<?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>ns_to_aK1.out</source>

<heading><![CDATA[
Prover9 (64) version 2017-09A, September 2017.
Process 30606 was started by veroff on b146-08,
Tue Apr 13 07:49:09 2021
The command was "prover9 -f ns_to_aK1.in".
]]></heading>

<proof number="1" length="19752" max_count="71">

<comments><![CDATA[
% Proof 1 at 5221.30 (+ 232.06) seconds: "aK1".
% Length of proof is 19752.
% Level of proof is 944.
% Maximum clause weight is 71.000.
% Given clauses 20810 (22.044 givens/level).

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

  <clause id="36" type="assumption">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      x * u != z
    ]]></literal>
    <literal><![CDATA[
      y = u
    ]]></literal>
    <attribute><![CDATA[
      label("*-Cancellation 1")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37" type="assumption">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      u * y != z
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <attribute><![CDATA[
      label("*-Cancellation 2")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="38" type="assumption">
    <literal><![CDATA[
      x / y != z
    ]]></literal>
    <literal><![CDATA[
      x / u != z
    ]]></literal>
    <literal><![CDATA[
      y = u
    ]]></literal>
    <attribute><![CDATA[
      label("/-Cancellation 1")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="39" type="assumption">
    <literal><![CDATA[
      x / y != z
    ]]></literal>
    <literal><![CDATA[
      u / y != z
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <attribute><![CDATA[
      label("/-Cancellation 2")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="40" type="assumption">
    <literal><![CDATA[
      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="41" 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="42" 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="43" 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="44" 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="45" type="assumption">
    <literal><![CDATA[
      x * y != x * z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <attribute><![CDATA[
      label("*-Cancellation 3")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="46" type="assumption">
    <literal><![CDATA[
      x * y != z * y
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <attribute><![CDATA[
      label("*-Cancellation 4")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="47" type="assumption">
    <literal><![CDATA[
      x / y != x / z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <attribute><![CDATA[
      label("/-Cancellation 3")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="48" type="assumption">
    <literal><![CDATA[
      x / y != z / y
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <attribute><![CDATA[
      label("/-Cancellation 4")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="49" type="assumption">
    <literal><![CDATA[
      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="50" 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="51" 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="52" 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="53" 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="54" 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="55" 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="56" 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="57" 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="58" 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="59" 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="60" 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="61" type="assumption">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      x / z = y / z
    ]]></literal>
    <attribute><![CDATA[
      label("Aux 3")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="62" type="assumption">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z / x = z / y
    ]]></literal>
    <attribute><![CDATA[
      label("Aux 4")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="63" 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="64" 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="65" 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="66" 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="67">
    <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 \ (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="70">
    <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="71">
    <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="72">
    <literal><![CDATA[
      x * (y * (y \ (x \ z))) = z
    ]]></literal>
    <justification jstring="[para(10(a,2),10(a,1,2))].">
      <j1 rule="para" parents="10 10"/>
    </justification>
  </clause>

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  <clause id="92">
    <literal><![CDATA[
      K(x * x,x) = a(x,x,x)
    ]]></literal>
    <justification jstring="[para(16(a,2),14(a,2)),flip(a)].">
      <j1 rule="para" parents="16 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="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[
      (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="100">
    <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="101">
    <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="102">
    <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="103">
    <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="104">
    <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="105">
    <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="106">
    <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="107">
    <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="108">
    <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="109">
    <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="110">
    <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="111">
    <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="112">
    <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="113">
    <literal><![CDATA[
      ((x * x) * (y * z)) / z = (x * x) * y
    ]]></literal>
    <justification jstring="[para(33(a,1),11(a,1,1))].">
      <j1 rule="para" parents="33 11"/>
    </justification>
  </clause>

  <clause id="114">
    <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="115">
    <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="116">
    <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="117">
    <literal><![CDATA[
      (x * (y * (z * z))) * u = (x * y) * ((z * z) * u)
    ]]></literal>
    <justification jstring="[para(35(a,1),34(a,1,1))].">
      <j1 rule="para" parents="35 34"/>
    </justification>
  </clause>

  <clause id="118">
    <literal><![CDATA[
      1 * x != y
    ]]></literal>
    <literal><![CDATA[
      z != y
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(7(a,1),36(b,1))].">
      <j1 rule="para" parents="7 36"/>
    </justification>
  </clause>

  <clause id="119">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z * u != y
    ]]></literal>
    <literal><![CDATA[
      z \ x = u
    ]]></literal>
    <justification jstring="[para(10(a,1),36(a,1))].">
      <j1 rule="para" parents="10 36"/>
    </justification>
  </clause>

  <clause id="120">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z * u != y
    ]]></literal>
    <literal><![CDATA[
      x / u = z
    ]]></literal>
    <justification jstring="[para(12(a,1),37(a,1))].">
      <j1 rule="para" parents="12 37"/>
    </justification>
  </clause>

  <clause id="121">
    <literal><![CDATA[
      1 * x != y
    ]]></literal>
    <literal><![CDATA[
      y = 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="122">
    <literal><![CDATA[
      1 * x != y
    ]]></literal>
    <literal><![CDATA[
      x = y
    ]]></literal>
    <justification jstring="[para(7(a,1),45(a,2))].">
      <j1 rule="para" parents="7 45"/>
    </justification>
  </clause>

  <clause id="123">
    <literal><![CDATA[
      x * y != x
    ]]></literal>
    <literal><![CDATA[
      1 = y
    ]]></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="124">
    <literal><![CDATA[
      x \ (x * (y * z)) != y * u
    ]]></literal>
    <literal><![CDATA[
      u = z
    ]]></literal>
    <justification jstring="[para(9(a,2),45(a,2)),flip(a)].">
      <j1 rule="para" parents="9 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="125">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      x \ z = y
    ]]></literal>
    <justification jstring="[para(10(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="10 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="128">
    <literal><![CDATA[
      ((x * x) * y) * z != (x * x) * u
    ]]></literal>
    <literal><![CDATA[
      y * z = u
    ]]></literal>
    <justification jstring="[para(33(a,2),45(a,1))].">
      <j1 rule="para" parents="33 45"/>
    </justification>
  </clause>

  <clause id="132">
    <literal><![CDATA[
      x * 1 != y
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(8(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="8 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="133">
    <literal><![CDATA[
      x * 1 != y
    ]]></literal>
    <literal><![CDATA[
      x = y
    ]]></literal>
    <justification jstring="[para(8(a,1),46(a,2))].">
      <j1 rule="para" parents="8 46"/>
    </justification>
  </clause>

  <clause id="134">
    <literal><![CDATA[
      x \ (x * (y * z)) != u * z
    ]]></literal>
    <literal><![CDATA[
      y = u
    ]]></literal>
    <justification jstring="[para(9(a,2),46(a,1))].">
      <j1 rule="para" parents="9 46"/>
    </justification>
  </clause>

  <clause id="136">
    <literal><![CDATA[
      x * (y \ z) != z
    ]]></literal>
    <literal><![CDATA[
      x = y
    ]]></literal>
    <justification jstring="[para(10(a,1),46(a,2))].">
      <j1 rule="para" parents="10 46"/>
    </justification>
  </clause>

  <clause id="137">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      z / y = x
    ]]></literal>
    <justification jstring="[para(12(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="12 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="140">
    <literal><![CDATA[
      x * (y * (z * z)) != u * (z * z)
    ]]></literal>
    <literal><![CDATA[
      x * y = u
    ]]></literal>
    <justification jstring="[para(35(a,1),46(a,1))].">
      <j1 rule="para" parents="35 46"/>
    </justification>
  </clause>

  <clause id="143">
    <literal><![CDATA[
      x / y != z
    ]]></literal>
    <literal><![CDATA[
      z * y = x
    ]]></literal>
    <justification jstring="[para(11(a,1),48(a,1)),flip(a)].">
      <j1 rule="para" parents="11 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="144">
    <literal><![CDATA[
      x \ y != z
    ]]></literal>
    <literal><![CDATA[
      x * z = y
    ]]></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="145">
    <literal><![CDATA[
      x \ (y * z) != z
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(9(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="9 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="146">
    <literal><![CDATA[
      x \ (y * z) != K(y,z)
    ]]></literal>
    <literal><![CDATA[
      z * y = x
    ]]></literal>
    <justification jstring="[para(16(a,2),50(a,1)),flip(a)].">
      <j1 rule="para" parents="16 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="147">
    <literal><![CDATA[
      x \ (y * (z * u)) != L(u,z,y)
    ]]></literal>
    <literal><![CDATA[
      y * z = x
    ]]></literal>
    <justification jstring="[para(18(a,2),50(a,1)),flip(a)].">
      <j1 rule="para" parents="18 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="148">
    <literal><![CDATA[
      T(T(x,y),z) != T(u,y)
    ]]></literal>
    <literal><![CDATA[
      T(x,z) = u
    ]]></literal>
    <justification jstring="[para(23(a,1),51(a,1))].">
      <j1 rule="para" parents="23 51"/>
    </justification>
  </clause>

  <clause id="149">
    <literal><![CDATA[
      T(x,y) != R(T(z,y),u,w)
    ]]></literal>
    <literal><![CDATA[
      R(z,u,w) = x
    ]]></literal>
    <justification jstring="[para(27(a,2),51(a,1)),flip(a)].">
      <j1 rule="para" parents="27 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="150">
    <literal><![CDATA[
      T(L(x,y,z),u) != L(w,y,z)
    ]]></literal>
    <literal><![CDATA[
      T(x,u) = w
    ]]></literal>
    <justification jstring="[para(25(a,1),52(a,1))].">
      <j1 rule="para" parents="25 52"/>
    </justification>
  </clause>

  <clause id="151">
    <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),52(a,1))].">
      <j1 rule="para" parents="29 52"/>
    </justification>
  </clause>

  <clause id="152">
    <literal><![CDATA[
      T(R(x,y,z),u) != R(w,y,z)
    ]]></literal>
    <literal><![CDATA[
      T(x,u) = w
    ]]></literal>
    <justification jstring="[para(27(a,1),53(a,1))].">
      <j1 rule="para" parents="27 53"/>
    </justification>
  </clause>

  <clause id="153">
    <literal><![CDATA[
      R(x,y,z) != L(R(u,y,z),w,v5)
    ]]></literal>
    <literal><![CDATA[
      L(u,w,v5) = x
    ]]></literal>
    <justification jstring="[para(29(a,1),53(a,1)),flip(a)].">
      <j1 rule="para" parents="29 53"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="154">
    <literal><![CDATA[
      ((x / y) * y) * z = x * z
    ]]></literal>
    <justification jstring="[hyper(59,a,12,a)].">
      <j1 rule="hyper" parents="59 12"/>
    </justification>
  </clause>

  <clause id="155">
    <literal><![CDATA[
      x * (y * (y \ z)) = x * z
    ]]></literal>
    <justification jstring="[hyper(60,a,10,a)].">
      <j1 rule="hyper" parents="60 10"/>
    </justification>
  </clause>

  <clause id="156">
    <literal><![CDATA[
      ((x / y) * y) / z = x / z
    ]]></literal>
    <justification jstring="[hyper(61,a,12,a)].">
      <j1 rule="hyper" parents="61 12"/>
    </justification>
  </clause>

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

  <clause id="158">
    <literal><![CDATA[
      (x * y) / y = (x / z) * z
    ]]></literal>
    <justification jstring="[hyper(65,a,12,a,b,11,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="65 12 11"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="159">
    <literal><![CDATA[
      (x / y) * y = x * 1
    ]]></literal>
    <justification jstring="[hyper(65,a,12,a,b,8,a(flip))].">
      <j1 rule="hyper" parents="65 12 8"/>
    </justification>
  </clause>

  <clause id="160">
    <literal><![CDATA[
      x \ (x * y) = z * (z \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,10,a,b,9,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="65 10 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="161">
    <literal><![CDATA[
      x * (x \ y) = y * 1
    ]]></literal>
    <justification jstring="[hyper(65,a,10,a,b,8,a(flip))].">
      <j1 rule="hyper" parents="65 10 8"/>
    </justification>
  </clause>

  <clause id="162">
    <literal><![CDATA[
      T(x,1) = x * 1
    ]]></literal>
    <justification jstring="[hyper(65,a,22,a,b,67,a)].">
      <j1 rule="hyper" parents="65 22 67"/>
    </justification>
  </clause>

  <clause id="163">
    <literal><![CDATA[
      1 \ (x * 1) = x
    ]]></literal>
    <justification jstring="[hyper(65,a,67,a,b,8,a)].">
      <j1 rule="hyper" parents="65 67 8"/>
    </justification>
  </clause>

  <clause id="164">
    <literal><![CDATA[
      (x * (x \ 1)) \ y = y
    ]]></literal>
    <justification jstring="[para(10(a,2),67(a,1,1))].">
      <j1 rule="para" parents="10 67"/>
    </justification>
  </clause>

  <clause id="165">
    <literal><![CDATA[
      ((1 / x) * x) \ y = y
    ]]></literal>
    <justification jstring="[para(12(a,2),67(a,1,1))].">
      <j1 rule="para" parents="12 67"/>
    </justification>
  </clause>

  <clause id="166">
    <literal><![CDATA[
      1 \ x != y
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(67(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="67 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="167">
    <literal><![CDATA[
      x \ y != y
    ]]></literal>
    <literal><![CDATA[
      1 = x
    ]]></literal>
    <justification jstring="[para(67(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="67 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="168">
    <literal><![CDATA[
      K(x,x) = 1
    ]]></literal>
    <justification jstring="[hyper(65,a,16,a,b,68,a)].">
      <j1 rule="hyper" parents="65 16 68"/>
    </justification>
  </clause>

  <clause id="169">
    <literal><![CDATA[
      x / (y * (y \ 1)) = x
    ]]></literal>
    <justification jstring="[para(10(a,2),74(a,1,2))].">
      <j1 rule="para" parents="10 74"/>
    </justification>
  </clause>

  <clause id="170">
    <literal><![CDATA[
      x / ((1 / y) * y) = x
    ]]></literal>
    <justification jstring="[para(12(a,2),74(a,1,2))].">
      <j1 rule="para" parents="12 74"/>
    </justification>
  </clause>

  <clause id="171">
    <literal><![CDATA[
      x / 1 != y
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(74(a,1),48(a,1)),flip(a)].">
      <j1 rule="para" parents="74 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="172">
    <literal><![CDATA[
      T(x,R(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(44,a,27,a,b,106,a(flip))].">
      <j1 rule="hyper" parents="44 27 106"/>
    </justification>
  </clause>

  <clause id="173">
    <literal><![CDATA[
      T(x,L(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(43,a,25,a,b,106,a(flip))].">
      <j1 rule="hyper" parents="43 25 106"/>
    </justification>
  </clause>

  <clause id="174">
    <literal><![CDATA[
      T(x,T(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(42,a,23,a,b,106,a(flip))].">
      <j1 rule="hyper" parents="42 23 106"/>
    </justification>
  </clause>

  <clause id="175">
    <literal><![CDATA[
      T(T(x,y),x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(106(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="106 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="176">
    <literal><![CDATA[
      T(L(x,y,z),x) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(106(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="106 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="177">
    <literal><![CDATA[
      x * K(y,y) = x
    ]]></literal>
    <justification jstring="[para(168(a,2),8(a,1,2))].">
      <j1 rule="para" parents="168 8"/>
    </justification>
  </clause>

  <clause id="178">
    <literal><![CDATA[
      x / (y \ x) = z / (y \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,76,a,b,76,a(flip))].">
      <j1 rule="hyper" parents="65 76 76"/>
    </justification>
  </clause>

  <clause id="179">
    <literal><![CDATA[
      (x * y) / y = z / (x \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,76,a,b,11,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="65 76 11"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="180">
    <literal><![CDATA[
      x / (y \ x) = z * (z \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,76,a,b,10,a(flip))].">
      <j1 rule="hyper" parents="65 76 10"/>
    </justification>
  </clause>

  <clause id="181">
    <literal><![CDATA[
      (x / (y \ x)) * z = y * z
    ]]></literal>
    <justification jstring="[hyper(59,a,76,a)].">
      <j1 rule="hyper" parents="59 76"/>
    </justification>
  </clause>

  <clause id="182">
    <literal><![CDATA[
      R(x,y,z) \ ((x * y) * z) = y * z
    ]]></literal>
    <justification jstring="[hyper(38,a,20,a(flip),b,76,a),flip(a)].">
      <j1 rule="hyper" parents="38 20 76"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="183">
    <literal><![CDATA[
      (x * y) / K(x,y) = y * x
    ]]></literal>
    <justification jstring="[para(16(a,2),76(a,1,2))].">
      <j1 rule="para" parents="16 76"/>
    </justification>
  </clause>

  <clause id="184">
    <literal><![CDATA[
      (x * (y * z)) / L(z,y,x) = x * y
    ]]></literal>
    <justification jstring="[para(18(a,2),76(a,1,2))].">
      <j1 rule="para" parents="18 76"/>
    </justification>
  </clause>

  <clause id="185">
    <literal><![CDATA[
      (x * y) / T(x,y) = y
    ]]></literal>
    <justification jstring="[para(22(a,2),76(a,1,2))].">
      <j1 rule="para" parents="22 76"/>
    </justification>
  </clause>

  <clause id="186">
    <literal><![CDATA[
      x / y != z
    ]]></literal>
    <literal><![CDATA[
      z \ x = y
    ]]></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="187">
    <literal><![CDATA[
      x / (y / ((z \ x) \ y)) = z
    ]]></literal>
    <justification jstring="[para(76(a,2),76(a,1,2))].">
      <j1 rule="para" parents="76 76"/>
    </justification>
  </clause>

  <clause id="188">
    <literal><![CDATA[
      (x / y) \ x = z * (z \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,79,a,b,10,a(flip))].">
      <j1 rule="hyper" parents="65 79 10"/>
    </justification>
  </clause>

  <clause id="189">
    <literal><![CDATA[
      ((x / y) \ x) * z = y * z
    ]]></literal>
    <justification jstring="[hyper(59,a,79,a)].">
      <j1 rule="hyper" parents="59 79"/>
    </justification>
  </clause>

  <clause id="190">
    <literal><![CDATA[
      x * ((y / (x \ z)) \ y) = z
    ]]></literal>
    <justification jstring="[hyper(40,a,9,a,b,79,a(flip))].">
      <j1 rule="hyper" parents="40 9 79"/>
    </justification>
  </clause>

  <clause id="191">
    <literal><![CDATA[
      ((x / (y / z)) \ x) \ y = z
    ]]></literal>
    <justification jstring="[hyper(38,a,76,a,b,79,a(flip))].">
      <j1 rule="hyper" parents="38 76 79"/>
    </justification>
  </clause>

  <clause id="192">
    <literal><![CDATA[
      x \ y != z
    ]]></literal>
    <literal><![CDATA[
      y / z = x
    ]]></literal>
    <justification jstring="[para(79(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="79 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="193">
    <literal><![CDATA[
      T(x,1) = x
    ]]></literal>
    <justification jstring="[hyper(65,a,162,a,b,8,a)].">
      <j1 rule="hyper" parents="65 162 8"/>
    </justification>
  </clause>

  <clause id="194">
    <literal><![CDATA[
      K(x,1) = 1
    ]]></literal>
    <justification jstring="[hyper(57,a,193,a)].">
      <j1 rule="hyper" parents="57 193"/>
    </justification>
  </clause>

  <clause id="195">
    <literal><![CDATA[
      T(1,x) = 1
    ]]></literal>
    <justification jstring="[hyper(56,a,193,a)].">
      <j1 rule="hyper" parents="56 193"/>
    </justification>
  </clause>

  <clause id="196">
    <literal><![CDATA[
      T(x,1) != y
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(193(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="193 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="197">
    <literal><![CDATA[
      T(x,1) != y
    ]]></literal>
    <literal><![CDATA[
      x = y
    ]]></literal>
    <justification jstring="[para(193(a,1),51(a,2))].">
      <j1 rule="para" parents="193 51"/>
    </justification>
  </clause>

  <clause id="198">
    <literal><![CDATA[
      T(x,y \ y) = x
    ]]></literal>
    <justification jstring="[para(68(a,2),193(a,1,2))].">
      <j1 rule="para" parents="68 193"/>
    </justification>
  </clause>

  <clause id="199">
    <literal><![CDATA[
      K(1,x) = 1
    ]]></literal>
    <justification jstring="[hyper(57,a,195,a)].">
      <j1 rule="hyper" parents="57 195"/>
    </justification>
  </clause>

  <clause id="200">
    <literal><![CDATA[
      T(x,T(T(x,y),z)) = x
    ]]></literal>
    <justification jstring="[hyper(42,a,23,a,b,174,a(flip))].">
      <j1 rule="hyper" parents="42 23 174"/>
    </justification>
  </clause>

  <clause id="202">
    <literal><![CDATA[
      (x * (x \ 1)) * y != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(10(a,2),122(a,1,1))].">
      <j1 rule="para" parents="10 122"/>
    </justification>
  </clause>

  <clause id="203">
    <literal><![CDATA[
      x * (y * (y \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(10(a,2),132(a,1,2))].">
      <j1 rule="para" parents="10 132"/>
    </justification>
  </clause>

  <clause id="204">
    <literal><![CDATA[
      x * ((1 / y) * y) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(12(a,2),132(a,1,2))].">
      <j1 rule="para" parents="12 132"/>
    </justification>
  </clause>

  <clause id="205">
    <literal><![CDATA[
      x * (y * (y \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(10(a,2),133(a,1,2))].">
      <j1 rule="para" parents="10 133"/>
    </justification>
  </clause>

  <clause id="206">
    <literal><![CDATA[
      x * ((1 / y) * y) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(12(a,2),133(a,1,2))].">
      <j1 rule="para" parents="12 133"/>
    </justification>
  </clause>

  <clause id="207">
    <literal><![CDATA[
      x * (y \ y) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(68(a,2),133(a,1,2))].">
      <j1 rule="para" parents="68 133"/>
    </justification>
  </clause>

  <clause id="208">
    <literal><![CDATA[
      x / (y * (y \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(10(a,2),171(a,1,2))].">
      <j1 rule="para" parents="10 171"/>
    </justification>
  </clause>

  <clause id="209">
    <literal><![CDATA[
      T(x,R(T(x,y),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(42,a,23,a,b,172,a(flip))].">
      <j1 rule="hyper" parents="42 23 172"/>
    </justification>
  </clause>

  <clause id="210">
    <literal><![CDATA[
      K(x,L(x,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(57,a,173,a)].">
      <j1 rule="hyper" parents="57 173"/>
    </justification>
  </clause>

  <clause id="211">
    <literal><![CDATA[
      T(x,L(L(x,y,z),u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(43,a,25,a,b,173,a(flip))].">
      <j1 rule="hyper" parents="43 25 173"/>
    </justification>
  </clause>

  <clause id="212">
    <literal><![CDATA[
      R(x,x \ 1,y) = y / ((x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(70(a,1),20(a,2,1))].">
      <j1 rule="para" parents="70 20"/>
    </justification>
  </clause>

  <clause id="213">
    <literal><![CDATA[
      x * (x \ y) = y * (z * (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(65,a,71,a,b,10,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="65 71 10"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="214">
    <literal><![CDATA[
      L(x \ 1,x,y) = (y * x) \ y
    ]]></literal>
    <justification jstring="[para(71(a,1),18(a,2,2))].">
      <j1 rule="para" parents="71 18"/>
    </justification>
  </clause>

  <clause id="215">
    <literal><![CDATA[
      x * ((1 / x) * (1 / x)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(36,a,35,a(flip),b,77,a(flip))].">
      <j1 rule="hyper" parents="36 35 77"/>
    </justification>
  </clause>

  <clause id="216">
    <literal><![CDATA[
      R(1 / x,x,y) = y / (x * y)
    ]]></literal>
    <justification jstring="[para(77(a,1),20(a,2,1))].">
      <j1 rule="para" parents="77 20"/>
    </justification>
  </clause>

  <clause id="217">
    <literal><![CDATA[
      (x * x) * (1 / x) = x
    ]]></literal>
    <justification jstring="[hyper(37,a,33,a,b,78,a(flip))].">
      <j1 rule="hyper" parents="37 33 78"/>
    </justification>
  </clause>

  <clause id="218">
    <literal><![CDATA[
      x \ ((x * (1 / y)) * y) = a(x,1 / y,y)
    ]]></literal>
    <justification jstring="[para(78(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="78 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="219">
    <literal><![CDATA[
      x * T(y / x,x) = y
    ]]></literal>
    <justification jstring="[hyper(65,a,107,a,b,12,a)].">
      <j1 rule="hyper" parents="65 107 12"/>
    </justification>
  </clause>

  <clause id="220">
    <literal><![CDATA[
      (x \ y) * T(x,x \ y) = y
    ]]></literal>
    <justification jstring="[hyper(65,a,107,a,b,10,a)].">
      <j1 rule="hyper" parents="65 107 10"/>
    </justification>
  </clause>

  <clause id="221">
    <literal><![CDATA[
      T((x * x) * y,x * x) = y * (x * x)
    ]]></literal>
    <justification jstring="[hyper(36,a,35,a(flip),b,107,a),flip(a)].">
      <j1 rule="hyper" parents="36 35 107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="222">
    <literal><![CDATA[
      T((x * y) / x,x) = y
    ]]></literal>
    <justification jstring="[hyper(36,a,12,a(flip),b,107,a),flip(a)].">
      <j1 rule="hyper" parents="36 12 107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="223">
    <literal><![CDATA[
      (x * T(y,x)) / x = y
    ]]></literal>
    <justification jstring="[hyper(37,a,12,a,b,107,a(flip))].">
      <j1 rule="hyper" parents="37 12 107"/>
    </justification>
  </clause>

  <clause id="224">
    <literal><![CDATA[
      x \ (y * T(x,y)) = y
    ]]></literal>
    <justification jstring="[hyper(36,a,10,a,b,107,a(flip))].">
      <j1 rule="hyper" parents="36 10 107"/>
    </justification>
  </clause>

  <clause id="225">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * z) * T(y,z)) = a(x,z,T(y,z))
    ]]></literal>
    <justification jstring="[para(107(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="107 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="226">
    <literal><![CDATA[
      (x * (T(y,x) * z)) \ ((y * x) * z) = a(x,T(y,x),z)
    ]]></literal>
    <justification jstring="[para(107(a,1),14(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="107 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="227">
    <literal><![CDATA[
      (x * (y * T(z,x * y))) \ (z * (x * y)) = a(x,y,T(z,x * y))
    ]]></literal>
    <justification jstring="[para(107(a,1),14(a,2,2)),flip(a)].">
      <j1 rule="para" parents="107 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="228">
    <literal><![CDATA[
      (x * y) \ (T(x,y) * y) = K(T(x,y),y)
    ]]></literal>
    <justification jstring="[para(107(a,1),16(a,2,1)),flip(a)].">
      <j1 rule="para" parents="107 16"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="229">
    <literal><![CDATA[
      (x * y) \ (y * (T(x,y) * z)) = L(z,T(x,y),y)
    ]]></literal>
    <justification jstring="[para(107(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="107 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="230">
    <literal><![CDATA[
      (x * y) \ (x * (z * y)) = L(T(z,y),y,x)
    ]]></literal>
    <justification jstring="[para(107(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="107 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="231">
    <literal><![CDATA[
      ((x * y) * z) / (T(x,y) * z) = R(y,T(x,y),z)
    ]]></literal>
    <justification jstring="[para(107(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="107 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="232">
    <literal><![CDATA[
      x * T(T(y,x),z) = T(y,z) * x
    ]]></literal>
    <justification jstring="[para(23(a,1),107(a,1,2))].">
      <j1 rule="para" parents="23 107"/>
    </justification>
  </clause>

  <clause id="233">
    <literal><![CDATA[
      x * L(T(y,x),z,u) = L(y,z,u) * x
    ]]></literal>
    <justification jstring="[para(25(a,2),107(a,1,2))].">
      <j1 rule="para" parents="25 107"/>
    </justification>
  </clause>

  <clause id="234">
    <literal><![CDATA[
      x * R(T(y,x),z,u) = R(y,z,u) * x
    ]]></literal>
    <justification jstring="[para(27(a,2),107(a,1,2))].">
      <j1 rule="para" parents="27 107"/>
    </justification>
  </clause>

  <clause id="235">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      y * u != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(107(a,1),36(a,1))].">
      <j1 rule="para" parents="107 36"/>
    </justification>
  </clause>

  <clause id="236">
    <literal><![CDATA[
      x * y != z * x
    ]]></literal>
    <literal><![CDATA[
      T(z,x) = y
    ]]></literal>
    <justification jstring="[para(107(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="107 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="237">
    <literal><![CDATA[
      x * T(y,x) != z * x
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(107(a,2),46(a,1))].">
      <j1 rule="para" parents="107 46"/>
    </justification>
  </clause>

  <clause id="238">
    <literal><![CDATA[
      x * T(y,x) != z * x
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(107(a,2),46(a,2)),flip(a)].">
      <j1 rule="para" parents="107 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="239">
    <literal><![CDATA[
      T(x,y) * x = x * T(x,y)
    ]]></literal>
    <justification jstring="[para(174(a,1),107(a,1,2))].">
      <j1 rule="para" parents="174 107"/>
    </justification>
  </clause>

  <clause id="241">
    <literal><![CDATA[
      T(x / (x / y),x / y) = y
    ]]></literal>
    <justification jstring="[hyper(65,a,109,a,b,79,a)].">
      <j1 rule="hyper" parents="65 109 79"/>
    </justification>
  </clause>

  <clause id="242">
    <literal><![CDATA[
      T(T(x / y,z),y) = T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(109(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="109 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="243">
    <literal><![CDATA[
      T(R(x / y,z,u),y) = R(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(109(a,1),27(a,1,1)),flip(a)].">
      <j1 rule="para" parents="109 27"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="244">
    <literal><![CDATA[
      T(x,y) != y \ z
    ]]></literal>
    <literal><![CDATA[
      z / y = x
    ]]></literal>
    <justification jstring="[para(109(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="109 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="245">
    <literal><![CDATA[
      x * 1 != y * z
    ]]></literal>
    <literal><![CDATA[
      x / z = y
    ]]></literal>
    <justification jstring="[para(159(a,1),46(a,1))].">
      <j1 rule="para" parents="159 46"/>
    </justification>
  </clause>

  <clause id="246">
    <literal><![CDATA[
      (x / y) * y != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(159(a,2),132(a,1))].">
      <j1 rule="para" parents="159 132"/>
    </justification>
  </clause>

  <clause id="247">
    <literal><![CDATA[
      (x / y) * y != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(159(a,2),133(a,1))].">
      <j1 rule="para" parents="159 133"/>
    </justification>
  </clause>

  <clause id="248">
    <literal><![CDATA[
      x \ (y * (y \ x)) = 1
    ]]></literal>
    <justification jstring="[hyper(36,a,10,a,b,161,a(flip))].">
      <j1 rule="hyper" parents="36 10 161"/>
    </justification>
  </clause>

  <clause id="249">
    <literal><![CDATA[
      x * 1 != y * z
    ]]></literal>
    <literal><![CDATA[
      y \ x = z
    ]]></literal>
    <justification jstring="[para(161(a,1),45(a,1))].">
      <j1 rule="para" parents="161 45"/>
    </justification>
  </clause>

  <clause id="250">
    <literal><![CDATA[
      x * (x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(161(a,2),132(a,1))].">
      <j1 rule="para" parents="161 132"/>
    </justification>
  </clause>

  <clause id="251">
    <literal><![CDATA[
      x * (x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(161(a,2),133(a,1))].">
      <j1 rule="para" parents="161 133"/>
    </justification>
  </clause>

  <clause id="252">
    <literal><![CDATA[
      x * ((x \ 1) * y) = L(y,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,18,a,b,164,a),flip(a)].">
      <j1 rule="hyper" parents="65 18 164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="253">
    <literal><![CDATA[
      K(x \ 1,x) = (x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(65,a,16,a,b,164,a)].">
      <j1 rule="hyper" parents="65 16 164"/>
    </justification>
  </clause>

  <clause id="254">
    <literal><![CDATA[
      (x * (x \ 1)) \ y != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(164(a,1),49(a,2))].">
      <j1 rule="para" parents="164 49"/>
    </justification>
  </clause>

  <clause id="255">
    <literal><![CDATA[
      (1 / x) * (x * y) = L(y,x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(65,a,18,a,b,165,a),flip(a)].">
      <j1 rule="hyper" parents="65 18 165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="256">
    <literal><![CDATA[
      K(x,1 / x) = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(65,a,16,a,b,165,a)].">
      <j1 rule="hyper" parents="65 16 165"/>
    </justification>
  </clause>

  <clause id="257">
    <literal><![CDATA[
      ((1 / x) * x) \ y != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(165(a,1),49(a,2))].">
      <j1 rule="para" parents="165 49"/>
    </justification>
  </clause>

  <clause id="258">
    <literal><![CDATA[
      (x * y) * (y \ 1) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,20,a,b,169,a),flip(a)].">
      <j1 rule="hyper" parents="65 20 169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="259">
    <literal><![CDATA[
      x / (y * (y \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(169(a,1),48(a,2))].">
      <j1 rule="para" parents="169 48"/>
    </justification>
  </clause>

  <clause id="260">
    <literal><![CDATA[
      (x * (1 / y)) * y = R(x,1 / y,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,20,a,b,170,a),flip(a)].">
      <j1 rule="hyper" parents="65 20 170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="262">
    <literal><![CDATA[
      x / T(y,y \ x) = y \ x
    ]]></literal>
    <justification jstring="[para(10(a,1),185(a,1,1))].">
      <j1 rule="para" parents="10 185"/>
    </justification>
  </clause>

  <clause id="263">
    <literal><![CDATA[
      (x * y) / z != y
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(185(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="185 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="264">
    <literal><![CDATA[
      (x * x) \ x = 1 / x
    ]]></literal>
    <justification jstring="[hyper(36,a,10,a,b,217,a)].">
      <j1 rule="hyper" parents="36 10 217"/>
    </justification>
  </clause>

  <clause id="265">
    <literal><![CDATA[
      (x * x) * ((1 / x) * y) = x * y
    ]]></literal>
    <justification jstring="[para(217(a,1),33(a,1,1)),flip(a)].">
      <j1 rule="para" parents="217 33"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="266">
    <literal><![CDATA[
      T(T((x * y) / x,z),x) = T(y,z)
    ]]></literal>
    <justification jstring="[para(222(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="222 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="267">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (y * z) / y = x
    ]]></literal>
    <justification jstring="[para(222(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="222 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="268">
    <literal><![CDATA[
      T((x * y) / x,y) = (x * y) / x
    ]]></literal>
    <justification jstring="[para(222(a,1),174(a,1,2))].">
      <j1 rule="para" parents="222 174"/>
    </justification>
  </clause>

  <clause id="269">
    <literal><![CDATA[
      x / y != z
    ]]></literal>
    <literal><![CDATA[
      y * T(z,y) = x
    ]]></literal>
    <justification jstring="[para(223(a,1),48(a,1)),flip(a)].">
      <j1 rule="para" parents="223 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="270">
    <literal><![CDATA[
      T(T(x,y),x * x) = T(L(x,x,x),y)
    ]]></literal>
    <justification jstring="[para(110(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="110 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="273">
    <literal><![CDATA[
      x \ y != z \ y
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(10(a,1),145(a,1,2))].">
      <j1 rule="para" parents="10 145"/>
    </justification>
  </clause>

  <clause id="274">
    <literal><![CDATA[
      x \ x != y
    ]]></literal>
    <literal><![CDATA[
      1 = y
    ]]></literal>
    <justification jstring="[para(7(a,1),207(a,1))].">
      <j1 rule="para" parents="7 207"/>
    </justification>
  </clause>

  <clause id="275">
    <literal><![CDATA[
      R(x,y,z) * (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      (x * y) * z = u
    ]]></literal>
    <justification jstring="[para(20(a,2),246(a,1,1)),flip(b)].">
      <j1 rule="para" parents="20 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="276">
    <literal><![CDATA[
      x * T(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      y * x = z
    ]]></literal>
    <justification jstring="[para(185(a,1),246(a,1,1)),flip(b)].">
      <j1 rule="para" parents="185 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="277">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      y * T(x,y) = z
    ]]></literal>
    <justification jstring="[para(223(a,1),246(a,1,1)),flip(b)].">
      <j1 rule="para" parents="223 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="279">
    <literal><![CDATA[
      (x * y) * L(z,y,x) != u
    ]]></literal>
    <literal><![CDATA[
      x * (y * z) = u
    ]]></literal>
    <justification jstring="[para(18(a,2),250(a,1,2)),flip(b)].">
      <j1 rule="para" parents="18 250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="280">
    <literal><![CDATA[
      x \ ((y * z) * (z \ (y \ x))) = a(y,z,z \ (y \ x))
    ]]></literal>
    <justification jstring="[para(72(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="72 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="281">
    <literal><![CDATA[
      L(x \ (y \ z),x,y) = (y * x) \ z
    ]]></literal>
    <justification jstring="[para(72(a,1),18(a,2,2))].">
      <j1 rule="para" parents="72 18"/>
    </justification>
  </clause>

  <clause id="283">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z * (z \ x) = y
    ]]></literal>
    <justification jstring="[para(81(a,1),246(a,1)),flip(b)].">
      <j1 rule="para" parents="81 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="284">
    <literal><![CDATA[
      (R(x,y,z) * (y * z)) / z = x * y
    ]]></literal>
    <justification jstring="[para(20(a,2),82(a,1,1,1))].">
      <j1 rule="para" parents="20 82"/>
    </justification>
  </clause>

  <clause id="285">
    <literal><![CDATA[
      R((x / y) / z,z,y) = x / (z * y)
    ]]></literal>
    <justification jstring="[para(83(a,1),20(a,2,1))].">
      <j1 rule="para" parents="83 20"/>
    </justification>
  </clause>

  <clause id="286">
    <literal><![CDATA[
      ((x / y) * y) * (x \ z) = z
    ]]></literal>
    <justification jstring="[para(76(a,1),83(a,1,1,1,1))].">
      <j1 rule="para" parents="76 83"/>
    </justification>
  </clause>

  <clause id="287">
    <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="288">
    <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="289">
    <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="290">
    <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="291">
    <literal><![CDATA[
      (x * y) / T(y * x,K(x,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(88(a,1),185(a,1,1))].">
      <j1 rule="para" parents="88 185"/>
    </justification>
  </clause>

  <clause id="292">
    <literal><![CDATA[
      (x \ y) \ y = z * (z \ T(x,x \ y))
    ]]></literal>
    <justification jstring="[hyper(283,a,108,a),flip(a)].">
      <j1 rule="hyper" parents="283 108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="293">
    <literal><![CDATA[
      x \ T(y,y \ z) = x \ ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,108,a)].">
      <j1 rule="hyper" parents="64 108"/>
    </justification>
  </clause>

  <clause id="294">
    <literal><![CDATA[
      x / T(y,y \ z) = x / ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(62,a,108,a)].">
      <j1 rule="hyper" parents="62 108"/>
    </justification>
  </clause>

  <clause id="295">
    <literal><![CDATA[
      x * T(y,y \ z) = x * ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(60,a,108,a)].">
      <j1 rule="hyper" parents="60 108"/>
    </justification>
  </clause>

  <clause id="296">
    <literal><![CDATA[
      T(x,x \ y) * z = ((x \ y) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(59,a,108,a)].">
      <j1 rule="hyper" parents="59 108"/>
    </justification>
  </clause>

  <clause id="297">
    <literal><![CDATA[
      T(T(x,y),x \ z) = T((x \ z) \ z,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="298">
    <literal><![CDATA[
      T(L(x,y,z),x \ u) = L((x \ u) \ u,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="299">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z != y
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(7(a,1),118(a,1))].">
      <j1 rule="para" parents="7 118"/>
    </justification>
  </clause>

  <clause id="300">
    <literal><![CDATA[
      ((x / y) * y) * z != u
    ]]></literal>
    <literal><![CDATA[
      x \ u = z
    ]]></literal>
    <justification jstring="[para(154(a,2),125(a,1))].">
      <j1 rule="para" parents="154 125"/>
    </justification>
  </clause>

  <clause id="301">
    <literal><![CDATA[
      (x / (y * (y \ z))) * z = x
    ]]></literal>
    <justification jstring="[hyper(247,a,155,a),flip(a)].">
      <j1 rule="hyper" parents="247 155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="302">
    <literal><![CDATA[
      x / (y \ ((x / z) * z)) = y
    ]]></literal>
    <justification jstring="[hyper(65,a,76,a(flip),b,156,a),flip(a)].">
      <j1 rule="hyper" parents="65 76 156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="304">
    <literal><![CDATA[
      (x * y) / y != z * u
    ]]></literal>
    <literal><![CDATA[
      x / u = z
    ]]></literal>
    <justification jstring="[para(158(a,2),46(a,1))].">
      <j1 rule="para" parents="158 46"/>
    </justification>
  </clause>

  <clause id="305">
    <literal><![CDATA[
      x / y != (z / u) * u
    ]]></literal>
    <literal><![CDATA[
      z * y = x
    ]]></literal>
    <justification jstring="[para(158(a,1),48(a,1)),flip(a)].">
      <j1 rule="para" parents="158 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="306">
    <literal><![CDATA[
      ((x / y) * y) * z != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(158(a,1),246(a,1,1)),flip(b)].">
      <j1 rule="para" parents="158 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="307">
    <literal><![CDATA[
      (x * y) / y != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(158(a,2),246(a,1))].">
      <j1 rule="para" parents="158 246"/>
    </justification>
  </clause>

  <clause id="308">
    <literal><![CDATA[
      (x * y) / y != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(158(a,2),247(a,1))].">
      <j1 rule="para" parents="158 247"/>
    </justification>
  </clause>

  <clause id="309">
    <literal><![CDATA[
      x / x != y
    ]]></literal>
    <literal><![CDATA[
      1 = y
    ]]></literal>
    <justification jstring="[para(7(a,1),307(a,1,1)),flip(b)].">
      <j1 rule="para" parents="7 307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="310">
    <literal><![CDATA[
      x / (y \ x) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(10(a,1),307(a,1,1))].">
      <j1 rule="para" parents="10 307"/>
    </justification>
  </clause>

  <clause id="311">
    <literal><![CDATA[
      (x * T(y,x)) / x != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(107(a,2),307(a,1,1))].">
      <j1 rule="para" parents="107 307"/>
    </justification>
  </clause>

  <clause id="312">
    <literal><![CDATA[
      x / (y \ x) != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(10(a,1),308(a,1,1))].">
      <j1 rule="para" parents="10 308"/>
    </justification>
  </clause>

  <clause id="313">
    <literal><![CDATA[
      x \ (x * y) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ y = u
    ]]></literal>
    <justification jstring="[para(160(a,2),45(a,1))].">
      <j1 rule="para" parents="160 45"/>
    </justification>
  </clause>

  <clause id="314">
    <literal><![CDATA[
      x \ (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(160(a,2),207(a,1))].">
      <j1 rule="para" parents="160 207"/>
    </justification>
  </clause>

  <clause id="315">
    <literal><![CDATA[
      x * (y * (y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(160(a,1),250(a,1,2)),flip(b)].">
      <j1 rule="para" parents="160 250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="316">
    <literal><![CDATA[
      x \ (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(160(a,2),250(a,1))].">
      <j1 rule="para" parents="160 250"/>
    </justification>
  </clause>

  <clause id="317">
    <literal><![CDATA[
      (x / y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(12(a,1),314(a,1,2))].">
      <j1 rule="para" parents="12 314"/>
    </justification>
  </clause>

  <clause id="318">
    <literal><![CDATA[
      x \ (y * x) != z
    ]]></literal>
    <literal><![CDATA[
      T(y,x) = z
    ]]></literal>
    <justification jstring="[para(107(a,1),314(a,1,2))].">
      <j1 rule="para" parents="107 314"/>
    </justification>
  </clause>

  <clause id="319">
    <literal><![CDATA[
      x \ (y * T(x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(107(a,2),314(a,1,2))].">
      <j1 rule="para" parents="107 314"/>
    </justification>
  </clause>

  <clause id="322">
    <literal><![CDATA[
      (x * y) \ (y * x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(88(a,1),314(a,1,2))].">
      <j1 rule="para" parents="88 314"/>
    </justification>
  </clause>

  <clause id="323">
    <literal><![CDATA[
      (x / y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(12(a,1),316(a,1,2))].">
      <j1 rule="para" parents="12 316"/>
    </justification>
  </clause>

  <clause id="324">
    <literal><![CDATA[
      T((x * y) / x,x) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(109(a,2),316(a,1))].">
      <j1 rule="para" parents="109 316"/>
    </justification>
  </clause>

  <clause id="327">
    <literal><![CDATA[
      (x / (y \ x)) * z != u
    ]]></literal>
    <literal><![CDATA[
      y * z = u
    ]]></literal>
    <justification jstring="[para(179(a,1),246(a,1,1)),flip(b)].">
      <j1 rule="para" parents="179 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="329">
    <literal><![CDATA[
      (x * (x \ y)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      y \ z = u
    ]]></literal>
    <justification jstring="[para(180(a,1),317(a,1,1))].">
      <j1 rule="para" parents="180 317"/>
    </justification>
  </clause>

  <clause id="330">
    <literal><![CDATA[
      (x / y) \ x != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ y = u
    ]]></literal>
    <justification jstring="[para(188(a,2),45(a,1))].">
      <j1 rule="para" parents="188 45"/>
    </justification>
  </clause>

  <clause id="331">
    <literal><![CDATA[
      x \ y != z * (z \ u)
    ]]></literal>
    <literal><![CDATA[
      y / u = x
    ]]></literal>
    <justification jstring="[para(188(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="188 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="332">
    <literal><![CDATA[
      ((x / y) \ x) * (y \ z) = z
    ]]></literal>
    <justification jstring="[hyper(299,a,10,a(flip),b,189,a),flip(a)].">
      <j1 rule="hyper" parents="299 10 189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="333">
    <literal><![CDATA[
      x * (((y / x) \ y) \ z) = z
    ]]></literal>
    <justification jstring="[hyper(251,a,189,a),flip(a)].">
      <j1 rule="hyper" parents="251 189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="334">
    <literal><![CDATA[
      ((x / y) \ x) * z != u
    ]]></literal>
    <literal><![CDATA[
      y \ u = z
    ]]></literal>
    <justification jstring="[para(189(a,2),125(a,1))].">
      <j1 rule="para" parents="189 125"/>
    </justification>
  </clause>

  <clause id="335">
    <literal><![CDATA[
      (x / y) * ((z / y) \ z) = x
    ]]></literal>
    <justification jstring="[para(79(a,1),190(a,1,2,1,2))].">
      <j1 rule="para" parents="79 190"/>
    </justification>
  </clause>

  <clause id="336">
    <literal><![CDATA[
      L(T(x,x \ y),x \ y,z) = (z * (x \ y)) \ (z * y)
    ]]></literal>
    <justification jstring="[para(220(a,1),18(a,2,2,2))].">
      <j1 rule="para" parents="220 18"/>
    </justification>
  </clause>

  <clause id="337">
    <literal><![CDATA[
      (x \ y) * z != y
    ]]></literal>
    <literal><![CDATA[
      T(x,x \ y) = z
    ]]></literal>
    <justification jstring="[para(220(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="220 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="338">
    <literal><![CDATA[
      (x \ y) \ y != z
    ]]></literal>
    <literal><![CDATA[
      T(x,x \ y) = z
    ]]></literal>
    <justification jstring="[para(220(a,1),314(a,1,2))].">
      <j1 rule="para" parents="220 314"/>
    </justification>
  </clause>

  <clause id="339">
    <literal><![CDATA[
      T(x,y / z) != z
    ]]></literal>
    <literal><![CDATA[
      y / (y / z) = x
    ]]></literal>
    <justification jstring="[para(241(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="241 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="340">
    <literal><![CDATA[
      T(x / (x / y),(z / (x / y)) \ z) = y
    ]]></literal>
    <justification jstring="[para(79(a,2),241(a,1,2))].">
      <j1 rule="para" parents="79 241"/>
    </justification>
  </clause>

  <clause id="341">
    <literal><![CDATA[
      T(x / (x / y),y) = x / (x / y)
    ]]></literal>
    <justification jstring="[para(241(a,1),174(a,1,2))].">
      <j1 rule="para" parents="241 174"/>
    </justification>
  </clause>

  <clause id="342">
    <literal><![CDATA[
      x * T(x \ 1,x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,107,a,b,253,a)].">
      <j1 rule="hyper" parents="299 107 253"/>
    </justification>
  </clause>

  <clause id="345">
    <literal><![CDATA[
      R(x / y,y,x \ z) = z / (y * (x \ z))
    ]]></literal>
    <justification jstring="[para(286(a,1),20(a,2,1))].">
      <j1 rule="para" parents="286 20"/>
    </justification>
  </clause>

  <clause id="347">
    <literal><![CDATA[
      R(x,y,y \ z) * z = (x * y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(20(a,2),301(a,1,1))].">
      <j1 rule="para" parents="20 301"/>
    </justification>
  </clause>

  <clause id="348">
    <literal><![CDATA[
      (x / ((y / z) * z)) * y = x
    ]]></literal>
    <justification jstring="[para(79(a,1),301(a,1,1,2,2))].">
      <j1 rule="para" parents="79 301"/>
    </justification>
  </clause>

  <clause id="349">
    <literal><![CDATA[
      x / L(y,z,x / (z * y)) = (x / (z * y)) * z
    ]]></literal>
    <justification jstring="[para(18(a,2),302(a,1,2))].">
      <j1 rule="para" parents="18 302"/>
    </justification>
  </clause>

  <clause id="350">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      (z / x) \ z = y
    ]]></literal>
    <justification jstring="[para(332(a,1),207(a,1))].">
      <j1 rule="para" parents="332 207"/>
    </justification>
  </clause>

  <clause id="351">
    <literal><![CDATA[
      ((x \ y) \ y) * (T(x,x \ y) \ z) = z
    ]]></literal>
    <justification jstring="[para(262(a,1),332(a,1,1,1))].">
      <j1 rule="para" parents="262 332"/>
    </justification>
  </clause>

  <clause id="352">
    <literal><![CDATA[
      x * ((y / z) \ y) != u
    ]]></literal>
    <literal><![CDATA[
      u / z = x
    ]]></literal>
    <justification jstring="[para(335(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="335 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="353">
    <literal><![CDATA[
      (x / T(y,y \ z)) * ((y \ z) \ z) = x
    ]]></literal>
    <justification jstring="[para(262(a,1),335(a,1,2,1))].">
      <j1 rule="para" parents="262 335"/>
    </justification>
  </clause>

  <clause id="354">
    <literal><![CDATA[
      R(x,y / z,z) * y = (x * (y / z)) * z
    ]]></literal>
    <justification jstring="[para(20(a,2),348(a,1,1))].">
      <j1 rule="para" parents="20 348"/>
    </justification>
  </clause>

  <clause id="355">
    <literal><![CDATA[
      L(1,x,y) = 1
    ]]></literal>
    <justification jstring="[hyper(274,a,93,a),flip(a)].">
      <j1 rule="hyper" parents="274 93"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="358">
    <literal><![CDATA[
      a(x,y,1) = 1
    ]]></literal>
    <justification jstring="[hyper(55,a,355,a)].">
      <j1 rule="hyper" parents="55 355"/>
    </justification>
  </clause>

  <clause id="359">
    <literal><![CDATA[
      a(x,y,K(1,z)) = 1
    ]]></literal>
    <justification jstring="[para(199(a,2),358(a,1,3))].">
      <j1 rule="para" parents="199 358"/>
    </justification>
  </clause>

  <clause id="360">
    <literal><![CDATA[
      R(1,x,y) = 1
    ]]></literal>
    <justification jstring="[hyper(309,a,99,a),flip(a)].">
      <j1 rule="hyper" parents="309 99"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="363">
    <literal><![CDATA[
      (x \ 1) * x != y
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(88(a,1),202(a,1))].">
      <j1 rule="para" parents="88 202"/>
    </justification>
  </clause>

  <clause id="366">
    <literal><![CDATA[
      L((x \ y) \ 1,x \ y,x) = y \ x
    ]]></literal>
    <justification jstring="[hyper(299,a,157,a(flip),b,214,a),flip(a)].">
      <j1 rule="hyper" parents="299 157 214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="367">
    <literal><![CDATA[
      L(x \ 1,x,y) \ z = ((y * x) \ y) \ z
    ]]></literal>
    <justification jstring="[hyper(63,a,214,a)].">
      <j1 rule="hyper" parents="63 214"/>
    </justification>
  </clause>

  <clause id="368">
    <literal><![CDATA[
      x / L(y \ 1,y,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(192,a,214,a(flip))].">
      <j1 rule="hyper" parents="192 214"/>
    </justification>
  </clause>

  <clause id="369">
    <literal><![CDATA[
      (x * y) * L(y \ 1,y,x) = x
    ]]></literal>
    <justification jstring="[hyper(144,a,214,a(flip))].">
      <j1 rule="hyper" parents="144 214"/>
    </justification>
  </clause>

  <clause id="370">
    <literal><![CDATA[
      L(x \ 1,x,y / x) = y \ (y / x)
    ]]></literal>
    <justification jstring="[para(12(a,1),214(a,2,1))].">
      <j1 rule="para" parents="12 214"/>
    </justification>
  </clause>

  <clause id="371">
    <literal><![CDATA[
      T((x * y) \ x,z) = L(T(y \ 1,z),y,x)
    ]]></literal>
    <justification jstring="[para(214(a,1),25(a,2,1)),flip(a)].">
      <j1 rule="para" parents="214 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="372">
    <literal><![CDATA[
      L(L(x \ 1,y,z),x,u) = L((u * x) \ u,y,z)
    ]]></literal>
    <justification jstring="[para(214(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="214 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="373">
    <literal><![CDATA[
      R(1 / x,x,y) * z = (y / (x * y)) * z
    ]]></literal>
    <justification jstring="[hyper(59,a,216,a)].">
      <j1 rule="hyper" parents="59 216"/>
    </justification>
  </clause>

  <clause id="374">
    <literal><![CDATA[
      R(1 / x,x,y) \ y = x * y
    ]]></literal>
    <justification jstring="[hyper(186,a,216,a(flip))].">
      <j1 rule="hyper" parents="186 216"/>
    </justification>
  </clause>

  <clause id="375">
    <literal><![CDATA[
      R(1 / x,x,x \ y) = (x \ y) / y
    ]]></literal>
    <justification jstring="[para(10(a,1),216(a,2,2))].">
      <j1 rule="para" parents="10 216"/>
    </justification>
  </clause>

  <clause id="376">
    <literal><![CDATA[
      R(1 / (x / y),x / y,y) = y / x
    ]]></literal>
    <justification jstring="[para(12(a,1),216(a,2,2))].">
      <j1 rule="para" parents="12 216"/>
    </justification>
  </clause>

  <clause id="377">
    <literal><![CDATA[
      T(x / (y * x),z) = R(T(1 / y,z),y,x)
    ]]></literal>
    <justification jstring="[para(216(a,1),27(a,2,1)),flip(a)].">
      <j1 rule="para" parents="216 27"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="378">
    <literal><![CDATA[
      x \ (x * (y * z)) != z * u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) = u
    ]]></literal>
    <justification jstring="[para(9(a,2),236(a,2)),flip(a)].">
      <j1 rule="para" parents="9 236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="379">
    <literal><![CDATA[
      ((x * y) / z) * z != y * u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(12(a,2),236(a,2)),flip(a)].">
      <j1 rule="para" parents="12 236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="381">
    <literal><![CDATA[
      T(x,y) * z != x * y
    ]]></literal>
    <literal><![CDATA[
      T(y,T(x,y)) = z
    ]]></literal>
    <justification jstring="[para(107(a,1),236(a,2))].">
      <j1 rule="para" parents="107 236"/>
    </justification>
  </clause>

  <clause id="384">
    <literal><![CDATA[
      x * T(T(y,x),z) != u * x
    ]]></literal>
    <literal><![CDATA[
      T(y,z) = u
    ]]></literal>
    <justification jstring="[para(23(a,1),237(a,1,2))].">
      <j1 rule="para" parents="23 237"/>
    </justification>
  </clause>

  <clause id="385">
    <literal><![CDATA[
      x * (y * (y \ 1)) != z * u
    ]]></literal>
    <literal><![CDATA[
      x / u = z
    ]]></literal>
    <justification jstring="[para(10(a,2),245(a,1,2))].">
      <j1 rule="para" parents="10 245"/>
    </justification>
  </clause>

  <clause id="386">
    <literal><![CDATA[
      x * ((1 / y) * y) != z * u
    ]]></literal>
    <literal><![CDATA[
      x / u = z
    ]]></literal>
    <justification jstring="[para(12(a,2),245(a,1,2))].">
      <j1 rule="para" parents="12 245"/>
    </justification>
  </clause>

  <clause id="387">
    <literal><![CDATA[
      (x / y) * y != z * u
    ]]></literal>
    <literal><![CDATA[
      x / u = z
    ]]></literal>
    <justification jstring="[para(159(a,2),245(a,1))].">
      <j1 rule="para" parents="159 245"/>
    </justification>
  </clause>

  <clause id="388">
    <literal><![CDATA[
      x * (x \ y) != z * u
    ]]></literal>
    <literal><![CDATA[
      y / u = z
    ]]></literal>
    <justification jstring="[para(161(a,2),245(a,1))].">
      <j1 rule="para" parents="161 245"/>
    </justification>
  </clause>

  <clause id="389">
    <literal><![CDATA[
      x * (y * (y \ 1)) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ x = u
    ]]></literal>
    <justification jstring="[para(10(a,2),249(a,1,2))].">
      <j1 rule="para" parents="10 249"/>
    </justification>
  </clause>

  <clause id="390">
    <literal><![CDATA[
      (x / y) * y != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ x = u
    ]]></literal>
    <justification jstring="[para(159(a,2),249(a,1))].">
      <j1 rule="para" parents="159 249"/>
    </justification>
  </clause>

  <clause id="391">
    <literal><![CDATA[
      x * (x \ y) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ y = u
    ]]></literal>
    <justification jstring="[para(161(a,2),249(a,1))].">
      <j1 rule="para" parents="161 249"/>
    </justification>
  </clause>

  <clause id="392">
    <literal><![CDATA[
      K(x \ 1,x) != y
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) * x = y
    ]]></literal>
    <justification jstring="[para(16(a,2),254(a,1))].">
      <j1 rule="para" parents="16 254"/>
    </justification>
  </clause>

  <clause id="393">
    <literal><![CDATA[
      K(x,1 / x) != y
    ]]></literal>
    <literal><![CDATA[
      x * (1 / x) = y
    ]]></literal>
    <justification jstring="[para(16(a,2),257(a,1))].">
      <j1 rule="para" parents="16 257"/>
    </justification>
  </clause>

  <clause id="394">
    <literal><![CDATA[
      L(x,y,1 / y) != z
    ]]></literal>
    <literal><![CDATA[
      (1 / y) * (y * x) = z
    ]]></literal>
    <justification jstring="[para(18(a,2),257(a,1))].">
      <j1 rule="para" parents="18 257"/>
    </justification>
  </clause>

  <clause id="395">
    <literal><![CDATA[
      x * T(T(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(23(a,1),276(a,1,2))].">
      <j1 rule="para" parents="23 276"/>
    </justification>
  </clause>

  <clause id="396">
    <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),276(a,1,2))].">
      <j1 rule="para" parents="25 276"/>
    </justification>
  </clause>

  <clause id="397">
    <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),276(a,1,2))].">
      <j1 rule="para" parents="27 276"/>
    </justification>
  </clause>

  <clause id="398">
    <literal><![CDATA[
      T(x,y) \ (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      T(y,T(x,y)) = z
    ]]></literal>
    <justification jstring="[para(107(a,1),318(a,1,2))].">
      <j1 rule="para" parents="107 318"/>
    </justification>
  </clause>

  <clause id="399">
    <literal><![CDATA[
      T(x,x \ y) \ y != z
    ]]></literal>
    <literal><![CDATA[
      T(x \ y,T(x,x \ y)) = z
    ]]></literal>
    <justification jstring="[para(220(a,1),318(a,1,2))].">
      <j1 rule="para" parents="220 318"/>
    </justification>
  </clause>

  <clause id="400">
    <literal><![CDATA[
      T(x / y,y) != z
    ]]></literal>
    <literal><![CDATA[
      y \ x = z
    ]]></literal>
    <justification jstring="[para(10(a,1),324(a,1,1,1)),flip(b)].">
      <j1 rule="para" parents="10 324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="401">
    <literal><![CDATA[
      x / L(y,1 / y,x) = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(79(a,1),368(a,1,2,1))].">
      <j1 rule="para" parents="79 368"/>
    </justification>
  </clause>

  <clause id="402">
    <literal><![CDATA[
      (x * y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      L(y \ 1,y,x) = z
    ]]></literal>
    <justification jstring="[para(368(a,1),317(a,1,1))].">
      <j1 rule="para" parents="368 317"/>
    </justification>
  </clause>

  <clause id="403">
    <literal><![CDATA[
      ((x * y) \ x) * (L(y \ 1,y,x) \ z) = z
    ]]></literal>
    <justification jstring="[para(368(a,1),332(a,1,1,1))].">
      <j1 rule="para" parents="368 332"/>
    </justification>
  </clause>

  <clause id="404">
    <literal><![CDATA[
      L(x \ 1,x,y) * (((y * x) \ y) \ z) = z
    ]]></literal>
    <justification jstring="[para(368(a,1),333(a,1,2,1,1))].">
      <j1 rule="para" parents="368 333"/>
    </justification>
  </clause>

  <clause id="405">
    <literal><![CDATA[
      L(L(x \ 1,x,y),y * x,z) = (z * (y * x)) \ (z * y)
    ]]></literal>
    <justification jstring="[para(369(a,1),18(a,2,2,2))].">
      <j1 rule="para" parents="369 18"/>
    </justification>
  </clause>

  <clause id="406">
    <literal><![CDATA[
      R(x,x \ 1,y) \ y = (x \ 1) * y
    ]]></literal>
    <justification jstring="[para(76(a,1),374(a,1,1,1))].">
      <j1 rule="para" parents="76 374"/>
    </justification>
  </clause>

  <clause id="407">
    <literal><![CDATA[
      x / (y * x) != z
    ]]></literal>
    <literal><![CDATA[
      R(1 / y,y,x) = z
    ]]></literal>
    <justification jstring="[para(374(a,1),310(a,1,2)),flip(b)].">
      <j1 rule="para" parents="374 310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="409">
    <literal><![CDATA[
      T(x,x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) \ y = z
    ]]></literal>
    <justification jstring="[para(76(a,1),400(a,1,1))].">
      <j1 rule="para" parents="76 400"/>
    </justification>
  </clause>

  <clause id="410">
    <literal><![CDATA[
      T(x * y,K(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) \ (y * x) = z
    ]]></literal>
    <justification jstring="[para(183(a,1),400(a,1,1))].">
      <j1 rule="para" parents="183 400"/>
    </justification>
  </clause>

  <clause id="411">
    <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="412">
    <literal><![CDATA[
      x \ (y * T(y \ x,y)) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(107(a,2),89(a,1,2))].">
      <j1 rule="para" parents="107 89"/>
    </justification>
  </clause>

  <clause id="414">
    <literal><![CDATA[
      K(x \ 1,x) \ 1 = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(253(a,2),90(a,1,1))].">
      <j1 rule="para" parents="253 90"/>
    </justification>
  </clause>

  <clause id="415">
    <literal><![CDATA[
      x \ L(y,x \ 1,x) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(119,a,18,a,b,164,a(flip))].">
      <j1 rule="hyper" parents="119 18 164"/>
    </justification>
  </clause>

  <clause id="416">
    <literal><![CDATA[
      (x / (y * y)) \ z = (y * y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(119,a,286,a(flip),b,34,a(flip))].">
      <j1 rule="hyper" parents="119 286 34"/>
    </justification>
  </clause>

  <clause id="417">
    <literal><![CDATA[
      (T(x,x \ y) / z) \ ((x \ y) \ y) = z
    ]]></literal>
    <justification jstring="[hyper(119,a,108,a(flip),b,12,a)].">
      <j1 rule="hyper" parents="119 108 12"/>
    </justification>
  </clause>

  <clause id="418">
    <literal><![CDATA[
      (1 / x) \ (y * y) = x * (y * y)
    ]]></literal>
    <justification jstring="[hyper(119,a,77,a(flip),b,35,a(flip))].">
      <j1 rule="hyper" parents="119 77 35"/>
    </justification>
  </clause>

  <clause id="419">
    <literal><![CDATA[
      (x * (y * y)) \ z = (y * y) \ (x \ z)
    ]]></literal>
    <justification jstring="[hyper(119,a,72,a(flip),b,34,a)].">
      <j1 rule="hyper" parents="119 72 34"/>
    </justification>
  </clause>

  <clause id="420">
    <literal><![CDATA[
      ((x * x) * y) \ z = y \ ((x * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(119,a,72,a(flip),b,33,a)].">
      <j1 rule="hyper" parents="119 72 33"/>
    </justification>
  </clause>

  <clause id="421">
    <literal><![CDATA[
      (x \ 1) * (y * y) = x \ (y * y)
    ]]></literal>
    <justification jstring="[hyper(119,a,70,a(flip),b,35,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 70 35"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="422">
    <literal><![CDATA[
      ((x * x) \ 1) * y = (x * x) \ y
    ]]></literal>
    <justification jstring="[hyper(119,a,70,a(flip),b,33,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 70 33"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="423">
    <literal><![CDATA[
      R(x,y,y \ 1) / (y \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(120,a,20,a,b,169,a(flip))].">
      <j1 rule="hyper" parents="120 20 169"/>
    </justification>
  </clause>

  <clause id="424">
    <literal><![CDATA[
      (x / (y * y)) / z = x / (z * (y * y))
    ]]></literal>
    <justification jstring="[hyper(120,a,83,a(flip),b,35,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="120 83 35"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="425">
    <literal><![CDATA[
      (x / y) / (z * z) = x / ((z * z) * y)
    ]]></literal>
    <justification jstring="[hyper(120,a,83,a(flip),b,34,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="120 83 34"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="426">
    <literal><![CDATA[
      (x * x) / (y \ 1) = (x * x) * y
    ]]></literal>
    <justification jstring="[hyper(120,a,71,a(flip),b,33,a)].">
      <j1 rule="hyper" parents="120 71 33"/>
    </justification>
  </clause>

  <clause id="427">
    <literal><![CDATA[
      (x \ y) * z != y * (u * (u \ 1))
    ]]></literal>
    <literal><![CDATA[
      T(x,x \ y) = z
    ]]></literal>
    <justification jstring="[para(213(a,1),236(a,2))].">
      <j1 rule="para" parents="213 236"/>
    </justification>
  </clause>

  <clause id="428">
    <literal><![CDATA[
      (1 / x) * (1 / x) = x \ (1 / x)
    ]]></literal>
    <justification jstring="[hyper(125,a,215,a),flip(a)].">
      <j1 rule="hyper" parents="125 215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="429">
    <literal><![CDATA[
      x * T(x \ (y * x),z) = T(y,z) * x
    ]]></literal>
    <justification jstring="[para(22(a,1),232(a,1,2,1))].">
      <j1 rule="para" parents="22 232"/>
    </justification>
  </clause>

  <clause id="430">
    <literal><![CDATA[
      x * T(T(T(y,x),z),u) = T(T(y,z),u) * x
    ]]></literal>
    <justification jstring="[para(23(a,1),232(a,1,2,1))].">
      <j1 rule="para" parents="23 232"/>
    </justification>
  </clause>

  <clause id="431">
    <literal><![CDATA[
      T(x,y) * z != z * u
    ]]></literal>
    <literal><![CDATA[
      T(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(232(a,1),45(a,1))].">
      <j1 rule="para" parents="232 45"/>
    </justification>
  </clause>

  <clause id="432">
    <literal><![CDATA[
      T(x / y,z) * y = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(109(a,1),232(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="109 232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="433">
    <literal><![CDATA[
      T((x * y) / x,z) * x = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(222(a,1),232(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="222 232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="434">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ y,z) = T(x,z) * (x \ y)
    ]]></literal>
    <justification jstring="[para(108(a,1),232(a,1,2,1))].">
      <j1 rule="para" parents="108 232"/>
    </justification>
  </clause>

  <clause id="435">
    <literal><![CDATA[
      T(x / (x / y),z) * (x / y) = (x / y) * T(y,z)
    ]]></literal>
    <justification jstring="[para(241(a,1),232(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="241 232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="436">
    <literal><![CDATA[
      (x * T(x \ y,z)) / x = T(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(267,a,242,a)].">
      <j1 rule="hyper" parents="267 242"/>
    </justification>
  </clause>

  <clause id="437">
    <literal><![CDATA[
      T(T(T(x / y,z),u),y) = T(T(y \ x,z),u)
    ]]></literal>
    <justification jstring="[para(242(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="242 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="438">
    <literal><![CDATA[
      T(x / y,z) \ (y * T(y \ x,z)) = y
    ]]></literal>
    <justification jstring="[para(242(a,1),224(a,1,2,2))].">
      <j1 rule="para" parents="242 224"/>
    </justification>
  </clause>

  <clause id="439">
    <literal><![CDATA[
      x * T(x \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y / x,z) * x = u
    ]]></literal>
    <justification jstring="[para(242(a,1),276(a,1,2))].">
      <j1 rule="para" parents="242 276"/>
    </justification>
  </clause>

  <clause id="440">
    <literal><![CDATA[
      (x * T(x \ y,z)) / x != u
    ]]></literal>
    <literal><![CDATA[
      T(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(242(a,1),311(a,1,1,2)),flip(b)].">
      <j1 rule="para" parents="242 311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="441">
    <literal><![CDATA[
      (1 / x) * (x \ y) = (x * x) \ y
    ]]></literal>
    <justification jstring="[hyper(119,a,10,a(flip),b,265,a),flip(a)].">
      <j1 rule="hyper" parents="119 10 265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="442">
    <literal><![CDATA[
      x * ((1 / x) \ y) = (x * x) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,155,a(flip),b,265,a),flip(a)].">
      <j1 rule="hyper" parents="65 155 265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="443">
    <literal><![CDATA[
      x \ ((x * x) * y) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[hyper(119,a,155,a(flip),b,265,a(flip))].">
      <j1 rule="hyper" parents="119 155 265"/>
    </justification>
  </clause>

  <clause id="445">
    <literal><![CDATA[
      (x * T(y,z)) / x = T((x * y) / x,z)
    ]]></literal>
    <justification jstring="[hyper(267,a,266,a)].">
      <j1 rule="hyper" parents="267 266"/>
    </justification>
  </clause>

  <clause id="446">
    <literal><![CDATA[
      T(x,y) != T(z,u)
    ]]></literal>
    <literal><![CDATA[
      T((y * z) / y,u) = x
    ]]></literal>
    <justification jstring="[para(266(a,1),51(a,2)),flip(b)].">
      <j1 rule="para" parents="266 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="448">
    <literal><![CDATA[
      (x * T(y,z)) / x != u
    ]]></literal>
    <literal><![CDATA[
      T((x * y) / x,z) = u
    ]]></literal>
    <justification jstring="[para(266(a,1),311(a,1,1,2)),flip(b)].">
      <j1 rule="para" parents="266 311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="449">
    <literal><![CDATA[
      T(x,(y * x) / y) = x
    ]]></literal>
    <justification jstring="[hyper(56,a,268,a)].">
      <j1 rule="hyper" parents="56 268"/>
    </justification>
  </clause>

  <clause id="450">
    <literal><![CDATA[
      T(x \ y,y / x) = x \ y
    ]]></literal>
    <justification jstring="[para(10(a,1),449(a,1,2,1))].">
      <j1 rule="para" parents="10 449"/>
    </justification>
  </clause>

  <clause id="451">
    <literal><![CDATA[
      T(x \ y,z) * (y / x) = (y / x) * T(x \ y,z)
    ]]></literal>
    <justification jstring="[para(450(a,1),232(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="450 232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="452">
    <literal><![CDATA[
      (x * y) \ (x * ((z \ y) * z)) = L(K(z \ y,z),y,x)
    ]]></literal>
    <justification jstring="[para(287(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="287 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="453">
    <literal><![CDATA[
      (x \ y) * x != y * z
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,x) = z
    ]]></literal>
    <justification jstring="[para(287(a,1),45(a,1))].">
      <j1 rule="para" parents="287 45"/>
    </justification>
  </clause>

  <clause id="454">
    <literal><![CDATA[
      x \ ((y \ x) * y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,y) = z
    ]]></literal>
    <justification jstring="[para(287(a,1),314(a,1,2))].">
      <j1 rule="para" parents="287 314"/>
    </justification>
  </clause>

  <clause id="455">
    <literal><![CDATA[
      x * (y / x) != y * z
    ]]></literal>
    <literal><![CDATA[
      K(x,y / x) = z
    ]]></literal>
    <justification jstring="[para(288(a,1),45(a,1))].">
      <j1 rule="para" parents="288 45"/>
    </justification>
  </clause>

  <clause id="457">
    <literal><![CDATA[
      x \ (y * (x / y)) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x / y) = z
    ]]></literal>
    <justification jstring="[para(288(a,1),314(a,1,2))].">
      <j1 rule="para" parents="288 314"/>
    </justification>
  </clause>

  <clause id="458">
    <literal><![CDATA[
      1 / (x * x) = (x * x) \ 1
    ]]></literal>
    <justification jstring="[hyper(120,a,68,a(flip),b,421,a)].">
      <j1 rule="hyper" parents="120 68 421"/>
    </justification>
  </clause>

  <clause id="459">
    <literal><![CDATA[
      x / (x * x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(120,a,9,a(flip),b,421,a)].">
      <j1 rule="hyper" parents="120 9 421"/>
    </justification>
  </clause>

  <clause id="460">
    <literal><![CDATA[
      (x \ 1) \ x = x * x
    ]]></literal>
    <justification jstring="[hyper(119,a,9,a(flip),b,421,a)].">
      <j1 rule="hyper" parents="119 9 421"/>
    </justification>
  </clause>

  <clause id="461">
    <literal><![CDATA[
      (x * x) \ (y \ (x * x)) = T(y \ 1,x * x)
    ]]></literal>
    <justification jstring="[hyper(119,a,421,a(flip),b,107,a)].">
      <j1 rule="hyper" parents="119 421 107"/>
    </justification>
  </clause>

  <clause id="462">
    <literal><![CDATA[
      (x \ 1) * ((y * y) * z) = (x \ (y * y)) * z
    ]]></literal>
    <justification jstring="[para(421(a,1),34(a,1,1)),flip(a)].">
      <j1 rule="para" parents="421 34"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="463">
    <literal><![CDATA[
      T(x \ 1,x * x) = (x * x) \ x
    ]]></literal>
    <justification jstring="[para(459(a,1),109(a,1,1))].">
      <j1 rule="para" parents="459 109"/>
    </justification>
  </clause>

  <clause id="464">
    <literal><![CDATA[
      ((x * x) \ y) \ 1 = y \ (x * x)
    ]]></literal>
    <justification jstring="[hyper(38,a,180,a,b,426,a),flip(a)].">
      <j1 rule="hyper" parents="38 180 426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="465">
    <literal><![CDATA[
      ((x \ 1) * (x \ 1)) \ y = x * ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,181,a(flip),b,441,a),flip(a)].">
      <j1 rule="hyper" parents="65 181 441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="466">
    <literal><![CDATA[
      T(x * x,x) = (1 / x) \ x
    ]]></literal>
    <justification jstring="[hyper(236,a,442,a)].">
      <j1 rule="hyper" parents="236 442"/>
    </justification>
  </clause>

  <clause id="468">
    <literal><![CDATA[
      ((x \ 1) * (x \ 1)) * y = (x \ 1) * (x \ y)
    ]]></literal>
    <justification jstring="[para(76(a,1),442(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="76 442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="469">
    <literal><![CDATA[
      T(x \ 1,x * x) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(299,a,264,a(flip),b,463,a),flip(a)].">
      <j1 rule="hyper" parents="299 264 463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="470">
    <literal><![CDATA[
      T(T(x \ 1,y),x * x) = T(1 / x,y)
    ]]></literal>
    <justification jstring="[para(469(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="469 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="471">
    <literal><![CDATA[
      1 / (x \ (y * y)) = (y * y) \ x
    ]]></literal>
    <justification jstring="[hyper(192,a,464,a)].">
      <j1 rule="hyper" parents="192 464"/>
    </justification>
  </clause>

  <clause id="472">
    <literal><![CDATA[
      1 / (x * (y * y)) = (y * y) \ (1 / x)
    ]]></literal>
    <justification jstring="[para(418(a,1),471(a,1,2))].">
      <j1 rule="para" parents="418 471"/>
    </justification>
  </clause>

  <clause id="473">
    <literal><![CDATA[
      x \ ((x * y) * L(z,y,x)) = y * z
    ]]></literal>
    <justification jstring="[hyper(119,a,94,a,b,xx)].">
      <j1 rule="hyper" parents="119 94"/>
    </justification>
  </clause>

  <clause id="474">
    <literal><![CDATA[
      x * L(y,z,x / z) = (x / z) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,154,a(flip),b,94,a)].">
      <j1 rule="hyper" parents="65 154 94"/>
    </justification>
  </clause>

  <clause id="475">
    <literal><![CDATA[
      (1 / x) * (x * y) = L(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(36,a,265,a,b,94,a)].">
      <j1 rule="hyper" parents="36 265 94"/>
    </justification>
  </clause>

  <clause id="476">
    <literal><![CDATA[
      L(x * x,y,z) = x * x
    ]]></literal>
    <justification jstring="[hyper(36,a,35,a,b,94,a),flip(a)].">
      <j1 rule="hyper" parents="36 35 94"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="477">
    <literal><![CDATA[
      L(x,y * y,z) = x
    ]]></literal>
    <justification jstring="[hyper(36,a,34,a,b,94,a),flip(a)].">
      <j1 rule="hyper" parents="36 34 94"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="478">
    <literal><![CDATA[
      L(x,y,z * z) = x
    ]]></literal>
    <justification jstring="[hyper(36,a,33,a,b,94,a),flip(a)].">
      <j1 rule="hyper" parents="36 33 94"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="479">
    <literal><![CDATA[
      L(x \ (y \ ((y * x) * z)),x,y) = z
    ]]></literal>
    <justification jstring="[hyper(36,a,72,a(flip),b,94,a),flip(a)].">
      <j1 rule="hyper" parents="36 72 94"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="480">
    <literal><![CDATA[
      L(x,y,z) \ (z * (y * x)) = T(z * y,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,94,a(flip),b,107,a)].">
      <j1 rule="hyper" parents="119 94 107"/>
    </justification>
  </clause>

  <clause id="481">
    <literal><![CDATA[
      (1 / x) \ L(y,x,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(36,a,442,a,b,94,a(flip))].">
      <j1 rule="hyper" parents="36 442 94"/>
    </justification>
  </clause>

  <clause id="482">
    <literal><![CDATA[
      x * L(y,z \ x,z) = z * ((z \ x) * y)
    ]]></literal>
    <justification jstring="[para(10(a,1),94(a,1,1))].">
      <j1 rule="para" parents="10 94"/>
    </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 * y) * T(L(z,y,x),u) = x * (y * T(z,u))
    ]]></literal>
    <justification jstring="[para(25(a,1),94(a,1,2))].">
      <j1 rule="para" parents="25 94"/>
    </justification>
  </clause>

  <clause id="488">
    <literal><![CDATA[
      (x * y) * R(L(z,y,x),u,w) = x * (y * R(z,u,w))
    ]]></literal>
    <justification jstring="[para(29(a,2),94(a,1,2))].">
      <j1 rule="para" parents="29 94"/>
    </justification>
  </clause>

  <clause id="489">
    <literal><![CDATA[
      (x * y) * L(L(z,y,x),u,w) = x * (y * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(30(a,1),94(a,1,2))].">
      <j1 rule="para" parents="30 94"/>
    </justification>
  </clause>

  <clause id="490">
    <literal><![CDATA[
      (x * y) * z != x * (y * u)
    ]]></literal>
    <literal><![CDATA[
      L(u,y,x) = z
    ]]></literal>
    <justification jstring="[para(94(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="94 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="491">
    <literal><![CDATA[
      (x * y) * L(z,T(x,y),y) = y * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[para(107(a,1),94(a,1,1))].">
      <j1 rule="para" parents="107 94"/>
    </justification>
  </clause>

  <clause id="492">
    <literal><![CDATA[
      (x * (y * z)) * K(L(z,y,x),x * y) = L(z,y,x) * (x * y)
    ]]></literal>
    <justification jstring="[para(94(a,1),88(a,1,1))].">
      <j1 rule="para" parents="94 88"/>
    </justification>
  </clause>

  <clause id="493">
    <literal><![CDATA[
      (x * y) \ (x * (y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,y,x) = u
    ]]></literal>
    <justification jstring="[para(94(a,1),314(a,1,2))].">
      <j1 rule="para" parents="94 314"/>
    </justification>
  </clause>

  <clause id="494">
    <literal><![CDATA[
      x * ((x \ 1) * y) != z
    ]]></literal>
    <literal><![CDATA[
      L(y,x \ 1,x) = z
    ]]></literal>
    <justification jstring="[para(94(a,1),202(a,1))].">
      <j1 rule="para" parents="94 202"/>
    </justification>
  </clause>

  <clause id="496">
    <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="497">
    <literal><![CDATA[
      L(x,y * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(477(a,1),52(a,2))].">
      <j1 rule="para" parents="477 52"/>
    </justification>
  </clause>

  <clause id="498">
    <literal><![CDATA[
      L(x,y \ (1 / y),z) = x
    ]]></literal>
    <justification jstring="[para(428(a,1),477(a,1,2))].">
      <j1 rule="para" parents="428 477"/>
    </justification>
  </clause>

  <clause id="499">
    <literal><![CDATA[
      L(x,1,y) = z \ (z * x)
    ]]></literal>
    <justification jstring="[hyper(299,a,9,a,b,496,a),flip(a)].">
      <j1 rule="hyper" parents="299 9 496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="500">
    <literal><![CDATA[
      L(x,1,y) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(496(a,1),52(a,1)),flip(a)].">
      <j1 rule="para" parents="496 52"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="502">
    <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="503">
    <literal><![CDATA[
      L(x,y,z * z) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(478(a,1),52(a,2))].">
      <j1 rule="para" parents="478 52"/>
    </justification>
  </clause>

  <clause id="504">
    <literal><![CDATA[
      L(x,y,z \ (1 / z)) = x
    ]]></literal>
    <justification jstring="[para(428(a,1),478(a,1,3))].">
      <j1 rule="para" parents="428 478"/>
    </justification>
  </clause>

  <clause id="505">
    <literal><![CDATA[
      L(x,y,1) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(502(a,1),52(a,2))].">
      <j1 rule="para" parents="502 52"/>
    </justification>
  </clause>

  <clause id="506">
    <literal><![CDATA[
      L(x,y \ (1 / y),z) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(498(a,1),52(a,2))].">
      <j1 rule="para" parents="498 52"/>
    </justification>
  </clause>

  <clause id="507">
    <literal><![CDATA[
      (x * (y \ (1 / y))) * z = x * ((y \ (1 / y)) * z)
    ]]></literal>
    <justification jstring="[para(498(a,1),94(a,1,2))].">
      <j1 rule="para" parents="498 94"/>
    </justification>
  </clause>

  <clause id="508">
    <literal><![CDATA[
      L(x,1,y) != z \ (z * u)
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(499(a,1),52(a,1)),flip(a)].">
      <j1 rule="para" parents="499 52"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="509">
    <literal><![CDATA[
      ((x \ (1 / x)) * y) * z = (x \ (1 / x)) * (y * z)
    ]]></literal>
    <justification jstring="[para(504(a,1),94(a,1,2))].">
      <j1 rule="para" parents="504 94"/>
    </justification>
  </clause>

  <clause id="510">
    <literal><![CDATA[
      (1 / (x \ (1 / x))) \ y = (x \ (1 / x)) * y
    ]]></literal>
    <justification jstring="[hyper(119,a,504,a(flip),b,475,a)].">
      <j1 rule="hyper" parents="119 504 475"/>
    </justification>
  </clause>

  <clause id="511">
    <literal><![CDATA[
      L(x \ y,x,x) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,155,a(flip),b,475,a),flip(a)].">
      <j1 rule="hyper" parents="65 155 475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="512">
    <literal><![CDATA[
      (1 / x) * ((x * x) * y) = L(x,x,x) * y
    ]]></literal>
    <justification jstring="[para(475(a,1),34(a,1,1)),flip(a)].">
      <j1 rule="para" parents="475 34"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="513">
    <literal><![CDATA[
      L(T(x,y),y,y) = (1 / y) * (x * y)
    ]]></literal>
    <justification jstring="[para(107(a,1),475(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="514">
    <literal><![CDATA[
      (1 / x) \ y != x * z
    ]]></literal>
    <literal><![CDATA[
      L(z,x,x) = y
    ]]></literal>
    <justification jstring="[para(481(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="481 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="515">
    <literal><![CDATA[
      L(T(x \ y,z),x,x) = T((1 / x) * y,z)
    ]]></literal>
    <justification jstring="[para(511(a,1),25(a,2,1))].">
      <j1 rule="para" parents="511 25"/>
    </justification>
  </clause>

  <clause id="516">
    <literal><![CDATA[
      L(R(x \ y,z,u),x,x) = R((1 / x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(511(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="511 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="517">
    <literal><![CDATA[
      L(x \ T(y * x,y),x,y) = y
    ]]></literal>
    <justification jstring="[hyper(299,a,224,a(flip),b,96,a),flip(a)].">
      <j1 rule="hyper" parents="299 224 96"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="518">
    <literal><![CDATA[
      L(x \ y,x,1 / x) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(299,a,165,a(flip),b,96,a),flip(a)].">
      <j1 rule="hyper" parents="299 165 96"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="519">
    <literal><![CDATA[
      L((x \ 1) \ y,x \ 1,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(299,a,164,a(flip),b,96,a),flip(a)].">
      <j1 rule="hyper" parents="299 164 96"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="520">
    <literal><![CDATA[
      L((x \ y) \ z,x \ y,x) = y \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(299,a,157,a(flip),b,96,a),flip(a)].">
      <j1 rule="hyper" parents="299 157 96"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="521">
    <literal><![CDATA[
      L(x \ ((y * x) / y),x,y) = K(y,(y * x) / y)
    ]]></literal>
    <justification jstring="[hyper(299,a,91,a(flip),b,96,a),flip(a)].">
      <j1 rule="hyper" parents="299 91 96"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="522">
    <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="523">
    <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="524">
    <literal><![CDATA[
      T((x * y) \ (x * z),u) = L(T(y \ z,u),y,x)
    ]]></literal>
    <justification jstring="[para(96(a,1),25(a,2,1)),flip(a)].">
      <j1 rule="para" parents="96 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="525">
    <literal><![CDATA[
      L(T(x,y) \ z,T(x,y),y) = (x * y) \ (y * z)
    ]]></literal>
    <justification jstring="[para(107(a,1),96(a,2,1))].">
      <j1 rule="para" parents="107 96"/>
    </justification>
  </clause>

  <clause id="526">
    <literal><![CDATA[
      L(x \ T(y,z),x,z) = (z * x) \ (y * z)
    ]]></literal>
    <justification jstring="[para(107(a,1),96(a,2,2))].">
      <j1 rule="para" parents="107 96"/>
    </justification>
  </clause>

  <clause id="527">
    <literal><![CDATA[
      L(K(x,y) \ z,K(x,y),y * x) = (x * y) \ ((y * x) * z)
    ]]></literal>
    <justification jstring="[para(88(a,1),96(a,2,1))].">
      <j1 rule="para" parents="88 96"/>
    </justification>
  </clause>

  <clause id="528">
    <literal><![CDATA[
      L(x \ (1 / y),x,y) = (y * x) \ K(y,1 / y)
    ]]></literal>
    <justification jstring="[para(256(a,2),96(a,2,2))].">
      <j1 rule="para" parents="256 96"/>
    </justification>
  </clause>

  <clause id="529">
    <literal><![CDATA[
      x / L(y \ z,y,x / z) = (x / z) * y
    ]]></literal>
    <justification jstring="[para(96(a,2),302(a,1,2))].">
      <j1 rule="para" parents="96 302"/>
    </justification>
  </clause>

  <clause id="530">
    <literal><![CDATA[
      L((x \ 1) \ y,x \ 1,x) != z
    ]]></literal>
    <literal><![CDATA[
      x * y = z
    ]]></literal>
    <justification jstring="[para(96(a,2),254(a,1))].">
      <j1 rule="para" parents="96 254"/>
    </justification>
  </clause>

  <clause id="531">
    <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="532">
    <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="533">
    <literal><![CDATA[
      R(x / y,y,x \ z) \ z = y * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(119,a,286,a(flip),b,103,a)].">
      <j1 rule="hyper" parents="119 286 103"/>
    </justification>
  </clause>

  <clause id="534">
    <literal><![CDATA[
      R(x / y,y,z) \ (x * z) = y * z
    ]]></literal>
    <justification jstring="[hyper(119,a,154,a(flip),b,103,a)].">
      <j1 rule="hyper" parents="119 154 103"/>
    </justification>
  </clause>

  <clause id="535">
    <literal><![CDATA[
      R(x,y,z * z) = x
    ]]></literal>
    <justification jstring="[hyper(37,a,35,a(flip),b,103,a),flip(a)].">
      <j1 rule="hyper" parents="37 35 103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="536">
    <literal><![CDATA[
      R(x,y * y,z) = x
    ]]></literal>
    <justification jstring="[hyper(37,a,34,a(flip),b,103,a),flip(a)].">
      <j1 rule="hyper" parents="37 34 103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="537">
    <literal><![CDATA[
      (R(x,y,z) * y) \ ((x * y) * z) = L(z,y,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,103,a(flip),b,94,a)].">
      <j1 rule="hyper" parents="119 103 94"/>
    </justification>
  </clause>

  <clause id="538">
    <literal><![CDATA[
      ((x * y) * z) \ ((y * z) * R(x,y,z)) = K(y * z,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(103(a,1),16(a,2,1)),flip(a)].">
      <j1 rule="para" parents="103 16"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="539">
    <literal><![CDATA[
      (((x * y) * z) * u) / ((y * z) * u) = R(R(x,y,z),y * z,u)
    ]]></literal>
    <justification jstring="[para(103(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="103 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="540">
    <literal><![CDATA[
      ((x * R(y,z,u)) * (z * u)) / ((y * z) * u) = R(x,R(y,z,u),z * u)
    ]]></literal>
    <justification jstring="[para(103(a,1),20(a,2,2)),flip(a)].">
      <j1 rule="para" parents="103 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="541">
    <literal><![CDATA[
      T(R(x,y,z),u) * (y * z) = (T(x,u) * y) * z
    ]]></literal>
    <justification jstring="[para(27(a,1),103(a,1,1))].">
      <j1 rule="para" parents="27 103"/>
    </justification>
  </clause>

  <clause id="542">
    <literal><![CDATA[
      L(R(x,y,z),u,w) * (y * z) = (L(x,u,w) * y) * z
    ]]></literal>
    <justification jstring="[para(29(a,1),103(a,1,1))].">
      <j1 rule="para" parents="29 103"/>
    </justification>
  </clause>

  <clause id="543">
    <literal><![CDATA[
      R(R(x,y,z),u,w) * (y * z) = (R(x,u,w) * y) * z
    ]]></literal>
    <justification jstring="[para(31(a,1),103(a,1,1))].">
      <j1 rule="para" parents="31 103"/>
    </justification>
  </clause>

  <clause id="544">
    <literal><![CDATA[
      (x * y) * z != u * (y * z)
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(103(a,1),46(a,1))].">
      <j1 rule="para" parents="103 46"/>
    </justification>
  </clause>

  <clause id="546">
    <literal><![CDATA[
      R(x,y,T(z,y)) * (z * y) = (x * y) * T(z,y)
    ]]></literal>
    <justification jstring="[para(107(a,1),103(a,1,2))].">
      <j1 rule="para" parents="107 103"/>
    </justification>
  </clause>

  <clause id="547">
    <literal><![CDATA[
      ((x * y) * z) * K(y * z,R(x,y,z)) = (y * z) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(103(a,1),88(a,1,1))].">
      <j1 rule="para" parents="103 88"/>
    </justification>
  </clause>

  <clause id="548">
    <literal><![CDATA[
      R(x,y * z,K(z,y)) * (z * y) = (x * (y * z)) * K(z,y)
    ]]></literal>
    <justification jstring="[para(88(a,1),103(a,1,2))].">
      <j1 rule="para" parents="88 103"/>
    </justification>
  </clause>

  <clause id="549">
    <literal><![CDATA[
      ((x * y) * z) / (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(103(a,1),307(a,1,1)),flip(b)].">
      <j1 rule="para" parents="103 307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="550">
    <literal><![CDATA[
      (R(x,y,z) * (y * z)) / z != u
    ]]></literal>
    <literal><![CDATA[
      x * y = u
    ]]></literal>
    <justification jstring="[para(103(a,2),307(a,1,1)),flip(b)].">
      <j1 rule="para" parents="103 307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="551">
    <literal><![CDATA[
      (x * y) * (y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      R(x,y,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(103(a,1),203(a,1)),flip(b)].">
      <j1 rule="para" parents="103 203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="552">
    <literal><![CDATA[
      (x * (1 / y)) * y != z
    ]]></literal>
    <literal><![CDATA[
      R(x,1 / y,y) = z
    ]]></literal>
    <justification jstring="[para(103(a,1),204(a,1)),flip(b)].">
      <j1 rule="para" parents="103 204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="554">
    <literal><![CDATA[
      R(x,R(y,z,u),z * u) * ((y * z) * u) = (x * R(y,z,u)) * (z * u)
    ]]></literal>
    <justification jstring="[para(103(a,1),103(a,1,2))].">
      <j1 rule="para" parents="103 103"/>
    </justification>
  </clause>

  <clause id="555">
    <literal><![CDATA[
      R(x * y,z,u * u) != x * w
    ]]></literal>
    <literal><![CDATA[
      w = y
    ]]></literal>
    <justification jstring="[para(535(a,2),45(a,2)),flip(a)].">
      <j1 rule="para" parents="535 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="556">
    <literal><![CDATA[
      R(x,y,z * z) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(535(a,1),53(a,2))].">
      <j1 rule="para" parents="535 53"/>
    </justification>
  </clause>

  <clause id="557">
    <literal><![CDATA[
      R(x,y,z \ (1 / z)) = x
    ]]></literal>
    <justification jstring="[para(428(a,1),535(a,1,3))].">
      <j1 rule="para" parents="428 535"/>
    </justification>
  </clause>

  <clause id="558">
    <literal><![CDATA[
      R(x,1,y) = x
    ]]></literal>
    <justification jstring="[para(7(a,1),536(a,1,2))].">
      <j1 rule="para" parents="7 536"/>
    </justification>
  </clause>

  <clause id="559">
    <literal><![CDATA[
      R(x,y * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(536(a,1),53(a,2))].">
      <j1 rule="para" parents="536 53"/>
    </justification>
  </clause>

  <clause id="560">
    <literal><![CDATA[
      R(x,1,y) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(558(a,1),53(a,1)),flip(a)].">
      <j1 rule="para" parents="558 53"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="562">
    <literal><![CDATA[
      R(x,y,z \ (1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(557(a,1),53(a,2))].">
      <j1 rule="para" parents="557 53"/>
    </justification>
  </clause>

  <clause id="563">
    <literal><![CDATA[
      (x * y) * (z \ (1 / z)) = x * (y * (z \ (1 / z)))
    ]]></literal>
    <justification jstring="[para(557(a,1),103(a,1,1)),flip(a)].">
      <j1 rule="para" parents="557 103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="564">
    <literal><![CDATA[
      R(x / (1 / y),1 / y,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(299,a,170,a(flip),b,104,a),flip(a)].">
      <j1 rule="hyper" parents="299 170 104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="565">
    <literal><![CDATA[
      R(x / y,y,y \ 1) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,169,a(flip),b,104,a),flip(a)].">
      <j1 rule="hyper" parents="299 169 104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="566">
    <literal><![CDATA[
      R(x / y,y,y \ z) = (x * (y \ z)) / z
    ]]></literal>
    <justification jstring="[para(10(a,1),104(a,2,2))].">
      <j1 rule="para" parents="10 104"/>
    </justification>
  </clause>

  <clause id="567">
    <literal><![CDATA[
      R(x / (y / z),y / z,z) = (x * z) / y
    ]]></literal>
    <justification jstring="[para(12(a,1),104(a,2,2))].">
      <j1 rule="para" parents="12 104"/>
    </justification>
  </clause>

  <clause id="568">
    <literal><![CDATA[
      T((x * y) / (z * y),u) = R(T(x / z,u),z,y)
    ]]></literal>
    <justification jstring="[para(104(a,1),27(a,2,1)),flip(a)].">
      <j1 rule="para" parents="104 27"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="569">
    <literal><![CDATA[
      T(R(x / y,y,z),y * z) = (y * z) \ (x * z)
    ]]></literal>
    <justification jstring="[para(104(a,2),109(a,1,1))].">
      <j1 rule="para" parents="104 109"/>
    </justification>
  </clause>

  <clause id="570">
    <literal><![CDATA[
      R(x / T(y,z),T(y,z),y) = (x * y) / (y * T(y,z))
    ]]></literal>
    <justification jstring="[para(239(a,1),104(a,2,2))].">
      <j1 rule="para" parents="239 104"/>
    </justification>
  </clause>

  <clause id="571">
    <literal><![CDATA[
      R(R(1 / x,x,y),x * y,z) = (y * z) / ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(216(a,2),104(a,1,1))].">
      <j1 rule="para" parents="216 104"/>
    </justification>
  </clause>

  <clause id="572">
    <literal><![CDATA[
      R(R(x,y,z) / u,u,y * z) = ((x * y) * z) / (u * (y * z))
    ]]></literal>
    <justification jstring="[para(103(a,1),104(a,2,1))].">
      <j1 rule="para" parents="103 104"/>
    </justification>
  </clause>

  <clause id="573">
    <literal><![CDATA[
      R(x / R(y,z,u),R(y,z,u),z * u) = (x * (z * u)) / ((y * z) * u)
    ]]></literal>
    <justification jstring="[para(103(a,1),104(a,2,2))].">
      <j1 rule="para" parents="103 104"/>
    </justification>
  </clause>

  <clause id="574">
    <literal><![CDATA[
      R(R(x / y,y,z),y * z,u) = ((x * z) * u) / ((y * z) * u)
    ]]></literal>
    <justification jstring="[para(104(a,2),104(a,1,1))].">
      <j1 rule="para" parents="104 104"/>
    </justification>
  </clause>

  <clause id="576">
    <literal><![CDATA[
      x \ (y * (y \ x)) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ 1 = u
    ]]></literal>
    <justification jstring="[para(213(a,2),124(a,1,2)),flip(b)].">
      <j1 rule="para" parents="213 124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="577">
    <literal><![CDATA[
      x \ (x * y) != z * u
    ]]></literal>
    <literal><![CDATA[
      y / u = z
    ]]></literal>
    <justification jstring="[para(12(a,1),134(a,1,2,2))].">
      <j1 rule="para" parents="12 134"/>
    </justification>
  </clause>

  <clause id="578">
    <literal><![CDATA[
      x \ x != y * z
    ]]></literal>
    <literal><![CDATA[
      1 / z = y
    ]]></literal>
    <justification jstring="[para(78(a,1),134(a,1,2))].">
      <j1 rule="para" parents="78 134"/>
    </justification>
  </clause>

  <clause id="579">
    <literal><![CDATA[
      x \ (y * (y \ x)) != z * u
    ]]></literal>
    <literal><![CDATA[
      1 / u = z
    ]]></literal>
    <justification jstring="[para(157(a,1),578(a,1))].">
      <j1 rule="para" parents="157 578"/>
    </justification>
  </clause>

  <clause id="580">
    <literal><![CDATA[
      R(x,x \ y,z) \ (y * z) = (x \ y) * z
    ]]></literal>
    <justification jstring="[para(10(a,1),182(a,1,2,1))].">
      <j1 rule="para" parents="10 182"/>
    </justification>
  </clause>

  <clause id="581">
    <literal><![CDATA[
      R(x,T(y,x),z) \ ((y * x) * z) = T(y,x) * z
    ]]></literal>
    <justification jstring="[para(107(a,1),182(a,1,2,1))].">
      <j1 rule="para" parents="107 182"/>
    </justification>
  </clause>

  <clause id="582">
    <literal><![CDATA[
      R(x * y,K(y,x),z) \ ((y * x) * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[para(88(a,1),182(a,1,2,1))].">
      <j1 rule="para" parents="88 182"/>
    </justification>
  </clause>

  <clause id="583">
    <literal><![CDATA[
      R(x,K(y \ x,y),z) \ (((y \ x) * y) * z) = K(y \ x,y) * z
    ]]></literal>
    <justification jstring="[para(287(a,1),182(a,1,2,1))].">
      <j1 rule="para" parents="287 182"/>
    </justification>
  </clause>

  <clause id="584">
    <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),182(a,1,2,1))].">
      <j1 rule="para" parents="94 182"/>
    </justification>
  </clause>

  <clause id="585">
    <literal><![CDATA[
      (x * y) / L(z,y / z,x) = x * (y / z)
    ]]></literal>
    <justification jstring="[para(12(a,1),184(a,1,1,2))].">
      <j1 rule="para" parents="12 184"/>
    </justification>
  </clause>

  <clause id="586">
    <literal><![CDATA[
      (x * (y * z)) / L(T(y,z),z,x) = x * z
    ]]></literal>
    <justification jstring="[para(107(a,1),184(a,1,1,2))].">
      <j1 rule="para" parents="107 184"/>
    </justification>
  </clause>

  <clause id="587">
    <literal><![CDATA[
      x / K(x \ 1,x) = R(x,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(253(a,2),212(a,2,2)),flip(a)].">
      <j1 rule="para" parents="253 212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="588">
    <literal><![CDATA[
      x \ L(L(y,x \ 1,x),z,u) = (x \ 1) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(119,a,30,a,b,252,a)].">
      <j1 rule="hyper" parents="119 30 252"/>
    </justification>
  </clause>

  <clause id="589">
    <literal><![CDATA[
      x \ T(L(y,x \ 1,x),z) = (x \ 1) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,25,a(flip),b,252,a)].">
      <j1 rule="hyper" parents="119 25 252"/>
    </justification>
  </clause>

  <clause id="590">
    <literal><![CDATA[
      x * K(x \ 1,x) = L(x,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(253(a,2),252(a,1,2))].">
      <j1 rule="para" parents="253 252"/>
    </justification>
  </clause>

  <clause id="591">
    <literal><![CDATA[
      L(R(x,y,y \ 1),z,u) / (y \ 1) = L(x,z,u) * y
    ]]></literal>
    <justification jstring="[hyper(120,a,29,a(flip),b,258,a)].">
      <j1 rule="hyper" parents="120 29 258"/>
    </justification>
  </clause>

  <clause id="592">
    <literal><![CDATA[
      (x \ 1) \ R(y,x,x \ 1) = T(y * x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,258,a(flip),b,107,a)].">
      <j1 rule="hyper" parents="119 258 107"/>
    </justification>
  </clause>

  <clause id="593">
    <literal><![CDATA[
      R(x,y,y \ 1) / (y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x * y = z
    ]]></literal>
    <justification jstring="[para(258(a,1),307(a,1,1)),flip(b)].">
      <j1 rule="para" parents="258 307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="594">
    <literal><![CDATA[
      L((x \ 1) \ 1,x \ 1,y * x) = R(y,x,x \ 1) \ (y * x)
    ]]></literal>
    <justification jstring="[para(258(a,1),214(a,2,1))].">
      <j1 rule="para" parents="258 214"/>
    </justification>
  </clause>

  <clause id="595">
    <literal><![CDATA[
      R(R(x,y,z),y * z,(y * z) \ 1) = ((x * y) * z) * ((y * z) \ 1)
    ]]></literal>
    <justification jstring="[para(103(a,1),258(a,1,1)),flip(a)].">
      <j1 rule="para" parents="103 258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="596">
    <literal><![CDATA[
      L(R(x,1 / y,y),z,u) / y = L(x,z,u) * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(120,a,29,a(flip),b,260,a)].">
      <j1 rule="hyper" parents="120 29 260"/>
    </justification>
  </clause>

  <clause id="597">
    <literal><![CDATA[
      T(R(x,1 / y,y),z) / y = T(x,z) * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(120,a,27,a(flip),b,260,a)].">
      <j1 rule="hyper" parents="120 27 260"/>
    </justification>
  </clause>

  <clause id="598">
    <literal><![CDATA[
      x \ R(y,1 / x,x) = T(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[hyper(119,a,260,a(flip),b,107,a)].">
      <j1 rule="hyper" parents="119 260 107"/>
    </justification>
  </clause>

  <clause id="599">
    <literal><![CDATA[
      T(T(x,y),x * x) = L(T(x,y),x,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,25,a,b,270,a),flip(a)].">
      <j1 rule="hyper" parents="299 25 270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="600">
    <literal><![CDATA[
      L(T(x \ (y \ z),u),x,y) = T((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[para(281(a,1),25(a,2,1))].">
      <j1 rule="para" parents="281 25"/>
    </justification>
  </clause>

  <clause id="601">
    <literal><![CDATA[
      L(L(x \ (y \ z),u,w),x,y) = L((y * x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(281(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="281 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="602">
    <literal><![CDATA[
      L(x,(y \ z) / x,y) = (y * ((y \ z) / x)) \ z
    ]]></literal>
    <justification jstring="[para(79(a,1),281(a,1,1))].">
      <j1 rule="para" parents="79 281"/>
    </justification>
  </clause>

  <clause id="603">
    <literal><![CDATA[
      (x * (y * y)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      (y * y) \ (x \ z) = u
    ]]></literal>
    <justification jstring="[para(281(a,1),497(a,1))].">
      <j1 rule="para" parents="281 497"/>
    </justification>
  </clause>

  <clause id="606">
    <literal><![CDATA[
      (x * (x \ y)) * z != u
    ]]></literal>
    <literal><![CDATA[
      y * z = u
    ]]></literal>
    <justification jstring="[para(76(a,1),306(a,1,1,1))].">
      <j1 rule="para" parents="76 306"/>
    </justification>
  </clause>

  <clause id="608">
    <literal><![CDATA[
      (x * (x \ 1)) * y != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ y = u
    ]]></literal>
    <justification jstring="[para(164(a,1),313(a,1))].">
      <j1 rule="para" parents="164 313"/>
    </justification>
  </clause>

  <clause id="612">
    <literal><![CDATA[
      R(x,y,z) \ ((x * y) * z) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (y * z) = w
    ]]></literal>
    <justification jstring="[para(103(a,1),313(a,1,2))].">
      <j1 rule="para" parents="103 313"/>
    </justification>
  </clause>

  <clause id="613">
    <literal><![CDATA[
      L(x \ y,x,x) != z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) * y = z
    ]]></literal>
    <justification jstring="[para(475(a,1),315(a,1))].">
      <j1 rule="para" parents="475 315"/>
    </justification>
  </clause>

  <clause id="615">
    <literal><![CDATA[
      L((x \ y) \ z,x \ y,x) != u
    ]]></literal>
    <literal><![CDATA[
      y \ (x * z) = u
    ]]></literal>
    <justification jstring="[para(96(a,2),329(a,1))].">
      <j1 rule="para" parents="96 329"/>
    </justification>
  </clause>

  <clause id="616">
    <literal><![CDATA[
      (x * (x \ y)) \ z != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (y \ z) = w
    ]]></literal>
    <justification jstring="[para(180(a,1),330(a,1,1))].">
      <j1 rule="para" parents="180 330"/>
    </justification>
  </clause>

  <clause id="617">
    <literal><![CDATA[
      x * T(x \ 1,x) != y
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(107(a,2),363(a,1))].">
      <j1 rule="para" parents="107 363"/>
    </justification>
  </clause>

  <clause id="618">
    <literal><![CDATA[
      T((x \ y) \ 1,y \ x) = (x \ y) \ 1
    ]]></literal>
    <justification jstring="[para(366(a,1),173(a,1,2))].">
      <j1 rule="para" parents="366 173"/>
    </justification>
  </clause>

  <clause id="619">
    <literal><![CDATA[
      K((x \ y) \ 1,y \ x) = 1
    ]]></literal>
    <justification jstring="[para(366(a,1),210(a,1,2))].">
      <j1 rule="para" parents="366 210"/>
    </justification>
  </clause>

  <clause id="620">
    <literal><![CDATA[
      K(((x * y) \ x) \ 1,y) = 1
    ]]></literal>
    <justification jstring="[para(9(a,1),619(a,1,2))].">
      <j1 rule="para" parents="9 619"/>
    </justification>
  </clause>

  <clause id="621">
    <literal><![CDATA[
      T(x \ (x / y),z) = L(T(y \ 1,z),y,x / y)
    ]]></literal>
    <justification jstring="[para(370(a,1),25(a,2,1)),flip(a)].">
      <j1 rule="para" parents="370 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="622">
    <literal><![CDATA[
      T((x \ y) / y,z) = R(T(1 / x,z),x,x \ y)
    ]]></literal>
    <justification jstring="[para(375(a,1),27(a,2,1)),flip(a)].">
      <j1 rule="para" parents="375 27"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="623">
    <literal><![CDATA[
      1 / (x / (y * y)) = (y * y) / x
    ]]></literal>
    <justification jstring="[hyper(556,a,376,a)].">
      <j1 rule="hyper" parents="556 376"/>
    </justification>
  </clause>

  <clause id="625">
    <literal><![CDATA[
      1 * x != y * z
    ]]></literal>
    <literal><![CDATA[
      x / z = y
    ]]></literal>
    <justification jstring="[para(73(a,1),387(a,1,1))].">
      <j1 rule="para" parents="73 387"/>
    </justification>
  </clause>

  <clause id="626">
    <literal><![CDATA[
      ((x / y) * y) * z != u * w
    ]]></literal>
    <literal><![CDATA[
      (x * z) / w = u
    ]]></literal>
    <justification jstring="[para(158(a,1),387(a,1,1))].">
      <j1 rule="para" parents="158 387"/>
    </justification>
  </clause>

  <clause id="629">
    <literal><![CDATA[
      ((1 / x) * x) * y != z * u
    ]]></literal>
    <literal><![CDATA[
      y / u = z
    ]]></literal>
    <justification jstring="[para(12(a,2),625(a,1,1))].">
      <j1 rule="para" parents="12 625"/>
    </justification>
  </clause>

  <clause id="630">
    <literal><![CDATA[
      x * (y * (y \ z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      (x * z) / w = u
    ]]></literal>
    <justification jstring="[para(160(a,1),388(a,1,2))].">
      <j1 rule="para" parents="160 388"/>
    </justification>
  </clause>

  <clause id="631">
    <literal><![CDATA[
      x * y != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ (x * y) = u
    ]]></literal>
    <justification jstring="[para(11(a,1),390(a,1,1))].">
      <j1 rule="para" parents="11 390"/>
    </justification>
  </clause>

  <clause id="634">
    <literal><![CDATA[
      ((x / y) * y) * z != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * z) = w
    ]]></literal>
    <justification jstring="[para(158(a,1),390(a,1,1))].">
      <j1 rule="para" parents="158 390"/>
    </justification>
  </clause>

  <clause id="635">
    <literal><![CDATA[
      (x * y) / y != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ x = u
    ]]></literal>
    <justification jstring="[para(158(a,2),390(a,1))].">
      <j1 rule="para" parents="158 390"/>
    </justification>
  </clause>

  <clause id="636">
    <literal><![CDATA[
      (x * y) * L(z,y,x) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * (y * z)) = w
    ]]></literal>
    <justification jstring="[para(184(a,1),390(a,1,1))].">
      <j1 rule="para" parents="184 390"/>
    </justification>
  </clause>

  <clause id="637">
    <literal><![CDATA[
      x * (y * (y \ (x \ z))) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ z = w
    ]]></literal>
    <justification jstring="[para(10(a,2),391(a,1,2))].">
      <j1 rule="para" parents="10 391"/>
    </justification>
  </clause>

  <clause id="640">
    <literal><![CDATA[
      x * (y * (y \ z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * z) = w
    ]]></literal>
    <justification jstring="[para(160(a,1),391(a,1,2))].">
      <j1 rule="para" parents="160 391"/>
    </justification>
  </clause>

  <clause id="642">
    <literal><![CDATA[
      x \ y != (z \ 1) * y
    ]]></literal>
    <literal><![CDATA[
      R(z,z \ 1,y) = x
    ]]></literal>
    <justification jstring="[para(406(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="406 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="644">
    <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),409(a,1))].">
      <j1 rule="para" parents="27 409"/>
    </justification>
  </clause>

  <clause id="645">
    <literal><![CDATA[
      T(x \ y,T(x,x \ y)) != z
    ]]></literal>
    <literal><![CDATA[
      ((x \ y) \ y) \ y = z
    ]]></literal>
    <justification jstring="[para(108(a,2),409(a,1,2))].">
      <j1 rule="para" parents="108 409"/>
    </justification>
  </clause>

  <clause id="646">
    <literal><![CDATA[
      x \ y != (x \ 1) * z
    ]]></literal>
    <literal><![CDATA[
      L(z,x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(415(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="415 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="647">
    <literal><![CDATA[
      R(x,y,y \ 1) / (y \ 1) != z * y
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(423(a,2),46(a,2)),flip(a)].">
      <j1 rule="para" parents="423 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="651">
    <literal><![CDATA[
      (x * y) / (z * y) != u
    ]]></literal>
    <literal><![CDATA[
      R(x / z,z,y) = u
    ]]></literal>
    <justification jstring="[para(534(a,1),310(a,1,2)),flip(b)].">
      <j1 rule="para" parents="534 310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="652">
    <literal><![CDATA[
      R(R(x / y,z,u),y,y \ 1) = R(x * (y \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(565(a,1),31(a,1,1)),flip(a)].">
      <j1 rule="para" parents="565 31"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="655">
    <literal><![CDATA[
      (x * y) \ x != z * u
    ]]></literal>
    <literal><![CDATA[
      L(y \ 1,y,x) / u = z
    ]]></literal>
    <justification jstring="[para(369(a,1),577(a,1,2))].">
      <j1 rule="para" parents="369 577"/>
    </justification>
  </clause>

  <clause id="656">
    <literal><![CDATA[
      R(x,y,z) \ ((x * y) * z) != u * w
    ]]></literal>
    <literal><![CDATA[
      (y * z) / w = u
    ]]></literal>
    <justification jstring="[para(103(a,1),577(a,1,2))].">
      <j1 rule="para" parents="103 577"/>
    </justification>
  </clause>

  <clause id="657">
    <literal><![CDATA[
      ((x / y) \ x) * z != u
    ]]></literal>
    <literal><![CDATA[
      y * z = u
    ]]></literal>
    <justification jstring="[para(188(a,2),606(a,1,1))].">
      <j1 rule="para" parents="188 606"/>
    </justification>
  </clause>

  <clause id="659">
    <literal><![CDATA[
      (x * (y * z)) / L(z,y,x) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * y) = w
    ]]></literal>
    <justification jstring="[para(184(a,2),631(a,1))].">
      <j1 rule="para" parents="184 631"/>
    </justification>
  </clause>

  <clause id="662">
    <literal><![CDATA[
      ((x \ y) \ y) * z != u
    ]]></literal>
    <literal><![CDATA[
      T(x,x \ y) * z = u
    ]]></literal>
    <justification jstring="[para(262(a,1),657(a,1,1,1))].">
      <j1 rule="para" parents="262 657"/>
    </justification>
  </clause>

  <clause id="663">
    <literal><![CDATA[
      ((x * x) \ y) * (x * x) = T(y,x * x)
    ]]></literal>
    <justification jstring="[hyper(236,a,112,a),flip(a)].">
      <j1 rule="hyper" parents="236 112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="664">
    <literal><![CDATA[
      (x * x) \ (y * z) = ((x * x) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(125,a,112,a)].">
      <j1 rule="hyper" parents="125 112"/>
    </justification>
  </clause>

  <clause id="665">
    <literal><![CDATA[
      ((x * x) \ (y / z)) * z = (x * x) \ y
    ]]></literal>
    <justification jstring="[hyper(119,a,12,a(flip),b,112,a),flip(a)].">
      <j1 rule="hyper" parents="119 12 112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="666">
    <literal><![CDATA[
      ((x * x) \ y) \ z = y \ ((x * x) * z)
    ]]></literal>
    <justification jstring="[hyper(119,a,155,a(flip),b,112,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 155 112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="667">
    <literal><![CDATA[
      (x * x) * y != z * u
    ]]></literal>
    <literal><![CDATA[
      ((x * x) \ z) * u = y
    ]]></literal>
    <justification jstring="[para(112(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="112 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="668">
    <literal><![CDATA[
      (x * x) \ (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      ((x * x) \ y) * z = u
    ]]></literal>
    <justification jstring="[para(112(a,1),314(a,1,2))].">
      <j1 rule="para" parents="112 314"/>
    </justification>
  </clause>

  <clause id="670">
    <literal><![CDATA[
      ((x * x) * y) / z = (x * x) * (y / z)
    ]]></literal>
    <justification jstring="[para(12(a,1),113(a,1,1,2))].">
      <j1 rule="para" parents="12 113"/>
    </justification>
  </clause>

  <clause id="671">
    <literal><![CDATA[
      ((x * x) * y) * z != u
    ]]></literal>
    <literal><![CDATA[
      (x * x) * (y * z) = u
    ]]></literal>
    <justification jstring="[para(113(a,1),246(a,1,1)),flip(b)].">
      <j1 rule="para" parents="113 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="672">
    <literal><![CDATA[
      (x * y) / (1 / y) = x * (y * y)
    ]]></literal>
    <justification jstring="[para(217(a,1),115(a,1,1,2))].">
      <j1 rule="para" parents="217 115"/>
    </justification>
  </clause>

  <clause id="673">
    <literal><![CDATA[
      (x * (y * y)) * z != u
    ]]></literal>
    <literal><![CDATA[
      x * ((y * y) * z) = u
    ]]></literal>
    <justification jstring="[para(115(a,1),246(a,1,1)),flip(b)].">
      <j1 rule="para" parents="115 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="674">
    <literal><![CDATA[
      (x * x) \ ((y * x) / (1 / x)) = T(y,x * x)
    ]]></literal>
    <justification jstring="[hyper(119,a,672,a,b,107,a)].">
      <j1 rule="hyper" parents="119 672 107"/>
    </justification>
  </clause>

  <clause id="675">
    <literal><![CDATA[
      (x / y) * (y * y) = x / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(65,a,156,a(flip),b,672,a),flip(a)].">
      <j1 rule="hyper" parents="65 156 672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="676">
    <literal><![CDATA[
      x * ((x \ y) * (x \ y)) = y / (1 / (x \ y))
    ]]></literal>
    <justification jstring="[para(10(a,1),672(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="677">
    <literal><![CDATA[
      x * ((y \ 1) * (y \ 1)) = (x * (y \ 1)) / y
    ]]></literal>
    <justification jstring="[para(76(a,1),672(a,1,2)),flip(a)].">
      <j1 rule="para" parents="76 672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="678">
    <literal><![CDATA[
      x * (T(y,y \ 1) * T(y,y \ 1)) = (x * T(y,y \ 1)) / (y \ 1)
    ]]></literal>
    <justification jstring="[para(262(a,1),672(a,1,2)),flip(a)].">
      <j1 rule="para" parents="262 672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="680">
    <literal><![CDATA[
      (x / y) * ((y * y) * z) = (x / (1 / y)) * z
    ]]></literal>
    <justification jstring="[para(675(a,1),34(a,1,1)),flip(a)].">
      <j1 rule="para" parents="675 34"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="681">
    <literal><![CDATA[
      x * (y * T(z,x * y)) = L(z,y,x) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,94,a(flip),b,233,a)].">
      <j1 rule="hyper" parents="65 94 233"/>
    </justification>
  </clause>

  <clause id="682">
    <literal><![CDATA[
      x * L(x \ (y * x),z,u) = L(y,z,u) * x
    ]]></literal>
    <justification jstring="[para(22(a,1),233(a,1,2,1))].">
      <j1 rule="para" parents="22 233"/>
    </justification>
  </clause>

  <clause id="683">
    <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),233(a,1,2,1))].">
      <j1 rule="para" parents="27 233"/>
    </justification>
  </clause>

  <clause id="685">
    <literal><![CDATA[
      L(x / y,z,u) * y = y * L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(109(a,1),233(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="109 233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="686">
    <literal><![CDATA[
      L((x * y) / x,z,u) * x = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(222(a,1),233(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="222 233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="687">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ y,z,u) = L(x,z,u) * (x \ y)
    ]]></literal>
    <justification jstring="[para(108(a,1),233(a,1,2,1))].">
      <j1 rule="para" parents="108 233"/>
    </justification>
  </clause>

  <clause id="688">
    <literal><![CDATA[
      (x * y) * R(T(z,x * y),x,y) = (z * x) * y
    ]]></literal>
    <justification jstring="[hyper(299,a,103,a(flip),b,234,a),flip(a)].">
      <j1 rule="hyper" parents="299 103 234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="689">
    <literal><![CDATA[
      (x * y) \ ((z * x) * y) = R(T(z,x * y),x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,103,a(flip),b,234,a)].">
      <j1 rule="hyper" parents="119 103 234"/>
    </justification>
  </clause>

  <clause id="690">
    <literal><![CDATA[
      x * R(T(T(y,x),z),u,w) = R(T(y,z),u,w) * x
    ]]></literal>
    <justification jstring="[para(23(a,1),234(a,1,2,1))].">
      <j1 rule="para" parents="23 234"/>
    </justification>
  </clause>

  <clause id="692">
    <literal><![CDATA[
      R(x / y,z,u) * y = y * R(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(109(a,1),234(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="109 234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="693">
    <literal><![CDATA[
      R((x * y) / x,z,u) * x = x * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(222(a,1),234(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="222 234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="694">
    <literal><![CDATA[
      (x \ y) * R((x \ y) \ y,z,u) = R(x,z,u) * (x \ y)
    ]]></literal>
    <justification jstring="[para(108(a,1),234(a,1,2,1))].">
      <j1 rule="para" parents="108 234"/>
    </justification>
  </clause>

  <clause id="695">
    <literal><![CDATA[
      (1 / x) * (y * (x * x)) = T(x * y,x * x)
    ]]></literal>
    <justification jstring="[hyper(235,a,35,a,b,265,a),flip(a)].">
      <j1 rule="hyper" parents="235 35 265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="696">
    <literal><![CDATA[
      ((x * x) \ y) * (z * (x * x)) = T(y * z,x * x)
    ]]></literal>
    <justification jstring="[hyper(235,a,35,a,b,112,a),flip(a)].">
      <j1 rule="hyper" parents="235 35 112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="697">
    <literal><![CDATA[
      T((x * y) / x,x * y) = L(y,x,(x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(235,a,94,a(flip),b,154,a(flip))].">
      <j1 rule="hyper" parents="235 94 154"/>
    </justification>
  </clause>

  <clause id="698">
    <literal><![CDATA[
      x \ ((y * y) \ (z * ((y * y) * x))) = T(z,(y * y) * x)
    ]]></literal>
    <justification jstring="[hyper(235,a,72,a(flip),b,33,a),flip(a)].">
      <j1 rule="hyper" parents="235 72 33"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="699">
    <literal><![CDATA[
      (x * R(x \ y,z,u)) / x = R(y / x,z,u)
    ]]></literal>
    <justification jstring="[hyper(267,a,243,a)].">
      <j1 rule="hyper" parents="267 243"/>
    </justification>
  </clause>

  <clause id="700">
    <literal><![CDATA[
      T(x / (y * x),y) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(216(a,1),243(a,1,1))].">
      <j1 rule="para" parents="216 243"/>
    </justification>
  </clause>

  <clause id="701">
    <literal><![CDATA[
      x * R(x \ y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      R(y / x,z,u) * x = w
    ]]></literal>
    <justification jstring="[para(243(a,1),276(a,1,2))].">
      <j1 rule="para" parents="243 276"/>
    </justification>
  </clause>

  <clause id="702">
    <literal><![CDATA[
      T((x * y) / (z * y),z) = R(z \ x,z,y)
    ]]></literal>
    <justification jstring="[para(104(a,1),243(a,1,1))].">
      <j1 rule="para" parents="104 243"/>
    </justification>
  </clause>

  <clause id="703">
    <literal><![CDATA[
      R(x \ (y / z),x,z) = T(y / (x * z),x)
    ]]></literal>
    <justification jstring="[para(285(a,1),243(a,1,1)),flip(a)].">
      <j1 rule="para" parents="285 243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="704">
    <literal><![CDATA[
      R((x / y) \ 1,x / y,y) = T(y / x,x / y)
    ]]></literal>
    <justification jstring="[para(376(a,1),243(a,1,1)),flip(a)].">
      <j1 rule="para" parents="376 243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="705">
    <literal><![CDATA[
      R(x \ y,x,x \ 1) = T(y * (x \ 1),x)
    ]]></literal>
    <justification jstring="[para(565(a,1),243(a,1,1)),flip(a)].">
      <j1 rule="para" parents="565 243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="706">
    <literal><![CDATA[
      (x / (y * x)) * y = y * R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(700(a,1),107(a,1,2)),flip(a)].">
      <j1 rule="para" parents="700 107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="707">
    <literal><![CDATA[
      x \ ((y \ z) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ T(y,y \ z) = u
    ]]></literal>
    <justification jstring="[para(292(a,2),314(a,1,2))].">
      <j1 rule="para" parents="292 314"/>
    </justification>
  </clause>

  <clause id="708">
    <literal><![CDATA[
      x / ((y \ z) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      u * T(y,y \ z) = x
    ]]></literal>
    <justification jstring="[para(294(a,1),143(a,1))].">
      <j1 rule="para" parents="294 143"/>
    </justification>
  </clause>

  <clause id="709">
    <literal><![CDATA[
      (T(x,x \ y) * z) \ (z * ((x \ y) \ y)) = K(z,T(x,x \ y))
    ]]></literal>
    <justification jstring="[hyper(119,a,295,a(flip),b,88,a)].">
      <j1 rule="hyper" parents="119 295 88"/>
    </justification>
  </clause>

  <clause id="711">
    <literal><![CDATA[
      ((x \ y) \ y) \ (T(x,x \ y) * z) = z
    ]]></literal>
    <justification jstring="[hyper(631,a,296,a)].">
      <j1 rule="hyper" parents="631 296"/>
    </justification>
  </clause>

  <clause id="712">
    <literal><![CDATA[
      ((x \ y) \ y) * T(z,T(x,x \ y)) = z * T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(276,a,296,a),flip(a)].">
      <j1 rule="hyper" parents="276 296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="713">
    <literal><![CDATA[
      (T(x,x \ y) * z) \ (((x \ y) \ y) * (z * u)) = L(u,z,T(x,x \ y))
    ]]></literal>
    <justification jstring="[hyper(119,a,296,a(flip),b,94,a)].">
      <j1 rule="hyper" parents="119 296 94"/>
    </justification>
  </clause>

  <clause id="714">
    <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(296(a,2),322(a,1,1))].">
      <j1 rule="para" parents="296 322"/>
    </justification>
  </clause>

  <clause id="716">
    <literal><![CDATA[
      T((x \ y) \ y,z) \ T(T(x,z),x \ y) = 1
    ]]></literal>
    <justification jstring="[hyper(119,a,297,a,b,8,a)].">
      <j1 rule="hyper" parents="119 297 8"/>
    </justification>
  </clause>

  <clause id="717">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) * (x \ y) = u
    ]]></literal>
    <justification jstring="[para(297(a,1),276(a,1,2))].">
      <j1 rule="para" parents="297 276"/>
    </justification>
  </clause>

  <clause id="720">
    <literal><![CDATA[
      T(x,y) / (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      R(1 / y,y,T(x,y)) = z
    ]]></literal>
    <justification jstring="[para(107(a,1),407(a,1,2))].">
      <j1 rule="para" parents="107 407"/>
    </justification>
  </clause>

  <clause id="721">
    <literal><![CDATA[
      K(x \ (x * y),x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,89,a(flip),b,411,a)].">
      <j1 rule="hyper" parents="299 89 411"/>
    </justification>
  </clause>

  <clause id="722">
    <literal><![CDATA[
      K(x \ (x * y),z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(69(a,1),721(a,1,1)),flip(a)].">
      <j1 rule="para" parents="69 721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="723">
    <literal><![CDATA[
      K((x / y) \ x,z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(12(a,1),722(a,1,1,2))].">
      <j1 rule="para" parents="12 722"/>
    </justification>
  </clause>

  <clause id="724">
    <literal><![CDATA[
      (x * x) * (x \ y) = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[para(459(a,1),416(a,1,1)),flip(a)].">
      <j1 rule="para" parents="459 416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="725">
    <literal><![CDATA[
      ((1 / x) * (1 / x)) * (y \ z) = (y / (x \ (1 / x))) \ z
    ]]></literal>
    <justification jstring="[para(428(a,1),416(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="428 416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="726">
    <literal><![CDATA[
      (x * x) \ T(y,x \ 1) = x \ (y * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(119,a,22,a,b,724,a)].">
      <j1 rule="hyper" parents="119 22 724"/>
    </justification>
  </clause>

  <clause id="727">
    <literal><![CDATA[
      (x * x) \ 1 = x \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,68,a(flip),b,724,a)].">
      <j1 rule="hyper" parents="119 68 724"/>
    </justification>
  </clause>

  <clause id="728">
    <literal><![CDATA[
      x \ ((x \ 1) * y) = (x * x) \ y
    ]]></literal>
    <justification jstring="[hyper(119,a,9,a(flip),b,724,a),flip(a)].">
      <j1 rule="hyper" parents="119 9 724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="729">
    <literal><![CDATA[
      (1 / x) \ (x \ y) = x \ ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(119,a,724,a(flip),b,442,a),flip(a)].">
      <j1 rule="hyper" parents="119 724 442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="730">
    <literal><![CDATA[
      (x \ 1) \ (x * y) = (x * x) * y
    ]]></literal>
    <justification jstring="[para(9(a,1),724(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="731">
    <literal><![CDATA[
      (x * x) * ((x \ y) * z) = ((x \ 1) \ y) * z
    ]]></literal>
    <justification jstring="[para(724(a,1),33(a,1,1)),flip(a)].">
      <j1 rule="para" parents="724 33"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="732">
    <literal><![CDATA[
      ((x * x) * (y * ((x * x) * y))) * (((x * x) * y) \ z) = (((x * x) * y) \ 1) \ z
    ]]></literal>
    <justification jstring="[para(33(a,1),724(a,1,1))].">
      <j1 rule="para" parents="33 724"/>
    </justification>
  </clause>

  <clause id="733">
    <literal><![CDATA[
      (x * ((y * y) * (x * (y * y)))) * ((x * (y * y)) \ z) = ((x * (y * y)) \ 1) \ z
    ]]></literal>
    <justification jstring="[para(34(a,1),724(a,1,1))].">
      <j1 rule="para" parents="34 724"/>
    </justification>
  </clause>

  <clause id="734">
    <literal><![CDATA[
      ((1 / x) * (1 / x)) * ((1 / x) \ y) = x \ y
    ]]></literal>
    <justification jstring="[para(79(a,1),724(a,2,1))].">
      <j1 rule="para" parents="79 724"/>
    </justification>
  </clause>

  <clause id="735">
    <literal><![CDATA[
      T((x \ 1) \ y,x * x) = (x \ y) * (x * x)
    ]]></literal>
    <justification jstring="[para(724(a,1),221(a,1,1))].">
      <j1 rule="para" parents="724 221"/>
    </justification>
  </clause>

  <clause id="736">
    <literal><![CDATA[
      1 / (x * x) = x \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,458,a,b,727,a)].">
      <j1 rule="hyper" parents="65 458 727"/>
    </justification>
  </clause>

  <clause id="737">
    <literal><![CDATA[
      (x \ (x \ 1)) * y = (x * x) \ y
    ]]></literal>
    <justification jstring="[para(727(a,1),422(a,1,1))].">
      <j1 rule="para" parents="727 422"/>
    </justification>
  </clause>

  <clause id="738">
    <literal><![CDATA[
      x * ((x * x) \ y) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(144,a,728,a)].">
      <j1 rule="hyper" parents="144 728"/>
    </justification>
  </clause>

  <clause id="739">
    <literal><![CDATA[
      (x * x) \ T(y,x \ (x \ 1)) = y * (x \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(276,a,737,a),flip(a)].">
      <j1 rule="hyper" parents="276 737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="740">
    <literal><![CDATA[
      (x \ (x \ 1)) \ y = (x * x) * y
    ]]></literal>
    <justification jstring="[hyper(119,a,9,a(flip),b,737,a)].">
      <j1 rule="hyper" parents="119 9 737"/>
    </justification>
  </clause>

  <clause id="741">
    <literal><![CDATA[
      ((x * (y \ (y \ 1))) * z) / ((y * y) \ z) = R(x,y \ (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(737(a,1),20(a,2,2)),flip(a)].">
      <j1 rule="para" parents="737 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="742">
    <literal><![CDATA[
      (x \ 1) * (y * (x * x)) = x * T(y,x * x)
    ]]></literal>
    <justification jstring="[para(22(a,2),738(a,1,2)),flip(a)].">
      <j1 rule="para" parents="22 738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="744">
    <literal><![CDATA[
      (x * (y * (z * z))) \ u = (z * z) \ ((x * y) \ u)
    ]]></literal>
    <justification jstring="[para(35(a,1),419(a,1,1))].">
      <j1 rule="para" parents="35 419"/>
    </justification>
  </clause>

  <clause id="745">
    <literal><![CDATA[
      (x * x) \ ((y \ 1) \ z) = (y \ (x * x)) \ z
    ]]></literal>
    <justification jstring="[para(421(a,1),419(a,1,1)),flip(a)].">
      <j1 rule="para" parents="421 419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="746">
    <literal><![CDATA[
      (x * x) \ ((y / x) \ z) = (y / (1 / x)) \ z
    ]]></literal>
    <justification jstring="[para(675(a,1),419(a,1,1)),flip(a)].">
      <j1 rule="para" parents="675 419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="747">
    <literal><![CDATA[
      (((x * x) * y) * z) \ u = (y * z) \ ((x * x) \ u)
    ]]></literal>
    <justification jstring="[para(33(a,2),420(a,1,1))].">
      <j1 rule="para" parents="33 420"/>
    </justification>
  </clause>

  <clause id="748">
    <literal><![CDATA[
      (x \ y) \ ((x * x) \ z) = ((x \ 1) \ y) \ z
    ]]></literal>
    <justification jstring="[para(724(a,1),420(a,1,1)),flip(a)].">
      <j1 rule="para" parents="724 420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="749">
    <literal><![CDATA[
      x / (y * (x * x)) = (x \ 1) / y
    ]]></literal>
    <justification jstring="[para(459(a,1),424(a,1,1)),flip(a)].">
      <j1 rule="para" parents="459 424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="750">
    <literal><![CDATA[
      (x / ((y * y) * z)) / u = (x / z) / (u * (y * y))
    ]]></literal>
    <justification jstring="[para(425(a,1),424(a,1,1))].">
      <j1 rule="para" parents="425 424"/>
    </justification>
  </clause>

  <clause id="751">
    <literal><![CDATA[
      ((((x * y) / x) \ z) \ z) * x = x * T(y,((x * y) / x) \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,296,a(flip),b,433,a)].">
      <j1 rule="hyper" parents="65 296 433"/>
    </justification>
  </clause>

  <clause id="752">
    <literal><![CDATA[
      T(x / y,z) * y != u
    ]]></literal>
    <literal><![CDATA[
      y * T(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(436(a,1),246(a,1,1)),flip(b)].">
      <j1 rule="para" parents="436 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="753">
    <literal><![CDATA[
      T(T(x / y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      T(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(436(a,1),324(a,1,1)),flip(b)].">
      <j1 rule="para" parents="436 324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="755">
    <literal><![CDATA[
      T((x * (y / z)) / x,z) = (x * (z \ y)) / x
    ]]></literal>
    <justification jstring="[para(109(a,1),445(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="109 445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="756">
    <literal><![CDATA[
      T((x * y) / x,z) * x != u
    ]]></literal>
    <literal><![CDATA[
      x * T(y,z) = u
    ]]></literal>
    <justification jstring="[para(445(a,1),246(a,1,1)),flip(b)].">
      <j1 rule="para" parents="445 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="757">
    <literal><![CDATA[
      T(T((x * y) / x,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) = u
    ]]></literal>
    <justification jstring="[para(445(a,1),324(a,1,1)),flip(b)].">
      <j1 rule="para" parents="445 324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="758">
    <literal><![CDATA[
      L(x,y,y) != z
    ]]></literal>
    <literal><![CDATA[
      (1 / y) * (y * x) = z
    ]]></literal>
    <justification jstring="[para(9(a,1),613(a,1,1))].">
      <j1 rule="para" parents="9 613"/>
    </justification>
  </clause>

  <clause id="760">
    <literal><![CDATA[
      ((x * x) \ y) * ((x * x) * z) = T(y,x * x) * z
    ]]></literal>
    <justification jstring="[para(663(a,1),34(a,1,1)),flip(a)].">
      <j1 rule="para" parents="663 34"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="761">
    <literal><![CDATA[
      L((x * x) \ (((x * x) \ y) \ z),x * x,(x * x) \ y) = T(y,x * x) \ z
    ]]></literal>
    <justification jstring="[para(663(a,1),281(a,2,1))].">
      <j1 rule="para" parents="663 281"/>
    </justification>
  </clause>

  <clause id="762">
    <literal><![CDATA[
      x * (((x * x) \ y) * z) = (x \ 1) * (y * z)
    ]]></literal>
    <justification jstring="[para(664(a,1),738(a,1,2))].">
      <j1 rule="para" parents="664 738"/>
    </justification>
  </clause>

  <clause id="763">
    <literal><![CDATA[
      ((x * x) \ y) / z = (x * x) \ (y / z)
    ]]></literal>
    <justification jstring="[hyper(137,a,665,a)].">
      <j1 rule="hyper" parents="137 665"/>
    </justification>
  </clause>

  <clause id="764">
    <literal><![CDATA[
      (((x * x) \ y) * z) / u = (x * x) \ ((y * z) / u)
    ]]></literal>
    <justification jstring="[hyper(120,a,664,a(flip),b,665,a)].">
      <j1 rule="hyper" parents="120 664 665"/>
    </justification>
  </clause>

  <clause id="765">
    <literal><![CDATA[
      (x * x) \ (x / y) = (1 / x) / y
    ]]></literal>
    <justification jstring="[hyper(120,a,264,a(flip),b,665,a),flip(a)].">
      <j1 rule="hyper" parents="120 264 665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="766">
    <literal><![CDATA[
      (1 / x) \ ((1 / x) / y) = x \ (x / y)
    ]]></literal>
    <justification jstring="[hyper(119,a,765,a(flip),b,441,a)].">
      <j1 rule="hyper" parents="119 765 441"/>
    </justification>
  </clause>

  <clause id="767">
    <literal><![CDATA[
      (((x * x) \ y) * z) \ u = (y * z) \ ((x * x) * u)
    ]]></literal>
    <justification jstring="[para(664(a,1),666(a,1,1))].">
      <j1 rule="para" parents="664 666"/>
    </justification>
  </clause>

  <clause id="768">
    <literal><![CDATA[
      ((1 / x) * (1 / x)) * (y / z) = ((x \ (1 / x)) * y) / z
    ]]></literal>
    <justification jstring="[para(428(a,1),670(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="428 670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="769">
    <literal><![CDATA[
      (x \ 1) \ (((x \ 1) \ 1) \ y) = x \ ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(76(a,1),729(a,1,1)),flip(a)].">
      <j1 rule="para" parents="76 729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="770">
    <literal><![CDATA[
      (x * x) \ y != ((x * x) \ z) / u
    ]]></literal>
    <literal><![CDATA[
      z / u = y
    ]]></literal>
    <justification jstring="[para(763(a,2),49(a,1)),flip(a)].">
      <j1 rule="para" parents="763 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="771">
    <literal><![CDATA[
      ((1 / x) * (1 / x)) \ (y / z) = ((x \ (1 / x)) \ y) / z
    ]]></literal>
    <justification jstring="[para(428(a,1),763(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="428 763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="772">
    <literal><![CDATA[
      (x * y) * a(x,z,z \ y) = (x * z) * (z \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),84(a,1,1,2))].">
      <j1 rule="para" parents="10 84"/>
    </justification>
  </clause>

  <clause id="773">
    <literal><![CDATA[
      x * a(x,y,y \ 1) = (x * y) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(71(a,1),84(a,1,1))].">
      <j1 rule="para" parents="71 84"/>
    </justification>
  </clause>

  <clause id="774">
    <literal><![CDATA[
      (x * (y * z)) * a(x,z,T(y,z)) = (x * z) * T(y,z)
    ]]></literal>
    <justification jstring="[para(107(a,1),84(a,1,1,2))].">
      <j1 rule="para" parents="107 84"/>
    </justification>
  </clause>

  <clause id="775">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(84(a,1),314(a,1,2))].">
      <j1 rule="para" parents="84 314"/>
    </justification>
  </clause>

  <clause id="776">
    <literal><![CDATA[
      ((x * y) * z) * a(R(x,y,z),y,z) = (R(x,y,z) * y) * z
    ]]></literal>
    <justification jstring="[para(103(a,1),84(a,1,1))].">
      <j1 rule="para" parents="103 84"/>
    </justification>
  </clause>

  <clause id="777">
    <literal><![CDATA[
      L(T(x,y \ z),y \ z,y) = z \ (y * (x * (y \ z)))
    ]]></literal>
    <justification jstring="[para(107(a,1),95(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 95"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="779">
    <literal><![CDATA[
      x * L(y,z,x / z) != u
    ]]></literal>
    <literal><![CDATA[
      (x / z) * (z * y) = u
    ]]></literal>
    <justification jstring="[para(97(a,1),250(a,1,2)),flip(b)].">
      <j1 rule="para" parents="97 250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="780">
    <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="781">
    <literal><![CDATA[
      R(x,x \ y,(x \ y) \ z) = (y * ((x \ y) \ z)) / z
    ]]></literal>
    <justification jstring="[para(10(a,1),100(a,2,2))].">
      <j1 rule="para" parents="10 100"/>
    </justification>
  </clause>

  <clause id="782">
    <literal><![CDATA[
      R(x,y,y \ z) != u / z
    ]]></literal>
    <literal><![CDATA[
      (x * y) * (y \ z) = u
    ]]></literal>
    <justification jstring="[para(102(a,1),48(a,1))].">
      <j1 rule="para" parents="102 48"/>
    </justification>
  </clause>

  <clause id="783">
    <literal><![CDATA[
      x \ R(x,1 / y,y) = a(x,1 / y,y)
    ]]></literal>
    <justification jstring="[para(260(a,1),218(a,1,2))].">
      <j1 rule="para" parents="260 218"/>
    </justification>
  </clause>

  <clause id="784">
    <literal><![CDATA[
      L(T(x,y),y,x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(318,a,230,a),flip(a)].">
      <j1 rule="hyper" parents="318 230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="785">
    <literal><![CDATA[
      (x * y) \ (x * (z * y)) = T(L(z,y,x),y)
    ]]></literal>
    <justification jstring="[hyper(299,a,25,a(flip),b,230,a),flip(a)].">
      <j1 rule="hyper" parents="299 25 230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="786">
    <literal><![CDATA[
      T(L(x,y,x),y) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,25,a(flip),b,784,a)].">
      <j1 rule="hyper" parents="65 25 784"/>
    </justification>
  </clause>

  <clause id="787">
    <literal><![CDATA[
      L(R(T(x,y),z,u),y,x) = R(T(x,x * y),z,u)
    ]]></literal>
    <justification jstring="[para(784(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="784 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="788">
    <literal><![CDATA[
      x * T(y,y * x) = L(y,x,y) * x
    ]]></literal>
    <justification jstring="[para(784(a,1),233(a,1,2))].">
      <j1 rule="para" parents="784 233"/>
    </justification>
  </clause>

  <clause id="789">
    <literal><![CDATA[
      (x * T(y,y * x)) / x = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(267,a,786,a)].">
      <j1 rule="hyper" parents="267 786"/>
    </justification>
  </clause>

  <clause id="790">
    <literal><![CDATA[
      T((x * y) / x,y * x) = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(42,a,266,a,b,786,a)].">
      <j1 rule="hyper" parents="42 266 786"/>
    </justification>
  </clause>

  <clause id="791">
    <literal><![CDATA[
      L(x,x \ y,x) * (x \ y) = (x \ y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),788(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="792">
    <literal><![CDATA[
      L(x,T(y,x),x) * T(y,x) = T(y,x) * T(x,y * x)
    ]]></literal>
    <justification jstring="[para(107(a,1),788(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="794">
    <literal><![CDATA[
      T(L(x,y,x),y) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,x * y) = z
    ]]></literal>
    <justification jstring="[para(789(a,1),324(a,1,1)),flip(b)].">
      <j1 rule="para" parents="789 324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="795">
    <literal><![CDATA[
      T(((x \ y) * x) / (x \ y),y) = L(x,x \ y,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),790(a,1,2))].">
      <j1 rule="para" parents="10 790"/>
    </justification>
  </clause>

  <clause id="796">
    <literal><![CDATA[
      T(T((x * y) / x,z),y * x) = T(L(y,x,y),z)
    ]]></literal>
    <justification jstring="[para(790(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="790 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="797">
    <literal><![CDATA[
      R((x * y) / z,z,K(y,x)) = (y * x) / (z * ((x * y) \ (y * x)))
    ]]></literal>
    <justification jstring="[para(16(a,2),345(a,1,3))].">
      <j1 rule="para" parents="16 345"/>
    </justification>
  </clause>

  <clause id="798">
    <literal><![CDATA[
      x * R(T(y,x),z,z \ x) = (y * z) * (z \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,234,a,b,347,a)].">
      <j1 rule="hyper" parents="65 234 347"/>
    </justification>
  </clause>

  <clause id="800">
    <literal><![CDATA[
      L(x \ 1,x,y) \ (z * ((y * x) \ y)) = T(z,(y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(299,a,22,a,b,367,a),flip(a)].">
      <j1 rule="hyper" parents="299 22 367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="801">
    <literal><![CDATA[
      (x * y) * T((x * y) \ x,z) = x * (y * T(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(371(a,2),94(a,1,2))].">
      <j1 rule="para" parents="371 94"/>
    </justification>
  </clause>

  <clause id="802">
    <literal><![CDATA[
      (x / (y * x)) * (R(1 / y,y,x) \ z) = z
    ]]></literal>
    <justification jstring="[hyper(251,a,373,a),flip(a)].">
      <j1 rule="hyper" parents="251 373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="803">
    <literal><![CDATA[
      R(T(1 / x,x * y),x,y) = (x * y) \ y
    ]]></literal>
    <justification jstring="[hyper(400,a,377,a),flip(a)].">
      <j1 rule="hyper" parents="400 377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="804">
    <literal><![CDATA[
      R(T(1 / x,y),x,x \ 1) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(169(a,1),377(a,1,1)),flip(a)].">
      <j1 rule="para" parents="169 377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="805">
    <literal><![CDATA[
      x * ((T(y,x) \ z) \ z) != u * x
    ]]></literal>
    <literal><![CDATA[
      T(y,T(y,x) \ z) = u
    ]]></literal>
    <justification jstring="[para(108(a,1),384(a,1,2))].">
      <j1 rule="para" parents="108 384"/>
    </justification>
  </clause>

  <clause id="806">
    <literal><![CDATA[
      (x / y) * T(y,z) != u * (x / y)
    ]]></literal>
    <literal><![CDATA[
      T(x / (x / y),z) = u
    ]]></literal>
    <justification jstring="[para(241(a,1),384(a,1,2,1))].">
      <j1 rule="para" parents="241 384"/>
    </justification>
  </clause>

  <clause id="807">
    <literal><![CDATA[
      x * T(x \ (y * x),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(22(a,1),395(a,1,2,1))].">
      <j1 rule="para" parents="22 395"/>
    </justification>
  </clause>

  <clause id="808">
    <literal><![CDATA[
      L(x \ 1,x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (y * x) \ y = z
    ]]></literal>
    <justification jstring="[para(403(a,1),207(a,1))].">
      <j1 rule="para" parents="403 207"/>
    </justification>
  </clause>

  <clause id="810">
    <literal><![CDATA[
      L(x,1 / x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (y * (1 / x)) \ y = z
    ]]></literal>
    <justification jstring="[para(79(a,1),808(a,1,1))].">
      <j1 rule="para" parents="79 808"/>
    </justification>
  </clause>

  <clause id="811">
    <literal><![CDATA[
      x \ (y * T(y \ x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,y) = z
    ]]></literal>
    <justification jstring="[para(107(a,2),454(a,1,2))].">
      <j1 rule="para" parents="107 454"/>
    </justification>
  </clause>

  <clause id="812">
    <literal><![CDATA[
      L(x \ y,x,y / x) = T(y / x,y)
    ]]></literal>
    <justification jstring="[hyper(235,a,155,a(flip),b,474,a),flip(a)].">
      <j1 rule="hyper" parents="235 155 474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="813">
    <literal><![CDATA[
      (x / y) * (y * T(z,x)) = L(z,y,x / y) * x
    ]]></literal>
    <justification jstring="[hyper(65,a,233,a(flip),b,474,a),flip(a)].">
      <j1 rule="hyper" parents="65 233 474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="814">
    <literal><![CDATA[
      x * L(L(y,z,x / z),u,w) = (x / z) * (z * L(y,u,w))
    ]]></literal>
    <justification jstring="[para(30(a,1),474(a,1,2))].">
      <j1 rule="para" parents="30 474"/>
    </justification>
  </clause>

  <clause id="816">
    <literal><![CDATA[
      x * L(L(y,z \ x,z),u,w) = z * ((z \ x) * L(y,u,w))
    ]]></literal>
    <justification jstring="[para(30(a,1),482(a,1,2))].">
      <j1 rule="para" parents="30 482"/>
    </justification>
  </clause>

  <clause id="817">
    <literal><![CDATA[
      x * ((x \ y) * z) != y * u
    ]]></literal>
    <literal><![CDATA[
      L(z,x \ y,x) = u
    ]]></literal>
    <justification jstring="[para(482(a,1),45(a,1))].">
      <j1 rule="para" parents="482 45"/>
    </justification>
  </clause>

  <clause id="818">
    <literal><![CDATA[
      x \ (y * ((y \ x) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,y \ x,y) = u
    ]]></literal>
    <justification jstring="[para(482(a,1),314(a,1,2))].">
      <j1 rule="para" parents="482 314"/>
    </justification>
  </clause>

  <clause id="819">
    <literal><![CDATA[
      L(x \ ((x * x) * y),x,x) = L(x,x,x) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,511,a,b,512,a)].">
      <j1 rule="hyper" parents="65 511 512"/>
    </justification>
  </clause>

  <clause id="820">
    <literal><![CDATA[
      (1 / x) * ((x \ y) * x) = T((1 / x) * y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,513,a(flip),b,515,a)].">
      <j1 rule="hyper" parents="65 513 515"/>
    </justification>
  </clause>

  <clause id="821">
    <literal><![CDATA[
      (1 / x) \ T((1 / x) * y,z) = x * T(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,515,a(flip),b,475,a)].">
      <j1 rule="hyper" parents="119 515 475"/>
    </justification>
  </clause>

  <clause id="822">
    <literal><![CDATA[
      L(T((x \ y) \ z,u),x \ y,x) = T(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[para(520(a,1),25(a,2,1))].">
      <j1 rule="para" parents="520 25"/>
    </justification>
  </clause>

  <clause id="823">
    <literal><![CDATA[
      L(R((x \ y) \ z,u,w),x \ y,x) = R(y \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[para(520(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="520 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="824">
    <literal><![CDATA[
      K(x,y) = L(x \ T(x,y),x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,16,a,b,526,a)].">
      <j1 rule="hyper" parents="299 16 526"/>
    </justification>
  </clause>

  <clause id="825">
    <literal><![CDATA[
      L(T(x \ T(y,z),u),x,z) = T((z * x) \ (y * z),u)
    ]]></literal>
    <justification jstring="[para(526(a,1),25(a,2,1))].">
      <j1 rule="para" parents="526 25"/>
    </justification>
  </clause>

  <clause id="827">
    <literal><![CDATA[
      x / ((y * y) \ z) = (x / z) * (y * y)
    ]]></literal>
    <justification jstring="[para(477(a,1),529(a,1,2))].">
      <j1 rule="para" parents="477 529"/>
    </justification>
  </clause>

  <clause id="828">
    <literal><![CDATA[
      (x * ((y * y) \ z)) / z = x / (y * y)
    ]]></literal>
    <justification jstring="[hyper(304,a,827,a),flip(a)].">
      <j1 rule="hyper" parents="304 827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="829">
    <literal><![CDATA[
      x / (((y * y) \ z) * u) = (x / (z * u)) * (y * y)
    ]]></literal>
    <justification jstring="[para(664(a,1),827(a,1,2))].">
      <j1 rule="para" parents="664 827"/>
    </justification>
  </clause>

  <clause id="830">
    <literal><![CDATA[
      (x / (y * y)) * z = x * ((y * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(143,a,828,a)].">
      <j1 rule="hyper" parents="143 828"/>
    </justification>
  </clause>

  <clause id="831">
    <literal><![CDATA[
      (x / (y * y)) * z != u
    ]]></literal>
    <literal><![CDATA[
      x * ((y * y) \ z) = u
    ]]></literal>
    <justification jstring="[para(828(a,1),246(a,1,1)),flip(b)].">
      <j1 rule="para" parents="828 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="832">
    <literal><![CDATA[
      (x * (y * ((z * z) \ u))) \ ((x * (y / (z * z))) * u) = a(x,y / (z * z),u)
    ]]></literal>
    <justification jstring="[para(830(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="830 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="833">
    <literal><![CDATA[
      (x * ((y * y) \ z)) \ ((x / (y * y)) * (z * u)) = L(u,z,x / (y * y))
    ]]></literal>
    <justification jstring="[para(830(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="830 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="834">
    <literal><![CDATA[
      x * ((y \ (y \ 1)) * z) = (x / (y * y)) * z
    ]]></literal>
    <justification jstring="[para(737(a,2),830(a,2,2)),flip(a)].">
      <j1 rule="para" parents="737 830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="835">
    <literal><![CDATA[
      (x / ((y * y) * z)) * u = (x / z) * ((y * y) \ u)
    ]]></literal>
    <justification jstring="[para(425(a,1),830(a,1,1))].">
      <j1 rule="para" parents="425 830"/>
    </justification>
  </clause>

  <clause id="836">
    <literal><![CDATA[
      (x / (y * y)) * (z * u) = x * (((y * y) \ z) * u)
    ]]></literal>
    <justification jstring="[para(664(a,1),830(a,2,2))].">
      <j1 rule="para" parents="664 830"/>
    </justification>
  </clause>

  <clause id="837">
    <literal><![CDATA[
      R(x,x \ y,y \ z) \ z = (x \ y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(76(a,1),533(a,1,1,1))].">
      <j1 rule="para" parents="76 533"/>
    </justification>
  </clause>

  <clause id="838">
    <literal><![CDATA[
      (x * (y \ (1 / y))) / z = x / (z / (y \ (1 / y)))
    ]]></literal>
    <justification jstring="[hyper(562,a,567,a),flip(a)].">
      <j1 rule="hyper" parents="562 567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="839">
    <literal><![CDATA[
      (x * (y * y)) / z = x / (z / (y * y))
    ]]></literal>
    <justification jstring="[hyper(556,a,567,a),flip(a)].">
      <j1 rule="hyper" parents="556 567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="840">
    <literal><![CDATA[
      R(T(x / (y / z),u),y / z,z) = T((x * z) / y,u)
    ]]></literal>
    <justification jstring="[para(567(a,1),27(a,2,1))].">
      <j1 rule="para" parents="567 27"/>
    </justification>
  </clause>

  <clause id="841">
    <literal><![CDATA[
      R(R(x / (y / z),u,w),y / z,z) = R((x * z) / y,u,w)
    ]]></literal>
    <justification jstring="[para(567(a,1),31(a,1,1)),flip(a)].">
      <j1 rule="para" parents="567 31"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="842">
    <literal><![CDATA[
      R(x / R(1 / y,y,z),z / (y * z),y * z) = (x * (y * z)) / z
    ]]></literal>
    <justification jstring="[para(216(a,2),567(a,1,1,2))].">
      <j1 rule="para" parents="216 567"/>
    </justification>
  </clause>

  <clause id="843">
    <literal><![CDATA[
      R(x / (y / (z * y)),R(1 / z,z,y),z * y) = (x * (z * y)) / y
    ]]></literal>
    <justification jstring="[para(216(a,2),567(a,1,2))].">
      <j1 rule="para" parents="216 567"/>
    </justification>
  </clause>

  <clause id="844">
    <literal><![CDATA[
      R((x / y) \ z,x / y,y) = T((z * y) / x,x / y)
    ]]></literal>
    <justification jstring="[para(567(a,1),243(a,1,1)),flip(a)].">
      <j1 rule="para" parents="567 243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="845">
    <literal><![CDATA[
      (x \ 1) / (y / (z * z)) = (x \ (z * z)) / y
    ]]></literal>
    <justification jstring="[para(421(a,1),839(a,1,1)),flip(a)].">
      <j1 rule="para" parents="421 839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="846">
    <literal><![CDATA[
      (x * y) / ((z \ x) * y) != u
    ]]></literal>
    <literal><![CDATA[
      R(z,z \ x,y) = u
    ]]></literal>
    <justification jstring="[para(580(a,1),310(a,1,2)),flip(b)].">
      <j1 rule="para" parents="580 310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="847">
    <literal><![CDATA[
      x \ (y * (z * z)) = (x \ y) * (z * z)
    ]]></literal>
    <justification jstring="[para(535(a,1),580(a,1,1))].">
      <j1 rule="para" parents="535 580"/>
    </justification>
  </clause>

  <clause id="848">
    <literal><![CDATA[
      x \ (y * (z \ (1 / z))) = (x \ y) * (z \ (1 / z))
    ]]></literal>
    <justification jstring="[para(557(a,1),580(a,1,1))].">
      <j1 rule="para" parents="557 580"/>
    </justification>
  </clause>

  <clause id="849">
    <literal><![CDATA[
      (x * y) / (z * z) = x * (y / (z * z))
    ]]></literal>
    <justification jstring="[para(476(a,1),585(a,1,2))].">
      <j1 rule="para" parents="476 585"/>
    </justification>
  </clause>

  <clause id="850">
    <literal><![CDATA[
      x / ((y * x) * (y * x)) = y \ ((y * x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,459,a(flip),b,849,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 459 849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="851">
    <literal><![CDATA[
      (x * y) / (z * z) != x * u
    ]]></literal>
    <literal><![CDATA[
      y / (z * z) = u
    ]]></literal>
    <justification jstring="[para(849(a,2),45(a,1))].">
      <j1 rule="para" parents="849 45"/>
    </justification>
  </clause>

  <clause id="852">
    <literal><![CDATA[
      (x * (y / (z * z))) \ u = (z * z) * ((x * y) \ u)
    ]]></literal>
    <justification jstring="[para(849(a,1),416(a,1,1))].">
      <j1 rule="para" parents="849 416"/>
    </justification>
  </clause>

  <clause id="853">
    <literal><![CDATA[
      (x * (y / (z * z))) / u = (x * y) / (u * (z * z))
    ]]></literal>
    <justification jstring="[para(849(a,1),424(a,1,1))].">
      <j1 rule="para" parents="849 424"/>
    </justification>
  </clause>

  <clause id="854">
    <literal><![CDATA[
      (x * (y / (z * z))) * u = (x * y) * ((z * z) \ u)
    ]]></literal>
    <justification jstring="[para(849(a,1),830(a,1,1))].">
      <j1 rule="para" parents="849 830"/>
    </justification>
  </clause>

  <clause id="855">
    <literal><![CDATA[
      (x * y) \ (x * (z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      L(T(z,y),y,x) = u
    ]]></literal>
    <justification jstring="[para(586(a,1),317(a,1,1))].">
      <j1 rule="para" parents="586 317"/>
    </justification>
  </clause>

  <clause id="857">
    <literal><![CDATA[
      R(x,y,z) = T(((y * x) * z) / (y * z),y)
    ]]></literal>
    <justification jstring="[para(9(a,1),702(a,2,1)),flip(a)].">
      <j1 rule="para" parents="9 702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="858">
    <literal><![CDATA[
      ((x \ y) * x) * (x \ 1) = T(y * (x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,258,a,b,705,a)].">
      <j1 rule="hyper" parents="65 258 705"/>
    </justification>
  </clause>

  <clause id="859">
    <literal><![CDATA[
      T(R(x \ y,x,z),x * z) != u
    ]]></literal>
    <literal><![CDATA[
      T((x * z) \ (y * z),x) = u
    ]]></literal>
    <justification jstring="[para(702(a,1),753(a,1,1))].">
      <j1 rule="para" parents="702 753"/>
    </justification>
  </clause>

  <clause id="860">
    <literal><![CDATA[
      T(T(x,y),x) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(11(a,1),757(a,1,1,1))].">
      <j1 rule="para" parents="11 757"/>
    </justification>
  </clause>

  <clause id="861">
    <literal><![CDATA[
      T(T(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(223(a,1),757(a,1,1,1))].">
      <j1 rule="para" parents="223 757"/>
    </justification>
  </clause>

  <clause id="862">
    <literal><![CDATA[
      T((((x * y) / x) \ z) \ z,x) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,((x * y) / x) \ z) = u
    ]]></literal>
    <justification jstring="[para(108(a,1),757(a,1,1))].">
      <j1 rule="para" parents="108 757"/>
    </justification>
  </clause>

  <clause id="863">
    <literal><![CDATA[
      T((x \ y) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(T(x,z),x \ y) = u
    ]]></literal>
    <justification jstring="[para(108(a,1),861(a,1,1))].">
      <j1 rule="para" parents="108 861"/>
    </justification>
  </clause>

  <clause id="864">
    <literal><![CDATA[
      x * a(x,y,y \ 1) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,258,a(flip),b,773,a),flip(a)].">
      <j1 rule="hyper" parents="299 258 773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="865">
    <literal><![CDATA[
      x \ R(x,y,y \ 1) = a(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,258,a(flip),b,773,a)].">
      <j1 rule="hyper" parents="119 258 773"/>
    </justification>
  </clause>

  <clause id="866">
    <literal><![CDATA[
      (x * y) * (y \ 1) != x * z
    ]]></literal>
    <literal><![CDATA[
      a(x,y,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(773(a,1),45(a,1))].">
      <j1 rule="para" parents="773 45"/>
    </justification>
  </clause>

  <clause id="868">
    <literal><![CDATA[
      x \ R(x,y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      a(x,y,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(864(a,1),314(a,1,2))].">
      <j1 rule="para" parents="864 314"/>
    </justification>
  </clause>

  <clause id="869">
    <literal><![CDATA[
      T(L(x,y \ z,y),y \ z) = z \ (y * (x * (y \ z)))
    ]]></literal>
    <justification jstring="[hyper(329,a,785,a),flip(a)].">
      <j1 rule="hyper" parents="329 785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="870">
    <literal><![CDATA[
      T(L(x,y,z / y),y) = z \ ((z / y) * (x * y))
    ]]></literal>
    <justification jstring="[para(12(a,1),785(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12 785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="871">
    <literal><![CDATA[
      ((x \ y) / y) * (R(1 / x,x,x \ y) \ z) = z
    ]]></literal>
    <justification jstring="[para(10(a,1),802(a,1,1,2))].">
      <j1 rule="para" parents="10 802"/>
    </justification>
  </clause>

  <clause id="872">
    <literal><![CDATA[
      R(1 / x,x,y) != z
    ]]></literal>
    <literal><![CDATA[
      y / (x * y) = z
    ]]></literal>
    <justification jstring="[para(802(a,1),207(a,1))].">
      <j1 rule="para" parents="802 207"/>
    </justification>
  </clause>

  <clause id="873">
    <literal><![CDATA[
      T(x,y) != R(z,y,u)
    ]]></literal>
    <literal><![CDATA[
      ((y * z) * u) / (y * u) = x
    ]]></literal>
    <justification jstring="[para(857(a,2),51(a,1)),flip(a)].">
      <j1 rule="para" parents="857 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="874">
    <literal><![CDATA[
      T(((1 / x) * y) * x,1 / x) = R(y,1 / x,x)
    ]]></literal>
    <justification jstring="[para(170(a,1),857(a,2,1)),flip(a)].">
      <j1 rule="para" parents="170 857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="875">
    <literal><![CDATA[
      T(R(x,y,x),y * x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(857(a,2),266(a,1,1))].">
      <j1 rule="para" parents="857 266"/>
    </justification>
  </clause>

  <clause id="876">
    <literal><![CDATA[
      R(x,y,x) * (y * x) = (y * x) * T(x,y)
    ]]></literal>
    <justification jstring="[para(857(a,2),433(a,1,1))].">
      <j1 rule="para" parents="857 433"/>
    </justification>
  </clause>

  <clause id="877">
    <literal><![CDATA[
      R(T(x,y * x),y,x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,27,a,b,875,a)].">
      <j1 rule="hyper" parents="65 27 875"/>
    </justification>
  </clause>

  <clause id="878">
    <literal><![CDATA[
      T(R(x,y,x),z) * (y * x) = (y * x) * T(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(875(a,1),232(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="875 232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="879">
    <literal><![CDATA[
      L(R(x,y,x),z,u) * (y * x) = (y * x) * L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(875(a,1),233(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="875 233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="880">
    <literal><![CDATA[
      R(R(x,y,x),z,u) * (y * x) = (y * x) * R(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(875(a,1),234(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="875 234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="881">
    <literal><![CDATA[
      R(T(x,y),y / x,x) = T(x,y / x)
    ]]></literal>
    <justification jstring="[para(12(a,1),877(a,1,1,2))].">
      <j1 rule="para" parents="12 877"/>
    </justification>
  </clause>

  <clause id="882">
    <literal><![CDATA[
      R(x,1 / x,x) = T(x,1 / x)
    ]]></literal>
    <justification jstring="[para(193(a,1),881(a,1,1))].">
      <j1 rule="para" parents="193 881"/>
    </justification>
  </clause>

  <clause id="883">
    <literal><![CDATA[
      T(x,1 / x) / x = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(120,a,882,a(flip),b,260,a)].">
      <j1 rule="hyper" parents="120 882 260"/>
    </justification>
  </clause>

  <clause id="884">
    <literal><![CDATA[
      R(R(x,y,z),1 / x,x) = R(T(x,1 / x),y,z)
    ]]></literal>
    <justification jstring="[para(882(a,1),31(a,1,1)),flip(a)].">
      <j1 rule="para" parents="882 31"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="885">
    <literal><![CDATA[
      T(x,1 / x) / x = K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(299,a,256,a,b,883,a),flip(a)].">
      <j1 rule="hyper" parents="299 256 883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="886">
    <literal><![CDATA[
      (x * y) * T(y,x) = (y * x) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,103,a(flip),b,876,a),flip(a)].">
      <j1 rule="hyper" parents="65 103 876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="887">
    <literal><![CDATA[
      (x * T(y,x)) * T(x,y) = R(x,y,x) * (y * x)
    ]]></literal>
    <justification jstring="[para(107(a,2),876(a,2,1)),flip(a)].">
      <j1 rule="para" parents="107 876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="888">
    <literal><![CDATA[
      ((x \ y) * x) * (x \ y) = y * T(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(606,a,886,a),flip(a)].">
      <j1 rule="hyper" parents="606 886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="889">
    <literal><![CDATA[
      (x * (y / x)) * x = y * T(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(306,a,886,a),flip(a)].">
      <j1 rule="hyper" parents="306 886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="890">
    <literal><![CDATA[
      ((x \ 1) * x) \ x = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,70,a(flip),b,886,a)].">
      <j1 rule="hyper" parents="119 70 886"/>
    </justification>
  </clause>

  <clause id="891">
    <literal><![CDATA[
      K(x \ 1,x) \ x = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(253(a,2),890(a,1,1))].">
      <j1 rule="para" parents="253 890"/>
    </justification>
  </clause>

  <clause id="892">
    <literal><![CDATA[
      K(x \ 1,x) \ x = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(299,a,108,a(flip),b,891,a),flip(a)].">
      <j1 rule="hyper" parents="299 108 891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="893">
    <literal><![CDATA[
      K(x \ 1,x) * T(x,x \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(144,a,891,a)].">
      <j1 rule="hyper" parents="144 891"/>
    </justification>
  </clause>

  <clause id="894">
    <literal><![CDATA[
      K(x \ 1,x) * ((x \ 1) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(144,a,892,a)].">
      <j1 rule="hyper" parents="144 892"/>
    </justification>
  </clause>

  <clause id="895">
    <literal><![CDATA[
      R(T(T(x,y),z),u,w) = T(T(R(x,u,w),z),y)
    ]]></literal>
    <justification jstring="[hyper(299,a,27,a,b,111,a)].">
      <j1 rule="hyper" parents="299 27 111"/>
    </justification>
  </clause>

  <clause id="899">
    <literal><![CDATA[
      R(x,y,T(z,y)) * (z * y) != u
    ]]></literal>
    <literal><![CDATA[
      (x * y) * T(z,y) = u
    ]]></literal>
    <justification jstring="[para(107(a,1),275(a,1,2))].">
      <j1 rule="para" parents="107 275"/>
    </justification>
  </clause>

  <clause id="901">
    <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),279(a,1,2))].">
      <j1 rule="para" parents="29 279"/>
    </justification>
  </clause>

  <clause id="902">
    <literal><![CDATA[
      K(x \ 1,x) * L(y,x,x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) * (x * y) = z
    ]]></literal>
    <justification jstring="[para(253(a,2),279(a,1,1))].">
      <j1 rule="para" parents="253 279"/>
    </justification>
  </clause>

  <clause id="903">
    <literal><![CDATA[
      (x * y) * (z * z) != u
    ]]></literal>
    <literal><![CDATA[
      x * (y * (z * z)) = u
    ]]></literal>
    <justification jstring="[para(476(a,1),279(a,1,2))].">
      <j1 rule="para" parents="476 279"/>
    </justification>
  </clause>

  <clause id="904">
    <literal><![CDATA[
      (x * y) * T((x * y) \ x,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * (y * T(y \ 1,z)) = u
    ]]></literal>
    <justification jstring="[para(371(a,2),279(a,1,2))].">
      <j1 rule="para" parents="371 279"/>
    </justification>
  </clause>

  <clause id="906">
    <literal><![CDATA[
      (((x \ 1) * (x \ 1)) \ y) * z = x * ((x \ 1) \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,664,a(flip),b,465,a)].">
      <j1 rule="hyper" parents="65 664 465"/>
    </justification>
  </clause>

  <clause id="907">
    <literal><![CDATA[
      (x * ((x \ 1) \ y)) * ((x \ 1) * (x \ 1)) = T(y,(x \ 1) * (x \ 1))
    ]]></literal>
    <justification jstring="[para(465(a,1),663(a,1,1))].">
      <j1 rule="para" parents="465 663"/>
    </justification>
  </clause>

  <clause id="908">
    <literal><![CDATA[
      (x \ 1) * (x \ ((x \ 1) \ y)) = ((x \ 1) \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(65,a,724,a(flip),b,468,a),flip(a)].">
      <j1 rule="hyper" parents="65 724 468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="909">
    <literal><![CDATA[
      (x * y) \ (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      L(y \ z,y,x) = u
    ]]></literal>
    <justification jstring="[para(10(a,1),493(a,1,2,2))].">
      <j1 rule="para" parents="10 493"/>
    </justification>
  </clause>

  <clause id="910">
    <literal><![CDATA[
      (x * y) \ (y * (T(x,y) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,T(x,y),y) = u
    ]]></literal>
    <justification jstring="[para(107(a,1),493(a,1,1))].">
      <j1 rule="para" parents="107 493"/>
    </justification>
  </clause>

  <clause id="911">
    <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),493(a,1,2,2))].">
      <j1 rule="para" parents="94 493"/>
    </justification>
  </clause>

  <clause id="912">
    <literal><![CDATA[
      (T(x,x \ y) * z) \ (((x \ y) \ y) * (z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(u,z,(x \ y) \ y) = w
    ]]></literal>
    <justification jstring="[para(296(a,2),493(a,1,1))].">
      <j1 rule="para" parents="296 493"/>
    </justification>
  </clause>

  <clause id="913">
    <literal><![CDATA[
      (x * (y * (z * u))) \ (x * ((y * z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(a(y,z,u),y * (z * u),x) = w
    ]]></literal>
    <justification jstring="[para(84(a,1),493(a,1,2,2))].">
      <j1 rule="para" parents="84 493"/>
    </justification>
  </clause>

  <clause id="914">
    <literal><![CDATA[
      (x * y) * K(z \ y,z) != u * ((z \ y) * z)
    ]]></literal>
    <literal><![CDATA[
      R(x,y,K(z \ y,z)) = u
    ]]></literal>
    <justification jstring="[para(287(a,1),544(a,2,2))].">
      <j1 rule="para" parents="287 544"/>
    </justification>
  </clause>

  <clause id="915">
    <literal><![CDATA[
      x / (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      R((x / z) / y,y,z) = u
    ]]></literal>
    <justification jstring="[para(83(a,1),549(a,1,1))].">
      <j1 rule="para" parents="83 549"/>
    </justification>
  </clause>

  <clause id="916">
    <literal><![CDATA[
      (K(x \ 1,x) * y) / (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      R(x \ 1,x,y) = z
    ]]></literal>
    <justification jstring="[para(253(a,2),549(a,1,1,1))].">
      <j1 rule="para" parents="253 549"/>
    </justification>
  </clause>

  <clause id="917">
    <literal><![CDATA[
      T(x \ 1,y) / (x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      T(1 / x,y) * x = z
    ]]></literal>
    <justification jstring="[para(804(a,1),593(a,1,1))].">
      <j1 rule="para" parents="804 593"/>
    </justification>
  </clause>

  <clause id="918">
    <literal><![CDATA[
      (x * y) / z != u
    ]]></literal>
    <literal><![CDATA[
      R(x / (z / y),z / y,y) = u
    ]]></literal>
    <justification jstring="[para(12(a,1),651(a,1,2))].">
      <j1 rule="para" parents="12 651"/>
    </justification>
  </clause>

  <clause id="919">
    <literal><![CDATA[
      (x * L(x \ y,z,u)) / x = L(y / x,z,u)
    ]]></literal>
    <justification jstring="[hyper(137,a,685,a)].">
      <j1 rule="hyper" parents="137 685"/>
    </justification>
  </clause>

  <clause id="920">
    <literal><![CDATA[
      L(1 / x,x,y) * x = x * ((y * x) \ y)
    ]]></literal>
    <justification jstring="[para(214(a,1),685(a,2,2))].">
      <j1 rule="para" parents="214 685"/>
    </justification>
  </clause>

  <clause id="921">
    <literal><![CDATA[
      L(1 / x,x,x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(37,a,738,a(flip),b,920,a),flip(a)].">
      <j1 rule="hyper" parents="37 738 920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="922">
    <literal><![CDATA[
      L(T(1 / x,y),x,x) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(921(a,1),25(a,2,1))].">
      <j1 rule="para" parents="921 25"/>
    </justification>
  </clause>

  <clause id="924">
    <literal><![CDATA[
      (x * x) * T(x \ 1,y) = x * (x * T(1 / x,y))
    ]]></literal>
    <justification jstring="[para(922(a,1),94(a,1,2))].">
      <j1 rule="para" parents="922 94"/>
    </justification>
  </clause>

  <clause id="925">
    <literal><![CDATA[
      L((x * y) / x,z,u) = (x * L(y,z,u)) / x
    ]]></literal>
    <justification jstring="[hyper(137,a,686,a),flip(a)].">
      <j1 rule="hyper" parents="137 686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="926">
    <literal><![CDATA[
      L((x * y) / x,z \ x,z) = (z * ((z \ x) * y)) / x
    ]]></literal>
    <justification jstring="[hyper(120,a,482,a(flip),b,686,a),flip(a)].">
      <j1 rule="hyper" parents="120 482 686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="927">
    <literal><![CDATA[
      L(((x * y) * z) / (x * y),y,x) = (x * (y * z)) / (x * y)
    ]]></literal>
    <justification jstring="[hyper(120,a,94,a(flip),b,686,a),flip(a)].">
      <j1 rule="hyper" parents="120 94 686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="928">
    <literal><![CDATA[
      (x * R(x \ y,z,u)) * (x \ 1) = R(R(y / x,z,u),x,x \ 1)
    ]]></literal>
    <justification jstring="[para(692(a,1),258(a,1,1))].">
      <j1 rule="para" parents="692 258"/>
    </justification>
  </clause>

  <clause id="929">
    <literal><![CDATA[
      (x * K(x,y)) * R((x * K(x,y)) \ (x * y),z,u) = R(R(y,x,K(x,y)),z,u) * (x * K(x,y))
    ]]></literal>
    <justification jstring="[para(290(a,1),692(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="290 692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="930">
    <literal><![CDATA[
      (x / y) * R((x / y) \ z,x / y,y) = ((z * y) / x) * (x / y)
    ]]></literal>
    <justification jstring="[para(567(a,1),692(a,1,1)),flip(a)].">
      <j1 rule="para" parents="567 692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="931">
    <literal><![CDATA[
      ((((x * y) * z) / (x * y)) * x) * y = (x * y) * R(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(275,a,693,a)].">
      <j1 rule="hyper" parents="275 693"/>
    </justification>
  </clause>

  <clause id="932">
    <literal><![CDATA[
      R((x * y) / x,z,u) = (x * R(y,z,u)) / x
    ]]></literal>
    <justification jstring="[hyper(137,a,693,a),flip(a)].">
      <j1 rule="hyper" parents="137 693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="933">
    <literal><![CDATA[
      L(x \ (y * (x * x)),x,x) = T(x * y,x * x)
    ]]></literal>
    <justification jstring="[hyper(65,a,511,a,b,695,a)].">
      <j1 rule="hyper" parents="65 511 695"/>
    </justification>
  </clause>

  <clause id="934">
    <literal><![CDATA[
      T(x * ((x * x) \ y),x * x) = (1 / x) * T(y,x * x)
    ]]></literal>
    <justification jstring="[para(663(a,1),695(a,1,2)),flip(a)].">
      <j1 rule="para" parents="663 695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="935">
    <literal><![CDATA[
      R(x / y,z,u) * y != w
    ]]></literal>
    <literal><![CDATA[
      y * R(y \ x,z,u) = w
    ]]></literal>
    <justification jstring="[para(699(a,1),246(a,1,1)),flip(b)].">
      <j1 rule="para" parents="699 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="936">
    <literal><![CDATA[
      (x \ y) * (((x \ 1) \ y) \ z) = (x * x) \ z
    ]]></literal>
    <justification jstring="[hyper(119,a,10,a(flip),b,731,a),flip(a)].">
      <j1 rule="hyper" parents="119 10 731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="937">
    <literal><![CDATA[
      (x / ((y \ 1) \ z)) * (u * u) = x / ((y \ (u * u)) \ z)
    ]]></literal>
    <justification jstring="[para(745(a,1),827(a,1,2)),flip(a)].">
      <j1 rule="para" parents="745 827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="938">
    <literal><![CDATA[
      ((x \ 1) \ y) \ (z * (x * x)) = (x \ y) \ T(z,x * x)
    ]]></literal>
    <justification jstring="[para(22(a,2),748(a,1,2)),flip(a)].">
      <j1 rule="para" parents="22 748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="939">
    <literal><![CDATA[
      (x \ y) \ (((x * x) \ z) * u) = ((x \ 1) \ y) \ (z * u)
    ]]></literal>
    <justification jstring="[para(664(a,1),748(a,1,2))].">
      <j1 rule="para" parents="664 748"/>
    </justification>
  </clause>

  <clause id="940">
    <literal><![CDATA[
      (x * ((y * (x \ z)) / y)) / x = (y * (z / x)) / y
    ]]></literal>
    <justification jstring="[hyper(267,a,755,a)].">
      <j1 rule="hyper" parents="267 755"/>
    </justification>
  </clause>

  <clause id="941">
    <literal><![CDATA[
      ((x * (y / z)) / x) * z = z * ((x * (z \ y)) / x)
    ]]></literal>
    <justification jstring="[para(755(a,1),107(a,1,2)),flip(a)].">
      <j1 rule="para" parents="755 107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="942">
    <literal><![CDATA[
      ((x * (y / z)) / x) \ (z * ((x * (z \ y)) / x)) = z
    ]]></literal>
    <justification jstring="[para(755(a,1),224(a,1,2,2))].">
      <j1 rule="para" parents="755 224"/>
    </justification>
  </clause>

  <clause id="944">
    <literal><![CDATA[
      (x \ 1) * (x * y) = x * ((1 / x) * y)
    ]]></literal>
    <justification jstring="[para(264(a,1),762(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="264 762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="945">
    <literal><![CDATA[
      ((x \ 1) * x) \ (x * ((1 / x) * y)) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,944,a(flip),b,94,a)].">
      <j1 rule="hyper" parents="119 944 94"/>
    </justification>
  </clause>

  <clause id="946">
    <literal><![CDATA[
      x * ((1 / x) * T(y,x)) = (x \ 1) * (y * x)
    ]]></literal>
    <justification jstring="[para(107(a,1),944(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="948">
    <literal><![CDATA[
      L(x,x,x) * L(y,x,x) = L(x * y,x,x)
    ]]></literal>
    <justification jstring="[para(473(a,1),819(a,1,1)),flip(a)].">
      <j1 rule="para" parents="473 819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="949">
    <literal><![CDATA[
      L(x,x,x) * L(x,x,x) = x * x
    ]]></literal>
    <justification jstring="[hyper(299,a,476,a(flip),b,948,a),flip(a)].">
      <j1 rule="hyper" parents="299 476 948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="950">
    <literal><![CDATA[
      T((1 / x) * ((x * x) * y),x) = (1 / x) * (((1 / x) \ y) * x)
    ]]></literal>
    <justification jstring="[para(443(a,1),820(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="443 820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="951">
    <literal><![CDATA[
      x * (y \ (y \ 1)) = x / (y * y)
    ]]></literal>
    <justification jstring="[hyper(37,a,35,a,b,834,a(flip))].">
      <j1 rule="hyper" parents="37 35 834"/>
    </justification>
  </clause>

  <clause id="953">
    <literal><![CDATA[
      (x * (y \ (y \ 1))) \ z = (y * y) * (x \ z)
    ]]></literal>
    <justification jstring="[para(951(a,2),416(a,1,1))].">
      <j1 rule="para" parents="951 416"/>
    </justification>
  </clause>

  <clause id="954">
    <literal><![CDATA[
      (x * (y \ (y \ 1))) * z = x * ((y * y) \ z)
    ]]></literal>
    <justification jstring="[para(951(a,2),830(a,1,1))].">
      <j1 rule="para" parents="951 830"/>
    </justification>
  </clause>

  <clause id="955">
    <literal><![CDATA[
      ((x \ (y * y)) / z) \ (x \ 1) = z / (y * y)
    ]]></literal>
    <justification jstring="[hyper(186,a,845,a)].">
      <j1 rule="hyper" parents="186 845"/>
    </justification>
  </clause>

  <clause id="956">
    <literal><![CDATA[
      (x * y) \ ((x * y) \ 1) = y \ (x \ ((x * y) \ 1))
    ]]></literal>
    <justification jstring="[hyper(119,a,850,a(flip),b,951,a),flip(a)].">
      <j1 rule="hyper" parents="119 850 951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="957">
    <literal><![CDATA[
      (x \ 1) \ T(y * (x \ 1),x) != z
    ]]></literal>
    <literal><![CDATA[
      T((x \ y) * x,x \ 1) = z
    ]]></literal>
    <justification jstring="[para(858(a,1),318(a,1,2))].">
      <j1 rule="para" parents="858 318"/>
    </justification>
  </clause>

  <clause id="958">
    <literal><![CDATA[
      (x * K(y \ x,y)) * (y \ 1) = T(x * (y \ 1),y)
    ]]></literal>
    <justification jstring="[para(287(a,2),858(a,1,1))].">
      <j1 rule="para" parents="287 858"/>
    </justification>
  </clause>

  <clause id="959">
    <literal><![CDATA[
      T(T(R(x / y,z,u),w),y) = R(T(y \ x,w),z,u)
    ]]></literal>
    <justification jstring="[para(109(a,1),895(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="109 895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="960">
    <literal><![CDATA[
      x \ (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      L((y \ x) \ z,y \ x,y) = u
    ]]></literal>
    <justification jstring="[para(10(a,1),909(a,1,1))].">
      <j1 rule="para" parents="10 909"/>
    </justification>
  </clause>

  <clause id="962">
    <literal><![CDATA[
      ((x * y) * L(L(z,y,x),u,w)) / (x * y) = L((x * (y * z)) / (x * y),u,w)
    ]]></literal>
    <justification jstring="[para(18(a,2),919(a,1,1,2,1))].">
      <j1 rule="para" parents="18 919"/>
    </justification>
  </clause>

  <clause id="963">
    <literal><![CDATA[
      L(x / y,z,u) != w / y
    ]]></literal>
    <literal><![CDATA[
      y * L(y \ x,z,u) = w
    ]]></literal>
    <justification jstring="[para(919(a,1),48(a,1))].">
      <j1 rule="para" parents="919 48"/>
    </justification>
  </clause>

  <clause id="964">
    <literal><![CDATA[
      L(x,y,z) != (u * L(u \ w,y,z)) / u
    ]]></literal>
    <literal><![CDATA[
      w / u = x
    ]]></literal>
    <justification jstring="[para(919(a,2),52(a,1)),flip(a)].">
      <j1 rule="para" parents="919 52"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="965">
    <literal><![CDATA[
      L(x / y,z,u) * y != w
    ]]></literal>
    <literal><![CDATA[
      y * L(y \ x,z,u) = w
    ]]></literal>
    <justification jstring="[para(919(a,1),246(a,1,1)),flip(b)].">
      <j1 rule="para" parents="919 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="966">
    <literal><![CDATA[
      T(L(x / y,z,u),y) != w
    ]]></literal>
    <literal><![CDATA[
      L(y \ x,z,u) = w
    ]]></literal>
    <justification jstring="[para(919(a,1),324(a,1,1)),flip(b)].">
      <j1 rule="para" parents="919 324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="967">
    <literal><![CDATA[
      (x * ((1 / x) * y)) / x = L(y / x,x,x)
    ]]></literal>
    <justification jstring="[para(511(a,1),919(a,1,1,2))].">
      <j1 rule="para" parents="511 919"/>
    </justification>
  </clause>

  <clause id="968">
    <literal><![CDATA[
      L((x \ y) / z,z,x) = (z * ((x * z) \ y)) / z
    ]]></literal>
    <justification jstring="[para(281(a,1),919(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="281 919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="969">
    <literal><![CDATA[
      (x * ((1 / x) * y)) / x = L(y / x,x,1 / x)
    ]]></literal>
    <justification jstring="[para(518(a,1),919(a,1,1,2))].">
      <j1 rule="para" parents="518 919"/>
    </justification>
  </clause>

  <clause id="970">
    <literal><![CDATA[
      L(T(x,y) / x,x,y) = (x * K(x,y)) / x
    ]]></literal>
    <justification jstring="[para(824(a,2),919(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="824 919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="971">
    <literal><![CDATA[
      L((x * y) / x,z,u) * x != w
    ]]></literal>
    <literal><![CDATA[
      x * L(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(925(a,2),246(a,1,1)),flip(b)].">
      <j1 rule="para" parents="925 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="972">
    <literal><![CDATA[
      (x * y) * ((z * L(u,y,x)) / z) = x * (y * ((z * u) / z))
    ]]></literal>
    <justification jstring="[para(925(a,1),94(a,1,2))].">
      <j1 rule="para" parents="925 94"/>
    </justification>
  </clause>

  <clause id="973">
    <literal><![CDATA[
      L((x * (y \ 1)) / x,y,z / y) = (x * (z \ (z / y))) / x
    ]]></literal>
    <justification jstring="[para(370(a,1),925(a,2,1,2))].">
      <j1 rule="para" parents="370 925"/>
    </justification>
  </clause>

  <clause id="974">
    <literal><![CDATA[
      L((x * ((y \ z) \ u)) / x,y \ z,y) = (x * (z \ (y * u))) / x
    ]]></literal>
    <justification jstring="[para(520(a,1),925(a,2,1,2))].">
      <j1 rule="para" parents="520 925"/>
    </justification>
  </clause>

  <clause id="975">
    <literal><![CDATA[
      R((x * y) / x,z,u) != w / x
    ]]></literal>
    <literal><![CDATA[
      x * R(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(932(a,2),48(a,1))].">
      <j1 rule="para" parents="932 48"/>
    </justification>
  </clause>

  <clause id="976">
    <literal><![CDATA[
      R((x * (1 / y)) / x,y,z) = (x * (z / (y * z))) / x
    ]]></literal>
    <justification jstring="[para(216(a,1),932(a,2,1,2))].">
      <j1 rule="para" parents="216 932"/>
    </justification>
  </clause>

  <clause id="977">
    <literal><![CDATA[
      ((x * R(y,z,u)) / x) * (z * u) = (((x * y) / x) * z) * u
    ]]></literal>
    <justification jstring="[para(932(a,1),103(a,1,1))].">
      <j1 rule="para" parents="932 103"/>
    </justification>
  </clause>

  <clause id="978">
    <literal><![CDATA[
      R((x * ((y / z) / u)) / x,u,z) = (x * (y / (u * z))) / x
    ]]></literal>
    <justification jstring="[para(285(a,1),932(a,2,1,2))].">
      <j1 rule="para" parents="285 932"/>
    </justification>
  </clause>

  <clause id="979">
    <literal><![CDATA[
      R((x * (y / z)) / x,z,z \ 1) = (x * (y * (z \ 1))) / x
    ]]></literal>
    <justification jstring="[para(565(a,1),932(a,2,1,2))].">
      <j1 rule="para" parents="565 932"/>
    </justification>
  </clause>

  <clause id="980">
    <literal><![CDATA[
      ((x * R(y,z,u)) / x) * (z * u) != w
    ]]></literal>
    <literal><![CDATA[
      (((x * y) / x) * z) * u = w
    ]]></literal>
    <justification jstring="[para(932(a,1),275(a,1,1))].">
      <j1 rule="para" parents="932 275"/>
    </justification>
  </clause>

  <clause id="981">
    <literal><![CDATA[
      (x * x) \ y != (x \ z) * u
    ]]></literal>
    <literal><![CDATA[
      ((x \ 1) \ z) \ y = u
    ]]></literal>
    <justification jstring="[para(936(a,1),45(a,1))].">
      <j1 rule="para" parents="936 45"/>
    </justification>
  </clause>

  <clause id="983">
    <literal><![CDATA[
      ((x * x) \ y) * x = (1 / x) * T(y,x)
    ]]></literal>
    <justification jstring="[hyper(36,a,762,a,b,946,a)].">
      <j1 rule="hyper" parents="36 762 946"/>
    </justification>
  </clause>

  <clause id="984">
    <literal><![CDATA[
      (x \ 1) * (y * x) != x * z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) * T(y,x) = z
    ]]></literal>
    <justification jstring="[para(946(a,1),45(a,1))].">
      <j1 rule="para" parents="946 45"/>
    </justification>
  </clause>

  <clause id="985">
    <literal><![CDATA[
      T(x,y) * T(1 / y,T(x,y)) = ((y * y) \ x) * y
    ]]></literal>
    <justification jstring="[hyper(299,a,107,a,b,983,a)].">
      <j1 rule="hyper" parents="299 107 983"/>
    </justification>
  </clause>

  <clause id="986">
    <literal><![CDATA[
      (1 / x) * T(T(y,x \ 1),x) = (x \ (y * (x \ 1))) * x
    ]]></literal>
    <justification jstring="[para(726(a,1),983(a,1,1)),flip(a)].">
      <j1 rule="para" parents="726 983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="987">
    <literal><![CDATA[
      ((1 / x) * (1 / x)) * (y \ z) = (y * ((1 / x) \ x)) \ z
    ]]></literal>
    <justification jstring="[para(79(a,1),953(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="79 953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="990">
    <literal><![CDATA[
      (x / y) \ (x \ 1) = y / (x * x)
    ]]></literal>
    <justification jstring="[para(9(a,1),955(a,1,1,1))].">
      <j1 rule="para" parents="9 955"/>
    </justification>
  </clause>

  <clause id="991">
    <literal><![CDATA[
      (x * y) \ (y * T(x,y / x)) = a(x,y / x,x)
    ]]></literal>
    <justification jstring="[para(889(a,1),86(a,1,2))].">
      <j1 rule="para" parents="889 86"/>
    </justification>
  </clause>

  <clause id="992">
    <literal><![CDATA[
      L(L(x \ 1,y * x,z),x,y) = (z * (y * x)) \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(299,a,96,a(flip),b,372,a),flip(a)].">
      <j1 rule="hyper" parents="299 96 372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="993">
    <literal><![CDATA[
      (x * y) * L((x * y) \ x,z,u) = x * (y * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(372(a,1),94(a,1,2))].">
      <j1 rule="para" parents="372 94"/>
    </justification>
  </clause>

  <clause id="994">
    <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),396(a,1,2,1))].">
      <j1 rule="para" parents="22 396"/>
    </justification>
  </clause>

  <clause id="996">
    <literal><![CDATA[
      (x * y) * T(z * z,u) = x * (y * T(z * z,u))
    ]]></literal>
    <justification jstring="[para(476(a,1),487(a,1,2,1))].">
      <j1 rule="para" parents="476 487"/>
    </justification>
  </clause>

  <clause id="997">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (x * z),u) = x * (y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(96(a,1),487(a,1,2,1))].">
      <j1 rule="para" parents="96 487"/>
    </justification>
  </clause>

  <clause id="998">
    <literal><![CDATA[
      (x * y) * T((x * y) \ z,u) = x * (y * T(y \ (x \ z),u))
    ]]></literal>
    <justification jstring="[para(281(a,1),487(a,1,2,1))].">
      <j1 rule="para" parents="281 487"/>
    </justification>
  </clause>

  <clause id="999">
    <literal><![CDATA[
      (x * y) * T(T(x,x * y),z) = x * (y * T(T(x,y),z))
    ]]></literal>
    <justification jstring="[para(784(a,1),487(a,1,2,1))].">
      <j1 rule="para" parents="784 487"/>
    </justification>
  </clause>

  <clause id="1000">
    <literal><![CDATA[
      x * (y * T(y \ T(y,x),z)) = (x * y) * T(K(y,x),z)
    ]]></literal>
    <justification jstring="[para(824(a,2),487(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="824 487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1001">
    <literal><![CDATA[
      x * (T(y,x) * T(z,y * x)) = L(z,T(y,x),x) * (y * x)
    ]]></literal>
    <justification jstring="[hyper(396,a,491,a),flip(a)].">
      <j1 rule="hyper" parents="396 491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1002">
    <literal><![CDATA[
      (1 / x) * (x * R(x \ y,z,u)) = R((1 / x) * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(758,a,516,a)].">
      <j1 rule="hyper" parents="758 516"/>
    </justification>
  </clause>

  <clause id="1003">
    <literal><![CDATA[
      L(T(T(x,y) \ z,u),T(x,y),y) = T((x * y) \ (y * z),u)
    ]]></literal>
    <justification jstring="[para(107(a,1),524(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="107 524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1004">
    <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(524(a,2),279(a,1,2))].">
      <j1 rule="para" parents="524 279"/>
    </justification>
  </clause>

  <clause id="1005">
    <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(525(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="525 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1006">
    <literal><![CDATA[
      L(L(T(x,y) \ z,u,w),T(x,y),y) = L((x * y) \ (y * z),u,w)
    ]]></literal>
    <justification jstring="[para(525(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="525 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1007">
    <literal><![CDATA[
      T(((x * y) * x) / (x * y),y) = R(x,y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(37,a,433,a,b,546,a)].">
      <j1 rule="hyper" parents="37 433 546"/>
    </justification>
  </clause>

  <clause id="1008">
    <literal><![CDATA[
      R(T(x,x * y),y,T(x,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,234,a,b,546,a(flip))].">
      <j1 rule="hyper" parents="36 234 546"/>
    </justification>
  </clause>

  <clause id="1009">
    <literal><![CDATA[
      (T(x,x * y) * y) * T(x,y) = T(x,y) * (x * y)
    ]]></literal>
    <justification jstring="[para(1008(a,1),546(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1008 546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1010">
    <literal><![CDATA[
      R(T(T(x / y,z),y * u),y,u) = T((y * u) \ (x * u),z)
    ]]></literal>
    <justification jstring="[para(569(a,1),895(a,2,1))].">
      <j1 rule="para" parents="569 895"/>
    </justification>
  </clause>

  <clause id="1011">
    <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(107(a,1),581(a,1,2))].">
      <j1 rule="para" parents="107 581"/>
    </justification>
  </clause>

  <clause id="1012">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ y,z) = x \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(519(a,1),589(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="519 589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1013">
    <literal><![CDATA[
      T(x / (1 / y),z) * (1 / y) = T(x * y,z) / y
    ]]></literal>
    <justification jstring="[para(564(a,1),597(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="564 597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1014">
    <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(600(a,1),279(a,1,2))].">
      <j1 rule="para" parents="600 279"/>
    </justification>
  </clause>

  <clause id="1015">
    <literal><![CDATA[
      (x * (y * (z * z))) \ u != w
    ]]></literal>
    <literal><![CDATA[
      (z * z) \ ((x * y) \ u) = w
    ]]></literal>
    <justification jstring="[para(35(a,1),603(a,1,1))].">
      <j1 rule="para" parents="35 603"/>
    </justification>
  </clause>

  <clause id="1018">
    <literal><![CDATA[
      (x / y) * (y * T(y \ 1,z)) = x * T(x \ (x / y),z)
    ]]></literal>
    <justification jstring="[para(621(a,2),474(a,1,2)),flip(a)].">
      <j1 rule="para" parents="621 474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1019">
    <literal><![CDATA[
      T((x \ y) / y,z) * y = (T(1 / x,z) * x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(622(a,2),347(a,1,1))].">
      <j1 rule="para" parents="622 347"/>
    </justification>
  </clause>

  <clause id="1020">
    <literal><![CDATA[
      (x * (x \ y)) * z != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (y * z) = w
    ]]></literal>
    <justification jstring="[para(76(a,1),634(a,1,1,1))].">
      <j1 rule="para" parents="76 634"/>
    </justification>
  </clause>

  <clause id="1022">
    <literal><![CDATA[
      ((x * y) \ x) * (x * y) = x * (y * T(y \ 1,x * y))
    ]]></literal>
    <justification jstring="[para(214(a,1),681(a,2,1)),flip(a)].">
      <j1 rule="para" parents="214 681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1023">
    <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(119,a,84,a(flip),b,688,a),flip(a)].">
      <j1 rule="hyper" parents="119 84 688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1025">
    <literal><![CDATA[
      (x * y) \ ((z * x) * y) != u
    ]]></literal>
    <literal><![CDATA[
      R(T(z,x * y),x,y) = u
    ]]></literal>
    <justification jstring="[para(688(a,1),314(a,1,2))].">
      <j1 rule="para" parents="688 314"/>
    </justification>
  </clause>

  <clause id="1026">
    <literal><![CDATA[
      L(x,y,(y * x) / y) * y = y * T(x,y * x)
    ]]></literal>
    <justification jstring="[para(697(a,1),433(a,1,1))].">
      <j1 rule="para" parents="697 433"/>
    </justification>
  </clause>

  <clause id="1027">
    <literal><![CDATA[
      T(x,y) * (x \ z) != u
    ]]></literal>
    <literal><![CDATA[
      (x \ z) * T((x \ z) \ z,y) = u
    ]]></literal>
    <justification jstring="[para(76(a,1),752(a,1,1,1))].">
      <j1 rule="para" parents="76 752"/>
    </justification>
  </clause>

  <clause id="1029">
    <literal><![CDATA[
      ((x * y) * (y \ z)) / T(x * z,a(x,y,y \ z)) = a(x,y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(120,a,772,a(flip),b,107,a)].">
      <j1 rule="hyper" parents="120 772 107"/>
    </justification>
  </clause>

  <clause id="1030">
    <literal><![CDATA[
      L(x,x \ y,x) * (x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) * T(x,y) = z
    ]]></literal>
    <justification jstring="[para(795(a,1),756(a,1,1))].">
      <j1 rule="para" parents="795 756"/>
    </justification>
  </clause>

  <clause id="1031">
    <literal><![CDATA[
      T(T((x * y) / x,z),y * x) = L(T(y,z),x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,25,a,b,796,a),flip(a)].">
      <j1 rule="hyper" parents="299 25 796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1032">
    <literal><![CDATA[
      R(T(x / y,z),y,y \ z) = z \ (x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(119,a,154,a(flip),b,798,a),flip(a)].">
      <j1 rule="hyper" parents="119 154 798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1033">
    <literal><![CDATA[
      x \ ((x / y) * ((y \ z) * y)) = T(x \ ((x / y) * z),y)
    ]]></literal>
    <justification jstring="[para(522(a,1),870(a,1,1)),flip(a)].">
      <j1 rule="para" parents="522 870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1034">
    <literal><![CDATA[
      R(1 / x,x,x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) / y = z
    ]]></literal>
    <justification jstring="[para(871(a,1),207(a,1))].">
      <j1 rule="para" parents="871 207"/>
    </justification>
  </clause>

  <clause id="1036">
    <literal><![CDATA[
      L(((x / y) \ z) / y,y,x / y) = (y * (x \ z)) / y
    ]]></literal>
    <justification jstring="[para(12(a,1),968(a,2,1,2,1))].">
      <j1 rule="para" parents="12 968"/>
    </justification>
  </clause>

  <clause id="1037">
    <literal><![CDATA[
      L((x \ (y * (x * z))) / z,z,x) = (z * T(y,x * z)) / z
    ]]></literal>
    <justification jstring="[para(22(a,2),968(a,2,1,2))].">
      <j1 rule="para" parents="22 968"/>
    </justification>
  </clause>

  <clause id="1038">
    <literal><![CDATA[
      L((x \ y) / z,z,x) != u / z
    ]]></literal>
    <literal><![CDATA[
      z * ((x * z) \ y) = u
    ]]></literal>
    <justification jstring="[para(968(a,2),48(a,1))].">
      <j1 rule="para" parents="968 48"/>
    </justification>
  </clause>

  <clause id="1039">
    <literal><![CDATA[
      L((x \ (T(x,y) * y)) / y,y,x) = (y * K(T(x,y),y)) / y
    ]]></literal>
    <justification jstring="[para(228(a,1),968(a,2,1,2))].">
      <j1 rule="para" parents="228 968"/>
    </justification>
  </clause>

  <clause id="1040">
    <literal><![CDATA[
      L((x \ y) / x,x,x) = ((x \ 1) * y) / x
    ]]></literal>
    <justification jstring="[para(738(a,1),968(a,2,1))].">
      <j1 rule="para" parents="738 968"/>
    </justification>
  </clause>

  <clause id="1041">
    <literal><![CDATA[
      x * T(y,x * y) != z * x
    ]]></literal>
    <literal><![CDATA[
      L(y,x,(x * y) / x) = z
    ]]></literal>
    <justification jstring="[para(1026(a,1),46(a,1))].">
      <j1 rule="para" parents="1026 46"/>
    </justification>
  </clause>

  <clause id="1042">
    <literal><![CDATA[
      (x \ (y * (z \ x))) * x = (T(y / z,x) * z) * (z \ x)
    ]]></literal>
    <justification jstring="[para(1032(a,1),347(a,1,1))].">
      <j1 rule="para" parents="1032 347"/>
    </justification>
  </clause>

  <clause id="1043">
    <literal><![CDATA[
      (x * (y * (z * (u * u)))) * w = (x * (y * z)) * ((u * u) * w)
    ]]></literal>
    <justification jstring="[para(35(a,1),117(a,1,1,2))].">
      <j1 rule="para" parents="35 117"/>
    </justification>
  </clause>

  <clause id="1044">
    <literal><![CDATA[
      (x * (y / z)) * ((z * z) * u) = (x * (y / (1 / z))) * u
    ]]></literal>
    <justification jstring="[para(675(a,1),117(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="675 117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1045">
    <literal><![CDATA[
      ((x \ 1) * y) * ((x * x) * z) = (x * T(y,x * x)) * z
    ]]></literal>
    <justification jstring="[para(742(a,1),117(a,1,1)),flip(a)].">
      <j1 rule="para" parents="742 117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1046">
    <literal><![CDATA[
      x * ((x \ y) * (z \ (1 / z))) = y * (z \ (1 / z))
    ]]></literal>
    <justification jstring="[hyper(606,a,563,a),flip(a)].">
      <j1 rule="hyper" parents="606 563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1047">
    <literal><![CDATA[
      L((x \ (1 / x)) \ ((y * z) \ u),x \ (1 / x),y * z) = (y * (z * (x \ (1 / x)))) \ u
    ]]></literal>
    <justification jstring="[para(563(a,1),281(a,2,1))].">
      <j1 rule="para" parents="563 281"/>
    </justification>
  </clause>

  <clause id="1049">
    <literal><![CDATA[
      (x * (y * (z \ (1 / z)))) * u = (x * y) * ((z \ (1 / z)) * u)
    ]]></literal>
    <justification jstring="[para(563(a,1),507(a,1,1))].">
      <j1 rule="para" parents="563 507"/>
    </justification>
  </clause>

  <clause id="1050">
    <literal><![CDATA[
      ((x * x) \ y) \ z != u
    ]]></literal>
    <literal><![CDATA[
      y \ ((x * x) * z) = u
    ]]></literal>
    <justification jstring="[para(478(a,1),615(a,1))].">
      <j1 rule="para" parents="478 615"/>
    </justification>
  </clause>

  <clause id="1051">
    <literal><![CDATA[
      T(x,(y * y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      z \ ((y * y) * (x * ((y * y) \ z))) = u
    ]]></literal>
    <justification jstring="[para(22(a,2),1050(a,1))].">
      <j1 rule="para" parents="22 1050"/>
    </justification>
  </clause>

  <clause id="1052">
    <literal><![CDATA[
      (1 / x) \ y != z
    ]]></literal>
    <literal><![CDATA[
      x \ ((x * x) * y) = z
    ]]></literal>
    <justification jstring="[para(264(a,1),1050(a,1,1))].">
      <j1 rule="para" parents="264 1050"/>
    </justification>
  </clause>

  <clause id="1053">
    <literal><![CDATA[
      T(x * (y / (z * z)),z * z) = ((z * z) \ x) * y
    ]]></literal>
    <justification jstring="[para(12(a,1),696(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1054">
    <literal><![CDATA[
      ((x * x) \ y) * L(x,x,x) = T(y * (1 / x),x * x)
    ]]></literal>
    <justification jstring="[para(475(a,1),696(a,1,2))].">
      <j1 rule="para" parents="475 696"/>
    </justification>
  </clause>

  <clause id="1055">
    <literal><![CDATA[
      T(x * ((y * y) \ z),y * y) = ((y * y) \ x) * T(z,y * y)
    ]]></literal>
    <justification jstring="[para(663(a,1),696(a,1,2)),flip(a)].">
      <j1 rule="para" parents="663 696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1056">
    <literal><![CDATA[
      (x * x) \ T(y,x \ (x \ 1)) = y / (x * x)
    ]]></literal>
    <justification jstring="[hyper(299,a,951,a(flip),b,739,a),flip(a)].">
      <j1 rule="hyper" parents="299 951 739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1057">
    <literal><![CDATA[
      T((x * x) \ y,x \ (x \ 1)) = y / (x * x)
    ]]></literal>
    <justification jstring="[hyper(770,a,1056,a),flip(a)].">
      <j1 rule="hyper" parents="770 1056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1058">
    <literal><![CDATA[
      (x * x) * (y / (x * x)) = T(y,x \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(144,a,1056,a)].">
      <j1 rule="hyper" parents="144 1056"/>
    </justification>
  </clause>

  <clause id="1059">
    <literal><![CDATA[
      (1 / x) \ (y / (x * x)) = x \ T(y,x \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(119,a,1056,a(flip),b,441,a)].">
      <j1 rule="hyper" parents="119 1056 441"/>
    </justification>
  </clause>

  <clause id="1060">
    <literal><![CDATA[
      (x * x) * (y / (x * x)) != z
    ]]></literal>
    <literal><![CDATA[
      T(y,x \ (x \ 1)) = z
    ]]></literal>
    <justification jstring="[para(1056(a,1),250(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1056 250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1061">
    <literal><![CDATA[
      (x * x) * ((y / (x * x)) * z) = T(y,x \ (x \ 1)) * z
    ]]></literal>
    <justification jstring="[para(1056(a,1),112(a,1,2,1))].">
      <j1 rule="para" parents="1056 112"/>
    </justification>
  </clause>

  <clause id="1062">
    <literal><![CDATA[
      (x * x) * R(y / x,x,x) = T(y * x,x \ (x \ 1))
    ]]></literal>
    <justification jstring="[para(104(a,2),1058(a,1,2))].">
      <j1 rule="para" parents="104 1058"/>
    </justification>
  </clause>

  <clause id="1064">
    <literal><![CDATA[
      (x * x) * (y / ((x * x) * z)) = T(y / z,x \ (x \ 1))
    ]]></literal>
    <justification jstring="[para(425(a,1),1058(a,1,2))].">
      <j1 rule="para" parents="425 1058"/>
    </justification>
  </clause>

  <clause id="1065">
    <literal><![CDATA[
      (x * x) * (y * (z / (x * x))) = T(y * z,x \ (x \ 1))
    ]]></literal>
    <justification jstring="[para(849(a,1),1058(a,1,2))].">
      <j1 rule="para" parents="849 1058"/>
    </justification>
  </clause>

  <clause id="1066">
    <literal><![CDATA[
      T(x,y * y) * ((y * y) \ z) = ((y * y) \ x) * z
    ]]></literal>
    <justification jstring="[hyper(315,a,760,a),flip(a)].">
      <j1 rule="hyper" parents="315 760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1067">
    <literal><![CDATA[
      (x * x) * (T(y,x * x) * z) = y * ((x * x) * z)
    ]]></literal>
    <justification jstring="[para(760(a,1),112(a,1,2))].">
      <j1 rule="para" parents="760 112"/>
    </justification>
  </clause>

  <clause id="1068">
    <literal><![CDATA[
      (x * y) \ ((x * x) * z) = ((1 / x) * y) \ z
    ]]></literal>
    <justification jstring="[para(264(a,1),767(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="264 767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1069">
    <literal><![CDATA[
      ((1 / x) * y) \ ((1 / x) * z) = (x * y) \ (x * z)
    ]]></literal>
    <justification jstring="[para(265(a,1),1068(a,1,2)),flip(a)].">
      <j1 rule="para" parents="265 1068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1070">
    <literal><![CDATA[
      ((1 / x) * y) \ (x \ z) = (x * y) \ ((x \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(724(a,1),1068(a,1,2)),flip(a)].">
      <j1 rule="para" parents="724 1068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1071">
    <literal><![CDATA[
      (x * ((y * y) * (z * u))) \ ((x * ((y * y) * z)) * u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,(y * y) * z,u) = w
    ]]></literal>
    <justification jstring="[para(33(a,1),775(a,1,1,2))].">
      <j1 rule="para" parents="33 775"/>
    </justification>
  </clause>

  <clause id="1072">
    <literal><![CDATA[
      K((x * y) \ 1,x * y) \ ((((x * y) \ 1) * x) * y) != z
    ]]></literal>
    <literal><![CDATA[
      a((x * y) \ 1,x,y) = z
    ]]></literal>
    <justification jstring="[para(253(a,2),775(a,1,1))].">
      <j1 rule="para" parents="253 775"/>
    </justification>
  </clause>

  <clause id="1074">
    <literal><![CDATA[
      (1 / x) \ T(1 / x,y) = x * T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(8(a,1),821(a,1,2,1))].">
      <j1 rule="para" parents="8 821"/>
    </justification>
  </clause>

  <clause id="1075">
    <literal><![CDATA[
      x * T(x \ ((1 / x) \ y),z) = (1 / x) \ T(y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),821(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1076">
    <literal><![CDATA[
      (x / (y * z)) * (y * y) = x / ((1 / y) * z)
    ]]></literal>
    <justification jstring="[para(264(a,1),829(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="264 829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1077">
    <literal><![CDATA[
      (x * (y * (z \ (1 / z)))) / u = (x * y) / (u / (z \ (1 / z)))
    ]]></literal>
    <justification jstring="[para(563(a,1),838(a,1,1))].">
      <j1 rule="para" parents="563 838"/>
    </justification>
  </clause>

  <clause id="1078">
    <literal><![CDATA[
      1 / (x \ (1 / x)) = (1 / x) \ x
    ]]></literal>
    <justification jstring="[hyper(579,a,848,a)].">
      <j1 rule="hyper" parents="579 848"/>
    </justification>
  </clause>

  <clause id="1079">
    <literal><![CDATA[
      x \ (y * (z * (u \ (1 / u)))) = (x \ (y * z)) * (u \ (1 / u))
    ]]></literal>
    <justification jstring="[para(563(a,1),848(a,1,2))].">
      <j1 rule="para" parents="563 848"/>
    </justification>
  </clause>

  <clause id="1080">
    <literal><![CDATA[
      ((1 / x) \ x) \ y = (x \ (1 / x)) * y
    ]]></literal>
    <justification jstring="[para(1078(a,1),510(a,1,1))].">
      <j1 rule="para" parents="1078 510"/>
    </justification>
  </clause>

  <clause id="1081">
    <literal><![CDATA[
      1 / ((1 / x) \ x) = x \ (1 / x)
    ]]></literal>
    <justification jstring="[hyper(578,a,1080,a)].">
      <j1 rule="hyper" parents="578 1080"/>
    </justification>
  </clause>

  <clause id="1082">
    <literal><![CDATA[
      ((x * x) * y) / (z * (x * x)) = T(y,x \ (x \ 1)) / z
    ]]></literal>
    <justification jstring="[para(1058(a,1),853(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1058 853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1083">
    <literal><![CDATA[
      (x * (y * ((z * z) \ u))) \ ((x * (y / (z * z))) * u) = a(x,y,(z * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(119,a,854,a,b,84,a)].">
      <j1 rule="hyper" parents="119 854 84"/>
    </justification>
  </clause>

  <clause id="1084">
    <literal><![CDATA[
      (x * y) * ((y * y) \ z) = (x * (y \ 1)) * z
    ]]></literal>
    <justification jstring="[para(459(a,1),854(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="459 854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1086">
    <literal><![CDATA[
      ((x * y) * ((y * y) \ ((y \ 1) \ z))) / z = R(x,y \ 1,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(120,a,1084,a,b,347,a)].">
      <j1 rule="hyper" parents="120 1084 347"/>
    </justification>
  </clause>

  <clause id="1087">
    <literal><![CDATA[
      (x * y) * (y \ (y \ 1)) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(37,a,954,a,b,1084,a(flip))].">
      <j1 rule="hyper" parents="37 954 1084"/>
    </justification>
  </clause>

  <clause id="1088">
    <literal><![CDATA[
      (x * (y \ 1)) * y = (x * y) * (1 / y)
    ]]></literal>
    <justification jstring="[para(264(a,1),1084(a,1,2)),flip(a)].">
      <j1 rule="para" parents="264 1084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1089">
    <literal><![CDATA[
      (x * y) \ (x * (y \ 1)) = y \ (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(125,a,1087,a)].">
      <j1 rule="hyper" parents="125 1087"/>
    </justification>
  </clause>

  <clause id="1090">
    <literal><![CDATA[
      (x * y) * (1 / y) != z * y
    ]]></literal>
    <literal><![CDATA[
      x * (y \ 1) = z
    ]]></literal>
    <justification jstring="[para(1088(a,1),46(a,1))].">
      <j1 rule="para" parents="1088 46"/>
    </justification>
  </clause>

  <clause id="1091">
    <literal><![CDATA[
      (x / (((y \ 1) * y) * (1 / y))) * z = (x / y) * (((y \ 1) * (y \ 1)) \ z)
    ]]></literal>
    <justification jstring="[para(1088(a,1),835(a,1,1,2))].">
      <j1 rule="para" parents="1088 835"/>
    </justification>
  </clause>

  <clause id="1092">
    <literal><![CDATA[
      (x \ y) \ ((x \ y) \ 1) = y \ (x * ((x \ y) \ 1))
    ]]></literal>
    <justification jstring="[hyper(329,a,1089,a),flip(a)].">
      <j1 rule="hyper" parents="329 1089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1093">
    <literal><![CDATA[
      (x * ((y * z) / y)) / x = (y * ((x * z) / x)) / y
    ]]></literal>
    <justification jstring="[para(9(a,1),940(a,1,1,2,1,2))].">
      <j1 rule="para" parents="9 940"/>
    </justification>
  </clause>

  <clause id="1095">
    <literal><![CDATA[
      ((x * (y / z)) / x) * z != u
    ]]></literal>
    <literal><![CDATA[
      z * ((x * (z \ y)) / x) = u
    ]]></literal>
    <justification jstring="[para(940(a,1),246(a,1,1)),flip(b)].">
      <j1 rule="para" parents="940 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1097">
    <literal><![CDATA[
      R((x * (y / z)) / x,z,z \ 1) / (z \ 1) = z * ((x * (z \ y)) / x)
    ]]></literal>
    <justification jstring="[hyper(65,a,423,a,b,941,a)].">
      <j1 rule="hyper" parents="65 423 941"/>
    </justification>
  </clause>

  <clause id="1098">
    <literal><![CDATA[
      (x \ y) * ((z * ((x \ y) \ y)) / z) = ((z * x) / z) * (x \ y)
    ]]></literal>
    <justification jstring="[para(76(a,1),941(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="76 941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1099">
    <literal><![CDATA[
      ((x * R(y / z,z,u)) / x) * (z * u) = (z * u) * ((x * ((z * u) \ (y * u))) / x)
    ]]></literal>
    <justification jstring="[para(104(a,2),941(a,1,1,1,2))].">
      <j1 rule="para" parents="104 941"/>
    </justification>
  </clause>

  <clause id="1100">
    <literal><![CDATA[
      ((x * (y / (y / z))) / x) \ ((y / z) * ((x * z) / x)) = y / z
    ]]></literal>
    <justification jstring="[para(79(a,1),942(a,1,2,2,1,2))].">
      <j1 rule="para" parents="79 942"/>
    </justification>
  </clause>

  <clause id="1101">
    <literal><![CDATA[
      T(T((x * y) / (z * y),u),z) = R(T(z \ x,u),z,y)
    ]]></literal>
    <justification jstring="[para(104(a,1),959(a,1,1,1))].">
      <j1 rule="para" parents="104 959"/>
    </justification>
  </clause>

  <clause id="1102">
    <literal><![CDATA[
      x \ (y * T(z * z,u)) = (x \ y) * T(z * z,u)
    ]]></literal>
    <justification jstring="[hyper(1020,a,996,a)].">
      <j1 rule="hyper" parents="1020 996"/>
    </justification>
  </clause>

  <clause id="1103">
    <literal><![CDATA[
      T(T(x,x * y) * y,T(x,y)) = x * y
    ]]></literal>
    <justification jstring="[hyper(235,a,1009,a,b,xx)].">
      <j1 rule="hyper" parents="235 1009"/>
    </justification>
  </clause>

  <clause id="1105">
    <literal><![CDATA[
      x \ T(x * (y * (x \ 1)),z) = T(y,z) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(807,a,1012,a),flip(a)].">
      <j1 rule="hyper" parents="807 1012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1106">
    <literal><![CDATA[
      x \ T(x * y,x \ 1) = ((x \ 1) \ y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(276,a,1012,a),flip(a)].">
      <j1 rule="hyper" parents="276 1012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1107">
    <literal><![CDATA[
      (x \ 1) \ (x \ T(x * y,z)) = T((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,1012,a)].">
      <j1 rule="hyper" parents="125 1012"/>
    </justification>
  </clause>

  <clause id="1108">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ 1,y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[para(8(a,1),1012(a,2,2,1))].">
      <j1 rule="para" parents="8 1012"/>
    </justification>
  </clause>

  <clause id="1109">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ (x \ y),z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),1012(a,2,2,1))].">
      <j1 rule="para" parents="10 1012"/>
    </justification>
  </clause>

  <clause id="1110">
    <literal><![CDATA[
      x \ T(x * y,x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      ((x \ 1) \ y) * (x \ 1) = z
    ]]></literal>
    <justification jstring="[para(1012(a,1),276(a,1))].">
      <j1 rule="para" parents="1012 276"/>
    </justification>
  </clause>

  <clause id="1111">
    <literal><![CDATA[
      T(1 / (x \ 1),y) * (x \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(439,a,1108,a)].">
      <j1 rule="hyper" parents="439 1108"/>
    </justification>
  </clause>

  <clause id="1112">
    <literal><![CDATA[
      T(x,y) * (x \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,434,a(flip),b,1108,a)].">
      <j1 rule="hyper" parents="65 434 1108"/>
    </justification>
  </clause>

  <clause id="1113">
    <literal><![CDATA[
      T(x,y) * R(T(x,y) \ 1,T(x,y),x \ 1) = ((x \ 1) / (x \ T(x,y))) * T(x,y)
    ]]></literal>
    <justification jstring="[para(1112(a,1),706(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1112 706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1114">
    <literal><![CDATA[
      (x * y) \ (y * (x \ T(x,y))) = L(x \ 1,T(x,y),y)
    ]]></literal>
    <justification jstring="[para(1112(a,1),229(a,1,2,2))].">
      <j1 rule="para" parents="1112 229"/>
    </justification>
  </clause>

  <clause id="1116">
    <literal><![CDATA[
      T(((1 / x) * y) * x,z) / x = (1 / x) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(756,a,1013,a),flip(a)].">
      <j1 rule="hyper" parents="756 1013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1117">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ y,z) = T(y * x,z) / x
    ]]></literal>
    <justification jstring="[hyper(752,a,1013,a)].">
      <j1 rule="hyper" parents="752 1013"/>
    </justification>
  </clause>

  <clause id="1118">
    <literal><![CDATA[
      T(1 / (1 / x),y) * (1 / x) = T(x,y) / x
    ]]></literal>
    <justification jstring="[para(7(a,1),1013(a,2,1,1))].">
      <j1 rule="para" parents="7 1013"/>
    </justification>
  </clause>

  <clause id="1119">
    <literal><![CDATA[
      x / y != T(z / (1 / y),u) * (1 / y)
    ]]></literal>
    <literal><![CDATA[
      T(z * y,u) = x
    ]]></literal>
    <justification jstring="[para(1013(a,2),48(a,1)),flip(a)].">
      <j1 rule="para" parents="1013 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1120">
    <literal><![CDATA[
      T(x * y,1 / y) / y = ((1 / y) \ x) * (1 / y)
    ]]></literal>
    <justification jstring="[para(109(a,1),1013(a,1,1)),flip(a)].">
      <j1 rule="para" parents="109 1013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1121">
    <literal><![CDATA[
      T(x * y,z) / y != u
    ]]></literal>
    <literal><![CDATA[
      (1 / y) * T((1 / y) \ x,z) = u
    ]]></literal>
    <justification jstring="[para(1013(a,1),752(a,1))].">
      <j1 rule="para" parents="1013 752"/>
    </justification>
  </clause>

  <clause id="1122">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ 1,y) = T(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(752,a,1118,a)].">
      <j1 rule="hyper" parents="752 1118"/>
    </justification>
  </clause>

  <clause id="1123">
    <literal><![CDATA[
      (1 / x) * T(x,y) = T(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(65,a,435,a(flip),b,1118,a)].">
      <j1 rule="hyper" parents="65 435 1118"/>
    </justification>
  </clause>

  <clause id="1124">
    <literal><![CDATA[
      (T(x,y) / x) / T(x,y) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(120,a,1118,a(flip),b,435,a(flip))].">
      <j1 rule="hyper" parents="120 1118 435"/>
    </justification>
  </clause>

  <clause id="1125">
    <literal><![CDATA[
      T(x \ 1,y) / (x \ 1) = x * T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(327,a,1123,a),flip(a)].">
      <j1 rule="hyper" parents="327 1123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1126">
    <literal><![CDATA[
      T(x,y) \ (T(x,y) / x) = T(1 / x,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(235,a,1123,a,b,10,a),flip(a)].">
      <j1 rule="hyper" parents="235 1123 10"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1128">
    <literal><![CDATA[
      T(x \ 1,y) / (x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x * T(x \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(1123(a,1),327(a,1))].">
      <j1 rule="para" parents="1123 327"/>
    </justification>
  </clause>

  <clause id="1129">
    <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(1123(a,1),790(a,1,2))].">
      <j1 rule="para" parents="1123 790"/>
    </justification>
  </clause>

  <clause id="1130">
    <literal><![CDATA[
      x * (y \ (1 / y)) != z * ((z \ u) * (y \ (1 / y)))
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(1046(a,2),46(a,2))].">
      <j1 rule="para" parents="1046 46"/>
    </justification>
  </clause>

  <clause id="1131">
    <literal><![CDATA[
      (x \ y) \ (((1 / x) * x) \ (x \ z)) = ((x \ 1) \ y) \ ((x \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(119,a,1070,a,b,936,a)].">
      <j1 rule="hyper" parents="119 1070 936"/>
    </justification>
  </clause>

  <clause id="1132">
    <literal><![CDATA[
      ((1 / x) \ y) \ ((1 / x) \ T(y,x)) = K(x \ ((1 / x) \ y),x)
    ]]></literal>
    <justification jstring="[para(1075(a,1),412(a,1,2))].">
      <j1 rule="para" parents="1075 412"/>
    </justification>
  </clause>

  <clause id="1133">
    <literal><![CDATA[
      (x \ (y * ((y \ x) \ 1))) \ z = ((y \ x) * (y \ x)) * z
    ]]></literal>
    <justification jstring="[para(1092(a,1),740(a,1,1))].">
      <j1 rule="para" parents="1092 740"/>
    </justification>
  </clause>

  <clause id="1134">
    <literal><![CDATA[
      x \ y != (x \ z) * T(u * u,w)
    ]]></literal>
    <literal><![CDATA[
      z * T(u * u,w) = y
    ]]></literal>
    <justification jstring="[para(1102(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="1102 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1135">
    <literal><![CDATA[
      T(x * (y * (x \ 1)),z) = x * (T(y,z) * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(144,a,1105,a),flip(a)].">
      <j1 rule="hyper" parents="144 1105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1136">
    <literal><![CDATA[
      x * (((x \ 1) \ y) * (x \ 1)) = T(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(144,a,1106,a)].">
      <j1 rule="hyper" parents="144 1106"/>
    </justification>
  </clause>

  <clause id="1137">
    <literal><![CDATA[
      ((x \ 1) \ (x \ y)) * (x \ 1) = x \ T(y,x \ 1)
    ]]></literal>
    <justification jstring="[para(10(a,1),1106(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 1106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1138">
    <literal><![CDATA[
      (x * x) \ T(x * y,x \ 1) = (1 / x) * (((x \ 1) \ y) * (x \ 1))
    ]]></literal>
    <justification jstring="[para(1106(a,1),441(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1106 441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1139">
    <literal><![CDATA[
      x \ T(x * (((x \ 1) \ 1) \ y),x \ 1) = ((1 / (x \ 1)) \ ((x \ 1) \ y)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(729(a,2),1106(a,2,1))].">
      <j1 rule="para" parents="729 1106"/>
    </justification>
  </clause>

  <clause id="1140">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ T(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(1107(a,1),250(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1107 250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1141">
    <literal><![CDATA[
      (x \ T(y,z)) / (x \ 1) = T((x \ y) / (x \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(120,a,1109,a(flip),b,432,a)].">
      <j1 rule="hyper" parents="120 1109 432"/>
    </justification>
  </clause>

  <clause id="1142">
    <literal><![CDATA[
      T(x * y,1 / y) / y != z
    ]]></literal>
    <literal><![CDATA[
      ((1 / y) \ x) * (1 / y) = z
    ]]></literal>
    <justification jstring="[para(1117(a,1),276(a,1))].">
      <j1 rule="para" parents="1117 276"/>
    </justification>
  </clause>

  <clause id="1143">
    <literal><![CDATA[
      ((1 / x) \ (y / x)) * (1 / x) = T(y,1 / x) / x
    ]]></literal>
    <justification jstring="[para(12(a,1),1120(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="12 1120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1145">
    <literal><![CDATA[
      K(1 / x,(1 / x) \ (y / x)) = (T(y,1 / x) / x) \ (y / x)
    ]]></literal>
    <justification jstring="[para(1143(a,1),90(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1143 90"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1146">
    <literal><![CDATA[
      a(x,x,x \ (x \ y)) = y \ ((x \ 1) \ (x \ y))
    ]]></literal>
    <justification jstring="[para(724(a,1),280(a,1,2)),flip(a)].">
      <j1 rule="para" parents="724 280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1147">
    <literal><![CDATA[
      (x * y) * R((x * y) \ x,z,u) = x * (y * R(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(214(a,1),488(a,1,2,1))].">
      <j1 rule="para" parents="214 488"/>
    </justification>
  </clause>

  <clause id="1148">
    <literal><![CDATA[
      (x * y) * R((x * y) \ (x * z),u,w) = x * (y * R(y \ z,u,w))
    ]]></literal>
    <justification jstring="[para(96(a,1),488(a,1,2,1))].">
      <j1 rule="para" parents="96 488"/>
    </justification>
  </clause>

  <clause id="1149">
    <literal><![CDATA[
      (x * y) * R((x * y) \ z,u,w) = x * (y * R(y \ (x \ z),u,w))
    ]]></literal>
    <justification jstring="[para(281(a,1),488(a,1,2,1))].">
      <j1 rule="para" parents="281 488"/>
    </justification>
  </clause>

  <clause id="1150">
    <literal><![CDATA[
      (x * y) * L((x * y) \ z,u,w) = x * (y * L(y \ (x \ z),u,w))
    ]]></literal>
    <justification jstring="[para(281(a,1),489(a,1,2,1))].">
      <j1 rule="para" parents="281 489"/>
    </justification>
  </clause>

  <clause id="1151">
    <literal><![CDATA[
      (x * y) * L(T(x,x * y),z,u) = x * (y * L(T(x,y),z,u))
    ]]></literal>
    <justification jstring="[para(784(a,1),489(a,1,2,1))].">
      <j1 rule="para" parents="784 489"/>
    </justification>
  </clause>

  <clause id="1152">
    <literal><![CDATA[
      L((x * y) / (z * y),u,w) * (z * y) = (L(x / z,u,w) * z) * y
    ]]></literal>
    <justification jstring="[para(104(a,1),542(a,1,1,1))].">
      <j1 rule="para" parents="104 542"/>
    </justification>
  </clause>

  <clause id="1153">
    <literal><![CDATA[
      R((x * y) / (z * y),u,w) * (z * y) = (R(x / z,u,w) * z) * y
    ]]></literal>
    <justification jstring="[para(104(a,1),543(a,1,1,1))].">
      <j1 rule="para" parents="104 543"/>
    </justification>
  </clause>

  <clause id="1154">
    <literal><![CDATA[
      (x \ 1) * L((x \ 1) \ y,z,u) = x \ L(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(519(a,1),588(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="519 588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1155">
    <literal><![CDATA[
      L(x * (y \ 1),z,u) / (y \ 1) = L(x / y,z,u) * y
    ]]></literal>
    <justification jstring="[para(565(a,1),591(a,1,1,1))].">
      <j1 rule="para" parents="565 591"/>
    </justification>
  </clause>

  <clause id="1156">
    <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(377(a,2),596(a,1,1,1))].">
      <j1 rule="para" parents="377 596"/>
    </justification>
  </clause>

  <clause id="1158">
    <literal><![CDATA[
      x * ((x \ y) * T((x \ y) \ z,u)) = y * T(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[para(822(a,1),482(a,1,2)),flip(a)].">
      <j1 rule="para" parents="822 482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1159">
    <literal><![CDATA[
      (T(x / (y / z),u) * (y / z)) * z = T((x * z) / y,u) * y
    ]]></literal>
    <justification jstring="[para(840(a,1),354(a,1,1)),flip(a)].">
      <j1 rule="para" parents="840 354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1161">
    <literal><![CDATA[
      (x * y) * T(T(y,x),z) = (T(y,z) * x) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,541,a(flip),b,878,a),flip(a)].">
      <j1 rule="hyper" parents="65 541 878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1162">
    <literal><![CDATA[
      (x * y) * T(T(y,z),x) = (T(y,z) * x) * y
    ]]></literal>
    <justification jstring="[para(23(a,1),1161(a,1,2))].">
      <j1 rule="para" parents="23 1161"/>
    </justification>
  </clause>

  <clause id="1163">
    <literal><![CDATA[
      R(T(T(x,y),z * x),z,x) = T(T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(36,a,688,a,b,1162,a)].">
      <j1 rule="hyper" parents="36 688 1162"/>
    </justification>
  </clause>

  <clause id="1164">
    <literal><![CDATA[
      L((x * y) / x,z \ x,z) != u / x
    ]]></literal>
    <literal><![CDATA[
      z * ((z \ x) * y) = u
    ]]></literal>
    <justification jstring="[para(926(a,2),48(a,1))].">
      <j1 rule="para" parents="926 48"/>
    </justification>
  </clause>

  <clause id="1165">
    <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(436(a,1),971(a,1,1,1))].">
      <j1 rule="para" parents="436 971"/>
    </justification>
  </clause>

  <clause id="1170">
    <literal><![CDATA[
      R(T(x,x \ y),z,u) = R((x \ y) \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(36,a,234,a,b,694,a)].">
      <j1 rule="hyper" parents="36 234 694"/>
    </justification>
  </clause>

  <clause id="1171">
    <literal><![CDATA[
      x \ R(T(y,y \ z),u,w) = x \ R((y \ z) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(119,a,1170,a,b,10,a)].">
      <j1 rule="hyper" parents="119 1170 10"/>
    </justification>
  </clause>

  <clause id="1172">
    <literal><![CDATA[
      x \ (((y * y) \ z) * ((y * y) * x)) = T(z,(y * y) * x)
    ]]></literal>
    <justification jstring="[para(664(a,1),698(a,1,2))].">
      <j1 rule="para" parents="664 698"/>
    </justification>
  </clause>

  <clause id="1174">
    <literal><![CDATA[
      (x * ((x \ 1) \ y)) * z = x * ((x \ 1) \ (y * z))
    ]]></literal>
    <justification jstring="[para(465(a,1),906(a,1,1))].">
      <j1 rule="para" parents="465 906"/>
    </justification>
  </clause>

  <clause id="1175">
    <literal><![CDATA[
      T(x * ((x \ 1) \ y),x) = (x \ 1) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(235,a,1174,a,b,xx)].">
      <j1 rule="hyper" parents="235 1174"/>
    </justification>
  </clause>

  <clause id="1176">
    <literal><![CDATA[
      ((x * ((x \ 1) \ (y * z))) * u) / (z * u) = R(x * ((x \ 1) \ y),z,u)
    ]]></literal>
    <justification jstring="[para(1174(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="1174 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1178">
    <literal><![CDATA[
      T((x \ 1) * y,x * x) = (1 / x) * T(y,x * x)
    ]]></literal>
    <justification jstring="[para(738(a,1),934(a,1,1))].">
      <j1 rule="para" parents="738 934"/>
    </justification>
  </clause>

  <clause id="1179">
    <literal><![CDATA[
      (1 / x) * T(T(y,x \ 1),x * x) = T(y * (x \ 1),x * x)
    ]]></literal>
    <justification jstring="[para(107(a,1),1178(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 1178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1180">
    <literal><![CDATA[
      (((x \ 1) \ y) \ z) * (x * x) = (x \ y) \ T(z,x * x)
    ]]></literal>
    <justification jstring="[hyper(65,a,847,a(flip),b,938,a)].">
      <j1 rule="hyper" parents="65 847 938"/>
    </justification>
  </clause>

  <clause id="1181">
    <literal><![CDATA[
      ((x \ 1) \ y) \ (x * z) = (x \ y) \ ((1 / x) * z)
    ]]></literal>
    <justification jstring="[para(264(a,1),939(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="264 939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1182">
    <literal><![CDATA[
      (x \ y) \ ((1 / x) * T(z,x)) = ((x \ 1) \ y) \ (z * x)
    ]]></literal>
    <justification jstring="[para(983(a,1),939(a,1,2))].">
      <j1 rule="para" parents="983 939"/>
    </justification>
  </clause>

  <clause id="1183">
    <literal><![CDATA[
      (1 / x) * T(T(y,x),x \ 1) = (x \ (y * (x \ 1))) * x
    ]]></literal>
    <justification jstring="[para(23(a,1),986(a,1,2))].">
      <j1 rule="para" parents="23 986"/>
    </justification>
  </clause>

  <clause id="1184">
    <literal><![CDATA[
      x / (y \ (1 / y)) = x * ((1 / y) \ y)
    ]]></literal>
    <justification jstring="[hyper(41,a,725,a(flip),b,987,a(flip))].">
      <j1 rule="hyper" parents="41 725 987"/>
    </justification>
  </clause>

  <clause id="1185">
    <literal><![CDATA[
      x / ((1 / y) \ y) = x * (y \ (1 / y))
    ]]></literal>
    <justification jstring="[hyper(305,a,1184,a),flip(a)].">
      <j1 rule="hyper" parents="305 1184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1186">
    <literal><![CDATA[
      x * (y * T(T(x,y),z)) = T(x,z) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(395,a,999,a),flip(a)].">
      <j1 rule="hyper" parents="395 999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1187">
    <literal><![CDATA[
      T(x,y) * (x * z) = x * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[para(232(a,1),1186(a,1,2)),flip(a)].">
      <j1 rule="para" parents="232 1186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1188">
    <literal><![CDATA[
      x \ (T(x,y) * z) = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(640,a,1187,a)].">
      <j1 rule="hyper" parents="640 1187"/>
    </justification>
  </clause>

  <clause id="1189">
    <literal><![CDATA[
      T(x,y) * (x \ (T(x,y) \ z)) = x \ z
    ]]></literal>
    <justification jstring="[hyper(637,a,1187,a),flip(a)].">
      <j1 rule="hyper" parents="637 1187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1190">
    <literal><![CDATA[
      x * (T(x,y) * (x \ z)) = T(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(315,a,1187,a),flip(a)].">
      <j1 rule="hyper" parents="315 1187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1191">
    <literal><![CDATA[
      T(x,y) * (x * (T(x,y) \ z)) = x * z
    ]]></literal>
    <justification jstring="[hyper(299,a,155,a(flip),b,1187,a),flip(a)].">
      <j1 rule="hyper" parents="299 155 1187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1192">
    <literal><![CDATA[
      T(x,y) \ (x * z) = x * (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(119,a,155,a(flip),b,1187,a)].">
      <j1 rule="hyper" parents="119 155 1187"/>
    </justification>
  </clause>

  <clause id="1193">
    <literal><![CDATA[
      x * (T(x,y) \ 1) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(119,a,71,a(flip),b,1187,a),flip(a)].">
      <j1 rule="hyper" parents="119 71 1187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1194">
    <literal><![CDATA[
      (x / y) * (T(x / y,z) * y) = T(x / y,z) * x
    ]]></literal>
    <justification jstring="[para(12(a,1),1187(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 1187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1195">
    <literal><![CDATA[
      T(x,y) * (x * z) != x * u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(1187(a,2),45(a,1))].">
      <j1 rule="para" parents="1187 45"/>
    </justification>
  </clause>

  <clause id="1196">
    <literal><![CDATA[
      x * (T(x,y) * T(z,x)) = T(x,y) * (z * x)
    ]]></literal>
    <justification jstring="[para(107(a,1),1187(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 1187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1197">
    <literal><![CDATA[
      (x / y) * (T(x / y,y) * z) = (y \ x) * ((x / y) * z)
    ]]></literal>
    <justification jstring="[para(109(a,1),1187(a,1,1)),flip(a)].">
      <j1 rule="para" parents="109 1187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1198">
    <literal><![CDATA[
      (T(x,y) \ x) / (T(x,y) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(137,a,1193,a)].">
      <j1 rule="hyper" parents="137 1193"/>
    </justification>
  </clause>

  <clause id="1199">
    <literal><![CDATA[
      x \ (T(x,y) \ x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(125,a,1193,a)].">
      <j1 rule="hyper" parents="125 1193"/>
    </justification>
  </clause>

  <clause id="1200">
    <literal><![CDATA[
      T(x / y,y) \ (x / y) = (x / y) * ((y \ x) \ 1)
    ]]></literal>
    <justification jstring="[para(109(a,1),1193(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="109 1193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1201">
    <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(1198(a,1),400(a,1,1))].">
      <j1 rule="para" parents="1198 400"/>
    </justification>
  </clause>

  <clause id="1202">
    <literal><![CDATA[
      (T(x,y) \ T(x,z)) / (T(x,y) \ 1) = T(x,z)
    ]]></literal>
    <justification jstring="[para(1198(a,1),1141(a,2,1))].">
      <j1 rule="para" parents="1198 1141"/>
    </justification>
  </clause>

  <clause id="1203">
    <literal><![CDATA[
      T(x,y) \ (x \ z) = x \ (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(125,a,1189,a)].">
      <j1 rule="hyper" parents="125 1189"/>
    </justification>
  </clause>

  <clause id="1204">
    <literal><![CDATA[
      T(x,y) * z != x * u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * (x \ z) = u
    ]]></literal>
    <justification jstring="[para(1190(a,1),45(a,1))].">
      <j1 rule="para" parents="1190 45"/>
    </justification>
  </clause>

  <clause id="1205">
    <literal><![CDATA[
      x * (T(x,y) \ y) = T(y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(381,a,1191,a),flip(a)].">
      <j1 rule="hyper" parents="381 1191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1206">
    <literal><![CDATA[
      T(T(x,y),x * (T(x,y) \ z)) = (x * (T(x,y) \ z)) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(235,a,1191,a,b,10,a)].">
      <j1 rule="hyper" parents="235 1191 10"/>
    </justification>
  </clause>

  <clause id="1207">
    <literal><![CDATA[
      x * (T(x,y) \ ((x \ T(x,y)) * z)) = L(z,x \ T(x,y),x)
    ]]></literal>
    <justification jstring="[hyper(36,a,482,a,b,1191,a),flip(a)].">
      <j1 rule="hyper" parents="36 482 1191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1208">
    <literal><![CDATA[
      T(x,y) \ (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      x * (T(x,y) \ z) = u
    ]]></literal>
    <justification jstring="[para(1191(a,1),314(a,1,2))].">
      <j1 rule="para" parents="1191 314"/>
    </justification>
  </clause>

  <clause id="1210">
    <literal><![CDATA[
      x * (T(x,y) \ (x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) \ z = u
    ]]></literal>
    <justification jstring="[para(1203(a,2),250(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1203 250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1211">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ x,x) = L(x,T(x,y) \ x,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(36,a,482,a,b,1196,a),flip(a)].">
      <j1 rule="hyper" parents="36 482 1196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1213">
    <literal><![CDATA[
      T(x,y) * (T(x,z) \ 1) = T(x,z) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(143,a,1202,a)].">
      <j1 rule="hyper" parents="143 1202"/>
    </justification>
  </clause>

  <clause id="1214">
    <literal><![CDATA[
      T(x / y,z) \ T(x / y,y) = (y \ x) * (T(x / y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(109(a,1),1213(a,1,1)),flip(a)].">
      <j1 rule="para" parents="109 1213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1216">
    <literal><![CDATA[
      x * (T(x,y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) \ (x * z) = u
    ]]></literal>
    <justification jstring="[para(9(a,1),1210(a,1,2,2))].">
      <j1 rule="para" parents="9 1210"/>
    </justification>
  </clause>

  <clause id="1217">
    <literal><![CDATA[
      (x / y) * (y * T(y \ x,z)) = T(x / y,z) * x
    ]]></literal>
    <justification jstring="[para(432(a,1),1194(a,1,2))].">
      <j1 rule="para" parents="432 1194"/>
    </justification>
  </clause>

  <clause id="1218">
    <literal><![CDATA[
      (x / y) * ((y \ x) \ 1) = (y \ x) \ (x / y)
    ]]></literal>
    <justification jstring="[para(109(a,1),1200(a,1,1)),flip(a)].">
      <j1 rule="para" parents="109 1200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1219">
    <literal><![CDATA[
      ((x \ y) \ (y / x)) * K((x \ y) \ 1,y / x) = ((x \ y) \ 1) * (y / x)
    ]]></literal>
    <justification jstring="[para(1218(a,1),88(a,1,1))].">
      <j1 rule="para" parents="1218 88"/>
    </justification>
  </clause>

  <clause id="1221">
    <literal><![CDATA[
      T(x / y,z) * u != (x / y) * (y * T(y \ x,z))
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(1217(a,2),45(a,2))].">
      <j1 rule="para" parents="1217 45"/>
    </justification>
  </clause>

  <clause id="1222">
    <literal><![CDATA[
      (1 / x) * (x * R(x \ 1,y,z)) = R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(8(a,1),1002(a,2,1))].">
      <j1 rule="para" parents="8 1002"/>
    </justification>
  </clause>

  <clause id="1223">
    <literal><![CDATA[
      (1 / x) \ R(1 / x,y,z) = x * R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,1222,a)].">
      <j1 rule="hyper" parents="125 1222"/>
    </justification>
  </clause>

  <clause id="1224">
    <literal><![CDATA[
      (x / y) * R((x / y) \ 1,x / y,y) = (1 / (x / y)) \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(119,a,376,a(flip),b,1222,a),flip(a)].">
      <j1 rule="hyper" parents="119 376 1222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1227">
    <literal><![CDATA[
      (1 / x) * ((y / (x * y)) * x) = R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[para(706(a,2),1222(a,1,2))].">
      <j1 rule="para" parents="706 1222"/>
    </justification>
  </clause>

  <clause id="1228">
    <literal><![CDATA[
      (x / (y * x)) / ((x / (y * x)) * y) = 1 / y
    ]]></literal>
    <justification jstring="[hyper(120,a,216,a(flip),b,1227,a)].">
      <j1 rule="hyper" parents="120 216 1227"/>
    </justification>
  </clause>

  <clause id="1229">
    <literal><![CDATA[
      ((x / (y * x)) * y) \ (x / (y * x)) = T(1 / y,(x / (y * x)) * y)
    ]]></literal>
    <justification jstring="[para(1228(a,1),109(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1228 109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1230">
    <literal><![CDATA[
      x * R(x \ 1,y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      a(1 / x,y,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(1223(a,1),868(a,1))].">
      <j1 rule="para" parents="1223 868"/>
    </justification>
  </clause>

  <clause id="1231">
    <literal><![CDATA[
      (x / y) \ (x * T(x \ (x / y),z)) = y * T(y \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,1018,a)].">
      <j1 rule="hyper" parents="125 1018"/>
    </justification>
  </clause>

  <clause id="1232">
    <literal><![CDATA[
      (x / y) * K(y \ 1,y) = x * T(x \ (x / y),y)
    ]]></literal>
    <justification jstring="[para(342(a,1),1018(a,1,2))].">
      <j1 rule="para" parents="342 1018"/>
    </justification>
  </clause>

  <clause id="1233">
    <literal><![CDATA[
      (T(1 / x,y) * x) * (x \ z) = z * T(z \ (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(752,a,1019,a),flip(a)].">
      <j1 rule="hyper" parents="752 1019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1234">
    <literal><![CDATA[
      K((x * y) \ x,x * y) = y * T(y \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(453,a,1022,a)].">
      <j1 rule="hyper" parents="453 1022"/>
    </justification>
  </clause>

  <clause id="1235">
    <literal><![CDATA[
      K((x * y) \ x,x * y) / y = T(1 / y,x * y)
    ]]></literal>
    <justification jstring="[hyper(120,a,1234,a,b,432,a)].">
      <j1 rule="hyper" parents="120 1234 432"/>
    </justification>
  </clause>

  <clause id="1236">
    <literal><![CDATA[
      (x \ (y * (z \ x))) * x = (z * T(z \ y,x)) * (z \ x)
    ]]></literal>
    <justification jstring="[para(432(a,1),1042(a,2,1))].">
      <j1 rule="para" parents="432 1042"/>
    </justification>
  </clause>

  <clause id="1237">
    <literal><![CDATA[
      (x * ((y * (z / (1 / u))) * w)) \ ((x * (y * (z / u))) * ((u * u) * w)) = a(x,y * (z / u),(u * u) * w)
    ]]></literal>
    <justification jstring="[para(1044(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="1044 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1238">
    <literal><![CDATA[
      (x * x) * (y * ((x * x) \ z)) = T(y,x \ (x \ 1)) * z
    ]]></literal>
    <justification jstring="[para(830(a,1),1061(a,1,2))].">
      <j1 rule="para" parents="830 1061"/>
    </justification>
  </clause>

  <clause id="1239">
    <literal><![CDATA[
      T((x \ y) * z,x \ (x \ 1)) = ((x \ 1) \ y) * (z / (x * x))
    ]]></literal>
    <justification jstring="[hyper(65,a,731,a(flip),b,1065,a),flip(a)].">
      <j1 rule="hyper" parents="65 731 1065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1240">
    <literal><![CDATA[
      T(x * y,y \ (y \ 1)) = (y * y) * (x * (y \ 1))
    ]]></literal>
    <justification jstring="[para(459(a,1),1065(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="459 1065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1241">
    <literal><![CDATA[
      (x * x) * (y * R(z / x,x,x)) = T(y * (z * x),x \ (x \ 1))
    ]]></literal>
    <justification jstring="[para(104(a,2),1065(a,1,2,2))].">
      <j1 rule="para" parents="104 1065"/>
    </justification>
  </clause>

  <clause id="1242">
    <literal><![CDATA[
      x \ T(y * x,x \ (x \ 1)) = (1 / x) \ (y * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(119,a,1240,a,b,442,a)].">
      <j1 rule="hyper" parents="119 1240 442"/>
    </justification>
  </clause>

  <clause id="1243">
    <literal><![CDATA[
      R(x / y,y,y) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(36,a,1062,a,b,1240,a(flip))].">
      <j1 rule="hyper" parents="36 1062 1240"/>
    </justification>
  </clause>

  <clause id="1244">
    <literal><![CDATA[
      T(x * y,y \ (y \ 1)) \ z = (x * (y \ 1)) \ ((y * y) \ z)
    ]]></literal>
    <justification jstring="[para(1240(a,2),420(a,1,1))].">
      <j1 rule="para" parents="1240 420"/>
    </justification>
  </clause>

  <clause id="1245">
    <literal><![CDATA[
      (x / y) * (y \ 1) = x / (y * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,285,a(flip),b,1243,a),flip(a)].">
      <j1 rule="hyper" parents="65 285 1243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1246">
    <literal><![CDATA[
      (x * y) * (y \ 1) = R(x,y,y)
    ]]></literal>
    <justification jstring="[para(11(a,1),1243(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 1243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1247">
    <literal><![CDATA[
      R(T(x / y,z),y,y) = T(x * (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(1243(a,1),27(a,2,1))].">
      <j1 rule="para" parents="1243 27"/>
    </justification>
  </clause>

  <clause id="1248">
    <literal><![CDATA[
      T(x * (y \ 1),y) = R(y \ x,y,y)
    ]]></literal>
    <justification jstring="[para(1243(a,1),243(a,1,1))].">
      <j1 rule="para" parents="1243 243"/>
    </justification>
  </clause>

  <clause id="1249">
    <literal><![CDATA[
      R(x,y,y \ 1) = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(551,a,1246,a)].">
      <j1 rule="hyper" parents="551 1246"/>
    </justification>
  </clause>

  <clause id="1250">
    <literal><![CDATA[
      (x \ 1) \ R(y,x,x) = T(y * x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(235,a,1246,a,b,10,a),flip(a)].">
      <j1 rule="hyper" parents="235 1246 10"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1251">
    <literal><![CDATA[
      R(x,y,y) / (y \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(137,a,1246,a)].">
      <j1 rule="hyper" parents="137 1246"/>
    </justification>
  </clause>

  <clause id="1254">
    <literal><![CDATA[
      (x * y) * (y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      R(x,y,y) = z
    ]]></literal>
    <justification jstring="[para(1251(a,1),246(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1251 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1255">
    <literal><![CDATA[
      (x \ 1) \ (y / (x * x)) = T(y / x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(235,a,1245,a,b,10,a),flip(a)].">
      <j1 rule="hyper" parents="235 1245 10"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1256">
    <literal><![CDATA[
      x / ((1 / y) * (1 / y)) = (x / (1 / y)) * y
    ]]></literal>
    <justification jstring="[para(79(a,1),1245(a,1,2)),flip(a)].">
      <j1 rule="para" parents="79 1245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1258">
    <literal><![CDATA[
      T((x * y) * (x \ 1),x) = R(y,x,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),1248(a,2,1))].">
      <j1 rule="para" parents="9 1248"/>
    </justification>
  </clause>

  <clause id="1259">
    <literal><![CDATA[
      R(x,y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      R(x,y,y) = z
    ]]></literal>
    <justification jstring="[para(258(a,1),1254(a,1))].">
      <j1 rule="para" parents="258 1254"/>
    </justification>
  </clause>

  <clause id="1260">
    <literal><![CDATA[
      T(x * (y \ 1),z) / (y \ 1) = T(x / y,z) * y
    ]]></literal>
    <justification jstring="[hyper(120,a,1247,a(flip),b,1246,a)].">
      <j1 rule="hyper" parents="120 1247 1246"/>
    </justification>
  </clause>

  <clause id="1261">
    <literal><![CDATA[
      (x \ 1) \ (((x \ 1) \ 1) \ R(y,x,x)) = x \ T(y * x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1250(a,1),769(a,2,2))].">
      <j1 rule="para" parents="1250 769"/>
    </justification>
  </clause>

  <clause id="1262">
    <literal><![CDATA[
      x / (y \ (1 / y)) = (x / (1 / y)) * y
    ]]></literal>
    <justification jstring="[para(428(a,1),1256(a,1,2))].">
      <j1 rule="para" parents="428 1256"/>
    </justification>
  </clause>

  <clause id="1263">
    <literal><![CDATA[
      (x / (1 / y)) * y = x * ((1 / y) \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,1184,a(flip),b,1262,a),flip(a)].">
      <j1 rule="hyper" parents="65 1184 1262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1264">
    <literal><![CDATA[
      T(x * (y \ 1),z) / (y \ 1) = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,432,a(flip),b,1260,a),flip(a)].">
      <j1 rule="hyper" parents="299 432 1260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1265">
    <literal><![CDATA[
      (x * T(x \ y,z)) * (x \ 1) = T(y * (x \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(143,a,1264,a)].">
      <j1 rule="hyper" parents="143 1264"/>
    </justification>
  </clause>

  <clause id="1266">
    <literal><![CDATA[
      T((x * y) * (x \ 1),z) = (x * T(y,z)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),1265(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 1265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1267">
    <literal><![CDATA[
      T((x * y) * (x \ 1),y) = (x * y) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(106(a,1),1266(a,2,1,2))].">
      <j1 rule="para" parents="106 1266"/>
    </justification>
  </clause>

  <clause id="1268">
    <literal><![CDATA[
      K((x * y) * (x \ 1),y) = 1
    ]]></literal>
    <justification jstring="[hyper(57,a,1267,a)].">
      <j1 rule="hyper" parents="57 1267"/>
    </justification>
  </clause>

  <clause id="1269">
    <literal><![CDATA[
      K(((1 / x) * y) * x,y) = 1
    ]]></literal>
    <justification jstring="[para(79(a,1),1268(a,1,1,2))].">
      <j1 rule="para" parents="79 1268"/>
    </justification>
  </clause>

  <clause id="1270">
    <literal><![CDATA[
      K(x * y,(1 / y) \ x) = 1
    ]]></literal>
    <justification jstring="[para(10(a,1),1269(a,1,1,1))].">
      <j1 rule="para" parents="10 1269"/>
    </justification>
  </clause>

  <clause id="1271">
    <literal><![CDATA[
      T(x * y,(1 / y) \ x) = x * y
    ]]></literal>
    <justification jstring="[hyper(58,a,1270,a)].">
      <j1 rule="hyper" parents="58 1270"/>
    </justification>
  </clause>

  <clause id="1272">
    <literal><![CDATA[
      (x * x) * (y / (z * (x * x))) = T(y,x \ (x \ 1)) / z
    ]]></literal>
    <justification jstring="[hyper(65,a,670,a(flip),b,1082,a)].">
      <j1 rule="hyper" parents="65 670 1082"/>
    </justification>
  </clause>

  <clause id="1273">
    <literal><![CDATA[
      (x \ 1) * L((x \ 1) \ 1,y,z) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(8(a,1),1154(a,2,2,1))].">
      <j1 rule="para" parents="8 1154"/>
    </justification>
  </clause>

  <clause id="1274">
    <literal><![CDATA[
      L(x,y,z) * (x \ 1) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,687,a(flip),b,1273,a)].">
      <j1 rule="hyper" parents="65 687 1273"/>
    </justification>
  </clause>

  <clause id="1275">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (L(x,y,z) * ((x \ 1) * u)) = L(u,x \ 1,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(1274(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1274 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1276">
    <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(1274(a,1),706(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1274 706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1277">
    <literal><![CDATA[
      x \ T(x * (x \ L(x,y,z)),u) = T(L(x,y,z),u) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(1274(a,1),1105(a,1,2,1,2))].">
      <j1 rule="para" parents="1274 1105"/>
    </justification>
  </clause>

  <clause id="1278">
    <literal><![CDATA[
      L(x * (y \ 1),z,u) / (y \ 1) = y * L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,685,a(flip),b,1155,a),flip(a)].">
      <j1 rule="hyper" parents="299 685 1155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1279">
    <literal><![CDATA[
      x \ (T(y,z * z) * x) = T(y,(z * z) * x)
    ]]></literal>
    <justification jstring="[para(760(a,1),1172(a,1,2))].">
      <j1 rule="para" parents="760 1172"/>
    </justification>
  </clause>

  <clause id="1280">
    <literal><![CDATA[
      T(T(x,y * y),z) = T(x,(y * y) * z)
    ]]></literal>
    <justification jstring="[hyper(318,a,1279,a)].">
      <j1 rule="hyper" parents="318 1279"/>
    </justification>
  </clause>

  <clause id="1281">
    <literal><![CDATA[
      T(x,(y * y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(T(x,y * y),z) = u
    ]]></literal>
    <justification jstring="[para(1279(a,1),318(a,1))].">
      <j1 rule="para" parents="1279 318"/>
    </justification>
  </clause>

  <clause id="1282">
    <literal><![CDATA[
      (x / y) * ((y \ x) * z) = (y \ x) * ((x / y) * z)
    ]]></literal>
    <justification jstring="[para(109(a,1),1197(a,1,2,1))].">
      <j1 rule="para" parents="109 1197"/>
    </justification>
  </clause>

  <clause id="1283">
    <literal><![CDATA[
      (x \ (x * y)) * (((x * y) / x) * z) = ((x * y) / x) * (y * z)
    ]]></literal>
    <justification jstring="[para(222(a,1),1197(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="222 1197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1284">
    <literal><![CDATA[
      ((x / y) \ x) * ((x / (x / y)) * z) = (x / (x / y)) * (y * z)
    ]]></literal>
    <justification jstring="[para(241(a,1),1197(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="241 1197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1285">
    <literal><![CDATA[
      (1 / x) * ((x \ 1) * x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(299,a,78,a(flip),b,1282,a),flip(a)].">
      <j1 rule="hyper" parents="299 78 1282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1286">
    <literal><![CDATA[
      (x \ y) * ((y / x) \ 1) = (y / x) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(119,a,71,a(flip),b,1282,a),flip(a)].">
      <j1 rule="hyper" parents="119 71 1282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1287">
    <literal><![CDATA[
      (1 / x) * K(x \ 1,x) = x \ 1
    ]]></literal>
    <justification jstring="[para(253(a,2),1285(a,1,2))].">
      <j1 rule="para" parents="253 1285"/>
    </justification>
  </clause>

  <clause id="1288">
    <literal><![CDATA[
      K(x \ 1,x) * y != x \ 1
    ]]></literal>
    <literal><![CDATA[
      T(1 / x,K(x \ 1,x)) = y
    ]]></literal>
    <justification jstring="[para(1287(a,1),236(a,2))].">
      <j1 rule="para" parents="1287 236"/>
    </justification>
  </clause>

  <clause id="1289">
    <literal><![CDATA[
      (x / y) \ (y \ x) != (y \ x) * z
    ]]></literal>
    <literal><![CDATA[
      (x / y) \ 1 = z
    ]]></literal>
    <justification jstring="[para(1286(a,1),45(a,1))].">
      <j1 rule="para" parents="1286 45"/>
    </justification>
  </clause>

  <clause id="1290">
    <literal><![CDATA[
      K(x \ (x / y),x) = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(811,a,1231,a)].">
      <j1 rule="hyper" parents="811 1231"/>
    </justification>
  </clause>

  <clause id="1291">
    <literal><![CDATA[
      x \ K(y \ (y / x),y) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,412,a(flip),b,1231,a(flip))].">
      <j1 rule="hyper" parents="119 412 1231"/>
    </justification>
  </clause>

  <clause id="1292">
    <literal><![CDATA[
      x * T(x \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ (y / x),y) = z
    ]]></literal>
    <justification jstring="[para(1231(a,1),811(a,1))].">
      <j1 rule="para" parents="1231 811"/>
    </justification>
  </clause>

  <clause id="1293">
    <literal><![CDATA[
      K(x \ (x / (1 / y)),x) = T(y,x) / y
    ]]></literal>
    <justification jstring="[hyper(299,a,1122,a(flip),b,1290,a),flip(a)].">
      <j1 rule="hyper" parents="299 1122 1290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1294">
    <literal><![CDATA[
      K(x \ (x / (y \ 1)),x) = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,1108,a(flip),b,1290,a),flip(a)].">
      <j1 rule="hyper" parents="299 1108 1290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1295">
    <literal><![CDATA[
      K(T(1 / x,T(x,y)),T(x,y)) = x * T(x \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[para(1126(a,1),1290(a,1,1))].">
      <j1 rule="para" parents="1126 1290"/>
    </justification>
  </clause>

  <clause id="1296">
    <literal><![CDATA[
      T(x,y) = K(y \ (y / (1 / x)),y) * x
    ]]></literal>
    <justification jstring="[hyper(143,a,1293,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="143 1293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1297">
    <literal><![CDATA[
      K(x \ (x / (1 / (y / (x * y)))),x) = R(x \ 1,x,y) / (y / (x * y))
    ]]></literal>
    <justification jstring="[para(700(a,1),1293(a,2,1))].">
      <j1 rule="para" parents="700 1293"/>
    </justification>
  </clause>

  <clause id="1298">
    <literal><![CDATA[
      K(x \ (x / (((x * y) / x) \ 1)),x) = ((x * y) / x) \ y
    ]]></literal>
    <justification jstring="[para(222(a,1),1294(a,2,2))].">
      <j1 rule="para" parents="222 1294"/>
    </justification>
  </clause>

  <clause id="1299">
    <literal><![CDATA[
      (x * T(x \ 1,y)) * (x \ z) = z * T(z \ (x \ z),y)
    ]]></literal>
    <justification jstring="[para(432(a,1),1233(a,1,1))].">
      <j1 rule="para" parents="432 1233"/>
    </justification>
  </clause>

  <clause id="1300">
    <literal><![CDATA[
      (x \ T(x,y)) * ((x \ 1) \ z) = z * T(z \ ((x \ 1) \ z),y)
    ]]></literal>
    <justification jstring="[para(1111(a,1),1233(a,1,1))].">
      <j1 rule="para" parents="1111 1233"/>
    </justification>
  </clause>

  <clause id="1301">
    <literal><![CDATA[
      (x \ (y \ x)) * x = (y * T(y \ 1,x)) * (y \ x)
    ]]></literal>
    <justification jstring="[para(7(a,1),1236(a,1,1,2))].">
      <j1 rule="para" parents="7 1236"/>
    </justification>
  </clause>

  <clause id="1302">
    <literal><![CDATA[
      T(x * T(x \ 1,y),x \ y) = K(y \ (x \ y),y)
    ]]></literal>
    <justification jstring="[hyper(235,a,1301,a(flip),b,287,a)].">
      <j1 rule="hyper" parents="235 1301 287"/>
    </justification>
  </clause>

  <clause id="1304">
    <literal><![CDATA[
      L(x * y,z,u) / ((1 / y) \ 1) = (1 / y) * L((1 / y) \ x,z,u)
    ]]></literal>
    <justification jstring="[para(79(a,1),1278(a,1,1,1,2))].">
      <j1 rule="para" parents="79 1278"/>
    </justification>
  </clause>

  <clause id="1305">
    <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(1298(a,2),409(a,1,2))].">
      <j1 rule="para" parents="1298 409"/>
    </justification>
  </clause>

  <clause id="1306">
    <literal><![CDATA[
      (x * T(x \ (y \ x),z)) / (y \ x) != u
    ]]></literal>
    <literal><![CDATA[
      y * T(y \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(1299(a,1),307(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1299 307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1307">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) = y * T(y \ (x \ y),x)
    ]]></literal>
    <justification jstring="[para(342(a,1),1299(a,1,1))].">
      <j1 rule="para" parents="342 1299"/>
    </justification>
  </clause>

  <clause id="1308">
    <literal><![CDATA[
      L(K(x,y) \ T(T(x,y),z),K(x,y),y * x) = (x * y) \ ((T(x,z) * y) * x)
    ]]></literal>
    <justification jstring="[para(1161(a,1),527(a,2,2))].">
      <j1 rule="para" parents="1161 527"/>
    </justification>
  </clause>

  <clause id="1310">
    <literal><![CDATA[
      (x / y) * (y * L(y \ 1,z,u)) = x * L(x \ (x / y),z,u)
    ]]></literal>
    <justification jstring="[para(370(a,1),814(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="370 814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1311">
    <literal><![CDATA[
      (x / y) * (y * L(y \ z,u,w)) = x * L(x \ ((x / y) * z),u,w)
    ]]></literal>
    <justification jstring="[para(522(a,1),814(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="522 814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1312">
    <literal><![CDATA[
      x * ((x \ y) * L((x \ y) \ z,u,w)) = y * L(y \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[para(520(a,1),816(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="520 816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1313">
    <literal><![CDATA[
      (x \ 1) * R((x \ 1) \ y,z,u) = x \ R(1 \ (x * y),z,u)
    ]]></literal>
    <justification jstring="[hyper(119,a,823,a(flip),b,252,a),flip(a)].">
      <j1 rule="hyper" parents="119 823 252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1314">
    <literal><![CDATA[
      x * ((x \ y) * R((x \ y) \ z,u,w)) = y * R(y \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[para(823(a,1),482(a,1,2)),flip(a)].">
      <j1 rule="para" parents="823 482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1315">
    <literal><![CDATA[
      (R(x / (y / z),u,w) * (y / z)) * z = R((x * z) / y,u,w) * y
    ]]></literal>
    <justification jstring="[para(841(a,1),354(a,1,1)),flip(a)].">
      <j1 rule="para" parents="841 354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1316">
    <literal><![CDATA[
      (x * y) * L(T(y,x),z,u) = (L(y,z,u) * x) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,542,a(flip),b,879,a),flip(a)].">
      <j1 rule="hyper" parents="65 542 879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1317">
    <literal><![CDATA[
      (x * y) * R(T(y,x),z,u) = (R(y,z,u) * x) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,543,a(flip),b,880,a),flip(a)].">
      <j1 rule="hyper" parents="65 543 880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1318">
    <literal><![CDATA[
      L(((x * y) * z) / (x * y),y,x) != u / (x * y)
    ]]></literal>
    <literal><![CDATA[
      x * (y * z) = u
    ]]></literal>
    <justification jstring="[para(927(a,2),48(a,1))].">
      <j1 rule="para" parents="927 48"/>
    </justification>
  </clause>

  <clause id="1319">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ x)) / z) = x * (y * ((z * (y \ 1)) / z))
    ]]></literal>
    <justification jstring="[para(214(a,1),972(a,1,2,1,2))].">
      <j1 rule="para" parents="214 972"/>
    </justification>
  </clause>

  <clause id="1320">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ (x * u))) / z) = x * (y * ((z * (y \ u)) / z))
    ]]></literal>
    <justification jstring="[para(96(a,1),972(a,1,2,1,2))].">
      <j1 rule="para" parents="96 972"/>
    </justification>
  </clause>

  <clause id="1321">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ u)) / z) = x * (y * ((z * (y \ (x \ u))) / z))
    ]]></literal>
    <justification jstring="[para(281(a,1),972(a,1,2,1,2))].">
      <j1 rule="para" parents="281 972"/>
    </justification>
  </clause>

  <clause id="1322">
    <literal><![CDATA[
      (x / y) * (y * ((z * (y \ 1)) / z)) = x * ((z * (x \ (x / y))) / z)
    ]]></literal>
    <justification jstring="[para(973(a,1),474(a,1,2)),flip(a)].">
      <j1 rule="para" parents="973 474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1323">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (y * z),u) = y * (T(x,y) * T(T(x,y) \ z,u))
    ]]></literal>
    <justification jstring="[para(1003(a,1),491(a,1,2))].">
      <j1 rule="para" parents="1003 491"/>
    </justification>
  </clause>

  <clause id="1324">
    <literal><![CDATA[
      T((x * y) \ ((x * z) * y),x) = R(T(z,x * y),x,y)
    ]]></literal>
    <justification jstring="[para(222(a,1),1010(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="222 1010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1325">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (z * y),u) = (T(z / x,u) * x) * y
    ]]></literal>
    <justification jstring="[para(1010(a,1),688(a,1,2))].">
      <j1 rule="para" parents="1010 688"/>
    </justification>
  </clause>

  <clause id="1326">
    <literal><![CDATA[
      R(T(x \ 1,x * y),x,y) = T((x * y) \ y,x)
    ]]></literal>
    <justification jstring="[para(70(a,1),1324(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="70 1324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1327">
    <literal><![CDATA[
      L((x \ (y * (x * z))) / z,z,x) = T((z * y) / z,x * z)
    ]]></literal>
    <justification jstring="[hyper(299,a,445,a(flip),b,1037,a),flip(a)].">
      <j1 rule="hyper" parents="299 445 1037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1328">
    <literal><![CDATA[
      L((T(x,y) * (x \ y)) / y,y,x) = (y * K(T(x,y),y)) / y
    ]]></literal>
    <justification jstring="[para(1188(a,1),1039(a,1,1,1))].">
      <j1 rule="para" parents="1188 1039"/>
    </justification>
  </clause>

  <clause id="1330">
    <literal><![CDATA[
      (x / y) \ T(x,(x / y) \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      (((x / y) \ 1) \ y) * ((x / y) \ 1) = z
    ]]></literal>
    <justification jstring="[para(12(a,1),1110(a,1,2,1))].">
      <j1 rule="para" parents="12 1110"/>
    </justification>
  </clause>

  <clause id="1331">
    <literal><![CDATA[
      ((x * x) \ (y * z)) \ (((x * x) \ 1) * (y * (z * u))) = L(L(u,z,y),y * z,(x * x) \ 1)
    ]]></literal>
    <justification jstring="[para(422(a,1),484(a,1,1))].">
      <j1 rule="para" parents="422 484"/>
    </justification>
  </clause>

  <clause id="1332">
    <literal><![CDATA[
      L(L(((x * x) \ y) * z,x * x,u),u * (x * x),w) = (w * (u * (x * x))) \ (w * (u * (y * z)))
    ]]></literal>
    <justification jstring="[para(112(a,1),484(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="112 484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1333">
    <literal><![CDATA[
      (x * y) \ ((z * y) * R(x / z,z,y)) = K(z * y,R(x / z,z,y))
    ]]></literal>
    <justification jstring="[para(12(a,1),538(a,1,1,1))].">
      <j1 rule="para" parents="12 538"/>
    </justification>
  </clause>

  <clause id="1334">
    <literal><![CDATA[
      ((((x * y) / x) \ z) \ z) * x != x * u
    ]]></literal>
    <literal><![CDATA[
      T(y,((x * y) / x) \ z) = u
    ]]></literal>
    <justification jstring="[para(751(a,2),45(a,1))].">
      <j1 rule="para" parents="751 45"/>
    </justification>
  </clause>

  <clause id="1335">
    <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),901(a,1,2,1))].">
      <j1 rule="para" parents="96 901"/>
    </justification>
  </clause>

  <clause id="1337">
    <literal><![CDATA[
      T(L(x,x,x) * y,x) = (1 / x) * (((1 / x) \ y) * x)
    ]]></literal>
    <justification jstring="[para(512(a,1),950(a,1,1))].">
      <j1 rule="para" parents="512 950"/>
    </justification>
  </clause>

  <clause id="1338">
    <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(253(a,2),998(a,1,1))].">
      <j1 rule="para" parents="253 998"/>
    </justification>
  </clause>

  <clause id="1339">
    <literal><![CDATA[
      (x * (y * (z / u))) * ((u * u) * w) = (x * (y * (z / (1 / u)))) * w
    ]]></literal>
    <justification jstring="[para(675(a,1),1043(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="675 1043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1340">
    <literal><![CDATA[
      (x * y) * ((y \ (1 / y)) * z) = (x * (1 / y)) * z
    ]]></literal>
    <justification jstring="[para(10(a,1),1049(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10 1049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1341">
    <literal><![CDATA[
      (x * (y * (z \ (1 / z)))) / u = (x * y) / (u * ((1 / z) \ z))
    ]]></literal>
    <justification jstring="[para(1184(a,1),1077(a,2,2))].">
      <j1 rule="para" parents="1184 1077"/>
    </justification>
  </clause>

  <clause id="1342">
    <literal><![CDATA[
      (x \ (y * z)) * (z \ (1 / z)) = x \ (y * (1 / z))
    ]]></literal>
    <justification jstring="[para(10(a,1),1079(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 1079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1343">
    <literal><![CDATA[
      ((x * (y / (y / T(z,x)))) / x) \ ((y / T(z,x)) * z) = y / T(z,x)
    ]]></literal>
    <justification jstring="[para(223(a,1),1100(a,1,2,2))].">
      <j1 rule="para" parents="223 1100"/>
    </justification>
  </clause>

  <clause id="1344">
    <literal><![CDATA[
      (x * y) * R((y * T(x,y)) \ y,z,u) = y * (T(x,y) * R(T(x,y) \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(107(a,1),1147(a,1,1))].">
      <j1 rule="para" parents="107 1147"/>
    </justification>
  </clause>

  <clause id="1345">
    <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),1147(a,1,1))].">
      <j1 rule="para" parents="94 1147"/>
    </justification>
  </clause>

  <clause id="1346">
    <literal><![CDATA[
      x * (y * L(T(x,y),z,u)) = L(x,z,u) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(396,a,1151,a),flip(a)].">
      <j1 rule="hyper" parents="396 1151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1347">
    <literal><![CDATA[
      L(x,y,z) * (x * u) = x * (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(233(a,1),1346(a,1,2)),flip(a)].">
      <j1 rule="para" parents="233 1346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1348">
    <literal><![CDATA[
      x \ (L(x,y,z) * u) = L(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(640,a,1347,a)].">
      <j1 rule="hyper" parents="640 1347"/>
    </justification>
  </clause>

  <clause id="1349">
    <literal><![CDATA[
      L(x,y,z) * (x \ (L(x,y,z) \ u)) = x \ u
    ]]></literal>
    <justification jstring="[hyper(637,a,1347,a),flip(a)].">
      <j1 rule="hyper" parents="637 1347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1350">
    <literal><![CDATA[
      x * (L(x,y,z) * (x \ u)) = L(x,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(315,a,1347,a),flip(a)].">
      <j1 rule="hyper" parents="315 1347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1351">
    <literal><![CDATA[
      L(x,y,z) \ (x * (L(x,y,z) * u)) = x * u
    ]]></literal>
    <justification jstring="[hyper(125,a,1347,a)].">
      <j1 rule="hyper" parents="125 1347"/>
    </justification>
  </clause>

  <clause id="1352">
    <literal><![CDATA[
      L(x,y,z) \ (x * u) = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(119,a,155,a(flip),b,1347,a)].">
      <j1 rule="hyper" parents="119 155 1347"/>
    </justification>
  </clause>

  <clause id="1353">
    <literal><![CDATA[
      x * (L(x,y,z) \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(119,a,71,a(flip),b,1347,a),flip(a)].">
      <j1 rule="hyper" parents="119 71 1347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1354">
    <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(119,a,1347,a(flip),b,88,a)].">
      <j1 rule="hyper" parents="119 1347 88"/>
    </justification>
  </clause>

  <clause id="1355">
    <literal><![CDATA[
      L(x,y,z) * u != x * (L(x,y,z) * w)
    ]]></literal>
    <literal><![CDATA[
      x * w = u
    ]]></literal>
    <justification jstring="[para(1347(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="1347 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1358">
    <literal><![CDATA[
      x \ (L(x,y,z) \ x) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(125,a,1353,a)].">
      <j1 rule="hyper" parents="125 1353"/>
    </justification>
  </clause>

  <clause id="1359">
    <literal><![CDATA[
      R(1 / x,x,L(x,y,z) \ 1) \ (L(x,y,z) \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(65,a,374,a,b,1353,a)].">
      <j1 rule="hyper" parents="65 374 1353"/>
    </justification>
  </clause>

  <clause id="1360">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ ((L(x,y,z) \ 1) * x) = K(L(x,y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[para(1353(a,1),16(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1353 16"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1361">
    <literal><![CDATA[
      L(L(x,y,z) \ 1,x,1 / x) = (1 / x) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(1353(a,1),255(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1353 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1362">
    <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(1353(a,2),1302(a,1,2))].">
      <j1 rule="para" parents="1353 1302"/>
    </justification>
  </clause>

  <clause id="1363">
    <literal><![CDATA[
      T((1 / x) * (L(x,y,z) \ x),x) = (1 / x) * ((L(x,y,z) \ 1) * x)
    ]]></literal>
    <justification jstring="[para(1358(a,1),820(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1358 820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1364">
    <literal><![CDATA[
      x \ (L(x,y,z) * (u * x)) = L(x,y,z) * T(u,x)
    ]]></literal>
    <justification jstring="[para(22(a,2),1348(a,2,2))].">
      <j1 rule="para" parents="22 1348"/>
    </justification>
  </clause>

  <clause id="1365">
    <literal><![CDATA[
      L(L(x,y,z) * (x \ u),x,x) != w
    ]]></literal>
    <literal><![CDATA[
      (1 / x) * (L(x,y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(1348(a,1),613(a,1,1))].">
      <j1 rule="para" parents="1348 613"/>
    </justification>
  </clause>

  <clause id="1366">
    <literal><![CDATA[
      L(x,y,z) \ (x \ u) = x \ (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(125,a,1349,a)].">
      <j1 rule="hyper" parents="125 1349"/>
    </justification>
  </clause>

  <clause id="1367">
    <literal><![CDATA[
      x \ (L(x,y,z) \ (u * x)) = L(x,y,z) \ T(u,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,22,a,b,1349,a),flip(a)].">
      <j1 rule="hyper" parents="119 22 1349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1368">
    <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(235,a,1350,a,b,10,a),flip(a)].">
      <j1 rule="hyper" parents="235 1350 10"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1371">
    <literal><![CDATA[
      T((x * y) / x,L(y,z,u) * x) = L((y * x) / x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(1351(a,1),1327(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1351 1327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1372">
    <literal><![CDATA[
      L(x \ 1,y,z) \ K(x \ 1,x) = (x \ 1) * (L(x \ 1,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(253(a,2),1352(a,1,2))].">
      <j1 rule="para" parents="253 1352"/>
    </justification>
  </clause>

  <clause id="1373">
    <literal><![CDATA[
      x \ (y * T(y \ (x * z),u)) = (x \ y) * T((x \ y) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(125,a,1158,a)].">
      <j1 rule="hyper" parents="125 1158"/>
    </justification>
  </clause>

  <clause id="1374">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ z,y) = x \ ((y \ (x * z)) * y)
    ]]></literal>
    <justification jstring="[hyper(119,a,107,a(flip),b,1158,a),flip(a)].">
      <j1 rule="hyper" parents="119 107 1158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1375">
    <literal><![CDATA[
      x * ((x \ y) * T((x \ y) \ 1,z)) = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(8(a,1),1158(a,2,2,1,2))].">
      <j1 rule="para" parents="8 1158"/>
    </justification>
  </clause>

  <clause id="1376">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ 1,y) = x \ ((y \ x) * y)
    ]]></literal>
    <justification jstring="[para(8(a,1),1374(a,2,2,1,2))].">
      <j1 rule="para" parents="8 1374"/>
    </justification>
  </clause>

  <clause id="1377">
    <literal><![CDATA[
      K(x,y) = ((y * x) \ y) * T(((y * x) \ y) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,411,a,b,1376,a)].">
      <j1 rule="hyper" parents="299 411 1376"/>
    </justification>
  </clause>

  <clause id="1378">
    <literal><![CDATA[
      T(((x * y) \ x) \ 1,x) = ((x * y) \ x) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,411,a,b,1376,a),flip(a)].">
      <j1 rule="hyper" parents="119 411 1376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1380">
    <literal><![CDATA[
      T(L(x \ 1,x,y) \ 1,y) = ((y * x) \ y) \ K(x,y)
    ]]></literal>
    <justification jstring="[para(214(a,2),1378(a,1,1,1))].">
      <j1 rule="para" parents="214 1378"/>
    </justification>
  </clause>

  <clause id="1381">
    <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(1378(a,1),1125(a,1,1))].">
      <j1 rule="para" parents="1378 1125"/>
    </justification>
  </clause>

  <clause id="1382">
    <literal><![CDATA[
      K(x,y) = L(x \ 1,x,y) * T(L(x \ 1,x,y) \ 1,y)
    ]]></literal>
    <justification jstring="[para(1380(a,2),404(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1380 404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1383">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ 1,z) = x \ (y * T(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(125,a,1375,a),flip(a)].">
      <j1 rule="hyper" parents="125 1375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1384">
    <literal><![CDATA[
      x * T(x \ y,y \ x) = y * K((y \ x) \ 1,y \ x)
    ]]></literal>
    <justification jstring="[para(342(a,1),1375(a,1,2)),flip(a)].">
      <j1 rule="para" parents="342 1375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1385">
    <literal><![CDATA[
      x * T(x \ y,z) = y * K(z \ (z / (y \ x)),z)
    ]]></literal>
    <justification jstring="[para(1290(a,2),1375(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1290 1375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1386">
    <literal><![CDATA[
      K(x \ (x / (y \ z)),x) = y \ (z * T(z \ y,x))
    ]]></literal>
    <justification jstring="[hyper(631,a,1385,a),flip(a)].">
      <j1 rule="hyper" parents="631 1385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1387">
    <literal><![CDATA[
      T(x * y,z) / y = x * K(z \ (z / (x \ (1 / y))),z)
    ]]></literal>
    <justification jstring="[hyper(65,a,1117,a(flip),b,1385,a)].">
      <j1 rule="hyper" parents="65 1117 1385"/>
    </justification>
  </clause>

  <clause id="1388">
    <literal><![CDATA[
      (x \ y) * K(z \ (z / ((x \ y) \ (x \ 1))),z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,1109,a(flip),b,1385,a),flip(a)].">
      <j1 rule="hyper" parents="65 1109 1385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1389">
    <literal><![CDATA[
      (x * y) * K(z \ (z / ((x * y) \ x)),z) = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),1385(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 1385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1390">
    <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),1385(a,2,2,1,2,2))].">
      <j1 rule="para" parents="16 1385"/>
    </justification>
  </clause>

  <clause id="1391">
    <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),1385(a,2,2,1,2,2))].">
      <j1 rule="para" parents="18 1385"/>
    </justification>
  </clause>

  <clause id="1392">
    <literal><![CDATA[
      K((x * (y \ z)) \ x,x * (y \ z)) = y \ (z * T(z \ y,x * (y \ z)))
    ]]></literal>
    <justification jstring="[para(11(a,1),1386(a,1,1,2))].">
      <j1 rule="para" parents="11 1386"/>
    </justification>
  </clause>

  <clause id="1393">
    <literal><![CDATA[
      K(x \ (x / (y \ (y / z))),x) = y \ ((y / z) * T(z,x))
    ]]></literal>
    <justification jstring="[para(79(a,1),1386(a,2,2,2,1))].">
      <j1 rule="para" parents="79 1386"/>
    </justification>
  </clause>

  <clause id="1394">
    <literal><![CDATA[
      (x / y) * K(z \ (z / ((x / y) \ (1 / y))),z) = T(x,z) / y
    ]]></literal>
    <justification jstring="[para(12(a,1),1387(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="12 1387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1396">
    <literal><![CDATA[
      (x * T(x \ (y * z),u)) / z = T(y / (x / z),u) * (x / z)
    ]]></literal>
    <justification jstring="[hyper(120,a,432,a(flip),b,1159,a)].">
      <j1 rule="hyper" parents="120 432 1159"/>
    </justification>
  </clause>

  <clause id="1397">
    <literal><![CDATA[
      (T(1 / (x / y),z) * (x / y)) * y = T(y / x,z) * x
    ]]></literal>
    <justification jstring="[para(7(a,1),1159(a,2,1,1,1))].">
      <j1 rule="para" parents="7 1159"/>
    </justification>
  </clause>

  <clause id="1398">
    <literal><![CDATA[
      (T(1 / (x / y),z) * (x / y)) * y = x * T(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,432,a(flip),b,1397,a),flip(a)].">
      <j1 rule="hyper" parents="299 432 1397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1399">
    <literal><![CDATA[
      ((x / y) * T((x / y) \ 1,z)) * y = x * T(x \ y,z)
    ]]></literal>
    <justification jstring="[para(432(a,1),1398(a,1,1))].">
      <j1 rule="para" parents="432 1398"/>
    </justification>
  </clause>

  <clause id="1400">
    <literal><![CDATA[
      K((x / y) \ 1,x / y) * y = x * T(x \ y,x / y)
    ]]></literal>
    <justification jstring="[para(342(a,1),1399(a,1,1))].">
      <j1 rule="para" parents="342 1399"/>
    </justification>
  </clause>

  <clause id="1401">
    <literal><![CDATA[
      K(x \ (x / (y / z)),x) * z = y * T(y \ z,x)
    ]]></literal>
    <justification jstring="[para(1290(a,2),1399(a,1,1))].">
      <j1 rule="para" parents="1290 1399"/>
    </justification>
  </clause>

  <clause id="1402">
    <literal><![CDATA[
      K(x \ (x / (y / z)),x) = (y * T(y \ z,x)) / z
    ]]></literal>
    <justification jstring="[hyper(137,a,1401,a),flip(a)].">
      <j1 rule="hyper" parents="137 1401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1403">
    <literal><![CDATA[
      K((x * (y / z)) \ x,x * (y / z)) = (y * T(y \ z,x * (y / z))) / z
    ]]></literal>
    <justification jstring="[para(11(a,1),1402(a,1,1,2))].">
      <j1 rule="para" parents="11 1402"/>
    </justification>
  </clause>

  <clause id="1404">
    <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),1402(a,1,1,2,2))].">
      <j1 rule="para" parents="20 1402"/>
    </justification>
  </clause>

  <clause id="1405">
    <literal><![CDATA[
      K((x / (y * x)) \ 1,x / (y * x)) * (y * x) = T(y,x / (y * x)) * x
    ]]></literal>
    <justification jstring="[hyper(299,a,429,a(flip),b,1400,a),flip(a)].">
      <j1 rule="hyper" parents="299 429 1400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1406">
    <literal><![CDATA[
      (x \ y) * (T(y / x,z) \ 1) = T(y / x,z) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(109(a,1),1214(a,1,2)),flip(a)].">
      <j1 rule="para" parents="109 1214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1407">
    <literal><![CDATA[
      T(x / (y \ x),z) \ ((y \ x) \ x) = ((y \ x) \ x) * (T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(76(a,1),1406(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="76 1406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1408">
    <literal><![CDATA[
      T(((1 / x) \ y) * z,(1 / x) \ ((1 / x) \ 1)) = (x \ y) * (z / ((1 / x) * (1 / x)))
    ]]></literal>
    <justification jstring="[para(79(a,1),1239(a,2,1,1))].">
      <j1 rule="para" parents="79 1239"/>
    </justification>
  </clause>

  <clause id="1409">
    <literal><![CDATA[
      T(L(x,y,z),u) * (x \ 1) = x \ T(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(10(a,1),1277(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 1277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1411">
    <literal><![CDATA[
      T(L(x,y,z),u) * (x \ 1) = x \ L(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(25(a,2),1409(a,2,2))].">
      <j1 rule="para" parents="25 1409"/>
    </justification>
  </clause>

  <clause id="1412">
    <literal><![CDATA[
      L(T(x,y),z,u) * (x \ 1) = x \ L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(25(a,2),1411(a,1,1))].">
      <j1 rule="para" parents="25 1411"/>
    </justification>
  </clause>

  <clause id="1413">
    <literal><![CDATA[
      ((x * y) / x) * (y * z) = y * (((x * y) / x) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),1283(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 1283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1414">
    <literal><![CDATA[
      ((x * y) / x) * (y \ 1) = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(389,a,1413,a),flip(a)].">
      <j1 rule="hyper" parents="389 1413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1415">
    <literal><![CDATA[
      (((x * y) * x) / (x * y)) * y = T(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(379,a,1413,a),flip(a)].">
      <j1 rule="hyper" parents="379 1413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1416">
    <literal><![CDATA[
      x * (((y * x) / y) * (x \ z)) = ((y * x) / y) * z
    ]]></literal>
    <justification jstring="[hyper(315,a,1413,a),flip(a)].">
      <j1 rule="hyper" parents="315 1413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1417">
    <literal><![CDATA[
      ((x * y) / x) \ (y * z) = y * (((x * y) / x) \ z)
    ]]></literal>
    <justification jstring="[hyper(119,a,155,a(flip),b,1413,a)].">
      <j1 rule="hyper" parents="119 155 1413"/>
    </justification>
  </clause>

  <clause id="1418">
    <literal><![CDATA[
      x * (((y * x) / y) \ 1) = ((y * x) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(119,a,71,a(flip),b,1413,a),flip(a)].">
      <j1 rule="hyper" parents="119 71 1413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1419">
    <literal><![CDATA[
      (x \ 1) * ((y * ((x \ 1) \ 1)) / y) = x \ ((y * x) / y)
    ]]></literal>
    <justification jstring="[hyper(65,a,1098,a,b,1414,a)].">
      <j1 rule="hyper" parents="65 1098 1414"/>
    </justification>
  </clause>

  <clause id="1420">
    <literal><![CDATA[
      ((x * y) * x) / (x * y) = T(x * y,x) / y
    ]]></literal>
    <justification jstring="[hyper(137,a,1415,a),flip(a)].">
      <j1 rule="hyper" parents="137 1415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1421">
    <literal><![CDATA[
      T(T(x * y,x) / y,x * y) = x
    ]]></literal>
    <justification jstring="[para(1420(a,1),222(a,1,1))].">
      <j1 rule="para" parents="1420 222"/>
    </justification>
  </clause>

  <clause id="1422">
    <literal><![CDATA[
      T(T(x * y,x) / y,y) = R(x,y,T(x,y))
    ]]></literal>
    <justification jstring="[para(1420(a,1),1007(a,1,1))].">
      <j1 rule="para" parents="1420 1007"/>
    </justification>
  </clause>

  <clause id="1423">
    <literal><![CDATA[
      T(T(R(x,y,y \ 1),x * y) / (y \ 1),(x * y) * (y \ 1)) = x * y
    ]]></literal>
    <justification jstring="[para(258(a,1),1421(a,1,1,1,1))].">
      <j1 rule="para" parents="258 1421"/>
    </justification>
  </clause>

  <clause id="1424">
    <literal><![CDATA[
      x * R(y,x,T(y,x)) = T(y * x,y)
    ]]></literal>
    <justification jstring="[para(1422(a,1),219(a,1,2))].">
      <j1 rule="para" parents="1422 219"/>
    </justification>
  </clause>

  <clause id="1425">
    <literal><![CDATA[
      x \ T(y * x,y) != z
    ]]></literal>
    <literal><![CDATA[
      R(y,x,T(y,x)) = z
    ]]></literal>
    <justification jstring="[para(1424(a,1),314(a,1,2))].">
      <j1 rule="para" parents="1424 314"/>
    </justification>
  </clause>

  <clause id="1426">
    <literal><![CDATA[
      T(x,y) = ((x * y) / x) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(235,a,12,a(flip),b,1416,a)].">
      <j1 rule="hyper" parents="235 12 1416"/>
    </justification>
  </clause>

  <clause id="1427">
    <literal><![CDATA[
      ((x * y) / x) * (y \ ((((x * y) / x) \ y) * z)) = L(z,((x * y) / x) \ y,(x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(36,a,482,a,b,1416,a),flip(a)].">
      <j1 rule="hyper" parents="36 482 1416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1428">
    <literal><![CDATA[
      x \ (((y * x) / y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      ((y * x) / y) * (x \ z) = u
    ]]></literal>
    <justification jstring="[para(1416(a,1),314(a,1,2))].">
      <j1 rule="para" parents="1416 314"/>
    </justification>
  </clause>

  <clause id="1429">
    <literal><![CDATA[
      T(x,y) / (y \ x) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(120,a,1426,a,b,xx)].">
      <j1 rule="hyper" parents="120 1426"/>
    </justification>
  </clause>

  <clause id="1430">
    <literal><![CDATA[
      T((x * y) / x,y \ x) = (y \ x) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,1426,a,b,107,a),flip(a)].">
      <j1 rule="hyper" parents="119 1426 107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1431">
    <literal><![CDATA[
      ((x * y) / x) \ T(x,y) = y \ x
    ]]></literal>
    <justification jstring="[hyper(119,a,1426,a,b,xx)].">
      <j1 rule="hyper" parents="119 1426"/>
    </justification>
  </clause>

  <clause id="1432">
    <literal><![CDATA[
      T(x,x / y) / y = (x * (x / y)) / x
    ]]></literal>
    <justification jstring="[hyper(352,a,1426,a(flip))].">
      <j1 rule="hyper" parents="352 1426"/>
    </justification>
  </clause>

  <clause id="1433">
    <literal><![CDATA[
      (x / (x / y)) * (y \ (x / y)) = T(x / y,y)
    ]]></literal>
    <justification jstring="[para(12(a,1),1426(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="12 1426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1434">
    <literal><![CDATA[
      ((x * (x / y)) / x) * y = T(x,x / y)
    ]]></literal>
    <justification jstring="[para(79(a,1),1426(a,2,2)),flip(a)].">
      <j1 rule="para" parents="79 1426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1436">
    <literal><![CDATA[
      ((x * R(1 / y,y,x)) / x) * (y * x) = T(x,R(1 / y,y,x))
    ]]></literal>
    <justification jstring="[para(374(a,1),1426(a,2,2)),flip(a)].">
      <j1 rule="para" parents="374 1426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1437">
    <literal><![CDATA[
      ((x * R(y,y \ 1,x)) / x) * ((y \ 1) * x) = T(x,R(y,y \ 1,x))
    ]]></literal>
    <justification jstring="[para(406(a,1),1426(a,2,2)),flip(a)].">
      <j1 rule="para" parents="406 1426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1440">
    <literal><![CDATA[
      (x \ y) \ K(T(y,x) \ ((y * x) / y),T(y,x)) = T((x \ y) \ 1,T(y,x))
    ]]></literal>
    <justification jstring="[para(1429(a,1),1291(a,1,2,1,2))].">
      <j1 rule="para" parents="1429 1291"/>
    </justification>
  </clause>

  <clause id="1441">
    <literal><![CDATA[
      x * ((y * (x \ y)) / y) = T(y,y / x)
    ]]></literal>
    <justification jstring="[hyper(39,a,940,a,b,1432,a)].">
      <j1 rule="hyper" parents="39 940 1432"/>
    </justification>
  </clause>

  <clause id="1442">
    <literal><![CDATA[
      T(T(x,x / y) / y,x) = x / y
    ]]></literal>
    <justification jstring="[para(1432(a,2),222(a,1,1))].">
      <j1 rule="para" parents="1432 222"/>
    </justification>
  </clause>

  <clause id="1443">
    <literal><![CDATA[
      (x / y) * ((x * y) / x) = T(x,x / (x / y))
    ]]></literal>
    <justification jstring="[para(79(a,1),1441(a,1,2,1,2))].">
      <j1 rule="para" parents="79 1441"/>
    </justification>
  </clause>

  <clause id="1444">
    <literal><![CDATA[
      T((x \ y) \ T(y,x),y) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(1430(a,1),266(a,1,1))].">
      <j1 rule="para" parents="1430 266"/>
    </justification>
  </clause>

  <clause id="1445">
    <literal><![CDATA[
      T((x \ y) \ T(y,x),x * y) = L(T(x,x \ y),y,x)
    ]]></literal>
    <justification jstring="[para(1430(a,1),1031(a,1,1))].">
      <j1 rule="para" parents="1430 1031"/>
    </justification>
  </clause>

  <clause id="1446">
    <literal><![CDATA[
      T((x \ y) \ T(y,x),y) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(299,a,108,a(flip),b,1444,a),flip(a)].">
      <j1 rule="hyper" parents="299 108 1444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1447">
    <literal><![CDATA[
      K(x \ (x / ((y \ x) / T(x,y))),x) = ((y \ x) * ((y \ x) \ x)) / T(x,y)
    ]]></literal>
    <justification jstring="[para(1446(a,1),1402(a,2,1,2))].">
      <j1 rule="para" parents="1446 1402"/>
    </justification>
  </clause>

  <clause id="1448">
    <literal><![CDATA[
      (x * y) / ((x * y) / x) = y / (x \ ((x * y) / x))
    ]]></literal>
    <justification jstring="[hyper(120,a,222,a(flip),b,1433,a),flip(a)].">
      <j1 rule="hyper" parents="120 222 1433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1449">
    <literal><![CDATA[
      T(x,x / (x / T(y,x))) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[para(223(a,1),1443(a,1,2)),flip(a)].">
      <j1 rule="para" parents="223 1443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1450">
    <literal><![CDATA[
      (x / (x / y)) * (y * z) = y * ((x / (x / y)) * z)
    ]]></literal>
    <justification jstring="[hyper(657,a,1284,a),flip(a)].">
      <j1 rule="hyper" parents="657 1284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1452">
    <literal><![CDATA[
      (1 / (1 / x)) * (x * (1 / x)) = x
    ]]></literal>
    <justification jstring="[hyper(299,a,78,a(flip),b,1450,a),flip(a)].">
      <j1 rule="hyper" parents="299 78 1450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1454">
    <literal><![CDATA[
      (x \ 1) * R((x \ 1) \ y,z,u) = x \ R(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(67(a,1),1313(a,2,2,1))].">
      <j1 rule="para" parents="67 1313"/>
    </justification>
  </clause>

  <clause id="1455">
    <literal><![CDATA[
      (x \ 1) * R((x \ 1) \ 1,y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(163(a,1),1313(a,2,2,1))].">
      <j1 rule="para" parents="163 1313"/>
    </justification>
  </clause>

  <clause id="1456">
    <literal><![CDATA[
      R(x,y,z) * (x \ 1) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,694,a(flip),b,1455,a)].">
      <j1 rule="hyper" parents="65 694 1455"/>
    </justification>
  </clause>

  <clause id="1457">
    <literal><![CDATA[
      (x \ R(x,y,z)) / R(T(x,x \ 1),y,z) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(120,a,1456,a(flip),b,234,a)].">
      <j1 rule="hyper" parents="120 1456 234"/>
    </justification>
  </clause>

  <clause id="1458">
    <literal><![CDATA[
      (x \ R(x,y,z)) * K(x \ 1,R(x,y,z)) = (x \ 1) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(1456(a,1),88(a,1,1))].">
      <j1 rule="para" parents="1456 88"/>
    </justification>
  </clause>

  <clause id="1459">
    <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(1456(a,1),706(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1456 706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1460">
    <literal><![CDATA[
      T((R(x,y,z) * (1 / x)) / R(x,y,z),x) = (x \ R(x,y,z)) / R(x,y,z)
    ]]></literal>
    <justification jstring="[para(1456(a,1),755(a,2,1))].">
      <j1 rule="para" parents="1456 755"/>
    </justification>
  </clause>

  <clause id="1461">
    <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),1454(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="22 1454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1462">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (z * y),u) = (x * T(x \ z,u)) * y
    ]]></literal>
    <justification jstring="[para(432(a,1),1325(a,2,1))].">
      <j1 rule="para" parents="432 1325"/>
    </justification>
  </clause>

  <clause id="1463">
    <literal><![CDATA[
      ((x * y) * z) / ((y * (z * (u \ (1 / u)))) * ((1 / u) \ u)) = R(x,y,z * (u \ (1 / u)))
    ]]></literal>
    <justification jstring="[hyper(549,a,1341,a),flip(a)].">
      <j1 rule="hyper" parents="549 1341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1464">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ (x \ z),u) = x \ (y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),1373(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="10 1373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1465">
    <literal><![CDATA[
      (x * T(x \ (y * z),u)) / z = (x / z) * T((x / z) \ y,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,432,a(flip),b,1396,a),flip(a)].">
      <j1 rule="hyper" parents="299 432 1396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1466">
    <literal><![CDATA[
      (((x * (1 / y)) / x) * y) * x = T(x,R(1 / y,y,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,977,a(flip),b,1436,a)].">
      <j1 rule="hyper" parents="65 977 1436"/>
    </justification>
  </clause>

  <clause id="1467">
    <literal><![CDATA[
      (x * ((y * (x \ 1)) / y)) * y = T(y,R(1 / x,x,y))
    ]]></literal>
    <justification jstring="[para(941(a,1),1466(a,1,1))].">
      <j1 rule="para" parents="941 1466"/>
    </justification>
  </clause>

  <clause id="1468">
    <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(1193(a,1),1467(a,1,1,2,1))].">
      <j1 rule="para" parents="1193 1467"/>
    </justification>
  </clause>

  <clause id="1469">
    <literal><![CDATA[
      x * (y * T(y \ (x \ (z * y)),u)) = (x * T(x \ z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,998,a(flip),b,1462,a)].">
      <j1 rule="hyper" parents="65 998 1462"/>
    </justification>
  </clause>

  <clause id="1470">
    <literal><![CDATA[
      ((x * y) * T((x * y) \ x,z)) * y = (x * y) * (y * T(y \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,801,a(flip),b,1462,a),flip(a)].">
      <j1 rule="hyper" parents="65 801 1462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1471">
    <literal><![CDATA[
      x * T(x \ (x \ (y * x)),z) = T(x * T(x \ y,z),x)
    ]]></literal>
    <justification jstring="[hyper(235,a,1462,a(flip),b,998,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="235 1462 998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1472">
    <literal><![CDATA[
      (x * y) * T((x * y) \ y,z) = (x * T(x \ 1,z)) * y
    ]]></literal>
    <justification jstring="[para(7(a,1),1462(a,1,2,1,2))].">
      <j1 rule="para" parents="7 1462"/>
    </justification>
  </clause>

  <clause id="1474">
    <literal><![CDATA[
      T(x * T(x \ y,z),x) = x * T(x \ T(y,x),z)
    ]]></literal>
    <justification jstring="[para(22(a,2),1471(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="22 1471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1475">
    <literal><![CDATA[
      x \ T(x * T(x \ y,z),x) = T(x \ T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(119,a,1474,a,b,xx)].">
      <j1 rule="hyper" parents="119 1474"/>
    </justification>
  </clause>

  <clause id="1476">
    <literal><![CDATA[
      T(x \ T(x * y,x),z) = x \ T(x * T(y,z),x)
    ]]></literal>
    <justification jstring="[para(9(a,1),1475(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 1475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1478">
    <literal><![CDATA[
      x * (y * T(y \ (x \ y),z)) = (x * T(x \ 1,z)) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,998,a(flip),b,1472,a)].">
      <j1 rule="hyper" parents="65 998 1472"/>
    </justification>
  </clause>

  <clause id="1479">
    <literal><![CDATA[
      T(x,x * T(x \ 1,y)) = x
    ]]></literal>
    <justification jstring="[hyper(235,a,801,a(flip),b,1472,a(flip))].">
      <j1 rule="hyper" parents="235 801 1472"/>
    </justification>
  </clause>

  <clause id="1480">
    <literal><![CDATA[
      T(x,(x \ 1) * x) = x
    ]]></literal>
    <justification jstring="[para(107(a,1),1479(a,1,2))].">
      <j1 rule="para" parents="107 1479"/>
    </justification>
  </clause>

  <clause id="1481">
    <literal><![CDATA[
      T(x \ 1,T(x,y) * (x \ 1)) = x \ 1
    ]]></literal>
    <justification jstring="[para(434(a,1),1479(a,1,2))].">
      <j1 rule="para" parents="434 1479"/>
    </justification>
  </clause>

  <clause id="1482">
    <literal><![CDATA[
      T(x \ 1,x \ T(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[para(1108(a,1),1479(a,1,2))].">
      <j1 rule="para" parents="1108 1479"/>
    </justification>
  </clause>

  <clause id="1483">
    <literal><![CDATA[
      T(1 / x,T(x,y) / x) = 1 / x
    ]]></literal>
    <justification jstring="[para(1122(a,1),1479(a,1,2))].">
      <j1 rule="para" parents="1122 1479"/>
    </justification>
  </clause>

  <clause id="1484">
    <literal><![CDATA[
      R(x,x \ 1,x) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1480(a,1),877(a,1,1))].">
      <j1 rule="para" parents="1480 877"/>
    </justification>
  </clause>

  <clause id="1485">
    <literal><![CDATA[
      R(x,x \ 1,x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(299,a,108,a(flip),b,1484,a),flip(a)].">
      <j1 rule="hyper" parents="299 108 1484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1486">
    <literal><![CDATA[
      T(x,x \ 1) \ x = (x \ 1) * x
    ]]></literal>
    <justification jstring="[para(1484(a,1),406(a,1,1))].">
      <j1 rule="para" parents="1484 406"/>
    </justification>
  </clause>

  <clause id="1487">
    <literal><![CDATA[
      x / K(x \ 1,x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,587,a,b,1485,a)].">
      <j1 rule="hyper" parents="65 587 1485"/>
    </justification>
  </clause>

  <clause id="1488">
    <literal><![CDATA[
      T(x \ T(x,y),x \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(56,a,1482,a)].">
      <j1 rule="hyper" parents="56 1482"/>
    </justification>
  </clause>

  <clause id="1489">
    <literal><![CDATA[
      T((x * (1 / y)) / x,T(y,z) / y) = (x * (1 / y)) / x
    ]]></literal>
    <justification jstring="[para(1483(a,1),445(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1483 445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1490">
    <literal><![CDATA[
      T(x,x \ 1) \ 1 = T(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(235,a,1486,a(flip),b,1193,a),flip(a)].">
      <j1 rule="hyper" parents="235 1486 1193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1492">
    <literal><![CDATA[
      ((x \ 1) \ 1) * K(x \ 1,x) = x
    ]]></literal>
    <justification jstring="[hyper(143,a,1487,a)].">
      <j1 rule="hyper" parents="143 1487"/>
    </justification>
  </clause>

  <clause id="1493">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ x != y
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(1487(a,1),317(a,1,1))].">
      <j1 rule="para" parents="1487 317"/>
    </justification>
  </clause>

  <clause id="1494">
    <literal><![CDATA[
      T(x \ 1,T(x,x \ 1)) = T(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(399,a,1490,a)].">
      <j1 rule="hyper" parents="399 1490"/>
    </justification>
  </clause>

  <clause id="1495">
    <literal><![CDATA[
      T(x \ 1,x) = ((x \ 1) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(108(a,1),1490(a,1,1)),flip(a)].">
      <j1 rule="para" parents="108 1490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1496">
    <literal><![CDATA[
      R(x \ 1,T(x,y),x \ 1) = T(x \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[para(1481(a,1),877(a,1,1))].">
      <j1 rule="para" parents="1481 877"/>
    </justification>
  </clause>

  <clause id="1497">
    <literal><![CDATA[
      T((x * y) \ (y * x),y \ 1) = L(y \ T(y,x),y,x)
    ]]></literal>
    <justification jstring="[para(1488(a,1),825(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1488 825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1498">
    <literal><![CDATA[
      K(x,y) = T((y * x) \ (x * y),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,824,a,b,1497,a)].">
      <j1 rule="hyper" parents="299 824 1497"/>
    </justification>
  </clause>

  <clause id="1499">
    <literal><![CDATA[
      T(K(x,y),x \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[para(16(a,2),1498(a,2,1)),flip(a)].">
      <j1 rule="para" parents="16 1498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1500">
    <literal><![CDATA[
      T(x \ 1,K(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(56,a,1499,a)].">
      <j1 rule="hyper" parents="56 1499"/>
    </justification>
  </clause>

  <clause id="1501">
    <literal><![CDATA[
      (x \ 1) * K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (x \ 1) = z
    ]]></literal>
    <justification jstring="[para(1499(a,1),276(a,1,2))].">
      <j1 rule="para" parents="1499 276"/>
    </justification>
  </clause>

  <clause id="1502">
    <literal><![CDATA[
      T(x,K(x \ 1,y)) * (x \ 1) = (x \ 1) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(1500(a,1),434(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1500 434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1503">
    <literal><![CDATA[
      (x * T(x \ 1,y)) * y = x * ((y \ (x \ y)) * y)
    ]]></literal>
    <justification jstring="[para(107(a,1),1478(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 1478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1504">
    <literal><![CDATA[
      T(x,K(x \ 1,y)) * (x \ 1) = 1
    ]]></literal>
    <justification jstring="[hyper(299,a,10,a(flip),b,1502,a),flip(a)].">
      <j1 rule="hyper" parents="299 10 1502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1506">
    <literal><![CDATA[
      T(x,K(x \ 1,y)) = x
    ]]></literal>
    <justification jstring="[hyper(136,a,1504,a)].">
      <j1 rule="hyper" parents="136 1504"/>
    </justification>
  </clause>

  <clause id="1507">
    <literal><![CDATA[
      T(1 / x,K(x,y)) = 1 / x
    ]]></literal>
    <justification jstring="[para(79(a,1),1506(a,1,2,1))].">
      <j1 rule="para" parents="79 1506"/>
    </justification>
  </clause>

  <clause id="1508">
    <literal><![CDATA[
      K(x \ 1,y) * x = x * K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(1506(a,1),107(a,1,2))].">
      <j1 rule="para" parents="1506 107"/>
    </justification>
  </clause>

  <clause id="1509">
    <literal><![CDATA[
      K(x,y) * (1 / x) = (1 / x) * K(x,y)
    ]]></literal>
    <justification jstring="[para(1507(a,1),107(a,1,2))].">
      <j1 rule="para" parents="1507 107"/>
    </justification>
  </clause>

  <clause id="1510">
    <literal><![CDATA[
      K(x,y) * (1 / x) != z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) * K(x,y) = z
    ]]></literal>
    <justification jstring="[para(1507(a,1),276(a,1,2))].">
      <j1 rule="para" parents="1507 276"/>
    </justification>
  </clause>

  <clause id="1511">
    <literal><![CDATA[
      T((1 * x) / y,K(y / x,z)) = R(1 / (y / x),y / x,x)
    ]]></literal>
    <justification jstring="[para(1507(a,1),840(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1507 840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1512">
    <literal><![CDATA[
      K(x,y) * z != (1 / x) * K(x,y)
    ]]></literal>
    <literal><![CDATA[
      1 / x = z
    ]]></literal>
    <justification jstring="[para(1509(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="1509 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1513">
    <literal><![CDATA[
      ((1 / x) * (K(x,y) * z)) * a(1 / x,K(x,y),z) = (K(x,y) * (1 / x)) * z
    ]]></literal>
    <justification jstring="[para(1509(a,2),84(a,2,1))].">
      <j1 rule="para" parents="1509 84"/>
    </justification>
  </clause>

  <clause id="1514">
    <literal><![CDATA[
      T((1 * x) / y,K(y / x,z)) = x / y
    ]]></literal>
    <justification jstring="[hyper(299,a,376,a(flip),b,1511,a),flip(a)].">
      <j1 rule="hyper" parents="299 376 1511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1515">
    <literal><![CDATA[
      T(x / y,K(y / x,z)) = x / y
    ]]></literal>
    <justification jstring="[para(7(a,1),1514(a,1,1,1))].">
      <j1 rule="para" parents="7 1514"/>
    </justification>
  </clause>

  <clause id="1516">
    <literal><![CDATA[
      T(x \ y,K(x / y,z)) = T(y / x,x)
    ]]></literal>
    <justification jstring="[para(1515(a,1),242(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1515 242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1517">
    <literal><![CDATA[
      T(x \ y,K(x / y,z)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(299,a,109,a(flip),b,1516,a),flip(a)].">
      <j1 rule="hyper" parents="299 109 1516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1518">
    <literal><![CDATA[
      T(x,y) * T((y \ (x * y)) \ (y \ z),u) = y \ ((x * y) * T((x * y) \ z,u))
    ]]></literal>
    <justification jstring="[para(22(a,2),1464(a,1,1))].">
      <j1 rule="para" parents="22 1464"/>
    </justification>
  </clause>

  <clause id="1519">
    <literal><![CDATA[
      (x / y) * T((x / y) \ x,z) = (x * T(y,z)) / y
    ]]></literal>
    <justification jstring="[para(9(a,1),1465(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 1465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1520">
    <literal><![CDATA[
      (x / y) * T((x / y) \ z,x) = ((x \ (z * y)) * x) / y
    ]]></literal>
    <justification jstring="[para(107(a,1),1465(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 1465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1521">
    <literal><![CDATA[
      ((x * y) / z) * T(((x * y) / z) \ x,u) = (x * (y * T(y \ z,u))) / z
    ]]></literal>
    <justification jstring="[para(997(a,1),1465(a,1,1)),flip(a)].">
      <j1 rule="para" parents="997 1465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1522">
    <literal><![CDATA[
      (x * (y * T(y \ (x \ (z * u)),w))) / u = ((x * y) / u) * T(((x * y) / u) \ z,w)
    ]]></literal>
    <justification jstring="[para(998(a,1),1465(a,1,1))].">
      <j1 rule="para" parents="998 1465"/>
    </justification>
  </clause>

  <clause id="1523">
    <literal><![CDATA[
      (x * T(y,z)) / y = (x / y) * T(y,z)
    ]]></literal>
    <justification jstring="[para(79(a,1),1519(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 1519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1524">
    <literal><![CDATA[
      ((x / y) * T(y,z)) \ (x * T(y,z)) = y
    ]]></literal>
    <justification jstring="[hyper(186,a,1523,a)].">
      <j1 rule="hyper" parents="186 1523"/>
    </justification>
  </clause>

  <clause id="1525">
    <literal><![CDATA[
      ((x / y) * T(y,z)) * y = x * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(143,a,1523,a)].">
      <j1 rule="hyper" parents="143 1523"/>
    </justification>
  </clause>

  <clause id="1526">
    <literal><![CDATA[
      ((x / T(y,z)) / y) * T(y,z) = x / y
    ]]></literal>
    <justification jstring="[hyper(65,a,156,a(flip),b,1523,a),flip(a)].">
      <j1 rule="hyper" parents="65 156 1523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1527">
    <literal><![CDATA[
      (x / y) * T(y,x) = (y * x) / y
    ]]></literal>
    <justification jstring="[para(107(a,1),1523(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 1523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1528">
    <literal><![CDATA[
      T((x / y) * T(y,z),y) = y \ (x * T(y,z))
    ]]></literal>
    <justification jstring="[para(1523(a,1),109(a,1,1))].">
      <j1 rule="para" parents="1523 109"/>
    </justification>
  </clause>

  <clause id="1529">
    <literal><![CDATA[
      ((x \ y) * y) / (x \ y) = x * T(x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(327,a,1527,a),flip(a)].">
      <j1 rule="hyper" parents="327 1527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1530">
    <literal><![CDATA[
      T(x,y) \ ((x * y) / x) = T(y / x,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(235,a,1527,a,b,10,a),flip(a)].">
      <j1 rule="hyper" parents="235 1527 10"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1531">
    <literal><![CDATA[
      T(x,y) = (y / x) \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(125,a,1527,a),flip(a)].">
      <j1 rule="hyper" parents="125 1527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1532">
    <literal><![CDATA[
      ((x * y) / x) / T(y / x,T(x,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(120,a,1527,a(flip),b,107,a)].">
      <j1 rule="hyper" parents="120 1527 107"/>
    </justification>
  </clause>

  <clause id="1533">
    <literal><![CDATA[
      (x * (y * x)) / x = y * T(x,y * x)
    ]]></literal>
    <justification jstring="[para(11(a,1),1527(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 1527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1535">
    <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(368(a,1),1527(a,1,1)),flip(a)].">
      <j1 rule="para" parents="368 1527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1536">
    <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(401(a,1),1527(a,1,1)),flip(a)].">
      <j1 rule="para" parents="401 1527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1537">
    <literal><![CDATA[
      K(x \ (x / (x \ (x / y))),x) = x \ ((y * x) / y)
    ]]></literal>
    <justification jstring="[para(1527(a,1),1393(a,2,2))].">
      <j1 rule="para" parents="1527 1393"/>
    </justification>
  </clause>

  <clause id="1538">
    <literal><![CDATA[
      x \ ((y * (x * y)) / y) = T(y,x * y)
    ]]></literal>
    <justification jstring="[para(11(a,1),1531(a,2,1)),flip(a)].">
      <j1 rule="para" parents="11 1531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1540">
    <literal><![CDATA[
      (x * T(y,z)) \ ((x * y) * T(y,z)) = y
    ]]></literal>
    <justification jstring="[para(11(a,1),1524(a,1,1,1))].">
      <j1 rule="para" parents="11 1524"/>
    </justification>
  </clause>

  <clause id="1542">
    <literal><![CDATA[
      (x * T(y,z)) * y = (x * y) * T(y,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),1525(a,1,1,1))].">
      <j1 rule="para" parents="11 1525"/>
    </justification>
  </clause>

  <clause id="1543">
    <literal><![CDATA[
      (x * T(T(y,x),z)) * T(y,x) = (y * x) * T(T(y,x),z)
    ]]></literal>
    <justification jstring="[para(185(a,1),1525(a,1,1,1))].">
      <j1 rule="para" parents="185 1525"/>
    </justification>
  </clause>

  <clause id="1544">
    <literal><![CDATA[
      (x * T(y,x * y)) * y = y * (x * y)
    ]]></literal>
    <justification jstring="[hyper(143,a,1533,a)].">
      <j1 rule="hyper" parents="143 1533"/>
    </justification>
  </clause>

  <clause id="1546">
    <literal><![CDATA[
      (1 / T(x,y)) * x = x / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(120,a,1540,a(flip),b,165,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="120 1540 165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1548">
    <literal><![CDATA[
      R(T(x,y * T(x,z)),y,T(x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1540(a,1),1324(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1540 1324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1549">
    <literal><![CDATA[
      ((x * T(y,z)) / T(y,z)) * T(((x * T(y,z)) / T(y,z)) \ (x * y),u) = ((x * T(y,z)) * T(y,u)) / T(y,z)
    ]]></literal>
    <justification jstring="[para(1540(a,1),1465(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1540 1465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1550">
    <literal><![CDATA[
      (1 / T(x,y)) \ (x / T(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(125,a,1546,a)].">
      <j1 rule="hyper" parents="125 1546"/>
    </justification>
  </clause>

  <clause id="1551">
    <literal><![CDATA[
      (1 / T(x,y)) * x != z
    ]]></literal>
    <literal><![CDATA[
      x / T(x,y) = z
    ]]></literal>
    <justification jstring="[para(1550(a,1),250(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1550 250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1552">
    <literal><![CDATA[
      T(x,1 / T(x,y)) / T(x,y) = x * (1 / T(x,y))
    ]]></literal>
    <justification jstring="[para(1550(a,1),1143(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1550 1143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1553">
    <literal><![CDATA[
      (x * y) / T(y,z) = (x / T(y,z)) * y
    ]]></literal>
    <justification jstring="[hyper(626,a,1542,a)].">
      <j1 rule="hyper" parents="626 1542"/>
    </justification>
  </clause>

  <clause id="1554">
    <literal><![CDATA[
      ((x / T(y,z)) * y) * T(y,z) = x * y
    ]]></literal>
    <justification jstring="[hyper(306,a,1542,a),flip(a)].">
      <j1 rule="hyper" parents="306 1542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1556">
    <literal><![CDATA[
      (x * (y / z)) * T(y / z,z) = (x * (z \ y)) * (y / z)
    ]]></literal>
    <justification jstring="[para(109(a,1),1542(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="109 1542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1559">
    <literal><![CDATA[
      (x * y) / T(y,z) != y * u
    ]]></literal>
    <literal><![CDATA[
      T(x / T(y,z),y) = u
    ]]></literal>
    <justification jstring="[para(1553(a,2),236(a,2)),flip(a)].">
      <j1 rule="para" parents="1553 236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1560">
    <literal><![CDATA[
      x * T(y,z) != u * y
    ]]></literal>
    <literal><![CDATA[
      (u / T(y,z)) * y = x
    ]]></literal>
    <justification jstring="[para(1554(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="1554 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1561">
    <literal><![CDATA[
      T(x,x / (x / T(y,x))) * T(y,x) = x * y
    ]]></literal>
    <justification jstring="[para(1449(a,2),1554(a,1,1))].">
      <j1 rule="para" parents="1449 1554"/>
    </justification>
  </clause>

  <clause id="1562">
    <literal><![CDATA[
      R(T(x,L(x,y,x) * y),y,T(x,x * y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(788(a,1),1548(a,1,1,2))].">
      <j1 rule="para" parents="788 1548"/>
    </justification>
  </clause>

  <clause id="1563">
    <literal><![CDATA[
      T(x,x / (x / T(y,x))) * (y * x) = x * (x * y)
    ]]></literal>
    <justification jstring="[para(1561(a,1),1196(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1561 1196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1564">
    <literal><![CDATA[
      T(x,x / (x / T(y,x))) = (x * (x * y)) / (y * x)
    ]]></literal>
    <justification jstring="[hyper(137,a,1563,a),flip(a)].">
      <j1 rule="hyper" parents="137 1563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1565">
    <literal><![CDATA[
      (x * (x * y)) / (y * x) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,1449,a(flip),b,1564,a),flip(a)].">
      <j1 rule="hyper" parents="65 1449 1564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1566">
    <literal><![CDATA[
      R(((x * (x * y)) / x) / y,y,x) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[hyper(915,a,1565,a)].">
      <j1 rule="hyper" parents="915 1565"/>
    </justification>
  </clause>

  <clause id="1567">
    <literal><![CDATA[
      (T(x,y) * z) * T(x,z) = (x * z) * T(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(232(a,1),1543(a,1,1))].">
      <j1 rule="para" parents="232 1543"/>
    </justification>
  </clause>

  <clause id="1568">
    <literal><![CDATA[
      T(T(x,x \ 1),y) / T(x,x \ 1) = T(x,y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(120,a,70,a(flip),b,1567,a)].">
      <j1 rule="hyper" parents="120 70 1567"/>
    </justification>
  </clause>

  <clause id="1570">
    <literal><![CDATA[
      (x * (y / z)) * (z \ y) = (x * (z \ y)) * (y / z)
    ]]></literal>
    <justification jstring="[para(109(a,1),1556(a,1,2))].">
      <j1 rule="para" parents="109 1556"/>
    </justification>
  </clause>

  <clause id="1571">
    <literal><![CDATA[
      (x * (y \ (y * z))) * ((y * z) / y) = (x * ((y * z) / y)) * z
    ]]></literal>
    <justification jstring="[para(222(a,1),1556(a,1,2)),flip(a)].">
      <j1 rule="para" parents="222 1556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1572">
    <literal><![CDATA[
      (1 / (x / y)) * (y \ x) = (y \ x) / (x / y)
    ]]></literal>
    <justification jstring="[hyper(629,a,1570,a),flip(a)].">
      <j1 rule="hyper" parents="629 1570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1573">
    <literal><![CDATA[
      (x * (y / z)) / (z \ y) = (x / (z \ y)) * (y / z)
    ]]></literal>
    <justification jstring="[hyper(120,a,154,a(flip),b,1570,a)].">
      <j1 rule="hyper" parents="120 154 1570"/>
    </justification>
  </clause>

  <clause id="1574">
    <literal><![CDATA[
      (x \ y) \ ((x \ y) / (y / x)) = T(1 / (y / x),x \ y)
    ]]></literal>
    <justification jstring="[hyper(235,a,1572,a,b,10,a),flip(a)].">
      <j1 rule="hyper" parents="235 1572 10"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1576">
    <literal><![CDATA[
      T(T(x,x \ 1),y) / T(x,x \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,1112,a(flip),b,1568,a),flip(a)].">
      <j1 rule="hyper" parents="299 1112 1568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1577">
    <literal><![CDATA[
      K(T(1 / (1 / x),x \ 1),x \ 1) = T(x,x \ 1) / x
    ]]></literal>
    <justification jstring="[para(1574(a,1),1293(a,1,1))].">
      <j1 rule="para" parents="1574 1293"/>
    </justification>
  </clause>

  <clause id="1578">
    <literal><![CDATA[
      x * ((y \ z) * T((y \ z) \ (x \ z),u)) = (x * T(x \ y,u)) * (y \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),1469(a,1,2,2,1,2,2))].">
      <j1 rule="para" parents="10 1469"/>
    </justification>
  </clause>

  <clause id="1579">
    <literal><![CDATA[
      (x * T(x \ (y / z),u)) * z = x * (z * T(z \ (x \ y),u))
    ]]></literal>
    <justification jstring="[para(12(a,1),1469(a,1,2,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 1469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1580">
    <literal><![CDATA[
      ((x * y) * T((x * y) \ x,z)) * u = (x * y) * (u * T(u \ L(y \ u,y,x),z))
    ]]></literal>
    <justification jstring="[para(96(a,2),1469(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="96 1469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1581">
    <literal><![CDATA[
      (x * ((y * z) / y)) * z = (x * z) * ((y * z) / y)
    ]]></literal>
    <justification jstring="[para(9(a,1),1571(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 1571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1582">
    <literal><![CDATA[
      (1 / ((x * y) / x)) * y = y / ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(629,a,1581,a),flip(a)].">
      <j1 rule="hyper" parents="629 1581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1583">
    <literal><![CDATA[
      (x * y) / ((z * y) / z) = (x / ((z * y) / z)) * y
    ]]></literal>
    <justification jstring="[hyper(626,a,1581,a)].">
      <j1 rule="hyper" parents="626 1581"/>
    </justification>
  </clause>

  <clause id="1584">
    <literal><![CDATA[
      (1 / x) * ((y * x) / y) = ((y * x) / y) / x
    ]]></literal>
    <justification jstring="[hyper(120,a,77,a(flip),b,1581,a),flip(a)].">
      <j1 rule="hyper" parents="120 77 1581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1585">
    <literal><![CDATA[
      ((x / y) * y) * ((x * y) / x) = T(x,x / (x / y)) * y
    ]]></literal>
    <justification jstring="[para(1443(a,1),1581(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1443 1581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1586">
    <literal><![CDATA[
      T(x,x / (x / y)) * y = x * ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(306,a,1585,a),flip(a)].">
      <j1 rule="hyper" parents="306 1585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1587">
    <literal><![CDATA[
      T(x,x / (x / y)) * (x \ y) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(1204,a,1586,a)].">
      <j1 rule="hyper" parents="1204 1586"/>
    </justification>
  </clause>

  <clause id="1590">
    <literal><![CDATA[
      ((x * y) / x) / (x \ y) = T(x,x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(137,a,1587,a)].">
      <j1 rule="hyper" parents="137 1587"/>
    </justification>
  </clause>

  <clause id="1592">
    <literal><![CDATA[
      x * (y * T(y \ (x \ z),x)) = ((x \ (z / y)) * x) * y
    ]]></literal>
    <justification jstring="[para(107(a,1),1579(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 1579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1593">
    <literal><![CDATA[
      x \ (y * (x * T(x \ (y \ z),u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(y * T(y \ (z / x),u),x) = w
    ]]></literal>
    <justification jstring="[para(1579(a,1),318(a,1,2))].">
      <j1 rule="para" parents="1579 318"/>
    </justification>
  </clause>

  <clause id="1594">
    <literal><![CDATA[
      (x \ 1) * (y * T(y \ ((x \ 1) \ z),u)) = (x \ T(x * (z / y),u)) * y
    ]]></literal>
    <justification jstring="[para(1012(a,1),1579(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1012 1579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1595">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,y)) * y = x * (y * T(y \ (x \ x),y))
    ]]></literal>
    <justification jstring="[para(1232(a,2),1579(a,1,1))].">
      <j1 rule="para" parents="1232 1579"/>
    </justification>
  </clause>

  <clause id="1596">
    <literal><![CDATA[
      (x * y) * T((x * y) \ z,x) = ((x \ (z / y)) * x) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,998,a,b,1592,a)].">
      <j1 rule="hyper" parents="65 998 1592"/>
    </justification>
  </clause>

  <clause id="1597">
    <literal><![CDATA[
      ((x \ ((x * y) / z)) * x) * z = x * (z * T(z \ y,x))
    ]]></literal>
    <justification jstring="[para(9(a,1),1592(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9 1592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1598">
    <literal><![CDATA[
      ((x \ (x / y)) * x) * y = x * (y * T(y \ 1,x))
    ]]></literal>
    <justification jstring="[para(68(a,1),1592(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="68 1592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1599">
    <literal><![CDATA[
      ((x \ (y / (z \ 1))) * x) * (z \ 1) = x * (z \ T(z * (x \ y),x))
    ]]></literal>
    <justification jstring="[para(1012(a,1),1592(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1012 1592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1600">
    <literal><![CDATA[
      ((x \ (y / (1 / z))) * x) * (1 / z) = x * (T((x \ y) * z,x) / z)
    ]]></literal>
    <justification jstring="[para(1117(a,1),1592(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1117 1592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1601">
    <literal><![CDATA[
      x * ((y \ x) * T((y \ x) \ 1,x)) = ((x \ y) * x) * (y \ x)
    ]]></literal>
    <justification jstring="[para(76(a,1),1598(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="76 1598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1602">
    <literal><![CDATA[
      x * (x * T(x \ T(y,x),x)) = ((x \ y) * x) * x
    ]]></literal>
    <justification jstring="[para(223(a,1),1597(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="223 1597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1603">
    <literal><![CDATA[
      x * ((x \ T(y,x)) * x) = ((x \ y) * x) * x
    ]]></literal>
    <justification jstring="[para(107(a,1),1602(a,1,2))].">
      <j1 rule="para" parents="107 1602"/>
    </justification>
  </clause>

  <clause id="1604">
    <literal><![CDATA[
      T((x \ y) * x,x) = (x \ T(y,x)) * x
    ]]></literal>
    <justification jstring="[hyper(236,a,1603,a)].">
      <j1 rule="hyper" parents="236 1603"/>
    </justification>
  </clause>

  <clause id="1605">
    <literal><![CDATA[
      x * (T((x \ y) * x,x) / x) = T(y,x)
    ]]></literal>
    <justification jstring="[para(1604(a,2),75(a,1,2,1))].">
      <j1 rule="para" parents="1604 75"/>
    </justification>
  </clause>

  <clause id="1606">
    <literal><![CDATA[
      x * (T(y * x,x) / x) = T(x * y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),1605(a,1,2,1,1,1))].">
      <j1 rule="para" parents="9 1605"/>
    </justification>
  </clause>

  <clause id="1607">
    <literal><![CDATA[
      T(x * (y / x),x) = x * (T(y,x) / x)
    ]]></literal>
    <justification jstring="[para(80(a,1),1605(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="80 1605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1608">
    <literal><![CDATA[
      T(x * y,y) / y = y \ T(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(125,a,1606,a),flip(a)].">
      <j1 rule="hyper" parents="125 1606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1609">
    <literal><![CDATA[
      T(x * ((1 / x) * y),x) = x * ((1 / x) * T(y,x))
    ]]></literal>
    <justification jstring="[para(1116(a,1),1606(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1116 1606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1610">
    <literal><![CDATA[
      x \ T(x * (y / x),x) = T(y,x) / x
    ]]></literal>
    <justification jstring="[hyper(119,a,1607,a,b,xx)].">
      <j1 rule="hyper" parents="119 1607"/>
    </justification>
  </clause>

  <clause id="1611">
    <literal><![CDATA[
      x \ T(x * T((x * y) / x,z),x) = T(x * T(y,z),x) / x
    ]]></literal>
    <justification jstring="[para(433(a,1),1608(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="433 1608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1612">
    <literal><![CDATA[
      x \ T(x * L((x * y) / x,z,u),x) = T(x * L(y,z,u),x) / x
    ]]></literal>
    <justification jstring="[para(686(a,1),1608(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="686 1608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1614">
    <literal><![CDATA[
      x \ T(x * T(y / x,z),x) = T(T(y,x) / x,z)
    ]]></literal>
    <justification jstring="[para(1610(a,1),1476(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1610 1476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1615">
    <literal><![CDATA[
      T(x * ((1 / x) * ((1 / x) \ (x \ (y * (1 / x))))),x) = (x * T(x \ y,x)) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(299,a,1469,a(flip),b,1609,a),flip(a)].">
      <j1 rule="hyper" parents="299 1469 1609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1616">
    <literal><![CDATA[
      T(x * T(y / x,z),x) = x * T(T(y,x) / x,z)
    ]]></literal>
    <justification jstring="[hyper(144,a,1614,a),flip(a)].">
      <j1 rule="hyper" parents="144 1614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1617">
    <literal><![CDATA[
      x \ T(x * T(y / x,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      T(T(y,x) / x,z) = u
    ]]></literal>
    <justification jstring="[para(1616(a,2),314(a,1,2))].">
      <j1 rule="para" parents="1616 314"/>
    </justification>
  </clause>

  <clause id="1618">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,y)) * y = x * (y * T(y \ 1,y))
    ]]></literal>
    <justification jstring="[para(68(a,1),1595(a,2,2,2,1,2))].">
      <j1 rule="para" parents="68 1595"/>
    </justification>
  </clause>

  <clause id="1620">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,y)) * y = x * ((y \ 1) * y)
    ]]></literal>
    <justification jstring="[para(107(a,1),1618(a,2,2))].">
      <j1 rule="para" parents="107 1618"/>
    </justification>
  </clause>

  <clause id="1621">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,y)) * y = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(342(a,1),1618(a,2,2))].">
      <j1 rule="para" parents="342 1618"/>
    </justification>
  </clause>

  <clause id="1622">
    <literal><![CDATA[
      (R(x,y \ 1,y) / y) * K(y \ 1,y) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(37,a,103,a(flip),b,1620,a),flip(a)].">
      <j1 rule="hyper" parents="37 103 1620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1623">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * y = (x * y) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(11(a,1),1621(a,1,1,1))].">
      <j1 rule="para" parents="11 1621"/>
    </justification>
  </clause>

  <clause id="1624">
    <literal><![CDATA[
      (L(1 / x,x,y) * K(x \ 1,x)) * x = (x * ((y * x) \ y)) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(920(a,1),1623(a,2,1))].">
      <j1 rule="para" parents="920 1623"/>
    </justification>
  </clause>

  <clause id="1625">
    <literal><![CDATA[
      x * K(y \ 1,y) != z * (y \ 1)
    ]]></literal>
    <literal><![CDATA[
      R(z,y \ 1,y) / y = x
    ]]></literal>
    <justification jstring="[para(1622(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="1622 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1626">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ x) = x * (y \ ((x \ y) * x))
    ]]></literal>
    <justification jstring="[para(1376(a,1),1601(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1376 1601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1627">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ x) = x * K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(89(a,1),1626(a,2,2))].">
      <j1 rule="para" parents="89 1626"/>
    </justification>
  </clause>

  <clause id="1628">
    <literal><![CDATA[
      (x * y) * ((y * x) \ y) = y * K(y \ (y * x),y)
    ]]></literal>
    <justification jstring="[para(9(a,1),1627(a,1,1,1))].">
      <j1 rule="para" parents="9 1627"/>
    </justification>
  </clause>

  <clause id="1629">
    <literal><![CDATA[
      (x * y) * ((y * x) \ y) = y * K(x,y)
    ]]></literal>
    <justification jstring="[para(9(a,1),1628(a,2,2,1))].">
      <j1 rule="para" parents="9 1628"/>
    </justification>
  </clause>

  <clause id="1630">
    <literal><![CDATA[
      x \ (y * K(x / y,y)) = (y * (x / y)) \ y
    ]]></literal>
    <justification jstring="[hyper(300,a,1629,a)].">
      <j1 rule="hyper" parents="300 1629"/>
    </justification>
  </clause>

  <clause id="1631">
    <literal><![CDATA[
      (x * y) * L(x \ 1,x,y) = y * K(x,y)
    ]]></literal>
    <justification jstring="[para(214(a,2),1629(a,1,2))].">
      <j1 rule="para" parents="214 1629"/>
    </justification>
  </clause>

  <clause id="1633">
    <literal><![CDATA[
      T(x * T(y,z),x) / x = T(T(x * y,x) / x,z)
    ]]></literal>
    <justification jstring="[hyper(1617,a,1611,a),flip(a)].">
      <j1 rule="hyper" parents="1617 1611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1634">
    <literal><![CDATA[
      (L(x,y,z) * (z * y)) \ (x * (z * y)) = a(z,y,T(x,z * y))
    ]]></literal>
    <justification jstring="[para(681(a,1),227(a,1,1))].">
      <j1 rule="para" parents="681 227"/>
    </justification>
  </clause>

  <clause id="1635">
    <literal><![CDATA[
      (L(x,y \ z,y) * z) \ (x * (y * (y \ z))) = a(y,y \ z,T(x,y * (y \ z)))
    ]]></literal>
    <justification jstring="[para(10(a,1),1634(a,1,1,2))].">
      <j1 rule="para" parents="10 1634"/>
    </justification>
  </clause>

  <clause id="1636">
    <literal><![CDATA[
      (x * ((y * y) \ z)) / ((y * y) \ z) = R(x,y \ (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(954(a,1),741(a,1,1))].">
      <j1 rule="para" parents="954 741"/>
    </justification>
  </clause>

  <clause id="1637">
    <literal><![CDATA[
      R(x,y \ (y \ 1),z) = x
    ]]></literal>
    <justification jstring="[hyper(308,a,1636,a),flip(a)].">
      <j1 rule="hyper" parents="308 1636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1639">
    <literal><![CDATA[
      R(x,(1 / y) \ y,z) = x
    ]]></literal>
    <justification jstring="[para(79(a,1),1637(a,1,2,2))].">
      <j1 rule="para" parents="79 1637"/>
    </justification>
  </clause>

  <clause id="1640">
    <literal><![CDATA[
      (x * ((1 / y) \ y)) * z = x * (((1 / y) \ y) * z)
    ]]></literal>
    <justification jstring="[para(1639(a,1),103(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1639 103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1641">
    <literal><![CDATA[
      ((x \ (x / y)) * x) * y != z
    ]]></literal>
    <literal><![CDATA[
      x * (y * T(y \ 1,x)) = z
    ]]></literal>
    <justification jstring="[para(1596(a,1),904(a,1))].">
      <j1 rule="para" parents="1596 904"/>
    </justification>
  </clause>

  <clause id="1642">
    <literal><![CDATA[
      R(x * (y \ 1),z,u) / (y \ 1) = y * R(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(120,a,652,a(flip),b,928,a)].">
      <j1 rule="hyper" parents="120 652 928"/>
    </justification>
  </clause>

  <clause id="1643">
    <literal><![CDATA[
      x * ((x \ y) * ((z * ((x \ y) \ u)) / z)) = y * ((z * (y \ (x * u))) / z)
    ]]></literal>
    <justification jstring="[para(974(a,1),482(a,1,2)),flip(a)].">
      <j1 rule="para" parents="974 482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1645">
    <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(1006(a,1),491(a,1,2))].">
      <j1 rule="para" parents="1006 491"/>
    </justification>
  </clause>

  <clause id="1646">
    <literal><![CDATA[
      (1 / (x / y)) \ (y / x) = ((1 * y) / x) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(65,a,930,a(flip),b,1224,a),flip(a)].">
      <j1 rule="hyper" parents="65 930 1224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1647">
    <literal><![CDATA[
      (1 / (x / y)) \ (y / x) = (y / x) * (x / y)
    ]]></literal>
    <justification jstring="[para(7(a,1),1646(a,2,1,1))].">
      <j1 rule="para" parents="7 1646"/>
    </justification>
  </clause>

  <clause id="1648">
    <literal><![CDATA[
      (1 / (x / y)) * ((y / x) * (x / y)) = y / x
    ]]></literal>
    <justification jstring="[hyper(144,a,1647,a)].">
      <j1 rule="hyper" parents="144 1647"/>
    </justification>
  </clause>

  <clause id="1649">
    <literal><![CDATA[
      (1 / ((x \ y) / y)) * ((y / (x \ y)) * ((x \ y) / y)) = x
    ]]></literal>
    <justification jstring="[hyper(299,a,76,a(flip),b,1648,a),flip(a)].">
      <j1 rule="hyper" parents="299 76 1648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1650">
    <literal><![CDATA[
      (1 / ((x \ y) / y)) * (x * ((x \ y) / y)) = x
    ]]></literal>
    <justification jstring="[para(76(a,1),1649(a,1,2,1))].">
      <j1 rule="para" parents="76 1649"/>
    </justification>
  </clause>

  <clause id="1652">
    <literal><![CDATA[
      T(1 / ((x \ y) / y),x * ((x \ y) / y)) = (x * ((x \ y) / y)) \ x
    ]]></literal>
    <justification jstring="[hyper(235,a,1650,a,b,10,a)].">
      <j1 rule="hyper" parents="235 1650 10"/>
    </justification>
  </clause>

  <clause id="1654">
    <literal><![CDATA[
      T(x * (y * z),z \ (z \ 1)) = (z * z) * (x * (y * (z \ 1)))
    ]]></literal>
    <justification jstring="[para(1243(a,1),1241(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1243 1241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1655">
    <literal><![CDATA[
      T((x \ y) * (z * x),x \ (x \ 1)) = ((x \ 1) \ y) * (z * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(299,a,731,a(flip),b,1654,a),flip(a)].">
      <j1 rule="hyper" parents="299 731 1654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1656">
    <literal><![CDATA[
      T((x * y) / x,L(y,z,u) * x) = L(y,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(11(a,1),1371(a,2,1))].">
      <j1 rule="para" parents="11 1371"/>
    </justification>
  </clause>

  <clause id="1657">
    <literal><![CDATA[
      x * T(y,L(y,z,u) * x) = L(y,x,L(y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(1656(a,1),433(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1656 433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1658">
    <literal><![CDATA[
      L(T(x,y),y,L(x,z,u)) = T(x,L(x,z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(36,a,233,a,b,1657,a)].">
      <j1 rule="hyper" parents="36 233 1657"/>
    </justification>
  </clause>

  <clause id="1659">
    <literal><![CDATA[
      ((x \ 1) \ y) \ ((x \ 1) \ z) = (x \ y) \ (x \ z)
    ]]></literal>
    <justification jstring="[para(165(a,1),1131(a,1,2)),flip(a)].">
      <j1 rule="para" parents="165 1131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1660">
    <literal><![CDATA[
      (((1 / x) \ 1) \ y) \ (x \ z) = ((1 / x) \ y) \ ((1 / x) \ z)
    ]]></literal>
    <justification jstring="[para(79(a,1),1659(a,1,2,1))].">
      <j1 rule="para" parents="79 1659"/>
    </justification>
  </clause>

  <clause id="1662">
    <literal><![CDATA[
      ((1 / x) \ y) \ ((1 / x) \ z) = (x \ y) \ (x \ z)
    ]]></literal>
    <justification jstring="[para(79(a,1),1660(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 1660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1663">
    <literal><![CDATA[
      (x \ 1) \ (x \ y) = x \ ((1 / x) \ y)
    ]]></literal>
    <justification jstring="[para(79(a,1),1662(a,1,1)),flip(a)].">
      <j1 rule="para" parents="79 1662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1664">
    <literal><![CDATA[
      x * ((x \ 1) \ (x \ y)) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[para(1662(a,1),333(a,1,2))].">
      <j1 rule="para" parents="1662 333"/>
    </justification>
  </clause>

  <clause id="1665">
    <literal><![CDATA[
      (x \ y) \ (x \ L(z,x,x)) = ((1 / x) \ y) \ (x * z)
    ]]></literal>
    <justification jstring="[para(481(a,1),1662(a,1,2)),flip(a)].">
      <j1 rule="para" parents="481 1662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1666">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ ((x \ 1) \ y) = x \ ((1 / x) \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,1659,a,b,1663,a)].">
      <j1 rule="hyper" parents="65 1659 1663"/>
    </justification>
  </clause>

  <clause id="1667">
    <literal><![CDATA[
      a(x,x,x \ (x \ y)) = y \ (x \ ((1 / x) \ y))
    ]]></literal>
    <justification jstring="[para(1663(a,1),1146(a,2,2))].">
      <j1 rule="para" parents="1663 1146"/>
    </justification>
  </clause>

  <clause id="1668">
    <literal><![CDATA[
      (1 / x) \ (x * y) = x * ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(9(a,1),1664(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 1664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1669">
    <literal><![CDATA[
      x * ((x \ 1) \ 1) = (1 / x) \ x
    ]]></literal>
    <justification jstring="[para(68(a,1),1664(a,1,2,2))].">
      <j1 rule="para" parents="68 1664"/>
    </justification>
  </clause>

  <clause id="1670">
    <literal><![CDATA[
      L((x \ 1) \ y,x,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(514,a,1668,a)].">
      <j1 rule="hyper" parents="514 1668"/>
    </justification>
  </clause>

  <clause id="1671">
    <literal><![CDATA[
      (1 / x) * (x * ((x \ 1) \ y)) = x * y
    ]]></literal>
    <justification jstring="[hyper(144,a,1668,a)].">
      <j1 rule="hyper" parents="144 1668"/>
    </justification>
  </clause>

  <clause id="1672">
    <literal><![CDATA[
      L(x \ (y * ((y \ 1) \ z)),x,1 / y) = ((1 / y) * x) \ (y * z)
    ]]></literal>
    <justification jstring="[para(1668(a,1),281(a,1,1,2))].">
      <j1 rule="para" parents="1668 281"/>
    </justification>
  </clause>

  <clause id="1673">
    <literal><![CDATA[
      x * ((x \ 1) * y) = L(y,x,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),1670(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 1670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1674">
    <literal><![CDATA[
      L(T(x,y \ 1),y,y) = y * (x * (y \ 1))
    ]]></literal>
    <justification jstring="[para(22(a,2),1670(a,1,1))].">
      <j1 rule="para" parents="22 1670"/>
    </justification>
  </clause>

  <clause id="1675">
    <literal><![CDATA[
      L((x * x) * y,x,x) = x * (x * y)
    ]]></literal>
    <justification jstring="[para(730(a,1),1670(a,1,1))].">
      <j1 rule="para" parents="730 1670"/>
    </justification>
  </clause>

  <clause id="1676">
    <literal><![CDATA[
      L(L(x \ 1,y,z) * ((x \ 1) \ u),x,x) = x * (L(x \ 1,y,z) * u)
    ]]></literal>
    <justification jstring="[para(1348(a,1),1670(a,1,1))].">
      <j1 rule="para" parents="1348 1670"/>
    </justification>
  </clause>

  <clause id="1677">
    <literal><![CDATA[
      (1 / x) * (x * y) = x * ((x \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(299,a,475,a,b,1673,a)].">
      <j1 rule="hyper" parents="299 475 1673"/>
    </justification>
  </clause>

  <clause id="1678">
    <literal><![CDATA[
      x * ((x \ 1) * (x \ y)) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(299,a,511,a(flip),b,1673,a),flip(a)].">
      <j1 rule="hyper" parents="299 511 1673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1679">
    <literal><![CDATA[
      x \ L(y,x,x) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(125,a,1673,a)].">
      <j1 rule="hyper" parents="125 1673"/>
    </justification>
  </clause>

  <clause id="1680">
    <literal><![CDATA[
      (x \ 1) * T(1 / x,y) = x \ T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,922,a(flip),b,1673,a),flip(a)].">
      <j1 rule="hyper" parents="119 922 1673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1681">
    <literal><![CDATA[
      (x \ 1) * (1 / x) = x \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,921,a(flip),b,1673,a),flip(a)].">
      <j1 rule="hyper" parents="119 921 1673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1682">
    <literal><![CDATA[
      x \ T((1 / x) * y,z) = (x \ 1) * T(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,515,a(flip),b,1673,a)].">
      <j1 rule="hyper" parents="119 515 1673"/>
    </justification>
  </clause>

  <clause id="1683">
    <literal><![CDATA[
      x \ ((1 / x) * y) = (x \ 1) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(119,a,511,a(flip),b,1673,a)].">
      <j1 rule="hyper" parents="119 511 1673"/>
    </justification>
  </clause>

  <clause id="1684">
    <literal><![CDATA[
      L(x,y,y) != y * z
    ]]></literal>
    <literal><![CDATA[
      (y \ 1) * x = z
    ]]></literal>
    <justification jstring="[para(1673(a,1),45(a,1))].">
      <j1 rule="para" parents="1673 45"/>
    </justification>
  </clause>

  <clause id="1686">
    <literal><![CDATA[
      x * ((x \ 1) * y) != z
    ]]></literal>
    <literal><![CDATA[
      L(y,x,x) = z
    ]]></literal>
    <justification jstring="[para(1679(a,1),250(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1679 250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1688">
    <literal><![CDATA[
      (x \ 1) * (1 / x) = (x * x) \ 1
    ]]></literal>
    <justification jstring="[hyper(299,a,727,a,b,1681,a),flip(a)].">
      <j1 rule="hyper" parents="299 727 1681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1689">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ 1 = 1 / x
    ]]></literal>
    <justification jstring="[hyper(36,a,936,a,b,1688,a)].">
      <j1 rule="hyper" parents="36 936 1688"/>
    </justification>
  </clause>

  <clause id="1690">
    <literal><![CDATA[
      T(x \ 1,(x \ 1) \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(338,a,1689,a)].">
      <j1 rule="hyper" parents="338 1689"/>
    </justification>
  </clause>

  <clause id="1691">
    <literal><![CDATA[
      1 / (1 / x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(192,a,1689,a)].">
      <j1 rule="hyper" parents="192 1689"/>
    </justification>
  </clause>

  <clause id="1692">
    <literal><![CDATA[
      T(x \ 1,x) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(65,a,1495,a,b,1689,a)].">
      <j1 rule="hyper" parents="65 1495 1689"/>
    </justification>
  </clause>

  <clause id="1693">
    <literal><![CDATA[
      x \ 1 != 1 / y
    ]]></literal>
    <literal><![CDATA[
      (y \ 1) \ 1 = x
    ]]></literal>
    <justification jstring="[para(1689(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="1689 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1695">
    <literal><![CDATA[
      (x * x) * ((y \ 1) \ 1) = (x * x) / (1 / y)
    ]]></literal>
    <justification jstring="[para(1689(a,1),426(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1689 426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1696">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ y) * (((x \ 1) \ 1) * ((x \ 1) \ 1)) = T((1 / x) \ y,((x \ 1) \ 1) * ((x \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(1689(a,1),735(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1689 735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1697">
    <literal><![CDATA[
      T(x \ 1,x) \ 1 = x
    ]]></literal>
    <justification jstring="[hyper(186,a,1692,a(flip))].">
      <j1 rule="hyper" parents="186 1692"/>
    </justification>
  </clause>

  <clause id="1698">
    <literal><![CDATA[
      T(T(x \ 1,y),x) = T(1 / x,y)
    ]]></literal>
    <justification jstring="[para(1692(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1692 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1699">
    <literal><![CDATA[
      K(x \ 1,x) = x * (1 / x)
    ]]></literal>
    <justification jstring="[para(1692(a,1),342(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1692 342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1700">
    <literal><![CDATA[
      x * (1 / x) != y
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(1692(a,1),617(a,1,2))].">
      <j1 rule="para" parents="1692 617"/>
    </justification>
  </clause>

  <clause id="1701">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ 1 != y
    ]]></literal>
    <literal><![CDATA[
      1 / x = y
    ]]></literal>
    <justification jstring="[para(1691(a,1),317(a,1,1))].">
      <j1 rule="para" parents="1691 317"/>
    </justification>
  </clause>

  <clause id="1702">
    <literal><![CDATA[
      L(((x \ 1) \ y) * z,x,x) = x * (x * ((x \ y) * z))
    ]]></literal>
    <justification jstring="[para(731(a,1),1675(a,1,1))].">
      <j1 rule="para" parents="731 1675"/>
    </justification>
  </clause>

  <clause id="1703">
    <literal><![CDATA[
      (x \ 1) \ 1 != y
    ]]></literal>
    <literal><![CDATA[
      1 / (1 / x) = y
    ]]></literal>
    <justification jstring="[para(79(a,1),1701(a,1,1,1))].">
      <j1 rule="para" parents="79 1701"/>
    </justification>
  </clause>

  <clause id="1704">
    <literal><![CDATA[
      T(x \ 1,x) != y
    ]]></literal>
    <literal><![CDATA[
      1 / x = y
    ]]></literal>
    <justification jstring="[para(1495(a,2),1701(a,1))].">
      <j1 rule="para" parents="1495 1701"/>
    </justification>
  </clause>

  <clause id="1705">
    <literal><![CDATA[
      (x \ 1) * (x \ 1) = x \ (1 / x)
    ]]></literal>
    <justification jstring="[hyper(389,a,1677,a),flip(a)].">
      <j1 rule="hyper" parents="389 1677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1706">
    <literal><![CDATA[
      (1 / x) * (x * y) = L(y,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,252,a(flip),b,1677,a),flip(a)].">
      <j1 rule="hyper" parents="299 252 1677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1707">
    <literal><![CDATA[
      (1 / x) * (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      L(y,x \ 1,x) = z
    ]]></literal>
    <justification jstring="[para(1677(a,2),494(a,1))].">
      <j1 rule="para" parents="1677 494"/>
    </justification>
  </clause>

  <clause id="1708">
    <literal><![CDATA[
      L(x \ 1,x \ 1,x) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(646,a,1705,a(flip))].">
      <j1 rule="hyper" parents="646 1705"/>
    </justification>
  </clause>

  <clause id="1709">
    <literal><![CDATA[
      (x \ (1 / x)) \ y = x * ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(1705(a,1),465(a,1,1))].">
      <j1 rule="para" parents="1705 465"/>
    </justification>
  </clause>

  <clause id="1710">
    <literal><![CDATA[
      (x \ (1 / x)) * y = (x \ 1) * (x \ y)
    ]]></literal>
    <justification jstring="[para(1705(a,1),468(a,1,1))].">
      <j1 rule="para" parents="1705 468"/>
    </justification>
  </clause>

  <clause id="1711">
    <literal><![CDATA[
      (x * (y \ 1)) / y = x * (y \ (1 / y))
    ]]></literal>
    <justification jstring="[para(1705(a,1),677(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1705 677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1712">
    <literal><![CDATA[
      (x \ (y * z)) * ((z \ 1) * (z \ 1)) = x \ (y * (1 / z))
    ]]></literal>
    <justification jstring="[para(1705(a,2),1342(a,1,2))].">
      <j1 rule="para" parents="1705 1342"/>
    </justification>
  </clause>

  <clause id="1713">
    <literal><![CDATA[
      (x * ((x \ 1) \ y)) * (x \ (1 / x)) = T(y,(x \ 1) * (x \ 1))
    ]]></literal>
    <justification jstring="[para(1705(a,1),907(a,1,2))].">
      <j1 rule="para" parents="1705 907"/>
    </justification>
  </clause>

  <clause id="1714">
    <literal><![CDATA[
      L(T(x \ 1,y),x \ 1,x) = T(1 / x,y)
    ]]></literal>
    <justification jstring="[para(1708(a,1),25(a,2,1))].">
      <j1 rule="para" parents="1708 25"/>
    </justification>
  </clause>

  <clause id="1715">
    <literal><![CDATA[
      L(x,x \ 1,x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(65,a,675,a(flip),b,1706,a),flip(a)].">
      <j1 rule="hyper" parents="65 675 1706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1716">
    <literal><![CDATA[
      x * K(x \ 1,x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(65,a,590,a,b,1715,a)].">
      <j1 rule="hyper" parents="65 590 1715"/>
    </justification>
  </clause>

  <clause id="1717">
    <literal><![CDATA[
      x \ (1 / (1 / x)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,1715,a(flip),b,590,a)].">
      <j1 rule="hyper" parents="119 1715 590"/>
    </justification>
  </clause>

  <clause id="1718">
    <literal><![CDATA[
      L(R(x,y,z),x \ 1,x) = R(1 / (1 / x),y,z)
    ]]></literal>
    <justification jstring="[para(1715(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1715 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1720">
    <literal><![CDATA[
      (1 / x) * y != x * z
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) * (x \ y) = z
    ]]></literal>
    <justification jstring="[para(1678(a,1),45(a,1))].">
      <j1 rule="para" parents="1678 45"/>
    </justification>
  </clause>

  <clause id="1722">
    <literal><![CDATA[
      (1 / x) * y != z
    ]]></literal>
    <literal><![CDATA[
      L(x \ y,x \ 1,x) = z
    ]]></literal>
    <justification jstring="[para(1678(a,1),494(a,1))].">
      <j1 rule="para" parents="1678 494"/>
    </justification>
  </clause>

  <clause id="1723">
    <literal><![CDATA[
      L((x \ 1) * (x \ y),x,x) != z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) * ((1 / x) * y) = z
    ]]></literal>
    <justification jstring="[para(1683(a,1),613(a,1,1))].">
      <j1 rule="para" parents="1683 613"/>
    </justification>
  </clause>

  <clause id="1725">
    <literal><![CDATA[
      ((1 / x) * (1 / x)) \ (y / z) = (x * ((x \ 1) \ y)) / z
    ]]></literal>
    <justification jstring="[para(1709(a,1),771(a,2,1))].">
      <j1 rule="para" parents="1709 771"/>
    </justification>
  </clause>

  <clause id="1726">
    <literal><![CDATA[
      ((1 / x) \ x) \ y = (x \ 1) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,1080,a,b,1710,a)].">
      <j1 rule="hyper" parents="65 1080 1710"/>
    </justification>
  </clause>

  <clause id="1727">
    <literal><![CDATA[
      ((x \ 1) * (x \ y)) * z = (x \ (1 / x)) * (y * z)
    ]]></literal>
    <justification jstring="[para(1710(a,1),509(a,1,1))].">
      <j1 rule="para" parents="1710 509"/>
    </justification>
  </clause>

  <clause id="1728">
    <literal><![CDATA[
      ((1 / x) * (1 / x)) * (y / z) = ((x \ 1) * (x \ y)) / z
    ]]></literal>
    <justification jstring="[para(1710(a,1),768(a,2,1))].">
      <j1 rule="para" parents="1710 768"/>
    </justification>
  </clause>

  <clause id="1729">
    <literal><![CDATA[
      (x * y) * ((y \ 1) * (y \ z)) = (x * (1 / y)) * z
    ]]></literal>
    <justification jstring="[para(1710(a,1),1340(a,1,2))].">
      <j1 rule="para" parents="1710 1340"/>
    </justification>
  </clause>

  <clause id="1730">
    <literal><![CDATA[
      T(x * (y \ (1 / y)),y) = y \ (x * (y \ 1))
    ]]></literal>
    <justification jstring="[para(1711(a,1),109(a,1,1))].">
      <j1 rule="para" parents="1711 109"/>
    </justification>
  </clause>

  <clause id="1731">
    <literal><![CDATA[
      (1 / ((1 / x) \ x)) * (((x \ 1) * (x \ y)) * ((1 / x) \ x)) = T((1 / ((1 / x) \ x)) * y,(1 / x) \ x)
    ]]></literal>
    <justification jstring="[para(1726(a,1),820(a,1,2,1))].">
      <j1 rule="para" parents="1726 820"/>
    </justification>
  </clause>

  <clause id="1732">
    <literal><![CDATA[
      L(T(x,x \ 1),x,x) = x
    ]]></literal>
    <justification jstring="[hyper(299,a,71,a(flip),b,1674,a),flip(a)].">
      <j1 rule="hyper" parents="299 71 1674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1733">
    <literal><![CDATA[
      T(L(x,y,y),y \ 1) = y * (x * (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(65,a,25,a(flip),b,1674,a)].">
      <j1 rule="hyper" parents="65 25 1674"/>
    </justification>
  </clause>

  <clause id="1735">
    <literal><![CDATA[
      (1 / x) \ T((1 / x) \ 1,y) = x * T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[hyper(657,a,1680,a),flip(a)].">
      <j1 rule="hyper" parents="657 1680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1736">
    <literal><![CDATA[
      L(T(1 / x,y),x \ 1,x) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(646,a,1680,a(flip))].">
      <j1 rule="hyper" parents="646 1680"/>
    </justification>
  </clause>

  <clause id="1737">
    <literal><![CDATA[
      (x \ ((1 / x) \ y)) / T(y,a(x,x,x \ (x \ y))) = y \ (x \ ((1 / x) \ y))
    ]]></literal>
    <justification jstring="[para(1667(a,2),262(a,1,2,2))].">
      <j1 rule="para" parents="1667 262"/>
    </justification>
  </clause>

  <clause id="1738">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ y != x \ ((1 / x) \ z)
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) \ z = y
    ]]></literal>
    <justification jstring="[para(1666(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="1666 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1740">
    <literal><![CDATA[
      ((x \ 1) * (x \ y)) * z = (x \ 1) * (x \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(299,a,1710,a(flip),b,1727,a),flip(a)].">
      <j1 rule="hyper" parents="299 1710 1727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1741">
    <literal><![CDATA[
      T((x \ 1) * (x \ y),x \ 1) = x \ (y * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(235,a,1727,a,b,1710,a(flip))].">
      <j1 rule="hyper" parents="235 1727 1710"/>
    </justification>
  </clause>

  <clause id="1743">
    <literal><![CDATA[
      ((x * y) * (y \ 1)) / y = (x * (1 / y)) * 1
    ]]></literal>
    <justification jstring="[hyper(65,a,677,a(flip),b,1729,a)].">
      <j1 rule="hyper" parents="65 677 1729"/>
    </justification>
  </clause>

  <clause id="1744">
    <literal><![CDATA[
      (x * ((y * (1 / z)) * u)) \ ((x * (y * z)) * ((z \ 1) * (z \ u))) = a(x,y * z,(z \ 1) * (z \ u))
    ]]></literal>
    <justification jstring="[para(1729(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="1729 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1745">
    <literal><![CDATA[
      ((x * y) * (((y \ 1) * (y \ z)) * u)) \ (((x * (1 / y)) * z) * u) = a(x * y,(y \ 1) * (y \ z),u)
    ]]></literal>
    <justification jstring="[para(1729(a,1),14(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="1729 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1746">
    <literal><![CDATA[
      (x * (y * z)) * (((z \ 1) * (z \ 1)) * u) = (x * ((y * (1 / z)) * 1)) * u
    ]]></literal>
    <justification jstring="[para(1729(a,1),117(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1729 117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1747">
    <literal><![CDATA[
      (x * (1 / y)) * ((y \ 1) \ z) = (x * y) * (((y \ 1) \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(908(a,1),1729(a,1,2)),flip(a)].">
      <j1 rule="para" parents="908 1729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1748">
    <literal><![CDATA[
      ((x \ 1) * (x \ 1)) * (y / ((z * (1 / x)) * 1)) = T(y,(x \ 1) \ ((x \ 1) \ 1)) / (z * x)
    ]]></literal>
    <justification jstring="[para(1729(a,1),1272(a,1,2,2))].">
      <j1 rule="para" parents="1729 1272"/>
    </justification>
  </clause>

  <clause id="1749">
    <literal><![CDATA[
      (x * y) * ((y \ 1) * ((y \ 1) * z)) = (x * (1 / y)) * L(z,y,y)
    ]]></literal>
    <justification jstring="[para(1679(a,1),1729(a,1,2,2))].">
      <j1 rule="para" parents="1679 1729"/>
    </justification>
  </clause>

  <clause id="1750">
    <literal><![CDATA[
      ((x * y) * (y \ 1)) / y = x * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(299,a,8,a(flip),b,1743,a),flip(a)].">
      <j1 rule="hyper" parents="299 8 1743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1751">
    <literal><![CDATA[
      T(x * (y \ 1),y) / y = (y \ x) * (1 / y)
    ]]></literal>
    <justification jstring="[para(858(a,1),1750(a,1,1))].">
      <j1 rule="para" parents="858 1750"/>
    </justification>
  </clause>

  <clause id="1752">
    <literal><![CDATA[
      R(x,y,y) / y = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(1246(a,1),1750(a,1,1))].">
      <j1 rule="para" parents="1246 1750"/>
    </justification>
  </clause>

  <clause id="1753">
    <literal><![CDATA[
      x * T(y * (1 / x),x) = R(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(269,a,1752,a)].">
      <j1 rule="hyper" parents="269 1752"/>
    </justification>
  </clause>

  <clause id="1754">
    <literal><![CDATA[
      (x * (1 / y)) * y = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(143,a,1752,a)].">
      <j1 rule="hyper" parents="143 1752"/>
    </justification>
  </clause>

  <clause id="1755">
    <literal><![CDATA[
      T(x * (1 / y),y) = y \ R(x,y,y)
    ]]></literal>
    <justification jstring="[para(1752(a,1),109(a,1,1))].">
      <j1 rule="para" parents="1752 109"/>
    </justification>
  </clause>

  <clause id="1757">
    <literal><![CDATA[
      ((1 / x) \ y) \ (x * z) = (x \ y) \ ((x \ 1) * z)
    ]]></literal>
    <justification jstring="[para(1679(a,1),1665(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1679 1665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1758">
    <literal><![CDATA[
      (x \ 1) * (((x \ 1) \ y) * z) = x * ((x \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(1684,a,1702,a)].">
      <j1 rule="hyper" parents="1684 1702"/>
    </justification>
  </clause>

  <clause id="1759">
    <literal><![CDATA[
      (1 / x) * T((x \ 1) \ y,x) = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(984,a,1758,a)].">
      <j1 rule="hyper" parents="984 1758"/>
    </justification>
  </clause>

  <clause id="1760">
    <literal><![CDATA[
      (1 / x) * (((1 / x) \ y) * z) = x * ((((1 / x) \ 1) \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(657,a,1758,a),flip(a)].">
      <j1 rule="hyper" parents="657 1758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1761">
    <literal><![CDATA[
      (x \ 1) \ L(y,x,x) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(119,a,1673,a(flip),b,1758,a)].">
      <j1 rule="hyper" parents="119 1673 1758"/>
    </justification>
  </clause>

  <clause id="1762">
    <literal><![CDATA[
      L(x,(y \ 1) \ z,y \ 1) = z \ (y * ((y \ z) * x))
    ]]></literal>
    <justification jstring="[hyper(119,a,1758,a(flip),b,482,a),flip(a)].">
      <j1 rule="hyper" parents="119 1758 482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1764">
    <literal><![CDATA[
      L(x,(y \ 1) \ z,y \ 1) = L(x,y \ z,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,95,a(flip),b,1762,a),flip(a)].">
      <j1 rule="hyper" parents="299 95 1762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1765">
    <literal><![CDATA[
      L(((x \ 1) \ y) \ z,x \ y,x) = y \ ((x \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(615,a,1764,a),flip(a)].">
      <j1 rule="hyper" parents="615 1764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1766">
    <literal><![CDATA[
      L(((x \ 1) * (x \ 1)) * y,x \ 1,x) = 1 \ ((x \ 1) * ((x \ 1) * y))
    ]]></literal>
    <justification jstring="[para(730(a,1),1765(a,1,1))].">
      <j1 rule="para" parents="730 1765"/>
    </justification>
  </clause>

  <clause id="1767">
    <literal><![CDATA[
      (x * ((x \ 1) \ y)) / z = (x \ (1 / x)) \ (y / z)
    ]]></literal>
    <justification jstring="[para(428(a,1),1725(a,1,1)),flip(a)].">
      <j1 rule="para" parents="428 1725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1768">
    <literal><![CDATA[
      (x * ((x \ 1) \ y)) / z = x * ((x \ 1) \ (y / z))
    ]]></literal>
    <justification jstring="[hyper(299,a,1709,a(flip),b,1767,a),flip(a)].">
      <j1 rule="hyper" parents="299 1709 1767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1769">
    <literal><![CDATA[
      ((x \ 1) * (x \ y)) / z = (x \ (1 / x)) * (y / z)
    ]]></literal>
    <justification jstring="[para(428(a,1),1728(a,1,1)),flip(a)].">
      <j1 rule="para" parents="428 1728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1770">
    <literal><![CDATA[
      ((x \ 1) * (x \ y)) / z = (x \ 1) * (x \ (y / z))
    ]]></literal>
    <justification jstring="[hyper(299,a,1710,a(flip),b,1769,a),flip(a)].">
      <j1 rule="hyper" parents="299 1710 1769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1771">
    <literal><![CDATA[
      (x \ y) / (z * z) = x \ (y / (z * z))
    ]]></literal>
    <justification jstring="[hyper(851,a,1770,a)].">
      <j1 rule="hyper" parents="851 1770"/>
    </justification>
  </clause>

  <clause id="1772">
    <literal><![CDATA[
      (x \ 1) / (y * y) = x \ (y \ (y \ 1))
    ]]></literal>
    <justification jstring="[para(736(a,1),1771(a,2,2))].">
      <j1 rule="para" parents="736 1771"/>
    </justification>
  </clause>

  <clause id="1773">
    <literal><![CDATA[
      (x * x) * (y \ (z / (x * x))) = T(y \ z,x \ (x \ 1))
    ]]></literal>
    <justification jstring="[para(1771(a,1),1058(a,1,2))].">
      <j1 rule="para" parents="1771 1058"/>
    </justification>
  </clause>

  <clause id="1774">
    <literal><![CDATA[
      (x \ (y \ (y \ 1))) \ z = (y * y) * ((x \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(1772(a,1),416(a,1,1))].">
      <j1 rule="para" parents="1772 416"/>
    </justification>
  </clause>

  <clause id="1775">
    <literal><![CDATA[
      (1 / x) \ T((1 / x) \ 1,y) = x * T((x \ 1) \ 1,y)
    ]]></literal>
    <justification jstring="[para(1691(a,1),1735(a,2,2,1))].">
      <j1 rule="para" parents="1691 1735"/>
    </justification>
  </clause>

  <clause id="1776">
    <literal><![CDATA[
      T(x \ y,y \ (y \ 1)) = (y * y) * (x \ (y \ 1))
    ]]></literal>
    <justification jstring="[para(459(a,1),1773(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="459 1773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1777">
    <literal><![CDATA[
      T(x \ y,y \ (y \ 1)) \ z = (x \ (y \ 1)) \ ((y * y) \ z)
    ]]></literal>
    <justification jstring="[para(1776(a,2),420(a,1,1))].">
      <j1 rule="para" parents="1776 420"/>
    </justification>
  </clause>

  <clause id="1778">
    <literal><![CDATA[
      x * T((x \ 1) \ 1,y) = (1 / x) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(79(a,1),1775(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 1775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1779">
    <literal><![CDATA[
      (x / y) * T(((x / y) \ 1) \ 1,y) = (1 / (x / y)) \ (y \ x)
    ]]></literal>
    <justification jstring="[para(109(a,1),1778(a,2,2))].">
      <j1 rule="para" parents="109 1778"/>
    </justification>
  </clause>

  <clause id="1780">
    <literal><![CDATA[
      x * (((x \ 1) \ y) * (x \ (1 / x))) = T(y,(x \ 1) * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(65,a,563,a(flip),b,1713,a)].">
      <j1 rule="hyper" parents="65 563 1713"/>
    </justification>
  </clause>

  <clause id="1781">
    <literal><![CDATA[
      (x * (y \ 1)) * ((T(y,y \ 1) \ 1) \ z) = (x * (1 / (y \ 1))) * (((y \ 1) \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(108(a,2),1747(a,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="108 1747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1782">
    <literal><![CDATA[
      (1 / x) * (((1 / x) \ y) * z) = x * ((x \ y) * z)
    ]]></literal>
    <justification jstring="[para(79(a,1),1760(a,2,2,1,1))].">
      <j1 rule="para" parents="79 1760"/>
    </justification>
  </clause>

  <clause id="1783">
    <literal><![CDATA[
      (x \ 1) * (x \ (((1 / x) \ y) * z)) = (x \ y) * z
    ]]></literal>
    <justification jstring="[hyper(1720,a,1782,a)].">
      <j1 rule="hyper" parents="1720 1782"/>
    </justification>
  </clause>

  <clause id="1784">
    <literal><![CDATA[
      T(L(x,x,x) * y,x) = x * ((x \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(65,a,1337,a,b,1782,a)].">
      <j1 rule="hyper" parents="65 1337 1782"/>
    </justification>
  </clause>

  <clause id="1785">
    <literal><![CDATA[
      (x \ 1) * T((1 / x) \ y,x) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(22(a,2),1783(a,1,2))].">
      <j1 rule="para" parents="22 1783"/>
    </justification>
  </clause>

  <clause id="1786">
    <literal><![CDATA[
      R((x * y) / (x * z),u,w) * (x * z) = x * (z * R(z \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(701,a,1148,a)].">
      <j1 rule="hyper" parents="701 1148"/>
    </justification>
  </clause>

  <clause id="1787">
    <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(253(a,2),1149(a,1,1))].">
      <j1 rule="para" parents="253 1149"/>
    </justification>
  </clause>

  <clause id="1788">
    <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(253(a,2),1150(a,1,1))].">
      <j1 rule="para" parents="253 1150"/>
    </justification>
  </clause>

  <clause id="1789">
    <literal><![CDATA[
      (L((x * y) / x,z,u) * x) * y = (x * y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(971,a,1152,a),flip(a)].">
      <j1 rule="hyper" parents="971 1152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1790">
    <literal><![CDATA[
      (x * y) * L((x * y) \ (z * y),u,w) = (L(z / x,u,w) * x) * y
    ]]></literal>
    <justification jstring="[hyper(965,a,1152,a)].">
      <j1 rule="hyper" parents="965 1152"/>
    </justification>
  </clause>

  <clause id="1791">
    <literal><![CDATA[
      (x * L(y,z,u)) * y = (x * y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(686(a,1),1789(a,1,1))].">
      <j1 rule="para" parents="686 1789"/>
    </justification>
  </clause>

  <clause id="1792">
    <literal><![CDATA[
      ((x / L(y,z,u)) * y) \ (x * y) = L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(634,a,1791,a)].">
      <j1 rule="hyper" parents="634 1791"/>
    </justification>
  </clause>

  <clause id="1793">
    <literal><![CDATA[
      (1 / L(x,y,z)) * x = x / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(629,a,1791,a),flip(a)].">
      <j1 rule="hyper" parents="629 1791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1794">
    <literal><![CDATA[
      (x * y) / L(y,z,u) = (x / L(y,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(626,a,1791,a)].">
      <j1 rule="hyper" parents="626 1791"/>
    </justification>
  </clause>

  <clause id="1795">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) * (x \ 1) = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,70,a(flip),b,1791,a),flip(a)].">
      <j1 rule="hyper" parents="299 70 1791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1796">
    <literal><![CDATA[
      (x * L(y,z,u)) \ ((x * y) * L(y,z,u)) = y
    ]]></literal>
    <justification jstring="[hyper(125,a,1791,a)].">
      <j1 rule="hyper" parents="125 1791"/>
    </justification>
  </clause>

  <clause id="1797">
    <literal><![CDATA[
      (x * L(y,z,u)) / y = (x / y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(120,a,154,a(flip),b,1791,a)].">
      <j1 rule="hyper" parents="120 154 1791"/>
    </justification>
  </clause>

  <clause id="1798">
    <literal><![CDATA[
      (1 / x) * L(x,y,z) = L(x,y,z) / x
    ]]></literal>
    <justification jstring="[hyper(120,a,77,a(flip),b,1791,a),flip(a)].">
      <j1 rule="hyper" parents="120 77 1791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1799">
    <literal><![CDATA[
      ((x / y) * L(y,z,u)) \ (x * L(y,z,u)) = y
    ]]></literal>
    <justification jstring="[hyper(119,a,154,a(flip),b,1791,a)].">
      <j1 rule="hyper" parents="119 154 1791"/>
    </justification>
  </clause>

  <clause id="1800">
    <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(1791(a,1),322(a,1,1))].">
      <j1 rule="para" parents="1791 322"/>
    </justification>
  </clause>

  <clause id="1801">
    <literal><![CDATA[
      T(1 / L(x,y,z),x) = x \ (x / L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(235,a,1793,a,b,10,a)].">
      <j1 rule="hyper" parents="235 1793 10"/>
    </justification>
  </clause>

  <clause id="1803">
    <literal><![CDATA[
      (L(x,y,z) / x) / L(x,y,z) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(137,a,1798,a)].">
      <j1 rule="hyper" parents="137 1798"/>
    </justification>
  </clause>

  <clause id="1804">
    <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(1798(a,1),96(a,2,1))].">
      <j1 rule="para" parents="1798 96"/>
    </justification>
  </clause>

  <clause id="1805">
    <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(1798(a,1),790(a,1,2))].">
      <j1 rule="para" parents="1798 790"/>
    </justification>
  </clause>

  <clause id="1806">
    <literal><![CDATA[
      (x * y) / L(y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      (x / L(y,z,u)) * y = w
    ]]></literal>
    <justification jstring="[para(1792(a,1),310(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1792 310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1807">
    <literal><![CDATA[
      ((x * L(y,z,u)) / L(y,z,u)) * T(((x * L(y,z,u)) / L(y,z,u)) \ (x * y),w) = ((x * L(y,z,u)) * T(y,w)) / L(y,z,u)
    ]]></literal>
    <justification jstring="[para(1796(a,1),1465(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1796 1465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1808">
    <literal><![CDATA[
      ((x * y) / z) * L(z,y,x) = (x * (y * z)) / z
    ]]></literal>
    <justification jstring="[para(94(a,1),1797(a,1,1)),flip(a)].">
      <j1 rule="para" parents="94 1797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1809">
    <literal><![CDATA[
      T(x \ (x / L(x,y,z)),L(x,y,z)) = T(L(x,y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[para(1801(a,1),242(a,1,1))].">
      <j1 rule="para" parents="1801 242"/>
    </justification>
  </clause>

  <clause id="1810">
    <literal><![CDATA[
      L(x,y,z) = ((z * y) / x) \ ((z * (y * x)) / x)
    ]]></literal>
    <justification jstring="[hyper(125,a,1808,a),flip(a)].">
      <j1 rule="hyper" parents="125 1808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1811">
    <literal><![CDATA[
      (x * y) / L(z,y,R(x,y,z)) = (R(x,y,z) * y) / z
    ]]></literal>
    <justification jstring="[hyper(120,a,284,a(flip),b,1808,a)].">
      <j1 rule="hyper" parents="120 284 1808"/>
    </justification>
  </clause>

  <clause id="1812">
    <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(1808(a,1),236(a,2)),flip(a)].">
      <j1 rule="para" parents="1808 236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1814">
    <literal><![CDATA[
      (x * ((y * x) \ y)) * (x \ 1) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[para(214(a,1),1795(a,1,1,2))].">
      <j1 rule="para" parents="214 1795"/>
    </justification>
  </clause>

  <clause id="1815">
    <literal><![CDATA[
      L(x \ 1,x,y) \ ((x \ 1) * (x * ((y * x) \ y))) = K(x \ 1,x * ((y * x) \ y))
    ]]></literal>
    <justification jstring="[para(1814(a,1),16(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1814 16"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1816">
    <literal><![CDATA[
      L(x,x,R(y,x,x)) = R(y,x,x) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(38,a,179,a(flip),b,1811,a),flip(a)].">
      <j1 rule="hyper" parents="38 179 1811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1817">
    <literal><![CDATA[
      (x * y) * R((x * y) \ (z * y),u,w) = (R(z / x,u,w) * x) * y
    ]]></literal>
    <justification jstring="[hyper(935,a,1153,a)].">
      <j1 rule="hyper" parents="935 1153"/>
    </justification>
  </clause>

  <clause id="1818">
    <literal><![CDATA[
      T(1 / x,(y / (x * y)) * x) != z
    ]]></literal>
    <literal><![CDATA[
      L(x \ 1,x,y / (x * y)) = z
    ]]></literal>
    <justification jstring="[para(1229(a,1),402(a,1))].">
      <j1 rule="para" parents="1229 402"/>
    </justification>
  </clause>

  <clause id="1819">
    <literal><![CDATA[
      (1 / x) * L((1 / x) \ y,z,u) = L(y * x,z,u) / x
    ]]></literal>
    <justification jstring="[para(79(a,1),1304(a,1,2)),flip(a)].">
      <j1 rule="para" parents="79 1304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1820">
    <literal><![CDATA[
      (1 / x) * L((1 / x) \ 1,y,z) = L(x,y,z) / x
    ]]></literal>
    <justification jstring="[para(7(a,1),1819(a,2,1,1))].">
      <j1 rule="para" parents="7 1819"/>
    </justification>
  </clause>

  <clause id="1821">
    <literal><![CDATA[
      (x / y) * (y * L(y \ ((x / y) \ z),u,w)) = x * L(x \ z,u,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),1311(a,2,2,1,2))].">
      <j1 rule="para" parents="10 1311"/>
    </justification>
  </clause>

  <clause id="1822">
    <literal><![CDATA[
      x \ (y * L(y \ (x * z),u,w)) = (x \ y) * L((x \ y) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(125,a,1312,a)].">
      <j1 rule="hyper" parents="125 1312"/>
    </justification>
  </clause>

  <clause id="1823">
    <literal><![CDATA[
      x \ (y * R(y \ (x * z),u,w)) = (x \ y) * R((x \ y) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(125,a,1314,a)].">
      <j1 rule="hyper" parents="125 1314"/>
    </justification>
  </clause>

  <clause id="1824">
    <literal><![CDATA[
      (R(x / (y / z),u,w) * (y / z)) * z = y * R(y \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[hyper(299,a,692,a(flip),b,1315,a),flip(a)].">
      <j1 rule="hyper" parents="299 692 1315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1825">
    <literal><![CDATA[
      (R(1 / (x / y),z,u) * (x / y)) * y = R(y / x,z,u) * x
    ]]></literal>
    <justification jstring="[para(7(a,1),1315(a,2,1,1,1))].">
      <j1 rule="para" parents="7 1315"/>
    </justification>
  </clause>

  <clause id="1826">
    <literal><![CDATA[
      R(1 / (1 / x),y,z) * (1 / x) = R(x / 1,y,z) / x
    ]]></literal>
    <justification jstring="[hyper(120,a,8,a(flip),b,1825,a),flip(a)].">
      <j1 rule="hyper" parents="120 8 1825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1827">
    <literal><![CDATA[
      R(1 / (1 / x),y,z) * (1 / x) = R(x,y,z) / x
    ]]></literal>
    <justification jstring="[para(74(a,1),1826(a,2,1,1))].">
      <j1 rule="para" parents="74 1826"/>
    </justification>
  </clause>

  <clause id="1828">
    <literal><![CDATA[
      (1 / x) * R((1 / x) \ 1,y,z) = R(x,y,z) / x
    ]]></literal>
    <justification jstring="[hyper(935,a,1827,a)].">
      <j1 rule="hyper" parents="935 1827"/>
    </justification>
  </clause>

  <clause id="1829">
    <literal><![CDATA[
      (1 / x) * R(x,y,z) = R(x,y,z) / x
    ]]></literal>
    <justification jstring="[para(79(a,1),1828(a,1,2,1))].">
      <j1 rule="para" parents="79 1828"/>
    </justification>
  </clause>

  <clause id="1830">
    <literal><![CDATA[
      (R(x,y,z) / x) / R(x,y,z) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(137,a,1829,a)].">
      <j1 rule="hyper" parents="137 1829"/>
    </justification>
  </clause>

  <clause id="1831">
    <literal><![CDATA[
      ((1 / x) * R(x,y,z)) * x = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(143,a,1829,a(flip))].">
      <j1 rule="hyper" parents="143 1829"/>
    </justification>
  </clause>

  <clause id="1832">
    <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(1829(a,1),236(a,2)),flip(a)].">
      <j1 rule="para" parents="1829 236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1833">
    <literal><![CDATA[
      L(R(x,y,z) \ u,R(x,y,z),1 / x) = (R(x,y,z) / x) \ ((1 / x) * u)
    ]]></literal>
    <justification jstring="[para(1829(a,1),96(a,2,1))].">
      <j1 rule="para" parents="1829 96"/>
    </justification>
  </clause>

  <clause id="1834">
    <literal><![CDATA[
      (1 / x) * R(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) / x = u
    ]]></literal>
    <justification jstring="[para(1830(a,1),246(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1830 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1835">
    <literal><![CDATA[
      x * (y * ((x * (y \ 1)) / x)) = T(x,x / (x * y))
    ]]></literal>
    <justification jstring="[hyper(65,a,1441,a(flip),b,1319,a),flip(a)].">
      <j1 rule="hyper" parents="65 1441 1319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1836">
    <literal><![CDATA[
      x \ T(x,x / (x * y)) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(119,a,1441,a(flip),b,1319,a(flip))].">
      <j1 rule="hyper" parents="119 1441 1319"/>
    </justification>
  </clause>

  <clause id="1837">
    <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),1319(a,1,1))].">
      <j1 rule="para" parents="94 1319"/>
    </justification>
  </clause>

  <clause id="1839">
    <literal><![CDATA[
      (x * ((y * (x \ 1)) / y)) / (y \ 1) = T(y,y / (y * x))
    ]]></literal>
    <justification jstring="[hyper(120,a,1836,a(flip),b,1112,a)].">
      <j1 rule="hyper" parents="120 1836 1112"/>
    </justification>
  </clause>

  <clause id="1840">
    <literal><![CDATA[
      T(x,R(1 / y,y,x)) = (x \ T(x,x / (x * y))) * x
    ]]></literal>
    <justification jstring="[para(1836(a,2),1467(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1836 1467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1841">
    <literal><![CDATA[
      (x * ((x \ R(x,y,z)) / R(x,y,z))) / (R(x,y,z) \ 1) = T(R(x,y,z),R(x,y,z) / (R(x,y,z) * x))
    ]]></literal>
    <justification jstring="[para(1456(a,1),1839(a,1,1,2,1))].">
      <j1 rule="para" parents="1456 1839"/>
    </justification>
  </clause>

  <clause id="1842">
    <literal><![CDATA[
      (x / y) \ (x * ((z * (x \ (x / y))) / z)) = y * ((z * (y \ 1)) / z)
    ]]></literal>
    <justification jstring="[hyper(125,a,1322,a)].">
      <j1 rule="hyper" parents="125 1322"/>
    </justification>
  </clause>

  <clause id="1843">
    <literal><![CDATA[
      ((x * (1 / (1 / T(y,x)))) / x) \ (y / T(y,x)) = 1 / T(y,x)
    ]]></literal>
    <justification jstring="[para(1546(a,1),1343(a,1,2))].">
      <j1 rule="para" parents="1546 1343"/>
    </justification>
  </clause>

  <clause id="1844">
    <literal><![CDATA[
      ((x \ y) \ y) * (T(x,z) \ 1) = T(x,z) \ ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(76(a,1),1407(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="76 1407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1846">
    <literal><![CDATA[
      (((x * y) / x) * (y \ 1)) * x = T(x,R(y,y \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(980,a,1437,a)].">
      <j1 rule="hyper" parents="980 1437"/>
    </justification>
  </clause>

  <clause id="1847">
    <literal><![CDATA[
      (x \ ((y * x) / y)) * y = T(y,R(x,x \ 1,y))
    ]]></literal>
    <justification jstring="[para(1414(a,1),1846(a,1,1))].">
      <j1 rule="para" parents="1414 1846"/>
    </justification>
  </clause>

  <clause id="1848">
    <literal><![CDATA[
      T(x,R(T(y,x),T(y,x) \ 1,x)) = (T(y,x) \ y) * x
    ]]></literal>
    <justification jstring="[para(223(a,1),1847(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="223 1847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1849">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) / x != z
    ]]></literal>
    <literal><![CDATA[
      y \ ((x * y) / x) = z
    ]]></literal>
    <justification jstring="[para(1847(a,1),307(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1847 307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1850">
    <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(1848(a,1),1199(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1848 1199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1851">
    <literal><![CDATA[
      x \ R(x * (y * (x \ 1)),z,u) = R(y,z,u) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,234,a(flip),b,1461,a),flip(a)].">
      <j1 rule="hyper" parents="299 234 1461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1852">
    <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(1193(a,1),1851(a,1,2,1,2))].">
      <j1 rule="para" parents="1193 1851"/>
    </justification>
  </clause>

  <clause id="1853">
    <literal><![CDATA[
      (x * (y * T(y \ 1,z))) * y = (x * y) * (y * T(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(801(a,1),1470(a,1,1))].">
      <j1 rule="para" parents="801 1470"/>
    </justification>
  </clause>

  <clause id="1854">
    <literal><![CDATA[
      (x \ (y / (1 / x))) * x = T(y,x) / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(120,a,1605,a(flip),b,1600,a),flip(a)].">
      <j1 rule="hyper" parents="120 1605 1600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1855">
    <literal><![CDATA[
      R((x * y) / (x * z),u,w) * (x * z) = x * (R(y / z,u,w) * z)
    ]]></literal>
    <justification jstring="[para(692(a,2),1786(a,2,2))].">
      <j1 rule="para" parents="692 1786"/>
    </justification>
  </clause>

  <clause id="1856">
    <literal><![CDATA[
      (x * y) * L((x * y) \ y,z,u) = (L(1 / x,z,u) * x) * y
    ]]></literal>
    <justification jstring="[para(7(a,1),1790(a,1,2,1,2))].">
      <j1 rule="para" parents="7 1790"/>
    </justification>
  </clause>

  <clause id="1857">
    <literal><![CDATA[
      (x * y) * L((x * y) \ (z * y),u,w) = (x * L(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[para(685(a,1),1790(a,2,1))].">
      <j1 rule="para" parents="685 1790"/>
    </justification>
  </clause>

  <clause id="1858">
    <literal><![CDATA[
      (x * y) * L((x * y) \ y,z,u) = (x * L(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[para(685(a,1),1856(a,2,1))].">
      <j1 rule="para" parents="685 1856"/>
    </justification>
  </clause>

  <clause id="1859">
    <literal><![CDATA[
      x * (y * L(y \ (x \ y),z,u)) = (x * L(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,1150,a(flip),b,1858,a)].">
      <j1 rule="hyper" parents="65 1150 1858"/>
    </justification>
  </clause>

  <clause id="1860">
    <literal><![CDATA[
      T(x,x * L(x \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(235,a,993,a(flip),b,1858,a(flip))].">
      <j1 rule="hyper" parents="235 993 1858"/>
    </justification>
  </clause>

  <clause id="1861">
    <literal><![CDATA[
      T(x * L(x \ 1,T(x,y),y),y) = T(x,y) * ((x * y) \ y)
    ]]></literal>
    <justification jstring="[hyper(235,a,1858,a(flip),b,491,a(flip))].">
      <j1 rule="hyper" parents="235 1858 491"/>
    </justification>
  </clause>

  <clause id="1863">
    <literal><![CDATA[
      K(x,x * L(x \ 1,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(57,a,1860,a)].">
      <j1 rule="hyper" parents="57 1860"/>
    </justification>
  </clause>

  <clause id="1864">
    <literal><![CDATA[
      T(x \ y,(x \ y) * (y \ x)) = x \ y
    ]]></literal>
    <justification jstring="[para(366(a,1),1860(a,1,2,2))].">
      <j1 rule="para" parents="366 1860"/>
    </justification>
  </clause>

  <clause id="1865">
    <literal><![CDATA[
      T(x \ 1,L(x,y,z) * (x \ 1)) = x \ 1
    ]]></literal>
    <justification jstring="[para(687(a,1),1860(a,1,2))].">
      <j1 rule="para" parents="687 1860"/>
    </justification>
  </clause>

  <clause id="1866">
    <literal><![CDATA[
      T(x \ 1,x \ L(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[para(1273(a,1),1860(a,1,2))].">
      <j1 rule="para" parents="1273 1860"/>
    </justification>
  </clause>

  <clause id="1867">
    <literal><![CDATA[
      T(1 / x,L(x,y,z) / x) = 1 / x
    ]]></literal>
    <justification jstring="[para(1820(a,1),1860(a,1,2))].">
      <j1 rule="para" parents="1820 1860"/>
    </justification>
  </clause>

  <clause id="1868">
    <literal><![CDATA[
      T((x * (1 / y)) / x,L(y,z,u) / y) = (x * (1 / y)) / x
    ]]></literal>
    <justification jstring="[para(1867(a,1),445(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1867 445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1869">
    <literal><![CDATA[
      R(x \ 1,L(x,y,z),x \ 1) = T(x \ 1,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(1865(a,1),877(a,1,1))].">
      <j1 rule="para" parents="1865 877"/>
    </justification>
  </clause>

  <clause id="1870">
    <literal><![CDATA[
      x * ((x * y) * L((x * y) \ y,z,u)) = (x * L(x \ 1,z,u)) * (x * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),1859(a,1,2,2,1,2))].">
      <j1 rule="para" parents="9 1859"/>
    </justification>
  </clause>

  <clause id="1871">
    <literal><![CDATA[
      (x * y) * R((x * y) \ (z * y),u,w) = (x * R(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[para(692(a,1),1817(a,2,1))].">
      <j1 rule="para" parents="692 1817"/>
    </justification>
  </clause>

  <clause id="1872">
    <literal><![CDATA[
      (x / y) * L((x / y) \ 1,z,u) = (x * L(x \ y,z,u)) / y
    ]]></literal>
    <justification jstring="[hyper(120,a,1821,a(flip),b,1859,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="120 1821 1859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1873">
    <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),1872(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20 1872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1874">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ 1,z,u) = x \ (y * L(y \ x,z,u))
    ]]></literal>
    <justification jstring="[para(8(a,1),1822(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="8 1822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1875">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ (x \ z),u,w) = x \ (y * L(y \ z,u,w))
    ]]></literal>
    <justification jstring="[para(10(a,1),1822(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="10 1822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1876">
    <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),1874(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18 1874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1877">
    <literal><![CDATA[
      (x \ y) * R((x \ y) \ 1,z,u) = x \ (y * R(y \ x,z,u))
    ]]></literal>
    <justification jstring="[para(8(a,1),1823(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="8 1823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1878">
    <literal><![CDATA[
      ((x / y) * R((x / y) \ z,u,w)) * y = x * R(x \ (z * y),u,w)
    ]]></literal>
    <justification jstring="[para(692(a,1),1824(a,1,1))].">
      <j1 rule="para" parents="692 1824"/>
    </justification>
  </clause>

  <clause id="1879">
    <literal><![CDATA[
      (x / y) \ (x * ((x / y) / x)) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[para(10(a,1),1842(a,1,2,2,1))].">
      <j1 rule="para" parents="10 1842"/>
    </justification>
  </clause>

  <clause id="1880">
    <literal><![CDATA[
      K(x,(x / y) / x) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(457,a,1879,a)].">
      <j1 rule="hyper" parents="457 1879"/>
    </justification>
  </clause>

  <clause id="1881">
    <literal><![CDATA[
      x * ((y * (x \ 1)) / y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,(y / x) / y) = z
    ]]></literal>
    <justification jstring="[para(1879(a,1),457(a,1))].">
      <j1 rule="para" parents="1879 457"/>
    </justification>
  </clause>

  <clause id="1882">
    <literal><![CDATA[
      K(x,(x / (y \ 1)) / x) = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(299,a,1419,a(flip),b,1880,a),flip(a)].">
      <j1 rule="hyper" parents="299 1419 1880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1883">
    <literal><![CDATA[
      (x \ y) * ((y * ((x \ y) \ 1)) / y) = K(y,x / y)
    ]]></literal>
    <justification jstring="[para(76(a,1),1880(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="76 1880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1884">
    <literal><![CDATA[
      x * ((T(x,y) * (x \ 1)) / T(x,y)) = K(T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[para(1124(a,1),1880(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1124 1880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1885">
    <literal><![CDATA[
      x * ((L(x,y,z) * (x \ 1)) / L(x,y,z)) = K(L(x,y,z),1 / x)
    ]]></literal>
    <justification jstring="[para(1803(a,1),1880(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1803 1880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1886">
    <literal><![CDATA[
      K(R(x,y,z),(R(x,y,z) / ((x \ 1) \ 1)) / R(x,y,z)) = (x \ 1) \ ((x \ R(x,y,z)) / R(x,y,z))
    ]]></literal>
    <justification jstring="[para(1456(a,1),1882(a,2,2,1))].">
      <j1 rule="para" parents="1456 1882"/>
    </justification>
  </clause>

  <clause id="1887">
    <literal><![CDATA[
      T(x,x / (x * (y \ x))) = x * K(x,y / x)
    ]]></literal>
    <justification jstring="[para(1883(a,1),1835(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1883 1835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1888">
    <literal><![CDATA[
      T(x,R(y,x,(y * x) \ x)) = x * K(x,(y * x) / x)
    ]]></literal>
    <justification jstring="[para(101(a,2),1887(a,1,2))].">
      <j1 rule="para" parents="101 1887"/>
    </justification>
  </clause>

  <clause id="1889">
    <literal><![CDATA[
      T(x,R(y,x,(y * x) \ x)) = x * K(x,y)
    ]]></literal>
    <justification jstring="[para(11(a,1),1888(a,2,2,2))].">
      <j1 rule="para" parents="11 1888"/>
    </justification>
  </clause>

  <clause id="1890">
    <literal><![CDATA[
      T(x,R(y,x,(y * x) \ x)) * (x \ z) = x \ ((x * K(x,y)) * z)
    ]]></literal>
    <justification jstring="[para(1889(a,1),1188(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1889 1188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1891">
    <literal><![CDATA[
      x * (((x \ 1) * T((x \ 1) \ 1,y)) / T(x,y)) = K(T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[para(434(a,2),1884(a,1,2,1))].">
      <j1 rule="para" parents="434 1884"/>
    </justification>
  </clause>

  <clause id="1892">
    <literal><![CDATA[
      x \ ((x * K(x,y)) * z) = (x * K(x,y)) * (x \ z)
    ]]></literal>
    <justification jstring="[para(1889(a,1),1890(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1889 1890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1893">
    <literal><![CDATA[
      (x * K(x,y)) * (x \ 1) = x \ (x * K(x,y))
    ]]></literal>
    <justification jstring="[para(8(a,1),1892(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8 1892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1894">
    <literal><![CDATA[
      (x * K(x,y)) * (x \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,9,a(flip),b,1893,a),flip(a)].">
      <j1 rule="hyper" parents="299 9 1893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1895">
    <literal><![CDATA[
      T(x * K(x,y),x \ 1) = (x \ 1) \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(235,a,1893,a,b,160,a(flip))].">
      <j1 rule="hyper" parents="235 1893 160"/>
    </justification>
  </clause>

  <clause id="1898">
    <literal><![CDATA[
      K(x,y) / (x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x * K(x,y) = z
    ]]></literal>
    <justification jstring="[para(1894(a,1),307(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1894 307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1900">
    <literal><![CDATA[
      R((x * (y * z)) / (x * z),u,w) * (x * z) = x * (R(y,u,w) * z)
    ]]></literal>
    <justification jstring="[para(11(a,1),1855(a,2,2,1,1))].">
      <j1 rule="para" parents="11 1855"/>
    </justification>
  </clause>

  <clause id="1901">
    <literal><![CDATA[
      x * (y * L(y \ (x \ (z * y)),u,w)) = (x * L(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,1150,a(flip),b,1857,a)].">
      <j1 rule="hyper" parents="65 1150 1857"/>
    </justification>
  </clause>

  <clause id="1902">
    <literal><![CDATA[
      x * L(x \ (x \ (y * x)),z,u) = T(x * L(x \ y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(235,a,1857,a(flip),b,1150,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="235 1857 1150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1904">
    <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),1902(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="22 1902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1905">
    <literal><![CDATA[
      x \ T(x * L(x \ y,z,u),x) = L(x \ T(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(119,a,1904,a,b,xx)].">
      <j1 rule="hyper" parents="119 1904"/>
    </justification>
  </clause>

  <clause id="1906">
    <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),1905(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 1905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1908">
    <literal><![CDATA[
      x \ T(x * L(y / x,z,u),x) = L(T(y,x) / x,z,u)
    ]]></literal>
    <justification jstring="[para(1610(a,1),1906(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1610 1906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1909">
    <literal><![CDATA[
      L(T(x * y,x) / x,z,u) = T(x * L(y,z,u),x) / x
    ]]></literal>
    <justification jstring="[hyper(65,a,1612,a(flip),b,1908,a),flip(a)].">
      <j1 rule="hyper" parents="65 1612 1908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1910">
    <literal><![CDATA[
      x * (y * R(y \ (x \ (z * y)),u,w)) = (x * R(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,1149,a(flip),b,1871,a)].">
      <j1 rule="hyper" parents="65 1149 1871"/>
    </justification>
  </clause>

  <clause id="1911">
    <literal><![CDATA[
      (x \ (y * x)) * R((x \ (y * x)) \ x,z,u) = T(y * R(y \ x,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(235,a,1871,a(flip),b,1314,a),flip(a)].">
      <j1 rule="hyper" parents="235 1871 1314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1912">
    <literal><![CDATA[
      x * R(x \ (x \ (y * x)),z,u) = T(x * R(x \ y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(235,a,1871,a(flip),b,1149,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="235 1871 1149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1913">
    <literal><![CDATA[
      (x \ (y * z)) * R((x \ (y * z)) \ z,u,w) = x \ ((y * R(y \ x,u,w)) * z)
    ]]></literal>
    <justification jstring="[hyper(119,a,1871,a(flip),b,1314,a),flip(a)].">
      <j1 rule="hyper" parents="119 1871 1314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1914">
    <literal><![CDATA[
      (x * y) * R((x * y) \ y,z,u) = (x * R(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[para(7(a,1),1871(a,1,2,1,2))].">
      <j1 rule="para" parents="7 1871"/>
    </justification>
  </clause>

  <clause id="1915">
    <literal><![CDATA[
      (x * R(x \ (x * y),z,u)) * y = (x * y) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),1871(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 1871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1918">
    <literal><![CDATA[
      (x * R(y,z,u)) * y = (x * y) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),1915(a,1,1,2,1))].">
      <j1 rule="para" parents="9 1915"/>
    </justification>
  </clause>

  <clause id="1919">
    <literal><![CDATA[
      (1 / R(x,y,z)) * x = x / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(629,a,1918,a),flip(a)].">
      <j1 rule="hyper" parents="629 1918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1920">
    <literal><![CDATA[
      ((x / R(y,z,u)) * y) * R(y,z,u) = x * y
    ]]></literal>
    <justification jstring="[hyper(306,a,1918,a),flip(a)].">
      <j1 rule="hyper" parents="306 1918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1921">
    <literal><![CDATA[
      (x * R(y,z,u)) \ ((x * y) * R(y,z,u)) = y
    ]]></literal>
    <justification jstring="[hyper(125,a,1918,a)].">
      <j1 rule="hyper" parents="125 1918"/>
    </justification>
  </clause>

  <clause id="1922">
    <literal><![CDATA[
      (x / R(x,y,z)) / x = 1 / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(137,a,1919,a)].">
      <j1 rule="hyper" parents="137 1919"/>
    </justification>
  </clause>

  <clause id="1923">
    <literal><![CDATA[
      (1 / R(x,y,z)) * x != u
    ]]></literal>
    <literal><![CDATA[
      x / R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(1922(a,1),246(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1922 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1924">
    <literal><![CDATA[
      (x * y) / R(y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      (x / R(y,z,u)) * y = w
    ]]></literal>
    <justification jstring="[para(1920(a,1),307(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1920 307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1925">
    <literal><![CDATA[
      R(T(x,y * R(x,z,u)),y,R(x,z,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1921(a,1),1324(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1921 1324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1926">
    <literal><![CDATA[
      R(x,y,R(x,z,u)) * (y * R(x,z,u)) = (y * R(x,z,u)) * T(x,y)
    ]]></literal>
    <justification jstring="[para(1925(a,1),234(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1925 234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1927">
    <literal><![CDATA[
      (x * R(y,z,u)) * T(y,x) = (y * x) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(1925(a,1),688(a,1,2))].">
      <j1 rule="para" parents="1925 688"/>
    </justification>
  </clause>

  <clause id="1928">
    <literal><![CDATA[
      R(x,y,z) / T(x,x \ 1) = (x \ 1) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(120,a,70,a(flip),b,1927,a)].">
      <j1 rule="hyper" parents="120 70 1927"/>
    </justification>
  </clause>

  <clause id="1929">
    <literal><![CDATA[
      (x * R(y / x,z,u)) \ (y * R(y / x,z,u)) = T(y / x,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,154,a(flip),b,1927,a)].">
      <j1 rule="hyper" parents="119 154 1927"/>
    </justification>
  </clause>

  <clause id="1931">
    <literal><![CDATA[
      R(x,y,z) / ((x \ 1) \ 1) = (x \ 1) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,294,a(flip),b,1928,a)].">
      <j1 rule="hyper" parents="65 294 1928"/>
    </justification>
  </clause>

  <clause id="1932">
    <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),1912(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="22 1912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1933">
    <literal><![CDATA[
      x \ T(x * R(x \ y,z,u),x) = R(x \ T(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(119,a,1932,a,b,xx)].">
      <j1 rule="hyper" parents="119 1932"/>
    </justification>
  </clause>

  <clause id="1934">
    <literal><![CDATA[
      T(x * R(x \ 1,y,z),x) = x * R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(195(a,1),1932(a,2,2,1,2))].">
      <j1 rule="para" parents="195 1932"/>
    </justification>
  </clause>

  <clause id="1935">
    <literal><![CDATA[
      T(x,x * R(x \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(56,a,1934,a)].">
      <j1 rule="hyper" parents="56 1934"/>
    </justification>
  </clause>

  <clause id="1936">
    <literal><![CDATA[
      T(x * ((x * R(x \ 1,y,z)) / x),x) = x * ((x * R(x \ 1,y,z)) / x)
    ]]></literal>
    <justification jstring="[para(1934(a,1),1607(a,2,2,1))].">
      <j1 rule="para" parents="1934 1607"/>
    </justification>
  </clause>

  <clause id="1937">
    <literal><![CDATA[
      T(1 / x,(1 / x) * R(x,y,z)) = 1 / x
    ]]></literal>
    <justification jstring="[para(79(a,1),1935(a,1,2,2,1))].">
      <j1 rule="para" parents="79 1935"/>
    </justification>
  </clause>

  <clause id="1938">
    <literal><![CDATA[
      T(x \ 1,R(x,y,z) * (x \ 1)) = x \ 1
    ]]></literal>
    <justification jstring="[para(694(a,1),1935(a,1,2))].">
      <j1 rule="para" parents="694 1935"/>
    </justification>
  </clause>

  <clause id="1939">
    <literal><![CDATA[
      T(x \ 1,x \ R(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[para(1455(a,1),1935(a,1,2))].">
      <j1 rule="para" parents="1455 1935"/>
    </justification>
  </clause>

  <clause id="1940">
    <literal><![CDATA[
      T(T(x \ 1,y),x \ R(x,z,u)) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(1939(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1939 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1941">
    <literal><![CDATA[
      (R(x,y,z) * (1 / x)) / R(x,y,z) = L(1 / x,R(x,y,z),1 / x)
    ]]></literal>
    <justification jstring="[para(1937(a,1),789(a,1,1,2))].">
      <j1 rule="para" parents="1937 789"/>
    </justification>
  </clause>

  <clause id="1942">
    <literal><![CDATA[
      R(x \ 1,R(x,y,z),x \ 1) = T(x \ 1,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(1938(a,1),877(a,1,1))].">
      <j1 rule="para" parents="1938 877"/>
    </justification>
  </clause>

  <clause id="1945">
    <literal><![CDATA[
      x * (y * R(y \ (x \ y),z,u)) = (x * R(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,1149,a(flip),b,1914,a)].">
      <j1 rule="hyper" parents="65 1149 1914"/>
    </justification>
  </clause>

  <clause id="1946">
    <literal><![CDATA[
      x * ((x * y) * R((x * y) \ y,z,u)) = (x * R(x \ 1,z,u)) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,1148,a(flip),b,1914,a)].">
      <j1 rule="hyper" parents="65 1148 1914"/>
    </justification>
  </clause>

  <clause id="1948">
    <literal><![CDATA[
      (x * R(y / x,z,u)) \ (y * R(y / x,z,u)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(299,a,109,a(flip),b,1929,a),flip(a)].">
      <j1 rule="hyper" parents="299 109 1929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1949">
    <literal><![CDATA[
      T(x,y) * L((y \ (x * y)) \ (y \ z),u,w) = y \ ((x * y) * L((x * y) \ z,u,w))
    ]]></literal>
    <justification jstring="[para(22(a,2),1875(a,1,1))].">
      <j1 rule="para" parents="22 1875"/>
    </justification>
  </clause>

  <clause id="1950">
    <literal><![CDATA[
      (x * R(x \ (y * z),u,w)) / z = (x / z) * R((x / z) \ y,u,w)
    ]]></literal>
    <justification jstring="[hyper(137,a,1878,a)].">
      <j1 rule="hyper" parents="137 1878"/>
    </justification>
  </clause>

  <clause id="1951">
    <literal><![CDATA[
      (((x * (y * z)) / (x * z)) * x) * z = x * (R(y,x,z) * z)
    ]]></literal>
    <justification jstring="[hyper(275,a,1900,a)].">
      <j1 rule="hyper" parents="275 1900"/>
    </justification>
  </clause>

  <clause id="1952">
    <literal><![CDATA[
      R(x,y,z) * (x * u) = x * (R(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(11(a,1),1900(a,1,1,1))].">
      <j1 rule="para" parents="11 1900"/>
    </justification>
  </clause>

  <clause id="1953">
    <literal><![CDATA[
      x \ (R(x,y,z) * u) = R(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(640,a,1952,a)].">
      <j1 rule="hyper" parents="640 1952"/>
    </justification>
  </clause>

  <clause id="1954">
    <literal><![CDATA[
      (R(x,y,z) * u) / (R(x,y,z) * (x \ u)) = x
    ]]></literal>
    <justification jstring="[hyper(630,a,1952,a)].">
      <j1 rule="hyper" parents="630 1952"/>
    </justification>
  </clause>

  <clause id="1955">
    <literal><![CDATA[
      x * (R(x,y,z) * (x \ u)) = R(x,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(315,a,1952,a),flip(a)].">
      <j1 rule="hyper" parents="315 1952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1956">
    <literal><![CDATA[
      R(x,y,z) \ (x * (R(x,y,z) * u)) = x * u
    ]]></literal>
    <justification jstring="[hyper(125,a,1952,a)].">
      <j1 rule="hyper" parents="125 1952"/>
    </justification>
  </clause>

  <clause id="1957">
    <literal><![CDATA[
      x * (R(x,y,z) \ 1) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(119,a,71,a(flip),b,1952,a),flip(a)].">
      <j1 rule="hyper" parents="119 71 1952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1958">
    <literal><![CDATA[
      x * (R(x,y,z) * T(u,x)) = R(x,y,z) * (u * x)
    ]]></literal>
    <justification jstring="[para(107(a,1),1952(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 1952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1959">
    <literal><![CDATA[
      (R(x,y,z) * u) \ (x * (R(x,y,z) * u)) = L(T(x,u),u,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(1952(a,1),230(a,1,2))].">
      <j1 rule="para" parents="1952 230"/>
    </justification>
  </clause>

  <clause id="1960">
    <literal><![CDATA[
      (R(x,y,z) \ 1) * T(x,R(x,y,z) \ 1) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(277,a,1957,a)].">
      <j1 rule="hyper" parents="277 1957"/>
    </justification>
  </clause>

  <clause id="1961">
    <literal><![CDATA[
      L(R(x,y,z) \ 1,x,1 / x) = (1 / x) * (R(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(1957(a,1),255(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1957 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1962">
    <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(1957(a,1),1105(a,1,2,1,2))].">
      <j1 rule="para" parents="1957 1105"/>
    </justification>
  </clause>

  <clause id="1963">
    <literal><![CDATA[
      R(x,y,z) * (x \ (y * z)) = x \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(103(a,1),1953(a,1,2)),flip(a)].">
      <j1 rule="para" parents="103 1953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1964">
    <literal><![CDATA[
      R(x,y,y \ z) * (x \ z) = x \ ((x * y) * (y \ z))
    ]]></literal>
    <justification jstring="[para(347(a,1),1953(a,1,2)),flip(a)].">
      <j1 rule="para" parents="347 1953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1965">
    <literal><![CDATA[
      (R(x,y,z) * (x \ u)) \ (R(x,y,z) * u) = T(x,R(x,y,z) * (x \ u))
    ]]></literal>
    <justification jstring="[para(1954(a,1),109(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1954 109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1966">
    <literal><![CDATA[
      x \ (R(x,y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) * (x \ u) = w
    ]]></literal>
    <justification jstring="[para(1954(a,1),317(a,1,1))].">
      <j1 rule="para" parents="1954 317"/>
    </justification>
  </clause>

  <clause id="1967">
    <literal><![CDATA[
      R(x,y,z) = (x \ ((x * y) * z)) / (x \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(137,a,1963,a),flip(a)].">
      <j1 rule="hyper" parents="137 1963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1968">
    <literal><![CDATA[
      R(x,y,x) * T(y,x) = T(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(235,a,103,a(flip),b,1958,a),flip(a)].">
      <j1 rule="hyper" parents="235 103 1958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1969">
    <literal><![CDATA[
      R(x,y,x) \ T(x * y,x) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(125,a,1968,a)].">
      <j1 rule="hyper" parents="125 1968"/>
    </justification>
  </clause>

  <clause id="1970">
    <literal><![CDATA[
      x \ ((x * (x \ y)) * ((x \ y) \ z)) = ((y * ((x \ y) \ z)) / z) * (x \ z)
    ]]></literal>
    <justification jstring="[para(781(a,1),1964(a,1,1)),flip(a)].">
      <j1 rule="para" parents="781 1964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1971">
    <literal><![CDATA[
      (x * L(x \ (y / z),u,w)) * z = x * (z * L(z \ (x \ y),u,w))
    ]]></literal>
    <justification jstring="[para(12(a,1),1901(a,1,2,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 1901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1972">
    <literal><![CDATA[
      R(x,y,z) * (z * R(z \ (y * z),u,w)) = (R(x,y,z) * R(R(x,y,z) \ (x * y),u,w)) * z
    ]]></literal>
    <justification jstring="[para(182(a,1),1910(a,1,2,2,1,2))].">
      <j1 rule="para" parents="182 1910"/>
    </justification>
  </clause>

  <clause id="1973">
    <literal><![CDATA[
      (x / y) * R((x / y) \ 1,z,u) = (x * R(x \ y,z,u)) / y
    ]]></literal>
    <justification jstring="[para(7(a,1),1950(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="7 1950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1974">
    <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),1973(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20 1973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1975">
    <literal><![CDATA[
      L(T(x,y),y,R(x,z,u)) = T(x,R(x,z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(318,a,1959,a),flip(a)].">
      <j1 rule="hyper" parents="318 1959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1976">
    <literal><![CDATA[
      (x * (y * L(y \ (x \ z),u,w))) / y = x * L(x \ (z / y),u,w)
    ]]></literal>
    <justification jstring="[hyper(137,a,1971,a)].">
      <j1 rule="hyper" parents="137 1971"/>
    </justification>
  </clause>

  <clause id="1977">
    <literal><![CDATA[
      (x / y) * L((x / y) \ (z / y),u,w) = (x * L(x \ z,u,w)) / y
    ]]></literal>
    <justification jstring="[hyper(120,a,1821,a(flip),b,1971,a),flip(a)].">
      <j1 rule="hyper" parents="120 1821 1971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1978">
    <literal><![CDATA[
      x \ (y * (x * L(x \ (y \ z),u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(y * L(y \ (z / x),u,w),x) = v5
    ]]></literal>
    <justification jstring="[para(1971(a,1),318(a,1,2))].">
      <j1 rule="para" parents="1971 318"/>
    </justification>
  </clause>

  <clause id="1979">
    <literal><![CDATA[
      (x * (y * L(y \ (x \ x),z,u))) / y = (x / y) * (y * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,1310,a,b,1976,a),flip(a)].">
      <j1 rule="hyper" parents="299 1310 1976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1980">
    <literal><![CDATA[
      (x * L(x \ (y * x),z,u)) / y = (x / y) * L(T(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(1531(a,2),1977(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1531 1977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1981">
    <literal><![CDATA[
      (x / y) * L(T(y,x),z,u) = (L(y,z,u) * x) / y
    ]]></literal>
    <justification jstring="[para(682(a,1),1980(a,1,1)),flip(a)].">
      <j1 rule="para" parents="682 1980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1982">
    <literal><![CDATA[
      (L(x,y,z) * (u * x)) / x = u * L(T(x,u * x),y,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),1981(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 1981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1983">
    <literal><![CDATA[
      T(x * L(T(y,x * y),z,u),y) = y \ (L(y,z,u) * (x * y))
    ]]></literal>
    <justification jstring="[para(1982(a,1),109(a,1,1))].">
      <j1 rule="para" parents="1982 109"/>
    </justification>
  </clause>

  <clause id="1984">
    <literal><![CDATA[
      T(x * L(T(y,x * y),z,u),y) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,1364,a(flip),b,1983,a),flip(a)].">
      <j1 rule="hyper" parents="299 1364 1983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1985">
    <literal><![CDATA[
      a(x,y,z) = L(L(z,y,x) \ z,L(z,y,x),x * y)
    ]]></literal>
    <justification jstring="[hyper(299,a,14,a,b,531,a)].">
      <j1 rule="hyper" parents="299 14 531"/>
    </justification>
  </clause>

  <clause id="1986">
    <literal><![CDATA[
      L(x,y,y) \ x = a(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,478,a(flip),b,1985,a)].">
      <j1 rule="hyper" parents="299 478 1985"/>
    </justification>
  </clause>

  <clause id="1987">
    <literal><![CDATA[
      L(x,y,y) * a(y,y,x) = x
    ]]></literal>
    <justification jstring="[hyper(144,a,1986,a)].">
      <j1 rule="hyper" parents="144 1986"/>
    </justification>
  </clause>

  <clause id="1988">
    <literal><![CDATA[
      L(x,y,y) * z != x
    ]]></literal>
    <literal><![CDATA[
      a(y,y,x) = z
    ]]></literal>
    <justification jstring="[para(1987(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="1987 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1989">
    <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(976(a,1),554(a,1,1))].">
      <j1 rule="para" parents="976 554"/>
    </justification>
  </clause>

  <clause id="1990">
    <literal><![CDATA[
      (x * ((y * y) \ z)) \ (x * (((y * y) \ z) * u)) = L(u,z,x / (y * y))
    ]]></literal>
    <justification jstring="[para(836(a,1),833(a,1,2))].">
      <j1 rule="para" parents="836 833"/>
    </justification>
  </clause>

  <clause id="1991">
    <literal><![CDATA[
      ((x * y) * ((y \ (y * y)) \ z)) / z = R(x,y \ 1,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(745(a,1),1086(a,1,1,2))].">
      <j1 rule="para" parents="745 1086"/>
    </justification>
  </clause>

  <clause id="1992">
    <literal><![CDATA[
      R(x,y \ 1,(y \ 1) \ z) = ((x * y) * (y \ z)) / z
    ]]></literal>
    <justification jstring="[para(9(a,1),1991(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 1991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1993">
    <literal><![CDATA[
      (x * (y \ 1)) * ((y \ 1) \ z) = (x * y) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(782,a,1992,a)].">
      <j1 rule="hyper" parents="782 1992"/>
    </justification>
  </clause>

  <clause id="1994">
    <literal><![CDATA[
      (x * (y \ 1)) * ((y \ 1) \ 1) = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,1246,a(flip),b,1993,a),flip(a)].">
      <j1 rule="hyper" parents="299 1246 1993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1995">
    <literal><![CDATA[
      (x * (y \ 1)) * ((y \ 1) \ 1) = (x * (1 / y)) * y
    ]]></literal>
    <justification jstring="[hyper(299,a,1754,a,b,1994,a),flip(a)].">
      <j1 rule="hyper" parents="299 1754 1994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1998">
    <literal><![CDATA[
      ((x * (y * (z \ 1))) / x) / (z \ 1) = z * ((x * (z \ y)) / x)
    ]]></literal>
    <justification jstring="[para(979(a,1),1097(a,1,1))].">
      <j1 rule="para" parents="979 1097"/>
    </justification>
  </clause>

  <clause id="1999">
    <literal><![CDATA[
      ((x * (y * ((1 / z) \ 1))) / x) / z = (1 / z) * ((x * ((1 / z) \ y)) / x)
    ]]></literal>
    <justification jstring="[para(79(a,1),1998(a,1,2))].">
      <j1 rule="para" parents="79 1998"/>
    </justification>
  </clause>

  <clause id="2000">
    <literal><![CDATA[
      (x * ((x \ 1) \ ((y * z) * u))) / (z * u) = R(x * ((x \ 1) \ y),z,u)
    ]]></literal>
    <justification jstring="[para(1174(a,1),1176(a,1,1))].">
      <j1 rule="para" parents="1174 1176"/>
    </justification>
  </clause>

  <clause id="2001">
    <literal><![CDATA[
      T(T(R(x,y,y \ 1),x * y) / (y \ 1),R(x,y,y \ 1)) = x * y
    ]]></literal>
    <justification jstring="[para(258(a,1),1423(a,1,2))].">
      <j1 rule="para" parents="258 1423"/>
    </justification>
  </clause>

  <clause id="2002">
    <literal><![CDATA[
      T(R(T(x,x * y),y,y \ 1) / (y \ 1),R(x,y,y \ 1)) = x * y
    ]]></literal>
    <justification jstring="[para(27(a,2),2001(a,1,1,1))].">
      <j1 rule="para" parents="27 2001"/>
    </justification>
  </clause>

  <clause id="2003">
    <literal><![CDATA[
      T(T(x,x * y) * y,R(x,y,y \ 1)) = x * y
    ]]></literal>
    <justification jstring="[para(423(a,1),2002(a,1,1))].">
      <j1 rule="para" parents="423 2002"/>
    </justification>
  </clause>

  <clause id="2004">
    <literal><![CDATA[
      T(T(T(x,x * y) * y,z),R(x,y,y \ 1)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(2003(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2003 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2005">
    <literal><![CDATA[
      T(x * y,R(x,y,y \ 1)) = T(x * y,T(x,y))
    ]]></literal>
    <justification jstring="[para(1103(a,1),2004(a,1,1))].">
      <j1 rule="para" parents="1103 2004"/>
    </justification>
  </clause>

  <clause id="2006">
    <literal><![CDATA[
      T((x / y) * y,T(x / y,y)) = T(x,R(x / y,y,y \ 1))
    ]]></literal>
    <justification jstring="[para(12(a,1),2005(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12 2005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2007">
    <literal><![CDATA[
      T((x / y) * y,T(x / y,y)) = T(x,x * (y \ 1))
    ]]></literal>
    <justification jstring="[para(565(a,1),2006(a,2,2))].">
      <j1 rule="para" parents="565 2006"/>
    </justification>
  </clause>

  <clause id="2008">
    <literal><![CDATA[
      T(x,T(x / y,y)) = T(x,x * (y \ 1))
    ]]></literal>
    <justification jstring="[para(12(a,1),2007(a,1,1))].">
      <j1 rule="para" parents="12 2007"/>
    </justification>
  </clause>

  <clause id="2009">
    <literal><![CDATA[
      T(x,x * (y \ 1)) = T(x,y \ x)
    ]]></literal>
    <justification jstring="[para(109(a,1),2008(a,1,2)),flip(a)].">
      <j1 rule="para" parents="109 2008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2010">
    <literal><![CDATA[
      T(x,(1 / y) \ x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[para(79(a,1),2009(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="79 2009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2011">
    <literal><![CDATA[
      (T(x,y) * ((T(x,y) \ x) / x)) * x = T(x,(1 * x) / (x * T(x,y)))
    ]]></literal>
    <justification jstring="[para(570(a,1),1468(a,2,2))].">
      <j1 rule="para" parents="570 1468"/>
    </justification>
  </clause>

  <clause id="2012">
    <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),2011(a,2,2,1))].">
      <j1 rule="para" parents="7 2011"/>
    </justification>
  </clause>

  <clause id="2013">
    <literal><![CDATA[
      L((x \ 1) * (x \ y),x \ 1,x) = 1 \ ((x \ 1) * ((x \ 1) * y))
    ]]></literal>
    <justification jstring="[para(468(a,1),1766(a,1,1))].">
      <j1 rule="para" parents="468 1766"/>
    </justification>
  </clause>

  <clause id="2014">
    <literal><![CDATA[
      x \ (((T(y,x) \ y) * x) \ x) = ((T(y,x) \ y) * x) \ 1
    ]]></literal>
    <justification jstring="[para(1848(a,1),1850(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1848 1850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2015">
    <literal><![CDATA[
      L(x,(y * y) \ z,u) = L(x,z,u / (y * y))
    ]]></literal>
    <justification jstring="[hyper(493,a,1990,a)].">
      <j1 rule="hyper" parents="493 1990"/>
    </justification>
  </clause>

  <clause id="2016">
    <literal><![CDATA[
      L(x,y,z / (u * u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,(u * u) \ y,z) = w
    ]]></literal>
    <justification jstring="[para(1990(a,1),493(a,1))].">
      <j1 rule="para" parents="1990 493"/>
    </justification>
  </clause>

  <clause id="2017">
    <literal><![CDATA[
      L(x,y,1 / (z * z)) = x
    ]]></literal>
    <justification jstring="[hyper(505,a,2015,a),flip(a)].">
      <j1 rule="hyper" parents="505 2015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2018">
    <literal><![CDATA[
      L(x,(y * y) \ 1,z) = x
    ]]></literal>
    <justification jstring="[hyper(299,a,496,a(flip),b,2015,a),flip(a)].">
      <j1 rule="hyper" parents="299 496 2015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2019">
    <literal><![CDATA[
      L(x,y,(z * z) \ 1) = x
    ]]></literal>
    <justification jstring="[para(458(a,1),2017(a,1,3))].">
      <j1 rule="para" parents="458 2017"/>
    </justification>
  </clause>

  <clause id="2020">
    <literal><![CDATA[
      L(x,y \ (y \ 1),z) = x
    ]]></literal>
    <justification jstring="[para(727(a,1),2018(a,1,2))].">
      <j1 rule="para" parents="727 2018"/>
    </justification>
  </clause>

  <clause id="2021">
    <literal><![CDATA[
      L(x,y,(z * z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(2019(a,1),52(a,2))].">
      <j1 rule="para" parents="2019 52"/>
    </justification>
  </clause>

  <clause id="2022">
    <literal><![CDATA[
      L(x,(y / (z * z)) \ ((z * z) * (y \ 1)),u) = x
    ]]></literal>
    <justification jstring="[para(416(a,1),2020(a,1,2,2))].">
      <j1 rule="para" parents="416 2020"/>
    </justification>
  </clause>

  <clause id="2023">
    <literal><![CDATA[
      L(x,(y * y) * (z \ ((y * y) * (z \ 1))),u) = x
    ]]></literal>
    <justification jstring="[para(416(a,1),2022(a,1,2))].">
      <j1 rule="para" parents="416 2022"/>
    </justification>
  </clause>

  <clause id="2024">
    <literal><![CDATA[
      L(x,(y * y) * (z \ ((y * y) * (z \ 1))),u) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(2023(a,1),52(a,2))].">
      <j1 rule="para" parents="2023 52"/>
    </justification>
  </clause>

  <clause id="2025">
    <literal><![CDATA[
      x * ((x \ 1) \ (((y * z) * u) / (z * u))) = R(x * ((x \ 1) \ y),z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,1768,a(flip),b,2000,a)].">
      <j1 rule="hyper" parents="65 1768 2000"/>
    </justification>
  </clause>

  <clause id="2026">
    <literal><![CDATA[
      R(x * ((x \ 1) \ y),z,u) = x * ((x \ 1) \ R(y,z,u))
    ]]></literal>
    <justification jstring="[para(20(a,2),2025(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="20 2025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2028">
    <literal><![CDATA[
      L(a(x,y,y),x * (y * y),z) != u
    ]]></literal>
    <literal><![CDATA[
      (y * y) \ ((z * x) \ (z * ((x * y) * y))) = u
    ]]></literal>
    <justification jstring="[para(523(a,1),1015(a,1))].">
      <j1 rule="para" parents="523 1015"/>
    </justification>
  </clause>

  <clause id="2029">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ y,z) = T(x * T(x \ y,z),y)
    ]]></literal>
    <justification jstring="[hyper(235,a,1462,a(flip),b,1323,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="235 1462 1323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2030">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (y * x),x) = y * L(x,T(x,y) \ x,T(x,y))
    ]]></literal>
    <justification jstring="[para(1211(a,1),1323(a,2,2))].">
      <j1 rule="para" parents="1211 1323"/>
    </justification>
  </clause>

  <clause id="2031">
    <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),2030(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="16 2030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2032">
    <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),1390(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="16 1390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2033">
    <literal><![CDATA[
      (x * y) * (K(y,x) * T(K(y,x) \ 1,z)) = (y * x) * T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(1290(a,1),2032(a,1,2))].">
      <j1 rule="para" parents="1290 2032"/>
    </justification>
  </clause>

  <clause id="2034">
    <literal><![CDATA[
      (x * y) \ ((y * x) * T(K(x,y),z)) = K(y,x) * T(K(y,x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,2033,a)].">
      <j1 rule="hyper" parents="125 2033"/>
    </justification>
  </clause>

  <clause id="2035">
    <literal><![CDATA[
      K(((x \ y) * (y \ x)) \ (x \ y),(x \ y) * (y \ x)) = y \ (x * (x \ y))
    ]]></literal>
    <justification jstring="[para(1864(a,1),1392(a,2,2,2))].">
      <j1 rule="para" parents="1864 1392"/>
    </justification>
  </clause>

  <clause id="2036">
    <literal><![CDATA[
      (x \ y) \ K(T(x / y,T(y,x)),T(y,x)) = T((x \ y) \ 1,T(y,x))
    ]]></literal>
    <justification jstring="[para(1530(a,1),1440(a,1,2,1))].">
      <j1 rule="para" parents="1530 1440"/>
    </justification>
  </clause>

  <clause id="2037">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ 1,T(y,x)) = K(T(x / y,T(y,x)),T(y,x))
    ]]></literal>
    <justification jstring="[hyper(144,a,2036,a)].">
      <j1 rule="hyper" parents="144 2036"/>
    </justification>
  </clause>

  <clause id="2038">
    <literal><![CDATA[
      K(T(x / y,T(y,x)),T(y,x)) = x \ (y * T(y \ x,T(y,x)))
    ]]></literal>
    <justification jstring="[hyper(65,a,1383,a(flip),b,2037,a),flip(a)].">
      <j1 rule="hyper" parents="65 1383 2037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2039">
    <literal><![CDATA[
      K(x \ (x / ((y \ x) / T(x,y))),x) = x / T(x,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),1447(a,2,1))].">
      <j1 rule="para" parents="10 1447"/>
    </justification>
  </clause>

  <clause id="2040">
    <literal><![CDATA[
      T(L(1 / x,R(x,y,z),1 / x),x) = (x \ R(x,y,z)) / R(x,y,z)
    ]]></literal>
    <justification jstring="[para(1941(a,1),1460(a,1,1))].">
      <j1 rule="para" parents="1941 1460"/>
    </justification>
  </clause>

  <clause id="2041">
    <literal><![CDATA[
      L(x \ 1,R(x,y,z),1 / x) = (x \ R(x,y,z)) / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(966,a,2040,a)].">
      <j1 rule="hyper" parents="966 2040"/>
    </justification>
  </clause>

  <clause id="2042">
    <literal><![CDATA[
      (x \ T(x * (y / z),z)) * z = (x \ 1) * ((z \ ((x \ 1) \ y)) * z)
    ]]></literal>
    <justification jstring="[para(107(a,1),1594(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 1594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2043">
    <literal><![CDATA[
      T((x \ (x * (y / x))) * x,x) = (x \ 1) * ((x \ ((x \ 1) \ y)) * x)
    ]]></literal>
    <justification jstring="[hyper(65,a,1604,a,b,2042,a)].">
      <j1 rule="hyper" parents="65 1604 2042"/>
    </justification>
  </clause>

  <clause id="2044">
    <literal><![CDATA[
      T(x,y) = (y \ 1) * ((y \ ((y \ 1) \ x)) * y)
    ]]></literal>
    <justification jstring="[para(80(a,1),2043(a,1,1))].">
      <j1 rule="para" parents="80 2043"/>
    </justification>
  </clause>

  <clause id="2045">
    <literal><![CDATA[
      (x \ ((x \ 1) \ y)) * x = (x \ 1) \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,2044,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="119 2044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2046">
    <literal><![CDATA[
      (x \ 1) * ((x \ y) * x) = T((x \ 1) * y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),2044(a,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9 2044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2048">
    <literal><![CDATA[
      T((x \ 1) * (x * y),x) = (x \ 1) * (y * x)
    ]]></literal>
    <justification jstring="[para(9(a,1),2046(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 2046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2049">
    <literal><![CDATA[
      T((x \ 1) * ((y \ x) * y),x) = (x \ 1) * (K(y \ x,y) * x)
    ]]></literal>
    <justification jstring="[para(89(a,1),2046(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="89 2046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2050">
    <literal><![CDATA[
      ((x \ 1) * y) \ T((x \ 1) * y,x) = L(K(x \ y,x),y,x \ 1)
    ]]></literal>
    <justification jstring="[para(2046(a,1),452(a,1,2))].">
      <j1 rule="para" parents="2046 452"/>
    </justification>
  </clause>

  <clause id="2051">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) * x = x * ((x \ 1) * (y * x))
    ]]></literal>
    <justification jstring="[para(2048(a,1),107(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2048 107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2052">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) * x = L(y * x,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,252,a(flip),b,2051,a),flip(a)].">
      <j1 rule="hyper" parents="299 252 2051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2053">
    <literal><![CDATA[
      x \ (y * ((z * (y \ (x * u))) / z)) = (x \ y) * ((z * ((x \ y) \ u)) / z)
    ]]></literal>
    <justification jstring="[hyper(125,a,1643,a)].">
      <j1 rule="hyper" parents="125 1643"/>
    </justification>
  </clause>

  <clause id="2054">
    <literal><![CDATA[
      x * ((x \ y) * ((z * ((x \ y) \ 1)) / z)) = y * ((z * (y \ x)) / z)
    ]]></literal>
    <justification jstring="[para(8(a,1),1643(a,2,2,1,2,2))].">
      <j1 rule="para" parents="8 1643"/>
    </justification>
  </clause>

  <clause id="2055">
    <literal><![CDATA[
      x * K(y,(y / (x \ z)) / y) = z * ((y * (z \ (x * 1))) / y)
    ]]></literal>
    <justification jstring="[para(1880(a,2),1643(a,1,2))].">
      <j1 rule="para" parents="1880 1643"/>
    </justification>
  </clause>

  <clause id="2056">
    <literal><![CDATA[
      x * K(y,(y / (x \ z)) / y) = z * ((y * (z \ x)) / y)
    ]]></literal>
    <justification jstring="[para(8(a,1),2055(a,2,2,1,2,2))].">
      <j1 rule="para" parents="8 2055"/>
    </justification>
  </clause>

  <clause id="2057">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ y)) / z) = y * K(z,(z / T(x,y)) / z)
    ]]></literal>
    <justification jstring="[para(22(a,2),2056(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="22 2056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2058">
    <literal><![CDATA[
      (x * (y * z)) * (((z \ 1) * (z \ 1)) * u) = (x * (y * (1 / z))) * u
    ]]></literal>
    <justification jstring="[para(8(a,1),1746(a,2,1,2))].">
      <j1 rule="para" parents="8 1746"/>
    </justification>
  </clause>

  <clause id="2059">
    <literal><![CDATA[
      (x * (y * z)) * ((z \ 1) * (z \ u)) = (x * (y * (1 / z))) * u
    ]]></literal>
    <justification jstring="[para(468(a,1),2058(a,1,2))].">
      <j1 rule="para" parents="468 2058"/>
    </justification>
  </clause>

  <clause id="2060">
    <literal><![CDATA[
      R(x,y,z) * (T(x,u) \ 1) = T(x,u) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),1852(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 1852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2061">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) * (x * u) = x * ((x * L(x \ 1,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(1858(a,1),1870(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1858 1870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2062">
    <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(1273(a,1),2061(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1273 2061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2063">
    <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),1911(a,1,1))].">
      <j1 rule="para" parents="22 1911"/>
    </justification>
  </clause>

  <clause id="2064">
    <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),2063(a,1,2,1,1))].">
      <j1 rule="para" parents="22 2063"/>
    </justification>
  </clause>

  <clause id="2065">
    <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),2064(a,2,1,2,1))].">
      <j1 rule="para" parents="9 2064"/>
    </justification>
  </clause>

  <clause id="2066">
    <literal><![CDATA[
      T(x * ((x * R(x \ 1,y,z)) / x),x) = x * R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(699(a,1),1936(a,2,2))].">
      <j1 rule="para" parents="699 1936"/>
    </justification>
  </clause>

  <clause id="2067">
    <literal><![CDATA[
      T(x * R(1 / x,y,z),x) = x * R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(699(a,1),2066(a,1,1,2))].">
      <j1 rule="para" parents="699 2066"/>
    </justification>
  </clause>

  <clause id="2068">
    <literal><![CDATA[
      T(x * (y / (x * y)),x) = x * R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[para(216(a,1),2067(a,1,1,2))].">
      <j1 rule="para" parents="216 2067"/>
    </justification>
  </clause>

  <clause id="2069">
    <literal><![CDATA[
      T(x * (y / (x * y)),x) = x * (y / (x * y))
    ]]></literal>
    <justification jstring="[para(216(a,1),2068(a,2,2))].">
      <j1 rule="para" parents="216 2068"/>
    </justification>
  </clause>

  <clause id="2070">
    <literal><![CDATA[
      T(x,x * (y / (x * y))) = x
    ]]></literal>
    <justification jstring="[hyper(56,a,2069,a)].">
      <j1 rule="hyper" parents="56 2069"/>
    </justification>
  </clause>

  <clause id="2071">
    <literal><![CDATA[
      T(x,x * ((x \ y) / y)) = x
    ]]></literal>
    <justification jstring="[para(10(a,1),2070(a,1,2,2,2))].">
      <j1 rule="para" parents="10 2070"/>
    </justification>
  </clause>

  <clause id="2072">
    <literal><![CDATA[
      T(x / y,(x / y) * (y / x)) = x / y
    ]]></literal>
    <justification jstring="[para(12(a,1),2070(a,1,2,2,2))].">
      <j1 rule="para" parents="12 2070"/>
    </justification>
  </clause>

  <clause id="2073">
    <literal><![CDATA[
      T((x \ y) \ y,x * ((x \ z) / z)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(2071(a,1),297(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2071 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2074">
    <literal><![CDATA[
      T(x \ y,(y / x) * (x / y)) = T(y / x,x)
    ]]></literal>
    <justification jstring="[para(2072(a,1),242(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2072 242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2075">
    <literal><![CDATA[
      T(x \ y,(y / x) * (x / y)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(299,a,109,a(flip),b,2074,a),flip(a)].">
      <j1 rule="hyper" parents="299 109 2074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2076">
    <literal><![CDATA[
      K(((x / y) * (y / x)) \ (x / y),(x / y) * (y / x)) = (y * (y \ x)) / x
    ]]></literal>
    <justification jstring="[para(2075(a,1),1403(a,2,1,2))].">
      <j1 rule="para" parents="2075 1403"/>
    </justification>
  </clause>

  <clause id="2077">
    <literal><![CDATA[
      K((x * ((x \ y) / y)) \ x,x * ((x \ y) / y)) = ((x \ y) * T(x,x \ y)) / y
    ]]></literal>
    <justification jstring="[para(2073(a,1),1403(a,2,1,2))].">
      <j1 rule="para" parents="2073 1403"/>
    </justification>
  </clause>

  <clause id="2078">
    <literal><![CDATA[
      (x * R(x \ 1,y,z)) * (x * u) = x * ((x * R(x \ 1,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(1914(a,1),1946(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1914 1946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2079">
    <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(1455(a,1),2078(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1455 2078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2080">
    <literal><![CDATA[
      ((x * ((y \ x) \ z)) / z) * (y \ z) = y \ (x * ((y \ x) \ z))
    ]]></literal>
    <justification jstring="[para(10(a,1),1970(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 1970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2081">
    <literal><![CDATA[
      (x * (y * L(y \ 1,z,u))) / y = (x / y) * (y * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(68(a,1),1979(a,1,1,2,2,1,2))].">
      <j1 rule="para" parents="68 1979"/>
    </justification>
  </clause>

  <clause id="2083">
    <literal><![CDATA[
      (1 / x) * ((y * ((1 / x) \ z)) / y) = ((y * (z * x)) / y) / x
    ]]></literal>
    <justification jstring="[para(79(a,1),1999(a,1,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="79 1999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2084">
    <literal><![CDATA[
      ((x * (x * y)) / x) / y = T(x,x / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(65,a,1441,a(flip),b,2083,a),flip(a)].">
      <j1 rule="hyper" parents="65 1441 2083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2085">
    <literal><![CDATA[
      (1 / x) * ((y * ((1 / x) \ 1)) / y) = ((y * x) / y) / x
    ]]></literal>
    <justification jstring="[para(7(a,1),2083(a,2,1,1,2))].">
      <j1 rule="para" parents="7 2083"/>
    </justification>
  </clause>

  <clause id="2086">
    <literal><![CDATA[
      T(x,x / (1 / (x \ y))) = ((x * y) / x) / (x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),2084(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10 2084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2087">
    <literal><![CDATA[
      R(T(x,x / (1 / y)),y,x) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[para(2084(a,1),1566(a,1,1))].">
      <j1 rule="para" parents="2084 1566"/>
    </justification>
  </clause>

  <clause id="2088">
    <literal><![CDATA[
      T(x,x / (1 / (x \ y))) = T(x,x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(299,a,1590,a(flip),b,2086,a),flip(a)].">
      <j1 rule="hyper" parents="299 1590 2086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2089">
    <literal><![CDATA[
      T(x,x / (x / (x * y))) = T(x,x / (1 / y))
    ]]></literal>
    <justification jstring="[para(9(a,1),2088(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="9 2088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2090">
    <literal><![CDATA[
      K(((x \ y) * (y \ x)) \ (x \ y),(x \ y) * (y \ x)) = 1
    ]]></literal>
    <justification jstring="[hyper(299,a,248,a(flip),b,2035,a),flip(a)].">
      <j1 rule="hyper" parents="299 248 2035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2092">
    <literal><![CDATA[
      T(1 / (x \ y),(y \ x) * (x \ y)) = 1 / (x \ y)
    ]]></literal>
    <justification jstring="[para(2090(a,1),1235(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2090 1235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2093">
    <literal><![CDATA[
      (x \ y) * ((z * ((x \ y) \ (x \ u))) / z) = x \ (y * ((z * (y \ u)) / z))
    ]]></literal>
    <justification jstring="[para(10(a,1),2053(a,1,2,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 2053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2094">
    <literal><![CDATA[
      K(((x / y) * (y / x)) \ (x / y),(x / y) * (y / x)) = x / x
    ]]></literal>
    <justification jstring="[para(10(a,1),2076(a,2,1))].">
      <j1 rule="para" parents="10 2076"/>
    </justification>
  </clause>

  <clause id="2095">
    <literal><![CDATA[
      K(((x / y) * (y / x)) \ (x / y),(x / y) * (y / x)) = 1
    ]]></literal>
    <justification jstring="[hyper(299,a,73,a(flip),b,2094,a),flip(a)].">
      <j1 rule="hyper" parents="299 73 2094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2097">
    <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),114(a,1,2,1))].">
      <j1 rule="para" parents="33 114"/>
    </justification>
  </clause>

  <clause id="2098">
    <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),116(a,1,2,1))].">
      <j1 rule="para" parents="34 116"/>
    </justification>
  </clause>

  <clause id="2099">
    <literal><![CDATA[
      L((x * x) \ (y \ ((x * x) * z)),x * x,(x * x) \ y) = T(y,x * x) \ z
    ]]></literal>
    <justification jstring="[para(666(a,1),761(a,1,1,2))].">
      <j1 rule="para" parents="666 761"/>
    </justification>
  </clause>

  <clause id="2100">
    <literal><![CDATA[
      L((x * (y * z)) / (x * y),u,w) = (x * (y * L(z,u,w))) / (x * y)
    ]]></literal>
    <justification jstring="[para(489(a,1),962(a,1,1)),flip(a)].">
      <j1 rule="para" parents="489 962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2101">
    <literal><![CDATA[
      L((x * (y * z)) / (x * y),u,w) != v5 / (x * y)
    ]]></literal>
    <literal><![CDATA[
      x * (y * L(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(2100(a,2),48(a,1))].">
      <j1 rule="para" parents="2100 48"/>
    </justification>
  </clause>

  <clause id="2102">
    <literal><![CDATA[
      a(x,y / (z * z),u) = a(x,y,(z * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,832,a(flip),b,1083,a)].">
      <j1 rule="hyper" parents="65 832 1083"/>
    </justification>
  </clause>

  <clause id="2103">
    <literal><![CDATA[
      a(x,y * (z * z),(z * z) \ u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(11(a,1),2102(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11 2102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2104">
    <literal><![CDATA[
      a(x,y * (z * z),u) = a(x,y,(z * z) * u)
    ]]></literal>
    <justification jstring="[para(9(a,1),2103(a,1,3))].">
      <j1 rule="para" parents="9 2103"/>
    </justification>
  </clause>

  <clause id="2105">
    <literal><![CDATA[
      (T(x,y) * (1 / x)) / T(x,y) = L(1 / x,T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[hyper(65,a,1489,a(flip),b,1129,a)].">
      <j1 rule="hyper" parents="65 1489 1129"/>
    </justification>
  </clause>

  <clause id="2107">
    <literal><![CDATA[
      T(L(1 / x,T(x,y),1 / x),x) = (T(x,y) * (x \ 1)) / T(x,y)
    ]]></literal>
    <justification jstring="[para(2105(a,1),755(a,1,1))].">
      <j1 rule="para" parents="2105 755"/>
    </justification>
  </clause>

  <clause id="2108">
    <literal><![CDATA[
      (T(x,y) * (x \ 1)) / T(x,y) = L(x \ 1,T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[hyper(966,a,2107,a),flip(a)].">
      <j1 rule="hyper" parents="966 2107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2109">
    <literal><![CDATA[
      x * L(x \ 1,T(x,y),1 / x) = K(T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[para(2108(a,1),1884(a,1,2))].">
      <j1 rule="para" parents="2108 1884"/>
    </justification>
  </clause>

  <clause id="2110">
    <literal><![CDATA[
      (L(x \ 1,x,y) * y) / L(x \ 1,x,y) = y * (x * T(x \ 1,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,487,a(flip),b,1535,a),flip(a)].">
      <j1 rule="hyper" parents="299 487 1535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2111">
    <literal><![CDATA[
      T(x,x * (y * T(y \ 1,x))) = x
    ]]></literal>
    <justification jstring="[para(2110(a,1),449(a,1,2))].">
      <j1 rule="para" parents="2110 449"/>
    </justification>
  </clause>

  <clause id="2112">
    <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(2110(a,1),1414(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2110 1414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2113">
    <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(2110(a,1),1584(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2110 1584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2114">
    <literal><![CDATA[
      T(x,x * K(y,x)) = x
    ]]></literal>
    <justification jstring="[para(1377(a,2),2111(a,1,2,2))].">
      <j1 rule="para" parents="1377 2111"/>
    </justification>
  </clause>

  <clause id="2115">
    <literal><![CDATA[
      T(x,x * (y \ (z * T(z \ y,x)))) = x
    ]]></literal>
    <justification jstring="[para(1383(a,1),2111(a,1,2,2))].">
      <j1 rule="para" parents="1383 2111"/>
    </justification>
  </clause>

  <clause id="2116">
    <literal><![CDATA[
      T(x * K(y,x),x) = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(56,a,2114,a)].">
      <j1 rule="hyper" parents="56 2114"/>
    </justification>
  </clause>

  <clause id="2117">
    <literal><![CDATA[
      T(x,x * (T(x,y) \ ((y \ x) * ((y \ x) \ x)))) = x
    ]]></literal>
    <justification jstring="[para(1446(a,1),2115(a,1,2,2,2,2))].">
      <j1 rule="para" parents="1446 2115"/>
    </justification>
  </clause>

  <clause id="2118">
    <literal><![CDATA[
      T(x,x * (T(x,y) \ x)) = x
    ]]></literal>
    <justification jstring="[para(10(a,1),2117(a,1,2,2,2))].">
      <j1 rule="para" parents="10 2117"/>
    </justification>
  </clause>

  <clause id="2119">
    <literal><![CDATA[
      T(T(x,y),x * (T(x,z) \ x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2118(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2118 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2120">
    <literal><![CDATA[
      (x * (T(x,y) \ x)) \ (x * x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,1206,a(flip),b,2119,a)].">
      <j1 rule="hyper" parents="65 1206 2119"/>
    </justification>
  </clause>

  <clause id="2121">
    <literal><![CDATA[
      (x * x) / T(x,y) = x * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(192,a,2120,a)].">
      <j1 rule="hyper" parents="192 2120"/>
    </justification>
  </clause>

  <clause id="2122">
    <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(1848(a,1),2120(a,1,1,2,1))].">
      <j1 rule="para" parents="1848 2120"/>
    </justification>
  </clause>

  <clause id="2123">
    <literal><![CDATA[
      T(x / T(x,y),x) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(1559,a,2121,a)].">
      <j1 rule="hyper" parents="1559 2121"/>
    </justification>
  </clause>

  <clause id="2124">
    <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(2121(a,2),790(a,1,2))].">
      <j1 rule="para" parents="2121 790"/>
    </justification>
  </clause>

  <clause id="2125">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ x,x) = (T(x,y) \ x) * T(x,y)
    ]]></literal>
    <justification jstring="[para(2123(a,1),432(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2123 432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2126">
    <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),2097(a,1,2))].">
      <j1 rule="para" parents="33 2097"/>
    </justification>
  </clause>

  <clause id="2127">
    <literal><![CDATA[
      (x * x) \ (y \ ((x * x) * z)) = T(y,x * x) \ z
    ]]></literal>
    <justification jstring="[hyper(497,a,2099,a)].">
      <j1 rule="hyper" parents="497 2099"/>
    </justification>
  </clause>

  <clause id="2129">
    <literal><![CDATA[
      (x * (((T(y,x) \ y) * x) \ x)) \ (x * x) = (T(y,x) \ y) * x
    ]]></literal>
    <justification jstring="[hyper(299,a,1848,a(flip),b,2122,a),flip(a)].">
      <j1 rule="hyper" parents="299 1848 2122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2130">
    <literal><![CDATA[
      L(a(x,y,z),x * (y * z),u * u) = a((u * u) * x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,523,a(flip),b,2126,a)].">
      <j1 rule="hyper" parents="65 523 2126"/>
    </justification>
  </clause>

  <clause id="2131">
    <literal><![CDATA[
      a((x * x) * y,z,u) = a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(503,a,2130,a),flip(a)].">
      <j1 rule="hyper" parents="503 2130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2133">
    <literal><![CDATA[
      a((x * x) \ y,z,u) = a(y,z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),2131(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 2131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2134">
    <literal><![CDATA[
      a(1 / x,y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(217(a,1),2131(a,1,1)),flip(a)].">
      <j1 rule="para" parents="217 2131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2135">
    <literal><![CDATA[
      a((1 / x) * y,z,u) = a(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(265(a,1),2131(a,1,1)),flip(a)].">
      <j1 rule="para" parents="265 2131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2136">
    <literal><![CDATA[
      a(x * (x * y),z,u) = a(L(y,x,x),z,u)
    ]]></literal>
    <justification jstring="[para(94(a,1),2131(a,1,1))].">
      <j1 rule="para" parents="94 2131"/>
    </justification>
  </clause>

  <clause id="2137">
    <literal><![CDATA[
      a((x \ 1) \ y,z,u) = a(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(724(a,1),2131(a,1,1))].">
      <j1 rule="para" parents="724 2131"/>
    </justification>
  </clause>

  <clause id="2138">
    <literal><![CDATA[
      a(x \ 1,y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(76(a,1),2134(a,1,1)),flip(a)].">
      <j1 rule="para" parents="76 2134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2139">
    <literal><![CDATA[
      ((1 / x) * (K(x,y) * z)) * a(x,K(x,y),z) = (K(x,y) * (1 / x)) * z
    ]]></literal>
    <justification jstring="[para(2134(a,1),1513(a,1,2))].">
      <j1 rule="para" parents="2134 1513"/>
    </justification>
  </clause>

  <clause id="2140">
    <literal><![CDATA[
      a(1 / x,y,z) = a(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,2134,a,b,2138,a)].">
      <j1 rule="hyper" parents="299 2134 2138"/>
    </justification>
  </clause>

  <clause id="2141">
    <literal><![CDATA[
      a((x * x) \ (y \ 1),z,u) = a(y * (x * x),z,u)
    ]]></literal>
    <justification jstring="[para(419(a,1),2138(a,1,1))].">
      <j1 rule="para" parents="419 2138"/>
    </justification>
  </clause>

  <clause id="2142">
    <literal><![CDATA[
      a(x * (y * y),z,u) = a(x \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,2133,a(flip),b,2141,a),flip(a)].">
      <j1 rule="hyper" parents="65 2133 2141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2144">
    <literal><![CDATA[
      a(x * (y * y),z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,2138,a(flip),b,2142,a),flip(a)].">
      <j1 rule="hyper" parents="299 2138 2142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2145">
    <literal><![CDATA[
      a(x / (1 / y),z,u) = a(x / y,z,u)
    ]]></literal>
    <justification jstring="[para(675(a,1),2144(a,1,1))].">
      <j1 rule="para" parents="675 2144"/>
    </justification>
  </clause>

  <clause id="2146">
    <literal><![CDATA[
      a(x \ (y * (1 / z)),u,w) = a(x \ (y * z),u,w)
    ]]></literal>
    <justification jstring="[para(1712(a,1),2144(a,1,1))].">
      <j1 rule="para" parents="1712 2144"/>
    </justification>
  </clause>

  <clause id="2147">
    <literal><![CDATA[
      ((x * x) * (y * ((x * x) * y))) * (y \ ((x * x) \ z)) = (((x * x) * y) \ 1) \ z
    ]]></literal>
    <justification jstring="[para(420(a,1),732(a,1,2))].">
      <j1 rule="para" parents="420 732"/>
    </justification>
  </clause>

  <clause id="2148">
    <literal><![CDATA[
      (x * ((y * y) * (x * (y * y)))) * ((y * y) \ (x \ z)) = ((x * (y * y)) \ 1) \ z
    ]]></literal>
    <justification jstring="[para(419(a,1),733(a,1,2))].">
      <j1 rule="para" parents="419 733"/>
    </justification>
  </clause>

  <clause id="2149">
    <literal><![CDATA[
      L(x,y,T(z,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(z \ u) \ u) = w
    ]]></literal>
    <justification jstring="[para(713(a,1),912(a,1))].">
      <j1 rule="para" parents="713 912"/>
    </justification>
  </clause>

  <clause id="2150">
    <literal><![CDATA[
      L(T(1 / (1 / x),y),z,u) * (1 / x) = L(T(x,y),z,u) / x
    ]]></literal>
    <justification jstring="[para(170(a,1),1156(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="170 1156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2151">
    <literal><![CDATA[
      (1 / x) * L(T((1 / x) \ 1,y),z,u) = L(T(x,y),z,u) / x
    ]]></literal>
    <justification jstring="[hyper(1165,a,2150,a)].">
      <j1 rule="hyper" parents="1165 2150"/>
    </justification>
  </clause>

  <clause id="2152">
    <literal><![CDATA[
      (1 / x) * L(T(x,y),z,u) = L(T(x,y),z,u) / x
    ]]></literal>
    <justification jstring="[para(79(a,1),2151(a,1,2,1,1))].">
      <j1 rule="para" parents="79 2151"/>
    </justification>
  </clause>

  <clause id="2153">
    <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(107(a,1),1344(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="107 1344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2154">
    <literal><![CDATA[
      T(x,y) * R(T(x,y) \ 1,z,u) = T(x * R(x \ 1,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(235,a,1914,a(flip),b,2153,a),flip(a)].">
      <j1 rule="hyper" parents="235 1914 2153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2155">
    <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(1866(a,1),2154(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="1866 2154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2156">
    <literal><![CDATA[
      x \ ((y * x) * T((y * x) \ z,u)) = T(y,x) * T(T(y,x) \ (x \ z),u)
    ]]></literal>
    <justification jstring="[para(22(a,2),1518(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="22 1518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2157">
    <literal><![CDATA[
      x \ (y * (x * T(x \ (y \ z),u))) = T(y,x) * T(T(y,x) \ (x \ z),u)
    ]]></literal>
    <justification jstring="[para(998(a,1),2156(a,1,2))].">
      <j1 rule="para" parents="998 2156"/>
    </justification>
  </clause>

  <clause id="2158">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ (y \ z),u) = T(x * T(x \ (z / y),u),y)
    ]]></literal>
    <justification jstring="[hyper(1593,a,2157,a),flip(a)].">
      <j1 rule="hyper" parents="1593 2157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2159">
    <literal><![CDATA[
      T(x * T(x \ ((y * z) / y),u),y) = T(x,y) * T(T(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),2158(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9 2158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2160">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ T(z,y),u) = T(x * T(x \ z,u),y)
    ]]></literal>
    <justification jstring="[para(223(a,1),2159(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="223 2159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2161">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ 1,z) = T(x * T(x \ 1,z),y)
    ]]></literal>
    <justification jstring="[para(195(a,1),2160(a,1,2,1,2))].">
      <j1 rule="para" parents="195 2160"/>
    </justification>
  </clause>

  <clause id="2162">
    <literal><![CDATA[
      T(x * T(x \ 1,y),z) = K(y \ (y / T(x,z)),y)
    ]]></literal>
    <justification jstring="[hyper(1292,a,2161,a),flip(a)].">
      <j1 rule="hyper" parents="1292 2161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2163">
    <literal><![CDATA[
      T(x * T(x \ 1,T(x,y)),y) = (T(x,y) \ 1) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(276,a,2161,a),flip(a)].">
      <j1 rule="hyper" parents="276 2161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2164">
    <literal><![CDATA[
      T(x,y) \ T(x * T(x \ 1,z),y) = T(T(x,y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,2161,a)].">
      <j1 rule="hyper" parents="125 2161"/>
    </justification>
  </clause>

  <clause id="2165">
    <literal><![CDATA[
      T(x,y) \ T(x * T(x \ 1,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      T(T(x,y) \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(2161(a,1),314(a,1,2))].">
      <j1 rule="para" parents="2161 314"/>
    </justification>
  </clause>

  <clause id="2167">
    <literal><![CDATA[
      (x * T(x \ 1,y)) * z = z * K(y \ (y / T(x,z)),y)
    ]]></literal>
    <justification jstring="[para(2162(a,1),107(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2162 107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2168">
    <literal><![CDATA[
      T(x \ T(x,y),z) = K(y \ (y / T(x \ 1,z)),y)
    ]]></literal>
    <justification jstring="[para(1108(a,1),2162(a,1,1))].">
      <j1 rule="para" parents="1108 2162"/>
    </justification>
  </clause>

  <clause id="2169">
    <literal><![CDATA[
      K(x \ (x / T(L(y \ 1,y,x),z)),x) = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[para(1382(a,2),2162(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1382 2162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2170">
    <literal><![CDATA[
      T(x \ T(x,y),T(x,x \ 1)) = K(y \ (y / T(x \ 1,x)),y)
    ]]></literal>
    <justification jstring="[para(1494(a,1),2168(a,2,1,2,2))].">
      <j1 rule="para" parents="1494 2168"/>
    </justification>
  </clause>

  <clause id="2171">
    <literal><![CDATA[
      K(x \ (x / T(y \ x,z)),x) = T(K(x \ y,x),z)
    ]]></literal>
    <justification jstring="[para(366(a,1),2169(a,1,1,2,2,1))].">
      <j1 rule="para" parents="366 2169"/>
    </justification>
  </clause>

  <clause id="2172">
    <literal><![CDATA[
      T(K(x \ y,x),(y \ x) \ z) = K(x \ (x / (((y \ x) \ z) \ z)),x)
    ]]></literal>
    <justification jstring="[para(108(a,1),2171(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="108 2171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2173">
    <literal><![CDATA[
      T(T(x,y) \ 1,x \ T(x,z)) = T(x,y) \ T(x * (x \ 1),y)
    ]]></literal>
    <justification jstring="[para(1482(a,1),2164(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="1482 2164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2174">
    <literal><![CDATA[
      T(x,y) \ T(x * T(x \ 1,x),y) = T(T(x,y) \ 1,T(x,x \ 1))
    ]]></literal>
    <justification jstring="[para(1494(a,1),2164(a,1,2,1,2))].">
      <j1 rule="para" parents="1494 2164"/>
    </justification>
  </clause>

  <clause id="2175">
    <literal><![CDATA[
      T(x \ T(x,y),T(x,x \ 1)) = T(x \ T(x,y),x)
    ]]></literal>
    <justification jstring="[hyper(299,a,2168,a,b,2170,a),flip(a)].">
      <j1 rule="hyper" parents="299 2168 2170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2176">
    <literal><![CDATA[
      T((x * y) \ (y * x),T(y,y \ 1)) = L(T(y \ T(y,x),y),y,x)
    ]]></literal>
    <justification jstring="[para(2175(a,1),825(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2175 825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2177">
    <literal><![CDATA[
      T(T(x,y) \ 1,x \ T(x,z)) = T(x,y) \ T(1,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),2173(a,2,2,1))].">
      <j1 rule="para" parents="10 2173"/>
    </justification>
  </clause>

  <clause id="2179">
    <literal><![CDATA[
      T(T(x,y) \ 1,x \ T(x,z)) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[para(195(a,1),2177(a,2,2))].">
      <j1 rule="para" parents="195 2177"/>
    </justification>
  </clause>

  <clause id="2181">
    <literal><![CDATA[
      T((x * y) \ (y * x),T(y,y \ 1)) = T((x * y) \ (y * x),y)
    ]]></literal>
    <justification jstring="[hyper(299,a,825,a(flip),b,2176,a),flip(a)].">
      <j1 rule="hyper" parents="299 825 2176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2182">
    <literal><![CDATA[
      T((x * y) \ (y * x),T(y,y \ 1)) = T(K(y,x),y)
    ]]></literal>
    <justification jstring="[para(16(a,2),2181(a,2,1))].">
      <j1 rule="para" parents="16 2181"/>
    </justification>
  </clause>

  <clause id="2183">
    <literal><![CDATA[
      T(K(x,y),T(x,x \ 1)) = T(K(x,y),x)
    ]]></literal>
    <justification jstring="[para(16(a,2),2182(a,1,1))].">
      <j1 rule="para" parents="16 2182"/>
    </justification>
  </clause>

  <clause id="2184">
    <literal><![CDATA[
      T(T(x,y) \ 1,T(x,x \ 1)) = T(T(x,y) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(2165,a,2174,a),flip(a)].">
      <j1 rule="hyper" parents="2165 2174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2185">
    <literal><![CDATA[
      T(T(x,y) \ 1,(x \ 1) \ 1) = T(T(x,y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(108(a,1),2184(a,1,2))].">
      <j1 rule="para" parents="108 2184"/>
    </justification>
  </clause>

  <clause id="2186">
    <literal><![CDATA[
      ((x \ 1) \ 1) * T(T(x,y) \ 1,x) = (T(x,y) \ 1) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2185(a,1),107(a,1,2))].">
      <j1 rule="para" parents="2185 107"/>
    </justification>
  </clause>

  <clause id="2187">
    <literal><![CDATA[
      a(x,x \ y,T(z,x * (x \ y))) = (L(z,x \ y,x) * y) \ (z * y)
    ]]></literal>
    <justification jstring="[para(10(a,1),1635(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 1635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2188">
    <literal><![CDATA[
      (L(x,y \ z,y) * z) \ (x * z) = a(y,y \ z,T(x,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),2187(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="10 2187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2190">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ y,z,u) = T(x * L(x \ y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(235,a,1857,a(flip),b,1645,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="235 1857 1645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2191">
    <literal><![CDATA[
      x * (T(y,x) * L(T(y,x) \ 1,z,u)) = (y * x) * L((y * x) \ x,z,u)
    ]]></literal>
    <justification jstring="[para(8(a,1),1645(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="8 1645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2192">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ 1,z,u) = T(x * L(x \ 1,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(235,a,1858,a(flip),b,2191,a),flip(a)].">
      <j1 rule="hyper" parents="235 1858 2191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2193">
    <literal><![CDATA[
      T(x,y) \ T(x * L(x \ 1,z,u),y) = L(T(x,y) \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(125,a,2192,a)].">
      <j1 rule="hyper" parents="125 2192"/>
    </justification>
  </clause>

  <clause id="2194">
    <literal><![CDATA[
      T(x * L(x \ 1,y,z),u) != T(x,u) * w
    ]]></literal>
    <literal><![CDATA[
      L(T(x,u) \ 1,y,z) = w
    ]]></literal>
    <justification jstring="[para(2192(a,1),45(a,1))].">
      <j1 rule="para" parents="2192 45"/>
    </justification>
  </clause>

  <clause id="2195">
    <literal><![CDATA[
      T(x * L(x \ 1,T(x,y),z),y) = T(x,y) * ((z * T(x,y)) \ z)
    ]]></literal>
    <justification jstring="[para(214(a,1),2192(a,1,2)),flip(a)].">
      <j1 rule="para" parents="214 2192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2196">
    <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(366(a,1),2193(a,1,2,1,2))].">
      <j1 rule="para" parents="366 2193"/>
    </justification>
  </clause>

  <clause id="2197">
    <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(1123(a,1),2195(a,2,2,1))].">
      <j1 rule="para" parents="1123 2195"/>
    </justification>
  </clause>

  <clause id="2198">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) / x) \ (1 / x)) = T(K(T(x,y),1 / x),y)
    ]]></literal>
    <justification jstring="[para(2109(a,1),2197(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2109 2197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2199">
    <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(694(a,1),1913(a,2,2,1))].">
      <j1 rule="para" parents="694 1913"/>
    </justification>
  </clause>

  <clause id="2200">
    <literal><![CDATA[
      T(x,y) * (R(x,z,u) \ 1) = R(x,z,u) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),1962(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 1962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2201">
    <literal><![CDATA[
      R(x / y,z,u) \ T(x / y,y) = (y \ x) * (R(x / y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(109(a,1),2200(a,1,1)),flip(a)].">
      <j1 rule="para" parents="109 2200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2202">
    <literal><![CDATA[
      (x \ y) * (R(y / x,z,u) \ 1) = R(y / x,z,u) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(109(a,1),2201(a,1,2)),flip(a)].">
      <j1 rule="para" parents="109 2201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2203">
    <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),2202(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 2202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2204">
    <literal><![CDATA[
      x * (R((y * x) / y,z,u) \ 1) = R((y * x) / y,z,u) \ x
    ]]></literal>
    <justification jstring="[para(9(a,1),2203(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 2203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2205">
    <literal><![CDATA[
      K((x * ((x \ y) / y)) \ x,x * ((x \ y) / y)) = y / y
    ]]></literal>
    <justification jstring="[para(220(a,1),2077(a,2,1))].">
      <j1 rule="para" parents="220 2077"/>
    </justification>
  </clause>

  <clause id="2206">
    <literal><![CDATA[
      K((x * ((x \ y) / y)) \ x,x * ((x \ y) / y)) = 1
    ]]></literal>
    <justification jstring="[hyper(299,a,73,a(flip),b,2205,a),flip(a)].">
      <j1 rule="hyper" parents="299 73 2205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2208">
    <literal><![CDATA[
      T(1 / ((x \ y) / y),x * ((x \ y) / y)) = 1 / ((x \ y) / y)
    ]]></literal>
    <justification jstring="[para(2206(a,1),1235(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2206 1235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2209">
    <literal><![CDATA[
      (x * ((x \ y) / y)) \ x = 1 / ((x \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(65,a,1652,a(flip),b,2208,a)].">
      <j1 rule="hyper" parents="65 1652 2208"/>
    </justification>
  </clause>

  <clause id="2210">
    <literal><![CDATA[
      ((x / y) * (y / x)) \ (x / y) = 1 / (((x / y) \ x) / x)
    ]]></literal>
    <justification jstring="[para(79(a,1),2209(a,1,1,2,1))].">
      <j1 rule="para" parents="79 2209"/>
    </justification>
  </clause>

  <clause id="2211">
    <literal><![CDATA[
      ((x / y) * (y / x)) \ (x / y) = 1 / (y / x)
    ]]></literal>
    <justification jstring="[para(79(a,1),2210(a,2,2,1))].">
      <j1 rule="para" parents="79 2210"/>
    </justification>
  </clause>

  <clause id="2212">
    <literal><![CDATA[
      ((x / y) * (y / x)) * (1 / (y / x)) = x / y
    ]]></literal>
    <justification jstring="[hyper(144,a,2211,a)].">
      <j1 rule="hyper" parents="144 2211"/>
    </justification>
  </clause>

  <clause id="2213">
    <literal><![CDATA[
      K(1 / (x / y),(y / x) * (x / y)) = 1
    ]]></literal>
    <justification jstring="[para(2211(a,1),2095(a,1,1))].">
      <j1 rule="para" parents="2211 2095"/>
    </justification>
  </clause>

  <clause id="2214">
    <literal><![CDATA[
      K(1 / x,(y / (x * y)) * ((x * y) / y)) = 1
    ]]></literal>
    <justification jstring="[para(11(a,1),2213(a,1,1,2))].">
      <j1 rule="para" parents="11 2213"/>
    </justification>
  </clause>

  <clause id="2215">
    <literal><![CDATA[
      ((x * y) / y) * (y / (x * y)) = x / (1 / (y / (x * y)))
    ]]></literal>
    <justification jstring="[hyper(120,a,11,a(flip),b,2212,a),flip(a)].">
      <j1 rule="hyper" parents="120 11 2212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2216">
    <literal><![CDATA[
      K(1 / x,(y / (x * y)) * x) = 1
    ]]></literal>
    <justification jstring="[para(11(a,1),2214(a,1,2,2))].">
      <j1 rule="para" parents="11 2214"/>
    </justification>
  </clause>

  <clause id="2217">
    <literal><![CDATA[
      T(1 / x,(y / (x * y)) * x) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(58,a,2216,a)].">
      <j1 rule="hyper" parents="58 2216"/>
    </justification>
  </clause>

  <clause id="2218">
    <literal><![CDATA[
      L(x \ 1,x,y / (x * y)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(1818,a,2217,a)].">
      <j1 rule="hyper" parents="1818 2217"/>
    </justification>
  </clause>

  <clause id="2219">
    <literal><![CDATA[
      L(x \ 1,x,(x \ y) / y) = 1 / x
    ]]></literal>
    <justification jstring="[para(10(a,1),2218(a,1,3,2))].">
      <j1 rule="para" parents="10 2218"/>
    </justification>
  </clause>

  <clause id="2220">
    <literal><![CDATA[
      L(x \ 1,x,x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[para(169(a,1),2218(a,1,3))].">
      <j1 rule="para" parents="169 2218"/>
    </justification>
  </clause>

  <clause id="2221">
    <literal><![CDATA[
      L(x \ 1,x,R(1 / x,x,y)) = 1 / x
    ]]></literal>
    <justification jstring="[para(216(a,2),2218(a,1,3))].">
      <j1 rule="para" parents="216 2218"/>
    </justification>
  </clause>

  <clause id="2222">
    <literal><![CDATA[
      ((x \ 1) * x) * (1 / x) = x \ 1
    ]]></literal>
    <justification jstring="[para(2220(a,1),369(a,1,2))].">
      <j1 rule="para" parents="2220 369"/>
    </justification>
  </clause>

  <clause id="2223">
    <literal><![CDATA[
      K(x \ 1,x) * (1 / x) = x \ 1
    ]]></literal>
    <justification jstring="[para(253(a,2),2222(a,1,1))].">
      <j1 rule="para" parents="253 2222"/>
    </justification>
  </clause>

  <clause id="2224">
    <literal><![CDATA[
      (x / y) * (((y \ 1) * (y \ 1)) \ z) = (x / (y \ 1)) * z
    ]]></literal>
    <justification jstring="[para(2222(a,1),1091(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2222 1091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2225">
    <literal><![CDATA[
      T(1 / x,K(x \ 1,x)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(1288,a,2223,a)].">
      <j1 rule="hyper" parents="1288 2223"/>
    </justification>
  </clause>

  <clause id="2226">
    <literal><![CDATA[
      (x \ 1) / (1 / x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(137,a,2223,a)].">
      <j1 rule="hyper" parents="137 2223"/>
    </justification>
  </clause>

  <clause id="2227">
    <literal><![CDATA[
      x * (1 / y) != y \ 1
    ]]></literal>
    <literal><![CDATA[
      K(y \ 1,y) = x
    ]]></literal>
    <justification jstring="[para(2223(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="2223 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2229">
    <literal><![CDATA[
      K(x \ 1,x) * L(1 / x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(1 / x,y,z) * K(x \ 1,x) = u
    ]]></literal>
    <justification jstring="[para(2225(a,1),396(a,1,2,1))].">
      <j1 rule="para" parents="2225 396"/>
    </justification>
  </clause>

  <clause id="2230">
    <literal><![CDATA[
      (((x \ y) / y) * x) * (1 / x) = (x \ y) / y
    ]]></literal>
    <justification jstring="[para(2219(a,1),369(a,1,2))].">
      <j1 rule="para" parents="2219 369"/>
    </justification>
  </clause>

  <clause id="2231">
    <literal><![CDATA[
      R(1 / x,x,y) / (1 / x) = R(1 / x,x,y) * x
    ]]></literal>
    <justification jstring="[para(2221(a,1),368(a,1,2))].">
      <j1 rule="para" parents="2221 368"/>
    </justification>
  </clause>

  <clause id="2232">
    <literal><![CDATA[
      T(1 / (1 / x),R(1 / x,x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(1832,a,2231,a)].">
      <j1 rule="hyper" parents="1832 2231"/>
    </justification>
  </clause>

  <clause id="2233">
    <literal><![CDATA[
      x / (1 / (y / (x * y))) = x * (y / (x * y))
    ]]></literal>
    <justification jstring="[para(11(a,1),2215(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 2215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2234">
    <literal><![CDATA[
      K(x \ (x * (y / (x * y))),x) = R(x \ 1,x,y) / (y / (x * y))
    ]]></literal>
    <justification jstring="[para(2233(a,1),1297(a,1,1,2))].">
      <j1 rule="para" parents="2233 1297"/>
    </justification>
  </clause>

  <clause id="2235">
    <literal><![CDATA[
      (x / y) * (y * ((y \ 1) \ z)) = (x / (y \ 1)) * z
    ]]></literal>
    <justification jstring="[para(465(a,1),2224(a,1,2))].">
      <j1 rule="para" parents="465 2224"/>
    </justification>
  </clause>

  <clause id="2237">
    <literal><![CDATA[
      R(x \ 1,x,y) / (y / (x * y)) = K(y / (x * y),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,722,a(flip),b,2234,a),flip(a)].">
      <j1 rule="hyper" parents="65 722 2234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2239">
    <literal><![CDATA[
      K(x / (y * x),y) * (x / (y * x)) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(143,a,2237,a)].">
      <j1 rule="hyper" parents="143 2237"/>
    </justification>
  </clause>

  <clause id="2241">
    <literal><![CDATA[
      (x * x) * ((y * ((x * x) * y)) * (y \ ((x * x) \ z))) = (((x * x) * y) \ 1) \ z
    ]]></literal>
    <justification jstring="[hyper(671,a,2147,a)].">
      <j1 rule="hyper" parents="671 2147"/>
    </justification>
  </clause>

  <clause id="2242">
    <literal><![CDATA[
      (x * ((y * y) * x)) * ((y * y) * ((y * y) \ (x \ z))) = ((x * (y * y)) \ 1) \ z
    ]]></literal>
    <justification jstring="[hyper(65,a,1043,a(flip),b,2148,a)].">
      <j1 rule="hyper" parents="65 1043 2148"/>
    </justification>
  </clause>

  <clause id="2243">
    <literal><![CDATA[
      (x * ((y * y) * x)) * (x \ z) = ((x * (y * y)) \ 1) \ z
    ]]></literal>
    <justification jstring="[hyper(315,a,2242,a)].">
      <j1 rule="hyper" parents="315 2242"/>
    </justification>
  </clause>

  <clause id="2245">
    <literal><![CDATA[
      (x * ((y * y) * x)) * (x \ z) = ((y * y) \ (x \ 1)) \ z
    ]]></literal>
    <justification jstring="[para(419(a,1),2243(a,2,1))].">
      <j1 rule="para" parents="419 2243"/>
    </justification>
  </clause>

  <clause id="2246">
    <literal><![CDATA[
      (x * ((y * y) * x)) * (x \ z) = (x \ 1) \ ((y * y) * z)
    ]]></literal>
    <justification jstring="[hyper(299,a,666,a(flip),b,2245,a),flip(a)].">
      <j1 rule="hyper" parents="299 666 2245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2247">
    <literal><![CDATA[
      (x * x) * ((y \ 1) \ ((x * x) * ((x * x) \ z))) = (((x * x) * y) \ 1) \ z
    ]]></literal>
    <justification jstring="[para(2246(a,1),2241(a,1,2))].">
      <j1 rule="para" parents="2246 2241"/>
    </justification>
  </clause>

  <clause id="2248">
    <literal><![CDATA[
      (((x * x) * y) \ 1) \ z = (x * x) * ((y \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),2247(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 2247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2249">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ (u * y))) / z) = (((z * (u / x)) / z) * x) * y
    ]]></literal>
    <justification jstring="[hyper(980,a,1099,a),flip(a)].">
      <j1 rule="hyper" parents="980 1099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2250">
    <literal><![CDATA[
      (((x * ((y / z) / u)) / x) * u) * z = (u * z) * ((x * ((u * z) \ y)) / x)
    ]]></literal>
    <justification jstring="[para(12(a,1),2249(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 2249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2251">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ (u * y))) / z) = (x * ((z * (x \ u)) / z)) * y
    ]]></literal>
    <justification jstring="[para(941(a,1),2249(a,2,1))].">
      <j1 rule="para" parents="941 2249"/>
    </justification>
  </clause>

  <clause id="2252">
    <literal><![CDATA[
      (x * y) * ((x * ((x * y) \ z)) / x) = (x * ((z / y) / x)) * y
    ]]></literal>
    <justification jstring="[hyper(306,a,2250,a),flip(a)].">
      <j1 rule="hyper" parents="306 2250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2254">
    <literal><![CDATA[
      x * (y * ((x * (y \ (x \ z))) / x)) = (x * ((z / y) / x)) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,1321,a(flip),b,2252,a)].">
      <j1 rule="hyper" parents="65 1321 2252"/>
    </justification>
  </clause>

  <clause id="2255">
    <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(345(a,2),2254(a,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="345 2254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2257">
    <literal><![CDATA[
      ((x / y) * ((z * ((x / y) \ u)) / z)) * y = x * ((z * (((x / y) * y) \ (u * y))) / z)
    ]]></literal>
    <justification jstring="[hyper(306,a,2251,a),flip(a)].">
      <j1 rule="hyper" parents="306 2251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2258">
    <literal><![CDATA[
      ((x * y) * ((z * ((x * y) \ x)) / z)) * y = (x * y) * (y * ((z * (y \ 1)) / z))
    ]]></literal>
    <justification jstring="[hyper(65,a,1319,a(flip),b,2251,a),flip(a)].">
      <j1 rule="hyper" parents="65 1319 2251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2259">
    <literal><![CDATA[
      (x \ (y * x)) * ((z * ((x \ (y * x)) \ x)) / z) = T(y * ((z * (y \ x)) / z),x)
    ]]></literal>
    <justification jstring="[hyper(235,a,2251,a(flip),b,1643,a),flip(a)].">
      <j1 rule="hyper" parents="235 2251 1643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2260">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ y)) / z) = (x * ((z * (x \ 1)) / z)) * y
    ]]></literal>
    <justification jstring="[para(7(a,1),2251(a,1,2,1,2,2))].">
      <j1 rule="para" parents="7 2251"/>
    </justification>
  </clause>

  <clause id="2262">
    <literal><![CDATA[
      x * ((x * y) * ((z * ((x * y) \ y)) / z)) = (x * ((z * (x \ 1)) / z)) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,1320,a(flip),b,2260,a)].">
      <j1 rule="hyper" parents="65 1320 2260"/>
    </justification>
  </clause>

  <clause id="2263">
    <literal><![CDATA[
      (x * ((y * (x \ 1)) / y)) * x = x * (x * ((y * (x \ 1)) / y))
    ]]></literal>
    <justification jstring="[hyper(65,a,1319,a(flip),b,2260,a),flip(a)].">
      <j1 rule="hyper" parents="65 1319 2260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2264">
    <literal><![CDATA[
      T(x * ((y * (x \ 1)) / y),z) = K(y,(y / T(x,z)) / y)
    ]]></literal>
    <justification jstring="[hyper(235,a,2260,a(flip),b,2057,a(flip))].">
      <j1 rule="hyper" parents="235 2260 2057"/>
    </justification>
  </clause>

  <clause id="2266">
    <literal><![CDATA[
      (x * ((y / (z * (x \ y))) / x)) * (z * (x \ y)) = x * ((z * ((x * (z \ 1)) / x)) * (x \ y))
    ]]></literal>
    <justification jstring="[para(2260(a,1),2254(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2260 2254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2267">
    <literal><![CDATA[
      T(x,y) * ((z * (T(x,y) \ 1)) / z) = T(x * ((z * (x \ 1)) / z),y)
    ]]></literal>
    <justification jstring="[hyper(299,a,1880,a(flip),b,2264,a)].">
      <j1 rule="hyper" parents="299 1880 2264"/>
    </justification>
  </clause>

  <clause id="2268">
    <literal><![CDATA[
      K(x,(x / T(y \ x,z)) / x) = T(K(x,y / x),z)
    ]]></literal>
    <justification jstring="[para(1883(a,1),2264(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1883 2264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2269">
    <literal><![CDATA[
      T(K(x,y / x),K(y / x,z)) = K(x,(x / (y \ x)) / x)
    ]]></literal>
    <justification jstring="[para(1517(a,1),2268(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="1517 2268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2270">
    <literal><![CDATA[
      T(K(x,y / x),K(y / x,z)) = K(x,y / x)
    ]]></literal>
    <justification jstring="[para(76(a,1),2269(a,2,2,1))].">
      <j1 rule="para" parents="76 2269"/>
    </justification>
  </clause>

  <clause id="2272">
    <literal><![CDATA[
      T(K(x,y),K((y * x) / x,z)) = K(x,(y * x) / x)
    ]]></literal>
    <justification jstring="[para(11(a,1),2270(a,1,1,2))].">
      <j1 rule="para" parents="11 2270"/>
    </justification>
  </clause>

  <clause id="2273">
    <literal><![CDATA[
      T(K(x,y),K(y,z)) = K(x,(y * x) / x)
    ]]></literal>
    <justification jstring="[para(11(a,1),2272(a,1,2,1))].">
      <j1 rule="para" parents="11 2272"/>
    </justification>
  </clause>

  <clause id="2274">
    <literal><![CDATA[
      T(K(x,y),K(y,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(11(a,1),2273(a,2,2))].">
      <j1 rule="para" parents="11 2273"/>
    </justification>
  </clause>

  <clause id="2275">
    <literal><![CDATA[
      K(K(x,y),K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(57,a,2274,a)].">
      <j1 rule="hyper" parents="57 2274"/>
    </justification>
  </clause>

  <clause id="2276">
    <literal><![CDATA[
      T(K(x,y),K(z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(56,a,2274,a)].">
      <j1 rule="hyper" parents="56 2274"/>
    </justification>
  </clause>

  <clause id="2277">
    <literal><![CDATA[
      T(x,K(y,z)) != K(u,y)
    ]]></literal>
    <literal><![CDATA[
      K(u,y) = x
    ]]></literal>
    <justification jstring="[para(2274(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="2274 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2278">
    <literal><![CDATA[
      K(x,y) * K(z,x) = K(z,x) * K(x,y)
    ]]></literal>
    <justification jstring="[para(2274(a,1),107(a,1,2))].">
      <j1 rule="para" parents="2274 107"/>
    </justification>
  </clause>

  <clause id="2279">
    <literal><![CDATA[
      K(x,y) * K(z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(2274(a,1),276(a,1,2))].">
      <j1 rule="para" parents="2274 276"/>
    </justification>
  </clause>

  <clause id="2280">
    <literal><![CDATA[
      L(K(x,y),z,u) * K(y,w) = K(y,w) * L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2274(a,1),233(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2274 233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2281">
    <literal><![CDATA[
      R(K(x,y),z,u) * K(y,w) = K(y,w) * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2274(a,1),234(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2274 234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2282">
    <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(2274(a,1),396(a,1,2,1))].">
      <j1 rule="para" parents="2274 396"/>
    </justification>
  </clause>

  <clause id="2283">
    <literal><![CDATA[
      T(x,K(y,z)) != K(z,u)
    ]]></literal>
    <literal><![CDATA[
      K(z,u) = x
    ]]></literal>
    <justification jstring="[para(2276(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="2276 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2285">
    <literal><![CDATA[
      K(x,y) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(2276(a,1),276(a,1,2))].">
      <j1 rule="para" parents="2276 276"/>
    </justification>
  </clause>

  <clause id="2286">
    <literal><![CDATA[
      R(K(x,y),z,u) * K(w,x) = K(w,x) * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2276(a,1),234(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2276 234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2287">
    <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(2276(a,1),397(a,1,2,1))].">
      <j1 rule="para" parents="2276 397"/>
    </justification>
  </clause>

  <clause id="2290">
    <literal><![CDATA[
      (1 / x) * ((1 / x) * ((y * ((1 / x) \ 1)) / y)) = (((y * x) / y) / x) * (1 / x)
    ]]></literal>
    <justification jstring="[para(2085(a,1),2263(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2085 2263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2291">
    <literal><![CDATA[
      T(x,y) * ((x * (T(x,y) \ 1)) / x) = T(x * (1 / x),y)
    ]]></literal>
    <justification jstring="[para(10(a,1),2267(a,2,1,2,1))].">
      <j1 rule="para" parents="10 2267"/>
    </justification>
  </clause>

  <clause id="2292">
    <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(434(a,2),2267(a,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="434 2267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2293">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ x) / x) = T(x * (1 / x),y)
    ]]></literal>
    <justification jstring="[para(1193(a,1),2291(a,1,2,1))].">
      <j1 rule="para" parents="1193 2291"/>
    </justification>
  </clause>

  <clause id="2294">
    <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),2259(a,1,1))].">
      <j1 rule="para" parents="22 2259"/>
    </justification>
  </clause>

  <clause id="2295">
    <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),2294(a,1,2,1,2,1))].">
      <j1 rule="para" parents="22 2294"/>
    </justification>
  </clause>

  <clause id="2296">
    <literal><![CDATA[
      (x * ((y * (x \ 1)) / y)) * (x * z) = x * ((x * ((y * (x \ 1)) / y)) * z)
    ]]></literal>
    <justification jstring="[para(2260(a,1),2262(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2260 2262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2297">
    <literal><![CDATA[
      K(x,(x / y) / x) * (y * z) = y * ((y * ((x * (y \ 1)) / x)) * z)
    ]]></literal>
    <justification jstring="[para(1880(a,2),2296(a,1,1))].">
      <j1 rule="para" parents="1880 2296"/>
    </justification>
  </clause>

  <clause id="2298">
    <literal><![CDATA[
      (((x * y) / x) / y) * (1 / y) = (1 / y) * (((x * y) / x) / y)
    ]]></literal>
    <justification jstring="[para(2085(a,1),2290(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2085 2290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2299">
    <literal><![CDATA[
      ((1 / x) * (((y * x) / y) / x)) / (1 / x) = ((y * x) / y) / x
    ]]></literal>
    <justification jstring="[hyper(137,a,2298,a)].">
      <j1 rule="hyper" parents="137 2298"/>
    </justification>
  </clause>

  <clause id="2300">
    <literal><![CDATA[
      R(((x * y) / x) / y,y,x) = ((1 / y) * ((x * y) / (y * x))) / (1 / y)
    ]]></literal>
    <justification jstring="[para(2299(a,1),978(a,1,1))].">
      <j1 rule="para" parents="2299 978"/>
    </justification>
  </clause>

  <clause id="2301">
    <literal><![CDATA[
      ((1 / x) * ((y * x) / (x * y))) / (1 / x) = (y * x) / (x * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,285,a(flip),b,2300,a),flip(a)].">
      <j1 rule="hyper" parents="65 285 2300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2302">
    <literal><![CDATA[
      T((x * y) / (y * x),y * x) = ((1 / y) * ((y * x) \ (x * y))) / (1 / y)
    ]]></literal>
    <justification jstring="[para(2301(a,1),755(a,1,1))].">
      <j1 rule="para" parents="2301 755"/>
    </justification>
  </clause>

  <clause id="2303">
    <literal><![CDATA[
      ((1 / x) * ((x * y) \ (y * x))) / (1 / x) = (x * y) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(400,a,2302,a),flip(a)].">
      <j1 rule="hyper" parents="400 2302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2304">
    <literal><![CDATA[
      K(x,y) = ((1 / y) * ((y * x) \ (x * y))) / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(299,a,16,a,b,2303,a)].">
      <j1 rule="hyper" parents="299 16 2303"/>
    </justification>
  </clause>

  <clause id="2305">
    <literal><![CDATA[
      ((1 / x) * K(y,x)) / (1 / x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(16(a,2),2304(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="16 2304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2306">
    <literal><![CDATA[
      T(1 / x,K(y,x)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(263,a,2305,a)].">
      <j1 rule="hyper" parents="263 2305"/>
    </justification>
  </clause>

  <clause id="2308">
    <literal><![CDATA[
      K(1 / x,K(y,x)) = 1
    ]]></literal>
    <justification jstring="[hyper(57,a,2306,a)].">
      <j1 rule="hyper" parents="57 2306"/>
    </justification>
  </clause>

  <clause id="2309">
    <literal><![CDATA[
      T(x \ 1,K(y,x)) = T(1 / x,x)
    ]]></literal>
    <justification jstring="[para(2306(a,1),242(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2306 242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2311">
    <literal><![CDATA[
      K(x,K(y,x \ 1)) = 1
    ]]></literal>
    <justification jstring="[para(76(a,1),2308(a,1,1))].">
      <j1 rule="para" parents="76 2308"/>
    </justification>
  </clause>

  <clause id="2312">
    <literal><![CDATA[
      T(x,K(y,x \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,2311,a)].">
      <j1 rule="hyper" parents="58 2311"/>
    </justification>
  </clause>

  <clause id="2313">
    <literal><![CDATA[
      K(x,y \ 1) * y != z
    ]]></literal>
    <literal><![CDATA[
      y * K(x,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(2312(a,1),276(a,1,2))].">
      <j1 rule="para" parents="2312 276"/>
    </justification>
  </clause>

  <clause id="2314">
    <literal><![CDATA[
      L(x,y,z) * K(u,x \ 1) = K(u,x \ 1) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(2312(a,1),233(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2312 233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2315">
    <literal><![CDATA[
      T(x \ 1,K(y,x)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(299,a,109,a(flip),b,2309,a),flip(a)].">
      <j1 rule="hyper" parents="299 109 2309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2316">
    <literal><![CDATA[
      T(K(x,y),y \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(56,a,2315,a)].">
      <j1 rule="hyper" parents="56 2315"/>
    </justification>
  </clause>

  <clause id="2317">
    <literal><![CDATA[
      T((x * y) \ x,K(z,y)) = L(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(2315(a,1),371(a,2,1))].">
      <j1 rule="para" parents="2315 371"/>
    </justification>
  </clause>

  <clause id="2318">
    <literal><![CDATA[
      T(x \ y,K(z,y \ x)) = L((y \ x) \ 1,y \ x,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),2317(a,1,1,1))].">
      <j1 rule="para" parents="10 2317"/>
    </justification>
  </clause>

  <clause id="2319">
    <literal><![CDATA[
      T(x \ y,K(z,y \ x)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(299,a,366,a(flip),b,2318,a),flip(a)].">
      <j1 rule="hyper" parents="299 366 2318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2320">
    <literal><![CDATA[
      K(x,y \ z) * (z \ y) = (z \ y) * K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(2319(a,1),107(a,1,2))].">
      <j1 rule="para" parents="2319 107"/>
    </justification>
  </clause>

  <clause id="2321">
    <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="[hyper(65,a,2154,a(flip),b,1113,a)].">
      <j1 rule="hyper" parents="65 2154 1113"/>
    </justification>
  </clause>

  <clause id="2322">
    <literal><![CDATA[
      ((x \ 1) / (x \ T(x,y))) * T(x,y) = T(x * T(x \ 1,T(x,y)),y)
    ]]></literal>
    <justification jstring="[para(1496(a,1),2321(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1496 2321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2323">
    <literal><![CDATA[
      (x \ 1) / (x \ T(x,y)) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(37,a,2163,a(flip),b,2322,a),flip(a)].">
      <j1 rule="hyper" parents="37 2163 2322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2324">
    <literal><![CDATA[
      T(T(x,y) \ 1,x \ T(x,y)) = (x \ T(x,y)) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(2323(a,1),109(a,1,1))].">
      <j1 rule="para" parents="2323 109"/>
    </justification>
  </clause>

  <clause id="2325">
    <literal><![CDATA[
      (x \ T(x,y)) \ (x \ 1) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,2179,a(flip),b,2324,a),flip(a)].">
      <j1 rule="hyper" parents="65 2179 2324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2327">
    <literal><![CDATA[
      (L(x,1 / x,y) * y) / L(x,1 / x,y) = y * ((1 / x) * T(x,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,487,a(flip),b,1536,a),flip(a)].">
      <j1 rule="hyper" parents="299 487 1536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2328">
    <literal><![CDATA[
      (L(x,1 / x,y) * y) / L(x,1 / x,y) = y * (T(x,y) / x)
    ]]></literal>
    <justification jstring="[para(1123(a,1),2327(a,2,2))].">
      <j1 rule="para" parents="1123 2327"/>
    </justification>
  </clause>

  <clause id="2329">
    <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(2328(a,1),1417(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2328 1417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2330">
    <literal><![CDATA[
      (x * y) * (z * T(z \ L(y \ z,y,x),u)) = (x * (y * T(y \ 1,u))) * z
    ]]></literal>
    <justification jstring="[para(801(a,1),1580(a,1,1)),flip(a)].">
      <j1 rule="para" parents="801 1580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2331">
    <literal><![CDATA[
      (x \ 1) * (L(x \ 1,x,y) \ (x * ((y * x) \ y))) = K(x \ 1,x * ((y * x) \ y))
    ]]></literal>
    <justification jstring="[hyper(65,a,1352,a(flip),b,1815,a)].">
      <j1 rule="hyper" parents="65 1352 1815"/>
    </justification>
  </clause>

  <clause id="2332">
    <literal><![CDATA[
      ((x * y) \ x) * K(y \ 1,y * ((x * y) \ x)) = (y \ 1) * (y * ((x * y) \ x))
    ]]></literal>
    <justification jstring="[para(1815(a,1),403(a,1,2))].">
      <j1 rule="para" parents="1815 403"/>
    </justification>
  </clause>

  <clause id="2333">
    <literal><![CDATA[
      ((x * y) \ x) * z != (y \ 1) * (y * ((x * y) \ x))
    ]]></literal>
    <literal><![CDATA[
      K(y \ 1,y * ((x * y) \ x)) = z
    ]]></literal>
    <justification jstring="[para(2332(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="2332 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2334">
    <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(1529(a,1),2124(a,1,1))].">
      <j1 rule="para" parents="1529 2124"/>
    </justification>
  </clause>

  <clause id="2335">
    <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(1211(a,1),2334(a,1,1))].">
      <j1 rule="para" parents="1211 2334"/>
    </justification>
  </clause>

  <clause id="2336">
    <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(2121(a,1),2335(a,1,2))].">
      <j1 rule="para" parents="2121 2335"/>
    </justification>
  </clause>

  <clause id="2337">
    <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(65,a,25,a,b,2336,a)].">
      <j1 rule="hyper" parents="65 25 2336"/>
    </justification>
  </clause>

  <clause id="2338">
    <literal><![CDATA[
      L(x,T(x,y) \ x,T(x,y)) = L(x,T(x,y) \ x,x)
    ]]></literal>
    <justification jstring="[para(2118(a,1),2337(a,1,1))].">
      <j1 rule="para" parents="2118 2337"/>
    </justification>
  </clause>

  <clause id="2339">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ x,x) = L(x,T(x,y) \ x,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,1211,a,b,2338,a)].">
      <j1 rule="hyper" parents="65 1211 2338"/>
    </justification>
  </clause>

  <clause id="2340">
    <literal><![CDATA[
      x * L(y,T(y,x) \ y,y) = (y * x) * T(K(x,y),y)
    ]]></literal>
    <justification jstring="[para(2338(a,1),2031(a,1,2))].">
      <j1 rule="para" parents="2338 2031"/>
    </justification>
  </clause>

  <clause id="2341">
    <literal><![CDATA[
      L(x,T(x,y) \ x,x) = (T(x,y) \ x) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2125,a(flip),b,2339,a),flip(a)].">
      <j1 rule="hyper" parents="65 2125 2339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2342">
    <literal><![CDATA[
      (x * y) * T(K(y,x),x) != y * z
    ]]></literal>
    <literal><![CDATA[
      L(x,T(x,y) \ x,x) = z
    ]]></literal>
    <justification jstring="[para(2340(a,1),45(a,1))].">
      <j1 rule="para" parents="2340 45"/>
    </justification>
  </clause>

  <clause id="2343">
    <literal><![CDATA[
      K(x \ 1,x * ((y * x) \ y)) = (x \ 1) * T(x,(y * x) \ y)
    ]]></literal>
    <justification jstring="[para(800(a,1),2331(a,1,2)),flip(a)].">
      <j1 rule="para" parents="800 2331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2344">
    <literal><![CDATA[
      a(x * (y * y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,(y * y) * z,u) = w
    ]]></literal>
    <justification jstring="[para(2098(a,1),1071(a,1))].">
      <j1 rule="para" parents="2098 1071"/>
    </justification>
  </clause>

  <clause id="2345">
    <literal><![CDATA[
      a(x,(y * y) * z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(2344,a,2144,a)].">
      <j1 rule="hyper" parents="2344 2144"/>
    </justification>
  </clause>

  <clause id="2346">
    <literal><![CDATA[
      a(x,(y * y) \ z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),2345(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 2345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2347">
    <literal><![CDATA[
      a(x,T(y,z * z),u) = a(x,y * (z * z),u)
    ]]></literal>
    <justification jstring="[para(107(a,1),2345(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 2345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2348">
    <literal><![CDATA[
      a(x,1 / y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(217(a,1),2345(a,1,2)),flip(a)].">
      <j1 rule="para" parents="217 2345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2349">
    <literal><![CDATA[
      a(x,(1 / y) * z,u) = a(x,y * z,u)
    ]]></literal>
    <justification jstring="[para(265(a,1),2345(a,1,2)),flip(a)].">
      <j1 rule="para" parents="265 2345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2350">
    <literal><![CDATA[
      a(x,y * (y * z),u) = a(x,L(z,y,y),u)
    ]]></literal>
    <justification jstring="[para(94(a,1),2345(a,1,2))].">
      <j1 rule="para" parents="94 2345"/>
    </justification>
  </clause>

  <clause id="2351">
    <literal><![CDATA[
      a(x,1 / (y * (z * z)),u) = a(x,y,(z * z) * u)
    ]]></literal>
    <justification jstring="[hyper(299,a,2104,a(flip),b,2348,a),flip(a)].">
      <j1 rule="hyper" parents="299 2104 2348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2352">
    <literal><![CDATA[
      a(x,(y \ 1) * z,u) = a(x,y * z,u)
    ]]></literal>
    <justification jstring="[para(76(a,1),2349(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="76 2349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2353">
    <literal><![CDATA[
      a(x,T(y,z * z),u) = a(x,y,(z * z) * u)
    ]]></literal>
    <justification jstring="[hyper(299,a,2104,a(flip),b,2347,a),flip(a)].">
      <j1 rule="hyper" parents="299 2104 2347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2354">
    <literal><![CDATA[
      a(x,(y * y) \ (1 / z),u) = a(x,z,(y * y) * u)
    ]]></literal>
    <justification jstring="[para(472(a,1),2351(a,1,2))].">
      <j1 rule="para" parents="472 2351"/>
    </justification>
  </clause>

  <clause id="2355">
    <literal><![CDATA[
      a(x,y,(z * z) * u) = a(x,1 / y,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,2346,a(flip),b,2354,a),flip(a)].">
      <j1 rule="hyper" parents="65 2346 2354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2357">
    <literal><![CDATA[
      a(x,y,(z * z) * u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,2348,a(flip),b,2355,a),flip(a)].">
      <j1 rule="hyper" parents="299 2348 2355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2358">
    <literal><![CDATA[
      a(x,T(y,z * z),u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,2353,a,b,2357,a)].">
      <j1 rule="hyper" parents="65 2353 2357"/>
    </justification>
  </clause>

  <clause id="2359">
    <literal><![CDATA[
      a(x,y,1 / z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(217(a,1),2357(a,1,3)),flip(a)].">
      <j1 rule="para" parents="217 2357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2360">
    <literal><![CDATA[
      a(x,y,(1 / z) * u) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(265(a,1),2357(a,1,3)),flip(a)].">
      <j1 rule="para" parents="265 2357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2361">
    <literal><![CDATA[
      a(x,y,(1 / z) \ u) = a(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(734(a,1),2357(a,1,3)),flip(a)].">
      <j1 rule="para" parents="734 2357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2362">
    <literal><![CDATA[
      a(x,y,T(z,u \ (u \ 1))) = a(x,y,z / (u * u))
    ]]></literal>
    <justification jstring="[para(1058(a,1),2357(a,1,3))].">
      <j1 rule="para" parents="1058 2357"/>
    </justification>
  </clause>

  <clause id="2363">
    <literal><![CDATA[
      a(x,y,z \ 1) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(76(a,1),2359(a,1,3)),flip(a)].">
      <j1 rule="para" parents="76 2359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2364">
    <literal><![CDATA[
      a(x,y,1 / z) = a(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,2359,a,b,2363,a)].">
      <j1 rule="hyper" parents="299 2359 2363"/>
    </justification>
  </clause>

  <clause id="2365">
    <literal><![CDATA[
      a(x,y,(z \ 1) \ 1) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,2363,a(flip),b,2363,a),flip(a)].">
      <j1 rule="hyper" parents="299 2363 2363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2367">
    <literal><![CDATA[
      a(x,1 / y,z) = a(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[para(469(a,1),2358(a,1,2))].">
      <j1 rule="para" parents="469 2358"/>
    </justification>
  </clause>

  <clause id="2369">
    <literal><![CDATA[
      a(x,y,(z \ 1) * u) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(76(a,1),2360(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="76 2360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2371">
    <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(253(a,2),1338(a,1,2,1,1))].">
      <j1 rule="para" parents="253 1338"/>
    </justification>
  </clause>

  <clause id="2372">
    <literal><![CDATA[
      T(x,(1 / y) \ ((1 / y) \ 1)) != (y \ z) * (u / ((1 / y) * (1 / y)))
    ]]></literal>
    <literal><![CDATA[
      ((1 / y) \ z) * u = x
    ]]></literal>
    <justification jstring="[para(1408(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="1408 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2373">
    <literal><![CDATA[
      T((x * ((x \ 1) \ y)) * z,(1 / x) \ ((1 / x) \ 1)) = (x \ (x * y)) * (z / ((1 / x) * (1 / x)))
    ]]></literal>
    <justification jstring="[para(1668(a,1),1408(a,1,1,1))].">
      <j1 rule="para" parents="1668 1408"/>
    </justification>
  </clause>

  <clause id="2374">
    <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),1522(a,1,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="22 1522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2375">
    <literal><![CDATA[
      (x * T(x \ y,x)) * (1 / x) = T(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[para(72(a,1),1615(a,1,1)),flip(a)].">
      <j1 rule="para" parents="72 1615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2376">
    <literal><![CDATA[
      ((x \ y) * x) * (1 / x) = T(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[para(107(a,1),2375(a,1,1))].">
      <j1 rule="para" parents="107 2375"/>
    </justification>
  </clause>

  <clause id="2378">
    <literal><![CDATA[
      T((x * y) * (1 / x),x) = (y * x) * (1 / x)
    ]]></literal>
    <justification jstring="[para(9(a,1),2376(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 2376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2379">
    <literal><![CDATA[
      T(x * (1 / y),y) != z * (1 / y)
    ]]></literal>
    <literal><![CDATA[
      (y \ x) * y = z
    ]]></literal>
    <justification jstring="[para(2376(a,1),46(a,1))].">
      <j1 rule="para" parents="2376 46"/>
    </justification>
  </clause>

  <clause id="2380">
    <literal><![CDATA[
      T((x * y) * (1 / x),x) != z * (1 / x)
    ]]></literal>
    <literal><![CDATA[
      y * x = z
    ]]></literal>
    <justification jstring="[para(2378(a,2),46(a,1))].">
      <j1 rule="para" parents="2378 46"/>
    </justification>
  </clause>

  <clause id="2381">
    <literal><![CDATA[
      x * ((y * x) * (1 / x)) = R(x * y,x,x)
    ]]></literal>
    <justification jstring="[para(2378(a,1),1753(a,1,2))].">
      <j1 rule="para" parents="2378 1753"/>
    </justification>
  </clause>

  <clause id="2382">
    <literal><![CDATA[
      (x * (y \ 1)) * ((T(y,y \ 1) \ 1) \ z) = (x * y) * (((y \ 1) \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(76(a,1),1781(a,2,1,2))].">
      <j1 rule="para" parents="76 1781"/>
    </justification>
  </clause>

  <clause id="2384">
    <literal><![CDATA[
      (x * (y \ 1)) * (T(y \ 1,y) \ z) = (x * y) * (((y \ 1) \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(1490(a,1),2382(a,1,2,1))].">
      <j1 rule="para" parents="1490 2382"/>
    </justification>
  </clause>

  <clause id="2385">
    <literal><![CDATA[
      (x * (y \ 1)) * ((1 / y) \ z) = (x * y) * (((y \ 1) \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(1692(a,1),2384(a,1,2,1))].">
      <j1 rule="para" parents="1692 2384"/>
    </justification>
  </clause>

  <clause id="2386">
    <literal><![CDATA[
      ((x \ 1) * (x \ 1)) * (y / (((x \ 1) * x) * (((x \ 1) \ 1) \ z))) = T(y / ((1 / x) \ z),(x \ 1) \ ((x \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(2385(a,1),1064(a,1,2,2))].">
      <j1 rule="para" parents="2385 1064"/>
    </justification>
  </clause>

  <clause id="2387">
    <literal><![CDATA[
      x \ ((y * x) * L((y * x) \ z,u,w)) = T(y,x) * L(T(y,x) \ (x \ z),u,w)
    ]]></literal>
    <justification jstring="[para(22(a,2),1949(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="22 1949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2388">
    <literal><![CDATA[
      x \ (y * (x * L(x \ (y \ z),u,w))) = T(y,x) * L(T(y,x) \ (x \ z),u,w)
    ]]></literal>
    <justification jstring="[para(1150(a,1),2387(a,1,2))].">
      <j1 rule="para" parents="1150 2387"/>
    </justification>
  </clause>

  <clause id="2389">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ (y \ z),u,w) = T(x * L(x \ (z / y),u,w),y)
    ]]></literal>
    <justification jstring="[hyper(1978,a,2388,a),flip(a)].">
      <j1 rule="hyper" parents="1978 2388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2390">
    <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="[para(9(a,1),2389(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9 2389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2391">
    <literal><![CDATA[
      (x \ L(x,y,z)) * ((x \ 1) * u) = (x \ 1) * ((x \ L(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(1273(a,1),2062(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1273 2062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2392">
    <literal><![CDATA[
      (x \ 1) * ((x \ L(x,y,z)) \ 1) = (x \ L(x,y,z)) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,71,a(flip),b,2391,a),flip(a)].">
      <j1 rule="hyper" parents="119 71 2391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2393">
    <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(2392(a,1),45(a,1))].">
      <j1 rule="para" parents="2392 45"/>
    </justification>
  </clause>

  <clause id="2394">
    <literal><![CDATA[
      (x \ R(x,y,z)) * ((x \ 1) * u) = (x \ 1) * ((x \ R(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(1455(a,1),2079(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1455 2079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2395">
    <literal><![CDATA[
      (x \ 1) * ((x \ R(x,y,z)) \ 1) = (x \ R(x,y,z)) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,71,a(flip),b,2394,a),flip(a)].">
      <j1 rule="hyper" parents="119 71 2394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2396">
    <literal><![CDATA[
      (x * (y * T(y \ 1,x))) * (x \ 1) = x \ (x * (y * T(y \ 1,x)))
    ]]></literal>
    <justification jstring="[para(2110(a,1),2112(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2110 2112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2397">
    <literal><![CDATA[
      (x * (y * T(y \ 1,x))) * (x \ 1) = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,9,a(flip),b,2396,a),flip(a)].">
      <j1 rule="hyper" parents="299 9 2396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2398">
    <literal><![CDATA[
      (x * (y * T(y \ 1,x))) \ (y * T(y \ 1,x)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(119,a,9,a(flip),b,2396,a)].">
      <j1 rule="hyper" parents="119 9 2396"/>
    </justification>
  </clause>

  <clause id="2400">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ 1,y) = (y * (x \ T(x,y))) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(1108(a,1),2397(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1108 2397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2401">
    <literal><![CDATA[
      (x * K(y,x)) \ (L(y \ 1,y,x) * T(L(y \ 1,y,x) \ 1,x)) = x \ 1
    ]]></literal>
    <justification jstring="[para(1382(a,2),2398(a,1,1,2))].">
      <j1 rule="para" parents="1382 2398"/>
    </justification>
  </clause>

  <clause id="2402">
    <literal><![CDATA[
      (x * (y \ T(y,x))) * (x \ 1) = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,1108,a(flip),b,2400,a),flip(a)].">
      <j1 rule="hyper" parents="65 1108 2400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2403">
    <literal><![CDATA[
      (x * K(y,x)) \ K(y,x) = x \ 1
    ]]></literal>
    <justification jstring="[para(1382(a,2),2401(a,1,2))].">
      <j1 rule="para" parents="1382 2401"/>
    </justification>
  </clause>

  <clause id="2404">
    <literal><![CDATA[
      K(x,y) / (y \ 1) = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(192,a,2403,a)].">
      <j1 rule="hyper" parents="192 2403"/>
    </justification>
  </clause>

  <clause id="2405">
    <literal><![CDATA[
      (x * K(y,x)) * (x \ 1) != z * u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) / u = z
    ]]></literal>
    <justification jstring="[para(2403(a,1),388(a,1,2))].">
      <j1 rule="para" parents="2403 388"/>
    </justification>
  </clause>

  <clause id="2406">
    <literal><![CDATA[
      (1 / x) * K(y,1 / x) = K(y,1 / x) / x
    ]]></literal>
    <justification jstring="[para(79(a,1),2404(a,1,2)),flip(a)].">
      <j1 rule="para" parents="79 2404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2407">
    <literal><![CDATA[
      T(x * K(y,x),x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) \ K(y,x) = z
    ]]></literal>
    <justification jstring="[para(2404(a,1),400(a,1,1))].">
      <j1 rule="para" parents="2404 400"/>
    </justification>
  </clause>

  <clause id="2408">
    <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(299,a,255,a(flip),b,2113,a),flip(a)].">
      <j1 rule="hyper" parents="299 255 2113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2409">
    <literal><![CDATA[
      L(x * T(x \ 1,y),y,1 / y) = (y * (x * T(x \ 1,y))) / y
    ]]></literal>
    <justification jstring="[para(2110(a,1),2408(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2110 2408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2410">
    <literal><![CDATA[
      (x * (((x * y) \ x) * T(((x * y) \ x) \ 1,x))) / x = L(K(y,x),x,1 / x)
    ]]></literal>
    <justification jstring="[para(1377(a,2),2409(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1377 2409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2411">
    <literal><![CDATA[
      L(K(x,y),y,1 / y) = (y * K(x,y)) / y
    ]]></literal>
    <justification jstring="[para(1377(a,2),2410(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1377 2410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2412">
    <literal><![CDATA[
      ((x / y) * ((z * ((x / y) \ u)) / z)) * y = x * ((z * (x \ (u * y))) / z)
    ]]></literal>
    <justification jstring="[para(12(a,1),2257(a,2,2,1,2,1))].">
      <j1 rule="para" parents="12 2257"/>
    </justification>
  </clause>

  <clause id="2413">
    <literal><![CDATA[
      (x * ((y * (x \ (z * u))) / y)) / u = (x / u) * ((y * ((x / u) \ z)) / y)
    ]]></literal>
    <justification jstring="[hyper(137,a,2412,a)].">
      <j1 rule="hyper" parents="137 2412"/>
    </justification>
  </clause>

  <clause id="2414">
    <literal><![CDATA[
      (x / y) * ((z * ((x / y) \ 1)) / z) = (x * ((z * (x \ y)) / z)) / y
    ]]></literal>
    <justification jstring="[para(7(a,1),2413(a,1,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 2413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2415">
    <literal><![CDATA[
      (x * (T(y,x) / y)) \ (x * z) = x * ((x * (T(y,x) / y)) \ z)
    ]]></literal>
    <justification jstring="[para(2328(a,1),2329(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2328 2329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2416">
    <literal><![CDATA[
      K(x \ 1,x) * T(K(x \ 1,x) \ y,z) = (x \ T(x * (y / x),z)) * x
    ]]></literal>
    <justification jstring="[hyper(299,a,1594,a(flip),b,2371,a),flip(a)].">
      <j1 rule="hyper" parents="299 1594 2371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2417">
    <literal><![CDATA[
      L(x * ((x \ 1) \ ((y * z) \ u)),x \ (1 / x),y * z) = (y * (z * (x \ (1 / x)))) \ u
    ]]></literal>
    <justification jstring="[para(1709(a,1),1047(a,1,1))].">
      <j1 rule="para" parents="1709 1047"/>
    </justification>
  </clause>

  <clause id="2418">
    <literal><![CDATA[
      (x * y) * K(z \ (z / L(u,y,x)),z) = x * ((y * u) * T((y * u) \ y,z))
    ]]></literal>
    <justification jstring="[hyper(1004,a,1391,a),flip(a)].">
      <j1 rule="hyper" parents="1004 1391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2419">
    <literal><![CDATA[
      (x * y) * K(z \ (z / L(u,y,x)),z) = x * (y * (u * T(u \ 1,z)))
    ]]></literal>
    <justification jstring="[para(801(a,1),2418(a,2,2))].">
      <j1 rule="para" parents="801 2418"/>
    </justification>
  </clause>

  <clause id="2420">
    <literal><![CDATA[
      L(x * T(x \ 1,y),z,u) = K(y \ (y / L(x,z,u)),y)
    ]]></literal>
    <justification jstring="[hyper(490,a,2419,a)].">
      <j1 rule="hyper" parents="490 2419"/>
    </justification>
  </clause>

  <clause id="2421">
    <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(299,a,1290,a(flip),b,2420,a)].">
      <j1 rule="hyper" parents="299 1290 2420"/>
    </justification>
  </clause>

  <clause id="2422">
    <literal><![CDATA[
      L(x * T(x \ 1,L(x,y,z)),y,z) = K(L(x,y,z) \ 1,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(73(a,1),2420(a,2,1,2))].">
      <j1 rule="para" parents="73 2420"/>
    </justification>
  </clause>

  <clause id="2423">
    <literal><![CDATA[
      L(x \ T(x,y),z,u) = K(y \ (y / L(x \ 1,z,u)),y)
    ]]></literal>
    <justification jstring="[para(1108(a,1),2420(a,1,1))].">
      <j1 rule="para" parents="1108 2420"/>
    </justification>
  </clause>

  <clause id="2424">
    <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),2423(a,2,1,2))].">
      <j1 rule="para" parents="11 2423"/>
    </justification>
  </clause>

  <clause id="2426">
    <literal><![CDATA[
      K(x \ (x / R(y,z,u)),x) = (((y * z) * T((y * z) \ z,x)) * u) / (z * u)
    ]]></literal>
    <justification jstring="[para(1462(a,1),1404(a,2,1))].">
      <j1 rule="para" parents="1462 1404"/>
    </justification>
  </clause>

  <clause id="2427">
    <literal><![CDATA[
      K(x \ (x / R(y,z,u)),x) = (((y * T(y \ 1,x)) * z) * u) / (z * u)
    ]]></literal>
    <justification jstring="[para(1472(a,1),2426(a,2,1,1))].">
      <j1 rule="para" parents="1472 2426"/>
    </justification>
  </clause>

  <clause id="2428">
    <literal><![CDATA[
      R(x * T(x \ 1,y),z,u) = K(y \ (y / R(x,z,u)),y)
    ]]></literal>
    <justification jstring="[hyper(299,a,20,a,b,2427,a)].">
      <j1 rule="hyper" parents="299 20 2427"/>
    </justification>
  </clause>

  <clause id="2429">
    <literal><![CDATA[
      K(x \ (x / R(y,z,u)),x) != w
    ]]></literal>
    <literal><![CDATA[
      R(y * T(y \ 1,x),z,u) = w
    ]]></literal>
    <justification jstring="[para(2427(a,2),549(a,1))].">
      <j1 rule="para" parents="2427 549"/>
    </justification>
  </clause>

  <clause id="2430">
    <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(299,a,1290,a(flip),b,2428,a)].">
      <j1 rule="hyper" parents="299 1290 2428"/>
    </justification>
  </clause>

  <clause id="2431">
    <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(1457(a,1),2428(a,2,1,2))].">
      <j1 rule="para" parents="1457 2428"/>
    </justification>
  </clause>

  <clause id="2432">
    <literal><![CDATA[
      R(x * T(x \ 1,R(x,y,z)),y,z) != u * R(x,y,z)
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) \ 1 = u
    ]]></literal>
    <justification jstring="[para(2430(a,1),237(a,1))].">
      <j1 rule="para" parents="2430 237"/>
    </justification>
  </clause>

  <clause id="2433">
    <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(65,a,1868,a(flip),b,1805,a)].">
      <j1 rule="hyper" parents="65 1868 1805"/>
    </justification>
  </clause>

  <clause id="2435">
    <literal><![CDATA[
      x * ((L(x,y,z) * (x \ 1)) / L(x,y,z)) = L(1 / x,L(x,y,z),1 / x) * x
    ]]></literal>
    <justification jstring="[para(2433(a,1),941(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2433 941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2436">
    <literal><![CDATA[
      x * ((L(x,y,z) * (x \ 1)) / L(x,y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x * L(x \ 1,L(x,y,z),1 / x) = u
    ]]></literal>
    <justification jstring="[para(2435(a,2),965(a,1))].">
      <j1 rule="para" parents="2435 965"/>
    </justification>
  </clause>

  <clause id="2437">
    <literal><![CDATA[
      (x * (y * (z \ (1 / z)))) \ u = z * ((z \ 1) \ ((x * y) \ u))
    ]]></literal>
    <justification jstring="[hyper(506,a,2417,a),flip(a)].">
      <j1 rule="hyper" parents="506 2417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2439">
    <literal><![CDATA[
      x * L(x \ 1,L(x,y,z),1 / x) = K(L(x,y,z),1 / x)
    ]]></literal>
    <justification jstring="[hyper(2436,a,1885,a)].">
      <j1 rule="hyper" parents="2436 1885"/>
    </justification>
  </clause>

  <clause id="2440">
    <literal><![CDATA[
      (((x * x) \ y) * z) \ (((x * x) \ 1) * (y * (z * u))) = L(L(u,z,y),y * z,(x * x) \ 1)
    ]]></literal>
    <justification jstring="[para(664(a,1),1331(a,1,1))].">
      <j1 rule="para" parents="664 1331"/>
    </justification>
  </clause>

  <clause id="2441">
    <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(2421(a,1),1362(a,1,1))].">
      <j1 rule="para" parents="2421 1362"/>
    </justification>
  </clause>

  <clause id="2442">
    <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(342(a,1),2441(a,1,1,1))].">
      <j1 rule="para" parents="342 2441"/>
    </justification>
  </clause>

  <clause id="2443">
    <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(1353(a,1),2442(a,1,2))].">
      <j1 rule="para" parents="1353 2442"/>
    </justification>
  </clause>

  <clause id="2444">
    <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(65,a,25,a,b,2443,a)].">
      <j1 rule="hyper" parents="65 25 2443"/>
    </justification>
  </clause>

  <clause id="2445">
    <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(1358(a,1),2444(a,2,1))].">
      <j1 rule="para" parents="1358 2444"/>
    </justification>
  </clause>

  <clause id="2446">
    <literal><![CDATA[
      (((x * y) \ x) \ K(y,x)) / (((x * y) \ x) \ 1) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,1377,a,b,1381,a),flip(a)].">
      <j1 rule="hyper" parents="299 1377 1381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2447">
    <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(2446(a,1),400(a,1,1))].">
      <j1 rule="para" parents="2446 400"/>
    </justification>
  </clause>

  <clause id="2448">
    <literal><![CDATA[
      T(x,(y \ 1) \ ((y \ 1) \ 1)) / (z * y) = (y \ (1 / y)) * (x / ((z * (1 / y)) * 1))
    ]]></literal>
    <justification jstring="[para(1705(a,1),1748(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1705 1748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2449">
    <literal><![CDATA[
      T(x,(y \ 1) \ ((y \ 1) \ 1)) / (z * y) = (y \ (1 / y)) * (x / (z * (1 / y)))
    ]]></literal>
    <justification jstring="[para(8(a,1),2448(a,2,2,2))].">
      <j1 rule="para" parents="8 2448"/>
    </justification>
  </clause>

  <clause id="2450">
    <literal><![CDATA[
      T(x,(y \ 1) \ ((y \ 1) \ 1)) / (z * y) = (y \ 1) * (y \ (x / (z * (1 / y))))
    ]]></literal>
    <justification jstring="[hyper(299,a,1710,a(flip),b,2449,a),flip(a)].">
      <j1 rule="hyper" parents="299 1710 2449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2451">
    <literal><![CDATA[
      T(x,1 \ (y * ((y \ 1) \ 1))) / (z * y) = (y \ 1) * (y \ (x / (z * (1 / y))))
    ]]></literal>
    <justification jstring="[para(1092(a,1),2450(a,1,1,2))].">
      <j1 rule="para" parents="1092 2450"/>
    </justification>
  </clause>

  <clause id="2452">
    <literal><![CDATA[
      T(x,1 \ ((1 / y) \ y)) / (z * y) = (y \ 1) * (y \ (x / (z * (1 / y))))
    ]]></literal>
    <justification jstring="[para(1669(a,1),2451(a,1,1,2,2))].">
      <j1 rule="para" parents="1669 2451"/>
    </justification>
  </clause>

  <clause id="2453">
    <literal><![CDATA[
      (x \ 1) * (x \ (y / (z * (1 / x)))) = T(y,(1 / x) \ x) / (z * x)
    ]]></literal>
    <justification jstring="[para(67(a,1),2452(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="67 2452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2454">
    <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(253(a,2),1787(a,1,2,1,1))].">
      <j1 rule="para" parents="253 1787"/>
    </justification>
  </clause>

  <clause id="2455">
    <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(253(a,2),1788(a,1,2,1,1))].">
      <j1 rule="para" parents="253 1788"/>
    </justification>
  </clause>

  <clause id="2456">
    <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),2199(a,1,1))].">
      <j1 rule="para" parents="89 2199"/>
    </justification>
  </clause>

  <clause id="2457">
    <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),2456(a,1,2,1,1))].">
      <j1 rule="para" parents="89 2456"/>
    </justification>
  </clause>

  <clause id="2458">
    <literal><![CDATA[
      (((x * x) \ y) * z) \ ((x * x) \ (y * (z * u))) = L(L(u,z,y),y * z,(x * x) \ 1)
    ]]></literal>
    <justification jstring="[para(422(a,1),2440(a,1,2))].">
      <j1 rule="para" parents="422 2440"/>
    </justification>
  </clause>

  <clause id="2459">
    <literal><![CDATA[
      (((x * x) \ y) * z) \ (((x * x) \ y) * (z * u)) = L(L(u,z,y),y * z,(x * x) \ 1)
    ]]></literal>
    <justification jstring="[para(664(a,1),2458(a,1,2))].">
      <j1 rule="para" parents="664 2458"/>
    </justification>
  </clause>

  <clause id="2460">
    <literal><![CDATA[
      L(L(x,y,z),z * y,(u * u) \ 1) = L(x,y,(u * u) \ z)
    ]]></literal>
    <justification jstring="[hyper(493,a,2459,a),flip(a)].">
      <j1 rule="hyper" parents="493 2459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2461">
    <literal><![CDATA[
      L(x,y,(z * z) \ u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(2021,a,2460,a),flip(a)].">
      <j1 rule="hyper" parents="2021 2460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2462">
    <literal><![CDATA[
      L(x,y,(z * z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(2460(a,1),2021(a,1))].">
      <j1 rule="para" parents="2460 2021"/>
    </justification>
  </clause>

  <clause id="2464">
    <literal><![CDATA[
      L(x,y,(z * z) * u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),2461(a,1,3)),flip(a)].">
      <j1 rule="para" parents="9 2461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2465">
    <literal><![CDATA[
      L(x,y,z * (z * u)) = L(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[para(18(a,2),2461(a,1,3)),flip(a)].">
      <j1 rule="para" parents="18 2461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2466">
    <literal><![CDATA[
      L(x,y,T(z,u * u)) = L(x,y,z * (u * u))
    ]]></literal>
    <justification jstring="[para(22(a,2),2461(a,1,3))].">
      <j1 rule="para" parents="22 2461"/>
    </justification>
  </clause>

  <clause id="2467">
    <literal><![CDATA[
      L(x,y,1 / z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(264(a,1),2461(a,1,3))].">
      <j1 rule="para" parents="264 2461"/>
    </justification>
  </clause>

  <clause id="2468">
    <literal><![CDATA[
      L(x,y,z * ((z \ 1) \ u)) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(465(a,1),2461(a,1,3))].">
      <j1 rule="para" parents="465 2461"/>
    </justification>
  </clause>

  <clause id="2469">
    <literal><![CDATA[
      L(x \ (y * ((y \ 1) \ z)),x,y) = ((1 / y) * x) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,1672,a(flip),b,2467,a),flip(a)].">
      <j1 rule="hyper" parents="65 1672 2467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2470">
    <literal><![CDATA[
      L(x,y,z \ 1) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(76(a,1),2467(a,1,3)),flip(a)].">
      <j1 rule="para" parents="76 2467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2471">
    <literal><![CDATA[
      L(x,y,1 / z) = L(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,2467,a,b,2470,a)].">
      <j1 rule="hyper" parents="299 2467 2470"/>
    </justification>
  </clause>

  <clause id="2472">
    <literal><![CDATA[
      (1 / x) * (x * y) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,475,a,b,2470,a)].">
      <j1 rule="hyper" parents="299 475 2470"/>
    </justification>
  </clause>

  <clause id="2473">
    <literal><![CDATA[
      L(T(x,y),y,y \ 1) = (1 / y) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(299,a,513,a(flip),b,2470,a),flip(a)].">
      <j1 rule="hyper" parents="299 513 2470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2474">
    <literal><![CDATA[
      L(x \ y,x,x \ 1) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(299,a,511,a(flip),b,2470,a),flip(a)].">
      <j1 rule="hyper" parents="299 511 2470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2475">
    <literal><![CDATA[
      (1 / x) \ L(y,x,x \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(119,a,2470,a,b,475,a)].">
      <j1 rule="hyper" parents="119 2470 475"/>
    </justification>
  </clause>

  <clause id="2476">
    <literal><![CDATA[
      L(x \ ((y \ 1) \ z),x,y) = ((y \ 1) * x) \ z
    ]]></literal>
    <justification jstring="[hyper(65,a,281,a(flip),b,2470,a),flip(a)].">
      <j1 rule="hyper" parents="65 281 2470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2477">
    <literal><![CDATA[
      ((x \ 1) * y) * L(z,y,x) = (x \ 1) * (y * z)
    ]]></literal>
    <justification jstring="[para(2470(a,1),94(a,1,2))].">
      <j1 rule="para" parents="2470 94"/>
    </justification>
  </clause>

  <clause id="2478">
    <literal><![CDATA[
      L(x,y,(z * z) \ (u \ 1)) = L(x,y,u * (z * z))
    ]]></literal>
    <justification jstring="[para(419(a,1),2470(a,1,3))].">
      <j1 rule="para" parents="419 2470"/>
    </justification>
  </clause>

  <clause id="2479">
    <literal><![CDATA[
      L(x,y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      (1 / y) * (y * x) = z
    ]]></literal>
    <justification jstring="[para(2470(a,2),758(a,1))].">
      <j1 rule="para" parents="2470 758"/>
    </justification>
  </clause>

  <clause id="2480">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ L(y,x \ 1,x) = (((x \ 1) \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[para(2470(a,1),1761(a,1,2))].">
      <j1 rule="para" parents="2470 1761"/>
    </justification>
  </clause>

  <clause id="2481">
    <literal><![CDATA[
      L(x,y,(1 / z) * u) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(265(a,1),2464(a,1,3)),flip(a)].">
      <j1 rule="para" parents="265 2464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2482">
    <literal><![CDATA[
      L(x,y,(z \ 1) \ u) = L(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(724(a,1),2464(a,1,3))].">
      <j1 rule="para" parents="724 2464"/>
    </justification>
  </clause>

  <clause id="2483">
    <literal><![CDATA[
      L(x,y,(1 / z) \ u) = L(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(734(a,1),2464(a,1,3)),flip(a)].">
      <j1 rule="para" parents="734 2464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2484">
    <literal><![CDATA[
      L(x,y,T(z,u * u) * w) = L(x,y,z * ((u * u) * w))
    ]]></literal>
    <justification jstring="[para(1067(a,1),2464(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1067 2464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2485">
    <literal><![CDATA[
      L(x,y,y \ 1) \ ((1 / y) * (x * y)) = L(K(x,y),y * x,1 / y)
    ]]></literal>
    <justification jstring="[para(2472(a,1),289(a,1,1))].">
      <j1 rule="para" parents="2472 289"/>
    </justification>
  </clause>

  <clause id="2486">
    <literal><![CDATA[
      L(L(x \ y,z,u),x,x \ 1) = L((1 / x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(2474(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2474 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2487">
    <literal><![CDATA[
      x * ((1 / x) * (y * x)) = L(y,x,x \ 1) * x
    ]]></literal>
    <justification jstring="[para(2474(a,1),682(a,1,2))].">
      <j1 rule="para" parents="2474 682"/>
    </justification>
  </clause>

  <clause id="2489">
    <literal><![CDATA[
      L(x,y,(z \ 1) * u) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(9(a,1),2468(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="9 2468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2490">
    <literal><![CDATA[
      L(x,y,z * (1 / z)) = x
    ]]></literal>
    <justification jstring="[hyper(503,a,2481,a),flip(a)].">
      <j1 rule="hyper" parents="503 2481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2491">
    <literal><![CDATA[
      L(x,y,K(z,1 / z)) = x
    ]]></literal>
    <justification jstring="[para(256(a,2),2490(a,1,3))].">
      <j1 rule="para" parents="256 2490"/>
    </justification>
  </clause>

  <clause id="2492">
    <literal><![CDATA[
      L(x,y,K(z \ 1,z)) = x
    ]]></literal>
    <justification jstring="[para(1699(a,2),2490(a,1,3))].">
      <j1 rule="para" parents="1699 2490"/>
    </justification>
  </clause>

  <clause id="2493">
    <literal><![CDATA[
      (K(x,1 / x) * y) * z = K(x,1 / x) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(1318,a,2491,a),flip(a)].">
      <j1 rule="hyper" parents="1318 2491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2494">
    <literal><![CDATA[
      K(x,1 / x) * (1 / y) = K(x,1 / x) / y
    ]]></literal>
    <justification jstring="[para(2491(a,1),401(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2491 401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2495">
    <literal><![CDATA[
      (K(x \ 1,x) * y) * z = K(x \ 1,x) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(1318,a,2492,a),flip(a)].">
      <j1 rule="hyper" parents="1318 2492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2496">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ (K(x \ 1,x) * z) = y \ z
    ]]></literal>
    <justification jstring="[hyper(65,a,96,a(flip),b,2492,a)].">
      <j1 rule="hyper" parents="65 96 2492"/>
    </justification>
  </clause>

  <clause id="2497">
    <literal><![CDATA[
      L(x,y,K(z \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(2492(a,1),52(a,2))].">
      <j1 rule="para" parents="2492 52"/>
    </justification>
  </clause>

  <clause id="2498">
    <literal><![CDATA[
      K(x \ 1,x) * (1 / y) = K(x \ 1,x) / y
    ]]></literal>
    <justification jstring="[para(2492(a,1),401(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2492 401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2499">
    <literal><![CDATA[
      (K(x \ 1,x) * y) / z = K(x \ 1,x) * (y / z)
    ]]></literal>
    <justification jstring="[para(2492(a,1),585(a,1,2))].">
      <j1 rule="para" parents="2492 585"/>
    </justification>
  </clause>

  <clause id="2500">
    <literal><![CDATA[
      L(x,y,((z \ 1) \ 1) * u) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[hyper(299,a,2489,a(flip),b,2489,a),flip(a)].">
      <j1 rule="hyper" parents="299 2489 2489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2501">
    <literal><![CDATA[
      L(x,y,1 / z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(264(a,1),2462(a,1,3))].">
      <j1 rule="para" parents="264 2462"/>
    </justification>
  </clause>

  <clause id="2502">
    <literal><![CDATA[
      L(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(76(a,1),2501(a,1,3))].">
      <j1 rule="para" parents="76 2501"/>
    </justification>
  </clause>

  <clause id="2503">
    <literal><![CDATA[
      L(x,y,z \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(2471(a,1),2501(a,1))].">
      <j1 rule="para" parents="2471 2501"/>
    </justification>
  </clause>

  <clause id="2504">
    <literal><![CDATA[
      L(x,y,1 / z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(2467(a,2),2502(a,1))].">
      <j1 rule="para" parents="2467 2502"/>
    </justification>
  </clause>

  <clause id="2505">
    <literal><![CDATA[
      L(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,1 / z) = u
    ]]></literal>
    <justification jstring="[para(79(a,1),2503(a,1,3))].">
      <j1 rule="para" parents="79 2503"/>
    </justification>
  </clause>

  <clause id="2506">
    <literal><![CDATA[
      ((x \ 1) * (x \ y)) \ z = y \ (x * ((x \ 1) \ z))
    ]]></literal>
    <justification jstring="[hyper(615,a,2476,a),flip(a)].">
      <j1 rule="hyper" parents="615 2476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2507">
    <literal><![CDATA[
      (x * y) \ (x * ((x \ 1) \ z)) = ((x \ 1) * y) \ z
    ]]></literal>
    <justification jstring="[hyper(65,a,96,a(flip),b,2476,a)].">
      <j1 rule="hyper" parents="65 96 2476"/>
    </justification>
  </clause>

  <clause id="2508">
    <literal><![CDATA[
      (x * ((1 / x) * y)) * L(z,x * y,x) = (x \ 1) * ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(944(a,1),2477(a,1,1))].">
      <j1 rule="para" parents="944 2477"/>
    </justification>
  </clause>

  <clause id="2509">
    <literal><![CDATA[
      L(x,y,z * (u * u)) = L(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(2462,a,2478,a),flip(a)].">
      <j1 rule="hyper" parents="2462 2478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2511">
    <literal><![CDATA[
      L(x,y,z * (u * u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,2470,a(flip),b,2509,a),flip(a)].">
      <j1 rule="hyper" parents="299 2470 2509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2512">
    <literal><![CDATA[
      L(x,y,z * (u * u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(2509(a,2),2503(a,1))].">
      <j1 rule="para" parents="2509 2503"/>
    </justification>
  </clause>

  <clause id="2513">
    <literal><![CDATA[
      L(x,y,T(z,u * u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,2466,a,b,2511,a)].">
      <j1 rule="hyper" parents="65 2466 2511"/>
    </justification>
  </clause>

  <clause id="2514">
    <literal><![CDATA[
      L(x,y,z / (u * u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(12(a,1),2511(a,1,3)),flip(a)].">
      <j1 rule="para" parents="12 2511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2515">
    <literal><![CDATA[
      L(x,y,z * (u * (w * w))) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(35(a,1),2511(a,1,3))].">
      <j1 rule="para" parents="35 2511"/>
    </justification>
  </clause>

  <clause id="2517">
    <literal><![CDATA[
      L(x,(y * y) \ z,u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(2016,a,2514,a)].">
      <j1 rule="hyper" parents="2016 2514"/>
    </justification>
  </clause>

  <clause id="2519">
    <literal><![CDATA[
      L(x,(y * y) * z,u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),2517(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 2517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2520">
    <literal><![CDATA[
      L(x,y * (y * z),u) = L(x,L(z,y,y),u)
    ]]></literal>
    <justification jstring="[para(18(a,2),2517(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18 2517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2521">
    <literal><![CDATA[
      L(x,1 / y,z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(264(a,1),2517(a,1,2))].">
      <j1 rule="para" parents="264 2517"/>
    </justification>
  </clause>

  <clause id="2522">
    <literal><![CDATA[
      L(x,((y * y) \ z) * u,w) = L(x,z * u,w)
    ]]></literal>
    <justification jstring="[para(664(a,1),2517(a,1,2))].">
      <j1 rule="para" parents="664 2517"/>
    </justification>
  </clause>

  <clause id="2523">
    <literal><![CDATA[
      L(x,y \ (z * (y \ 1)),u) = L(x,T(z,y \ 1),u)
    ]]></literal>
    <justification jstring="[para(726(a,1),2517(a,1,2))].">
      <j1 rule="para" parents="726 2517"/>
    </justification>
  </clause>

  <clause id="2524">
    <literal><![CDATA[
      L(x,x,y) = (y * (1 / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(810,a,2521,a),flip(a)].">
      <j1 rule="hyper" parents="810 2521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2525">
    <literal><![CDATA[
      L(T(x,x \ 1),1 / x,x) = x
    ]]></literal>
    <justification jstring="[hyper(299,a,1732,a(flip),b,2521,a),flip(a)].">
      <j1 rule="hyper" parents="299 1732 2521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2526">
    <literal><![CDATA[
      L(x,y \ 1,z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(76(a,1),2521(a,1,2)),flip(a)].">
      <j1 rule="para" parents="76 2521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2527">
    <literal><![CDATA[
      L(x,x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (y * (1 / x)) \ y = z
    ]]></literal>
    <justification jstring="[para(2521(a,1),810(a,1))].">
      <j1 rule="para" parents="2521 810"/>
    </justification>
  </clause>

  <clause id="2528">
    <literal><![CDATA[
      L(x,1 / y,z) = L(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,2521,a,b,2526,a)].">
      <j1 rule="hyper" parents="299 2521 2526"/>
    </justification>
  </clause>

  <clause id="2529">
    <literal><![CDATA[
      L(x,(y \ 1) \ 1,z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,2526,a(flip),b,2526,a),flip(a)].">
      <j1 rule="hyper" parents="299 2526 2526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2530">
    <literal><![CDATA[
      L((x \ 1) * (x \ y),x,x) = 1 \ ((x \ 1) * ((x \ 1) * y))
    ]]></literal>
    <justification jstring="[hyper(65,a,2013,a(flip),b,2526,a),flip(a)].">
      <j1 rule="hyper" parents="65 2013 2526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2531">
    <literal><![CDATA[
      L((x \ 1) \ y,x,z) = (z * (x \ 1)) \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,96,a(flip),b,2526,a),flip(a)].">
      <j1 rule="hyper" parents="65 96 2526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2532">
    <literal><![CDATA[
      L(x,x \ 1,y) = (y * (1 / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(65,a,2526,a,b,2524,a)].">
      <j1 rule="hyper" parents="65 2526 2524"/>
    </justification>
  </clause>

  <clause id="2534">
    <literal><![CDATA[
      T(L(x,1 / x,x),x \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(65,a,25,a(flip),b,2525,a)].">
      <j1 rule="hyper" parents="65 25 2525"/>
    </justification>
  </clause>

  <clause id="2536">
    <literal><![CDATA[
      L(x,(y * y) * z,u) = L(x,z,u * (w * w))
    ]]></literal>
    <justification jstring="[hyper(299,a,2511,a,b,2519,a),flip(a)].">
      <j1 rule="hyper" parents="299 2511 2519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2537">
    <literal><![CDATA[
      L(x,(1 / y) * z,u) = L(x,y * z,u)
    ]]></literal>
    <justification jstring="[para(265(a,1),2519(a,1,2)),flip(a)].">
      <j1 rule="para" parents="265 2519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2538">
    <literal><![CDATA[
      L(x,(y \ 1) \ z,u) = L(x,y \ z,u)
    ]]></literal>
    <justification jstring="[para(724(a,1),2519(a,1,2))].">
      <j1 rule="para" parents="724 2519"/>
    </justification>
  </clause>

  <clause id="2539">
    <literal><![CDATA[
      L(x,y \ ((z * z) * (y \ 1)),u) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(2519(a,1),2024(a,1))].">
      <j1 rule="para" parents="2519 2024"/>
    </justification>
  </clause>

  <clause id="2540">
    <literal><![CDATA[
      L(x,1 / x,x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(299,a,1715,a(flip),b,2528,a),flip(a)].">
      <j1 rule="hyper" parents="299 1715 2528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2541">
    <literal><![CDATA[
      x / L(y,y \ 1,x) = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(2528(a,1),401(a,1,2))].">
      <j1 rule="para" parents="2528 401"/>
    </justification>
  </clause>

  <clause id="2542">
    <literal><![CDATA[
      L(x,((y \ z) \ z) \ 1,u) = L(x,1 / T(y,y \ z),u)
    ]]></literal>
    <justification jstring="[para(294(a,2),2528(a,1,2)),flip(a)].">
      <j1 rule="para" parents="294 2528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2543">
    <literal><![CDATA[
      L(x,y \ 1,T(z,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,1 / y,(z \ u) \ u) = w
    ]]></literal>
    <justification jstring="[para(2528(a,1),2149(a,1))].">
      <j1 rule="para" parents="2528 2149"/>
    </justification>
  </clause>

  <clause id="2544">
    <literal><![CDATA[
      x / (1 / (1 / x)) = x * (1 / x)
    ]]></literal>
    <justification jstring="[para(2540(a,1),401(a,1,2))].">
      <j1 rule="para" parents="2540 401"/>
    </justification>
  </clause>

  <clause id="2545">
    <literal><![CDATA[
      T(1 / (1 / x),x \ 1) = x
    ]]></literal>
    <justification jstring="[para(2540(a,1),2534(a,1,1))].">
      <j1 rule="para" parents="2540 2534"/>
    </justification>
  </clause>

  <clause id="2546">
    <literal><![CDATA[
      T(T(1 / (1 / x),y),x \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2545(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2545 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2547">
    <literal><![CDATA[
      T(x,y \ 1) != T(y,z)
    ]]></literal>
    <literal><![CDATA[
      T(1 / (1 / y),z) = x
    ]]></literal>
    <justification jstring="[para(2545(a,1),148(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2545 148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2548">
    <literal><![CDATA[
      T(x,x \ 1) / x = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(2545(a,1),1577(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2545 1577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2549">
    <literal><![CDATA[
      L(x,T(y,y \ 1),z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(108(a,2),2529(a,1,2))].">
      <j1 rule="para" parents="108 2529"/>
    </justification>
  </clause>

  <clause id="2550">
    <literal><![CDATA[
      x / (1 / (1 / x)) = K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(299,a,256,a,b,2544,a),flip(a)].">
      <j1 rule="hyper" parents="299 256 2544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2551">
    <literal><![CDATA[
      K(x,x \ 1) * x = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(143,a,2548,a)].">
      <j1 rule="hyper" parents="143 2548"/>
    </justification>
  </clause>

  <clause id="2552">
    <literal><![CDATA[
      ((x \ 1) \ 1) / x = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(108(a,1),2548(a,1,1))].">
      <j1 rule="para" parents="108 2548"/>
    </justification>
  </clause>

  <clause id="2553">
    <literal><![CDATA[
      (x * T(y,y \ 1)) * L(z,y,x) = x * (T(y,y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(2549(a,1),94(a,1,2))].">
      <j1 rule="para" parents="2549 94"/>
    </justification>
  </clause>

  <clause id="2554">
    <literal><![CDATA[
      K(x,1 / x) * (1 / (1 / x)) = x
    ]]></literal>
    <justification jstring="[hyper(143,a,2550,a)].">
      <j1 rule="hyper" parents="143 2550"/>
    </justification>
  </clause>

  <clause id="2555">
    <literal><![CDATA[
      x * K(x,x \ 1) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(2313,a,2551,a)].">
      <j1 rule="hyper" parents="2313 2551"/>
    </justification>
  </clause>

  <clause id="2556">
    <literal><![CDATA[
      K(x,x \ 1) * x = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(299,a,108,a(flip),b,2551,a),flip(a)].">
      <j1 rule="hyper" parents="299 108 2551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2558">
    <literal><![CDATA[
      x * K(x,x \ 1) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(299,a,108,a(flip),b,2555,a),flip(a)].">
      <j1 rule="hyper" parents="299 108 2555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2559">
    <literal><![CDATA[
      ((x \ 1) \ 1) / x != y
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(2556(a,1),307(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2556 307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2562">
    <literal><![CDATA[
      K(x \ (x / L(y,y \ 1,x)),z) = K(1 / y,z)
    ]]></literal>
    <justification jstring="[para(2541(a,2),722(a,1,1,2))].">
      <j1 rule="para" parents="2541 722"/>
    </justification>
  </clause>

  <clause id="2563">
    <literal><![CDATA[
      L(x,y * (1 / y),z) = x
    ]]></literal>
    <justification jstring="[hyper(497,a,2537,a),flip(a)].">
      <j1 rule="hyper" parents="497 2537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2564">
    <literal><![CDATA[
      L(x,(1 / (y * (z * z))) * u,w) = L(x,y * ((z * z) * u),w)
    ]]></literal>
    <justification jstring="[para(34(a,1),2537(a,2,2))].">
      <j1 rule="para" parents="34 2537"/>
    </justification>
  </clause>

  <clause id="2565">
    <literal><![CDATA[
      L(x,(y \ 1) * z,u) = L(x,y * z,u)
    ]]></literal>
    <justification jstring="[para(76(a,1),2537(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="76 2537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2566">
    <literal><![CDATA[
      (x * ((1 / y) * z)) * L(u,y * z,x) = x * (((1 / y) * z) * u)
    ]]></literal>
    <justification jstring="[para(2537(a,1),94(a,1,2))].">
      <j1 rule="para" parents="2537 94"/>
    </justification>
  </clause>

  <clause id="2567">
    <literal><![CDATA[
      L(x,y * (1 / y),z) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(2537(a,1),497(a,1))].">
      <j1 rule="para" parents="2537 497"/>
    </justification>
  </clause>

  <clause id="2568">
    <literal><![CDATA[
      L(x,T((1 / y) * z,y),u) = L(x,y * ((y \ z) * y),u)
    ]]></literal>
    <justification jstring="[para(820(a,1),2537(a,1,2))].">
      <j1 rule="para" parents="820 2537"/>
    </justification>
  </clause>

  <clause id="2569">
    <literal><![CDATA[
      L(x,K(y \ 1,y),z) = x
    ]]></literal>
    <justification jstring="[para(1699(a,2),2563(a,1,2))].">
      <j1 rule="para" parents="1699 2563"/>
    </justification>
  </clause>

  <clause id="2570">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * z = x * (K(y \ 1,y) * z)
    ]]></literal>
    <justification jstring="[hyper(1318,a,2569,a),flip(a)].">
      <j1 rule="hyper" parents="1318 2569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2571">
    <literal><![CDATA[
      K(x \ 1,x) * ((y * K(x \ 1,x)) \ z) = y \ z
    ]]></literal>
    <justification jstring="[hyper(1038,a,2569,a)].">
      <j1 rule="hyper" parents="1038 2569"/>
    </justification>
  </clause>

  <clause id="2572">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * z != u
    ]]></literal>
    <literal><![CDATA[
      x * (K(y \ 1,y) * z) = u
    ]]></literal>
    <justification jstring="[para(2569(a,1),279(a,1,2))].">
      <j1 rule="para" parents="2569 279"/>
    </justification>
  </clause>

  <clause id="2574">
    <literal><![CDATA[
      L(x,(y * y) * ((z \ 1) \ u),w) = L(x,((y * y) * z) \ u,w)
    ]]></literal>
    <justification jstring="[para(2248(a,1),2538(a,1,2))].">
      <j1 rule="para" parents="2248 2538"/>
    </justification>
  </clause>

  <clause id="2575">
    <literal><![CDATA[
      T(x,1 / x) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(241(a,1),2546(a,1,1)),flip(a)].">
      <j1 rule="para" parents="241 2546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2576">
    <literal><![CDATA[
      T(x,R(1 / x,x,y)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(2232(a,1),2546(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2232 2546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2577">
    <literal><![CDATA[
      T(x,1 / x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(299,a,108,a(flip),b,2575,a),flip(a)].">
      <j1 rule="hyper" parents="299 108 2575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2578">
    <literal><![CDATA[
      (x * T(y,y \ 1)) / x = T((x * y) / x,1 / y)
    ]]></literal>
    <justification jstring="[para(2575(a,1),445(a,1,1,2))].">
      <j1 rule="para" parents="2575 445"/>
    </justification>
  </clause>

  <clause id="2579">
    <literal><![CDATA[
      T(x,x \ 1) / x = K(x,1 / x)
    ]]></literal>
    <justification jstring="[para(2575(a,1),885(a,1,1))].">
      <j1 rule="para" parents="2575 885"/>
    </justification>
  </clause>

  <clause id="2580">
    <literal><![CDATA[
      R(R(x,y,z),1 / x,x) = R(T(x,x \ 1),y,z)
    ]]></literal>
    <justification jstring="[para(2575(a,1),884(a,2,1))].">
      <j1 rule="para" parents="2575 884"/>
    </justification>
  </clause>

  <clause id="2581">
    <literal><![CDATA[
      R(x,1 / x,x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,882,a,b,2577,a)].">
      <j1 rule="hyper" parents="65 882 2577"/>
    </justification>
  </clause>

  <clause id="2582">
    <literal><![CDATA[
      ((x \ 1) \ 1) / x = K(x,1 / x)
    ]]></literal>
    <justification jstring="[para(2577(a,1),885(a,1,1))].">
      <j1 rule="para" parents="2577 885"/>
    </justification>
  </clause>

  <clause id="2583">
    <literal><![CDATA[
      L((x \ 1) \ 1,y,z) / x = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[para(2581(a,1),596(a,1,1,1))].">
      <j1 rule="para" parents="2581 596"/>
    </justification>
  </clause>

  <clause id="2584">
    <literal><![CDATA[
      K(x,1 / x) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,2548,a(flip),b,2579,a),flip(a)].">
      <j1 rule="hyper" parents="65 2548 2579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2585">
    <literal><![CDATA[
      K(x,x \ 1) = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(393,a,2584,a),flip(a)].">
      <j1 rule="hyper" parents="393 2584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2586">
    <literal><![CDATA[
      x \ K(x,x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(119,a,2584,a(flip),b,256,a(flip))].">
      <j1 rule="hyper" parents="119 2584 256"/>
    </justification>
  </clause>

  <clause id="2587">
    <literal><![CDATA[
      K(x \ 1,(x \ 1) \ 1) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(76(a,1),2584(a,1,2)),flip(a)].">
      <j1 rule="para" parents="76 2584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2588">
    <literal><![CDATA[
      K(x,x \ 1) != y
    ]]></literal>
    <literal><![CDATA[
      x * (1 / x) = y
    ]]></literal>
    <justification jstring="[para(2584(a,1),393(a,1))].">
      <j1 rule="para" parents="2584 393"/>
    </justification>
  </clause>

  <clause id="2589">
    <literal><![CDATA[
      L(x,y,K(z,z \ 1)) = x
    ]]></literal>
    <justification jstring="[para(2584(a,1),2491(a,1,3))].">
      <j1 rule="para" parents="2584 2491"/>
    </justification>
  </clause>

  <clause id="2590">
    <literal><![CDATA[
      K(x,x \ 1) * (1 / (1 / x)) = x
    ]]></literal>
    <justification jstring="[para(2584(a,1),2554(a,1,1))].">
      <j1 rule="para" parents="2584 2554"/>
    </justification>
  </clause>

  <clause id="2591">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * z = K(x,x \ 1) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(1318,a,2589,a),flip(a)].">
      <j1 rule="hyper" parents="1318 2589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2592">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ (K(x,x \ 1) * z) = y \ z
    ]]></literal>
    <justification jstring="[hyper(65,a,96,a(flip),b,2589,a)].">
      <j1 rule="hyper" parents="65 96 2589"/>
    </justification>
  </clause>

  <clause id="2593">
    <literal><![CDATA[
      K(x,x \ 1) * (1 / y) = K(x,x \ 1) / y
    ]]></literal>
    <justification jstring="[para(2589(a,1),401(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2589 401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2594">
    <literal><![CDATA[
      (K(x,x \ 1) * y) / z = K(x,x \ 1) * (y / z)
    ]]></literal>
    <justification jstring="[para(2589(a,1),585(a,1,2))].">
      <j1 rule="para" parents="2589 585"/>
    </justification>
  </clause>

  <clause id="2595">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * z != u
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) * (y * z) = u
    ]]></literal>
    <justification jstring="[para(2589(a,1),279(a,1,2))].">
      <j1 rule="para" parents="2589 279"/>
    </justification>
  </clause>

  <clause id="2596">
    <literal><![CDATA[
      K(x \ 1,x) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,1699,a,b,2585,a)].">
      <j1 rule="hyper" parents="299 1699 2585"/>
    </justification>
  </clause>

  <clause id="2597">
    <literal><![CDATA[
      K(x \ 1,x) \ 1 = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(65,a,414,a,b,2585,a)].">
      <j1 rule="hyper" parents="65 414 2585"/>
    </justification>
  </clause>

  <clause id="2598">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ ((x * y) * (1 / y)) = a(x,y,1 / y)
    ]]></literal>
    <justification jstring="[para(2585(a,2),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="2585 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2600">
    <literal><![CDATA[
      (x * y) * (1 / y) != z * K(y,y \ 1)
    ]]></literal>
    <literal><![CDATA[
      R(x,y,1 / y) = z
    ]]></literal>
    <justification jstring="[para(2585(a,2),544(a,2,2))].">
      <j1 rule="para" parents="2585 544"/>
    </justification>
  </clause>

  <clause id="2601">
    <literal><![CDATA[
      T(x,y) \ K(x,x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x * (T(x,y) \ (1 / x)) = z
    ]]></literal>
    <justification jstring="[para(2585(a,2),1208(a,1,2))].">
      <j1 rule="para" parents="2585 1208"/>
    </justification>
  </clause>

  <clause id="2602">
    <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(2585(a,2),998(a,1,1))].">
      <j1 rule="para" parents="2585 998"/>
    </justification>
  </clause>

  <clause id="2603">
    <literal><![CDATA[
      L(x,y,z) * K(x,x \ 1) = x * (L(x,y,z) * (1 / x))
    ]]></literal>
    <justification jstring="[para(2585(a,2),1347(a,1,2))].">
      <j1 rule="para" parents="2585 1347"/>
    </justification>
  </clause>

  <clause id="2604">
    <literal><![CDATA[
      L(x,y,z) \ K(x,x \ 1) = x * (L(x,y,z) \ (1 / x))
    ]]></literal>
    <justification jstring="[para(2585(a,2),1352(a,1,2))].">
      <j1 rule="para" parents="2585 1352"/>
    </justification>
  </clause>

  <clause id="2605">
    <literal><![CDATA[
      (1 / (1 / x)) * K(x,x \ 1) = x
    ]]></literal>
    <justification jstring="[para(2585(a,2),1452(a,1,2))].">
      <j1 rule="para" parents="2585 1452"/>
    </justification>
  </clause>

  <clause id="2606">
    <literal><![CDATA[
      K(x,x \ 1) != y
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(2585(a,2),1700(a,1))].">
      <j1 rule="para" parents="2585 1700"/>
    </justification>
  </clause>

  <clause id="2607">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ x) / x) = T(K(x,x \ 1),y)
    ]]></literal>
    <justification jstring="[para(2585(a,2),2293(a,2,1))].">
      <j1 rule="para" parents="2585 2293"/>
    </justification>
  </clause>

  <clause id="2608">
    <literal><![CDATA[
      L(x,K(y,y \ 1),z) = x
    ]]></literal>
    <justification jstring="[para(2585(a,2),2563(a,1,2))].">
      <j1 rule="para" parents="2585 2563"/>
    </justification>
  </clause>

  <clause id="2609">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * z = x * (K(y,y \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(1318,a,2608,a),flip(a)].">
      <j1 rule="hyper" parents="1318 2608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2610">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * z != u
    ]]></literal>
    <literal><![CDATA[
      x * (K(y,y \ 1) * z) = u
    ]]></literal>
    <justification jstring="[para(2608(a,1),279(a,1,2))].">
      <j1 rule="para" parents="2608 279"/>
    </justification>
  </clause>

  <clause id="2611">
    <literal><![CDATA[
      x * (1 / x) != y
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(2586(a,1),250(a,1,2)),flip(b)].">
      <j1 rule="para" parents="2586 250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2612">
    <literal><![CDATA[
      K(x,x \ 1) = (x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(392,a,2596,a),flip(a)].">
      <j1 rule="hyper" parents="392 2596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2613">
    <literal><![CDATA[
      K(x,x \ 1) / x = x \ 1
    ]]></literal>
    <justification jstring="[hyper(120,a,2596,a(flip),b,253,a(flip))].">
      <j1 rule="hyper" parents="120 2596 253"/>
    </justification>
  </clause>

  <clause id="2614">
    <literal><![CDATA[
      K(x,x \ 1) \ (x * ((1 / x) * y)) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(2612(a,2),945(a,1,1))].">
      <j1 rule="para" parents="2612 945"/>
    </justification>
  </clause>

  <clause id="2616">
    <literal><![CDATA[
      K(1 / x,1 / (1 / x)) = (x \ 1) / (1 / x)
    ]]></literal>
    <justification jstring="[para(79(a,1),2582(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 2582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2617">
    <literal><![CDATA[
      T(x,y / (x * y)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(216(a,1),2576(a,1,2))].">
      <j1 rule="para" parents="216 2576"/>
    </justification>
  </clause>

  <clause id="2618">
    <literal><![CDATA[
      T(x,y / (x * y)) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(299,a,108,a(flip),b,2617,a),flip(a)].">
      <j1 rule="hyper" parents="299 108 2617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2619">
    <literal><![CDATA[
      K((x / (y * x)) \ 1,x / (y * x)) * (y * x) = T(y,y \ 1) * x
    ]]></literal>
    <justification jstring="[para(2617(a,1),1405(a,2,1))].">
      <j1 rule="para" parents="2617 1405"/>
    </justification>
  </clause>

  <clause id="2620">
    <literal><![CDATA[
      T(x / y,y / x) = ((x / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(12(a,1),2618(a,1,2,2))].">
      <j1 rule="para" parents="12 2618"/>
    </justification>
  </clause>

  <clause id="2621">
    <literal><![CDATA[
      K(x,1 / x) != y
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(256(a,2),2611(a,1))].">
      <j1 rule="para" parents="256 2611"/>
    </justification>
  </clause>

  <clause id="2623">
    <literal><![CDATA[
      ((((x * y) / x) \ 1) \ 1) * x = x * T(y,x / (x * y))
    ]]></literal>
    <justification jstring="[para(2620(a,1),433(a,1,1))].">
      <j1 rule="para" parents="2620 433"/>
    </justification>
  </clause>

  <clause id="2624">
    <literal><![CDATA[
      L(x,y,(z * u) * u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,R(z,u,u)) = w
    ]]></literal>
    <justification jstring="[para(103(a,1),2512(a,1,3))].">
      <j1 rule="para" parents="103 2512"/>
    </justification>
  </clause>

  <clause id="2625">
    <literal><![CDATA[
      L(x,y,z * (1 / u)) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(215(a,1),2515(a,1,3,2))].">
      <j1 rule="para" parents="215 2515"/>
    </justification>
  </clause>

  <clause id="2626">
    <literal><![CDATA[
      L(x,y \ 1,z * u) = L(x,y,z * (1 / u))
    ]]></literal>
    <justification jstring="[hyper(299,a,2526,a,b,2625,a)].">
      <j1 rule="hyper" parents="299 2526 2625"/>
    </justification>
  </clause>

  <clause id="2627">
    <literal><![CDATA[
      L(x,y,z * (u \ 1)) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(76(a,1),2625(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="76 2625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2628">
    <literal><![CDATA[
      L(x,y,z * ((u * u) * (w \ 1))) = L(x,y,(z * (u * u)) * w)
    ]]></literal>
    <justification jstring="[para(34(a,1),2627(a,1,3))].">
      <j1 rule="para" parents="34 2627"/>
    </justification>
  </clause>

  <clause id="2629">
    <literal><![CDATA[
      L(x,y,z * ((u / (w * w)) \ 1)) = L(x,y,(z * u) / (w * w))
    ]]></literal>
    <justification jstring="[para(849(a,2),2627(a,2,3))].">
      <j1 rule="para" parents="849 2627"/>
    </justification>
  </clause>

  <clause id="2630">
    <literal><![CDATA[
      L(x,(y * y) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,u) = w
    ]]></literal>
    <justification jstring="[para(2536(a,2),2512(a,1))].">
      <j1 rule="para" parents="2536 2512"/>
    </justification>
  </clause>

  <clause id="2632">
    <literal><![CDATA[
      L(x,(y \ 1) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ z,u) = w
    ]]></literal>
    <justification jstring="[para(724(a,1),2630(a,1,2))].">
      <j1 rule="para" parents="724 2630"/>
    </justification>
  </clause>

  <clause id="2634">
    <literal><![CDATA[
      K(1 / x,1 / (1 / x)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,2226,a(flip),b,2616,a),flip(a)].">
      <j1 rule="hyper" parents="299 2226 2616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2635">
    <literal><![CDATA[
      K(1 / x,(1 / x) \ 1) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(2621,a,2634,a)].">
      <j1 rule="hyper" parents="2621 2634"/>
    </justification>
  </clause>

  <clause id="2636">
    <literal><![CDATA[
      K(1 / x,x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(79(a,1),2635(a,1,2))].">
      <j1 rule="para" parents="79 2635"/>
    </justification>
  </clause>

  <clause id="2637">
    <literal><![CDATA[
      x * K(1 / x,x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[para(2636(a,2),1716(a,1,2))].">
      <j1 rule="para" parents="2636 1716"/>
    </justification>
  </clause>

  <clause id="2638">
    <literal><![CDATA[
      L((x \ 1) \ 1,x,y * (1 / x)) = R(y,x,x \ 1) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(65,a,594,a(flip),b,2626,a),flip(a)].">
      <j1 rule="hyper" parents="65 594 2626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2639">
    <literal><![CDATA[
      L(x * T(x \ 1,y),x \ 1,y) = K(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2420,a,b,2562,a)].">
      <j1 rule="hyper" parents="65 2420 2562"/>
    </justification>
  </clause>

  <clause id="2640">
    <literal><![CDATA[
      R(x,y,z) \ R(T(x,x \ 1),y,z) = a(R(x,y,z),1 / x,x)
    ]]></literal>
    <justification jstring="[para(2580(a,1),783(a,1,2))].">
      <j1 rule="para" parents="2580 783"/>
    </justification>
  </clause>

  <clause id="2641">
    <literal><![CDATA[
      L(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(2529(a,1),2632(a,1))].">
      <j1 rule="para" parents="2529 2632"/>
    </justification>
  </clause>

  <clause id="2642">
    <literal><![CDATA[
      x \ ((x / (y \ 1)) * ((y \ 1) * (y * T(y \ 1,x / (y \ 1))))) = K(1 / y,x / (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(65,a,97,a,b,2639,a)].">
      <j1 rule="hyper" parents="65 97 2639"/>
    </justification>
  </clause>

  <clause id="2643">
    <literal><![CDATA[
      L((1 / x) * T((1 / x) \ 1,y),x,y) = K(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(79(a,1),2639(a,1,2))].">
      <j1 rule="para" parents="79 2639"/>
    </justification>
  </clause>

  <clause id="2644">
    <literal><![CDATA[
      T(K(x \ 1,x) * y,K(x \ 1,x)) = y * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(235,a,2495,a,b,xx)].">
      <j1 rule="hyper" parents="235 2495"/>
    </justification>
  </clause>

  <clause id="2645">
    <literal><![CDATA[
      ((K(x \ 1,x) * (y * z)) * u) / (z * u) = R(K(x \ 1,x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(2495(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="2495 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2646">
    <literal><![CDATA[
      K(x \ 1,x) * y != (K(x \ 1,x) * z) * u
    ]]></literal>
    <literal><![CDATA[
      z * u = y
    ]]></literal>
    <justification jstring="[para(2495(a,2),45(a,1)),flip(a)].">
      <j1 rule="para" parents="2495 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2648">
    <literal><![CDATA[
      K(x \ 1,x) * (T(x,x \ 1) * y) = x * y
    ]]></literal>
    <justification jstring="[para(893(a,1),2495(a,1,1)),flip(a)].">
      <j1 rule="para" parents="893 2495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2649">
    <literal><![CDATA[
      K(x \ 1,x) * (((x \ 1) \ 1) * y) = x * y
    ]]></literal>
    <justification jstring="[para(894(a,1),2495(a,1,1)),flip(a)].">
      <j1 rule="para" parents="894 2495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2650">
    <literal><![CDATA[
      K(x \ 1,x) * ((1 / x) * y) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[para(2223(a,1),2495(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2223 2495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2651">
    <literal><![CDATA[
      x \ (K(x \ 1,x) * y) = ((x \ 1) \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(640,a,2649,a)].">
      <j1 rule="hyper" parents="640 2649"/>
    </justification>
  </clause>

  <clause id="2652">
    <literal><![CDATA[
      x * (((x \ 1) \ 1) \ y) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[hyper(315,a,2649,a),flip(a)].">
      <j1 rule="hyper" parents="315 2649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2653">
    <literal><![CDATA[
      (x \ 1) * ((1 / x) \ y) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[hyper(315,a,2650,a),flip(a)].">
      <j1 rule="hyper" parents="315 2650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2654">
    <literal><![CDATA[
      ((x \ 1) * y) / L(T(1 / x,y),y,K(x \ 1,x)) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[para(2650(a,1),586(a,1,1))].">
      <j1 rule="para" parents="2650 586"/>
    </justification>
  </clause>

  <clause id="2655">
    <literal><![CDATA[
      K(x \ 1,x) * ((x \ 1) \ y) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[hyper(40,a,1666,a(flip),b,2651,a),flip(a)].">
      <j1 rule="hyper" parents="40 1666 2651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2658">
    <literal><![CDATA[
      x \ T(K(x \ 1,x) * y,x \ 1) = ((1 / (x \ 1)) \ ((x \ 1) \ y)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(2652(a,1),1139(a,1,2,1))].">
      <j1 rule="para" parents="2652 1139"/>
    </justification>
  </clause>

  <clause id="2659">
    <literal><![CDATA[
      K(x \ 1,x) * T(1 / x,y) = (x \ 1) * (x * T(x \ 1,y))
    ]]></literal>
    <justification jstring="[para(1074(a,1),2653(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1074 2653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2660">
    <literal><![CDATA[
      ((x \ 1) * y) \ (K(x \ 1,x) * z) = ((1 / x) * y) \ z
    ]]></literal>
    <justification jstring="[para(2650(a,1),2496(a,1,1))].">
      <j1 rule="para" parents="2650 2496"/>
    </justification>
  </clause>

  <clause id="2661">
    <literal><![CDATA[
      K(x \ 1,x) * (y / (x * y)) = R(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(916,a,2499,a),flip(a)].">
      <j1 rule="hyper" parents="916 2499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2662">
    <literal><![CDATA[
      K(x \ 1,x) * (y / (x * y)) != z
    ]]></literal>
    <literal><![CDATA[
      R(x \ 1,x,y) = z
    ]]></literal>
    <justification jstring="[para(2499(a,1),916(a,1))].">
      <j1 rule="para" parents="2499 916"/>
    </justification>
  </clause>

  <clause id="2663">
    <literal><![CDATA[
      K(x / (y * x),y) = K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(37,a,2239,a,b,2661,a)].">
      <j1 rule="hyper" parents="37 2239 2661"/>
    </justification>
  </clause>

  <clause id="2664">
    <literal><![CDATA[
      K((x / y) \ 1,x / y) = K(y / x,x / y)
    ]]></literal>
    <justification jstring="[para(12(a,1),2663(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12 2663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2666">
    <literal><![CDATA[
      K((x / (y * x)) \ 1,x / (y * x)) = K(y,x / (y * x))
    ]]></literal>
    <justification jstring="[para(11(a,1),2664(a,2,1))].">
      <j1 rule="para" parents="11 2664"/>
    </justification>
  </clause>

  <clause id="2667">
    <literal><![CDATA[
      ((x \ 1) * y) \ (x \ z) = (x * y) \ ((1 / x) \ z)
    ]]></literal>
    <justification jstring="[para(1664(a,1),2507(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1664 2507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2668">
    <literal><![CDATA[
      L(x,T(y * y,z \ 1),u) = x
    ]]></literal>
    <justification jstring="[hyper(2539,a,2523,a),flip(a)].">
      <j1 rule="hyper" parents="2539 2523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2669">
    <literal><![CDATA[
      L(x,T(y * y,z),u) = x
    ]]></literal>
    <justification jstring="[para(79(a,1),2668(a,1,2,2))].">
      <j1 rule="para" parents="79 2668"/>
    </justification>
  </clause>

  <clause id="2670">
    <literal><![CDATA[
      (x * T(y * y,z)) \ u = T(y * y,z) \ (x \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,281,a(flip),b,2669,a)].">
      <j1 rule="hyper" parents="65 281 2669"/>
    </justification>
  </clause>

  <clause id="2671">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * ((y \ 1) \ 1) = x * y
    ]]></literal>
    <justification jstring="[para(894(a,1),2570(a,2,2))].">
      <j1 rule="para" parents="894 2570"/>
    </justification>
  </clause>

  <clause id="2672">
    <literal><![CDATA[
      (1 / x) * (K(x \ 1,x) * y) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[para(1287(a,1),2570(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1287 2570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2673">
    <literal><![CDATA[
      ((x \ 1) \ 1) * (K(x \ 1,x) * y) = x * y
    ]]></literal>
    <justification jstring="[para(1492(a,1),2570(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1492 2570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2674">
    <literal><![CDATA[
      x * (K(x \ 1,x) * y) = (1 / (1 / x)) * y
    ]]></literal>
    <justification jstring="[para(1716(a,1),2570(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1716 2570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2675">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * (1 / y) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[para(2223(a,1),2570(a,2,2))].">
      <j1 rule="para" parents="2223 2570"/>
    </justification>
  </clause>

  <clause id="2676">
    <literal><![CDATA[
      (x / y) * K(y \ 1,y) = x / ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(120,a,12,a(flip),b,2671,a),flip(a)].">
      <j1 rule="hyper" parents="120 12 2671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2677">
    <literal><![CDATA[
      (x * (1 / y)) * K(y \ 1,y) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(37,a,1995,a,b,2671,a),flip(a)].">
      <j1 rule="hyper" parents="37 1995 2671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2680">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) = ((x \ 1) \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(119,a,10,a(flip),b,2673,a),flip(a)].">
      <j1 rule="hyper" parents="119 10 2673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2681">
    <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(2673(a,1),16(a,2,1)),flip(a)].">
      <j1 rule="para" parents="2673 16"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2682">
    <literal><![CDATA[
      K(x \ 1,x) * (x * y) = x * (K(x \ 1,x) * y)
    ]]></literal>
    <justification jstring="[para(2673(a,1),2649(a,1,2))].">
      <j1 rule="para" parents="2673 2649"/>
    </justification>
  </clause>

  <clause id="2683">
    <literal><![CDATA[
      ((x \ 1) \ 1) * ((x \ 1) * y) = x * ((1 / x) * y)
    ]]></literal>
    <justification jstring="[para(2650(a,1),2673(a,1,2))].">
      <j1 rule="para" parents="2650 2673"/>
    </justification>
  </clause>

  <clause id="2684">
    <literal><![CDATA[
      K(x \ 1,x) * ((1 / (1 / x)) \ y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(119,a,10,a(flip),b,2674,a),flip(a)].">
      <j1 rule="hyper" parents="119 10 2674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2685">
    <literal><![CDATA[
      K(x \ 1,x) * (x * y) = (1 / (1 / x)) * y
    ]]></literal>
    <justification jstring="[hyper(36,a,1450,a(flip),b,2674,a),flip(a)].">
      <j1 rule="hyper" parents="36 1450 2674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2686">
    <literal><![CDATA[
      (x * ((y * x) \ y)) * K(x \ 1,x) = L(x \ 1,x,y) / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(120,a,1814,a(flip),b,2675,a),flip(a)].">
      <j1 rule="hyper" parents="120 1814 2675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2687">
    <literal><![CDATA[
      (x / (y \ 1)) * K(y \ 1,y) = x / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(120,a,12,a(flip),b,2675,a),flip(a)].">
      <j1 rule="hyper" parents="120 12 2675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2688">
    <literal><![CDATA[
      x * T(x \ (x / y),y) = x / ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,1232,a(flip),b,2676,a)].">
      <j1 rule="hyper" parents="65 1232 2676"/>
    </justification>
  </clause>

  <clause id="2689">
    <literal><![CDATA[
      T(x \ (x / y),y) = x \ (x / ((y \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(119,a,2676,a(flip),b,1232,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 2676 1232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2690">
    <literal><![CDATA[
      R(x,y \ 1,y) / y = x * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(1625,a,2677,a)].">
      <j1 rule="hyper" parents="1625 2677"/>
    </justification>
  </clause>

  <clause id="2691">
    <literal><![CDATA[
      (x / (1 / y)) * (y \ 1) = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(306,a,2677,a),flip(a)].">
      <j1 rule="hyper" parents="306 2677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2692">
    <literal><![CDATA[
      R(T(x / (1 / y),z),y \ 1,y) = T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(1119,a,2690,a),flip(a)].">
      <j1 rule="hyper" parents="1119 2690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2693">
    <literal><![CDATA[
      R(x / (1 / y),y \ 1,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(305,a,2690,a),flip(a)].">
      <j1 rule="hyper" parents="305 2690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2694">
    <literal><![CDATA[
      (x * (1 / y)) * y = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(143,a,2690,a)].">
      <j1 rule="hyper" parents="143 2690"/>
    </justification>
  </clause>

  <clause id="2695">
    <literal><![CDATA[
      R(x,(1 / y) \ 1,1 / y) / (1 / y) = x * (y * K(y \ 1,y))
    ]]></literal>
    <justification jstring="[para(1716(a,2),2690(a,2,2))].">
      <j1 rule="para" parents="1716 2690"/>
    </justification>
  </clause>

  <clause id="2696">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ (y * R(y / (1 / x),x \ 1,x)) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[para(2693(a,1),1948(a,1,1,2))].">
      <j1 rule="para" parents="2693 1948"/>
    </justification>
  </clause>

  <clause id="2697">
    <literal><![CDATA[
      ((1 / x) * K(y,x)) * x = R(K(y,x),x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2305(a,1),2693(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2305 2693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2698">
    <literal><![CDATA[
      R(x,1 / y,y) = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(552,a,2694,a)].">
      <j1 rule="hyper" parents="552 2694"/>
    </justification>
  </clause>

  <clause id="2699">
    <literal><![CDATA[
      (x * (y \ 1)) * ((y \ 1) \ 1) = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,1995,a,b,2694,a)].">
      <j1 rule="hyper" parents="65 1995 2694"/>
    </justification>
  </clause>

  <clause id="2700">
    <literal><![CDATA[
      x \ R(x,y \ 1,y) = a(x,1 / y,y)
    ]]></literal>
    <justification jstring="[para(2694(a,1),218(a,1,2))].">
      <j1 rule="para" parents="2694 218"/>
    </justification>
  </clause>

  <clause id="2702">
    <literal><![CDATA[
      R(x * K(y \ 1,y),y \ 1,y) = (x * (y \ 1)) * y
    ]]></literal>
    <justification jstring="[para(2675(a,1),2694(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2675 2694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2703">
    <literal><![CDATA[
      R(x,(y \ 1) \ 1,y \ 1) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(76(a,1),2698(a,1,2)),flip(a)].">
      <j1 rule="para" parents="76 2698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2704">
    <literal><![CDATA[
      x \ R(x,y \ 1,y) = a(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,2367,a(flip),b,2700,a),flip(a)].">
      <j1 rule="hyper" parents="299 2367 2700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2705">
    <literal><![CDATA[
      x * T(x \ (y \ x),y) = ((y \ 1) \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(65,a,1307,a(flip),b,2680,a)].">
      <j1 rule="hyper" parents="65 1307 2680"/>
    </justification>
  </clause>

  <clause id="2706">
    <literal><![CDATA[
      K(x,x \ 1) * (x \ y) = ((x \ 1) \ 1) \ y
    ]]></literal>
    <justification jstring="[para(2596(a,1),2680(a,1,1))].">
      <j1 rule="para" parents="2596 2680"/>
    </justification>
  </clause>

  <clause id="2707">
    <literal><![CDATA[
      1 / (1 / x) != y
    ]]></literal>
    <literal><![CDATA[
      x * K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(2687(a,1),327(a,1))].">
      <j1 rule="para" parents="2687 327"/>
    </justification>
  </clause>

  <clause id="2709">
    <literal><![CDATA[
      x \ (x / T(y,y \ 1)) = T(x \ (x / y),y)
    ]]></literal>
    <justification jstring="[hyper(119,a,294,a,b,2688,a)].">
      <j1 rule="hyper" parents="119 294 2688"/>
    </justification>
  </clause>

  <clause id="2710">
    <literal><![CDATA[
      T(x \ (x / (1 / y)),1 / y) = x \ (x / (y \ 1))
    ]]></literal>
    <justification jstring="[para(79(a,1),2689(a,2,2,2,1))].">
      <j1 rule="para" parents="79 2689"/>
    </justification>
  </clause>

  <clause id="2711">
    <literal><![CDATA[
      x * (y \ (y / ((x \ 1) \ 1))) = (y \ (y / x)) * x
    ]]></literal>
    <justification jstring="[para(2689(a,1),107(a,1,2))].">
      <j1 rule="para" parents="2689 107"/>
    </justification>
  </clause>

  <clause id="2712">
    <literal><![CDATA[
      K(x,x \ 1) * (x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(299,a,1689,a(flip),b,2706,a),flip(a)].">
      <j1 rule="hyper" parents="299 1689 2706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2714">
    <literal><![CDATA[
      K(x,x \ 1) * (x \ y) = (1 / (1 / x)) \ y
    ]]></literal>
    <justification jstring="[para(1691(a,2),2706(a,2,1))].">
      <j1 rule="para" parents="1691 2706"/>
    </justification>
  </clause>

  <clause id="2715">
    <literal><![CDATA[
      x * R(x \ K(x,x \ 1),y,z) = R(1 / x,y,z) / (x \ 1)
    ]]></literal>
    <justification jstring="[para(2712(a,1),1642(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2712 1642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2716">
    <literal><![CDATA[
      R(x,y \ 1,(y \ 1) \ 1) = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(551,a,2699,a)].">
      <j1 rule="hyper" parents="551 2699"/>
    </justification>
  </clause>

  <clause id="2717">
    <literal><![CDATA[
      (x * ((y / z) \ 1)) * T(y / z,z / y) = R(x,(y / z) \ 1,y / z)
    ]]></literal>
    <justification jstring="[para(2620(a,2),2699(a,1,2))].">
      <j1 rule="para" parents="2620 2699"/>
    </justification>
  </clause>

  <clause id="2718">
    <literal><![CDATA[
      R(x,y \ 1,(y \ 1) \ 1) = R(x,1 / y,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,2698,a,b,2716,a),flip(a)].">
      <j1 rule="hyper" parents="299 2698 2716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2719">
    <literal><![CDATA[
      R(x,(y \ 1) \ 1,T(y \ 1,y)) = R(x,1 / (y \ 1),y \ 1)
    ]]></literal>
    <justification jstring="[para(1495(a,2),2718(a,1,3))].">
      <j1 rule="para" parents="1495 2718"/>
    </justification>
  </clause>

  <clause id="2720">
    <literal><![CDATA[
      T((x * y) / x,1 / y) = T((x * y) / x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(448,a,2578,a),flip(a)].">
      <j1 rule="hyper" parents="448 2578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2721">
    <literal><![CDATA[
      T(L(x,y,z) * (1 / x),x) = x \ L((x \ 1) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(2583(a,1),109(a,1,1))].">
      <j1 rule="para" parents="2583 109"/>
    </justification>
  </clause>

  <clause id="2722">
    <literal><![CDATA[
      R(K(x,x \ 1),y,z) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(544,a,2591,a)].">
      <j1 rule="hyper" parents="544 2591"/>
    </justification>
  </clause>

  <clause id="2723">
    <literal><![CDATA[
      x * T(K(y,y \ 1) * z,x) = K(y,y \ 1) * (z * x)
    ]]></literal>
    <justification jstring="[hyper(277,a,2591,a)].">
      <j1 rule="hyper" parents="277 2591"/>
    </justification>
  </clause>

  <clause id="2724">
    <literal><![CDATA[
      K(x,x \ 1) * (x * y) = T(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[para(2551(a,1),2591(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2551 2591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2725">
    <literal><![CDATA[
      K(x,x \ 1) * (x * y) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[para(2556(a,1),2591(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2556 2591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2726">
    <literal><![CDATA[
      K(x,x \ 1) * ((1 / (1 / x)) * y) = x * y
    ]]></literal>
    <justification jstring="[para(2590(a,1),2591(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2590 2591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2727">
    <literal><![CDATA[
      K(x,x \ 1) * ((x \ 1) * y) = (1 / x) * y
    ]]></literal>
    <justification jstring="[para(2712(a,1),2591(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2712 2591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2729">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ (K(x,x \ 1) * y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(640,a,2725,a)].">
      <j1 rule="hyper" parents="640 2725"/>
    </justification>
  </clause>

  <clause id="2730">
    <literal><![CDATA[
      ((x \ 1) \ 1) * (x \ y) = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(315,a,2725,a),flip(a)].">
      <j1 rule="hyper" parents="315 2725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2731">
    <literal><![CDATA[
      K(x,x \ 1) * (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,x \ 1) * y = z
    ]]></literal>
    <justification jstring="[para(2725(a,2),662(a,1))].">
      <j1 rule="para" parents="2725 662"/>
    </justification>
  </clause>

  <clause id="2732">
    <literal><![CDATA[
      K(x,x \ 1) * ((y \ (1 / (1 / x))) * y) = x * K(y \ (1 / (1 / x)),y)
    ]]></literal>
    <justification jstring="[para(287(a,1),2726(a,1,2))].">
      <j1 rule="para" parents="287 2726"/>
    </justification>
  </clause>

  <clause id="2733">
    <literal><![CDATA[
      (x \ 1) * K(x,x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(1512,a,2727,a),flip(a)].">
      <j1 rule="hyper" parents="1512 2727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2734">
    <literal><![CDATA[
      (1 / x) * ((x \ 1) \ y) = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(315,a,2727,a),flip(a)].">
      <j1 rule="hyper" parents="315 2727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2735">
    <literal><![CDATA[
      K(x,x \ 1) * (((x \ 1) * y) * z) = ((1 / x) * y) * z
    ]]></literal>
    <justification jstring="[para(2727(a,1),2591(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2727 2591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2736">
    <literal><![CDATA[
      K(x,x \ 1) * ((1 / x) \ y) = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(1738,a,2729,a),flip(a)].">
      <j1 rule="hyper" parents="1738 2729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2737">
    <literal><![CDATA[
      K(x,x \ 1) * (K(x \ 1,x) * y) = y
    ]]></literal>
    <justification jstring="[hyper(40,a,2651,a(flip),b,2729,a),flip(a)].">
      <j1 rule="hyper" parents="40 2651 2729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2738">
    <literal><![CDATA[
      K(x \ 1,x) * (K(x,x \ 1) * y) = y
    ]]></literal>
    <justification jstring="[hyper(40,a,2651,a,b,2729,a(flip))].">
      <j1 rule="hyper" parents="40 2651 2729"/>
    </justification>
  </clause>

  <clause id="2739">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ (((x \ 1) \ 1) \ y) = x \ (x \ y)
    ]]></literal>
    <justification jstring="[para(2706(a,1),2729(a,1,2))].">
      <j1 rule="para" parents="2706 2729"/>
    </justification>
  </clause>

  <clause id="2740">
    <literal><![CDATA[
      K(x \ 1,x) \ y = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(315,a,2737,a),flip(a)].">
      <j1 rule="hyper" parents="315 2737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2741">
    <literal><![CDATA[
      K(x,x \ 1) \ y = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[hyper(125,a,2737,a)].">
      <j1 rule="hyper" parents="125 2737"/>
    </justification>
  </clause>

  <clause id="2742">
    <literal><![CDATA[
      K(x,x \ 1) * y != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) * z = y
    ]]></literal>
    <justification jstring="[para(2737(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="2737 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2743">
    <literal><![CDATA[
      K(x,x \ 1) \ y != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) * y = z
    ]]></literal>
    <justification jstring="[para(2737(a,1),314(a,1,2))].">
      <j1 rule="para" parents="2737 314"/>
    </justification>
  </clause>

  <clause id="2744">
    <literal><![CDATA[
      K(x,x \ 1) * ((K(x \ 1,x) * y) * z) = y * z
    ]]></literal>
    <justification jstring="[para(2495(a,2),2737(a,1,2))].">
      <j1 rule="para" parents="2495 2737"/>
    </justification>
  </clause>

  <clause id="2745">
    <literal><![CDATA[
      K(x,x \ 1) * (((x \ 1) \ 1) \ y) = x \ y
    ]]></literal>
    <justification jstring="[para(2680(a,1),2737(a,1,2))].">
      <j1 rule="para" parents="2680 2737"/>
    </justification>
  </clause>

  <clause id="2746">
    <literal><![CDATA[
      K(x \ 1,x) * y != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) * z = y
    ]]></literal>
    <justification jstring="[para(2738(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="2738 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2747">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ z = y \ (K(x \ 1,x) * z)
    ]]></literal>
    <justification jstring="[para(2738(a,1),2496(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2738 2496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2748">
    <literal><![CDATA[
      (x \ 1) * (K(x,x \ 1) * y) = (1 / x) * y
    ]]></literal>
    <justification jstring="[para(2738(a,1),2672(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2738 2672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2749">
    <literal><![CDATA[
      x * (K(x,x \ 1) * y) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[para(2738(a,1),2673(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2738 2673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2750">
    <literal><![CDATA[
      K(x * y,(x * y) \ 1) * ((((x * y) \ 1) * x) * y) = a((x * y) \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(1072,a,2740,a),flip(a)].">
      <j1 rule="hyper" parents="1072 2740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2751">
    <literal><![CDATA[
      K(x \ 1,x) * T(K(x,x \ 1) * y,z) = (x \ T(x * (y / x),z)) * x
    ]]></literal>
    <justification jstring="[para(2740(a,1),2416(a,1,2,1))].">
      <j1 rule="para" parents="2740 2416"/>
    </justification>
  </clause>

  <clause id="2752">
    <literal><![CDATA[
      (x \ 1) * T(x \ ((x \ 1) \ y),z) = x \ T(K(x,x \ 1) * y,z)
    ]]></literal>
    <justification jstring="[para(2734(a,1),1682(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2734 1682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2753">
    <literal><![CDATA[
      K(x,x \ 1) * (T(x,x \ 1) \ y) = x \ y
    ]]></literal>
    <justification jstring="[para(108(a,2),2745(a,1,2,1))].">
      <j1 rule="para" parents="108 2745"/>
    </justification>
  </clause>

  <clause id="2754">
    <literal><![CDATA[
      L(K(x,x \ 1) * y,x \ 1,x) = x * ((1 / x) * y)
    ]]></literal>
    <justification jstring="[para(2748(a,1),252(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2748 252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2755">
    <literal><![CDATA[
      K(x,x \ 1) * ((x \ 1) / y) = (1 / x) / y
    ]]></literal>
    <justification jstring="[para(2712(a,1),2594(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2712 2594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2756">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * y = x * T(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(2551(a,1),2609(a,2,2))].">
      <j1 rule="para" parents="2551 2609"/>
    </justification>
  </clause>

  <clause id="2757">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * y = x * ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2556(a,1),2609(a,2,2))].">
      <j1 rule="para" parents="2556 2609"/>
    </justification>
  </clause>

  <clause id="2758">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * (y \ 1) = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(2712(a,1),2609(a,2,2))].">
      <j1 rule="para" parents="2712 2609"/>
    </justification>
  </clause>

  <clause id="2759">
    <literal><![CDATA[
      (x / T(y,y \ 1)) * K(y,y \ 1) = x / y
    ]]></literal>
    <justification jstring="[hyper(120,a,12,a(flip),b,2756,a),flip(a)].">
      <j1 rule="hyper" parents="120 12 2756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2760">
    <literal><![CDATA[
      (x * y) * K(y,y \ 1) = x * T(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(37,a,1542,a,b,2756,a),flip(a)].">
      <j1 rule="hyper" parents="37 1542 2756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2761">
    <literal><![CDATA[
      (x / y) * T(y,y \ 1) = x * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(37,a,1525,a,b,2756,a)].">
      <j1 rule="hyper" parents="37 1525 2756"/>
    </justification>
  </clause>

  <clause id="2762">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * K(y,y \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(37,a,2671,a(flip),b,2757,a),flip(a)].">
      <j1 rule="hyper" parents="37 2671 2757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2763">
    <literal><![CDATA[
      (x * (y \ 1)) * K(y,y \ 1) = x * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(37,a,1995,a(flip),b,2757,a),flip(a)].">
      <j1 rule="hyper" parents="37 1995 2757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2764">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * K(y \ 1,y) = x
    ]]></literal>
    <justification jstring="[hyper(37,a,2671,a,b,2757,a(flip))].">
      <j1 rule="hyper" parents="37 2671 2757"/>
    </justification>
  </clause>

  <clause id="2765">
    <literal><![CDATA[
      x * K(y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      z * K(y \ 1,y) = x
    ]]></literal>
    <justification jstring="[para(2762(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="2762 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2766">
    <literal><![CDATA[
      (x / (1 / y)) * K(y,y \ 1) = x / (y \ 1)
    ]]></literal>
    <justification jstring="[para(2687(a,1),2762(a,1,1))].">
      <j1 rule="para" parents="2687 2762"/>
    </justification>
  </clause>

  <clause id="2767">
    <literal><![CDATA[
      x * K(y \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      z * K(y,y \ 1) = x
    ]]></literal>
    <justification jstring="[para(2764(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="2764 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2768">
    <literal><![CDATA[
      R((x * K(y,y \ 1)) / z,z,K(y \ 1,y)) = x / (z * K(y \ 1,y))
    ]]></literal>
    <justification jstring="[para(2764(a,1),104(a,2,1))].">
      <j1 rule="para" parents="2764 104"/>
    </justification>
  </clause>

  <clause id="2769">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ z = K(y \ 1,y) * (x \ z)
    ]]></literal>
    <justification jstring="[para(2764(a,1),2571(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2764 2571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2770">
    <literal><![CDATA[
      (x * y) * K(y,y \ 1) = x * ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,295,a(flip),b,2760,a),flip(a)].">
      <j1 rule="hyper" parents="299 295 2760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2771">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ ((x * y) * K(y,y \ 1)) = y
    ]]></literal>
    <justification jstring="[hyper(119,a,2760,a,b,2756,a)].">
      <j1 rule="hyper" parents="119 2760 2756"/>
    </justification>
  </clause>

  <clause id="2772">
    <literal><![CDATA[
      (x * T(y,y \ 1)) * K(y \ 1,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(37,a,2762,a,b,2760,a)].">
      <j1 rule="hyper" parents="37 2762 2760"/>
    </justification>
  </clause>

  <clause id="2775">
    <literal><![CDATA[
      (x * K(y \ 1,y)) / y = x / T(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(120,a,2762,a(flip),b,2761,a),flip(a)].">
      <j1 rule="hyper" parents="120 2762 2761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2776">
    <literal><![CDATA[
      (x / y) * ((y \ 1) \ 1) = x * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,295,a(flip),b,2761,a)].">
      <j1 rule="hyper" parents="65 295 2761"/>
    </justification>
  </clause>

  <clause id="2777">
    <literal><![CDATA[
      (x * K(y,y \ 1)) / y = (x / y) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(120,a,2761,a(flip),b,2756,a)].">
      <j1 rule="hyper" parents="120 2761 2756"/>
    </justification>
  </clause>

  <clause id="2778">
    <literal><![CDATA[
      (x / (y \ 1)) * (1 / y) = x * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(306,a,2763,a),flip(a)].">
      <j1 rule="hyper" parents="306 2763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2779">
    <literal><![CDATA[
      ((x * y) * (1 / z)) / ((y * (z \ 1)) * K(z,z \ 1)) = R(R(x,y,z \ 1),y * (z \ 1),K(z,z \ 1))
    ]]></literal>
    <justification jstring="[para(2763(a,1),539(a,1,1))].">
      <j1 rule="para" parents="2763 539"/>
    </justification>
  </clause>

  <clause id="2780">
    <literal><![CDATA[
      (R(x,y,y \ 1) / (1 / y)) * K(y,y \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(299,a,423,a(flip),b,2766,a),flip(a)].">
      <j1 rule="hyper" parents="299 423 2766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2781">
    <literal><![CDATA[
      (x * ((y \ 1) \ 1)) * K(y \ 1,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(37,a,2762,a,b,2770,a)].">
      <j1 rule="hyper" parents="37 2762 2770"/>
    </justification>
  </clause>

  <clause id="2782">
    <literal><![CDATA[
      (x / T(y,y \ 1)) * y = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(306,a,2772,a),flip(a)].">
      <j1 rule="hyper" parents="306 2772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2783">
    <literal><![CDATA[
      x * K(y \ 1,y) != z * y
    ]]></literal>
    <literal><![CDATA[
      z * T(y,y \ 1) = x
    ]]></literal>
    <justification jstring="[para(2772(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="2772 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2784">
    <literal><![CDATA[
      K(x \ 1,x) * ((y * x) \ z) = (y * ((x \ 1) \ 1)) \ z
    ]]></literal>
    <justification jstring="[para(2781(a,1),2571(a,1,2,1))].">
      <j1 rule="para" parents="2781 2571"/>
    </justification>
  </clause>

  <clause id="2786">
    <literal><![CDATA[
      (x * y) \ ((1 / x) \ (z * x)) = ((x \ 1) * y) \ T(z,x)
    ]]></literal>
    <justification jstring="[para(22(a,2),2667(a,1,2)),flip(a)].">
      <j1 rule="para" parents="22 2667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2787">
    <literal><![CDATA[
      ((x \ 1) * y) \ (x \ 1) = (x * y) \ x
    ]]></literal>
    <justification jstring="[para(79(a,1),2667(a,2,2))].">
      <j1 rule="para" parents="79 2667"/>
    </justification>
  </clause>

  <clause id="2788">
    <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(2682(a,1),230(a,1,2))].">
      <j1 rule="para" parents="2682 230"/>
    </justification>
  </clause>

  <clause id="2789">
    <literal><![CDATA[
      T((x * T(y,x)) / x,T(y,x) \ 1) = T(y,1 / T(y,x))
    ]]></literal>
    <justification jstring="[para(223(a,1),2720(a,1,1)),flip(a)].">
      <j1 rule="para" parents="223 2720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2790">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ 1) * T((1 / ((x \ 1) \ 1)) \ (((x \ 1) \ 1) \ y),(x \ 1) \ 1) = (x \ (x \ y)) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2739(a,1),1785(a,2,1))].">
      <j1 rule="para" parents="2739 1785"/>
    </justification>
  </clause>

  <clause id="2791">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ 1 = y \ K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(389,a,2744,a),flip(a)].">
      <j1 rule="hyper" parents="389 2744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2792">
    <literal><![CDATA[
      K(x,x \ 1) * y != z * u
    ]]></literal>
    <literal><![CDATA[
      (K(x \ 1,x) * z) * u = y
    ]]></literal>
    <justification jstring="[para(2744(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="2744 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2793">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ 1 = y \ K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(8(a,1),2747(a,2,2))].">
      <j1 rule="para" parents="8 2747"/>
    </justification>
  </clause>

  <clause id="2794">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ z = K(y,y \ 1) * (x \ z)
    ]]></literal>
    <justification jstring="[para(2596(a,1),2769(a,2,1))].">
      <j1 rule="para" parents="2596 2769"/>
    </justification>
  </clause>

  <clause id="2795">
    <literal><![CDATA[
      R(T(x,y * K(x,x \ 1)),y,K(x,x \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2771(a,1),1324(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2771 1324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2796">
    <literal><![CDATA[
      T((x / y) * K(y,y \ 1),y) != z
    ]]></literal>
    <literal><![CDATA[
      y \ (x * K(y,y \ 1)) = z
    ]]></literal>
    <justification jstring="[para(2777(a,1),400(a,1,1))].">
      <j1 rule="para" parents="2777 400"/>
    </justification>
  </clause>

  <clause id="2797">
    <literal><![CDATA[
      K(x,x \ 1) * ((y * (x \ 1)) \ z) = (y * (1 / x)) \ z
    ]]></literal>
    <justification jstring="[para(2763(a,1),2794(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2763 2794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2798">
    <literal><![CDATA[
      (1 / x) * (x * L(x \ y,z,u)) = L((1 / x) * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(2479,a,2486,a)].">
      <j1 rule="hyper" parents="2479 2486"/>
    </justification>
  </clause>

  <clause id="2799">
    <literal><![CDATA[
      (1 / x) \ L((1 / x) * y,z,u) = x * L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(119,a,2486,a(flip),b,2472,a)].">
      <j1 rule="hyper" parents="119 2486 2472"/>
    </justification>
  </clause>

  <clause id="2800">
    <literal><![CDATA[
      K(x \ 1,x) * (x * ((1 / x) * y)) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(2743,a,2614,a)].">
      <j1 rule="hyper" parents="2743 2614"/>
    </justification>
  </clause>

  <clause id="2801">
    <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(1598(a,1),2702(a,2,1))].">
      <j1 rule="para" parents="1598 2702"/>
    </justification>
  </clause>

  <clause id="2802">
    <literal><![CDATA[
      K(x,x \ 1) * (x * ((1 / x) * y)) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(2596(a,1),2800(a,1,1))].">
      <j1 rule="para" parents="2596 2800"/>
    </justification>
  </clause>

  <clause id="2803">
    <literal><![CDATA[
      T(x,x \ 1) * ((1 / x) * y) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(2731,a,2802,a)].">
      <j1 rule="hyper" parents="2731 2802"/>
    </justification>
  </clause>

  <clause id="2804">
    <literal><![CDATA[
      T(x,x \ 1) * ((1 / x) * y) = L(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,2470,a(flip),b,2803,a),flip(a)].">
      <j1 rule="hyper" parents="299 2470 2803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2805">
    <literal><![CDATA[
      T(x,x \ 1) = L(x,x,x)
    ]]></literal>
    <justification jstring="[hyper(206,a,2804,a)].">
      <j1 rule="hyper" parents="206 2804"/>
    </justification>
  </clause>

  <clause id="2806">
    <literal><![CDATA[
      L(x,x,x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(409,a,2805,a),flip(a)].">
      <j1 rule="hyper" parents="409 2805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2807">
    <literal><![CDATA[
      T(x,x \ 1) * y = L(x,x,x) * y
    ]]></literal>
    <justification jstring="[hyper(59,a,2805,a)].">
      <j1 rule="hyper" parents="59 2805"/>
    </justification>
  </clause>

  <clause id="2808">
    <literal><![CDATA[
      1 / L(x,x,x) = x \ 1
    ]]></literal>
    <justification jstring="[para(2805(a,1),262(a,1,2))].">
      <j1 rule="para" parents="2805 262"/>
    </justification>
  </clause>

  <clause id="2809">
    <literal><![CDATA[
      T(T(x,x \ 1) * y,x) = x * ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(2805(a,2),1784(a,1,1,1))].">
      <j1 rule="para" parents="2805 1784"/>
    </justification>
  </clause>

  <clause id="2810">
    <literal><![CDATA[
      x \ (x / L(y,y,y)) = T(x \ (x / y),y)
    ]]></literal>
    <justification jstring="[para(2805(a,1),2709(a,1,2,2))].">
      <j1 rule="para" parents="2805 2709"/>
    </justification>
  </clause>

  <clause id="2811">
    <literal><![CDATA[
      T((x \ 1) \ 1,y) = L(T(x,y),x,x)
    ]]></literal>
    <justification jstring="[para(2806(a,1),25(a,2,1)),flip(a)].">
      <j1 rule="para" parents="2806 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2812">
    <literal><![CDATA[
      ((x \ 1) \ 1) * L(y,x,x) = L(x * y,x,x)
    ]]></literal>
    <justification jstring="[para(2806(a,1),948(a,1,1))].">
      <j1 rule="para" parents="2806 948"/>
    </justification>
  </clause>

  <clause id="2813">
    <literal><![CDATA[
      (x \ 1) * L(L(x,x,x),y,z) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(2806(a,2),1273(a,1,2,1))].">
      <j1 rule="para" parents="2806 1273"/>
    </justification>
  </clause>

  <clause id="2814">
    <literal><![CDATA[
      L(x,x,x) \ 1 = 1 / x
    ]]></literal>
    <justification jstring="[para(2806(a,2),1689(a,1,1))].">
      <j1 rule="para" parents="2806 1689"/>
    </justification>
  </clause>

  <clause id="2816">
    <literal><![CDATA[
      (x \ 1) \ L(y,x,x) = L(x,x,x) * y
    ]]></literal>
    <justification jstring="[para(2806(a,2),1761(a,2,1))].">
      <j1 rule="para" parents="2806 1761"/>
    </justification>
  </clause>

  <clause id="2818">
    <literal><![CDATA[
      ((L(x,x,x) * L(x,x,x)) \ y) * L(x,x,x) = (x \ 1) * T(y,L(x,x,x))
    ]]></literal>
    <justification jstring="[para(2808(a,1),983(a,2,1))].">
      <j1 rule="para" parents="2808 983"/>
    </justification>
  </clause>

  <clause id="2819">
    <literal><![CDATA[
      L(1 / x,L(x,x,x),y) = (y * L(x,x,x)) \ y
    ]]></literal>
    <justification jstring="[para(2814(a,1),214(a,1,1))].">
      <j1 rule="para" parents="2814 214"/>
    </justification>
  </clause>

  <clause id="2821">
    <literal><![CDATA[
      T(T(x,y),x \ 1) = L(T(x,y),x,x)
    ]]></literal>
    <justification jstring="[hyper(863,a,2811,a)].">
      <j1 rule="hyper" parents="863 2811"/>
    </justification>
  </clause>

  <clause id="2822">
    <literal><![CDATA[
      (x \ L(x,y,z)) * L(u,L(L(x,x,x),y,z),x) = (x \ 1) * (L(L(x,x,x),y,z) * u)
    ]]></literal>
    <justification jstring="[para(2813(a,1),2477(a,1,1))].">
      <j1 rule="para" parents="2813 2477"/>
    </justification>
  </clause>

  <clause id="2823">
    <literal><![CDATA[
      K(x,x \ 1) * L(x,y,z) = x * (L(x,y,z) * (1 / x))
    ]]></literal>
    <justification jstring="[hyper(65,a,2314,a(flip),b,2603,a)].">
      <j1 rule="hyper" parents="65 2314 2603"/>
    </justification>
  </clause>

  <clause id="2824">
    <literal><![CDATA[
      T(x,((y * x) / y) \ 1) = T(x,y / (y * x))
    ]]></literal>
    <justification jstring="[hyper(1334,a,2623,a)].">
      <j1 rule="hyper" parents="1334 2623"/>
    </justification>
  </clause>

  <clause id="2825">
    <literal><![CDATA[
      T((x \ 1) * y,K(x \ 1,x)) = ((1 / x) * y) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2650(a,1),2644(a,1,1))].">
      <j1 rule="para" parents="2650 2644"/>
    </justification>
  </clause>

  <clause id="2826">
    <literal><![CDATA[
      T(x,1 / T(x,y)) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(223(a,1),2789(a,1,1)),flip(a)].">
      <j1 rule="para" parents="223 2789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2827">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) / T(x,y) = x * (1 / T(x,y))
    ]]></literal>
    <justification jstring="[para(2826(a,1),1552(a,1,1))].">
      <j1 rule="para" parents="2826 1552"/>
    </justification>
  </clause>

  <clause id="2828">
    <literal><![CDATA[
      ((x * (1 / T(x,y))) / x) * T(x,y) = T(x,T(x,y) \ 1) / x
    ]]></literal>
    <justification jstring="[para(2827(a,1),1526(a,1,1,1))].">
      <j1 rule="para" parents="2827 1526"/>
    </justification>
  </clause>

  <clause id="2829">
    <literal><![CDATA[
      L((1 / x) * (y * x),z,u) = (1 / x) * (L(y,z,u) * x)
    ]]></literal>
    <justification jstring="[para(682(a,1),2798(a,1,2)),flip(a)].">
      <j1 rule="para" parents="682 2798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2830">
    <literal><![CDATA[
      (1 / x) \ L(1 / x,y,z) = x * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(8(a,1),2799(a,1,2,1))].">
      <j1 rule="para" parents="8 2799"/>
    </justification>
  </clause>

  <clause id="2831">
    <literal><![CDATA[
      x * L(x \ ((1 / x) \ y),z,u) = (1 / x) \ L(y,z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),2799(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 2799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2832">
    <literal><![CDATA[
      K(x \ 1,x) * L(1 / x,y,z) = (x \ 1) * (x * L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[para(2830(a,1),2653(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2830 2653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2833">
    <literal><![CDATA[
      (1 / x) * (L(x \ 1,y,z) * x) = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(1285(a,1),2829(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1285 2829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2834">
    <literal><![CDATA[
      L((x \ y) \ 1,x \ y,x) * (x \ y) = (1 / (x \ y)) \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(119,a,366,a(flip),b,2833,a),flip(a)].">
      <j1 rule="hyper" parents="119 366 2833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2835">
    <literal><![CDATA[
      L(x \ ((1 / x) \ y),z,u) = x \ ((1 / x) \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(125,a,2831,a),flip(a)].">
      <j1 rule="hyper" parents="125 2831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2836">
    <literal><![CDATA[
      L((x \ 1) \ ((1 / (x \ 1)) \ y),z,u) = (x \ 1) \ (x \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(76(a,1),2835(a,2,2,1))].">
      <j1 rule="para" parents="76 2835"/>
    </justification>
  </clause>

  <clause id="2837">
    <literal><![CDATA[
      1 \ ((x \ 1) * ((x \ 1) * y)) = (1 / x) * ((1 / x) * y)
    ]]></literal>
    <justification jstring="[hyper(1723,a,2530,a),flip(a)].">
      <j1 rule="hyper" parents="1723 2530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2838">
    <literal><![CDATA[
      (1 / x) * ((1 / x) * y) = (x \ 1) * ((x \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(166,a,2837,a)].">
      <j1 rule="hyper" parents="166 2837"/>
    </justification>
  </clause>

  <clause id="2839">
    <literal><![CDATA[
      (x \ 1) * ((x \ 1) * y) != (1 / x) * z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) * y = z
    ]]></literal>
    <justification jstring="[para(2838(a,1),45(a,1))].">
      <j1 rule="para" parents="2838 45"/>
    </justification>
  </clause>

  <clause id="2840">
    <literal><![CDATA[
      x * ((1 / x) * ((1 / x) * y)) = L((x \ 1) * y,x,x)
    ]]></literal>
    <justification jstring="[para(2838(a,2),1673(a,1,2))].">
      <j1 rule="para" parents="2838 1673"/>
    </justification>
  </clause>

  <clause id="2841">
    <literal><![CDATA[
      (x * T(y,y \ 1)) * z != x * (T(y,y \ 1) * u)
    ]]></literal>
    <literal><![CDATA[
      L(u,y,x) = z
    ]]></literal>
    <justification jstring="[para(2553(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="2553 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2842">
    <literal><![CDATA[
      (K(x \ 1,x) * y) * z != u
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) * (y * z) = u
    ]]></literal>
    <justification jstring="[para(2596(a,2),2595(a,1,1,1))].">
      <j1 rule="para" parents="2596 2595"/>
    </justification>
  </clause>

  <clause id="2843">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ z != a(x,y,1 / y)
    ]]></literal>
    <literal><![CDATA[
      (x * y) * (1 / y) = z
    ]]></literal>
    <justification jstring="[para(2598(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="2598 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2844">
    <literal><![CDATA[
      L(T(x,y) / x,x,y) = K(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(1122(a,1),2643(a,1,1))].">
      <j1 rule="para" parents="1122 2643"/>
    </justification>
  </clause>

  <clause id="2845">
    <literal><![CDATA[
      K(1 / (1 / x),y) = (x * K(x,y)) / x
    ]]></literal>
    <justification jstring="[hyper(65,a,970,a(flip),b,2844,a),flip(a)].">
      <j1 rule="hyper" parents="65 970 2844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2846">
    <literal><![CDATA[
      T(K(1 / (1 / x),y),x) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2845(a,2),222(a,1,1))].">
      <j1 rule="para" parents="2845 222"/>
    </justification>
  </clause>

  <clause id="2847">
    <literal><![CDATA[
      T(K(1 / x,y),x \ 1) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(76(a,1),2846(a,1,1,1,2))].">
      <j1 rule="para" parents="76 2846"/>
    </justification>
  </clause>

  <clause id="2848">
    <literal><![CDATA[
      T(K(1 / (x \ 1),y),T(x,x \ 1)) = K(T(x,x \ 1),y)
    ]]></literal>
    <justification jstring="[para(262(a,1),2846(a,1,1,1,2))].">
      <j1 rule="para" parents="262 2846"/>
    </justification>
  </clause>

  <clause id="2849">
    <literal><![CDATA[
      T(K(x,y),T(x,x \ 1)) = K(T(x,x \ 1),y)
    ]]></literal>
    <justification jstring="[para(76(a,1),2848(a,1,1,1))].">
      <j1 rule="para" parents="76 2848"/>
    </justification>
  </clause>

  <clause id="2851">
    <literal><![CDATA[
      K(T(x,x \ 1),y) = T(K(x,y),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,2183,a(flip),b,2849,a),flip(a)].">
      <j1 rule="hyper" parents="65 2183 2849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2852">
    <literal><![CDATA[
      T(K(x,y),x) = K((x \ 1) \ 1,y)
    ]]></literal>
    <justification jstring="[para(108(a,1),2851(a,1,1)),flip(a)].">
      <j1 rule="para" parents="108 2851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2853">
    <literal><![CDATA[
      K(x \ 1,x) * y != (K(x \ 1,x) / z) * u
    ]]></literal>
    <literal><![CDATA[
      (1 / z) * u = y
    ]]></literal>
    <justification jstring="[para(2498(a,1),2646(a,2,1))].">
      <j1 rule="para" parents="2498 2646"/>
    </justification>
  </clause>

  <clause id="2854">
    <literal><![CDATA[
      L(x,((y * y) \ (1 / z)) * u,w) = L(x,z * ((y * y) * u),w)
    ]]></literal>
    <justification jstring="[para(472(a,1),2564(a,1,2,1))].">
      <j1 rule="para" parents="472 2564"/>
    </justification>
  </clause>

  <clause id="2855">
    <literal><![CDATA[
      L(x,((y * y) * z) \ u,w) = L(x,(z \ 1) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(2630,a,2574,a),flip(a)].">
      <j1 rule="hyper" parents="2630 2574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2857">
    <literal><![CDATA[
      L(x,((y * y) * z) \ u,w) = L(x,z \ u,w)
    ]]></literal>
    <justification jstring="[hyper(299,a,2538,a(flip),b,2855,a),flip(a)].">
      <j1 rule="hyper" parents="299 2538 2855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2858">
    <literal><![CDATA[
      L(x,((y \ 1) \ z) \ u,w) = L(x,(y \ z) \ u,w)
    ]]></literal>
    <justification jstring="[para(724(a,1),2857(a,1,2,1))].">
      <j1 rule="para" parents="724 2857"/>
    </justification>
  </clause>

  <clause id="2859">
    <literal><![CDATA[
      L(x,y \ ((z * z) \ u),w) = L(x,y \ u,w)
    ]]></literal>
    <justification jstring="[para(420(a,1),2857(a,1,2))].">
      <j1 rule="para" parents="420 2857"/>
    </justification>
  </clause>

  <clause id="2860">
    <literal><![CDATA[
      L(x,y \ (1 / z),u) = L(x,y \ z,u)
    ]]></literal>
    <justification jstring="[para(264(a,1),2859(a,1,2,2))].">
      <j1 rule="para" parents="264 2859"/>
    </justification>
  </clause>

  <clause id="2861">
    <literal><![CDATA[
      L(x,y \ (((1 / z) * z) \ (z \ u)),w) = L(x,y \ ((z \ 1) \ u),w)
    ]]></literal>
    <justification jstring="[para(1070(a,2),2859(a,1,2,2))].">
      <j1 rule="para" parents="1070 2859"/>
    </justification>
  </clause>

  <clause id="2862">
    <literal><![CDATA[
      L(x,y \ (z \ 1),u) = L(x,y \ z,u)
    ]]></literal>
    <justification jstring="[para(76(a,1),2860(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="76 2860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2863">
    <literal><![CDATA[
      L((x \ (y \ 1)) \ z,x \ y,x) = (y \ 1) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(615,a,2862,a),flip(a)].">
      <j1 rule="hyper" parents="615 2862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2864">
    <literal><![CDATA[
      L(x,((y \ 1) * z) \ y,u) = L(x,(y * z) \ y,u)
    ]]></literal>
    <justification jstring="[para(2787(a,1),2862(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2787 2862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2865">
    <literal><![CDATA[
      L(((x * y) \ x) \ z,((x \ 1) * y) \ x,(x \ 1) * y) = (x \ 1) \ (((x \ 1) * y) * z)
    ]]></literal>
    <justification jstring="[para(2787(a,1),2863(a,1,1,1))].">
      <j1 rule="para" parents="2787 2863"/>
    </justification>
  </clause>

  <clause id="2866">
    <literal><![CDATA[
      (x * y) * (y \ 1) = R(x,y,1 / y)
    ]]></literal>
    <justification jstring="[hyper(2600,a,2763,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="2600 2763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2867">
    <literal><![CDATA[
      R(x,y,1 / y) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(551,a,2866,a),flip(a)].">
      <j1 rule="hyper" parents="551 2866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2868">
    <literal><![CDATA[
      R(x \ y,x,1 / x) = T(y * (x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,858,a(flip),b,2866,a),flip(a)].">
      <j1 rule="hyper" parents="65 858 2866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2869">
    <literal><![CDATA[
      R(1 / L(x,y,z),x,1 / x) = (x / L(x,y,z)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(1793(a,1),2866(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1793 2866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2870">
    <literal><![CDATA[
      (L(x,y,z) * R(L(x,y,z) \ 1,x,1 / x)) / L(x,y,z) = (x / L(x,y,z)) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,699,a,b,2869,a)].">
      <j1 rule="hyper" parents="65 699 2869"/>
    </justification>
  </clause>

  <clause id="2871">
    <literal><![CDATA[
      L(x,y,z * ((u * u) * (w \ 1))) = L(x,y,z * ((u * u) * w))
    ]]></literal>
    <justification jstring="[para(34(a,1),2628(a,2,3))].">
      <j1 rule="para" parents="34 2628"/>
    </justification>
  </clause>

  <clause id="2872">
    <literal><![CDATA[
      L(x,y,z * ((u * u) * (w \ 1))) = L(x,y,(z * w) / (u * u))
    ]]></literal>
    <justification jstring="[para(416(a,1),2629(a,1,3,2))].">
      <j1 rule="para" parents="416 2629"/>
    </justification>
  </clause>

  <clause id="2873">
    <literal><![CDATA[
      L((x \ 1) \ 1,x,y * (1 / x)) = R(y,x,x) \ (y * x)
    ]]></literal>
    <justification jstring="[para(1249(a,1),2638(a,2,1))].">
      <j1 rule="para" parents="1249 2638"/>
    </justification>
  </clause>

  <clause id="2874">
    <literal><![CDATA[
      L((x \ 1) \ 1,x,y * x) = R(y,x,x) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(65,a,2625,a(flip),b,2873,a)].">
      <j1 rule="hyper" parents="65 2625 2873"/>
    </justification>
  </clause>

  <clause id="2875">
    <literal><![CDATA[
      x * ((y \ 1) * (y * T(y \ 1,x * K(y \ 1,y)))) = L(1 / y,K(y \ 1,y),x) * (x * K(y \ 1,y))
    ]]></literal>
    <justification jstring="[para(2659(a,1),681(a,1,2))].">
      <j1 rule="para" parents="2659 681"/>
    </justification>
  </clause>

  <clause id="2876">
    <literal><![CDATA[
      R(1 / x,y,z) / (x \ 1) = x * R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(2586(a,1),2715(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2586 2715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2877">
    <literal><![CDATA[
      (x / y) * R(1 / (x / y),x / y,y) = (y / x) / ((x / y) \ 1)
    ]]></literal>
    <justification jstring="[para(376(a,1),2876(a,1,1)),flip(a)].">
      <j1 rule="para" parents="376 2876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2878">
    <literal><![CDATA[
      R(x,(y \ 1) \ 1,T(y \ 1,y)) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(76(a,1),2719(a,2,2))].">
      <j1 rule="para" parents="76 2719"/>
    </justification>
  </clause>

  <clause id="2880">
    <literal><![CDATA[
      R(x,T(y,y \ 1),T(y \ 1,y)) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(108(a,2),2878(a,1,2))].">
      <j1 rule="para" parents="108 2878"/>
    </justification>
  </clause>

  <clause id="2881">
    <literal><![CDATA[
      T(x,y) * ((x * (T(x,y) \ 1)) / x) = T(x,T(x,y) \ 1) / x
    ]]></literal>
    <justification jstring="[hyper(1095,a,2828,a)].">
      <j1 rule="hyper" parents="1095 2828"/>
    </justification>
  </clause>

  <clause id="2882">
    <literal><![CDATA[
      L(x,y * ((z * z) * u),w) = L(x,(1 / y) * u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,2522,a(flip),b,2854,a),flip(a)].">
      <j1 rule="hyper" parents="65 2522 2854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2884">
    <literal><![CDATA[
      L(x,y * ((z * z) * u),w) = L(x,y * u,w)
    ]]></literal>
    <justification jstring="[hyper(299,a,2537,a(flip),b,2882,a),flip(a)].">
      <j1 rule="hyper" parents="299 2537 2882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2885">
    <literal><![CDATA[
      L(x,y * ((z * z) \ 1),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(71(a,1),2884(a,1,2)),flip(a)].">
      <j1 rule="para" parents="71 2884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2886">
    <literal><![CDATA[
      L(x,y * (1 / z),u) = L(x,y * z,u)
    ]]></literal>
    <justification jstring="[para(217(a,1),2884(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="217 2884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2887">
    <literal><![CDATA[
      L(x,y * ((1 / z) \ u),w) = L(x,y * (z \ u),w)
    ]]></literal>
    <justification jstring="[para(734(a,1),2884(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="734 2884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2888">
    <literal><![CDATA[
      L(x,y * (z \ 1),u) = L(x,y * z,u)
    ]]></literal>
    <justification jstring="[para(76(a,1),2886(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="76 2886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2889">
    <literal><![CDATA[
      L(x,y * (1 / z),u) = L(x,y * (z \ 1),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,2886,a,b,2888,a)].">
      <j1 rule="hyper" parents="299 2886 2888"/>
    </justification>
  </clause>

  <clause id="2890">
    <literal><![CDATA[
      L(x,y * (z * z),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,2885,a(flip),b,2888,a),flip(a)].">
      <j1 rule="hyper" parents="65 2885 2888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2891">
    <literal><![CDATA[
      (x * x) \ ((y * z) \ (y * ((z * x) * x))) = L(a(z,x,x),z,y)
    ]]></literal>
    <justification jstring="[hyper(2028,a,2890,a)].">
      <j1 rule="hyper" parents="2028 2890"/>
    </justification>
  </clause>

  <clause id="2892">
    <literal><![CDATA[
      L(x,y / (z * z),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(12(a,1),2890(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 2890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2893">
    <literal><![CDATA[
      L(x,y * (z / (u * u)),w) = L(x,y * z,w)
    ]]></literal>
    <justification jstring="[para(849(a,1),2892(a,1,2))].">
      <j1 rule="para" parents="849 2892"/>
    </justification>
  </clause>

  <clause id="2894">
    <literal><![CDATA[
      L(x,y,(z * u) / (w * w)) = L(x,y,z * ((w * w) * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,2871,a(flip),b,2872,a),flip(a)].">
      <j1 rule="hyper" parents="65 2871 2872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2895">
    <literal><![CDATA[
      L(x,y,z * ((u * u) * w)) = L(x,y,z * w)
    ]]></literal>
    <justification jstring="[hyper(65,a,2514,a(flip),b,2894,a),flip(a)].">
      <j1 rule="hyper" parents="65 2514 2894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2897">
    <literal><![CDATA[
      L(x,y,T(z,u * u) * w) = L(x,y,z * w)
    ]]></literal>
    <justification jstring="[hyper(65,a,2484,a,b,2895,a)].">
      <j1 rule="hyper" parents="65 2484 2895"/>
    </justification>
  </clause>

  <clause id="2900">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ x) / x) = T(x,T(x,y) \ 1) / x
    ]]></literal>
    <justification jstring="[para(1193(a,1),2881(a,1,2,1))].">
      <j1 rule="para" parents="1193 2881"/>
    </justification>
  </clause>

  <clause id="2901">
    <literal><![CDATA[
      x * (T(x,T(x,y) \ 1) / x) = T(x,x / (x * T(x,y)))
    ]]></literal>
    <justification jstring="[para(2881(a,1),1835(a,1,2))].">
      <j1 rule="para" parents="2881 1835"/>
    </justification>
  </clause>

  <clause id="2902">
    <literal><![CDATA[
      (T(x,T(x,y) \ 1) / x) * x = T(x,x / (x * T(x,y)))
    ]]></literal>
    <justification jstring="[para(2900(a,1),2012(a,1,1))].">
      <j1 rule="para" parents="2900 2012"/>
    </justification>
  </clause>

  <clause id="2903">
    <literal><![CDATA[
      T(x,x / (x * T(x,y))) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(247,a,2902,a),flip(a)].">
      <j1 rule="hyper" parents="247 2902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2905">
    <literal><![CDATA[
      x * (T(x,T(x,y) \ 1) / x) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,2901,a,b,2903,a)].">
      <j1 rule="hyper" parents="65 2901 2903"/>
    </justification>
  </clause>

  <clause id="2906">
    <literal><![CDATA[
      x * (T(x,y) * ((T(x,y) \ x) / x)) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(2900(a,2),2905(a,1,2))].">
      <j1 rule="para" parents="2900 2905"/>
    </justification>
  </clause>

  <clause id="2907">
    <literal><![CDATA[
      x * T(K(x,x \ 1),y) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(2607(a,1),2906(a,1,2))].">
      <j1 rule="para" parents="2607 2906"/>
    </justification>
  </clause>

  <clause id="2908">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) != x * z
    ]]></literal>
    <literal><![CDATA[
      T(K(x,x \ 1),y) = z
    ]]></literal>
    <justification jstring="[para(2907(a,1),45(a,1))].">
      <j1 rule="para" parents="2907 45"/>
    </justification>
  </clause>

  <clause id="2910">
    <literal><![CDATA[
      (x \ 1) * ((x * y) * z) = x * (((1 / x) * y) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,2508,a(flip),b,2566,a)].">
      <j1 rule="hyper" parents="65 2508 2566"/>
    </justification>
  </clause>

  <clause id="2911">
    <literal><![CDATA[
      R(x,y,1 / y) / (1 / y) = x * (y * K(y \ 1,y))
    ]]></literal>
    <justification jstring="[para(79(a,1),2695(a,1,1,2))].">
      <j1 rule="para" parents="79 2695"/>
    </justification>
  </clause>

  <clause id="2912">
    <literal><![CDATA[
      R(x,y,y \ 1) / (1 / y) = x * (y * K(y \ 1,y))
    ]]></literal>
    <justification jstring="[para(2867(a,1),2911(a,1,1))].">
      <j1 rule="para" parents="2867 2911"/>
    </justification>
  </clause>

  <clause id="2913">
    <literal><![CDATA[
      R(x,y,y \ 1) / (1 / y) = x * (1 / (1 / y))
    ]]></literal>
    <justification jstring="[para(1716(a,1),2912(a,2,2))].">
      <j1 rule="para" parents="1716 2912"/>
    </justification>
  </clause>

  <clause id="2914">
    <literal><![CDATA[
      (x * (1 / (1 / y))) * K(y,y \ 1) = x * y
    ]]></literal>
    <justification jstring="[para(2913(a,1),2780(a,1,1))].">
      <j1 rule="para" parents="2913 2780"/>
    </justification>
  </clause>

  <clause id="2915">
    <literal><![CDATA[
      (x * y) * K(y \ 1,y) = x * (1 / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(2765,a,2914,a)].">
      <j1 rule="hyper" parents="2765 2914"/>
    </justification>
  </clause>

  <clause id="2916">
    <literal><![CDATA[
      (x * K(y,y \ 1)) / y = x / (1 / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(626,a,2914,a)].">
      <j1 rule="hyper" parents="626 2914"/>
    </justification>
  </clause>

  <clause id="2917">
    <literal><![CDATA[
      (x / y) * K(y,y \ 1) = x / (1 / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(65,a,2777,a(flip),b,2916,a)].">
      <j1 rule="hyper" parents="65 2777 2916"/>
    </justification>
  </clause>

  <clause id="2918">
    <literal><![CDATA[
      (1 / (x \ y)) \ (y \ x) = (y \ x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(366(a,1),2834(a,1,1)),flip(a)].">
      <j1 rule="para" parents="366 2834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2919">
    <literal><![CDATA[
      (1 / (x \ y)) * ((y \ x) * (x \ y)) = y \ x
    ]]></literal>
    <justification jstring="[hyper(144,a,2918,a)].">
      <j1 rule="hyper" parents="144 2918"/>
    </justification>
  </clause>

  <clause id="2920">
    <literal><![CDATA[
      (x \ (x * y)) * ((x * y) \ x) = (1 / ((x * y) \ x)) \ y
    ]]></literal>
    <justification jstring="[para(9(a,1),2918(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 2918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2921">
    <literal><![CDATA[
      T(1 / (x \ y),(y \ x) * (x \ y)) = ((y \ x) * (x \ y)) \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(235,a,2919,a,b,10,a)].">
      <j1 rule="hyper" parents="235 2919 10"/>
    </justification>
  </clause>

  <clause id="2923">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) \ y = y * ((x * y) \ x)
    ]]></literal>
    <justification jstring="[para(9(a,1),2920(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 2920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2924">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) * (y * ((x * y) \ x)) = y
    ]]></literal>
    <justification jstring="[hyper(144,a,2923,a)].">
      <j1 rule="hyper" parents="144 2923"/>
    </justification>
  </clause>

  <clause id="2925">
    <literal><![CDATA[
      (x / y) / ((y / x) \ 1) = (y / x) * (x / y)
    ]]></literal>
    <justification jstring="[para(376(a,1),2877(a,1,2)),flip(a)].">
      <j1 rule="para" parents="376 2877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2926">
    <literal><![CDATA[
      ((x / y) * (y / x)) * ((x / y) \ 1) = y / x
    ]]></literal>
    <justification jstring="[hyper(143,a,2925,a)].">
      <j1 rule="hyper" parents="143 2925"/>
    </justification>
  </clause>

  <clause id="2927">
    <literal><![CDATA[
      (x / (y \ x)) * ((y \ x) / x) = ((y \ x) / x) / (y \ 1)
    ]]></literal>
    <justification jstring="[para(76(a,1),2925(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="76 2925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2929">
    <literal><![CDATA[
      ((x \ y) / y) / (x \ 1) = x * ((x \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(327,a,2927,a),flip(a)].">
      <j1 rule="hyper" parents="327 2927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2931">
    <literal><![CDATA[
      (x * ((x \ y) / y)) * (x \ 1) = (x \ y) / y
    ]]></literal>
    <justification jstring="[hyper(143,a,2929,a)].">
      <j1 rule="hyper" parents="143 2929"/>
    </justification>
  </clause>

  <clause id="2932">
    <literal><![CDATA[
      (x * ((x \ y) / y)) * (x \ 1) = R(1 / x,x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(299,a,375,a,b,2931,a),flip(a)].">
      <j1 rule="hyper" parents="299 375 2931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2933">
    <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(2485(a,2),2504(a,1))].">
      <j1 rule="para" parents="2485 2504"/>
    </justification>
  </clause>

  <clause id="2934">
    <literal><![CDATA[
      K((x / (y * x)) \ 1,x / (y * x)) = K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(37,a,2724,a,b,2619,a),flip(a)].">
      <j1 rule="hyper" parents="37 2724 2619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2936">
    <literal><![CDATA[
      K(x,y / (x * y)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,2666,a(flip),b,2934,a)].">
      <j1 rule="hyper" parents="65 2666 2934"/>
    </justification>
  </clause>

  <clause id="2939">
    <literal><![CDATA[
      K(x / y,(x / y) \ 1) = K(x / y,y / x)
    ]]></literal>
    <justification jstring="[para(12(a,1),2936(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 2936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2940">
    <literal><![CDATA[
      K((x / y) \ 1,x / y) = K(y / x,(y / x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,2664,a,b,2939,a)].">
      <j1 rule="hyper" parents="299 2664 2939"/>
    </justification>
  </clause>

  <clause id="2941">
    <literal><![CDATA[
      K(x / (y * x),(x / (y * x)) \ 1) = K(x / (y * x),y)
    ]]></literal>
    <justification jstring="[para(11(a,1),2939(a,2,2))].">
      <j1 rule="para" parents="11 2939"/>
    </justification>
  </clause>

  <clause id="2942">
    <literal><![CDATA[
      K(x / (y * x),(x / (y * x)) \ 1) = K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,2663,a(flip),b,2941,a),flip(a)].">
      <j1 rule="hyper" parents="299 2663 2941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2944">
    <literal><![CDATA[
      K(x \ 1,x) * (y / (x * y)) = ((y / (x * y)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(2942(a,1),2556(a,1,1))].">
      <j1 rule="para" parents="2942 2556"/>
    </justification>
  </clause>

  <clause id="2945">
    <literal><![CDATA[
      R(x \ 1,x,y) = ((y / (x * y)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(2662,a,2944,a)].">
      <j1 rule="hyper" parents="2662 2944"/>
    </justification>
  </clause>

  <clause id="2947">
    <literal><![CDATA[
      R(R(x,y,z) \ 1,R(x,y,z),y * z) = (((y * z) / ((x * y) * z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(103(a,1),2945(a,2,1,1,2))].">
      <j1 rule="para" parents="103 2945"/>
    </justification>
  </clause>

  <clause id="2948">
    <literal><![CDATA[
      L(1 / x,y,z) * K(x \ 1,x) = (x \ 1) * (x * L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[hyper(2229,a,2832,a)].">
      <j1 rule="hyper" parents="2229 2832"/>
    </justification>
  </clause>

  <clause id="2949">
    <literal><![CDATA[
      L((x \ 1) \ (x \ y),z,u) = (x \ 1) \ (x \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(76(a,1),2836(a,1,1,2,1))].">
      <j1 rule="para" parents="76 2836"/>
    </justification>
  </clause>

  <clause id="2951">
    <literal><![CDATA[
      L(x,y \ ((z \ 1) \ u),w) = L(x,y \ (z \ u),w)
    ]]></literal>
    <justification jstring="[para(165(a,1),2861(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="165 2861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2952">
    <literal><![CDATA[
      L(x,y \ ((1 / z) \ u),w) = L(x,y \ (z \ u),w)
    ]]></literal>
    <justification jstring="[para(79(a,1),2951(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="79 2951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2954">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ (x \ y) = 1 / (y \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,2092,a(flip),b,2921,a),flip(a)].">
      <j1 rule="hyper" parents="65 2092 2921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2955">
    <literal><![CDATA[
      L((x \ y) \ 1,x \ y,y \ x) = 1 / (x \ y)
    ]]></literal>
    <justification jstring="[hyper(402,a,2954,a)].">
      <j1 rule="hyper" parents="402 2954"/>
    </justification>
  </clause>

  <clause id="2956">
    <literal><![CDATA[
      (((x * y) \ x) * y) \ ((x * y) \ x) = 1 / (x \ (x * y))
    ]]></literal>
    <justification jstring="[para(9(a,1),2954(a,1,1,2))].">
      <j1 rule="para" parents="9 2954"/>
    </justification>
  </clause>

  <clause id="2957">
    <literal><![CDATA[
      L(((x * y) \ x) \ 1,(x * y) \ x,y) = 1 / ((x * y) \ x)
    ]]></literal>
    <justification jstring="[para(9(a,1),2955(a,1,3))].">
      <j1 rule="para" parents="9 2955"/>
    </justification>
  </clause>

  <clause id="2958">
    <literal><![CDATA[
      (((x * y) \ x) * y) \ ((x * y) \ x) = 1 / y
    ]]></literal>
    <justification jstring="[para(9(a,1),2956(a,2,2))].">
      <j1 rule="para" parents="9 2956"/>
    </justification>
  </clause>

  <clause id="2959">
    <literal><![CDATA[
      ((x * y) \ x) / (1 / y) = ((x * y) \ x) * y
    ]]></literal>
    <justification jstring="[hyper(192,a,2958,a)].">
      <j1 rule="hyper" parents="192 2958"/>
    </justification>
  </clause>

  <clause id="2960">
    <literal><![CDATA[
      (((x * y) \ x) * y) * (1 / y) = (x * y) \ x
    ]]></literal>
    <justification jstring="[hyper(144,a,2958,a)].">
      <j1 rule="hyper" parents="144 2958"/>
    </justification>
  </clause>

  <clause id="2961">
    <literal><![CDATA[
      K(((x * y) \ x) \ (((x * y) \ x) * y),(x * y) \ x) * y = T(y,(x * y) \ x)
    ]]></literal>
    <justification jstring="[para(2959(a,1),1296(a,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2959 1296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2962">
    <literal><![CDATA[
      (x * y) \ x = (L(y \ 1,y,x) * y) * (1 / y)
    ]]></literal>
    <justification jstring="[para(214(a,2),2960(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="214 2960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2963">
    <literal><![CDATA[
      L(x \ 1,x,y) / (1 / x) = L(x \ 1,x,y) * x
    ]]></literal>
    <justification jstring="[hyper(655,a,2962,a)].">
      <j1 rule="hyper" parents="655 2962"/>
    </justification>
  </clause>

  <clause id="2964">
    <literal><![CDATA[
      (x * ((y * x) \ y)) * K(x \ 1,x) = L(x \ 1,x,y) * x
    ]]></literal>
    <justification jstring="[hyper(65,a,2686,a,b,2963,a)].">
      <j1 rule="hyper" parents="65 2686 2963"/>
    </justification>
  </clause>

  <clause id="2965">
    <literal><![CDATA[
      (x * ((y * x) \ y)) \ x = 1 / ((y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(808,a,2957,a)].">
      <j1 rule="hyper" parents="808 2957"/>
    </justification>
  </clause>

  <clause id="2967">
    <literal><![CDATA[
      ((x \ 1) * (x * L(x \ 1,x,y))) * x = (x * ((y * x) \ y)) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2948(a,1),1624(a,1,1))].">
      <j1 rule="para" parents="2948 1624"/>
    </justification>
  </clause>

  <clause id="2968">
    <literal><![CDATA[
      (K(x \ 1,x) * ((y * z) * u)) / (z * u) = R(K(x \ 1,x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(2495(a,1),2645(a,1,1))].">
      <j1 rule="para" parents="2495 2645"/>
    </justification>
  </clause>

  <clause id="2969">
    <literal><![CDATA[
      ((x \ 1) * y) / T(1 / x,y) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[para(2492(a,1),2654(a,1,2))].">
      <j1 rule="para" parents="2492 2654"/>
    </justification>
  </clause>

  <clause id="2970">
    <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(2969(a,1),2167(a,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="2969 2167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2972">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ (y * (y * x)) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[para(2693(a,1),2696(a,1,2,2))].">
      <j1 rule="para" parents="2693 2696"/>
    </justification>
  </clause>

  <clause id="2973">
    <literal><![CDATA[
      K(x \ 1,x) * (((y * z) * u) / (z * u)) = R(K(x \ 1,x) * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,2499,a(flip),b,2968,a)].">
      <j1 rule="hyper" parents="65 2499 2968"/>
    </justification>
  </clause>

  <clause id="2974">
    <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),2973(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20 2973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2975">
    <literal><![CDATA[
      K(x,x \ 1) * R(K(x \ 1,x) * y,z,u) = R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(2746,a,2974,a(flip))].">
      <j1 rule="hyper" parents="2746 2974"/>
    </justification>
  </clause>

  <clause id="2976">
    <literal><![CDATA[
      K(x,x \ 1) * R(x \ 1,y,z) = R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(2223(a,1),2975(a,1,2,1))].">
      <j1 rule="para" parents="2223 2975"/>
    </justification>
  </clause>

  <clause id="2977">
    <literal><![CDATA[
      R(K(x,x \ 1) * y,z,u) = K(x,x \ 1) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(2738(a,1),2975(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2738 2975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2978">
    <literal><![CDATA[
      ((x * x) \ y) * L(x,x,x) = (x \ 1) * T(y,L(x,x,x))
    ]]></literal>
    <justification jstring="[para(949(a,1),2818(a,1,1,1))].">
      <j1 rule="para" parents="949 2818"/>
    </justification>
  </clause>

  <clause id="2979">
    <literal><![CDATA[
      (x \ 1) * T(y,L(x,x,x)) = T(y * (1 / x),x * x)
    ]]></literal>
    <justification jstring="[hyper(65,a,1054,a(flip),b,2978,a),flip(a)].">
      <j1 rule="hyper" parents="65 1054 2978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2980">
    <literal><![CDATA[
      a((x * y) \ 1,x,y) / y = (1 / (x * y)) * x
    ]]></literal>
    <justification jstring="[hyper(120,a,2750,a(flip),b,2735,a(flip))].">
      <j1 rule="hyper" parents="120 2750 2735"/>
    </justification>
  </clause>

  <clause id="2981">
    <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(2788(a,1),318(a,1))].">
      <j1 rule="para" parents="2788 318"/>
    </justification>
  </clause>

  <clause id="2982">
    <literal><![CDATA[
      T(x,K(x \ 1,x) * y) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(2981,a,2492,a)].">
      <j1 rule="hyper" parents="2981 2492"/>
    </justification>
  </clause>

  <clause id="2983">
    <literal><![CDATA[
      T(x,(1 / x) * y) = T(x,(x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(2650(a,1),2982(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2650 2982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2984">
    <literal><![CDATA[
      ((((x * y) / ((z * x) * y)) \ 1) \ 1) * ((z * x) * y) = ((R(z,x,y) \ 1) * R(z,x,y)) * (x * y)
    ]]></literal>
    <justification jstring="[para(2947(a,1),554(a,1,1))].">
      <j1 rule="para" parents="2947 554"/>
    </justification>
  </clause>

  <clause id="2985">
    <literal><![CDATA[
      (x \ 1) * (x * L(x \ 1,x,y)) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(37,a,2964,a(flip),b,2967,a),flip(a)].">
      <j1 rule="hyper" parents="37 2964 2967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2986">
    <literal><![CDATA[
      (x * y) \ x = (y \ 1) * (y * L(y \ 1,y,x))
    ]]></literal>
    <justification jstring="[hyper(299,a,214,a(flip),b,2985,a)].">
      <j1 rule="hyper" parents="299 214 2985"/>
    </justification>
  </clause>

  <clause id="2987">
    <literal><![CDATA[
      (x \ 1) * (x * ((y * x) \ y)) = (y * x) \ y
    ]]></literal>
    <justification jstring="[para(214(a,1),2986(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="214 2986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2988">
    <literal><![CDATA[
      (x \ 1) * (x * ((y * x) \ y)) = ((y * x) \ y) * 1
    ]]></literal>
    <justification jstring="[hyper(299,a,8,a,b,2987,a),flip(a)].">
      <j1 rule="hyper" parents="299 8 2987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2989">
    <literal><![CDATA[
      (x \ 1) \ ((y * x) \ y) = x * ((y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(125,a,2987,a)].">
      <j1 rule="hyper" parents="125 2987"/>
    </justification>
  </clause>

  <clause id="2990">
    <literal><![CDATA[
      L(x * ((y * x) \ y),x \ 1,y * x) = ((y * x) * (x \ 1)) \ y
    ]]></literal>
    <justification jstring="[para(2989(a,1),281(a,1,1))].">
      <j1 rule="para" parents="2989 281"/>
    </justification>
  </clause>

  <clause id="2991">
    <literal><![CDATA[
      K(x \ 1,x * ((y * x) \ y)) = 1
    ]]></literal>
    <justification jstring="[hyper(2333,a,2988,a(flip))].">
      <j1 rule="hyper" parents="2333 2988"/>
    </justification>
  </clause>

  <clause id="2992">
    <literal><![CDATA[
      T(x,(y * x) \ y) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(119,a,2991,a(flip),b,2343,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 2991 2343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2994">
    <literal><![CDATA[
      T(x,(y * x) \ y) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,108,a,b,2992,a),flip(a)].">
      <j1 rule="hyper" parents="299 108 2992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2995">
    <literal><![CDATA[
      T(x \ y,y \ x) = ((x \ y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(10(a,1),2992(a,1,2,1))].">
      <j1 rule="para" parents="10 2992"/>
    </justification>
  </clause>

  <clause id="2996">
    <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),2994(a,1,2,1))].">
      <j1 rule="para" parents="88 2994"/>
    </justification>
  </clause>

  <clause id="2997">
    <literal><![CDATA[
      1 / T(x \ y,y \ x) = (x \ y) \ 1
    ]]></literal>
    <justification jstring="[hyper(192,a,2995,a(flip))].">
      <j1 rule="hyper" parents="192 2995"/>
    </justification>
  </clause>

  <clause id="2998">
    <literal><![CDATA[
      T(x \ (x / y),y) = ((x \ (x / y)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(79(a,1),2995(a,1,2))].">
      <j1 rule="para" parents="79 2995"/>
    </justification>
  </clause>

  <clause id="2999">
    <literal><![CDATA[
      x * K((x \ y) \ 1,x \ y) = y * (((y \ x) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2995(a,1),1384(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2995 1384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3000">
    <literal><![CDATA[
      T(x \ y,y \ x) \ 1 = 1 / (x \ y)
    ]]></literal>
    <justification jstring="[para(2995(a,2),1689(a,1,1))].">
      <j1 rule="para" parents="2995 1689"/>
    </justification>
  </clause>

  <clause id="3001">
    <literal><![CDATA[
      K(x \ (x / T(y \ x,x \ y)),x) = T(K(x \ y,x),(y \ x) \ 1)
    ]]></literal>
    <justification jstring="[para(2995(a,2),2172(a,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2995 2172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3002">
    <literal><![CDATA[
      1 / T((x * y) \ x,y) = ((x * y) \ x) \ 1
    ]]></literal>
    <justification jstring="[para(9(a,1),2997(a,1,2,2))].">
      <j1 rule="para" parents="9 2997"/>
    </justification>
  </clause>

  <clause id="3003">
    <literal><![CDATA[
      ((x \ (x / y)) \ 1) \ 1 = x \ (x / ((y \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(65,a,2689,a(flip),b,2998,a),flip(a)].">
      <j1 rule="hyper" parents="65 2689 2998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3004">
    <literal><![CDATA[
      x * (((x \ (x / y)) \ 1) \ 1) = x / ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2998(a,1),2688(a,1,2))].">
      <j1 rule="para" parents="2998 2688"/>
    </justification>
  </clause>

  <clause id="3005">
    <literal><![CDATA[
      1 / (x \ (x / ((y \ 1) \ 1))) = (x \ (x / y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(192,a,3003,a)].">
      <j1 rule="hyper" parents="192 3003"/>
    </justification>
  </clause>

  <clause id="3006">
    <literal><![CDATA[
      x / (((y \ x) \ 1) \ 1) = x * (((x \ y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(76(a,1),3004(a,1,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="76 3004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3007">
    <literal><![CDATA[
      x \ (x / ((y \ 1) \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      ((x \ (x / y)) \ 1) \ 1 = z
    ]]></literal>
    <justification jstring="[para(3004(a,1),314(a,1,2))].">
      <j1 rule="para" parents="3004 314"/>
    </justification>
  </clause>

  <clause id="3008">
    <literal><![CDATA[
      (x \ (x / (1 / (1 / y)))) \ 1 = 1 / (x \ (x / y))
    ]]></literal>
    <justification jstring="[para(191(a,1),3005(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="191 3005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3009">
    <literal><![CDATA[
      1 / (1 / (x \ (x / y))) = x \ (x / (1 / (1 / y)))
    ]]></literal>
    <justification jstring="[hyper(192,a,3008,a)].">
      <j1 rule="hyper" parents="192 3008"/>
    </justification>
  </clause>

  <clause id="3010">
    <literal><![CDATA[
      x * (1 / (1 / (x \ (x / y)))) = x / (1 / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(144,a,3009,a(flip))].">
      <j1 rule="hyper" parents="144 3009"/>
    </justification>
  </clause>

  <clause id="3011">
    <literal><![CDATA[
      1 / (1 / (x \ (x / (y \ 1)))) = x \ (x / (1 / y))
    ]]></literal>
    <justification jstring="[para(76(a,1),3009(a,2,2,2,2))].">
      <j1 rule="para" parents="76 3009"/>
    </justification>
  </clause>

  <clause id="3012">
    <literal><![CDATA[
      x / (1 / (1 / (y \ x))) = x * (1 / (1 / (x \ y)))
    ]]></literal>
    <justification jstring="[para(76(a,1),3010(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="76 3010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3013">
    <literal><![CDATA[
      (x * (1 / (1 / (x \ y)))) \ x = 1 / (1 / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(186,a,3012,a)].">
      <j1 rule="hyper" parents="186 3012"/>
    </justification>
  </clause>

  <clause id="3014">
    <literal><![CDATA[
      (x * (1 / (1 / T(y,x)))) \ x = 1 / (1 / ((y * x) \ x))
    ]]></literal>
    <justification jstring="[para(22(a,2),3013(a,1,1,2,2,2))].">
      <j1 rule="para" parents="22 3013"/>
    </justification>
  </clause>

  <clause id="3015">
    <literal><![CDATA[
      T(K(x,y),K(x,y) \ 1) = T(K(x,y),K(y,x))
    ]]></literal>
    <justification jstring="[para(16(a,2),2996(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16 2996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3016">
    <literal><![CDATA[
      T(K(x,y),K(y,x)) = (K(x,y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(409,a,3015,a),flip(a)].">
      <j1 rule="hyper" parents="409 3015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3017">
    <literal><![CDATA[
      (K(x,y) \ 1) \ 1 = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2276,a(flip),b,3016,a),flip(a)].">
      <j1 rule="hyper" parents="65 2276 3016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3018">
    <literal><![CDATA[
      1 / (1 / K(x,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(1703,a,3017,a)].">
      <j1 rule="hyper" parents="1703 3017"/>
    </justification>
  </clause>

  <clause id="3022">
    <literal><![CDATA[
      L(x * ((y * x) \ y),x \ 1,y * x) = R(y,x,x \ 1) \ y
    ]]></literal>
    <justification jstring="[para(258(a,1),2990(a,2,1))].">
      <j1 rule="para" parents="258 2990"/>
    </justification>
  </clause>

  <clause id="3023">
    <literal><![CDATA[
      T(K(x \ y,x),(y \ x) \ 1) = T(K(x \ y,x),x \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2171,a(flip),b,3001,a),flip(a)].">
      <j1 rule="hyper" parents="65 2171 3001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3024">
    <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),3023(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 3023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3025">
    <literal><![CDATA[
      T(K(x,y),((y * x) \ y) \ 1) = T(K(x,y),y \ (y * x))
    ]]></literal>
    <justification jstring="[para(9(a,1),3024(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 3024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3026">
    <literal><![CDATA[
      T(K(x,y),((y * x) \ y) \ 1) = T(K(x,y),x)
    ]]></literal>
    <justification jstring="[para(9(a,1),3025(a,2,2))].">
      <j1 rule="para" parents="9 3025"/>
    </justification>
  </clause>

  <clause id="3028">
    <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(3026(a,1),2447(a,1))].">
      <j1 rule="para" parents="3026 2447"/>
    </justification>
  </clause>

  <clause id="3030">
    <literal><![CDATA[
      x \ T(K(x,x \ 1) * y,x \ 1) = ((1 / (x \ 1)) \ ((x \ 1) \ y)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(2596(a,1),2658(a,1,2,1,1))].">
      <j1 rule="para" parents="2596 2658"/>
    </justification>
  </clause>

  <clause id="3031">
    <literal><![CDATA[
      K(x,(y * x) \ y) * x = T(x,(y * x) \ y)
    ]]></literal>
    <justification jstring="[para(9(a,1),2961(a,1,1,1))].">
      <j1 rule="para" parents="9 2961"/>
    </justification>
  </clause>

  <clause id="3032">
    <literal><![CDATA[
      K(x,(y * x) \ y) = ((x \ 1) \ 1) / x
    ]]></literal>
    <justification jstring="[hyper(120,a,2992,a(flip),b,3031,a),flip(a)].">
      <j1 rule="hyper" parents="120 2992 3031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3034">
    <literal><![CDATA[
      K(x,(y * x) \ y) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,2552,a(flip),b,3032,a),flip(a)].">
      <j1 rule="hyper" parents="299 2552 3032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3035">
    <literal><![CDATA[
      K(x,(y * x) \ y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) = z
    ]]></literal>
    <justification jstring="[para(3032(a,2),2559(a,1))].">
      <j1 rule="para" parents="3032 2559"/>
    </justification>
  </clause>

  <clause id="3036">
    <literal><![CDATA[
      K(x \ y,(x \ y) \ 1) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[para(10(a,1),3034(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 3034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3037">
    <literal><![CDATA[
      K(x,y \ (y / x)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(12(a,1),3034(a,1,2,1))].">
      <j1 rule="para" parents="12 3034"/>
    </justification>
  </clause>

  <clause id="3038">
    <literal><![CDATA[
      K(x \ y,T(y,x) \ ((y * x) / y)) = K(x \ y,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(1426(a,2),3034(a,1,2,1))].">
      <j1 rule="para" parents="1426 3034"/>
    </justification>
  </clause>

  <clause id="3039">
    <literal><![CDATA[
      K((x / y) \ x,z \ (z / y)) = K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,723,a,b,3037,a)].">
      <j1 rule="hyper" parents="65 723 3037"/>
    </justification>
  </clause>

  <clause id="3040">
    <literal><![CDATA[
      (x \ y) * (1 / (x \ y)) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(2588,a,3036,a)].">
      <j1 rule="hyper" parents="2588 3036"/>
    </justification>
  </clause>

  <clause id="3041">
    <literal><![CDATA[
      L(x,y,K(z \ u,u \ z)) = x
    ]]></literal>
    <justification jstring="[para(3036(a,1),2589(a,1,3))].">
      <j1 rule="para" parents="3036 2589"/>
    </justification>
  </clause>

  <clause id="3042">
    <literal><![CDATA[
      (K(x \ y,y \ x) * z) * u = K(x \ y,y \ x) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(1318,a,3041,a),flip(a)].">
      <j1 rule="hyper" parents="1318 3041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3043">
    <literal><![CDATA[
      K(x \ y,T(x / y,T(y,x))) = K(x \ y,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(1530(a,1),3038(a,1,2))].">
      <j1 rule="para" parents="1530 3038"/>
    </justification>
  </clause>

  <clause id="3044">
    <literal><![CDATA[
      K(x \ y,T(x / y,T(y,x))) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(299,a,3036,a(flip),b,3043,a),flip(a)].">
      <j1 rule="hyper" parents="299 3036 3043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3046">
    <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(2585(a,2),2602(a,1,2,1,1))].">
      <j1 rule="para" parents="2585 2602"/>
    </justification>
  </clause>

  <clause id="3047">
    <literal><![CDATA[
      K(x,x \ 1) * T(K(x,x \ 1) \ y,z) = x * (T((x \ y) * x,z) / x)
    ]]></literal>
    <justification jstring="[para(1117(a,1),3046(a,2,2))].">
      <j1 rule="para" parents="1117 3046"/>
    </justification>
  </clause>

  <clause id="3048">
    <literal><![CDATA[
      K(x,x \ 1) * T(K(x,x \ 1) \ y,x) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,1605,a(flip),b,3047,a),flip(a)].">
      <j1 rule="hyper" parents="299 1605 3047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3049">
    <literal><![CDATA[
      T(x * K(y,y \ 1),y) = T(x,y) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(807,a,3048,a),flip(a)].">
      <j1 rule="hyper" parents="807 3048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3050">
    <literal><![CDATA[
      T(K(x,x \ 1) * y,x) = K(x,x \ 1) * T(y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),3048(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 3048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3051">
    <literal><![CDATA[
      T((x / y) * K(y,y \ 1),y) = (y \ x) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(109(a,1),3049(a,2,1))].">
      <j1 rule="para" parents="109 3049"/>
    </justification>
  </clause>

  <clause id="3052">
    <literal><![CDATA[
      x \ (y * K(x,x \ 1)) = (x \ y) * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(2796,a,3051,a)].">
      <j1 rule="hyper" parents="2796 3051"/>
    </justification>
  </clause>

  <clause id="3053">
    <literal><![CDATA[
      x * ((x \ y) * K(x,x \ 1)) = y * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(144,a,3052,a)].">
      <j1 rule="hyper" parents="144 3052"/>
    </justification>
  </clause>

  <clause id="3054">
    <literal><![CDATA[
      (x * y) * K(x,x \ 1) = x * (y * K(x,x \ 1))
    ]]></literal>
    <justification jstring="[para(9(a,1),3053(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 3053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3055">
    <literal><![CDATA[
      R(x,y,K(x,x \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(544,a,3054,a)].">
      <j1 rule="hyper" parents="544 3054"/>
    </justification>
  </clause>

  <clause id="3056">
    <literal><![CDATA[
      R(T(x,y),z,K(x,x \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(3055(a,1),27(a,2,1))].">
      <j1 rule="para" parents="3055 27"/>
    </justification>
  </clause>

  <clause id="3057">
    <literal><![CDATA[
      R(x,y,K(x \ 1,x)) = x
    ]]></literal>
    <justification jstring="[para(2596(a,2),3055(a,1,3))].">
      <j1 rule="para" parents="2596 3055"/>
    </justification>
  </clause>

  <clause id="3058">
    <literal><![CDATA[
      x * (y * K(x \ 1,x)) != z
    ]]></literal>
    <literal><![CDATA[
      (x * y) * K(x \ 1,x) = z
    ]]></literal>
    <justification jstring="[para(3057(a,1),275(a,1,1))].">
      <j1 rule="para" parents="3057 275"/>
    </justification>
  </clause>

  <clause id="3059">
    <literal><![CDATA[
      T(x,y * K(x,x \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2795,a(flip),b,3056,a),flip(a)].">
      <j1 rule="hyper" parents="65 2795 3056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3061">
    <literal><![CDATA[
      T(x \ 1,y * K(x \ 1,x)) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(2587(a,1),3059(a,1,2,2))].">
      <j1 rule="para" parents="2587 3059"/>
    </justification>
  </clause>

  <clause id="3062">
    <literal><![CDATA[
      L(((x * y) \ x) \ z,((x \ 1) * y) \ x,x * y) = (x \ 1) \ (((x \ 1) * y) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,2489,a(flip),b,2865,a)].">
      <j1 rule="hyper" parents="65 2489 2865"/>
    </justification>
  </clause>

  <clause id="3063">
    <literal><![CDATA[
      L(((x * y) \ x) \ z,(x * y) \ x,x * y) = (x \ 1) \ (((x \ 1) * y) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,2864,a(flip),b,3062,a)].">
      <j1 rule="hyper" parents="65 2864 3062"/>
    </justification>
  </clause>

  <clause id="3064">
    <literal><![CDATA[
      (x \ 1) \ (((x \ 1) * y) * z) = x \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[hyper(615,a,3063,a),flip(a)].">
      <j1 rule="hyper" parents="615 3063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3065">
    <literal><![CDATA[
      ((x \ 1) * y) \ (((x \ 1) * z) * u) = (x * y) \ (x * (x \ ((x * z) * u)))
    ]]></literal>
    <justification jstring="[para(3064(a,1),2507(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3064 2507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3066">
    <literal><![CDATA[
      ((x \ 1) * y) \ (((x \ 1) * z) * u) = (x * y) \ ((x * z) * u)
    ]]></literal>
    <justification jstring="[para(10(a,1),3065(a,2,2))].">
      <j1 rule="para" parents="10 3065"/>
    </justification>
  </clause>

  <clause id="3068">
    <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(299,a,1910,a(flip),b,2454,a),flip(a)].">
      <j1 rule="hyper" parents="299 1910 2454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3069">
    <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(299,a,1901,a(flip),b,2455,a),flip(a)].">
      <j1 rule="hyper" parents="299 1901 2455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3070">
    <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(1454(a,1),3068(a,2,1))].">
      <j1 rule="para" parents="1454 3068"/>
    </justification>
  </clause>

  <clause id="3071">
    <literal><![CDATA[
      K(x \ 1,x) * R(K(x,x \ 1) * (y * x),z,u) = (x \ R(x * y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(2740(a,1),3070(a,1,2,1))].">
      <j1 rule="para" parents="2740 3070"/>
    </justification>
  </clause>

  <clause id="3072">
    <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(1154(a,1),3069(a,2,1))].">
      <j1 rule="para" parents="1154 3069"/>
    </justification>
  </clause>

  <clause id="3073">
    <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(2740(a,1),3072(a,1,2,1))].">
      <j1 rule="para" parents="2740 3072"/>
    </justification>
  </clause>

  <clause id="3074">
    <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),3073(a,1,2,1,2))].">
      <j1 rule="para" parents="12 3073"/>
    </justification>
  </clause>

  <clause id="3075">
    <literal><![CDATA[
      (x * K(x,y)) * R((x * K(x,y)) \ (x * y),z,u) = (R(y,z,u) * x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,543,a(flip),b,929,a),flip(a)].">
      <j1 rule="hyper" parents="299 543 929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3076">
    <literal><![CDATA[
      x * (K(x,y) * R(K(x,y) \ y,z,u)) = (R(y,z,u) * x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(1335,a,3075,a)].">
      <j1 rule="hyper" parents="1335 3075"/>
    </justification>
  </clause>

  <clause id="3077">
    <literal><![CDATA[
      x * (K(x,y) * R(K(x,y) \ y,y \ 1,y)) = (T(y,y \ 1) * x) * K(x,y)
    ]]></literal>
    <justification jstring="[para(1484(a,1),3076(a,2,1,1))].">
      <j1 rule="para" parents="1484 3076"/>
    </justification>
  </clause>

  <clause id="3078">
    <literal><![CDATA[
      (R(x,y,z) * R(R(x,y,z) \ (x * y),u,w)) * z = R(x,y,z) * (z * R(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(22(a,2),1972(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="22 1972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3079">
    <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(234(a,1),3078(a,2,2))].">
      <j1 rule="para" parents="234 3078"/>
    </justification>
  </clause>

  <clause id="3080">
    <literal><![CDATA[
      L(L(((x * x) \ y) * z,x * x,u),u * (x * x),w) = (x * x) \ ((w * u) \ (w * (u * (y * z))))
    ]]></literal>
    <justification jstring="[hyper(299,a,744,a(flip),b,1332,a),flip(a)].">
      <j1 rule="hyper" parents="299 744 1332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3081">
    <literal><![CDATA[
      T((x * ((x \ 1) \ y)) * z,(1 / x) \ ((1 / x) \ 1)) = y * (z / ((1 / x) * (1 / x)))
    ]]></literal>
    <justification jstring="[para(9(a,1),2373(a,2,1))].">
      <j1 rule="para" parents="9 2373"/>
    </justification>
  </clause>

  <clause id="3082">
    <literal><![CDATA[
      T((x * ((x \ 1) \ y)) * z,(1 / x) \ ((1 / x) \ 1)) = y * (z / (x \ (1 / x)))
    ]]></literal>
    <justification jstring="[para(428(a,1),3081(a,2,2,2))].">
      <j1 rule="para" parents="428 3081"/>
    </justification>
  </clause>

  <clause id="3083">
    <literal><![CDATA[
      T((x * ((x \ 1) \ y)) * z,(1 / x) \ ((1 / x) \ 1)) = y * (z * ((1 / x) \ x))
    ]]></literal>
    <justification jstring="[para(1184(a,1),3082(a,2,2))].">
      <j1 rule="para" parents="1184 3082"/>
    </justification>
  </clause>

  <clause id="3084">
    <literal><![CDATA[
      T(x * ((x \ 1) \ (y * z)),(1 / x) \ ((1 / x) \ 1)) = y * (z * ((1 / x) \ x))
    ]]></literal>
    <justification jstring="[para(1174(a,1),3083(a,1,1))].">
      <j1 rule="para" parents="1174 3083"/>
    </justification>
  </clause>

  <clause id="3085">
    <literal><![CDATA[
      T(((1 / x) \ y) * z,(1 / x) \ ((1 / x) \ 1)) = (x \ y) * (z * ((1 / x) \ x))
    ]]></literal>
    <justification jstring="[para(1664(a,1),3083(a,1,1,1))].">
      <j1 rule="para" parents="1664 3083"/>
    </justification>
  </clause>

  <clause id="3086">
    <literal><![CDATA[
      T(x * ((x \ 1) \ y),(1 / x) \ ((1 / x) \ 1)) = 1 * (y * ((1 / x) \ x))
    ]]></literal>
    <justification jstring="[para(7(a,1),3084(a,1,1,2,2))].">
      <j1 rule="para" parents="7 3084"/>
    </justification>
  </clause>

  <clause id="3087">
    <literal><![CDATA[
      (x * y) * ((1 / z) \ z) = x * (y * ((1 / z) \ z))
    ]]></literal>
    <justification jstring="[hyper(118,a,3086,a(flip),b,3084,a(flip))].">
      <j1 rule="hyper" parents="118 3086 3084"/>
    </justification>
  </clause>

  <clause id="3088">
    <literal><![CDATA[
      T(x * ((x \ 1) \ y),(1 / x) \ ((1 / x) \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      y * ((1 / x) \ x) = z
    ]]></literal>
    <justification jstring="[para(3086(a,2),121(a,1)),flip(b)].">
      <j1 rule="para" parents="3086 121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3089">
    <literal><![CDATA[
      T(x * ((x \ 1) \ y),(1 / x) \ ((1 / x) \ 1)) = 1 * (y / (x \ (1 / x)))
    ]]></literal>
    <justification jstring="[para(1184(a,2),3086(a,2,2))].">
      <j1 rule="para" parents="1184 3086"/>
    </justification>
  </clause>

  <clause id="3090">
    <literal><![CDATA[
      x \ (y * ((1 / z) \ z)) = (x \ y) * ((1 / z) \ z)
    ]]></literal>
    <justification jstring="[hyper(1020,a,3087,a)].">
      <j1 rule="hyper" parents="1020 3087"/>
    </justification>
  </clause>

  <clause id="3092">
    <literal><![CDATA[
      ((x * y) * z) / (y * ((z * (u \ (1 / u))) * ((1 / u) \ u))) = R(x,y,z * (u \ (1 / u)))
    ]]></literal>
    <justification jstring="[para(3087(a,1),1463(a,1,2))].">
      <j1 rule="para" parents="3087 1463"/>
    </justification>
  </clause>

  <clause id="3093">
    <literal><![CDATA[
      T(x * ((x \ 1) \ y),(1 / x) \ ((1 / x) \ 1)) = 1 * (y / ((1 / x) * (1 / x)))
    ]]></literal>
    <justification jstring="[para(428(a,2),3089(a,2,2,2))].">
      <j1 rule="para" parents="428 3089"/>
    </justification>
  </clause>

  <clause id="3094">
    <literal><![CDATA[
      T(x * ((x \ 1) \ y),(1 / x) \ x) != z
    ]]></literal>
    <literal><![CDATA[
      y * ((1 / x) \ x) = z
    ]]></literal>
    <justification jstring="[para(79(a,1),3088(a,1,2,2))].">
      <j1 rule="para" parents="79 3088"/>
    </justification>
  </clause>

  <clause id="3096">
    <literal><![CDATA[
      T(((1 / x) \ y) * z,(1 / x) \ x) = (x \ y) * (z * ((1 / x) \ x))
    ]]></literal>
    <justification jstring="[para(79(a,1),3085(a,1,2,2))].">
      <j1 rule="para" parents="79 3085"/>
    </justification>
  </clause>

  <clause id="3097">
    <literal><![CDATA[
      T(x * ((x \ 1) \ y),(1 / x) \ ((1 / x) \ 1)) = (z \ z) * (y / ((1 / x) * (1 / x)))
    ]]></literal>
    <justification jstring="[para(68(a,2),3093(a,2,1))].">
      <j1 rule="para" parents="68 3093"/>
    </justification>
  </clause>

  <clause id="3098">
    <literal><![CDATA[
      ((1 / x) \ x) * y = x * ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(2372,a,3097,a)].">
      <j1 rule="hyper" parents="2372 3097"/>
    </justification>
  </clause>

  <clause id="3099">
    <literal><![CDATA[
      (x * ((1 / y) \ y)) * z = x * (y * ((y \ 1) \ z))
    ]]></literal>
    <justification jstring="[para(3098(a,1),1640(a,2,2))].">
      <j1 rule="para" parents="3098 1640"/>
    </justification>
  </clause>

  <clause id="3100">
    <literal><![CDATA[
      (x / y) * ((1 / y) \ y) = x / (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(37,a,2235,a(flip),b,3099,a),flip(a)].">
      <j1 rule="hyper" parents="37 2235 3099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3101">
    <literal><![CDATA[
      (x * y) / (y \ 1) = x * ((1 / y) \ y)
    ]]></literal>
    <justification jstring="[para(11(a,1),3100(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 3100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3102">
    <literal><![CDATA[
      ((x * y) * z) / (y * (z * ((u \ (1 / u)) * ((1 / u) \ u)))) = R(x,y,z * (u \ (1 / u)))
    ]]></literal>
    <justification jstring="[para(507(a,1),3092(a,1,2,2))].">
      <j1 rule="para" parents="507 3092"/>
    </justification>
  </clause>

  <clause id="3103">
    <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(1860(a,1),2424(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1860 2424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3104">
    <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),3103(a,2,1))].">
      <j1 rule="para" parents="68 3103"/>
    </justification>
  </clause>

  <clause id="3105">
    <literal><![CDATA[
      K((x * L(x \ 1,y,z)) \ x,x * L(x \ 1,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(299,a,355,a(flip),b,3104,a),flip(a)].">
      <j1 rule="hyper" parents="299 355 3104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3108">
    <literal><![CDATA[
      ((x * L(x \ 1,y,z)) \ x) * (x * L(x \ 1,y,z)) = x * 1
    ]]></literal>
    <justification jstring="[para(3105(a,1),287(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3105 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3109">
    <literal><![CDATA[
      ((x * L(x \ 1,y,z)) \ x) * (x * L(x \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(299,a,8,a(flip),b,3108,a),flip(a)].">
      <j1 rule="hyper" parents="299 8 3108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3110">
    <literal><![CDATA[
      x * (y * L(y \ 1,z,u)) != y
    ]]></literal>
    <literal><![CDATA[
      (y * L(y \ 1,z,u)) \ y = x
    ]]></literal>
    <justification jstring="[para(3109(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="3109 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3111">
    <literal><![CDATA[
      L(L(((x * x) \ y) * z,x * x,u),u * (x * x),w) = (x * x) \ L(y * z,u,w)
    ]]></literal>
    <justification jstring="[para(18(a,2),3080(a,2,2))].">
      <j1 rule="para" parents="18 3080"/>
    </justification>
  </clause>

  <clause id="3112">
    <literal><![CDATA[
      L(((x * x) \ y) * z,u * (x * x),w) = (x * x) \ L(y * z,u,w)
    ]]></literal>
    <justification jstring="[para(477(a,1),3111(a,1,1))].">
      <j1 rule="para" parents="477 3111"/>
    </justification>
  </clause>

  <clause id="3113">
    <literal><![CDATA[
      L(((x * x) \ y) * z,u,w) = (x * x) \ L(y * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,2890,a(flip),b,3112,a)].">
      <j1 rule="hyper" parents="65 2890 3112"/>
    </justification>
  </clause>

  <clause id="3116">
    <literal><![CDATA[
      a(x,y * z,(z \ 1) * (z \ u)) = (x * ((y * (1 / z)) * u)) \ ((x * (y * (1 / z))) * u)
    ]]></literal>
    <justification jstring="[para(2059(a,1),1744(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2059 1744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3117">
    <literal><![CDATA[
      a(x,y * z,(z \ 1) * (z \ u)) = a(x,y * (1 / z),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,14,a,b,3116,a),flip(a)].">
      <j1 rule="hyper" parents="299 14 3116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3118">
    <literal><![CDATA[
      a(x,y * z,z * (z \ u)) = a(x,y * (1 / z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,2369,a(flip),b,3117,a)].">
      <j1 rule="hyper" parents="65 2369 3117"/>
    </justification>
  </clause>

  <clause id="3119">
    <literal><![CDATA[
      a(x,y * (1 / z),u) = a(x,y * z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),3118(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10 3118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3120">
    <literal><![CDATA[
      ((x * y) * ((y \ 1) * (y \ (z * u)))) \ (((x * (1 / y)) * z) * u) = a(x * y,(y \ 1) * (y \ z),u)
    ]]></literal>
    <justification jstring="[para(1740(a,1),1745(a,1,1,2))].">
      <j1 rule="para" parents="1740 1745"/>
    </justification>
  </clause>

  <clause id="3121">
    <literal><![CDATA[
      K(R(x,y,z),((x \ 1) * R(x,y,z)) / R(x,y,z)) = (x \ 1) \ ((x \ R(x,y,z)) / R(x,y,z))
    ]]></literal>
    <justification jstring="[para(1931(a,1),1886(a,1,2,1))].">
      <j1 rule="para" parents="1931 1886"/>
    </justification>
  </clause>

  <clause id="3122">
    <literal><![CDATA[
      (x \ 1) \ ((x \ R(x,y,z)) / R(x,y,z)) = K(R(x,y,z),x \ 1)
    ]]></literal>
    <justification jstring="[para(11(a,1),3121(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11 3121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3124">
    <literal><![CDATA[
      (x \ 1) * K(R(x,y,z),x \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      (x \ R(x,y,z)) / R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(3122(a,1),250(a,1,2)),flip(b)].">
      <j1 rule="para" parents="3122 250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3125">
    <literal><![CDATA[
      a(x * y,(y \ 1) * (y \ z),u) = ((x * (1 / y)) * (z * u)) \ (((x * (1 / y)) * z) * u)
    ]]></literal>
    <justification jstring="[para(1729(a,1),3120(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1729 3120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3126">
    <literal><![CDATA[
      a(x * y,(y \ 1) * (y \ z),u) = a(x * (1 / y),z,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,14,a,b,3125,a),flip(a)].">
      <j1 rule="hyper" parents="299 14 3125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3127">
    <literal><![CDATA[
      a(x * y,y * (y \ z),u) = a(x * (1 / y),z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,2352,a(flip),b,3126,a)].">
      <j1 rule="hyper" parents="65 2352 3126"/>
    </justification>
  </clause>

  <clause id="3128">
    <literal><![CDATA[
      a(x * (1 / y),z,u) = a(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),3127(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 3127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3129">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ y) * (((x \ 1) \ 1) * ((x \ 1) \ 1)) = T((1 / x) \ y,(x \ 1) \ (1 / (x \ 1)))
    ]]></literal>
    <justification jstring="[para(1705(a,1),1696(a,2,2))].">
      <j1 rule="para" parents="1705 1696"/>
    </justification>
  </clause>

  <clause id="3130">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ y) * (((x \ 1) \ 1) * ((x \ 1) \ 1)) = T((1 / x) \ y,(x \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(76(a,1),3129(a,2,2,2))].">
      <j1 rule="para" parents="76 3129"/>
    </justification>
  </clause>

  <clause id="3132">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ y) * (((x \ 1) \ 1) * ((x \ 1) \ 1)) = T((1 / x) \ y,x * x)
    ]]></literal>
    <justification jstring="[para(460(a,1),3130(a,2,2))].">
      <j1 rule="para" parents="460 3130"/>
    </justification>
  </clause>

  <clause id="3133">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ y) * ((x \ 1) \ (1 / (x \ 1))) = T((1 / x) \ y,x * x)
    ]]></literal>
    <justification jstring="[para(1705(a,1),3132(a,1,2))].">
      <j1 rule="para" parents="1705 3132"/>
    </justification>
  </clause>

  <clause id="3134">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ y) * ((x \ 1) \ x) = T((1 / x) \ y,x * x)
    ]]></literal>
    <justification jstring="[para(76(a,1),3133(a,1,2,2))].">
      <j1 rule="para" parents="76 3133"/>
    </justification>
  </clause>

  <clause id="3136">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ y) * (x * x) = T((1 / x) \ y,x * x)
    ]]></literal>
    <justification jstring="[para(460(a,1),3134(a,1,2))].">
      <j1 rule="para" parents="460 3134"/>
    </justification>
  </clause>

  <clause id="3137">
    <literal><![CDATA[
      T((1 / x) \ y,x * x) = (x \ 1) \ T(y,x * x)
    ]]></literal>
    <justification jstring="[hyper(65,a,1180,a(flip),b,3136,a),flip(a)].">
      <j1 rule="hyper" parents="65 1180 3136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3138">
    <literal><![CDATA[
      (x \ (1 / x)) * (((x \ 1) * (x \ y)) * ((1 / x) \ x)) = T((1 / ((1 / x) \ x)) * y,(1 / x) \ x)
    ]]></literal>
    <justification jstring="[para(1081(a,1),1731(a,1,1))].">
      <j1 rule="para" parents="1081 1731"/>
    </justification>
  </clause>

  <clause id="3139">
    <literal><![CDATA[
      (x \ (1 / x)) * ((x \ 1) * ((x \ y) * ((1 / x) \ x))) = T((1 / ((1 / x) \ x)) * y,(1 / x) \ x)
    ]]></literal>
    <justification jstring="[para(3087(a,1),3138(a,1,2))].">
      <j1 rule="para" parents="3087 3138"/>
    </justification>
  </clause>

  <clause id="3140">
    <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(1213(a,1),2292(a,2,2,1))].">
      <j1 rule="para" parents="1213 2292"/>
    </justification>
  </clause>

  <clause id="3141">
    <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(1891(a,1),3140(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1891 3140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3142">
    <literal><![CDATA[
      R(R(x,y,z \ 1),y * (z \ 1),K(z,z \ 1)) = ((x * y) * (1 / z)) / (y * (1 / z))
    ]]></literal>
    <justification jstring="[para(2763(a,1),2779(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2763 2779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3143">
    <literal><![CDATA[
      R(R(x,y,z \ 1),y * (z \ 1),K(z,z \ 1)) = R(x,y,1 / z)
    ]]></literal>
    <justification jstring="[hyper(299,a,20,a,b,3142,a),flip(a)].">
      <j1 rule="hyper" parents="299 20 3142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3144">
    <literal><![CDATA[
      R(R(x,y,z \ 1),y * (z \ 1),K(z,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,1 / z) = u
    ]]></literal>
    <justification jstring="[para(3142(a,2),549(a,1))].">
      <j1 rule="para" parents="3142 549"/>
    </justification>
  </clause>

  <clause id="3145">
    <literal><![CDATA[
      R(R(x,y,(z \ 1) \ 1),y * T(z,z \ 1),K(z \ 1,(z \ 1) \ 1)) = R(x,y,1 / (z \ 1))
    ]]></literal>
    <justification jstring="[para(108(a,2),3143(a,1,2,2))].">
      <j1 rule="para" parents="108 3143"/>
    </justification>
  </clause>

  <clause id="3147">
    <literal><![CDATA[
      R(R(x,y,(z \ 1) \ 1),y * T(z,z \ 1),K(z \ 1,z)) = R(x,y,1 / (z \ 1))
    ]]></literal>
    <justification jstring="[para(2587(a,1),3145(a,1,3))].">
      <j1 rule="para" parents="2587 3145"/>
    </justification>
  </clause>

  <clause id="3148">
    <literal><![CDATA[
      R(R(x,y,(z \ 1) \ 1),y * T(z,z \ 1),K(z \ 1,z)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(76(a,1),3147(a,2,3))].">
      <j1 rule="para" parents="76 3147"/>
    </justification>
  </clause>

  <clause id="3150">
    <literal><![CDATA[
      (x * ((y * (z / (1 / u))) * w)) \ ((x * (y * (z / u))) * ((u * u) * w)) = a(x,y * (z / u),w)
    ]]></literal>
    <justification jstring="[hyper(299,a,2357,a(flip),b,1237,a),flip(a)].">
      <j1 rule="hyper" parents="299 2357 1237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3152">
    <literal><![CDATA[
      (x * ((y * (z / (1 / u))) * w)) \ ((x * (y * (z / (1 / u)))) * w) = a(x,y * (z / u),w)
    ]]></literal>
    <justification jstring="[para(1339(a,1),3150(a,1,2))].">
      <j1 rule="para" parents="1339 3150"/>
    </justification>
  </clause>

  <clause id="3153">
    <literal><![CDATA[
      a(x,y * (z / (1 / u)),w) = a(x,y * (z / u),w)
    ]]></literal>
    <justification jstring="[hyper(775,a,3152,a)].">
      <j1 rule="hyper" parents="775 3152"/>
    </justification>
  </clause>

  <clause id="3154">
    <literal><![CDATA[
      L(1 / x,K(x \ 1,x),y) * (y * K(x \ 1,x)) = y * ((x \ 1) * (x * T(x \ 1,y)))
    ]]></literal>
    <justification jstring="[para(3061(a,1),2875(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="3061 2875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3155">
    <literal><![CDATA[
      x * ((y \ 1) * (y * T(y \ 1,x))) = (1 / y) * (x * K(y \ 1,y))
    ]]></literal>
    <justification jstring="[para(2569(a,1),3154(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2569 3154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3157">
    <literal><![CDATA[
      x * T(((x * T(y,z)) / T(y,z)) \ (x * y),u) = ((x * T(y,z)) * T(y,u)) / T(y,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),1549(a,1,1))].">
      <j1 rule="para" parents="11 1549"/>
    </justification>
  </clause>

  <clause id="3158">
    <literal><![CDATA[
      ((x * T(y,z)) * T(y,u)) / T(y,z) = x * T(x \ (x * y),u)
    ]]></literal>
    <justification jstring="[para(11(a,1),3157(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="11 3157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3159">
    <literal><![CDATA[
      ((x * T(y,z)) * T(y,u)) / T(y,z) = x * T(y,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),3158(a,2,2,1))].">
      <j1 rule="para" parents="9 3158"/>
    </justification>
  </clause>

  <clause id="3160">
    <literal><![CDATA[
      (1 / T(x,y)) * T(x,z) = T(x,z) / T(x,y)
    ]]></literal>
    <justification jstring="[para(77(a,1),3159(a,1,1)),flip(a)].">
      <j1 rule="para" parents="77 3159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3161">
    <literal><![CDATA[
      (T(x,y) / T(x,z)) / T(x,y) = 1 / T(x,z)
    ]]></literal>
    <justification jstring="[hyper(137,a,3160,a)].">
      <j1 rule="hyper" parents="137 3160"/>
    </justification>
  </clause>

  <clause id="3162">
    <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(3161(a,1),1880(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3161 1880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3163">
    <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(1213(a,1),3162(a,1,2,1))].">
      <j1 rule="para" parents="1213 3162"/>
    </justification>
  </clause>

  <clause id="3164">
    <literal><![CDATA[
      K(T(x,y),1 / T(x,z)) = T(K(T(x,y),1 / x),z)
    ]]></literal>
    <justification jstring="[hyper(65,a,3141,a(flip),b,3163,a),flip(a)].">
      <j1 rule="hyper" parents="65 3141 3163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3165">
    <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(3164(a,1),2621(a,1))].">
      <j1 rule="para" parents="3164 2621"/>
    </justification>
  </clause>

  <clause id="3166">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) / x) \ (1 / x)) = K(T(x,y),T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(3165,a,2198,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="3165 2198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3167">
    <literal><![CDATA[
      (T(x,y) / x) \ (1 / x) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,2585,a(flip),b,3166,a),flip(a)].">
      <j1 rule="hyper" parents="36 2585 3166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3168">
    <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(262(a,1),3167(a,1,2))].">
      <j1 rule="para" parents="262 3167"/>
    </justification>
  </clause>

  <clause id="3169">
    <literal><![CDATA[
      (x \ T(x,y)) \ (x \ 1) = 1 / T(T(x,x \ 1),y)
    ]]></literal>
    <justification jstring="[para(1576(a,1),3168(a,1,1))].">
      <j1 rule="para" parents="1576 3168"/>
    </justification>
  </clause>

  <clause id="3170">
    <literal><![CDATA[
      1 / T(T(x,x \ 1),y) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,2325,a(flip),b,3169,a),flip(a)].">
      <j1 rule="hyper" parents="65 2325 3169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3171">
    <literal><![CDATA[
      T(T(x,x \ 1),y) = (T(x,y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(186,a,3170,a),flip(a)].">
      <j1 rule="hyper" parents="186 3170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3172">
    <literal><![CDATA[
      1 / T((x \ 1) \ 1,y) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[para(108(a,1),3170(a,1,2,1))].">
      <j1 rule="para" parents="108 3170"/>
    </justification>
  </clause>

  <clause id="3173">
    <literal><![CDATA[
      T(1 / (1 / x),y) \ 1 = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[para(340(a,1),3170(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="340 3170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3174">
    <literal><![CDATA[
      T((x \ 1) \ 1,y) = (T(x,y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(108(a,1),3171(a,1,1))].">
      <j1 rule="para" parents="108 3171"/>
    </justification>
  </clause>

  <clause id="3175">
    <literal><![CDATA[
      1 / T(x \ 1,y) = T(1 / x,y) \ 1
    ]]></literal>
    <justification jstring="[para(79(a,1),3172(a,1,2,1,1))].">
      <j1 rule="para" parents="79 3172"/>
    </justification>
  </clause>

  <clause id="3176">
    <literal><![CDATA[
      1 / (1 / T(x,y)) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[hyper(192,a,3173,a)].">
      <j1 rule="hyper" parents="192 3173"/>
    </justification>
  </clause>

  <clause id="3177">
    <literal><![CDATA[
      x \ 1 != 1 / T(y,z)
    ]]></literal>
    <literal><![CDATA[
      T(1 / (1 / y),z) = x
    ]]></literal>
    <justification jstring="[para(3173(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="3173 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3178">
    <literal><![CDATA[
      T((x \ 1) \ 1,y) \ 1 = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[para(1691(a,1),3173(a,1,1,1))].">
      <j1 rule="para" parents="1691 3173"/>
    </justification>
  </clause>

  <clause id="3179">
    <literal><![CDATA[
      (T(1 / x,y) \ 1) \ 1 = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(79(a,1),3174(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 3174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3180">
    <literal><![CDATA[
      x * ((T(y,x) \ 1) \ 1) = ((y \ 1) \ 1) * x
    ]]></literal>
    <justification jstring="[para(3174(a,1),107(a,1,2))].">
      <j1 rule="para" parents="3174 107"/>
    </justification>
  </clause>

  <clause id="3181">
    <literal><![CDATA[
      T(((x / y) \ 1) \ 1,y) = ((y \ x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(109(a,1),3174(a,2,1,1))].">
      <j1 rule="para" parents="109 3174"/>
    </justification>
  </clause>

  <clause id="3182">
    <literal><![CDATA[
      (T(x,y) \ 1) \ L(z,T(x,y),T(x,y)) = T((x \ 1) \ 1,y) * z
    ]]></literal>
    <justification jstring="[para(3174(a,2),1761(a,2,1))].">
      <j1 rule="para" parents="3174 1761"/>
    </justification>
  </clause>

  <clause id="3183">
    <literal><![CDATA[
      T(x,y) * K(T(x,y) \ 1,T(x,y)) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[hyper(2707,a,3176,a)].">
      <j1 rule="hyper" parents="2707 3176"/>
    </justification>
  </clause>

  <clause id="3184">
    <literal><![CDATA[
      ((x * T(1 / (1 / y),x)) / x) \ (y / T(y,x)) = 1 / T(y,x)
    ]]></literal>
    <justification jstring="[para(3176(a,1),1843(a,1,1,1,2))].">
      <j1 rule="para" parents="3176 1843"/>
    </justification>
  </clause>

  <clause id="3185">
    <literal><![CDATA[
      (x * T(1 / (1 / y),x)) \ x = 1 / (1 / ((y * x) \ x))
    ]]></literal>
    <justification jstring="[para(3176(a,1),3014(a,1,1,2))].">
      <j1 rule="para" parents="3176 3014"/>
    </justification>
  </clause>

  <clause id="3186">
    <literal><![CDATA[
      T(T(x,y),x \ 1) \ 1 = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[para(297(a,2),3178(a,1,1))].">
      <j1 rule="para" parents="297 3178"/>
    </justification>
  </clause>

  <clause id="3187">
    <literal><![CDATA[
      L(T(T(x,y),x \ 1) * z,T(T(x,y),x \ 1),T(T(x,y),x \ 1)) = ((1 / T(x,y)) \ 1) * L(z,T(T(x,y),x \ 1),T(T(x,y),x \ 1))
    ]]></literal>
    <justification jstring="[para(3186(a,1),2812(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3186 2812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3188">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(805,a,3180,a)].">
      <j1 rule="hyper" parents="805 3180"/>
    </justification>
  </clause>

  <clause id="3189">
    <literal><![CDATA[
      (((x / y) \ 1) \ 1) * y = y * (((y \ x) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(109(a,1),3180(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="109 3180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3190">
    <literal><![CDATA[
      ((R(x / y,y,z) \ 1) \ 1) * (y * z) = (y * z) * ((((y * z) \ (x * z)) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(569(a,1),3180(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="569 3180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3191">
    <literal><![CDATA[
      (T(x,y) \ 1) \ (T(x,y) \ x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(1201,a,3188,a)].">
      <j1 rule="hyper" parents="1201 3188"/>
    </justification>
  </clause>

  <clause id="3192">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) = x * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,2558,a,b,3188,a),flip(a)].">
      <j1 rule="hyper" parents="299 2558 3188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3193">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,108,a,b,3188,a),flip(a)].">
      <j1 rule="hyper" parents="299 108 3188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3194">
    <literal><![CDATA[
      T(K(x,x \ 1),y) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(2908,a,3192,a)].">
      <j1 rule="hyper" parents="2908 3192"/>
    </justification>
  </clause>

  <clause id="3195">
    <literal><![CDATA[
      T(x,K(y,y \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(56,a,3194,a)].">
      <j1 rule="hyper" parents="56 3194"/>
    </justification>
  </clause>

  <clause id="3196">
    <literal><![CDATA[
      T(x,y) \ K(x,x \ 1) = (T(x,y) \ x) / x
    ]]></literal>
    <justification jstring="[hyper(119,a,3194,a(flip),b,2607,a)].">
      <j1 rule="hyper" parents="119 3194 2607"/>
    </justification>
  </clause>

  <clause id="3197">
    <literal><![CDATA[
      K(x,x \ 1) * y = y * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(3194(a,1),107(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3194 107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3198">
    <literal><![CDATA[
      x * K(y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,y \ 1) * x = z
    ]]></literal>
    <justification jstring="[para(3194(a,1),276(a,1,2))].">
      <j1 rule="para" parents="3194 276"/>
    </justification>
  </clause>

  <clause id="3200">
    <literal><![CDATA[
      T(x,K(1 / y,y)) = x
    ]]></literal>
    <justification jstring="[para(79(a,1),3195(a,1,2,2))].">
      <j1 rule="para" parents="79 3195"/>
    </justification>
  </clause>

  <clause id="3201">
    <literal><![CDATA[
      K(x,x \ 1) * y != z
    ]]></literal>
    <literal><![CDATA[
      y * K(x,x \ 1) = z
    ]]></literal>
    <justification jstring="[para(3195(a,1),276(a,1,2))].">
      <j1 rule="para" parents="3195 276"/>
    </justification>
  </clause>

  <clause id="3202">
    <literal><![CDATA[
      T(x,K(y \ 1,y)) = x
    ]]></literal>
    <justification jstring="[para(2596(a,2),3195(a,1,2))].">
      <j1 rule="para" parents="2596 3195"/>
    </justification>
  </clause>

  <clause id="3203">
    <literal><![CDATA[
      T(x,(y \ 1) * y) = x
    ]]></literal>
    <justification jstring="[para(2612(a,1),3195(a,1,2))].">
      <j1 rule="para" parents="2612 3195"/>
    </justification>
  </clause>

  <clause id="3204">
    <literal><![CDATA[
      T(x,K(y \ z,z \ y)) = x
    ]]></literal>
    <justification jstring="[para(3036(a,1),3195(a,1,2))].">
      <j1 rule="para" parents="3036 3195"/>
    </justification>
  </clause>

  <clause id="3205">
    <literal><![CDATA[
      K(x \ 1,x) * y = y * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(2380,a,3202,a),flip(a)].">
      <j1 rule="hyper" parents="2380 3202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3206">
    <literal><![CDATA[
      ((1 / x) * y) * K(x \ 1,x) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,2825,a(flip),b,3202,a)].">
      <j1 rule="hyper" parents="65 2825 3202"/>
    </justification>
  </clause>

  <clause id="3207">
    <literal><![CDATA[
      T(K(x \ 1,x),y) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(56,a,3202,a)].">
      <j1 rule="hyper" parents="56 3202"/>
    </justification>
  </clause>

  <clause id="3208">
    <literal><![CDATA[
      K(x \ 1,x) * y != z
    ]]></literal>
    <literal><![CDATA[
      y * K(x \ 1,x) = z
    ]]></literal>
    <justification jstring="[para(3202(a,1),276(a,1,2))].">
      <j1 rule="para" parents="3202 276"/>
    </justification>
  </clause>

  <clause id="3209">
    <literal><![CDATA[
      ((x \ 1) * x) * y = y * ((x \ 1) * x)
    ]]></literal>
    <justification jstring="[hyper(2380,a,3203,a),flip(a)].">
      <j1 rule="hyper" parents="2380 3203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3210">
    <literal><![CDATA[
      K(x \ y,y \ x) * z = z * K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(2380,a,3204,a),flip(a)].">
      <j1 rule="hyper" parents="2380 3204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3211">
    <literal><![CDATA[
      x * K(y \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ 1,y) * x = z
    ]]></literal>
    <justification jstring="[para(3207(a,1),276(a,1,2))].">
      <j1 rule="para" parents="3207 276"/>
    </justification>
  </clause>

  <clause id="3212">
    <literal><![CDATA[
      L(K(x \ 1,x),y,z) = K(L(x,y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[para(3207(a,1),2445(a,1,1))].">
      <j1 rule="para" parents="3207 2445"/>
    </justification>
  </clause>

  <clause id="3213">
    <literal><![CDATA[
      (K(x \ 1,x) * y) * K(x,x \ 1) = y
    ]]></literal>
    <justification jstring="[hyper(2792,a,3197,a)].">
      <j1 rule="hyper" parents="2792 3197"/>
    </justification>
  </clause>

  <clause id="3214">
    <literal><![CDATA[
      K(x \ 1,x) * (y * K(x,x \ 1)) = y
    ]]></literal>
    <justification jstring="[hyper(2742,a,3197,a)].">
      <j1 rule="hyper" parents="2742 3197"/>
    </justification>
  </clause>

  <clause id="3215">
    <literal><![CDATA[
      (x * y) * K(x,x \ 1) = T(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(2731,a,3197,a),flip(a)].">
      <j1 rule="hyper" parents="2731 3197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3216">
    <literal><![CDATA[
      K(x,x \ 1) * (y * x) = y * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,2770,a(flip),b,3197,a),flip(a)].">
      <j1 rule="hyper" parents="299 2770 3197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3217">
    <literal><![CDATA[
      K(x,x \ 1) * (y / (1 / x)) = y / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,2766,a(flip),b,3197,a),flip(a)].">
      <j1 rule="hyper" parents="299 2766 3197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3218">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (x \ 1)) = y * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(299,a,2763,a(flip),b,3197,a),flip(a)].">
      <j1 rule="hyper" parents="299 2763 3197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3219">
    <literal><![CDATA[
      K(x,x \ 1) * (y * K(x \ 1,x)) = y
    ]]></literal>
    <justification jstring="[hyper(299,a,2762,a(flip),b,3197,a),flip(a)].">
      <j1 rule="hyper" parents="299 2762 3197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3220">
    <literal><![CDATA[
      K(x,x \ 1) * (y * x) = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,2760,a(flip),b,3197,a),flip(a)].">
      <j1 rule="hyper" parents="299 2760 3197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3221">
    <literal><![CDATA[
      R(K(x,x \ 1) * y,z,u) = R(y,z,u) * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,2977,a,b,3197,a)].">
      <j1 rule="hyper" parents="65 2977 3197"/>
    </justification>
  </clause>

  <clause id="3222">
    <literal><![CDATA[
      ((1 / x) \ y) * K(x,x \ 1) = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(65,a,2736,a(flip),b,3197,a),flip(a)].">
      <j1 rule="hyper" parents="65 2736 3197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3223">
    <literal><![CDATA[
      ((x \ 1) * y) * K(x,x \ 1) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,2727,a(flip),b,3197,a),flip(a)].">
      <j1 rule="hyper" parents="65 2727 3197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3224">
    <literal><![CDATA[
      (x * y) * K(x,x \ 1) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,2725,a(flip),b,3197,a),flip(a)].">
      <j1 rule="hyper" parents="65 2725 3197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3225">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * z = K(y,y \ 1) * (x * z)
    ]]></literal>
    <justification jstring="[para(3197(a,1),2591(a,1,1))].">
      <j1 rule="para" parents="3197 2591"/>
    </justification>
  </clause>

  <clause id="3226">
    <literal><![CDATA[
      x * (y * K(x,x \ 1)) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[para(3197(a,1),2749(a,1,2))].">
      <j1 rule="para" parents="3197 2749"/>
    </justification>
  </clause>

  <clause id="3227">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * z = x * (z * K(y,y \ 1))
    ]]></literal>
    <justification jstring="[para(3197(a,1),2609(a,2,2))].">
      <j1 rule="para" parents="3197 2609"/>
    </justification>
  </clause>

  <clause id="3228">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * x = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(3197(a,2),2756(a,1,1))].">
      <j1 rule="para" parents="3197 2756"/>
    </justification>
  </clause>

  <clause id="3229">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * x = y * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(3197(a,2),2757(a,1,1))].">
      <j1 rule="para" parents="3197 2757"/>
    </justification>
  </clause>

  <clause id="3230">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * (x \ 1) = y * (1 / x)
    ]]></literal>
    <justification jstring="[para(3197(a,2),2758(a,1,1))].">
      <j1 rule="para" parents="3197 2758"/>
    </justification>
  </clause>

  <clause id="3231">
    <literal><![CDATA[
      K(x,x \ 1) * y != z
    ]]></literal>
    <literal><![CDATA[
      z * K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(3197(a,2),2765(a,1))].">
      <j1 rule="para" parents="3197 2765"/>
    </justification>
  </clause>

  <clause id="3232">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ 1 = x \ K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(3197(a,1),2793(a,1,1))].">
      <j1 rule="para" parents="3197 2793"/>
    </justification>
  </clause>

  <clause id="3233">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ z = K(x \ 1,x) * (y \ z)
    ]]></literal>
    <justification jstring="[para(3197(a,2),2769(a,1,1))].">
      <j1 rule="para" parents="3197 2769"/>
    </justification>
  </clause>

  <clause id="3234">
    <literal><![CDATA[
      R((K(x,x \ 1) * y) / z,z,K(x \ 1,x)) = y / (z * K(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(3197(a,2),2768(a,1,1,1))].">
      <j1 rule="para" parents="3197 2768"/>
    </justification>
  </clause>

  <clause id="3235">
    <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(3197(a,1),3074(a,1,2,1))].">
      <j1 rule="para" parents="3197 3074"/>
    </justification>
  </clause>

  <clause id="3236">
    <literal><![CDATA[
      (1 / x) * K(y \ 1,y) = K(y \ 1,y) / x
    ]]></literal>
    <justification jstring="[hyper(2853,a,3205,a)].">
      <j1 rule="hyper" parents="2853 3205"/>
    </justification>
  </clause>

  <clause id="3237">
    <literal><![CDATA[
      K(x \ 1,x) * (y * x) = y * (1 / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(299,a,2915,a(flip),b,3205,a),flip(a)].">
      <j1 rule="hyper" parents="299 2915 3205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3238">
    <literal><![CDATA[
      K(x \ 1,x) * (y * T(x,x \ 1)) = y * x
    ]]></literal>
    <justification jstring="[hyper(299,a,2772,a(flip),b,3205,a),flip(a)].">
      <j1 rule="hyper" parents="299 2772 3205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3239">
    <literal><![CDATA[
      K(x \ 1,x) * (y * (1 / x)) = y * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,2677,a(flip),b,3205,a),flip(a)].">
      <j1 rule="hyper" parents="299 2677 3205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3240">
    <literal><![CDATA[
      K(x \ 1,x) * (y / x) = y / ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,2676,a(flip),b,3205,a),flip(a)].">
      <j1 rule="hyper" parents="299 2676 3205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3241">
    <literal><![CDATA[
      K(x \ 1,x) * (y / x) = y * T(y \ (y / x),x)
    ]]></literal>
    <justification jstring="[hyper(299,a,1232,a(flip),b,3205,a),flip(a)].">
      <j1 rule="hyper" parents="299 1232 3205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3243">
    <literal><![CDATA[
      (x * y) * K(x \ 1,x) = (1 / (1 / x)) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,2685,a(flip),b,3205,a),flip(a)].">
      <j1 rule="hyper" parents="65 2685 3205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3244">
    <literal><![CDATA[
      (x \ y) * K(x \ 1,x) = ((x \ 1) \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(65,a,2680,a(flip),b,3205,a),flip(a)].">
      <j1 rule="hyper" parents="65 2680 3205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3245">
    <literal><![CDATA[
      ((x \ 1) \ y) * K(x \ 1,x) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[hyper(65,a,2655,a(flip),b,3205,a),flip(a)].">
      <j1 rule="hyper" parents="65 2655 3205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3246">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * z = K(y \ 1,y) * (x * z)
    ]]></literal>
    <justification jstring="[para(3205(a,1),2495(a,1,1))].">
      <j1 rule="para" parents="3205 2495"/>
    </justification>
  </clause>

  <clause id="3247">
    <literal><![CDATA[
      (K(x \ 1,x) * y) * ((x \ 1) \ 1) = y * x
    ]]></literal>
    <justification jstring="[para(3205(a,2),2671(a,1,1))].">
      <j1 rule="para" parents="3205 2671"/>
    </justification>
  </clause>

  <clause id="3248">
    <literal><![CDATA[
      (1 / x) * (y * K(x \ 1,x)) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[para(3205(a,1),2672(a,1,2))].">
      <j1 rule="para" parents="3205 2672"/>
    </justification>
  </clause>

  <clause id="3249">
    <literal><![CDATA[
      x * K(y \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,y \ 1) * z = x
    ]]></literal>
    <justification jstring="[para(3205(a,1),2746(a,1))].">
      <j1 rule="para" parents="3205 2746"/>
    </justification>
  </clause>

  <clause id="3250">
    <literal><![CDATA[
      K(x \ 1,x) * y != z
    ]]></literal>
    <literal><![CDATA[
      z * K(x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(3205(a,2),2767(a,1))].">
      <j1 rule="para" parents="3205 2767"/>
    </justification>
  </clause>

  <clause id="3251">
    <literal><![CDATA[
      (x * K(y \ 1,y)) \ 1 = x \ K(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(3205(a,1),2791(a,1,1))].">
      <j1 rule="para" parents="3205 2791"/>
    </justification>
  </clause>

  <clause id="3252">
    <literal><![CDATA[
      a(x \ 1,x,x \ 1) = (x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(866,a,3209,a)].">
      <j1 rule="hyper" parents="866 3209"/>
    </justification>
  </clause>

  <clause id="3253">
    <literal><![CDATA[
      a(x \ 1,x,x \ 1) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,253,a,b,3252,a),flip(a)].">
      <j1 rule="hyper" parents="299 253 3252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3254">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ z = y \ (z * K(x,x \ 1))
    ]]></literal>
    <justification jstring="[para(3214(a,1),2496(a,1,2))].">
      <j1 rule="para" parents="3214 2496"/>
    </justification>
  </clause>

  <clause id="3255">
    <literal><![CDATA[
      (x * K(y \ 1,y)) \ z = x \ (K(y,y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(3219(a,1),2592(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3219 2592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3256">
    <literal><![CDATA[
      T(x,((y * x) / y) \ 1) = ((y \ (y * x)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(862,a,3181,a)].">
      <j1 rule="hyper" parents="862 3181"/>
    </justification>
  </clause>

  <clause id="3257">
    <literal><![CDATA[
      (x * (((x \ y) \ 1) \ 1)) / x = ((y / x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(267,a,3181,a)].">
      <j1 rule="hyper" parents="267 3181"/>
    </justification>
  </clause>

  <clause id="3259">
    <literal><![CDATA[
      (x / y) * (((y \ x) \ 1) \ 1) = (1 / (x / y)) \ (y \ x)
    ]]></literal>
    <justification jstring="[para(3181(a,1),1779(a,1,2))].">
      <j1 rule="para" parents="3181 1779"/>
    </justification>
  </clause>

  <clause id="3260">
    <literal><![CDATA[
      (T(x,y) \ 1) * ((x \ 1) \ 1) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(144,a,3191,a)].">
      <j1 rule="hyper" parents="144 3191"/>
    </justification>
  </clause>

  <clause id="3262">
    <literal><![CDATA[
      ((1 / x) * y) / (1 / x) = ((x \ 1) * y) / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(120,a,3206,a(flip),b,2691,a),flip(a)].">
      <j1 rule="hyper" parents="120 3206 2691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3264">
    <literal><![CDATA[
      ((x \ 1) * y) * ((x \ 1) \ 1) = ((1 / x) * y) * x
    ]]></literal>
    <justification jstring="[para(3206(a,1),2671(a,1,1))].">
      <j1 rule="para" parents="3206 2671"/>
    </justification>
  </clause>

  <clause id="3265">
    <literal><![CDATA[
      K(x \ 1,x) * (((x \ 1) * y) \ z) = ((1 / x) * y) \ z
    ]]></literal>
    <justification jstring="[para(3206(a,1),2571(a,1,2,1))].">
      <j1 rule="para" parents="3206 2571"/>
    </justification>
  </clause>

  <clause id="3267">
    <literal><![CDATA[
      (T(x,x \ 1) * y) * (x \ 1) = (x * y) * (1 / x)
    ]]></literal>
    <justification jstring="[para(3215(a,1),2758(a,1,1))].">
      <j1 rule="para" parents="3215 2758"/>
    </justification>
  </clause>

  <clause id="3268">
    <literal><![CDATA[
      (x \ 1) * (y * ((x \ 1) \ 1)) = (1 / x) * (y * x)
    ]]></literal>
    <justification jstring="[para(3216(a,1),2748(a,1,2))].">
      <j1 rule="para" parents="3216 2748"/>
    </justification>
  </clause>

  <clause id="3269">
    <literal><![CDATA[
      (1 / x) * (y / (1 / x)) = (x \ 1) * (y / (x \ 1))
    ]]></literal>
    <justification jstring="[para(3217(a,1),2748(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3217 2748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3270">
    <literal><![CDATA[
      K(1 / T(x,y),(1 / T(x,y)) \ 1) * (z / T(1 / (1 / x),y)) = z / ((1 / T(x,y)) \ 1)
    ]]></literal>
    <justification jstring="[para(3176(a,1),3217(a,1,2,2))].">
      <j1 rule="para" parents="3176 3217"/>
    </justification>
  </clause>

  <clause id="3271">
    <literal><![CDATA[
      T(K(x,x \ 1) * y,x \ 1) = (x \ 1) \ (y * (1 / x))
    ]]></literal>
    <justification jstring="[hyper(119,a,3218,a(flip),b,2723,a),flip(a)].">
      <j1 rule="hyper" parents="119 3218 2723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3273">
    <literal><![CDATA[
      (1 / x) * (y * (x \ 1)) = (x \ 1) * (y * (1 / x))
    ]]></literal>
    <justification jstring="[para(3218(a,1),2748(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3218 2748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3274">
    <literal><![CDATA[
      ((x \ 1) \ 1) * (y * (x \ 1)) = x * (y * (1 / x))
    ]]></literal>
    <justification jstring="[para(3218(a,1),2749(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3218 2749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3275">
    <literal><![CDATA[
      (x \ 1) * (y * T(x,x \ 1)) = (1 / x) * (y * x)
    ]]></literal>
    <justification jstring="[para(3220(a,1),2748(a,1,2))].">
      <j1 rule="para" parents="3220 2748"/>
    </justification>
  </clause>

  <clause id="3276">
    <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(3220(a,1),3071(a,1,2,1))].">
      <j1 rule="para" parents="3220 3071"/>
    </justification>
  </clause>

  <clause id="3277">
    <literal><![CDATA[
      (x \ y) * K(x \ 1,(x \ 1) \ 1) = ((x \ 1) \ 1) \ y
    ]]></literal>
    <justification jstring="[para(76(a,1),3222(a,1,1,1))].">
      <j1 rule="para" parents="76 3222"/>
    </justification>
  </clause>

  <clause id="3278">
    <literal><![CDATA[
      ((1 / x) \ y) * (1 / x) = ((x \ 1) \ y) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(3222(a,1),2758(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3222 2758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3279">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) * K(x,x \ 1) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,2472,a(flip),b,3223,a),flip(a)].">
      <j1 rule="hyper" parents="299 2472 3223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3280">
    <literal><![CDATA[
      K(x,x \ 1) * ((x * y) \ z) = (((x \ 1) \ 1) * y) \ z
    ]]></literal>
    <justification jstring="[para(3224(a,1),2794(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3224 2794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3281">
    <literal><![CDATA[
      (T(x,x \ 1) \ y) * T(x,x \ 1) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(2753(a,1),3228(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2753 3228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3282">
    <literal><![CDATA[
      ((1 / (1 / x)) \ y) * x = (x \ y) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2714(a,1),3229(a,1,1))].">
      <j1 rule="para" parents="2714 3229"/>
    </justification>
  </clause>

  <clause id="3283">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ y) * ((x \ 1) \ 1) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(2745(a,1),3229(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2745 3229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3284">
    <literal><![CDATA[
      (x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ (1 / (1 / x))) * y) * (1 / x)
    ]]></literal>
    <justification jstring="[para(2732(a,1),3230(a,1,1))].">
      <j1 rule="para" parents="2732 3230"/>
    </justification>
  </clause>

  <clause id="3285">
    <literal><![CDATA[
      K(x \ 1,x) * (y \ 1) = y \ K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,2769,a(flip),b,3232,a)].">
      <j1 rule="hyper" parents="65 2769 3232"/>
    </justification>
  </clause>

  <clause id="3287">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (1 / x)) = y * (x \ 1)
    ]]></literal>
    <justification jstring="[para(2596(a,1),3239(a,1,1))].">
      <j1 rule="para" parents="2596 3239"/>
    </justification>
  </clause>

  <clause id="3288">
    <literal><![CDATA[
      K(x \ 1,x) * ((y * (1 / x)) * z) = (y * (x \ 1)) * z
    ]]></literal>
    <justification jstring="[para(3239(a,1),2495(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3239 2495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3289">
    <literal><![CDATA[
      ((x \ 1) \ 1) * (y / ((x \ 1) \ 1)) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(3240(a,1),2673(a,1,2))].">
      <j1 rule="para" parents="3240 2673"/>
    </justification>
  </clause>

  <clause id="3290">
    <literal><![CDATA[
      K(K(x \ 1,x) * y,(x \ 1) \ 1) = (x * y) \ (y * x)
    ]]></literal>
    <justification jstring="[para(3247(a,1),2681(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3247 2681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3291">
    <literal><![CDATA[
      T((x \ 1) * y,K(z \ 1,z)) = (1 / x) * (y * K(x \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(299,a,3202,a,b,3248,a)].">
      <j1 rule="hyper" parents="299 3202 3248"/>
    </justification>
  </clause>

  <clause id="3292">
    <literal><![CDATA[
      ((x \ 1) \ 1) * T(T(x,y) \ 1,x) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(65,a,2186,a,b,3260,a)].">
      <j1 rule="hyper" parents="65 2186 3260"/>
    </justification>
  </clause>

  <clause id="3293">
    <literal><![CDATA[
      (x \ 1) * K(y \ 1,y) = x \ K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,3205,a(flip),b,3285,a)].">
      <j1 rule="hyper" parents="65 3205 3285"/>
    </justification>
  </clause>

  <clause id="3294">
    <literal><![CDATA[
      (1 / x) \ (y * (x \ 1)) = (x \ 1) \ (y * (1 / x))
    ]]></literal>
    <justification jstring="[hyper(119,a,3287,a(flip),b,2734,a)].">
      <j1 rule="hyper" parents="119 3287 2734"/>
    </justification>
  </clause>

  <clause id="3296">
    <literal><![CDATA[
      (1 / x) * (y * (1 / x)) = (x \ 1) * (y * (x \ 1))
    ]]></literal>
    <justification jstring="[para(3287(a,1),2748(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3287 2748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3297">
    <literal><![CDATA[
      K(x,x \ 1) / y != z
    ]]></literal>
    <literal><![CDATA[
      (1 / y) * K(x,x \ 1) = z
    ]]></literal>
    <justification jstring="[para(2593(a,1),3201(a,1))].">
      <j1 rule="para" parents="2593 3201"/>
    </justification>
  </clause>

  <clause id="3298">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ y != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) * K(x \ 1,x) = z
    ]]></literal>
    <justification jstring="[para(2680(a,1),3208(a,1))].">
      <j1 rule="para" parents="2680 3208"/>
    </justification>
  </clause>

  <clause id="3299">
    <literal><![CDATA[
      ((x * y) * z) * (((((x * y) * z) \ (y * z)) \ 1) \ 1) = ((R(x,y,z) \ 1) * R(x,y,z)) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,2984,a(flip),b,3189,a),flip(a)].">
      <j1 rule="hyper" parents="65 2984 3189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3300">
    <literal><![CDATA[
      (x * K(y \ z,z \ y)) * u = K(y \ z,z \ y) * (x * u)
    ]]></literal>
    <justification jstring="[para(3210(a,1),3042(a,1,1))].">
      <j1 rule="para" parents="3210 3042"/>
    </justification>
  </clause>

  <clause id="3301">
    <literal><![CDATA[
      K(x,x \ 1) * (y * z) = y * (K(x,x \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(2610,a,3225,a),flip(a)].">
      <j1 rule="hyper" parents="2610 3225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3303">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ (x * (z * K(y,y \ 1))) = z
    ]]></literal>
    <justification jstring="[hyper(125,a,3227,a)].">
      <j1 rule="hyper" parents="125 3227"/>
    </justification>
  </clause>

  <clause id="3304">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ z = (y \ z) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,3205,a(flip),b,3233,a),flip(a)].">
      <j1 rule="hyper" parents="299 3205 3233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3305">
    <literal><![CDATA[
      K(x \ 1,x) * (R(x \ 1,y,z) \ u) = R(1 / x,y,z) \ u
    ]]></literal>
    <justification jstring="[para(2976(a,1),3233(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2976 3233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3306">
    <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(1809(a,1),3241(a,2,2))].">
      <j1 rule="para" parents="1809 3241"/>
    </justification>
  </clause>

  <clause id="3307">
    <literal><![CDATA[
      K(x \ 1,x) * (y * z) = y * (K(x \ 1,x) * z)
    ]]></literal>
    <justification jstring="[hyper(2572,a,3246,a),flip(a)].">
      <j1 rule="hyper" parents="2572 3246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3309">
    <literal><![CDATA[
      (K(x \ 1,x) * (y * (z * u))) \ (((y * K(x \ 1,x)) * z) * u) = a(y * K(x \ 1,x),z,u)
    ]]></literal>
    <justification jstring="[para(3246(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="3246 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3310">
    <literal><![CDATA[
      (x * (y * K(z \ 1,z))) \ (x * (K(z \ 1,z) * (y * u))) = L(u,y * K(z \ 1,z),x)
    ]]></literal>
    <justification jstring="[para(3246(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="3246 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3312">
    <literal><![CDATA[
      K(x \ 1,x) * ((y / (x \ 1)) * z) = (y / (1 / x)) * z
    ]]></literal>
    <justification jstring="[para(2687(a,1),3246(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2687 3246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3313">
    <literal><![CDATA[
      (x * K(y \ 1,y)) \ (z * K(y \ 1,y)) = x \ z
    ]]></literal>
    <justification jstring="[para(3219(a,1),3255(a,2,2))].">
      <j1 rule="para" parents="3219 3255"/>
    </justification>
  </clause>

  <clause id="3314">
    <literal><![CDATA[
      T(x,((y * x) / y) \ 1) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(9(a,1),3256(a,2,1,1))].">
      <j1 rule="para" parents="9 3256"/>
    </justification>
  </clause>

  <clause id="3315">
    <literal><![CDATA[
      T(x,y / (y * x)) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,2824,a(flip),b,3314,a)].">
      <j1 rule="hyper" parents="65 2824 3314"/>
    </justification>
  </clause>

  <clause id="3317">
    <literal><![CDATA[
      T(x,y / (y * x)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,108,a,b,3315,a),flip(a)].">
      <j1 rule="hyper" parents="299 108 3315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3318">
    <literal><![CDATA[
      T(x \ y,x / y) = ((x \ y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(10(a,1),3315(a,1,2,2))].">
      <j1 rule="para" parents="10 3315"/>
    </justification>
  </clause>

  <clause id="3319">
    <literal><![CDATA[
      T(1 / (1 / x),y / (y * x)) = x
    ]]></literal>
    <justification jstring="[hyper(2547,a,3317,a(flip))].">
      <j1 rule="hyper" parents="2547 3317"/>
    </justification>
  </clause>

  <clause id="3320">
    <literal><![CDATA[
      T(1 / (1 / x),(y / x) / y) = x
    ]]></literal>
    <justification jstring="[para(12(a,1),3319(a,1,2,2))].">
      <j1 rule="para" parents="12 3319"/>
    </justification>
  </clause>

  <clause id="3321">
    <literal><![CDATA[
      (1 / (1 / x)) \ (((y / x) / y) * x) = (y / x) / y
    ]]></literal>
    <justification jstring="[para(3320(a,1),224(a,1,2,2))].">
      <j1 rule="para" parents="3320 224"/>
    </justification>
  </clause>

  <clause id="3322">
    <literal><![CDATA[
      T((x * y) \ y,x) = (((x * y) \ y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(11(a,1),3318(a,1,2))].">
      <j1 rule="para" parents="11 3318"/>
    </justification>
  </clause>

  <clause id="3323">
    <literal><![CDATA[
      T(x \ (y \ x),y) = ((x \ (y \ x)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(76(a,1),3318(a,1,2))].">
      <j1 rule="para" parents="76 3318"/>
    </justification>
  </clause>

  <clause id="3324">
    <literal><![CDATA[
      x * (((x \ (y \ x)) \ 1) \ 1) = ((y \ 1) \ 1) \ x
    ]]></literal>
    <justification jstring="[para(3323(a,1),2705(a,1,2))].">
      <j1 rule="para" parents="3323 2705"/>
    </justification>
  </clause>

  <clause id="3325">
    <literal><![CDATA[
      (x * T(x \ y,y \ x)) / x = ((y / x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(2995(a,2),3257(a,1,1,2))].">
      <j1 rule="para" parents="2995 3257"/>
    </justification>
  </clause>

  <clause id="3326">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) / (x \ 1) = L(y,x,x \ 1) / (1 / x)
    ]]></literal>
    <justification jstring="[para(2472(a,1),3262(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2472 3262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3327">
    <literal><![CDATA[
      ((1 / x) * (K(x,x \ 1) * y)) / (1 / x) = ((1 / x) * y) / (x \ 1)
    ]]></literal>
    <justification jstring="[para(2748(a,1),3262(a,2,1))].">
      <j1 rule="para" parents="2748 3262"/>
    </justification>
  </clause>

  <clause id="3328">
    <literal><![CDATA[
      (1 / x) * K(y,x \ 1) = K(y,x \ 1) / x
    ]]></literal>
    <justification jstring="[hyper(2405,a,3264,a),flip(a)].">
      <j1 rule="hyper" parents="2405 3264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3329">
    <literal><![CDATA[
      T((x \ 1) * (y / (x \ 1)),K(z \ 1,z)) = (1 / x) * (y / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(299,a,3202,a,b,3269,a)].">
      <j1 rule="hyper" parents="299 3202 3269"/>
    </justification>
  </clause>

  <clause id="3330">
    <literal><![CDATA[
      (x * x) \ T(x * y,x \ 1) = (x \ 1) * (((x \ 1) \ y) * (1 / x))
    ]]></literal>
    <justification jstring="[hyper(65,a,1138,a,b,3273,a)].">
      <j1 rule="hyper" parents="65 1138 3273"/>
    </justification>
  </clause>

  <clause id="3331">
    <literal><![CDATA[
      ((x \ 1) \ 1) * R(y,x,x) = x * ((y * x) * (1 / x))
    ]]></literal>
    <justification jstring="[para(1246(a,1),3274(a,1,2))].">
      <j1 rule="para" parents="1246 3274"/>
    </justification>
  </clause>

  <clause id="3332">
    <literal><![CDATA[
      (T(x,x \ 1) \ ((x \ 1) \ y)) * T(x,x \ 1) = ((1 / x) \ (x \ y)) * x
    ]]></literal>
    <justification jstring="[para(729(a,2),3281(a,2,1))].">
      <j1 rule="para" parents="729 3281"/>
    </justification>
  </clause>

  <clause id="3333">
    <literal><![CDATA[
      x \ T(y * x,x \ (x \ 1)) = (x \ 1) \ (y * (1 / x))
    ]]></literal>
    <justification jstring="[hyper(65,a,1242,a,b,3294,a)].">
      <j1 rule="hyper" parents="65 1242 3294"/>
    </justification>
  </clause>

  <clause id="3334">
    <literal><![CDATA[
      (x \ 1) * ((x \ 1) * T(y,x \ 1)) = (1 / x) * (y * (1 / x))
    ]]></literal>
    <justification jstring="[para(107(a,2),3296(a,2,2)),flip(a)].">
      <j1 rule="para" parents="107 3296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3335">
    <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(3301(a,2),14(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="3301 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3336">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (K(x \ 1,x) * z)) = y * z
    ]]></literal>
    <justification jstring="[para(2737(a,1),3301(a,2,2))].">
      <j1 rule="para" parents="2737 3301"/>
    </justification>
  </clause>

  <clause id="3337">
    <literal><![CDATA[
      K(x,x \ 1) * (y * ((1 / x) \ z)) = y * ((x \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(2736(a,1),3301(a,2,2))].">
      <j1 rule="para" parents="2736 3301"/>
    </justification>
  </clause>

  <clause id="3338">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (z * K(x \ 1,x))) = y * z
    ]]></literal>
    <justification jstring="[para(3219(a,1),3301(a,2,2))].">
      <j1 rule="para" parents="3219 3301"/>
    </justification>
  </clause>

  <clause id="3339">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (z / (1 / x))) = y * (z / (x \ 1))
    ]]></literal>
    <justification jstring="[para(3217(a,1),3301(a,2,2))].">
      <j1 rule="para" parents="3217 3301"/>
    </justification>
  </clause>

  <clause id="3340">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (z * (x \ 1))) = y * (z * (1 / x))
    ]]></literal>
    <justification jstring="[para(3218(a,1),3301(a,2,2))].">
      <j1 rule="para" parents="3218 3301"/>
    </justification>
  </clause>

  <clause id="3341">
    <literal><![CDATA[
      x * (a(x,y,1 / y) * K(y,y \ 1)) = (x * y) * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(2843,a,3303,a),flip(a)].">
      <j1 rule="hyper" parents="2843 3303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3342">
    <literal><![CDATA[
      x \ (K(y \ 1,y) * z) = (x \ z) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2747,a(flip),b,3304,a)].">
      <j1 rule="hyper" parents="65 2747 3304"/>
    </justification>
  </clause>

  <clause id="3343">
    <literal><![CDATA[
      (((1 / x) \ y) \ z) * K(x \ 1,x) = ((x \ 1) \ y) \ z
    ]]></literal>
    <justification jstring="[para(2736(a,1),3304(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2736 3304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3344">
    <literal><![CDATA[
      (x * (K(y,y \ 1) * z)) \ u = ((x * z) \ u) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(3301(a,1),3304(a,1,1))].">
      <j1 rule="para" parents="3301 3304"/>
    </justification>
  </clause>

  <clause id="3345">
    <literal><![CDATA[
      x * (K(y \ 1,y) * T(z,x)) = K(y \ 1,y) * (z * x)
    ]]></literal>
    <justification jstring="[para(107(a,1),3307(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 3307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3346">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ (z * (K(x \ 1,x) * y)) = L(T(z,y),y,K(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(3307(a,1),230(a,1,2))].">
      <j1 rule="para" parents="3307 230"/>
    </justification>
  </clause>

  <clause id="3347">
    <literal><![CDATA[
      K(x \ 1,x) * (y * z) = y * (z * K(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(3205(a,1),3307(a,2,2))].">
      <j1 rule="para" parents="3205 3307"/>
    </justification>
  </clause>

  <clause id="3348">
    <literal><![CDATA[
      T(x,x \ y) = ((x \ y) * K(z \ 1,z)) \ (y * K(z \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,108,a,b,3313,a)].">
      <j1 rule="hyper" parents="299 108 3313"/>
    </justification>
  </clause>

  <clause id="3349">
    <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(2081(a,2),3321(a,1,2))].">
      <j1 rule="para" parents="2081 3321"/>
    </justification>
  </clause>

  <clause id="3350">
    <literal><![CDATA[
      (x \ y) * K(x \ 1,x) = y * (((y \ (x \ y)) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,3244,a,b,3324,a)].">
      <j1 rule="hyper" parents="299 3244 3324"/>
    </justification>
  </clause>

  <clause id="3351">
    <literal><![CDATA[
      ((x \ (y \ x)) \ 1) \ 1 = x \ (((y \ 1) \ 1) \ x)
    ]]></literal>
    <justification jstring="[hyper(125,a,3324,a),flip(a)].">
      <j1 rule="hyper" parents="125 3324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3352">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ y) / y = (((x \ y) / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(120,a,3324,a(flip),b,3189,a)].">
      <j1 rule="hyper" parents="120 3324 3189"/>
    </justification>
  </clause>

  <clause id="3353">
    <literal><![CDATA[
      (((x / y) \ 1) \ 1) \ x = x * (((x \ y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(79(a,1),3324(a,1,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="79 3324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3354">
    <literal><![CDATA[
      ((x * y) * z) * (((((x * y) * z) \ (y * z)) \ 1) \ 1) = ((R(x,y,z) \ 1) \ 1) \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(182(a,1),3324(a,1,2,1,1,2))].">
      <j1 rule="para" parents="182 3324"/>
    </justification>
  </clause>

  <clause id="3355">
    <literal><![CDATA[
      T(x / y,x \ y) = ((x / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(440,a,3325,a)].">
      <j1 rule="hyper" parents="440 3325"/>
    </justification>
  </clause>

  <clause id="3356">
    <literal><![CDATA[
      T(x / y,y / x) = T(x / y,x \ y)
    ]]></literal>
    <justification jstring="[hyper(299,a,2620,a,b,3355,a)].">
      <j1 rule="hyper" parents="299 2620 3355"/>
    </justification>
  </clause>

  <clause id="3357">
    <literal><![CDATA[
      T(x / (x * y),y) = ((x / (x * y)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(9(a,1),3355(a,1,2))].">
      <j1 rule="para" parents="9 3355"/>
    </justification>
  </clause>

  <clause id="3358">
    <literal><![CDATA[
      T(x * y,x \ (1 / y)) = R(((x / (1 / y)) \ 1) \ 1,y \ 1,y)
    ]]></literal>
    <justification jstring="[para(3355(a,1),2692(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3355 2692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3359">
    <literal><![CDATA[
      (x * y) * K(z \ 1,z) = x * (y * K(z \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(3231,a,3338,a)].">
      <j1 rule="hyper" parents="3231 3338"/>
    </justification>
  </clause>

  <clause id="3360">
    <literal><![CDATA[
      1 / (x * K(y \ 1,y)) = K(y,y \ 1) / x
    ]]></literal>
    <justification jstring="[hyper(386,a,3338,a),flip(a)].">
      <j1 rule="hyper" parents="386 3338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3361">
    <literal><![CDATA[
      (x * (y * K(z \ 1,z))) \ u = (x * y) \ (K(z,z \ 1) * u)
    ]]></literal>
    <justification jstring="[para(3338(a,1),2592(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3338 2592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3362">
    <literal><![CDATA[
      (x \ ((y \ 1) \ 1)) * K(y \ 1,y) = x \ y
    ]]></literal>
    <justification jstring="[para(894(a,1),3342(a,1,2)),flip(a)].">
      <j1 rule="para" parents="894 3342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3363">
    <literal><![CDATA[
      (x \ (1 / y)) * K(y \ 1,y) = x \ (y \ 1)
    ]]></literal>
    <justification jstring="[para(2223(a,1),3342(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2223 3342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3364">
    <literal><![CDATA[
      x \ (y * K(z \ 1,z)) = (x \ y) * K(z \ 1,z)
    ]]></literal>
    <justification jstring="[para(3205(a,1),3342(a,1,2))].">
      <j1 rule="para" parents="3205 3342"/>
    </justification>
  </clause>

  <clause id="3365">
    <literal><![CDATA[
      x \ (y * (K(z \ 1,z) * u)) = (x \ (y * u)) * K(z \ 1,z)
    ]]></literal>
    <justification jstring="[para(3307(a,1),3342(a,1,2))].">
      <j1 rule="para" parents="3307 3342"/>
    </justification>
  </clause>

  <clause id="3366">
    <literal><![CDATA[
      (x \ y) * K(y,y \ 1) = x \ ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(2767,a,3362,a)].">
      <j1 rule="hyper" parents="2767 3362"/>
    </justification>
  </clause>

  <clause id="3368">
    <literal><![CDATA[
      (x \ ((y \ 1) \ 1)) * (y \ 1) = (x \ y) * (1 / y)
    ]]></literal>
    <justification jstring="[para(3362(a,1),2675(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3362 2675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3369">
    <literal><![CDATA[
      K(x,x \ 1) * (y \ (x \ 1)) = y \ (1 / x)
    ]]></literal>
    <justification jstring="[hyper(3249,a,3363,a)].">
      <j1 rule="hyper" parents="3249 3363"/>
    </justification>
  </clause>

  <clause id="3370">
    <literal><![CDATA[
      K(x \ 1,x) * (y \ (1 / x)) = y \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(3211,a,3363,a)].">
      <j1 rule="hyper" parents="3211 3363"/>
    </justification>
  </clause>

  <clause id="3371">
    <literal><![CDATA[
      (x \ y) * K(y,y \ 1) = x \ T(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,293,a,b,3366,a),flip(a)].">
      <j1 rule="hyper" parents="299 293 3366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3372">
    <literal><![CDATA[
      (x \ y) * K(y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x \ T(y,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(3366(a,2),707(a,1))].">
      <j1 rule="para" parents="3366 707"/>
    </justification>
  </clause>

  <clause id="3373">
    <literal><![CDATA[
      K(x,x \ 1) * ((y \ x) * z) = (y \ ((x \ 1) \ 1)) * z
    ]]></literal>
    <justification jstring="[para(3366(a,1),3225(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3366 3225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3374">
    <literal><![CDATA[
      (x * (1 / y)) \ (y \ 1) = (x * (y \ 1)) \ (1 / y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2797,a(flip),b,3369,a)].">
      <j1 rule="hyper" parents="65 2797 3369"/>
    </justification>
  </clause>

  <clause id="3375">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ (1 / y) = x \ (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,2769,a,b,3370,a)].">
      <j1 rule="hyper" parents="65 2769 3370"/>
    </justification>
  </clause>

  <clause id="3376">
    <literal><![CDATA[
      K(x,x \ 1) * (y \ x) = y \ T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(3198,a,3371,a)].">
      <j1 rule="hyper" parents="3198 3371"/>
    </justification>
  </clause>

  <clause id="3377">
    <literal><![CDATA[
      (x * y) \ (x * (K(z \ 1,z) * (y * u))) = L(u * K(z \ 1,z),y,x)
    ]]></literal>
    <justification jstring="[para(3347(a,2),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="3347 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3379">
    <literal><![CDATA[
      (x * (y * K(z \ 1,z))) * u = K(z \ 1,z) * ((x * y) * u)
    ]]></literal>
    <justification jstring="[para(3347(a,1),2495(a,1,1))].">
      <j1 rule="para" parents="3347 2495"/>
    </justification>
  </clause>

  <clause id="3382">
    <literal><![CDATA[
      ((((1 / x) \ y) / y) \ 1) \ 1 = ((x \ 1) \ y) / y
    ]]></literal>
    <justification jstring="[para(79(a,1),3352(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 3352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3383">
    <literal><![CDATA[
      (((x / y) \ 1) \ 1) \ x = (((y / x) \ 1) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(299,a,3189,a,b,3353,a),flip(a)].">
      <j1 rule="hyper" parents="299 3189 3353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3384">
    <literal><![CDATA[
      x / (x * (((x \ y) \ 1) \ 1)) = ((x / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(192,a,3353,a)].">
      <j1 rule="hyper" parents="192 3353"/>
    </justification>
  </clause>

  <clause id="3385">
    <literal><![CDATA[
      L(K(x \ 1,x),y,z) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(2841,a,3359,a)].">
      <j1 rule="hyper" parents="2841 3359"/>
    </justification>
  </clause>

  <clause id="3386">
    <literal><![CDATA[
      R(x,y,K(z \ 1,z)) = x
    ]]></literal>
    <justification jstring="[hyper(544,a,3359,a)].">
      <j1 rule="hyper" parents="544 3359"/>
    </justification>
  </clause>

  <clause id="3387">
    <literal><![CDATA[
      R(x,y,(z \ 1) \ 1) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,3148,a(flip),b,3386,a),flip(a)].">
      <j1 rule="hyper" parents="65 3148 3386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3388">
    <literal><![CDATA[
      (x * K(y,y \ 1)) / z = x / (z * K(y \ 1,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,2768,a(flip),b,3386,a),flip(a)].">
      <j1 rule="hyper" parents="65 2768 3386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3389">
    <literal><![CDATA[
      R(x,y,K(z \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(3386(a,1),53(a,2))].">
      <j1 rule="para" parents="3386 53"/>
    </justification>
  </clause>

  <clause id="3390">
    <literal><![CDATA[
      R(x,y,K(z,1 / z)) = x
    ]]></literal>
    <justification jstring="[para(79(a,1),3386(a,1,3,1))].">
      <j1 rule="para" parents="79 3386"/>
    </justification>
  </clause>

  <clause id="3391">
    <literal><![CDATA[
      R(x,y,K(z,z \ 1)) = x
    ]]></literal>
    <justification jstring="[para(2596(a,1),3386(a,1,3))].">
      <j1 rule="para" parents="2596 3386"/>
    </justification>
  </clause>

  <clause id="3392">
    <literal><![CDATA[
      R(x,y,K(1 / z,z)) = x
    ]]></literal>
    <justification jstring="[para(2636(a,2),3386(a,1,3))].">
      <j1 rule="para" parents="2636 3386"/>
    </justification>
  </clause>

  <clause id="3393">
    <literal><![CDATA[
      R(x,y,K(z,1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(3390(a,1),53(a,2))].">
      <j1 rule="para" parents="3390 53"/>
    </justification>
  </clause>

  <clause id="3394">
    <literal><![CDATA[
      (x * y) * K(z,1 / z) = x * (y * K(z,1 / z))
    ]]></literal>
    <justification jstring="[para(3390(a,1),103(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3390 103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3395">
    <literal><![CDATA[
      R(x,y,1 / z) = R(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(3144,a,3391,a)].">
      <j1 rule="hyper" parents="3144 3391"/>
    </justification>
  </clause>

  <clause id="3397">
    <literal><![CDATA[
      (x * y) * K(z,z \ 1) = x * (y * K(z,z \ 1))
    ]]></literal>
    <justification jstring="[para(3391(a,1),103(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3391 103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3398">
    <literal><![CDATA[
      (x \ 1) * K(y,y \ 1) = x \ K(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(3391(a,1),406(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3391 406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3399">
    <literal><![CDATA[
      x \ (y * K(z,z \ 1)) = (x \ y) * K(z,z \ 1)
    ]]></literal>
    <justification jstring="[para(3391(a,1),580(a,1,1))].">
      <j1 rule="para" parents="3391 580"/>
    </justification>
  </clause>

  <clause id="3400">
    <literal><![CDATA[
      (x * y) * K(1 / z,z) = x * (y * K(1 / z,z))
    ]]></literal>
    <justification jstring="[para(3392(a,1),103(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3392 103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3401">
    <literal><![CDATA[
      (x * y) \ ((x * (y * z)) * K(1 / u,u)) = L(z,y,x) * K(1 / u,u)
    ]]></literal>
    <justification jstring="[para(3392(a,1),584(a,1,1))].">
      <j1 rule="para" parents="3392 584"/>
    </justification>
  </clause>

  <clause id="3403">
    <literal><![CDATA[
      R(x,y,1 / (1 / z)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(191(a,1),3387(a,1,3)),flip(a)].">
      <j1 rule="para" parents="191 3387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3404">
    <literal><![CDATA[
      R(x,y,z) * (y * ((z \ 1) \ 1)) = (x * y) * ((z \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(3387(a,1),103(a,1,1))].">
      <j1 rule="para" parents="3387 103"/>
    </justification>
  </clause>

  <clause id="3405">
    <literal><![CDATA[
      R(x,y,L(z,z,z)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(2806(a,2),3387(a,1,3))].">
      <j1 rule="para" parents="2806 3387"/>
    </justification>
  </clause>

  <clause id="3407">
    <literal><![CDATA[
      R(R(x,y,z \ 1),u,K(w \ 1,w)) = R(x,y,1 / z)
    ]]></literal>
    <justification jstring="[hyper(299,a,3386,a,b,3395,a)].">
      <j1 rule="hyper" parents="299 3386 3395"/>
    </justification>
  </clause>

  <clause id="3408">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,3212,a(flip),b,3385,a)].">
      <j1 rule="hyper" parents="65 3212 3385"/>
    </justification>
  </clause>

  <clause id="3410">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ ((L(x,y,z) \ 1) * x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,1360,a,b,3408,a)].">
      <j1 rule="hyper" parents="65 1360 3408"/>
    </justification>
  </clause>

  <clause id="3411">
    <literal><![CDATA[
      (x \ K(y,y \ 1)) * y = (x \ 1) * ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(3398(a,1),2757(a,1,1))].">
      <j1 rule="para" parents="3398 2757"/>
    </justification>
  </clause>

  <clause id="3412">
    <literal><![CDATA[
      x / ((((y / x) \ 1) \ 1) * x) = ((x / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(192,a,3383,a)].">
      <j1 rule="hyper" parents="192 3383"/>
    </justification>
  </clause>

  <clause id="3413">
    <literal><![CDATA[
      x / (x * ((y \ 1) \ 1)) = ((x / (x * y)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(9(a,1),3384(a,1,2,2,1,1))].">
      <j1 rule="para" parents="9 3384"/>
    </justification>
  </clause>

  <clause id="3415">
    <literal><![CDATA[
      (x * K(y,y \ 1)) / (z * ((y \ 1) \ 1)) = x / (z * y)
    ]]></literal>
    <justification jstring="[para(2781(a,1),3388(a,2,2))].">
      <j1 rule="para" parents="2781 3388"/>
    </justification>
  </clause>

  <clause id="3416">
    <literal><![CDATA[
      L(K(x,x \ 1),y,z) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(2841,a,3397,a)].">
      <j1 rule="hyper" parents="2841 3397"/>
    </justification>
  </clause>

  <clause id="3418">
    <literal><![CDATA[
      L(K(x,x \ 1),y,z) = K(x,(u * x) \ u)
    ]]></literal>
    <justification jstring="[hyper(299,a,3034,a,b,3416,a),flip(a)].">
      <j1 rule="hyper" parents="299 3034 3416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3419">
    <literal><![CDATA[
      L(K(x,x \ 1),y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) = u
    ]]></literal>
    <justification jstring="[para(3418(a,2),3035(a,1))].">
      <j1 rule="para" parents="3418 3035"/>
    </justification>
  </clause>

  <clause id="3420">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ z = (y \ z) * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,3254,a,b,3399,a)].">
      <j1 rule="hyper" parents="65 3254 3399"/>
    </justification>
  </clause>

  <clause id="3421">
    <literal><![CDATA[
      (x \ (1 / (1 / y))) * K(y,y \ 1) = x \ y
    ]]></literal>
    <justification jstring="[para(2605(a,1),3399(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2605 3399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3422">
    <literal><![CDATA[
      x \ (K(y,y \ 1) * z) = (x \ z) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(3197(a,2),3399(a,1,2))].">
      <j1 rule="para" parents="3197 3399"/>
    </justification>
  </clause>

  <clause id="3423">
    <literal><![CDATA[
      K(x,x \ 1) * ((y \ (1 / (1 / x))) * z) = (y \ x) * z
    ]]></literal>
    <justification jstring="[para(3421(a,1),3225(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3421 3225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3424">
    <literal><![CDATA[
      (x * y) * z != x * (y * K(1 / u,u))
    ]]></literal>
    <literal><![CDATA[
      K(1 / u,u) = z
    ]]></literal>
    <justification jstring="[para(3400(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="3400 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3425">
    <literal><![CDATA[
      x / (((y \ 1) \ 1) * x) = ((x / (y * x)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(11(a,1),3412(a,1,2,1,1,1))].">
      <j1 rule="para" parents="11 3412"/>
    </justification>
  </clause>

  <clause id="3426">
    <literal><![CDATA[
      T(x / (x * y),y) = x / (x * ((y \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(299,a,3357,a,b,3413,a)].">
      <j1 rule="hyper" parents="299 3357 3413"/>
    </justification>
  </clause>

  <clause id="3427">
    <literal><![CDATA[
      x / (x * T(y,y \ 1)) = T(x / (x * y),y)
    ]]></literal>
    <justification jstring="[para(108(a,2),3426(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="108 3426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3428">
    <literal><![CDATA[
      T(x / (x * y),y) \ x = x * T(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(186,a,3427,a)].">
      <j1 rule="hyper" parents="186 3427"/>
    </justification>
  </clause>

  <clause id="3429">
    <literal><![CDATA[
      x \ (y * (K(z,z \ 1) * u)) = (x \ (y * u)) * K(z,z \ 1)
    ]]></literal>
    <justification jstring="[para(3301(a,1),3422(a,1,2))].">
      <j1 rule="para" parents="3301 3422"/>
    </justification>
  </clause>

  <clause id="3430">
    <literal><![CDATA[
      R(x \ 1,x,y) = y / (((x \ 1) \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(299,a,2945,a,b,3425,a)].">
      <j1 rule="hyper" parents="299 2945 3425"/>
    </justification>
  </clause>

  <clause id="3431">
    <literal><![CDATA[
      R(x \ 1,(x \ 1) \ 1,y) = R(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,212,a,b,3430,a)].">
      <j1 rule="hyper" parents="299 212 3430"/>
    </justification>
  </clause>

  <clause id="3432">
    <literal><![CDATA[
      R(x \ 1,x,y) \ y = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(186,a,3430,a(flip))].">
      <j1 rule="hyper" parents="186 3430"/>
    </justification>
  </clause>

  <clause id="3433">
    <literal><![CDATA[
      T(R(x \ 1,x,y),((x \ 1) \ 1) * y) = (((x \ 1) \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[para(3430(a,2),109(a,1,1))].">
      <j1 rule="para" parents="3430 109"/>
    </justification>
  </clause>

  <clause id="3434">
    <literal><![CDATA[
      x / (T(y,y \ 1) * x) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(108(a,2),3430(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="108 3430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3435">
    <literal><![CDATA[
      R(x,1 / x,y) \ y = (((1 / x) \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[para(79(a,1),3432(a,1,1,1))].">
      <j1 rule="para" parents="79 3432"/>
    </justification>
  </clause>

  <clause id="3436">
    <literal><![CDATA[
      R(x,1 / x,y) \ y = (x \ 1) * y
    ]]></literal>
    <justification jstring="[para(79(a,1),3435(a,2,1,1))].">
      <j1 rule="para" parents="79 3435"/>
    </justification>
  </clause>

  <clause id="3437">
    <literal><![CDATA[
      R(x,1 / x,y) = R(x,x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(642,a,3436,a),flip(a)].">
      <j1 rule="hyper" parents="642 3436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3438">
    <literal><![CDATA[
      L(R(x,x \ 1,y),x \ 1,x) = R(1 / (1 / x),1 / x,y)
    ]]></literal>
    <justification jstring="[para(3437(a,1),1718(a,1,1))].">
      <j1 rule="para" parents="3437 1718"/>
    </justification>
  </clause>

  <clause id="3439">
    <literal><![CDATA[
      ((x \ 1) \ 1) * R(y,x,x) = R(x * y,x,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,2381,a(flip),b,3331,a),flip(a)].">
      <j1 rule="hyper" parents="299 2381 3331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3442">
    <literal><![CDATA[
      R(x,y,1 / z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(3407(a,1),560(a,1)),flip(b)].">
      <j1 rule="para" parents="3407 560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3443">
    <literal><![CDATA[
      1 / (1 / ((x * y) \ y)) = ((1 / (1 / x)) * y) \ y
    ]]></literal>
    <justification jstring="[para(107(a,1),3185(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 3185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3444">
    <literal><![CDATA[
      (((1 / (1 / x)) * y) \ y) \ 1 = 1 / ((x * y) \ y)
    ]]></literal>
    <justification jstring="[hyper(186,a,3443,a)].">
      <j1 rule="hyper" parents="186 3443"/>
    </justification>
  </clause>

  <clause id="3445">
    <literal><![CDATA[
      1 / (((x \ 1) * y) \ y) = (((1 / x) * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(76(a,1),3444(a,1,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="76 3444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3446">
    <literal><![CDATA[
      ((((1 / x) * y) \ y) \ 1) \ 1 = ((x \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[hyper(186,a,3445,a)].">
      <j1 rule="hyper" parents="186 3445"/>
    </justification>
  </clause>

  <clause id="3447">
    <literal><![CDATA[
      ((L(x,y,y \ 1) \ (y * x)) \ 1) \ 1 = ((y \ 1) * (y * x)) \ (y * x)
    ]]></literal>
    <justification jstring="[para(2472(a,1),3446(a,1,1,1,1))].">
      <j1 rule="para" parents="2472 3446"/>
    </justification>
  </clause>

  <clause id="3448">
    <literal><![CDATA[
      ((1 / (x \ 1)) \ ((x \ 1) \ y)) * (x \ 1) = x \ ((x \ 1) \ (y * (1 / x)))
    ]]></literal>
    <justification jstring="[para(3271(a,1),3030(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3271 3030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3449">
    <literal><![CDATA[
      K(K(x \ 1,x) * y,(x \ 1) \ 1) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,16,a,b,3290,a),flip(a)].">
      <j1 rule="hyper" parents="299 16 3290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3450">
    <literal><![CDATA[
      K(((x \ 1) \ 1) \ y,(x \ 1) \ 1) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(2680(a,1),3449(a,1,1))].">
      <j1 rule="para" parents="2680 3449"/>
    </justification>
  </clause>

  <clause id="3451">
    <literal><![CDATA[
      K(K(x,x \ 1) * y,x) = K(y,(x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2738(a,1),3449(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2738 3449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3452">
    <literal><![CDATA[
      x * ((x \ 1) \ (y * (1 / x))) = T(y * x,x \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(144,a,3333,a)].">
      <j1 rule="hyper" parents="144 3333"/>
    </justification>
  </clause>

  <clause id="3453">
    <literal><![CDATA[
      K(x,x \ 1) * (((x \ 1) \ y) \ z) = ((1 / x) \ y) \ z
    ]]></literal>
    <justification jstring="[hyper(3249,a,3343,a)].">
      <j1 rule="hyper" parents="3249 3343"/>
    </justification>
  </clause>

  <clause id="3454">
    <literal><![CDATA[
      T(K(x \ 1,x) * y,z) = K(x \ 1,x) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(235,a,2495,a,b,3345,a)].">
      <j1 rule="hyper" parents="235 2495 3345"/>
    </justification>
  </clause>

  <clause id="3455">
    <literal><![CDATA[
      K(x \ 1,x) * T(K(x,x \ 1) * y,z) = T(y,z)
    ]]></literal>
    <justification jstring="[para(2738(a,1),3454(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2738 3454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3456">
    <literal><![CDATA[
      T(K(x,x \ 1) * y,z) = T(y,z) * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(3250,a,3455,a),flip(a)].">
      <j1 rule="hyper" parents="3250 3455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3458">
    <literal><![CDATA[
      x \ T(x * (y / x),z) = T(y,z) / x
    ]]></literal>
    <justification jstring="[hyper(120,a,3455,a(flip),b,2751,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="120 3455 2751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3459">
    <literal><![CDATA[
      T(x * (y / x),z) = x * (T(y,z) / x)
    ]]></literal>
    <justification jstring="[hyper(144,a,3458,a),flip(a)].">
      <j1 rule="hyper" parents="144 3458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3460">
    <literal><![CDATA[
      T(x * y,z) / y = y \ T(y * x,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),3458(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="11 3458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3461">
    <literal><![CDATA[
      (x \ y) \ T((x \ y) * x,z) = T(y,z) / (x \ y)
    ]]></literal>
    <justification jstring="[para(76(a,1),3458(a,1,2,1,2))].">
      <j1 rule="para" parents="76 3458"/>
    </justification>
  </clause>

  <clause id="3463">
    <literal><![CDATA[
      T((x \ y) * x,z) / x = x \ T(y,z)
    ]]></literal>
    <justification jstring="[para(75(a,1),3458(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 3458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3468">
    <literal><![CDATA[
      x * (T(y * x,z) / x) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),3459(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11 3459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3469">
    <literal><![CDATA[
      T(x * (y / x),y) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(106(a,1),3459(a,2,2,1))].">
      <j1 rule="para" parents="106 3459"/>
    </justification>
  </clause>

  <clause id="3470">
    <literal><![CDATA[
      (x \ y) * (T(y,z) / (x \ y)) = T((x \ y) * x,z)
    ]]></literal>
    <justification jstring="[para(76(a,1),3459(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="76 3459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3471">
    <literal><![CDATA[
      T(x * ((y / z) / x),z) = x * ((z \ y) / x)
    ]]></literal>
    <justification jstring="[para(109(a,1),3459(a,2,2,1))].">
      <j1 rule="para" parents="109 3459"/>
    </justification>
  </clause>

  <clause id="3472">
    <literal><![CDATA[
      x * (T((x \ y) * x,z) / x) = T(y,z)
    ]]></literal>
    <justification jstring="[para(75(a,1),3459(a,1,1)),flip(a)].">
      <j1 rule="para" parents="75 3459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3473">
    <literal><![CDATA[
      x \ T(x * (y / x),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) / x = u
    ]]></literal>
    <justification jstring="[para(3459(a,2),314(a,1,2))].">
      <j1 rule="para" parents="3459 314"/>
    </justification>
  </clause>

  <clause id="3474">
    <literal><![CDATA[
      x \ T(x * (y / x),z) != u * w
    ]]></literal>
    <literal><![CDATA[
      (T(y,z) / x) / w = u
    ]]></literal>
    <justification jstring="[para(3459(a,2),577(a,1,2))].">
      <j1 rule="para" parents="3459 577"/>
    </justification>
  </clause>

  <clause id="3476">
    <literal><![CDATA[
      x \ T(x * y,1 / x) = ((1 / x) \ y) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(1142,a,3460,a),flip(a)].">
      <j1 rule="hyper" parents="1142 3460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3477">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ y,z) = x \ T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(1121,a,3460,a)].">
      <j1 rule="hyper" parents="1121 3460"/>
    </justification>
  </clause>

  <clause id="3478">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ y,z) = T(y * x,z) / x
    ]]></literal>
    <justification jstring="[hyper(299,a,1012,a,b,3460,a)].">
      <j1 rule="hyper" parents="299 1012 3460"/>
    </justification>
  </clause>

  <clause id="3479">
    <literal><![CDATA[
      (x \ T(x * y,z)) * x = T(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(143,a,3460,a)].">
      <j1 rule="hyper" parents="143 3460"/>
    </justification>
  </clause>

  <clause id="3480">
    <literal><![CDATA[
      T(x \ T(x * y,z),x) = x \ T(y * x,z)
    ]]></literal>
    <justification jstring="[para(3460(a,1),109(a,1,1))].">
      <j1 rule="para" parents="3460 109"/>
    </justification>
  </clause>

  <clause id="3481">
    <literal><![CDATA[
      T(K(x,y) * (y * x),z) / (y * x) = (y * x) \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(88(a,1),3460(a,2,2,1))].">
      <j1 rule="para" parents="88 3460"/>
    </justification>
  </clause>

  <clause id="3482">
    <literal><![CDATA[
      T(x \ T(x * y,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      x \ T(y * x,z) = u
    ]]></literal>
    <justification jstring="[para(3460(a,1),400(a,1,1))].">
      <j1 rule="para" parents="3460 400"/>
    </justification>
  </clause>

  <clause id="3483">
    <literal><![CDATA[
      T((x \ y) * x,z) = (x \ T(y,z)) * x
    ]]></literal>
    <justification jstring="[hyper(143,a,3463,a),flip(a)].">
      <j1 rule="hyper" parents="143 3463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3484">
    <literal><![CDATA[
      (x \ T(y,z)) / (1 / x) = T((x \ y) / (1 / x),z)
    ]]></literal>
    <justification jstring="[hyper(120,a,3463,a(flip),b,1013,a)].">
      <j1 rule="hyper" parents="120 3463 1013"/>
    </justification>
  </clause>

  <clause id="3485">
    <literal><![CDATA[
      x \ T((x \ y) * x,z) = T(x \ T(y,z),x)
    ]]></literal>
    <justification jstring="[para(3463(a,1),109(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3463 109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3490">
    <literal><![CDATA[
      x * ((1 / x) * T((1 / x) \ y,z)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(1117(a,2),3468(a,1,2))].">
      <j1 rule="para" parents="1117 3468"/>
    </justification>
  </clause>

  <clause id="3491">
    <literal><![CDATA[
      K(x,x \ 1) * T(K(x,x \ 1) \ y,z) = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,3047,a,b,3472,a)].">
      <j1 rule="hyper" parents="65 3047 3472"/>
    </justification>
  </clause>

  <clause id="3493">
    <literal><![CDATA[
      T(x * y,z) / y != u
    ]]></literal>
    <literal><![CDATA[
      y \ T(y * x,z) = u
    ]]></literal>
    <justification jstring="[para(3479(a,1),307(a,1,1)),flip(b)].">
      <j1 rule="para" parents="3479 307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3495">
    <literal><![CDATA[
      T((x \ y) * x,z) != u * x
    ]]></literal>
    <literal><![CDATA[
      x \ T(y,z) = u
    ]]></literal>
    <justification jstring="[para(3483(a,2),46(a,1))].">
      <j1 rule="para" parents="3483 46"/>
    </justification>
  </clause>

  <clause id="3496">
    <literal><![CDATA[
      T((x \ y) * x,y) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(106(a,1),3483(a,2,1,2))].">
      <j1 rule="para" parents="106 3483"/>
    </justification>
  </clause>

  <clause id="3497">
    <literal><![CDATA[
      x * ((y \ T(z,x)) * y) = ((y \ z) * y) * x
    ]]></literal>
    <justification jstring="[para(3483(a,1),107(a,1,2))].">
      <j1 rule="para" parents="3483 107"/>
    </justification>
  </clause>

  <clause id="3498">
    <literal><![CDATA[
      T((x \ y) * x,z) \ T(y,z) = K(x,x \ T(y,z))
    ]]></literal>
    <justification jstring="[para(3483(a,2),90(a,1,1))].">
      <j1 rule="para" parents="3483 90"/>
    </justification>
  </clause>

  <clause id="3500">
    <literal><![CDATA[
      T(x,(y \ x) * y) = x
    ]]></literal>
    <justification jstring="[hyper(56,a,3496,a)].">
      <j1 rule="hyper" parents="56 3496"/>
    </justification>
  </clause>

  <clause id="3501">
    <literal><![CDATA[
      (x * ((y / z) / x)) * z = z * (x * ((z \ y) / x))
    ]]></literal>
    <justification jstring="[para(3471(a,1),107(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3471 107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3503">
    <literal><![CDATA[
      ((x \ (y / z)) * x) * z = z * ((x \ (z \ y)) * x)
    ]]></literal>
    <justification jstring="[para(109(a,1),3497(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="109 3497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3504">
    <literal><![CDATA[
      (x \ y) * ((z \ ((x \ y) \ y)) * z) = ((z \ x) * z) * (x \ y)
    ]]></literal>
    <justification jstring="[para(108(a,1),3497(a,1,2,1,2))].">
      <j1 rule="para" parents="108 3497"/>
    </justification>
  </clause>

  <clause id="3505">
    <literal><![CDATA[
      (x \ y) \ T((x \ y) * x,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) / (x \ y) = u
    ]]></literal>
    <justification jstring="[para(76(a,1),3473(a,1,2,1,2))].">
      <j1 rule="para" parents="76 3473"/>
    </justification>
  </clause>

  <clause id="3507">
    <literal><![CDATA[
      T(((x \ 1) \ 1) \ y,z) * K(x,x \ 1) = T(x \ y,z)
    ]]></literal>
    <justification jstring="[para(2745(a,1),3456(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2745 3456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3508">
    <literal><![CDATA[
      T(x * K(y,y \ 1),z) = T(x,z) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(3197(a,1),3456(a,1,1))].">
      <j1 rule="para" parents="3197 3456"/>
    </justification>
  </clause>

  <clause id="3509">
    <literal><![CDATA[
      (x \ y) \ T((x \ y) * x,x) = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(299,a,1429,a(flip),b,3461,a),flip(a)].">
      <j1 rule="hyper" parents="299 1429 3461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3510">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ 1,y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[para(8(a,1),3477(a,2,2,1))].">
      <j1 rule="para" parents="8 3477"/>
    </justification>
  </clause>

  <clause id="3512">
    <literal><![CDATA[
      ((1 / x) / y) * T(((1 / x) / y) \ z,u) = (x \ T(x * (z * y),u)) / y
    ]]></literal>
    <justification jstring="[para(3477(a,1),1465(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3477 1465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3513">
    <literal><![CDATA[
      T(x,y) / x = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,1122,a(flip),b,3510,a)].">
      <j1 rule="hyper" parents="65 1122 3510"/>
    </justification>
  </clause>

  <clause id="3514">
    <literal><![CDATA[
      (1 / x) * T(x,y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[para(79(a,1),3510(a,1,2,1))].">
      <j1 rule="para" parents="79 3510"/>
    </justification>
  </clause>

  <clause id="3515">
    <literal><![CDATA[
      x \ T(x,R(y,y \ 1,x)) = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(1849,a,3513,a),flip(a)].">
      <j1 rule="hyper" parents="1849 3513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3516">
    <literal><![CDATA[
      (x \ 1) \ T(x \ 1,y) = x * T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(1128,a,3513,a),flip(a)].">
      <j1 rule="hyper" parents="1128 3513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3517">
    <literal><![CDATA[
      (x \ T(x,y)) * x = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(143,a,3513,a)].">
      <j1 rule="hyper" parents="143 3513"/>
    </justification>
  </clause>

  <clause id="3518">
    <literal><![CDATA[
      T(x,x \ T(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(38,a,262,a,b,3513,a)].">
      <j1 rule="hyper" parents="38 262 3513"/>
    </justification>
  </clause>

  <clause id="3520">
    <literal><![CDATA[
      (x \ T(x,y)) * x != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(3513(a,1),246(a,1,1)),flip(b)].">
      <j1 rule="para" parents="3513 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3521">
    <literal><![CDATA[
      R(x \ T(x,y),x,z) = (T(x,y) * z) / (x * z)
    ]]></literal>
    <justification jstring="[para(3513(a,1),104(a,1,1))].">
      <j1 rule="para" parents="3513 104"/>
    </justification>
  </clause>

  <clause id="3522">
    <literal><![CDATA[
      R((x / y) \ T(x / y,z),x / y,y) = (T(x / y,z) * y) / x
    ]]></literal>
    <justification jstring="[para(3513(a,1),567(a,1,1))].">
      <j1 rule="para" parents="3513 567"/>
    </justification>
  </clause>

  <clause id="3525">
    <literal><![CDATA[
      (x * (y \ T(y,x))) \ (x * z) = x * ((x * (T(y,x) / y)) \ z)
    ]]></literal>
    <justification jstring="[para(3513(a,1),2415(a,1,1,2))].">
      <j1 rule="para" parents="3513 2415"/>
    </justification>
  </clause>

  <clause id="3526">
    <literal><![CDATA[
      T(x,K(y \ (y / (x \ 1)),y)) = x
    ]]></literal>
    <justification jstring="[para(1294(a,2),3518(a,1,2))].">
      <j1 rule="para" parents="1294 3518"/>
    </justification>
  </clause>

  <clause id="3527">
    <literal><![CDATA[
      T(x,R(1 / y,y,x)) = T(x,x / (x * y))
    ]]></literal>
    <justification jstring="[hyper(65,a,1840,a,b,3517,a)].">
      <j1 rule="hyper" parents="65 1840 3517"/>
    </justification>
  </clause>

  <clause id="3528">
    <literal><![CDATA[
      T(x,y) \ ((x \ T(x,y)) * (x * z)) = L(z,x,x \ T(x,y))
    ]]></literal>
    <justification jstring="[para(3517(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="3517 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3529">
    <literal><![CDATA[
      T(x,y) * L(z,x,x \ T(x,y)) = (x \ T(x,y)) * (x * z)
    ]]></literal>
    <justification jstring="[para(3517(a,1),94(a,1,1))].">
      <j1 rule="para" parents="3517 94"/>
    </justification>
  </clause>

  <clause id="3530">
    <literal><![CDATA[
      (T(x,y) * z) / (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x \ T(x,y),x,z) = u
    ]]></literal>
    <justification jstring="[para(3517(a,1),549(a,1,1,1))].">
      <j1 rule="para" parents="3517 549"/>
    </justification>
  </clause>

  <clause id="3531">
    <literal><![CDATA[
      L(x \ T(x,y),x \ 1,x) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(1722,a,3514,a)].">
      <j1 rule="hyper" parents="1722 3514"/>
    </justification>
  </clause>

  <clause id="3532">
    <literal><![CDATA[
      T(1 / x,T(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(235,a,3514,a,b,1112,a)].">
      <j1 rule="hyper" parents="235 3514 1112"/>
    </justification>
  </clause>

  <clause id="3533">
    <literal><![CDATA[
      T(x \ 1,T(x,y)) = T(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(3532(a,1),242(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3532 242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3534">
    <literal><![CDATA[
      T(x / (y * x),T(y,z)) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(3532(a,1),377(a,2,1))].">
      <j1 rule="para" parents="3532 377"/>
    </justification>
  </clause>

  <clause id="3535">
    <literal><![CDATA[
      x * T(x \ 1,T(x,y)) = K(x \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[para(3532(a,1),1295(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3532 1295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3536">
    <literal><![CDATA[
      (((x * y) / x) \ y) \ y = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(1305,a,3526,a)].">
      <j1 rule="hyper" parents="1305 3526"/>
    </justification>
  </clause>

  <clause id="3537">
    <literal><![CDATA[
      T(x \ 1,T(x,y)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(299,a,1692,a(flip),b,3533,a),flip(a)].">
      <j1 rule="hyper" parents="299 1692 3533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3538">
    <literal><![CDATA[
      T(x \ 1,T(x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      1 / x = z
    ]]></literal>
    <justification jstring="[para(3533(a,2),1704(a,1))].">
      <j1 rule="para" parents="3533 1704"/>
    </justification>
  </clause>

  <clause id="3542">
    <literal><![CDATA[
      T(L(x,y,z) \ 1,L(T(x,u),y,z)) != w
    ]]></literal>
    <literal><![CDATA[
      1 / L(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(25(a,2),3538(a,1,2))].">
      <j1 rule="para" parents="25 3538"/>
    </justification>
  </clause>

  <clause id="3543">
    <literal><![CDATA[
      x / ((y * x) / y) = ((y * x) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(192,a,3536,a)].">
      <j1 rule="hyper" parents="192 3536"/>
    </justification>
  </clause>

  <clause id="3544">
    <literal><![CDATA[
      (((x * y) / x) \ y) * ((x * y) / x) = y
    ]]></literal>
    <justification jstring="[hyper(144,a,3536,a)].">
      <j1 rule="hyper" parents="144 3536"/>
    </justification>
  </clause>

  <clause id="3545">
    <literal><![CDATA[
      (((x * y) / x) \ y) / y = 1 / ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(120,a,3543,a(flip),b,1582,a)].">
      <j1 rule="hyper" parents="120 3543 1582"/>
    </justification>
  </clause>

  <clause id="3547">
    <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(2487(a,1),3544(a,1,1,1,1))].">
      <j1 rule="para" parents="2487 3544"/>
    </justification>
  </clause>

  <clause id="3548">
    <literal><![CDATA[
      T(x,x / (y * x)) = T(x,x / (x * y))
    ]]></literal>
    <justification jstring="[para(216(a,1),3527(a,1,2))].">
      <j1 rule="para" parents="216 3527"/>
    </justification>
  </clause>

  <clause id="3550">
    <literal><![CDATA[
      L(x \ (x * K(x,y)),x \ 1,x) = x \ T(x,R(y,x,(y * x) \ x))
    ]]></literal>
    <justification jstring="[para(1889(a,1),3531(a,1,1,2))].">
      <j1 rule="para" parents="1889 3531"/>
    </justification>
  </clause>

  <clause id="3551">
    <literal><![CDATA[
      L(x * T(x \ 1,y),x \ 1,y) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(3516(a,1),824(a,2,1)),flip(a)].">
      <j1 rule="para" parents="3516 824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3553">
    <literal><![CDATA[
      K(x \ 1,T(x,y)) = x * T(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(3533(a,1),3535(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3533 3535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3554">
    <literal><![CDATA[
      K(x \ 1,T(x,y)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,342,a(flip),b,3553,a),flip(a)].">
      <j1 rule="hyper" parents="299 342 3553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3557">
    <literal><![CDATA[
      x \ ((y * x) / y) != y \ z
    ]]></literal>
    <literal><![CDATA[
      T(y,R(x,x \ 1,y)) = z
    ]]></literal>
    <justification jstring="[para(3515(a,1),49(a,1))].">
      <j1 rule="para" parents="3515 49"/>
    </justification>
  </clause>

  <clause id="3558">
    <literal><![CDATA[
      T(x,y \ ((x * y) / x)) = x
    ]]></literal>
    <justification jstring="[para(3515(a,1),3518(a,1,2))].">
      <j1 rule="para" parents="3515 3518"/>
    </justification>
  </clause>

  <clause id="3559">
    <literal><![CDATA[
      T(x,T(y,x) \ y) = x
    ]]></literal>
    <justification jstring="[para(223(a,1),3558(a,1,2,2))].">
      <j1 rule="para" parents="223 3558"/>
    </justification>
  </clause>

  <clause id="3560">
    <literal><![CDATA[
      (T(x,y) \ x) * y = y * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[para(3559(a,1),107(a,1,2))].">
      <j1 rule="para" parents="3559 107"/>
    </justification>
  </clause>

  <clause id="3561">
    <literal><![CDATA[
      (T(x,y) \ x) * y != z
    ]]></literal>
    <literal><![CDATA[
      y * (T(x,y) \ x) = z
    ]]></literal>
    <justification jstring="[para(3559(a,1),276(a,1,2))].">
      <j1 rule="para" parents="3559 276"/>
    </justification>
  </clause>

  <clause id="3562">
    <literal><![CDATA[
      T(x,R(T(y,x),T(y,x) \ 1,x)) = x * (T(y,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,1848,a,b,3560,a)].">
      <j1 rule="hyper" parents="65 1848 3560"/>
    </justification>
  </clause>

  <clause id="3563">
    <literal><![CDATA[
      x \ ((x * (T(y,x) \ y)) \ x) = ((T(y,x) \ y) * x) \ 1
    ]]></literal>
    <justification jstring="[para(3560(a,1),2014(a,1,2,1))].">
      <j1 rule="para" parents="3560 2014"/>
    </justification>
  </clause>

  <clause id="3564">
    <literal><![CDATA[
      (x * ((x * (T(y,x) \ y)) \ x)) \ (x * x) = (T(y,x) \ y) * x
    ]]></literal>
    <justification jstring="[para(3560(a,1),2129(a,1,1,2,1))].">
      <j1 rule="para" parents="3560 2129"/>
    </justification>
  </clause>

  <clause id="3565">
    <literal><![CDATA[
      K(1 / x,y) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2639,a(flip),b,3551,a)].">
      <j1 rule="hyper" parents="65 2639 3551"/>
    </justification>
  </clause>

  <clause id="3566">
    <literal><![CDATA[
      K(x \ 1,(1 / x) \ (y / x)) = (T(y,1 / x) / x) \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(65,a,1145,a(flip),b,3565,a),flip(a)].">
      <j1 rule="hyper" parents="65 1145 3565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3567">
    <literal><![CDATA[
      K((x \ 1) \ 1,y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(76(a,1),3565(a,1,1)),flip(a)].">
      <j1 rule="para" parents="76 3565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3568">
    <literal><![CDATA[
      K(T(1 / x,y) \ 1,z) = K(T(x \ 1,y) \ 1,z)
    ]]></literal>
    <justification jstring="[para(3175(a,1),3565(a,1,1))].">
      <j1 rule="para" parents="3175 3565"/>
    </justification>
  </clause>

  <clause id="3569">
    <literal><![CDATA[
      T(K(x,y),x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2852,a,b,3567,a)].">
      <j1 rule="hyper" parents="65 2852 3567"/>
    </justification>
  </clause>

  <clause id="3570">
    <literal><![CDATA[
      K(T(x \ y,y \ x),z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(2995(a,2),3567(a,1,1))].">
      <j1 rule="para" parents="2995 3567"/>
    </justification>
  </clause>

  <clause id="3571">
    <literal><![CDATA[
      K(((1 / x) * y) \ y,z) = K(((x \ 1) * y) \ y,z)
    ]]></literal>
    <justification jstring="[para(3446(a,1),3567(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3446 3567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3572">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) \ (((x * y) \ x) \ K(y,x)) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(3028,a,3569,a)].">
      <j1 rule="hyper" parents="3028 3569"/>
    </justification>
  </clause>

  <clause id="3573">
    <literal><![CDATA[
      T(x,K(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(56,a,3569,a)].">
      <j1 rule="hyper" parents="56 3569"/>
    </justification>
  </clause>

  <clause id="3574">
    <literal><![CDATA[
      R(K(x,y),z,u) * x = x * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(3569(a,1),234(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3569 234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3575">
    <literal><![CDATA[
      T(T(x,y),K(x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(3573(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3573 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3576">
    <literal><![CDATA[
      K(x,y) * x != z
    ]]></literal>
    <literal><![CDATA[
      x * K(x,y) = z
    ]]></literal>
    <justification jstring="[para(3573(a,1),276(a,1,2))].">
      <j1 rule="para" parents="3573 276"/>
    </justification>
  </clause>

  <clause id="3577">
    <literal><![CDATA[
      T(x,y) * K(x,z) = K(x,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(3573(a,1),232(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3573 232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3578">
    <literal><![CDATA[
      L(x,y,z) * K(x,u) = K(x,u) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(3573(a,1),233(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3573 233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3579">
    <literal><![CDATA[
      R(x,y,z) * K(x,u) = K(x,u) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(3573(a,1),234(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3573 234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3580">
    <literal><![CDATA[
      K(x,y) * L(x,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,u) * K(x,y) = w
    ]]></literal>
    <justification jstring="[para(3573(a,1),396(a,1,2,1))].">
      <j1 rule="para" parents="3573 396"/>
    </justification>
  </clause>

  <clause id="3581">
    <literal><![CDATA[
      T(x * (y / x),K(y,z)) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(3573(a,1),3459(a,2,2,1))].">
      <j1 rule="para" parents="3573 3459"/>
    </justification>
  </clause>

  <clause id="3583">
    <literal><![CDATA[
      K(T(x,y),K(x,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(57,a,3575,a)].">
      <j1 rule="hyper" parents="57 3575"/>
    </justification>
  </clause>

  <clause id="3584">
    <literal><![CDATA[
      T(K(x,y),T(x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(56,a,3575,a)].">
      <j1 rule="hyper" parents="56 3575"/>
    </justification>
  </clause>

  <clause id="3585">
    <literal><![CDATA[
      K(T(x,y),K(x,z)) = T((u \ w) \ w,v5) \ T(T(u,v5),u \ w)
    ]]></literal>
    <justification jstring="[hyper(299,a,716,a,b,3583,a),flip(a)].">
      <j1 rule="hyper" parents="299 716 3583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3587">
    <literal><![CDATA[
      T(T(K(x,y),z),T(x,u)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(3584(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3584 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3588">
    <literal><![CDATA[
      T(x,y) * K(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * T(x,y) = u
    ]]></literal>
    <justification jstring="[para(3584(a,1),276(a,1,2))].">
      <j1 rule="para" parents="3584 276"/>
    </justification>
  </clause>

  <clause id="3589">
    <literal><![CDATA[
      T(x,y) * K(x,z) != K(x,z) * u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(3577(a,2),45(a,1))].">
      <j1 rule="para" parents="3577 45"/>
    </justification>
  </clause>

  <clause id="3590">
    <literal><![CDATA[
      T(K(x,y),z * (x / z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(56,a,3581,a)].">
      <j1 rule="hyper" parents="56 3581"/>
    </justification>
  </clause>

  <clause id="3591">
    <literal><![CDATA[
      T(K(x * y,z),y * x) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),3590(a,1,2,2))].">
      <j1 rule="para" parents="11 3590"/>
    </justification>
  </clause>

  <clause id="3592">
    <literal><![CDATA[
      (x * y) * K(y * x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * x,z) * (x * y) = u
    ]]></literal>
    <justification jstring="[para(3591(a,1),276(a,1,2))].">
      <j1 rule="para" parents="3591 276"/>
    </justification>
  </clause>

  <clause id="3593">
    <literal><![CDATA[
      (x * y) * R(K(x * y,z),y,T(x,y)) = (K(x * y,z) * y) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(899,a,3574,a),flip(a)].">
      <j1 rule="hyper" parents="899 3574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3594">
    <literal><![CDATA[
      T(x,R(K(x,y),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(236,a,3574,a)].">
      <j1 rule="hyper" parents="236 3574"/>
    </justification>
  </clause>

  <clause id="3595">
    <literal><![CDATA[
      K(x,R(K(x,y),z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(57,a,3594,a)].">
      <j1 rule="hyper" parents="57 3594"/>
    </justification>
  </clause>

  <clause id="3596">
    <literal><![CDATA[
      R(K(x,y),z,u) * L(x,w,v5) = L(x,w,v5) * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(3594(a,1),233(a,1,2,1))].">
      <j1 rule="para" parents="3594 233"/>
    </justification>
  </clause>

  <clause id="3597">
    <literal><![CDATA[
      T(K(x,y),R(x,z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(236,a,3579,a)].">
      <j1 rule="hyper" parents="236 3579"/>
    </justification>
  </clause>

  <clause id="3598">
    <literal><![CDATA[
      T(x,R(T(y,x),T(y,x) \ 1,x)) != z
    ]]></literal>
    <literal><![CDATA[
      x * (T(y,x) \ y) = z
    ]]></literal>
    <justification jstring="[para(1848(a,2),3561(a,1))].">
      <j1 rule="para" parents="1848 3561"/>
    </justification>
  </clause>

  <clause id="3599">
    <literal><![CDATA[
      ((x * ((y * x) \ y)) \ 1) * T(((x * ((y * x) \ y)) \ 1) \ (1 / ((y * x) \ y)),z) = T(x,z) / (x * ((y * x) \ y))
    ]]></literal>
    <justification jstring="[para(2924(a,1),3478(a,2,1,1))].">
      <j1 rule="para" parents="2924 3478"/>
    </justification>
  </clause>

  <clause id="3600">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ T(x * y,z) = (x \ 1) * T((1 / x) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,3490,a(flip),b,2683,a)].">
      <j1 rule="hyper" parents="119 3490 2683"/>
    </justification>
  </clause>

  <clause id="3602">
    <literal><![CDATA[
      (x * (((y * z) / y) / x)) * y = y * (x * (z / x))
    ]]></literal>
    <justification jstring="[para(9(a,1),3501(a,2,2,2,1))].">
      <j1 rule="para" parents="9 3501"/>
    </justification>
  </clause>

  <clause id="3603">
    <literal><![CDATA[
      (x * ((y / (y * z)) / x)) * (y * z) = (y * z) * (x * (L(z \ 1,z,y) / x))
    ]]></literal>
    <justification jstring="[para(214(a,2),3501(a,2,2,2,1))].">
      <j1 rule="para" parents="214 3501"/>
    </justification>
  </clause>

  <clause id="3604">
    <literal><![CDATA[
      x * ((y \ (x \ y)) * y) = y * (x * T(x \ 1,y))
    ]]></literal>
    <justification jstring="[hyper(1641,a,3503,a),flip(a)].">
      <j1 rule="hyper" parents="1641 3503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3605">
    <literal><![CDATA[
      (x * ((y \ (x \ z)) * y)) / x = (y \ (z / x)) * y
    ]]></literal>
    <justification jstring="[hyper(137,a,3503,a)].">
      <j1 rule="hyper" parents="137 3503"/>
    </justification>
  </clause>

  <clause id="3606">
    <literal><![CDATA[
      ((x \ R(1 / y,y,z)) * x) * (y * z) = (y * z) * ((x \ ((y * z) \ z)) * x)
    ]]></literal>
    <justification jstring="[para(216(a,2),3503(a,1,1,1,2))].">
      <j1 rule="para" parents="216 3503"/>
    </justification>
  </clause>

  <clause id="3607">
    <literal><![CDATA[
      x * ((y \ (x \ y)) * y) != z
    ]]></literal>
    <literal><![CDATA[
      y * (x * T(x \ 1,y)) = z
    ]]></literal>
    <justification jstring="[para(3503(a,1),1641(a,1))].">
      <j1 rule="para" parents="3503 1641"/>
    </justification>
  </clause>

  <clause id="3608">
    <literal><![CDATA[
      T((x / y) * K(z,z \ 1),y) = (y \ x) * K(z,z \ 1)
    ]]></literal>
    <justification jstring="[para(109(a,1),3508(a,2,1))].">
      <j1 rule="para" parents="109 3508"/>
    </justification>
  </clause>

  <clause id="3609">
    <literal><![CDATA[
      T(x,y * T(y \ 1,x)) = x
    ]]></literal>
    <justification jstring="[hyper(235,a,3604,a(flip),b,1503,a)].">
      <j1 rule="hyper" parents="235 3604 1503"/>
    </justification>
  </clause>

  <clause id="3611">
    <literal><![CDATA[
      T(x,y \ T(y,x)) = x
    ]]></literal>
    <justification jstring="[para(1108(a,1),3609(a,1,2))].">
      <j1 rule="para" parents="1108 3609"/>
    </justification>
  </clause>

  <clause id="3612">
    <literal><![CDATA[
      T(x,K(y,x)) = x
    ]]></literal>
    <justification jstring="[para(1377(a,2),3609(a,1,2))].">
      <j1 rule="para" parents="1377 3609"/>
    </justification>
  </clause>

  <clause id="3613">
    <literal><![CDATA[
      T(x,K(y,R(x,z,u))) = x
    ]]></literal>
    <justification jstring="[hyper(152,a,3612,a)].">
      <j1 rule="hyper" parents="152 3612"/>
    </justification>
  </clause>

  <clause id="3614">
    <literal><![CDATA[
      T(x,K(y,L(x,z,u))) = x
    ]]></literal>
    <justification jstring="[hyper(150,a,3612,a)].">
      <j1 rule="hyper" parents="150 3612"/>
    </justification>
  </clause>

  <clause id="3615">
    <literal><![CDATA[
      T(x,K(y,T(x,z))) = x
    ]]></literal>
    <justification jstring="[hyper(148,a,3612,a)].">
      <j1 rule="hyper" parents="148 3612"/>
    </justification>
  </clause>

  <clause id="3616">
    <literal><![CDATA[
      T(K(x,y),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(56,a,3612,a)].">
      <j1 rule="hyper" parents="56 3612"/>
    </justification>
  </clause>

  <clause id="3617">
    <literal><![CDATA[
      T(T(x,y),K(z,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(3612(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3612 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3618">
    <literal><![CDATA[
      K(x,y) * y = y * K(x,y)
    ]]></literal>
    <justification jstring="[para(3612(a,1),107(a,1,2))].">
      <j1 rule="para" parents="3612 107"/>
    </justification>
  </clause>

  <clause id="3619">
    <literal><![CDATA[
      (x * K(y,x)) / x = K(y,x)
    ]]></literal>
    <justification jstring="[para(3612(a,1),185(a,1,2))].">
      <j1 rule="para" parents="3612 185"/>
    </justification>
  </clause>

  <clause id="3621">
    <literal><![CDATA[
      T(x,y) * K(z,x) = K(z,x) * T(x,y)
    ]]></literal>
    <justification jstring="[para(3612(a,1),232(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3612 232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3622">
    <literal><![CDATA[
      L(x,y,z) * K(u,x) = K(u,x) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(3612(a,1),233(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3612 233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3623">
    <literal><![CDATA[
      R(x,y,z) * K(u,x) = K(u,x) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(3612(a,1),234(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3612 234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3624">
    <literal><![CDATA[
      K(x,y) * T(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(3612(a,1),395(a,1,2,1))].">
      <j1 rule="para" parents="3612 395"/>
    </justification>
  </clause>

  <clause id="3626">
    <literal><![CDATA[
      T(T(x,y),z) * K(u,x) = K(u,x) * T(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(3612(a,1),430(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="3612 430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3627">
    <literal><![CDATA[
      R(T(x,y),z,u) * K(w,x) = K(w,x) * R(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(3612(a,1),690(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="3612 690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3628">
    <literal><![CDATA[
      T(x,x \ ((y * x) / y)) = x
    ]]></literal>
    <justification jstring="[para(1537(a,1),3612(a,1,2))].">
      <j1 rule="para" parents="1537 3612"/>
    </justification>
  </clause>

  <clause id="3629">
    <literal><![CDATA[
      (x \ T(x,y)) * y = y * (x \ T(x,y))
    ]]></literal>
    <justification jstring="[para(3611(a,1),107(a,1,2))].">
      <j1 rule="para" parents="3611 107"/>
    </justification>
  </clause>

  <clause id="3630">
    <literal><![CDATA[
      T(x,y) * (z \ T(z,x)) = (z \ T(z,x)) * T(x,y)
    ]]></literal>
    <justification jstring="[para(3611(a,1),232(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3611 232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3631">
    <literal><![CDATA[
      (x \ T(x,y)) * T(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) * (x \ T(x,y)) = u
    ]]></literal>
    <justification jstring="[para(3611(a,1),395(a,1,2,1))].">
      <j1 rule="para" parents="3611 395"/>
    </justification>
  </clause>

  <clause id="3632">
    <literal><![CDATA[
      K(x,T(y,z)) * y = y * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(3615(a,1),107(a,1,2))].">
      <j1 rule="para" parents="3615 107"/>
    </justification>
  </clause>

  <clause id="3633">
    <literal><![CDATA[
      T(x / y,K(z,y \ x)) = x / y
    ]]></literal>
    <justification jstring="[para(109(a,1),3615(a,1,2,2))].">
      <j1 rule="para" parents="109 3615"/>
    </justification>
  </clause>

  <clause id="3634">
    <literal><![CDATA[
      (x * y) * T(K(y,x),x) = y * x
    ]]></literal>
    <justification jstring="[para(3616(a,2),88(a,1,2))].">
      <j1 rule="para" parents="3616 88"/>
    </justification>
  </clause>

  <clause id="3636">
    <literal><![CDATA[
      L(K(x,y),z,u) * y = y * L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(3616(a,1),233(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3616 233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3637">
    <literal><![CDATA[
      T(T(x,y),K(z,R(x,u,w))) = T(x,y)
    ]]></literal>
    <justification jstring="[para(3613(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3613 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3638">
    <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(3617(a,1),395(a,1,2,1))].">
      <j1 rule="para" parents="3617 395"/>
    </justification>
  </clause>

  <clause id="3639">
    <literal><![CDATA[
      (x * K(y,x)) * L(z,x,K(y,x)) = K(y,x) * (x * z)
    ]]></literal>
    <justification jstring="[para(3618(a,1),94(a,1,1))].">
      <j1 rule="para" parents="3618 94"/>
    </justification>
  </clause>

  <clause id="3640">
    <literal><![CDATA[
      (((x / y) * K(z,x / y)) * y) / x = R(K(z,x / y),x / y,y)
    ]]></literal>
    <justification jstring="[para(3618(a,1),105(a,1,1,1))].">
      <j1 rule="para" parents="3618 105"/>
    </justification>
  </clause>

  <clause id="3641">
    <literal><![CDATA[
      L(K(x,y),y,1 / y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2411,a,b,3619,a)].">
      <j1 rule="hyper" parents="65 2411 3619"/>
    </justification>
  </clause>

  <clause id="3642">
    <literal><![CDATA[
      L((T(x,y) * (x \ y)) / y,y,x) = K(T(x,y),y)
    ]]></literal>
    <justification jstring="[hyper(65,a,1328,a,b,3619,a)].">
      <j1 rule="hyper" parents="65 1328 3619"/>
    </justification>
  </clause>

  <clause id="3644">
    <literal><![CDATA[
      R(K(x,y),y,(y * K(x,y)) \ z) \ z = y * ((y * K(x,y)) \ z)
    ]]></literal>
    <justification jstring="[para(3619(a,1),533(a,1,1,1))].">
      <j1 rule="para" parents="3619 533"/>
    </justification>
  </clause>

  <clause id="3645">
    <literal><![CDATA[
      ((x * y) / x) / y = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[para(3628(a,1),262(a,1,2))].">
      <j1 rule="para" parents="3628 262"/>
    </justification>
  </clause>

  <clause id="3646">
    <literal><![CDATA[
      (1 / x) * (x * K(y,x)) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(394,a,3641,a)].">
      <j1 rule="hyper" parents="394 3641"/>
    </justification>
  </clause>

  <clause id="3647">
    <literal><![CDATA[
      K(x,y) / (y * K(x,y)) = 1 / y
    ]]></literal>
    <justification jstring="[hyper(120,a,3641,a(flip),b,255,a)].">
      <j1 rule="hyper" parents="120 3641 255"/>
    </justification>
  </clause>

  <clause id="3648">
    <literal><![CDATA[
      (1 / x) \ K(y,x) = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,3641,a(flip),b,255,a)].">
      <j1 rule="hyper" parents="119 3641 255"/>
    </justification>
  </clause>

  <clause id="3649">
    <literal><![CDATA[
      L(x,T(x,y) \ x,x) = x
    ]]></literal>
    <justification jstring="[hyper(2342,a,3634,a)].">
      <j1 rule="hyper" parents="2342 3634"/>
    </justification>
  </clause>

  <clause id="3650">
    <literal><![CDATA[
      (T(x,y) \ x) * T(x,y) = x
    ]]></literal>
    <justification jstring="[hyper(65,a,2341,a(flip),b,3649,a)].">
      <j1 rule="hyper" parents="65 2341 3649"/>
    </justification>
  </clause>

  <clause id="3651">
    <literal><![CDATA[
      x / T(x,y) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(120,a,3649,a(flip),b,2341,a(flip))].">
      <j1 rule="hyper" parents="120 3649 2341"/>
    </justification>
  </clause>

  <clause id="3652">
    <literal><![CDATA[
      (T(x,y) \ x) \ x = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,3649,a(flip),b,2341,a(flip))].">
      <j1 rule="hyper" parents="119 3649 2341"/>
    </justification>
  </clause>

  <clause id="3655">
    <literal><![CDATA[
      x \ (x / T(x,y)) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(119,a,3651,a,b,1193,a)].">
      <j1 rule="hyper" parents="119 3651 1193"/>
    </justification>
  </clause>

  <clause id="3656">
    <literal><![CDATA[
      K(x \ (x / ((y \ x) / T(x,y))),x) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(65,a,2039,a,b,3651,a)].">
      <j1 rule="hyper" parents="65 2039 3651"/>
    </justification>
  </clause>

  <clause id="3657">
    <literal><![CDATA[
      (1 / T(x,y)) * x = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(65,a,1546,a,b,3651,a)].">
      <j1 rule="hyper" parents="65 1546 3651"/>
    </justification>
  </clause>

  <clause id="3658">
    <literal><![CDATA[
      (T(x,y) \ x) / x = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(120,a,3651,a(flip),b,1546,a)].">
      <j1 rule="hyper" parents="120 3651 1546"/>
    </justification>
  </clause>

  <clause id="3659">
    <literal><![CDATA[
      L(K(x,y),y \ 1,y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(1707,a,3646,a)].">
      <j1 rule="hyper" parents="1707 3646"/>
    </justification>
  </clause>

  <clause id="3660">
    <literal><![CDATA[
      (x \ 1) * K(y,x) = x \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,3646,a(flip),b,1677,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 3646 1677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3661">
    <literal><![CDATA[
      (x \ 1) * K(y,x \ 1) = x \ K(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,3646,a(flip),b,181,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 3646 181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3662">
    <literal><![CDATA[
      K(x,y) = L((y * x) \ (x * y),y \ 1,y)
    ]]></literal>
    <justification jstring="[para(16(a,1),3659(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16 3659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3664">
    <literal><![CDATA[
      T(x,y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      x / T(x,y) = z
    ]]></literal>
    <justification jstring="[para(3657(a,1),1551(a,1))].">
      <j1 rule="para" parents="3657 1551"/>
    </justification>
  </clause>

  <clause id="3665">
    <literal><![CDATA[
      T(x,y) \ K(x,x \ 1) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,3196,a,b,3658,a)].">
      <j1 rule="hyper" parents="65 3196 3658"/>
    </justification>
  </clause>

  <clause id="3666">
    <literal><![CDATA[
      x * (((y * x) / y) / x) = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(144,a,3645,a(flip))].">
      <j1 rule="hyper" parents="144 3645"/>
    </justification>
  </clause>

  <clause id="3667">
    <literal><![CDATA[
      x * (T(x,y) \ (1 / x)) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(2601,a,3665,a)].">
      <j1 rule="hyper" parents="2601 3665"/>
    </justification>
  </clause>

  <clause id="3669">
    <literal><![CDATA[
      L((x * y) \ (y * x),x \ 1,x) = (x * y) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(65,a,16,a(flip),b,3662,a),flip(a)].">
      <j1 rule="hyper" parents="65 16 3662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3670">
    <literal><![CDATA[
      T(K(x,y),L(y,z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(236,a,3622,a)].">
      <j1 rule="hyper" parents="236 3622"/>
    </justification>
  </clause>

  <clause id="3671">
    <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(3623(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="3623 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3672">
    <literal><![CDATA[
      T(x,L(K(y,x),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(236,a,3636,a)].">
      <j1 rule="hyper" parents="236 3636"/>
    </justification>
  </clause>

  <clause id="3673">
    <literal><![CDATA[
      (x \ R(x,y,z)) / R(x,y,z) = x \ K(R(x,y,z),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(3124,a,3661,a)].">
      <j1 rule="hyper" parents="3124 3661"/>
    </justification>
  </clause>

  <clause id="3674">
    <literal><![CDATA[
      (x * ((y \ z) * y)) / x = (y \ ((x * z) / x)) * y
    ]]></literal>
    <justification jstring="[para(9(a,1),3605(a,1,1,2,1,2))].">
      <j1 rule="para" parents="9 3605"/>
    </justification>
  </clause>

  <clause id="3675">
    <literal><![CDATA[
      ((x \ (y / z)) * x) * z != u
    ]]></literal>
    <literal><![CDATA[
      z * ((x \ (z \ y)) * x) = u
    ]]></literal>
    <justification jstring="[para(3605(a,1),246(a,1,1)),flip(b)].">
      <j1 rule="para" parents="3605 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3676">
    <literal><![CDATA[
      T(x \ T(x,y),T(y,z)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(236,a,3630,a)].">
      <j1 rule="hyper" parents="236 3630"/>
    </justification>
  </clause>

  <clause id="3677">
    <literal><![CDATA[
      T(x \ 1,T(x,y) \ x) = x \ 1
    ]]></literal>
    <justification jstring="[para(3656(a,1),2315(a,1,2))].">
      <j1 rule="para" parents="3656 2315"/>
    </justification>
  </clause>

  <clause id="3678">
    <literal><![CDATA[
      R(K(x \ (x / ((y \ x) / T(x,y))),x),x \ 1,x) = ((1 / x) * (T(x,y) \ x)) * x
    ]]></literal>
    <justification jstring="[para(3656(a,1),2697(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3656 2697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3679">
    <literal><![CDATA[
      T(T(x,y) \ x,x \ 1) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(56,a,3677,a)].">
      <j1 rule="hyper" parents="56 3677"/>
    </justification>
  </clause>

  <clause id="3681">
    <literal><![CDATA[
      L(T(x,y) \ x,T(x,y),y) = L((x * y) \ (y * x),x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,525,a,b,3669,a)].">
      <j1 rule="hyper" parents="299 525 3669"/>
    </justification>
  </clause>

  <clause id="3682">
    <literal><![CDATA[
      K(((x \ y) \ y) \ 1,(x \ y) \ y) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(36,a,2999,a,b,3350,a)].">
      <j1 rule="hyper" parents="36 2999 3350"/>
    </justification>
  </clause>

  <clause id="3683">
    <literal><![CDATA[
      (x \ 1) * ((y \ ((x \ 1) \ 1)) * z) = (1 / x) * ((y \ x) * z)
    ]]></literal>
    <justification jstring="[para(3373(a,1),2748(a,1,2))].">
      <j1 rule="para" parents="3373 2748"/>
    </justification>
  </clause>

  <clause id="3684">
    <literal><![CDATA[
      L((x \ ((y \ 1) \ 1)) * z,y \ 1,y) = y * ((1 / y) * ((x \ y) * z))
    ]]></literal>
    <justification jstring="[para(3373(a,1),2754(a,1,1))].">
      <j1 rule="para" parents="3373 2754"/>
    </justification>
  </clause>

  <clause id="3686">
    <literal><![CDATA[
      (L(x,y,z) \ x) * K(x \ 1,x) = (L(x,y,z) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(144,a,3410,a)].">
      <j1 rule="hyper" parents="144 3410"/>
    </justification>
  </clause>

  <clause id="3687">
    <literal><![CDATA[
      (1 / (1 / x)) / (y * x) = x / (y * ((x \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(2605(a,1),3415(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2605 3415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3688">
    <literal><![CDATA[
      x * K(y \ (1 / (1 / x)),y) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,2732,a(flip),b,3423,a)].">
      <j1 rule="hyper" parents="65 2732 3423"/>
    </justification>
  </clause>

  <clause id="3689">
    <literal><![CDATA[
      ((1 / x) \ y) \ (x * (((x \ 1) \ 1) \ (z * (1 / (x \ 1))))) = (x \ y) \ T(z * (x \ 1),(x \ 1) \ ((x \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(3452(a,1),1757(a,2,2))].">
      <j1 rule="para" parents="3452 1757"/>
    </justification>
  </clause>

  <clause id="3690">
    <literal><![CDATA[
      T(1 / x,y) * K(x,x \ 1) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(1689(a,1),3507(a,1,1,1))].">
      <j1 rule="para" parents="1689 3507"/>
    </justification>
  </clause>

  <clause id="3691">
    <literal><![CDATA[
      T(1 / x,y) * K(x \ 1,x) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(2596(a,2),3690(a,1,2))].">
      <j1 rule="para" parents="2596 3690"/>
    </justification>
  </clause>

  <clause id="3692">
    <literal><![CDATA[
      K(x,x \ 1) * (T(1 / x,y) \ z) = T(x \ 1,y) \ z
    ]]></literal>
    <justification jstring="[para(3690(a,1),2794(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3690 2794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3693">
    <literal><![CDATA[
      K(x,x \ 1) * T(x \ 1,y) = T(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(3249,a,3691,a)].">
      <j1 rule="hyper" parents="3249 3691"/>
    </justification>
  </clause>

  <clause id="3694">
    <literal><![CDATA[
      (T(x \ 1,y) \ z) * K(x \ 1,x) = T(1 / x,y) \ z
    ]]></literal>
    <justification jstring="[para(3693(a,1),3304(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3693 3304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3695">
    <literal><![CDATA[
      x \ ((x * (T(y,x) \ y)) \ x) = (x * (T(y,x) \ y)) \ 1
    ]]></literal>
    <justification jstring="[para(3560(a,1),3563(a,2,1))].">
      <j1 rule="para" parents="3560 3563"/>
    </justification>
  </clause>

  <clause id="3696">
    <literal><![CDATA[
      T((x / y) * K(z,z \ 1),y) != u * K(z,z \ 1)
    ]]></literal>
    <literal><![CDATA[
      y \ x = u
    ]]></literal>
    <justification jstring="[para(3608(a,2),46(a,1))].">
      <j1 rule="para" parents="3608 46"/>
    </justification>
  </clause>

  <clause id="3697">
    <literal><![CDATA[
      (R(T(x,y),z,u) * K(w,x)) * v5 = (K(w,x) * R(T(x,y),z,u)) * v5
    ]]></literal>
    <justification jstring="[hyper(59,a,3627,a)].">
      <j1 rule="hyper" parents="59 3627"/>
    </justification>
  </clause>

  <clause id="3698">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * T(x,x \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(2783,a,3686,a)].">
      <j1 rule="hyper" parents="2783 3686"/>
    </justification>
  </clause>

  <clause id="3699">
    <literal><![CDATA[
      ((L(x,y,z) \ 1) * x) * (1 / x) = (L(x,y,z) \ x) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(3686(a,1),2675(a,1,1))].">
      <j1 rule="para" parents="3686 2675"/>
    </justification>
  </clause>

  <clause id="3700">
    <literal><![CDATA[
      T(1 / x,y) \ ((x \ 1) \ 1) = T(x \ 1,y) \ x
    ]]></literal>
    <justification jstring="[hyper(65,a,3362,a(flip),b,3694,a),flip(a)].">
      <j1 rule="hyper" parents="65 3362 3694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3701">
    <literal><![CDATA[
      (x * y) * ((z \ 1) \ 1) != u * (y * ((z \ 1) \ 1))
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(3404(a,1),46(a,1))].">
      <j1 rule="para" parents="3404 46"/>
    </justification>
  </clause>

  <clause id="3702">
    <literal><![CDATA[
      R(1 / (1 / x),1 / x,y) = R(1 / (1 / x),x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,1718,a(flip),b,3438,a),flip(a)].">
      <j1 rule="hyper" parents="65 1718 3438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3703">
    <literal><![CDATA[
      R(1 / (1 / x),x \ 1,(1 / x) \ y) = ((1 / x) \ y) / y
    ]]></literal>
    <justification jstring="[hyper(1034,a,3702,a),flip(a)].">
      <j1 rule="hyper" parents="1034 3702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3705">
    <literal><![CDATA[
      L(x * y,x \ T(x,z),x) = x * L(y,x,x \ T(x,z))
    ]]></literal>
    <justification jstring="[para(3528(a,1),1207(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3528 1207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3706">
    <literal><![CDATA[
      x * L(x \ y,x,x \ T(x,z)) = L(y,x \ T(x,z),x)
    ]]></literal>
    <justification jstring="[para(10(a,1),3705(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 3705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3707">
    <literal><![CDATA[
      T(x * L(x \ ((y * z) / y),x,x \ T(x,y)),y) = (x \ T(x,y)) * (x * (T(x,y) \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,2390,a,b,3529,a)].">
      <j1 rule="hyper" parents="65 2390 3529"/>
    </justification>
  </clause>

  <clause id="3708">
    <literal><![CDATA[
      x * ((x \ R(x,y,z)) / R(x,y,z)) = K(R(x,y,z),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(144,a,3673,a(flip))].">
      <j1 rule="hyper" parents="144 3673"/>
    </justification>
  </clause>

  <clause id="3709">
    <literal><![CDATA[
      ((1 / x) \ y) \ (y * R(1 / (1 / x),x \ 1,(1 / x) \ y)) = K(y,((1 / x) \ y) / y)
    ]]></literal>
    <justification jstring="[para(3703(a,2),91(a,1,2,2))].">
      <j1 rule="para" parents="3703 91"/>
    </justification>
  </clause>

  <clause id="3710">
    <literal><![CDATA[
      T(R(x,y,z),R(x,y,z) / (R(x,y,z) * x)) = K(R(x,y,z),x \ 1) / (R(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(3708(a,1),1841(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3708 1841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3711">
    <literal><![CDATA[
      (1 / (1 / x)) \ (x / T(x,y)) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[para(223(a,1),3184(a,1,1))].">
      <j1 rule="para" parents="223 3184"/>
    </justification>
  </clause>

  <clause id="3713">
    <literal><![CDATA[
      K(x \ 1,x) * (1 / T(x,y)) = x \ (x / T(x,y))
    ]]></literal>
    <justification jstring="[para(3711(a,1),2684(a,1,2))].">
      <j1 rule="para" parents="3711 2684"/>
    </justification>
  </clause>

  <clause id="3714">
    <literal><![CDATA[
      K(x \ 1,x) * (1 / T(x,y)) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(299,a,3655,a(flip),b,3713,a),flip(a)].">
      <j1 rule="hyper" parents="299 3655 3713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3715">
    <literal><![CDATA[
      (1 / T(x,y)) * K(x \ 1,x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(3208,a,3714,a)].">
      <j1 rule="hyper" parents="3208 3714"/>
    </justification>
  </clause>

  <clause id="3716">
    <literal><![CDATA[
      K(T(x,y) \ 1,T(x,y)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(2227,a,3714,a)].">
      <j1 rule="hyper" parents="2227 3714"/>
    </justification>
  </clause>

  <clause id="3717">
    <literal><![CDATA[
      K(x \ 1,x) * (y * T(x,z)) = y * (1 / (1 / T(x,z)))
    ]]></literal>
    <justification jstring="[para(3716(a,1),3237(a,1,1))].">
      <j1 rule="para" parents="3716 3237"/>
    </justification>
  </clause>

  <clause id="3718">
    <literal><![CDATA[
      T(x,y) * K(x \ 1,x) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(3716(a,1),3183(a,1,2))].">
      <j1 rule="para" parents="3716 3183"/>
    </justification>
  </clause>

  <clause id="3719">
    <literal><![CDATA[
      x * ((1 / T(x,y)) * K(x \ 1,x)) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[para(3715(a,2),1193(a,1,2))].">
      <j1 rule="para" parents="3715 1193"/>
    </justification>
  </clause>

  <clause id="3720">
    <literal><![CDATA[
      K(x \ 1,x) * (T(1 / (1 / x),y) \ z) = T(x,y) \ z
    ]]></literal>
    <justification jstring="[para(3718(a,1),2571(a,1,2,1))].">
      <j1 rule="para" parents="3718 2571"/>
    </justification>
  </clause>

  <clause id="3721">
    <literal><![CDATA[
      K(x \ 1,x) * (y * T(x,z)) = y * T(1 / (1 / x),z)
    ]]></literal>
    <justification jstring="[para(3718(a,1),3347(a,2,2))].">
      <j1 rule="para" parents="3718 3347"/>
    </justification>
  </clause>

  <clause id="3723">
    <literal><![CDATA[
      (x * (1 / T(x,y))) * K(x \ 1,x) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(3058,a,3719,a)].">
      <j1 rule="hyper" parents="3058 3719"/>
    </justification>
  </clause>

  <clause id="3724">
    <literal><![CDATA[
      T(x,y) \ ((x \ 1) \ 1) = x * (1 / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(37,a,3362,a,b,3723,a)].">
      <j1 rule="hyper" parents="37 3362 3723"/>
    </justification>
  </clause>

  <clause id="3725">
    <literal><![CDATA[
      (x \ 1) * (x * (1 / T(x,y))) = (1 / x) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[para(3723(a,1),3248(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3723 3248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3726">
    <literal><![CDATA[
      K(x \ 1,x) * (y * T((x \ z) \ z,u)) = y * (1 / (1 / T((x \ z) \ z,u)))
    ]]></literal>
    <justification jstring="[para(3682(a,1),3717(a,1,1))].">
      <j1 rule="para" parents="3682 3717"/>
    </justification>
  </clause>

  <clause id="3727">
    <literal><![CDATA[
      ((x \ 1) \ 1) * (T(x,y) \ z) = x * (T(1 / (1 / x),y) \ z)
    ]]></literal>
    <justification jstring="[para(3720(a,1),2673(a,1,2))].">
      <j1 rule="para" parents="3720 2673"/>
    </justification>
  </clause>

  <clause id="3728">
    <literal><![CDATA[
      K(x \ 1,x) * (y * ((x \ z) \ z)) = y * T(1 / (1 / x),x \ z)
    ]]></literal>
    <justification jstring="[para(108(a,1),3721(a,1,2,2))].">
      <j1 rule="para" parents="108 3721"/>
    </justification>
  </clause>

  <clause id="3729">
    <literal><![CDATA[
      L((1 / T(x,y)) * x,x \ 1,x) = ((1 / x) * (T(x,y) \ x)) * x
    ]]></literal>
    <justification jstring="[para(3725(a,1),2052(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3725 2052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3730">
    <literal><![CDATA[
      T((x \ 1) * y,K(z \ 1,z)) = y * ((x \ 1) * (x * T(x \ 1,y)))
    ]]></literal>
    <justification jstring="[hyper(299,a,3155,a,b,3291,a),flip(a)].">
      <j1 rule="hyper" parents="299 3155 3291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3731">
    <literal><![CDATA[
      (x * K(y \ z,z \ y)) * (x \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ z,z \ y) = u
    ]]></literal>
    <justification jstring="[para(3300(a,2),203(a,1)),flip(b)].">
      <j1 rule="para" parents="3300 203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3732">
    <literal><![CDATA[
      (1 / x) * T(y,x \ 1) = y * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(2839,a,3334,a)].">
      <j1 rule="hyper" parents="2839 3334"/>
    </justification>
  </clause>

  <clause id="3733">
    <literal><![CDATA[
      T(x,1 / y) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(384,a,3732,a),flip(a)].">
      <j1 rule="hyper" parents="384 3732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3734">
    <literal><![CDATA[
      T(x / (1 / y),y \ 1) = (1 / y) \ x
    ]]></literal>
    <justification jstring="[hyper(119,a,12,a(flip),b,3732,a),flip(a)].">
      <j1 rule="hyper" parents="119 12 3732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3735">
    <literal><![CDATA[
      (x \ (y * (x \ 1))) * x = T(y,x) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(65,a,1183,a(flip),b,3732,a)].">
      <j1 rule="hyper" parents="65 1183 3732"/>
    </justification>
  </clause>

  <clause id="3736">
    <literal><![CDATA[
      K(1 / x,y) * (1 / x) = (1 / x) * K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(2847(a,1),3732(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2847 3732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3738">
    <literal><![CDATA[
      T(((1 / x) * y) * x,x \ 1) = R(y,1 / x,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,874,a(flip),b,3733,a),flip(a)].">
      <j1 rule="hyper" parents="65 874 3733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3739">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[para(76(a,1),3733(a,1,2)),flip(a)].">
      <j1 rule="para" parents="76 3733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3740">
    <literal><![CDATA[
      T(x,1 / (1 / y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(79(a,1),3733(a,2,2))].">
      <j1 rule="para" parents="79 3733"/>
    </justification>
  </clause>

  <clause id="3741">
    <literal><![CDATA[
      T(x,T(y \ 1,y)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(1692(a,2),3733(a,1,2))].">
      <j1 rule="para" parents="1692 3733"/>
    </justification>
  </clause>

  <clause id="3742">
    <literal><![CDATA[
      ((x \ 1) \ 1) * T(y,x) = y * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(3739(a,1),107(a,1,2))].">
      <j1 rule="para" parents="3739 107"/>
    </justification>
  </clause>

  <clause id="3743">
    <literal><![CDATA[
      T(x,T(y,y \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(108(a,2),3739(a,1,2))].">
      <j1 rule="para" parents="108 3739"/>
    </justification>
  </clause>

  <clause id="3744">
    <literal><![CDATA[
      T(x,T(y \ (z \ y),z)) = T(x,y \ (z \ y))
    ]]></literal>
    <justification jstring="[para(3323(a,2),3739(a,1,2))].">
      <j1 rule="para" parents="3323 3739"/>
    </justification>
  </clause>

  <clause id="3748">
    <literal><![CDATA[
      T(x,x \ 1) * T(y,x) = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(3743(a,1),107(a,1,2))].">
      <j1 rule="para" parents="3743 107"/>
    </justification>
  </clause>

  <clause id="3749">
    <literal><![CDATA[
      ((x \ 1) \ 1) * T(y,x) = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(3743(a,1),712(a,1,2))].">
      <j1 rule="para" parents="3743 712"/>
    </justification>
  </clause>

  <clause id="3750">
    <literal><![CDATA[
      T(x * (y * y),y \ 1) = (1 / y) \ (x * y)
    ]]></literal>
    <justification jstring="[para(672(a,1),3734(a,1,1))].">
      <j1 rule="para" parents="672 3734"/>
    </justification>
  </clause>

  <clause id="3751">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ R(y,x,x) = T(y * (x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(119,a,1994,a(flip),b,3742,a)].">
      <j1 rule="hyper" parents="119 1994 3742"/>
    </justification>
  </clause>

  <clause id="3752">
    <literal><![CDATA[
      x * (x * ((x \ 1) * T(y,x))) = L(y * ((x \ 1) \ 1),x,x)
    ]]></literal>
    <justification jstring="[para(3742(a,1),1702(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3742 1702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3753">
    <literal><![CDATA[
      (T(x,x \ 1) \ 1) \ R(y,T(x,x \ 1),T(x,x \ 1) \ 1) = T(((x \ 1) \ 1) * T(y,x),T(x,x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(3749(a,2),592(a,2,1))].">
      <j1 rule="para" parents="3749 592"/>
    </justification>
  </clause>

  <clause id="3754">
    <literal><![CDATA[
      (x * x) \ ((1 / x) \ (y * x)) = x \ ((y * (x * x)) * (x \ 1))
    ]]></literal>
    <justification jstring="[para(3750(a,1),726(a,1,2))].">
      <j1 rule="para" parents="3750 726"/>
    </justification>
  </clause>

  <clause id="3755">
    <literal><![CDATA[
      T((K(x,x \ 1) * y) * x,x \ 1) = R((x \ 1) \ y,1 / x,x)
    ]]></literal>
    <justification jstring="[para(2734(a,1),3738(a,1,1,1))].">
      <j1 rule="para" parents="2734 3738"/>
    </justification>
  </clause>

  <clause id="3756">
    <literal><![CDATA[
      (x \ 1) \ T(y * (x \ 1),x) = x \ T(y * x,x \ 1)
    ]]></literal>
    <justification jstring="[para(3751(a,1),1261(a,1,2))].">
      <j1 rule="para" parents="3751 1261"/>
    </justification>
  </clause>

  <clause id="3757">
    <literal><![CDATA[
      T((x \ y) * x,x \ 1) = x \ T(y * x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(957,a,3756,a)].">
      <j1 rule="hyper" parents="957 3756"/>
    </justification>
  </clause>

  <clause id="3758">
    <literal><![CDATA[
      L(x * ((y \ 1) \ 1),y,y) = y * L(T(x,y),y,y)
    ]]></literal>
    <justification jstring="[para(1673(a,1),3752(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1673 3752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3759">
    <literal><![CDATA[
      L(x * ((y \ 1) \ 1),y,y) = L(x,y,y) * y
    ]]></literal>
    <justification jstring="[hyper(299,a,233,a(flip),b,3758,a),flip(a)].">
      <j1 rule="hyper" parents="299 233 3758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3760">
    <literal><![CDATA[
      (1 / x) \ L(y * ((x \ 1) \ 1),x,x) = x * ((x \ 1) \ L(T(y,x),x,x))
    ]]></literal>
    <justification jstring="[hyper(119,a,3758,a,b,1671,a)].">
      <j1 rule="hyper" parents="119 3758 1671"/>
    </justification>
  </clause>

  <clause id="3761">
    <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),3365(a,2,1))].">
      <j1 rule="para" parents="18 3365"/>
    </justification>
  </clause>

  <clause id="3762">
    <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(120,a,3379,a(flip),b,103,a)].">
      <j1 rule="hyper" parents="120 3379 103"/>
    </justification>
  </clause>

  <clause id="3763">
    <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(775,a,3429,a),flip(a)].">
      <j1 rule="hyper" parents="775 3429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3764">
    <literal><![CDATA[
      (x * (y \ T(y,x))) \ (x * z) = x * ((x * (y \ T(y,x))) \ z)
    ]]></literal>
    <justification jstring="[para(3513(a,1),3525(a,2,2,1,2))].">
      <j1 rule="para" parents="3513 3525"/>
    </justification>
  </clause>

  <clause id="3765">
    <literal><![CDATA[
      (x * ((x * (T(y,x) \ y)) \ x)) \ (x * x) = x * (T(y,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(299,a,3560,a(flip),b,3564,a),flip(a)].">
      <j1 rule="hyper" parents="299 3560 3564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3766">
    <literal><![CDATA[
      K(x \ 1,(1 / x) \ (y / x)) = (T(y,x \ 1) / x) \ (y / x)
    ]]></literal>
    <justification jstring="[para(3733(a,1),3566(a,2,1,1))].">
      <j1 rule="para" parents="3733 3566"/>
    </justification>
  </clause>

  <clause id="3767">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ T(x * y,x) = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(299,a,1785,a(flip),b,3600,a),flip(a)].">
      <j1 rule="hyper" parents="299 1785 3600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3768">
    <literal><![CDATA[
      L(T(x,y) \ x,x \ 1,x) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(43,a,1006,a,b,3681,a)].">
      <j1 rule="hyper" parents="43 1006 3681"/>
    </justification>
  </clause>

  <clause id="3769">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ 1) = (1 / y) * ((x \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(65,a,3504,a(flip),b,3683,a)].">
      <j1 rule="hyper" parents="65 3504 3683"/>
    </justification>
  </clause>

  <clause id="3771">
    <literal><![CDATA[
      x \ ((y * (x * x)) * (x \ 1)) = (1 / (1 / x)) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(65,a,746,a(flip),b,3754,a),flip(a)].">
      <j1 rule="hyper" parents="65 746 3754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3772">
    <literal><![CDATA[
      x \ ((y * (x * x)) * (x \ 1)) = ((x \ 1) \ 1) \ (y * x)
    ]]></literal>
    <justification jstring="[para(1691(a,1),3771(a,2,1))].">
      <j1 rule="para" parents="1691 3771"/>
    </justification>
  </clause>

  <clause id="3773">
    <literal><![CDATA[
      x \ (y * ((x * x) * (x \ 1))) = ((x \ 1) \ 1) \ (y * x)
    ]]></literal>
    <justification jstring="[para(34(a,1),3772(a,1,2))].">
      <j1 rule="para" parents="34 3772"/>
    </justification>
  </clause>

  <clause id="3774">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ (y * x) = x \ (y * ((x \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(724(a,1),3773(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="724 3773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3775">
    <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(3764(a,2),45(a,1))].">
      <j1 rule="para" parents="3764 45"/>
    </justification>
  </clause>

  <clause id="3776">
    <literal><![CDATA[
      R(T(x \ 1,((x \ 1) \ 1) * y),x,y) = (((x \ 1) \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[hyper(65,a,27,a,b,3433,a)].">
      <j1 rule="hyper" parents="65 27 3433"/>
    </justification>
  </clause>

  <clause id="3777">
    <literal><![CDATA[
      R((x / y) \ T(x / y,z),x / y,y) = (y * T(y \ x,z)) / x
    ]]></literal>
    <justification jstring="[para(432(a,1),3522(a,2,1))].">
      <j1 rule="para" parents="432 3522"/>
    </justification>
  </clause>

  <clause id="3778">
    <literal><![CDATA[
      T((x * K(y,x)) * (R(K(y,x),x,(x * K(y,x)) \ 1) \ 1),z) = (x * K(y,x)) * (T(x,z) * ((x * K(y,x)) \ 1))
    ]]></literal>
    <justification jstring="[para(3644(a,2),1135(a,1,1,2))].">
      <j1 rule="para" parents="3644 1135"/>
    </justification>
  </clause>

  <clause id="3779">
    <literal><![CDATA[
      ((1 / x) * (T(x,y) \ x)) * x = L(T(x,y) \ x,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(3657(a,1),3729(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3657 3729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3780">
    <literal><![CDATA[
      T(x * T(y,y \ 1),y \ 1) = R((y \ 1) \ x,1 / y,y)
    ]]></literal>
    <justification jstring="[para(3228(a,1),3755(a,1,1))].">
      <j1 rule="para" parents="3228 3755"/>
    </justification>
  </clause>

  <clause id="3781">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ T(x * y,x \ 1) = ((x \ 1) \ y) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(981,a,3330,a)].">
      <j1 rule="hyper" parents="981 3330"/>
    </justification>
  </clause>

  <clause id="3782">
    <literal><![CDATA[
      x \ T(x,R(y,x,(y * x) \ x)) = L(K(x,y),x \ 1,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),3550(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 3550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3784">
    <literal><![CDATA[
      L(K(x,y),x \ 1,x) = x \ (x * K(x,y))
    ]]></literal>
    <justification jstring="[para(1889(a,1),3782(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1889 3782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3785">
    <literal><![CDATA[
      L(K(x,y),x \ 1,x) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ K(x,y) = u
    ]]></literal>
    <justification jstring="[para(3784(a,2),313(a,1))].">
      <j1 rule="para" parents="3784 313"/>
    </justification>
  </clause>

  <clause id="3786">
    <literal><![CDATA[
      (x \ 1) * K(x,y) = x \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3785,a,252,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="3785 252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3787">
    <literal><![CDATA[
      K(x,y) * (x \ 1) = x \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(1501,a,3786,a)].">
      <j1 rule="hyper" parents="1501 3786"/>
    </justification>
  </clause>

  <clause id="3788">
    <literal><![CDATA[
      x \ K(x,y) != z * K(x,y)
    ]]></literal>
    <literal><![CDATA[
      x \ 1 = z
    ]]></literal>
    <justification jstring="[para(3786(a,1),46(a,1))].">
      <j1 rule="para" parents="3786 46"/>
    </justification>
  </clause>

  <clause id="3790">
    <literal><![CDATA[
      (x \ K(x,y)) * L(z,x \ 1,K(x,y)) = K(x,y) * ((x \ 1) * z)
    ]]></literal>
    <justification jstring="[para(3787(a,1),94(a,1,1))].">
      <j1 rule="para" parents="3787 94"/>
    </justification>
  </clause>

  <clause id="3791">
    <literal><![CDATA[
      K(x,y) \ (x \ K(x,y)) != z * u
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) / u = z
    ]]></literal>
    <justification jstring="[para(3787(a,1),577(a,1,2))].">
      <j1 rule="para" parents="3787 577"/>
    </justification>
  </clause>

  <clause id="3792">
    <literal><![CDATA[
      (K(x,y) * R(T(y,z),u,w)) * v5 != R(T(y,z),u,w) * K(x,y)
    ]]></literal>
    <literal><![CDATA[
      1 = v5
    ]]></literal>
    <justification jstring="[para(3697(a,1),123(a,1))].">
      <j1 rule="para" parents="3697 123"/>
    </justification>
  </clause>

  <clause id="3793">
    <literal><![CDATA[
      x \ T((y \ 1) * (x / (y \ 1)),K(z \ 1,z)) = K(1 / y,x / (y \ 1))
    ]]></literal>
    <justification jstring="[para(3730(a,2),2642(a,1,2))].">
      <j1 rule="para" parents="3730 2642"/>
    </justification>
  </clause>

  <clause id="3794">
    <literal><![CDATA[
      R(K(x,x \ 1) * (y / z),z,K(x \ 1,x)) = y / (z * K(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(2594(a,1),3234(a,1,1))].">
      <j1 rule="para" parents="2594 3234"/>
    </justification>
  </clause>

  <clause id="3795">
    <literal><![CDATA[
      (x * y) \ (x * ((y * z) * K(1 / u,u))) = L(z,y,x) * K(1 / u,u)
    ]]></literal>
    <justification jstring="[para(3400(a,1),3401(a,1,2))].">
      <j1 rule="para" parents="3400 3401"/>
    </justification>
  </clause>

  <clause id="3796">
    <literal><![CDATA[
      (x * y) * R(K(x * y,z),y,T(x,y)) = (K(y * T(x,y),z) * y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(107(a,2),3593(a,2,1,1,1))].">
      <j1 rule="para" parents="107 3593"/>
    </justification>
  </clause>

  <clause id="3797">
    <literal><![CDATA[
      L(x * K(y \ 1,y),z,u) = L(x,z,u) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,3377,a(flip),b,3761,a)].">
      <j1 rule="hyper" parents="65 3377 3761"/>
    </justification>
  </clause>

  <clause id="3798">
    <literal><![CDATA[
      L(x * K(y \ 1,y),z,u) = K(y \ 1,y) * L(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,3205,a,b,3797,a),flip(a)].">
      <j1 rule="hyper" parents="299 3205 3797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3800">
    <literal><![CDATA[
      L(x * K(y \ 1,y),y,y \ 1) = (y \ 1) * (y * x)
    ]]></literal>
    <justification jstring="[hyper(902,a,3798,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="902 3798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3801">
    <literal><![CDATA[
      K(x \ 1,x) * L(y * K(x,x \ 1),z,u) = L(y,z,u)
    ]]></literal>
    <justification jstring="[para(2764(a,1),3798(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2764 3798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3802">
    <literal><![CDATA[
      L(x * K(y,y \ 1),z,u) = L(x,z,u) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(3250,a,3801,a),flip(a)].">
      <j1 rule="hyper" parents="3250 3801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3803">
    <literal><![CDATA[
      L(x * K(y,y \ 1),z,u) = K(y,y \ 1) * L(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(2746,a,3801,a),flip(a)].">
      <j1 rule="hyper" parents="2746 3801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3805">
    <literal><![CDATA[
      L(x \ 1,y,z) * K(x,x \ 1) = L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(2733(a,1),3802(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2733 3802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3806">
    <literal><![CDATA[
      L(x * K(y \ z,(y \ z) \ 1),u,w) = L(x,u,w) * K(y \ z,z \ y)
    ]]></literal>
    <justification jstring="[para(3036(a,1),3802(a,2,2))].">
      <j1 rule="para" parents="3036 3802"/>
    </justification>
  </clause>

  <clause id="3807">
    <literal><![CDATA[
      x \ L(y * K(z,z \ 1),u,w) = (x \ L(y,u,w)) * K(z,z \ 1)
    ]]></literal>
    <justification jstring="[para(3802(a,2),3399(a,1,2))].">
      <j1 rule="para" parents="3802 3399"/>
    </justification>
  </clause>

  <clause id="3808">
    <literal><![CDATA[
      L(x \ 1,y,z) \ K(x \ 1,x) = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(3805(a,1),3232(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3805 3232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3809">
    <literal><![CDATA[
      L(1 / x,y,z) \ (1 / x) = L(x \ 1,y,z) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(3805(a,1),3375(a,1,1))].">
      <j1 rule="para" parents="3805 3375"/>
    </justification>
  </clause>

  <clause id="3810">
    <literal><![CDATA[
      K(x,x \ 1) * L(x,y,z) = L(T(x,x \ 1),y,z)
    ]]></literal>
    <justification jstring="[para(2555(a,1),3803(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2555 3803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3811">
    <literal><![CDATA[
      x * (L(x,y,z) * (1 / x)) = L(T(x,x \ 1),y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,2823,a(flip),b,3810,a)].">
      <j1 rule="hyper" parents="65 2823 3810"/>
    </justification>
  </clause>

  <clause id="3812">
    <literal><![CDATA[
      x * (L(x,y,z) * (1 / x)) = L((x \ 1) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(108(a,1),3811(a,2,1))].">
      <j1 rule="para" parents="108 3811"/>
    </justification>
  </clause>

  <clause id="3813">
    <literal><![CDATA[
      x \ L((x \ 1) \ 1,y,z) = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(125,a,3812,a)].">
      <j1 rule="hyper" parents="125 3812"/>
    </justification>
  </clause>

  <clause id="3814">
    <literal><![CDATA[
      T(L(x,y,z) * (1 / x),x) = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(65,a,2721,a,b,3813,a)].">
      <j1 rule="hyper" parents="65 2721 3813"/>
    </justification>
  </clause>

  <clause id="3815">
    <literal><![CDATA[
      (x \ L(x,y,z)) * x = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(2379,a,3814,a)].">
      <j1 rule="hyper" parents="2379 3814"/>
    </justification>
  </clause>

  <clause id="3816">
    <literal><![CDATA[
      T(x,x \ L(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(337,a,3815,a)].">
      <j1 rule="hyper" parents="337 3815"/>
    </justification>
  </clause>

  <clause id="3817">
    <literal><![CDATA[
      (x \ L(x,y,z)) * x = u * (u \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,10,a,b,3815,a),flip(a)].">
      <j1 rule="hyper" parents="299 10 3815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3818">
    <literal><![CDATA[
      T(x \ L(x,y,z),x) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(235,a,3815,a,b,10,a)].">
      <j1 rule="hyper" parents="235 3815 10"/>
    </justification>
  </clause>

  <clause id="3819">
    <literal><![CDATA[
      L(x,y,z) / x = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(137,a,3815,a)].">
      <j1 rule="hyper" parents="137 3815"/>
    </justification>
  </clause>

  <clause id="3820">
    <literal><![CDATA[
      (x \ 1) \ L(x \ 1,y,z) = x * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(37,a,1795,a,b,3815,a),flip(a)].">
      <j1 rule="hyper" parents="37 1795 3815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3822">
    <literal><![CDATA[
      T(x,y) * (x \ L(x,z,u)) = (x \ L(x,z,u)) * T(x,y)
    ]]></literal>
    <justification jstring="[para(3816(a,1),232(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3816 232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3823">
    <literal><![CDATA[
      (1 / x) * L(x,y,z) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,1798,a,b,3819,a)].">
      <j1 rule="hyper" parents="65 1798 3819"/>
    </justification>
  </clause>

  <clause id="3825">
    <literal><![CDATA[
      (x \ L(x,y,z)) * L(u,L(x,y,z),1 / x) = (1 / x) * (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(3823(a,1),94(a,1,1))].">
      <j1 rule="para" parents="3823 94"/>
    </justification>
  </clause>

  <clause id="3828">
    <literal><![CDATA[
      (x \ 1) * (L(x \ 1,y,z) \ x) = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,1372,a(flip),b,3808,a)].">
      <j1 rule="hyper" parents="65 1372 3808"/>
    </justification>
  </clause>

  <clause id="3829">
    <literal><![CDATA[
      x \ ((x \ L(x,y,z)) * T(x,u)) = T(x,u) * (x \ (x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(119,a,3822,a(flip),b,1190,a)].">
      <j1 rule="hyper" parents="119 3822 1190"/>
    </justification>
  </clause>

  <clause id="3831">
    <literal><![CDATA[
      x / (y * K(z \ 1,z)) = K(z,z \ 1) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(3389,a,3794,a),flip(a)].">
      <j1 rule="hyper" parents="3389 3794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3833">
    <literal><![CDATA[
      x / (K(y \ 1,y) * z) = K(y,y \ 1) * (x / z)
    ]]></literal>
    <justification jstring="[para(3205(a,2),3831(a,1,2))].">
      <j1 rule="para" parents="3205 3831"/>
    </justification>
  </clause>

  <clause id="3834">
    <literal><![CDATA[
      x / (y * (z * K(u \ 1,u))) = K(u,u \ 1) * (x / (y * z))
    ]]></literal>
    <justification jstring="[para(3359(a,1),3831(a,1,2))].">
      <j1 rule="para" parents="3359 3831"/>
    </justification>
  </clause>

  <clause id="3835">
    <literal><![CDATA[
      K(x \ 1,x) * (y / (z * (u * K(x \ 1,x)))) = y / (z * u)
    ]]></literal>
    <justification jstring="[hyper(2742,a,3834,a(flip))].">
      <j1 rule="hyper" parents="2742 3834"/>
    </justification>
  </clause>

  <clause id="3836">
    <literal><![CDATA[
      x / (K(y,y \ 1) * z) = K(y \ 1,y) * (x / z)
    ]]></literal>
    <justification jstring="[para(3219(a,1),3835(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3219 3835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3837">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z * K(1 / u,u)))) = L(z,y,x) * K(1 / u,u)
    ]]></literal>
    <justification jstring="[para(3400(a,1),3795(a,1,2,2))].">
      <j1 rule="para" parents="3400 3795"/>
    </justification>
  </clause>

  <clause id="3838">
    <literal><![CDATA[
      L(x * K(1 / y,y),z,u) = L(x,z,u) * K(1 / y,y)
    ]]></literal>
    <justification jstring="[hyper(493,a,3837,a)].">
      <j1 rule="hyper" parents="493 3837"/>
    </justification>
  </clause>

  <clause id="3840">
    <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(65,a,2974,a,b,3276,a)].">
      <j1 rule="hyper" parents="65 2974 3276"/>
    </justification>
  </clause>

  <clause id="3842">
    <literal><![CDATA[
      ((1 / x) / y) * T(((1 / x) / y) \ (y \ 1),z) = (x \ T(x * K(y \ 1,y),z)) / y
    ]]></literal>
    <justification jstring="[para(253(a,2),3512(a,2,1,2,1,2))].">
      <j1 rule="para" parents="253 3512"/>
    </justification>
  </clause>

  <clause id="3843">
    <literal><![CDATA[
      (1 / x) \ L(y * ((x \ 1) \ 1),x,x) = x * (L(x,x,x) * T(y,x))
    ]]></literal>
    <justification jstring="[para(2816(a,1),3760(a,2,2))].">
      <j1 rule="para" parents="2816 3760"/>
    </justification>
  </clause>

  <clause id="3844">
    <literal><![CDATA[
      x \ ((1 / y) * (x / (1 / y))) = K(1 / y,x / (y \ 1))
    ]]></literal>
    <justification jstring="[para(3329(a,1),3793(a,1,2))].">
      <j1 rule="para" parents="3329 3793"/>
    </justification>
  </clause>

  <clause id="3845">
    <literal><![CDATA[
      L(x * K(y \ z,z \ y),u,w) = L(x,u,w) * K(y \ z,z \ y)
    ]]></literal>
    <justification jstring="[para(3036(a,1),3806(a,1,1,2))].">
      <j1 rule="para" parents="3036 3806"/>
    </justification>
  </clause>

  <clause id="3847">
    <literal><![CDATA[
      (x \ L(x,y,z)) * L(u,L(x,y,z),x) = (1 / x) * (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(2467(a,1),3825(a,1,2))].">
      <j1 rule="para" parents="2467 3825"/>
    </justification>
  </clause>

  <clause id="3848">
    <literal><![CDATA[
      (x \ R(x * y,z,u)) * x = R(y * x,z,u)
    ]]></literal>
    <justification jstring="[para(3238(a,1),3840(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3238 3840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3849">
    <literal><![CDATA[
      R((x \ y) * x,z,u) = (x \ R(y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(10(a,1),3848(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 3848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3850">
    <literal><![CDATA[
      R((x \ y) * x,z,u) / x = x \ R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(120,a,3849,a,b,xx)].">
      <j1 rule="hyper" parents="120 3849"/>
    </justification>
  </clause>

  <clause id="3851">
    <literal><![CDATA[
      R((x \ (y / z)) * x,z,z \ 1) = (x \ (y * (z \ 1))) * x
    ]]></literal>
    <justification jstring="[para(565(a,1),3849(a,2,1,2))].">
      <j1 rule="para" parents="565 3849"/>
    </justification>
  </clause>

  <clause id="3852">
    <literal><![CDATA[
      R((x \ (y / (1 / z))) * x,z \ 1,z) = (x \ (y * z)) * x
    ]]></literal>
    <justification jstring="[para(2693(a,1),3849(a,2,1,2))].">
      <j1 rule="para" parents="2693 3849"/>
    </justification>
  </clause>

  <clause id="3853">
    <literal><![CDATA[
      x \ R(x * (y / x),z,u) = R(y,z,u) / x
    ]]></literal>
    <justification jstring="[para(80(a,1),3850(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="80 3850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3855">
    <literal><![CDATA[
      R(x * (y / x),z,u) = x * (R(y,z,u) / x)
    ]]></literal>
    <justification jstring="[hyper(144,a,3853,a),flip(a)].">
      <j1 rule="hyper" parents="144 3853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3856">
    <literal><![CDATA[
      ((x \ (y * (z \ 1))) * x) / (z \ 1) = ((x \ (y / z)) * x) * z
    ]]></literal>
    <justification jstring="[hyper(120,a,3851,a(flip),b,258,a)].">
      <j1 rule="hyper" parents="120 3851 258"/>
    </justification>
  </clause>

  <clause id="3857">
    <literal><![CDATA[
      ((x \ (y / (1 / z))) * x) * (1 / z) = ((x \ (y * z)) * x) / z
    ]]></literal>
    <justification jstring="[hyper(120,a,3852,a(flip),b,2694,a),flip(a)].">
      <j1 rule="hyper" parents="120 3852 2694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3858">
    <literal><![CDATA[
      ((x \ (y * (z \ 1))) * x) / (z \ 1) = z * ((x \ (z \ y)) * x)
    ]]></literal>
    <justification jstring="[hyper(299,a,3503,a(flip),b,3856,a),flip(a)].">
      <j1 rule="hyper" parents="299 3503 3856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3859">
    <literal><![CDATA[
      x * (T((x \ y) * z,x) / z) = ((x \ (y * z)) * x) / z
    ]]></literal>
    <justification jstring="[hyper(65,a,1600,a(flip),b,3857,a)].">
      <j1 rule="hyper" parents="65 1600 3857"/>
    </justification>
  </clause>

  <clause id="3860">
    <literal><![CDATA[
      x * (y \ T(y * (x \ z),x)) = ((x \ (z * y)) * x) / y
    ]]></literal>
    <justification jstring="[para(3460(a,1),3859(a,1,2))].">
      <j1 rule="para" parents="3460 3859"/>
    </justification>
  </clause>

  <clause id="3861">
    <literal><![CDATA[
      ((x \ (y / (z \ 1))) * x) * (z \ 1) = ((x \ (y * z)) * x) / z
    ]]></literal>
    <justification jstring="[hyper(65,a,1599,a,b,3860,a)].">
      <j1 rule="hyper" parents="65 1599 3860"/>
    </justification>
  </clause>

  <clause id="3862">
    <literal><![CDATA[
      (x \ 1) * ((y \ ((x \ 1) \ z)) * y) = ((y \ (z * x)) * y) / x
    ]]></literal>
    <justification jstring="[hyper(3675,a,3861,a)].">
      <j1 rule="hyper" parents="3675 3861"/>
    </justification>
  </clause>

  <clause id="3863">
    <literal><![CDATA[
      L(T(x,y),y,K(z \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z \ 1,z) * y) = u
    ]]></literal>
    <justification jstring="[para(3346(a,1),318(a,1))].">
      <j1 rule="para" parents="3346 318"/>
    </justification>
  </clause>

  <clause id="3864">
    <literal><![CDATA[
      T(x,K(y \ 1,y) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(3863,a,2492,a)].">
      <j1 rule="hyper" parents="3863 2492"/>
    </justification>
  </clause>

  <clause id="3865">
    <literal><![CDATA[
      T(x,K(y,y \ 1) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(2596(a,1),3864(a,1,2,1))].">
      <j1 rule="para" parents="2596 3864"/>
    </justification>
  </clause>

  <clause id="3866">
    <literal><![CDATA[
      T(x,T(y,y \ 1) * z) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(2648(a,1),3864(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2648 3864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3867">
    <literal><![CDATA[
      T(x,((y \ 1) \ 1) * z) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(2649(a,1),3864(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2649 3864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3868">
    <literal><![CDATA[
      T(x,(1 / y) * z) = T(x,(y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(2650(a,1),3864(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2650 3864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3869">
    <literal><![CDATA[
      T(x,(1 / y) \ z) = T(x,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(2655(a,1),3864(a,1,2))].">
      <j1 rule="para" parents="2655 3864"/>
    </justification>
  </clause>

  <clause id="3870">
    <literal><![CDATA[
      T(x,((y \ 1) \ 1) \ z) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(2680(a,1),3864(a,1,2))].">
      <j1 rule="para" parents="2680 3864"/>
    </justification>
  </clause>

  <clause id="3871">
    <literal><![CDATA[
      T(x,(1 / (1 / y)) * z) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(2685(a,1),3864(a,1,2))].">
      <j1 rule="para" parents="2685 3864"/>
    </justification>
  </clause>

  <clause id="3872">
    <literal><![CDATA[
      T(x,y * K(z \ 1,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(3205(a,1),3864(a,1,2))].">
      <j1 rule="para" parents="3205 3864"/>
    </justification>
  </clause>

  <clause id="3873">
    <literal><![CDATA[
      T(x,y * K(z,z \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(3214(a,1),3864(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3214 3864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3874">
    <literal><![CDATA[
      T(x,y * (1 / z)) = T(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[para(3239(a,1),3864(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3239 3864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3875">
    <literal><![CDATA[
      T(x,y \ (1 / z)) = T(x,y \ (z \ 1))
    ]]></literal>
    <justification jstring="[para(3370(a,1),3864(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3370 3864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3876">
    <literal><![CDATA[
      T(x,((1 / y) * z) \ u) = T(x,((y \ 1) * z) \ u)
    ]]></literal>
    <justification jstring="[para(3265(a,1),3864(a,1,2))].">
      <j1 rule="para" parents="3265 3864"/>
    </justification>
  </clause>

  <clause id="3877">
    <literal><![CDATA[
      T(x,(y * (1 / z)) * u) = T(x,(y * (z \ 1)) * u)
    ]]></literal>
    <justification jstring="[para(3288(a,1),3864(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3288 3864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3878">
    <literal><![CDATA[
      T(x,(y / (1 / z)) * u) = T(x,(y / (z \ 1)) * u)
    ]]></literal>
    <justification jstring="[para(3312(a,1),3864(a,1,2))].">
      <j1 rule="para" parents="3312 3864"/>
    </justification>
  </clause>

  <clause id="3879">
    <literal><![CDATA[
      T(x,((1 / y) * z) * u) = T(x,((y \ 1) * z) * u)
    ]]></literal>
    <justification jstring="[para(2735(a,1),3865(a,1,2))].">
      <j1 rule="para" parents="2735 3865"/>
    </justification>
  </clause>

  <clause id="3880">
    <literal><![CDATA[
      T(x,(y * (1 / z)) \ u) = T(x,(y * (z \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(2797(a,1),3865(a,1,2))].">
      <j1 rule="para" parents="2797 3865"/>
    </justification>
  </clause>

  <clause id="3881">
    <literal><![CDATA[
      T(x,R(1 / y,z,u)) = T(x,R(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(2976(a,1),3865(a,1,2))].">
      <j1 rule="para" parents="2976 3865"/>
    </justification>
  </clause>

  <clause id="3882">
    <literal><![CDATA[
      T(x,y / (1 / z)) = T(x,y / (z \ 1))
    ]]></literal>
    <justification jstring="[para(3217(a,1),3865(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3217 3865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3883">
    <literal><![CDATA[
      T(x,y * (K(z,z \ 1) * u)) = T(x,y * u)
    ]]></literal>
    <justification jstring="[para(3301(a,1),3865(a,1,2))].">
      <j1 rule="para" parents="3301 3865"/>
    </justification>
  </clause>

  <clause id="3884">
    <literal><![CDATA[
      T(x,y * ((1 / z) \ u)) = T(x,y * ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(3337(a,1),3865(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3337 3865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3885">
    <literal><![CDATA[
      T(x,y * (z * (1 / u))) = T(x,y * (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(3340(a,1),3865(a,1,2))].">
      <j1 rule="para" parents="3340 3865"/>
    </justification>
  </clause>

  <clause id="3886">
    <literal><![CDATA[
      T(x,((1 / y) \ z) \ u) = T(x,((y \ 1) \ z) \ u)
    ]]></literal>
    <justification jstring="[para(3453(a,1),3865(a,1,2))].">
      <j1 rule="para" parents="3453 3865"/>
    </justification>
  </clause>

  <clause id="3887">
    <literal><![CDATA[
      T(x,y * (((y \ z) \ 1) \ 1)) = T(x,z)
    ]]></literal>
    <justification jstring="[para(2999(a,1),3872(a,1,2))].">
      <j1 rule="para" parents="2999 3872"/>
    </justification>
  </clause>

  <clause id="3890">
    <literal><![CDATA[
      T(x,T(((y \ 1) \ 1) \ z,u)) = T(x,T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(3507(a,1),3873(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3507 3873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3891">
    <literal><![CDATA[
      R(T(x \ 1,x * y),x,y) = (((x \ 1) \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[para(3867(a,1),3776(a,1,1))].">
      <j1 rule="para" parents="3867 3776"/>
    </justification>
  </clause>

  <clause id="3892">
    <literal><![CDATA[
      T(x,(y \ 1) \ K(z,y)) = T(x,y * K(z,y))
    ]]></literal>
    <justification jstring="[para(3648(a,1),3869(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3648 3869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3893">
    <literal><![CDATA[
      T(x,R(y \ 1,y,z) \ u) = T(x,(z / (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(2945(a,2),3870(a,1,2,1))].">
      <j1 rule="para" parents="2945 3870"/>
    </justification>
  </clause>

  <clause id="3894">
    <literal><![CDATA[
      (1 / x) / T(y,y \ (x \ 1)) = y \ (1 / x)
    ]]></literal>
    <justification jstring="[para(3875(a,1),262(a,1,2))].">
      <j1 rule="para" parents="3875 262"/>
    </justification>
  </clause>

  <clause id="3895">
    <literal><![CDATA[
      T(x,R(1 / y,z,u) * K(w,w \ 1)) = T(x,R(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,3873,a,b,3881,a)].">
      <j1 rule="hyper" parents="65 3873 3881"/>
    </justification>
  </clause>

  <clause id="3896">
    <literal><![CDATA[
      (x * ((y * (x \ 1)) / y)) * y = T(y,R(x \ 1,x,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,1467,a,b,3881,a)].">
      <j1 rule="hyper" parents="65 1467 3881"/>
    </justification>
  </clause>

  <clause id="3897">
    <literal><![CDATA[
      T(x,R((y \ 1) \ 1,z,u)) = T(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(76(a,1),3881(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="76 3881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3898">
    <literal><![CDATA[
      T(x,R((y * K(z \ 1,z)) \ 1,u,w)) = T(x,R(K(z,z \ 1) / y,u,w))
    ]]></literal>
    <justification jstring="[para(3360(a,1),3881(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3360 3881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3899">
    <literal><![CDATA[
      T(x,y * ((1 / z) * u)) = T(x,y * ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[para(2727(a,1),3883(a,1,2,2))].">
      <j1 rule="para" parents="2727 3883"/>
    </justification>
  </clause>

  <clause id="3900">
    <literal><![CDATA[
      T(x,y * (((1 / z) * u) * w)) = T(x,y * (((z \ 1) * u) * w))
    ]]></literal>
    <justification jstring="[para(2735(a,1),3883(a,1,2,2))].">
      <j1 rule="para" parents="2735 3883"/>
    </justification>
  </clause>

  <clause id="3901">
    <literal><![CDATA[
      T(x,y * ((((z \ 1) \ 1) * u) \ w)) = T(x,y * ((z * u) \ w))
    ]]></literal>
    <justification jstring="[para(3280(a,1),3883(a,1,2,2))].">
      <j1 rule="para" parents="3280 3883"/>
    </justification>
  </clause>

  <clause id="3902">
    <literal><![CDATA[
      T(x,y * (z * (u * (1 / w)))) = T(x,y * (z * (u * (w \ 1))))
    ]]></literal>
    <justification jstring="[para(3340(a,1),3883(a,1,2,2))].">
      <j1 rule="para" parents="3340 3883"/>
    </justification>
  </clause>

  <clause id="3903">
    <literal><![CDATA[
      T(x,(y * z) \ ((y * y) * u)) = T(x,((y \ 1) * z) \ u)
    ]]></literal>
    <justification jstring="[para(1068(a,2),3876(a,1,2))].">
      <j1 rule="para" parents="1068 3876"/>
    </justification>
  </clause>

  <clause id="3904">
    <literal><![CDATA[
      T(x,(((y \ 1) \ 1) \ z) \ u) = T(x,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[para(76(a,1),3886(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="76 3886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3905">
    <literal><![CDATA[
      T(x,T((1 / y) \ z,u)) = T(x,T((y \ 1) \ z,u))
    ]]></literal>
    <justification jstring="[para(79(a,1),3890(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 3890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3906">
    <literal><![CDATA[
      T((x * y) \ y,x) = (((x \ 1) \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[hyper(65,a,1326,a(flip),b,3891,a)].">
      <j1 rule="hyper" parents="65 1326 3891"/>
    </justification>
  </clause>

  <clause id="3907">
    <literal><![CDATA[
      (T(x,x \ 1) * y) \ y = T((x * y) \ y,x)
    ]]></literal>
    <justification jstring="[para(108(a,2),3906(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="108 3906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3908">
    <literal><![CDATA[
      T(x,R(y \ 1,(y \ 1) \ 1,x)) = (y * ((x * (y \ 1)) / x)) * x
    ]]></literal>
    <justification jstring="[para(3431(a,2),3896(a,2,2)),flip(a)].">
      <j1 rule="para" parents="3431 3896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3909">
    <literal><![CDATA[
      T(x,((y \ 1) * z) \ 1) = T(x,(y * z) \ (y * y))
    ]]></literal>
    <justification jstring="[para(8(a,1),3903(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8 3903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3910">
    <literal><![CDATA[
      T(x,R(K(y,y \ 1) * (1 / z),u,w)) = T(x,R(z \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(3221(a,2),3895(a,1,2))].">
      <j1 rule="para" parents="3221 3895"/>
    </justification>
  </clause>

  <clause id="3911">
    <literal><![CDATA[
      T(x,y * (((z \ 1) * u) * T(w,(1 / z) * u))) = T(x,y * (w * ((1 / z) * u)))
    ]]></literal>
    <justification jstring="[para(107(a,1),3900(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 3900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3912">
    <literal><![CDATA[
      T(x,R(K(y,y \ 1) / z,u,w)) = T(x,R(z \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(2593(a,1),3910(a,1,2,1))].">
      <j1 rule="para" parents="2593 3910"/>
    </justification>
  </clause>

  <clause id="3913">
    <literal><![CDATA[
      T(x,R(y \ 1,(y \ 1) \ 1,x)) != z * x
    ]]></literal>
    <literal><![CDATA[
      y * ((x * (y \ 1)) / x) = z
    ]]></literal>
    <justification jstring="[para(3908(a,2),46(a,1))].">
      <j1 rule="para" parents="3908 46"/>
    </justification>
  </clause>

  <clause id="3914">
    <literal><![CDATA[
      T(x,R((y \ x) \ 1,((y \ x) \ 1) \ 1,x)) = K(x,y / x) * x
    ]]></literal>
    <justification jstring="[para(1883(a,1),3908(a,2,1))].">
      <j1 rule="para" parents="1883 3908"/>
    </justification>
  </clause>

  <clause id="3915">
    <literal><![CDATA[
      T(x,R((y \ x) \ 1,((y \ x) \ 1) \ 1,x)) != z
    ]]></literal>
    <literal><![CDATA[
      x * K(x,y / x) = z
    ]]></literal>
    <justification jstring="[para(3914(a,2),3576(a,1))].">
      <j1 rule="para" parents="3914 3576"/>
    </justification>
  </clause>

  <clause id="3916">
    <literal><![CDATA[
      T(x,R(K(y,y \ 1) / z,u,w)) = T(x,R(z \ K(y,y \ 1),u,w))
    ]]></literal>
    <justification jstring="[para(3251(a,1),3898(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3251 3898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3917">
    <literal><![CDATA[
      T(x,R(y \ K(z,z \ 1),u,w)) = T(x,R(y \ 1,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,3912,a(flip),b,3916,a),flip(a)].">
      <j1 rule="hyper" parents="65 3912 3916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3919">
    <literal><![CDATA[
      (x * y) * (z * (L(y \ 1,y,x) / z)) = (x * y) * (z * (((x * y) \ x) / z))
    ]]></literal>
    <justification jstring="[hyper(65,a,3501,a(flip),b,3603,a),flip(a)].">
      <j1 rule="hyper" parents="65 3501 3603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3920">
    <literal><![CDATA[
      R((x \ (1 / y)) * x,y,z) * (y * z) = (y * z) * ((x \ ((y * z) \ z)) * x)
    ]]></literal>
    <justification jstring="[para(3849(a,2),3606(a,1,1))].">
      <j1 rule="para" parents="3849 3606"/>
    </justification>
  </clause>

  <clause id="3921">
    <literal><![CDATA[
      (x * y) * ((z \ ((x * y) \ y)) * z) = (((z \ (1 / x)) * z) * x) * y
    ]]></literal>
    <justification jstring="[hyper(275,a,3920,a),flip(a)].">
      <j1 rule="hyper" parents="275 3920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3922">
    <literal><![CDATA[
      x * ((y * x) * T((y * x) \ 1,x)) = (((x \ (1 / y)) * x) * y) * x
    ]]></literal>
    <justification jstring="[hyper(3607,a,3921,a)].">
      <j1 rule="hyper" parents="3607 3921"/>
    </justification>
  </clause>

  <clause id="3923">
    <literal><![CDATA[
      x * (y * (x * T(x \ (y \ 1),x))) = (((x \ (1 / y)) * x) * y) * x
    ]]></literal>
    <justification jstring="[para(998(a,1),3922(a,1,2))].">
      <j1 rule="para" parents="998 3922"/>
    </justification>
  </clause>

  <clause id="3924">
    <literal><![CDATA[
      (((x \ (1 / y)) * x) * y) * x = x * (y * ((x \ (y \ 1)) * x))
    ]]></literal>
    <justification jstring="[para(107(a,1),3923(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 3923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3925">
    <literal><![CDATA[
      (x \ L(x * (y / x),z,u)) * x = L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,3801,a(flip),b,3235,a),flip(a)].">
      <j1 rule="hyper" parents="65 3801 3235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3927">
    <literal><![CDATA[
      (x \ L(x * y,z,u)) * x = L(y * x,z,u)
    ]]></literal>
    <justification jstring="[para(11(a,1),3925(a,1,1,2,1,2))].">
      <j1 rule="para" parents="11 3925"/>
    </justification>
  </clause>

  <clause id="3928">
    <literal><![CDATA[
      L(x * (y / x),z,u) = x * (L(y,z,u) / x)
    ]]></literal>
    <justification jstring="[para(3925(a,1),75(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3925 75"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3929">
    <literal><![CDATA[
      L((x \ y) * x,z,u) = (x \ L(y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(75(a,1),3925(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 3925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3930">
    <literal><![CDATA[
      (x * y) * L(z * ((y \ 1) / z),y,x) = (x * y) * (z * (((x * y) \ x) / z))
    ]]></literal>
    <justification jstring="[para(3928(a,2),3919(a,1,2))].">
      <j1 rule="para" parents="3928 3919"/>
    </justification>
  </clause>

  <clause id="3931">
    <literal><![CDATA[
      L((x \ y) * x,z,u) != w * x
    ]]></literal>
    <literal><![CDATA[
      x \ L(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(3929(a,2),46(a,1))].">
      <j1 rule="para" parents="3929 46"/>
    </justification>
  </clause>

  <clause id="3932">
    <literal><![CDATA[
      L((x \ (y \ (z \ u))) * x,y,z) = (x \ ((z * y) \ u)) * x
    ]]></literal>
    <justification jstring="[para(281(a,1),3929(a,2,1,2))].">
      <j1 rule="para" parents="281 3929"/>
    </justification>
  </clause>

  <clause id="3933">
    <literal><![CDATA[
      L((x \ ((y \ 1) \ z)) * x,y \ 1,y) = (x \ (y * z)) * x
    ]]></literal>
    <justification jstring="[para(519(a,1),3929(a,2,1,2))].">
      <j1 rule="para" parents="519 3929"/>
    </justification>
  </clause>

  <clause id="3934">
    <literal><![CDATA[
      L((x \ ((y \ z) \ u)) * x,y \ z,y) = (x \ (z \ (y * u))) * x
    ]]></literal>
    <justification jstring="[para(520(a,1),3929(a,2,1,2))].">
      <j1 rule="para" parents="520 3929"/>
    </justification>
  </clause>

  <clause id="3935">
    <literal><![CDATA[
      L((x \ ((y \ 1) \ (y \ z))) * x,y \ 1,y) = (x \ z) * x
    ]]></literal>
    <justification jstring="[para(164(a,1),3932(a,2,1,2))].">
      <j1 rule="para" parents="164 3932"/>
    </justification>
  </clause>

  <clause id="3936">
    <literal><![CDATA[
      (x * y) * ((z \ ((x * y) \ u)) * z) = x * (y * ((z \ (y \ (x \ u))) * z))
    ]]></literal>
    <justification jstring="[para(3932(a,1),94(a,1,2))].">
      <j1 rule="para" parents="3932 94"/>
    </justification>
  </clause>

  <clause id="3937">
    <literal><![CDATA[
      (x \ 1) * ((y \ ((x \ 1) \ z)) * y) = x \ ((y \ (x * z)) * y)
    ]]></literal>
    <justification jstring="[hyper(119,a,3933,a(flip),b,252,a),flip(a)].">
      <j1 rule="hyper" parents="119 3933 252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3939">
    <literal><![CDATA[
      ((x \ (y * z)) * x) / z = z \ ((x \ (z * y)) * x)
    ]]></literal>
    <justification jstring="[hyper(65,a,3862,a(flip),b,3937,a)].">
      <j1 rule="hyper" parents="65 3862 3937"/>
    </justification>
  </clause>

  <clause id="3940">
    <literal><![CDATA[
      (x \ ((y \ (x * z)) * y)) * x = (y \ (z * x)) * y
    ]]></literal>
    <justification jstring="[hyper(143,a,3939,a)].">
      <j1 rule="hyper" parents="143 3939"/>
    </justification>
  </clause>

  <clause id="3941">
    <literal><![CDATA[
      (x \ ((y \ (x * z)) * y)) * x != u
    ]]></literal>
    <literal><![CDATA[
      (y \ (z * x)) * y = u
    ]]></literal>
    <justification jstring="[para(3939(a,1),246(a,1,1)),flip(b)].">
      <j1 rule="para" parents="3939 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3943">
    <literal><![CDATA[
      (x * y) * (z * (((x * y) \ x) / z)) = x * (y * (z * ((y \ 1) / z)))
    ]]></literal>
    <justification jstring="[hyper(279,a,3930,a),flip(a)].">
      <j1 rule="hyper" parents="279 3930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3944">
    <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(299,a,423,a,b,3284,a)].">
      <j1 rule="hyper" parents="299 423 3284"/>
    </justification>
  </clause>

  <clause id="3945">
    <literal><![CDATA[
      K(x \ 1,x) * (y * T((x \ 1) \ 1,z)) = y * (1 / (T(x,z) \ 1))
    ]]></literal>
    <justification jstring="[para(3172(a,1),3726(a,2,2,2))].">
      <j1 rule="para" parents="3172 3726"/>
    </justification>
  </clause>

  <clause id="3946">
    <literal><![CDATA[
      K(x \ 1,x) * (y * T((x \ 1) \ 1,z)) = y * T(x,z)
    ]]></literal>
    <justification jstring="[para(76(a,1),3945(a,2,2))].">
      <j1 rule="para" parents="76 3945"/>
    </justification>
  </clause>

  <clause id="3948">
    <literal><![CDATA[
      R(K(x \ (x / ((y \ x) / T(x,y))),x),x \ 1,x) = L(T(x,y) \ x,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,3779,a(flip),b,3678,a),flip(a)].">
      <j1 rule="hyper" parents="299 3779 3678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3949">
    <literal><![CDATA[
      R(T(x,y) \ x,x \ 1,x) = L(T(x,y) \ x,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(3656(a,1),3948(a,1,1))].">
      <j1 rule="para" parents="3656 3948"/>
    </justification>
  </clause>

  <clause id="3950">
    <literal><![CDATA[
      R(T(x,y) \ x,x \ 1,x) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(299,a,3768,a(flip),b,3949,a),flip(a)].">
      <j1 rule="hyper" parents="299 3768 3949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3951">
    <literal><![CDATA[
      R(x,y \ 1,y) != T(y,z) \ y
    ]]></literal>
    <literal><![CDATA[
      T(y,z) \ y = x
    ]]></literal>
    <justification jstring="[para(3950(a,1),53(a,1)),flip(a)].">
      <j1 rule="para" parents="3950 53"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3952">
    <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(65,a,3361,a(flip),b,3310,a)].">
      <j1 rule="hyper" parents="65 3361 3310"/>
    </justification>
  </clause>

  <clause id="3953">
    <literal><![CDATA[
      T(L((x * y) / x,z \ T(z,x),z),x) = (z \ T(z,x)) * (z * (T(z,x) \ y))
    ]]></literal>
    <justification jstring="[para(3706(a,1),3707(a,1,1))].">
      <j1 rule="para" parents="3706 3707"/>
    </justification>
  </clause>

  <clause id="3954">
    <literal><![CDATA[
      L(x \ (x * y),z \ T(z,x),z) = (z \ T(z,x)) * (z * (T(z,x) \ y))
    ]]></literal>
    <justification jstring="[hyper(966,a,3953,a)].">
      <j1 rule="hyper" parents="966 3953"/>
    </justification>
  </clause>

  <clause id="3955">
    <literal><![CDATA[
      (x \ T(x,y)) * (x * (T(x,y) \ z)) = L(z,x \ T(x,y),x)
    ]]></literal>
    <justification jstring="[para(9(a,1),3954(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 3954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3956">
    <literal><![CDATA[
      (x \ T(x,y)) * T(y,T(x,y)) = L(y,x \ T(x,y),x)
    ]]></literal>
    <justification jstring="[para(1205(a,1),3955(a,1,2))].">
      <j1 rule="para" parents="1205 3955"/>
    </justification>
  </clause>

  <clause id="3957">
    <literal><![CDATA[
      T(x,T(y,x)) * (y \ T(y,x)) = L(x,y \ T(y,x),y)
    ]]></literal>
    <justification jstring="[hyper(3631,a,3956,a)].">
      <j1 rule="hyper" parents="3631 3956"/>
    </justification>
  </clause>

  <clause id="3958">
    <literal><![CDATA[
      T(R(x,y,z),R(x,y,z) / (R(x,y,z) * x)) = R(x,y,z) * K(R(x,y,z),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(1898,a,3710,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="1898 3710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3959">
    <literal><![CDATA[
      T(R(x,y,z),R(x,y,z) / (x * R(x,y,z))) = R(x,y,z) * K(R(x,y,z),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,3548,a,b,3958,a)].">
      <j1 rule="hyper" parents="65 3548 3958"/>
    </justification>
  </clause>

  <clause id="3960">
    <literal><![CDATA[
      R(T(x,R(x,y,z) / (x * R(x,y,z))),y,z) = R(x,y,z) * K(R(x,y,z),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,27,a,b,3959,a)].">
      <j1 rule="hyper" parents="65 27 3959"/>
    </justification>
  </clause>

  <clause id="3961">
    <literal><![CDATA[
      R(x,y,z) * K(R(x,y,z),x \ 1) = R((x \ 1) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(2618(a,1),3960(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2618 3960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3962">
    <literal><![CDATA[
      R(x,y,z) \ R(T(x,x \ 1),y,z) = K(R(x,y,z),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,1170,a,b,3961,a)].">
      <j1 rule="hyper" parents="119 1170 3961"/>
    </justification>
  </clause>

  <clause id="3964">
    <literal><![CDATA[
      a(R(x,y,z),1 / x,x) = K(R(x,y,z),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,2640,a(flip),b,3962,a)].">
      <j1 rule="hyper" parents="65 2640 3962"/>
    </justification>
  </clause>

  <clause id="3965">
    <literal><![CDATA[
      x * ((x \ R(x,y,z)) / R(x,y,z)) = a(R(x,y,z),1 / x,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,3708,a,b,3964,a)].">
      <j1 rule="hyper" parents="299 3708 3964"/>
    </justification>
  </clause>

  <clause id="3966">
    <literal><![CDATA[
      x * L(x \ 1,R(x,y,z),1 / x) = a(R(x,y,z),1 / x,x)
    ]]></literal>
    <justification jstring="[para(2041(a,2),3965(a,1,2))].">
      <j1 rule="para" parents="2041 3965"/>
    </justification>
  </clause>

  <clause id="3967">
    <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(3246(a,1),3762(a,1,2))].">
      <j1 rule="para" parents="3246 3762"/>
    </justification>
  </clause>

  <clause id="3968">
    <literal><![CDATA[
      L(x,y * K(z \ 1,z),u) = (u * y) \ (u * (y * x))
    ]]></literal>
    <justification jstring="[para(3336(a,1),3952(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3336 3952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3969">
    <literal><![CDATA[
      L(x,y * K(z \ 1,z),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,18,a,b,3968,a),flip(a)].">
      <j1 rule="hyper" parents="299 18 3968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3971">
    <literal><![CDATA[
      L(x,K(y \ 1,y) * z,u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(3205(a,2),3969(a,1,2))].">
      <j1 rule="para" parents="3205 3969"/>
    </justification>
  </clause>

  <clause id="3972">
    <literal><![CDATA[
      L(x,T(1 / y,z) \ u,w) = L(x,T(y \ 1,z) \ u,w)
    ]]></literal>
    <justification jstring="[para(3694(a,1),3969(a,1,2))].">
      <j1 rule="para" parents="3694 3969"/>
    </justification>
  </clause>

  <clause id="3973">
    <literal><![CDATA[
      L(x,T((y \ 1) \ 1,z) \ u,w) = L(x,T(y,z) \ u,w)
    ]]></literal>
    <justification jstring="[para(76(a,1),3972(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="76 3972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3974">
    <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(65,a,3833,a(flip),b,3967,a)].">
      <j1 rule="hyper" parents="65 3833 3967"/>
    </justification>
  </clause>

  <clause id="3975">
    <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(2968(a,1),3974(a,1,2))].">
      <j1 rule="para" parents="2968 3974"/>
    </justification>
  </clause>

  <clause id="3976">
    <literal><![CDATA[
      R(x,y * K(z \ 1,z),u) = R(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,2975,a(flip),b,3975,a),flip(a)].">
      <j1 rule="hyper" parents="65 2975 3975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3978">
    <literal><![CDATA[
      R(x,1 / y,z) = R(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[para(1287(a,1),3976(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1287 3976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3979">
    <literal><![CDATA[
      R(x,(y \ 1) \ 1,z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(1492(a,1),3976(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1492 3976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3982">
    <literal><![CDATA[
      R(x,1 / y,1 / (1 / z)) = R(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,3403,a(flip),b,3978,a),flip(a)].">
      <j1 rule="hyper" parents="299 3403 3978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3983">
    <literal><![CDATA[
      R(x,y,z) * (((y \ 1) \ 1) * z) = (x * ((y \ 1) \ 1)) * z
    ]]></literal>
    <justification jstring="[para(3979(a,1),103(a,1,1))].">
      <j1 rule="para" parents="3979 103"/>
    </justification>
  </clause>

  <clause id="3984">
    <literal><![CDATA[
      R(x,1 / y,(1 / z) \ 1) = R(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(3442,a,3982,a)].">
      <j1 rule="hyper" parents="3442 3982"/>
    </justification>
  </clause>

  <clause id="3985">
    <literal><![CDATA[
      (x * ((y \ 1) \ 1)) * z != u * (((y \ 1) \ 1) * z)
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(3983(a,1),46(a,1))].">
      <j1 rule="para" parents="3983 46"/>
    </justification>
  </clause>

  <clause id="3986">
    <literal><![CDATA[
      K(T(x,y) \ 1,T(x,y)) * (z / T(1 / (1 / x),y)) = z / ((1 / T(x,y)) \ 1)
    ]]></literal>
    <justification jstring="[para(2635(a,1),3270(a,1,1))].">
      <j1 rule="para" parents="2635 3270"/>
    </justification>
  </clause>

  <clause id="3987">
    <literal><![CDATA[
      K(x \ 1,x) * (y / T(1 / (1 / x),z)) = y / ((1 / T(x,z)) \ 1)
    ]]></literal>
    <justification jstring="[para(3716(a,1),3986(a,1,1))].">
      <j1 rule="para" parents="3716 3986"/>
    </justification>
  </clause>

  <clause id="3988">
    <literal><![CDATA[
      K(x \ 1,x) * (y / T(1 / (1 / x),z)) = y / T(x,z)
    ]]></literal>
    <justification jstring="[para(79(a,1),3987(a,2,2))].">
      <j1 rule="para" parents="79 3987"/>
    </justification>
  </clause>

  <clause id="3991">
    <literal><![CDATA[
      ((x \ 1) \ 1) * (y / T(x,z)) = x * (y / T(1 / (1 / x),z))
    ]]></literal>
    <justification jstring="[para(3988(a,1),2673(a,1,2))].">
      <j1 rule="para" parents="3988 2673"/>
    </justification>
  </clause>

  <clause id="3992">
    <literal><![CDATA[
      (K(x \ 1,x) * (y * (z * u))) \ ((K(x \ 1,x) * (y * z)) * u) = a(y * K(x \ 1,x),z,u)
    ]]></literal>
    <justification jstring="[para(3246(a,1),3309(a,1,2,1))].">
      <j1 rule="para" parents="3246 3309"/>
    </justification>
  </clause>

  <clause id="3993">
    <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(2591(a,1),3335(a,1,1,2))].">
      <j1 rule="para" parents="2591 3335"/>
    </justification>
  </clause>

  <clause id="3994">
    <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(3301(a,2),3763(a,1,1,1,2))].">
      <j1 rule="para" parents="3301 3763"/>
    </justification>
  </clause>

  <clause id="3995">
    <literal><![CDATA[
      (K(x \ 1,x) * (y * (z * u))) \ (K(x \ 1,x) * ((y * z) * u)) = a(y * K(x \ 1,x),z,u)
    ]]></literal>
    <justification jstring="[para(2495(a,1),3992(a,1,2))].">
      <j1 rule="para" parents="2495 3992"/>
    </justification>
  </clause>

  <clause id="3996">
    <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(2591(a,1),3993(a,1,2))].">
      <j1 rule="para" parents="2591 3993"/>
    </justification>
  </clause>

  <clause id="3997">
    <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(3344(a,1),3994(a,1,1))].">
      <j1 rule="para" parents="3344 3994"/>
    </justification>
  </clause>

  <clause id="3998">
    <literal><![CDATA[
      L(a(x,y,z),x * (y * z),K(u \ 1,u)) = a(x * K(u \ 1,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(913,a,3995,a)].">
      <j1 rule="hyper" parents="913 3995"/>
    </justification>
  </clause>

  <clause id="3999">
    <literal><![CDATA[
      a(x * K(y \ 1,y),z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(2497,a,3998,a),flip(a)].">
      <j1 rule="hyper" parents="2497 3998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4001">
    <literal><![CDATA[
      a(T(1 / x,y),z,u) = a(T(x \ 1,y),z,u)
    ]]></literal>
    <justification jstring="[para(3691(a,1),3999(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3691 3999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4002">
    <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(65,a,3422,a(flip),b,3996,a)].">
      <j1 rule="hyper" parents="65 3422 3996"/>
    </justification>
  </clause>

  <clause id="4003">
    <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),3997(a,1,1,1))].">
      <j1 rule="para" parents="14 3997"/>
    </justification>
  </clause>

  <clause id="4004">
    <literal><![CDATA[
      a(x,y,K(z,z \ 1) * u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,2762,a(flip),b,4003,a),flip(a)].">
      <j1 rule="hyper" parents="65 2762 4003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4006">
    <literal><![CDATA[
      ((x * (y * (K(z,z \ 1) * u))) \ ((x * y) * u)) * K(z,z \ 1) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,3763,a,b,4004,a)].">
      <j1 rule="hyper" parents="65 3763 4004"/>
    </justification>
  </clause>

  <clause id="4007">
    <literal><![CDATA[
      a(x,y,z * (u * (1 / w))) = a(x,y,z * (u * (w \ 1)))
    ]]></literal>
    <justification jstring="[para(3340(a,1),4004(a,1,3))].">
      <j1 rule="para" parents="3340 4004"/>
    </justification>
  </clause>

  <clause id="4009">
    <literal><![CDATA[
      ((x * (y * (z * K(u,u \ 1)))) \ ((x * y) * z)) * K(u,u \ 1) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(3197(a,1),4006(a,1,1,1,2,2))].">
      <j1 rule="para" parents="3197 4006"/>
    </justification>
  </clause>

  <clause id="4010">
    <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(3344(a,1),4002(a,1,1))].">
      <j1 rule="para" parents="3344 4002"/>
    </justification>
  </clause>

  <clause id="4011">
    <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),4010(a,1,1,1))].">
      <j1 rule="para" parents="14 4010"/>
    </justification>
  </clause>

  <clause id="4012">
    <literal><![CDATA[
      a(x,K(y,y \ 1) * z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,2762,a(flip),b,4011,a),flip(a)].">
      <j1 rule="hyper" parents="65 2762 4011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4014">
    <literal><![CDATA[
      a(x,y * K(z \ 1,z),u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(3219(a,1),4012(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3219 4012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4015">
    <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),3547(a,1,1,1))].">
      <j1 rule="para" parents="11 3547"/>
    </justification>
  </clause>

  <clause id="4017">
    <literal><![CDATA[
      x * ((y * ((1 / y) * (z * y))) / y) != (1 / y) * (z * y)
    ]]></literal>
    <literal><![CDATA[
      L(z,y,y \ 1) \ ((1 / y) * (z * y)) = x
    ]]></literal>
    <justification jstring="[para(4015(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="4015 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4018">
    <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(1866(a,1),2155(a,2,1))].">
      <j1 rule="para" parents="1866 2155"/>
    </justification>
  </clause>

  <clause id="4019">
    <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(299,a,1455,a(flip),b,4018,a),flip(a)].">
      <j1 rule="hyper" parents="299 1455 4018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4021">
    <literal><![CDATA[
      T(x \ R(x,y,z),x \ L(x,u,w)) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(1455(a,1),4019(a,1,1))].">
      <j1 rule="para" parents="1455 4019"/>
    </justification>
  </clause>

  <clause id="4022">
    <literal><![CDATA[
      T(x \ L(x,y,z),x \ R(x,u,w)) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(56,a,4021,a)].">
      <j1 rule="hyper" parents="56 4021"/>
    </justification>
  </clause>

  <clause id="4023">
    <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(3510(a,1),2970(a,2,1))].">
      <j1 rule="para" parents="3510 2970"/>
    </justification>
  </clause>

  <clause id="4024">
    <literal><![CDATA[
      (x \ T(x,(x \ 1) * y)) * y = y * K(((1 / x) * y) \ y,(x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(2660(a,1),4023(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2660 4023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4025">
    <literal><![CDATA[
      (x \ T(x,(x \ 1) * y)) * y = y * K(((x \ 1) * y) \ y,(x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(3571(a,1),4024(a,2,2))].">
      <j1 rule="para" parents="3571 4024"/>
    </justification>
  </clause>

  <clause id="4026">
    <literal><![CDATA[
      (((x \ 1) * y) \ y) * ((x \ 1) * y) = (x \ T(x,(x \ 1) * y)) * y
    ]]></literal>
    <justification jstring="[hyper(299,a,287,a(flip),b,4025,a)].">
      <j1 rule="hyper" parents="299 287 4025"/>
    </justification>
  </clause>

  <clause id="4027">
    <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),1345(a,1,2,1,1))].">
      <j1 rule="para" parents="94 1345"/>
    </justification>
  </clause>

  <clause id="4028">
    <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(1335,a,4027,a),flip(a)].">
      <j1 rule="hyper" parents="1335 4027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4029">
    <literal><![CDATA[
      (x * y) \ ((x * (y * z)) * R((x * (y * z)) \ (x * y),u,w)) = L(z,y,x) * R(L(z,y,x) \ 1,u,w)
    ]]></literal>
    <justification jstring="[hyper(631,a,4027,a)].">
      <j1 rule="hyper" parents="631 4027"/>
    </justification>
  </clause>

  <clause id="4030">
    <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(1147(a,1),4028(a,2,2))].">
      <j1 rule="para" parents="1147 4028"/>
    </justification>
  </clause>

  <clause id="4031">
    <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(490,a,4030,a),flip(a)].">
      <j1 rule="hyper" parents="490 4030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4032">
    <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(65,a,1276,a(flip),b,4031,a),flip(a)].">
      <j1 rule="hyper" parents="65 1276 4031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4033">
    <literal><![CDATA[
      L(x * R(x \ 1,x,1 / x),y,z) / L(x,y,z) = (x / L(x,y,z)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(4031(a,1),2870(a,1,1))].">
      <j1 rule="para" parents="4031 2870"/>
    </justification>
  </clause>

  <clause id="4034">
    <literal><![CDATA[
      L(x * T(1 * (x \ 1),x),y,z) / L(x,y,z) = (x / L(x,y,z)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(2868(a,1),4033(a,1,1,1,2))].">
      <j1 rule="para" parents="2868 4033"/>
    </justification>
  </clause>

  <clause id="4035">
    <literal><![CDATA[
      L(x * T(x \ 1,x),y,z) / L(x,y,z) = (x / L(x,y,z)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(7(a,1),4034(a,1,1,1,2,1))].">
      <j1 rule="para" parents="7 4034"/>
    </justification>
  </clause>

  <clause id="4036">
    <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(1869(a,1),4032(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1869 4032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4037">
    <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(299,a,2422,a(flip),b,4036,a),flip(a)].">
      <j1 rule="hyper" parents="299 2422 4036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4038">
    <literal><![CDATA[
      (x \ 1) / (x \ L(x,y,z)) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(37,a,253,a(flip),b,4037,a),flip(a)].">
      <j1 rule="hyper" parents="37 253 4037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4039">
    <literal><![CDATA[
      x / ((1 / x) \ L(1 / x,y,z)) = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(79(a,1),4038(a,1,1))].">
      <j1 rule="para" parents="79 4038"/>
    </justification>
  </clause>

  <clause id="4040">
    <literal><![CDATA[
      x / (x * L(x \ 1,y,z)) = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(2830(a,1),4039(a,1,2))].">
      <j1 rule="para" parents="2830 4039"/>
    </justification>
  </clause>

  <clause id="4041">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) * (x * L(x \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(143,a,4040,a)].">
      <j1 rule="hyper" parents="143 4040"/>
    </justification>
  </clause>

  <clause id="4042">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) \ x = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(3110,a,4041,a)].">
      <j1 rule="hyper" parents="3110 4041"/>
    </justification>
  </clause>

  <clause id="4043">
    <literal><![CDATA[
      L(1 / (1 / x),y,z) \ 1 = (L(x,y,z) / x) \ (1 / x)
    ]]></literal>
    <justification jstring="[para(1820(a,1),4042(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1820 4042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4044">
    <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(299,a,2254,a(flip),b,2255,a),flip(a)].">
      <j1 rule="hyper" parents="299 2254 2255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4045">
    <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(3855(a,2),4044(a,1,1))].">
      <j1 rule="para" parents="3855 4044"/>
    </justification>
  </clause>

  <clause id="4046">
    <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(4045(a,1),275(a,1))].">
      <j1 rule="para" parents="4045 275"/>
    </justification>
  </clause>

  <clause id="4047">
    <literal><![CDATA[
      (x * (y \ z)) * (u * (((x * (y \ z)) \ z) / u)) = ((u * ((y / x) / u)) * x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(4046,a,3501,a),flip(a)].">
      <j1 rule="hyper" parents="4046 3501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4048">
    <literal><![CDATA[
      (x * (y \ z)) * (u * (((x * (y \ z)) \ z) / u)) = (x * (u * ((x \ y) / u))) * (y \ z)
    ]]></literal>
    <justification jstring="[para(3501(a,1),4047(a,2,1))].">
      <j1 rule="para" parents="3501 4047"/>
    </justification>
  </clause>

  <clause id="4049">
    <literal><![CDATA[
      (x * (y * ((x \ (z / u)) / y))) * ((z / u) \ z) = (x * u) * (y * (((x * ((z / u) \ z)) \ z) / y))
    ]]></literal>
    <justification jstring="[para(79(a,1),4048(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="79 4048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4050">
    <literal><![CDATA[
      (x * (y * ((x \ (z / u)) / y))) * ((z / u) \ z) = (x * u) * (y * (((x * u) \ z) / y))
    ]]></literal>
    <justification jstring="[para(79(a,1),4049(a,2,2,2,1,1,2))].">
      <j1 rule="para" parents="79 4049"/>
    </justification>
  </clause>

  <clause id="4051">
    <literal><![CDATA[
      (x * (y * ((x \ (z / u)) / y))) * u = (x * u) * (y * (((x * u) \ z) / y))
    ]]></literal>
    <justification jstring="[para(79(a,1),4050(a,1,2))].">
      <j1 rule="para" parents="79 4050"/>
    </justification>
  </clause>

  <clause id="4052">
    <literal><![CDATA[
      T(x \ 1,x) \ R(y,T(x,x \ 1),T(x,x \ 1) \ 1) = T(((x \ 1) \ 1) * T(y,x),T(x,x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(1490(a,1),3753(a,1,1))].">
      <j1 rule="para" parents="1490 3753"/>
    </justification>
  </clause>

  <clause id="4053">
    <literal><![CDATA[
      T(x \ 1,x) \ R(y,T(x,x \ 1),T(x \ 1,x)) = T(((x \ 1) \ 1) * T(y,x),T(x,x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(1490(a,1),4052(a,1,2,3))].">
      <j1 rule="para" parents="1490 4052"/>
    </justification>
  </clause>

  <clause id="4054">
    <literal><![CDATA[
      T(((x \ 1) \ 1) * T(y,x),T(x,x \ 1) \ 1) = T(x \ 1,x) \ R(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(2880(a,1),4053(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2880 4053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4055">
    <literal><![CDATA[
      T(x \ 1,x) \ R(T(x,y) \ 1,x,x \ 1) = T(T(x,y) \ x,T(x,x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(3292(a,1),4054(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3292 4054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4056">
    <literal><![CDATA[
      T(x * T(y,y \ 1),T(y,y \ 1) \ 1) = T(y \ 1,y) \ R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(3749(a,1),4054(a,1,1))].">
      <j1 rule="para" parents="3749 4054"/>
    </justification>
  </clause>

  <clause id="4057">
    <literal><![CDATA[
      T(x * T(y,y \ 1),T(y \ 1,y)) = T(y \ 1,y) \ R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(1490(a,1),4056(a,1,2))].">
      <j1 rule="para" parents="1490 4056"/>
    </justification>
  </clause>

  <clause id="4058">
    <literal><![CDATA[
      T(x \ 1,x) \ R(y,x,x \ 1) = T(y * T(x,x \ 1),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,3741,a(flip),b,4057,a),flip(a)].">
      <j1 rule="hyper" parents="65 3741 4057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4059">
    <literal><![CDATA[
      T(x \ 1,x) \ R(y,x,x \ 1) = R((x \ 1) \ y,1 / x,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,3780,a(flip),b,4058,a),flip(a)].">
      <j1 rule="hyper" parents="299 3780 4058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4060">
    <literal><![CDATA[
      T(x \ 1,x) \ R(y,x,x \ 1) = R((x \ 1) \ y,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,3978,a(flip),b,4059,a),flip(a)].">
      <j1 rule="hyper" parents="299 3978 4059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4061">
    <literal><![CDATA[
      R((x \ 1) \ (T(x,y) \ 1),x \ 1,x) = T(T(x,y) \ x,T(x,x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,4060,a(flip),b,4055,a)].">
      <j1 rule="hyper" parents="65 4060 4055"/>
    </justification>
  </clause>

  <clause id="4062">
    <literal><![CDATA[
      R((x \ 1) \ (T(x,y) \ 1),x \ 1,x) = T(T(x,y) \ x,T(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(1490(a,1),4061(a,2,2))].">
      <j1 rule="para" parents="1490 4061"/>
    </justification>
  </clause>

  <clause id="4063">
    <literal><![CDATA[
      R((x \ 1) \ (T(x,y) \ 1),x \ 1,x) = T(T(x,y) \ x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,3741,a(flip),b,4062,a),flip(a)].">
      <j1 rule="hyper" parents="299 3741 4062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4064">
    <literal><![CDATA[
      R((x \ 1) \ (T(x,y) \ 1),x \ 1,x) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(299,a,3679,a(flip),b,4063,a),flip(a)].">
      <j1 rule="hyper" parents="299 3679 4063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4065">
    <literal><![CDATA[
      (x \ 1) \ (T(x,y) \ 1) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(3951,a,4064,a),flip(a)].">
      <j1 rule="hyper" parents="3951 4064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4066">
    <literal><![CDATA[
      (x \ 1) * (T(x,y) \ x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(144,a,4065,a)].">
      <j1 rule="hyper" parents="144 4065"/>
    </justification>
  </clause>

  <clause id="4067">
    <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(3984(a,1),3944(a,1,1))].">
      <j1 rule="para" parents="3984 3944"/>
    </justification>
  </clause>

  <clause id="4068">
    <literal><![CDATA[
      (x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ (1 * x)) * y) / ((1 / x) \ 1)
    ]]></literal>
    <justification jstring="[para(3852(a,1),4067(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3852 4067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4069">
    <literal><![CDATA[
      (x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ x) * y) / ((1 / x) \ 1)
    ]]></literal>
    <justification jstring="[para(7(a,1),4068(a,2,1,1,2))].">
      <j1 rule="para" parents="7 4068"/>
    </justification>
  </clause>

  <clause id="4070">
    <literal><![CDATA[
      (x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ x) * y) / x
    ]]></literal>
    <justification jstring="[para(79(a,1),4069(a,2,2))].">
      <j1 rule="para" parents="79 4069"/>
    </justification>
  </clause>

  <clause id="4071">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ 1) = ((x \ y) * x) / y
    ]]></literal>
    <justification jstring="[para(3688(a,1),4070(a,1,1))].">
      <j1 rule="para" parents="3688 4070"/>
    </justification>
  </clause>

  <clause id="4072">
    <literal><![CDATA[
      (1 / x) * ((y \ x) * y) = ((y \ x) * y) / x
    ]]></literal>
    <justification jstring="[hyper(65,a,3769,a(flip),b,4071,a)].">
      <j1 rule="hyper" parents="65 3769 4071"/>
    </justification>
  </clause>

  <clause id="4073">
    <literal><![CDATA[
      ((x \ y) * x) / y != ((x \ y) * x) * z
    ]]></literal>
    <literal><![CDATA[
      y \ 1 = z
    ]]></literal>
    <justification jstring="[para(4071(a,1),45(a,1))].">
      <j1 rule="para" parents="4071 45"/>
    </justification>
  </clause>

  <clause id="4074">
    <literal><![CDATA[
      (x \ (1 / x)) * (y / (((x \ 1) * x) * (((x \ 1) \ 1) \ z))) = T(y / ((1 / x) \ z),(x \ 1) \ ((x \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(1705(a,1),2386(a,1,1))].">
      <j1 rule="para" parents="1705 2386"/>
    </justification>
  </clause>

  <clause id="4075">
    <literal><![CDATA[
      (x \ (1 / x)) * (y / (K(x,x \ 1) * (((x \ 1) \ 1) \ z))) = T(y / ((1 / x) \ z),(x \ 1) \ ((x \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(2612(a,2),4074(a,1,2,2,1))].">
      <j1 rule="para" parents="2612 4074"/>
    </justification>
  </clause>

  <clause id="4076">
    <literal><![CDATA[
      T(x / ((1 / y) \ z),(y \ 1) \ ((y \ 1) \ 1)) = (y \ (1 / y)) * (x / (y \ z))
    ]]></literal>
    <justification jstring="[para(2745(a,1),4075(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2745 4075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4077">
    <literal><![CDATA[
      T(x / ((1 / y) \ z),(y \ 1) \ ((y \ 1) \ 1)) = (y \ 1) * (y \ (x / (y \ z)))
    ]]></literal>
    <justification jstring="[hyper(299,a,1710,a(flip),b,4076,a),flip(a)].">
      <j1 rule="hyper" parents="299 1710 4076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4078">
    <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(1490(a,1),2431(a,1,1,2,1))].">
      <j1 rule="para" parents="1490 2431"/>
    </justification>
  </clause>

  <clause id="4079">
    <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(1940(a,1),4078(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1940 4078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4081">
    <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(3748(a,1),4079(a,2,1))].">
      <j1 rule="para" parents="3748 4079"/>
    </justification>
  </clause>

  <clause id="4082">
    <literal><![CDATA[
      K((x \ R(x,y,z)) \ (x \ 1),x \ R(x,y,z)) = R(1,y,z)
    ]]></literal>
    <justification jstring="[para(220(a,1),4081(a,2,1))].">
      <j1 rule="para" parents="220 4081"/>
    </justification>
  </clause>

  <clause id="4083">
    <literal><![CDATA[
      K((x \ R(x,y,z)) \ (x \ 1),x \ R(x,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(299,a,360,a(flip),b,4082,a),flip(a)].">
      <j1 rule="hyper" parents="299 360 4082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4086">
    <literal><![CDATA[
      ((x \ R(x,y,z)) \ (x \ 1)) * (x \ R(x,y,z)) = (x \ 1) * 1
    ]]></literal>
    <justification jstring="[para(4083(a,1),287(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4083 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4087">
    <literal><![CDATA[
      (x \ 1) / (x \ R(x,y,z)) = (x \ R(x,y,z)) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(120,a,8,a(flip),b,4086,a)].">
      <j1 rule="hyper" parents="120 8 4086"/>
    </justification>
  </clause>

  <clause id="4089">
    <literal><![CDATA[
      (1 / x) * T((1 / ((x \ 1) \ 1)) \ (((x \ 1) \ 1) \ y),(x \ 1) \ 1) = (x \ (x \ y)) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(1689(a,1),2790(a,1,1))].">
      <j1 rule="para" parents="1689 2790"/>
    </justification>
  </clause>

  <clause id="4090">
    <literal><![CDATA[
      (1 / x) * T((x \ 1) \ (((x \ 1) \ 1) \ y),(x \ 1) \ 1) = (x \ (x \ y)) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(76(a,1),4089(a,1,2,1,1))].">
      <j1 rule="para" parents="76 4089"/>
    </justification>
  </clause>

  <clause id="4092">
    <literal><![CDATA[
      (1 / x) * T(x \ ((x \ 1) \ y),(x \ 1) \ 1) = (x \ (x \ y)) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(769(a,1),4090(a,1,2,1))].">
      <j1 rule="para" parents="769 4090"/>
    </justification>
  </clause>

  <clause id="4093">
    <literal><![CDATA[
      (1 / x) * T(x \ ((x \ 1) \ y),x) = (x \ (x \ y)) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(3739(a,1),4092(a,1,2))].">
      <j1 rule="para" parents="3739 4092"/>
    </justification>
  </clause>

  <clause id="4094">
    <literal><![CDATA[
      (x \ y) \ T(z * (x \ 1),(x \ 1) \ ((x \ 1) \ 1)) = ((1 / x) \ y) \ (x * (((x \ 1) \ 1) \ (z * x)))
    ]]></literal>
    <justification jstring="[para(76(a,1),3689(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="76 3689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4096">
    <literal><![CDATA[
      (x \ y) \ T(z * (x \ 1),(x \ 1) \ ((x \ 1) \ 1)) = ((1 / x) \ y) \ (x * (x \ (z * ((x \ 1) \ 1))))
    ]]></literal>
    <justification jstring="[para(3774(a,1),4094(a,2,2,2))].">
      <j1 rule="para" parents="3774 4094"/>
    </justification>
  </clause>

  <clause id="4097">
    <literal><![CDATA[
      (x \ y) \ T(z * (x \ 1),(x \ 1) \ ((x \ 1) \ 1)) = ((1 / x) \ y) \ (z * ((x \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(10(a,1),4096(a,2,2))].">
      <j1 rule="para" parents="10 4096"/>
    </justification>
  </clause>

  <clause id="4099">
    <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),1837(a,1,2,1,2,1))].">
      <j1 rule="para" parents="94 1837"/>
    </justification>
  </clause>

  <clause id="4100">
    <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(65,a,1320,a(flip),b,4099,a),flip(a)].">
      <j1 rule="hyper" parents="65 1320 4099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4101">
    <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(1319(a,1),4100(a,2,2))].">
      <j1 rule="para" parents="1319 4100"/>
    </justification>
  </clause>

  <clause id="4102">
    <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(490,a,4101,a),flip(a)].">
      <j1 rule="hyper" parents="490 4101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4103">
    <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),4102(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 4102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4104">
    <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(299,a,2585,a,b,4103,a),flip(a)].">
      <j1 rule="hyper" parents="299 2585 4103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4105">
    <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(1885(a,1),4104(a,1,1))].">
      <j1 rule="para" parents="1885 4104"/>
    </justification>
  </clause>

  <clause id="4106">
    <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),1873(a,2,2,1,1))].">
      <j1 rule="para" parents="20 1873"/>
    </justification>
  </clause>

  <clause id="4107">
    <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(1857(a,1),4106(a,1,1))].">
      <j1 rule="para" parents="1857 4106"/>
    </justification>
  </clause>

  <clause id="4108">
    <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(1858(a,1),4107(a,1,1,1))].">
      <j1 rule="para" parents="1858 4107"/>
    </justification>
  </clause>

  <clause id="4109">
    <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(549,a,4108,a),flip(a)].">
      <j1 rule="hyper" parents="549 4108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4110">
    <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(812(a,1),4109(a,2,1,2))].">
      <j1 rule="para" parents="812 4109"/>
    </justification>
  </clause>

  <clause id="4111">
    <literal><![CDATA[
      R(x,y,z) * ((R(x,y,z) / x) \ ((1 / x) * 1)) = R(x * L(x \ 1,R(x,y,z),1 / x),y,z)
    ]]></literal>
    <justification jstring="[para(1833(a,1),4109(a,1,2))].">
      <j1 rule="para" parents="1833 4109"/>
    </justification>
  </clause>

  <clause id="4112">
    <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(1961(a,1),4110(a,1,2))].">
      <j1 rule="para" parents="1961 4110"/>
    </justification>
  </clause>

  <clause id="4113">
    <literal><![CDATA[
      R(x,y,z) * ((1 / x) * (R(x,y,z) \ x)) = R(x * (1 / x),y,z)
    ]]></literal>
    <justification jstring="[para(193(a,1),4112(a,2,1,2))].">
      <j1 rule="para" parents="193 4112"/>
    </justification>
  </clause>

  <clause id="4114">
    <literal><![CDATA[
      R(x,y,z) * ((1 / x) * (R(x,y,z) \ x)) = R(K(x,x \ 1),y,z)
    ]]></literal>
    <justification jstring="[para(2585(a,2),4113(a,2,1))].">
      <j1 rule="para" parents="2585 4113"/>
    </justification>
  </clause>

  <clause id="4115">
    <literal><![CDATA[
      R(x,y,z) * ((1 / x) * (R(x,y,z) \ x)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,2722,a(flip),b,4114,a),flip(a)].">
      <j1 rule="hyper" parents="299 2722 4114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4118">
    <literal><![CDATA[
      R(x * L(x \ 1,R(x,y,z),1 / x),y,z) = R(x,y,z) * ((R(x,y,z) / x) \ (1 / x))
    ]]></literal>
    <justification jstring="[para(8(a,1),4111(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8 4111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4119">
    <literal><![CDATA[
      R(x,y,z) * ((R(x,y,z) / x) \ (1 / x)) = R(a(R(x,y,z),1 / x,x),y,z)
    ]]></literal>
    <justification jstring="[para(3966(a,1),4118(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3966 4118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4120">
    <literal><![CDATA[
      R(x,y,z) * ((R(x,y,z) / x) \ (1 / x)) = R(K(R(x,y,z),x \ 1),y,z)
    ]]></literal>
    <justification jstring="[para(3964(a,1),4119(a,2,1))].">
      <j1 rule="para" parents="3964 4119"/>
    </justification>
  </clause>

  <clause id="4121">
    <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),1876(a,2,2,1,1))].">
      <j1 rule="para" parents="18 1876"/>
    </justification>
  </clause>

  <clause id="4122">
    <literal><![CDATA[
      (x * y) \ (x * ((y * z) * L((y * z) \ (x \ (x * y)),u,w))) = L(z,y,x) * L(L(z,y,x) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(1150(a,1),4121(a,1,2))].">
      <j1 rule="para" parents="1150 4121"/>
    </justification>
  </clause>

  <clause id="4123">
    <literal><![CDATA[
      (x * y) \ (x * ((y * z) * L((y * z) \ y,u,w))) = L(z,y,x) * L(L(z,y,x) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(9(a,1),4122(a,1,2,2,2,1,2))].">
      <j1 rule="para" parents="9 4122"/>
    </justification>
  </clause>

  <clause id="4124">
    <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(993(a,1),4123(a,1,2,2))].">
      <j1 rule="para" parents="993 4123"/>
    </justification>
  </clause>

  <clause id="4125">
    <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(493,a,4124,a),flip(a)].">
      <j1 rule="hyper" parents="493 4124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4127">
    <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(812(a,1),4125(a,2,1,2))].">
      <j1 rule="para" parents="812 4125"/>
    </justification>
  </clause>

  <clause id="4128">
    <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(1804(a,1),4125(a,1,2))].">
      <j1 rule="para" parents="1804 4125"/>
    </justification>
  </clause>

  <clause id="4129">
    <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(1361(a,1),4127(a,1,2))].">
      <j1 rule="para" parents="1361 4127"/>
    </justification>
  </clause>

  <clause id="4130">
    <literal><![CDATA[
      L(x,y,z) * ((1 / x) * (L(x,y,z) \ x)) = L(x * (1 / x),y,z)
    ]]></literal>
    <justification jstring="[para(193(a,1),4129(a,2,1,2))].">
      <j1 rule="para" parents="193 4129"/>
    </justification>
  </clause>

  <clause id="4131">
    <literal><![CDATA[
      L(x,y,z) * ((1 / x) * (L(x,y,z) \ x)) = L(K(x,x \ 1),y,z)
    ]]></literal>
    <justification jstring="[para(2585(a,2),4130(a,2,1))].">
      <j1 rule="para" parents="2585 4130"/>
    </justification>
  </clause>

  <clause id="4132">
    <literal><![CDATA[
      L(x,y,z) * ((1 / x) * (L(x,y,z) \ x)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,3416,a(flip),b,4131,a),flip(a)].">
      <j1 rule="hyper" parents="299 3416 4131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4134">
    <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),4128(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8 4128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4135">
    <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(2439(a,1),4134(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2439 4134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4136">
    <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(299,a,4105,a(flip),b,4135,a),flip(a)].">
      <j1 rule="hyper" parents="299 4105 4135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4137">
    <literal><![CDATA[
      (L(x,y,z) / x) \ (1 / x) = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,2585,a(flip),b,4136,a),flip(a)].">
      <j1 rule="hyper" parents="36 2585 4136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4138">
    <literal><![CDATA[
      L(1 / (1 / x),y,z) \ 1 = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,4043,a,b,4137,a)].">
      <j1 rule="hyper" parents="65 4043 4137"/>
    </justification>
  </clause>

  <clause id="4139">
    <literal><![CDATA[
      L(1 / (1 / x),y,z) = 1 / (1 / L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(192,a,4138,a),flip(a)].">
      <j1 rule="hyper" parents="192 4138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4140">
    <literal><![CDATA[
      1 / L(x \ 1,y,z) = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(76(a,1),4138(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="76 4138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4141">
    <literal><![CDATA[
      1 / (1 / L(x \ 1,y,z)) = L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(76(a,1),4139(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="76 4139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4142">
    <literal><![CDATA[
      L(1 / (1 / (x \ y)),x,1 / x) = 1 / (1 / ((1 / x) * y))
    ]]></literal>
    <justification jstring="[para(518(a,1),4139(a,2,2,2))].">
      <j1 rule="para" parents="518 4139"/>
    </justification>
  </clause>

  <clause id="4143">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) \ 1 = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(186,a,4140,a)].">
      <j1 rule="hyper" parents="186 4140"/>
    </justification>
  </clause>

  <clause id="4144">
    <literal><![CDATA[
      L(1 / x,x,y) \ 1 = 1 / ((y * x) \ y)
    ]]></literal>
    <justification jstring="[para(214(a,1),4140(a,1,2)),flip(a)].">
      <j1 rule="para" parents="214 4140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4145">
    <literal><![CDATA[
      1 / L(x \ 1,y,z \ 1) = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(2470(a,1),4140(a,2,1))].">
      <j1 rule="para" parents="2470 4140"/>
    </justification>
  </clause>

  <clause id="4146">
    <literal><![CDATA[
      x \ 1 != 1 / ((y * z) \ y)
    ]]></literal>
    <literal><![CDATA[
      L(1 / z,z,y) = x
    ]]></literal>
    <justification jstring="[para(4144(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="4144 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4147">
    <literal><![CDATA[
      L(1 / (x \ y),x \ y,x) = 1 / (1 / (y \ x))
    ]]></literal>
    <justification jstring="[para(366(a,1),4141(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="366 4141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4148">
    <literal><![CDATA[
      T(x,L(1 / y,z,u) * w) = T(x,L(y \ 1,z,u) * w)
    ]]></literal>
    <justification jstring="[para(4141(a,1),3871(a,1,2,1))].">
      <j1 rule="para" parents="4141 3871"/>
    </justification>
  </clause>

  <clause id="4149">
    <literal><![CDATA[
      L((x \ 1) \ 1,y,z) = (L(x,y,z) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(76(a,1),4143(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="76 4143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4150">
    <literal><![CDATA[
      L(L(x,y,z),L(x,y,z),L(x,y,z)) = L((x \ 1) \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,2806,a,b,4149,a)].">
      <j1 rule="hyper" parents="299 2806 4149"/>
    </justification>
  </clause>

  <clause id="4151">
    <literal><![CDATA[
      L(1 / (x \ y),x \ y,x) = ((y \ x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(299,a,1691,a(flip),b,4147,a),flip(a)].">
      <j1 rule="hyper" parents="299 1691 4147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4152">
    <literal><![CDATA[
      x * ((x \ y) * (1 / (x \ y))) = y * (1 / (1 / (y \ x)))
    ]]></literal>
    <justification jstring="[para(4147(a,1),482(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4147 482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4154">
    <literal><![CDATA[
      x * K(x \ y,y \ x) = y * (1 / (1 / (y \ x)))
    ]]></literal>
    <justification jstring="[para(3040(a,1),4152(a,1,2))].">
      <j1 rule="para" parents="3040 4152"/>
    </justification>
  </clause>

  <clause id="4155">
    <literal><![CDATA[
      x \ (y * K(y \ x,x \ y)) = 1 / (1 / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(631,a,4154,a)].">
      <j1 rule="hyper" parents="631 4154"/>
    </justification>
  </clause>

  <clause id="4156">
    <literal><![CDATA[
      L(x \ (1 / (1 / (y \ (y * x)))),x,y) = K((y * x) \ y,y \ (y * x))
    ]]></literal>
    <justification jstring="[para(4155(a,1),479(a,1,1,2))].">
      <j1 rule="para" parents="4155 479"/>
    </justification>
  </clause>

  <clause id="4157">
    <literal><![CDATA[
      (1 / x) \ (1 / (1 / ((1 / x) * y))) = x * (1 / (1 / (x \ y)))
    ]]></literal>
    <justification jstring="[hyper(119,a,4142,a(flip),b,255,a)].">
      <j1 rule="hyper" parents="119 4142 255"/>
    </justification>
  </clause>

  <clause id="4158">
    <literal><![CDATA[
      L(x \ (1 / (1 / x)),x,y) = K((y * x) \ y,y \ (y * x))
    ]]></literal>
    <justification jstring="[para(9(a,1),4156(a,1,1,2,2,2))].">
      <j1 rule="para" parents="9 4156"/>
    </justification>
  </clause>

  <clause id="4159">
    <literal><![CDATA[
      L(K(x \ 1,x),x,y) = K((y * x) \ y,y \ (y * x))
    ]]></literal>
    <justification jstring="[para(1717(a,1),4158(a,1,1))].">
      <j1 rule="para" parents="1717 4158"/>
    </justification>
  </clause>

  <clause id="4160">
    <literal><![CDATA[
      K((x * y) \ x,x \ (x * y)) = K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,3385,a(flip),b,4159,a),flip(a)].">
      <j1 rule="hyper" parents="65 3385 4159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4162">
    <literal><![CDATA[
      K((x * y) \ x,y) = K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(9(a,1),4160(a,1,2))].">
      <j1 rule="para" parents="9 4160"/>
    </justification>
  </clause>

  <clause id="4163">
    <literal><![CDATA[
      K((x \ y) \ 1,x \ y) = K(y \ x,x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),4162(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 4162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4164">
    <literal><![CDATA[
      K(x \ (x / y),y) = K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(12(a,1),4162(a,1,1,1))].">
      <j1 rule="para" parents="12 4162"/>
    </justification>
  </clause>

  <clause id="4165">
    <literal><![CDATA[
      K(T(x / y,T(y,x)) \ 1,T(x / y,T(y,x))) = K(((y * x) / y) \ T(y,x),T(x / y,T(y,x)))
    ]]></literal>
    <justification jstring="[para(1532(a,1),4164(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1532 4164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4166">
    <literal><![CDATA[
      x * K(y \ x,x \ y) = y * (((y \ x) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(4163(a,1),2999(a,1,2))].">
      <j1 rule="para" parents="4163 2999"/>
    </justification>
  </clause>

  <clause id="4167">
    <literal><![CDATA[
      ((x \ y) * z) * K(y \ x,x \ y) = (1 / (1 / (x \ y))) * z
    ]]></literal>
    <justification jstring="[para(4163(a,1),3243(a,1,2))].">
      <j1 rule="para" parents="4163 3243"/>
    </justification>
  </clause>

  <clause id="4168">
    <literal><![CDATA[
      L(K(x \ y,y \ x),z,u) = K((y \ x) \ 1,y \ x)
    ]]></literal>
    <justification jstring="[para(4163(a,1),3385(a,1,1))].">
      <j1 rule="para" parents="4163 3385"/>
    </justification>
  </clause>

  <clause id="4169">
    <literal><![CDATA[
      K((x \ y) \ 1,x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,x \ y) = z
    ]]></literal>
    <justification jstring="[para(4168(a,1),500(a,1)),flip(b)].">
      <j1 rule="para" parents="4168 500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4170">
    <literal><![CDATA[
      L(K(x \ y,y \ x),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,y \ x) = w
    ]]></literal>
    <justification jstring="[para(4168(a,2),4169(a,1))].">
      <j1 rule="para" parents="4168 4169"/>
    </justification>
  </clause>

  <clause id="4171">
    <literal><![CDATA[
      ((x \ (x / y)) * z) * K(y,y \ 1) = (1 / (1 / (x \ (x / y)))) * z
    ]]></literal>
    <justification jstring="[para(3039(a,1),4167(a,1,2))].">
      <j1 rule="para" parents="3039 4167"/>
    </justification>
  </clause>

  <clause id="4172">
    <literal><![CDATA[
      ((x \ (x / (y \ 1))) * z) * K(y \ 1,y) = (1 / (1 / (x \ (x / (y \ 1))))) * z
    ]]></literal>
    <justification jstring="[para(2587(a,1),4171(a,1,2))].">
      <j1 rule="para" parents="2587 4171"/>
    </justification>
  </clause>

  <clause id="4173">
    <literal><![CDATA[
      ((x \ (x / (y \ 1))) * z) * K(y \ 1,y) = (x \ (x / (1 / y))) * z
    ]]></literal>
    <justification jstring="[para(3011(a,1),4172(a,2,1))].">
      <j1 rule="para" parents="3011 4172"/>
    </justification>
  </clause>

  <clause id="4174">
    <literal><![CDATA[
      R((x \ (x / (1 / y))) * x,y \ 1,y) = (x * ((y \ 1) * T((y \ 1) \ 1,x))) * y
    ]]></literal>
    <justification jstring="[para(4173(a,1),2801(a,1,1))].">
      <j1 rule="para" parents="4173 2801"/>
    </justification>
  </clause>

  <clause id="4175">
    <literal><![CDATA[
      R((x \ (x / (1 / y))) * x,y \ 1,y) = (x * (y \ T(y,x))) * y
    ]]></literal>
    <justification jstring="[para(1108(a,1),4174(a,2,1,2))].">
      <j1 rule="para" parents="1108 4174"/>
    </justification>
  </clause>

  <clause id="4176">
    <literal><![CDATA[
      (x \ (x * y)) * x = (x * (y \ T(y,x))) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,3852,a(flip),b,4175,a)].">
      <j1 rule="hyper" parents="65 3852 4175"/>
    </justification>
  </clause>

  <clause id="4177">
    <literal><![CDATA[
      (x * (y \ T(y,x))) * y = y * x
    ]]></literal>
    <justification jstring="[para(9(a,1),4176(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 4176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4178">
    <literal><![CDATA[
      x * (y \ T(y,x)) = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(137,a,4177,a),flip(a)].">
      <j1 rule="hyper" parents="137 4177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4179">
    <literal><![CDATA[
      (x \ y) * (x \ T(x,x \ y)) = y / x
    ]]></literal>
    <justification jstring="[hyper(120,a,10,a(flip),b,4177,a),flip(a)].">
      <j1 rule="hyper" parents="120 10 4177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4180">
    <literal><![CDATA[
      T(x,y) * (y \ T(y,T(x,y))) = x
    ]]></literal>
    <justification jstring="[hyper(37,a,107,a(flip),b,4177,a),flip(a)].">
      <j1 rule="hyper" parents="37 107 4177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4182">
    <literal><![CDATA[
      x \ ((y * x) / y) = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(125,a,4178,a)].">
      <j1 rule="hyper" parents="125 4178"/>
    </justification>
  </clause>

  <clause id="4183">
    <literal><![CDATA[
      T(x,y) \ x = y \ T(y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,223,a(flip),b,4178,a)].">
      <j1 rule="hyper" parents="119 223 4178"/>
    </justification>
  </clause>

  <clause id="4184">
    <literal><![CDATA[
      (x \ T(x,y)) * y = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(65,a,3629,a,b,4178,a)].">
      <j1 rule="hyper" parents="65 3629 4178"/>
    </justification>
  </clause>

  <clause id="4185">
    <literal><![CDATA[
      ((x * y) / x) / y = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,3666,a,b,4178,a)].">
      <j1 rule="hyper" parents="36 3666 4178"/>
    </justification>
  </clause>

  <clause id="4186">
    <literal><![CDATA[
      (x * y) \ ((x * y) / x) = L(x \ 1,T(x,y),y)
    ]]></literal>
    <justification jstring="[para(4178(a,1),1114(a,1,2))].">
      <j1 rule="para" parents="4178 1114"/>
    </justification>
  </clause>

  <clause id="4187">
    <literal><![CDATA[
      ((x * y) / x) * (y \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[para(4178(a,1),2402(a,1,1))].">
      <j1 rule="para" parents="4178 2402"/>
    </justification>
  </clause>

  <clause id="4188">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(3557,a,4182,a)].">
      <j1 rule="hyper" parents="3557 4182"/>
    </justification>
  </clause>

  <clause id="4189">
    <literal><![CDATA[
      L(x \ T(x,y),y,x) = K(x,(x * y) / x)
    ]]></literal>
    <justification jstring="[para(4182(a,1),521(a,1,1))].">
      <j1 rule="para" parents="4182 521"/>
    </justification>
  </clause>

  <clause id="4190">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) = (x \ T(x,y)) * x
    ]]></literal>
    <justification jstring="[para(4182(a,1),1847(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4182 1847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4191">
    <literal><![CDATA[
      T(x,(y \ x) \ 1) = x * K(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(3915,a,4188,a),flip(a)].">
      <j1 rule="hyper" parents="3915 4188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4192">
    <literal><![CDATA[
      x * (T(y,x) \ y) = T(x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(3598,a,4188,a)].">
      <j1 rule="hyper" parents="3598 4188"/>
    </justification>
  </clause>

  <clause id="4194">
    <literal><![CDATA[
      T(x,T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      x * (T(y,x) \ y) = z
    ]]></literal>
    <justification jstring="[para(4188(a,1),3598(a,1))].">
      <j1 rule="para" parents="4188 3598"/>
    </justification>
  </clause>

  <clause id="4195">
    <literal><![CDATA[
      T(x,(y \ x) \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x * K(x,y / x) = z
    ]]></literal>
    <justification jstring="[para(4188(a,1),3915(a,1))].">
      <j1 rule="para" parents="4188 3915"/>
    </justification>
  </clause>

  <clause id="4196">
    <literal><![CDATA[
      R(T(x,y) \ x,y,z) = (T(y,T(x,y)) * z) / (y * z)
    ]]></literal>
    <justification jstring="[para(4183(a,2),3521(a,1,1))].">
      <j1 rule="para" parents="4183 3521"/>
    </justification>
  </clause>

  <clause id="4197">
    <literal><![CDATA[
      R(x \ T(x,y),y,z) \ (((x * y) / x) * z) = y * z
    ]]></literal>
    <justification jstring="[para(4184(a,1),182(a,1,2,1))].">
      <j1 rule="para" parents="4184 182"/>
    </justification>
  </clause>

  <clause id="4198">
    <literal><![CDATA[
      (a((x * y) \ 1,x,y) / y) / (1 / (x * y)) = ((1 / (x * y)) \ T(1 / (x * y),x)) * x
    ]]></literal>
    <justification jstring="[para(2980(a,2),4184(a,2,1)),flip(a)].">
      <j1 rule="para" parents="2980 4184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4199">
    <literal><![CDATA[
      R(x \ T(x,y),y,((x * y) / x) \ z) \ z = y * (((x * y) / x) \ z)
    ]]></literal>
    <justification jstring="[para(4185(a,1),533(a,1,1,1))].">
      <j1 rule="para" parents="4185 533"/>
    </justification>
  </clause>

  <clause id="4200">
    <literal><![CDATA[
      (x \ y) * (x \ ((x \ y) \ y)) = y / x
    ]]></literal>
    <justification jstring="[para(108(a,1),4179(a,1,2,2))].">
      <j1 rule="para" parents="108 4179"/>
    </justification>
  </clause>

  <clause id="4201">
    <literal><![CDATA[
      (x \ T(x,y)) \ (((x * y) / x) * ((y \ 1) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,y \ 1,(x * y) / x) = u
    ]]></literal>
    <justification jstring="[para(4187(a,1),493(a,1,1))].">
      <j1 rule="para" parents="4187 493"/>
    </justification>
  </clause>

  <clause id="4202">
    <literal><![CDATA[
      T(x,T(y,y \ x) \ 1) = x * K(x,(y \ x) / x)
    ]]></literal>
    <justification jstring="[para(108(a,2),4191(a,1,2,1))].">
      <j1 rule="para" parents="108 4191"/>
    </justification>
  </clause>

  <clause id="4203">
    <literal><![CDATA[
      (x \ y) \ (y / x) = x \ ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[hyper(125,a,4200,a)].">
      <j1 rule="hyper" parents="125 4200"/>
    </justification>
  </clause>

  <clause id="4205">
    <literal><![CDATA[
      K(x,y) = L(x \ T(x,T(y,x)),T(y,x),x)
    ]]></literal>
    <justification jstring="[para(223(a,1),4189(a,2,2)),flip(a)].">
      <j1 rule="para" parents="223 4189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4206">
    <literal><![CDATA[
      x * ((y * (x \ 1)) / y) = y \ T(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(3913,a,4190,a)].">
      <j1 rule="hyper" parents="3913 4190"/>
    </justification>
  </clause>

  <clause id="4207">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4190(a,2),3520(a,1))].">
      <j1 rule="para" parents="4190 3520"/>
    </justification>
  </clause>

  <clause id="4208">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y),x) = z
    ]]></literal>
    <justification jstring="[para(3597(a,1),4207(a,1))].">
      <j1 rule="para" parents="3597 4207"/>
    </justification>
  </clause>

  <clause id="4211">
    <literal><![CDATA[
      K(x,(x / y) / x) = x \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(1881,a,4206,a)].">
      <j1 rule="hyper" parents="1881 4206"/>
    </justification>
  </clause>

  <clause id="4212">
    <literal><![CDATA[
      L(x * ((y * (x \ 1)) / y),z,u) = y \ T(y,L(x,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,4102,a(flip),b,4206,a)].">
      <j1 rule="hyper" parents="65 4102 4206"/>
    </justification>
  </clause>

  <clause id="4214">
    <literal><![CDATA[
      x \ T(x,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,(x / y) / x) = z
    ]]></literal>
    <justification jstring="[para(4206(a,1),1881(a,1))].">
      <j1 rule="para" parents="4206 1881"/>
    </justification>
  </clause>

  <clause id="4215">
    <literal><![CDATA[
      T(x \ T(x,y \ 1),z) = K(x,(x / T(y,z)) / x)
    ]]></literal>
    <justification jstring="[para(4206(a,1),2264(a,1,1))].">
      <j1 rule="para" parents="4206 2264"/>
    </justification>
  </clause>

  <clause id="4216">
    <literal><![CDATA[
      K(x,(x / y) / x) * (y * z) = y * ((x \ T(x,y \ 1)) * z)
    ]]></literal>
    <justification jstring="[para(4206(a,1),2297(a,2,2,1))].">
      <j1 rule="para" parents="4206 2297"/>
    </justification>
  </clause>

  <clause id="4217">
    <literal><![CDATA[
      (x * ((y / (z * (x \ y))) / x)) * (z * (x \ y)) = x * ((x \ T(x,z \ 1)) * (x \ y))
    ]]></literal>
    <justification jstring="[para(4206(a,1),2266(a,2,2,1))].">
      <j1 rule="para" parents="4206 2266"/>
    </justification>
  </clause>

  <clause id="4218">
    <literal><![CDATA[
      T(x,T(y,y \ x) \ 1) != x * z
    ]]></literal>
    <literal><![CDATA[
      K(x,(y \ x) / x) = z
    ]]></literal>
    <justification jstring="[para(4202(a,2),45(a,1))].">
      <j1 rule="para" parents="4202 45"/>
    </justification>
  </clause>

  <clause id="4219">
    <literal><![CDATA[
      T(x \ T(x,y \ 1),z) = x \ T(x,T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,4211,a(flip),b,4215,a),flip(a)].">
      <j1 rule="hyper" parents="299 4211 4215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4220">
    <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(3534(a,1),4219(a,2,2,2,1))].">
      <j1 rule="para" parents="3534 4219"/>
    </justification>
  </clause>

  <clause id="4221">
    <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(4196(a,1),1005(a,1,1))].">
      <j1 rule="para" parents="4196 1005"/>
    </justification>
  </clause>

  <clause id="4222">
    <literal><![CDATA[
      (x \ T(x,y \ 1)) * (y * z) = y * ((x \ T(x,y \ 1)) * z)
    ]]></literal>
    <justification jstring="[para(4211(a,1),4216(a,1,1))].">
      <j1 rule="para" parents="4211 4216"/>
    </justification>
  </clause>

  <clause id="4223">
    <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),4221(a,2,1))].">
      <j1 rule="para" parents="16 4221"/>
    </justification>
  </clause>

  <clause id="4224">
    <literal><![CDATA[
      ((x * ((x / y) / x)) * y) * (x \ z) = x * ((x \ T(x,y \ 1)) * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(4046,a,4217,a)].">
      <j1 rule="hyper" parents="4046 4217"/>
    </justification>
  </clause>

  <clause id="4225">
    <literal><![CDATA[
      (x * ((x / y) / x)) * y = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(1130,a,4224,a)].">
      <j1 rule="hyper" parents="1130 4224"/>
    </justification>
  </clause>

  <clause id="4226">
    <literal><![CDATA[
      T(x * ((x / y) / x),y) = y \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(235,a,4225,a,b,10,a)].">
      <j1 rule="hyper" parents="235 4225 10"/>
    </justification>
  </clause>

  <clause id="4227">
    <literal><![CDATA[
      T(x,y \ 1) / y = x * ((x / y) / x)
    ]]></literal>
    <justification jstring="[hyper(137,a,4225,a)].">
      <j1 rule="hyper" parents="137 4225"/>
    </justification>
  </clause>

  <clause id="4228">
    <literal><![CDATA[
      x * ((x * y) * (y / (x * y))) = T(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,3602,a(flip),b,4225,a)].">
      <j1 rule="hyper" parents="65 3602 4225"/>
    </justification>
  </clause>

  <clause id="4229">
    <literal><![CDATA[
      x \ T(y,x \ 1) = y * ((x \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4225,a(flip),b,3501,a(flip))].">
      <j1 rule="hyper" parents="119 4225 3501"/>
    </justification>
  </clause>

  <clause id="4231">
    <literal><![CDATA[
      x * ((x \ T(x,y \ 1)) * (x \ z)) = T(x,y \ 1) * (x \ z)
    ]]></literal>
    <justification jstring="[para(4225(a,1),4224(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4225 4224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4232">
    <literal><![CDATA[
      T(x,y) / (1 / y) = x * ((x / (1 / y)) / x)
    ]]></literal>
    <justification jstring="[para(79(a,1),4227(a,1,1,2))].">
      <j1 rule="para" parents="79 4227"/>
    </justification>
  </clause>

  <clause id="4233">
    <literal><![CDATA[
      L(((x / y) / x) \ 1,(x / y) / x,x) = (T(x,y \ 1) / y) \ x
    ]]></literal>
    <justification jstring="[para(4227(a,2),214(a,2,1))].">
      <j1 rule="para" parents="4227 214"/>
    </justification>
  </clause>

  <clause id="4235">
    <literal><![CDATA[
      x \ (y \ T(x,y \ 1)) = (y \ x) / x
    ]]></literal>
    <justification jstring="[hyper(119,a,4229,a,b,xx)].">
      <j1 rule="hyper" parents="119 4229"/>
    </justification>
  </clause>

  <clause id="4236">
    <literal><![CDATA[
      (x / y) \ T(x,(x / y) \ 1) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(79(a,1),4229(a,2,2,1))].">
      <j1 rule="para" parents="79 4229"/>
    </justification>
  </clause>

  <clause id="4237">
    <literal><![CDATA[
      x * R(1 / y,y,y \ x) = y \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(375(a,2),4229(a,2,2)),flip(a)].">
      <j1 rule="para" parents="375 4229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4238">
    <literal><![CDATA[
      R(x,(y \ x) / x,x) = ((y \ T(x,y \ 1)) * x) / (y \ x)
    ]]></literal>
    <justification jstring="[para(4229(a,2),105(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4229 105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4241">
    <literal><![CDATA[
      x \ (T(x,y) / (1 / y)) = (x / (1 / y)) / x
    ]]></literal>
    <justification jstring="[hyper(119,a,4232,a,b,xx)].">
      <j1 rule="hyper" parents="119 4232"/>
    </justification>
  </clause>

  <clause id="4242">
    <literal><![CDATA[
      (((x / y) \ 1) \ y) * ((x / y) \ 1) = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(1330,a,4236,a)].">
      <j1 rule="hyper" parents="1330 4236"/>
    </justification>
  </clause>

  <clause id="4244">
    <literal><![CDATA[
      x * R(1 / (1 / y),1 / y,(1 / y) \ x) = (1 / y) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(79(a,1),4237(a,2,2,2))].">
      <j1 rule="para" parents="79 4237"/>
    </justification>
  </clause>

  <clause id="4245">
    <literal><![CDATA[
      ((x \ 1) \ y) * (x \ 1) = (x * y) * (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(36,a,1136,a,b,4228,a)].">
      <j1 rule="hyper" parents="36 1136 4228"/>
    </justification>
  </clause>

  <clause id="4248">
    <literal><![CDATA[
      x \ (y * (x / y)) != z
    ]]></literal>
    <literal><![CDATA[
      K(((y / x) \ 1) \ x,(y / x) \ 1) = z
    ]]></literal>
    <justification jstring="[para(4242(a,1),454(a,1,2))].">
      <j1 rule="para" parents="4242 454"/>
    </justification>
  </clause>

  <clause id="4249">
    <literal><![CDATA[
      ((x \ 1) * y) * (y / ((x \ 1) * y)) = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(65,a,3283,a(flip),b,4245,a),flip(a)].">
      <j1 rule="hyper" parents="65 3283 4245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4250">
    <literal><![CDATA[
      ((x \ 1) * y) * R(x,x \ 1,y) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(212(a,2),4249(a,1,2))].">
      <j1 rule="para" parents="212 4249"/>
    </justification>
  </clause>

  <clause id="4251">
    <literal><![CDATA[
      ((((x \ 1) * y) * x) / ((x \ 1) * y)) * (x \ 1) = ((x \ y) * x) / y
    ]]></literal>
    <justification jstring="[hyper(120,a,4250,a(flip),b,931,a),flip(a)].">
      <j1 rule="hyper" parents="120 4250 931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4252">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) * (x \ z) = x * ((x \ T(x,y)) * (x \ z))
    ]]></literal>
    <justification jstring="[para(3739(a,1),4231(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="3739 4231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4253">
    <literal><![CDATA[
      x * ((x \ T(x,y)) * (x \ z)) = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[para(3739(a,1),4252(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3739 4252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4254">
    <literal><![CDATA[
      T(x,y) * (x \ (x * z)) = x * ((x \ T(x,y)) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),4253(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 4253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4255">
    <literal><![CDATA[
      x * ((x \ T(x,y)) * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[para(9(a,1),4254(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 4254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4256">
    <literal><![CDATA[
      L(x,y \ T(y,z),y) = x
    ]]></literal>
    <justification jstring="[hyper(817,a,4255,a)].">
      <j1 rule="hyper" parents="817 4255"/>
    </justification>
  </clause>

  <clause id="4258">
    <literal><![CDATA[
      (x \ T(x,y)) \ 1 = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(389,a,4255,a),flip(a)].">
      <j1 rule="hyper" parents="389 4255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4259">
    <literal><![CDATA[
      (T(x,y) * z) / ((x \ T(x,y)) * z) = x
    ]]></literal>
    <justification jstring="[hyper(137,a,4255,a)].">
      <j1 rule="hyper" parents="137 4255"/>
    </justification>
  </clause>

  <clause id="4260">
    <literal><![CDATA[
      (x \ T(x,y)) * z = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(36,a,1190,a,b,4255,a),flip(a)].">
      <j1 rule="hyper" parents="36 1190 4255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4261">
    <literal><![CDATA[
      (x \ T(x,y)) * (x * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(36,a,1187,a(flip),b,4255,a),flip(a)].">
      <j1 rule="hyper" parents="36 1187 4255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4263">
    <literal><![CDATA[
      T(x,y) * y = x * ((x * y) / x)
    ]]></literal>
    <justification jstring="[para(4184(a,1),4255(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4184 4255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4265">
    <literal><![CDATA[
      T(x,T(y,x)) \ x = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,4256,a(flip),b,3957,a)].">
      <j1 rule="hyper" parents="119 4256 3957"/>
    </justification>
  </clause>

  <clause id="4266">
    <literal><![CDATA[
      (x \ T(x,y)) \ y = T(y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,4256,a(flip),b,3956,a)].">
      <j1 rule="hyper" parents="119 4256 3956"/>
    </justification>
  </clause>

  <clause id="4267">
    <literal><![CDATA[
      (x \ T(x,y)) \ z = x * (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(119,a,4256,a(flip),b,3955,a)].">
      <j1 rule="hyper" parents="119 4256 3955"/>
    </justification>
  </clause>

  <clause id="4268">
    <literal><![CDATA[
      (x * T(x \ 1,y)) \ 1 = T(x \ 1,y) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(3516(a,1),4258(a,1,1))].">
      <j1 rule="para" parents="3516 4258"/>
    </justification>
  </clause>

  <clause id="4269">
    <literal><![CDATA[
      T(x,y) * (x \ y) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(1204,a,4263,a)].">
      <j1 rule="hyper" parents="1204 4263"/>
    </justification>
  </clause>

  <clause id="4270">
    <literal><![CDATA[
      (x * (x * y)) / x = T(x,x * y) * y
    ]]></literal>
    <justification jstring="[hyper(1195,a,4263,a),flip(a)].">
      <j1 rule="hyper" parents="1195 4263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4271">
    <literal><![CDATA[
      T(x,x / (x / y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(37,a,1586,a,b,4263,a)].">
      <j1 rule="hyper" parents="37 1586 4263"/>
    </justification>
  </clause>

  <clause id="4272">
    <literal><![CDATA[
      T(x,x \ y) * (x \ y) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(10(a,1),4263(a,2,2,1))].">
      <j1 rule="para" parents="10 4263"/>
    </justification>
  </clause>

  <clause id="4273">
    <literal><![CDATA[
      L(x,L(y,T(z,y),T(z,y)),u) = L(x,T(z,y) * (z * ((z * y) / z)),u)
    ]]></literal>
    <justification jstring="[para(4263(a,1),2520(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4263 2520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4274">
    <literal><![CDATA[
      T(x,x / (1 / y)) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2089,a(flip),b,4271,a)].">
      <j1 rule="hyper" parents="65 2089 4271"/>
    </justification>
  </clause>

  <clause id="4275">
    <literal><![CDATA[
      (x / T(y,x)) * y = T(x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,1449,a(flip),b,4271,a)].">
      <j1 rule="hyper" parents="65 1449 4271"/>
    </justification>
  </clause>

  <clause id="4276">
    <literal><![CDATA[
      (x / y) \ T(x,y) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(119,a,4271,a(flip),b,1443,a)].">
      <j1 rule="hyper" parents="119 4271 1443"/>
    </justification>
  </clause>

  <clause id="4277">
    <literal><![CDATA[
      T(x,x / y) = T(x,y \ x)
    ]]></literal>
    <justification jstring="[para(76(a,1),4271(a,1,2,2))].">
      <j1 rule="para" parents="76 4271"/>
    </justification>
  </clause>

  <clause id="4278">
    <literal><![CDATA[
      T(x,(y \ x) \ x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(187(a,1),4271(a,1,2)),flip(a)].">
      <j1 rule="para" parents="187 4271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4279">
    <literal><![CDATA[
      T(x,y \ x) / y = (x * (x / y)) / x
    ]]></literal>
    <justification jstring="[hyper(120,a,4277,a(flip),b,1434,a)].">
      <j1 rule="hyper" parents="120 4277 1434"/>
    </justification>
  </clause>

  <clause id="4280">
    <literal><![CDATA[
      x \ T(y,x \ y) = (y * (x \ y)) / y
    ]]></literal>
    <justification jstring="[hyper(119,a,4277,a(flip),b,1441,a)].">
      <j1 rule="hyper" parents="119 4277 1441"/>
    </justification>
  </clause>

  <clause id="4281">
    <literal><![CDATA[
      T(T(x,y \ x) / y,x) = x / y
    ]]></literal>
    <justification jstring="[para(4277(a,1),1442(a,1,1,1))].">
      <j1 rule="para" parents="4277 1442"/>
    </justification>
  </clause>

  <clause id="4282">
    <literal><![CDATA[
      T(x,T(y,y \ x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(108(a,2),4278(a,1,2))].">
      <j1 rule="para" parents="108 4278"/>
    </justification>
  </clause>

  <clause id="4283">
    <literal><![CDATA[
      T(x * y,T(x,y)) = T(x * y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),4282(a,1,2,2))].">
      <j1 rule="para" parents="9 4282"/>
    </justification>
  </clause>

  <clause id="4284">
    <literal><![CDATA[
      (x * (T(x,T(y,x)) \ x)) * y = y * x
    ]]></literal>
    <justification jstring="[para(4265(a,2),4177(a,1,1,2))].">
      <j1 rule="para" parents="4265 4177"/>
    </justification>
  </clause>

  <clause id="4285">
    <literal><![CDATA[
      (x * y) / x = y * (T(y,T(x,y)) \ y)
    ]]></literal>
    <justification jstring="[para(4265(a,2),4178(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4265 4178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4286">
    <literal><![CDATA[
      T(x,R(T(y,x),T(y,x) \ 1,x)) \ x = y \ T(y,x)
    ]]></literal>
    <justification jstring="[para(4188(a,2),4265(a,1,1))].">
      <j1 rule="para" parents="4188 4265"/>
    </justification>
  </clause>

  <clause id="4287">
    <literal><![CDATA[
      (x * (T(y,x) \ y)) \ x = y \ T(y,x)
    ]]></literal>
    <justification jstring="[para(4192(a,2),4265(a,1,1))].">
      <j1 rule="para" parents="4192 4265"/>
    </justification>
  </clause>

  <clause id="4288">
    <literal><![CDATA[
      L(x,T(y,T(z,y)) \ y,z) = x
    ]]></literal>
    <justification jstring="[para(4265(a,2),4256(a,1,2))].">
      <j1 rule="para" parents="4265 4256"/>
    </justification>
  </clause>

  <clause id="4289">
    <literal><![CDATA[
      L(x,T(y,z) \ y,(y * z) / y) = x
    ]]></literal>
    <justification jstring="[para(222(a,1),4288(a,1,2,1,2))].">
      <j1 rule="para" parents="222 4288"/>
    </justification>
  </clause>

  <clause id="4290">
    <literal><![CDATA[
      (x * T(x \ 1,y)) \ y = T(y,T(x \ 1,y))
    ]]></literal>
    <justification jstring="[para(3516(a,1),4266(a,1,1))].">
      <j1 rule="para" parents="3516 4266"/>
    </justification>
  </clause>

  <clause id="4291">
    <literal><![CDATA[
      T(x / y,T(y,x)) = y \ x
    ]]></literal>
    <justification jstring="[hyper(235,a,1527,a,b,4269,a)].">
      <j1 rule="hyper" parents="235 1527 4269"/>
    </justification>
  </clause>

  <clause id="4292">
    <literal><![CDATA[
      T(x,T(y,x * y)) = y \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(235,a,1533,a(flip),b,4269,a)].">
      <j1 rule="hyper" parents="235 1533 4269"/>
    </justification>
  </clause>

  <clause id="4293">
    <literal><![CDATA[
      T(x,y) \ (y * (x \ T(x,y))) = x \ y
    ]]></literal>
    <justification jstring="[hyper(119,a,4178,a,b,4269,a)].">
      <j1 rule="hyper" parents="119 4178 4269"/>
    </justification>
  </clause>

  <clause id="4294">
    <literal><![CDATA[
      T(x,(y \ x) * y) * K(y \ x,y) = (x * ((y \ x) * y)) / x
    ]]></literal>
    <justification jstring="[para(89(a,1),4269(a,1,2))].">
      <j1 rule="para" parents="89 4269"/>
    </justification>
  </clause>

  <clause id="4295">
    <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(4269(a,1),493(a,1,1))].">
      <j1 rule="para" parents="4269 493"/>
    </justification>
  </clause>

  <clause id="4296">
    <literal><![CDATA[
      L(((x * y) / x) / y,y,x) = K(T(x,y),y)
    ]]></literal>
    <justification jstring="[para(4269(a,1),3642(a,1,1,1))].">
      <j1 rule="para" parents="4269 3642"/>
    </justification>
  </clause>

  <clause id="4297">
    <literal><![CDATA[
      T(x \ y,T(x,y)) = T(x \ y,x)
    ]]></literal>
    <justification jstring="[para(4291(a,1),242(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4291 242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4298">
    <literal><![CDATA[
      x \ (y * T(y \ x,T(y,x))) = K(y \ x,T(y,x))
    ]]></literal>
    <justification jstring="[para(4291(a,1),2038(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4291 2038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4299">
    <literal><![CDATA[
      R(T(x,x * y),y,x) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[para(4274(a,1),2087(a,1,1))].">
      <j1 rule="para" parents="4274 2087"/>
    </justification>
  </clause>

  <clause id="4300">
    <literal><![CDATA[
      T(x / T(y,x),y) = T(y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(235,a,4275,a,b,1205,a)].">
      <j1 rule="hyper" parents="235 4275 1205"/>
    </justification>
  </clause>

  <clause id="4302">
    <literal><![CDATA[
      ((x * y) * y) / (x * y) = x \ T(x * y,y)
    ]]></literal>
    <justification jstring="[para(11(a,1),4276(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 4276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4303">
    <literal><![CDATA[
      T(x,T(y,x * y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,22,a,b,4292,a),flip(a)].">
      <j1 rule="hyper" parents="299 22 4292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4304">
    <literal><![CDATA[
      T(x,T(x \ y,y)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),4303(a,1,2,2))].">
      <j1 rule="para" parents="10 4303"/>
    </justification>
  </clause>

  <clause id="4305">
    <literal><![CDATA[
      T(x,y) * T(x \ y,x) = (x \ y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(4297(a,1),107(a,1,2))].">
      <j1 rule="para" parents="4297 107"/>
    </justification>
  </clause>

  <clause id="4307">
    <literal><![CDATA[
      x \ (y * T(y \ x,T(y,x))) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,y) = z
    ]]></literal>
    <justification jstring="[para(4297(a,2),811(a,1,2,2))].">
      <j1 rule="para" parents="4297 811"/>
    </justification>
  </clause>

  <clause id="4308">
    <literal><![CDATA[
      R(x,x \ T(x,y),z) = x
    ]]></literal>
    <justification jstring="[hyper(846,a,4259,a)].">
      <j1 rule="hyper" parents="846 4259"/>
    </justification>
  </clause>

  <clause id="4309">
    <literal><![CDATA[
      T(x,y \ 1) * (x \ (y * z)) = y * ((x \ T(x,y \ 1)) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,4222,a(flip),b,4260,a),flip(a)].">
      <j1 rule="hyper" parents="65 4222 4260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4311">
    <literal><![CDATA[
      (T(x,y) * z) / (x * z) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(137,a,4261,a)].">
      <j1 rule="hyper" parents="137 4261"/>
    </justification>
  </clause>

  <clause id="4312">
    <literal><![CDATA[
      (x \ T(x,y)) \ (T(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(4261(a,1),314(a,1,2))].">
      <j1 rule="para" parents="4261 314"/>
    </justification>
  </clause>

  <clause id="4313">
    <literal><![CDATA[
      (x \ T(x,y)) \ (T(x,y) * z) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * z) = w
    ]]></literal>
    <justification jstring="[para(4261(a,1),313(a,1,2))].">
      <j1 rule="para" parents="4261 313"/>
    </justification>
  </clause>

  <clause id="4316">
    <literal><![CDATA[
      T(T(x,x * y) * y,x) = x * y
    ]]></literal>
    <justification jstring="[para(4270(a,1),222(a,1,1))].">
      <j1 rule="para" parents="4270 222"/>
    </justification>
  </clause>

  <clause id="4317">
    <literal><![CDATA[
      T(x,x \ (y \ x)) \ (y \ T(x,y \ 1)) = x \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(119,a,4229,a,b,4272,a)].">
      <j1 rule="hyper" parents="119 4229 4272"/>
    </justification>
  </clause>

  <clause id="4318">
    <literal><![CDATA[
      (x \ T(x,x \ y)) * y = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(65,a,4260,a,b,4272,a)].">
      <j1 rule="hyper" parents="65 4260 4272"/>
    </justification>
  </clause>

  <clause id="4319">
    <literal><![CDATA[
      (x * (y / x)) \ (T(x,x \ y) * ((x \ y) * z)) = L(z,x \ y,T(x,x \ y))
    ]]></literal>
    <justification jstring="[para(4272(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4272 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4320">
    <literal><![CDATA[
      T(x * (T(x,T(y,x)) \ x),y) = x
    ]]></literal>
    <justification jstring="[hyper(235,a,4284,a,b,xx)].">
      <j1 rule="hyper" parents="235 4284"/>
    </justification>
  </clause>

  <clause id="4322">
    <literal><![CDATA[
      x / (y \ T(y,x)) = x * (T(y,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(192,a,4287,a)].">
      <j1 rule="hyper" parents="192 4287"/>
    </justification>
  </clause>

  <clause id="4323">
    <literal><![CDATA[
      (x * (T(y,x) \ y)) \ 1 = x \ (y \ T(y,x))
    ]]></literal>
    <justification jstring="[para(4287(a,1),3695(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4287 3695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4324">
    <literal><![CDATA[
      (x * (y \ T(y,x))) \ (x * x) = x * (T(y,x) \ y)
    ]]></literal>
    <justification jstring="[para(4287(a,1),3765(a,1,1,2))].">
      <j1 rule="para" parents="4287 3765"/>
    </justification>
  </clause>

  <clause id="4325">
    <literal><![CDATA[
      T(x,x \ y) \ (y / x) = x \ (x \ y)
    ]]></literal>
    <justification jstring="[para(4179(a,1),4293(a,1,2))].">
      <j1 rule="para" parents="4179 4293"/>
    </justification>
  </clause>

  <clause id="4326">
    <literal><![CDATA[
      R(x \ T(x,y),x,z) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(3530,a,4311,a)].">
      <j1 rule="hyper" parents="3530 4311"/>
    </justification>
  </clause>

  <clause id="4327">
    <literal><![CDATA[
      R(K(x,y),x,z) = L(x \ T(x,T(y,x)),T(y,x),x)
    ]]></literal>
    <justification jstring="[para(4311(a,1),4223(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4311 4223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4329">
    <literal><![CDATA[
      (x * T(x \ y,z)) / y = (y / x) \ T(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,3777,a(flip),b,4326,a)].">
      <j1 rule="hyper" parents="65 3777 4326"/>
    </justification>
  </clause>

  <clause id="4330">
    <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(1378(a,1),4322(a,1,2,2))].">
      <j1 rule="para" parents="1378 4322"/>
    </justification>
  </clause>

  <clause id="4331">
    <literal><![CDATA[
      T(1 / x,(1 / x) \ y) \ (y / (1 / x)) = x \ ((x * x) * ((1 / x) \ y))
    ]]></literal>
    <justification jstring="[hyper(299,a,443,a,b,4325,a),flip(a)].">
      <j1 rule="hyper" parents="299 443 4325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4332">
    <literal><![CDATA[
      ((x \ y) \ y) \ (y / x) = x \ (x \ y)
    ]]></literal>
    <justification jstring="[para(108(a,1),4325(a,1,1))].">
      <j1 rule="para" parents="108 4325"/>
    </justification>
  </clause>

  <clause id="4333">
    <literal><![CDATA[
      L(x \ T(x,y),y,x) = K(T(x,y),y)
    ]]></literal>
    <justification jstring="[para(4185(a,1),4296(a,1,1))].">
      <j1 rule="para" parents="4185 4296"/>
    </justification>
  </clause>

  <clause id="4334">
    <literal><![CDATA[
      K(T(x,T(y,x)),T(y,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,4205,a,b,4333,a),flip(a)].">
      <j1 rule="hyper" parents="65 4205 4333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4336">
    <literal><![CDATA[
      T(x,T(L(y \ 1,y,x) \ 1,x)) = K(y,x) \ x
    ]]></literal>
    <justification jstring="[para(1382(a,2),4290(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1382 4290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4337">
    <literal><![CDATA[
      T(x \ T(x * y,y),x) = R(y,x,y)
    ]]></literal>
    <justification jstring="[para(4302(a,1),857(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4302 857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4338">
    <literal><![CDATA[
      x \ T(y * x,y) = R(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(3482,a,4337,a)].">
      <j1 rule="hyper" parents="3482 4337"/>
    </justification>
  </clause>

  <clause id="4340">
    <literal><![CDATA[
      R(x,y,T(x,y)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(1425,a,4338,a)].">
      <j1 rule="hyper" parents="1425 4338"/>
    </justification>
  </clause>

  <clause id="4341">
    <literal><![CDATA[
      x * R(y,x,y) = T(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(144,a,4338,a)].">
      <j1 rule="hyper" parents="144 4338"/>
    </justification>
  </clause>

  <clause id="4342">
    <literal><![CDATA[
      (x * y) \ ((1 / x) \ ((x * ((x \ 1) * y)) * x)) = R(x,(x \ 1) * y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,2786,a,b,4338,a)].">
      <j1 rule="hyper" parents="65 2786 4338"/>
    </justification>
  </clause>

  <clause id="4343">
    <literal><![CDATA[
      R(x,x \ y,x) = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),4338(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 4338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4344">
    <literal><![CDATA[
      (x * y) \ T(L(y,x,x),1 / x) = R(1 / x,x * y,1 / x)
    ]]></literal>
    <justification jstring="[para(475(a,1),4338(a,1,2,1))].">
      <j1 rule="para" parents="475 4338"/>
    </justification>
  </clause>

  <clause id="4345">
    <literal><![CDATA[
      (x * y) \ (x * T(z * y,z)) = L(R(z,y,z),y,x)
    ]]></literal>
    <justification jstring="[para(4338(a,1),96(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4338 96"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4346">
    <literal><![CDATA[
      L(R(x,y,x),y,x) = x
    ]]></literal>
    <justification jstring="[para(4338(a,1),517(a,1,1))].">
      <j1 rule="para" parents="4338 517"/>
    </justification>
  </clause>

  <clause id="4347">
    <literal><![CDATA[
      (L(x,y,x) * y) * x = x * (y * x)
    ]]></literal>
    <justification jstring="[para(4346(a,1),542(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4346 542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4348">
    <literal><![CDATA[
      x \ T(y * x,y) != z
    ]]></literal>
    <literal><![CDATA[
      R(y,x,y) = z
    ]]></literal>
    <justification jstring="[para(4341(a,1),314(a,1,2))].">
      <j1 rule="para" parents="4341 314"/>
    </justification>
  </clause>

  <clause id="4349">
    <literal><![CDATA[
      T(x * y,x) * T(x,y) = (x * y) * R(x,y,x)
    ]]></literal>
    <justification jstring="[para(4341(a,1),1927(a,1,1))].">
      <j1 rule="para" parents="4341 1927"/>
    </justification>
  </clause>

  <clause id="4350">
    <literal><![CDATA[
      T(T(x,x \ 1) * y,L(x,x,x)) = y * R(L(x,x,x),y,L(x,x,x))
    ]]></literal>
    <justification jstring="[para(2807(a,2),4341(a,2,1)),flip(a)].">
      <j1 rule="para" parents="2807 4341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4351">
    <literal><![CDATA[
      T(L(x,y,x) * y,x) = y * x
    ]]></literal>
    <justification jstring="[hyper(235,a,4347,a,b,xx)].">
      <j1 rule="hyper" parents="235 4347"/>
    </justification>
  </clause>

  <clause id="4352">
    <literal><![CDATA[
      (x * (y * x)) / x = L(x,y,x) * y
    ]]></literal>
    <justification jstring="[hyper(137,a,4347,a)].">
      <j1 rule="hyper" parents="137 4347"/>
    </justification>
  </clause>

  <clause id="4353">
    <literal><![CDATA[
      x * T(y,x * y) = L(y,x,y) * x
    ]]></literal>
    <justification jstring="[hyper(37,a,1544,a,b,4347,a)].">
      <j1 rule="hyper" parents="37 1544 4347"/>
    </justification>
  </clause>

  <clause id="4355">
    <literal><![CDATA[
      T((x * y) / x,L(x,y,x)) = y
    ]]></literal>
    <justification jstring="[hyper(1812,a,4352,a)].">
      <j1 rule="hyper" parents="1812 4352"/>
    </justification>
  </clause>

  <clause id="4356">
    <literal><![CDATA[
      (x * (y * x)) / x = y * T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(299,a,788,a,b,4352,a),flip(a)].">
      <j1 rule="hyper" parents="299 788 4352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4357">
    <literal><![CDATA[
      ((x * (y * x)) / x) / T(x,x * y) = y
    ]]></literal>
    <justification jstring="[hyper(120,a,4352,a,b,788,a)].">
      <j1 rule="hyper" parents="120 4352 788"/>
    </justification>
  </clause>

  <clause id="4358">
    <literal><![CDATA[
      ((x * (y * x)) / x) / y = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(120,a,4352,a,b,xx)].">
      <j1 rule="hyper" parents="120 4352"/>
    </justification>
  </clause>

  <clause id="4359">
    <literal><![CDATA[
      L(x,y,x) \ ((x * (y * x)) / x) = y
    ]]></literal>
    <justification jstring="[hyper(119,a,4352,a,b,xx)].">
      <j1 rule="hyper" parents="119 4352"/>
    </justification>
  </clause>

  <clause id="4360">
    <literal><![CDATA[
      T(L(x,y,x),y) = T(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(235,a,4352,a(flip),b,1533,a(flip))].">
      <j1 rule="hyper" parents="235 4352 1533"/>
    </justification>
  </clause>

  <clause id="4362">
    <literal><![CDATA[
      (x * ((x \ y) * x)) / x != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) * T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4352(a,2),1030(a,1))].">
      <j1 rule="para" parents="4352 1030"/>
    </justification>
  </clause>

  <clause id="4363">
    <literal><![CDATA[
      T(x,L(y,x,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4355(a,1),266(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4355 266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4364">
    <literal><![CDATA[
      L(x,y,x) * T(y,x) = y * L(x,y,x)
    ]]></literal>
    <justification jstring="[para(4363(a,1),107(a,1,2))].">
      <j1 rule="para" parents="4363 107"/>
    </justification>
  </clause>

  <clause id="4366">
    <literal><![CDATA[
      T(x,y * x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(794,a,4360,a),flip(a)].">
      <j1 rule="hyper" parents="794 4360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4368">
    <literal><![CDATA[
      x * L(T(y,x * y),z,u) = L(L(y,x,y),z,u) * x
    ]]></literal>
    <justification jstring="[para(4360(a,1),233(a,1,2,1))].">
      <j1 rule="para" parents="4360 233"/>
    </justification>
  </clause>

  <clause id="4370">
    <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(65,a,27,a,b,4366,a)].">
      <j1 rule="hyper" parents="65 27 4366"/>
    </justification>
  </clause>

  <clause id="4371">
    <literal><![CDATA[
      T(x,(x \ y) * x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),4366(a,2,2))].">
      <j1 rule="para" parents="10 4366"/>
    </justification>
  </clause>

  <clause id="4372">
    <literal><![CDATA[
      T(x,x * (y / x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(12(a,1),4366(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 4366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4373">
    <literal><![CDATA[
      T(T(x,x * y),z) = T(T(x,z),y * x)
    ]]></literal>
    <justification jstring="[para(4366(a,1),23(a,1,1))].">
      <j1 rule="para" parents="4366 23"/>
    </justification>
  </clause>

  <clause id="4374">
    <literal><![CDATA[
      T(T(x,y * x),z) = T(T(x,z),x * y)
    ]]></literal>
    <justification jstring="[para(4366(a,2),23(a,1,1))].">
      <j1 rule="para" parents="4366 23"/>
    </justification>
  </clause>

  <clause id="4375">
    <literal><![CDATA[
      R(T(x,x * y),y,x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4366(a,1),877(a,1,1))].">
      <j1 rule="para" parents="4366 877"/>
    </justification>
  </clause>

  <clause id="4376">
    <literal><![CDATA[
      T(x,T(y,y * x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4366(a,1),4303(a,1,2))].">
      <j1 rule="para" parents="4366 4303"/>
    </justification>
  </clause>

  <clause id="4377">
    <literal><![CDATA[
      R(T(x,y),x \ y,x) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(4371(a,1),877(a,1,1))].">
      <j1 rule="para" parents="4371 877"/>
    </justification>
  </clause>

  <clause id="4378">
    <literal><![CDATA[
      T(x,T(y * x,z)) = T(x,T(x * y,z))
    ]]></literal>
    <justification jstring="[para(3479(a,1),4371(a,1,2))].">
      <j1 rule="para" parents="3479 4371"/>
    </justification>
  </clause>

  <clause id="4379">
    <literal><![CDATA[
      T(x,x * y) * L(T(y,x),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(y,z,u) * T(x,x * y) = w
    ]]></literal>
    <justification jstring="[para(4376(a,1),396(a,1,2,1))].">
      <j1 rule="para" parents="4376 396"/>
    </justification>
  </clause>

  <clause id="4380">
    <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(4376(a,1),397(a,1,2,1))].">
      <j1 rule="para" parents="4376 397"/>
    </justification>
  </clause>

  <clause id="4381">
    <literal><![CDATA[
      (x / T(y,x)) * y = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,4299,a(flip),b,4375,a)].">
      <j1 rule="hyper" parents="65 4299 4375"/>
    </justification>
  </clause>

  <clause id="4382">
    <literal><![CDATA[
      T(x,y) / y = x / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(120,a,4375,a(flip),b,4299,a(flip))].">
      <j1 rule="hyper" parents="120 4375 4299"/>
    </justification>
  </clause>

  <clause id="4383">
    <literal><![CDATA[
      T(x / T(y,x),y) = y \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(235,a,4381,a,b,10,a)].">
      <j1 rule="hyper" parents="235 4381 10"/>
    </justification>
  </clause>

  <clause id="4384">
    <literal><![CDATA[
      (x / y) / T(y,x / y) = (y \ x) / y
    ]]></literal>
    <justification jstring="[hyper(120,a,109,a(flip),b,4381,a),flip(a)].">
      <j1 rule="hyper" parents="120 109 4381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4385">
    <literal><![CDATA[
      (x * y) / T(y,x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,1553,a,b,4381,a)].">
      <j1 rule="hyper" parents="65 1553 4381"/>
    </justification>
  </clause>

  <clause id="4386">
    <literal><![CDATA[
      T(x,T(y,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,4275,a(flip),b,4381,a)].">
      <j1 rule="hyper" parents="65 4275 4381"/>
    </justification>
  </clause>

  <clause id="4389">
    <literal><![CDATA[
      T(x,y) * T(y,x) = x * y
    ]]></literal>
    <justification jstring="[para(4381(a,1),1554(a,1,1))].">
      <j1 rule="para" parents="4381 1554"/>
    </justification>
  </clause>

  <clause id="4390">
    <literal><![CDATA[
      (((x \ y) * x) / T(x,y)) * x = T((x \ y) * x,x)
    ]]></literal>
    <justification jstring="[para(4371(a,1),4381(a,1,1,2))].">
      <j1 rule="para" parents="4371 4381"/>
    </justification>
  </clause>

  <clause id="4391">
    <literal><![CDATA[
      T(x \ y,x) = ((x \ y) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(645,a,4386,a),flip(a)].">
      <j1 rule="hyper" parents="645 4386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4392">
    <literal><![CDATA[
      T((T(x,y) * y) / T(x,y),x) = y
    ]]></literal>
    <justification jstring="[hyper(446,a,4386,a)].">
      <j1 rule="hyper" parents="446 4386"/>
    </justification>
  </clause>

  <clause id="4393">
    <literal><![CDATA[
      T(x,y) / T(y,x) = x / T(T(y,x),x)
    ]]></literal>
    <justification jstring="[hyper(120,a,4386,a(flip),b,4381,a)].">
      <j1 rule="hyper" parents="120 4386 4381"/>
    </justification>
  </clause>

  <clause id="4394">
    <literal><![CDATA[
      T(x,y) / (T(y,x) \ x) = y
    ]]></literal>
    <justification jstring="[hyper(120,a,4386,a(flip),b,1205,a)].">
      <j1 rule="hyper" parents="120 4386 1205"/>
    </justification>
  </clause>

  <clause id="4395">
    <literal><![CDATA[
      T(x,y) \ x = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,4386,a(flip),b,4192,a),flip(a)].">
      <j1 rule="hyper" parents="119 4386 4192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4396">
    <literal><![CDATA[
      T(x,y) \ y = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,4386,a(flip),b,1205,a),flip(a)].">
      <j1 rule="hyper" parents="119 4386 1205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4397">
    <literal><![CDATA[
      T(T(x,y),T(z,x)) = T(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(4386(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4386 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4398">
    <literal><![CDATA[
      T(x,T(T(y,x),z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(23(a,1),4386(a,1,2))].">
      <j1 rule="para" parents="23 4386"/>
    </justification>
  </clause>

  <clause id="4399">
    <literal><![CDATA[
      T(x,L(T(y,x),z,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(25(a,2),4386(a,1,2))].">
      <j1 rule="para" parents="25 4386"/>
    </justification>
  </clause>

  <clause id="4400">
    <literal><![CDATA[
      T(x,y / x) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(109(a,1),4386(a,1,2)),flip(a)].">
      <j1 rule="para" parents="109 4386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4401">
    <literal><![CDATA[
      T(x,y) * T(T(y,x),z) = T(y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(4386(a,1),232(a,1,2,1))].">
      <j1 rule="para" parents="4386 232"/>
    </justification>
  </clause>

  <clause id="4402">
    <literal><![CDATA[
      T(x,y) * L(T(y,x),z,u) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(4386(a,1),233(a,1,2,1))].">
      <j1 rule="para" parents="4386 233"/>
    </justification>
  </clause>

  <clause id="4403">
    <literal><![CDATA[
      T(x,y) * R(T(y,x),z,u) = R(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(4386(a,1),234(a,1,2,1))].">
      <j1 rule="para" parents="4386 234"/>
    </justification>
  </clause>

  <clause id="4404">
    <literal><![CDATA[
      T((x \ y) \ y,T(z,x)) = T(T(x,z),x \ y)
    ]]></literal>
    <justification jstring="[para(4386(a,1),297(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4386 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4405">
    <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(4386(a,1),395(a,1,2,1))].">
      <j1 rule="para" parents="4386 395"/>
    </justification>
  </clause>

  <clause id="4409">
    <literal><![CDATA[
      T(x * (T(x,y) \ x),y) = x
    ]]></literal>
    <justification jstring="[para(4386(a,1),4320(a,1,1,2,1))].">
      <j1 rule="para" parents="4386 4320"/>
    </justification>
  </clause>

  <clause id="4410">
    <literal><![CDATA[
      (x * y) / x = y * (T(y,x) \ y)
    ]]></literal>
    <justification jstring="[para(4386(a,1),4285(a,2,2,1))].">
      <j1 rule="para" parents="4386 4285"/>
    </justification>
  </clause>

  <clause id="4411">
    <literal><![CDATA[
      K(T(x,y),T(y,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4386(a,1),4334(a,1,1))].">
      <j1 rule="para" parents="4386 4334"/>
    </justification>
  </clause>

  <clause id="4412">
    <literal><![CDATA[
      R(x,T(y,x),T(x,y)) = R(x,T(y,x),x)
    ]]></literal>
    <justification jstring="[para(4386(a,1),4340(a,1,3))].">
      <j1 rule="para" parents="4386 4340"/>
    </justification>
  </clause>

  <clause id="4413">
    <literal><![CDATA[
      T(x,L(x,y,x) * y) = T(x,y * x)
    ]]></literal>
    <justification jstring="[para(4351(a,1),4386(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4351 4386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4414">
    <literal><![CDATA[
      (T(x,y) / y) * z = (x / T(y,x)) * z
    ]]></literal>
    <justification jstring="[hyper(59,a,4382,a)].">
      <j1 rule="hyper" parents="59 4382"/>
    </justification>
  </clause>

  <clause id="4415">
    <literal><![CDATA[
      (T(x,y) / y) \ x = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(186,a,4382,a(flip))].">
      <j1 rule="hyper" parents="186 4382"/>
    </justification>
  </clause>

  <clause id="4416">
    <literal><![CDATA[
      T(x,y / x) / (y / x) = x / (x \ y)
    ]]></literal>
    <justification jstring="[para(109(a,1),4382(a,2,2))].">
      <j1 rule="para" parents="109 4382"/>
    </justification>
  </clause>

  <clause id="4417">
    <literal><![CDATA[
      T(x * (y / x),x) = x * (y / T(x,y))
    ]]></literal>
    <justification jstring="[para(4382(a,1),1607(a,2,2))].">
      <j1 rule="para" parents="4382 1607"/>
    </justification>
  </clause>

  <clause id="4418">
    <literal><![CDATA[
      T(x,T(y,x) \ x) / T(y,x) = (x * (T(x,y) / y)) / x
    ]]></literal>
    <justification jstring="[para(4382(a,2),4279(a,2,1,2))].">
      <j1 rule="para" parents="4382 4279"/>
    </justification>
  </clause>

  <clause id="4419">
    <literal><![CDATA[
      T(x,y) \ (x * y) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(186,a,4385,a)].">
      <j1 rule="hyper" parents="186 4385"/>
    </justification>
  </clause>

  <clause id="4420">
    <literal><![CDATA[
      (x * R(y,z,u)) / R(T(y,x),z,u) = T(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(27(a,2),4385(a,1,2))].">
      <j1 rule="para" parents="27 4385"/>
    </justification>
  </clause>

  <clause id="4424">
    <literal><![CDATA[
      (T(x,y) * (y * x)) / T(x,y) = T(y,x) * T(T(x,y),y * x)
    ]]></literal>
    <justification jstring="[para(4385(a,1),1527(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4385 1527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4425">
    <literal><![CDATA[
      T(x,y) * (x \ T(y,x)) = y
    ]]></literal>
    <justification jstring="[hyper(1204,a,4389,a)].">
      <j1 rule="hyper" parents="1204 4389"/>
    </justification>
  </clause>

  <clause id="4426">
    <literal><![CDATA[
      T(x,x \ y) \ y = T(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,10,a(flip),b,4389,a)].">
      <j1 rule="hyper" parents="119 10 4389"/>
    </justification>
  </clause>

  <clause id="4427">
    <literal><![CDATA[
      (T(x,y) * (T(y,x) * z)) \ ((x * y) * z) = a(T(x,y),T(y,x),z)
    ]]></literal>
    <justification jstring="[para(4389(a,1),14(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4389 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4428">
    <literal><![CDATA[
      R(x,T(y,z),T(z,y)) * (y * z) = (x * T(y,z)) * T(z,y)
    ]]></literal>
    <justification jstring="[para(4389(a,1),103(a,1,2))].">
      <j1 rule="para" parents="4389 103"/>
    </justification>
  </clause>

  <clause id="4429">
    <literal><![CDATA[
      T(x,y) * (T(y,x) * z) != (x * y) * u
    ]]></literal>
    <literal><![CDATA[
      L(z,T(y,x),T(x,y)) = u
    ]]></literal>
    <justification jstring="[para(4389(a,1),490(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4389 490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4430">
    <literal><![CDATA[
      T(x,y) * (y * x) = x * (x * y)
    ]]></literal>
    <justification jstring="[para(4389(a,1),1196(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4389 1196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4431">
    <literal><![CDATA[
      T(x,T(y,z)) / (T(T(y,x),z) \ x) = T(y,z)
    ]]></literal>
    <justification jstring="[para(23(a,1),4394(a,1,2,1))].">
      <j1 rule="para" parents="23 4394"/>
    </justification>
  </clause>

  <clause id="4432">
    <literal><![CDATA[
      T(x,y \ 1) \ x = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,3516,a(flip),b,4395,a),flip(a)].">
      <j1 rule="hyper" parents="299 3516 4395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4434">
    <literal><![CDATA[
      x * ((T(y,x) \ y) * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[para(4395(a,2),4255(a,1,2,1))].">
      <j1 rule="para" parents="4395 4255"/>
    </justification>
  </clause>

  <clause id="4435">
    <literal><![CDATA[
      T(x,y) * (x \ z) = (T(y,x) \ y) * z
    ]]></literal>
    <justification jstring="[para(4395(a,2),4260(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4395 4260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4436">
    <literal><![CDATA[
      T(x,y) \ ((T(y,x) \ x) * y) = K(y \ T(x,y),y)
    ]]></literal>
    <justification jstring="[para(4396(a,2),89(a,1,2,1))].">
      <j1 rule="para" parents="4396 89"/>
    </justification>
  </clause>

  <clause id="4437">
    <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(4396(a,1),85(a,1,1,2,1))].">
      <j1 rule="para" parents="4396 85"/>
    </justification>
  </clause>

  <clause id="4438">
    <literal><![CDATA[
      T(x,y) * L(x \ T(y,x),z,u) = T(x * L(x \ y,z,u),y)
    ]]></literal>
    <justification jstring="[para(4396(a,1),2190(a,1,2,1))].">
      <j1 rule="para" parents="4396 2190"/>
    </justification>
  </clause>

  <clause id="4439">
    <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(4396(a,1),2065(a,1,2,1))].">
      <j1 rule="para" parents="4396 2065"/>
    </justification>
  </clause>

  <clause id="4440">
    <literal><![CDATA[
      T(x,y / x) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(299,a,108,a(flip),b,4400,a),flip(a)].">
      <j1 rule="hyper" parents="299 108 4400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4441">
    <literal><![CDATA[
      (x / y) * T(y,y \ x) = y * (x / y)
    ]]></literal>
    <justification jstring="[para(4400(a,1),107(a,1,2))].">
      <j1 rule="para" parents="4400 107"/>
    </justification>
  </clause>

  <clause id="4442">
    <literal><![CDATA[
      (x * (y / x)) / T(x,x \ y) = y / x
    ]]></literal>
    <justification jstring="[para(4400(a,1),185(a,1,2))].">
      <j1 rule="para" parents="4400 185"/>
    </justification>
  </clause>

  <clause id="4443">
    <literal><![CDATA[
      T(T(x / y,(x / y) \ z),y) = T(y \ x,z / (x / y))
    ]]></literal>
    <justification jstring="[para(4400(a,1),242(a,1,1))].">
      <j1 rule="para" parents="4400 242"/>
    </justification>
  </clause>

  <clause id="4445">
    <literal><![CDATA[
      (x * (y / x)) * x = y * T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(4400(a,1),889(a,2,2))].">
      <j1 rule="para" parents="4400 889"/>
    </justification>
  </clause>

  <clause id="4446">
    <literal><![CDATA[
      (x * y) \ (y * T(x,x \ y)) = a(x,y / x,x)
    ]]></literal>
    <justification jstring="[para(4400(a,1),991(a,1,2,2))].">
      <j1 rule="para" parents="4400 991"/>
    </justification>
  </clause>

  <clause id="4447">
    <literal><![CDATA[
      T(x * (y / x),z / y) = x * (T(y,y \ z) / x)
    ]]></literal>
    <justification jstring="[para(4400(a,1),3459(a,2,2,1))].">
      <j1 rule="para" parents="4400 3459"/>
    </justification>
  </clause>

  <clause id="4448">
    <literal><![CDATA[
      x \ (T(x,y / x) / (1 / (x \ y))) = (x / (1 / (x \ y))) / x
    ]]></literal>
    <justification jstring="[para(4400(a,2),4241(a,1,2,1))].">
      <j1 rule="para" parents="4400 4241"/>
    </justification>
  </clause>

  <clause id="4449">
    <literal><![CDATA[
      T(x * (T(x,y) \ x),y) = L(R(x,z,x),z,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,4346,a,b,4409,a),flip(a)].">
      <j1 rule="hyper" parents="299 4346 4409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4450">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      z * (T(z,y) \ z) = x
    ]]></literal>
    <justification jstring="[para(4409(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="4409 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4452">
    <literal><![CDATA[
      T(x,y) = (x \ (y * x)) \ (y * x)
    ]]></literal>
    <justification jstring="[para(22(a,1),4419(a,1,1)),flip(a)].">
      <j1 rule="para" parents="22 4419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4453">
    <literal><![CDATA[
      T(x,y) \ z != T(y,x)
    ]]></literal>
    <literal><![CDATA[
      x * y = z
    ]]></literal>
    <justification jstring="[para(4419(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="4419 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4454">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,x)) = z
    ]]></literal>
    <justification jstring="[para(4419(a,1),398(a,1))].">
      <j1 rule="para" parents="4419 398"/>
    </justification>
  </clause>

  <clause id="4455">
    <literal><![CDATA[
      T(x,y) * (x \ T(x * (y / x),x)) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(4372(a,1),4425(a,1,1))].">
      <j1 rule="para" parents="4372 4425"/>
    </justification>
  </clause>

  <clause id="4456">
    <literal><![CDATA[
      T(x,y / x) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,x \ y) = z
    ]]></literal>
    <justification jstring="[para(4440(a,2),338(a,1))].">
      <j1 rule="para" parents="4440 338"/>
    </justification>
  </clause>

  <clause id="4457">
    <literal><![CDATA[
      (x * (y / x)) * x = y * ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(4440(a,1),889(a,2,2))].">
      <j1 rule="para" parents="4440 889"/>
    </justification>
  </clause>

  <clause id="4459">
    <literal><![CDATA[
      ((x \ y) \ y) * T(x \ y,x) = y
    ]]></literal>
    <justification jstring="[hyper(144,a,4391,a(flip))].">
      <j1 rule="hyper" parents="144 4391"/>
    </justification>
  </clause>

  <clause id="4460">
    <literal><![CDATA[
      L((((x \ y) \ z) \ z) \ z,x \ y,x) = T(y \ (x * z),x \ y)
    ]]></literal>
    <justification jstring="[para(4391(a,1),822(a,1,1))].">
      <j1 rule="para" parents="4391 822"/>
    </justification>
  </clause>

  <clause id="4461">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (T(y,z) * z) / T(y,z) = x
    ]]></literal>
    <justification jstring="[para(4392(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="4392 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4462">
    <literal><![CDATA[
      T(x,T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4392(a,1),757(a,1,1))].">
      <j1 rule="para" parents="4392 757"/>
    </justification>
  </clause>

  <clause id="4464">
    <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),4397(a,1,2))].">
      <j1 rule="para" parents="25 4397"/>
    </justification>
  </clause>

  <clause id="4465">
    <literal><![CDATA[
      T(x,T(y,T(z,T(y,x)))) = T(x,T(T(y,x),z))
    ]]></literal>
    <justification jstring="[para(4386(a,1),4398(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4386 4398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4466">
    <literal><![CDATA[
      T(x,y / x) \ x = x \ (y / (y / x))
    ]]></literal>
    <justification jstring="[hyper(119,a,156,a(flip),b,4410,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 156 4410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4467">
    <literal><![CDATA[
      T(x,x \ T(x * y,y)) \ T(x * y,y) = R(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,4337,a(flip),b,4426,a),flip(a)].">
      <j1 rule="hyper" parents="299 4337 4426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4469">
    <literal><![CDATA[
      T(x * y,T(y,x)) = T(x * y,y)
    ]]></literal>
    <justification jstring="[para(4452(a,2),4278(a,1,2))].">
      <j1 rule="para" parents="4452 4278"/>
    </justification>
  </clause>

  <clause id="4471">
    <literal><![CDATA[
      L(x,L(T(y \ z,y),(y \ z) \ z,(y \ z) \ z),u) = L(x,((y \ z) \ z) * z,u)
    ]]></literal>
    <justification jstring="[para(4459(a,1),2520(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4459 2520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4472">
    <literal><![CDATA[
      L(x,y,(y * x) / y) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(1041,a,4353,a)].">
      <j1 rule="hyper" parents="1041 4353"/>
    </justification>
  </clause>

  <clause id="4475">
    <literal><![CDATA[
      R(T(x,y),x \ y,x) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(299,a,108,a(flip),b,4377,a),flip(a)].">
      <j1 rule="hyper" parents="299 108 4377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4477">
    <literal><![CDATA[
      T(x,L(x,y,x) * y) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(299,a,4366,a(flip),b,4413,a),flip(a)].">
      <j1 rule="hyper" parents="299 4366 4413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4478">
    <literal><![CDATA[
      T(x,(x \ y) * T(x,y)) = T(x,(x \ y) * x)
    ]]></literal>
    <justification jstring="[para(791(a,1),4413(a,1,2))].">
      <j1 rule="para" parents="791 4413"/>
    </justification>
  </clause>

  <clause id="4479">
    <literal><![CDATA[
      R(T(x,x * y),y,T(x,x * y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4477(a,1),1562(a,1,1))].">
      <j1 rule="para" parents="4477 1562"/>
    </justification>
  </clause>

  <clause id="4481">
    <literal><![CDATA[
      (((1 / x) * ((y * (x * x)) * (1 / x))) / (1 / x)) / T(1 / x,T(x * y,x * x)) = y * (x * x)
    ]]></literal>
    <justification jstring="[para(695(a,1),4357(a,1,2,2))].">
      <j1 rule="para" parents="695 4357"/>
    </justification>
  </clause>

  <clause id="4482">
    <literal><![CDATA[
      x * T(y,z) != y * L(z,y,z)
    ]]></literal>
    <literal><![CDATA[
      L(z,y,z) = x
    ]]></literal>
    <justification jstring="[para(4364(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="4364 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4483">
    <literal><![CDATA[
      T(T(x,y),z * x) = T(T(x,y),x * z)
    ]]></literal>
    <justification jstring="[hyper(861,a,4373,a),flip(a)].">
      <j1 rule="hyper" parents="861 4373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4484">
    <literal><![CDATA[
      T(T(x,y),x * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(T(x,y),z * x) = u
    ]]></literal>
    <justification jstring="[para(4374(a,1),861(a,1))].">
      <j1 rule="para" parents="4374 861"/>
    </justification>
  </clause>

  <clause id="4485">
    <literal><![CDATA[
      (x / y) / T(y,y \ x) = (y \ x) / y
    ]]></literal>
    <justification jstring="[para(4400(a,1),4384(a,1,2))].">
      <j1 rule="para" parents="4400 4384"/>
    </justification>
  </clause>

  <clause id="4486">
    <literal><![CDATA[
      K(x \ (x / y),x) = T(x,y \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(299,a,1290,a,b,4432,a)].">
      <j1 rule="hyper" parents="299 1290 4432"/>
    </justification>
  </clause>

  <clause id="4488">
    <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(4432(a,2),493(a,1,1))].">
      <j1 rule="para" parents="4432 493"/>
    </justification>
  </clause>

  <clause id="4490">
    <literal><![CDATA[
      (T(x,y / z) \ x) * y = z * T(z \ y,x)
    ]]></literal>
    <justification jstring="[hyper(36,a,1217,a,b,4434,a),flip(a)].">
      <j1 rule="hyper" parents="36 1217 4434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4491">
    <literal><![CDATA[
      (T(x,y) \ x) * (x * y) = y * x
    ]]></literal>
    <justification jstring="[hyper(36,a,4430,a(flip),b,4434,a),flip(a)].">
      <j1 rule="hyper" parents="36 4430 4434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4492">
    <literal><![CDATA[
      K(x,y) = T(T(y,x) \ y,y * x)
    ]]></literal>
    <justification jstring="[hyper(235,a,4491,a,b,88,a),flip(a)].">
      <j1 rule="hyper" parents="235 4491 88"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4493">
    <literal><![CDATA[
      (x * y) / (y * x) = T(y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(137,a,4491,a)].">
      <j1 rule="hyper" parents="137 4491"/>
    </justification>
  </clause>

  <clause id="4494">
    <literal><![CDATA[
      T(x,y / x) \ x = y / (x * (y / x))
    ]]></literal>
    <justification jstring="[hyper(120,a,12,a(flip),b,4491,a),flip(a)].">
      <j1 rule="hyper" parents="120 12 4491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4497">
    <literal><![CDATA[
      T(T(x,x \ y) \ x,y) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),4492(a,2,2)),flip(a)].">
      <j1 rule="para" parents="10 4492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4498">
    <literal><![CDATA[
      K(x,y) = T(x \ T(x,y),y * x)
    ]]></literal>
    <justification jstring="[para(4395(a,1),4492(a,2,1))].">
      <j1 rule="para" parents="4395 4492"/>
    </justification>
  </clause>

  <clause id="4499">
    <literal><![CDATA[
      T(x / y,y) \ (x / y) = (y * (x / y)) / x
    ]]></literal>
    <justification jstring="[para(12(a,1),4493(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 4493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4500">
    <literal><![CDATA[
      x \ y != (z * y) / (y * z)
    ]]></literal>
    <literal><![CDATA[
      T(y,z) = x
    ]]></literal>
    <justification jstring="[para(4493(a,2),50(a,1)),flip(a)].">
      <j1 rule="para" parents="4493 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4501">
    <literal><![CDATA[
      x \ T(x,T(y,(y \ 1) * x) \ 1) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,4219,a(flip),b,4498,a)].">
      <j1 rule="hyper" parents="299 4219 4498"/>
    </justification>
  </clause>

  <clause id="4502">
    <literal><![CDATA[
      T(x / (x / y),y \ x) = y
    ]]></literal>
    <justification jstring="[hyper(806,a,4441,a)].">
      <j1 rule="hyper" parents="806 4441"/>
    </justification>
  </clause>

  <clause id="4503">
    <literal><![CDATA[
      x / (x / y) = y * (T(y,y \ x) \ y)
    ]]></literal>
    <justification jstring="[hyper(4450,a,4502,a),flip(a)].">
      <j1 rule="hyper" parents="4450 4502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4504">
    <literal><![CDATA[
      ((x \ y) * x) / (x \ y) = y / (y / x)
    ]]></literal>
    <justification jstring="[hyper(267,a,4502,a)].">
      <j1 rule="hyper" parents="267 4502"/>
    </justification>
  </clause>

  <clause id="4506">
    <literal><![CDATA[
      T(x / (x / (x / y)),y) = x / y
    ]]></literal>
    <justification jstring="[para(79(a,1),4502(a,1,2))].">
      <j1 rule="para" parents="79 4502"/>
    </justification>
  </clause>

  <clause id="4508">
    <literal><![CDATA[
      (x * (y / x)) / x = y / (y / (y / x))
    ]]></literal>
    <justification jstring="[hyper(267,a,4506,a)].">
      <j1 rule="hyper" parents="267 4506"/>
    </justification>
  </clause>

  <clause id="4509">
    <literal><![CDATA[
      R(x / y,x / (x / y),x / y) = T((x * (x / y)) / x,y)
    ]]></literal>
    <justification jstring="[para(4506(a,1),840(a,1,1))].">
      <j1 rule="para" parents="4506 840"/>
    </justification>
  </clause>

  <clause id="4510">
    <literal><![CDATA[
      (x \ y) * T(y,y \ (x \ y)) = (x \ T(y,x \ 1)) * y
    ]]></literal>
    <justification jstring="[para(4229(a,2),4445(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4229 4445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4511">
    <literal><![CDATA[
      T(x * (y / x),x) = x \ (y * ((x \ y) \ y))
    ]]></literal>
    <justification jstring="[hyper(235,a,4457,a,b,10,a)].">
      <j1 rule="hyper" parents="235 4457 10"/>
    </justification>
  </clause>

  <clause id="4513">
    <literal><![CDATA[
      T(x,x \ y) \ x = x \ (y / (y / x))
    ]]></literal>
    <justification jstring="[para(4400(a,1),4466(a,1,1))].">
      <j1 rule="para" parents="4400 4466"/>
    </justification>
  </clause>

  <clause id="4514">
    <literal><![CDATA[
      T(T(x,y),z * x) != u
    ]]></literal>
    <literal><![CDATA[
      T(T(x,x * z),y) = u
    ]]></literal>
    <justification jstring="[para(4483(a,2),861(a,1))].">
      <j1 rule="para" parents="4483 861"/>
    </justification>
  </clause>

  <clause id="4515">
    <literal><![CDATA[
      T((x / y) / T(y,y \ x),y \ 1) = (y \ 1) \ ((y \ x) / (y * y))
    ]]></literal>
    <justification jstring="[para(4485(a,2),1255(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4485 1255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4516">
    <literal><![CDATA[
      K(x \ (x / y),x) \ x = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(4486(a,2),3652(a,1,1))].">
      <j1 rule="para" parents="4486 3652"/>
    </justification>
  </clause>

  <clause id="4517">
    <literal><![CDATA[
      x / (y * (x / y)) = y \ (x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(65,a,4466,a(flip),b,4494,a),flip(a)].">
      <j1 rule="hyper" parents="65 4466 4494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4518">
    <literal><![CDATA[
      (x * y) / ((x * y) / x) = x * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[para(9(a,1),4503(a,2,2,1,2))].">
      <j1 rule="para" parents="9 4503"/>
    </justification>
  </clause>

  <clause id="4519">
    <literal><![CDATA[
      T(x / (x / y),x) = L(y,y \ x,y)
    ]]></literal>
    <justification jstring="[para(4504(a,1),795(a,1,1))].">
      <j1 rule="para" parents="4504 795"/>
    </justification>
  </clause>

  <clause id="4520">
    <literal><![CDATA[
      T(T(x / (x / y),x),z) = L(T(y,z),y \ x,y)
    ]]></literal>
    <justification jstring="[para(4519(a,2),25(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4519 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4521">
    <literal><![CDATA[
      L(x \ y,(x \ y) \ y,x \ y) = T(y / x,y)
    ]]></literal>
    <justification jstring="[para(76(a,1),4519(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="76 4519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4523">
    <literal><![CDATA[
      R(1 / (1 / (1 / x)),x,y) = (x * (y / (x * y))) / x
    ]]></literal>
    <justification jstring="[para(4508(a,1),976(a,1,1))].">
      <j1 rule="para" parents="4508 976"/>
    </justification>
  </clause>

  <clause id="4524">
    <literal><![CDATA[
      T(x \ (y / (y / x)),y) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(4513(a,1),4497(a,1,1))].">
      <j1 rule="para" parents="4513 4497"/>
    </justification>
  </clause>

  <clause id="4525">
    <literal><![CDATA[
      T(x,(y \ x) \ 1) = K(x \ y,x) \ x
    ]]></literal>
    <justification jstring="[para(76(a,1),4516(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="76 4516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4526">
    <literal><![CDATA[
      K(x \ y,x) \ x = x * K(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(4195,a,4525,a),flip(a)].">
      <j1 rule="hyper" parents="4195 4525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4528">
    <literal><![CDATA[
      T(x,y) * T(T(y,x),x) = y * x
    ]]></literal>
    <justification jstring="[hyper(299,a,4389,a(flip),b,4401,a),flip(a)].">
      <j1 rule="hyper" parents="299 4389 4401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4529">
    <literal><![CDATA[
      (x * y) / T(T(x,y),y) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(120,a,4389,a(flip),b,4401,a)].">
      <j1 rule="hyper" parents="120 4389 4401"/>
    </justification>
  </clause>

  <clause id="4530">
    <literal><![CDATA[
      T(x,y) \ (y * x) = T(T(y,x),x)
    ]]></literal>
    <justification jstring="[hyper(119,a,4389,a(flip),b,4401,a)].">
      <j1 rule="hyper" parents="119 4389 4401"/>
    </justification>
  </clause>

  <clause id="4531">
    <literal><![CDATA[
      T(x,y) * T(T(y,z),x) = T(y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(23(a,1),4401(a,1,2))].">
      <j1 rule="para" parents="23 4401"/>
    </justification>
  </clause>

  <clause id="4532">
    <literal><![CDATA[
      T(T(x,x \ y),x \ y) = T(x \ y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(119,a,10,a(flip),b,4528,a),flip(a)].">
      <j1 rule="hyper" parents="119 10 4528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4533">
    <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),4530(a,1,1))].">
      <j1 rule="para" parents="25 4530"/>
    </justification>
  </clause>

  <clause id="4534">
    <literal><![CDATA[
      T(x,T(y,T(z,T(y,x)))) / (T(T(y,x),z) \ x) = T(y,T(z,T(y,x)))
    ]]></literal>
    <justification jstring="[para(4386(a,1),4431(a,1,2,1))].">
      <j1 rule="para" parents="4386 4431"/>
    </justification>
  </clause>

  <clause id="4535">
    <literal><![CDATA[
      T((x * y) / x,T(x,y)) = L(R(y,z,y),z,y)
    ]]></literal>
    <justification jstring="[para(4285(a,2),4449(a,1,1))].">
      <j1 rule="para" parents="4285 4449"/>
    </justification>
  </clause>

  <clause id="4536">
    <literal><![CDATA[
      T(x,T(y,T(z,T(y,x)))) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,4398,a(flip),b,4465,a),flip(a)].">
      <j1 rule="hyper" parents="299 4398 4465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4537">
    <literal><![CDATA[
      T(x,(x \ y) * T(x,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,4371,a(flip),b,4478,a),flip(a)].">
      <j1 rule="hyper" parents="299 4371 4478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4538">
    <literal><![CDATA[
      R(T(x,y),x \ y,T(x,y)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(4537(a,1),1548(a,1,1))].">
      <j1 rule="para" parents="4537 1548"/>
    </justification>
  </clause>

  <clause id="4539">
    <literal><![CDATA[
      x * K(y \ (y / (x \ z)),y) = (T(y,x / z) \ y) * x
    ]]></literal>
    <justification jstring="[hyper(299,a,1385,a(flip),b,4490,a)].">
      <j1 rule="hyper" parents="299 1385 4490"/>
    </justification>
  </clause>

  <clause id="4540">
    <literal><![CDATA[
      (x * (y / x)) / y = (x \ y) \ (y / x)
    ]]></literal>
    <justification jstring="[para(109(a,1),4499(a,1,1)),flip(a)].">
      <j1 rule="para" parents="109 4499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4541">
    <literal><![CDATA[
      (x * (y / x)) / y = x \ ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[hyper(299,a,4203,a(flip),b,4540,a),flip(a)].">
      <j1 rule="hyper" parents="299 4203 4540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4542">
    <literal><![CDATA[
      x \ (y * ((x \ y) \ y)) = x * (y / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,4417,a(flip),b,4511,a),flip(a)].">
      <j1 rule="hyper" parents="65 4417 4511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4543">
    <literal><![CDATA[
      x / (y \ ((y * x) / y)) = y * (T(y,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,1448,a(flip),b,4518,a)].">
      <j1 rule="hyper" parents="65 1448 4518"/>
    </justification>
  </clause>

  <clause id="4544">
    <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="[para(4531(a,1),813(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4531 813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4545">
    <literal><![CDATA[
      T(x \ T(x * y,y),T(x * y,y)) = L(R(y,z,y),z,y)
    ]]></literal>
    <justification jstring="[para(4302(a,1),4535(a,1,1))].">
      <j1 rule="para" parents="4302 4535"/>
    </justification>
  </clause>

  <clause id="4546">
    <literal><![CDATA[
      (x * (T(x,y) \ x)) \ y = x \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(186,a,4543,a)].">
      <j1 rule="hyper" parents="186 4543"/>
    </justification>
  </clause>

  <clause id="4547">
    <literal><![CDATA[
      ((x * y) / x) * T(((x * y) / x) \ x,y) = x * K(y \ (x * (T(x,y) \ x)),y)
    ]]></literal>
    <justification jstring="[para(4543(a,1),1385(a,2,2,1,2))].">
      <j1 rule="para" parents="4543 1385"/>
    </justification>
  </clause>

  <clause id="4548">
    <literal><![CDATA[
      ((x * y) / x) \ x = y \ ((y * x) / y)
    ]]></literal>
    <justification jstring="[para(4410(a,2),4546(a,1,1))].">
      <j1 rule="para" parents="4410 4546"/>
    </justification>
  </clause>

  <clause id="4549">
    <literal><![CDATA[
      x \ (y * (T(y,x) \ y)) = ((y * x) / y) \ y
    ]]></literal>
    <justification jstring="[para(4410(a,1),4548(a,2,2)),flip(a)].">
      <j1 rule="para" parents="4410 4548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4550">
    <literal><![CDATA[
      (x \ T(x,y)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      x * (T(x,y) \ z) = u
    ]]></literal>
    <justification jstring="[para(10(a,1),4312(a,1,2))].">
      <j1 rule="para" parents="10 4312"/>
    </justification>
  </clause>

  <clause id="4551">
    <literal><![CDATA[
      x * (T(L(y \ 1,y,x) \ 1,x) \ (L(y \ 1,y,x) \ 1)) = K(y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(4194,a,4336,a)].">
      <j1 rule="hyper" parents="4194 4336"/>
    </justification>
  </clause>

  <clause id="4554">
    <literal><![CDATA[
      T(L(x \ 1,x,y) \ 1,y) \ (L(x \ 1,x,y) \ 1) = K(x,y) \ 1
    ]]></literal>
    <justification jstring="[para(1382(a,2),4268(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1382 4268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4555">
    <literal><![CDATA[
      T((x \ y) \ 1,z) \ ((x \ y) \ 1) = (x \ (y * T(y \ x,z))) \ 1
    ]]></literal>
    <justification jstring="[para(1383(a,1),4268(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1383 4268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4556">
    <literal><![CDATA[
      (x * (y \ T(y,x))) \ x = T(y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(3775,a,4324,a)].">
      <j1 rule="hyper" parents="3775 4324"/>
    </justification>
  </clause>

  <clause id="4557">
    <literal><![CDATA[
      ((x * y) / x) \ y = T(x,y) \ x
    ]]></literal>
    <justification jstring="[para(4178(a,1),4556(a,1,1))].">
      <j1 rule="para" parents="4178 4556"/>
    </justification>
  </clause>

  <clause id="4558">
    <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(4557(a,1),1236(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4557 1236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4559">
    <literal><![CDATA[
      ((x * y) / x) * (y \ ((T(x,y) \ x) * z)) = L(z,((x * y) / x) \ y,(x * y) / x)
    ]]></literal>
    <justification jstring="[para(4557(a,1),1427(a,1,2,2,1))].">
      <j1 rule="para" parents="4557 1427"/>
    </justification>
  </clause>

  <clause id="4560">
    <literal><![CDATA[
      (T(x,y) \ x) * ((x * y) / x) = y
    ]]></literal>
    <justification jstring="[para(4557(a,1),3544(a,1,1))].">
      <j1 rule="para" parents="4557 3544"/>
    </justification>
  </clause>

  <clause id="4561">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) \ x = ((x * y) / x) \ y
    ]]></literal>
    <justification jstring="[para(4188(a,2),4557(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4188 4557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4562">
    <literal><![CDATA[
      L(x,y,y \ 1) \ ((1 / y) * (x * y)) = T(y,(1 / y) * (x * y)) \ y
    ]]></literal>
    <justification jstring="[hyper(4017,a,4560,a)].">
      <j1 rule="hyper" parents="4017 4560"/>
    </justification>
  </clause>

  <clause id="4563">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) \ 1 = x \ (((x * y) / x) \ y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4561,a(flip),b,1193,a),flip(a)].">
      <j1 rule="hyper" parents="119 4561 1193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4564">
    <literal><![CDATA[
      R(K(x,y),x,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,4205,a,b,4327,a),flip(a)].">
      <j1 rule="hyper" parents="299 4205 4327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4565">
    <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(4327(a,1),556(a,1))].">
      <j1 rule="para" parents="4327 556"/>
    </justification>
  </clause>

  <clause id="4567">
    <literal><![CDATA[
      K(x,y) * (1 / x) = K(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(120,a,4564,a(flip),b,1754,a),flip(a)].">
      <j1 rule="hyper" parents="120 4564 1754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4568">
    <literal><![CDATA[
      (K(x,y) * x) * z = K(x,y) * (x * z)
    ]]></literal>
    <justification jstring="[para(4564(a,1),103(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4564 103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4569">
    <literal><![CDATA[
      (1 / x) * K(x,y) = K(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(1510,a,4567,a)].">
      <j1 rule="hyper" parents="1510 4567"/>
    </justification>
  </clause>

  <clause id="4570">
    <literal><![CDATA[
      L(x,y,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(490,a,4568,a)].">
      <j1 rule="hyper" parents="490 4568"/>
    </justification>
  </clause>

  <clause id="4571">
    <literal><![CDATA[
      L(x,y \ 1,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(2641,a,4570,a)].">
      <j1 rule="hyper" parents="2641 4570"/>
    </justification>
  </clause>

  <clause id="4572">
    <literal><![CDATA[
      L(x,y,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(4570(a,1),52(a,2))].">
      <j1 rule="para" parents="4570 52"/>
    </justification>
  </clause>

  <clause id="4573">
    <literal><![CDATA[
      K(x,y) * ((x \ 1) * z) = (x \ K(x,y)) * z
    ]]></literal>
    <justification jstring="[para(4571(a,1),3790(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4571 3790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4574">
    <literal><![CDATA[
      K(x,y) / ((x \ 1) \ 1) = x \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(385,a,4573,a)].">
      <j1 rule="hyper" parents="385 4573"/>
    </justification>
  </clause>

  <clause id="4575">
    <literal><![CDATA[
      T(x,x \ K(x,y)) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(427,a,4573,a(flip))].">
      <j1 rule="hyper" parents="427 4573"/>
    </justification>
  </clause>

  <clause id="4576">
    <literal><![CDATA[
      (x \ K(x,y)) * T((x \ 1) \ 1,z) = T(x,z) * (x \ K(x,y))
    ]]></literal>
    <justification jstring="[para(4575(a,1),232(a,1,2,1))].">
      <j1 rule="para" parents="4575 232"/>
    </justification>
  </clause>

  <clause id="4577">
    <literal><![CDATA[
      (x \ K(x,y)) * T(x,x \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(708,a,4574,a)].">
      <j1 rule="hyper" parents="708 4574"/>
    </justification>
  </clause>

  <clause id="4578">
    <literal><![CDATA[
      ((x \ y) / y) \ T((x \ y) / y,z) = x * T(x \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(1306,a,4329,a),flip(a)].">
      <j1 rule="hyper" parents="1306 4329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4582">
    <literal><![CDATA[
      ((x \ y) * x) / T(x,y) = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(37,a,3483,a(flip),b,4390,a),flip(a)].">
      <j1 rule="hyper" parents="37 3483 4390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4583">
    <literal><![CDATA[
      (x \ T(y,x)) * T(x,y) = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(143,a,4582,a)].">
      <j1 rule="hyper" parents="143 4582"/>
    </justification>
  </clause>

  <clause id="4586">
    <literal><![CDATA[
      T(x,y) * T(y,y * x) = L(y,x,y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(784(a,1),4402(a,1,2))].">
      <j1 rule="para" parents="784 4402"/>
    </justification>
  </clause>

  <clause id="4587">
    <literal><![CDATA[
      T(x,y) * T(y,y * x) = x * L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,4364,a(flip),b,4586,a),flip(a)].">
      <j1 rule="hyper" parents="299 4364 4586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4589">
    <literal><![CDATA[
      T(x,y) * T(y,x * y) = x * L(y,x,y)
    ]]></literal>
    <justification jstring="[para(4366(a,2),4587(a,1,2))].">
      <j1 rule="para" parents="4366 4587"/>
    </justification>
  </clause>

  <clause id="4590">
    <literal><![CDATA[
      L(x,T(y,x),x) * T(y,x) = y * L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,792,a,b,4589,a)].">
      <j1 rule="hyper" parents="65 792 4589"/>
    </justification>
  </clause>

  <clause id="4592">
    <literal><![CDATA[
      L(x,T(y,x),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(4482,a,4590,a),flip(a)].">
      <j1 rule="hyper" parents="4482 4590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4593">
    <literal><![CDATA[
      ((x * (y * x)) / x) / y = L(x,T(y,x),x)
    ]]></literal>
    <justification jstring="[hyper(299,a,4358,a,b,4592,a)].">
      <j1 rule="hyper" parents="299 4358 4592"/>
    </justification>
  </clause>

  <clause id="4594">
    <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(4403(a,1),226(a,1,1,2))].">
      <j1 rule="para" parents="4403 226"/>
    </justification>
  </clause>

  <clause id="4595">
    <literal><![CDATA[
      R(x,y,x) * T(x * y,x) = T(x * y,x) * T(x,y)
    ]]></literal>
    <justification jstring="[para(4375(a,1),4403(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4375 4403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4596">
    <literal><![CDATA[
      T(x * (y / x),z / y) = T(x * (y / x),y \ z)
    ]]></literal>
    <justification jstring="[hyper(299,a,3459,a,b,4447,a),flip(a)].">
      <j1 rule="hyper" parents="299 3459 4447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4598">
    <literal><![CDATA[
      T(x,y) * (T(y,x) / x) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(1610(a,1),4455(a,1,2))].">
      <j1 rule="para" parents="1610 4455"/>
    </justification>
  </clause>

  <clause id="4599">
    <literal><![CDATA[
      T(x,y) * z != x * (y / x)
    ]]></literal>
    <literal><![CDATA[
      T(y,x) / x = z
    ]]></literal>
    <justification jstring="[para(4598(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="4598 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4600">
    <literal><![CDATA[
      T(x,y) * (y / T(x,y)) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(4382(a,1),4598(a,1,2))].">
      <j1 rule="para" parents="4382 4598"/>
    </justification>
  </clause>

  <clause id="4601">
    <literal><![CDATA[
      T(x,y) * z != x * (y / x)
    ]]></literal>
    <literal><![CDATA[
      y / T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4600(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="4600 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4602">
    <literal><![CDATA[
      L(x,K(y,z \ 1),y) = x
    ]]></literal>
    <justification jstring="[para(4501(a,1),4256(a,1,2))].">
      <j1 rule="para" parents="4501 4256"/>
    </justification>
  </clause>

  <clause id="4603">
    <literal><![CDATA[
      R(x,K(x,y \ 1),z) = x
    ]]></literal>
    <justification jstring="[para(4501(a,1),4308(a,1,2))].">
      <j1 rule="para" parents="4501 4308"/>
    </justification>
  </clause>

  <clause id="4604">
    <literal><![CDATA[
      L(x,K(y,z),y) = x
    ]]></literal>
    <justification jstring="[para(79(a,1),4602(a,1,2,2))].">
      <j1 rule="para" parents="79 4602"/>
    </justification>
  </clause>

  <clause id="4605">
    <literal><![CDATA[
      a(x,K(x,y),z) = 1
    ]]></literal>
    <justification jstring="[hyper(55,a,4604,a)].">
      <j1 rule="hyper" parents="55 4604"/>
    </justification>
  </clause>

  <clause id="4606">
    <literal><![CDATA[
      L(x,K(y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(4604(a,1),52(a,2))].">
      <j1 rule="para" parents="4604 52"/>
    </justification>
  </clause>

  <clause id="4607">
    <literal><![CDATA[
      ((1 / x) * (K(x,y) * z)) * 1 = (K(x,y) * (1 / x)) * z
    ]]></literal>
    <justification jstring="[para(4605(a,1),2139(a,1,2))].">
      <j1 rule="para" parents="4605 2139"/>
    </justification>
  </clause>

  <clause id="4608">
    <literal><![CDATA[
      R(x,K(x,y),z) = x
    ]]></literal>
    <justification jstring="[para(79(a,1),4603(a,1,2,2))].">
      <j1 rule="para" parents="79 4603"/>
    </justification>
  </clause>

  <clause id="4609">
    <literal><![CDATA[
      R(T(x,y),K(x,z),u) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4608(a,1),27(a,2,1))].">
      <j1 rule="para" parents="4608 27"/>
    </justification>
  </clause>

  <clause id="4610">
    <literal><![CDATA[
      (L(x,y,z) * K(x,u)) * w = L(x,y,z) * (K(x,u) * w)
    ]]></literal>
    <justification jstring="[para(4608(a,1),542(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4608 542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4611">
    <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(4609(a,1),543(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4609 543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4612">
    <literal><![CDATA[
      K(T(x,T(y,x)),T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(4333(a,1),4565(a,1))].">
      <j1 rule="para" parents="4333 4565"/>
    </justification>
  </clause>

  <clause id="4613">
    <literal><![CDATA[
      R(K(x,y),x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(4327(a,2),4565(a,1))].">
      <j1 rule="para" parents="4327 4565"/>
    </justification>
  </clause>

  <clause id="4614">
    <literal><![CDATA[
      1 / T(x,R(T(y,x),T(y,x) \ 1,x)) = (y \ T(y,x)) / x
    ]]></literal>
    <justification jstring="[hyper(120,a,4286,a(flip),b,3657,a),flip(a)].">
      <j1 rule="hyper" parents="120 4286 3657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4615">
    <literal><![CDATA[
      K(x \ y,T(x,y)) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(4307,a,4298,a),flip(a)].">
      <j1 rule="hyper" parents="4307 4298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4616">
    <literal><![CDATA[
      K(x \ (x * y),x) = K(y,T(x,x * y))
    ]]></literal>
    <justification jstring="[hyper(65,a,722,a(flip),b,4615,a),flip(a)].">
      <j1 rule="hyper" parents="65 722 4615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4617">
    <literal><![CDATA[
      K(x,T(y,y * x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,722,a(flip),b,4616,a),flip(a)].">
      <j1 rule="hyper" parents="65 722 4616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4619">
    <literal><![CDATA[
      K(x,T(y,x * y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4366(a,2),4617(a,1,2))].">
      <j1 rule="para" parents="4366 4617"/>
    </justification>
  </clause>

  <clause id="4620">
    <literal><![CDATA[
      (x \ ((x * y) / x)) * x = (x \ y) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(4362,a,3674,a),flip(a)].">
      <j1 rule="hyper" parents="4362 3674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4621">
    <literal><![CDATA[
      T(L(L(x,y,x),z,u) * y,x) = L(x,z,u) * T(y,x)
    ]]></literal>
    <justification jstring="[para(4368(a,1),1984(a,1,1))].">
      <j1 rule="para" parents="4368 1984"/>
    </justification>
  </clause>

  <clause id="4622">
    <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(2116(a,1),4420(a,1,2,1))].">
      <j1 rule="para" parents="2116 4420"/>
    </justification>
  </clause>

  <clause id="4623">
    <literal><![CDATA[
      T(x,x \ (((x * y) / x) \ y)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(4563(a,1),3193(a,1,2))].">
      <j1 rule="para" parents="4563 3193"/>
    </justification>
  </clause>

  <clause id="4624">
    <literal><![CDATA[
      T(x,x \ (y \ T(y,x))) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(223(a,1),4623(a,1,2,2,1))].">
      <j1 rule="para" parents="223 4623"/>
    </justification>
  </clause>

  <clause id="4625">
    <literal><![CDATA[
      T(x,x \ ((((x * y) \ x) \ 1) \ (((x * y) \ x) \ K(y,x)))) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1378(a,1),4624(a,1,2,2,2))].">
      <j1 rule="para" parents="1378 4624"/>
    </justification>
  </clause>

  <clause id="4626">
    <literal><![CDATA[
      R(x,y,x) * T(x * y,x) = (x * y) * R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,4349,a(flip),b,4595,a),flip(a)].">
      <j1 rule="hyper" parents="299 4349 4595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4627">
    <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(4626(a,1),4345(a,1,2))].">
      <j1 rule="para" parents="4626 4345"/>
    </justification>
  </clause>

  <clause id="4628">
    <literal><![CDATA[
      T(x \ y,z / (y / x)) = T(x \ y,(y / x) \ z)
    ]]></literal>
    <justification jstring="[hyper(753,a,4443,a),flip(a)].">
      <j1 rule="hyper" parents="753 4443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4629">
    <literal><![CDATA[
      (T(x,(y / z) / (1 / z)) \ x) * (y / z) = T(y,x) / z
    ]]></literal>
    <justification jstring="[hyper(65,a,1394,a(flip),b,4539,a),flip(a)].">
      <j1 rule="hyper" parents="65 1394 4539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4630">
    <literal><![CDATA[
      T(x \ T(x * y,y),T(x * y,y)) = y
    ]]></literal>
    <justification jstring="[hyper(299,a,4346,a(flip),b,4545,a),flip(a)].">
      <j1 rule="hyper" parents="299 4346 4545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4631">
    <literal><![CDATA[
      T(x,x \ T(x * y,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4630(a,1),4304(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4630 4304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4632">
    <literal><![CDATA[
      T(x,y) \ T(x * y,y) = R(y,x,y)
    ]]></literal>
    <justification jstring="[para(4631(a,1),4467(a,1,1))].">
      <j1 rule="para" parents="4631 4467"/>
    </justification>
  </clause>

  <clause id="4633">
    <literal><![CDATA[
      (x \ (y * x)) \ T(y * x,x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(22(a,1),4632(a,1,1))].">
      <j1 rule="para" parents="22 4632"/>
    </justification>
  </clause>

  <clause id="4634">
    <literal><![CDATA[
      T(x,T((y \ z) / z,x)) = (y * T(y \ 1,x)) \ x
    ]]></literal>
    <justification jstring="[para(4578(a,1),4266(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4578 4266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4635">
    <literal><![CDATA[
      T(x,T((y \ z) / z,x)) = T(x,T(y \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(299,a,4290,a(flip),b,4634,a),flip(a)].">
      <j1 rule="hyper" parents="299 4290 4634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4636">
    <literal><![CDATA[
      T(x,T(y \ 1,x)) = T(x,(y \ z) / z)
    ]]></literal>
    <justification jstring="[hyper(4462,a,4635,a),flip(a)].">
      <j1 rule="hyper" parents="4462 4635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4637">
    <literal><![CDATA[
      T(x,(y \ z) / z) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(4462,a,4636,a),flip(a)].">
      <j1 rule="hyper" parents="4462 4636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4638">
    <literal><![CDATA[
      T(x,(y \ z) / z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ 1) = u
    ]]></literal>
    <justification jstring="[para(4636(a,1),4462(a,1))].">
      <j1 rule="para" parents="4636 4462"/>
    </justification>
  </clause>

  <clause id="4639">
    <literal><![CDATA[
      T(x,x \ (y \ x)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(4456,a,4637,a)].">
      <j1 rule="hyper" parents="4456 4637"/>
    </justification>
  </clause>

  <clause id="4641">
    <literal><![CDATA[
      T(x,(y / z) \ 1) = T(x,z / y)
    ]]></literal>
    <justification jstring="[para(79(a,1),4637(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 4637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4642">
    <literal><![CDATA[
      T(x * y,(x * y) \ y) = T(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),4639(a,1,2,2))].">
      <j1 rule="para" parents="9 4639"/>
    </justification>
  </clause>

  <clause id="4643">
    <literal><![CDATA[
      T(x,(x / y) \ 1) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(79(a,1),4639(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="79 4639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4644">
    <literal><![CDATA[
      (x \ (y \ x)) * T(x,y \ 1) = y \ x
    ]]></literal>
    <justification jstring="[para(4639(a,1),220(a,1,2))].">
      <j1 rule="para" parents="4639 220"/>
    </justification>
  </clause>

  <clause id="4645">
    <literal><![CDATA[
      x \ ((y \ (z \ y)) \ (z \ y)) = x \ T(y,z \ 1)
    ]]></literal>
    <justification jstring="[para(4639(a,1),293(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4639 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4646">
    <literal><![CDATA[
      T(x,y \ 1) \ (y \ T(x,y \ 1)) = x \ (y \ x)
    ]]></literal>
    <justification jstring="[para(4639(a,1),4317(a,1,1))].">
      <j1 rule="para" parents="4639 4317"/>
    </justification>
  </clause>

  <clause id="4647">
    <literal><![CDATA[
      (x \ T(y,x \ 1)) * y = (x \ y) * T(y,x \ 1)
    ]]></literal>
    <justification jstring="[para(4639(a,1),4510(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4639 4510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4648">
    <literal><![CDATA[
      T(x * (y / x),(y / z) \ 1) = T(x * (y / x),y \ z)
    ]]></literal>
    <justification jstring="[hyper(299,a,4596,a(flip),b,4641,a),flip(a)].">
      <j1 rule="hyper" parents="299 4596 4641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4649">
    <literal><![CDATA[
      T(x,(L(y,z,y) * z) \ 1) = T(x,y / (y * (z * y)))
    ]]></literal>
    <justification jstring="[para(4352(a,1),4641(a,1,2,1))].">
      <j1 rule="para" parents="4352 4641"/>
    </justification>
  </clause>

  <clause id="4650">
    <literal><![CDATA[
      (x / y) \ T(x,x \ y) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(4643(a,1),4236(a,1,2))].">
      <j1 rule="para" parents="4643 4236"/>
    </justification>
  </clause>

  <clause id="4651">
    <literal><![CDATA[
      (x \ ((1 / y) \ x)) * T(x,y) = (1 / y) \ x
    ]]></literal>
    <justification jstring="[para(79(a,1),4644(a,1,2,2))].">
      <j1 rule="para" parents="79 4644"/>
    </justification>
  </clause>

  <clause id="4652">
    <literal><![CDATA[
      (x \ ((y \ 1) \ x)) * T(x,y) = (y \ 1) \ x
    ]]></literal>
    <justification jstring="[para(3739(a,1),4644(a,1,2))].">
      <j1 rule="para" parents="3739 4644"/>
    </justification>
  </clause>

  <clause id="4653">
    <literal><![CDATA[
      T(x,y * (((((z \ (u \ z)) \ 1) \ 1) * T(z,u \ 1)) \ w)) = T(x,y * ((u \ z) \ w))
    ]]></literal>
    <justification jstring="[para(4644(a,1),3901(a,2,2,2,1))].">
      <j1 rule="para" parents="4644 3901"/>
    </justification>
  </clause>

  <clause id="4654">
    <literal><![CDATA[
      (x / (y * x)) \ T(x,x \ (y * x)) = x * y
    ]]></literal>
    <justification jstring="[para(11(a,1),4650(a,2,2))].">
      <j1 rule="para" parents="11 4650"/>
    </justification>
  </clause>

  <clause id="4655">
    <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(4650(a,1),2932(a,1,1,2,1))].">
      <j1 rule="para" parents="4650 2932"/>
    </justification>
  </clause>

  <clause id="4656">
    <literal><![CDATA[
      T(x,1 / y) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(68(a,1),4638(a,1,2,1))].">
      <j1 rule="para" parents="68 4638"/>
    </justification>
  </clause>

  <clause id="4659">
    <literal><![CDATA[
      T(x * y,x \ 1) = ((x * y) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(409,a,4642,a),flip(a)].">
      <j1 rule="hyper" parents="409 4642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4660">
    <literal><![CDATA[
      x / T(y * x,y \ 1) = (y * x) \ x
    ]]></literal>
    <justification jstring="[para(4642(a,1),262(a,1,2))].">
      <j1 rule="para" parents="4642 262"/>
    </justification>
  </clause>

  <clause id="4661">
    <literal><![CDATA[
      T((x \ 1) * y,x) = (((x \ 1) * y) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(65,a,3739,a(flip),b,4659,a)].">
      <j1 rule="hyper" parents="65 3739 4659"/>
    </justification>
  </clause>

  <clause id="4662">
    <literal><![CDATA[
      ((x \ 1) \ y) / T(y,x) = y \ ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(137,a,4652,a)].">
      <j1 rule="hyper" parents="137 4652"/>
    </justification>
  </clause>

  <clause id="4663">
    <literal><![CDATA[
      (x / (y * x)) \ T(x,T(y,x)) = x * y
    ]]></literal>
    <justification jstring="[para(22(a,2),4654(a,1,2,2))].">
      <j1 rule="para" parents="22 4654"/>
    </justification>
  </clause>

  <clause id="4664">
    <literal><![CDATA[
      (x / (y * x)) \ T(x,y) = x * y
    ]]></literal>
    <justification jstring="[para(4386(a,1),4663(a,1,2))].">
      <j1 rule="para" parents="4386 4663"/>
    </justification>
  </clause>

  <clause id="4665">
    <literal><![CDATA[
      T(x,x \ y) / y = x / ((x \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(331,a,4664,a)].">
      <j1 rule="hyper" parents="331 4664"/>
    </justification>
  </clause>

  <clause id="4666">
    <literal><![CDATA[
      T(x,y) / (x * y) = x / (y * x)
    ]]></literal>
    <justification jstring="[hyper(192,a,4664,a)].">
      <j1 rule="hyper" parents="192 4664"/>
    </justification>
  </clause>

  <clause id="4667">
    <literal><![CDATA[
      R(1 / x,x,y) \ T(y,x) = y * x
    ]]></literal>
    <justification jstring="[para(216(a,2),4664(a,1,1))].">
      <j1 rule="para" parents="216 4664"/>
    </justification>
  </clause>

  <clause id="4668">
    <literal><![CDATA[
      T(x,y) / (x * y) = R(1 / y,y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,216,a,b,4666,a),flip(a)].">
      <j1 rule="hyper" parents="299 216 4666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4669">
    <literal><![CDATA[
      R(1 / x,x,T(y,x)) = R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(720,a,4668,a)].">
      <j1 rule="hyper" parents="720 4668"/>
    </justification>
  </clause>

  <clause id="4670">
    <literal><![CDATA[
      (T(x,y) * R(T(x,y) \ (x * y),z,u)) / (x * y) = R(1 / y,y,x) * R((T(x,y) / (x * y)) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(4668(a,1),1973(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4668 1973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4671">
    <literal><![CDATA[
      T(x,y \ 1) / (y \ x) = x / ((x \ (y \ x)) * x)
    ]]></literal>
    <justification jstring="[para(4639(a,1),4665(a,1,1))].">
      <j1 rule="para" parents="4639 4665"/>
    </justification>
  </clause>

  <clause id="4672">
    <literal><![CDATA[
      R(1 / x,x,y / x) = R(1 / x,x,x \ y)
    ]]></literal>
    <justification jstring="[para(109(a,1),4669(a,1,3)),flip(a)].">
      <j1 rule="para" parents="109 4669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4673">
    <literal><![CDATA[
      R(1 / x,x,y / x) = (x \ y) / y
    ]]></literal>
    <justification jstring="[hyper(299,a,375,a(flip),b,4672,a),flip(a)].">
      <j1 rule="hyper" parents="299 375 4672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4674">
    <literal><![CDATA[
      (x / y) / (y * (x / y)) = (y \ x) / x
    ]]></literal>
    <justification jstring="[hyper(872,a,4673,a)].">
      <j1 rule="hyper" parents="872 4673"/>
    </justification>
  </clause>

  <clause id="4675">
    <literal><![CDATA[
      ((x \ y) / y) * (x * (y / x)) = y / x
    ]]></literal>
    <justification jstring="[hyper(143,a,4674,a)].">
      <j1 rule="hyper" parents="143 4674"/>
    </justification>
  </clause>

  <clause id="4676">
    <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(2475(a,1),4646(a,2,2))].">
      <j1 rule="para" parents="2475 4646"/>
    </justification>
  </clause>

  <clause id="4677">
    <literal><![CDATA[
      T(x,y) / ((y \ 1) \ x) = x / ((x \ ((y \ 1) \ x)) * x)
    ]]></literal>
    <justification jstring="[para(3739(a,1),4671(a,1,1))].">
      <j1 rule="para" parents="3739 4671"/>
    </justification>
  </clause>

  <clause id="4678">
    <literal><![CDATA[
      (K(x,y) * (1 / x)) * z = (1 / x) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(133,a,4607,a),flip(a)].">
      <j1 rule="hyper" parents="133 4607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4680">
    <literal><![CDATA[
      (1 / x) * (K(x,y) * z) = (K(x,y) / x) * z
    ]]></literal>
    <justification jstring="[para(4567(a,1),4678(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4567 4678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4681">
    <literal><![CDATA[
      (1 / x) \ K(x,y) = K(x,y) * x
    ]]></literal>
    <justification jstring="[hyper(119,a,12,a(flip),b,4680,a)].">
      <j1 rule="hyper" parents="119 12 4680"/>
    </justification>
  </clause>

  <clause id="4682">
    <literal><![CDATA[
      ((K(x,x \ 1) / x) * y) / (1 / x) = ((1 / x) * y) / (x \ 1)
    ]]></literal>
    <justification jstring="[para(4680(a,1),3327(a,1,1))].">
      <j1 rule="para" parents="4680 3327"/>
    </justification>
  </clause>

  <clause id="4683">
    <literal><![CDATA[
      K(x \ 1,x) * (K(1 / x,y) * (1 / x)) = x \ K(1 / x,y)
    ]]></literal>
    <justification jstring="[para(4681(a,1),2684(a,1,2))].">
      <j1 rule="para" parents="4681 2684"/>
    </justification>
  </clause>

  <clause id="4684">
    <literal><![CDATA[
      L(x,K(y,z),L(y,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(490,a,4610,a)].">
      <j1 rule="hyper" parents="490 4610"/>
    </justification>
  </clause>

  <clause id="4685">
    <literal><![CDATA[
      (K(x,y) * L(x,z,u)) * w = L(x,z,u) * (K(x,y) * w)
    ]]></literal>
    <justification jstring="[para(3578(a,1),4610(a,1,1))].">
      <j1 rule="para" parents="3578 4610"/>
    </justification>
  </clause>

  <clause id="4686">
    <literal><![CDATA[
      L(x,K(y,z),L(y,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x = v5
    ]]></literal>
    <justification jstring="[para(4684(a,1),52(a,2))].">
      <j1 rule="para" parents="4684 52"/>
    </justification>
  </clause>

  <clause id="4687">
    <literal><![CDATA[
      R(x,T(y,x),T(x,y)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(37,a,887,a(flip),b,4428,a),flip(a)].">
      <j1 rule="hyper" parents="37 887 4428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4688">
    <literal><![CDATA[
      R(x,T(y,x),x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,4412,a(flip),b,4687,a)].">
      <j1 rule="hyper" parents="65 4412 4687"/>
    </justification>
  </clause>

  <clause id="4689">
    <literal><![CDATA[
      R(R(x,y,z),T(u,x),T(x,u)) = R(R(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[para(4687(a,1),31(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4687 31"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4690">
    <literal><![CDATA[
      R(x,y / x,x) = R(x,x \ y,x)
    ]]></literal>
    <justification jstring="[para(109(a,1),4688(a,1,2)),flip(a)].">
      <j1 rule="para" parents="109 4688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4691">
    <literal><![CDATA[
      R(x,x \ (y \ x),x) = ((y \ T(x,y \ 1)) * x) / (y \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,4238,a(flip),b,4690,a),flip(a)].">
      <j1 rule="hyper" parents="65 4238 4690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4692">
    <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(4689(a,1),4428(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4689 4428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4693">
    <literal><![CDATA[
      R(x / y,x / (x / y),x / y) = (x * (y \ x)) / x
    ]]></literal>
    <justification jstring="[hyper(299,a,755,a(flip),b,4509,a),flip(a)].">
      <j1 rule="hyper" parents="299 755 4509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4694">
    <literal><![CDATA[
      R(x / (x / y),(y * (x / y)) / y,x / (x / y)) = (x * ((x / y) \ x)) / x
    ]]></literal>
    <justification jstring="[para(4508(a,2),4693(a,1,2))].">
      <j1 rule="para" parents="4508 4693"/>
    </justification>
  </clause>

  <clause id="4695">
    <literal><![CDATA[
      1 / (x * (T(y,x) \ y)) = (y \ T(y,x)) / x
    ]]></literal>
    <justification jstring="[para(3562(a,1),4614(a,1,2))].">
      <j1 rule="para" parents="3562 4614"/>
    </justification>
  </clause>

  <clause id="4696">
    <literal><![CDATA[
      1 / (x * (T(y \ 1,x) \ (y \ 1))) = (y * T(y \ 1,x)) / x
    ]]></literal>
    <justification jstring="[para(3516(a,1),4695(a,2,1))].">
      <j1 rule="para" parents="3516 4695"/>
    </justification>
  </clause>

  <clause id="4697">
    <literal><![CDATA[
      R(x,x \ (y \ x),x) = ((y \ x) * T(x,y \ 1)) / (y \ x)
    ]]></literal>
    <justification jstring="[para(4647(a,1),4691(a,2,1))].">
      <j1 rule="para" parents="4647 4691"/>
    </justification>
  </clause>

  <clause id="4698">
    <literal><![CDATA[
      (x * ((y \ x) * y)) / x = x * K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(3500(a,1),4294(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3500 4294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4700">
    <literal><![CDATA[
      T(x,y \ 1) * (x \ (y * z)) = y * (T(x,y \ 1) * (x \ z))
    ]]></literal>
    <justification jstring="[para(4260(a,1),4309(a,2,2))].">
      <j1 rule="para" parents="4260 4309"/>
    </justification>
  </clause>

  <clause id="4701">
    <literal><![CDATA[
      (x * y) \ T(L(y,x,x),x \ 1) = R(1 / x,x * y,1 / x)
    ]]></literal>
    <justification jstring="[para(3733(a,1),4344(a,1,2))].">
      <j1 rule="para" parents="3733 4344"/>
    </justification>
  </clause>

  <clause id="4702">
    <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(4424(a,2),4405(a,1))].">
      <j1 rule="para" parents="4424 4405"/>
    </justification>
  </clause>

  <clause id="4703">
    <literal><![CDATA[
      ((1 / x) * y) / (x \ 1) = ((x \ 1) * y) / (1 / x)
    ]]></literal>
    <justification jstring="[para(2613(a,1),4682(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2613 4682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4704">
    <literal><![CDATA[
      K(x \ 1,x) * ((1 / x) * K(x \ 1,y)) = x \ K(1 / x,y)
    ]]></literal>
    <justification jstring="[para(3736(a,1),4683(a,1,2))].">
      <j1 rule="para" parents="3736 4683"/>
    </justification>
  </clause>

  <clause id="4705">
    <literal><![CDATA[
      (x * y) \ (x * (y * (x \ 1))) = R(1 / x,x * y,1 / x)
    ]]></literal>
    <justification jstring="[para(1733(a,1),4701(a,1,2))].">
      <j1 rule="para" parents="1733 4701"/>
    </justification>
  </clause>

  <clause id="4706">
    <literal><![CDATA[
      R(1 / x,x * y,1 / x) = L(x \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(493,a,4705,a),flip(a)].">
      <j1 rule="hyper" parents="493 4705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4707">
    <literal><![CDATA[
      (x \ 1) * K(x \ 1,y) = x \ K(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2650,a(flip),b,4704,a)].">
      <j1 rule="hyper" parents="65 2650 4704"/>
    </justification>
  </clause>

  <clause id="4708">
    <literal><![CDATA[
      (x \ K(1 / x,y)) * ((x \ 1) \ 1) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(4707(a,1),1894(a,1,1))].">
      <j1 rule="para" parents="4707 1894"/>
    </justification>
  </clause>

  <clause id="4709">
    <literal><![CDATA[
      (x \ (y \ ((1 / x) * (y / (1 / x))))) * ((x \ 1) \ 1) = K(x \ 1,y / (1 / x))
    ]]></literal>
    <justification jstring="[para(91(a,2),4708(a,1,1,2))].">
      <j1 rule="para" parents="91 4708"/>
    </justification>
  </clause>

  <clause id="4710">
    <literal><![CDATA[
      x * R(1 / (1 / y),y \ 1,(1 / y) \ x) = (1 / y) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(3702(a,1),4244(a,1,2))].">
      <j1 rule="para" parents="3702 4244"/>
    </justification>
  </clause>

  <clause id="4711">
    <literal><![CDATA[
      (R(x,y,z) * T(u,x)) * T(x,u) = (R(x,y,z) * u) * x
    ]]></literal>
    <justification jstring="[hyper(299,a,543,a(flip),b,4692,a),flip(a)].">
      <j1 rule="hyper" parents="299 543 4692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4712">
    <literal><![CDATA[
      T(x * y,x) * T(x,y) = (R(x,y,x) * y) * x
    ]]></literal>
    <justification jstring="[para(1968(a,1),4711(a,1,1))].">
      <j1 rule="para" parents="1968 4711"/>
    </justification>
  </clause>

  <clause id="4713">
    <literal><![CDATA[
      (R(x,y,x) * y) * x = (x * y) * R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,4349,a(flip),b,4712,a),flip(a)].">
      <j1 rule="hyper" parents="65 4349 4712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4714">
    <literal><![CDATA[
      (R(x,y,x) * y) \ ((x * y) * R(x,y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(4713(a,1),314(a,1,2))].">
      <j1 rule="para" parents="4713 314"/>
    </justification>
  </clause>

  <clause id="4715">
    <literal><![CDATA[
      ((x \ 1) * y) \ T((x \ 1) * y,x) = ((x \ y) * x) / y
    ]]></literal>
    <justification jstring="[hyper(65,a,4187,a(flip),b,4251,a)].">
      <j1 rule="hyper" parents="65 4187 4251"/>
    </justification>
  </clause>

  <clause id="4716">
    <literal><![CDATA[
      L(K(x \ y,x),y,x \ 1) = ((x \ y) * x) / y
    ]]></literal>
    <justification jstring="[hyper(65,a,2050,a(flip),b,4715,a)].">
      <j1 rule="hyper" parents="65 2050 4715"/>
    </justification>
  </clause>

  <clause id="4717">
    <literal><![CDATA[
      ((x \ (x * y)) * x) / (x * y) = L(K(y,x),x * y,x \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),4716(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 4716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4718">
    <literal><![CDATA[
      L(K(x,y),y * x,y \ 1) = (x * y) / (y * x)
    ]]></literal>
    <justification jstring="[para(9(a,1),4717(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 4717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4719">
    <literal><![CDATA[
      T(T(x,x \ 1) * y,L(x,x,x)) = y * L(R(x,y,L(x,x,x)),x,x)
    ]]></literal>
    <justification jstring="[para(29(a,1),4350(a,2,2))].">
      <j1 rule="para" parents="29 4350"/>
    </justification>
  </clause>

  <clause id="4720">
    <literal><![CDATA[
      T((x / y) / T(y,y \ x),y \ 1) = (y \ 1) \ (y \ (x / (y * y)))
    ]]></literal>
    <justification jstring="[para(1771(a,1),4515(a,2,2))].">
      <j1 rule="para" parents="1771 4515"/>
    </justification>
  </clause>

  <clause id="4721">
    <literal><![CDATA[
      T(x,T(y,z)) / (T(T(y,x),z) \ x) = T(y,T(z,T(y,x)))
    ]]></literal>
    <justification jstring="[para(4536(a,1),4534(a,1,1))].">
      <j1 rule="para" parents="4536 4534"/>
    </justification>
  </clause>

  <clause id="4722">
    <literal><![CDATA[
      T(x,T(y,T(x,z))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,4431,a(flip),b,4721,a),flip(a)].">
      <j1 rule="hyper" parents="65 4431 4721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4725">
    <literal><![CDATA[
      T(x / (x / y),T(z,y)) = T(x / (x / y),z)
    ]]></literal>
    <justification jstring="[para(241(a,1),4722(a,1,2,2))].">
      <j1 rule="para" parents="241 4722"/>
    </justification>
  </clause>

  <clause id="4728">
    <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(4725(a,1),4520(a,1,1))].">
      <j1 rule="para" parents="4725 4520"/>
    </justification>
  </clause>

  <clause id="4729">
    <literal><![CDATA[
      T(x,K(y,x) \ 1) = x
    ]]></literal>
    <justification jstring="[para(4554(a,1),3559(a,1,2))].">
      <j1 rule="para" parents="4554 3559"/>
    </justification>
  </clause>

  <clause id="4730">
    <literal><![CDATA[
      (K(x,y) \ 1) * y = y * (K(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(4729(a,1),107(a,1,2))].">
      <j1 rule="para" parents="4729 107"/>
    </justification>
  </clause>

  <clause id="4731">
    <literal><![CDATA[
      (x * (K(y,x) \ 1)) \ (K(y,x) \ 1) = L(x \ 1,x,K(y,x) \ 1)
    ]]></literal>
    <justification jstring="[para(4730(a,1),214(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4730 214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4732">
    <literal><![CDATA[
      T((x / y) / T(y,y \ x),y \ 1) = y \ ((1 / y) \ (x / (y * y)))
    ]]></literal>
    <justification jstring="[hyper(299,a,1663,a(flip),b,4720,a),flip(a)].">
      <j1 rule="hyper" parents="299 1663 4720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4733">
    <literal><![CDATA[
      T((x / y) / T(y,y \ x),y \ 1) = y \ (y \ T(x,y \ (y \ 1)))
    ]]></literal>
    <justification jstring="[para(1059(a,1),4732(a,2,2))].">
      <j1 rule="para" parents="1059 4732"/>
    </justification>
  </clause>

  <clause id="4734">
    <literal><![CDATA[
      x \ (x \ T(y,x \ (x \ 1))) = T((x \ y) / x,x \ 1)
    ]]></literal>
    <justification jstring="[para(4485(a,1),4733(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4485 4733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4735">
    <literal><![CDATA[
      x \ (x \ T(y * x,x \ (x \ 1))) = T(T(y,x) / x,x \ 1)
    ]]></literal>
    <justification jstring="[para(22(a,2),4734(a,2,1,1))].">
      <j1 rule="para" parents="22 4734"/>
    </justification>
  </clause>

  <clause id="4736">
    <literal><![CDATA[
      x \ ((x \ 1) \ (y * (1 / x))) = T(T(y,x) / x,x \ 1)
    ]]></literal>
    <justification jstring="[para(3333(a,1),4735(a,1,2))].">
      <j1 rule="para" parents="3333 4735"/>
    </justification>
  </clause>

  <clause id="4737">
    <literal><![CDATA[
      ((1 / (x \ 1)) \ ((x \ 1) \ y)) * (x \ 1) = T(T(y,x) / x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,3448,a,b,4736,a)].">
      <j1 rule="hyper" parents="65 3448 4736"/>
    </justification>
  </clause>

  <clause id="4739">
    <literal><![CDATA[
      L(x,L(y,T(z,y),T(z,y)),u) = L(x,z * (T(z,y) * ((z * y) / z)),u)
    ]]></literal>
    <justification jstring="[para(1187(a,1),4273(a,2,2))].">
      <j1 rule="para" parents="1187 4273"/>
    </justification>
  </clause>

  <clause id="4740">
    <literal><![CDATA[
      (x * y) \ ((1 / x) \ (L(y,x,x) * x)) = R(x,(x \ 1) * y,x)
    ]]></literal>
    <justification jstring="[para(1673(a,1),4342(a,1,2,2,1))].">
      <j1 rule="para" parents="1673 4342"/>
    </justification>
  </clause>

  <clause id="4741">
    <literal><![CDATA[
      L(K(x,y),y * x,y \ 1) = T(y,(1 / y) * (x * y)) \ y
    ]]></literal>
    <justification jstring="[hyper(2933,a,4562,a)].">
      <j1 rule="hyper" parents="2933 4562"/>
    </justification>
  </clause>

  <clause id="4742">
    <literal><![CDATA[
      L(K(x,y),y * x,y \ 1) = T(y,(y \ 1) * (x * y)) \ y
    ]]></literal>
    <justification jstring="[para(2983(a,1),4741(a,2,1))].">
      <j1 rule="para" parents="2983 4741"/>
    </justification>
  </clause>

  <clause id="4743">
    <literal><![CDATA[
      T(x,(x \ 1) * (y * x)) \ x = (y * x) / (x * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,4718,a(flip),b,4742,a),flip(a)].">
      <j1 rule="hyper" parents="65 4718 4742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4744">
    <literal><![CDATA[
      T(x,(x \ 1) * (y * x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(4500,a,4743,a),flip(a)].">
      <j1 rule="hyper" parents="4500 4743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4745">
    <literal><![CDATA[
      T(x,T((x \ 1) * y,x)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(2046(a,1),4744(a,1,2))].">
      <j1 rule="para" parents="2046 4744"/>
    </justification>
  </clause>

  <clause id="4746">
    <literal><![CDATA[
      T(x,(x \ 1) * y) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(4462,a,4745,a)].">
      <j1 rule="hyper" parents="4462 4745"/>
    </justification>
  </clause>

  <clause id="4747">
    <literal><![CDATA[
      T(x,(1 / x) * y) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,3868,a,b,4746,a)].">
      <j1 rule="hyper" parents="65 3868 4746"/>
    </justification>
  </clause>

  <clause id="4748">
    <literal><![CDATA[
      (((x \ 1) * y) \ y) * ((x \ 1) * y) = (x \ T(x,x \ y)) * y
    ]]></literal>
    <justification jstring="[para(4746(a,1),4026(a,2,1,2))].">
      <j1 rule="para" parents="4746 4026"/>
    </justification>
  </clause>

  <clause id="4749">
    <literal><![CDATA[
      x \ T(x,T(y,y \ x) \ 1) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(4746(a,1),4501(a,1,2,2,1))].">
      <j1 rule="para" parents="4746 4501"/>
    </justification>
  </clause>

  <clause id="4750">
    <literal><![CDATA[
      x / T(y,(1 / y) * x) = y \ x
    ]]></literal>
    <justification jstring="[para(4747(a,2),262(a,1,2))].">
      <j1 rule="para" parents="4747 262"/>
    </justification>
  </clause>

  <clause id="4751">
    <literal><![CDATA[
      x / T(y \ 1,y * x) = (y \ 1) \ x
    ]]></literal>
    <justification jstring="[para(76(a,1),4750(a,1,2,2,1))].">
      <j1 rule="para" parents="76 4750"/>
    </justification>
  </clause>

  <clause id="4752">
    <literal><![CDATA[
      x / T(1 / y,y * x) = (1 / y) \ x
    ]]></literal>
    <justification jstring="[para(3871(a,1),4750(a,1,2))].">
      <j1 rule="para" parents="3871 4750"/>
    </justification>
  </clause>

  <clause id="4753">
    <literal><![CDATA[
      T(x \ 1,x * y) = ((x \ 1) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(186,a,4751,a),flip(a)].">
      <j1 rule="hyper" parents="186 4751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4755">
    <literal><![CDATA[
      T(1 / x,x * y) = ((1 / x) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(186,a,4752,a),flip(a)].">
      <j1 rule="hyper" parents="186 4752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4756">
    <literal><![CDATA[
      T(1 / (x / y),x) = ((1 / (x / y)) \ y) \ y
    ]]></literal>
    <justification jstring="[para(12(a,1),4755(a,1,2))].">
      <j1 rule="para" parents="12 4755"/>
    </justification>
  </clause>

  <clause id="4757">
    <literal><![CDATA[
      T(x,T(y,y \ x) \ 1) = x * K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(144,a,4749,a),flip(a)].">
      <j1 rule="hyper" parents="144 4749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4758">
    <literal><![CDATA[
      K(x,(y \ x) / x) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(4218,a,4757,a)].">
      <j1 rule="hyper" parents="4218 4757"/>
    </justification>
  </clause>

  <clause id="4759">
    <literal><![CDATA[
      (((x \ 1) * y) \ y) * ((x \ 1) * y) = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(299,a,4318,a(flip),b,4748,a),flip(a)].">
      <j1 rule="hyper" parents="299 4318 4748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4760">
    <literal><![CDATA[
      L(R(x,y,x),y,R(x,y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(4714,a,4627,a),flip(a)].">
      <j1 rule="hyper" parents="4714 4627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4761">
    <literal><![CDATA[
      x * (K(y,x) \ 1) = K(y,x) \ x
    ]]></literal>
    <justification jstring="[para(4554(a,1),4551(a,1,2))].">
      <j1 rule="para" parents="4554 4551"/>
    </justification>
  </clause>

  <clause id="4762">
    <literal><![CDATA[
      K(x \ y,x) \ 1 = K(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(36,a,4526,a(flip),b,4761,a),flip(a)].">
      <j1 rule="hyper" parents="36 4526 4761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4763">
    <literal><![CDATA[
      (K(x,y) \ 1) \ (K(x,y) \ y) = y
    ]]></literal>
    <justification jstring="[hyper(119,a,4761,a(flip),b,4730,a)].">
      <j1 rule="hyper" parents="119 4761 4730"/>
    </justification>
  </clause>

  <clause id="4764">
    <literal><![CDATA[
      K(x,(x * y) / x) = K(y,x) \ 1
    ]]></literal>
    <justification jstring="[para(9(a,1),4762(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 4762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4765">
    <literal><![CDATA[
      (K(x,y) \ 1) * T(y,z) = K(x,y) \ T(y,z)
    ]]></literal>
    <justification jstring="[para(4763(a,1),1109(a,1,2,1))].">
      <j1 rule="para" parents="4763 1109"/>
    </justification>
  </clause>

  <clause id="4766">
    <literal><![CDATA[
      K(T(x,y),y) \ 1 = K(y,x)
    ]]></literal>
    <justification jstring="[para(223(a,1),4764(a,1,2)),flip(a)].">
      <j1 rule="para" parents="223 4764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4767">
    <literal><![CDATA[
      L(x,y,K(z,y) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(4764(a,1),4572(a,1,3))].">
      <j1 rule="para" parents="4764 4572"/>
    </justification>
  </clause>

  <clause id="4768">
    <literal><![CDATA[
      K(T(x,y),y) * K(y,x) = 1
    ]]></literal>
    <justification jstring="[hyper(144,a,4766,a)].">
      <j1 rule="hyper" parents="144 4766"/>
    </justification>
  </clause>

  <clause id="4769">
    <literal><![CDATA[
      K(T(x,y),y) * z != 1
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(4768(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="4768 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4770">
    <literal><![CDATA[
      K(T(x,y),y) \ 1 != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(4768(a,1),314(a,1,2))].">
      <j1 rule="para" parents="4768 314"/>
    </justification>
  </clause>

  <clause id="4771">
    <literal><![CDATA[
      L(x,y,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(4767,a,2470,a),flip(a)].">
      <j1 rule="hyper" parents="4767 2470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4772">
    <literal><![CDATA[
      (x * (K(y,x) \ 1)) \ (K(y,x) \ 1) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(4767,a,4731,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="4767 4731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4773">
    <literal><![CDATA[
      (K(x,y) * y) * z = K(x,y) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(1318,a,4771,a),flip(a)].">
      <j1 rule="hyper" parents="1318 4771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4774">
    <literal><![CDATA[
      a(K(x,y),y,z) = 1
    ]]></literal>
    <justification jstring="[hyper(55,a,4771,a)].">
      <j1 rule="hyper" parents="55 4771"/>
    </justification>
  </clause>

  <clause id="4775">
    <literal><![CDATA[
      L(x,y,K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(4771(a,1),52(a,1)),flip(a)].">
      <j1 rule="para" parents="4771 52"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4776">
    <literal><![CDATA[
      (x * K(y,x)) * z = K(y,x) * (x * z)
    ]]></literal>
    <justification jstring="[para(4771(a,1),3639(a,1,2))].">
      <j1 rule="para" parents="4771 3639"/>
    </justification>
  </clause>

  <clause id="4777">
    <literal><![CDATA[
      L(x,T(y,z),K(z,y)) = x
    ]]></literal>
    <justification jstring="[para(4334(a,1),4771(a,1,3))].">
      <j1 rule="para" parents="4334 4771"/>
    </justification>
  </clause>

  <clause id="4778">
    <literal><![CDATA[
      R(K(x,y),y,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3701,a,4773,a)].">
      <j1 rule="hyper" parents="3701 4773"/>
    </justification>
  </clause>

  <clause id="4779">
    <literal><![CDATA[
      (x * K(y,x)) \ z = x \ (K(y,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(119,a,72,a(flip),b,4776,a)].">
      <j1 rule="hyper" parents="119 72 4776"/>
    </justification>
  </clause>

  <clause id="4780">
    <literal><![CDATA[
      K(x,y) \ T(y,y \ z) = (K(x,y) \ 1) * ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,295,a(flip),b,4765,a),flip(a)].">
      <j1 rule="hyper" parents="65 295 4765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4781">
    <literal><![CDATA[
      (K(x,y) \ y) \ (K(x,y) \ 1) = y \ 1
    ]]></literal>
    <justification jstring="[para(4761(a,1),4772(a,1,1))].">
      <j1 rule="para" parents="4761 4772"/>
    </justification>
  </clause>

  <clause id="4782">
    <literal><![CDATA[
      (K(x,y) \ y) * (y \ 1) = K(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(144,a,4781,a)].">
      <j1 rule="hyper" parents="144 4781"/>
    </justification>
  </clause>

  <clause id="4783">
    <literal><![CDATA[
      R(K(x,y) \ y,y \ 1,y) = (K(x,y) \ 1) * ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(4782(a,1),2699(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4782 2699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4784">
    <literal><![CDATA[
      (K(x,y) \ 1) * ((y \ z) \ z) = K(x,y) \ ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,293,a(flip),b,4780,a),flip(a)].">
      <j1 rule="hyper" parents="65 293 4780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4785">
    <literal><![CDATA[
      R(K(x,y) \ y,y \ 1,y) = K(x,y) \ ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,4784,a(flip),b,4783,a),flip(a)].">
      <j1 rule="hyper" parents="299 4784 4783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4786">
    <literal><![CDATA[
      x * (K(x,y) * (K(x,y) \ ((y \ 1) \ 1))) = (T(y,y \ 1) * x) * K(x,y)
    ]]></literal>
    <justification jstring="[para(4785(a,1),3077(a,1,2,2))].">
      <j1 rule="para" parents="4785 3077"/>
    </justification>
  </clause>

  <clause id="4787">
    <literal><![CDATA[
      T(x,x \ K(y,x)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(3572(a,1),4625(a,1,2,2))].">
      <j1 rule="para" parents="3572 4625"/>
    </justification>
  </clause>

  <clause id="4788">
    <literal><![CDATA[
      K(x,y) / T(y,y \ 1) = y \ K(x,y)
    ]]></literal>
    <justification jstring="[para(4787(a,1),262(a,1,2))].">
      <j1 rule="para" parents="4787 262"/>
    </justification>
  </clause>

  <clause id="4789">
    <literal><![CDATA[
      (x \ K(y,x)) * K(x,x \ 1) = K(y,x) / x
    ]]></literal>
    <justification jstring="[para(4788(a,1),2759(a,1,1))].">
      <j1 rule="para" parents="4788 2759"/>
    </justification>
  </clause>

  <clause id="4790">
    <literal><![CDATA[
      K(x,y) * K(y \ 1,y) = (y \ K(x,y)) * y
    ]]></literal>
    <justification jstring="[para(4788(a,1),2782(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4788 2782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4791">
    <literal><![CDATA[
      K(x,y) * K(y,y \ 1) = y * (K(x,y) / y)
    ]]></literal>
    <justification jstring="[para(4789(a,1),3053(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4789 3053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4792">
    <literal><![CDATA[
      K(x,y) = (T(y,y \ 1) * x) \ (x * ((y \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(640,a,4786,a),flip(a)].">
      <j1 rule="hyper" parents="640 4786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4793">
    <literal><![CDATA[
      K(x,(y \ 1) \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(714,a,4792,a(flip))].">
      <j1 rule="hyper" parents="714 4792"/>
    </justification>
  </clause>

  <clause id="4794">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,(y \ 1) \ 1) = z
    ]]></literal>
    <justification jstring="[para(4792(a,2),714(a,1))].">
      <j1 rule="para" parents="4792 714"/>
    </justification>
  </clause>

  <clause id="4795">
    <literal><![CDATA[
      K(K(x,x \ 1) * y,x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,3451,a,b,4793,a)].">
      <j1 rule="hyper" parents="65 3451 4793"/>
    </justification>
  </clause>

  <clause id="4796">
    <literal><![CDATA[
      K(((x \ 1) \ 1) \ y,x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,3450,a(flip),b,4793,a),flip(a)].">
      <j1 rule="hyper" parents="65 3450 4793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4797">
    <literal><![CDATA[
      K(x,1 / y) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(79(a,1),4793(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 4793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4798">
    <literal><![CDATA[
      K(x,1 / (1 / y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(191(a,1),4793(a,1,2)),flip(a)].">
      <j1 rule="para" parents="191 4793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4799">
    <literal><![CDATA[
      K(x,T(y,1 / y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2577(a,2),4793(a,1,2))].">
      <j1 rule="para" parents="2577 4793"/>
    </justification>
  </clause>

  <clause id="4800">
    <literal><![CDATA[
      K(x,T(y / z,z / y)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(2620(a,2),4793(a,1,2))].">
      <j1 rule="para" parents="2620 4793"/>
    </justification>
  </clause>

  <clause id="4801">
    <literal><![CDATA[
      K(x,T(1 / y,z)) = K(x,T(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(3179(a,1),4793(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3179 4793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4802">
    <literal><![CDATA[
      K(x,T(y / z,y \ z)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(3355(a,2),4793(a,1,2))].">
      <j1 rule="para" parents="3355 4793"/>
    </justification>
  </clause>

  <clause id="4803">
    <literal><![CDATA[
      K(x,((1 / y) \ z) / z) = K(x,((y \ 1) \ z) / z)
    ]]></literal>
    <justification jstring="[para(3382(a,1),4793(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3382 4793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4804">
    <literal><![CDATA[
      ((x \ 1) \ 1) * K(y,(x \ 1) \ 1) = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[para(4793(a,1),3661(a,2,2))].">
      <j1 rule="para" parents="4793 3661"/>
    </justification>
  </clause>

  <clause id="4805">
    <literal><![CDATA[
      K(x,L(1 / y,z,u)) = K(x,L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(4143(a,1),4793(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4143 4793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4806">
    <literal><![CDATA[
      (1 / x) * K(y,1 / x) = K(y,x \ 1) / x
    ]]></literal>
    <justification jstring="[para(4797(a,1),2406(a,2,1))].">
      <j1 rule="para" parents="4797 2406"/>
    </justification>
  </clause>

  <clause id="4807">
    <literal><![CDATA[
      (x \ 1) * K(y,x \ 1) = x \ K(y,1 / x)
    ]]></literal>
    <justification jstring="[para(4797(a,2),3661(a,2,2))].">
      <j1 rule="para" parents="4797 3661"/>
    </justification>
  </clause>

  <clause id="4809">
    <literal><![CDATA[
      K(T(K(x,x \ 1) * y,x),x) = K(T(y,x),x)
    ]]></literal>
    <justification jstring="[para(3050(a,2),4795(a,1,1))].">
      <j1 rule="para" parents="3050 4795"/>
    </justification>
  </clause>

  <clause id="4810">
    <literal><![CDATA[
      K(x \ ((1 / x) \ y),x) = K(x \ ((x \ 1) \ y),x)
    ]]></literal>
    <justification jstring="[para(1666(a,1),4796(a,1,1))].">
      <j1 rule="para" parents="1666 4796"/>
    </justification>
  </clause>

  <clause id="4811">
    <literal><![CDATA[
      K(T((1 / x) * y,x),x) = K(T((x \ 1) * y,x),x)
    ]]></literal>
    <justification jstring="[para(2727(a,1),4809(a,1,1,1))].">
      <j1 rule="para" parents="2727 4809"/>
    </justification>
  </clause>

  <clause id="4812">
    <literal><![CDATA[
      ((1 / x) \ y) \ (y * R(1 / (1 / x),x \ 1,(1 / x) \ y)) = K(y,((x \ 1) \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(65,a,3709,a,b,4803,a)].">
      <j1 rule="hyper" parents="65 3709 4803"/>
    </justification>
  </clause>

  <clause id="4813">
    <literal><![CDATA[
      ((1 / x) \ y) \ ((1 / x) \ T(y,x)) = K(x \ ((x \ 1) \ y),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,1132,a,b,4810,a)].">
      <j1 rule="hyper" parents="65 1132 4810"/>
    </justification>
  </clause>

  <clause id="4814">
    <literal><![CDATA[
      ((x \ 1) \ 1) * K(y,x) = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[para(4793(a,1),4804(a,1,2))].">
      <j1 rule="para" parents="4793 4804"/>
    </justification>
  </clause>

  <clause id="4815">
    <literal><![CDATA[
      x * (K(y,x) * K(x,x \ 1)) = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,3226,a,b,4814,a)].">
      <j1 rule="hyper" parents="65 3226 4814"/>
    </justification>
  </clause>

  <clause id="4816">
    <literal><![CDATA[
      x * (x * (K(y,x) / x)) = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[para(4791(a,1),4815(a,1,2))].">
      <j1 rule="para" parents="4791 4815"/>
    </justification>
  </clause>

  <clause id="4817">
    <literal><![CDATA[
      x * (T(x,y) \ (x * (K(z,x) / x))) = T(x,y) \ ((x \ 1) \ K(z,x))
    ]]></literal>
    <justification jstring="[hyper(119,a,4816,a(flip),b,1191,a),flip(a)].">
      <j1 rule="hyper" parents="119 4816 1191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4818">
    <literal><![CDATA[
      x * (x * (T(x,y) \ (K(z,x) / x))) = T(x,y) \ ((x \ 1) \ K(z,x))
    ]]></literal>
    <justification jstring="[para(1192(a,1),4817(a,1,2))].">
      <j1 rule="para" parents="1192 4817"/>
    </justification>
  </clause>

  <clause id="4819">
    <literal><![CDATA[
      R(x / (x / y),(y * (x / y)) / y,x / (x / y)) = (x * y) / x
    ]]></literal>
    <justification jstring="[para(79(a,1),4694(a,2,1,2))].">
      <j1 rule="para" parents="79 4694"/>
    </justification>
  </clause>

  <clause id="4820">
    <literal><![CDATA[
      x * K(y \ (x * (T(x,y) \ x)),y) = (x * (y * T(y \ x,y))) / x
    ]]></literal>
    <justification jstring="[hyper(65,a,1521,a(flip),b,4547,a),flip(a)].">
      <j1 rule="hyper" parents="65 1521 4547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4821">
    <literal><![CDATA[
      x * K(y \ (x * (T(x,y) \ x)),y) = (x * ((y \ x) * y)) / x
    ]]></literal>
    <justification jstring="[para(107(a,1),4820(a,2,1,2))].">
      <j1 rule="para" parents="107 4820"/>
    </justification>
  </clause>

  <clause id="4822">
    <literal><![CDATA[
      x * K(((x * y) / x) \ x,y) = (x * ((y \ x) * y)) / x
    ]]></literal>
    <justification jstring="[para(4549(a,1),4821(a,1,2,1))].">
      <j1 rule="para" parents="4549 4821"/>
    </justification>
  </clause>

  <clause id="4823">
    <literal><![CDATA[
      K(((x * y) / x) \ x,y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,4698,a(flip),b,4822,a),flip(a)].">
      <j1 rule="hyper" parents="36 4698 4822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4824">
    <literal><![CDATA[
      K(x \ ((x * y) / x),x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(4548(a,1),4823(a,1,1))].">
      <j1 rule="para" parents="4548 4823"/>
    </justification>
  </clause>

  <clause id="4825">
    <literal><![CDATA[
      K(x \ T(y,x),x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(223(a,1),4824(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="223 4824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4826">
    <literal><![CDATA[
      T(x,y) \ ((T(y,x) \ x) * y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,4436,a,b,4825,a)].">
      <j1 rule="hyper" parents="65 4436 4825"/>
    </justification>
  </clause>

  <clause id="4827">
    <literal><![CDATA[
      (T(x,y) \ y) * x != z * K(x \ y,x)
    ]]></literal>
    <literal><![CDATA[
      T(y,x) = z
    ]]></literal>
    <justification jstring="[para(4826(a,1),136(a,1,2)),flip(a),flip(b)].">
      <j1 rule="para" parents="4826 136"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4828">
    <literal><![CDATA[
      (x \ K(1 / x,y / (x \ 1))) * ((x \ 1) \ 1) = K(x \ 1,y / (1 / x))
    ]]></literal>
    <justification jstring="[para(3844(a,1),4709(a,1,1,2))].">
      <j1 rule="para" parents="3844 4709"/>
    </justification>
  </clause>

  <clause id="4829">
    <literal><![CDATA[
      K(x \ 1,y / (1 / x)) = K(x \ 1,y / (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(65,a,4708,a(flip),b,4828,a),flip(a)].">
      <j1 rule="hyper" parents="65 4708 4828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4830">
    <literal><![CDATA[
      K(x \ 1,(y * (1 / x)) / (x \ 1)) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(11(a,1),4829(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11 4829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4831">
    <literal><![CDATA[
      K(x \ 1,(y / (x \ 1)) * (1 / x)) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(1573(a,1),4830(a,1,2))].">
      <j1 rule="para" parents="1573 4830"/>
    </justification>
  </clause>

  <clause id="4832">
    <literal><![CDATA[
      K(x \ 1,y * K(x,x \ 1)) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(2778(a,1),4831(a,1,2))].">
      <j1 rule="para" parents="2778 4831"/>
    </justification>
  </clause>

  <clause id="4833">
    <literal><![CDATA[
      K(x \ 1,((x \ 1) \ 1) * y) = K(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[para(3224(a,1),4832(a,1,2))].">
      <j1 rule="para" parents="3224 4832"/>
    </justification>
  </clause>

  <clause id="4834">
    <literal><![CDATA[
      ((x * y) / x) * (y \ ((T(x,y) \ x) * z)) = L(z,T(x,y) \ x,(x * y) / x)
    ]]></literal>
    <justification jstring="[para(4557(a,1),4559(a,2,2))].">
      <j1 rule="para" parents="4557 4559"/>
    </justification>
  </clause>

  <clause id="4835">
    <literal><![CDATA[
      x \ ((T(y,x) \ y) * z) = ((y * x) / y) \ z
    ]]></literal>
    <justification jstring="[hyper(119,a,4289,a(flip),b,4834,a),flip(a)].">
      <j1 rule="hyper" parents="119 4289 4834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4836">
    <literal><![CDATA[
      x * (((y * x) / y) \ z) = (T(y,x) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(144,a,4835,a)].">
      <j1 rule="hyper" parents="144 4835"/>
    </justification>
  </clause>

  <clause id="4837">
    <literal><![CDATA[
      x * (((y * x) / y) \ z) = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(299,a,4435,a,b,4836,a),flip(a)].">
      <j1 rule="hyper" parents="299 4435 4836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4838">
    <literal><![CDATA[
      R(x \ T(x,y),y,((x * y) / x) \ z) \ z = (T(x,y) \ x) * z
    ]]></literal>
    <justification jstring="[hyper(65,a,4199,a,b,4836,a)].">
      <j1 rule="hyper" parents="65 4199 4836"/>
    </justification>
  </clause>

  <clause id="4839">
    <literal><![CDATA[
      ((x * y) / x) \ (y * z) = T(y,x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,1417,a,b,4837,a)].">
      <j1 rule="hyper" parents="65 1417 4837"/>
    </justification>
  </clause>

  <clause id="4841">
    <literal><![CDATA[
      T(x,R(x * K(y,x),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(308,a,4622,a),flip(a)].">
      <j1 rule="hyper" parents="308 4622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4843">
    <literal><![CDATA[
      T(x,y * (((z \ (((u \ 1) \ 1) \ z)) * T(z,u \ 1)) \ w)) = T(x,y * ((u \ z) \ w))
    ]]></literal>
    <justification jstring="[para(3351(a,1),4653(a,1,2,2,1,1))].">
      <j1 rule="para" parents="3351 4653"/>
    </justification>
  </clause>

  <clause id="4844">
    <literal><![CDATA[
      T(x,y * ((((z \ 1) \ 1) \ u) \ w)) = T(x,y * ((z \ u) \ w))
    ]]></literal>
    <justification jstring="[para(4652(a,1),4843(a,1,2,2,1))].">
      <j1 rule="para" parents="4652 4843"/>
    </justification>
  </clause>

  <clause id="4845">
    <literal><![CDATA[
      (a((x * y) \ 1,x,y) / y) / (1 / (x * y)) = ((x * y) * T((x * y) \ 1,x)) * x
    ]]></literal>
    <justification jstring="[para(1074(a,1),4198(a,2,1))].">
      <j1 rule="para" parents="1074 4198"/>
    </justification>
  </clause>

  <clause id="4846">
    <literal><![CDATA[
      (a((x * y) \ 1,x,y) / y) / (1 / (x * y)) = (((x \ (1 / y)) * x) * y) * x
    ]]></literal>
    <justification jstring="[para(1596(a,1),4845(a,2,1))].">
      <j1 rule="para" parents="1596 4845"/>
    </justification>
  </clause>

  <clause id="4847">
    <literal><![CDATA[
      (a((x * y) \ 1,x,y) / y) / (1 / (x * y)) = x * (y * ((x \ (y \ 1)) * x))
    ]]></literal>
    <justification jstring="[hyper(299,a,3924,a(flip),b,4846,a),flip(a)].">
      <j1 rule="hyper" parents="299 3924 4846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4848">
    <literal><![CDATA[
      (a((x * y) \ 1,x,y) / y) / (1 / (x * y)) = x * (((x \ (1 / y)) * x) * y)
    ]]></literal>
    <justification jstring="[para(3503(a,2),4847(a,2,2))].">
      <j1 rule="para" parents="3503 4847"/>
    </justification>
  </clause>

  <clause id="4849">
    <literal><![CDATA[
      ((1 / (x * y)) * x) / (1 / (x * y)) = x * (((x \ (1 / y)) * x) * y)
    ]]></literal>
    <justification jstring="[para(2980(a,1),4848(a,1,1))].">
      <j1 rule="para" parents="2980 4848"/>
    </justification>
  </clause>

  <clause id="4850">
    <literal><![CDATA[
      (((x * y) \ 1) * x) / ((x * y) \ 1) = x * (((x \ (1 / y)) * x) * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,3262,a(flip),b,4849,a)].">
      <j1 rule="hyper" parents="65 3262 4849"/>
    </justification>
  </clause>

  <clause id="4851">
    <literal><![CDATA[
      (((x * y) \ 1) * x) / ((x * y) \ 1) != x * z
    ]]></literal>
    <literal><![CDATA[
      ((x \ (1 / y)) * x) * y = z
    ]]></literal>
    <justification jstring="[para(4850(a,2),45(a,1))].">
      <j1 rule="para" parents="4850 45"/>
    </justification>
  </clause>

  <clause id="4852">
    <literal><![CDATA[
      K(x,((y \ 1) \ x) / x) = ((1 / y) \ x) \ ((1 / y) \ T(x,y))
    ]]></literal>
    <justification jstring="[para(4710(a,1),4812(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4710 4812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4853">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),x) = K(y,((x \ 1) \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(299,a,4813,a(flip),b,4852,a)].">
      <j1 rule="hyper" parents="299 4813 4852"/>
    </justification>
  </clause>

  <clause id="4854">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),x) = K(y,(x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,4758,a(flip),b,4853,a),flip(a)].">
      <j1 rule="hyper" parents="299 4758 4853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4855">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,4793,a(flip),b,4854,a),flip(a)].">
      <j1 rule="hyper" parents="299 4793 4854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4856">
    <literal><![CDATA[
      K(x \ ((1 / x) \ y),x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,4810,a,b,4855,a)].">
      <j1 rule="hyper" parents="65 4810 4855"/>
    </justification>
  </clause>

  <clause id="4857">
    <literal><![CDATA[
      K((x \ 1) * y,x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),4855(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 4855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4858">
    <literal><![CDATA[
      K((1 / x) * y,x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),4856(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 4856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4859">
    <literal><![CDATA[
      K((1 / x) * (y * x),x) = K(T(y,x),x)
    ]]></literal>
    <justification jstring="[para(22(a,2),4858(a,2,1))].">
      <j1 rule="para" parents="22 4858"/>
    </justification>
  </clause>

  <clause id="4860">
    <literal><![CDATA[
      K(T((1 / x) * y,x),x) = K(T(x \ y,x),x)
    ]]></literal>
    <justification jstring="[para(820(a,1),4859(a,1,1))].">
      <j1 rule="para" parents="820 4859"/>
    </justification>
  </clause>

  <clause id="4861">
    <literal><![CDATA[
      K(T((x \ 1) * y,x),x) = K(T(x \ y,x),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,4811,a(flip),b,4860,a)].">
      <j1 rule="hyper" parents="65 4811 4860"/>
    </justification>
  </clause>

  <clause id="4862">
    <literal><![CDATA[
      K(T(x \ y,x),x) \ 1 = K(x,(x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(4861(a,1),4766(a,1,1))].">
      <j1 rule="para" parents="4861 4766"/>
    </justification>
  </clause>

  <clause id="4863">
    <literal><![CDATA[
      K(x,(x \ 1) * y) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(4770,a,4862,a),flip(a)].">
      <j1 rule="hyper" parents="4770 4862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4864">
    <literal><![CDATA[
      K(x \ 1,(x \ 1) \ y) = K(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,4833,a(flip),b,4863,a),flip(a)].">
      <j1 rule="hyper" parents="65 4833 4863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4865">
    <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(2945(a,2),4863(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2945 4863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4866">
    <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(1958(a,1),4594(a,1,1))].">
      <j1 rule="para" parents="1958 4594"/>
    </justification>
  </clause>

  <clause id="4867">
    <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(1317(a,1),4866(a,1,2))].">
      <j1 rule="para" parents="1317 4866"/>
    </justification>
  </clause>

  <clause id="4868">
    <literal><![CDATA[
      a(x,T(y,x),R(T(x,y),z,u)) = a(R(x,z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(775,a,4867,a),flip(a)].">
      <j1 rule="hyper" parents="775 4867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4870">
    <literal><![CDATA[
      K(T(x / y,T(y,x)) \ 1,T(x / y,T(y,x))) = K(x \ y,T(x / y,T(y,x)))
    ]]></literal>
    <justification jstring="[para(1431(a,1),4165(a,2,1))].">
      <j1 rule="para" parents="1431 4165"/>
    </justification>
  </clause>

  <clause id="4871">
    <literal><![CDATA[
      K(T(x / y,T(y,x)) \ 1,T(x / y,T(y,x))) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(299,a,3044,a(flip),b,4870,a),flip(a)].">
      <j1 rule="hyper" parents="299 3044 4870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4872">
    <literal><![CDATA[
      K((x / y) \ 1,x / y) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,3716,a(flip),b,4871,a)].">
      <j1 rule="hyper" parents="65 3716 4871"/>
    </justification>
  </clause>

  <clause id="4874">
    <literal><![CDATA[
      K(x / y,(x / y) \ 1) = K(y \ x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2940,a(flip),b,4872,a)].">
      <j1 rule="hyper" parents="65 2940 4872"/>
    </justification>
  </clause>

  <clause id="4875">
    <literal><![CDATA[
      x * K(x / y,(x / y) \ 1) = y * (((y \ x) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(4874(a,2),4166(a,1,2))].">
      <j1 rule="para" parents="4874 4166"/>
    </justification>
  </clause>

  <clause id="4876">
    <literal><![CDATA[
      (x * y) * ((((x * y) \ y) \ 1) \ 1) = y * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2942(a,1),4875(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2942 4875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4877">
    <literal><![CDATA[
      (((1 / x) * (y * ((x * x) * (1 / x)))) / (1 / x)) / T(1 / x,T(x * y,x * x)) = y * (x * x)
    ]]></literal>
    <justification jstring="[para(34(a,1),4481(a,1,1,1,2))].">
      <j1 rule="para" parents="34 4481"/>
    </justification>
  </clause>

  <clause id="4878">
    <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(2374(a,1),4558(a,1,1))].">
      <j1 rule="para" parents="2374 4558"/>
    </justification>
  </clause>

  <clause id="4879">
    <literal><![CDATA[
      ((x * ((y \ T(z,x)) * y)) / x) * (((x * y) / x) \ y) = (y \ (z * (T(x,y) \ x))) * y
    ]]></literal>
    <justification jstring="[para(107(a,1),4878(a,1,1,1,2))].">
      <j1 rule="para" parents="107 4878"/>
    </justification>
  </clause>

  <clause id="4880">
    <literal><![CDATA[
      ((x * ((y \ T(z,x)) * y)) / x) * (T(x,y) \ x) = (y \ (z * (T(x,y) \ x))) * y
    ]]></literal>
    <justification jstring="[para(4557(a,1),4879(a,1,2))].">
      <j1 rule="para" parents="4557 4879"/>
    </justification>
  </clause>

  <clause id="4881">
    <literal><![CDATA[
      ((x * T((y \ z) * y,x)) / x) * (T(x,y) \ x) = (y \ (z * (T(x,y) \ x))) * y
    ]]></literal>
    <justification jstring="[para(3483(a,2),4880(a,1,1,1,2))].">
      <j1 rule="para" parents="3483 4880"/>
    </justification>
  </clause>

  <clause id="4882">
    <literal><![CDATA[
      (x \ (y * (T(z,x) \ z))) * x = ((x \ y) * x) * (T(z,x) \ z)
    ]]></literal>
    <justification jstring="[para(223(a,1),4881(a,1,1)),flip(a)].">
      <j1 rule="para" parents="223 4881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4884">
    <literal><![CDATA[
      (((1 / x) * (y * x)) / (1 / x)) / T(1 / x,T(x * y,x * x)) = y * (x * x)
    ]]></literal>
    <justification jstring="[para(217(a,1),4877(a,1,1,1,2,2))].">
      <j1 rule="para" parents="217 4877"/>
    </justification>
  </clause>

  <clause id="4885">
    <literal><![CDATA[
      (((x \ 1) * (y * x)) / (x \ 1)) / T(1 / x,T(x * y,x * x)) = y * (x * x)
    ]]></literal>
    <justification jstring="[para(3262(a,1),4884(a,1,1))].">
      <j1 rule="para" parents="3262 4884"/>
    </justification>
  </clause>

  <clause id="4886">
    <literal><![CDATA[
      (T(x,y) * R(T(x,y) \ (x * y),z,u)) / (x * y) = R(1 / y,y,x) * R(R(1 / y,y,x) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(4668(a,1),4670(a,2,2,1,1))].">
      <j1 rule="para" parents="4668 4670"/>
    </justification>
  </clause>

  <clause id="4887">
    <literal><![CDATA[
      x * (T(((x * y) \ x) \ 1,x) \ (((x * y) \ x) \ 1)) = x / K(y,x)
    ]]></literal>
    <justification jstring="[para(3572(a,1),4330(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3572 4330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4888">
    <literal><![CDATA[
      x * (((x * y) \ (x * T(x \ (x * y),x))) \ 1) = x / K(y,x)
    ]]></literal>
    <justification jstring="[para(4555(a,1),4887(a,1,2))].">
      <j1 rule="para" parents="4555 4887"/>
    </justification>
  </clause>

  <clause id="4889">
    <literal><![CDATA[
      x * (((x * y) \ (x * T(y,x))) \ 1) = x / K(y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),4888(a,1,2,1,2,2,1))].">
      <j1 rule="para" parents="9 4888"/>
    </justification>
  </clause>

  <clause id="4890">
    <literal><![CDATA[
      x * (((x * y) \ (y * x)) \ 1) = x / K(y,x)
    ]]></literal>
    <justification jstring="[para(107(a,1),4889(a,1,2,1,2))].">
      <j1 rule="para" parents="107 4889"/>
    </justification>
  </clause>

  <clause id="4891">
    <literal><![CDATA[
      x * (K(y,x) \ 1) = x / K(y,x)
    ]]></literal>
    <justification jstring="[para(16(a,2),4890(a,1,2,1))].">
      <j1 rule="para" parents="16 4890"/>
    </justification>
  </clause>

  <clause id="4892">
    <literal><![CDATA[
      x / K(y,x) = K(y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(65,a,4761,a(flip),b,4891,a),flip(a)].">
      <j1 rule="hyper" parents="65 4761 4891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4893">
    <literal><![CDATA[
      x * (T(((x * y) \ x) \ 1,x) \ (((x * y) \ x) \ 1)) = K(y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(65,a,4887,a,b,4892,a)].">
      <j1 rule="hyper" parents="65 4887 4892"/>
    </justification>
  </clause>

  <clause id="4894">
    <literal><![CDATA[
      x \ ((((x * y) \ x) \ 1) \ T(((x * y) \ x) \ 1,x)) = (K(y,x) \ x) \ 1
    ]]></literal>
    <justification jstring="[para(4893(a,1),4323(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4893 4323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4895">
    <literal><![CDATA[
      (((x * y) \ x) * T(((x * y) \ x) \ 1,x)) / x = 1 / (K(y,x) \ x)
    ]]></literal>
    <justification jstring="[para(4893(a,1),4696(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4893 4696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4896">
    <literal><![CDATA[
      1 / (K(x,y) \ y) = K(x,y) / y
    ]]></literal>
    <justification jstring="[para(1377(a,2),4895(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1377 4895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4897">
    <literal><![CDATA[
      (K(x,y) / y) \ 1 = K(x,y) \ y
    ]]></literal>
    <justification jstring="[hyper(186,a,4896,a)].">
      <j1 rule="hyper" parents="186 4896"/>
    </justification>
  </clause>

  <clause id="4898">
    <literal><![CDATA[
      x \ (((x * y) \ x) * T(((x * y) \ x) \ 1,x)) = (K(y,x) \ x) \ 1
    ]]></literal>
    <justification jstring="[para(3516(a,1),4894(a,1,2))].">
      <j1 rule="para" parents="3516 4894"/>
    </justification>
  </clause>

  <clause id="4899">
    <literal><![CDATA[
      (K(x,y) \ y) \ 1 = y \ K(x,y)
    ]]></literal>
    <justification jstring="[para(1377(a,2),4898(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1377 4898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4900">
    <literal><![CDATA[
      1 / (x \ K(y,x)) = K(y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(192,a,4899,a)].">
      <j1 rule="hyper" parents="192 4899"/>
    </justification>
  </clause>

  <clause id="4901">
    <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(4442(a,1),4655(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4442 4655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4902">
    <literal><![CDATA[
      R(1 / (x / y),x / y,(x / y) \ T(x,x \ y)) = y / x
    ]]></literal>
    <justification jstring="[hyper(299,a,2926,a(flip),b,4901,a),flip(a)].">
      <j1 rule="hyper" parents="299 2926 4901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4903">
    <literal><![CDATA[
      R(1 / (x / y),x / y,x * (y / x)) = y / x
    ]]></literal>
    <justification jstring="[para(4650(a,1),4902(a,1,3))].">
      <j1 rule="para" parents="4650 4902"/>
    </justification>
  </clause>

  <clause id="4904">
    <literal><![CDATA[
      T(L(x,y,y \ 1),y) \ ((1 / y) \ T(L(x,y,y \ 1),(1 / y) \ 1)) = L(x,y,y \ 1) \ (y * x)
    ]]></literal>
    <justification jstring="[para(79(a,1),4676(a,1,1,2))].">
      <j1 rule="para" parents="79 4676"/>
    </justification>
  </clause>

  <clause id="4905">
    <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),4904(a,1,1))].">
      <j1 rule="para" parents="25 4904"/>
    </justification>
  </clause>

  <clause id="4906">
    <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(2473(a,1),4905(a,1,1))].">
      <j1 rule="para" parents="2473 4905"/>
    </justification>
  </clause>

  <clause id="4907">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ ((1 / x) \ T(L(y,x,x \ 1),x)) = L(y,x,x \ 1) \ (x * y)
    ]]></literal>
    <justification jstring="[para(79(a,1),4906(a,1,2,2,2))].">
      <j1 rule="para" parents="79 4906"/>
    </justification>
  </clause>

  <clause id="4908">
    <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),4907(a,1,2,2))].">
      <j1 rule="para" parents="25 4907"/>
    </justification>
  </clause>

  <clause id="4909">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ ((1 / x) \ ((1 / x) * (y * x))) = L(y,x,x \ 1) \ (x * y)
    ]]></literal>
    <justification jstring="[para(2473(a,1),4908(a,1,2,2))].">
      <j1 rule="para" parents="2473 4908"/>
    </justification>
  </clause>

  <clause id="4910">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ (y * x) = L(y,x,x \ 1) \ (x * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),4909(a,1,2))].">
      <j1 rule="para" parents="9 4909"/>
    </justification>
  </clause>

  <clause id="4912">
    <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),1974(a,2,2,1,1))].">
      <j1 rule="para" parents="20 1974"/>
    </justification>
  </clause>

  <clause id="4913">
    <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(1871(a,1),4912(a,1,1))].">
      <j1 rule="para" parents="1871 4912"/>
    </justification>
  </clause>

  <clause id="4914">
    <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(1914(a,1),4913(a,1,1,1))].">
      <j1 rule="para" parents="1914 4913"/>
    </justification>
  </clause>

  <clause id="4915">
    <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(549,a,4914,a),flip(a)].">
      <j1 rule="hyper" parents="549 4914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4916">
    <literal><![CDATA[
      (T(x,y) * R(T(x,y) \ (x * y),z,u)) / (x * y) = R((1 / y) * R((1 / y) \ 1,z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,4886,a,b,4915,a)].">
      <j1 rule="hyper" parents="65 4886 4915"/>
    </justification>
  </clause>

  <clause id="4917">
    <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(65,a,1459,a(flip),b,4915,a),flip(a)].">
      <j1 rule="hyper" parents="65 1459 4915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4918">
    <literal><![CDATA[
      R(x,y,z) * R(R(x,y,z) \ 1,x,x \ 1) = R(x * T(1 * (x \ 1),x),y,z)
    ]]></literal>
    <justification jstring="[para(705(a,1),4915(a,2,1,2))].">
      <j1 rule="para" parents="705 4915"/>
    </justification>
  </clause>

  <clause id="4919">
    <literal><![CDATA[
      R(x * T(1 * (x \ 1),x),y,z) = a(1 / R(x,y,z),x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(1230,a,4918,a),flip(a)].">
      <j1 rule="hyper" parents="1230 4918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4920">
    <literal><![CDATA[
      a(1 / R(x,y,z),x,x \ 1) = R(x * T(x \ 1,x),y,z)
    ]]></literal>
    <justification jstring="[para(7(a,1),4919(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 4919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4921">
    <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(1942(a,1),4917(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1942 4917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4922">
    <literal><![CDATA[
      (x \ 1) / (x \ R(x,y,z)) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(2432,a,4921,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="2432 4921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4923">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ (x \ 1) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,4087,a(flip),b,4922,a)].">
      <j1 rule="hyper" parents="65 4087 4922"/>
    </justification>
  </clause>

  <clause id="4924">
    <literal><![CDATA[
      (x \ 1) \ (R(x,y,z) \ 1) = (x \ R(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(119,a,4923,a(flip),b,2395,a)].">
      <j1 rule="hyper" parents="119 4923 2395"/>
    </justification>
  </clause>

  <clause id="4925">
    <literal><![CDATA[
      ((1 / x) \ R(1 / x,y,z)) \ x = R(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(79(a,1),4923(a,1,2))].">
      <j1 rule="para" parents="79 4923"/>
    </justification>
  </clause>

  <clause id="4926">
    <literal><![CDATA[
      (x * R(x \ 1,y,z)) \ x = R(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(1223(a,1),4925(a,1,1))].">
      <j1 rule="para" parents="1223 4925"/>
    </justification>
  </clause>

  <clause id="4927">
    <literal><![CDATA[
      R(1 / (1 / x),y,z) \ 1 = (R(x,y,z) / x) \ (1 / x)
    ]]></literal>
    <justification jstring="[para(1828(a,1),4926(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1828 4926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4928">
    <literal><![CDATA[
      (T(x,y) * R(T(x,y) \ (x * y),z,u)) / (x * y) = R(R(y,z,u) / y,y,x)
    ]]></literal>
    <justification jstring="[para(1828(a,1),4916(a,2,1))].">
      <j1 rule="para" parents="1828 4916"/>
    </justification>
  </clause>

  <clause id="4929">
    <literal><![CDATA[
      (T(x,y) * R(T(y,x),z,u)) / (x * y) = R(R(y,z,u) / y,y,x)
    ]]></literal>
    <justification jstring="[para(4419(a,1),4928(a,1,1,2,1))].">
      <j1 rule="para" parents="4419 4928"/>
    </justification>
  </clause>

  <clause id="4930">
    <literal><![CDATA[
      (R(x,y,z) * T(u,x)) / (u * x) = R(R(x,y,z) / x,x,u)
    ]]></literal>
    <justification jstring="[para(4403(a,1),4929(a,1,1))].">
      <j1 rule="para" parents="4403 4929"/>
    </justification>
  </clause>

  <clause id="4931">
    <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(103(a,1),1989(a,1,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="103 1989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4932">
    <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(299,a,941,a(flip),b,4931,a),flip(a)].">
      <j1 rule="hyper" parents="299 941 4931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4933">
    <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(299,a,2251,a(flip),b,4932,a),flip(a)].">
      <j1 rule="hyper" parents="299 2251 4932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4934">
    <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(941(a,1),4933(a,1,1))].">
      <j1 rule="para" parents="941 4933"/>
    </justification>
  </clause>

  <clause id="4935">
    <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(2260(a,1),4934(a,2,1))].">
      <j1 rule="para" parents="2260 4934"/>
    </justification>
  </clause>

  <clause id="4936">
    <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(37,a,103,a,b,4935,a),flip(a)].">
      <j1 rule="hyper" parents="37 103 4935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4937">
    <literal><![CDATA[
      R(x * ((y * (x \ 1)) / y),z,u) = K(y,(y / R(x,z,u)) / y)
    ]]></literal>
    <justification jstring="[hyper(1881,a,4936,a),flip(a)].">
      <j1 rule="hyper" parents="1881 4936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4938">
    <literal><![CDATA[
      R(x \ T(x,y \ 1),z,u) = K(x,(x / R(y,z,u)) / x)
    ]]></literal>
    <justification jstring="[para(4206(a,1),4937(a,1,1))].">
      <j1 rule="para" parents="4206 4937"/>
    </justification>
  </clause>

  <clause id="4939">
    <literal><![CDATA[
      R(x \ T(x,y \ 1),z,u) = x \ T(x,R(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,4211,a(flip),b,4938,a),flip(a)].">
      <j1 rule="hyper" parents="299 4211 4938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4940">
    <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(299,a,4220,a,b,4939,a)].">
      <j1 rule="hyper" parents="299 4220 4939"/>
    </justification>
  </clause>

  <clause id="4941">
    <literal><![CDATA[
      T(x \ T(x,(y / (z * y)) \ 1),T(z,u)) = R(x \ T(x,z),z,y)
    ]]></literal>
    <justification jstring="[para(3739(a,1),4940(a,2,1,2))].">
      <j1 rule="para" parents="3739 4940"/>
    </justification>
  </clause>

  <clause id="4942">
    <literal><![CDATA[
      T(x \ T(x,(y * z) / z),T(y,u)) = R(x \ T(x,y),y,z)
    ]]></literal>
    <justification jstring="[para(4641(a,1),4941(a,1,1,2))].">
      <j1 rule="para" parents="4641 4941"/>
    </justification>
  </clause>

  <clause id="4943">
    <literal><![CDATA[
      T(x \ T(x,y),T(y,z)) = R(x \ T(x,y),y,u)
    ]]></literal>
    <justification jstring="[para(11(a,1),4942(a,1,1,2,2))].">
      <j1 rule="para" parents="11 4942"/>
    </justification>
  </clause>

  <clause id="4944">
    <literal><![CDATA[
      R(x \ T(x,y),y,z) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,3676,a(flip),b,4943,a),flip(a)].">
      <j1 rule="hyper" parents="65 3676 4943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4946">
    <literal><![CDATA[
      (x \ T(x,y)) \ (((x * y) / x) * z) = y * z
    ]]></literal>
    <justification jstring="[para(4944(a,1),4197(a,1,1))].">
      <j1 rule="para" parents="4944 4197"/>
    </justification>
  </clause>

  <clause id="4947">
    <literal><![CDATA[
      (x \ T(x,y)) \ z = (T(x,y) \ x) * z
    ]]></literal>
    <justification jstring="[para(4944(a,1),4838(a,1,1))].">
      <j1 rule="para" parents="4944 4838"/>
    </justification>
  </clause>

  <clause id="4948">
    <literal><![CDATA[
      (T(x,y) \ x) * z = x * (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(4550,a,4947,a),flip(a)].">
      <j1 rule="hyper" parents="4550 4947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4949">
    <literal><![CDATA[
      (T(x,y) \ x) * (T(x,y) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(4312,a,4947,a),flip(a)].">
      <j1 rule="hyper" parents="4312 4947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4950">
    <literal><![CDATA[
      (x \ T(x,y)) \ z = T(y,x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(299,a,4435,a,b,4947,a),flip(a)].">
      <j1 rule="hyper" parents="299 4435 4947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4953">
    <literal><![CDATA[
      T(x,y) * (x \ z) = y * (T(y,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,4435,a,b,4948,a)].">
      <j1 rule="hyper" parents="65 4435 4948"/>
    </justification>
  </clause>

  <clause id="4954">
    <literal><![CDATA[
      x * (T(x,(y / z) / (1 / z)) \ (y / z)) = T(y,x) / z
    ]]></literal>
    <justification jstring="[hyper(65,a,4629,a(flip),b,4948,a),flip(a)].">
      <j1 rule="hyper" parents="65 4629 4948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4955">
    <literal><![CDATA[
      x * T(x \ y,z) = z * (T(z,y / x) \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,4490,a(flip),b,4948,a)].">
      <j1 rule="hyper" parents="65 4490 4948"/>
    </justification>
  </clause>

  <clause id="4957">
    <literal><![CDATA[
      (T(x,y) \ x) \ z = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(119,a,10,a(flip),b,4949,a)].">
      <j1 rule="hyper" parents="119 10 4949"/>
    </justification>
  </clause>

  <clause id="4958">
    <literal><![CDATA[
      T(x,y) * (x \ (T(y,x) * z)) = y * z
    ]]></literal>
    <justification jstring="[hyper(65,a,4435,a,b,4949,a)].">
      <j1 rule="hyper" parents="65 4435 4949"/>
    </justification>
  </clause>

  <clause id="4959">
    <literal><![CDATA[
      ((x * y) / x) \ (T(x,y) * z) = y \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(119,a,4949,a(flip),b,4836,a),flip(a)].">
      <j1 rule="hyper" parents="119 4949 4836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4960">
    <literal><![CDATA[
      T(x,y) \ (y * z) = x \ (T(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(119,a,4949,a(flip),b,4435,a)].">
      <j1 rule="hyper" parents="119 4949 4435"/>
    </justification>
  </clause>

  <clause id="4961">
    <literal><![CDATA[
      T(x,y) * (T(y,x) * z) = x * (y * z)
    ]]></literal>
    <justification jstring="[para(4949(a,1),4434(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4949 4434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4962">
    <literal><![CDATA[
      T(x,y) * (x \ (T(y,x) * z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (y * z) = w
    ]]></literal>
    <justification jstring="[para(4950(a,1),4313(a,1))].">
      <j1 rule="para" parents="4950 4313"/>
    </justification>
  </clause>

  <clause id="4963">
    <literal><![CDATA[
      T(x,y \ 1) * (x \ (y * (T(y \ 1,x) * z))) = L(z,T(y \ 1,x),y)
    ]]></literal>
    <justification jstring="[hyper(4488,a,4957,a),flip(a)].">
      <j1 rule="hyper" parents="4488 4957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4964">
    <literal><![CDATA[
      T(x,y) * (x \ (T(y,x) * z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      (y * z) / w = u
    ]]></literal>
    <justification jstring="[para(4960(a,1),388(a,1,2))].">
      <j1 rule="para" parents="4960 388"/>
    </justification>
  </clause>

  <clause id="4965">
    <literal><![CDATA[
      T(x,y) * (T(y,x) * z) = (x * y) * L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,94,a,b,4961,a),flip(a)].">
      <j1 rule="hyper" parents="299 94 4961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4966">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) = a(T(x,y),T(y,x),z)
    ]]></literal>
    <justification jstring="[para(4961(a,1),4427(a,1,1))].">
      <j1 rule="para" parents="4961 4427"/>
    </justification>
  </clause>

  <clause id="4967">
    <literal><![CDATA[
      L(x,y \ 1,(z * y) / z) = y * ((y \ 1) * x)
    ]]></literal>
    <justification jstring="[hyper(4201,a,4946,a)].">
      <j1 rule="hyper" parents="4201 4946"/>
    </justification>
  </clause>

  <clause id="4968">
    <literal><![CDATA[
      x \ (((y * x) / y) * z) = T(x,y) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(119,a,4946,a(flip),b,4950,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 4946 4950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4969">
    <literal><![CDATA[
      (x \ T(x,x \ y)) \ y = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(81(a,1),4946(a,1,2))].">
      <j1 rule="para" parents="81 4946"/>
    </justification>
  </clause>

  <clause id="4972">
    <literal><![CDATA[
      (x \ ((x \ y) \ y)) \ y = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(108(a,1),4969(a,1,1,2))].">
      <j1 rule="para" parents="108 4969"/>
    </justification>
  </clause>

  <clause id="4973">
    <literal><![CDATA[
      x / ((y \ x) * y) = y \ ((y \ x) \ x)
    ]]></literal>
    <justification jstring="[hyper(192,a,4972,a)].">
      <j1 rule="hyper" parents="192 4972"/>
    </justification>
  </clause>

  <clause id="4974">
    <literal><![CDATA[
      (x * (y / x)) / y = y / ((x \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(299,a,4541,a,b,4973,a)].">
      <j1 rule="hyper" parents="299 4541 4973"/>
    </justification>
  </clause>

  <clause id="4975">
    <literal><![CDATA[
      T(x * (y / x),y) / y = y / ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(3469(a,2),4974(a,1,1))].">
      <j1 rule="para" parents="3469 4974"/>
    </justification>
  </clause>

  <clause id="4976">
    <literal><![CDATA[
      x \ (y * ((y \ x) * z)) = L(z,y \ x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(4295,a,4959,a),flip(a)].">
      <j1 rule="hyper" parents="4295 4959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4977">
    <literal><![CDATA[
      x \ (((y * x) / y) * z) = x * (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(299,a,1192,a(flip),b,4968,a),flip(a)].">
      <j1 rule="hyper" parents="299 1192 4968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4978">
    <literal><![CDATA[
      T(x,y) \ z != x \ (((y * x) / y) * u)
    ]]></literal>
    <literal><![CDATA[
      x * u = z
    ]]></literal>
    <justification jstring="[para(4968(a,2),49(a,1)),flip(a)].">
      <j1 rule="para" parents="4968 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4979">
    <literal><![CDATA[
      x / ((((y \ 1) * x) \ x) * ((y \ 1) * x)) = T((y \ x) * y,x) / x
    ]]></literal>
    <justification jstring="[para(4249(a,1),4975(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4249 4975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4980">
    <literal><![CDATA[
      x * (T(x,y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      ((y * x) / y) * (x \ z) = u
    ]]></literal>
    <justification jstring="[para(4977(a,1),1428(a,1))].">
      <j1 rule="para" parents="4977 1428"/>
    </justification>
  </clause>

  <clause id="4981">
    <literal><![CDATA[
      L(x,T(y,z),T(z,y)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(4429,a,4965,a)].">
      <j1 rule="hyper" parents="4429 4965"/>
    </justification>
  </clause>

  <clause id="4982">
    <literal><![CDATA[
      L(T(x,y) \ 1,x,y) = (y * x) \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(389,a,4965,a),flip(a)].">
      <j1 rule="hyper" parents="389 4965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4983">
    <literal><![CDATA[
      L(x,y \ z,T(y,z / y)) = L(x,z / y,y)
    ]]></literal>
    <justification jstring="[para(109(a,1),4981(a,1,2))].">
      <j1 rule="para" parents="109 4981"/>
    </justification>
  </clause>

  <clause id="4984">
    <literal><![CDATA[
      L(x,y \ z,T(y,y \ z)) = L(x,z / y,y)
    ]]></literal>
    <justification jstring="[para(4400(a,1),4983(a,1,3))].">
      <j1 rule="para" parents="4400 4983"/>
    </justification>
  </clause>

  <clause id="4985">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ 1) * z) = L(z,T(x,y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(223(a,1),4967(a,1,3)),flip(a)].">
      <j1 rule="para" parents="223 4967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4986">
    <literal><![CDATA[
      L(x,y \ z,T(y,z)) = L(x,y \ z,y)
    ]]></literal>
    <justification jstring="[hyper(818,a,4976,a),flip(a)].">
      <j1 rule="hyper" parents="818 4976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4987">
    <literal><![CDATA[
      a(T(x,y),T(y,x),z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(775,a,4966,a),flip(a)].">
      <j1 rule="hyper" parents="775 4966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4988">
    <literal><![CDATA[
      a(T(x,y),T(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(4966(a,1),775(a,1))].">
      <j1 rule="para" parents="4966 775"/>
    </justification>
  </clause>

  <clause id="4989">
    <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(299,a,4868,a(flip),b,4987,a),flip(a)].">
      <j1 rule="hyper" parents="299 4868 4987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4990">
    <literal><![CDATA[
      a(T(x,T(y,z)),T(T(y,x),z),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,T(y,z),u) = w
    ]]></literal>
    <justification jstring="[para(23(a,1),4988(a,1,2))].">
      <j1 rule="para" parents="23 4988"/>
    </justification>
  </clause>

  <clause id="4991">
    <literal><![CDATA[
      L(x,T(y,z) \ 1,T(y,z)) = L(x,T(y,z) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(494,a,4985,a)].">
      <j1 rule="hyper" parents="494 4985"/>
    </justification>
  </clause>

  <clause id="4992">
    <literal><![CDATA[
      L(x,1 / T(y,y \ z),(y \ z) \ z) = L(x,T(y,y \ z) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(2543,a,4991,a)].">
      <j1 rule="hyper" parents="2543 4991"/>
    </justification>
  </clause>

  <clause id="4993">
    <literal><![CDATA[
      x * (T(x,(y / z) / (z \ 1)) \ (y / z)) = T(y,x) / z
    ]]></literal>
    <justification jstring="[para(3882(a,1),4954(a,1,2,1))].">
      <j1 rule="para" parents="3882 4954"/>
    </justification>
  </clause>

  <clause id="4994">
    <literal><![CDATA[
      T((x \ y) * x,y) / y = y / (x * (y / x))
    ]]></literal>
    <justification jstring="[para(4759(a,1),4979(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4759 4979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4995">
    <literal><![CDATA[
      ((x \ y) * x) / y = y / (x * (y / x))
    ]]></literal>
    <justification jstring="[para(3496(a,1),4994(a,1,1))].">
      <j1 rule="para" parents="3496 4994"/>
    </justification>
  </clause>

  <clause id="4996">
    <literal><![CDATA[
      ((x \ y) * x) / y = x \ (y / (y / x))
    ]]></literal>
    <justification jstring="[hyper(299,a,4517,a(flip),b,4995,a),flip(a)].">
      <j1 rule="hyper" parents="299 4517 4995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4997">
    <literal><![CDATA[
      (1 / x) * ((y \ x) * y) = y \ (x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(65,a,4072,a,b,4996,a)].">
      <j1 rule="hyper" parents="65 4072 4996"/>
    </justification>
  </clause>

  <clause id="4998">
    <literal><![CDATA[
      L((x \ ((y \ 1) \ 1)) * x,y \ 1,y) = y * (x \ (y / (y / x)))
    ]]></literal>
    <justification jstring="[para(4997(a,1),3684(a,2,2))].">
      <j1 rule="para" parents="4997 3684"/>
    </justification>
  </clause>

  <clause id="4999">
    <literal><![CDATA[
      (x \ (1 \ (y * 1))) * x = y * (x \ (y / (y / x)))
    ]]></literal>
    <justification jstring="[hyper(65,a,3934,a(flip),b,4998,a)].">
      <j1 rule="hyper" parents="65 3934 4998"/>
    </justification>
  </clause>

  <clause id="5000">
    <literal><![CDATA[
      x * (y \ (x / (x / y))) = (y \ x) * y
    ]]></literal>
    <justification jstring="[para(163(a,1),4999(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="163 4999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5001">
    <literal><![CDATA[
      x \ (y / (y / x)) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(36,a,287,a,b,5000,a),flip(a)].">
      <j1 rule="hyper" parents="36 287 5000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5002">
    <literal><![CDATA[
      x / (x / y) = y * K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(144,a,5001,a),flip(a)].">
      <j1 rule="hyper" parents="144 5001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5003">
    <literal><![CDATA[
      (1 / x) * ((y \ x) * y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,4997,a,b,5001,a)].">
      <j1 rule="hyper" parents="65 4997 5001"/>
    </justification>
  </clause>

  <clause id="5004">
    <literal><![CDATA[
      ((x \ y) * x) / y = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,4996,a,b,5001,a)].">
      <j1 rule="hyper" parents="65 4996 5001"/>
    </justification>
  </clause>

  <clause id="5006">
    <literal><![CDATA[
      T(K(x \ y,x),y) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(5001(a,1),4524(a,1,1))].">
      <j1 rule="para" parents="5001 4524"/>
    </justification>
  </clause>

  <clause id="5007">
    <literal><![CDATA[
      x / (x / y) = K(y \ x,y) * y
    ]]></literal>
    <justification jstring="[hyper(299,a,3618,a,b,5002,a),flip(a)].">
      <j1 rule="hyper" parents="299 3618 5002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5009">
    <literal><![CDATA[
      L(x,y \ 1,y) / (L(x,y \ 1,y) / y) = y * K((y \ 1) * x,y)
    ]]></literal>
    <justification jstring="[para(415(a,1),5002(a,2,2,1))].">
      <j1 rule="para" parents="415 5002"/>
    </justification>
  </clause>

  <clause id="5010">
    <literal><![CDATA[
      T(x,(y / (y / (1 / z))) * u) = T(x,((z \ 1) * K((1 / z) \ y,1 / z)) * u)
    ]]></literal>
    <justification jstring="[para(5002(a,2),3879(a,1,2,1))].">
      <j1 rule="para" parents="5002 3879"/>
    </justification>
  </clause>

  <clause id="5011">
    <literal><![CDATA[
      T(x * K(x \ y,x),y) = L(x,x \ y,x)
    ]]></literal>
    <justification jstring="[para(5002(a,1),4519(a,1,1))].">
      <j1 rule="para" parents="5002 4519"/>
    </justification>
  </clause>

  <clause id="5012">
    <literal><![CDATA[
      K(x \ y,x) * (x * z) = (y / (y / x)) * z
    ]]></literal>
    <justification jstring="[para(5002(a,2),4776(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5002 4776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5013">
    <literal><![CDATA[
      T(x,y) / (T(x,y) / y) = y * K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(4825(a,1),5002(a,2,2))].">
      <j1 rule="para" parents="4825 5002"/>
    </justification>
  </clause>

  <clause id="5014">
    <literal><![CDATA[
      K(x \ y,x) * y = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(143,a,5004,a)].">
      <j1 rule="hyper" parents="143 5004"/>
    </justification>
  </clause>

  <clause id="5015">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ 1) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,4071,a,b,5004,a)].">
      <j1 rule="hyper" parents="65 4071 5004"/>
    </justification>
  </clause>

  <clause id="5016">
    <literal><![CDATA[
      T(x,K(y \ x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(56,a,5006,a)].">
      <j1 rule="hyper" parents="56 5006"/>
    </justification>
  </clause>

  <clause id="5017">
    <literal><![CDATA[
      T(x * y,K(y,x)) = x * y
    ]]></literal>
    <justification jstring="[para(9(a,1),5016(a,1,2,1))].">
      <j1 rule="para" parents="9 5016"/>
    </justification>
  </clause>

  <clause id="5018">
    <literal><![CDATA[
      K(x,y) \ (x * y) = y * x
    ]]></literal>
    <justification jstring="[hyper(410,a,5017,a)].">
      <j1 rule="hyper" parents="410 5017"/>
    </justification>
  </clause>

  <clause id="5019">
    <literal><![CDATA[
      K(x,y) = (x * y) / (y * x)
    ]]></literal>
    <justification jstring="[para(5017(a,1),291(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5017 291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5020">
    <literal><![CDATA[
      K(x,y) * (y * x) = x * y
    ]]></literal>
    <justification jstring="[hyper(144,a,5018,a)].">
      <j1 rule="hyper" parents="144 5018"/>
    </justification>
  </clause>

  <clause id="5021">
    <literal><![CDATA[
      x * (y * z) != z * y
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = x
    ]]></literal>
    <justification jstring="[para(5018(a,1),136(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5018 136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5024">
    <literal><![CDATA[
      K(x,y) = T(y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(299,a,4493,a(flip),b,5019,a),flip(a)].">
      <j1 rule="hyper" parents="299 4493 5019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5025">
    <literal><![CDATA[
      x / ((y \ x) * y) = K(y,y \ x)
    ]]></literal>
    <justification jstring="[para(10(a,1),5019(a,2,1)),flip(a)].">
      <j1 rule="para" parents="10 5019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5026">
    <literal><![CDATA[
      K(x,y / x) * y = x * (y / x)
    ]]></literal>
    <justification jstring="[para(5019(a,2),348(a,1,1))].">
      <j1 rule="para" parents="5019 348"/>
    </justification>
  </clause>

  <clause id="5028">
    <literal><![CDATA[
      K(x,y) != z \ y
    ]]></literal>
    <literal><![CDATA[
      T(y,x) = z
    ]]></literal>
    <justification jstring="[para(5019(a,2),4500(a,2)),flip(a)].">
      <j1 rule="para" parents="5019 4500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5029">
    <literal><![CDATA[
      K(x,y) = ((y * x) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(299,a,4557,a,b,5024,a),flip(a)].">
      <j1 rule="hyper" parents="299 4557 5024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5030">
    <literal><![CDATA[
      K(x \ (x / y),x) = K(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,4486,a,b,5024,a)].">
      <j1 rule="hyper" parents="299 4486 5024"/>
    </justification>
  </clause>

  <clause id="5031">
    <literal><![CDATA[
      (x * T(x \ 1,y)) \ 1 = K(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,4268,a,b,5024,a)].">
      <j1 rule="hyper" parents="299 4268 5024"/>
    </justification>
  </clause>

  <clause id="5032">
    <literal><![CDATA[
      K(x,y) = (1 / T(y,x)) * y
    ]]></literal>
    <justification jstring="[hyper(299,a,3657,a,b,5024,a),flip(a)].">
      <j1 rule="hyper" parents="299 3657 5024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5033">
    <literal><![CDATA[
      K(x,y) = y / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,3651,a,b,5024,a),flip(a)].">
      <j1 rule="hyper" parents="299 3651 5024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5034">
    <literal><![CDATA[
      K(x,y) = y * (T(y,x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,1193,a,b,5024,a),flip(a)].">
      <j1 rule="hyper" parents="299 1193 5024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5035">
    <literal><![CDATA[
      x * T(x \ 1,y) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,4432,a(flip),b,5024,a)].">
      <j1 rule="hyper" parents="299 4432 5024"/>
    </justification>
  </clause>

  <clause id="5036">
    <literal><![CDATA[
      K(x,y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,4395,a(flip),b,5024,a),flip(a)].">
      <j1 rule="hyper" parents="299 4395 5024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5037">
    <literal><![CDATA[
      K(T(x,y),y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,4265,a(flip),b,5024,a),flip(a)].">
      <j1 rule="hyper" parents="299 4265 5024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5038">
    <literal><![CDATA[
      K(x,y) / y = 1 / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(120,a,5024,a,b,3657,a)].">
      <j1 rule="hyper" parents="120 5024 3657"/>
    </justification>
  </clause>

  <clause id="5039">
    <literal><![CDATA[
      T(x,y) \ 1 = x \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,5024,a,b,1193,a),flip(a)].">
      <j1 rule="hyper" parents="119 5024 1193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5040">
    <literal><![CDATA[
      x \ K(x \ 1,y) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,5024,a,b,4432,a(flip))].">
      <j1 rule="hyper" parents="119 5024 4432"/>
    </justification>
  </clause>

  <clause id="5041">
    <literal><![CDATA[
      T(x,y) = x / K(y,x)
    ]]></literal>
    <justification jstring="[hyper(192,a,5024,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="192 5024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5042">
    <literal><![CDATA[
      T(x,y) * K(y,x) = x
    ]]></literal>
    <justification jstring="[hyper(144,a,5024,a(flip))].">
      <j1 rule="hyper" parents="144 5024"/>
    </justification>
  </clause>

  <clause id="5043">
    <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),5024(a,2,1)),flip(a)].">
      <j1 rule="para" parents="25 5024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5044">
    <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),5024(a,2,1)),flip(a)].">
      <j1 rule="para" parents="27 5024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5045">
    <literal><![CDATA[
      x * K(y,z) != z
    ]]></literal>
    <literal><![CDATA[
      T(z,y) = x
    ]]></literal>
    <justification jstring="[para(5024(a,2),136(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5024 136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5046">
    <literal><![CDATA[
      x / K(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(5024(a,2),310(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5024 310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5047">
    <literal><![CDATA[
      ((x \ y) \ y) * K(x \ y,x) = x
    ]]></literal>
    <justification jstring="[para(5024(a,2),351(a,1,2))].">
      <j1 rule="para" parents="5024 351"/>
    </justification>
  </clause>

  <clause id="5048">
    <literal><![CDATA[
      K((1 / x) \ y,y) = T(y,y * x) \ y
    ]]></literal>
    <justification jstring="[para(2010(a,1),5024(a,2,1))].">
      <j1 rule="para" parents="2010 5024"/>
    </justification>
  </clause>

  <clause id="5049">
    <literal><![CDATA[
      K(x,y) * T(y,x) = y
    ]]></literal>
    <justification jstring="[para(5024(a,2),3650(a,1,1))].">
      <j1 rule="para" parents="5024 3650"/>
    </justification>
  </clause>

  <clause id="5050">
    <literal><![CDATA[
      T(x,y) = K(y,x) \ x
    ]]></literal>
    <justification jstring="[para(5024(a,2),3652(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5024 3652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5051">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      y / T(y,x) = z
    ]]></literal>
    <justification jstring="[para(5024(a,2),3664(a,1))].">
      <j1 rule="para" parents="5024 3664"/>
    </justification>
  </clause>

  <clause id="5052">
    <literal><![CDATA[
      (x \ 1) * K(y,x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[para(5024(a,2),4066(a,1,2))].">
      <j1 rule="para" parents="5024 4066"/>
    </justification>
  </clause>

  <clause id="5053">
    <literal><![CDATA[
      T(x * K(y,x),y) = x
    ]]></literal>
    <justification jstring="[para(5024(a,2),4409(a,1,1,2))].">
      <j1 rule="para" parents="5024 4409"/>
    </justification>
  </clause>

  <clause id="5054">
    <literal><![CDATA[
      (x * y) / x = y * K(x,y)
    ]]></literal>
    <justification jstring="[para(5024(a,2),4410(a,2,2))].">
      <j1 rule="para" parents="5024 4410"/>
    </justification>
  </clause>

  <clause id="5055">
    <literal><![CDATA[
      x * (K(x,y) * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[para(5024(a,2),4434(a,1,2,1))].">
      <j1 rule="para" parents="5024 4434"/>
    </justification>
  </clause>

  <clause id="5056">
    <literal><![CDATA[
      T(x,y) * (x \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(5024(a,2),4435(a,2,1))].">
      <j1 rule="para" parents="5024 4435"/>
    </justification>
  </clause>

  <clause id="5057">
    <literal><![CDATA[
      K(x / y,z) * x = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(5024(a,2),4490(a,1,1))].">
      <j1 rule="para" parents="5024 4490"/>
    </justification>
  </clause>

  <clause id="5058">
    <literal><![CDATA[
      K(x,y) * ((y * x) / y) = x
    ]]></literal>
    <justification jstring="[para(5024(a,2),4560(a,1,1))].">
      <j1 rule="para" parents="5024 4560"/>
    </justification>
  </clause>

  <clause id="5059">
    <literal><![CDATA[
      ((x \ y) * x) * (T(z,x) \ z) = (x \ (y * K(x,z))) * x
    ]]></literal>
    <justification jstring="[para(5024(a,2),4882(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5024 4882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5060">
    <literal><![CDATA[
      x * (T(x,y) \ z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[para(5024(a,2),4948(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5024 4948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5061">
    <literal><![CDATA[
      K(x,y) * (T(y,x) * z) = y * z
    ]]></literal>
    <justification jstring="[para(5024(a,2),4949(a,1,1))].">
      <j1 rule="para" parents="5024 4949"/>
    </justification>
  </clause>

  <clause id="5062">
    <literal><![CDATA[
      K(x,y) != y / z
    ]]></literal>
    <literal><![CDATA[
      T(y,x) = z
    ]]></literal>
    <justification jstring="[para(5033(a,2),47(a,1))].">
      <j1 rule="para" parents="5033 47"/>
    </justification>
  </clause>

  <clause id="5063">
    <literal><![CDATA[
      K(x,y) \ y != z
    ]]></literal>
    <literal><![CDATA[
      T(y,x) = z
    ]]></literal>
    <justification jstring="[para(5033(a,2),317(a,1,1))].">
      <j1 rule="para" parents="5033 317"/>
    </justification>
  </clause>

  <clause id="5065">
    <literal><![CDATA[
      (1 / (1 / x)) \ K(y,x) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[para(5033(a,2),3711(a,1,2))].">
      <j1 rule="para" parents="5033 3711"/>
    </justification>
  </clause>

  <clause id="5066">
    <literal><![CDATA[
      K(x * K(y,y \ 1),z) = z / T(z,x)
    ]]></literal>
    <justification jstring="[para(3873(a,1),5033(a,2,2))].">
      <j1 rule="para" parents="3873 5033"/>
    </justification>
  </clause>

  <clause id="5067">
    <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(5033(a,2),4544(a,2,1))].">
      <j1 rule="para" parents="5033 4544"/>
    </justification>
  </clause>

  <clause id="5068">
    <literal><![CDATA[
      T(K(x,y),x) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(4208,a,5036,a)].">
      <j1 rule="hyper" parents="4208 5036"/>
    </justification>
  </clause>

  <clause id="5069">
    <literal><![CDATA[
      (T(x,y) * z) / (x * z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,4311,a,b,5036,a)].">
      <j1 rule="hyper" parents="299 4311 5036"/>
    </justification>
  </clause>

  <clause id="5070">
    <literal><![CDATA[
      T(x \ T(x,y \ 1),z) = K(x,T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,4219,a,b,5036,a)].">
      <j1 rule="hyper" parents="299 4219 5036"/>
    </justification>
  </clause>

  <clause id="5071">
    <literal><![CDATA[
      L(x * ((y * (x \ 1)) / y),z,u) = K(y,L(x,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,4212,a,b,5036,a)].">
      <j1 rule="hyper" parents="299 4212 5036"/>
    </justification>
  </clause>

  <clause id="5072">
    <literal><![CDATA[
      x * ((y * (x \ 1)) / y) = K(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,4206,a,b,5036,a)].">
      <j1 rule="hyper" parents="299 4206 5036"/>
    </justification>
  </clause>

  <clause id="5073">
    <literal><![CDATA[
      K(x,y) = ((x * y) / x) * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,4187,a,b,5036,a),flip(a)].">
      <j1 rule="hyper" parents="299 4187 5036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5074">
    <literal><![CDATA[
      K(x,y) = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(299,a,4182,a,b,5036,a),flip(a)].">
      <j1 rule="hyper" parents="299 4182 5036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5075">
    <literal><![CDATA[
      K(x,y) = (1 / x) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,3514,a,b,5036,a),flip(a)].">
      <j1 rule="hyper" parents="299 3514 5036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5076">
    <literal><![CDATA[
      K(x,y) = T(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(299,a,3513,a,b,5036,a),flip(a)].">
      <j1 rule="hyper" parents="299 3513 5036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5077">
    <literal><![CDATA[
      K(x,y) = T(x,y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,1112,a,b,5036,a),flip(a)].">
      <j1 rule="hyper" parents="299 1112 5036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5078">
    <literal><![CDATA[
      x * T(x \ 1,y) = K(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,1074,a(flip),b,5036,a)].">
      <j1 rule="hyper" parents="299 1074 5036"/>
    </justification>
  </clause>

  <clause id="5079">
    <literal><![CDATA[
      x \ K(y,x \ 1) = (y * (x \ 1)) / y
    ]]></literal>
    <justification jstring="[hyper(119,a,5036,a,b,4206,a)].">
      <j1 rule="hyper" parents="119 5036 4206"/>
    </justification>
  </clause>

  <clause id="5080">
    <literal><![CDATA[
      ((x * y) / x) \ K(x,y) = y \ 1
    ]]></literal>
    <justification jstring="[hyper(119,a,5036,a,b,4187,a)].">
      <j1 rule="hyper" parents="119 5036 4187"/>
    </justification>
  </clause>

  <clause id="5081">
    <literal><![CDATA[
      T(x,y) = (1 / x) \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,5036,a,b,3514,a),flip(a)].">
      <j1 rule="hyper" parents="119 5036 3514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5082">
    <literal><![CDATA[
      x \ T(x,y \ 1) = K(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(65,a,4797,a,b,5036,a),flip(a)].">
      <j1 rule="hyper" parents="65 4797 5036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5083">
    <literal><![CDATA[
      T(x,y) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(144,a,5036,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="144 5036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5084">
    <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),5036(a,2,2)),flip(a)].">
      <j1 rule="para" parents="25 5036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5085">
    <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),5036(a,2,2)),flip(a)].">
      <j1 rule="para" parents="27 5036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5086">
    <literal><![CDATA[
      K(x,y) != x \ z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(5036(a,2),49(a,1))].">
      <j1 rule="para" parents="5036 49"/>
    </justification>
  </clause>

  <clause id="5087">
    <literal><![CDATA[
      x * K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(5036(a,2),250(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5036 250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5088">
    <literal><![CDATA[
      (x * y) \ (x * T(y,z)) = L(K(y,z),y,x)
    ]]></literal>
    <justification jstring="[para(5036(a,2),96(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5036 96"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5090">
    <literal><![CDATA[
      x * K(x,y) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ T(x,y) = u
    ]]></literal>
    <justification jstring="[para(5036(a,2),391(a,1,2))].">
      <j1 rule="para" parents="5036 391"/>
    </justification>
  </clause>

  <clause id="5092">
    <literal><![CDATA[
      (x * y) * T(K(y,x),z) = x * (y * T(K(y,x),z))
    ]]></literal>
    <justification jstring="[para(5036(a,2),1000(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5036 1000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5093">
    <literal><![CDATA[
      K(x,y) * ((x \ 1) \ z) = z * T(z \ ((x \ 1) \ z),y)
    ]]></literal>
    <justification jstring="[para(5036(a,2),1300(a,1,1))].">
      <j1 rule="para" parents="5036 1300"/>
    </justification>
  </clause>

  <clause id="5094">
    <literal><![CDATA[
      K(x,x * (y \ 1)) = x \ T(x,y \ x)
    ]]></literal>
    <justification jstring="[para(2009(a,1),5036(a,2,2))].">
      <j1 rule="para" parents="2009 5036"/>
    </justification>
  </clause>

  <clause id="5095">
    <literal><![CDATA[
      L(x,y,K(z * z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,T(z * z,u)) = w
    ]]></literal>
    <justification jstring="[para(5036(a,2),2462(a,1,3))].">
      <j1 rule="para" parents="5036 2462"/>
    </justification>
  </clause>

  <clause id="5096">
    <literal><![CDATA[
      T(x,y) = K(x,y) * x
    ]]></literal>
    <justification jstring="[para(5036(a,2),3517(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5036 3517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5097">
    <literal><![CDATA[
      K(x,y) * x != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(5036(a,2),3520(a,1,1))].">
      <j1 rule="para" parents="5036 3520"/>
    </justification>
  </clause>

  <clause id="5098">
    <literal><![CDATA[
      K(x,y * K(z,z \ 1)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[para(3873(a,1),5036(a,2,2))].">
      <j1 rule="para" parents="3873 5036"/>
    </justification>
  </clause>

  <clause id="5099">
    <literal><![CDATA[
      (x * K(y,x)) * y = y * x
    ]]></literal>
    <justification jstring="[para(5036(a,2),4177(a,1,1,2))].">
      <j1 rule="para" parents="5036 4177"/>
    </justification>
  </clause>

  <clause id="5100">
    <literal><![CDATA[
      T(x,y) * K(y,T(x,y)) = x
    ]]></literal>
    <justification jstring="[para(5036(a,2),4180(a,1,2))].">
      <j1 rule="para" parents="5036 4180"/>
    </justification>
  </clause>

  <clause id="5101">
    <literal><![CDATA[
      (x * y) / x = K(x,y) * y
    ]]></literal>
    <justification jstring="[para(5036(a,2),4184(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5036 4184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5102">
    <literal><![CDATA[
      (x \ y) * K(x,x \ y) = y / x
    ]]></literal>
    <justification jstring="[para(5036(a,2),4179(a,1,2))].">
      <j1 rule="para" parents="5036 4179"/>
    </justification>
  </clause>

  <clause id="5103">
    <literal><![CDATA[
      K(x,y) * (x * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[para(5036(a,2),4261(a,1,1))].">
      <j1 rule="para" parents="5036 4261"/>
    </justification>
  </clause>

  <clause id="5104">
    <literal><![CDATA[
      x * (T(x,y) \ z) = K(x,y) \ z
    ]]></literal>
    <justification jstring="[para(5036(a,2),4267(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5036 4267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5105">
    <literal><![CDATA[
      K(x,x \ y) * y = x * (y / x)
    ]]></literal>
    <justification jstring="[para(5036(a,2),4318(a,1,1))].">
      <j1 rule="para" parents="5036 4318"/>
    </justification>
  </clause>

  <clause id="5106">
    <literal><![CDATA[
      K(x,y) \ (T(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(5036(a,2),4312(a,1,1))].">
      <j1 rule="para" parents="5036 4312"/>
    </justification>
  </clause>

  <clause id="5107">
    <literal><![CDATA[
      K(x,y) \ z != u
    ]]></literal>
    <literal><![CDATA[
      x * (T(x,y) \ z) = u
    ]]></literal>
    <justification jstring="[para(5036(a,2),4550(a,1,1))].">
      <j1 rule="para" parents="5036 4550"/>
    </justification>
  </clause>

  <clause id="5109">
    <literal><![CDATA[
      T(x,y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(5041(a,2),317(a,1,1))].">
      <j1 rule="para" parents="5041 317"/>
    </justification>
  </clause>

  <clause id="5111">
    <literal><![CDATA[
      (1 / (1 / x)) / K(y,x) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(4798(a,1),5041(a,2,2)),flip(a)].">
      <j1 rule="para" parents="4798 5041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5112">
    <literal><![CDATA[
      (x \ y) * K(x,y / x) = y / x
    ]]></literal>
    <justification jstring="[para(109(a,1),5042(a,1,1))].">
      <j1 rule="para" parents="109 5042"/>
    </justification>
  </clause>

  <clause id="5114">
    <literal><![CDATA[
      ((x \ y) \ y) * K(y / x,x) = x
    ]]></literal>
    <justification jstring="[para(4440(a,1),5042(a,1,1))].">
      <j1 rule="para" parents="4440 5042"/>
    </justification>
  </clause>

  <clause id="5115">
    <literal><![CDATA[
      x * (y * K(x,y)) = T(x,y) * y
    ]]></literal>
    <justification jstring="[para(5042(a,1),4961(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5042 4961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5117">
    <literal><![CDATA[
      K(x,y / x) * (x \ y) = y / x
    ]]></literal>
    <justification jstring="[para(109(a,1),5049(a,1,2))].">
      <j1 rule="para" parents="109 5049"/>
    </justification>
  </clause>

  <clause id="5118">
    <literal><![CDATA[
      x / T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(5049(a,1),307(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5049 307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5119">
    <literal><![CDATA[
      T(x,y) = 1 / (x \ K(y,x))
    ]]></literal>
    <justification jstring="[hyper(299,a,4900,a,b,5050,a),flip(a)].">
      <j1 rule="hyper" parents="299 4900 5050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5120">
    <literal><![CDATA[
      T(x,y) = (K(y,x) / x) \ 1
    ]]></literal>
    <justification jstring="[hyper(299,a,4897,a,b,5050,a),flip(a)].">
      <j1 rule="hyper" parents="299 4897 5050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5121">
    <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(5050(a,2),2457(a,1,2,1))].">
      <j1 rule="para" parents="5050 2457"/>
    </justification>
  </clause>

  <clause id="5122">
    <literal><![CDATA[
      (T(x,y) * y) / T(x,y) = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4461,a,5053,a)].">
      <j1 rule="hyper" parents="4461 5053"/>
    </justification>
  </clause>

  <clause id="5123">
    <literal><![CDATA[
      T((x * y) / x,z) = T(y,z) * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(446,a,5053,a)].">
      <j1 rule="hyper" parents="446 5053"/>
    </justification>
  </clause>

  <clause id="5124">
    <literal><![CDATA[
      x / (x / y) = y * K(x / y,y)
    ]]></literal>
    <justification jstring="[hyper(339,a,5053,a)].">
      <j1 rule="hyper" parents="339 5053"/>
    </justification>
  </clause>

  <clause id="5125">
    <literal><![CDATA[
      T(T(x * K(y,x),z),y) = T(x,z)
    ]]></literal>
    <justification jstring="[para(5053(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5053 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5126">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      z * K(y,z) = x
    ]]></literal>
    <justification jstring="[para(5053(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="5053 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5127">
    <literal><![CDATA[
      (x * K(y,x)) \ (y * x) = y
    ]]></literal>
    <justification jstring="[para(5053(a,1),224(a,1,2,2))].">
      <j1 rule="para" parents="5053 224"/>
    </justification>
  </clause>

  <clause id="5129">
    <literal><![CDATA[
      (x * y) / x != z
    ]]></literal>
    <literal><![CDATA[
      y * K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5053(a,1),311(a,1,1,2)),flip(b)].">
      <j1 rule="para" parents="5053 311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5130">
    <literal><![CDATA[
      T(x * K(y,x),z) * y = y * T(x,z)
    ]]></literal>
    <justification jstring="[para(5053(a,1),232(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5053 232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5131">
    <literal><![CDATA[
      L(x * K(y,x),z,u) * y = y * L(x,z,u)
    ]]></literal>
    <justification jstring="[para(5053(a,1),233(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5053 233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5132">
    <literal><![CDATA[
      R(x * K(y,x),z,u) * y = y * R(x,z,u)
    ]]></literal>
    <justification jstring="[para(5053(a,1),234(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5053 234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5133">
    <literal><![CDATA[
      T(x * K(y,x),(x * K(y,x)) * y) = L(x,y,x * K(y,x))
    ]]></literal>
    <justification jstring="[para(5053(a,1),784(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5053 784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5135">
    <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(5053(a,1),2152(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5053 2152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5136">
    <literal><![CDATA[
      T(1 / (1 / (x * K(y,x))),y) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[para(5053(a,1),3176(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5053 3176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5137">
    <literal><![CDATA[
      ((x \ (y * K(z,y))) * x) * z = z * ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(5053(a,1),3497(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="5053 3497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5138">
    <literal><![CDATA[
      T(K(x,y) * y,x) = y
    ]]></literal>
    <justification jstring="[para(3618(a,2),5053(a,1,1))].">
      <j1 rule="para" parents="3618 5053"/>
    </justification>
  </clause>

  <clause id="5139">
    <literal><![CDATA[
      T(x \ K(y,x \ 1),y) = x \ 1
    ]]></literal>
    <justification jstring="[para(3661(a,1),5053(a,1,1))].">
      <j1 rule="para" parents="3661 5053"/>
    </justification>
  </clause>

  <clause id="5140">
    <literal><![CDATA[
      (x * K(y,x)) * ((y \ 1) \ 1) = ((y \ 1) \ 1) * x
    ]]></literal>
    <justification jstring="[para(5053(a,1),3742(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5053 3742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5141">
    <literal><![CDATA[
      T(x,y * K(x,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(5053(a,1),4386(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5053 4386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5142">
    <literal><![CDATA[
      T(x,L(y * K(x,y),z,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(5053(a,1),4399(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5053 4399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5143">
    <literal><![CDATA[
      T(K(x,y \ 1) / y,x) = 1 / y
    ]]></literal>
    <justification jstring="[para(4806(a,1),5053(a,1,1))].">
      <j1 rule="para" parents="4806 5053"/>
    </justification>
  </clause>

  <clause id="5145">
    <literal><![CDATA[
      T(1 / x,y) * x = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(917,a,5076,a(flip))].">
      <j1 rule="hyper" parents="917 5076"/>
    </justification>
  </clause>

  <clause id="5146">
    <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),5076(a,2,1)),flip(a)].">
      <j1 rule="para" parents="27 5076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5150">
    <literal><![CDATA[
      T(x,y) * K(T(x,y),z) = T(T(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(861,a,5083,a),flip(a)].">
      <j1 rule="hyper" parents="861 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5151">
    <literal><![CDATA[
      T(x * y,z) / a(x,y,K(x * y,z)) = x * (y * K(x * y,z))
    ]]></literal>
    <justification jstring="[hyper(120,a,5083,a,b,84,a)].">
      <j1 rule="hyper" parents="120 5083 84"/>
    </justification>
  </clause>

  <clause id="5152">
    <literal><![CDATA[
      T(x,T(y,T(x,z))) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,4722,a,b,5083,a)].">
      <j1 rule="hyper" parents="65 4722 5083"/>
    </justification>
  </clause>

  <clause id="5153">
    <literal><![CDATA[
      ((x * y) * K(y,z)) / T(y,z) = R(x,y,K(y,z))
    ]]></literal>
    <justification jstring="[para(5083(a,2),20(a,2,2)),flip(a)].">
      <j1 rule="para" parents="5083 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5154">
    <literal><![CDATA[
      T(x,y) != x * z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5083(a,2),45(a,1))].">
      <j1 rule="para" parents="5083 45"/>
    </justification>
  </clause>

  <clause id="5155">
    <literal><![CDATA[
      x \ T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5083(a,2),314(a,1,2))].">
      <j1 rule="para" parents="5083 314"/>
    </justification>
  </clause>

  <clause id="5156">
    <literal><![CDATA[
      (x * y) * L(K(y,z),y,x) = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(5083(a,2),94(a,2,2))].">
      <j1 rule="para" parents="5083 94"/>
    </justification>
  </clause>

  <clause id="5157">
    <literal><![CDATA[
      R(x / y,y,K(x,z)) = T(x,z) / (y * K(x,z))
    ]]></literal>
    <justification jstring="[para(5083(a,2),104(a,2,1))].">
      <j1 rule="para" parents="5083 104"/>
    </justification>
  </clause>

  <clause id="5159">
    <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(5083(a,2),544(a,2,2))].">
      <j1 rule="para" parents="5083 544"/>
    </justification>
  </clause>

  <clause id="5160">
    <literal><![CDATA[
      T(T(x,y),x \ 1) = (x \ 1) \ K(x,y)
    ]]></literal>
    <justification jstring="[para(5083(a,2),1895(a,1,1))].">
      <j1 rule="para" parents="5083 1895"/>
    </justification>
  </clause>

  <clause id="5161">
    <literal><![CDATA[
      (1 / x) * K(x \ 1,y) = T(1 / x,y)
    ]]></literal>
    <justification jstring="[para(3565(a,1),5083(a,2,2)),flip(a)].">
      <j1 rule="para" parents="3565 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5162">
    <literal><![CDATA[
      K(T(x,y),z) * T(x,y) = T(T(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(861,a,5096,a),flip(a)].">
      <j1 rule="hyper" parents="861 5096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5164">
    <literal><![CDATA[
      (x * K(x * y,x)) * y = T(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,4776,a,b,5096,a)].">
      <j1 rule="hyper" parents="299 4776 5096"/>
    </justification>
  </clause>

  <clause id="5165">
    <literal><![CDATA[
      K(L(x,y,z),u) * L(x,y,z) = L(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,25,a,b,5096,a),flip(a)].">
      <j1 rule="hyper" parents="65 25 5096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5166">
    <literal><![CDATA[
      x * (K(y,x) * y) = y * x
    ]]></literal>
    <justification jstring="[para(5096(a,1),107(a,1,2))].">
      <j1 rule="para" parents="5096 107"/>
    </justification>
  </clause>

  <clause id="5167">
    <literal><![CDATA[
      T(x,y) / x != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5096(a,2),307(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5096 307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5168">
    <literal><![CDATA[
      L(x \ y,x,K(y,z)) = (K(y,z) * x) \ T(y,z)
    ]]></literal>
    <justification jstring="[para(5096(a,2),96(a,2,2))].">
      <j1 rule="para" parents="5096 96"/>
    </justification>
  </clause>

  <clause id="5170">
    <literal><![CDATA[
      T(x,y) \ (K(x,y) * (z * x)) = L(T(z,x),x,K(x,y))
    ]]></literal>
    <justification jstring="[para(5096(a,2),230(a,1,1))].">
      <j1 rule="para" parents="5096 230"/>
    </justification>
  </clause>

  <clause id="5171">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(y,K(y,z),x) = u
    ]]></literal>
    <justification jstring="[para(5096(a,2),493(a,1,2,2))].">
      <j1 rule="para" parents="5096 493"/>
    </justification>
  </clause>

  <clause id="5172">
    <literal><![CDATA[
      (K(x,y) * z) \ T(x,y) != u
    ]]></literal>
    <literal><![CDATA[
      L(z \ x,z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(5096(a,2),909(a,1,2))].">
      <j1 rule="para" parents="5096 909"/>
    </justification>
  </clause>

  <clause id="5173">
    <literal><![CDATA[
      T(x * y,z) * a(K(x * y,z),y,T(x,y)) = (K(x * y,z) * y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(5096(a,2),774(a,1,1))].">
      <j1 rule="para" parents="5096 774"/>
    </justification>
  </clause>

  <clause id="5174">
    <literal><![CDATA[
      ((K(x,y) * z) * (z \ x)) / T(T(x,y),a(K(x,y),z,z \ x)) = a(K(x,y),z,z \ x)
    ]]></literal>
    <justification jstring="[para(5096(a,2),1029(a,1,2,1))].">
      <j1 rule="para" parents="5096 1029"/>
    </justification>
  </clause>

  <clause id="5175">
    <literal><![CDATA[
      T(x,y) / R(x,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      (K(x,y) / R(x,z,u)) * x = w
    ]]></literal>
    <justification jstring="[para(5096(a,2),1924(a,1,1))].">
      <j1 rule="para" parents="5096 1924"/>
    </justification>
  </clause>

  <clause id="5176">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      x * K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5096(a,2),3576(a,1))].">
      <j1 rule="para" parents="5096 3576"/>
    </justification>
  </clause>

  <clause id="5177">
    <literal><![CDATA[
      K(x,x \ y) * (x \ y) = y / x
    ]]></literal>
    <justification jstring="[hyper(244,a,5138,a),flip(a)].">
      <j1 rule="hyper" parents="244 5138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5178">
    <literal><![CDATA[
      K(x,y) * ((y * x) * z) != (x * y) * u
    ]]></literal>
    <literal><![CDATA[
      L(z,y * x,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(5020(a,1),490(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5020 490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5179">
    <literal><![CDATA[
      T(x * y,z) / (y * x) = (y * x) \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(5020(a,1),3481(a,1,1,1))].">
      <j1 rule="para" parents="5020 3481"/>
    </justification>
  </clause>

  <clause id="5180">
    <literal><![CDATA[
      K(x,y) = x / ((y * x) / y)
    ]]></literal>
    <justification jstring="[hyper(299,a,3543,a,b,5029,a),flip(a)].">
      <j1 rule="hyper" parents="299 3543 5029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5181">
    <literal><![CDATA[
      K(x,y) = x * (((y * x) / y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,1418,a,b,5029,a),flip(a)].">
      <j1 rule="hyper" parents="299 1418 5029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5182">
    <literal><![CDATA[
      ((x * y) / x) \ 1 = y \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,5029,a,b,1418,a),flip(a)].">
      <j1 rule="hyper" parents="119 5029 1418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5183">
    <literal><![CDATA[
      T((x * y) / x,z) \ T(y,z) = K(T(y,z),x)
    ]]></literal>
    <justification jstring="[para(445(a,1),5029(a,2,1)),flip(a)].">
      <j1 rule="para" parents="445 5029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5184">
    <literal><![CDATA[
      K(x,y) / x = 1 / ((y * x) / y)
    ]]></literal>
    <justification jstring="[para(5029(a,2),3545(a,1,1))].">
      <j1 rule="para" parents="5029 3545"/>
    </justification>
  </clause>

  <clause id="5186">
    <literal><![CDATA[
      (x * y) \ (x * K(z,y)) = L(T(y,z) \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(5034(a,2),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5034 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5187">
    <literal><![CDATA[
      L(T(x \ y,z) \ 1,x \ y,x) = y \ (x * K(z,x \ y))
    ]]></literal>
    <justification jstring="[para(5034(a,2),95(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5034 95"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5188">
    <literal><![CDATA[
      K(T(x,y),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,5036,a,b,5037,a),flip(a)].">
      <j1 rule="hyper" parents="299 5036 5037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5190">
    <literal><![CDATA[
      K(x,T(y,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4612,a,5188,a),flip(a)].">
      <j1 rule="hyper" parents="4612 5188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5191">
    <literal><![CDATA[
      K(x \ (y * x),x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(22(a,1),5188(a,1,1))].">
      <j1 rule="para" parents="22 5188"/>
    </justification>
  </clause>

  <clause id="5192">
    <literal><![CDATA[
      K(x / y,y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(109(a,1),5188(a,1,1)),flip(a)].">
      <j1 rule="para" parents="109 5188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5193">
    <literal><![CDATA[
      K((x \ y) \ y,x \ y) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(108(a,1),5188(a,1,1))].">
      <j1 rule="para" parents="108 5188"/>
    </justification>
  </clause>

  <clause id="5194">
    <literal><![CDATA[
      K(R(x,y,x),y * x) = K(T(x,y),y * x)
    ]]></literal>
    <justification jstring="[para(875(a,1),5188(a,1,1)),flip(a)].">
      <j1 rule="para" parents="875 5188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5195">
    <literal><![CDATA[
      K(x / (x / y),y \ x) = K(y,y \ x)
    ]]></literal>
    <justification jstring="[para(4502(a,1),5188(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4502 5188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5196">
    <literal><![CDATA[
      K(x,T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5188(a,1),4612(a,1))].">
      <j1 rule="para" parents="5188 4612"/>
    </justification>
  </clause>

  <clause id="5197">
    <literal><![CDATA[
      K(x,y) \ 1 = K(y,x)
    ]]></literal>
    <justification jstring="[para(5188(a,1),4766(a,1,1))].">
      <j1 rule="para" parents="5188 4766"/>
    </justification>
  </clause>

  <clause id="5198">
    <literal><![CDATA[
      K(x,y) * K(y,x) = 1
    ]]></literal>
    <justification jstring="[para(5188(a,1),4768(a,1,1))].">
      <j1 rule="para" parents="5188 4768"/>
    </justification>
  </clause>

  <clause id="5199">
    <literal><![CDATA[
      K(x,y) * z != 1
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(5188(a,1),4769(a,1,1))].">
      <j1 rule="para" parents="5188 4769"/>
    </justification>
  </clause>

  <clause id="5200">
    <literal><![CDATA[
      K(x,y) \ 1 != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(5188(a,1),4770(a,1,1))].">
      <j1 rule="para" parents="5188 4770"/>
    </justification>
  </clause>

  <clause id="5201">
    <literal><![CDATA[
      K(x * K(y,x),y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5053(a,1),5188(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5053 5188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5202">
    <literal><![CDATA[
      K(x,y) * T(x,y) = T(T(x,y),y)
    ]]></literal>
    <justification jstring="[para(5188(a,1),5096(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5188 5096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5203">
    <literal><![CDATA[
      K(x,x \ (y * x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(22(a,1),5190(a,1,2))].">
      <j1 rule="para" parents="22 5190"/>
    </justification>
  </clause>

  <clause id="5204">
    <literal><![CDATA[
      K(x,L(T(y,x),z,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(25(a,2),5190(a,1,2))].">
      <j1 rule="para" parents="25 5190"/>
    </justification>
  </clause>

  <clause id="5205">
    <literal><![CDATA[
      K(x,y / x) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(109(a,1),5190(a,1,2)),flip(a)].">
      <j1 rule="para" parents="109 5190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5206">
    <literal><![CDATA[
      K(x \ y,(x \ y) \ y) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(108(a,1),5190(a,1,2))].">
      <j1 rule="para" parents="108 5190"/>
    </justification>
  </clause>

  <clause id="5207">
    <literal><![CDATA[
      K(x,R(y / x,z,u)) = K(x,R(x \ y,z,u))
    ]]></literal>
    <justification jstring="[para(243(a,1),5190(a,1,2)),flip(a)].">
      <j1 rule="para" parents="243 5190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5208">
    <literal><![CDATA[
      K(x,y * K(x,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5053(a,1),5190(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5053 5190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5209">
    <literal><![CDATA[
      1 / K(x,y) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(192,a,5197,a)].">
      <j1 rule="hyper" parents="192 5197"/>
    </justification>
  </clause>

  <clause id="5210">
    <literal><![CDATA[
      x * (K(y,z) * K(z,y)) = x
    ]]></literal>
    <justification jstring="[para(5197(a,1),71(a,1,2,2))].">
      <j1 rule="para" parents="5197 71"/>
    </justification>
  </clause>

  <clause id="5211">
    <literal><![CDATA[
      1 / K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(5197(a,1),310(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5197 310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5212">
    <literal><![CDATA[
      x * (K(y,z) * K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(5197(a,1),205(a,1,2,2))].">
      <j1 rule="para" parents="5197 205"/>
    </justification>
  </clause>

  <clause id="5214">
    <literal><![CDATA[
      L(L(K(x,y),z,u),K(y,x),w) = L((w * K(y,x)) \ w,z,u)
    ]]></literal>
    <justification jstring="[para(5197(a,1),372(a,1,1,1))].">
      <j1 rule="para" parents="5197 372"/>
    </justification>
  </clause>

  <clause id="5215">
    <literal><![CDATA[
      K(x,y) * ((K(x,y) \ 1) \ (z / u)) = (K(x,y) * (K(y,x) \ z)) / u
    ]]></literal>
    <justification jstring="[para(5197(a,1),1768(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5197 1768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5216">
    <literal><![CDATA[
      (x * y) \ ((y * x) * T(K(x,y),z)) = K(y,x) * T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(5197(a,1),2034(a,2,2,1))].">
      <j1 rule="para" parents="5197 2034"/>
    </justification>
  </clause>

  <clause id="5217">
    <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(5197(a,1),2154(a,2,1,2,1))].">
      <j1 rule="para" parents="5197 2154"/>
    </justification>
  </clause>

  <clause id="5218">
    <literal><![CDATA[
      L(x,y,K(z,u)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(5197(a,1),2470(a,1,3))].">
      <j1 rule="para" parents="5197 2470"/>
    </justification>
  </clause>

  <clause id="5219">
    <literal><![CDATA[
      L(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(5197(a,1),2503(a,1,3))].">
      <j1 rule="para" parents="5197 2503"/>
    </justification>
  </clause>

  <clause id="5220">
    <literal><![CDATA[
      L(x,K(y,z),u) = L(x,K(z,y),u)
    ]]></literal>
    <justification jstring="[para(5197(a,1),2526(a,1,2))].">
      <j1 rule="para" parents="5197 2526"/>
    </justification>
  </clause>

  <clause id="5221">
    <literal><![CDATA[
      L(x,y,z * K(u,w)) = L(x,y,z * K(w,u))
    ]]></literal>
    <justification jstring="[para(5197(a,1),2627(a,1,3,2))].">
      <j1 rule="para" parents="5197 2627"/>
    </justification>
  </clause>

  <clause id="5223">
    <literal><![CDATA[
      (x * K(y,x)) \ 1 = x \ K(x,y)
    ]]></literal>
    <justification jstring="[para(5197(a,1),4779(a,2,2))].">
      <j1 rule="para" parents="5197 4779"/>
    </justification>
  </clause>

  <clause id="5224">
    <literal><![CDATA[
      K(x,y) \ 1 != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ K(y,x) = u
    ]]></literal>
    <justification jstring="[para(5198(a,1),313(a,1,2))].">
      <j1 rule="para" parents="5198 313"/>
    </justification>
  </clause>

  <clause id="5226">
    <literal><![CDATA[
      1 / (x \ K(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(5039(a,1),310(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5039 310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5227">
    <literal><![CDATA[
      T(x,y) * L(x \ K(y,x),z,u) = T(x * L(x \ 1,z,u),y)
    ]]></literal>
    <justification jstring="[para(5039(a,1),2192(a,1,2,1))].">
      <j1 rule="para" parents="5039 2192"/>
    </justification>
  </clause>

  <clause id="5228">
    <literal><![CDATA[
      K(x,y) * K(y \ 1,y) = (T(y,x) \ 1) * y
    ]]></literal>
    <justification jstring="[para(5039(a,2),4790(a,2,1))].">
      <j1 rule="para" parents="5039 4790"/>
    </justification>
  </clause>

  <clause id="5229">
    <literal><![CDATA[
      ((x \ (1 / y)) * x) * y = K((x * y) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(4851,a,5054,a)].">
      <j1 rule="hyper" parents="4851 5054"/>
    </justification>
  </clause>

  <clause id="5230">
    <literal><![CDATA[
      (x * y) * K(T(y,x),x * y) = T(y,x * y) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(4702,a,5054,a),flip(a)].">
      <j1 rule="hyper" parents="4702 5054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5231">
    <literal><![CDATA[
      x \ K(y,1 / x) = (y * (x \ 1)) / y
    ]]></literal>
    <justification jstring="[hyper(299,a,4807,a(flip),b,5054,a)].">
      <j1 rule="hyper" parents="299 4807 5054"/>
    </justification>
  </clause>

  <clause id="5232">
    <literal><![CDATA[
      K(x,1 / y) / y = (x * (1 / y)) / x
    ]]></literal>
    <justification jstring="[hyper(299,a,2406,a(flip),b,5054,a)].">
      <j1 rule="hyper" parents="299 2406 5054"/>
    </justification>
  </clause>

  <clause id="5233">
    <literal><![CDATA[
      (x * y) \ ((x * y) / x) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,5054,a,b,1631,a)].">
      <j1 rule="hyper" parents="119 5054 1631"/>
    </justification>
  </clause>

  <clause id="5234">
    <literal><![CDATA[
      T(x,y) \ ((z * x) / z) = x * (T(x,y) \ K(z,x))
    ]]></literal>
    <justification jstring="[hyper(119,a,5054,a,b,1191,a)].">
      <j1 rule="hyper" parents="119 5054 1191"/>
    </justification>
  </clause>

  <clause id="5235">
    <literal><![CDATA[
      (x * y) * K(x \ 1,x * y) = L(y,x,x \ 1) / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(65,a,3326,a(flip),b,5054,a),flip(a)].">
      <j1 rule="hyper" parents="65 3326 5054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5236">
    <literal><![CDATA[
      (x * x) * (y / (x * x)) = y * K(x * x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,849,a(flip),b,5054,a)].">
      <j1 rule="hyper" parents="65 849 5054"/>
    </justification>
  </clause>

  <clause id="5237">
    <literal><![CDATA[
      x * ((y * z) / y) = x * (z * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,5054,a)].">
      <j1 rule="hyper" parents="60 5054"/>
    </justification>
  </clause>

  <clause id="5238">
    <literal><![CDATA[
      (x * y) / x != y * z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5054(a,2),45(a,1))].">
      <j1 rule="para" parents="5054 45"/>
    </justification>
  </clause>

  <clause id="5239">
    <literal><![CDATA[
      T(x,y) * K(y,T(x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(5054(a,1),311(a,1))].">
      <j1 rule="para" parents="5054 311"/>
    </justification>
  </clause>

  <clause id="5240">
    <literal><![CDATA[
      T(x * K(y,x),y) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(5054(a,1),324(a,1,1))].">
      <j1 rule="para" parents="5054 324"/>
    </justification>
  </clause>

  <clause id="5241">
    <literal><![CDATA[
      ((x * y) * z) / R(x,y,z) = (y * z) * K(R(x,y,z),y * z)
    ]]></literal>
    <justification jstring="[para(103(a,1),5054(a,1,1))].">
      <j1 rule="para" parents="103 5054"/>
    </justification>
  </clause>

  <clause id="5242">
    <literal><![CDATA[
      R(x * K(y,x),y,z) = ((y * x) * z) / (y * z)
    ]]></literal>
    <justification jstring="[para(5054(a,1),104(a,1,1))].">
      <j1 rule="para" parents="5054 104"/>
    </justification>
  </clause>

  <clause id="5243">
    <literal><![CDATA[
      R(x / y,y,K(z,x)) \ ((z * x) / z) = y * K(z,x)
    ]]></literal>
    <justification jstring="[para(5054(a,2),534(a,1,2))].">
      <j1 rule="para" parents="5054 534"/>
    </justification>
  </clause>

  <clause id="5244">
    <literal><![CDATA[
      R(x * K(y,x),y,y \ 1) = (y * x) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(5054(a,1),565(a,1,1))].">
      <j1 rule="para" parents="5054 565"/>
    </justification>
  </clause>

  <clause id="5245">
    <literal><![CDATA[
      T(x * K(y,x),z) = (y * T(x,z)) / y
    ]]></literal>
    <justification jstring="[para(5054(a,1),445(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5054 445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5246">
    <literal><![CDATA[
      T(x * K(y,x),x * y) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(5054(a,1),790(a,1,1))].">
      <j1 rule="para" parents="5054 790"/>
    </justification>
  </clause>

  <clause id="5247">
    <literal><![CDATA[
      T(T(x * K(y,x),z),y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) = u
    ]]></literal>
    <justification jstring="[para(5054(a,1),757(a,1,1,1))].">
      <j1 rule="para" parents="5054 757"/>
    </justification>
  </clause>

  <clause id="5248">
    <literal><![CDATA[
      T(x * K(y * x,x),y) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(5054(a,1),857(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5054 857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5249">
    <literal><![CDATA[
      L(x * K(y,x),z,u) = (y * L(x,z,u)) / y
    ]]></literal>
    <justification jstring="[para(5054(a,1),925(a,1,1))].">
      <j1 rule="para" parents="5054 925"/>
    </justification>
  </clause>

  <clause id="5250">
    <literal><![CDATA[
      R(x * K(y,x),z,u) = (y * R(x,z,u)) / y
    ]]></literal>
    <justification jstring="[para(5054(a,1),932(a,1,1))].">
      <j1 rule="para" parents="5054 932"/>
    </justification>
  </clause>

  <clause id="5251">
    <literal><![CDATA[
      ((x / y) * (y * K(z,x))) \ ((z * x) / z) = a(x / y,y,K(z,x))
    ]]></literal>
    <justification jstring="[para(5054(a,2),87(a,1,2))].">
      <j1 rule="para" parents="5054 87"/>
    </justification>
  </clause>

  <clause id="5252">
    <literal><![CDATA[
      R(T(x,y * K(z,y)),y,K(z,y)) = ((z * y) / z) \ ((x * y) * K(z,y))
    ]]></literal>
    <justification jstring="[para(5054(a,2),689(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5054 689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5253">
    <literal><![CDATA[
      T(T(x * K(y,x),z),x * y) = L(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[para(5054(a,1),1031(a,1,1,1))].">
      <j1 rule="para" parents="5054 1031"/>
    </justification>
  </clause>

  <clause id="5254">
    <literal><![CDATA[
      L(x * K(y * z,x),z,y) = (y * (z * x)) / (y * z)
    ]]></literal>
    <justification jstring="[para(5054(a,1),927(a,1,1))].">
      <j1 rule="para" parents="5054 927"/>
    </justification>
  </clause>

  <clause id="5255">
    <literal><![CDATA[
      (x * y) / ((z * y) / z) = (x / (y * K(z,y))) * y
    ]]></literal>
    <justification jstring="[para(5054(a,1),1583(a,2,1,2))].">
      <j1 rule="para" parents="5054 1583"/>
    </justification>
  </clause>

  <clause id="5256">
    <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(1791(a,1),5054(a,1,1))].">
      <j1 rule="para" parents="1791 5054"/>
    </justification>
  </clause>

  <clause id="5257">
    <literal><![CDATA[
      (x * K(y,x)) \ ((y * (x * y)) / y) = L(y,x,y)
    ]]></literal>
    <justification jstring="[para(5054(a,1),1810(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5054 1810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5258">
    <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(1918(a,1),5054(a,1,1))].">
      <j1 rule="para" parents="1918 5054"/>
    </justification>
  </clause>

  <clause id="5259">
    <literal><![CDATA[
      K(x,y) = (1 / y) * ((x * y) / x)
    ]]></literal>
    <justification jstring="[para(5054(a,2),3646(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5054 3646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5260">
    <literal><![CDATA[
      L(x,y,x * K(y,x)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(5054(a,1),4472(a,1,3))].">
      <j1 rule="para" parents="5054 4472"/>
    </justification>
  </clause>

  <clause id="5261">
    <literal><![CDATA[
      (x \ (y * K(x,y))) * x = (x \ y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(5054(a,1),4620(a,1,1,2))].">
      <j1 rule="para" parents="5054 4620"/>
    </justification>
  </clause>

  <clause id="5263">
    <literal><![CDATA[
      K(x \ y,x) * (y / x) = x \ y
    ]]></literal>
    <justification jstring="[para(10(a,1),5058(a,1,2,1))].">
      <j1 rule="para" parents="10 5058"/>
    </justification>
  </clause>

  <clause id="5265">
    <literal><![CDATA[
      K(a(x,y,z),x * (y * z)) * (((x * y) * z) / (x * (y * z))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(84(a,1),5058(a,1,2,1))].">
      <j1 rule="para" parents="84 5058"/>
    </justification>
  </clause>

  <clause id="5267">
    <literal><![CDATA[
      (x \ y) \ (y / x) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),5074(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 5074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5268">
    <literal><![CDATA[
      x * K(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      (y * x) / y = z
    ]]></literal>
    <justification jstring="[para(5074(a,2),250(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5074 250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5269">
    <literal><![CDATA[
      x * (y * K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x * ((z * y) / z) = u
    ]]></literal>
    <justification jstring="[para(5074(a,2),315(a,1,2,2))].">
      <j1 rule="para" parents="5074 315"/>
    </justification>
  </clause>

  <clause id="5272">
    <literal><![CDATA[
      K(1 / x,y) / x = T(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(352,a,5077,a(flip))].">
      <j1 rule="hyper" parents="352 5077"/>
    </justification>
  </clause>

  <clause id="5273">
    <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(5077(a,2),493(a,1,2,2))].">
      <j1 rule="para" parents="5077 493"/>
    </justification>
  </clause>

  <clause id="5274">
    <literal><![CDATA[
      K(x,y) \ (T(x,y) * ((T(x,y) \ 1) \ z)) = ((T(x,y) \ 1) * (x \ 1)) \ z
    ]]></literal>
    <justification jstring="[para(5077(a,2),2507(a,1,1))].">
      <j1 rule="para" parents="5077 2507"/>
    </justification>
  </clause>

  <clause id="5276">
    <literal><![CDATA[
      T(x,y * x) * (x \ 1) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(4366(a,2),5077(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4366 5077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5277">
    <literal><![CDATA[
      T(K(x,y),z) * K(y,x) = K(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(5197(a,1),5077(a,2,2)),flip(a)].">
      <j1 rule="para" parents="5197 5077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5278">
    <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(37,a,1926,a,b,5099,a),flip(a)].">
      <j1 rule="hyper" parents="37 1926 5099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5279">
    <literal><![CDATA[
      (x \ K(y,x \ 1)) * y = y * (x \ 1)
    ]]></literal>
    <justification jstring="[para(3661(a,1),5099(a,1,1))].">
      <j1 rule="para" parents="3661 5099"/>
    </justification>
  </clause>

  <clause id="5280">
    <literal><![CDATA[
      x / ((y * K(x,y)) * ((x \ 1) \ 1)) = (1 / (1 / x)) / (x * y)
    ]]></literal>
    <justification jstring="[para(5099(a,1),3687(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5099 3687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5281">
    <literal><![CDATA[
      (x / (x * y)) \ T(x,y * K(x,y)) = x * (y * K(x,y))
    ]]></literal>
    <justification jstring="[para(5099(a,1),4664(a,1,1,2))].">
      <j1 rule="para" parents="5099 4664"/>
    </justification>
  </clause>

  <clause id="5282">
    <literal><![CDATA[
      ((x * ((y * z) / y)) / x) / ((x * z) / x) = K(y,(x * z) / x)
    ]]></literal>
    <justification jstring="[hyper(120,a,1093,a,b,5101,a(flip))].">
      <j1 rule="hyper" parents="120 1093 5101"/>
    </justification>
  </clause>

  <clause id="5283">
    <literal><![CDATA[
      (x \ T(x * y,y)) / y = K(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(120,a,4302,a(flip),b,5101,a(flip))].">
      <j1 rule="hyper" parents="120 4302 5101"/>
    </justification>
  </clause>

  <clause id="5284">
    <literal><![CDATA[
      ((x * y) / x) / y != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5101(a,2),307(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5101 307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5285">
    <literal><![CDATA[
      T(L(L(x * K(y,x),y,x * K(y,x)),z,u) * y,x * K(y,x)) = L(x * K(y,x),z,u) * T(y,x)
    ]]></literal>
    <justification jstring="[para(5141(a,1),4621(a,2,2))].">
      <j1 rule="para" parents="5141 4621"/>
    </justification>
  </clause>

  <clause id="5289">
    <literal><![CDATA[
      x * K(x / y,y) = (y \ x) * y
    ]]></literal>
    <justification jstring="[para(5192(a,2),287(a,1,2))].">
      <j1 rule="para" parents="5192 287"/>
    </justification>
  </clause>

  <clause id="5290">
    <literal><![CDATA[
      x \ (y * K(y \ x,y)) = (y * (x / y)) \ y
    ]]></literal>
    <justification jstring="[para(5192(a,1),1630(a,1,2,2))].">
      <j1 rule="para" parents="5192 1630"/>
    </justification>
  </clause>

  <clause id="5292">
    <literal><![CDATA[
      x \ (y * (x / y)) = K(y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,91,a,b,5205,a)].">
      <j1 rule="hyper" parents="65 91 5205"/>
    </justification>
  </clause>

  <clause id="5293">
    <literal><![CDATA[
      x * K(y,y \ x) = y * (x / y)
    ]]></literal>
    <justification jstring="[para(5205(a,1),288(a,1,2))].">
      <j1 rule="para" parents="5205 288"/>
    </justification>
  </clause>

  <clause id="5294">
    <literal><![CDATA[
      a(L(K(x,y),K(y,x),K(y,x)),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(5210(a,1),2136(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5210 2136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5296">
    <literal><![CDATA[
      (1 / x) * K(x \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      T(1 / x,y) = z
    ]]></literal>
    <justification jstring="[para(3565(a,1),5087(a,1,2))].">
      <j1 rule="para" parents="3565 5087"/>
    </justification>
  </clause>

  <clause id="5297">
    <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),5109(a,1,1))].">
      <j1 rule="para" parents="25 5109"/>
    </justification>
  </clause>

  <clause id="5298">
    <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),5109(a,1,1))].">
      <j1 rule="para" parents="27 5109"/>
    </justification>
  </clause>

  <clause id="5300">
    <literal><![CDATA[
      x * T(x \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(4432(a,1),5109(a,1))].">
      <j1 rule="para" parents="4432 5109"/>
    </justification>
  </clause>

  <clause id="5301">
    <literal><![CDATA[
      L(x,y,z) \ L(T(x,u),y,z) != w
    ]]></literal>
    <literal><![CDATA[
      K(L(x,y,z),u) = w
    ]]></literal>
    <justification jstring="[para(25(a,2),5155(a,1,2))].">
      <j1 rule="para" parents="25 5155"/>
    </justification>
  </clause>

  <clause id="5302">
    <literal><![CDATA[
      x \ L(x,x,x) != y
    ]]></literal>
    <literal><![CDATA[
      K(x,x * x) = y
    ]]></literal>
    <justification jstring="[para(110(a,1),5155(a,1,2))].">
      <j1 rule="para" parents="110 5155"/>
    </justification>
  </clause>

  <clause id="5303">
    <literal><![CDATA[
      x \ L(T(x,y),y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x * y) = z
    ]]></literal>
    <justification jstring="[para(784(a,2),5155(a,1,2))].">
      <j1 rule="para" parents="784 5155"/>
    </justification>
  </clause>

  <clause id="5304">
    <literal><![CDATA[
      T(x,y) * (x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(1112(a,2),5155(a,1))].">
      <j1 rule="para" parents="1112 5155"/>
    </justification>
  </clause>

  <clause id="5305">
    <literal><![CDATA[
      K(T(x,y),y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5037(a,2),5155(a,1))].">
      <j1 rule="para" parents="5037 5155"/>
    </justification>
  </clause>

  <clause id="5306">
    <literal><![CDATA[
      T(K(x,y),x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5068(a,2),5155(a,1))].">
      <j1 rule="para" parents="5068 5155"/>
    </justification>
  </clause>

  <clause id="5309">
    <literal><![CDATA[
      K(x,x \ (y * x)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(22(a,1),5196(a,1,2))].">
      <j1 rule="para" parents="22 5196"/>
    </justification>
  </clause>

  <clause id="5311">
    <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),5196(a,1,2))].">
      <j1 rule="para" parents="27 5196"/>
    </justification>
  </clause>

  <clause id="5312">
    <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(1324(a,1),5196(a,1,2))].">
      <j1 rule="para" parents="1324 5196"/>
    </justification>
  </clause>

  <clause id="5317">
    <literal><![CDATA[
      K((x \ y) * (x * x),x * x) != z
    ]]></literal>
    <literal><![CDATA[
      K((x \ 1) \ y,x * x) = z
    ]]></literal>
    <justification jstring="[para(735(a,1),5305(a,1,1))].">
      <j1 rule="para" parents="735 5305"/>
    </justification>
  </clause>

  <clause id="5318">
    <literal><![CDATA[
      K((x \ 1) \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(2852(a,1),5306(a,1))].">
      <j1 rule="para" parents="2852 5306"/>
    </justification>
  </clause>

  <clause id="5320">
    <literal><![CDATA[
      T((x \ 1) * ((y \ x) * y),x) = (x \ 1) * ((y \ x) * y)
    ]]></literal>
    <justification jstring="[para(5014(a,1),2049(a,2,2))].">
      <j1 rule="para" parents="5014 2049"/>
    </justification>
  </clause>

  <clause id="5321">
    <literal><![CDATA[
      x / L((y \ ((z \ 1) \ (z \ x))) * y,z \ 1,z) = K(y,y \ x)
    ]]></literal>
    <justification jstring="[para(3935(a,2),5025(a,1,2))].">
      <j1 rule="para" parents="3935 5025"/>
    </justification>
  </clause>

  <clause id="5322">
    <literal><![CDATA[
      K(x,y \ 1) * (y \ x) = x * ((y \ x) / x)
    ]]></literal>
    <justification jstring="[para(4758(a,1),5026(a,1,1))].">
      <j1 rule="para" parents="4758 5026"/>
    </justification>
  </clause>

  <clause id="5323">
    <literal><![CDATA[
      R(x * T(x \ 1,y),z,u) = K(R(x,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(2429,a,5030,a)].">
      <j1 rule="hyper" parents="2429 5030"/>
    </justification>
  </clause>

  <clause id="5325">
    <literal><![CDATA[
      (x * T(x \ y,z)) / y = K((x / y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,1402,a(flip),b,5030,a)].">
      <j1 rule="hyper" parents="65 1402 5030"/>
    </justification>
  </clause>

  <clause id="5326">
    <literal><![CDATA[
      x \ (y * T(y \ x,z)) = K((x \ y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,1386,a(flip),b,5030,a)].">
      <j1 rule="hyper" parents="65 1386 5030"/>
    </justification>
  </clause>

  <clause id="5327">
    <literal><![CDATA[
      K((x * y) \ x,x * y) = K(y \ 1,x * y)
    ]]></literal>
    <justification jstring="[para(11(a,1),5030(a,1,1,2))].">
      <j1 rule="para" parents="11 5030"/>
    </justification>
  </clause>

  <clause id="5328">
    <literal><![CDATA[
      x * T(x \ y,z) = y * K((y \ x) \ 1,z)
    ]]></literal>
    <justification jstring="[para(5030(a,1),1385(a,2,2))].">
      <j1 rule="para" parents="5030 1385"/>
    </justification>
  </clause>

  <clause id="5329">
    <literal><![CDATA[
      K((x / y) \ 1,z) * y = x * T(x \ y,z)
    ]]></literal>
    <justification jstring="[para(5030(a,1),1401(a,1,1))].">
      <j1 rule="para" parents="5030 1401"/>
    </justification>
  </clause>

  <clause id="5330">
    <literal><![CDATA[
      (x \ y) * K(((x \ y) \ (x \ 1)) \ 1,z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[para(5030(a,1),1388(a,1,2))].">
      <j1 rule="para" parents="5030 1388"/>
    </justification>
  </clause>

  <clause id="5331">
    <literal><![CDATA[
      (x / y) * K(((x / y) \ (1 / y)) \ 1,z) = T(x,z) / y
    ]]></literal>
    <justification jstring="[para(5030(a,1),1394(a,1,2))].">
      <j1 rule="para" parents="5030 1394"/>
    </justification>
  </clause>

  <clause id="5333">
    <literal><![CDATA[
      x * (y * T(y \ (x \ 1),z)) = K((x * y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(1014,a,5035,a)].">
      <j1 rule="hyper" parents="1014 5035"/>
    </justification>
  </clause>

  <clause id="5334">
    <literal><![CDATA[
      x \ K((x * y) \ 1,z) = y * T(y \ (x \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(119,a,5035,a(flip),b,998,a(flip))].">
      <j1 rule="hyper" parents="119 5035 998"/>
    </justification>
  </clause>

  <clause id="5335">
    <literal><![CDATA[
      L(x \ 1,x,y) * (y * x) = y * K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[para(5035(a,1),681(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5035 681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5336">
    <literal><![CDATA[
      (x * y) * T((x * y) \ x,z) = x * K(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(5035(a,1),801(a,2,2))].">
      <j1 rule="para" parents="5035 801"/>
    </justification>
  </clause>

  <clause id="5338">
    <literal><![CDATA[
      ((x * y) \ x) * (x * y) = x * K(y \ 1,x * y)
    ]]></literal>
    <justification jstring="[para(5035(a,1),1022(a,2,2))].">
      <j1 rule="para" parents="5035 1022"/>
    </justification>
  </clause>

  <clause id="5339">
    <literal><![CDATA[
      K(x \ 1,y) * (x \ z) = z * T(z \ (x \ z),y)
    ]]></literal>
    <justification jstring="[para(5035(a,1),1299(a,1,1))].">
      <j1 rule="para" parents="5035 1299"/>
    </justification>
  </clause>

  <clause id="5340">
    <literal><![CDATA[
      (x * y) * T((x * y) \ y,z) = K(x \ 1,z) * y
    ]]></literal>
    <justification jstring="[para(5035(a,1),1472(a,2,1))].">
      <j1 rule="para" parents="5035 1472"/>
    </justification>
  </clause>

  <clause id="5341">
    <literal><![CDATA[
      x * (y * T(y \ (x \ y),z)) = K(x \ 1,z) * y
    ]]></literal>
    <justification jstring="[para(5035(a,1),1478(a,2,1))].">
      <j1 rule="para" parents="5035 1478"/>
    </justification>
  </clause>

  <clause id="5342">
    <literal><![CDATA[
      (x * (y * T(y \ 1,z))) * y = (x * y) * K(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(5035(a,1),1853(a,2,2))].">
      <j1 rule="para" parents="5035 1853"/>
    </justification>
  </clause>

  <clause id="5343">
    <literal><![CDATA[
      (x * y) * (z * T(z \ L(y \ z,y,x),u)) = (x * K(y \ 1,u)) * z
    ]]></literal>
    <justification jstring="[para(5035(a,1),2330(a,2,1,2))].">
      <j1 rule="para" parents="5035 2330"/>
    </justification>
  </clause>

  <clause id="5346">
    <literal><![CDATA[
      (T(1 / x,y) \ 1) / K(y,1 / x) = x
    ]]></literal>
    <justification jstring="[hyper(120,a,5052,a(flip),b,189,a(flip))].">
      <j1 rule="hyper" parents="120 5052 189"/>
    </justification>
  </clause>

  <clause id="5347">
    <literal><![CDATA[
      (x * (y \ 1)) \ (x * (T(y,z) \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      L(K(z,y),y \ 1,x) = u
    ]]></literal>
    <justification jstring="[para(5052(a,1),493(a,1,2,2))].">
      <j1 rule="para" parents="5052 493"/>
    </justification>
  </clause>

  <clause id="5348">
    <literal><![CDATA[
      K(x,y) \ (x \ z) = T(x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(637,a,5055,a),flip(a)].">
      <j1 rule="hyper" parents="637 5055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5350">
    <literal><![CDATA[
      x \ (T(x,y) * z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(125,a,5055,a)].">
      <j1 rule="hyper" parents="125 5055"/>
    </justification>
  </clause>

  <clause id="5351">
    <literal><![CDATA[
      K(x,y) * (T(x,y) \ z) = x \ z
    ]]></literal>
    <justification jstring="[hyper(119,a,10,a(flip),b,5055,a),flip(a)].">
      <j1 rule="hyper" parents="119 10 5055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5352">
    <literal><![CDATA[
      ((x * y) / x) \ z = K(y,x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(36,a,4837,a,b,5055,a)].">
      <j1 rule="hyper" parents="36 4837 5055"/>
    </justification>
  </clause>

  <clause id="5353">
    <literal><![CDATA[
      K(x,y) * (z * x) = T(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(36,a,1196,a,b,5055,a),flip(a)].">
      <j1 rule="hyper" parents="36 1196 5055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5354">
    <literal><![CDATA[
      K(x,y) * T(y,x * y) = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,4589,a(flip),b,5055,a),flip(a)].">
      <j1 rule="hyper" parents="36 4589 5055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5355">
    <literal><![CDATA[
      K(x,y) * T(y,y * x) = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,4587,a(flip),b,5055,a),flip(a)].">
      <j1 rule="hyper" parents="36 4587 5055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5356">
    <literal><![CDATA[
      K(x * y,x) * T(x,y) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(36,a,4349,a(flip),b,5055,a),flip(a)].">
      <j1 rule="hyper" parents="36 4349 5055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5357">
    <literal><![CDATA[
      (x * ((K(x,y) * z) * u)) \ ((T(x,y) * z) * u) = a(x,K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(5055(a,1),14(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5055 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5358">
    <literal><![CDATA[
      T(x,y) * T(z,K(x,y)) = x * (z * K(x,y))
    ]]></literal>
    <justification jstring="[para(107(a,1),5055(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 5055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5359">
    <literal><![CDATA[
      (x / y) * (K(x / y,y) * z) = (y \ x) * z
    ]]></literal>
    <justification jstring="[para(109(a,1),5055(a,2,1))].">
      <j1 rule="para" parents="109 5055"/>
    </justification>
  </clause>

  <clause id="5360">
    <literal><![CDATA[
      x \ (T(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(5055(a,1),314(a,1,2))].">
      <j1 rule="para" parents="5055 314"/>
    </justification>
  </clause>

  <clause id="5361">
    <literal><![CDATA[
      (x \ y) * (K(y,z) * K(y,z)) = x \ (T(y,z) * K(y,z))
    ]]></literal>
    <justification jstring="[para(5055(a,1),847(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5055 847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5362">
    <literal><![CDATA[
      x * (K(y,x) * K(x,z)) = T(x,z) * K(y,x)
    ]]></literal>
    <justification jstring="[para(2278(a,1),5055(a,1,2))].">
      <j1 rule="para" parents="2278 5055"/>
    </justification>
  </clause>

  <clause id="5363">
    <literal><![CDATA[
      (x * y) / (T(x,z) * y) = K(z,x)
    ]]></literal>
    <justification jstring="[hyper(4964,a,5056,a)].">
      <j1 rule="hyper" parents="4964 5056"/>
    </justification>
  </clause>

  <clause id="5364">
    <literal><![CDATA[
      K(x,y) \ (y * z) = T(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(4962,a,5056,a)].">
      <j1 rule="hyper" parents="4962 5056"/>
    </justification>
  </clause>

  <clause id="5365">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ y,z) = K(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(1027,a,5056,a)].">
      <j1 rule="hyper" parents="1027 5056"/>
    </justification>
  </clause>

  <clause id="5366">
    <literal><![CDATA[
      T(x,y) \ (K(x,y) * z) = x \ z
    ]]></literal>
    <justification jstring="[hyper(125,a,5056,a)].">
      <j1 rule="hyper" parents="125 5056"/>
    </justification>
  </clause>

  <clause id="5367">
    <literal><![CDATA[
      x * (K(x,y) * (x \ z)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(65,a,5055,a,b,5056,a)].">
      <j1 rule="hyper" parents="65 5055 5056"/>
    </justification>
  </clause>

  <clause id="5368">
    <literal><![CDATA[
      ((x * y) / x) \ (y * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(65,a,4839,a,b,5056,a)].">
      <j1 rule="hyper" parents="65 4839 5056"/>
    </justification>
  </clause>

  <clause id="5369">
    <literal><![CDATA[
      (x \ L(x,y,z)) * T(x,u) = K(x,u) * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,3822,a(flip),b,5056,a)].">
      <j1 rule="hyper" parents="65 3822 5056"/>
    </justification>
  </clause>

  <clause id="5371">
    <literal><![CDATA[
      x \ (K(x,y) * z) = K(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(119,a,5056,a(flip),b,5055,a)].">
      <j1 rule="hyper" parents="119 5056 5055"/>
    </justification>
  </clause>

  <clause id="5372">
    <literal><![CDATA[
      x \ (K(y,x) * z) = T(x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(119,a,5056,a(flip),b,4953,a(flip))].">
      <j1 rule="hyper" parents="119 5056 4953"/>
    </justification>
  </clause>

  <clause id="5374">
    <literal><![CDATA[
      K(x * y,z) * (x * (y * u)) = T(x * y,z) * L(u,y,x)
    ]]></literal>
    <justification jstring="[para(18(a,2),5056(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18 5056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5375">
    <literal><![CDATA[
      (x \ y) * ((y / x) \ z) = K(y / x,x) * z
    ]]></literal>
    <justification jstring="[para(109(a,1),5056(a,1,1))].">
      <j1 rule="para" parents="109 5056"/>
    </justification>
  </clause>

  <clause id="5376">
    <literal><![CDATA[
      T(x,y) * ((1 / x) \ z) = K(x,y) * ((x * x) * z)
    ]]></literal>
    <justification jstring="[para(443(a,1),5056(a,1,2))].">
      <j1 rule="para" parents="443 5056"/>
    </justification>
  </clause>

  <clause id="5378">
    <literal><![CDATA[
      T(L(x,y,y),z) * a(y,y,x) = K(L(x,y,y),z) * x
    ]]></literal>
    <justification jstring="[para(1986(a,1),5056(a,1,2))].">
      <j1 rule="para" parents="1986 5056"/>
    </justification>
  </clause>

  <clause id="5379">
    <literal><![CDATA[
      K(x,y) * T(x,z) = T(x,y) * K(x,z)
    ]]></literal>
    <justification jstring="[para(5036(a,2),5056(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5036 5056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5380">
    <literal><![CDATA[
      K(x,y) * ((z * x) / z) = T(x,y) * K(z,x)
    ]]></literal>
    <justification jstring="[para(5074(a,2),5056(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5074 5056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5381">
    <literal><![CDATA[
      ((x * y) / x) * (y \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(4980,a,5060,a)].">
      <j1 rule="hyper" parents="4980 5060"/>
    </justification>
  </clause>

  <clause id="5382">
    <literal><![CDATA[
      T(x,y) \ (x * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(1216,a,5060,a)].">
      <j1 rule="hyper" parents="1216 5060"/>
    </justification>
  </clause>

  <clause id="5383">
    <literal><![CDATA[
      K(x,y) * (y \ z) = T(y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(1210,a,5060,a),flip(a)].">
      <j1 rule="hyper" parents="1210 5060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5384">
    <literal><![CDATA[
      K(x,y) * (1 / y) = 1 / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,3667,a(flip),b,5060,a),flip(a)].">
      <j1 rule="hyper" parents="65 3667 5060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5385">
    <literal><![CDATA[
      K((x / y) / (y \ 1),z) = (T(x,z) / y) / (x / y)
    ]]></literal>
    <justification jstring="[hyper(120,a,4993,a(flip),b,5060,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="120 4993 5060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5387">
    <literal><![CDATA[
      T(x,y) * (K(y,x) * z) = x * z
    ]]></literal>
    <justification jstring="[para(5060(a,1),1191(a,1,2))].">
      <j1 rule="para" parents="5060 1191"/>
    </justification>
  </clause>

  <clause id="5388">
    <literal><![CDATA[
      K(x,y) * (y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,x) \ z = u
    ]]></literal>
    <justification jstring="[para(5060(a,1),1210(a,1))].">
      <j1 rule="para" parents="5060 1210"/>
    </justification>
  </clause>

  <clause id="5390">
    <literal><![CDATA[
      L(x,y,z * (T(z \ 1,u) \ w)) = L(x,y,K(u,z \ 1) * w)
    ]]></literal>
    <justification jstring="[para(5060(a,1),2489(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5060 2489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5391">
    <literal><![CDATA[
      (x / T(y,x)) * ((y \ T(x,y)) \ z) = K(y,x / T(y,x)) * z
    ]]></literal>
    <justification jstring="[para(4383(a,1),5060(a,1,2,1))].">
      <j1 rule="para" parents="4383 5060"/>
    </justification>
  </clause>

  <clause id="5392">
    <literal><![CDATA[
      K(x,y) * T(T(y,x),z) = y * K(T(y,x),z)
    ]]></literal>
    <justification jstring="[para(5036(a,2),5060(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5036 5060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5394">
    <literal><![CDATA[
      K(x,y) \ (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,x) * z = u
    ]]></literal>
    <justification jstring="[para(5061(a,1),314(a,1,2))].">
      <j1 rule="para" parents="5061 314"/>
    </justification>
  </clause>

  <clause id="5395">
    <literal><![CDATA[
      x * (T(x,y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * z = u
    ]]></literal>
    <justification jstring="[para(5061(a,1),315(a,1))].">
      <j1 rule="para" parents="5061 315"/>
    </justification>
  </clause>

  <clause id="5396">
    <literal><![CDATA[
      L(L(x,y,T(z,u)),T(z,u) * y,K(u,z)) = (z * y) \ (K(u,z) * (T(z,u) * (y * x)))
    ]]></literal>
    <justification jstring="[para(5061(a,1),484(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5061 484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5397">
    <literal><![CDATA[
      K(x,y) * (K(z,T(y,x)) * u) = y * (T(T(y,x),z) \ u)
    ]]></literal>
    <justification jstring="[para(5060(a,1),5061(a,1,2))].">
      <j1 rule="para" parents="5060 5061"/>
    </justification>
  </clause>

  <clause id="5398">
    <literal><![CDATA[
      K(x,y) * (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(5069(a,1),246(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5069 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5399">
    <literal><![CDATA[
      ((T(x,y) * z) * u) / ((x * z) * u) = R(K(x,y),x * z,u)
    ]]></literal>
    <justification jstring="[para(5069(a,1),104(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5069 104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5400">
    <literal><![CDATA[
      (x * T(x \ y,y)) * (y \ 1) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[para(1529(a,1),5073(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1529 5073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5404">
    <literal><![CDATA[
      L(K(1 / x,x),y,z) / L(x,y,z) = (x / L(x,y,z)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(5078(a,1),4035(a,1,1,1))].">
      <j1 rule="para" parents="5078 4035"/>
    </justification>
  </clause>

  <clause id="5405">
    <literal><![CDATA[
      K(1 / x,y / (x \ 1)) = x * (((x \ 1) \ y) \ y)
    ]]></literal>
    <justification jstring="[para(4440(a,1),5078(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4440 5078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5406">
    <literal><![CDATA[
      K(x,(x / y) / x) = K(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(4214,a,5082,a)].">
      <j1 rule="hyper" parents="4214 5082"/>
    </justification>
  </clause>

  <clause id="5408">
    <literal><![CDATA[
      K(x,1 / y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(5082(a,1),5155(a,1))].">
      <j1 rule="para" parents="5082 5155"/>
    </justification>
  </clause>

  <clause id="5409">
    <literal><![CDATA[
      K(x,x \ y) / (y / x) = 1 / (x \ y)
    ]]></literal>
    <justification jstring="[para(5102(a,1),3647(a,1,2))].">
      <j1 rule="para" parents="5102 3647"/>
    </justification>
  </clause>

  <clause id="5410">
    <literal><![CDATA[
      K(x,x \ y) * ((x \ y) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[para(5102(a,1),4776(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5102 4776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5411">
    <literal><![CDATA[
      T(x \ y,R(y / x,z,u)) = x \ y
    ]]></literal>
    <justification jstring="[para(5102(a,1),4841(a,1,2,1))].">
      <j1 rule="para" parents="5102 4841"/>
    </justification>
  </clause>

  <clause id="5413">
    <literal><![CDATA[
      K(x,y) \ (z * T(x,y)) = x * T(z,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,107,a(flip),b,5103,a)].">
      <j1 rule="hyper" parents="119 107 5103"/>
    </justification>
  </clause>

  <clause id="5414">
    <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),5103(a,2,1))].">
      <j1 rule="para" parents="27 5103"/>
    </justification>
  </clause>

  <clause id="5415">
    <literal><![CDATA[
      K(x,y) * ((x * x) * z) = (T(x,y) * x) * z
    ]]></literal>
    <justification jstring="[para(5103(a,1),34(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5103 34"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5417">
    <literal><![CDATA[
      T(x,y) * (x \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(5103(a,1),315(a,1))].">
      <j1 rule="para" parents="5103 315"/>
    </justification>
  </clause>

  <clause id="5418">
    <literal><![CDATA[
      K(x,y) * (L(z,u,w) * x) = T(x,y) * L(T(z,x),u,w)
    ]]></literal>
    <justification jstring="[para(233(a,1),5103(a,1,2))].">
      <j1 rule="para" parents="233 5103"/>
    </justification>
  </clause>

  <clause id="5419">
    <literal><![CDATA[
      K(x,y) * (R(z,u,w) * x) = T(x,y) * R(T(z,x),u,w)
    ]]></literal>
    <justification jstring="[para(234(a,1),5103(a,1,2))].">
      <j1 rule="para" parents="234 5103"/>
    </justification>
  </clause>

  <clause id="5420">
    <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(5103(a,1),549(a,1,1,1))].">
      <j1 rule="para" parents="5103 549"/>
    </justification>
  </clause>

  <clause id="5421">
    <literal><![CDATA[
      (T(x,y) * z) \ (K(x,y) * (x * (z * u))) = L(L(u,z,x),x * z,K(x,y))
    ]]></literal>
    <justification jstring="[para(5103(a,1),484(a,1,1))].">
      <j1 rule="para" parents="5103 484"/>
    </justification>
  </clause>

  <clause id="5423">
    <literal><![CDATA[
      (K(x,y) / x) * (x * z) = (1 / x) * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[para(5103(a,1),4680(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5103 4680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5424">
    <literal><![CDATA[
      K(x,y) * (T(x,y) * z) = T(T(x,y),y) * z
    ]]></literal>
    <justification jstring="[para(5188(a,1),5103(a,1,1))].">
      <j1 rule="para" parents="5188 5103"/>
    </justification>
  </clause>

  <clause id="5425">
    <literal><![CDATA[
      K(x,y) * (T(x,z) * u) = T(x,y) * (K(x,z) * u)
    ]]></literal>
    <justification jstring="[para(5055(a,1),5103(a,1,2))].">
      <j1 rule="para" parents="5055 5103"/>
    </justification>
  </clause>

  <clause id="5426">
    <literal><![CDATA[
      K(x,y) \ z = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(65,a,5060,a(flip),b,5104,a),flip(a)].">
      <j1 rule="hyper" parents="65 5060 5104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5427">
    <literal><![CDATA[
      K(x,y) \ (K(y,x) \ z) = z
    ]]></literal>
    <justification jstring="[hyper(119,a,5104,a(flip),b,5060,a(flip))].">
      <j1 rule="hyper" parents="119 5104 5060"/>
    </justification>
  </clause>

  <clause id="5428">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,y)) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(3791,a,5426,a)].">
      <j1 rule="hyper" parents="3791 5426"/>
    </justification>
  </clause>

  <clause id="5429">
    <literal><![CDATA[
      K(x,y) * R(K(y,x),z,z \ 1) = a(K(y,x),z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(868,a,5426,a),flip(a)].">
      <j1 rule="hyper" parents="868 5426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5430">
    <literal><![CDATA[
      x / (K(y,z) * x) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(577,a,5426,a)].">
      <j1 rule="hyper" parents="577 5426"/>
    </justification>
  </clause>

  <clause id="5431">
    <literal><![CDATA[
      K(x,y) * (z * K(y,x)) = T(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(378,a,5426,a),flip(a)].">
      <j1 rule="hyper" parents="378 5426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5432">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * z) = z
    ]]></literal>
    <justification jstring="[hyper(316,a,5426,a)].">
      <j1 rule="hyper" parents="316 5426"/>
    </justification>
  </clause>

  <clause id="5433">
    <literal><![CDATA[
      K(x,y) \ T(T(x,z),u) = T(T(x,z),u) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,3626,a,b,5426,a),flip(a)].">
      <j1 rule="hyper" parents="299 3626 5426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5434">
    <literal><![CDATA[
      x \ (K(y,z) \ x) = T(K(z,y),x)
    ]]></literal>
    <justification jstring="[hyper(119,a,5426,a,b,107,a)].">
      <j1 rule="hyper" parents="119 5426 107"/>
    </justification>
  </clause>

  <clause id="5435">
    <literal><![CDATA[
      K(x,y) * R(K(y,x),z \ 1,z) = a(K(y,x),z \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,2704,a(flip),b,5426,a),flip(a)].">
      <j1 rule="hyper" parents="65 2704 5426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5436">
    <literal><![CDATA[
      x * (K(y,z) * u) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = x
    ]]></literal>
    <justification jstring="[para(5426(a,1),136(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5426 136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5437">
    <literal><![CDATA[
      K(x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * u = z
    ]]></literal>
    <justification jstring="[para(5426(a,1),144(a,1))].">
      <j1 rule="para" parents="5426 144"/>
    </justification>
  </clause>

  <clause id="5438">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      u = z
    ]]></literal>
    <justification jstring="[para(5426(a,1),250(a,1,2))].">
      <j1 rule="para" parents="5426 250"/>
    </justification>
  </clause>

  <clause id="5439">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      z = u
    ]]></literal>
    <justification jstring="[para(5426(a,1),251(a,1,2))].">
      <j1 rule="para" parents="5426 251"/>
    </justification>
  </clause>

  <clause id="5440">
    <literal><![CDATA[
      x / (K(y,z) * x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = u
    ]]></literal>
    <justification jstring="[para(5426(a,1),310(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5426 310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5441">
    <literal><![CDATA[
      (K(x,y) \ z) * L(u,z,K(y,x)) = K(y,x) * (z * u)
    ]]></literal>
    <justification jstring="[para(5426(a,2),94(a,1,1))].">
      <j1 rule="para" parents="5426 94"/>
    </justification>
  </clause>

  <clause id="5442">
    <literal><![CDATA[
      L(x \ (K(y,z) * u),x,K(z,y)) = (K(z,y) * x) \ u
    ]]></literal>
    <justification jstring="[para(5426(a,1),281(a,1,1,2))].">
      <j1 rule="para" parents="5426 281"/>
    </justification>
  </clause>

  <clause id="5443">
    <literal><![CDATA[
      L(K(x,y) * (z \ u),K(y,x),z) = (z * K(y,x)) \ u
    ]]></literal>
    <justification jstring="[para(5426(a,1),281(a,1,1))].">
      <j1 rule="para" parents="5426 281"/>
    </justification>
  </clause>

  <clause id="5445">
    <literal><![CDATA[
      T((x \ K(y,z)) \ 1,K(z,y) * x) = (x \ K(y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(5426(a,1),618(a,1,2))].">
      <j1 rule="para" parents="5426 618"/>
    </justification>
  </clause>

  <clause id="5446">
    <literal><![CDATA[
      R(x,K(y,z),K(z,y) * u) * u = (x * K(y,z)) * (K(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(5426(a,1),347(a,1,1,3))].">
      <j1 rule="para" parents="5426 347"/>
    </justification>
  </clause>

  <clause id="5447">
    <literal><![CDATA[
      (K(x,y) \ 1) \ z = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(5197(a,2),5426(a,1,1))].">
      <j1 rule="para" parents="5197 5426"/>
    </justification>
  </clause>

  <clause id="5449">
    <literal><![CDATA[
      K(x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) \ z = u
    ]]></literal>
    <justification jstring="[para(5427(a,1),250(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5427 250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5452">
    <literal><![CDATA[
      K(x,y) \ z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * z = u
    ]]></literal>
    <justification jstring="[para(5430(a,1),317(a,1,1))].">
      <j1 rule="para" parents="5430 317"/>
    </justification>
  </clause>

  <clause id="5453">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) \ 1 = z
    ]]></literal>
    <justification jstring="[para(5430(a,1),208(a,1)),flip(b)].">
      <j1 rule="para" parents="5430 208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5454">
    <literal><![CDATA[
      a(x,y * K(z \ 1,z),u) = K(w,v5) * (K(v5,w) * a(x,y,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,4014,a,b,5432,a)].">
      <j1 rule="hyper" parents="299 4014 5432"/>
    </justification>
  </clause>

  <clause id="5455">
    <literal><![CDATA[
      K(x,y) * (y \ K(y,x)) = y \ 1
    ]]></literal>
    <justification jstring="[hyper(36,a,3787,a,b,5432,a),flip(a)].">
      <j1 rule="hyper" parents="36 3787 5432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5456">
    <literal><![CDATA[
      K(x,y) * (K(z,y) * K(y,x)) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,2278,a,b,5432,a),flip(a)].">
      <j1 rule="hyper" parents="36 2278 5432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5457">
    <literal><![CDATA[
      K(x,y) * (K(x,z) * K(y,x)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,2278,a(flip),b,5432,a),flip(a)].">
      <j1 rule="hyper" parents="36 2278 5432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5458">
    <literal><![CDATA[
      L((K(x,y) * z) \ u,K(x,y) * z,K(y,x)) = z \ (K(y,x) * u)
    ]]></literal>
    <justification jstring="[para(5432(a,1),96(a,2,1))].">
      <j1 rule="para" parents="5432 96"/>
    </justification>
  </clause>

  <clause id="5459">
    <literal><![CDATA[
      R(x,K(y,z),K(z,y) * u) * u = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(5432(a,1),103(a,1,2))].">
      <j1 rule="para" parents="5432 103"/>
    </justification>
  </clause>

  <clause id="5460">
    <literal><![CDATA[
      T(x * (y / x),z) / T(y,z) = K(x,x \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(120,a,3459,a,b,5105,a)].">
      <j1 rule="hyper" parents="120 3459 5105"/>
    </justification>
  </clause>

  <clause id="5461">
    <literal><![CDATA[
      K(x \ y,x) \ y = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(65,a,5426,a,b,5105,a)].">
      <j1 rule="hyper" parents="65 5426 5105"/>
    </justification>
  </clause>

  <clause id="5462">
    <literal><![CDATA[
      K(x \ y,x) * (x * (y / x)) = y
    ]]></literal>
    <justification jstring="[hyper(36,a,5432,a,b,5105,a)].">
      <j1 rule="hyper" parents="36 5432 5105"/>
    </justification>
  </clause>

  <clause id="5463">
    <literal><![CDATA[
      K(x,(x \ 1) * y) * y = x * (y / x)
    ]]></literal>
    <justification jstring="[para(4863(a,2),5105(a,1,1))].">
      <j1 rule="para" parents="4863 5105"/>
    </justification>
  </clause>

  <clause id="5464">
    <literal><![CDATA[
      L((x \ 1) \ 1,y,z) * K(1 / x,x) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(5114(a,1),3838(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5114 3838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5465">
    <literal><![CDATA[
      ((x * y) * (z * K(y,z))) / (T(y,z) * z) = R(x,y,z * K(y,z))
    ]]></literal>
    <justification jstring="[para(5115(a,1),20(a,2,2)),flip(a)].">
      <j1 rule="para" parents="5115 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5466">
    <literal><![CDATA[
      L((x * K(y,x)) \ z,x * K(y,x),y) = (T(y,x) * x) \ (y * z)
    ]]></literal>
    <justification jstring="[para(5115(a,1),96(a,2,1))].">
      <j1 rule="para" parents="5115 96"/>
    </justification>
  </clause>

  <clause id="5467">
    <literal><![CDATA[
      (x * (y / x)) \ x = y \ (y / (y / x))
    ]]></literal>
    <justification jstring="[para(5124(a,2),1630(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5124 1630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5468">
    <literal><![CDATA[
      T(x,y) * K(z,T(x,y)) = T(x * K(z,x),y)
    ]]></literal>
    <justification jstring="[hyper(5126,a,5125,a)].">
      <j1 rule="hyper" parents="5126 5125"/>
    </justification>
  </clause>

  <clause id="5469">
    <literal><![CDATA[
      T((x * y) / x,z) = T(y * K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(446,a,5125,a)].">
      <j1 rule="hyper" parents="446 5125"/>
    </justification>
  </clause>

  <clause id="5470">
    <literal><![CDATA[
      T(x * K(y,x),y * x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(42,a,4360,a,b,5125,a),flip(a)].">
      <j1 rule="hyper" parents="42 4360 5125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5471">
    <literal><![CDATA[
      T(x,y) != T(z,u)
    ]]></literal>
    <literal><![CDATA[
      T(z * K(y,z),u) = x
    ]]></literal>
    <justification jstring="[para(5125(a,1),51(a,2)),flip(b)].">
      <j1 rule="para" parents="5125 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5473">
    <literal><![CDATA[
      L(x,y,T(z * K(u * u,z),w)) = L(x,y,T(z,w))
    ]]></literal>
    <justification jstring="[para(5125(a,1),2513(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5125 2513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5474">
    <literal><![CDATA[
      T(1 / ((x * y) \ x),y) = 1 / ((x * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(120,a,620,a(flip),b,5145,a),flip(a)].">
      <j1 rule="hyper" parents="120 620 5145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5475">
    <literal><![CDATA[
      K(x,T(y,T(x,z))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5154,a,5152,a)].">
      <j1 rule="hyper" parents="5154 5152"/>
    </justification>
  </clause>

  <clause id="5476">
    <literal><![CDATA[
      T(x,T(y,T(x,z))) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(5152(a,2),5087(a,1))].">
      <j1 rule="para" parents="5152 5087"/>
    </justification>
  </clause>

  <clause id="5477">
    <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(5181(a,2),1952(a,2,2))].">
      <j1 rule="para" parents="5181 1952"/>
    </justification>
  </clause>

  <clause id="5478">
    <literal><![CDATA[
      ((1 / x) * y) \ K((1 / x) * y,x) = L(y / x,x,x) \ 1
    ]]></literal>
    <justification jstring="[para(967(a,1),5182(a,1,1)),flip(a)].">
      <j1 rule="para" parents="967 5182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5479">
    <literal><![CDATA[
      L(x,y * (z \ K(z,u)),w) = L(x,y * ((u * z) / u),w)
    ]]></literal>
    <justification jstring="[para(5182(a,1),2888(a,1,2,2))].">
      <j1 rule="para" parents="5182 2888"/>
    </justification>
  </clause>

  <clause id="5480">
    <literal><![CDATA[
      (x * y) \ K(x * y,y) = (L(y,x,y) * x) \ 1
    ]]></literal>
    <justification jstring="[para(4352(a,1),5182(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4352 5182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5481">
    <literal><![CDATA[
      T(x,y \ K(y,z)) = T(x,z / (z * y))
    ]]></literal>
    <justification jstring="[para(5182(a,1),4641(a,1,2))].">
      <j1 rule="para" parents="5182 4641"/>
    </justification>
  </clause>

  <clause id="5482">
    <literal><![CDATA[
      1 / (x * K(y,x)) = K(x,y) / x
    ]]></literal>
    <justification jstring="[para(5054(a,1),5184(a,2,2)),flip(a)].">
      <j1 rule="para" parents="5054 5184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5483">
    <literal><![CDATA[
      T(x,y) * T(x,y) = x * T(T(x,y),y)
    ]]></literal>
    <justification jstring="[para(5202(a,1),5055(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5202 5055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5484">
    <literal><![CDATA[
      L(x,K(y,z),z) = x
    ]]></literal>
    <justification jstring="[hyper(4606,a,5220,a),flip(a)].">
      <j1 rule="hyper" parents="4606 5220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5485">
    <literal><![CDATA[
      L(x,K(y,z),u) * w = L(x,K(z,y),u) * w
    ]]></literal>
    <justification jstring="[hyper(59,a,5220,a)].">
      <j1 rule="hyper" parents="59 5220"/>
    </justification>
  </clause>

  <clause id="5486">
    <literal><![CDATA[
      L(x,K(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(5220(a,1),4606(a,1))].">
      <j1 rule="para" parents="5220 4606"/>
    </justification>
  </clause>

  <clause id="5487">
    <literal><![CDATA[
      L(x,K(y,z),1 / z) = x
    ]]></literal>
    <justification jstring="[hyper(2505,a,5484,a)].">
      <j1 rule="hyper" parents="2505 5484"/>
    </justification>
  </clause>

  <clause id="5488">
    <literal><![CDATA[
      (x * K(y,x)) * z = x * (K(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(1318,a,5484,a),flip(a)].">
      <j1 rule="hyper" parents="1318 5484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5489">
    <literal><![CDATA[
      (x * K(y,x)) * z != u
    ]]></literal>
    <literal><![CDATA[
      x * (K(y,x) * z) = u
    ]]></literal>
    <justification jstring="[para(5484(a,1),279(a,1,2))].">
      <j1 rule="para" parents="5484 279"/>
    </justification>
  </clause>

  <clause id="5491">
    <literal><![CDATA[
      L(x,K(y,z),1 / z) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(5487(a,1),52(a,2))].">
      <j1 rule="para" parents="5487 52"/>
    </justification>
  </clause>

  <clause id="5492">
    <literal><![CDATA[
      1 / (x \ K(x,y)) = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(192,a,5223,a)].">
      <j1 rule="hyper" parents="192 5223"/>
    </justification>
  </clause>

  <clause id="5493">
    <literal><![CDATA[
      T((x * K(y,x)) * (R(K(y,x),x,(x * K(y,x)) \ 1) \ 1),z) = (x * K(y,x)) * (T(x,z) * (x \ K(x,y)))
    ]]></literal>
    <justification jstring="[para(5223(a,1),3778(a,2,2,2))].">
      <j1 rule="para" parents="5223 3778"/>
    </justification>
  </clause>

  <clause id="5494">
    <literal><![CDATA[
      T(1 / x,(y * x) / y) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(235,a,5259,a(flip),b,5073,a(flip))].">
      <j1 rule="hyper" parents="235 5259 5073"/>
    </justification>
  </clause>

  <clause id="5498">
    <literal><![CDATA[
      (x \ y) * K(x,x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      y / x = z
    ]]></literal>
    <justification jstring="[para(5267(a,1),250(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5267 250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5500">
    <literal><![CDATA[
      T((x \ (1 / x)) * y,x \ (x \ 1)) = K(x,x \ 1) * (y / (x * x))
    ]]></literal>
    <justification jstring="[para(5267(a,1),1239(a,2,1))].">
      <j1 rule="para" parents="5267 1239"/>
    </justification>
  </clause>

  <clause id="5501">
    <literal><![CDATA[
      K(((x / y) \ 1) \ y,(x / y) \ 1) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(4248,a,5292,a)].">
      <j1 rule="hyper" parents="4248 5292"/>
    </justification>
  </clause>

  <clause id="5503">
    <literal><![CDATA[
      T(x,K(y,y \ x)) = x
    ]]></literal>
    <justification jstring="[hyper(235,a,5293,a,b,5105,a)].">
      <j1 rule="hyper" parents="235 5293 5105"/>
    </justification>
  </clause>

  <clause id="5504">
    <literal><![CDATA[
      (x * (y / x)) \ (y * (K(x,x \ y) * z)) = L(z,K(x,x \ y),y)
    ]]></literal>
    <justification jstring="[para(5293(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5293 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5507">
    <literal><![CDATA[
      R(x,x \ y,K(z,z \ y)) \ (z * (y / z)) = (x \ y) * K(z,z \ y)
    ]]></literal>
    <justification jstring="[para(5293(a,1),580(a,1,2))].">
      <j1 rule="para" parents="5293 580"/>
    </justification>
  </clause>

  <clause id="5508">
    <literal><![CDATA[
      a(x,y * (1 / K(z,z \ y)),u) = a(x,z * (y / z),u)
    ]]></literal>
    <justification jstring="[para(5293(a,1),3119(a,2,2))].">
      <j1 rule="para" parents="5293 3119"/>
    </justification>
  </clause>

  <clause id="5509">
    <literal><![CDATA[
      K(x,y) * (T(x,y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ z = u
    ]]></literal>
    <justification jstring="[para(5348(a,1),250(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5348 250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5510">
    <literal><![CDATA[
      x \ y != K(x,z) * u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) * u = y
    ]]></literal>
    <justification jstring="[para(5350(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="5350 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5511">
    <literal><![CDATA[
      x * (K(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(5350(a,1),250(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5350 250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5512">
    <literal><![CDATA[
      x \ y != K(x,z) * u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) \ y = u
    ]]></literal>
    <justification jstring="[para(5351(a,1),45(a,1))].">
      <j1 rule="para" parents="5351 45"/>
    </justification>
  </clause>

  <clause id="5513">
    <literal><![CDATA[
      K(x,x \ y) * (((x \ y) \ y) \ z) = x \ z
    ]]></literal>
    <justification jstring="[para(108(a,1),5351(a,1,2,1))].">
      <j1 rule="para" parents="108 5351"/>
    </justification>
  </clause>

  <clause id="5514">
    <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),5363(a,1,2,1))].">
      <j1 rule="para" parents="27 5363"/>
    </justification>
  </clause>

  <clause id="5515">
    <literal><![CDATA[
      K(x,y) * (((y * x) / y) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(4978,a,5366,a),flip(a)].">
      <j1 rule="hyper" parents="4978 5366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5517">
    <literal><![CDATA[
      (x * y) / (K(z,x) * y) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(192,a,5382,a)].">
      <j1 rule="hyper" parents="192 5382"/>
    </justification>
  </clause>

  <clause id="5518">
    <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),5382(a,1,1))].">
      <j1 rule="para" parents="25 5382"/>
    </justification>
  </clause>

  <clause id="5519">
    <literal><![CDATA[
      (x * y) / (K(z,x) * y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) = u
    ]]></literal>
    <justification jstring="[para(5382(a,1),310(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5382 310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5521">
    <literal><![CDATA[
      K(x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      y * (T(y,x) \ z) = u
    ]]></literal>
    <justification jstring="[para(5382(a,1),1208(a,1))].">
      <j1 rule="para" parents="5382 1208"/>
    </justification>
  </clause>

  <clause id="5522">
    <literal><![CDATA[
      K(x,T(y,z)) * K(z,y) = T(T(y,z),x) \ y
    ]]></literal>
    <justification jstring="[para(5042(a,1),5382(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5042 5382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5523">
    <literal><![CDATA[
      T(x,y) \ T(x,z) = K(y,x) * K(x,z)
    ]]></literal>
    <justification jstring="[para(5083(a,2),5382(a,1,2))].">
      <j1 rule="para" parents="5083 5382"/>
    </justification>
  </clause>

  <clause id="5524">
    <literal><![CDATA[
      K(x,y) * (y * z) = y * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(5382(a,1),5060(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5382 5060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5525">
    <literal><![CDATA[
      T(x,y) \ z != u * (x \ z)
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = u
    ]]></literal>
    <justification jstring="[para(5383(a,1),46(a,1))].">
      <j1 rule="para" parents="5383 46"/>
    </justification>
  </clause>

  <clause id="5527">
    <literal><![CDATA[
      K(x,y) * (T(y,x) \ z) = T(T(y,x),x) \ z
    ]]></literal>
    <justification jstring="[para(5190(a,1),5383(a,1,1))].">
      <j1 rule="para" parents="5190 5383"/>
    </justification>
  </clause>

  <clause id="5528">
    <literal><![CDATA[
      x * (K(y,x) * (x \ z)) = K(y,x) * z
    ]]></literal>
    <justification jstring="[para(5383(a,2),5060(a,1,2))].">
      <j1 rule="para" parents="5383 5060"/>
    </justification>
  </clause>

  <clause id="5529">
    <literal><![CDATA[
      T(x,y) * (1 / y) = x * (1 / T(y,x))
    ]]></literal>
    <justification jstring="[para(5384(a,1),5055(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5384 5055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5530">
    <literal><![CDATA[
      K(x,y) * (x / y) = x / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(4601,a,5387,a),flip(a)].">
      <j1 rule="hyper" parents="4601 5387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5531">
    <literal><![CDATA[
      K(x,y) * (x / y) = T(x,y) / y
    ]]></literal>
    <justification jstring="[hyper(4599,a,5387,a),flip(a)].">
      <j1 rule="hyper" parents="4599 5387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5532">
    <literal><![CDATA[
      K(x,y / z) * (z * T(z \ y,x)) = y
    ]]></literal>
    <justification jstring="[hyper(1221,a,5387,a)].">
      <j1 rule="hyper" parents="1221 5387"/>
    </justification>
  </clause>

  <clause id="5533">
    <literal><![CDATA[
      T(x,y) \ (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * z = u
    ]]></literal>
    <justification jstring="[para(5387(a,1),314(a,1,2))].">
      <j1 rule="para" parents="5387 314"/>
    </justification>
  </clause>

  <clause id="5534">
    <literal><![CDATA[
      (x * T(y,z)) * ((K(z,y) * K(z,y)) * u) = (x * (y * K(z,y))) * u
    ]]></literal>
    <justification jstring="[para(5387(a,1),117(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5387 117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5535">
    <literal><![CDATA[
      a(x * K(y,x),z,u) = a(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(5387(a,1),2144(a,1,1))].">
      <j1 rule="para" parents="5387 2144"/>
    </justification>
  </clause>

  <clause id="5536">
    <literal><![CDATA[
      T(x \ y,z) * ((y \ x) * K(z,x \ y)) = (x \ y) * (y \ x)
    ]]></literal>
    <justification jstring="[para(2320(a,1),5387(a,1,2))].">
      <j1 rule="para" parents="2320 5387"/>
    </justification>
  </clause>

  <clause id="5537">
    <literal><![CDATA[
      L(x,y,z * K(u,z)) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(5387(a,1),2511(a,1,3))].">
      <j1 rule="para" parents="5387 2511"/>
    </justification>
  </clause>

  <clause id="5538">
    <literal><![CDATA[
      L(x,y * K(z,y),u) = L(x,T(y,z),u)
    ]]></literal>
    <justification jstring="[para(5387(a,1),2890(a,1,2))].">
      <j1 rule="para" parents="5387 2890"/>
    </justification>
  </clause>

  <clause id="5539">
    <literal><![CDATA[
      T(x,y) * (K(y,T(x,y)) * z) = x * z
    ]]></literal>
    <justification jstring="[para(5190(a,2),5387(a,1,2,1))].">
      <j1 rule="para" parents="5190 5387"/>
    </justification>
  </clause>

  <clause id="5540">
    <literal><![CDATA[
      K(x,1 / (y \ x)) = K(x,y / x)
    ]]></literal>
    <justification jstring="[para(76(a,1),5406(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="76 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5541">
    <literal><![CDATA[
      (x / y) * K(x,1 / y) = x * ((x / y) / x)
    ]]></literal>
    <justification jstring="[para(5406(a,1),288(a,1,2))].">
      <j1 rule="para" parents="5406 288"/>
    </justification>
  </clause>

  <clause id="5542">
    <literal><![CDATA[
      x * K(y,1 / (x \ z)) = z * ((y * (z \ x)) / y)
    ]]></literal>
    <justification jstring="[para(5406(a,1),2056(a,1,2))].">
      <j1 rule="para" parents="5406 2056"/>
    </justification>
  </clause>

  <clause id="5543">
    <literal><![CDATA[
      K(x,y) * (z * L(T(K(y,x),z),u,w)) = (K(x,y) * L(K(x,y) \ 1,u,w)) * z
    ]]></literal>
    <justification jstring="[para(5434(a,1),1859(a,1,2,2,1))].">
      <j1 rule="para" parents="5434 1859"/>
    </justification>
  </clause>

  <clause id="5544">
    <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(5434(a,1),1945(a,1,2,2,1))].">
      <j1 rule="para" parents="5434 1945"/>
    </justification>
  </clause>

  <clause id="5545">
    <literal><![CDATA[
      (K(x,y) \ 1) * (z * K(x,y)) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(378,a,5447,a),flip(a)].">
      <j1 rule="hyper" parents="378 5447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5546">
    <literal><![CDATA[
      (K(x,y) * z) \ (K(x,y) * (K(x,y) * u)) = ((K(x,y) \ 1) * z) \ u
    ]]></literal>
    <justification jstring="[para(5447(a,1),2507(a,1,2,2))].">
      <j1 rule="para" parents="5447 2507"/>
    </justification>
  </clause>

  <clause id="5547">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(5455(a,1),307(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5455 307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5548">
    <literal><![CDATA[
      (K(x,y) / x) \ 1 = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(186,a,5482,a)].">
      <j1 rule="hyper" parents="186 5482"/>
    </justification>
  </clause>

  <clause id="5549">
    <literal><![CDATA[
      1 / ((x \ 1) * K(y,x \ 1)) = K(1 / x,y) / (x \ 1)
    ]]></literal>
    <justification jstring="[para(3565(a,2),5482(a,2,1))].">
      <j1 rule="para" parents="3565 5482"/>
    </justification>
  </clause>

  <clause id="5550">
    <literal><![CDATA[
      (x / T(y,x)) * L(z,x / y,K(x,y)) = K(x,y) * ((x / y) * z)
    ]]></literal>
    <justification jstring="[para(5530(a,1),94(a,1,1))].">
      <j1 rule="para" parents="5530 94"/>
    </justification>
  </clause>

  <clause id="5551">
    <literal><![CDATA[
      R(K(x,y),x / y,z) \ ((x / T(y,x)) * z) = (x / y) * z
    ]]></literal>
    <justification jstring="[para(5530(a,1),182(a,1,2,1))].">
      <j1 rule="para" parents="5530 182"/>
    </justification>
  </clause>

  <clause id="5552">
    <literal><![CDATA[
      (x * x) * (y / (x * x)) != z
    ]]></literal>
    <literal><![CDATA[
      y * K(x * x,y) = z
    ]]></literal>
    <justification jstring="[para(670(a,1),5129(a,1))].">
      <j1 rule="para" parents="670 5129"/>
    </justification>
  </clause>

  <clause id="5554">
    <literal><![CDATA[
      T(K(x,y),z) * K(y,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(K(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(5103(a,1),5212(a,1))].">
      <j1 rule="para" parents="5103 5212"/>
    </justification>
  </clause>

  <clause id="5555">
    <literal><![CDATA[
      x \ T(x * y,y) != y * z
    ]]></literal>
    <literal><![CDATA[
      K(x * y,y) = z
    ]]></literal>
    <justification jstring="[para(4302(a,1),5238(a,1))].">
      <j1 rule="para" parents="4302 5238"/>
    </justification>
  </clause>

  <clause id="5556">
    <literal><![CDATA[
      T(K(x * (1 / y),y \ 1) / y,x) = R(1 / y,x,1 / y)
    ]]></literal>
    <justification jstring="[para(4806(a,1),5248(a,1,1))].">
      <j1 rule="para" parents="4806 5248"/>
    </justification>
  </clause>

  <clause id="5559">
    <literal><![CDATA[
      K(x \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(1 / x,y) = z
    ]]></literal>
    <justification jstring="[para(79(a,1),5318(a,1,1,1))].">
      <j1 rule="para" parents="79 5318"/>
    </justification>
  </clause>

  <clause id="5560">
    <literal><![CDATA[
      K(1 / x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(1689(a,1),5318(a,1,1))].">
      <j1 rule="para" parents="1689 5318"/>
    </justification>
  </clause>

  <clause id="5561">
    <literal><![CDATA[
      T(x,x * y) * K(y,x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(3624,a,5355,a)].">
      <j1 rule="hyper" parents="3624 5355"/>
    </justification>
  </clause>

  <clause id="5562">
    <literal><![CDATA[
      K(x,y) = T(y,y * x) \ L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,5355,a(flip),b,3621,a),flip(a)].">
      <j1 rule="hyper" parents="119 5355 3621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5563">
    <literal><![CDATA[
      T(x,y) * K(x * y,x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(3624,a,5356,a)].">
      <j1 rule="hyper" parents="3624 5356"/>
    </justification>
  </clause>

  <clause id="5570">
    <literal><![CDATA[
      K(x \ 1,x) * ((x \ 1) \ y) != z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) \ y = z
    ]]></literal>
    <justification jstring="[para(2736(a,1),5438(a,1,2)),flip(b)].">
      <j1 rule="para" parents="2736 5438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5576">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) * (x * K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(22(a,2),5452(a,1))].">
      <j1 rule="para" parents="22 5452"/>
    </justification>
  </clause>

  <clause id="5579">
    <literal><![CDATA[
      T(x,R(T(x,y) \ z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,R(z / T(x,y),u,w)) = v5
    ]]></literal>
    <justification jstring="[para(243(a,1),5476(a,1,2))].">
      <j1 rule="para" parents="243 5476"/>
    </justification>
  </clause>

  <clause id="5583">
    <literal><![CDATA[
      K(x,x * y) * K(y,x) = x \ L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,5561,a(flip),b,5055,a),flip(a)].">
      <j1 rule="hyper" parents="119 5561 5055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5584">
    <literal><![CDATA[
      T(x,y \ x) * K(y \ 1,x) = L(x,y \ 1,x)
    ]]></literal>
    <justification jstring="[para(2009(a,1),5561(a,1,1))].">
      <j1 rule="para" parents="2009 5561"/>
    </justification>
  </clause>

  <clause id="5585">
    <literal><![CDATA[
      T(x,x * y) * K(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      L(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(5562(a,2),250(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5562 250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5587">
    <literal><![CDATA[
      K(x,y) * K(x * y,x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,5563,a(flip),b,5055,a),flip(a)].">
      <j1 rule="hyper" parents="119 5563 5055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5588">
    <literal><![CDATA[
      (x * T(y,z)) \ (x * R(y,z,y)) = L(K(y * z,y),T(y,z),x)
    ]]></literal>
    <justification jstring="[para(5563(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5563 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5589">
    <literal><![CDATA[
      K(x \ (x * y),x) = (y * x) * ((x * y) \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),5015(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 5015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5590">
    <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(5031(a,1),4915(a,2,1,2,1))].">
      <j1 rule="para" parents="5031 4915"/>
    </justification>
  </clause>

  <clause id="5591">
    <literal><![CDATA[
      K((1 / x) \ y,y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,5024,a,b,5048,a),flip(a)].">
      <j1 rule="hyper" parents="299 5024 5048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5592">
    <literal><![CDATA[
      K(x * (y \ 1),x) = K(y \ x,x)
    ]]></literal>
    <justification jstring="[para(76(a,1),5591(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="76 5591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5593">
    <literal><![CDATA[
      K(((x * y) / x) \ z,z) = K(z * (y \ K(y,x)),z)
    ]]></literal>
    <justification jstring="[para(5182(a,1),5592(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5182 5592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5594">
    <literal><![CDATA[
      (x * (y * T(y \ z,u))) / (x * z) = K((x * z) / (x * y),u)
    ]]></literal>
    <justification jstring="[hyper(120,a,997,a(flip),b,5057,a)].">
      <j1 rule="hyper" parents="120 997 5057"/>
    </justification>
  </clause>

  <clause id="5596">
    <literal><![CDATA[
      x * T(x \ y,z) != y * u
    ]]></literal>
    <literal><![CDATA[
      T(K(y / x,z),y) = u
    ]]></literal>
    <justification jstring="[para(5057(a,1),236(a,2)),flip(a)].">
      <j1 rule="para" parents="5057 236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5597">
    <literal><![CDATA[
      x / (y * T(y \ x,z)) = K(z,x / y)
    ]]></literal>
    <justification jstring="[para(5057(a,1),5430(a,1,2))].">
      <j1 rule="para" parents="5057 5430"/>
    </justification>
  </clause>

  <clause id="5598">
    <literal><![CDATA[
      x / (y * T(y \ x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x / y) = u
    ]]></literal>
    <justification jstring="[para(5057(a,1),5440(a,1,2))].">
      <j1 rule="para" parents="5057 5440"/>
    </justification>
  </clause>

  <clause id="5599">
    <literal><![CDATA[
      K(x,y) / (1 / T(y,x)) = 1 / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(192,a,5065,a)].">
      <j1 rule="hyper" parents="192 5065"/>
    </justification>
  </clause>

  <clause id="5600">
    <literal><![CDATA[
      K(x * K(y,y \ 1),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,5033,a,b,5066,a),flip(a)].">
      <j1 rule="hyper" parents="299 5033 5066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5601">
    <literal><![CDATA[
      K(x * (1 / y),z) = K(x * (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(2763(a,1),5600(a,1,1))].">
      <j1 rule="para" parents="2763 5600"/>
    </justification>
  </clause>

  <clause id="5602">
    <literal><![CDATA[
      K(x / (1 / y),z) = K(x / (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(2766(a,1),5600(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2766 5600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5603">
    <literal><![CDATA[
      K(x * ((y \ 1) \ 1),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(2770(a,1),5600(a,1,1))].">
      <j1 rule="para" parents="2770 5600"/>
    </justification>
  </clause>

  <clause id="5604">
    <literal><![CDATA[
      K(x * (1 / (1 / y)),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(2914(a,1),5600(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2914 5600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5605">
    <literal><![CDATA[
      K(K(x,x \ 1) * y,z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(3197(a,2),5600(a,1,1))].">
      <j1 rule="para" parents="3197 5600"/>
    </justification>
  </clause>

  <clause id="5606">
    <literal><![CDATA[
      K(K(x \ 1,x) * y,z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(3213(a,1),5600(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3213 5600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5607">
    <literal><![CDATA[
      K((1 / x) \ y,z) = K((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[para(3222(a,1),5600(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3222 5600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5608">
    <literal><![CDATA[
      K((1 / x) * y,z) = K((x \ 1) * y,z)
    ]]></literal>
    <justification jstring="[para(3223(a,1),5600(a,1,1))].">
      <j1 rule="para" parents="3223 5600"/>
    </justification>
  </clause>

  <clause id="5609">
    <literal><![CDATA[
      K(((x \ 1) \ 1) * y,z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(3224(a,1),5600(a,1,1))].">
      <j1 rule="para" parents="3224 5600"/>
    </justification>
  </clause>

  <clause id="5610">
    <literal><![CDATA[
      K(x \ (y * K(z,z \ 1)),u) = K(x \ y,u)
    ]]></literal>
    <justification jstring="[para(3399(a,2),5600(a,1,1))].">
      <j1 rule="para" parents="3399 5600"/>
    </justification>
  </clause>

  <clause id="5611">
    <literal><![CDATA[
      K(x \ (K(y,y \ 1) * z),u) = K(x \ z,u)
    ]]></literal>
    <justification jstring="[para(3422(a,2),5600(a,1,1))].">
      <j1 rule="para" parents="3422 5600"/>
    </justification>
  </clause>

  <clause id="5615">
    <literal><![CDATA[
      K((1 / (1 / x)) * y,z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(2726(a,1),5605(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2726 5605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5616">
    <literal><![CDATA[
      K(R(1 / x,y,z),u) = K(R(x \ 1,y,z),u)
    ]]></literal>
    <justification jstring="[para(2976(a,1),5605(a,1,1))].">
      <j1 rule="para" parents="2976 5605"/>
    </justification>
  </clause>

  <clause id="5617">
    <literal><![CDATA[
      K(x \ (1 / y),z) = K(x \ (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(3369(a,1),5605(a,1,1))].">
      <j1 rule="para" parents="3369 5605"/>
    </justification>
  </clause>

  <clause id="5618">
    <literal><![CDATA[
      K(x * ((1 / y) \ z),u) = K(x * ((y \ 1) \ z),u)
    ]]></literal>
    <justification jstring="[para(3337(a,1),5605(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3337 5605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5619">
    <literal><![CDATA[
      K(x * (y * (1 / z)),u) = K(x * (y * (z \ 1)),u)
    ]]></literal>
    <justification jstring="[para(3340(a,1),5605(a,1,1))].">
      <j1 rule="para" parents="3340 5605"/>
    </justification>
  </clause>

  <clause id="5622">
    <literal><![CDATA[
      K((K(x,x \ 1) * y) \ z,u) = K(y \ z,u)
    ]]></literal>
    <justification jstring="[para(3233(a,2),5606(a,1,1))].">
      <j1 rule="para" parents="3233 5606"/>
    </justification>
  </clause>

  <clause id="5623">
    <literal><![CDATA[
      K(((1 / x) * y) \ z,u) = K(((x \ 1) * y) \ z,u)
    ]]></literal>
    <justification jstring="[para(3265(a,1),5606(a,1,1))].">
      <j1 rule="para" parents="3265 5606"/>
    </justification>
  </clause>

  <clause id="5624">
    <literal><![CDATA[
      K((x / (1 / y)) * z,u) = K((x / (y \ 1)) * z,u)
    ]]></literal>
    <justification jstring="[para(3312(a,1),5606(a,1,1))].">
      <j1 rule="para" parents="3312 5606"/>
    </justification>
  </clause>

  <clause id="5625">
    <literal><![CDATA[
      K(x / (K(y,y \ 1) * z),u) = K(x / z,u)
    ]]></literal>
    <justification jstring="[para(3836(a,2),5606(a,1,1))].">
      <j1 rule="para" parents="3836 5606"/>
    </justification>
  </clause>

  <clause id="5626">
    <literal><![CDATA[
      R(x * ((y * (x \ 1)) / y),z,u) = K(y,R(x,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,4936,a(flip),b,5072,a)].">
      <j1 rule="hyper" parents="65 4936 5072"/>
    </justification>
  </clause>

  <clause id="5627">
    <literal><![CDATA[
      (x * ((y * (x \ z)) / y)) / z = K(y,(x / z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,2414,a(flip),b,5072,a)].">
      <j1 rule="hyper" parents="65 2414 5072"/>
    </justification>
  </clause>

  <clause id="5628">
    <literal><![CDATA[
      x * (y * ((z * (y \ (x \ 1))) / z)) = K(z,(x * y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,1321,a(flip),b,5072,a)].">
      <j1 rule="hyper" parents="65 1321 5072"/>
    </justification>
  </clause>

  <clause id="5629">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ x)) / z) = x * K(z,y \ 1)
    ]]></literal>
    <justification jstring="[para(5072(a,1),1319(a,2,2))].">
      <j1 rule="para" parents="5072 1319"/>
    </justification>
  </clause>

  <clause id="5632">
    <literal><![CDATA[
      x * K(y,(x \ z) \ 1) = z * ((y * (z \ x)) / y)
    ]]></literal>
    <justification jstring="[para(5072(a,1),2054(a,1,2))].">
      <j1 rule="para" parents="5072 2054"/>
    </justification>
  </clause>

  <clause id="5633">
    <literal><![CDATA[
      ((x * y) * ((z * ((x * y) \ x)) / z)) * y = (x * y) * K(z,y \ 1)
    ]]></literal>
    <justification jstring="[para(5072(a,1),2258(a,2,2))].">
      <j1 rule="para" parents="5072 2258"/>
    </justification>
  </clause>

  <clause id="5634">
    <literal><![CDATA[
      L(x,y,z) \ K(x,L(x,y,z) \ 1) = (L(x,y,z) \ x) / x
    ]]></literal>
    <justification jstring="[para(1353(a,1),5079(a,2,1))].">
      <j1 rule="para" parents="1353 5079"/>
    </justification>
  </clause>

  <clause id="5635">
    <literal><![CDATA[
      K(x,x * (y \ 1)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(299,a,5036,a,b,5094,a),flip(a)].">
      <j1 rule="hyper" parents="299 5036 5094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5637">
    <literal><![CDATA[
      K(x,y * K(z,z \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,5036,a,b,5098,a),flip(a)].">
      <j1 rule="hyper" parents="299 5036 5098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5638">
    <literal><![CDATA[
      K(x,y * T(z,z \ 1)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(2760(a,1),5637(a,1,2))].">
      <j1 rule="para" parents="2760 5637"/>
    </justification>
  </clause>

  <clause id="5639">
    <literal><![CDATA[
      K(x,y * (1 / z)) = K(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[para(2763(a,1),5637(a,1,2))].">
      <j1 rule="para" parents="2763 5637"/>
    </justification>
  </clause>

  <clause id="5640">
    <literal><![CDATA[
      K(x,y / (1 / z)) = K(x,y / (z \ 1))
    ]]></literal>
    <justification jstring="[para(2766(a,1),5637(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2766 5637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5641">
    <literal><![CDATA[
      K(x,y * ((z \ 1) \ 1)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(2770(a,1),5637(a,1,2))].">
      <j1 rule="para" parents="2770 5637"/>
    </justification>
  </clause>

  <clause id="5643">
    <literal><![CDATA[
      K(x,y / (1 / (1 / z))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(2917(a,1),5637(a,1,2))].">
      <j1 rule="para" parents="2917 5637"/>
    </justification>
  </clause>

  <clause id="5644">
    <literal><![CDATA[
      K(x,K(y,y \ 1) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(3197(a,2),5637(a,1,2))].">
      <j1 rule="para" parents="3197 5637"/>
    </justification>
  </clause>

  <clause id="5645">
    <literal><![CDATA[
      K(x,K(y \ 1,y) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(3213(a,1),5637(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3213 5637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5646">
    <literal><![CDATA[
      K(x,T(y,y \ 1) * z) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(3215(a,1),5637(a,1,2))].">
      <j1 rule="para" parents="3215 5637"/>
    </justification>
  </clause>

  <clause id="5647">
    <literal><![CDATA[
      K(x,(1 / y) \ z) = K(x,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(3222(a,1),5637(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3222 5637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5648">
    <literal><![CDATA[
      K(x,(1 / y) * z) = K(x,(y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(3223(a,1),5637(a,1,2))].">
      <j1 rule="para" parents="3223 5637"/>
    </justification>
  </clause>

  <clause id="5649">
    <literal><![CDATA[
      K(x,((y \ 1) \ 1) * z) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(3224(a,1),5637(a,1,2))].">
      <j1 rule="para" parents="3224 5637"/>
    </justification>
  </clause>

  <clause id="5650">
    <literal><![CDATA[
      K(x,(K(y \ 1,y) * z) \ u) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(3420(a,2),5637(a,1,2))].">
      <j1 rule="para" parents="3420 5637"/>
    </justification>
  </clause>

  <clause id="5651">
    <literal><![CDATA[
      K(x,y \ (K(z,z \ 1) * u)) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(3422(a,2),5637(a,1,2))].">
      <j1 rule="para" parents="3422 5637"/>
    </justification>
  </clause>

  <clause id="5652">
    <literal><![CDATA[
      K(x,(y \ 1) * (y * z)) = K(x,L(z,y,y \ 1))
    ]]></literal>
    <justification jstring="[para(3279(a,1),5637(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3279 5637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5653">
    <literal><![CDATA[
      K(x,((y \ 1) \ 1) \ z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(3277(a,1),5637(a,1,2))].">
      <j1 rule="para" parents="3277 5637"/>
    </justification>
  </clause>

  <clause id="5654">
    <literal><![CDATA[
      K(x,T(y * K(z,z \ 1),u)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(3508(a,2),5637(a,1,2))].">
      <j1 rule="para" parents="3508 5637"/>
    </justification>
  </clause>

  <clause id="5655">
    <literal><![CDATA[
      K(x,K(y,1 / y) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(2584(a,2),5644(a,1,2,1))].">
      <j1 rule="para" parents="2584 5644"/>
    </justification>
  </clause>

  <clause id="5656">
    <literal><![CDATA[
      K(x,(y * (1 / z)) \ u) = K(x,(y * (z \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(2797(a,1),5644(a,1,2))].">
      <j1 rule="para" parents="2797 5644"/>
    </justification>
  </clause>

  <clause id="5657">
    <literal><![CDATA[
      K(x,y * (K(z,z \ 1) * u)) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(3301(a,1),5644(a,1,2))].">
      <j1 rule="para" parents="3301 5644"/>
    </justification>
  </clause>

  <clause id="5658">
    <literal><![CDATA[
      K(x,y * ((1 / z) \ u)) = K(x,y * ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(3337(a,1),5644(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3337 5644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5659">
    <literal><![CDATA[
      K(x,y * (z * (1 / u))) = K(x,y * (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(3340(a,1),5644(a,1,2))].">
      <j1 rule="para" parents="3340 5644"/>
    </justification>
  </clause>

  <clause id="5660">
    <literal><![CDATA[
      K(x,((1 / y) \ z) \ u) = K(x,((y \ 1) \ z) \ u)
    ]]></literal>
    <justification jstring="[para(3453(a,1),5644(a,1,2))].">
      <j1 rule="para" parents="3453 5644"/>
    </justification>
  </clause>

  <clause id="5661">
    <literal><![CDATA[
      K(x,(K(y \ 1,y) * z) / u) = K(x,z / u)
    ]]></literal>
    <justification jstring="[para(2499(a,2),5645(a,1,2))].">
      <j1 rule="para" parents="2499 5645"/>
    </justification>
  </clause>

  <clause id="5662">
    <literal><![CDATA[
      K(x,(y * ((z \ 1) \ 1)) \ u) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[para(2784(a,1),5645(a,1,2))].">
      <j1 rule="para" parents="2784 5645"/>
    </justification>
  </clause>

  <clause id="5663">
    <literal><![CDATA[
      K(x,(K(y,y \ 1) * z) \ u) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(3233(a,2),5645(a,1,2))].">
      <j1 rule="para" parents="3233 5645"/>
    </justification>
  </clause>

  <clause id="5664">
    <literal><![CDATA[
      K(x,((1 / y) * z) \ u) = K(x,((y \ 1) * z) \ u)
    ]]></literal>
    <justification jstring="[para(3265(a,1),5645(a,1,2))].">
      <j1 rule="para" parents="3265 5645"/>
    </justification>
  </clause>

  <clause id="5665">
    <literal><![CDATA[
      K(x,(y / (1 / z)) * u) = K(x,(y / (z \ 1)) * u)
    ]]></literal>
    <justification jstring="[para(3312(a,1),5645(a,1,2))].">
      <j1 rule="para" parents="3312 5645"/>
    </justification>
  </clause>

  <clause id="5666">
    <literal><![CDATA[
      K(x,R(1 / y,z,u) \ w) = K(x,R(y \ 1,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(3305(a,1),5645(a,1,2))].">
      <j1 rule="para" parents="3305 5645"/>
    </justification>
  </clause>

  <clause id="5667">
    <literal><![CDATA[
      K(x,y / (K(z,z \ 1) * u)) = K(x,y / u)
    ]]></literal>
    <justification jstring="[para(3836(a,2),5645(a,1,2))].">
      <j1 rule="para" parents="3836 5645"/>
    </justification>
  </clause>

  <clause id="5668">
    <literal><![CDATA[
      K(x,K(y,1 / y) / z) = K(x,1 / z)
    ]]></literal>
    <justification jstring="[para(2494(a,1),5655(a,1,2))].">
      <j1 rule="para" parents="2494 5655"/>
    </justification>
  </clause>

  <clause id="5669">
    <literal><![CDATA[
      L(x * K(y,x),z,u) * T(y,x) = T(y,x) * L(x,z,u)
    ]]></literal>
    <justification jstring="[para(5122(a,1),686(a,1,1,1))].">
      <j1 rule="para" parents="5122 686"/>
    </justification>
  </clause>

  <clause id="5671">
    <literal><![CDATA[
      ((T(x,(1 / y) \ z) * (z * y)) / T(x,(1 / y) \ z)) / y = (1 / y) * (((1 / y) \ z) * K(x,(1 / y) \ z))
    ]]></literal>
    <justification jstring="[para(5122(a,1),2083(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5122 2083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5672">
    <literal><![CDATA[
      T(x * K(1 / y,x),y) = (((y * y) \ x) * y) / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(120,a,983,a,b,5130,a),flip(a)].">
      <j1 rule="hyper" parents="120 983 5130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5673">
    <literal><![CDATA[
      T(x * K(y * R(x,z,u),x),y) = R(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(37,a,1926,a,b,5130,a),flip(a)].">
      <j1 rule="hyper" parents="37 1926 5130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5674">
    <literal><![CDATA[
      T(x * K(x * y,x),y) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(235,a,5164,a,b,4341,a)].">
      <j1 rule="hyper" parents="235 5164 4341"/>
    </justification>
  </clause>

  <clause id="5675">
    <literal><![CDATA[
      x \ T(x * y,y) = y * K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(37,a,3479,a,b,5164,a)].">
      <j1 rule="hyper" parents="37 3479 5164"/>
    </justification>
  </clause>

  <clause id="5677">
    <literal><![CDATA[
      T(x * K(y,x),x \ y) = R(x,x \ y,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),5674(a,1,1,2,1))].">
      <j1 rule="para" parents="10 5674"/>
    </justification>
  </clause>

  <clause id="5678">
    <literal><![CDATA[
      T(T(x * K(x * y,x),z),y) = T(R(x,y,x),z)
    ]]></literal>
    <justification jstring="[para(5674(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5674 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5679">
    <literal><![CDATA[
      T(x * K(y \ x,x),y \ 1) = R(x,y \ 1,x)
    ]]></literal>
    <justification jstring="[para(5592(a,1),5674(a,1,1,2))].">
      <j1 rule="para" parents="5592 5674"/>
    </justification>
  </clause>

  <clause id="5680">
    <literal><![CDATA[
      K(x,(1 / x) * (y * x)) = K(x,L(y,x,x \ 1))
    ]]></literal>
    <justification jstring="[para(2473(a,1),5204(a,1,2))].">
      <j1 rule="para" parents="2473 5204"/>
    </justification>
  </clause>

  <clause id="5681">
    <literal><![CDATA[
      T(x * K(y \ x,x),y \ 1) = R(x,x \ (y \ x),x)
    ]]></literal>
    <justification jstring="[hyper(299,a,4697,a,b,5245,a),flip(a)].">
      <j1 rule="hyper" parents="299 4697 5245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5682">
    <literal><![CDATA[
      T(x,y) \ T(x * K(z,x),y) = K(z,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,5245,a,b,5054,a(flip))].">
      <j1 rule="hyper" parents="119 5245 5054"/>
    </justification>
  </clause>

  <clause id="5683">
    <literal><![CDATA[
      T(x * K(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      T((y * x) / y,z) = u
    ]]></literal>
    <justification jstring="[para(5245(a,2),448(a,1))].">
      <j1 rule="para" parents="5245 448"/>
    </justification>
  </clause>

  <clause id="5684">
    <literal><![CDATA[
      T(x * K(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) * K(y,T(x,z)) = u
    ]]></literal>
    <justification jstring="[para(5245(a,2),5129(a,1))].">
      <j1 rule="para" parents="5245 5129"/>
    </justification>
  </clause>

  <clause id="5685">
    <literal><![CDATA[
      K(x,y * x) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(5304,a,5276,a)].">
      <j1 rule="hyper" parents="5304 5276"/>
    </justification>
  </clause>

  <clause id="5687">
    <literal><![CDATA[
      K(x,x * (y / x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(12(a,1),5685(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 5685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5688">
    <literal><![CDATA[
      K(x * (y * z),a(x,y,z) * (x * (y * z))) = K(x * (y * z),(x * y) * z)
    ]]></literal>
    <justification jstring="[para(84(a,1),5685(a,2,2))].">
      <j1 rule="para" parents="84 5685"/>
    </justification>
  </clause>

  <clause id="5689">
    <literal><![CDATA[
      K(x,T(y * x,z)) = K(x,T(x * y,z))
    ]]></literal>
    <justification jstring="[para(3468(a,1),5687(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3468 5687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5690">
    <literal><![CDATA[
      R(K(x * (y / (z * y)),y / (z * y)),R(1 / z,z,y),z * y) = ((x \ T(x * (y / (z * y)),y / (z * y))) * (z * y)) / y
    ]]></literal>
    <justification jstring="[para(5283(a,1),843(a,1,1))].">
      <j1 rule="para" parents="5283 843"/>
    </justification>
  </clause>

  <clause id="5691">
    <literal><![CDATA[
      (T(1 / x,y) \ 1) / K(y,x \ 1) = x
    ]]></literal>
    <justification jstring="[para(4797(a,1),5346(a,1,2))].">
      <j1 rule="para" parents="4797 5346"/>
    </justification>
  </clause>

  <clause id="5692">
    <literal><![CDATA[
      K(x \ y,x) * ((x \ y) \ z) = (y / x) \ z
    ]]></literal>
    <justification jstring="[para(10(a,1),5352(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 5352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5693">
    <literal><![CDATA[
      (x / (x / y)) \ z = K(y,x / y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(12(a,1),5352(a,1,1,1))].">
      <j1 rule="para" parents="12 5352"/>
    </justification>
  </clause>

  <clause id="5695">
    <literal><![CDATA[
      (x * K(y,x)) \ z = K(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[para(5054(a,1),5352(a,1,1))].">
      <j1 rule="para" parents="5054 5352"/>
    </justification>
  </clause>

  <clause id="5696">
    <literal><![CDATA[
      K(x \ 1,y) * ((x \ 1) \ z) = (x \ K(y,x \ 1)) \ z
    ]]></literal>
    <justification jstring="[para(5079(a,2),5352(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5079 5352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5697">
    <literal><![CDATA[
      x * (K(x,y) * T(z,x)) = K(x,y) * (z * x)
    ]]></literal>
    <justification jstring="[hyper(299,a,5055,a,b,5353,a)].">
      <j1 rule="hyper" parents="299 5055 5353"/>
    </justification>
  </clause>

  <clause id="5698">
    <literal><![CDATA[
      K(x,y) * (x \ (y \ z)) = x \ (T(y,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(119,a,5383,a(flip),b,5367,a),flip(a)].">
      <j1 rule="hyper" parents="119 5383 5367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5699">
    <literal><![CDATA[
      x \ (y * K(x,y)) = K(x,y) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(119,a,3618,a(flip),b,5367,a)].">
      <j1 rule="hyper" parents="119 3618 5367"/>
    </justification>
  </clause>

  <clause id="5700">
    <literal><![CDATA[
      x \ (K(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (x \ z) = u
    ]]></literal>
    <justification jstring="[para(5367(a,1),314(a,1,2))].">
      <j1 rule="para" parents="5367 314"/>
    </justification>
  </clause>

  <clause id="5701">
    <literal><![CDATA[
      K(x,y) * T(x,z) = K(x,z) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,3577,a(flip),b,5379,a)].">
      <j1 rule="hyper" parents="299 3577 5379"/>
    </justification>
  </clause>

  <clause id="5702">
    <literal><![CDATA[
      K(x,y) * T(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * T(x,y) = u
    ]]></literal>
    <justification jstring="[para(5379(a,2),3588(a,1))].">
      <j1 rule="para" parents="5379 3588"/>
    </justification>
  </clause>

  <clause id="5703">
    <literal><![CDATA[
      K(x,y) * T(x,z) != K(x,z) * u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(5379(a,2),3589(a,1))].">
      <j1 rule="para" parents="5379 3589"/>
    </justification>
  </clause>

  <clause id="5705">
    <literal><![CDATA[
      ((x * y) / x) * z = y * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(5381(a,1),1416(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5381 1416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5707">
    <literal><![CDATA[
      x * ((y * (x / y)) \ y) = x / (x / y)
    ]]></literal>
    <justification jstring="[hyper(144,a,5467,a(flip))].">
      <j1 rule="hyper" parents="144 5467"/>
    </justification>
  </clause>

  <clause id="5708">
    <literal><![CDATA[
      ((x * T(T(x,y),y)) \ z) * T(x,y) = (1 / T(x,y)) * T(z,T(x,y))
    ]]></literal>
    <justification jstring="[para(5483(a,1),983(a,1,1,1))].">
      <j1 rule="para" parents="5483 983"/>
    </justification>
  </clause>

  <clause id="5709">
    <literal><![CDATA[
      x * (y * T(T(y,y \ 1),y \ 1)) = (x * T(y,y \ 1)) / (y \ 1)
    ]]></literal>
    <justification jstring="[para(5483(a,1),678(a,1,2))].">
      <j1 rule="para" parents="5483 678"/>
    </justification>
  </clause>

  <clause id="5710">
    <literal><![CDATA[
      R(x,K(y,x),z) = x
    ]]></literal>
    <justification jstring="[hyper(3701,a,5488,a)].">
      <j1 rule="hyper" parents="3701 5488"/>
    </justification>
  </clause>

  <clause id="5711">
    <literal><![CDATA[
      (x * (K(y,x) * z)) \ ((x * K(y,x)) * (z * u)) = L(u,z,x * K(y,x))
    ]]></literal>
    <justification jstring="[para(5488(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5488 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5712">
    <literal><![CDATA[
      L(x,y,z * (K(u,z) * (w \ 1))) = L(x,y,(z * K(u,z)) * w)
    ]]></literal>
    <justification jstring="[para(5488(a,1),2627(a,1,3))].">
      <j1 rule="para" parents="5488 2627"/>
    </justification>
  </clause>

  <clause id="5713">
    <literal><![CDATA[
      (x / (x / y)) * z = y * (K(y \ x,y) * z)
    ]]></literal>
    <justification jstring="[para(5002(a,2),5488(a,1,1))].">
      <j1 rule="para" parents="5002 5488"/>
    </justification>
  </clause>

  <clause id="5714">
    <literal><![CDATA[
      (x \ y) * (K(x,x \ y) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[para(5102(a,1),5488(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5102 5488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5716">
    <literal><![CDATA[
      (T(x,y) * K(z,x)) * u = T(x,y) * (K(z,x) * u)
    ]]></literal>
    <justification jstring="[para(5710(a,1),541(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5710 541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5717">
    <literal><![CDATA[
      (R(x,y,z) * K(u,x)) * w = R(x,y,z) * (K(u,x) * w)
    ]]></literal>
    <justification jstring="[para(5710(a,1),543(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5710 543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5718">
    <literal><![CDATA[
      K(x \ y,x) * ((y / x) * z) = (x \ y) * z
    ]]></literal>
    <justification jstring="[para(10(a,1),5515(a,1,2,1,1))].">
      <j1 rule="para" parents="10 5515"/>
    </justification>
  </clause>

  <clause id="5720">
    <literal><![CDATA[
      T(x,y) \ T(x,z) = K(x,z) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,2278,a,b,5523,a),flip(a)].">
      <j1 rule="hyper" parents="299 2278 5523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5721">
    <literal><![CDATA[
      R(K(x,y),y * z,u) * ((y * z) * u) = (y * (K(x,y) * z)) * u
    ]]></literal>
    <justification jstring="[para(5524(a,1),103(a,2,1))].">
      <j1 rule="para" parents="5524 103"/>
    </justification>
  </clause>

  <clause id="5722">
    <literal><![CDATA[
      x * (K(y,x) * (x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * z = u
    ]]></literal>
    <justification jstring="[para(5524(a,1),315(a,1))].">
      <j1 rule="para" parents="5524 315"/>
    </justification>
  </clause>

  <clause id="5724">
    <literal><![CDATA[
      (1 / T(x,y)) \ (T(y,x) * (1 / x)) = T(y,1 / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,5529,a,b,107,a)].">
      <j1 rule="hyper" parents="119 5529 107"/>
    </justification>
  </clause>

  <clause id="5725">
    <literal><![CDATA[
      L((1 / T(x,y)) \ z,1 / T(x,y),y) = (T(y,x) * (1 / x)) \ (y * z)
    ]]></literal>
    <justification jstring="[para(5529(a,2),96(a,2,1))].">
      <j1 rule="para" parents="5529 96"/>
    </justification>
  </clause>

  <clause id="5727">
    <literal><![CDATA[
      K(x,y / (z \ 1)) * (z \ T(z * y,x)) = y
    ]]></literal>
    <justification jstring="[para(1012(a,1),5532(a,1,2))].">
      <j1 rule="para" parents="1012 5532"/>
    </justification>
  </clause>

  <clause id="5728">
    <literal><![CDATA[
      K(x,(y \ z) / (y \ 1)) * (y \ T(z,x)) = y \ z
    ]]></literal>
    <justification jstring="[para(1109(a,1),5532(a,1,2))].">
      <j1 rule="para" parents="1109 5532"/>
    </justification>
  </clause>

  <clause id="5729">
    <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(336(a,2),5532(a,1,2,2,1))].">
      <j1 rule="para" parents="336 5532"/>
    </justification>
  </clause>

  <clause id="5730">
    <literal><![CDATA[
      L(x,y,T(T(z,u),u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(5100(a,1),5537(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5100 5537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5731">
    <literal><![CDATA[
      L(x,y,T(z \ u,z)) = L(x,y,u / z)
    ]]></literal>
    <justification jstring="[para(5102(a,1),5537(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5102 5537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5732">
    <literal><![CDATA[
      L(x,y,T(T(z,z * u),u)) = L(x,y,L(z,u,z))
    ]]></literal>
    <justification jstring="[para(786(a,1),5730(a,1,3,1))].">
      <j1 rule="para" parents="786 5730"/>
    </justification>
  </clause>

  <clause id="5733">
    <literal><![CDATA[
      L(x,y,T(T(z,u),u * z)) = L(x,y,R(z,u,z))
    ]]></literal>
    <justification jstring="[para(875(a,1),5730(a,1,3,1))].">
      <j1 rule="para" parents="875 5730"/>
    </justification>
  </clause>

  <clause id="5734">
    <literal><![CDATA[
      L(x,(y * z) / y,u) = L(x,T(z,y),u)
    ]]></literal>
    <justification jstring="[para(5054(a,2),5538(a,1,2))].">
      <j1 rule="para" parents="5054 5538"/>
    </justification>
  </clause>

  <clause id="5735">
    <literal><![CDATA[
      L(x,T(y \ z,y),u) = L(x,z / y,u)
    ]]></literal>
    <justification jstring="[para(5102(a,1),5538(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5102 5538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5736">
    <literal><![CDATA[
      T(x,y) * (T(x,y) * z) = x * (T(T(x,y),y) * z)
    ]]></literal>
    <justification jstring="[para(5061(a,1),5539(a,1,2))].">
      <j1 rule="para" parents="5061 5539"/>
    </justification>
  </clause>

  <clause id="5737">
    <literal><![CDATA[
      x / (y * (z * T(z \ (y \ x),u))) = K(u,x / (y * z))
    ]]></literal>
    <justification jstring="[para(998(a,1),5597(a,1,2))].">
      <j1 rule="para" parents="998 5597"/>
    </justification>
  </clause>

  <clause id="5738">
    <literal><![CDATA[
      x / (((y \ (x * z)) * y) / z) = K(y,x / (y / z))
    ]]></literal>
    <justification jstring="[para(1520(a,1),5597(a,1,2))].">
      <j1 rule="para" parents="1520 5597"/>
    </justification>
  </clause>

  <clause id="5739">
    <literal><![CDATA[
      x / (((y \ (x / z)) * y) * z) = K(y,x / (y * z))
    ]]></literal>
    <justification jstring="[para(1596(a,1),5597(a,1,2))].">
      <j1 rule="para" parents="1596 5597"/>
    </justification>
  </clause>

  <clause id="5740">
    <literal><![CDATA[
      K(x,y) / (K(x,y) / y) = 1 / (1 / y)
    ]]></literal>
    <justification jstring="[para(5038(a,2),5599(a,1,2))].">
      <j1 rule="para" parents="5038 5599"/>
    </justification>
  </clause>

  <clause id="5741">
    <literal><![CDATA[
      K((x \ 1) \ y,y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,5592,a(flip),b,5603,a)].">
      <j1 rule="hyper" parents="65 5592 5603"/>
    </justification>
  </clause>

  <clause id="5742">
    <literal><![CDATA[
      K(x * T(1 / y,z),u) = K(x * T(y \ 1,z),u)
    ]]></literal>
    <justification jstring="[para(3179(a,1),5603(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3179 5603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5743">
    <literal><![CDATA[
      K(x * T((y * z) \ z,y),u) = K(x * ((y * z) \ z),u)
    ]]></literal>
    <justification jstring="[para(3322(a,2),5603(a,1,1,2))].">
      <j1 rule="para" parents="3322 5603"/>
    </justification>
  </clause>

  <clause id="5744">
    <literal><![CDATA[
      K((1 / (1 / x)) * (x \ y),z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(332(a,1),5608(a,2,1))].">
      <j1 rule="para" parents="332 5608"/>
    </justification>
  </clause>

  <clause id="5745">
    <literal><![CDATA[
      K(((x * K(y,x)) \ 1) * z,u) = K((K(x,y) / x) * z,u)
    ]]></literal>
    <justification jstring="[para(5482(a,1),5608(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5482 5608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5746">
    <literal><![CDATA[
      K((1 / (1 / x)) * y,1 / z) = K(x * y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,4797,a(flip),b,5615,a),flip(a)].">
      <j1 rule="hyper" parents="299 4797 5615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5749">
    <literal><![CDATA[
      K(x,(y \ 1) \ x) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,5635,a(flip),b,5641,a)].">
      <j1 rule="hyper" parents="65 5635 5641"/>
    </justification>
  </clause>

  <clause id="5750">
    <literal><![CDATA[
      K(x,y * L(1 / z,u,w)) = K(x,y * L(z \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(4143(a,1),5641(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4143 5641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5751">
    <literal><![CDATA[
      K(x,(y \ 1) \ x) = K(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(299,a,5685,a,b,5749,a),flip(a)].">
      <j1 rule="hyper" parents="299 5685 5749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5752">
    <literal><![CDATA[
      K(x,y / L(1 / z,u,w)) = K(x,y / L(z \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(4141(a,1),5643(a,1,2,2))].">
      <j1 rule="para" parents="4141 5643"/>
    </justification>
  </clause>

  <clause id="5753">
    <literal><![CDATA[
      K(x,(1 / x) * y) * y = x * (y / x)
    ]]></literal>
    <justification jstring="[para(5648(a,2),5463(a,1,1))].">
      <j1 rule="para" parents="5648 5463"/>
    </justification>
  </clause>

  <clause id="5754">
    <literal><![CDATA[
      K(x,L(1 / y,z,u) * w) = K(x,L(y \ 1,z,u) * w)
    ]]></literal>
    <justification jstring="[para(4143(a,1),5649(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4143 5649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5755">
    <literal><![CDATA[
      K(x,L(1 / y,z,u) \ w) = K(x,L(y \ 1,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(4143(a,1),5653(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4143 5653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5756">
    <literal><![CDATA[
      T(1 / x,y) \ 1 = x * K(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(143,a,5691,a),flip(a)].">
      <j1 rule="hyper" parents="143 5691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5757">
    <literal><![CDATA[
      (x * K(y,x)) \ y = x \ (y * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,5695,a,b,5699,a)].">
      <j1 rule="hyper" parents="299 5695 5699"/>
    </justification>
  </clause>

  <clause id="5758">
    <literal><![CDATA[
      (x / (K(y,z) * T(y,u))) \ x = K(y,u) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(350,a,5701,a)].">
      <j1 rule="hyper" parents="350 5701"/>
    </justification>
  </clause>

  <clause id="5759">
    <literal><![CDATA[
      (x * (K(y * z,x) * y)) * z = (y * z) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(5705(a,1),931(a,1,1))].">
      <j1 rule="para" parents="5705 931"/>
    </justification>
  </clause>

  <clause id="5760">
    <literal><![CDATA[
      ((x * y) / x) * (x / y) = y * (x / T(y,x))
    ]]></literal>
    <justification jstring="[para(5530(a,1),5705(a,2,2))].">
      <j1 rule="para" parents="5530 5705"/>
    </justification>
  </clause>

  <clause id="5761">
    <literal><![CDATA[
      K(x / (x / y),y \ x) * K(z,x / (x / y)) = T(x / (x / y),z) \ y
    ]]></literal>
    <justification jstring="[para(4502(a,1),5720(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4502 5720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5765">
    <literal><![CDATA[
      L(x \ 1,T(x,y),y) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,4186,a(flip),b,5233,a)].">
      <j1 rule="hyper" parents="65 4186 5233"/>
    </justification>
  </clause>

  <clause id="5766">
    <literal><![CDATA[
      T(x * L(x \ 1,x,y),y) = T(x,y) * ((x * y) \ y)
    ]]></literal>
    <justification jstring="[para(5765(a,1),1861(a,1,1,2))].">
      <j1 rule="para" parents="5765 1861"/>
    </justification>
  </clause>

  <clause id="5767">
    <literal><![CDATA[
      x \ (y * T(y \ x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K((x \ y) \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(1383(a,1),5300(a,1))].">
      <j1 rule="para" parents="1383 5300"/>
    </justification>
  </clause>

  <clause id="5768">
    <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(2421(a,1),5300(a,1))].">
      <j1 rule="para" parents="2421 5300"/>
    </justification>
  </clause>

  <clause id="5769">
    <literal><![CDATA[
      x \ R(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * K(x * y,x) = z
    ]]></literal>
    <justification jstring="[para(5563(a,1),5360(a,1,2))].">
      <j1 rule="para" parents="5563 5360"/>
    </justification>
  </clause>

  <clause id="5770">
    <literal><![CDATA[
      K(x,y \ 1) * (y * y) != z
    ]]></literal>
    <literal><![CDATA[
      T(y \ 1,x) \ y = z
    ]]></literal>
    <justification jstring="[para(460(a,1),5388(a,1,2))].">
      <j1 rule="para" parents="460 5388"/>
    </justification>
  </clause>

  <clause id="5771">
    <literal><![CDATA[
      K(x,y \ z) * K(y,y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y \ z,x) \ (z / y) = u
    ]]></literal>
    <justification jstring="[para(5267(a,1),5388(a,1,2))].">
      <j1 rule="para" parents="5267 5388"/>
    </justification>
  </clause>

  <clause id="5772">
    <literal><![CDATA[
      x * T(x \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) * y = u
    ]]></literal>
    <justification jstring="[para(4955(a,2),5395(a,1))].">
      <j1 rule="para" parents="4955 5395"/>
    </justification>
  </clause>

  <clause id="5773">
    <literal><![CDATA[
      x * K(T(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * T(T(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(5036(a,2),5395(a,1,2))].">
      <j1 rule="para" parents="5036 5395"/>
    </justification>
  </clause>

  <clause id="5774">
    <literal><![CDATA[
      x * (K(y,x) * K(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * T(x,z) = u
    ]]></literal>
    <justification jstring="[para(5523(a,1),5395(a,1,2))].">
      <j1 rule="para" parents="5523 5395"/>
    </justification>
  </clause>

  <clause id="5775">
    <literal><![CDATA[
      K(x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * (x \ z) = u
    ]]></literal>
    <justification jstring="[para(10(a,1),5398(a,1,2))].">
      <j1 rule="para" parents="10 5398"/>
    </justification>
  </clause>

  <clause id="5777">
    <literal><![CDATA[
      K(x,y) * ((x \ 1) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * ((x * x) \ z) = u
    ]]></literal>
    <justification jstring="[para(738(a,1),5398(a,1,2))].">
      <j1 rule="para" parents="738 5398"/>
    </justification>
  </clause>

  <clause id="5779">
    <literal><![CDATA[
      T(x,y) * T(z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (z * x) = u
    ]]></literal>
    <justification jstring="[para(22(a,2),5417(a,1,2))].">
      <j1 rule="para" parents="22 5417"/>
    </justification>
  </clause>

  <clause id="5781">
    <literal><![CDATA[
      T(x,y) * K(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * T(x,z) = u
    ]]></literal>
    <justification jstring="[para(5036(a,2),5417(a,1,2))].">
      <j1 rule="para" parents="5036 5417"/>
    </justification>
  </clause>

  <clause id="5783">
    <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(5372(a,1),5417(a,1,2))].">
      <j1 rule="para" parents="5372 5417"/>
    </justification>
  </clause>

  <clause id="5789">
    <literal><![CDATA[
      K(x,y) * K(y,y * x) = y \ L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(2279,a,5583,a)].">
      <j1 rule="hyper" parents="2279 5583"/>
    </justification>
  </clause>

  <clause id="5790">
    <literal><![CDATA[
      K(x * y,x) * K(x,y) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(2279,a,5587,a)].">
      <j1 rule="hyper" parents="2279 5587"/>
    </justification>
  </clause>

  <clause id="5791">
    <literal><![CDATA[
      x \ R(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x * y,x) * K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5587(a,1),2279(a,1))].">
      <j1 rule="para" parents="5587 2279"/>
    </justification>
  </clause>

  <clause id="5792">
    <literal><![CDATA[
      T(x * K(L(y,x,x),x),(x \ 1) * y) = R(x,x \ L(y,x,x),x)
    ]]></literal>
    <justification jstring="[para(1679(a,1),5677(a,1,2))].">
      <j1 rule="para" parents="1679 5677"/>
    </justification>
  </clause>

  <clause id="5795">
    <literal><![CDATA[
      K(x,y) * K(y,x * y) = y \ L(y,x,y)
    ]]></literal>
    <justification jstring="[para(5685(a,2),5789(a,1,2))].">
      <j1 rule="para" parents="5685 5789"/>
    </justification>
  </clause>

  <clause id="5796">
    <literal><![CDATA[
      x \ R(x,x \ y,x) = K(y,x) * K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),5790(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 5790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5797">
    <literal><![CDATA[
      T(T(x * K(x \ y,x),y),z) = L(T(x,z),x \ T(y,x),x)
    ]]></literal>
    <justification jstring="[para(5013(a,1),4728(a,1,1,1))].">
      <j1 rule="para" parents="5013 4728"/>
    </justification>
  </clause>

  <clause id="5798">
    <literal><![CDATA[
      K(x,T(y,z) \ 1) = T(K(x,y \ 1),z)
    ]]></literal>
    <justification jstring="[para(5036(a,2),5070(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5036 5070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5800">
    <literal><![CDATA[
      K(x,T(1 / y,z) \ 1) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(79(a,1),5798(a,2,1,2))].">
      <j1 rule="para" parents="79 5798"/>
    </justification>
  </clause>

  <clause id="5801">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ 1) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(4793(a,1),5798(a,2,1))].">
      <j1 rule="para" parents="4793 5798"/>
    </justification>
  </clause>

  <clause id="5803">
    <literal><![CDATA[
      K(x,1 / T(1 / y,z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(65,a,4797,a,b,5800,a)].">
      <j1 rule="hyper" parents="65 4797 5800"/>
    </justification>
  </clause>

  <clause id="5804">
    <literal><![CDATA[
      K(x,1 / T(y,z)) = T(K(x,1 / y),z)
    ]]></literal>
    <justification jstring="[para(3173(a,1),5800(a,1,2))].">
      <j1 rule="para" parents="3173 5800"/>
    </justification>
  </clause>

  <clause id="5805">
    <literal><![CDATA[
      K(x,R(T(K(x,y),z),u,w)) = 1
    ]]></literal>
    <justification jstring="[para(5800(a,1),3595(a,1,2,1))].">
      <j1 rule="para" parents="5800 3595"/>
    </justification>
  </clause>

  <clause id="5806">
    <literal><![CDATA[
      K(x,y * K(z,y \ 1)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(5756(a,1),5800(a,1,2))].">
      <j1 rule="para" parents="5756 5800"/>
    </justification>
  </clause>

  <clause id="5807">
    <literal><![CDATA[
      T(x,y) != K(z,1 / T(u,y))
    ]]></literal>
    <literal><![CDATA[
      K(z,1 / u) = x
    ]]></literal>
    <justification jstring="[para(5804(a,2),51(a,1)),flip(a)].">
      <j1 rule="para" parents="5804 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5809">
    <literal><![CDATA[
      L(x,y,z) * K(u,L(x,y,z)) = L(x * K(u,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(37,a,5099,a,b,5131,a)].">
      <j1 rule="hyper" parents="37 5099 5131"/>
    </justification>
  </clause>

  <clause id="5810">
    <literal><![CDATA[
      L(L(x,y,z) * K(u,L(x,y,z)),w,v5) * u = u * L(L(x,w,v5),y,z)
    ]]></literal>
    <justification jstring="[para(30(a,1),5131(a,2,2))].">
      <j1 rule="para" parents="30 5131"/>
    </justification>
  </clause>

  <clause id="5813">
    <literal><![CDATA[
      R(x,y,z) * K(u,R(x,y,z)) = R(x * K(u,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(37,a,5099,a,b,5132,a)].">
      <j1 rule="hyper" parents="37 5099 5132"/>
    </justification>
  </clause>

  <clause id="5815">
    <literal><![CDATA[
      T(1 / (K(x,y) / x),y) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[para(5482(a,1),5136(a,1,1,2))].">
      <j1 rule="para" parents="5482 5136"/>
    </justification>
  </clause>

  <clause id="5816">
    <literal><![CDATA[
      (1 / (K(x,y) / x)) * y = y * (1 / (1 / x))
    ]]></literal>
    <justification jstring="[para(5815(a,1),107(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5815 107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5817">
    <literal><![CDATA[
      T(T(x * K(y,x),z),u) \ T(T(x,z),u) = K(T(T(x,z),u),y)
    ]]></literal>
    <justification jstring="[para(5245(a,2),5183(a,1,1,1))].">
      <j1 rule="para" parents="5245 5183"/>
    </justification>
  </clause>

  <clause id="5818">
    <literal><![CDATA[
      L(x,y,z * K(u,u \ z)) = L(x,y,(u \ z) * u)
    ]]></literal>
    <justification jstring="[para(287(a,1),5221(a,1,3)),flip(a)].">
      <j1 rule="para" parents="287 5221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5819">
    <literal><![CDATA[
      K(x,y) = (T(y,x) \ 1) * T(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(2783,a,5228,a),flip(a)].">
      <j1 rule="hyper" parents="2783 5228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5820">
    <literal><![CDATA[
      (T(x,y) \ 1) \ K(y,x) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,5819,a,b,xx)].">
      <j1 rule="hyper" parents="119 5819"/>
    </justification>
  </clause>

  <clause id="5822">
    <literal><![CDATA[
      T(x * K(y,x),(x * K(y,x)) \ 1) = (x \ 1) \ K(y,x * K(y,x))
    ]]></literal>
    <justification jstring="[para(5053(a,1),5820(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5053 5820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5823">
    <literal><![CDATA[
      T(x,y \ (y \ 1)) = x * K(y * y,x)
    ]]></literal>
    <justification jstring="[hyper(1060,a,5236,a)].">
      <j1 rule="hyper" parents="1060 5236"/>
    </justification>
  </clause>

  <clause id="5824">
    <literal><![CDATA[
      ((x * x) \ y) * K(x * x,y) = y / (x * x)
    ]]></literal>
    <justification jstring="[hyper(667,a,5236,a)].">
      <j1 rule="hyper" parents="667 5236"/>
    </justification>
  </clause>

  <clause id="5825">
    <literal><![CDATA[
      x * K(y * y,x) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (y \ 1)) = z
    ]]></literal>
    <justification jstring="[para(5236(a,1),1060(a,1))].">
      <j1 rule="para" parents="5236 1060"/>
    </justification>
  </clause>

  <clause id="5826">
    <literal><![CDATA[
      a(x,y,T(1 / z,u \ (u \ 1))) = a(x,y,z * K(u * u,1 / z))
    ]]></literal>
    <justification jstring="[para(5823(a,2),2360(a,1,3))].">
      <j1 rule="para" parents="5823 2360"/>
    </justification>
  </clause>

  <clause id="5827">
    <literal><![CDATA[
      L(x * K(y,x),z,u) / L(x,z,u) = K(y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(120,a,5249,a,b,5101,a(flip))].">
      <j1 rule="hyper" parents="120 5249 5101"/>
    </justification>
  </clause>

  <clause id="5828">
    <literal><![CDATA[
      (x * x) \ L(y * K(x * x,y),z,u) = L(y,z,u) / (x * x)
    ]]></literal>
    <justification jstring="[hyper(119,a,5249,a,b,849,a(flip))].">
      <j1 rule="hyper" parents="119 5249 849"/>
    </justification>
  </clause>

  <clause id="5829">
    <literal><![CDATA[
      L(x,y,z) / L(x * K(u,x),y,z) = K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(5249(a,2),5180(a,2,2)),flip(a)].">
      <j1 rule="para" parents="5249 5180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5830">
    <literal><![CDATA[
      L(x * K(y,x),z,u) / L(x,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,L(x,z,u)) = w
    ]]></literal>
    <justification jstring="[para(5249(a,2),5284(a,1,1))].">
      <j1 rule="para" parents="5249 5284"/>
    </justification>
  </clause>

  <clause id="5831">
    <literal><![CDATA[
      R(x,y,z) \ R(x * K(u,x),y,z) = K(u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,5250,a,b,5054,a(flip))].">
      <j1 rule="hyper" parents="119 5250 5054"/>
    </justification>
  </clause>

  <clause id="5832">
    <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(5250(a,2),4548(a,1,1))].">
      <j1 rule="para" parents="5250 4548"/>
    </justification>
  </clause>

  <clause id="5833">
    <literal><![CDATA[
      R(x * K(y,x),z,u) \ R(x,z,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(5250(a,2),5029(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5250 5029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5835">
    <literal><![CDATA[
      (x \ T(y,x \ 1)) / (x \ y) = K(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(120,a,4229,a,b,5322,a)].">
      <j1 rule="hyper" parents="120 4229 5322"/>
    </justification>
  </clause>

  <clause id="5836">
    <literal><![CDATA[
      (x * T(x \ y,z)) / y = K(1 / (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(299,a,3565,a,b,5325,a),flip(a)].">
      <j1 rule="hyper" parents="299 3565 5325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5837">
    <literal><![CDATA[
      (x * (y * T(y \ (x \ z),u))) / z = K(((x * y) / z) \ 1,u)
    ]]></literal>
    <justification jstring="[para(998(a,1),5325(a,1,1))].">
      <j1 rule="para" parents="998 5325"/>
    </justification>
  </clause>

  <clause id="5838">
    <literal><![CDATA[
      x \ (y * (z * T(z \ (y \ x),u))) = K((x \ (y * z)) \ 1,u)
    ]]></literal>
    <justification jstring="[para(998(a,1),5326(a,1,2))].">
      <j1 rule="para" parents="998 5326"/>
    </justification>
  </clause>

  <clause id="5839">
    <literal><![CDATA[
      x \ (((y \ (x * z)) * y) / z) = K((x \ (y / z)) \ 1,y)
    ]]></literal>
    <justification jstring="[para(1520(a,1),5326(a,1,2))].">
      <j1 rule="para" parents="1520 5326"/>
    </justification>
  </clause>

  <clause id="5840">
    <literal><![CDATA[
      T(x,y) \ T(z * T(z \ x,u),y) = K((T(x,y) \ T(z,y)) \ 1,u)
    ]]></literal>
    <justification jstring="[para(2160(a,1),5326(a,1,2))].">
      <j1 rule="para" parents="2160 5326"/>
    </justification>
  </clause>

  <clause id="5841">
    <literal><![CDATA[
      x \ T(x * y,z) = y * K((y \ (x \ 1)) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(1140,a,5328,a)].">
      <j1 rule="hyper" parents="1140 5328"/>
    </justification>
  </clause>

  <clause id="5842">
    <literal><![CDATA[
      x * K((x \ (y * z)) \ 1,u) = y * (z * T(z \ (y \ x),u))
    ]]></literal>
    <justification jstring="[hyper(1014,a,5328,a),flip(a)].">
      <j1 rule="hyper" parents="1014 5328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5843">
    <literal><![CDATA[
      (x * y) * K(((x * y) \ y) \ 1,z) = T(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(807,a,5328,a),flip(a)].">
      <j1 rule="hyper" parents="807 5328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5844">
    <literal><![CDATA[
      x \ (y * K((y \ x) \ 1,z)) = T(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,5328,a)].">
      <j1 rule="hyper" parents="125 5328"/>
    </justification>
  </clause>

  <clause id="5845">
    <literal><![CDATA[
      ((x \ (y / z)) * x) * z = y * K((y \ (x * z)) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,1596,a(flip),b,5328,a)].">
      <j1 rule="hyper" parents="65 1596 5328"/>
    </justification>
  </clause>

  <clause id="5846">
    <literal><![CDATA[
      T(K(x / y,z),x) = K((x \ y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(235,a,5057,a,b,5328,a(flip))].">
      <j1 rule="hyper" parents="235 5057 5328"/>
    </justification>
  </clause>

  <clause id="5847">
    <literal><![CDATA[
      (x * K((x \ y) \ 1,z)) / y = T(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(120,a,5328,a(flip),b,432,a)].">
      <j1 rule="hyper" parents="120 5328 432"/>
    </justification>
  </clause>

  <clause id="5848">
    <literal><![CDATA[
      x * T(x \ y,z) != y * u
    ]]></literal>
    <literal><![CDATA[
      K((y \ x) \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(5328(a,2),45(a,1))].">
      <j1 rule="para" parents="5328 45"/>
    </justification>
  </clause>

  <clause id="5849">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ y,z) = y * K((T(y,x) \ x) \ 1,z)
    ]]></literal>
    <justification jstring="[para(4396(a,2),5328(a,2,2,1,1))].">
      <j1 rule="para" parents="4396 5328"/>
    </justification>
  </clause>

  <clause id="5850">
    <literal><![CDATA[
      K(((x \ 1) / (x \ y)) \ 1,z) * (x \ y) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,1109,a(flip),b,5329,a),flip(a)].">
      <j1 rule="hyper" parents="299 1109 5329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5852">
    <literal><![CDATA[
      K((x / y) \ 1,z) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(37,a,5057,a,b,5329,a),flip(a)].">
      <j1 rule="hyper" parents="37 5057 5329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5853">
    <literal><![CDATA[
      K((x / (x * y)) \ 1,z) * (x * y) = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),5329(a,2,2,1))].">
      <j1 rule="para" parents="9 5329"/>
    </justification>
  </clause>

  <clause id="5854">
    <literal><![CDATA[
      x / (y * T(y \ x,z)) = K(z,(y / x) \ 1)
    ]]></literal>
    <justification jstring="[para(5329(a,1),5430(a,1,2))].">
      <j1 rule="para" parents="5329 5430"/>
    </justification>
  </clause>

  <clause id="5855">
    <literal><![CDATA[
      K(1 / (x / y),z) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(5559,a,5852,a)].">
      <j1 rule="hyper" parents="5559 5852"/>
    </justification>
  </clause>

  <clause id="5856">
    <literal><![CDATA[
      R(K(x / y,z),x / y,u) = K((y / x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,4564,a,b,5852,a)].">
      <j1 rule="hyper" parents="299 4564 5852"/>
    </justification>
  </clause>

  <clause id="5857">
    <literal><![CDATA[
      K((x / y) \ 1,x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,5192,a(flip),b,5852,a),flip(a)].">
      <j1 rule="hyper" parents="299 5192 5852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5858">
    <literal><![CDATA[
      K(x / (y * x),z) = K(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),5852(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11 5852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5859">
    <literal><![CDATA[
      K((x / (y * x)) \ 1,z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),5852(a,2,1))].">
      <j1 rule="para" parents="11 5852"/>
    </justification>
  </clause>

  <clause id="5860">
    <literal><![CDATA[
      K((x \ y) / y,z) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(76(a,1),5852(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="76 5852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5861">
    <literal><![CDATA[
      K(x / y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K((y / x) \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(5855(a,1),5560(a,1))].">
      <j1 rule="para" parents="5855 5560"/>
    </justification>
  </clause>

  <clause id="5862">
    <literal><![CDATA[
      ((x * y) \ y) * (x * y) = y * K(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[para(5858(a,1),5289(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5858 5289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5863">
    <literal><![CDATA[
      K(x / (y * x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(1 / y,z) = u
    ]]></literal>
    <justification jstring="[para(5858(a,2),5559(a,1))].">
      <j1 rule="para" parents="5858 5559"/>
    </justification>
  </clause>

  <clause id="5866">
    <literal><![CDATA[
      (x \ (y \ x)) * x = (y \ x) * K(y \ 1,x)
    ]]></literal>
    <justification jstring="[para(5860(a,1),5289(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5860 5289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5867">
    <literal><![CDATA[
      (x / y) * (K(y \ x,y) * z) = (y \ x) * z
    ]]></literal>
    <justification jstring="[para(5192(a,1),5359(a,1,2,1))].">
      <j1 rule="para" parents="5192 5359"/>
    </justification>
  </clause>

  <clause id="5868">
    <literal><![CDATA[
      (x * K(y,x)) * K(x,z) = T(x,z) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,5488,a,b,5362,a)].">
      <j1 rule="hyper" parents="65 5488 5362"/>
    </justification>
  </clause>

  <clause id="5869">
    <literal><![CDATA[
      x * K(y,z) != z * (K(y,z) * K(z,u))
    ]]></literal>
    <literal><![CDATA[
      T(z,u) = x
    ]]></literal>
    <justification jstring="[para(5362(a,2),46(a,1)),flip(a)].">
      <j1 rule="para" parents="5362 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5870">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ y,z) != y * u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(5365(a,2),236(a,2)),flip(a)].">
      <j1 rule="para" parents="5365 236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5871">
    <literal><![CDATA[
      (x \ y) * ((y / x) \ z) = K(x \ y,x) * z
    ]]></literal>
    <justification jstring="[para(5192(a,1),5375(a,2,1))].">
      <j1 rule="para" parents="5192 5375"/>
    </justification>
  </clause>

  <clause id="5872">
    <literal><![CDATA[
      T(T(x,y),z) * K(y,x) = x * K(T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(3638,a,5392,a)].">
      <j1 rule="hyper" parents="3638 5392"/>
    </justification>
  </clause>

  <clause id="5873">
    <literal><![CDATA[
      (x \ y) \ ((y / x) * z) = K(x,x \ y) * z
    ]]></literal>
    <justification jstring="[hyper(119,a,5410,a(flip),b,5524,a(flip))].">
      <j1 rule="hyper" parents="119 5410 5524"/>
    </justification>
  </clause>

  <clause id="5875">
    <literal><![CDATA[
      T(x,x \ y) * ((x \ y) * z) = x * ((y / x) * z)
    ]]></literal>
    <justification jstring="[para(5410(a,1),5055(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5410 5055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5877">
    <literal><![CDATA[
      K(x,y) * ((x * x) * z) = (x * T(x,y)) * z
    ]]></literal>
    <justification jstring="[para(239(a,1),5415(a,2,1))].">
      <j1 rule="para" parents="239 5415"/>
    </justification>
  </clause>

  <clause id="5878">
    <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(5468(a,1),314(a,1,2))].">
      <j1 rule="para" parents="5468 314"/>
    </justification>
  </clause>

  <clause id="5879">
    <literal><![CDATA[
      T(T(x,(x * K(y,x)) * z) * K(y,T(x,(x * K(y,x)) * z)),u) = T(T(x * K(y,x),u),z * (x * K(y,x)))
    ]]></literal>
    <justification jstring="[para(5468(a,2),4373(a,1,1))].">
      <j1 rule="para" parents="5468 4373"/>
    </justification>
  </clause>

  <clause id="5880">
    <literal><![CDATA[
      T(T(1 / ((x * y) \ x),z),y) = T(1 / ((x * y) \ x),z)
    ]]></literal>
    <justification jstring="[para(5474(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5474 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5882">
    <literal><![CDATA[
      K(x \ y,x) * (x \ z) != u
    ]]></literal>
    <literal><![CDATA[
      ((x \ y) \ y) \ z = u
    ]]></literal>
    <justification jstring="[para(5513(a,1),5438(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5513 5438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5883">
    <literal><![CDATA[
      T(x,y) \ (T(x,y) \ z) = x \ (T(T(x,y),y) \ z)
    ]]></literal>
    <justification jstring="[hyper(119,a,5527,a(flip),b,5060,a),flip(a)].">
      <j1 rule="hyper" parents="119 5527 5060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5884">
    <literal><![CDATA[
      ((x / y) / x) * z != (x / y) * K(x,1 / y)
    ]]></literal>
    <literal><![CDATA[
      T(x,(x / y) / x) = z
    ]]></literal>
    <justification jstring="[para(5541(a,2),236(a,2))].">
      <j1 rule="para" parents="5541 236"/>
    </justification>
  </clause>

  <clause id="5886">
    <literal><![CDATA[
      K(x,y) = (x * y) * ((y * x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,722,a(flip),b,5589,a)].">
      <j1 rule="hyper" parents="65 722 5589"/>
    </justification>
  </clause>

  <clause id="5888">
    <literal><![CDATA[
      K(x \ (y * ((z \ 1) \ 1)),u) = K(x \ (y * z),u)
    ]]></literal>
    <justification jstring="[para(2770(a,1),5610(a,1,1,2))].">
      <j1 rule="para" parents="2770 5610"/>
    </justification>
  </clause>

  <clause id="5889">
    <literal><![CDATA[
      K(x \ ((1 / y) \ z),u) = K(x \ ((y \ 1) \ z),u)
    ]]></literal>
    <justification jstring="[para(3222(a,1),5610(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3222 5610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5890">
    <literal><![CDATA[
      K(x \ ((1 / y) * z),u) = K(x \ ((y \ 1) * z),u)
    ]]></literal>
    <justification jstring="[para(3223(a,1),5610(a,1,1,2))].">
      <j1 rule="para" parents="3223 5610"/>
    </justification>
  </clause>

  <clause id="5891">
    <literal><![CDATA[
      K(x \ (y * (((y \ z) \ 1) \ 1)),u) = K(x \ z,u)
    ]]></literal>
    <justification jstring="[para(4875(a,1),5610(a,1,1,2))].">
      <j1 rule="para" parents="4875 5610"/>
    </justification>
  </clause>

  <clause id="5892">
    <literal><![CDATA[
      K(x \ R(1 / y,z,u),w) = K(x \ R(y \ 1,z,u),w)
    ]]></literal>
    <justification jstring="[para(2976(a,1),5611(a,1,1,2))].">
      <j1 rule="para" parents="2976 5611"/>
    </justification>
  </clause>

  <clause id="5893">
    <literal><![CDATA[
      K((((x \ 1) \ 1) \ y) \ z,u) = K((x \ y) \ z,u)
    ]]></literal>
    <justification jstring="[para(2706(a,1),5622(a,1,1,1))].">
      <j1 rule="para" parents="2706 5622"/>
    </justification>
  </clause>

  <clause id="5894">
    <literal><![CDATA[
      K(((1 / x) / y) \ z,u) = K(((x \ 1) / y) \ z,u)
    ]]></literal>
    <justification jstring="[para(2755(a,1),5622(a,1,1,1))].">
      <j1 rule="para" parents="2755 5622"/>
    </justification>
  </clause>

  <clause id="5895">
    <literal><![CDATA[
      K((x * (K(y,y \ 1) * z)) \ u,w) = K((x * z) \ u,w)
    ]]></literal>
    <justification jstring="[para(3301(a,1),5622(a,1,1,1))].">
      <j1 rule="para" parents="3301 5622"/>
    </justification>
  </clause>

  <clause id="5896">
    <literal><![CDATA[
      K((((1 / x) \ y) \ z) \ u,w) = K((((x \ 1) \ y) \ z) \ u,w)
    ]]></literal>
    <justification jstring="[para(3453(a,1),5622(a,1,1,1))].">
      <j1 rule="para" parents="3453 5622"/>
    </justification>
  </clause>

  <clause id="5897">
    <literal><![CDATA[
      K(x / ((1 / y) * z),u) = K(x / ((y \ 1) * z),u)
    ]]></literal>
    <justification jstring="[para(2727(a,1),5625(a,1,1,2))].">
      <j1 rule="para" parents="2727 5625"/>
    </justification>
  </clause>

  <clause id="5898">
    <literal><![CDATA[
      K(x / (y * (1 / z)),u) = K(x / (y * (z \ 1)),u)
    ]]></literal>
    <justification jstring="[para(3218(a,1),5625(a,1,1,2))].">
      <j1 rule="para" parents="3218 5625"/>
    </justification>
  </clause>

  <clause id="5899">
    <literal><![CDATA[
      K(x,(y \ (1 / z)) \ u) = K(x,(y \ (z \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(3370(a,1),5650(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3370 5650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5900">
    <literal><![CDATA[
      K(x,y \ (((z \ 1) \ 1) * u)) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[para(2725(a,1),5651(a,1,2,2))].">
      <j1 rule="para" parents="2725 5651"/>
    </justification>
  </clause>

  <clause id="5901">
    <literal><![CDATA[
      K(x,T((1 / y) * z,u)) = K(x,T((y \ 1) * z,u))
    ]]></literal>
    <justification jstring="[para(3223(a,1),5654(a,1,2,1))].">
      <j1 rule="para" parents="3223 5654"/>
    </justification>
  </clause>

  <clause id="5902">
    <literal><![CDATA[
      K(x,y * (((z \ 1) \ 1) \ u)) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[para(2706(a,1),5657(a,1,2,2))].">
      <j1 rule="para" parents="2706 5657"/>
    </justification>
  </clause>

  <clause id="5903">
    <literal><![CDATA[
      K(x,y * ((1 / z) * u)) = K(x,y * ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[para(2727(a,1),5657(a,1,2,2))].">
      <j1 rule="para" parents="2727 5657"/>
    </justification>
  </clause>

  <clause id="5904">
    <literal><![CDATA[
      K(x,y * (((1 / z) * u) * w)) = K(x,y * (((z \ 1) * u) * w))
    ]]></literal>
    <justification jstring="[para(2735(a,1),5657(a,1,2,2))].">
      <j1 rule="para" parents="2735 5657"/>
    </justification>
  </clause>

  <clause id="5905">
    <literal><![CDATA[
      K(x,y * (z * ((1 / u) \ w))) = K(x,y * (z * ((u \ 1) \ w)))
    ]]></literal>
    <justification jstring="[para(3337(a,1),5657(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3337 5657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5906">
    <literal><![CDATA[
      K(x,y * (z * (u * (1 / w)))) = K(x,y * (z * (u * (w \ 1))))
    ]]></literal>
    <justification jstring="[para(3340(a,1),5657(a,1,2,2))].">
      <j1 rule="para" parents="3340 5657"/>
    </justification>
  </clause>

  <clause id="5907">
    <literal><![CDATA[
      K(x,y * (T(1 / z,u) \ w)) = K(x,y * (T(z \ 1,u) \ w))
    ]]></literal>
    <justification jstring="[para(3692(a,1),5657(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3692 5657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5909">
    <literal><![CDATA[
      K(x,(y / ((z \ 1) \ 1)) / u) = K(x,(y / z) / u)
    ]]></literal>
    <justification jstring="[para(3240(a,1),5661(a,1,2,1))].">
      <j1 rule="para" parents="3240 5661"/>
    </justification>
  </clause>

  <clause id="5910">
    <literal><![CDATA[
      K(x,((((y \ 1) \ 1) * z) \ u) \ w) = K(x,((y * z) \ u) \ w)
    ]]></literal>
    <justification jstring="[para(3280(a,1),5663(a,1,2,1))].">
      <j1 rule="para" parents="3280 5663"/>
    </justification>
  </clause>

  <clause id="5911">
    <literal><![CDATA[
      K(x,(y * (z / (1 / u))) \ w) = K(x,(y * (z / (u \ 1))) \ w)
    ]]></literal>
    <justification jstring="[para(3339(a,1),5663(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3339 5663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5912">
    <literal><![CDATA[
      K(x,y / (((z \ 1) \ 1) * u)) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[para(2725(a,1),5667(a,1,2,2))].">
      <j1 rule="para" parents="2725 5667"/>
    </justification>
  </clause>

  <clause id="5913">
    <literal><![CDATA[
      K(x,y / ((1 / z) * u)) = K(x,y / ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[para(2727(a,1),5667(a,1,2,2))].">
      <j1 rule="para" parents="2727 5667"/>
    </justification>
  </clause>

  <clause id="5914">
    <literal><![CDATA[
      K(x,y / ((1 / z) \ u)) = K(x,y / ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(2736(a,1),5667(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2736 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5915">
    <literal><![CDATA[
      K(x,y / (z * (1 / u))) = K(x,y / (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(3218(a,1),5667(a,1,2,2))].">
      <j1 rule="para" parents="3218 5667"/>
    </justification>
  </clause>

  <clause id="5917">
    <literal><![CDATA[
      T(x,y) \ T(z / (z / x),y) = K(x \ z,T(x,y))
    ]]></literal>
    <justification jstring="[para(5002(a,2),5682(a,1,2,1))].">
      <j1 rule="para" parents="5002 5682"/>
    </justification>
  </clause>

  <clause id="5918">
    <literal><![CDATA[
      K(x,x \ y) * ((y / x) \ z) = (x \ y) \ z
    ]]></literal>
    <justification jstring="[hyper(5437,a,5692,a)].">
      <j1 rule="hyper" parents="5437 5692"/>
    </justification>
  </clause>

  <clause id="5919">
    <literal><![CDATA[
      T(x,x \ y) \ ((x \ y) \ z) = x \ ((y / x) \ z)
    ]]></literal>
    <justification jstring="[hyper(119,a,5692,a(flip),b,5060,a),flip(a)].">
      <j1 rule="hyper" parents="119 5692 5060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5920">
    <literal><![CDATA[
      K(x \ y,x) * T(z,x \ y) = (y / x) \ (z * (x \ y))
    ]]></literal>
    <justification jstring="[para(22(a,2),5692(a,1,2))].">
      <j1 rule="para" parents="22 5692"/>
    </justification>
  </clause>

  <clause id="5921">
    <literal><![CDATA[
      K(T(x,y),T(y,x) / x) * (((T(y,x) / x) \ y) \ z) = (y / (T(y,x) / x)) \ z
    ]]></literal>
    <justification jstring="[para(4415(a,1),5692(a,1,1,1))].">
      <j1 rule="para" parents="4415 5692"/>
    </justification>
  </clause>

  <clause id="5922">
    <literal><![CDATA[
      T(x,x \ y) * ((y / x) \ z) = x * ((x \ y) \ z)
    ]]></literal>
    <justification jstring="[para(5692(a,1),5387(a,1,2))].">
      <j1 rule="para" parents="5692 5387"/>
    </justification>
  </clause>

  <clause id="5924">
    <literal><![CDATA[
      x * (K(x \ y,x) * K(y / (y / x),z)) = T(y / (y / x),z)
    ]]></literal>
    <justification jstring="[hyper(5087,a,5713,a),flip(a)].">
      <j1 rule="hyper" parents="5087 5713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5928">
    <literal><![CDATA[
      (x / y) * T(y \ x,y) = (y \ x) * (y \ x)
    ]]></literal>
    <justification jstring="[para(5049(a,1),5714(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5049 5714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5929">
    <literal><![CDATA[
      (x \ y) * (T(x,x \ y) * z) = (y / x) * (x * z)
    ]]></literal>
    <justification jstring="[para(5103(a,1),5714(a,1,2))].">
      <j1 rule="para" parents="5103 5714"/>
    </justification>
  </clause>

  <clause id="5931">
    <literal><![CDATA[
      K(x,x \ y) * ((x \ y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      (y / x) * z = u
    ]]></literal>
    <justification jstring="[para(5718(a,1),5438(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5718 5438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5932">
    <literal><![CDATA[
      (x / (x / y)) * ((x / y) * z) = y * ((y \ x) * z)
    ]]></literal>
    <justification jstring="[para(5718(a,1),5713(a,2,2))].">
      <j1 rule="para" parents="5718 5713"/>
    </justification>
  </clause>

  <clause id="5933">
    <literal><![CDATA[
      (x \ y) * (y / T(x \ y,y)) = ((y * (x \ y)) / y) * x
    ]]></literal>
    <justification jstring="[para(76(a,1),5760(a,1,2)),flip(a)].">
      <j1 rule="para" parents="76 5760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5934">
    <literal><![CDATA[
      K(1 / ((1 / x) / y),z) = (T(y * x,z) / x) / y
    ]]></literal>
    <justification jstring="[para(1117(a,1),5836(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1117 5836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5935">
    <literal><![CDATA[
      (x * y) \ (y * K(T(x,y) \ 1,z)) = T((x * y) \ y,z)
    ]]></literal>
    <justification jstring="[para(22(a,2),5844(a,1,2,2,1,1))].">
      <j1 rule="para" parents="22 5844"/>
    </justification>
  </clause>

  <clause id="5937">
    <literal><![CDATA[
      K(x,(y / z) \ 1) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(65,a,5597,a(flip),b,5854,a),flip(a)].">
      <j1 rule="hyper" parents="65 5597 5854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5939">
    <literal><![CDATA[
      R(K(x,y / z),y / z,u) = K(x,(z / y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,4778,a,b,5937,a)].">
      <j1 rule="hyper" parents="299 4778 5937"/>
    </justification>
  </clause>

  <clause id="5940">
    <literal><![CDATA[
      K(x,1 / (y / z)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(65,a,4797,a,b,5937,a)].">
      <j1 rule="hyper" parents="65 4797 5937"/>
    </justification>
  </clause>

  <clause id="5941">
    <literal><![CDATA[
      K(x,y / (z * y)) = K(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(11(a,1),5937(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11 5937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5943">
    <literal><![CDATA[
      K(x,(y \ z) / z) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(76(a,1),5937(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="76 5937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5944">
    <literal><![CDATA[
      K(x,y / (z * y)) = K(x,1 / z)
    ]]></literal>
    <justification jstring="[para(11(a,1),5940(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 5940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5946">
    <literal><![CDATA[
      R(K(x,y / (z * y)),y / (z * y),u) = K(x,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,4778,a,b,5941,a)].">
      <j1 rule="hyper" parents="65 4778 5941"/>
    </justification>
  </clause>

  <clause id="5948">
    <literal><![CDATA[
      K(x * y,x \ 1) * ((x * y) \ y) = y / (x * y)
    ]]></literal>
    <justification jstring="[para(5941(a,1),5117(a,1,1))].">
      <j1 rule="para" parents="5941 5117"/>
    </justification>
  </clause>

  <clause id="5951">
    <literal><![CDATA[
      ((x * y) \ y) * K(x * y,1 / x) = y / (x * y)
    ]]></literal>
    <justification jstring="[para(5944(a,1),5112(a,1,2))].">
      <j1 rule="para" parents="5944 5112"/>
    </justification>
  </clause>

  <clause id="5952">
    <literal><![CDATA[
      K(x,y / (z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(5944(a,2),5408(a,1))].">
      <j1 rule="para" parents="5944 5408"/>
    </justification>
  </clause>

  <clause id="5953">
    <literal><![CDATA[
      K(x,(y \ z) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ 1) = u
    ]]></literal>
    <justification jstring="[para(10(a,1),5952(a,1,2,2))].">
      <j1 rule="para" parents="10 5952"/>
    </justification>
  </clause>

  <clause id="5954">
    <literal><![CDATA[
      (x * K(y,x)) \ L(x,y,x) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(119,a,5561,a(flip),b,5868,a)].">
      <j1 rule="hyper" parents="119 5561 5868"/>
    </justification>
  </clause>

  <clause id="5955">
    <literal><![CDATA[
      (x \ y) \ (y / (y / x)) = (y / x) \ x
    ]]></literal>
    <justification jstring="[hyper(119,a,5007,a,b,5871,a)].">
      <j1 rule="hyper" parents="119 5007 5871"/>
    </justification>
  </clause>

  <clause id="5956">
    <literal><![CDATA[
      (x / (x / y)) \ (x / y) = y \ (x / (x / (x / y)))
    ]]></literal>
    <justification jstring="[para(79(a,1),5955(a,1,1)),flip(a)].">
      <j1 rule="para" parents="79 5955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5957">
    <literal><![CDATA[
      (x \ 1) \ ((x \ 1) \ 1) = (1 / x) \ x
    ]]></literal>
    <justification jstring="[para(1691(a,1),5955(a,1,2))].">
      <j1 rule="para" parents="1691 5955"/>
    </justification>
  </clause>

  <clause id="5958">
    <literal><![CDATA[
      T(x / ((1 / y) \ z),(1 / y) \ y) = (y \ 1) * (y \ (x / (y \ z)))
    ]]></literal>
    <justification jstring="[para(5957(a,1),4077(a,1,2))].">
      <j1 rule="para" parents="5957 4077"/>
    </justification>
  </clause>

  <clause id="5959">
    <literal><![CDATA[
      (x \ y) \ T(z * (x \ 1),(1 / x) \ x) = ((1 / x) \ y) \ (z * ((x \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(5957(a,1),4097(a,1,2,2))].">
      <j1 rule="para" parents="5957 4097"/>
    </justification>
  </clause>

  <clause id="5960">
    <literal><![CDATA[
      L(x,y,(z * T(z,u)) * w) = L(x,y,K(z,u) * w)
    ]]></literal>
    <justification jstring="[para(5877(a,1),2895(a,1,3))].">
      <j1 rule="para" parents="5877 2895"/>
    </justification>
  </clause>

  <clause id="5963">
    <literal><![CDATA[
      (R(T(x,y),z,u) * (z * u)) / ((x * z) * u) = R(K(R(x,z,u),y),R(x,z,u),z * u)
    ]]></literal>
    <justification jstring="[para(5146(a,1),573(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5146 573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5966">
    <literal><![CDATA[
      R(x * K(y,x),y,x) = x * K(y * x,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,5054,a(flip),b,5242,a),flip(a)].">
      <j1 rule="hyper" parents="299 5054 5242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5967">
    <literal><![CDATA[
      K(x * (y * y),y * y) = K(x,y * y)
    ]]></literal>
    <justification jstring="[hyper(555,a,5966,a)].">
      <j1 rule="hyper" parents="555 5966"/>
    </justification>
  </clause>

  <clause id="5968">
    <literal><![CDATA[
      ((x * K(y,x)) \ ((y * (x * y)) / y)) \ ((y * (x * y)) / y) = x
    ]]></literal>
    <justification jstring="[para(5257(a,2),4359(a,1,1))].">
      <j1 rule="para" parents="5257 4359"/>
    </justification>
  </clause>

  <clause id="5975">
    <literal><![CDATA[
      ((x * y) / x) * z != u
    ]]></literal>
    <literal><![CDATA[
      y * (K(x,y) * z) = u
    ]]></literal>
    <justification jstring="[para(5054(a,2),5489(a,1,1))].">
      <j1 rule="para" parents="5054 5489"/>
    </justification>
  </clause>

  <clause id="5980">
    <literal><![CDATA[
      K(x * y,y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(5555,a,5675,a)].">
      <j1 rule="hyper" parents="5555 5675"/>
    </justification>
  </clause>

  <clause id="5981">
    <literal><![CDATA[
      K((x \ 1) \ y,y) = K(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,5741,a,b,5980,a)].">
      <j1 rule="hyper" parents="299 5741 5980"/>
    </justification>
  </clause>

  <clause id="5982">
    <literal><![CDATA[
      K(x * (y / x),x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(12(a,1),5980(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12 5980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5983">
    <literal><![CDATA[
      K(x,y) * K(y * x,x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[para(5980(a,2),5587(a,1,2))].">
      <j1 rule="para" parents="5980 5587"/>
    </justification>
  </clause>

  <clause id="5984">
    <literal><![CDATA[
      K(x * y,y) * K(y,x) = y \ R(y,x,y)
    ]]></literal>
    <justification jstring="[para(5980(a,2),5790(a,1,1))].">
      <j1 rule="para" parents="5980 5790"/>
    </justification>
  </clause>

  <clause id="5985">
    <literal><![CDATA[
      T(x,y) \ T(x * K(x * z,x),y) = K(z * x,T(x,y))
    ]]></literal>
    <justification jstring="[para(5980(a,1),5682(a,1,2,1,2))].">
      <j1 rule="para" parents="5980 5682"/>
    </justification>
  </clause>

  <clause id="5986">
    <literal><![CDATA[
      K((1 / x) * y,y) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[para(79(a,1),5981(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 5981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5987">
    <literal><![CDATA[
      ((x \ 1) \ y) * K(x * y,y) = T((x \ 1) \ y,y)
    ]]></literal>
    <justification jstring="[para(5981(a,1),5083(a,2,2)),flip(a)].">
      <j1 rule="para" parents="5981 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5988">
    <literal><![CDATA[
      T(x,T(1 / y,z) \ x) * K(T(y \ 1,z) \ 1,x) = L(x,T(1 / y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[para(3568(a,1),5584(a,1,2))].">
      <j1 rule="para" parents="3568 5584"/>
    </justification>
  </clause>

  <clause id="5989">
    <literal><![CDATA[
      K(x,(y / z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(5854(a,1),5598(a,1))].">
      <j1 rule="para" parents="5854 5598"/>
    </justification>
  </clause>

  <clause id="5991">
    <literal><![CDATA[
      K(x,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,1 / y) = z
    ]]></literal>
    <justification jstring="[para(74(a,1),5989(a,1,2,1))].">
      <j1 rule="para" parents="74 5989"/>
    </justification>
  </clause>

  <clause id="5992">
    <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(104(a,2),5989(a,1,2,1))].">
      <j1 rule="para" parents="104 5989"/>
    </justification>
  </clause>

  <clause id="5993">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,1 / (1 / y)) = z
    ]]></literal>
    <justification jstring="[para(79(a,1),5991(a,1,2))].">
      <j1 rule="para" parents="79 5991"/>
    </justification>
  </clause>

  <clause id="5995">
    <literal><![CDATA[
      T(T(x * K(x * y,x),z),y) = R(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,27,a,b,5678,a),flip(a)].">
      <j1 rule="hyper" parents="299 27 5678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5996">
    <literal><![CDATA[
      K(x,L(y,x,x \ 1)) * (y * x) = x * ((y * x) / x)
    ]]></literal>
    <justification jstring="[para(5680(a,1),5753(a,1,1))].">
      <j1 rule="para" parents="5680 5753"/>
    </justification>
  </clause>

  <clause id="5997">
    <literal><![CDATA[
      x \ (y * K(x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (x \ y) = z
    ]]></literal>
    <justification jstring="[para(3618(a,1),5700(a,1,2))].">
      <j1 rule="para" parents="3618 5700"/>
    </justification>
  </clause>

  <clause id="5999">
    <literal><![CDATA[
      L(x,y,T(T(z,u),u * z)) = L(x,y,L(z,u,z))
    ]]></literal>
    <justification jstring="[para(4373(a,1),5732(a,1,3))].">
      <j1 rule="para" parents="4373 5732"/>
    </justification>
  </clause>

  <clause id="6000">
    <literal><![CDATA[
      T(x,y) * L(T(z,x),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (L(z,u,w) * x) = v5
    ]]></literal>
    <justification jstring="[para(25(a,2),5779(a,1,2))].">
      <j1 rule="para" parents="25 5779"/>
    </justification>
  </clause>

  <clause id="6001">
    <literal><![CDATA[
      K((x / y) \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(5856(a,1),556(a,1))].">
      <j1 rule="para" parents="5856 556"/>
    </justification>
  </clause>

  <clause id="6003">
    <literal><![CDATA[
      L(x,y,R(z,u,z)) = L(x,y,L(z,u,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,5733,a(flip),b,5999,a)].">
      <j1 rule="hyper" parents="65 5733 5999"/>
    </justification>
  </clause>

  <clause id="6004">
    <literal><![CDATA[
      ((x \ y) * x) * K(z,(x \ y) * x) = (x \ (y * K(z,y))) * x
    ]]></literal>
    <justification jstring="[hyper(37,a,5099,a,b,5137,a)].">
      <j1 rule="hyper" parents="37 5099 5137"/>
    </justification>
  </clause>

  <clause id="6005">
    <literal><![CDATA[
      ((x * y) \ T(y * x,z)) * (x * y) = T(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(143,a,5179,a)].">
      <j1 rule="hyper" parents="143 5179"/>
    </justification>
  </clause>

  <clause id="6006">
    <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(5255(a,1),400(a,1,1))].">
      <j1 rule="para" parents="5255 400"/>
    </justification>
  </clause>

  <clause id="6007">
    <literal><![CDATA[
      a(1 / R(x,y,z),x,x \ 1) = K(R(x,y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,4920,a,b,5323,a)].">
      <j1 rule="hyper" parents="65 4920 5323"/>
    </justification>
  </clause>

  <clause id="6008">
    <literal><![CDATA[
      R(K(x \ 1,y),z,u) = K(R(x,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[para(5035(a,1),5323(a,1,1))].">
      <j1 rule="para" parents="5035 5323"/>
    </justification>
  </clause>

  <clause id="6009">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,y) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,4778,a(flip),b,6008,a),flip(a)].">
      <j1 rule="hyper" parents="65 4778 6008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6010">
    <literal><![CDATA[
      R(K((x / y) \ 1,z),y,u) = K(((x * u) / (y * u)) \ 1,z)
    ]]></literal>
    <justification jstring="[para(104(a,1),6008(a,2,1,1))].">
      <j1 rule="para" parents="104 6008"/>
    </justification>
  </clause>

  <clause id="6011">
    <literal><![CDATA[
      K(R(x \ 1,y,z) \ 1,u) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(3567(a,1),6008(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3567 6008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6012">
    <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(842(a,1),6009(a,1,1,1))].">
      <j1 rule="para" parents="842 6009"/>
    </justification>
  </clause>

  <clause id="6013">
    <literal><![CDATA[
      K(x,R(y \ 1,z,u) \ 1) * w = R(K(y,x),z,u) \ w
    ]]></literal>
    <justification jstring="[para(6011(a,1),5426(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6011 5426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6014">
    <literal><![CDATA[
      (x * T(x \ y,z)) * (y \ 1) = K((x * (y \ 1)) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,1578,a(flip),b,5333,a)].">
      <j1 rule="hyper" parents="65 1578 5333"/>
    </justification>
  </clause>

  <clause id="6015">
    <literal><![CDATA[
      (1 / x) * (y * T(y \ x,z)) = K(((1 / x) * y) \ 1,z)
    ]]></literal>
    <justification jstring="[para(79(a,1),5333(a,1,2,2,1,2))].">
      <j1 rule="para" parents="79 5333"/>
    </justification>
  </clause>

  <clause id="6016">
    <literal><![CDATA[
      x * ((y \ (x \ 1)) * y) = K((x * y) \ 1,y)
    ]]></literal>
    <justification jstring="[para(107(a,1),5333(a,1,2))].">
      <j1 rule="para" parents="107 5333"/>
    </justification>
  </clause>

  <clause id="6017">
    <literal><![CDATA[
      x \ K((x * ((1 / y) / x)) \ 1,z) = (y \ T(y * K(x \ 1,x),z)) / x
    ]]></literal>
    <justification jstring="[hyper(299,a,3842,a(flip),b,5334,a),flip(a)].">
      <j1 rule="hyper" parents="299 3842 5334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6018">
    <literal><![CDATA[
      x \ T(x * (y \ 1),z) = y \ K((y * (x \ 1)) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,1012,a(flip),b,5334,a)].">
      <j1 rule="hyper" parents="299 1012 5334"/>
    </justification>
  </clause>

  <clause id="6019">
    <literal><![CDATA[
      (R(x,y,y \ 1) \ (x * y)) * ((x * y) * (y \ 1)) = (x * y) * K((y \ 1) \ 1,(x * y) * (y \ 1))
    ]]></literal>
    <justification jstring="[para(258(a,1),5338(a,1,1,1))].">
      <j1 rule="para" parents="258 5338"/>
    </justification>
  </clause>

  <clause id="6020">
    <literal><![CDATA[
      K(x,y) * ((1 / x) \ z) = z * T(z \ ((1 / x) \ z),y)
    ]]></literal>
    <justification jstring="[para(79(a,1),5339(a,1,1,1))].">
      <j1 rule="para" parents="79 5339"/>
    </justification>
  </clause>

  <clause id="6021">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) = y * T(y \ (x \ y),T(x,z))
    ]]></literal>
    <justification jstring="[para(3554(a,1),5339(a,1,1))].">
      <j1 rule="para" parents="3554 5339"/>
    </justification>
  </clause>

  <clause id="6022">
    <literal><![CDATA[
      (x * y) \ (K(x \ 1,z) * y) = T((x * y) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,5340,a)].">
      <j1 rule="hyper" parents="125 5340"/>
    </justification>
  </clause>

  <clause id="6024">
    <literal><![CDATA[
      x * (y \ T(y * (x \ (y \ 1)),z)) = K(x \ 1,z) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(1012(a,1),5341(a,1,2))].">
      <j1 rule="para" parents="1012 5341"/>
    </justification>
  </clause>

  <clause id="6025">
    <literal><![CDATA[
      T(x,y) * ((1 / x) \ z) = (x * T(x,y)) * z
    ]]></literal>
    <justification jstring="[hyper(299,a,5877,a(flip),b,5376,a),flip(a)].">
      <j1 rule="hyper" parents="299 5877 5376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6026">
    <literal><![CDATA[
      ((x \ 1) * T(x \ 1,y)) * z = T(x \ 1,y) * (x \ z)
    ]]></literal>
    <justification jstring="[para(76(a,1),6025(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="76 6025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6027">
    <literal><![CDATA[
      K(((x \ 1) / (y / x)) \ 1,z) = (T(y,z) / x) / (y / x)
    ]]></literal>
    <justification jstring="[hyper(5861,a,5385,a)].">
      <j1 rule="hyper" parents="5861 5385"/>
    </justification>
  </clause>

  <clause id="6028">
    <literal><![CDATA[
      K(1 / x,y / (1 / x)) = x * (((x \ 1) \ y) \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,5640,a,b,5405,a)].">
      <j1 rule="hyper" parents="65 5640 5405"/>
    </justification>
  </clause>

  <clause id="6029">
    <literal><![CDATA[
      L(x \ (T(x,y) * z),x,x) = (K(x,y) / x) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(299,a,511,a,b,5423,a)].">
      <j1 rule="hyper" parents="299 511 5423"/>
    </justification>
  </clause>

  <clause id="6031">
    <literal><![CDATA[
      x \ (y * ((z * (y \ x)) / z)) = K(z,1 / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(125,a,5542,a)].">
      <j1 rule="hyper" parents="125 5542"/>
    </justification>
  </clause>

  <clause id="6032">
    <literal><![CDATA[
      K(x * (((y \ 1) \ 1) \ z),u) = K(x * (y \ z),u)
    ]]></literal>
    <justification jstring="[para(76(a,1),5618(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="76 5618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6033">
    <literal><![CDATA[
      K(x * ((x \ 1) \ y),z) = K((x * x) * y,z)
    ]]></literal>
    <justification jstring="[para(442(a,1),5618(a,1,1)),flip(a)].">
      <j1 rule="para" parents="442 5618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6034">
    <literal><![CDATA[
      K(((x \ 1) * (x * y)) \ z,u) = K(L(y,x,x \ 1) \ z,u)
    ]]></literal>
    <justification jstring="[para(2472(a,1),5623(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2472 5623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6035">
    <literal><![CDATA[
      K((x / (y \ 1)) * T((x / (1 / y)) \ 1,z),u) = K(K((x / (1 / y)) \ 1,z),u)
    ]]></literal>
    <justification jstring="[para(5035(a,1),5624(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5035 5624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6036">
    <literal><![CDATA[
      K(x,(y / z) \ 1) * z = y * ((x * (y \ z)) / x)
    ]]></literal>
    <justification jstring="[hyper(143,a,5627,a)].">
      <j1 rule="hyper" parents="143 5627"/>
    </justification>
  </clause>

  <clause id="6037">
    <literal><![CDATA[
      (x * (y * ((z * (y \ (x \ u))) / z))) / u = K(z,((x * y) / u) \ 1)
    ]]></literal>
    <justification jstring="[para(1321(a,1),5627(a,1,1))].">
      <j1 rule="para" parents="1321 5627"/>
    </justification>
  </clause>

  <clause id="6038">
    <literal><![CDATA[
      T(x * ((y * (x \ z)) / y),z) / z = K(y,(T(x,z) / z) \ 1)
    ]]></literal>
    <justification jstring="[para(2295(a,1),5627(a,1,1))].">
      <j1 rule="para" parents="2295 5627"/>
    </justification>
  </clause>

  <clause id="6039">
    <literal><![CDATA[
      x * ((x \ y) * K(z,x \ y)) = y * K(z,(y \ x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,5237,a(flip),b,5632,a)].">
      <j1 rule="hyper" parents="299 5237 5632"/>
    </justification>
  </clause>

  <clause id="6040">
    <literal><![CDATA[
      K(x,y * ((1 / z) \ z)) = K(x,y * (z * z))
    ]]></literal>
    <justification jstring="[para(460(a,1),5658(a,2,2,2))].">
      <j1 rule="para" parents="460 5658"/>
    </justification>
  </clause>

  <clause id="6041">
    <literal><![CDATA[
      K(x,y * (((1 / z) * (u * z)) \ (u * (u * z)))) = K(x,y * ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(2972(a,2),5658(a,1,2,2))].">
      <j1 rule="para" parents="2972 5658"/>
    </justification>
  </clause>

  <clause id="6042">
    <literal><![CDATA[
      K(x,y * (((z * (u \ 1)) / z) \ 1)) = K(x,y * ((1 / u) \ K(u \ 1,z)))
    ]]></literal>
    <justification jstring="[para(5182(a,2),5658(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5182 5658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6043">
    <literal><![CDATA[
      K(x,(y * L(1 / z,u,w)) \ v5) = K(x,(y * L(z \ 1,u,w)) \ v5)
    ]]></literal>
    <justification jstring="[para(4143(a,1),5662(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="4143 5662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6044">
    <literal><![CDATA[
      x / (y * ((z \ (y \ x)) * z)) = K(z,x / (z / (y \ 1)))
    ]]></literal>
    <justification jstring="[para(3858(a,1),5738(a,1,2))].">
      <j1 rule="para" parents="3858 5738"/>
    </justification>
  </clause>

  <clause id="6045">
    <literal><![CDATA[
      x / (y * ((z \ (y \ x)) * z)) = K(z,x / (z * y))
    ]]></literal>
    <justification jstring="[para(3503(a,1),5739(a,1,2))].">
      <j1 rule="para" parents="3503 5739"/>
    </justification>
  </clause>

  <clause id="6046">
    <literal><![CDATA[
      K((1 / x) \ y,1 / x) = K(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,4858,a(flip),b,5746,a)].">
      <j1 rule="hyper" parents="65 4858 5746"/>
    </justification>
  </clause>

  <clause id="6047">
    <literal><![CDATA[
      L(x,y,(z \ u) * z) = L(x,y,z * (u / z))
    ]]></literal>
    <justification jstring="[para(5293(a,1),5818(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5293 5818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6048">
    <literal><![CDATA[
      L(x,y,z * ((z * u) / z)) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),6047(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="9 6047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6049">
    <literal><![CDATA[
      L(x,y,((1 / z) \ (z \ u)) * z) = L(x,y,z * (((z \ 1) \ u) / z))
    ]]></literal>
    <justification jstring="[para(729(a,2),6047(a,1,3,1))].">
      <j1 rule="para" parents="729 6047"/>
    </justification>
  </clause>

  <clause id="6050">
    <literal><![CDATA[
      L(x,y,z * (((z \ 1) \ u) / z)) = L(x,y,(z \ 1) \ T(u,z))
    ]]></literal>
    <justification jstring="[para(2045(a,1),6047(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2045 6047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6051">
    <literal><![CDATA[
      L(x,y,T(z,u) * u) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[para(223(a,1),6048(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="223 6048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6052">
    <literal><![CDATA[
      L(x,y,z * ((T(z,u \ 1) / u) / z)) = L(x,y,((z / u) / z) * z)
    ]]></literal>
    <justification jstring="[para(4227(a,2),6048(a,1,3,2,1))].">
      <j1 rule="para" parents="4227 6048"/>
    </justification>
  </clause>

  <clause id="6053">
    <literal><![CDATA[
      x * (y * K((y \ (x \ 1)) \ 1,z)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(144,a,5841,a)].">
      <j1 rule="hyper" parents="144 5841"/>
    </justification>
  </clause>

  <clause id="6054">
    <literal><![CDATA[
      ((x \ y) \ y) * ((x \ y) * z) = x * ((y / x) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,296,a(flip),b,5875,a)].">
      <j1 rule="hyper" parents="65 296 5875"/>
    </justification>
  </clause>

  <clause id="6055">
    <literal><![CDATA[
      (x \ 1) \ (T(T(x \ 1,x),x) \ y) = (1 / x) \ (T(x \ 1,x) \ y)
    ]]></literal>
    <justification jstring="[para(1692(a,1),5883(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1692 5883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6056">
    <literal><![CDATA[
      K(x \ ((y \ 1) * y),z) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),5888(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10 5888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6057">
    <literal><![CDATA[
      x / T(x,y \ ((z \ 1) \ u)) = K(y \ ((1 / z) \ u),x)
    ]]></literal>
    <justification jstring="[hyper(299,a,5033,a(flip),b,5889,a)].">
      <j1 rule="hyper" parents="299 5033 5889"/>
    </justification>
  </clause>

  <clause id="6058">
    <literal><![CDATA[
      K((x \ ((1 / x) \ y)) \ z,u) = K((x \ ((x \ 1) \ y)) \ z,u)
    ]]></literal>
    <justification jstring="[para(1666(a,1),5893(a,1,1,1))].">
      <j1 rule="para" parents="1666 5893"/>
    </justification>
  </clause>

  <clause id="6059">
    <literal><![CDATA[
      K(x,y \ (z * ((1 / z) * u))) = K(x,y \ (z * ((z \ 1) * u)))
    ]]></literal>
    <justification jstring="[para(2683(a,1),5900(a,1,2,2))].">
      <j1 rule="para" parents="2683 5900"/>
    </justification>
  </clause>

  <clause id="6060">
    <literal><![CDATA[
      K(x,T((y \ 1) * ((z \ y) * z),u)) = K(x,T(K(z \ y,z),u))
    ]]></literal>
    <justification jstring="[para(5003(a,1),5901(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5003 5901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6061">
    <literal><![CDATA[
      K(x,y * (z \ ((1 / z) \ u))) = K(x,y * (z \ ((z \ 1) \ u)))
    ]]></literal>
    <justification jstring="[para(1666(a,1),5902(a,1,2,2))].">
      <j1 rule="para" parents="1666 5902"/>
    </justification>
  </clause>

  <clause id="6062">
    <literal><![CDATA[
      K(x,y * ((z \ 1) * (z * u))) = K(x,y * L(u,z,z))
    ]]></literal>
    <justification jstring="[para(475(a,1),5903(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="475 5903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6063">
    <literal><![CDATA[
      K(x,(y / (1 / (1 / z))) / u) = K(x,(y / z) / u)
    ]]></literal>
    <justification jstring="[para(191(a,1),5909(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="191 5909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6065">
    <literal><![CDATA[
      (x \ ((1 / x) \ y)) * T(x,x \ 1) = ((1 / x) \ (x \ y)) * x
    ]]></literal>
    <justification jstring="[para(5919(a,1),3332(a,1,1))].">
      <j1 rule="para" parents="5919 3332"/>
    </justification>
  </clause>

  <clause id="6066">
    <literal><![CDATA[
      (x \ K(x,y)) * (T(x,x \ 1) * z) = K(x,y) * ((1 / x) * (x * z))
    ]]></literal>
    <justification jstring="[para(5929(a,1),4573(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5929 4573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6069">
    <literal><![CDATA[
      T((x * y) \ y,T(x,z)) = (x * y) \ (K(x \ 1,x) * y)
    ]]></literal>
    <justification jstring="[para(3554(a,1),6022(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3554 6022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6070">
    <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(374(a,1),6031(a,1,2,2,1,2))].">
      <j1 rule="para" parents="374 6031"/>
    </justification>
  </clause>

  <clause id="6071">
    <literal><![CDATA[
      K(x,(y / z) \ 1) * z = z * K(x,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,5632,a,b,6036,a),flip(a)].">
      <j1 rule="hyper" parents="299 5632 6036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6072">
    <literal><![CDATA[
      K(x,y) * (z * K((z \ K(y,x)) \ 1,u)) = T(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(5197(a,1),6053(a,1,2,2,1,1,2))].">
      <j1 rule="para" parents="5197 6053"/>
    </justification>
  </clause>

  <clause id="6075">
    <literal><![CDATA[
      K(x,y \ K(y,z)) * z = z * K(x,(z \ (z * y)) \ 1)
    ]]></literal>
    <justification jstring="[para(5182(a,1),6071(a,1,1,2))].">
      <j1 rule="para" parents="5182 6071"/>
    </justification>
  </clause>

  <clause id="6076">
    <literal><![CDATA[
      x * K(y,(x \ z) \ 1) = K(y,x / z) * x
    ]]></literal>
    <justification jstring="[para(5937(a,1),6071(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5937 6071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6077">
    <literal><![CDATA[
      T(K(x,y / z),y) = K(x,(y \ z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(236,a,6076,a)].">
      <j1 rule="hyper" parents="236 6076"/>
    </justification>
  </clause>

  <clause id="6078">
    <literal><![CDATA[
      T(x,y) != K(z,(y \ u) \ 1)
    ]]></literal>
    <literal><![CDATA[
      K(z,y / u) = x
    ]]></literal>
    <justification jstring="[para(6077(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="6077 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6079">
    <literal><![CDATA[
      L(x \ 1,x,y) * ((x \ 1) \ (y * x)) = (x \ 1) \ (y * K(x \ 1,y * x))
    ]]></literal>
    <justification jstring="[hyper(119,a,5335,a(flip),b,1350,a),flip(a)].">
      <j1 rule="hyper" parents="119 5335 1350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6081">
    <literal><![CDATA[
      (K(x,y) \ z) * L(u,z,K(y,x)) = K(x,y) \ (z * u)
    ]]></literal>
    <justification jstring="[hyper(299,a,5426,a,b,5441,a),flip(a)].">
      <j1 rule="hyper" parents="299 5426 5441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6082">
    <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(5426(a,1),5442(a,1,1))].">
      <j1 rule="para" parents="5426 5442"/>
    </justification>
  </clause>

  <clause id="6083">
    <literal><![CDATA[
      ((1 / x) * K(y,x)) \ z = K(x,y) * ((1 / x) \ z)
    ]]></literal>
    <justification jstring="[hyper(5491,a,5443,a),flip(a)].">
      <j1 rule="hyper" parents="5491 5443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6084">
    <literal><![CDATA[
      (L(x,y,z) * K(x,u)) \ w = K(u,x) * (L(x,y,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(4686,a,5443,a),flip(a)].">
      <j1 rule="hyper" parents="4686 5443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6085">
    <literal><![CDATA[
      L(K(x \ 1,y) * ((1 / x) \ z),K(y,x \ 1),1 / x) = (K(y,x \ 1) / x) \ z
    ]]></literal>
    <justification jstring="[para(3328(a,1),5443(a,2,1))].">
      <j1 rule="para" parents="3328 5443"/>
    </justification>
  </clause>

  <clause id="6086">
    <literal><![CDATA[
      (x * K(y,x)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (x \ z) = u
    ]]></literal>
    <justification jstring="[para(5443(a,1),5486(a,1))].">
      <j1 rule="para" parents="5443 5486"/>
    </justification>
  </clause>

  <clause id="6088">
    <literal><![CDATA[
      T(x,y \ (y \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      x * K(y * y,x) = z
    ]]></literal>
    <justification jstring="[para(1058(a,1),5552(a,1))].">
      <j1 rule="para" parents="1058 5552"/>
    </justification>
  </clause>

  <clause id="6090">
    <literal><![CDATA[
      ((x \ 1) \ y) * K(x \ 1,x) != z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) \ y = z
    ]]></literal>
    <justification jstring="[para(3205(a,1),5570(a,1))].">
      <j1 rule="para" parents="3205 5570"/>
    </justification>
  </clause>

  <clause id="6092">
    <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(216(a,1),5673(a,2,3))].">
      <j1 rule="para" parents="216 5673"/>
    </justification>
  </clause>

  <clause id="6093">
    <literal><![CDATA[
      R(x,x \ (y \ x),x) = R(x,y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,5679,a(flip),b,5681,a),flip(a)].">
      <j1 rule="hyper" parents="65 5679 5681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6094">
    <literal><![CDATA[
      L(T(x,y) \ 1,x,y) = (x * y) \ y
    ]]></literal>
    <justification jstring="[hyper(2194,a,5766,a)].">
      <j1 rule="hyper" parents="2194 5766"/>
    </justification>
  </clause>

  <clause id="6095">
    <literal><![CDATA[
      (x * y) \ T(x,y) = (y * x) \ x
    ]]></literal>
    <justification jstring="[hyper(65,a,4982,a(flip),b,6094,a)].">
      <j1 rule="hyper" parents="65 4982 6094"/>
    </justification>
  </clause>

  <clause id="6096">
    <literal><![CDATA[
      T(x,y) / ((y * x) \ x) = x * y
    ]]></literal>
    <justification jstring="[hyper(192,a,6095,a)].">
      <j1 rule="hyper" parents="192 6095"/>
    </justification>
  </clause>

  <clause id="6097">
    <literal><![CDATA[
      T(x,y) = (x * y) * ((y * x) \ x)
    ]]></literal>
    <justification jstring="[hyper(144,a,6095,a),flip(a)].">
      <j1 rule="hyper" parents="144 6095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6098">
    <literal><![CDATA[
      T(x,y / x) / (y \ x) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(12(a,1),6096(a,1,2,1))].">
      <j1 rule="para" parents="12 6096"/>
    </justification>
  </clause>

  <clause id="6099">
    <literal><![CDATA[
      T(x,(x / y) / x) / ((x / y) \ x) = (x / y) * K(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(299,a,5541,a,b,6098,a),flip(a)].">
      <j1 rule="hyper" parents="299 5541 6098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6100">
    <literal><![CDATA[
      x \ (((y \ (x / z)) * y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K((x \ (y * z)) \ 1,y) = u
    ]]></literal>
    <justification jstring="[para(1596(a,1),5767(a,1,2))].">
      <j1 rule="para" parents="1596 5767"/>
    </justification>
  </clause>

  <clause id="6101">
    <literal><![CDATA[
      K(x \ y,L(y \ x,z,u)) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(36,a,3845,a(flip),b,5809,a),flip(a)].">
      <j1 rule="hyper" parents="36 3845 5809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6102">
    <literal><![CDATA[
      K(1 / x,L(x,y,z)) = K(1 / x,x)
    ]]></literal>
    <justification jstring="[hyper(36,a,3838,a(flip),b,5809,a),flip(a)].">
      <j1 rule="hyper" parents="36 3838 5809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6103">
    <literal><![CDATA[
      K(x,L(x \ 1,y,z)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(36,a,3802,a(flip),b,5809,a),flip(a)].">
      <j1 rule="hyper" parents="36 3802 5809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6104">
    <literal><![CDATA[
      K(x \ 1,L(x,y,z)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(36,a,3797,a(flip),b,5809,a),flip(a)].">
      <j1 rule="hyper" parents="36 3797 5809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6105">
    <literal><![CDATA[
      K(1 / x,x) / L(x,y,z) = 1 / T(L(x,y,z),1 / x)
    ]]></literal>
    <justification jstring="[hyper(120,a,6102,a(flip),b,5032,a(flip))].">
      <j1 rule="hyper" parents="120 6102 5032"/>
    </justification>
  </clause>

  <clause id="6107">
    <literal><![CDATA[
      K(x \ 1,L(x,y,z)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,2596,a(flip),b,6104,a),flip(a)].">
      <j1 rule="hyper" parents="299 2596 6104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6108">
    <literal><![CDATA[
      L(K(x \ 1,L(x,y,z)),u,w) = K(L(x,u,w) \ 1,x)
    ]]></literal>
    <justification jstring="[para(6104(a,2),3212(a,1,1))].">
      <j1 rule="para" parents="6104 3212"/>
    </justification>
  </clause>

  <clause id="6109">
    <literal><![CDATA[
      K(x \ (y \ 1),(y \ 1) \ x) = K(x \ (y \ 1),y * x)
    ]]></literal>
    <justification jstring="[para(519(a,1),6101(a,1,2)),flip(a)].">
      <j1 rule="para" parents="519 6101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6111">
    <literal><![CDATA[
      R(x,y,z) * K(x \ 1,R(x,y,z)) = R(1 / (1 / x),y,z)
    ]]></literal>
    <justification jstring="[para(1716(a,1),5813(a,2,1))].">
      <j1 rule="para" parents="1716 5813"/>
    </justification>
  </clause>

  <clause id="6112">
    <literal><![CDATA[
      R(x / (x / y),z,u) = R(y,z,u) * K(y \ x,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(5002(a,2),5813(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5002 5813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6114">
    <literal><![CDATA[
      T(x,y) \ T(z * T(z \ x,x),y) != u
    ]]></literal>
    <literal><![CDATA[
      K((x \ z) \ 1,T(x,y)) = u
    ]]></literal>
    <justification jstring="[para(5328(a,2),5878(a,1,2,1))].">
      <j1 rule="para" parents="5328 5878"/>
    </justification>
  </clause>

  <clause id="6115">
    <literal><![CDATA[
      T(x,x \ y) \ z != u
    ]]></literal>
    <literal><![CDATA[
      ((x \ y) \ y) \ z = u
    ]]></literal>
    <justification jstring="[para(5383(a,1),5882(a,1))].">
      <j1 rule="para" parents="5383 5882"/>
    </justification>
  </clause>

  <clause id="6116">
    <literal><![CDATA[
      T(x,x \ y) \ R(T(z,z \ u),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      ((x \ y) \ y) \ R((z \ u) \ u,w,v5) = v6
    ]]></literal>
    <justification jstring="[para(1171(a,2),6115(a,1))].">
      <j1 rule="para" parents="1171 6115"/>
    </justification>
  </clause>

  <clause id="6117">
    <literal><![CDATA[
      R(K(x,y / (z * y)),R(1 / z,z,y),u) = K(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(216(a,2),5946(a,1,2))].">
      <j1 rule="para" parents="216 5946"/>
    </justification>
  </clause>

  <clause id="6120">
    <literal><![CDATA[
      K(x,L(y,x,x \ 1)) * (y * x) = x * y
    ]]></literal>
    <justification jstring="[para(11(a,1),5996(a,2,2))].">
      <j1 rule="para" parents="11 5996"/>
    </justification>
  </clause>

  <clause id="6121">
    <literal><![CDATA[
      K(x,L(y,x,x \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5021,a,6120,a),flip(a)].">
      <j1 rule="hyper" parents="5021 6120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6122">
    <literal><![CDATA[
      (1 / R(x,y,z)) * K(R(x,y,z) \ 1,x) = ((1 / R(x,y,z)) * x) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(6007(a,1),773(a,1,2))].">
      <j1 rule="para" parents="6007 773"/>
    </justification>
  </clause>

  <clause id="6123">
    <literal><![CDATA[
      (K(x,y) / x) * (x * z) = L(K(x,y) * z,x,x)
    ]]></literal>
    <justification jstring="[para(5350(a,1),6029(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5350 6029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6124">
    <literal><![CDATA[
      K(x,y * (z * ((1 / z) * u))) = K(x,y * L(u,z,z))
    ]]></literal>
    <justification jstring="[para(944(a,1),6062(a,1,2,2))].">
      <j1 rule="para" parents="944 6062"/>
    </justification>
  </clause>

  <clause id="6125">
    <literal><![CDATA[
      K(x,y * L((1 / z) * u,z,z)) = K(x,y * L((z \ 1) * u,z,z))
    ]]></literal>
    <justification jstring="[para(2840(a,1),6124(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2840 6124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6126">
    <literal><![CDATA[
      (x \ (y * K(x,z))) * x = ((x \ y) * x) * K(x,z)
    ]]></literal>
    <justification jstring="[para(5024(a,2),5059(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5024 5059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6129">
    <literal><![CDATA[
      L(K(x,y \ 1),z,u) = K(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(5072(a,1),5071(a,1,1))].">
      <j1 rule="para" parents="5072 5071"/>
    </justification>
  </clause>

  <clause id="6130">
    <literal><![CDATA[
      K(x,L(x,y,z) \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(3419,a,6129,a),flip(a)].">
      <j1 rule="hyper" parents="3419 6129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6131">
    <literal><![CDATA[
      K(x,L(y \ 1,z,u) \ 1) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(4793(a,1),6129(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4793 6129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6132">
    <literal><![CDATA[
      L(K(x,1 / y),z,u) = K(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(4797(a,2),6129(a,1,1))].">
      <j1 rule="para" parents="4797 6129"/>
    </justification>
  </clause>

  <clause id="6133">
    <literal><![CDATA[
      K(x,L(T(y \ 1,z),u,w) \ 1) = L(T(K(x,y),z),u,w)
    ]]></literal>
    <justification jstring="[para(5801(a,1),6129(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5801 6129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6134">
    <literal><![CDATA[
      L(x,y,z) \ K(x,L(x,u,w) \ 1) = (1 / x) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(119,a,6130,a,b,4132,a)].">
      <j1 rule="hyper" parents="119 6130 4132"/>
    </justification>
  </clause>

  <clause id="6135">
    <literal><![CDATA[
      T(x,L(x,y,z) \ 1) = K(x,x \ 1) * x
    ]]></literal>
    <justification jstring="[para(6130(a,1),5096(a,2,1))].">
      <j1 rule="para" parents="6130 5096"/>
    </justification>
  </clause>

  <clause id="6136">
    <literal><![CDATA[
      K(x,T(y,L(y,z,u) \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6135(a,2),5644(a,1,2))].">
      <j1 rule="para" parents="6135 5644"/>
    </justification>
  </clause>

  <clause id="6137">
    <literal><![CDATA[
      L(K(x,y \ z),y \ z,y) = K(x,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(366(a,1),6131(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="366 6131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6138">
    <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(6131(a,1),6129(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6131 6129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6139">
    <literal><![CDATA[
      L(K(x,1 / y),z,u) = K(x,1 / L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,4797,a,b,6132,a),flip(a)].">
      <j1 rule="hyper" parents="299 4797 6132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6141">
    <literal><![CDATA[
      L(K(x,1 / y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u) \ 1) = w
    ]]></literal>
    <justification jstring="[para(6139(a,2),5408(a,1))].">
      <j1 rule="para" parents="6139 5408"/>
    </justification>
  </clause>

  <clause id="6142">
    <literal><![CDATA[
      L(T(K(x,y \ z),u),y \ z,y) = T(K(x,(z \ y) \ 1),u)
    ]]></literal>
    <justification jstring="[para(6137(a,1),25(a,2,1))].">
      <j1 rule="para" parents="6137 25"/>
    </justification>
  </clause>

  <clause id="6144">
    <literal><![CDATA[
      L(K(x,y \ 1),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u) \ 1) = w
    ]]></literal>
    <justification jstring="[para(4797(a,1),6141(a,1,1))].">
      <j1 rule="para" parents="4797 6141"/>
    </justification>
  </clause>

  <clause id="6146">
    <literal><![CDATA[
      K(x,y) * ((x \ 1) \ y) != z
    ]]></literal>
    <literal><![CDATA[
      (y \ ((x \ 1) \ y)) * y = z
    ]]></literal>
    <justification jstring="[para(5093(a,2),276(a,1))].">
      <j1 rule="para" parents="5093 276"/>
    </justification>
  </clause>

  <clause id="6147">
    <literal><![CDATA[
      (x \ 1) * (K(x,y) * ((x \ 1) \ z)) = K((x \ 1) \ 1,y) * z
    ]]></literal>
    <justification jstring="[para(5093(a,2),5341(a,1,2))].">
      <j1 rule="para" parents="5093 5341"/>
    </justification>
  </clause>

  <clause id="6148">
    <literal><![CDATA[
      (x / (x * y)) \ T(x,y) = x * (y * K(x,y))
    ]]></literal>
    <justification jstring="[para(5141(a,1),5281(a,1,2))].">
      <j1 rule="para" parents="5141 5281"/>
    </justification>
  </clause>

  <clause id="6149">
    <literal><![CDATA[
      (x / (x * y)) \ T(x,y) = T(x,y) * y
    ]]></literal>
    <justification jstring="[hyper(299,a,5115,a(flip),b,6148,a),flip(a)].">
      <j1 rule="hyper" parents="299 5115 6148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6150">
    <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),5330(a,2,2))].">
      <j1 rule="para" parents="27 5330"/>
    </justification>
  </clause>

  <clause id="6151">
    <literal><![CDATA[
      (x * K(y \ 1,z)) * y = (x * y) * K(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(5035(a,1),5342(a,1,1,2))].">
      <j1 rule="para" parents="5035 5342"/>
    </justification>
  </clause>

  <clause id="6153">
    <literal><![CDATA[
      (x * K(y \ 1,z)) \ ((x * y) * K(y \ 1,z)) = y
    ]]></literal>
    <justification jstring="[hyper(125,a,6151,a)].">
      <j1 rule="hyper" parents="125 6151"/>
    </justification>
  </clause>

  <clause id="6154">
    <literal><![CDATA[
      (x * K(y \ 1,z)) / y = (x / y) * K(y \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(120,a,154,a(flip),b,6151,a)].">
      <j1 rule="hyper" parents="120 154 6151"/>
    </justification>
  </clause>

  <clause id="6156">
    <literal><![CDATA[
      R(T(x,y * K(x \ 1,z)),y,K(x \ 1,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(6153(a,1),1324(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6153 1324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6157">
    <literal><![CDATA[
      (T(x,y \ 1) / y) * K(y \ 1,x) = x / y
    ]]></literal>
    <justification jstring="[para(5042(a,1),6154(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5042 6154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6158">
    <literal><![CDATA[
      (T(x,y \ 1) / y) \ (x / y) = K(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(125,a,6157,a)].">
      <j1 rule="hyper" parents="125 6157"/>
    </justification>
  </clause>

  <clause id="6159">
    <literal><![CDATA[
      K(x \ 1,(1 / x) \ (y / x)) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,3766,a,b,6158,a)].">
      <j1 rule="hyper" parents="65 3766 6158"/>
    </justification>
  </clause>

  <clause id="6160">
    <literal><![CDATA[
      K(x \ 1,(1 / x) \ y) = K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[para(11(a,1),6159(a,1,2,2))].">
      <j1 rule="para" parents="11 6159"/>
    </justification>
  </clause>

  <clause id="6161">
    <literal><![CDATA[
      K(x \ 1,(x \ 1) \ y) = K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(65,a,5647,a(flip),b,6160,a)].">
      <j1 rule="hyper" parents="65 5647 6160"/>
    </justification>
  </clause>

  <clause id="6162">
    <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(65,a,4865,a(flip),b,6161,a)].">
      <j1 rule="hyper" parents="65 4865 6161"/>
    </justification>
  </clause>

  <clause id="6163">
    <literal><![CDATA[
      K(x \ 1,y * x) = K(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,4864,a(flip),b,6161,a),flip(a)].">
      <j1 rule="hyper" parents="65 4864 6161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6164">
    <literal><![CDATA[
      ((x \ 1) \ y) * K(x \ 1,y * x) = y / (x \ 1)
    ]]></literal>
    <justification jstring="[para(6161(a,1),5102(a,1,2))].">
      <j1 rule="para" parents="6161 5102"/>
    </justification>
  </clause>

  <clause id="6165">
    <literal><![CDATA[
      (x \ 1) * (y / (x \ 1)) = y * K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[para(6161(a,1),5293(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6161 5293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6167">
    <literal><![CDATA[
      ((x * y) \ y) * (x * y) = y * K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[para(6163(a,2),5862(a,2,2))].">
      <j1 rule="para" parents="6163 5862"/>
    </justification>
  </clause>

  <clause id="6168">
    <literal><![CDATA[
      (1 / x) * (y / (1 / x)) = y * K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(65,a,3269,a,b,6165,a)].">
      <j1 rule="hyper" parents="65 3269 6165"/>
    </justification>
  </clause>

  <clause id="6169">
    <literal><![CDATA[
      x * K((y \ 1) \ 1,x * (y \ 1)) = y * (x / y)
    ]]></literal>
    <justification jstring="[hyper(65,a,3289,a(flip),b,6165,a),flip(a)].">
      <j1 rule="hyper" parents="65 3289 6165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6170">
    <literal><![CDATA[
      x * (y * K(x \ 1,y * x)) = L(y / (x \ 1),x,x)
    ]]></literal>
    <justification jstring="[para(6165(a,1),1673(a,1,2))].">
      <j1 rule="para" parents="6165 1673"/>
    </justification>
  </clause>

  <clause id="6171">
    <literal><![CDATA[
      x * (y * K(x \ 1,y * x)) != z
    ]]></literal>
    <literal><![CDATA[
      L(y / (x \ 1),x,x) = z
    ]]></literal>
    <justification jstring="[para(6165(a,1),1686(a,1,2))].">
      <j1 rule="para" parents="6165 1686"/>
    </justification>
  </clause>

  <clause id="6172">
    <literal><![CDATA[
      a(x,y * K(z \ 1,y * z),u) = a(x,z * (y / (1 / z)),u)
    ]]></literal>
    <justification jstring="[para(6168(a,1),2349(a,1,2))].">
      <j1 rule="para" parents="6168 2349"/>
    </justification>
  </clause>

  <clause id="6173">
    <literal><![CDATA[
      (1 / x) * (y / (1 / x)) = y * K(1 / x,y * x)
    ]]></literal>
    <justification jstring="[para(3565(a,2),6168(a,2,2))].">
      <j1 rule="para" parents="3565 6168"/>
    </justification>
  </clause>

  <clause id="6174">
    <literal><![CDATA[
      x * K(y,x * (y \ 1)) = y * (x / y)
    ]]></literal>
    <justification jstring="[para(3567(a,1),6169(a,1,2))].">
      <j1 rule="para" parents="3567 6169"/>
    </justification>
  </clause>

  <clause id="6175">
    <literal><![CDATA[
      K(x,y * (x \ 1)) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(36,a,5293,a,b,6174,a),flip(a)].">
      <j1 rule="hyper" parents="36 5293 6174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6176">
    <literal><![CDATA[
      (x / (y \ 1)) * K(y,x) = y * ((x / (y \ 1)) / y)
    ]]></literal>
    <justification jstring="[para(12(a,1),6174(a,1,2,2))].">
      <j1 rule="para" parents="12 6174"/>
    </justification>
  </clause>

  <clause id="6177">
    <literal><![CDATA[
      (x / y) * z != x * K(y,x * (y \ 1))
    ]]></literal>
    <literal><![CDATA[
      T(y,x / y) = z
    ]]></literal>
    <justification jstring="[para(6174(a,2),236(a,2))].">
      <j1 rule="para" parents="6174 236"/>
    </justification>
  </clause>

  <clause id="6178">
    <literal><![CDATA[
      K(x,y * (1 / x)) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,5639,a,b,6175,a)].">
      <j1 rule="hyper" parents="65 5639 6175"/>
    </justification>
  </clause>

  <clause id="6179">
    <literal><![CDATA[
      K(x * (1 / y),y) = 1 / K(y,y \ x)
    ]]></literal>
    <justification jstring="[para(6178(a,1),5209(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6178 5209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6180">
    <literal><![CDATA[
      K(x * (1 / y),y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,5209,a(flip),b,6179,a),flip(a)].">
      <j1 rule="hyper" parents="299 5209 6179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6181">
    <literal><![CDATA[
      K(x * (1 / y),y) = K(x / y,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,5192,a,b,6180,a),flip(a)].">
      <j1 rule="hyper" parents="299 5192 6180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6182">
    <literal><![CDATA[
      K((1 / x) * y,x) = K(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[hyper(299,a,4858,a,b,6180,a)].">
      <j1 rule="hyper" parents="299 4858 6180"/>
    </justification>
  </clause>

  <clause id="6183">
    <literal><![CDATA[
      K(x * (y \ 1),y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,5601,a(flip),b,6180,a)].">
      <j1 rule="hyper" parents="65 5601 6180"/>
    </justification>
  </clause>

  <clause id="6184">
    <literal><![CDATA[
      K((x \ 1) \ y,x \ 1) = K(y * x,x \ 1)
    ]]></literal>
    <justification jstring="[para(76(a,1),6180(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="76 6180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6185">
    <literal><![CDATA[
      K(x / (1 / y),1 / y) = K(x * y,1 / y)
    ]]></literal>
    <justification jstring="[hyper(65,a,5604,a(flip),b,6181,a),flip(a)].">
      <j1 rule="hyper" parents="65 5604 6181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6186">
    <literal><![CDATA[
      x * K(x * (y \ 1),y) = (y \ x) * y
    ]]></literal>
    <justification jstring="[para(6183(a,2),287(a,1,2))].">
      <j1 rule="para" parents="6183 287"/>
    </justification>
  </clause>

  <clause id="6187">
    <literal><![CDATA[
      K((1 / (1 / x)) * y,1 / x) = K(y * x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(299,a,5604,a(flip),b,6182,a),flip(a)].">
      <j1 rule="hyper" parents="299 5604 6182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6188">
    <literal><![CDATA[
      ((1 / x) \ y) * (1 / x) = y * K(y * x,1 / x)
    ]]></literal>
    <justification jstring="[para(79(a,1),6186(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="79 6186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6189">
    <literal><![CDATA[
      K(1 / x,y / (1 / x)) = K(1 / x,y * x)
    ]]></literal>
    <justification jstring="[hyper(455,a,6173,a)].">
      <j1 rule="hyper" parents="455 6173"/>
    </justification>
  </clause>

  <clause id="6190">
    <literal><![CDATA[
      x * (((x \ 1) \ y) \ y) = K(1 / x,y * x)
    ]]></literal>
    <justification jstring="[hyper(65,a,6028,a(flip),b,6189,a)].">
      <j1 rule="hyper" parents="65 6028 6189"/>
    </justification>
  </clause>

  <clause id="6191">
    <literal><![CDATA[
      T(x \ 1,y * x) = ((x \ 1) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(36,a,5078,a,b,6190,a)].">
      <j1 rule="hyper" parents="36 5078 6190"/>
    </justification>
  </clause>

  <clause id="6192">
    <literal><![CDATA[
      T(x \ 1,y * x) = T(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(299,a,4753,a,b,6191,a),flip(a)].">
      <j1 rule="hyper" parents="299 4753 6191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6193">
    <literal><![CDATA[
      T((x \ y) \ 1,y) = (((x \ y) \ 1) \ x) \ x
    ]]></literal>
    <justification jstring="[para(10(a,1),6191(a,1,2))].">
      <j1 rule="para" parents="10 6191"/>
    </justification>
  </clause>

  <clause id="6194">
    <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(6192(a,1),2192(a,1,2,1,1))].">
      <j1 rule="para" parents="6192 2192"/>
    </justification>
  </clause>

  <clause id="6195">
    <literal><![CDATA[
      T(x \ 1,y * x) * L(T(x \ 1,x * y) \ 1,z,u) = T((x \ 1) * L((x \ 1) \ 1,z,u),x * y)
    ]]></literal>
    <justification jstring="[para(6192(a,2),2192(a,1,1))].">
      <j1 rule="para" parents="6192 2192"/>
    </justification>
  </clause>

  <clause id="6196">
    <literal><![CDATA[
      K((x \ y) * x,1 / x) = K(y,1 / x)
    ]]></literal>
    <justification jstring="[hyper(65,a,5744,a(flip),b,6187,a),flip(a)].">
      <j1 rule="hyper" parents="65 5744 6187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6197">
    <literal><![CDATA[
      x * (y * K(x \ 1,x * y)) = L(y / (x \ 1),x,x)
    ]]></literal>
    <justification jstring="[para(6163(a,1),6170(a,1,2,2))].">
      <j1 rule="para" parents="6163 6170"/>
    </justification>
  </clause>

  <clause id="6198">
    <literal><![CDATA[
      (x \ y) * (K(y,z) * K(y,z)) = x \ (K(y,z) * T(y,z))
    ]]></literal>
    <justification jstring="[para(3577(a,1),5361(a,2,2))].">
      <j1 rule="para" parents="3577 5361"/>
    </justification>
  </clause>

  <clause id="6199">
    <literal><![CDATA[
      K(x,y) * (K(x,y) * z) = y * (T(T(y,x),x) \ z)
    ]]></literal>
    <justification jstring="[para(5190(a,1),5397(a,1,2,1))].">
      <j1 rule="para" parents="5190 5397"/>
    </justification>
  </clause>

  <clause id="6200">
    <literal><![CDATA[
      (K(x,y) * (K(x,y) * z)) \ ((u * K(x,y)) * (K(x,y) * z)) = R(T(u,y * (T(T(y,x),x) \ z)),K(x,y),K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(6199(a,1),689(a,2,1,2))].">
      <j1 rule="para" parents="6199 689"/>
    </justification>
  </clause>

  <clause id="6201">
    <literal><![CDATA[
      K(x,x * y) * (L(y,z,u) * x) = L(y,z,u) * T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(4379,a,5418,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="4379 5418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6202">
    <literal><![CDATA[
      K(x,y) * (R(y,z,u) * x) = R(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,4403,a(flip),b,5419,a),flip(a)].">
      <j1 rule="hyper" parents="299 4403 5419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6203">
    <literal><![CDATA[
      K(x,x * y) * (R(y,z,u) * x) = R(y,z,u) * T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(4380,a,5419,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="4380 5419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6204">
    <literal><![CDATA[
      K(x * y,z) * ((z * x) * y) = R(z,x,y) * T(x * y,z)
    ]]></literal>
    <justification jstring="[para(103(a,1),6202(a,1,2))].">
      <j1 rule="para" parents="103 6202"/>
    </justification>
  </clause>

  <clause id="6205">
    <literal><![CDATA[
      a(x,y * K(z \ y,z),u) = a(x,z * (y / z),u)
    ]]></literal>
    <justification jstring="[para(5209(a,1),5508(a,1,2,2))].">
      <j1 rule="para" parents="5209 5508"/>
    </justification>
  </clause>

  <clause id="6206">
    <literal><![CDATA[
      a(x,(y * z) * (y / (y * z)),u) = a(x,y * K(z \ 1,y * z),u)
    ]]></literal>
    <justification jstring="[para(5327(a,1),6205(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5327 6205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6207">
    <literal><![CDATA[
      K(1 / x,y) / (x \ 1) = 1 / (x \ K(y,1 / x))
    ]]></literal>
    <justification jstring="[para(4807(a,1),5549(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4807 5549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6209">
    <literal><![CDATA[
      R(K(x,y \ 1),z,u) = K(x,R(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(5072(a,1),5626(a,1,1))].">
      <j1 rule="para" parents="5072 5626"/>
    </justification>
  </clause>

  <clause id="6210">
    <literal><![CDATA[
      K(x,R(y,x,z) \ 1) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(4613,a,6209,a),flip(a)].">
      <j1 rule="hyper" parents="4613 6209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6211">
    <literal><![CDATA[
      R(x,y,z) * ((R(x,y,z) / x) \ (1 / x)) = K(R(x,y,z),R(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,4120,a,b,6209,a)].">
      <j1 rule="hyper" parents="65 4120 6209"/>
    </justification>
  </clause>

  <clause id="6212">
    <literal><![CDATA[
      K(x,R(x,y,z) \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,2722,a(flip),b,6209,a),flip(a)].">
      <j1 rule="hyper" parents="65 2722 6209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6213">
    <literal><![CDATA[
      K(x,R(y \ 1,z,u) \ 1) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(4793(a,1),6209(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4793 6209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6214">
    <literal><![CDATA[
      K(x,R(y / z,u,w) \ 1) = R(K(x,z / y),u,w)
    ]]></literal>
    <justification jstring="[para(5937(a,1),6209(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5937 6209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6215">
    <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),6210(a,1,2,1))].">
      <j1 rule="para" parents="31 6210"/>
    </justification>
  </clause>

  <clause id="6216">
    <literal><![CDATA[
      T(x,R(y \ 1,z,u) \ 1) = x * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(6213(a,1),5083(a,2,2))].">
      <j1 rule="para" parents="6213 5083"/>
    </justification>
  </clause>

  <clause id="6217">
    <literal><![CDATA[
      R(K(x,y / z),y,y \ 1) = K(x,(z * (y \ 1)) \ 1)
    ]]></literal>
    <justification jstring="[para(565(a,1),6214(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="565 6214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6218">
    <literal><![CDATA[
      R(K(x,y / z),y,z \ 1) = K(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[para(533(a,1),6214(a,1,2)),flip(a)].">
      <j1 rule="para" parents="533 6214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6219">
    <literal><![CDATA[
      K(x,R(y / x,x * z,u) \ 1) = K(x,(((y * z) * u) / ((x * z) * u)) \ 1)
    ]]></literal>
    <justification jstring="[para(574(a,1),6215(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="574 6215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6220">
    <literal><![CDATA[
      K(x,((y \ z) * (z \ 1)) \ 1) = R(K(x,y),z,z \ 1)
    ]]></literal>
    <justification jstring="[para(76(a,1),6217(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="76 6217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6221">
    <literal><![CDATA[
      x * (y * ((x \ 1) / y)) = K(y,(x * y) \ 1)
    ]]></literal>
    <justification jstring="[para(10(a,1),5628(a,1,2,2,1))].">
      <j1 rule="para" parents="10 5628"/>
    </justification>
  </clause>

  <clause id="6222">
    <literal><![CDATA[
      (x * y) * (x / (x * y)) = x * K(x * y,y \ 1)
    ]]></literal>
    <justification jstring="[para(10(a,1),5629(a,1,2,1))].">
      <j1 rule="para" parents="10 5629"/>
    </justification>
  </clause>

  <clause id="6223">
    <literal><![CDATA[
      T(x * K(y \ 1,x),y) = (((y * y) \ x) * y) / (1 / y)
    ]]></literal>
    <justification jstring="[para(3565(a,1),5672(a,1,1,2))].">
      <j1 rule="para" parents="3565 5672"/>
    </justification>
  </clause>

  <clause id="6224">
    <literal><![CDATA[
      (K(x,y) * R(y,z,u)) * w = R(y,z,u) * (K(x,y) * w)
    ]]></literal>
    <justification jstring="[para(3623(a,1),5717(a,1,1))].">
      <j1 rule="para" parents="3623 5717"/>
    </justification>
  </clause>

  <clause id="6225">
    <literal><![CDATA[
      x / (y * (z * (u * T(u \ (z \ (y \ x)),w)))) = K(w,x / (y * (z * u)))
    ]]></literal>
    <justification jstring="[para(998(a,1),5737(a,1,2,2))].">
      <j1 rule="para" parents="998 5737"/>
    </justification>
  </clause>

  <clause id="6226">
    <literal><![CDATA[
      x / (y * (((z \ ((y \ x) * u)) * z) / u)) = K(z,x / (y * (z / u)))
    ]]></literal>
    <justification jstring="[para(1520(a,1),5737(a,1,2,2))].">
      <j1 rule="para" parents="1520 5737"/>
    </justification>
  </clause>

  <clause id="6227">
    <literal><![CDATA[
      K((K(x,y) / x) * z,u) = K((x \ K(x,y)) * z,u)
    ]]></literal>
    <justification jstring="[para(5223(a,1),5745(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5223 5745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6228">
    <literal><![CDATA[
      K(x,L(y \ 1,z,u) \ (K(w,L(1 / y,z,u)) * v5)) = K(x,T(L(1 / y,z,u),w) \ v5)
    ]]></literal>
    <justification jstring="[para(5372(a,1),5755(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5372 5755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6229">
    <literal><![CDATA[
      K((x \ (y / (z \ 1))) \ 1,y) = x \ (((y \ (x / z)) * y) * z)
    ]]></literal>
    <justification jstring="[para(3856(a,1),5839(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3856 5839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6230">
    <literal><![CDATA[
      x * K((x \ (y * z)) \ 1,y) = z * ((y \ (z \ x)) * y)
    ]]></literal>
    <justification jstring="[hyper(3675,a,5845,a),flip(a)].">
      <j1 rule="hyper" parents="3675 5845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6231">
    <literal><![CDATA[
      K((x * ((1 / y) / z)) \ u,w) = K((x * ((y \ 1) / z)) \ u,w)
    ]]></literal>
    <justification jstring="[para(2755(a,1),5895(a,1,1,1,2))].">
      <j1 rule="para" parents="2755 5895"/>
    </justification>
  </clause>

  <clause id="6232">
    <literal><![CDATA[
      ((x \ y) \ y) * (y / T(T(x,x \ y),y)) = ((y * ((x \ y) \ y)) / y) * (x \ y)
    ]]></literal>
    <justification jstring="[para(108(a,2),5933(a,1,2,2,1))].">
      <j1 rule="para" parents="108 5933"/>
    </justification>
  </clause>

  <clause id="6233">
    <literal><![CDATA[
      x * K(T(y,x) \ 1,z) = K(y \ 1,z) * x
    ]]></literal>
    <justification jstring="[hyper(40,a,6022,a,b,5935,a),flip(a)].">
      <j1 rule="hyper" parents="40 6022 5935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6234">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) = T(K(x \ 1,z),y)
    ]]></literal>
    <justification jstring="[hyper(236,a,6233,a),flip(a)].">
      <j1 rule="hyper" parents="236 6233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6235">
    <literal><![CDATA[
      K(T(1 / x,y) \ 1,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[para(79(a,1),6234(a,2,1,1))].">
      <j1 rule="para" parents="79 6234"/>
    </justification>
  </clause>

  <clause id="6236">
    <literal><![CDATA[
      K(T(x \ 1,y) \ 1,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[para(3567(a,1),6234(a,2,1))].">
      <j1 rule="para" parents="3567 6234"/>
    </justification>
  </clause>

  <clause id="6237">
    <literal><![CDATA[
      K(1 / T(x,y),z) = T(K(1 / x,z),y)
    ]]></literal>
    <justification jstring="[para(3173(a,1),6235(a,1,1))].">
      <j1 rule="para" parents="3173 6235"/>
    </justification>
  </clause>

  <clause id="6238">
    <literal><![CDATA[
      K(x * K(y,x \ 1),z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[para(5756(a,1),6235(a,1,1))].">
      <j1 rule="para" parents="5756 6235"/>
    </justification>
  </clause>

  <clause id="6239">
    <literal><![CDATA[
      T(x,y) != K(1 / T(z,y),u)
    ]]></literal>
    <literal><![CDATA[
      K(1 / z,u) = x
    ]]></literal>
    <justification jstring="[para(6237(a,2),51(a,1)),flip(a)].">
      <j1 rule="para" parents="6237 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6240">
    <literal><![CDATA[
      K(x,y * K(z,y \ 1)) = T(K(y,x),z) \ 1
    ]]></literal>
    <justification jstring="[para(6238(a,1),5197(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6238 5197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6241">
    <literal><![CDATA[
      T(K(x,y),z) \ 1 = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(65,a,5806,a(flip),b,6240,a),flip(a)].">
      <j1 rule="hyper" parents="65 5806 6240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6242">
    <literal><![CDATA[
      1 / T(K(x,y),z) = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(192,a,6241,a)].">
      <j1 rule="hyper" parents="192 6241"/>
    </justification>
  </clause>

  <clause id="6243">
    <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="[para(6241(a,1),258(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6241 258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6244">
    <literal><![CDATA[
      K(x,y) * T(K(y,x),z) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(6241(a,1),5034(a,2,2)),flip(a)].">
      <j1 rule="para" parents="6241 5034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6245">
    <literal><![CDATA[
      T(K(x,y),z) * K(y,x) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[para(6242(a,1),5032(a,2,1)),flip(a)].">
      <j1 rule="para" parents="6242 5032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6246">
    <literal><![CDATA[
      K(x,y) * K(z,K(y,x)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(5437,a,6244,a)].">
      <j1 rule="hyper" parents="5437 6244"/>
    </justification>
  </clause>

  <clause id="6247">
    <literal><![CDATA[
      K(K(x,y),z) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(5554,a,6245,a)].">
      <j1 rule="hyper" parents="5554 6245"/>
    </justification>
  </clause>

  <clause id="6248">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(K(z,y),x) = u
    ]]></literal>
    <justification jstring="[para(6245(a,1),5554(a,1))].">
      <j1 rule="para" parents="6245 5554"/>
    </justification>
  </clause>

  <clause id="6249">
    <literal><![CDATA[
      K(x,K(y,z)) \ 1 = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(5453,a,6247,a)].">
      <j1 rule="hyper" parents="5453 6247"/>
    </justification>
  </clause>

  <clause id="6250">
    <literal><![CDATA[
      x * K(K(y,z),x) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(6247(a,2),5083(a,2,2)),flip(a)].">
      <j1 rule="para" parents="6247 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6251">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z,y) = T(K(z,y),x)
    ]]></literal>
    <justification jstring="[para(6247(a,1),5096(a,2,1)),flip(a)].">
      <j1 rule="para" parents="6247 5096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6252">
    <literal><![CDATA[
      K(x,K(y,z)) \ 1 != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(6247(a,1),5200(a,1,1))].">
      <j1 rule="para" parents="6247 5200"/>
    </justification>
  </clause>

  <clause id="6253">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,y) * u) = T(K(z,y),x) * u
    ]]></literal>
    <justification jstring="[para(6247(a,1),5103(a,1,1))].">
      <j1 rule="para" parents="6247 5103"/>
    </justification>
  </clause>

  <clause id="6254">
    <literal><![CDATA[
      T(K(x,y) \ z,K(y,x)) = z / K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5498,a,6250,a),flip(a)].">
      <j1 rule="hyper" parents="5498 6250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6255">
    <literal><![CDATA[
      (K(x,y) * z) / K(x,y) = T(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(5268,a,6250,a)].">
      <j1 rule="hyper" parents="5268 6250"/>
    </justification>
  </clause>

  <clause id="6256">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(5239,a,6250,a)].">
      <j1 rule="hyper" parents="5239 6250"/>
    </justification>
  </clause>

  <clause id="6257">
    <literal><![CDATA[
      T(x,K(y,z)) * K(z,y) = K(z,y) * x
    ]]></literal>
    <justification jstring="[para(6250(a,1),5099(a,1,1))].">
      <j1 rule="para" parents="6250 5099"/>
    </justification>
  </clause>

  <clause id="6258">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(6250(a,1),5240(a,1,1))].">
      <j1 rule="para" parents="6250 5240"/>
    </justification>
  </clause>

  <clause id="6259">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      (K(z,y) * x) / K(z,y) = u
    ]]></literal>
    <justification jstring="[para(6250(a,1),5268(a,1))].">
      <j1 rule="para" parents="6250 5268"/>
    </justification>
  </clause>

  <clause id="6260">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y) * x) = L(x,K(z,y),x)
    ]]></literal>
    <justification jstring="[para(6250(a,1),5470(a,1,1))].">
      <j1 rule="para" parents="6250 5470"/>
    </justification>
  </clause>

  <clause id="6261">
    <literal><![CDATA[
      T(K(x,y),K(x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2283,a,6256,a),flip(a)].">
      <j1 rule="hyper" parents="2283 6256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6262">
    <literal><![CDATA[
      T(K(x,y),K(z,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2277,a,6256,a),flip(a)].">
      <j1 rule="hyper" parents="2277 6256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6264">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(u,K(z,y)) = x
    ]]></literal>
    <justification jstring="[para(6256(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="6256 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6265">
    <literal><![CDATA[
      K(x,y) * z != u * K(x,y)
    ]]></literal>
    <literal><![CDATA[
      T(z,K(y,x)) = u
    ]]></literal>
    <justification jstring="[para(6256(a,1),237(a,1,2))].">
      <j1 rule="para" parents="6256 237"/>
    </justification>
  </clause>

  <clause id="6266">
    <literal><![CDATA[
      K(x,y) * K(x,z) = K(x,z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(6261(a,1),107(a,1,2))].">
      <j1 rule="para" parents="6261 107"/>
    </justification>
  </clause>

  <clause id="6267">
    <literal><![CDATA[
      K(x,y) * K(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(6261(a,1),276(a,1,2))].">
      <j1 rule="para" parents="6261 276"/>
    </justification>
  </clause>

  <clause id="6268">
    <literal><![CDATA[
      K(x,y) \ K(z,x) = K(z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,6262,a(flip),b,5431,a)].">
      <j1 rule="hyper" parents="119 6262 5431"/>
    </justification>
  </clause>

  <clause id="6269">
    <literal><![CDATA[
      K(x,y) * K(z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(6262(a,1),276(a,1,2))].">
      <j1 rule="para" parents="6262 276"/>
    </justification>
  </clause>

  <clause id="6271">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x * K(K(z,y),x) = u
    ]]></literal>
    <justification jstring="[para(5053(a,1),6258(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5053 6258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6275">
    <literal><![CDATA[
      K(x,y) * T(K(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(6246(a,1),5438(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6246 5438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6276">
    <literal><![CDATA[
      (x * T(x \ y,z)) / K((x / y) \ 1,z) = T(y,K(z,(x / y) \ 1))
    ]]></literal>
    <justification jstring="[para(5329(a,1),6255(a,1,1))].">
      <j1 rule="para" parents="5329 6255"/>
    </justification>
  </clause>

  <clause id="6277">
    <literal><![CDATA[
      (K(x,y) * z) / K(x,y) != u * w
    ]]></literal>
    <literal><![CDATA[
      T(z,K(y,x)) / w = u
    ]]></literal>
    <justification jstring="[para(6257(a,1),304(a,1,1))].">
      <j1 rule="para" parents="6257 304"/>
    </justification>
  </clause>

  <clause id="6278">
    <literal><![CDATA[
      K(x,1 / x) * y = y * K(x,1 / x)
    ]]></literal>
    <justification jstring="[para(3200(a,1),6257(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3200 6257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6279">
    <literal><![CDATA[
      T(x,y) * (x \ K(x,z)) = K(x,z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5775,a,6266,a)].">
      <j1 rule="hyper" parents="5775 6266"/>
    </justification>
  </clause>

  <clause id="6280">
    <literal><![CDATA[
      x * (T(x,y) \ K(z,x)) = K(z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(5107,a,6268,a)].">
      <j1 rule="hyper" parents="5107 6268"/>
    </justification>
  </clause>

  <clause id="6281">
    <literal><![CDATA[
      x \ K(y,z) != K(y,z) * K(u,z)
    ]]></literal>
    <literal><![CDATA[
      K(z,u) = x
    ]]></literal>
    <justification jstring="[para(6268(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="6268 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6282">
    <literal><![CDATA[
      K(x,1 / x) * (y * z) = y * (z * K(x,1 / x))
    ]]></literal>
    <justification jstring="[hyper(299,a,3394,a(flip),b,6278,a),flip(a)].">
      <j1 rule="hyper" parents="299 3394 6278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6283">
    <literal><![CDATA[
      (x \ y) * K(x,1 / x) = (1 / (1 / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(65,a,5693,a,b,6278,a),flip(a)].">
      <j1 rule="hyper" parents="65 5693 6278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6284">
    <literal><![CDATA[
      (K(x,1 / x) * y) * z = (y * z) * K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(65,a,2493,a,b,6278,a)].">
      <j1 rule="hyper" parents="65 2493 6278"/>
    </justification>
  </clause>

  <clause id="6285">
    <literal><![CDATA[
      K(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(y,x)) = u
    ]]></literal>
    <justification jstring="[para(5197(a,1),6252(a,1))].">
      <j1 rule="para" parents="5197 6252"/>
    </justification>
  </clause>

  <clause id="6286">
    <literal><![CDATA[
      T(K(x,y),z) * K(y,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(y,x)) = u
    ]]></literal>
    <justification jstring="[para(5277(a,2),6285(a,1))].">
      <j1 rule="para" parents="5277 6285"/>
    </justification>
  </clause>

  <clause id="6287">
    <literal><![CDATA[
      (x \ K(x,y)) * T((x \ 1) \ 1,z) = K(x,y) * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,4576,a,b,6279,a)].">
      <j1 rule="hyper" parents="65 4576 6279"/>
    </justification>
  </clause>

  <clause id="6288">
    <literal><![CDATA[
      T(x,y) \ ((z * x) / z) = K(z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,5234,a,b,6280,a)].">
      <j1 rule="hyper" parents="65 5234 6280"/>
    </justification>
  </clause>

  <clause id="6289">
    <literal><![CDATA[
      L(x,y,((z \ 1) \ 1) * (T(z,u) \ K(w,z))) = L(x,y,K(w,z) * K(u,z))
    ]]></literal>
    <justification jstring="[para(6280(a,1),2500(a,2,3))].">
      <j1 rule="para" parents="6280 2500"/>
    </justification>
  </clause>

  <clause id="6290">
    <literal><![CDATA[
      ((x * y) / x) \ (T(y,z) * ((K(x,y) * K(z,y)) * u)) = L(u,T(y,z) \ ((x * y) / x),T(y,z))
    ]]></literal>
    <justification jstring="[para(6288(a,1),95(a,1,2,2,1))].">
      <j1 rule="para" parents="6288 95"/>
    </justification>
  </clause>

  <clause id="6291">
    <literal><![CDATA[
      (x * K(y,1 / y)) / z = K(y,1 / y) * (x / z)
    ]]></literal>
    <justification jstring="[hyper(120,a,154,a(flip),b,6284,a)].">
      <j1 rule="hyper" parents="120 154 6284"/>
    </justification>
  </clause>

  <clause id="6292">
    <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(918,a,6291,a)].">
      <j1 rule="hyper" parents="918 6291"/>
    </justification>
  </clause>

  <clause id="6293">
    <literal><![CDATA[
      K(x * y,T(y,z)) = K(y * x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(5878,a,5985,a),flip(a)].">
      <j1 rule="hyper" parents="5878 5985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6294">
    <literal><![CDATA[
      R(K(x,y),z,u) \ w = R(K(y,x),z,u) * w
    ]]></literal>
    <justification jstring="[para(6213(a,1),6013(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6213 6013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6295">
    <literal><![CDATA[
      R(K(x,y),z,u) \ 1 = R(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(3788,a,6294,a)].">
      <j1 rule="hyper" parents="3788 6294"/>
    </justification>
  </clause>

  <clause id="6296">
    <literal><![CDATA[
      (x * y) / ((K(z,u) * x) * y) = R(K(u,z),x,y)
    ]]></literal>
    <justification jstring="[hyper(656,a,6294,a)].">
      <j1 rule="hyper" parents="656 6294"/>
    </justification>
  </clause>

  <clause id="6297">
    <literal><![CDATA[
      R(K(x,y),z,u) \ (z * u) = (K(y,x) * z) * u
    ]]></literal>
    <justification jstring="[hyper(612,a,6294,a)].">
      <j1 rule="hyper" parents="612 6294"/>
    </justification>
  </clause>

  <clause id="6298">
    <literal><![CDATA[
      x / (R(K(y,z),u,w) * x) = R(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(577,a,6294,a)].">
      <j1 rule="hyper" parents="577 6294"/>
    </justification>
  </clause>

  <clause id="6299">
    <literal><![CDATA[
      R(K(x,y),z,u) \ 1 != w
    ]]></literal>
    <literal><![CDATA[
      R(K(y,x),z,u) = w
    ]]></literal>
    <justification jstring="[para(6294(a,2),132(a,1)),flip(b)].">
      <j1 rule="para" parents="6294 132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6300">
    <literal><![CDATA[
      R(K(x,y),z,u) \ w != v5
    ]]></literal>
    <literal><![CDATA[
      R(K(y,x),z,u) * w = v5
    ]]></literal>
    <justification jstring="[para(6298(a,1),317(a,1,1))].">
      <j1 rule="para" parents="6298 317"/>
    </justification>
  </clause>

  <clause id="6301">
    <literal><![CDATA[
      R(K(x,y),z,(K(y,x) * z) \ 1) = z * ((K(y,x) * z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(259,a,6296,a),flip(a)].">
      <j1 rule="hyper" parents="259 6296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6302">
    <literal><![CDATA[
      R(K(x,y),z,u) != (z * u) / w
    ]]></literal>
    <literal><![CDATA[
      (K(y,x) * z) * u = w
    ]]></literal>
    <justification jstring="[para(6296(a,1),47(a,1))].">
      <j1 rule="para" parents="6296 47"/>
    </justification>
  </clause>

  <clause id="6303">
    <literal><![CDATA[
      K((x * (y \ 1)) \ 1,y) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,5400,a(flip),b,6014,a),flip(a)].">
      <j1 rule="hyper" parents="65 5400 6014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6304">
    <literal><![CDATA[
      (x * K((x \ y) \ 1,z)) * (x \ 1) = K((y * (x \ 1)) \ 1,z)
    ]]></literal>
    <justification jstring="[para(5328(a,1),6014(a,1,1))].">
      <j1 rule="para" parents="5328 6014"/>
    </justification>
  </clause>

  <clause id="6305">
    <literal><![CDATA[
      (1 / x) * (y * T(y \ x,z)) = K(((x \ 1) * y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,5623,a(flip),b,6015,a),flip(a)].">
      <j1 rule="hyper" parents="299 5623 6015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6306">
    <literal><![CDATA[
      K(((1 / x) * (y \ 1)) \ 1,z) = (1 / x) * (y \ T(y * x,z))
    ]]></literal>
    <justification jstring="[para(1012(a,1),6015(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1012 6015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6307">
    <literal><![CDATA[
      x * (y \ K((y * (x \ 1)) \ 1,z)) = T(x * (y \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(144,a,6018,a)].">
      <j1 rule="hyper" parents="144 6018"/>
    </justification>
  </clause>

  <clause id="6308">
    <literal><![CDATA[
      (1 / x) * (K(x,y) * ((1 / x) \ z)) = K((1 / x) \ 1,y) * z
    ]]></literal>
    <justification jstring="[para(6020(a,2),5341(a,1,2))].">
      <j1 rule="para" parents="6020 5341"/>
    </justification>
  </clause>

  <clause id="6309">
    <literal><![CDATA[
      x * T(x \ (y \ x),T(y,z)) = ((y \ 1) \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(5882,a,6021,a),flip(a)].">
      <j1 rule="hyper" parents="5882 6021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6310">
    <literal><![CDATA[
      L(x,y,T(z \ 1,u) * (z \ w)) = L(x,y,K(z \ 1,u) * w)
    ]]></literal>
    <justification jstring="[para(6026(a,1),5960(a,1,3))].">
      <j1 rule="para" parents="6026 5960"/>
    </justification>
  </clause>

  <clause id="6311">
    <literal><![CDATA[
      K(((1 / x) / (y / x)) \ 1,z) = (T(y,z) / x) / (y / x)
    ]]></literal>
    <justification jstring="[hyper(65,a,5894,a,b,6027,a)].">
      <j1 rule="hyper" parents="65 5894 6027"/>
    </justification>
  </clause>

  <clause id="6312">
    <literal><![CDATA[
      K(x,y / (x / (z \ 1))) = K(x,y / (x * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,6045,a(flip),b,6044,a),flip(a)].">
      <j1 rule="hyper" parents="65 6045 6044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6313">
    <literal><![CDATA[
      K(x \ ((1 / y) \ z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ ((y \ 1) \ z),u) = w
    ]]></literal>
    <justification jstring="[para(6057(a,1),5118(a,1))].">
      <j1 rule="para" parents="6057 5118"/>
    </justification>
  </clause>

  <clause id="6314">
    <literal><![CDATA[
      T((x * y) \ y,T(x,z)) = T((x * y) \ y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,6022,a(flip),b,6069,a),flip(a)].">
      <j1 rule="hyper" parents="299 6022 6069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6315">
    <literal><![CDATA[
      K(x,y \ K(y,z)) * z = z * K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),6075(a,2,2,2,1))].">
      <j1 rule="para" parents="9 6075"/>
    </justification>
  </clause>

  <clause id="6316">
    <literal><![CDATA[
      (x \ y) * (K(y,z) * K(y,z)) = x \ T(T(y,z),z)
    ]]></literal>
    <justification jstring="[para(5202(a,1),6198(a,2,2))].">
      <j1 rule="para" parents="5202 6198"/>
    </justification>
  </clause>

  <clause id="6317">
    <literal><![CDATA[
      T(x * K(y \ 1,x),y) = (y * y) \ ((x * y) / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(299,a,764,a(flip),b,6223,a),flip(a)].">
      <j1 rule="hyper" parents="299 764 6223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6318">
    <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(6224(a,1),544(a,1))].">
      <j1 rule="para" parents="6224 544"/>
    </justification>
  </clause>

  <clause id="6319">
    <literal><![CDATA[
      K(x \ 1,x) * (K(x,y) * K(x,z)) = (x \ K(x,y)) * T(x,z)
    ]]></literal>
    <justification jstring="[para(6287(a,1),3946(a,1,2))].">
      <j1 rule="para" parents="6287 3946"/>
    </justification>
  </clause>

  <clause id="6320">
    <literal><![CDATA[
      K((((x \ y) \ 1) * (x \ 1)) \ 1,z) = (1 / (x \ y)) * (x \ T(y,z))
    ]]></literal>
    <justification jstring="[para(1109(a,1),6305(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1109 6305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6321">
    <literal><![CDATA[
      x * (y \ K(y \ x,x)) = T(x * (y \ 1),x)
    ]]></literal>
    <justification jstring="[para(6303(a,1),6307(a,1,2,2))].">
      <j1 rule="para" parents="6303 6307"/>
    </justification>
  </clause>

  <clause id="6322">
    <literal><![CDATA[
      ((x * (K(y \ x,x) * (y \ 1))) / x) / (y \ 1) = y * (T(x * (y \ 1),x) / x)
    ]]></literal>
    <justification jstring="[para(6321(a,1),1998(a,2,2,1))].">
      <j1 rule="para" parents="6321 1998"/>
    </justification>
  </clause>

  <clause id="6323">
    <literal><![CDATA[
      K(((1 / x) / (y / x)) \ 1,z) * (y / x) = T(y,z) / x
    ]]></literal>
    <justification jstring="[hyper(143,a,6311,a(flip))].">
      <j1 rule="hyper" parents="143 6311"/>
    </justification>
  </clause>

  <clause id="6324">
    <literal><![CDATA[
      T(x * K(y \ 1,x),y) = T(x,y * y)
    ]]></literal>
    <justification jstring="[hyper(299,a,674,a(flip),b,6317,a),flip(a)].">
      <j1 rule="hyper" parents="299 674 6317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6325">
    <literal><![CDATA[
      T(((x \ 1) * y) / (x \ 1),x) = T(y,x * x)
    ]]></literal>
    <justification jstring="[hyper(5683,a,6324,a)].">
      <j1 rule="hyper" parents="5683 6324"/>
    </justification>
  </clause>

  <clause id="6326">
    <literal><![CDATA[
      T(x * K(y / z,x),z / y) = T(x,(z / y) * (z / y))
    ]]></literal>
    <justification jstring="[para(5852(a,1),6324(a,1,1,2))].">
      <j1 rule="para" parents="5852 6324"/>
    </justification>
  </clause>

  <clause id="6327">
    <literal><![CDATA[
      T((K(x \ 1,x) * y) / (x \ 1),x) = T((1 / x) \ y,x * x)
    ]]></literal>
    <justification jstring="[para(2653(a,1),6325(a,1,1,1))].">
      <j1 rule="para" parents="2653 6325"/>
    </justification>
  </clause>

  <clause id="6328">
    <literal><![CDATA[
      T(x \ y,z) \ T((x \ y) * (y \ x),z) = y \ (x * K(z,x \ y))
    ]]></literal>
    <justification jstring="[hyper(65,a,2196,a,b,5187,a)].">
      <j1 rule="hyper" parents="65 2196 5187"/>
    </justification>
  </clause>

  <clause id="6329">
    <literal><![CDATA[
      (T(x * y,z) * L(u,y,x)) \ (K(x * y,z) * ((x * y) * u)) = L(a(x,y,u),x * (y * u),K(x * y,z))
    ]]></literal>
    <justification jstring="[para(5374(a,1),523(a,1,1))].">
      <j1 rule="para" parents="5374 523"/>
    </justification>
  </clause>

  <clause id="6330">
    <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(5414(a,1),5440(a,1,2))].">
      <j1 rule="para" parents="5414 5440"/>
    </justification>
  </clause>

  <clause id="6331">
    <literal><![CDATA[
      ((1 / x) * y) \ K(x \ y,x) = L(y / x,x,x) \ 1
    ]]></literal>
    <justification jstring="[para(4858(a,1),5478(a,1,2))].">
      <j1 rule="para" parents="4858 5478"/>
    </justification>
  </clause>

  <clause id="6332">
    <literal><![CDATA[
      R(K(x,y),y / x,z) * ((y / T(x,y)) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[hyper(6300,a,5551,a)].">
      <j1 rule="hyper" parents="6300 5551"/>
    </justification>
  </clause>

  <clause id="6333">
    <literal><![CDATA[
      T(K(x * (y \ 1),y \ 1) / y,x) = R(1 / y,x,1 / y)
    ]]></literal>
    <justification jstring="[para(5601(a,1),5556(a,1,1,1))].">
      <j1 rule="para" parents="5601 5556"/>
    </justification>
  </clause>

  <clause id="6335">
    <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(5035(a,1),5768(a,1,1))].">
      <j1 rule="para" parents="5035 5768"/>
    </justification>
  </clause>

  <clause id="6336">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,L(x,u,w)) = K(L(x,y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(6335,a,6108,a)].">
      <j1 rule="hyper" parents="6335 6108"/>
    </justification>
  </clause>

  <clause id="6337">
    <literal><![CDATA[
      L(K(x \ 1,y),z,u) = K(L(x,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(6335,a,xx),flip(a)].">
      <j1 rule="hyper" parents="6335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6338">
    <literal><![CDATA[
      (x * y) * K(L(z,y,x) \ 1,u) = x * (y * K(z \ 1,u))
    ]]></literal>
    <justification jstring="[para(6337(a,1),94(a,1,2))].">
      <j1 rule="para" parents="6337 94"/>
    </justification>
  </clause>

  <clause id="6339">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,(x \ 1) * L((x \ 1) \ 1,u,w)) = L(1,y,z)
    ]]></literal>
    <justification jstring="[para(1863(a,1),6337(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1863 6337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6340">
    <literal><![CDATA[
      L(K(1 / x,y),z,u) = K(L(x,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[para(3565(a,2),6337(a,1,1))].">
      <j1 rule="para" parents="3565 6337"/>
    </justification>
  </clause>

  <clause id="6341">
    <literal><![CDATA[
      K(L(x \ 1,y,z) \ 1,u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(3567(a,1),6337(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3567 6337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6342">
    <literal><![CDATA[
      K(L(T(1 / x,y),z,u) \ 1,w) = L(T(K(x,w),y),z,u)
    ]]></literal>
    <justification jstring="[para(6235(a,1),6337(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6235 6337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6343">
    <literal><![CDATA[
      K(L(T(x \ 1,y),z,u) \ 1,w) = L(T(K(x,w),y),z,u)
    ]]></literal>
    <justification jstring="[para(6236(a,1),6337(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6236 6337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6344">
    <literal><![CDATA[
      L(K(1 / x,y),z,u) = K(1 / L(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(299,a,3565,a,b,6340,a),flip(a)].">
      <j1 rule="hyper" parents="299 3565 6340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6346">
    <literal><![CDATA[
      K(x,L(y \ 1,z,u) \ 1) = L(K(y,x),z,u) \ 1
    ]]></literal>
    <justification jstring="[para(6341(a,1),5197(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6341 5197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6347">
    <literal><![CDATA[
      K(x,L(y \ 1,z,u) \ 1) * w = L(K(y,x),z,u) \ w
    ]]></literal>
    <justification jstring="[para(6341(a,1),5426(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6341 5426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6348">
    <literal><![CDATA[
      (x * y) * K(1 / L(z,y,x),u) = x * (y * K(1 / z,u))
    ]]></literal>
    <justification jstring="[para(6344(a,1),94(a,1,2))].">
      <j1 rule="para" parents="6344 94"/>
    </justification>
  </clause>

  <clause id="6349">
    <literal><![CDATA[
      K(1 / L(x,y,z),L(x,u,w)) = L(K(1 / x,x),y,z)
    ]]></literal>
    <justification jstring="[para(6102(a,1),6344(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6102 6344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6350">
    <literal><![CDATA[
      L(K(x,y),z,u) \ 1 = L(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,6131,a(flip),b,6346,a),flip(a)].">
      <j1 rule="hyper" parents="65 6131 6346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6351">
    <literal><![CDATA[
      1 / L(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(y,x),z,u) = w
    ]]></literal>
    <justification jstring="[para(6350(a,1),310(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6350 310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6352">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,L(x,u,w)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,3408,a(flip),b,6336,a),flip(a)].">
      <j1 rule="hyper" parents="299 3408 6336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6353">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,L(x,u,w)) = K(x \ 1,L(x,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(299,a,6104,a,b,6352,a),flip(a)].">
      <j1 rule="hyper" parents="299 6104 6352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6355">
    <literal><![CDATA[
      K(x \ 1,x) / L(x,y,z) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(120,a,6352,a(flip),b,253,a(flip))].">
      <j1 rule="hyper" parents="120 6352 253"/>
    </justification>
  </clause>

  <clause id="6356">
    <literal><![CDATA[
      K(x,x \ 1) / L(x,y,z) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(2596(a,1),6355(a,1,1))].">
      <j1 rule="para" parents="2596 6355"/>
    </justification>
  </clause>

  <clause id="6357">
    <literal><![CDATA[
      K(1 / x,x) / L(x,y,z) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(2636(a,2),6355(a,1,1))].">
      <j1 rule="para" parents="2636 6355"/>
    </justification>
  </clause>

  <clause id="6358">
    <literal><![CDATA[
      K(L(x,y,z),L(x,y,z) \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(39,a,2613,a,b,6356,a)].">
      <j1 rule="hyper" parents="39 2613 6356"/>
    </justification>
  </clause>

  <clause id="6359">
    <literal><![CDATA[
      1 / T(L(x,y,z),1 / x) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,6105,a(flip),b,6357,a)].">
      <j1 rule="hyper" parents="65 6105 6357"/>
    </justification>
  </clause>

  <clause id="6360">
    <literal><![CDATA[
      L(x,y,z) \ K(x,x \ 1) = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,6358,a(flip),b,2585,a(flip))].">
      <j1 rule="hyper" parents="119 6358 2585"/>
    </justification>
  </clause>

  <clause id="6361">
    <literal><![CDATA[
      T(1 / (1 / L(x,y,z)),1 / x) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(3177,a,6359,a(flip))].">
      <j1 rule="hyper" parents="3177 6359"/>
    </justification>
  </clause>

  <clause id="6362">
    <literal><![CDATA[
      L(x,y,z) \ (1 / x) = x \ (1 / L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,6360,a(flip),b,2604,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 6360 2604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6363">
    <literal><![CDATA[
      L(x,y,z) \ K(x,L(x,u,w) \ 1) = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[para(6130(a,2),6360(a,1,2))].">
      <j1 rule="para" parents="6130 6360"/>
    </justification>
  </clause>

  <clause id="6364">
    <literal><![CDATA[
      T(T(1 / (1 / L(x,y,z)),u),1 / x) = T(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(6361(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6361 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6365">
    <literal><![CDATA[
      K(1 / L(x,y,z),L(x,u,w)) = K(1 / L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(299,a,6344,a(flip),b,6349,a),flip(a)].">
      <j1 rule="hyper" parents="299 6344 6349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6366">
    <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(6353(a,1),3240(a,1,1))].">
      <j1 rule="para" parents="6353 3240"/>
    </justification>
  </clause>

  <clause id="6367">
    <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(6353(a,1),3306(a,1,1))].">
      <j1 rule="para" parents="6353 3306"/>
    </justification>
  </clause>

  <clause id="6368">
    <literal><![CDATA[
      (L(x,y,z) \ x) / x = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,5634,a(flip),b,6363,a)].">
      <j1 rule="hyper" parents="65 5634 6363"/>
    </justification>
  </clause>

  <clause id="6369">
    <literal><![CDATA[
      T(1 / L(x,y,z),x) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(6363(a,1),5139(a,1,1))].">
      <j1 rule="para" parents="6363 5139"/>
    </justification>
  </clause>

  <clause id="6371">
    <literal><![CDATA[
      (1 / L(x,y,z)) * x = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(143,a,6368,a)].">
      <j1 rule="hyper" parents="143 6368"/>
    </justification>
  </clause>

  <clause id="6372">
    <literal><![CDATA[
      x / L(x,y,z) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(65,a,1793,a(flip),b,6371,a)].">
      <j1 rule="hyper" parents="65 1793 6371"/>
    </justification>
  </clause>

  <clause id="6373">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ x = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(186,a,6372,a)].">
      <j1 rule="hyper" parents="186 6372"/>
    </justification>
  </clause>

  <clause id="6374">
    <literal><![CDATA[
      a(x,x,y) \ y = L(y,x,x)
    ]]></literal>
    <justification jstring="[para(1986(a,1),6373(a,1,1))].">
      <j1 rule="para" parents="1986 6373"/>
    </justification>
  </clause>

  <clause id="6375">
    <literal><![CDATA[
      a(x,x,y) * L(y,x,x) = y
    ]]></literal>
    <justification jstring="[hyper(144,a,6374,a)].">
      <j1 rule="hyper" parents="144 6374"/>
    </justification>
  </clause>

  <clause id="6376">
    <literal><![CDATA[
      a(x,x,x) = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(41,a,2524,a(flip),b,6374,a),flip(a)].">
      <j1 rule="hyper" parents="41 2524 6374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6377">
    <literal><![CDATA[
      K(x,x \ 1) = a(x,x,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,2585,a,b,6376,a)].">
      <j1 rule="hyper" parents="299 2585 6376"/>
    </justification>
  </clause>

  <clause id="6378">
    <literal><![CDATA[
      (x \ 1) \ a(x,x,x) = x
    ]]></literal>
    <justification jstring="[hyper(119,a,6377,a(flip),b,2612,a(flip))].">
      <j1 rule="hyper" parents="119 6377 2612"/>
    </justification>
  </clause>

  <clause id="6379">
    <literal><![CDATA[
      T(a(x,x,x) * y,x \ 1) = (x \ 1) \ (y * (1 / x))
    ]]></literal>
    <justification jstring="[para(6377(a,1),3271(a,1,1,1))].">
      <j1 rule="para" parents="6377 3271"/>
    </justification>
  </clause>

  <clause id="6380">
    <literal><![CDATA[
      x * a(x,x,x) = L(x,x,x)
    ]]></literal>
    <justification jstring="[para(6378(a,1),1670(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6378 1670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6381">
    <literal><![CDATA[
      x \ L(x,x,x) = a(x,x,x)
    ]]></literal>
    <justification jstring="[hyper(125,a,6380,a)].">
      <j1 rule="hyper" parents="125 6380"/>
    </justification>
  </clause>

  <clause id="6382">
    <literal><![CDATA[
      x * K(x * x,x) = L(x,x,x)
    ]]></literal>
    <justification jstring="[para(92(a,2),6380(a,1,2))].">
      <j1 rule="para" parents="92 6380"/>
    </justification>
  </clause>

  <clause id="6383">
    <literal><![CDATA[
      K(x,x * x) = a(x,x,x)
    ]]></literal>
    <justification jstring="[hyper(5302,a,6381,a)].">
      <j1 rule="hyper" parents="5302 6381"/>
    </justification>
  </clause>

  <clause id="6384">
    <literal><![CDATA[
      T(x,x \ (x \ 1)) = L(x,x,x)
    ]]></literal>
    <justification jstring="[hyper(5825,a,6382,a)].">
      <j1 rule="hyper" parents="5825 6382"/>
    </justification>
  </clause>

  <clause id="6385">
    <literal><![CDATA[
      a((a(x,x,x) * y) * K(x \ 1,a(x,x,x) * y),z,u) = a((x \ 1) \ (y * (1 / x)),z,u)
    ]]></literal>
    <justification jstring="[para(6379(a,1),5535(a,2,1))].">
      <j1 rule="para" parents="6379 5535"/>
    </justification>
  </clause>

  <clause id="6386">
    <literal><![CDATA[
      K(x,L(T(y \ 1,z),u,w) \ 1) * v5 = L(T(K(y,x),z),u,w) \ v5
    ]]></literal>
    <justification jstring="[para(6343(a,1),5426(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6343 5426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6387">
    <literal><![CDATA[
      L(K(x,y),z,u) \ w = L(K(y,x),z,u) * w
    ]]></literal>
    <justification jstring="[para(6131(a,1),6347(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6131 6347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6388">
    <literal><![CDATA[
      L(K(x,y),z,u) * (L(K(y,x),z,u) * w) = w
    ]]></literal>
    <justification jstring="[hyper(316,a,6387,a)].">
      <j1 rule="hyper" parents="316 6387"/>
    </justification>
  </clause>

  <clause id="6389">
    <literal><![CDATA[
      L(K(x,y),z,u) \ K(x,w) = K(x,w) * L(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,2280,a(flip),b,6387,a),flip(a)].">
      <j1 rule="hyper" parents="299 2280 6387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6390">
    <literal><![CDATA[
      L(K(x,y),z,u) \ 1 != w
    ]]></literal>
    <literal><![CDATA[
      L(K(y,x),z,u) = w
    ]]></literal>
    <justification jstring="[para(6387(a,2),132(a,1)),flip(b)].">
      <j1 rule="para" parents="6387 132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6391">
    <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(6387(a,1),144(a,1))].">
      <j1 rule="para" parents="6387 144"/>
    </justification>
  </clause>

  <clause id="6392">
    <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(6388(a,1),314(a,1,2))].">
      <j1 rule="para" parents="6388 314"/>
    </justification>
  </clause>

  <clause id="6394">
    <literal><![CDATA[
      T(x,x \ 1) * ((x * x) \ y) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(5777,a,5410,a)].">
      <j1 rule="hyper" parents="5777 5410"/>
    </justification>
  </clause>

  <clause id="6395">
    <literal><![CDATA[
      T(x,y) * ((x * x) \ z) = (x \ K(x,y)) * z
    ]]></literal>
    <justification jstring="[hyper(5777,a,4573,a)].">
      <j1 rule="hyper" parents="5777 4573"/>
    </justification>
  </clause>

  <clause id="6396">
    <literal><![CDATA[
      L(T(x,y),x \ T(z,x),x) = T(L(x,x \ z,x),y)
    ]]></literal>
    <justification jstring="[para(5011(a,1),5797(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5011 5797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6397">
    <literal><![CDATA[
      L(T(x,y),x \ T(z,x),x) = L(T(x,y),x \ z,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,25,a,b,6396,a),flip(a)].">
      <j1 rule="hyper" parents="299 25 6396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6398">
    <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(6397(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6397 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6399">
    <literal><![CDATA[
      R(K(x \ y,x),y,z) = K(((x * z) / (y * z)) \ 1,x)
    ]]></literal>
    <justification jstring="[para(5857(a,1),6010(a,1,1))].">
      <j1 rule="para" parents="5857 6010"/>
    </justification>
  </clause>

  <clause id="6400">
    <literal><![CDATA[
      R(K(x \ (y / z),x),y / z,z) = K(((x * z) / y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(12(a,1),6399(a,2,1,1,2))].">
      <j1 rule="para" parents="12 6399"/>
    </justification>
  </clause>

  <clause id="6401">
    <literal><![CDATA[
      L(T(K(x,y \ z),u),y \ z,y) = K(x,T(z \ y,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,5798,a,b,6142,a),flip(a)].">
      <j1 rule="hyper" parents="299 5798 6142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6402">
    <literal><![CDATA[
      x / (R(K(y,z),u,(K(y,z) * u) \ 1) * x) = u * ((K(y,z) * u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,6298,a,b,6301,a)].">
      <j1 rule="hyper" parents="65 6298 6301"/>
    </justification>
  </clause>

  <clause id="6404">
    <literal><![CDATA[
      T(K(x * (y \ 1),y \ 1) / y,x) = R(1 / y,x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,3395,a(flip),b,6333,a),flip(a)].">
      <j1 rule="hyper" parents="299 3395 6333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6405">
    <literal><![CDATA[
      (x * y) * z != x * (y * K(u \ 1,w))
    ]]></literal>
    <literal><![CDATA[
      K(L(u,y,x) \ 1,w) = z
    ]]></literal>
    <justification jstring="[para(6338(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="6338 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6406">
    <literal><![CDATA[
      K(1 / L(x,y,z),x) = K(1 / x,x)
    ]]></literal>
    <justification jstring="[hyper(3424,a,6348,a),flip(a)].">
      <j1 rule="hyper" parents="3424 6348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6407">
    <literal><![CDATA[
      K(1 / L(x,y,z),L(x,u,w)) = K(1 / x,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,6365,a,b,6406,a)].">
      <j1 rule="hyper" parents="65 6365 6406"/>
    </justification>
  </clause>

  <clause id="6409">
    <literal><![CDATA[
      L(x,y,z) * K(1 / x,x) = 1 / (1 / L(x,y,z))
    ]]></literal>
    <justification jstring="[para(6407(a,1),2637(a,1,2))].">
      <j1 rule="para" parents="6407 2637"/>
    </justification>
  </clause>

  <clause id="6410">
    <literal><![CDATA[
      R(K(x \ (y / z),x),y / z,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / (x * z),x) = u
    ]]></literal>
    <justification jstring="[para(6400(a,2),6001(a,1))].">
      <j1 rule="para" parents="6400 6001"/>
    </justification>
  </clause>

  <clause id="6411">
    <literal><![CDATA[
      (x * y) \ (y * (x * T(K(x,y),z))) = K(y,x) * T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(5092(a,1),5216(a,1,2))].">
      <j1 rule="para" parents="5092 5216"/>
    </justification>
  </clause>

  <clause id="6412">
    <literal><![CDATA[
      (x * y) * K(R(y,x,y),x * y) = ((y * x) / R(y,x,y)) * y
    ]]></literal>
    <justification jstring="[hyper(1924,a,5241,a),flip(a)].">
      <j1 rule="hyper" parents="1924 5241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6413">
    <literal><![CDATA[
      (1 / (1 / x)) / (x * y) = x / (((x \ 1) \ 1) * y)
    ]]></literal>
    <justification jstring="[para(5140(a,1),5280(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5140 5280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6414">
    <literal><![CDATA[
      (1 / (1 / x)) / (x * (T(x,y) \ 1)) = x / (T(x,y) \ ((x \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(1844(a,1),6413(a,2,2))].">
      <j1 rule="para" parents="1844 6413"/>
    </justification>
  </clause>

  <clause id="6415">
    <literal><![CDATA[
      a(x,y * K(z \ 1,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(5454(a,2),5438(a,1)),flip(b)].">
      <j1 rule="para" parents="5454 5438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6416">
    <literal><![CDATA[
      a(x,y * K(z,z \ 1),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(2596(a,1),6415(a,1,2,2))].">
      <j1 rule="para" parents="2596 6415"/>
    </justification>
  </clause>

  <clause id="6417">
    <literal><![CDATA[
      a(x,(y \ 1) \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(2558(a,1),6416(a,1,2))].">
      <j1 rule="para" parents="2558 6416"/>
    </justification>
  </clause>

  <clause id="6421">
    <literal><![CDATA[
      (x * (y \ T(y * z,u))) / (x * z) = K((x * z) / (x * (y \ 1)),u)
    ]]></literal>
    <justification jstring="[para(1012(a,1),5594(a,1,1,2))].">
      <j1 rule="para" parents="1012 5594"/>
    </justification>
  </clause>

  <clause id="6422">
    <literal><![CDATA[
      L(((x * x) \ y) * K(x * x,y),z,u) = L(y,z,u) / (x * x)
    ]]></literal>
    <justification jstring="[hyper(65,a,3113,a,b,5828,a)].">
      <j1 rule="hyper" parents="65 3113 5828"/>
    </justification>
  </clause>

  <clause id="6423">
    <literal><![CDATA[
      ((x \ T(x * (y / z),u)) * z) / y = K((((x \ 1) * z) / y) \ 1,u)
    ]]></literal>
    <justification jstring="[para(1594(a,1),5837(a,1,1))].">
      <j1 rule="para" parents="1594 5837"/>
    </justification>
  </clause>

  <clause id="6424">
    <literal><![CDATA[
      x * K((x \ (y * z)) \ 1,z) = y * ((z \ (y \ x)) * z)
    ]]></literal>
    <justification jstring="[para(107(a,1),5842(a,2,2))].">
      <j1 rule="para" parents="107 5842"/>
    </justification>
  </clause>

  <clause id="6425">
    <literal><![CDATA[
      x * K((T(x,y) \ y) \ 1,z) = T(y * T(y \ x,z),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,2029,a(flip),b,5849,a),flip(a)].">
      <j1 rule="hyper" parents="65 2029 5849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6426">
    <literal><![CDATA[
      T(x * T(x \ y,z),y) != y * u
    ]]></literal>
    <literal><![CDATA[
      K((T(y,x) \ x) \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(6425(a,1),45(a,1))].">
      <j1 rule="para" parents="6425 45"/>
    </justification>
  </clause>

  <clause id="6427">
    <literal><![CDATA[
      K(x,y * ((((K(z,u) / z) \ 1) * u) * w)) = K(x,y * ((u * (1 / (1 / z))) * w))
    ]]></literal>
    <justification jstring="[para(5816(a,1),5904(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5816 5904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6428">
    <literal><![CDATA[
      R(K(x,y / z),y,u) = K(x,(y * u) / (z * u))
    ]]></literal>
    <justification jstring="[hyper(5992,a,6214,a),flip(a)].">
      <j1 rule="hyper" parents="5992 6214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6429">
    <literal><![CDATA[
      R(K(x,(y / z) / u),y / z,z) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[para(12(a,1),6428(a,2,2,1))].">
      <j1 rule="para" parents="12 6428"/>
    </justification>
  </clause>

  <clause id="6430">
    <literal><![CDATA[
      R(K(x,y / (z / u)),y,u) = K(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[para(12(a,1),6428(a,2,2,2))].">
      <j1 rule="para" parents="12 6428"/>
    </justification>
  </clause>

  <clause id="6431">
    <literal><![CDATA[
      K(x,(y * z) / ((u \ y) * z)) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(76(a,1),6428(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="76 6428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6432">
    <literal><![CDATA[
      K(x,R(y,y \ z,u)) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(100(a,2),6431(a,1,2))].">
      <j1 rule="para" parents="100 6431"/>
    </justification>
  </clause>

  <clause id="6433">
    <literal><![CDATA[
      R(K(x,y),T(y,z),u) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4259(a,1),6431(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4259 6431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6434">
    <literal><![CDATA[
      (K(x,y) * T(x,z)) \ 1 = T(x,z) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,6433,a(flip),b,6301,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 6433 6301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6435">
    <literal><![CDATA[
      (K(x,y) * T(y,z)) * u = K(x,y) * (T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(6433(a,1),103(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6433 103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6436">
    <literal><![CDATA[
      K(x,R(y,T(y,x) \ z,u)) = R(K(x,T(y,x)),z,u)
    ]]></literal>
    <justification jstring="[hyper(5311,a,6432,a)].">
      <j1 rule="hyper" parents="5311 6432"/>
    </justification>
  </clause>

  <clause id="6437">
    <literal><![CDATA[
      R(K(x,y),y * z,u) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),6432(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 6432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6438">
    <literal><![CDATA[
      R(K(x,y),z * y,u) = K(x,R(y,T(z,y),u))
    ]]></literal>
    <justification jstring="[para(22(a,2),6432(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="22 6432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6439">
    <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(182(a,1),6432(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="182 6432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6440">
    <literal><![CDATA[
      R(K(x,y),y \ 1,z) = K(x,y)
    ]]></literal>
    <justification jstring="[para(1637(a,1),6432(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1637 6432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6441">
    <literal><![CDATA[
      R(K(x,y),K(z,y) * u,w) = K(x,R(y,T(y,z) \ u,w))
    ]]></literal>
    <justification jstring="[para(5372(a,1),6432(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5372 6432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6442">
    <literal><![CDATA[
      K(x * y,R(x,y,z)) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(4613,a,6437,a),flip(a)].">
      <j1 rule="hyper" parents="4613 6437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6443">
    <literal><![CDATA[
      K(R(x,y * z,u) \ 1,y) = K(x \ 1,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,6008,a(flip),b,6437,a)].">
      <j1 rule="hyper" parents="65 6008 6437"/>
    </justification>
  </clause>

  <clause id="6444">
    <literal><![CDATA[
      K(x,R(x \ 1,y,z)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,2722,a(flip),b,6437,a),flip(a)].">
      <j1 rule="hyper" parents="65 2722 6437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6445">
    <literal><![CDATA[
      R(T(K(x,y),z),y * u,w) = T(K(x,R(y,u,w)),z)
    ]]></literal>
    <justification jstring="[para(6437(a,1),27(a,2,1))].">
      <j1 rule="para" parents="6437 27"/>
    </justification>
  </clause>

  <clause id="6446">
    <literal><![CDATA[
      (K(x,y) * T(x,z)) \ 1 = T(x,y) \ K(z,x)
    ]]></literal>
    <justification jstring="[para(5701(a,1),6434(a,1,1))].">
      <j1 rule="para" parents="5701 6434"/>
    </justification>
  </clause>

  <clause id="6447">
    <literal><![CDATA[
      L(x,T(y,z),K(u,y)) = x
    ]]></literal>
    <justification jstring="[hyper(490,a,6435,a)].">
      <j1 rule="hyper" parents="490 6435"/>
    </justification>
  </clause>

  <clause id="6448">
    <literal><![CDATA[
      K(x,R(y,T(y,x) \ z,u)) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(5190(a,1),6436(a,2,1))].">
      <j1 rule="para" parents="5190 6436"/>
    </justification>
  </clause>

  <clause id="6449">
    <literal><![CDATA[
      K(x / y,(x / y) / z) = K(x / y,x / (z * y))
    ]]></literal>
    <justification jstring="[hyper(4613,a,6429,a)].">
      <j1 rule="hyper" parents="4613 6429"/>
    </justification>
  </clause>

  <clause id="6450">
    <literal><![CDATA[
      R(K(x,y),K(x,y) * z,u) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,6448,a(flip),b,6441,a),flip(a)].">
      <j1 rule="hyper" parents="299 6448 6441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6451">
    <literal><![CDATA[
      R(K(x,y),y \ K(y,x),z) = R(K(x,y),y \ 1,z)
    ]]></literal>
    <justification jstring="[para(5455(a,1),6450(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5455 6450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6452">
    <literal><![CDATA[
      (x \ 1) * (R(K(y,x),x \ K(x,y),z) * z) = ((((x \ 1) * (K(y,x) * z)) / ((x \ 1) * z)) * (x \ 1)) * z
    ]]></literal>
    <justification jstring="[para(6451(a,2),1951(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="6451 1951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6454">
    <literal><![CDATA[
      T(((x * y) / x) * (y \ z),z) / z = K(x,(T(y \ z,z) / z) \ 1)
    ]]></literal>
    <justification jstring="[para(1098(a,1),6038(a,1,1,1))].">
      <j1 rule="para" parents="1098 6038"/>
    </justification>
  </clause>

  <clause id="6455">
    <literal><![CDATA[
      L(x,y,z * (((z \ 1) \ u) / z)) = L(x,y,z \ T(u,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,2482,a(flip),b,6050,a),flip(a)].">
      <j1 rule="hyper" parents="299 2482 6050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6456">
    <literal><![CDATA[
      K(x,y \ (z * ((1 / z) * u))) = K(x,y \ L(u,z,z))
    ]]></literal>
    <justification jstring="[para(1673(a,1),6059(a,2,2,2))].">
      <j1 rule="para" parents="1673 6059"/>
    </justification>
  </clause>

  <clause id="6457">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * T(K(y,x) \ z,u)) = T(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(5328(a,2),6072(a,1,2))].">
      <j1 rule="para" parents="5328 6072"/>
    </justification>
  </clause>

  <clause id="6458">
    <literal><![CDATA[
      T(K(x,y) * (z * K(y,x)),u) = K(x,y) * (T(z,u) * K(y,x))
    ]]></literal>
    <justification jstring="[para(5843(a,1),6072(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5843 6072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6459">
    <literal><![CDATA[
      (x \ 1) * (K(x,y) * ((x \ 1) \ z)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(3567(a,1),6147(a,2,1))].">
      <j1 rule="para" parents="3567 6147"/>
    </justification>
  </clause>

  <clause id="6460">
    <literal><![CDATA[
      K(x,x \ y) * ((x \ 1) \ (x \ y)) = (x \ 1) \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(119,a,5177,a(flip),b,6459,a),flip(a)].">
      <j1 rule="hyper" parents="119 5177 6459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6461">
    <literal><![CDATA[
      K(x,y) * ((x \ 1) * z) = (x \ 1) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),6459(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 6459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6462">
    <literal><![CDATA[
      (x \ 1) * (K(x,y) * T(z,x \ 1)) = K(x,y) * (z * (x \ 1))
    ]]></literal>
    <justification jstring="[para(22(a,2),6459(a,1,2,2))].">
      <j1 rule="para" parents="22 6459"/>
    </justification>
  </clause>

  <clause id="6463">
    <literal><![CDATA[
      (x \ 1) * (K(x,y) * z) = (x \ K(x,y)) * z
    ]]></literal>
    <justification jstring="[hyper(65,a,4573,a(flip),b,6461,a),flip(a)].">
      <j1 rule="hyper" parents="65 4573 6461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6464">
    <literal><![CDATA[
      x * (K(x,y) * ((x \ 1) * z)) = L(K(x,y) * z,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(6461(a,2),252(a,1,2))].">
      <j1 rule="para" parents="6461 252"/>
    </justification>
  </clause>

  <clause id="6465">
    <literal><![CDATA[
      ((x \ 1) * y) / ((x \ 1) * (K(x,z) * y)) = K(z,x)
    ]]></literal>
    <justification jstring="[para(6461(a,1),5430(a,1,2))].">
      <j1 rule="para" parents="6461 5430"/>
    </justification>
  </clause>

  <clause id="6466">
    <literal><![CDATA[
      (x \ K(x,y)) * K(y,x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(5212,a,6463,a),flip(a)].">
      <j1 rule="hyper" parents="5212 6463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6467">
    <literal><![CDATA[
      (x \ K(x,y)) * x = (x \ 1) * T(x,y)
    ]]></literal>
    <justification jstring="[para(5096(a,2),6463(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5096 6463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6468">
    <literal><![CDATA[
      R(x / (y \ K(y,z)),y \ K(y,z),K(z,y)) = (x * K(z,y)) / (y \ 1)
    ]]></literal>
    <justification jstring="[para(6466(a,1),104(a,2,2))].">
      <j1 rule="para" parents="6466 104"/>
    </justification>
  </clause>

  <clause id="6469">
    <literal><![CDATA[
      ((x \ 1) * (K(y,x) * z)) / ((x \ 1) * z) = K(y,x)
    ]]></literal>
    <justification jstring="[para(5432(a,1),6465(a,1,2,2))].">
      <j1 rule="para" parents="5432 6465"/>
    </justification>
  </clause>

  <clause id="6470">
    <literal><![CDATA[
      ((x \ y) \ ((x \ 1) \ (x \ y))) * (x \ y) = (x \ 1) \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(6146,a,6460,a)].">
      <j1 rule="hyper" parents="6146 6460"/>
    </justification>
  </clause>

  <clause id="6471">
    <literal><![CDATA[
      L(K(x,y) * z,x \ 1,x) = T(x,y) * ((x \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(5511,a,6464,a),flip(a)].">
      <j1 rule="hyper" parents="5511 6464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6472">
    <literal><![CDATA[
      T(x,y) * ((x \ 1) * (K(y,x) * z)) = L(z,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(5432(a,1),6471(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5432 6471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6473">
    <literal><![CDATA[
      a(x,y * K(z \ 1,y * z),u) = a(x,z * (y / z),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,3153,a(flip),b,6172,a),flip(a)].">
      <j1 rule="hyper" parents="299 3153 6172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6474">
    <literal><![CDATA[
      K(R(x,L(y,z,u),x),R(x,L(y,z,u),x) * y) * T(x * L(y,z,u),x) = L(y,z,u) * T(R(x,L(y,z,u),x),R(x,L(y,z,u),x) * y)
    ]]></literal>
    <justification jstring="[para(4341(a,1),6201(a,1,2))].">
      <j1 rule="para" parents="4341 6201"/>
    </justification>
  </clause>

  <clause id="6475">
    <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(4341(a,1),6203(a,1,2))].">
      <j1 rule="para" parents="4341 6203"/>
    </justification>
  </clause>

  <clause id="6476">
    <literal><![CDATA[
      K((x * ((1 / y) \ 1)) \ 1,z) / y = (1 / y) * K(((1 / y) \ x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(352,a,6304,a)].">
      <j1 rule="hyper" parents="352 6304"/>
    </justification>
  </clause>

  <clause id="6477">
    <literal><![CDATA[
      ((1 / x) * T((1 / x) \ y,z)) * (y \ 1) = (1 / x) * (y \ T(y * x,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,6014,a,b,6306,a)].">
      <j1 rule="hyper" parents="65 6014 6306"/>
    </justification>
  </clause>

  <clause id="6478">
    <literal><![CDATA[
      (1 / x) * (K(x,y) * ((1 / x) \ z)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(79(a,1),6308(a,2,1,1))].">
      <j1 rule="para" parents="79 6308"/>
    </justification>
  </clause>

  <clause id="6479">
    <literal><![CDATA[
      K(x,y) * ((1 / x) * z) = (1 / x) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),6478(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 6478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6481">
    <literal><![CDATA[
      (K(x,y) * z) \ (K(x,y) * ((1 / x) * z)) = T(1 / x,K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(119,a,6479,a,b,107,a)].">
      <j1 rule="hyper" parents="119 6479 107"/>
    </justification>
  </clause>

  <clause id="6483">
    <literal><![CDATA[
      (K(x,y) * K(x,z)) \ K(x,x \ 1) = ((x \ K(x,y)) * T(x,z)) \ 1
    ]]></literal>
    <justification jstring="[para(6319(a,1),2791(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6319 2791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6484">
    <literal><![CDATA[
      L(x,(y \ K(y,z)) * T(y,u),w) = L(x,K(y,z) * K(y,u),w)
    ]]></literal>
    <justification jstring="[para(6319(a,1),3971(a,1,2))].">
      <j1 rule="para" parents="6319 3971"/>
    </justification>
  </clause>

  <clause id="6485">
    <literal><![CDATA[
      T((K(x,x \ 1) * y) / (x \ 1),x) = T((1 / x) \ y,x * x)
    ]]></literal>
    <justification jstring="[para(2596(a,1),6327(a,1,1,1,1))].">
      <j1 rule="para" parents="2596 6327"/>
    </justification>
  </clause>

  <clause id="6486">
    <literal><![CDATA[
      (x * y) \ (y * (x * T(K(x,y),z))) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(299,a,6244,a(flip),b,6411,a),flip(a)].">
      <j1 rule="hyper" parents="299 6244 6411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6487">
    <literal><![CDATA[
      ((x * y) / R(x,y,x)) * x = (y * x) * K(T(x,y),y * x)
    ]]></literal>
    <justification jstring="[para(5194(a,1),6412(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5194 6412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6488">
    <literal><![CDATA[
      ((x * y) / R(x,y,x)) * x = T(x,y * x) * T(y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,5230,a(flip),b,6487,a),flip(a)].">
      <j1 rule="hyper" parents="299 5230 6487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6489">
    <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),6488(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 6488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6490">
    <literal><![CDATA[
      L(x / (y * y),z,u) = L(x,z,u) / (y * y)
    ]]></literal>
    <justification jstring="[para(5824(a,1),6422(a,1,1))].">
      <j1 rule="para" parents="5824 6422"/>
    </justification>
  </clause>

  <clause id="6491">
    <literal><![CDATA[
      L(x * (x * y),z,u) = x * (x * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(2101,a,6490,a),flip(a)].">
      <j1 rule="hyper" parents="2101 6490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6492">
    <literal><![CDATA[
      (x * x) * L((x * x) \ y,z,u) = L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(963,a,6490,a)].">
      <j1 rule="hyper" parents="963 6490"/>
    </justification>
  </clause>

  <clause id="6493">
    <literal><![CDATA[
      L(x,y,z) / (x * x) = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(459(a,1),6490(a,1,1)),flip(a)].">
      <j1 rule="para" parents="459 6490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6494">
    <literal><![CDATA[
      L(x,y,L(z \ 1,u,w)) = L(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(6493(a,1),2514(a,1,3))].">
      <j1 rule="para" parents="6493 2514"/>
    </justification>
  </clause>

  <clause id="6495">
    <literal><![CDATA[
      L(x,L(y \ 1,z,u),w) = L(x,L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(6493(a,1),2892(a,1,2))].">
      <j1 rule="para" parents="6493 2892"/>
    </justification>
  </clause>

  <clause id="6496">
    <literal><![CDATA[
      x * (x * L(x \ y,z,u)) = L(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),6491(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10 6491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6497">
    <literal><![CDATA[
      L(x * (y * y),z,u) = L(x,z,u) * (y * y)
    ]]></literal>
    <justification jstring="[hyper(994,a,6492,a),flip(a)].">
      <j1 rule="hyper" parents="994 6492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6498">
    <literal><![CDATA[
      L((x * x) \ y,z,u) = (x * x) \ L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(125,a,6492,a),flip(a)].">
      <j1 rule="hyper" parents="125 6492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6499">
    <literal><![CDATA[
      x * L(x \ 1,y,z) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,6492,a(flip),b,993,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 6492 993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6500">
    <literal><![CDATA[
      (1 / x) * L(x,y,z) = x * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,3823,a,b,6499,a)].">
      <j1 rule="hyper" parents="299 3823 6499"/>
    </justification>
  </clause>

  <clause id="6501">
    <literal><![CDATA[
      x \ (x \ L(x,y,z)) = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,6499,a)].">
      <j1 rule="hyper" parents="125 6499"/>
    </justification>
  </clause>

  <clause id="6502">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z * L(z \ 1,u,w)))) = L(z,y,x) \ L(L(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,4124,a,b,6499,a)].">
      <j1 rule="hyper" parents="65 4124 6499"/>
    </justification>
  </clause>

  <clause id="6503">
    <literal><![CDATA[
      (x \ 1) \ L(x \ 1,y,z) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,3820,a,b,6499,a)].">
      <j1 rule="hyper" parents="65 3820 6499"/>
    </justification>
  </clause>

  <clause id="6504">
    <literal><![CDATA[
      (1 / x) \ L(1 / x,y,z) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,2830,a,b,6499,a)].">
      <j1 rule="hyper" parents="65 2830 6499"/>
    </justification>
  </clause>

  <clause id="6505">
    <literal><![CDATA[
      (x \ y) \ L(x \ y,z,u) = x \ (y * L(y \ x,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,1874,a(flip),b,6499,a),flip(a)].">
      <j1 rule="hyper" parents="65 1874 6499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6506">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (x \ 1) = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(6499(a,1),1795(a,1,1))].">
      <j1 rule="para" parents="6499 1795"/>
    </justification>
  </clause>

  <clause id="6507">
    <literal><![CDATA[
      x * (y * L(y \ (x \ y),z,u)) = (x \ L(x,z,u)) * y
    ]]></literal>
    <justification jstring="[para(6499(a,1),1859(a,2,1))].">
      <j1 rule="para" parents="6499 1859"/>
    </justification>
  </clause>

  <clause id="6508">
    <literal><![CDATA[
      x * ((x * L(x \ 1,y,z)) * u) = (x \ L(x,y,z)) * (x * u)
    ]]></literal>
    <justification jstring="[para(6499(a,1),2061(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6499 2061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6509">
    <literal><![CDATA[
      x * L(x \ 1,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(6501(a,1),250(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6501 250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6510">
    <literal><![CDATA[
      L(x,y,L(1 / z,u,w)) = L(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(79(a,1),6494(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="79 6494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6511">
    <literal><![CDATA[
      L(x,y,L(z \ 1,z,u * z)) = L(x,y,R(u,z,z) \ (u * z))
    ]]></literal>
    <justification jstring="[para(2874(a,1),6494(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2874 6494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6512">
    <literal><![CDATA[
      L(x,L(1 / y,z,u),w) = L(x,L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(79(a,1),6495(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 6495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6513">
    <literal><![CDATA[
      L(x,L(L(y,y,y),z,u),w) = L(x,L(y \ 1,z,u),w)
    ]]></literal>
    <justification jstring="[para(2806(a,2),6495(a,1,2,1))].">
      <j1 rule="para" parents="2806 6495"/>
    </justification>
  </clause>

  <clause id="6514">
    <literal><![CDATA[
      x \ L(x * y,z,u) = x * L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(125,a,6496,a)].">
      <j1 rule="hyper" parents="125 6496"/>
    </justification>
  </clause>

  <clause id="6515">
    <literal><![CDATA[
      L(x * (y * x),z,u) = x * (L(y,z,u) * x)
    ]]></literal>
    <justification jstring="[para(682(a,1),6496(a,1,2)),flip(a)].">
      <j1 rule="para" parents="682 6496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6516">
    <literal><![CDATA[
      L(x * (y * y),z,u) * w = L(x,z,u) * ((y * y) * w)
    ]]></literal>
    <justification jstring="[para(6497(a,2),34(a,1,1))].">
      <j1 rule="para" parents="6497 34"/>
    </justification>
  </clause>

  <clause id="6517">
    <literal><![CDATA[
      (x * L(y * (z * z),u,w)) * v5 = (x * L(y,u,w)) * ((z * z) * v5)
    ]]></literal>
    <justification jstring="[para(6497(a,2),117(a,1,1,2))].">
      <j1 rule="para" parents="6497 117"/>
    </justification>
  </clause>

  <clause id="6518">
    <literal><![CDATA[
      (x * x) \ L(x,y,z) = L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(264(a,1),6498(a,1,1)),flip(a)].">
      <j1 rule="para" parents="264 6498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6520">
    <literal><![CDATA[
      L(1 / x,y,z) \ 1 = L(x,y,z) \ (x * x)
    ]]></literal>
    <justification jstring="[para(6518(a,1),464(a,1,1))].">
      <j1 rule="para" parents="6518 464"/>
    </justification>
  </clause>

  <clause id="6521">
    <literal><![CDATA[
      (x \ 1) * L(x,y,z) = x * L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(6518(a,1),738(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6518 738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6522">
    <literal><![CDATA[
      K(x,y * (z * ((u \ 1) \ L(1 / u,w,v5)))) = K(x,y * (z * (u \ L(u,w,v5))))
    ]]></literal>
    <justification jstring="[para(6504(a,1),5905(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6504 5905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6523">
    <literal><![CDATA[
      L(x \ 1,y,z) * ((x \ 1) \ u) = ((x \ L(x,y,z)) * x) * (x \ u)
    ]]></literal>
    <justification jstring="[para(6506(a,1),1993(a,1,1))].">
      <j1 rule="para" parents="6506 1993"/>
    </justification>
  </clause>

  <clause id="6524">
    <literal><![CDATA[
      L(L(1 / x,y,z),L(x,y,z),L(1 / x,y,z)) = L(((1 / x) \ 1) \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,4150,a(flip),b,6512,a),flip(a)].">
      <j1 rule="hyper" parents="65 4150 6512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6525">
    <literal><![CDATA[
      (x \ 1) \ L((x \ 1) * a(x,x,x),y,z) = (x \ 1) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(6378(a,1),6514(a,2,2,1))].">
      <j1 rule="para" parents="6378 6514"/>
    </justification>
  </clause>

  <clause id="6526">
    <literal><![CDATA[
      L(x * (y * x),z,u) != x * w
    ]]></literal>
    <literal><![CDATA[
      L(y,z,u) * x = w
    ]]></literal>
    <justification jstring="[para(6515(a,2),45(a,1))].">
      <j1 rule="para" parents="6515 45"/>
    </justification>
  </clause>

  <clause id="6527">
    <literal><![CDATA[
      L(1 / x,y,z) \ 1 = x * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(299,a,1352,a(flip),b,6520,a),flip(a)].">
      <j1 rule="hyper" parents="299 1352 6520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6529">
    <literal><![CDATA[
      (x \ 1) \ L(x \ 1,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(3820(a,2),6509(a,1))].">
      <j1 rule="para" parents="3820 6509"/>
    </justification>
  </clause>

  <clause id="6530">
    <literal><![CDATA[
      L(x,L(L(y,y,y),z,u),w) = L(x,L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(299,a,6495,a(flip),b,6513,a),flip(a)].">
      <j1 rule="hyper" parents="299 6495 6513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6531">
    <literal><![CDATA[
      (x \ L(x,y,z)) * L(u,L(x,y,z),x) = (x \ 1) * (L(L(x,x,x),y,z) * u)
    ]]></literal>
    <justification jstring="[para(6530(a,1),2822(a,1,2))].">
      <j1 rule="para" parents="6530 2822"/>
    </justification>
  </clause>

  <clause id="6532">
    <literal><![CDATA[
      x \ ((y * x) * L((y * x) \ x,z,u)) = T(y,x) \ L(x \ (y * x),z,u)
    ]]></literal>
    <justification jstring="[para(22(a,2),6505(a,1,1)),flip(a)].">
      <j1 rule="para" parents="22 6505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6533">
    <literal><![CDATA[
      (1 / x) \ ((y * y) * L((y * y) \ (1 / x),z,u)) = (x * (y * y)) \ L((1 / x) \ (y * y),z,u)
    ]]></literal>
    <justification jstring="[para(418(a,1),6505(a,1,1)),flip(a)].">
      <j1 rule="para" parents="418 6505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6534">
    <literal><![CDATA[
      K(x,y) \ T(K(x,y) * z,u) = K(y,x) * T(K(y,x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(125,a,6457,a)].">
      <j1 rule="hyper" parents="125 6457"/>
    </justification>
  </clause>

  <clause id="6535">
    <literal><![CDATA[
      T(K(x,y) * (z * K(y,x)),u) != K(x,y) * w
    ]]></literal>
    <literal><![CDATA[
      T(z,u) * K(y,x) = w
    ]]></literal>
    <justification jstring="[para(6458(a,2),45(a,1))].">
      <j1 rule="para" parents="6458 45"/>
    </justification>
  </clause>

  <clause id="6536">
    <literal><![CDATA[
      T(x \ y,x) / ((x \ 1) \ (x \ y)) = (x \ y) / ((x \ 1) \ (y / x))
    ]]></literal>
    <justification jstring="[para(6470(a,1),4677(a,2,2))].">
      <j1 rule="para" parents="6470 4677"/>
    </justification>
  </clause>

  <clause id="6537">
    <literal><![CDATA[
      T(K(x,x \ 1) * (y / (x \ 1)),x) = T((1 / x) \ y,x * x)
    ]]></literal>
    <justification jstring="[para(2594(a,1),6485(a,1,1))].">
      <j1 rule="para" parents="2594 6485"/>
    </justification>
  </clause>

  <clause id="6538">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (x * u) = x * ((x \ L(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(6499(a,1),6508(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6499 6508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6539">
    <literal><![CDATA[
      L(x,y,R(z,u,u) \ (z * u)) = L(x,y,L(u,u,z * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,6494,a(flip),b,6511,a),flip(a)].">
      <j1 rule="hyper" parents="65 6494 6511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6540">
    <literal><![CDATA[
      (K(x,y) * T(K(x,y) \ z,u)) * K(y,x) = T(z * K(y,x),u)
    ]]></literal>
    <justification jstring="[para(6534(a,1),3479(a,1,1))].">
      <j1 rule="para" parents="6534 3479"/>
    </justification>
  </clause>

  <clause id="6541">
    <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),6540(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 6540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6542">
    <literal><![CDATA[
      T(x * K(y \ 1,y),z) = T(x,z) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(3491(a,1),6540(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3491 6540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6543">
    <literal><![CDATA[
      x \ T(y * K(z \ 1,z),u) = (x \ T(y,u)) * K(z \ 1,z)
    ]]></literal>
    <justification jstring="[para(6542(a,2),3364(a,1,2))].">
      <j1 rule="para" parents="6542 3364"/>
    </justification>
  </clause>

  <clause id="6544">
    <literal><![CDATA[
      T((K(x,y) * z) * K(y,x),u) != w * K(y,x)
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * T(z,u) = w
    ]]></literal>
    <justification jstring="[para(6541(a,2),46(a,1))].">
      <j1 rule="para" parents="6541 46"/>
    </justification>
  </clause>

  <clause id="6545">
    <literal><![CDATA[
      K((x \ 1) \ y,x * x) = K(x \ y,x * x)
    ]]></literal>
    <justification jstring="[hyper(5317,a,5967,a)].">
      <j1 rule="hyper" parents="5317 5967"/>
    </justification>
  </clause>

  <clause id="6546">
    <literal><![CDATA[
      K(1 / L(x,y,z),x) / L(x,y,z) = (x / L(x,y,z)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(6344(a,1),5404(a,1,1))].">
      <j1 rule="para" parents="6344 5404"/>
    </justification>
  </clause>

  <clause id="6547">
    <literal><![CDATA[
      L(K(x,y) * (x \ z),x * K(y,x),y) = (T(y,x) * x) \ (y * z)
    ]]></literal>
    <justification jstring="[para(5695(a,1),5466(a,1,1))].">
      <j1 rule="para" parents="5695 5466"/>
    </justification>
  </clause>

  <clause id="6548">
    <literal><![CDATA[
      L(K(x \ y,x) * z,K(x,x \ y),y) = (x * (y / x)) \ (y * z)
    ]]></literal>
    <justification jstring="[para(5432(a,1),5504(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5432 5504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6550">
    <literal><![CDATA[
      K(x,R(y,z,u)) * ((y * z) * u) = (y * (K(x,y) * z)) * u
    ]]></literal>
    <justification jstring="[para(6437(a,1),5721(a,1,1))].">
      <j1 rule="para" parents="6437 5721"/>
    </justification>
  </clause>

  <clause id="6551">
    <literal><![CDATA[
      K((x \ (y / (z \ 1))) \ 1,y) != u
    ]]></literal>
    <literal><![CDATA[
      K((x \ (y * z)) \ 1,y) = u
    ]]></literal>
    <justification jstring="[para(6229(a,2),6100(a,1))].">
      <j1 rule="para" parents="6229 6100"/>
    </justification>
  </clause>

  <clause id="6552">
    <literal><![CDATA[
      (1 / x) * (L(x,y,z) \ x) = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,6363,a(flip),b,6134,a),flip(a)].">
      <j1 rule="hyper" parents="65 6363 6134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6553">
    <literal><![CDATA[
      (1 / x) * ((L(x,y,z) \ 1) * x) = T(1 / L(x,y,z),x)
    ]]></literal>
    <justification jstring="[para(6552(a,1),1363(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6552 1363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6554">
    <literal><![CDATA[
      (1 / x) * a(y,y,x) = 1 / L(x,y,y)
    ]]></literal>
    <justification jstring="[para(1986(a,1),6552(a,1,2))].">
      <j1 rule="para" parents="1986 6552"/>
    </justification>
  </clause>

  <clause id="6555">
    <literal><![CDATA[
      (x \ 1) \ T(1 / L(x,y,z),x) = (L(x,y,z) \ 1) * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,6553,a(flip),b,3275,a)].">
      <j1 rule="hyper" parents="119 6553 3275"/>
    </justification>
  </clause>

  <clause id="6556">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,(x \ 1) * L((x \ 1) \ 1,u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(299,a,355,a(flip),b,6339,a),flip(a)].">
      <j1 rule="hyper" parents="299 355 6339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6558">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,x \ L(x,u,w)) = 1
    ]]></literal>
    <justification jstring="[para(1273(a,1),6556(a,1,2))].">
      <j1 rule="para" parents="1273 6556"/>
    </justification>
  </clause>

  <clause id="6559">
    <literal><![CDATA[
      T(L(x,y,z) \ 1,x \ L(x,u,w)) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,6558,a)].">
      <j1 rule="hyper" parents="58 6558"/>
    </justification>
  </clause>

  <clause id="6560">
    <literal><![CDATA[
      T(x \ L(x,y,z),L(x,u,w) \ 1) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(56,a,6559,a)].">
      <j1 rule="hyper" parents="56 6559"/>
    </justification>
  </clause>

  <clause id="6561">
    <literal><![CDATA[
      T(L(x,y,z) * (x \ 1),L(x,u,w) \ 1) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1274(a,2),6560(a,1,1))].">
      <j1 rule="para" parents="1274 6560"/>
    </justification>
  </clause>

  <clause id="6562">
    <literal><![CDATA[
      (L(x,y,z) * (x \ 1)) \ (x \ 1) = (x \ 1) / (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(6561(a,1),4660(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6561 4660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6563">
    <literal><![CDATA[
      (L(x,y,z) * (x \ 1)) \ (x \ 1) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(299,a,4038,a(flip),b,6562,a),flip(a)].">
      <j1 rule="hyper" parents="299 4038 6562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6564">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (x \ 1) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(1274(a,1),6563(a,1,1))].">
      <j1 rule="para" parents="1274 6563"/>
    </justification>
  </clause>

  <clause id="6565">
    <literal><![CDATA[
      (x / R(y,y \ x,y)) * y = T(y,x) * T(y \ x,y)
    ]]></literal>
    <justification jstring="[para(4371(a,1),6489(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4371 6489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6566">
    <literal><![CDATA[
      (x / R(y,y \ x,y)) * y = (y \ x) * T(y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,4305,a(flip),b,6565,a),flip(a)].">
      <j1 rule="hyper" parents="299 4305 6565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6567">
    <literal><![CDATA[
      x / R(y,y \ x,y) = y \ (x * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(37,a,5261,a,b,6566,a),flip(a)].">
      <j1 rule="hyper" parents="37 5261 6566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6568">
    <literal><![CDATA[
      x / R(y,y \ x,y) = (y * K(x,y)) \ x
    ]]></literal>
    <justification jstring="[hyper(299,a,5757,a,b,6567,a),flip(a)].">
      <j1 rule="hyper" parents="299 5757 6567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6569">
    <literal><![CDATA[
      x / ((y \ x) \ T(x,y)) = (y * K(x,y)) \ x
    ]]></literal>
    <justification jstring="[para(4343(a,1),6568(a,1,2))].">
      <j1 rule="para" parents="4343 6568"/>
    </justification>
  </clause>

  <clause id="6570">
    <literal><![CDATA[
      ((x * K(y,x)) \ y) \ y = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(186,a,6569,a)].">
      <j1 rule="hyper" parents="186 6569"/>
    </justification>
  </clause>

  <clause id="6571">
    <literal><![CDATA[
      (x \ (y * K(x,y))) \ y = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(5757(a,1),6570(a,1,1))].">
      <j1 rule="para" parents="5757 6570"/>
    </justification>
  </clause>

  <clause id="6572">
    <literal><![CDATA[
      (x \ ((x * y) / x)) \ y = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(5054(a,2),6571(a,1,1,2))].">
      <j1 rule="para" parents="5054 6571"/>
    </justification>
  </clause>

  <clause id="6573">
    <literal><![CDATA[
      K(1 / x,x) / L(x,y,z) = (x / L(x,y,z)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(6406(a,1),6546(a,1,1))].">
      <j1 rule="para" parents="6406 6546"/>
    </justification>
  </clause>

  <clause id="6574">
    <literal><![CDATA[
      (x / L(x,y,z)) * (x \ 1) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,6357,a(flip),b,6573,a),flip(a)].">
      <j1 rule="hyper" parents="65 6357 6573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6576">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (x \ 1) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(6372(a,1),6574(a,1,1))].">
      <j1 rule="para" parents="6372 6574"/>
    </justification>
  </clause>

  <clause id="6577">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) / x = L(1 / x,y,z) \ (1 / x)
    ]]></literal>
    <justification jstring="[hyper(352,a,6576,a)].">
      <j1 rule="hyper" parents="352 6576"/>
    </justification>
  </clause>

  <clause id="6578">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ (L(x,y,z) \ 1) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(125,a,6576,a)].">
      <j1 rule="hyper" parents="125 6576"/>
    </justification>
  </clause>

  <clause id="6579">
    <literal><![CDATA[
      (L(x \ 1,y,z) \ (x \ 1)) * T(1 / (1 / x),x \ 1) = K(x \ 1,x) * (L(x \ 1,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(6576(a,1),3728(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6576 3728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6580">
    <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(4386(a,1),4989(a,1,1))].">
      <j1 rule="para" parents="4386 4989"/>
    </justification>
  </clause>

  <clause id="6581">
    <literal><![CDATA[
      L(x,T(y,y \ z) \ 1,y) = L(x,((y \ z) \ z) \ 1,(y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,2542,a,b,4992,a),flip(a)].">
      <j1 rule="hyper" parents="65 2542 4992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6582">
    <literal><![CDATA[
      L(x,y \ 1,y) / (L(x,y \ 1,y) / y) = y * K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(4857(a,1),5009(a,2,2))].">
      <j1 rule="para" parents="4857 5009"/>
    </justification>
  </clause>

  <clause id="6583">
    <literal><![CDATA[
      K(x,y) * ((K(x,y) \ 1) \ (x / z)) = (K(x,y) * T(x,y)) / z
    ]]></literal>
    <justification jstring="[para(5050(a,2),5215(a,2,1,2))].">
      <j1 rule="para" parents="5050 5215"/>
    </justification>
  </clause>

  <clause id="6584">
    <literal><![CDATA[
      K(x,y) * ((K(x,y) \ 1) \ (x / z)) = T(T(x,y),y) / z
    ]]></literal>
    <justification jstring="[para(5202(a,1),6583(a,2,1))].">
      <j1 rule="para" parents="5202 6583"/>
    </justification>
  </clause>

  <clause id="6585">
    <literal><![CDATA[
      K(x,y) * (K(x,y) * (x / z)) = T(T(x,y),y) / z
    ]]></literal>
    <justification jstring="[para(5447(a,1),6584(a,1,2))].">
      <j1 rule="para" parents="5447 6584"/>
    </justification>
  </clause>

  <clause id="6586">
    <literal><![CDATA[
      T((x \ 1) * (x \ y),x \ (x \ 1)) = K(x,x \ 1) * (y / (x * x))
    ]]></literal>
    <justification jstring="[para(1710(a,1),5500(a,1,1))].">
      <j1 rule="para" parents="1710 5500"/>
    </justification>
  </clause>

  <clause id="6587">
    <literal><![CDATA[
      (K(x,y) * z) \ (y * (T(T(y,x),x) \ u)) = ((K(x,y) \ 1) * z) \ u
    ]]></literal>
    <justification jstring="[para(6199(a,1),5546(a,1,2))].">
      <j1 rule="para" parents="6199 5546"/>
    </justification>
  </clause>

  <clause id="6588">
    <literal><![CDATA[
      (x * K(y,z \ 1)) * z = (x * z) * K(y,z \ 1)
    ]]></literal>
    <justification jstring="[para(5629(a,1),5633(a,1,1))].">
      <j1 rule="para" parents="5629 5633"/>
    </justification>
  </clause>

  <clause id="6591">
    <literal><![CDATA[
      (x * K(y,(z \ 1) \ 1)) * (z \ 1) = (x * (z \ 1)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(4793(a,1),6588(a,2,2))].">
      <j1 rule="para" parents="4793 6588"/>
    </justification>
  </clause>

  <clause id="6592">
    <literal><![CDATA[
      (x * K(y,z)) * (z \ 1) = (x * (z \ 1)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(4793(a,1),6591(a,1,1,2))].">
      <j1 rule="para" parents="4793 6591"/>
    </justification>
  </clause>

  <clause id="6593">
    <literal><![CDATA[
      ((x * T(T(x,x \ 1),x \ 1)) \ y) * T(x,x \ 1) = (x \ 1) * T(y,T(x,x \ 1))
    ]]></literal>
    <justification jstring="[para(262(a,1),5708(a,2,1))].">
      <j1 rule="para" parents="262 5708"/>
    </justification>
  </clause>

  <clause id="6594">
    <literal><![CDATA[
      (x * T(y,y \ 1)) / (y \ 1) = x * (y * (T(y \ 1,y) \ 1))
    ]]></literal>
    <justification jstring="[para(4532(a,1),5709(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4532 5709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6595">
    <literal><![CDATA[
      (x * T(y,y \ 1)) / (y \ 1) = x * (y * y)
    ]]></literal>
    <justification jstring="[para(1697(a,1),6594(a,2,2,2))].">
      <j1 rule="para" parents="1697 6594"/>
    </justification>
  </clause>

  <clause id="6596">
    <literal><![CDATA[
      (x \ 1) \ (y * T(x,x \ 1)) = T(y * (x * x),x \ 1)
    ]]></literal>
    <justification jstring="[para(6595(a,1),109(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6595 109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6597">
    <literal><![CDATA[
      (x \ 1) \ (y * T(x,x \ 1)) = (1 / x) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(299,a,3750,a(flip),b,6596,a),flip(a)].">
      <j1 rule="hyper" parents="299 3750 6596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6598">
    <literal><![CDATA[
      (x \ 1) \ (y * ((x \ 1) \ 1)) = (1 / x) \ (y * x)
    ]]></literal>
    <justification jstring="[para(108(a,1),6597(a,1,2,2))].">
      <j1 rule="para" parents="108 6597"/>
    </justification>
  </clause>

  <clause id="6599">
    <literal><![CDATA[
      T(x,y \ 1) * (1 / (y \ 1)) = ((1 / y) \ (x * y)) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(6598(a,1),3735(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6598 3735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6600">
    <literal><![CDATA[
      ((1 / x) \ (y * x)) * (x \ 1) = T(y,x \ 1) * x
    ]]></literal>
    <justification jstring="[para(76(a,1),6599(a,1,2)),flip(a)].">
      <j1 rule="para" parents="76 6599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6602">
    <literal><![CDATA[
      T(x * K(y,x),(x * K(y,x)) \ 1) = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[para(5208(a,1),5822(a,2,2))].">
      <j1 rule="para" parents="5208 5822"/>
    </justification>
  </clause>

  <clause id="6603">
    <literal><![CDATA[
      ((x * K(y,x)) \ 1) \ 1 = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(409,a,6602,a)].">
      <j1 rule="hyper" parents="409 6602"/>
    </justification>
  </clause>

  <clause id="6604">
    <literal><![CDATA[
      T(x * K(y,x),x \ K(x,y)) = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[para(5223(a,1),6602(a,1,2))].">
      <j1 rule="para" parents="5223 6602"/>
    </justification>
  </clause>

  <clause id="6605">
    <literal><![CDATA[
      (x \ K(x,y)) \ 1 = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[para(5223(a,1),6603(a,1,1))].">
      <j1 rule="para" parents="5223 6603"/>
    </justification>
  </clause>

  <clause id="6606">
    <literal><![CDATA[
      a(x,y,z * K(u * u,1 / z)) = a(x,y,(1 / z) / (u * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,2362,a(flip),b,5826,a),flip(a)].">
      <j1 rule="hyper" parents="65 2362 5826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6607">
    <literal><![CDATA[
      a(x,y,z * K(u * u,1 / z)) = a(x,y,1 / ((u * u) * z))
    ]]></literal>
    <justification jstring="[para(425(a,1),6606(a,2,3))].">
      <j1 rule="para" parents="425 6606"/>
    </justification>
  </clause>

  <clause id="6608">
    <literal><![CDATA[
      a(x,y,z * K(u * u,1 / z)) = a(x,y,(u * u) * z)
    ]]></literal>
    <justification jstring="[hyper(299,a,2359,a(flip),b,6607,a),flip(a)].">
      <j1 rule="hyper" parents="299 2359 6607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6609">
    <literal><![CDATA[
      a(x,y,z * K(u * u,1 / z)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,2357,a(flip),b,6608,a),flip(a)].">
      <j1 rule="hyper" parents="299 2357 6608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6611">
    <literal><![CDATA[
      a(x,y,z * K(u * u,z \ 1)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(4797(a,1),6609(a,1,3,2))].">
      <j1 rule="para" parents="4797 6609"/>
    </justification>
  </clause>

  <clause id="6612">
    <literal><![CDATA[
      (x * (y * ((x \ z) / y))) / z = K(y,((x * y) / z) \ 1)
    ]]></literal>
    <justification jstring="[para(10(a,1),6037(a,1,1,2,2,1))].">
      <j1 rule="para" parents="10 6037"/>
    </justification>
  </clause>

  <clause id="6613">
    <literal><![CDATA[
      (x * (y * ((x \ z) / y))) / z = K(y,z / (x * y))
    ]]></literal>
    <justification jstring="[hyper(299,a,5937,a(flip),b,6612,a),flip(a)].">
      <j1 rule="hyper" parents="299 5937 6612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6614">
    <literal><![CDATA[
      (x * (y * ((x \ z) / y))) / z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z / (x * y)) = u
    ]]></literal>
    <justification jstring="[para(6612(a,2),5989(a,1))].">
      <j1 rule="para" parents="6612 5989"/>
    </justification>
  </clause>

  <clause id="6615">
    <literal><![CDATA[
      R(K(x,(y / z) / (u * x)),y / z,z) = ((u * (x * ((u \ (y / z)) / x))) * z) / y
    ]]></literal>
    <justification jstring="[para(6613(a,1),567(a,1,1))].">
      <j1 rule="para" parents="6613 567"/>
    </justification>
  </clause>

  <clause id="6616">
    <literal><![CDATA[
      L(x,y,(z \ 1) * ((((z \ 1) \ 1) \ u) / (z \ 1))) = L(x,y,T(T(u,z) / z,z \ 1))
    ]]></literal>
    <justification jstring="[para(4737(a,1),6049(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4737 6049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6617">
    <literal><![CDATA[
      L(x,y,z * ((T(z,u \ 1) / u) / z)) = L(x,y,z / u)
    ]]></literal>
    <justification jstring="[para(12(a,1),6052(a,2,3))].">
      <j1 rule="para" parents="12 6052"/>
    </justification>
  </clause>

  <clause id="6619">
    <literal><![CDATA[
      (x \ 1) \ (T(T(x \ 1,x),x) \ y) = (1 / x) \ ((1 / x) \ y)
    ]]></literal>
    <justification jstring="[para(1692(a,1),6055(a,2,2,1))].">
      <j1 rule="para" parents="1692 6055"/>
    </justification>
  </clause>

  <clause id="6620">
    <literal><![CDATA[
      (x \ 1) \ (T(1 / x,x) \ y) = (1 / x) \ ((1 / x) \ y)
    ]]></literal>
    <justification jstring="[para(1692(a,1),6619(a,1,2,1,1))].">
      <j1 rule="para" parents="1692 6619"/>
    </justification>
  </clause>

  <clause id="6621">
    <literal><![CDATA[
      (1 / x) \ ((1 / x) \ y) = (x \ 1) \ ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(109(a,1),6620(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="109 6620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6622">
    <literal><![CDATA[
      x \ ((x * x) * ((1 / x) \ y)) = (x \ 1) \ ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(1052,a,6621,a)].">
      <j1 rule="hyper" parents="1052 6621"/>
    </justification>
  </clause>

  <clause id="6623">
    <literal><![CDATA[
      (x \ K(x,y)) * (T(x,x \ 1) * z) = K(x,y) * L(z,x,x)
    ]]></literal>
    <justification jstring="[para(475(a,1),6066(a,2,2))].">
      <j1 rule="para" parents="475 6066"/>
    </justification>
  </clause>

  <clause id="6624">
    <literal><![CDATA[
      a(x,(y * z) * (y / (y * z)),u) = a(x,z * (y / z),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,6473,a(flip),b,6206,a),flip(a)].">
      <j1 rule="hyper" parents="299 6473 6206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6625">
    <literal><![CDATA[
      x / (y * (z * ((u \ (z \ (y \ x))) * u))) = K(u,x / (y * (u / (z \ 1))))
    ]]></literal>
    <justification jstring="[para(3858(a,1),6226(a,1,2,2))].">
      <j1 rule="para" parents="3858 6226"/>
    </justification>
  </clause>

  <clause id="6626">
    <literal><![CDATA[
      T(x \ y,z) * (y \ (x * K(z,x \ y))) = T((x \ y) * (y \ x),z)
    ]]></literal>
    <justification jstring="[hyper(144,a,6328,a)].">
      <j1 rule="hyper" parents="144 6328"/>
    </justification>
  </clause>

  <clause id="6627">
    <literal><![CDATA[
      L(T(K(x,y),z),u,w) \ v5 = L(T(K(y,x),z),u,w) * v5
    ]]></literal>
    <justification jstring="[para(6133(a,1),6386(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6133 6386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6628">
    <literal><![CDATA[
      L(T(K(x,y),z),z,z \ 1) * u = ((1 / z) * (K(y,x) * z)) \ u
    ]]></literal>
    <justification jstring="[para(2473(a,1),6627(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2473 6627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6629">
    <literal><![CDATA[
      ((1 / x) * (K(y,z) * x)) \ u = ((1 / x) * (K(z,y) * x)) * u
    ]]></literal>
    <justification jstring="[para(2473(a,1),6628(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2473 6628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6630">
    <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(299,a,29,a(flip),b,6398,a),flip(a)].">
      <j1 rule="hyper" parents="299 29 6398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6631">
    <literal><![CDATA[
      x / (T(x,y) \ ((x \ 1) \ 1)) = (1 / (1 / x)) / K(y,x)
    ]]></literal>
    <justification jstring="[para(5034(a,2),6414(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5034 6414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6632">
    <literal><![CDATA[
      x / (T(x,y) \ ((x \ 1) \ 1)) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[hyper(299,a,5111,a(flip),b,6631,a),flip(a)].">
      <j1 rule="hyper" parents="299 5111 6631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6633">
    <literal><![CDATA[
      x / (x * (1 / T(x,y))) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(3724(a,1),6632(a,1,2))].">
      <j1 rule="para" parents="3724 6632"/>
    </justification>
  </clause>

  <clause id="6634">
    <literal><![CDATA[
      T(1 / (1 / x),y) \ x = x * (1 / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(186,a,6633,a)].">
      <j1 rule="hyper" parents="186 6633"/>
    </justification>
  </clause>

  <clause id="6635">
    <literal><![CDATA[
      R(K(x * y,x),(x * y) * z,u) = K(x * y,R(R(x,y,z),y * z,u))
    ]]></literal>
    <justification jstring="[para(6442(a,1),6439(a,1,1))].">
      <j1 rule="para" parents="6442 6439"/>
    </justification>
  </clause>

  <clause id="6636">
    <literal><![CDATA[
      K(x,(T(y \ z,z) / z) \ 1) = T(K(x,y) * z,z) / z
    ]]></literal>
    <justification jstring="[para(5381(a,1),6454(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5381 6454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6637">
    <literal><![CDATA[
      K(x,(T(y \ z,z) / z) \ 1) = z \ T(z * K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(299,a,3460,a(flip),b,6636,a),flip(a)].">
      <j1 rule="hyper" parents="299 3460 6636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6638">
    <literal><![CDATA[
      K(x,y / T(z \ y,y)) = y \ T(y * K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(5989,a,6637,a)].">
      <j1 rule="hyper" parents="5989 6637"/>
    </justification>
  </clause>

  <clause id="6639">
    <literal><![CDATA[
      L(T(1 / x,y),y,K(x,z)) = T(1 / x,K(x,z) * y)
    ]]></literal>
    <justification jstring="[hyper(855,a,6481,a)].">
      <j1 rule="hyper" parents="855 6481"/>
    </justification>
  </clause>

  <clause id="6640">
    <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(6639(a,1),6342(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6639 6342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6641">
    <literal><![CDATA[
      L(T(K(x,y),z),z,K(x,u)) = T(K(x,y),K(x,u) * z)
    ]]></literal>
    <justification jstring="[hyper(299,a,6235,a(flip),b,6640,a),flip(a)].">
      <j1 rule="hyper" parents="299 6235 6640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6642">
    <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(6641(a,1),816(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6641 816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6643">
    <literal><![CDATA[
      L(x \ 1,y,z) * ((x \ 1) \ u) = L(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[para(3815(a,1),6523(a,2,1))].">
      <j1 rule="para" parents="3815 6523"/>
    </justification>
  </clause>

  <clause id="6644">
    <literal><![CDATA[
      L(L(x,y,z) * (x \ u),x,x) = x * (L(x \ 1,y,z) * u)
    ]]></literal>
    <justification jstring="[para(6643(a,1),1676(a,1,1))].">
      <j1 rule="para" parents="6643 1676"/>
    </justification>
  </clause>

  <clause id="6645">
    <literal><![CDATA[
      (1 / x) * (L(x,y,z) * u) = x * (L(x \ 1,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(1365,a,6644,a)].">
      <j1 rule="hyper" parents="1365 6644"/>
    </justification>
  </clause>

  <clause id="6646">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (x * (L(x \ 1,y,z) * u)) = L(u,L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(119,a,6645,a(flip),b,3847,a)].">
      <j1 rule="hyper" parents="119 6645 3847"/>
    </justification>
  </clause>

  <clause id="6648">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * T(x,x \ 1) = (x \ 1) \ (L(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(6369(a,1),6555(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6369 6555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6649">
    <literal><![CDATA[
      (x \ 1) \ (L(x,y,z) \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(65,a,3698,a(flip),b,6648,a),flip(a)].">
      <j1 rule="hyper" parents="65 3698 6648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6650">
    <literal><![CDATA[
      (x \ (L(x \ 1,y,z) \ 1)) * K(x \ 1,x) = L(x \ 1,y,z) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(3298,a,6649,a)].">
      <j1 rule="hyper" parents="3298 6649"/>
    </justification>
  </clause>

  <clause id="6651">
    <literal><![CDATA[
      (x \ 1) * (L(x,y,z) \ x) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(144,a,6649,a)].">
      <j1 rule="hyper" parents="144 6649"/>
    </justification>
  </clause>

  <clause id="6653">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (x \ 1) = (x \ 1) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(299,a,6564,a,b,6651,a)].">
      <j1 rule="hyper" parents="299 6564 6651"/>
    </justification>
  </clause>

  <clause id="6654">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ 1 = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(2393,a,6653,a)].">
      <j1 rule="hyper" parents="2393 6653"/>
    </justification>
  </clause>

  <clause id="6655">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ 1 = (1 / L(x,y,z)) * x
    ]]></literal>
    <justification jstring="[hyper(299,a,6371,a,b,6654,a),flip(a)].">
      <j1 rule="hyper" parents="299 6371 6654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6656">
    <literal><![CDATA[
      x * (T(y,x \ 1) * (y \ (T(x \ 1,y) * z))) = L(z,T(x \ 1,y),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,4700,a(flip),b,4963,a)].">
      <j1 rule="hyper" parents="65 4700 4963"/>
    </justification>
  </clause>

  <clause id="6657">
    <literal><![CDATA[
      L(T(x,y),T(z,x),K(x,z)) * z = K(x,z) * (T(x,y) * T(z,x))
    ]]></literal>
    <justification jstring="[para(5033(a,2),5067(a,1,1,3))].">
      <j1 rule="para" parents="5033 5067"/>
    </justification>
  </clause>

  <clause id="6658">
    <literal><![CDATA[
      K(x,y) * (T(x,z) * T(y,x)) = T(x,z) * y
    ]]></literal>
    <justification jstring="[para(4777(a,1),6657(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4777 6657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6660">
    <literal><![CDATA[
      K(x,y) * (K(x,z) * (y * x)) = T(x,z) * y
    ]]></literal>
    <justification jstring="[para(5353(a,2),6658(a,1,2))].">
      <j1 rule="para" parents="5353 6658"/>
    </justification>
  </clause>

  <clause id="6662">
    <literal><![CDATA[
      T(x * K(y * L(x,z,u),x),y) = R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(5256(a,1),857(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5256 857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6663">
    <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(5684,a,6662,a)].">
      <j1 rule="hyper" parents="5684 6662"/>
    </justification>
  </clause>

  <clause id="6664">
    <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(5258(a,1),1101(a,1,1,1))].">
      <j1 rule="para" parents="5258 1101"/>
    </justification>
  </clause>

  <clause id="6665">
    <literal><![CDATA[
      (x * y) * (z \ T(z * L(y \ (z \ 1),y,x),u)) = (x * K(y \ 1,u)) * (z \ 1)
    ]]></literal>
    <justification jstring="[para(1012(a,1),5343(a,1,2))].">
      <j1 rule="para" parents="1012 5343"/>
    </justification>
  </clause>

  <clause id="6666">
    <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(932(a,2),5477(a,1,2,2,1))].">
      <j1 rule="para" parents="932 5477"/>
    </justification>
  </clause>

  <clause id="6667">
    <literal><![CDATA[
      (x * (K(y,x) * z)) \ (x * (K(y,x) * (z * u))) = L(u,z,x * K(y,x))
    ]]></literal>
    <justification jstring="[para(5488(a,1),5711(a,1,2))].">
      <j1 rule="para" parents="5488 5711"/>
    </justification>
  </clause>

  <clause id="6668">
    <literal><![CDATA[
      L((1 / T(x,y)) \ z,T(x,y),y) = (T(y,x) * (1 / x)) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,2521,a(flip),b,5725,a)].">
      <j1 rule="hyper" parents="65 2521 5725"/>
    </justification>
  </clause>

  <clause id="6669">
    <literal><![CDATA[
      L(L(x * K(y,x),z,u),w,v5) * y = y * L(L(x,w,v5),z,u)
    ]]></literal>
    <justification jstring="[para(5809(a,1),5810(a,1,1,1))].">
      <j1 rule="para" parents="5809 5810"/>
    </justification>
  </clause>

  <clause id="6670">
    <literal><![CDATA[
      K((T(x,y) \ T(z,y)) \ 1,x) = K((x \ z) \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(6114,a,5840,a),flip(a)].">
      <j1 rule="hyper" parents="6114 5840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6671">
    <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(4149(a,2),6366(a,2,2))].">
      <j1 rule="para" parents="4149 6366"/>
    </justification>
  </clause>

  <clause id="6672">
    <literal><![CDATA[
      K(x \ 1,L(x,y,z)) * (x / L(x,u,w)) = (L(x,u,w) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(299,a,107,a(flip),b,6367,a),flip(a)].">
      <j1 rule="hyper" parents="299 107 6367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6675">
    <literal><![CDATA[
      L(x,T(y \ 1,z),y) = y * ((y \ 1) * x)
    ]]></literal>
    <justification jstring="[para(4958(a,1),6656(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4958 6656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6676">
    <literal><![CDATA[
      L(x,T(y \ 1,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,y) = u
    ]]></literal>
    <justification jstring="[para(6675(a,2),1686(a,1))].">
      <j1 rule="para" parents="6675 1686"/>
    </justification>
  </clause>

  <clause id="6678">
    <literal><![CDATA[
      R(x,y,z) * (R((u * x) / u,y,z) \ x) = x * K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(2204(a,1),6666(a,1,2))].">
      <j1 rule="para" parents="2204 6666"/>
    </justification>
  </clause>

  <clause id="6679">
    <literal><![CDATA[
      x / L((x \ 1) \ 1,y,z) = (L(x,y,z) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(65,a,6672,a(flip),b,6671,a),flip(a)].">
      <j1 rule="hyper" parents="65 6672 6671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6680">
    <literal><![CDATA[
      ((L(x,y,z) \ 1) * x) \ x = L((x \ 1) \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(186,a,6679,a)].">
      <j1 rule="hyper" parents="186 6679"/>
    </justification>
  </clause>

  <clause id="6681">
    <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(119,a,5121,a(flip),b,5060,a),flip(a)].">
      <j1 rule="hyper" parents="119 5121 5060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6682">
    <literal><![CDATA[
      ((T(x,y) \ 1) * (x \ 1)) \ z = x * ((T(x,y) \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(5106,a,5274,a),flip(a)].">
      <j1 rule="hyper" parents="5106 5274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6683">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(z,u)) = (T(z,u) * y) \ (T(z,u) * (y * x))
    ]]></literal>
    <justification jstring="[para(5103(a,1),5421(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5103 5421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6684">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(6683(a,2),493(a,1))].">
      <j1 rule="para" parents="6683 493"/>
    </justification>
  </clause>

  <clause id="6685">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(u,z)) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(6684,a,5218,a),flip(a)].">
      <j1 rule="hyper" parents="6684 5218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6686">
    <literal><![CDATA[
      L(x,y,T(y,z)) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(6684,a,477,a)].">
      <j1 rule="hyper" parents="6684 477"/>
    </justification>
  </clause>

  <clause id="6687">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(5218(a,1),6684(a,1))].">
      <j1 rule="para" parents="5218 6684"/>
    </justification>
  </clause>

  <clause id="6688">
    <literal><![CDATA[
      L(x,y \ z,z / y) = L(x,y \ z,y \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,5731,a(flip),b,6686,a)].">
      <j1 rule="hyper" parents="65 5731 6686"/>
    </justification>
  </clause>

  <clause id="6689">
    <literal><![CDATA[
      L(x,(y \ z) \ z,(y \ z) \ z) = L(x,(y \ z) \ z,y)
    ]]></literal>
    <justification jstring="[para(76(a,1),6688(a,1,3)),flip(a)].">
      <j1 rule="para" parents="76 6688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6690">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(u,z)) = L(x,y,z * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,5537,a,b,6685,a),flip(a)].">
      <j1 rule="hyper" parents="299 5537 6685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6691">
    <literal><![CDATA[
      L(x,y,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,y) = u
    ]]></literal>
    <justification jstring="[para(6685(a,1),497(a,1))].">
      <j1 rule="para" parents="6685 497"/>
    </justification>
  </clause>

  <clause id="6692">
    <literal><![CDATA[
      L(x,T(y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,T(y,z),T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(5730(a,1),6691(a,1))].">
      <j1 rule="para" parents="5730 6691"/>
    </justification>
  </clause>

  <clause id="6693">
    <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="[hyper(299,a,6667,a,b,6690,a)].">
      <j1 rule="hyper" parents="299 6667 6690"/>
    </justification>
  </clause>

  <clause id="6694">
    <literal><![CDATA[
      K(x,x \ y) * K(z,y / (y / x)) = T(y / (y / x),z) \ x
    ]]></literal>
    <justification jstring="[para(5195(a,1),5761(a,1,1))].">
      <j1 rule="para" parents="5195 5761"/>
    </justification>
  </clause>

  <clause id="6695">
    <literal><![CDATA[
      x \ K((x * ((y \ 1) / x)) \ 1,z) = (y \ T(y * K(x \ 1,x),z)) / x
    ]]></literal>
    <justification jstring="[para(6231(a,1),6017(a,1,2))].">
      <j1 rule="para" parents="6231 6017"/>
    </justification>
  </clause>

  <clause id="6696">
    <literal><![CDATA[
      K(x,y * (((1 / z) * (K(u,w) * z)) \ (w * (T(T(w,u),u) \ z)))) = K(x,y * ((z \ 1) \ K(u,w)))
    ]]></literal>
    <justification jstring="[para(6199(a,1),6041(a,1,2,2,2))].">
      <j1 rule="para" parents="6199 6041"/>
    </justification>
  </clause>

  <clause id="6697">
    <literal><![CDATA[
      (R(x,y,z) / x) \ (1 / x) = 1 / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,2585,a(flip),b,6211,a),flip(a)].">
      <j1 rule="hyper" parents="36 2585 6211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6698">
    <literal><![CDATA[
      R(1 / (1 / x),y,z) \ 1 = 1 / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,4927,a,b,6697,a)].">
      <j1 rule="hyper" parents="65 4927 6697"/>
    </justification>
  </clause>

  <clause id="6699">
    <literal><![CDATA[
      R(1 / (1 / x),y,z) = 1 / (1 / R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(192,a,6698,a),flip(a)].">
      <j1 rule="hyper" parents="192 6698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6700">
    <literal><![CDATA[
      1 / R(x \ 1,y,z) = R(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(76(a,1),6698(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="76 6698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6701">
    <literal><![CDATA[
      R(T(1 / (1 / x),y),z,u) \ 1 = 1 / R(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(3176(a,1),6698(a,1,1,1))].">
      <j1 rule="para" parents="3176 6698"/>
    </justification>
  </clause>

  <clause id="6702">
    <literal><![CDATA[
      R(x,y,z) * K(x \ 1,R(x,y,z)) = 1 / (1 / R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,6111,a,b,6699,a)].">
      <j1 rule="hyper" parents="65 6111 6699"/>
    </justification>
  </clause>

  <clause id="6703">
    <literal><![CDATA[
      1 / (1 / R(x \ 1,y,z)) = R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(76(a,1),6699(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="76 6699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6704">
    <literal><![CDATA[
      (R(1 / x,y,z) \ 1) \ 1 = R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(186,a,6700,a)].">
      <j1 rule="hyper" parents="186 6700"/>
    </justification>
  </clause>

  <clause id="6705">
    <literal><![CDATA[
      K(x * R(1 / y,z,u),w) = K(x * R(y \ 1,z,u),w)
    ]]></literal>
    <justification jstring="[para(6703(a,1),5604(a,1,1,2))].">
      <j1 rule="para" parents="6703 5604"/>
    </justification>
  </clause>

  <clause id="6706">
    <literal><![CDATA[
      R((x \ 1) \ 1,y,z) = (R(x,y,z) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(76(a,1),6704(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="76 6704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6707">
    <literal><![CDATA[
      R(((x / y) \ 1) \ 1,y,y \ 1) = ((x * (y \ 1)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(565(a,1),6706(a,2,1,1))].">
      <j1 rule="para" parents="565 6706"/>
    </justification>
  </clause>

  <clause id="6708">
    <literal><![CDATA[
      R(((x / (1 / y)) \ 1) \ 1,y \ 1,y) = ((x * y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(2693(a,1),6706(a,2,1,1))].">
      <j1 rule="para" parents="2693 6706"/>
    </justification>
  </clause>

  <clause id="6709">
    <literal><![CDATA[
      R(((x / y) \ 1) \ 1,y,z) * (y * z) = (y * z) * ((((y * z) \ (x * z)) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(6706(a,2),3190(a,1,1))].">
      <j1 rule="para" parents="6706 3190"/>
    </justification>
  </clause>

  <clause id="6710">
    <literal><![CDATA[
      1 / R(T(x,(1 / x) * y),1 / x,y) = (((1 / x) * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(803(a,1),6701(a,1,1)),flip(a)].">
      <j1 rule="para" parents="803 6701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6711">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,R(x,y,z)) = K(x \ 1,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(36,a,1716,a,b,6702,a)].">
      <j1 rule="hyper" parents="36 1716 6702"/>
    </justification>
  </clause>

  <clause id="6712">
    <literal><![CDATA[
      (R(x,y,z) \ 1) * R(x,y,z) = K(x \ 1,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(392,a,6711,a)].">
      <j1 rule="hyper" parents="392 6711"/>
    </justification>
  </clause>

  <clause id="6713">
    <literal><![CDATA[
      K(x \ 1,R(x,y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(R(x,y,z) \ 1,R(x,y,z)) = u
    ]]></literal>
    <justification jstring="[para(6712(a,1),363(a,1))].">
      <j1 rule="para" parents="6712 363"/>
    </justification>
  </clause>

  <clause id="6714">
    <literal><![CDATA[
      T(x * y,x \ (1 / y)) = ((x * y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,3358,a,b,6708,a)].">
      <j1 rule="hyper" parents="65 3358 6708"/>
    </justification>
  </clause>

  <clause id="6715">
    <literal><![CDATA[
      T(x * K(y,z),x \ K(z,y)) = ((x * K(y,z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(5209(a,1),6714(a,1,2,2))].">
      <j1 rule="para" parents="5209 6714"/>
    </justification>
  </clause>

  <clause id="6716">
    <literal><![CDATA[
      T(K(x,y) * K(x,z),K(x,y) \ K(z,x)) = ((K(x,z) * K(x,y)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(6266(a,1),6715(a,2,1,1))].">
      <j1 rule="para" parents="6266 6715"/>
    </justification>
  </clause>

  <clause id="6717">
    <literal><![CDATA[
      1 / R(T(x,(1 / x) * y),x \ 1,y) = (((1 / x) * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(3978(a,1),6710(a,1,2))].">
      <j1 rule="para" parents="3978 6710"/>
    </justification>
  </clause>

  <clause id="6718">
    <literal><![CDATA[
      1 / R(T(x,(x \ 1) * y),x \ 1,y) = (((1 / x) * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(2983(a,1),6717(a,1,2,1))].">
      <j1 rule="para" parents="2983 6717"/>
    </justification>
  </clause>

  <clause id="6719">
    <literal><![CDATA[
      (((1 / x) * (y * x)) \ (y * x)) \ 1 = 1 / R(T(x,y),x \ 1,y * x)
    ]]></literal>
    <justification jstring="[para(4744(a,1),6718(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4744 6718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6720">
    <literal><![CDATA[
      1 / R(T(x,y),x \ 1,y * x) = (L(y,x,x \ 1) \ (x * y)) \ 1
    ]]></literal>
    <justification jstring="[para(4910(a,1),6719(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4910 6719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6721">
    <literal><![CDATA[
      ((L(x,y,y \ 1) \ (y * x)) \ 1) \ 1 = R(T(y,x),y \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(186,a,6720,a)].">
      <j1 rule="hyper" parents="186 6720"/>
    </justification>
  </clause>

  <clause id="6722">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) \ (x * y) = R(T(x,y),x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(65,a,3447,a(flip),b,6721,a)].">
      <j1 rule="hyper" parents="65 3447 6721"/>
    </justification>
  </clause>

  <clause id="6723">
    <literal><![CDATA[
      x / (y * (z * ((u \ (z \ (y \ x))) * u))) = K(u,x / (y * (z * u)))
    ]]></literal>
    <justification jstring="[para(107(a,1),6225(a,1,2,2,2))].">
      <j1 rule="para" parents="107 6225"/>
    </justification>
  </clause>

  <clause id="6724">
    <literal><![CDATA[
      L(x,y,z * (T(1 / (1 / z),u) \ K(w,z))) = L(x,y,K(w,z) * K(u,z))
    ]]></literal>
    <justification jstring="[para(3727(a,1),6289(a,1,3))].">
      <j1 rule="para" parents="3727 6289"/>
    </justification>
  </clause>

  <clause id="6725">
    <literal><![CDATA[
      (1 / x) * K(((1 / x) \ y) \ 1,z) = K((y * x) \ 1,z) / x
    ]]></literal>
    <justification jstring="[para(79(a,1),6476(a,1,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="79 6476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6726">
    <literal><![CDATA[
      (T(x * y,z) / y) * (x \ 1) = (1 / y) * (x \ T(x * y,z))
    ]]></literal>
    <justification jstring="[para(1117(a,1),6477(a,1,1))].">
      <j1 rule="para" parents="1117 6477"/>
    </justification>
  </clause>

  <clause id="6727">
    <literal><![CDATA[
      (1 / x) * ((x \ y) \ T((x \ y) * x,z)) = (x \ T(y,z)) * ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(3463(a,1),6726(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3463 6726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6728">
    <literal><![CDATA[
      x \ ((y * x) * L((y * x) \ x,z,u)) = T(y,x) \ L(T(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(22(a,2),6532(a,2,2,1))].">
      <j1 rule="para" parents="22 6532"/>
    </justification>
  </clause>

  <clause id="6729">
    <literal><![CDATA[
      x \ (y * (x * L(x \ (y \ x),z,u))) = T(y,x) \ L(T(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(1150(a,1),6728(a,1,2))].">
      <j1 rule="para" parents="1150 6728"/>
    </justification>
  </clause>

  <clause id="6730">
    <literal><![CDATA[
      T(x,y) \ L(T(x,y),z,u) = y \ ((x \ L(x,z,u)) * y)
    ]]></literal>
    <justification jstring="[para(6507(a,1),6729(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6507 6729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6731">
    <literal><![CDATA[
      T(x,y) \ L(T(x,y),z,u) = T(x \ L(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(299,a,22,a,b,6730,a),flip(a)].">
      <j1 rule="hyper" parents="299 22 6730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6733">
    <literal><![CDATA[
      T(((x * x) * y) \ L((x * x) * y,z,u),x * x) = (y * (x * x)) \ L(T((x * x) * y,x * x),z,u)
    ]]></literal>
    <justification jstring="[para(221(a,1),6731(a,1,1)),flip(a)].">
      <j1 rule="para" parents="221 6731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6734">
    <literal><![CDATA[
      K(x,y) * L(T(y,x),z,u) = y * T(y \ L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(6731(a,1),5060(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6731 5060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6735">
    <literal><![CDATA[
      T(x \ L(x,y,z),u) * (T(x,u) \ 1) = L(T(x,u) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(6731(a,1),6506(a,1,1))].">
      <j1 rule="para" parents="6731 6506"/>
    </justification>
  </clause>

  <clause id="6736">
    <literal><![CDATA[
      K(x,y / (z * (x / (u \ 1)))) = K(x,y / (z * (u * x)))
    ]]></literal>
    <justification jstring="[hyper(65,a,6723,a(flip),b,6625,a),flip(a)].">
      <j1 rule="hyper" parents="65 6723 6625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6737">
    <literal><![CDATA[
      x / L((y \ ((z \ 1) \ (z \ x))) * y,z \ 1,z) = K(y,x / (z * (y / ((z \ 1) \ 1))))
    ]]></literal>
    <justification jstring="[para(252(a,1),6625(a,1,2))].">
      <j1 rule="para" parents="252 6625"/>
    </justification>
  </clause>

  <clause id="6738">
    <literal><![CDATA[
      (L(x \ 1,y,z) \ (x \ 1)) \ ((L(x \ 1,y,z) \ 1) * K(x \ 1,x)) = T(x,x \ (L(x \ 1,y,z) \ 1))
    ]]></literal>
    <justification jstring="[para(6650(a,1),3348(a,2,1)),flip(a)].">
      <j1 rule="para" parents="6650 3348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6739">
    <literal><![CDATA[
      x \ K((x * ((y \ 1) / x)) \ 1,z) = ((y \ T(y,z)) * K(x \ 1,x)) / x
    ]]></literal>
    <justification jstring="[para(6543(a,1),6695(a,2,1))].">
      <j1 rule="para" parents="6543 6695"/>
    </justification>
  </clause>

  <clause id="6740">
    <literal><![CDATA[
      T(K(x,y) * K(x,z),K(z,x) * K(y,x)) = ((K(x,z) * K(x,y)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(6268(a,1),6716(a,1,2))].">
      <j1 rule="para" parents="6268 6716"/>
    </justification>
  </clause>

  <clause id="6741">
    <literal><![CDATA[
      (x \ T(y,x)) * ((x \ y) \ 1) = (1 / x) * ((y * x) / y)
    ]]></literal>
    <justification jstring="[para(3509(a,1),6727(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3509 6727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6742">
    <literal><![CDATA[
      K(x,y) = (y \ T(x,y)) * ((y \ x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,5259,a,b,6741,a)].">
      <j1 rule="hyper" parents="299 5259 6741"/>
    </justification>
  </clause>

  <clause id="6743">
    <literal><![CDATA[
      (x \ T(x * y,x)) * (y \ 1) = K(x * y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),6742(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="9 6742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6744">
    <literal><![CDATA[
      (x \ T(x * K(y,z),x)) * (K(z,y) * 1) = K(x * K(y,z),x)
    ]]></literal>
    <justification jstring="[para(5426(a,1),6743(a,1,2))].">
      <j1 rule="para" parents="5426 6743"/>
    </justification>
  </clause>

  <clause id="6745">
    <literal><![CDATA[
      x \ K((x * ((y \ 1) / x)) \ 1,z) = (K(y,z) * K(x \ 1,x)) / x
    ]]></literal>
    <justification jstring="[para(5036(a,2),6739(a,2,1,1))].">
      <j1 rule="para" parents="5036 6739"/>
    </justification>
  </clause>

  <clause id="6746">
    <literal><![CDATA[
      x \ K((x * ((y \ 1) / x)) \ 1,z) = K(y,z) / T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,2775,a(flip),b,6745,a),flip(a)].">
      <j1 rule="hyper" parents="299 2775 6745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6747">
    <literal><![CDATA[
      K((x * ((y \ 1) / x)) \ 1,z) = x * (K(y,z) / T(x,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(144,a,6746,a),flip(a)].">
      <j1 rule="hyper" parents="144 6746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6748">
    <literal><![CDATA[
      K((x * ((y \ 1) / x)) \ 1,z) = x * (K(y,z) / ((x \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(108(a,1),6747(a,2,2,2))].">
      <j1 rule="para" parents="108 6747"/>
    </justification>
  </clause>

  <clause id="6749">
    <literal><![CDATA[
      ((1 / R(x,y,z)) * x) * (x \ 1) = T(1 / R(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(5296,a,6122,a),flip(a)].">
      <j1 rule="hyper" parents="5296 6122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6750">
    <literal><![CDATA[
      (x / R(x,y,z)) * (x \ 1) = T(1 / R(x,y,z),x)
    ]]></literal>
    <justification jstring="[para(1919(a,1),6749(a,1,1))].">
      <j1 rule="para" parents="1919 6749"/>
    </justification>
  </clause>

  <clause id="6751">
    <literal><![CDATA[
      K(x,R(y / x,x * z,u) \ 1) = K(x,((x * z) * u) / ((y * z) * u))
    ]]></literal>
    <justification jstring="[hyper(299,a,5937,a(flip),b,6219,a),flip(a)].">
      <j1 rule="hyper" parents="299 5937 6219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6752">
    <literal><![CDATA[
      R(K(x,x / y),x * z,u) = K(x,((x * z) * u) / ((y * z) * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,6214,a(flip),b,6751,a)].">
      <j1 rule="hyper" parents="65 6214 6751"/>
    </justification>
  </clause>

  <clause id="6753">
    <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(6241(a,1),6243(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6241 6243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6754">
    <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(6753(a,1),46(a,1))].">
      <j1 rule="para" parents="6753 46"/>
    </justification>
  </clause>

  <clause id="6755">
    <literal><![CDATA[
      L(L(1 / x,y,z),L(x,y,z),L(1 / x,y,z)) = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(79(a,1),6524(a,2,1,1))].">
      <j1 rule="para" parents="79 6524"/>
    </justification>
  </clause>

  <clause id="6756">
    <literal><![CDATA[
      (x \ 1) * (L(L(x,x,x),y,z) * u) = (1 / x) * (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,3847,a(flip),b,6531,a),flip(a)].">
      <j1 rule="hyper" parents="65 3847 6531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6757">
    <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),6664(a,2,1,1))].">
      <j1 rule="para" parents="9 6664"/>
    </justification>
  </clause>

  <clause id="6758">
    <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(5482(a,1),5135(a,2,1))].">
      <j1 rule="para" parents="5482 5135"/>
    </justification>
  </clause>

  <clause id="6759">
    <literal><![CDATA[
      L(x,y,z) / (x * K(u,x)) = (K(x,u) / x) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(5053(a,1),6758(a,1,1,1))].">
      <j1 rule="para" parents="5053 6758"/>
    </justification>
  </clause>

  <clause id="6760">
    <literal><![CDATA[
      ((K(x,y) / x) * L(x,z,u)) \ L(x,z,u) = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(186,a,6759,a)].">
      <j1 rule="hyper" parents="186 6759"/>
    </justification>
  </clause>

  <clause id="6761">
    <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(4346(a,1),6760(a,1,1,2))].">
      <j1 rule="para" parents="4346 6760"/>
    </justification>
  </clause>

  <clause id="6762">
    <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(6241(a,1),5217(a,1,2,1))].">
      <j1 rule="para" parents="6241 5217"/>
    </justification>
  </clause>

  <clause id="6763">
    <literal><![CDATA[
      (K(x,y) * L(K(x,y) \ 1,z,u)) * w = K(x,y) * (L(K(y,x),z,u) * w)
    ]]></literal>
    <justification jstring="[para(233(a,1),5543(a,1,2)),flip(a)].">
      <j1 rule="para" parents="233 5543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6764">
    <literal><![CDATA[
      (K(x,y) * L(K(y,x),z,u)) * w = K(x,y) * (L(K(y,x),z,u) * w)
    ]]></literal>
    <justification jstring="[para(5197(a,1),6763(a,1,1,2,1))].">
      <j1 rule="para" parents="5197 6763"/>
    </justification>
  </clause>

  <clause id="6765">
    <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(234(a,1),5544(a,1,2)),flip(a)].">
      <j1 rule="para" parents="234 5544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6766">
    <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(5197(a,1),6765(a,1,1,2,1))].">
      <j1 rule="para" parents="5197 6765"/>
    </justification>
  </clause>

  <clause id="6767">
    <literal><![CDATA[
      K((x / (y \ 1)) * T((x / (1 / y)) \ 1,z),u) = K(K((1 / y) / x,z),u)
    ]]></literal>
    <justification jstring="[para(5852(a,1),6035(a,2,1))].">
      <j1 rule="para" parents="5852 6035"/>
    </justification>
  </clause>

  <clause id="6768">
    <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(6409(a,1),6070(a,1,2,2,1,2))].">
      <j1 rule="para" parents="6409 6070"/>
    </justification>
  </clause>

  <clause id="6769">
    <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(4806(a,1),6092(a,1,1))].">
      <j1 rule="para" parents="4806 6092"/>
    </justification>
  </clause>

  <clause id="6770">
    <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(6705(a,1),6769(a,1,1,1))].">
      <j1 rule="para" parents="6705 6769"/>
    </justification>
  </clause>

  <clause id="6771">
    <literal><![CDATA[
      ((x \ y) \ y) * (y / T(T(x,x \ y),y)) = x \ (y * ((x \ y) \ y))
    ]]></literal>
    <justification jstring="[hyper(299,a,2080,a(flip),b,6232,a),flip(a)].">
      <j1 rule="hyper" parents="299 2080 6232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6772">
    <literal><![CDATA[
      ((x \ y) \ y) * (y / T(T(x,x \ y),y)) = x * (y / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,4542,a(flip),b,6771,a),flip(a)].">
      <j1 rule="hyper" parents="299 4542 6771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6773">
    <literal><![CDATA[
      K(x,y * (((z * K(u,z)) * u) * w)) = K(x,y * ((u * (1 / (1 / z))) * w))
    ]]></literal>
    <justification jstring="[para(5548(a,1),6427(a,1,2,2,1,1))].">
      <j1 rule="para" parents="5548 6427"/>
    </justification>
  </clause>

  <clause id="6774">
    <literal><![CDATA[
      K(x,y * ((z * (1 / (1 / u))) * w)) = K(x,y * ((z * u) * w))
    ]]></literal>
    <justification jstring="[para(5099(a,1),6773(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5099 6773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6775">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z \ L(z,u,w)))) = L(z,y,x) \ L(L(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(6499(a,1),6502(a,1,2,2,2))].">
      <j1 rule="para" parents="6499 6502"/>
    </justification>
  </clause>

  <clause id="6776">
    <literal><![CDATA[
      L(x,y,z) \ L(L(x,y,z),u,w) = L(x \ L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(493,a,6775,a),flip(a)].">
      <j1 rule="hyper" parents="493 6775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6777">
    <literal><![CDATA[
      L(x,y,z) \ L(L(x,y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x \ L(x,u,w),y,z) = v5
    ]]></literal>
    <justification jstring="[para(6775(a,1),493(a,1))].">
      <j1 rule="para" parents="6775 493"/>
    </justification>
  </clause>

  <clause id="6778">
    <literal><![CDATA[
      (x * y) \ (y * (K(x,y) * (x * z))) = L(L(z,x,y),y * x,K(x,y))
    ]]></literal>
    <justification jstring="[para(5166(a,1),6693(a,1,1))].">
      <j1 rule="para" parents="5166 6693"/>
    </justification>
  </clause>

  <clause id="6779">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(y,z)) = (y * z) \ (z * (T(y,z) * x))
    ]]></literal>
    <justification jstring="[para(5103(a,1),6778(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5103 6778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6780">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(y,z)) = L(x,T(y,z),z)
    ]]></literal>
    <justification jstring="[hyper(299,a,229,a(flip),b,6779,a),flip(a)].">
      <j1 rule="hyper" parents="299 229 6779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6781">
    <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(6779(a,2),910(a,1))].">
      <j1 rule="para" parents="6779 910"/>
    </justification>
  </clause>

  <clause id="6782">
    <literal><![CDATA[
      L(x,T(y,z),z) = L(x,y,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(6687,a,6780,a),flip(a)].">
      <j1 rule="hyper" parents="6687 6780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6783">
    <literal><![CDATA[
      L(x,y * K(z,y),z) = L(x,y,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,5538,a,b,6782,a)].">
      <j1 rule="hyper" parents="65 5538 6782"/>
    </justification>
  </clause>

  <clause id="6784">
    <literal><![CDATA[
      L(K(x,y) * (x \ z),x,T(y,x)) = (T(y,x) * x) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,6547,a(flip),b,6783,a),flip(a)].">
      <j1 rule="hyper" parents="65 6547 6783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6785">
    <literal><![CDATA[
      L(x,y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,T(y,z),z) = u
    ]]></literal>
    <justification jstring="[para(6685(a,1),6781(a,1))].">
      <j1 rule="para" parents="6685 6781"/>
    </justification>
  </clause>

  <clause id="6786">
    <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(4923(a,1),6150(a,1,2,1,1))].">
      <j1 rule="para" parents="4923 6150"/>
    </justification>
  </clause>

  <clause id="6787">
    <literal><![CDATA[
      (x \ R(x,y,z)) * K(R(x,y,z),u) = x \ R(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(3567(a,1),6786(a,1,2))].">
      <j1 rule="para" parents="3567 6786"/>
    </justification>
  </clause>

  <clause id="6788">
    <literal><![CDATA[
      ((x * (y * ((x \ (z / u)) / y))) * u) / z = K(y,z / ((x * y) * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,6429,a(flip),b,6615,a),flip(a)].">
      <j1 rule="hyper" parents="65 6429 6615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6789">
    <literal><![CDATA[
      ((x * y) * (z * (((x * y) \ u) / z))) / u = K(z,u / ((x * z) * y))
    ]]></literal>
    <justification jstring="[para(4051(a,1),6788(a,1,1))].">
      <j1 rule="para" parents="4051 6788"/>
    </justification>
  </clause>

  <clause id="6790">
    <literal><![CDATA[
      K(x,y / ((z * u) * x)) = K(x,y / ((z * x) * u))
    ]]></literal>
    <justification jstring="[hyper(6614,a,6789,a)].">
      <j1 rule="hyper" parents="6614 6789"/>
    </justification>
  </clause>

  <clause id="6791">
    <literal><![CDATA[
      K(T(x,y * z),u / ((y * T(x,y * z)) * z)) = K(T(x,y * z),u / (x * (y * z)))
    ]]></literal>
    <justification jstring="[para(107(a,1),6790(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 6790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6792">
    <literal><![CDATA[
      (x * y) * L(z \ T(z * (y \ (z \ 1)),z),y,x) = (x * K(y \ 1,z)) * (z \ 1)
    ]]></literal>
    <justification jstring="[para(1906(a,2),6665(a,1,2))].">
      <j1 rule="para" parents="1906 6665"/>
    </justification>
  </clause>

  <clause id="6793">
    <literal><![CDATA[
      (x * y) * ((((x * y) \ (z * y)) \ 1) \ 1) = ((((z / x) \ 1) \ 1) * x) * y
    ]]></literal>
    <justification jstring="[hyper(275,a,6709,a),flip(a)].">
      <j1 rule="hyper" parents="275 6709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6794">
    <literal><![CDATA[
      (x * y) * ((((x * y) \ (z * y)) \ 1) \ 1) = (x * (((x \ z) \ 1) \ 1)) * y
    ]]></literal>
    <justification jstring="[para(3189(a,1),6793(a,2,1))].">
      <j1 rule="para" parents="3189 6793"/>
    </justification>
  </clause>

  <clause id="6795">
    <literal><![CDATA[
      ((R(x,y,z) \ 1) \ 1) \ ((x * y) * z) = ((x * y) * ((((x * y) \ y) \ 1) \ 1)) * z
    ]]></literal>
    <justification jstring="[hyper(65,a,3354,a(flip),b,6794,a)].">
      <j1 rule="hyper" parents="65 3354 6794"/>
    </justification>
  </clause>

  <clause id="6796">
    <literal><![CDATA[
      ((R(x,y,z) \ 1) * R(x,y,z)) * (y * z) = ((x * y) * ((((x * y) \ y) \ 1) \ 1)) * z
    ]]></literal>
    <justification jstring="[hyper(65,a,3299,a(flip),b,6794,a)].">
      <j1 rule="hyper" parents="65 3299 6794"/>
    </justification>
  </clause>

  <clause id="6797">
    <literal><![CDATA[
      x * (y * (z \ T(z * (y \ (z \ 1)),z))) = (x * K(y \ 1,z)) * (z \ 1)
    ]]></literal>
    <justification jstring="[hyper(279,a,6792,a)].">
      <j1 rule="hyper" parents="279 6792"/>
    </justification>
  </clause>

  <clause id="6798">
    <literal><![CDATA[
      (x * K(y \ 1,z)) * (z \ 1) = x * (K(y \ 1,z) * (z \ 1))
    ]]></literal>
    <justification jstring="[para(6024(a,1),6797(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6024 6797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6799">
    <literal><![CDATA[
      (x * K(y \ 1,z)) * (z \ 1) = x * (T(z,y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(5383(a,1),6798(a,2,2))].">
      <j1 rule="para" parents="5383 6798"/>
    </justification>
  </clause>

  <clause id="6800">
    <literal><![CDATA[
      (x * K(y,z)) * (z \ 1) = x * (T(z,(1 / y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(79(a,1),6799(a,1,1,2,1))].">
      <j1 rule="para" parents="79 6799"/>
    </justification>
  </clause>

  <clause id="6801">
    <literal><![CDATA[
      (x * K(y,z)) * (z \ 1) = x * (T(z,y) \ 1)
    ]]></literal>
    <justification jstring="[para(79(a,1),6800(a,2,2,1,2))].">
      <j1 rule="para" parents="79 6800"/>
    </justification>
  </clause>

  <clause id="6802">
    <literal><![CDATA[
      x \ T(x * (y \ 1),y) = T(y,y \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(119,a,958,a(flip),b,6801,a(flip))].">
      <j1 rule="hyper" parents="119 958 6801"/>
    </justification>
  </clause>

  <clause id="6803">
    <literal><![CDATA[
      (x * (y \ 1)) \ (x * (T(y,z) \ 1)) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,6801,a(flip),b,6592,a(flip))].">
      <j1 rule="hyper" parents="119 6801 6592"/>
    </justification>
  </clause>

  <clause id="6807">
    <literal><![CDATA[
      x \ T(x * (y \ 1),y) = ((y \ x) \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(6115,a,6802,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="6115 6802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6808">
    <literal><![CDATA[
      L(K(x,y),y \ 1,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5347,a,6803,a)].">
      <j1 rule="hyper" parents="5347 6803"/>
    </justification>
  </clause>

  <clause id="6809">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      L(K(x,y),y \ 1,u) = z
    ]]></literal>
    <justification jstring="[para(6803(a,1),5347(a,1))].">
      <j1 rule="para" parents="6803 5347"/>
    </justification>
  </clause>

  <clause id="6810">
    <literal><![CDATA[
      L(K(x,y \ 1),y,z) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,2529,a(flip),b,6808,a)].">
      <j1 rule="hyper" parents="65 2529 6808"/>
    </justification>
  </clause>

  <clause id="6811">
    <literal><![CDATA[
      L(K(x,y),y,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2526,a(flip),b,6808,a)].">
      <j1 rule="hyper" parents="65 2526 6808"/>
    </justification>
  </clause>

  <clause id="6812">
    <literal><![CDATA[
      L(K(x,y),y,z) = L(K(x,y),y,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,6811,a,b,6811,a)].">
      <j1 rule="hyper" parents="299 6811 6811"/>
    </justification>
  </clause>

  <clause id="6814">
    <literal><![CDATA[
      K(x,(y \ z) \ 1) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,6137,a(flip),b,6811,a)].">
      <j1 rule="hyper" parents="65 6137 6811"/>
    </justification>
  </clause>

  <clause id="6815">
    <literal><![CDATA[
      a(x,y,K(z,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(55,a,6811,a)].">
      <j1 rule="hyper" parents="55 6811"/>
    </justification>
  </clause>

  <clause id="6816">
    <literal><![CDATA[
      (x * y) * K(z,y) = x * (y * K(z,y))
    ]]></literal>
    <justification jstring="[para(6811(a,1),94(a,1,2))].">
      <j1 rule="para" parents="6811 94"/>
    </justification>
  </clause>

  <clause id="6817">
    <literal><![CDATA[
      x * ((x \ y) * K(z,x \ y)) = y * K(z,x \ y)
    ]]></literal>
    <justification jstring="[para(6811(a,1),482(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6811 482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6820">
    <literal><![CDATA[
      L(K(x,y),x,z) = K(y,x) \ 1
    ]]></literal>
    <justification jstring="[para(6811(a,1),6350(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6811 6350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6821">
    <literal><![CDATA[
      L(K(x,y),x,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,5197,a(flip),b,6820,a),flip(a)].">
      <j1 rule="hyper" parents="299 5197 6820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6822">
    <literal><![CDATA[
      L(K(x,y),x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(6820(a,2),5200(a,1))].">
      <j1 rule="para" parents="6820 5200"/>
    </justification>
  </clause>

  <clause id="6824">
    <literal><![CDATA[
      L(K(x,y),x \ 1,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2641,a,6821,a)].">
      <j1 rule="hyper" parents="2641 6821"/>
    </justification>
  </clause>

  <clause id="6825">
    <literal><![CDATA[
      L(K(x,y),x,z) = (T(x,y) * u) / (x * u)
    ]]></literal>
    <justification jstring="[hyper(299,a,5069,a,b,6821,a),flip(a)].">
      <j1 rule="hyper" parents="299 5069 6821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6826">
    <literal><![CDATA[
      (x * y) \ (x * T(y,z)) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,5088,a,b,6821,a)].">
      <j1 rule="hyper" parents="65 5088 6821"/>
    </justification>
  </clause>

  <clause id="6827">
    <literal><![CDATA[
      L(K(x \ 1,y),x,z) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2526,a(flip),b,6821,a)].">
      <j1 rule="hyper" parents="65 2526 6821"/>
    </justification>
  </clause>

  <clause id="6828">
    <literal><![CDATA[
      a(x,y,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(55,a,6821,a)].">
      <j1 rule="hyper" parents="55 6821"/>
    </justification>
  </clause>

  <clause id="6829">
    <literal><![CDATA[
      (1 / x) \ K(x \ 1,y) = x * K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,6821,a(flip),b,1706,a)].">
      <j1 rule="hyper" parents="119 6821 1706"/>
    </justification>
  </clause>

  <clause id="6832">
    <literal><![CDATA[
      (x * y) * K(y,z) = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(6821(a,1),5156(a,1,2))].">
      <j1 rule="para" parents="6821 5156"/>
    </justification>
  </clause>

  <clause id="6834">
    <literal><![CDATA[
      a(x,y \ 1,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(55,a,6824,a)].">
      <j1 rule="hyper" parents="55 6824"/>
    </justification>
  </clause>

  <clause id="6835">
    <literal><![CDATA[
      a(x,y,K(y \ 1,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(6417,a,6834,a)].">
      <j1 rule="hyper" parents="6417 6834"/>
    </justification>
  </clause>

  <clause id="6838">
    <literal><![CDATA[
      L(K(x,y),y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(6812(a,1),505(a,1))].">
      <j1 rule="para" parents="6812 505"/>
    </justification>
  </clause>

  <clause id="6840">
    <literal><![CDATA[
      K(x,1 / (y \ z)) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(5991,a,6814,a)].">
      <j1 rule="hyper" parents="5991 6814"/>
    </justification>
  </clause>

  <clause id="6841">
    <literal><![CDATA[
      T(K(x,y / z),y) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,6077,a,b,6814,a)].">
      <j1 rule="hyper" parents="65 6077 6814"/>
    </justification>
  </clause>

  <clause id="6842">
    <literal><![CDATA[
      K(x,(y * z) \ y) = K(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),6814(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 6814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6843">
    <literal><![CDATA[
      K(x,((y * z) \ y) \ 1) = K(x,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),6814(a,2,2))].">
      <j1 rule="para" parents="9 6814"/>
    </justification>
  </clause>

  <clause id="6844">
    <literal><![CDATA[
      K(x,((y * z) * u) \ (y * (z * u))) = K(x,a(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(14(a,2),6814(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14 6814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6845">
    <literal><![CDATA[
      K(x,y \ (y / z)) = K(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(79(a,1),6814(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 6814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6846">
    <literal><![CDATA[
      K(x,L(y,z \ 1,z) \ z) = K(x,((z \ 1) * y) \ 1)
    ]]></literal>
    <justification jstring="[para(415(a,1),6814(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="415 6814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6847">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1) \ y) = K(x,a(y,z,z \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(865(a,1),6814(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="865 6814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6848">
    <literal><![CDATA[
      K(x,(T(y,z) * (y \ u)) \ 1) = K(x,(T(y,z) * u) \ y)
    ]]></literal>
    <justification jstring="[para(1188(a,1),6814(a,1,2,1))].">
      <j1 rule="para" parents="1188 6814"/>
    </justification>
  </clause>

  <clause id="6851">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ 1) = K(x,u \ K(z,y))
    ]]></literal>
    <justification jstring="[para(5426(a,1),6814(a,1,2,1))].">
      <j1 rule="para" parents="5426 6814"/>
    </justification>
  </clause>

  <clause id="6852">
    <literal><![CDATA[
      K(x,y \ z) * K(x * ((z \ y) \ 1),x) = x \ R(x,(z \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(6814(a,1),5587(a,1,1))].">
      <j1 rule="para" parents="6814 5587"/>
    </justification>
  </clause>

  <clause id="6853">
    <literal><![CDATA[
      x * K(y,z \ x) = z * ((y * (z \ x)) / y)
    ]]></literal>
    <justification jstring="[para(6814(a,1),5632(a,1,2))].">
      <j1 rule="para" parents="6814 5632"/>
    </justification>
  </clause>

  <clause id="6854">
    <literal><![CDATA[
      T(x,y) != K(z,u \ y)
    ]]></literal>
    <literal><![CDATA[
      K(z,y / u) = x
    ]]></literal>
    <justification jstring="[para(6814(a,1),6078(a,2))].">
      <j1 rule="para" parents="6814 6078"/>
    </justification>
  </clause>

  <clause id="6855">
    <literal><![CDATA[
      K(x,L(y \ z,u,w) \ 1) = L(K(x,z \ y),u,w)
    ]]></literal>
    <justification jstring="[para(6814(a,1),6129(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6814 6129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6856">
    <literal><![CDATA[
      K(x,R(y \ z,u,w) \ 1) = R(K(x,z \ y),u,w)
    ]]></literal>
    <justification jstring="[para(6814(a,1),6209(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6814 6209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6861">
    <literal><![CDATA[
      ((x / T(y,z)) * y) \ x = K(y,z)
    ]]></literal>
    <justification jstring="[para(12(a,1),6826(a,1,2))].">
      <j1 rule="para" parents="12 6826"/>
    </justification>
  </clause>

  <clause id="6862">
    <literal><![CDATA[
      (x * y) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * T(y,z) = u
    ]]></literal>
    <justification jstring="[para(6826(a,1),250(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6826 250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6865">
    <literal><![CDATA[
      (x * (y / x)) \ (K(x,x \ y) * T(y,z)) = K(y,z)
    ]]></literal>
    <justification jstring="[para(5105(a,1),6826(a,1,1))].">
      <j1 rule="para" parents="5105 6826"/>
    </justification>
  </clause>

  <clause id="6866">
    <literal><![CDATA[
      R(x,y,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(5159,a,6832,a)].">
      <j1 rule="hyper" parents="5159 6832"/>
    </justification>
  </clause>

  <clause id="6867">
    <literal><![CDATA[
      (x / y) \ (x * K(y,z)) = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(634,a,6832,a)].">
      <j1 rule="hyper" parents="634 6832"/>
    </justification>
  </clause>

  <clause id="6868">
    <literal><![CDATA[
      x * T(x \ y,z) = y * K(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(606,a,6832,a),flip(a)].">
      <j1 rule="hyper" parents="606 6832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6869">
    <literal><![CDATA[
      (x / y) * T(y,z) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(306,a,6832,a),flip(a)].">
      <j1 rule="hyper" parents="306 6832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6872">
    <literal><![CDATA[
      K(x,y) \ (z * T(x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(z * x,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(6832(a,1),318(a,1,2))].">
      <j1 rule="para" parents="6832 318"/>
    </justification>
  </clause>

  <clause id="6873">
    <literal><![CDATA[
      (x * (y * z)) * K(L(z,y,x),u) = (x * y) * T(L(z,y,x),u)
    ]]></literal>
    <justification jstring="[para(94(a,1),6832(a,1,1))].">
      <j1 rule="para" parents="94 6832"/>
    </justification>
  </clause>

  <clause id="6876">
    <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(6832(a,1),582(a,1,2))].">
      <j1 rule="para" parents="6832 582"/>
    </justification>
  </clause>

  <clause id="6877">
    <literal><![CDATA[
      (x / (y * y)) * K(y \ 1,z) = (x / y) * T(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(1245(a,1),6832(a,1,1))].">
      <j1 rule="para" parents="1245 6832"/>
    </justification>
  </clause>

  <clause id="6878">
    <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(6832(a,1),539(a,1,1))].">
      <j1 rule="para" parents="6832 539"/>
    </justification>
  </clause>

  <clause id="6879">
    <literal><![CDATA[
      ((x \ 1) * ((x \ 1) * y)) * K((1 / x) * y,z) = (1 / x) * T((1 / x) * y,z)
    ]]></literal>
    <justification jstring="[para(2838(a,1),6832(a,1,1))].">
      <j1 rule="para" parents="2838 6832"/>
    </justification>
  </clause>

  <clause id="6880">
    <literal><![CDATA[
      ((x * y) / x) * K(x \ y,z) = T(x,y) * T(x \ y,z)
    ]]></literal>
    <justification jstring="[para(4269(a,1),6832(a,1,1))].">
      <j1 rule="para" parents="4269 6832"/>
    </justification>
  </clause>

  <clause id="6881">
    <literal><![CDATA[
      K(x,y) * T(y * x,z) = (x * y) * K(y * x,z)
    ]]></literal>
    <justification jstring="[para(5020(a,1),6832(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5020 6832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6884">
    <literal><![CDATA[
      (x * R(R(x,y,K(y,z)) \ (x * y),u,w)) * K(y,z) = R(x,y,K(y,z)) * (R(y,u,w) * K(y,z))
    ]]></literal>
    <justification jstring="[para(6866(a,1),3079(a,1,1,1))].">
      <j1 rule="para" parents="6866 3079"/>
    </justification>
  </clause>

  <clause id="6885">
    <literal><![CDATA[
      K(x,(y \ z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(6137(a,1),6838(a,1))].">
      <j1 rule="para" parents="6137 6838"/>
    </justification>
  </clause>

  <clause id="6886">
    <literal><![CDATA[
      K(x,(y * (z * u)) \ (y * z)) = K(x,1 / L(u,z,y))
    ]]></literal>
    <justification jstring="[para(18(a,2),6840(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="18 6840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6887">
    <literal><![CDATA[
      ((1 / (x \ y)) \ z) * (1 / (x \ y)) = z * K(z * (x \ y),y \ x)
    ]]></literal>
    <justification jstring="[para(6840(a,1),6188(a,2,2))].">
      <j1 rule="para" parents="6840 6188"/>
    </justification>
  </clause>

  <clause id="6888">
    <literal><![CDATA[
      K(x,x / y) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(5306,a,6841,a)].">
      <j1 rule="hyper" parents="5306 6841"/>
    </justification>
  </clause>

  <clause id="6889">
    <literal><![CDATA[
      K(x,(y \ z) \ z) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(76(a,1),6841(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="76 6841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6890">
    <literal><![CDATA[
      K(x / y,x / (z * y)) = K(x / y,z \ (x / y))
    ]]></literal>
    <justification jstring="[hyper(65,a,6449,a(flip),b,6888,a)].">
      <j1 rule="hyper" parents="65 6449 6888"/>
    </justification>
  </clause>

  <clause id="6891">
    <literal><![CDATA[
      K(x,(y \ x) \ x) = K(x,y)
    ]]></literal>
    <justification jstring="[para(76(a,1),6888(a,1,2)),flip(a)].">
      <j1 rule="para" parents="76 6888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6892">
    <literal><![CDATA[
      R(K(x,(y / z) \ x),x,z) = K(x,(x * z) / y)
    ]]></literal>
    <justification jstring="[para(6888(a,1),6430(a,1,1))].">
      <j1 rule="para" parents="6888 6430"/>
    </justification>
  </clause>

  <clause id="6893">
    <literal><![CDATA[
      R(K(x,y \ x),x * z,u) = K(x,((x * z) * u) / ((y * z) * u))
    ]]></literal>
    <justification jstring="[para(6888(a,1),6752(a,1,1))].">
      <j1 rule="para" parents="6888 6752"/>
    </justification>
  </clause>

  <clause id="6894">
    <literal><![CDATA[
      K(x,T(y,y \ x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(108(a,2),6891(a,1,2))].">
      <j1 rule="para" parents="108 6891"/>
    </justification>
  </clause>

  <clause id="6895">
    <literal><![CDATA[
      K(x * y,T(x,y)) = K(x * y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),6894(a,1,2,2))].">
      <j1 rule="para" parents="9 6894"/>
    </justification>
  </clause>

  <clause id="6896">
    <literal><![CDATA[
      K(x,y \ 1) / ((z * y) \ z) = 1 / T((z * y) \ z,x)
    ]]></literal>
    <justification jstring="[hyper(120,a,6842,a(flip),b,5032,a(flip))].">
      <j1 rule="hyper" parents="120 6842 5032"/>
    </justification>
  </clause>

  <clause id="6897">
    <literal><![CDATA[
      K(x,(y * (z / u)) \ y) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / z) = w
    ]]></literal>
    <justification jstring="[para(6842(a,2),5989(a,1))].">
      <j1 rule="para" parents="6842 5989"/>
    </justification>
  </clause>

  <clause id="6898">
    <literal><![CDATA[
      L(K(x,y),y,z) = K(x,((u * y) \ u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,6811,a,b,6843,a)].">
      <j1 rule="hyper" parents="299 6811 6843"/>
    </justification>
  </clause>

  <clause id="6899">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) \ z,((x * y) \ x) \ 1) = K(z * ((x * y) \ x),y)
    ]]></literal>
    <justification jstring="[hyper(65,a,6184,a,b,6843,a)].">
      <j1 rule="hyper" parents="65 6184 6843"/>
    </justification>
  </clause>

  <clause id="6900">
    <literal><![CDATA[
      K(x,y \ (y / z)) = K(x,u / (z * u))
    ]]></literal>
    <justification jstring="[hyper(299,a,5941,a,b,6845,a),flip(a)].">
      <j1 rule="hyper" parents="299 5941 6845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6902">
    <literal><![CDATA[
      (x / y) \ T(x * K(y,z),(x / y) \ 1) = (((x / y) \ 1) \ T(y,z)) * ((x / y) \ 1)
    ]]></literal>
    <justification jstring="[para(6867(a,1),1137(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6867 1137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6903">
    <literal><![CDATA[
      ((x / y) \ T(x * K(y,z),(x / y) \ 1)) / T(y,z) = K(x * K(y,z),(x / y) \ 1)
    ]]></literal>
    <justification jstring="[para(6867(a,1),5835(a,1,2))].">
      <j1 rule="para" parents="6867 5835"/>
    </justification>
  </clause>

  <clause id="6904">
    <literal><![CDATA[
      T(x,y * (x \ 1)) = T(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(6177,a,6869,a),flip(a)].">
      <j1 rule="hyper" parents="6177 6869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6905">
    <literal><![CDATA[
      T(x,(x / y) / x) = T(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(5884,a,6869,a)].">
      <j1 rule="hyper" parents="5884 6869"/>
    </justification>
  </clause>

  <clause id="6906">
    <literal><![CDATA[
      (x * T(y,z)) / y = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,1523,a,b,6869,a)].">
      <j1 rule="hyper" parents="65 1523 6869"/>
    </justification>
  </clause>

  <clause id="6907">
    <literal><![CDATA[
      (x / T(y,z)) * K(y,z) = x / y
    ]]></literal>
    <justification jstring="[hyper(65,a,1526,a(flip),b,6869,a),flip(a)].">
      <j1 rule="hyper" parents="65 1526 6869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6909">
    <literal><![CDATA[
      (x * K(y,z)) / (x / y) = T(x / (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(120,a,6869,a(flip),b,435,a)].">
      <j1 rule="hyper" parents="120 6869 435"/>
    </justification>
  </clause>

  <clause id="6911">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * T(y,z)) = y
    ]]></literal>
    <justification jstring="[para(6869(a,1),1524(a,1,1))].">
      <j1 rule="para" parents="6869 1524"/>
    </justification>
  </clause>

  <clause id="6912">
    <literal><![CDATA[
      (x * K(y,z)) * y = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(6869(a,1),1525(a,1,1))].">
      <j1 rule="para" parents="6869 1525"/>
    </justification>
  </clause>

  <clause id="6913">
    <literal><![CDATA[
      T(x * K(y,z),y) = y \ (x * T(y,z))
    ]]></literal>
    <justification jstring="[para(6869(a,1),1528(a,1,1))].">
      <j1 rule="para" parents="6869 1528"/>
    </justification>
  </clause>

  <clause id="6914">
    <literal><![CDATA[
      K(x,(y \ 1) \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(6889(a,2),196(a,1)),flip(b)].">
      <j1 rule="para" parents="6889 196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6915">
    <literal><![CDATA[
      K(x,T(y,y \ z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(108(a,2),6889(a,1,2))].">
      <j1 rule="para" parents="108 6889"/>
    </justification>
  </clause>

  <clause id="6916">
    <literal><![CDATA[
      K(x,T(y,z / y)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(4440(a,2),6889(a,1,2))].">
      <j1 rule="para" parents="4440 6889"/>
    </justification>
  </clause>

  <clause id="6917">
    <literal><![CDATA[
      T(K(x,y),z * y) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4452(a,2),6889(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4452 6889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6918">
    <literal><![CDATA[
      T(x,y * (1 / x)) = T(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(65,a,3874,a,b,6904,a)].">
      <j1 rule="hyper" parents="65 3874 6904"/>
    </justification>
  </clause>

  <clause id="6919">
    <literal><![CDATA[
      T(x,1 / y) / ((x / y) \ x) = (x / y) * K(x,1 / y)
    ]]></literal>
    <justification jstring="[para(6905(a,1),6099(a,1,1))].">
      <j1 rule="para" parents="6905 6099"/>
    </justification>
  </clause>

  <clause id="6920">
    <literal><![CDATA[
      x * T(y * K(x,z),x) = y * T(x,z)
    ]]></literal>
    <justification jstring="[hyper(269,a,6906,a)].">
      <j1 rule="hyper" parents="269 6906"/>
    </justification>
  </clause>

  <clause id="6921">
    <literal><![CDATA[
      (x * K(y,z)) * y != u
    ]]></literal>
    <literal><![CDATA[
      x * T(y,z) = u
    ]]></literal>
    <justification jstring="[para(6906(a,1),246(a,1,1)),flip(b)].">
      <j1 rule="para" parents="6906 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6922">
    <literal><![CDATA[
      T(x * K(y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      y \ (x * T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6906(a,1),400(a,1,1))].">
      <j1 rule="para" parents="6906 400"/>
    </justification>
  </clause>

  <clause id="6923">
    <literal><![CDATA[
      (x * T(y \ z,u)) / T(z / y,u) = x * K(T(z / y,u),y)
    ]]></literal>
    <justification jstring="[para(242(a,1),6906(a,1,1,2))].">
      <j1 rule="para" parents="242 6906"/>
    </justification>
  </clause>

  <clause id="6925">
    <literal><![CDATA[
      T(x / T(y,z),K(y,z)) = K(z,y) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(235,a,6907,a,b,5432,a)].">
      <j1 rule="hyper" parents="235 6907 5432"/>
    </justification>
  </clause>

  <clause id="6927">
    <literal><![CDATA[
      L(x,K(x,y),z) = x
    ]]></literal>
    <justification jstring="[hyper(5171,a,6911,a)].">
      <j1 rule="hyper" parents="5171 6911"/>
    </justification>
  </clause>

  <clause id="6928">
    <literal><![CDATA[
      x * T(y,z) != u * y
    ]]></literal>
    <literal><![CDATA[
      x * K(y,z) = u
    ]]></literal>
    <justification jstring="[para(6911(a,1),136(a,1,2)),flip(a),flip(b)].">
      <j1 rule="para" parents="6911 136"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6930">
    <literal><![CDATA[
      L(x,K(y,x),z) = x
    ]]></literal>
    <justification jstring="[hyper(65,a,5220,a,b,6927,a)].">
      <j1 rule="hyper" parents="65 5220 6927"/>
    </justification>
  </clause>

  <clause id="6931">
    <literal><![CDATA[
      L(T(x,y),K(x,z),u) = T(x,y)
    ]]></literal>
    <justification jstring="[para(6927(a,1),25(a,2,1))].">
      <j1 rule="para" parents="6927 25"/>
    </justification>
  </clause>

  <clause id="6932">
    <literal><![CDATA[
      (x * K(y,z)) * L(y,u,w) = x * (K(y,z) * L(y,u,w))
    ]]></literal>
    <justification jstring="[para(6927(a,1),489(a,1,2,1))].">
      <j1 rule="para" parents="6927 489"/>
    </justification>
  </clause>

  <clause id="6933">
    <literal><![CDATA[
      L(x * y,K(y * x,z),u) = (y \ (y * x)) * y
    ]]></literal>
    <justification jstring="[para(6927(a,1),3927(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6927 3927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6934">
    <literal><![CDATA[
      L(T(x,y),K(z,x),u) = T(x,y)
    ]]></literal>
    <justification jstring="[para(6930(a,1),25(a,2,1))].">
      <j1 rule="para" parents="6930 25"/>
    </justification>
  </clause>

  <clause id="6935">
    <literal><![CDATA[
      (x * K(y,z)) * T(z,u) = x * (K(y,z) * T(z,u))
    ]]></literal>
    <justification jstring="[para(6930(a,1),487(a,1,2,1))].">
      <j1 rule="para" parents="6930 487"/>
    </justification>
  </clause>

  <clause id="6936">
    <literal><![CDATA[
      (x * K(y,z)) * R(z,u,w) = x * (K(y,z) * R(z,u,w))
    ]]></literal>
    <justification jstring="[para(6930(a,1),488(a,1,2,1))].">
      <j1 rule="para" parents="6930 488"/>
    </justification>
  </clause>

  <clause id="6937">
    <literal><![CDATA[
      (x * K(y,z)) * L(z,u,w) = x * (K(y,z) * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(6930(a,1),489(a,1,2,1))].">
      <j1 rule="para" parents="6930 489"/>
    </justification>
  </clause>

  <clause id="6939">
    <literal><![CDATA[
      L(L(T(x,y),z,u),K(x,w),v5) = L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(6931(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6931 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6940">
    <literal><![CDATA[
      L(T(x,K(y,x)),K(z,x),u) = x
    ]]></literal>
    <justification jstring="[hyper(299,a,3612,a(flip),b,6934,a),flip(a)].">
      <j1 rule="hyper" parents="299 3612 6934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6941">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * (z * K(y,z))) = z
    ]]></literal>
    <justification jstring="[hyper(65,a,230,a,b,6940,a)].">
      <j1 rule="hyper" parents="65 230 6940"/>
    </justification>
  </clause>

  <clause id="6942">
    <literal><![CDATA[
      (x * K(y,z)) * y = (x * y) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,6832,a,b,6912,a),flip(a)].">
      <j1 rule="hyper" parents="299 6832 6912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6943">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) * y = T(y,z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,3621,a,b,6912,a),flip(a)].">
      <j1 rule="hyper" parents="299 3621 6912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6945">
    <literal><![CDATA[
      (x * y) * K(T(x,y),z) = T(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(37,a,1567,a,b,6912,a),flip(a)].">
      <j1 rule="hyper" parents="37 1567 6912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6946">
    <literal><![CDATA[
      (x \ T(y,x)) * K(x,y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(37,a,4583,a(flip),b,6912,a),flip(a)].">
      <j1 rule="hyper" parents="37 4583 6912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6947">
    <literal><![CDATA[
      (x * (y * T(z,u))) \ ((x * (y * K(z,u))) * z) = a(x,y * K(z,u),z)
    ]]></literal>
    <justification jstring="[para(6912(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="6912 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6948">
    <literal><![CDATA[
      L(x \ 1,x,y * K(x,z)) = (y * T(x,z)) \ (y * K(x,z))
    ]]></literal>
    <justification jstring="[para(6912(a,1),214(a,2,1))].">
      <j1 rule="para" parents="6912 214"/>
    </justification>
  </clause>

  <clause id="6950">
    <literal><![CDATA[
      (T(x,y) \ 1) * y = (x \ 1) * T(y,x)
    ]]></literal>
    <justification jstring="[para(5052(a,1),6912(a,1,1))].">
      <j1 rule="para" parents="5052 6912"/>
    </justification>
  </clause>

  <clause id="6951">
    <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(6912(a,1),5983(a,1,2,1))].">
      <j1 rule="para" parents="6912 5983"/>
    </justification>
  </clause>

  <clause id="6952">
    <literal><![CDATA[
      T(K(x,y),y * z) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),6915(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 6915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6953">
    <literal><![CDATA[
      T(x,(y / (1 / x)) / x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(12(a,1),6918(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 6918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6954">
    <literal><![CDATA[
      K(x,y) = (x \ T(y,x)) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(125,a,6946,a),flip(a)].">
      <j1 rule="hyper" parents="125 6946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6955">
    <literal><![CDATA[
      T(K(x,y),z * y) = T(K(x,y),y * z)
    ]]></literal>
    <justification jstring="[hyper(299,a,6917,a,b,6952,a)].">
      <j1 rule="hyper" parents="299 6917 6952"/>
    </justification>
  </clause>

  <clause id="6956">
    <literal><![CDATA[
      (x * y) * K(z,T(x,y)) = K(z,x) * (x * y)
    ]]></literal>
    <justification jstring="[para(6952(a,1),107(a,1,2))].">
      <j1 rule="para" parents="6952 107"/>
    </justification>
  </clause>

  <clause id="6957">
    <literal><![CDATA[
      K(x * y,T(x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x * y,x) = z
    ]]></literal>
    <justification jstring="[para(6952(a,1),5306(a,1))].">
      <j1 rule="para" parents="6952 5306"/>
    </justification>
  </clause>

  <clause id="6959">
    <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(6952(a,1),6275(a,1,2))].">
      <j1 rule="para" parents="6952 6275"/>
    </justification>
  </clause>

  <clause id="6960">
    <literal><![CDATA[
      (x * y) * K(z,y \ 1) = x * (y * K(z,y \ 1))
    ]]></literal>
    <justification jstring="[para(6810(a,1),94(a,1,2))].">
      <j1 rule="para" parents="6810 94"/>
    </justification>
  </clause>

  <clause id="6961">
    <literal><![CDATA[
      (x * y) * K(y \ 1,z) = x * (y * K(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(6827(a,1),94(a,1,2))].">
      <j1 rule="para" parents="6827 94"/>
    </justification>
  </clause>

  <clause id="6962">
    <literal><![CDATA[
      K(x,T(y / z,z / y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(2620(a,2),6914(a,1,2))].">
      <j1 rule="para" parents="2620 6914"/>
    </justification>
  </clause>

  <clause id="6964">
    <literal><![CDATA[
      K(K(x \ 1,x) * y,(z \ 1) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(5606(a,2),6914(a,1))].">
      <j1 rule="para" parents="5606 6914"/>
    </justification>
  </clause>

  <clause id="6966">
    <literal><![CDATA[
      x \ (y * K(z,x \ y)) = (x \ y) * K(z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(1020,a,6816,a)].">
      <j1 rule="hyper" parents="1020 6816"/>
    </justification>
  </clause>

  <clause id="6967">
    <literal><![CDATA[
      R(x,y,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(544,a,6816,a)].">
      <j1 rule="hyper" parents="544 6816"/>
    </justification>
  </clause>

  <clause id="6968">
    <literal><![CDATA[
      (x * y) * K(z,y) = x * ((z * y) / z)
    ]]></literal>
    <justification jstring="[hyper(299,a,5237,a,b,6816,a),flip(a)].">
      <j1 rule="hyper" parents="299 5237 6816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6970">
    <literal><![CDATA[
      (x * (y \ z)) * K(y,y \ z) = x * (z / y)
    ]]></literal>
    <justification jstring="[para(5102(a,1),6816(a,2,2))].">
      <j1 rule="para" parents="5102 6816"/>
    </justification>
  </clause>

  <clause id="6971">
    <literal><![CDATA[
      R(T(x,y * K(z,y)),y,K(z,y)) = ((z * y) / z) \ (x * (y * K(z,y)))
    ]]></literal>
    <justification jstring="[para(6816(a,1),5252(a,2,2))].">
      <j1 rule="para" parents="6816 5252"/>
    </justification>
  </clause>

  <clause id="6972">
    <literal><![CDATA[
      (x * (y * K(z,y))) * z = (x * y) * T(z,y)
    ]]></literal>
    <justification jstring="[para(6816(a,1),6912(a,1,1))].">
      <j1 rule="para" parents="6816 6912"/>
    </justification>
  </clause>

  <clause id="6973">
    <literal><![CDATA[
      (x * K(y,z)) * (y * K(u,y)) = (x * T(y,z)) * K(u,y)
    ]]></literal>
    <justification jstring="[para(6912(a,1),6816(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6912 6816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6975">
    <literal><![CDATA[
      x * (y * K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      (x * y) * K(z,y) = u
    ]]></literal>
    <justification jstring="[para(6967(a,1),275(a,1,1))].">
      <j1 rule="para" parents="6967 275"/>
    </justification>
  </clause>

  <clause id="6976">
    <literal><![CDATA[
      K((x \ y) \ y,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(5870,a,6868,a),flip(a)].">
      <j1 rule="hyper" parents="5870 6868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6977">
    <literal><![CDATA[
      K((x \ y) \ 1,z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(5848,a,6868,a)].">
      <j1 rule="hyper" parents="5848 6868"/>
    </justification>
  </clause>

  <clause id="6978">
    <literal><![CDATA[
      K(x / y,z) * x = x * K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(5772,a,6868,a)].">
      <j1 rule="hyper" parents="5772 6868"/>
    </justification>
  </clause>

  <clause id="6979">
    <literal><![CDATA[
      T(K(x / y,z),x) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(5596,a,6868,a)].">
      <j1 rule="hyper" parents="5596 6868"/>
    </justification>
  </clause>

  <clause id="6980">
    <literal><![CDATA[
      x \ T(x * y,z) = y * K((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(1140,a,6868,a)].">
      <j1 rule="hyper" parents="1140 6868"/>
    </justification>
  </clause>

  <clause id="6981">
    <literal><![CDATA[
      (x \ y) * K((x \ 1) \ (x \ y),z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,1109,a(flip),b,6868,a),flip(a)].">
      <j1 rule="hyper" parents="65 1109 6868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6983">
    <literal><![CDATA[
      x \ (((y \ (x * z)) * y) / z) = K((y / z) \ x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,1520,a(flip),b,6868,a(flip))].">
      <j1 rule="hyper" parents="119 1520 6868"/>
    </justification>
  </clause>

  <clause id="6984">
    <literal><![CDATA[
      x \ (y \ ((z \ (y * x)) * z)) = K((y \ z) \ x,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,1374,a(flip),b,6868,a(flip))].">
      <j1 rule="hyper" parents="119 1374 6868"/>
    </justification>
  </clause>

  <clause id="6989">
    <literal><![CDATA[
      x \ (y * T(y \ x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(6868(a,2),314(a,1,2))].">
      <j1 rule="para" parents="6868 314"/>
    </justification>
  </clause>

  <clause id="6991">
    <literal><![CDATA[
      (x \ y) * K((1 / x) \ (x \ y),z) = (1 / x) * T(x \ ((x \ 1) \ y),z)
    ]]></literal>
    <justification jstring="[para(729(a,1),6868(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="729 6868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6992">
    <literal><![CDATA[
      L(K(x \ (y \ z),u),y \ z,y) = z \ (y * (x * T(x \ (y \ z),u)))
    ]]></literal>
    <justification jstring="[para(6868(a,2),95(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6868 95"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6993">
    <literal><![CDATA[
      (x * K(y \ x,z)) * (y \ 1) = T(x * (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(6868(a,1),1265(a,1,1))].">
      <j1 rule="para" parents="6868 1265"/>
    </justification>
  </clause>

  <clause id="6994">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ y,z) = T(y * K(x \ y,z),y)
    ]]></literal>
    <justification jstring="[para(6868(a,1),2029(a,2,1))].">
      <j1 rule="para" parents="6868 2029"/>
    </justification>
  </clause>

  <clause id="6995">
    <literal><![CDATA[
      R(K(x \ (y / z),y / z),y / z,z) = ((x * T(x \ (y / z),y / z)) * z) / y
    ]]></literal>
    <justification jstring="[para(6868(a,2),3640(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6868 3640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6998">
    <literal><![CDATA[
      (L(x,y,z) \ x) * T((L(x,y,z) \ x) \ x,u) = x * K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(6373(a,1),6868(a,2,2,1))].">
      <j1 rule="para" parents="6373 6868"/>
    </justification>
  </clause>

  <clause id="6999">
    <literal><![CDATA[
      K((x \ y) \ y,y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,3616,a(flip),b,6976,a),flip(a)].">
      <j1 rule="hyper" parents="299 3616 6976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7000">
    <literal><![CDATA[
      K(T(x,x \ y),z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[para(108(a,2),6976(a,1,1))].">
      <j1 rule="para" parents="108 6976"/>
    </justification>
  </clause>

  <clause id="7001">
    <literal><![CDATA[
      K(x / y,x) = K(y \ x,x)
    ]]></literal>
    <justification jstring="[para(79(a,1),6999(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 6999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7002">
    <literal><![CDATA[
      K((x / y) \ 1,y) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(5861,a,7001,a)].">
      <j1 rule="hyper" parents="5861 7001"/>
    </justification>
  </clause>

  <clause id="7003">
    <literal><![CDATA[
      K((x \ (y * z)) \ 1,y) = K((y / (z \ 1)) \ x,y)
    ]]></literal>
    <justification jstring="[hyper(6551,a,6977,a)].">
      <j1 rule="hyper" parents="6551 6977"/>
    </justification>
  </clause>

  <clause id="7004">
    <literal><![CDATA[
      K(1 / (x \ y),z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(5559,a,6977,a)].">
      <j1 rule="hyper" parents="5559 6977"/>
    </justification>
  </clause>

  <clause id="7005">
    <literal><![CDATA[
      K((x \ y) \ 1,(z \ u) \ 1) = K(y \ x,u \ z)
    ]]></literal>
    <justification jstring="[hyper(299,a,6814,a(flip),b,6977,a),flip(a)].">
      <j1 rule="hyper" parents="299 6814 6977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7006">
    <literal><![CDATA[
      K(((x * y) \ x) \ 1,z) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,722,a(flip),b,6977,a),flip(a)].">
      <j1 rule="hyper" parents="299 722 6977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7007">
    <literal><![CDATA[
      K((T(x,y) \ T(z,y)) \ 1,x) = K(z \ x,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,6670,a,b,6977,a)].">
      <j1 rule="hyper" parents="65 6670 6977"/>
    </justification>
  </clause>

  <clause id="7008">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) = K((x * y) \ y,z)
    ]]></literal>
    <justification jstring="[para(22(a,2),6977(a,1,1,1))].">
      <j1 rule="para" parents="22 6977"/>
    </justification>
  </clause>

  <clause id="7010">
    <literal><![CDATA[
      K(L(x \ y,x,z) \ 1,u) = K((z * y) \ (z * x),u)
    ]]></literal>
    <justification jstring="[para(96(a,2),6977(a,1,1,1))].">
      <j1 rule="para" parents="96 6977"/>
    </justification>
  </clause>

  <clause id="7013">
    <literal><![CDATA[
      T(x,y \ z) * K((z \ y) \ 1,x) = x
    ]]></literal>
    <justification jstring="[para(6977(a,2),5042(a,1,2))].">
      <j1 rule="para" parents="6977 5042"/>
    </justification>
  </clause>

  <clause id="7014">
    <literal><![CDATA[
      T(x,(y \ z) \ 1) = K(z \ y,x) \ x
    ]]></literal>
    <justification jstring="[para(6977(a,1),5050(a,2,1))].">
      <j1 rule="para" parents="6977 5050"/>
    </justification>
  </clause>

  <clause id="7015">
    <literal><![CDATA[
      K((K(x,y) * z) \ 1,u) = K(z \ K(y,x),u)
    ]]></literal>
    <justification jstring="[para(5426(a,1),6977(a,1,1,1))].">
      <j1 rule="para" parents="5426 6977"/>
    </justification>
  </clause>

  <clause id="7016">
    <literal><![CDATA[
      x * (y * K((x \ 1) \ y,z)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(6977(a,1),6053(a,1,2,2))].">
      <j1 rule="para" parents="6977 6053"/>
    </justification>
  </clause>

  <clause id="7017">
    <literal><![CDATA[
      (1 / (x \ y)) * (z / (1 / (x \ y))) = z * K(y \ x,z * (x \ y))
    ]]></literal>
    <justification jstring="[para(6977(a,1),6168(a,2,2))].">
      <j1 rule="para" parents="6977 6168"/>
    </justification>
  </clause>

  <clause id="7018">
    <literal><![CDATA[
      x * K((y * z) \ x,y) = z * ((y \ (z \ x)) * y)
    ]]></literal>
    <justification jstring="[para(6977(a,1),6230(a,1,2))].">
      <j1 rule="para" parents="6977 6230"/>
    </justification>
  </clause>

  <clause id="7019">
    <literal><![CDATA[
      T(x * K(y \ z,x),z \ y) = T(x,(z \ y) * (z \ y))
    ]]></literal>
    <justification jstring="[para(6977(a,1),6324(a,1,1,2))].">
      <j1 rule="para" parents="6977 6324"/>
    </justification>
  </clause>

  <clause id="7020">
    <literal><![CDATA[
      K(L(x \ y,z,u) \ 1,w) = L(K(y \ x,w),z,u)
    ]]></literal>
    <justification jstring="[para(6977(a,1),6337(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6977 6337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7021">
    <literal><![CDATA[
      x * K((y * z) \ x,z) = y * ((z \ (y \ x)) * z)
    ]]></literal>
    <justification jstring="[para(6977(a,1),6424(a,1,2))].">
      <j1 rule="para" parents="6977 6424"/>
    </justification>
  </clause>

  <clause id="7022">
    <literal><![CDATA[
      (1 / x) * K(y \ (1 / x),z) = K((y * x) \ 1,z) / x
    ]]></literal>
    <justification jstring="[para(6977(a,1),6725(a,1,2))].">
      <j1 rule="para" parents="6977 6725"/>
    </justification>
  </clause>

  <clause id="7023">
    <literal><![CDATA[
      K(L(x,y,z) / u,x) = K(u \ L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,3670,a(flip),b,6979,a)].">
      <j1 rule="hyper" parents="65 3670 6979"/>
    </justification>
  </clause>

  <clause id="7024">
    <literal><![CDATA[
      K(x \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K((y \ x) \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(7004(a,1),5560(a,1))].">
      <j1 rule="para" parents="7004 5560"/>
    </justification>
  </clause>

  <clause id="7025">
    <literal><![CDATA[
      T(((x * y) \ x) \ 1,z) = ((x * y) \ x) \ K(y,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,7006,a(flip),b,5035,a),flip(a)].">
      <j1 rule="hyper" parents="119 7006 5035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7026">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) * K(y,z) = T(1 / ((x * y) \ x),z)
    ]]></literal>
    <justification jstring="[para(7006(a,1),5161(a,1,2))].">
      <j1 rule="para" parents="7006 5161"/>
    </justification>
  </clause>

  <clause id="7027">
    <literal><![CDATA[
      K(x,y \ (y / z)) = K(x,((z * u) \ u) * K(z * u,1 / z))
    ]]></literal>
    <justification jstring="[para(5951(a,2),6900(a,2,2))].">
      <j1 rule="para" parents="5951 6900"/>
    </justification>
  </clause>

  <clause id="7028">
    <literal><![CDATA[
      (x * K(y,z)) * z = x * (z * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(144,a,6941,a)].">
      <j1 rule="hyper" parents="144 6941"/>
    </justification>
  </clause>

  <clause id="7029">
    <literal><![CDATA[
      x \ (y * K(x,z)) = (x \ y) * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(37,a,6126,a,b,6942,a)].">
      <j1 rule="hyper" parents="37 6126 6942"/>
    </justification>
  </clause>

  <clause id="7031">
    <literal><![CDATA[
      ((x \ y) \ y) * z = (x * z) * K(T(x,z),y / x)
    ]]></literal>
    <justification jstring="[para(4440(a,1),6945(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4440 6945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7032">
    <literal><![CDATA[
      T(K(x,y),z * y) * K(y,x) = K(K(x,y),y * z)
    ]]></literal>
    <justification jstring="[para(6955(a,2),5277(a,1,1))].">
      <j1 rule="para" parents="6955 5277"/>
    </justification>
  </clause>

  <clause id="7033">
    <literal><![CDATA[
      (x / y) * ((z * y) / z) = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(306,a,6968,a),flip(a)].">
      <j1 rule="hyper" parents="306 6968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7034">
    <literal><![CDATA[
      (x * ((y * z) / y)) * y = (x * z) * T(y,z)
    ]]></literal>
    <justification jstring="[para(6968(a,1),6912(a,1,1))].">
      <j1 rule="para" parents="6968 6912"/>
    </justification>
  </clause>

  <clause id="7035">
    <literal><![CDATA[
      K((x * T(x \ y,z)) / T(y / x,z),u) * (x * T(x \ y,z)) = (x * T(x \ y,z)) * K(x,u)
    ]]></literal>
    <justification jstring="[para(438(a,1),6978(a,2,2,1))].">
      <j1 rule="para" parents="438 6978"/>
    </justification>
  </clause>

  <clause id="7036">
    <literal><![CDATA[
      K(((x \ 1) * y) \ y,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(65,a,6236,a(flip),b,7008,a),flip(a)].">
      <j1 rule="hyper" parents="65 6236 7008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7037">
    <literal><![CDATA[
      T(x,(y \ z) \ 1) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(5045,a,7013,a)].">
      <j1 rule="hyper" parents="5045 7013"/>
    </justification>
  </clause>

  <clause id="7040">
    <literal><![CDATA[
      T(x,(y * z) \ y) = T(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),7037(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 7037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7041">
    <literal><![CDATA[
      T(x,((y * z) \ y) \ 1) = T(x,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),7037(a,2,2))].">
      <j1 rule="para" parents="9 7037"/>
    </justification>
  </clause>

  <clause id="7043">
    <literal><![CDATA[
      T(x,T(y,z) \ 1) = T(x,(y * z) \ z)
    ]]></literal>
    <justification jstring="[para(22(a,2),7037(a,1,2,1))].">
      <j1 rule="para" parents="22 7037"/>
    </justification>
  </clause>

  <clause id="7044">
    <literal><![CDATA[
      T(x,y \ (y / z)) = T(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(79(a,1),7037(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 7037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7045">
    <literal><![CDATA[
      ((x \ y) \ 1) * T(z,y \ x) = z * ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(7037(a,1),107(a,1,2))].">
      <j1 rule="para" parents="7037 107"/>
    </justification>
  </clause>

  <clause id="7046">
    <literal><![CDATA[
      T(x \ y,y \ x) != z
    ]]></literal>
    <literal><![CDATA[
      ((x \ y) \ 1) \ 1 = z
    ]]></literal>
    <justification jstring="[para(7037(a,1),409(a,1))].">
      <j1 rule="para" parents="7037 409"/>
    </justification>
  </clause>

  <clause id="7047">
    <literal><![CDATA[
      T(x,(y / (z * z)) \ 1) = T(x,(z \ 1) \ (z / y))
    ]]></literal>
    <justification jstring="[para(990(a,1),7037(a,1,2,1))].">
      <j1 rule="para" parents="990 7037"/>
    </justification>
  </clause>

  <clause id="7048">
    <literal><![CDATA[
      T(x * y,y \ 1) = ((x * y) \ x) \ x
    ]]></literal>
    <justification jstring="[hyper(409,a,7040,a),flip(a)].">
      <j1 rule="hyper" parents="409 7040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7049">
    <literal><![CDATA[
      T(x,L(y,y \ 1,z)) = T(x,(1 / y) \ 1)
    ]]></literal>
    <justification jstring="[para(2532(a,2),7040(a,1,2))].">
      <j1 rule="para" parents="2532 7040"/>
    </justification>
  </clause>

  <clause id="7050">
    <literal><![CDATA[
      T(x,L(y \ 1,y,z) \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[para(214(a,2),7041(a,1,2,1))].">
      <j1 rule="para" parents="214 7041"/>
    </justification>
  </clause>

  <clause id="7052">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) * T(z,y) = z * (1 / ((x * y) \ x))
    ]]></literal>
    <justification jstring="[para(7041(a,1),3732(a,1,2))].">
      <j1 rule="para" parents="7041 3732"/>
    </justification>
  </clause>

  <clause id="7053">
    <literal><![CDATA[
      T(x,y \ (y / z)) = T(x,1 / z)
    ]]></literal>
    <justification jstring="[hyper(299,a,3733,a,b,7044,a),flip(a)].">
      <j1 rule="hyper" parents="299 3733 7044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7057">
    <literal><![CDATA[
      T(x,y \ (y / z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(7053(a,2),4656(a,1))].">
      <j1 rule="para" parents="7053 4656"/>
    </justification>
  </clause>

  <clause id="7059">
    <literal><![CDATA[
      T(x,(y \ z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(7014(a,2),5063(a,1))].">
      <j1 rule="para" parents="7014 5063"/>
    </justification>
  </clause>

  <clause id="7061">
    <literal><![CDATA[
      (x \ 1) * (x * K(y,x)) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[para(5052(a,1),7028(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5052 7028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7063">
    <literal><![CDATA[
      (x * y) * (z * K(y,z)) = (x * T(y,z)) * z
    ]]></literal>
    <justification jstring="[para(6832(a,1),7028(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6832 7028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7064">
    <literal><![CDATA[
      K(x,y) * (x \ y) = (x \ y) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5997,a,7029,a)].">
      <j1 rule="hyper" parents="5997 7029"/>
    </justification>
  </clause>

  <clause id="7065">
    <literal><![CDATA[
      x * ((x \ y) * K(x,z)) = y * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(144,a,7029,a)].">
      <j1 rule="hyper" parents="144 7029"/>
    </justification>
  </clause>

  <clause id="7066">
    <literal><![CDATA[
      L(x \ 1,x,y) * ((x \ 1) \ (y * x)) = ((x \ 1) \ y) * K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(65,a,6079,a,b,7029,a)].">
      <j1 rule="hyper" parents="65 6079 7029"/>
    </justification>
  </clause>

  <clause id="7067">
    <literal><![CDATA[
      (x / (y \ z)) * (z / y) = x * K(y,y \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),7033(a,1,2,1))].">
      <j1 rule="para" parents="10 7033"/>
    </justification>
  </clause>

  <clause id="7068">
    <literal><![CDATA[
      L(x,(y / z) * ((u * u) * z),w) = L(x,y * K(u * u,z),w)
    ]]></literal>
    <justification jstring="[para(7033(a,1),2893(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7033 2893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7069">
    <literal><![CDATA[
      x / T(y * x,T(y,x) \ 1) = (y * x) \ x
    ]]></literal>
    <justification jstring="[para(7043(a,2),262(a,1,2))].">
      <j1 rule="para" parents="7043 262"/>
    </justification>
  </clause>

  <clause id="7070">
    <literal><![CDATA[
      L(x \ 1,x,y) \ y = T(y * x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,367,a,b,7048,a)].">
      <j1 rule="hyper" parents="299 367 7048"/>
    </justification>
  </clause>

  <clause id="7071">
    <literal><![CDATA[
      T(x * (1 / y),y) = ((x * (1 / y)) \ x) \ x
    ]]></literal>
    <justification jstring="[para(79(a,1),7048(a,1,2))].">
      <j1 rule="para" parents="79 7048"/>
    </justification>
  </clause>

  <clause id="7072">
    <literal><![CDATA[
      L(K(x,y) * ((y \ x) \ z),K(y,x),y \ x) = (K(y,x) * (y \ x)) \ z
    ]]></literal>
    <justification jstring="[para(7064(a,2),5443(a,2,1))].">
      <j1 rule="para" parents="7064 5443"/>
    </justification>
  </clause>

  <clause id="7073">
    <literal><![CDATA[
      x * ((x \ y) * K(x \ 1,z)) = y * K(x \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,1758,a(flip),b,7065,a)].">
      <j1 rule="hyper" parents="65 1758 7065"/>
    </justification>
  </clause>

  <clause id="7074">
    <literal><![CDATA[
      (x * y) * K(x,z) = x * (y * K(x,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),7065(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 7065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7075">
    <literal><![CDATA[
      R(x,y,K(x,z)) = x
    ]]></literal>
    <justification jstring="[hyper(3985,a,7074,a)].">
      <j1 rule="hyper" parents="3985 7074"/>
    </justification>
  </clause>

  <clause id="7076">
    <literal><![CDATA[
      L(K(x,y),z,x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2841,a,7074,a)].">
      <j1 rule="hyper" parents="2841 7074"/>
    </justification>
  </clause>

  <clause id="7077">
    <literal><![CDATA[
      T(x,y) * T(z,K(x,y)) = (x * z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,5358,a,b,7074,a)].">
      <j1 rule="hyper" parents="299 5358 7074"/>
    </justification>
  </clause>

  <clause id="7078">
    <literal><![CDATA[
      (x * (y * K(x,z))) * x = (x * y) * T(x,z)
    ]]></literal>
    <justification jstring="[para(7074(a,1),6912(a,1,1))].">
      <j1 rule="para" parents="7074 6912"/>
    </justification>
  </clause>

  <clause id="7079">
    <literal><![CDATA[
      R(T(x,y),z,K(x,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(7075(a,1),27(a,2,1))].">
      <j1 rule="para" parents="7075 27"/>
    </justification>
  </clause>

  <clause id="7080">
    <literal><![CDATA[
      (T(x,y) * z) * K(x,u) = T(x,y) * (z * K(x,u))
    ]]></literal>
    <justification jstring="[para(7075(a,1),541(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7075 541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7081">
    <literal><![CDATA[
      (L(x,y,z) * u) * K(x,w) = L(x,y,z) * (u * K(x,w))
    ]]></literal>
    <justification jstring="[para(7075(a,1),542(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7075 542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7082">
    <literal><![CDATA[
      (R(x,y,z) * u) * K(x,w) = R(x,y,z) * (u * K(x,w))
    ]]></literal>
    <justification jstring="[para(7075(a,1),543(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7075 543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7083">
    <literal><![CDATA[
      L(K(x,y),z,x) = u \ (u * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,9,a,b,7076,a),flip(a)].">
      <j1 rule="hyper" parents="299 9 7076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7084">
    <literal><![CDATA[
      a(x,y,K(x,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(55,a,7076,a)].">
      <j1 rule="hyper" parents="55 7076"/>
    </justification>
  </clause>

  <clause id="7087">
    <literal><![CDATA[
      L(K(x,y),z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7083(a,2),314(a,1))].">
      <j1 rule="para" parents="7083 314"/>
    </justification>
  </clause>

  <clause id="7090">
    <literal><![CDATA[
      T(L(K(x,y),x,z),x * u) != w
    ]]></literal>
    <literal><![CDATA[
      (x * u) \ (T(x,y) * u) = w
    ]]></literal>
    <justification jstring="[para(6825(a,2),400(a,1,1))].">
      <j1 rule="para" parents="6825 400"/>
    </justification>
  </clause>

  <clause id="7092">
    <literal><![CDATA[
      ((x * y) * z) * K(y * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) * T(y * z,u) = w
    ]]></literal>
    <justification jstring="[para(103(a,1),6862(a,1,1))].">
      <j1 rule="para" parents="103 6862"/>
    </justification>
  </clause>

  <clause id="7094">
    <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),6885(a,1,2,1))].">
      <j1 rule="para" parents="22 6885"/>
    </justification>
  </clause>

  <clause id="7095">
    <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),6885(a,1,2,1))].">
      <j1 rule="para" parents="96 6885"/>
    </justification>
  </clause>

  <clause id="7096">
    <literal><![CDATA[
      K(x,1 / (y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(4797(a,2),6885(a,1))].">
      <j1 rule="para" parents="4797 6885"/>
    </justification>
  </clause>

  <clause id="7097">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u \ K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(5426(a,1),6885(a,1,2,1))].">
      <j1 rule="para" parents="5426 6885"/>
    </justification>
  </clause>

  <clause id="7098">
    <literal><![CDATA[
      T(K(x,y / z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(6077(a,2),6885(a,1))].">
      <j1 rule="para" parents="6077 6885"/>
    </justification>
  </clause>

  <clause id="7099">
    <literal><![CDATA[
      K(x,((y * z) \ y) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(6898(a,1),505(a,1))].">
      <j1 rule="para" parents="6898 505"/>
    </justification>
  </clause>

  <clause id="7101">
    <literal><![CDATA[
      (x * ((y * z) / y)) * y != u
    ]]></literal>
    <literal><![CDATA[
      (x * z) * T(y,z) = u
    ]]></literal>
    <justification jstring="[para(6968(a,1),6921(a,1,1))].">
      <j1 rule="para" parents="6968 6921"/>
    </justification>
  </clause>

  <clause id="7102">
    <literal><![CDATA[
      T(x,L(y,y \ 1,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(79(a,1),7049(a,2,2))].">
      <j1 rule="para" parents="79 7049"/>
    </justification>
  </clause>

  <clause id="7103">
    <literal><![CDATA[
      T(x,L(y,y,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2526(a,1),7102(a,1,2))].">
      <j1 rule="para" parents="2526 7102"/>
    </justification>
  </clause>

  <clause id="7104">
    <literal><![CDATA[
      L(x,x,y) * T(z,x) = z * L(x,x,y)
    ]]></literal>
    <justification jstring="[para(7103(a,1),107(a,1,2))].">
      <j1 rule="para" parents="7103 107"/>
    </justification>
  </clause>

  <clause id="7105">
    <literal><![CDATA[
      T(x * (1 / y),y * y) = (y \ 1) * T(x,y)
    ]]></literal>
    <justification jstring="[para(7103(a,1),2979(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7103 2979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7106">
    <literal><![CDATA[
      (1 / x) \ L(y * ((x \ 1) \ 1),x,x) = x * (y * L(x,x,x))
    ]]></literal>
    <justification jstring="[para(7104(a,1),3843(a,2,2))].">
      <j1 rule="para" parents="7104 3843"/>
    </justification>
  </clause>

  <clause id="7107">
    <literal><![CDATA[
      T(x,y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,(z \ y) \ 1) = u
    ]]></literal>
    <justification jstring="[para(76(a,1),7057(a,1,2,2))].">
      <j1 rule="para" parents="76 7057"/>
    </justification>
  </clause>

  <clause id="7108">
    <literal><![CDATA[
      T(x,(y * z) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z) \ 1) = u
    ]]></literal>
    <justification jstring="[para(185(a,1),7057(a,1,2,2))].">
      <j1 rule="para" parents="185 7057"/>
    </justification>
  </clause>

  <clause id="7110">
    <literal><![CDATA[
      x / T(x * y,y \ 1) = L(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(192,a,7070,a)].">
      <j1 rule="hyper" parents="192 7070"/>
    </justification>
  </clause>

  <clause id="7111">
    <literal><![CDATA[
      T(x,x \ T(x * y,y \ 1)) = T(x,L(y \ 1,y,x) \ 1)
    ]]></literal>
    <justification jstring="[para(7070(a,1),4639(a,1,2,2))].">
      <j1 rule="para" parents="7070 4639"/>
    </justification>
  </clause>

  <clause id="7112">
    <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(3597(a,1),7098(a,1))].">
      <j1 rule="para" parents="3597 7098"/>
    </justification>
  </clause>

  <clause id="7113">
    <literal><![CDATA[
      K(x,(y \ K(z,u)) \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,z) * y) = w
    ]]></literal>
    <justification jstring="[para(5432(a,1),7099(a,1,2,1,1))].">
      <j1 rule="para" parents="5432 7099"/>
    </justification>
  </clause>

  <clause id="7114">
    <literal><![CDATA[
      x / T(x * (y / x),y \ x) = L((y / x) \ 1,y / x,x)
    ]]></literal>
    <justification jstring="[para(4648(a,1),7110(a,1,2))].">
      <j1 rule="para" parents="4648 7110"/>
    </justification>
  </clause>

  <clause id="7115">
    <literal><![CDATA[
      T((x \ 1) * y,x) = (((x \ y) \ y) \ 1) * y
    ]]></literal>
    <justification jstring="[para(6807(a,1),3479(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6807 3479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7117">
    <literal><![CDATA[
      K(x,y * (((z * (u \ 1)) / z) \ 1)) = K(x,y * (u * K(u \ 1,z)))
    ]]></literal>
    <justification jstring="[para(6829(a,1),6042(a,2,2,2))].">
      <j1 rule="para" parents="6829 6042"/>
    </justification>
  </clause>

  <clause id="7118">
    <literal><![CDATA[
      K(x,(T(y,z) * (y \ u)) \ 1) = K(x,u \ K(z,y))
    ]]></literal>
    <justification jstring="[para(5056(a,2),6851(a,1,2,1))].">
      <j1 rule="para" parents="5056 6851"/>
    </justification>
  </clause>

  <clause id="7119">
    <literal><![CDATA[
      (x * ((y / z) / x)) * z = y * K(x,(x * z) \ y)
    ]]></literal>
    <justification jstring="[hyper(299,a,2252,a(flip),b,6853,a)].">
      <j1 rule="hyper" parents="299 2252 6853"/>
    </justification>
  </clause>

  <clause id="7120">
    <literal><![CDATA[
      T(x / (x / y),z) != u / (x / y)
    ]]></literal>
    <literal><![CDATA[
      x * K(y,z) = u
    ]]></literal>
    <justification jstring="[para(6909(a,1),48(a,1))].">
      <j1 rule="para" parents="6909 48"/>
    </justification>
  </clause>

  <clause id="7121">
    <literal><![CDATA[
      T(x * K(x \ y,x),z) = (y * K(x,z)) / (y / x)
    ]]></literal>
    <justification jstring="[para(5002(a,1),6909(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5002 6909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7122">
    <literal><![CDATA[
      T(x,x \ 1) * K(y,x) = (x * (K(y,x) / x)) * x
    ]]></literal>
    <justification jstring="[para(4791(a,1),6943(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4791 6943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7123">
    <literal><![CDATA[
      ((x \ y) * z) * K(x,T(x \ y,z)) = (y / x) * z
    ]]></literal>
    <justification jstring="[hyper(299,a,5410,a(flip),b,6956,a),flip(a)].">
      <j1 rule="hyper" parents="299 5410 6956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7126">
    <literal><![CDATA[
      ((x * y) * T(z,y)) / ((y * K(z,y)) * z) = R(x,y * K(z,y),z)
    ]]></literal>
    <justification jstring="[hyper(120,a,6972,a(flip),b,103,a)].">
      <j1 rule="hyper" parents="120 6972 103"/>
    </justification>
  </clause>

  <clause id="7127">
    <literal><![CDATA[
      (T(x,y) * y) * x = (x * y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(5115(a,1),6972(a,1,1))].">
      <j1 rule="para" parents="5115 6972"/>
    </justification>
  </clause>

  <clause id="7128">
    <literal><![CDATA[
      T(x,y) / (z \ x) = z * K(((z \ x) \ 1) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(3505,a,6980,a)].">
      <j1 rule="hyper" parents="3505 6980"/>
    </justification>
  </clause>

  <clause id="7129">
    <literal><![CDATA[
      (T(x,y) / z) / K((z \ 1) \ (x / z),y) = x / z
    ]]></literal>
    <justification jstring="[hyper(3474,a,6980,a)].">
      <j1 rule="hyper" parents="3474 6980"/>
    </justification>
  </clause>

  <clause id="7130">
    <literal><![CDATA[
      (x / y) * K((y \ 1) \ (x / y),z) = T(x,z) / y
    ]]></literal>
    <justification jstring="[hyper(3473,a,6980,a),flip(a)].">
      <j1 rule="hyper" parents="3473 6980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7132">
    <literal><![CDATA[
      T(x * K((y \ 1) \ x,z),y) = y \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(6980(a,1),3480(a,1,1))].">
      <j1 rule="para" parents="6980 3480"/>
    </justification>
  </clause>

  <clause id="7134">
    <literal><![CDATA[
      K(T(K(x,y) * z,u) \ 1,w) = T(K(z \ K(y,x),w),u)
    ]]></literal>
    <justification jstring="[para(7015(a,1),6234(a,2,1))].">
      <j1 rule="para" parents="7015 6234"/>
    </justification>
  </clause>

  <clause id="7135">
    <literal><![CDATA[
      (K(x * y,z) * ((x * y) / x)) * x = (x * y) * R(K(x * y,z),y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,3593,a,b,7034,a),flip(a)].">
      <j1 rule="hyper" parents="299 3593 7034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7136">
    <literal><![CDATA[
      (x \ 1) * ((y * x) / y) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(5269,a,7061,a)].">
      <j1 rule="hyper" parents="5269 7061"/>
    </justification>
  </clause>

  <clause id="7137">
    <literal><![CDATA[
      ((x * T(y,z)) * z) / (T(y,z) * z) = R(x,y,z * K(y,z))
    ]]></literal>
    <justification jstring="[para(7063(a,1),5465(a,1,1))].">
      <j1 rule="para" parents="7063 5465"/>
    </justification>
  </clause>

  <clause id="7138">
    <literal><![CDATA[
      (((x * y) * (1 / x)) \ (x * y)) \ (x * y) = (y * x) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(65,a,2378,a(flip),b,7071,a),flip(a)].">
      <j1 rule="hyper" parents="65 2378 7071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7139">
    <literal><![CDATA[
      T((x * y) / x,T(x,z)) = T(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(235,a,6869,a,b,7077,a)].">
      <j1 rule="hyper" parents="235 6869 7077"/>
    </justification>
  </clause>

  <clause id="7140">
    <literal><![CDATA[
      T(T(x,y),K(y,z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(223(a,1),7139(a,1,1)),flip(a)].">
      <j1 rule="para" parents="223 7139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7141">
    <literal><![CDATA[
      T(T(x,K(y,z)),y) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7139(a,1),266(a,1,1))].">
      <j1 rule="para" parents="7139 266"/>
    </justification>
  </clause>

  <clause id="7142">
    <literal><![CDATA[
      T(x,K(y,z)) * y = y * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7139(a,1),433(a,1,1))].">
      <j1 rule="para" parents="7139 433"/>
    </justification>
  </clause>

  <clause id="7143">
    <literal><![CDATA[
      T(T(x,K(y,z)),y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7139(a,1),757(a,1,1))].">
      <j1 rule="para" parents="7139 757"/>
    </justification>
  </clause>

  <clause id="7144">
    <literal><![CDATA[
      T(T(x,T(y,z)),K(T(y,z),u)) = T(x,T(T(y,u),z))
    ]]></literal>
    <justification jstring="[para(23(a,1),7140(a,2,2))].">
      <j1 rule="para" parents="23 7140"/>
    </justification>
  </clause>

  <clause id="7145">
    <literal><![CDATA[
      T(x,T(y,z)) != T(u,K(y,z))
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(7140(a,1),51(a,1))].">
      <j1 rule="para" parents="7140 51"/>
    </justification>
  </clause>

  <clause id="7148">
    <literal><![CDATA[
      T(1 / x,T(y,x)) = T(1 / x,y)
    ]]></literal>
    <justification jstring="[para(2306(a,1),7141(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2306 7141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7149">
    <literal><![CDATA[
      T(x \ 1,T(y,x)) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(2315(a,1),7141(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2315 7141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7150">
    <literal><![CDATA[
      L(x,T(y,K(x,z)),x) = L(x,T(y,T(x,z)),x)
    ]]></literal>
    <justification jstring="[para(7141(a,1),4592(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7141 4592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7151">
    <literal><![CDATA[
      T(K(x,y),T(z,y)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(6262(a,1),7141(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6262 7141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7152">
    <literal><![CDATA[
      T(x,y) * T(1 / y,x) = ((y * y) \ x) * y
    ]]></literal>
    <justification jstring="[para(7148(a,1),985(a,1,2))].">
      <j1 rule="para" parents="7148 985"/>
    </justification>
  </clause>

  <clause id="7153">
    <literal><![CDATA[
      T(x \ 1,y / x) = T(x \ 1,x \ y)
    ]]></literal>
    <justification jstring="[para(109(a,1),7149(a,1,2)),flip(a)].">
      <j1 rule="para" parents="109 7149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7154">
    <literal><![CDATA[
      T(T(x,y),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(23(a,1),7143(a,1))].">
      <j1 rule="para" parents="23 7143"/>
    </justification>
  </clause>

  <clause id="7157">
    <literal><![CDATA[
      (x \ 1) * T((1 / x) \ (((1 / x) \ 1) \ y),x) = T(((1 / x) \ 1) \ T(y,1 / x),x * x)
    ]]></literal>
    <justification jstring="[para(2045(a,1),7105(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2045 7105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7159">
    <literal><![CDATA[
      (((x \ 1) * y) \ y) \ y = (((x \ y) \ y) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,4661,a(flip),b,7115,a)].">
      <j1 rule="hyper" parents="65 4661 7115"/>
    </justification>
  </clause>

  <clause id="7160">
    <literal><![CDATA[
      K(x,y) * ((1 / y) * x) = ((y * y) \ x) * y
    ]]></literal>
    <justification jstring="[hyper(5779,a,7152,a)].">
      <j1 rule="hyper" parents="5779 7152"/>
    </justification>
  </clause>

  <clause id="7161">
    <literal><![CDATA[
      K(x,(x * y) / z) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(4613,a,6892,a),flip(a)].">
      <j1 rule="hyper" parents="4613 6892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7162">
    <literal><![CDATA[
      K(x,(x * y) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) \ x) = u
    ]]></literal>
    <justification jstring="[para(6892(a,1),4613(a,1))].">
      <j1 rule="para" parents="6892 4613"/>
    </justification>
  </clause>

  <clause id="7164">
    <literal><![CDATA[
      K(x,(L(y,z,u) / y) \ x) = K(x,(x / L(y,z,u)) * y)
    ]]></literal>
    <justification jstring="[para(1794(a,1),7161(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1794 7161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7165">
    <literal><![CDATA[
      L(x * y,K(y * x,z),u) = x * y
    ]]></literal>
    <justification jstring="[para(9(a,1),6933(a,2,1))].">
      <j1 rule="para" parents="9 6933"/>
    </justification>
  </clause>

  <clause id="7166">
    <literal><![CDATA[
      (x * K(y * z,u)) * (z * y) = x * (K(y * z,u) * (z * y))
    ]]></literal>
    <justification jstring="[para(7165(a,1),94(a,1,2))].">
      <j1 rule="para" parents="7165 94"/>
    </justification>
  </clause>

  <clause id="7167">
    <literal><![CDATA[
      (x * K(y,z)) * L(T(y,u),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      x * (K(y,z) * L(T(y,u),w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(6939(a,1),279(a,1,2))].">
      <j1 rule="para" parents="6939 279"/>
    </justification>
  </clause>

  <clause id="7168">
    <literal><![CDATA[
      x * ((y * z) / y) != u
    ]]></literal>
    <literal><![CDATA[
      (x * z) * K(y,z) = u
    ]]></literal>
    <justification jstring="[para(5054(a,2),6975(a,1,2))].">
      <j1 rule="para" parents="5054 6975"/>
    </justification>
  </clause>

  <clause id="7170">
    <literal><![CDATA[
      x \ (y * (z * T(z \ (y \ x),u))) != w
    ]]></literal>
    <literal><![CDATA[
      K((y * z) \ x,u) = w
    ]]></literal>
    <justification jstring="[para(998(a,1),6989(a,1,2))].">
      <j1 rule="para" parents="998 6989"/>
    </justification>
  </clause>

  <clause id="7172">
    <literal><![CDATA[
      K((x \ y) \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(5326(a,1),6989(a,1))].">
      <j1 rule="para" parents="5326 6989"/>
    </justification>
  </clause>

  <clause id="7174">
    <literal><![CDATA[
      T(K(x / y,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(5846(a,2),7172(a,1))].">
      <j1 rule="para" parents="5846 7172"/>
    </justification>
  </clause>

  <clause id="7176">
    <literal><![CDATA[
      K(x / y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,x) = z
    ]]></literal>
    <justification jstring="[para(3616(a,1),7174(a,1))].">
      <j1 rule="para" parents="3616 7174"/>
    </justification>
  </clause>

  <clause id="7179">
    <literal><![CDATA[
      L(K(x,y \ z),z,z \ 1) = K(x,((1 / z) * y) \ 1)
    ]]></literal>
    <justification jstring="[para(2474(a,1),6855(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2474 6855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7180">
    <literal><![CDATA[
      K(x * y,z) * (y * x) = K(y,x) * T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(3592,a,6881,a(flip))].">
      <j1 rule="hyper" parents="3592 6881"/>
    </justification>
  </clause>

  <clause id="7181">
    <literal><![CDATA[
      R(x,K(y,z),T(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(544,a,6935,a)].">
      <j1 rule="hyper" parents="544 6935"/>
    </justification>
  </clause>

  <clause id="7182">
    <literal><![CDATA[
      (x * K(y,z)) * T(z,y) = x * z
    ]]></literal>
    <justification jstring="[para(5049(a,1),6935(a,2,2))].">
      <j1 rule="para" parents="5049 6935"/>
    </justification>
  </clause>

  <clause id="7183">
    <literal><![CDATA[
      R(x,K(y,z),T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(7181(a,1),53(a,2))].">
      <j1 rule="para" parents="7181 53"/>
    </justification>
  </clause>

  <clause id="7184">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,y) = x
    ]]></literal>
    <justification jstring="[hyper(6928,a,7182,a)].">
      <j1 rule="hyper" parents="6928 7182"/>
    </justification>
  </clause>

  <clause id="7185">
    <literal><![CDATA[
      (x / T(y,z)) * y = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(1560,a,7182,a)].">
      <j1 rule="hyper" parents="1560 7182"/>
    </justification>
  </clause>

  <clause id="7186">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * z) = T(z,y)
    ]]></literal>
    <justification jstring="[hyper(125,a,7182,a)].">
      <j1 rule="hyper" parents="125 7182"/>
    </justification>
  </clause>

  <clause id="7187">
    <literal><![CDATA[
      K(x,x \ y) * K(z,x \ y) = (y / x) / T(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(120,a,5177,a(flip),b,7182,a),flip(a)].">
      <j1 rule="hyper" parents="120 5177 7182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7188">
    <literal><![CDATA[
      (x * y) / T(y * x,z) = K(x,y) * K(z,y * x)
    ]]></literal>
    <justification jstring="[hyper(120,a,5020,a(flip),b,7182,a)].">
      <j1 rule="hyper" parents="120 5020 7182"/>
    </justification>
  </clause>

  <clause id="7189">
    <literal><![CDATA[
      (x / y) * K(z,y) = x / T(y,z)
    ]]></literal>
    <justification jstring="[hyper(120,a,12,a(flip),b,7182,a),flip(a)].">
      <j1 rule="hyper" parents="120 12 7182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7190">
    <literal><![CDATA[
      x / T(y \ x,z) = y * K(z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(120,a,10,a(flip),b,7182,a)].">
      <j1 rule="hyper" parents="120 10 7182"/>
    </justification>
  </clause>

  <clause id="7191">
    <literal><![CDATA[
      (K(x,y) * K(z,y * x)) \ (x * y) = T(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,5020,a(flip),b,7182,a)].">
      <j1 rule="hyper" parents="119 5020 7182"/>
    </justification>
  </clause>

  <clause id="7193">
    <literal><![CDATA[
      (x \ y) * K(y,x) = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(37,a,4583,a,b,7182,a),flip(a)].">
      <j1 rule="hyper" parents="37 4583 7182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7194">
    <literal><![CDATA[
      (x * T(y,z)) * K(z,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(37,a,1542,a(flip),b,7182,a),flip(a)].">
      <j1 rule="hyper" parents="37 1542 7182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7195">
    <literal><![CDATA[
      (x * T(y,z)) * T(z,y) = (x * y) * z
    ]]></literal>
    <justification jstring="[para(6832(a,1),7182(a,1,1))].">
      <j1 rule="para" parents="6832 7182"/>
    </justification>
  </clause>

  <clause id="7196">
    <literal><![CDATA[
      x / K(y,z) = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(306,a,7184,a),flip(a)].">
      <j1 rule="hyper" parents="306 7184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7199">
    <literal><![CDATA[
      T(x * K(y,z),K(z,y)) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(235,a,7184,a,b,5432,a)].">
      <j1 rule="hyper" parents="235 7184 5432"/>
    </justification>
  </clause>

  <clause id="7200">
    <literal><![CDATA[
      (x * K(y,z)) \ x = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(125,a,7184,a)].">
      <j1 rule="hyper" parents="125 7184"/>
    </justification>
  </clause>

  <clause id="7201">
    <literal><![CDATA[
      (((x \ y) \ y) * K(z,u)) \ T(x,x \ y) = K(u,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,108,a,b,7184,a)].">
      <j1 rule="hyper" parents="119 108 7184"/>
    </justification>
  </clause>

  <clause id="7202">
    <literal><![CDATA[
      (x * (y / z)) * K(z \ y,z) = x * (z \ y)
    ]]></literal>
    <justification jstring="[hyper(37,a,6970,a,b,7184,a),flip(a)].">
      <j1 rule="hyper" parents="37 6970 7184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7203">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,x) = T(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(37,a,6257,a,b,7184,a),flip(a)].">
      <j1 rule="hyper" parents="37 6257 7184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7204">
    <literal><![CDATA[
      L(x,y,z) * K(x,1 / x) = L((x \ 1) \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(37,a,5464,a,b,7184,a),flip(a)].">
      <j1 rule="hyper" parents="37 5464 7184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7205">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) * K(y,x) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(37,a,2278,a,b,7184,a),flip(a)].">
      <j1 rule="hyper" parents="37 2278 7184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7206">
    <literal><![CDATA[
      (x * K(y,z)) / z = x / T(z,y)
    ]]></literal>
    <justification jstring="[hyper(120,a,7184,a(flip),b,6869,a),flip(a)].">
      <j1 rule="hyper" parents="120 7184 6869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7207">
    <literal><![CDATA[
      x * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      u * K(z,y) = x
    ]]></literal>
    <justification jstring="[para(7184(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="7184 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7208">
    <literal><![CDATA[
      x / K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * K(z,y) = u
    ]]></literal>
    <justification jstring="[para(7184(a,1),307(a,1,1)),flip(b)].">
      <j1 rule="para" parents="7184 307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7209">
    <literal><![CDATA[
      (x * K(y,z)) \ x != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = u
    ]]></literal>
    <justification jstring="[para(7184(a,1),314(a,1,2))].">
      <j1 rule="para" parents="7184 314"/>
    </justification>
  </clause>

  <clause id="7211">
    <literal><![CDATA[
      R((x * K(y,z)) / u,u,K(z,y)) = x / (u * K(z,y))
    ]]></literal>
    <justification jstring="[para(7184(a,1),104(a,2,1))].">
      <j1 rule="para" parents="7184 104"/>
    </justification>
  </clause>

  <clause id="7212">
    <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(7184(a,1),775(a,1,1,2))].">
      <j1 rule="para" parents="7184 775"/>
    </justification>
  </clause>

  <clause id="7213">
    <literal><![CDATA[
      L(x,K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,K(z,y),u) = w
    ]]></literal>
    <justification jstring="[para(7184(a,1),2630(a,1,2))].">
      <j1 rule="para" parents="7184 2630"/>
    </justification>
  </clause>

  <clause id="7214">
    <literal><![CDATA[
      (x * K(y,z)) * (T(y,z) \ 1) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[para(7184(a,1),6801(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7184 6801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7215">
    <literal><![CDATA[
      T(x,K(y,z)) / K(y,z) = K(z,y) * x
    ]]></literal>
    <justification jstring="[hyper(6277,a,7196,a)].">
      <j1 rule="hyper" parents="6277 7196"/>
    </justification>
  </clause>

  <clause id="7216">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,y) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(7196(a,1),246(a,1,1))].">
      <j1 rule="para" parents="7196 246"/>
    </justification>
  </clause>

  <clause id="7217">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,y) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(7196(a,1),247(a,1,1))].">
      <j1 rule="para" parents="7196 247"/>
    </justification>
  </clause>

  <clause id="7218">
    <literal><![CDATA[
      R((x / y) * K(z,u),K(u,z),y) = x / (K(u,z) * y)
    ]]></literal>
    <justification jstring="[para(7196(a,1),285(a,1,1))].">
      <j1 rule="para" parents="7196 285"/>
    </justification>
  </clause>

  <clause id="7220">
    <literal><![CDATA[
      ((K(x,y) / z) * (z * K(y,x))) \ (K(x,y) / z) = 1 / (z / K(x,y))
    ]]></literal>
    <justification jstring="[para(7196(a,1),2211(a,1,1,2))].">
      <j1 rule="para" parents="7196 2211"/>
    </justification>
  </clause>

  <clause id="7221">
    <literal><![CDATA[
      x / (K(y,z) \ 1) = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(5197(a,2),7196(a,1,2))].">
      <j1 rule="para" parents="5197 7196"/>
    </justification>
  </clause>

  <clause id="7223">
    <literal><![CDATA[
      K(x,1 / (K(y,z) / u)) = K(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[para(7196(a,1),5940(a,2,2))].">
      <j1 rule="para" parents="7196 5940"/>
    </justification>
  </clause>

  <clause id="7224">
    <literal><![CDATA[
      (x * K(L(y \ 1,z,u) \ 1,w)) \ x = L(K(w,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,6131,a(flip),b,7200,a),flip(a)].">
      <j1 rule="hyper" parents="299 6131 7200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7225">
    <literal><![CDATA[
      ((x * K(y,z)) \ x) \ u = K(y,z) * u
    ]]></literal>
    <justification jstring="[para(7200(a,2),5426(a,1,1))].">
      <j1 rule="para" parents="7200 5426"/>
    </justification>
  </clause>

  <clause id="7226">
    <literal><![CDATA[
      (x \ R(x,y,x)) \ K(x * y,x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(5790(a,1),7200(a,1,1))].">
      <j1 rule="para" parents="5790 7200"/>
    </justification>
  </clause>

  <clause id="7227">
    <literal><![CDATA[
      L(L(K(x,y),z,u),K(y,x),w) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(7200(a,1),5214(a,2,1))].">
      <j1 rule="para" parents="7200 5214"/>
    </justification>
  </clause>

  <clause id="7228">
    <literal><![CDATA[
      (x * T(x \ y,z)) \ y = K(z,x \ y)
    ]]></literal>
    <justification jstring="[para(6868(a,2),7200(a,1,1))].">
      <j1 rule="para" parents="6868 7200"/>
    </justification>
  </clause>

  <clause id="7229">
    <literal><![CDATA[
      (x \ T(x * y,z)) \ y = K(z,(x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(6980(a,2),7200(a,1,1))].">
      <j1 rule="para" parents="6980 7200"/>
    </justification>
  </clause>

  <clause id="7230">
    <literal><![CDATA[
      (K(x,y) / T(x,x * y)) * x = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,5587,a(flip),b,7185,a),flip(a)].">
      <j1 rule="hyper" parents="299 5587 7185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7231">
    <literal><![CDATA[
      T(x / T(y,z),y) = y \ (x * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(235,a,7185,a,b,10,a)].">
      <j1 rule="hyper" parents="235 7185 10"/>
    </justification>
  </clause>

  <clause id="7232">
    <literal><![CDATA[
      x * K(y,z) != u * z
    ]]></literal>
    <literal><![CDATA[
      x / T(z,y) = u
    ]]></literal>
    <justification jstring="[para(7185(a,1),46(a,1))].">
      <j1 rule="para" parents="7185 46"/>
    </justification>
  </clause>

  <clause id="7235">
    <literal><![CDATA[
      x \ (y * K(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      T(y / T(x,z),x) = u
    ]]></literal>
    <justification jstring="[para(7185(a,1),318(a,1,2))].">
      <j1 rule="para" parents="7185 318"/>
    </justification>
  </clause>

  <clause id="7236">
    <literal><![CDATA[
      R(x / T(y,z),y,y \ 1) = (x * K(z,y)) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(7185(a,1),258(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7185 258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7237">
    <literal><![CDATA[
      (x / T(y,z)) * T(y,u) = (x * K(z,y)) * K(y,u)
    ]]></literal>
    <justification jstring="[para(7185(a,1),6832(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7185 6832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7239">
    <literal><![CDATA[
      K(x,y) * (x / y) = (x / y) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,5530,a,b,7189,a)].">
      <j1 rule="hyper" parents="299 5530 7189"/>
    </justification>
  </clause>

  <clause id="7240">
    <literal><![CDATA[
      (x / y) * K(x,y) = T(x,y) / y
    ]]></literal>
    <justification jstring="[hyper(299,a,4382,a,b,7189,a),flip(a)].">
      <j1 rule="hyper" parents="299 4382 7189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7242">
    <literal><![CDATA[
      (x \ 1) * (x \ K(y,x)) = x \ (1 / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,7189,a(flip),b,1678,a),flip(a)].">
      <j1 rule="hyper" parents="119 7189 1678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7243">
    <literal><![CDATA[
      K(x \ y,x) * K(z,y / x) = x \ (y / T(y / x,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,7189,a(flip),b,5713,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 7189 5713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7244">
    <literal><![CDATA[
      (x * (y * y)) * K(z,1 / y) = (x * y) / T(1 / y,z)
    ]]></literal>
    <justification jstring="[para(672(a,1),7189(a,1,1))].">
      <j1 rule="para" parents="672 7189"/>
    </justification>
  </clause>

  <clause id="7245">
    <literal><![CDATA[
      (x / ((y \ 1) \ 1)) * K(z,y) = x / T((y \ 1) \ 1,z)
    ]]></literal>
    <justification jstring="[para(4793(a,1),7189(a,1,2))].">
      <j1 rule="para" parents="4793 7189"/>
    </justification>
  </clause>

  <clause id="7246">
    <literal><![CDATA[
      K(x,y) * ((1 / x) \ z) = (1 / T(x,y)) \ z
    ]]></literal>
    <justification jstring="[para(7189(a,1),6083(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7189 6083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7248">
    <literal><![CDATA[
      x \ T(x * y,x) = y * K(x * y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),7193(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 7193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7249">
    <literal><![CDATA[
      (x \ T(y,x)) \ ((x \ y) * (K(y,x) * z)) = L(z,K(y,x),x \ y)
    ]]></literal>
    <justification jstring="[para(7193(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7193 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7251">
    <literal><![CDATA[
      (x * ((y \ z) \ z)) * K(y \ z,y) = x * y
    ]]></literal>
    <justification jstring="[para(108(a,1),7194(a,1,1,2))].">
      <j1 rule="para" parents="108 7194"/>
    </justification>
  </clause>

  <clause id="7253">
    <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(7194(a,1),539(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7194 539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7254">
    <literal><![CDATA[
      (x * K(y,z / y)) / (z / y) = x / (y \ z)
    ]]></literal>
    <justification jstring="[para(109(a,1),7206(a,2,2))].">
      <j1 rule="para" parents="109 7206"/>
    </justification>
  </clause>

  <clause id="7255">
    <literal><![CDATA[
      T((x * K(y,z)) / (x / T(z,y)),x * K(y,z)) = L(z,z \ (x * K(y,z)),z)
    ]]></literal>
    <justification jstring="[para(7206(a,1),4519(a,1,1,2))].">
      <j1 rule="para" parents="7206 4519"/>
    </justification>
  </clause>

  <clause id="7256">
    <literal><![CDATA[
      T(T((x * K(y,z)) / (x / T(z,y)),x * K(y,z)),u) = L(T(z,u),z \ (x * K(y,z)),z)
    ]]></literal>
    <justification jstring="[para(7206(a,1),4520(a,1,1,1,2))].">
      <j1 rule="para" parents="7206 4520"/>
    </justification>
  </clause>

  <clause id="7257">
    <literal><![CDATA[
      K(x,y) * (z / (K(y,x) \ 1)) = T(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(235,a,7221,a(flip),b,5432,a),flip(a)].">
      <j1 rule="hyper" parents="235 7221 5432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7259">
    <literal><![CDATA[
      x * (K(y,x) * K(y * x,y)) = T(y * x,y) / y
    ]]></literal>
    <justification jstring="[hyper(5975,a,7240,a)].">
      <j1 rule="hyper" parents="5975 7240"/>
    </justification>
  </clause>

  <clause id="7260">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      (K(z,y) * x) * K(y,z) = u
    ]]></literal>
    <justification jstring="[para(6255(a,1),7208(a,1))].">
      <j1 rule="para" parents="6255 7208"/>
    </justification>
  </clause>

  <clause id="7262">
    <literal><![CDATA[
      (x \ K(y,x)) \ (x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(3660(a,1),7209(a,1,1))].">
      <j1 rule="para" parents="3660 7209"/>
    </justification>
  </clause>

  <clause id="7263">
    <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(5813(a,1),7209(a,1,1))].">
      <j1 rule="para" parents="5813 7209"/>
    </justification>
  </clause>

  <clause id="7265">
    <literal><![CDATA[
      x * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x / K(z,y) = u
    ]]></literal>
    <justification jstring="[para(12(a,1),7216(a,1,1)),flip(b)].">
      <j1 rule="para" parents="12 7216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7271">
    <literal><![CDATA[
      (x / y) * K(z,y) != u
    ]]></literal>
    <literal><![CDATA[
      x / T(y,z) = u
    ]]></literal>
    <justification jstring="[para(6907(a,1),7216(a,1,1)),flip(b)].">
      <j1 rule="para" parents="6907 7216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7277">
    <literal><![CDATA[
      (x * T(y,L(z,y,x))) \ (x * (y * z)) = T(L(z,y,x),y)
    ]]></literal>
    <justification jstring="[hyper(119,a,94,a(flip),b,7195,a)].">
      <j1 rule="hyper" parents="119 94 7195"/>
    </justification>
  </clause>

  <clause id="7279">
    <literal><![CDATA[
      T(K(x,y) * z,K(x,y)) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6264,a,7199,a)].">
      <j1 rule="hyper" parents="6264 7199"/>
    </justification>
  </clause>

  <clause id="7280">
    <literal><![CDATA[
      T(K(x,y) * z,K(x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      z * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7199(a,1),6258(a,1,1)),flip(b)].">
      <j1 rule="para" parents="7199 6258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7281">
    <literal><![CDATA[
      (K(x,y) \ z) * K(x,y) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(5426(a,2),7203(a,1,1))].">
      <j1 rule="para" parents="5426 7203"/>
    </justification>
  </clause>

  <clause id="7283">
    <literal><![CDATA[
      T((x / y) * z,K(y,y \ x)) = ((y \ x) * z) * K(y,y \ x)
    ]]></literal>
    <justification jstring="[para(5718(a,1),7203(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5718 7203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7284">
    <literal><![CDATA[
      (K(x,y) * z) \ z = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[para(7215(a,1),4415(a,1,1))].">
      <j1 rule="para" parents="7215 4415"/>
    </justification>
  </clause>

  <clause id="7285">
    <literal><![CDATA[
      (K(x,y) * z) * T(K(y,x),z) = z
    ]]></literal>
    <justification jstring="[hyper(144,a,7284,a)].">
      <j1 rule="hyper" parents="144 7284"/>
    </justification>
  </clause>

  <clause id="7287">
    <literal><![CDATA[
      (x * (y * T(y \ (x \ z),u))) \ z = K(u,(x * y) \ z)
    ]]></literal>
    <justification jstring="[para(998(a,1),7228(a,1,1))].">
      <j1 rule="para" parents="998 7228"/>
    </justification>
  </clause>

  <clause id="7288">
    <literal><![CDATA[
      ((x * T(x \ y,z)) * u) \ (y * u) = K(z,(x * u) \ (y * u))
    ]]></literal>
    <justification jstring="[para(1462(a,1),7228(a,1,1))].">
      <j1 rule="para" parents="1462 7228"/>
    </justification>
  </clause>

  <clause id="7289">
    <literal><![CDATA[
      T(x / y,K(y,x)) = x / y
    ]]></literal>
    <justification jstring="[hyper(6265,a,7239,a)].">
      <j1 rule="hyper" parents="6265 7239"/>
    </justification>
  </clause>

  <clause id="7290">
    <literal><![CDATA[
      x * (y * K(x * y,x)) = T(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(144,a,7248,a)].">
      <j1 rule="hyper" parents="144 7248"/>
    </justification>
  </clause>

  <clause id="7291">
    <literal><![CDATA[
      K((x \ 1) \ y,x) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(36,a,6980,a(flip),b,7248,a(flip))].">
      <j1 rule="hyper" parents="36 6980 7248"/>
    </justification>
  </clause>

  <clause id="7292">
    <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(7248(a,2),5186(a,1,1))].">
      <j1 rule="para" parents="7248 5186"/>
    </justification>
  </clause>

  <clause id="7293">
    <literal><![CDATA[
      K((1 / x) \ y,x) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,5607,a,b,7291,a)].">
      <j1 rule="hyper" parents="65 5607 7291"/>
    </justification>
  </clause>

  <clause id="7294">
    <literal><![CDATA[
      K((x \ 1) * y,x \ 1) = K(x \ y,x \ 1)
    ]]></literal>
    <justification jstring="[para(76(a,1),7293(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="76 7293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7295">
    <literal><![CDATA[
      T(x * K(y,z),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(7279(a,1),6258(a,1,1)),flip(b)].">
      <j1 rule="para" parents="7279 6258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7296">
    <literal><![CDATA[
      T(K(x,y) * z,T(x,y)) = T(z * K(x,y),x)
    ]]></literal>
    <justification jstring="[para(7279(a,1),7141(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7279 7141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7297">
    <literal><![CDATA[
      x / T(K(y,z),x) = K(y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(37,a,4381,a,b,7281,a)].">
      <j1 rule="hyper" parents="37 4381 7281"/>
    </justification>
  </clause>

  <clause id="7299">
    <literal><![CDATA[
      x * (y * K(y * x,x)) = T(x * y,x)
    ]]></literal>
    <justification jstring="[para(5980(a,2),7290(a,1,2,2))].">
      <j1 rule="para" parents="5980 7290"/>
    </justification>
  </clause>

  <clause id="7300">
    <literal><![CDATA[
      x * (K(x / y,z) * K(x * K(y \ x,z),x)) = T(x * K(x / y,z),x)
    ]]></literal>
    <justification jstring="[para(6978(a,1),7299(a,1,2,2,1))].">
      <j1 rule="para" parents="6978 7299"/>
    </justification>
  </clause>

  <clause id="7302">
    <literal><![CDATA[
      x * K(y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      (z * x) / T(T(z,x),y) = u
    ]]></literal>
    <justification jstring="[para(185(a,1),7271(a,1,1))].">
      <j1 rule="para" parents="185 7271"/>
    </justification>
  </clause>

  <clause id="7303">
    <literal><![CDATA[
      (x \ y) * K(z,T(x,x \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      y / T(T(x,x \ y),z) = u
    ]]></literal>
    <justification jstring="[para(262(a,1),7271(a,1,1))].">
      <j1 rule="para" parents="262 7271"/>
    </justification>
  </clause>

  <clause id="7304">
    <literal><![CDATA[
      (x / (y / z)) * (z \ y) = x * K(z \ y,z)
    ]]></literal>
    <justification jstring="[hyper(306,a,7202,a),flip(a)].">
      <j1 rule="hyper" parents="306 7202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7307">
    <literal><![CDATA[
      (x / (y \ 1)) * K(y,z) = x / (T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(120,a,12,a(flip),b,7214,a),flip(a)].">
      <j1 rule="hyper" parents="120 12 7214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7308">
    <literal><![CDATA[
      K(x,1 / ((y * (1 / z)) / y)) = K(x,z * K(1 / z,y))
    ]]></literal>
    <justification jstring="[para(5232(a,1),7223(a,1,2,2))].">
      <j1 rule="para" parents="5232 7223"/>
    </justification>
  </clause>

  <clause id="7309">
    <literal><![CDATA[
      K(x,((y / z) \ 1) \ z) = ((y / z) \ T(y,x)) \ z
    ]]></literal>
    <justification jstring="[para(12(a,1),7229(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 7229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7310">
    <literal><![CDATA[
      K(x,y) \ (y * ((y \ 1) \ z)) = (y \ (1 / T(y,x))) \ z
    ]]></literal>
    <justification jstring="[para(7242(a,1),2506(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7242 2506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7311">
    <literal><![CDATA[
      (x \ 1) * (T(x,y) \ 1) = x \ (1 / T(x,y))
    ]]></literal>
    <justification jstring="[para(5039(a,2),7242(a,1,2))].">
      <j1 rule="para" parents="5039 7242"/>
    </justification>
  </clause>

  <clause id="7312">
    <literal><![CDATA[
      (T(x,y) \ y) * ((x \ y) \ y) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(4827,a,7251,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="4827 7251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7314">
    <literal><![CDATA[
      ((1 / (1 / x)) \ y) / (1 / x) = (x \ y) / (x \ 1)
    ]]></literal>
    <justification jstring="[para(6283(a,1),7254(a,1,1))].">
      <j1 rule="para" parents="6283 7254"/>
    </justification>
  </clause>

  <clause id="7315">
    <literal><![CDATA[
      (1 / K(x,y)) * (z / (K(x,y) \ 1)) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(5209(a,2),7257(a,1,1))].">
      <j1 rule="para" parents="5209 7257"/>
    </justification>
  </clause>

  <clause id="7316">
    <literal><![CDATA[
      K(x * (y \ 1),y \ 1) = K(y \ x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,5980,a,b,7294,a)].">
      <j1 rule="hyper" parents="65 5980 7294"/>
    </justification>
  </clause>

  <clause id="7317">
    <literal><![CDATA[
      (x / (x / y)) / (y \ x) = y / (x / y)
    ]]></literal>
    <justification jstring="[hyper(120,a,5002,a,b,7304,a)].">
      <j1 rule="hyper" parents="120 5002 7304"/>
    </justification>
  </clause>

  <clause id="7318">
    <literal><![CDATA[
      x / (T(y,x) \ 1) = y * ((x / (y \ 1)) / y)
    ]]></literal>
    <justification jstring="[hyper(65,a,6176,a(flip),b,7307,a),flip(a)].">
      <j1 rule="hyper" parents="65 6176 7307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7319">
    <literal><![CDATA[
      (T(x,y) \ 1) * T(x \ 1,T(x,y) \ 1) = x \ (1 / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(277,a,7311,a)].">
      <j1 rule="hyper" parents="277 7311"/>
    </justification>
  </clause>

  <clause id="7320">
    <literal><![CDATA[
      T(K(x \ y,x \ 1) / x,y) = R(1 / x,y,x \ 1)
    ]]></literal>
    <justification jstring="[para(7316(a,1),6404(a,1,1,1))].">
      <j1 rule="para" parents="7316 6404"/>
    </justification>
  </clause>

  <clause id="7325">
    <literal><![CDATA[
      T(x * T(y,z),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * (x * y) = u
    ]]></literal>
    <justification jstring="[para(6832(a,1),7295(a,1,1))].">
      <j1 rule="para" parents="6832 7295"/>
    </justification>
  </clause>

  <clause id="7326">
    <literal><![CDATA[
      R(x,y,K(z,y \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(544,a,6960,a)].">
      <j1 rule="hyper" parents="544 6960"/>
    </justification>
  </clause>

  <clause id="7327">
    <literal><![CDATA[
      R(x,y \ 1,K(z,y)) = x
    ]]></literal>
    <justification jstring="[para(3449(a,1),7326(a,1,3))].">
      <j1 rule="para" parents="3449 7326"/>
    </justification>
  </clause>

  <clause id="7328">
    <literal><![CDATA[
      R(x,y \ z,K(u,z \ y)) = x
    ]]></literal>
    <justification jstring="[para(6814(a,1),7326(a,1,3))].">
      <j1 rule="para" parents="6814 7326"/>
    </justification>
  </clause>

  <clause id="7329">
    <literal><![CDATA[
      T(x,y) / ((y \ 1) * K(x,y)) = x / (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,5157,a(flip),b,7327,a)].">
      <j1 rule="hyper" parents="65 5157 7327"/>
    </justification>
  </clause>

  <clause id="7330">
    <literal><![CDATA[
      x \ (y * K(z,y \ x)) = (x \ y) * K(z,y \ x)
    ]]></literal>
    <justification jstring="[para(7328(a,1),580(a,1,1))].">
      <j1 rule="para" parents="7328 580"/>
    </justification>
  </clause>

  <clause id="7331">
    <literal><![CDATA[
      T(x,y) / (T(y,x) \ 1) = x / (y \ 1)
    ]]></literal>
    <justification jstring="[para(5052(a,1),7329(a,1,2))].">
      <j1 rule="para" parents="5052 7329"/>
    </justification>
  </clause>

  <clause id="7333">
    <literal><![CDATA[
      (x / (y \ 1)) \ T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      T(y,x) \ 1 = z
    ]]></literal>
    <justification jstring="[para(7331(a,1),317(a,1,1))].">
      <j1 rule="para" parents="7331 317"/>
    </justification>
  </clause>

  <clause id="7334">
    <literal><![CDATA[
      R(x,y,K(y \ 1,z)) = x
    ]]></literal>
    <justification jstring="[hyper(544,a,6961,a)].">
      <j1 rule="hyper" parents="544 6961"/>
    </justification>
  </clause>

  <clause id="7335">
    <literal><![CDATA[
      (x \ T(y,z)) * K(z,(x \ 1) \ (x \ y)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(7207,a,6981,a)].">
      <j1 rule="hyper" parents="7207 6981"/>
    </justification>
  </clause>

  <clause id="7336">
    <literal><![CDATA[
      L(K((x \ 1) \ (x \ y),z),x \ y,T(x,x \ y)) = (x * (y / x)) \ (T(x,x \ y) * (x \ T(y,z)))
    ]]></literal>
    <justification jstring="[para(6981(a,1),4319(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6981 4319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7337">
    <literal><![CDATA[
      x \ (y \ ((z \ (y * x)) * z)) = K((z / y) \ x,z)
    ]]></literal>
    <justification jstring="[para(3939(a,1),6983(a,1,2))].">
      <j1 rule="para" parents="3939 6983"/>
    </justification>
  </clause>

  <clause id="7338">
    <literal><![CDATA[
      x * (K(y \ x,x) * (y \ 1)) = T(x * (y \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(5489,a,6993,a)].">
      <j1 rule="hyper" parents="5489 6993"/>
    </justification>
  </clause>

  <clause id="7339">
    <literal><![CDATA[
      K((x / (y \ 1)) \ z,x) = K((x * y) \ z,x)
    ]]></literal>
    <justification jstring="[hyper(7172,a,7003,a),flip(a)].">
      <j1 rule="hyper" parents="7172 7003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7340">
    <literal><![CDATA[
      K(T(x,y) \ T(z,y),z) = K(x \ z,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(7172,a,7007,a)].">
      <j1 rule="hyper" parents="7172 7007"/>
    </justification>
  </clause>

  <clause id="7341">
    <literal><![CDATA[
      K(x,T(y,z) \ T(x,z)) = 1 / K(y \ x,T(x,z))
    ]]></literal>
    <justification jstring="[para(7340(a,1),5209(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7340 5209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7342">
    <literal><![CDATA[
      x / K(y \ x,T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z) \ T(x,z)) = u
    ]]></literal>
    <justification jstring="[para(7340(a,1),5046(a,1,2))].">
      <j1 rule="para" parents="7340 5046"/>
    </justification>
  </clause>

  <clause id="7344">
    <literal><![CDATA[
      K((x * y) \ z,y) = K((y * x) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,7018,a,b,7021,a),flip(a)].">
      <j1 rule="hyper" parents="36 7018 7021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7345">
    <literal><![CDATA[
      (x * ((y \ (x \ z)) * y)) \ z = K(y,(x * y) \ z)
    ]]></literal>
    <justification jstring="[para(7021(a,1),7200(a,1,1))].">
      <j1 rule="para" parents="7021 7200"/>
    </justification>
  </clause>

  <clause id="7346">
    <literal><![CDATA[
      1 / K((x * y) \ z,x) = K(x,(y * x) \ z)
    ]]></literal>
    <justification jstring="[para(7344(a,1),5209(a,1,2))].">
      <j1 rule="para" parents="7344 5209"/>
    </justification>
  </clause>

  <clause id="7347">
    <literal><![CDATA[
      K(x,(y * x) \ z) = K(x,(x * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(5211,a,7346,a),flip(a)].">
      <j1 rule="hyper" parents="5211 7346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7349">
    <literal><![CDATA[
      T(L(x \ 1,x,y) \ 1,z) = ((y * x) \ y) \ K(x,z)
    ]]></literal>
    <justification jstring="[para(214(a,2),7025(a,1,1,1))].">
      <j1 rule="para" parents="214 7025"/>
    </justification>
  </clause>

  <clause id="7353">
    <literal><![CDATA[
      K(K(x,y),y * z) = K(z * y,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(6286,a,7032,a),flip(a)].">
      <j1 rule="hyper" parents="6286 7032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7354">
    <literal><![CDATA[
      K(x * y,K(y,z)) = K(y * x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(6285,a,7353,a),flip(a)].">
      <j1 rule="hyper" parents="6285 7353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7355">
    <literal><![CDATA[
      T(x,(y \ 1) \ (y / z)) = T(x,(y * y) / z)
    ]]></literal>
    <justification jstring="[hyper(65,a,4641,a(flip),b,7047,a),flip(a)].">
      <j1 rule="hyper" parents="65 4641 7047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7356">
    <literal><![CDATA[
      (x * y) * K(x \ 1,z) = x * (y * K(x \ 1,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),7073(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 7073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7357">
    <literal><![CDATA[
      L(K(x,y),z,T(x,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2841,a,7080,a)].">
      <j1 rule="hyper" parents="2841 7080"/>
    </justification>
  </clause>

  <clause id="7358">
    <literal><![CDATA[
      (T(x,y) * z) * K(x,u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * (z * K(x,u)) = w
    ]]></literal>
    <justification jstring="[para(7357(a,1),279(a,1,2))].">
      <j1 rule="para" parents="7357 279"/>
    </justification>
  </clause>

  <clause id="7359">
    <literal><![CDATA[
      T(x,y) / ((1 / z) \ x) = (1 / z) * K((((1 / z) \ x) \ 1) \ (z \ 1),y)
    ]]></literal>
    <justification jstring="[para(5617(a,1),7128(a,2,2))].">
      <j1 rule="para" parents="5617 7128"/>
    </justification>
  </clause>

  <clause id="7360">
    <literal><![CDATA[
      (((L(x,y,z) \ 1) * x) \ x) \ x = (L(x,y,z) \ 1) * x
    ]]></literal>
    <justification jstring="[para(6373(a,1),7159(a,2,1,1))].">
      <j1 rule="para" parents="6373 7159"/>
    </justification>
  </clause>

  <clause id="7361">
    <literal><![CDATA[
      (x * y) / T(y * x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * K(z,y * x) = u
    ]]></literal>
    <justification jstring="[para(7191(a,1),310(a,1,2)),flip(b)].">
      <j1 rule="para" parents="7191 310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7362">
    <literal><![CDATA[
      K(x,1 / x) * (y * L(x,z,u)) = y * L((x \ 1) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(7204(a,1),6282(a,2,2))].">
      <j1 rule="para" parents="7204 6282"/>
    </justification>
  </clause>

  <clause id="7363">
    <literal><![CDATA[
      x * (y \ R(y,x,y)) = T(y * x,y) / y
    ]]></literal>
    <justification jstring="[para(5587(a,1),7259(a,1,2))].">
      <j1 rule="para" parents="5587 7259"/>
    </justification>
  </clause>

  <clause id="7364">
    <literal><![CDATA[
      R(x,x \ 1,y \ R(y,x \ 1,y)) = (y \ R(y,x \ 1,y)) / (T(y * (x \ 1),y) / y)
    ]]></literal>
    <justification jstring="[para(7363(a,1),212(a,2,2))].">
      <j1 rule="para" parents="7363 212"/>
    </justification>
  </clause>

  <clause id="7365">
    <literal><![CDATA[
      T(x / (1 / (1 / y)),1 / (1 / y)) / (1 / y) = (y \ x) / (y \ 1)
    ]]></literal>
    <justification jstring="[para(109(a,2),7314(a,1,1))].">
      <j1 rule="para" parents="109 7314"/>
    </justification>
  </clause>

  <clause id="7366">
    <literal><![CDATA[
      T(x \ y,z) * ((y \ x) * K(z,x \ y)) = T((x \ y) * (y \ x),z)
    ]]></literal>
    <justification jstring="[para(7330(a,1),6626(a,1,2))].">
      <j1 rule="para" parents="7330 6626"/>
    </justification>
  </clause>

  <clause id="7367">
    <literal><![CDATA[
      K(x,((T(y,x) / z) \ 1) \ ((T(y,x) / z) \ y)) = z \ ((T(y,x) / z) \ y)
    ]]></literal>
    <justification jstring="[hyper(334,a,7335,a),flip(a)].">
      <j1 rule="hyper" parents="334 7335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7368">
    <literal><![CDATA[
      (x \ y) * K((x \ 1) \ (x \ y),z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ T(y,z) = u
    ]]></literal>
    <justification jstring="[para(7335(a,1),7216(a,1,1)),flip(b)].">
      <j1 rule="para" parents="7335 7216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7369">
    <literal><![CDATA[
      K((x / y) \ z,x) = K((y \ x) \ z,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,6984,a(flip),b,7337,a),flip(a)].">
      <j1 rule="hyper" parents="65 6984 7337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7370">
    <literal><![CDATA[
      (T(x * (y \ 1),x) / x) / (y \ 1) = y * (T(x * (y \ 1),x) / x)
    ]]></literal>
    <justification jstring="[para(7338(a,1),6322(a,1,1,1))].">
      <j1 rule="para" parents="7338 6322"/>
    </justification>
  </clause>

  <clause id="7371">
    <literal><![CDATA[
      K(x,T(y,z) \ T(x,z)) = K(T(x,z),y \ x)
    ]]></literal>
    <justification jstring="[hyper(299,a,5209,a(flip),b,7341,a),flip(a)].">
      <j1 rule="hyper" parents="299 5209 7341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7372">
    <literal><![CDATA[
      K(L(x,y,x) \ 1,z) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(6405,a,7356,a)].">
      <j1 rule="hyper" parents="6405 7356"/>
    </justification>
  </clause>

  <clause id="7373">
    <literal><![CDATA[
      R(x,y,K(x \ 1,z)) = x
    ]]></literal>
    <justification jstring="[hyper(3985,a,7356,a)].">
      <j1 rule="hyper" parents="3985 7356"/>
    </justification>
  </clause>

  <clause id="7374">
    <literal><![CDATA[
      R(T(x,y),z,K(x \ 1,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(7373(a,1),27(a,2,1))].">
      <j1 rule="para" parents="7373 27"/>
    </justification>
  </clause>

  <clause id="7376">
    <literal><![CDATA[
      K(R(x,y,x) \ 1,z) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(4760(a,1),7372(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4760 7372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7377">
    <literal><![CDATA[
      T(x,y * K(x \ 1,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,6156,a(flip),b,7374,a),flip(a)].">
      <j1 rule="hyper" parents="65 6156 7374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7379">
    <literal><![CDATA[
      K(x,y * K(x \ 1,z)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,7377,a(flip),b,5083,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 7377 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7381">
    <literal><![CDATA[
      R(K(x,y),z,x \ 1) = K((x \ 1) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,6011,a(flip),b,7376,a)].">
      <j1 rule="hyper" parents="65 6011 7376"/>
    </justification>
  </clause>

  <clause id="7382">
    <literal><![CDATA[
      K(x,y * K(x \ 1,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,5036,a,b,7379,a),flip(a)].">
      <j1 rule="hyper" parents="299 5036 7379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7384">
    <literal><![CDATA[
      K(x \ y,T(z,y \ x)) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(7013(a,1),7382(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7013 7382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7385">
    <literal><![CDATA[
      K(x,y * K(z,x \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7184(a,1),7382(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7184 7382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7386">
    <literal><![CDATA[
      K(x \ y,z * K(u,y \ x)) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(6814(a,1),7385(a,1,2,2))].">
      <j1 rule="para" parents="6814 7385"/>
    </justification>
  </clause>

  <clause id="7387">
    <literal><![CDATA[
      R(K(x,y),z,x \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,3567,a(flip),b,7381,a),flip(a)].">
      <j1 rule="hyper" parents="299 3567 7381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7388">
    <literal><![CDATA[
      K(x,R(y,z,x \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,6437,a(flip),b,7387,a)].">
      <j1 rule="hyper" parents="65 6437 7387"/>
    </justification>
  </clause>

  <clause id="7389">
    <literal><![CDATA[
      (K(x,y) * z) * (x \ 1) = K(x,y) * (z * (x \ 1))
    ]]></literal>
    <justification jstring="[para(7387(a,1),103(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7387 103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7391">
    <literal><![CDATA[
      R(x * K(y,x),z,y \ 1) = R(x,z,y \ 1) * K(y,x)
    ]]></literal>
    <justification jstring="[para(7388(a,1),5813(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7388 5813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7392">
    <literal><![CDATA[
      K(x \ y,z * (x / y)) = K(x \ y,z * (y \ x))
    ]]></literal>
    <justification jstring="[para(6970(a,1),7386(a,1,2))].">
      <j1 rule="para" parents="6970 7386"/>
    </justification>
  </clause>

  <clause id="7393">
    <literal><![CDATA[
      L(x \ 1,y,K(x,z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(2841,a,7389,a)].">
      <j1 rule="hyper" parents="2841 7389"/>
    </justification>
  </clause>

  <clause id="7394">
    <literal><![CDATA[
      T(K(x,y) * z,x \ 1) = K(x,y) * T(z,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(235,a,7389,a,b,6462,a)].">
      <j1 rule="hyper" parents="235 7389 6462"/>
    </justification>
  </clause>

  <clause id="7395">
    <literal><![CDATA[
      (K(x,y) * (z * x)) \ (K(x,y) * z) = L(x \ 1,x,z)
    ]]></literal>
    <justification jstring="[para(7393(a,1),992(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7393 992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7396">
    <literal><![CDATA[
      T(x * K(y,z),z \ 1) = T(x,z \ 1) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(6535,a,7394,a),flip(a)].">
      <j1 rule="hyper" parents="6535 7394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7397">
    <literal><![CDATA[
      T(x * K(y,x),x \ 1) = (x * (K(y,x) / x)) * x
    ]]></literal>
    <justification jstring="[hyper(299,a,7122,a(flip),b,7396,a),flip(a)].">
      <j1 rule="hyper" parents="299 7122 7396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7398">
    <literal><![CDATA[
      (x * (K(y,x) / x)) * x = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(2407,a,7397,a),flip(a)].">
      <j1 rule="hyper" parents="2407 7397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7399">
    <literal><![CDATA[
      (x * (1 / T(x,y))) * x = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[para(5038(a,1),7398(a,1,1,2))].">
      <j1 rule="para" parents="5038 7398"/>
    </justification>
  </clause>

  <clause id="7400">
    <literal><![CDATA[
      T(x * y,K(y,z)) = y * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(6872,a,5413,a)].">
      <j1 rule="hyper" parents="6872 5413"/>
    </justification>
  </clause>

  <clause id="7401">
    <literal><![CDATA[
      T(x * y,K(y,z)) = T(x,K(y,z)) * y
    ]]></literal>
    <justification jstring="[hyper(299,a,7142,a,b,7400,a),flip(a)].">
      <j1 rule="hyper" parents="299 7142 7400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7402">
    <literal><![CDATA[
      K(x,L(L(y \ 1,y,z),z * y,u)) = K(x,1 / L(y,z,u))
    ]]></literal>
    <justification jstring="[para(405(a,2),6886(a,1,2))].">
      <j1 rule="para" parents="405 6886"/>
    </justification>
  </clause>

  <clause id="7404">
    <literal><![CDATA[
      K(K(x \ 1,x) * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(4793(a,1),6964(a,1))].">
      <j1 rule="para" parents="4793 6964"/>
    </justification>
  </clause>

  <clause id="7405">
    <literal><![CDATA[
      K((1 / x) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K((x \ 1) \ y,z) = u
    ]]></literal>
    <justification jstring="[para(2655(a,1),7404(a,1,1))].">
      <j1 rule="para" parents="2655 7404"/>
    </justification>
  </clause>

  <clause id="7406">
    <literal><![CDATA[
      K(((x \ 1) \ 1) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(2680(a,1),7404(a,1,1))].">
      <j1 rule="para" parents="2680 7404"/>
    </justification>
  </clause>

  <clause id="7407">
    <literal><![CDATA[
      K((x * ((y \ 1) \ 1)) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K((x * y) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(2784(a,1),7404(a,1,1))].">
      <j1 rule="para" parents="2784 7404"/>
    </justification>
  </clause>

  <clause id="7408">
    <literal><![CDATA[
      K(x * (1 / (1 / y)),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(3237(a,1),7404(a,1,1))].">
      <j1 rule="para" parents="3237 7404"/>
    </justification>
  </clause>

  <clause id="7409">
    <literal><![CDATA[
      K(x * (y \ 1),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * (1 / y),z) = u
    ]]></literal>
    <justification jstring="[para(3239(a,1),7404(a,1,1))].">
      <j1 rule="para" parents="3239 7404"/>
    </justification>
  </clause>

  <clause id="7410">
    <literal><![CDATA[
      K(x \ (y \ 1),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ (1 / y),z) = u
    ]]></literal>
    <justification jstring="[para(3370(a,1),7404(a,1,1))].">
      <j1 rule="para" parents="3370 7404"/>
    </justification>
  </clause>

  <clause id="7411">
    <literal><![CDATA[
      K(((1 / x) * y) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(((x \ 1) * y) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(3265(a,1),7404(a,1,1))].">
      <j1 rule="para" parents="3265 7404"/>
    </justification>
  </clause>

  <clause id="7415">
    <literal><![CDATA[
      K(x * (y \ 1),x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,x) = z
    ]]></literal>
    <justification jstring="[para(5741(a,1),7406(a,1))].">
      <j1 rule="para" parents="5741 7406"/>
    </justification>
  </clause>

  <clause id="7416">
    <literal><![CDATA[
      K(x * (1 / y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * (y \ 1),z) = u
    ]]></literal>
    <justification jstring="[para(76(a,1),7408(a,1,1,2,2))].">
      <j1 rule="para" parents="76 7408"/>
    </justification>
  </clause>

  <clause id="7417">
    <literal><![CDATA[
      K(x * L(1 / y,z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x * L(y \ 1,z,u),w) = v5
    ]]></literal>
    <justification jstring="[para(4141(a,1),7408(a,1,1,2))].">
      <j1 rule="para" parents="4141 7408"/>
    </justification>
  </clause>

  <clause id="7418">
    <literal><![CDATA[
      K(x \ (y \ 1),z * T(u,u \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ (1 / y),z * u) = w
    ]]></literal>
    <justification jstring="[para(5638(a,2),7410(a,1))].">
      <j1 rule="para" parents="5638 7410"/>
    </justification>
  </clause>

  <clause id="7419">
    <literal><![CDATA[
      L(K(x \ y,z),y,u) = K((u * x) \ (u * y),z)
    ]]></literal>
    <justification jstring="[hyper(65,a,7020,a(flip),b,7010,a)].">
      <j1 rule="hyper" parents="65 7020 7010"/>
    </justification>
  </clause>

  <clause id="7420">
    <literal><![CDATA[
      L(K(x \ y,z),y,y \ 1) = K(((y \ 1) * x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,6056,a(flip),b,7419,a),flip(a)].">
      <j1 rule="hyper" parents="299 6056 7419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7421">
    <literal><![CDATA[
      L(K((x \ y) \ z,u),z,x) = K(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[para(10(a,1),7419(a,2,1,1))].">
      <j1 rule="para" parents="10 7419"/>
    </justification>
  </clause>

  <clause id="7422">
    <literal><![CDATA[
      L(K(x \ (y \ z),u),y \ z,y) = K((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),7419(a,2,1,2))].">
      <j1 rule="para" parents="10 7419"/>
    </justification>
  </clause>

  <clause id="7423">
    <literal><![CDATA[
      K((x * (y / z)) \ (x * y),u) = L(K(z,u),y,x)
    ]]></literal>
    <justification jstring="[para(79(a,1),7419(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 7419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7424">
    <literal><![CDATA[
      L(K(x \ y,z),y,u) = K(L(x \ y,x,u),z)
    ]]></literal>
    <justification jstring="[para(96(a,2),7419(a,2,1))].">
      <j1 rule="para" parents="96 7419"/>
    </justification>
  </clause>

  <clause id="7425">
    <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(5432(a,1),7419(a,2,1,1))].">
      <j1 rule="para" parents="5432 7419"/>
    </justification>
  </clause>

  <clause id="7426">
    <literal><![CDATA[
      L(K(x * y,x),y,z) = K((z * (x \ 1)) \ (z * y),x)
    ]]></literal>
    <justification jstring="[para(7291(a,1),7419(a,1,1))].">
      <j1 rule="para" parents="7291 7419"/>
    </justification>
  </clause>

  <clause id="7427">
    <literal><![CDATA[
      L(K(L(x,y,z) \ x,u),x,z * y) = K(a(z,y,x),u)
    ]]></literal>
    <justification jstring="[para(1985(a,2),7424(a,2,1))].">
      <j1 rule="para" parents="1985 7424"/>
    </justification>
  </clause>

  <clause id="7428">
    <literal><![CDATA[
      L(K(x \ y,z),y,x \ 1) = K((1 / x) * y,z)
    ]]></literal>
    <justification jstring="[para(2474(a,1),7424(a,2,1))].">
      <j1 rule="para" parents="2474 7424"/>
    </justification>
  </clause>

  <clause id="7429">
    <literal><![CDATA[
      K((x \ y) \ z,z) = K(y \ (x * z),z)
    ]]></literal>
    <justification jstring="[hyper(6838,a,7421,a)].">
      <j1 rule="hyper" parents="6838 7421"/>
    </justification>
  </clause>

  <clause id="7430">
    <literal><![CDATA[
      K(x \ (y * z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K((y \ x) \ z,z) = u
    ]]></literal>
    <justification jstring="[para(7421(a,1),6838(a,1))].">
      <j1 rule="para" parents="7421 6838"/>
    </justification>
  </clause>

  <clause id="7431">
    <literal><![CDATA[
      K(L(x,y / x,z),u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(98(a,2),7423(a,1,1))].">
      <j1 rule="para" parents="98 7423"/>
    </justification>
  </clause>

  <clause id="7432">
    <literal><![CDATA[
      K(L(x,y / x,z),u) = (z * y) \ (z * (y * K(x,u)))
    ]]></literal>
    <justification jstring="[hyper(299,a,18,a(flip),b,7431,a),flip(a)].">
      <j1 rule="hyper" parents="299 18 7431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7433">
    <literal><![CDATA[
      L(K(x,y),z * x,u) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(11(a,1),7431(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11 7431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7434">
    <literal><![CDATA[
      K(x,L(y,z / y,u)) = L(K(y,x),z,u) \ 1
    ]]></literal>
    <justification jstring="[para(7431(a,1),5197(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7431 5197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7435">
    <literal><![CDATA[
      K(L(x,y,x),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(7087,a,7433,a),flip(a)].">
      <j1 rule="hyper" parents="7087 7433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7436">
    <literal><![CDATA[
      K(L(x,y,z),y * x) = K(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(6838,a,7433,a),flip(a)].">
      <j1 rule="hyper" parents="6838 7433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7438">
    <literal><![CDATA[
      K(L(x,y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(7433(a,1),7087(a,1))].">
      <j1 rule="para" parents="7433 7087"/>
    </justification>
  </clause>

  <clause id="7439">
    <literal><![CDATA[
      K(T(x / (x / y),x),z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(4519(a,2),7435(a,1,1))].">
      <j1 rule="para" parents="4519 7435"/>
    </justification>
  </clause>

  <clause id="7440">
    <literal><![CDATA[
      K(T(x / y,x),z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(4521(a,1),7435(a,1,1))].">
      <j1 rule="para" parents="4521 7435"/>
    </justification>
  </clause>

  <clause id="7441">
    <literal><![CDATA[
      K(R(x,y,x),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(4760(a,1),7435(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4760 7435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7442">
    <literal><![CDATA[
      T(x,L(y,z,y)) = x / K(y,x)
    ]]></literal>
    <justification jstring="[para(7435(a,1),5041(a,2,2))].">
      <j1 rule="para" parents="7435 5041"/>
    </justification>
  </clause>

  <clause id="7443">
    <literal><![CDATA[
      K(x,y) * L(x,z,x) = L(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[para(7435(a,1),5165(a,1,1))].">
      <j1 rule="para" parents="7435 5165"/>
    </justification>
  </clause>

  <clause id="7444">
    <literal><![CDATA[
      K((x \ y) \ T(y,x),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(4343(a,1),7441(a,1,1))].">
      <j1 rule="para" parents="4343 7441"/>
    </justification>
  </clause>

  <clause id="7445">
    <literal><![CDATA[
      x * K(R(x,y,x),z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(7441(a,2),5083(a,2,2)),flip(a)].">
      <j1 rule="para" parents="7441 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7446">
    <literal><![CDATA[
      K(x,R(y,z,y)) = 1 / K(y,x)
    ]]></literal>
    <justification jstring="[para(7441(a,1),5209(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7441 5209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7448">
    <literal><![CDATA[
      K(x,y) * (R(x,z,x) * u) = R(T(x,y),z,x) * u
    ]]></literal>
    <justification jstring="[para(7441(a,1),5414(a,1,1))].">
      <j1 rule="para" parents="7441 5414"/>
    </justification>
  </clause>

  <clause id="7449">
    <literal><![CDATA[
      T(x,L(y,z,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,5041,a,b,7442,a),flip(a)].">
      <j1 rule="hyper" parents="299 5041 7442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7450">
    <literal><![CDATA[
      T(x,L(y,z,y)) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,7196,a(flip),b,7442,a),flip(a)].">
      <j1 rule="hyper" parents="299 7196 7442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7451">
    <literal><![CDATA[
      T(x,L(y,z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(7442(a,2),5046(a,1))].">
      <j1 rule="para" parents="7442 5046"/>
    </justification>
  </clause>

  <clause id="7452">
    <literal><![CDATA[
      T(x / L(y,z,y),y) = L(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(400,a,7449,a),flip(a)].">
      <j1 rule="hyper" parents="400 7449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7454">
    <literal><![CDATA[
      L(x,y,x) * T(z,x) = z * L(x,y,x)
    ]]></literal>
    <justification jstring="[para(7449(a,1),107(a,1,2))].">
      <j1 rule="para" parents="7449 107"/>
    </justification>
  </clause>

  <clause id="7456">
    <literal><![CDATA[
      T(x,T(y / z,y)) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[para(4521(a,1),7449(a,1,2))].">
      <j1 rule="para" parents="4521 7449"/>
    </justification>
  </clause>

  <clause id="7457">
    <literal><![CDATA[
      T(x,R(y,z,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4760(a,1),7449(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4760 7449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7459">
    <literal><![CDATA[
      T(x / R(y,z,y),y) = R(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(400,a,7457,a),flip(a)].">
      <j1 rule="hyper" parents="400 7457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7460">
    <literal><![CDATA[
      T(x / y,R(y,z,y)) = y \ x
    ]]></literal>
    <justification jstring="[hyper(299,a,109,a(flip),b,7457,a),flip(a)].">
      <j1 rule="hyper" parents="299 109 7457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7461">
    <literal><![CDATA[
      R(x,y,x) * T(z,x) = z * R(x,y,x)
    ]]></literal>
    <justification jstring="[para(7457(a,1),107(a,1,2))].">
      <j1 rule="para" parents="7457 107"/>
    </justification>
  </clause>

  <clause id="7462">
    <literal><![CDATA[
      T(x,T(y,y * z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4479(a,1),7457(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4479 7457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7463">
    <literal><![CDATA[
      T(x,T(y,y \ z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4538(a,1),7457(a,1,2))].">
      <j1 rule="para" parents="4538 7457"/>
    </justification>
  </clause>

  <clause id="7464">
    <literal><![CDATA[
      T(x,(y * z) / y) = T(x,y / (y / z))
    ]]></literal>
    <justification jstring="[para(4819(a,1),7457(a,1,2))].">
      <j1 rule="para" parents="4819 7457"/>
    </justification>
  </clause>

  <clause id="7465">
    <literal><![CDATA[
      R((x * y) / x,z,y) \ y = R(y,z,y) \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,7445,a(flip),b,6678,a),flip(a)].">
      <j1 rule="hyper" parents="119 7445 6678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7466">
    <literal><![CDATA[
      K(x,R(y,z,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,5209,a(flip),b,7446,a),flip(a)].">
      <j1 rule="hyper" parents="299 5209 7446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7467">
    <literal><![CDATA[
      K(x,R(y,z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7446(a,2),5211(a,1))].">
      <j1 rule="para" parents="7446 5211"/>
    </justification>
  </clause>

  <clause id="7468">
    <literal><![CDATA[
      R(K(x,y),z,y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,6448,a(flip),b,7466,a)].">
      <j1 rule="hyper" parents="65 6448 7466"/>
    </justification>
  </clause>

  <clause id="7469">
    <literal><![CDATA[
      K(x,T(y,y * z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4479(a,1),7466(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4479 7466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7470">
    <literal><![CDATA[
      K(x,T(y,y \ z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4538(a,1),7466(a,1,2))].">
      <j1 rule="para" parents="4538 7466"/>
    </justification>
  </clause>

  <clause id="7471">
    <literal><![CDATA[
      R(x * K(y,x),z,x) = R(x,z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[para(7466(a,1),5813(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7466 5813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7472">
    <literal><![CDATA[
      (K(x,y) * z) * y = K(x,y) * (z * y)
    ]]></literal>
    <justification jstring="[para(7468(a,1),103(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7468 103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7473">
    <literal><![CDATA[
      K(x,L(y,z,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5154,a,7450,a)].">
      <j1 rule="hyper" parents="5154 7450"/>
    </justification>
  </clause>

  <clause id="7474">
    <literal><![CDATA[
      K(x,T(y / z,y)) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(4521(a,1),7473(a,1,2))].">
      <j1 rule="para" parents="4521 7473"/>
    </justification>
  </clause>

  <clause id="7475">
    <literal><![CDATA[
      R(x,y,x) * (x \ z) = (z / x) * R(x,y,x)
    ]]></literal>
    <justification jstring="[para(7460(a,1),107(a,1,2))].">
      <j1 rule="para" parents="7460 107"/>
    </justification>
  </clause>

  <clause id="7476">
    <literal><![CDATA[
      K(x \ (x * y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(499(a,1),7438(a,1,1))].">
      <j1 rule="para" parents="499 7438"/>
    </justification>
  </clause>

  <clause id="7477">
    <literal><![CDATA[
      K(T(x / (x / y),x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(4519(a,2),7438(a,1,1))].">
      <j1 rule="para" parents="4519 7438"/>
    </justification>
  </clause>

  <clause id="7478">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(R(x,u,x),y) = z
    ]]></literal>
    <justification jstring="[para(4760(a,1),7438(a,1,1))].">
      <j1 rule="para" parents="4760 7438"/>
    </justification>
  </clause>

  <clause id="7479">
    <literal><![CDATA[
      K((x \ y) \ y,z) = K(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(187(a,1),7439(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="187 7439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7481">
    <literal><![CDATA[
      T(x,T(y / z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(4521(a,1),7451(a,1,2))].">
      <j1 rule="para" parents="4521 7451"/>
    </justification>
  </clause>

  <clause id="7482">
    <literal><![CDATA[
      T(x,(y \ z) \ z) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(76(a,1),7456(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="76 7456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7483">
    <literal><![CDATA[
      T(x,y \ T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(x,z) / y) = u
    ]]></literal>
    <justification jstring="[para(7456(a,1),5476(a,1))].">
      <j1 rule="para" parents="7456 5476"/>
    </justification>
  </clause>

  <clause id="7485">
    <literal><![CDATA[
      K(x,T(y,y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(4538(a,1),7467(a,1,2))].">
      <j1 rule="para" parents="4538 7467"/>
    </justification>
  </clause>

  <clause id="7486">
    <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(1350(a,1),7469(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1350 7469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7487">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) = K(x,T(y,z \ y))
    ]]></literal>
    <justification jstring="[para(2009(a,1),7469(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2009 7469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7488">
    <literal><![CDATA[
      K(x,T(y,z * y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4366(a,2),7469(a,1,2))].">
      <j1 rule="para" parents="4366 7469"/>
    </justification>
  </clause>

  <clause id="7489">
    <literal><![CDATA[
      K(x,T(y,z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(65,a,6915,a(flip),b,7470,a),flip(a)].">
      <j1 rule="hyper" parents="65 6915 7470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7490">
    <literal><![CDATA[
      K(x,(y \ z) \ z) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(108(a,1),7470(a,1,2))].">
      <j1 rule="para" parents="108 7470"/>
    </justification>
  </clause>

  <clause id="7491">
    <literal><![CDATA[
      T(K(x * y,x),y) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(6957,a,7489,a),flip(a)].">
      <j1 rule="hyper" parents="6957 7489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7492">
    <literal><![CDATA[
      (K(x,y) * z) \ z = K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,7284,a,b,7489,a)].">
      <j1 rule="hyper" parents="299 7284 7489"/>
    </justification>
  </clause>

  <clause id="7493">
    <literal><![CDATA[
      K((x \ y) \ y,z) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,6976,a,b,7489,a)].">
      <j1 rule="hyper" parents="299 6976 7489"/>
    </justification>
  </clause>

  <clause id="7494">
    <literal><![CDATA[
      R(T(K(x,y),z),y * u,w) = K(x,T(R(y,u,w),z))
    ]]></literal>
    <justification jstring="[hyper(299,a,6445,a,b,7489,a)].">
      <j1 rule="hyper" parents="299 6445 7489"/>
    </justification>
  </clause>

  <clause id="7495">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z,y) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(299,a,6251,a,b,7489,a)].">
      <j1 rule="hyper" parents="299 6251 7489"/>
    </justification>
  </clause>

  <clause id="7496">
    <literal><![CDATA[
      K(x,y) * K(z,K(y,x)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,6246,a,b,7489,a)].">
      <j1 rule="hyper" parents="299 6246 7489"/>
    </justification>
  </clause>

  <clause id="7497">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) = K(x \ 1,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,6234,a,b,7489,a)].">
      <j1 rule="hyper" parents="299 6234 7489"/>
    </justification>
  </clause>

  <clause id="7498">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) = K(x,T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,5798,a,b,7489,a),flip(a)].">
      <j1 rule="hyper" parents="299 5798 7489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7499">
    <literal><![CDATA[
      K(x / y,T(z,x)) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,6979,a(flip),b,7489,a),flip(a)].">
      <j1 rule="hyper" parents="299 6979 7489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7500">
    <literal><![CDATA[
      K(x,T(y,K(x,z))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,6261,a(flip),b,7489,a),flip(a)].">
      <j1 rule="hyper" parents="299 6261 7489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7501">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,3597,a(flip),b,7489,a),flip(a)].">
      <j1 rule="hyper" parents="299 3597 7489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7502">
    <literal><![CDATA[
      K(x,T(y,K(z,x))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,2276,a(flip),b,7489,a),flip(a)].">
      <j1 rule="hyper" parents="299 2276 7489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7503">
    <literal><![CDATA[
      x * K(y,T(z,u)) = x * T(K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,7489,a)].">
      <j1 rule="hyper" parents="60 7489"/>
    </justification>
  </clause>

  <clause id="7504">
    <literal><![CDATA[
      K(x,T(T(y,z),u)) = T(K(x,T(y,u)),z)
    ]]></literal>
    <justification jstring="[para(23(a,1),7489(a,1,2))].">
      <j1 rule="para" parents="23 7489"/>
    </justification>
  </clause>

  <clause id="7505">
    <literal><![CDATA[
      L(K(x,T(y,z)),u,w) = T(L(K(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[para(7489(a,2),25(a,1,1))].">
      <j1 rule="para" parents="7489 25"/>
    </justification>
  </clause>

  <clause id="7506">
    <literal><![CDATA[
      K(x,L(T(y,z),u,w)) = T(K(x,L(y,u,w)),z)
    ]]></literal>
    <justification jstring="[para(25(a,2),7489(a,1,2))].">
      <j1 rule="para" parents="25 7489"/>
    </justification>
  </clause>

  <clause id="7507">
    <literal><![CDATA[
      x * K(y,T(z,x)) = K(y,z) * x
    ]]></literal>
    <justification jstring="[para(7489(a,2),107(a,1,2))].">
      <j1 rule="para" parents="7489 107"/>
    </justification>
  </clause>

  <clause id="7509">
    <literal><![CDATA[
      x * K(y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(7489(a,2),276(a,1,2))].">
      <j1 rule="para" parents="7489 276"/>
    </justification>
  </clause>

  <clause id="7510">
    <literal><![CDATA[
      x * L(K(y,T(z,x)),u,w) = L(K(y,z),u,w) * x
    ]]></literal>
    <justification jstring="[para(7489(a,2),233(a,1,2,1))].">
      <j1 rule="para" parents="7489 233"/>
    </justification>
  </clause>

  <clause id="7512">
    <literal><![CDATA[
      x * (y * K(z,T(u,x * y))) = L(K(z,u),y,x) * (x * y)
    ]]></literal>
    <justification jstring="[para(7489(a,2),681(a,1,2,2))].">
      <j1 rule="para" parents="7489 681"/>
    </justification>
  </clause>

  <clause id="7513">
    <literal><![CDATA[
      L(K(x,T(y,z \ u)),z \ u,z) = u \ (z * (K(x,y) * (z \ u)))
    ]]></literal>
    <justification jstring="[para(7489(a,2),777(a,1,1))].">
      <j1 rule="para" parents="7489 777"/>
    </justification>
  </clause>

  <clause id="7514">
    <literal><![CDATA[
      T(x,K(y,T(z,x))) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7489(a,2),4462(a,1,2))].">
      <j1 rule="para" parents="7489 4462"/>
    </justification>
  </clause>

  <clause id="7515">
    <literal><![CDATA[
      T(x,K(y,z)) * (K(y,T(z,x)) * u) = x * (K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(7489(a,2),4961(a,1,2,1))].">
      <j1 rule="para" parents="7489 4961"/>
    </justification>
  </clause>

  <clause id="7516">
    <literal><![CDATA[
      x * T(K(x,y),z) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7489(a,1),5083(a,2,2)),flip(a)].">
      <j1 rule="para" parents="7489 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7517">
    <literal><![CDATA[
      K(x,y) * (K(z,u) * x) = T(x,y) * K(z,T(u,x))
    ]]></literal>
    <justification jstring="[para(7489(a,2),5353(a,2,2))].">
      <j1 rule="para" parents="7489 5353"/>
    </justification>
  </clause>

  <clause id="7518">
    <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(7489(a,2),5917(a,1,1))].">
      <j1 rule="para" parents="7489 5917"/>
    </justification>
  </clause>

  <clause id="7519">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(7489(a,2),6244(a,1,2))].">
      <j1 rule="para" parents="7489 6244"/>
    </justification>
  </clause>

  <clause id="7520">
    <literal><![CDATA[
      K(x,T(y,K(z,u))) * K(u,z) = K(u,z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(7489(a,2),6257(a,1,1))].">
      <j1 rule="para" parents="7489 6257"/>
    </justification>
  </clause>

  <clause id="7521">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,y) * u) = K(z,T(y,x)) * u
    ]]></literal>
    <justification jstring="[para(7489(a,2),6253(a,2,1))].">
      <j1 rule="para" parents="7489 6253"/>
    </justification>
  </clause>

  <clause id="7522">
    <literal><![CDATA[
      L(K(x,T(y \ z,u)),y \ z,y) = K(x,T(z \ y,u) \ 1)
    ]]></literal>
    <justification jstring="[para(7489(a,2),6401(a,1,1))].">
      <j1 rule="para" parents="7489 6401"/>
    </justification>
  </clause>

  <clause id="7523">
    <literal><![CDATA[
      K(x,T((y \ 1) * ((z \ y) * z),u)) = K(x,K(z \ y,T(z,u)))
    ]]></literal>
    <justification jstring="[para(7489(a,2),6060(a,2,2))].">
      <j1 rule="para" parents="7489 6060"/>
    </justification>
  </clause>

  <clause id="7524">
    <literal><![CDATA[
      K(x,T(y,z)) * R(T(K(y,x),z),u,w) = T(K(x,y) * R(K(y,x),u,w),z)
    ]]></literal>
    <justification jstring="[para(7489(a,2),6762(a,1,1))].">
      <j1 rule="para" parents="7489 6762"/>
    </justification>
  </clause>

  <clause id="7525">
    <literal><![CDATA[
      K(x,T(y / z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(7489(a,2),7098(a,1))].">
      <j1 rule="para" parents="7489 7098"/>
    </justification>
  </clause>

  <clause id="7526">
    <literal><![CDATA[
      K(x / y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(7489(a,2),7174(a,1))].">
      <j1 rule="para" parents="7489 7174"/>
    </justification>
  </clause>

  <clause id="7527">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,T(x,z)) = z
    ]]></literal>
    <justification jstring="[para(7489(a,2),7285(a,1,2))].">
      <j1 rule="para" parents="7489 7285"/>
    </justification>
  </clause>

  <clause id="7528">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = T(K(x,K(y,z)),u)
    ]]></literal>
    <justification jstring="[para(7489(a,2),7489(a,1,2))].">
      <j1 rule="para" parents="7489 7489"/>
    </justification>
  </clause>

  <clause id="7529">
    <literal><![CDATA[
      K(x,R(T(y,K(x,z)),u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(27(a,2),7500(a,1,2))].">
      <j1 rule="para" parents="27 7500"/>
    </justification>
  </clause>

  <clause id="7530">
    <literal><![CDATA[
      K(x,T(y,T(z,x))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7140(a,1),7502(a,1,2))].">
      <j1 rule="para" parents="7140 7502"/>
    </justification>
  </clause>

  <clause id="7531">
    <literal><![CDATA[
      K(x,y / R(x,z,u)) = K(x,R(x,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(109(a,1),7501(a,1,2)),flip(a)].">
      <j1 rule="para" parents="109 7501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7532">
    <literal><![CDATA[
      K(x,R(T(y / z,y * u),z,u)) = K(x,(z * u) \ (y * u))
    ]]></literal>
    <justification jstring="[para(568(a,1),7474(a,1,2))].">
      <j1 rule="para" parents="568 7474"/>
    </justification>
  </clause>

  <clause id="7533">
    <literal><![CDATA[
      K(T(x,y),z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(65,a,6976,a(flip),b,7479,a),flip(a)].">
      <j1 rule="hyper" parents="65 6976 7479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7534">
    <literal><![CDATA[
      K(T(R(x,x \ y,y \ z),z),u) = K(((x \ y) * (y \ z)) \ z,u)
    ]]></literal>
    <justification jstring="[para(837(a,1),7479(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="837 7479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7535">
    <literal><![CDATA[
      K(T(x * K(y,z),x),u) = K(K(y,z) * x,u)
    ]]></literal>
    <justification jstring="[para(7225(a,1),7479(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7225 7479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7536">
    <literal><![CDATA[
      K((x * (y \ z)) \ (x * z),u) = L(K(T(y,z),u),z,x)
    ]]></literal>
    <justification jstring="[para(7479(a,1),7419(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7479 7419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7537">
    <literal><![CDATA[
      K(T(x,y),z) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,7489,a,b,7533,a),flip(a)].">
      <j1 rule="hyper" parents="299 7489 7533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7538">
    <literal><![CDATA[
      K(T(x,y),y / z) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(299,a,6841,a(flip),b,7533,a),flip(a)].">
      <j1 rule="hyper" parents="299 6841 7533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7539">
    <literal><![CDATA[
      K(T(x,y \ 1),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,2316,a(flip),b,7533,a),flip(a)].">
      <j1 rule="hyper" parents="299 2316 7533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7540">
    <literal><![CDATA[
      K(T(x,K(y,z)),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,2274,a(flip),b,7533,a),flip(a)].">
      <j1 rule="hyper" parents="299 2274 7533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7541">
    <literal><![CDATA[
      x * K(T(y,x),z) = K(y,z) * x
    ]]></literal>
    <justification jstring="[para(7533(a,2),107(a,1,2))].">
      <j1 rule="para" parents="7533 107"/>
    </justification>
  </clause>

  <clause id="7542">
    <literal><![CDATA[
      T(K(x,y),z) * T(x,z) = T(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(7533(a,1),5096(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7533 5096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7543">
    <literal><![CDATA[
      (K(x,y) * z) * K(T(y,z),x) = z
    ]]></literal>
    <justification jstring="[para(7533(a,2),7285(a,1,2))].">
      <j1 rule="para" parents="7533 7285"/>
    </justification>
  </clause>

  <clause id="7544">
    <literal><![CDATA[
      K(x,T(y,z)) \ 1 = K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(5453,a,7537,a)].">
      <j1 rule="hyper" parents="5453 7537"/>
    </justification>
  </clause>

  <clause id="7545">
    <literal><![CDATA[
      x / T(x,T(y,z)) = K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(5051,a,7537,a)].">
      <j1 rule="hyper" parents="5051 7537"/>
    </justification>
  </clause>

  <clause id="7546">
    <literal><![CDATA[
      (x * K(y,T(z,u))) \ x = K(z,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,7200,a,b,7537,a)].">
      <j1 rule="hyper" parents="65 7200 7537"/>
    </justification>
  </clause>

  <clause id="7547">
    <literal><![CDATA[
      T(T(x * K(y,x),z),u) \ T(T(x,z),u) = K(T(x,z),T(y,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,5817,a,b,7537,a)].">
      <j1 rule="hyper" parents="65 5817 7537"/>
    </justification>
  </clause>

  <clause id="7548">
    <literal><![CDATA[
      K(x,T(y,x \ z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(65,a,7000,a(flip),b,7537,a),flip(a)].">
      <j1 rule="hyper" parents="65 7000 7537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7549">
    <literal><![CDATA[
      x * K(T(y,z),u) = x * K(y,T(u,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,7537,a)].">
      <j1 rule="hyper" parents="60 7537"/>
    </justification>
  </clause>

  <clause id="7550">
    <literal><![CDATA[
      T(x,T(y,z)) \ 1 = x \ K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,7537,a(flip),b,5034,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 7537 5034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7551">
    <literal><![CDATA[
      K(T(x,y),T(z,u)) = K(x,T(T(z,y),u))
    ]]></literal>
    <justification jstring="[para(23(a,1),7537(a,2,2))].">
      <j1 rule="para" parents="23 7537"/>
    </justification>
  </clause>

  <clause id="7552">
    <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),7537(a,1,1))].">
      <j1 rule="para" parents="27 7537"/>
    </justification>
  </clause>

  <clause id="7553">
    <literal><![CDATA[
      K(x / y,T(z,y)) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(109(a,1),7537(a,1,1)),flip(a)].">
      <j1 rule="para" parents="109 7537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7554">
    <literal><![CDATA[
      K(T(x,y),z / y) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(109(a,1),7537(a,2,2))].">
      <j1 rule="para" parents="109 7537"/>
    </justification>
  </clause>

  <clause id="7555">
    <literal><![CDATA[
      K(x,T(y,T(T(x,z),u))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(200(a,1),7537(a,1,1)),flip(a)].">
      <j1 rule="para" parents="200 7537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7556">
    <literal><![CDATA[
      K((x * y) / x,T(z,x)) = K(y,z)
    ]]></literal>
    <justification jstring="[para(222(a,1),7537(a,1,1)),flip(a)].">
      <j1 rule="para" parents="222 7537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7557">
    <literal><![CDATA[
      K(x,T(y,R(T(x,z),u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(209(a,1),7537(a,1,1)),flip(a)].">
      <j1 rule="para" parents="209 7537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7558">
    <literal><![CDATA[
      K(L((x \ y) \ y,z,u),w) = K(L(x,z,u),T(w,x \ y))
    ]]></literal>
    <justification jstring="[para(298(a,1),7537(a,1,1))].">
      <j1 rule="para" parents="298 7537"/>
    </justification>
  </clause>

  <clause id="7559">
    <literal><![CDATA[
      K(T(x,(1 / y) \ z),z * y) = K(x,z * y)
    ]]></literal>
    <justification jstring="[para(1271(a,1),7537(a,2,2))].">
      <j1 rule="para" parents="1271 7537"/>
    </justification>
  </clause>

  <clause id="7560">
    <literal><![CDATA[
      K(x,T(y,K(z,L(x,u,w)))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3614(a,1),7537(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3614 7537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7561">
    <literal><![CDATA[
      x / K(y,T(x,z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7537(a,1),5041(a,2,2)),flip(a)].">
      <j1 rule="para" parents="7537 5041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7562">
    <literal><![CDATA[
      T(x * K(y,T(x,z)),T(y,z)) = x
    ]]></literal>
    <justification jstring="[para(7537(a,1),5053(a,1,1,2))].">
      <j1 rule="para" parents="7537 5053"/>
    </justification>
  </clause>

  <clause id="7563">
    <literal><![CDATA[
      x * K(T(x,y),z) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(7537(a,2),5083(a,2,2)),flip(a)].">
      <j1 rule="para" parents="7537 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7564">
    <literal><![CDATA[
      K(x,T(y,z)) * T(x,z) = T(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(7537(a,1),5096(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7537 5096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7565">
    <literal><![CDATA[
      (T(x,y) * z) / T(x,y) = z * K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(7537(a,1),5054(a,2,2))].">
      <j1 rule="para" parents="7537 5054"/>
    </justification>
  </clause>

  <clause id="7566">
    <literal><![CDATA[
      x / K(y,T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7537(a,1),5046(a,1,2))].">
      <j1 rule="para" parents="7537 5046"/>
    </justification>
  </clause>

  <clause id="7568">
    <literal><![CDATA[
      x * K(T(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(7537(a,2),5087(a,1,2))].">
      <j1 rule="para" parents="7537 5087"/>
    </justification>
  </clause>

  <clause id="7570">
    <literal><![CDATA[
      K(x,T(y,z)) \ u = K(y,T(x,z)) * u
    ]]></literal>
    <justification jstring="[para(7537(a,1),5426(a,1,1))].">
      <j1 rule="para" parents="7537 5426"/>
    </justification>
  </clause>

  <clause id="7571">
    <literal><![CDATA[
      K(x,T(y,z)) * (K(y,T(x,z)) * u) = u
    ]]></literal>
    <justification jstring="[para(7537(a,1),5432(a,1,1))].">
      <j1 rule="para" parents="7537 5432"/>
    </justification>
  </clause>

  <clause id="7572">
    <literal><![CDATA[
      K(x,T(y,K(z,z \ x))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5503(a,1),7537(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5503 7537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7573">
    <literal><![CDATA[
      K(x,T(y,z)) \ (y * u) = T(y,T(x,z)) * u
    ]]></literal>
    <justification jstring="[para(7537(a,1),5364(a,1,1))].">
      <j1 rule="para" parents="7537 5364"/>
    </justification>
  </clause>

  <clause id="7574">
    <literal><![CDATA[
      K(x,T(y,z)) * (y \ u) = T(y,T(x,z)) \ u
    ]]></literal>
    <justification jstring="[para(7537(a,1),5383(a,1,1))].">
      <j1 rule="para" parents="7537 5383"/>
    </justification>
  </clause>

  <clause id="7575">
    <literal><![CDATA[
      1 / (x \ K(y,T(x,z))) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7537(a,1),5226(a,1,2,2))].">
      <j1 rule="para" parents="7537 5226"/>
    </justification>
  </clause>

  <clause id="7578">
    <literal><![CDATA[
      T(x,y) * K(x,T(z,y)) = T(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(7537(a,1),5150(a,1,2))].">
      <j1 rule="para" parents="7537 5150"/>
    </justification>
  </clause>

  <clause id="7579">
    <literal><![CDATA[
      K(x,T(y,z)) * T(x,z) = T(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(7537(a,1),5162(a,1,1))].">
      <j1 rule="para" parents="7537 5162"/>
    </justification>
  </clause>

  <clause id="7580">
    <literal><![CDATA[
      K(x,T(y,z)) \ (y * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(y,T(x,z)) * u = w
    ]]></literal>
    <justification jstring="[para(7537(a,1),5394(a,1,1))].">
      <j1 rule="para" parents="7537 5394"/>
    </justification>
  </clause>

  <clause id="7581">
    <literal><![CDATA[
      (x * y) / (K(z,T(x,u)) * y) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(7537(a,1),5519(a,1,2,1))].">
      <j1 rule="para" parents="7537 5519"/>
    </justification>
  </clause>

  <clause id="7582">
    <literal><![CDATA[
      a(x,y,K(z,T(y,u))) = 1
    ]]></literal>
    <justification jstring="[para(7537(a,1),6815(a,1,3))].">
      <j1 rule="para" parents="7537 6815"/>
    </justification>
  </clause>

  <clause id="7583">
    <literal><![CDATA[
      x / K(y,T(z,u)) = x * K(z,T(y,u))
    ]]></literal>
    <justification jstring="[para(7537(a,1),7196(a,1,2))].">
      <j1 rule="para" parents="7537 7196"/>
    </justification>
  </clause>

  <clause id="7584">
    <literal><![CDATA[
      (x * K(y,T(z,u))) \ (x * z) = T(z,T(y,u))
    ]]></literal>
    <justification jstring="[para(7537(a,1),7186(a,1,1,2))].">
      <j1 rule="para" parents="7537 7186"/>
    </justification>
  </clause>

  <clause id="7585">
    <literal><![CDATA[
      x * K(y,T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      w * K(z,T(y,u)) = x
    ]]></literal>
    <justification jstring="[para(7537(a,1),7207(a,1,2))].">
      <j1 rule="para" parents="7537 7207"/>
    </justification>
  </clause>

  <clause id="7586">
    <literal><![CDATA[
      x / K(y,T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x * K(z,T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(7537(a,1),7208(a,1,2))].">
      <j1 rule="para" parents="7537 7208"/>
    </justification>
  </clause>

  <clause id="7588">
    <literal><![CDATA[
      T(x / T(y,T(z,u)),y) = y \ (x * K(z,T(y,u)))
    ]]></literal>
    <justification jstring="[para(7537(a,1),7231(a,2,2,2))].">
      <j1 rule="para" parents="7537 7231"/>
    </justification>
  </clause>

  <clause id="7589">
    <literal><![CDATA[
      R(x,y \ 1,K(z,T(y,u))) = x
    ]]></literal>
    <justification jstring="[para(7537(a,1),7327(a,1,3))].">
      <j1 rule="para" parents="7537 7327"/>
    </justification>
  </clause>

  <clause id="7590">
    <literal><![CDATA[
      L(K(x,T(y,z)),y,u) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(54,a,7582,a)].">
      <j1 rule="hyper" parents="54 7582"/>
    </justification>
  </clause>

  <clause id="7591">
    <literal><![CDATA[
      K(x,y) * T(x,K(y,z)) = T(T(x,K(y,z)),y)
    ]]></literal>
    <justification jstring="[para(7540(a,1),5096(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7540 5096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7592">
    <literal><![CDATA[
      T(x,x * T(y,K(x,z))) * K(y,x) = L(x,T(y,K(x,z)),x)
    ]]></literal>
    <justification jstring="[para(7540(a,1),5561(a,1,2))].">
      <j1 rule="para" parents="7540 5561"/>
    </justification>
  </clause>

  <clause id="7593">
    <literal><![CDATA[
      R(x,(y * K(z,y)) \ 1,K(u,y)) = x
    ]]></literal>
    <justification jstring="[para(5053(a,1),7589(a,1,3,2))].">
      <j1 rule="para" parents="5053 7589"/>
    </justification>
  </clause>

  <clause id="7594">
    <literal><![CDATA[
      T(x,(y \ (z \ y)) \ 1) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(7107,a,7482,a)].">
      <j1 rule="hyper" parents="7107 7482"/>
    </justification>
  </clause>

  <clause id="7595">
    <literal><![CDATA[
      T(x / ((y \ z) \ z),T(y,z)) = ((y \ z) \ z) \ x
    ]]></literal>
    <justification jstring="[hyper(400,a,7482,a),flip(a)].">
      <j1 rule="hyper" parents="400 7482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7596">
    <literal><![CDATA[
      T(x,T(y \ 1,y * z)) = T(x,T(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(4753(a,2),7482(a,1,2))].">
      <j1 rule="para" parents="4753 7482"/>
    </justification>
  </clause>

  <clause id="7597">
    <literal><![CDATA[
      K(x,T(y \ 1,y * z)) = K(x,T(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(4753(a,2),7490(a,1,2))].">
      <j1 rule="para" parents="4753 7490"/>
    </justification>
  </clause>

  <clause id="7599">
    <literal><![CDATA[
      (x \ y) * K(z,T(x,x \ y)) = T(x,z) \ y
    ]]></literal>
    <justification jstring="[hyper(299,a,5383,a(flip),b,7507,a),flip(a)].">
      <j1 rule="hyper" parents="299 5383 7507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7600">
    <literal><![CDATA[
      x \ (y * K(z,T(x,y))) = T(x,z) \ y
    ]]></literal>
    <justification jstring="[hyper(119,a,7507,a,b,5060,a)].">
      <j1 rule="hyper" parents="119 7507 5060"/>
    </justification>
  </clause>

  <clause id="7601">
    <literal><![CDATA[
      x * (y * K(z,T(u,y))) = x * (K(z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,7507,a)].">
      <j1 rule="hyper" parents="60 7507"/>
    </justification>
  </clause>

  <clause id="7602">
    <literal><![CDATA[
      K(x,T((y / z) \ 1,z)) = K(x,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(36,a,6071,a(flip),b,7507,a),flip(a)].">
      <j1 rule="hyper" parents="36 6071 7507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7603">
    <literal><![CDATA[
      K(x,y) * (z * K(y,T(x,z))) = z
    ]]></literal>
    <justification jstring="[hyper(5437,a,7507,a(flip))].">
      <j1 rule="hyper" parents="5437 7507"/>
    </justification>
  </clause>

  <clause id="7604">
    <literal><![CDATA[
      ((x * y) * K(z,T(u,y))) / (K(z,u) * y) = R(x,y,K(z,T(u,y)))
    ]]></literal>
    <justification jstring="[para(7507(a,1),20(a,2,2)),flip(a)].">
      <j1 rule="para" parents="7507 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7605">
    <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),7507(a,1,2,2))].">
      <j1 rule="para" parents="25 7507"/>
    </justification>
  </clause>

  <clause id="7606">
    <literal><![CDATA[
      K(x,y) * z != z * u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7507(a,1),45(a,1))].">
      <j1 rule="para" parents="7507 45"/>
    </justification>
  </clause>

  <clause id="7607">
    <literal><![CDATA[
      K(x,y / z) * z = z * K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(109(a,1),7507(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="109 7507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7610">
    <literal><![CDATA[
      K(x,K(x \ 1,y) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(7507(a,1),7382(a,1,2))].">
      <j1 rule="para" parents="7507 7382"/>
    </justification>
  </clause>

  <clause id="7611">
    <literal><![CDATA[
      x * K(y,K(z,T(u,x))) = K(y,K(z,u)) * x
    ]]></literal>
    <justification jstring="[para(7489(a,2),7507(a,1,2,2))].">
      <j1 rule="para" parents="7489 7507"/>
    </justification>
  </clause>

  <clause id="7612">
    <literal><![CDATA[
      T(T(x,y),K(y,z)) = x * T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(299,a,7140,a,b,7516,a)].">
      <j1 rule="hyper" parents="299 7140 7516"/>
    </justification>
  </clause>

  <clause id="7613">
    <literal><![CDATA[
      (x * y) \ (y * T(x,T(y,z))) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[para(7516(a,1),6486(a,1,2,2))].">
      <j1 rule="para" parents="7516 6486"/>
    </justification>
  </clause>

  <clause id="7614">
    <literal><![CDATA[
      (K(x,y) * z) \ z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(x,z)) = u
    ]]></literal>
    <justification jstring="[para(7527(a,1),314(a,1,2))].">
      <j1 rule="para" parents="7527 314"/>
    </justification>
  </clause>

  <clause id="7615">
    <literal><![CDATA[
      T(x,K(y,x \ 1) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(7527(a,1),7377(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7527 7377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7616">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) / w) = K(x,w \ R(T(x,y),z,u))
    ]]></literal>
    <justification jstring="[para(209(a,1),7538(a,1,1))].">
      <j1 rule="para" parents="209 7538"/>
    </justification>
  </clause>

  <clause id="7617">
    <literal><![CDATA[
      K(x,L(L(x,y,z),u,w) / v5) = K(x,v5 \ L(L(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[para(211(a,1),7538(a,1,1))].">
      <j1 rule="para" parents="211 7538"/>
    </justification>
  </clause>

  <clause id="7618">
    <literal><![CDATA[
      K(x,y \ z) * T(x,z) = T(T(x,z),z / y)
    ]]></literal>
    <justification jstring="[para(7538(a,1),5096(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7538 5096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7619">
    <literal><![CDATA[
      L(x,K(y,z \ u),u / z) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(7538(a,1),5486(a,1,2))].">
      <j1 rule="para" parents="7538 5486"/>
    </justification>
  </clause>

  <clause id="7620">
    <literal><![CDATA[
      K(x / y,z) * y = y * K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(109(a,1),7541(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="109 7541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7621">
    <literal><![CDATA[
      K((x * y) / x,z) * x = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(222(a,1),7541(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="222 7541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7622">
    <literal><![CDATA[
      K(x,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(7544(a,1),5200(a,1))].">
      <j1 rule="para" parents="7544 5200"/>
    </justification>
  </clause>

  <clause id="7623">
    <literal><![CDATA[
      K(x,T(y,x \ z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,7489,a,b,7548,a),flip(a)].">
      <j1 rule="hyper" parents="299 7489 7548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7624">
    <literal><![CDATA[
      K(x / y,y \ z) = K(y \ x,z / y)
    ]]></literal>
    <justification jstring="[para(109(a,1),7553(a,1,2))].">
      <j1 rule="para" parents="109 7553"/>
    </justification>
  </clause>

  <clause id="7625">
    <literal><![CDATA[
      K(x / y,T(y,z)) = K(y \ x,T(y,z))
    ]]></literal>
    <justification jstring="[para(175(a,1),7553(a,1,2))].">
      <j1 rule="para" parents="175 7553"/>
    </justification>
  </clause>

  <clause id="7626">
    <literal><![CDATA[
      K(x / y,L(y,z,u)) = K(y \ x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(176(a,1),7553(a,1,2))].">
      <j1 rule="para" parents="176 7553"/>
    </justification>
  </clause>

  <clause id="7627">
    <literal><![CDATA[
      (x / y) * K(y \ x,z) = T(x / y,T(z,y))
    ]]></literal>
    <justification jstring="[para(7553(a,1),5083(a,2,2)),flip(a)].">
      <j1 rule="para" parents="7553 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7628">
    <literal><![CDATA[
      K(x \ y,z) * (y / x) = T(y / x,T(z,x))
    ]]></literal>
    <justification jstring="[para(7553(a,1),5096(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7553 5096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7629">
    <literal><![CDATA[
      K(x \ y,z) * (y / x) != u
    ]]></literal>
    <literal><![CDATA[
      T(y / x,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(7553(a,1),5097(a,1,1))].">
      <j1 rule="para" parents="7553 5097"/>
    </justification>
  </clause>

  <clause id="7630">
    <literal><![CDATA[
      K(x,y / L(x,z,u)) = K(x,L(x,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(173(a,1),7554(a,1,1))].">
      <j1 rule="para" parents="173 7554"/>
    </justification>
  </clause>

  <clause id="7631">
    <literal><![CDATA[
      K(x,y / R(T(x,z),u,w)) = K(x,R(T(x,z),u,w) \ y)
    ]]></literal>
    <justification jstring="[para(209(a,1),7554(a,1,1))].">
      <j1 rule="para" parents="209 7554"/>
    </justification>
  </clause>

  <clause id="7632">
    <literal><![CDATA[
      (x / (y / z)) * K(u,z \ y) = x / T(y / z,T(u,z))
    ]]></literal>
    <justification jstring="[para(7554(a,1),7189(a,1,2))].">
      <j1 rule="para" parents="7554 7189"/>
    </justification>
  </clause>

  <clause id="7633">
    <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(7554(a,1),7271(a,1,2))].">
      <j1 rule="para" parents="7554 7271"/>
    </justification>
  </clause>

  <clause id="7634">
    <literal><![CDATA[
      T(x,T(y,T(T(x,z),u))) = K(x,y) * x
    ]]></literal>
    <justification jstring="[para(7555(a,1),5096(a,2,1))].">
      <j1 rule="para" parents="7555 5096"/>
    </justification>
  </clause>

  <clause id="7635">
    <literal><![CDATA[
      L(x,T(T(y,z),u),K(w,y)) = x
    ]]></literal>
    <justification jstring="[para(7556(a,1),6447(a,1,3))].">
      <j1 rule="para" parents="7556 6447"/>
    </justification>
  </clause>

  <clause id="7636">
    <literal><![CDATA[
      a(x,T(y,z),K(u,y)) = 1
    ]]></literal>
    <justification jstring="[para(7556(a,1),6815(a,1,3))].">
      <j1 rule="para" parents="7556 6815"/>
    </justification>
  </clause>

  <clause id="7637">
    <literal><![CDATA[
      L(K(x,y),T(y,z),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(54,a,7636,a)].">
      <j1 rule="hyper" parents="54 7636"/>
    </justification>
  </clause>

  <clause id="7638">
    <literal><![CDATA[
      L(x,T(T(y,z),u),K(w,y)) != v5
    ]]></literal>
    <literal><![CDATA[
      x = v5
    ]]></literal>
    <justification jstring="[para(7635(a,1),52(a,2))].">
      <j1 rule="para" parents="7635 52"/>
    </justification>
  </clause>

  <clause id="7639">
    <literal><![CDATA[
      (x * T(y,z)) \ (x * R(y,z,y)) = K(y * z,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,5588,a,b,7637,a)].">
      <j1 rule="hyper" parents="65 5588 7637"/>
    </justification>
  </clause>

  <clause id="7640">
    <literal><![CDATA[
      (x * T(y,z)) * L(K(u,y),w,v5) = x * (T(y,z) * L(K(u,y),w,v5))
    ]]></literal>
    <justification jstring="[para(7637(a,1),489(a,1,2,1))].">
      <j1 rule="para" parents="7637 489"/>
    </justification>
  </clause>

  <clause id="7641">
    <literal><![CDATA[
      K(x,y) * T(T(y,x),z) = T(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(5773,a,7563,a)].">
      <j1 rule="hyper" parents="5773 7563"/>
    </justification>
  </clause>

  <clause id="7643">
    <literal><![CDATA[
      K(x,T(y,x \ 1) \ z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(5383(a,1),7610(a,1,2))].">
      <j1 rule="para" parents="5383 7610"/>
    </justification>
  </clause>

  <clause id="7644">
    <literal><![CDATA[
      T(x,K(y,1 / x) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(4797(a,2),7615(a,1,2,1))].">
      <j1 rule="para" parents="4797 7615"/>
    </justification>
  </clause>

  <clause id="7645">
    <literal><![CDATA[
      K(x,T(y,x * z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),7623(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 7623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7646">
    <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),7623(a,1,2))].">
      <j1 rule="para" parents="27 7623"/>
    </justification>
  </clause>

  <clause id="7647">
    <literal><![CDATA[
      T(x,T(y,x \ z)) = x * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7623(a,1),5083(a,2,2))].">
      <j1 rule="para" parents="7623 5083"/>
    </justification>
  </clause>

  <clause id="7648">
    <literal><![CDATA[
      K(x * y,T(z,y \ 1)) = K(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[para(7040(a,1),7623(a,1,2))].">
      <j1 rule="para" parents="7040 7623"/>
    </justification>
  </clause>

  <clause id="7649">
    <literal><![CDATA[
      K(K(x,1 / y) * z,y) = y / T(y,z)
    ]]></literal>
    <justification jstring="[para(7644(a,1),5033(a,2,2))].">
      <j1 rule="para" parents="7644 5033"/>
    </justification>
  </clause>

  <clause id="7650">
    <literal><![CDATA[
      K(x,T(y / (x * z),z)) = K(x,(x * z) \ y)
    ]]></literal>
    <justification jstring="[para(109(a,1),7645(a,1,2)),flip(a)].">
      <j1 rule="para" parents="109 7645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7651">
    <literal><![CDATA[
      K(L(x,y,z),y * x) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(299,a,5685,a(flip),b,7436,a),flip(a)].">
      <j1 rule="hyper" parents="299 5685 7436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7652">
    <literal><![CDATA[
      K((x / y) \ x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(12(a,1),7476(a,1,1,2))].">
      <j1 rule="para" parents="12 7476"/>
    </justification>
  </clause>

  <clause id="7653">
    <literal><![CDATA[
      K(T(x,y) \ (y * z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ (T(y,x) * z),u) = w
    ]]></literal>
    <justification jstring="[para(4958(a,1),7476(a,1,1,2))].">
      <j1 rule="para" parents="4958 7476"/>
    </justification>
  </clause>

  <clause id="7654">
    <literal><![CDATA[
      K((x * y) / x,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(7553(a,2),7476(a,1))].">
      <j1 rule="para" parents="7553 7476"/>
    </justification>
  </clause>

  <clause id="7657">
    <literal><![CDATA[
      K(x,T(y,T(z,L(x,u,w)))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7140(a,1),7560(a,1,2))].">
      <j1 rule="para" parents="7140 7560"/>
    </justification>
  </clause>

  <clause id="7658">
    <literal><![CDATA[
      K((x \ y) \ z,T(z,u)) = K(y \ (x * z),T(z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,7421,a(flip),b,7590,a),flip(a)].">
      <j1 rule="hyper" parents="65 7421 7590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7659">
    <literal><![CDATA[
      R(x,y \ K(y,z),K(u,y)) = x
    ]]></literal>
    <justification jstring="[para(5223(a,1),7593(a,1,2))].">
      <j1 rule="para" parents="5223 7593"/>
    </justification>
  </clause>

  <clause id="7660">
    <literal><![CDATA[
      (x * K(y,z)) / (z \ 1) = x / (z \ K(z,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,6468,a(flip),b,7659,a)].">
      <j1 rule="hyper" parents="65 6468 7659"/>
    </justification>
  </clause>

  <clause id="7661">
    <literal><![CDATA[
      T(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(7489(a,1),7622(a,1))].">
      <j1 rule="para" parents="7489 7622"/>
    </justification>
  </clause>

  <clause id="7662">
    <literal><![CDATA[
      L(x,y,x) * K(x,z) = L(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(3580,a,7443,a)].">
      <j1 rule="hyper" parents="3580 7443"/>
    </justification>
  </clause>

  <clause id="7663">
    <literal><![CDATA[
      T(x,y) \ L(T(x,y),z,x) = x \ L(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,7443,a(flip),b,5056,a)].">
      <j1 rule="hyper" parents="119 7443 5056"/>
    </justification>
  </clause>

  <clause id="7664">
    <literal><![CDATA[
      (x / L(y,z,y)) * y = y * (L(y,z,y) \ x)
    ]]></literal>
    <justification jstring="[para(7452(a,1),107(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7452 107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7666">
    <literal><![CDATA[
      L(x,y,x) * (x \ z) = (z / x) * L(x,y,x)
    ]]></literal>
    <justification jstring="[para(109(a,1),7454(a,1,2))].">
      <j1 rule="para" parents="109 7454"/>
    </justification>
  </clause>

  <clause id="7668">
    <literal><![CDATA[
      (x / R(y,z,y)) * y = y * (R(y,z,y) \ x)
    ]]></literal>
    <justification jstring="[para(7459(a,1),107(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7459 107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7670">
    <literal><![CDATA[
      R(R(x,y,x) / x,x,z) = (z * R(x,y,x)) / (z * x)
    ]]></literal>
    <justification jstring="[para(7461(a,1),4930(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7461 4930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7671">
    <literal><![CDATA[
      T((x / (y * K(z,y))) * y,z / (z / y)) = ((z * y) / z) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(6006,a,7464,a),flip(a)].">
      <j1 rule="hyper" parents="6006 7464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7672">
    <literal><![CDATA[
      L(x,y,K(z,x)) = x
    ]]></literal>
    <justification jstring="[hyper(2841,a,7472,a)].">
      <j1 rule="hyper" parents="2841 7472"/>
    </justification>
  </clause>

  <clause id="7673">
    <literal><![CDATA[
      K(x,y) * ((y \ z) * y) = (T(y,x) \ z) * y
    ]]></literal>
    <justification jstring="[para(5383(a,1),7472(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5383 7472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7674">
    <literal><![CDATA[
      K(K(x,y) * z,y) * T(y,K(x,y) * (z * y)) = L(y,K(x,y) * z,y)
    ]]></literal>
    <justification jstring="[para(7472(a,1),5354(a,1,2,2))].">
      <j1 rule="para" parents="7472 5354"/>
    </justification>
  </clause>

  <clause id="7675">
    <literal><![CDATA[
      L(x,y,K(x,z)) = x
    ]]></literal>
    <justification jstring="[hyper(5219,a,7672,a)].">
      <j1 rule="hyper" parents="5219 7672"/>
    </justification>
  </clause>

  <clause id="7676">
    <literal><![CDATA[
      L(L(x,y,z),u,K(w,x)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(7672(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7672 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7677">
    <literal><![CDATA[
      L(K(x,y),z,K(u,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7672(a,1),7431(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7672 7431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7678">
    <literal><![CDATA[
      L(x,y,K(R(x,z,u),w)) = x
    ]]></literal>
    <justification jstring="[hyper(153,a,7675,a(flip))].">
      <j1 rule="hyper" parents="153 7675"/>
    </justification>
  </clause>

  <clause id="7679">
    <literal><![CDATA[
      L(T(x,y),z,K(x,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(7675(a,1),25(a,2,1))].">
      <j1 rule="para" parents="7675 25"/>
    </justification>
  </clause>

  <clause id="7680">
    <literal><![CDATA[
      (K(x,y) * z) * x = K(x,y) * (z * x)
    ]]></literal>
    <justification jstring="[para(7675(a,1),94(a,1,2))].">
      <j1 rule="para" parents="7675 94"/>
    </justification>
  </clause>

  <clause id="7681">
    <literal><![CDATA[
      (K(x,y) * z) / x = K(x,y) * (z / x)
    ]]></literal>
    <justification jstring="[para(7675(a,1),585(a,1,2))].">
      <j1 rule="para" parents="7675 585"/>
    </justification>
  </clause>

  <clause id="7682">
    <literal><![CDATA[
      (K(x,y) * z) * R(x,u,w) = K(x,y) * (z * R(x,u,w))
    ]]></literal>
    <justification jstring="[para(7675(a,1),488(a,1,2,1))].">
      <j1 rule="para" parents="7675 488"/>
    </justification>
  </clause>

  <clause id="7683">
    <literal><![CDATA[
      (K(x,y) * z) * L(x,u,w) = K(x,y) * (z * L(x,u,w))
    ]]></literal>
    <justification jstring="[para(7675(a,1),489(a,1,2,1))].">
      <j1 rule="para" parents="7675 489"/>
    </justification>
  </clause>

  <clause id="7684">
    <literal><![CDATA[
      L(K(x,y),z,K(x,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7675(a,1),7431(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7675 7431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7685">
    <literal><![CDATA[
      R(K(R(x,y,z),u),w,L(x,w,K(R(x,y,z),u))) = (K(R(x,y,z),u) * (w * x)) / (w * x)
    ]]></literal>
    <justification jstring="[para(7678(a,1),486(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7678 486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7686">
    <literal><![CDATA[
      (K(x,y) * z) / T(x,u) = K(x,y) * (z / T(x,u))
    ]]></literal>
    <justification jstring="[para(7679(a,1),585(a,1,2))].">
      <j1 rule="para" parents="7679 585"/>
    </justification>
  </clause>

  <clause id="7688">
    <literal><![CDATA[
      T(x / (x / K(y,z)),x) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,4519,a,b,7684,a)].">
      <j1 rule="hyper" parents="65 4519 7684"/>
    </justification>
  </clause>

  <clause id="7689">
    <literal><![CDATA[
      (K(x,y) * z) * K(x,u) = K(x,y) * (z * K(x,u))
    ]]></literal>
    <justification jstring="[para(7684(a,1),94(a,1,2))].">
      <j1 rule="para" parents="7684 94"/>
    </justification>
  </clause>

  <clause id="7690">
    <literal><![CDATA[
      T((T(x,y) / z) / (x / z),T(x,y) / z) = K((z \ 1) \ (x / z),y)
    ]]></literal>
    <justification jstring="[para(7129(a,1),7688(a,1,1,2))].">
      <j1 rule="para" parents="7129 7688"/>
    </justification>
  </clause>

  <clause id="7691">
    <literal><![CDATA[
      L(x,y,T(x,z)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(6687,a,7676,a)].">
      <j1 rule="hyper" parents="6687 7676"/>
    </justification>
  </clause>

  <clause id="7695">
    <literal><![CDATA[
      L(x \ y,z,y / x) = L(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,5731,a(flip),b,7691,a)].">
      <j1 rule="hyper" parents="65 5731 7691"/>
    </justification>
  </clause>

  <clause id="7696">
    <literal><![CDATA[
      L(T(x,y),z,T(x,u)) = T(L(x,z,x),y)
    ]]></literal>
    <justification jstring="[para(7691(a,1),25(a,2,1))].">
      <j1 rule="para" parents="7691 25"/>
    </justification>
  </clause>

  <clause id="7698">
    <literal><![CDATA[
      K(x,T(y,(z \ u) \ y)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[para(7037(a,1),7487(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7037 7487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7699">
    <literal><![CDATA[
      x / T(x,T(y \ 1,z)) = K(T(y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,7545,a,b,7497,a)].">
      <j1 rule="hyper" parents="299 7545 7497"/>
    </justification>
  </clause>

  <clause id="7700">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) = K(x,(y * z) \ z)
    ]]></literal>
    <justification jstring="[hyper(7094,a,7498,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="7094 7498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7702">
    <literal><![CDATA[
      K(x,T(T(y,z),u)) = T(T(K(x,y),u),z)
    ]]></literal>
    <justification jstring="[para(7489(a,1),7504(a,2,1))].">
      <j1 rule="para" parents="7489 7504"/>
    </justification>
  </clause>

  <clause id="7703">
    <literal><![CDATA[
      K(x * y,K(x,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(6959,a,7519,a)].">
      <j1 rule="hyper" parents="6959 7519"/>
    </justification>
  </clause>

  <clause id="7704">
    <literal><![CDATA[
      K(x * y,K(y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,7354,a,b,7703,a)].">
      <j1 rule="hyper" parents="65 7354 7703"/>
    </justification>
  </clause>

  <clause id="7705">
    <literal><![CDATA[
      K(x \ y,K(x,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),7703(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 7703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7706">
    <literal><![CDATA[
      K(x * y,K(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(x,z)) = u
    ]]></literal>
    <justification jstring="[para(7705(a,1),7476(a,1))].">
      <j1 rule="para" parents="7705 7476"/>
    </justification>
  </clause>

  <clause id="7707">
    <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(7550(a,1),2060(a,1,2))].">
      <j1 rule="para" parents="7550 2060"/>
    </justification>
  </clause>

  <clause id="7708">
    <literal><![CDATA[
      K(x,y) \ T(T(x,y),z) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,7564,a(flip),b,5701,a)].">
      <j1 rule="hyper" parents="119 7564 5701"/>
    </justification>
  </clause>

  <clause id="7709">
    <literal><![CDATA[
      K(T(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(7571(a,1),5212(a,1))].">
      <j1 rule="para" parents="7571 5212"/>
    </justification>
  </clause>

  <clause id="7710">
    <literal><![CDATA[
      K(T(x,y),z) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) * u = w
    ]]></literal>
    <justification jstring="[para(7571(a,1),5438(a,1,2)),flip(b)].">
      <j1 rule="para" parents="7571 5438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7711">
    <literal><![CDATA[
      K(L(T(x,y),z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(L(x,z,u),T(w,y)) = v5
    ]]></literal>
    <justification jstring="[para(25(a,2),7709(a,1,1))].">
      <j1 rule="para" parents="25 7709"/>
    </justification>
  </clause>

  <clause id="7712">
    <literal><![CDATA[
      K(x,T(y,z) \ T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y \ x,z)) = u
    ]]></literal>
    <justification jstring="[para(7371(a,2),7709(a,1))].">
      <j1 rule="para" parents="7371 7709"/>
    </justification>
  </clause>

  <clause id="7713">
    <literal><![CDATA[
      K((x \ y) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(7479(a,2),7709(a,1))].">
      <j1 rule="para" parents="7479 7709"/>
    </justification>
  </clause>

  <clause id="7714">
    <literal><![CDATA[
      T(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7533(a,1),7709(a,1))].">
      <j1 rule="para" parents="7533 7709"/>
    </justification>
  </clause>

  <clause id="7715">
    <literal><![CDATA[
      K(x,T(T(y,z),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(T(y,u),z)) = w
    ]]></literal>
    <justification jstring="[para(7551(a,1),7709(a,1))].">
      <j1 rule="para" parents="7551 7709"/>
    </justification>
  </clause>

  <clause id="7717">
    <literal><![CDATA[
      K(x,T(y,x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7548(a,2),7714(a,1))].">
      <j1 rule="para" parents="7548 7714"/>
    </justification>
  </clause>

  <clause id="7718">
    <literal><![CDATA[
      K(x,y) * T(x,T(z,y)) = T(T(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(5781,a,7578,a)].">
      <j1 rule="hyper" parents="5781 7578"/>
    </justification>
  </clause>

  <clause id="7719">
    <literal><![CDATA[
      K(x,T(y,z)) * T(x,x \ z) = T(T(x,y),x \ z)
    ]]></literal>
    <justification jstring="[para(7623(a,1),7579(a,1,1))].">
      <j1 rule="para" parents="7623 7579"/>
    </justification>
  </clause>

  <clause id="7721">
    <literal><![CDATA[
      x * K(y,x \ (z \ x)) = K(y,z \ 1) * x
    ]]></literal>
    <justification jstring="[para(5943(a,1),7607(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5943 7607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7722">
    <literal><![CDATA[
      T(T(x,1 / y),K(1 / y,z)) = x * K(x,1 / T(y,z))
    ]]></literal>
    <justification jstring="[para(5804(a,2),7612(a,2,2))].">
      <j1 rule="para" parents="5804 7612"/>
    </justification>
  </clause>

  <clause id="7723">
    <literal><![CDATA[
      K(x \ 1,y) * ((1 / x) \ z) = (K(y,x \ 1) / x) \ z
    ]]></literal>
    <justification jstring="[hyper(7619,a,6085,a)].">
      <j1 rule="hyper" parents="7619 6085"/>
    </justification>
  </clause>

  <clause id="7725">
    <literal><![CDATA[
      K(T(x / y,z),y) = K(y \ x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(7622,a,7625,a)].">
      <j1 rule="hyper" parents="7622 7625"/>
    </justification>
  </clause>

  <clause id="7726">
    <literal><![CDATA[
      T(x,T(y,T(T(x,z),u))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,5096,a,b,7634,a),flip(a)].">
      <j1 rule="hyper" parents="299 5096 7634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7727">
    <literal><![CDATA[
      T(x * K(y,x),T(z,T(x,u))) = T(x * K(y,x),z)
    ]]></literal>
    <justification jstring="[para(5053(a,1),7726(a,1,2,2,1))].">
      <j1 rule="para" parents="5053 7726"/>
    </justification>
  </clause>

  <clause id="7728">
    <literal><![CDATA[
      L(T(T(x,y),z) \ (K(x,y) * u),T(T(x,y),z),K(y,x)) = T(x,T(z,y)) \ u
    ]]></literal>
    <justification jstring="[para(7641(a,1),5442(a,2,1))].">
      <j1 rule="para" parents="7641 5442"/>
    </justification>
  </clause>

  <clause id="7729">
    <literal><![CDATA[
      T(x,T(y,x \ z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,5083,a,b,7647,a),flip(a)].">
      <j1 rule="hyper" parents="299 5083 7647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7730">
    <literal><![CDATA[
      T(x,T(y,x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7647(a,2),5087(a,1))].">
      <j1 rule="para" parents="7647 5087"/>
    </justification>
  </clause>

  <clause id="7731">
    <literal><![CDATA[
      T(x,T(y,x \ y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(106(a,1),7729(a,2,2))].">
      <j1 rule="para" parents="106 7729"/>
    </justification>
  </clause>

  <clause id="7732">
    <literal><![CDATA[
      L(x,y,z) \ L(T(x,T(u,w)),y,z) = K(L(x,y,z),T(u,x \ w))
    ]]></literal>
    <justification jstring="[para(7729(a,1),5084(a,1,2,1))].">
      <j1 rule="para" parents="7729 5084"/>
    </justification>
  </clause>

  <clause id="7733">
    <literal><![CDATA[
      T(x,T(x * y,y)) = T(x,x * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),7731(a,1,2,2))].">
      <j1 rule="para" parents="9 7731"/>
    </justification>
  </clause>

  <clause id="7734">
    <literal><![CDATA[
      K(K(x,1 / y) * z,y) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,5033,a,b,7649,a),flip(a)].">
      <j1 rule="hyper" parents="299 5033 7649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7735">
    <literal><![CDATA[
      K(K(x,y \ 1) * z,y) = K(z,y)
    ]]></literal>
    <justification jstring="[para(4797(a,1),7734(a,1,1,1))].">
      <j1 rule="para" parents="4797 7734"/>
    </justification>
  </clause>

  <clause id="7736">
    <literal><![CDATA[
      K(T(x,1 / y) / z,y) = K(x / z,y)
    ]]></literal>
    <justification jstring="[para(6323(a,1),7734(a,1,1))].">
      <j1 rule="para" parents="6323 7734"/>
    </justification>
  </clause>

  <clause id="7738">
    <literal><![CDATA[
      K(T(x,y \ 1) \ z,y) = K(x \ z,y)
    ]]></literal>
    <justification jstring="[para(5351(a,1),7735(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5351 7735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7739">
    <literal><![CDATA[
      K(K(x,x \ y) * z,x / y) = K(z,x / y)
    ]]></literal>
    <justification jstring="[para(5501(a,1),7735(a,1,1,1))].">
      <j1 rule="para" parents="5501 7735"/>
    </justification>
  </clause>

  <clause id="7740">
    <literal><![CDATA[
      K(x \ T(y,z \ 1),z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(5850(a,1),7735(a,1,1))].">
      <j1 rule="para" parents="5850 7735"/>
    </justification>
  </clause>

  <clause id="7741">
    <literal><![CDATA[
      K(x * K(y,z \ 1),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(7621(a,1),7735(a,1,1))].">
      <j1 rule="para" parents="7621 7735"/>
    </justification>
  </clause>

  <clause id="7742">
    <literal><![CDATA[
      K(x * K(y,z \ u),u \ z) = K(x,u \ z)
    ]]></literal>
    <justification jstring="[para(6814(a,1),7741(a,1,1,2))].">
      <j1 rule="para" parents="6814 7741"/>
    </justification>
  </clause>

  <clause id="7743">
    <literal><![CDATA[
      K(x / T(y,z \ 1),z) = K(x / y,z)
    ]]></literal>
    <justification jstring="[para(6907(a,1),7741(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6907 7741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7744">
    <literal><![CDATA[
      L(x,y,x) * K(x,R(z \ 1,u,w) \ 1) = L(x * R(K(x,z),u,w),y,x)
    ]]></literal>
    <justification jstring="[para(6216(a,1),7662(a,2,1))].">
      <j1 rule="para" parents="6216 7662"/>
    </justification>
  </clause>

  <clause id="7745">
    <literal><![CDATA[
      K(x,y) * (L(y,z,y) \ u) = L(T(y,x),z,y) \ u
    ]]></literal>
    <justification jstring="[para(7662(a,1),6084(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7662 6084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7746">
    <literal><![CDATA[
      R(K(x,y),z,x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3985,a,7680,a)].">
      <j1 rule="hyper" parents="3985 7680"/>
    </justification>
  </clause>

  <clause id="7747">
    <literal><![CDATA[
      (K(x,y) * z) * x = T(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,5353,a(flip),b,7680,a),flip(a)].">
      <j1 rule="hyper" parents="299 5353 7680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7748">
    <literal><![CDATA[
      T(K(x \ y,x) * z,x \ y) = (y / x) \ (z * (x \ y))
    ]]></literal>
    <justification jstring="[hyper(235,a,7680,a,b,5871,a)].">
      <j1 rule="hyper" parents="235 7680 5871"/>
    </justification>
  </clause>

  <clause id="7749">
    <literal><![CDATA[
      T(K(x,y) * z,x) = K(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(235,a,7680,a,b,5697,a)].">
      <j1 rule="hyper" parents="235 7680 5697"/>
    </justification>
  </clause>

  <clause id="7750">
    <literal><![CDATA[
      (K(x,y) * (z * x)) \ (K(x,y) * z) = L(x \ 1,x,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(7680(a,1),214(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7680 214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7752">
    <literal><![CDATA[
      (x * (K(y,x) * z)) * y = K(y,x) * ((x * z) * y)
    ]]></literal>
    <justification jstring="[para(5524(a,1),7680(a,1,1))].">
      <j1 rule="para" parents="5524 7680"/>
    </justification>
  </clause>

  <clause id="7753">
    <literal><![CDATA[
      K(x,R(y,z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,6437,a(flip),b,7746,a)].">
      <j1 rule="hyper" parents="65 6437 7746"/>
    </justification>
  </clause>

  <clause id="7754">
    <literal><![CDATA[
      K(x,(y * x) / z) = K(x,y / (z / x))
    ]]></literal>
    <justification jstring="[hyper(65,a,6430,a(flip),b,7746,a)].">
      <j1 rule="hyper" parents="65 6430 7746"/>
    </justification>
  </clause>

  <clause id="7755">
    <literal><![CDATA[
      T(x,R(y,z,x)) = x * K(x,y)
    ]]></literal>
    <justification jstring="[para(7753(a,1),5083(a,2,2))].">
      <j1 rule="para" parents="7753 5083"/>
    </justification>
  </clause>

  <clause id="7756">
    <literal><![CDATA[
      K(x,K(y,R(z,u,x))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(6437(a,1),7753(a,1,2))].">
      <j1 rule="para" parents="6437 7753"/>
    </justification>
  </clause>

  <clause id="7757">
    <literal><![CDATA[
      T(x,R(y,z,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,5083,a,b,7755,a),flip(a)].">
      <j1 rule="hyper" parents="299 5083 7755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7761">
    <literal><![CDATA[
      T(x,(y * x) / z) = T(x,y / (z / x))
    ]]></literal>
    <justification jstring="[para(567(a,1),7757(a,1,2))].">
      <j1 rule="para" parents="567 7757"/>
    </justification>
  </clause>

  <clause id="7762">
    <literal><![CDATA[
      T(x,T((y * x) / z,u)) = T(x,T(y / (z / x),u))
    ]]></literal>
    <justification jstring="[para(840(a,1),7757(a,1,2))].">
      <j1 rule="para" parents="840 7757"/>
    </justification>
  </clause>

  <clause id="7768">
    <literal><![CDATA[
      K(x,K(y,T((z * x) / u,u / x))) = K(x,K(y,(u / x) \ z))
    ]]></literal>
    <justification jstring="[para(844(a,1),7756(a,1,2,2))].">
      <j1 rule="para" parents="844 7756"/>
    </justification>
  </clause>

  <clause id="7769">
    <literal><![CDATA[
      K(x,y) * ((x * z) / x) = (T(x,y) * z) / x
    ]]></literal>
    <justification jstring="[para(5103(a,1),7681(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5103 7681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7770">
    <literal><![CDATA[
      L(T(x,y),z,T(x,u)) = L(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,25,a,b,7696,a),flip(a)].">
      <j1 rule="hyper" parents="299 25 7696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7771">
    <literal><![CDATA[
      L(T(x,T(y,z)),K(x,z),z * x) = (x * z) \ ((T(x,y) * z) * x)
    ]]></literal>
    <justification jstring="[para(7708(a,1),1308(a,1,1))].">
      <j1 rule="para" parents="7708 1308"/>
    </justification>
  </clause>

  <clause id="7772">
    <literal><![CDATA[
      (T(x,y) * (x \ z)) * x = T(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[para(5056(a,2),7747(a,1,1))].">
      <j1 rule="para" parents="5056 7747"/>
    </justification>
  </clause>

  <clause id="7773">
    <literal><![CDATA[
      T(x * K(y,z),z) = T(x,z) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(6535,a,7749,a),flip(a)].">
      <j1 rule="hyper" parents="6535 7749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7774">
    <literal><![CDATA[
      K(x,y) * T(K(x,y) \ z,x) = T(z,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),7749(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 7749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7775">
    <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),7749(a,2,2))].">
      <j1 rule="para" parents="25 7749"/>
    </justification>
  </clause>

  <clause id="7776">
    <literal><![CDATA[
      x \ T(K(x,y) * z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (x \ T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(7749(a,2),5700(a,1,2))].">
      <j1 rule="para" parents="7749 5700"/>
    </justification>
  </clause>

  <clause id="7778">
    <literal><![CDATA[
      L(T(x,y),T(z,x),x) = L(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(6785,a,7770,a)].">
      <j1 rule="hyper" parents="6785 7770"/>
    </justification>
  </clause>

  <clause id="7780">
    <literal><![CDATA[
      T(x,L(T(y,z),u,y)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7770(a,1),7449(a,1,2))].">
      <j1 rule="para" parents="7770 7449"/>
    </justification>
  </clause>

  <clause id="7781">
    <literal><![CDATA[
      T(L(x,y,x) \ 1,T(x,z)) = 1 / L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(3542,a,7780,a),flip(a)].">
      <j1 rule="hyper" parents="3542 7780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7782">
    <literal><![CDATA[
      T(x * K(y,z),z) * z = T(x,z) * (z * K(y,z))
    ]]></literal>
    <justification jstring="[para(7773(a,2),7028(a,1,1))].">
      <j1 rule="para" parents="7773 7028"/>
    </justification>
  </clause>

  <clause id="7784">
    <literal><![CDATA[
      T(T(x,y) * K(z,y),K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x * K(z,y),T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(7773(a,1),7154(a,1,1))].">
      <j1 rule="para" parents="7773 7154"/>
    </justification>
  </clause>

  <clause id="7785">
    <literal><![CDATA[
      T(x * K(y,z),y) = T(x,y) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(807,a,7774,a),flip(a)].">
      <j1 rule="hyper" parents="807 7774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7786">
    <literal><![CDATA[
      (x \ K(y,z)) * T((x \ K(y,z)) \ u,y) = x \ T(x * u,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,7774,a(flip),b,1158,a),flip(a)].">
      <j1 rule="hyper" parents="119 7774 1158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7787">
    <literal><![CDATA[
      T(K(x,y) * z,y) = K(x,y) * T(z,y)
    ]]></literal>
    <justification jstring="[para(7774(a,1),6457(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7774 6457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7788">
    <literal><![CDATA[
      x \ (y * T(x,z)) = T(y,x) * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(6922,a,7785,a)].">
      <j1 rule="hyper" parents="6922 7785"/>
    </justification>
  </clause>

  <clause id="7789">
    <literal><![CDATA[
      (T(x,y) / y) * T(y,z) = T(x * K(y,z),y)
    ]]></literal>
    <justification jstring="[hyper(299,a,6869,a,b,7785,a)].">
      <j1 rule="hyper" parents="299 6869 7785"/>
    </justification>
  </clause>

  <clause id="7791">
    <literal><![CDATA[
      x \ T(x * K(y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * K(y,z) = u
    ]]></literal>
    <justification jstring="[para(7785(a,2),5360(a,1,2))].">
      <j1 rule="para" parents="7785 5360"/>
    </justification>
  </clause>

  <clause id="7792">
    <literal><![CDATA[
      T(x * K(y,z),y) * y = T(x,y) * T(y,z)
    ]]></literal>
    <justification jstring="[para(7785(a,2),6912(a,1,1))].">
      <j1 rule="para" parents="7785 6912"/>
    </justification>
  </clause>

  <clause id="7793">
    <literal><![CDATA[
      K(x,y) * T(K(x * y,x),y) = T(x \ R(x,y,x),y)
    ]]></literal>
    <justification jstring="[para(5587(a,1),7787(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5587 7787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7795">
    <literal><![CDATA[
      (T(x,x \ y) * z) \ (z * ((x \ y) \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,T(x,y)) = u
    ]]></literal>
    <justification jstring="[para(709(a,2),7485(a,1))].">
      <j1 rule="para" parents="709 7485"/>
    </justification>
  </clause>

  <clause id="7797">
    <literal><![CDATA[
      K(x,T(y * z,y \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y * z,z)) = u
    ]]></literal>
    <justification jstring="[para(4642(a,1),7485(a,1,2))].">
      <j1 rule="para" parents="4642 7485"/>
    </justification>
  </clause>

  <clause id="7800">
    <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(5411(a,1),7526(a,1,2))].">
      <j1 rule="para" parents="5411 7526"/>
    </justification>
  </clause>

  <clause id="7801">
    <literal><![CDATA[
      K(x / y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(10(a,1),7654(a,1,1,1))].">
      <j1 rule="para" parents="10 7654"/>
    </justification>
  </clause>

  <clause id="7802">
    <literal><![CDATA[
      K(x,T(y,z / L(x,u,w))) = K(x,T(y,L(x,u,w) \ z))
    ]]></literal>
    <justification jstring="[para(109(a,1),7657(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="109 7657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7803">
    <literal><![CDATA[
      K(x * y,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7354(a,2),7706(a,1))].">
      <j1 rule="para" parents="7354 7706"/>
    </justification>
  </clause>

  <clause id="7806">
    <literal><![CDATA[
      T(x * y,T(z,y \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x * y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(7040(a,1),7730(a,1,2))].">
      <j1 rule="para" parents="7040 7730"/>
    </justification>
  </clause>

  <clause id="7808">
    <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(176(a,1),7801(a,1,2))].">
      <j1 rule="para" parents="176 7801"/>
    </justification>
  </clause>

  <clause id="7809">
    <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(3460(a,1),7801(a,1,1))].">
      <j1 rule="para" parents="3460 7801"/>
    </justification>
  </clause>

  <clause id="7810">
    <literal><![CDATA[
      K(x,L(y,z / y,u)) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,6350,a(flip),b,7434,a),flip(a)].">
      <j1 rule="hyper" parents="299 6350 7434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7811">
    <literal><![CDATA[
      K(x,L(y,z / y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,y),z,u) = w
    ]]></literal>
    <justification jstring="[para(7434(a,2),6390(a,1))].">
      <j1 rule="para" parents="7434 6390"/>
    </justification>
  </clause>

  <clause id="7812">
    <literal><![CDATA[
      L(K(x,y),z,y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,7473,a(flip),b,7810,a),flip(a)].">
      <j1 rule="hyper" parents="65 7473 7810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7813">
    <literal><![CDATA[
      L(K(x,y),z * y,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(11(a,1),7810(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 7810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7814">
    <literal><![CDATA[
      L(K(x,y \ z),z,u) = K(x,L(y \ z,y,u))
    ]]></literal>
    <justification jstring="[para(76(a,1),7810(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="76 7810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7815">
    <literal><![CDATA[
      L(K(x,y),z * T(y,u),w) = K(x,L(y,z * K(y,u),w))
    ]]></literal>
    <justification jstring="[para(6906(a,1),7810(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6906 7810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7816">
    <literal><![CDATA[
      L(K(x,y),z,K(u,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7672(a,1),7810(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7672 7810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7817">
    <literal><![CDATA[
      L(K(x,y),z,K(y,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7675(a,1),7810(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7675 7810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7818">
    <literal><![CDATA[
      L(K(x,T(y,z)),u,K(y,w)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7679(a,1),7810(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7679 7810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7820">
    <literal><![CDATA[
      K(L(x,y,z),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,7433,a(flip),b,7812,a)].">
      <j1 rule="hyper" parents="65 7433 7812"/>
    </justification>
  </clause>

  <clause id="7821">
    <literal><![CDATA[
      K((x \ y) \ z,x) = K(y \ (x * z),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,7421,a(flip),b,7812,a),flip(a)].">
      <j1 rule="hyper" parents="65 7421 7812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7822">
    <literal><![CDATA[
      (x * y) * K(z,x) = x * (y * K(z,x))
    ]]></literal>
    <justification jstring="[para(7812(a,1),94(a,1,2))].">
      <j1 rule="para" parents="7812 94"/>
    </justification>
  </clause>

  <clause id="7826">
    <literal><![CDATA[
      K(L(L(x,y,z),u,w),z) = K(L(x,u,w),z)
    ]]></literal>
    <justification jstring="[para(30(a,1),7820(a,1,1))].">
      <j1 rule="para" parents="30 7820"/>
    </justification>
  </clause>

  <clause id="7827">
    <literal><![CDATA[
      K((x * y) \ z,x) = K(y \ (x \ z),x)
    ]]></literal>
    <justification jstring="[para(281(a,1),7820(a,1,1))].">
      <j1 rule="para" parents="281 7820"/>
    </justification>
  </clause>

  <clause id="7829">
    <literal><![CDATA[
      K(L(x,y,z \ 1),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(2470(a,2),7820(a,1,1))].">
      <j1 rule="para" parents="2470 7820"/>
    </justification>
  </clause>

  <clause id="7830">
    <literal><![CDATA[
      T(x * K(y,x),L(y,z,x)) = x
    ]]></literal>
    <justification jstring="[para(7820(a,1),5053(a,1,1,2))].">
      <j1 rule="para" parents="7820 5053"/>
    </justification>
  </clause>

  <clause id="7831">
    <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(7820(a,1),5831(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="7820 5831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7832">
    <literal><![CDATA[
      T(x * K(y,x),(x \ 1) * y) = R(x,x \ L(y,x,x),x)
    ]]></literal>
    <justification jstring="[para(7820(a,1),5792(a,1,1,2))].">
      <j1 rule="para" parents="7820 5792"/>
    </justification>
  </clause>

  <clause id="7833">
    <literal><![CDATA[
      K((x * (y / x)) \ (y * z),y) = K(K(x \ y,x) * z,y)
    ]]></literal>
    <justification jstring="[para(6548(a,1),7820(a,1,1))].">
      <j1 rule="para" parents="6548 7820"/>
    </justification>
  </clause>

  <clause id="7834">
    <literal><![CDATA[
      K(L(x,y,K(z,u)),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,7433,a(flip),b,7816,a)].">
      <j1 rule="hyper" parents="65 7433 7816"/>
    </justification>
  </clause>

  <clause id="7835">
    <literal><![CDATA[
      (K(x,y) * z) * K(u,y) = K(x,y) * (z * K(u,y))
    ]]></literal>
    <justification jstring="[para(7816(a,1),94(a,1,2))].">
      <j1 rule="para" parents="7816 94"/>
    </justification>
  </clause>

  <clause id="7836">
    <literal><![CDATA[
      K((K(x,y) * z) \ (K(x,y) * u),x) = K(z \ u,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,7419,a(flip),b,7817,a)].">
      <j1 rule="hyper" parents="65 7419 7817"/>
    </justification>
  </clause>

  <clause id="7837">
    <literal><![CDATA[
      K(((x \ 1) * y) \ (z * (x \ 1)),x) = K(y \ T(z,x \ 1),x)
    ]]></literal>
    <justification jstring="[para(526(a,1),7829(a,1,1))].">
      <j1 rule="para" parents="526 7829"/>
    </justification>
  </clause>

  <clause id="7838">
    <literal><![CDATA[
      T(x,L(y,z,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(7830(a,1),5125(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7830 5125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7839">
    <literal><![CDATA[
      T(x,L(y,z,x)) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,5083,a(flip),b,7838,a),flip(a)].">
      <j1 rule="hyper" parents="299 5083 7838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7840">
    <literal><![CDATA[
      T(x,(x * y) \ z) = T(x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[para(281(a,1),7838(a,1,2))].">
      <j1 rule="para" parents="281 7838"/>
    </justification>
  </clause>

  <clause id="7841">
    <literal><![CDATA[
      T(x,(x \ y) \ z) = T(x,y \ (x * z))
    ]]></literal>
    <justification jstring="[para(520(a,1),7838(a,1,2)),flip(a)].">
      <j1 rule="para" parents="520 7838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7842">
    <literal><![CDATA[
      T(x,L(y,z,K(u,x))) = (K(y,x) / x) \ 1
    ]]></literal>
    <justification jstring="[para(7834(a,1),5120(a,2,1,1))].">
      <j1 rule="para" parents="7834 5120"/>
    </justification>
  </clause>

  <clause id="7843">
    <literal><![CDATA[
      K(x,L(y,z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5154,a,7839,a)].">
      <j1 rule="hyper" parents="5154 7839"/>
    </justification>
  </clause>

  <clause id="7844">
    <literal><![CDATA[
      K(x,L(L(y,z,x),u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(30(a,1),7843(a,1,2))].">
      <j1 rule="para" parents="30 7843"/>
    </justification>
  </clause>

  <clause id="7845">
    <literal><![CDATA[
      K(x,(x * y) \ z) = K(x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[para(281(a,1),7843(a,1,2))].">
      <j1 rule="para" parents="281 7843"/>
    </justification>
  </clause>

  <clause id="7846">
    <literal><![CDATA[
      K(x,(x \ y) \ z) = K(x,y \ (x * z))
    ]]></literal>
    <justification jstring="[para(520(a,1),7843(a,1,2)),flip(a)].">
      <j1 rule="para" parents="520 7843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7847">
    <literal><![CDATA[
      K(x,T((x \ y) \ z,u)) = K(x,T(y \ (x * z),u))
    ]]></literal>
    <justification jstring="[para(822(a,1),7843(a,1,2)),flip(a)].">
      <j1 rule="para" parents="822 7843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7850">
    <literal><![CDATA[
      K(L(x,y,z),L(u,w,x)) = L(K(x,u),y * x,z)
    ]]></literal>
    <justification jstring="[para(7843(a,1),7433(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7843 7433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7851">
    <literal><![CDATA[
      K(x,L(1 / y,y,z)) = K(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(2567,a,7813,a),flip(a)].">
      <j1 rule="hyper" parents="2567 7813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7852">
    <literal><![CDATA[
      K(x,L(y,y,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(497,a,7813,a),flip(a)].">
      <j1 rule="hyper" parents="497 7813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7853">
    <literal><![CDATA[
      K(x,L(y,z,K(x,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,7684,a(flip),b,7813,a),flip(a)].">
      <j1 rule="hyper" parents="65 7684 7813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7854">
    <literal><![CDATA[
      K(x,L(y,z,K(u,x))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,7677,a(flip),b,7813,a),flip(a)].">
      <j1 rule="hyper" parents="65 7677 7813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7855">
    <literal><![CDATA[
      K(x,L(y,z,T(x,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,7357,a(flip),b,7813,a),flip(a)].">
      <j1 rule="hyper" parents="65 7357 7813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7856">
    <literal><![CDATA[
      K(x,L(y,z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7813(a,1),7087(a,1))].">
      <j1 rule="para" parents="7813 7087"/>
    </justification>
  </clause>

  <clause id="7857">
    <literal><![CDATA[
      K(x,(K(y,x) * z) \ u) = K(x,z \ (K(x,y) * u))
    ]]></literal>
    <justification jstring="[para(5458(a,1),7853(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5458 7853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7858">
    <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),7854(a,1,2))].">
      <j1 rule="para" parents="30 7854"/>
    </justification>
  </clause>

  <clause id="7859">
    <literal><![CDATA[
      K(x,T(L(y,z,T(x,u)),w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(25(a,1),7855(a,1,2))].">
      <j1 rule="para" parents="25 7855"/>
    </justification>
  </clause>

  <clause id="7860">
    <literal><![CDATA[
      K(x,(T(x,y) * z) \ u) = K(x,z \ (T(x,y) \ u))
    ]]></literal>
    <justification jstring="[para(281(a,1),7855(a,1,2))].">
      <j1 rule="para" parents="281 7855"/>
    </justification>
  </clause>

  <clause id="7862">
    <literal><![CDATA[
      K(x,(x * y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(281(a,1),7856(a,1,2))].">
      <j1 rule="para" parents="281 7856"/>
    </justification>
  </clause>

  <clause id="7864">
    <literal><![CDATA[
      K(x,L(y,z,x \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(2470(a,2),7856(a,1,2))].">
      <j1 rule="para" parents="2470 7856"/>
    </justification>
  </clause>

  <clause id="7865">
    <literal><![CDATA[
      K(x,(y * (x / y)) \ (x * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y \ x,y) * z) = u
    ]]></literal>
    <justification jstring="[para(6548(a,1),7856(a,1,2))].">
      <j1 rule="para" parents="6548 7856"/>
    </justification>
  </clause>

  <clause id="7866">
    <literal><![CDATA[
      K((x \ y) \ (x \ z),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),7821(a,2,1,2))].">
      <j1 rule="para" parents="10 7821"/>
    </justification>
  </clause>

  <clause id="7867">
    <literal><![CDATA[
      L(x * K(y \ (x * z),x),u,w) / L(x,u,w) = K((x \ y) \ z,L(x,u,w))
    ]]></literal>
    <justification jstring="[para(7821(a,1),5827(a,1,1,1,2))].">
      <j1 rule="para" parents="7821 5827"/>
    </justification>
  </clause>

  <clause id="7868">
    <literal><![CDATA[
      R(x,y,K(z,x)) = x
    ]]></literal>
    <justification jstring="[hyper(3985,a,7822,a)].">
      <j1 rule="hyper" parents="3985 7822"/>
    </justification>
  </clause>

  <clause id="7869">
    <literal><![CDATA[
      x \ (y * K(z,x)) = (x \ y) * K(z,x)
    ]]></literal>
    <justification jstring="[hyper(1020,a,7822,a)].">
      <j1 rule="hyper" parents="1020 7822"/>
    </justification>
  </clause>

  <clause id="7871">
    <literal><![CDATA[
      R(x,y,K(z,T(x,u))) = x
    ]]></literal>
    <justification jstring="[hyper(149,a,7868,a(flip))].">
      <j1 rule="hyper" parents="149 7868"/>
    </justification>
  </clause>

  <clause id="7873">
    <literal><![CDATA[
      (T(x,y) * z) * K(u,x) = T(x,y) * (z * K(u,x))
    ]]></literal>
    <justification jstring="[para(7868(a,1),541(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7868 541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7874">
    <literal><![CDATA[
      R(x,y,T(K(z,x),u)) = x
    ]]></literal>
    <justification jstring="[para(2169(a,1),7868(a,1,3))].">
      <j1 rule="para" parents="2169 7868"/>
    </justification>
  </clause>

  <clause id="7875">
    <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(7871(a,1),542(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7871 542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7876">
    <literal><![CDATA[
      x \ (y * T(K(z,x),u)) = (x \ y) * T(K(z,x),u)
    ]]></literal>
    <justification jstring="[para(7874(a,1),580(a,1,1))].">
      <j1 rule="para" parents="7874 580"/>
    </justification>
  </clause>

  <clause id="7877">
    <literal><![CDATA[
      K((x * y) \ z,y) = K(x \ (y \ z),y)
    ]]></literal>
    <justification jstring="[hyper(65,a,7344,a,b,7827,a)].">
      <j1 rule="hyper" parents="65 7344 7827"/>
    </justification>
  </clause>

  <clause id="7878">
    <literal><![CDATA[
      K((x / (y \ 1)) \ z,x) = K(y \ (x \ z),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,7339,a,b,7827,a)].">
      <j1 rule="hyper" parents="65 7339 7827"/>
    </justification>
  </clause>

  <clause id="7879">
    <literal><![CDATA[
      ((x \ (1 / y)) * x) * y = K(y \ (x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,5229,a,b,7827,a)].">
      <j1 rule="hyper" parents="65 5229 7827"/>
    </justification>
  </clause>

  <clause id="7880">
    <literal><![CDATA[
      x * K(y \ (z \ x),z) = y * ((z \ (y \ x)) * z)
    ]]></literal>
    <justification jstring="[para(7827(a,1),7018(a,1,2))].">
      <j1 rule="para" parents="7827 7018"/>
    </justification>
  </clause>

  <clause id="7881">
    <literal><![CDATA[
      T(x,(x \ y) \ (x \ z)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),7840(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 7840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7882">
    <literal><![CDATA[
      T(x,T(y,x) \ (x \ z)) = T(x,(y * x) \ z)
    ]]></literal>
    <justification jstring="[para(107(a,1),7840(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="107 7840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7883">
    <literal><![CDATA[
      K(x * y,T(x,y \ (x \ z))) = K(x * y,T(x,z))
    ]]></literal>
    <justification jstring="[para(7840(a,1),7623(a,1,2))].">
      <j1 rule="para" parents="7840 7623"/>
    </justification>
  </clause>

  <clause id="7885">
    <literal><![CDATA[
      K(x,(y * x) \ z) = K(x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,7347,a,b,7845,a)].">
      <j1 rule="hyper" parents="65 7347 7845"/>
    </justification>
  </clause>

  <clause id="7886">
    <literal><![CDATA[
      K(x,(x \ y) \ (x \ z)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),7845(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 7845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7887">
    <literal><![CDATA[
      K(x,((x \ 1) * y) \ (x \ z)) = K(x,L(y,x \ 1,x) \ z)
    ]]></literal>
    <justification jstring="[para(252(a,1),7845(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="252 7845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7888">
    <literal><![CDATA[
      (x * ((y / z) / x)) * z = y * K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[para(7845(a,1),7119(a,2,2))].">
      <j1 rule="para" parents="7845 7119"/>
    </justification>
  </clause>

  <clause id="7889">
    <literal><![CDATA[
      T(x / T(y,z),y) = (y \ x) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(7235,a,7869,a)].">
      <j1 rule="hyper" parents="7235 7869"/>
    </justification>
  </clause>

  <clause id="7890">
    <literal><![CDATA[
      (x \ y) * K(z,x) != u
    ]]></literal>
    <literal><![CDATA[
      T(y / T(x,z),x) = u
    ]]></literal>
    <justification jstring="[para(7869(a,1),7235(a,1))].">
      <j1 rule="para" parents="7869 7235"/>
    </justification>
  </clause>

  <clause id="7891">
    <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(7877(a,1),5827(a,1,1,1,2))].">
      <j1 rule="para" parents="7877 5827"/>
    </justification>
  </clause>

  <clause id="7892">
    <literal><![CDATA[
      (x * ((y \ (x \ z)) * y)) \ z = K(y,x \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,7345,a,b,7885,a)].">
      <j1 rule="hyper" parents="65 7345 7885"/>
    </justification>
  </clause>

  <clause id="7893">
    <literal><![CDATA[
      x * (y * ((x \ 1) / y)) = K(y,x \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(65,a,6221,a,b,7885,a)].">
      <j1 rule="hyper" parents="65 6221 7885"/>
    </justification>
  </clause>

  <clause id="7894">
    <literal><![CDATA[
      K(x,y \ (x \ (y * (x * z)))) = K(x,L(z,x,y))
    ]]></literal>
    <justification jstring="[para(18(a,2),7885(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18 7885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7895">
    <literal><![CDATA[
      K(x,L(x \ y,x,z)) = K(x,z \ (x \ (z * y)))
    ]]></literal>
    <justification jstring="[para(96(a,2),7885(a,1,2))].">
      <j1 rule="para" parents="96 7885"/>
    </justification>
  </clause>

  <clause id="7896">
    <literal><![CDATA[
      K(x,y \ (x \ (y * (z * x)))) = K(x,L(T(z,x),x,y))
    ]]></literal>
    <justification jstring="[para(230(a,1),7885(a,1,2)),flip(a)].">
      <j1 rule="para" parents="230 7885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7897">
    <literal><![CDATA[
      (K(x,y) * z) * K(u,T(x,w)) = K(x,y) * (z * K(u,T(x,w)))
    ]]></literal>
    <justification jstring="[para(7818(a,1),94(a,1,2))].">
      <j1 rule="para" parents="7818 94"/>
    </justification>
  </clause>

  <clause id="7899">
    <literal><![CDATA[
      T(x,L(y,z,K(u,x))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,5120,a,b,7842,a),flip(a)].">
      <j1 rule="hyper" parents="299 5120 7842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7900">
    <literal><![CDATA[
      T(x,(K(y,x) * z) \ (K(y,x) * u)) = T(x,z \ u)
    ]]></literal>
    <justification jstring="[para(96(a,1),7899(a,1,2))].">
      <j1 rule="para" parents="96 7899"/>
    </justification>
  </clause>

  <clause id="7901">
    <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(299,a,7067,a,b,7471,a)].">
      <j1 rule="hyper" parents="299 7067 7471"/>
    </justification>
  </clause>

  <clause id="7902">
    <literal><![CDATA[
      R(x * K(y,x),z,x) = K(y,x) * R(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,3623,a(flip),b,7471,a),flip(a)].">
      <j1 rule="hyper" parents="299 3623 7471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7903">
    <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(6011(a,1),7471(a,2,2))].">
      <j1 rule="para" parents="6011 7471"/>
    </justification>
  </clause>

  <clause id="7904">
    <literal><![CDATA[
      T(L(K(x,y),z,u),x * w) = L(K(x,T(y,w)),z,u)
    ]]></literal>
    <justification jstring="[para(7645(a,1),7505(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7645 7505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7905">
    <literal><![CDATA[
      T(x,y) != K(z,L(T(u,y),w,v5))
    ]]></literal>
    <literal><![CDATA[
      K(z,L(u,w,v5)) = x
    ]]></literal>
    <justification jstring="[para(7506(a,2),51(a,1)),flip(a)].">
      <j1 rule="para" parents="7506 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7906">
    <literal><![CDATA[
      K(x,R(K(y,x) * z,u,w)) = K(x,R(z * K(y,x),u,w))
    ]]></literal>
    <justification jstring="[para(7199(a,1),7529(a,1,2,1))].">
      <j1 rule="para" parents="7199 7529"/>
    </justification>
  </clause>

  <clause id="7907">
    <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(176(a,1),7552(a,2,2))].">
      <j1 rule="para" parents="176 7552"/>
    </justification>
  </clause>

  <clause id="7908">
    <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(1925(a,1),7552(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1925 7552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7909">
    <literal><![CDATA[
      K(R(T(x,K(y,z)),u,w),z) = K(R(x,u,w),z)
    ]]></literal>
    <justification jstring="[para(3612(a,1),7552(a,2,2))].">
      <j1 rule="para" parents="3612 7552"/>
    </justification>
  </clause>

  <clause id="7910">
    <literal><![CDATA[
      K(x,y) * T(x,K(y,z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,7141,a(flip),b,7591,a),flip(a)].">
      <j1 rule="hyper" parents="299 7141 7591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7911">
    <literal><![CDATA[
      K(x,K(y,z)) * T(x,y) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(5702,a,7910,a)].">
      <j1 rule="hyper" parents="5702 7910"/>
    </justification>
  </clause>

  <clause id="7912">
    <literal><![CDATA[
      K(x,T(y \ 1,y \ z)) = K(x,T(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),7597(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 7597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7913">
    <literal><![CDATA[
      (x * y) \ T(x * y,K(y,z)) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[para(7400(a,2),7613(a,1,2))].">
      <j1 rule="para" parents="7400 7613"/>
    </justification>
  </clause>

  <clause id="7914">
    <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(4281(a,1),7618(a,1,2))].">
      <j1 rule="para" parents="4281 7618"/>
    </justification>
  </clause>

  <clause id="7915">
    <literal><![CDATA[
      T(x / y,T(z,y)) != (x / y) * u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(7627(a,1),45(a,1))].">
      <j1 rule="para" parents="7627 45"/>
    </justification>
  </clause>

  <clause id="7916">
    <literal><![CDATA[
      ((x \ ((1 / x) \ y)) / y) * K(a(x,x,x \ (x \ y)),z) = T((x \ ((1 / x) \ y)) / y,T(z,y))
    ]]></literal>
    <justification jstring="[para(1667(a,2),7627(a,1,2,1))].">
      <j1 rule="para" parents="1667 7627"/>
    </justification>
  </clause>

  <clause id="7917">
    <literal><![CDATA[
      K(x * L(y,z,u),T(y,x)) = K(x * L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(65,a,6136,a(flip),b,7648,a),flip(a)].">
      <j1 rule="hyper" parents="65 6136 7648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7918">
    <literal><![CDATA[
      K(x,T(y / (x * z),z)) = K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(299,a,7845,a(flip),b,7650,a),flip(a)].">
      <j1 rule="hyper" parents="299 7845 7650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7920">
    <literal><![CDATA[
      T(x,y) / (y \ 1) = x / (y \ K(y,x))
    ]]></literal>
    <justification jstring="[para(5083(a,2),7660(a,1,1))].">
      <j1 rule="para" parents="5083 7660"/>
    </justification>
  </clause>

  <clause id="7921">
    <literal><![CDATA[
      (T(x,y) / (y \ 1)) \ x = y \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(186,a,7920,a(flip))].">
      <j1 rule="hyper" parents="186 7920"/>
    </justification>
  </clause>

  <clause id="7922">
    <literal><![CDATA[
      (T(x / y,y) / (y \ 1)) \ (x / y) = y \ K(y,y \ x)
    ]]></literal>
    <justification jstring="[para(5205(a,1),7921(a,2,2))].">
      <j1 rule="para" parents="5205 7921"/>
    </justification>
  </clause>

  <clause id="7923">
    <literal><![CDATA[
      K(x,y) * (x \ L(x,z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      x \ L(T(x,y),z,x) = u
    ]]></literal>
    <justification jstring="[para(7663(a,1),5509(a,1,2))].">
      <j1 rule="para" parents="7663 5509"/>
    </justification>
  </clause>

  <clause id="7924">
    <literal><![CDATA[
      (x / R(y,z,y)) * y != y * u
    ]]></literal>
    <literal><![CDATA[
      R(y,z,y) \ x = u
    ]]></literal>
    <justification jstring="[para(7668(a,2),45(a,1))].">
      <j1 rule="para" parents="7668 45"/>
    </justification>
  </clause>

  <clause id="7925">
    <literal><![CDATA[
      L(x \ y,z,T(x \ y,u)) = L(x \ y,z,y / x)
    ]]></literal>
    <justification jstring="[hyper(299,a,7691,a,b,7695,a)].">
      <j1 rule="hyper" parents="299 7691 7695"/>
    </justification>
  </clause>

  <clause id="7926">
    <literal><![CDATA[
      T(x,T(y \ 1,z)) = T(x,T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(38,a,5033,a(flip),b,7699,a),flip(a)].">
      <j1 rule="hyper" parents="38 5033 7699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7927">
    <literal><![CDATA[
      T(x,T(y \ 1,z)) = T(x,(y * z) \ z)
    ]]></literal>
    <justification jstring="[hyper(299,a,7043,a(flip),b,7926,a),flip(a)].">
      <j1 rule="hyper" parents="299 7043 7926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7928">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) = K(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(36,a,7507,a,b,7721,a)].">
      <j1 rule="hyper" parents="36 7507 7721"/>
    </justification>
  </clause>

  <clause id="7929">
    <literal><![CDATA[
      K(x,(y * z) \ z) = K(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,7700,a(flip),b,7928,a)].">
      <j1 rule="hyper" parents="65 7700 7928"/>
    </justification>
  </clause>

  <clause id="7930">
    <literal><![CDATA[
      K(x,T((y / z) \ 1,y)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(79(a,1),7928(a,2,2,2))].">
      <j1 rule="para" parents="79 7928"/>
    </justification>
  </clause>

  <clause id="7931">
    <literal><![CDATA[
      x * K(x,y \ (z \ y)) = T(x,(z * y) \ y)
    ]]></literal>
    <justification jstring="[para(7929(a,1),5083(a,2,2)),flip(a)].">
      <j1 rule="para" parents="7929 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7932">
    <literal><![CDATA[
      K((x / y) \ z,y / x) = K((y \ x) \ z,y / x)
    ]]></literal>
    <justification jstring="[para(5918(a,1),7739(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5918 7739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7933">
    <literal><![CDATA[
      K(x * (y / z),y \ z) = K(x * (z \ y),y \ z)
    ]]></literal>
    <justification jstring="[para(6970(a,1),7742(a,1,1))].">
      <j1 rule="para" parents="6970 7742"/>
    </justification>
  </clause>

  <clause id="7934">
    <literal><![CDATA[
      (K(x,y) * z) * K(x,z) = (T(x,y) * z) / x
    ]]></literal>
    <justification jstring="[hyper(7168,a,7769,a)].">
      <j1 rule="hyper" parents="7168 7769"/>
    </justification>
  </clause>

  <clause id="7935">
    <literal><![CDATA[
      K(x,y) * (z * K(x,z)) = (T(x,y) * z) / x
    ]]></literal>
    <justification jstring="[hyper(65,a,5237,a(flip),b,7769,a)].">
      <j1 rule="hyper" parents="65 5237 7769"/>
    </justification>
  </clause>

  <clause id="7936">
    <literal><![CDATA[
      T(x,y) * ((x * z) / x) = x * ((T(x,y) * z) / x)
    ]]></literal>
    <justification jstring="[para(7769(a,1),5055(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7769 5055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7937">
    <literal><![CDATA[
      T(T(x,y) * (x \ z),x) = T(x,y) * (x \ T(z,x))
    ]]></literal>
    <justification jstring="[hyper(235,a,7772,a,b,1190,a)].">
      <j1 rule="hyper" parents="235 7772 1190"/>
    </justification>
  </clause>

  <clause id="7939">
    <literal><![CDATA[
      T(x,T(y,z)) != 1 / L(y,u,y)
    ]]></literal>
    <literal><![CDATA[
      L(y,u,y) \ 1 = x
    ]]></literal>
    <justification jstring="[para(7781(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="7781 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7940">
    <literal><![CDATA[
      T((1 / ((x * y) \ x)) * K(y,z),y) = ((1 / ((x * y) \ x)) / y) * T(y,z)
    ]]></literal>
    <justification jstring="[para(5474(a,1),7789(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5474 7789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7941">
    <literal><![CDATA[
      K(x,L(y \ z,y,K(z,u))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(4572,a,7814,a),flip(a)].">
      <j1 rule="hyper" parents="4572 7814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7942">
    <literal><![CDATA[
      L(K(x,y \ z),z,u) = K(x,(u * y) \ (u * z))
    ]]></literal>
    <justification jstring="[para(96(a,1),7814(a,2,2))].">
      <j1 rule="para" parents="96 7814"/>
    </justification>
  </clause>

  <clause id="7943">
    <literal><![CDATA[
      L(K(x,y \ (z \ u)),z \ u,z) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[para(281(a,1),7814(a,2,2))].">
      <j1 rule="para" parents="281 7814"/>
    </justification>
  </clause>

  <clause id="7944">
    <literal><![CDATA[
      L(K(x,(y \ z) \ u),u,y) = K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[para(520(a,1),7814(a,2,2))].">
      <j1 rule="para" parents="520 7814"/>
    </justification>
  </clause>

  <clause id="7945">
    <literal><![CDATA[
      L(K(x,y \ z),z,y \ 1) = K(x,(1 / y) * z)
    ]]></literal>
    <justification jstring="[para(2474(a,1),7814(a,2,2))].">
      <j1 rule="para" parents="2474 7814"/>
    </justification>
  </clause>

  <clause id="7946">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ T(y,z)) = K(x,u \ y)
    ]]></literal>
    <justification jstring="[para(5168(a,1),7941(a,1,2))].">
      <j1 rule="para" parents="5168 7941"/>
    </justification>
  </clause>

  <clause id="7947">
    <literal><![CDATA[
      K(((x \ 1) \ y) \ z,y) = K(x \ (y \ z),y)
    ]]></literal>
    <justification jstring="[hyper(65,a,7369,a(flip),b,7878,a)].">
      <j1 rule="hyper" parents="65 7369 7878"/>
    </justification>
  </clause>

  <clause id="7948">
    <literal><![CDATA[
      (x * y) * ((z \ ((x * y) \ y)) * z) = K(x \ (z \ 1),z) * y
    ]]></literal>
    <justification jstring="[para(7879(a,1),3921(a,2,1))].">
      <j1 rule="para" parents="7879 3921"/>
    </justification>
  </clause>

  <clause id="7949">
    <literal><![CDATA[
      (x * y) * (z * (((x * y) \ x) / z)) = x * K(z,y \ (z \ 1))
    ]]></literal>
    <justification jstring="[para(7893(a,1),3943(a,2,2))].">
      <j1 rule="para" parents="7893 3943"/>
    </justification>
  </clause>

  <clause id="7950">
    <literal><![CDATA[
      K(R(K(x,y) * z,u,w),y) = K(R(z * K(x,y),u,w),y)
    ]]></literal>
    <justification jstring="[para(7279(a,1),7909(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7279 7909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7951">
    <literal><![CDATA[
      K(x * y,K(y,z)) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(5155,a,7913,a)].">
      <j1 rule="hyper" parents="5155 7913"/>
    </justification>
  </clause>

  <clause id="7952">
    <literal><![CDATA[
      K(x,K(y,z)) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(7803,a,7951,a)].">
      <j1 rule="hyper" parents="7803 7951"/>
    </justification>
  </clause>

  <clause id="7953">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(y,x)) = u
    ]]></literal>
    <justification jstring="[para(7951(a,1),7803(a,1))].">
      <j1 rule="para" parents="7951 7803"/>
    </justification>
  </clause>

  <clause id="7954">
    <literal><![CDATA[
      K(K(x,y),z) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(6248,a,7952,a)].">
      <j1 rule="hyper" parents="6248 7952"/>
    </justification>
  </clause>

  <clause id="7955">
    <literal><![CDATA[
      K(x,K(y,z * y)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,7951,a(flip),b,7952,a),flip(a)].">
      <j1 rule="hyper" parents="299 7951 7952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7956">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,K(x,z)) = z * K(x,y)
    ]]></literal>
    <justification jstring="[para(7952(a,1),88(a,1,2))].">
      <j1 rule="para" parents="7952 88"/>
    </justification>
  </clause>

  <clause id="7957">
    <literal><![CDATA[
      K(x,K(y,z)) \ K(y,x) = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[para(7952(a,1),5050(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7952 5050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7958">
    <literal><![CDATA[
      x * K(y,K(z,x)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(7952(a,1),5083(a,2,2)),flip(a)].">
      <j1 rule="para" parents="7952 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7959">
    <literal><![CDATA[
      K(x,K(y,z)) * z = T(z,K(y,x))
    ]]></literal>
    <justification jstring="[para(7952(a,1),5096(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7952 5096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7960">
    <literal><![CDATA[
      K(x,K(y,z)) \ K(y,x) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(y,x),z) = u
    ]]></literal>
    <justification jstring="[para(7952(a,1),5063(a,1,1))].">
      <j1 rule="para" parents="7952 5063"/>
    </justification>
  </clause>

  <clause id="7962">
    <literal><![CDATA[
      K(x,K(y,z)) \ 1 = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(7952(a,1),6249(a,1,1))].">
      <j1 rule="para" parents="7952 6249"/>
    </justification>
  </clause>

  <clause id="7964">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(7952(a,1),6246(a,1,2))].">
      <j1 rule="para" parents="7952 6246"/>
    </justification>
  </clause>

  <clause id="7965">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,y) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(7952(a,1),6251(a,1,1))].">
      <j1 rule="para" parents="7952 6251"/>
    </justification>
  </clause>

  <clause id="7966">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,y) * u) = T(K(x,y),z) * u
    ]]></literal>
    <justification jstring="[para(7952(a,1),6253(a,1,1))].">
      <j1 rule="para" parents="7952 6253"/>
    </justification>
  </clause>

  <clause id="7967">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7952(a,1),7496(a,1,2))].">
      <j1 rule="para" parents="7952 7496"/>
    </justification>
  </clause>

  <clause id="7968">
    <literal><![CDATA[
      K(x,K(y,z)) * T(z,y) = T(z,T(y,x))
    ]]></literal>
    <justification jstring="[para(7952(a,1),7911(a,1,1))].">
      <j1 rule="para" parents="7952 7911"/>
    </justification>
  </clause>

  <clause id="7969">
    <literal><![CDATA[
      K(K(L(x \ 1,y,z) \ 1,u),w) = L(K(x,K(u,w)),y,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,6341,a(flip),b,7954,a),flip(a)].">
      <j1 rule="hyper" parents="299 6341 7954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7970">
    <literal><![CDATA[
      K(K(R(x \ 1,y,z) \ 1,u),w) = R(K(x,K(u,w)),y,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,6011,a(flip),b,7954,a),flip(a)].">
      <j1 rule="hyper" parents="299 6011 7954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7971">
    <literal><![CDATA[
      R(K(K(x,y),z \ 1),u,w) = K(x,K(y,R(z,u,w) \ 1))
    ]]></literal>
    <justification jstring="[hyper(65,a,6209,a,b,7954,a)].">
      <j1 rule="hyper" parents="65 6209 7954"/>
    </justification>
  </clause>

  <clause id="7972">
    <literal><![CDATA[
      T(x,K(y,z)) * K(y,K(z,x)) = x
    ]]></literal>
    <justification jstring="[para(7954(a,1),5042(a,1,2))].">
      <j1 rule="para" parents="7954 5042"/>
    </justification>
  </clause>

  <clause id="7973">
    <literal><![CDATA[
      K(x,K(y,z)) \ z = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(7954(a,1),5050(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7954 5050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7974">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(7954(a,1),5087(a,1,2))].">
      <j1 rule="para" parents="7954 5087"/>
    </justification>
  </clause>

  <clause id="7976">
    <literal><![CDATA[
      K(x,K(y,z)) * (z \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(z,K(x,y)) \ u = w
    ]]></literal>
    <justification jstring="[para(7954(a,1),5388(a,1,1))].">
      <j1 rule="para" parents="7954 5388"/>
    </justification>
  </clause>

  <clause id="7977">
    <literal><![CDATA[
      (x * K(y,z)) * K(y,K(z,u)) = x * T(K(y,z),u)
    ]]></literal>
    <justification jstring="[para(7954(a,1),6832(a,1,2))].">
      <j1 rule="para" parents="7954 6832"/>
    </justification>
  </clause>

  <clause id="7979">
    <literal><![CDATA[
      K(x,K(a(y,z,u),(y * z) * u)) = K(x,K(a(y,z,u),y * (z * u)))
    ]]></literal>
    <justification jstring="[para(84(a,1),7955(a,1,2,2))].">
      <j1 rule="para" parents="84 7955"/>
    </justification>
  </clause>

  <clause id="7980">
    <literal><![CDATA[
      K(x,K(y,y * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(5685(a,1),7955(a,1,2))].">
      <j1 rule="para" parents="5685 7955"/>
    </justification>
  </clause>

  <clause id="7982">
    <literal><![CDATA[
      T(x,K(y,z)) != u * x
    ]]></literal>
    <literal><![CDATA[
      K(z,K(y,x)) = u
    ]]></literal>
    <justification jstring="[para(7959(a,1),46(a,1))].">
      <j1 rule="para" parents="7959 46"/>
    </justification>
  </clause>

  <clause id="7983">
    <literal><![CDATA[
      K(x,K(y,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(6252,a,7962,a)].">
      <j1 rule="hyper" parents="6252 7962"/>
    </justification>
  </clause>

  <clause id="7984">
    <literal><![CDATA[
      K(K(x,y),z) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(5200,a,7962,a)].">
      <j1 rule="hyper" parents="5200 7962"/>
    </justification>
  </clause>

  <clause id="7985">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(x,z)) = u
    ]]></literal>
    <justification jstring="[para(7962(a,1),6252(a,1))].">
      <j1 rule="para" parents="7962 6252"/>
    </justification>
  </clause>

  <clause id="7986">
    <literal><![CDATA[
      K(x,K(x * y,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(7706,a,7983,a),flip(a)].">
      <j1 rule="hyper" parents="7706 7983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7987">
    <literal><![CDATA[
      K(x,K(y,z * y)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,7955,a,b,7983,a)].">
      <j1 rule="hyper" parents="299 7955 7983"/>
    </justification>
  </clause>

  <clause id="7988">
    <literal><![CDATA[
      K(K(x,y),z) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,7954,a,b,7983,a)].">
      <j1 rule="hyper" parents="299 7954 7983"/>
    </justification>
  </clause>

  <clause id="7989">
    <literal><![CDATA[
      K(x,K(y,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,7952,a,b,7983,a),flip(a)].">
      <j1 rule="hyper" parents="299 7952 7983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7990">
    <literal><![CDATA[
      x * K(y,K(x,z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(7983(a,1),5083(a,2,2)),flip(a)].">
      <j1 rule="para" parents="7983 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7991">
    <literal><![CDATA[
      K(x,K(y,z)) * y = T(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(7983(a,1),5096(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7983 5096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7992">
    <literal><![CDATA[
      x * K(y,K(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7983(a,1),5087(a,1,2))].">
      <j1 rule="para" parents="7983 5087"/>
    </justification>
  </clause>

  <clause id="7993">
    <literal><![CDATA[
      K(x,K(y,z)) * y != u
    ]]></literal>
    <literal><![CDATA[
      T(y,K(x,z)) = u
    ]]></literal>
    <justification jstring="[para(7983(a,1),5097(a,1,1))].">
      <j1 rule="para" parents="7983 5097"/>
    </justification>
  </clause>

  <clause id="7994">
    <literal><![CDATA[
      K(x,K(y,z)) * (y * u) = T(y,K(x,z)) * u
    ]]></literal>
    <justification jstring="[para(7983(a,1),5103(a,1,1))].">
      <j1 rule="para" parents="7983 5103"/>
    </justification>
  </clause>

  <clause id="7995">
    <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(7983(a,1),5480(a,1,2))].">
      <j1 rule="para" parents="7983 5480"/>
    </justification>
  </clause>

  <clause id="7996">
    <literal><![CDATA[
      K(x,y) * K(y,K(z,x)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(7983(a,1),6246(a,1,2))].">
      <j1 rule="para" parents="7983 6246"/>
    </justification>
  </clause>

  <clause id="7997">
    <literal><![CDATA[
      K(x,K(T(y,z),u)) = K(y,K(x,T(u,z)))
    ]]></literal>
    <justification jstring="[para(7537(a,2),7983(a,1,2))].">
      <j1 rule="para" parents="7537 7983"/>
    </justification>
  </clause>

  <clause id="7998">
    <literal><![CDATA[
      K(x,K(y,L(z,u,K(x,w)))) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(7853(a,1),7983(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7853 7983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7999">
    <literal><![CDATA[
      x * K(y,K(z,x)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(7983(a,1),7958(a,1,2))].">
      <j1 rule="para" parents="7983 7958"/>
    </justification>
  </clause>

  <clause id="8000">
    <literal><![CDATA[
      K(x,K(y,z)) * z = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(7983(a,1),7959(a,1,1))].">
      <j1 rule="para" parents="7983 7959"/>
    </justification>
  </clause>

  <clause id="8001">
    <literal><![CDATA[
      K(K(x,y),z) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,7952,a,b,7984,a),flip(a)].">
      <j1 rule="hyper" parents="299 7952 7984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8003">
    <literal><![CDATA[
      K(K(x,y),z) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,7952,a,b,7988,a),flip(a)].">
      <j1 rule="hyper" parents="299 7952 7988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8004">
    <literal><![CDATA[
      K(x,K(y,z)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,7984,a(flip),b,7988,a)].">
      <j1 rule="hyper" parents="65 7984 7988"/>
    </justification>
  </clause>

  <clause id="8005">
    <literal><![CDATA[
      K(x,K(y,z)) * (z * K(y,x)) = K(y,x) * z
    ]]></literal>
    <justification jstring="[para(7988(a,1),5020(a,1,1))].">
      <j1 rule="para" parents="7988 5020"/>
    </justification>
  </clause>

  <clause id="8006">
    <literal><![CDATA[
      K(x,K(R(y \ 1,z,u) \ 1,w)) = K(R(K(y,x),z,u),w)
    ]]></literal>
    <justification jstring="[para(6011(a,1),7988(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6011 7988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8007">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(7988(a,1),6285(a,1))].">
      <j1 rule="para" parents="7988 6285"/>
    </justification>
  </clause>

  <clause id="8008">
    <literal><![CDATA[
      K(x,K(L(y \ 1,z,u) \ 1,w)) = K(L(K(y,x),z,u),w)
    ]]></literal>
    <justification jstring="[para(6341(a,1),7988(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6341 7988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8009">
    <literal><![CDATA[
      x * K(K(y,z),x) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(7988(a,2),7958(a,1,2))].">
      <j1 rule="para" parents="7988 7958"/>
    </justification>
  </clause>

  <clause id="8010">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,7519,a,b,7989,a)].">
      <j1 rule="hyper" parents="299 7519 7989"/>
    </justification>
  </clause>

  <clause id="8011">
    <literal><![CDATA[
      K((x \ y) \ 1,K(z,u)) = K(z,K(u,y \ x))
    ]]></literal>
    <justification jstring="[hyper(299,a,6977,a,b,7989,a)].">
      <j1 rule="hyper" parents="299 6977 7989"/>
    </justification>
  </clause>

  <clause id="8012">
    <literal><![CDATA[
      K(x,K(y,x \ z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,7705,a(flip),b,7989,a),flip(a)].">
      <j1 rule="hyper" parents="299 7705 7989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8013">
    <literal><![CDATA[
      K(x,K(y * z,z)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,7951,a(flip),b,7989,a),flip(a)].">
      <j1 rule="hyper" parents="65 7951 7989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8014">
    <literal><![CDATA[
      K(x,K(y,z)) * (z * u) = T(z,K(x,y)) * u
    ]]></literal>
    <justification jstring="[para(7989(a,2),5103(a,1,1))].">
      <j1 rule="para" parents="7989 5103"/>
    </justification>
  </clause>

  <clause id="8015">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[para(7989(a,1),6251(a,1,1))].">
      <j1 rule="para" parents="7989 6251"/>
    </justification>
  </clause>

  <clause id="8016">
    <literal><![CDATA[
      K(x,K(y,((1 / z) / (u / z)) \ 1)) * (u / z) = T(u,K(x,y)) / z
    ]]></literal>
    <justification jstring="[para(7989(a,2),6323(a,1,1))].">
      <j1 rule="para" parents="7989 6323"/>
    </justification>
  </clause>

  <clause id="8017">
    <literal><![CDATA[
      x \ T(x * y,K(z,u)) = y * K(z,K(u,(x \ 1) \ y))
    ]]></literal>
    <justification jstring="[para(7989(a,2),6980(a,2,2))].">
      <j1 rule="para" parents="7989 6980"/>
    </justification>
  </clause>

  <clause id="8018">
    <literal><![CDATA[
      (x * K(y,K(z,u))) / K(y,z) = x / T(K(y,z),u)
    ]]></literal>
    <justification jstring="[para(7989(a,2),7206(a,1,1,2))].">
      <j1 rule="para" parents="7989 7206"/>
    </justification>
  </clause>

  <clause id="8019">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(z,K(x,T(y,u)))
    ]]></literal>
    <justification jstring="[para(7537(a,1),7989(a,1,2))].">
      <j1 rule="para" parents="7537 7989"/>
    </justification>
  </clause>

  <clause id="8020">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,x) = K(y,T(x,z))
    ]]></literal>
    <justification jstring="[para(7989(a,2),7495(a,1,1))].">
      <j1 rule="para" parents="7989 7495"/>
    </justification>
  </clause>

  <clause id="8021">
    <literal><![CDATA[
      K(x,y) * K(x,K(z,y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7989(a,1),7496(a,1,2))].">
      <j1 rule="para" parents="7989 7496"/>
    </justification>
  </clause>

  <clause id="8022">
    <literal><![CDATA[
      x * K(x,K(y,z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(7989(a,1),7958(a,1,2))].">
      <j1 rule="para" parents="7989 7958"/>
    </justification>
  </clause>

  <clause id="8023">
    <literal><![CDATA[
      K(x,K(y,z)) * x = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(7989(a,1),7959(a,1,1))].">
      <j1 rule="para" parents="7989 7959"/>
    </justification>
  </clause>

  <clause id="8024">
    <literal><![CDATA[
      K(x,K(y,z)) \ y = T(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(8001(a,1),5050(a,2,1)),flip(a)].">
      <j1 rule="para" parents="8001 5050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8025">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,x)) = u
    ]]></literal>
    <justification jstring="[para(8001(a,1),6285(a,1))].">
      <j1 rule="para" parents="8001 6285"/>
    </justification>
  </clause>

  <clause id="8026">
    <literal><![CDATA[
      (x / y) * K(z,K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x / T(y,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(8001(a,1),7271(a,1,2))].">
      <j1 rule="para" parents="8001 7271"/>
    </justification>
  </clause>

  <clause id="8027">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[para(8003(a,1),5198(a,1,1))].">
      <j1 rule="para" parents="8003 5198"/>
    </justification>
  </clause>

  <clause id="8028">
    <literal><![CDATA[
      K(x,K(y,z)) \ u = K(x,K(y,z)) * u
    ]]></literal>
    <justification jstring="[para(8003(a,1),5426(a,1,1))].">
      <j1 rule="para" parents="8003 5426"/>
    </justification>
  </clause>

  <clause id="8029">
    <literal><![CDATA[
      K(x,K(y,z)) * (x \ u) = T(x,K(y,z)) \ u
    ]]></literal>
    <justification jstring="[para(8003(a,1),5383(a,1,1))].">
      <j1 rule="para" parents="8003 5383"/>
    </justification>
  </clause>

  <clause id="8030">
    <literal><![CDATA[
      K(x,K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) * w = u
    ]]></literal>
    <justification jstring="[para(8003(a,1),5437(a,1,1))].">
      <j1 rule="para" parents="8003 5437"/>
    </justification>
  </clause>

  <clause id="8031">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,K(y,z)) * u) != w
    ]]></literal>
    <literal><![CDATA[
      w = u
    ]]></literal>
    <justification jstring="[para(8003(a,1),5438(a,1,1))].">
      <j1 rule="para" parents="8003 5438"/>
    </justification>
  </clause>

  <clause id="8032">
    <literal><![CDATA[
      K(x,K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) \ u = w
    ]]></literal>
    <justification jstring="[para(8003(a,1),5449(a,1,1))].">
      <j1 rule="para" parents="8003 5449"/>
    </justification>
  </clause>

  <clause id="8033">
    <literal><![CDATA[
      K(x,K(y,z)) * (x \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) \ u = w
    ]]></literal>
    <justification jstring="[para(8003(a,1),5388(a,1,1))].">
      <j1 rule="para" parents="8003 5388"/>
    </justification>
  </clause>

  <clause id="8034">
    <literal><![CDATA[
      K(x,K(y,z)) \ (x * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) * u = w
    ]]></literal>
    <justification jstring="[para(8003(a,1),5394(a,1,1))].">
      <j1 rule="para" parents="8003 5394"/>
    </justification>
  </clause>

  <clause id="8035">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(8003(a,1),6285(a,1))].">
      <j1 rule="para" parents="8003 6285"/>
    </justification>
  </clause>

  <clause id="8036">
    <literal><![CDATA[
      K(x,K(y,z * y)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,7955,a,b,8004,a)].">
      <j1 rule="hyper" parents="299 7955 8004"/>
    </justification>
  </clause>

  <clause id="8039">
    <literal><![CDATA[
      K(x,K(y,((1 / z) / (u / z)) \ 1)) = K(x,(T(u,y) / z) / (u / z))
    ]]></literal>
    <justification jstring="[para(6311(a,1),8004(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6311 8004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8040">
    <literal><![CDATA[
      K(x,y) * K(z,K(x,y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(8004(a,1),7496(a,1,2))].">
      <j1 rule="para" parents="8004 7496"/>
    </justification>
  </clause>

  <clause id="8041">
    <literal><![CDATA[
      K(x,K(y,L(z,z,u))) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(7852(a,2),8004(a,1,2))].">
      <j1 rule="para" parents="7852 8004"/>
    </justification>
  </clause>

  <clause id="8042">
    <literal><![CDATA[
      K(x,K(y,y * z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,7983,a,b,7980,a),flip(a)].">
      <j1 rule="hyper" parents="299 7983 7980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8043">
    <literal><![CDATA[
      K(x,K(y,y \ z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),7980(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 7980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8044">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = K(x,K(y,z \ y))
    ]]></literal>
    <justification jstring="[para(5635(a,1),7980(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5635 7980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8045">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y * z,y) = K(y * z,T(y,x))
    ]]></literal>
    <justification jstring="[para(7980(a,1),7495(a,1,1))].">
      <j1 rule="para" parents="7980 7495"/>
    </justification>
  </clause>

  <clause id="8046">
    <literal><![CDATA[
      K(x * y,x) * K(z,K(x,y)) = K(x * y,T(x,z))
    ]]></literal>
    <justification jstring="[para(7980(a,1),7496(a,1,2))].">
      <j1 rule="para" parents="7980 7496"/>
    </justification>
  </clause>

  <clause id="8047">
    <literal><![CDATA[
      K(x,K(x * y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,7983,a,b,7986,a),flip(a)].">
      <j1 rule="hyper" parents="299 7983 7986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8048">
    <literal><![CDATA[
      K(x,K(y,z * x)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,7983,a,b,7987,a)].">
      <j1 rule="hyper" parents="65 7983 7987"/>
    </justification>
  </clause>

  <clause id="8049">
    <literal><![CDATA[
      x * K(y,K(x,x * z)) = T(x,K(y,z * x))
    ]]></literal>
    <justification jstring="[para(5685(a,1),7990(a,1,2,2))].">
      <j1 rule="para" parents="5685 7990"/>
    </justification>
  </clause>

  <clause id="8050">
    <literal><![CDATA[
      T(x,K(y,z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,7958,a(flip),b,7999,a)].">
      <j1 rule="hyper" parents="65 7958 7999"/>
    </justification>
  </clause>

  <clause id="8051">
    <literal><![CDATA[
      T(x / y,K(((x / y) \ (1 / y)) \ 1,z)) = T(x,K(z,x / y)) / y
    ]]></literal>
    <justification jstring="[hyper(65,a,5331,a(flip),b,7999,a),flip(a)].">
      <j1 rule="hyper" parents="65 5331 7999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8052">
    <literal><![CDATA[
      T(x,K(y,z)) != x * u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,x)) = u
    ]]></literal>
    <justification jstring="[para(7999(a,1),45(a,1))].">
      <j1 rule="para" parents="7999 45"/>
    </justification>
  </clause>

  <clause id="8053">
    <literal><![CDATA[
      T(x * K(y,z),K(y,z)) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(7295,a,8050,a),flip(a)].">
      <j1 rule="hyper" parents="7295 8050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8054">
    <literal><![CDATA[
      T(K(x,y) * z,K(y,x)) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7280,a,8050,a),flip(a)].">
      <j1 rule="hyper" parents="7280 8050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8055">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,x) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(7260,a,8050,a)].">
      <j1 rule="hyper" parents="7260 8050"/>
    </justification>
  </clause>

  <clause id="8056">
    <literal><![CDATA[
      T(T(x,y),K(z,y)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(7154,a,8050,a),flip(a)].">
      <j1 rule="hyper" parents="7154 8050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8057">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(6264,a,8050,a)].">
      <j1 rule="hyper" parents="6264 8050"/>
    </justification>
  </clause>

  <clause id="8058">
    <literal><![CDATA[
      (K(x,y) * z) / K(x,y) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(6259,a,8050,a)].">
      <j1 rule="hyper" parents="6259 8050"/>
    </justification>
  </clause>

  <clause id="8059">
    <literal><![CDATA[
      K(x,y) * (z * K(y,x)) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(5576,a,8050,a)].">
      <j1 rule="hyper" parents="5576 8050"/>
    </justification>
  </clause>

  <clause id="8060">
    <literal><![CDATA[
      T(T(x,K(y,z)),u) = T(T(x,u),K(z,y))
    ]]></literal>
    <justification jstring="[hyper(861,a,8050,a)].">
      <j1 rule="hyper" parents="861 8050"/>
    </justification>
  </clause>

  <clause id="8061">
    <literal><![CDATA[
      T(T(x,y),K(z,y)) = x * T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(299,a,7612,a(flip),b,8050,a),flip(a)].">
      <j1 rule="hyper" parents="299 7612 8050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8062">
    <literal><![CDATA[
      T(x * y,K(z,y)) = y * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,7400,a(flip),b,8050,a),flip(a)].">
      <j1 rule="hyper" parents="299 7400 8050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8063">
    <literal><![CDATA[
      K(x,y) * T(z,K(y,x)) = z * K(x,y)
    ]]></literal>
    <justification jstring="[para(8050(a,1),107(a,1,2))].">
      <j1 rule="para" parents="8050 107"/>
    </justification>
  </clause>

  <clause id="8064">
    <literal><![CDATA[
      T(T(x,K(y,z)),u) != w
    ]]></literal>
    <literal><![CDATA[
      T(T(x,u),K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(8050(a,1),861(a,1,1))].">
      <j1 rule="para" parents="8050 861"/>
    </justification>
  </clause>

  <clause id="8065">
    <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(8050(a,1),861(a,1))].">
      <j1 rule="para" parents="8050 861"/>
    </justification>
  </clause>

  <clause id="8066">
    <literal><![CDATA[
      T(K(x,y) * z,T(z,K(y,x))) = T(K(x,y) * z,z)
    ]]></literal>
    <justification jstring="[para(8050(a,1),4469(a,1,2))].">
      <j1 rule="para" parents="8050 4469"/>
    </justification>
  </clause>

  <clause id="8068">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(u,K(y,z)) = x
    ]]></literal>
    <justification jstring="[para(8050(a,1),6264(a,1))].">
      <j1 rule="para" parents="8050 6264"/>
    </justification>
  </clause>

  <clause id="8069">
    <literal><![CDATA[
      T(x,K(y,z)) * K(y,z) = K(y,z) * x
    ]]></literal>
    <justification jstring="[para(8050(a,1),6257(a,1,1))].">
      <j1 rule="para" parents="8050 6257"/>
    </justification>
  </clause>

  <clause id="8070">
    <literal><![CDATA[
      T(T(x,K(y,z)),z) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(8050(a,1),7141(a,1,1))].">
      <j1 rule="para" parents="8050 7141"/>
    </justification>
  </clause>

  <clause id="8071">
    <literal><![CDATA[
      T(x,K(y,z)) * z = z * T(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(8050(a,1),7142(a,1,1))].">
      <j1 rule="para" parents="8050 7142"/>
    </justification>
  </clause>

  <clause id="8072">
    <literal><![CDATA[
      T(T(x,y),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8050(a,1),7154(a,1))].">
      <j1 rule="para" parents="8050 7154"/>
    </justification>
  </clause>

  <clause id="8074">
    <literal><![CDATA[
      T(x * K(y,z),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(8050(a,1),7295(a,1))].">
      <j1 rule="para" parents="8050 7295"/>
    </justification>
  </clause>

  <clause id="8075">
    <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(873,a,8057,a)].">
      <j1 rule="hyper" parents="873 8057"/>
    </justification>
  </clause>

  <clause id="8076">
    <literal><![CDATA[
      T(T(x,T(y,z)),K(y,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(42,a,7140,a,b,8057,a),flip(a)].">
      <j1 rule="hyper" parents="42 7140 8057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8078">
    <literal><![CDATA[
      K(x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      T(z,K(x,y)) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(8057(a,1),276(a,1,2))].">
      <j1 rule="para" parents="8057 276"/>
    </justification>
  </clause>

  <clause id="8079">
    <literal><![CDATA[
      T(K(x,y),z) * z = z * K(x,y)
    ]]></literal>
    <justification jstring="[para(8057(a,1),4528(a,1,2))].">
      <j1 rule="para" parents="8057 4528"/>
    </justification>
  </clause>

  <clause id="8080">
    <literal><![CDATA[
      (x * K(y,z)) / x = T(K(y,z),x)
    ]]></literal>
    <justification jstring="[para(8057(a,1),4529(a,1,2))].">
      <j1 rule="para" parents="8057 4529"/>
    </justification>
  </clause>

  <clause id="8081">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(8057(a,1),6258(a,1,1)),flip(b)].">
      <j1 rule="para" parents="8057 6258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8082">
    <literal><![CDATA[
      K(x,K(y,z)) * z = (1 / K(x,y)) * (z / (K(x,y) \ 1))
    ]]></literal>
    <justification jstring="[hyper(299,a,7315,a,b,8000,a),flip(a)].">
      <j1 rule="hyper" parents="299 7315 8000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8083">
    <literal><![CDATA[
      K(x,K(y,x \ z)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,7983,a,b,8012,a),flip(a)].">
      <j1 rule="hyper" parents="299 7983 8012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8084">
    <literal><![CDATA[
      T(x,K(y,z)) != u \ x
    ]]></literal>
    <literal><![CDATA[
      K(y,K(x,z)) = u
    ]]></literal>
    <justification jstring="[para(8024(a,1),50(a,1))].">
      <j1 rule="para" parents="8024 50"/>
    </justification>
  </clause>

  <clause id="8086">
    <literal><![CDATA[
      K(x,K(y,x * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,7983,a,b,8042,a)].">
      <j1 rule="hyper" parents="65 7983 8042"/>
    </justification>
  </clause>

  <clause id="8087">
    <literal><![CDATA[
      T(x,K(y,y \ z)) = x * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(8043(a,1),5083(a,2,2))].">
      <j1 rule="para" parents="8043 5083"/>
    </justification>
  </clause>

  <clause id="8088">
    <literal><![CDATA[
      K(x,K(x \ y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),8047(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 8047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8089">
    <literal><![CDATA[
      T(x,T(y,z)) * K(y,z) = K(y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(8056(a,1),6257(a,1,1))].">
      <j1 rule="para" parents="8056 6257"/>
    </justification>
  </clause>

  <clause id="8090">
    <literal><![CDATA[
      T(T(x,(y \ z) \ 1),K(u,z \ y)) = T(x,T((y \ z) \ 1,u))
    ]]></literal>
    <justification jstring="[para(6814(a,1),8056(a,1,2))].">
      <j1 rule="para" parents="6814 8056"/>
    </justification>
  </clause>

  <clause id="8091">
    <literal><![CDATA[
      T(T(x,y / z),K(y,y / z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(8056(a,2),7481(a,1))].">
      <j1 rule="para" parents="8056 7481"/>
    </justification>
  </clause>

  <clause id="8092">
    <literal><![CDATA[
      T(T(x,y) \ z,K(x,y)) = T(z / T(x,y),x)
    ]]></literal>
    <justification jstring="[para(109(a,1),8076(a,1,1))].">
      <j1 rule="para" parents="109 8076"/>
    </justification>
  </clause>

  <clause id="8093">
    <literal><![CDATA[
      T(x * K(y,T(x,z)),y) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(7562(a,1),8076(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7562 8076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8094">
    <literal><![CDATA[
      T(T(K(x,y),z),z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(431,a,8079,a)].">
      <j1 rule="hyper" parents="431 8079"/>
    </justification>
  </clause>

  <clause id="8095">
    <literal><![CDATA[
      T(K(x \ y,z),x) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(37,a,7620,a,b,8079,a),flip(a)].">
      <j1 rule="hyper" parents="37 7620 8079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8096">
    <literal><![CDATA[
      T(K(x,y \ z),y) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(37,a,7607,a,b,8079,a),flip(a)].">
      <j1 rule="hyper" parents="37 7607 8079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8097">
    <literal><![CDATA[
      T(K(x \ y,z),y) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(37,a,6978,a,b,8079,a),flip(a)].">
      <j1 rule="hyper" parents="37 6978 8079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8098">
    <literal><![CDATA[
      T(K(x,T(y,z)),z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(37,a,7507,a(flip),b,8079,a),flip(a)].">
      <j1 rule="hyper" parents="37 7507 8079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8099">
    <literal><![CDATA[
      K(x,y \ z) * z = z * K(x,z / y)
    ]]></literal>
    <justification jstring="[para(6841(a,1),8079(a,1,1))].">
      <j1 rule="para" parents="6841 8079"/>
    </justification>
  </clause>

  <clause id="8100">
    <literal><![CDATA[
      K(x \ y,z) * y = y * K(y / x,z)
    ]]></literal>
    <justification jstring="[para(6979(a,1),8079(a,1,1))].">
      <j1 rule="para" parents="6979 8079"/>
    </justification>
  </clause>

  <clause id="8101">
    <literal><![CDATA[
      K(x,T(y,z)) * z = z * K(x,y)
    ]]></literal>
    <justification jstring="[para(7489(a,2),8079(a,1,1))].">
      <j1 rule="para" parents="7489 8079"/>
    </justification>
  </clause>

  <clause id="8102">
    <literal><![CDATA[
      T(K(1 / T(x,y),z),y) = K(1 / x,z)
    ]]></literal>
    <justification jstring="[hyper(6239,a,8094,a),flip(a)].">
      <j1 rule="hyper" parents="6239 8094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8103">
    <literal><![CDATA[
      T(K(x,1 / T(y,z)),z) = K(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(5807,a,8094,a),flip(a)].">
      <j1 rule="hyper" parents="5807 8094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8104">
    <literal><![CDATA[
      K(x,T(T(y,z),z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,7702,a,b,8094,a)].">
      <j1 rule="hyper" parents="65 7702 8094"/>
    </justification>
  </clause>

  <clause id="8105">
    <literal><![CDATA[
      L(T(K(x,y),z),u,w) * z = z * L(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(8094(a,1),233(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8094 233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8106">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(7661,a,8098,a)].">
      <j1 rule="hyper" parents="7661 8098"/>
    </justification>
  </clause>

  <clause id="8107">
    <literal><![CDATA[
      K(x \ y,T(z,y)) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(7174,a,8098,a)].">
      <j1 rule="hyper" parents="7174 8098"/>
    </justification>
  </clause>

  <clause id="8108">
    <literal><![CDATA[
      K(x,T(y \ z,z)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(6854,a,8098,a),flip(a)].">
      <j1 rule="hyper" parents="6854 8098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8109">
    <literal><![CDATA[
      K(x,T((y \ z) \ 1,y)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(6078,a,8098,a),flip(a)].">
      <j1 rule="hyper" parents="6078 8098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8111">
    <literal><![CDATA[
      K(x,T(L(T(y,z),u,w),z)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(42,a,7506,a(flip),b,8098,a),flip(a)].">
      <j1 rule="hyper" parents="42 7506 8098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8112">
    <literal><![CDATA[
      T(x,y) != K(z,u)
    ]]></literal>
    <literal><![CDATA[
      K(z,T(u,y)) = x
    ]]></literal>
    <justification jstring="[para(8098(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="8098 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8113">
    <literal><![CDATA[
      x * K(y,z) != u * x
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(8098(a,1),237(a,1,2))].">
      <j1 rule="para" parents="8098 237"/>
    </justification>
  </clause>

  <clause id="8114">
    <literal><![CDATA[
      R(K(x,T(y,z)),u,w) * z = z * R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(8098(a,1),234(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8098 234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8115">
    <literal><![CDATA[
      T(T(x,y),T(z,y)) = K(x,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(8098(a,1),7542(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8098 7542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8116">
    <literal><![CDATA[
      K(x \ y,T(z,x)) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(7801,a,8104,a)].">
      <j1 rule="hyper" parents="7801 8104"/>
    </justification>
  </clause>

  <clause id="8117">
    <literal><![CDATA[
      K((x * y) / x,z) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(7654,a,8104,a),flip(a)].">
      <j1 rule="hyper" parents="7654 8104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8118">
    <literal><![CDATA[
      K(R(T(x,y),z,u),T(w,y)) = K(R(x,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,7552,a,b,8104,a)].">
      <j1 rule="hyper" parents="65 7552 8104"/>
    </justification>
  </clause>

  <clause id="8119">
    <literal><![CDATA[
      K(x,T(y \ z,y)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(109(a,1),8104(a,1,2,1))].">
      <j1 rule="para" parents="109 8104"/>
    </justification>
  </clause>

  <clause id="8120">
    <literal><![CDATA[
      K(x,(y * z) / y) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(222(a,1),8104(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="222 8104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8121">
    <literal><![CDATA[
      K((x * y) / x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(8104(a,1),7654(a,1))].">
      <j1 rule="para" parents="8104 7654"/>
    </justification>
  </clause>

  <clause id="8122">
    <literal><![CDATA[
      K(T(x,y),z \ y) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(7525,a,8106,a)].">
      <j1 rule="hyper" parents="7525 8106"/>
    </justification>
  </clause>

  <clause id="8123">
    <literal><![CDATA[
      K(x / (x / y),z) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(7477,a,8106,a),flip(a)].">
      <j1 rule="hyper" parents="7477 8106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8124">
    <literal><![CDATA[
      K(K(x,y) * z,T(u,z)) = K(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,7535,a(flip),b,8106,a)].">
      <j1 rule="hyper" parents="65 7535 8106"/>
    </justification>
  </clause>

  <clause id="8126">
    <literal><![CDATA[
      K(L(T(x,y),z,u),T(w,y)) = K(L(x,z,u),w)
    ]]></literal>
    <justification jstring="[para(25(a,2),8106(a,1,1))].">
      <j1 rule="para" parents="25 8106"/>
    </justification>
  </clause>

  <clause id="8127">
    <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),8106(a,1,2))].">
      <j1 rule="para" parents="25 8106"/>
    </justification>
  </clause>

  <clause id="8128">
    <literal><![CDATA[
      K(T(x,y),y \ z) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(109(a,1),8106(a,1,2))].">
      <j1 rule="para" parents="109 8106"/>
    </justification>
  </clause>

  <clause id="8129">
    <literal><![CDATA[
      K(x,(y * z) / y) = K(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(222(a,1),8106(a,1,2)),flip(a)].">
      <j1 rule="para" parents="222 8106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8130">
    <literal><![CDATA[
      K(T(x,y),R(T(z,y * u),y,u)) = K(x,(y * u) \ ((y * z) * u))
    ]]></literal>
    <justification jstring="[para(1324(a,1),8106(a,1,2))].">
      <j1 rule="para" parents="1324 8106"/>
    </justification>
  </clause>

  <clause id="8131">
    <literal><![CDATA[
      K(T(x,y \ z),y) = K(x,z / (z / y))
    ]]></literal>
    <justification jstring="[para(4502(a,1),8106(a,1,2))].">
      <j1 rule="para" parents="4502 8106"/>
    </justification>
  </clause>

  <clause id="8132">
    <literal><![CDATA[
      K(x * K(y,x),z) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(5053(a,1),8106(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5053 8106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8133">
    <literal><![CDATA[
      K(x,y * K(z,y)) = K(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(5053(a,1),8106(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5053 8106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8134">
    <literal><![CDATA[
      T(T(x,y),T(z,y)) = T(x,y) * K(x,z)
    ]]></literal>
    <justification jstring="[para(8106(a,1),5083(a,2,2))].">
      <j1 rule="para" parents="8106 5083"/>
    </justification>
  </clause>

  <clause id="8135">
    <literal><![CDATA[
      x * K(T(x,y),T(z,y)) = T(x,z)
    ]]></literal>
    <justification jstring="[para(8106(a,2),5083(a,2,2)),flip(a)].">
      <j1 rule="para" parents="8106 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8136">
    <literal><![CDATA[
      x * K(T(x,y),T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) = u
    ]]></literal>
    <justification jstring="[para(8106(a,2),5087(a,1,2))].">
      <j1 rule="para" parents="8106 5087"/>
    </justification>
  </clause>

  <clause id="8137">
    <literal><![CDATA[
      T(T(x,y),T(z,y)) \ x = K(z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[para(8106(a,1),5522(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8106 5522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8138">
    <literal><![CDATA[
      R(x,T(y,z),K(y,u)) = x
    ]]></literal>
    <justification jstring="[para(8106(a,1),6866(a,1,3))].">
      <j1 rule="para" parents="8106 6866"/>
    </justification>
  </clause>

  <clause id="8139">
    <literal><![CDATA[
      L(K(x,y),z * T(x,u),w) = K(L(T(x,u),z,w),T(y,u))
    ]]></literal>
    <justification jstring="[para(8106(a,1),7433(a,1,1))].">
      <j1 rule="para" parents="8106 7433"/>
    </justification>
  </clause>

  <clause id="8140">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * K(y,x)) = z
    ]]></literal>
    <justification jstring="[para(8106(a,1),7603(a,1,2,2))].">
      <j1 rule="para" parents="8106 7603"/>
    </justification>
  </clause>

  <clause id="8141">
    <literal><![CDATA[
      K(x,T(y,L(z,u,x))) = K(x * K(z,x),y)
    ]]></literal>
    <justification jstring="[para(7830(a,1),8106(a,1,1))].">
      <j1 rule="para" parents="7830 8106"/>
    </justification>
  </clause>

  <clause id="8142">
    <literal><![CDATA[
      R(x,T(y,z),T(K(y,u),w)) = x
    ]]></literal>
    <justification jstring="[para(5800(a,1),8138(a,1,3))].">
      <j1 rule="para" parents="5800 8138"/>
    </justification>
  </clause>

  <clause id="8143">
    <literal><![CDATA[
      x * ((x * K(y,z)) / x) = K(y,z) * x
    ]]></literal>
    <justification jstring="[para(8080(a,2),107(a,1,2))].">
      <j1 rule="para" parents="8080 107"/>
    </justification>
  </clause>

  <clause id="8144">
    <literal><![CDATA[
      T(K(x \ y,z),x) = K((x / y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,5852,a,b,8095,a),flip(a)].">
      <j1 rule="hyper" parents="299 5852 8095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8145">
    <literal><![CDATA[
      K(x \ y,T(T(z,x),u)) = K(y / x,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,7504,a,b,8095,a)].">
      <j1 rule="hyper" parents="65 7504 8095"/>
    </justification>
  </clause>

  <clause id="8146">
    <literal><![CDATA[
      K(x,y \ z) * y = y * K(x,z / y)
    ]]></literal>
    <justification jstring="[para(8096(a,1),107(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8096 107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8147">
    <literal><![CDATA[
      K(x / y,x / z) = K(y \ x,z \ x)
    ]]></literal>
    <justification jstring="[hyper(7098,a,8097,a),flip(a)].">
      <j1 rule="hyper" parents="7098 8097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8148">
    <literal><![CDATA[
      K(x \ y,z) \ (y * K(y / x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      y = u
    ]]></literal>
    <justification jstring="[para(8097(a,1),319(a,1,2,2))].">
      <j1 rule="para" parents="8097 319"/>
    </justification>
  </clause>

  <clause id="8149">
    <literal><![CDATA[
      x / K(x / y,z) = K(y \ x,z) \ x
    ]]></literal>
    <justification jstring="[para(8097(a,1),7297(a,1,2))].">
      <j1 rule="para" parents="8097 7297"/>
    </justification>
  </clause>

  <clause id="8150">
    <literal><![CDATA[
      T(x,T(y,z)) * (x \ z) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5775,a,8101,a)].">
      <j1 rule="hyper" parents="5775 8101"/>
    </justification>
  </clause>

  <clause id="8151">
    <literal><![CDATA[
      K(x,T((y \ z) \ 1,y)) = K(x,(z / y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(37,a,6071,a,b,8101,a),flip(a)].">
      <j1 rule="hyper" parents="37 6071 8101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8152">
    <literal><![CDATA[
      (x * K(y,z)) / (y \ x) = T(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(120,a,8101,a(flip),b,5056,a)].">
      <j1 rule="hyper" parents="120 8101 5056"/>
    </justification>
  </clause>

  <clause id="8153">
    <literal><![CDATA[
      K(x,T(y,z)) * z != z * u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(8101(a,2),45(a,1))].">
      <j1 rule="para" parents="8101 45"/>
    </justification>
  </clause>

  <clause id="8154">
    <literal><![CDATA[
      R(T(K(x,T(y,z)),z * u),z,u) = (z * u) \ ((z * K(x,y)) * u)
    ]]></literal>
    <justification jstring="[para(8101(a,1),689(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8101 689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8155">
    <literal><![CDATA[
      (K(x,T(y,z \ 1)) * z) * (1 / z) = ((z \ 1) * K(x,y)) * z
    ]]></literal>
    <justification jstring="[para(8101(a,1),1088(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8101 1088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8156">
    <literal><![CDATA[
      T(x,T(y,z)) * z = x * (z * K(x,y))
    ]]></literal>
    <justification jstring="[para(8101(a,1),5055(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8101 5055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8157">
    <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(8101(a,1),5459(a,1,1,3)),flip(a)].">
      <j1 rule="para" parents="8101 5459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8158">
    <literal><![CDATA[
      T(K(x,y),z) * (z / y) = (z / y) * K(x,y)
    ]]></literal>
    <justification jstring="[para(6916(a,1),8101(a,1,1))].">
      <j1 rule="para" parents="6916 8101"/>
    </justification>
  </clause>

  <clause id="8159">
    <literal><![CDATA[
      K(x \ (y \ z),T(y,z)) = K((y \ z) / x,y)
    ]]></literal>
    <justification jstring="[hyper(7485,a,8107,a)].">
      <j1 rule="hyper" parents="7485 8107"/>
    </justification>
  </clause>

  <clause id="8161">
    <literal><![CDATA[
      K(x,T(y \ (x * z),z)) = K(x,(x * z) / y)
    ]]></literal>
    <justification jstring="[hyper(65,a,7645,a(flip),b,8108,a)].">
      <j1 rule="hyper" parents="65 7645 8108"/>
    </justification>
  </clause>

  <clause id="8162">
    <literal><![CDATA[
      K(x,y / (y / z)) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(79(a,1),8108(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 8108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8163">
    <literal><![CDATA[
      K(x,T(((y \ 1) * z) \ u,y * ((y \ 1) \ u))) = K(x,(y * ((y \ 1) \ u)) / (y * z))
    ]]></literal>
    <justification jstring="[para(2507(a,1),8108(a,1,2,1))].">
      <j1 rule="para" parents="2507 8108"/>
    </justification>
  </clause>

  <clause id="8165">
    <literal><![CDATA[
      K((x \ y) \ 1,T(z,y)) = K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(7024,a,8116,a)].">
      <j1 rule="hyper" parents="7024 8116"/>
    </justification>
  </clause>

  <clause id="8166">
    <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),8116(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14 8116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8167">
    <literal><![CDATA[
      K(x / (y \ z),z / (z / y)) = K((y \ z) \ x,y)
    ]]></literal>
    <justification jstring="[para(4502(a,1),8116(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4502 8116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8168">
    <literal><![CDATA[
      K(x \ y,T(z,x)) / (x \ y) = (1 / (x \ y)) * K(y / x,z)
    ]]></literal>
    <justification jstring="[para(8116(a,1),4569(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8116 4569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8169">
    <literal><![CDATA[
      K(L((x \ y) / z,z,x),u) = K((x * z) \ y,T(u,z))
    ]]></literal>
    <justification jstring="[para(968(a,2),8117(a,1,1))].">
      <j1 rule="para" parents="968 8117"/>
    </justification>
  </clause>

  <clause id="8170">
    <literal><![CDATA[
      K(x \ T(x * y,y),z) = K(y,T(z,x * y))
    ]]></literal>
    <justification jstring="[para(4302(a,1),8117(a,1,1))].">
      <j1 rule="para" parents="4302 8117"/>
    </justification>
  </clause>

  <clause id="8171">
    <literal><![CDATA[
      K(x,T(T(y,z),z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(8117(a,1),7654(a,1))].">
      <j1 rule="para" parents="8117 7654"/>
    </justification>
  </clause>

  <clause id="8172">
    <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),8119(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="18 8119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8173">
    <literal><![CDATA[
      x * (K(x \ y,x) * K(x,T(z,y))) = T(y / (y / x),z)
    ]]></literal>
    <justification jstring="[para(8123(a,1),5924(a,1,2,2))].">
      <j1 rule="para" parents="8123 5924"/>
    </justification>
  </clause>

  <clause id="8174">
    <literal><![CDATA[
      ((x * ((y * z) / y)) / x) / ((x * z) / x) = K(T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(65,a,5282,a,b,8129,a)].">
      <j1 rule="hyper" parents="65 5282 8129"/>
    </justification>
  </clause>

  <clause id="8175">
    <literal><![CDATA[
      K(x,R((y * z) / y,u,w)) = K(T(x,y),R(z,u,w))
    ]]></literal>
    <justification jstring="[para(932(a,2),8129(a,1,2))].">
      <j1 rule="para" parents="932 8129"/>
    </justification>
  </clause>

  <clause id="8176">
    <literal><![CDATA[
      K(x,(y * z) / y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(8129(a,2),7709(a,1))].">
      <j1 rule="para" parents="8129 7709"/>
    </justification>
  </clause>

  <clause id="8177">
    <literal><![CDATA[
      (x * K(y,x)) * K(x,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x * K(y,x),z) = u
    ]]></literal>
    <justification jstring="[para(8132(a,1),5087(a,1,2))].">
      <j1 rule="para" parents="8132 5087"/>
    </justification>
  </clause>

  <clause id="8178">
    <literal><![CDATA[
      K(R(x / (x / y),z,u),w) = K(R(y,z,u),T(w,y \ x))
    ]]></literal>
    <justification jstring="[para(6112(a,2),8132(a,1,1))].">
      <j1 rule="para" parents="6112 8132"/>
    </justification>
  </clause>

  <clause id="8179">
    <literal><![CDATA[
      T(x,T(T(y,z),z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(7568,a,8135,a)].">
      <j1 rule="hyper" parents="7568 8135"/>
    </justification>
  </clause>

  <clause id="8180">
    <literal><![CDATA[
      T(T(x,y) \ 1,x) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(3538,a,8179,a),flip(a)].">
      <j1 rule="hyper" parents="3538 8179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8181">
    <literal><![CDATA[
      T(x,T(y \ z,y)) = T(x,z / y)
    ]]></literal>
    <justification jstring="[para(109(a,1),8179(a,1,2,1))].">
      <j1 rule="para" parents="109 8179"/>
    </justification>
  </clause>

  <clause id="8182">
    <literal><![CDATA[
      T(x,(y * z) / y) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(222(a,1),8179(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="222 8179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8183">
    <literal><![CDATA[
      T(x,T(T(y \ z,u),y)) = T(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[para(242(a,1),8179(a,1,2,1))].">
      <j1 rule="para" parents="242 8179"/>
    </justification>
  </clause>

  <clause id="8184">
    <literal><![CDATA[
      T(x,y * K(z,y)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(5053(a,1),8179(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5053 8179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8186">
    <literal><![CDATA[
      K(x,x \ y) * K(z,T(x,y)) = T(y / (y / x),z) \ x
    ]]></literal>
    <justification jstring="[para(8162(a,1),6694(a,1,2))].">
      <j1 rule="para" parents="8162 6694"/>
    </justification>
  </clause>

  <clause id="8187">
    <literal><![CDATA[
      K(x,y / (y / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(8162(a,2),7622(a,1))].">
      <j1 rule="para" parents="8162 7622"/>
    </justification>
  </clause>

  <clause id="8188">
    <literal><![CDATA[
      (T(x,y) \ 1) * x = x * (1 / T(x,y))
    ]]></literal>
    <justification jstring="[para(8180(a,1),107(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8180 107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8189">
    <literal><![CDATA[
      T(x,y / (y / z)) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,7464,a(flip),b,8182,a)].">
      <j1 rule="hyper" parents="65 7464 8182"/>
    </justification>
  </clause>

  <clause id="8190">
    <literal><![CDATA[
      T(x,T(y * z,y * y) / (1 / y)) = T(x,T(z * (y * y),1 / y))
    ]]></literal>
    <justification jstring="[para(695(a,1),8182(a,1,2,1))].">
      <j1 rule="para" parents="695 8182"/>
    </justification>
  </clause>

  <clause id="8191">
    <literal><![CDATA[
      T(x,R((y * z) / y,u,w)) = T(x,T(R(z,u,w),y))
    ]]></literal>
    <justification jstring="[para(932(a,2),8182(a,1,2))].">
      <j1 rule="para" parents="932 8182"/>
    </justification>
  </clause>

  <clause id="8192">
    <literal><![CDATA[
      T(x,K(y,1 / z) / z) = T(x,T(1 / z,y))
    ]]></literal>
    <justification jstring="[para(5232(a,2),8182(a,1,2))].">
      <j1 rule="para" parents="5232 8182"/>
    </justification>
  </clause>

  <clause id="8193">
    <literal><![CDATA[
      T(x,T(T(y \ (z \ y),T(z,u)),y)) = T(x,(((z \ 1) \ 1) \ y) / y)
    ]]></literal>
    <justification jstring="[para(6309(a,1),8182(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6309 8182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8194">
    <literal><![CDATA[
      T(x,(y \ 1) \ K(z,y)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,3892,a,b,8184,a)].">
      <j1 rule="hyper" parents="65 3892 8184"/>
    </justification>
  </clause>

  <clause id="8195">
    <literal><![CDATA[
      a(T(x,T(y,z)),T(y * K(z,y),x),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y * K(z,y),u) = w
    ]]></literal>
    <justification jstring="[para(8184(a,1),4988(a,1,1))].">
      <j1 rule="para" parents="8184 4988"/>
    </justification>
  </clause>

  <clause id="8196">
    <literal><![CDATA[
      T(x,T(y \ z,z)) = T(x,z / y)
    ]]></literal>
    <justification jstring="[para(76(a,1),8189(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="76 8189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8198">
    <literal><![CDATA[
      K(x * y,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(y,x)) = u
    ]]></literal>
    <justification jstring="[para(7704(a,2),7953(a,1))].">
      <j1 rule="para" parents="7704 7953"/>
    </justification>
  </clause>

  <clause id="8200">
    <literal><![CDATA[
      K(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(7984(a,2),7953(a,1))].">
      <j1 rule="para" parents="7984 7953"/>
    </justification>
  </clause>

  <clause id="8201">
    <literal><![CDATA[
      K(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(7988(a,2),7953(a,1))].">
      <j1 rule="para" parents="7988 7953"/>
    </justification>
  </clause>

  <clause id="8205">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7519(a,2),8025(a,1))].">
      <j1 rule="para" parents="7519 8025"/>
    </justification>
  </clause>

  <clause id="8206">
    <literal><![CDATA[
      K(x,K(y,z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(7987(a,2),8025(a,1))].">
      <j1 rule="para" parents="7987 8025"/>
    </justification>
  </clause>

  <clause id="8207">
    <literal><![CDATA[
      K(x,K(y,y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(8042(a,2),8025(a,1))].">
      <j1 rule="para" parents="8042 8025"/>
    </justification>
  </clause>

  <clause id="8208">
    <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(7537(a,1),8035(a,1,2))].">
      <j1 rule="para" parents="7537 8035"/>
    </justification>
  </clause>

  <clause id="8209">
    <literal><![CDATA[
      K(x,K(y / z,T(u,z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,z \ y)) = w
    ]]></literal>
    <justification jstring="[para(7553(a,2),8035(a,1,2))].">
      <j1 rule="para" parents="7553 8035"/>
    </justification>
  </clause>

  <clause id="8211">
    <literal><![CDATA[
      K(x,K(y * z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8013(a,2),8035(a,1))].">
      <j1 rule="para" parents="8013 8035"/>
    </justification>
  </clause>

  <clause id="8213">
    <literal><![CDATA[
      K(x,T(T(T(y,z),u),z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(23(a,1),8171(a,1,2,1))].">
      <j1 rule="para" parents="23 8171"/>
    </justification>
  </clause>

  <clause id="8214">
    <literal><![CDATA[
      K(x,T(L(T(y,z),u,w),z)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(25(a,2),8171(a,1,2,1))].">
      <j1 rule="para" parents="25 8171"/>
    </justification>
  </clause>

  <clause id="8215">
    <literal><![CDATA[
      K(x,T(y \ z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(109(a,1),8171(a,1,2,1))].">
      <j1 rule="para" parents="109 8171"/>
    </justification>
  </clause>

  <clause id="8217">
    <literal><![CDATA[
      T(K(x,T(y,z)),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7489(a,1),8171(a,1))].">
      <j1 rule="para" parents="7489 8171"/>
    </justification>
  </clause>

  <clause id="8218">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(7537(a,2),8171(a,1))].">
      <j1 rule="para" parents="7537 8171"/>
    </justification>
  </clause>

  <clause id="8219">
    <literal><![CDATA[
      K(x \ y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(7499(a,1),8171(a,1))].">
      <j1 rule="para" parents="7499 8171"/>
    </justification>
  </clause>

  <clause id="8220">
    <literal><![CDATA[
      K(x \ y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(7553(a,1),8171(a,1))].">
      <j1 rule="para" parents="7553 8171"/>
    </justification>
  </clause>

  <clause id="8221">
    <literal><![CDATA[
      K(x,T(y,K(z,z \ x))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7572(a,1),8171(a,1))].">
      <j1 rule="para" parents="7572 8171"/>
    </justification>
  </clause>

  <clause id="8222">
    <literal><![CDATA[
      K(x,T(y,R(T(x,z),u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(7557(a,1),8171(a,1))].">
      <j1 rule="para" parents="7557 8171"/>
    </justification>
  </clause>

  <clause id="8224">
    <literal><![CDATA[
      K(R(T(x,y),z,u),T(w,y)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(R(x,z,u),w) = v5
    ]]></literal>
    <justification jstring="[para(7552(a,2),8171(a,1))].">
      <j1 rule="para" parents="7552 8171"/>
    </justification>
  </clause>

  <clause id="8226">
    <literal><![CDATA[
      T(K(x,y \ z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(109(a,1),8217(a,1,1,2))].">
      <j1 rule="para" parents="109 8217"/>
    </justification>
  </clause>

  <clause id="8228">
    <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),8218(a,1,2))].">
      <j1 rule="para" parents="23 8218"/>
    </justification>
  </clause>

  <clause id="8229">
    <literal><![CDATA[
      K(L(T(x,y),z,u),T(w,y)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(L(x,z,u),w) = v5
    ]]></literal>
    <justification jstring="[para(25(a,2),8218(a,1,1))].">
      <j1 rule="para" parents="25 8218"/>
    </justification>
  </clause>

  <clause id="8230">
    <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),8218(a,1,2))].">
      <j1 rule="para" parents="27 8218"/>
    </justification>
  </clause>

  <clause id="8231">
    <literal><![CDATA[
      K(T(x,y),y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(109(a,1),8218(a,1,2))].">
      <j1 rule="para" parents="109 8218"/>
    </justification>
  </clause>

  <clause id="8232">
    <literal><![CDATA[
      K(T(x,y),z \ y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(7474(a,1),8218(a,1))].">
      <j1 rule="para" parents="7474 8218"/>
    </justification>
  </clause>

  <clause id="8233">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) \ K(y,x) = T(K(y,x),T(z,y \ u))
    ]]></literal>
    <justification jstring="[para(7623(a,1),7957(a,1,1,2))].">
      <j1 rule="para" parents="7623 7957"/>
    </justification>
  </clause>

  <clause id="8234">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7964(a,2),7714(a,1))].">
      <j1 rule="para" parents="7964 7714"/>
    </justification>
  </clause>

  <clause id="8235">
    <literal><![CDATA[
      T(K(x,y),T(z,K(y,u))) = K(x,K(y,z)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(7500(a,1),7965(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7500 7965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8236">
    <literal><![CDATA[
      K(x,T(y,z)) * K(y,x) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(36,a,5457,a,b,7967,a)].">
      <j1 rule="hyper" parents="36 5457 7967"/>
    </justification>
  </clause>

  <clause id="8237">
    <literal><![CDATA[
      K(x,T(y,z)) != K(x,y) * u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7967(a,1),45(a,1))].">
      <j1 rule="para" parents="7967 45"/>
    </justification>
  </clause>

  <clause id="8238">
    <literal><![CDATA[
      K(x,y) * K(y,K(z,T(x,u))) = T(K(x,y),T(z,u))
    ]]></literal>
    <justification jstring="[para(7537(a,1),7996(a,1,2,2))].">
      <j1 rule="para" parents="7537 7996"/>
    </justification>
  </clause>

  <clause id="8239">
    <literal><![CDATA[
      K(x,K(T(y,z),u)) = K(y,K(u,T(x,z)))
    ]]></literal>
    <justification jstring="[hyper(7953,a,7997,a)].">
      <j1 rule="hyper" parents="7953 7997"/>
    </justification>
  </clause>

  <clause id="8240">
    <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(7997(a,1),7953(a,1))].">
      <j1 rule="para" parents="7997 7953"/>
    </justification>
  </clause>

  <clause id="8241">
    <literal><![CDATA[
      K(x,T(y,z)) * K(y,x) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(2285,a,8010,a)].">
      <j1 rule="hyper" parents="2285 8010"/>
    </justification>
  </clause>

  <clause id="8242">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,y \ z) = T(K(x,y \ z),y)
    ]]></literal>
    <justification jstring="[para(8043(a,1),8015(a,1,1))].">
      <j1 rule="para" parents="8043 8015"/>
    </justification>
  </clause>

  <clause id="8243">
    <literal><![CDATA[
      K(x,y / z) * K(x,K(u,z \ y)) = K(x,T(y / z,T(u,z)))
    ]]></literal>
    <justification jstring="[para(7554(a,1),8021(a,1,2,2))].">
      <j1 rule="para" parents="7554 8021"/>
    </justification>
  </clause>

  <clause id="8244">
    <literal><![CDATA[
      (x * L(K(y,z),u,w)) / x = L(K(y,T(z,x)),u,w)
    ]]></literal>
    <justification jstring="[para(8040(a,1),5249(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8040 5249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8245">
    <literal><![CDATA[
      (x * (y * K(z,u))) / (x * y) = L(K(z,T(u,x * y)),y,x)
    ]]></literal>
    <justification jstring="[para(8040(a,1),5254(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8040 5254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8246">
    <literal><![CDATA[
      (x * T(y,K(z,u))) * K(z,u) = (x * y) * K(z,T(u,y))
    ]]></literal>
    <justification jstring="[para(8040(a,1),7063(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8040 7063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8247">
    <literal><![CDATA[
      K(x,y) * (z / K(x,y)) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(12(a,1),8053(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12 8053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8248">
    <literal><![CDATA[
      T(K(x,y) * z,K(y,x) * (z * K(x,y))) = L(z * K(x,y),K(y,x),z * K(x,y))
    ]]></literal>
    <justification jstring="[para(8053(a,1),6260(a,1,1))].">
      <j1 rule="para" parents="8053 6260"/>
    </justification>
  </clause>

  <clause id="8249">
    <literal><![CDATA[
      T(x * T(y,z),K(y,z)) = K(y,z) * (x * y)
    ]]></literal>
    <justification jstring="[para(6832(a,1),8053(a,1,1))].">
      <j1 rule="para" parents="6832 8053"/>
    </justification>
  </clause>

  <clause id="8250">
    <literal><![CDATA[
      T(K(x,y) * z,u) * K(y,x) = K(y,x) * T(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[para(8054(a,1),232(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8054 232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8251">
    <literal><![CDATA[
      T(T(x,y) * z,K(y,x)) = (x * z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(5103(a,1),8054(a,1,1))].">
      <j1 rule="para" parents="5103 8054"/>
    </justification>
  </clause>

  <clause id="8252">
    <literal><![CDATA[
      T(K(x,y) \ z,K(x,y)) = z * K(y,x)
    ]]></literal>
    <justification jstring="[para(5426(a,2),8054(a,1,1))].">
      <j1 rule="para" parents="5426 8054"/>
    </justification>
  </clause>

  <clause id="8253">
    <literal><![CDATA[
      T(T(x,y) \ z,K(x,y)) = (x \ z) * K(y,x)
    ]]></literal>
    <justification jstring="[para(5383(a,1),8054(a,1,1))].">
      <j1 rule="para" parents="5383 8054"/>
    </justification>
  </clause>

  <clause id="8254">
    <literal><![CDATA[
      T(T(x,1 / (y / z)),K(u,z / y)) = x * T(K(x,1 / (y / z)),u)
    ]]></literal>
    <justification jstring="[para(5940(a,1),8061(a,1,2))].">
      <j1 rule="para" parents="5940 8061"/>
    </justification>
  </clause>

  <clause id="8255">
    <literal><![CDATA[
      ((1 / K(x,y)) * (z / (K(x,y) \ 1))) * K(x,y) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(7315(a,2),8069(a,1,1))].">
      <j1 rule="para" parents="7315 8069"/>
    </justification>
  </clause>

  <clause id="8256">
    <literal><![CDATA[
      T(x * y,K(z,y)) = T(x,K(z,y)) * y
    ]]></literal>
    <justification jstring="[hyper(299,a,8062,a,b,8071,a)].">
      <j1 rule="hyper" parents="299 8062 8071"/>
    </justification>
  </clause>

  <clause id="8257">
    <literal><![CDATA[
      T(x,K(y,y \ z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,5083,a,b,8087,a),flip(a)].">
      <j1 rule="hyper" parents="299 5083 8087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8258">
    <literal><![CDATA[
      T(x,K(y,y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8087(a,2),5087(a,1))].">
      <j1 rule="para" parents="8087 5087"/>
    </justification>
  </clause>

  <clause id="8259">
    <literal><![CDATA[
      T(x,K(y,y * z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),8257(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 8257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8260">
    <literal><![CDATA[
      T(x,K(y,y * z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,8050,a,b,8259,a),flip(a)].">
      <j1 rule="hyper" parents="299 8050 8259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8261">
    <literal><![CDATA[
      T(x,K(y,y * T(x,z))) = x
    ]]></literal>
    <justification jstring="[hyper(299,a,3615,a(flip),b,8259,a),flip(a)].">
      <j1 rule="hyper" parents="299 3615 8259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8262">
    <literal><![CDATA[
      T(K(x * y,x) * z,K(x,y)) = z * K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,8054,a(flip),b,8259,a),flip(a)].">
      <j1 rule="hyper" parents="65 8054 8259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8263">
    <literal><![CDATA[
      T(K(x,x * T(y,z)),y) = K(x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(56,a,8261,a)].">
      <j1 rule="hyper" parents="56 8261"/>
    </justification>
  </clause>

  <clause id="8264">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * y) = T(x,T(z * y,z))
    ]]></literal>
    <justification jstring="[para(8260(a,1),8070(a,1,1))].">
      <j1 rule="para" parents="8260 8070"/>
    </justification>
  </clause>

  <clause id="8265">
    <literal><![CDATA[
      T(x * K(y,x),K(y,z)) = x * K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(5471,a,8093,a)].">
      <j1 rule="hyper" parents="5471 8093"/>
    </justification>
  </clause>

  <clause id="8266">
    <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(8100(a,2),7248(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="8100 7248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8267">
    <literal><![CDATA[
      K(x \ (y \ z),y) * z = z * K(z / (y * x),y)
    ]]></literal>
    <justification jstring="[para(7827(a,1),8100(a,1,1))].">
      <j1 rule="para" parents="7827 8100"/>
    </justification>
  </clause>

  <clause id="8268">
    <literal><![CDATA[
      K(1 / T(T(x,y),y),z) = K(1 / x,z)
    ]]></literal>
    <justification jstring="[hyper(6239,a,8102,a),flip(a)].">
      <j1 rule="hyper" parents="6239 8102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8269">
    <literal><![CDATA[
      K(x,1 / T(T(y,z),z)) = K(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(5807,a,8103,a),flip(a)].">
      <j1 rule="hyper" parents="5807 8103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8270">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) = K(x,z / (z * y))
    ]]></literal>
    <justification jstring="[para(9(a,1),8109(a,1,2,1,1))].">
      <j1 rule="para" parents="9 8109"/>
    </justification>
  </clause>

  <clause id="8271">
    <literal><![CDATA[
      T(T(x,y),T(z,y)) = K(x,y) * T(x,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,5701,a,b,8115,a),flip(a)].">
      <j1 rule="hyper" parents="299 5701 8115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8272">
    <literal><![CDATA[
      T(x,y) \ T(T(x,z),T(y,z)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,8115,a,b,5379,a(flip))].">
      <j1 rule="hyper" parents="119 8115 5379"/>
    </justification>
  </clause>

  <clause id="8273">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) / T(z,y) = 1 / (K(z,x) * T(z,y))
    ]]></literal>
    <justification jstring="[para(8115(a,1),5038(a,2,2))].">
      <j1 rule="para" parents="8115 5038"/>
    </justification>
  </clause>

  <clause id="8274">
    <literal><![CDATA[
      T(T(x,y),T(z,y)) != T(x,y) * u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(8134(a,2),45(a,1))].">
      <j1 rule="para" parents="8134 45"/>
    </justification>
  </clause>

  <clause id="8275">
    <literal><![CDATA[
      T(x * K(y,z),u) / x = x \ T(K(y,z) * x,u)
    ]]></literal>
    <justification jstring="[para(8143(a,1),3458(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8143 3458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8277">
    <literal><![CDATA[
      K((x / (y * x)) \ 1,z) = T(K(T(y,x),z),x)
    ]]></literal>
    <justification jstring="[para(22(a,2),8144(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="22 8144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8279">
    <literal><![CDATA[
      K(x / y,z \ (x / y)) = K(y \ x,(z * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,6890,a(flip),b,8147,a)].">
      <j1 rule="hyper" parents="65 6890 8147"/>
    </justification>
  </clause>

  <clause id="8280">
    <literal><![CDATA[
      (x * K(y,z)) / (y \ x) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(8150(a,1),307(a,1,1)),flip(b)].">
      <j1 rule="para" parents="8150 307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8281">
    <literal><![CDATA[
      (x * K(y,z \ (u \ z))) / (y \ x) = T(y,T((u * z) \ z,x))
    ]]></literal>
    <justification jstring="[para(7929(a,1),8152(a,1,1,2))].">
      <j1 rule="para" parents="7929 8152"/>
    </justification>
  </clause>

  <clause id="8282">
    <literal><![CDATA[
      (x * (K(y,z) * K(x,u))) * K(z,y) = T(x,T(u,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(7207,a,8156,a)].">
      <j1 rule="hyper" parents="7207 8156"/>
    </justification>
  </clause>

  <clause id="8283">
    <literal><![CDATA[
      T(x,T(y,K(z,x))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(5869,a,8156,a),flip(a)].">
      <j1 rule="hyper" parents="5869 8156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8284">
    <literal><![CDATA[
      (x * (K(y,z) * K(x,u))) * K(z,y) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(u,K(y,z))) = w
    ]]></literal>
    <justification jstring="[para(8156(a,1),7216(a,1,1)),flip(b)].">
      <j1 rule="para" parents="8156 7216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8285">
    <literal><![CDATA[
      T(x,T(y,T(z,x))) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7140(a,1),8283(a,1,2))].">
      <j1 rule="para" parents="7140 8283"/>
    </justification>
  </clause>

  <clause id="8286">
    <literal><![CDATA[
      T(x,T(y,z / x)) = T(x,T(y,x \ z))
    ]]></literal>
    <justification jstring="[para(109(a,1),8285(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="109 8285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8287">
    <literal><![CDATA[
      R(x,y \ z,K(y / z,u)) = x
    ]]></literal>
    <justification jstring="[para(8165(a,1),7334(a,1,3))].">
      <j1 rule="para" parents="8165 7334"/>
    </justification>
  </clause>

  <clause id="8288">
    <literal><![CDATA[
      x \ (y * K(x / y,z)) = (x \ y) * K(x / y,z)
    ]]></literal>
    <justification jstring="[para(8287(a,1),580(a,1,1))].">
      <j1 rule="para" parents="8287 580"/>
    </justification>
  </clause>

  <clause id="8289">
    <literal><![CDATA[
      (x / y) * (1 / T(x / y,y)) = ((y \ x) \ 1) * (x / y)
    ]]></literal>
    <justification jstring="[para(109(a,1),8188(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="109 8188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8291">
    <literal><![CDATA[
      K(x,K(y \ z,T(y,u))) = K(y,K(z,T(x,u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,8083,a(flip),b,8239,a),flip(a)].">
      <j1 rule="hyper" parents="65 8083 8239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8292">
    <literal><![CDATA[
      K(x,T(y,z)) * K(x,K(y,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,7571,a,b,8241,a)].">
      <j1 rule="hyper" parents="36 7571 8241"/>
    </justification>
  </clause>

  <clause id="8294">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(x,z)) = u
    ]]></literal>
    <justification jstring="[para(8241(a,1),7216(a,1,1)),flip(b)].">
      <j1 rule="para" parents="8241 7216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8295">
    <literal><![CDATA[
      K(x,T(y,z)) * K(y,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8241(a,2),7985(a,1))].">
      <j1 rule="para" parents="8241 7985"/>
    </justification>
  </clause>

  <clause id="8296">
    <literal><![CDATA[
      T(x \ y,K(z,x)) = x \ T(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(3495,a,8256,a),flip(a)].">
      <j1 rule="hyper" parents="3495 8256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8297">
    <literal><![CDATA[
      T(x,1 / T(T(y,z),z)) = x / K(1 / y,x)
    ]]></literal>
    <justification jstring="[para(8268(a,1),5041(a,2,2))].">
      <j1 rule="para" parents="8268 5041"/>
    </justification>
  </clause>

  <clause id="8298">
    <literal><![CDATA[
      K(x,1 / ((y * z) / y)) = K(x,1 / T(z,y))
    ]]></literal>
    <justification jstring="[para(222(a,1),8269(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="222 8269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8299">
    <literal><![CDATA[
      K(x,1 / T(y,z / y)) = K(x,1 / (z / (z / y)))
    ]]></literal>
    <justification jstring="[para(241(a,1),8269(a,1,2,2,1))].">
      <j1 rule="para" parents="241 8269"/>
    </justification>
  </clause>

  <clause id="8300">
    <literal><![CDATA[
      K(x,y / (y * z)) = K(x,(z * y) \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,7700,a(flip),b,8270,a),flip(a)].">
      <j1 rule="hyper" parents="65 7700 8270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8301">
    <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(8271(a,2),231(a,1,1,1))].">
      <j1 rule="para" parents="8271 231"/>
    </justification>
  </clause>

  <clause id="8302">
    <literal><![CDATA[
      T(x,T(y,z / x)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,7729,a(flip),b,8286,a),flip(a)].">
      <j1 rule="hyper" parents="299 7729 8286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8303">
    <literal><![CDATA[
      T(x \ y,T(z,y)) = T(x \ y,T(z,x))
    ]]></literal>
    <justification jstring="[para(76(a,1),8302(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="76 8302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8304">
    <literal><![CDATA[
      T(x \ K(x,y),K(z,x)) = x \ K(x,y)
    ]]></literal>
    <justification jstring="[para(2276(a,1),8296(a,2,2))].">
      <j1 rule="para" parents="2276 8296"/>
    </justification>
  </clause>

  <clause id="8305">
    <literal><![CDATA[
      K(x,T(y \ x,T(z,y))) = K(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[para(8303(a,1),7530(a,1,2))].">
      <j1 rule="para" parents="8303 7530"/>
    </justification>
  </clause>

  <clause id="8306">
    <literal><![CDATA[
      T(x \ K(x,y),T(x,z)) = T(x \ K(x,y),x)
    ]]></literal>
    <justification jstring="[para(8304(a,1),8070(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8304 8070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8307">
    <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(968(a,2),8121(a,1,1))].">
      <j1 rule="para" parents="968 8121"/>
    </justification>
  </clause>

  <clause id="8309">
    <literal><![CDATA[
      K(K(x,y) * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(5101(a,1),8121(a,1,1))].">
      <j1 rule="para" parents="5101 8121"/>
    </justification>
  </clause>

  <clause id="8310">
    <literal><![CDATA[
      T(x,T(T(y,z),z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(7563(a,1),8136(a,1))].">
      <j1 rule="para" parents="7563 8136"/>
    </justification>
  </clause>

  <clause id="8311">
    <literal><![CDATA[
      T(x,T(y \ z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(109(a,1),8310(a,1,2,1))].">
      <j1 rule="para" parents="109 8310"/>
    </justification>
  </clause>

  <clause id="8312">
    <literal><![CDATA[
      T(x,T(T(y \ z,u),y)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(z / y,u)) = w
    ]]></literal>
    <justification jstring="[para(242(a,1),8310(a,1,2,1))].">
      <j1 rule="para" parents="242 8310"/>
    </justification>
  </clause>

  <clause id="8313">
    <literal><![CDATA[
      T(K(x,y),T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(7151(a,1),8310(a,1))].">
      <j1 rule="para" parents="7151 8310"/>
    </justification>
  </clause>

  <clause id="8314">
    <literal><![CDATA[
      K(x,T(y,L(z,u,x))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,8132,a(flip),b,8141,a),flip(a)].">
      <j1 rule="hyper" parents="299 8132 8141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8315">
    <literal><![CDATA[
      K(x,T(y,(x \ z) \ u)) = K(x,T(y,z \ (x * u)))
    ]]></literal>
    <justification jstring="[para(520(a,1),8314(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="520 8314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8316">
    <literal><![CDATA[
      K(T(x,y \ z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(8131(a,2),8187(a,1))].">
      <j1 rule="para" parents="8131 8187"/>
    </justification>
  </clause>

  <clause id="8317">
    <literal><![CDATA[
      K(x,T(a(y,z,u),y * (z * u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,((y * z) * u) / (y * (z * u))) = w
    ]]></literal>
    <justification jstring="[para(14(a,2),8215(a,1,2,1))].">
      <j1 rule="para" parents="14 8215"/>
    </justification>
  </clause>

  <clause id="8318">
    <literal><![CDATA[
      K(x,L(T(y \ z,u * y),y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * z) / (u * y)) = w
    ]]></literal>
    <justification jstring="[para(524(a,1),8215(a,1,2))].">
      <j1 rule="para" parents="524 8215"/>
    </justification>
  </clause>

  <clause id="8319">
    <literal><![CDATA[
      K(x,y \ T(z * y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y * z,u) / y) = w
    ]]></literal>
    <justification jstring="[para(3480(a,1),8215(a,1,2))].">
      <j1 rule="para" parents="3480 8215"/>
    </justification>
  </clause>

  <clause id="8320">
    <literal><![CDATA[
      K(x,T(x,y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / T(x,y)) = u
    ]]></literal>
    <justification jstring="[para(5475(a,1),8215(a,1))].">
      <j1 rule="para" parents="5475 8215"/>
    </justification>
  </clause>

  <clause id="8321">
    <literal><![CDATA[
      K(x \ y,L(T(z,y),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(y / x,L(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(25(a,2),8219(a,1,2))].">
      <j1 rule="para" parents="25 8219"/>
    </justification>
  </clause>

  <clause id="8322">
    <literal><![CDATA[
      K(((x \ y) \ y) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(7493(a,2),8219(a,1))].">
      <j1 rule="para" parents="7493 8219"/>
    </justification>
  </clause>

  <clause id="8323">
    <literal><![CDATA[
      K(L(x,y,z) \ u,x) != w
    ]]></literal>
    <literal><![CDATA[
      K(u / L(x,y,z),x) = w
    ]]></literal>
    <justification jstring="[para(173(a,1),8220(a,1,2))].">
      <j1 rule="para" parents="173 8220"/>
    </justification>
  </clause>

  <clause id="8324">
    <literal><![CDATA[
      K(T(x \ y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(7537(a,2),8220(a,1))].">
      <j1 rule="para" parents="7537 8220"/>
    </justification>
  </clause>

  <clause id="8325">
    <literal><![CDATA[
      K(x,K(y \ x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * K(y \ x,y)) = u
    ]]></literal>
    <justification jstring="[para(7199(a,1),8221(a,1,2))].">
      <j1 rule="para" parents="7199 8221"/>
    </justification>
  </clause>

  <clause id="8326">
    <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(209(a,1),8232(a,1,1))].">
      <j1 rule="para" parents="209 8232"/>
    </justification>
  </clause>

  <clause id="8327">
    <literal><![CDATA[
      K(x,T(y \ z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(7537(a,1),8232(a,1))].">
      <j1 rule="para" parents="7537 8232"/>
    </justification>
  </clause>

  <clause id="8328">
    <literal><![CDATA[
      T(x,K(y,z / y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(5205(a,2),8258(a,1,2))].">
      <j1 rule="para" parents="5205 8258"/>
    </justification>
  </clause>

  <clause id="8329">
    <literal><![CDATA[
      T(1 / x,x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      T(1 / x,y / x) = z
    ]]></literal>
    <justification jstring="[para(7148(a,1),8311(a,1))].">
      <j1 rule="para" parents="7148 8311"/>
    </justification>
  </clause>

  <clause id="8330">
    <literal><![CDATA[
      T(K(x,y \ z),T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y \ z),y) = u
    ]]></literal>
    <justification jstring="[para(7463(a,1),8313(a,1))].">
      <j1 rule="para" parents="7463 8313"/>
    </justification>
  </clause>

  <clause id="8332">
    <literal><![CDATA[
      T(x,(y * z) \ z) = T(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(5087,a,7931,a),flip(a)].">
      <j1 rule="hyper" parents="5087 7931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8333">
    <literal><![CDATA[
      T(x,T(y,z) \ 1) = T(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(7108,a,8332,a)].">
      <j1 rule="hyper" parents="7108 8332"/>
    </justification>
  </clause>

  <clause id="8334">
    <literal><![CDATA[
      T(x,T(y \ 1,z)) = T(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,7927,a,b,8332,a)].">
      <j1 rule="hyper" parents="65 7927 8332"/>
    </justification>
  </clause>

  <clause id="8335">
    <literal><![CDATA[
      (x * (K(x,y) * z)) / x = (K(x,y) * z) * K(x,z)
    ]]></literal>
    <justification jstring="[para(5055(a,2),7934(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5055 7934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8336">
    <literal><![CDATA[
      K(x \ 1,x * x) * (y * K(x \ 1,y)) = ((1 / x) * y) / (x \ 1)
    ]]></literal>
    <justification jstring="[para(469(a,1),7935(a,2,1,1))].">
      <j1 rule="para" parents="469 7935"/>
    </justification>
  </clause>

  <clause id="8337">
    <literal><![CDATA[
      K((x \ 1) \ (y \ z),y) = K((x \ y) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,5893,a(flip),b,7947,a),flip(a)].">
      <j1 rule="hyper" parents="65 5893 7947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8338">
    <literal><![CDATA[
      K(x,K(y,R(T(x,z),u,w))) = 1
    ]]></literal>
    <justification jstring="[hyper(3792,a,7956,a),flip(a)].">
      <j1 rule="hyper" parents="3792 7956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8340">
    <literal><![CDATA[
      L((K(x,K(y,z)) \ u) \ (y * w),K(x,K(y,z)) \ u,K(x,K(y,z))) = u \ (T(y,K(x,z)) * w)
    ]]></literal>
    <justification jstring="[para(7994(a,1),520(a,2,2))].">
      <j1 rule="para" parents="7994 520"/>
    </justification>
  </clause>

  <clause id="8341">
    <literal><![CDATA[
      K(x,K(y,z)) * (z / K(x,y)) = K(y,x) * z
    ]]></literal>
    <justification jstring="[para(7196(a,2),8005(a,1,2))].">
      <j1 rule="para" parents="7196 8005"/>
    </justification>
  </clause>

  <clause id="8342">
    <literal><![CDATA[
      (x * K(y,K(z,u \ x))) / u = T(x / u,K(y,z))
    ]]></literal>
    <justification jstring="[para(8011(a,1),5847(a,1,1,2))].">
      <j1 rule="para" parents="8011 5847"/>
    </justification>
  </clause>

  <clause id="8344">
    <literal><![CDATA[
      K(x,K(y,z)) * (T(z,y) * u) = T(T(z,y),K(x,y)) * u
    ]]></literal>
    <justification jstring="[para(5190(a,1),8014(a,1,1,2))].">
      <j1 rule="para" parents="5190 8014"/>
    </justification>
  </clause>

  <clause id="8345">
    <literal><![CDATA[
      T(x,K(y,z * x)) = T(x,K(y,x * z))
    ]]></literal>
    <justification jstring="[hyper(7992,a,8049,a),flip(a)].">
      <j1 rule="hyper" parents="7992 8049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8346">
    <literal><![CDATA[
      T(x,K(y,x * z)) * K(y,z * x) = K(y,z * x) * x
    ]]></literal>
    <justification jstring="[para(8345(a,1),8069(a,1,1))].">
      <j1 rule="para" parents="8345 8069"/>
    </justification>
  </clause>

  <clause id="8347">
    <literal><![CDATA[
      T(x,y / z) * K(z \ y,z) = K(z \ y,z) * T(x,z \ y)
    ]]></literal>
    <justification jstring="[para(8181(a,1),8089(a,1,1))].">
      <j1 rule="para" parents="8181 8089"/>
    </justification>
  </clause>

  <clause id="8348">
    <literal><![CDATA[
      K(x,L(T(T(y,z),z),u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(25(a,2),8111(a,1,2))].">
      <j1 rule="para" parents="25 8111"/>
    </justification>
  </clause>

  <clause id="8349">
    <literal><![CDATA[
      T(K(x,L(y,z,u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(y,w),z,u)) = v5
    ]]></literal>
    <justification jstring="[para(8111(a,1),8217(a,1,1))].">
      <j1 rule="para" parents="8111 8217"/>
    </justification>
  </clause>

  <clause id="8351">
    <literal><![CDATA[
      K(x * K(y,z),(x / u) \ 1) = K(K(y,z) * x,x \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,7930,a(flip),b,8124,a),flip(a)].">
      <j1 rule="hyper" parents="65 7930 8124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8352">
    <literal><![CDATA[
      K(T(x,L(x,y,z) * u),T(w,u)) = K(L(x,u,L(x,y,z)),w)
    ]]></literal>
    <justification jstring="[para(1658(a,1),8126(a,1,1))].">
      <j1 rule="para" parents="1658 8126"/>
    </justification>
  </clause>

  <clause id="8353">
    <literal><![CDATA[
      L(K(T(x,y),T(z,y)),u,w) = K(x,L(z,u / T(z,y),w))
    ]]></literal>
    <justification jstring="[hyper(65,a,7810,a(flip),b,8127,a)].">
      <j1 rule="hyper" parents="65 7810 8127"/>
    </justification>
  </clause>

  <clause id="8354">
    <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(1658(a,1),8127(a,1,2))].">
      <j1 rule="para" parents="1658 8127"/>
    </justification>
  </clause>

  <clause id="8355">
    <literal><![CDATA[
      (K(x,y) * T(x,z)) \ x = K(z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[para(8271(a,1),8137(a,1,1))].">
      <j1 rule="para" parents="8271 8137"/>
    </justification>
  </clause>

  <clause id="8356">
    <literal><![CDATA[
      K(x / y,T(z,x \ y)) = K(y \ x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,7384,a(flip),b,8145,a),flip(a)].">
      <j1 rule="hyper" parents="65 7384 8145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8357">
    <literal><![CDATA[
      K(x,T((y \ z) \ 1,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(8151(a,2),5989(a,1))].">
      <j1 rule="para" parents="8151 5989"/>
    </justification>
  </clause>

  <clause id="8358">
    <literal><![CDATA[
      T(K(x,y),z) * (z / y) = z / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,7189,a(flip),b,8158,a),flip(a)].">
      <j1 rule="hyper" parents="299 7189 8158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8359">
    <literal><![CDATA[
      K(x,y) * (K(z,y) / y) = K(z,y) / T(y,x)
    ]]></literal>
    <justification jstring="[para(6262(a,1),8358(a,1,1))].">
      <j1 rule="para" parents="6262 8358"/>
    </justification>
  </clause>

  <clause id="8360">
    <literal><![CDATA[
      K(x,T(y,z)) * (z / y) = z / T(y,x)
    ]]></literal>
    <justification jstring="[para(7489(a,2),8358(a,1,1))].">
      <j1 rule="para" parents="7489 8358"/>
    </justification>
  </clause>

  <clause id="8361">
    <literal><![CDATA[
      (x / T(y,z)) / (x / y) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(137,a,8360,a)].">
      <j1 rule="hyper" parents="137 8360"/>
    </justification>
  </clause>

  <clause id="8362">
    <literal><![CDATA[
      K(x \ (y \ z),y) * z = z * K((y \ z) / x,y)
    ]]></literal>
    <justification jstring="[para(8159(a,1),7507(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8159 7507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8363">
    <literal><![CDATA[
      K(x,T(y \ (x * z),z)) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(299,a,7161,a(flip),b,8161,a),flip(a)].">
      <j1 rule="hyper" parents="299 7161 8161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8365">
    <literal><![CDATA[
      K(T(x * y,y) / x,z) = K(y,T(T(z,x),x * y))
    ]]></literal>
    <justification jstring="[hyper(8220,a,8170,a)].">
      <j1 rule="hyper" parents="8220 8170"/>
    </justification>
  </clause>

  <clause id="8367">
    <literal><![CDATA[
      T(x,K(y,z / y) / (z \ y)) = T(x,T(1 / (z \ y),y))
    ]]></literal>
    <justification jstring="[para(5540(a,1),8192(a,1,2,1))].">
      <j1 rule="para" parents="5540 8192"/>
    </justification>
  </clause>

  <clause id="8368">
    <literal><![CDATA[
      K(x * T(y,z),T(u,K(y,z))) = K(K(y,z) * (x * y),u)
    ]]></literal>
    <justification jstring="[para(8249(a,1),7537(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8249 7537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8369">
    <literal><![CDATA[
      K(K(x,y) * (z * x),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(z * T(x,y),T(u,K(x,y))) = w
    ]]></literal>
    <justification jstring="[para(8249(a,1),7709(a,1,1))].">
      <j1 rule="para" parents="8249 7709"/>
    </justification>
  </clause>

  <clause id="8370">
    <literal><![CDATA[
      T(T(x,y) * z,K(y,x)) = x * (z * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,7074,a(flip),b,8251,a),flip(a)].">
      <j1 rule="hyper" parents="299 7074 8251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8371">
    <literal><![CDATA[
      K(x,T(T(x * T(y,z),u),y)) = T(K(x,x * T(y,z)),u)
    ]]></literal>
    <justification jstring="[para(8263(a,1),7702(a,2,1))].">
      <j1 rule="para" parents="8263 7702"/>
    </justification>
  </clause>

  <clause id="8372">
    <literal><![CDATA[
      T(x * K(y,x),K(z,y)) = x * K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(8081,a,8265,a)].">
      <j1 rule="hyper" parents="8081 8265"/>
    </justification>
  </clause>

  <clause id="8373">
    <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(8265(a,2),45(a,1))].">
      <j1 rule="para" parents="8265 45"/>
    </justification>
  </clause>

  <clause id="8374">
    <literal><![CDATA[
      T(x * K(y,T(x,z)),y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8265(a,1),5247(a,1,1))].">
      <j1 rule="para" parents="8265 5247"/>
    </justification>
  </clause>

  <clause id="8375">
    <literal><![CDATA[
      T(x,1 / T(T(y,z),z)) = T(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(299,a,5041,a,b,8297,a),flip(a)].">
      <j1 rule="hyper" parents="299 5041 8297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8376">
    <literal><![CDATA[
      T(x,1 / T(y \ z,y)) = T(x,1 / (z / y))
    ]]></literal>
    <justification jstring="[para(109(a,1),8375(a,1,2,2,1))].">
      <j1 rule="para" parents="109 8375"/>
    </justification>
  </clause>

  <clause id="8377">
    <literal><![CDATA[
      K(x,T(y \ x,z / y)) = K(x,T(y \ x,y \ z))
    ]]></literal>
    <justification jstring="[para(109(a,1),8305(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="109 8305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8378">
    <literal><![CDATA[
      T(x,y) * T(x \ K(x,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      (x \ K(x,z)) * T(x,y) = u
    ]]></literal>
    <justification jstring="[para(8306(a,1),276(a,1,2))].">
      <j1 rule="para" parents="8306 276"/>
    </justification>
  </clause>

  <clause id="8379">
    <literal><![CDATA[
      K(x,L(T(y \ z,y),u,w)) = K(x,L(z / y,u,w))
    ]]></literal>
    <justification jstring="[para(109(a,1),8348(a,1,2,1,1))].">
      <j1 rule="para" parents="109 8348"/>
    </justification>
  </clause>

  <clause id="8380">
    <literal><![CDATA[
      K(x,L((y * z) / y,u,w)) = K(x,L(T(z,y),u,w))
    ]]></literal>
    <justification jstring="[para(222(a,1),8348(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="222 8348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8381">
    <literal><![CDATA[
      K(x,L(y * K(z,y),u,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(5053(a,1),8348(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5053 8348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8382">
    <literal><![CDATA[
      (K(x,y) * T(x,K(z,u))) \ x = K(z,K(u,x)) * K(y,x)
    ]]></literal>
    <justification jstring="[para(7954(a,1),8355(a,2,1))].">
      <j1 rule="para" parents="7954 8355"/>
    </justification>
  </clause>

  <clause id="8383">
    <literal><![CDATA[
      K(x / y,T(z,x \ y)) = K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,8116,a(flip),b,8356,a),flip(a)].">
      <j1 rule="hyper" parents="299 8116 8356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8384">
    <literal><![CDATA[
      x * (T(x,y) \ (K(z,x) / x)) = K(z,x) / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(5521,a,8359,a)].">
      <j1 rule="hyper" parents="5521 8359"/>
    </justification>
  </clause>

  <clause id="8385">
    <literal><![CDATA[
      K(x,T(y \ (x * z),z)) * u = u * K(x,T((y / z) \ x,u))
    ]]></literal>
    <justification jstring="[para(8363(a,2),7507(a,2,1)),flip(a)].">
      <j1 rule="para" parents="8363 7507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8386">
    <literal><![CDATA[
      T(x * (y * K(x,z)),K(x,z)) = T(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(6264,a,8370,a)].">
      <j1 rule="hyper" parents="6264 8370"/>
    </justification>
  </clause>

  <clause id="8387">
    <literal><![CDATA[
      T(x * K(y,x),K(z,y)) != x * u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(x,z)) = u
    ]]></literal>
    <justification jstring="[para(8372(a,2),45(a,1))].">
      <j1 rule="para" parents="8372 45"/>
    </justification>
  </clause>

  <clause id="8388">
    <literal><![CDATA[
      T(x,1 / (((y \ z) \ z) \ z)) = T(x,1 / (z / y))
    ]]></literal>
    <justification jstring="[para(4391(a,1),8376(a,1,2,2))].">
      <j1 rule="para" parents="4391 8376"/>
    </justification>
  </clause>

  <clause id="8389">
    <literal><![CDATA[
      K((1 / x) * y,y \ x) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(4170,a,7428,a),flip(a)].">
      <j1 rule="hyper" parents="4170 7428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8390">
    <literal><![CDATA[
      L(K(x \ y,z),y,x \ 1) = K((x \ 1) * y,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,5608,a(flip),b,7428,a),flip(a)].">
      <j1 rule="hyper" parents="299 5608 7428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8391">
    <literal><![CDATA[
      K((x \ 1) \ y,y \ (x \ 1)) = K(x * y,y \ (x \ 1))
    ]]></literal>
    <justification jstring="[para(76(a,1),8389(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="76 8389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8392">
    <literal><![CDATA[
      x * K(T(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      x * K(y,T(u,z)) = w
    ]]></literal>
    <justification jstring="[para(7196(a,1),7586(a,1))].">
      <j1 rule="para" parents="7196 7586"/>
    </justification>
  </clause>

  <clause id="8394">
    <literal><![CDATA[
      T(K(x,y),z) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) * u = w
    ]]></literal>
    <justification jstring="[para(7533(a,1),7710(a,1,1))].">
      <j1 rule="para" parents="7533 7710"/>
    </justification>
  </clause>

  <clause id="8395">
    <literal><![CDATA[
      T(K(x,T(y,z)),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(T(y,u),z)) = w
    ]]></literal>
    <justification jstring="[para(7489(a,1),7715(a,1))].">
      <j1 rule="para" parents="7489 7715"/>
    </justification>
  </clause>

  <clause id="8396">
    <literal><![CDATA[
      K(x,L(y \ z,y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,y \ z),z,u) = w
    ]]></literal>
    <justification jstring="[para(76(a,1),7811(a,1,2,2))].">
      <j1 rule="para" parents="76 7811"/>
    </justification>
  </clause>

  <clause id="8397">
    <literal><![CDATA[
      K(x,(y * (z / u)) \ (y * z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,u),z,y) = w
    ]]></literal>
    <justification jstring="[para(98(a,1),7811(a,1,2))].">
      <j1 rule="para" parents="98 7811"/>
    </justification>
  </clause>

  <clause id="8398">
    <literal><![CDATA[
      K(L(x,y,z),L(u,w,x)) = K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,7433,a(flip),b,7850,a),flip(a)].">
      <j1 rule="hyper" parents="299 7433 7850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8399">
    <literal><![CDATA[
      K(x,(y * x) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(7347(a,2),7862(a,1))].">
      <j1 rule="para" parents="7347 7862"/>
    </justification>
  </clause>

  <clause id="8401">
    <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(1901(a,1),7894(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="1901 7894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8402">
    <literal><![CDATA[
      L(K(x,x \ y),y,z) = K(x,z \ (x \ (z * y)))
    ]]></literal>
    <justification jstring="[hyper(65,a,7814,a,b,7895,a)].">
      <j1 rule="hyper" parents="65 7814 7895"/>
    </justification>
  </clause>

  <clause id="8403">
    <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(4651(a,1),7895(a,2,2,2,2))].">
      <j1 rule="para" parents="4651 7895"/>
    </justification>
  </clause>

  <clause id="8404">
    <literal><![CDATA[
      K(x,L(y \ z,y,u)) = K(x,(u * y) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,7814,a(flip),b,7942,a)].">
      <j1 rule="hyper" parents="65 7814 7942"/>
    </justification>
  </clause>

  <clause id="8405">
    <literal><![CDATA[
      K(x,(y * z) \ (y * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ x) = u
    ]]></literal>
    <justification jstring="[para(7942(a,1),6822(a,1))].">
      <j1 rule="para" parents="7942 6822"/>
    </justification>
  </clause>

  <clause id="8406">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ (y * u)) = L(K(x,T(z,u)),u,y)
    ]]></literal>
    <justification jstring="[para(7490(a,1),7942(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7490 7942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8407">
    <literal><![CDATA[
      K(x,(y \ z) \ x) = K(x,z \ (y * x))
    ]]></literal>
    <justification jstring="[hyper(6822,a,7944,a)].">
      <j1 rule="hyper" parents="6822 7944"/>
    </justification>
  </clause>

  <clause id="8408">
    <literal><![CDATA[
      K((x \ y) \ z,u \ (x * z)) = K(y \ (x * z),(x \ u) \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,7421,a(flip),b,7944,a),flip(a)].">
      <j1 rule="hyper" parents="65 7421 7944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8409">
    <literal><![CDATA[
      L(T(K(x,(y \ z) \ u),w),u,y) = T(K(x,z \ (y * u)),w)
    ]]></literal>
    <justification jstring="[para(7944(a,1),25(a,2,1))].">
      <j1 rule="para" parents="7944 25"/>
    </justification>
  </clause>

  <clause id="8410">
    <literal><![CDATA[
      (x * y) * K(z,u \ (x * y)) = x * (y * K(z,(x \ u) \ y))
    ]]></literal>
    <justification jstring="[para(7944(a,1),94(a,1,2))].">
      <j1 rule="para" parents="7944 94"/>
    </justification>
  </clause>

  <clause id="8411">
    <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(7944(a,1),5486(a,1))].">
      <j1 rule="para" parents="7944 5486"/>
    </justification>
  </clause>

  <clause id="8412">
    <literal><![CDATA[
      x * K(x,y \ (z * x)) = T(x,(z \ y) \ x)
    ]]></literal>
    <justification jstring="[para(8407(a,1),5083(a,2,2)),flip(a)].">
      <j1 rule="para" parents="8407 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8413">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ x) = K(x,u \ (K(z,y) * x))
    ]]></literal>
    <justification jstring="[para(5426(a,1),8407(a,1,2,1))].">
      <j1 rule="para" parents="5426 8407"/>
    </justification>
  </clause>

  <clause id="8414">
    <literal><![CDATA[
      K(x,T((y \ z) \ 1,z) \ x) = K(x,y \ ((((y \ z) \ 1) \ y) * x))
    ]]></literal>
    <justification jstring="[para(6193(a,2),8407(a,1,2,1))].">
      <j1 rule="para" parents="6193 8407"/>
    </justification>
  </clause>

  <clause id="8415">
    <literal><![CDATA[
      T(x,(y \ z) \ x) = T(x,z \ (y * x))
    ]]></literal>
    <justification jstring="[hyper(5087,a,8412,a),flip(a)].">
      <j1 rule="hyper" parents="5087 8412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8416">
    <literal><![CDATA[
      K(x,T(y,z \ (u * y))) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(8415(a,1),7698(a,1,2))].">
      <j1 rule="para" parents="8415 7698"/>
    </justification>
  </clause>

  <clause id="8417">
    <literal><![CDATA[
      K(x,T(y \ z,u \ z)) = K(x,T(y \ z,u \ y))
    ]]></literal>
    <justification jstring="[para(10(a,1),8416(a,1,2,2,2))].">
      <j1 rule="para" parents="10 8416"/>
    </justification>
  </clause>

  <clause id="8418">
    <literal><![CDATA[
      L(K(x,y \ z),z,y \ 1) = K(x,(y \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(299,a,5648,a(flip),b,7945,a),flip(a)].">
      <j1 rule="hyper" parents="299 5648 7945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8419">
    <literal><![CDATA[
      K(x,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(7967(a,1),7974(a,1))].">
      <j1 rule="para" parents="7967 7974"/>
    </justification>
  </clause>

  <clause id="8420">
    <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(8019(a,2),7974(a,1,2))].">
      <j1 rule="para" parents="8019 7974"/>
    </justification>
  </clause>

  <clause id="8422">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(K(x,K(y,z)),u) = w
    ]]></literal>
    <justification jstring="[para(7489(a,2),8419(a,1,2))].">
      <j1 rule="para" parents="7489 8419"/>
    </justification>
  </clause>

  <clause id="8426">
    <literal><![CDATA[
      K(x,y / z) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,z \ y),z) = u
    ]]></literal>
    <justification jstring="[para(8119(a,1),8419(a,1))].">
      <j1 rule="para" parents="8119 8419"/>
    </justification>
  </clause>

  <clause id="8429">
    <literal><![CDATA[
      T(x / T(y,z),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) * (x / y) = u
    ]]></literal>
    <justification jstring="[para(7189(a,1),8074(a,1,1))].">
      <j1 rule="para" parents="7189 8074"/>
    </justification>
  </clause>

  <clause id="8430">
    <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(8291(a,2),8208(a,1))].">
      <j1 rule="para" parents="8291 8208"/>
    </justification>
  </clause>

  <clause id="8431">
    <literal><![CDATA[
      K(x,T(T(y \ z,y),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z / y,u)) = w
    ]]></literal>
    <justification jstring="[para(437(a,1),8213(a,1,2))].">
      <j1 rule="para" parents="437 8213"/>
    </justification>
  </clause>

  <clause id="8432">
    <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(7704(a,1),8234(a,1,2))].">
      <j1 rule="para" parents="7704 8234"/>
    </justification>
  </clause>

  <clause id="8434">
    <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),8357(a,1,2,1,1))].">
      <j1 rule="para" parents="9 8357"/>
    </justification>
  </clause>

  <clause id="8435">
    <literal><![CDATA[
      K(x,((y \ z) * y) \ y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(7700(a,1),8357(a,1))].">
      <j1 rule="para" parents="7700 8357"/>
    </justification>
  </clause>

  <clause id="8436">
    <literal><![CDATA[
      ((x \ 1) * y) \ T((x \ 1) * y,z) = L(K(x \ y,z),y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,5036,a(flip),b,8390,a)].">
      <j1 rule="hyper" parents="299 5036 8390"/>
    </justification>
  </clause>

  <clause id="8437">
    <literal><![CDATA[
      x * T(K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      x * K(y,T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(7533(a,1),8392(a,1,2))].">
      <j1 rule="para" parents="7533 8392"/>
    </justification>
  </clause>

  <clause id="8438">
    <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(6253(a,2),8394(a,1))].">
      <j1 rule="para" parents="6253 8394"/>
    </justification>
  </clause>

  <clause id="8440">
    <literal><![CDATA[
      (x * ((y \ (x \ z)) * y)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x \ (y \ z)) = u
    ]]></literal>
    <justification jstring="[para(7345(a,2),8399(a,1))].">
      <j1 rule="para" parents="7345 8399"/>
    </justification>
  </clause>

  <clause id="8441">
    <literal><![CDATA[
      L(K(x,x \ y),y,x \ z) = K(x,z \ ((x \ z) * y))
    ]]></literal>
    <justification jstring="[hyper(299,a,7886,a(flip),b,8402,a),flip(a)].">
      <j1 rule="hyper" parents="299 7886 8402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8442">
    <literal><![CDATA[
      K(x,T(1 / y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / (z * y)) = u
    ]]></literal>
    <justification jstring="[para(4801(a,2),8434(a,1))].">
      <j1 rule="para" parents="4801 8434"/>
    </justification>
  </clause>

  <clause id="8443">
    <literal><![CDATA[
      T(K(x,y) * K(z,u),x) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * K(z,T(u,x)) = w
    ]]></literal>
    <justification jstring="[para(7749(a,2),8437(a,1))].">
      <j1 rule="para" parents="7749 8437"/>
    </justification>
  </clause>

  <clause id="8444">
    <literal><![CDATA[
      K(x,y) * R(x,z,x) = R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(140,a,7448,a)].">
      <j1 rule="hyper" parents="140 7448"/>
    </justification>
  </clause>

  <clause id="8445">
    <literal><![CDATA[
      K(x,y) * (x \ R(x,z,x)) = x \ R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,8444,a(flip),b,5367,a),flip(a)].">
      <j1 rule="hyper" parents="119 8444 5367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8446">
    <literal><![CDATA[
      T(x,y) \ R(T(x,y),z,x) = x \ R(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,8444,a(flip),b,5056,a)].">
      <j1 rule="hyper" parents="119 8444 5056"/>
    </justification>
  </clause>

  <clause id="8447">
    <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),7494(a,2,2))].">
      <j1 rule="para" parents="27 7494"/>
    </justification>
  </clause>

  <clause id="8448">
    <literal><![CDATA[
      K(x \ y,z) * K(u,y / x) = K(u,y / x) * K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(3633(a,1),7520(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3633 7520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8449">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,y) * u) = K(x,T(y,z)) * u
    ]]></literal>
    <justification jstring="[para(7952(a,1),7521(a,1,1))].">
      <j1 rule="para" parents="7952 7521"/>
    </justification>
  </clause>

  <clause id="8450">
    <literal><![CDATA[
      T(x / T(y,T(z,x)),y) = T(y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(299,a,7600,a(flip),b,7588,a),flip(a)].">
      <j1 rule="hyper" parents="299 7600 7588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8451">
    <literal><![CDATA[
      T(x / T(y,z),y) = T(y,T(z,x)) \ x
    ]]></literal>
    <justification jstring="[para(8179(a,1),8450(a,1,1,2))].">
      <j1 rule="para" parents="8179 8450"/>
    </justification>
  </clause>

  <clause id="8452">
    <literal><![CDATA[
      x * K(y,(1 / x) * (z * x)) = K(y,L(z,x,x \ 1)) * x
    ]]></literal>
    <justification jstring="[para(2473(a,1),7605(a,1,2,2))].">
      <j1 rule="para" parents="2473 7605"/>
    </justification>
  </clause>

  <clause id="8453">
    <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),7646(a,2,2))].">
      <j1 rule="para" parents="27 7646"/>
    </justification>
  </clause>

  <clause id="8454">
    <literal><![CDATA[
      T(K(x,y) * (z / T(x,u)),T(x,u)) = T(x,u) \ (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(7686(a,1),109(a,1,1))].">
      <j1 rule="para" parents="7686 109"/>
    </justification>
  </clause>

  <clause id="8457">
    <literal><![CDATA[
      K(T(x,y),K(x,z)) = T((u \ w) \ w,v5) \ (K(u,T(v5,w)) * T(u,u \ w))
    ]]></literal>
    <justification jstring="[para(7719(a,2),3585(a,2,2))].">
      <j1 rule="para" parents="7719 3585"/>
    </justification>
  </clause>

  <clause id="8458">
    <literal><![CDATA[
      T(x * K(y,x),T(z,T(x,u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x * K(y,x),z) = w
    ]]></literal>
    <justification jstring="[para(7727(a,1),8310(a,1))].">
      <j1 rule="para" parents="7727 8310"/>
    </justification>
  </clause>

  <clause id="8459">
    <literal><![CDATA[
      T(x,y) * (L(T(x,y),z,x) \ u) = x * (L(x,z,x) \ u)
    ]]></literal>
    <justification jstring="[para(7745(a,1),5387(a,1,2))].">
      <j1 rule="para" parents="7745 5387"/>
    </justification>
  </clause>

  <clause id="8460">
    <literal><![CDATA[
      K(x,y) * (K(z,x) * (u * K(y,x))) = T(K(z,x) * u,K(x,y))
    ]]></literal>
    <justification jstring="[para(7835(a,1),8059(a,1,2))].">
      <j1 rule="para" parents="7835 8059"/>
    </justification>
  </clause>

  <clause id="8461">
    <literal><![CDATA[
      K(x,T(y \ (x * z),z)) = K(x,z / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(8327,a,7847,a),flip(a)].">
      <j1 rule="hyper" parents="8327 7847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8462">
    <literal><![CDATA[
      K(x,y / (x \ z)) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,8363,a(flip),b,8461,a),flip(a)].">
      <j1 rule="hyper" parents="65 8363 8461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8463">
    <literal><![CDATA[
      K(x,(x * y) / z) = K(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,8161,a(flip),b,8461,a)].">
      <j1 rule="hyper" parents="65 8161 8461"/>
    </justification>
  </clause>

  <clause id="8464">
    <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(8461(a,2),7606(a,1,1))].">
      <j1 rule="para" parents="8461 7606"/>
    </justification>
  </clause>

  <clause id="8465">
    <literal><![CDATA[
      K(x,y / (x \ z)) * u = K(x,(z / y) \ x) * u
    ]]></literal>
    <justification jstring="[hyper(59,a,8462,a)].">
      <j1 rule="hyper" parents="59 8462"/>
    </justification>
  </clause>

  <clause id="8466">
    <literal><![CDATA[
      K(x,((x * y) / z) \ x) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(9(a,1),8462(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 8462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8467">
    <literal><![CDATA[
      R(K(x,(y / (z / u)) \ x),z / u,u) = K(x,z / ((x \ y) * u))
    ]]></literal>
    <justification jstring="[para(8462(a,1),6429(a,1,1))].">
      <j1 rule="para" parents="8462 6429"/>
    </justification>
  </clause>

  <clause id="8468">
    <literal><![CDATA[
      K(x,(x \ y) / (x \ z)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(10(a,1),8463(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 8463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8469">
    <literal><![CDATA[
      K(x,y / (x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) \ x) = u
    ]]></literal>
    <justification jstring="[para(8463(a,1),7162(a,1))].">
      <j1 rule="para" parents="8463 7162"/>
    </justification>
  </clause>

  <clause id="8470">
    <literal><![CDATA[
      K(x,(y \ (x * z)) / z) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[para(76(a,1),8466(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="76 8466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8471">
    <literal><![CDATA[
      K(x,(y \ R(x,z,z \ 1)) / a(x,z,z \ 1)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[para(864(a,1),8470(a,1,2,1,2))].">
      <j1 rule="para" parents="864 8470"/>
    </justification>
  </clause>

  <clause id="8472">
    <literal><![CDATA[
      L(K(x,y),z,T(y,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2841,a,7873,a)].">
      <j1 rule="hyper" parents="2841 7873"/>
    </justification>
  </clause>

  <clause id="8473">
    <literal><![CDATA[
      L(K(x,T(y,z)),u,y) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,5730,a(flip),b,8472,a)].">
      <j1 rule="hyper" parents="65 5730 8472"/>
    </justification>
  </clause>

  <clause id="8474">
    <literal><![CDATA[
      K((x \ 1) * y,T(x \ 1,z)) = K(x \ y,T(x \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,8390,a(flip),b,8473,a)].">
      <j1 rule="hyper" parents="65 8390 8473"/>
    </justification>
  </clause>

  <clause id="8475">
    <literal><![CDATA[
      K((x \ y) \ z,T(x,u)) = K(y \ (x * z),T(x,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,7421,a(flip),b,8473,a),flip(a)].">
      <j1 rule="hyper" parents="65 7421 8473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8476">
    <literal><![CDATA[
      x \ (y * K(z,T(x,u))) = (x \ y) * T(K(z,x),u)
    ]]></literal>
    <justification jstring="[para(7489(a,2),7876(a,1,2,2))].">
      <j1 rule="para" parents="7489 7876"/>
    </justification>
  </clause>

  <clause id="8477">
    <literal><![CDATA[
      (x * K(y \ (z \ x),z)) * u = (y * ((z \ (y \ x)) * z)) * u
    ]]></literal>
    <justification jstring="[hyper(59,a,7880,a)].">
      <j1 rule="hyper" parents="59 7880"/>
    </justification>
  </clause>

  <clause id="8478">
    <literal><![CDATA[
      (x * y) * K(x \ (z \ (x * y)),z) = x * ((z \ y) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),7880(a,2,2,1,2))].">
      <j1 rule="para" parents="9 7880"/>
    </justification>
  </clause>

  <clause id="8479">
    <literal><![CDATA[
      x * K(y,z \ (y \ x)) = z * (y * ((z \ x) / y))
    ]]></literal>
    <justification jstring="[hyper(65,a,3501,a(flip),b,7888,a),flip(a)].">
      <j1 rule="hyper" parents="65 3501 7888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8480">
    <literal><![CDATA[
      (((x \ (y / z)) * x) * z) \ y = K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[para(3503(a,2),7892(a,1,1))].">
      <j1 rule="para" parents="3503 7892"/>
    </justification>
  </clause>

  <clause id="8481">
    <literal><![CDATA[
      T(x,y) * K(y * L(x,z,u),x) = R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(7917(a,1),6663(a,1,2))].">
      <j1 rule="para" parents="7917 6663"/>
    </justification>
  </clause>

  <clause id="8482">
    <literal><![CDATA[
      L(x,L(y,T(z,y),T(z,y)),u) = L(x,z * (z * ((T(z,y) * y) / z)),u)
    ]]></literal>
    <justification jstring="[para(7936(a,1),4739(a,2,2,2))].">
      <j1 rule="para" parents="7936 4739"/>
    </justification>
  </clause>

  <clause id="8483">
    <literal><![CDATA[
      T(x,y) * (x \ T(x * z,x)) = T(T(x,y) * z,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),7937(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 7937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8484">
    <literal><![CDATA[
      K(x,K(y,z)) * (x \ R(x,y,x)) = T(K(x,y),z) * K(x * y,x)
    ]]></literal>
    <justification jstring="[para(5587(a,1),7966(a,1,2))].">
      <j1 rule="para" parents="5587 7966"/>
    </justification>
  </clause>

  <clause id="8486">
    <literal><![CDATA[
      (x * K(y,z)) * T(K(z,y),u) = x * K(z,K(y,u))
    ]]></literal>
    <justification jstring="[para(7184(a,1),7977(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7184 7977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8487">
    <literal><![CDATA[
      K(x * y,x) * K(x,K(y,z)) = K(x * y,T(x,z))
    ]]></literal>
    <justification jstring="[para(7989(a,2),8046(a,1,2))].">
      <j1 rule="para" parents="7989 8046"/>
    </justification>
  </clause>

  <clause id="8488">
    <literal><![CDATA[
      L(T(K(x,y),z),u,w) \ (z * L(K(x,y),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      z = v5
    ]]></literal>
    <justification jstring="[para(8105(a,1),314(a,1,2))].">
      <j1 rule="para" parents="8105 314"/>
    </justification>
  </clause>

  <clause id="8489">
    <literal><![CDATA[
      ((1 / x) * (K(y,z) * x)) * x = x * L(K(y,z),x,x \ 1)
    ]]></literal>
    <justification jstring="[para(2473(a,1),8105(a,1,1))].">
      <j1 rule="para" parents="2473 8105"/>
    </justification>
  </clause>

  <clause id="8490">
    <literal><![CDATA[
      K(x / ((y \ 1) * z),L(z,y \ 1,y) / (L(z,y \ 1,y) / y)) = K((y \ L(z,y \ 1,y)) \ x,y)
    ]]></literal>
    <justification jstring="[para(415(a,1),8167(a,1,1,2))].">
      <j1 rule="para" parents="415 8167"/>
    </justification>
  </clause>

  <clause id="8491">
    <literal><![CDATA[
      T(x,R((y * z) / y,u,w)) = x * K(T(x,y),R(z,u,w))
    ]]></literal>
    <justification jstring="[para(8175(a,1),5083(a,2,2))].">
      <j1 rule="para" parents="8175 5083"/>
    </justification>
  </clause>

  <clause id="8493">
    <literal><![CDATA[
      T(x,R((y * z) / y,u,w)) = T(x,R(T(z,y),u,w))
    ]]></literal>
    <justification jstring="[para(27(a,2),8191(a,2,2))].">
      <j1 rule="para" parents="27 8191"/>
    </justification>
  </clause>

  <clause id="8494">
    <literal><![CDATA[
      T(K(x,y),T(z,K(y,u))) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(299,a,7965,a(flip),b,8235,a),flip(a)].">
      <j1 rule="hyper" parents="299 7965 8235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8495">
    <literal><![CDATA[
      T(K(x,y),z / K(u,y)) = T(K(x,y),K(u,y) \ z)
    ]]></literal>
    <justification jstring="[para(6254(a,1),8494(a,1,2))].">
      <j1 rule="para" parents="6254 8494"/>
    </justification>
  </clause>

  <clause id="8496">
    <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(4366(a,1),8238(a,1,2,2,2))].">
      <j1 rule="para" parents="4366 8238"/>
    </justification>
  </clause>

  <clause id="8497">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,y \ z) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(299,a,8096,a(flip),b,8242,a),flip(a)].">
      <j1 rule="hyper" parents="299 8096 8242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8498">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(8242(a,2),8226(a,1))].">
      <j1 rule="para" parents="8242 8226"/>
    </justification>
  </clause>

  <clause id="8499">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,z / y) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(8030,a,8497,a)].">
      <j1 rule="hyper" parents="8030 8497"/>
    </justification>
  </clause>

  <clause id="8500">
    <literal><![CDATA[
      K(x,K(y,z)) * u != K(x,z / y)
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(8497(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="8497 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8501">
    <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(8497(a,1),5153(a,1,1,1))].">
      <j1 rule="para" parents="8497 5153"/>
    </justification>
  </clause>

  <clause id="8502">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,x \ z) = K(y,z / x)
    ]]></literal>
    <justification jstring="[para(7983(a,1),8497(a,1,1))].">
      <j1 rule="para" parents="7983 8497"/>
    </justification>
  </clause>

  <clause id="8503">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,z \ x) = K(y,x / z)
    ]]></literal>
    <justification jstring="[para(7989(a,1),8497(a,1,1))].">
      <j1 rule="para" parents="7989 8497"/>
    </justification>
  </clause>

  <clause id="8504">
    <literal><![CDATA[
      K(x,K(y * z,(y * u) * z)) * K(x,R(u * K(y,u),y,z)) = K(x,(y * z) \ ((y * u) * z))
    ]]></literal>
    <justification jstring="[para(5242(a,2),8499(a,1,2,2))].">
      <j1 rule="para" parents="5242 8499"/>
    </justification>
  </clause>

  <clause id="8505">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,z / x) = K(y,x \ z)
    ]]></literal>
    <justification jstring="[para(7983(a,1),8499(a,1,1))].">
      <j1 rule="para" parents="7983 8499"/>
    </justification>
  </clause>

  <clause id="8506">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,x / z) = K(y,z \ x)
    ]]></literal>
    <justification jstring="[para(7989(a,1),8499(a,1,1))].">
      <j1 rule="para" parents="7989 8499"/>
    </justification>
  </clause>

  <clause id="8507">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,y / z) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(8004(a,1),8499(a,1,1))].">
      <j1 rule="para" parents="8004 8499"/>
    </justification>
  </clause>

  <clause id="8508">
    <literal><![CDATA[
      K(x,K(y,z * (u * (z \ x)))) * K(y,L(T(u,z \ x),z \ x,z)) = K(y,(z * (u * (z \ x))) / x)
    ]]></literal>
    <justification jstring="[para(777(a,2),8502(a,1,2,2))].">
      <j1 rule="para" parents="777 8502"/>
    </justification>
  </clause>

  <clause id="8509">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,z / x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x \ z) = u
    ]]></literal>
    <justification jstring="[para(8502(a,1),8031(a,1,2)),flip(b)].">
      <j1 rule="para" parents="8502 8031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8510">
    <literal><![CDATA[
      T(x,K(y,z)) * K(y,z \ x) = x * K(y,x / z)
    ]]></literal>
    <justification jstring="[para(8503(a,1),5055(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8503 5055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8511">
    <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(5951(a,2),8503(a,2,2)),flip(a)].">
      <j1 rule="para" parents="5951 8503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8512">
    <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(3009(a,2),8505(a,2,2))].">
      <j1 rule="para" parents="3009 8505"/>
    </justification>
  </clause>

  <clause id="8513">
    <literal><![CDATA[
      K(x,y / z) * K(x,K(y,z)) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(6267,a,8507,a)].">
      <j1 rule="hyper" parents="6267 8507"/>
    </justification>
  </clause>

  <clause id="8514">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) * K(x,((y \ u) \ u) / z) = K(x,z \ ((y \ u) \ u))
    ]]></literal>
    <justification jstring="[para(7493(a,1),8507(a,1,1,2))].">
      <j1 rule="para" parents="7493 8507"/>
    </justification>
  </clause>

  <clause id="8515">
    <literal><![CDATA[
      K(x,(y * (z * u)) / (y * z)) * K(x,K(y * (z * u),y * z)) = K(x,L(u,z,y))
    ]]></literal>
    <justification jstring="[para(18(a,2),8513(a,2,2))].">
      <j1 rule="para" parents="18 8513"/>
    </justification>
  </clause>

  <clause id="8517">
    <literal><![CDATA[
      (x \ y) * K(x / y,y) = (y * (x / y)) \ y
    ]]></literal>
    <justification jstring="[hyper(65,a,1630,a(flip),b,8288,a),flip(a)].">
      <j1 rule="hyper" parents="65 1630 8288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8518">
    <literal><![CDATA[
      T(K(x,y),z / (1 / y)) = K(x,1 / (z / (z / (1 / y))))
    ]]></literal>
    <justification jstring="[hyper(65,a,5803,a(flip),b,8299,a)].">
      <j1 rule="hyper" parents="65 5803 8299"/>
    </justification>
  </clause>

  <clause id="8519">
    <literal><![CDATA[
      K(x,K(x,y) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(5238,a,8335,a)].">
      <j1 rule="hyper" parents="5238 8335"/>
    </justification>
  </clause>

  <clause id="8520">
    <literal><![CDATA[
      K(x,K(x,y) \ z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),8519(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 8519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8521">
    <literal><![CDATA[
      K(x,T(x,y) * z) = K(x,x * z)
    ]]></literal>
    <justification jstring="[para(5103(a,1),8519(a,1,2))].">
      <j1 rule="para" parents="5103 8519"/>
    </justification>
  </clause>

  <clause id="8522">
    <literal><![CDATA[
      K(x,K(y,x) \ z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(5426(a,2),8519(a,1,2))].">
      <j1 rule="para" parents="5426 8519"/>
    </justification>
  </clause>

  <clause id="8523">
    <literal><![CDATA[
      K(x,K(y,x) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(5432(a,1),8519(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5432 8519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8524">
    <literal><![CDATA[
      K(x,T(x,y) \ z) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(5351(a,1),8519(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5351 8519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8525">
    <literal><![CDATA[
      K(x,y \ T(y * z,x)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(5727(a,1),8519(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5727 8519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8526">
    <literal><![CDATA[
      K(x,K(y,K(x,z) * u)) = K(y,K(x,u))
    ]]></literal>
    <justification jstring="[para(8519(a,1),7983(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8519 7983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8527">
    <literal><![CDATA[
      K(x,y * K(x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(8101(a,1),8519(a,1,2))].">
      <j1 rule="para" parents="8101 8519"/>
    </justification>
  </clause>

  <clause id="8528">
    <literal><![CDATA[
      K(x,y * K(z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(8140(a,1),8519(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8140 8519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8529">
    <literal><![CDATA[
      K(x,K(K(x,y) \ z,u)) = K(K(x,z),u)
    ]]></literal>
    <justification jstring="[para(8520(a,1),7954(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8520 7954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8530">
    <literal><![CDATA[
      T(K(x,y),K(z,y) \ u) = K(x,y) * K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(8522(a,1),7964(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8522 7964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8531">
    <literal><![CDATA[
      T(x,K(y,x) * z) = x * K(x,z)
    ]]></literal>
    <justification jstring="[para(8523(a,1),5083(a,2,2))].">
      <j1 rule="para" parents="8523 5083"/>
    </justification>
  </clause>

  <clause id="8532">
    <literal><![CDATA[
      K(x,R(K(y,x),z,u) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(6011(a,1),8523(a,1,2,1))].">
      <j1 rule="para" parents="6011 8523"/>
    </justification>
  </clause>

  <clause id="8533">
    <literal><![CDATA[
      K(x,y * K(x,z)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,5036,a(flip),b,8527,a),flip(a)].">
      <j1 rule="hyper" parents="299 5036 8527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8534">
    <literal><![CDATA[
      T(x,K(y,x * K(y,z))) = x
    ]]></literal>
    <justification jstring="[para(8527(a,2),3612(a,1,2))].">
      <j1 rule="para" parents="8527 3612"/>
    </justification>
  </clause>

  <clause id="8536">
    <literal><![CDATA[
      K(x,y / K(z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7196(a,2),8527(a,1,2))].">
      <j1 rule="para" parents="7196 8527"/>
    </justification>
  </clause>

  <clause id="8537">
    <literal><![CDATA[
      K(x,(y * z) * (z \ K(u,x))) = K(x,R(y,z,z \ K(u,x)))
    ]]></literal>
    <justification jstring="[para(347(a,1),8528(a,1,2))].">
      <j1 rule="para" parents="347 8528"/>
    </justification>
  </clause>

  <clause id="8538">
    <literal><![CDATA[
      R(K(x,y),y * K(z,x),u) = K(x,y * K(z,x))
    ]]></literal>
    <justification jstring="[para(8528(a,1),4778(a,1,1))].">
      <j1 rule="para" parents="8528 4778"/>
    </justification>
  </clause>

  <clause id="8539">
    <literal><![CDATA[
      K(x * K(y,z),z) = 1 / K(z,x)
    ]]></literal>
    <justification jstring="[para(8528(a,1),5209(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8528 5209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8541">
    <literal><![CDATA[
      K(x,K(y,x * K(y,z))) = 1
    ]]></literal>
    <justification jstring="[hyper(57,a,8534,a)].">
      <j1 rule="hyper" parents="57 8534"/>
    </justification>
  </clause>

  <clause id="8542">
    <literal><![CDATA[
      K(x,y \ K(z,x)) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(5953,a,8536,a),flip(a)].">
      <j1 rule="hyper" parents="5953 8536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8543">
    <literal><![CDATA[
      K(x,T(x * K(y,z),y)) = K(x,x * K(y,z))
    ]]></literal>
    <justification jstring="[para(7785(a,2),8521(a,1,2))].">
      <j1 rule="para" parents="7785 8521"/>
    </justification>
  </clause>

  <clause id="8544">
    <literal><![CDATA[
      K(x,y / T(x,z)) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(8320,a,8524,a)].">
      <j1 rule="hyper" parents="8320 8524"/>
    </justification>
  </clause>

  <clause id="8545">
    <literal><![CDATA[
      K(x / y,(x / y) \ z) = K(x / y,(y \ x) \ z)
    ]]></literal>
    <justification jstring="[para(109(a,1),8524(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="109 8524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8547">
    <literal><![CDATA[
      T(x,K(y,x) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,5083,a,b,8531,a),flip(a)].">
      <j1 rule="hyper" parents="299 5083 8531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8548">
    <literal><![CDATA[
      L(x,y \ (K(z,y) * u),T(y,u)) = L(x,y \ (K(z,y) * u),y)
    ]]></literal>
    <justification jstring="[para(8547(a,1),4986(a,1,3))].">
      <j1 rule="para" parents="8547 4986"/>
    </justification>
  </clause>

  <clause id="8549">
    <literal><![CDATA[
      T(x,T(x,y) * z) = T(x,x * z)
    ]]></literal>
    <justification jstring="[para(5061(a,1),8547(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5061 8547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8550">
    <literal><![CDATA[
      T(x,K(x,y) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(5432(a,1),8547(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5432 8547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8551">
    <literal><![CDATA[
      T(x,T(y,x) \ z) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(5351(a,1),8547(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5351 8547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8552">
    <literal><![CDATA[
      T(x,T(x,y) \ z) = T(x,x \ z)
    ]]></literal>
    <justification jstring="[para(5383(a,1),8547(a,1,2))].">
      <j1 rule="para" parents="5383 8547"/>
    </justification>
  </clause>

  <clause id="8553">
    <literal><![CDATA[
      T(x,(y / x) \ z) = T(x,(x \ y) \ z)
    ]]></literal>
    <justification jstring="[para(5692(a,1),8547(a,1,2))].">
      <j1 rule="para" parents="5692 8547"/>
    </justification>
  </clause>

  <clause id="8555">
    <literal><![CDATA[
      T(x \ y,(y / x) \ z) = T(x \ y,(x \ y) \ z)
    ]]></literal>
    <justification jstring="[para(5918(a,1),8547(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5918 8547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8556">
    <literal><![CDATA[
      T(x,y \ T(z,x)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(5850(a,1),8547(a,1,2))].">
      <j1 rule="para" parents="5850 8547"/>
    </justification>
  </clause>

  <clause id="8557">
    <literal><![CDATA[
      T(x,y * K(z,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(7621(a,1),8547(a,1,2))].">
      <j1 rule="para" parents="7621 8547"/>
    </justification>
  </clause>

  <clause id="8558">
    <literal><![CDATA[
      T(x,K(x,y) * L(K(z,x),u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(299,a,3672,a(flip),b,8550,a),flip(a)].">
      <j1 rule="hyper" parents="299 3672 8550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8559">
    <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(8550(a,1),5468(a,1,1))].">
      <j1 rule="para" parents="8550 5468"/>
    </justification>
  </clause>

  <clause id="8561">
    <literal><![CDATA[
      K(x,T(y,K(x,z) * u)) = K(T(x,u),y)
    ]]></literal>
    <justification jstring="[para(8550(a,1),7537(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8550 7537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8562">
    <literal><![CDATA[
      T(x,y * K(x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(8101(a,1),8550(a,1,2))].">
      <j1 rule="para" parents="8101 8550"/>
    </justification>
  </clause>

  <clause id="8563">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),T(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K((K(y,z) * u) / x,y) = w
    ]]></literal>
    <justification jstring="[para(8550(a,1),8219(a,1,2))].">
      <j1 rule="para" parents="8550 8219"/>
    </justification>
  </clause>

  <clause id="8564">
    <literal><![CDATA[
      T(x,y / T(z,x)) = T(x,y / z)
    ]]></literal>
    <justification jstring="[para(8360(a,1),8550(a,1,2))].">
      <j1 rule="para" parents="8360 8550"/>
    </justification>
  </clause>

  <clause id="8565">
    <literal><![CDATA[
      T(x,y * T(x,z)) = T(x,y * x)
    ]]></literal>
    <justification jstring="[para(7194(a,1),8557(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7194 8557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8566">
    <literal><![CDATA[
      K(T(x,y),(y * K(z,x)) \ u) = K(x,u / (y * K(z,x)))
    ]]></literal>
    <justification jstring="[para(8557(a,1),8128(a,1,1))].">
      <j1 rule="para" parents="8557 8128"/>
    </justification>
  </clause>

  <clause id="8569">
    <literal><![CDATA[
      (x * K(y,z)) * L(T(y,x),u,w) = L(y,u,w) * (x * K(y,z))
    ]]></literal>
    <justification jstring="[para(8562(a,1),233(a,1,2,1))].">
      <j1 rule="para" parents="8562 233"/>
    </justification>
  </clause>

  <clause id="8571">
    <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(8562(a,1),4399(a,1,2,1))].">
      <j1 rule="para" parents="8562 4399"/>
    </justification>
  </clause>

  <clause id="8573">
    <literal><![CDATA[
      T(x,y * L(K(x,z),u,w)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(6131(a,1),8562(a,1,2,2))].">
      <j1 rule="para" parents="6131 8562"/>
    </justification>
  </clause>

  <clause id="8575">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,T(y,x)) = K(u / (x * K(y,z)),y)
    ]]></literal>
    <justification jstring="[para(8562(a,1),8116(a,1,2))].">
      <j1 rule="para" parents="8562 8116"/>
    </justification>
  </clause>

  <clause id="8576">
    <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(8562(a,1),8114(a,1,1,1,2))].">
      <j1 rule="para" parents="8562 8114"/>
    </justification>
  </clause>

  <clause id="8577">
    <literal><![CDATA[
      K(x,y * K(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(8533(a,2),5155(a,1))].">
      <j1 rule="para" parents="8533 5155"/>
    </justification>
  </clause>

  <clause id="8578">
    <literal><![CDATA[
      K(x * K(y,z),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,5209,a(flip),b,8539,a),flip(a)].">
      <j1 rule="hyper" parents="299 5209 8539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8579">
    <literal><![CDATA[
      K(x * K(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(8539(a,2),5211(a,1))].">
      <j1 rule="para" parents="8539 5211"/>
    </justification>
  </clause>

  <clause id="8580">
    <literal><![CDATA[
      K(x * T(y,z),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(1389(a,1),8578(a,1,1))].">
      <j1 rule="para" parents="1389 8578"/>
    </justification>
  </clause>

  <clause id="8583">
    <literal><![CDATA[
      R(K(x,y),x * K(z,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x * K(z,y),y) = w
    ]]></literal>
    <justification jstring="[para(8578(a,1),4613(a,1,1))].">
      <j1 rule="para" parents="8578 4613"/>
    </justification>
  </clause>

  <clause id="8584">
    <literal><![CDATA[
      K(T(x,y) * z,y) = K(x * z,y)
    ]]></literal>
    <justification jstring="[para(5843(a,1),8578(a,1,1))].">
      <j1 rule="para" parents="5843 8578"/>
    </justification>
  </clause>

  <clause id="8585">
    <literal><![CDATA[
      K(x * L(K(y,z),u,w),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(6341(a,1),8578(a,1,1,2))].">
      <j1 rule="para" parents="6341 8578"/>
    </justification>
  </clause>

  <clause id="8586">
    <literal><![CDATA[
      K(x * (y / z),z \ y) = K(x * (z \ y),z \ y)
    ]]></literal>
    <justification jstring="[para(6970(a,1),8578(a,1,1))].">
      <j1 rule="para" parents="6970 8578"/>
    </justification>
  </clause>

  <clause id="8587">
    <literal><![CDATA[
      K(x * K(y,z),y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7184(a,1),8578(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7184 8578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8588">
    <literal><![CDATA[
      K(x * T(y,z),y) = K(x * y,y)
    ]]></literal>
    <justification jstring="[para(7194(a,1),8578(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7194 8578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8589">
    <literal><![CDATA[
      K(x * K(y,z \ u),u / z) = K(x,u / z)
    ]]></literal>
    <justification jstring="[para(7538(a,1),8578(a,1,1,2))].">
      <j1 rule="para" parents="7538 8578"/>
    </justification>
  </clause>

  <clause id="8590">
    <literal><![CDATA[
      K(K(x,y) * z,y) = K(z,y)
    ]]></literal>
    <justification jstring="[para(7541(a,1),8578(a,1,1))].">
      <j1 rule="para" parents="7541 8578"/>
    </justification>
  </clause>

  <clause id="8591">
    <literal><![CDATA[
      K(K(x,y) * z,x) = K(z,x)
    ]]></literal>
    <justification jstring="[para(7543(a,1),8578(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7543 8578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8592">
    <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(8587(a,1),5833(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="8587 5833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8594">
    <literal><![CDATA[
      K(T(x,y) * z,x) = K(x * z,x)
    ]]></literal>
    <justification jstring="[para(5061(a,1),8590(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5061 8590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8595">
    <literal><![CDATA[
      K(K(x,y) \ z,x) = K(z,x)
    ]]></literal>
    <justification jstring="[para(5426(a,2),8590(a,1,1))].">
      <j1 rule="para" parents="5426 8590"/>
    </justification>
  </clause>

  <clause id="8596">
    <literal><![CDATA[
      K(K(x,y) * z,T(y,u)) = K(z,T(y,u))
    ]]></literal>
    <justification jstring="[para(7556(a,1),8590(a,1,1,1))].">
      <j1 rule="para" parents="7556 8590"/>
    </justification>
  </clause>

  <clause id="8600">
    <literal><![CDATA[
      K(R(K(x,y),z,u) * w,x) = K(w,x)
    ]]></literal>
    <justification jstring="[para(6213(a,1),8591(a,1,1,1))].">
      <j1 rule="para" parents="6213 8591"/>
    </justification>
  </clause>

  <clause id="8601">
    <literal><![CDATA[
      L(K(x,y),K(y,z) * x,u) = K(K(y,z) * x,y)
    ]]></literal>
    <justification jstring="[para(8591(a,1),6821(a,1,1))].">
      <j1 rule="para" parents="8591 6821"/>
    </justification>
  </clause>

  <clause id="8603">
    <literal><![CDATA[
      K(K(x,y) * z,K(x,u)) = K(K(z,x),u)
    ]]></literal>
    <justification jstring="[para(8591(a,1),7954(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8591 7954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8604">
    <literal><![CDATA[
      K(K(x,y) * z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x) = u
    ]]></literal>
    <justification jstring="[para(8595(a,1),7476(a,1))].">
      <j1 rule="para" parents="8595 7476"/>
    </justification>
  </clause>

  <clause id="8605">
    <literal><![CDATA[
      K(T(x,T(y,z)) * u,y) = K(x * u,y)
    ]]></literal>
    <justification jstring="[para(7573(a,1),8595(a,1,1))].">
      <j1 rule="para" parents="7573 8595"/>
    </justification>
  </clause>

  <clause id="8606">
    <literal><![CDATA[
      (x / T(y,x)) * ((y \ T(x,y)) \ z) = K(y,y \ x) * z
    ]]></literal>
    <justification jstring="[para(8544(a,1),5391(a,2,1))].">
      <j1 rule="para" parents="8544 5391"/>
    </justification>
  </clause>

  <clause id="8607">
    <literal><![CDATA[
      T(x,(y * x) \ z) = T(x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,7882,a(flip),b,8551,a)].">
      <j1 rule="hyper" parents="65 7882 8551"/>
    </justification>
  </clause>

  <clause id="8608">
    <literal><![CDATA[
      (x * (T(x,y) / y)) / x = T(x,y \ x) / T(y,x)
    ]]></literal>
    <justification jstring="[para(8551(a,1),4418(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8551 4418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8611">
    <literal><![CDATA[
      T(x,y) / T(y,y \ x) = y \ T(x,y)
    ]]></literal>
    <justification jstring="[para(8556(a,1),262(a,1,2))].">
      <j1 rule="para" parents="8556 262"/>
    </justification>
  </clause>

  <clause id="8612">
    <literal><![CDATA[
      (1 / T(x,y)) \ (T(y,x) * (1 / x)) = T(y,1 / x)
    ]]></literal>
    <justification jstring="[hyper(65,a,5724,a,b,8564,a)].">
      <j1 rule="hyper" parents="65 5724 8564"/>
    </justification>
  </clause>

  <clause id="8613">
    <literal><![CDATA[
      T(x,y / (z / x)) = T(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[para(109(a,1),8564(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="109 8564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8615">
    <literal><![CDATA[
      T(x,y * T(x,z)) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(299,a,4366,a(flip),b,8565,a),flip(a)].">
      <j1 rule="hyper" parents="299 4366 8565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8616">
    <literal><![CDATA[
      K(x \ (y * T(z,u)),T(z,y * z)) = K((y * T(z,u)) / x,z)
    ]]></literal>
    <justification jstring="[para(8565(a,1),8107(a,1,2))].">
      <j1 rule="para" parents="8565 8107"/>
    </justification>
  </clause>

  <clause id="8617">
    <literal><![CDATA[
      K(x * (y / R(z,u,z)),z) = K(x * (R(z,u,z) \ y),z)
    ]]></literal>
    <justification jstring="[para(7459(a,1),8580(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7459 8580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8618">
    <literal><![CDATA[
      K(x * T(y,z),y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,5980,a(flip),b,8588,a),flip(a)].">
      <j1 rule="hyper" parents="299 5980 8588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8619">
    <literal><![CDATA[
      T(x,x * (y / T(x,z))) = T(x,y)
    ]]></literal>
    <justification jstring="[para(12(a,1),8615(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 8615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8621">
    <literal><![CDATA[
      T(x * K(y,x),(x * K(y,x)) * z) = T(x * K(y,x),z * x)
    ]]></literal>
    <justification jstring="[para(5053(a,1),8615(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5053 8615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8622">
    <literal><![CDATA[
      K(T(x,y) * z,x) = K(z * T(x,u),x)
    ]]></literal>
    <justification jstring="[hyper(299,a,8594,a,b,8618,a)].">
      <j1 rule="hyper" parents="299 8594 8618"/>
    </justification>
  </clause>

  <clause id="8623">
    <literal><![CDATA[
      K(x * (y / T(x,z)),x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(12(a,1),8618(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12 8618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8624">
    <literal><![CDATA[
      K(x,K(y,R(x,z,u)) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(6437(a,1),8532(a,1,2,1))].">
      <j1 rule="para" parents="6437 8532"/>
    </justification>
  </clause>

  <clause id="8625">
    <literal><![CDATA[
      T(x,y * (z * K(x,u))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(94(a,1),8573(a,1,2))].">
      <j1 rule="para" parents="94 8573"/>
    </justification>
  </clause>

  <clause id="8626">
    <literal><![CDATA[
      T(x,y * K(L(x,z,u),w)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(7433(a,1),8573(a,1,2,2))].">
      <j1 rule="para" parents="7433 8573"/>
    </justification>
  </clause>

  <clause id="8629">
    <literal><![CDATA[
      K(x \ T(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(1388(a,1),8579(a,1,1))].">
      <j1 rule="para" parents="1388 8579"/>
    </justification>
  </clause>

  <clause id="8630">
    <literal><![CDATA[
      K(x * K(y,L(z,u,w)),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(7813(a,1),8585(a,1,1,2))].">
      <j1 rule="para" parents="7813 8585"/>
    </justification>
  </clause>

  <clause id="8631">
    <literal><![CDATA[
      K((K(x,y) * z) * u,x) = K(z * u,x)
    ]]></literal>
    <justification jstring="[para(103(a,1),8600(a,1,1))].">
      <j1 rule="para" parents="103 8600"/>
    </justification>
  </clause>

  <clause id="8632">
    <literal><![CDATA[
      K(x * y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y * x,x) = z
    ]]></literal>
    <justification jstring="[para(5020(a,1),8604(a,1,1))].">
      <j1 rule="para" parents="5020 8604"/>
    </justification>
  </clause>

  <clause id="8633">
    <literal><![CDATA[
      K(x,R(x,y,z) * u) = K(x,u * R(x,y,z))
    ]]></literal>
    <justification jstring="[para(5020(a,1),8624(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5020 8624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8634">
    <literal><![CDATA[
      K(x,K(R(x,y,z),u) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(5432(a,1),8624(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5432 8624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8635">
    <literal><![CDATA[
      K(x,T(R(x,y,z),u) \ w) = K(x,R(x,y,z) \ w)
    ]]></literal>
    <justification jstring="[para(5383(a,1),8624(a,1,2))].">
      <j1 rule="para" parents="5383 8624"/>
    </justification>
  </clause>

  <clause id="8636">
    <literal><![CDATA[
      K(x,y * K(z,R(x,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7621(a,1),8624(a,1,2))].">
      <j1 rule="para" parents="7621 8624"/>
    </justification>
  </clause>

  <clause id="8637">
    <literal><![CDATA[
      T(x,L(x,y,z) * (z * y)) = T(x,z * (y * x))
    ]]></literal>
    <justification jstring="[para(492(a,1),8626(a,1,2))].">
      <j1 rule="para" parents="492 8626"/>
    </justification>
  </clause>

  <clause id="8638">
    <literal><![CDATA[
      K(L(x,y,z) * u,x) = K(u * L(x,y,z),x)
    ]]></literal>
    <justification jstring="[para(88(a,1),8630(a,1,1)),flip(a)].">
      <j1 rule="para" parents="88 8630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8639">
    <literal><![CDATA[
      K((L(x,y,z) \ u) * L(x,y,z),x) = K(u,x)
    ]]></literal>
    <justification jstring="[para(287(a,1),8630(a,1,1))].">
      <j1 rule="para" parents="287 8630"/>
    </justification>
  </clause>

  <clause id="8640">
    <literal><![CDATA[
      K((x \ 1) \ y,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x * y,y) = z
    ]]></literal>
    <justification jstring="[para(5741(a,2),8632(a,1))].">
      <j1 rule="para" parents="5741 8632"/>
    </justification>
  </clause>

  <clause id="8641">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) * w) = K(x,R(x,z,u) * w)
    ]]></literal>
    <justification jstring="[para(5414(a,1),8634(a,1,2))].">
      <j1 rule="para" parents="5414 8634"/>
    </justification>
  </clause>

  <clause id="8642">
    <literal><![CDATA[
      K(x,T(y,T(z,R(x,u,w)))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7968(a,1),8634(a,1,2))].">
      <j1 rule="para" parents="7968 8634"/>
    </justification>
  </clause>

  <clause id="8643">
    <literal><![CDATA[
      K(x,K(y,K(x,z) * u)) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,7983,a,b,8526,a),flip(a)].">
      <j1 rule="hyper" parents="299 7983 8526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8644">
    <literal><![CDATA[
      K(x,K(K(x,y) \ z,u)) = K(x,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,7954,a(flip),b,8529,a),flip(a)].">
      <j1 rule="hyper" parents="299 7954 8529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8645">
    <literal><![CDATA[
      T(x,(y / x) \ z) = T(x,y \ (x * z))
    ]]></literal>
    <justification jstring="[hyper(299,a,7841,a(flip),b,8553,a),flip(a)].">
      <j1 rule="hyper" parents="299 7841 8553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8646">
    <literal><![CDATA[
      K(x,T(y,K(x,z) * u)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,7537,a(flip),b,8561,a),flip(a)].">
      <j1 rule="hyper" parents="299 7537 8561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8647">
    <literal><![CDATA[
      K(T(x,y) * z,T(x,u)) = K(x * z,T(x,u))
    ]]></literal>
    <justification jstring="[para(5061(a,1),8596(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5061 8596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8648">
    <literal><![CDATA[
      K(K(x,y) * z,K(x,u)) = K(x,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,7984,a(flip),b,8603,a),flip(a)].">
      <j1 rule="hyper" parents="299 7984 8603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8649">
    <literal><![CDATA[
      K(K(x,y) * z,K(x,u)) = K(z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,7954,a(flip),b,8603,a),flip(a)].">
      <j1 rule="hyper" parents="299 7954 8603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8650">
    <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(8605(a,1),5673(a,1,1,2))].">
      <j1 rule="para" parents="8605 5673"/>
    </justification>
  </clause>

  <clause id="8651">
    <literal><![CDATA[
      T(x,L(x \ y,x,z)) = T(x,z \ (x \ (z * y)))
    ]]></literal>
    <justification jstring="[para(96(a,2),8607(a,1,2))].">
      <j1 rule="para" parents="96 8607"/>
    </justification>
  </clause>

  <clause id="8652">
    <literal><![CDATA[
      T(x * y,x) / T(x,y) = x \ T(x * y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),8611(a,1,2,2))].">
      <j1 rule="para" parents="9 8611"/>
    </justification>
  </clause>

  <clause id="8653">
    <literal><![CDATA[
      T(x,(y * x) / z) = T(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,7761,a,b,8613,a)].">
      <j1 rule="hyper" parents="65 7761 8613"/>
    </justification>
  </clause>

  <clause id="8654">
    <literal><![CDATA[
      T(x,y * (z * x)) = T(x,y * (x * z))
    ]]></literal>
    <justification jstring="[para(88(a,1),8625(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="88 8625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8655">
    <literal><![CDATA[
      T(x,y * (K(z,x) * u)) = T(x,y * u)
    ]]></literal>
    <justification jstring="[para(7527(a,1),8625(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7527 8625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8656">
    <literal><![CDATA[
      T(x,y * T(z,K(x,u))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(7972(a,1),8625(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7972 8625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8657">
    <literal><![CDATA[
      K(x,K(y,(z / x) \ u)) = K(x,K(y,(x \ z) \ u))
    ]]></literal>
    <justification jstring="[para(5918(a,1),8643(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5918 8643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8658">
    <literal><![CDATA[
      K(K(x,y) \ z,K(x,u)) = K(x,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(7985,a,8644,a)].">
      <j1 rule="hyper" parents="7985 8644"/>
    </justification>
  </clause>

  <clause id="8659">
    <literal><![CDATA[
      K(x,T(y,K(z,x) * u)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(5432(a,1),8646(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5432 8646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8660">
    <literal><![CDATA[
      K(x,T(y,T(z,K(u,x)))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7959(a,1),8646(a,1,2,2))].">
      <j1 rule="para" parents="7959 8646"/>
    </justification>
  </clause>

  <clause id="8661">
    <literal><![CDATA[
      K(x,T(y,z * K(x,u))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(8101(a,1),8646(a,1,2,2))].">
      <j1 rule="para" parents="8101 8646"/>
    </justification>
  </clause>

  <clause id="8662">
    <literal><![CDATA[
      K(K(x,y) * z,K(y,u)) = K(z,K(y,u))
    ]]></literal>
    <justification jstring="[para(5432(a,1),8649(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5432 8649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8663">
    <literal><![CDATA[
      R(x,K(y,z) * u,K(u,K(y,w))) = x
    ]]></literal>
    <justification jstring="[para(8649(a,1),6866(a,1,3))].">
      <j1 rule="para" parents="8649 6866"/>
    </justification>
  </clause>

  <clause id="8664">
    <literal><![CDATA[
      K(K(x,y) \ z,T(K(x,u),w)) = K(x,K(z,T(u,w)))
    ]]></literal>
    <justification jstring="[para(7489(a,1),8658(a,1,2))].">
      <j1 rule="para" parents="7489 8658"/>
    </justification>
  </clause>

  <clause id="8665">
    <literal><![CDATA[
      K(x,T(y,K(z,x) * u)) = T(K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,7489,a(flip),b,8659,a),flip(a)].">
      <j1 rule="hyper" parents="299 7489 8659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8666">
    <literal><![CDATA[
      T(K(x,y),T(z,K(u,x))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(8419,a,8660,a)].">
      <j1 rule="hyper" parents="8419 8660"/>
    </justification>
  </clause>

  <clause id="8667">
    <literal><![CDATA[
      T(K(x,y),K(z,x) * u) = T(K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(8419,a,8665,a)].">
      <j1 rule="hyper" parents="8419 8665"/>
    </justification>
  </clause>

  <clause id="8668">
    <literal><![CDATA[
      T(K(x,y),(x \ z) * x) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(5014(a,1),8667(a,1,2))].">
      <j1 rule="para" parents="5014 8667"/>
    </justification>
  </clause>

  <clause id="8669">
    <literal><![CDATA[
      T(K(x,y),z * K(u,x)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(7621(a,1),8667(a,1,2))].">
      <j1 rule="para" parents="7621 8667"/>
    </justification>
  </clause>

  <clause id="8670">
    <literal><![CDATA[
      T(K(x,y),z * T(x,u)) = T(K(x,y),z * x)
    ]]></literal>
    <justification jstring="[para(7194(a,1),8669(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7194 8669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8671">
    <literal><![CDATA[
      K(x \ (y \ (z * y)),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ z,y) = u
    ]]></literal>
    <justification jstring="[para(22(a,1),8629(a,1,1,2))].">
      <j1 rule="para" parents="22 8629"/>
    </justification>
  </clause>

  <clause id="8672">
    <literal><![CDATA[
      K(x,T(y,z / R(x,u,w))) = K(x,T(y,R(x,u,w) \ z))
    ]]></literal>
    <justification jstring="[para(109(a,1),8642(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="109 8642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8673">
    <literal><![CDATA[
      K(x * T(y,z \ u),u / z) = K(x * y,u / z)
    ]]></literal>
    <justification jstring="[para(1389(a,1),8589(a,1,1))].">
      <j1 rule="para" parents="1389 8589"/>
    </justification>
  </clause>

  <clause id="8674">
    <literal><![CDATA[
      K(T(x,y) * z,T(T(x,u),w)) = T(T(x,u),w) \ T(T(x,u) * K(x * z,T(x,u)),w)
    ]]></literal>
    <justification jstring="[para(8647(a,1),5682(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="8647 5682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8675">
    <literal><![CDATA[
      T(x * y,x) / T(x,y) = y * K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,7248,a(flip),b,8652,a),flip(a)].">
      <j1 rule="hyper" parents="299 7248 8652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8676">
    <literal><![CDATA[
      T(K(x,y),(x \ z) * T(x,u)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(299,a,8668,a(flip),b,8670,a),flip(a)].">
      <j1 rule="hyper" parents="299 8668 8670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8677">
    <literal><![CDATA[
      L(K(x * y,x) * K(z * y,K(x * y,x)),y,z) = (z * (T(x * y,x) / T(x,y))) / (z * y)
    ]]></literal>
    <justification jstring="[para(8675(a,2),5254(a,2,1,2))].">
      <j1 rule="para" parents="8675 5254"/>
    </justification>
  </clause>

  <clause id="8678">
    <literal><![CDATA[
      ((x \ y) * T(x,z)) * T(K(x,u),y) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u) * ((x \ y) * T(x,z)) = w
    ]]></literal>
    <justification jstring="[para(8676(a,1),276(a,1,2))].">
      <j1 rule="para" parents="8676 276"/>
    </justification>
  </clause>

  <clause id="8679">
    <literal><![CDATA[
      K(x,R(y,K(z,x),u)) = K(x,y * K(z,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,6437,a(flip),b,8538,a)].">
      <j1 rule="hyper" parents="65 6437 8538"/>
    </justification>
  </clause>

  <clause id="8680">
    <literal><![CDATA[
      K(x,y * K(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(8538(a,1),556(a,1))].">
      <j1 rule="para" parents="8538 556"/>
    </justification>
  </clause>

  <clause id="8681">
    <literal><![CDATA[
      K(x,y * x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x * y) = z
    ]]></literal>
    <justification jstring="[para(88(a,1),8680(a,1,2))].">
      <j1 rule="para" parents="88 8680"/>
    </justification>
  </clause>

  <clause id="8682">
    <literal><![CDATA[
      K(x,y \ T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(1388(a,1),8680(a,1,2))].">
      <j1 rule="para" parents="1388 8680"/>
    </justification>
  </clause>

  <clause id="8685">
    <literal><![CDATA[
      K(x,(y \ 1) \ x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x * y) = z
    ]]></literal>
    <justification jstring="[para(5751(a,2),8681(a,1))].">
      <j1 rule="para" parents="5751 8681"/>
    </justification>
  </clause>

  <clause id="8686">
    <literal><![CDATA[
      K(L(x,y,z),y * x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,x * y) = u
    ]]></literal>
    <justification jstring="[para(7436(a,2),8681(a,1))].">
      <j1 rule="para" parents="7436 8681"/>
    </justification>
  </clause>

  <clause id="8687">
    <literal><![CDATA[
      K(x,R(y,K(z,x),u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,8528,a(flip),b,8679,a),flip(a)].">
      <j1 rule="hyper" parents="299 8528 8679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8689">
    <literal><![CDATA[
      K(x,R(R(y,K(z,x),u),w,v5)) = K(x,R(y,w,v5))
    ]]></literal>
    <justification jstring="[para(31(a,1),8687(a,1,2))].">
      <j1 rule="para" parents="31 8687"/>
    </justification>
  </clause>

  <clause id="8690">
    <literal><![CDATA[
      K(L(x,K(y,z),u),y) = K(K(y,z) * x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,7433,a(flip),b,8601,a)].">
      <j1 rule="hyper" parents="65 7433 8601"/>
    </justification>
  </clause>

  <clause id="8691">
    <literal><![CDATA[
      K(L(x,K(y,z),u),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,8591,a(flip),b,8690,a),flip(a)].">
      <j1 rule="hyper" parents="299 8591 8690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8693">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,y) = K(K(y,z) \ (x \ u),y)
    ]]></literal>
    <justification jstring="[para(281(a,1),8691(a,1,1))].">
      <j1 rule="para" parents="281 8691"/>
    </justification>
  </clause>

  <clause id="8694">
    <literal><![CDATA[
      K((x \ y) \ (z * y),y) = K((x \ 1) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(8671,a,8337,a),flip(a)].">
      <j1 rule="hyper" parents="8671 8337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8695">
    <literal><![CDATA[
      K((x \ y) \ z,x) = K(y \ (z * x),x)
    ]]></literal>
    <justification jstring="[hyper(8671,a,7866,a)].">
      <j1 rule="hyper" parents="8671 7866"/>
    </justification>
  </clause>

  <clause id="8696">
    <literal><![CDATA[
      K((x * y) \ (z * y),y) = K(x \ z,y)
    ]]></literal>
    <justification jstring="[hyper(8671,a,7877,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="8671 7877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8697">
    <literal><![CDATA[
      K(x \ (y * z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K((z \ x) \ y,z) = u
    ]]></literal>
    <justification jstring="[para(7866(a,1),8671(a,1))].">
      <j1 rule="para" parents="7866 8671"/>
    </justification>
  </clause>

  <clause id="8698">
    <literal><![CDATA[
      K((x * y) \ (z * y),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ z,y) = u
    ]]></literal>
    <justification jstring="[para(7877(a,2),8671(a,1))].">
      <j1 rule="para" parents="7877 8671"/>
    </justification>
  </clause>

  <clause id="8699">
    <literal><![CDATA[
      K(x \ ((y \ z) * y),y) = K(x \ z,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,7866,a(flip),b,8695,a),flip(a)].">
      <j1 rule="hyper" parents="65 7866 8695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8700">
    <literal><![CDATA[
      T(x,(y \ x) \ (z * x)) = 1 / (x \ K((y \ 1) \ z,x))
    ]]></literal>
    <justification jstring="[para(8694(a,1),5119(a,2,2,2))].">
      <j1 rule="para" parents="8694 5119"/>
    </justification>
  </clause>

  <clause id="8701">
    <literal><![CDATA[
      K(x \ (y * z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K((x / z) \ y,z) = u
    ]]></literal>
    <justification jstring="[para(12(a,1),8698(a,1,1,1))].">
      <j1 rule="para" parents="12 8698"/>
    </justification>
  </clause>

  <clause id="8703">
    <literal><![CDATA[
      K((x * y) \ z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ (y \ z),y) = u
    ]]></literal>
    <justification jstring="[para(8699(a,1),8698(a,1))].">
      <j1 rule="para" parents="8699 8698"/>
    </justification>
  </clause>

  <clause id="8704">
    <literal><![CDATA[
      K((x * y) \ z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ (x \ z),x) = u
    ]]></literal>
    <justification jstring="[para(7344(a,1),8703(a,1))].">
      <j1 rule="para" parents="7344 8703"/>
    </justification>
  </clause>

  <clause id="8705">
    <literal><![CDATA[
      L(K(x \ y,x),y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(z \ (x \ (z * y)),x) = u
    ]]></literal>
    <justification jstring="[para(7419(a,2),8703(a,1))].">
      <j1 rule="para" parents="7419 8703"/>
    </justification>
  </clause>

  <clause id="8706">
    <literal><![CDATA[
      T(x,K(y,z \ x)) / z = T(x / z,K(x,y))
    ]]></literal>
    <justification jstring="[para(5083(a,2),8342(a,1,1))].">
      <j1 rule="para" parents="5083 8342"/>
    </justification>
  </clause>

  <clause id="8707">
    <literal><![CDATA[
      K((x \ y) / z,x) = K(y / (x * z),x)
    ]]></literal>
    <justification jstring="[hyper(36,a,8267,a(flip),b,8362,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="36 8267 8362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8708">
    <literal><![CDATA[
      K(x,T((y * z) \ (y * u),z)) = K(x,L(u / z,z,y))
    ]]></literal>
    <justification jstring="[para(524(a,2),8379(a,1,2))].">
      <j1 rule="para" parents="524 8379"/>
    </justification>
  </clause>

  <clause id="8709">
    <literal><![CDATA[
      T(x,y) \ ((x \ 1) \ K(z,x)) = x * (K(z,x) / T(x,y))
    ]]></literal>
    <justification jstring="[para(8384(a,1),4818(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8384 4818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8710">
    <literal><![CDATA[
      T(x,K(y,z)) \ R(x,u,x) = x \ R(T(x,K(y,z)),u,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,8029,a(flip),b,8445,a)].">
      <j1 rule="hyper" parents="65 8029 8445"/>
    </justification>
  </clause>

  <clause id="8711">
    <literal><![CDATA[
      R(K(x,T(y,z)),y * u,w) = K(x,R(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(7489(a,2),8447(a,1,1))].">
      <j1 rule="para" parents="7489 8447"/>
    </justification>
  </clause>

  <clause id="8712">
    <literal><![CDATA[
      K(x,T(y,z)) * (T(x,y) \ u) = K(x,K(y,z)) * (x \ u)
    ]]></literal>
    <justification jstring="[para(5351(a,1),8449(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5351 8449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8713">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,x \ y) * u) = K(x,T(x \ y,z)) * u
    ]]></literal>
    <justification jstring="[para(8088(a,1),8449(a,1,1))].">
      <j1 rule="para" parents="8088 8449"/>
    </justification>
  </clause>

  <clause id="8714">
    <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),8453(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9 8453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8715">
    <literal><![CDATA[
      T(x,y / (x \ z)) = T(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(5703,a,8465,a)].">
      <j1 rule="hyper" parents="5703 8465"/>
    </justification>
  </clause>

  <clause id="8716">
    <literal><![CDATA[
      T(x,(y * x) / z) = T(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,8653,a,b,8715,a)].">
      <j1 rule="hyper" parents="65 8653 8715"/>
    </justification>
  </clause>

  <clause id="8717">
    <literal><![CDATA[
      K(x \ (y * z),T(y,z)) = K(z / (y \ x),y)
    ]]></literal>
    <justification jstring="[hyper(8219,a,8475,a),flip(a)].">
      <j1 rule="hyper" parents="8219 8475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8718">
    <literal><![CDATA[
      K(x \ (y * z),T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z / (y \ x),y) = u
    ]]></literal>
    <justification jstring="[para(8475(a,1),8219(a,1))].">
      <j1 rule="para" parents="8475 8219"/>
    </justification>
  </clause>

  <clause id="8719">
    <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(1966,a,8476,a),flip(a)].">
      <j1 rule="hyper" parents="1966 8476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8720">
    <literal><![CDATA[
      x * (y * ((x \ z) / y)) != z * u
    ]]></literal>
    <literal><![CDATA[
      K(y,x \ (y \ z)) = u
    ]]></literal>
    <justification jstring="[para(8479(a,1),45(a,1))].">
      <j1 rule="para" parents="8479 45"/>
    </justification>
  </clause>

  <clause id="8721">
    <literal><![CDATA[
      (((x \ y) * x) * z) \ (y * z) = K(x,z \ (x \ (y * z)))
    ]]></literal>
    <justification jstring="[para(11(a,1),8480(a,1,1,1,1,2))].">
      <j1 rule="para" parents="11 8480"/>
    </justification>
  </clause>

  <clause id="8722">
    <literal><![CDATA[
      T(T(x,y) * L(x \ z,u,w),x) = T(x,y) * L(x \ T(z,x),u,w)
    ]]></literal>
    <justification jstring="[para(1905(a,1),8483(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1905 8483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8723">
    <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(1933(a,1),8483(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1933 8483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8724">
    <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(5984(a,1),8486(a,1,1))].">
      <j1 rule="para" parents="5984 8486"/>
    </justification>
  </clause>

  <clause id="8725">
    <literal><![CDATA[
      T(x,R(T(y,y \ z),u,w)) = T(x,R(z / (z / y),u,w))
    ]]></literal>
    <justification jstring="[para(4504(a,1),8493(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4504 8493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8726">
    <literal><![CDATA[
      T(x,K(y,z)) * K(y,z \ x) = K(y,z \ x) * x
    ]]></literal>
    <justification jstring="[hyper(299,a,8099,a,b,8510,a),flip(a)].">
      <j1 rule="hyper" parents="299 8099 8510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8727">
    <literal><![CDATA[
      T(K(x,y),K(z,y) \ u) = T(K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,7964,a(flip),b,8530,a),flip(a)].">
      <j1 rule="hyper" parents="299 7964 8530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8728">
    <literal><![CDATA[
      T(K(x,y),z / K(u,y)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(65,a,8495,a,b,8727,a)].">
      <j1 rule="hyper" parents="65 8495 8727"/>
    </justification>
  </clause>

  <clause id="8730">
    <literal><![CDATA[
      T(K(x,y),z * K(y,u)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(7196(a,1),8728(a,1,2))].">
      <j1 rule="para" parents="7196 8728"/>
    </justification>
  </clause>

  <clause id="8731">
    <literal><![CDATA[
      x * K(y / z,(z \ y) \ x) = (y / z) * (x / (y / z))
    ]]></literal>
    <justification jstring="[para(8545(a,1),5293(a,1,2))].">
      <j1 rule="para" parents="8545 5293"/>
    </justification>
  </clause>

  <clause id="8732">
    <literal><![CDATA[
      L(x \ y,x \ y,x \ y) = T(x \ y,(y / x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,2805,a(flip),b,8555,a)].">
      <j1 rule="hyper" parents="299 2805 8555"/>
    </justification>
  </clause>

  <clause id="8733">
    <literal><![CDATA[
      T(x \ y,z / (y / x)) = T(x \ y,(x \ y) \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,4628,a,b,8555,a)].">
      <j1 rule="hyper" parents="65 4628 8555"/>
    </justification>
  </clause>

  <clause id="8734">
    <literal><![CDATA[
      T(x \ y,(y / x) \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      T(x \ y,y \ x) = z
    ]]></literal>
    <justification jstring="[para(8555(a,2),7059(a,1))].">
      <j1 rule="para" parents="8555 7059"/>
    </justification>
  </clause>

  <clause id="8735">
    <literal><![CDATA[
      K(x,K(y * (x \ z),x \ z)) = K(z,K(x,y * (z / x)))
    ]]></literal>
    <justification jstring="[para(8586(a,1),8012(a,1,2))].">
      <j1 rule="para" parents="8586 8012"/>
    </justification>
  </clause>

  <clause id="8736">
    <literal><![CDATA[
      (1 / T(x,y)) \ (T(y,x) * (1 / x)) = T(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,3733,a(flip),b,8612,a),flip(a)].">
      <j1 rule="hyper" parents="299 3733 8612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8737">
    <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),8635(a,1,2,1))].">
      <j1 rule="para" parents="27 8635"/>
    </justification>
  </clause>

  <clause id="8738">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,x / y) = K(z * ((x \ y) \ 1),x / y)
    ]]></literal>
    <justification jstring="[para(7045(a,1),8673(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7045 8673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8739">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,y) = K(x \ u,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,8595,a(flip),b,8693,a),flip(a)].">
      <j1 rule="hyper" parents="299 8595 8693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8741">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,z) = K(x \ u,z)
    ]]></literal>
    <justification jstring="[para(7184(a,1),8739(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7184 8739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8742">
    <literal><![CDATA[
      K((K(x,y) * z) \ u,x) = K(z \ u,x)
    ]]></literal>
    <justification jstring="[para(7507(a,1),8739(a,1,1,1))].">
      <j1 rule="para" parents="7507 8739"/>
    </justification>
  </clause>

  <clause id="8743">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,T(y,w)) = K(x \ u,T(y,w))
    ]]></literal>
    <justification jstring="[para(8106(a,1),8739(a,1,1,1,2))].">
      <j1 rule="para" parents="8106 8739"/>
    </justification>
  </clause>

  <clause id="8744">
    <literal><![CDATA[
      K(x,(y * K(z,x)) \ u) = (w * K(y \ u,x)) \ w
    ]]></literal>
    <justification jstring="[para(8741(a,1),7200(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="8741 7200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8745">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),y) = K(x \ u,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,7836,a(flip),b,8742,a),flip(a)].">
      <j1 rule="hyper" parents="65 7836 8742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8746">
    <literal><![CDATA[
      K(x \ K(y,z),z) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,7015,a(flip),b,8742,a)].">
      <j1 rule="hyper" parents="65 7015 8742"/>
    </justification>
  </clause>

  <clause id="8747">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) * (y \ K(u,z)) = T(y \ K(u,z),K(x,z))
    ]]></literal>
    <justification jstring="[para(8746(a,1),7991(a,1,1,2))].">
      <j1 rule="para" parents="8746 7991"/>
    </justification>
  </clause>

  <clause id="8750">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),z) = K(x \ u,z)
    ]]></literal>
    <justification jstring="[para(5432(a,1),8745(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5432 8745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8751">
    <literal><![CDATA[
      K(x \ (y / z),z) = K(x \ (z \ y),z)
    ]]></literal>
    <justification jstring="[para(5117(a,1),8745(a,1,1,2))].">
      <j1 rule="para" parents="5117 8745"/>
    </justification>
  </clause>

  <clause id="8752">
    <literal><![CDATA[
      K(x \ (y / z),z \ y) = K(x \ (z \ y),z \ y)
    ]]></literal>
    <justification jstring="[para(5263(a,1),8745(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5263 8745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8753">
    <literal><![CDATA[
      K(x \ (T(y,z) \ u),y) = K(x \ (y \ u),y)
    ]]></literal>
    <justification jstring="[para(5351(a,1),8745(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5351 8745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8756">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),T(y,w)) = K(x \ u,T(y,w))
    ]]></literal>
    <justification jstring="[para(8106(a,1),8745(a,1,1,2,1))].">
      <j1 rule="para" parents="8106 8745"/>
    </justification>
  </clause>

  <clause id="8757">
    <literal><![CDATA[
      K(x \ (y * K(z,u)),z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(8101(a,1),8745(a,1,1,2))].">
      <j1 rule="para" parents="8101 8745"/>
    </justification>
  </clause>

  <clause id="8758">
    <literal><![CDATA[
      K(x \ (y * T(z,u)),u) = K(x \ (y * z),u)
    ]]></literal>
    <justification jstring="[para(5853(a,1),8750(a,1,1,2))].">
      <j1 rule="para" parents="5853 8750"/>
    </justification>
  </clause>

  <clause id="8759">
    <literal><![CDATA[
      K(x \ (y / (z * y)),z \ 1) = K(x \ ((z * y) \ y),z \ 1)
    ]]></literal>
    <justification jstring="[para(5948(a,1),8750(a,1,1,2))].">
      <j1 rule="para" parents="5948 8750"/>
    </justification>
  </clause>

  <clause id="8760">
    <literal><![CDATA[
      L(x * K(y \ (x \ z),x),u,w) / L(x,u,w) = K(y \ (z / x),L(x,u,w))
    ]]></literal>
    <justification jstring="[para(8751(a,1),5827(a,1,1,1,2))].">
      <j1 rule="para" parents="8751 5827"/>
    </justification>
  </clause>

  <clause id="8761">
    <literal><![CDATA[
      K(x \ (y * K(z,u)),T(z,w)) = K(x \ y,T(z,w))
    ]]></literal>
    <justification jstring="[para(8106(a,1),8757(a,1,1,2,2))].">
      <j1 rule="para" parents="8106 8757"/>
    </justification>
  </clause>

  <clause id="8762">
    <literal><![CDATA[
      K((x * (y * z)) \ ((x * z) * y),z) = K(a(x,z,T(y,z)),z)
    ]]></literal>
    <justification jstring="[para(225(a,1),8758(a,1,1)),flip(a)].">
      <j1 rule="para" parents="225 8758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8763">
    <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),8711(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 8711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8764">
    <literal><![CDATA[
      R(K(x,y),(y * K(z,y)) * u,w) = K(x,R(T(y * K(z,y),z),u,w))
    ]]></literal>
    <justification jstring="[para(5053(a,1),8711(a,1,1,2))].">
      <j1 rule="para" parents="5053 8711"/>
    </justification>
  </clause>

  <clause id="8765">
    <literal><![CDATA[
      K(x,(x * y) \ ((x * z) * y)) = K(x,R(T(z,y),x,y))
    ]]></literal>
    <justification jstring="[hyper(5312,a,8714,a)].">
      <j1 rule="hyper" parents="5312 8714"/>
    </justification>
  </clause>

  <clause id="8766">
    <literal><![CDATA[
      T(x,K(y,z \ x)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(37,a,8069,a,b,8726,a)].">
      <j1 rule="hyper" parents="37 8069 8726"/>
    </justification>
  </clause>

  <clause id="8767">
    <literal><![CDATA[
      T(x,K(y,z \ x)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,8050,a,b,8766,a),flip(a)].">
      <j1 rule="hyper" parents="299 8050 8766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8768">
    <literal><![CDATA[
      T(x,K(y,z \ x)) = x * K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,8022,a,b,8766,a),flip(a)].">
      <j1 rule="hyper" parents="299 8022 8766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8769">
    <literal><![CDATA[
      T(x,K(y,x / z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(79(a,1),8766(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="79 8766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8770">
    <literal><![CDATA[
      (K(x \ y,z) * y) \ T(y,K(x,z)) = K(z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(119,a,8767,a(flip),b,7203,a)].">
      <j1 rule="hyper" parents="119 8767 7203"/>
    </justification>
  </clause>

  <clause id="8771">
    <literal><![CDATA[
      K(1 / ((1 / x) / y),K(z,(y * x) / u)) = (T(y * x,K(z,u)) / x) / y
    ]]></literal>
    <justification jstring="[para(8769(a,1),5934(a,2,1,1))].">
      <j1 rule="para" parents="8769 5934"/>
    </justification>
  </clause>

  <clause id="8772">
    <literal><![CDATA[
      K(x,K(y \ z,z)) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(8052,a,8768,a)].">
      <j1 rule="hyper" parents="8052 8768"/>
    </justification>
  </clause>

  <clause id="8773">
    <literal><![CDATA[
      K(x,K(y,z \ x)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(5154,a,8768,a)].">
      <j1 rule="hyper" parents="5154 8768"/>
    </justification>
  </clause>

  <clause id="8775">
    <literal><![CDATA[
      K(x,K(y \ z,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,7952,a,b,8772,a),flip(a)].">
      <j1 rule="hyper" parents="299 7952 8772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8776">
    <literal><![CDATA[
      K(x,K(y \ z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8772(a,2),7953(a,1))].">
      <j1 rule="para" parents="8772 7953"/>
    </justification>
  </clause>

  <clause id="8777">
    <literal><![CDATA[
      K(x,K(x / y,z)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(79(a,1),8773(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="79 8773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8778">
    <literal><![CDATA[
      K(x,K(y,x / z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8035,a,8777,a)].">
      <j1 rule="hyper" parents="8035 8777"/>
    </justification>
  </clause>

  <clause id="8779">
    <literal><![CDATA[
      K(x,K(y,y / z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(8007,a,8777,a)].">
      <j1 rule="hyper" parents="8007 8777"/>
    </justification>
  </clause>

  <clause id="8780">
    <literal><![CDATA[
      K(x,K(x / y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8777(a,2),8035(a,1))].">
      <j1 rule="para" parents="8777 8035"/>
    </justification>
  </clause>

  <clause id="8781">
    <literal><![CDATA[
      K(x,K(y,y / z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,7983,a,b,8779,a),flip(a)].">
      <j1 rule="hyper" parents="299 7983 8779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8782">
    <literal><![CDATA[
      K(x,K(y,z \ y)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(76(a,1),8781(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="76 8781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8783">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,8044,a,b,8782,a)].">
      <j1 rule="hyper" parents="65 8044 8782"/>
    </justification>
  </clause>

  <clause id="8784">
    <literal><![CDATA[
      K(x,K(y,z)) * (z \ y) = T(z \ y,K(x,y))
    ]]></literal>
    <justification jstring="[para(8782(a,1),8000(a,1,1))].">
      <j1 rule="para" parents="8782 8000"/>
    </justification>
  </clause>

  <clause id="8785">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(8035,a,8783,a)].">
      <j1 rule="hyper" parents="8035 8783"/>
    </justification>
  </clause>

  <clause id="8786">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(8025,a,8783,a)].">
      <j1 rule="hyper" parents="8025 8783"/>
    </justification>
  </clause>

  <clause id="8787">
    <literal><![CDATA[
      K(x \ 1,K(y,z)) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(8007,a,8783,a)].">
      <j1 rule="hyper" parents="8007 8783"/>
    </justification>
  </clause>

  <clause id="8788">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,8004,a,b,8783,a),flip(a)].">
      <j1 rule="hyper" parents="299 8004 8783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8789">
    <literal><![CDATA[
      K(x,K(y,1 / z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(79(a,1),8783(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="79 8783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8790">
    <literal><![CDATA[
      T(x,K(y,z \ 1)) = x * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(8783(a,1),5083(a,2,2))].">
      <j1 rule="para" parents="8783 5083"/>
    </justification>
  </clause>

  <clause id="8791">
    <literal><![CDATA[
      K(x,K(y,z / u)) = K(x,K(y,u / z))
    ]]></literal>
    <justification jstring="[para(5937(a,1),8783(a,1,2))].">
      <j1 rule="para" parents="5937 8783"/>
    </justification>
  </clause>

  <clause id="8792">
    <literal><![CDATA[
      K(x,K(y,z / (u * z))) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(5941(a,2),8783(a,1,2))].">
      <j1 rule="para" parents="5941 8783"/>
    </justification>
  </clause>

  <clause id="8793">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) = T(K(x,y),z \ 1)
    ]]></literal>
    <justification jstring="[para(8783(a,1),7964(a,1,2))].">
      <j1 rule="para" parents="8783 7964"/>
    </justification>
  </clause>

  <clause id="8794">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,8004,a,b,8785,a),flip(a)].">
      <j1 rule="hyper" parents="299 8004 8785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8795">
    <literal><![CDATA[
      K(x,K(y,1 / z)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(79(a,1),8785(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 8785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8796">
    <literal><![CDATA[
      K(x,K(y \ z,u)) = K(x,K(u,z \ y))
    ]]></literal>
    <justification jstring="[para(6977(a,1),8785(a,1,2))].">
      <j1 rule="para" parents="6977 8785"/>
    </justification>
  </clause>

  <clause id="8797">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) / (u / z))) = K(y,(T(u,x) / z) / (u / z))
    ]]></literal>
    <justification jstring="[para(6027(a,1),8786(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6027 8786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8798">
    <literal><![CDATA[
      K(x,K(y,1 / z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(7652,a,8787,a),flip(a)].">
      <j1 rule="hyper" parents="7652 8787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8799">
    <literal><![CDATA[
      K(1 / x,K(y,z)) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(5559,a,8787,a)].">
      <j1 rule="hyper" parents="5559 8787"/>
    </justification>
  </clause>

  <clause id="8800">
    <literal><![CDATA[
      K(x \ 1,K(y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,7989,a(flip),b,8787,a),flip(a)].">
      <j1 rule="hyper" parents="299 7989 8787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8801">
    <literal><![CDATA[
      L(K(x \ 1,K(y,z)),u,w) = K(y,K(z,L(x,u,w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,6337,a,b,8787,a)].">
      <j1 rule="hyper" parents="65 6337 8787"/>
    </justification>
  </clause>

  <clause id="8802">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8788(a,2),8035(a,1))].">
      <j1 rule="para" parents="8788 8035"/>
    </justification>
  </clause>

  <clause id="8803">
    <literal><![CDATA[
      (x * K(y \ 1,z)) \ K(x,K(y,z)) = (K(y \ 1,z) * x) \ 1
    ]]></literal>
    <justification jstring="[hyper(119,a,8794,a(flip),b,5886,a(flip))].">
      <j1 rule="hyper" parents="119 8794 5886"/>
    </justification>
  </clause>

  <clause id="8804">
    <literal><![CDATA[
      K(x,y * ((z \ (y \ 1)) * z)) = K(x,K(y * z,z))
    ]]></literal>
    <justification jstring="[para(6016(a,2),8794(a,1,2))].">
      <j1 rule="para" parents="6016 8794"/>
    </justification>
  </clause>

  <clause id="8805">
    <literal><![CDATA[
      K(1 / x,K(y,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(8007,a,8795,a)].">
      <j1 rule="hyper" parents="8007 8795"/>
    </justification>
  </clause>

  <clause id="8806">
    <literal><![CDATA[
      (1 / x) * K(y,K(x,z)) = T(1 / x,K(y,z))
    ]]></literal>
    <justification jstring="[para(8795(a,1),7999(a,1,2))].">
      <j1 rule="para" parents="8795 7999"/>
    </justification>
  </clause>

  <clause id="8807">
    <literal><![CDATA[
      K(x,K(y,1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8795(a,2),8035(a,1))].">
      <j1 rule="para" parents="8795 8035"/>
    </justification>
  </clause>

  <clause id="8808">
    <literal><![CDATA[
      K(1 / x,K(y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8007,a,8798,a)].">
      <j1 rule="hyper" parents="8007 8798"/>
    </justification>
  </clause>

  <clause id="8809">
    <literal><![CDATA[
      (T(x * y,K(z,u)) / y) / x = K(z,K(u,(1 / y) / x))
    ]]></literal>
    <justification jstring="[hyper(65,a,5934,a(flip),b,8799,a)].">
      <j1 rule="hyper" parents="65 5934 8799"/>
    </justification>
  </clause>

  <clause id="8810">
    <literal><![CDATA[
      K(1 / x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(x,z)) = u
    ]]></literal>
    <justification jstring="[para(8799(a,2),8035(a,1))].">
      <j1 rule="para" parents="8799 8035"/>
    </justification>
  </clause>

  <clause id="8811">
    <literal><![CDATA[
      K(x \ 1,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,x)) = u
    ]]></literal>
    <justification jstring="[para(8800(a,2),8025(a,1))].">
      <j1 rule="para" parents="8800 8025"/>
    </justification>
  </clause>

  <clause id="8812">
    <literal><![CDATA[
      T(x,K(y,z \ 1)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,5083,a,b,8790,a),flip(a)].">
      <j1 rule="hyper" parents="299 5083 8790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8813">
    <literal><![CDATA[
      T(x,K(y,z \ 1)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,8022,a(flip),b,8790,a),flip(a)].">
      <j1 rule="hyper" parents="299 8022 8790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8814">
    <literal><![CDATA[
      T(x,K(y \ 1,z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(8081,a,8812,a)].">
      <j1 rule="hyper" parents="8081 8812"/>
    </justification>
  </clause>

  <clause id="8815">
    <literal><![CDATA[
      K(x,y \ 1) * T(z,K(x,y)) = z * K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(8812(a,1),107(a,1,2))].">
      <j1 rule="para" parents="8812 107"/>
    </justification>
  </clause>

  <clause id="8816">
    <literal><![CDATA[
      T(T(x,y),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z \ 1)) = u
    ]]></literal>
    <justification jstring="[para(8812(a,1),7154(a,1))].">
      <j1 rule="para" parents="8812 7154"/>
    </justification>
  </clause>

  <clause id="8817">
    <literal><![CDATA[
      T(T(x,K(y,z)),z \ 1) = T(x,T(z \ 1,y))
    ]]></literal>
    <justification jstring="[para(8812(a,1),8070(a,1,1))].">
      <j1 rule="para" parents="8812 8070"/>
    </justification>
  </clause>

  <clause id="8818">
    <literal><![CDATA[
      T(x,K(y \ 1,z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8081,a,8813,a)].">
      <j1 rule="hyper" parents="8081 8813"/>
    </justification>
  </clause>

  <clause id="8819">
    <literal><![CDATA[
      T(x,K(y \ z,u)) = T(x,K(u,z \ y))
    ]]></literal>
    <justification jstring="[para(6814(a,1),8813(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6814 8813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8820">
    <literal><![CDATA[
      T(x,K(y \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8814(a,2),8081(a,1))].">
      <j1 rule="para" parents="8814 8081"/>
    </justification>
  </clause>

  <clause id="8821">
    <literal><![CDATA[
      T(x,K(y \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(8818(a,2),8081(a,1))].">
      <j1 rule="para" parents="8818 8081"/>
    </justification>
  </clause>

  <clause id="8822">
    <literal><![CDATA[
      K(x,K(y,z / (u * z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(8792(a,2),8035(a,1))].">
      <j1 rule="para" parents="8792 8035"/>
    </justification>
  </clause>

  <clause id="8823">
    <literal><![CDATA[
      K(x,K(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(8796(a,1),8035(a,1))].">
      <j1 rule="para" parents="8796 8035"/>
    </justification>
  </clause>

  <clause id="8824">
    <literal><![CDATA[
      T(x,K(y \ z,z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,8257,a(flip),b,8819,a),flip(a)].">
      <j1 rule="hyper" parents="299 8257 8819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8825">
    <literal><![CDATA[
      T(x,K(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(8819(a,1),8081(a,1))].">
      <j1 rule="para" parents="8819 8081"/>
    </justification>
  </clause>

  <clause id="8826">
    <literal><![CDATA[
      T(x,K(y,y / z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(79(a,1),8824(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 8824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8827">
    <literal><![CDATA[
      K(x / y,K(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7983(a,1),8780(a,1))].">
      <j1 rule="para" parents="7983 8780"/>
    </justification>
  </clause>

  <clause id="8828">
    <literal><![CDATA[
      K(x,K(y,z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u / z)) = w
    ]]></literal>
    <justification jstring="[para(5937(a,1),8802(a,1,2))].">
      <j1 rule="para" parents="5937 8802"/>
    </justification>
  </clause>

  <clause id="8829">
    <literal><![CDATA[
      K(x,K(y,z / (u * z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(5941(a,2),8802(a,1,2))].">
      <j1 rule="para" parents="5941 8802"/>
    </justification>
  </clause>

  <clause id="8830">
    <literal><![CDATA[
      T(K(x,y),z \ 1) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(8234,a,8793,a),flip(a)].">
      <j1 rule="hyper" parents="8234 8793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8831">
    <literal><![CDATA[
      T(K(x,y),z \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(8793(a,1),7974(a,1))].">
      <j1 rule="para" parents="8793 7974"/>
    </justification>
  </clause>

  <clause id="8832">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(7714,a,8830,a)].">
      <j1 rule="hyper" parents="7714 8830"/>
    </justification>
  </clause>

  <clause id="8834">
    <literal><![CDATA[
      T(x,T(y,z \ 1)) = x * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(8830(a,1),7516(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8830 7516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8835">
    <literal><![CDATA[
      K(x * y,T(z,y)) = K(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,7648,a(flip),b,8832,a),flip(a)].">
      <j1 rule="hyper" parents="65 7648 8832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8836">
    <literal><![CDATA[
      K(x,T(y,1 / z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(79(a,1),8832(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="79 8832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8837">
    <literal><![CDATA[
      K(x,T(y / (z \ 1),z)) = K(x,(z \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(109(a,1),8832(a,1,2)),flip(a)].">
      <j1 rule="para" parents="109 8832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8838">
    <literal><![CDATA[
      K(x,T(y,z \ u)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[para(7037(a,1),8832(a,1,2))].">
      <j1 rule="para" parents="7037 8832"/>
    </justification>
  </clause>

  <clause id="8839">
    <literal><![CDATA[
      T(x,T(y,z \ 1)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,5083,a,b,8834,a),flip(a)].">
      <j1 rule="hyper" parents="299 5083 8834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8840">
    <literal><![CDATA[
      T(x,T(y,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8834(a,2),5087(a,1))].">
      <j1 rule="para" parents="8834 5087"/>
    </justification>
  </clause>

  <clause id="8841">
    <literal><![CDATA[
      K(x * R(y,z,u),T(y,x)) = K(x * R(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(172(a,1),8835(a,1,2)),flip(a)].">
      <j1 rule="para" parents="172 8835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8842">
    <literal><![CDATA[
      K(R(x,y,z) * u,T(x,u)) = K(R(x,y,z) * u,x)
    ]]></literal>
    <justification jstring="[para(172(a,1),8835(a,2,2))].">
      <j1 rule="para" parents="172 8835"/>
    </justification>
  </clause>

  <clause id="8843">
    <literal><![CDATA[
      K(L(x,y,z) * u,T(x,u)) = K(L(x,y,z) * u,x)
    ]]></literal>
    <justification jstring="[para(173(a,1),8835(a,2,2))].">
      <j1 rule="para" parents="173 8835"/>
    </justification>
  </clause>

  <clause id="8844">
    <literal><![CDATA[
      K(x,T(y,z \ x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8838(a,1),7717(a,1))].">
      <j1 rule="para" parents="8838 7717"/>
    </justification>
  </clause>

  <clause id="8846">
    <literal><![CDATA[
      K(x,T(x \ y,z \ y)) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(8844,a,8417,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="8844 8417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8848">
    <literal><![CDATA[
      T(T(x,K(y,z)),(y \ z) \ 1) = T(x,T((y \ z) \ 1,y))
    ]]></literal>
    <justification jstring="[para(8257(a,1),8817(a,1,1))].">
      <j1 rule="para" parents="8257 8817"/>
    </justification>
  </clause>

  <clause id="8849">
    <literal><![CDATA[
      T(x,K(y,x \ z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8825,a,8766,a)].">
      <j1 rule="hyper" parents="8825 8766"/>
    </justification>
  </clause>

  <clause id="8850">
    <literal><![CDATA[
      T(x,K(y,x * z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),8849(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 8849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8851">
    <literal><![CDATA[
      T(x,K(y,x * z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,8050,a,b,8850,a),flip(a)].">
      <j1 rule="hyper" parents="299 8050 8850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8852">
    <literal><![CDATA[
      x * K(K(x * y,z),x) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(6271,a,8851,a)].">
      <j1 rule="hyper" parents="6271 8851"/>
    </justification>
  </clause>

  <clause id="8853">
    <literal><![CDATA[
      T(T(x,K(y,z)),x * y) = T(x,T(x * y,z))
    ]]></literal>
    <justification jstring="[para(8851(a,1),8070(a,1,1))].">
      <j1 rule="para" parents="8851 8070"/>
    </justification>
  </clause>

  <clause id="8854">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * x) = T(x,T(x * y,z))
    ]]></literal>
    <justification jstring="[hyper(4484,a,8853,a)].">
      <j1 rule="hyper" parents="4484 8853"/>
    </justification>
  </clause>

  <clause id="8855">
    <literal><![CDATA[
      K(x,y) * T(z,T(z * x,y)) = T(z,x * z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(8854(a,1),232(a,1,2))].">
      <j1 rule="para" parents="8854 232"/>
    </justification>
  </clause>

  <clause id="8856">
    <literal><![CDATA[
      K(x,(y * K(z,x)) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(299,a,7200,a(flip),b,8744,a),flip(a)].">
      <j1 rule="hyper" parents="299 7200 8744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8857">
    <literal><![CDATA[
      T(x,(y * K(z,x)) \ u) = x * K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(8856(a,1),5083(a,2,2))].">
      <j1 rule="para" parents="8856 5083"/>
    </justification>
  </clause>

  <clause id="8858">
    <literal><![CDATA[
      K(x,(y * K(x,z)) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(7184(a,1),8856(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7184 8856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8859">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ u) = K(x,(y * (x \ z)) \ u)
    ]]></literal>
    <justification jstring="[para(7202(a,1),8856(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7202 8856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8860">
    <literal><![CDATA[
      K(x,(K(y,x) * z) \ u) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(7541(a,1),8856(a,1,2,1))].">
      <j1 rule="para" parents="7541 8856"/>
    </justification>
  </clause>

  <clause id="8861">
    <literal><![CDATA[
      K(x,(K(x,y) * z) \ u) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(7543(a,1),8856(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7543 8856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8862">
    <literal><![CDATA[
      K(T(x,y),(z * K(u,x)) \ w) = K(T(x,y),z \ w)
    ]]></literal>
    <justification jstring="[para(7556(a,1),8856(a,1,2,1,2))].">
      <j1 rule="para" parents="7556 8856"/>
    </justification>
  </clause>

  <clause id="8863">
    <literal><![CDATA[
      K(x,y \ (K(x,z) * u)) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,7857,a(flip),b,8860,a)].">
      <j1 rule="hyper" parents="65 7857 8860"/>
    </justification>
  </clause>

  <clause id="8864">
    <literal><![CDATA[
      K(x,y \ T(x,z)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,7946,a(flip),b,8861,a),flip(a)].">
      <j1 rule="hyper" parents="65 7946 8861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8865">
    <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),8861(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14 8861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8866">
    <literal><![CDATA[
      K(x / y,z \ (x / y)) = K(x / y,z \ (y \ x))
    ]]></literal>
    <justification jstring="[para(109(a,1),8864(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="109 8864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8868">
    <literal><![CDATA[
      K(x,y \ (z * x)) = K(x,y \ (x * z))
    ]]></literal>
    <justification jstring="[para(5020(a,1),8863(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5020 8863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8869">
    <literal><![CDATA[
      K(x,y \ (T(x,z) \ u)) = K(x,y \ (x \ u))
    ]]></literal>
    <justification jstring="[para(5351(a,1),8863(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5351 8863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8870">
    <literal><![CDATA[
      K(x,y \ (z \ T(u,x))) = K(x,y \ (z \ u))
    ]]></literal>
    <justification jstring="[para(5728(a,1),8863(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5728 8863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8871">
    <literal><![CDATA[
      K(x,T(y \ (K(x,z) * u),w)) = T(K(x,y \ u),w)
    ]]></literal>
    <justification jstring="[para(8863(a,1),7489(a,2,1))].">
      <j1 rule="para" parents="8863 7489"/>
    </justification>
  </clause>

  <clause id="8872">
    <literal><![CDATA[
      K(x,y \ (z * K(x,u))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(8101(a,1),8863(a,1,2,2))].">
      <j1 rule="para" parents="8101 8863"/>
    </justification>
  </clause>

  <clause id="8873">
    <literal><![CDATA[
      K(x,(x \ y) \ z) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(299,a,7846,a,b,8868,a)].">
      <j1 rule="hyper" parents="299 7846 8868"/>
    </justification>
  </clause>

  <clause id="8874">
    <literal><![CDATA[
      K(x,y \ ((x \ z) * x)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),8868(a,2,2,2))].">
      <j1 rule="para" parents="10 8868"/>
    </justification>
  </clause>

  <clause id="8875">
    <literal><![CDATA[
      K(x,y \ (z * (u / x))) = K(x,y \ (z * (x \ u)))
    ]]></literal>
    <justification jstring="[para(6970(a,1),8872(a,1,2,2))].">
      <j1 rule="para" parents="6970 8872"/>
    </justification>
  </clause>

  <clause id="8876">
    <literal><![CDATA[
      K(x,(x * y) \ (z * x)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(9(a,1),8873(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 8873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8877">
    <literal><![CDATA[
      K(x,y \ (((x \ y) * z) * x)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),8873(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 8873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8878">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z \ (u * y))) = K(x,T(y,(y \ z) \ u))
    ]]></literal>
    <justification jstring="[para(8873(a,1),7967(a,1,2,2))].">
      <j1 rule="para" parents="8873 7967"/>
    </justification>
  </clause>

  <clause id="8879">
    <literal><![CDATA[
      K(x,(y * x) \ (z * x)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,7347,a,b,8876,a)].">
      <j1 rule="hyper" parents="65 7347 8876"/>
    </justification>
  </clause>

  <clause id="8880">
    <literal><![CDATA[
      K(x,(y / x) \ z) = K(x,y \ (z * 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[
      T(x,(y * K(z,x)) \ u) = T(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(299,a,5083,a,b,8857,a),flip(a)].">
      <j1 rule="hyper" parents="299 5083 8857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8882">
    <literal><![CDATA[
      T(x,(K(y,x) * z) \ u) = T(x,z \ u)
    ]]></literal>
    <justification jstring="[para(7541(a,1),8881(a,1,2,1))].">
      <j1 rule="para" parents="7541 8881"/>
    </justification>
  </clause>

  <clause id="8883">
    <literal><![CDATA[
      T(x,y \ (K(z,x) * u)) = T(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,7900,a(flip),b,8882,a),flip(a)].">
      <j1 rule="hyper" parents="65 7900 8882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8886">
    <literal><![CDATA[
      T(x,y \ K(x,z)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(4768(a,1),8883(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4768 8883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8887">
    <literal><![CDATA[
      T(x,y \ T(x,z)) = T(x,y \ x)
    ]]></literal>
    <justification jstring="[para(5049(a,1),8883(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5049 8883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8888">
    <literal><![CDATA[
      T(x,y \ (z * x)) = T(x,y \ (x * z))
    ]]></literal>
    <justification jstring="[para(5020(a,1),8883(a,1,2,2))].">
      <j1 rule="para" parents="5020 8883"/>
    </justification>
  </clause>

  <clause id="8889">
    <literal><![CDATA[
      T(x,y \ ((x \ z) * x)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(5014(a,1),8883(a,1,2,2))].">
      <j1 rule="para" parents="5014 8883"/>
    </justification>
  </clause>

  <clause id="8890">
    <literal><![CDATA[
      T(x,y \ ((z / x) \ u)) = T(x,y \ ((x \ z) \ u))
    ]]></literal>
    <justification jstring="[para(5692(a,1),8883(a,1,2,2))].">
      <j1 rule="para" parents="5692 8883"/>
    </justification>
  </clause>

  <clause id="8891">
    <literal><![CDATA[
      (x \ K(x,y)) * (T(x,x \ 1) * z) = (K(x,y) / x) * (x * z)
    ]]></literal>
    <justification jstring="[para(8886(a,1),5929(a,1,2,1))].">
      <j1 rule="para" parents="8886 5929"/>
    </justification>
  </clause>

  <clause id="8892">
    <literal><![CDATA[
      T(x,T(x,y) / z) = T(x,z \ x)
    ]]></literal>
    <justification jstring="[hyper(7483,a,8887,a)].">
      <j1 rule="hyper" parents="7483 8887"/>
    </justification>
  </clause>

  <clause id="8893">
    <literal><![CDATA[
      T(x,(y / x) \ z) = T(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(299,a,8645,a,b,8888,a)].">
      <j1 rule="hyper" parents="299 8645 8888"/>
    </justification>
  </clause>

  <clause id="8894">
    <literal><![CDATA[
      T(x,y \ ((x \ z) * x)) != u
    ]]></literal>
    <literal><![CDATA[
      x * K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(8889(a,2),5176(a,1))].">
      <j1 rule="para" parents="8889 5176"/>
    </justification>
  </clause>

  <clause id="8895">
    <literal><![CDATA[
      K(x \ ((y \ z) * y),L(y,u,w)) = L(T(y,x \ z),u,w) \ L(y,u,w)
    ]]></literal>
    <justification jstring="[para(8889(a,1),5043(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="8889 5043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8896">
    <literal><![CDATA[
      K(x,T(y,z \ (y \ u))) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(8889(a,1),8416(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8889 8416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8897">
    <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(8893(a,1),5043(a,1,1,1))].">
      <j1 rule="para" parents="8893 5043"/>
    </justification>
  </clause>

  <clause id="8898">
    <literal><![CDATA[
      K(x,(T(x,y) * z) \ u) = K(x,z \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,7860,a,b,8869,a)].">
      <j1 rule="hyper" parents="65 7860 8869"/>
    </justification>
  </clause>

  <clause id="8899">
    <literal><![CDATA[
      K(x,y \ ((T(z,x) / u) \ z)) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(79(a,1),8870(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="79 8870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8900">
    <literal><![CDATA[
      K(x * y,T(x,y \ z)) = K(x * y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,7883,a(flip),b,8896,a),flip(a)].">
      <j1 rule="hyper" parents="65 7883 8896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8901">
    <literal><![CDATA[
      K(x,T(y,(y \ z) \ u)) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(7881(a,1),8896(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7881 8896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8903">
    <literal><![CDATA[
      K(x * y,T(x,y \ z)) = K(y * x,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,6293,a,b,8900,a),flip(a)].">
      <j1 rule="hyper" parents="299 6293 8900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8904">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z \ u)) = K(x,T(y,(y \ z) \ u))
    ]]></literal>
    <justification jstring="[hyper(299,a,7967,a,b,8901,a)].">
      <j1 rule="hyper" parents="299 7967 8901"/>
    </justification>
  </clause>

  <clause id="8906">
    <literal><![CDATA[
      K(x * y,T(y,x \ z)) = K(x * y,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,6293,a,b,8903,a)].">
      <j1 rule="hyper" parents="65 6293 8903"/>
    </justification>
  </clause>

  <clause id="8907">
    <literal><![CDATA[
      K(x * y,T(y,x * z)) = K(x * y,T(y,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),8906(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 8906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8908">
    <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(8752(a,1),5833(a,1,1,1,2))].">
      <j1 rule="para" parents="8752 5833"/>
    </justification>
  </clause>

  <clause id="8909">
    <literal><![CDATA[
      K(x \ (y * z),T(z,u)) = K(x \ (z * y),T(z,u))
    ]]></literal>
    <justification jstring="[para(5020(a,1),8756(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5020 8756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8910">
    <literal><![CDATA[
      K(x,R(T(y,z),y \ 1,u)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,558,a(flip),b,8763,a),flip(a)].">
      <j1 rule="hyper" parents="299 558 8763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8911">
    <literal><![CDATA[
      K(x,R(T(y,z),y \ 1,u)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(299,a,7489,a(flip),b,8910,a),flip(a)].">
      <j1 rule="hyper" parents="299 7489 8910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8912">
    <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(4667(a,1),8770(a,1,1,1,1))].">
      <j1 rule="para" parents="4667 8770"/>
    </justification>
  </clause>

  <clause id="8913">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(8787(a,1),8801(a,1,1))].">
      <j1 rule="para" parents="8787 8801"/>
    </justification>
  </clause>

  <clause id="8914">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(y,K(z,L(x,u,w)))
    ]]></literal>
    <justification jstring="[para(8800(a,1),8801(a,1,1))].">
      <j1 rule="para" parents="8800 8801"/>
    </justification>
  </clause>

  <clause id="8915">
    <literal><![CDATA[
      (x * y) * K(z,K(u,L(w,y,x))) = x * (y * K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(8913(a,1),94(a,1,2))].">
      <j1 rule="para" parents="8913 94"/>
    </justification>
  </clause>

  <clause id="8916">
    <literal><![CDATA[
      (x * y) * K(z,K(u,L(w,y,x))) != v5
    ]]></literal>
    <literal><![CDATA[
      x * (y * K(z,K(u,w))) = v5
    ]]></literal>
    <justification jstring="[para(8913(a,1),279(a,1,2))].">
      <j1 rule="para" parents="8913 279"/>
    </justification>
  </clause>

  <clause id="8917">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(z,K(x,L(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,8913,a(flip),b,8914,a),flip(a)].">
      <j1 rule="hyper" parents="65 8913 8914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8918">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(z,K(y,L(x,u,w)))
    ]]></literal>
    <justification jstring="[hyper(7985,a,8917,a)].">
      <j1 rule="hyper" parents="7985 8917"/>
    </justification>
  </clause>

  <clause id="8919">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(x,K(z,L(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(299,a,7983,a,b,8917,a)].">
      <j1 rule="hyper" parents="299 7983 8917"/>
    </justification>
  </clause>

  <clause id="8920">
    <literal><![CDATA[
      K(x,K(y \ (z \ u),L(w,y,z))) = K(w,K(x,(z * y) \ u))
    ]]></literal>
    <justification jstring="[para(281(a,1),8917(a,2,2,2))].">
      <j1 rule="para" parents="281 8917"/>
    </justification>
  </clause>

  <clause id="8921">
    <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(8917(a,2),7985(a,1))].">
      <j1 rule="para" parents="8917 7985"/>
    </justification>
  </clause>

  <clause id="8922">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(L(y,u,w),z)) = v5
    ]]></literal>
    <justification jstring="[para(8917(a,2),8025(a,1))].">
      <j1 rule="para" parents="8917 8025"/>
    </justification>
  </clause>

  <clause id="8923">
    <literal><![CDATA[
      K(x,K(y,L(z,1 / u,w))) = K(x,K(z,L(y,u,w)))
    ]]></literal>
    <justification jstring="[para(2521(a,1),8919(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2521 8919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8924">
    <literal><![CDATA[
      K(x,(1 / y) * ((z \ ((1 / y) \ 1)) * z)) = K(x,K(y \ z,z))
    ]]></literal>
    <justification jstring="[para(5986(a,1),8804(a,2,2))].">
      <j1 rule="para" parents="5986 8804"/>
    </justification>
  </clause>

  <clause id="8925">
    <literal><![CDATA[
      T(x,y) * K(y * R(x,z,u),x) = R(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(8841(a,1),5278(a,1,2))].">
      <j1 rule="para" parents="8841 5278"/>
    </justification>
  </clause>

  <clause id="8926">
    <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(8841(a,2),7996(a,2,1))].">
      <j1 rule="para" parents="8841 7996"/>
    </justification>
  </clause>

  <clause id="8927">
    <literal><![CDATA[
      K(T(L(x,y,z) * u,u),x) = K(L(x,y,z) * u,x)
    ]]></literal>
    <justification jstring="[hyper(7622,a,8843,a)].">
      <j1 rule="hyper" parents="7622 8843"/>
    </justification>
  </clause>

  <clause id="8928">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,(y * (x \ z)) \ u)) = K((y * (z / x)) \ u,x)
    ]]></literal>
    <justification jstring="[para(8859(a,1),5428(a,1,2,2))].">
      <j1 rule="para" parents="8859 5428"/>
    </justification>
  </clause>

  <clause id="8929">
    <literal><![CDATA[
      K(x / y,z \ (y \ x)) = K(y \ x,(z * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,8279,a(flip),b,8866,a),flip(a)].">
      <j1 rule="hyper" parents="65 8279 8866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8930">
    <literal><![CDATA[
      K(x,T(y \ (K(x,z) * u),w)) = K(x,T(y \ u,w))
    ]]></literal>
    <justification jstring="[hyper(299,a,7489,a,b,8871,a),flip(a)].">
      <j1 rule="hyper" parents="299 7489 8871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8931">
    <literal><![CDATA[
      K(x,(y * (z * (u / x))) \ (z * (x \ u))) = K(x,(z * (u / x)) \ (y \ (z * (u / x))))
    ]]></literal>
    <justification jstring="[hyper(65,a,7929,a(flip),b,8875,a),flip(a)].">
      <j1 rule="hyper" parents="65 7929 8875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8932">
    <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(8890(a,1),5043(a,1,1,1))].">
      <j1 rule="para" parents="8890 5043"/>
    </justification>
  </clause>

  <clause id="8933">
    <literal><![CDATA[
      K((x \ y) \ z,T(z,u)) = K(y \ (z * x),T(z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,7658,a,b,8909,a)].">
      <j1 rule="hyper" parents="65 7658 8909"/>
    </justification>
  </clause>

  <clause id="8934">
    <literal><![CDATA[
      K(x \ (y * (z * K(y,u))),T(y,w)) = K(x \ (z * T(y,u)),T(y,w))
    ]]></literal>
    <justification jstring="[para(6912(a,1),8909(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6912 8909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8935">
    <literal><![CDATA[
      K(x,T(y \ T(x,z),u)) = K(x,T(y \ x,u))
    ]]></literal>
    <justification jstring="[para(5096(a,2),8930(a,1,2,1,2))].">
      <j1 rule="para" parents="5096 8930"/>
    </justification>
  </clause>

  <clause id="8936">
    <literal><![CDATA[
      K(x,T(y \ T(T(x,z),u),w)) = K(x,T(y \ T(x,u),w))
    ]]></literal>
    <justification jstring="[para(7579(a,1),8930(a,1,2,1,2))].">
      <j1 rule="para" parents="7579 8930"/>
    </justification>
  </clause>

  <clause id="8938">
    <literal><![CDATA[
      L(K(x,y \ z),z,z \ 1) = K(x,((z \ 1) * y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,5664,a(flip),b,7179,a),flip(a)].">
      <j1 rule="hyper" parents="299 5664 7179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8939">
    <literal><![CDATA[
      x / (K(y,z) * T(z,u)) = (x / T(z,u)) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(7183,a,7218,a),flip(a)].">
      <j1 rule="hyper" parents="7183 7218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8940">
    <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(5429(a,1),7218(a,2,2))].">
      <j1 rule="para" parents="5429 7218"/>
    </justification>
  </clause>

  <clause id="8941">
    <literal><![CDATA[
      (x / T(y \ 1,z)) * K(y \ 1,y) = x / T(1 / y,z)
    ]]></literal>
    <justification jstring="[para(3693(a,1),8939(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3693 8939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8942">
    <literal><![CDATA[
      (x / T(y,y * z)) * K(y,z) = x / L(y,z,y)
    ]]></literal>
    <justification jstring="[para(5355(a,1),8939(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5355 8939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8943">
    <literal><![CDATA[
      (x / T(y,z)) * K(y,y * z) = x / R(y,z,y)
    ]]></literal>
    <justification jstring="[para(5356(a,1),8939(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5356 8939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8945">
    <literal><![CDATA[
      (x / T(y,z)) * T(y,y * z) = (x / R(y,z,y)) * y
    ]]></literal>
    <justification jstring="[para(8943(a,1),6912(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8943 6912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8946">
    <literal><![CDATA[
      R(x / T(y,z),y,y \ 1) = x * (T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,6801,a(flip),b,7236,a),flip(a)].">
      <j1 rule="hyper" parents="299 6801 7236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8947">
    <literal><![CDATA[
      R(x / T(y,z),y,y) = x * (T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(1259,a,8946,a)].">
      <j1 rule="hyper" parents="1259 8946"/>
    </justification>
  </clause>

  <clause id="8948">
    <literal><![CDATA[
      (x * y) * (T(x,y) \ 1) = R(y,x,x)
    ]]></literal>
    <justification jstring="[para(185(a,1),8947(a,1,1)),flip(a)].">
      <j1 rule="para" parents="185 8947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8949">
    <literal><![CDATA[
      L(x,(y * z) * T(y,z),u) = L(x,R(z,y,y),u)
    ]]></literal>
    <justification jstring="[para(8948(a,1),2888(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8948 2888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8950">
    <literal><![CDATA[
      (x * y) / T(T(x,y),z) = K(z,x) * y
    ]]></literal>
    <justification jstring="[hyper(7302,a,7507,a)].">
      <j1 rule="hyper" parents="7302 7507"/>
    </justification>
  </clause>

  <clause id="8951">
    <literal><![CDATA[
      (x * L(y,z,y)) / T(T(x,y),u) = K(u,x) * L(y,z,y)
    ]]></literal>
    <justification jstring="[para(7449(a,1),8950(a,1,2,1))].">
      <j1 rule="para" parents="7449 8950"/>
    </justification>
  </clause>

  <clause id="8952">
    <literal><![CDATA[
      T(L(x \ 1,x,y) \ 1,x * L(x \ 1,z,u)) = ((y * x) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(1863(a,1),7349(a,2,2))].">
      <j1 rule="para" parents="1863 7349"/>
    </justification>
  </clause>

  <clause id="8953">
    <literal><![CDATA[
      K((T(x,y) * z) \ u,x) = K(z \ (T(x,y) \ u),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,8472,a(flip),b,7422,a),flip(a)].">
      <j1 rule="hyper" parents="65 8472 7422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8954">
    <literal><![CDATA[
      x * ((x \ y) * K(z \ (x \ y),u)) = y * K((x * z) \ y,u)
    ]]></literal>
    <justification jstring="[para(7422(a,1),482(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7422 482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8955">
    <literal><![CDATA[
      L(K(x * (y \ z),x),y \ z,y) = K((y * (x \ 1)) \ z,x)
    ]]></literal>
    <justification jstring="[para(7291(a,1),7422(a,1,1))].">
      <j1 rule="para" parents="7291 7422"/>
    </justification>
  </clause>

  <clause id="8956">
    <literal><![CDATA[
      L(K((x \ y) \ (z \ u),y),z \ u,z) = K((z * (y / x)) \ u,y)
    ]]></literal>
    <justification jstring="[para(7369(a,1),7422(a,1,1))].">
      <j1 rule="para" parents="7369 7422"/>
    </justification>
  </clause>

  <clause id="8957">
    <literal><![CDATA[
      K((T(x,y) * z) \ u,x) = K(z \ (x \ u),x)
    ]]></literal>
    <justification jstring="[hyper(299,a,8753,a(flip),b,8953,a),flip(a)].">
      <j1 rule="hyper" parents="299 8753 8953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8959">
    <literal><![CDATA[
      K((T(x,y) * z) \ u,K(x,w)) = K(w,K(z \ (x \ u),x))
    ]]></literal>
    <justification jstring="[para(8957(a,1),7989(a,2,2))].">
      <j1 rule="para" parents="8957 7989"/>
    </justification>
  </clause>

  <clause id="8960">
    <literal><![CDATA[
      K(L(x,y / x,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,u),y,z) = w
    ]]></literal>
    <justification jstring="[para(7432(a,2),493(a,1))].">
      <j1 rule="para" parents="7432 493"/>
    </justification>
  </clause>

  <clause id="8961">
    <literal><![CDATA[
      K(L(x \ y,x,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x \ y,u),y,z) = w
    ]]></literal>
    <justification jstring="[para(76(a,1),8960(a,1,1,2))].">
      <j1 rule="para" parents="76 8960"/>
    </justification>
  </clause>

  <clause id="8962">
    <literal><![CDATA[
      K(x,T(y \ x,z)) = K(x,T(y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(7712,a,8864,a)].">
      <j1 rule="hyper" parents="7712 8864"/>
    </justification>
  </clause>

  <clause id="8963">
    <literal><![CDATA[
      K(x,T(y,z) \ x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y \ x,z)) = u
    ]]></literal>
    <justification jstring="[para(8864(a,1),7712(a,1))].">
      <j1 rule="para" parents="8864 7712"/>
    </justification>
  </clause>

  <clause id="8964">
    <literal><![CDATA[
      K(x,T(y,K(z,z \ x)) \ x) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(8221,a,8962,a),flip(a)].">
      <j1 rule="hyper" parents="8221 8962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8965">
    <literal><![CDATA[
      K(x,T(y,z) \ T(x,u)) = K(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,8864,a,b,8962,a)].">
      <j1 rule="hyper" parents="299 8864 8962"/>
    </justification>
  </clause>

  <clause id="8966">
    <literal><![CDATA[
      K(x,(K(y \ x,y) * z) \ x) = K(x,(z * K(y \ x,y)) \ x)
    ]]></literal>
    <justification jstring="[para(7199(a,1),8964(a,1,2,1))].">
      <j1 rule="para" parents="7199 8964"/>
    </justification>
  </clause>

  <clause id="8968">
    <literal><![CDATA[
      K(x,T(y \ x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) \ x) = u
    ]]></literal>
    <justification jstring="[para(8965(a,1),8682(a,1))].">
      <j1 rule="para" parents="8965 8682"/>
    </justification>
  </clause>

  <clause id="8970">
    <literal><![CDATA[
      K(x,y) * K(x * y,x) = T(x \ R(x,y,x),y)
    ]]></literal>
    <justification jstring="[para(7491(a,1),7793(a,1,2))].">
      <j1 rule="para" parents="7491 7793"/>
    </justification>
  </clause>

  <clause id="8971">
    <literal><![CDATA[
      T(x \ R(x,y,x),y) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,5587,a(flip),b,8970,a),flip(a)].">
      <j1 rule="hyper" parents="65 5587 8970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8972">
    <literal><![CDATA[
      (x * (y \ R(y,x,y))) / x = y \ R(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(267,a,8971,a)].">
      <j1 rule="hyper" parents="267 8971"/>
    </justification>
  </clause>

  <clause id="8973">
    <literal><![CDATA[
      (T(x * y,x) / x) / y = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[para(7363(a,1),8972(a,1,1))].">
      <j1 rule="para" parents="7363 8972"/>
    </justification>
  </clause>

  <clause id="8974">
    <literal><![CDATA[
      K(x,T(y * z,z)) = K(x,T(y * z,y))
    ]]></literal>
    <justification jstring="[hyper(7797,a,8832,a)].">
      <j1 rule="hyper" parents="7797 8832"/>
    </justification>
  </clause>

  <clause id="8975">
    <literal><![CDATA[
      T(x * y,T(z,y)) = T(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(7806,a,8839,a),flip(a)].">
      <j1 rule="hyper" parents="7806 8839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8976">
    <literal><![CDATA[
      T(x * L(L(y,z,u),w,v5),T(y,x)) = T(x * L(L(y,z,u),w,v5),y)
    ]]></literal>
    <justification jstring="[para(211(a,1),8975(a,1,2)),flip(a)].">
      <j1 rule="para" parents="211 8975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8977">
    <literal><![CDATA[
      K(x,y \ (x \ (y * (z * x)))) = K(x,L(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,5204,a(flip),b,7896,a),flip(a)].">
      <j1 rule="hyper" parents="299 5204 7896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8979">
    <literal><![CDATA[
      K(x \ y,(x * z) \ y) = K(x \ y,z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(6822,a,7943,a),flip(a)].">
      <j1 rule="hyper" parents="6822 7943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8980">
    <literal><![CDATA[
      L(K(x,R(y,z,y) \ (z \ u)),z \ u,z) = K(x,T(y * z,y) \ u)
    ]]></literal>
    <justification jstring="[para(4341(a,1),7943(a,2,2,1))].">
      <j1 rule="para" parents="4341 7943"/>
    </justification>
  </clause>

  <clause id="8981">
    <literal><![CDATA[
      L(K(x,K(y,z) * (u \ w)),u \ w,u) = K(x,(u * K(z,y)) \ w)
    ]]></literal>
    <justification jstring="[para(5426(a,1),7943(a,1,1,2))].">
      <j1 rule="para" parents="5426 7943"/>
    </justification>
  </clause>

  <clause id="8982">
    <literal><![CDATA[
      L(K(x,y \ (z \ u)),z \ u,z) = K(x,(z * T(y,x \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(7643(a,1),7943(a,1,1))].">
      <j1 rule="para" parents="7643 7943"/>
    </justification>
  </clause>

  <clause id="8983">
    <literal><![CDATA[
      L(K(x,x \ (y \ z)),y \ z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(7943(a,2),8399(a,1))].">
      <j1 rule="para" parents="7943 8399"/>
    </justification>
  </clause>

  <clause id="8984">
    <literal><![CDATA[
      L(K(x,y \ ((z \ u) * x)),z \ u,z) = K(x,(z * (x \ y)) \ u)
    ]]></literal>
    <justification jstring="[para(8873(a,1),7943(a,1,1))].">
      <j1 rule="para" parents="8873 7943"/>
    </justification>
  </clause>

  <clause id="8985">
    <literal><![CDATA[
      L(K(x,y \ ((z \ u) * x)),z \ u,z) = K(x,(z * (y / x)) \ u)
    ]]></literal>
    <justification jstring="[para(8880(a,1),7943(a,1,1))].">
      <j1 rule="para" parents="8880 7943"/>
    </justification>
  </clause>

  <clause id="8986">
    <literal><![CDATA[
      L(K(x,(y * (x \ z)) \ (u \ w)),u \ w,u) = K(x,(u * (y * (z / x))) \ w)
    ]]></literal>
    <justification jstring="[para(8859(a,1),7943(a,1,1))].">
      <j1 rule="para" parents="8859 7943"/>
    </justification>
  </clause>

  <clause id="8987">
    <literal><![CDATA[
      K(x \ y,z \ (x \ y)) * (y / x) = T(y / x,T((x * z) \ y,x))
    ]]></literal>
    <justification jstring="[para(8979(a,1),7628(a,1,1))].">
      <j1 rule="para" parents="8979 7628"/>
    </justification>
  </clause>

  <clause id="8988">
    <literal><![CDATA[
      T(x \ y,K(z,y)) = T(x,K(z,y)) \ y
    ]]></literal>
    <justification jstring="[hyper(7976,a,8784,a),flip(a)].">
      <j1 rule="hyper" parents="7976 8784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8989">
    <literal><![CDATA[
      T((K(x,y) * z) \ y,K(x,y)) = (z * K(x,y)) \ y
    ]]></literal>
    <justification jstring="[para(7279(a,1),8988(a,2,1))].">
      <j1 rule="para" parents="7279 8988"/>
    </justification>
  </clause>

  <clause id="8990">
    <literal><![CDATA[
      1 / T(x,K(y,z)) = T(1 / x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8026,a,8806,a)].">
      <j1 rule="hyper" parents="8026 8806"/>
    </justification>
  </clause>

  <clause id="8991">
    <literal><![CDATA[
      T(1 / x,K(y,z)) \ 1 = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(186,a,8990,a)].">
      <j1 rule="hyper" parents="186 8990"/>
    </justification>
  </clause>

  <clause id="8992">
    <literal><![CDATA[
      T(1 / (x * K(y,z)),K(z,y)) = 1 / (K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(7199(a,1),8990(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7199 8990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8993">
    <literal><![CDATA[
      T(x \ 1,K(y,z)) = T(x,K(y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(76(a,1),8991(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="76 8991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8994">
    <literal><![CDATA[
      a(T(x \ 1,K(y,z)),u,w) = a(T(x,K(y,z)),u,w)
    ]]></literal>
    <justification jstring="[para(8993(a,2),2138(a,1,1))].">
      <j1 rule="para" parents="8993 2138"/>
    </justification>
  </clause>

  <clause id="8995">
    <literal><![CDATA[
      T(T(x,y / z),K(z,y)) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(8091,a,8826,a),flip(a)].">
      <j1 rule="hyper" parents="8091 8826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8996">
    <literal><![CDATA[
      T(T(x,y / z),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(8826(a,1),8091(a,1))].">
      <j1 rule="para" parents="8826 8091"/>
    </justification>
  </clause>

  <clause id="8997">
    <literal><![CDATA[
      T(T(x,K(y,z)),y / z) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(8065,a,8995,a)].">
      <j1 rule="hyper" parents="8065 8995"/>
    </justification>
  </clause>

  <clause id="8998">
    <literal><![CDATA[
      T(T(x,K(y,z)),z / y) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(861,a,8995,a)].">
      <j1 rule="hyper" parents="861 8995"/>
    </justification>
  </clause>

  <clause id="9000">
    <literal><![CDATA[
      T(x / (y / z),z \ y) = T((y / z) \ x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(753,a,8997,a),flip(a)].">
      <j1 rule="hyper" parents="753 8997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9001">
    <literal><![CDATA[
      T(T(x,K(y,z)),y \ z) = T(x,z / y)
    ]]></literal>
    <justification jstring="[para(6256(a,1),8997(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6256 8997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9002">
    <literal><![CDATA[
      T(T(x,K(y,z)),z \ y) = T(x,y / z)
    ]]></literal>
    <justification jstring="[para(8057(a,1),8997(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8057 8997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9003">
    <literal><![CDATA[
      T(T(x,K(y,z \ (y * u))),y \ ((y \ z) \ u)) = T(x,((y \ z) \ u) / y)
    ]]></literal>
    <justification jstring="[para(7846(a,1),9001(a,1,1,2))].">
      <j1 rule="para" parents="7846 9001"/>
    </justification>
  </clause>

  <clause id="9004">
    <literal><![CDATA[
      T(T(x,K(y,z)),(y \ z) \ 1) = T(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(7107,a,9002,a)].">
      <j1 rule="hyper" parents="7107 9002"/>
    </justification>
  </clause>

  <clause id="9005">
    <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(5653(a,1),9002(a,1,1,2))].">
      <j1 rule="para" parents="5653 9002"/>
    </justification>
  </clause>

  <clause id="9006">
    <literal><![CDATA[
      T(T(x,K(y,z)),(y \ z) \ 1) = T(x,(z / y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,4641,a,b,9004,a),flip(a)].">
      <j1 rule="hyper" parents="299 4641 9004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9008">
    <literal><![CDATA[
      T(x / (y / z),T(z \ y,x / (y / z))) = T((y / z) \ x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(4454,a,9000,a)].">
      <j1 rule="hyper" parents="4454 9000"/>
    </justification>
  </clause>

  <clause id="9009">
    <literal><![CDATA[
      K(((x \ 1) * y) \ z,T(x,y)) = K(((x \ 1) \ z) / y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,7829,a(flip),b,8169,a),flip(a)].">
      <j1 rule="hyper" parents="65 7829 8169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9010">
    <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(1368(a,1),8406(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1368 8406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9011">
    <literal><![CDATA[
      T(x / T(y \ z,y),K(y,z)) = K(y,y \ z) * (x / (y \ z))
    ]]></literal>
    <justification jstring="[hyper(8429,a,8257,a),flip(a)].">
      <j1 rule="hyper" parents="8429 8257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9012">
    <literal><![CDATA[
      K(x,T(T(y \ z,y),u)) = K(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[hyper(8431,a,xx),flip(a)].">
      <j1 rule="hyper" parents="8431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9013">
    <literal><![CDATA[
      K(x,T((y * z) / y,u)) = K(x,T(T(z,y),u))
    ]]></literal>
    <justification jstring="[para(9(a,1),9012(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="9 9012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9014">
    <literal><![CDATA[
      K(x,T(y * K(z,y),u)) = K(x,T(T(y,z),u))
    ]]></literal>
    <justification jstring="[para(5054(a,1),9013(a,1,2,1))].">
      <j1 rule="para" parents="5054 9013"/>
    </justification>
  </clause>

  <clause id="9015">
    <literal><![CDATA[
      K(x,T(T(y,z) * K(u,T(y,z)),w)) = K(x,T(T(T(y,u),z),w))
    ]]></literal>
    <justification jstring="[para(23(a,1),9014(a,2,2,1))].">
      <j1 rule="para" parents="23 9014"/>
    </justification>
  </clause>

  <clause id="9016">
    <literal><![CDATA[
      K(x * L(y,z,u),y) * K(y,x) = y \ R(y,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,8481,a(flip),b,5362,a),flip(a)].">
      <j1 rule="hyper" parents="119 8481 5362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9017">
    <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(8481(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="8481 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9018">
    <literal><![CDATA[
      K(x,y \ (x \ ((x * z) * y))) = K(x,R(T(z,y),x,y))
    ]]></literal>
    <justification jstring="[hyper(7862,a,8765,a)].">
      <j1 rule="hyper" parents="7862 8765"/>
    </justification>
  </clause>

  <clause id="9020">
    <literal><![CDATA[
      K(x,K(L(y,z,u),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,L(w,z,u))) = v5
    ]]></literal>
    <justification jstring="[para(8004(a,1),8921(a,1))].">
      <j1 rule="para" parents="8004 8921"/>
    </justification>
  </clause>

  <clause id="9021">
    <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(8913(a,2),8921(a,1))].">
      <j1 rule="para" parents="8913 8921"/>
    </justification>
  </clause>

  <clause id="9022">
    <literal><![CDATA[
      K(x * R(y,z,u),y) * K(y,x) = y \ R(y,x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,8925,a(flip),b,5362,a),flip(a)].">
      <j1 rule="hyper" parents="119 8925 5362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9023">
    <literal><![CDATA[
      K(x,y) * K(y * R(x,z,u),x) = x \ R(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,8925,a(flip),b,5055,a),flip(a)].">
      <j1 rule="hyper" parents="119 8925 5055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9024">
    <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(8925(a,1),5716(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8925 5716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9025">
    <literal><![CDATA[
      K(x,((y \ 1) * (y / z)) \ 1) = L(K(x,z),y,y \ 1)
    ]]></literal>
    <justification jstring="[para(79(a,1),8938(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="79 8938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9026">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,z * y) = (x / R(z,y,z)) * z
    ]]></literal>
    <justification jstring="[hyper(65,a,7237,a(flip),b,8945,a)].">
      <j1 rule="hyper" parents="65 7237 8945"/>
    </justification>
  </clause>

  <clause id="9027">
    <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(531(a,1),8961(a,1,1))].">
      <j1 rule="para" parents="531 8961"/>
    </justification>
  </clause>

  <clause id="9028">
    <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(7983(a,1),9021(a,1,1))].">
      <j1 rule="para" parents="7983 9021"/>
    </justification>
  </clause>

  <clause id="9030">
    <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(3022(a,2),6847(a,1,2))].">
      <j1 rule="para" parents="3022 6847"/>
    </justification>
  </clause>

  <clause id="9031">
    <literal><![CDATA[
      K(x,(T(y,z) * u) \ y) = K(x,u \ K(z,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,7118,a(flip),b,6848,a),flip(a)].">
      <j1 rule="hyper" parents="65 7118 6848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9032">
    <literal><![CDATA[
      K(x,(T(y,z) \ u) \ K(z,y)) = K(x,u \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),9031(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 9031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9033">
    <literal><![CDATA[
      x * ((y * y) \ K(y \ 1,z)) = (x / y) * T(y \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(831,a,6877,a)].">
      <j1 rule="hyper" parents="831 6877"/>
    </justification>
  </clause>

  <clause id="9034">
    <literal><![CDATA[
      K(x,x \ 1) / ((y * x) \ y) = ((y * x) \ y) \ 1
    ]]></literal>
    <justification jstring="[hyper(299,a,3002,a(flip),b,6896,a),flip(a)].">
      <j1 rule="hyper" parents="299 3002 6896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9035">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) * K(y,y \ 1) = ((x * y) \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(3297,a,9034,a)].">
      <j1 rule="hyper" parents="3297 9034"/>
    </justification>
  </clause>

  <clause id="9036">
    <literal><![CDATA[
      (x / y) * K(x,1 / y) = T(x,1 / y) / y
    ]]></literal>
    <justification jstring="[para(79(a,1),6919(a,1,2)),flip(a)].">
      <j1 rule="para" parents="79 6919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9037">
    <literal><![CDATA[
      (K(x,y) / z) * K(x,K(y,1 / z)) = T(K(x,y),1 / z) / z
    ]]></literal>
    <justification jstring="[para(7954(a,1),9036(a,1,2))].">
      <j1 rule="para" parents="7954 9036"/>
    </justification>
  </clause>

  <clause id="9038">
    <literal><![CDATA[
      R(x,K(y,z),R(z,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(544,a,6936,a)].">
      <j1 rule="hyper" parents="544 6936"/>
    </justification>
  </clause>

  <clause id="9039">
    <literal><![CDATA[
      x / (K(y,z) * R(z,u,w)) = (x / R(z,u,w)) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,7218,a(flip),b,9038,a)].">
      <j1 rule="hyper" parents="65 7218 9038"/>
    </justification>
  </clause>

  <clause id="9040">
    <literal><![CDATA[
      R(x,K(y,z),L(z,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(544,a,6937,a)].">
      <j1 rule="hyper" parents="544 6937"/>
    </justification>
  </clause>

  <clause id="9041">
    <literal><![CDATA[
      R(x,K(y,z),L(T(z,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[para(7556(a,1),9040(a,1,2))].">
      <j1 rule="para" parents="7556 9040"/>
    </justification>
  </clause>

  <clause id="9042">
    <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(9041(a,1),583(a,1,1))].">
      <j1 rule="para" parents="9041 583"/>
    </justification>
  </clause>

  <clause id="9043">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * y) = y * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,7194,a(flip),b,6973,a)].">
      <j1 rule="hyper" parents="119 7194 6973"/>
    </justification>
  </clause>

  <clause id="9044">
    <literal><![CDATA[
      x / (y * K(z,y)) = (x / y) * K(y,z)
    ]]></literal>
    <justification jstring="[para(9043(a,1),302(a,1,2))].">
      <j1 rule="para" parents="9043 302"/>
    </justification>
  </clause>

  <clause id="9045">
    <literal><![CDATA[
      x / (y / (y / z)) = (x / z) * K(z,z \ y)
    ]]></literal>
    <justification jstring="[para(5002(a,2),9044(a,1,2))].">
      <j1 rule="para" parents="5002 9044"/>
    </justification>
  </clause>

  <clause id="9046">
    <literal><![CDATA[
      x / ((y * z) / y) = (x / z) * K(z,y)
    ]]></literal>
    <justification jstring="[para(5054(a,2),9044(a,1,2))].">
      <j1 rule="para" parents="5054 9044"/>
    </justification>
  </clause>

  <clause id="9047">
    <literal><![CDATA[
      (x / (y \ z)) * K(y \ z,y) = x / (z / y)
    ]]></literal>
    <justification jstring="[para(5102(a,1),9044(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5102 9044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9048">
    <literal><![CDATA[
      x / (y * K(z,T(y,u))) = (x / y) * K(y,T(z,u))
    ]]></literal>
    <justification jstring="[para(7537(a,1),9044(a,1,2,2))].">
      <j1 rule="para" parents="7537 9044"/>
    </justification>
  </clause>

  <clause id="9049">
    <literal><![CDATA[
      (x / ((y * z) / y)) * K(y,z) = x / z
    ]]></literal>
    <justification jstring="[hyper(7207,a,9046,a(flip))].">
      <j1 rule="hyper" parents="7207 9046"/>
    </justification>
  </clause>

  <clause id="9050">
    <literal><![CDATA[
      (x * y) / ((z * y) / z) = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),9046(a,2,1))].">
      <j1 rule="para" parents="11 9046"/>
    </justification>
  </clause>

  <clause id="9052">
    <literal><![CDATA[
      (x / (y / z)) * K(z,z \ y) = x / (z \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),9049(a,1,1,2,1))].">
      <j1 rule="para" parents="10 9049"/>
    </justification>
  </clause>

  <clause id="9053">
    <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(9049(a,1),1033(a,2,1,2))].">
      <j1 rule="para" parents="9049 1033"/>
    </justification>
  </clause>

  <clause id="9054">
    <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(9049(a,1),3476(a,1,2,1))].">
      <j1 rule="para" parents="9049 3476"/>
    </justification>
  </clause>

  <clause id="9055">
    <literal><![CDATA[
      (x / (y * K(z,y))) * y = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,5255,a(flip),b,9050,a)].">
      <j1 rule="hyper" parents="65 5255 9050"/>
    </justification>
  </clause>

  <clause id="9057">
    <literal><![CDATA[
      (x / (y / (y / z))) * z = x * K(z,z \ y)
    ]]></literal>
    <justification jstring="[para(5002(a,2),9055(a,1,1,2))].">
      <j1 rule="para" parents="5002 9055"/>
    </justification>
  </clause>

  <clause id="9058">
    <literal><![CDATA[
      (x / (y / (y / z))) / (y / z) = (x / z) / (z \ y)
    ]]></literal>
    <justification jstring="[hyper(120,a,9045,a,b,7067,a)].">
      <j1 rule="hyper" parents="120 9045 7067"/>
    </justification>
  </clause>

  <clause id="9061">
    <literal><![CDATA[
      K(x,y / (z / x)) = K(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[para(9047(a,1),8528(a,1,2))].">
      <j1 rule="para" parents="9047 8528"/>
    </justification>
  </clause>

  <clause id="9062">
    <literal><![CDATA[
      K(x,y / (z / R(x,u,w))) = K(x,y / (R(x,u,w) \ z))
    ]]></literal>
    <justification jstring="[para(9047(a,1),8636(a,1,2))].">
      <j1 rule="para" parents="9047 8636"/>
    </justification>
  </clause>

  <clause id="9063">
    <literal><![CDATA[
      K(x,(x \ y) / (z / x)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(299,a,8468,a(flip),b,9061,a),flip(a)].">
      <j1 rule="hyper" parents="299 8468 9061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9064">
    <literal><![CDATA[
      K(x,(y * x) / z) = K(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,7754,a,b,9061,a)].">
      <j1 rule="hyper" parents="65 7754 9061"/>
    </justification>
  </clause>

  <clause id="9065">
    <literal><![CDATA[
      K(x,(x \ y) / z) = K(x,y / (z * x))
    ]]></literal>
    <justification jstring="[para(11(a,1),9063(a,1,2,2))].">
      <j1 rule="para" parents="11 9063"/>
    </justification>
  </clause>

  <clause id="9066">
    <literal><![CDATA[
      K(x,(y * x) / z) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(299,a,8462,a(flip),b,9064,a),flip(a)].">
      <j1 rule="hyper" parents="299 8462 9064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9067">
    <literal><![CDATA[
      K(x,(y * x) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) \ x) = u
    ]]></literal>
    <justification jstring="[para(9064(a,2),8469(a,1))].">
      <j1 rule="para" parents="9064 8469"/>
    </justification>
  </clause>

  <clause id="9068">
    <literal><![CDATA[
      T(K(x,y \ (z * x)),y) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(8426,a,9066,a)].">
      <j1 rule="hyper" parents="8426 9066"/>
    </justification>
  </clause>

  <clause id="9070">
    <literal><![CDATA[
      (x \ y) / (y / (y / x)) = (y / x) / x
    ]]></literal>
    <justification jstring="[hyper(120,a,5102,a(flip),b,9057,a),flip(a)].">
      <j1 rule="hyper" parents="120 5102 9057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9072">
    <literal><![CDATA[
      (x * K(y,z / (z / u))) * K(u,u \ z) = (x / T(z / (z / u),y)) * u
    ]]></literal>
    <justification jstring="[para(7206(a,1),9057(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7206 9057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9073">
    <literal><![CDATA[
      K(x,T((y / z) \ x,y)) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(8112,a,9068,a)].">
      <j1 rule="hyper" parents="8112 9068"/>
    </justification>
  </clause>

  <clause id="9074">
    <literal><![CDATA[
      K(x,y \ ((z \ y) * x)) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[para(76(a,1),9073(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="76 9073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9076">
    <literal><![CDATA[
      K(x,(y / x) \ (z \ y)) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,8880,a,b,9074,a)].">
      <j1 rule="hyper" parents="65 8880 9074"/>
    </justification>
  </clause>

  <clause id="9077">
    <literal><![CDATA[
      K(x \ y,T(z \ (x \ y),y)) = K(x \ y,x \ (z \ y))
    ]]></literal>
    <justification jstring="[para(76(a,1),9076(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="76 9076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9078">
    <literal><![CDATA[
      K(T(x / (y / (y / z)),1 / u) / (y / z),u) = K((x / z) / (z \ y),u)
    ]]></literal>
    <justification jstring="[para(9058(a,1),7736(a,2,1))].">
      <j1 rule="para" parents="9058 7736"/>
    </justification>
  </clause>

  <clause id="9079">
    <literal><![CDATA[
      x \ T(x * K(y \ x,z),x) = K(T(y,x) \ x,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,6994,a(flip),b,6868,a(flip))].">
      <j1 rule="hyper" parents="119 6994 6868"/>
    </justification>
  </clause>

  <clause id="9080">
    <literal><![CDATA[
      K(T(x / y,x) \ x,z) = x \ T(x * K(y,z),x)
    ]]></literal>
    <justification jstring="[para(79(a,1),9079(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 9079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9081">
    <literal><![CDATA[
      K((x * y) \ 1,x * y) = K(x \ (1 / y),x * y)
    ]]></literal>
    <justification jstring="[hyper(36,a,3236,a,b,7022,a)].">
      <j1 rule="hyper" parents="36 3236 7022"/>
    </justification>
  </clause>

  <clause id="9082">
    <literal><![CDATA[
      (1 / x) * K(y \ (x \ 1),z) = K((y * x) \ 1,z) / x
    ]]></literal>
    <justification jstring="[para(5617(a,1),7022(a,1,2))].">
      <j1 rule="para" parents="5617 7022"/>
    </justification>
  </clause>

  <clause id="9083">
    <literal><![CDATA[
      K((x * (y \ 1)) \ 1,x * (y \ 1)) = K(x \ y,x * (y \ 1))
    ]]></literal>
    <justification jstring="[para(76(a,1),9081(a,2,1,2))].">
      <j1 rule="para" parents="76 9081"/>
    </justification>
  </clause>

  <clause id="9084">
    <literal><![CDATA[
      K((1 / ((x * y) \ x)) * z,y) = K(z * (1 / ((x * y) \ x)),y)
    ]]></literal>
    <justification jstring="[para(7052(a,1),8580(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7052 8580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9085">
    <literal><![CDATA[
      L(K(x,y),z,L(x,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2841,a,7081,a)].">
      <j1 rule="hyper" parents="2841 7081"/>
    </justification>
  </clause>

  <clause id="9086">
    <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(7081(a,1),7209(a,1,1))].">
      <j1 rule="para" parents="7081 7209"/>
    </justification>
  </clause>

  <clause id="9087">
    <literal><![CDATA[
      K(x,y) * (L(y,z,u) * (w * K(y,x))) = T(L(y,z,u) * w,K(x,y))
    ]]></literal>
    <justification jstring="[para(7081(a,1),8059(a,1,2))].">
      <j1 rule="para" parents="7081 8059"/>
    </justification>
  </clause>

  <clause id="9088">
    <literal><![CDATA[
      K(L(x,y,L(x,z,u)),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,7433,a(flip),b,9085,a)].">
      <j1 rule="hyper" parents="65 7433 9085"/>
    </justification>
  </clause>

  <clause id="9089">
    <literal><![CDATA[
      (R(x,y,z) \ 1) * K(x,u) = R(x,y,z) \ K(x,u)
    ]]></literal>
    <justification jstring="[hyper(608,a,7082,a),flip(a)].">
      <j1 rule="hyper" parents="608 7082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9090">
    <literal><![CDATA[
      (R(x,y,z) \ 1) \ (R(x,y,z) \ K(x,u)) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(125,a,9089,a)].">
      <j1 rule="hyper" parents="125 9089"/>
    </justification>
  </clause>

  <clause id="9092">
    <literal><![CDATA[
      T(K(x \ K(x,y),z),y) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(5138(a,1),7134(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5138 7134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9093">
    <literal><![CDATA[
      K(x \ K(x,y),z) * y = y * K(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(9092(a,1),107(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9092 107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9094">
    <literal><![CDATA[
      K(x,(y \ L(y,z,u)) \ x) = K(x,(x / L(y,z,u)) * y)
    ]]></literal>
    <justification jstring="[para(3819(a,1),7164(a,1,2,1))].">
      <j1 rule="para" parents="3819 7164"/>
    </justification>
  </clause>

  <clause id="9095">
    <literal><![CDATA[
      K(x,y \ z) * K(y,y \ z) = (z / y) / T(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(6269,a,7187,a)].">
      <j1 rule="hyper" parents="6269 7187"/>
    </justification>
  </clause>

  <clause id="9096">
    <literal><![CDATA[
      (x * L(K(y,z),u,w)) \ x = L(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[para(6341(a,1),7224(a,1,1,2))].">
      <j1 rule="para" parents="6341 7224"/>
    </justification>
  </clause>

  <clause id="9097">
    <literal><![CDATA[
      (((x \ y) \ y) * L(K(z,u),w,v5)) \ T(x,x \ y) = L(K(u,z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(707,a,9096,a)].">
      <j1 rule="hyper" parents="707 9096"/>
    </justification>
  </clause>

  <clause id="9098">
    <literal><![CDATA[
      x / L(K(y,z),u,w) = x * L(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(192,a,9096,a)].">
      <j1 rule="hyper" parents="192 9096"/>
    </justification>
  </clause>

  <clause id="9099">
    <literal><![CDATA[
      (x * (y * K(z,u))) * L(K(u,z),y,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(147,a,9096,a),flip(a)].">
      <j1 rule="hyper" parents="147 9096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9100">
    <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(9096(a,1),136(a,1,2)),flip(b)].">
      <j1 rule="para" parents="9096 136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9101">
    <literal><![CDATA[
      x / L(K(y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      x * L(K(z,y),u,w) = v5
    ]]></literal>
    <justification jstring="[para(9096(a,1),310(a,1,2)),flip(b)].">
      <j1 rule="para" parents="9096 310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9102">
    <literal><![CDATA[
      (x * (y * K(z,u))) \ (x * y) = L(K(u,z),y,x)
    ]]></literal>
    <justification jstring="[para(94(a,1),9096(a,1,1))].">
      <j1 rule="para" parents="94 9096"/>
    </justification>
  </clause>

  <clause id="9103">
    <literal><![CDATA[
      (x * ((x \ y) * K(z,u))) \ y = L(K(u,z),x \ y,x)
    ]]></literal>
    <justification jstring="[para(482(a,1),9096(a,1,1))].">
      <j1 rule="para" parents="482 9096"/>
    </justification>
  </clause>

  <clause id="9104">
    <literal><![CDATA[
      x / L(K(y,z),u,w) != x * v5
    ]]></literal>
    <literal><![CDATA[
      L(K(z,y),u,w) = v5
    ]]></literal>
    <justification jstring="[para(9098(a,2),45(a,1))].">
      <j1 rule="para" parents="9098 45"/>
    </justification>
  </clause>

  <clause id="9105">
    <literal><![CDATA[
      x / L(L(K(y,z),u,w),K(z,y),v5) = x * L(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[para(7227(a,2),9098(a,1,2))].">
      <j1 rule="para" parents="7227 9098"/>
    </justification>
  </clause>

  <clause id="9106">
    <literal><![CDATA[
      L(T(K(x,y),z * (u * K(y,x))),u,z) = (z * u) / (z * (u * K(y,x)))
    ]]></literal>
    <justification jstring="[hyper(120,a,9099,a(flip),b,8105,a),flip(a)].">
      <j1 rule="hyper" parents="120 9099 8105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9107">
    <literal><![CDATA[
      (x * (K(y,z) * u)) * L(K(z,T(y,u)),u,x) = x * u
    ]]></literal>
    <justification jstring="[para(7541(a,1),9099(a,1,1,2))].">
      <j1 rule="para" parents="7541 9099"/>
    </justification>
  </clause>

  <clause id="9108">
    <literal><![CDATA[
      K(x * (y * K(z,u)),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(9099(a,1),8585(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9099 8585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9109">
    <literal><![CDATA[
      K(x * (y / T(z,u)),u) = K(x * (y / z),u)
    ]]></literal>
    <justification jstring="[para(7189(a,1),9108(a,1,1,2))].">
      <j1 rule="para" parents="7189 9108"/>
    </justification>
  </clause>

  <clause id="9110">
    <literal><![CDATA[
      K(x * (y \ T(z,u)),u) = K(x * (y \ z),u)
    ]]></literal>
    <justification jstring="[para(7335(a,1),9108(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7335 9108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9111">
    <literal><![CDATA[
      K(x * (K(y,z) * u),y) = K(x * u,y)
    ]]></literal>
    <justification jstring="[para(7507(a,1),9108(a,1,1,2))].">
      <j1 rule="para" parents="7507 9108"/>
    </justification>
  </clause>

  <clause id="9112">
    <literal><![CDATA[
      K(x * (y / R(z,u,z)),z) = K(x * (y / T(z,u)),z)
    ]]></literal>
    <justification jstring="[para(8943(a,1),9108(a,1,1,2))].">
      <j1 rule="para" parents="8943 9108"/>
    </justification>
  </clause>

  <clause id="9113">
    <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(9111(a,1),5829(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9111 5829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9114">
    <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(9111(a,1),5831(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9111 5831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9115">
    <literal><![CDATA[
      K(x * (y / (z * y)),z \ 1) = K(x * ((z * y) \ y),z \ 1)
    ]]></literal>
    <justification jstring="[para(4660(a,1),9109(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4660 9109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9116">
    <literal><![CDATA[
      K(x * (((y \ 1) \ z) / z),y) = K(x * (z \ ((y \ 1) \ z)),y)
    ]]></literal>
    <justification jstring="[para(4662(a,1),9109(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4662 9109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9117">
    <literal><![CDATA[
      K(x * ((y * z) \ z),y) = K(x * ((z * y) \ z),y)
    ]]></literal>
    <justification jstring="[para(6095(a,1),9110(a,1,1,2))].">
      <j1 rule="para" parents="6095 9110"/>
    </justification>
  </clause>

  <clause id="9119">
    <literal><![CDATA[
      (x * (y \ T(y * z,y))) \ (x * z) = L(K(y,y * z),z,x)
    ]]></literal>
    <justification jstring="[para(7248(a,2),9102(a,1,1,2))].">
      <j1 rule="para" parents="7248 9102"/>
    </justification>
  </clause>

  <clause id="9120">
    <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(9107(a,1),314(a,1,2))].">
      <j1 rule="para" parents="9107 314"/>
    </justification>
  </clause>

  <clause id="9121">
    <literal><![CDATA[
      L(K(x,T(T(y,z),u * (K(y,x) * z))),z,u) = (u * z) / (u * (K(y,x) * z))
    ]]></literal>
    <justification jstring="[para(9107(a,1),8244(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9107 8244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9122">
    <literal><![CDATA[
      (x * (y * y)) * K(z,y \ 1) = (x * y) / T(1 / y,z)
    ]]></literal>
    <justification jstring="[para(4797(a,1),7244(a,1,2))].">
      <j1 rule="para" parents="4797 7244"/>
    </justification>
  </clause>

  <clause id="9123">
    <literal><![CDATA[
      (x * T(y,L(z,y,x))) \ (x * (y * z)) = L(T(z,y),y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,25,a,b,7277,a),flip(a)].">
      <j1 rule="hyper" parents="299 25 7277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9124">
    <literal><![CDATA[
      (x * (y * (z * T(z \ (y \ (x \ u)),w)))) \ u = K(w,(x * (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(998(a,1),7287(a,1,1,2))].">
      <j1 rule="para" parents="998 7287"/>
    </justification>
  </clause>

  <clause id="9125">
    <literal><![CDATA[
      (x * (((y \ ((x \ z) * u)) * y) / u)) \ z = K(y,(x * (y / u)) \ z)
    ]]></literal>
    <justification jstring="[para(1520(a,1),7287(a,1,1,2))].">
      <j1 rule="para" parents="1520 7287"/>
    </justification>
  </clause>

  <clause id="9126">
    <literal><![CDATA[
      K(x,1 / T(1 / y,z)) = K(x,y * K(1 / y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,8298,a(flip),b,7308,a)].">
      <j1 rule="hyper" parents="65 8298 7308"/>
    </justification>
  </clause>

  <clause id="9127">
    <literal><![CDATA[
      K(x,y * K(1 / y,z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(65,a,5803,a(flip),b,9126,a),flip(a)].">
      <j1 rule="hyper" parents="65 5803 9126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9128">
    <literal><![CDATA[
      K(x,y * K(1 / y,z * y)) = T(K(x,y),z / (1 / y))
    ]]></literal>
    <justification jstring="[para(6189(a,1),9127(a,1,2,2))].">
      <j1 rule="para" parents="6189 9127"/>
    </justification>
  </clause>

  <clause id="9129">
    <literal><![CDATA[
      (x \ (1 / T(x,y))) \ z != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * ((x \ 1) \ z) = u
    ]]></literal>
    <justification jstring="[para(7310(a,1),5394(a,1))].">
      <j1 rule="para" parents="7310 5394"/>
    </justification>
  </clause>

  <clause id="9130">
    <literal><![CDATA[
      L((x \ 1) \ 1,y,z) \ x = (L(x,y,z) \ 1) * x
    ]]></literal>
    <justification jstring="[para(6680(a,1),7360(a,1,1))].">
      <j1 rule="para" parents="6680 7360"/>
    </justification>
  </clause>

  <clause id="9131">
    <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(9130(a,1),3368(a,2,1))].">
      <j1 rule="para" parents="9130 3368"/>
    </justification>
  </clause>

  <clause id="9132">
    <literal><![CDATA[
      R(x * K(y,x),z,y \ 1) = K(y,x) * R(x,z,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,3623,a(flip),b,7391,a),flip(a)].">
      <j1 rule="hyper" parents="299 3623 7391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9133">
    <literal><![CDATA[
      K(x,y / R(T(x,z),u,w)) = K(x,R(x,u,w) \ y)
    ]]></literal>
    <justification jstring="[hyper(299,a,8737,a(flip),b,7631,a),flip(a)].">
      <j1 rule="hyper" parents="299 8737 7631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9135">
    <literal><![CDATA[
      R(K(x,y),z,R(x,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3985,a,7682,a)].">
      <j1 rule="hyper" parents="3985 7682"/>
    </justification>
  </clause>

  <clause id="9136">
    <literal><![CDATA[
      K(x,y) * ((y * x) * R(x,z,u)) = (x * y) * R(x,z,u)
    ]]></literal>
    <justification jstring="[para(5020(a,1),7682(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5020 7682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9137">
    <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(7682(a,1),5357(a,1,1,2))].">
      <j1 rule="para" parents="7682 5357"/>
    </justification>
  </clause>

  <clause id="9138">
    <literal><![CDATA[
      K(x,(y * R(x,z,u)) / w) = K(x,y / (w / R(x,z,u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,6430,a(flip),b,9135,a)].">
      <j1 rule="hyper" parents="65 6430 9135"/>
    </justification>
  </clause>

  <clause id="9139">
    <literal><![CDATA[
      R(K(x,y),z,L(x,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3985,a,7683,a)].">
      <j1 rule="hyper" parents="3985 7683"/>
    </justification>
  </clause>

  <clause id="9140">
    <literal><![CDATA[
      T(T(x,1 / y),K(1 / y,z)) = T(x,1 / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,5083,a,b,7722,a),flip(a)].">
      <j1 rule="hyper" parents="299 5083 7722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9141">
    <literal><![CDATA[
      T(x,1 / T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(1 / y,z)) = u
    ]]></literal>
    <justification jstring="[para(9140(a,1),7154(a,1))].">
      <j1 rule="para" parents="9140 7154"/>
    </justification>
  </clause>

  <clause id="9142">
    <literal><![CDATA[
      T(K(x,y) * L(y,z,u),x) = y * T(y \ L(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(299,a,6734,a(flip),b,7775,a),flip(a)].">
      <j1 rule="hyper" parents="299 6734 7775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9144">
    <literal><![CDATA[
      ((x \ y) / (x \ 1)) \ (y / x) = x \ K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(109(a,1),7922(a,1,1,1))].">
      <j1 rule="para" parents="109 7922"/>
    </justification>
  </clause>

  <clause id="9145">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(L(K(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[para(6341(a,1),7969(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6341 7969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9146">
    <literal><![CDATA[
      K(L(K(x,y),z,u),w) = K(y,K(w,L(x,z,u)))
    ]]></literal>
    <justification jstring="[hyper(9028,a,9145,a),flip(a)].">
      <j1 rule="hyper" parents="9028 9145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9147">
    <literal><![CDATA[
      K(L(K(x,y),z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(y,K(w,L(x,z,u))) = v5
    ]]></literal>
    <justification jstring="[para(9145(a,1),9028(a,1))].">
      <j1 rule="para" parents="9145 9028"/>
    </justification>
  </clause>

  <clause id="9148">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) = K(R(K(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[para(6011(a,1),7970(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6011 7970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9149">
    <literal><![CDATA[
      R(K(x,K(y,z \ 1)),u,w) = K(x,K(y,R(z,u,w) \ 1))
    ]]></literal>
    <justification jstring="[para(7954(a,1),7971(a,1,1))].">
      <j1 rule="para" parents="7954 7971"/>
    </justification>
  </clause>

  <clause id="9150">
    <literal><![CDATA[
      K(R(K(x,y),z,u),w) = K(y,R(K(x,w),z,u))
    ]]></literal>
    <justification jstring="[para(6011(a,1),8006(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6011 8006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9151">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) = K(y,R(K(x,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,9148,a,b,9150,a)].">
      <j1 rule="hyper" parents="65 9148 9150"/>
    </justification>
  </clause>

  <clause id="9152">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) = K(x,R(K(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(7983(a,1),9151(a,1,1))].">
      <j1 rule="para" parents="7983 9151"/>
    </justification>
  </clause>

  <clause id="9153">
    <literal><![CDATA[
      x * R(K(x,K(y,z)),u,w) = T(x,R(K(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(9152(a,2),5083(a,2,2)),flip(a)].">
      <j1 rule="para" parents="9152 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9155">
    <literal><![CDATA[
      K(L(K(x,y),z,u),w) = K(y,L(K(x,w),z,u))
    ]]></literal>
    <justification jstring="[para(6341(a,1),8008(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6341 8008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9156">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w)) = K(x,K(z,L(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(9147,a,9155,a),flip(a)].">
      <j1 rule="hyper" parents="9147 9155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9157">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(y,L(K(x,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,9145,a,b,9155,a)].">
      <j1 rule="hyper" parents="65 9145 9155"/>
    </justification>
  </clause>

  <clause id="9158">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) * y = T(y,L(K(x,z),u,w))
    ]]></literal>
    <justification jstring="[para(9157(a,2),5096(a,2,1)),flip(a)].">
      <j1 rule="para" parents="9157 5096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9159">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) * y = T(y,L(K(x,z),u,w))
    ]]></literal>
    <justification jstring="[para(8913(a,1),9158(a,1,1))].">
      <j1 rule="para" parents="8913 9158"/>
    </justification>
  </clause>

  <clause id="9160">
    <literal><![CDATA[
      T(x,L(K(y,z),u,w)) = T(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(7993,a,9159,a),flip(a)].">
      <j1 rule="hyper" parents="7993 9159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9161">
    <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),8017(a,1,2,1))].">
      <j1 rule="para" parents="12 8017"/>
    </justification>
  </clause>

  <clause id="9162">
    <literal><![CDATA[
      L(K(x,y),z * T(x,u),w) = K(L(x,z,w),y)
    ]]></literal>
    <justification jstring="[hyper(299,a,8126,a(flip),b,8139,a),flip(a)].">
      <j1 rule="hyper" parents="299 8126 8139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9164">
    <literal><![CDATA[
      L(K(x,y),x * z,u) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(107(a,1),9162(a,1,2))].">
      <j1 rule="para" parents="107 9162"/>
    </justification>
  </clause>

  <clause id="9165">
    <literal><![CDATA[
      K(L(x,y,z),x * y) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(6838,a,9164,a),flip(a)].">
      <j1 rule="hyper" parents="6838 9164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9166">
    <literal><![CDATA[
      K(L(x,y,z),(z \ u) \ (x * y)) = K(x,u \ (z * (x * y)))
    ]]></literal>
    <justification jstring="[hyper(65,a,7944,a(flip),b,9164,a),flip(a)].">
      <j1 rule="hyper" parents="65 7944 9164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9167">
    <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(8106(a,1),9164(a,1,1))].">
      <j1 rule="para" parents="8106 9164"/>
    </justification>
  </clause>

  <clause id="9168">
    <literal><![CDATA[
      K(x \ y,x) * T(x,T(z,y)) = T(y / (y / x),z)
    ]]></literal>
    <justification jstring="[hyper(5774,a,8173,a)].">
      <j1 rule="hyper" parents="5774 8173"/>
    </justification>
  </clause>

  <clause id="9169">
    <literal><![CDATA[
      T(x,T(y,z)) \ T(z / (z / x),y) = K(x \ z,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,8173,a(flip),b,5362,a(flip))].">
      <j1 rule="hyper" parents="119 8173 5362"/>
    </justification>
  </clause>

  <clause id="9170">
    <literal><![CDATA[
      ((x * (y * K(z,y))) / x) / ((x * y) / x) = K(T(z,x),y)
    ]]></literal>
    <justification jstring="[para(5054(a,1),8174(a,1,1,1,2))].">
      <j1 rule="para" parents="5054 8174"/>
    </justification>
  </clause>

  <clause id="9171">
    <literal><![CDATA[
      K(R(x,y / x,z),T(u,x \ y)) = K((y * z) / ((y / x) * z),u)
    ]]></literal>
    <justification jstring="[para(104(a,1),8178(a,1,1)),flip(a)].">
      <j1 rule="para" parents="104 8178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9172">
    <literal><![CDATA[
      T(K(x,y),T(z,x \ u)) = T(K(x,y),T(z,u))
    ]]></literal>
    <justification jstring="[hyper(7960,a,8233,a),flip(a)].">
      <j1 rule="hyper" parents="7960 8233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9173">
    <literal><![CDATA[
      T(K(x,y),T(z,x * u)) = T(K(x,y),T(z,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),9172(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 9172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9175">
    <literal><![CDATA[
      1 / (K(x,y) * T(x,z)) = K(y,x) / T(x,z)
    ]]></literal>
    <justification jstring="[para(8106(a,1),8273(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8106 8273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9176">
    <literal><![CDATA[
      L(x,y * ((K(z,u) * T(z,w)) \ 1),v5) = L(x,y * (K(u,z) / T(z,w)),v5)
    ]]></literal>
    <justification jstring="[para(9175(a,1),2889(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9175 2889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9177">
    <literal><![CDATA[
      (K(x,y) / T(y,z)) \ 1 = K(y,z) * T(y,x)
    ]]></literal>
    <justification jstring="[para(9175(a,1),5758(a,1,1))].">
      <j1 rule="para" parents="9175 5758"/>
    </justification>
  </clause>

  <clause id="9179">
    <literal><![CDATA[
      ((x \ y) \ 1) * (y / x) = (y / x) * (1 / (x \ y))
    ]]></literal>
    <justification jstring="[para(109(a,1),8289(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="109 8289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9180">
    <literal><![CDATA[
      ((x \ y) \ (y / x)) * K((x \ y) \ 1,y / x) = (y / x) * (1 / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(65,a,1219,a,b,9179,a)].">
      <j1 rule="hyper" parents="65 1219 9179"/>
    </justification>
  </clause>

  <clause id="9181">
    <literal><![CDATA[
      K(x,K(y,z)) * (T(z,y) * u) = T(z,T(y,x)) * u
    ]]></literal>
    <justification jstring="[para(8056(a,1),8344(a,2,1))].">
      <j1 rule="para" parents="8056 8344"/>
    </justification>
  </clause>

  <clause id="9182">
    <literal><![CDATA[
      T(x,K(y,z)) * K(y,z * x) = K(y,z * x) * x
    ]]></literal>
    <justification jstring="[para(8850(a,1),8346(a,1,1))].">
      <j1 rule="para" parents="8850 8346"/>
    </justification>
  </clause>

  <clause id="9183">
    <literal><![CDATA[
      K(x,L(y,z / T(y,u),w)) = L(K(x,y),z,w)
    ]]></literal>
    <justification jstring="[para(8106(a,1),8353(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8106 8353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9184">
    <literal><![CDATA[
      L(K(x,y),z * T(y,u),w) = K(x,L(y,z,w))
    ]]></literal>
    <justification jstring="[para(11(a,1),9183(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 9183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9185">
    <literal><![CDATA[
      L(K(x,y),y * z,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(185(a,1),9183(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="185 9183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9186">
    <literal><![CDATA[
      K(x,L(y,y \ z,u)) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(262(a,1),9183(a,1,2,2))].">
      <j1 rule="para" parents="262 9183"/>
    </justification>
  </clause>

  <clause id="9188">
    <literal><![CDATA[
      K(x * y,L(x,y,z)) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(6822,a,9185,a),flip(a)].">
      <j1 rule="hyper" parents="6822 9185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9189">
    <literal><![CDATA[
      K((x \ y) \ (z * u),L(z,u,x)) = K(y \ (x * (z * u)),z)
    ]]></literal>
    <justification jstring="[hyper(65,a,7421,a(flip),b,9185,a),flip(a)].">
      <j1 rule="hyper" parents="65 7421 9185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9190">
    <literal><![CDATA[
      L(K(x,y / z),y,u) = K(x,L(y / z,z,u))
    ]]></literal>
    <justification jstring="[para(12(a,1),9185(a,1,2))].">
      <j1 rule="para" parents="12 9185"/>
    </justification>
  </clause>

  <clause id="9191">
    <literal><![CDATA[
      (x * (y * z)) * K(u,L(y,z,x)) = x * ((y * z) * K(u,y))
    ]]></literal>
    <justification jstring="[para(9185(a,1),94(a,1,2))].">
      <j1 rule="para" parents="9185 94"/>
    </justification>
  </clause>

  <clause id="9192">
    <literal><![CDATA[
      L(K(x,y),T(y,z) * u,w) = K(x,L(y,K(y,z) * u,w))
    ]]></literal>
    <justification jstring="[para(5055(a,1),9185(a,1,2))].">
      <j1 rule="para" parents="5055 9185"/>
    </justification>
  </clause>

  <clause id="9193">
    <literal><![CDATA[
      K(x,L(y,z * K(y,u),w)) = K(x,L(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,7815,a(flip),b,9184,a)].">
      <j1 rule="hyper" parents="65 7815 9184"/>
    </justification>
  </clause>

  <clause id="9194">
    <literal><![CDATA[
      L(K(x,y),z * K(y,u),w) = K(x,L(y,z / y,w))
    ]]></literal>
    <justification jstring="[para(6869(a,1),9184(a,1,2))].">
      <j1 rule="para" parents="6869 9184"/>
    </justification>
  </clause>

  <clause id="9195">
    <literal><![CDATA[
      K(x,K(y / z,L(u,y,w))) = K(x,K(u,L(y / z,z,w)))
    ]]></literal>
    <justification jstring="[para(9190(a,1),9156(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9190 9156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9197">
    <literal><![CDATA[
      K(x,L(y,K(y,z) * u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(7507(a,1),9193(a,1,2,2))].">
      <j1 rule="para" parents="7507 9193"/>
    </justification>
  </clause>

  <clause id="9198">
    <literal><![CDATA[
      L(K(x,y),z * K(y,u),w) = L(K(x,y),z,w)
    ]]></literal>
    <justification jstring="[hyper(299,a,7810,a(flip),b,9194,a),flip(a)].">
      <j1 rule="hyper" parents="299 7810 9194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9199">
    <literal><![CDATA[
      L(K(x,y),K(y,z),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(497,a,9198,a),flip(a)].">
      <j1 rule="hyper" parents="497 9198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9200">
    <literal><![CDATA[
      L(K(x,y),K(z,y),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7213,a,9199,a)].">
      <j1 rule="hyper" parents="7213 9199"/>
    </justification>
  </clause>

  <clause id="9202">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,y) = x * (K(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[para(9199(a,1),94(a,1,2))].">
      <j1 rule="para" parents="9199 94"/>
    </justification>
  </clause>

  <clause id="9203">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,y) != w
    ]]></literal>
    <literal><![CDATA[
      x * (K(y,z) * K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(9199(a,1),279(a,1,2))].">
      <j1 rule="para" parents="9199 279"/>
    </justification>
  </clause>

  <clause id="9204">
    <literal><![CDATA[
      (x * K(y,z)) * L(K(u,y),w,v5) = x * (K(y,z) * L(K(u,y),w,v5))
    ]]></literal>
    <justification jstring="[para(9199(a,1),489(a,1,2,1))].">
      <j1 rule="para" parents="9199 489"/>
    </justification>
  </clause>

  <clause id="9205">
    <literal><![CDATA[
      L(K(x,T(y,z)),K(y,u),w) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(8106(a,1),9199(a,1,2))].">
      <j1 rule="para" parents="8106 9199"/>
    </justification>
  </clause>

  <clause id="9206">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,z) = x * (K(y,z) * K(u,z))
    ]]></literal>
    <justification jstring="[para(9200(a,1),94(a,1,2))].">
      <j1 rule="para" parents="9200 94"/>
    </justification>
  </clause>

  <clause id="9207">
    <literal><![CDATA[
      (x * (K(y,z) * K(z,u))) * K(u,z) = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(9200(a,1),9099(a,1,2))].">
      <j1 rule="para" parents="9200 9099"/>
    </justification>
  </clause>

  <clause id="9209">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,T(y,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x * (K(y,z) * K(u,T(y,w))) = v5
    ]]></literal>
    <justification jstring="[para(9205(a,1),279(a,1,2))].">
      <j1 rule="para" parents="9205 279"/>
    </justification>
  </clause>

  <clause id="9210">
    <literal><![CDATA[
      R(x,K(y,z),K(u,y)) = x
    ]]></literal>
    <justification jstring="[hyper(544,a,9202,a)].">
      <j1 rule="hyper" parents="544 9202"/>
    </justification>
  </clause>

  <clause id="9211">
    <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(3282(a,1),9202(a,1,1))].">
      <j1 rule="para" parents="3282 9202"/>
    </justification>
  </clause>

  <clause id="9212">
    <literal><![CDATA[
      (x * K(y,z)) * (K(z,y) * K(u,z)) = x * K(u,z)
    ]]></literal>
    <justification jstring="[para(7184(a,1),9202(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7184 9202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9213">
    <literal><![CDATA[
      (K(x,y) * z) * (K(y,x) * K(u,y)) = T(z,K(x,y)) * K(u,y)
    ]]></literal>
    <justification jstring="[para(8055(a,1),9202(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8055 9202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9215">
    <literal><![CDATA[
      K(K(x,y) * K(z,x),R(u / K(x,y),K(x,y),K(z,x))) = (u * K(z,x)) \ ((K(x,y) * K(z,x)) * (u / K(x,y)))
    ]]></literal>
    <justification jstring="[para(9210(a,1),1333(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9210 1333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9216">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,u) = x * (K(y,z) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(7207,a,9207,a)].">
      <j1 rule="hyper" parents="7207 9207"/>
    </justification>
  </clause>

  <clause id="9218">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,y))) * K(z,y) = x * K(u,y)
    ]]></literal>
    <justification jstring="[para(2278(a,2),9207(a,1,1,2))].">
      <j1 rule="para" parents="2278 9207"/>
    </justification>
  </clause>

  <clause id="9219">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,u) != w
    ]]></literal>
    <literal><![CDATA[
      x * (K(y,z) * K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(9207(a,1),7216(a,1,1)),flip(b)].">
      <j1 rule="para" parents="9207 7216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9220">
    <literal><![CDATA[
      ((x * K(y,z)) / (x * K(u,z))) \ 1 = (K(z,u) * K(y,z)) \ K(K(z,u) * K(y,z),x * K(u,z))
    ]]></literal>
    <justification jstring="[para(9212(a,1),5182(a,1,1,1))].">
      <j1 rule="para" parents="9212 5182"/>
    </justification>
  </clause>

  <clause id="9221">
    <literal><![CDATA[
      R(x,K(y,z),K(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(544,a,9216,a)].">
      <j1 rule="hyper" parents="544 9216"/>
    </justification>
  </clause>

  <clause id="9222">
    <literal><![CDATA[
      L(K(x,y),K(z,x),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(490,a,9216,a)].">
      <j1 rule="hyper" parents="490 9216"/>
    </justification>
  </clause>

  <clause id="9223">
    <literal><![CDATA[
      x * (K(y,z) * K(z,z * y)) = (x / R(z,y,z)) * z
    ]]></literal>
    <justification jstring="[hyper(65,a,9026,a(flip),b,9216,a),flip(a)].">
      <j1 rule="hyper" parents="65 9026 9216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9224">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,u) = x * (K(z,u) * K(y,z))
    ]]></literal>
    <justification jstring="[para(2278(a,2),9216(a,2,2))].">
      <j1 rule="para" parents="2278 9216"/>
    </justification>
  </clause>

  <clause id="9225">
    <literal><![CDATA[
      R(x,T(K(y,z),u),K(z,w)) = x
    ]]></literal>
    <justification jstring="[para(2169(a,1),9221(a,1,2))].">
      <j1 rule="para" parents="2169 9221"/>
    </justification>
  </clause>

  <clause id="9226">
    <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(9221(a,1),3079(a,1,1,1))].">
      <j1 rule="para" parents="9221 3079"/>
    </justification>
  </clause>

  <clause id="9227">
    <literal><![CDATA[
      R(x,K(y,z),R(K(z,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[para(6213(a,1),9221(a,1,3))].">
      <j1 rule="para" parents="6213 9221"/>
    </justification>
  </clause>

  <clause id="9228">
    <literal><![CDATA[
      R(x,L(K(y,z),u,w),K(z,v5)) = x
    ]]></literal>
    <justification jstring="[para(6341(a,1),9221(a,1,2))].">
      <j1 rule="para" parents="6341 9221"/>
    </justification>
  </clause>

  <clause id="9230">
    <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(9222(a,1),488(a,1,2,1))].">
      <j1 rule="para" parents="9222 488"/>
    </justification>
  </clause>

  <clause id="9231">
    <literal><![CDATA[
      R(x,T(K(y,z),u),T(K(z,w),v5)) = x
    ]]></literal>
    <justification jstring="[para(5800(a,1),9225(a,1,3))].">
      <j1 rule="para" parents="5800 9225"/>
    </justification>
  </clause>

  <clause id="9232">
    <literal><![CDATA[
      R(x,K(y,z),R(K(z,u),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      x = v6
    ]]></literal>
    <justification jstring="[para(9227(a,1),53(a,2))].">
      <j1 rule="para" parents="9227 53"/>
    </justification>
  </clause>

  <clause id="9233">
    <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="[para(9228(a,1),103(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9228 103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9234">
    <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(9228(a,1),584(a,1,1))].">
      <j1 rule="para" parents="9228 584"/>
    </justification>
  </clause>

  <clause id="9235">
    <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(9231(a,1),1011(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9231 1011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9236">
    <literal><![CDATA[
      x * T(K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      w * T(K(z,y),u) = x
    ]]></literal>
    <justification jstring="[para(9231(a,1),6754(a,1)),flip(a)].">
      <j1 rule="para" parents="9231 6754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9237">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,y))) * (K(z,y) * K(y,u)) = x
    ]]></literal>
    <justification jstring="[hyper(37,a,9207,a,b,9218,a(flip))].">
      <j1 rule="hyper" parents="37 9207 9218"/>
    </justification>
  </clause>

  <clause id="9238">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,u) != w
    ]]></literal>
    <literal><![CDATA[
      x * (K(z,u) * K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(9218(a,1),7216(a,1,1)),flip(b)].">
      <j1 rule="para" parents="9218 7216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9239">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,y) = (x * K(u,y)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,9202,a,b,9224,a)].">
      <j1 rule="hyper" parents="299 9202 9224"/>
    </justification>
  </clause>

  <clause id="9240">
    <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(235,a,9224,a,b,681,a)].">
      <j1 rule="hyper" parents="235 9224 681"/>
    </justification>
  </clause>

  <clause id="9242">
    <literal><![CDATA[
      (x / y) * (K(y,z) * K(u,y)) = (x / T(y,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(7189(a,1),9224(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7189 9224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9243">
    <literal><![CDATA[
      x / (K(y,z) * K(z,u)) = x * (K(z,y) * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(137,a,9237,a)].">
      <j1 rule="hyper" parents="137 9237"/>
    </justification>
  </clause>

  <clause id="9244">
    <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(9237(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="9237 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9245">
    <literal><![CDATA[
      (x * K(T(y,z),u)) * K(u,w) = (x * K(u,w)) * K(y,T(u,z))
    ]]></literal>
    <justification jstring="[hyper(8392,a,9239,a),flip(a)].">
      <j1 rule="hyper" parents="8392 9239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9246">
    <literal><![CDATA[
      ((x * K(y,z)) * K(y,u)) * K(z,y) = x * K(y,u)
    ]]></literal>
    <justification jstring="[para(7184(a,1),9239(a,2,1))].">
      <j1 rule="para" parents="7184 9239"/>
    </justification>
  </clause>

  <clause id="9247">
    <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(9239(a,2),7216(a,1,1)),flip(b)].">
      <j1 rule="para" parents="9239 7216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9248">
    <literal><![CDATA[
      x / (K(y,z) * K(z,u)) = x * (K(u,z) * K(z,y))
    ]]></literal>
    <justification jstring="[para(2278(a,1),9243(a,2,2))].">
      <j1 rule="para" parents="2278 9243"/>
    </justification>
  </clause>

  <clause id="9249">
    <literal><![CDATA[
      x / (K(y,z) * K(u,y)) = x * (K(y,u) * K(z,y))
    ]]></literal>
    <justification jstring="[para(2278(a,2),9243(a,1,2))].">
      <j1 rule="para" parents="2278 9243"/>
    </justification>
  </clause>

  <clause id="9250">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * K(y,u)) = K(y,u) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,9246,a(flip),b,9202,a(flip))].">
      <j1 rule="hyper" parents="119 9246 9202"/>
    </justification>
  </clause>

  <clause id="9252">
    <literal><![CDATA[
      (x * (K(y,z) * K(z,u))) \ x = K(u,z) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(635,a,9248,a)].">
      <j1 rule="hyper" parents="635 9248"/>
    </justification>
  </clause>

  <clause id="9253">
    <literal><![CDATA[
      x / (K(y,z) * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x * (K(u,z) * K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(9252(a,1),310(a,1,2)),flip(b)].">
      <j1 rule="para" parents="9252 310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9254">
    <literal><![CDATA[
      (x / R(y,z,y)) * y = x * (y \ L(y,z,y))
    ]]></literal>
    <justification jstring="[para(5789(a,1),9223(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5789 9223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9255">
    <literal><![CDATA[
      R(x,y,x) \ x = x \ L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(7924,a,9254,a)].">
      <j1 rule="hyper" parents="7924 9254"/>
    </justification>
  </clause>

  <clause id="9256">
    <literal><![CDATA[
      x / R(x,y,x) = x \ L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(37,a,3817,a,b,9254,a),flip(a)].">
      <j1 rule="hyper" parents="37 3817 9254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9257">
    <literal><![CDATA[
      x \ (x \ L(x,y,x)) = R(x,y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(119,a,9255,a(flip),b,1957,a)].">
      <j1 rule="hyper" parents="119 9255 1957"/>
    </justification>
  </clause>

  <clause id="9258">
    <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(9256(a,1),2717(a,1,1,2,1))].">
      <j1 rule="para" parents="9256 2717"/>
    </justification>
  </clause>

  <clause id="9259">
    <literal><![CDATA[
      x \ ((x \ L(x,y,x)) * T(x,z)) = T(x,z) * (R(x,y,x) \ 1)
    ]]></literal>
    <justification jstring="[para(9257(a,1),3829(a,2,2))].">
      <j1 rule="para" parents="9257 3829"/>
    </justification>
  </clause>

  <clause id="9260">
    <literal><![CDATA[
      K(x,T(T(x * T(y,z),u),y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(x * T(y,z),u)) = w
    ]]></literal>
    <justification jstring="[para(8371(a,2),7714(a,1))].">
      <j1 rule="para" parents="8371 7714"/>
    </justification>
  </clause>

  <clause id="9261">
    <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(7984(a,1),8382(a,2,2))].">
      <j1 rule="para" parents="7984 8382"/>
    </justification>
  </clause>

  <clause id="9262">
    <literal><![CDATA[
      ((x \ 1) \ y) \ K(x * y,y \ (x \ 1)) = 1 / ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(119,a,8391,a(flip),b,3040,a)].">
      <j1 rule="hyper" parents="119 8391 3040"/>
    </justification>
  </clause>

  <clause id="9263">
    <literal><![CDATA[
      T(x,R(y / (y / z),u,w)) = x * K(T(x,z \ y),R(z,u,w))
    ]]></literal>
    <justification jstring="[para(4504(a,1),8491(a,1,2,1))].">
      <j1 rule="para" parents="4504 8491"/>
    </justification>
  </clause>

  <clause id="9264">
    <literal><![CDATA[
      K(T(x,y),y \ z) = K(x,z / (y * K(u,x)))
    ]]></literal>
    <justification jstring="[hyper(65,a,8862,a(flip),b,8566,a)].">
      <j1 rule="hyper" parents="65 8862 8566"/>
    </justification>
  </clause>

  <clause id="9265">
    <literal><![CDATA[
      K(x,y / (z * K(u,x))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(8231,a,9264,a),flip(a)].">
      <j1 rule="hyper" parents="8231 9264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9267">
    <literal><![CDATA[
      K(x,y / (z * x)) = K(x,y / (x * z))
    ]]></literal>
    <justification jstring="[para(88(a,1),9265(a,1,2,2))].">
      <j1 rule="para" parents="88 9265"/>
    </justification>
  </clause>

  <clause id="9268">
    <literal><![CDATA[
      K(x,y / K(z,z \ K(u,x))) = K(x,y / (z * (K(u,x) / z)))
    ]]></literal>
    <justification jstring="[para(5105(a,1),9265(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5105 9265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9269">
    <literal><![CDATA[
      K(x,y / (z * K(x,u))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(7184(a,1),9265(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7184 9265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9270">
    <literal><![CDATA[
      K(x,y / ((z * x) * u)) = K(x,y / (x * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,6790,a(flip),b,9267,a)].">
      <j1 rule="hyper" parents="65 6790 9267"/>
    </justification>
  </clause>

  <clause id="9271">
    <literal><![CDATA[
      K(x,R(y / x,x,z)) = K(x,(y * z) / (z * x))
    ]]></literal>
    <justification jstring="[para(104(a,2),9267(a,2,2)),flip(a)].">
      <j1 rule="para" parents="104 9267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9272">
    <literal><![CDATA[
      K(x,R(x \ y,x,z)) = K(x,(y * z) / (z * x))
    ]]></literal>
    <justification jstring="[hyper(65,a,5207,a(flip),b,9271,a)].">
      <j1 rule="hyper" parents="65 5207 9271"/>
    </justification>
  </clause>

  <clause id="9273">
    <literal><![CDATA[
      K(x \ y,T(z,x)) = K(y / (x * K(z,u)),z)
    ]]></literal>
    <justification jstring="[hyper(65,a,8743,a(flip),b,8575,a)].">
      <j1 rule="hyper" parents="65 8743 8575"/>
    </justification>
  </clause>

  <clause id="9274">
    <literal><![CDATA[
      K(x / (y * K(z,u)),z) = K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(8220,a,9273,a),flip(a)].">
      <j1 rule="hyper" parents="8220 9273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9277">
    <literal><![CDATA[
      K(x * (R(y,z,y) \ u),y) = K(x * (u / T(y,z)),y)
    ]]></literal>
    <justification jstring="[hyper(65,a,9112,a(flip),b,8617,a),flip(a)].">
      <j1 rule="hyper" parents="65 9112 8617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9278">
    <literal><![CDATA[
      K(x * (R(x,y,x) \ z),x) = K(z,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,8623,a(flip),b,9277,a),flip(a)].">
      <j1 rule="hyper" parents="299 8623 9277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9279">
    <literal><![CDATA[
      K(R(x,y,x) * z,x) = K(x * z,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),9278(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 9278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9280">
    <literal><![CDATA[
      T(x,(y \ x) \ (z * x)) = T(x,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(299,a,5119,a,b,8700,a),flip(a)].">
      <j1 rule="hyper" parents="299 5119 8700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9281">
    <literal><![CDATA[
      T(x,(y \ 1) \ (x \ z)) = x * K(x,(y \ x) \ z)
    ]]></literal>
    <justification jstring="[hyper(8894,a,9280,a),flip(a)].">
      <j1 rule="hyper" parents="8894 9280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9282">
    <literal><![CDATA[
      K(x,(y \ 1) \ (x \ z)) = K(x,(y \ x) \ z)
    ]]></literal>
    <justification jstring="[hyper(5154,a,9281,a)].">
      <j1 rule="hyper" parents="5154 9281"/>
    </justification>
  </clause>

  <clause id="9283">
    <literal><![CDATA[
      K(x,(y \ x) \ (x * z)) = K(x,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(9(a,1),9282(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 9282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9284">
    <literal><![CDATA[
      K(x,(y \ x) \ (z * x)) = K(x,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,8868,a,b,9283,a)].">
      <j1 rule="hyper" parents="65 8868 9283"/>
    </justification>
  </clause>

  <clause id="9285">
    <literal><![CDATA[
      L((x * (K(y,x) / T(x,z))) \ u,T(x,z) \ ((x \ 1) \ K(y,x)),T(x,z)) = ((x \ 1) \ K(y,x)) \ (T(x,z) * u)
    ]]></literal>
    <justification jstring="[para(8709(a,1),520(a,1,1,1))].">
      <j1 rule="para" parents="8709 520"/>
    </justification>
  </clause>

  <clause id="9286">
    <literal><![CDATA[
      K(x,T(y,z)) * (T(x,y) \ u) = T(x,K(y,z)) \ u
    ]]></literal>
    <justification jstring="[hyper(299,a,8029,a(flip),b,8712,a),flip(a)].">
      <j1 rule="hyper" parents="299 8029 8712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9287">
    <literal><![CDATA[
      K(x,y \ (x \ ((x * z) * y))) = ((z * x) * y) \ ((x * z) * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),8721(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 8721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9288">
    <literal><![CDATA[
      (((x * (y * x)) / x) / y) * (z / (((x * (y * x)) / x) / y)) = z * K(((x * (y * x)) / x) / y,T(x,y * x) \ z)
    ]]></literal>
    <justification jstring="[para(1538(a,1),8731(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="1538 8731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9289">
    <literal><![CDATA[
      K(x * (y \ z),K(y,y \ z)) = K(z,K(y,x * (z / y)))
    ]]></literal>
    <justification jstring="[hyper(7985,a,8735,a)].">
      <j1 rule="hyper" parents="7985 8735"/>
    </justification>
  </clause>

  <clause id="9290">
    <literal><![CDATA[
      T(x,T((y \ z) \ 1,y)) = T(x,(z / y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,9006,a(flip),b,8848,a),flip(a)].">
      <j1 rule="hyper" parents="65 9006 8848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9291">
    <literal><![CDATA[
      T(x,((y * z) / y) \ 1) = T(x,T(z \ 1,y))
    ]]></literal>
    <justification jstring="[para(9(a,1),9290(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="9 9290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9292">
    <literal><![CDATA[
      T(x,T(y \ 1,z)) = T(x,y \ K(y,z))
    ]]></literal>
    <justification jstring="[para(5182(a,1),9291(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5182 9291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9293">
    <literal><![CDATA[
      T(x,y \ K(y,z)) = T(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,8334,a(flip),b,9292,a),flip(a)].">
      <j1 rule="hyper" parents="65 8334 9292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9294">
    <literal><![CDATA[
      T(x,y / (y * z)) = T(x,y \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(65,a,5481,a(flip),b,9293,a)].">
      <j1 rule="hyper" parents="65 5481 9293"/>
    </justification>
  </clause>

  <clause id="9296">
    <literal><![CDATA[
      K(x,y) * T(z,T(x * z,y)) = T(z,x * z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(4378(a,2),8855(a,1,2))].">
      <j1 rule="para" parents="4378 8855"/>
    </justification>
  </clause>

  <clause id="9297">
    <literal><![CDATA[
      K(x,T(y \ T(T(x,z),u),w)) = K(T(x,w),y \ T(x,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,7537,a,b,8936,a),flip(a)].">
      <j1 rule="hyper" parents="299 7537 8936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9298">
    <literal><![CDATA[
      K(x,T(y \ T(T(x,z),u),w)) = K(x,T(y \ x,w))
    ]]></literal>
    <justification jstring="[hyper(299,a,8935,a(flip),b,8936,a),flip(a)].">
      <j1 rule="hyper" parents="299 8935 8936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9300">
    <literal><![CDATA[
      (x / T(y \ 1,z)) \ K(y,y \ 1) = (x / T(1 / y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(8941(a,1),3251(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8941 3251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9301">
    <literal><![CDATA[
      L(x,y / T(1 / z,u),w) = L(x,y / T(z \ 1,u),w)
    ]]></literal>
    <justification jstring="[para(8941(a,1),3969(a,1,2))].">
      <j1 rule="para" parents="8941 3969"/>
    </justification>
  </clause>

  <clause id="9302">
    <literal><![CDATA[
      K((T(x,y) * z) \ u,K(x,w)) = K(x,K(w,z \ (x \ u)))
    ]]></literal>
    <justification jstring="[hyper(299,a,7989,a(flip),b,8959,a),flip(a)].">
      <j1 rule="hyper" parents="299 7989 8959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9303">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) / ((y \ 1) \ 1) = (1 / ((x * y) \ x)) / y
    ]]></literal>
    <justification jstring="[hyper(120,a,9035,a(flip),b,2776,a)].">
      <j1 rule="hyper" parents="120 9035 2776"/>
    </justification>
  </clause>

  <clause id="9304">
    <literal><![CDATA[
      x / R(y * K(z,y),u,y) = (x / R(y,u,y)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(7902(a,2),9039(a,1,2))].">
      <j1 rule="para" parents="7902 9039"/>
    </justification>
  </clause>

  <clause id="9305">
    <literal><![CDATA[
      K(x / y,z \ (y \ x)) = K(y \ x,y \ (z \ x))
    ]]></literal>
    <justification jstring="[hyper(8219,a,9077,a)].">
      <j1 rule="hyper" parents="8219 9077"/>
    </justification>
  </clause>

  <clause id="9306">
    <literal><![CDATA[
      K(x \ y,(z * x) \ y) = K(x \ y,x \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(65,a,8929,a(flip),b,9305,a)].">
      <j1 rule="hyper" parents="65 8929 9305"/>
    </justification>
  </clause>

  <clause id="9307">
    <literal><![CDATA[
      K(((x \ y) / z) \ y,(x * ((x \ y) / z)) \ y) = K(((x \ y) / z) \ y,z)
    ]]></literal>
    <justification jstring="[para(79(a,1),9306(a,2,2))].">
      <j1 rule="para" parents="79 9306"/>
    </justification>
  </clause>

  <clause id="9308">
    <literal><![CDATA[
      K(x,L(y,z,u) \ (y * x)) = K(x,(x / L(y,z,u)) * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,8407,a(flip),b,9094,a)].">
      <j1 rule="hyper" parents="65 8407 9094"/>
    </justification>
  </clause>

  <clause id="9309">
    <literal><![CDATA[
      (x / y) / T(y \ x,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y \ x,z) \ (x / y) = u
    ]]></literal>
    <justification jstring="[para(9095(a,1),5771(a,1))].">
      <j1 rule="para" parents="9095 5771"/>
    </justification>
  </clause>

  <clause id="9310">
    <literal><![CDATA[
      x * ((y * y) * K(z,y \ 1)) = (x * y) / T(1 / y,z)
    ]]></literal>
    <justification jstring="[hyper(673,a,9122,a)].">
      <j1 rule="hyper" parents="673 9122"/>
    </justification>
  </clause>

  <clause id="9311">
    <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(5053(a,1),9123(a,2,1))].">
      <j1 rule="para" parents="5053 9123"/>
    </justification>
  </clause>

  <clause id="9312">
    <literal><![CDATA[
      T(K(x,y),z / (1 / y)) = T(K(x,y),z * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,9127,a(flip),b,9128,a),flip(a)].">
      <j1 rule="hyper" parents="65 9127 9128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9313">
    <literal><![CDATA[
      T(K(x,y),z * y) = K(x,1 / (z / (z / (1 / y))))
    ]]></literal>
    <justification jstring="[hyper(65,a,8518,a(flip),b,9312,a),flip(a)].">
      <j1 rule="hyper" parents="65 8518 9312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9314">
    <literal><![CDATA[
      K(x,1 / (y / (y / (1 / z)))) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,6917,a(flip),b,9313,a),flip(a)].">
      <j1 rule="hyper" parents="65 6917 9313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9315">
    <literal><![CDATA[
      x \ R(x * K(y,x),z,y \ 1) = K(y,x) * (x \ R(x,z,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(119,a,9132,a,b,5528,a)].">
      <j1 rule="hyper" parents="119 9132 5528"/>
    </justification>
  </clause>

  <clause id="9316">
    <literal><![CDATA[
      K(x,y) * ((y * R(x,z,u)) * x) = (x * y) * R(x,z,u)
    ]]></literal>
    <justification jstring="[para(1918(a,2),9136(a,1,2))].">
      <j1 rule="para" parents="1918 9136"/>
    </justification>
  </clause>

  <clause id="9317">
    <literal><![CDATA[
      K(x,(y * R(x,z,u)) / w) = K(x,y / (R(x,z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(299,a,9062,a(flip),b,9138,a),flip(a)].">
      <j1 rule="hyper" parents="299 9062 9138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9318">
    <literal><![CDATA[
      R(K(x,K(y,z \ 1)),u,w) = K(x,K(y,R(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(299,a,8783,a(flip),b,9149,a),flip(a)].">
      <j1 rule="hyper" parents="299 8783 9149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9319">
    <literal><![CDATA[
      R(K(x,K(y,z \ 1)),u,w) * x = T(x,K(R(z,u,w) \ 1,y))
    ]]></literal>
    <justification jstring="[para(9149(a,2),8023(a,1,1))].">
      <j1 rule="para" parents="9149 8023"/>
    </justification>
  </clause>

  <clause id="9320">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) = K(x,K(y,R(z,u,w)))
    ]]></literal>
    <justification jstring="[para(8783(a,1),9318(a,1,1))].">
      <j1 rule="para" parents="8783 9318"/>
    </justification>
  </clause>

  <clause id="9321">
    <literal><![CDATA[
      K(x,R(K(y,z),u,w)) = K(x,K(y,R(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,9152,a(flip),b,9320,a)].">
      <j1 rule="hyper" parents="65 9152 9320"/>
    </justification>
  </clause>

  <clause id="9322">
    <literal><![CDATA[
      x * R(K(x,K(y,z)),u,w) = T(x,K(y,R(z,u,w)))
    ]]></literal>
    <justification jstring="[para(9320(a,2),5083(a,2,2)),flip(a)].">
      <j1 rule="para" parents="9320 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9323">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) = K(y,K(z,R(x,u,w)))
    ]]></literal>
    <justification jstring="[para(7989(a,1),9320(a,1,1))].">
      <j1 rule="para" parents="7989 9320"/>
    </justification>
  </clause>

  <clause id="9324">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w))) = K(z,K(x,R(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,9320,a(flip),b,9323,a),flip(a)].">
      <j1 rule="hyper" parents="65 9320 9323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9325">
    <literal><![CDATA[
      K(x,R(K(y,z),u,w)) = K(x,K(z,R(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,9151,a(flip),b,9323,a)].">
      <j1 rule="hyper" parents="65 9151 9323"/>
    </justification>
  </clause>

  <clause id="9326">
    <literal><![CDATA[
      T(x,R(K(y,z),u,w)) = T(x,K(y,R(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,9153,a(flip),b,9322,a)].">
      <j1 rule="hyper" parents="65 9153 9322"/>
    </justification>
  </clause>

  <clause id="9327">
    <literal><![CDATA[
      L(K(x,y),T(x,z) * u,w) = K(L(x,u,w),y)
    ]]></literal>
    <justification jstring="[hyper(299,a,8126,a(flip),b,9167,a),flip(a)].">
      <j1 rule="hyper" parents="299 8126 9167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9328">
    <literal><![CDATA[
      L(K(x,y),T(x,z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(L(x,u,w),y) = v5
    ]]></literal>
    <justification jstring="[para(9167(a,2),8229(a,1))].">
      <j1 rule="para" parents="9167 8229"/>
    </justification>
  </clause>

  <clause id="9330">
    <literal><![CDATA[
      K(L(x,T(x,y) \ z,u),w) = L(K(x,w),z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),9327(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 9327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9331">
    <literal><![CDATA[
      K(L(x,T(x,y) \ 1,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u) = w
    ]]></literal>
    <justification jstring="[para(9330(a,2),500(a,1)),flip(b)].">
      <j1 rule="para" parents="9330 500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9333">
    <literal><![CDATA[
      K(T(x,y),z) * ((y * z) / y) = (y * (z * K(x,z))) / y
    ]]></literal>
    <justification jstring="[hyper(143,a,9170,a)].">
      <j1 rule="hyper" parents="143 9170"/>
    </justification>
  </clause>

  <clause id="9334">
    <literal><![CDATA[
      L(K(x,y),T(y,z) * u,w) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(299,a,9197,a(flip),b,9192,a),flip(a)].">
      <j1 rule="hyper" parents="299 9197 9192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9336">
    <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(528(a,1),9195(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="528 9195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9337">
    <literal><![CDATA[
      (x / y) * (K(y,z) * K(y * z,y)) = x / L(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,8942,a(flip),b,9242,a),flip(a)].">
      <j1 rule="hyper" parents="299 8942 9242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9338">
    <literal><![CDATA[
      K(x * (y \ z),K(y,y \ z)) = K(K(z,y),x * (z / y))
    ]]></literal>
    <justification jstring="[hyper(299,a,7954,a,b,9289,a),flip(a)].">
      <j1 rule="hyper" parents="299 7954 9289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9339">
    <literal><![CDATA[
      K(x,(x / L(y,z,u)) * y) = K(x,y * (L(y,z,u) \ x))
    ]]></literal>
    <justification jstring="[para(1352(a,1),9308(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1352 9308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9340">
    <literal><![CDATA[
      x * (y * (y * K(z,y \ 1))) = (x * y) / T(1 / y,z)
    ]]></literal>
    <justification jstring="[para(6960(a,1),9310(a,1,2))].">
      <j1 rule="para" parents="6960 9310"/>
    </justification>
  </clause>

  <clause id="9341">
    <literal><![CDATA[
      ((x * y) / x) / ((x * (y * K(z,y))) / x) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[para(9333(a,1),5430(a,1,2))].">
      <j1 rule="para" parents="9333 5430"/>
    </justification>
  </clause>

  <clause id="9342">
    <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(9333(a,1),5440(a,1,2))].">
      <j1 rule="para" parents="9333 5440"/>
    </justification>
  </clause>

  <clause id="9343">
    <literal><![CDATA[
      T(x * (y / z),K(y,z)) \ (x * (y / z)) = K(x * (z \ y),K(z,z \ y))
    ]]></literal>
    <justification jstring="[hyper(299,a,5024,a(flip),b,9338,a)].">
      <j1 rule="hyper" parents="299 5024 9338"/>
    </justification>
  </clause>

  <clause id="9344">
    <literal><![CDATA[
      K(x,T((y \ z) / z,u)) = ((u * x) / u) / ((u * (x * K(y \ 1,x))) / u)
    ]]></literal>
    <justification jstring="[para(5860(a,1),9341(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5860 9341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9345">
    <literal><![CDATA[
      K(x,T((y \ z) \ z,u)) = ((u * x) / u) / ((u * (x * K(y,T(x,z)))) / u)
    ]]></literal>
    <justification jstring="[para(7493(a,1),9341(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7493 9341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9346">
    <literal><![CDATA[
      K(x,L(y \ L(y,z,u),y,u * z)) = K(x,a(u,z,y) \ 1)
    ]]></literal>
    <justification jstring="[para(532(a,2),6844(a,1,2))].">
      <j1 rule="para" parents="532 6844"/>
    </justification>
  </clause>

  <clause id="9347">
    <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(6948(a,2),5273(a,1))].">
      <j1 rule="para" parents="6948 5273"/>
    </justification>
  </clause>

  <clause id="9349">
    <literal><![CDATA[
      T(x,x \ T(x * y,y \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,7050,a(flip),b,7111,a),flip(a)].">
      <j1 rule="hyper" parents="299 7050 7111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9351">
    <literal><![CDATA[
      T(x / y,(x / y) \ T(x,y \ 1)) = T(x / y,y)
    ]]></literal>
    <justification jstring="[para(12(a,1),9349(a,1,2,2,1))].">
      <j1 rule="para" parents="12 9349"/>
    </justification>
  </clause>

  <clause id="9352">
    <literal><![CDATA[
      T(x / y,(x / y) \ T(x,y \ 1)) = y \ x
    ]]></literal>
    <justification jstring="[hyper(299,a,109,a(flip),b,9351,a),flip(a)].">
      <j1 rule="hyper" parents="299 109 9351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9353">
    <literal><![CDATA[
      T(x,y \ 1) / (y \ x) = (x / y) \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(9352(a,1),262(a,1,2))].">
      <j1 rule="para" parents="9352 262"/>
    </justification>
  </clause>

  <clause id="9354">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) / ((y \ 1) \ x) = (x / (y \ 1)) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(3739(a,1),9353(a,2,2))].">
      <j1 rule="para" parents="3739 9353"/>
    </justification>
  </clause>

  <clause id="9355">
    <literal><![CDATA[
      L(((x / y) / x) \ 1,(x / y) / x,x) = x / T(x * ((x / y) / x),y)
    ]]></literal>
    <justification jstring="[para(79(a,1),7114(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="79 7114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9356">
    <literal><![CDATA[
      R(x,y,z * K(y,z)) = R(x,T(y,z),z)
    ]]></literal>
    <justification jstring="[hyper(549,a,7137,a),flip(a)].">
      <j1 rule="hyper" parents="549 7137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9357">
    <literal><![CDATA[
      R(x,T(K(y,z),u),u) = R(x,K(y,z),T(u,K(y,z)))
    ]]></literal>
    <justification jstring="[para(8009(a,1),9356(a,1,3)),flip(a)].">
      <j1 rule="para" parents="8009 9356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9359">
    <literal><![CDATA[
      T(x,T(y,z) \ T(x,z)) = T(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(7342,a,7561,a)].">
      <j1 rule="hyper" parents="7342 7561"/>
    </justification>
  </clause>

  <clause id="9360">
    <literal><![CDATA[
      T(x,T(y \ x,z)) = T(x,T(y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,8887,a(flip),b,9359,a),flip(a)].">
      <j1 rule="hyper" parents="65 8887 9359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9362">
    <literal><![CDATA[
      T(x,T((1 / y) \ x,z)) * K(T(y \ 1,z) \ 1,x) = L(x,T(1 / y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[para(9360(a,2),5988(a,1,1))].">
      <j1 rule="para" parents="9360 5988"/>
    </justification>
  </clause>

  <clause id="9364">
    <literal><![CDATA[
      L(K(x,T(y \ z,u)),y \ z,y) = K(x,T((z \ y) \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,7498,a,b,7522,a),flip(a)].">
      <j1 rule="hyper" parents="299 7498 7522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9365">
    <literal><![CDATA[
      K(x,R(T(y,z * u),y \ z,u)) = K(x,((y \ z) * u) \ (z * u))
    ]]></literal>
    <justification jstring="[para(76(a,1),7532(a,1,2,1,1))].">
      <j1 rule="para" parents="76 7532"/>
    </justification>
  </clause>

  <clause id="9366">
    <literal><![CDATA[
      L(x,T(y,K(x,z)),x) = T(x,x * y) * K(y,x)
    ]]></literal>
    <justification jstring="[para(8656(a,1),7592(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8656 7592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9367">
    <literal><![CDATA[
      L(x,T(y,K(x,z)),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,5561,a(flip),b,9366,a),flip(a)].">
      <j1 rule="hyper" parents="299 5561 9366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9369">
    <literal><![CDATA[
      L(x,T(y,T(x,z)),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,7150,a(flip),b,9367,a)].">
      <j1 rule="hyper" parents="65 7150 9367"/>
    </justification>
  </clause>

  <clause id="9371">
    <literal><![CDATA[
      L(x,y / T(x,z),x) = L(x,T(x,z) \ y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,5735,a(flip),b,9369,a)].">
      <j1 rule="hyper" parents="65 5735 9369"/>
    </justification>
  </clause>

  <clause id="9372">
    <literal><![CDATA[
      K(R(x,y,R(x,z,u)),T(w,y * R(x,z,u))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(w,y)) = v5
    ]]></literal>
    <justification jstring="[para(7908(a,2),7709(a,1))].">
      <j1 rule="para" parents="7908 7709"/>
    </justification>
  </clause>

  <clause id="9373">
    <literal><![CDATA[
      x * (K(y,x) * K(x,T(z,y))) = T(x * K(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(8177,a,9216,a),flip(a)].">
      <j1 rule="hyper" parents="8177 9216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9374">
    <literal><![CDATA[
      K(x,y) * T(y,T(z,x)) = T(y * K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(5774,a,9373,a)].">
      <j1 rule="hyper" parents="5774 9373"/>
    </justification>
  </clause>

  <clause id="9375">
    <literal><![CDATA[
      T(x * K(y,x),z) \ x = K(T(z,y),x) * K(x,y)
    ]]></literal>
    <justification jstring="[para(9373(a,1),9252(a,1,1))].">
      <j1 rule="para" parents="9373 9252"/>
    </justification>
  </clause>

  <clause id="9376">
    <literal><![CDATA[
      K(x,y) * T(x * K(y,x),z) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(5437,a,9374,a)].">
      <j1 rule="hyper" parents="5437 9374"/>
    </justification>
  </clause>

  <clause id="9377">
    <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(9374(a,1),5438(a,1,2)),flip(b)].">
      <j1 rule="para" parents="9374 5438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9378">
    <literal><![CDATA[
      a(x,L(T(y * K(z,y),u),K(y,z),K(y,z)),w) = a(x,K(y,z) * T(y,T(u,z)),w)
    ]]></literal>
    <justification jstring="[para(9376(a,1),2350(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9376 2350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9379">
    <literal><![CDATA[
      K(x \ y,x) * T(y / x,z) = T(x \ y,T(z,x))
    ]]></literal>
    <justification jstring="[para(5102(a,1),9376(a,1,2,1))].">
      <j1 rule="para" parents="5102 9376"/>
    </justification>
  </clause>

  <clause id="9380">
    <literal><![CDATA[
      T((x * y) / x,z) \ y = K(T(z,x),y) * K(y,x)
    ]]></literal>
    <justification jstring="[para(5054(a,2),9375(a,1,1,1))].">
      <j1 rule="para" parents="5054 9375"/>
    </justification>
  </clause>

  <clause id="9381">
    <literal><![CDATA[
      (x / y) * T(y \ x,T(z,y)) = (y \ x) * T(x / y,z)
    ]]></literal>
    <justification jstring="[para(9379(a,1),5867(a,1,2))].">
      <j1 rule="para" parents="9379 5867"/>
    </justification>
  </clause>

  <clause id="9382">
    <literal><![CDATA[
      T((x * y) / x,z) \ y = K(y,x) * K(T(z,x),y)
    ]]></literal>
    <justification jstring="[hyper(299,a,2278,a,b,9380,a),flip(a)].">
      <j1 rule="hyper" parents="299 2278 9380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9383">
    <literal><![CDATA[
      K(x,y) * K(T(L(x,z,u) * y,y),x) = L(x,y,L(x,z,u)) \ x
    ]]></literal>
    <justification jstring="[para(1656(a,1),9382(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1656 9382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9384">
    <literal><![CDATA[
      (x / y) * T(y \ x,z \ y) = (y \ x) * T(x / y,y / z)
    ]]></literal>
    <justification jstring="[para(7456(a,1),9381(a,1,2))].">
      <j1 rule="para" parents="7456 9381"/>
    </justification>
  </clause>

  <clause id="9385">
    <literal><![CDATA[
      L(K(x,T(T(y,z),u * z)),z,u) = (u * (K(x,y) * z)) / (u * z)
    ]]></literal>
    <justification jstring="[para(7507(a,1),8245(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7507 8245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9386">
    <literal><![CDATA[
      K(L(x,y,L(x,z,u)),T(w,L(x,z,u) * y)) = K(x,T(w,y))
    ]]></literal>
    <justification jstring="[hyper(8228,a,8352,a),flip(a)].">
      <j1 rule="hyper" parents="8228 8352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9387">
    <literal><![CDATA[
      L(T(K(x,(y \ z) \ u),w),u,y) = K(x,T(z \ (y * u),w))
    ]]></literal>
    <justification jstring="[hyper(299,a,7489,a,b,8409,a),flip(a)].">
      <j1 rule="hyper" parents="299 7489 8409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9388">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,x) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,T(x,y)) * u = w
    ]]></literal>
    <justification jstring="[para(7983(a,1),8438(a,1,1))].">
      <j1 rule="para" parents="7983 8438"/>
    </justification>
  </clause>

  <clause id="9389">
    <literal><![CDATA[
      x * K(y,(x \ 1) * (z * x)) = K(y,L(z,x,x \ 1)) * x
    ]]></literal>
    <justification jstring="[para(5648(a,1),8452(a,1,2))].">
      <j1 rule="para" parents="5648 8452"/>
    </justification>
  </clause>

  <clause id="9390">
    <literal><![CDATA[
      T(T(x,L(K(y,z),u,w)),L(K(y,z),u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(8488,a,4533,a),flip(a)].">
      <j1 rule="hyper" parents="8488 4533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9391">
    <literal><![CDATA[
      x * K(L(K(y,z),u,w),x) = T(x,L(K(y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(5247,a,9390,a),flip(a)].">
      <j1 rule="hyper" parents="5247 9390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9392">
    <literal><![CDATA[
      T(L(K(x,y),z,u) \ w,L(K(x,y),z,u)) != v5
    ]]></literal>
    <literal><![CDATA[
      w / L(K(x,y),z,u) = v5
    ]]></literal>
    <justification jstring="[para(9391(a,1),5498(a,1))].">
      <j1 rule="para" parents="9391 5498"/>
    </justification>
  </clause>

  <clause id="9394">
    <literal><![CDATA[
      K((x * (y * z)) \ ((x * z) * y),K(z,u)) = K(K(a(x,z,T(y,z)),z),u)
    ]]></literal>
    <justification jstring="[para(8762(a,1),7954(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8762 7954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9395">
    <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(689(a,1),8865(a,1,2))].">
      <j1 rule="para" parents="689 8865"/>
    </justification>
  </clause>

  <clause id="9396">
    <literal><![CDATA[
      K(x,a(K(x,y),z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(65,a,5805,a(flip),b,9395,a),flip(a)].">
      <j1 rule="hyper" parents="65 5805 9395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9398">
    <literal><![CDATA[
      T(x,a(K(x,y),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,9396,a)].">
      <j1 rule="hyper" parents="58 9396"/>
    </justification>
  </clause>

  <clause id="9399">
    <literal><![CDATA[
      T(a(K(x,y),z,u),x) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(56,a,9398,a)].">
      <j1 rule="hyper" parents="56 9398"/>
    </justification>
  </clause>

  <clause id="9400">
    <literal><![CDATA[
      T(T(x,y),a(K(x,z),u,w)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(9398(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9398 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9401">
    <literal><![CDATA[
      a(K(x,y),z,u) * x = x * a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(9398(a,1),107(a,1,2))].">
      <j1 rule="para" parents="9398 107"/>
    </justification>
  </clause>

  <clause id="9402">
    <literal><![CDATA[
      K(x,y) * a(K(x,z),u,w) = a(K(x,z),u,w) * K(x,y)
    ]]></literal>
    <justification jstring="[para(9398(a,1),7541(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9398 7541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9403">
    <literal><![CDATA[
      K(a(K(x,y),z,u),w) * x = x * K(a(K(x,y),z,u),w)
    ]]></literal>
    <justification jstring="[para(9399(a,1),7541(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9399 7541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9404">
    <literal><![CDATA[
      K(x,y) * (y \ R(y,x,L(y,z,u))) = K(x * L(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(9016(a,1),5456(a,1,2))].">
      <j1 rule="para" parents="9016 5456"/>
    </justification>
  </clause>

  <clause id="9405">
    <literal><![CDATA[
      K(R(x,y,z) * u,T(x,u)) * K(T(x,u),u) = T(x,u) \ R(T(x,u),u,R(T(x,u),y,z))
    ]]></literal>
    <justification jstring="[para(234(a,1),9022(a,1,1,1))].">
      <j1 rule="para" parents="234 9022"/>
    </justification>
  </clause>

  <clause id="9406">
    <literal><![CDATA[
      x \ R(x,y,R(x,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(y * R(x,z,u),x) * K(x,y) = w
    ]]></literal>
    <justification jstring="[para(9023(a,1),2279(a,1))].">
      <j1 rule="para" parents="9023 2279"/>
    </justification>
  </clause>

  <clause id="9407">
    <literal><![CDATA[
      (x / (K(y,z) * L(K(z,y),u,w))) * K(y,z) = x * L(K(y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,349,a(flip),b,9105,a)].">
      <j1 rule="hyper" parents="65 349 9105"/>
    </justification>
  </clause>

  <clause id="9408">
    <literal><![CDATA[
      K(x * (y \ T(y * z,y)),L(K(y,y * z),z,x)) / ((x * z) / (x * (y \ T(y * z,y)))) = 1 / ((x * (y \ T(y * z,y))) \ (x * z))
    ]]></literal>
    <justification jstring="[para(9119(a,1),5409(a,1,1,2))].">
      <j1 rule="para" parents="9119 5409"/>
    </justification>
  </clause>

  <clause id="9409">
    <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),9166(a,2,2))].">
      <j1 rule="para" parents="484 9166"/>
    </justification>
  </clause>

  <clause id="9410">
    <literal><![CDATA[
      (x * (y * z)) * K(z,L(y,z,x)) = x * (z * y)
    ]]></literal>
    <justification jstring="[para(88(a,1),9191(a,2,2))].">
      <j1 rule="para" parents="88 9191"/>
    </justification>
  </clause>

  <clause id="9411">
    <literal><![CDATA[
      (x * (y * z)) * K(u,L(y,z,x)) = x * (y * (z * K(u,y)))
    ]]></literal>
    <justification jstring="[para(7822(a,1),9191(a,2,2))].">
      <j1 rule="para" parents="7822 9191"/>
    </justification>
  </clause>

  <clause id="9412">
    <literal><![CDATA[
      (x * (y * z)) * K(L(z,y,x),y) = x * (z * y)
    ]]></literal>
    <justification jstring="[hyper(7207,a,9410,a)].">
      <j1 rule="hyper" parents="7207 9410"/>
    </justification>
  </clause>

  <clause id="9413">
    <literal><![CDATA[
      (x * (y * z)) * u != x * (z * y)
    ]]></literal>
    <literal><![CDATA[
      K(z,L(y,z,x)) = u
    ]]></literal>
    <justification jstring="[para(9410(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="9410 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9414">
    <literal><![CDATA[
      K(x,T(y,z * (u * x))) = K(x,T(y,z * (x * u)))
    ]]></literal>
    <justification jstring="[para(9410(a,1),8661(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9410 8661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9415">
    <literal><![CDATA[
      K((x * (y * z)) \ u,z) = K((x * (z * y)) \ u,z)
    ]]></literal>
    <justification jstring="[para(9410(a,1),8739(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9410 8739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9416">
    <literal><![CDATA[
      K(x \ (y * (z * u)),u) = K(x \ (y * (u * z)),u)
    ]]></literal>
    <justification jstring="[para(9410(a,1),8757(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9410 8757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9417">
    <literal><![CDATA[
      (x * (y * z)) * u != x * (z * y)
    ]]></literal>
    <literal><![CDATA[
      K(L(z,y,x),y) = u
    ]]></literal>
    <justification jstring="[para(9412(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="9412 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9418">
    <literal><![CDATA[
      (x * (y * z)) * K(z,L(y,z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      x * (z * y) = u
    ]]></literal>
    <justification jstring="[para(9412(a,1),7216(a,1,1)),flip(b)].">
      <j1 rule="para" parents="9412 7216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9419">
    <literal><![CDATA[
      T(x,(y * (z * x)) \ u) = T(x,(y * (x * z)) \ u)
    ]]></literal>
    <justification jstring="[para(9412(a,1),8881(a,1,2,1))].">
      <j1 rule="para" parents="9412 8881"/>
    </justification>
  </clause>

  <clause id="9420">
    <literal><![CDATA[
      K(((x \ 1) * (y * x)) \ z,x) = K(L(y,x,x \ 1) \ z,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,6034,a(flip),b,9415,a),flip(a)].">
      <j1 rule="hyper" parents="299 6034 9415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9421">
    <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),9416(a,2,1))].">
      <j1 rule="para" parents="484 9416"/>
    </justification>
  </clause>

  <clause id="9422">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,y) != w
    ]]></literal>
    <literal><![CDATA[
      x * (K(u,y) * K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(9239(a,2),9219(a,1))].">
      <j1 rule="para" parents="9239 9219"/>
    </justification>
  </clause>

  <clause id="9423">
    <literal><![CDATA[
      (x * K(y,z)) * (K(u,y) * K(z,y)) = x * K(u,y)
    ]]></literal>
    <justification jstring="[hyper(9247,a,9206,a),flip(a)].">
      <j1 rule="hyper" parents="9247 9206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9424">
    <literal><![CDATA[
      (K(x,y) * K(x,z)) \ 1 = K(y,x) * K(z,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,5198,a(flip),b,9423,a)].">
      <j1 rule="hyper" parents="119 5198 9423"/>
    </justification>
  </clause>

  <clause id="9425">
    <literal><![CDATA[
      L(x,y,z * K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z * K(w,u)) = v5
    ]]></literal>
    <justification jstring="[para(9423(a,1),2512(a,1,3))].">
      <j1 rule="para" parents="9423 2512"/>
    </justification>
  </clause>

  <clause id="9426">
    <literal><![CDATA[
      (K(x,y) * K(x,z)) \ 1 = K(z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(6269,a,9424,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="6269 9424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9427">
    <literal><![CDATA[
      T(K(x,y) * K(x,z),K(z,x) * K(y,x)) = (K(z,x) * K(y,x)) \ 1
    ]]></literal>
    <justification jstring="[para(9424(a,1),6740(a,2,1))].">
      <j1 rule="para" parents="9424 6740"/>
    </justification>
  </clause>

  <clause id="9428">
    <literal><![CDATA[
      L(x,y,T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z * K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(5083(a,2),9425(a,1,3))].">
      <j1 rule="para" parents="5083 9425"/>
    </justification>
  </clause>

  <clause id="9429">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z * K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(6685(a,2),9428(a,1))].">
      <j1 rule="para" parents="6685 9428"/>
    </justification>
  </clause>

  <clause id="9430">
    <literal><![CDATA[
      K(x,T((y \ z) \ 1,u)) = K(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,7590,a(flip),b,9364,a),flip(a)].">
      <j1 rule="hyper" parents="65 7590 9364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9432">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,T((x \ y) \ 1,u)) = K((x \ y) \ z,T(y \ x,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,8474,a,b,9430,a)].">
      <j1 rule="hyper" parents="65 8474 9430"/>
    </justification>
  </clause>

  <clause id="9433">
    <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(65,a,6293,a,b,9430,a)].">
      <j1 rule="hyper" parents="65 6293 9430"/>
    </justification>
  </clause>

  <clause id="9434">
    <literal><![CDATA[
      K(x,T(y,L(x,z,u) * w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,9088,a(flip),b,9386,a)].">
      <j1 rule="hyper" parents="65 9088 9386"/>
    </justification>
  </clause>

  <clause id="9436">
    <literal><![CDATA[
      K(x,T(y,L(x,z,u) \ w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(10(a,1),9434(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 9434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9437">
    <literal><![CDATA[
      K(x,T(y,z / L(x,u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,7802,a,b,9436,a)].">
      <j1 rule="hyper" parents="65 7802 9436"/>
    </justification>
  </clause>

  <clause id="9439">
    <literal><![CDATA[
      K(x,T(y,z / x)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(477(a,1),9437(a,1,2,2,2))].">
      <j1 rule="para" parents="477 9437"/>
    </justification>
  </clause>

  <clause id="9440">
    <literal><![CDATA[
      K(x,T(y,z * (u * x))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(184(a,1),9437(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="184 9437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9441">
    <literal><![CDATA[
      K(x,T(y,z * (u / x))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(585(a,1),9437(a,1,2,2))].">
      <j1 rule="para" parents="585 9437"/>
    </justification>
  </clause>

  <clause id="9442">
    <literal><![CDATA[
      K(x,T(y,z * x)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(11(a,1),9439(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 9439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9443">
    <literal><![CDATA[
      K(L(x,y,z),T(u,z * (y * x))) = K(L(x,y,z),T(u,z * y))
    ]]></literal>
    <justification jstring="[para(184(a,1),9439(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="184 9439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9444">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) = K(x,T(y,z \ x))
    ]]></literal>
    <justification jstring="[para(4637(a,1),9439(a,1,2))].">
      <j1 rule="para" parents="4637 9439"/>
    </justification>
  </clause>

  <clause id="9445">
    <literal><![CDATA[
      K(x,K(y,T(z,u / x))) = K(z,K(x,T(y,u)))
    ]]></literal>
    <justification jstring="[para(9439(a,1),8019(a,2,2))].">
      <j1 rule="para" parents="9439 8019"/>
    </justification>
  </clause>

  <clause id="9446">
    <literal><![CDATA[
      K(x,T(y \ (z * x),z)) = K(x,(z * x) / y)
    ]]></literal>
    <justification jstring="[hyper(8327,a,9442,a),flip(a)].">
      <j1 rule="hyper" parents="8327 9442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9447">
    <literal><![CDATA[
      K(L(x,y,x),T(z,u)) = K(x,T(z,u * x))
    ]]></literal>
    <justification jstring="[hyper(299,a,7435,a,b,9442,a)].">
      <j1 rule="hyper" parents="299 7435 9442"/>
    </justification>
  </clause>

  <clause id="9448">
    <literal><![CDATA[
      K(a(x,y,z),T(u,(x * y) * z)) = K(a(x,y,z),T(u,x * (y * z)))
    ]]></literal>
    <justification jstring="[para(84(a,1),9442(a,1,2,2))].">
      <j1 rule="para" parents="84 9442"/>
    </justification>
  </clause>

  <clause id="9449">
    <literal><![CDATA[
      (x * y) * K(y,T(z,x)) = K(y,z) * (x * y)
    ]]></literal>
    <justification jstring="[para(9442(a,1),7507(a,1,2))].">
      <j1 rule="para" parents="9442 7507"/>
    </justification>
  </clause>

  <clause id="9450">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(9444(a,2),8844(a,1))].">
      <j1 rule="para" parents="9444 8844"/>
    </justification>
  </clause>

  <clause id="9451">
    <literal><![CDATA[
      K(L(x,y,x),z) = K(x,T(T(z,u),u * x))
    ]]></literal>
    <justification jstring="[hyper(8171,a,9447,a)].">
      <j1 rule="hyper" parents="8171 9447"/>
    </justification>
  </clause>

  <clause id="9452">
    <literal><![CDATA[
      K(x,T(y,z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(9447(a,1),7438(a,1))].">
      <j1 rule="para" parents="9447 7438"/>
    </justification>
  </clause>

  <clause id="9453">
    <literal><![CDATA[
      K(x,T(y,z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u / z)) = w
    ]]></literal>
    <justification jstring="[para(4641(a,1),9450(a,1,2))].">
      <j1 rule="para" parents="4641 9450"/>
    </justification>
  </clause>

  <clause id="9454">
    <literal><![CDATA[
      K(x,T(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(7037(a,1),9450(a,1,2))].">
      <j1 rule="para" parents="7037 9450"/>
    </justification>
  </clause>

  <clause id="9455">
    <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(8333(a,1),9450(a,1,2))].">
      <j1 rule="para" parents="8333 9450"/>
    </justification>
  </clause>

  <clause id="9456">
    <literal><![CDATA[
      K(L(x,y,x),z) = K(T(u * x,x) / u,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,8365,a,b,9451,a),flip(a)].">
      <j1 rule="hyper" parents="299 8365 9451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9457">
    <literal><![CDATA[
      K(T(x * y,y) / x,z) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(9331,a,9456,a),flip(a)].">
      <j1 rule="hyper" parents="9331 9456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9459">
    <literal><![CDATA[
      K(T(x,y \ x) / y,z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),9457(a,1,1,1,1))].">
      <j1 rule="para" parents="10 9457"/>
    </justification>
  </clause>

  <clause id="9460">
    <literal><![CDATA[
      K(x,T(y,z * (x * u))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,9414,a(flip),b,9440,a)].">
      <j1 rule="hyper" parents="65 9414 9440"/>
    </justification>
  </clause>

  <clause id="9461">
    <literal><![CDATA[
      K(x,K(y,T(z,u / x))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,T(y,u))) = w
    ]]></literal>
    <justification jstring="[para(9445(a,2),7985(a,1))].">
      <j1 rule="para" parents="9445 7985"/>
    </justification>
  </clause>

  <clause id="9462">
    <literal><![CDATA[
      K(x,T(y \ (z * x),z)) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(299,a,9066,a(flip),b,9446,a),flip(a)].">
      <j1 rule="hyper" parents="299 9066 9446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9463">
    <literal><![CDATA[
      K(x,T(y \ (z * x),z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(y / z) \ x) = u
    ]]></literal>
    <justification jstring="[para(9446(a,2),9067(a,1))].">
      <j1 rule="para" parents="9446 9067"/>
    </justification>
  </clause>

  <clause id="9464">
    <literal><![CDATA[
      K(x,y) * (z * x) = z * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(6862,a,9449,a),flip(a)].">
      <j1 rule="hyper" parents="6862 9449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9465">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * x) = z * T(x,y)
    ]]></literal>
    <justification jstring="[para(8179(a,1),9464(a,2,2))].">
      <j1 rule="para" parents="8179 9464"/>
    </justification>
  </clause>

  <clause id="9466">
    <literal><![CDATA[
      (x * T(y,z)) / (x * y) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(137,a,9465,a)].">
      <j1 rule="hyper" parents="137 9465"/>
    </justification>
  </clause>

  <clause id="9467">
    <literal><![CDATA[
      T(K(x,y) * L(y,z,u),x) / (y * (y \ L(y,z,u))) = K(y \ L(y,z,u),T(x,y))
    ]]></literal>
    <justification jstring="[hyper(120,a,9142,a,b,9465,a)].">
      <j1 rule="hyper" parents="120 9142 9465"/>
    </justification>
  </clause>

  <clause id="9468">
    <literal><![CDATA[
      (x * T(y,z)) / T(x,y) = T(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(120,a,9465,a(flip),b,5353,a(flip))].">
      <j1 rule="hyper" parents="120 9465 5353"/>
    </justification>
  </clause>

  <clause id="9469">
    <literal><![CDATA[
      (x * T(y,z)) / (x * y) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(9465(a,1),307(a,1,1)),flip(b)].">
      <j1 rule="para" parents="9465 307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9470">
    <literal><![CDATA[
      K(x,T(y,z)) * ((z * y) * x) = (z * y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(7488(a,1),9465(a,1,1))].">
      <j1 rule="para" parents="7488 9465"/>
    </justification>
  </clause>

  <clause id="9471">
    <literal><![CDATA[
      T(K(x,y),z) * ((x \ z) * x) = (x \ z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(7548(a,1),9465(a,1,1))].">
      <j1 rule="para" parents="7548 9465"/>
    </justification>
  </clause>

  <clause id="9473">
    <literal><![CDATA[
      (K(x,y) * T(z,u)) / T(K(x,y),z) = (z * (K(x,y) * K(z,u))) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,8282,a,b,9468,a),flip(a)].">
      <j1 rule="hyper" parents="299 8282 9468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9474">
    <literal><![CDATA[
      (x * ((y \ z) \ z)) / T(x,y) = T(y,T(y \ z,x))
    ]]></literal>
    <justification jstring="[para(108(a,1),9468(a,1,1,2))].">
      <j1 rule="para" parents="108 9468"/>
    </justification>
  </clause>

  <clause id="9475">
    <literal><![CDATA[
      (x * T(y,z \ y)) / T(x,y) = T(y,T(y * (z \ 1),x))
    ]]></literal>
    <justification jstring="[para(2009(a,1),9468(a,1,1,2))].">
      <j1 rule="para" parents="2009 9468"/>
    </justification>
  </clause>

  <clause id="9476">
    <literal><![CDATA[
      T(x,T(y * K(x,z),u)) = (u * T(x,y)) / T(u,x)
    ]]></literal>
    <justification jstring="[para(8562(a,1),9468(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="8562 9468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9477">
    <literal><![CDATA[
      K(x,T(x * y,z * y)) = K(x,T(x * y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,7488,a(flip),b,9460,a),flip(a)].">
      <j1 rule="hyper" parents="65 7488 9460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9478">
    <literal><![CDATA[
      K(x,T(y,z * (x \ u))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(10(a,1),9460(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10 9460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9479">
    <literal><![CDATA[
      K(x,T(x * y,z * y)) = K(x,T(y * x,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,5689,a,b,9477,a),flip(a)].">
      <j1 rule="hyper" parents="299 5689 9477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9480">
    <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(9478(a,1),8215(a,1))].">
      <j1 rule="para" parents="9478 8215"/>
    </justification>
  </clause>

  <clause id="9481">
    <literal><![CDATA[
      K(x,T(y,K(y * T(x,y),z))) * ((K(y * T(x,y),z) * y) * x) = (x * y) * R(K(x * y,z),y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,3796,a,b,9470,a),flip(a)].">
      <j1 rule="hyper" parents="299 3796 9470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9482">
    <literal><![CDATA[
      (T(x,T(x \ y,z)) * z) \ (z * ((x \ y) \ y)) = K(z,x)
    ]]></literal>
    <justification jstring="[para(9474(a,1),6861(a,1,1,1))].">
      <j1 rule="para" parents="9474 6861"/>
    </justification>
  </clause>

  <clause id="9483">
    <literal><![CDATA[
      T(x,T(y * K(x,z),u)) = T(x,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,9468,a(flip),b,9476,a),flip(a)].">
      <j1 rule="hyper" parents="299 9468 9476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9484">
    <literal><![CDATA[
      T(x,T(y / (z / x),u)) = T(x,T(y / (x \ z),u))
    ]]></literal>
    <justification jstring="[para(9052(a,1),9483(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9052 9483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9485">
    <literal><![CDATA[
      T(x,T((y * x) / z,u)) = T(x,T(y / (x \ z),u))
    ]]></literal>
    <justification jstring="[hyper(65,a,7762,a,b,9484,a)].">
      <j1 rule="hyper" parents="65 7762 9484"/>
    </justification>
  </clause>

  <clause id="9486">
    <literal><![CDATA[
      T(x,T(x * (y \ 1),z)) = T(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,9468,a(flip),b,9475,a),flip(a)].">
      <j1 rule="hyper" parents="65 9468 9475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9487">
    <literal><![CDATA[
      L(K(x,T((y \ z) \ u,w)),u,y) = K(x,T(z \ (y * u),w))
    ]]></literal>
    <justification jstring="[para(7489(a,2),9387(a,1,1))].">
      <j1 rule="para" parents="7489 9387"/>
    </justification>
  </clause>

  <clause id="9488">
    <literal><![CDATA[
      K(x,T((y \ 1) * (z * y),y)) = K(x,L(z,y,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(8113,a,9389,a)].">
      <j1 rule="hyper" parents="8113 9389"/>
    </justification>
  </clause>

  <clause id="9489">
    <literal><![CDATA[
      (x * (y * (K(z,y) \ (y \ u)))) * K(z,L(y,K(z,y) \ (y \ u),x)) = x * (((K(z,y) \ (u / y)) * K(z,y)) * y)
    ]]></literal>
    <justification jstring="[para(3503(a,2),9411(a,2,2))].">
      <j1 rule="para" parents="3503 9411"/>
    </justification>
  </clause>

  <clause id="9490">
    <literal><![CDATA[
      K(x,T((y \ z) \ x,u)) = K(x,T(z \ (y * x),u))
    ]]></literal>
    <justification jstring="[hyper(6822,a,9487,a)].">
      <j1 rule="hyper" parents="6822 9487"/>
    </justification>
  </clause>

  <clause id="9491">
    <literal><![CDATA[
      K(x,T((y \ z) \ x,y)) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(299,a,9462,a(flip),b,9490,a),flip(a)].">
      <j1 rule="hyper" parents="299 9462 9490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9492">
    <literal><![CDATA[
      K(x,T((y \ z) \ x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) \ x) = u
    ]]></literal>
    <justification jstring="[para(9490(a,2),9463(a,1))].">
      <j1 rule="para" parents="9490 9463"/>
    </justification>
  </clause>

  <clause id="9493">
    <literal><![CDATA[
      K(x,((y * z) / y) \ x) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[para(9(a,1),9491(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="9 9491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9494">
    <literal><![CDATA[
      K(x,T(y \ x,y \ z)) = K(x,(z / (z / y)) \ x)
    ]]></literal>
    <justification jstring="[para(4504(a,1),9493(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4504 9493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9495">
    <literal><![CDATA[
      K(x,T((y / (z * y)) \ x,z)) = K(x,R(1 / (1 / (1 / z)),z,y) \ x)
    ]]></literal>
    <justification jstring="[para(4523(a,2),9493(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4523 9493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9496">
    <literal><![CDATA[
      (x * (y * z)) * K(L(z,y,x),u) = x * (y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,487,a(flip),b,6873,a),flip(a)].">
      <j1 rule="hyper" parents="299 487 6873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9497">
    <literal><![CDATA[
      K(L(x,y,z),u) \ ((z * (y * T(x,u))) / (z * (y * x))) = K(z * (y * x),K(L(x,y,z),u))
    ]]></literal>
    <justification jstring="[para(9496(a,1),5074(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="9496 5074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9498">
    <literal><![CDATA[
      (x * (y * T(z,u))) \ (x * (y * z)) = K(u,L(z,y,x))
    ]]></literal>
    <justification jstring="[para(9496(a,1),7200(a,1,1))].">
      <j1 rule="para" parents="9496 7200"/>
    </justification>
  </clause>

  <clause id="9499">
    <literal><![CDATA[
      (x * (y * T(z,u))) \ (x * (y * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(u,L(z,y,x)) = w
    ]]></literal>
    <justification jstring="[para(9496(a,1),7209(a,1,1))].">
      <j1 rule="para" parents="9496 7209"/>
    </justification>
  </clause>

  <clause id="9500">
    <literal><![CDATA[
      (x * T(y \ z,u)) / T(z / y,u) = x * K(y \ z,T(y,u))
    ]]></literal>
    <justification jstring="[para(7725(a,1),6923(a,2,2))].">
      <j1 rule="para" parents="7725 6923"/>
    </justification>
  </clause>

  <clause id="9501">
    <literal><![CDATA[
      L(x,(y / z) * z,u) = L(x,y * K(w * w,z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,2884,a(flip),b,7068,a)].">
      <j1 rule="hyper" parents="65 2884 7068"/>
    </justification>
  </clause>

  <clause id="9503">
    <literal><![CDATA[
      L(x,y * K(z * z,u),w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[para(12(a,1),9501(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 9501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9505">
    <literal><![CDATA[
      L(K(x,T(y,z)),x,u) = (x * z) \ (T(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(7090,a,7904,a),flip(a)].">
      <j1 rule="hyper" parents="7090 7904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9506">
    <literal><![CDATA[
      L(K(x,y \ z),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * y) \ (u * z)) = w
    ]]></literal>
    <justification jstring="[para(6855(a,1),7095(a,1))].">
      <j1 rule="para" parents="6855 7095"/>
    </justification>
  </clause>

  <clause id="9507">
    <literal><![CDATA[
      (1 / x) \ (L(y,x,x) * x) = x * (y * L(x,x,x))
    ]]></literal>
    <justification jstring="[para(3759(a,1),7106(a,1,2))].">
      <j1 rule="para" parents="3759 7106"/>
    </justification>
  </clause>

  <clause id="9508">
    <literal><![CDATA[
      (x * y) \ (x * (y * L(x,x,x))) = R(x,(x \ 1) * y,x)
    ]]></literal>
    <justification jstring="[para(9507(a,1),4740(a,1,2))].">
      <j1 rule="para" parents="9507 4740"/>
    </justification>
  </clause>

  <clause id="9509">
    <literal><![CDATA[
      R(x,(x \ 1) * y,x) = L(L(x,x,x),y,x)
    ]]></literal>
    <justification jstring="[hyper(493,a,9508,a),flip(a)].">
      <j1 rule="hyper" parents="493 9508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9510">
    <literal><![CDATA[
      (x * K(y * z,u)) * (z * y) = x * (K(z,y) * T(y * z,u))
    ]]></literal>
    <justification jstring="[para(7180(a,1),7166(a,2,2))].">
      <j1 rule="para" parents="7180 7166"/>
    </justification>
  </clause>

  <clause id="9511">
    <literal><![CDATA[
      (((x / y) * T(y,z)) * u) \ (x * u) = K(z,((x / y) * u) \ (x * u))
    ]]></literal>
    <justification jstring="[para(79(a,1),7288(a,1,1,1,2,1))].">
      <j1 rule="para" parents="79 7288"/>
    </justification>
  </clause>

  <clause id="9512">
    <literal><![CDATA[
      (T(x,y) \ 1) * T(x \ 1,T(x \ 1,y)) = x \ (1 / T(x,y))
    ]]></literal>
    <justification jstring="[para(7926(a,2),7319(a,1,2))].">
      <j1 rule="para" parents="7926 7319"/>
    </justification>
  </clause>

  <clause id="9513">
    <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(7523(a,2),8430(a,1))].">
      <j1 rule="para" parents="7523 8430"/>
    </justification>
  </clause>

  <clause id="9514">
    <literal><![CDATA[
      T(T(x * K(y,x),z),u) \ T(T(x,z),u) = K(x,T(T(y,u),z))
    ]]></literal>
    <justification jstring="[hyper(299,a,7537,a(flip),b,7547,a),flip(a)].">
      <j1 rule="hyper" parents="299 7537 7547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9516">
    <literal><![CDATA[
      K(x,K((y * x) / z,T(u,z))) = K(x,K(u,(z / x) \ y))
    ]]></literal>
    <justification jstring="[hyper(9461,a,7768,a)].">
      <j1 rule="hyper" parents="9461 7768"/>
    </justification>
  </clause>

  <clause id="9517">
    <literal><![CDATA[
      K(x,K(y,(z / x) \ u)) = K(x,K(y,z \ (u * x)))
    ]]></literal>
    <justification jstring="[hyper(8209,a,9516,a),flip(a)].">
      <j1 rule="hyper" parents="8209 9516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9518">
    <literal><![CDATA[
      K(x,(y \ K(x,z)) \ u) = (y \ T(y * u,x)) \ u
    ]]></literal>
    <justification jstring="[para(7786(a,1),7228(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7786 7228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9519">
    <literal><![CDATA[
      K(x,(y \ K(x,z)) \ u) = K(x,(y \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(299,a,7229,a(flip),b,9518,a),flip(a)].">
      <j1 rule="hyper" parents="299 7229 9518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9520">
    <literal><![CDATA[
      K(x,((y \ 1) \ K(x,z)) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(299,a,5653,a(flip),b,9519,a),flip(a)].">
      <j1 rule="hyper" parents="299 5653 9519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9521">
    <literal><![CDATA[
      K(L(x,y,z),R(z,u,w)) = K(x,R(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(299,a,5831,a(flip),b,7831,a),flip(a)].">
      <j1 rule="hyper" parents="299 5831 7831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9522">
    <literal><![CDATA[
      K((x \ 1) \ y,R(x,z,u)) = K(x * y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(519(a,1),9521(a,1,1)),flip(a)].">
      <j1 rule="para" parents="519 9521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9523">
    <literal><![CDATA[
      K((x \ 1) * y,R(x \ 1,z,u)) = K(x \ y,R(x \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(7406,a,9522,a),flip(a)].">
      <j1 rule="hyper" parents="7406 9522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9524">
    <literal><![CDATA[
      K(x,y / (x / ((z * y) \ 1))) = y / (K(z \ (x \ 1),x) * y)
    ]]></literal>
    <justification jstring="[para(7948(a,1),6044(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7948 6044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9525">
    <literal><![CDATA[
      K(x,(y * z) \ (x \ y)) = K(x,z \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(8720,a,7949,a)].">
      <j1 rule="hyper" parents="8720 7949"/>
    </justification>
  </clause>

  <clause id="9526">
    <literal><![CDATA[
      K((x * y) \ (z \ x),z) = (u * K(z,y \ (z \ 1))) \ u
    ]]></literal>
    <justification jstring="[para(9525(a,1),7200(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9525 7200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9527">
    <literal><![CDATA[
      K((x * y) \ (z \ x),z) = K(y \ (z \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(299,a,7200,a(flip),b,9526,a),flip(a)].">
      <j1 rule="hyper" parents="299 7200 9526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9528">
    <literal><![CDATA[
      K((x \ y) \ (z \ 1),z) = K(y \ (z \ x),z)
    ]]></literal>
    <justification jstring="[para(10(a,1),9527(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 9527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9529">
    <literal><![CDATA[
      L(K((x \ y) \ (z \ 1),z),z \ 1,u) = K(y \ (z \ x),z)
    ]]></literal>
    <justification jstring="[hyper(6809,a,9528,a)].">
      <j1 rule="hyper" parents="6809 9528"/>
    </justification>
  </clause>

  <clause id="9530">
    <literal><![CDATA[
      K(x \ (y * (z \ 1)),z) = K(x \ (z \ y),z)
    ]]></literal>
    <justification jstring="[hyper(65,a,7421,a(flip),b,9529,a)].">
      <j1 rule="hyper" parents="65 7421 9529"/>
    </justification>
  </clause>

  <clause id="9531">
    <literal><![CDATA[
      K(((x \ 1) * y) \ (x \ z),x) = K(y \ T(z,x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,7837,a(flip),b,9530,a),flip(a)].">
      <j1 rule="hyper" parents="65 7837 9530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9532">
    <literal><![CDATA[
      K(((x \ 1) * y) \ (x \ z),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,7740,a(flip),b,9531,a),flip(a)].">
      <j1 rule="hyper" parents="299 7740 9531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9533">
    <literal><![CDATA[
      K(((x \ 1) * y) \ z,x) = K(y \ (z * x),x)
    ]]></literal>
    <justification jstring="[hyper(8671,a,9532,a)].">
      <j1 rule="hyper" parents="8671 9532"/>
    </justification>
  </clause>

  <clause id="9534">
    <literal><![CDATA[
      K(L(x,y,y \ 1) \ z,y) = K((x * y) \ (z * y),y)
    ]]></literal>
    <justification jstring="[hyper(65,a,9420,a(flip),b,9533,a)].">
      <j1 rule="hyper" parents="65 9420 9533"/>
    </justification>
  </clause>

  <clause id="9535">
    <literal><![CDATA[
      K(T(x,y \ 1) \ (z * y),y) = K((x * (y \ 1)) \ z,y)
    ]]></literal>
    <justification jstring="[para(107(a,1),9533(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="107 9533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9536">
    <literal><![CDATA[
      K(L(x,y,y \ 1) \ z,y) = K(x \ z,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,8696,a(flip),b,9534,a),flip(a)].">
      <j1 rule="hyper" parents="299 8696 9534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9537">
    <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(9536(a,1),5682(a,1,2,1,2))].">
      <j1 rule="para" parents="9536 5682"/>
    </justification>
  </clause>

  <clause id="9538">
    <literal><![CDATA[
      K((x * (y \ 1)) \ z,y) = K(x \ (z * y),y)
    ]]></literal>
    <justification jstring="[hyper(65,a,7738,a(flip),b,9535,a),flip(a)].">
      <j1 rule="hyper" parents="65 7738 9535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9539">
    <literal><![CDATA[
      L(K(x * (y \ z),x),y \ z,y) = K(y \ (z * x),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,8955,a,b,9538,a)].">
      <j1 rule="hyper" parents="65 8955 9538"/>
    </justification>
  </clause>

  <clause id="9540">
    <literal><![CDATA[
      L(K(x * y,x),y,z) = K(z \ ((z * y) * x),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,7426,a,b,9538,a)].">
      <j1 rule="hyper" parents="65 7426 9538"/>
    </justification>
  </clause>

  <clause id="9541">
    <literal><![CDATA[
      T(T(x,y \ z),K(u,y \ z)) = T(x,T((z \ y) \ 1,u))
    ]]></literal>
    <justification jstring="[para(7037(a,1),8090(a,1,1))].">
      <j1 rule="para" parents="7037 8090"/>
    </justification>
  </clause>

  <clause id="9542">
    <literal><![CDATA[
      T(x,T((y \ z) \ 1,u)) = T(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[hyper(8072,a,9541,a),flip(a)].">
      <j1 rule="hyper" parents="8072 9541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9543">
    <literal><![CDATA[
      (1 / (x \ y)) * K(y / x,z) = K(y / x,z) / (x \ y)
    ]]></literal>
    <justification jstring="[para(8116(a,1),8168(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8116 8168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9544">
    <literal><![CDATA[
      K(1 / x,y) / (x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x * K(1 / x,y) = z
    ]]></literal>
    <justification jstring="[para(9543(a,1),327(a,1))].">
      <j1 rule="para" parents="9543 327"/>
    </justification>
  </clause>

  <clause id="9545">
    <literal><![CDATA[
      1 / (x \ K(y,1 / x)) = x * K(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(9544,a,6207,a),flip(a)].">
      <j1 rule="hyper" parents="9544 6207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9546">
    <literal><![CDATA[
      1 / ((x * (y \ 1)) / x) = y * K(1 / y,x)
    ]]></literal>
    <justification jstring="[para(5231(a,1),9545(a,1,2))].">
      <j1 rule="para" parents="5231 9545"/>
    </justification>
  </clause>

  <clause id="9547">
    <literal><![CDATA[
      1 / ((x * ((y / z) \ 1)) / x) = (y / z) * K(z / y,x)
    ]]></literal>
    <justification jstring="[para(5855(a,1),9546(a,2,2))].">
      <j1 rule="para" parents="5855 9546"/>
    </justification>
  </clause>

  <clause id="9548">
    <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(8250(a,1),9464(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8250 9464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9549">
    <literal><![CDATA[
      T(x,T((y * z) \ z,u)) = T(x,T(z \ (y \ z),u))
    ]]></literal>
    <justification jstring="[hyper(8280,a,8281,a),flip(a)].">
      <j1 rule="hyper" parents="8280 8281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9550">
    <literal><![CDATA[
      T(x,y / z) * K(z \ y,z) = (y / z) \ (x * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(299,a,5920,a(flip),b,8347,a),flip(a)].">
      <j1 rule="hyper" parents="299 5920 8347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9551">
    <literal><![CDATA[
      x \ ((y / z) \ (x * (z \ y))) = K(x,y / z) * K(z \ y,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,9550,a(flip),b,5055,a)].">
      <j1 rule="hyper" parents="119 9550 5055"/>
    </justification>
  </clause>

  <clause id="9552">
    <literal><![CDATA[
      K((x \ 1) \ y,z \ (x * y)) = K(x * y,(x \ z) \ y)
    ]]></literal>
    <justification jstring="[para(67(a,1),8408(a,2,1))].">
      <j1 rule="para" parents="67 8408"/>
    </justification>
  </clause>

  <clause id="9553">
    <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(1965(a,1),8408(a,2,1))].">
      <j1 rule="para" parents="1965 8408"/>
    </justification>
  </clause>

  <clause id="9554">
    <literal><![CDATA[
      K(x,K(y \ (z * u),u \ (z \ 1))) = K(x,K(z * u,(z \ y) \ u))
    ]]></literal>
    <justification jstring="[para(9552(a,1),8796(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9552 8796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9555">
    <literal><![CDATA[
      x * (y * K(z,(x \ 1) \ y)) = (x * y) * K(z,x * y)
    ]]></literal>
    <justification jstring="[para(67(a,1),8410(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="67 8410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9556">
    <literal><![CDATA[
      K(x,y / z) * K(z \ y,z) = z \ (y / T(y / z,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,7243,a(flip),b,8448,a),flip(a)].">
      <j1 rule="hyper" parents="65 7243 8448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9557">
    <literal><![CDATA[
      (x \ ((y \ (x * z)) * y)) * u = (z * K((x \ 1) \ (y \ z),y)) * u
    ]]></literal>
    <justification jstring="[para(3937(a,1),8477(a,2,1)),flip(a)].">
      <j1 rule="para" parents="3937 8477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9558">
    <literal><![CDATA[
      T(K(x,y),T(z,u * x)) = T(K(x,y),T(z,x * u))
    ]]></literal>
    <justification jstring="[hyper(8420,a,8496,a),flip(a)].">
      <j1 rule="hyper" parents="8420 8496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9559">
    <literal><![CDATA[
      T(K(x,y \ (z * x)),T(y,x * z)) = T(K(x,y \ (z * x)),y)
    ]]></literal>
    <justification jstring="[hyper(8330,a,9558,a),flip(a)].">
      <j1 rule="hyper" parents="8330 9558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9560">
    <literal><![CDATA[
      L(x,T(y,z) \ u,T(y,u)) = L(x,y \ (K(z,y) * u),y)
    ]]></literal>
    <justification jstring="[para(5372(a,1),8548(a,1,2))].">
      <j1 rule="para" parents="5372 8548"/>
    </justification>
  </clause>

  <clause id="9561">
    <literal><![CDATA[
      L(x,T(y,z) \ u,T(y,u)) = L(x,T(y,z) \ u,y)
    ]]></literal>
    <justification jstring="[para(5372(a,1),9560(a,2,2))].">
      <j1 rule="para" parents="5372 9560"/>
    </justification>
  </clause>

  <clause id="9562">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ y) * z) = y * L(z,T(x,y) \ y,x)
    ]]></literal>
    <justification jstring="[para(9561(a,1),482(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9561 482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9563">
    <literal><![CDATA[
      T(x,y) * ((x \ T(y,x)) * z) = y * L(z,T(x,y) \ y,x)
    ]]></literal>
    <justification jstring="[para(4396(a,1),9562(a,1,2,1))].">
      <j1 rule="para" parents="4396 9562"/>
    </justification>
  </clause>

  <clause id="9564">
    <literal><![CDATA[
      T(x,y) * ((x \ T(y,x)) * z) = y * L(z,x \ T(y,x),x)
    ]]></literal>
    <justification jstring="[para(4396(a,1),9563(a,2,2,2))].">
      <j1 rule="para" parents="4396 9563"/>
    </justification>
  </clause>

  <clause id="9565">
    <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(9564(a,1),4437(a,1,1))].">
      <j1 rule="para" parents="9564 4437"/>
    </justification>
  </clause>

  <clause id="9566">
    <literal><![CDATA[
      K(x \ (y * T(z,u)),T(z,y)) = K((y * T(z,u)) / x,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,7488,a(flip),b,8616,a)].">
      <j1 rule="hyper" parents="65 7488 8616"/>
    </justification>
  </clause>

  <clause id="9567">
    <literal><![CDATA[
      T(T(x * K(y,x),z),u * (x * K(y,x))) = T(T(x * K(y,x),u * x),z)
    ]]></literal>
    <justification jstring="[para(8621(a,1),4373(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8621 4373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9568">
    <literal><![CDATA[
      K(x,T(x \ y,z)) * (K(y,z) * x) = T(x,x \ y) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,6660,a(flip),b,8713,a),flip(a)].">
      <j1 rule="hyper" parents="65 6660 8713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9569">
    <literal><![CDATA[
      K(x,K(y,z)) * (z \ K(u,y)) = T(z \ K(u,y),K(x,y))
    ]]></literal>
    <justification jstring="[para(8785(a,1),8747(a,1,1))].">
      <j1 rule="para" parents="8785 8747"/>
    </justification>
  </clause>

  <clause id="9570">
    <literal><![CDATA[
      T(x \ K(y,z),K(u,z)) = T(x,K(u,z)) \ K(y,z)
    ]]></literal>
    <justification jstring="[hyper(7976,a,9569,a),flip(a)].">
      <j1 rule="hyper" parents="7976 9569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9571">
    <literal><![CDATA[
      K(x,K(y,z \ (u * y))) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(36,a,8904,a,b,8878,a),flip(a)].">
      <j1 rule="hyper" parents="36 8904 8878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9572">
    <literal><![CDATA[
      K(x,K(y,z \ (u * y))) = K(y,K(x,z \ u))
    ]]></literal>
    <justification jstring="[hyper(299,a,7983,a,b,9571,a),flip(a)].">
      <j1 rule="hyper" parents="299 7983 9571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9573">
    <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(1953(a,1),9571(a,1,2,2))].">
      <j1 rule="para" parents="1953 9571"/>
    </justification>
  </clause>

  <clause id="9574">
    <literal><![CDATA[
      K(x,K(y,z \ (y \ u))) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(8874(a,1),9571(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8874 9571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9575">
    <literal><![CDATA[
      K(x,K(y,z \ (u * x))) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(7985,a,9572,a)].">
      <j1 rule="hyper" parents="7985 9572"/>
    </justification>
  </clause>

  <clause id="9576">
    <literal><![CDATA[
      K(x,K(y,(z / x) \ u)) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,9517,a,b,9575,a)].">
      <j1 rule="hyper" parents="65 9517 9575"/>
    </justification>
  </clause>

  <clause id="9577">
    <literal><![CDATA[
      T(K(x,y),(z \ (u * x)) \ 1) = K(x,y) * K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(9575(a,1),8793(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9575 8793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9578">
    <literal><![CDATA[
      K(x,K(y,(x \ z) \ u)) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,8657,a(flip),b,9576,a)].">
      <j1 rule="hyper" parents="65 8657 9576"/>
    </justification>
  </clause>

  <clause id="9579">
    <literal><![CDATA[
      K(x,K(y,z \ (x \ u))) = K(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[hyper(8823,a,9578,a)].">
      <j1 rule="hyper" parents="8823 9578"/>
    </justification>
  </clause>

  <clause id="9580">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z \ u)) = K(x,T(y,(x \ z) \ u))
    ]]></literal>
    <justification jstring="[para(9578(a,1),7967(a,1,2))].">
      <j1 rule="para" parents="9578 7967"/>
    </justification>
  </clause>

  <clause id="9581">
    <literal><![CDATA[
      K((T(x,y) * z) \ u,K(x,w)) = K(x,K(w,u \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,9302,a,b,9579,a)].">
      <j1 rule="hyper" parents="65 9302 9579"/>
    </justification>
  </clause>

  <clause id="9582">
    <literal><![CDATA[
      K(x,K(y,(T(x,z) * u) \ w)) = K(x,K(y,w \ u))
    ]]></literal>
    <justification jstring="[hyper(8025,a,9581,a)].">
      <j1 rule="hyper" parents="8025 9581"/>
    </justification>
  </clause>

  <clause id="9583">
    <literal><![CDATA[
      K(x,T(y,(x \ z) \ u)) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(8234,a,9580,a),flip(a)].">
      <j1 rule="hyper" parents="8234 9580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9584">
    <literal><![CDATA[
      K(x,T(y,z \ (x * u))) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,8315,a(flip),b,9583,a)].">
      <j1 rule="hyper" parents="65 8315 9583"/>
    </justification>
  </clause>

  <clause id="9585">
    <literal><![CDATA[
      K(x,T(y,(x * z) \ u)) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(9(a,1),9583(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="9 9583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9586">
    <literal><![CDATA[
      K(x,T(y,z \ (x \ u))) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(10(a,1),9584(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10 9584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9587">
    <literal><![CDATA[
      K(x,T(y,(z * u) \ ((x * z) * u))) = K(x,T(y,a(x,z,u)))
    ]]></literal>
    <justification jstring="[para(14(a,2),9585(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14 9585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9588">
    <literal><![CDATA[
      K(x,T(y,R(T(x,z * u),z,u))) = K(x,T(y,a(x,z,u)))
    ]]></literal>
    <justification jstring="[para(689(a,1),9587(a,1,2,2))].">
      <j1 rule="para" parents="689 9587"/>
    </justification>
  </clause>

  <clause id="9589">
    <literal><![CDATA[
      K(x,T(y,a(x,z,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8222,a,9588,a),flip(a)].">
      <j1 rule="hyper" parents="8222 9588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9590">
    <literal><![CDATA[
      K(x,y / a(x,z,u)) = K(x,a(x,z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(8215,a,9589,a)].">
      <j1 rule="hyper" parents="8215 9589"/>
    </justification>
  </clause>

  <clause id="9592">
    <literal><![CDATA[
      T(x,T(y,a(x,z,u))) = x * K(x,y)
    ]]></literal>
    <justification jstring="[para(9589(a,1),5083(a,2,2))].">
      <j1 rule="para" parents="9589 5083"/>
    </justification>
  </clause>

  <clause id="9593">
    <literal><![CDATA[
      T(x,T(y,a(x,z,u))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,5083,a,b,9592,a),flip(a)].">
      <j1 rule="hyper" parents="299 5083 9592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9594">
    <literal><![CDATA[
      (T(x,x \ y) * a(x,z,u)) \ (a(x,z,u) * ((x \ y) \ y)) = K(a(x,z,u),x)
    ]]></literal>
    <justification jstring="[para(9593(a,1),9482(a,1,1,1))].">
      <j1 rule="para" parents="9593 9482"/>
    </justification>
  </clause>

  <clause id="9595">
    <literal><![CDATA[
      K(x,a(x,y,y \ 1) \ (z \ R(x,y,y \ 1))) = K(x,z \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,8471,a(flip),b,9590,a),flip(a)].">
      <j1 rule="hyper" parents="65 8471 9590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9596">
    <literal><![CDATA[
      (K(x,y) / x) * (x * z) = K(x,y) * L(z,x,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,6623,a(flip),b,8891,a),flip(a)].">
      <j1 rule="hyper" parents="65 6623 8891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9597">
    <literal><![CDATA[
      (((x \ K(x,y)) \ 1) \ (T(x,x \ 1) * z)) * K((K(x,y) / x) * (x * z),T(x,x \ 1) * z) = T(((x \ K(x,y)) \ 1) \ (T(x,x \ 1) * z),T(x,x \ 1) * z)
    ]]></literal>
    <justification jstring="[para(8891(a,1),5987(a,1,2,1))].">
      <j1 rule="para" parents="8891 5987"/>
    </justification>
  </clause>

  <clause id="9598">
    <literal><![CDATA[
      L(K(x,y) * z,x,x) = K(x,y) * L(z,x,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,6123,a(flip),b,9596,a)].">
      <j1 rule="hyper" parents="65 6123 9596"/>
    </justification>
  </clause>

  <clause id="9599">
    <literal><![CDATA[
      L(x * K(y,z),y,y) = L(x,y,y) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(6526,a,9598,a),flip(a)].">
      <j1 rule="hyper" parents="6526 9598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9600">
    <literal><![CDATA[
      K(x,(1 / y) * ((z \ ((1 / y) \ 1)) * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,8775,a(flip),b,8924,a),flip(a)].">
      <j1 rule="hyper" parents="299 8775 8924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9601">
    <literal><![CDATA[
      K(x,(1 / y) * ((z \ y) * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(79(a,1),9600(a,1,2,2,1,2))].">
      <j1 rule="para" parents="79 9600"/>
    </justification>
  </clause>

  <clause id="9602">
    <literal><![CDATA[
      K(x,(y \ 1) * ((z \ y) * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,5648,a(flip),b,9601,a)].">
      <j1 rule="hyper" parents="65 5648 9601"/>
    </justification>
  </clause>

  <clause id="9603">
    <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(8954(a,2),7209(a,1,1))].">
      <j1 rule="para" parents="8954 7209"/>
    </justification>
  </clause>

  <clause id="9604">
    <literal><![CDATA[
      T(T(x / T(y \ 1,y),K(y,1)),y) = T((1 / y) \ x,y * y)
    ]]></literal>
    <justification jstring="[para(9011(a,2),6537(a,1,1))].">
      <j1 rule="para" parents="9011 6537"/>
    </justification>
  </clause>

  <clause id="9605">
    <literal><![CDATA[
      K(x,T(T((y * z) / y,u),w)) = K(x,T(T(T(z,y),u),w))
    ]]></literal>
    <justification jstring="[para(5123(a,2),9015(a,1,2,1))].">
      <j1 rule="para" parents="5123 9015"/>
    </justification>
  </clause>

  <clause id="9606">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) * z,y) = K(z * (1 / ((x * y) \ x)),y)
    ]]></literal>
    <justification jstring="[hyper(65,a,5608,a(flip),b,9084,a)].">
      <j1 rule="hyper" parents="65 5608 9084"/>
    </justification>
  </clause>

  <clause id="9607">
    <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(711(a,1),9116(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="711 9116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9608">
    <literal><![CDATA[
      (x * K(y,T(z,u))) * K(z,w) = (x * K(z,w)) * K(y,T(z,u))
    ]]></literal>
    <justification jstring="[para(7537(a,1),9245(a,1,1,2))].">
      <j1 rule="para" parents="7537 9245"/>
    </justification>
  </clause>

  <clause id="9609">
    <literal><![CDATA[
      x \ ((x \ L(x,y,x)) * T(x,z)) = R(x,y,x) \ T(x,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,2200,a(flip),b,9259,a),flip(a)].">
      <j1 rule="hyper" parents="299 2200 9259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9610">
    <literal><![CDATA[
      x \ (K(x,y) * L(x,z,x)) = R(x,z,x) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(5369(a,1),9609(a,1,2))].">
      <j1 rule="para" parents="5369 9609"/>
    </justification>
  </clause>

  <clause id="9611">
    <literal><![CDATA[
      R(x,y,x) \ T(x,z) = x \ L(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[para(7443(a,1),9610(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7443 9610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9612">
    <literal><![CDATA[
      R((x * y) / x,z,y) \ y = y \ L(T(y,x),z,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,7465,a,b,9611,a)].">
      <j1 rule="hyper" parents="65 7465 9611"/>
    </justification>
  </clause>

  <clause id="9613">
    <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(9612(a,1),7595(a,1,1,2,1))].">
      <j1 rule="para" parents="9612 7595"/>
    </justification>
  </clause>

  <clause id="9614">
    <literal><![CDATA[
      K(x,y / (z * (K(u,x) / z))) = K(x,y * K(z \ K(u,x),z))
    ]]></literal>
    <justification jstring="[para(7196(a,1),9268(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7196 9268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9615">
    <literal><![CDATA[
      ((x * y) * z) \ ((y * x) * z) = K(y,R(T(x,z),y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,9018,a(flip),b,9287,a),flip(a)].">
      <j1 rule="hyper" parents="65 9018 9287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9616">
    <literal><![CDATA[
      T(x,K(R(y,z,u) \ 1,w)) = R(K(x,K(y,w)),z,u) * x
    ]]></literal>
    <justification jstring="[para(8788(a,1),9319(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="8788 9319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9617">
    <literal><![CDATA[
      T(x,K(R(y,z,u) \ 1,w)) = K(x,R(K(y,w),z,u)) * x
    ]]></literal>
    <justification jstring="[para(9152(a,1),9616(a,2,1))].">
      <j1 rule="para" parents="9152 9616"/>
    </justification>
  </clause>

  <clause id="9618">
    <literal><![CDATA[
      T(x,K(R(y,z,u) \ 1,w)) = T(x,R(K(y,w),z,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,5096,a,b,9617,a),flip(a)].">
      <j1 rule="hyper" parents="299 5096 9617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9619">
    <literal><![CDATA[
      T(x,R(K(y,z),u,w)) = T(x,K(z,R(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(8821,a,9618,a),flip(a)].">
      <j1 rule="hyper" parents="8821 9618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9620">
    <literal><![CDATA[
      T(x,K(y,R(z,u,w))) = T(x,K(z,R(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,9326,a(flip),b,9619,a)].">
      <j1 rule="hyper" parents="65 9326 9619"/>
    </justification>
  </clause>

  <clause id="9621">
    <literal><![CDATA[
      T(x,K(y,R(z \ 1,u,w))) = T(x,K(z,R(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(8820,a,9620,a),flip(a)].">
      <j1 rule="hyper" parents="8820 9620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9622">
    <literal><![CDATA[
      T(x,K(y \ z,R(u,y,y \ 1))) = T(x,K(u,T(z * (y \ 1),y)))
    ]]></literal>
    <justification jstring="[para(705(a,1),9620(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="705 9620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9623">
    <literal><![CDATA[
      T(x,y) / ((y \ 1) \ x) = (x / (y \ 1)) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(3739(a,1),9354(a,1,1))].">
      <j1 rule="para" parents="3739 9354"/>
    </justification>
  </clause>

  <clause id="9624">
    <literal><![CDATA[
      ((x \ y) / (x \ 1)) \ T(x \ y,x) = (x \ y) / ((x \ 1) \ (y / x))
    ]]></literal>
    <justification jstring="[hyper(65,a,6536,a(flip),b,9623,a),flip(a)].">
      <j1 rule="hyper" parents="65 6536 9623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9625">
    <literal><![CDATA[
      ((x / y) / (y \ 1)) \ T(x / y,y) = (y \ x) / ((y \ 1) \ (x / y))
    ]]></literal>
    <justification jstring="[para(109(a,1),9623(a,1,1)),flip(a)].">
      <j1 rule="para" parents="109 9623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9626">
    <literal><![CDATA[
      K(L(x,y,z),u) \ K(L(x,y,z),T(u,z * y)) = K(z * (y * x),K(L(x,y,z),u))
    ]]></literal>
    <justification jstring="[hyper(119,a,9443,a(flip),b,8040,a)].">
      <j1 rule="hyper" parents="119 9443 8040"/>
    </justification>
  </clause>

  <clause id="9627">
    <literal><![CDATA[
      (K(x,y) * K(x * y,z)) * (y * x) = T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,5432,a(flip),b,9510,a),flip(a)].">
      <j1 rule="hyper" parents="299 5432 9510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9628">
    <literal><![CDATA[
      (x * y) \ T(y * x,z) = K(y,x) * K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(37,a,6005,a,b,9627,a)].">
      <j1 rule="hyper" parents="37 6005 9627"/>
    </justification>
  </clause>

  <clause id="9629">
    <literal><![CDATA[
      (x * y) * (K(y,x) * K(y * x,z)) = T(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(144,a,9628,a)].">
      <j1 rule="hyper" parents="144 9628"/>
    </justification>
  </clause>

  <clause id="9631">
    <literal><![CDATA[
      (T(x,y) \ 1) * (x \ 1) = x \ (1 / T(x,y))
    ]]></literal>
    <justification jstring="[para(174(a,1),9512(a,1,2))].">
      <j1 rule="para" parents="174 9512"/>
    </justification>
  </clause>

  <clause id="9633">
    <literal><![CDATA[
      (x \ (1 / T(x,y))) \ z = x * ((T(x,y) \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(9631(a,1),6682(a,1,1))].">
      <j1 rule="para" parents="9631 6682"/>
    </justification>
  </clause>

  <clause id="9634">
    <literal><![CDATA[
      T(x,y) * ((x \ 1) \ z) = x * ((T(x,y) \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(9129,a,9633,a)].">
      <j1 rule="hyper" parents="9129 9633"/>
    </justification>
  </clause>

  <clause id="9635">
    <literal><![CDATA[
      (x / y) * ((T(x / y,y) \ 1) \ z) = (y \ x) * (((x / y) \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(109(a,1),9634(a,1,1)),flip(a)].">
      <j1 rule="para" parents="109 9634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9636">
    <literal><![CDATA[
      K(x,T(T(T(x,y) * z,u),w)) = T(T(x * K(z * T(x,v5),x),w),u) \ T(T(x,w),u)
    ]]></literal>
    <justification jstring="[para(8622(a,1),9514(a,1,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="8622 9514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9637">
    <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(704(a,1),9523(a,1,2)),flip(a)].">
      <j1 rule="para" parents="704 9523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9638">
    <literal><![CDATA[
      K(x,y / (x / ((z * y) \ 1))) = K(x,z \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(299,a,5430,a(flip),b,9524,a),flip(a)].">
      <j1 rule="hyper" parents="299 5430 9524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9640">
    <literal><![CDATA[
      K(x,y / (x * (z * y))) = K(x,z \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(65,a,6312,a(flip),b,9638,a)].">
      <j1 rule="hyper" parents="65 6312 9638"/>
    </justification>
  </clause>

  <clause id="9641">
    <literal><![CDATA[
      K(x,y / ((z * y) * x)) = K(x,z \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(65,a,9267,a,b,9640,a)].">
      <j1 rule="hyper" parents="65 9267 9640"/>
    </justification>
  </clause>

  <clause id="9642">
    <literal><![CDATA[
      K(x,(y / z) \ (x \ 1)) = K(x,z / (y * x))
    ]]></literal>
    <justification jstring="[para(12(a,1),9641(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="12 9641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9643">
    <literal><![CDATA[
      K(x,(y * (z / y)) / ((z / y) * x)) = K(x,((y \ z) / z) \ (x \ 1))
    ]]></literal>
    <justification jstring="[para(4675(a,1),9641(a,1,2,2,1))].">
      <j1 rule="para" parents="4675 9641"/>
    </justification>
  </clause>

  <clause id="9644">
    <literal><![CDATA[
      x \ ((y / z) \ (x * (z \ y))) = z \ (y / T(y / z,x))
    ]]></literal>
    <justification jstring="[hyper(299,a,9556,a(flip),b,9551,a),flip(a)].">
      <j1 rule="hyper" parents="299 9556 9551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9645">
    <literal><![CDATA[
      T(K(x,y \ (z * x)),T(y,z)) = T(K(x,y \ (z * x)),y)
    ]]></literal>
    <justification jstring="[hyper(65,a,9173,a(flip),b,9559,a)].">
      <j1 rule="hyper" parents="65 9173 9559"/>
    </justification>
  </clause>

  <clause id="9646">
    <literal><![CDATA[
      K(x,T(y \ (z * x),T(y,z))) = T(K(x,y \ (z * x)),y)
    ]]></literal>
    <justification jstring="[hyper(7714,a,9645,a)].">
      <j1 rule="hyper" parents="7714 9645"/>
    </justification>
  </clause>

  <clause id="9647">
    <literal><![CDATA[
      K(x,T(y \ (z * x),T(y,z))) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(299,a,9068,a(flip),b,9646,a),flip(a)].">
      <j1 rule="hyper" parents="299 9068 9646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9648">
    <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(9573(a,2),8823(a,1))].">
      <j1 rule="para" parents="9573 8823"/>
    </justification>
  </clause>

  <clause id="9649">
    <literal><![CDATA[
      T(K(x,y),(z \ (u * x)) \ 1) = T(K(x,y),z \ u)
    ]]></literal>
    <justification jstring="[hyper(299,a,7964,a(flip),b,9577,a),flip(a)].">
      <j1 rule="hyper" parents="299 7964 9577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9650">
    <literal><![CDATA[
      T(K(x,y),z \ (u * x)) = T(K(x,y),z \ u)
    ]]></literal>
    <justification jstring="[hyper(8831,a,9649,a)].">
      <j1 rule="hyper" parents="8831 9649"/>
    </justification>
  </clause>

  <clause id="9651">
    <literal><![CDATA[
      T(K(x,y),z \ (u / x)) = T(K(x,y),z \ u)
    ]]></literal>
    <justification jstring="[para(12(a,1),9650(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 9650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9652">
    <literal><![CDATA[
      L(K(x,y),z,u) \ L(T(K(x,y),w \ v5),z,u) = K(L(K(x,y),z,u),w \ (v5 / x))
    ]]></literal>
    <justification jstring="[para(9651(a,1),5084(a,1,2,1))].">
      <j1 rule="para" parents="9651 5084"/>
    </justification>
  </clause>

  <clause id="9653">
    <literal><![CDATA[
      T(T(x / (1 / y),K(y,1)),y) = T((1 / y) \ x,y * y)
    ]]></literal>
    <justification jstring="[para(1692(a,1),9604(a,1,1,1,2))].">
      <j1 rule="para" parents="1692 9604"/>
    </justification>
  </clause>

  <clause id="9654">
    <literal><![CDATA[
      T(T(x / (1 / y),1),y) = T((1 / y) \ x,y * y)
    ]]></literal>
    <justification jstring="[para(194(a,1),9653(a,1,1,2))].">
      <j1 rule="para" parents="194 9653"/>
    </justification>
  </clause>

  <clause id="9655">
    <literal><![CDATA[
      T((1 / x) \ y,x * x) = T(y / (1 / x),x)
    ]]></literal>
    <justification jstring="[para(193(a,1),9654(a,1,1)),flip(a)].">
      <j1 rule="para" parents="193 9654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9657">
    <literal><![CDATA[
      (x \ 1) \ T(y,x * x) = T(y / (1 / x),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,3137,a(flip),b,9655,a)].">
      <j1 rule="hyper" parents="65 3137 9655"/>
    </justification>
  </clause>

  <clause id="9658">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) * z,y) = K(z * (((x * y) \ x) \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(299,a,5601,a(flip),b,9606,a),flip(a)].">
      <j1 rule="hyper" parents="299 5601 9606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9660">
    <literal><![CDATA[
      K(x,y * K(((z \ 1) \ 1) \ K(u,x),(z \ 1) \ 1)) = K(x,y / (z * (K(u,x) / ((z \ 1) \ 1))))
    ]]></literal>
    <justification jstring="[hyper(65,a,5912,a(flip),b,9614,a),flip(a)].">
      <j1 rule="hyper" parents="65 5912 9614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9661">
    <literal><![CDATA[
      (x * y) \ (y * T(x,z)) = K(y,x) * K(x,z)
    ]]></literal>
    <justification jstring="[para(9221(a,1),6876(a,1,1))].">
      <j1 rule="para" parents="9221 6876"/>
    </justification>
  </clause>

  <clause id="9662">
    <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(299,a,9022,a(flip),b,9661,a),flip(a)].">
      <j1 rule="hyper" parents="299 9022 9661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9663">
    <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(299,a,9016,a(flip),b,9661,a),flip(a)].">
      <j1 rule="hyper" parents="299 9016 9661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9664">
    <literal><![CDATA[
      K(x,y) * K(y,y \ x) = a(y,x / y,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,4446,a(flip),b,9661,a),flip(a)].">
      <j1 rule="hyper" parents="65 4446 9661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9665">
    <literal><![CDATA[
      (x * y) \ (y * T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * K(y,x) = u
    ]]></literal>
    <justification jstring="[para(9661(a,2),2285(a,1))].">
      <j1 rule="para" parents="9661 2285"/>
    </justification>
  </clause>

  <clause id="9667">
    <literal><![CDATA[
      x \ R(x,x \ y,x) = a(x,y / x,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,5796,a,b,9664,a)].">
      <j1 rule="hyper" parents="65 5796 9664"/>
    </justification>
  </clause>

  <clause id="9668">
    <literal><![CDATA[
      a(x,y / x,x) \ K(y,x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(9664(a,1),7200(a,1,1))].">
      <j1 rule="para" parents="9664 7200"/>
    </justification>
  </clause>

  <clause id="9669">
    <literal><![CDATA[
      a(x,(x * y) / x,x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),9667(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 9667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9670">
    <literal><![CDATA[
      x \ R(x,T(y,x),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[para(223(a,1),9669(a,1,2)),flip(a)].">
      <j1 rule="para" parents="223 9669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9671">
    <literal><![CDATA[
      x \ R(x,y,x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[para(4688(a,1),9670(a,1,2))].">
      <j1 rule="para" parents="4688 9670"/>
    </justification>
  </clause>

  <clause id="9672">
    <literal><![CDATA[
      K(x * y,x) * K(x,y) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(5791,a,9671,a)].">
      <j1 rule="hyper" parents="5791 9671"/>
    </justification>
  </clause>

  <clause id="9673">
    <literal><![CDATA[
      K(x,y) * K(x * y,x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(5769,a,9671,a)].">
      <j1 rule="hyper" parents="5769 9671"/>
    </justification>
  </clause>

  <clause id="9674">
    <literal><![CDATA[
      x * a(x,y,x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(144,a,9671,a)].">
      <j1 rule="hyper" parents="144 9671"/>
    </justification>
  </clause>

  <clause id="9675">
    <literal><![CDATA[
      T(x,y) \ R(T(x,y),z,x) = a(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,8446,a,b,9671,a)].">
      <j1 rule="hyper" parents="65 8446 9671"/>
    </justification>
  </clause>

  <clause id="9676">
    <literal><![CDATA[
      K(x,y) * K(y,y \ x) = a(y,y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,5796,a(flip),b,9671,a)].">
      <j1 rule="hyper" parents="65 5796 9671"/>
    </justification>
  </clause>

  <clause id="9679">
    <literal><![CDATA[
      a(x,x \ (y \ x),x) = x \ R(x,y \ 1,x)
    ]]></literal>
    <justification jstring="[para(6093(a,1),9671(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6093 9671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9680">
    <literal><![CDATA[
      a(x,y,x) \ K(x * y,x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(9671(a,1),7226(a,1,1))].">
      <j1 rule="para" parents="9671 7226"/>
    </justification>
  </clause>

  <clause id="9681">
    <literal><![CDATA[
      T(x * y,x) / x = y * a(x,y,x)
    ]]></literal>
    <justification jstring="[para(9671(a,1),7363(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9671 7363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9682">
    <literal><![CDATA[
      T(x,T(y,z)) \ R(x,u,x) = K(y,T(x,z)) * a(x,u,x)
    ]]></literal>
    <justification jstring="[para(9671(a,1),7574(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9671 7574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9683">
    <literal><![CDATA[
      x \ R(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(9674(a,1),314(a,1,2))].">
      <j1 rule="para" parents="9674 314"/>
    </justification>
  </clause>

  <clause id="9684">
    <literal><![CDATA[
      a(x,y,x) * K(y,x) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(7207,a,9672,a)].">
      <j1 rule="hyper" parents="7207 9672"/>
    </justification>
  </clause>

  <clause id="9685">
    <literal><![CDATA[
      K(x,x * y) * a(x,y,x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5437,a,9672,a)].">
      <j1 rule="hyper" parents="5437 9672"/>
    </justification>
  </clause>

  <clause id="9686">
    <literal><![CDATA[
      K(x,y) * a(y,x,y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[para(9672(a,1),5456(a,1,2))].">
      <j1 rule="para" parents="9672 5456"/>
    </justification>
  </clause>

  <clause id="9688">
    <literal><![CDATA[
      a(x,y,x) * K(x,x * y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(9672(a,1),7205(a,1,1))].">
      <j1 rule="para" parents="9672 7205"/>
    </justification>
  </clause>

  <clause id="9689">
    <literal><![CDATA[
      (x / y) * a(y,z,y) = x / L(y,z,y)
    ]]></literal>
    <justification jstring="[para(9673(a,1),9337(a,1,2))].">
      <j1 rule="para" parents="9673 9337"/>
    </justification>
  </clause>

  <clause id="9690">
    <literal><![CDATA[
      a(x,y,x) * (y * x) = T(x * y,x)
    ]]></literal>
    <justification jstring="[para(9673(a,1),9627(a,1,1))].">
      <j1 rule="para" parents="9673 9627"/>
    </justification>
  </clause>

  <clause id="9691">
    <literal><![CDATA[
      (x * y) * a(y,x,y) = T(y * x,y)
    ]]></literal>
    <justification jstring="[para(9673(a,1),9629(a,1,2))].">
      <j1 rule="para" parents="9673 9629"/>
    </justification>
  </clause>

  <clause id="9692">
    <literal><![CDATA[
      a(x,y \ 1,x) \ K(y \ x,x) = K(y \ 1,x)
    ]]></literal>
    <justification jstring="[para(5592(a,1),9680(a,1,2))].">
      <j1 rule="para" parents="5592 9680"/>
    </justification>
  </clause>

  <clause id="9693">
    <literal><![CDATA[
      (x \ y) * a(x,x \ y,x) = T(y,x) / x
    ]]></literal>
    <justification jstring="[para(10(a,1),9681(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 9681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9694">
    <literal><![CDATA[
      T(x * a(y,x,y),y) = y \ T(y * x,y)
    ]]></literal>
    <justification jstring="[para(9681(a,1),109(a,1,1))].">
      <j1 rule="para" parents="9681 109"/>
    </justification>
  </clause>

  <clause id="9695">
    <literal><![CDATA[
      R(x * a(y,x,y),z,u) * y = y * R(y \ T(y * x,y),z,u)
    ]]></literal>
    <justification jstring="[para(9681(a,1),692(a,1,1,1))].">
      <j1 rule="para" parents="9681 692"/>
    </justification>
  </clause>

  <clause id="9696">
    <literal><![CDATA[
      (x * y) \ (y * (T(z * T(x,y),z) / z)) = L(a(z,T(x,y),z),T(x,y),y)
    ]]></literal>
    <justification jstring="[para(9681(a,2),229(a,1,2,2))].">
      <j1 rule="para" parents="9681 229"/>
    </justification>
  </clause>

  <clause id="9697">
    <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(9681(a,2),483(a,1,2,2))].">
      <j1 rule="para" parents="9681 483"/>
    </justification>
  </clause>

  <clause id="9698">
    <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(9681(a,2),911(a,1,2,2,2))].">
      <j1 rule="para" parents="9681 911"/>
    </justification>
  </clause>

  <clause id="9699">
    <literal><![CDATA[
      K(x,y) * K(x * y,x) != z
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(5587(a,2),9683(a,1))].">
      <j1 rule="para" parents="5587 9683"/>
    </justification>
  </clause>

  <clause id="9700">
    <literal><![CDATA[
      K(x * y,x) * K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(5790(a,2),9683(a,1))].">
      <j1 rule="para" parents="5790 9683"/>
    </justification>
  </clause>

  <clause id="9701">
    <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(7052(a,1),9684(a,2,1))].">
      <j1 rule="para" parents="7052 9684"/>
    </justification>
  </clause>

  <clause id="9702">
    <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(9442(a,1),9684(a,1,2))].">
      <j1 rule="para" parents="9442 9684"/>
    </justification>
  </clause>

  <clause id="9703">
    <literal><![CDATA[
      K(x,y) * a(x,x \ y,x) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),9685(a,1,1,2))].">
      <j1 rule="para" parents="10 9685"/>
    </justification>
  </clause>

  <clause id="9704">
    <literal><![CDATA[
      (x * K(y,y * z)) \ (x * K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(a(y,z,y),K(y,y * z),x) = u
    ]]></literal>
    <justification jstring="[para(9685(a,1),493(a,1,2,2))].">
      <j1 rule="para" parents="9685 493"/>
    </justification>
  </clause>

  <clause id="9705">
    <literal><![CDATA[
      K(x,y) * a(y,x,y) = K(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,5980,a,b,9686,a),flip(a)].">
      <j1 rule="hyper" parents="299 5980 9686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9706">
    <literal><![CDATA[
      a(x,x \ y,x) * K(x,y) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),9688(a,1,2,2))].">
      <j1 rule="para" parents="10 9688"/>
    </justification>
  </clause>

  <clause id="9708">
    <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(9691(a,1),1023(a,1,1,2))].">
      <j1 rule="para" parents="9691 1023"/>
    </justification>
  </clause>

  <clause id="9709">
    <literal><![CDATA[
      a(x,x \ y,x) = T(x,y) \ ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(4475(a,1),9675(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4475 9675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9710">
    <literal><![CDATA[
      (x * y) / L(y,z,y) = x * a(y,z,y)
    ]]></literal>
    <justification jstring="[para(11(a,1),9689(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 9689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9711">
    <literal><![CDATA[
      (x / L(y,z,y)) * y = x * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(1806,a,9710,a)].">
      <j1 rule="hyper" parents="1806 9710"/>
    </justification>
  </clause>

  <clause id="9712">
    <literal><![CDATA[
      (x * a(y,z,y)) \ (x * y) = L(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(186,a,9710,a)].">
      <j1 rule="hyper" parents="186 9710"/>
    </justification>
  </clause>

  <clause id="9713">
    <literal><![CDATA[
      x * (L(x,y,x) \ z) = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,7664,a(flip),b,9711,a)].">
      <j1 rule="hyper" parents="65 7664 9711"/>
    </justification>
  </clause>

  <clause id="9714">
    <literal><![CDATA[
      (x * L(y,z,y)) * a(y,z,y) = x * y
    ]]></literal>
    <justification jstring="[para(11(a,1),9711(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 9711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9715">
    <literal><![CDATA[
      a(x,y,x) \ x = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,2592,a(flip),b,9712,a)].">
      <j1 rule="hyper" parents="65 2592 9712"/>
    </justification>
  </clause>

  <clause id="9716">
    <literal><![CDATA[
      (x * y) / L(y,z,y) != u
    ]]></literal>
    <literal><![CDATA[
      x * a(y,z,y) = u
    ]]></literal>
    <justification jstring="[para(9712(a,1),310(a,1,2)),flip(b)].">
      <j1 rule="para" parents="9712 310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9717">
    <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(886(a,1),9712(a,1,2))].">
      <j1 rule="para" parents="886 9712"/>
    </justification>
  </clause>

  <clause id="9718">
    <literal><![CDATA[
      (T(x * y,x) / x) \ (y * x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(9681(a,2),9712(a,1,1))].">
      <j1 rule="para" parents="9681 9712"/>
    </justification>
  </clause>

  <clause id="9719">
    <literal><![CDATA[
      a(x,y,x) \ (x * L(x \ a(x,y,x),z,u)) = L(x,y,x) \ L(a(x,y,x) \ x,z,u)
    ]]></literal>
    <justification jstring="[para(9715(a,1),6505(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9715 6505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9720">
    <literal><![CDATA[
      T(x,y) * (L(T(x,y),z,x) \ u) = u * a(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,8459,a,b,9713,a)].">
      <j1 rule="hyper" parents="65 8459 9713"/>
    </justification>
  </clause>

  <clause id="9721">
    <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(7770(a,1),9713(a,1,2,1))].">
      <j1 rule="para" parents="7770 9713"/>
    </justification>
  </clause>

  <clause id="9724">
    <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(8100(a,1),9718(a,1,2))].">
      <j1 rule="para" parents="8100 9718"/>
    </justification>
  </clause>

  <clause id="9725">
    <literal><![CDATA[
      a(x,x \ (y \ x),x) = a(x,y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,9671,a(flip),b,9679,a),flip(a)].">
      <j1 rule="hyper" parents="299 9671 9679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9726">
    <literal><![CDATA[
      T(x,y \ x) \ ((x \ (y \ x)) \ (y \ x)) = a(x,y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,9709,a(flip),b,9725,a)].">
      <j1 rule="hyper" parents="65 9709 9725"/>
    </justification>
  </clause>

  <clause id="9727">
    <literal><![CDATA[
      T(x,y) * (L(T(x,y),z,x) \ u) != u * w
    ]]></literal>
    <literal><![CDATA[
      a(x,z,x) = w
    ]]></literal>
    <justification jstring="[para(9720(a,2),45(a,1))].">
      <j1 rule="para" parents="9720 45"/>
    </justification>
  </clause>

  <clause id="9728">
    <literal><![CDATA[
      K(x,y) * (z * a(y,u,y)) = y * (L(T(y,x),u,y) \ z)
    ]]></literal>
    <justification jstring="[para(9720(a,1),5061(a,1,2))].">
      <j1 rule="para" parents="9720 5061"/>
    </justification>
  </clause>

  <clause id="9729">
    <literal><![CDATA[
      a(T(x,y),z,T(x,y)) = a(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(9727,a,9721,a),flip(a)].">
      <j1 rule="hyper" parents="9727 9721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9731">
    <literal><![CDATA[
      ((x * y) * T(z,y)) / (y * T(z,y)) = R(x,y * K(z,y),z)
    ]]></literal>
    <justification jstring="[para(6912(a,1),7126(a,1,2))].">
      <j1 rule="para" parents="6912 7126"/>
    </justification>
  </clause>

  <clause id="9732">
    <literal><![CDATA[
      R(x,y * K(z,y),z) = R(x,y,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(549,a,9731,a),flip(a)].">
      <j1 rule="hyper" parents="549 9731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9733">
    <literal><![CDATA[
      R(x,y \ z,T(y,y \ z)) = R(x,z / y,y)
    ]]></literal>
    <justification jstring="[para(5102(a,1),9732(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5102 9732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9735">
    <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(7249(a,1),8606(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7249 8606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9736">
    <literal><![CDATA[
      x / T(T(y,y \ x),z) = T(y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(7303,a,7599,a)].">
      <j1 rule="hyper" parents="7303 7599"/>
    </justification>
  </clause>

  <clause id="9738">
    <literal><![CDATA[
      x / T((y \ x) \ x,z) = T(y,z) \ x
    ]]></literal>
    <justification jstring="[para(108(a,1),9736(a,1,2,1))].">
      <j1 rule="para" parents="108 9736"/>
    </justification>
  </clause>

  <clause id="9739">
    <literal><![CDATA[
      T(x / (x / y),z) \ x = x / T(y,z)
    ]]></literal>
    <justification jstring="[para(340(a,1),9736(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="340 9736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9740">
    <literal><![CDATA[
      ((x \ y) \ y) * (T(x,y) \ y) = x * (y / T(x,y))
    ]]></literal>
    <justification jstring="[para(9736(a,1),6772(a,1,2))].">
      <j1 rule="para" parents="9736 6772"/>
    </justification>
  </clause>

  <clause id="9741">
    <literal><![CDATA[
      T((x \ y) \ y,z) = (T(x,z) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(186,a,9738,a),flip(a)].">
      <j1 rule="hyper" parents="186 9738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9743">
    <literal><![CDATA[
      x / T(y \ x,z) = T(x / y,z) \ x
    ]]></literal>
    <justification jstring="[para(79(a,1),9738(a,1,2,1,1))].">
      <j1 rule="para" parents="79 9738"/>
    </justification>
  </clause>

  <clause id="9744">
    <literal><![CDATA[
      x / (x / T(y,z)) = T(x / (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(192,a,9739,a)].">
      <j1 rule="hyper" parents="192 9739"/>
    </justification>
  </clause>

  <clause id="9746">
    <literal><![CDATA[
      L(x,x \ y,x) \ y = y / T(x,y)
    ]]></literal>
    <justification jstring="[para(4519(a,1),9739(a,1,1))].">
      <j1 rule="para" parents="4519 9739"/>
    </justification>
  </clause>

  <clause id="9747">
    <literal><![CDATA[
      T(1 / (1 / x),y) \ K(z,x) = K(z,x) / T(x,y)
    ]]></literal>
    <justification jstring="[para(5740(a,1),9739(a,1,1,1))].">
      <j1 rule="para" parents="5740 9739"/>
    </justification>
  </clause>

  <clause id="9751">
    <literal><![CDATA[
      T((x \ y) \ y,x \ z) = (((x \ z) \ z) \ y) \ y
    ]]></literal>
    <justification jstring="[para(108(a,1),9741(a,2,1,1))].">
      <j1 rule="para" parents="108 9741"/>
    </justification>
  </clause>

  <clause id="9754">
    <literal><![CDATA[
      x \ (T(y / x,z) \ y) = K(z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(119,a,9743,a(flip),b,7190,a(flip))].">
      <j1 rule="hyper" parents="119 9743 7190"/>
    </justification>
  </clause>

  <clause id="9755">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) = y \ T(y * K(x,z),y)
    ]]></literal>
    <justification jstring="[para(9743(a,1),6638(a,1,2))].">
      <j1 rule="para" parents="9743 6638"/>
    </justification>
  </clause>

  <clause id="9757">
    <literal><![CDATA[
      T(x / (x / (y / z)),z) = x / (x / (z \ y))
    ]]></literal>
    <justification jstring="[para(109(a,1),9744(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="109 9744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9758">
    <literal><![CDATA[
      T(x * K(x \ y,x),z) = y / (y / T(x,z))
    ]]></literal>
    <justification jstring="[para(5002(a,1),9744(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5002 9744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9760">
    <literal><![CDATA[
      L(K(x,(y \ 1) \ z),y \ 1,y) != u
    ]]></literal>
    <literal><![CDATA[
      y * (T(z / (y \ 1),x) \ z) = u
    ]]></literal>
    <justification jstring="[para(9754(a,1),530(a,1,1))].">
      <j1 rule="para" parents="9754 530"/>
    </justification>
  </clause>

  <clause id="9761">
    <literal><![CDATA[
      (x * (y / (y / (x \ z)))) / x = y / (y / (z / x))
    ]]></literal>
    <justification jstring="[hyper(267,a,9757,a)].">
      <j1 rule="hyper" parents="267 9757"/>
    </justification>
  </clause>

  <clause id="9762">
    <literal><![CDATA[
      T(x * K(x \ y,x),y) = y / (T(y,x) / x)
    ]]></literal>
    <justification jstring="[para(4382(a,2),9758(a,2,2))].">
      <j1 rule="para" parents="4382 9758"/>
    </justification>
  </clause>

  <clause id="9763">
    <literal><![CDATA[
      (x * K(y,x)) / (x / y) = x / (T(x,y) / y)
    ]]></literal>
    <justification jstring="[hyper(65,a,7121,a(flip),b,9762,a)].">
      <j1 rule="hyper" parents="65 7121 9762"/>
    </justification>
  </clause>

  <clause id="9764">
    <literal><![CDATA[
      L(x,x \ y,x) = y / (T(y,x) / x)
    ]]></literal>
    <justification jstring="[hyper(65,a,5011,a(flip),b,9762,a)].">
      <j1 rule="hyper" parents="65 5011 9762"/>
    </justification>
  </clause>

  <clause id="9765">
    <literal><![CDATA[
      T(x * K(x \ (x \ y),x),x \ y) = (x \ y) / ((((x \ y) \ y) \ y) / x)
    ]]></literal>
    <justification jstring="[para(4391(a,1),9762(a,2,2,1))].">
      <j1 rule="para" parents="4391 9762"/>
    </justification>
  </clause>

  <clause id="9766">
    <literal><![CDATA[
      (x * y) / (T(x * y,x) / x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),9764(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 9764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9767">
    <literal><![CDATA[
      ((x * y) / x) / (y / x) = y / (T(y,x) / x)
    ]]></literal>
    <justification jstring="[para(5054(a,2),9763(a,1,1))].">
      <j1 rule="para" parents="5054 9763"/>
    </justification>
  </clause>

  <clause id="9768">
    <literal><![CDATA[
      (x \ y) / ((((x \ y) \ y) \ y) / x) = ((x * (x \ y)) / x) / ((x \ y) / x)
    ]]></literal>
    <justification jstring="[para(4391(a,1),9767(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4391 9767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9769">
    <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(9740(a,1),790(a,1,2))].">
      <j1 rule="para" parents="9740 790"/>
    </justification>
  </clause>

  <clause id="9770">
    <literal><![CDATA[
      L(x,y,z * (K(u,z) / T(z,w))) = L(x,y,K(u,z) * K(w,z))
    ]]></literal>
    <justification jstring="[para(9747(a,1),6724(a,1,3,2))].">
      <j1 rule="para" parents="9747 6724"/>
    </justification>
  </clause>

  <clause id="9771">
    <literal><![CDATA[
      K(T(x / y,x) \ x,z) = K(y,T(x / z,x) \ x)
    ]]></literal>
    <justification jstring="[hyper(299,a,9080,a,b,9755,a)].">
      <j1 rule="hyper" parents="299 9080 9755"/>
    </justification>
  </clause>

  <clause id="9772">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) * (K(z,x) * 1) = K(y * K(x,z),y)
    ]]></literal>
    <justification jstring="[para(9755(a,2),6744(a,1,1))].">
      <j1 rule="para" parents="9755 6744"/>
    </justification>
  </clause>

  <clause id="9773">
    <literal><![CDATA[
      (x * (y / (y / z))) / x = y / (y / ((x * z) / x))
    ]]></literal>
    <justification jstring="[para(9(a,1),9761(a,1,1,2,2,2))].">
      <j1 rule="para" parents="9 9761"/>
    </justification>
  </clause>

  <clause id="9774">
    <literal><![CDATA[
      (x / (1 / (1 / y))) / x = 1 / (1 / ((x / y) / x))
    ]]></literal>
    <justification jstring="[para(3010(a,1),9761(a,1,1))].">
      <j1 rule="para" parents="3010 9761"/>
    </justification>
  </clause>

  <clause id="9775">
    <literal><![CDATA[
      1 / (1 / ((x / (y \ 1)) / x)) = (x / (1 / y)) / x
    ]]></literal>
    <justification jstring="[para(76(a,1),9774(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="76 9774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9776">
    <literal><![CDATA[
      1 / ((x / (y \ 1)) / x) = ((x / (1 / y)) / x) \ 1
    ]]></literal>
    <justification jstring="[hyper(186,a,9775,a),flip(a)].">
      <j1 rule="hyper" parents="186 9775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9777">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) * K(z,x) = K(y * K(x,z),y)
    ]]></literal>
    <justification jstring="[para(8(a,1),9772(a,1,2))].">
      <j1 rule="para" parents="8 9772"/>
    </justification>
  </clause>

  <clause id="9778">
    <literal><![CDATA[
      K(R(T(x,y),x \ z,z \ y),u) = K(((x \ z) * (z \ y)) \ y,u)
    ]]></literal>
    <justification jstring="[para(27(a,2),7534(a,1,1))].">
      <j1 rule="para" parents="27 7534"/>
    </justification>
  </clause>

  <clause id="9779">
    <literal><![CDATA[
      K(L(x,y,z),T(u,x \ w)) = K(L(x,y,z),T(u,w))
    ]]></literal>
    <justification jstring="[hyper(5301,a,7732,a),flip(a)].">
      <j1 rule="hyper" parents="5301 7732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9780">
    <literal><![CDATA[
      K(L((x \ y) \ y,z,u),w) = K(L(x,z,u),T(w,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,7558,a,b,9779,a)].">
      <j1 rule="hyper" parents="65 7558 9779"/>
    </justification>
  </clause>

  <clause id="9781">
    <literal><![CDATA[
      K(T(x,y \ z),L(y,u,w)) = 1 / K(L(y,u,w),T(x,z))
    ]]></literal>
    <justification jstring="[para(9779(a,1),5209(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9779 5209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9782">
    <literal><![CDATA[
      T(x,L((y \ z) \ z,u,w)) = (v5 * K(L(y,u,w),T(x,z))) \ (v5 * x)
    ]]></literal>
    <justification jstring="[para(9780(a,1),7186(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9780 7186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9783">
    <literal><![CDATA[
      K(T(x,y \ z),L(y,u,w)) = K(x,T(L(y,u,w),z))
    ]]></literal>
    <justification jstring="[hyper(118,a,7583,a(flip),b,9781,a),flip(a)].">
      <j1 rule="hyper" parents="118 7583 9781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9784">
    <literal><![CDATA[
      K(T(x,y \ z),L(y,u,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(25(a,2),9783(a,2,2))].">
      <j1 rule="para" parents="25 9783"/>
    </justification>
  </clause>

  <clause id="9785">
    <literal><![CDATA[
      K(x,T(L(y,z,u),y \ w)) = K(x,L(T(y,w),z,u))
    ]]></literal>
    <justification jstring="[hyper(7709,a,9784,a)].">
      <j1 rule="hyper" parents="7709 9784"/>
    </justification>
  </clause>

  <clause id="9786">
    <literal><![CDATA[
      K(x,L(T(y,y \ z),u,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(25(a,2),9785(a,1,2))].">
      <j1 rule="para" parents="25 9785"/>
    </justification>
  </clause>

  <clause id="9787">
    <literal><![CDATA[
      K(x,L(T(y,y * z),u,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(9(a,1),9786(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9 9786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9788">
    <literal><![CDATA[
      K(x,L(L(y,z,y * K(z,y)),u,w)) = K(x,L(T(y * K(z,y),z),u,w))
    ]]></literal>
    <justification jstring="[para(5133(a,1),9787(a,1,2,1))].">
      <j1 rule="para" parents="5133 9787"/>
    </justification>
  </clause>

  <clause id="9789">
    <literal><![CDATA[
      L(x \ 1,x,K(x,y) * z) = L(x \ 1,x,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,7395,a(flip),b,7750,a),flip(a)].">
      <j1 rule="hyper" parents="65 7395 7750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9791">
    <literal><![CDATA[
      L(x \ 1,x,y * K(x,z)) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[para(8101(a,1),9789(a,1,3))].">
      <j1 rule="para" parents="8101 9789"/>
    </justification>
  </clause>

  <clause id="9792">
    <literal><![CDATA[
      L(x \ 1,T(x,y),z) = L(x \ 1,x,z)
    ]]></literal>
    <justification jstring="[hyper(9347,a,9791,a)].">
      <j1 rule="hyper" parents="9347 9791"/>
    </justification>
  </clause>

  <clause id="9794">
    <literal><![CDATA[
      T(x * L(x \ 1,x,y),z) = T(x,z) * ((y * T(x,z)) \ y)
    ]]></literal>
    <justification jstring="[para(9792(a,1),2195(a,1,1,2))].">
      <j1 rule="para" parents="9792 2195"/>
    </justification>
  </clause>

  <clause id="9795">
    <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(9792(a,1),4125(a,1,1))].">
      <j1 rule="para" parents="9792 4125"/>
    </justification>
  </clause>

  <clause id="9798">
    <literal><![CDATA[
      (x * y) \ ((T(x,z) * y) * x) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,6931,a(flip),b,7771,a),flip(a)].">
      <j1 rule="hyper" parents="65 6931 7771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9800">
    <literal><![CDATA[
      (x * y) \ ((T(x,z \ (u * x)) * y) * x) = T(x,T((u \ z) \ x,y))
    ]]></literal>
    <justification jstring="[para(8415(a,1),9798(a,1,2,1,1))].">
      <j1 rule="para" parents="8415 9798"/>
    </justification>
  </clause>

  <clause id="9801">
    <literal><![CDATA[
      K(x,K(y,(z * u) \ ((z * x) * u))) = 1
    ]]></literal>
    <justification jstring="[para(8130(a,1),8338(a,1,2))].">
      <j1 rule="para" parents="8130 8338"/>
    </justification>
  </clause>

  <clause id="9802">
    <literal><![CDATA[
      R(K(x,T(T(y,z),z * u)),z,u) = (z * u) \ ((z * K(x,y)) * u)
    ]]></literal>
    <justification jstring="[para(7489(a,2),8154(a,1,1))].">
      <j1 rule="para" parents="7489 8154"/>
    </justification>
  </clause>

  <clause id="9803">
    <literal><![CDATA[
      L(K(x \ y,z),y,x \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K((x \ 1) * y,z) = u
    ]]></literal>
    <justification jstring="[para(8436(a,1),5155(a,1))].">
      <j1 rule="para" parents="8436 5155"/>
    </justification>
  </clause>

  <clause id="9804">
    <literal><![CDATA[
      K((1 / x) * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K((x \ 1) * y,z) = u
    ]]></literal>
    <justification jstring="[para(7428(a,1),9803(a,1))].">
      <j1 rule="para" parents="7428 9803"/>
    </justification>
  </clause>

  <clause id="9806">
    <literal><![CDATA[
      T(K(x,y),z) * K(x * y,x) = T(x,K(y,z)) \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(8033,a,8484,a),flip(a)].">
      <j1 rule="hyper" parents="8033 8484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9807">
    <literal><![CDATA[
      K(x \ y,T(z,y)) = K((K(z,u) * y) / x,z)
    ]]></literal>
    <justification jstring="[hyper(8563,a,8756,a),flip(a)].">
      <j1 rule="hyper" parents="8563 8756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9808">
    <literal><![CDATA[
      K((K(x,y) * z) / u,x) = K(z / u,x)
    ]]></literal>
    <justification jstring="[hyper(8219,a,9807,a),flip(a)].">
      <j1 rule="hyper" parents="8219 9807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9809">
    <literal><![CDATA[
      K(x,(K(x,y) * z) / u) = (w * K(z / u,x)) \ w
    ]]></literal>
    <justification jstring="[para(9808(a,1),7200(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9808 7200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9810">
    <literal><![CDATA[
      K(x,(K(x,y) * z) / u) = K(x,z / u)
    ]]></literal>
    <justification jstring="[hyper(299,a,7200,a(flip),b,9809,a),flip(a)].">
      <j1 rule="hyper" parents="299 7200 9809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9811">
    <literal><![CDATA[
      K(x,(y * K(z,x)) / u) = K(x,y / u)
    ]]></literal>
    <justification jstring="[para(8140(a,1),9810(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8140 9810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9812">
    <literal><![CDATA[
      K(x,K(y,(z * K(u,y)) / w)) = K(x,K(y,1 / (z / w)))
    ]]></literal>
    <justification jstring="[para(9811(a,2),8789(a,2,2)),flip(a)].">
      <j1 rule="para" parents="9811 8789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9813">
    <literal><![CDATA[
      K(x,K(y,(z * K(u,y)) / w)) = K(x,K(y,z / w))
    ]]></literal>
    <justification jstring="[hyper(299,a,8789,a(flip),b,9812,a),flip(a)].">
      <j1 rule="hyper" parents="299 8789 9812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9814">
    <literal><![CDATA[
      K(x,K(y,K(z,y) / u)) = K(x,K(y,1 / u))
    ]]></literal>
    <justification jstring="[para(7(a,1),9813(a,1,2,2,1))].">
      <j1 rule="para" parents="7 9813"/>
    </justification>
  </clause>

  <clause id="9815">
    <literal><![CDATA[
      (K(x,y) / z) * K(u,K(y,1 / z)) = T(K(x,y) / z,K(u,y))
    ]]></literal>
    <justification jstring="[para(9814(a,1),7999(a,1,2))].">
      <j1 rule="para" parents="9814 7999"/>
    </justification>
  </clause>

  <clause id="9816">
    <literal><![CDATA[
      T(K(x,y) / z,K(x,y)) = T(K(x,y),1 / z) / z
    ]]></literal>
    <justification jstring="[hyper(65,a,9037,a(flip),b,9815,a),flip(a)].">
      <j1 rule="hyper" parents="65 9037 9815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9817">
    <literal><![CDATA[
      T(K(x,y) / z,K(x,y)) = K(x,T(y,1 / z)) / z
    ]]></literal>
    <justification jstring="[para(7489(a,2),9816(a,2,1))].">
      <j1 rule="para" parents="7489 9816"/>
    </justification>
  </clause>

  <clause id="9818">
    <literal><![CDATA[
      T(K(x,y) / z,K(x,y)) = K(x,T(y,z)) / z
    ]]></literal>
    <justification jstring="[para(8836(a,1),9817(a,2,1))].">
      <j1 rule="para" parents="8836 9817"/>
    </justification>
  </clause>

  <clause id="9819">
    <literal><![CDATA[
      T(K(x,y) / z,K(x,y)) != u / z
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(9818(a,2),48(a,1))].">
      <j1 rule="para" parents="9818 48"/>
    </justification>
  </clause>

  <clause id="9820">
    <literal><![CDATA[
      T(K(x,y) / z,K(x,y)) * K(u,z) = K(x,T(y,z)) / T(z,u)
    ]]></literal>
    <justification jstring="[para(9818(a,2),7189(a,1,1))].">
      <j1 rule="para" parents="9818 7189"/>
    </justification>
  </clause>

  <clause id="9821">
    <literal><![CDATA[
      K(R(x,y,z),u * K(x,w)) = K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,5833,a(flip),b,8592,a),flip(a)].">
      <j1 rule="hyper" parents="299 5833 8592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9822">
    <literal><![CDATA[
      K(R(x,y,z),u * K(w,x)) = K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(7184(a,1),9821(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7184 9821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9823">
    <literal><![CDATA[
      K((x * (y / z)) \ u,y) = K((x * (z \ y)) \ u,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,7422,a(flip),b,8956,a),flip(a)].">
      <j1 rule="hyper" parents="65 7422 8956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9824">
    <literal><![CDATA[
      K((x * (y / x)) \ z,y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),9823(a,2,1,1))].">
      <j1 rule="para" parents="10 9823"/>
    </justification>
  </clause>

  <clause id="9825">
    <literal><![CDATA[
      K(x \ (x * y),x) = K(K(z \ x,z) * y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,7833,a(flip),b,9824,a),flip(a)].">
      <j1 rule="hyper" parents="65 7833 9824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9826">
    <literal><![CDATA[
      K(K(x \ y,x) * z,y) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(7476,a,9825,a),flip(a)].">
      <j1 rule="hyper" parents="7476 9825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9829">
    <literal><![CDATA[
      (K(x \ y,x) * z) * K(z,y) = T(K(x \ y,x) * z,y)
    ]]></literal>
    <justification jstring="[para(9826(a,1),5083(a,2,2)),flip(a)].">
      <j1 rule="para" parents="9826 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9830">
    <literal><![CDATA[
      T(K(x \ y,x) * z,y) = K(x \ y,x) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(6862,a,9829,a),flip(a)].">
      <j1 rule="hyper" parents="6862 9829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9831">
    <literal><![CDATA[
      T(K(x \ (y * x),x) * z,y * x) = K(y,x) * T(z,y * x)
    ]]></literal>
    <justification jstring="[para(5191(a,1),9830(a,2,1))].">
      <j1 rule="para" parents="5191 9830"/>
    </justification>
  </clause>

  <clause id="9832">
    <literal><![CDATA[
      T(K(x,y) * z,x * y) = K(x,y) * T(z,x * y)
    ]]></literal>
    <justification jstring="[para(5191(a,1),9831(a,1,1,1))].">
      <j1 rule="para" parents="5191 9831"/>
    </justification>
  </clause>

  <clause id="9833">
    <literal><![CDATA[
      T(x * K(y,z),z * y) = T(x,z * y) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(6535,a,9832,a),flip(a)].">
      <j1 rule="hyper" parents="6535 9832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9834">
    <literal><![CDATA[
      (x * (y * z)) * L(K(z,y),T(x,y * z),y * z) = (y * z) * T(x * K(z,y),y * z)
    ]]></literal>
    <justification jstring="[para(9833(a,2),491(a,2,2))].">
      <j1 rule="para" parents="9833 491"/>
    </justification>
  </clause>

  <clause id="9835">
    <literal><![CDATA[
      T(x * K(y,x),x * y) != z
    ]]></literal>
    <literal><![CDATA[
      L(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(9833(a,2),5585(a,1))].">
      <j1 rule="para" parents="9833 5585"/>
    </justification>
  </clause>

  <clause id="9837">
    <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(6315(a,2),8981(a,2,2,1))].">
      <j1 rule="para" parents="6315 8981"/>
    </justification>
  </clause>

  <clause id="9838">
    <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(9093(a,2),8981(a,2,2,1))].">
      <j1 rule="para" parents="9093 8981"/>
    </justification>
  </clause>

  <clause id="9839">
    <literal><![CDATA[
      K(x,(y * T(z,x \ 1)) \ u) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,7943,a(flip),b,8982,a),flip(a)].">
      <j1 rule="hyper" parents="65 7943 8982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9840">
    <literal><![CDATA[
      K(x,((x \ 1) * y) \ z) = K(x,(y * (x \ 1)) \ z)
    ]]></literal>
    <justification jstring="[para(107(a,1),9839(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="107 9839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9841">
    <literal><![CDATA[
      L(K(x,y \ ((z \ u) * x)),z \ u,z) = K((x \ 1) \ 1,(z * (y / x)) \ u)
    ]]></literal>
    <justification jstring="[hyper(299,a,3567,a,b,8985,a),flip(a)].">
      <j1 rule="hyper" parents="299 3567 8985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9842">
    <literal><![CDATA[
      L(K(x,(y \ x) \ ((z \ u) * x)),z \ u,z) = K(x,(z * ((((y \ x) / x) * y) * (1 / y))) \ u)
    ]]></literal>
    <justification jstring="[para(2230(a,2),8985(a,2,2,1,2))].">
      <j1 rule="para" parents="2230 8985"/>
    </justification>
  </clause>

  <clause id="9843">
    <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(299,a,7486,a(flip),b,9010,a),flip(a)].">
      <j1 rule="hyper" parents="299 7486 9010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9844">
    <literal><![CDATA[
      L(K(x,y),z,L(y,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(9086,a,9102,a),flip(a)].">
      <j1 rule="hyper" parents="9086 9102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9845">
    <literal><![CDATA[
      K(L(x,y,L(z,u,w)),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(9328,a,9844,a)].">
      <j1 rule="hyper" parents="9328 9844"/>
    </justification>
  </clause>

  <clause id="9846">
    <literal><![CDATA[
      K(x,L(y,z,L(y,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,9334,a(flip),b,9844,a)].">
      <j1 rule="hyper" parents="65 9334 9844"/>
    </justification>
  </clause>

  <clause id="9847">
    <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(4460(a,1),9845(a,1,1))].">
      <j1 rule="para" parents="4460 9845"/>
    </justification>
  </clause>

  <clause id="9848">
    <literal><![CDATA[
      K(x,((y \ z) * u) \ (z * u)) = R(K(x,T(y,z * u)),z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,8763,a(flip),b,9365,a),flip(a)].">
      <j1 rule="hyper" parents="65 8763 9365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9849">
    <literal><![CDATA[
      K(x,y) * K(L(x,z,u) * y,x) = L(x,y,L(x,z,u)) \ x
    ]]></literal>
    <justification jstring="[para(8927(a,1),9383(a,1,2))].">
      <j1 rule="para" parents="8927 9383"/>
    </justification>
  </clause>

  <clause id="9850">
    <literal><![CDATA[
      K(L(x,y,z) * u,x) * K(x,u) = L(x,u,L(x,y,z)) \ x
    ]]></literal>
    <justification jstring="[hyper(2279,a,9849,a)].">
      <j1 rule="hyper" parents="2279 9849"/>
    </justification>
  </clause>

  <clause id="9851">
    <literal><![CDATA[
      L(T(K(x,T(y,z * u)),u),u,z) = (z * (K(x,y) * u)) / (z * u)
    ]]></literal>
    <justification jstring="[para(7504(a,1),9385(a,1,1))].">
      <j1 rule="para" parents="7504 9385"/>
    </justification>
  </clause>

  <clause id="9852">
    <literal><![CDATA[
      T(x * R(x \ (x * y),z,u),x) = R(y * a(x,y,x),z,u) * x
    ]]></literal>
    <justification jstring="[hyper(299,a,1932,a,b,9695,a)].">
      <j1 rule="hyper" parents="299 1932 9695"/>
    </justification>
  </clause>

  <clause id="9853">
    <literal><![CDATA[
      K(R(T(x,y / (((x \ y) \ 1) \ 1)),x \ y,y \ (y / (((x \ y) \ 1) \ 1))),z) = K(((y \ (y / (x \ y))) * (x \ y)) \ (y / (((x \ y) \ 1) \ 1)),z)
    ]]></literal>
    <justification jstring="[para(2711(a,1),9778(a,2,1,1))].">
      <j1 rule="para" parents="2711 9778"/>
    </justification>
  </clause>

  <clause id="9854">
    <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(9802(a,1),6295(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9802 6295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9855">
    <literal><![CDATA[
      R(x * a(y,x,y),z,u) * y = T(y * R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(9(a,1),9852(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 9852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9856">
    <literal><![CDATA[
      ((1 / (x \ y)) \ z) * (1 / (x \ y)) = z * K(z * (y / x),y \ x)
    ]]></literal>
    <justification jstring="[para(7933(a,2),6887(a,2,2))].">
      <j1 rule="para" parents="7933 6887"/>
    </justification>
  </clause>

  <clause id="9857">
    <literal><![CDATA[
      (1 / (x \ y)) * (z / (1 / (x \ y))) = z * K(y \ x,z * (y / x))
    ]]></literal>
    <justification jstring="[para(7392(a,2),7017(a,2,2))].">
      <j1 rule="para" parents="7392 7017"/>
    </justification>
  </clause>

  <clause id="9858">
    <literal><![CDATA[
      ((K(x,y) / z) * (z * K(y,x))) \ (K(x,y) / z) = 1 / (z * K(y,x))
    ]]></literal>
    <justification jstring="[para(7196(a,1),7220(a,2,2))].">
      <j1 rule="para" parents="7196 7220"/>
    </justification>
  </clause>

  <clause id="9859">
    <literal><![CDATA[
      T((x \ y) * (y \ x),z) = (x \ y) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,5536,a(flip),b,7366,a),flip(a)].">
      <j1 rule="hyper" parents="65 5536 7366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9861">
    <literal><![CDATA[
      T(x,(y \ z) * (z \ y)) = x
    ]]></literal>
    <justification jstring="[hyper(56,a,9859,a)].">
      <j1 rule="hyper" parents="56 9859"/>
    </justification>
  </clause>

  <clause id="9864">
    <literal><![CDATA[
      T(x,y * ((z * y) \ z)) = x
    ]]></literal>
    <justification jstring="[para(9(a,1),9861(a,1,2,1))].">
      <j1 rule="para" parents="9 9861"/>
    </justification>
  </clause>

  <clause id="9866">
    <literal><![CDATA[
      x / (y * ((z * y) \ z)) = (y * ((z * y) \ z)) \ x
    ]]></literal>
    <justification jstring="[hyper(3696,a,9864,a),flip(a)].">
      <j1 rule="hyper" parents="3696 9864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9867">
    <literal><![CDATA[
      K(x,y * ((z * y) \ z)) = 1
    ]]></literal>
    <justification jstring="[hyper(57,a,9864,a)].">
      <j1 rule="hyper" parents="57 9864"/>
    </justification>
  </clause>

  <clause id="9868">
    <literal><![CDATA[
      T(x * ((y * x) \ y),z) = x * ((y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(56,a,9864,a)].">
      <j1 rule="hyper" parents="56 9864"/>
    </justification>
  </clause>

  <clause id="9871">
    <literal><![CDATA[
      T(x * L(x \ 1,x,y),z) = x * ((y * x) \ y)
    ]]></literal>
    <justification jstring="[para(214(a,2),9868(a,1,1,2))].">
      <j1 rule="para" parents="214 9868"/>
    </justification>
  </clause>

  <clause id="9872">
    <literal><![CDATA[
      T(x,y) * ((z * T(x,y)) \ z) = x * ((z * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,9794,a(flip),b,9871,a)].">
      <j1 rule="hyper" parents="65 9794 9871"/>
    </justification>
  </clause>

  <clause id="9873">
    <literal><![CDATA[
      T(x,y) * ((x * y) \ y) = x * ((y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,5766,a(flip),b,9871,a)].">
      <j1 rule="hyper" parents="65 5766 9871"/>
    </justification>
  </clause>

  <clause id="9876">
    <literal><![CDATA[
      (x * ((y * x) \ y)) \ T(x,z) = 1 / ((y * T(x,z)) \ y)
    ]]></literal>
    <justification jstring="[para(9872(a,1),2965(a,1,1))].">
      <j1 rule="para" parents="9872 2965"/>
    </justification>
  </clause>

  <clause id="9877">
    <literal><![CDATA[
      (x \ R(x,y \ 1,x)) / (T(x * (y \ 1),x) / x) = y
    ]]></literal>
    <justification jstring="[hyper(120,a,8973,a(flip),b,7370,a(flip))].">
      <j1 rule="hyper" parents="120 8973 7370"/>
    </justification>
  </clause>

  <clause id="9878">
    <literal><![CDATA[
      T(x * K(y,z),z / (z / y)) = ((z * y) / z) \ (x * y)
    ]]></literal>
    <justification jstring="[para(9055(a,1),7671(a,1,1))].">
      <j1 rule="para" parents="9055 7671"/>
    </justification>
  </clause>

  <clause id="9879">
    <literal><![CDATA[
      L(K(x,T(y,z)),u,L(y,w,v5)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(2841,a,7875,a)].">
      <j1 rule="hyper" parents="2841 7875"/>
    </justification>
  </clause>

  <clause id="9880">
    <literal><![CDATA[
      K(x,T(y,L(y,z,u) * w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,9843,a(flip),b,9879,a)].">
      <j1 rule="hyper" parents="65 9843 9879"/>
    </justification>
  </clause>

  <clause id="9882">
    <literal><![CDATA[
      K(x,T(y,L(y,z,u) \ w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(10(a,1),9880(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 9880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9883">
    <literal><![CDATA[
      K(x,T(y,z * (u * y))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(8637(a,1),9880(a,1,2))].">
      <j1 rule="para" parents="8637 9880"/>
    </justification>
  </clause>

  <clause id="9884">
    <literal><![CDATA[
      L(K(x,y),z,L(y,u,w)) * (L(y,u,w) * z) = L(y,u,w) * (z * K(x,T(y,z)))
    ]]></literal>
    <justification jstring="[para(9880(a,1),7512(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9880 7512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9885">
    <literal><![CDATA[
      K(x,T(y \ z,u * z)) = K(x,T(y \ z,u * y))
    ]]></literal>
    <justification jstring="[para(10(a,1),9883(a,1,2,2,2))].">
      <j1 rule="para" parents="10 9883"/>
    </justification>
  </clause>

  <clause id="9886">
    <literal><![CDATA[
      K(x,T(y,z * (y * u))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(8654(a,1),9883(a,1,2))].">
      <j1 rule="para" parents="8654 9883"/>
    </justification>
  </clause>

  <clause id="9887">
    <literal><![CDATA[
      K(x * y,T(x,z * y)) = K(x * y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(9452,a,9886,a),flip(a)].">
      <j1 rule="hyper" parents="9452 9886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9889">
    <literal><![CDATA[
      K(T(x,y) * z,T(x,u * z)) = K(x * z,T(x,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,8647,a,b,9887,a)].">
      <j1 rule="hyper" parents="65 8647 9887"/>
    </justification>
  </clause>

  <clause id="9890">
    <literal><![CDATA[
      K(x * (y \ z),T(x,z)) = K(x * (y \ z),T(x,y))
    ]]></literal>
    <justification jstring="[para(10(a,1),9887(a,1,2,2))].">
      <j1 rule="para" parents="10 9887"/>
    </justification>
  </clause>

  <clause id="9891">
    <literal><![CDATA[
      K(x,T(y \ x,z * y)) = K(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(9452,a,9885,a),flip(a)].">
      <j1 rule="hyper" parents="9452 9885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9892">
    <literal><![CDATA[
      K(x,T(y \ x,z / y)) = K(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[para(12(a,1),9891(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 9891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9893">
    <literal><![CDATA[
      K(x,T(y \ x,y \ z)) = K(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,8377,a(flip),b,9892,a)].">
      <j1 rule="hyper" parents="65 8377 9892"/>
    </justification>
  </clause>

  <clause id="9894">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ x) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,9494,a(flip),b,9893,a)].">
      <j1 rule="hyper" parents="65 9494 9893"/>
    </justification>
  </clause>

  <clause id="9895">
    <literal><![CDATA[
      K(x,T(y \ x,x * z)) = K(x,((x * z) / y) / z)
    ]]></literal>
    <justification jstring="[hyper(65,a,8466,a(flip),b,9894,a),flip(a)].">
      <j1 rule="hyper" parents="65 8466 9894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9896">
    <literal><![CDATA[
      K(x,((x * y) / z) / y) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,7645,a(flip),b,9895,a),flip(a)].">
      <j1 rule="hyper" parents="65 7645 9895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9897">
    <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(65,a,9133,a(flip),b,9896,a)].">
      <j1 rule="hyper" parents="65 9133 9896"/>
    </justification>
  </clause>

  <clause id="9898">
    <literal><![CDATA[
      K(x,(T(y,z) / u) / (y / u)) * (y / u) = T(y,K(x,z)) / u
    ]]></literal>
    <justification jstring="[para(8039(a,1),8016(a,1,1))].">
      <j1 rule="para" parents="8039 8016"/>
    </justification>
  </clause>

  <clause id="9899">
    <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(9898(a,1),105(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9898 105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9900">
    <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(9898(a,1),5436(a,1,2))].">
      <j1 rule="para" parents="9898 5436"/>
    </justification>
  </clause>

  <clause id="9901">
    <literal><![CDATA[
      T(x,T(y * z,y * y) / (1 / y)) = T(x,T(z * (y * y),y \ 1))
    ]]></literal>
    <justification jstring="[para(3733(a,1),8190(a,2,2))].">
      <j1 rule="para" parents="3733 8190"/>
    </justification>
  </clause>

  <clause id="9902">
    <literal><![CDATA[
      T(x,T((y \ z) / z,T(y,u))) = T(x,(((y \ 1) \ 1) \ z) / z)
    ]]></literal>
    <justification jstring="[hyper(8312,a,8193,a)].">
      <j1 rule="hyper" parents="8312 8193"/>
    </justification>
  </clause>

  <clause id="9903">
    <literal><![CDATA[
      T(x,T((y \ z) / z,T(y,u))) = T(x,((y \ 1) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,4637,a(flip),b,9902,a),flip(a)].">
      <j1 rule="hyper" parents="299 4637 9902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9905">
    <literal><![CDATA[
      T(x,T((y \ z) / z,T(y,u))) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,3870,a(flip),b,9903,a),flip(a)].">
      <j1 rule="hyper" parents="299 3870 9903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9906">
    <literal><![CDATA[
      T(T(x,1 / (y / z)),K(u,z / y)) = x * K(x,1 / T(y / z,u))
    ]]></literal>
    <justification jstring="[para(5804(a,2),8254(a,2,2))].">
      <j1 rule="para" parents="5804 8254"/>
    </justification>
  </clause>

  <clause id="9907">
    <literal><![CDATA[
      K(x,L(T(T(y,z),u * z),z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * (y * z)) / (u * z)) = w
    ]]></literal>
    <justification jstring="[para(22(a,2),8318(a,1,2,1,1))].">
      <j1 rule="para" parents="22 8318"/>
    </justification>
  </clause>

  <clause id="9908">
    <literal><![CDATA[
      K(x,T(((y \ z) \ 1) \ x,z)) = K(x,y \ ((((y \ z) \ 1) \ y) * x))
    ]]></literal>
    <justification jstring="[hyper(8963,a,8414,a)].">
      <j1 rule="hyper" parents="8963 8414"/>
    </justification>
  </clause>

  <clause id="9909">
    <literal><![CDATA[
      T(x * K(y,x),K(x,z) * u) = T(x,u) * K(y,T(x,u))
    ]]></literal>
    <justification jstring="[para(8550(a,1),8559(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8550 8559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9910">
    <literal><![CDATA[
      T(x * K(y,x),K(x,z) * u) = T(x * K(y,x),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,5468,a(flip),b,9909,a),flip(a)].">
      <j1 rule="hyper" parents="299 5468 9909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9912">
    <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(65,a,5673,a(flip),b,9910,a),flip(a)].">
      <j1 rule="hyper" parents="65 5673 9910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9913">
    <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(299,a,7707,a(flip),b,8719,a),flip(a)].">
      <j1 rule="hyper" parents="299 7707 8719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9914">
    <literal><![CDATA[
      K(x * y,y) * K(x,K(y,z)) = T(y,T(x,z)) \ R(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,8724,a(flip),b,9913,a)].">
      <j1 rule="hyper" parents="65 8724 9913"/>
    </justification>
  </clause>

  <clause id="9915">
    <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(9914(a,1),8432(a,1))].">
      <j1 rule="para" parents="9914 8432"/>
    </justification>
  </clause>

  <clause id="9916">
    <literal><![CDATA[
      K(x,T(y,z)) * a(y,x,y) = K(x * y,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(9915,a,9682,a),flip(a)].">
      <j1 rule="hyper" parents="9915 9682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9917">
    <literal><![CDATA[
      K(x / y,z) * a(z,y \ x,z) = K((y \ x) * z,T(z,y))
    ]]></literal>
    <justification jstring="[para(8116(a,1),9916(a,1,1))].">
      <j1 rule="para" parents="8116 9916"/>
    </justification>
  </clause>

  <clause id="9918">
    <literal><![CDATA[
      K(x * y,T(y,z)) \ (K(x,T(y,z)) * y) = L(y,x,y)
    ]]></literal>
    <justification jstring="[para(9916(a,1),9712(a,1,1))].">
      <j1 rule="para" parents="9916 9712"/>
    </justification>
  </clause>

  <clause id="9919">
    <literal><![CDATA[
      K(x * y,T(y,z)) \ (y * K(x,T(y,z))) = L(y,x,y)
    ]]></literal>
    <justification jstring="[para(3632(a,1),9918(a,1,2))].">
      <j1 rule="para" parents="3632 9918"/>
    </justification>
  </clause>

  <clause id="9920">
    <literal><![CDATA[
      T(x,T(y * x,z)) * K(y,T(x,z)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(7580,a,9919,a)].">
      <j1 rule="hyper" parents="7580 9919"/>
    </justification>
  </clause>

  <clause id="9921">
    <literal><![CDATA[
      T(T(x,y) * L(x \ y,z,u),x) = T(x * L(x \ y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(299,a,4438,a(flip),b,8722,a),flip(a)].">
      <j1 rule="hyper" parents="299 4438 8722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9922">
    <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),9921(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 9921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9923">
    <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(299,a,4439,a(flip),b,8723,a),flip(a)].">
      <j1 rule="hyper" parents="299 4439 8723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9924">
    <literal><![CDATA[
      R(K(x,y),y * (K(z,y) * u),w) = K(x,R(T(y * K(z,y),z),u,w))
    ]]></literal>
    <justification jstring="[para(5488(a,1),8764(a,1,2))].">
      <j1 rule="para" parents="5488 8764"/>
    </justification>
  </clause>

  <clause id="9925">
    <literal><![CDATA[
      K((x * (y / z)) \ u,z) != w
    ]]></literal>
    <literal><![CDATA[
      K((x * (z \ y)) \ u,z) = w
    ]]></literal>
    <justification jstring="[para(8928(a,1),5547(a,1))].">
      <j1 rule="para" parents="8928 5547"/>
    </justification>
  </clause>

  <clause id="9926">
    <literal><![CDATA[
      K(x \ ((y * z) * K(y,u)),T(y,w)) = K(x \ (z * T(y,u)),T(y,w))
    ]]></literal>
    <justification jstring="[para(7074(a,2),8934(a,1,1,2))].">
      <j1 rule="para" parents="7074 8934"/>
    </justification>
  </clause>

  <clause id="9927">
    <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(8987(a,1),7629(a,1))].">
      <j1 rule="para" parents="8987 7629"/>
    </justification>
  </clause>

  <clause id="9928">
    <literal><![CDATA[
      (x * (y \ ((z \ (y * (x \ u))) * z))) \ u = K(z,(x * (z / y)) \ u)
    ]]></literal>
    <justification jstring="[para(3939(a,1),9125(a,1,1,2))].">
      <j1 rule="para" parents="3939 9125"/>
    </justification>
  </clause>

  <clause id="9929">
    <literal><![CDATA[
      (x * K(y,z)) * (K(z,y) * L(K(u,z),w,v5)) = x * L(K(u,z),w,v5)
    ]]></literal>
    <justification jstring="[para(7184(a,1),9204(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7184 9204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9930">
    <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(2286(a,2),9230(a,2,2))].">
      <j1 rule="para" parents="2286 9230"/>
    </justification>
  </clause>

  <clause id="9931">
    <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(7184(a,1),9230(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7184 9230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9932">
    <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(2280(a,1),9233(a,2,2))].">
      <j1 rule="para" parents="2280 9233"/>
    </justification>
  </clause>

  <clause id="9933">
    <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(7989(a,1),9261(a,1,1,1))].">
      <j1 rule="para" parents="7989 9261"/>
    </justification>
  </clause>

  <clause id="9934">
    <literal><![CDATA[
      x \ R(x * K(y,x),y,y \ 1) = K(y,x) * a(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(865(a,1),9315(a,2,2))].">
      <j1 rule="para" parents="865 9315"/>
    </justification>
  </clause>

  <clause id="9935">
    <literal><![CDATA[
      K(x,y) * a(y,x,x \ 1) = y \ ((x * y) * (x \ 1))
    ]]></literal>
    <justification jstring="[para(5244(a,1),9934(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5244 9934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9936">
    <literal><![CDATA[
      K(x,(x \ ((y * x) * (y \ 1))) \ z) = K(x,a(x,y,y \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(9935(a,1),8860(a,1,2,1))].">
      <j1 rule="para" parents="9935 8860"/>
    </justification>
  </clause>

  <clause id="9937">
    <literal><![CDATA[
      K(x,((y * x) * (y \ 1)) \ (x * z)) = K(x,a(x,y,y \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,7846,a(flip),b,9936,a)].">
      <j1 rule="hyper" parents="65 7846 9936"/>
    </justification>
  </clause>

  <clause id="9938">
    <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(5320(a,1),9448(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5320 9448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9939">
    <literal><![CDATA[
      K(x,((y / z) * u) \ (y * u)) = ((y * K(z,x)) * u) \ (y * u)
    ]]></literal>
    <justification jstring="[para(6869(a,1),9511(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6869 9511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9940">
    <literal><![CDATA[
      ((x * K(y,z)) * u) * K(z,((x / y) * u) \ (x * u)) = x * u
    ]]></literal>
    <justification jstring="[hyper(144,a,9939,a(flip))].">
      <j1 rule="hyper" parents="144 9939"/>
    </justification>
  </clause>

  <clause id="9941">
    <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(6932(a,1),9939(a,2,1))].">
      <j1 rule="para" parents="6932 9939"/>
    </justification>
  </clause>

  <clause id="9942">
    <literal><![CDATA[
      K(((x / y) * z) \ (x * z),u) = (x * z) \ ((x * K(y,u)) * z)
    ]]></literal>
    <justification jstring="[para(9940(a,1),7200(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9940 7200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9943">
    <literal><![CDATA[
      K(x,T(y,(z * K(u,x)) * w)) = K(x,T(y,z * w))
    ]]></literal>
    <justification jstring="[para(9940(a,1),8661(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9940 8661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9944">
    <literal><![CDATA[
      K(x,((y * K(z,x)) * u) \ w) = K(x,(y * u) \ w)
    ]]></literal>
    <justification jstring="[para(9940(a,1),8858(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9940 8858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9945">
    <literal><![CDATA[
      K(x,y \ ((z * K(u,x)) * w)) = K(x,y \ (z * w))
    ]]></literal>
    <justification jstring="[para(9940(a,1),8872(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9940 8872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9946">
    <literal><![CDATA[
      K(x,y / ((z * K(u,x)) * w)) = K(x,y / (z * w))
    ]]></literal>
    <justification jstring="[para(9940(a,1),9269(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9940 9269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9947">
    <literal><![CDATA[
      K(x / ((y * K(z,u)) * w),u) = K(x / (y * w),u)
    ]]></literal>
    <justification jstring="[para(9940(a,1),9274(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9940 9274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9948">
    <literal><![CDATA[
      K(x,T(y,(z * x) * u)) = K(x,T(y,(x * z) * u))
    ]]></literal>
    <justification jstring="[para(88(a,1),9943(a,1,2,2,1))].">
      <j1 rule="para" parents="88 9943"/>
    </justification>
  </clause>

  <clause id="9949">
    <literal><![CDATA[
      K(x,(((x \ y) * x) * z) \ u) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[para(287(a,1),9944(a,1,2,1,1))].">
      <j1 rule="para" parents="287 9944"/>
    </justification>
  </clause>

  <clause id="9950">
    <literal><![CDATA[
      K(x,y \ ((z * K(x,u)) * w)) = K(x,y \ (z * w))
    ]]></literal>
    <justification jstring="[para(7184(a,1),9945(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7184 9945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9951">
    <literal><![CDATA[
      K(x,y / ((z * x) * u)) = K(x,y / ((x * z) * u))
    ]]></literal>
    <justification jstring="[para(88(a,1),9946(a,1,2,2,1))].">
      <j1 rule="para" parents="88 9946"/>
    </justification>
  </clause>

  <clause id="9952">
    <literal><![CDATA[
      K(x,y / (((x \ z) * x) * u)) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[para(287(a,1),9946(a,1,2,2,1))].">
      <j1 rule="para" parents="287 9946"/>
    </justification>
  </clause>

  <clause id="9953">
    <literal><![CDATA[
      K(x,y / ((K(z,x) * u) * w)) = K(x,y / (u * w))
    ]]></literal>
    <justification jstring="[para(7541(a,1),9946(a,1,2,2,1))].">
      <j1 rule="para" parents="7541 9946"/>
    </justification>
  </clause>

  <clause id="9954">
    <literal><![CDATA[
      K(x,y / ((K(x,z) * u) * w)) = K(x,y / (u * w))
    ]]></literal>
    <justification jstring="[para(7543(a,1),9946(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7543 9946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9955">
    <literal><![CDATA[
      K(x / ((T(y,z) \ 1) * u),y) = K(x / ((y \ 1) * u),y)
    ]]></literal>
    <justification jstring="[para(5052(a,1),9947(a,1,1,2,1))].">
      <j1 rule="para" parents="5052 9947"/>
    </justification>
  </clause>

  <clause id="9956">
    <literal><![CDATA[
      K(x / ((K(y,z) * u) * w),z) = K(x / (u * w),z)
    ]]></literal>
    <justification jstring="[para(7541(a,1),9947(a,1,1,2,1))].">
      <j1 rule="para" parents="7541 9947"/>
    </justification>
  </clause>

  <clause id="9957">
    <literal><![CDATA[
      K(x / ((K(y,z) * u) * w),y) = K(x / (u * w),y)
    ]]></literal>
    <justification jstring="[para(7543(a,1),9947(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7543 9947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9958">
    <literal><![CDATA[
      K(x,y \ (((z / x) * u) * w)) = K(x,y \ (((x \ z) * u) * w))
    ]]></literal>
    <justification jstring="[para(7123(a,1),9950(a,1,2,2,1))].">
      <j1 rule="para" parents="7123 9950"/>
    </justification>
  </clause>

  <clause id="9959">
    <literal><![CDATA[
      K(x,y / ((x * z) * u)) = K(x,y / (x * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,9270,a(flip),b,9951,a),flip(a)].">
      <j1 rule="hyper" parents="65 9270 9951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9960">
    <literal><![CDATA[
      K(x,R(R(y,K(z,x),u),K(z,x) * u,w)) = K(x,(((y * K(z,x)) * u) * w) / (u * w))
    ]]></literal>
    <justification jstring="[para(539(a,1),9953(a,1,2))].">
      <j1 rule="para" parents="539 9953"/>
    </justification>
  </clause>

  <clause id="9961">
    <literal><![CDATA[
      K(R(R(x,K(y,z),u),K(y,z) * u,w),z) = K((((x * K(y,z)) * u) * w) / (u * w),z)
    ]]></literal>
    <justification jstring="[para(539(a,1),9956(a,1,1))].">
      <j1 rule="para" parents="539 9956"/>
    </justification>
  </clause>

  <clause id="9963">
    <literal><![CDATA[
      K(x,T(y / ((K(x,z) * u) * w),v5)) = ((v5 * x) / v5) / ((v5 * (x * K(y / (u * w),x))) / v5)
    ]]></literal>
    <justification jstring="[para(9957(a,1),9341(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9957 9341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9964">
    <literal><![CDATA[
      x * K(x,y / (x * (z * u))) = T(x,y / ((x * z) * u))
    ]]></literal>
    <justification jstring="[para(9959(a,1),5083(a,2,2)),flip(a)].">
      <j1 rule="para" parents="9959 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9965">
    <literal><![CDATA[
      (x * y) \ ((x * K(z \ x,u)) * y) = K((z * y) \ (x * y),u)
    ]]></literal>
    <justification jstring="[para(76(a,1),9942(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="76 9942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9966">
    <literal><![CDATA[
      (x * y) * K((z * y) \ (x * y),u) = (x * K(z \ x,u)) * y
    ]]></literal>
    <justification jstring="[hyper(144,a,9965,a)].">
      <j1 rule="hyper" parents="144 9965"/>
    </justification>
  </clause>

  <clause id="9968">
    <literal><![CDATA[
      (x * K((y \ 1) \ (z \ x),z)) * y = (z \ (x * y)) * z
    ]]></literal>
    <justification jstring="[hyper(3941,a,9557,a),flip(a)].">
      <j1 rule="hyper" parents="3941 9557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9969">
    <literal><![CDATA[
      (x * K((y \ z) \ x,z)) * y = (z \ (x * y)) * z
    ]]></literal>
    <justification jstring="[para(8337(a,1),9968(a,1,1,2))].">
      <j1 rule="para" parents="8337 9968"/>
    </justification>
  </clause>

  <clause id="9970">
    <literal><![CDATA[
      (x \ y) / ((x \ 1) \ (y / x)) = ((y / x) / (x \ 1)) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(109(a,1),9625(a,1,2)),flip(a)].">
      <j1 rule="para" parents="109 9625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9971">
    <literal><![CDATA[
      ((x \ y) / (x \ 1)) \ T(x \ y,x) = ((y / x) / (x \ 1)) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,9624,a,b,9970,a)].">
      <j1 rule="hyper" parents="65 9624 9970"/>
    </justification>
  </clause>

  <clause id="9972">
    <literal><![CDATA[
      (x / y) * (((y \ x) \ 1) \ z) = (y \ x) * (((x / y) \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(109(a,1),9635(a,1,2,1,1))].">
      <j1 rule="para" parents="109 9635"/>
    </justification>
  </clause>

  <clause id="9973">
    <literal><![CDATA[
      (x \ y) * (((y / x) \ 1) \ 1) = (1 / (y / x)) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,3259,a(flip),b,9972,a),flip(a)].">
      <j1 rule="hyper" parents="65 3259 9972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9974">
    <literal><![CDATA[
      K(x,(y * (z / y)) / ((z / y) * x)) = K(x,z / ((y \ z) * x))
    ]]></literal>
    <justification jstring="[hyper(299,a,9642,a(flip),b,9643,a),flip(a)].">
      <j1 rule="hyper" parents="299 9642 9643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9975">
    <literal><![CDATA[
      K(x,R(x \ y,x,z / y)) = K(x,z / ((y \ z) * x))
    ]]></literal>
    <justification jstring="[hyper(65,a,9272,a,b,9974,a)].">
      <j1 rule="hyper" parents="65 9272 9974"/>
    </justification>
  </clause>

  <clause id="9976">
    <literal><![CDATA[
      K(x,R(x \ (y / z),x,y / (y / z))) = K(x,y / (z * x))
    ]]></literal>
    <justification jstring="[para(79(a,1),9975(a,2,2,2,1))].">
      <j1 rule="para" parents="79 9975"/>
    </justification>
  </clause>

  <clause id="9977">
    <literal><![CDATA[
      T(x,L((y \ z) \ z,u,w)) = T(x,T(L(y,u,w),z))
    ]]></literal>
    <justification jstring="[hyper(299,a,7584,a(flip),b,9782,a),flip(a)].">
      <j1 rule="hyper" parents="299 7584 9782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9978">
    <literal><![CDATA[
      T(x,L((y \ z) \ z,u,w)) = T(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(25(a,2),9977(a,2,2))].">
      <j1 rule="para" parents="25 9977"/>
    </justification>
  </clause>

  <clause id="9979">
    <literal><![CDATA[
      T(x,L(T(y,z * y),u,w)) = T(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(4452(a,2),9978(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4452 9978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9980">
    <literal><![CDATA[
      T(x,T((y \ z) \ x,u)) = T(x,T(z \ (y * x),u))
    ]]></literal>
    <justification jstring="[hyper(65,a,9798,a(flip),b,9800,a),flip(a)].">
      <j1 rule="hyper" parents="65 9798 9800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9981">
    <literal><![CDATA[
      ((K(x,y) / z) * (z * K(y,x))) * (1 / (z * K(y,x))) = K(x,y) / z
    ]]></literal>
    <justification jstring="[hyper(144,a,9858,a)].">
      <j1 rule="hyper" parents="144 9858"/>
    </justification>
  </clause>

  <clause id="9982">
    <literal><![CDATA[
      T(x,T(y * z,y * y) / (1 / y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(z * (y * y),y)) = u
    ]]></literal>
    <justification jstring="[para(9901(a,2),8840(a,1))].">
      <j1 rule="para" parents="9901 8840"/>
    </justification>
  </clause>

  <clause id="9983">
    <literal><![CDATA[
      T(T(x,1 / (y / z)),K(u,z / y)) = T(x,1 / T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,5083,a,b,9906,a),flip(a)].">
      <j1 rule="hyper" parents="299 5083 9906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9984">
    <literal><![CDATA[
      T(T(x,1 / (y / z)),K(y,z)) = T(x,1 / T(y / z,y))
    ]]></literal>
    <justification jstring="[hyper(8328,a,9983,a)].">
      <j1 rule="hyper" parents="8328 9983"/>
    </justification>
  </clause>

  <clause id="9985">
    <literal><![CDATA[
      T(T(x,1 / (y / z)),K(z,z / y)) = T(x,1 / (z \ y))
    ]]></literal>
    <justification jstring="[para(109(a,1),9983(a,2,2,2))].">
      <j1 rule="para" parents="109 9983"/>
    </justification>
  </clause>

  <clause id="9986">
    <literal><![CDATA[
      T(T(x,1 / (y / z)),K(y,z)) = T(x,1 / (z \ y))
    ]]></literal>
    <justification jstring="[hyper(65,a,8826,a(flip),b,9985,a)].">
      <j1 rule="hyper" parents="65 8826 9985"/>
    </justification>
  </clause>

  <clause id="9987">
    <literal><![CDATA[
      T(x,1 / T(y / z,y)) = T(x,1 / (z \ y))
    ]]></literal>
    <justification jstring="[hyper(65,a,9984,a(flip),b,9986,a)].">
      <j1 rule="hyper" parents="65 9984 9986"/>
    </justification>
  </clause>

  <clause id="9988">
    <literal><![CDATA[
      T(x,T(1 / (y / z),y)) = T(x,1 / (z \ y))
    ]]></literal>
    <justification jstring="[hyper(9141,a,9987,a)].">
      <j1 rule="hyper" parents="9141 9987"/>
    </justification>
  </clause>

  <clause id="9989">
    <literal><![CDATA[
      T(x,1 / ((y \ z) \ z)) = T(x,T(1 / y,z))
    ]]></literal>
    <justification jstring="[para(76(a,1),9988(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="76 9988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9990">
    <literal><![CDATA[
      T(x,T(1 / (y \ z),z)) = T(x,1 / (z / y))
    ]]></literal>
    <justification jstring="[hyper(65,a,8388,a(flip),b,9989,a),flip(a)].">
      <j1 rule="hyper" parents="65 8388 9989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9991">
    <literal><![CDATA[
      T(x,K(y,z / y) / (z \ y)) = T(x,1 / (y / z))
    ]]></literal>
    <justification jstring="[hyper(65,a,8367,a,b,9990,a)].">
      <j1 rule="hyper" parents="65 8367 9990"/>
    </justification>
  </clause>

  <clause id="9992">
    <literal><![CDATA[
      K(x,T(1 \ ((y \ z) * x),z)) = K(x,y \ ((((y \ z) \ 1) \ y) * x))
    ]]></literal>
    <justification jstring="[hyper(65,a,9490,a(flip),b,9908,a)].">
      <j1 rule="hyper" parents="65 9490 9908"/>
    </justification>
  </clause>

  <clause id="9993">
    <literal><![CDATA[
      K(x,R(T(y * K(z,y),z),u,w)) = K(x,R(y,K(z,y) * u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,6437,a(flip),b,9924,a),flip(a)].">
      <j1 rule="hyper" parents="65 6437 9924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9994">
    <literal><![CDATA[
      K(x,R(y,K(z,y) * u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(5053(a,1),9993(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5053 9993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9995">
    <literal><![CDATA[
      K(x,R(y,T(z,y),u)) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(1296(a,2),9994(a,1,2,2))].">
      <j1 rule="para" parents="1296 9994"/>
    </justification>
  </clause>

  <clause id="9996">
    <literal><![CDATA[
      K(x,R(y,K(y,z) * u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(5432(a,1),9994(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5432 9994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9997">
    <literal><![CDATA[
      R(K(x,y),z * y,u) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,6438,a,b,9995,a)].">
      <j1 rule="hyper" parents="65 6438 9995"/>
    </justification>
  </clause>

  <clause id="9998">
    <literal><![CDATA[
      R(K(x,y \ z),z,u) = K(x,R(y \ z,y,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),9997(a,1,2))].">
      <j1 rule="para" parents="10 9997"/>
    </justification>
  </clause>

  <clause id="9999">
    <literal><![CDATA[
      R(K(x,y),z * T(y,u),w) = K(x,R(y,z * K(y,u),w))
    ]]></literal>
    <justification jstring="[para(6912(a,1),9997(a,1,2))].">
      <j1 rule="para" parents="6912 9997"/>
    </justification>
  </clause>

  <clause id="10000">
    <literal><![CDATA[
      R(K(x,y),z * K(u,y),w) = K(x,R(y,z / T(y,u),w))
    ]]></literal>
    <justification jstring="[para(7185(a,1),9997(a,1,2))].">
      <j1 rule="para" parents="7185 9997"/>
    </justification>
  </clause>

  <clause id="10001">
    <literal><![CDATA[
      R(K(x,y),z * (y * K(u,x)),w) = K(x,R(y * K(u,x),z,w))
    ]]></literal>
    <justification jstring="[para(8528(a,1),9997(a,1,1))].">
      <j1 rule="para" parents="8528 9997"/>
    </justification>
  </clause>

  <clause id="10002">
    <literal><![CDATA[
      K(R(x,K(x,y) * z,u),w) = (v5 * K(w,R(x,z,u))) \ v5
    ]]></literal>
    <justification jstring="[para(9996(a,1),7200(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9996 7200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10003">
    <literal><![CDATA[
      K(x,R(y,z * K(y,u),w)) = K(x,R(y,z,w))
    ]]></literal>
    <justification jstring="[para(8101(a,1),9996(a,1,2,2))].">
      <j1 rule="para" parents="8101 9996"/>
    </justification>
  </clause>

  <clause id="10004">
    <literal><![CDATA[
      R(K(x,y),z * T(y,u),w) = K(x,R(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(299,a,10003,a(flip),b,9999,a),flip(a)].">
      <j1 rule="hyper" parents="299 10003 9999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10006">
    <literal><![CDATA[
      K(x,R(y,z / T(y,u),w)) = R(K(x,y),z,w)
    ]]></literal>
    <justification jstring="[para(12(a,1),10004(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 10004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10007">
    <literal><![CDATA[
      R(K(x,y),z * K(u,y),w) = R(K(x,y),z,w)
    ]]></literal>
    <justification jstring="[hyper(299,a,10006,a(flip),b,10000,a),flip(a)].">
      <j1 rule="hyper" parents="299 10006 10000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10008">
    <literal><![CDATA[
      R(K(x,y),K(z,y),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(559,a,10007,a),flip(a)].">
      <j1 rule="hyper" parents="559 10007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10012">
    <literal><![CDATA[
      R(K(x,y),K(y,z) * u,w) = R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(7543(a,1),10007(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7543 10007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10013">
    <literal><![CDATA[
      R(K(x,y),K(z,y),u) = w / (K(y,x) * w)
    ]]></literal>
    <justification jstring="[hyper(299,a,5430,a,b,10008,a),flip(a)].">
      <j1 rule="hyper" parents="299 5430 10008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10014">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) * u = K(x,y) * (K(z,x) * u)
    ]]></literal>
    <justification jstring="[hyper(6302,a,10013,a)].">
      <j1 rule="hyper" parents="6302 10013"/>
    </justification>
  </clause>

  <clause id="10015">
    <literal><![CDATA[
      R(K(x,y),K(y,z),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(559,a,10012,a),flip(a)].">
      <j1 rule="hyper" parents="559 10012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10016">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) * u = K(x,y) * (K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(10015(a,1),103(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10015 103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10017">
    <literal><![CDATA[
      (K(x,y) * (K(y,z) * u)) / u = K(x,y) * K(y,z)
    ]]></literal>
    <justification jstring="[para(10015(a,1),284(a,1,1,1))].">
      <j1 rule="para" parents="10015 284"/>
    </justification>
  </clause>

  <clause id="10018">
    <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(10015(a,1),4915(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10015 4915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10019">
    <literal><![CDATA[
      L(x,K(y,z),K(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(490,a,10014,a)].">
      <j1 rule="hyper" parents="490 10014"/>
    </justification>
  </clause>

  <clause id="10020">
    <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(10014(a,1),318(a,1,2))].">
      <j1 rule="para" parents="10014 318"/>
    </justification>
  </clause>

  <clause id="10021">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) * u = K(y,z) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(2278(a,1),10014(a,1,1))].">
      <j1 rule="para" parents="2278 10014"/>
    </justification>
  </clause>

  <clause id="10022">
    <literal><![CDATA[
      K(x,y) * (K(x * y,x) * z) = (x \ R(x,y,x)) * z
    ]]></literal>
    <justification jstring="[para(5587(a,1),10014(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5587 10014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10023">
    <literal><![CDATA[
      L(x,K(y,z),K(y,u)) = x
    ]]></literal>
    <justification jstring="[hyper(7213,a,10019,a)].">
      <j1 rule="hyper" parents="7213 10019"/>
    </justification>
  </clause>

  <clause id="10024">
    <literal><![CDATA[
      L(T(x / (x / y),y \ x),K(z,u),K(u,w)) = y
    ]]></literal>
    <justification jstring="[hyper(299,a,4502,a(flip),b,10019,a),flip(a)].">
      <j1 rule="hyper" parents="299 4502 10019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10025">
    <literal><![CDATA[
      L(x,L(K(y,z),u,w),K(z,v5)) = x
    ]]></literal>
    <justification jstring="[para(6341(a,1),10019(a,1,2))].">
      <j1 rule="para" parents="6341 10019"/>
    </justification>
  </clause>

  <clause id="10026">
    <literal><![CDATA[
      L(x,K(y,T(z,u)),K(z,w)) = x
    ]]></literal>
    <justification jstring="[para(7537(a,1),10019(a,1,2))].">
      <j1 rule="para" parents="7537 10019"/>
    </justification>
  </clause>

  <clause id="10027">
    <literal><![CDATA[
      L(x,K(y,z),K(u,K(z,w))) = x
    ]]></literal>
    <justification jstring="[para(7983(a,1),10019(a,1,3))].">
      <j1 rule="para" parents="7983 10019"/>
    </justification>
  </clause>

  <clause id="10028">
    <literal><![CDATA[
      L(x,K(y,z),K(u,y)) = x
    ]]></literal>
    <justification jstring="[hyper(5219,a,10023,a)].">
      <j1 rule="hyper" parents="5219 10023"/>
    </justification>
  </clause>

  <clause id="10029">
    <literal><![CDATA[
      (K(x,y) * K(x,z)) * u = K(x,y) * (K(x,z) * u)
    ]]></literal>
    <justification jstring="[hyper(1318,a,10023,a),flip(a)].">
      <j1 rule="hyper" parents="1318 10023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10030">
    <literal><![CDATA[
      (K(x,y) * K(x,z)) \ u = K(z,x) * (K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,6082,a(flip),b,10023,a)].">
      <j1 rule="hyper" parents="65 6082 10023"/>
    </justification>
  </clause>

  <clause id="10031">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) \ u = K(z,y) * (K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,6082,a(flip),b,10028,a)].">
      <j1 rule="hyper" parents="65 6082 10028"/>
    </justification>
  </clause>

  <clause id="10033">
    <literal><![CDATA[
      (K(x,y) * K(z,T(x,u))) * w = K(x,y) * (K(z,T(x,u)) * w)
    ]]></literal>
    <justification jstring="[hyper(1318,a,10026,a),flip(a)].">
      <j1 rule="hyper" parents="1318 10026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10034">
    <literal><![CDATA[
      (K(x,K(y,z)) * K(u,y)) * w = K(x,K(y,z)) * (K(u,y) * w)
    ]]></literal>
    <justification jstring="[hyper(1318,a,10027,a),flip(a)].">
      <j1 rule="hyper" parents="1318 10027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10035">
    <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(1318,a,10025,a),flip(a)].">
      <j1 rule="hyper" parents="1318 10025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10036">
    <literal><![CDATA[
      x \ (K(y,z) * (K(z,u) * x)) != w
    ]]></literal>
    <literal><![CDATA[
      T(K(y,z) * K(z,u),x) = w
    ]]></literal>
    <justification jstring="[para(10016(a,1),318(a,1,2))].">
      <j1 rule="para" parents="10016 318"/>
    </justification>
  </clause>

  <clause id="10037">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) * u = K(z,x) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(2278(a,2),10016(a,1,1))].">
      <j1 rule="para" parents="2278 10016"/>
    </justification>
  </clause>

  <clause id="10038">
    <literal><![CDATA[
      (K(x,y) * (K(y,z) * u)) / (K(x,y) * K(y,z)) != w
    ]]></literal>
    <literal><![CDATA[
      u * K(K(x,y) * K(y,z),u) = w
    ]]></literal>
    <justification jstring="[para(10016(a,1),5129(a,1,1))].">
      <j1 rule="para" parents="10016 5129"/>
    </justification>
  </clause>

  <clause id="10039">
    <literal><![CDATA[
      K(x,y) * (K(y,x * y) * z) = (y \ L(y,x,y)) * z
    ]]></literal>
    <justification jstring="[para(5795(a,1),10016(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5795 10016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10040">
    <literal><![CDATA[
      K(x * y,x) * (K(x,y) * z) = a(x,y,x) * z
    ]]></literal>
    <justification jstring="[para(9672(a,1),10016(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9672 10016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10041">
    <literal><![CDATA[
      K(x * y,x) * (K(x,y) * z) != z * u
    ]]></literal>
    <literal><![CDATA[
      T(a(x,y,x),z) = u
    ]]></literal>
    <justification jstring="[para(10040(a,2),236(a,2)),flip(a)].">
      <j1 rule="para" parents="10040 236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10042">
    <literal><![CDATA[
      K(x * y,y) * (K(y,x) * z) = a(y,x,y) * z
    ]]></literal>
    <justification jstring="[para(5980(a,2),10040(a,1,1))].">
      <j1 rule="para" parents="5980 10040"/>
    </justification>
  </clause>

  <clause id="10043">
    <literal><![CDATA[
      K(x * y,y) * (x * (K(y,x) * z)) = a(y,x,y) * (x * z)
    ]]></literal>
    <justification jstring="[para(5524(a,1),10042(a,1,2))].">
      <j1 rule="para" parents="5524 10042"/>
    </justification>
  </clause>

  <clause id="10044">
    <literal><![CDATA[
      (K(x,y) * z) / (K(u,y) * z) = K(x,y) * K(y,u)
    ]]></literal>
    <justification jstring="[para(5432(a,1),10017(a,1,1,2))].">
      <j1 rule="para" parents="5432 10017"/>
    </justification>
  </clause>

  <clause id="10045">
    <literal><![CDATA[
      K(x,y) * (K(z,x) * u) = K(z,x) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,10016,a(flip),b,10021,a),flip(a)].">
      <j1 rule="hyper" parents="65 10016 10021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10046">
    <literal><![CDATA[
      K(x,y) * (K(z,x) * K(K(z,x) * K(x,y),u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(K(z,x) * K(x,y),u) = w
    ]]></literal>
    <justification jstring="[para(10021(a,1),5087(a,1))].">
      <j1 rule="para" parents="10021 5087"/>
    </justification>
  </clause>

  <clause id="10047">
    <literal><![CDATA[
      K(x,x \ y) * (K(y,x) * z) = a(x,x \ y,x) * z
    ]]></literal>
    <justification jstring="[para(9676(a,1),10021(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9676 10021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10048">
    <literal><![CDATA[
      (K(x,y) * K(x,y)) * z = y * (T(T(y,x),x) \ z)
    ]]></literal>
    <justification jstring="[hyper(299,a,6199,a(flip),b,10029,a),flip(a)].">
      <j1 rule="hyper" parents="299 6199 10029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10049">
    <literal><![CDATA[
      K(x,y) * (K(x,K(y,z)) * u) = K(x,T(y,z)) * u
    ]]></literal>
    <justification jstring="[para(7967(a,1),10029(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7967 10029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10050">
    <literal><![CDATA[
      K(x,y) * (K(z,y) * K(y,y \ 1)) = ((y \ K(y,z)) * T(y,x)) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,6483,a(flip),b,10030,a),flip(a)].">
      <j1 rule="hyper" parents="65 6483 10030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10051">
    <literal><![CDATA[
      (K(x,y) * (K(x,y) * z)) \ u = z \ ((K(y,x) * K(y,x)) * u)
    ]]></literal>
    <justification jstring="[para(10030(a,1),666(a,1,1))].">
      <j1 rule="para" parents="10030 666"/>
    </justification>
  </clause>

  <clause id="10052">
    <literal><![CDATA[
      K(x,y) * (K(y,y * x) * z) = a(y,x,y) \ z
    ]]></literal>
    <justification jstring="[para(9672(a,1),10031(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9672 10031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10053">
    <literal><![CDATA[
      K(x,y) * (K(y,x * y) * z) = a(y,x,y) \ z
    ]]></literal>
    <justification jstring="[para(5685(a,2),10052(a,1,2,1))].">
      <j1 rule="para" parents="5685 10052"/>
    </justification>
  </clause>

  <clause id="10054">
    <literal><![CDATA[
      T(K(x,y) * K(z,x),u) * u = (K(x,y) * K(z,x)) * ((K(z,x) * (K(x,y) * u)) / (K(x,y) * K(z,x)))
    ]]></literal>
    <justification jstring="[para(10037(a,1),4263(a,2,2,1))].">
      <j1 rule="para" parents="10037 4263"/>
    </justification>
  </clause>

  <clause id="10055">
    <literal><![CDATA[
      (x * K(y,z)) / (K(u,T(z,x)) * x) = K(y,T(z,x)) * K(T(z,x),u)
    ]]></literal>
    <justification jstring="[para(8101(a,1),10044(a,1,1))].">
      <j1 rule="para" parents="8101 10044"/>
    </justification>
  </clause>

  <clause id="10056">
    <literal><![CDATA[
      T(K(x,y) * z,K(y,u)) * K(y,u) = K(x,y) * (K(y,u) * z)
    ]]></literal>
    <justification jstring="[hyper(8078,a,10045,a)].">
      <j1 rule="hyper" parents="8078 10045"/>
    </justification>
  </clause>

  <clause id="10057">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) \ u = K(y,x) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(299,a,10031,a,b,10045,a)].">
      <j1 rule="hyper" parents="299 10031 10045"/>
    </justification>
  </clause>

  <clause id="10058">
    <literal><![CDATA[
      T(x,y) \ (x * (K(x,z) * u)) = K(x,z) * (K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(299,a,5382,a,b,10045,a)].">
      <j1 rule="hyper" parents="299 5382 10045"/>
    </justification>
  </clause>

  <clause id="10059">
    <literal><![CDATA[
      K(x,y) * (K(y,z) * (K(y,x) * u)) = K(y,z) * u
    ]]></literal>
    <justification jstring="[para(5432(a,1),10045(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5432 10045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10060">
    <literal><![CDATA[
      K(x,y) * (K(z,x) * (K(y,x) * u)) = K(z,x) * u
    ]]></literal>
    <justification jstring="[para(5432(a,1),10045(a,2,2))].">
      <j1 rule="para" parents="5432 10045"/>
    </justification>
  </clause>

  <clause id="10061">
    <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(7431(a,1),10045(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7431 10045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10062">
    <literal><![CDATA[
      T(K(x,y) \ T(K(x,T(y,z)) * u,w),K(x,y)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) \ T((K(x,K(y,z)) * u) * K(x,y),w) = v5
    ]]></literal>
    <justification jstring="[para(10049(a,1),3482(a,1,1,2,1))].">
      <j1 rule="para" parents="10049 3482"/>
    </justification>
  </clause>

  <clause id="10063">
    <literal><![CDATA[
      (K(x,T(y,z)) * K(y,u)) \ w = K(y,T(x,z)) * (K(u,y) * w)
    ]]></literal>
    <justification jstring="[para(7537(a,1),10057(a,1,1,1))].">
      <j1 rule="para" parents="7537 10057"/>
    </justification>
  </clause>

  <clause id="10064">
    <literal><![CDATA[
      K(x,y) * (K(x,z) * u) = K(x,z) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(5437,a,10059,a)].">
      <j1 rule="hyper" parents="5437 10059"/>
    </justification>
  </clause>

  <clause id="10065">
    <literal><![CDATA[
      a(x,y,x) * (K(x,x * y) * z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(65,a,10040,a(flip),b,10059,a)].">
      <j1 rule="hyper" parents="65 10040 10059"/>
    </justification>
  </clause>

  <clause id="10066">
    <literal><![CDATA[
      (K(x,y) * z) / (K(x,u) * z) = K(u,x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(120,a,10059,a(flip),b,10016,a)].">
      <j1 rule="hyper" parents="120 10059 10016"/>
    </justification>
  </clause>

  <clause id="10067">
    <literal><![CDATA[
      K(x,y) * (K(z,y) * u) = K(z,y) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(5437,a,10060,a)].">
      <j1 rule="hyper" parents="5437 10060"/>
    </justification>
  </clause>

  <clause id="10068">
    <literal><![CDATA[
      K(x,y) * (K(x,z) * u) != K(x,z) * w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * u = w
    ]]></literal>
    <justification jstring="[para(10064(a,1),45(a,1))].">
      <j1 rule="para" parents="10064 45"/>
    </justification>
  </clause>

  <clause id="10069">
    <literal><![CDATA[
      K(x,y) * (K(x,z) * T(u,K(x,y))) = K(x,z) * (u * K(x,y))
    ]]></literal>
    <justification jstring="[para(107(a,1),10064(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 10064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10070">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,u) * w) = K(z,u) * (K(z,K(x,y)) * w)
    ]]></literal>
    <justification jstring="[para(7989(a,2),10064(a,1,1))].">
      <j1 rule="para" parents="7989 10064"/>
    </justification>
  </clause>

  <clause id="10071">
    <literal><![CDATA[
      x / (K(y \ x,z) * (y * (x / y))) = K(z,y \ x) * K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(5462(a,1),10066(a,1,1))].">
      <j1 rule="para" parents="5462 10066"/>
    </justification>
  </clause>

  <clause id="10072">
    <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(10067(a,1),1951(a,1,1,1,1))].">
      <j1 rule="para" parents="10067 1951"/>
    </justification>
  </clause>

  <clause id="10073">
    <literal><![CDATA[
      (x \ R(x,y,x)) * T(z,K(x,x * y)) = K(x,y) * (z * K(x * y,x))
    ]]></literal>
    <justification jstring="[para(8063(a,1),10022(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8063 10022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10074">
    <literal><![CDATA[
      (x \ L(x,y,x)) * z = a(x,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(65,a,10053,a(flip),b,10039,a),flip(a)].">
      <j1 rule="hyper" parents="65 10053 10039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10075">
    <literal><![CDATA[
      a(x,y,x) \ 1 = x \ L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,10074,a),flip(a)].">
      <j1 rule="hyper" parents="133 10074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10076">
    <literal><![CDATA[
      (x \ L(x,y,x)) \ z = a(x,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(119,a,9,a(flip),b,10074,a)].">
      <j1 rule="hyper" parents="119 9 10074"/>
    </justification>
  </clause>

  <clause id="10078">
    <literal><![CDATA[
      (a(x,y,x) \ 1) * z = a(x,y,x) \ z
    ]]></literal>
    <justification jstring="[para(10075(a,2),10074(a,1,1))].">
      <j1 rule="para" parents="10075 10074"/>
    </justification>
  </clause>

  <clause id="10079">
    <literal><![CDATA[
      (1 / a(x,y,x)) * z = a(x,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(36,a,1683,a(flip),b,10078,a),flip(a)].">
      <j1 rule="hyper" parents="36 1683 10078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10080">
    <literal><![CDATA[
      (x \ y) * (a(x,x \ y,x) * z) = (y / x) * (K(y,x) * z)
    ]]></literal>
    <justification jstring="[para(10047(a,1),5714(a,1,2))].">
      <j1 rule="para" parents="10047 5714"/>
    </justification>
  </clause>

  <clause id="10081">
    <literal><![CDATA[
      K(R(x,K(x,y) * z,u),w) = K(R(x,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(299,a,7200,a(flip),b,10002,a),flip(a)].">
      <j1 rule="hyper" parents="299 7200 10002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10082">
    <literal><![CDATA[
      K(R(x,K(x,y) * z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(R(x,z,u),w) = v5
    ]]></literal>
    <justification jstring="[para(10002(a,2),7209(a,1))].">
      <j1 rule="para" parents="10002 7209"/>
    </justification>
  </clause>

  <clause id="10083">
    <literal><![CDATA[
      K(R(x,K(y,x) * z,u),w) = K(R(x,z,u),w)
    ]]></literal>
    <justification jstring="[para(5432(a,1),10081(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5432 10081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10084">
    <literal><![CDATA[
      T(x,y) \ (T(x,z) * u) = K(x,z) * (K(y,x) * u)
    ]]></literal>
    <justification jstring="[para(5055(a,1),10058(a,1,2))].">
      <j1 rule="para" parents="5055 10058"/>
    </justification>
  </clause>

  <clause id="10086">
    <literal><![CDATA[
      R(x,T(K(y,z),x),T(K(u,K(z,w)),K(y,z) * x)) \ ((K(u,K(z,w)) * K(y,z)) * x) = T(K(y,z),x) * T(K(u,K(z,w)),K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(10034(a,2),1011(a,1,2))].">
      <j1 rule="para" parents="10034 1011"/>
    </justification>
  </clause>

  <clause id="10087">
    <literal><![CDATA[
      (K(x,y) * (K(x,y) * z)) \ u = z \ (K(y,x) * (K(y,x) * u))
    ]]></literal>
    <justification jstring="[para(10029(a,1),10051(a,2,2))].">
      <j1 rule="para" parents="10029 10051"/>
    </justification>
  </clause>

  <clause id="10088">
    <literal><![CDATA[
      (x * K(y * z,y)) * K(y,z) = K(y * z,y) * (K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(8262(a,1),10056(a,1,1))].">
      <j1 rule="para" parents="8262 10056"/>
    </justification>
  </clause>

  <clause id="10089">
    <literal><![CDATA[
      T(K(x,y) * z,K(x,u)) = K(x,y) * T(z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(235,a,7689,a,b,10069,a)].">
      <j1 rule="hyper" parents="235 7689 10069"/>
    </justification>
  </clause>

  <clause id="10090">
    <literal><![CDATA[
      K(x,K(y,z)) * T(y,K(x,u)) = T(T(y,K(x,z)),K(x,u))
    ]]></literal>
    <justification jstring="[hyper(235,a,7994,a(flip),b,10069,a),flip(a)].">
      <j1 rule="hyper" parents="235 7994 10069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10091">
    <literal><![CDATA[
      T(x * K(y,z),K(z,u)) = T(x,K(z,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(6535,a,10089,a),flip(a)].">
      <j1 rule="hyper" parents="6535 10089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10092">
    <literal><![CDATA[
      K(x,y) * T(K(x,y) \ z,K(x,u)) = T(z,K(x,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),10089(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 10089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10093">
    <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(9620(a,1),10089(a,2,2))].">
      <j1 rule="para" parents="9620 10089"/>
    </justification>
  </clause>

  <clause id="10094">
    <literal><![CDATA[
      T(T(x,y),K(y,z)) * K(u,y) = T(x * K(u,y),T(y,z))
    ]]></literal>
    <justification jstring="[hyper(7784,a,10091,a),flip(a)].">
      <j1 rule="hyper" parents="7784 10091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10095">
    <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(6341(a,1),10091(a,2,2))].">
      <j1 rule="para" parents="6341 10091"/>
    </justification>
  </clause>

  <clause id="10096">
    <literal><![CDATA[
      T(x * K(y,z),K(y,u)) = T(x,K(y,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(807,a,10092,a),flip(a)].">
      <j1 rule="hyper" parents="807 10092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10097">
    <literal><![CDATA[
      T(x * K(y,z * x),K(y,z)) = K(y,z * x) * x
    ]]></literal>
    <justification jstring="[hyper(299,a,9182,a(flip),b,10096,a),flip(a)].">
      <j1 rule="hyper" parents="299 9182 10096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10098">
    <literal><![CDATA[
      K(x,y) * (T(z,K(y,x)) * K(y,u)) = (z * K(y,u)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(10096(a,1),8063(a,1,2))].">
      <j1 rule="para" parents="10096 8063"/>
    </justification>
  </clause>

  <clause id="10099">
    <literal><![CDATA[
      (x * K(y,z * x)) / T(T(K(y,z),x * K(y,z * x)),x * K(y,z * x)) = (K(y,z * x) * x) / T(K(y,z),x * K(y,z * x))
    ]]></literal>
    <justification jstring="[para(10097(a,1),4393(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10097 4393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10100">
    <literal><![CDATA[
      T(x * K(y,z),T(z,u)) = T(x,T(z,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(7140(a,1),10094(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7140 10094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10101">
    <literal><![CDATA[
      T(K(x,y) * z,T(x,u)) = K(x,y) * T(z,T(x,u))
    ]]></literal>
    <justification jstring="[hyper(6544,a,10100,a),flip(a)].">
      <j1 rule="hyper" parents="6544 10100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10102">
    <literal><![CDATA[
      K(x,y) * T(z / T(x,u),T(x,u)) = T(x,u) \ (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,8454,a(flip),b,10101,a),flip(a)].">
      <j1 rule="hyper" parents="65 8454 10101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10103">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,u) * w) = K(z,u) * (K(x,K(y,z)) * w)
    ]]></literal>
    <justification jstring="[para(7989(a,2),10070(a,2,2,1))].">
      <j1 rule="para" parents="7989 10070"/>
    </justification>
  </clause>

  <clause id="10104">
    <literal><![CDATA[
      (x * (T(T(x,y),y) \ z)) \ u = z \ (K(x,y) * (K(x,y) * u))
    ]]></literal>
    <justification jstring="[para(6199(a,1),10087(a,1,1))].">
      <j1 rule="para" parents="6199 10087"/>
    </justification>
  </clause>

  <clause id="10105">
    <literal><![CDATA[
      K(x * y,x) * (K(x,y) * z) = z * (K(x,y) * K(x * y,x))
    ]]></literal>
    <justification jstring="[hyper(9238,a,10088,a),flip(a)].">
      <j1 rule="hyper" parents="9238 10088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10106">
    <literal><![CDATA[
      K(x,y) * (T(z,K(y,x)) * K(y,u)) = z * (K(y,u) * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,9202,a(flip),b,10098,a),flip(a)].">
      <j1 rule="hyper" parents="299 9202 10098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10107">
    <literal><![CDATA[
      T(x,y) \ (K(x,z) * u) = K(x,z) * (T(x,y) \ u)
    ]]></literal>
    <justification jstring="[para(109(a,1),10102(a,1,2)),flip(a)].">
      <j1 rule="para" parents="109 10102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10108">
    <literal><![CDATA[
      K(x,y) * (T(x,z) \ 1) = T(x,z) \ K(x,y)
    ]]></literal>
    <justification jstring="[para(8(a,1),10107(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8 10107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10109">
    <literal><![CDATA[
      K(x,y) * (T(y,z) \ K(y,x)) = T(y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(5437,a,10108,a)].">
      <j1 rule="hyper" parents="5437 10108"/>
    </justification>
  </clause>

  <clause id="10110">
    <literal><![CDATA[
      K(x,y) * (T(x,z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) \ K(x,y) = u
    ]]></literal>
    <justification jstring="[para(10109(a,1),5438(a,1,2)),flip(b)].">
      <j1 rule="para" parents="10109 5438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10111">
    <literal><![CDATA[
      K(x,y) * (K(z,K(u,x)) * (K(x,y) \ w)) = K(z,K(u,x)) * w
    ]]></literal>
    <justification jstring="[hyper(315,a,10103,a),flip(a)].">
      <j1 rule="hyper" parents="315 10103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10112">
    <literal><![CDATA[
      (x * (T(T(x,y),y) \ z)) \ u = z \ (y * (T(T(y,x),x) \ u))
    ]]></literal>
    <justification jstring="[para(6199(a,1),10104(a,2,2))].">
      <j1 rule="para" parents="6199 10104"/>
    </justification>
  </clause>

  <clause id="10113">
    <literal><![CDATA[
      K(x * y,x) * (K(x,y) * z) = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[para(9673(a,1),10105(a,2,2))].">
      <j1 rule="para" parents="9673 10105"/>
    </justification>
  </clause>

  <clause id="10114">
    <literal><![CDATA[
      T(a(x,y,x),z) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(10041,a,10113,a)].">
      <j1 rule="hyper" parents="10041 10113"/>
    </justification>
  </clause>

  <clause id="10115">
    <literal><![CDATA[
      K(x,x * y) * (z * a(x,y,x)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(5437,a,10113,a)].">
      <j1 rule="hyper" parents="5437 10113"/>
    </justification>
  </clause>

  <clause id="10116">
    <literal><![CDATA[
      a(x,y,x) * z = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,10040,a(flip),b,10113,a)].">
      <j1 rule="hyper" parents="65 10040 10113"/>
    </justification>
  </clause>

  <clause id="10117">
    <literal><![CDATA[
      T(x,a(y,z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(235,a,10113,a(flip),b,10040,a(flip))].">
      <j1 rule="hyper" parents="235 10113 10040"/>
    </justification>
  </clause>

  <clause id="10118">
    <literal><![CDATA[
      (a(x,y,x) * z) / a(x,y,x) = z
    ]]></literal>
    <justification jstring="[hyper(120,a,10040,a(flip),b,10113,a(flip))].">
      <j1 rule="hyper" parents="120 10040 10113"/>
    </justification>
  </clause>

  <clause id="10120">
    <literal><![CDATA[
      x * K(y,a(z,u,z)) = x
    ]]></literal>
    <justification jstring="[hyper(7120,a,10117,a)].">
      <j1 rule="hyper" parents="7120 10117"/>
    </justification>
  </clause>

  <clause id="10121">
    <literal><![CDATA[
      x / a(y,z,y) = a(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(3696,a,10117,a),flip(a)].">
      <j1 rule="hyper" parents="3696 10117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10122">
    <literal><![CDATA[
      (a(x,y,x) \ z) * a(x,y,x) = z
    ]]></literal>
    <justification jstring="[hyper(2379,a,10117,a)].">
      <j1 rule="hyper" parents="2379 10117"/>
    </justification>
  </clause>

  <clause id="10123">
    <literal><![CDATA[
      K(x,a(y,z,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(57,a,10117,a)].">
      <j1 rule="hyper" parents="57 10117"/>
    </justification>
  </clause>

  <clause id="10125">
    <literal><![CDATA[
      a(x,y,x) * z != u
    ]]></literal>
    <literal><![CDATA[
      z * a(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(10117(a,1),276(a,1,2))].">
      <j1 rule="para" parents="10117 276"/>
    </justification>
  </clause>

  <clause id="10126">
    <literal><![CDATA[
      x / a(y,z,y) != u
    ]]></literal>
    <literal><![CDATA[
      a(y,z,y) \ x = u
    ]]></literal>
    <justification jstring="[para(10117(a,1),400(a,1))].">
      <j1 rule="para" parents="10117 400"/>
    </justification>
  </clause>

  <clause id="10127">
    <literal><![CDATA[
      T(x,y \ R(y,z,y)) = x
    ]]></literal>
    <justification jstring="[para(9669(a,1),10117(a,1,2))].">
      <j1 rule="para" parents="9669 10117"/>
    </justification>
  </clause>

  <clause id="10128">
    <literal><![CDATA[
      R(a(x,y,x),z,u) * w = w * R(a(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(10120(a,1),5132(a,1,1,1))].">
      <j1 rule="para" parents="10120 5132"/>
    </justification>
  </clause>

  <clause id="10129">
    <literal><![CDATA[
      (x * (y * a(z,u,z))) / (x * y) = L(a(z,u,z),y,x)
    ]]></literal>
    <justification jstring="[para(10120(a,1),5254(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10120 5254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10130">
    <literal><![CDATA[
      x / (y \ R(y,z,y)) = (y \ R(y,z,y)) \ x
    ]]></literal>
    <justification jstring="[hyper(3696,a,10127,a),flip(a)].">
      <j1 rule="hyper" parents="3696 10127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10133">
    <literal><![CDATA[
      T(a(x,y,x),z) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,9671,a,b,10114,a),flip(a)].">
      <j1 rule="hyper" parents="299 9671 10114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10134">
    <literal><![CDATA[
      x * a(y,z,y) != u
    ]]></literal>
    <literal><![CDATA[
      a(y,z,y) * x = u
    ]]></literal>
    <justification jstring="[para(10114(a,1),276(a,1,2))].">
      <j1 rule="para" parents="10114 276"/>
    </justification>
  </clause>

  <clause id="10135">
    <literal><![CDATA[
      (x * (a(y,z,y) * u)) / L(a(y,z,y),u,x) = x * u
    ]]></literal>
    <justification jstring="[para(10114(a,1),586(a,1,2,1))].">
      <j1 rule="para" parents="10114 586"/>
    </justification>
  </clause>

  <clause id="10137">
    <literal><![CDATA[
      a(x,y,x) * x = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,9674,a(flip),b,10116,a),flip(a)].">
      <j1 rule="hyper" parents="299 9674 10116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10138">
    <literal><![CDATA[
      a(x,y,x) \ (z * x) = z * L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,9714,a(flip),b,10116,a)].">
      <j1 rule="hyper" parents="119 9714 10116"/>
    </justification>
  </clause>

  <clause id="10139">
    <literal><![CDATA[
      a(x,y,x) \ R(x,y,x) = x
    ]]></literal>
    <justification jstring="[hyper(119,a,9674,a(flip),b,10116,a)].">
      <j1 rule="hyper" parents="119 9674 10116"/>
    </justification>
  </clause>

  <clause id="10140">
    <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(119,a,10116,a,b,688,a)].">
      <j1 rule="hyper" parents="119 10116 688"/>
    </justification>
  </clause>

  <clause id="10141">
    <literal><![CDATA[
      (x \ L(x,y,x)) \ z = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,10076,a,b,10116,a)].">
      <j1 rule="hyper" parents="65 10076 10116"/>
    </justification>
  </clause>

  <clause id="10142">
    <literal><![CDATA[
      a(x,y,x) * z != z * u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(10116(a,2),45(a,1))].">
      <j1 rule="para" parents="10116 45"/>
    </justification>
  </clause>

  <clause id="10143">
    <literal><![CDATA[
      (x * y) \ ((x * a(z,u,z)) * y) = R(T(a(z,u,z),x * y),x,y)
    ]]></literal>
    <justification jstring="[para(10116(a,1),689(a,1,2,1))].">
      <j1 rule="para" parents="10116 689"/>
    </justification>
  </clause>

  <clause id="10144">
    <literal><![CDATA[
      (x / (y * a(z,u,z))) * (a(z,u,z) * a(z,u,z)) = x / ((1 / a(z,u,z)) * y)
    ]]></literal>
    <justification jstring="[para(10116(a,1),1076(a,1,1,2))].">
      <j1 rule="para" parents="10116 1076"/>
    </justification>
  </clause>

  <clause id="10145">
    <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(10116(a,1),855(a,1,1))].">
      <j1 rule="para" parents="10116 855"/>
    </justification>
  </clause>

  <clause id="10146">
    <literal><![CDATA[
      x * (y \ R(y,z,y)) = a(y,z,y) * x
    ]]></literal>
    <justification jstring="[para(9671(a,2),10116(a,2,2)),flip(a)].">
      <j1 rule="para" parents="9671 10116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10147">
    <literal><![CDATA[
      x / a(y,z,y) != u
    ]]></literal>
    <literal><![CDATA[
      a(y,z,y) * u = x
    ]]></literal>
    <justification jstring="[para(10118(a,1),48(a,1)),flip(a)].">
      <j1 rule="para" parents="10118 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10148">
    <literal><![CDATA[
      T(a(1 / x,y,1 / x),z) = (1 / x) \ R(1 / x,y,x \ 1)
    ]]></literal>
    <justification jstring="[para(3395(a,1),10133(a,2,2))].">
      <j1 rule="para" parents="3395 10133"/>
    </justification>
  </clause>

  <clause id="10149">
    <literal><![CDATA[
      (x * (y \ R(y,z,y))) / (K(y,z) * x) = K(y * z,y)
    ]]></literal>
    <justification jstring="[hyper(120,a,10146,a,b,10040,a)].">
      <j1 rule="hyper" parents="120 10146 10040"/>
    </justification>
  </clause>

  <clause id="10150">
    <literal><![CDATA[
      (x \ L(x,y,x)) \ 1 = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(118,a,10146,a,b,10076,a),flip(a)].">
      <j1 rule="hyper" parents="118 10146 10076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10158">
    <literal><![CDATA[
      K(x,y) * (z * L(x,y,x)) = K(x,x * y) * (z * x)
    ]]></literal>
    <justification jstring="[para(9714(a,1),10115(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9714 10115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10159">
    <literal><![CDATA[
      T(x,R(a(y,z,y),u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(238,a,10128,a)].">
      <j1 rule="hyper" parents="238 10128"/>
    </justification>
  </clause>

  <clause id="10161">
    <literal><![CDATA[
      T(K(x * y,x),K(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      (K(x,y) * z) \ (z * (x \ R(x,y,x))) = u
    ]]></literal>
    <justification jstring="[para(10149(a,1),400(a,1,1))].">
      <j1 rule="para" parents="10149 400"/>
    </justification>
  </clause>

  <clause id="10162">
    <literal><![CDATA[
      ((K(x,y) * z) \ (z * (x \ R(x,y,x)))) / ((z * (x \ R(x,y,x))) / K(x * y,x)) = ((z * (x \ R(x,y,x))) / (K(x,y) * z)) / (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(10149(a,1),9070(a,1,2,2))].">
      <j1 rule="para" parents="10149 9070"/>
    </justification>
  </clause>

  <clause id="10163">
    <literal><![CDATA[
      K(x,y) * (K(z,K(x,u)) * (K(x,y) \ w)) = K(u,K(z,x)) * w
    ]]></literal>
    <justification jstring="[para(7989(a,2),10111(a,1,2,1))].">
      <j1 rule="para" parents="7989 10111"/>
    </justification>
  </clause>

  <clause id="10164">
    <literal><![CDATA[
      (x * y) \ ((x * a(z,u,z)) * y) = R(a(z,u,z),x,y)
    ]]></literal>
    <justification jstring="[para(10114(a,1),10143(a,2,1))].">
      <j1 rule="para" parents="10114 10143"/>
    </justification>
  </clause>

  <clause id="10165">
    <literal><![CDATA[
      (x * y) \ ((T(z * x,z) / z) * y) = R(a(z,x,z),x,y)
    ]]></literal>
    <justification jstring="[para(9681(a,2),10164(a,1,2,1))].">
      <j1 rule="para" parents="9681 10164"/>
    </justification>
  </clause>

  <clause id="10167">
    <literal><![CDATA[
      K(x \ (y * T(z,u)),T(z,w)) = K(x \ (z * y),T(z,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,8761,a(flip),b,9926,a),flip(a)].">
      <j1 rule="hyper" parents="65 8761 9926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10169">
    <literal><![CDATA[
      K(x \ (y * z),T(y,z)) = K((z * T(y,u)) / x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,9566,a(flip),b,10167,a),flip(a)].">
      <j1 rule="hyper" parents="65 9566 10167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10170">
    <literal><![CDATA[
      K((x * T(y,z)) / u,y) = K(x / (y \ u),y)
    ]]></literal>
    <justification jstring="[hyper(8718,a,10169,a),flip(a)].">
      <j1 rule="hyper" parents="8718 10169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10172">
    <literal><![CDATA[
      K((x * T(y,z)) / u,y) != w
    ]]></literal>
    <literal><![CDATA[
      K(x / (y \ u),y) = w
    ]]></literal>
    <justification jstring="[para(10169(a,1),8718(a,1))].">
      <j1 rule="para" parents="10169 8718"/>
    </justification>
  </clause>

  <clause id="10173">
    <literal><![CDATA[
      K((x * y) / z,x) = K(y / (x \ z),x)
    ]]></literal>
    <justification jstring="[para(107(a,1),10170(a,1,1,1))].">
      <j1 rule="para" parents="107 10170"/>
    </justification>
  </clause>

  <clause id="10174">
    <literal><![CDATA[
      K(x / (y \ T(z,y \ 1)),y) = K((y * x) / z,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,7743,a(flip),b,10173,a),flip(a)].">
      <j1 rule="hyper" parents="65 7743 10173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10175">
    <literal><![CDATA[
      K((x * y) / z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / (x \ z),x) = u
    ]]></literal>
    <justification jstring="[para(107(a,1),10172(a,1,1,1))].">
      <j1 rule="para" parents="107 10172"/>
    </justification>
  </clause>

  <clause id="10176">
    <literal><![CDATA[
      K(x / (y \ T(z,y \ 1)),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x / (y \ z),y) = u
    ]]></literal>
    <justification jstring="[para(10174(a,2),10175(a,1))].">
      <j1 rule="para" parents="10174 10175"/>
    </justification>
  </clause>

  <clause id="10177">
    <literal><![CDATA[
      (T(x,L(K(y,z),u,w)) * K(v5,z)) * (K(z,v5) * L(K(y,z),u,w)) = x * ((x * L(K(y,z),u,w)) / x)
    ]]></literal>
    <justification jstring="[hyper(299,a,4263,a(flip),b,9929,a),flip(a)].">
      <j1 rule="hyper" parents="299 4263 9929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10178">
    <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(7207,a,9932,a)].">
      <j1 rule="hyper" parents="7207 9932"/>
    </justification>
  </clause>

  <clause id="10179">
    <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(10090(a,1),9933(a,1,1))].">
      <j1 rule="para" parents="10090 9933"/>
    </justification>
  </clause>

  <clause id="10180">
    <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(7989(a,1),10179(a,2,1))].">
      <j1 rule="para" parents="7989 10179"/>
    </justification>
  </clause>

  <clause id="10181">
    <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(7983(a,1),10180(a,2,2))].">
      <j1 rule="para" parents="7983 10180"/>
    </justification>
  </clause>

  <clause id="10182">
    <literal><![CDATA[
      ((x / y) / (y \ 1)) \ (y \ x) = T(y,y \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(7333,a,9971,a),flip(a)].">
      <j1 rule="hyper" parents="7333 9971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10183">
    <literal><![CDATA[
      (x \ y) / (T(x,x \ y) \ 1) = (y / x) / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(192,a,10182,a)].">
      <j1 rule="hyper" parents="192 10182"/>
    </justification>
  </clause>

  <clause id="10184">
    <literal><![CDATA[
      K(x,T((y \ z) * x,z)) = K(x,y \ ((((y \ z) \ 1) \ y) * x))
    ]]></literal>
    <justification jstring="[para(67(a,1),9992(a,1,2,1))].">
      <j1 rule="para" parents="67 9992"/>
    </justification>
  </clause>

  <clause id="10185">
    <literal><![CDATA[
      K(x,T(((y \ z) \ 1) \ x,y)) = K(x,T((y \ z) * x,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,9074,a(flip),b,10184,a)].">
      <j1 rule="hyper" parents="299 9074 10184"/>
    </justification>
  </clause>

  <clause id="10186">
    <literal><![CDATA[
      K(x,T(1 \ ((y \ z) * x),y)) = K(x,T((y \ z) * x,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,9490,a(flip),b,10185,a)].">
      <j1 rule="hyper" parents="65 9490 10185"/>
    </justification>
  </clause>

  <clause id="10187">
    <literal><![CDATA[
      K(x,T((y \ z) * x,z)) = K(x,T((y \ z) * x,y))
    ]]></literal>
    <justification jstring="[para(67(a,1),10186(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="67 10186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10188">
    <literal><![CDATA[
      (K(x,y) * L(K(x,z) \ 1,u,w)) * v5 = K(x,y) * (L(K(z,x),u,w) * v5)
    ]]></literal>
    <justification jstring="[para(5197(a,2),10035(a,1,1,2,1))].">
      <j1 rule="para" parents="5197 10035"/>
    </justification>
  </clause>

  <clause id="10189">
    <literal><![CDATA[
      ((x \ K(x,y)) * T(x,z)) \ 1 = K(z,x) * (x * (K(y,x) / x))
    ]]></literal>
    <justification jstring="[para(4791(a,1),10050(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4791 10050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10190">
    <literal><![CDATA[
      ((x \ K(x,y)) * T(x,z)) \ 1 = x * (K(z,x) * (K(y,x) / x))
    ]]></literal>
    <justification jstring="[hyper(299,a,5524,a(flip),b,10189,a),flip(a)].">
      <j1 rule="hyper" parents="299 5524 10189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10191">
    <literal><![CDATA[
      ((x \ K(x,y)) * T(x,z)) \ 1 = x * (K(y,x) / T(x,z))
    ]]></literal>
    <justification jstring="[para(8359(a,1),10190(a,2,2))].">
      <j1 rule="para" parents="8359 10190"/>
    </justification>
  </clause>

  <clause id="10192">
    <literal><![CDATA[
      (x * K(y,z)) / (x * K(u,z)) = K(y,T(z,x)) * K(T(z,x),u)
    ]]></literal>
    <justification jstring="[para(8101(a,1),10055(a,1,2))].">
      <j1 rule="para" parents="8101 10055"/>
    </justification>
  </clause>

  <clause id="10193">
    <literal><![CDATA[
      (x * K(y,z)) / (x * K(u,z)) = K(y,T(z,x)) * K(z,T(u,x))
    ]]></literal>
    <justification jstring="[hyper(299,a,7549,a(flip),b,10192,a),flip(a)].">
      <j1 rule="hyper" parents="299 7549 10192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10194">
    <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(212(a,2),10071(a,1,2,2,2))].">
      <j1 rule="para" parents="212 10071"/>
    </justification>
  </clause>

  <clause id="10195">
    <literal><![CDATA[
      K(x,y \ z) * K((z \ y) \ x,x) = x \ R(x,(z \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(5592(a,1),6852(a,1,2))].">
      <j1 rule="para" parents="5592 6852"/>
    </justification>
  </clause>

  <clause id="10196">
    <literal><![CDATA[
      K(x,y \ z) * K(y \ (z * x),x) = x \ R(x,(z \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(7429(a,1),10195(a,1,2))].">
      <j1 rule="para" parents="7429 10195"/>
    </justification>
  </clause>

  <clause id="10197">
    <literal><![CDATA[
      K(x,y \ z) * K(y \ (z * x),x) = a(x,(z \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,9671,a(flip),b,10196,a),flip(a)].">
      <j1 rule="hyper" parents="299 9671 10196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10198">
    <literal><![CDATA[
      (x * (y * T(x,z))) \ ((x * y) * T(x,z)) = a(x,y * K(x,z),x)
    ]]></literal>
    <justification jstring="[para(7078(a,1),6947(a,1,2))].">
      <j1 rule="para" parents="7078 6947"/>
    </justification>
  </clause>

  <clause id="10199">
    <literal><![CDATA[
      a(x,y * K(x,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,T(x,z)) = u
    ]]></literal>
    <justification jstring="[para(10198(a,1),775(a,1))].">
      <j1 rule="para" parents="10198 775"/>
    </justification>
  </clause>

  <clause id="10200">
    <literal><![CDATA[
      x \ R(x,y * K(x,z),x) = K(x,y) * K(y * T(x,z),x)
    ]]></literal>
    <justification jstring="[para(8527(a,1),6951(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8527 6951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10202">
    <literal><![CDATA[
      x \ R(x,y * K(x,z),x) = K(x,y) * K(y * x,x)
    ]]></literal>
    <justification jstring="[para(8588(a,1),10200(a,2,2))].">
      <j1 rule="para" parents="8588 10200"/>
    </justification>
  </clause>

  <clause id="10203">
    <literal><![CDATA[
      x \ R(x,y * K(x,z),x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,5983,a(flip),b,10202,a),flip(a)].">
      <j1 rule="hyper" parents="299 5983 10202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10205">
    <literal><![CDATA[
      a(x,y * K(x,z),x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(9683,a,10203,a)].">
      <j1 rule="hyper" parents="9683 10203"/>
    </justification>
  </clause>

  <clause id="10206">
    <literal><![CDATA[
      a(x,y,T(x,z)) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(10199,a,10205,a)].">
      <j1 rule="hyper" parents="10199 10205"/>
    </justification>
  </clause>

  <clause id="10207">
    <literal><![CDATA[
      a(x,y,T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(10206(a,2),9683(a,1))].">
      <j1 rule="para" parents="10206 9683"/>
    </justification>
  </clause>

  <clause id="10208">
    <literal><![CDATA[
      ((x * y) / x) \ (z * (y * K(x,y))) = R(T(z,T(y,x)),y,K(x,y))
    ]]></literal>
    <justification jstring="[para(8184(a,1),6971(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8184 6971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10209">
    <literal><![CDATA[
      ((x * y) / x) \ (z * (y * K(x,y))) = T(z,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(299,a,6967,a(flip),b,10208,a),flip(a)].">
      <j1 rule="hyper" parents="299 6967 10208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10211">
    <literal><![CDATA[
      L(K(x \ (y \ z),u),y \ z,y) != w
    ]]></literal>
    <literal><![CDATA[
      K((y * x) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(6992(a,2),7170(a,1))].">
      <j1 rule="para" parents="6992 7170"/>
    </justification>
  </clause>

  <clause id="10212">
    <literal><![CDATA[
      T(L(x,y,z),u) * (L(x,y,z) \ x) = x * K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(717,a,6998,a)].">
      <j1 rule="hyper" parents="717 6998"/>
    </justification>
  </clause>

  <clause id="10213">
    <literal><![CDATA[
      L(T(x,y),z,u) * (L(x,z,u) \ x) = x * K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(25(a,2),10212(a,1,1))].">
      <j1 rule="para" parents="25 10212"/>
    </justification>
  </clause>

  <clause id="10214">
    <literal><![CDATA[
      L(T(x,y),z,u) \ (x * K(L(x,z,u),y)) = L(x,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(125,a,10213,a)].">
      <j1 rule="hyper" parents="125 10213"/>
    </justification>
  </clause>

  <clause id="10215">
    <literal><![CDATA[
      T(x,R(x,y,z) * u) \ (x * K(L(x,u,R(x,y,z)),u)) = L(x,u,R(x,y,z)) \ x
    ]]></literal>
    <justification jstring="[para(1975(a,1),10214(a,1,1))].">
      <j1 rule="para" parents="1975 10214"/>
    </justification>
  </clause>

  <clause id="10216">
    <literal><![CDATA[
      K(x,y) * T(y,K(z,y) * (x * y)) = L(y,K(z,y) * x,y)
    ]]></literal>
    <justification jstring="[para(8590(a,1),7674(a,1,1))].">
      <j1 rule="para" parents="8590 7674"/>
    </justification>
  </clause>

  <clause id="10217">
    <literal><![CDATA[
      L(x,K(y,x) * z,x) = K(z,x) * T(x,z * x)
    ]]></literal>
    <justification jstring="[para(8547(a,1),10216(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8547 10216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10219">
    <literal><![CDATA[
      L(x,K(y,x) * z,x) = L(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,5354,a(flip),b,10217,a),flip(a)].">
      <j1 rule="hyper" parents="299 5354 10217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10221">
    <literal><![CDATA[
      L(x,T(x,y) \ z,x) = L(x,x \ z,x)
    ]]></literal>
    <justification jstring="[para(5383(a,1),10219(a,1,2))].">
      <j1 rule="para" parents="5383 10219"/>
    </justification>
  </clause>

  <clause id="10222">
    <literal><![CDATA[
      L(x,y / T(x,z),x) = L(x,x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,9371,a,b,10221,a)].">
      <j1 rule="hyper" parents="65 9371 10221"/>
    </justification>
  </clause>

  <clause id="10225">
    <literal><![CDATA[
      K(x,T(y / (x \ z),u)) = K(x,T((z / y) \ x,u))
    ]]></literal>
    <justification jstring="[hyper(8464,a,8385,a)].">
      <j1 rule="hyper" parents="8464 8385"/>
    </justification>
  </clause>

  <clause id="10226">
    <literal><![CDATA[
      x * K(x,T((y / z) \ x,u)) = T(x,T(z / (x \ y),u))
    ]]></literal>
    <justification jstring="[para(10225(a,1),5083(a,2,2)),flip(a)].">
      <j1 rule="para" parents="10225 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10227">
    <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(10226(a,1),5087(a,1))].">
      <j1 rule="para" parents="10226 5087"/>
    </justification>
  </clause>

  <clause id="10228">
    <literal><![CDATA[
      K(x \ ((y \ z) * y),L(y,u,w)) = K(x \ z,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(299,a,5043,a(flip),b,8895,a),flip(a)].">
      <j1 rule="hyper" parents="299 5043 8895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10229">
    <literal><![CDATA[
      K(x \ (y * z),L(z,u,w)) = K(x \ (z * y),L(z,u,w))
    ]]></literal>
    <justification jstring="[para(9(a,1),10228(a,1,1,2,1))].">
      <j1 rule="para" parents="9 10228"/>
    </justification>
  </clause>

  <clause id="10230">
    <literal><![CDATA[
      K((x / y) \ z,L(y,u,w)) = K(x \ (z * y),L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(5297,a,8897,a),flip(a)].">
      <j1 rule="hyper" parents="5297 8897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10232">
    <literal><![CDATA[
      (x * K(y,T(z,u))) * K(z,w) != v5
    ]]></literal>
    <literal><![CDATA[
      x * (K(z,w) * K(y,T(z,u))) = v5
    ]]></literal>
    <justification jstring="[para(9608(a,2),9209(a,1))].">
      <j1 rule="para" parents="9608 9209"/>
    </justification>
  </clause>

  <clause id="10233">
    <literal><![CDATA[
      L(((x / y) / x) \ 1,(x / y) / x,x) = x / (y \ T(x,y \ 1))
    ]]></literal>
    <justification jstring="[para(4226(a,1),9355(a,2,2))].">
      <j1 rule="para" parents="4226 9355"/>
    </justification>
  </clause>

  <clause id="10234">
    <literal><![CDATA[
      x / (y \ T(x,y \ 1)) = (T(x,y \ 1) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(65,a,4233,a(flip),b,10233,a),flip(a)].">
      <j1 rule="hyper" parents="65 4233 10233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10235">
    <literal><![CDATA[
      (T(x,(y \ 1) \ 1) / (y \ 1)) \ x = x / ((y \ 1) \ T(x,y))
    ]]></literal>
    <justification jstring="[para(3739(a,1),10234(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3739 10234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10236">
    <literal><![CDATA[
      x / ((y \ 1) \ T(x,y)) = (T(x,y) / (y \ 1)) \ x
    ]]></literal>
    <justification jstring="[para(3739(a,1),10235(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3739 10235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10237">
    <literal><![CDATA[
      ((T(x,y) / (y \ 1)) \ x) \ x = (y \ 1) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(186,a,10236,a)].">
      <j1 rule="hyper" parents="186 10236"/>
    </justification>
  </clause>

  <clause id="10238">
    <literal><![CDATA[
      (((x \ y) / (x \ 1)) \ (y / x)) \ (y / x) = (x \ 1) \ T(y / x,x)
    ]]></literal>
    <justification jstring="[para(109(a,1),10237(a,1,1,1,1))].">
      <j1 rule="para" parents="109 10237"/>
    </justification>
  </clause>

  <clause id="10239">
    <literal><![CDATA[
      (((x \ y) / (x \ 1)) \ (y / x)) \ (y / x) = (x \ 1) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(109(a,1),10238(a,2,2))].">
      <j1 rule="para" parents="109 10238"/>
    </justification>
  </clause>

  <clause id="10240">
    <literal><![CDATA[
      (x \ K(x,x \ y)) \ (y / x) = (x \ 1) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(9144(a,1),10239(a,1,1))].">
      <j1 rule="para" parents="9144 10239"/>
    </justification>
  </clause>

  <clause id="10241">
    <literal><![CDATA[
      (x \ K(x,(x \ 1) * y)) \ (y / x) = (x \ 1) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(4863(a,2),10240(a,1,1,2))].">
      <j1 rule="para" parents="4863 10240"/>
    </justification>
  </clause>

  <clause id="10242">
    <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(9821(a,1),10241(a,1,1,2))].">
      <j1 rule="para" parents="9821 10241"/>
    </justification>
  </clause>

  <clause id="10243">
    <literal><![CDATA[
      K((x * (y * z)) \ ((x * z) * y),K(z,u)) = K(z,K(u,a(x,z,T(y,z))))
    ]]></literal>
    <justification jstring="[hyper(299,a,7984,a(flip),b,9394,a),flip(a)].">
      <j1 rule="hyper" parents="299 7984 9394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10244">
    <literal><![CDATA[
      K(L(x,y,y \ 1) \ z,T(y,u)) = K(x \ z,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(5878,a,9537,a),flip(a)].">
      <j1 rule="hyper" parents="5878 9537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10245">
    <literal><![CDATA[
      K(((1 / x) * y) \ z,T(x,u)) = K((x \ y) \ z,T(x,u))
    ]]></literal>
    <justification jstring="[para(2474(a,1),10244(a,1,1,1))].">
      <j1 rule="para" parents="2474 10244"/>
    </justification>
  </clause>

  <clause id="10246">
    <literal><![CDATA[
      K(((x \ 1) * y) \ z,T(x,u)) = K((x \ y) \ z,T(x,u))
    ]]></literal>
    <justification jstring="[hyper(7411,a,10245,a)].">
      <j1 rule="hyper" parents="7411 10245"/>
    </justification>
  </clause>

  <clause id="10247">
    <literal><![CDATA[
      K(((x \ 1) * y) \ z,T(x,u)) = K(y \ (x * z),T(x,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,8475,a(flip),b,10246,a),flip(a)].">
      <j1 rule="hyper" parents="299 8475 10246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10248">
    <literal><![CDATA[
      K(x \ (y * z),T(y,x)) = K(((y \ 1) \ z) / x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,9009,a(flip),b,10247,a),flip(a)].">
      <j1 rule="hyper" parents="65 9009 10247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10249">
    <literal><![CDATA[
      K(((x \ 1) \ y) / z,x) = K((x * y) / z,x)
    ]]></literal>
    <justification jstring="[hyper(8220,a,10248,a),flip(a)].">
      <j1 rule="hyper" parents="8220 10248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10250">
    <literal><![CDATA[
      (x * (y * T(y \ (x \ z),u))) \ z != w
    ]]></literal>
    <literal><![CDATA[
      K(u,(x * y) \ z) = w
    ]]></literal>
    <justification jstring="[para(6868(a,2),9603(a,1,1,2))].">
      <j1 rule="para" parents="6868 9603"/>
    </justification>
  </clause>

  <clause id="10251">
    <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(9103(a,1),9603(a,1))].">
      <j1 rule="para" parents="9103 9603"/>
    </justification>
  </clause>

  <clause id="10252">
    <literal><![CDATA[
      L(K(x,y),z \ u,z) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * ((z \ u) / y)) \ u) = w
    ]]></literal>
    <justification jstring="[para(79(a,1),10251(a,1,1,2))].">
      <j1 rule="para" parents="79 10251"/>
    </justification>
  </clause>

  <clause id="10253">
    <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(5426(a,1),10251(a,1,1,2))].">
      <j1 rule="para" parents="5426 10251"/>
    </justification>
  </clause>

  <clause id="10255">
    <literal><![CDATA[
      L(K(x,y \ ((z \ u) * x)),z \ u,z) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * (x \ y)) \ u) = w
    ]]></literal>
    <justification jstring="[para(8873(a,1),10251(a,1,1))].">
      <j1 rule="para" parents="8873 10251"/>
    </justification>
  </clause>

  <clause id="10256">
    <literal><![CDATA[
      L(K(x,y \ ((z \ u) * x)),z \ u,z) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * (y / x)) \ u) = w
    ]]></literal>
    <justification jstring="[para(8880(a,1),10251(a,1,1))].">
      <j1 rule="para" parents="8880 10251"/>
    </justification>
  </clause>

  <clause id="10257">
    <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(1374(a,1),10250(a,1,1,2))].">
      <j1 rule="para" parents="1374 10250"/>
    </justification>
  </clause>

  <clause id="10258">
    <literal><![CDATA[
      K(x,L(L(y,z,y * K(z,y)),u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(5053(a,1),9788(a,2,2,1))].">
      <j1 rule="para" parents="5053 9788"/>
    </justification>
  </clause>

  <clause id="10259">
    <literal><![CDATA[
      K(x,L(L(y,z,y),u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(5260(a,1),10258(a,1,2,1))].">
      <j1 rule="para" parents="5260 10258"/>
    </justification>
  </clause>

  <clause id="10260">
    <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(6755(a,1),10259(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6755 10259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10261">
    <literal><![CDATA[
      K(x,L(L(1 / y,y,z),z * y,u)) = K(x,1 / L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,7402,a(flip),b,10260,a),flip(a)].">
      <j1 rule="hyper" parents="299 7402 10260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10262">
    <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(7537(a,1),9854(a,1,1))].">
      <j1 rule="para" parents="7537 9854"/>
    </justification>
  </clause>

  <clause id="10263">
    <literal><![CDATA[
      (x \ R(x,y,x)) * T(z,K(x,y)) = K(x,y) * (z * K(x * y,x))
    ]]></literal>
    <justification jstring="[para(8259(a,1),10073(a,1,2))].">
      <j1 rule="para" parents="8259 10073"/>
    </justification>
  </clause>

  <clause id="10264">
    <literal><![CDATA[
      K(x,K(y,(z * (u * x)) \ ((z * x) * u))) = K(x,K(y,a(z,x,T(u,x))))
    ]]></literal>
    <justification jstring="[hyper(8025,a,10243,a)].">
      <j1 rule="hyper" parents="8025 10243"/>
    </justification>
  </clause>

  <clause id="10265">
    <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(7551(a,1),10262(a,1,1))].">
      <j1 rule="para" parents="7551 10262"/>
    </justification>
  </clause>

  <clause id="10266">
    <literal><![CDATA[
      ((x * y) \ ((x * K(z,u)) * y)) \ 1 = (x * y) \ ((x * K(u,z)) * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,9802,a(flip),b,10265,a),flip(a)].">
      <j1 rule="hyper" parents="65 9802 10265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10267">
    <literal><![CDATA[
      K(((x / y) * z) \ (x * z),u) \ 1 = (x * z) \ ((x * K(u,y)) * z)
    ]]></literal>
    <justification jstring="[para(9942(a,2),10266(a,1,1))].">
      <j1 rule="para" parents="9942 10266"/>
    </justification>
  </clause>

  <clause id="10268">
    <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(10267(a,1),5200(a,1))].">
      <j1 rule="para" parents="10267 5200"/>
    </justification>
  </clause>

  <clause id="10269">
    <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(6832(a,1),6878(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6832 6878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10270">
    <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(10269(a,2),549(a,1))].">
      <j1 rule="para" parents="10269 549"/>
    </justification>
  </clause>

  <clause id="10271">
    <literal><![CDATA[
      R(x,K(y,z),T(u,K(y,w))) = R(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(10270,a,8663,a)].">
      <j1 rule="hyper" parents="10270 8663"/>
    </justification>
  </clause>

  <clause id="10272">
    <literal><![CDATA[
      R(R(x,y * z,K(z,u)),y,z) = R(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(10270,a,31,a),flip(a)].">
      <j1 rule="hyper" parents="10270 31"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10273">
    <literal><![CDATA[
      R(x,T(K(y,z),u),u) = R(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,9357,a,b,10271,a)].">
      <j1 rule="hyper" parents="65 9357 10271"/>
    </justification>
  </clause>

  <clause id="10274">
    <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(10271(a,2),5446(a,1,1))].">
      <j1 rule="para" parents="10271 5446"/>
    </justification>
  </clause>

  <clause id="10276">
    <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(8730(a,1),10273(a,1,2))].">
      <j1 rule="para" parents="8730 10273"/>
    </justification>
  </clause>

  <clause id="10277">
    <literal><![CDATA[
      R(x,y,T(x,z)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(7075(a,1),10272(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7075 10272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10278">
    <literal><![CDATA[
      R(T(x,y),z,T(x,u)) = R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[para(7079(a,1),10272(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7079 10272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10280">
    <literal><![CDATA[
      R(x / y,z,x / y) = R(x / y,z,y \ x)
    ]]></literal>
    <justification jstring="[para(109(a,1),10277(a,1,3)),flip(a)].">
      <j1 rule="para" parents="109 10277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10281">
    <literal><![CDATA[
      R(x,y,(x \ z) \ z) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(108(a,1),10277(a,1,3))].">
      <j1 rule="para" parents="108 10277"/>
    </justification>
  </clause>

  <clause id="10283">
    <literal><![CDATA[
      R(T(x,y),x \ y,T(x,z)) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(299,a,4475,a(flip),b,10278,a),flip(a)].">
      <j1 rule="hyper" parents="299 4475 10278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10285">
    <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(10278(a,1),1969(a,1,1))].">
      <j1 rule="para" parents="10278 1969"/>
    </justification>
  </clause>

  <clause id="10286">
    <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(5053(a,1),10278(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5053 10278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10287">
    <literal><![CDATA[
      K(x,R(T(y,z),u,y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(10278(a,1),7466(a,1,2))].">
      <j1 rule="para" parents="10278 7466"/>
    </justification>
  </clause>

  <clause id="10288">
    <literal><![CDATA[
      K(x,T(R(y,z,y),u)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(27(a,1),10287(a,1,2))].">
      <j1 rule="para" parents="27 10287"/>
    </justification>
  </clause>

  <clause id="10289">
    <literal><![CDATA[
      K(x,T((y \ z) \ z,u)) = K(x,T(T(y,z),u))
    ]]></literal>
    <justification jstring="[para(10283(a,1),10288(a,1,2,1))].">
      <j1 rule="para" parents="10283 10288"/>
    </justification>
  </clause>

  <clause id="10290">
    <literal><![CDATA[
      R(T(x / y,K(y,x)),z,x / y) = R(x / y,z,y \ x)
    ]]></literal>
    <justification jstring="[para(7289(a,2),10280(a,1,1))].">
      <j1 rule="para" parents="7289 10280"/>
    </justification>
  </clause>

  <clause id="10292">
    <literal><![CDATA[
      K(x,T((y \ z) \ z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(T(y,u),z)) = w
    ]]></literal>
    <justification jstring="[para(10289(a,2),7715(a,1))].">
      <j1 rule="para" parents="10289 7715"/>
    </justification>
  </clause>

  <clause id="10293">
    <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(6257(a,1),10285(a,1,2,1))].">
      <j1 rule="para" parents="6257 10285"/>
    </justification>
  </clause>

  <clause id="10294">
    <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(7489(a,2),10276(a,1,2))].">
      <j1 rule="para" parents="7489 10276"/>
    </justification>
  </clause>

  <clause id="10295">
    <literal><![CDATA[
      R(x,y,T(x * K(z,x),u)) = R(x,y,x * K(z,x))
    ]]></literal>
    <justification jstring="[para(5053(a,1),10286(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5053 10286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10296">
    <literal><![CDATA[
      R(x,y,x * K(z,x)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(5053(a,1),10295(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5053 10295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10297">
    <literal><![CDATA[
      R(x \ y,z,y / x) = R(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[para(5102(a,1),10296(a,1,3))].">
      <j1 rule="para" parents="5102 10296"/>
    </justification>
  </clause>

  <clause id="10298">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) \ z,y) = K(z * ((x * y) \ x),y)
    ]]></literal>
    <justification jstring="[hyper(7099,a,6899,a)].">
      <j1 rule="hyper" parents="7099 6899"/>
    </justification>
  </clause>

  <clause id="10300">
    <literal><![CDATA[
      (x \ y) * K(x \ ((x \ 1) \ y),z) = (1 / x) * T(x \ ((x \ 1) \ y),z)
    ]]></literal>
    <justification jstring="[para(729(a,1),6991(a,1,2,1))].">
      <j1 rule="para" parents="729 6991"/>
    </justification>
  </clause>

  <clause id="10301">
    <literal><![CDATA[
      T(x,y) / ((1 / z) \ x) = (1 / z) * K((((z \ 1) \ x) \ 1) \ (z \ 1),y)
    ]]></literal>
    <justification jstring="[para(5896(a,1),7359(a,2,2))].">
      <j1 rule="para" parents="5896 7359"/>
    </justification>
  </clause>

  <clause id="10302">
    <literal><![CDATA[
      K(x,((T(y,x) / z) \ 1) \ z) = z \ ((T(y,x) / z) \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,8899,a(flip),b,7367,a)].">
      <j1 rule="hyper" parents="65 8899 7367"/>
    </justification>
  </clause>

  <clause id="10304">
    <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(8149(a,1),7518(a,1,2,1,2))].">
      <j1 rule="para" parents="8149 7518"/>
    </justification>
  </clause>

  <clause id="10305">
    <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(7489(a,2),7524(a,1,2,1))].">
      <j1 rule="para" parents="7489 7524"/>
    </justification>
  </clause>

  <clause id="10306">
    <literal><![CDATA[
      L(x * R(K(x,y),z,u),w,x) = L(x,w,x) * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(6213(a,1),7744(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6213 7744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10307">
    <literal><![CDATA[
      L(x * R(K(x,y),z,u),w,x) = R(K(x,y),z,u) * L(x,w,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,3596,a,b,10306,a),flip(a)].">
      <j1 rule="hyper" parents="299 3596 10306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10308">
    <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(6011(a,1),7903(a,1,1,2))].">
      <j1 rule="para" parents="6011 7903"/>
    </justification>
  </clause>

  <clause id="10309">
    <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(299,a,9080,a,b,8266,a),flip(a)].">
      <j1 rule="hyper" parents="299 9080 8266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10310">
    <literal><![CDATA[
      K(T(x,y),K(x,z)) = T((u \ w) \ w,v5) \ (T(u,T(v5,w)) * K(u,u \ w))
    ]]></literal>
    <justification jstring="[para(5379(a,1),8457(a,2,2))].">
      <j1 rule="para" parents="5379 8457"/>
    </justification>
  </clause>

  <clause id="10311">
    <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(299,a,9930,a(flip),b,8576,a),flip(a)].">
      <j1 rule="hyper" parents="299 9930 8576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10312">
    <literal><![CDATA[
      K(x,K((1 / y) / z,(z * y) / u)) = (T(z * y,K(x,u)) / y) / z
    ]]></literal>
    <justification jstring="[hyper(8810,a,8771,a)].">
      <j1 rule="hyper" parents="8810 8771"/>
    </justification>
  </clause>

  <clause id="10313">
    <literal><![CDATA[
      K(x,K((1 / y) / z,(z * y) / u)) = K(x,K(u,(1 / y) / z))
    ]]></literal>
    <justification jstring="[hyper(299,a,8809,a(flip),b,10312,a),flip(a)].">
      <j1 rule="hyper" parents="299 8809 10312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10314">
    <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(566(a,2),10313(a,1,2,2))].">
      <j1 rule="para" parents="566 10313"/>
    </justification>
  </clause>

  <clause id="10315">
    <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(1316(a,1),9042(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1316 9042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10316">
    <literal><![CDATA[
      (x * K(y,T(z,u))) * K(z,z \ u) = (x / T(u / (u / z),y)) * z
    ]]></literal>
    <justification jstring="[para(8162(a,1),9072(a,1,1,2))].">
      <j1 rule="para" parents="8162 9072"/>
    </justification>
  </clause>

  <clause id="10317">
    <literal><![CDATA[
      x * (K(y,y \ z) * K(u,T(y,z))) = (x / T(z / (z / y),u)) * y
    ]]></literal>
    <justification jstring="[hyper(10232,a,10316,a)].">
      <j1 rule="hyper" parents="10232 10316"/>
    </justification>
  </clause>

  <clause id="10318">
    <literal><![CDATA[
      (x / T(y / (y / z),u)) * z = x * (T(y / (y / z),u) \ z)
    ]]></literal>
    <justification jstring="[para(8186(a,1),10317(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8186 10317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10319">
    <literal><![CDATA[
      (x / T(1 / (1 / y),z)) * y = x * (y * (1 / T(y,z)))
    ]]></literal>
    <justification jstring="[para(6634(a,1),10318(a,2,2))].">
      <j1 rule="para" parents="6634 10318"/>
    </justification>
  </clause>

  <clause id="10320">
    <literal><![CDATA[
      K((x / y) / (y \ 1),1 / y) = K((y \ x) / (y \ 1),1 / y)
    ]]></literal>
    <justification jstring="[para(7365(a,1),9078(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7365 9078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10321">
    <literal><![CDATA[
      K((x / y) / (y \ 1),1 / y) = K((y \ x) / (1 / y),1 / y)
    ]]></literal>
    <justification jstring="[hyper(299,a,5602,a,b,10320,a),flip(a)].">
      <j1 rule="hyper" parents="299 5602 10320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10322">
    <literal><![CDATA[
      K((x / y) / (1 / y),1 / y) = K((y \ x) / (1 / y),1 / y)
    ]]></literal>
    <justification jstring="[hyper(65,a,5602,a,b,10321,a)].">
      <j1 rule="hyper" parents="65 5602 10321"/>
    </justification>
  </clause>

  <clause id="10323">
    <literal><![CDATA[
      (x / y) / ((x / y) / (1 / y)) = (1 / y) * K((y \ x) / (1 / y),1 / y)
    ]]></literal>
    <justification jstring="[para(10322(a,1),5124(a,2,2))].">
      <j1 rule="para" parents="10322 5124"/>
    </justification>
  </clause>

  <clause id="10324">
    <literal><![CDATA[
      (x * (y * ((z \ (y \ (x \ u))) * z))) \ u = K(z,(x * (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(107(a,1),9124(a,1,1,2,2))].">
      <j1 rule="para" parents="107 9124"/>
    </justification>
  </clause>

  <clause id="10325">
    <literal><![CDATA[
      ((x * y) * ((z \ ((x * y) \ u)) * z)) \ u = K(z,(x * (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(3936(a,2),10324(a,1,1))].">
      <j1 rule="para" parents="3936 10324"/>
    </justification>
  </clause>

  <clause id="10326">
    <literal><![CDATA[
      K(x,(y * (z * x)) \ u) = K(x,(y * z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(8440,a,10325,a),flip(a)].">
      <j1 rule="hyper" parents="8440 10325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10327">
    <literal><![CDATA[
      K(x,(y * (z * x)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * z) \ (x \ u)) = w
    ]]></literal>
    <justification jstring="[para(10325(a,1),8440(a,1))].">
      <j1 rule="para" parents="10325 8440"/>
    </justification>
  </clause>

  <clause id="10328">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ (x \ u)) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[para(12(a,1),10326(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="12 10326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10329">
    <literal><![CDATA[
      (x * K(y,(z * u) \ (y \ w))) \ x = K((z * (u * y)) \ w,y)
    ]]></literal>
    <justification jstring="[para(10326(a,1),7200(a,1,1,2))].">
      <j1 rule="para" parents="10326 7200"/>
    </justification>
  </clause>

  <clause id="10330">
    <literal><![CDATA[
      K(x,(y * (x \ z)) \ (x \ u)) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,8859,a(flip),b,10328,a)].">
      <j1 rule="hyper" parents="65 8859 10328"/>
    </justification>
  </clause>

  <clause id="10331">
    <literal><![CDATA[
      K(x,(y * (x \ 1)) \ (x \ z)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(8(a,1),10330(a,2,2,1))].">
      <j1 rule="para" parents="8 10330"/>
    </justification>
  </clause>

  <clause id="10332">
    <literal><![CDATA[
      K(x,((x \ 1) * y) \ (x \ z)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,9840,a,b,10331,a)].">
      <j1 rule="hyper" parents="65 9840 10331"/>
    </justification>
  </clause>

  <clause id="10333">
    <literal><![CDATA[
      K(x,L(y,x \ 1,x) \ z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,7887,a(flip),b,10332,a)].">
      <j1 rule="hyper" parents="65 7887 10332"/>
    </justification>
  </clause>

  <clause id="10334">
    <literal><![CDATA[
      K((x * (y * z)) \ u,z) = K((x * y) \ (z \ u),z)
    ]]></literal>
    <justification jstring="[hyper(7209,a,10329,a),flip(a)].">
      <j1 rule="hyper" parents="7209 10329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10335">
    <literal><![CDATA[
      K((x * (y * z)) \ u,z) != w
    ]]></literal>
    <literal><![CDATA[
      K((x * y) \ (z \ u),z) = w
    ]]></literal>
    <justification jstring="[para(10329(a,1),7209(a,1))].">
      <j1 rule="para" parents="10329 7209"/>
    </justification>
  </clause>

  <clause id="10336">
    <literal><![CDATA[
      K((x * (y * z)) \ u,y) = K((x * z) \ (y \ u),y)
    ]]></literal>
    <justification jstring="[hyper(65,a,9415,a(flip),b,10334,a)].">
      <j1 rule="hyper" parents="65 9415 10334"/>
    </justification>
  </clause>

  <clause id="10337">
    <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(10334(a,1),5827(a,1,1,1,2))].">
      <j1 rule="para" parents="10334 5827"/>
    </justification>
  </clause>

  <clause id="10338">
    <literal><![CDATA[
      K((x * y) \ ((1 / y) \ z),1 / y) = K(x \ z,1 / y)
    ]]></literal>
    <justification jstring="[para(78(a,1),10336(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="78 10336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10339">
    <literal><![CDATA[
      1 / (x \ K((y * z) \ (x \ u),x)) = T(x,(y * (x * z)) \ u)
    ]]></literal>
    <justification jstring="[para(10336(a,1),5119(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10336 5119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10340">
    <literal><![CDATA[
      K((x * (y \ z)) \ ((1 / (y \ z)) \ u),1 / (y \ z)) = K(x \ u,z \ y)
    ]]></literal>
    <justification jstring="[hyper(299,a,6840,a(flip),b,10338,a),flip(a)].">
      <j1 rule="hyper" parents="299 6840 10338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10341">
    <literal><![CDATA[
      K((x * (y * z)) \ u,y) != w
    ]]></literal>
    <literal><![CDATA[
      K((x * z) \ (y \ u),y) = w
    ]]></literal>
    <justification jstring="[para(9415(a,1),10335(a,1))].">
      <j1 rule="para" parents="9415 10335"/>
    </justification>
  </clause>

  <clause id="10342">
    <literal><![CDATA[
      T(x,(y * (x * z)) \ u) = T(x,(y * z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(5226,a,10339,a),flip(a)].">
      <j1 rule="hyper" parents="5226 10339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10343">
    <literal><![CDATA[
      T(x,(y * (z * x)) \ u) = T(x,(y * z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,9419,a,b,10342,a)].">
      <j1 rule="hyper" parents="65 9419 10342"/>
    </justification>
  </clause>

  <clause id="10344">
    <literal><![CDATA[
      L(x,y * (K(z,u) / T(u,w)),v5) = L(x,y * (T(u,z) \ K(w,u)),v5)
    ]]></literal>
    <justification jstring="[para(6446(a,1),9176(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6446 9176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10345">
    <literal><![CDATA[
      K(x,x \ y) * K((x \ y) \ 1,y / x) = (y / x) * (1 / (x \ y))
    ]]></literal>
    <justification jstring="[para(5267(a,1),9180(a,1,1))].">
      <j1 rule="para" parents="5267 9180"/>
    </justification>
  </clause>

  <clause id="10346">
    <literal><![CDATA[
      x \ (K(y,z) * (K(u,y) * x)) = T(K(u,y),x) * T(K(y,z),x)
    ]]></literal>
    <justification jstring="[para(8667(a,1),9235(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8667 9235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10348">
    <literal><![CDATA[
      T(K(x,y),z) * T(K(y,u),z) != w
    ]]></literal>
    <literal><![CDATA[
      T(K(y,u) * K(x,y),z) = w
    ]]></literal>
    <justification jstring="[para(10346(a,1),10020(a,1))].">
      <j1 rule="para" parents="10346 10020"/>
    </justification>
  </clause>

  <clause id="10349">
    <literal><![CDATA[
      (x * T(y,L(z,y,x))) \ (x * (y * (z * K(y,z)))) = L(z,y,x)
    ]]></literal>
    <justification jstring="[para(5142(a,1),9311(a,1,1,2))].">
      <j1 rule="para" parents="5142 9311"/>
    </justification>
  </clause>

  <clause id="10350">
    <literal><![CDATA[
      (x * T(y,L(z,y,x))) \ (x * (T(y,z) * z)) = L(z,y,x)
    ]]></literal>
    <justification jstring="[para(5115(a,1),10349(a,1,2,2))].">
      <j1 rule="para" parents="5115 10349"/>
    </justification>
  </clause>

  <clause id="10351">
    <literal><![CDATA[
      T(x * (y / z),K(y,z)) \ ((x * (z \ y)) * K(z,z \ y)) = K(x * (z \ y),K(z,z \ y))
    ]]></literal>
    <justification jstring="[para(6970(a,2),9343(a,1,2))].">
      <j1 rule="para" parents="6970 9343"/>
    </justification>
  </clause>

  <clause id="10352">
    <literal><![CDATA[
      K(x,T((y \ z) / z,u)) = K(x,T(y \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,9341,a(flip),b,9344,a),flip(a)].">
      <j1 rule="hyper" parents="299 9341 9344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10353">
    <literal><![CDATA[
      K(x,T((y / z) \ 1,u)) = K(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[para(79(a,1),10352(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="79 10352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10354">
    <literal><![CDATA[
      ((x * y) / x) / ((x * (y * K(z,T(y,u)))) / x) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,T(T(z,x),u)) = w
    ]]></literal>
    <justification jstring="[para(9345(a,1),10292(a,1))].">
      <j1 rule="para" parents="9345 10292"/>
    </justification>
  </clause>

  <clause id="10355">
    <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="[hyper(9392,a,9160,a),flip(a)].">
      <j1 rule="hyper" parents="9392 9160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10356">
    <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(6387(a,1),10355(a,1,1))].">
      <j1 rule="para" parents="6387 10355"/>
    </justification>
  </clause>

  <clause id="10357">
    <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(299,a,9098,a(flip),b,10356,a),flip(a)].">
      <j1 rule="hyper" parents="299 9098 10356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10358">
    <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(8068,a,10357,a)].">
      <j1 rule="hyper" parents="8068 10357"/>
    </justification>
  </clause>

  <clause id="10359">
    <literal><![CDATA[
      K((x * (y * z)) \ (x * ((z * u) * y)),y) = K(L(u,y * z,x),y)
    ]]></literal>
    <justification jstring="[hyper(299,a,7826,a(flip),b,9421,a),flip(a)].">
      <j1 rule="hyper" parents="299 7826 9421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10360">
    <literal><![CDATA[
      K((x * y) \ (z \ (x * ((y * u) * z))),z) = K(L(u,z * y,x),z)
    ]]></literal>
    <justification jstring="[hyper(10341,a,10359,a)].">
      <j1 rule="hyper" parents="10341 10359"/>
    </justification>
  </clause>

  <clause id="10362">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,T(y \ x,u)) = K((x \ y) \ z,T(y \ x,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,9430,a(flip),b,9432,a)].">
      <j1 rule="hyper" parents="65 9430 9432"/>
    </justification>
  </clause>

  <clause id="10363">
    <literal><![CDATA[
      (K(x,y) * T(z,u)) / K(x,T(y,z)) = (z * (K(x,y) * K(z,u))) * K(y,x)
    ]]></literal>
    <justification jstring="[para(7489(a,2),9473(a,1,2))].">
      <j1 rule="para" parents="7489 9473"/>
    </justification>
  </clause>

  <clause id="10364">
    <literal><![CDATA[
      T(T(x * K(y,x),z),u * (x * K(y,x))) != T(w,z)
    ]]></literal>
    <literal><![CDATA[
      T(x * K(y,x),u * x) = w
    ]]></literal>
    <justification jstring="[para(9567(a,2),51(a,1))].">
      <j1 rule="para" parents="9567 51"/>
    </justification>
  </clause>

  <clause id="10365">
    <literal><![CDATA[
      (x * y) \ (y * T(T(z * x,z) / z,y)) = L(a(z,T(x,y),z),T(x,y),y)
    ]]></literal>
    <justification jstring="[para(1633(a,1),9696(a,1,2,2))].">
      <j1 rule="para" parents="1633 9696"/>
    </justification>
  </clause>

  <clause id="10366">
    <literal><![CDATA[
      ((x * y) * a(y,z,y)) \ ((y * x) * y) = L(T(y,x),z,T(y,x))
    ]]></literal>
    <justification jstring="[para(9729(a,1),9717(a,1,1,2))].">
      <j1 rule="para" parents="9729 9717"/>
    </justification>
  </clause>

  <clause id="10368">
    <literal><![CDATA[
      (x \ y) / ((((x \ y) \ y) \ y) / x) = (y / x) / ((x \ y) / x)
    ]]></literal>
    <justification jstring="[para(10(a,1),9768(a,2,1,1))].">
      <j1 rule="para" parents="10 9768"/>
    </justification>
  </clause>

  <clause id="10369">
    <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),9922(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 9922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10370">
    <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),9923(a,1,1,2,1))].">
      <j1 rule="para" parents="9 9923"/>
    </justification>
  </clause>

  <clause id="10371">
    <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(7431(a,1),10061(a,1,1))].">
      <j1 rule="para" parents="7431 10061"/>
    </justification>
  </clause>

  <clause id="10373">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * (x \ z)) \ u) = w
    ]]></literal>
    <justification jstring="[para(8985(a,1),10255(a,1))].">
      <j1 rule="para" parents="8985 10255"/>
    </justification>
  </clause>

  <clause id="10374">
    <literal><![CDATA[
      K(x,(y * (x \ z)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * (z / x)) \ u) = w
    ]]></literal>
    <justification jstring="[para(8984(a,1),10256(a,1))].">
      <j1 rule="para" parents="8984 10256"/>
    </justification>
  </clause>

  <clause id="10375">
    <literal><![CDATA[
      T(x,y) / ((1 / z) \ x) = K(((((z \ 1) \ x) \ 1) * z) \ 1,y) / z
    ]]></literal>
    <justification jstring="[hyper(299,a,9082,a(flip),b,10301,a),flip(a)].">
      <j1 rule="hyper" parents="299 9082 10301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10376">
    <literal><![CDATA[
      K(x / y,z) * K(K(y \ x,z) * x,x) = K(x / T(y,x),z)
    ]]></literal>
    <justification jstring="[para(9739(a,1),10309(a,2,1))].">
      <j1 rule="para" parents="9739 10309"/>
    </justification>
  </clause>

  <clause id="10377">
    <literal><![CDATA[
      K(x / y,z) * K(x * K(y \ x,z),x) = K(x / T(y,x),z)
    ]]></literal>
    <justification jstring="[para(5980(a,1),10376(a,1,2))].">
      <j1 rule="para" parents="5980 10376"/>
    </justification>
  </clause>

  <clause id="10378">
    <literal><![CDATA[
      T(x * K(x / y,z),x) = x * K(x / T(y,x),z)
    ]]></literal>
    <justification jstring="[para(10377(a,1),7300(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10377 7300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10380">
    <literal><![CDATA[
      T(x * K(x / y,z),x) = x * K(T(x,y) / y,z)
    ]]></literal>
    <justification jstring="[para(4382(a,2),10378(a,2,2,1))].">
      <j1 rule="para" parents="4382 10378"/>
    </justification>
  </clause>

  <clause id="10381">
    <literal><![CDATA[
      K(T(x,y) / y,z) = K(x / T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(36,a,10378,a(flip),b,10380,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="36 10378 10380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10382">
    <literal><![CDATA[
      K(T(x * K(y,x),z) / z,u) = K(((y * x) / y) / T(z,(y * x) / y),u)
    ]]></literal>
    <justification jstring="[para(5469(a,1),10381(a,1,1,1))].">
      <j1 rule="para" parents="5469 10381"/>
    </justification>
  </clause>

  <clause id="10383">
    <literal><![CDATA[
      K(x,x \ y) * T(x,T(z,y)) = T((x \ y) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(146,a,10310,a(flip))].">
      <j1 rule="hyper" parents="146 10310"/>
    </justification>
  </clause>

  <clause id="10384">
    <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(65,a,7775,a,b,10315,a)].">
      <j1 rule="hyper" parents="65 7775 10315"/>
    </justification>
  </clause>

  <clause id="10385">
    <literal><![CDATA[
      (x / y) / ((x / y) / (1 / y)) = (1 / y) * K((y \ x) * y,1 / y)
    ]]></literal>
    <justification jstring="[para(6185(a,1),10323(a,2,2))].">
      <j1 rule="para" parents="6185 10323"/>
    </justification>
  </clause>

  <clause id="10386">
    <literal><![CDATA[
      (x / y) / ((x / y) / (1 / y)) = (1 / y) * K(x,1 / y)
    ]]></literal>
    <justification jstring="[para(6196(a,1),10385(a,2,2))].">
      <j1 rule="para" parents="6196 10385"/>
    </justification>
  </clause>

  <clause id="10387">
    <literal><![CDATA[
      (x / y) / ((x / y) / (1 / y)) = K(x,1 / y) / y
    ]]></literal>
    <justification jstring="[hyper(299,a,2406,a(flip),b,10386,a),flip(a)].">
      <j1 rule="hyper" parents="299 2406 10386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10388">
    <literal><![CDATA[
      x / ((y / (x \ y)) / (1 / (x \ y))) = K(y,1 / (x \ y)) / (x \ y)
    ]]></literal>
    <justification jstring="[para(76(a,1),10387(a,1,1))].">
      <j1 rule="para" parents="76 10387"/>
    </justification>
  </clause>

  <clause id="10389">
    <literal><![CDATA[
      K(x,1 / (y \ x)) / (y \ x) = y / (y / (1 / (y \ x)))
    ]]></literal>
    <justification jstring="[para(76(a,1),10388(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="76 10388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10391">
    <literal><![CDATA[
      K(x,y / x) / (y \ x) = y / (y / (1 / (y \ x)))
    ]]></literal>
    <justification jstring="[para(5540(a,1),10389(a,1,1))].">
      <j1 rule="para" parents="5540 10389"/>
    </justification>
  </clause>

  <clause id="10392">
    <literal><![CDATA[
      T((x / (1 / (x \ y))) / x,K(y,x / y) / (x \ y)) = (((x / (1 / (x \ y))) / x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(10391(a,2),2620(a,1,2))].">
      <j1 rule="para" parents="10391 2620"/>
    </justification>
  </clause>

  <clause id="10393">
    <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),10340(a,2,2))].">
      <j1 rule="para" parents="9 10340"/>
    </justification>
  </clause>

  <clause id="10394">
    <literal><![CDATA[
      (x * (K(y,z) * K(x,u))) * K(z,y) = (K(y,z) * T(x,u)) * K(z,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(7586,a,10363,a),flip(a)].">
      <j1 rule="hyper" parents="7586 10363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10395">
    <literal><![CDATA[
      L(a(x,T(y,z),x),T(y,z),z) = (y * z) \ ((T(x * y,x) / x) * z)
    ]]></literal>
    <justification jstring="[para(107(a,1),10365(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 10365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10396">
    <literal><![CDATA[
      L(a(x,T(y,z),x),T(y,z),z) = R(a(x,y,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,10165,a(flip),b,10395,a),flip(a)].">
      <j1 rule="hyper" parents="299 10165 10395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10397">
    <literal><![CDATA[
      R(a(x,y * K(z,y),x),y * K(z,y),z) = L(a(x,y,x),T(y * K(z,y),z),z)
    ]]></literal>
    <justification jstring="[para(5053(a,1),10396(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5053 10396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10398">
    <literal><![CDATA[
      K(T(x * K(y,x),z) / z,u) = K(((y * x) / y) / T(z,T(x,y)),u)
    ]]></literal>
    <justification jstring="[para(8182(a,1),10382(a,2,1,2))].">
      <j1 rule="para" parents="8182 10382"/>
    </justification>
  </clause>

  <clause id="10399">
    <literal><![CDATA[
      (x / y) \ (L(y,z,u) * (y \ x)) = x \ ((L(y,z,u) * (y \ x)) * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,7748,a(flip),b,10384,a)].">
      <j1 rule="hyper" parents="65 7748 10384"/>
    </justification>
  </clause>

  <clause id="10400">
    <literal><![CDATA[
      (x * (K(y,z) * K(x,u))) * K(z,y) = K(y,z) * (T(x,u) * K(z,T(y,x)))
    ]]></literal>
    <justification jstring="[hyper(299,a,7897,a(flip),b,10394,a),flip(a)].">
      <j1 rule="hyper" parents="299 7897 10394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10401">
    <literal><![CDATA[
      (x * (K(y,z) * K(x,u))) * K(z,y) = K(y,z) * (K(x,u) * (K(z,y) * x))
    ]]></literal>
    <justification jstring="[para(7517(a,2),10400(a,2,2))].">
      <j1 rule="para" parents="7517 10400"/>
    </justification>
  </clause>

  <clause id="10402">
    <literal><![CDATA[
      K(x,y) * (K(z,u) * (K(y,x) * z)) = T(z,T(u,K(x,y)))
    ]]></literal>
    <justification jstring="[hyper(8284,a,10401,a),flip(a)].">
      <j1 rule="hyper" parents="8284 10401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10403">
    <literal><![CDATA[
      K(x,y) * (K(K(x,y) * z,u) * z) = T(K(x,y) * z,T(u,K(x,y)))
    ]]></literal>
    <justification jstring="[para(5432(a,1),10402(a,1,2,2))].">
      <j1 rule="para" parents="5432 10402"/>
    </justification>
  </clause>

  <clause id="10404">
    <literal><![CDATA[
      L(x \ 1,x,y) * ((x \ 1) \ (y * x)) = y / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,6164,a(flip),b,7066,a),flip(a)].">
      <j1 rule="hyper" parents="299 6164 7066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10405">
    <literal><![CDATA[
      L(x,x,y) * (x \ (y * x)) = y / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,6643,a(flip),b,10404,a)].">
      <j1 rule="hyper" parents="65 6643 10404"/>
    </justification>
  </clause>

  <clause id="10406">
    <literal><![CDATA[
      L(x,x,y) * T(y,x) = y / (x \ 1)
    ]]></literal>
    <justification jstring="[para(22(a,2),10405(a,1,2))].">
      <j1 rule="para" parents="22 10405"/>
    </justification>
  </clause>

  <clause id="10407">
    <literal><![CDATA[
      L(x,x,y) = y \ (y / (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(119,a,10406,a(flip),b,7104,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 10406 7104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10408">
    <literal><![CDATA[
      (x * (1 / y)) \ x = x \ (x / (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(2527,a,10407,a)].">
      <j1 rule="hyper" parents="2527 10407"/>
    </justification>
  </clause>

  <clause id="10409">
    <literal><![CDATA[
      x \ (x / ((y \ 1) \ 1)) = (x * y) \ x
    ]]></literal>
    <justification jstring="[para(76(a,1),10408(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="76 10408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10410">
    <literal><![CDATA[
      ((x \ (x / y)) \ 1) \ 1 = (x * y) \ x
    ]]></literal>
    <justification jstring="[hyper(3007,a,10409,a)].">
      <j1 rule="hyper" parents="3007 10409"/>
    </justification>
  </clause>

  <clause id="10411">
    <literal><![CDATA[
      (x * (y \ 1)) \ x = x \ (x / (1 / y))
    ]]></literal>
    <justification jstring="[para(1689(a,1),10409(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1689 10409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10412">
    <literal><![CDATA[
      1 / ((x * y) \ x) = (x \ (x / y)) \ 1
    ]]></literal>
    <justification jstring="[para(10409(a,1),3005(a,1,2))].">
      <j1 rule="para" parents="10409 3005"/>
    </justification>
  </clause>

  <clause id="10413">
    <literal><![CDATA[
      ((x * y) * (y \ 1)) \ (x * y) = (x * y) \ (x * (y * y))
    ]]></literal>
    <justification jstring="[para(672(a,1),10411(a,2,2))].">
      <j1 rule="para" parents="672 10411"/>
    </justification>
  </clause>

  <clause id="10414">
    <literal><![CDATA[
      L(1 / x,x,y) = y \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(4146,a,10412,a(flip))].">
      <j1 rule="hyper" parents="4146 10412"/>
    </justification>
  </clause>

  <clause id="10415">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) \ 1 = x \ (x / y)
    ]]></literal>
    <justification jstring="[hyper(1693,a,10412,a(flip))].">
      <j1 rule="hyper" parents="1693 10412"/>
    </justification>
  </clause>

  <clause id="10416">
    <literal><![CDATA[
      x * L(1 / y,y,x) = x / y
    ]]></literal>
    <justification jstring="[hyper(144,a,10414,a(flip))].">
      <j1 rule="hyper" parents="144 10414"/>
    </justification>
  </clause>

  <clause id="10417">
    <literal><![CDATA[
      T(x \ (x / y),y) != z
    ]]></literal>
    <literal><![CDATA[
      L(y \ 1,y,x) = z
    ]]></literal>
    <justification jstring="[para(10414(a,1),966(a,1,1))].">
      <j1 rule="para" parents="10414 966"/>
    </justification>
  </clause>

  <clause id="10418">
    <literal><![CDATA[
      x * (((y \ x) \ 1) \ 1) = x / (x \ y)
    ]]></literal>
    <justification jstring="[para(4151(a,1),10416(a,1,2))].">
      <j1 rule="para" parents="4151 10416"/>
    </justification>
  </clause>

  <clause id="10419">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) \ (1 * L(1 \ (((x * y) \ x) \ 1),z,u)) = (x \ (x / y)) \ L((((x * y) \ x) \ 1) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(10415(a,1),6505(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10415 6505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10420">
    <literal><![CDATA[
      x * T(y \ x,x \ y) = x / (x \ y)
    ]]></literal>
    <justification jstring="[para(2995(a,2),10418(a,1,2))].">
      <j1 rule="para" parents="2995 10418"/>
    </justification>
  </clause>

  <clause id="10421">
    <literal><![CDATA[
      (x * y) \ (x * (y * y)) = R(x,y,y) \ (x * y)
    ]]></literal>
    <justification jstring="[para(1246(a,1),10413(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1246 10413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10422">
    <literal><![CDATA[
      R(x,y,y) \ (x * y) = L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(493,a,10421,a),flip(a)].">
      <j1 rule="hyper" parents="493 10421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10424">
    <literal><![CDATA[
      x * (K(y,z) * L(T(y,x),u,w)) = L(y,u,w) * (x * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(7167,a,8569,a)].">
      <j1 rule="hyper" parents="7167 8569"/>
    </justification>
  </clause>

  <clause id="10425">
    <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="[para(10424(a,1),480(a,1,2))].">
      <j1 rule="para" parents="10424 480"/>
    </justification>
  </clause>

  <clause id="10426">
    <literal><![CDATA[
      T((x * K(y,z)) / (x / T(z,y)),x * K(y,z)) = L(z,T(x / T(z,y),z),z)
    ]]></literal>
    <justification jstring="[para(7231(a,2),7255(a,2,2))].">
      <j1 rule="para" parents="7231 7255"/>
    </justification>
  </clause>

  <clause id="10427">
    <literal><![CDATA[
      T(T(x,y),z) \ (K(x,y) * u) = T(x,T(z,y)) \ u
    ]]></literal>
    <justification jstring="[hyper(7638,a,7728,a)].">
      <j1 rule="hyper" parents="7638 7728"/>
    </justification>
  </clause>

  <clause id="10429">
    <literal><![CDATA[
      K((x \ y) \ z,L(x,u,w)) = K(y \ (x * z),L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(5830,a,7867,a),flip(a)].">
      <j1 rule="hyper" parents="5830 7867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10431">
    <literal><![CDATA[
      K((x * y) \ z,L(y,u,w)) = K(x \ (y \ z),L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(5830,a,7891,a),flip(a)].">
      <j1 rule="hyper" parents="5830 7891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10432">
    <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(8458,a,8650,a)].">
      <j1 rule="hyper" parents="8458 8650"/>
    </justification>
  </clause>

  <clause id="10434">
    <literal><![CDATA[
      R(x,T(y,T(x,z)),R(x,u,w)) = R(x,y,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,5673,a(flip),b,10432,a),flip(a)].">
      <j1 rule="hyper" parents="65 5673 10432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10435">
    <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(8179(a,1),10434(a,1,2))].">
      <j1 rule="para" parents="8179 10434"/>
    </justification>
  </clause>

  <clause id="10436">
    <literal><![CDATA[
      K(x \ (y / z),L(z,u,w)) = K(x \ (z \ y),L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(5830,a,8760,a),flip(a)].">
      <j1 rule="hyper" parents="5830 8760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10437">
    <literal><![CDATA[
      K(L(x,y,z),u * (K(x,w) * v5)) = K(L(x,y,z),u * v5)
    ]]></literal>
    <justification jstring="[hyper(299,a,5829,a(flip),b,9113,a),flip(a)].">
      <j1 rule="hyper" parents="299 5829 9113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10438">
    <literal><![CDATA[
      K(x * (K(y,z) * u),R(y,w,v5)) = K(x * u,R(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(299,a,5831,a(flip),b,9114,a),flip(a)].">
      <j1 rule="hyper" parents="299 5831 9114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10439">
    <literal><![CDATA[
      K(x * y,R(y,z,u)) = K(y * x,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(5166(a,1),10438(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5166 10438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10440">
    <literal><![CDATA[
      K(a(x,y,z),T(x,u)) = K(a(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(7795,a,9594,a)].">
      <j1 rule="hyper" parents="7795 9594"/>
    </justification>
  </clause>

  <clause id="10441">
    <literal><![CDATA[
      L(a(x,y,x),K(x,x * y),z) = K(x,y) * K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(9704,a,9250,a)].">
      <j1 rule="hyper" parents="9704 9250"/>
    </justification>
  </clause>

  <clause id="10442">
    <literal><![CDATA[
      L(a(x,y,x),K(x,x * y),z) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,9673,a(flip),b,10441,a),flip(a)].">
      <j1 rule="hyper" parents="299 9673 10441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10443">
    <literal><![CDATA[
      (x / (K(y,y * z) * a(y,z,y))) * K(y,y * z) = x / a(y,z,y)
    ]]></literal>
    <justification jstring="[para(10442(a,1),349(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10442 349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10444">
    <literal><![CDATA[
      (x / (K(y,y * z) * a(y,z,y))) * K(y,y * z) = a(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(299,a,10121,a(flip),b,10443,a),flip(a)].">
      <j1 rule="hyper" parents="299 10121 10443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10445">
    <literal><![CDATA[
      (x / K(y,z)) * K(y,y * z) = a(y,z,y) \ x
    ]]></literal>
    <justification jstring="[para(9685(a,1),10444(a,1,1,2))].">
      <j1 rule="para" parents="9685 10444"/>
    </justification>
  </clause>

  <clause id="10446">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,z * y) = a(z,y,z) \ x
    ]]></literal>
    <justification jstring="[para(7196(a,1),10445(a,1,1))].">
      <j1 rule="para" parents="7196 10445"/>
    </justification>
  </clause>

  <clause id="10447">
    <literal><![CDATA[
      (x / R(y,z,y)) * y = a(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(65,a,9026,a(flip),b,10446,a)].">
      <j1 rule="hyper" parents="65 9026 10446"/>
    </justification>
  </clause>

  <clause id="10448">
    <literal><![CDATA[
      x * (y \ L(y,z,y)) = a(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(65,a,9254,a(flip),b,10447,a)].">
      <j1 rule="hyper" parents="65 9254 10447"/>
    </justification>
  </clause>

  <clause id="10449">
    <literal><![CDATA[
      (a(x,y,x) * (z * x)) / R(x,y,x) = z
    ]]></literal>
    <justification jstring="[hyper(37,a,9,a(flip),b,10447,a),flip(a)].">
      <j1 rule="hyper" parents="37 9 10447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10450">
    <literal><![CDATA[
      x * (y \ L(y,z,y)) = x / a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,10121,a,b,10448,a),flip(a)].">
      <j1 rule="hyper" parents="299 10121 10448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10451">
    <literal><![CDATA[
      a(x,y,x) \ K(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ L(T(x,z),y,x) = u
    ]]></literal>
    <justification jstring="[para(10448(a,1),7923(a,1))].">
      <j1 rule="para" parents="10448 7923"/>
    </justification>
  </clause>

  <clause id="10452">
    <literal><![CDATA[
      a(x,y,x) * (z * x) = z * R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(143,a,10449,a),flip(a)].">
      <j1 rule="hyper" parents="143 10449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10453">
    <literal><![CDATA[
      (x * R(y,z,y)) / (x * y) = a(y,z,y)
    ]]></literal>
    <justification jstring="[para(10449(a,1),82(a,1,1,1))].">
      <j1 rule="para" parents="10449 82"/>
    </justification>
  </clause>

  <clause id="10454">
    <literal><![CDATA[
      x / (y \ L(y,z,y)) = x * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(120,a,11,a(flip),b,10450,a)].">
      <j1 rule="hyper" parents="120 11 10450"/>
    </justification>
  </clause>

  <clause id="10455">
    <literal><![CDATA[
      x * (y \ L(y,z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      a(y,z,y) \ x = u
    ]]></literal>
    <justification jstring="[para(10450(a,2),10126(a,1))].">
      <j1 rule="para" parents="10450 10126"/>
    </justification>
  </clause>

  <clause id="10456">
    <literal><![CDATA[
      (x * y) * a(y,z,y) = x * R(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(10125,a,10452,a)].">
      <j1 rule="hyper" parents="10125 10452"/>
    </justification>
  </clause>

  <clause id="10457">
    <literal><![CDATA[
      (x * R(x \ y,z,x \ y)) / y = a(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(120,a,10452,a(flip),b,155,a(flip))].">
      <j1 rule="hyper" parents="120 10452 155"/>
    </justification>
  </clause>

  <clause id="10458">
    <literal><![CDATA[
      (x * y) \ (x * R(y,z,y)) = a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,10452,a(flip),b,10116,a(flip))].">
      <j1 rule="hyper" parents="119 10452 10116"/>
    </justification>
  </clause>

  <clause id="10459">
    <literal><![CDATA[
      (x * R(y,z,y)) / (x * y) != u
    ]]></literal>
    <literal><![CDATA[
      a(y,z,y) = u
    ]]></literal>
    <justification jstring="[para(10452(a,1),307(a,1,1)),flip(b)].">
      <j1 rule="para" parents="10452 307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10461">
    <literal><![CDATA[
      a(x,y,x) * (z * x) != u
    ]]></literal>
    <literal><![CDATA[
      z * R(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(10453(a,1),246(a,1,1)),flip(b)].">
      <j1 rule="para" parents="10453 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10462">
    <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),10453(a,1,2))].">
      <j1 rule="para" parents="94 10453"/>
    </justification>
  </clause>

  <clause id="10464">
    <literal><![CDATA[
      x / (a(y,z,y) \ 1) = x * a(y,z,y)
    ]]></literal>
    <justification jstring="[para(10075(a,2),10454(a,1,2))].">
      <j1 rule="para" parents="10075 10454"/>
    </justification>
  </clause>

  <clause id="10465">
    <literal><![CDATA[
      (x / y) * R(y,z,y) = x * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(306,a,10456,a),flip(a)].">
      <j1 rule="hyper" parents="306 10456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10466">
    <literal><![CDATA[
      (x * (y * R(z,u,z))) / (x * (y * z)) = L(a(z,u,z),y * z,x)
    ]]></literal>
    <justification jstring="[para(10456(a,1),10129(a,1,1,2))].">
      <j1 rule="para" parents="10456 10129"/>
    </justification>
  </clause>

  <clause id="10467">
    <literal><![CDATA[
      (x * R(y,z,y)) \ ((y * x) * y) = L(T(y,x),z,T(y,x))
    ]]></literal>
    <justification jstring="[para(10456(a,1),10366(a,1,1))].">
      <j1 rule="para" parents="10456 10366"/>
    </justification>
  </clause>

  <clause id="10468">
    <literal><![CDATA[
      R(x,a(y,z,y),a(y,z,y) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(647,a,10464,a)].">
      <j1 rule="hyper" parents="647 10464"/>
    </justification>
  </clause>

  <clause id="10469">
    <literal><![CDATA[
      R(x,a(y,z,y),y \ L(y,z,y)) = x
    ]]></literal>
    <justification jstring="[para(10075(a,1),10468(a,1,3))].">
      <j1 rule="para" parents="10075 10468"/>
    </justification>
  </clause>

  <clause id="10470">
    <literal><![CDATA[
      R(x,y \ R(y,z,y),y \ L(y,z,y)) = x
    ]]></literal>
    <justification jstring="[para(9671(a,2),10469(a,1,2))].">
      <j1 rule="para" parents="9671 10469"/>
    </justification>
  </clause>

  <clause id="10471">
    <literal><![CDATA[
      R(x,y,x) * (x \ z) = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,7475,a,b,10465,a)].">
      <j1 rule="hyper" parents="65 7475 10465"/>
    </justification>
  </clause>

  <clause id="10472">
    <literal><![CDATA[
      (x / y) * ((y \ z) \ T(z,y)) = x * a(y,y \ z,y)
    ]]></literal>
    <justification jstring="[para(4343(a,1),10465(a,1,2))].">
      <j1 rule="para" parents="4343 10465"/>
    </justification>
  </clause>

  <clause id="10473">
    <literal><![CDATA[
      K(x,y) * ((z / y) * R(y,u,y)) = y * (L(T(y,x),u,y) \ z)
    ]]></literal>
    <justification jstring="[para(10465(a,2),9728(a,1,2))].">
      <j1 rule="para" parents="10465 9728"/>
    </justification>
  </clause>

  <clause id="10474">
    <literal><![CDATA[
      (x * y) * a(x,z,x) = R(x,z,x) * y
    ]]></literal>
    <justification jstring="[para(9(a,1),10471(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 10471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10475">
    <literal><![CDATA[
      x * (y * a(x,z,x)) = R(x,z,x) * y
    ]]></literal>
    <justification jstring="[para(10471(a,1),1955(a,1,2))].">
      <j1 rule="para" parents="10471 1955"/>
    </justification>
  </clause>

  <clause id="10476">
    <literal><![CDATA[
      a(x,y,x) * (x * z) = R(x,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(10134,a,10474,a)].">
      <j1 rule="hyper" parents="10134 10474"/>
    </justification>
  </clause>

  <clause id="10477">
    <literal><![CDATA[
      (x * y) \ (R(x,z,x) * y) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,z,x) = u
    ]]></literal>
    <justification jstring="[para(10474(a,1),314(a,1,2))].">
      <j1 rule="para" parents="10474 314"/>
    </justification>
  </clause>

  <clause id="10478">
    <literal><![CDATA[
      (R(x,y,x) \ z) * a(x,y,x) = x \ z
    ]]></literal>
    <justification jstring="[hyper(119,a,10,a(flip),b,10475,a),flip(a)].">
      <j1 rule="hyper" parents="119 10 10475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10479">
    <literal><![CDATA[
      (x * y) \ (R(x,z,x) * y) = L(a(x,z,x),y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,10475,a(flip),b,94,a)].">
      <j1 rule="hyper" parents="119 10475 94"/>
    </justification>
  </clause>

  <clause id="10481">
    <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(10476(a,1),549(a,1,1,1))].">
      <j1 rule="para" parents="10476 549"/>
    </justification>
  </clause>

  <clause id="10484">
    <literal><![CDATA[
      L(a(x,y,x),z,x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(10477,a,10479,a),flip(a)].">
      <j1 rule="hyper" parents="10477 10479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10485">
    <literal><![CDATA[
      L(a(x,y,x),z,x) = (u * x) \ (u * R(x,y,x))
    ]]></literal>
    <justification jstring="[hyper(299,a,10458,a,b,10484,a),flip(a)].">
      <j1 rule="hyper" parents="299 10458 10484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10486">
    <literal><![CDATA[
      L(a(x \ y,z,x \ y),u,x \ y) = y \ (x * R(x \ y,z,x \ y))
    ]]></literal>
    <justification jstring="[hyper(299,a,157,a(flip),b,10485,a),flip(a)].">
      <j1 rule="hyper" parents="299 157 10485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10487">
    <literal><![CDATA[
      (x * R(y,z,y)) \ ((y * x) * y) = L(T(y,x),z,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,7770,a(flip),b,10467,a),flip(a)].">
      <j1 rule="hyper" parents="299 7770 10467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10489">
    <literal><![CDATA[
      L(a((x \ y) \ y,z,(x \ y) \ y),u,(x \ y) \ y) = y \ (R(x,z,(x \ y) \ y) * (x \ y))
    ]]></literal>
    <justification jstring="[para(694(a,1),10486(a,2,2))].">
      <j1 rule="para" parents="694 10486"/>
    </justification>
  </clause>

  <clause id="10490">
    <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(8275(a,1),9724(a,1,1))].">
      <j1 rule="para" parents="8275 9724"/>
    </justification>
  </clause>

  <clause id="10491">
    <literal><![CDATA[
      L(K(x,y \ ((z \ u) * x)),z \ u,z) = K((x \ 1) \ 1,(z * (L(y,x \ 1,x) / x)) \ u)
    ]]></literal>
    <justification jstring="[para(10333(a,1),9841(a,1,1))].">
      <j1 rule="para" parents="10333 9841"/>
    </justification>
  </clause>

  <clause id="10492">
    <literal><![CDATA[
      R(K(x,(T(y,z) / u) / (y / u)),y / u,u) = T(y,K(x,z)) / y
    ]]></literal>
    <justification jstring="[hyper(299,a,156,a(flip),b,9899,a),flip(a)].">
      <j1 rule="hyper" parents="299 156 9899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10493">
    <literal><![CDATA[
      R(K(x,(T(y,z) / u) / (y / u)),y / u,u) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,5076,a,b,10492,a),flip(a)].">
      <j1 rule="hyper" parents="299 5076 10492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10495">
    <literal><![CDATA[
      R(K(x,(T(y,z) / u) / (y / u)),y / u,u) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,7983,a,b,10493,a),flip(a)].">
      <j1 rule="hyper" parents="299 7983 10493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10496">
    <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(8631(a,1),9912(a,1,1,2))].">
      <j1 rule="para" parents="8631 9912"/>
    </justification>
  </clause>

  <clause id="10497">
    <literal><![CDATA[
      R(x,K(x,y) * z,R(x,u,w)) = R(x,z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,5673,a(flip),b,10496,a),flip(a)].">
      <j1 rule="hyper" parents="65 5673 10496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10499">
    <literal><![CDATA[
      K(x,(y * (x / z)) \ u) = K(x,(y * (z \ x)) \ u)
    ]]></literal>
    <justification jstring="[hyper(10257,a,9928,a),flip(a)].">
      <j1 rule="hyper" parents="10257 9928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10500">
    <literal><![CDATA[
      K(x,(y * (x / y)) \ z) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),10499(a,2,2,1))].">
      <j1 rule="para" parents="10 10499"/>
    </justification>
  </clause>

  <clause id="10501">
    <literal><![CDATA[
      K(x,(y * ((z \ x) \ x)) \ u) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[para(76(a,1),10499(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="76 10499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10502">
    <literal><![CDATA[
      K(x,x \ (x * y)) = K(x,K(z \ x,z) * y)
    ]]></literal>
    <justification jstring="[hyper(7865,a,10500,a),flip(a)].">
      <j1 rule="hyper" parents="7865 10500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10504">
    <literal><![CDATA[
      K(x,K(y \ x,y) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),10502(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 10502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10505">
    <literal><![CDATA[
      K(x,y * K(z \ x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8325,a,10504,a)].">
      <j1 rule="hyper" parents="8325 10504"/>
    </justification>
  </clause>

  <clause id="10506">
    <literal><![CDATA[
      K(x * y,K(y,x) * z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),10504(a,1,2,1,1))].">
      <j1 rule="para" parents="9 10504"/>
    </justification>
  </clause>

  <clause id="10507">
    <literal><![CDATA[
      K(x,(x / y) * z) = K(x,(y \ x) * z)
    ]]></literal>
    <justification jstring="[para(5718(a,1),10504(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5718 10504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10509">
    <literal><![CDATA[
      K(x,y * (x / z)) = K(x,y * (z \ x))
    ]]></literal>
    <justification jstring="[para(7202(a,1),10505(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7202 10505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10510">
    <literal><![CDATA[
      K(x,y \ T(z,((y \ 1) \ (y \ z)) \ x)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(7335(a,1),10505(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7335 10505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10511">
    <literal><![CDATA[
      T((K(x,y) * z) * K(y * x,z),y * x) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(10506(a,1),5053(a,1,1,2))].">
      <j1 rule="para" parents="10506 5053"/>
    </justification>
  </clause>

  <clause id="10512">
    <literal><![CDATA[
      x * K(x,y * (z \ x)) = T(x,y * (x / z))
    ]]></literal>
    <justification jstring="[para(10509(a,1),5083(a,2,2)),flip(a)].">
      <j1 rule="para" parents="10509 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10513">
    <literal><![CDATA[
      (x * K(y,z * (u \ y))) \ x = K(z * (y / u),y)
    ]]></literal>
    <justification jstring="[para(10509(a,1),7200(a,1,1,2))].">
      <j1 rule="para" parents="10509 7200"/>
    </justification>
  </clause>

  <clause id="10514">
    <literal><![CDATA[
      T(x,y * (x / z)) = T(x,y * (z \ x))
    ]]></literal>
    <justification jstring="[hyper(5087,a,10512,a),flip(a)].">
      <j1 rule="hyper" parents="5087 10512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10515">
    <literal><![CDATA[
      K(x,((y / T(z,z \ x)) * z) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(353(a,1),10501(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="353 10501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10516">
    <literal><![CDATA[
      K(x * (y / z),y) = K(x * (z \ y),y)
    ]]></literal>
    <justification jstring="[hyper(7209,a,10513,a),flip(a)].">
      <j1 rule="hyper" parents="7209 10513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10517">
    <literal><![CDATA[
      K(x,(y * K(z \ x,z)) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(7185(a,1),10515(a,1,2,1))].">
      <j1 rule="para" parents="7185 10515"/>
    </justification>
  </clause>

  <clause id="10518">
    <literal><![CDATA[
      K(x,(K(y \ x,y) * z) \ x) = K(x,z \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,8966,a,b,10517,a)].">
      <j1 rule="hyper" parents="65 8966 10517"/>
    </justification>
  </clause>

  <clause id="10519">
    <literal><![CDATA[
      K(x,((y \ x) \ x) \ z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(5047(a,1),10517(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5047 10517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10521">
    <literal><![CDATA[
      K(x,y \ (K(z,z \ x) * x)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,8413,a(flip),b,10518,a)].">
      <j1 rule="hyper" parents="65 8413 10518"/>
    </justification>
  </clause>

  <clause id="10522">
    <literal><![CDATA[
      K(x,y \ (z * (x / z))) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[para(5105(a,1),10521(a,1,2,2))].">
      <j1 rule="para" parents="5105 10521"/>
    </justification>
  </clause>

  <clause id="10523">
    <literal><![CDATA[
      K(x,y \ ((z \ x) * z)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[para(76(a,1),10522(a,1,2,2,2))].">
      <j1 rule="para" parents="76 10522"/>
    </justification>
  </clause>

  <clause id="10524">
    <literal><![CDATA[
      K(x,((y \ x) * (y / z)) \ x) != u
    ]]></literal>
    <literal><![CDATA[
      L(K(x,z),y,y \ x) = u
    ]]></literal>
    <justification jstring="[para(10523(a,1),8397(a,1))].">
      <j1 rule="para" parents="10523 8397"/>
    </justification>
  </clause>

  <clause id="10525">
    <literal><![CDATA[
      (K(x,y) * z) * T(y * x,z) = (y * x) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(10511(a,1),6920(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10511 6920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10526">
    <literal><![CDATA[
      R(x,K(y,z),u * K(z,y)) * u = (x * K(y,z)) * (K(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(8054(a,1),10274(a,1,1,3))].">
      <j1 rule="para" parents="8054 10274"/>
    </justification>
  </clause>

  <clause id="10527">
    <literal><![CDATA[
      R(x,K(y,z),u * K(z,y)) * u = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(5426(a,1),10526(a,2,2))].">
      <j1 rule="para" parents="5426 10526"/>
    </justification>
  </clause>

  <clause id="10528">
    <literal><![CDATA[
      T((x * K(y,z)) / (x / T(z,y)),x * K(y,z)) = L(z,x / T(z,y),z)
    ]]></literal>
    <justification jstring="[hyper(299,a,4592,a(flip),b,10426,a),flip(a)].">
      <j1 rule="hyper" parents="299 4592 10426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10529">
    <literal><![CDATA[
      T((x * K(y,z)) / (x / T(z,y)),x * K(y,z)) = L(z,z \ x,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,10222,a(flip),b,10528,a),flip(a)].">
      <j1 rule="hyper" parents="299 10222 10528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10531">
    <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(8100(a,1),10490(a,1,1,2,1))].">
      <j1 rule="para" parents="8100 10490"/>
    </justification>
  </clause>

  <clause id="10532">
    <literal><![CDATA[
      a(x,y * K(z,u),K(u,z)) = L(K(z,u),y,x) * K(u,z)
    ]]></literal>
    <justification jstring="[hyper(7212,a,9234,a)].">
      <j1 rule="hyper" parents="7212 9234"/>
    </justification>
  </clause>

  <clause id="10533">
    <literal><![CDATA[
      a(x,y * K(z,u),K(u,z)) = K(u,z) * L(K(z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,2280,a(flip),b,10532,a),flip(a)].">
      <j1 rule="hyper" parents="299 2280 10532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10534">
    <literal><![CDATA[
      K(x,y) * L(K(y,x),z * K(x,y),u) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(7184(a,1),10533(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7184 10533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10535">
    <literal><![CDATA[
      T(x,a(y,z,K(x,u))) = x
    ]]></literal>
    <justification jstring="[para(10534(a,1),8558(a,1,2))].">
      <j1 rule="para" parents="10534 8558"/>
    </justification>
  </clause>

  <clause id="10536">
    <literal><![CDATA[
      K(x,y) * L(K(y,x),z,u) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(9198(a,1),10534(a,1,2))].">
      <j1 rule="para" parents="9198 10534"/>
    </justification>
  </clause>

  <clause id="10537">
    <literal><![CDATA[
      K(x,y) * a(z,u,K(y,w)) = a(z,u,K(y,w)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(10535(a,1),7507(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10535 7507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10539">
    <literal><![CDATA[
      a(x,y,K(z,u)) * L(K(z,u),y,x) = K(z,u)
    ]]></literal>
    <justification jstring="[hyper(9100,a,10536,a)].">
      <j1 rule="hyper" parents="9100 10536"/>
    </justification>
  </clause>

  <clause id="10540">
    <literal><![CDATA[
      K(x,y) * a(z,u,K(y,x)) = L(K(x,y),u,z)
    ]]></literal>
    <justification jstring="[hyper(5437,a,10536,a)].">
      <j1 rule="hyper" parents="5437 10536"/>
    </justification>
  </clause>

  <clause id="10541">
    <literal><![CDATA[
      L(K(x,y),z,u) * K(y,x) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(2282,a,10536,a)].">
      <j1 rule="hyper" parents="2282 10536"/>
    </justification>
  </clause>

  <clause id="10542">
    <literal><![CDATA[
      (K(x,y) / z) * (z * K(y,x)) = a(K(x,y) / z,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(779,a,10536,a)].">
      <j1 rule="hyper" parents="779 10536"/>
    </justification>
  </clause>

  <clause id="10543">
    <literal><![CDATA[
      L(K(x,y),z,u) \ K(x,y) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,6389,a,b,10536,a)].">
      <j1 rule="hyper" parents="65 6389 10536"/>
    </justification>
  </clause>

  <clause id="10545">
    <literal><![CDATA[
      T(x,y) * L(K(y,x),z,u) = x * a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(10536(a,1),5055(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10536 5055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10546">
    <literal><![CDATA[
      K(x \ 1,y) * K(y,L(x,z,u) \ 1) = a(u,z,K(x \ 1,y))
    ]]></literal>
    <justification jstring="[para(6129(a,1),10536(a,1,2))].">
      <j1 rule="para" parents="6129 10536"/>
    </justification>
  </clause>

  <clause id="10547">
    <literal><![CDATA[
      K(1 / x,y) * K(y,1 / L(x,z,u)) = a(u,z,K(1 / x,y))
    ]]></literal>
    <justification jstring="[para(6139(a,1),10536(a,1,2))].">
      <j1 rule="para" parents="6139 10536"/>
    </justification>
  </clause>

  <clause id="10548">
    <literal><![CDATA[
      K(x,y) * (L(K(y,x),z,u) * w) = a(u,z,K(x,y)) * w
    ]]></literal>
    <justification jstring="[para(10536(a,1),6764(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10536 6764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10549">
    <literal><![CDATA[
      K(x,y) * K(L(y,z,u),x) = a(u,z * y,K(x,y))
    ]]></literal>
    <justification jstring="[para(7433(a,1),10536(a,1,2))].">
      <j1 rule="para" parents="7433 10536"/>
    </justification>
  </clause>

  <clause id="10551">
    <literal><![CDATA[
      K(x,x * y) * K(z \ ((z * y) * x),x) = a(z,y,K(x,x * y))
    ]]></literal>
    <justification jstring="[para(9540(a,1),10536(a,1,2))].">
      <j1 rule="para" parents="9540 10536"/>
    </justification>
  </clause>

  <clause id="10552">
    <literal><![CDATA[
      (x / a(y,z,K(u,w))) * K(u,w) = x * L(K(u,w),z,y)
    ]]></literal>
    <justification jstring="[para(10536(a,1),9407(a,1,1,2))].">
      <j1 rule="para" parents="10536 9407"/>
    </justification>
  </clause>

  <clause id="10553">
    <literal><![CDATA[
      (x * K(y,z)) * a(u,w,K(z,y)) = x * L(K(y,z),w,u)
    ]]></literal>
    <justification jstring="[para(10536(a,1),9929(a,1,2))].">
      <j1 rule="para" parents="10536 9929"/>
    </justification>
  </clause>

  <clause id="10554">
    <literal><![CDATA[
      (x * a(y,z,K(u,w))) * K(w,u) = x * L(K(w,u),z,y)
    ]]></literal>
    <justification jstring="[para(10536(a,1),10178(a,1,1,2))].">
      <j1 rule="para" parents="10536 10178"/>
    </justification>
  </clause>

  <clause id="10555">
    <literal><![CDATA[
      L(K(x,y),z,u) * a(u,z,K(x,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6391,a,10541,a)].">
      <j1 rule="hyper" parents="6391 10541"/>
    </justification>
  </clause>

  <clause id="10556">
    <literal><![CDATA[
      (x * y) \ ((x * (y * K(z,u))) * K(u,z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,9234,a,b,10541,a)].">
      <j1 rule="hyper" parents="65 9234 10541"/>
    </justification>
  </clause>

  <clause id="10557">
    <literal><![CDATA[
      K(L(x,y,z),u) * K(u,x) = a(z,y * x,K(u,x))
    ]]></literal>
    <justification jstring="[para(7433(a,1),10541(a,1,1))].">
      <j1 rule="para" parents="7433 10541"/>
    </justification>
  </clause>

  <clause id="10558">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(y,x) = a(u,z * y,K(y,x))
    ]]></literal>
    <justification jstring="[para(7813(a,1),10541(a,1,1))].">
      <j1 rule="para" parents="7813 10541"/>
    </justification>
  </clause>

  <clause id="10559">
    <literal><![CDATA[
      x * a(y,z,K(u,w)) != K(u,w)
    ]]></literal>
    <literal><![CDATA[
      L(K(u,w),z,y) = x
    ]]></literal>
    <justification jstring="[para(10543(a,1),136(a,1,2)),flip(b)].">
      <j1 rule="para" parents="10543 136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10560">
    <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(7427(a,1),10555(a,1,1))].">
      <j1 rule="para" parents="7427 10555"/>
    </justification>
  </clause>

  <clause id="10561">
    <literal><![CDATA[
      (x / (x / y)) * K(L(y,z,u),y \ x) = y * a(u,z * y,K(y \ x,y))
    ]]></literal>
    <justification jstring="[para(10549(a,1),5713(a,2,2))].">
      <j1 rule="para" parents="10549 5713"/>
    </justification>
  </clause>

  <clause id="10562">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (L(K(z,u),y,x) * w) = K(z,u) * w
    ]]></literal>
    <justification jstring="[para(6388(a,1),10548(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6388 10548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10564">
    <literal><![CDATA[
      (x * T(y,z)) * L(K(z,y),u,w) = (x * y) * a(w,u,K(y,z))
    ]]></literal>
    <justification jstring="[para(7194(a,1),10553(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7194 10553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10565">
    <literal><![CDATA[
      x / a(y,z,K(u,w)) = x * a(y,z,K(w,u))
    ]]></literal>
    <justification jstring="[hyper(37,a,10552,a,b,10554,a)].">
      <j1 rule="hyper" parents="37 10552 10554"/>
    </justification>
  </clause>

  <clause id="10566">
    <literal><![CDATA[
      T(x * y,z) * a(x,y,K(z,x * y)) = x * (y * K(x * y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,5151,a(flip),b,10565,a),flip(a)].">
      <j1 rule="hyper" parents="65 5151 10565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10567">
    <literal><![CDATA[
      (T(x,x \ y) * a(z,u,K(w,v5))) \ ((x \ y) \ y) = a(z,u,K(v5,w))
    ]]></literal>
    <justification jstring="[para(10565(a,1),417(a,1,1))].">
      <j1 rule="para" parents="10565 417"/>
    </justification>
  </clause>

  <clause id="10568">
    <literal><![CDATA[
      L(K(x,y),z,u) * (K(y,x) * w) = a(u,z,K(x,y)) \ w
    ]]></literal>
    <justification jstring="[hyper(119,a,5432,a(flip),b,10562,a),flip(a)].">
      <j1 rule="hyper" parents="119 5432 10562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10569">
    <literal><![CDATA[
      K(x,y) * (L(K(y,x),z,u) * w) = a(u,z,K(y,x)) \ w
    ]]></literal>
    <justification jstring="[hyper(65,a,10371,a(flip),b,10568,a)].">
      <j1 rule="hyper" parents="65 10371 10568"/>
    </justification>
  </clause>

  <clause id="10570">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ w = a(x,y,K(u,z)) * w
    ]]></literal>
    <justification jstring="[hyper(65,a,10548,a(flip),b,10569,a),flip(a)].">
      <j1 rule="hyper" parents="65 10548 10569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10571">
    <literal><![CDATA[
      x / (a(y,z,K(u,w)) * x) = a(y,z,K(w,u))
    ]]></literal>
    <justification jstring="[hyper(577,a,10570,a)].">
      <j1 rule="hyper" parents="577 10570"/>
    </justification>
  </clause>

  <clause id="10572">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ K(w,u) = K(w,u) * a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,10537,a,b,10570,a),flip(a)].">
      <j1 rule="hyper" parents="299 10537 10570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10573">
    <literal><![CDATA[
      a(x,y,K(z,u)) * w != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(u,z)) * v5 = w
    ]]></literal>
    <justification jstring="[para(10570(a,1),144(a,1))].">
      <j1 rule="para" parents="10570 144"/>
    </justification>
  </clause>

  <clause id="10575">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ K(w,u) != K(w,u) * v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(u,z)) = v5
    ]]></literal>
    <justification jstring="[para(10572(a,2),45(a,1))].">
      <j1 rule="para" parents="10572 45"/>
    </justification>
  </clause>

  <clause id="10576">
    <literal><![CDATA[
      a(K(x,y) / z,z,K(x,y)) * (1 / (z * K(y,x))) = K(x,y) / z
    ]]></literal>
    <justification jstring="[para(10542(a,1),9981(a,1,1))].">
      <j1 rule="para" parents="10542 9981"/>
    </justification>
  </clause>

  <clause id="10577">
    <literal><![CDATA[
      ((x / y) * (y * K(z,x))) \ ((z * x) / z) = ((x / y) * y) \ (((x / y) * (y * K(x,z))) * K(z,x))
    ]]></literal>
    <justification jstring="[hyper(299,a,5251,a,b,10556,a)].">
      <j1 rule="hyper" parents="299 5251 10556"/>
    </justification>
  </clause>

  <clause id="10578">
    <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(6341(a,1),10546(a,1,1))].">
      <j1 rule="para" parents="6341 10546"/>
    </justification>
  </clause>

  <clause id="10579">
    <literal><![CDATA[
      K(1 / x,K(y,z)) * K(y,K(z,1 / L(x,u,w))) = a(w,u,K(1 / x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(7954(a,1),10547(a,1,2))].">
      <j1 rule="para" parents="7954 10547"/>
    </justification>
  </clause>

  <clause id="10580">
    <literal><![CDATA[
      x * (T(y,z) * L(K(z,y),u,w)) = (x * y) * a(w,u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,7640,a(flip),b,10564,a)].">
      <j1 rule="hyper" parents="65 7640 10564"/>
    </justification>
  </clause>

  <clause id="10581">
    <literal><![CDATA[
      (x * y) * a(z,u,K(y,w)) = x * (y * a(z,u,K(y,w)))
    ]]></literal>
    <justification jstring="[para(10545(a,1),10580(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10545 10580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10582">
    <literal><![CDATA[
      L(a(x,y,K(z,u)),z,w) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(490,a,10581,a)].">
      <j1 rule="hyper" parents="490 10581"/>
    </justification>
  </clause>

  <clause id="10583">
    <literal><![CDATA[
      a(x,y,a(z,u,K(y,w))) = 1
    ]]></literal>
    <justification jstring="[hyper(55,a,10582,a)].">
      <j1 rule="hyper" parents="55 10582"/>
    </justification>
  </clause>

  <clause id="10584">
    <literal><![CDATA[
      a(x,T(y,z),a(u,w,K(y,v5))) = 1
    ]]></literal>
    <justification jstring="[para(8106(a,1),10583(a,1,3,3))].">
      <j1 rule="para" parents="8106 10583"/>
    </justification>
  </clause>

  <clause id="10585">
    <literal><![CDATA[
      K(x,y \ ((y * z) * x)) * a(y,z,K(x,x * z)) = K(x,x * z)
    ]]></literal>
    <justification jstring="[para(10551(a,1),5457(a,1,2))].">
      <j1 rule="para" parents="10551 5457"/>
    </justification>
  </clause>

  <clause id="10586">
    <literal><![CDATA[
      a(K(x,y) / z,z,K(y,x)) * (K(x,y) / z) = 1 / (z * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(10573,a,10576,a)].">
      <j1 rule="hyper" parents="10573 10576"/>
    </justification>
  </clause>

  <clause id="10587">
    <literal><![CDATA[
      L(K(x,x * y),y,z) = K(x,z \ ((z * y) * x))
    ]]></literal>
    <justification jstring="[hyper(10559,a,10585,a)].">
      <j1 rule="hyper" parents="10559 10585"/>
    </justification>
  </clause>

  <clause id="10588">
    <literal><![CDATA[
      L(K(x,x * (y \ z)),y \ z,y) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[para(10(a,1),10587(a,2,2,2,1))].">
      <j1 rule="para" parents="10 10587"/>
    </justification>
  </clause>

  <clause id="10589">
    <literal><![CDATA[
      L(K(x,y * x),y,z) = K(x,z \ ((z * y) * x))
    ]]></literal>
    <justification jstring="[para(5685(a,2),10587(a,1,1))].">
      <j1 rule="para" parents="5685 10587"/>
    </justification>
  </clause>

  <clause id="10590">
    <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(473(a,1),10589(a,2,2))].">
      <j1 rule="para" parents="473 10589"/>
    </justification>
  </clause>

  <clause id="10591">
    <literal><![CDATA[
      L(K(L(x,y,z),y * L(x,y,z)),y,z) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(299,a,7651,a(flip),b,10590,a),flip(a)].">
      <j1 rule="hyper" parents="299 7651 10590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10593">
    <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(7633,a,10561,a)].">
      <j1 rule="hyper" parents="7633 10561"/>
    </justification>
  </clause>

  <clause id="10594">
    <literal><![CDATA[
      x / T(x / y,L(y,z,u)) = y * a(u,z * y,K(y \ x,y))
    ]]></literal>
    <justification jstring="[para(176(a,1),10593(a,1,2,2))].">
      <j1 rule="para" parents="176 10593"/>
    </justification>
  </clause>

  <clause id="10595">
    <literal><![CDATA[
      T(T(T(x,y \ x) / y,x),x / z) = K(y \ x,z \ x) * (x / y)
    ]]></literal>
    <justification jstring="[para(9459(a,1),7914(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9459 7914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10596">
    <literal><![CDATA[
      T(T(T(x,y \ x) / y,x),x / z) = T(x / y,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,7628,a(flip),b,10595,a),flip(a)].">
      <j1 rule="hyper" parents="299 7628 10595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10597">
    <literal><![CDATA[
      T(x / y,T(z \ x,y)) = T(x / y,x / z)
    ]]></literal>
    <justification jstring="[para(4281(a,1),10596(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4281 10596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10598">
    <literal><![CDATA[
      T(x / y,T(z \ (y \ x),y)) = T(x / y,x / (y * z))
    ]]></literal>
    <justification jstring="[hyper(9927,a,10597,a)].">
      <j1 rule="hyper" parents="9927 10597"/>
    </justification>
  </clause>

  <clause id="10599">
    <literal><![CDATA[
      T(T(x,K(y,z \ u)),(z \ u) \ y) = T(x,y / (((z \ 1) \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,3904,a(flip),b,9005,a)].">
      <j1 rule="hyper" parents="65 3904 9005"/>
    </justification>
  </clause>

  <clause id="10600">
    <literal><![CDATA[
      T(x,y / (((z \ 1) \ 1) \ u)) = T(x,y / (z \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,9002,a(flip),b,10599,a),flip(a)].">
      <j1 rule="hyper" parents="65 9002 10599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10601">
    <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(299,a,7637,a(flip),b,9017,a),flip(a)].">
      <j1 rule="hyper" parents="299 7637 9017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10603">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,T(y \ x,u)) = K(z * ((x \ y) \ 1),T(y \ x,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,9430,a(flip),b,9433,a),flip(a)].">
      <j1 rule="hyper" parents="65 9430 9433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10604">
    <literal><![CDATA[
      K(x * ((y \ z) \ 1),T(z \ y,u)) = K((y \ z) \ x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,10362,a(flip),b,10603,a),flip(a)].">
      <j1 rule="hyper" parents="65 10362 10603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10605">
    <literal><![CDATA[
      K(x * ((y \ z) \ 1),T(z \ y,z)) = K((y \ z) \ x,y / z)
    ]]></literal>
    <justification jstring="[hyper(299,a,8119,a(flip),b,10604,a),flip(a)].">
      <j1 rule="hyper" parents="299 8119 10604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10606">
    <literal><![CDATA[
      K(x * ((y \ z) \ 1),y / z) = K((y \ z) \ x,y / z)
    ]]></literal>
    <justification jstring="[hyper(8215,a,10605,a)].">
      <j1 rule="hyper" parents="8215 10605"/>
    </justification>
  </clause>

  <clause id="10607">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,x / y) = K((x \ y) \ z,x / y)
    ]]></literal>
    <justification jstring="[hyper(65,a,8738,a,b,10606,a)].">
      <j1 rule="hyper" parents="65 8738 10606"/>
    </justification>
  </clause>

  <clause id="10608">
    <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(1927(a,1),9662(a,1,2))].">
      <j1 rule="para" parents="1927 9662"/>
    </justification>
  </clause>

  <clause id="10609">
    <literal><![CDATA[
      x \ R(x,y,R(x,z,u)) = a(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(775,a,10608,a),flip(a)].">
      <j1 rule="hyper" parents="775 10608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10610">
    <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(10608(a,1),775(a,1))].">
      <j1 rule="para" parents="10608 775"/>
    </justification>
  </clause>

  <clause id="10611">
    <literal><![CDATA[
      K(x * R(y,z,u),y) * K(y,x) = a(y,x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(9406,a,10609,a)].">
      <j1 rule="hyper" parents="9406 10609"/>
    </justification>
  </clause>

  <clause id="10612">
    <literal><![CDATA[
      x * a(x,y,R(x,z,u)) = R(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(144,a,10609,a)].">
      <j1 rule="hyper" parents="144 10609"/>
    </justification>
  </clause>

  <clause id="10613">
    <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(10435(a,2),10609(a,1,2))].">
      <j1 rule="para" parents="10435 10609"/>
    </justification>
  </clause>

  <clause id="10615">
    <literal><![CDATA[
      a(x,y,R(x,z,u)) * K(x,y * R(x,z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(10611(a,1),7205(a,1,1))].">
      <j1 rule="para" parents="10611 7205"/>
    </justification>
  </clause>

  <clause id="10616">
    <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(10611(a,1),8486(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10611 8486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10617">
    <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),10615(a,1,2,2))].">
      <j1 rule="para" parents="12 10615"/>
    </justification>
  </clause>

  <clause id="10618">
    <literal><![CDATA[
      L(K(x,y),z,L(y,u,w)) * (L(y,u,w) * z) = L(y,u,w) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(299,a,7601,a(flip),b,9884,a),flip(a)].">
      <j1 rule="hyper" parents="299 7601 9884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10619">
    <literal><![CDATA[
      L(x,y,z) * (K(u,x) * w) = K(u,x) * (L(x,y,z) * w)
    ]]></literal>
    <justification jstring="[para(9844(a,1),10618(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9844 10618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10620">
    <literal><![CDATA[
      K(x,y) * (L(y,z,u) * (w * K(y,x))) = L(y,z,u) * T(w,K(y,x))
    ]]></literal>
    <justification jstring="[para(5431(a,1),10619(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5431 10619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10622">
    <literal><![CDATA[
      T(L(x,y,z) * u,K(w,x)) = L(x,y,z) * T(u,K(x,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,9087,a(flip),b,10620,a)].">
      <j1 rule="hyper" parents="65 9087 10620"/>
    </justification>
  </clause>

  <clause id="10623">
    <literal><![CDATA[
      T(L(x,y,z) * u,K(x,w)) = L(x,y,z) * T(u,K(x,w))
    ]]></literal>
    <justification jstring="[hyper(8081,a,10622,a)].">
      <j1 rule="hyper" parents="8081 10622"/>
    </justification>
  </clause>

  <clause id="10624">
    <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(6341(a,1),10095(a,1,1,2))].">
      <j1 rule="para" parents="6341 10095"/>
    </justification>
  </clause>

  <clause id="10625">
    <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(3495,a,10624,a),flip(a)].">
      <j1 rule="hyper" parents="3495 10624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10626">
    <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(6387(a,1),10625(a,1,1))].">
      <j1 rule="para" parents="6387 10625"/>
    </justification>
  </clause>

  <clause id="10627">
    <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(299,a,6387,a(flip),b,10626,a),flip(a)].">
      <j1 rule="hyper" parents="299 6387 10626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10628">
    <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(299,a,232,a(flip),b,10627,a),flip(a)].">
      <j1 rule="hyper" parents="299 232 10627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10630">
    <literal><![CDATA[
      R(a(x,y * K(z,y),x),y * K(z,y),z) = L(a(x,y,x),y,z)
    ]]></literal>
    <justification jstring="[para(5053(a,1),10397(a,2,2))].">
      <j1 rule="para" parents="5053 10397"/>
    </justification>
  </clause>

  <clause id="10631">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,K(z,1 / L(x,u,w))) = a(w,u,K(1 / x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(8808(a,1),10579(a,1,1))].">
      <j1 rule="para" parents="8808 10579"/>
    </justification>
  </clause>

  <clause id="10632">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,K(z,L(x,u,w))) = a(w,u,K(1 / x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(8789(a,1),10631(a,1,2))].">
      <j1 rule="para" parents="8789 10631"/>
    </justification>
  </clause>

  <clause id="10633">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(z,L(y,u,w))) = a(w,u,K(1 / y,K(x,z)))
    ]]></literal>
    <justification jstring="[para(7983(a,1),10632(a,1,1))].">
      <j1 rule="para" parents="7983 10632"/>
    </justification>
  </clause>

  <clause id="10634">
    <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(8805(a,1),10633(a,2,3))].">
      <j1 rule="para" parents="8805 10633"/>
    </justification>
  </clause>

  <clause id="10635">
    <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(10634(a,1),6267(a,1))].">
      <j1 rule="para" parents="10634 6267"/>
    </justification>
  </clause>

  <clause id="10636">
    <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(10610,a,10613,a)].">
      <j1 rule="hyper" parents="10610 10613"/>
    </justification>
  </clause>

  <clause id="10637">
    <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(65,a,6580,a(flip),b,10636,a),flip(a)].">
      <j1 rule="hyper" parents="65 6580 10636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10638">
    <literal><![CDATA[
      a(x,y,R(T(x,y),z,u)) = a(R(x,z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(4988,a,10637,a)].">
      <j1 rule="hyper" parents="4988 10637"/>
    </justification>
  </clause>

  <clause id="10639">
    <literal><![CDATA[
      R((x \ 1) \ 1,y,z) \ ((x * y) * z) = ((x * y) * ((((x * y) \ y) \ 1) \ 1)) * z
    ]]></literal>
    <justification jstring="[para(6706(a,2),6795(a,1,1))].">
      <j1 rule="para" parents="6706 6795"/>
    </justification>
  </clause>

  <clause id="10640">
    <literal><![CDATA[
      ((x * T(x \ (y / z),y / z)) * z) / y = K(x \ (y / z),(z / y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,5939,a(flip),b,6995,a),flip(a)].">
      <j1 rule="hyper" parents="65 5939 6995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10642">
    <literal><![CDATA[
      (x * (y * T(y \ (x \ z),z / y))) / z = K(x \ (z / y),(y / z) \ 1)
    ]]></literal>
    <justification jstring="[para(1579(a,1),10640(a,1,1))].">
      <j1 rule="para" parents="1579 10640"/>
    </justification>
  </clause>

  <clause id="10643">
    <literal><![CDATA[
      K(((x * y) / z) \ 1,z / y) = K(x \ (z / y),(y / z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,5837,a(flip),b,10642,a)].">
      <j1 rule="hyper" parents="65 5837 10642"/>
    </justification>
  </clause>

  <clause id="10644">
    <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(7537(a,1),8157(a,2,1,2))].">
      <j1 rule="para" parents="7537 8157"/>
    </justification>
  </clause>

  <clause id="10645">
    <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(5431(a,1),8248(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5431 8248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10646">
    <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(8932(a,1),5297(a,1))].">
      <j1 rule="para" parents="8932 5297"/>
    </justification>
  </clause>

  <clause id="10647">
    <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(10019(a,1),9240(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10019 9240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10648">
    <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(2278(a,1),10647(a,1,2,2))].">
      <j1 rule="para" parents="2278 10647"/>
    </justification>
  </clause>

  <clause id="10649">
    <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(10648(a,1),7228(a,1,1))].">
      <j1 rule="para" parents="10648 7228"/>
    </justification>
  </clause>

  <clause id="10650">
    <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(7281(a,1),10649(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7281 10649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10651">
    <literal><![CDATA[
      T(x,T((y \ 1) \ x,z)) * K(T(y \ 1,z) \ 1,x) = L(x,T(1 / y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[para(3905(a,1),9362(a,1,1))].">
      <j1 rule="para" parents="3905 9362"/>
    </justification>
  </clause>

  <clause id="10652">
    <literal><![CDATA[
      a(x,L(T(y * K(z,y),u),K(y,z),K(y,z)),w) = a(x,T(T(y,u),z),w)
    ]]></literal>
    <justification jstring="[para(7718(a,1),9378(a,2,2))].">
      <j1 rule="para" parents="7718 9378"/>
    </justification>
  </clause>

  <clause id="10653">
    <literal><![CDATA[
      a(x,T(y * K(z,y),u),w) = a(x,T(T(y,u),z),w)
    ]]></literal>
    <justification jstring="[para(10023(a,1),10652(a,1,2))].">
      <j1 rule="para" parents="10023 10652"/>
    </justification>
  </clause>

  <clause id="10654">
    <literal><![CDATA[
      a(T(x,T(y,z)),T(T(y,x),z),u) = a(x,y * K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(8195,a,10653,a),flip(a)].">
      <j1 rule="hyper" parents="8195 10653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10656">
    <literal><![CDATA[
      a(x,y * K(z,y),u) = a(x,T(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(4990,a,10654,a),flip(a)].">
      <j1 rule="hyper" parents="4990 10654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10657">
    <literal><![CDATA[
      a(x,(y * z) / y,u) = a(x,T(z,y),u)
    ]]></literal>
    <justification jstring="[para(5054(a,2),10656(a,1,2))].">
      <j1 rule="para" parents="5054 10656"/>
    </justification>
  </clause>

  <clause id="10658">
    <literal><![CDATA[
      T(K(x,y) * L(y,z,u),x) / L(y,z,u) = K(y \ L(y,z,u),T(x,y))
    ]]></literal>
    <justification jstring="[para(10(a,1),9467(a,1,2))].">
      <j1 rule="para" parents="10 9467"/>
    </justification>
  </clause>

  <clause id="10659">
    <literal><![CDATA[
      L(x,y,z) \ T(L(x,y,z) * K(u,x),u) = K(x \ L(x,y,z),T(u,x))
    ]]></literal>
    <justification jstring="[hyper(3493,a,10658,a)].">
      <j1 rule="hyper" parents="3493 10658"/>
    </justification>
  </clause>

  <clause id="10661">
    <literal><![CDATA[
      K(x \ L(x,y,z),T(u,x)) = K(L(x,y,z),u) * K(u,x)
    ]]></literal>
    <justification jstring="[hyper(7791,a,10659,a),flip(a)].">
      <j1 rule="hyper" parents="7791 10659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10663">
    <literal><![CDATA[
      K(L(K(x,y),z,u),w \ (v5 / x)) = K(L(K(x,y),z,u),w \ v5)
    ]]></literal>
    <justification jstring="[hyper(5301,a,9652,a),flip(a)].">
      <j1 rule="hyper" parents="5301 9652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10664">
    <literal><![CDATA[
      K(L(K(x,y),z,u),w \ (v5 / x)) = K(y,K(w \ v5,L(x,z,u)))
    ]]></literal>
    <justification jstring="[hyper(299,a,9146,a(flip),b,10663,a),flip(a)].">
      <j1 rule="hyper" parents="299 9146 10663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10665">
    <literal><![CDATA[
      K(x,K(y \ (z / u),L(u,w,v5))) = K(x,K(y \ z,L(u,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(9147,a,10664,a)].">
      <j1 rule="hyper" parents="9147 10664"/>
    </justification>
  </clause>

  <clause id="10666">
    <literal><![CDATA[
      K(x,K(y \ (z \ u),L(z,w,v5))) = K(x,K(y \ u,L(z,w,v5)))
    ]]></literal>
    <justification jstring="[para(10436(a,1),10665(a,1,2))].">
      <j1 rule="para" parents="10436 10665"/>
    </justification>
  </clause>

  <clause id="10667">
    <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(4386(a,1),9708(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4386 9708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10668">
    <literal><![CDATA[
      (x / T(y,x)) * L(z,K(x,y),y \ x) = (x / y) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(5931,a,9735,a),flip(a)].">
      <j1 rule="hyper" parents="5931 9735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10669">
    <literal><![CDATA[
      (x \ y) * (a(x,x \ y,x) * z) = (y / T(x,y)) * L(z,K(y,x),x \ y)
    ]]></literal>
    <justification jstring="[hyper(299,a,10080,a,b,10668,a)].">
      <j1 rule="hyper" parents="299 10080 10668"/>
    </justification>
  </clause>

  <clause id="10670">
    <literal><![CDATA[
      ((x \ y) * a(x,x \ y,x)) \ ((y / T(x,y)) * L(z,K(y,x),x \ y)) = L(z,a(x,x \ y,x),x \ y)
    ]]></literal>
    <justification jstring="[hyper(119,a,10669,a(flip),b,94,a)].">
      <j1 rule="hyper" parents="119 10669 94"/>
    </justification>
  </clause>

  <clause id="10672">
    <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(9897(a,2),8222(a,1))].">
      <j1 rule="para" parents="9897 8222"/>
    </justification>
  </clause>

  <clause id="10673">
    <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(10140(a,1),10145(a,1))].">
      <j1 rule="para" parents="10140 10145"/>
    </justification>
  </clause>

  <clause id="10674">
    <literal><![CDATA[
      R((x \ 1) \ 1,y,z) \ ((x * y) * z) = (y * K(x \ 1,x)) * z
    ]]></literal>
    <justification jstring="[para(4876(a,1),10639(a,2,1))].">
      <j1 rule="para" parents="4876 10639"/>
    </justification>
  </clause>

  <clause id="10675">
    <literal><![CDATA[
      (((x * (y \ 1)) \ 1) \ 1) \ (((x / y) * y) * (y \ 1)) = (y * K((x / y) \ 1,x / y)) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(6707(a,1),10674(a,1,1))].">
      <j1 rule="para" parents="6707 10674"/>
    </justification>
  </clause>

  <clause id="10676">
    <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(10294(a,1),10644(a,2,1))].">
      <j1 rule="para" parents="10294 10644"/>
    </justification>
  </clause>

  <clause id="10677">
    <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(299,a,10527,a(flip),b,10676,a),flip(a)].">
      <j1 rule="hyper" parents="299 10527 10676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10678">
    <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(7537(a,1),10677(a,1,1,2))].">
      <j1 rule="para" parents="7537 10677"/>
    </justification>
  </clause>

  <clause id="10679">
    <literal><![CDATA[
      (x * K(y,T(z,u))) * (u * K(z,y)) = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(8101(a,1),10678(a,1,2))].">
      <j1 rule="para" parents="8101 10678"/>
    </justification>
  </clause>

  <clause id="10680">
    <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(9402(a,2),10679(a,1,1))].">
      <j1 rule="para" parents="9402 10679"/>
    </justification>
  </clause>

  <clause id="10681">
    <literal><![CDATA[
      T(x,T(1 \ (y * x),z)) * K(T(y \ 1,z) \ 1,x) = L(x,T(1 / y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[para(9980(a,1),10651(a,1,1))].">
      <j1 rule="para" parents="9980 10651"/>
    </justification>
  </clause>

  <clause id="10682">
    <literal><![CDATA[
      T(x,T(y * x,z)) * K(T(y \ 1,z) \ 1,x) = L(x,T(1 / y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[para(67(a,1),10681(a,1,1,2,1))].">
      <j1 rule="para" parents="67 10681"/>
    </justification>
  </clause>

  <clause id="10683">
    <literal><![CDATA[
      T(x,T(y * x,z)) * K((y \ 1) \ 1,T(x,z)) = L(x,T(1 / y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[para(7497(a,1),10682(a,1,2))].">
      <j1 rule="para" parents="7497 10682"/>
    </justification>
  </clause>

  <clause id="10684">
    <literal><![CDATA[
      T(x,T(y * x,z)) * K(y,T(x,z)) = L(x,T(1 / y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[para(3567(a,1),10683(a,1,2))].">
      <j1 rule="para" parents="3567 10683"/>
    </justification>
  </clause>

  <clause id="10685">
    <literal><![CDATA[
      T(x,T(y * x,z)) * K(y,T(x,z)) = L(x,T(y \ 1,z) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,3972,a(flip),b,10684,a),flip(a)].">
      <j1 rule="hyper" parents="299 3972 10684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10686">
    <literal><![CDATA[
      L(x,T(y \ 1,z) \ 1,x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,9920,a(flip),b,10685,a),flip(a)].">
      <j1 rule="hyper" parents="65 9920 10685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10688">
    <literal><![CDATA[
      L(x,T(y,z) \ 1,x) = L(x,y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,3973,a(flip),b,10686,a)].">
      <j1 rule="hyper" parents="65 3973 10686"/>
    </justification>
  </clause>

  <clause id="10689">
    <literal><![CDATA[
      L(x,(y / z) \ 1,x) = L(x,(z \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(109(a,1),10688(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="109 10688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10690">
    <literal><![CDATA[
      ((K(x,y) * z) * (z \ x)) / T(x,y) = a(K(x,y),z,z \ x)
    ]]></literal>
    <justification jstring="[para(9400(a,1),5174(a,1,2))].">
      <j1 rule="para" parents="9400 5174"/>
    </justification>
  </clause>

  <clause id="10692">
    <literal><![CDATA[
      L(L(x,y,T(z,u)),T(z,u) * y,K(u,z)) = (z * y) \ (z * (y * x))
    ]]></literal>
    <justification jstring="[para(5061(a,1),5396(a,2,2))].">
      <j1 rule="para" parents="5061 5396"/>
    </justification>
  </clause>

  <clause id="10693">
    <literal><![CDATA[
      L(L(x,y,T(z,u)),T(z,u) * y,K(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(10692(a,2),493(a,1))].">
      <j1 rule="para" parents="10692 493"/>
    </justification>
  </clause>

  <clause id="10695">
    <literal><![CDATA[
      R(K(R(x,y,z),u),R(x,y,z),y * z) = ((T(x,u) * y) * z) / ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(103(a,1),5963(a,1,1)),flip(a)].">
      <j1 rule="para" parents="103 5963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10696">
    <literal><![CDATA[
      ((T(x,y) * z) * u) / ((x * z) * u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(4613,a,10695,a),flip(a)].">
      <j1 rule="hyper" parents="4613 10695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10697">
    <literal><![CDATA[
      ((T(x,y) * z) * u) / ((x * z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(R(x,z,u),y) = w
    ]]></literal>
    <justification jstring="[para(10695(a,1),4613(a,1))].">
      <j1 rule="para" parents="10695 4613"/>
    </justification>
  </clause>

  <clause id="10698">
    <literal><![CDATA[
      R(K(x,y),x * z,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(5420,a,10696,a)].">
      <j1 rule="hyper" parents="5420 10696"/>
    </justification>
  </clause>

  <clause id="10700">
    <literal><![CDATA[
      K(R(x,K(y,z),u),z) = K(x * K(y,z),z)
    ]]></literal>
    <justification jstring="[hyper(8583,a,10698,a),flip(a)].">
      <j1 rule="hyper" parents="8583 10698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10701">
    <literal><![CDATA[
      K(R(x,y,z),y) = K(x,R(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,9997,a(flip),b,10698,a),flip(a)].">
      <j1 rule="hyper" parents="65 9997 10698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10702">
    <literal><![CDATA[
      K(R(x,y,L(x,z,u)),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,9139,a(flip),b,10698,a),flip(a)].">
      <j1 rule="hyper" parents="65 9139 10698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10703">
    <literal><![CDATA[
      K(R(x,y,R(x,z,u)),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,9135,a(flip),b,10698,a),flip(a)].">
      <j1 rule="hyper" parents="65 9135 10698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10704">
    <literal><![CDATA[
      K(x,((x * y) * z) / ((u * y) * z)) = K(R(x,y,z),u \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,6893,a(flip),b,10698,a)].">
      <j1 rule="hyper" parents="65 6893 10698"/>
    </justification>
  </clause>

  <clause id="10705">
    <literal><![CDATA[
      K(x * y,R(R(x,y,z),y * z,u)) = K(R(x * y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,6635,a(flip),b,10698,a)].">
      <j1 rule="hyper" parents="65 6635 10698"/>
    </justification>
  </clause>

  <clause id="10706">
    <literal><![CDATA[
      K(R(x,x \ y,z),u) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),10698(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 10698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10707">
    <literal><![CDATA[
      R(R(K(x,y),z,u),x * w,v5) = R(K(R(x,w,v5),y),z,u)
    ]]></literal>
    <justification jstring="[para(10698(a,1),31(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10698 31"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10708">
    <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(5367(a,1),10698(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5367 10698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10709">
    <literal><![CDATA[
      R(K(x,T(y,z)),x * u,w) = K(R(x,u,w),T(y,x \ z))
    ]]></literal>
    <justification jstring="[para(7623(a,1),10698(a,1,1))].">
      <j1 rule="para" parents="7623 10698"/>
    </justification>
  </clause>

  <clause id="10710">
    <literal><![CDATA[
      K(K(R(x,y,z),u) * w,x) = K(w,x)
    ]]></literal>
    <justification jstring="[para(10698(a,1),8600(a,1,1,1))].">
      <j1 rule="para" parents="10698 8600"/>
    </justification>
  </clause>

  <clause id="10711">
    <literal><![CDATA[
      K(x,R(y,x,z)) * R(x,y,z) = T(R(x,y,z),y)
    ]]></literal>
    <justification jstring="[para(10701(a,1),5096(a,2,1)),flip(a)].">
      <j1 rule="para" parents="10701 5096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10712">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) = K(R(x,u,L(T(x,y),w,v5)),z)
    ]]></literal>
    <justification jstring="[hyper(8224,a,10702,a),flip(a)].">
      <j1 rule="hyper" parents="8224 10702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10713">
    <literal><![CDATA[
      K(x,T(y,z * R(x,u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(9372,a,10703,a),flip(a)].">
      <j1 rule="hyper" parents="9372 10703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10714">
    <literal><![CDATA[
      K(x,y) * R(x,z,R(x,u,w)) = T(R(x,z,R(x,u,w)),y)
    ]]></literal>
    <justification jstring="[para(10703(a,1),5096(a,2,1)),flip(a)].">
      <j1 rule="para" parents="10703 5096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10715">
    <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(10703(a,1),5548(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10703 5548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10716">
    <literal><![CDATA[
      K(R(x,y,z) * u,x) = K(u * R(x,y,z),x)
    ]]></literal>
    <justification jstring="[para(5020(a,1),10710(a,1,1))].">
      <j1 rule="para" parents="5020 10710"/>
    </justification>
  </clause>

  <clause id="10717">
    <literal><![CDATA[
      K(T(x,R(y,z,u)) * w,y) = K(x * w,y)
    ]]></literal>
    <justification jstring="[para(5061(a,1),10710(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5061 10710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10718">
    <literal><![CDATA[
      K(K(R(x,y,z),u) * w,T(x,v5)) = K(w,T(x,v5))
    ]]></literal>
    <justification jstring="[para(8118(a,1),10710(a,1,1,1))].">
      <j1 rule="para" parents="8118 10710"/>
    </justification>
  </clause>

  <clause id="10719">
    <literal><![CDATA[
      K(R(x,x \ 1,y),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,558,a(flip),b,10706,a),flip(a)].">
      <j1 rule="hyper" parents="299 558 10706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10720">
    <literal><![CDATA[
      K(R(x,x \ y,z),u) * (y * z) = (K(x,u) * y) * z
    ]]></literal>
    <justification jstring="[para(10706(a,2),103(a,1,1))].">
      <j1 rule="para" parents="10706 103"/>
    </justification>
  </clause>

  <clause id="10721">
    <literal><![CDATA[
      K((x * y) / ((z \ x) * y),u) = R(K(z,u),x,y)
    ]]></literal>
    <justification jstring="[para(100(a,1),10706(a,1,1))].">
      <j1 rule="para" parents="100 10706"/>
    </justification>
  </clause>

  <clause id="10722">
    <literal><![CDATA[
      K(x,R(y,y \ z,u)) = (w * R(K(y,x),z,u)) \ w
    ]]></literal>
    <justification jstring="[para(10706(a,1),7200(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10706 7200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10723">
    <literal><![CDATA[
      K(R(x,x \ 1,y),L(z,x,x \ 1)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,6121,a(flip),b,10719,a),flip(a)].">
      <j1 rule="hyper" parents="299 6121 10719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10725">
    <literal><![CDATA[
      K(R(x,K(y,z),u),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,8578,a(flip),b,10700,a),flip(a)].">
      <j1 rule="hyper" parents="299 8578 10700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10727">
    <literal><![CDATA[
      K(R(R(x,K(y,z),u),w,v5),z) = K(R(x,w,v5),z)
    ]]></literal>
    <justification jstring="[para(31(a,1),10725(a,1,1))].">
      <j1 rule="para" parents="31 10725"/>
    </justification>
  </clause>

  <clause id="10728">
    <literal><![CDATA[
      K(x,T(y,z / R(x,u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(12(a,1),10713(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 10713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10729">
    <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(10717(a,1),10611(a,1,1))].">
      <j1 rule="para" parents="10717 10611"/>
    </justification>
  </clause>

  <clause id="10730">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u) \ w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,8672,a(flip),b,10728,a)].">
      <j1 rule="hyper" parents="65 8672 10728"/>
    </justification>
  </clause>

  <clause id="10732">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u) * w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(9(a,1),10730(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 10730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10733">
    <literal><![CDATA[
      K(x,T(y,(x * z) * u)) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(182(a,1),10730(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="182 10730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10734">
    <literal><![CDATA[
      K(x,T(y \ (R(x,z,u) * w),w)) = K(x,(R(x,z,u) * w) / y)
    ]]></literal>
    <justification jstring="[hyper(8327,a,10732,a),flip(a)].">
      <j1 rule="hyper" parents="8327 10732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10735">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u) * w)) = K(x,y) * K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(299,a,7967,a,b,10732,a),flip(a)].">
      <j1 rule="hyper" parents="299 7967 10732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10737">
    <literal><![CDATA[
      K(x * R(y,z,y),y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,9279,a(flip),b,10716,a),flip(a)].">
      <j1 rule="hyper" parents="65 9279 10716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10738">
    <literal><![CDATA[
      T(x,y * R(x,z,x)) = 1 / (x \ K(x * y,x))
    ]]></literal>
    <justification jstring="[para(10737(a,1),5119(a,2,2,2))].">
      <j1 rule="para" parents="10737 5119"/>
    </justification>
  </clause>

  <clause id="10739">
    <literal><![CDATA[
      K(x,T(y,(z * x) * u)) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,9948,a,b,10733,a)].">
      <j1 rule="hyper" parents="65 9948 10733"/>
    </justification>
  </clause>

  <clause id="10740">
    <literal><![CDATA[
      K(x,T(y / ((z * x) * u),z * u)) = K(x,((z * x) * u) \ y)
    ]]></literal>
    <justification jstring="[para(109(a,1),10739(a,1,2)),flip(a)].">
      <j1 rule="para" parents="109 10739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10741">
    <literal><![CDATA[
      K(x,R(y,x,z)) * R(x,y,z) = R(T(x,y),y,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,27,a,b,10711,a),flip(a)].">
      <j1 rule="hyper" parents="299 27 10711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10742">
    <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(8369,a,10718,a)].">
      <j1 rule="hyper" parents="8369 10718"/>
    </justification>
  </clause>

  <clause id="10743">
    <literal><![CDATA[
      R(K(x / y,z),x,u) = K((x * u) / (y * u),z)
    ]]></literal>
    <justification jstring="[para(79(a,1),10721(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 10721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10744">
    <literal><![CDATA[
      T(x,y * R(x,z,x)) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(299,a,5119,a,b,10738,a),flip(a)].">
      <j1 rule="hyper" parents="299 5119 10738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10745">
    <literal><![CDATA[
      T(x,y * R(x,z,x)) = x * K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(299,a,5083,a(flip),b,10744,a),flip(a)].">
      <j1 rule="hyper" parents="299 5083 10744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10746">
    <literal><![CDATA[
      K(x,y * R(x,z,x)) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(5154,a,10745,a)].">
      <j1 rule="hyper" parents="5154 10745"/>
    </justification>
  </clause>

  <clause id="10747">
    <literal><![CDATA[
      K(x,R(x,y,x) * z) = K(x,x * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,8633,a,b,10746,a)].">
      <j1 rule="hyper" parents="65 8633 10746"/>
    </justification>
  </clause>

  <clause id="10748">
    <literal><![CDATA[
      K(R(x,y,x),R(x,z,x) * u) = K(x,x * u)
    ]]></literal>
    <justification jstring="[hyper(7478,a,10747,a)].">
      <j1 rule="hyper" parents="7478 10747"/>
    </justification>
  </clause>

  <clause id="10749">
    <literal><![CDATA[
      T(x,R(y,x,z)) \ R(T(x,y),y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,10741,a(flip),b,5056,a)].">
      <j1 rule="hyper" parents="119 10741 5056"/>
    </justification>
  </clause>

  <clause id="10750">
    <literal><![CDATA[
      R(K(x / (y / z),u),x,z) = K((x * z) / y,u)
    ]]></literal>
    <justification jstring="[para(12(a,1),10743(a,2,1,2))].">
      <j1 rule="para" parents="12 10743"/>
    </justification>
  </clause>

  <clause id="10751">
    <literal><![CDATA[
      K((x * y) / (z * y),T(u,x)) = R(K(z \ x,u),x,y)
    ]]></literal>
    <justification jstring="[para(7499(a,1),10743(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7499 10743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10752">
    <literal><![CDATA[
      K((x * y) / z,x) = K(x / (z / y),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,4778,a(flip),b,10750,a),flip(a)].">
      <j1 rule="hyper" parents="65 4778 10750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10753">
    <literal><![CDATA[
      K((x * y) / z,x) = K((z / y) \ x,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,7001,a(flip),b,10752,a),flip(a)].">
      <j1 rule="hyper" parents="299 7001 10752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10754">
    <literal><![CDATA[
      K(x / (y \ z),y) = K((z / x) \ y,y)
    ]]></literal>
    <justification jstring="[hyper(10175,a,10753,a)].">
      <j1 rule="hyper" parents="10175 10753"/>
    </justification>
  </clause>

  <clause id="10755">
    <literal><![CDATA[
      K(((x \ 1) \ y) / z,x) = K((z / y) \ x,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,10249,a,b,10753,a)].">
      <j1 rule="hyper" parents="65 10249 10753"/>
    </justification>
  </clause>

  <clause id="10756">
    <literal><![CDATA[
      K(x \ (y * z),T(y,z)) = K((x / z) \ y,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,8717,a,b,10754,a)].">
      <j1 rule="hyper" parents="65 8717 10754"/>
    </justification>
  </clause>

  <clause id="10757">
    <literal><![CDATA[
      K((x / ((y \ 1) * z)) \ y,y) = K(z / x,y)
    ]]></literal>
    <justification jstring="[para(9(a,1),10755(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 10755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10758">
    <literal><![CDATA[
      K((x \ y) \ z,T(z,x)) = K((y / x) \ z,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,8933,a,b,10756,a)].">
      <j1 rule="hyper" parents="65 8933 10756"/>
    </justification>
  </clause>

  <clause id="10759">
    <literal><![CDATA[
      K(x / (y * ((z \ 1) * x)),z) = K(y \ z,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),10757(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11 10757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10760">
    <literal><![CDATA[
      K(((x * y) / x) \ z,z) = K(y \ z,T(z,x))
    ]]></literal>
    <justification jstring="[para(9(a,1),10758(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 10758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10761">
    <literal><![CDATA[
      K(x / (y * ((z \ 1) * x)),(z \ 1) \ 1) = K(y \ z,z)
    ]]></literal>
    <justification jstring="[hyper(4794,a,10759,a)].">
      <j1 rule="hyper" parents="4794 10759"/>
    </justification>
  </clause>

  <clause id="10762">
    <literal><![CDATA[
      K(x * (y \ K(y,z)),x) = K(y \ x,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,5593,a(flip),b,10760,a)].">
      <j1 rule="hyper" parents="65 5593 10760"/>
    </justification>
  </clause>

  <clause id="10763">
    <literal><![CDATA[
      K((x \ K(x,y)) * z,z) = K(x \ z,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(8632,a,10762,a)].">
      <j1 rule="hyper" parents="8632 10762"/>
    </justification>
  </clause>

  <clause id="10764">
    <literal><![CDATA[
      K(R(x,y,L(T(x,z),u,w)),v5) = K(x,v5)
    ]]></literal>
    <justification jstring="[hyper(8218,a,10712,a),flip(a)].">
      <j1 rule="hyper" parents="8218 10712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10766">
    <literal><![CDATA[
      T(x,R(y,z,L(T(y,u),w,v5))) = (K(y,x) / x) \ 1
    ]]></literal>
    <justification jstring="[para(10764(a,1),5120(a,2,1,1))].">
      <j1 rule="para" parents="10764 5120"/>
    </justification>
  </clause>

  <clause id="10767">
    <literal><![CDATA[
      (x * R(K(y,z),u,w)) \ x = R(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,6432,a(flip),b,10722,a),flip(a)].">
      <j1 rule="hyper" parents="65 6432 10722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10768">
    <literal><![CDATA[
      x / R(K(y,z),u,w) = x * R(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(192,a,10767,a)].">
      <j1 rule="hyper" parents="192 10767"/>
    </justification>
  </clause>

  <clause id="10769">
    <literal><![CDATA[
      (x * R(K(y,z),u,w)) * R(K(z,y),u,w) = x
    ]]></literal>
    <justification jstring="[hyper(145,a,10767,a),flip(a)].">
      <j1 rule="hyper" parents="145 10767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10771">
    <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(10308(a,2),10767(a,1,1))].">
      <j1 rule="para" parents="10308 10767"/>
    </justification>
  </clause>

  <clause id="10772">
    <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(120,a,10769,a(flip),b,9931,a)].">
      <j1 rule="hyper" parents="120 10769 9931"/>
    </justification>
  </clause>

  <clause id="10773">
    <literal><![CDATA[
      T(x,R(y,z,L(T(y,u),w,v5))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,5120,a,b,10766,a),flip(a)].">
      <j1 rule="hyper" parents="299 5120 10766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10774">
    <literal><![CDATA[
      T(x,R(y / (y / z),u,z)) = T(x,y / (y / z))
    ]]></literal>
    <justification jstring="[para(10024(a,1),10773(a,1,2,3))].">
      <j1 rule="para" parents="10024 10773"/>
    </justification>
  </clause>

  <clause id="10775">
    <literal><![CDATA[
      K(x,K(y,R(x,z,u) * w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(8237,a,10735,a)].">
      <j1 rule="hyper" parents="8237 10735"/>
    </justification>
  </clause>

  <clause id="10776">
    <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(10735(a,2),8234(a,1))].">
      <j1 rule="para" parents="10735 8234"/>
    </justification>
  </clause>

  <clause id="10777">
    <literal><![CDATA[
      K(x,K(y,R(x,z,u) \ w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[para(10(a,1),10775(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 10775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10778">
    <literal><![CDATA[
      K(x,K(y,(x * z) * u)) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(103(a,1),10775(a,1,2,2))].">
      <j1 rule="para" parents="103 10775"/>
    </justification>
  </clause>

  <clause id="10779">
    <literal><![CDATA[
      K(x,K(y,z \ R(x,u,w))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8823,a,10777,a)].">
      <j1 rule="hyper" parents="8823 10777"/>
    </justification>
  </clause>

  <clause id="10780">
    <literal><![CDATA[
      K(x,K(y,R(x,z,u) / w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[para(79(a,1),10779(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="79 10779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10781">
    <literal><![CDATA[
      K(x,K(y,z * R(x,u,w))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8829,a,10780,a),flip(a)].">
      <j1 rule="hyper" parents="8829 10780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10782">
    <literal><![CDATA[
      K(x,K(y,(y * z) * u)) = K(y,K(x,z * u))
    ]]></literal>
    <justification jstring="[hyper(7985,a,10778,a)].">
      <j1 rule="hyper" parents="7985 10778"/>
    </justification>
  </clause>

  <clause id="10783">
    <literal><![CDATA[
      K(x,K(y,z * u)) * K(y,x) = K(y,T(x,(x * z) * u))
    ]]></literal>
    <justification jstring="[para(10778(a,1),8020(a,1,1))].">
      <j1 rule="para" parents="10778 8020"/>
    </justification>
  </clause>

  <clause id="10784">
    <literal><![CDATA[
      K(x,T(y,x * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(535(a,1),10776(a,1,2,2,1))].">
      <j1 rule="para" parents="535 10776"/>
    </justification>
  </clause>

  <clause id="10785">
    <literal><![CDATA[
      K(R(x,y,z),T(u,x \ w)) = K(R(x,y,z),T(u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,10698,a(flip),b,10709,a),flip(a)].">
      <j1 rule="hyper" parents="65 10698 10709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10786">
    <literal><![CDATA[
      K(R(x,y / x,z),T(u,y)) = K((y * z) / ((y / x) * z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,9171,a(flip),b,10785,a),flip(a)].">
      <j1 rule="hyper" parents="65 9171 10785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10787">
    <literal><![CDATA[
      K(R(x,y,z),T(u,w)) * K(T(u,x \ w),R(x,y,z)) = 1
    ]]></literal>
    <justification jstring="[para(10785(a,1),5198(a,1,1))].">
      <j1 rule="para" parents="10785 5198"/>
    </justification>
  </clause>

  <clause id="10788">
    <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(299,a,27,a,b,10714,a),flip(a)].">
      <j1 rule="hyper" parents="299 27 10714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10789">
    <literal><![CDATA[
      K(x,T(y,(y * z) * u)) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(8294,a,10783,a),flip(a)].">
      <j1 rule="hyper" parents="8294 10783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10790">
    <literal><![CDATA[
      K(x,T(y,(y \ z) * u)) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(10(a,1),10789(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 10789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10791">
    <literal><![CDATA[
      K(x \ y,T(x,y * z)) = K(x \ y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(10784,a,10790,a),flip(a)].">
      <j1 rule="hyper" parents="10784 10790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10792">
    <literal><![CDATA[
      K(x \ (y / z),T(x,z)) = K(x \ (y / z),T(x,y))
    ]]></literal>
    <justification jstring="[para(12(a,1),10791(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 10791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10793">
    <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(10791(a,1),9851(a,1,1,1))].">
      <j1 rule="para" parents="10791 9851"/>
    </justification>
  </clause>

  <clause id="10794">
    <literal><![CDATA[
      K(T(x,y \ z),R(y,u,w)) = K(T(x,z),R(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(5199,a,10787,a),flip(a)].">
      <j1 rule="hyper" parents="5199 10787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10795">
    <literal><![CDATA[
      T(x,R(y / (y / z),u,w)) = x * K(T(x,y),R(z,u,w))
    ]]></literal>
    <justification jstring="[para(10794(a,1),9263(a,2,2))].">
      <j1 rule="para" parents="10794 9263"/>
    </justification>
  </clause>

  <clause id="10796">
    <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(119,a,10788,a(flip),b,5367,a),flip(a)].">
      <j1 rule="hyper" parents="119 10788 5367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10797">
    <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(10788(a,1),7752(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10788 7752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10798">
    <literal><![CDATA[
      T(x,R((y * z) / y,u,w)) = T(x,R(y / (y / z),u,w))
    ]]></literal>
    <justification jstring="[hyper(299,a,8491,a,b,10795,a)].">
      <j1 rule="hyper" parents="299 8491 10795"/>
    </justification>
  </clause>

  <clause id="10799">
    <literal><![CDATA[
      T(x,R(y / (y / z),u,w)) = T(x,R(T(z,y),u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,8493,a(flip),b,10798,a),flip(a)].">
      <j1 rule="hyper" parents="65 8493 10798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10800">
    <literal><![CDATA[
      T(x,R(T(y,y \ z),u,w)) = T(x,R(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,8725,a,b,10799,a)].">
      <j1 rule="hyper" parents="65 8725 10799"/>
    </justification>
  </clause>

  <clause id="10801">
    <literal><![CDATA[
      T(x,R((y \ z) \ z,u,w)) = T(x,R(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(108(a,1),10800(a,1,2,1))].">
      <j1 rule="para" parents="108 10800"/>
    </justification>
  </clause>

  <clause id="10802">
    <literal><![CDATA[
      T(x,R(((y / T(1 / z,u)) \ 1) \ K(z,z \ 1),w,v5)) = T(x,R(T(y / T(z \ 1,u),K(z,z \ 1)),w,v5))
    ]]></literal>
    <justification jstring="[para(9300(a,1),10801(a,1,2,1,1))].">
      <j1 rule="para" parents="9300 10801"/>
    </justification>
  </clause>

  <clause id="10803">
    <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),10704(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 10704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10804">
    <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(5759(a,1),10704(a,1,2,1))].">
      <j1 rule="para" parents="5759 10704"/>
    </justification>
  </clause>

  <clause id="10805">
    <literal><![CDATA[
      K(R(R(x,y,z),y * z,u),x * y) = w / (K(R(x * y,z,u),x) * w)
    ]]></literal>
    <justification jstring="[para(10705(a,1),5430(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10705 5430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10806">
    <literal><![CDATA[
      K(R(x,y / x,z),u) = K((y * z) / ((y / x) * z),T(u,y))
    ]]></literal>
    <justification jstring="[hyper(8171,a,10786,a)].">
      <j1 rule="hyper" parents="8171 10786"/>
    </justification>
  </clause>

  <clause id="10807">
    <literal><![CDATA[
      R(K((x / y) \ x,z),x,u) = K(R(y,x / y,u),z)
    ]]></literal>
    <justification jstring="[hyper(299,a,10751,a(flip),b,10806,a)].">
      <j1 rule="hyper" parents="299 10751 10806"/>
    </justification>
  </clause>

  <clause id="10808">
    <literal><![CDATA[
      K(R(x,y / x,z),u) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(79(a,1),10807(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 10807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10809">
    <literal><![CDATA[
      R(K(x,y),z * x,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(11(a,1),10808(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11 10808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10811">
    <literal><![CDATA[
      R(K(x,y),z * (K(u,y) * x),w) = K(R(K(u,y) * x,z,w),y)
    ]]></literal>
    <justification jstring="[para(8590(a,1),10809(a,1,1))].">
      <j1 rule="para" parents="8590 10809"/>
    </justification>
  </clause>

  <clause id="10812">
    <literal><![CDATA[
      R(K(x,y),x * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(R(x,z,u),y) = w
    ]]></literal>
    <justification jstring="[para(5399(a,1),10697(a,1))].">
      <j1 rule="para" parents="5399 10697"/>
    </justification>
  </clause>

  <clause id="10813">
    <literal><![CDATA[
      R(K(x,y),K(x,z) * u,w) = K(R(x,x \ u,w),y)
    ]]></literal>
    <justification jstring="[hyper(10082,a,10708,a),flip(a)].">
      <j1 rule="hyper" parents="10082 10708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10815">
    <literal><![CDATA[
      R(K(x,y),K(x,z) * u,w) = R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(299,a,10706,a(flip),b,10813,a),flip(a)].">
      <j1 rule="hyper" parents="299 10706 10813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10816">
    <literal><![CDATA[
      R(K(x,y),K(x,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(10815(a,1),559(a,1))].">
      <j1 rule="para" parents="10815 559"/>
    </justification>
  </clause>

  <clause id="10817">
    <literal><![CDATA[
      R(K(x,y),z / x,u) = R(K(x,y),x \ z,u)
    ]]></literal>
    <justification jstring="[para(5117(a,1),10815(a,1,2))].">
      <j1 rule="para" parents="5117 10815"/>
    </justification>
  </clause>

  <clause id="10819">
    <literal><![CDATA[
      R(K(x,y),x \ y,z) * ((y / T(x,y)) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[para(10817(a,1),6332(a,1,1))].">
      <j1 rule="para" parents="10817 6332"/>
    </justification>
  </clause>

  <clause id="10820">
    <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(10819(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="10819 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10821">
    <literal><![CDATA[
      K(x,(y * z) / ((u * (x \ y)) * z)) = R(K(x,u \ x),y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,10706,a(flip),b,10803,a),flip(a)].">
      <j1 rule="hyper" parents="65 10706 10803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10822">
    <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(10609(a,1),10796(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10609 10796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10823">
    <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(5512,a,10822,a)].">
      <j1 rule="hyper" parents="5512 10822"/>
    </justification>
  </clause>

  <clause id="10824">
    <literal><![CDATA[
      T(x,y) * a(x,z,R(x,u,w)) = R(T(x,y),z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(5510,a,10822,a)].">
      <j1 rule="hyper" parents="5510 10822"/>
    </justification>
  </clause>

  <clause id="10825">
    <literal><![CDATA[
      (x * (K(y \ x,y) * z)) / (x * z) = L(K(y \ x,y),z,x)
    ]]></literal>
    <justification jstring="[para(8098(a,1),10793(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8098 10793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10826">
    <literal><![CDATA[
      L(K(x \ y,x),z,y) * (y * z) = y * (K(x \ y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(143,a,10825,a)].">
      <j1 rule="hyper" parents="143 10825"/>
    </justification>
  </clause>

  <clause id="10828">
    <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),10826(a,1,1,1,1))].">
      <j1 rule="para" parents="9 10826"/>
    </justification>
  </clause>

  <clause id="10829">
    <literal><![CDATA[
      K(R(R(x,y,z),y * z,u),x * y) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,R(x * y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(10805(a,2),5440(a,1))].">
      <j1 rule="para" parents="10805 5440"/>
    </justification>
  </clause>

  <clause id="10830">
    <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),10828(a,2,2,1,1))].">
      <j1 rule="para" parents="9 10828"/>
    </justification>
  </clause>

  <clause id="10831">
    <literal><![CDATA[
      ((x * y) * (K(y,x) * z)) / ((x * y) * z) = L(K(y,x),z,x * y)
    ]]></literal>
    <justification jstring="[hyper(137,a,10830,a)].">
      <j1 rule="hyper" parents="137 10830"/>
    </justification>
  </clause>

  <clause id="10832">
    <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(10830(a,1),307(a,1,1)),flip(b)].">
      <j1 rule="para" parents="10830 307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10834">
    <literal><![CDATA[
      ((x * y) * (K(y,x) * z)) / (z * T(x * y,z)) = L(K(y,x),z,x * y)
    ]]></literal>
    <justification jstring="[para(107(a,2),10831(a,1,2))].">
      <j1 rule="para" parents="107 10831"/>
    </justification>
  </clause>

  <clause id="10835">
    <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(10525(a,2),10834(a,1,1))].">
      <j1 rule="para" parents="10525 10834"/>
    </justification>
  </clause>

  <clause id="10836">
    <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(10835(a,1),549(a,1))].">
      <j1 rule="para" parents="10835 549"/>
    </justification>
  </clause>

  <clause id="10837">
    <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(234(a,1),10797(a,2,1))].">
      <j1 rule="para" parents="234 10797"/>
    </justification>
  </clause>

  <clause id="10838">
    <literal><![CDATA[
      (R(x,y,R(x,z,u)) * w) * x = (x * w) * R(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,9316,a(flip),b,10837,a),flip(a)].">
      <j1 rule="hyper" parents="65 9316 10837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10839">
    <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(7501(a,1),10729(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7501 10729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10840">
    <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(299,a,10611,a(flip),b,10839,a),flip(a)].">
      <j1 rule="hyper" parents="299 10611 10839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10842">
    <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(109(a,1),10840(a,1,2)),flip(a)].">
      <j1 rule="para" parents="109 10840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10843">
    <literal><![CDATA[
      a(x,T(y,x),R(x,z,u)) = a(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(535(a,1),10840(a,1,2,2))].">
      <j1 rule="para" parents="535 10840"/>
    </justification>
  </clause>

  <clause id="10844">
    <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(10842(a,1),10617(a,1,1))].">
      <j1 rule="para" parents="10842 10617"/>
    </justification>
  </clause>

  <clause id="10845">
    <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(299,a,7531,a(flip),b,10844,a),flip(a)].">
      <j1 rule="hyper" parents="299 7531 10844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10846">
    <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),10742(a,1,1,2))].">
      <j1 rule="para" parents="27 10742"/>
    </justification>
  </clause>

  <clause id="10847">
    <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(8050(a,1),10846(a,1,2))].">
      <j1 rule="para" parents="8050 10846"/>
    </justification>
  </clause>

  <clause id="10848">
    <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(3637(a,1),10847(a,1,2))].">
      <j1 rule="para" parents="3637 10847"/>
    </justification>
  </clause>

  <clause id="10850">
    <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(10848(a,1),5673(a,1,1,2))].">
      <j1 rule="para" parents="10848 5673"/>
    </justification>
  </clause>

  <clause id="10851">
    <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(5468(a,1),10850(a,1,1))].">
      <j1 rule="para" parents="5468 10850"/>
    </justification>
  </clause>

  <clause id="10852">
    <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(65,a,6757,a(flip),b,10851,a),flip(a)].">
      <j1 rule="hyper" parents="65 6757 10851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10853">
    <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(10852(a,1),9024(a,2,1))].">
      <j1 rule="para" parents="10852 9024"/>
    </justification>
  </clause>

  <clause id="10854">
    <literal><![CDATA[
      ((x * (T(x \ 1,x) \ 1)) \ y) * T(x,x \ 1) = (x \ 1) * T(y,T(x,x \ 1))
    ]]></literal>
    <justification jstring="[para(4532(a,1),6593(a,1,1,1,2))].">
      <j1 rule="para" parents="4532 6593"/>
    </justification>
  </clause>

  <clause id="10855">
    <literal><![CDATA[
      ((x * x) \ y) * T(x,x \ 1) = (x \ 1) * T(y,T(x,x \ 1))
    ]]></literal>
    <justification jstring="[para(1697(a,1),10854(a,1,1,1,2))].">
      <j1 rule="para" parents="1697 10854"/>
    </justification>
  </clause>

  <clause id="10856">
    <literal><![CDATA[
      ((x * x) \ y) * T(x,x \ 1) = (x \ 1) * T(y,x)
    ]]></literal>
    <justification jstring="[para(3743(a,1),10855(a,2,2))].">
      <j1 rule="para" parents="3743 10855"/>
    </justification>
  </clause>

  <clause id="10857">
    <literal><![CDATA[
      K(T(x,y * z),u / ((y * T(x,y * z)) * z)) = K(x,T(u / (x * (y * z)),y * z))
    ]]></literal>
    <justification jstring="[hyper(299,a,7537,a(flip),b,6791,a),flip(a)].">
      <j1 rule="hyper" parents="299 7537 6791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10858">
    <literal><![CDATA[
      ((R(x,y,z) \ 1) * R(x,y,z)) * (y * z) = (y * K(x \ 1,x)) * z
    ]]></literal>
    <justification jstring="[para(4876(a,1),6796(a,2,1))].">
      <j1 rule="para" parents="4876 6796"/>
    </justification>
  </clause>

  <clause id="10859">
    <literal><![CDATA[
      K(x \ 1,R(x,y,z)) * (y * z) = (y * K(x \ 1,x)) * z
    ]]></literal>
    <justification jstring="[para(6712(a,1),10858(a,1,1))].">
      <j1 rule="para" parents="6712 10858"/>
    </justification>
  </clause>

  <clause id="10860">
    <literal><![CDATA[
      K(x \ 1,R(x,y,z)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(37,a,3246,a(flip),b,10859,a),flip(a)].">
      <j1 rule="hyper" parents="37 3246 10859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10861">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,R(x,y,z)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(6713,a,10860,a)].">
      <j1 rule="hyper" parents="6713 10860"/>
    </justification>
  </clause>

  <clause id="10862">
    <literal><![CDATA[
      (x \ R(x,y,z)) * K(x \ 1,x) = (x \ 1) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(10860(a,1),1458(a,1,2))].">
      <j1 rule="para" parents="10860 1458"/>
    </justification>
  </clause>

  <clause id="10864">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,R(x,y,z)) = K(x \ 1,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(299,a,10860,a,b,10861,a),flip(a)].">
      <j1 rule="hyper" parents="299 10860 10861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10865">
    <literal><![CDATA[
      (x \ (1 / R(y,z,u))) * K(y \ 1,y) = x \ (R(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(10861(a,1),3363(a,1,2))].">
      <j1 rule="para" parents="10861 3363"/>
    </justification>
  </clause>

  <clause id="10868">
    <literal><![CDATA[
      K(x \ 1,R(x,y,z)) \ 1 = R(x,u,w) * (1 / R(x,u,w))
    ]]></literal>
    <justification jstring="[para(10864(a,1),2597(a,1,1))].">
      <j1 rule="para" parents="10864 2597"/>
    </justification>
  </clause>

  <clause id="10869">
    <literal><![CDATA[
      (1 / x) * R(x,y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(37,a,3206,a,b,10862,a)].">
      <j1 rule="hyper" parents="37 3206 10862"/>
    </justification>
  </clause>

  <clause id="10871">
    <literal><![CDATA[
      R(x,y,z) / x = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(1834,a,10869,a)].">
      <j1 rule="hyper" parents="1834 10869"/>
    </justification>
  </clause>

  <clause id="10872">
    <literal><![CDATA[
      (x \ R(x,y,z)) * x = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(10869(a,1),1831(a,1,1))].">
      <j1 rule="para" parents="10869 1831"/>
    </justification>
  </clause>

  <clause id="10873">
    <literal><![CDATA[
      T(x,x \ R(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(38,a,262,a,b,10871,a)].">
      <j1 rule="hyper" parents="38 262 10871"/>
    </justification>
  </clause>

  <clause id="10874">
    <literal><![CDATA[
      R(x \ R(x,y,z),x,y * z) = ((x * y) * z) / (x * (y * z))
    ]]></literal>
    <justification jstring="[para(10871(a,1),572(a,1,1))].">
      <j1 rule="para" parents="10871 572"/>
    </justification>
  </clause>

  <clause id="10875">
    <literal><![CDATA[
      R(x \ R(x,y,x),x,z) = (z * R(x,y,x)) / (z * x)
    ]]></literal>
    <justification jstring="[para(10871(a,1),7670(a,1,1))].">
      <j1 rule="para" parents="10871 7670"/>
    </justification>
  </clause>

  <clause id="10876">
    <literal><![CDATA[
      K(x \ R(x,y,z),x) = (1 / x) * x
    ]]></literal>
    <justification jstring="[para(10873(a,1),5032(a,2,1,2))].">
      <j1 rule="para" parents="10873 5032"/>
    </justification>
  </clause>

  <clause id="10877">
    <literal><![CDATA[
      K(x \ R(x,y,z),R(x,u,w)) = R(x,u,w) \ R(x,u,w)
    ]]></literal>
    <justification jstring="[para(10873(a,1),5044(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10873 5044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10878">
    <literal><![CDATA[
      K(R(x,y,z),x \ R(x,u,w)) = R(x,y,z) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(10873(a,1),5085(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10873 5085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10879">
    <literal><![CDATA[
      (x \ ((x * x) * R(1 / x,y,z))) * (1 / x) = R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(443(a,2),10872(a,1,1))].">
      <j1 rule="para" parents="443 10872"/>
    </justification>
  </clause>

  <clause id="10880">
    <literal><![CDATA[
      (x \ 1) \ ((x \ R(x,y,z)) * (1 / x)) = x \ T(R(x,y,z),x \ (x \ 1))
    ]]></literal>
    <justification jstring="[para(10872(a,1),3333(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10872 3333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10881">
    <literal><![CDATA[
      a(x,y,x) * T(x,z) = R(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[para(9675(a,1),10872(a,1,1))].">
      <j1 rule="para" parents="9675 10872"/>
    </justification>
  </clause>

  <clause id="10882">
    <literal><![CDATA[
      K(x \ R(x,y,z),x) = (x \ K(x,x \ 1)) * x
    ]]></literal>
    <justification jstring="[para(2586(a,2),10876(a,2,1))].">
      <j1 rule="para" parents="2586 10876"/>
    </justification>
  </clause>

  <clause id="10883">
    <literal><![CDATA[
      R(T(x / y,K(y,x)),z,x / y) = a(x / y,z,x / y) * (x / y)
    ]]></literal>
    <justification jstring="[para(7289(a,1),10881(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7289 10881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10884">
    <literal><![CDATA[
      K(x \ R(x,y,z),x) = (x \ K(x,R(x,u,w) \ 1)) * x
    ]]></literal>
    <justification jstring="[para(6212(a,2),10882(a,2,1,2))].">
      <j1 rule="para" parents="6212 10882"/>
    </justification>
  </clause>

  <clause id="10885">
    <literal><![CDATA[
      K(x \ R(x,y,z),x) = (x \ K(x,R(x \ 1,u,w))) * x
    ]]></literal>
    <justification jstring="[para(6444(a,2),10882(a,2,1,2))].">
      <j1 rule="para" parents="6444 10882"/>
    </justification>
  </clause>

  <clause id="10886">
    <literal><![CDATA[
      (x * R(y,z,y)) / (x * y) = R(a(y,z,y),y,x)
    ]]></literal>
    <justification jstring="[para(9671(a,1),10875(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9671 10875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10887">
    <literal><![CDATA[
      R(a(x,y,x),x,z) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(10459,a,10886,a),flip(a)].">
      <j1 rule="hyper" parents="10459 10886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10889">
    <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(65,a,540,a,b,10887,a)].">
      <j1 rule="hyper" parents="65 540 10887"/>
    </justification>
  </clause>

  <clause id="10890">
    <literal><![CDATA[
      K(x \ R(x,y,z),R(x,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      1 = v5
    ]]></literal>
    <justification jstring="[para(10877(a,2),274(a,1))].">
      <j1 rule="para" parents="10877 274"/>
    </justification>
  </clause>

  <clause id="10891">
    <literal><![CDATA[
      K(R(x,y,z),x \ R(x,u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(299,a,68,a(flip),b,10878,a),flip(a)].">
      <j1 rule="hyper" parents="299 68 10878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10893">
    <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(10891(a,1),8341(a,1,1,2))].">
      <j1 rule="para" parents="10891 8341"/>
    </justification>
  </clause>

  <clause id="10894">
    <literal><![CDATA[
      K(x \ R(x,y,z),x) = (x \ 1) * T(x,R(x,u,w) \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,6467,a(flip),b,10884,a),flip(a)].">
      <j1 rule="hyper" parents="299 6467 10884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10895">
    <literal><![CDATA[
      K(x \ R(x,y,z),x) = (x \ 1) * T(x,R(x \ 1,u,w))
    ]]></literal>
    <justification jstring="[hyper(299,a,6467,a(flip),b,10885,a),flip(a)].">
      <j1 rule="hyper" parents="299 6467 10885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10897">
    <literal><![CDATA[
      T(x,R(x \ 1,y,z)) = T(x,R(x,u,w) \ 1)
    ]]></literal>
    <justification jstring="[hyper(36,a,10894,a(flip),b,10895,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="36 10894 10895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10898">
    <literal><![CDATA[
      T(x,R(x,y,z) \ 1) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(4207,a,10897,a),flip(a)].">
      <j1 rule="hyper" parents="4207 10897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10899">
    <literal><![CDATA[
      (R(x,y,z) \ 1) * T(x,x \ 1) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[para(10898(a,1),1960(a,1,2))].">
      <j1 rule="para" parents="10898 1960"/>
    </justification>
  </clause>

  <clause id="10900">
    <literal><![CDATA[
      (R(x,y,z) \ 1) * ((x \ 1) \ 1) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(65,a,295,a(flip),b,10899,a)].">
      <j1 rule="hyper" parents="65 295 10899"/>
    </justification>
  </clause>

  <clause id="10902">
    <literal><![CDATA[
      R(x,y,z) \ K(R(x,u,w),x \ 1) = 1 / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(5224,a,10868,a)].">
      <j1 rule="hyper" parents="5224 10868"/>
    </justification>
  </clause>

  <clause id="10903">
    <literal><![CDATA[
      R(x,y,z) \ K(x,x \ 1) = 1 / R(x,y,z)
    ]]></literal>
    <justification jstring="[para(535(a,1),10902(a,1,2,1))].">
      <j1 rule="para" parents="535 10902"/>
    </justification>
  </clause>

  <clause id="10904">
    <literal><![CDATA[
      R(x,y,z) * (1 / R(x,y,z)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(144,a,10903,a)].">
      <j1 rule="hyper" parents="144 10903"/>
    </justification>
  </clause>

  <clause id="10905">
    <literal><![CDATA[
      (R(x,y,z) \ 1) * ((x \ 1) \ 1) = (1 / R(x,y,z)) * x
    ]]></literal>
    <justification jstring="[para(10903(a,1),3411(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10903 3411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10906">
    <literal><![CDATA[
      (1 / x) * (R(x,y,z) \ x) = 1 / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,4115,a,b,10904,a)].">
      <j1 rule="hyper" parents="36 4115 10904"/>
    </justification>
  </clause>

  <clause id="10908">
    <literal><![CDATA[
      (1 / x) \ (1 / R(x,y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) \ x = u
    ]]></literal>
    <justification jstring="[para(10906(a,1),314(a,1,2))].">
      <j1 rule="para" parents="10906 314"/>
    </justification>
  </clause>

  <clause id="10909">
    <literal><![CDATA[
      (1 / R(x,y,z)) * x = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(65,a,10900,a(flip),b,10905,a),flip(a)].">
      <j1 rule="hyper" parents="65 10900 10905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10910">
    <literal><![CDATA[
      x / R(x,y,z) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(1923,a,10909,a)].">
      <j1 rule="hyper" parents="1923 10909"/>
    </justification>
  </clause>

  <clause id="10911">
    <literal><![CDATA[
      T(1 / R(x,y,z),x) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(235,a,10909,a,b,1957,a)].">
      <j1 rule="hyper" parents="235 10909 1957"/>
    </justification>
  </clause>

  <clause id="10913">
    <literal><![CDATA[
      (R(x,y,z) \ x) * R(x,y,z) = x
    ]]></literal>
    <justification jstring="[hyper(143,a,10910,a)].">
      <j1 rule="hyper" parents="143 10910"/>
    </justification>
  </clause>

  <clause id="10914">
    <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(10910(a,1),6428(a,1,1,2))].">
      <j1 rule="para" parents="10910 6428"/>
    </justification>
  </clause>

  <clause id="10915">
    <literal><![CDATA[
      T(x,y) / R(x,z,u) = R(x,z,u) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(10913(a,1),3463(a,1,1,1))].">
      <j1 rule="para" parents="10913 3463"/>
    </justification>
  </clause>

  <clause id="10916">
    <literal><![CDATA[
      ((x / y) \ (1 / (y / x))) * R(1 / (y / x),y / x,y * (x / y)) = 1 / (y / x)
    ]]></literal>
    <justification jstring="[para(4903(a,1),10913(a,1,1,1))].">
      <j1 rule="para" parents="4903 10913"/>
    </justification>
  </clause>

  <clause id="10917">
    <literal><![CDATA[
      (x / R(x,y,z)) * (x \ 1) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,6750,a,b,10911,a)].">
      <j1 rule="hyper" parents="65 6750 10911"/>
    </justification>
  </clause>

  <clause id="10918">
    <literal><![CDATA[
      (K(x,y) / R(x,z,u)) * x = R(x,z,u) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(5175,a,10915,a)].">
      <j1 rule="hyper" parents="5175 10915"/>
    </justification>
  </clause>

  <clause id="10919">
    <literal><![CDATA[
      (R(x,y,z) \ x) * (x \ 1) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(10910(a,1),10917(a,1,1))].">
      <j1 rule="para" parents="10910 10917"/>
    </justification>
  </clause>

  <clause id="10920">
    <literal><![CDATA[
      T(R(x,y,z) \ x,x \ 1) = (x \ 1) \ (R(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(235,a,10919,a,b,10,a)].">
      <j1 rule="hyper" parents="235 10919 10"/>
    </justification>
  </clause>

  <clause id="10923">
    <literal><![CDATA[
      (1 / x) \ (1 / R(x,y,z)) = (x \ 1) \ (R(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(6090,a,10865,a)].">
      <j1 rule="hyper" parents="6090 10865"/>
    </justification>
  </clause>

  <clause id="10924">
    <literal><![CDATA[
      (x \ 1) \ (R(x,y,z) \ 1) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(10908,a,10923,a),flip(a)].">
      <j1 rule="hyper" parents="10908 10923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10925">
    <literal><![CDATA[
      T(R(x,y,z) \ x,x \ 1) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(65,a,10920,a,b,10924,a)].">
      <j1 rule="hyper" parents="65 10920 10924"/>
    </justification>
  </clause>

  <clause id="10926">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ 1 = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(65,a,4924,a(flip),b,10924,a)].">
      <j1 rule="hyper" parents="65 4924 10924"/>
    </justification>
  </clause>

  <clause id="10927">
    <literal><![CDATA[
      K(x,(R(y,z,u) \ y) \ x) = K(x,x * (y \ R(y,z,u)))
    ]]></literal>
    <justification jstring="[para(10926(a,1),5749(a,1,2,1))].">
      <j1 rule="para" parents="10926 5749"/>
    </justification>
  </clause>

  <clause id="10928">
    <literal><![CDATA[
      R(x,y,R(x,z,u)) \ x = a(x,y,R(x,z,u)) \ 1
    ]]></literal>
    <justification jstring="[para(10609(a,1),10926(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10609 10926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10929">
    <literal><![CDATA[
      K(R(x,y,z) \ x,x \ 1) = 1
    ]]></literal>
    <justification jstring="[hyper(57,a,10925,a)].">
      <j1 rule="hyper" parents="57 10925"/>
    </justification>
  </clause>

  <clause id="10930">
    <literal><![CDATA[
      T(1 / x,R(x,y,z) \ x) = 1 / x
    ]]></literal>
    <justification jstring="[para(10929(a,1),5143(a,1,1,1))].">
      <j1 rule="para" parents="10929 5143"/>
    </justification>
  </clause>

  <clause id="10931">
    <literal><![CDATA[
      T((1 / x) * R((1 / x) \ 1,y,z),R(x,u,w) \ x) = (1 / x) * R(T(1 / x,R(x,u,w) \ x) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(10930(a,1),2154(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10930 2154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10932">
    <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(4987(a,1),10928(a,2,1))].">
      <j1 rule="para" parents="4987 10928"/>
    </justification>
  </clause>

  <clause id="10933">
    <literal><![CDATA[
      K(x,(y / R(y,z,u)) \ x) = K(x,x * (y \ R(y,z,u)))
    ]]></literal>
    <justification jstring="[para(10910(a,2),10927(a,1,2,1))].">
      <j1 rule="para" parents="10910 10927"/>
    </justification>
  </clause>

  <clause id="10934">
    <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(65,a,9647,a,b,10933,a)].">
      <j1 rule="hyper" parents="65 9647 10933"/>
    </justification>
  </clause>

  <clause id="10935">
    <literal><![CDATA[
      T((R(x \ R(x,y,z),x,y * z) \ 1) \ 1,x * (y * z)) = (((x * (y * z)) \ ((x * y) * z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(10874(a,2),3181(a,1,1,1,1))].">
      <j1 rule="para" parents="10874 3181"/>
    </justification>
  </clause>

  <clause id="10936">
    <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(5426(a,1),10874(a,1,1))].">
      <j1 rule="para" parents="5426 10874"/>
    </justification>
  </clause>

  <clause id="10937">
    <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(10874(a,1),9998(a,2,2))].">
      <j1 rule="para" parents="10874 9998"/>
    </justification>
  </clause>

  <clause id="10938">
    <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(10874(a,2),8166(a,1,1))].">
      <j1 rule="para" parents="10874 8166"/>
    </justification>
  </clause>

  <clause id="10939">
    <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(10914(a,1),9325(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10914 9325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10940">
    <literal><![CDATA[
      R(T(x / y,K(y,x)),z,x / y) != u * (x / y)
    ]]></literal>
    <literal><![CDATA[
      a(x / y,z,x / y) = u
    ]]></literal>
    <justification jstring="[para(10883(a,2),46(a,1))].">
      <j1 rule="para" parents="10883 46"/>
    </justification>
  </clause>

  <clause id="10941">
    <literal><![CDATA[
      K(x \ R(x,y,z),R(x,x \ R(x,y,z),y * z)) = K(a(x,y,z),T(x,x * (y * z)))
    ]]></literal>
    <justification jstring="[hyper(65,a,10701,a(flip),b,10938,a)].">
      <j1 rule="hyper" parents="65 10701 10938"/>
    </justification>
  </clause>

  <clause id="10942">
    <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(5445(a,1),10938(a,2,2))].">
      <j1 rule="para" parents="5445 10938"/>
    </justification>
  </clause>

  <clause id="10943">
    <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(10938(a,1),8788(a,2,2))].">
      <j1 rule="para" parents="10938 8788"/>
    </justification>
  </clause>

  <clause id="10944">
    <literal><![CDATA[
      (x \ 1) \ ((x \ R(x,y,z)) * (1 / x)) = x \ R(T(x,x \ (x \ 1)),y,z)
    ]]></literal>
    <justification jstring="[para(27(a,2),10880(a,2,2))].">
      <j1 rule="para" parents="27 10880"/>
    </justification>
  </clause>

  <clause id="10945">
    <literal><![CDATA[
      (x \ 1) \ ((x \ R(x,y,z)) * (1 / x)) = x \ R(L(x,x,x),y,z)
    ]]></literal>
    <justification jstring="[para(6384(a,1),10944(a,2,2,1))].">
      <j1 rule="para" parents="6384 10944"/>
    </justification>
  </clause>

  <clause id="10946">
    <literal><![CDATA[
      (x \ 1) \ ((x \ R(x,y,z)) * (1 / x)) = x \ L(R(x,y,z),x,x)
    ]]></literal>
    <justification jstring="[para(29(a,1),10945(a,2,2))].">
      <j1 rule="para" parents="29 10945"/>
    </justification>
  </clause>

  <clause id="10947">
    <literal><![CDATA[
      (x \ 1) \ ((x \ R(x,y,z)) * (1 / x)) = (x \ 1) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,1679,a(flip),b,10946,a),flip(a)].">
      <j1 rule="hyper" parents="299 1679 10946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10948">
    <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(1953(a,1),10934(a,1,2,1))].">
      <j1 rule="para" parents="1953 10934"/>
    </justification>
  </clause>

  <clause id="10949">
    <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(8035,a,10939,a)].">
      <j1 rule="hyper" parents="8035 10939"/>
    </justification>
  </clause>

  <clause id="10950">
    <literal><![CDATA[
      K(x,T(R(y,z,u) * (y \ x),y)) = K(x,x * (y \ R(y,z,u)))
    ]]></literal>
    <justification jstring="[para(172(a,1),10948(a,1,2,2))].">
      <j1 rule="para" parents="172 10948"/>
    </justification>
  </clause>

  <clause id="10951">
    <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(10949(a,1),8035(a,1))].">
      <j1 rule="para" parents="10949 8035"/>
    </justification>
  </clause>

  <clause id="10952">
    <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(10435(a,1),10932(a,1,1))].">
      <j1 rule="para" parents="10435 10932"/>
    </justification>
  </clause>

  <clause id="10953">
    <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(10638(a,1),10952(a,2,1))].">
      <j1 rule="para" parents="10638 10952"/>
    </justification>
  </clause>

  <clause id="10954">
    <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(65,a,10928,a(flip),b,10953,a)].">
      <j1 rule="hyper" parents="65 10928 10953"/>
    </justification>
  </clause>

  <clause id="10955">
    <literal><![CDATA[
      ((x / y) \ (1 / (y / x))) * (x / y) = 1 / (y / x)
    ]]></literal>
    <justification jstring="[para(4903(a,1),10916(a,1,2))].">
      <j1 rule="para" parents="4903 10916"/>
    </justification>
  </clause>

  <clause id="10956">
    <literal><![CDATA[
      T(x / y,(x / y) \ (1 / (y / x))) = x / y
    ]]></literal>
    <justification jstring="[hyper(337,a,10955,a)].">
      <j1 rule="hyper" parents="337 10955"/>
    </justification>
  </clause>

  <clause id="10957">
    <literal><![CDATA[
      T(x / y,(x / y) \ ((y / x) \ 1)) = x / y
    ]]></literal>
    <justification jstring="[hyper(65,a,3875,a(flip),b,10956,a)].">
      <j1 rule="hyper" parents="65 3875 10956"/>
    </justification>
  </clause>

  <clause id="10958">
    <literal><![CDATA[
      ((x / y) \ ((y / x) \ 1)) * (x / y) = (y / x) \ 1
    ]]></literal>
    <justification jstring="[para(10957(a,1),220(a,1,2))].">
      <j1 rule="para" parents="10957 220"/>
    </justification>
  </clause>

  <clause id="10959">
    <literal><![CDATA[
      T((((x / y) \ 1) \ y) * ((x / y) \ 1),z) = (x / y) \ T(x * K(y,z),(x / y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,3483,a,b,6902,a)].">
      <j1 rule="hyper" parents="299 3483 6902"/>
    </justification>
  </clause>

  <clause id="10960">
    <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(7194(a,1),7253(a,2,1))].">
      <j1 rule="para" parents="7194 7253"/>
    </justification>
  </clause>

  <clause id="10961">
    <literal><![CDATA[
      R(R(x,y,T(z,u)),y * T(z,u),K(u,z)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,20,a,b,10960,a),flip(a)].">
      <j1 rule="hyper" parents="299 20 10960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10964">
    <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(220(a,1),10961(a,1,2))].">
      <j1 rule="para" parents="220 10961"/>
    </justification>
  </clause>

  <clause id="10965">
    <literal><![CDATA[
      R(R(x,y / z,z),y,K(z \ y,z)) = R(x,z \ y,z)
    ]]></literal>
    <justification jstring="[para(9733(a,1),10964(a,1,1))].">
      <j1 rule="para" parents="9733 10964"/>
    </justification>
  </clause>

  <clause id="10966">
    <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(10871(a,1),7901(a,1,1))].">
      <j1 rule="para" parents="10871 7901"/>
    </justification>
  </clause>

  <clause id="10967">
    <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(8048(a,1),8511(a,2,1))].">
      <j1 rule="para" parents="8048 8511"/>
    </justification>
  </clause>

  <clause id="10968">
    <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(8300(a,2),10967(a,2,2))].">
      <j1 rule="para" parents="8300 10967"/>
    </justification>
  </clause>

  <clause id="10969">
    <literal><![CDATA[
      K(x,y \ (y / z)) = K(u,K(x,z)) * K(x,u / (u * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,7027,a,b,10968,a)].">
      <j1 rule="hyper" parents="65 7027 10968"/>
    </justification>
  </clause>

  <clause id="10970">
    <literal><![CDATA[
      K(x,1 / (1 / (y \ (y / z)))) = K(u,K(x,z)) * K(x,u / (u * z))
    ]]></literal>
    <justification jstring="[hyper(5993,a,10969,a)].">
      <j1 rule="hyper" parents="5993 10969"/>
    </justification>
  </clause>

  <clause id="10973">
    <literal><![CDATA[
      K(T(x,y) * z,T(T(x,u),w)) = K(x * z,T(T(x,u),w))
    ]]></literal>
    <justification jstring="[hyper(299,a,5682,a(flip),b,8674,a),flip(a)].">
      <j1 rule="hyper" parents="299 5682 8674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10974">
    <literal><![CDATA[
      K(((x \ y) \ y) * z,T(T(x,u),w)) = K(x * z,T(T(x,u),w))
    ]]></literal>
    <justification jstring="[para(108(a,1),10973(a,1,1,1))].">
      <j1 rule="para" parents="108 10973"/>
    </justification>
  </clause>

  <clause id="10975">
    <literal><![CDATA[
      L((x \ 1) \ 1,y,z) \ ((x \ 1) \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(37,a,3699,a(flip),b,9131,a),flip(a)].">
      <j1 rule="hyper" parents="37 3699 9131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10976">
    <literal><![CDATA[
      K(x,T(T(T(x,y) * z,u),w)) = K(x,T(T(z * T(x,v5),u),w))
    ]]></literal>
    <justification jstring="[hyper(299,a,9514,a(flip),b,9636,a),flip(a)].">
      <j1 rule="hyper" parents="299 9514 9636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10977">
    <literal><![CDATA[
      K(x,T(T(y * T(x,z),u),w)) = K(x,T(T(x * y,u),w))
    ]]></literal>
    <justification jstring="[para(106(a,1),10976(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="106 10976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10978">
    <literal><![CDATA[
      a(x,y,x) \ (x * L(x \ a(x,y,x),z,u)) = L(x,y,x) \ L(L(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(9715(a,1),9719(a,2,2,1))].">
      <j1 rule="para" parents="9715 9719"/>
    </justification>
  </clause>

  <clause id="10979">
    <literal><![CDATA[
      a(x,y,x) \ (x * L(x \ a(x,y,x),z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x \ L(x,z,u),y,x) = w
    ]]></literal>
    <justification jstring="[para(10978(a,2),6777(a,1))].">
      <j1 rule="para" parents="10978 6777"/>
    </justification>
  </clause>

  <clause id="10980">
    <literal><![CDATA[
      K(x,(((y * K(z,x)) * u) * w) / (u * w)) = K(x,R(y,K(z,x) * u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,8689,a(flip),b,9960,a),flip(a)].">
      <j1 rule="hyper" parents="65 8689 9960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10982">
    <literal><![CDATA[
      K(x,R(y * K(z,x),u,w)) = K(x,R(y,K(z,x) * u,w))
    ]]></literal>
    <justification jstring="[para(20(a,2),10980(a,1,2))].">
      <j1 rule="para" parents="20 10980"/>
    </justification>
  </clause>

  <clause id="10983">
    <literal><![CDATA[
      K(x,R(K(y,x) * z,u,w)) = K(x,R(z,K(y,x) * u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,7906,a,b,10982,a)].">
      <j1 rule="hyper" parents="65 7906 10982"/>
    </justification>
  </clause>

  <clause id="10984">
    <literal><![CDATA[
      x * K(x,R(y,K(z,x) * u,w)) = T(x,R(K(z,x) * y,u,w))
    ]]></literal>
    <justification jstring="[para(10983(a,1),5083(a,2,2)),flip(a)].">
      <j1 rule="para" parents="10983 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10985">
    <literal><![CDATA[
      T(x,R(K(y,x) * z,u,w)) = T(x,R(z,K(y,x) * u,w))
    ]]></literal>
    <justification jstring="[hyper(5087,a,10984,a),flip(a)].">
      <j1 rule="hyper" parents="5087 10984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10986">
    <literal><![CDATA[
      T(x,R(x \ y,K(z,x) * u,w)) = T(x,R(T(x,z) \ y,u,w))
    ]]></literal>
    <justification jstring="[para(5383(a,1),10985(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5383 10985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10987">
    <literal><![CDATA[
      K((((x * K(y,z)) * u) * w) / (u * w),z) = K(R(x,K(y,z) * u,w),z)
    ]]></literal>
    <justification jstring="[hyper(65,a,10727,a(flip),b,9961,a),flip(a)].">
      <j1 rule="hyper" parents="65 10727 9961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10989">
    <literal><![CDATA[
      K(R(x * K(y,z),u,w),z) = K(R(x,K(y,z) * u,w),z)
    ]]></literal>
    <justification jstring="[para(20(a,2),10987(a,1,1))].">
      <j1 rule="para" parents="20 10987"/>
    </justification>
  </clause>

  <clause id="10990">
    <literal><![CDATA[
      K(R(K(x,y) * z,u,w),y) = K(R(z,K(x,y) * u,w),y)
    ]]></literal>
    <justification jstring="[hyper(65,a,7950,a,b,10989,a)].">
      <j1 rule="hyper" parents="65 7950 10989"/>
    </justification>
  </clause>

  <clause id="10991">
    <literal><![CDATA[
      R(K(x,y),z * (K(u,y) * x),w) = K(R(x,K(u,y) * z,w),y)
    ]]></literal>
    <justification jstring="[hyper(65,a,10811,a,b,10990,a)].">
      <j1 rule="hyper" parents="65 10811 10990"/>
    </justification>
  </clause>

  <clause id="10992">
    <literal><![CDATA[
      K((x * ((y * z) \ y)) \ ((1 / ((y * z) \ y)) \ u),y \ (y * z)) = K(x \ u,z)
    ]]></literal>
    <justification jstring="[hyper(7096,a,10393,a)].">
      <j1 rule="hyper" parents="7096 10393"/>
    </justification>
  </clause>

  <clause id="10993">
    <literal><![CDATA[
      K((x * ((y * z) \ y)) \ ((1 / ((y * z) \ y)) \ u),z) = K(x \ u,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),10992(a,1,2))].">
      <j1 rule="para" parents="9 10992"/>
    </justification>
  </clause>

  <clause id="10994">
    <literal><![CDATA[
      K(((x * y) \ x) \ (y \ ((1 / ((x * y) \ x)) \ z)),y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[hyper(8704,a,10993,a)].">
      <j1 rule="hyper" parents="8704 10993"/>
    </justification>
  </clause>

  <clause id="10995">
    <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(488(a,1),10462(a,1,1))].">
      <j1 rule="para" parents="488 10462"/>
    </justification>
  </clause>

  <clause id="10996">
    <literal><![CDATA[
      K(T(x,y * z),u / ((y * T(x,y * z)) * z)) = K(x,(y * z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(299,a,7918,a(flip),b,10857,a),flip(a)].">
      <j1 rule="hyper" parents="299 7918 10857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10997">
    <literal><![CDATA[
      K(x,T(y / ((z * T(x,z * u)) * u),z * u)) = K(x,(z * u) \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(7709,a,10996,a)].">
      <j1 rule="hyper" parents="7709 10996"/>
    </justification>
  </clause>

  <clause id="10998">
    <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(194(a,1),10893(a,1,1))].">
      <j1 rule="para" parents="194 10893"/>
    </justification>
  </clause>

  <clause id="11000">
    <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(7196(a,1),10998(a,1,2))].">
      <j1 rule="para" parents="7196 10998"/>
    </justification>
  </clause>

  <clause id="11001">
    <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(6787(a,1),11000(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6787 11000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11002">
    <literal><![CDATA[
      K(R(x,y,z),u) * (x \ R(x,y,z)) = x \ R(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,7,a(flip),b,11001,a),flip(a)].">
      <j1 rule="hyper" parents="299 7 11001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11003">
    <literal><![CDATA[
      K(x,R(y,z,u)) * (y \ R(T(y,x),z,u)) = y \ R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(5437,a,11002,a)].">
      <j1 rule="hyper" parents="5437 11002"/>
    </justification>
  </clause>

  <clause id="11004">
    <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(1163(a,1),11003(a,1,2,2))].">
      <j1 rule="para" parents="1163 11003"/>
    </justification>
  </clause>

  <clause id="11005">
    <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(9325(a,1),11003(a,1,1))].">
      <j1 rule="para" parents="9325 11003"/>
    </justification>
  </clause>

  <clause id="11006">
    <literal><![CDATA[
      K(x \ R(x,y,z),R(x,x \ R(x,y,z),y * z)) = K(a(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(299,a,10440,a(flip),b,10941,a),flip(a)].">
      <j1 rule="hyper" parents="299 10440 10941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11007">
    <literal><![CDATA[
      K(a(x,y,z),x) = 1
    ]]></literal>
    <justification jstring="[hyper(10890,a,11006,a),flip(a)].">
      <j1 rule="hyper" parents="10890 11006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11009">
    <literal><![CDATA[
      T(a(x,y,z),x) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,11007,a)].">
      <j1 rule="hyper" parents="58 11007"/>
    </justification>
  </clause>

  <clause id="11010">
    <literal><![CDATA[
      a(x,y,z) * x = x * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(11009(a,1),107(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11009 107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11011">
    <literal><![CDATA[
      T(a(1 / x,y,z),x \ 1) = a(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(2140(a,2),11009(a,1,1))].">
      <j1 rule="para" parents="2140 11009"/>
    </justification>
  </clause>

  <clause id="11012">
    <literal><![CDATA[
      (K(x,y) / z) * a(K(x,y) / z,z,K(y,x)) = 1 / (z * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,10586,a(flip),b,11010,a),flip(a)].">
      <j1 rule="hyper" parents="65 10586 11010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11013">
    <literal><![CDATA[
      (x / y) \ T(x * K(y,z),(x / y) \ 1) = T(x * (y / x),z)
    ]]></literal>
    <justification jstring="[para(4242(a,1),10959(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4242 10959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11014">
    <literal><![CDATA[
      K(x * K(y,z),(x / y) \ 1) = T(x * (y / x),z) / T(y,z)
    ]]></literal>
    <justification jstring="[para(11013(a,1),6903(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11013 6903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11015">
    <literal><![CDATA[
      K(x * K(y,z),(x / y) \ 1) = K(x,x \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,5460,a(flip),b,11014,a),flip(a)].">
      <j1 rule="hyper" parents="299 5460 11014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11016">
    <literal><![CDATA[
      K(K(x,y) * z,z \ x) = K(z,z \ T(x,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,8351,a(flip),b,11015,a)].">
      <j1 rule="hyper" parents="65 8351 11015"/>
    </justification>
  </clause>

  <clause id="11017">
    <literal><![CDATA[
      ((x \ y) \ R(x \ y,z,x \ y)) * (y / x) = R(y / x,z,x \ y)
    ]]></literal>
    <justification jstring="[para(5102(a,1),10966(a,2,1))].">
      <j1 rule="para" parents="5102 10966"/>
    </justification>
  </clause>

  <clause id="11018">
    <literal><![CDATA[
      a(x \ y,z,x \ y) * (y / x) = R(y / x,z,x \ y)
    ]]></literal>
    <justification jstring="[para(9671(a,1),11017(a,1,1))].">
      <j1 rule="para" parents="9671 11017"/>
    </justification>
  </clause>

  <clause id="11019">
    <literal><![CDATA[
      R(T(x / y,K(y,x)),z,x / y) = a(y \ x,z,y \ x) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(299,a,10290,a,b,11018,a)].">
      <j1 rule="hyper" parents="299 10290 11018"/>
    </justification>
  </clause>

  <clause id="11020">
    <literal><![CDATA[
      a(x / y,z,x / y) = a(y \ x,z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(10940,a,11019,a)].">
      <j1 rule="hyper" parents="10940 11019"/>
    </justification>
  </clause>

  <clause id="11021">
    <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(10287(a,1),11004(a,1,1))].">
      <j1 rule="para" parents="10287 11004"/>
    </justification>
  </clause>

  <clause id="11022">
    <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(5036(a,2),11021(a,1,2))].">
      <j1 rule="para" parents="5036 11021"/>
    </justification>
  </clause>

  <clause id="11024">
    <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(6293(a,1),11022(a,1,1))].">
      <j1 rule="para" parents="6293 11022"/>
    </justification>
  </clause>

  <clause id="11025">
    <literal><![CDATA[
      K(x * y,T(x,z)) * K(T(x,z),y) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,8446,a(flip),b,11024,a),flip(a)].">
      <j1 rule="hyper" parents="299 8446 11024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11026">
    <literal><![CDATA[
      K(T(x,y),z) * K(x * z,T(x,y)) = x \ R(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(2285,a,11025,a)].">
      <j1 rule="hyper" parents="2285 11025"/>
    </justification>
  </clause>

  <clause id="11028">
    <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(5952,a,6012,a),flip(a)].">
      <j1 rule="hyper" parents="5952 6012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11030">
    <literal><![CDATA[
      K((x / R(1 / y,y,z)) \ 1,z / (y * z)) = K(z / (x * (y * z)),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,5852,a(flip),b,11028,a),flip(a)].">
      <j1 rule="hyper" parents="299 5852 11028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11031">
    <literal><![CDATA[
      K((x / R(1 / y,y,z)) \ 1,y \ 1) = K(z / (x * (y * z)),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(5952,a,11030,a)].">
      <j1 rule="hyper" parents="5952 11030"/>
    </justification>
  </clause>

  <clause id="11032">
    <literal><![CDATA[
      K(R(1 / x,x,y) / z,x \ 1) = K(y / (z * (x * y)),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(6001,a,11031,a)].">
      <j1 rule="hyper" parents="6001 11031"/>
    </justification>
  </clause>

  <clause id="11034">
    <literal><![CDATA[
      K(x \ R(1 / y,y,z),y \ 1) = K(z / (x * (y * z)),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(7800,a,11032,a)].">
      <j1 rule="hyper" parents="7800 11032"/>
    </justification>
  </clause>

  <clause id="11035">
    <literal><![CDATA[
      K(x \ R(y \ 1,y,z),y \ 1) = K(z / (x * (y * z)),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,5892,a(flip),b,11034,a)].">
      <j1 rule="hyper" parents="65 5892 11034"/>
    </justification>
  </clause>

  <clause id="11036">
    <literal><![CDATA[
      K(x / (y * (z * x)),z \ 1) = K(y \ (x / (z * x)),z \ 1)
    ]]></literal>
    <justification jstring="[para(216(a,1),11034(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="216 11034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11037">
    <literal><![CDATA[
      K(x / (y * (z * x)),z \ 1) = K(y \ ((z * x) \ x),z \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,8759,a(flip),b,11036,a),flip(a)].">
      <j1 rule="hyper" parents="299 8759 11036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11038">
    <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(11036(a,2),6914(a,1))].">
      <j1 rule="para" parents="11036 6914"/>
    </justification>
  </clause>

  <clause id="11039">
    <literal><![CDATA[
      K(x \ (y / ((z \ 1) * y)),z) = K(x \ z,z)
    ]]></literal>
    <justification jstring="[hyper(11038,a,10761,a)].">
      <j1 rule="hyper" parents="11038 10761"/>
    </justification>
  </clause>

  <clause id="11040">
    <literal><![CDATA[
      K(x \ R(y \ 1,y,z),y \ 1) = K(x \ (y \ 1),y \ 1)
    ]]></literal>
    <justification jstring="[para(3430(a,2),11039(a,1,1,2))].">
      <j1 rule="para" parents="3430 11039"/>
    </justification>
  </clause>

  <clause id="11041">
    <literal><![CDATA[
      K(x / (y * (z * x)),z \ 1) = K(y \ (z \ 1),z \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,11035,a(flip),b,11040,a)].">
      <j1 rule="hyper" parents="65 11035 11040"/>
    </justification>
  </clause>

  <clause id="11043">
    <literal><![CDATA[
      K(x \ ((y * z) \ z),y \ 1) = K(x \ (y \ 1),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,11037,a(flip),b,11041,a)].">
      <j1 rule="hyper" parents="65 11037 11041"/>
    </justification>
  </clause>

  <clause id="11045">
    <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(6116,a,10823,a)].">
      <j1 rule="hyper" parents="6116 10823"/>
    </justification>
  </clause>

  <clause id="11046">
    <literal><![CDATA[
      ((x \ y) \ y) \ R((x \ y) \ y,z,u) = x \ (y \ ((R(x,z,u) * (x \ y)) * x))
    ]]></literal>
    <justification jstring="[hyper(6116,a,6681,a)].">
      <j1 rule="hyper" parents="6116 6681"/>
    </justification>
  </clause>

  <clause id="11047">
    <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(10497(a,1),11046(a,2,2,2,1,1))].">
      <j1 rule="para" parents="10497 11046"/>
    </justification>
  </clause>

  <clause id="11048">
    <literal><![CDATA[
      K((x / (y * x)) \ 1,z * (x / (y * x))) = K(y,R(y \ 1,y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,5859,a(flip),b,6162,a),flip(a)].">
      <j1 rule="hyper" parents="65 5859 6162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11050">
    <literal><![CDATA[
      T(K(T(x,y),z * (y / (x * y))),y) = K(x,R(x \ 1,x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,8277,a(flip),b,11048,a)].">
      <j1 rule="hyper" parents="65 8277 11048"/>
    </justification>
  </clause>

  <clause id="11051">
    <literal><![CDATA[
      K(x,R(x \ 1,x,y) * z) = K(x,z * (y / (x * y)))
    ]]></literal>
    <justification jstring="[hyper(65,a,5859,a(flip),b,11048,a),flip(a)].">
      <j1 rule="hyper" parents="65 5859 11048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11053">
    <literal><![CDATA[
      K(x,L(y \ 1,z,u) \ (K(w,L(1 / y,z,u)) * v5)) = K(x,L(T(1 / y,w),z,u) \ v5)
    ]]></literal>
    <justification jstring="[para(25(a,2),6228(a,2,2,1))].">
      <j1 rule="para" parents="25 6228"/>
    </justification>
  </clause>

  <clause id="11054">
    <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(7196(a,1),6292(a,1,1,2))].">
      <j1 rule="para" parents="7196 6292"/>
    </justification>
  </clause>

  <clause id="11055">
    <literal><![CDATA[
      K(x,y / (z * (x / ((z \ 1) \ 1)))) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,5321,a(flip),b,6737,a),flip(a)].">
      <j1 rule="hyper" parents="65 5321 6737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11057">
    <literal><![CDATA[
      K(x,y / (z * ((z \ 1) * x))) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,6736,a(flip),b,11055,a)].">
      <j1 rule="hyper" parents="65 6736 11055"/>
    </justification>
  </clause>

  <clause id="11058">
    <literal><![CDATA[
      K(x,y / L(x,z \ 1,z)) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(252(a,1),11057(a,1,2,2))].">
      <j1 rule="para" parents="252 11057"/>
    </justification>
  </clause>

  <clause id="11059">
    <literal><![CDATA[
      K(x,L(x,y \ 1,y) \ z) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,7630,a(flip),b,11058,a)].">
      <j1 rule="hyper" parents="65 7630 11058"/>
    </justification>
  </clause>

  <clause id="11060">
    <literal><![CDATA[
      K((x \ 1) \ y,((x \ 1) \ y) \ z) = K((x \ 1) \ y,(x * y) \ z)
    ]]></literal>
    <justification jstring="[para(519(a,1),11059(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="519 11059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11061">
    <literal><![CDATA[
      (x \ y) * K((x \ 1) \ (x \ y),(x * (x \ y)) \ z) = x \ T(y,((x \ 1) \ (x \ y)) \ z)
    ]]></literal>
    <justification jstring="[para(11060(a,1),6981(a,1,2))].">
      <j1 rule="para" parents="11060 6981"/>
    </justification>
  </clause>

  <clause id="11062">
    <literal><![CDATA[
      L(T(x,y),x \ (z * K(u,x)),x) = T(L(x,x \ z,x),y)
    ]]></literal>
    <justification jstring="[para(10529(a,1),7256(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10529 7256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11063">
    <literal><![CDATA[
      L(T(x,y),x \ (K(z,x) * u),x) = T(L(x,x \ u,x),y)
    ]]></literal>
    <justification jstring="[para(7541(a,1),11062(a,1,2,2))].">
      <j1 rule="para" parents="7541 11062"/>
    </justification>
  </clause>

  <clause id="11065">
    <literal><![CDATA[
      L(T(x,y),x \ (K(z,x) * u),x) = L(T(x,y),x \ u,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,25,a,b,11063,a),flip(a)].">
      <j1 rule="hyper" parents="299 25 11063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11066">
    <literal><![CDATA[
      L(T(x,y),T(x,z) \ u,x) = L(T(x,y),x \ u,x)
    ]]></literal>
    <justification jstring="[para(5372(a,1),11065(a,1,2))].">
      <j1 rule="para" parents="5372 11065"/>
    </justification>
  </clause>

  <clause id="11067">
    <literal><![CDATA[
      L(T(x,y),T(z / T(x,u),x),x) = L(T(x,y),x \ z,x)
    ]]></literal>
    <justification jstring="[para(8451(a,2),11066(a,1,2))].">
      <j1 rule="para" parents="8451 11066"/>
    </justification>
  </clause>

  <clause id="11068">
    <literal><![CDATA[
      L(T(x,y),z / T(x,u),x) = L(T(x,y),x \ z,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,7778,a(flip),b,11067,a)].">
      <j1 rule="hyper" parents="65 7778 11067"/>
    </justification>
  </clause>

  <clause id="11069">
    <literal><![CDATA[
      R(x,x \ 1,y \ R(y,x \ 1,y)) = x
    ]]></literal>
    <justification jstring="[hyper(299,a,9877,a(flip),b,7364,a),flip(a)].">
      <j1 rule="hyper" parents="299 9877 7364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11071">
    <literal><![CDATA[
      R(x,x \ 1,a(y,x \ 1,y)) = x
    ]]></literal>
    <justification jstring="[para(9671(a,1),11069(a,1,3))].">
      <j1 rule="para" parents="9671 11069"/>
    </justification>
  </clause>

  <clause id="11072">
    <literal><![CDATA[
      (x \ 1) * a(y,x \ 1,y) = x \ a(y,x \ 1,y)
    ]]></literal>
    <justification jstring="[para(11071(a,1),406(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11071 406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11073">
    <literal><![CDATA[
      T(x \ a(y,x \ 1,y),y) = y \ T(y * (x \ 1),y)
    ]]></literal>
    <justification jstring="[para(11072(a,1),9694(a,1,1))].">
      <j1 rule="para" parents="11072 9694"/>
    </justification>
  </clause>

  <clause id="11074">
    <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(11073(a,1),2154(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11073 2154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11075">
    <literal><![CDATA[
      R(K(R(x,y,z),u),w,L(x,w,K(R(x,y,z),u))) = K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,11,a(flip),b,7685,a),flip(a)].">
      <j1 rule="hyper" parents="299 11 7685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11077">
    <literal><![CDATA[
      R(K(R(x,y,z),u),w,x) = K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(7678(a,1),11075(a,1,3))].">
      <j1 rule="para" parents="7678 11075"/>
    </justification>
  </clause>

  <clause id="11078">
    <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(3584(a,1),8301(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3584 8301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11079">
    <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(3584(a,1),11078(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3584 11078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11081">
    <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(11079(a,1),692(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11079 692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11083">
    <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),8401(a,2,2,2))].">
      <j1 rule="para" parents="22 8401"/>
    </justification>
  </clause>

  <clause id="11084">
    <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(299,a,8525,a(flip),b,11083,a),flip(a)].">
      <j1 rule="hyper" parents="299 8525 11083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11086">
    <literal><![CDATA[
      K(x,L((y * x) \ (z * x),u,w)) = K(x,L(y \ z,u,w))
    ]]></literal>
    <justification jstring="[para(601(a,1),11084(a,1,2))].">
      <j1 rule="para" parents="601 11084"/>
    </justification>
  </clause>

  <clause id="11087">
    <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),11086(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="12 11086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11088">
    <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),11087(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 11087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11089">
    <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(8396,a,11088,a)].">
      <j1 rule="hyper" parents="8396 11088"/>
    </justification>
  </clause>

  <clause id="11090">
    <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(9958(a,1),11089(a,1,1))].">
      <j1 rule="para" parents="9958 11089"/>
    </justification>
  </clause>

  <clause id="11091">
    <literal><![CDATA[
      L(K(x,y),((z / x) * y) * x,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(8877(a,1),11090(a,1,1))].">
      <j1 rule="para" parents="8877 11090"/>
    </justification>
  </clause>

  <clause id="11092">
    <literal><![CDATA[
      K(L(x,(y / x) * z,u),z) = K(x,L(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,7433,a(flip),b,11091,a)].">
      <j1 rule="hyper" parents="65 7433 11091"/>
    </justification>
  </clause>

  <clause id="11094">
    <literal><![CDATA[
      K(x,L(y * ((z * y) \ z),u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(65,a,9867,a(flip),b,11092,a),flip(a)].">
      <j1 rule="hyper" parents="65 9867 11092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11095">
    <literal><![CDATA[
      K(x,y \ K(z,L(x,u,w))) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(11092(a,1),8542(a,1,2,2))].">
      <j1 rule="para" parents="11092 8542"/>
    </justification>
  </clause>

  <clause id="11096">
    <literal><![CDATA[
      K(x,a(y,z,z \ 1) \ 1) = 1
    ]]></literal>
    <justification jstring="[hyper(65,a,9030,a(flip),b,11094,a)].">
      <j1 rule="hyper" parents="65 9030 11094"/>
    </justification>
  </clause>

  <clause id="11098">
    <literal><![CDATA[
      K(x,(T(L(x,y,z),u) \ w) \ 1) = K(x,w \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,9032,a(flip),b,11095,a),flip(a)].">
      <j1 rule="hyper" parents="65 9032 11095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11099">
    <literal><![CDATA[
      K(x,y \ K(z,L(L(x,u,w),v5,v6))) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(11092(a,1),11095(a,1,2,2))].">
      <j1 rule="para" parents="11092 11095"/>
    </justification>
  </clause>

  <clause id="11100">
    <literal><![CDATA[
      K(x,(L(T(x,y),z,u) \ w) \ 1) = K(x,w \ L(x,z,u))
    ]]></literal>
    <justification jstring="[para(25(a,2),11098(a,1,2,1,1))].">
      <j1 rule="para" parents="25 11098"/>
    </justification>
  </clause>

  <clause id="11101">
    <literal><![CDATA[
      K(x,y \ L(T(x,z),u,w)) = K(x,y \ L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(6885,a,11100,a)].">
      <j1 rule="hyper" parents="6885 11100"/>
    </justification>
  </clause>

  <clause id="11102">
    <literal><![CDATA[
      K((x \ y) \ T(y,x),z \ L((x \ y) \ T(y,x),u,w)) = K((x \ y) \ T(y,x),z \ L(T(x,x \ y),u,w))
    ]]></literal>
    <justification jstring="[para(1444(a,1),11101(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="1444 11101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11103">
    <literal><![CDATA[
      K((x \ y) \ T(y,x),z \ L(L(T(x,x \ y),y,x),u,w)) = K((x \ y) \ T(y,x),z \ L((x \ y) \ T(y,x),u,w))
    ]]></literal>
    <justification jstring="[para(1445(a,1),11101(a,1,2,2,1))].">
      <j1 rule="para" parents="1445 11101"/>
    </justification>
  </clause>

  <clause id="11104">
    <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(10781(a,1),8926(a,1,2))].">
      <j1 rule="para" parents="10781 8926"/>
    </justification>
  </clause>

  <clause id="11105">
    <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(7989(a,1),11104(a,1,2))].">
      <j1 rule="para" parents="7989 11104"/>
    </justification>
  </clause>

  <clause id="11107">
    <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(8841(a,1),11105(a,2,1))].">
      <j1 rule="para" parents="8841 11105"/>
    </justification>
  </clause>

  <clause id="11108">
    <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(65,a,10616,a(flip),b,11107,a)].">
      <j1 rule="hyper" parents="65 10616 11107"/>
    </justification>
  </clause>

  <clause id="11109">
    <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(9236,a,11108,a)].">
      <j1 rule="hyper" parents="9236 11108"/>
    </justification>
  </clause>

  <clause id="11110">
    <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(10348,a,11109,a)].">
      <j1 rule="hyper" parents="10348 11109"/>
    </justification>
  </clause>

  <clause id="11111">
    <literal><![CDATA[
      T(x,y) \ R(T(x,y),y,R(T(x,y),z,u)) = K(R(x,z,u) * y,x) * K(T(x,y),y)
    ]]></literal>
    <justification jstring="[para(8842(a,1),9405(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8842 9405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11112">
    <literal><![CDATA[
      T(x,y) \ R(T(x,y),y,R(T(x,y),z,u)) = K(R(x,z,u) * y,x) * K(x,y)
    ]]></literal>
    <justification jstring="[para(5188(a,1),11111(a,2,2))].">
      <j1 rule="para" parents="5188 11111"/>
    </justification>
  </clause>

  <clause id="11113">
    <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),9409(a,1,2,1))].">
      <j1 rule="para" parents="9 9409"/>
    </justification>
  </clause>

  <clause id="11115">
    <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),11113(a,1,2))].">
      <j1 rule="para" parents="18 11113"/>
    </justification>
  </clause>

  <clause id="11116">
    <literal><![CDATA[
      K(L(x,y * z,u),z) = K(x,L(L(z,y,x),x * y,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,8398,a(flip),b,11115,a)].">
      <j1 rule="hyper" parents="65 8398 11115"/>
    </justification>
  </clause>

  <clause id="11117">
    <literal><![CDATA[
      K(L(x,y * z,u),z) = K(x,L(z,x * y,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,7844,a(flip),b,11116,a),flip(a)].">
      <j1 rule="hyper" parents="299 7844 11116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11120">
    <literal><![CDATA[
      K(L(x,(x \ y) * z,u),z) = K(x,L(z,y,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),11117(a,2,2,2))].">
      <j1 rule="para" parents="10 11117"/>
    </justification>
  </clause>

  <clause id="11121">
    <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(4341(a,1),11120(a,1,1,2))].">
      <j1 rule="para" parents="4341 11120"/>
    </justification>
  </clause>

  <clause id="11122">
    <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(7467,a,11121,a)].">
      <j1 rule="hyper" parents="7467 11121"/>
    </justification>
  </clause>

  <clause id="11124">
    <literal><![CDATA[
      K((x / y) \ z,R((x / y) \ 1,x / y,y)) = K(((x / y) \ 1) * z,y / x)
    ]]></literal>
    <justification jstring="[hyper(299,a,4800,a(flip),b,9637,a),flip(a)].">
      <j1 rule="hyper" parents="299 4800 9637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11125">
    <literal><![CDATA[
      K((x / y) \ z,T(y / x,x / y)) = K(((x / y) \ 1) * z,y / x)
    ]]></literal>
    <justification jstring="[para(704(a,1),11124(a,1,2))].">
      <j1 rule="para" parents="704 11124"/>
    </justification>
  </clause>

  <clause id="11126">
    <literal><![CDATA[
      K(((x / y) \ 1) * z,y / x) = K((x / y) \ z,y / x)
    ]]></literal>
    <justification jstring="[hyper(6962,a,11125,a),flip(a)].">
      <j1 rule="hyper" parents="6962 11125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11127">
    <literal><![CDATA[
      K(((x / y) \ 1) * z,y / x) = K((y \ x) \ z,y / x)
    ]]></literal>
    <justification jstring="[hyper(299,a,7932,a(flip),b,11126,a),flip(a)].">
      <j1 rule="hyper" parents="299 7932 11126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11128">
    <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(9729(a,1),9702(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9729 9702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11129">
    <literal><![CDATA[
      a(x,y,x) * K(y,T(x,z)) = K(x * y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,9889,a(flip),b,11128,a),flip(a)].">
      <j1 rule="hyper" parents="65 9889 11128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11131">
    <literal><![CDATA[
      K(x * y,T(x,z)) * K(x,T(y,z)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(7585,a,11129,a)].">
      <j1 rule="hyper" parents="7585 11129"/>
    </justification>
  </clause>

  <clause id="11133">
    <literal><![CDATA[
      K(x * T(y,z),T(x,u)) * K(x,T(T(y,u),z)) = a(x,T(y,z),x)
    ]]></literal>
    <justification jstring="[para(23(a,1),11131(a,1,2,2))].">
      <j1 rule="para" parents="23 11131"/>
    </justification>
  </clause>

  <clause id="11134">
    <literal><![CDATA[
      K(((x \ y) \ y) * z,T(T(x,y),u)) * K((x \ y) \ y,T(z,u)) = a((x \ y) \ y,z,(x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(10289(a,1),11131(a,1,1))].">
      <j1 rule="para" parents="10289 11131"/>
    </justification>
  </clause>

  <clause id="11135">
    <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(10353(a,1),11131(a,1,1))].">
      <j1 rule="para" parents="10353 11131"/>
    </justification>
  </clause>

  <clause id="11136">
    <literal><![CDATA[
      a(x,T(y,z),x) != u * K(x,T(T(y,w),z))
    ]]></literal>
    <literal><![CDATA[
      K(x * T(y,z),T(x,w)) = u
    ]]></literal>
    <justification jstring="[para(11133(a,1),46(a,1))].">
      <j1 rule="para" parents="11133 46"/>
    </justification>
  </clause>

  <clause id="11137">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * K(z,y)) * (y * z)) = L(K(z,y),T(x,y * z),y * z)
    ]]></literal>
    <justification jstring="[hyper(119,a,107,a(flip),b,9834,a)].">
      <j1 rule="hyper" parents="119 107 9834"/>
    </justification>
  </clause>

  <clause id="11138">
    <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(10268,a,11137,a)].">
      <j1 rule="hyper" parents="10268 11137"/>
    </justification>
  </clause>

  <clause id="11139">
    <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(10327,a,11138,a)].">
      <j1 rule="hyper" parents="10327 11138"/>
    </justification>
  </clause>

  <clause id="11140">
    <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),11139(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 11139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11141">
    <literal><![CDATA[
      L(K(x,y),T(z,y * x),y * x) = K(x,L(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,8977,a(flip),b,11140,a),flip(a)].">
      <j1 rule="hyper" parents="299 8977 11140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11142">
    <literal><![CDATA[
      K(x,L(y,x,((y * x) * z) / (y * x))) = L(K(x,y),z,y * x)
    ]]></literal>
    <justification jstring="[para(222(a,1),11141(a,1,2)),flip(a)].">
      <j1 rule="para" parents="222 11141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11143">
    <literal><![CDATA[
      (x * (y * z)) * K(z,L(y,z,x)) = (y * z) * T(x * K(z,y),y * z)
    ]]></literal>
    <justification jstring="[para(11141(a,1),9834(a,1,2))].">
      <j1 rule="para" parents="11141 9834"/>
    </justification>
  </clause>

  <clause id="11144">
    <literal><![CDATA[
      (x * y) * T(z * K(y,x),x * y) = z * (y * x)
    ]]></literal>
    <justification jstring="[hyper(9418,a,11143,a),flip(a)].">
      <j1 rule="hyper" parents="9418 11143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11145">
    <literal><![CDATA[
      (x * (y * z)) / (z * y) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(120,a,11144,a(flip),b,107,a(flip))].">
      <j1 rule="hyper" parents="120 11144 107"/>
    </justification>
  </clause>

  <clause id="11147">
    <literal><![CDATA[
      (x / (y * z)) * K(y,z) = x / (z * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,156,a(flip),b,11145,a),flip(a)].">
      <j1 rule="hyper" parents="65 156 11145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11149">
    <literal><![CDATA[
      (x * K(y \ z,y)) * z = x * ((y \ z) * y)
    ]]></literal>
    <justification jstring="[para(11145(a,1),301(a,1,1))].">
      <j1 rule="para" parents="11145 301"/>
    </justification>
  </clause>

  <clause id="11150">
    <literal><![CDATA[
      (x / y) * K(y / z,z) = x / (z * (y / z))
    ]]></literal>
    <justification jstring="[para(12(a,1),11147(a,1,1,2))].">
      <j1 rule="para" parents="12 11147"/>
    </justification>
  </clause>

  <clause id="11152">
    <literal><![CDATA[
      K(x,y / (z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (x * z)) = u
    ]]></literal>
    <justification jstring="[para(11147(a,1),8577(a,1,2))].">
      <j1 rule="para" parents="11147 8577"/>
    </justification>
  </clause>

  <clause id="11155">
    <literal><![CDATA[
      1 / ((x * ((x / y) \ 1)) / x) = x / (x * (y / x))
    ]]></literal>
    <justification jstring="[hyper(65,a,9547,a,b,11150,a)].">
      <j1 rule="hyper" parents="65 9547 11150"/>
    </justification>
  </clause>

  <clause id="11157">
    <literal><![CDATA[
      (x * ((x / y) \ 1)) / x = (x / (x * (y / x))) \ 1
    ]]></literal>
    <justification jstring="[hyper(186,a,11155,a),flip(a)].">
      <j1 rule="hyper" parents="186 11155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11158">
    <literal><![CDATA[
      x / (x * (((y / x) \ 1) \ 1)) = ((x * ((x / y) \ 1)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(11157(a,2),3413(a,2,1))].">
      <j1 rule="para" parents="11157 3413"/>
    </justification>
  </clause>

  <clause id="11159">
    <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(10391(a,2),11158(a,2,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10391 11158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11160">
    <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(7709,a,9847,a),flip(a)].">
      <j1 rule="hyper" parents="7709 9847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11161">
    <literal><![CDATA[
      (K(x,y) * (K(y,z) * u)) * (K(y,x) * K(z,y)) != w
    ]]></literal>
    <literal><![CDATA[
      u * K(K(x,y) * K(y,z),u) = w
    ]]></literal>
    <justification jstring="[para(9243(a,1),10038(a,1))].">
      <j1 rule="para" parents="9243 10038"/>
    </justification>
  </clause>

  <clause id="11162">
    <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(8066(a,1),10293(a,1,2))].">
      <j1 rule="para" parents="8066 10293"/>
    </justification>
  </clause>

  <clause id="11163">
    <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(299,a,8666,a(flip),b,11162,a),flip(a)].">
      <j1 rule="hyper" parents="299 8666 11162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11165">
    <literal><![CDATA[
      K((x * (y * z)) \ u,L(z,w,v5)) = K((x * y) \ (z \ u),L(z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(5830,a,10337,a),flip(a)].">
      <j1 rule="hyper" parents="5830 10337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11166">
    <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(9027,a,11165,a)].">
      <j1 rule="hyper" parents="9027 11165"/>
    </justification>
  </clause>

  <clause id="11167">
    <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(107(a,1),10628(a,1,1))].">
      <j1 rule="para" parents="107 10628"/>
    </justification>
  </clause>

  <clause id="11168">
    <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(10848(a,1),10853(a,1,2,1))].">
      <j1 rule="para" parents="10848 10853"/>
    </justification>
  </clause>

  <clause id="11169">
    <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(5383(a,1),11168(a,1,2))].">
      <j1 rule="para" parents="5383 11168"/>
    </justification>
  </clause>

  <clause id="11171">
    <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(6856(a,1),10943(a,1,2))].">
      <j1 rule="para" parents="6856 10943"/>
    </justification>
  </clause>

  <clause id="11172">
    <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(65,a,9325,a(flip),b,11171,a)].">
      <j1 rule="hyper" parents="65 9325 11171"/>
    </justification>
  </clause>

  <clause id="11173">
    <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(7489(a,2),11005(a,1,2,2,1))].">
      <j1 rule="para" parents="7489 11005"/>
    </justification>
  </clause>

  <clause id="11174">
    <literal><![CDATA[
      K(x,L(y \ 1,z,u) \ (K(w,L(y \ 1,z,u)) * v5)) = K(x,L(T(1 / y,w),z,u) \ v5)
    ]]></literal>
    <justification jstring="[para(4805(a,1),11053(a,1,2,2,1))].">
      <j1 rule="para" parents="4805 11053"/>
    </justification>
  </clause>

  <clause id="11175">
    <literal><![CDATA[
      x / (y * K(1 / z,z)) = K(z,1 / z) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(3393,a,11054,a)].">
      <j1 rule="hyper" parents="3393 11054"/>
    </justification>
  </clause>

  <clause id="11177">
    <literal><![CDATA[
      K(x,1 / x) * (y / L(x,z,u)) = y / (1 / (1 / L(x,z,u)))
    ]]></literal>
    <justification jstring="[para(6409(a,1),11175(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6409 11175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11178">
    <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(299,a,9882,a(flip),b,11160,a),flip(a)].">
      <j1 rule="hyper" parents="299 9882 11160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11180">
    <literal><![CDATA[
      K((((L(x,y,z) \ u) \ w) \ w) \ w,x) = K((L(x,y,z) * w) / u,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,8116,a(flip),b,11178,a),flip(a)].">
      <j1 rule="hyper" parents="299 8116 11178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11181">
    <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(5426(a,1),11173(a,1,2))].">
      <j1 rule="para" parents="5426 11173"/>
    </justification>
  </clause>

  <clause id="11182">
    <literal><![CDATA[
      K(x,L(T(1 / y,z),u,w) \ v5) = K(x,T(L(y \ 1,u,w),z) \ v5)
    ]]></literal>
    <justification jstring="[para(5372(a,1),11174(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5372 11174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11183">
    <literal><![CDATA[
      K(x,L(T(1 / y,z),u,w) \ v5) = K(x,L(T(y \ 1,z),u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(25(a,2),11182(a,2,2,1))].">
      <j1 rule="para" parents="25 11182"/>
    </justification>
  </clause>

  <clause id="11184">
    <literal><![CDATA[
      x * (K(y,z) * R(K(z,T(y,u)),w,v5)) != K(z,y) \ R(K(z,y),w,v5)
    ]]></literal>
    <literal><![CDATA[
      K(u,K(y,R(z,w,v5))) = x
    ]]></literal>
    <justification jstring="[para(11181(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="11181 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11185">
    <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(4346(a,1),6761(a,1,2))].">
      <j1 rule="para" parents="4346 6761"/>
    </justification>
  </clause>

  <clause id="11186">
    <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(299,a,5813,a(flip),b,11185,a),flip(a)].">
      <j1 rule="hyper" parents="299 5813 11185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11187">
    <literal><![CDATA[
      ((K(x,y) / R(x,z,x)) * x) \ x = R(x * K(y,x),z,x)
    ]]></literal>
    <justification jstring="[para(7441(a,1),11186(a,1,1,1,1))].">
      <j1 rule="para" parents="7441 11186"/>
    </justification>
  </clause>

  <clause id="11189">
    <literal><![CDATA[
      (R(x,y,x) \ T(x,z)) \ x = R(x * K(z,x),y,x)
    ]]></literal>
    <justification jstring="[para(10918(a,1),11187(a,1,1))].">
      <j1 rule="para" parents="10918 11187"/>
    </justification>
  </clause>

  <clause id="11190">
    <literal><![CDATA[
      (x \ L(T(x,y),z,x)) \ x = R(x * K(y,x),z,x)
    ]]></literal>
    <justification jstring="[para(9611(a,1),11189(a,1,1))].">
      <j1 rule="para" parents="9611 11189"/>
    </justification>
  </clause>

  <clause id="11191">
    <literal><![CDATA[
      (x \ 1) * T((1 / x) \ (((1 / x) \ 1) \ y),x) = T(x \ T(y,1 / x),x * x)
    ]]></literal>
    <justification jstring="[para(79(a,1),7157(a,2,1,1))].">
      <j1 rule="para" parents="79 7157"/>
    </justification>
  </clause>

  <clause id="11192">
    <literal><![CDATA[
      (x \ 1) * T((1 / x) \ (((1 / x) \ 1) \ y),x) = T(x \ T(y,x \ 1),x * x)
    ]]></literal>
    <justification jstring="[para(3733(a,1),11191(a,2,1,2))].">
      <j1 rule="para" parents="3733 11191"/>
    </justification>
  </clause>

  <clause id="11193">
    <literal><![CDATA[
      (x \ 1) * T((1 / x) \ (x \ y),x) = T(x \ T(y,x \ 1),x * x)
    ]]></literal>
    <justification jstring="[para(79(a,1),11192(a,1,2,1,2,1))].">
      <j1 rule="para" parents="79 11192"/>
    </justification>
  </clause>

  <clause id="11194">
    <literal><![CDATA[
      (x \ 1) * T(x \ ((x \ 1) \ y),x) = T(x \ T(y,x \ 1),x * x)
    ]]></literal>
    <justification jstring="[para(729(a,1),11193(a,1,2,1))].">
      <j1 rule="para" parents="729 11193"/>
    </justification>
  </clause>

  <clause id="11195">
    <literal><![CDATA[
      T(x \ T(y,x \ 1),x * x) = x \ T(K(x,x \ 1) * y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,2752,a(flip),b,11194,a),flip(a)].">
      <j1 rule="hyper" parents="65 2752 11194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11196">
    <literal><![CDATA[
      T(x \ T(y,x \ 1),x * x) = K(x,x \ 1) * (x \ T(y,x))
    ]]></literal>
    <justification jstring="[hyper(7776,a,11195,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="7776 11195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11197">
    <literal><![CDATA[
      T(x \ T(y,x \ 1),x * x) = ((x \ 1) \ 1) \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,2706,a(flip),b,11196,a),flip(a)].">
      <j1 rule="hyper" parents="299 2706 11196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11198">
    <literal><![CDATA[
      T(x \ T(x * y,x \ 1),x * x) = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(299,a,3767,a(flip),b,11197,a),flip(a)].">
      <j1 rule="hyper" parents="299 3767 11197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11199">
    <literal><![CDATA[
      (x * (y * T(z,u))) / (x * (y * z)) = K(L(z,y,x),T(u,x * y))
    ]]></literal>
    <justification jstring="[hyper(40,a,9626,a,b,9497,a),flip(a)].">
      <j1 rule="hyper" parents="40 9626 9497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11200">
    <literal><![CDATA[
      K(x,T(y / ((K(x,z) * u) * w),v5)) = K(x,T(y / (u * w),v5))
    ]]></literal>
    <justification jstring="[hyper(299,a,9341,a(flip),b,9963,a),flip(a)].">
      <j1 rule="hyper" parents="299 9341 9963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11201">
    <literal><![CDATA[
      K(x,T(y / ((z * T(x,u)) * w),v5)) = K(x,T(y / ((z * x) * w),v5))
    ]]></literal>
    <justification jstring="[para(9465(a,1),11200(a,1,2,1,2,1))].">
      <j1 rule="para" parents="9465 11200"/>
    </justification>
  </clause>

  <clause id="11202">
    <literal><![CDATA[
      K(x,T(y / ((z * x) * u),z * u)) = K(x,(z * u) \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(65,a,10997,a(flip),b,11201,a),flip(a)].">
      <j1 rule="hyper" parents="65 10997 11201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11204">
    <literal><![CDATA[
      K(x,((y * x) * z) \ u) = K(x,(y * z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,10740,a(flip),b,11202,a)].">
      <j1 rule="hyper" parents="65 10740 11202"/>
    </justification>
  </clause>

  <clause id="11205">
    <literal><![CDATA[
      K(x,((x \ y) * z) \ (x \ u)) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,9949,a(flip),b,11204,a),flip(a)].">
      <j1 rule="hyper" parents="65 9949 11204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11206">
    <literal><![CDATA[
      K(x,((y * x) * (y \ 1)) \ z) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(164(a,1),11204(a,2,2))].">
      <j1 rule="para" parents="164 11204"/>
    </justification>
  </clause>

  <clause id="11207">
    <literal><![CDATA[
      K(x,a(x,y,y \ 1) \ z) = K(x,x \ (x * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,9937,a(flip),b,11206,a)].">
      <j1 rule="hyper" parents="65 9937 11206"/>
    </justification>
  </clause>

  <clause id="11209">
    <literal><![CDATA[
      K(x,a(x,y,y \ 1) \ z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),11207(a,2,2))].">
      <j1 rule="para" parents="9 11207"/>
    </justification>
  </clause>

  <clause id="11210">
    <literal><![CDATA[
      K(x,y \ R(x,z,z \ 1)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,9595,a(flip),b,11209,a),flip(a)].">
      <j1 rule="hyper" parents="65 9595 11209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11212">
    <literal><![CDATA[
      K(x,((x \ y) * z) \ 1) = K(x,(y * z) \ x)
    ]]></literal>
    <justification jstring="[para(68(a,1),11205(a,1,2,2))].">
      <j1 rule="para" parents="68 11205"/>
    </justification>
  </clause>

  <clause id="11213">
    <literal><![CDATA[
      K(x,x \ y) * (z * (x \ y)) = T(z * (y / x),K(y,x))
    ]]></literal>
    <justification jstring="[hyper(146,a,10351,a)].">
      <j1 rule="hyper" parents="146 10351"/>
    </justification>
  </clause>

  <clause id="11214">
    <literal><![CDATA[
      K(x,x \ y) * (z * (x \ y)) = T(z * (y / x),K(x,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,8050,a,b,11213,a),flip(a)].">
      <j1 rule="hyper" parents="299 8050 11213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11215">
    <literal><![CDATA[
      K(L(x,y,z),L(x,y,z) \ 1) * (L(x,y,z) \ x) = T(x * (1 / L(x,y,z)),K(L(x,y,z),1))
    ]]></literal>
    <justification jstring="[para(1353(a,1),11214(a,1,2))].">
      <j1 rule="para" parents="1353 11214"/>
    </justification>
  </clause>

  <clause id="11216">
    <literal><![CDATA[
      T(((x \ 1) \ 1) \ T(x * y,x \ 1),K(x,1)) = K(x,x \ 1) * (((x \ 1) \ y) * (x \ 1))
    ]]></literal>
    <justification jstring="[para(3781(a,2),11214(a,2,1)),flip(a)].">
      <j1 rule="para" parents="3781 11214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11217">
    <literal><![CDATA[
      T((x / (1 / (x \ y))) / x,1 / (y / x)) = (((x / (1 / (x \ y))) / x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,9991,a(flip),b,10392,a)].">
      <j1 rule="hyper" parents="65 9991 10392"/>
    </justification>
  </clause>

  <clause id="11218">
    <literal><![CDATA[
      T((x / (1 / (x \ y))) / x,1 / (y / x)) = (1 / ((x / ((x \ y) \ 1)) / x)) \ 1
    ]]></literal>
    <justification jstring="[para(9776(a,2),11217(a,2,1))].">
      <j1 rule="para" parents="9776 11217"/>
    </justification>
  </clause>

  <clause id="11220">
    <literal><![CDATA[
      T((x / (1 / (x \ y))) / x,1 / (y / x)) != z
    ]]></literal>
    <literal><![CDATA[
      (x / ((x \ y) \ 1)) / x = z
    ]]></literal>
    <justification jstring="[para(11218(a,2),317(a,1))].">
      <j1 rule="para" parents="11218 317"/>
    </justification>
  </clause>

  <clause id="11222">
    <literal><![CDATA[
      K((x \ 1) \ 1,(y * (L(z,x \ 1,x) / x)) \ u) = K(x,(y * (x \ z)) \ u)
    ]]></literal>
    <justification jstring="[hyper(10255,a,10491,a),flip(a)].">
      <j1 rule="hyper" parents="10255 10491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11223">
    <literal><![CDATA[
      K(x,(y * (L(z,x \ 1,x) / x)) \ u) = K(x,(y * (x \ z)) \ u)
    ]]></literal>
    <justification jstring="[hyper(5318,a,11222,a)].">
      <j1 rule="hyper" parents="5318 11222"/>
    </justification>
  </clause>

  <clause id="11224">
    <literal><![CDATA[
      K(x,(y * (x \ L(z,x \ 1,x))) \ u) = K(x,(y * (x \ z)) \ u)
    ]]></literal>
    <justification jstring="[hyper(10373,a,11223,a)].">
      <j1 rule="hyper" parents="10373 11223"/>
    </justification>
  </clause>

  <clause id="11225">
    <literal><![CDATA[
      K(x,(y * ((x \ 1) * z)) \ u) = K(x,(y * (x \ z)) \ u)
    ]]></literal>
    <justification jstring="[para(415(a,1),11224(a,1,2,1,2))].">
      <j1 rule="para" parents="415 11224"/>
    </justification>
  </clause>

  <clause id="11226">
    <literal><![CDATA[
      K(x,(y * ((x \ 1) * z)) \ (x \ u)) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(299,a,10330,a(flip),b,11225,a),flip(a)].">
      <j1 rule="hyper" parents="299 10330 11225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11227">
    <literal><![CDATA[
      K(x,(y * ((x \ 1) * z)) \ T(u,x)) = K(x,(y * z) \ (u * x))
    ]]></literal>
    <justification jstring="[para(22(a,2),11226(a,1,2,2))].">
      <j1 rule="para" parents="22 11226"/>
    </justification>
  </clause>

  <clause id="11228">
    <literal><![CDATA[
      K(x,(y * ((x \ 1) * z)) \ u) = K(x,(y * z) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(8682,a,11227,a)].">
      <j1 rule="hyper" parents="8682 11227"/>
    </justification>
  </clause>

  <clause id="11229">
    <literal><![CDATA[
      K(x,(y * (x \ z)) \ u) = K(x,(y * z) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(65,a,11225,a(flip),b,11228,a)].">
      <j1 rule="hyper" parents="65 11225 11228"/>
    </justification>
  </clause>

  <clause id="11230">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ u) = K(x,(y * z) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(10374,a,11229,a)].">
      <j1 rule="hyper" parents="10374 11229"/>
    </justification>
  </clause>

  <clause id="11231">
    <literal><![CDATA[
      L(K(x,y \ ((z \ u) * x)),z \ u,z) = K(x,(z * y) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(65,a,8984,a,b,11229,a)].">
      <j1 rule="hyper" parents="65 8984 11229"/>
    </justification>
  </clause>

  <clause id="11232">
    <literal><![CDATA[
      K(x,((y * K(x \ z,y)) * z) \ (u * x)) = K(x,((x \ z) * y) \ u)
    ]]></literal>
    <justification jstring="[para(5099(a,1),11229(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5099 11229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11233">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,(y * z) \ (u * x))) = K((y * (z / x)) \ u,x)
    ]]></literal>
    <justification jstring="[para(11229(a,1),8928(a,1,2,2))].">
      <j1 rule="para" parents="11229 8928"/>
    </justification>
  </clause>

  <clause id="11234">
    <literal><![CDATA[
      L(K(x,(y * z) \ ((u \ w) * x)),u \ w,u) = K(x,(u * (y * (z / x))) \ w)
    ]]></literal>
    <justification jstring="[para(11229(a,1),8986(a,1,1))].">
      <j1 rule="para" parents="11229 8986"/>
    </justification>
  </clause>

  <clause id="11235">
    <literal><![CDATA[
      K(x,(((K(y,x \ z) / y) \ 1) * z) \ (u * x)) = K(x,((x \ z) * y) \ u)
    ]]></literal>
    <justification jstring="[para(5548(a,2),11232(a,1,2,1,1))].">
      <j1 rule="para" parents="5548 11232"/>
    </justification>
  </clause>

  <clause id="11236">
    <literal><![CDATA[
      K((x * (y / z)) \ u,z) = K((x * y) \ (u * z),z)
    ]]></literal>
    <justification jstring="[hyper(5547,a,11233,a),flip(a)].">
      <j1 rule="hyper" parents="5547 11233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11237">
    <literal><![CDATA[
      K((x * (y \ z)) \ u,y) = K((x * z) \ (u * y),y)
    ]]></literal>
    <justification jstring="[hyper(9925,a,11236,a)].">
      <j1 rule="hyper" parents="9925 11236"/>
    </justification>
  </clause>

  <clause id="11238">
    <literal><![CDATA[
      K(x,((1 / (K(y,x \ z) / y)) * z) \ (u * x)) = K(x,((x \ z) * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,5664,a,b,11235,a)].">
      <j1 rule="hyper" parents="65 5664 11235"/>
    </justification>
  </clause>

  <clause id="11239">
    <literal><![CDATA[
      K(x,(y * (z * (u / x))) \ w) = K(x,(y * (z * u)) \ (w * x))
    ]]></literal>
    <justification jstring="[hyper(65,a,11231,a(flip),b,11234,a),flip(a)].">
      <j1 rule="hyper" parents="65 11231 11234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11240">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ (u \ (y * (z / x)))) = K(x,(u * (y * z)) \ ((y * (x \ z)) * x))
    ]]></literal>
    <justification jstring="[hyper(65,a,8931,a(flip),b,11239,a)].">
      <j1 rule="hyper" parents="65 8931 11239"/>
    </justification>
  </clause>

  <clause id="11241">
    <literal><![CDATA[
      K(x,(y * (z * u)) \ ((z * (x \ u)) * x)) = K(x,T(y \ 1,z * (u / x)))
    ]]></literal>
    <justification jstring="[hyper(65,a,7928,a,b,11240,a),flip(a)].">
      <j1 rule="hyper" parents="65 7928 11240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11242">
    <literal><![CDATA[
      K(x,(y * (z * u)) \ ((z * (x \ u)) * x)) = K(x,T(y \ 1,z * u))
    ]]></literal>
    <justification jstring="[hyper(299,a,9441,a(flip),b,11241,a),flip(a)].">
      <j1 rule="hyper" parents="299 9441 11241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11243">
    <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),11242(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 11242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11244">
    <literal><![CDATA[
      K(x,y \ ((z * (x \ u)) * x)) = K(x,((z * u) \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,7602,a(flip),b,11243,a),flip(a)].">
      <j1 rule="hyper" parents="65 7602 11243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11245">
    <literal><![CDATA[
      K(x,y \ ((z * (x \ u)) * x)) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(299,a,6814,a(flip),b,11244,a),flip(a)].">
      <j1 rule="hyper" parents="299 6814 11244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11246">
    <literal><![CDATA[
      K(x,x \ (y * z)) = K(x,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(5309,a,11245,a),flip(a)].">
      <j1 rule="hyper" parents="5309 11245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11247">
    <literal><![CDATA[
      K(x,y \ ((x \ y) * z)) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,8877,a(flip),b,11245,a),flip(a)].">
      <j1 rule="hyper" parents="65 8877 11245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11248">
    <literal><![CDATA[
      (x * K(y,z * (y \ u))) \ x = K(y \ (z * u),y)
    ]]></literal>
    <justification jstring="[para(11246(a,1),7200(a,1,1,2))].">
      <j1 rule="para" parents="11246 7200"/>
    </justification>
  </clause>

  <clause id="11249">
    <literal><![CDATA[
      T(x,K(y,z * (y \ u))) = T(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(11246(a,1),8257(a,1,2))].">
      <j1 rule="para" parents="11246 8257"/>
    </justification>
  </clause>

  <clause id="11250">
    <literal><![CDATA[
      L(K(x,x \ y),y,x \ z) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,8441,a,b,11247,a)].">
      <j1 rule="hyper" parents="65 8441 11247"/>
    </justification>
  </clause>

  <clause id="11252">
    <literal><![CDATA[
      L(K(x,x \ y),y,z) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(9(a,1),11250(a,1,3))].">
      <j1 rule="para" parents="9 11250"/>
    </justification>
  </clause>

  <clause id="11253">
    <literal><![CDATA[
      K(x,(y * x) \ z) = K(x,x \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(10251,a,11252,a)].">
      <j1 rule="hyper" parents="10251 11252"/>
    </justification>
  </clause>

  <clause id="11254">
    <literal><![CDATA[
      K(x,y \ (x \ z)) = K(x,x \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(8983,a,11252,a)].">
      <j1 rule="hyper" parents="8983 11252"/>
    </justification>
  </clause>

  <clause id="11256">
    <literal><![CDATA[
      a(x,y,K(z,z \ y)) = 1
    ]]></literal>
    <justification jstring="[hyper(55,a,11252,a)].">
      <j1 rule="hyper" parents="55 11252"/>
    </justification>
  </clause>

  <clause id="11257">
    <literal><![CDATA[
      a(x,y,K(z \ y,z)) = 1
    ]]></literal>
    <justification jstring="[para(5206(a,1),11256(a,1,3))].">
      <j1 rule="para" parents="5206 11256"/>
    </justification>
  </clause>

  <clause id="11258">
    <literal><![CDATA[
      L(K(x \ y,x),y,z) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(54,a,11257,a)].">
      <j1 rule="hyper" parents="54 11257"/>
    </justification>
  </clause>

  <clause id="11259">
    <literal><![CDATA[
      K(x \ (y \ (x * z)),y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[hyper(8705,a,11258,a)].">
      <j1 rule="hyper" parents="8705 11258"/>
    </justification>
  </clause>

  <clause id="11261">
    <literal><![CDATA[
      K((x \ y) \ z,x \ y) = K(y \ (x * z),x \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,7421,a(flip),b,11258,a),flip(a)].">
      <j1 rule="hyper" parents="65 7421 11258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11262">
    <literal><![CDATA[
      K(x,x \ (y \ (x * z))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(9(a,1),11254(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 11254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11264">
    <literal><![CDATA[
      K(x \ (y \ z),y) = K(y \ (x \ z),y)
    ]]></literal>
    <justification jstring="[para(10(a,1),11259(a,1,1,2,2))].">
      <j1 rule="para" parents="10 11259"/>
    </justification>
  </clause>

  <clause id="11265">
    <literal><![CDATA[
      (x * y) * K(z \ y,z) = x * ((z \ y) * z)
    ]]></literal>
    <justification jstring="[para(11259(a,1),8478(a,1,2))].">
      <j1 rule="para" parents="11259 8478"/>
    </justification>
  </clause>

  <clause id="11266">
    <literal><![CDATA[
      K(x \ ((x \ y) \ z),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,7866,a(flip),b,11264,a),flip(a)].">
      <j1 rule="hyper" parents="65 7866 11264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11267">
    <literal><![CDATA[
      K(L(x,y,z) \ ((x \ (L(x,y,z) \ u)) \ w),L(x,y,z)) = K((x \ u) \ w,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(1366(a,1),11266(a,1,1,2,1))].">
      <j1 rule="para" parents="1366 11266"/>
    </justification>
  </clause>

  <clause id="11268">
    <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(6362(a,1),11266(a,1,1,2,1))].">
      <j1 rule="para" parents="6362 11266"/>
    </justification>
  </clause>

  <clause id="11269">
    <literal><![CDATA[
      R(x,y,K(z \ y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(914,a,11265,a)].">
      <j1 rule="hyper" parents="914 11265"/>
    </justification>
  </clause>

  <clause id="11271">
    <literal><![CDATA[
      R(x,y / z,z) = R(x,z \ y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,10965,a(flip),b,11269,a),flip(a)].">
      <j1 rule="hyper" parents="65 10965 11269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11272">
    <literal><![CDATA[
      R(x,y * z,K(z,y)) = x
    ]]></literal>
    <justification jstring="[para(9(a,1),11269(a,1,3,1))].">
      <j1 rule="para" parents="9 11269"/>
    </justification>
  </clause>

  <clause id="11273">
    <literal><![CDATA[
      R(x,y,T(z,y)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(10270,a,11272,a)].">
      <j1 rule="hyper" parents="10270 11272"/>
    </justification>
  </clause>

  <clause id="11274">
    <literal><![CDATA[
      (x * (y * z)) * K(z,y) = x * (z * y)
    ]]></literal>
    <justification jstring="[para(11272(a,1),548(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11272 548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11279">
    <literal><![CDATA[
      R(x,y,z) * (z * y) = (x * y) * T(z,y)
    ]]></literal>
    <justification jstring="[para(11273(a,1),546(a,1,1))].">
      <j1 rule="para" parents="11273 546"/>
    </justification>
  </clause>

  <clause id="11281">
    <literal><![CDATA[
      R(x,y,K(z,T(u,y))) = R(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(7489(a,2),11273(a,1,3))].">
      <j1 rule="para" parents="7489 11273"/>
    </justification>
  </clause>

  <clause id="11284">
    <literal><![CDATA[
      R(K(x,(y / (z / u)) \ x),u \ z,u) = K(x,z / ((x \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,8467,a(flip),b,11271,a),flip(a)].">
      <j1 rule="hyper" parents="65 8467 11271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11285">
    <literal><![CDATA[
      R(K(x,(y / z) / u),z \ y,z) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,6429,a(flip),b,11271,a),flip(a)].">
      <j1 rule="hyper" parents="65 6429 11271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11287">
    <literal><![CDATA[
      R(x,y \ z,y) * z = (x * (z / y)) * y
    ]]></literal>
    <justification jstring="[para(11271(a,1),354(a,1,1))].">
      <j1 rule="para" parents="11271 354"/>
    </justification>
  </clause>

  <clause id="11288">
    <literal><![CDATA[
      K(L(x,y,z),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(9417,a,11274,a)].">
      <j1 rule="hyper" parents="9417 11274"/>
    </justification>
  </clause>

  <clause id="11289">
    <literal><![CDATA[
      K(x,L(y,x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(9413,a,11274,a)].">
      <j1 rule="hyper" parents="9413 11274"/>
    </justification>
  </clause>

  <clause id="11290">
    <literal><![CDATA[
      (x * K(y,z)) / (y * z) = x / (z * y)
    ]]></literal>
    <justification jstring="[hyper(626,a,11274,a)].">
      <j1 rule="hyper" parents="626 11274"/>
    </justification>
  </clause>

  <clause id="11291">
    <literal><![CDATA[
      ((x * (y * z)) / z) \ (x * (z * y)) = T(z,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,11274,a(flip),b,6869,a)].">
      <j1 rule="hyper" parents="119 11274 6869"/>
    </justification>
  </clause>

  <clause id="11292">
    <literal><![CDATA[
      (x * y) * K(z,y / z) = x * (z * (y / z))
    ]]></literal>
    <justification jstring="[para(12(a,1),11274(a,1,1,2))].">
      <j1 rule="para" parents="12 11274"/>
    </justification>
  </clause>

  <clause id="11293">
    <literal><![CDATA[
      ((x * y) * z) * K(z,y) = R(x,y,z) * (z * y)
    ]]></literal>
    <justification jstring="[para(103(a,1),11274(a,1,1))].">
      <j1 rule="para" parents="103 11274"/>
    </justification>
  </clause>

  <clause id="11295">
    <literal><![CDATA[
      L(x,(y * (z * u)) * (K(u,z) \ 1),w) = L(x,y * (u * z),w)
    ]]></literal>
    <justification jstring="[para(11274(a,1),2888(a,2,2))].">
      <j1 rule="para" parents="11274 2888"/>
    </justification>
  </clause>

  <clause id="11296">
    <literal><![CDATA[
      (x * (K(y,z) * (K(y,u) * w))) * K(K(y,u) * w,K(y,z)) = x * (K(y,u) * (w * K(y,z)))
    ]]></literal>
    <justification jstring="[para(7689(a,1),11274(a,2,2))].">
      <j1 rule="para" parents="7689 11274"/>
    </justification>
  </clause>

  <clause id="11297">
    <literal><![CDATA[
      K(x,y) * L(x,y,z) = L(T(x,y),y,z)
    ]]></literal>
    <justification jstring="[para(11288(a,1),5165(a,1,1))].">
      <j1 rule="para" parents="11288 5165"/>
    </justification>
  </clause>

  <clause id="11299">
    <literal><![CDATA[
      L(K(x,y),T(y,z) * u,w) = K(L(x,y,v5),L(y,u,w))
    ]]></literal>
    <justification jstring="[para(11288(a,1),9334(a,1,1))].">
      <j1 rule="para" parents="11288 9334"/>
    </justification>
  </clause>

  <clause id="11300">
    <literal><![CDATA[
      T(x,R(x,y,z) * u) \ (x * K(x,u)) = L(x,u,R(x,y,z)) \ x
    ]]></literal>
    <justification jstring="[para(11288(a,1),10215(a,1,2,2))].">
      <j1 rule="para" parents="11288 10215"/>
    </justification>
  </clause>

  <clause id="11303">
    <literal><![CDATA[
      L(K(x,y),z,y * x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,11142,a(flip),b,11289,a)].">
      <j1 rule="hyper" parents="65 11142 11289"/>
    </justification>
  </clause>

  <clause id="11304">
    <literal><![CDATA[
      T(x,L(y,x,z)) = x * K(x,y)
    ]]></literal>
    <justification jstring="[para(11289(a,1),5083(a,2,2))].">
      <j1 rule="para" parents="11289 5083"/>
    </justification>
  </clause>

  <clause id="11307">
    <literal><![CDATA[
      L(K(x,y),z,y * x) = K(x,L(y,x,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,11289,a,b,11303,a),flip(a)].">
      <j1 rule="hyper" parents="299 11289 11303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11308">
    <literal><![CDATA[
      K(x,y) * ((y * x) * z) = (y * x) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(11303(a,1),10830(a,1,1))].">
      <j1 rule="para" parents="11303 10830"/>
    </justification>
  </clause>

  <clause id="11309">
    <literal><![CDATA[
      T(x,L(y,x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,5083,a,b,11304,a),flip(a)].">
      <j1 rule="hyper" parents="299 5083 11304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11310">
    <literal><![CDATA[
      T(x,y \ (x \ (y * z))) = T(x,x \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,8651,a(flip),b,11309,a)].">
      <j1 rule="hyper" parents="65 8651 11309"/>
    </justification>
  </clause>

  <clause id="11312">
    <literal><![CDATA[
      L(x,y,z) * T(y,x) = y * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(11309(a,1),107(a,1,2))].">
      <j1 rule="para" parents="11309 107"/>
    </justification>
  </clause>

  <clause id="11314">
    <literal><![CDATA[
      T(x \ y,(x \ y) \ z) = T(x \ y,y \ (x * z))
    ]]></literal>
    <justification jstring="[para(520(a,1),11309(a,1,2)),flip(a)].">
      <j1 rule="para" parents="520 11309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11315">
    <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(531(a,1),11309(a,1,2))].">
      <j1 rule="para" parents="531 11309"/>
    </justification>
  </clause>

  <clause id="11316">
    <literal><![CDATA[
      L(x,y,z) = (z * T(y,x)) \ (z * (T(y,x) * x))
    ]]></literal>
    <justification jstring="[para(11309(a,1),10350(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11309 10350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11317">
    <literal><![CDATA[
      T(x / (y * z),z * y) != u
    ]]></literal>
    <literal><![CDATA[
      (z * y) \ (x * K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(11290(a,1),400(a,1,1))].">
      <j1 rule="para" parents="11290 400"/>
    </justification>
  </clause>

  <clause id="11320">
    <literal><![CDATA[
      K(x,L(y,x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(11307(a,1),500(a,1)),flip(b)].">
      <j1 rule="para" parents="11307 500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11322">
    <literal><![CDATA[
      L(K(x,y),z,y * x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(11307(a,2),7856(a,1))].">
      <j1 rule="para" parents="11307 7856"/>
    </justification>
  </clause>

  <clause id="11325">
    <literal><![CDATA[
      L(K(x,y),z * x,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(L(x,z,u),y) = w
    ]]></literal>
    <justification jstring="[para(7850(a,1),11320(a,1))].">
      <j1 rule="para" parents="7850 11320"/>
    </justification>
  </clause>

  <clause id="11326">
    <literal><![CDATA[
      L(K(x \ y,x),y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,x) = u
    ]]></literal>
    <justification jstring="[para(9186(a,1),11320(a,1))].">
      <j1 rule="para" parents="9186 11320"/>
    </justification>
  </clause>

  <clause id="11328">
    <literal><![CDATA[
      K(x \ (y \ (x * z)),L(y,u,w)) = (w * (u * T(y,y \ z))) \ (w * (u * y))
    ]]></literal>
    <justification jstring="[para(11310(a,1),9498(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11310 9498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11330">
    <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(11312(a,1),1354(a,1,2,2))].">
      <j1 rule="para" parents="11312 1354"/>
    </justification>
  </clause>

  <clause id="11332">
    <literal><![CDATA[
      (x * T(y,z)) * T(T(K(y,u),w),T(y,z)) = x * (T(K(y,u),w) * T(y,z))
    ]]></literal>
    <justification jstring="[para(8142(a,1),11279(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8142 11279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11333">
    <literal><![CDATA[
      (x * y) * K(z,z \ y) = x * (z * (y / z))
    ]]></literal>
    <justification jstring="[para(5205(a,1),11292(a,1,2))].">
      <j1 rule="para" parents="5205 11292"/>
    </justification>
  </clause>

  <clause id="11334">
    <literal><![CDATA[
      K(x / y,z * (y * (x / y))) = K(x / y,z * x)
    ]]></literal>
    <justification jstring="[para(11292(a,1),8528(a,1,2))].">
      <j1 rule="para" parents="11292 8528"/>
    </justification>
  </clause>

  <clause id="11336">
    <literal><![CDATA[
      (x * (y * z)) * K(y,y \ (y * z)) = x * (T(y,z) * z)
    ]]></literal>
    <justification jstring="[para(4263(a,2),11333(a,2,2))].">
      <j1 rule="para" parents="4263 11333"/>
    </justification>
  </clause>

  <clause id="11337">
    <literal><![CDATA[
      L(x,T(y,x),z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,18,a,b,11316,a)].">
      <j1 rule="hyper" parents="299 18 11316"/>
    </justification>
  </clause>

  <clause id="11339">
    <literal><![CDATA[
      L(x,y / x,z) = L(x,x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,5735,a(flip),b,11337,a)].">
      <j1 rule="hyper" parents="65 5735 11337"/>
    </justification>
  </clause>

  <clause id="11342">
    <literal><![CDATA[
      L(x,x \ (y \ z),y) = (y * ((y \ z) / x)) \ z
    ]]></literal>
    <justification jstring="[hyper(65,a,602,a(flip),b,11339,a),flip(a)].">
      <j1 rule="hyper" parents="65 602 11339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11343">
    <literal><![CDATA[
      K(L(x,x \ y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,u),y,z) = w
    ]]></literal>
    <justification jstring="[para(11339(a,1),8960(a,1,1))].">
      <j1 rule="para" parents="11339 8960"/>
    </justification>
  </clause>

  <clause id="11345">
    <literal><![CDATA[
      K(x \ (y * z),x) = K(y * (x \ z),x)
    ]]></literal>
    <justification jstring="[hyper(7209,a,11248,a),flip(a)].">
      <j1 rule="hyper" parents="7209 11248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11346">
    <literal><![CDATA[
      K(x * (y \ (x \ z)),y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),11345(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10 11345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11347">
    <literal><![CDATA[
      K((x \ y) \ T(z,x),x \ y) = K(y \ (z * x),x \ y)
    ]]></literal>
    <justification jstring="[para(107(a,1),11261(a,2,1,2))].">
      <j1 rule="para" parents="107 11261"/>
    </justification>
  </clause>

  <clause id="11349">
    <literal><![CDATA[
      T(x \ y,z / (y / x)) = T(x \ y,y \ (x * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,8733,a,b,11314,a)].">
      <j1 rule="hyper" parents="65 8733 11314"/>
    </justification>
  </clause>

  <clause id="11350">
    <literal><![CDATA[
      T(x / (y / z),T(z \ y,y \ (z * x))) = T((y / z) \ x,K(y,z))
    ]]></literal>
    <justification jstring="[para(11349(a,1),9008(a,1,2))].">
      <j1 rule="para" parents="11349 9008"/>
    </justification>
  </clause>

  <clause id="11351">
    <literal><![CDATA[
      K(L(x,y,z),L(y,u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,9334,a(flip),b,11299,a),flip(a)].">
      <j1 rule="hyper" parents="65 9334 11299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11353">
    <literal><![CDATA[
      K(((x / y) \ z) / y,L(y,u,w)) = K((y * (x \ z)) / y,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(1036(a,1),11351(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1036 11351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11357">
    <literal><![CDATA[
      (x * (y * z)) * K(y,z) = x * (T(y,z) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),11336(a,1,2,2))].">
      <j1 rule="para" parents="9 11336"/>
    </justification>
  </clause>

  <clause id="11358">
    <literal><![CDATA[
      L(x,(y * (z * u)) * K(z,u),w) = L(x,y * (u * z),w)
    ]]></literal>
    <justification jstring="[para(5197(a,1),11295(a,1,2,2))].">
      <j1 rule="para" parents="5197 11295"/>
    </justification>
  </clause>

  <clause id="11359">
    <literal><![CDATA[
      L(x,y * (T(z,u) * u),w) = L(x,y * (u * z),w)
    ]]></literal>
    <justification jstring="[para(11357(a,1),11358(a,1,2))].">
      <j1 rule="para" parents="11357 11358"/>
    </justification>
  </clause>

  <clause id="11360">
    <literal><![CDATA[
      L(x,y * ((z \ u) * z),w) = L(x,y * (z * (u / z)),w)
    ]]></literal>
    <justification jstring="[para(109(a,1),11359(a,1,2,2,1))].">
      <j1 rule="para" parents="109 11359"/>
    </justification>
  </clause>

  <clause id="11361">
    <literal><![CDATA[
      K(R(x,y,z) * u,x) * K(x,u) = L(x,u,R(x,y,z)) \ x
    ]]></literal>
    <justification jstring="[hyper(5533,a,11300,a)].">
      <j1 rule="hyper" parents="5533 11300"/>
    </justification>
  </clause>

  <clause id="11363">
    <literal><![CDATA[
      K(((x / y) \ z) / y,L(y,u,w)) = K(y \ (y * (x \ z)),L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(299,a,7626,a(flip),b,11353,a),flip(a)].">
      <j1 rule="hyper" parents="299 7626 11353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11364">
    <literal><![CDATA[
      K(((x / y) \ z) / y,L(y,u,w)) = K(x \ z,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(299,a,722,a(flip),b,11363,a),flip(a)].">
      <j1 rule="hyper" parents="299 722 11363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11365">
    <literal><![CDATA[
      K(x \ ((y / x) \ z),L(x,u,w)) = K(y \ z,L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(7808,a,11364,a)].">
      <j1 rule="hyper" parents="7808 11364"/>
    </justification>
  </clause>

  <clause id="11367">
    <literal><![CDATA[
      K(x \ ((x \ y) \ z),L(x,u,w)) = K(y \ z,L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(10646,a,11365,a)].">
      <j1 rule="hyper" parents="10646 11365"/>
    </justification>
  </clause>

  <clause id="11368">
    <literal><![CDATA[
      (x * T(y,z)) * T(K(y,u),w) = x * (T(K(y,u),w) * T(y,z))
    ]]></literal>
    <justification jstring="[para(3587(a,1),11332(a,1,2))].">
      <j1 rule="para" parents="3587 11332"/>
    </justification>
  </clause>

  <clause id="11369">
    <literal><![CDATA[
      (x \ y) * (T(K(x,z),y) * T(x,u)) = K(x,z) * ((x \ y) * T(x,u))
    ]]></literal>
    <justification jstring="[hyper(8678,a,11368,a),flip(a)].">
      <j1 rule="hyper" parents="8678 11368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11371">
    <literal><![CDATA[
      K(x,y) * ((x \ z) * T(x,z)) = (x \ z) * T(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(7542(a,1),11369(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7542 11369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11372">
    <literal><![CDATA[
      K((T(x,y) / z) / (x / z),u) * ((((T(x,y) / z) / (x / z)) \ (T(x,y) / z)) * K((z \ 1) \ (x / z),y)) = (((T(x,y) / z) / (x / z)) \ (T(x,y) / z)) * T(T((T(x,y) / z) / (x / z),T(x,y) / z),u)
    ]]></literal>
    <justification jstring="[para(7690(a,1),11371(a,1,2,2))].">
      <j1 rule="para" parents="7690 11371"/>
    </justification>
  </clause>

  <clause id="11373">
    <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(65,a,25,a,b,11315,a)].">
      <j1 rule="hyper" parents="65 25 11315"/>
    </justification>
  </clause>

  <clause id="11375">
    <literal><![CDATA[
      K(x \ (y \ (x * z)),L(y,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(y \ z,L(y,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(11328(a,2),9499(a,1))].">
      <j1 rule="para" parents="11328 9499"/>
    </justification>
  </clause>

  <clause id="11376">
    <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(10343(a,1),11373(a,1,1))].">
      <j1 rule="para" parents="10343 11373"/>
    </justification>
  </clause>

  <clause id="11377">
    <literal><![CDATA[
      T(L(x,y,z),L(x,y,z) \ u) = L(T(x,x \ u),y,z)
    ]]></literal>
    <justification jstring="[para(11310(a,1),11376(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11310 11376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11379">
    <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(107(a,1),11330(a,1,1,1))].">
      <j1 rule="para" parents="107 11330"/>
    </justification>
  </clause>

  <clause id="11380">
    <literal><![CDATA[
      K(L(x,y,z),x * T(y,x)) = K(x,y * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(1800,a,11379,a),flip(a)].">
      <j1 rule="hyper" parents="1800 11379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11381">
    <literal><![CDATA[
      K(L(x,y,z),y * x) = K(x,y * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(107(a,1),11380(a,1,2))].">
      <j1 rule="para" parents="107 11380"/>
    </justification>
  </clause>

  <clause id="11382">
    <literal><![CDATA[
      K(x,y * L(x,y,z)) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(8686,a,11381,a),flip(a)].">
      <j1 rule="hyper" parents="8686 11381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11384">
    <literal><![CDATA[
      L(K(x,x * y),z * x,u) = K(L(x,z,u),y * L(x,y,w))
    ]]></literal>
    <justification jstring="[para(11382(a,1),7433(a,1,1))].">
      <j1 rule="para" parents="11382 7433"/>
    </justification>
  </clause>

  <clause id="11385">
    <literal><![CDATA[
      K(L(x,y,z),u * L(x,u,w)) = K(L(x,y,z),x * u)
    ]]></literal>
    <justification jstring="[hyper(11325,a,11384,a),flip(a)].">
      <j1 rule="hyper" parents="11325 11384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11386">
    <literal><![CDATA[
      L(K(L(x,y,z),x * y),y,z) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(11385(a,1),10591(a,1,1))].">
      <j1 rule="para" parents="11385 10591"/>
    </justification>
  </clause>

  <clause id="11387">
    <literal><![CDATA[
      L(K(x,x * y),y,z) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(9165(a,1),11386(a,1,1))].">
      <j1 rule="para" parents="9165 11386"/>
    </justification>
  </clause>

  <clause id="11389">
    <literal><![CDATA[
      K(x,y \ (z * x)) = K(x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,10588,a(flip),b,11387,a)].">
      <j1 rule="hyper" parents="65 10588 11387"/>
    </justification>
  </clause>

  <clause id="11390">
    <literal><![CDATA[
      1 / L(K(x,x * y),y,z) = K(x * y,x)
    ]]></literal>
    <justification jstring="[para(11387(a,2),5209(a,1,2))].">
      <j1 rule="para" parents="11387 5209"/>
    </justification>
  </clause>

  <clause id="11394">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ x)) = K(x,x * (L(y,z,u) \ y))
    ]]></literal>
    <justification jstring="[para(1352(a,1),11389(a,1,2))].">
      <j1 rule="para" parents="1352 11389"/>
    </justification>
  </clause>

  <clause id="11395">
    <literal><![CDATA[
      K(x,x * ((y * z) \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ x) = u
    ]]></literal>
    <justification jstring="[para(11389(a,1),8405(a,1))].">
      <j1 rule="para" parents="11389 8405"/>
    </justification>
  </clause>

  <clause id="11396">
    <literal><![CDATA[
      L(K(x * y,x),y,z) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(6351,a,11390,a)].">
      <j1 rule="hyper" parents="6351 11390"/>
    </justification>
  </clause>

  <clause id="11397">
    <literal><![CDATA[
      1 / ((x * (y \ T(y * z,y))) \ (x * z)) = K(y * z,y)
    ]]></literal>
    <justification jstring="[para(9119(a,2),11390(a,1,2))].">
      <j1 rule="para" parents="9119 11390"/>
    </justification>
  </clause>

  <clause id="11398">
    <literal><![CDATA[
      L(K(x * y,x),y,z) = K(y * x,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,5980,a,b,11396,a),flip(a)].">
      <j1 rule="hyper" parents="299 5980 11396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11399">
    <literal><![CDATA[
      K(x \ (y * z),z) = K(z * (x \ y),z)
    ]]></literal>
    <justification jstring="[hyper(65,a,9539,a(flip),b,11396,a)].">
      <j1 rule="hyper" parents="65 9539 11396"/>
    </justification>
  </clause>

  <clause id="11400">
    <literal><![CDATA[
      L(K(x * y,y),x,z) = K(x * y,y)
    ]]></literal>
    <justification jstring="[para(5980(a,2),11398(a,1,1))].">
      <j1 rule="para" parents="5980 11398"/>
    </justification>
  </clause>

  <clause id="11401">
    <literal><![CDATA[
      (x * y) * K(y * z,z) = x * (y * K(y * z,z))
    ]]></literal>
    <justification jstring="[para(11400(a,1),94(a,1,2))].">
      <j1 rule="para" parents="11400 94"/>
    </justification>
  </clause>

  <clause id="11402">
    <literal><![CDATA[
      K((x / y) \ z,y) = K(y * (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(8701,a,11399,a)].">
      <j1 rule="hyper" parents="8701 11399"/>
    </justification>
  </clause>

  <clause id="11403">
    <literal><![CDATA[
      K(x * ((y * x) \ z),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(8698,a,11399,a),flip(a)].">
      <j1 rule="hyper" parents="8698 11399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11404">
    <literal><![CDATA[
      K((x \ y) \ z,x) = K(x * (y \ z),x)
    ]]></literal>
    <justification jstring="[hyper(8697,a,11399,a)].">
      <j1 rule="hyper" parents="8697 11399"/>
    </justification>
  </clause>

  <clause id="11405">
    <literal><![CDATA[
      K((x \ y) \ z,z) = K(z * (y \ x),z)
    ]]></literal>
    <justification jstring="[hyper(7430,a,11399,a)].">
      <j1 rule="hyper" parents="7430 11399"/>
    </justification>
  </clause>

  <clause id="11407">
    <literal><![CDATA[
      K(x * (y \ (x \ z)),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,8699,a(flip),b,11399,a),flip(a)].">
      <j1 rule="hyper" parents="65 8699 11399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11409">
    <literal><![CDATA[
      K(x,y \ z) * K(x * (y \ z),x) = a(x,(z \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(11399(a,1),10197(a,1,2))].">
      <j1 rule="para" parents="11399 10197"/>
    </justification>
  </clause>

  <clause id="11410">
    <literal><![CDATA[
      T(K(x * y,T(x,z)),z) = 1 / ((u * (x \ T(x * y,x))) \ (u * y))
    ]]></literal>
    <justification jstring="[hyper(299,a,8098,a,b,11397,a)].">
      <j1 rule="hyper" parents="299 8098 11397"/>
    </justification>
  </clause>

  <clause id="11412">
    <literal><![CDATA[
      a(x,(y \ z) \ 1,x) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,z \ y,x) = u
    ]]></literal>
    <justification jstring="[para(11409(a,1),9699(a,1))].">
      <j1 rule="para" parents="11409 9699"/>
    </justification>
  </clause>

  <clause id="11413">
    <literal><![CDATA[
      T(K(x,K(y,z)) * K(y * z,y),x) = 1 / ((u * (y \ T(y * z,y))) \ (u * z))
    ]]></literal>
    <justification jstring="[para(8045(a,2),11410(a,1,1))].">
      <j1 rule="para" parents="8045 11410"/>
    </justification>
  </clause>

  <clause id="11414">
    <literal><![CDATA[
      1 / ((x * (y \ T(y * z,y))) \ (x * z)) = K(u,K(y,z)) * K(y * z,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(8443,a,11413,a),flip(a)].">
      <j1 rule="hyper" parents="8443 11413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11416">
    <literal><![CDATA[
      (x \ y) * K((x \ 1) \ (x \ y),y \ z) = x \ T(y,((x \ 1) \ (x \ y)) \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),11061(a,1,2,2,1))].">
      <j1 rule="para" parents="10 11061"/>
    </justification>
  </clause>

  <clause id="11417">
    <literal><![CDATA[
      x \ T(y,((x \ 1) \ (x \ y)) \ z) = x \ T(y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(7368,a,11416,a),flip(a)].">
      <j1 rule="hyper" parents="7368 11416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11419">
    <literal><![CDATA[
      K(x,y \ T(z,z \ x)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(11417(a,1),10510(a,1,2))].">
      <j1 rule="para" parents="11417 10510"/>
    </justification>
  </clause>

  <clause id="11420">
    <literal><![CDATA[
      K(x,y \ ((z \ x) \ x)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(108(a,1),11419(a,1,2,2))].">
      <j1 rule="para" parents="108 11419"/>
    </justification>
  </clause>

  <clause id="11421">
    <literal><![CDATA[
      K(x,L(y,((z \ x) \ x) \ 1,(z \ x) \ x) \ z) = K(x,((((z \ x) \ x) \ 1) * y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,6846,a(flip),b,11420,a),flip(a)].">
      <j1 rule="hyper" parents="65 6846 11420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11422">
    <literal><![CDATA[
      K((x * y) \ (z \ ((x * y) * u)),L(z,y,x)) = K(L(z,y,x) \ u,L(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(11326,a,11166,a),flip(a)].">
      <j1 rule="hyper" parents="11326 11166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11423">
    <literal><![CDATA[
      K(L(x,y,z) \ u,L(x,y,z)) = K(x \ u,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(11375,a,11422,a),flip(a)].">
      <j1 rule="hyper" parents="11375 11422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11425">
    <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(65,a,11268,a(flip),b,11423,a),flip(a)].">
      <j1 rule="hyper" parents="65 11268 11423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11426">
    <literal><![CDATA[
      K(x \ ((x \ (L(x,y,z) \ u)) \ w),L(x,y,z)) = K((x \ u) \ w,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,11267,a(flip),b,11423,a),flip(a)].">
      <j1 rule="hyper" parents="65 11267 11423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11427">
    <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(65,a,11367,a(flip),b,11425,a)].">
      <j1 rule="hyper" parents="65 11367 11425"/>
    </justification>
  </clause>

  <clause id="11428">
    <literal><![CDATA[
      K(L(x,y,z) * u,L(x,y,z)) = K((1 / x) \ u,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,7293,a(flip),b,11427,a)].">
      <j1 rule="hyper" parents="65 7293 11427"/>
    </justification>
  </clause>

  <clause id="11429">
    <literal><![CDATA[
      K(x * L(y,z,u),L(y,z,u)) = K((1 / y) \ x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(8632,a,11428,a)].">
      <j1 rule="hyper" parents="8632 11428"/>
    </justification>
  </clause>

  <clause id="11430">
    <literal><![CDATA[
      K(x * L(y,z,u),L(y,z,u)) = K(1 \ (x * y),L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,10230,a(flip),b,11429,a),flip(a)].">
      <j1 rule="hyper" parents="299 10230 11429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11431">
    <literal><![CDATA[
      K(x * L(y,z,u),L(y,z,u)) = K(x * y,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(67(a,1),11430(a,2,1))].">
      <j1 rule="para" parents="67 11430"/>
    </justification>
  </clause>

  <clause id="11432">
    <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(11431(a,1),5248(a,1,1,2))].">
      <j1 rule="para" parents="11431 5248"/>
    </justification>
  </clause>

  <clause id="11433">
    <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(5809(a,1),11432(a,1,1))].">
      <j1 rule="para" parents="5809 11432"/>
    </justification>
  </clause>

  <clause id="11434">
    <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(5980(a,1),11433(a,1,1,1,2))].">
      <j1 rule="para" parents="5980 11433"/>
    </justification>
  </clause>

  <clause id="11435">
    <literal><![CDATA[
      T(L(x * K(x * y,x),z,u),y) = y \ T(L(x,z,u) * y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,4338,a,b,11434,a),flip(a)].">
      <j1 rule="hyper" parents="299 4338 11434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11436">
    <literal><![CDATA[
      L(T(x * K(x * y,x),y),z,u) = y \ T(L(x,z,u) * y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,25,a,b,11435,a)].">
      <j1 rule="hyper" parents="65 25 11435"/>
    </justification>
  </clause>

  <clause id="11437">
    <literal><![CDATA[
      x \ T(L(y,z,u) * x,L(y,z,u)) = L(R(y,x,y),z,u)
    ]]></literal>
    <justification jstring="[para(5674(a,1),11436(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5674 11436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11438">
    <literal><![CDATA[
      R(L(x,y,z),u,L(x,y,z)) = L(R(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(4348,a,11437,a)].">
      <j1 rule="hyper" parents="4348 11437"/>
    </justification>
  </clause>

  <clause id="11439">
    <literal><![CDATA[
      R(x,y,L(x,z,u)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(151,a,11438,a)].">
      <j1 rule="hyper" parents="151 11438"/>
    </justification>
  </clause>

  <clause id="11440">
    <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(11438(a,1),7467(a,1,2))].">
      <j1 rule="para" parents="11438 7467"/>
    </justification>
  </clause>

  <clause id="11441">
    <literal><![CDATA[
      T(x * K(y * x,x),y) = R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,5248,a,b,11439,a)].">
      <j1 rule="hyper" parents="299 5248 11439"/>
    </justification>
  </clause>

  <clause id="11443">
    <literal><![CDATA[
      K(x * L(y,z,u),y) = (w * T(y,x)) \ (w * R(y,x,y))
    ]]></literal>
    <justification jstring="[para(11439(a,1),10601(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11439 10601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11444">
    <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(11439(a,1),10995(a,1,1,2,2))].">
      <j1 rule="para" parents="11439 10995"/>
    </justification>
  </clause>

  <clause id="11445">
    <literal><![CDATA[
      K(x * L(y,z,u),y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,7639,a(flip),b,11443,a),flip(a)].">
      <j1 rule="hyper" parents="299 7639 11443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11447">
    <literal><![CDATA[
      K(x * L(y,z,u),y) = K(x,y) * a(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,9686,a,b,11445,a),flip(a)].">
      <j1 rule="hyper" parents="299 9686 11445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11448">
    <literal><![CDATA[
      K(x * (L(x,y,z) \ u),x) = K(u,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,8639,a(flip),b,11445,a),flip(a)].">
      <j1 rule="hyper" parents="65 8639 11445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11450">
    <literal><![CDATA[
      K(L(x,y,z) \ u,x) = K(x \ u,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,11407,a(flip),b,11448,a)].">
      <j1 rule="hyper" parents="65 11407 11448"/>
    </justification>
  </clause>

  <clause id="11451">
    <literal><![CDATA[
      K(x / L(y,z,u),y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(8323,a,11450,a)].">
      <j1 rule="hyper" parents="8323 11450"/>
    </justification>
  </clause>

  <clause id="11454">
    <literal><![CDATA[
      L(a(x,y,x),z * x,u) = a(L(x,z,u),y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,10466,a(flip),b,11444,a)].">
      <j1 rule="hyper" parents="65 10466 11444"/>
    </justification>
  </clause>

  <clause id="11456">
    <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),11454(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 11454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11457">
    <literal><![CDATA[
      K((L(x,y,z) \ u) \ w,L(x,y,z)) = K((x \ u) \ w,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,11367,a(flip),b,11426,a)].">
      <j1 rule="hyper" parents="65 11367 11426"/>
    </justification>
  </clause>

  <clause id="11458">
    <literal><![CDATA[
      K(L(x,y,z) * (u \ w),L(x,y,z)) = K((x \ u) \ w,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,11404,a(flip),b,11457,a)].">
      <j1 rule="hyper" parents="65 11404 11457"/>
    </justification>
  </clause>

  <clause id="11459">
    <literal><![CDATA[
      K(L(x,y,z) * (u \ w),L(x,y,z)) = K(u \ (x * w),L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,10429,a(flip),b,11458,a),flip(a)].">
      <j1 rule="hyper" parents="299 10429 11458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11460">
    <literal><![CDATA[
      K((x \ y) * L(z,u,w),L(z,u,w)) = K(x \ (z * y),L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(8632,a,11459,a)].">
      <j1 rule="hyper" parents="8632 11459"/>
    </justification>
  </clause>

  <clause id="11461">
    <literal><![CDATA[
      K(x \ (y * z),L(y,u,w)) = K((x \ z) * y,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,11431,a(flip),b,11460,a),flip(a)].">
      <j1 rule="hyper" parents="65 11431 11460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11462">
    <literal><![CDATA[
      K((x \ y) \ z,L(x,u,w)) = K((y \ z) * x,L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,10429,a,b,11461,a)].">
      <j1 rule="hyper" parents="65 10429 11461"/>
    </justification>
  </clause>

  <clause id="11463">
    <literal><![CDATA[
      K(x \ (y * z),L(z,u,w)) = K((x \ y) * z,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,10229,a,b,11461,a)].">
      <j1 rule="hyper" parents="65 10229 11461"/>
    </justification>
  </clause>

  <clause id="11464">
    <literal><![CDATA[
      K(((x \ y) \ z) * u,L(u,z,x)) = K(y \ (x * (u * z)),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,9189,a(flip),b,11461,a),flip(a)].">
      <j1 rule="hyper" parents="65 9189 11461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11465">
    <literal><![CDATA[
      K((x / y) \ z,L(y,u,w)) = K((x \ z) * y,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,10230,a,b,11463,a)].">
      <j1 rule="hyper" parents="65 10230 11463"/>
    </justification>
  </clause>

  <clause id="11466">
    <literal><![CDATA[
      T(((x \ 1) \ 1) \ T(x * y,x \ 1),K(x,1)) = (T(x \ 1,x) \ y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,7673,a(flip),b,11216,a),flip(a)].">
      <j1 rule="hyper" parents="299 7673 11216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11467">
    <literal><![CDATA[
      T(((x \ 1) \ 1) \ T(x * y,x \ 1),K(x,1)) = ((1 / x) \ y) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(1692(a,1),11466(a,2,1,1))].">
      <j1 rule="para" parents="1692 11466"/>
    </justification>
  </clause>

  <clause id="11468">
    <literal><![CDATA[
      T(((x \ 1) \ y) * (1 / x),K(x,1)) = ((1 / x) \ y) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(3781(a,1),11467(a,1,1))].">
      <j1 rule="para" parents="3781 11467"/>
    </justification>
  </clause>

  <clause id="11469">
    <literal><![CDATA[
      T(((x \ 1) \ y) * (1 / x),1) = ((1 / x) \ y) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(194(a,1),11468(a,1,2))].">
      <j1 rule="para" parents="194 11468"/>
    </justification>
  </clause>

  <clause id="11470">
    <literal><![CDATA[
      ((1 / x) \ y) * (x \ 1) = ((x \ 1) \ y) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(197,a,11469,a),flip(a)].">
      <j1 rule="hyper" parents="197 11469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11472">
    <literal><![CDATA[
      ((x \ 1) \ (y * x)) * (1 / x) = T(y,x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(65,a,6600,a(flip),b,11470,a),flip(a)].">
      <j1 rule="hyper" parents="65 6600 11470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11473">
    <literal><![CDATA[
      T(((x \ 1) \ y) * (1 / x),(1 / x) \ ((1 / x) \ 1)) = (x \ y) * ((x \ 1) * ((1 / x) \ x))
    ]]></literal>
    <justification jstring="[para(11470(a,1),3085(a,1,1))].">
      <j1 rule="para" parents="11470 3085"/>
    </justification>
  </clause>

  <clause id="11474">
    <literal><![CDATA[
      (x * (y * (T(T(y,z),z) \ u))) * K(K(z,y) * u,K(z,y)) = x * (K(z,y) * (u * K(z,y)))
    ]]></literal>
    <justification jstring="[para(6199(a,1),11296(a,1,1,2))].">
      <j1 rule="para" parents="6199 11296"/>
    </justification>
  </clause>

  <clause id="11475">
    <literal><![CDATA[
      T(((x \ 1) \ y) * (1 / x),(1 / x) \ ((1 / x) \ 1)) = (x \ y) * (K(x \ 1,x) * x)
    ]]></literal>
    <justification jstring="[para(2653(a,1),11473(a,2,2))].">
      <j1 rule="para" parents="2653 11473"/>
    </justification>
  </clause>

  <clause id="11476">
    <literal><![CDATA[
      T(((x \ 1) \ y) * (1 / x),(1 / x) \ ((1 / x) \ 1)) = (x \ y) * (K(x,x \ 1) * x)
    ]]></literal>
    <justification jstring="[para(2596(a,1),11475(a,2,2,1))].">
      <j1 rule="para" parents="2596 11475"/>
    </justification>
  </clause>

  <clause id="11477">
    <literal><![CDATA[
      T(((x \ 1) \ y) * (1 / x),(1 / x) \ ((1 / x) \ 1)) = (x \ y) * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(2551(a,1),11476(a,2,2))].">
      <j1 rule="para" parents="2551 11476"/>
    </justification>
  </clause>

  <clause id="11478">
    <literal><![CDATA[
      T(((x \ 1) \ y) * (1 / x),(1 / x) \ x) = (x \ y) * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(79(a,1),11477(a,1,2,2))].">
      <j1 rule="para" parents="79 11477"/>
    </justification>
  </clause>

  <clause id="11479">
    <literal><![CDATA[
      (x * (y * (T(T(y,z),z) \ u))) * K(z,K(y,u)) = x * (K(z,y) * (u * K(z,y)))
    ]]></literal>
    <justification jstring="[para(8648(a,1),11474(a,1,2))].">
      <j1 rule="para" parents="8648 11474"/>
    </justification>
  </clause>

  <clause id="11480">
    <literal><![CDATA[
      (x * (y * (T(T(y,z),z) \ u))) * K(y,K(z,u)) = x * (K(z,y) * (u * K(z,y)))
    ]]></literal>
    <justification jstring="[para(7983(a,1),11479(a,1,2))].">
      <j1 rule="para" parents="7983 11479"/>
    </justification>
  </clause>

  <clause id="11482">
    <literal><![CDATA[
      K(x,(y * z) / (y * (u \ z))) * (y * ((u \ z) * T(T(u,u \ z),x))) = y * z
    ]]></literal>
    <justification jstring="[para(487(a,1),5729(a,1,2))].">
      <j1 rule="para" parents="487 5729"/>
    </justification>
  </clause>

  <clause id="11483">
    <literal><![CDATA[
      K(x,(y * z) / (y * (u \ z))) * (y * (T(u,x) * (u \ z))) = y * z
    ]]></literal>
    <justification jstring="[para(232(a,1),11482(a,1,2,2))].">
      <j1 rule="para" parents="232 11482"/>
    </justification>
  </clause>

  <clause id="11484">
    <literal><![CDATA[
      K(x,(y * z) / (y * (u \ z))) * (y * (K(u,x) * z)) = y * z
    ]]></literal>
    <justification jstring="[para(5056(a,1),11483(a,1,2,2))].">
      <j1 rule="para" parents="5056 11483"/>
    </justification>
  </clause>

  <clause id="11485">
    <literal><![CDATA[
      (x * y) / (x * (K(z,u) * y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(u,(x * y) / (x * (z \ y))) = w
    ]]></literal>
    <justification jstring="[para(11484(a,1),307(a,1,1)),flip(b)].">
      <j1 rule="para" parents="11484 307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11486">
    <literal><![CDATA[
      K(x,y) * (R(y,z,u) * (K(y,x) * w)) = R(y,z,u) * w
    ]]></literal>
    <justification jstring="[para(1954(a,1),11484(a,1,1,2))].">
      <j1 rule="para" parents="1954 11484"/>
    </justification>
  </clause>

  <clause id="11487">
    <literal><![CDATA[
      K(x,y * (K(z,x \ 1) * u)) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(11484(a,1),7610(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11484 7610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11488">
    <literal><![CDATA[
      K(x,T(y,z * (K(u,x) * w))) = K(x,T(y,z * w))
    ]]></literal>
    <justification jstring="[para(11484(a,1),8646(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11484 8646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11489">
    <literal><![CDATA[
      K(x,(y * (K(z,x) * u)) \ w) = K(x,(y * u) \ w)
    ]]></literal>
    <justification jstring="[para(11484(a,1),8861(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11484 8861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11490">
    <literal><![CDATA[
      K(x,y \ (z * (K(u,x) * w))) = K(x,y \ (z * w))
    ]]></literal>
    <justification jstring="[para(11484(a,1),8863(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11484 8863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11491">
    <literal><![CDATA[
      K(x,y / ((z * (K(u,x) * w)) * v5)) = K(x,y / ((z * w) * v5))
    ]]></literal>
    <justification jstring="[para(11484(a,1),9954(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="11484 9954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11492">
    <literal><![CDATA[
      R(K(x,y),z * (K(u,y) * w),v5) = R(K(x,y),z * w,v5)
    ]]></literal>
    <justification jstring="[para(11484(a,1),10012(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11484 10012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11493">
    <literal><![CDATA[
      R(K(x,y),z * (K(u,x) * w),v5) = R(K(x,y),z * w,v5)
    ]]></literal>
    <justification jstring="[para(11484(a,1),10815(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11484 10815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11494">
    <literal><![CDATA[
      K(x,y * (K(x \ 1,z) * u)) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(5432(a,1),11487(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5432 11487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11495">
    <literal><![CDATA[
      K(x,y * (z / T(u,x \ 1))) = K(x,y * (z / u))
    ]]></literal>
    <justification jstring="[para(8360(a,1),11494(a,1,2,2))].">
      <j1 rule="para" parents="8360 11494"/>
    </justification>
  </clause>

  <clause id="11496">
    <literal><![CDATA[
      L(K(x,T(T(y,z),u * z)),z,u) = (u * z) / (u * (K(y,x) * z))
    ]]></literal>
    <justification jstring="[para(11488(a,1),9121(a,1,1))].">
      <j1 rule="para" parents="11488 9121"/>
    </justification>
  </clause>

  <clause id="11497">
    <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),11490(a,1,2))].">
      <j1 rule="para" parents="484 11490"/>
    </justification>
  </clause>

  <clause id="11498">
    <literal><![CDATA[
      K(T(x,y),z * (y / (x * y))) = K(T(x,y),z * ((x * y) \ y))
    ]]></literal>
    <justification jstring="[para(7069(a,1),11495(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7069 11495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11499">
    <literal><![CDATA[
      R(x,y,z) * (K(x,u) * w) = K(x,u) * (R(x,y,z) * w)
    ]]></literal>
    <justification jstring="[hyper(5437,a,11486,a),flip(a)].">
      <j1 rule="hyper" parents="5437 11486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11500">
    <literal><![CDATA[
      R(x,y,z) * (K(u,x) * w) = K(u,x) * (R(x,y,z) * w)
    ]]></literal>
    <justification jstring="[para(5432(a,1),11486(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5432 11486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11501">
    <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(8106(a,1),11486(a,1,1))].">
      <j1 rule="para" parents="8106 11486"/>
    </justification>
  </clause>

  <clause id="11502">
    <literal><![CDATA[
      R(K(x,y),z * x,u) = K(R(x,K(w,y) * z,u),y)
    ]]></literal>
    <justification jstring="[hyper(65,a,10991,a(flip),b,11492,a),flip(a)].">
      <j1 rule="hyper" parents="65 10991 11492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11504">
    <literal><![CDATA[
      K(R(x,K(y,z) * u,w),z) = K(R(x,u,w),z)
    ]]></literal>
    <justification jstring="[hyper(65,a,10809,a(flip),b,11502,a),flip(a)].">
      <j1 rule="hyper" parents="65 10809 11502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11506">
    <literal><![CDATA[
      T(x,R(y,K(z,x) * u,w)) = 1 / (x \ K(R(y,u,w),x))
    ]]></literal>
    <justification jstring="[para(11504(a,1),5119(a,2,2,2))].">
      <j1 rule="para" parents="11504 5119"/>
    </justification>
  </clause>

  <clause id="11507">
    <literal><![CDATA[
      R(K(x,y),z * (u * K(w,x)),v5) = R(K(x,y),z * u,v5)
    ]]></literal>
    <justification jstring="[para(7621(a,1),11493(a,1,2,2))].">
      <j1 rule="para" parents="7621 11493"/>
    </justification>
  </clause>

  <clause id="11508">
    <literal><![CDATA[
      K(x,y) * (R(x,z,u) \ 1) = R(x,z,u) \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,71,a(flip),b,11499,a),flip(a)].">
      <j1 rule="hyper" parents="119 71 11499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11509">
    <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(119,a,11508,a,b,2919,a)].">
      <j1 rule="hyper" parents="119 11508 2919"/>
    </justification>
  </clause>

  <clause id="11511">
    <literal><![CDATA[
      R(K(x,y),R(y,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6318,a,11500,a)].">
      <j1 rule="hyper" parents="6318 11500"/>
    </justification>
  </clause>

  <clause id="11512">
    <literal><![CDATA[
      R(x,y,x) * (K(z,x) * (x \ u)) = K(z,x) * ((u / x) * R(x,y,x))
    ]]></literal>
    <justification jstring="[para(7475(a,1),11500(a,2,2))].">
      <j1 rule="para" parents="7475 11500"/>
    </justification>
  </clause>

  <clause id="11513">
    <literal><![CDATA[
      R(K(x,y),R(x,z,u),w) = (v5 * K(y,x)) \ v5
    ]]></literal>
    <justification jstring="[para(11511(a,1),10767(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11511 10767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11514">
    <literal><![CDATA[
      R(K(x,y),R(x,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,7200,a(flip),b,11513,a),flip(a)].">
      <j1 rule="hyper" parents="299 7200 11513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11515">
    <literal><![CDATA[
      K(x,(R(x,y,z) * u) / w) = K(x,R(x,y,z) / (w / u))
    ]]></literal>
    <justification jstring="[hyper(65,a,6430,a(flip),b,11514,a)].">
      <j1 rule="hyper" parents="65 6430 11514"/>
    </justification>
  </clause>

  <clause id="11516">
    <literal><![CDATA[
      T(x,R(y,K(z,x) * u,w)) = T(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(299,a,5119,a,b,11506,a),flip(a)].">
      <j1 rule="hyper" parents="299 5119 11506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11517">
    <literal><![CDATA[
      T(x,R(T(x,y) \ z,u,w)) = T(x,R(x \ z,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,10986,a(flip),b,11516,a)].">
      <j1 rule="hyper" parents="65 10986 11516"/>
    </justification>
  </clause>

  <clause id="11518">
    <literal><![CDATA[
      T(x,R(y / T(x,z),u,w)) = T(x,R(x \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(5579,a,11517,a)].">
      <j1 rule="hyper" parents="5579 11517"/>
    </justification>
  </clause>

  <clause id="11520">
    <literal><![CDATA[
      R(K(x,y),z * y,u) = K(x,R(y * K(w,x),z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,10001,a(flip),b,11507,a),flip(a)].">
      <j1 rule="hyper" parents="65 10001 11507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11522">
    <literal><![CDATA[
      K(x,R(y * K(z,x),u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,9997,a(flip),b,11520,a),flip(a)].">
      <j1 rule="hyper" parents="65 9997 11520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11523">
    <literal><![CDATA[
      K(x,R(y,K(z,x) * u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,10982,a(flip),b,11522,a)].">
      <j1 rule="hyper" parents="65 10982 11522"/>
    </justification>
  </clause>

  <clause id="11524">
    <literal><![CDATA[
      K(x,R(y * K(x,z),u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(7184(a,1),11522(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7184 11522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11526">
    <literal><![CDATA[
      K(x,R(y,K(x,z) * u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(5432(a,1),11523(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5432 11523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11527">
    <literal><![CDATA[
      K(x,R(y,K(x,z),u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(536(a,1),11526(a,1,2)),flip(a)].">
      <j1 rule="para" parents="536 11526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11528">
    <literal><![CDATA[
      K(x,R(R(y,K(x,z),u),u,(K(x,z) * u) \ 1)) = K(x,((y * K(x,z)) * u) * ((K(x,z) * u) \ 1))
    ]]></literal>
    <justification jstring="[para(595(a,1),11526(a,1,2)),flip(a)].">
      <j1 rule="para" parents="595 11526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11529">
    <literal><![CDATA[
      K(x,R(R(y,K(x,z),u),w,v5)) = K(x,R(y,w,v5))
    ]]></literal>
    <justification jstring="[para(31(a,1),11527(a,1,2))].">
      <j1 rule="para" parents="31 11527"/>
    </justification>
  </clause>

  <clause id="11530">
    <literal><![CDATA[
      T(K(T(x,y),z * ((x * y) \ y)),y) = K(x,R(x \ 1,x,y) * z)
    ]]></literal>
    <justification jstring="[para(11498(a,1),11050(a,1,1))].">
      <j1 rule="para" parents="11498 11050"/>
    </justification>
  </clause>

  <clause id="11532">
    <literal><![CDATA[
      K(T(x,y),T(z * ((x * y) \ y),y)) = K(x,R(x \ 1,x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(7714,a,11530,a)].">
      <j1 rule="hyper" parents="7714 11530"/>
    </justification>
  </clause>

  <clause id="11533">
    <literal><![CDATA[
      K(x,R(x \ 1,x,y) * z) = K(x,z * ((x * y) \ y))
    ]]></literal>
    <justification jstring="[hyper(8218,a,11532,a),flip(a)].">
      <j1 rule="hyper" parents="8218 11532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11535">
    <literal><![CDATA[
      K(x,y) * ((z / y) * R(y,u,y)) = R(y,u,y) * (T(y,x) \ z)
    ]]></literal>
    <justification jstring="[para(5383(a,1),11512(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5383 11512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11536">
    <literal><![CDATA[
      R(x,y,x) * (T(x,z) \ u) = x * (L(T(x,z),y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,10473,a(flip),b,11535,a),flip(a)].">
      <j1 rule="hyper" parents="65 10473 11535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11537">
    <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(11536(a,1),7448(a,1,2))].">
      <j1 rule="para" parents="11536 7448"/>
    </justification>
  </clause>

  <clause id="11538">
    <literal><![CDATA[
      L(K(x,T(T(y,z),u * z)),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * z) / (u * (y \ z))) = w
    ]]></literal>
    <justification jstring="[para(11496(a,2),11485(a,1))].">
      <j1 rule="para" parents="11496 11485"/>
    </justification>
  </clause>

  <clause id="11539">
    <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(5398,a,11537,a),flip(a)].">
      <j1 rule="hyper" parents="5398 11537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11540">
    <literal><![CDATA[
      K(x,(y * z) / (y * (u \ z))) = (y * (K(x,u) * z)) / (y * z)
    ]]></literal>
    <justification jstring="[hyper(11538,a,9385,a)].">
      <j1 rule="hyper" parents="11538 9385"/>
    </justification>
  </clause>

  <clause id="11541">
    <literal><![CDATA[
      K(x,(y * z) / (y * (u \ z))) * (y * z) = y * (K(x,u) * z)
    ]]></literal>
    <justification jstring="[hyper(143,a,11540,a(flip))].">
      <j1 rule="hyper" parents="143 11540"/>
    </justification>
  </clause>

  <clause id="11542">
    <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(11540(a,2),10832(a,1))].">
      <j1 rule="para" parents="11540 10832"/>
    </justification>
  </clause>

  <clause id="11543">
    <literal><![CDATA[
      K(x,y * (K(x,z) * u)) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(11541(a,1),8519(a,1,2))].">
      <j1 rule="para" parents="11541 8519"/>
    </justification>
  </clause>

  <clause id="11544">
    <literal><![CDATA[
      K(x,y * (z * K(x,u))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(8101(a,1),11543(a,1,2,2))].">
      <j1 rule="para" parents="8101 11543"/>
    </justification>
  </clause>

  <clause id="11545">
    <literal><![CDATA[
      K(x,y * (z * K(u,x))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(8140(a,1),11543(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8140 11543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11546">
    <literal><![CDATA[
      K(x,y * (z * (K(u,x) * w))) = K(x,y * (z * w))
    ]]></literal>
    <justification jstring="[para(11484(a,1),11543(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11484 11543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11547">
    <literal><![CDATA[
      K(x,y * (z * L(K(x,u),w,v5))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(6131(a,1),11544(a,1,2,2,2))].">
      <j1 rule="para" parents="6131 11544"/>
    </justification>
  </clause>

  <clause id="11548">
    <literal><![CDATA[
      K(x,y * (z * (K(u,x) * (w * K(u,x))))) = K(x,y * (z * (x * (T(T(x,u),u) \ w))))
    ]]></literal>
    <justification jstring="[para(11480(a,1),11544(a,1,2,2))].">
      <j1 rule="para" parents="11480 11544"/>
    </justification>
  </clause>

  <clause id="11549">
    <literal><![CDATA[
      K(x,y * (T(z,x) / u)) = K(x,y * (z / u))
    ]]></literal>
    <justification jstring="[para(1394(a,1),11545(a,1,2,2))].">
      <j1 rule="para" parents="1394 11545"/>
    </justification>
  </clause>

  <clause id="11550">
    <literal><![CDATA[
      K(x \ y,z * (x / ((x \ y) * x))) = K(x \ y,z * (x / y))
    ]]></literal>
    <justification jstring="[para(4665(a,1),11549(a,1,2,2))].">
      <j1 rule="para" parents="4665 11549"/>
    </justification>
  </clause>

  <clause id="11551">
    <literal><![CDATA[
      K(x,y * (z * (u * K(w,x)))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(9099(a,1),11547(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9099 11547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11552">
    <literal><![CDATA[
      K(x,((y * x) * z) / (x * (y * (y \ z)))) = L(K(x,y),z,y * x)
    ]]></literal>
    <justification jstring="[hyper(11542,a,9270,a),flip(a)].">
      <j1 rule="hyper" parents="11542 9270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11553">
    <literal><![CDATA[
      L(K(x,y),z,y * x) = K(x,((y * x) * z) / (x * z))
    ]]></literal>
    <justification jstring="[para(10(a,1),11552(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10 11552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11554">
    <literal><![CDATA[
      L(K(x,y),z,y * x) = K(x,R(y,x,z))
    ]]></literal>
    <justification jstring="[para(20(a,2),11553(a,2,2))].">
      <j1 rule="para" parents="20 11553"/>
    </justification>
  </clause>

  <clause id="11556">
    <literal><![CDATA[
      K(x,R(y,x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(11322,a,11554,a),flip(a)].">
      <j1 rule="hyper" parents="11322 11554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11557">
    <literal><![CDATA[
      R(K(x,y),z,T(y * x,z)) = K(x,R(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(10836,a,11554,a)].">
      <j1 rule="hyper" parents="10836 11554"/>
    </justification>
  </clause>

  <clause id="11558">
    <literal><![CDATA[
      K(x,R(y,x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(11554(a,1),11322(a,1))].">
      <j1 rule="para" parents="11554 11322"/>
    </justification>
  </clause>

  <clause id="11560">
    <literal><![CDATA[
      K(x,y / (z * x)) = K(x,x \ (y / z))
    ]]></literal>
    <justification jstring="[hyper(65,a,9976,a(flip),b,11556,a)].">
      <j1 rule="hyper" parents="65 9976 11556"/>
    </justification>
  </clause>

  <clause id="11561">
    <literal><![CDATA[
      R(K(x \ y,x),y,z) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,6432,a(flip),b,11556,a)].">
      <j1 rule="hyper" parents="65 6432 11556"/>
    </justification>
  </clause>

  <clause id="11562">
    <literal><![CDATA[
      K(x,R(R(y,x,z),u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(31(a,1),11556(a,1,2))].">
      <j1 rule="para" parents="31 11556"/>
    </justification>
  </clause>

  <clause id="11563">
    <literal><![CDATA[
      T(x,R(y,x,z)) = x * K(x,y)
    ]]></literal>
    <justification jstring="[para(11556(a,1),5083(a,2,2))].">
      <j1 rule="para" parents="11556 5083"/>
    </justification>
  </clause>

  <clause id="11564">
    <literal><![CDATA[
      T(x,R(y,x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,5083,a,b,11563,a),flip(a)].">
      <j1 rule="hyper" parents="299 5083 11563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11572">
    <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(573(a,1),11564(a,1,2))].">
      <j1 rule="para" parents="573 11564"/>
    </justification>
  </clause>

  <clause id="11573">
    <literal><![CDATA[
      T(x,y) \ R(T(x,y),y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(11564(a,1),10749(a,1,1))].">
      <j1 rule="para" parents="11564 10749"/>
    </justification>
  </clause>

  <clause id="11574">
    <literal><![CDATA[
      ((x * y) * z) \ ((y * x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(x,z)) = u
    ]]></literal>
    <justification jstring="[para(9615(a,2),11558(a,1))].">
      <j1 rule="para" parents="9615 11558"/>
    </justification>
  </clause>

  <clause id="11575">
    <literal><![CDATA[
      K(x / (y * z),y) = K(y \ (x / z),y)
    ]]></literal>
    <justification jstring="[hyper(6410,a,11561,a)].">
      <j1 rule="hyper" parents="6410 11561"/>
    </justification>
  </clause>

  <clause id="11576">
    <literal><![CDATA[
      K(x,y / (x * z)) = K(x,x \ (y / z))
    ]]></literal>
    <justification jstring="[hyper(11152,a,11560,a)].">
      <j1 rule="hyper" parents="11152 11560"/>
    </justification>
  </clause>

  <clause id="11578">
    <literal><![CDATA[
      K(x,(x \ y) / z) = K(x,x \ (y / z))
    ]]></literal>
    <justification jstring="[hyper(65,a,9065,a,b,11560,a)].">
      <j1 rule="hyper" parents="65 9065 11560"/>
    </justification>
  </clause>

  <clause id="11579">
    <literal><![CDATA[
      K(x,y / ((z * x) * u)) = K(x,x \ (y / (z * u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,6790,a(flip),b,11560,a)].">
      <j1 rule="hyper" parents="65 6790 11560"/>
    </justification>
  </clause>

  <clause id="11580">
    <literal><![CDATA[
      K((x \ y) / z,x) = K(x \ (y / z),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,8707,a,b,11575,a)].">
      <j1 rule="hyper" parents="65 8707 11575"/>
    </justification>
  </clause>

  <clause id="11581">
    <literal><![CDATA[
      x * K(x,x \ (y / (z * u))) = T(x,y / ((x * z) * u))
    ]]></literal>
    <justification jstring="[para(11576(a,1),9964(a,1,2))].">
      <j1 rule="para" parents="11576 9964"/>
    </justification>
  </clause>

  <clause id="11582">
    <literal><![CDATA[
      K(x,x \ ((x * y) / z)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(9(a,1),11578(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 11578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11583">
    <literal><![CDATA[
      K(x \ (y / z),x) * z = z * K(z \ (x \ y),x)
    ]]></literal>
    <justification jstring="[para(11580(a,1),7620(a,1,1))].">
      <j1 rule="para" parents="11580 7620"/>
    </justification>
  </clause>

  <clause id="11584">
    <literal><![CDATA[
      K(x,x \ ((y \ 1) \ (x * z))) = K(x,z / T(y \ 1,y * (x * z)))
    ]]></literal>
    <justification jstring="[para(4751(a,1),11582(a,1,2,2))].">
      <j1 rule="para" parents="4751 11582"/>
    </justification>
  </clause>

  <clause id="11585">
    <literal><![CDATA[
      R(K(x,R(y,x,z)),(y * x) * z,u) = K(x,R(y,x * z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,6439,a,b,11562,a)].">
      <j1 rule="hyper" parents="65 6439 11562"/>
    </justification>
  </clause>

  <clause id="11586">
    <literal><![CDATA[
      K(x,R(y,x,z)) * ((y * x) * z) = (K(x,y) * z) * T(y * x,z)
    ]]></literal>
    <justification jstring="[para(11557(a,1),546(a,1,1))].">
      <j1 rule="para" parents="11557 546"/>
    </justification>
  </clause>

  <clause id="11587">
    <literal><![CDATA[
      K(R(x,y,z) * u,x) * K(x,u) = x \ R(x,u,R(T(x,u),y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,11112,a(flip),b,11573,a)].">
      <j1 rule="hyper" parents="65 11112 11573"/>
    </justification>
  </clause>

  <clause id="11589">
    <literal><![CDATA[
      K(x,x \ (y / ((x \ z) * u))) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,9952,a(flip),b,11579,a),flip(a)].">
      <j1 rule="hyper" parents="65 9952 11579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11590">
    <literal><![CDATA[
      K(x \ (y / z),T(x,z)) = K(z \ (x \ y),x)
    ]]></literal>
    <justification jstring="[hyper(7606,a,11583,a)].">
      <j1 rule="hyper" parents="7606 11583"/>
    </justification>
  </clause>

  <clause id="11591">
    <literal><![CDATA[
      K(x \ (y / z),T(x,y)) = K(z \ (x \ y),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,10792,a(flip),b,11590,a)].">
      <j1 rule="hyper" parents="65 10792 11590"/>
    </justification>
  </clause>

  <clause id="11592">
    <literal><![CDATA[
      K(T(x,y),x \ (y / z)) = (u * K(z \ (x \ y),x)) \ u
    ]]></literal>
    <justification jstring="[para(11591(a,1),7200(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11591 7200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11593">
    <literal><![CDATA[
      K(x,(x * y) / (z * u)) = K(x,y / ((x \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,11582,a(flip),b,11589,a),flip(a)].">
      <j1 rule="hyper" parents="65 11582 11589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11594">
    <literal><![CDATA[
      K(x,y / ((x \ z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,((z * u) / y) \ x) = w
    ]]></literal>
    <justification jstring="[para(11593(a,1),7162(a,1))].">
      <j1 rule="para" parents="11593 7162"/>
    </justification>
  </clause>

  <clause id="11595">
    <literal><![CDATA[
      T(x,y / ((x * z) * u)) = T(x,x \ (y / (z * u)))
    ]]></literal>
    <justification jstring="[hyper(5087,a,11581,a),flip(a)].">
      <j1 rule="hyper" parents="5087 11581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11596">
    <literal><![CDATA[
      K(T(x,y),x \ (y / z)) = K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(299,a,7200,a(flip),b,11592,a),flip(a)].">
      <j1 rule="hyper" parents="299 7200 11592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11597">
    <literal><![CDATA[
      K(x,T(x \ (y / z),y)) = K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(7709,a,11596,a)].">
      <j1 rule="hyper" parents="7709 11596"/>
    </justification>
  </clause>

  <clause id="11598">
    <literal><![CDATA[
      K(x,(y \ z) \ (x \ z)) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[para(76(a,1),11597(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="76 11597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11599">
    <literal><![CDATA[
      R(K(x,y),(y * x) * z,u) = K(x,R(y,x * z,u))
    ]]></literal>
    <justification jstring="[para(11556(a,1),11585(a,1,1))].">
      <j1 rule="para" parents="11556 11585"/>
    </justification>
  </clause>

  <clause id="11601">
    <literal><![CDATA[
      (K(x,y) * z) * T(y * x,z) = (y * (K(x,y) * x)) * z
    ]]></literal>
    <justification jstring="[hyper(65,a,6550,a(flip),b,11586,a),flip(a)].">
      <j1 rule="hyper" parents="65 6550 11586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11602">
    <literal><![CDATA[
      (K(x,y) * z) * T(y * x,z) = (x * y) * z
    ]]></literal>
    <justification jstring="[para(5166(a,1),11601(a,2,1))].">
      <j1 rule="para" parents="5166 11601"/>
    </justification>
  </clause>

  <clause id="11603">
    <literal><![CDATA[
      (x * y) * (K(y,x) * z) = (y * x) * z
    ]]></literal>
    <justification jstring="[hyper(65,a,10525,a(flip),b,11602,a)].">
      <j1 rule="hyper" parents="65 10525 11602"/>
    </justification>
  </clause>

  <clause id="11605">
    <literal><![CDATA[
      K(x / y,y) * (x \ z) = (y * (x / y)) \ z
    ]]></literal>
    <justification jstring="[hyper(119,a,286,a(flip),b,11603,a),flip(a)].">
      <j1 rule="hyper" parents="119 286 11603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11606">
    <literal><![CDATA[
      K(x,y) * ((x * y) \ z) = (y * x) \ z
    ]]></literal>
    <justification jstring="[hyper(119,a,10,a(flip),b,11603,a),flip(a)].">
      <j1 rule="hyper" parents="119 10 11603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11607">
    <literal><![CDATA[
      K(x,y) * ((y * x) * z) = (x * y) * z
    ]]></literal>
    <justification jstring="[hyper(65,a,11308,a,b,11603,a)].">
      <j1 rule="hyper" parents="65 11308 11603"/>
    </justification>
  </clause>

  <clause id="11608">
    <literal><![CDATA[
      (x * y) * (1 / T(x,y)) = (y * x) * (1 / x)
    ]]></literal>
    <justification jstring="[para(5384(a,1),11603(a,1,2))].">
      <j1 rule="para" parents="5384 11603"/>
    </justification>
  </clause>

  <clause id="11609">
    <literal><![CDATA[
      K(x,x \ y) * (y \ z) = ((x \ y) * x) \ z
    ]]></literal>
    <justification jstring="[para(10(a,1),11606(a,1,2,1))].">
      <j1 rule="para" parents="10 11606"/>
    </justification>
  </clause>

  <clause id="11610">
    <literal><![CDATA[
      (K(x,y) * (((x * y) \ z) * (u * u))) * w = ((y * x) \ z) * ((u * u) * w)
    ]]></literal>
    <justification jstring="[para(11606(a,1),117(a,2,1))].">
      <j1 rule="para" parents="11606 117"/>
    </justification>
  </clause>

  <clause id="11611">
    <literal><![CDATA[
      T(x,y) * ((x * y) \ z) = x * ((y * x) \ z)
    ]]></literal>
    <justification jstring="[para(11606(a,1),5055(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11606 5055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11612">
    <literal><![CDATA[
      K(x,y) * (((x * y) \ z) * y) = ((y * x) \ z) * y
    ]]></literal>
    <justification jstring="[para(11606(a,1),7472(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11606 7472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11613">
    <literal><![CDATA[
      K(x,K(y,z)) * ((K(x,y) * z) \ u) = (z * K(x,y)) \ u
    ]]></literal>
    <justification jstring="[para(7954(a,1),11606(a,1,1))].">
      <j1 rule="para" parents="7954 11606"/>
    </justification>
  </clause>

  <clause id="11615">
    <literal><![CDATA[
      L(x,y * z,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(5178,a,11607,a)].">
      <j1 rule="hyper" parents="5178 11607"/>
    </justification>
  </clause>

  <clause id="11616">
    <literal><![CDATA[
      (x * y) \ (K(x,y) * z) = (y * x) \ z
    ]]></literal>
    <justification jstring="[hyper(640,a,11607,a)].">
      <j1 rule="hyper" parents="640 11607"/>
    </justification>
  </clause>

  <clause id="11617">
    <literal><![CDATA[
      K(x,y) * ((y * x) * (y \ 1)) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,258,a(flip),b,11607,a),flip(a)].">
      <j1 rule="hyper" parents="299 258 11607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11618">
    <literal><![CDATA[
      K(x,y) * ((y * x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      (x * y) * z = u
    ]]></literal>
    <justification jstring="[para(11607(a,1),5438(a,1,2)),flip(b)].">
      <j1 rule="para" parents="11607 5438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11620">
    <literal><![CDATA[
      L(x,y,z * K(y,z)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(9429,a,11615,a)].">
      <j1 rule="hyper" parents="9429 11615"/>
    </justification>
  </clause>

  <clause id="11621">
    <literal><![CDATA[
      L(x,T(y,z),z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(6781,a,11615,a)].">
      <j1 rule="hyper" parents="6781 11615"/>
    </justification>
  </clause>

  <clause id="11622">
    <literal><![CDATA[
      L(x,y,T(z,y)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(6687,a,11615,a)].">
      <j1 rule="hyper" parents="6687 11615"/>
    </justification>
  </clause>

  <clause id="11623">
    <literal><![CDATA[
      L(x,y,z) = (y * z) \ (z * (T(y,z) * x))
    ]]></literal>
    <justification jstring="[hyper(65,a,6779,a(flip),b,11615,a),flip(a)].">
      <j1 rule="hyper" parents="65 6779 11615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11624">
    <literal><![CDATA[
      L(x,y,K(z \ y,z)) = x
    ]]></literal>
    <justification jstring="[para(10(a,1),11615(a,1,2))].">
      <j1 rule="para" parents="10 11615"/>
    </justification>
  </clause>

  <clause id="11625">
    <literal><![CDATA[
      L(x,T(y,z) * z,K(z,y)) = x
    ]]></literal>
    <justification jstring="[para(5190(a,1),11615(a,1,3))].">
      <j1 rule="para" parents="5190 11615"/>
    </justification>
  </clause>

  <clause id="11626">
    <literal><![CDATA[
      L(x,y,K(z \ 1,y * z)) = x
    ]]></literal>
    <justification jstring="[para(5327(a,1),11624(a,1,3))].">
      <j1 rule="para" parents="5327 11624"/>
    </justification>
  </clause>

  <clause id="11627">
    <literal><![CDATA[
      L(L(x,y,z),u * w,K(w,u)) = L(x,T(y,z),z)
    ]]></literal>
    <justification jstring="[hyper(299,a,11615,a,b,11621,a)].">
      <j1 rule="hyper" parents="299 11615 11621"/>
    </justification>
  </clause>

  <clause id="11628">
    <literal><![CDATA[
      (T(x,y) * (1 / y)) \ (x * z) = L((1 / T(y,x)) \ z,y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,6668,a(flip),b,11621,a)].">
      <j1 rule="hyper" parents="65 6668 11621"/>
    </justification>
  </clause>

  <clause id="11629">
    <literal><![CDATA[
      L(x,y / z,z) = L(x,z \ y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,5735,a(flip),b,11621,a)].">
      <j1 rule="hyper" parents="65 5735 11621"/>
    </justification>
  </clause>

  <clause id="11630">
    <literal><![CDATA[
      L(T(x,y) \ z,x,y) = (x * y) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,525,a(flip),b,11621,a),flip(a)].">
      <j1 rule="hyper" parents="65 525 11621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11631">
    <literal><![CDATA[
      L(x,(y \ z) \ z,y \ z) = L(x,y,y \ z)
    ]]></literal>
    <justification jstring="[para(108(a,1),11621(a,1,2))].">
      <j1 rule="para" parents="108 11621"/>
    </justification>
  </clause>

  <clause id="11632">
    <literal><![CDATA[
      (x * y) * L(z,x,y) = y * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[para(11621(a,1),491(a,1,2))].">
      <j1 rule="para" parents="11621 491"/>
    </justification>
  </clause>

  <clause id="11635">
    <literal><![CDATA[
      L(x,y \ z,(y \ z) \ z) = L(x,y \ z,y)
    ]]></literal>
    <justification jstring="[hyper(2149,a,11622,a)].">
      <j1 rule="hyper" parents="2149 11622"/>
    </justification>
  </clause>

  <clause id="11636">
    <literal><![CDATA[
      L(K(x,y) * (x \ z),x,y) = (T(y,x) * x) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,6784,a(flip),b,11622,a),flip(a)].">
      <j1 rule="hyper" parents="65 6784 11622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11637">
    <literal><![CDATA[
      L(x,y,z / y) = L(x,y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,5731,a(flip),b,11622,a)].">
      <j1 rule="hyper" parents="65 5731 11622"/>
    </justification>
  </clause>

  <clause id="11639">
    <literal><![CDATA[
      L(x,y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(11625(a,1),10693(a,1))].">
      <j1 rule="para" parents="11625 10693"/>
    </justification>
  </clause>

  <clause id="11640">
    <literal><![CDATA[
      L(x,y \ z,(y \ z) \ (z / (z / y))) = L(x,y \ z,y / (z / y))
    ]]></literal>
    <justification jstring="[para(7317(a,1),11637(a,1,3)),flip(a)].">
      <j1 rule="para" parents="7317 11637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11641">
    <literal><![CDATA[
      L(x,y \ z,(y \ z) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ z,y) = u
    ]]></literal>
    <justification jstring="[para(108(a,1),11639(a,1,3))].">
      <j1 rule="para" parents="108 11639"/>
    </justification>
  </clause>

  <clause id="11643">
    <literal><![CDATA[
      L(x,T(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(6782(a,2),11639(a,1))].">
      <j1 rule="para" parents="6782 11639"/>
    </justification>
  </clause>

  <clause id="11644">
    <literal><![CDATA[
      L(x \ y,z,y / x) != u
    ]]></literal>
    <literal><![CDATA[
      L(x \ y,z,x \ y) = u
    ]]></literal>
    <justification jstring="[para(7925(a,1),11639(a,1))].">
      <j1 rule="para" parents="7925 11639"/>
    </justification>
  </clause>

  <clause id="11645">
    <literal><![CDATA[
      x \ (K(y,y \ x) * z) = ((y \ x) * y) \ z
    ]]></literal>
    <justification jstring="[hyper(329,a,11616,a)].">
      <j1 rule="hyper" parents="329 11616"/>
    </justification>
  </clause>

  <clause id="11647">
    <literal><![CDATA[
      (x * (T(y,x) * z)) / L(z,y,x) = y * x
    ]]></literal>
    <justification jstring="[hyper(192,a,11623,a(flip))].">
      <j1 rule="hyper" parents="192 11623"/>
    </justification>
  </clause>

  <clause id="11648">
    <literal><![CDATA[
      L(T(x,y / x) \ z,x,x \ y) = (x * (y / x)) \ ((y / x) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,11637,a(flip),b,11630,a)].">
      <j1 rule="hyper" parents="65 11637 11630"/>
    </justification>
  </clause>

  <clause id="11649">
    <literal><![CDATA[
      L(T(x,(y * y) \ 1) \ z,x,(y * y) \ 1) = (x * ((y * y) \ 1)) \ ((y * y) \ z)
    ]]></literal>
    <justification jstring="[para(422(a,1),11630(a,2,2))].">
      <j1 rule="para" parents="422 11630"/>
    </justification>
  </clause>

  <clause id="11650">
    <literal><![CDATA[
      K(x,L(T(y,1 / z) \ u,y,1 / z)) = K(x,(y * (z \ 1)) \ ((1 / z) * u))
    ]]></literal>
    <justification jstring="[para(11630(a,2),5656(a,1,2))].">
      <j1 rule="para" parents="11630 5656"/>
    </justification>
  </clause>

  <clause id="11651">
    <literal><![CDATA[
      L(T(x \ L(x,y,z),u),x,u) = (x * u) \ (u * L(T(x,u),y,z))
    ]]></literal>
    <justification jstring="[para(6731(a,1),11630(a,1,1))].">
      <j1 rule="para" parents="6731 11630"/>
    </justification>
  </clause>

  <clause id="11652">
    <literal><![CDATA[
      (K(x,y) * z) * L(u,K(y,x),z) = z * (T(K(x,y),z) * u)
    ]]></literal>
    <justification jstring="[para(5220(a,1),11632(a,1,2))].">
      <j1 rule="para" parents="5220 11632"/>
    </justification>
  </clause>

  <clause id="11653">
    <literal><![CDATA[
      K(x \ y,x) * (y \ z) = (x * (y / x)) \ z
    ]]></literal>
    <justification jstring="[para(5192(a,1),11605(a,1,1))].">
      <j1 rule="para" parents="5192 11605"/>
    </justification>
  </clause>

  <clause id="11654">
    <literal><![CDATA[
      (x * (x \ (y / (1 / x)))) * (1 / T(x,x \ (y / (1 / x)))) = (T(y,x) / (1 / x)) * (1 / x)
    ]]></literal>
    <justification jstring="[para(1854(a,1),11608(a,2,1))].">
      <j1 rule="para" parents="1854 11608"/>
    </justification>
  </clause>

  <clause id="11655">
    <literal><![CDATA[
      L(((x \ y) \ y) \ z,x,x \ y) = y \ ((x \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(615,a,11631,a),flip(a)].">
      <j1 rule="hyper" parents="615 11631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11656">
    <literal><![CDATA[
      ((x \ y) * x) \ (x \ y) = y \ (y / x)
    ]]></literal>
    <justification jstring="[para(5177(a,1),11645(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5177 11645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11657">
    <literal><![CDATA[
      x \ (((y \ x) * (K(y,y \ x) * z)) * y) = ((y \ x) * y) \ (((y \ x) * z) * y)
    ]]></literal>
    <justification jstring="[para(7752(a,2),11645(a,1,2))].">
      <j1 rule="para" parents="7752 11645"/>
    </justification>
  </clause>

  <clause id="11658">
    <literal><![CDATA[
      K(x,y \ ((z * x) * (z \ 1))) = K(x,y \ R(x,z,z \ 1))
    ]]></literal>
    <justification jstring="[para(11617(a,1),8863(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11617 8863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11659">
    <literal><![CDATA[
      K(x * y,z) * ((z * x) * y) != u
    ]]></literal>
    <literal><![CDATA[
      ((x * y) * z) * a(z,x,y) = u
    ]]></literal>
    <justification jstring="[para(84(a,1),11618(a,1,2))].">
      <j1 rule="para" parents="84 11618"/>
    </justification>
  </clause>

  <clause id="11661">
    <literal><![CDATA[
      K(x,L(y,T(z,u),u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(11627(a,1),7853(a,1,2))].">
      <j1 rule="para" parents="11627 7853"/>
    </justification>
  </clause>

  <clause id="11662">
    <literal><![CDATA[
      K(x,L(y,z / u,u)) = K(x,L(y,u \ z,u))
    ]]></literal>
    <justification jstring="[para(109(a,1),11661(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="109 11661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11663">
    <literal><![CDATA[
      K(x,L(T(y,z) \ u,y,z)) = K(x,(y * z) \ (z * u))
    ]]></literal>
    <justification jstring="[para(525(a,1),11661(a,1,2)),flip(a)].">
      <j1 rule="para" parents="525 11661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11664">
    <literal><![CDATA[
      T(x,y) * (((x * y) \ z) * y) = x * (((y * x) \ z) * y)
    ]]></literal>
    <justification jstring="[para(11612(a,1),5055(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11612 5055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11665">
    <literal><![CDATA[
      L(((x \ K(x,y)) \ K(x,y)) \ z,x,x \ K(x,y)) = K(x,y) \ ((((y * x) / y) \ 1) * z)
    ]]></literal>
    <justification jstring="[para(5182(a,2),11655(a,2,2,1))].">
      <j1 rule="para" parents="5182 11655"/>
    </justification>
  </clause>

  <clause id="11666">
    <literal><![CDATA[
      K(x,y * ((K(x,z) * u) \ w)) = K(x,y * ((u * K(x,z)) \ w))
    ]]></literal>
    <justification jstring="[para(11613(a,1),11543(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11613 11543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11667">
    <literal><![CDATA[
      L((1 / T(x,y)) \ (T(y,x) * (1 / x)),x,y) = T(y,T(y,x) * (1 / x))
    ]]></literal>
    <justification jstring="[hyper(318,a,11628,a),flip(a)].">
      <j1 rule="hyper" parents="318 11628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11668">
    <literal><![CDATA[
      (K(x,y) * z) * L(u,K(y,x),z) = z * (K(x,T(y,z)) * u)
    ]]></literal>
    <justification jstring="[para(7489(a,2),11652(a,2,2,1))].">
      <j1 rule="para" parents="7489 11652"/>
    </justification>
  </clause>

  <clause id="11669">
    <literal><![CDATA[
      K(x,y \ ((z * x) * (z \ 1))) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(299,a,11210,a(flip),b,11658,a),flip(a)].">
      <j1 rule="hyper" parents="299 11210 11658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11671">
    <literal><![CDATA[
      R(K(x,T(y,(z * x) * (z \ 1))),z * x,z \ 1) = K(x,((y \ (z * x)) * (z \ 1)) \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,9848,a(flip),b,11669,a)].">
      <j1 rule="hyper" parents="65 9848 11669"/>
    </justification>
  </clause>

  <clause id="11672">
    <literal><![CDATA[
      x \ R(x,y,R(T(x,y),z,u)) = L(x,y,R(x,z,u)) \ x
    ]]></literal>
    <justification jstring="[hyper(65,a,11361,a(flip),b,11587,a),flip(a)].">
      <j1 rule="hyper" parents="65 11361 11587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11673">
    <literal><![CDATA[
      L(T(x,x \ y) \ z,x,x \ y) = (x * (y / x)) \ ((y / x) * z)
    ]]></literal>
    <justification jstring="[para(4400(a,1),11648(a,1,1,1))].">
      <j1 rule="para" parents="4400 11648"/>
    </justification>
  </clause>

  <clause id="11674">
    <literal><![CDATA[
      L(T(x \ L(x,y,z),u),x,u) = (x * u) \ (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(233(a,1),11651(a,2,2))].">
      <j1 rule="para" parents="233 11651"/>
    </justification>
  </clause>

  <clause id="11675">
    <literal><![CDATA[
      (x * (y / x)) \ ((y / x) * z) = (x * (x \ y)) \ ((x \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,11630,a(flip),b,11673,a),flip(a)].">
      <j1 rule="hyper" parents="65 11630 11673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11676">
    <literal><![CDATA[
      (x * (y / x)) \ ((y / x) * z) = y \ ((x \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(299,a,157,a(flip),b,11675,a),flip(a)].">
      <j1 rule="hyper" parents="299 157 11675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11678">
    <literal><![CDATA[
      K(x,y / T(z \ 1,z * (x * y))) = K(x,(z \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,11262,a(flip),b,11584,a),flip(a)].">
      <j1 rule="hyper" parents="65 11262 11584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11679">
    <literal><![CDATA[
      L(x,y \ z,y / (z / y)) = L(x,y \ z,(z / y) \ y)
    ]]></literal>
    <justification jstring="[para(5955(a,1),11640(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5955 11640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11680">
    <literal><![CDATA[
      R(x,y,z) * T(y * z,x) != u
    ]]></literal>
    <literal><![CDATA[
      ((y * z) * x) * a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(6204(a,1),11659(a,1))].">
      <j1 rule="para" parents="6204 11659"/>
    </justification>
  </clause>

  <clause id="11681">
    <literal><![CDATA[
      T(x,T(x,y) * (1 / y)) = L(T(x,y \ 1),y,x)
    ]]></literal>
    <justification jstring="[para(8736(a,1),11667(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8736 11667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11682">
    <literal><![CDATA[
      (K(x,y * y) * (((y * y) \ (x \ z)) * (u * u))) * w = (((y * y) * x) \ z) * ((u * u) * w)
    ]]></literal>
    <justification jstring="[para(419(a,1),11610(a,1,1,2,1))].">
      <j1 rule="para" parents="419 11610"/>
    </justification>
  </clause>

  <clause id="11683">
    <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(65,a,27,a,b,11572,a)].">
      <j1 rule="hyper" parents="65 27 11572"/>
    </justification>
  </clause>

  <clause id="11684">
    <literal><![CDATA[
      K(x,L(T(y,z \ 1) \ u,y,1 / z)) = K(x,(y * (z \ 1)) \ ((1 / z) * u))
    ]]></literal>
    <justification jstring="[para(3733(a,1),11650(a,1,2,1,1))].">
      <j1 rule="para" parents="3733 11650"/>
    </justification>
  </clause>

  <clause id="11685">
    <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(299,a,4400,a(flip),b,11683,a),flip(a)].">
      <j1 rule="hyper" parents="299 4400 11683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11686">
    <literal><![CDATA[
      K(x,L(T(y,z \ 1) \ u,y,z)) = K(x,(y * (z \ 1)) \ ((1 / z) * u))
    ]]></literal>
    <justification jstring="[para(2467(a,1),11684(a,1,2))].">
      <j1 rule="para" parents="2467 11684"/>
    </justification>
  </clause>

  <clause id="11687">
    <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(299,a,27,a,b,11685,a),flip(a)].">
      <j1 rule="hyper" parents="299 27 11685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11688">
    <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(11595(a,1),11687(a,1,1))].">
      <j1 rule="para" parents="11595 11687"/>
    </justification>
  </clause>

  <clause id="11689">
    <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),11688(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 11688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11690">
    <literal><![CDATA[
      R(T(x,x \ y),z,u) = (R(x,z,u) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(644,a,11689,a),flip(a)].">
      <j1 rule="hyper" parents="644 11689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11692">
    <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(11689(a,1),5514(a,1,2,1))].">
      <j1 rule="para" parents="11689 5514"/>
    </justification>
  </clause>

  <clause id="11693">
    <literal><![CDATA[
      R((x \ y) \ y,z,u) = (R(x,z,u) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(65,a,1170,a(flip),b,11690,a)].">
      <j1 rule="hyper" parents="65 1170 11690"/>
    </justification>
  </clause>

  <clause id="11694">
    <literal><![CDATA[
      (R(x,y,z) \ (x * u)) \ (x * u) = R(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),11690(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 11690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11695">
    <literal><![CDATA[
      (R(K(x,y),z,u) \ w) \ w = R(T(K(x,y),w),z,u)
    ]]></literal>
    <justification jstring="[para(8727(a,1),11690(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8727 11690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11696">
    <literal><![CDATA[
      (R(x / y,z,u) \ x) \ x = R(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(79(a,1),11693(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 11693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11699">
    <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(5832(a,1),11693(a,2,1))].">
      <j1 rule="para" parents="5832 11693"/>
    </justification>
  </clause>

  <clause id="11702">
    <literal><![CDATA[
      K(x,R(x / y,z,u) \ w) = K(x,R(y \ x,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(11696(a,1),10519(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11696 10519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11703">
    <literal><![CDATA[
      R(T(x,R(x,y,z) * u),y,z) = (x * u) \ (x * (R(x,y,z) * u))
    ]]></literal>
    <justification jstring="[para(1956(a,1),11694(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1956 11694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11704">
    <literal><![CDATA[
      ((K(x,y) * z) * u) \ (z * u) = R(T(K(y,x),z * u),z,u)
    ]]></literal>
    <justification jstring="[para(6297(a,1),11695(a,1,1))].">
      <j1 rule="para" parents="6297 11695"/>
    </justification>
  </clause>

  <clause id="11705">
    <literal><![CDATA[
      ((K(x,y) * z) * u) \ (z * u) = R(K(y,T(x,z * u)),z,u)
    ]]></literal>
    <justification jstring="[para(7489(a,2),11704(a,2,1))].">
      <j1 rule="para" parents="7489 11704"/>
    </justification>
  </clause>

  <clause id="11706">
    <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(8354(a,1),11705(a,2,1))].">
      <j1 rule="para" parents="8354 11705"/>
    </justification>
  </clause>

  <clause id="11707">
    <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(299,a,230,a(flip),b,11703,a),flip(a)].">
      <j1 rule="hyper" parents="299 230 11703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11708">
    <literal><![CDATA[
      R(T(x,R(x,y,z) * u),y,z) = L(R(T(x,u),y,z),u,x)
    ]]></literal>
    <justification jstring="[para(27(a,2),11707(a,2,1))].">
      <j1 rule="para" parents="27 11707"/>
    </justification>
  </clause>

  <clause id="11709">
    <literal><![CDATA[
      R(T(x,R(x,y,z) * u),y,z) = R(T(x,x * u),y,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,787,a(flip),b,11708,a),flip(a)].">
      <j1 rule="hyper" parents="299 787 11708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11710">
    <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(11709(a,1),5044(a,1,1))].">
      <j1 rule="para" parents="11709 5044"/>
    </justification>
  </clause>

  <clause id="11711">
    <literal><![CDATA[
      K(R(x,y,z) * u,R(x,y,z)) = K(x * u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(5298,a,11710,a),flip(a)].">
      <j1 rule="hyper" parents="5298 11710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11712">
    <literal><![CDATA[
      K(x * R(y,z,u),R(y,z,u)) = K(y * x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(8632,a,11711,a)].">
      <j1 rule="hyper" parents="8632 11711"/>
    </justification>
  </clause>

  <clause id="11713">
    <literal><![CDATA[
      K(x * R(y,z,u),R(y,z,u)) = K(x * y,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,10439,a,b,11712,a),flip(a)].">
      <j1 rule="hyper" parents="299 10439 11712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11714">
    <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(11713(a,1),11441(a,1,1,2))].">
      <j1 rule="para" parents="11713 11441"/>
    </justification>
  </clause>

  <clause id="11715">
    <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(8106(a,1),11501(a,1,2,2,1))].">
      <j1 rule="para" parents="8106 11501"/>
    </justification>
  </clause>

  <clause id="11717">
    <literal><![CDATA[
      ((x \ y) * x) \ (((x \ y) * z) * x) = y \ (((y / x) * z) * x)
    ]]></literal>
    <justification jstring="[para(5714(a,1),11657(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5714 11657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11718">
    <literal><![CDATA[
      K(R(x,y,z) \ u,R(x,y,z)) = K(x \ u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(6330,a,11692,a),flip(a)].">
      <j1 rule="hyper" parents="6330 11692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11720">
    <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(11718(a,1),5011(a,1,1,2))].">
      <j1 rule="para" parents="11718 5011"/>
    </justification>
  </clause>

  <clause id="11721">
    <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(5813(a,1),11714(a,1,1))].">
      <j1 rule="para" parents="5813 11714"/>
    </justification>
  </clause>

  <clause id="11722">
    <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(5980(a,1),11721(a,1,1,1,2))].">
      <j1 rule="para" parents="5980 11721"/>
    </justification>
  </clause>

  <clause id="11723">
    <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(65,a,27,a,b,11722,a)].">
      <j1 rule="hyper" parents="65 27 11722"/>
    </justification>
  </clause>

  <clause id="11724">
    <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(5674(a,1),11723(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5674 11723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11725">
    <literal><![CDATA[
      R(R(x,y,z),u,R(x,y,z)) = R(R(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,11439,a(flip),b,11724,a)].">
      <j1 rule="hyper" parents="65 11439 11724"/>
    </justification>
  </clause>

  <clause id="11726">
    <literal><![CDATA[
      (R(x,y,R(x,z,u)) * z) * u = R(R(x,y,x),z,u) * (z * u)
    ]]></literal>
    <justification jstring="[para(11725(a,1),543(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11725 543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11727">
    <literal><![CDATA[
      (R(x,y,R(x,z,u)) * z) * u = (R(x,y,x) * z) * u
    ]]></literal>
    <justification jstring="[hyper(299,a,103,a(flip),b,11726,a),flip(a)].">
      <j1 rule="hyper" parents="299 103 11726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11728">
    <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(10852(a,1),11727(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10852 11727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11729">
    <literal><![CDATA[
      (x * ((y * y) \ 1)) \ ((y * y) \ z) = T(x,(y * y) \ 1) \ z
    ]]></literal>
    <justification jstring="[hyper(2021,a,11649,a),flip(a)].">
      <j1 rule="hyper" parents="2021 11649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11731">
    <literal><![CDATA[
      (x * ((y * y) \ 1)) \ ((y * y) \ z) = T(x,y \ (y \ 1)) \ z
    ]]></literal>
    <justification jstring="[para(727(a,1),11729(a,2,1,2))].">
      <j1 rule="para" parents="727 11729"/>
    </justification>
  </clause>

  <clause id="11732">
    <literal><![CDATA[
      (x * (y \ (y \ 1))) \ ((y * y) \ z) = T(x,y \ (y \ 1)) \ z
    ]]></literal>
    <justification jstring="[para(727(a,1),11731(a,1,1,2))].">
      <j1 rule="para" parents="727 11731"/>
    </justification>
  </clause>

  <clause id="11733">
    <literal><![CDATA[
      (x * x) * (y \ ((x * x) \ z)) = T(y,x \ (x \ 1)) \ z
    ]]></literal>
    <justification jstring="[hyper(65,a,953,a(flip),b,11732,a)].">
      <j1 rule="hyper" parents="65 953 11732"/>
    </justification>
  </clause>

  <clause id="11734">
    <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(65,a,7858,a(flip),b,11497,a),flip(a)].">
      <j1 rule="hyper" parents="65 7858 11497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11736">
    <literal><![CDATA[
      K(x,L(y,K(z,x) * u,w)) = K(x,(w * u) \ (w * (u * y)))
    ]]></literal>
    <justification jstring="[hyper(65,a,11489,a(flip),b,11734,a),flip(a)].">
      <j1 rule="hyper" parents="65 11489 11734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11738">
    <literal><![CDATA[
      K(x,L(y,K(z,x) * u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(18(a,2),11736(a,2,2))].">
      <j1 rule="para" parents="18 11736"/>
    </justification>
  </clause>

  <clause id="11739">
    <literal><![CDATA[
      K(x,L(y,K(x,z) \ u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(5426(a,2),11738(a,1,2,2))].">
      <j1 rule="para" parents="5426 11738"/>
    </justification>
  </clause>

  <clause id="11740">
    <literal><![CDATA[
      K(x,L(y,K(x,z) * u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(5432(a,1),11738(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5432 11738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11741">
    <literal><![CDATA[
      K(L(x,K(y,z) * u,w),y) = (y \ 1) / (y \ K(y,L(x,u,w)))
    ]]></literal>
    <justification jstring="[para(11740(a,1),5428(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11740 5428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11742">
    <literal><![CDATA[
      K(L(x,K(y,z) * u,w),y) = K(L(x,u,w),y)
    ]]></literal>
    <justification jstring="[hyper(299,a,5428,a(flip),b,11741,a),flip(a)].">
      <j1 rule="hyper" parents="299 5428 11741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11743">
    <literal><![CDATA[
      K(L(x,T(y,z),u),z) = K(L(x,y,u),z)
    ]]></literal>
    <justification jstring="[para(5049(a,1),11742(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5049 11742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11744">
    <literal><![CDATA[
      K(x,L(R(y,x \ z,y),z,u)) = K(L(x,y * (x \ z),u),y)
    ]]></literal>
    <justification jstring="[hyper(65,a,11122,a(flip),b,11743,a)].">
      <j1 rule="hyper" parents="65 11122 11743"/>
    </justification>
  </clause>

  <clause id="11745">
    <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(11744(a,1),11440(a,1))].">
      <j1 rule="para" parents="11744 11440"/>
    </justification>
  </clause>

  <clause id="11746">
    <literal><![CDATA[
      K(x,y * (z * (x * (T(T(x,u),u) \ w)))) = K(x,y * (z * (w * K(u,x))))
    ]]></literal>
    <justification jstring="[hyper(65,a,11546,a(flip),b,11548,a),flip(a)].">
      <j1 rule="hyper" parents="65 11546 11548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11748">
    <literal><![CDATA[
      K(x,y * (z * (x * (T(T(x,u),u) \ w)))) = K(x,y * (z * w))
    ]]></literal>
    <justification jstring="[hyper(299,a,11551,a(flip),b,11746,a),flip(a)].">
      <j1 rule="hyper" parents="299 11551 11746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11750">
    <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(299,a,6572,a(flip),b,11699,a),flip(a)].">
      <j1 rule="hyper" parents="299 6572 11699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11751">
    <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(6570(a,1),11750(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6570 11750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11752">
    <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(11751(a,1),10472(a,1,2))].">
      <j1 rule="para" parents="11751 10472"/>
    </justification>
  </clause>

  <clause id="11753">
    <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(5813(a,1),11720(a,1,1))].">
      <j1 rule="para" parents="5813 11720"/>
    </justification>
  </clause>

  <clause id="11754">
    <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(65,a,27,a,b,11753,a)].">
      <j1 rule="hyper" parents="65 27 11753"/>
    </justification>
  </clause>

  <clause id="11755">
    <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(5011(a,1),11754(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5011 11754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11756">
    <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(299,a,29,a(flip),b,11755,a),flip(a)].">
      <j1 rule="hyper" parents="299 29 11755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11757">
    <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(11756(a,1),2188(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11756 2188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11758">
    <literal><![CDATA[
      L(T(x,x \ K(x,y)) \ z,x,x \ K(x,y)) = K(x,y) \ ((((y * x) / y) \ 1) * z)
    ]]></literal>
    <justification jstring="[para(108(a,2),11665(a,1,1,1))].">
      <j1 rule="para" parents="108 11665"/>
    </justification>
  </clause>

  <clause id="11759">
    <literal><![CDATA[
      L(T(x,x \ 1) \ y,x,x \ K(x,z)) = K(x,z) \ ((((z * x) / z) \ 1) * y)
    ]]></literal>
    <justification jstring="[para(8886(a,1),11758(a,1,1,1))].">
      <j1 rule="para" parents="8886 11758"/>
    </justification>
  </clause>

  <clause id="11761">
    <literal><![CDATA[
      (x / (1 / y)) * (1 / T(y,y \ (x / (1 / y)))) = (T(x,y) / (1 / y)) * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(606,a,11654,a)].">
      <j1 rule="hyper" parents="606 11654"/>
    </justification>
  </clause>

  <clause id="11763">
    <literal><![CDATA[
      (x / (1 / y)) * (1 / T(y,(x / (1 / y)) / y)) = (T(x,y) / (1 / y)) * (1 / y)
    ]]></literal>
    <justification jstring="[para(4400(a,2),11761(a,1,2,2))].">
      <j1 rule="para" parents="4400 11761"/>
    </justification>
  </clause>

  <clause id="11764">
    <literal><![CDATA[
      (T(x,y) / (1 / y)) * (1 / y) = (x / (1 / y)) * (1 / T(y,x))
    ]]></literal>
    <justification jstring="[para(6953(a,1),11763(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6953 11763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11765">
    <literal><![CDATA[
      T(x,y) / (1 / T(y,x)) = x / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(387,a,11764,a)].">
      <j1 rule="hyper" parents="387 11764"/>
    </justification>
  </clause>

  <clause id="11766">
    <literal><![CDATA[
      T(x,y / x) / (1 / (x \ y)) = x / (1 / (y / x))
    ]]></literal>
    <justification jstring="[para(109(a,1),11765(a,1,2,2))].">
      <j1 rule="para" parents="109 11765"/>
    </justification>
  </clause>

  <clause id="11767">
    <literal><![CDATA[
      (x / (1 / (x \ y))) / x = x \ (x / (1 / (y / x)))
    ]]></literal>
    <justification jstring="[para(11766(a,1),4448(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11766 4448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11768">
    <literal><![CDATA[
      T((x / (1 / (x \ y))) / x,1 / (y / x)) = x \ (x / ((y / x) \ 1))
    ]]></literal>
    <justification jstring="[para(11767(a,2),2710(a,1,1))].">
      <j1 rule="para" parents="11767 2710"/>
    </justification>
  </clause>

  <clause id="11769">
    <literal><![CDATA[
      (x / ((x \ y) \ 1)) / x = x \ (x / ((y / x) \ 1))
    ]]></literal>
    <justification jstring="[hyper(11220,a,11768,a)].">
      <j1 rule="hyper" parents="11220 11768"/>
    </justification>
  </clause>

  <clause id="11770">
    <literal><![CDATA[
      x * ((x / ((x \ y) \ 1)) / x) = x / ((y / x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(144,a,11769,a(flip))].">
      <j1 rule="hyper" parents="144 11769"/>
    </justification>
  </clause>

  <clause id="11771">
    <literal><![CDATA[
      (K(x,y * y) * T(x \ z,y * y)) * u = (((y * y) * x) \ z) * ((y * y) * u)
    ]]></literal>
    <justification jstring="[para(663(a,1),11682(a,1,1,2))].">
      <j1 rule="para" parents="663 11682"/>
    </justification>
  </clause>

  <clause id="11772">
    <literal><![CDATA[
      T(K(x,y * y) * (x \ z),y * y) * u = (((y * y) * x) \ z) * ((y * y) * u)
    ]]></literal>
    <justification jstring="[para(7787(a,2),11771(a,1,1))].">
      <j1 rule="para" parents="7787 11771"/>
    </justification>
  </clause>

  <clause id="11773">
    <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(7989(a,1),7292(a,1,2,2))].">
      <j1 rule="para" parents="7989 7292"/>
    </justification>
  </clause>

  <clause id="11774">
    <literal><![CDATA[
      L((K(x,K(y,z)) * u) \ (y * w),K(x,K(y,z)) \ u,K(x,K(y,z))) = u \ (T(y,K(x,z)) * w)
    ]]></literal>
    <justification jstring="[para(8028(a,1),8340(a,1,1,1))].">
      <j1 rule="para" parents="8028 8340"/>
    </justification>
  </clause>

  <clause id="11775">
    <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(299,a,11598,a(flip),b,8403,a),flip(a)].">
      <j1 rule="hyper" parents="299 11598 8403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11776">
    <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(3869(a,1),11775(a,2,2))].">
      <j1 rule="para" parents="3869 11775"/>
    </justification>
  </clause>

  <clause id="11777">
    <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(299,a,8846,a(flip),b,11776,a),flip(a)].">
      <j1 rule="hyper" parents="299 8846 11776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11778">
    <literal><![CDATA[
      K(x,L(x \ T(y,z),x,y \ ((1 / z) \ y))) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,8832,a(flip),b,11777,a),flip(a)].">
      <j1 rule="hyper" parents="299 8832 11777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11779">
    <literal><![CDATA[
      K(x,T(x \ y,z)) = K(x,x \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(11320,a,11778,a),flip(a)].">
      <j1 rule="hyper" parents="11320 11778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11781">
    <literal><![CDATA[
      K(K(x,y) * z,z \ x) = K(z,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,11016,a,b,11779,a)].">
      <j1 rule="hyper" parents="299 11016 11779"/>
    </justification>
  </clause>

  <clause id="11782">
    <literal><![CDATA[
      T((x \ y) * x,z) \ T(y,z) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,3498,a,b,11779,a)].">
      <j1 rule="hyper" parents="299 3498 11779"/>
    </justification>
  </clause>

  <clause id="11783">
    <literal><![CDATA[
      K(x,x \ T(y,z)) \ 1 = K(x \ y,T(x,z))
    ]]></literal>
    <justification jstring="[para(11779(a,1),7544(a,1,1))].">
      <j1 rule="para" parents="11779 7544"/>
    </justification>
  </clause>

  <clause id="11784">
    <literal><![CDATA[
      K(x,T(x \ y,z)) * (K(y,z) * x) = T(K(y,z) * x,x \ y)
    ]]></literal>
    <justification jstring="[para(11781(a,1),5096(a,2,1)),flip(a)].">
      <j1 rule="para" parents="11781 5096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11785">
    <literal><![CDATA[
      K(x \ T(y,z),x) = K(x \ y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(5200,a,11783,a)].">
      <j1 rule="hyper" parents="5200 11783"/>
    </justification>
  </clause>

  <clause id="11786">
    <literal><![CDATA[
      K((x \ y) \ z,T(x \ y,x)) = K(y \ (z * x),x \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,11347,a(flip),b,11785,a),flip(a)].">
      <j1 rule="hyper" parents="65 11347 11785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11787">
    <literal><![CDATA[
      K((x \ y) \ z,y / x) = K(y \ (z * x),x \ y)
    ]]></literal>
    <justification jstring="[hyper(8215,a,11786,a)].">
      <j1 rule="hyper" parents="8215 11786"/>
    </justification>
  </clause>

  <clause id="11788">
    <literal><![CDATA[
      K(x,x \ y) * K(y \ (1 * x),x \ y) = (y / x) * (1 / (x \ y))
    ]]></literal>
    <justification jstring="[para(11787(a,1),10345(a,1,2))].">
      <j1 rule="para" parents="11787 10345"/>
    </justification>
  </clause>

  <clause id="11789">
    <literal><![CDATA[
      T(K(x,y) * z,z \ x) = T(z,z \ x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,9568,a(flip),b,11784,a),flip(a)].">
      <j1 rule="hyper" parents="65 9568 11784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11790">
    <literal><![CDATA[
      (x \ y) * T(K(y,z) * x,x \ y) = (y / x) * (x * K(y,z))
    ]]></literal>
    <justification jstring="[para(11789(a,2),5929(a,1,2))].">
      <j1 rule="para" parents="11789 5929"/>
    </justification>
  </clause>

  <clause id="11791">
    <literal><![CDATA[
      (K(x,y) * z) * (z \ x) = (x / z) * (z * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(276,a,11790,a)].">
      <j1 rule="hyper" parents="276 11790"/>
    </justification>
  </clause>

  <clause id="11792">
    <literal><![CDATA[
      ((x / y) * (y * K(x,z))) / T(x,z) = a(K(x,z),y,y \ x)
    ]]></literal>
    <justification jstring="[para(11791(a,1),10690(a,1,1))].">
      <j1 rule="para" parents="11791 10690"/>
    </justification>
  </clause>

  <clause id="11793">
    <literal><![CDATA[
      K(x,x \ y) * K(y \ x,x \ y) = (y / x) * (1 / (x \ y))
    ]]></literal>
    <justification jstring="[para(7(a,1),11788(a,1,2,1,2))].">
      <j1 rule="para" parents="7 11788"/>
    </justification>
  </clause>

  <clause id="11794">
    <literal><![CDATA[
      (x / y) / T(y \ x,x \ y) = (x / y) * (1 / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(65,a,7187,a(flip),b,11793,a)].">
      <j1 rule="hyper" parents="65 7187 11793"/>
    </justification>
  </clause>

  <clause id="11795">
    <literal><![CDATA[
      T(x \ y,y \ x) \ (y / x) = (y / x) * (1 / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(9309,a,11794,a)].">
      <j1 rule="hyper" parents="9309 11794"/>
    </justification>
  </clause>

  <clause id="11796">
    <literal><![CDATA[
      L(K(x * y,x) * K(x,K(z * y,x * y)),y,z) = (z * (T(x * y,x) / T(x,y))) / (z * y)
    ]]></literal>
    <justification jstring="[para(7989(a,1),8677(a,1,1,2))].">
      <j1 rule="para" parents="7989 8677"/>
    </justification>
  </clause>

  <clause id="11797">
    <literal><![CDATA[
      L(K(x,(y \ 1) \ (z \ u)),z \ u,z) = K(x,(z * ((((y \ x) / x) * y) * (1 / y))) \ u)
    ]]></literal>
    <justification jstring="[para(9284(a,1),9842(a,1,1))].">
      <j1 rule="para" parents="9284 9842"/>
    </justification>
  </clause>

  <clause id="11798">
    <literal><![CDATA[
      K(x,(y * ((((z \ x) / x) * z) * (1 / z))) \ u) = K(x,(y * (z \ 1)) \ u)
    ]]></literal>
    <justification jstring="[hyper(10251,a,11797,a),flip(a)].">
      <j1 rule="hyper" parents="10251 11797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11799">
    <literal><![CDATA[
      K(x,(y * ((z \ x) / x)) \ u) = K(x,(y * (z \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(2230(a,1),11798(a,1,2,1,2))].">
      <j1 rule="para" parents="2230 11798"/>
    </justification>
  </clause>

  <clause id="11800">
    <literal><![CDATA[
      K(x,(y * (z \ x)) \ (u * x)) = K(x,(y * (z \ 1)) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,11230,a(flip),b,11799,a)].">
      <j1 rule="hyper" parents="65 11230 11799"/>
    </justification>
  </clause>

  <clause id="11801">
    <literal><![CDATA[
      K(x,(y * ((z \ x) \ 1)) \ u) = K(x,(y * z) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(65,a,10501,a(flip),b,11800,a),flip(a)].">
      <j1 rule="hyper" parents="65 10501 11800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11802">
    <literal><![CDATA[
      K(x,((1 / (K(y,(z \ x) \ 1) / y)) * z) \ (u * x)) = K(x,(((z \ x) \ 1) * (1 / (1 / y))) \ u)
    ]]></literal>
    <justification jstring="[para(5816(a,1),11801(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5816 11801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11803">
    <literal><![CDATA[
      L(a((x \ y) \ y,z,(x \ y) \ y),u,(x \ y) \ y) = y \ (R(x,z,x) * (x \ y))
    ]]></literal>
    <justification jstring="[para(10281(a,1),10489(a,2,2,1))].">
      <j1 rule="para" parents="10281 10489"/>
    </justification>
  </clause>

  <clause id="11805">
    <literal><![CDATA[
      L(a((x \ y) \ y,z,(x \ y) \ y),u,(x \ y) \ y) = y \ (y * a(x,z,x))
    ]]></literal>
    <justification jstring="[para(10471(a,1),11803(a,2,2))].">
      <j1 rule="para" parents="10471 11803"/>
    </justification>
  </clause>

  <clause id="11806">
    <literal><![CDATA[
      a((x \ y) \ y,z,(x \ y) \ y) = a(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(508,a,11805,a),flip(a)].">
      <j1 rule="hyper" parents="508 11805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11807">
    <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(6138(a,1),10578(a,1,2))].">
      <j1 rule="para" parents="6138 10578"/>
    </justification>
  </clause>

  <clause id="11808">
    <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(6341(a,1),11807(a,2,3))].">
      <j1 rule="para" parents="6341 11807"/>
    </justification>
  </clause>

  <clause id="11809">
    <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(5783,a,11169,a)].">
      <j1 rule="hyper" parents="5783 11169"/>
    </justification>
  </clause>

  <clause id="11810">
    <literal><![CDATA[
      T(x * (1 / L(x,y,z)),K(L(x,y,z),1)) = K(x,x \ 1) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(6358(a,1),11215(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6358 11215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11811">
    <literal><![CDATA[
      T(x * (1 / L(x,y,z)),K(L(x,y,z),1)) = L(x,y,z) \ T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,3376,a(flip),b,11810,a),flip(a)].">
      <j1 rule="hyper" parents="299 3376 11810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11813">
    <literal><![CDATA[
      (x \ T(x * y,x)) \ (y * K(x,K(z,x * y))) = L(K(x * y,T(x,z)) \ 1,K(x * y,x),y)
    ]]></literal>
    <justification jstring="[para(7489(a,2),11773(a,2,1,1))].">
      <j1 rule="para" parents="7489 11773"/>
    </justification>
  </clause>

  <clause id="11814">
    <literal><![CDATA[
      L(K(x * y,x) * K(x,K(z * y,y)),y,z) = (z * (T(x * y,x) / T(x,y))) / (z * y)
    ]]></literal>
    <justification jstring="[para(8086(a,1),11796(a,1,1,2))].">
      <j1 rule="para" parents="8086 11796"/>
    </justification>
  </clause>

  <clause id="11815">
    <literal><![CDATA[
      (x * (T(y * z,y) / T(y,z))) / (x * z) = L(K(y * z,y) * K(y,K(z,x)),z,x)
    ]]></literal>
    <justification jstring="[para(8013(a,1),11814(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="8013 11814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11816">
    <literal><![CDATA[
      L(K(x * y,x) * K(x,K(y,z)),y,z) = (z * (x \ T(x * y,x))) / (z * y)
    ]]></literal>
    <justification jstring="[para(8652(a,1),11815(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="8652 11815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11817">
    <literal><![CDATA[
      (x * (y \ T(y * z,y))) / (x * z) = L(K(y * z,T(y,x)),z,x)
    ]]></literal>
    <justification jstring="[para(8487(a,1),11816(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8487 11816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11818">
    <literal><![CDATA[
      L(K(x * y,T(x,z)),y,z) = K((z * y) / (z * (x \ 1)),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,6421,a(flip),b,11817,a),flip(a)].">
      <j1 rule="hyper" parents="65 6421 11817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11819">
    <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(7710,a,11809,a)].">
      <j1 rule="hyper" parents="7710 11809"/>
    </justification>
  </clause>

  <clause id="11820">
    <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(7544(a,1),11813(a,2,1))].">
      <j1 rule="para" parents="7544 11813"/>
    </justification>
  </clause>

  <clause id="11821">
    <literal><![CDATA[
      (x \ T(x * y,x)) \ (y * K(x,K(z,x * y))) = K(x,T(x * y,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,9222,a(flip),b,11820,a),flip(a)].">
      <j1 rule="hyper" parents="299 9222 11820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11824">
    <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(9755(a,2),11821(a,1,1))].">
      <j1 rule="para" parents="9755 11821"/>
    </justification>
  </clause>

  <clause id="11825">
    <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(8541(a,1),11824(a,1,2,2))].">
      <j1 rule="para" parents="8541 11824"/>
    </justification>
  </clause>

  <clause id="11826">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) \ K(x,z) = K(y,T(y * K(x,z),x))
    ]]></literal>
    <justification jstring="[para(8(a,1),11825(a,1,2))].">
      <j1 rule="para" parents="8 11825"/>
    </justification>
  </clause>

  <clause id="11827">
    <literal><![CDATA[
      K(T(x / y,x) \ x,z) * K(z,y) = K(x,T(x * K(z,y),z))
    ]]></literal>
    <justification jstring="[hyper(5452,a,11826,a)].">
      <j1 rule="hyper" parents="5452 11826"/>
    </justification>
  </clause>

  <clause id="11828">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) * K(z,x) = K(y,T(y * K(z,x),z))
    ]]></literal>
    <justification jstring="[para(9771(a,1),11827(a,1,1))].">
      <j1 rule="para" parents="9771 11827"/>
    </justification>
  </clause>

  <clause id="11829">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) * K(z,x) = K(y,y * K(z,x))
    ]]></literal>
    <justification jstring="[hyper(299,a,8543,a(flip),b,11828,a),flip(a)].">
      <j1 rule="hyper" parents="299 8543 11828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11830">
    <literal><![CDATA[
      K(x * K(y,z),x) = K(x,x * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,9777,a(flip),b,11829,a)].">
      <j1 rule="hyper" parents="65 9777 11829"/>
    </justification>
  </clause>

  <clause id="11831">
    <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(11830(a,1),5995(a,1,1,1,2))].">
      <j1 rule="para" parents="11830 5995"/>
    </justification>
  </clause>

  <clause id="11832">
    <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(5083(a,2),11831(a,1,1,1))].">
      <j1 rule="para" parents="5083 11831"/>
    </justification>
  </clause>

  <clause id="11833">
    <literal><![CDATA[
      R(T(x,K(y,z)),K(z,y),x) = T(x,x * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(6258,a,11832,a)].">
      <j1 rule="hyper" parents="6258 11832"/>
    </justification>
  </clause>

  <clause id="11834">
    <literal><![CDATA[
      T(x,x * K(y,z)) \ T(K(z,y) * x,x) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[para(11833(a,1),11163(a,1,1))].">
      <j1 rule="para" parents="11833 11163"/>
    </justification>
  </clause>

  <clause id="11835">
    <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(11237(a,1),11834(a,1,1,2,2))].">
      <j1 rule="para" parents="11237 11834"/>
    </justification>
  </clause>

  <clause id="11836">
    <literal><![CDATA[
      (1 / x) \ ((y * y) * L((y * y) \ (1 / x),z,u)) = (x * (y * y)) \ L(x * (y * y),z,u)
    ]]></literal>
    <justification jstring="[para(418(a,1),6533(a,2,2,1))].">
      <j1 rule="para" parents="418 6533"/>
    </justification>
  </clause>

  <clause id="11837">
    <literal><![CDATA[
      (1 / x) \ ((y * y) * L((y * y) \ (1 / x),z,u)) = (y * y) \ (x \ L(x * (y * y),z,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,419,a(flip),b,11836,a),flip(a)].">
      <j1 rule="hyper" parents="299 419 11836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11838">
    <literal><![CDATA[
      (x * x) \ (y \ L(y * (x * x),z,u)) = (1 / y) \ L(1 / y,z,u)
    ]]></literal>
    <justification jstring="[para(6492(a,1),11837(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6492 11837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11839">
    <literal><![CDATA[
      (x * x) \ (y \ L(y * (x * x),z,u)) = y \ L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,6504,a(flip),b,11838,a),flip(a)].">
      <j1 rule="hyper" parents="299 6504 11838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11842">
    <literal><![CDATA[
      (L(x \ 1,y,z) \ (x \ 1)) * T(1 / (1 / x),x \ 1) = L(x \ 1,y,z) \ K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,3285,a(flip),b,6579,a),flip(a)].">
      <j1 rule="hyper" parents="299 3285 6579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11843">
    <literal><![CDATA[
      (L(x \ 1,y,z) \ (x \ 1)) * T(1 / (1 / x),x \ 1) = (x \ 1) * (L(x \ 1,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(299,a,1372,a(flip),b,11842,a),flip(a)].">
      <j1 rule="hyper" parents="299 1372 11842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11844">
    <literal><![CDATA[
      (L(x \ 1,y,z) \ (x \ 1)) * x = (x \ 1) * (L(x \ 1,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(2545(a,1),11843(a,1,2))].">
      <j1 rule="para" parents="2545 11843"/>
    </justification>
  </clause>

  <clause id="11845">
    <literal><![CDATA[
      (L(x \ 1,y,z) \ (x \ 1)) \ (L(1 / x,y,z) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(119,a,3828,a(flip),b,11844,a)].">
      <j1 rule="hyper" parents="119 3828 11844"/>
    </justification>
  </clause>

  <clause id="11846">
    <literal><![CDATA[
      K(x,y * (((1 / z) * (K(u,w) * z)) * (u * (T(T(u,w),w) \ z)))) = K(x,y * ((z \ 1) \ K(w,u)))
    ]]></literal>
    <justification jstring="[para(6629(a,1),6696(a,1,2,2))].">
      <j1 rule="para" parents="6629 6696"/>
    </justification>
  </clause>

  <clause id="11847">
    <literal><![CDATA[
      R(x,y,K(y,z)) * (R(y,u,w) * K(y,z)) = (x * R(x \ (x * y),u,w)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(6866(a,1),6884(a,1,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="6866 6884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11848">
    <literal><![CDATA[
      R(x,y,K(y,z)) * (R(y,u,w) * K(y,z)) = (x * R(y,u,w)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),11847(a,2,1,2,1))].">
      <j1 rule="para" parents="9 11847"/>
    </justification>
  </clause>

  <clause id="11849">
    <literal><![CDATA[
      (x * R(y,z,u)) * K(y,w) = x * (R(y,z,u) * K(y,w))
    ]]></literal>
    <justification jstring="[para(6866(a,1),11848(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6866 11848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11850">
    <literal><![CDATA[
      L(K(x,y),R(x,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(490,a,11849,a)].">
      <j1 rule="hyper" parents="490 11849"/>
    </justification>
  </clause>

  <clause id="11851">
    <literal><![CDATA[
      K(x,(y \ 1) * R(x,z,u)) = K(x,y \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,8418,a(flip),b,11850,a)].">
      <j1 rule="hyper" parents="65 8418 11850"/>
    </justification>
  </clause>

  <clause id="11852">
    <literal><![CDATA[
      K(x,R(x,y,z) * (u \ 1)) = K(x,u \ R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,8633,a,b,11851,a)].">
      <j1 rule="hyper" parents="65 8633 11851"/>
    </justification>
  </clause>

  <clause id="11853">
    <literal><![CDATA[
      K(x * K(x \ y,T(x,z)),u) * (x * T(x \ y,z)) = (x * T(x \ y,z)) * K(x,u)
    ]]></literal>
    <justification jstring="[para(9500(a,1),7035(a,1,1,1))].">
      <j1 rule="para" parents="9500 7035"/>
    </justification>
  </clause>

  <clause id="11854">
    <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(5643(a,1),8512(a,1,1,2))].">
      <j1 rule="para" parents="5643 8512"/>
    </justification>
  </clause>

  <clause id="11855">
    <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(8778(a,1),11854(a,1,1))].">
      <j1 rule="para" parents="8778 11854"/>
    </justification>
  </clause>

  <clause id="11856">
    <literal><![CDATA[
      K(x,(y / (1 / (1 / z))) / y) = K(x,y / (y * z))
    ]]></literal>
    <justification jstring="[hyper(36,a,10970,a(flip),b,11855,a),flip(a)].">
      <j1 rule="hyper" parents="36 10970 11855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11857">
    <literal><![CDATA[
      K(x,(y / z) / y) = K(x,y / (y * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,6063,a(flip),b,11856,a)].">
      <j1 rule="hyper" parents="65 6063 11856"/>
    </justification>
  </clause>

  <clause id="11859">
    <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(5616(a,1),8912(a,1,2,2))].">
      <j1 rule="para" parents="5616 8912"/>
    </justification>
  </clause>

  <clause id="11860">
    <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(5055(a,1),9137(a,1,1))].">
      <j1 rule="para" parents="5055 9137"/>
    </justification>
  </clause>

  <clause id="11861">
    <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(775,a,11860,a),flip(a)].">
      <j1 rule="hyper" parents="775 11860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11862">
    <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(11860(a,1),775(a,1))].">
      <j1 rule="para" parents="11860 775"/>
    </justification>
  </clause>

  <clause id="11863">
    <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(5351(a,1),11861(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5351 11861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11864">
    <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(5426(a,1),9211(a,1,1,1))].">
      <j1 rule="para" parents="5426 9211"/>
    </justification>
  </clause>

  <clause id="11865">
    <literal><![CDATA[
      (K(x,T(y,z)) * K(y,T(u,z))) \ 1 = (K(y,u) * K(x,y)) \ K(K(y,u) * K(x,y),z * K(u,y))
    ]]></literal>
    <justification jstring="[para(10193(a,1),9220(a,1,1))].">
      <j1 rule="para" parents="10193 9220"/>
    </justification>
  </clause>

  <clause id="11866">
    <literal><![CDATA[
      K(x,y * K(((z \ 1) \ 1) \ K(u,x),(z \ 1) \ 1)) = K(x,y / K((z * ((u \ 1) / z)) \ 1,x))
    ]]></literal>
    <justification jstring="[para(6748(a,2),9660(a,2,2,2))].">
      <j1 rule="para" parents="6748 9660"/>
    </justification>
  </clause>

  <clause id="11867">
    <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(9120,a,9941,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="9120 9941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11868">
    <literal><![CDATA[
      K(x,((y / z) * L(z,u,w)) \ (y * L(z,u,w))) = L(K(x,z),L(z,u,w),y)
    ]]></literal>
    <justification jstring="[para(173(a,1),11867(a,2,1,2))].">
      <j1 rule="para" parents="173 11867"/>
    </justification>
  </clause>

  <clause id="11869">
    <literal><![CDATA[
      L(K(x,y),L(y,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[para(1799(a,1),11868(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1799 11868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11870">
    <literal><![CDATA[
      K((x \ 1) * L(y,z,u),y) = K(x \ L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(9803,a,11869,a)].">
      <j1 rule="hyper" parents="9803 11869"/>
    </justification>
  </clause>

  <clause id="11871">
    <literal><![CDATA[
      K((x \ y) \ L(z,u,w),z) = K(y \ (x * L(z,u,w)),z)
    ]]></literal>
    <justification jstring="[hyper(65,a,7421,a(flip),b,11869,a),flip(a)].">
      <j1 rule="hyper" parents="65 7421 11869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11872">
    <literal><![CDATA[
      L(K(x,y),L(x,z,u),w) = (((v5 \ v6) \ v6) * K(y,x)) \ T(v5,v5 \ v6)
    ]]></literal>
    <justification jstring="[para(11869(a,1),9097(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11869 9097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11873">
    <literal><![CDATA[
      K(x \ L(y,z,u),y) = K(y * (x \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(65,a,11445,a(flip),b,11870,a),flip(a)].">
      <j1 rule="hyper" parents="65 11445 11870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11875">
    <literal><![CDATA[
      K(x \ L(y,z,u),y) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,5592,a(flip),b,11873,a),flip(a)].">
      <j1 rule="hyper" parents="299 5592 11873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11876">
    <literal><![CDATA[
      K(x \ L(y,z,u),y) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,y) = w
    ]]></literal>
    <justification jstring="[para(11873(a,2),7415(a,1))].">
      <j1 rule="para" parents="11873 7415"/>
    </justification>
  </clause>

  <clause id="11877">
    <literal><![CDATA[
      (L(x,y,z) * K((u \ x) \ x,x)) * u = (x \ (L(x,y,z) * u)) * x
    ]]></literal>
    <justification jstring="[para(11875(a,1),9969(a,1,1,2))].">
      <j1 rule="para" parents="11875 9969"/>
    </justification>
  </clause>

  <clause id="11878">
    <literal><![CDATA[
      K(x \ (y * L(z,u,w)),z) = K((y \ x) \ z,z)
    ]]></literal>
    <justification jstring="[hyper(11876,a,11871,a),flip(a)].">
      <j1 rule="hyper" parents="11876 11871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11880">
    <literal><![CDATA[
      K(x \ (y * L(z,u,w)),z) = K(z * (x \ y),z)
    ]]></literal>
    <justification jstring="[hyper(299,a,11405,a(flip),b,11878,a),flip(a)].">
      <j1 rule="hyper" parents="299 11405 11878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11881">
    <literal><![CDATA[
      K(x \ (y * (z * u)),u) = K(u * (x \ (y * z)),u)
    ]]></literal>
    <justification jstring="[para(94(a,1),11880(a,1,1,2))].">
      <j1 rule="para" parents="94 11880"/>
    </justification>
  </clause>

  <clause id="11882">
    <literal><![CDATA[
      K(x \ (y \ (z * (u * y))),y) = K(y * ((x * y) \ (z * u)),y)
    ]]></literal>
    <justification jstring="[hyper(8703,a,11881,a)].">
      <j1 rule="hyper" parents="8703 11881"/>
    </justification>
  </clause>

  <clause id="11883">
    <literal><![CDATA[
      K(x \ (y * (z * u)),z) = K(z * (x \ (y * u)),z)
    ]]></literal>
    <justification jstring="[hyper(65,a,9416,a(flip),b,11881,a)].">
      <j1 rule="hyper" parents="65 9416 11881"/>
    </justification>
  </clause>

  <clause id="11884">
    <literal><![CDATA[
      K(((x \ y) \ z) * u,L(u,z,x)) = K(u * (y \ (x * z)),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,11464,a,b,11883,a)].">
      <j1 rule="hyper" parents="65 11464 11883"/>
    </justification>
  </clause>

  <clause id="11885">
    <literal><![CDATA[
      K(x \ (y \ (z * (u * y))),y) = K(x \ (z * u),y)
    ]]></literal>
    <justification jstring="[hyper(299,a,11403,a(flip),b,11882,a),flip(a)].">
      <j1 rule="hyper" parents="299 11403 11882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11886">
    <literal><![CDATA[
      K(L(x,y * z,u),y) = K((u * z) \ (u * (z * x)),y)
    ]]></literal>
    <justification jstring="[hyper(65,a,10360,a(flip),b,11885,a)].">
      <j1 rule="hyper" parents="65 10360 11885"/>
    </justification>
  </clause>

  <clause id="11887">
    <literal><![CDATA[
      K(L(x,y * z,u),y) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(18(a,2),11886(a,2,1))].">
      <j1 rule="para" parents="18 11886"/>
    </justification>
  </clause>

  <clause id="11888">
    <literal><![CDATA[
      K(L(x,x \ y,z),u) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(11745,a,11887,a),flip(a)].">
      <j1 rule="hyper" parents="11745 11887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11889">
    <literal><![CDATA[
      L(K(x,y),z,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(11343,a,11888,a)].">
      <j1 rule="hyper" parents="11343 11888"/>
    </justification>
  </clause>

  <clause id="11890">
    <literal><![CDATA[
      K(x,L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,y),z,u) = w
    ]]></literal>
    <justification jstring="[para(11888(a,1),11343(a,1))].">
      <j1 rule="para" parents="11888 11343"/>
    </justification>
  </clause>

  <clause id="11891">
    <literal><![CDATA[
      K(x,(y * ((y \ z) / u)) \ z) = K(x,L(u,y \ z,y))
    ]]></literal>
    <justification jstring="[hyper(10252,a,11889,a)].">
      <j1 rule="hyper" parents="10252 11889"/>
    </justification>
  </clause>

  <clause id="11892">
    <literal><![CDATA[
      K(x,L((y \ 1) \ z,y \ 1,y)) = y * (T(z / (y \ 1),x) \ z)
    ]]></literal>
    <justification jstring="[hyper(9760,a,11889,a),flip(a)].">
      <j1 rule="hyper" parents="9760 11889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11893">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,u) = K(x \ 1,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(6335,a,11889,a)].">
      <j1 rule="hyper" parents="6335 11889"/>
    </justification>
  </clause>

  <clause id="11894">
    <literal><![CDATA[
      K(x,L(y \ 1,z,u)) = K(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(6144,a,11889,a),flip(a)].">
      <j1 rule="hyper" parents="6144 11889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11895">
    <literal><![CDATA[
      K(x,L(T(y \ z,y),u,w)) = L(K(x,z / y),u,w)
    ]]></literal>
    <justification jstring="[hyper(299,a,8379,a,b,11889,a)].">
      <j1 rule="hyper" parents="299 8379 11889"/>
    </justification>
  </clause>

  <clause id="11896">
    <literal><![CDATA[
      K(x,y) * a(z,u,K(y,x)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,10540,a,b,11889,a)].">
      <j1 rule="hyper" parents="65 10540 11889"/>
    </justification>
  </clause>

  <clause id="11897">
    <literal><![CDATA[
      K(x,L(y,z / T(y,u),w)) = K(x,L(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,9183,a,b,11889,a)].">
      <j1 rule="hyper" parents="65 9183 11889"/>
    </justification>
  </clause>

  <clause id="11898">
    <literal><![CDATA[
      K(x,L(y,L(y,z,u),w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,11869,a(flip),b,11889,a),flip(a)].">
      <j1 rule="hyper" parents="65 11869 11889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11899">
    <literal><![CDATA[
      K(x,L((y \ z) \ u,u,y)) = K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,7944,a(flip),b,11889,a),flip(a)].">
      <j1 rule="hyper" parents="65 7944 11889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11900">
    <literal><![CDATA[
      K(x,L(y,z * y,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,7813,a(flip),b,11889,a),flip(a)].">
      <j1 rule="hyper" parents="65 7813 11889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11901">
    <literal><![CDATA[
      K(x \ y,L(z,y,y \ 1)) = K(((y \ 1) * x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,7420,a(flip),b,11889,a),flip(a)].">
      <j1 rule="hyper" parents="65 7420 11889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11902">
    <literal><![CDATA[
      L(K(x,T(y \ z,u * y)),y,u) = K(x,(u * z) / (u * y))
    ]]></literal>
    <justification jstring="[hyper(8318,a,11889,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="8318 11889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11903">
    <literal><![CDATA[
      (x * y) * K(z,L(u,y,x)) = x * (y * K(z,u))
    ]]></literal>
    <justification jstring="[para(11889(a,1),94(a,1,2))].">
      <j1 rule="para" parents="11889 94"/>
    </justification>
  </clause>

  <clause id="11904">
    <literal><![CDATA[
      L(K(x,y \ (z \ u)),y,z) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[para(281(a,1),11889(a,2,2))].">
      <j1 rule="para" parents="281 11889"/>
    </justification>
  </clause>

  <clause id="11905">
    <literal><![CDATA[
      L(K(x,(y \ z) \ u),y \ z,y) = K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[para(520(a,1),11889(a,2,2))].">
      <j1 rule="para" parents="520 11889"/>
    </justification>
  </clause>

  <clause id="11906">
    <literal><![CDATA[
      K(x,y) \ (K(x,L(y,z,u)) \ (w * K(x,y))) = L(K(x,y),z,u) \ T(w,K(x,y))
    ]]></literal>
    <justification jstring="[para(11889(a,1),1367(a,1,2,1))].">
      <j1 rule="para" parents="11889 1367"/>
    </justification>
  </clause>

  <clause id="11907">
    <literal><![CDATA[
      x * L(K(x,y),z,u) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(11889(a,2),5083(a,2,2)),flip(a)].">
      <j1 rule="para" parents="11889 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11908">
    <literal><![CDATA[
      K(x,L((y \ z) \ 1,u,w)) = L(K(x,z \ y),u,w)
    ]]></literal>
    <justification jstring="[para(6814(a,1),11889(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6814 11889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11909">
    <literal><![CDATA[
      x / L(K(y,z),u,w) = x * K(L(z,u,w),y)
    ]]></literal>
    <justification jstring="[para(11889(a,2),7196(a,1,2))].">
      <j1 rule="para" parents="11889 7196"/>
    </justification>
  </clause>

  <clause id="11910">
    <literal><![CDATA[
      (x * (y * K(z,u))) * K(u,L(z,y,x)) = x * y
    ]]></literal>
    <justification jstring="[para(11889(a,1),9099(a,1,2))].">
      <j1 rule="para" parents="11889 9099"/>
    </justification>
  </clause>

  <clause id="11911">
    <literal><![CDATA[
      K(x,y) * K(y,L(x,z,u)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(11889(a,1),10536(a,1,2))].">
      <j1 rule="para" parents="11889 10536"/>
    </justification>
  </clause>

  <clause id="11912">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(z,L(u,y,x)) = K(z,u)
    ]]></literal>
    <justification jstring="[para(11889(a,1),10539(a,1,2))].">
      <j1 rule="para" parents="11889 10539"/>
    </justification>
  </clause>

  <clause id="11913">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(y,x) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[para(11889(a,1),10541(a,1,1))].">
      <j1 rule="para" parents="11889 10541"/>
    </justification>
  </clause>

  <clause id="11914">
    <literal><![CDATA[
      K(x,L(T(T(y,z),u * z),z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * z) / (u * (y \ z))) = w
    ]]></literal>
    <justification jstring="[para(11889(a,1),11538(a,1))].">
      <j1 rule="para" parents="11889 11538"/>
    </justification>
  </clause>

  <clause id="11915">
    <literal><![CDATA[
      (x * y) * K(z,L(u,x,y)) = y * (T(x,y) * K(z,u))
    ]]></literal>
    <justification jstring="[para(11889(a,1),11632(a,1,2))].">
      <j1 rule="para" parents="11889 11632"/>
    </justification>
  </clause>

  <clause id="11916">
    <literal><![CDATA[
      L(K(x,((y \ z) \ z) \ u),y,y \ z) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[para(11655(a,1),11889(a,2,2))].">
      <j1 rule="para" parents="11655 11889"/>
    </justification>
  </clause>

  <clause id="11917">
    <literal><![CDATA[
      T(x,L(y,z * y,u)) = x * K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(11900(a,1),5083(a,2,2))].">
      <j1 rule="para" parents="11900 5083"/>
    </justification>
  </clause>

  <clause id="11918">
    <literal><![CDATA[
      K(x,K(y,L(z,u * x,w))) = K(z,K(y,L(x,u,w)))
    ]]></literal>
    <justification jstring="[para(11900(a,1),8918(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11900 8918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11919">
    <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(11889(a,1),11890(a,1,2))].">
      <j1 rule="para" parents="11889 11890"/>
    </justification>
  </clause>

  <clause id="11920">
    <literal><![CDATA[
      (L(x,y,z) \ u) * K(x \ 1,L(u,y,z)) = (u \ (L(x,y,z) \ u)) * u
    ]]></literal>
    <justification jstring="[para(11893(a,1),5866(a,2,2)),flip(a)].">
      <j1 rule="para" parents="11893 5866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11921">
    <literal><![CDATA[
      (x * K(y \ 1,L(z,u,w))) \ (x * z) = T(z,L(y,u,w) \ 1)
    ]]></literal>
    <justification jstring="[para(11893(a,1),7186(a,1,1,2))].">
      <j1 rule="para" parents="11893 7186"/>
    </justification>
  </clause>

  <clause id="11923">
    <literal><![CDATA[
      K(x,L((T(y,z) \ u) \ 1,y,z)) = K(x,((y * z) \ (z * u)) \ 1)
    ]]></literal>
    <justification jstring="[para(11630(a,1),11894(a,2,2,1))].">
      <j1 rule="para" parents="11630 11894"/>
    </justification>
  </clause>

  <clause id="11925">
    <literal><![CDATA[
      T(x,L(y,z / T(y,u),w)) = x * K(x,L(y,z,w))
    ]]></literal>
    <justification jstring="[para(11897(a,1),5083(a,2,2))].">
      <j1 rule="para" parents="11897 5083"/>
    </justification>
  </clause>

  <clause id="11926">
    <literal><![CDATA[
      L(K(x,y),z,u) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(9104,a,11909,a)].">
      <j1 rule="hyper" parents="9104 11909"/>
    </justification>
  </clause>

  <clause id="11927">
    <literal><![CDATA[
      (x * (y * K(z,u))) \ (x * y) = K(L(u,y,x),z)
    ]]></literal>
    <justification jstring="[hyper(659,a,11909,a)].">
      <j1 rule="hyper" parents="659 11909"/>
    </justification>
  </clause>

  <clause id="11928">
    <literal><![CDATA[
      L(K(x,y * x),y,z) = K(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(299,a,7436,a(flip),b,11926,a),flip(a)].">
      <j1 rule="hyper" parents="299 7436 11926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11929">
    <literal><![CDATA[
      K(L(x,y,z),u) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,11889,a(flip),b,11926,a),flip(a)].">
      <j1 rule="hyper" parents="65 11889 11926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11930">
    <literal><![CDATA[
      (x * y) * K(L(z,y,x),u) = x * (y * K(z,u))
    ]]></literal>
    <justification jstring="[para(11926(a,1),94(a,1,2))].">
      <j1 rule="para" parents="11926 94"/>
    </justification>
  </clause>

  <clause id="11931">
    <literal><![CDATA[
      L(K(x \ (y \ z),u),x,y) = K((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[para(281(a,1),11926(a,2,1))].">
      <j1 rule="para" parents="281 11926"/>
    </justification>
  </clause>

  <clause id="11932">
    <literal><![CDATA[
      K(L(x,y,z),u) * K(u,x) = a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[para(11926(a,1),10541(a,1,1))].">
      <j1 rule="para" parents="11926 10541"/>
    </justification>
  </clause>

  <clause id="11933">
    <literal><![CDATA[
      K((x \ y) / z,L(u,z,x)) = K((x * z) \ y,T(u,z))
    ]]></literal>
    <justification jstring="[hyper(8307,a,11929,a),flip(a)].">
      <j1 rule="hyper" parents="8307 11929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11934">
    <literal><![CDATA[
      K(L(x,y,z),(u * (w \ 1)) \ v5) = K(x,L((u * (1 / w)) \ v5,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,5656,a(flip),b,11929,a)].">
      <j1 rule="hyper" parents="65 5656 11929"/>
    </justification>
  </clause>

  <clause id="11935">
    <literal><![CDATA[
      K(x \ (y \ z),L(u,x,y)) = K((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[para(281(a,1),11929(a,1,1)),flip(a)].">
      <j1 rule="para" parents="281 11929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11936">
    <literal><![CDATA[
      K((x \ 1) \ y,L(z,x \ 1,x)) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(519(a,1),11929(a,1,1)),flip(a)].">
      <j1 rule="para" parents="519 11929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11937">
    <literal><![CDATA[
      K((x \ y) \ z,L(u,x \ y,x)) = K(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[para(520(a,1),11929(a,1,1)),flip(a)].">
      <j1 rule="para" parents="520 11929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11938">
    <literal><![CDATA[
      (x * (y * z)) * K(z,L(x * y,y,x)) = L(z,y,x) * (x * y)
    ]]></literal>
    <justification jstring="[para(11929(a,1),492(a,1,2))].">
      <j1 rule="para" parents="11929 492"/>
    </justification>
  </clause>

  <clause id="11939">
    <literal><![CDATA[
      (x * K(y,L(z,u,w))) \ (x * z) = T(z,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(11929(a,1),7186(a,1,1,2))].">
      <j1 rule="para" parents="11929 7186"/>
    </justification>
  </clause>

  <clause id="11940">
    <literal><![CDATA[
      (x / y) * K(z,L(y,u,w)) = x / T(y,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(11929(a,1),7189(a,1,2))].">
      <j1 rule="para" parents="11929 7189"/>
    </justification>
  </clause>

  <clause id="11942">
    <literal><![CDATA[
      (x * (y * z)) * K(z,L(u,y,x)) = x * (y * T(z,u))
    ]]></literal>
    <justification jstring="[para(11929(a,1),9496(a,1,2))].">
      <j1 rule="para" parents="11929 9496"/>
    </justification>
  </clause>

  <clause id="11943">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(y,x) = a(u,z * x,K(y,x))
    ]]></literal>
    <justification jstring="[para(11929(a,1),10557(a,1,1))].">
      <j1 rule="para" parents="11929 10557"/>
    </justification>
  </clause>

  <clause id="11944">
    <literal><![CDATA[
      K(T(x,y) \ z,L(u,x,y)) = K((x * y) \ (y * z),u)
    ]]></literal>
    <justification jstring="[para(11630(a,1),11929(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11630 11929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11945">
    <literal><![CDATA[
      K(L(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,u),y,z) = w
    ]]></literal>
    <justification jstring="[para(11929(a,2),11890(a,1))].">
      <j1 rule="para" parents="11929 11890"/>
    </justification>
  </clause>

  <clause id="11946">
    <literal><![CDATA[
      a(x,y,K(z,y * z)) = 1
    ]]></literal>
    <justification jstring="[hyper(55,a,11928,a)].">
      <j1 rule="hyper" parents="55 11928"/>
    </justification>
  </clause>

  <clause id="11947">
    <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(7989(a,2),11945(a,1))].">
      <j1 rule="para" parents="7989 11945"/>
    </justification>
  </clause>

  <clause id="11949">
    <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(11911(a,1),2285(a,1))].">
      <j1 rule="para" parents="11911 2285"/>
    </justification>
  </clause>

  <clause id="11950">
    <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(11911(a,1),5438(a,1,2)),flip(b)].">
      <j1 rule="para" parents="11911 5438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11951">
    <literal><![CDATA[
      ((x * y) / x) * K(y,L(x,z,u)) = y * a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(11911(a,1),5705(a,2,2))].">
      <j1 rule="para" parents="11911 5705"/>
    </justification>
  </clause>

  <clause id="11952">
    <literal><![CDATA[
      T(x,L(y,z,u)) * K(y,x) = x * a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[para(11911(a,1),5362(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11911 5362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11953">
    <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(11912(a,1),7216(a,1,1)),flip(b)].">
      <j1 rule="para" parents="11912 7216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11954">
    <literal><![CDATA[
      a(x,y * z,K(z,u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,10558,a(flip),b,11913,a)].">
      <j1 rule="hyper" parents="65 10558 11913"/>
    </justification>
  </clause>

  <clause id="11956">
    <literal><![CDATA[
      a(x,y * z,K(u,K(w,z))) = a(x,y,K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(7989(a,2),11954(a,1,3))].">
      <j1 rule="para" parents="7989 11954"/>
    </justification>
  </clause>

  <clause id="11957">
    <literal><![CDATA[
      T(x,L(y,z * y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(11917(a,2),5087(a,1))].">
      <j1 rule="para" parents="11917 5087"/>
    </justification>
  </clause>

  <clause id="11958">
    <literal><![CDATA[
      K(x \ L(x,y,z),T(u,x)) = a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,10661,a,b,11932,a)].">
      <j1 rule="hyper" parents="65 10661 11932"/>
    </justification>
  </clause>

  <clause id="11959">
    <literal><![CDATA[
      a(x,y * z,K(u,z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,10557,a(flip),b,11932,a)].">
      <j1 rule="hyper" parents="65 10557 11932"/>
    </justification>
  </clause>

  <clause id="11960">
    <literal><![CDATA[
      x / T(x / y,L(y,z,u)) = y * a(u,z,K(y \ x,y))
    ]]></literal>
    <justification jstring="[para(11959(a,1),10594(a,2,2))].">
      <j1 rule="para" parents="11959 10594"/>
    </justification>
  </clause>

  <clause id="11961">
    <literal><![CDATA[
      K(L(x,y,z) / x,u) = a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(8220,a,11958,a)].">
      <j1 rule="hyper" parents="8220 11958"/>
    </justification>
  </clause>

  <clause id="11962">
    <literal><![CDATA[
      K(x \ L(x,y,z),u) = a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[para(3819(a,1),11961(a,1,1))].">
      <j1 rule="para" parents="3819 11961"/>
    </justification>
  </clause>

  <clause id="11963">
    <literal><![CDATA[
      K(x,y * (z * a(u,w,K(x,v5)))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(11961(a,1),11545(a,1,2,2,2))].">
      <j1 rule="para" parents="11961 11545"/>
    </justification>
  </clause>

  <clause id="11964">
    <literal><![CDATA[
      (x * y) * z != x * (y * K(u,w))
    ]]></literal>
    <literal><![CDATA[
      K(u,L(w,y,x)) = z
    ]]></literal>
    <justification jstring="[para(11903(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="11903 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11965">
    <literal><![CDATA[
      (x * y) * K(z,u * u) = x * (y * K(z,u * u))
    ]]></literal>
    <justification jstring="[para(476(a,1),11903(a,1,2,2))].">
      <j1 rule="para" parents="476 11903"/>
    </justification>
  </clause>

  <clause id="11966">
    <literal><![CDATA[
      (x * (y * z)) * K(u,L(z,y * z,x)) = x * (y * (z * K(u,z)))
    ]]></literal>
    <justification jstring="[para(6816(a,1),11903(a,2,2))].">
      <j1 rule="para" parents="6816 11903"/>
    </justification>
  </clause>

  <clause id="11967">
    <literal><![CDATA[
      (x * (y * K(z,u))) \ (x * y) != w
    ]]></literal>
    <literal><![CDATA[
      K(L(u,y,x),z) = w
    ]]></literal>
    <justification jstring="[para(11903(a,1),7209(a,1,1))].">
      <j1 rule="para" parents="11903 7209"/>
    </justification>
  </clause>

  <clause id="11968">
    <literal><![CDATA[
      T(x * (y * K(z,u)),K(L(u,y,x),z)) = ((x * (y * K(z,u))) \ (x * y)) \ (x * y)
    ]]></literal>
    <justification jstring="[para(11927(a,1),108(a,1,2))].">
      <j1 rule="para" parents="11927 108"/>
    </justification>
  </clause>

  <clause id="11969">
    <literal><![CDATA[
      (x * y) * K(z * z,u) = x * (y * K(z * z,u))
    ]]></literal>
    <justification jstring="[para(476(a,1),11930(a,1,2,1))].">
      <j1 rule="para" parents="476 11930"/>
    </justification>
  </clause>

  <clause id="11970">
    <literal><![CDATA[
      T(K(x,y),z * (u * K(w,x))) = T(K(x,y),z * u)
    ]]></literal>
    <justification jstring="[para(11930(a,1),8669(a,1,2))].">
      <j1 rule="para" parents="11930 8669"/>
    </justification>
  </clause>

  <clause id="11971">
    <literal><![CDATA[
      K((x * y) \ z,T(y,u)) = K(y \ (x \ z),T(y,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,7590,a(flip),b,11931,a),flip(a)].">
      <j1 rule="hyper" parents="65 7590 11931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11972">
    <literal><![CDATA[
      K((x * y) \ z,T(u,x \ z)) = K((x \ z) / y,L(u,y,x))
    ]]></literal>
    <justification jstring="[hyper(8321,a,11935,a),flip(a)].">
      <j1 rule="hyper" parents="8321 11935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11973">
    <literal><![CDATA[
      K(x \ ((y \ 1) * (y \ z)),L(u,x,y)) = K((y * x) \ ((1 / y) * z),u)
    ]]></literal>
    <justification jstring="[para(1683(a,1),11935(a,1,1,2))].">
      <j1 rule="para" parents="1683 11935"/>
    </justification>
  </clause>

  <clause id="11974">
    <literal><![CDATA[
      K(x \ ((1 / y) \ z),L(u,x,y)) = K(((1 / y) * x) \ z,u)
    ]]></literal>
    <justification jstring="[para(2467(a,1),11935(a,1,2))].">
      <j1 rule="para" parents="2467 11935"/>
    </justification>
  </clause>

  <clause id="11975">
    <literal><![CDATA[
      K(x,K(y \ (z \ u),L(w,y,z))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(w,K(x,(z * y) \ u)) = v5
    ]]></literal>
    <justification jstring="[para(11935(a,2),8007(a,1,2))].">
      <j1 rule="para" parents="11935 8007"/>
    </justification>
  </clause>

  <clause id="11976">
    <literal><![CDATA[
      K((x \ 1) \ y,x * z) = K(x * y,(x \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(519(a,1),11936(a,1,2))].">
      <j1 rule="para" parents="519 11936"/>
    </justification>
  </clause>

  <clause id="11977">
    <literal><![CDATA[
      K(x,y * (1 / (z * K(x,u)))) = K(x,y * (K(u,x) / z))
    ]]></literal>
    <justification jstring="[para(11012(a,1),11963(a,1,2,2))].">
      <j1 rule="para" parents="11012 11963"/>
    </justification>
  </clause>

  <clause id="11978">
    <literal><![CDATA[
      K(x,L((y \ z) \ 1,u,w)) = K(x,L(z \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(299,a,11889,a(flip),b,11908,a),flip(a)].">
      <j1 rule="hyper" parents="299 11889 11908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11979">
    <literal><![CDATA[
      K(x,K((y * z) \ (u \ w),L(z,y,u))) = K(x,K(z,(u * (y * z)) \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,8920,a(flip),b,11918,a),flip(a)].">
      <j1 rule="hyper" parents="65 8920 11918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11980">
    <literal><![CDATA[
      T(x,L(y,z / T(y,u),w)) = T(x,L(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(299,a,5083,a,b,11925,a),flip(a)].">
      <j1 rule="hyper" parents="299 5083 11925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11981">
    <literal><![CDATA[
      T(x,L(y,y \ z,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(262(a,1),11980(a,1,2,2))].">
      <j1 rule="para" parents="262 11980"/>
    </justification>
  </clause>

  <clause id="11982">
    <literal><![CDATA[
      K(K(x,L(y,z,u)),w) * ((v5 / T(y,L(x,z,u))) / (v5 / y)) = T(K(x,L(y,z,u)),w) * K(v5 / y,K(x,L(y,z,u)))
    ]]></literal>
    <justification jstring="[para(11940(a,1),5380(a,1,2,1))].">
      <j1 rule="para" parents="11940 5380"/>
    </justification>
  </clause>

  <clause id="11983">
    <literal><![CDATA[
      K(x,L(y,z * x,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(37,a,11913,a,b,11943,a)].">
      <j1 rule="hyper" parents="37 11913 11943"/>
    </justification>
  </clause>

  <clause id="11984">
    <literal><![CDATA[
      K(x \ y,L(z,y,u)) = K(x \ y,L(z,x,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),11983(a,1,2,2))].">
      <j1 rule="para" parents="10 11983"/>
    </justification>
  </clause>

  <clause id="11985">
    <literal><![CDATA[
      K((x \ (y \ z)) \ u,L(x,u,y)) = K((x \ (y \ z)) \ u,(y * ((y \ z) / x)) \ z)
    ]]></literal>
    <justification jstring="[para(11342(a,1),11984(a,2,2))].">
      <j1 rule="para" parents="11342 11984"/>
    </justification>
  </clause>

  <clause id="11986">
    <literal><![CDATA[
      x * (T(T(y,x),z) * K(u,w * w)) = (T(y,z) * x) * K(u,w * w)
    ]]></literal>
    <justification jstring="[para(232(a,1),11965(a,1,1)),flip(a)].">
      <j1 rule="para" parents="232 11965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11988">
    <literal><![CDATA[
      (x * y) / (x * (y * K(z,u))) = L(T(K(u,z),x * y),y,x)
    ]]></literal>
    <justification jstring="[para(11970(a,1),9106(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11970 9106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11989">
    <literal><![CDATA[
      K(x * y,(x \ 1) \ (x \ z)) = K((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),11976(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 11976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11990">
    <literal><![CDATA[
      K((x \ 1) \ (x \ y),z) = K(y,(x \ 1) \ (x \ z))
    ]]></literal>
    <justification jstring="[para(10(a,1),11989(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 11989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11991">
    <literal><![CDATA[
      K(((x \ 1) \ 1) \ ((x \ 1) \ y),z) = K(y,((1 / x) \ 1) \ ((x \ 1) \ z))
    ]]></literal>
    <justification jstring="[hyper(299,a,5660,a,b,11990,a),flip(a)].">
      <j1 rule="hyper" parents="299 5660 11990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11992">
    <literal><![CDATA[
      K(((x \ y) / z) \ y,L(z,x \ y,x)) = K(((x \ y) / z) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,9307,a(flip),b,11891,a),flip(a)].">
      <j1 rule="hyper" parents="65 9307 11891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11993">
    <literal><![CDATA[
      K(x,(y \ 1) \ (y \ L(z,y \ x,(y \ x) \ 1))) = K((((y \ x) \ 1) * (y \ 1)) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,11990,a(flip),b,11901,a)].">
      <j1 rule="hyper" parents="65 11990 11901"/>
    </justification>
  </clause>

  <clause id="11995">
    <literal><![CDATA[
      L(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(10540(a,1),11950(a,1))].">
      <j1 rule="para" parents="10540 11950"/>
    </justification>
  </clause>

  <clause id="11997">
    <literal><![CDATA[
      K(x,(y * z) \ (y * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(z \ u,u,y)) = w
    ]]></literal>
    <justification jstring="[para(7942(a,1),11995(a,1))].">
      <j1 rule="para" parents="7942 11995"/>
    </justification>
  </clause>

  <clause id="11998">
    <literal><![CDATA[
      (x * (y * K(z,u))) / (x * y) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,L(T(u,x * y),y,x)) = w
    ]]></literal>
    <justification jstring="[para(8245(a,2),11995(a,1))].">
      <j1 rule="para" parents="8245 11995"/>
    </justification>
  </clause>

  <clause id="11999">
    <literal><![CDATA[
      K(L(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(11926(a,1),11995(a,1))].">
      <j1 rule="para" parents="11926 11995"/>
    </justification>
  </clause>

  <clause id="12000">
    <literal><![CDATA[
      K((x * y) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(y \ (x \ z),L(u,y,x)) = w
    ]]></literal>
    <justification jstring="[para(11931(a,1),11995(a,1))].">
      <j1 rule="para" parents="11931 11995"/>
    </justification>
  </clause>

  <clause id="12001">
    <literal><![CDATA[
      K(x,L(T(y \ z,y),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(z / y,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(11895(a,2),11995(a,1))].">
      <j1 rule="para" parents="11895 11995"/>
    </justification>
  </clause>

  <clause id="12003">
    <literal><![CDATA[
      a(x,y * z,K(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(10549(a,1),11953(a,1))].">
      <j1 rule="para" parents="10549 11953"/>
    </justification>
  </clause>

  <clause id="12004">
    <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(11943(a,2),12003(a,1))].">
      <j1 rule="para" parents="11943 12003"/>
    </justification>
  </clause>

  <clause id="12006">
    <literal><![CDATA[
      (x * y) / T(x,L(y,z,u)) = y * a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,11940,a(flip),b,11951,a)].">
      <j1 rule="hyper" parents="65 11940 11951"/>
    </justification>
  </clause>

  <clause id="12007">
    <literal><![CDATA[
      (x * L(y,x,y)) / T(T(x,y),L(T(y,x * y),z,u)) = T(y,x * y) * a(u,z,K(T(x,y),T(y,x * y)))
    ]]></literal>
    <justification jstring="[para(4589(a,1),12006(a,1,1))].">
      <j1 rule="para" parents="4589 12006"/>
    </justification>
  </clause>

  <clause id="12008">
    <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(11960(a,1),9644(a,2,2))].">
      <j1 rule="para" parents="11960 9644"/>
    </justification>
  </clause>

  <clause id="12009">
    <literal><![CDATA[
      L(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(L(x,z,u),y) = w
    ]]></literal>
    <justification jstring="[para(9102(a,1),11967(a,1))].">
      <j1 rule="para" parents="9102 11967"/>
    </justification>
  </clause>

  <clause id="12010">
    <literal><![CDATA[
      K(x,L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(L(x,z,u),y) = w
    ]]></literal>
    <justification jstring="[para(11889(a,1),12009(a,1))].">
      <j1 rule="para" parents="11889 12009"/>
    </justification>
  </clause>

  <clause id="12011">
    <literal><![CDATA[
      K(x,y * ((z * K(x,u)) \ 1)) = K(x,y * (K(u,x) / z))
    ]]></literal>
    <justification jstring="[hyper(65,a,5639,a(flip),b,11977,a)].">
      <j1 rule="hyper" parents="65 5639 11977"/>
    </justification>
  </clause>

  <clause id="12012">
    <literal><![CDATA[
      K(x,((y * z) * y) \ ((z * y) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(y,z) \ u,u,z * y)) = w
    ]]></literal>
    <justification jstring="[para(886(a,1),11997(a,1,2,1))].">
      <j1 rule="para" parents="886 11997"/>
    </justification>
  </clause>

  <clause id="12013">
    <literal><![CDATA[
      K(x,y * ((K(x,z) * u) \ 1)) = K(x,y * (K(z,x) / u))
    ]]></literal>
    <justification jstring="[hyper(65,a,11666,a,b,12011,a)].">
      <j1 rule="hyper" parents="65 11666 12011"/>
    </justification>
  </clause>

  <clause id="12014">
    <literal><![CDATA[
      L(K(x,T(y \ z,K(u,w) \ y)),y,K(w,u)) = K(x,(K(w,u) * z) / (K(w,u) * y))
    ]]></literal>
    <justification jstring="[para(5426(a,2),11902(a,1,1,2,2))].">
      <j1 rule="para" parents="5426 11902"/>
    </justification>
  </clause>

  <clause id="12015">
    <literal><![CDATA[
      K((x * y) \ ((1 / x) \ z),L(u,x * y,x)) = K((x * ((x \ 1) * y)) \ z,u)
    ]]></literal>
    <justification jstring="[para(1677(a,1),11974(a,2,1,1))].">
      <j1 rule="para" parents="1677 11974"/>
    </justification>
  </clause>

  <clause id="12016">
    <literal><![CDATA[
      (x * y) / (x * (y * K(z,u))) = L(K(u,T(z,x * y)),y,x)
    ]]></literal>
    <justification jstring="[para(7489(a,2),11988(a,2,1))].">
      <j1 rule="para" parents="7489 11988"/>
    </justification>
  </clause>

  <clause id="12018">
    <literal><![CDATA[
      K(x,L(T(((y / z) \ 1) \ u,z / y),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(u / ((y / z) \ 1),w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(4641(a,1),12001(a,1,2,1))].">
      <j1 rule="para" parents="4641 12001"/>
    </justification>
  </clause>

  <clause id="12019">
    <literal><![CDATA[
      L(K(x,T(x * y,z * y)),y,z) = (z * y) / (z * (x \ T(x * y,x)))
    ]]></literal>
    <justification jstring="[para(7248(a,2),12016(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7248 12016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12020">
    <literal><![CDATA[
      T(x,L(y \ 1,z,u)) = T(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,11939,a(flip),b,11921,a)].">
      <j1 rule="hyper" parents="65 11939 11921"/>
    </justification>
  </clause>

  <clause id="12021">
    <literal><![CDATA[
      T(x / (L(y,z,u) \ 1),L(y \ 1,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      (L(y,z,u) \ 1) \ x = w
    ]]></literal>
    <justification jstring="[para(12020(a,2),400(a,1))].">
      <j1 rule="para" parents="12020 400"/>
    </justification>
  </clause>

  <clause id="12022">
    <literal><![CDATA[
      T(x,L((y \ z) \ 1,y,y)) = T(x,((1 / y) * z) \ 1)
    ]]></literal>
    <justification jstring="[para(511(a,1),12020(a,2,2,1))].">
      <j1 rule="para" parents="511 12020"/>
    </justification>
  </clause>

  <clause id="12023">
    <literal><![CDATA[
      T(x,L((y \ z) \ 1,y,y)) = T(x,((y \ 1) * z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,3876,a(flip),b,12022,a),flip(a)].">
      <j1 rule="hyper" parents="299 3876 12022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12024">
    <literal><![CDATA[
      x * (T(y / (x \ 1),z) \ y) = K(z,x * y)
    ]]></literal>
    <justification jstring="[para(519(a,1),11892(a,1,2)),flip(a)].">
      <j1 rule="para" parents="519 11892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12025">
    <literal><![CDATA[
      x * (1 / (1 / (x \ (T(y / ((1 / x) \ 1),z) \ y)))) = (1 / x) \ (1 / (1 / K(z,(1 / x) * y)))
    ]]></literal>
    <justification jstring="[para(12024(a,1),4157(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="12024 4157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12026">
    <literal><![CDATA[
      K(x,L((T(y,z) \ u) \ 1,y,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * u) \ (y * z)) = w
    ]]></literal>
    <justification jstring="[para(11923(a,2),6885(a,1))].">
      <j1 rule="para" parents="11923 6885"/>
    </justification>
  </clause>

  <clause id="12027">
    <literal><![CDATA[
      (x * (y * z)) * K(u,L(z,y,x)) = x * (y * (z * K(u,z)))
    ]]></literal>
    <justification jstring="[para(11900(a,1),11966(a,1,2))].">
      <j1 rule="para" parents="11900 11966"/>
    </justification>
  </clause>

  <clause id="12028">
    <literal><![CDATA[
      K(((x \ y) \ y) * z,L(z,x \ y,x)) = K(((x \ y) / z) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,11465,a(flip),b,11992,a)].">
      <j1 rule="hyper" parents="65 11465 11992"/>
    </justification>
  </clause>

  <clause id="12029">
    <literal><![CDATA[
      L(K(x,y),L(x,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,7201,a(flip),b,11872,a),flip(a)].">
      <j1 rule="hyper" parents="299 7201 11872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12030">
    <literal><![CDATA[
      K(x,(y \ z) \ L(x,u,w)) = K(x,z \ (y * L(x,u,w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,7944,a(flip),b,12029,a),flip(a)].">
      <j1 rule="hyper" parents="65 7944 12029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12031">
    <literal><![CDATA[
      (x \ (L(x,y,z) * u)) * x = (L(x,y,z) * K(u,x)) * u
    ]]></literal>
    <justification jstring="[para(6999(a,1),11877(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6999 11877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12032">
    <literal><![CDATA[
      (x \ (L(x,y,z) * u)) * x = L(x,y,z) * T(u,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,6912,a(flip),b,12031,a),flip(a)].">
      <j1 rule="hyper" parents="299 6912 12031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12033">
    <literal><![CDATA[
      (x \ (L(x,y,x) * z)) * x = z * L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,7454,a(flip),b,12032,a),flip(a)].">
      <j1 rule="hyper" parents="299 7454 12032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12034">
    <literal><![CDATA[
      (L(x,y,z) * (x \ u)) * x = L(x,y,z) * T(u,x)
    ]]></literal>
    <justification jstring="[para(1348(a,1),12032(a,1,1))].">
      <j1 rule="para" parents="1348 12032"/>
    </justification>
  </clause>

  <clause id="12035">
    <literal><![CDATA[
      (L(x,y,x) \ z) * L(x,y,x) = (x \ z) * x
    ]]></literal>
    <justification jstring="[para(10(a,1),12033(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10 12033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12036">
    <literal><![CDATA[
      ((x \ y) * x) / L(x,z,x) = L(x,z,x) \ y
    ]]></literal>
    <justification jstring="[hyper(137,a,12035,a)].">
      <j1 rule="hyper" parents="137 12035"/>
    </justification>
  </clause>

  <clause id="12037">
    <literal><![CDATA[
      L(1 / x,L(x,x,x),L(x,x,x) \ y) = ((x \ y) * x) \ (L(x,x,x) \ y)
    ]]></literal>
    <justification jstring="[para(12035(a,1),2819(a,2,1))].">
      <j1 rule="para" parents="12035 2819"/>
    </justification>
  </clause>

  <clause id="12038">
    <literal><![CDATA[
      ((x \ y) * x) \ (L(x,z,x) \ y) = y \ (y / L(x,z,x))
    ]]></literal>
    <justification jstring="[para(12035(a,1),11656(a,1,1))].">
      <j1 rule="para" parents="12035 11656"/>
    </justification>
  </clause>

  <clause id="12039">
    <literal><![CDATA[
      (x \ y) * a(x,z,x) = L(x,z,x) \ y
    ]]></literal>
    <justification jstring="[hyper(9716,a,12036,a)].">
      <j1 rule="hyper" parents="9716 12036"/>
    </justification>
  </clause>

  <clause id="12040">
    <literal><![CDATA[
      a(x,y,x) * (x \ z) = L(x,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(10134,a,12039,a)].">
      <j1 rule="hyper" parents="10134 12039"/>
    </justification>
  </clause>

  <clause id="12041">
    <literal><![CDATA[
      (x / y) \ (L(y,z,u) * (y \ x)) = x \ (L(y,z,u) * T(x,y))
    ]]></literal>
    <justification jstring="[para(12034(a,1),10399(a,2,2))].">
      <j1 rule="para" parents="12034 10399"/>
    </justification>
  </clause>

  <clause id="12042">
    <literal><![CDATA[
      (x / y) \ (L(y,z,u) * (y \ x)) = T(L(y,z,u) * K(x,y),x)
    ]]></literal>
    <justification jstring="[hyper(299,a,6913,a,b,12041,a),flip(a)].">
      <j1 rule="hyper" parents="299 6913 12041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12043">
    <literal><![CDATA[
      K(x,L((y * (1 / z)) \ u,w,v5)) = K(x,L((y * (z \ 1)) \ u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(11999,a,11934,a),flip(a)].">
      <j1 rule="hyper" parents="11999 11934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12045">
    <literal><![CDATA[
      x * (T(T(y,x),z) * K(u,w * w)) = T(y,z) * (x * K(u,w * w))
    ]]></literal>
    <justification jstring="[hyper(299,a,11965,a(flip),b,11986,a),flip(a)].">
      <j1 rule="hyper" parents="299 11965 11986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12046">
    <literal><![CDATA[
      K(x,L(y \ T(z,u),z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * y) \ (z * u)) = w
    ]]></literal>
    <justification jstring="[para(11978(a,1),12026(a,1))].">
      <j1 rule="para" parents="11978 12026"/>
    </justification>
  </clause>

  <clause id="12047">
    <literal><![CDATA[
      (L(x,y,z) \ x) * K(x,x \ 1) = (x \ (L(x,y,z) \ x)) * x
    ]]></literal>
    <justification jstring="[para(6107(a,1),11920(a,1,2))].">
      <j1 rule="para" parents="6107 11920"/>
    </justification>
  </clause>

  <clause id="12048">
    <literal><![CDATA[
      L(x,y,z) \ T(x,x \ 1) = (x \ (L(x,y,z) \ x)) * x
    ]]></literal>
    <justification jstring="[hyper(3372,a,12047,a)].">
      <j1 rule="hyper" parents="3372 12047"/>
    </justification>
  </clause>

  <clause id="12049">
    <literal><![CDATA[
      L(x,y,z) \ T(x,x \ 1) = (L(x,y,z) \ 1) * x
    ]]></literal>
    <justification jstring="[para(1358(a,1),12048(a,2,1))].">
      <j1 rule="para" parents="1358 12048"/>
    </justification>
  </clause>

  <clause id="12050">
    <literal><![CDATA[
      T(x * (1 / L(x,y,z)),K(L(x,y,z),1)) = (L(x,y,z) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(65,a,11811,a,b,12049,a)].">
      <j1 rule="hyper" parents="65 11811 12049"/>
    </justification>
  </clause>

  <clause id="12051">
    <literal><![CDATA[
      T(x * (1 / L(x,y,z)),1) = (L(x,y,z) \ 1) * x
    ]]></literal>
    <justification jstring="[para(194(a,1),12050(a,1,2))].">
      <j1 rule="para" parents="194 12050"/>
    </justification>
  </clause>

  <clause id="12052">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * x = x * (1 / L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(197,a,12051,a),flip(a)].">
      <j1 rule="hyper" parents="197 12051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12054">
    <literal><![CDATA[
      T(x,((L(y,z,u) \ 1) * y) * w) = T(x,(y * (L(y,z,u) \ 1)) * w)
    ]]></literal>
    <justification jstring="[para(12052(a,2),3877(a,1,2,1))].">
      <j1 rule="para" parents="12052 3877"/>
    </justification>
  </clause>

  <clause id="12055">
    <literal><![CDATA[
      K(x,K(y \ (z \ (u \ w)),L(z,y,u))) = K(x,K(z,(u * (y * z)) \ w))
    ]]></literal>
    <justification jstring="[para(10431(a,1),11979(a,1,2))].">
      <j1 rule="para" parents="10431 11979"/>
    </justification>
  </clause>

  <clause id="12056">
    <literal><![CDATA[
      (x * y) / (x * (z \ T(z * y,z))) = L(K(z,T(y * z,x)),y,x)
    ]]></literal>
    <justification jstring="[para(9479(a,1),12019(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9479 12019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12057">
    <literal><![CDATA[
      K(x,K(y \ (z \ u),L(w,y,z))) = K(x,K(w,(z * (y * w)) \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,10666,a(flip),b,12055,a)].">
      <j1 rule="hyper" parents="65 10666 12055"/>
    </justification>
  </clause>

  <clause id="12058">
    <literal><![CDATA[
      K(x,K(y,(z * (u * y)) \ w)) = K(y,K(x,(z * u) \ w))
    ]]></literal>
    <justification jstring="[hyper(11975,a,12057,a),flip(a)].">
      <j1 rule="hyper" parents="11975 12057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12059">
    <literal><![CDATA[
      K(x,K(y,(z * (u * x)) \ w)) = K(x,K(y,(z * u) \ w))
    ]]></literal>
    <justification jstring="[hyper(7985,a,12058,a)].">
      <j1 rule="hyper" parents="7985 12058"/>
    </justification>
  </clause>

  <clause id="12060">
    <literal><![CDATA[
      K(x,K(y,a(z,x,T(u,x)))) = K(x,K(y,(z * u) \ ((z * x) * u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,10264,a(flip),b,12059,a)].">
      <j1 rule="hyper" parents="65 10264 12059"/>
    </justification>
  </clause>

  <clause id="12061">
    <literal><![CDATA[
      K(x,K(y,a(z,x,T(u,x)))) = 1
    ]]></literal>
    <justification jstring="[hyper(299,a,9801,a(flip),b,12060,a),flip(a)].">
      <j1 rule="hyper" parents="299 9801 12060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12063">
    <literal><![CDATA[
      K(x,K(y,a(z,x,u))) = 1
    ]]></literal>
    <justification jstring="[para(222(a,1),12061(a,1,2,2,3))].">
      <j1 rule="para" parents="222 12061"/>
    </justification>
  </clause>

  <clause id="12065">
    <literal><![CDATA[
      T(a(x,y,z),K(u,y)) = a(x,y,z) * 1
    ]]></literal>
    <justification jstring="[para(12063(a,1),7958(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12063 7958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12066">
    <literal><![CDATA[
      T(a(x,y,z),K(u,y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,8,a(flip),b,12065,a),flip(a)].">
      <j1 rule="hyper" parents="299 8 12065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12067">
    <literal><![CDATA[
      T(a(x,y \ z,u),K(y,z)) = a(x,y \ z,u)
    ]]></literal>
    <justification jstring="[hyper(8258,a,12066,a)].">
      <j1 rule="hyper" parents="8258 12066"/>
    </justification>
  </clause>

  <clause id="12068">
    <literal><![CDATA[
      a(x,y \ z,u) * K(y,z) = K(y,z) * a(x,y \ z,u)
    ]]></literal>
    <justification jstring="[para(12067(a,1),107(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12067 107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12069">
    <literal><![CDATA[
      K(x,((1 / y) \ 1) \ ((y \ 1) \ z)) = K(y \ ((y \ 1) \ x),z)
    ]]></literal>
    <justification jstring="[hyper(7406,a,11991,a),flip(a)].">
      <j1 rule="hyper" parents="7406 11991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12070">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),z) = K(y,x \ ((x \ 1) \ z))
    ]]></literal>
    <justification jstring="[para(79(a,1),12069(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 12069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12071">
    <literal><![CDATA[
      K(x,y) \ (K(L(y,z,u),x) * (w * K(x,y))) = L(K(x,y),z,u) \ T(w,K(x,y))
    ]]></literal>
    <justification jstring="[para(5426(a,1),11906(a,1,2))].">
      <j1 rule="para" parents="5426 11906"/>
    </justification>
  </clause>

  <clause id="12072">
    <literal><![CDATA[
      K(x,y) \ (K(y,L(x,z,u)) * (w * K(x,y))) = L(K(x,y),z,u) \ T(w,K(x,y))
    ]]></literal>
    <justification jstring="[para(11929(a,1),12071(a,1,2,1))].">
      <j1 rule="para" parents="11929 12071"/>
    </justification>
  </clause>

  <clause id="12073">
    <literal><![CDATA[
      K(x,y) \ (T(y,L(x,z,u)) * K(x,y)) = L(K(x,y),z,u) \ T(y,K(x,y))
    ]]></literal>
    <justification jstring="[para(5103(a,1),12072(a,1,2))].">
      <j1 rule="para" parents="5103 12072"/>
    </justification>
  </clause>

  <clause id="12074">
    <literal><![CDATA[
      L(K(x,y),z,u) \ T(y,K(x,y)) = K(x,y) \ (y * a(u,z,K(x,y)))
    ]]></literal>
    <justification jstring="[para(11952(a,1),12073(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11952 12073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12075">
    <literal><![CDATA[
      T(x * (y * K(z,u)),K(z,L(u,y,x))) = ((x * (y * K(z,u))) \ (x * y)) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(8081,a,11968,a)].">
      <j1 rule="hyper" parents="8081 11968"/>
    </justification>
  </clause>

  <clause id="12076">
    <literal><![CDATA[
      K((x \ (y \ z)) \ u,(y * ((y \ z) / x)) \ z) = K(((y \ z) \ u) * x,L(x,u,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,11462,a(flip),b,11985,a),flip(a)].">
      <j1 rule="hyper" parents="65 11462 11985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12077">
    <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(12042(a,1),12008(a,1,2))].">
      <j1 rule="para" parents="12042 12008"/>
    </justification>
  </clause>

  <clause id="12078">
    <literal><![CDATA[
      x \ (x * a(y,z,K(x \ u,x))) = K(L(x,z,y),u) * K(u,x)
    ]]></literal>
    <justification jstring="[hyper(7791,a,12077,a),flip(a)].">
      <j1 rule="hyper" parents="7791 12077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12079">
    <literal><![CDATA[
      x \ (x * a(y,z,K(x \ u,x))) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(299,a,11932,a(flip),b,12078,a),flip(a)].">
      <j1 rule="hyper" parents="299 11932 12078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12080">
    <literal><![CDATA[
      a(x,y,K(z \ u,z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,12079,a),flip(a)].">
      <j1 rule="hyper" parents="316 12079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12082">
    <literal><![CDATA[
      a(x,y,K(z * u,z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),12080(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="9 12080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12083">
    <literal><![CDATA[
      a(x,y,K(z * u,u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(5191(a,1),12080(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5191 12080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12084">
    <literal><![CDATA[
      a(x,y,K(z \ 1,u * z)) = a(x,y,K(u,u * z))
    ]]></literal>
    <justification jstring="[para(5327(a,1),12080(a,1,3))].">
      <j1 rule="para" parents="5327 12080"/>
    </justification>
  </clause>

  <clause id="12085">
    <literal><![CDATA[
      K(x,y) * K(y,L(x,z,u)) = a(u,z,K(y * x,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,11911,a,b,12082,a)].">
      <j1 rule="hyper" parents="299 11911 12082"/>
    </justification>
  </clause>

  <clause id="12086">
    <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(12082(a,2),10572(a,1,1))].">
      <j1 rule="para" parents="12082 10572"/>
    </justification>
  </clause>

  <clause id="12087">
    <literal><![CDATA[
      a(x,y,K(x * z,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(299,a,7084,a(flip),b,12083,a),flip(a)].">
      <j1 rule="hyper" parents="299 7084 12083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12088">
    <literal><![CDATA[
      L(K(x * y,y),z,u) \ T(y,K(x * y,y)) = K(x * y,y) \ (y * a(u,z,K(x,y)))
    ]]></literal>
    <justification jstring="[para(12083(a,1),12074(a,2,2,2))].">
      <j1 rule="para" parents="12083 12074"/>
    </justification>
  </clause>

  <clause id="12089">
    <literal><![CDATA[
      L(K(x * y,y),z,x) = K(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(54,a,12087,a)].">
      <j1 rule="hyper" parents="54 12087"/>
    </justification>
  </clause>

  <clause id="12090">
    <literal><![CDATA[
      x * (y * K(x * z,T(z,x * y))) = K(x * z,z) * (x * y)
    ]]></literal>
    <justification jstring="[para(12089(a,1),7512(a,2,1))].">
      <j1 rule="para" parents="12089 7512"/>
    </justification>
  </clause>

  <clause id="12091">
    <literal><![CDATA[
      a(x,y,K(z,z * u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(10575,a,12086,a)].">
      <j1 rule="hyper" parents="10575 12086"/>
    </justification>
  </clause>

  <clause id="12092">
    <literal><![CDATA[
      a(x,y,K(z \ 1,u * z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,12084,a,b,12091,a)].">
      <j1 rule="hyper" parents="65 12084 12091"/>
    </justification>
  </clause>

  <clause id="12093">
    <literal><![CDATA[
      a(x,y,K(z,z \ u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),12091(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="10 12091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12094">
    <literal><![CDATA[
      a(x,y,K(z \ 1,u * z)) = a(x,y,K(z \ 1,u))
    ]]></literal>
    <justification jstring="[para(6161(a,1),12093(a,1,3))].">
      <j1 rule="para" parents="6161 12093"/>
    </justification>
  </clause>

  <clause id="12095">
    <literal><![CDATA[
      a(x,y,K(z \ 1,u)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,12092,a(flip),b,12094,a),flip(a)].">
      <j1 rule="hyper" parents="65 12092 12094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12096">
    <literal><![CDATA[
      a(x,y,K(z \ u,w)) = a(x,y,K(w,u \ z))
    ]]></literal>
    <justification jstring="[para(6977(a,1),12095(a,1,3))].">
      <j1 rule="para" parents="6977 12095"/>
    </justification>
  </clause>

  <clause id="12097">
    <literal><![CDATA[
      x * (y * K(x * z,T(z,y))) = K(x * z,z) * (x * y)
    ]]></literal>
    <justification jstring="[para(8907(a,1),12090(a,1,2,2))].">
      <j1 rule="para" parents="8907 12090"/>
    </justification>
  </clause>

  <clause id="12098">
    <literal><![CDATA[
      K(x * y,y) * (x * z) = x * (K(x * y,y) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,7601,a(flip),b,12097,a),flip(a)].">
      <j1 rule="hyper" parents="65 7601 12097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12099">
    <literal><![CDATA[
      x * (K(x * y,y) * (K(y,x) * z)) = a(y,x,y) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,10043,a(flip),b,12098,a),flip(a)].">
      <j1 rule="hyper" parents="65 10043 12098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12100">
    <literal><![CDATA[
      a(x,y,x) * (y * z) = y * (a(x,y,x) * z)
    ]]></literal>
    <justification jstring="[para(10042(a,1),12099(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10042 12099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12101">
    <literal><![CDATA[
      K((x \ (y \ z)) \ u,(y * ((y \ z) / x)) \ z) = K(x * (z \ (y * u)),x)
    ]]></literal>
    <justification jstring="[hyper(299,a,11884,a(flip),b,12076,a),flip(a)].">
      <j1 rule="hyper" parents="299 11884 12076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12102">
    <literal><![CDATA[
      K((x \ (y \ z)) \ u,L(x,y \ z,y)) = K(x * (z \ (y * u)),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,11891,a(flip),b,12101,a)].">
      <j1 rule="hyper" parents="65 11891 12101"/>
    </justification>
  </clause>

  <clause id="12103">
    <literal><![CDATA[
      K(((x \ y) \ z) * u,L(u,x \ y,x)) = K(u * (y \ (x * z)),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,11462,a(flip),b,12102,a)].">
      <j1 rule="hyper" parents="65 11462 12102"/>
    </justification>
  </clause>

  <clause id="12104">
    <literal><![CDATA[
      K(((x \ y) / z) \ y,z) = K(z * (y \ (x * y)),z)
    ]]></literal>
    <justification jstring="[hyper(65,a,12028,a(flip),b,12103,a)].">
      <j1 rule="hyper" parents="65 12028 12103"/>
    </justification>
  </clause>

  <clause id="12105">
    <literal><![CDATA[
      K(((x \ y) / z) \ y,z) = K(z * T(x,y),z)
    ]]></literal>
    <justification jstring="[para(22(a,2),12104(a,2,1,2))].">
      <j1 rule="para" parents="22 12104"/>
    </justification>
  </clause>

  <clause id="12106">
    <literal><![CDATA[
      K(x * ((y \ z) \ z),x) = K(x * T(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,11402,a(flip),b,12105,a)].">
      <j1 rule="hyper" parents="65 11402 12105"/>
    </justification>
  </clause>

  <clause id="12107">
    <literal><![CDATA[
      K(x,x * ((y \ z) \ z)) = u / (K(x * T(y,z),x) * u)
    ]]></literal>
    <justification jstring="[para(12106(a,1),5430(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12106 5430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12108">
    <literal><![CDATA[
      T(x,x * K(y * T(z,u),y)) \ T(K(y,y * ((z \ u) \ u)) * x,x) = K(y,T(y * ((z \ u) \ u),x))
    ]]></literal>
    <justification jstring="[para(12106(a,1),11834(a,1,1,2,2))].">
      <j1 rule="para" parents="12106 11834"/>
    </justification>
  </clause>

  <clause id="12109">
    <literal><![CDATA[
      K(x,x * ((y \ z) \ z)) = K(x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,5430,a(flip),b,12107,a),flip(a)].">
      <j1 rule="hyper" parents="299 5430 12107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12110">
    <literal><![CDATA[
      L(K(x * y,y),z,u) \ T(y,K(x * y,y)) = T(y,x * y) * a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,5364,a(flip),b,12088,a),flip(a)].">
      <j1 rule="hyper" parents="299 5364 12088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12111">
    <literal><![CDATA[
      K(x,L((y \ 1) \ (y \ z),y \ x,(y \ x) \ 1)) = K((((y \ x) \ 1) * (y \ 1)) \ 1,z)
    ]]></literal>
    <justification jstring="[para(2949(a,2),11993(a,1,2))].">
      <j1 rule="para" parents="2949 11993"/>
    </justification>
  </clause>

  <clause id="12112">
    <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(10015(a,1),10018(a,2,2,1,1))].">
      <j1 rule="para" parents="10015 10018"/>
    </justification>
  </clause>

  <clause id="12113">
    <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(5197(a,1),12112(a,2,2,1))].">
      <j1 rule="para" parents="5197 12112"/>
    </justification>
  </clause>

  <clause id="12115">
    <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(5197(a,1),12113(a,1,1,2,1))].">
      <j1 rule="para" parents="5197 12113"/>
    </justification>
  </clause>

  <clause id="12116">
    <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(65,a,10936,a(flip),b,12115,a)].">
      <j1 rule="hyper" parents="65 10936 12115"/>
    </justification>
  </clause>

  <clause id="12117">
    <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(12115(a,1),537(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="12115 537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12118">
    <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(12115(a,2),6766(a,1,1))].">
      <j1 rule="para" parents="12115 6766"/>
    </justification>
  </clause>

  <clause id="12120">
    <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(7954(a,1),12118(a,1,1,1,2,1))].">
      <j1 rule="para" parents="7954 12118"/>
    </justification>
  </clause>

  <clause id="12121">
    <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(76(a,1),10304(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="76 10304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12123">
    <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(7489(a,2),12121(a,2,2))].">
      <j1 rule="para" parents="7489 12121"/>
    </justification>
  </clause>

  <clause id="12124">
    <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(299,a,7570,a(flip),b,12123,a),flip(a)].">
      <j1 rule="hyper" parents="299 7570 12123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12125">
    <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(65,a,8664,a(flip),b,12124,a),flip(a)].">
      <j1 rule="hyper" parents="65 8664 12124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12127">
    <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(12125(a,2),8827(a,1))].">
      <j1 rule="para" parents="12125 8827"/>
    </justification>
  </clause>

  <clause id="12128">
    <literal><![CDATA[
      ((x / y) * (y * K(z,x))) \ ((z * x) / z) = x \ (((x / y) * (y * K(x,z))) * K(z,x))
    ]]></literal>
    <justification jstring="[para(12(a,1),10577(a,2,1))].">
      <j1 rule="para" parents="12 10577"/>
    </justification>
  </clause>

  <clause id="12129">
    <literal><![CDATA[
      T(((x / y) * (y * K(x,z))) / T(x,z),x) = ((x / y) * (y * K(z,x))) \ ((z * x) / z)
    ]]></literal>
    <justification jstring="[hyper(299,a,7231,a,b,12128,a)].">
      <j1 rule="hyper" parents="299 7231 12128"/>
    </justification>
  </clause>

  <clause id="12130">
    <literal><![CDATA[
      ((x / y) * (y * K(z,x))) \ ((z * x) / z) = T(a(K(x,z),y,y \ x),x)
    ]]></literal>
    <justification jstring="[para(11792(a,1),12129(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11792 12129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12131">
    <literal><![CDATA[
      ((x / y) * (y * K(z,x))) \ ((z * x) / z) = a(K(x,z),y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(299,a,9399,a(flip),b,12130,a),flip(a)].">
      <j1 rule="hyper" parents="299 9399 12130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12132">
    <literal><![CDATA[
      a(K(x,y),z,z \ x) = a(x / z,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,5251,a(flip),b,12131,a),flip(a)].">
      <j1 rule="hyper" parents="65 5251 12131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12133">
    <literal><![CDATA[
      a(K(x * y,z),y,y \ (x * y)) = a(x,y,K(z,x * y))
    ]]></literal>
    <justification jstring="[para(11(a,1),12132(a,2,1))].">
      <j1 rule="para" parents="11 12132"/>
    </justification>
  </clause>

  <clause id="12134">
    <literal><![CDATA[
      a(K(x * y,z),y,T(x,y)) = a(x,y,K(z,x * y))
    ]]></literal>
    <justification jstring="[para(22(a,2),12133(a,1,3))].">
      <j1 rule="para" parents="22 12133"/>
    </justification>
  </clause>

  <clause id="12135">
    <literal><![CDATA[
      T(x * y,z) * a(x,y,K(z,x * y)) = (K(x * y,z) * y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(12134(a,1),5173(a,1,2))].">
      <j1 rule="para" parents="12134 5173"/>
    </justification>
  </clause>

  <clause id="12136">
    <literal><![CDATA[
      (K(x * y,z) * y) * T(x,y) = x * (y * K(x * y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,10566,a(flip),b,12135,a),flip(a)].">
      <j1 rule="hyper" parents="65 10566 12135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12137">
    <literal><![CDATA[
      T(K(x * y,z) * y,T(x,y)) = T(y,x) * K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(235,a,12136,a,b,4961,a)].">
      <j1 rule="hyper" parents="235 12136 4961"/>
    </justification>
  </clause>

  <clause id="12138">
    <literal><![CDATA[
      (K(x * y,z) * y) * T(x,y) != x * u
    ]]></literal>
    <literal><![CDATA[
      y * K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(12136(a,2),45(a,1))].">
      <j1 rule="para" parents="12136 45"/>
    </justification>
  </clause>

  <clause id="12140">
    <literal><![CDATA[
      (((x * (y \ 1)) \ 1) \ 1) \ (x * (y \ 1)) = (y * K((x / y) \ 1,x / y)) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(12(a,1),10675(a,1,2,1))].">
      <j1 rule="para" parents="12 10675"/>
    </justification>
  </clause>

  <clause id="12141">
    <literal><![CDATA[
      (x * K((y / x) \ 1,y / x)) * (x \ 1) = K((y * (x \ 1)) \ 1,y * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(1493,a,12140,a),flip(a)].">
      <j1 rule="hyper" parents="1493 12140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12143">
    <literal><![CDATA[
      (x * K((y / x) \ 1,y / x)) * (x \ 1) = K(y \ x,y * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(299,a,9083,a(flip),b,12141,a),flip(a)].">
      <j1 rule="hyper" parents="299 9083 12141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12144">
    <literal><![CDATA[
      (x * K(y \ x,x \ y)) * (x \ 1) = K(y \ x,y * (x \ 1))
    ]]></literal>
    <justification jstring="[para(4872(a,1),12143(a,1,1,2))].">
      <j1 rule="para" parents="4872 12143"/>
    </justification>
  </clause>

  <clause id="12145">
    <literal><![CDATA[
      K(x \ y,x * (y \ 1)) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(3731,a,12144,a),flip(a)].">
      <j1 rule="hyper" parents="3731 12144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12146">
    <literal><![CDATA[
      K(x \ (y \ 1),x * T(y,y \ 1)) = K(x \ (y \ 1),(y \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(108(a,2),12145(a,1,2,2))].">
      <j1 rule="para" parents="108 12145"/>
    </justification>
  </clause>

  <clause id="12147">
    <literal><![CDATA[
      K(x \ (y \ 1),(y \ 1) \ x) = K(x \ (1 / y),x * y)
    ]]></literal>
    <justification jstring="[hyper(7418,a,12146,a),flip(a)].">
      <j1 rule="hyper" parents="7418 12146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12148">
    <literal><![CDATA[
      K(x \ (1 / y),x * y) = K(x \ (y \ 1),y * x)
    ]]></literal>
    <justification jstring="[hyper(65,a,6109,a(flip),b,12147,a),flip(a)].">
      <j1 rule="hyper" parents="65 6109 12147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12149">
    <literal><![CDATA[
      K((x * y) \ 1,x * y) = K(x \ (y \ 1),y * x)
    ]]></literal>
    <justification jstring="[hyper(65,a,9081,a,b,12148,a)].">
      <j1 rule="hyper" parents="65 9081 12148"/>
    </justification>
  </clause>

  <clause id="12150">
    <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(4685(a,1),11706(a,1,1))].">
      <j1 rule="para" parents="4685 11706"/>
    </justification>
  </clause>

  <clause id="12151">
    <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(4633(a,1),11752(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4633 11752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12152">
    <literal><![CDATA[
      K(x,((1 / (K(y,(z \ x) \ 1) / y)) * z) \ (u * x)) = K(x,(((z \ x) \ 1) * (1 / (y \ 1))) \ u)
    ]]></literal>
    <justification jstring="[hyper(299,a,5911,a(flip),b,11802,a),flip(a)].">
      <j1 rule="hyper" parents="299 5911 11802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12153">
    <literal><![CDATA[
      K(x,y * (((1 / z) * (K(x,u) * z)) * z)) = K(x,y * ((z \ 1) \ K(u,x)))
    ]]></literal>
    <justification jstring="[hyper(65,a,11748,a(flip),b,11846,a)].">
      <j1 rule="hyper" parents="65 11748 11846"/>
    </justification>
  </clause>

  <clause id="12154">
    <literal><![CDATA[
      K(x,y * (z * L(K(x,u),z,z \ 1))) = K(x,y * ((z \ 1) \ K(u,x)))
    ]]></literal>
    <justification jstring="[para(8489(a,1),12153(a,1,2,2))].">
      <j1 rule="para" parents="8489 12153"/>
    </justification>
  </clause>

  <clause id="12155">
    <literal><![CDATA[
      K(x,y * ((z \ 1) \ K(u,x))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,11547,a(flip),b,12154,a),flip(a)].">
      <j1 rule="hyper" parents="65 11547 12154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12157">
    <literal><![CDATA[
      K(x,y * (z \ K(u,x))) = K(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(65,a,5902,a(flip),b,12155,a)].">
      <j1 rule="hyper" parents="65 5902 12155"/>
    </justification>
  </clause>

  <clause id="12158">
    <literal><![CDATA[
      K((x * (y \ 1)) \ 1,K(z,u)) = K(z,K(u,x * (y \ K(w,u))))
    ]]></literal>
    <justification jstring="[para(12157(a,2),8787(a,2,2))].">
      <j1 rule="para" parents="12157 8787"/>
    </justification>
  </clause>

  <clause id="12159">
    <literal><![CDATA[
      K(x,K(y,z * (u \ K(w,y)))) = K(x,K(y,z * (u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(8811,a,12158,a),flip(a)].">
      <j1 rule="hyper" parents="8811 12158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12160">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ K(w,y)))) = K(x,K(y,(z * u) * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(8537(a,1),12159(a,1,2))].">
      <j1 rule="para" parents="8537 12159"/>
    </justification>
  </clause>

  <clause id="12161">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ K(w,y)))) = K(x,K(y,R(z,u,u \ 1)))
    ]]></literal>
    <justification jstring="[para(258(a,1),12160(a,2,2,2))].">
      <j1 rule="para" parents="258 12160"/>
    </justification>
  </clause>

  <clause id="12162">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ K(w,x)))) = K(z,K(x,R(y,u,u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(65,a,9324,a,b,12161,a)].">
      <j1 rule="hyper" parents="65 9324 12161"/>
    </justification>
  </clause>

  <clause id="12163">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ K(w,x)))) = K(x,K(z,R(y,u,u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(299,a,7983,a,b,12162,a),flip(a)].">
      <j1 rule="hyper" parents="299 7983 12162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12164">
    <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(8050(a,1),11859(a,1,2))].">
      <j1 rule="para" parents="8050 11859"/>
    </justification>
  </clause>

  <clause id="12165">
    <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(3017(a,1),11864(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3017 11864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12166">
    <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(7203(a,1),12165(a,2,1))].">
      <j1 rule="para" parents="7203 12165"/>
    </justification>
  </clause>

  <clause id="12167">
    <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(299,a,10091,a,b,12166,a),flip(a)].">
      <j1 rule="hyper" parents="299 10091 12166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12168">
    <literal><![CDATA[
      (K(x,y) \ z) * (K(x,y) * K(u,x)) = T(z * K(u,x),K(x,y))
    ]]></literal>
    <justification jstring="[para(3018(a,1),12167(a,1,1,1))].">
      <j1 rule="para" parents="3018 12167"/>
    </justification>
  </clause>

  <clause id="12169">
    <literal><![CDATA[
      (K(x,y) * z) * (K(y,x) * K(u,y)) = T(z * K(u,y),K(y,x))
    ]]></literal>
    <justification jstring="[para(5426(a,1),12168(a,1,1))].">
      <j1 rule="para" parents="5426 12168"/>
    </justification>
  </clause>

  <clause id="12170">
    <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(11161,a,12169,a),flip(a)].">
      <j1 rule="hyper" parents="11161 12169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12171">
    <literal><![CDATA[
      x * K(K(y,z) * K(z,u),x) = T(T(x,K(z,u)),K(z,y))
    ]]></literal>
    <justification jstring="[para(8055(a,1),12170(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8055 12170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12172">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) \ K(K(x,y) * K(z,x),u * K(y,x)) = K(x,T(z,u)) * (K(T(y,u),x) * 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,10063,a(flip),b,11865,a),flip(a)].">
      <j1 rule="hyper" parents="65 10063 11865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12173">
    <literal><![CDATA[
      K(x,y * K(((z \ 1) \ 1) \ K(u,x),(z \ 1) \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,8536,a(flip),b,11866,a),flip(a)].">
      <j1 rule="hyper" parents="299 8536 11866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12175">
    <literal><![CDATA[
      K(x,y * K(z \ K(u,x),z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3450(a,1),12173(a,1,2,2))].">
      <j1 rule="para" parents="3450 12173"/>
    </justification>
  </clause>

  <clause id="12177">
    <literal><![CDATA[
      K(x,y * (K(z,x) / u)) = K(x,y * (u \ K(z,x)))
    ]]></literal>
    <justification jstring="[para(7202(a,1),12175(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7202 12175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12178">
    <literal><![CDATA[
      K(x,y * (K(z,x) / u)) = K(x,y * (u \ 1))
    ]]></literal>
    <justification jstring="[hyper(299,a,12157,a(flip),b,12177,a),flip(a)].">
      <j1 rule="hyper" parents="299 12157 12177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12180">
    <literal><![CDATA[
      K(x,y * ((K(x,z) * u) \ 1)) = K(x,y * (u \ 1))
    ]]></literal>
    <justification jstring="[hyper(65,a,12013,a,b,12178,a)].">
      <j1 rule="hyper" parents="65 12013 12178"/>
    </justification>
  </clause>

  <clause id="12182">
    <literal><![CDATA[
      K(x,R(R(y,K(x,z),u),u,(K(x,z) * u) \ 1)) = K(x,((y * K(x,z)) * u) * (u \ 1))
    ]]></literal>
    <justification jstring="[hyper(65,a,11528,a,b,12180,a)].">
      <j1 rule="hyper" parents="65 11528 12180"/>
    </justification>
  </clause>

  <clause id="12184">
    <literal><![CDATA[
      K(x,R(R(y,K(x,z),u),u,(K(x,z) * u) \ 1)) = K(x,R(y * K(x,z),u,u \ 1))
    ]]></literal>
    <justification jstring="[para(258(a,1),12182(a,2,2))].">
      <j1 rule="para" parents="258 12182"/>
    </justification>
  </clause>

  <clause id="12185">
    <literal><![CDATA[
      K(x,R(R(y,K(x,z),u),u,(K(x,z) * u) \ 1)) = K(x,R(y,u,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(299,a,11524,a(flip),b,12184,a),flip(a)].">
      <j1 rule="hyper" parents="299 11524 12184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12187">
    <literal><![CDATA[
      K(x,R(y,z,(K(x,u) * z) \ 1)) = K(x,R(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(65,a,11529,a(flip),b,12185,a)].">
      <j1 rule="hyper" parents="65 11529 12185"/>
    </justification>
  </clause>

  <clause id="12189">
    <literal><![CDATA[
      x * (1 / (1 / (x \ (T(y / ((1 / x) \ 1),z) \ y)))) = (1 / x) \ (1 / (1 / K(z,(x \ 1) * y)))
    ]]></literal>
    <justification jstring="[para(5648(a,1),12025(a,2,2,2,2))].">
      <j1 rule="para" parents="5648 12025"/>
    </justification>
  </clause>

  <clause id="12190">
    <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(8101(a,1),12150(a,1,1,2))].">
      <j1 rule="para" parents="8101 12150"/>
    </justification>
  </clause>

  <clause id="12191">
    <literal><![CDATA[
      R(K(x,L(y,z,L(y,u,w))),L(y,u,w),z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(9086,a,12190,a),flip(a)].">
      <j1 rule="hyper" parents="9086 12190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12192">
    <literal><![CDATA[
      R(K(x,y),L(y,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[para(9846(a,1),12191(a,1,1))].">
      <j1 rule="para" parents="9846 12191"/>
    </justification>
  </clause>

  <clause id="12193">
    <literal><![CDATA[
      K((L(x,y,z) * u) / w,x) = K(L(x,y,z) / (w / u),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,10750,a(flip),b,12192,a)].">
      <j1 rule="hyper" parents="65 10750 12192"/>
    </justification>
  </clause>

  <clause id="12195">
    <literal><![CDATA[
      K((L(x,y,z) * u) / w,x) = K((w / u) \ L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(299,a,7023,a(flip),b,12193,a),flip(a)].">
      <j1 rule="hyper" parents="299 7023 12193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12196">
    <literal><![CDATA[
      K((((L(x,y,z) \ u) \ w) \ w) \ w,x) = K((u / w) \ L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,11180,a,b,12195,a)].">
      <j1 rule="hyper" parents="65 11180 12195"/>
    </justification>
  </clause>

  <clause id="12197">
    <literal><![CDATA[
      K((x / y) \ L(z,u,w),z) != v5
    ]]></literal>
    <literal><![CDATA[
      K(y / (L(z,u,w) \ x),z) = v5
    ]]></literal>
    <justification jstring="[para(12196(a,1),8322(a,1))].">
      <j1 rule="para" parents="12196 8322"/>
    </justification>
  </clause>

  <clause id="12198">
    <literal><![CDATA[
      K(x / (L(y,z,u) \ w),y) = K((w / x) \ y,y)
    ]]></literal>
    <justification jstring="[hyper(12197,a,11875,a)].">
      <j1 rule="hyper" parents="12197 11875"/>
    </justification>
  </clause>

  <clause id="12199">
    <literal><![CDATA[
      K(x,((1 / (K(y,(z \ x) \ 1) / y)) * z) \ (u * x)) = K(x,(((z \ x) \ 1) * y) \ u)
    ]]></literal>
    <justification jstring="[para(76(a,1),12152(a,2,2,1,2))].">
      <j1 rule="para" parents="76 12152"/>
    </justification>
  </clause>

  <clause id="12201">
    <literal><![CDATA[
      K(x,((1 / (K(y,x \ z) / y)) * z) \ (u * x)) = K(x,(((z \ x) \ 1) * y) \ u)
    ]]></literal>
    <justification jstring="[para(6814(a,1),12199(a,1,2,1,1,2,1))].">
      <j1 rule="para" parents="6814 12199"/>
    </justification>
  </clause>

  <clause id="12202">
    <literal><![CDATA[
      K(x,(((y \ x) \ 1) * z) \ u) = K(x,((x \ y) * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,11238,a(flip),b,12201,a),flip(a)].">
      <j1 rule="hyper" parents="65 11238 12201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12203">
    <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(9621(a,1),12164(a,1,2))].">
      <j1 rule="para" parents="9621 12164"/>
    </justification>
  </clause>

  <clause id="12204">
    <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(11556(a,1),12203(a,1,2,2))].">
      <j1 rule="para" parents="11556 12203"/>
    </justification>
  </clause>

  <clause id="12205">
    <literal><![CDATA[
      (K(x * y,z) * T(x,y)) \ T(T(x,y),K(y,z)) = K(z,x * y)
    ]]></literal>
    <justification jstring="[para(4667(a,1),12204(a,2,2))].">
      <j1 rule="para" parents="4667 12204"/>
    </justification>
  </clause>

  <clause id="12207">
    <literal><![CDATA[
      (K(x * y,z) * T(x,y)) \ T(x,T(y,z)) = K(z,x * y)
    ]]></literal>
    <justification jstring="[para(7140(a,1),12205(a,1,2))].">
      <j1 rule="para" parents="7140 12205"/>
    </justification>
  </clause>

  <clause id="12208">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) \ K(K(x,y) * K(z,x),u * K(y,x)) = K(x,T(z,u)) * (K(y,T(x,u)) * 1)
    ]]></literal>
    <justification jstring="[para(7537(a,1),12172(a,2,2,1))].">
      <j1 rule="para" parents="7537 12172"/>
    </justification>
  </clause>

  <clause id="12209">
    <literal><![CDATA[
      x * (1 / (1 / (x \ (T(y / ((1 / x) \ 1),z) \ y)))) = (1 / x) \ K(z,(x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(3018(a,1),12189(a,2,2))].">
      <j1 rule="para" parents="3018 12189"/>
    </justification>
  </clause>

  <clause id="12210">
    <literal><![CDATA[
      x * (1 / (1 / (x \ (T(y / x,z) \ y)))) = (1 / x) \ K(z,(x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(79(a,1),12209(a,1,2,2,2,2,1,1,2))].">
      <j1 rule="para" parents="79 12209"/>
    </justification>
  </clause>

  <clause id="12211">
    <literal><![CDATA[
      (1 / x) \ K(y,(x \ 1) * z) = x * (1 / (1 / K(y,x \ z)))
    ]]></literal>
    <justification jstring="[para(9754(a,1),12210(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="9754 12210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12212">
    <literal><![CDATA[
      (1 / x) \ K(y,(x \ 1) * z) = x * K(y,x \ z)
    ]]></literal>
    <justification jstring="[para(3018(a,1),12211(a,2,2))].">
      <j1 rule="para" parents="3018 12211"/>
    </justification>
  </clause>

  <clause id="12213">
    <literal><![CDATA[
      x * K(y,x \ ((x \ 1) \ z)) = (1 / x) \ K(y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),12212(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 12212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12214">
    <literal><![CDATA[
      (1 / x) \ K(y,(x \ 1) * z) != x * u
    ]]></literal>
    <literal><![CDATA[
      K(y,x \ z) = u
    ]]></literal>
    <justification jstring="[para(12212(a,2),45(a,1))].">
      <j1 rule="para" parents="12212 45"/>
    </justification>
  </clause>

  <clause id="12215">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),z) = ((1 / x) \ K(z,y)) \ x
    ]]></literal>
    <justification jstring="[para(12213(a,1),7200(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12213 7200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12216">
    <literal><![CDATA[
      K(x,y \ ((y \ 1) \ z)) = ((1 / y) \ K(z,x)) \ y
    ]]></literal>
    <justification jstring="[hyper(65,a,12070,a(flip),b,12215,a)].">
      <j1 rule="hyper" parents="65 12070 12215"/>
    </justification>
  </clause>

  <clause id="12217">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) \ K(K(x,y) * K(z,x),u * K(y,x)) = K(x,T(z,u)) * K(y,T(x,u))
    ]]></literal>
    <justification jstring="[para(8(a,1),12208(a,2,2))].">
      <j1 rule="para" parents="8 12208"/>
    </justification>
  </clause>

  <clause id="12218">
    <literal><![CDATA[
      T(L(L(x * K(y,x),y,x),z,u) * y,x * K(y,x)) = L(x * K(y,x),z,u) * T(y,x)
    ]]></literal>
    <justification jstring="[para(11620(a,1),5285(a,1,1,1,1))].">
      <j1 rule="para" parents="11620 5285"/>
    </justification>
  </clause>

  <clause id="12219">
    <literal><![CDATA[
      T(x * L(L(y,z,u),x,y),y * K(x,y)) = L(y * K(x,y),z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(6669(a,1),12218(a,1,1))].">
      <j1 rule="para" parents="6669 12218"/>
    </justification>
  </clause>

  <clause id="12220">
    <literal><![CDATA[
      T(x * L(L(y,z,u),x,y),y * K(x,y)) = T(x,y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,5669,a(flip),b,12219,a),flip(a)].">
      <j1 rule="hyper" parents="299 5669 12219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12221">
    <literal><![CDATA[
      T(x * L(L(y,x,y),z,u),y * K(x,y)) = T(x,y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(30(a,1),12220(a,1,1,2))].">
      <j1 rule="para" parents="30 12220"/>
    </justification>
  </clause>

  <clause id="12222">
    <literal><![CDATA[
      T(x * L(L(y,x,y),z,u),T(y,x)) = T(x,y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,8184,a(flip),b,12221,a)].">
      <j1 rule="hyper" parents="65 8184 12221"/>
    </justification>
  </clause>

  <clause id="12223">
    <literal><![CDATA[
      T(x * L(L(y,x,y),z,u),y) = T(x,y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,8976,a(flip),b,12222,a)].">
      <j1 rule="hyper" parents="65 8976 12222"/>
    </justification>
  </clause>

  <clause id="12224">
    <literal><![CDATA[
      K(x,L(L(x,y,x),z,u) / (y \ 1)) * (y \ (T(y,x) * L(x,z,u))) = L(L(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(12223(a,1),5727(a,1,2,2))].">
      <j1 rule="para" parents="12223 5727"/>
    </justification>
  </clause>

  <clause id="12225">
    <literal><![CDATA[
      K(x,(y \ 1) \ L(L(x,y,x),z,u)) * (y \ (T(y,x) * L(x,z,u))) = L(L(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(7617(a,1),12224(a,1,1))].">
      <j1 rule="para" parents="7617 12224"/>
    </justification>
  </clause>

  <clause id="12226">
    <literal><![CDATA[
      (R(x,y,y \ 1) \ (x * y)) * R(x,y,y \ 1) = (x * y) * K((y \ 1) \ 1,(x * y) * (y \ 1))
    ]]></literal>
    <justification jstring="[para(258(a,1),6019(a,1,2))].">
      <j1 rule="para" parents="258 6019"/>
    </justification>
  </clause>

  <clause id="12227">
    <literal><![CDATA[
      (R(x,y,y \ 1) \ (x * y)) * R(x,y,y \ 1) = (x * y) * K((y \ 1) \ 1,R(x,y,y \ 1))
    ]]></literal>
    <justification jstring="[para(258(a,1),12226(a,2,2,2))].">
      <j1 rule="para" parents="258 12226"/>
    </justification>
  </clause>

  <clause id="12228">
    <literal><![CDATA[
      L(K((x \ 1) \ (x \ y),z),x \ y,T(x,x \ y)) = (x * (y / x)) \ (K(x,x \ y) * T(y,z))
    ]]></literal>
    <justification jstring="[para(5056(a,1),7336(a,2,2))].">
      <j1 rule="para" parents="5056 7336"/>
    </justification>
  </clause>

  <clause id="12229">
    <literal><![CDATA[
      L(K((x \ 1) \ (x \ y),z),x \ y,T(x,x \ y)) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,6865,a(flip),b,12228,a),flip(a)].">
      <j1 rule="hyper" parents="299 6865 12228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12231">
    <literal><![CDATA[
      L(K((x \ 1) \ (x \ y),z),y / x,x) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,4984,a(flip),b,12229,a)].">
      <j1 rule="hyper" parents="65 4984 12229"/>
    </justification>
  </clause>

  <clause id="12232">
    <literal><![CDATA[
      K((x \ 1) \ (x \ y),L(z,y / x,x)) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(11995,a,12231,a)].">
      <j1 rule="hyper" parents="11995 12231"/>
    </justification>
  </clause>

  <clause id="12233">
    <literal><![CDATA[
      K(x,(y \ 1) \ (y \ L(z,x / y,y))) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,11990,a(flip),b,12232,a)].">
      <j1 rule="hyper" parents="65 11990 12232"/>
    </justification>
  </clause>

  <clause id="12234">
    <literal><![CDATA[
      K(x,L((y \ 1) \ (y \ z),x / y,y)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(2949(a,2),12233(a,1,2))].">
      <j1 rule="para" parents="2949 12233"/>
    </justification>
  </clause>

  <clause id="12235">
    <literal><![CDATA[
      K(x,L((y \ 1) \ (y \ z),y \ x,y)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,11662,a(flip),b,12234,a)].">
      <j1 rule="hyper" parents="65 11662 12234"/>
    </justification>
  </clause>

  <clause id="12236">
    <literal><![CDATA[
      K(x / ((y \ 1) * z),y * K(y \ z,y)) = K((y \ L(z,y \ 1,y)) \ x,y)
    ]]></literal>
    <justification jstring="[para(6582(a,1),8490(a,1,2))].">
      <j1 rule="para" parents="6582 8490"/>
    </justification>
  </clause>

  <clause id="12237">
    <literal><![CDATA[
      K(T(x / ((y \ 1) * z),y \ z),y) = K((y \ L(z,y \ 1,y)) \ x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,8133,a(flip),b,12236,a)].">
      <j1 rule="hyper" parents="65 8133 12236"/>
    </justification>
  </clause>

  <clause id="12238">
    <literal><![CDATA[
      K(T(x / ((y \ 1) * z),y \ z),y) = K(((y \ 1) * z) \ x,y)
    ]]></literal>
    <justification jstring="[para(415(a,1),12237(a,2,1,1))].">
      <j1 rule="para" parents="415 12237"/>
    </justification>
  </clause>

  <clause id="12239">
    <literal><![CDATA[
      K(T(x / ((y \ 1) * z),z),y) = K(((y \ 1) * z) \ x,y)
    ]]></literal>
    <justification jstring="[hyper(8316,a,12238,a)].">
      <j1 rule="hyper" parents="8316 12238"/>
    </justification>
  </clause>

  <clause id="12240">
    <literal><![CDATA[
      K(((T(x,y) \ 1) * y) \ z,T(x,y)) = K(z / ((T(x,y) \ 1) * y),x)
    ]]></literal>
    <justification jstring="[hyper(8218,a,12239,a),flip(a)].">
      <j1 rule="hyper" parents="8218 12239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12241">
    <literal><![CDATA[
      K(((T(x,y) \ 1) * y) \ z,T(x,y)) = K(z / ((x \ 1) * y),x)
    ]]></literal>
    <justification jstring="[hyper(299,a,9955,a(flip),b,12240,a),flip(a)].">
      <j1 rule="hyper" parents="299 9955 12240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12243">
    <literal><![CDATA[
      K(x \ (y * T(z,x)),T(z,x)) = K(y / ((z \ 1) * x),z)
    ]]></literal>
    <justification jstring="[hyper(65,a,9533,a(flip),b,12241,a)].">
      <j1 rule="hyper" parents="65 9533 12241"/>
    </justification>
  </clause>

  <clause id="12244">
    <literal><![CDATA[
      K((x * T(y,z)) / z,y) = K(x / ((y \ 1) * z),y)
    ]]></literal>
    <justification jstring="[hyper(8220,a,12243,a)].">
      <j1 rule="hyper" parents="8220 12243"/>
    </justification>
  </clause>

  <clause id="12245">
    <literal><![CDATA[
      K(x / ((y \ 1) * z),y) = K(x / (y \ z),y)
    ]]></literal>
    <justification jstring="[hyper(10172,a,12244,a),flip(a)].">
      <j1 rule="hyper" parents="10172 12244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12247">
    <literal><![CDATA[
      K(x / (y \ T(z,y \ 1)),y) = K(x / (z * (y \ 1)),y)
    ]]></literal>
    <justification jstring="[para(107(a,1),12245(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="107 12245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12248">
    <literal><![CDATA[
      K(x / (y * (z \ 1)),z) = K(x / (z \ y),z)
    ]]></literal>
    <justification jstring="[hyper(10176,a,12247,a),flip(a)].">
      <j1 rule="hyper" parents="10176 12247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12249">
    <literal><![CDATA[
      L(K(x * y,T(x,z)),y,z) = K((z * y) / (x \ z),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,11818,a,b,12248,a)].">
      <j1 rule="hyper" parents="65 11818 12248"/>
    </justification>
  </clause>

  <clause id="12250">
    <literal><![CDATA[
      L(K(x * y,T(x,z)),y,z) = K((z / (z * y)) \ x,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,10754,a(flip),b,12249,a),flip(a)].">
      <j1 rule="hyper" parents="299 10754 12249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12251">
    <literal><![CDATA[
      L(K(x * y,T(y,z)),x,z) = K((z / (z * x)) \ y,y)
    ]]></literal>
    <justification jstring="[para(6293(a,2),12250(a,1,1))].">
      <j1 rule="para" parents="6293 12250"/>
    </justification>
  </clause>

  <clause id="12252">
    <literal><![CDATA[
      K(R(x \ y,z,u),w \ (y / x)) = K(R(x \ y,z,u),w \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(7263,a,8908,a),flip(a)].">
      <j1 rule="hyper" parents="7263 8908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12253">
    <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(5243(a,1),12252(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5243 12252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12254">
    <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(1909(a,2),9697(a,1,2,2))].">
      <j1 rule="para" parents="1909 9697"/>
    </justification>
  </clause>

  <clause id="12255">
    <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),10072(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11 10072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12257">
    <literal><![CDATA[
      (K(x,y) * K(z,y)) * u = K(z,y) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(10008(a,1),12255(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10008 12255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12259">
    <literal><![CDATA[
      ((x * y) / x) \ (T(y,z) * (K(z,y) * (K(x,y) * u))) = L(u,T(y,z) \ ((x * y) / x),T(y,z))
    ]]></literal>
    <justification jstring="[para(12257(a,1),6290(a,1,2,2))].">
      <j1 rule="para" parents="12257 6290"/>
    </justification>
  </clause>

  <clause id="12260">
    <literal><![CDATA[
      L(x,T(y,z) \ ((u * y) / u),T(y,z)) = ((u * y) / u) \ (y * (K(u,y) * x))
    ]]></literal>
    <justification jstring="[para(5387(a,1),12259(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5387 12259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12261">
    <literal><![CDATA[
      L(x,T(y,z) \ ((u * y) / u),T(y,z)) = K(y,u) * (K(u,y) * x)
    ]]></literal>
    <justification jstring="[hyper(299,a,5368,a(flip),b,12260,a),flip(a)].">
      <j1 rule="hyper" parents="299 5368 12260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12263">
    <literal><![CDATA[
      L(x,T(y,z) \ ((u * y) / u),T(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(299,a,5432,a(flip),b,12261,a),flip(a)].">
      <j1 rule="hyper" parents="299 5432 12261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12265">
    <literal><![CDATA[
      L(x,K(y,z) * K(u,z),T(z,u)) = x
    ]]></literal>
    <justification jstring="[para(6288(a,1),12263(a,1,2))].">
      <j1 rule="para" parents="6288 12263"/>
    </justification>
  </clause>

  <clause id="12266">
    <literal><![CDATA[
      L(x,K(y,z) * K(u,z),T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(12265(a,1),52(a,2))].">
      <j1 rule="para" parents="12265 52"/>
    </justification>
  </clause>

  <clause id="12267">
    <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(10137(a,1),10889(a,1,1,1))].">
      <j1 rule="para" parents="10137 10889"/>
    </justification>
  </clause>

  <clause id="12268">
    <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(543(a,1),12267(a,1,1))].">
      <j1 rule="para" parents="543 12267"/>
    </justification>
  </clause>

  <clause id="12269">
    <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(11727(a,1),12268(a,1,1))].">
      <j1 rule="para" parents="11727 12268"/>
    </justification>
  </clause>

  <clause id="12270">
    <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(12269(a,1),10481(a,1))].">
      <j1 rule="para" parents="12269 10481"/>
    </justification>
  </clause>

  <clause id="12271">
    <literal><![CDATA[
      a((x \ y) \ y,z,(x \ y) \ y) = K(x * z,T(T(x,y),u)) * K((x \ y) \ y,T(z,u))
    ]]></literal>
    <justification jstring="[para(10974(a,1),11134(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10974 11134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12272">
    <literal><![CDATA[
      a((x \ y) \ y,z,(x \ y) \ y) = K(x * z,T(T(x,y),u)) * K(x,T(T(z,u),y))
    ]]></literal>
    <justification jstring="[para(7493(a,1),12271(a,2,2))].">
      <j1 rule="para" parents="7493 12271"/>
    </justification>
  </clause>

  <clause id="12274">
    <literal><![CDATA[
      K(x * y,T(T(x,z),u)) * K(x,T(T(y,u),z)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,11806,a(flip),b,12272,a),flip(a)].">
      <j1 rule="hyper" parents="65 11806 12272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12276">
    <literal><![CDATA[
      K(x * y,T(T(x,z),u)) * K(x,T(T(y,z),u)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[para(23(a,1),12274(a,1,1,2))].">
      <j1 rule="para" parents="23 12274"/>
    </justification>
  </clause>

  <clause id="12277">
    <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(4802(a,1),11135(a,1,1))].">
      <j1 rule="para" parents="4802 11135"/>
    </justification>
  </clause>

  <clause id="12278">
    <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(299,a,2188,a(flip),b,11757,a),flip(a)].">
      <j1 rule="hyper" parents="299 2188 11757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12279">
    <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),12278(a,2,3))].">
      <j1 rule="para" parents="27 12278"/>
    </justification>
  </clause>

  <clause id="12280">
    <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),12254(a,1,2)),flip(a)].">
      <j1 rule="para" parents="94 12254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12281">
    <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(11127(a,1),12277(a,1,1))].">
      <j1 rule="para" parents="11127 12277"/>
    </justification>
  </clause>

  <clause id="12282">
    <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(5852(a,1),12281(a,1,2))].">
      <j1 rule="para" parents="5852 12281"/>
    </justification>
  </clause>

  <clause id="12283">
    <literal><![CDATA[
      K((x \ y) \ z,x / y) * K(x / y,z) = a((y / x) \ 1,z,(y / x) \ 1)
    ]]></literal>
    <justification jstring="[para(8383(a,1),12282(a,1,2))].">
      <j1 rule="para" parents="8383 12282"/>
    </justification>
  </clause>

  <clause id="12284">
    <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(1273(a,1),6194(a,2,1))].">
      <j1 rule="para" parents="1273 6194"/>
    </justification>
  </clause>

  <clause id="12285">
    <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(65,a,12284,a(flip),b,6195,a),flip(a)].">
      <j1 rule="hyper" parents="65 12284 6195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12286">
    <literal><![CDATA[
      T(x \ L(x,y,z),u * x) = T(x \ L(x,y,z),x * u)
    ]]></literal>
    <justification jstring="[para(1273(a,1),12285(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1273 12285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12287">
    <literal><![CDATA[
      T(((x * x) * y) \ L((x * x) * y,z,u),x * x) = (y * (x * x)) \ L(y * (x * x),z,u)
    ]]></literal>
    <justification jstring="[para(221(a,1),6733(a,2,2,1))].">
      <j1 rule="para" parents="221 6733"/>
    </justification>
  </clause>

  <clause id="12288">
    <literal><![CDATA[
      T(((x * x) * y) \ L((x * x) * y,z,u),x * x) = (x * x) \ (y \ L(y * (x * x),z,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,419,a(flip),b,12287,a),flip(a)].">
      <j1 rule="hyper" parents="299 419 12287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12289">
    <literal><![CDATA[
      T(((x * x) * y) \ L((x * x) * y,z,u),x * x) = y \ L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,11839,a(flip),b,12288,a),flip(a)].">
      <j1 rule="hyper" parents="299 11839 12288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12291">
    <literal><![CDATA[
      T(x \ ((y * y) \ L((y * y) * x,z,u)),y * y) = x \ L(x,z,u)
    ]]></literal>
    <justification jstring="[para(420(a,1),12289(a,1,1))].">
      <j1 rule="para" parents="420 12289"/>
    </justification>
  </clause>

  <clause id="12292">
    <literal><![CDATA[
      T(x \ L((y * y) \ ((y * y) * x),z,u),y * y) = x \ L(x,z,u)
    ]]></literal>
    <justification jstring="[para(6498(a,2),12291(a,1,1,2))].">
      <j1 rule="para" parents="6498 12291"/>
    </justification>
  </clause>

  <clause id="12293">
    <literal><![CDATA[
      T(x \ L(x,y,z),u * u) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),12292(a,1,1,2,1))].">
      <j1 rule="para" parents="9 12292"/>
    </justification>
  </clause>

  <clause id="12294">
    <literal><![CDATA[
      (x \ L(x,y,z)) * ((u * u) * w) = (u * u) * ((x \ L(x,y,z)) * w)
    ]]></literal>
    <justification jstring="[para(12293(a,1),1067(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12293 1067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12295">
    <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(10768(a,1),8940(a,1,1,1))].">
      <j1 rule="para" parents="10768 8940"/>
    </justification>
  </clause>

  <clause id="12296">
    <literal><![CDATA[
      x \ ((x / ((y * z) / y)) * ((z \ 1) * ((y * z) / y))) = T(x \ (x / z),(y * z) / y)
    ]]></literal>
    <justification jstring="[para(5080(a,1),9053(a,1,2,2,1))].">
      <j1 rule="para" parents="5080 9053"/>
    </justification>
  </clause>

  <clause id="12298">
    <literal><![CDATA[
      x \ ((x / ((y * z) / y)) * ((T(z,y) \ 1) * z)) = T(x \ (x / z),(y * z) / y)
    ]]></literal>
    <justification jstring="[para(7136(a,1),12296(a,1,2,2))].">
      <j1 rule="para" parents="7136 12296"/>
    </justification>
  </clause>

  <clause id="12299">
    <literal><![CDATA[
      (1 / ((x * y) / x)) * ((T(y,x) \ 1) * y) = T(1 \ (1 / y),(x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(166,a,12298,a),flip(a)].">
      <j1 rule="hyper" parents="166 12298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12300">
    <literal><![CDATA[
      (1 / ((x * y) / x)) * ((T(y,x) \ 1) * y) = T(1 / y,(x * y) / x)
    ]]></literal>
    <justification jstring="[para(67(a,1),12299(a,2,1))].">
      <j1 rule="para" parents="67 12299"/>
    </justification>
  </clause>

  <clause id="12301">
    <literal><![CDATA[
      (1 / ((x * y) / x)) \ (y \ 1) = (T(y,x) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(119,a,5494,a(flip),b,12300,a)].">
      <j1 rule="hyper" parents="119 5494 12300"/>
    </justification>
  </clause>

  <clause id="12302">
    <literal><![CDATA[
      T(K(x,y) * K(z,x),u) * u = (K(x,y) * K(z,x)) * ((K(z,x) * (K(x,y) * u)) * (K(x,z) * K(y,x)))
    ]]></literal>
    <justification jstring="[para(9249(a,1),10054(a,2,2))].">
      <j1 rule="para" parents="9249 10054"/>
    </justification>
  </clause>

  <clause id="12303">
    <literal><![CDATA[
      (L(x,x \ y,x) \ y) \ ((y / T(x,y)) * L(z,K(y,x),x \ y)) = L(z,a(x,x \ y,x),x \ y)
    ]]></literal>
    <justification jstring="[para(12039(a,1),10670(a,1,1))].">
      <j1 rule="para" parents="12039 10670"/>
    </justification>
  </clause>

  <clause id="12304">
    <literal><![CDATA[
      (x / T(y,x)) \ ((x / T(y,x)) * L(z,K(x,y),y \ x)) = L(z,a(y,y \ x,y),y \ x)
    ]]></literal>
    <justification jstring="[para(9746(a,1),12303(a,1,1))].">
      <j1 rule="para" parents="9746 12303"/>
    </justification>
  </clause>

  <clause id="12305">
    <literal><![CDATA[
      L(x,a(y,y \ z,y),y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,K(z,y),y \ z) = u
    ]]></literal>
    <justification jstring="[para(12304(a,1),314(a,1))].">
      <j1 rule="para" parents="12304 314"/>
    </justification>
  </clause>

  <clause id="12306">
    <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(65,a,11491,a(flip),b,10804,a),flip(a)].">
      <j1 rule="hyper" parents="65 11491 10804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12308">
    <literal><![CDATA[
      T(R(((x \ R(x,y,z)) \ 1) \ 1,x,y * z),x * (y * z)) = (((x * (y * z)) \ ((x * y) * z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(6706(a,2),10935(a,1,1))].">
      <j1 rule="para" parents="6706 10935"/>
    </justification>
  </clause>

  <clause id="12309">
    <literal><![CDATA[
      T(x,x * K(y * T(z,u),y)) \ T(K(y,y * T(z,u)) * x,x) = K(y,T(y * ((z \ u) \ u),x))
    ]]></literal>
    <justification jstring="[para(12109(a,1),12108(a,1,2,1,1))].">
      <j1 rule="para" parents="12109 12108"/>
    </justification>
  </clause>

  <clause id="12310">
    <literal><![CDATA[
      K(x,T(x * ((y \ z) \ z),u)) = K(x,T(x * T(y,z),u))
    ]]></literal>
    <justification jstring="[hyper(65,a,11834,a(flip),b,12309,a),flip(a)].">
      <j1 rule="hyper" parents="65 11834 12309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12311">
    <literal><![CDATA[
      T(K(x,y) * K(z,x),u) * u = (K(x,y) * K(z,x)) * (T(K(x,y) * u,K(z,x)) * K(y,x))
    ]]></literal>
    <justification jstring="[para(9213(a,1),12302(a,2,2))].">
      <j1 rule="para" parents="9213 12302"/>
    </justification>
  </clause>

  <clause id="12312">
    <literal><![CDATA[
      T(K(x,y) * K(z,x),u) * u = (K(x,y) * K(z,x)) * (T(K(x,y) * u,K(x,z)) * K(y,x))
    ]]></literal>
    <justification jstring="[para(8050(a,1),12311(a,2,2,1))].">
      <j1 rule="para" parents="8050 12311"/>
    </justification>
  </clause>

  <clause id="12313">
    <literal><![CDATA[
      T(K(x,y) * K(z,x),u) * u = (K(x,y) * K(z,x)) * ((K(x,y) * T(u,K(x,z))) * K(y,x))
    ]]></literal>
    <justification jstring="[para(10089(a,1),12312(a,2,2,1))].">
      <j1 rule="para" parents="10089 12312"/>
    </justification>
  </clause>

  <clause id="12314">
    <literal><![CDATA[
      T(K(x,y) * K(z,x),u) * u = (K(x,y) * K(z,x)) * T(T(u,K(x,z)),K(x,y))
    ]]></literal>
    <justification jstring="[para(8055(a,1),12313(a,2,2))].">
      <j1 rule="para" parents="8055 12313"/>
    </justification>
  </clause>

  <clause id="12315">
    <literal><![CDATA[
      T(K(x,y) * K(z,x),u) * u = K(z,x) * (K(x,y) * T(T(u,K(x,z)),K(x,y)))
    ]]></literal>
    <justification jstring="[hyper(299,a,10037,a(flip),b,12314,a),flip(a)].">
      <j1 rule="hyper" parents="299 10037 12314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12316">
    <literal><![CDATA[
      T(K(x,y) * K(z,x),u) * u = K(z,x) * (T(u,K(x,z)) * K(x,y))
    ]]></literal>
    <justification jstring="[para(107(a,1),12315(a,2,2))].">
      <j1 rule="para" parents="107 12315"/>
    </justification>
  </clause>

  <clause id="12317">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,y))) / x = T(K(y,z) * K(u,y),x)
    ]]></literal>
    <justification jstring="[hyper(120,a,10106,a(flip),b,12316,a)].">
      <j1 rule="hyper" parents="120 10106 12316"/>
    </justification>
  </clause>

  <clause id="12318">
    <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(5129,a,12317,a)].">
      <j1 rule="hyper" parents="5129 12317"/>
    </justification>
  </clause>

  <clause id="12319">
    <literal><![CDATA[
      K(K(x,y) * K(z,x),u) = K(u,K(x,y) * K(z,x))
    ]]></literal>
    <justification jstring="[hyper(36,a,5083,a(flip),b,12318,a)].">
      <j1 rule="hyper" parents="36 5083 12318"/>
    </justification>
  </clause>

  <clause id="12320">
    <literal><![CDATA[
      x * K(K(y,z) * K(u,y),x) = T(x,K(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[para(12319(a,2),5083(a,2,2)),flip(a)].">
      <j1 rule="para" parents="12319 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12322">
    <literal><![CDATA[
      x * K(K(y,z) * K(z,u),x) = T(x,K(z,u) * K(y,z))
    ]]></literal>
    <justification jstring="[para(2278(a,1),12320(a,1,2,1))].">
      <j1 rule="para" parents="2278 12320"/>
    </justification>
  </clause>

  <clause id="12323">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,u)) = T(x,K(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,12171,a(flip),b,12322,a)].">
      <j1 rule="hyper" parents="65 12171 12322"/>
    </justification>
  </clause>

  <clause id="12325">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,u)) = T(x,K(z,u) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8065,a,12323,a)].">
      <j1 rule="hyper" parents="8065 12323"/>
    </justification>
  </clause>

  <clause id="12326">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,u)) = T(x,K(y,u) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(861,a,12323,a)].">
      <j1 rule="hyper" parents="861 12323"/>
    </justification>
  </clause>

  <clause id="12327">
    <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(65,a,9620,a,b,12323,a)].">
      <j1 rule="hyper" parents="65 9620 12323"/>
    </justification>
  </clause>

  <clause id="12328">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,u)) = T(x,K(u,y) * K(y,z))
    ]]></literal>
    <justification jstring="[para(2278(a,1),12323(a,2,2))].">
      <j1 rule="para" parents="2278 12323"/>
    </justification>
  </clause>

  <clause id="12329">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,u)) = T(x,K(y,z) * K(z,u))
    ]]></literal>
    <justification jstring="[para(2278(a,1),12325(a,2,2))].">
      <j1 rule="para" parents="2278 12325"/>
    </justification>
  </clause>

  <clause id="12330">
    <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(12325(a,1),10650(a,2,1))].">
      <j1 rule="para" parents="12325 10650"/>
    </justification>
  </clause>

  <clause id="12331">
    <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(10808(a,1),12325(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10808 12325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12332">
    <literal><![CDATA[
      T(x,K(y,z) * K(u,y)) = T(x,K(y,u) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,12323,a(flip),b,12326,a)].">
      <j1 rule="hyper" parents="65 12323 12326"/>
    </justification>
  </clause>

  <clause id="12333">
    <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(12328(a,1),10181(a,1,1))].">
      <j1 rule="para" parents="12328 10181"/>
    </justification>
  </clause>

  <clause id="12334">
    <literal><![CDATA[
      x * K(x,K(y,z) * K(u,y)) = T(x,K(y,u) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(5176,a,12332,a)].">
      <j1 rule="hyper" parents="5176 12332"/>
    </justification>
  </clause>

  <clause id="12335">
    <literal><![CDATA[
      K(K(x,y) * K(y,z),u) = K(u,K(y,x) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(36,a,12322,a,b,12334,a)].">
      <j1 rule="hyper" parents="36 12322 12334"/>
    </justification>
  </clause>

  <clause id="12336">
    <literal><![CDATA[
      K(K(x,y) * K(z,x),u) = K(u,K(x,z) * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(36,a,12320,a,b,12334,a)].">
      <j1 rule="hyper" parents="36 12320 12334"/>
    </justification>
  </clause>

  <clause id="12337">
    <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(12334(a,1),5087(a,1))].">
      <j1 rule="para" parents="12334 5087"/>
    </justification>
  </clause>

  <clause id="12338">
    <literal><![CDATA[
      K(K(x,y) * K(z,x),u) = K(u,K(y,x) * K(x,z))
    ]]></literal>
    <justification jstring="[para(2278(a,1),12336(a,2,2))].">
      <j1 rule="para" parents="2278 12336"/>
    </justification>
  </clause>

  <clause id="12339">
    <literal><![CDATA[
      K(K(x,y) * K(z,x),u) / (K(y,x) * K(x,z)) = 1 / T(K(y,x) * K(x,z),u)
    ]]></literal>
    <justification jstring="[hyper(120,a,12338,a,b,5032,a(flip))].">
      <j1 rule="hyper" parents="120 12338 5032"/>
    </justification>
  </clause>

  <clause id="12340">
    <literal><![CDATA[
      K(x,K(y,z) * K(u,y)) = K(x,K(z,y) * K(y,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,12319,a(flip),b,12338,a)].">
      <j1 rule="hyper" parents="65 12319 12338"/>
    </justification>
  </clause>

  <clause id="12341">
    <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(12323(a,2),12337(a,1))].">
      <j1 rule="para" parents="12323 12337"/>
    </justification>
  </clause>

  <clause id="12343">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(y,u)) = K(K(z,y) * K(y,u),x)
    ]]></literal>
    <justification jstring="[hyper(5109,a,12333,a),flip(a)].">
      <j1 rule="hyper" parents="5109 12333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12345">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(y,u)) = K(x,K(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,12335,a(flip),b,12343,a),flip(a)].">
      <j1 rule="hyper" parents="299 12335 12343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12346">
    <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(6431(a,1),12343(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6431 12343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12347">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(y,u)) = K(K(y,z) * K(u,y),x)
    ]]></literal>
    <justification jstring="[hyper(299,a,12319,a,b,12345,a),flip(a)].">
      <j1 rule="hyper" parents="299 12319 12345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12348">
    <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(65,a,10163,a,b,12345,a)].">
      <j1 rule="hyper" parents="65 10163 12345"/>
    </justification>
  </clause>

  <clause id="12349">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(z,u)) = K(x,K(z,y) * K(u,z))
    ]]></literal>
    <justification jstring="[para(8004(a,1),12345(a,1,1))].">
      <j1 rule="para" parents="8004 12345"/>
    </justification>
  </clause>

  <clause id="12350">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(z,u)) = K(x,K(y,z) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,12340,a(flip),b,12349,a),flip(a)].">
      <j1 rule="hyper" parents="299 12340 12349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12351">
    <literal><![CDATA[
      T(x,K(y,z) * K(R(z,u,w),y)) = T(x,K(y,z) * K(z,R(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,12329,a(flip),b,12327,a),flip(a)].">
      <j1 rule="hyper" parents="65 12329 12327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12352">
    <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(299,a,5024,a,b,12330,a),flip(a)].">
      <j1 rule="hyper" parents="299 5024 12330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12353">
    <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(5426(a,1),12352(a,1,2))].">
      <j1 rule="para" parents="5426 12352"/>
    </justification>
  </clause>

  <clause id="12354">
    <literal><![CDATA[
      K(K(x,y) * K(y,z),K(y,x) * u) = K(u,K(y,z) * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,12319,a(flip),b,12353,a),flip(a)].">
      <j1 rule="hyper" parents="299 12319 12353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12355">
    <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(12337,a,12351,a)].">
      <j1 rule="hyper" parents="12337 12351"/>
    </justification>
  </clause>

  <clause id="12356">
    <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(299,a,5083,a(flip),b,12355,a)].">
      <j1 rule="hyper" parents="299 5083 12355"/>
    </justification>
  </clause>

  <clause id="12357">
    <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(9619(a,1),12331(a,2,1))].">
      <j1 rule="para" parents="9619 12331"/>
    </justification>
  </clause>

  <clause id="12358">
    <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(36,a,5083,a(flip),b,12356,a)].">
      <j1 rule="hyper" parents="36 5083 12356"/>
    </justification>
  </clause>

  <clause id="12359">
    <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(299,a,12326,a(flip),b,12357,a),flip(a)].">
      <j1 rule="hyper" parents="299 12326 12357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12360">
    <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(10808(a,1),12359(a,1,2,2))].">
      <j1 rule="para" parents="10808 12359"/>
    </justification>
  </clause>

  <clause id="12361">
    <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(299,a,12332,a,b,12360,a)].">
      <j1 rule="hyper" parents="299 12332 12360"/>
    </justification>
  </clause>

  <clause id="12362">
    <literal><![CDATA[
      K(K(x,y) * K(z,x),u) * (K(z,x) * K(x,y)) = 1 / T(K(y,x) * K(x,z),u)
    ]]></literal>
    <justification jstring="[hyper(9253,a,12339,a)].">
      <j1 rule="hyper" parents="9253 12339"/>
    </justification>
  </clause>

  <clause id="12363">
    <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(7983(a,1),12348(a,1,2,2,2))].">
      <j1 rule="para" parents="7983 12348"/>
    </justification>
  </clause>

  <clause id="12364">
    <literal><![CDATA[
      K(K(x,y),K(y,z)) * T(K(y,z) * K(x,y),u) = 1 / T(K(z,y) * K(y,x),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,7180,a(flip),b,12362,a)].">
      <j1 rule="hyper" parents="65 7180 12362"/>
    </justification>
  </clause>

  <clause id="12365">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(z,u)) = K(z,K(x,y) * K(u,x))
    ]]></literal>
    <justification jstring="[hyper(5722,a,12363,a)].">
      <j1 rule="hyper" parents="5722 12363"/>
    </justification>
  </clause>

  <clause id="12366">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,K(z,u)) = K(z,K(y,x) * K(u,y))
    ]]></literal>
    <justification jstring="[para(7983(a,1),12365(a,1,1))].">
      <j1 rule="para" parents="7983 12365"/>
    </justification>
  </clause>

  <clause id="12367">
    <literal><![CDATA[
      1 / T(K(x,y) * K(y,z),u) = 1 * T(K(y,x) * K(z,y),u)
    ]]></literal>
    <justification jstring="[para(2275(a,1),12364(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2275 12364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12368">
    <literal><![CDATA[
      1 / T(K(x,y) * K(y,z),u) = T(K(y,x) * K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,7,a(flip),b,12367,a),flip(a)].">
      <j1 rule="hyper" parents="299 7 12367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12370">
    <literal><![CDATA[
      1 / T(K(x,y) * K(y,z),u) = T(K(z,y) * K(y,x),u)
    ]]></literal>
    <justification jstring="[para(2278(a,1),12368(a,2,1))].">
      <j1 rule="para" parents="2278 12368"/>
    </justification>
  </clause>

  <clause id="12371">
    <literal><![CDATA[
      1 / T(K(x,y) * K(z,x),u) = T(K(y,x) * K(x,z),u)
    ]]></literal>
    <justification jstring="[para(2278(a,2),12370(a,1,2,1))].">
      <j1 rule="para" parents="2278 12370"/>
    </justification>
  </clause>

  <clause id="12372">
    <literal><![CDATA[
      T(K(x,y) * K(y,z),u) \ 1 != w
    ]]></literal>
    <literal><![CDATA[
      T(K(y,x) * K(z,y),u) = w
    ]]></literal>
    <justification jstring="[para(12371(a,1),317(a,1,1))].">
      <j1 rule="para" parents="12371 317"/>
    </justification>
  </clause>

  <clause id="12373">
    <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(9321(a,1),12346(a,2,2))].">
      <j1 rule="para" parents="9321 12346"/>
    </justification>
  </clause>

  <clause id="12374">
    <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(299,a,12343,a(flip),b,12373,a),flip(a)].">
      <j1 rule="hyper" parents="299 12343 12373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12375">
    <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(6431(a,1),12374(a,1,1,2))].">
      <j1 rule="para" parents="6431 12374"/>
    </justification>
  </clause>

  <clause id="12376">
    <literal><![CDATA[
      (x * K(y,x)) * (T(x,z) * (x \ K(x,y))) = T((x * K(y,x)) * (K(y,x) \ 1),z)
    ]]></literal>
    <justification jstring="[para(4778(a,1),5493(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4778 5493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12378">
    <literal><![CDATA[
      (x * K(y,x)) * (T(x,z) * (x \ K(x,y))) = T((x * K(y,x)) * K(x,y),z)
    ]]></literal>
    <justification jstring="[para(5197(a,1),12376(a,2,1,2))].">
      <j1 rule="para" parents="5197 12376"/>
    </justification>
  </clause>

  <clause id="12379">
    <literal><![CDATA[
      (x * K(y,x)) * (T(x,z) * (x \ K(x,y))) = T(x,z)
    ]]></literal>
    <justification jstring="[para(7184(a,1),12378(a,2,1))].">
      <j1 rule="para" parents="7184 12378"/>
    </justification>
  </clause>

  <clause id="12380">
    <literal><![CDATA[
      T(x,y) / (T(x,y) * (x \ K(x,z))) = x * K(z,x)
    ]]></literal>
    <justification jstring="[hyper(137,a,12379,a)].">
      <j1 rule="hyper" parents="137 12379"/>
    </justification>
  </clause>

  <clause id="12381">
    <literal><![CDATA[
      T(x,y) * T(x \ K(x,z),(x \ K(x,z)) \ 1) = T(x * K(z,x),x \ K(x,z)) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(12380(a,1),3428(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="12380 3428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12382">
    <literal><![CDATA[
      T(x,y) * T(x \ K(x,z),(x \ K(x,z)) \ 1) = ((x \ 1) \ K(z,x)) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(6604(a,1),12381(a,2,1))].">
      <j1 rule="para" parents="6604 12381"/>
    </justification>
  </clause>

  <clause id="12383">
    <literal><![CDATA[
      T(x,y) * T(x \ K(x,z),(x \ 1) \ K(z,x)) = ((x \ 1) \ K(z,x)) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(6605(a,1),12382(a,1,2,2))].">
      <j1 rule="para" parents="6605 12382"/>
    </justification>
  </clause>

  <clause id="12384">
    <literal><![CDATA[
      T(x,y) * T(x \ K(x,z),T(x,z)) = ((x \ 1) \ K(z,x)) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(8194(a,1),12383(a,1,2))].">
      <j1 rule="para" parents="8194 12383"/>
    </justification>
  </clause>

  <clause id="12385">
    <literal><![CDATA[
      ((x \ 1) \ K(y,x)) \ T(x,z) = T(x,z) * T(x \ K(x,y),x)
    ]]></literal>
    <justification jstring="[para(8306(a,1),12384(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8306 12384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12386">
    <literal><![CDATA[
      ((x \ 1) \ K(y,x)) \ T(x,z) = (x \ K(x,y)) * T(x,z)
    ]]></literal>
    <justification jstring="[hyper(8378,a,12385,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="8378 12385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12388">
    <literal><![CDATA[
      K((x \ y) \ 1,((z \ K(z,u)) * T(z,w)) \ 1) = K(y \ x,T(z,w) \ ((z \ 1) \ K(u,z)))
    ]]></literal>
    <justification jstring="[para(12386(a,1),7005(a,1,2,1))].">
      <j1 rule="para" parents="12386 7005"/>
    </justification>
  </clause>

  <clause id="12389">
    <literal><![CDATA[
      (((x \ K(x,y)) \ 1) \ T(x,z)) \ K(((x \ 1) \ K(y,x)) \ T(x,z),T(x,z) \ ((x \ K(x,y)) \ 1)) = 1 / (((x \ K(x,y)) \ 1) \ T(x,z))
    ]]></literal>
    <justification jstring="[para(12386(a,2),9262(a,1,2,1))].">
      <j1 rule="para" parents="12386 9262"/>
    </justification>
  </clause>

  <clause id="12390">
    <literal><![CDATA[
      K((x * (K(y,x) / T(x,z))) \ 1,((u \ K(u,w)) * T(u,v5)) \ 1) = K(((x \ 1) \ K(y,x)) \ T(x,z),T(u,v5) \ ((u \ 1) \ K(w,u)))
    ]]></literal>
    <justification jstring="[para(8709(a,1),12388(a,1,1,1))].">
      <j1 rule="para" parents="8709 12388"/>
    </justification>
  </clause>

  <clause id="12391">
    <literal><![CDATA[
      (T(x * y,z) * L(u,y,x)) \ (T(x * y,z) * u) = L(a(x,y,u),x * (y * u),K(x * y,z))
    ]]></literal>
    <justification jstring="[para(5103(a,1),6329(a,1,2))].">
      <j1 rule="para" parents="5103 6329"/>
    </justification>
  </clause>

  <clause id="12392">
    <literal><![CDATA[
      K(x * y,K(z,L(a(x,y,u),x * (y * u),K(x * y,w)))) = K(x * y,K(z,(T(x * y,w) * u) \ L(u,y,x)))
    ]]></literal>
    <justification jstring="[para(12391(a,1),9582(a,1,2,2))].">
      <j1 rule="para" parents="12391 9582"/>
    </justification>
  </clause>

  <clause id="12393">
    <literal><![CDATA[
      (x \ 1) * (R(K(y,x),x \ K(x,y),z) * z) = (K(y,x) * (x \ 1)) * z
    ]]></literal>
    <justification jstring="[para(6469(a,1),6452(a,2,1,1))].">
      <j1 rule="para" parents="6469 6452"/>
    </justification>
  </clause>

  <clause id="12394">
    <literal><![CDATA[
      (x \ 1) * (R(K(y,x),x \ K(x,y),z) * z) = (T(x,y) \ 1) * z
    ]]></literal>
    <justification jstring="[para(5383(a,1),12393(a,2,1))].">
      <j1 rule="para" parents="5383 12393"/>
    </justification>
  </clause>

  <clause id="12396">
    <literal><![CDATA[
      (x \ 1) * (R(K(y,x),x \ 1,z) * z) = (T(x,y) \ 1) * z
    ]]></literal>
    <justification jstring="[para(6451(a,1),12394(a,1,2,1))].">
      <j1 rule="para" parents="6451 12394"/>
    </justification>
  </clause>

  <clause id="12397">
    <literal><![CDATA[
      (x \ 1) * (K(y,x) * z) = (T(x,y) \ 1) * z
    ]]></literal>
    <justification jstring="[para(6440(a,1),12396(a,1,2,1))].">
      <j1 rule="para" parents="6440 12396"/>
    </justification>
  </clause>

  <clause id="12399">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ 1) * z) = L(z,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(12397(a,1),6472(a,1,2))].">
      <j1 rule="para" parents="12397 6472"/>
    </justification>
  </clause>

  <clause id="12400">
    <literal><![CDATA[
      L(x,T(y,z) \ 1,y) = L(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,4985,a(flip),b,12399,a)].">
      <j1 rule="hyper" parents="65 4985 12399"/>
    </justification>
  </clause>

  <clause id="12402">
    <literal><![CDATA[
      L(x,((y \ z) \ z) \ 1,(y \ z) \ z) = L(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,6581,a(flip),b,12400,a)].">
      <j1 rule="hyper" parents="65 6581 12400"/>
    </justification>
  </clause>

  <clause id="12405">
    <literal><![CDATA[
      K(x,L(y,z \ 1,z) \ z) = K(x,((((z \ x) \ x) \ 1) * y) \ 1)
    ]]></literal>
    <justification jstring="[para(12402(a,1),11421(a,1,2,1))].">
      <j1 rule="para" parents="12402 11421"/>
    </justification>
  </clause>

  <clause id="12406">
    <literal><![CDATA[
      K(x,((((y \ x) \ x) \ 1) * z) \ 1) = K(x,((y \ 1) * z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,6846,a(flip),b,12405,a),flip(a)].">
      <j1 rule="hyper" parents="65 6846 12405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12408">
    <literal><![CDATA[
      K(x,((x \ (y \ x)) * z) \ 1) = K(x,((y \ 1) * z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,12202,a(flip),b,12406,a)].">
      <j1 rule="hyper" parents="65 12202 12406"/>
    </justification>
  </clause>

  <clause id="12409">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ 1) = K(x,((y \ x) * z) \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,11212,a(flip),b,12408,a),flip(a)].">
      <j1 rule="hyper" parents="65 11212 12408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12410">
    <literal><![CDATA[
      K(x,((y \ x) * (y / z)) \ x) = L(K(x,z),y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,9025,a(flip),b,12409,a),flip(a)].">
      <j1 rule="hyper" parents="65 9025 12409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12411">
    <literal><![CDATA[
      L(K(x,y),z,z \ 1) = L(K(x,y),z,z \ x)
    ]]></literal>
    <justification jstring="[hyper(10524,a,12410,a),flip(a)].">
      <j1 rule="hyper" parents="10524 12410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12412">
    <literal><![CDATA[
      L(K(x,y),z,z \ x) = K(x,L(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(11995,a,12411,a),flip(a)].">
      <j1 rule="hyper" parents="11995 12411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12413">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1)) = K(x,L(y,z,z \ x))
    ]]></literal>
    <justification jstring="[hyper(11995,a,12412,a),flip(a)].">
      <j1 rule="hyper" parents="11995 12412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12414">
    <literal><![CDATA[
      K(x,L(y,z \ x,(z \ x) \ 1)) = K(x,L(y,z \ x,z))
    ]]></literal>
    <justification jstring="[para(11635(a,1),12413(a,2,2))].">
      <j1 rule="para" parents="11635 12413"/>
    </justification>
  </clause>

  <clause id="12415">
    <literal><![CDATA[
      K(x,L((y \ 1) \ (y \ z),y \ x,y)) = K((((y \ x) \ 1) * (y \ 1)) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,12111,a(flip),b,12414,a),flip(a)].">
      <j1 rule="hyper" parents="65 12111 12414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12416">
    <literal><![CDATA[
      K((((x \ y) \ 1) * (x \ 1)) \ 1,z) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,12235,a(flip),b,12415,a),flip(a)].">
      <j1 rule="hyper" parents="65 12235 12415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12417">
    <literal><![CDATA[
      K(((((x \ 1) \ y) \ 1) * x) \ 1,z) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(7407,a,12416,a)].">
      <j1 rule="hyper" parents="7407 12416"/>
    </justification>
  </clause>

  <clause id="12419">
    <literal><![CDATA[
      (1 / (x \ y)) * (x \ T(y,z)) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,6320,a(flip),b,12416,a)].">
      <j1 rule="hyper" parents="65 6320 12416"/>
    </justification>
  </clause>

  <clause id="12422">
    <literal><![CDATA[
      (1 / x) * ((y / x) \ T(y,z)) = K(y,z)
    ]]></literal>
    <justification jstring="[para(79(a,1),12419(a,1,1,2))].">
      <j1 rule="para" parents="79 12419"/>
    </justification>
  </clause>

  <clause id="12423">
    <literal><![CDATA[
      (1 / x) \ K(y,z) = (y / x) \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,12422,a)].">
      <j1 rule="hyper" parents="125 12422"/>
    </justification>
  </clause>

  <clause id="12425">
    <literal><![CDATA[
      K(x,((y / z) \ 1) \ z) = ((1 / z) \ K(y,x)) \ z
    ]]></literal>
    <justification jstring="[para(12423(a,2),7309(a,2,1))].">
      <j1 rule="para" parents="12423 7309"/>
    </justification>
  </clause>

  <clause id="12426">
    <literal><![CDATA[
      T(x,y) / ((1 / z) \ x) = K(x,y) / z
    ]]></literal>
    <justification jstring="[para(12417(a,1),10375(a,2,1))].">
      <j1 rule="para" parents="12417 10375"/>
    </justification>
  </clause>

  <clause id="12427">
    <literal><![CDATA[
      T(x,y) / ((1 / y) \ x) = 1 / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,5038,a(flip),b,12426,a),flip(a)].">
      <j1 rule="hyper" parents="299 5038 12426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12428">
    <literal><![CDATA[
      (1 / (x \ K(y,z))) \ y = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(38,a,178,a,b,12426,a),flip(a)].">
      <j1 rule="hyper" parents="38 178 12426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12430">
    <literal><![CDATA[
      T(x,y * L(y \ 1,y,z)) / ((1 / (y * L(y \ 1,y,z))) \ x) = 1 / (y * ((z * y) \ z))
    ]]></literal>
    <justification jstring="[para(9871(a,1),12427(a,2,2))].">
      <j1 rule="para" parents="9871 12427"/>
    </justification>
  </clause>

  <clause id="12431">
    <literal><![CDATA[
      (1 / T(x,y)) \ x = (1 / x) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(5081(a,2),12428(a,1,1,2))].">
      <j1 rule="para" parents="5081 12428"/>
    </justification>
  </clause>

  <clause id="12432">
    <literal><![CDATA[
      (1 / (x / y)) \ T(x / y,y) = (1 / (y \ x)) \ (x / y)
    ]]></literal>
    <justification jstring="[para(109(a,1),12431(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="109 12431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12433">
    <literal><![CDATA[
      ((1 / x) \ K(y * x,z)) \ x = K(z,(y \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(11(a,1),12425(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="11 12425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12434">
    <literal><![CDATA[
      K(x,y \ ((y \ 1) \ (z * y))) = K(x,(z \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,12216,a,b,12433,a)].">
      <j1 rule="hyper" parents="65 12216 12433"/>
    </justification>
  </clause>

  <clause id="12435">
    <literal><![CDATA[
      (1 / x) \ K(y,z * x) = x * K(y,(z \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(12434(a,1),12213(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12434 12213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12436">
    <literal><![CDATA[
      x * K(y,((z / x) \ 1) \ x) = (1 / x) \ K(y,z)
    ]]></literal>
    <justification jstring="[para(12(a,1),12435(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 12435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12437">
    <literal><![CDATA[
      (1 / (x / y)) \ (y \ x) = (1 / (y \ x)) \ (x / y)
    ]]></literal>
    <justification jstring="[para(109(a,1),12432(a,1,2))].">
      <j1 rule="para" parents="109 12432"/>
    </justification>
  </clause>

  <clause id="12438">
    <literal><![CDATA[
      (x \ y) * (((y / x) \ 1) \ 1) = (1 / (x \ y)) \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(65,a,9973,a,b,12437,a)].">
      <j1 rule="hyper" parents="65 9973 12437"/>
    </justification>
  </clause>

  <clause id="12439">
    <literal><![CDATA[
      (x \ y) * T(y / x,y \ x) = (1 / (x \ y)) \ (y / x)
    ]]></literal>
    <justification jstring="[para(3355(a,2),12438(a,1,2))].">
      <j1 rule="para" parents="3355 12438"/>
    </justification>
  </clause>

  <clause id="12440">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) / ((1 / (y * L(y \ 1,y,z))) \ (L(y \ 1,y,x) \ 1)) = 1 / (y * ((z * y) \ z))
    ]]></literal>
    <justification jstring="[para(8952(a,1),12430(a,1,1))].">
      <j1 rule="para" parents="8952 12430"/>
    </justification>
  </clause>

  <clause id="12441">
    <literal><![CDATA[
      (L(x \ 1,y,z) \ (x \ 1)) \ (L(x \ 1,y,z) \ K(x \ 1,x)) = T(x,x \ (L(x \ 1,y,z) \ 1))
    ]]></literal>
    <justification jstring="[para(3293(a,1),6738(a,1,2))].">
      <j1 rule="para" parents="3293 6738"/>
    </justification>
  </clause>

  <clause id="12442">
    <literal><![CDATA[
      (L(x \ 1,y,z) \ (x \ 1)) \ (L(1 / x,y,z) \ 1) = T(x,x \ (L(x \ 1,y,z) \ 1))
    ]]></literal>
    <justification jstring="[para(3808(a,1),12441(a,1,2))].">
      <j1 rule="para" parents="3808 12441"/>
    </justification>
  </clause>

  <clause id="12443">
    <literal><![CDATA[
      T(x,x \ (L(x \ 1,y,z) \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(65,a,11845,a(flip),b,12442,a),flip(a)].">
      <j1 rule="hyper" parents="65 11845 12442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12445">
    <literal><![CDATA[
      T(x,x \ (((y * x) \ y) \ 1)) = x
    ]]></literal>
    <justification jstring="[para(214(a,1),12443(a,1,2,2,1))].">
      <j1 rule="para" parents="214 12443"/>
    </justification>
  </clause>

  <clause id="12446">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) / y = y \ (1 / ((x * y) \ x))
    ]]></literal>
    <justification jstring="[para(12445(a,1),3894(a,1,2))].">
      <j1 rule="para" parents="12445 3894"/>
    </justification>
  </clause>

  <clause id="12447">
    <literal><![CDATA[
      T((1 / ((x * y) \ x)) * K(y,z),y) = (y \ (1 / ((x * y) \ x))) * T(y,z)
    ]]></literal>
    <justification jstring="[para(12446(a,1),7940(a,2,1))].">
      <j1 rule="para" parents="12446 7940"/>
    </justification>
  </clause>

  <clause id="12448">
    <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(11190(a,1),9613(a,1,1,2))].">
      <j1 rule="para" parents="11190 9613"/>
    </justification>
  </clause>

  <clause id="12449">
    <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(9304(a,1),12448(a,1,1))].">
      <j1 rule="para" parents="9304 12448"/>
    </justification>
  </clause>

  <clause id="12450">
    <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),12449(a,1,2))].">
      <j1 rule="para" parents="27 12449"/>
    </justification>
  </clause>

  <clause id="12451">
    <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(268(a,1),12450(a,1,2,1))].">
      <j1 rule="para" parents="268 12450"/>
    </justification>
  </clause>

  <clause id="12452">
    <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(65,a,10798,a(flip),b,12451,a)].">
      <j1 rule="hyper" parents="65 10798 12451"/>
    </justification>
  </clause>

  <clause id="12453">
    <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(65,a,10774,a(flip),b,12452,a)].">
      <j1 rule="hyper" parents="65 10774 12452"/>
    </justification>
  </clause>

  <clause id="12455">
    <literal><![CDATA[
      ((R((x * y) / x,z,y) \ y) \ y) \ u = ((x * y) / x) \ ((u / R(y,z,y)) * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,9878,a(flip),b,12453,a),flip(a)].">
      <j1 rule="hyper" parents="65 9878 12453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12456">
    <literal><![CDATA[
      ((R((x * y) / x,z,y) \ y) \ y) \ u = ((x * y) / x) \ (y * (R(y,z,y) \ u))
    ]]></literal>
    <justification jstring="[para(7668(a,1),12455(a,2,2))].">
      <j1 rule="para" parents="7668 12455"/>
    </justification>
  </clause>

  <clause id="12457">
    <literal><![CDATA[
      ((R((x * y) / x,z,y) \ y) \ y) \ u = T(y,x) * (y \ (R(y,z,y) \ u))
    ]]></literal>
    <justification jstring="[hyper(299,a,4839,a(flip),b,12456,a),flip(a)].">
      <j1 rule="hyper" parents="299 4839 12456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12458">
    <literal><![CDATA[
      ((x \ L(T(x,y),z,x)) \ x) \ u = T(x,y) * (x \ (R(x,z,x) \ u))
    ]]></literal>
    <justification jstring="[para(9612(a,1),12457(a,1,1,1))].">
      <j1 rule="para" parents="9612 12457"/>
    </justification>
  </clause>

  <clause id="12459">
    <literal><![CDATA[
      T(x,y) * (x \ (R(x,z,x) \ u)) = R(x * K(y,x),z,x) \ u
    ]]></literal>
    <justification jstring="[para(11190(a,1),12458(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11190 12458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12460">
    <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(12459(a,1),5417(a,1))].">
      <j1 rule="para" parents="12459 5417"/>
    </justification>
  </clause>

  <clause id="12461">
    <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(9792(a,1),9795(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="9792 9795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12462">
    <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(299,a,4125,a(flip),b,12461,a),flip(a)].">
      <j1 rule="hyper" parents="299 4125 12461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12464">
    <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(1273(a,1),12462(a,2,1))].">
      <j1 rule="para" parents="1273 12462"/>
    </justification>
  </clause>

  <clause id="12465">
    <literal><![CDATA[
      L(x \ L(x,y,z),T(x,u),w) = L(x \ L(x,y,z),x,w)
    ]]></literal>
    <justification jstring="[para(1273(a,1),12464(a,1,1))].">
      <j1 rule="para" parents="1273 12464"/>
    </justification>
  </clause>

  <clause id="12466">
    <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(12465(a,1),11912(a,1,2,2))].">
      <j1 rule="para" parents="12465 11912"/>
    </justification>
  </clause>

  <clause id="12467">
    <literal><![CDATA[
      T(K(x,T(y,z)) * u,w) * K(y,x) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) \ T((K(x,K(y,z)) * u) * K(x,y),w) = v5
    ]]></literal>
    <justification jstring="[para(8252(a,1),10062(a,1))].">
      <j1 rule="para" parents="8252 10062"/>
    </justification>
  </clause>

  <clause id="12468">
    <literal><![CDATA[
      (x * L(y,x,y)) / T(T(x,y),L(T(y,x),z,u)) = T(y,x * y) * a(u,z,K(T(x,y),T(y,x * y)))
    ]]></literal>
    <justification jstring="[para(9979(a,1),12007(a,1,2))].">
      <j1 rule="para" parents="9979 12007"/>
    </justification>
  </clause>

  <clause id="12469">
    <literal><![CDATA[
      T(x,y * x) * a(z,u,K(T(y,x),T(x,y * x))) = (y * L(x,y,x)) / T(T(y,L(x,u,z)),x)
    ]]></literal>
    <justification jstring="[para(4464(a,1),12468(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4464 12468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12470">
    <literal><![CDATA[
      T(x,y * x) * a(z,u,K(T(y,x),T(x,y * x))) = (y * L(x,y,x)) / T(T(y,x),L(x,u,z))
    ]]></literal>
    <justification jstring="[para(23(a,1),12469(a,2,2))].">
      <j1 rule="para" parents="23 12469"/>
    </justification>
  </clause>

  <clause id="12471">
    <literal><![CDATA[
      T(x,y * x) * a(z,u,K(T(y,x),T(x,y * x))) = K(L(x,u,z),y) * L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,8951,a(flip),b,12470,a),flip(a)].">
      <j1 rule="hyper" parents="299 8951 12470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12472">
    <literal><![CDATA[
      T(x,y * x) * a(z,u,K(T(y,x),T(x,y * x))) = K(x,L(y,u,z)) * L(x,y,x)
    ]]></literal>
    <justification jstring="[para(11929(a,1),12471(a,2,1))].">
      <j1 rule="para" parents="11929 12471"/>
    </justification>
  </clause>

  <clause id="12473">
    <literal><![CDATA[
      T(x,y * x) * a(z,u,K(T(y,x),T(x,y * x))) = L(T(x,L(y,u,z)),y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,7443,a(flip),b,12472,a),flip(a)].">
      <j1 rule="hyper" parents="299 7443 12472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12474">
    <literal><![CDATA[
      T(x,y * x) * a(z,u,K(T(y,x),T(x,y))) = L(T(x,L(y,u,z)),y,x)
    ]]></literal>
    <justification jstring="[para(7488(a,1),12473(a,1,2,3))].">
      <j1 rule="para" parents="7488 12473"/>
    </justification>
  </clause>

  <clause id="12475">
    <literal><![CDATA[
      T(x,y * x) * a(z,u,K(y,x)) = L(T(x,L(y,u,z)),y,x)
    ]]></literal>
    <justification jstring="[para(4411(a,1),12474(a,1,2,3))].">
      <j1 rule="para" parents="4411 12474"/>
    </justification>
  </clause>

  <clause id="12476">
    <literal><![CDATA[
      L(K(x * y,y),z,u) \ T(y,K(x * y,y)) = L(T(y,L(x,z,u)),x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,12110,a,b,12475,a)].">
      <j1 rule="hyper" parents="65 12110 12475"/>
    </justification>
  </clause>

  <clause id="12477">
    <literal><![CDATA[
      K(x * y,L(y,z,u)) \ T(y,K(x * y,y)) = L(T(y,L(x,z,u)),x,y)
    ]]></literal>
    <justification jstring="[para(11889(a,1),12476(a,1,1))].">
      <j1 rule="para" parents="11889 12476"/>
    </justification>
  </clause>

  <clause id="12478">
    <literal><![CDATA[
      L(T(x,L(y,z,u)),y,x) = K(y * x,L(x,z,u)) \ x
    ]]></literal>
    <justification jstring="[para(3612(a,1),12477(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3612 12477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12479">
    <literal><![CDATA[
      L(T(x,L(y,z,u)),y,x) = K(L(x,z,u),y * x) * x
    ]]></literal>
    <justification jstring="[hyper(299,a,5426,a(flip),b,12478,a),flip(a)].">
      <j1 rule="hyper" parents="299 5426 12478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12480">
    <literal><![CDATA[
      L(T(x,L(y,z,u)),y,x) = K(x,L(y * x,z,u)) * x
    ]]></literal>
    <justification jstring="[para(11929(a,1),12479(a,2,1))].">
      <j1 rule="para" parents="11929 12479"/>
    </justification>
  </clause>

  <clause id="12481">
    <literal><![CDATA[
      L(T(x,L(y,z,u)),y,x) = T(x,L(y * x,z,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,5096,a,b,12480,a),flip(a)].">
      <j1 rule="hyper" parents="299 5096 12480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12483">
    <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),12253(a,2,1,1))].">
      <j1 rule="para" parents="9 12253"/>
    </justification>
  </clause>

  <clause id="12484">
    <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(299,a,9822,a(flip),b,12483,a),flip(a)].">
      <j1 rule="hyper" parents="299 9822 12483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12486">
    <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),12484(a,1,1,1))].">
      <j1 rule="para" parents="9 12484"/>
    </justification>
  </clause>

  <clause id="12487">
    <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),12486(a,1,2,2))].">
      <j1 rule="para" parents="9 12486"/>
    </justification>
  </clause>

  <clause id="12488">
    <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(6341(a,1),12487(a,1,2,1,3))].">
      <j1 rule="para" parents="6341 12487"/>
    </justification>
  </clause>

  <clause id="12489">
    <literal><![CDATA[
      ((T(x,(1 / y) \ z) * (z * y)) / T(x,(1 / y) \ z)) / y = z * K(x,(z \ (1 / y)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,6039,a(flip),b,5671,a),flip(a)].">
      <j1 rule="hyper" parents="299 6039 5671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12490">
    <literal><![CDATA[
      ((x * y) * K(T(z,(1 / y) \ x),x * y)) / y = x * K(z,(x \ (1 / y)) \ 1)
    ]]></literal>
    <justification jstring="[para(5054(a,1),12489(a,1,1))].">
      <j1 rule="para" parents="5054 12489"/>
    </justification>
  </clause>

  <clause id="12491">
    <literal><![CDATA[
      ((x * y) * K(z,x * y)) / y = x * K(z,(x \ (1 / y)) \ 1)
    ]]></literal>
    <justification jstring="[para(7559(a,1),12490(a,1,1,2))].">
      <j1 rule="para" parents="7559 12490"/>
    </justification>
  </clause>

  <clause id="12492">
    <literal><![CDATA[
      ((x * y) * K(z,x * y)) / y = x * K(z,(1 / y) \ x)
    ]]></literal>
    <justification jstring="[para(6814(a,1),12491(a,2,2))].">
      <j1 rule="para" parents="6814 12491"/>
    </justification>
  </clause>

  <clause id="12493">
    <literal><![CDATA[
      ((x * y) * K(z,x * y)) / y = x * K(z,(y \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(5647(a,1),12492(a,2,2))].">
      <j1 rule="para" parents="5647 12492"/>
    </justification>
  </clause>

  <clause id="12494">
    <literal><![CDATA[
      (x * K(y,(z \ 1) \ x)) * z = (x * z) * K(y,x * z)
    ]]></literal>
    <justification jstring="[hyper(143,a,12493,a)].">
      <j1 rule="hyper" parents="143 12493"/>
    </justification>
  </clause>

  <clause id="12495">
    <literal><![CDATA[
      (x \ y) * K(z,(x \ 1) \ (x \ y)) = x \ (y * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(37,a,6004,a(flip),b,12494,a),flip(a)].">
      <j1 rule="hyper" parents="37 6004 12494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12496">
    <literal><![CDATA[
      (x \ y) \ (x \ (y * K(z,y))) = K(z,(x \ 1) \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(125,a,12495,a)].">
      <j1 rule="hyper" parents="125 12495"/>
    </justification>
  </clause>

  <clause id="12497">
    <literal><![CDATA[
      (x \ K(y,z)) \ (x \ K(y,T(z,u))) = K(u,(x \ 1) \ (x \ K(y,z)))
    ]]></literal>
    <justification jstring="[para(8040(a,1),12496(a,1,2,2))].">
      <j1 rule="para" parents="8040 12496"/>
    </justification>
  </clause>

  <clause id="12498">
    <literal><![CDATA[
      T(T(x,x * (K(y,x) * z)) * K(y,T(x,(x * K(y,x)) * z)),u) = T(T(x * K(y,x),u),z * (x * K(y,x)))
    ]]></literal>
    <justification jstring="[para(5488(a,1),5879(a,1,1,1,2))].">
      <j1 rule="para" parents="5488 5879"/>
    </justification>
  </clause>

  <clause id="12499">
    <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(7954(a,1),9548(a,2,1))].">
      <j1 rule="para" parents="7954 9548"/>
    </justification>
  </clause>

  <clause id="12500">
    <literal><![CDATA[
      T(x,R(T(y / T(z \ 1,u),K(z,z \ 1)),w,v5)) = T(x,R(((y / T(1 / z,u)) \ 1) \ 1,w,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,3917,a(flip),b,10802,a),flip(a)].">
      <j1 rule="hyper" parents="65 3917 10802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12502">
    <literal><![CDATA[
      T(x,R(T(y / T(z \ 1,u),K(z,z \ 1)),w,v5)) = T(x,R(y / T(1 / z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(299,a,3897,a(flip),b,12500,a),flip(a)].">
      <j1 rule="hyper" parents="299 3897 12500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12503">
    <literal><![CDATA[
      T(x,R(y / T(1 / z,u),w,v5)) = T(x,R(y / T(z \ 1,u),w,v5))
    ]]></literal>
    <justification jstring="[para(3195(a,1),12502(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3195 12502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12505">
    <literal><![CDATA[
      T((1 / x) * R((1 / x) \ 1,y,z),R(x,u,w) \ x) = (1 / x) * R((1 / x) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(10930(a,1),10931(a,2,2,1,1))].">
      <j1 rule="para" parents="10930 10931"/>
    </justification>
  </clause>

  <clause id="12506">
    <literal><![CDATA[
      T((1 / x) * R((1 / x) \ 1,y,z),R(x,u,w) \ x) = (1 / x) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(79(a,1),12505(a,2,2,1))].">
      <j1 rule="para" parents="79 12505"/>
    </justification>
  </clause>

  <clause id="12508">
    <literal><![CDATA[
      T((1 / x) * R((1 / x) \ 1,y,z),R(x,u,w) \ x) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,10869,a(flip),b,12506,a),flip(a)].">
      <j1 rule="hyper" parents="299 10869 12506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12509">
    <literal><![CDATA[
      T((1 / x) * R(x,y,z),R(x,u,w) \ x) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(79(a,1),12508(a,1,1,2,1))].">
      <j1 rule="para" parents="79 12508"/>
    </justification>
  </clause>

  <clause id="12510">
    <literal><![CDATA[
      T(x \ R(x,y,z),R(x,u,w) \ x) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(10869(a,1),12509(a,1,1))].">
      <j1 rule="para" parents="10869 12509"/>
    </justification>
  </clause>

  <clause id="12511">
    <literal><![CDATA[
      ((x \ R(x,y,z)) \ 1) \ 1 = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(7046,a,12510,a)].">
      <j1 rule="hyper" parents="7046 12510"/>
    </justification>
  </clause>

  <clause id="12512">
    <literal><![CDATA[
      T(R(x \ R(x,y,z),x,y * z),x * (y * z)) = (((x * (y * z)) \ ((x * y) * z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(12511(a,1),12308(a,1,1,1))].">
      <j1 rule="para" parents="12511 12308"/>
    </justification>
  </clause>

  <clause id="12513">
    <literal><![CDATA[
      T((x * (y * z)) \ (R(x,y,z) * (y * z)),x) = (((x * (y * z)) \ ((x * y) * z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(859,a,12512,a)].">
      <j1 rule="hyper" parents="859 12512"/>
    </justification>
  </clause>

  <clause id="12514">
    <literal><![CDATA[
      T((x * (y * z)) \ ((x * y) * z),x) = (((x * (y * z)) \ ((x * y) * z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(103(a,1),12513(a,1,1,2))].">
      <j1 rule="para" parents="103 12513"/>
    </justification>
  </clause>

  <clause id="12515">
    <literal><![CDATA[
      (((x * (y * z)) \ ((x * y) * z)) \ 1) \ 1 = T(a(x,y,z),x)
    ]]></literal>
    <justification jstring="[para(14(a,2),12514(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14 12514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12516">
    <literal><![CDATA[
      a(x,y,z) = (((x * (y * z)) \ ((x * y) * z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(299,a,11009,a(flip),b,12515,a)].">
      <j1 rule="hyper" parents="299 11009 12515"/>
    </justification>
  </clause>

  <clause id="12517">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ 1 = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(14(a,2),12516(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="14 12516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12518">
    <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(65,a,11045,a(flip),b,11047,a)].">
      <j1 rule="hyper" parents="65 11045 11047"/>
    </justification>
  </clause>

  <clause id="12519">
    <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(11862,a,12518,a)].">
      <j1 rule="hyper" parents="11862 12518"/>
    </justification>
  </clause>

  <clause id="12522">
    <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(10838(a,1),12519(a,2,2,2))].">
      <j1 rule="para" parents="10838 12519"/>
    </justification>
  </clause>

  <clause id="12523">
    <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),12522(a,2,2,2,1))].">
      <j1 rule="para" parents="10 12522"/>
    </justification>
  </clause>

  <clause id="12524">
    <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),12523(a,2,2))].">
      <j1 rule="para" parents="9 12523"/>
    </justification>
  </clause>

  <clause id="12526">
    <literal><![CDATA[
      a(T(x,y),z,R(x,u,w)) = a(x,z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(299,a,10609,a(flip),b,12524,a),flip(a)].">
      <j1 rule="hyper" parents="299 10609 12524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12527">
    <literal><![CDATA[
      a(x,T(x,y) \ z,R(x,u,w)) = a(x,x \ z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,11863,a(flip),b,12526,a),flip(a)].">
      <j1 rule="hyper" parents="65 11863 12526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12529">
    <literal><![CDATA[
      K((x \ y) \ T(y,x),z \ L((x \ y) \ T(y,x),u,w)) = K(x,z \ L(T(x,x \ y),u,w))
    ]]></literal>
    <justification jstring="[hyper(299,a,7444,a(flip),b,11102,a),flip(a)].">
      <j1 rule="hyper" parents="299 7444 11102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12531">
    <literal><![CDATA[
      K((x \ y) \ T(y,x),z \ L((x \ y) \ T(y,x),u,w)) = K(x,z \ L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(299,a,11101,a(flip),b,12529,a),flip(a)].">
      <j1 rule="hyper" parents="299 11101 12529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12533">
    <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(5426(a,1),11509(a,1,1,2))].">
      <j1 rule="para" parents="5426 11509"/>
    </justification>
  </clause>

  <clause id="12534">
    <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(11229(a,1),11835(a,1,2,1,1))].">
      <j1 rule="para" parents="11229 11835"/>
    </justification>
  </clause>

  <clause id="12535">
    <literal><![CDATA[
      T(T(x,x * y) * K(z,T(x,(x * K(z,x)) * y)),u) = T(T(x * K(z,x),u),y * (x * K(z,x)))
    ]]></literal>
    <justification jstring="[para(8655(a,1),12498(a,1,1,1))].">
      <j1 rule="para" parents="8655 12498"/>
    </justification>
  </clause>

  <clause id="12536">
    <literal><![CDATA[
      T(T(x,x * y) * K(z,T(x,x * (K(z,x) * y))),u) = T(T(x * K(z,x),u),y * (x * K(z,x)))
    ]]></literal>
    <justification jstring="[para(5488(a,1),12535(a,1,1,2,2,2))].">
      <j1 rule="para" parents="5488 12535"/>
    </justification>
  </clause>

  <clause id="12538">
    <literal><![CDATA[
      T(T(x * K(y,x),z),u * (x * K(y,x))) = T(T(x,x * u) * K(y,T(x,x * u)),z)
    ]]></literal>
    <justification jstring="[para(8655(a,1),12536(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8655 12536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12539">
    <literal><![CDATA[
      T(T(x * K(y,x),z),u * (x * K(y,x))) = T(T(x,x * u) * K(y,T(x,u)),z)
    ]]></literal>
    <justification jstring="[para(7469(a,1),12538(a,2,1,2))].">
      <j1 rule="para" parents="7469 12538"/>
    </justification>
  </clause>

  <clause id="12541">
    <literal><![CDATA[
      T(x,x * y) * K(z,T(x,y)) = T(x * K(z,x),y * x)
    ]]></literal>
    <justification jstring="[hyper(10364,a,12539,a),flip(a)].">
      <j1 rule="hyper" parents="10364 12539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12542">
    <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(299,a,8449,a(flip),b,12499,a),flip(a)].">
      <j1 rule="hyper" parents="299 8449 12499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12543">
    <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(9039(a,1),12533(a,1,1))].">
      <j1 rule="para" parents="9039 12533"/>
    </justification>
  </clause>

  <clause id="12544">
    <literal><![CDATA[
      K(x,T((y * (x \ z)) \ u,w)) = K(x,T((y * z) \ (u * x),w))
    ]]></literal>
    <justification jstring="[hyper(65,a,11834,a(flip),b,12534,a),flip(a)].">
      <j1 rule="hyper" parents="65 11834 12534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12545">
    <literal><![CDATA[
      K(x,T((y * z) \ (u * x),y * z)) = K(x,u / (y * (x \ z)))
    ]]></literal>
    <justification jstring="[hyper(9480,a,12544,a),flip(a)].">
      <j1 rule="hyper" parents="9480 12544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12546">
    <literal><![CDATA[
      K(x,(y * x) / (z * u)) = K(x,y / (z * (x \ u)))
    ]]></literal>
    <justification jstring="[hyper(8215,a,12545,a)].">
      <j1 rule="hyper" parents="8215 12545"/>
    </justification>
  </clause>

  <clause id="12547">
    <literal><![CDATA[
      K(x,y / (z * (x \ u))) = K(x,((z * u) / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(9067,a,12546,a),flip(a)].">
      <j1 rule="hyper" parents="9067 12546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12548">
    <literal><![CDATA[
      R(K(x,((y * z) / (u / w)) \ x),w \ u,w) = K(x,u / ((y * (x \ z)) * w))
    ]]></literal>
    <justification jstring="[para(12547(a,1),11285(a,1,1))].">
      <j1 rule="para" parents="12547 11285"/>
    </justification>
  </clause>

  <clause id="12549">
    <literal><![CDATA[
      K(x,y / ((x \ (z * u)) * w)) = K(x,y / ((z * (x \ u)) * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,11284,a(flip),b,12548,a)].">
      <j1 rule="hyper" parents="65 11284 12548"/>
    </justification>
  </clause>

  <clause id="12550">
    <literal><![CDATA[
      K(x,y / ((z * (x \ u)) * w)) = K(x,(((z * u) * w) / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(11594,a,12549,a),flip(a)].">
      <j1 rule="hyper" parents="11594 12549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12551">
    <literal><![CDATA[
      K(x,(((y * z) * u) / (z * u)) \ x) = R(K(x,y \ x),z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,10821,a(flip),b,12550,a),flip(a)].">
      <j1 rule="hyper" parents="65 10821 12550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12552">
    <literal><![CDATA[
      R(K(x,y \ x),z,u) = K(x,R(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[para(20(a,2),12551(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="20 12551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12553">
    <literal><![CDATA[
      R(K(x,R(1 / y,y,z) \ x),y * z,u) = K(x,((z * u) / ((y * z) * u)) \ x)
    ]]></literal>
    <justification jstring="[para(571(a,1),12552(a,2,2,1))].">
      <j1 rule="para" parents="571 12552"/>
    </justification>
  </clause>

  <clause id="12554">
    <literal><![CDATA[
      K(x,R(y \ 1,z,u) \ x) = R(K(x,x * y),z,u)
    ]]></literal>
    <justification jstring="[para(5749(a,1),12552(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5749 12552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12555">
    <literal><![CDATA[
      K(x,R(y \ x,z,u) \ x) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(6891(a,1),12552(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6891 12552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12556">
    <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(11702(a,1),12552(a,1,1))].">
      <j1 rule="para" parents="11702 12552"/>
    </justification>
  </clause>

  <clause id="12557">
    <literal><![CDATA[
      K(x,R(1 / y,z,u) \ x) = R(K(x,x * y),z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,5666,a,b,12554,a)].">
      <j1 rule="hyper" parents="65 5666 12554"/>
    </justification>
  </clause>

  <clause id="12558">
    <literal><![CDATA[
      T(x,R(y \ 1,z,u) \ x) = x * R(K(x,x * y),z,u)
    ]]></literal>
    <justification jstring="[para(12554(a,1),5083(a,2,2))].">
      <j1 rule="para" parents="12554 5083"/>
    </justification>
  </clause>

  <clause id="12559">
    <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(12555(a,1),12556(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12555 12556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12560">
    <literal><![CDATA[
      R(K(x,R(y \ 1,y,z) \ x),y * z,u) = K(x,((z * u) / ((y * z) * u)) \ x)
    ]]></literal>
    <justification jstring="[para(5666(a,1),12553(a,1,1))].">
      <j1 rule="para" parents="5666 12553"/>
    </justification>
  </clause>

  <clause id="12561">
    <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(8001(a,1),8501(a,1,1,2))].">
      <j1 rule="para" parents="8001 8501"/>
    </justification>
  </clause>

  <clause id="12562">
    <literal><![CDATA[
      K(K(x,y) * K(z,x),R(u / K(x,y),K(x,y),K(z,x))) = (u * K(z,x)) \ ((K(x,y) * K(z,x)) * (u * K(y,x)))
    ]]></literal>
    <justification jstring="[para(7196(a,1),9215(a,2,2,2))].">
      <j1 rule="para" parents="7196 9215"/>
    </justification>
  </clause>

  <clause id="12563">
    <literal><![CDATA[
      (x * (y * (K(y,z) * (y \ u)))) * K(z,L(y,K(z,y) \ (y \ u),x)) = x * (((K(z,y) \ (u / y)) * K(z,y)) * y)
    ]]></literal>
    <justification jstring="[para(5426(a,1),9489(a,1,1,2,2))].">
      <j1 rule="para" parents="5426 9489"/>
    </justification>
  </clause>

  <clause id="12564">
    <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(6939(a,1),10425(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6939 10425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12565">
    <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(299,a,5518,a(flip),b,12564,a),flip(a)].">
      <j1 rule="hyper" parents="299 5518 12564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12567">
    <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(299,a,5103,a(flip),b,12565,a),flip(a)].">
      <j1 rule="hyper" parents="299 5103 12565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12568">
    <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(6939(a,1),12567(a,1,2))].">
      <j1 rule="para" parents="6939 12567"/>
    </justification>
  </clause>

  <clause id="12569">
    <literal><![CDATA[
      T(x * K(y,z),L(y,u,w)) = T(x,L(y,u,w)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,8571,a(flip),b,12568,a)].">
      <j1 rule="hyper" parents="65 8571 12568"/>
    </justification>
  </clause>

  <clause id="12571">
    <literal><![CDATA[
      T(x * K(y,x),L(y,z,u)) = x * a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(299,a,11952,a(flip),b,12569,a),flip(a)].">
      <j1 rule="hyper" parents="299 11952 12569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12572">
    <literal><![CDATA[
      T(x * a(y,z,K(u,x)),u) = T(x,L(u,z,y))
    ]]></literal>
    <justification jstring="[para(12571(a,1),5125(a,1,1))].">
      <j1 rule="para" parents="12571 5125"/>
    </justification>
  </clause>

  <clause id="12573">
    <literal><![CDATA[
      T(x * a(y,z,K(u,x)),x * u) = L(T(x,L(u,z,y)),u,x)
    ]]></literal>
    <justification jstring="[para(12571(a,1),5253(a,1,1))].">
      <j1 rule="para" parents="12571 5253"/>
    </justification>
  </clause>

  <clause id="12574">
    <literal><![CDATA[
      T(x * a(y,z,K(u,x)),x * u) = T(x,L(u * x,z,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,12481,a(flip),b,12573,a),flip(a)].">
      <j1 rule="hyper" parents="299 12481 12573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12575">
    <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(9320(a,1),12120(a,1,1,1,2))].">
      <j1 rule="para" parents="9320 12120"/>
    </justification>
  </clause>

  <clause id="12576">
    <literal><![CDATA[
      K(x * y,K(z,(T(x * y,u) * w) \ L(w,y,x))) = K(z,K(x * y,a(x,y,w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,7998,a(flip),b,12392,a),flip(a)].">
      <j1 rule="hyper" parents="65 7998 12392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12577">
    <literal><![CDATA[
      K(x,K(y * z,(T(y * z,u) * w) \ L(w,z,y))) = K(x,K(y * z,a(y,z,w)))
    ]]></literal>
    <justification jstring="[hyper(7985,a,12576,a)].">
      <j1 rule="hyper" parents="7985 12576"/>
    </justification>
  </clause>

  <clause id="12579">
    <literal><![CDATA[
      K(x,K(y * z,u \ ((y * z) \ L(u,z,y)))) = K(x,K(y * z,a(y,z,u)))
    ]]></literal>
    <justification jstring="[para(8898(a,1),12577(a,1,2))].">
      <j1 rule="para" parents="8898 12577"/>
    </justification>
  </clause>

  <clause id="12580">
    <literal><![CDATA[
      K(x,K(y * z,u \ L(u,z,y))) = K(x,K(y * z,a(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,9574,a(flip),b,12579,a)].">
      <j1 rule="hyper" parents="65 9574 12579"/>
    </justification>
  </clause>

  <clause id="12581">
    <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(8243(a,1),12561(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8243 12561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12582">
    <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(7489(a,2),12581(a,2,2))].">
      <j1 rule="para" parents="7489 12581"/>
    </justification>
  </clause>

  <clause id="12583">
    <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(299,a,7583,a(flip),b,12582,a),flip(a)].">
      <j1 rule="hyper" parents="299 7583 12582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12584">
    <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(8004(a,1),12583(a,1,1))].">
      <j1 rule="para" parents="8004 12583"/>
    </justification>
  </clause>

  <clause id="12585">
    <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(10816,a,12584,a),flip(a)].">
      <j1 rule="hyper" parents="10816 12584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12587">
    <literal><![CDATA[
      K(K(x,y) * K(z,x),R(u / K(x,y),K(x,y),K(z,x))) = (u * K(z,x)) \ (K(x,y) * (K(z,x) * (u * K(y,x))))
    ]]></literal>
    <justification jstring="[para(10014(a,1),12562(a,2,2))].">
      <j1 rule="para" parents="10014 12562"/>
    </justification>
  </clause>

  <clause id="12588">
    <literal><![CDATA[
      (x * (K(y,z) * u)) * K(z,L(y,K(z,y) \ (y \ u),x)) = x * (((K(z,y) \ (u / y)) * K(z,y)) * y)
    ]]></literal>
    <justification jstring="[para(5367(a,1),12563(a,1,1,2))].">
      <j1 rule="para" parents="5367 12563"/>
    </justification>
  </clause>

  <clause id="12589">
    <literal><![CDATA[
      (x * (K(y,z) * u)) * K(z,L(y,y \ u,x)) = x * (((K(z,y) \ (u / y)) * K(z,y)) * y)
    ]]></literal>
    <justification jstring="[para(11739(a,1),12588(a,1,2))].">
      <j1 rule="para" parents="11739 12588"/>
    </justification>
  </clause>

  <clause id="12590">
    <literal><![CDATA[
      (x * (K(y,z) * u)) * L(K(z,y),u,x) = x * (((K(z,y) \ (u / y)) * K(z,y)) * y)
    ]]></literal>
    <justification jstring="[para(9186(a,1),12589(a,1,2))].">
      <j1 rule="para" parents="9186 12589"/>
    </justification>
  </clause>

  <clause id="12592">
    <literal><![CDATA[
      (x * (K(y,z) * u)) * L(K(z,y),u,x) = x * (((K(y,z) * (u / y)) * K(z,y)) * y)
    ]]></literal>
    <justification jstring="[para(5426(a,1),12590(a,2,2,1,1))].">
      <j1 rule="para" parents="5426 12590"/>
    </justification>
  </clause>

  <clause id="12593">
    <literal><![CDATA[
      (x * (K(y,z) * u)) * L(K(z,y),u,x) = x * (T(u / y,K(y,z)) * y)
    ]]></literal>
    <justification jstring="[para(8055(a,1),12592(a,2,2,1))].">
      <j1 rule="para" parents="8055 12592"/>
    </justification>
  </clause>

  <clause id="12594">
    <literal><![CDATA[
      (x * (K(y,z) * u)) * L(K(z,y),u,x) = x * T((u / y) * y,K(y,z))
    ]]></literal>
    <justification jstring="[para(7401(a,2),12593(a,2,2))].">
      <j1 rule="para" parents="7401 12593"/>
    </justification>
  </clause>

  <clause id="12595">
    <literal><![CDATA[
      (x * (K(y,z) * u)) * L(K(z,y),u,x) = x * T(u,K(y,z))
    ]]></literal>
    <justification jstring="[para(12(a,1),12594(a,2,2,1))].">
      <j1 rule="para" parents="12 12594"/>
    </justification>
  </clause>

  <clause id="12596">
    <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(12595(a,1),6149(a,1,1,2))].">
      <j1 rule="para" parents="12595 6149"/>
    </justification>
  </clause>

  <clause id="12597">
    <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(12366(a,1),12575(a,1,1,1))].">
      <j1 rule="para" parents="12366 12575"/>
    </justification>
  </clause>

  <clause id="12598">
    <literal><![CDATA[
      K(K(x,y) * K(z,x),R(u / K(x,y),K(x,y),K(z,x))) = (u * K(z,x)) \ T(K(z,x) * u,K(x,y))
    ]]></literal>
    <justification jstring="[para(8460(a,1),12587(a,2,2))].">
      <j1 rule="para" parents="8460 12587"/>
    </justification>
  </clause>

  <clause id="12599">
    <literal><![CDATA[
      K(K(x,y) * K(z,x),R(u / K(x,y),K(x,y),K(z,x))) = K(K(z,x),u) * K(K(z,x) * u,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,9628,a(flip),b,12598,a),flip(a)].">
      <j1 rule="hyper" parents="299 9628 12598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12600">
    <literal><![CDATA[
      K(K(x,y) * K(z,x),R(u / K(x,y),K(x,y),K(z,x))) = K(u,K(z,x)) * K(K(z,x) * u,K(x,y))
    ]]></literal>
    <justification jstring="[para(8003(a,1),12599(a,2,1))].">
      <j1 rule="para" parents="8003 12599"/>
    </justification>
  </clause>

  <clause id="12601">
    <literal><![CDATA[
      K(K(x,y) * K(z,x),R(u / K(x,y),K(x,y),K(z,x))) = K(u,K(z,x)) * K(u,K(x,y))
    ]]></literal>
    <justification jstring="[para(8662(a,1),12600(a,2,2))].">
      <j1 rule="para" parents="8662 12600"/>
    </justification>
  </clause>

  <clause id="12602">
    <literal><![CDATA[
      K(K(x,y) * K(z,x),R(u / K(x,y),K(x,y),K(z,x))) = K(u,K(z,x) * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,12350,a(flip),b,12601,a),flip(a)].">
      <j1 rule="hyper" parents="299 12350 12601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12604">
    <literal><![CDATA[
      K(K(x,y) * K(z,x),R(u * K(y,x),K(x,y),K(z,x))) = K(u,K(z,x) * K(x,y))
    ]]></literal>
    <justification jstring="[para(7196(a,1),12602(a,1,2,1))].">
      <j1 rule="para" parents="7196 12602"/>
    </justification>
  </clause>

  <clause id="12605">
    <literal><![CDATA[
      K(K(x,y) * K(z,x),u * K(y,x)) = K(u,K(z,x) * K(x,y))
    ]]></literal>
    <justification jstring="[para(9210(a,1),12604(a,1,2))].">
      <j1 rule="para" parents="9210 12604"/>
    </justification>
  </clause>

  <clause id="12607">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) \ K(u,K(z,x) * K(x,y)) = K(x,T(z,u)) * K(y,T(x,u))
    ]]></literal>
    <justification jstring="[para(12605(a,1),12217(a,1,2))].">
      <j1 rule="para" parents="12605 12217"/>
    </justification>
  </clause>

  <clause id="12608">
    <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),6642(a,2,2,1,2))].">
      <j1 rule="para" parents="10 6642"/>
    </justification>
  </clause>

  <clause id="12609">
    <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(299,a,233,a(flip),b,12608,a),flip(a)].">
      <j1 rule="hyper" parents="299 233 12608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12610">
    <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(233(a,1),12609(a,1,2))].">
      <j1 rule="para" parents="233 12609"/>
    </justification>
  </clause>

  <clause id="12611">
    <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(5426(a,1),12610(a,1,2,2))].">
      <j1 rule="para" parents="5426 12610"/>
    </justification>
  </clause>

  <clause id="12612">
    <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(299,a,4125,a(flip),b,12611,a),flip(a)].">
      <j1 rule="hyper" parents="299 4125 12611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12613">
    <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(10150(a,1),9258(a,1,1,2))].">
      <j1 rule="para" parents="10150 9258"/>
    </justification>
  </clause>

  <clause id="12614">
    <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(9256(a,1),12613(a,1,2,1))].">
      <j1 rule="para" parents="9256 12613"/>
    </justification>
  </clause>

  <clause id="12615">
    <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(10871(a,1),12614(a,1,2,2))].">
      <j1 rule="para" parents="10871 12614"/>
    </justification>
  </clause>

  <clause id="12616">
    <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(4022(a,1),12615(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4022 12615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12618">
    <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(9256(a,1),12616(a,1,2,1))].">
      <j1 rule="para" parents="9256 12616"/>
    </justification>
  </clause>

  <clause id="12620">
    <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(10150(a,1),12618(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10150 12618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12621">
    <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(9256(a,1),12620(a,2,3))].">
      <j1 rule="para" parents="9256 12620"/>
    </justification>
  </clause>

  <clause id="12622">
    <literal><![CDATA[
      (x * (y \ R(y,z,y))) * (y \ L(y,z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(299,a,10470,a(flip),b,12621,a),flip(a)].">
      <j1 rule="hyper" parents="299 10470 12621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12624">
    <literal><![CDATA[
      (x * (K(T(y,z),u) * K(y * u,T(y,z)))) * (y \ L(y,u,y)) = x
    ]]></literal>
    <justification jstring="[para(11026(a,2),12622(a,1,1,2))].">
      <j1 rule="para" parents="11026 12622"/>
    </justification>
  </clause>

  <clause id="12625">
    <literal><![CDATA[
      K(x,T(y,z)) * K(T(y,z),y * x) = y \ L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(9244,a,12624,a)].">
      <j1 rule="hyper" parents="9244 12624"/>
    </justification>
  </clause>

  <clause id="12626">
    <literal><![CDATA[
      K(x,T(y,z)) * K(y,T(y * x,z)) = y \ L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(8392,a,12625,a)].">
      <j1 rule="hyper" parents="8392 12625"/>
    </justification>
  </clause>

  <clause id="12627">
    <literal><![CDATA[
      K(x,T(y,z)) * T(y,T(y * x,z)) = (y \ L(y,x,y)) * y
    ]]></literal>
    <justification jstring="[para(12626(a,1),6912(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12626 6912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12628">
    <literal><![CDATA[
      K(x,T(y,z)) * T(y,T(y * x,z)) = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,3815,a(flip),b,12627,a),flip(a)].">
      <j1 rule="hyper" parents="299 3815 12627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12629">
    <literal><![CDATA[
      (((x * (y * x)) / x) / y) * (z / (((x * (y * x)) / x) / y)) = z * K(L(x,T(y,x),x),T(x,y * x) \ z)
    ]]></literal>
    <justification jstring="[para(4593(a,1),9288(a,2,2,1))].">
      <j1 rule="para" parents="4593 9288"/>
    </justification>
  </clause>

  <clause id="12630">
    <literal><![CDATA[
      (((x * (y * x)) / x) / y) * (z / (((x * (y * x)) / x) / y)) = z * K(L(x,T(y,x),x),T(x,x * y) \ z)
    ]]></literal>
    <justification jstring="[para(4366(a,1),12629(a,2,2,2,1))].">
      <j1 rule="para" parents="4366 12629"/>
    </justification>
  </clause>

  <clause id="12631">
    <literal><![CDATA[
      (((x * (y * x)) / x) / y) * (z / (((x * (y * x)) / x) / y)) = z * K(x,T(x,x * y) \ z)
    ]]></literal>
    <justification jstring="[para(7435(a,1),12630(a,2,2))].">
      <j1 rule="para" parents="7435 12630"/>
    </justification>
  </clause>

  <clause id="12633">
    <literal><![CDATA[
      (((x * (y * x)) / x) / y) * (z / (((x * (y * x)) / x) / y)) = z * K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(8524(a,1),12631(a,2,2))].">
      <j1 rule="para" parents="8524 12631"/>
    </justification>
  </clause>

  <clause id="12634">
    <literal><![CDATA[
      (((x * (y * x)) / x) / y) * (z / (((x * (y * x)) / x) / y)) = x * (z / x)
    ]]></literal>
    <justification jstring="[hyper(299,a,5293,a(flip),b,12633,a),flip(a)].">
      <j1 rule="hyper" parents="299 5293 12633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12636">
    <literal><![CDATA[
      L(x,T(y,x),x) * (z / (((x * (y * x)) / x) / y)) = x * (z / x)
    ]]></literal>
    <justification jstring="[para(4593(a,1),12634(a,1,1))].">
      <j1 rule="para" parents="4593 12634"/>
    </justification>
  </clause>

  <clause id="12637">
    <literal><![CDATA[
      L(x,T(y,x),x) * (z / L(x,T(y,x),x)) = x * (z / x)
    ]]></literal>
    <justification jstring="[para(4593(a,1),12636(a,1,2,2))].">
      <j1 rule="para" parents="4593 12636"/>
    </justification>
  </clause>

  <clause id="12638">
    <literal><![CDATA[
      L(x,y,x) * (z / L(x,T(y,x),x)) = x * (z / x)
    ]]></literal>
    <justification jstring="[para(4592(a,1),12637(a,1,1))].">
      <j1 rule="para" parents="4592 12637"/>
    </justification>
  </clause>

  <clause id="12639">
    <literal><![CDATA[
      L(x,y,x) * (z / L(x,y,x)) = x * (z / x)
    ]]></literal>
    <justification jstring="[para(4592(a,1),12638(a,1,2,2))].">
      <j1 rule="para" parents="4592 12638"/>
    </justification>
  </clause>

  <clause id="12640">
    <literal><![CDATA[
      L(x,y,x) * ((z * x) / L(x,y,x)) = x * z
    ]]></literal>
    <justification jstring="[para(11(a,1),12639(a,2,2))].">
      <j1 rule="para" parents="11 12639"/>
    </justification>
  </clause>

  <clause id="12641">
    <literal><![CDATA[
      L(x,y,x) * (z * a(x,y,x)) = x * z
    ]]></literal>
    <justification jstring="[para(9710(a,1),12640(a,1,2))].">
      <j1 rule="para" parents="9710 12640"/>
    </justification>
  </clause>

  <clause id="12642">
    <literal><![CDATA[
      x * (y / a(x,z,x)) = L(x,z,x) * y
    ]]></literal>
    <justification jstring="[para(12(a,1),12641(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 12641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12643">
    <literal><![CDATA[
      L(x,y,x) * (a(x,y,x) * z) = x * z
    ]]></literal>
    <justification jstring="[para(10116(a,2),12641(a,1,2))].">
      <j1 rule="para" parents="10116 12641"/>
    </justification>
  </clause>

  <clause id="12644">
    <literal><![CDATA[
      L(x,y,x) * (x \ z) = z / a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(36,a,1350,a,b,12642,a)].">
      <j1 rule="hyper" parents="36 1350 12642"/>
    </justification>
  </clause>

  <clause id="12645">
    <literal><![CDATA[
      a(x,y,x) * (L(x,y,x) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(1355,a,12643,a),flip(a)].">
      <j1 rule="hyper" parents="1355 12643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12646">
    <literal><![CDATA[
      (x / y) \ (x / a(y,z,y)) = L(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,12644,a(flip),b,7666,a(flip))].">
      <j1 rule="hyper" parents="119 12644 7666"/>
    </justification>
  </clause>

  <clause id="12647">
    <literal><![CDATA[
      (x / y) \ (a(y,z,y) \ x) = L(y,z,y)
    ]]></literal>
    <justification jstring="[para(10121(a,1),12646(a,1,2))].">
      <j1 rule="para" parents="10121 12646"/>
    </justification>
  </clause>

  <clause id="12648">
    <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(2586(a,1),10242(a,1,1))].">
      <j1 rule="para" parents="2586 10242"/>
    </justification>
  </clause>

  <clause id="12649">
    <literal><![CDATA[
      (1 / R(x,y,z)) \ (K(x,u) / R(x,y,z)) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,9090,a(flip),b,12648,a),flip(a)].">
      <j1 rule="hyper" parents="299 9090 12648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12651">
    <literal><![CDATA[
      (1 / R(x,y,z)) * K(x,u) = K(x,u) / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(144,a,12649,a)].">
      <j1 rule="hyper" parents="144 12649"/>
    </justification>
  </clause>

  <clause id="12652">
    <literal><![CDATA[
      K(x,x * y) / T(x,y) = 1 / R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(37,a,8943,a,b,12651,a)].">
      <j1 rule="hyper" parents="37 8943 12651"/>
    </justification>
  </clause>

  <clause id="12653">
    <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(12651(a,1),12543(a,1,1))].">
      <j1 rule="para" parents="12651 12543"/>
    </justification>
  </clause>

  <clause id="12654">
    <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(11508(a,1),12653(a,1,2))].">
      <j1 rule="para" parents="11508 12653"/>
    </justification>
  </clause>

  <clause id="12655">
    <literal><![CDATA[
      (K(x,y) / R(x,z,u)) \ 1 = K(x,y) \ R(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(1289,a,12654,a)].">
      <j1 rule="hyper" parents="1289 12654"/>
    </justification>
  </clause>

  <clause id="12656">
    <literal><![CDATA[
      (K(x,y) / R(x,z,u)) \ 1 = K(y,x) * R(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,5426,a(flip),b,12655,a),flip(a)].">
      <j1 rule="hyper" parents="299 5426 12655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12657">
    <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(65,a,10715,a,b,12656,a)].">
      <j1 rule="hyper" parents="65 10715 12656"/>
    </justification>
  </clause>

  <clause id="12658">
    <literal><![CDATA[
      K(x,R(y,z,R(y,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3671,a,12657,a),flip(a)].">
      <j1 rule="hyper" parents="3671 12657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12659">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) = K(x,R(z,u,R(T(z,y),w,v5)))
    ]]></literal>
    <justification jstring="[hyper(8230,a,12658,a),flip(a)].">
      <j1 rule="hyper" parents="8230 12658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12661">
    <literal><![CDATA[
      K(x,R(y,z,R(T(y,u),w,v5))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8218,a,12659,a),flip(a)].">
      <j1 rule="hyper" parents="8218 12659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12663">
    <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(12661(a,1),11003(a,1,1))].">
      <j1 rule="para" parents="12661 11003"/>
    </justification>
  </clause>

  <clause id="12664">
    <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(5388,a,12663,a)].">
      <j1 rule="hyper" parents="5388 12663"/>
    </justification>
  </clause>

  <clause id="12665">
    <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(10852(a,1),12663(a,1,2,2))].">
      <j1 rule="para" parents="10852 12663"/>
    </justification>
  </clause>

  <clause id="12667">
    <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(12664(a,1),10610(a,1))].">
      <j1 rule="para" parents="12664 10610"/>
    </justification>
  </clause>

  <clause id="12668">
    <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(10822(a,1),12665(a,1,2))].">
      <j1 rule="para" parents="10822 12665"/>
    </justification>
  </clause>

  <clause id="12669">
    <literal><![CDATA[
      x \ R(x,y,R(T(x,z),u,w)) = a(x,y,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(5439,a,12668,a),flip(a)].">
      <j1 rule="hyper" parents="5439 12668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12670">
    <literal><![CDATA[
      a(T(x,y),z,R(T(x,y),u,w)) = a(x,z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(12667,a,12669,a)].">
      <j1 rule="hyper" parents="12667 12669"/>
    </justification>
  </clause>

  <clause id="12672">
    <literal><![CDATA[
      L(x,y,R(x,z,u)) \ x = a(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,11672,a(flip),b,12669,a)].">
      <j1 rule="hyper" parents="65 11672 12669"/>
    </justification>
  </clause>

  <clause id="12674">
    <literal><![CDATA[
      a(x,y,R(x,z,u)) \ x = L(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(12672(a,1),6373(a,1,1))].">
      <j1 rule="para" parents="12672 6373"/>
    </justification>
  </clause>

  <clause id="12675">
    <literal><![CDATA[
      a(R(x,y,z),u,x) \ 1 = a(x,u,R(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(12670(a,1),10954(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12670 10954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12676">
    <literal><![CDATA[
      a(R(x,y,z),u,x) = a(x,u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(273,a,12675,a),flip(a)].">
      <j1 rule="hyper" parents="273 12675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12678">
    <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(299,a,9565,a,b,12676,a)].">
      <j1 rule="hyper" parents="299 9565 12676"/>
    </justification>
  </clause>

  <clause id="12680">
    <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(6630(a,1),12678(a,1,1,2))].">
      <j1 rule="para" parents="6630 12678"/>
    </justification>
  </clause>

  <clause id="12681">
    <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(683(a,1),12680(a,1,1))].">
      <j1 rule="para" parents="683 12680"/>
    </justification>
  </clause>

  <clause id="12682">
    <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(234(a,1),12681(a,1,2)),flip(a)].">
      <j1 rule="para" parents="234 12681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12683">
    <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(299,a,2188,a(flip),b,12682,a),flip(a)].">
      <j1 rule="hyper" parents="299 2188 12682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12684">
    <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),12683(a,2,3))].">
      <j1 rule="para" parents="27 12683"/>
    </justification>
  </clause>

  <clause id="12685">
    <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(65,a,12676,a(flip),b,12684,a)].">
      <j1 rule="hyper" parents="65 12676 12684"/>
    </justification>
  </clause>

  <clause id="12686">
    <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(65,a,12670,a(flip),b,12685,a)].">
      <j1 rule="hyper" parents="65 12670 12685"/>
    </justification>
  </clause>

  <clause id="12688">
    <literal><![CDATA[
      a(x,x \ y,R(T(x,y),z,u)) = a(x,x \ y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,12527,a(flip),b,12686,a),flip(a)].">
      <j1 rule="hyper" parents="65 12527 12686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12690">
    <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(65,a,12279,a,b,12688,a)].">
      <j1 rule="hyper" parents="65 12279 12688"/>
    </justification>
  </clause>

  <clause id="12691">
    <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(10207,a,12690,a)].">
      <j1 rule="hyper" parents="10207 12690"/>
    </justification>
  </clause>

  <clause id="12692">
    <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(12691(a,1),12151(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12691 12151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12693">
    <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),12692(a,2,2,2))].">
      <j1 rule="para" parents="22 12692"/>
    </justification>
  </clause>

  <clause id="12694">
    <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(10843(a,1),12693(a,2,2))].">
      <j1 rule="para" parents="10843 12693"/>
    </justification>
  </clause>

  <clause id="12695">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) \ (1 * L(1 \ (((x * y) \ x) \ 1),z,u)) = (x \ (x / y)) \ L(x \ (x / y),z,u)
    ]]></literal>
    <justification jstring="[para(10415(a,1),10419(a,2,2,1))].">
      <j1 rule="para" parents="10415 10419"/>
    </justification>
  </clause>

  <clause id="12696">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) \ (1 * L(1 \ (((x * y) \ x) \ 1),z,u)) = x \ ((x / y) * L((x / y) \ x,z,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,6505,a(flip),b,12695,a),flip(a)].">
      <j1 rule="hyper" parents="299 6505 12695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12697">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) \ (1 * L(1 \ (((x * y) \ x) \ 1),z,u)) = x \ ((x / y) * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(79(a,1),12696(a,2,2,2,1))].">
      <j1 rule="para" parents="79 12696"/>
    </justification>
  </clause>

  <clause id="12698">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) \ (1 * L(((x * y) \ x) \ 1,z,u)) = x \ ((x / y) * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(67(a,1),12697(a,1,2,2,1))].">
      <j1 rule="para" parents="67 12697"/>
    </justification>
  </clause>

  <clause id="12699">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) \ L(((x * y) \ x) \ 1,z,u) = x \ ((x / y) * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(7(a,1),12698(a,1,2))].">
      <j1 rule="para" parents="7 12698"/>
    </justification>
  </clause>

  <clause id="12700">
    <literal><![CDATA[
      ((x * y) \ x) \ L((x * y) \ x,z,u) = x \ ((x / y) * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(6529,a,12699,a)].">
      <j1 rule="hyper" parents="6529 12699"/>
    </justification>
  </clause>

  <clause id="12701">
    <literal><![CDATA[
      (x * y) \ (x * L(x \ (x * y),z,u)) = x \ ((x / y) * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,6505,a(flip),b,12700,a)].">
      <j1 rule="hyper" parents="65 6505 12700"/>
    </justification>
  </clause>

  <clause id="12702">
    <literal><![CDATA[
      (x * y) \ (x * L(y,z,u)) = x \ ((x / y) * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),12701(a,1,2,2,1))].">
      <j1 rule="para" parents="9 12701"/>
    </justification>
  </clause>

  <clause id="12703">
    <literal><![CDATA[
      ((x * (y / x)) * x) \ (y * L(T(x,x \ y),z,u)) = y \ ((y / T(x,x \ y)) * L(T(x,x \ y),z,u))
    ]]></literal>
    <justification jstring="[para(4445(a,2),12702(a,1,1))].">
      <j1 rule="para" parents="4445 12702"/>
    </justification>
  </clause>

  <clause id="12704">
    <literal><![CDATA[
      K(x,K(L(y,z,u),w)) * ((v5 / T(y,L(x,z,u))) / (v5 / y)) = T(K(x,L(y,z,u)),w) * K(v5 / y,K(x,L(y,z,u)))
    ]]></literal>
    <justification jstring="[para(7954(a,1),11982(a,1,1))].">
      <j1 rule="para" parents="7954 11982"/>
    </justification>
  </clause>

  <clause id="12705">
    <literal><![CDATA[
      (x * (T(T(x,y),y) \ z)) \ ((u * K(y,x)) * (K(y,x) * z)) = R(T(u,x * (T(T(x,y),y) \ z)),K(y,x),K(y,x) * z)
    ]]></literal>
    <justification jstring="[para(6199(a,1),6200(a,1,1))].">
      <j1 rule="para" parents="6199 6200"/>
    </justification>
  </clause>

  <clause id="12706">
    <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(7312(a,1),9769(a,1,1,1))].">
      <j1 rule="para" parents="7312 9769"/>
    </justification>
  </clause>

  <clause id="12707">
    <literal><![CDATA[
      L((x \ y) \ y,T(x,y) \ y,(x \ y) \ y) = T(x,x * (y / T(x,y)))
    ]]></literal>
    <justification jstring="[para(4394(a,1),12706(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4394 12706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12708">
    <literal><![CDATA[
      L((x \ y) \ y,T(x,y) \ y,(x \ y) \ y) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,8619,a(flip),b,12707,a),flip(a)].">
      <j1 rule="hyper" parents="299 8619 12707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12710">
    <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(299,a,543,a(flip),b,11081,a),flip(a)].">
      <j1 rule="hyper" parents="299 543 11081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12711">
    <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(65,a,1871,a(flip),b,12710,a)].">
      <j1 rule="hyper" parents="65 1871 12710"/>
    </justification>
  </clause>

  <clause id="12712">
    <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(5433(a,1),12711(a,1,1,2,1))].">
      <j1 rule="para" parents="5433 12711"/>
    </justification>
  </clause>

  <clause id="12713">
    <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(5872(a,1),12712(a,1,1,2,1))].">
      <j1 rule="para" parents="5872 12712"/>
    </justification>
  </clause>

  <clause id="12714">
    <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(8135(a,1),12713(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8135 12713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12715">
    <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(65,a,4611,a(flip),b,12714,a),flip(a)].">
      <j1 rule="hyper" parents="65 4611 12714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12717">
    <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(12715(a,1),1967(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="12715 1967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12718">
    <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(5426(a,1),12717(a,1,1))].">
      <j1 rule="para" parents="5426 12717"/>
    </justification>
  </clause>

  <clause id="12719">
    <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(11715(a,1),12718(a,1,1))].">
      <j1 rule="para" parents="11715 12718"/>
    </justification>
  </clause>

  <clause id="12720">
    <literal><![CDATA[
      R(K(x,y),R(T(x,z),u,w),v5) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(312,a,12719,a),flip(a)].">
      <j1 rule="hyper" parents="312 12719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12723">
    <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(65,a,6218,a(flip),b,12720,a)].">
      <j1 rule="hyper" parents="65 6218 12720"/>
    </justification>
  </clause>

  <clause id="12724">
    <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(299,a,7616,a(flip),b,12723,a),flip(a)].">
      <j1 rule="hyper" parents="299 7616 12723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12725">
    <literal><![CDATA[
      K(x,y \ R(T(x,z),u,w)) = K(x,R(x,u,w) * (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(65,a,8641,a(flip),b,12724,a),flip(a)].">
      <j1 rule="hyper" parents="65 8641 12724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12727">
    <literal><![CDATA[
      K(x,y \ R(T(x,z),u,w)) = K(x,y \ R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(299,a,11852,a(flip),b,12725,a),flip(a)].">
      <j1 rule="hyper" parents="299 11852 12725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12728">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) / w) = K(x,w \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(8326,a,12727,a)].">
      <j1 rule="hyper" parents="8326 12727"/>
    </justification>
  </clause>

  <clause id="12730">
    <literal><![CDATA[
      K((x \ y) \ T(y,x),z \ L((x \ y) \ T(y,x),u,w)) = K(x,z \ L(L(T(x,x \ y),y,x),u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,7444,a(flip),b,11103,a),flip(a)].">
      <j1 rule="hyper" parents="65 7444 11103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12732">
    <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(5197(a,1),12612(a,2,1,2,1))].">
      <j1 rule="para" parents="5197 12612"/>
    </justification>
  </clause>

  <clause id="12733">
    <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(10536(a,1),12732(a,2,1))].">
      <j1 rule="para" parents="10536 12732"/>
    </justification>
  </clause>

  <clause id="12734">
    <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(6350(a,1),12733(a,1,2,2,2,1))].">
      <j1 rule="para" parents="6350 12733"/>
    </justification>
  </clause>

  <clause id="12735">
    <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(65,a,12611,a(flip),b,12734,a)].">
      <j1 rule="hyper" parents="65 12611 12734"/>
    </justification>
  </clause>

  <clause id="12736">
    <literal><![CDATA[
      a(x,y,L(K(z,u),w,v5)) = L(a(x,y,K(z,u)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,11808,a(flip),b,12735,a)].">
      <j1 rule="hyper" parents="65 11808 12735"/>
    </justification>
  </clause>

  <clause id="12737">
    <literal><![CDATA[
      a(x,y,K(z,L(u,w,v5))) = L(a(x,y,K(z,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(11889(a,1),12736(a,1,3))].">
      <j1 rule="para" parents="11889 12736"/>
    </justification>
  </clause>

  <clause id="12738">
    <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(9221(a,1),9226(a,1,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="9221 9226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12739">
    <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),12738(a,2,1,2,1))].">
      <j1 rule="para" parents="9 12738"/>
    </justification>
  </clause>

  <clause id="12741">
    <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(9221(a,1),12739(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9221 12739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12742">
    <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(2281(a,1),12741(a,2,2))].">
      <j1 rule="para" parents="2281 12741"/>
    </justification>
  </clause>

  <clause id="12743">
    <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(65,a,10772,a,b,12742,a)].">
      <j1 rule="hyper" parents="65 10772 12742"/>
    </justification>
  </clause>

  <clause id="12744">
    <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(12742(a,1),12295(a,1,1))].">
      <j1 rule="para" parents="12742 12295"/>
    </justification>
  </clause>

  <clause id="12745">
    <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(308,a,12743,a),flip(a)].">
      <j1 rule="hyper" parents="308 12743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12746">
    <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(5429(a,1),12744(a,1,1,2))].">
      <j1 rule="para" parents="5429 12744"/>
    </justification>
  </clause>

  <clause id="12747">
    <literal><![CDATA[
      x / a(K(y,z),u,u \ 1) = x * a(K(z,y),u,u \ 1)
    ]]></literal>
    <justification jstring="[hyper(9232,a,12746,a),flip(a)].">
      <j1 rule="hyper" parents="9232 12746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12748">
    <literal><![CDATA[
      a(K(x,y),z,z \ 1) \ 1 = a(K(y,x),z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(4073,a,12747,a)].">
      <j1 rule="hyper" parents="4073 12747"/>
    </justification>
  </clause>

  <clause id="12750">
    <literal><![CDATA[
      K(x,a(K(y,z),u,u \ 1)) = 1
    ]]></literal>
    <justification jstring="[para(12748(a,1),11096(a,1,2))].">
      <j1 rule="para" parents="12748 11096"/>
    </justification>
  </clause>

  <clause id="12751">
    <literal><![CDATA[
      T(x,a(K(y,z),u,u \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,12750,a)].">
      <j1 rule="hyper" parents="58 12750"/>
    </justification>
  </clause>

  <clause id="12752">
    <literal><![CDATA[
      T(x,a(K(y,z),u \ 1,u)) = x
    ]]></literal>
    <justification jstring="[para(2365(a,1),12751(a,1,2))].">
      <j1 rule="para" parents="2365 12751"/>
    </justification>
  </clause>

  <clause id="12753">
    <literal><![CDATA[
      T(a(K(x,y),z \ 1,z),u) = a(K(x,y),z \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(56,a,12752,a)].">
      <j1 rule="hyper" parents="56 12752"/>
    </justification>
  </clause>

  <clause id="12754">
    <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(299,a,2704,a,b,12753,a),flip(a)].">
      <j1 rule="hyper" parents="299 2704 12753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12755">
    <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(5435(a,2),12754(a,1,1))].">
      <j1 rule="para" parents="5435 12754"/>
    </justification>
  </clause>

  <clause id="12756">
    <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(65,a,10305,a,b,12755,a)].">
      <j1 rule="hyper" parents="65 10305 12755"/>
    </justification>
  </clause>

  <clause id="12757">
    <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(65,a,7521,a,b,12756,a)].">
      <j1 rule="hyper" parents="65 7521 12756"/>
    </justification>
  </clause>

  <clause id="12758">
    <literal><![CDATA[
      K(x,K(y,R(z,u \ 1,u))) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(11184,a,12757,a)].">
      <j1 rule="hyper" parents="11184 12757"/>
    </justification>
  </clause>

  <clause id="12759">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ 1))) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(2703(a,1),12758(a,1,2,2))].">
      <j1 rule="para" parents="2703 12758"/>
    </justification>
  </clause>

  <clause id="12760">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ 1))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,8004,a,b,12759,a),flip(a)].">
      <j1 rule="hyper" parents="299 8004 12759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12761">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ K(w,x)))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,12163,a,b,12759,a)].">
      <j1 rule="hyper" parents="65 12163 12759"/>
    </justification>
  </clause>

  <clause id="12762">
    <literal><![CDATA[
      T(x,K(y,R(z,u,u \ 1))) = x * K(y,K(z,x))
    ]]></literal>
    <justification jstring="[para(12759(a,1),7990(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12759 7990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12763">
    <literal><![CDATA[
      K(x,K(y,z * (u \ 1))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[para(565(a,1),12760(a,1,2,2))].">
      <j1 rule="para" parents="565 12760"/>
    </justification>
  </clause>

  <clause id="12764">
    <literal><![CDATA[
      K(x,K(y,z / (1 / u))) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(79(a,1),12763(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="79 12763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12765">
    <literal><![CDATA[
      K(x,K(y,z * (1 / u))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[para(5639(a,2),12763(a,1,2))].">
      <j1 rule="para" parents="5639 12763"/>
    </justification>
  </clause>

  <clause id="12766">
    <literal><![CDATA[
      K(x,K(y,z / (u \ 1))) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(5641(a,1),12763(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5641 12763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12767">
    <literal><![CDATA[
      K(x,K(y,(1 / z) / u)) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(8828,a,12764,a)].">
      <j1 rule="hyper" parents="8828 12764"/>
    </justification>
  </clause>

  <clause id="12768">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) / u)) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(8828,a,12766,a)].">
      <j1 rule="hyper" parents="8828 12766"/>
    </justification>
  </clause>

  <clause id="12769">
    <literal><![CDATA[
      K(x,K(y / (z \ 1),u)) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(8035,a,12766,a)].">
      <j1 rule="hyper" parents="8035 12766"/>
    </justification>
  </clause>

  <clause id="12770">
    <literal><![CDATA[
      K(x,K(T(y,z),z * u)) = K(x,K(y,(u \ 1) \ z))
    ]]></literal>
    <justification jstring="[para(7538(a,1),12766(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7538 12766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12771">
    <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(12767(a,1),11956(a,1,3))].">
      <j1 rule="para" parents="12767 11956"/>
    </justification>
  </clause>

  <clause id="12772">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) / (u / z))) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(12(a,1),12768(a,2,2,2))].">
      <j1 rule="para" parents="12 12768"/>
    </justification>
  </clause>

  <clause id="12773">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) / (u / z))) = K(y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(7985,a,12772,a)].">
      <j1 rule="hyper" parents="7985 12772"/>
    </justification>
  </clause>

  <clause id="12774">
    <literal><![CDATA[
      K(x,(T(y,z) / u) / (y / u)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,8797,a(flip),b,12773,a)].">
      <j1 rule="hyper" parents="65 8797 12773"/>
    </justification>
  </clause>

  <clause id="12776">
    <literal><![CDATA[
      K(x,K(y,z)) * (z / u) = T(z,K(x,y)) / u
    ]]></literal>
    <justification jstring="[para(12774(a,1),9898(a,1,1))].">
      <j1 rule="para" parents="12774 9898"/>
    </justification>
  </clause>

  <clause id="12777">
    <literal><![CDATA[
      R(K(x,K(y,z)),z / u,u) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(12774(a,1),10495(a,1,1))].">
      <j1 rule="para" parents="12774 10495"/>
    </justification>
  </clause>

  <clause id="12778">
    <literal><![CDATA[
      R(K(x,K(y,z)),y / u,u) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(8004(a,1),12777(a,1,1))].">
      <j1 rule="para" parents="8004 12777"/>
    </justification>
  </clause>

  <clause id="12780">
    <literal><![CDATA[
      K(x,K(y,R(z,x / u,u))) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,9323,a(flip),b,12778,a)].">
      <j1 rule="hyper" parents="65 9323 12778"/>
    </justification>
  </clause>

  <clause id="12781">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ x))) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(76(a,1),12780(a,1,2,2,2))].">
      <j1 rule="para" parents="76 12780"/>
    </justification>
  </clause>

  <clause id="12782">
    <literal><![CDATA[
      K(x,K(y,z)) * (T(z,K(x,y)) / u) = z / u
    ]]></literal>
    <justification jstring="[hyper(8030,a,12776,a)].">
      <j1 rule="hyper" parents="8030 12776"/>
    </justification>
  </clause>

  <clause id="12783">
    <literal><![CDATA[
      T(x,K(y,z)) / (u \ x) = K(y,K(z,x)) * u
    ]]></literal>
    <justification jstring="[para(76(a,1),12776(a,1,2)),flip(a)].">
      <j1 rule="para" parents="76 12776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12785">
    <literal><![CDATA[
      K(x,K(y,z)) * (T(x,K(z,y)) / u) = x / u
    ]]></literal>
    <justification jstring="[para(7952(a,1),12782(a,1,1))].">
      <j1 rule="para" parents="7952 12782"/>
    </justification>
  </clause>

  <clause id="12786">
    <literal><![CDATA[
      T(x,K(y,z)) / (u \ x) = K(x,K(y,z)) * u
    ]]></literal>
    <justification jstring="[para(7989(a,1),12783(a,2,1))].">
      <j1 rule="para" parents="7989 12783"/>
    </justification>
  </clause>

  <clause id="12787">
    <literal><![CDATA[
      K((T(x,y) / z) / (x / z),u) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(9900,a,12785,a)].">
      <j1 rule="hyper" parents="9900 12785"/>
    </justification>
  </clause>

  <clause id="12788">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) \ T(x,K(y,z)) = u \ x
    ]]></literal>
    <justification jstring="[hyper(186,a,12786,a)].">
      <j1 rule="hyper" parents="186 12786"/>
    </justification>
  </clause>

  <clause id="12789">
    <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(12286(a,1),12787(a,1,1,1,1))].">
      <j1 rule="para" parents="12286 12787"/>
    </justification>
  </clause>

  <clause id="12790">
    <literal><![CDATA[
      L(x \ y,x,K(y,K(z,u))) = x \ y
    ]]></literal>
    <justification jstring="[hyper(5172,a,12788,a)].">
      <j1 rule="hyper" parents="5172 12788"/>
    </justification>
  </clause>

  <clause id="12791">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,u \ x) = 1
    ]]></literal>
    <justification jstring="[hyper(55,a,12790,a)].">
      <j1 rule="hyper" parents="55 12790"/>
    </justification>
  </clause>

  <clause id="12792">
    <literal><![CDATA[
      a(K(x * y,K(z,u)),x,y) = 1
    ]]></literal>
    <justification jstring="[para(9(a,1),12791(a,1,3))].">
      <j1 rule="para" parents="9 12791"/>
    </justification>
  </clause>

  <clause id="12793">
    <literal><![CDATA[
      a(K(K(x,y),z),u,u \ z) = 1
    ]]></literal>
    <justification jstring="[para(6247(a,2),12791(a,1,1))].">
      <j1 rule="para" parents="6247 12791"/>
    </justification>
  </clause>

  <clause id="12794">
    <literal><![CDATA[
      a(K(x,K(y,z * u)),z,u) = 1
    ]]></literal>
    <justification jstring="[para(7952(a,1),12792(a,1,1))].">
      <j1 rule="para" parents="7952 12792"/>
    </justification>
  </clause>

  <clause id="12795">
    <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(299,a,8027,a,b,12793,a),flip(a)].">
      <j1 rule="hyper" parents="299 8027 12793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12797">
    <literal><![CDATA[
      T(x,K(y,R(z,u,u \ 1))) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,7958,a(flip),b,12762,a),flip(a)].">
      <j1 rule="hyper" parents="299 7958 12762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12798">
    <literal><![CDATA[
      T(x,K(y,T(z * (u \ 1),u))) = T(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,9622,a(flip),b,12797,a)].">
      <j1 rule="hyper" parents="65 9622 12797"/>
    </justification>
  </clause>

  <clause id="12799">
    <literal><![CDATA[
      K(x,K(y,T(z * u,z))) = K(x,K(y,(u \ 1) \ z))
    ]]></literal>
    <justification jstring="[para(7537(a,1),12770(a,1,2))].">
      <j1 rule="para" parents="7537 12770"/>
    </justification>
  </clause>

  <clause id="12800">
    <literal><![CDATA[
      T(x,K(y,z * (x \ 1))) = T(x,K(y,x \ z))
    ]]></literal>
    <justification jstring="[hyper(7514,a,12798,a)].">
      <j1 rule="hyper" parents="7514 12798"/>
    </justification>
  </clause>

  <clause id="12802">
    <literal><![CDATA[
      T(x,K(T(y,z),z \ u)) = T(x,K(y,u * (z \ 1)))
    ]]></literal>
    <justification jstring="[para(8106(a,1),12798(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8106 12798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12803">
    <literal><![CDATA[
      T(x,K(y,z * (x \ 1))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,8849,a(flip),b,12800,a),flip(a)].">
      <j1 rule="hyper" parents="299 8849 12800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12804">
    <literal><![CDATA[
      T(x \ 1,K(y,z * x)) = T(x \ 1,K(y,z))
    ]]></literal>
    <justification jstring="[para(5641(a,1),12803(a,1,2))].">
      <j1 rule="para" parents="5641 12803"/>
    </justification>
  </clause>

  <clause id="12805">
    <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(12804(a,1),5227(a,1,1))].">
      <j1 rule="para" parents="12804 5227"/>
    </justification>
  </clause>

  <clause id="12806">
    <literal><![CDATA[
      T(x,K(y,z * (u \ 1))) = T(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[para(8128(a,1),12802(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8128 12802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12807">
    <literal><![CDATA[
      T(T(x,y),K(y,z / u)) = T(x,T(y,(z * (u \ 1)) \ 1))
    ]]></literal>
    <justification jstring="[hyper(8816,a,12806,a),flip(a)].">
      <j1 rule="hyper" parents="8816 12806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12808">
    <literal><![CDATA[
      T(x,T(y,(z * (u \ 1)) \ 1)) = T(x,T(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(7154,a,12807,a),flip(a)].">
      <j1 rule="hyper" parents="7154 12807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12809">
    <literal><![CDATA[
      T(x,T(y,z * (u \ 1))) = T(x,T(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(8840,a,12808,a)].">
      <j1 rule="hyper" parents="8840 12808"/>
    </justification>
  </clause>

  <clause id="12810">
    <literal><![CDATA[
      T(x,T(y,z * (u \ 1))) = x * K(x,T(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(299,a,5083,a(flip),b,12809,a),flip(a)].">
      <j1 rule="hyper" parents="299 5083 12809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12811">
    <literal><![CDATA[
      K(x,T(y,z * (u \ 1))) = K(x,T(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(5154,a,12810,a)].">
      <j1 rule="hyper" parents="5154 12810"/>
    </justification>
  </clause>

  <clause id="12812">
    <literal><![CDATA[
      R(K(x,T(y,(z * x) / z)),z * x,z \ 1) = K(x,((y \ (z * x)) * (z \ 1)) \ x)
    ]]></literal>
    <justification jstring="[para(12811(a,1),11671(a,1,1))].">
      <j1 rule="para" parents="12811 11671"/>
    </justification>
  </clause>

  <clause id="12813">
    <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(12781(a,1),12795(a,2,2))].">
      <j1 rule="para" parents="12781 12795"/>
    </justification>
  </clause>

  <clause id="12814">
    <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(7989(a,2),12813(a,2,2))].">
      <j1 rule="para" parents="7989 12813"/>
    </justification>
  </clause>

  <clause id="12815">
    <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(6247(a,1),12814(a,1,1))].">
      <j1 rule="para" parents="6247 12814"/>
    </justification>
  </clause>

  <clause id="12816">
    <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(299,a,12345,a(flip),b,12815,a)].">
      <j1 rule="hyper" parents="299 12345 12815"/>
    </justification>
  </clause>

  <clause id="12817">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ x)) * K(z,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(299,a,12794,a(flip),b,12816,a),flip(a)].">
      <j1 rule="hyper" parents="299 12794 12816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12818">
    <literal><![CDATA[
      K(x,K(y,z) * K(z,R(y,u,u \ x))) = 1
    ]]></literal>
    <justification jstring="[hyper(65,a,12358,a(flip),b,12817,a)].">
      <j1 rule="hyper" parents="65 12358 12817"/>
    </justification>
  </clause>

  <clause id="12819">
    <literal><![CDATA[
      K(x * y,K(z,u) * K(u,R(z,x,y))) = 1
    ]]></literal>
    <justification jstring="[para(9(a,1),12818(a,1,2,2,2,3))].">
      <j1 rule="para" parents="9 12818"/>
    </justification>
  </clause>

  <clause id="12820">
    <literal><![CDATA[
      R(K(x,T(y,T(x,z))),z * x,z \ 1) = K(x,((y \ (z * x)) * (z \ 1)) \ x)
    ]]></literal>
    <justification jstring="[para(8182(a,1),12812(a,1,1,2))].">
      <j1 rule="para" parents="8182 12812"/>
    </justification>
  </clause>

  <clause id="12821">
    <literal><![CDATA[
      K(x,((y \ (z * x)) * (z \ 1)) \ x) = R(K(x,y),z * x,z \ 1)
    ]]></literal>
    <justification jstring="[para(5475(a,1),12820(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5475 12820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12822">
    <literal><![CDATA[
      K(x,((y \ (z * x)) * (z \ 1)) \ x) = K(R(x,z,z \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(299,a,10809,a(flip),b,12821,a),flip(a)].">
      <j1 rule="hyper" parents="299 10809 12821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12824">
    <literal><![CDATA[
      K(R(x,y,y \ 1),R(z,z \ y,x)) = K(x,(((z \ y) * x) * (y \ 1)) \ x)
    ]]></literal>
    <justification jstring="[para(580(a,1),12822(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="580 12822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12825">
    <literal><![CDATA[
      R(K(R(x,y,y \ 1),z),y,x) = K(x,(((z \ y) * x) * (y \ 1)) \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,6432,a(flip),b,12824,a)].">
      <j1 rule="hyper" parents="65 6432 12824"/>
    </justification>
  </clause>

  <clause id="12826">
    <literal><![CDATA[
      K(x,(((y \ z) * x) * (z \ 1)) \ x) = K(R(x,z,z \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(65,a,11077,a(flip),b,12825,a),flip(a)].">
      <j1 rule="hyper" parents="65 11077 12825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12828">
    <literal><![CDATA[
      K(x,((y \ z) * (z \ 1)) \ (x \ x)) = K(R(x,z,z \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(65,a,11204,a(flip),b,12826,a)].">
      <j1 rule="hyper" parents="65 11204 12826"/>
    </justification>
  </clause>

  <clause id="12829">
    <literal><![CDATA[
      K(x,((y \ z) * (z \ 1)) \ 1) = K(R(x,z,z \ 1),y)
    ]]></literal>
    <justification jstring="[para(68(a,1),12828(a,1,2,2))].">
      <j1 rule="para" parents="68 12828"/>
    </justification>
  </clause>

  <clause id="12830">
    <literal><![CDATA[
      R(K(x,y),z,z \ 1) = K(R(x,z,z \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(65,a,6220,a(flip),b,12829,a)].">
      <j1 rule="hyper" parents="65 6220 12829"/>
    </justification>
  </clause>

  <clause id="12832">
    <literal><![CDATA[
      R(K(x,y),z,z \ 1) \ 1 = K(y,R(x,z,z \ 1))
    ]]></literal>
    <justification jstring="[para(12830(a,2),5197(a,1,1))].">
      <j1 rule="para" parents="12830 5197"/>
    </justification>
  </clause>

  <clause id="12833">
    <literal><![CDATA[
      R(K(x,y),z,z \ 1) = K(x,R(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(6299,a,12832,a)].">
      <j1 rule="hyper" parents="6299 12832"/>
    </justification>
  </clause>

  <clause id="12834">
    <literal><![CDATA[
      K(x,(y * z) * (z \ 1)) = R(K(x,y),z,z \ 1)
    ]]></literal>
    <justification jstring="[para(258(a,2),12833(a,2,2)),flip(a)].">
      <j1 rule="para" parents="258 12833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12835">
    <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(5385(a,2),12789(a,1,1))].">
      <j1 rule="para" parents="5385 12789"/>
    </justification>
  </clause>

  <clause id="12836">
    <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(8201,a,12835,a)].">
      <j1 rule="hyper" parents="8201 12835"/>
    </justification>
  </clause>

  <clause id="12837">
    <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(65,a,12769,a(flip),b,12836,a)].">
      <j1 rule="hyper" parents="65 12769 12836"/>
    </justification>
  </clause>

  <clause id="12838">
    <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),12837(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 12837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12839">
    <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(12838(a,1),7953(a,1))].">
      <j1 rule="para" parents="12838 7953"/>
    </justification>
  </clause>

  <clause id="12840">
    <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(3434(a,1),9607(a,2,1,2))].">
      <j1 rule="para" parents="3434 9607"/>
    </justification>
  </clause>

  <clause id="12841">
    <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(711(a,1),12840(a,1,1,2,2))].">
      <j1 rule="para" parents="711 12840"/>
    </justification>
  </clause>

  <clause id="12842">
    <literal><![CDATA[
      K(x * T((y * z) \ z,y),y \ 1) = K(x * R(y \ 1,y,z),y \ 1)
    ]]></literal>
    <justification jstring="[para(3907(a,1),12841(a,1,1,2))].">
      <j1 rule="para" parents="3907 12841"/>
    </justification>
  </clause>

  <clause id="12843">
    <literal><![CDATA[
      K(x * R(y \ 1,y,z),y \ 1) = K(x * ((y * z) \ z),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,5743,a(flip),b,12842,a),flip(a)].">
      <j1 rule="hyper" parents="65 5743 12842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12844">
    <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(7954(a,1),12805(a,1,2,1,2))].">
      <j1 rule="para" parents="7954 12805"/>
    </justification>
  </clause>

  <clause id="12845">
    <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(8788(a,1),12844(a,1,2,1,2))].">
      <j1 rule="para" parents="8788 12844"/>
    </justification>
  </clause>

  <clause id="12846">
    <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(7987(a,1),12845(a,1,2,1,2))].">
      <j1 rule="para" parents="7987 12845"/>
    </justification>
  </clause>

  <clause id="12847">
    <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(5160(a,2),12846(a,1,2,1))].">
      <j1 rule="para" parents="5160 12846"/>
    </justification>
  </clause>

  <clause id="12848">
    <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(6000,a,12847,a)].">
      <j1 rule="hyper" parents="6000 12847"/>
    </justification>
  </clause>

  <clause id="12849">
    <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(8800(a,1),12848(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8800 12848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12850">
    <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(1412(a,1),12849(a,2,2))].">
      <j1 rule="para" parents="1412 12849"/>
    </justification>
  </clause>

  <clause id="12851">
    <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(299,a,8029,a(flip),b,12850,a),flip(a)].">
      <j1 rule="hyper" parents="299 8029 12850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12852">
    <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(299,a,6731,a(flip),b,12851,a),flip(a)].">
      <j1 rule="hyper" parents="299 6731 12851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12853">
    <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(1273(a,1),12852(a,1,1))].">
      <j1 rule="para" parents="1273 12852"/>
    </justification>
  </clause>

  <clause id="12854">
    <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),9553(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 9553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12855">
    <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(299,a,7493,a(flip),b,12854,a),flip(a)].">
      <j1 rule="hyper" parents="299 7493 12854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12857">
    <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(299,a,10734,a(flip),b,12855,a),flip(a)].">
      <j1 rule="hyper" parents="299 10734 12855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12858">
    <literal><![CDATA[
      K(x,T((R(x,y,z) \ u) \ w,R(x,y,z) * (x \ w))) = K(x,(R(x,y,z) * w) / u)
    ]]></literal>
    <justification jstring="[hyper(7709,a,12857,a)].">
      <j1 rule="hyper" parents="7709 12857"/>
    </justification>
  </clause>

  <clause id="12859">
    <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(65,a,9478,a(flip),b,12858,a)].">
      <j1 rule="hyper" parents="65 9478 12858"/>
    </justification>
  </clause>

  <clause id="12860">
    <literal><![CDATA[
      K(x,T((R(x,y,z) \ u) \ w,w)) = K(x,(R(x,y,z) * w) / u)
    ]]></literal>
    <justification jstring="[hyper(10776,a,12859,a)].">
      <j1 rule="hyper" parents="10776 12859"/>
    </justification>
  </clause>

  <clause id="12861">
    <literal><![CDATA[
      K(x,(R(x,y,z) * u) / w) = K(x,u / (R(x,y,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(8327,a,12860,a),flip(a)].">
      <j1 rule="hyper" parents="8327 12860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12863">
    <literal><![CDATA[
      K(x,R(x,y,z) / (u / w)) = K(x,w / (R(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,11515,a(flip),b,12861,a)].">
      <j1 rule="hyper" parents="65 11515 12861"/>
    </justification>
  </clause>

  <clause id="12864">
    <literal><![CDATA[
      K(x,y / (R(x,z,u) \ w)) = K(x,(w / y) \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(7112,a,12863,a),flip(a)].">
      <j1 rule="hyper" parents="7112 12863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12865">
    <literal><![CDATA[
      K(x,(y * R(x,z,u)) / w) = K(x,(w / y) \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,9317,a,b,12864,a)].">
      <j1 rule="hyper" parents="65 9317 12864"/>
    </justification>
  </clause>

  <clause id="12866">
    <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(65,a,12306,a,b,12865,a)].">
      <j1 rule="hyper" parents="65 12306 12865"/>
    </justification>
  </clause>

  <clause id="12867">
    <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),12866(a,2,2,1))].">
      <j1 rule="para" parents="20 12866"/>
    </justification>
  </clause>

  <clause id="12868">
    <literal><![CDATA[
      K(x,R(y,z,u) \ R(x,z,u)) = K(R(x,z,u),y \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,10083,a(flip),b,12867,a),flip(a)].">
      <j1 rule="hyper" parents="65 10083 12867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12870">
    <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(5426(a,1),10942(a,1,1,1))].">
      <j1 rule="para" parents="5426 10942"/>
    </justification>
  </clause>

  <clause id="12871">
    <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(12115(a,1),12870(a,1,1))].">
      <j1 rule="para" parents="12115 12870"/>
    </justification>
  </clause>

  <clause id="12872">
    <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(7113,a,12871,a)].">
      <j1 rule="hyper" parents="7113 12871"/>
    </justification>
  </clause>

  <clause id="12874">
    <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(65,a,12375,a(flip),b,12872,a)].">
      <j1 rule="hyper" parents="65 12375 12872"/>
    </justification>
  </clause>

  <clause id="12875">
    <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(65,a,12354,a(flip),b,12874,a),flip(a)].">
      <j1 rule="hyper" parents="65 12354 12874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12876">
    <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(299,a,12358,a(flip),b,12875,a),flip(a)].">
      <j1 rule="hyper" parents="299 12358 12875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12877">
    <literal><![CDATA[
      K(a(K(x,y),z,u),((z * u) \ K(y,x)) \ 1) = 1
    ]]></literal>
    <justification jstring="[hyper(299,a,12819,a(flip),b,12876,a),flip(a)].">
      <j1 rule="hyper" parents="299 12819 12876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12878">
    <literal><![CDATA[
      K(a(K(x,y),z,u),K(x,y) * (z * u)) = 1
    ]]></literal>
    <justification jstring="[hyper(7113,a,12877,a)].">
      <j1 rule="hyper" parents="7113 12877"/>
    </justification>
  </clause>

  <clause id="12880">
    <literal><![CDATA[
      1 * (((K(x,y) * z) * u) / (K(x,y) * (z * u))) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(12878(a,1),5265(a,1,1))].">
      <j1 rule="para" parents="12878 5265"/>
    </justification>
  </clause>

  <clause id="12881">
    <literal><![CDATA[
      1 * (K(x,y) * R(K(y,x),z,u)) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(12116(a,1),12880(a,1,2))].">
      <j1 rule="para" parents="12116 12880"/>
    </justification>
  </clause>

  <clause id="12882">
    <literal><![CDATA[
      K(x,y) * R(K(y,x),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(122,a,12881,a)].">
      <j1 rule="hyper" parents="122 12881"/>
    </justification>
  </clause>

  <clause id="12883">
    <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(8003(a,1),12881(a,1,2,1))].">
      <j1 rule="para" parents="8003 12881"/>
    </justification>
  </clause>

  <clause id="12884">
    <literal><![CDATA[
      K(x,y) * a(K(x,y),z,u) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(5437,a,12882,a)].">
      <j1 rule="hyper" parents="5437 12882"/>
    </justification>
  </clause>

  <clause id="12885">
    <literal><![CDATA[
      R(K(x,y),z,u) * K(y,x) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(2287,a,12882,a)].">
      <j1 rule="hyper" parents="2287 12882"/>
    </justification>
  </clause>

  <clause id="12886">
    <literal><![CDATA[
      K(x \ 1,y) * K(y,R(x,z,u) \ 1) = a(K(y,x \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(6209(a,1),12882(a,1,2))].">
      <j1 rule="para" parents="6209 12882"/>
    </justification>
  </clause>

  <clause id="12887">
    <literal><![CDATA[
      K(x,y) * (R(K(y,x),z,u) * w) = a(K(y,x),z,u) * w
    ]]></literal>
    <justification jstring="[para(12882(a,1),6766(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12882 6766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12889">
    <literal><![CDATA[
      K(x,y) * K(y,R(x,z,u)) = a(K(y,x),z * x,u)
    ]]></literal>
    <justification jstring="[para(9997(a,1),12882(a,1,2))].">
      <j1 rule="para" parents="9997 12882"/>
    </justification>
  </clause>

  <clause id="12890">
    <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(12882(a,1),12361(a,2,2))].">
      <j1 rule="para" parents="12882 12361"/>
    </justification>
  </clause>

  <clause id="12891">
    <literal><![CDATA[
      K(K(x,y) * K(y,R(x,z,u)),w) = K(a(K(y,x),z,u),w)
    ]]></literal>
    <justification jstring="[para(12882(a,1),12375(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12882 12375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12892">
    <literal><![CDATA[
      (x * a(K(y,z),u,w)) * (K(y,z) * R(K(z,y),u,w)) = x
    ]]></literal>
    <justification jstring="[para(12882(a,1),12745(a,1,1,2))].">
      <j1 rule="para" parents="12882 12745"/>
    </justification>
  </clause>

  <clause id="12893">
    <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(12884(a,1),10680(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12884 10680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12894">
    <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(12885(a,1),10311(a,2,2))].">
      <j1 rule="para" parents="12885 10311"/>
    </justification>
  </clause>

  <clause id="12895">
    <literal><![CDATA[
      K(x,y) * (a(K(x,y),z,u) * w) = R(K(x,y),z,u) * w
    ]]></literal>
    <justification jstring="[hyper(5437,a,12887,a)].">
      <j1 rule="hyper" parents="5437 12887"/>
    </justification>
  </clause>

  <clause id="12898">
    <literal><![CDATA[
      K(x,K(y,z) * K(R(z,u,w),y)) = K(a(K(y,z),u,w),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,12335,a(flip),b,12891,a)].">
      <j1 rule="hyper" parents="65 12335 12891"/>
    </justification>
  </clause>

  <clause id="12899">
    <literal><![CDATA[
      (x * a(K(y,z),u,w)) * a(K(z,y),u,w) = x
    ]]></literal>
    <justification jstring="[para(12882(a,1),12892(a,1,2))].">
      <j1 rule="para" parents="12882 12892"/>
    </justification>
  </clause>

  <clause id="12901">
    <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(119,a,108,a(flip),b,12899,a)].">
      <j1 rule="hyper" parents="119 108 12899"/>
    </justification>
  </clause>

  <clause id="12902">
    <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(12899(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="12899 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12903">
    <literal><![CDATA[
      K(x,x * y) * (a(K(x,y),z,u) * x) = R(K(x,y),z,u) * L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,10158,a(flip),b,12895,a)].">
      <j1 rule="hyper" parents="65 10158 12895"/>
    </justification>
  </clause>

  <clause id="12904">
    <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(12898(a,1),12597(a,1,1,1))].">
      <j1 rule="para" parents="12898 12597"/>
    </justification>
  </clause>

  <clause id="12905">
    <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(9323(a,1),12883(a,1,2,2))].">
      <j1 rule="para" parents="9323 12883"/>
    </justification>
  </clause>

  <clause id="12906">
    <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(12366(a,1),12905(a,1,2))].">
      <j1 rule="para" parents="12366 12905"/>
    </justification>
  </clause>

  <clause id="12907">
    <literal><![CDATA[
      K(x,x * y) * (x * a(K(x,y),z,u)) = R(K(x,y),z,u) * L(x,y,x)
    ]]></literal>
    <justification jstring="[para(9401(a,1),12903(a,1,2))].">
      <j1 rule="para" parents="9401 12903"/>
    </justification>
  </clause>

  <clause id="12908">
    <literal><![CDATA[
      T(x,x * y) * a(K(x,y),z,u) = R(K(x,y),z,u) * L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(5398,a,12907,a)].">
      <j1 rule="hyper" parents="5398 12907"/>
    </justification>
  </clause>

  <clause id="12909">
    <literal><![CDATA[
      T(x,x * y) * a(K(x,y),z,u) = L(x * R(K(x,y),z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,10307,a,b,12908,a),flip(a)].">
      <j1 rule="hyper" parents="299 10307 12908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12910">
    <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(299,a,12894,a(flip),b,12893,a),flip(a)].">
      <j1 rule="hyper" parents="299 12894 12893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12911">
    <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(535(a,1),12904(a,1,1)),flip(a)].">
      <j1 rule="para" parents="535 12904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12912">
    <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(299,a,9403,a(flip),b,12911,a),flip(a)].">
      <j1 rule="hyper" parents="299 9403 12911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12913">
    <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(7954(a,1),12912(a,1,2,1,1))].">
      <j1 rule="para" parents="7954 12912"/>
    </justification>
  </clause>

  <clause id="12914">
    <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(9320(a,1),12913(a,1,2,1))].">
      <j1 rule="para" parents="9320 12913"/>
    </justification>
  </clause>

  <clause id="12915">
    <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(5096(a,2),12914(a,1,2))].">
      <j1 rule="para" parents="5096 12914"/>
    </justification>
  </clause>

  <clause id="12916">
    <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(65,a,10093,a,b,12915,a)].">
      <j1 rule="hyper" parents="65 10093 12915"/>
    </justification>
  </clause>

  <clause id="12917">
    <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(7991(a,1),12916(a,1,1))].">
      <j1 rule="para" parents="7991 12916"/>
    </justification>
  </clause>

  <clause id="12918">
    <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(12341,a,12917,a)].">
      <j1 rule="hyper" parents="12341 12917"/>
    </justification>
  </clause>

  <clause id="12919">
    <literal><![CDATA[
      x * K(a(K(x,y),z,u),w) = T(x,a(K(w,y),z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,12890,a(flip),b,12918,a),flip(a)].">
      <j1 rule="hyper" parents="65 12890 12918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12920">
    <literal><![CDATA[
      K(a(K(x,y),z,u),w) = K(x,a(K(w,y),z,u))
    ]]></literal>
    <justification jstring="[hyper(36,a,5083,a(flip),b,12919,a),flip(a)].">
      <j1 rule="hyper" parents="36 5083 12919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12921">
    <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(65,a,12898,a,b,12920,a)].">
      <j1 rule="hyper" parents="65 12898 12920"/>
    </justification>
  </clause>

  <clause id="12922">
    <literal><![CDATA[
      1 * K(x,a(K(y,z),u,w)) = a(K(z,K(x,y)),u,w)
    ]]></literal>
    <justification jstring="[para(12921(a,1),12906(a,1,2))].">
      <j1 rule="para" parents="12921 12906"/>
    </justification>
  </clause>

  <clause id="12923">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,w) = K(y,a(K(z,x),u,w))
    ]]></literal>
    <justification jstring="[hyper(122,a,12922,a),flip(a)].">
      <j1 rule="hyper" parents="122 12922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12924">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,w) = K(a(K(y,x),u,w),z)
    ]]></literal>
    <justification jstring="[hyper(299,a,12920,a,b,12923,a),flip(a)].">
      <j1 rule="hyper" parents="299 12920 12923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12925">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,w) = K(x,a(K(z,y),u,w))
    ]]></literal>
    <justification jstring="[para(7983(a,1),12923(a,1,1))].">
      <j1 rule="para" parents="7983 12923"/>
    </justification>
  </clause>

  <clause id="12926">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,w) = K(a(K(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[para(7983(a,1),12924(a,1,1))].">
      <j1 rule="para" parents="7983 12924"/>
    </justification>
  </clause>

  <clause id="12927">
    <literal><![CDATA[
      x * T(((x * L(y,z,u)) / L(y,z,u)) \ (x * y),w) = ((x * L(y,z,u)) * T(y,w)) / L(y,z,u)
    ]]></literal>
    <justification jstring="[para(11(a,1),1807(a,1,1))].">
      <j1 rule="para" parents="11 1807"/>
    </justification>
  </clause>

  <clause id="12928">
    <literal><![CDATA[
      ((x * L(y,z,u)) * T(y,w)) / L(y,z,u) = x * T(x \ (x * y),w)
    ]]></literal>
    <justification jstring="[para(11(a,1),12927(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="11 12927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12929">
    <literal><![CDATA[
      ((x * L(y,z,u)) * T(y,w)) / L(y,z,u) = x * T(y,w)
    ]]></literal>
    <justification jstring="[para(9(a,1),12928(a,2,2,1))].">
      <j1 rule="para" parents="9 12928"/>
    </justification>
  </clause>

  <clause id="12930">
    <literal><![CDATA[
      (x * T(y,z)) * L(y,u,w) = (x * L(y,u,w)) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(143,a,12929,a)].">
      <j1 rule="hyper" parents="143 12929"/>
    </justification>
  </clause>

  <clause id="12931">
    <literal><![CDATA[
      (x * L(y,z,u)) * T(y,x) = (y * x) * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(107(a,1),12930(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 12930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12932">
    <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(12931(a,1),9663(a,1,2))].">
      <j1 rule="para" parents="12931 9663"/>
    </justification>
  </clause>

  <clause id="12933">
    <literal><![CDATA[
      x \ R(x,y,L(x,z,u)) = a(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(775,a,12932,a),flip(a)].">
      <j1 rule="hyper" parents="775 12932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12934">
    <literal><![CDATA[
      K(x * L(y,z,u),y) * K(y,x) = a(y,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,9016,a,b,12933,a)].">
      <j1 rule="hyper" parents="65 9016 12933"/>
    </justification>
  </clause>

  <clause id="12935">
    <literal><![CDATA[
      K(x,y) * a(y,x,L(y,z,u)) = K(x * L(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(12933(a,1),9404(a,1,2))].">
      <j1 rule="para" parents="12933 9404"/>
    </justification>
  </clause>

  <clause id="12936">
    <literal><![CDATA[
      K(L(x,y,z) * u,x) * K(x,u) = a(x,u,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(8638(a,2),12934(a,1,1))].">
      <j1 rule="para" parents="8638 12934"/>
    </justification>
  </clause>

  <clause id="12937">
    <literal><![CDATA[
      x * (K(y,z) * K(z,y * L(z,u,w))) = x / a(z,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(12934(a,1),9248(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12934 9248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12938">
    <literal><![CDATA[
      a(x,y,L(x,z,u)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(36,a,11447,a(flip),b,12935,a),flip(a)].">
      <j1 rule="hyper" parents="36 11447 12935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12939">
    <literal><![CDATA[
      (x / y) * R(y,z,y) = x * a(y,z,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(12938(a,2),10465(a,2,2))].">
      <j1 rule="para" parents="12938 10465"/>
    </justification>
  </clause>

  <clause id="12941">
    <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(11725(a,1),12939(a,1,2))].">
      <j1 rule="para" parents="11725 12939"/>
    </justification>
  </clause>

  <clause id="12942">
    <literal><![CDATA[
      L(x,y,L(x,z,u)) \ x = a(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,9850,a(flip),b,12936,a)].">
      <j1 rule="hyper" parents="65 9850 12936"/>
    </justification>
  </clause>

  <clause id="12943">
    <literal><![CDATA[
      a(x,y,L(x,z,u)) \ x = L(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(12942(a,1),6373(a,1,1))].">
      <j1 rule="para" parents="12942 6373"/>
    </justification>
  </clause>

  <clause id="12944">
    <literal><![CDATA[
      K(x,y) * K(y,x * L(y,z,u)) = a(y,x,L(y,z,u)) \ 1
    ]]></literal>
    <justification jstring="[hyper(119,a,73,a(flip),b,12937,a),flip(a)].">
      <j1 rule="hyper" parents="119 73 12937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12945">
    <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(65,a,12694,a(flip),b,12941,a),flip(a)].">
      <j1 rule="hyper" parents="65 12694 12941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12946">
    <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),12945(a,1,2,3))].">
      <j1 rule="para" parents="477 12945"/>
    </justification>
  </clause>

  <clause id="12947">
    <literal><![CDATA[
      a(R(x,y,z),u,R(x,y,z)) = a(x,u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(10142,a,12946,a)].">
      <j1 rule="hyper" parents="10142 12946"/>
    </justification>
  </clause>

  <clause id="12948">
    <literal><![CDATA[
      R(a(x,y,x),x * z,u) = a(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(12270,a,12947,a)].">
      <j1 rule="hyper" parents="12270 12947"/>
    </justification>
  </clause>

  <clause id="12949">
    <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(65,a,12691,a(flip),b,12947,a),flip(a)].">
      <j1 rule="hyper" parents="65 12691 12947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12950">
    <literal><![CDATA[
      a(x,y,R(x,x \ z,u)) = R(a(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),12948(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 12948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12951">
    <literal><![CDATA[
      R(x,y,R(x,x \ z,u)) = x * R(a(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(12950(a,1),10612(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12950 10612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12952">
    <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="[para(12950(a,1),10824(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12950 10824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12953">
    <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(65,a,10852,a(flip),b,12951,a),flip(a)].">
      <j1 rule="hyper" parents="65 10852 12951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12954">
    <literal><![CDATA[
      a(x,x \ y,R(x,z,u)) * K(x,y) = K(x,R(x,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(12949(a,1),10845(a,1,1))].">
      <j1 rule="para" parents="12949 10845"/>
    </justification>
  </clause>

  <clause id="12955">
    <literal><![CDATA[
      K(x,y) * a(x,x \ y,R(x,z,u)) = K(x,R(x,z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,12068,a(flip),b,12954,a)].">
      <j1 rule="hyper" parents="65 12068 12954"/>
    </justification>
  </clause>

  <clause id="12956">
    <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(9729(a,1),12953(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9729 12953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12957">
    <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(299,a,12952,a,b,12956,a),flip(a)].">
      <j1 rule="hyper" parents="299 12952 12956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12959">
    <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(12957(a,1),11728(a,2,1,1))].">
      <j1 rule="para" parents="12957 11728"/>
    </justification>
  </clause>

  <clause id="12960">
    <literal><![CDATA[
      ((x \ T(x * (y / (z * y)),y / (z * y))) * (z * y)) / y = K(x * (y / (z * y)),z \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,6117,a(flip),b,5690,a),flip(a)].">
      <j1 rule="hyper" parents="65 6117 5690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12962">
    <literal><![CDATA[
      K((((x \ 1) * (y * z)) / z) \ 1,z / (y * z)) = K(x * (z / (y * z)),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,6423,a(flip),b,12960,a)].">
      <j1 rule="hyper" parents="65 6423 12960"/>
    </justification>
  </clause>

  <clause id="12963">
    <literal><![CDATA[
      K((x \ 1) \ (y / (z * y)),((z * y) / y) \ 1) = K(x * (y / (z * y)),z \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,10643,a(flip),b,12962,a)].">
      <j1 rule="hyper" parents="65 10643 12962"/>
    </justification>
  </clause>

  <clause id="12964">
    <literal><![CDATA[
      K((x \ 1) \ (y / (z * y)),z \ 1) = K(x * (y / (z * y)),z \ 1)
    ]]></literal>
    <justification jstring="[para(11(a,1),12963(a,1,2,1))].">
      <j1 rule="para" parents="11 12963"/>
    </justification>
  </clause>

  <clause id="12965">
    <literal><![CDATA[
      K((x \ 1) \ ((y * z) \ z),y \ 1) = K(x * (z / (y * z)),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,8759,a(flip),b,12964,a)].">
      <j1 rule="hyper" parents="65 8759 12964"/>
    </justification>
  </clause>

  <clause id="12966">
    <literal><![CDATA[
      K((x \ 1) \ ((y * z) \ z),y \ 1) = K(x * ((y * z) \ z),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,9115,a(flip),b,12965,a),flip(a)].">
      <j1 rule="hyper" parents="299 9115 12965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12967">
    <literal><![CDATA[
      K((x \ 1) \ (y \ 1),y \ 1) = K(x * ((y * z) \ z),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,11043,a(flip),b,12966,a)].">
      <j1 rule="hyper" parents="65 11043 12966"/>
    </justification>
  </clause>

  <clause id="12968">
    <literal><![CDATA[
      K(x * ((y * z) \ z),y \ 1) = K(x * (y \ 1),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(8640,a,12967,a),flip(a)].">
      <j1 rule="hyper" parents="8640 12967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12970">
    <literal><![CDATA[
      K(x * ((y * z) \ z),y \ 1) = K(y \ x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,7316,a(flip),b,12968,a),flip(a)].">
      <j1 rule="hyper" parents="299 7316 12968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12971">
    <literal><![CDATA[
      K(x * R(y \ 1,y,z),y \ 1) = K(y \ x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,12843,a,b,12970,a)].">
      <j1 rule="hyper" parents="65 12843 12970"/>
    </justification>
  </clause>

  <clause id="12973">
    <literal><![CDATA[
      T(K(x \ y,x \ 1) / x,y) = R(1 / x,y,z / (x * z))
    ]]></literal>
    <justification jstring="[para(12971(a,1),6770(a,1,1,1))].">
      <j1 rule="para" parents="12971 6770"/>
    </justification>
  </clause>

  <clause id="12974">
    <literal><![CDATA[
      R(1 / x,y,z / (x * z)) = R(1 / x,y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,7320,a(flip),b,12973,a),flip(a)].">
      <j1 rule="hyper" parents="65 7320 12973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12976">
    <literal><![CDATA[
      R(1 / (x / y),z,(x / y) \ 1) = R(1 / (x / y),z,y / x)
    ]]></literal>
    <justification jstring="[para(12(a,1),12974(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="12 12974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12977">
    <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(12976(a,1),10148(a,2,2))].">
      <j1 rule="para" parents="12976 10148"/>
    </justification>
  </clause>

  <clause id="12978">
    <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(299,a,1223,a(flip),b,12977,a),flip(a)].">
      <j1 rule="hyper" parents="299 1223 12977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12979">
    <literal><![CDATA[
      T(a(1 / (x / y),z,1 / (x / y)),u) = (x * R(x \ y,z,y / x)) / y
    ]]></literal>
    <justification jstring="[hyper(299,a,1973,a(flip),b,12978,a),flip(a)].">
      <j1 rule="hyper" parents="299 1973 12978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12980">
    <literal><![CDATA[
      T(a(1 / (x / y),z,1 / (x / y)),u) = (x * R(x \ y,z,x \ y)) / y
    ]]></literal>
    <justification jstring="[para(10297(a,1),12979(a,2,1,2))].">
      <j1 rule="para" parents="10297 12979"/>
    </justification>
  </clause>

  <clause id="12981">
    <literal><![CDATA[
      T(a(1 / (x / y),z,1 / (x / y)),u) = a(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(299,a,10457,a(flip),b,12980,a),flip(a)].">
      <j1 rule="hyper" parents="299 10457 12980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12982">
    <literal><![CDATA[
      T(a(1 / (x / y),z,(x / y) \ 1),u) = a(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[para(2364(a,1),12981(a,1,1))].">
      <j1 rule="para" parents="2364 12981"/>
    </justification>
  </clause>

  <clause id="12983">
    <literal><![CDATA[
      a((x / y) \ 1,z,(x / y) \ 1) = a(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,11011,a(flip),b,12982,a)].">
      <j1 rule="hyper" parents="65 11011 12982"/>
    </justification>
  </clause>

  <clause id="12984">
    <literal><![CDATA[
      K((x \ y) \ z,x / y) * K(x / y,z) = a(y \ x,z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,12283,a,b,12983,a)].">
      <j1 rule="hyper" parents="65 12283 12983"/>
    </justification>
  </clause>

  <clause id="12985">
    <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(5323(a,1),5590(a,1,1))].">
      <j1 rule="para" parents="5323 5590"/>
    </justification>
  </clause>

  <clause id="12986">
    <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(5323(a,1),12985(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5323 12985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12987">
    <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(5197(a,1),12986(a,2,2,1))].">
      <j1 rule="para" parents="5197 12986"/>
    </justification>
  </clause>

  <clause id="12988">
    <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(6209(a,1),12987(a,2,2))].">
      <j1 rule="para" parents="6209 12987"/>
    </justification>
  </clause>

  <clause id="12989">
    <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(5035(a,1),12988(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5035 12988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12990">
    <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(6209(a,1),12989(a,2,1,2))].">
      <j1 rule="para" parents="6209 12989"/>
    </justification>
  </clause>

  <clause id="12991">
    <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(65,a,12886,a(flip),b,12990,a),flip(a)].">
      <j1 rule="hyper" parents="65 12886 12990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12992">
    <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),3349(a,1,2,1))].">
      <j1 rule="para" parents="12 3349"/>
    </justification>
  </clause>

  <clause id="12993">
    <literal><![CDATA[
      (1 / (1 / (x * L(x \ 1,y,z)))) \ 1 = (x / (x * L(x \ 1,y,z))) / x
    ]]></literal>
    <justification jstring="[para(73(a,1),12992(a,1,2))].">
      <j1 rule="para" parents="73 12992"/>
    </justification>
  </clause>

  <clause id="12995">
    <literal><![CDATA[
      (x / (x * L(x \ 1,y,z))) / x = 1 / (x * L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[hyper(323,a,12993,a)].">
      <j1 rule="hyper" parents="323 12993"/>
    </justification>
  </clause>

  <clause id="12998">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) / x = 1 / (x * L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[para(4040(a,1),12995(a,1,1))].">
      <j1 rule="para" parents="4040 12995"/>
    </justification>
  </clause>

  <clause id="12999">
    <literal><![CDATA[
      1 / (x * L(x \ 1,y,z)) = L(1 / x,y,z) \ (1 / x)
    ]]></literal>
    <justification jstring="[hyper(65,a,6577,a(flip),b,12998,a),flip(a)].">
      <j1 rule="hyper" parents="65 6577 12998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13000">
    <literal><![CDATA[
      1 / (x * L(x \ 1,y,z)) = L(x \ 1,y,z) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,3809,a(flip),b,12999,a),flip(a)].">
      <j1 rule="hyper" parents="299 3809 12999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13001">
    <literal><![CDATA[
      1 / ((x \ 1) * L((x \ 1) \ 1,y,z)) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(299,a,10975,a(flip),b,13000,a),flip(a)].">
      <j1 rule="hyper" parents="299 10975 13000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13002">
    <literal><![CDATA[
      (1 / (x * L(x \ 1,y,z))) \ (L(x \ 1,y,z) \ 1) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(13000(a,2),6578(a,1,1))].">
      <j1 rule="para" parents="13000 6578"/>
    </justification>
  </clause>

  <clause id="13003">
    <literal><![CDATA[
      1 / (x \ L(x,y,z)) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[para(1273(a,1),13001(a,1,2))].">
      <j1 rule="para" parents="1273 13001"/>
    </justification>
  </clause>

  <clause id="13004">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ 1 = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(186,a,13003,a)].">
      <j1 rule="hyper" parents="186 13003"/>
    </justification>
  </clause>

  <clause id="13005">
    <literal><![CDATA[
      (L(x,y,z) \ x) * T(x \ L(x,y,z),u) = K(x \ L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(13003(a,1),5075(a,2,1)),flip(a)].">
      <j1 rule="para" parents="13003 5075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13006">
    <literal><![CDATA[
      a(x,x,y) \ 1 = y \ L(y,x,x)
    ]]></literal>
    <justification jstring="[para(1986(a,1),13004(a,1,1))].">
      <j1 rule="para" parents="1986 13004"/>
    </justification>
  </clause>

  <clause id="13007">
    <literal><![CDATA[
      (x \ (x \ y)) \ L(x \ (x \ y),x,x) = (y \ (x \ ((1 / x) \ y))) \ 1
    ]]></literal>
    <justification jstring="[para(1667(a,1),13006(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1667 13006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13008">
    <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(299,a,8004,a,b,13005,a),flip(a)].">
      <j1 rule="hyper" parents="299 8004 13005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13010">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) / ((y \ 1) \ 1) = 1 / (y * ((x * y) \ x))
    ]]></literal>
    <justification jstring="[para(13002(a,1),12440(a,1,2))].">
      <j1 rule="para" parents="13002 12440"/>
    </justification>
  </clause>

  <clause id="13011">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) / y = 1 / (y * ((x * y) \ x))
    ]]></literal>
    <justification jstring="[hyper(65,a,9303,a(flip),b,13010,a)].">
      <j1 rule="hyper" parents="65 9303 13010"/>
    </justification>
  </clause>

  <clause id="13012">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) / y = (y * ((x * y) \ x)) \ 1
    ]]></literal>
    <justification jstring="[hyper(299,a,9866,a(flip),b,13011,a),flip(a)].">
      <j1 rule="hyper" parents="299 9866 13011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13013">
    <literal><![CDATA[
      ((x * ((y * x) \ y)) \ 1) \ (1 / ((y * x) \ y)) = x
    ]]></literal>
    <justification jstring="[hyper(186,a,13012,a)].">
      <j1 rule="hyper" parents="186 13012"/>
    </justification>
  </clause>

  <clause id="13014">
    <literal><![CDATA[
      (x * ((y * x) \ y)) \ 1 = x \ (1 / ((y * x) \ y))
    ]]></literal>
    <justification jstring="[hyper(65,a,12446,a(flip),b,13012,a),flip(a)].">
      <j1 rule="hyper" parents="65 12446 13012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13015">
    <literal><![CDATA[
      ((x * ((y * x) \ y)) \ 1) * T(x,z) = T(x,z) / (x * ((y * x) \ y))
    ]]></literal>
    <justification jstring="[para(13013(a,1),3599(a,1,2,1))].">
      <j1 rule="para" parents="13013 3599"/>
    </justification>
  </clause>

  <clause id="13016">
    <literal><![CDATA[
      ((x * ((y * x) \ y)) \ 1) * T(x,z) = (x * ((y * x) \ y)) \ T(x,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,9866,a(flip),b,13015,a),flip(a)].">
      <j1 rule="hyper" parents="299 9866 13015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13017">
    <literal><![CDATA[
      (x \ (1 / ((y * x) \ y))) * T(x,z) = (x * ((y * x) \ y)) \ T(x,z)
    ]]></literal>
    <justification jstring="[para(13014(a,1),13016(a,1,1))].">
      <j1 rule="para" parents="13014 13016"/>
    </justification>
  </clause>

  <clause id="13018">
    <literal><![CDATA[
      T((1 / ((x * y) \ x)) * K(y,z),y) = (y * ((x * y) \ x)) \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,12447,a,b,13017,a)].">
      <j1 rule="hyper" parents="65 12447 13017"/>
    </justification>
  </clause>

  <clause id="13019">
    <literal><![CDATA[
      T(T(1 / ((x * y) \ x),z),y) = (y * ((x * y) \ x)) \ T(y,z)
    ]]></literal>
    <justification jstring="[para(7026(a,1),13018(a,1,1))].">
      <j1 rule="para" parents="7026 13018"/>
    </justification>
  </clause>

  <clause id="13020">
    <literal><![CDATA[
      (x * ((y * x) \ y)) \ T(x,z) = T(1 / ((y * x) \ y),z)
    ]]></literal>
    <justification jstring="[hyper(65,a,5880,a(flip),b,13019,a),flip(a)].">
      <j1 rule="hyper" parents="65 5880 13019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13021">
    <literal><![CDATA[
      1 / ((x * T(y,z)) \ x) = T(1 / ((x * y) \ x),z)
    ]]></literal>
    <justification jstring="[hyper(65,a,9876,a(flip),b,13020,a)].">
      <j1 rule="hyper" parents="65 9876 13020"/>
    </justification>
  </clause>

  <clause id="13022">
    <literal><![CDATA[
      T(1 / ((x * y) \ x),z) \ 1 = (x * T(y,z)) \ x
    ]]></literal>
    <justification jstring="[hyper(186,a,13021,a)].">
      <j1 rule="hyper" parents="186 13021"/>
    </justification>
  </clause>

  <clause id="13023">
    <literal><![CDATA[
      T(((x * y) \ x) \ 1,z) = ((x * T(y,z)) \ x) \ 1
    ]]></literal>
    <justification jstring="[para(13022(a,1),3179(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13022 3179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13024">
    <literal><![CDATA[
      K(x,T(((y * z) \ y) \ 1,u) \ x) = K(x,1 \ (((y * T(z,u)) \ y) * x))
    ]]></literal>
    <justification jstring="[para(13023(a,2),8407(a,1,2,1))].">
      <j1 rule="para" parents="13023 8407"/>
    </justification>
  </clause>

  <clause id="13025">
    <literal><![CDATA[
      (x \ (y \ ((1 / y) \ x))) \ 1 = (y \ (y \ x)) \ ((y * y) \ x)
    ]]></literal>
    <justification jstring="[para(281(a,1),13007(a,1,2)),flip(a)].">
      <j1 rule="para" parents="281 13007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13026">
    <literal><![CDATA[
      (x \ (y \ ((1 / y) \ x))) \ 1 = ((y \ 1) \ (y \ x)) \ x
    ]]></literal>
    <justification jstring="[hyper(299,a,748,a(flip),b,13025,a),flip(a)].">
      <j1 rule="hyper" parents="299 748 13025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13027">
    <literal><![CDATA[
      (x \ (y \ ((1 / y) \ x))) \ 1 = (y \ ((1 / y) \ x)) \ x
    ]]></literal>
    <justification jstring="[para(1663(a,1),13026(a,2,1))].">
      <j1 rule="para" parents="1663 13026"/>
    </justification>
  </clause>

  <clause id="13028">
    <literal><![CDATA[
      a(x,x,x \ (x \ y)) \ 1 = (x \ ((1 / x) \ y)) \ y
    ]]></literal>
    <justification jstring="[para(1667(a,2),13027(a,1,1))].">
      <j1 rule="para" parents="1667 13027"/>
    </justification>
  </clause>

  <clause id="13029">
    <literal><![CDATA[
      K(x,T((((y * z) \ y) \ 1) \ x,u)) = K(x,1 \ (((y * T(z,u)) \ y) * x))
    ]]></literal>
    <justification jstring="[hyper(8963,a,13024,a)].">
      <j1 rule="hyper" parents="8963 13024"/>
    </justification>
  </clause>

  <clause id="13030">
    <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(12853(a,1),13008(a,1,2))].">
      <j1 rule="para" parents="12853 13008"/>
    </justification>
  </clause>

  <clause id="13031">
    <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(65,a,13008,a(flip),b,13030,a),flip(a)].">
      <j1 rule="hyper" parents="65 13008 13030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13032">
    <literal><![CDATA[
      K(x \ L(x,y,z),K(u * x,w)) = K(u,K(w,x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(299,a,7989,a,b,13031,a),flip(a)].">
      <j1 rule="hyper" parents="299 7989 13031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13033">
    <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(65,a,12838,a(flip),b,13032,a)].">
      <j1 rule="hyper" parents="65 12838 13032"/>
    </justification>
  </clause>

  <clause id="13034">
    <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(299,a,7983,a,b,13033,a),flip(a)].">
      <j1 rule="hyper" parents="299 7983 13033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13035">
    <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(12839,a,13034,a)].">
      <j1 rule="hyper" parents="12839 13034"/>
    </justification>
  </clause>

  <clause id="13036">
    <literal><![CDATA[
      (x * K(y,z * x)) / T(T(K(y,z),x * K(y,z * x)),x * K(y,z * x)) = (K(y,z * x) * x) / K(y,T(z,x * K(y,z * x)))
    ]]></literal>
    <justification jstring="[para(7489(a,2),10099(a,2,2))].">
      <j1 rule="para" parents="7489 10099"/>
    </justification>
  </clause>

  <clause id="13037">
    <literal><![CDATA[
      K(((x \ 1) \ K(y,x)) \ T(x,z),T(u,w) \ ((u \ 1) \ K(v5,u))) = K((x * (K(y,x) / T(x,z))) \ 1,u * (K(v5,u) / T(u,w)))
    ]]></literal>
    <justification jstring="[para(10191(a,1),12390(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10191 12390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13038">
    <literal><![CDATA[
      K(((x \ 1) \ K(y,x)) \ T(x,z),T(x,z) \ ((x \ 1) \ K(y,x))) = K(x \ ((K(y,x) / T(x,z)) \ 1),(K(y,x) / T(x,z)) * x)
    ]]></literal>
    <justification jstring="[hyper(299,a,12149,a(flip),b,13037,a),flip(a)].">
      <j1 rule="hyper" parents="299 12149 13037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13039">
    <literal><![CDATA[
      K(((x \ 1) \ K(y,x)) \ T(x,z),T(x,z) \ ((x \ 1) \ K(y,x))) = K(x \ (K(x,z) * T(x,y)),(K(y,x) / T(x,z)) * x)
    ]]></literal>
    <justification jstring="[para(9177(a,1),13038(a,2,1,2))].">
      <j1 rule="para" parents="9177 13038"/>
    </justification>
  </clause>

  <clause id="13040">
    <literal><![CDATA[
      K(((x \ 1) \ K(y,x)) \ T(x,z),T(x,z) \ ((x \ 1) \ K(y,x))) = K(T(K(x,z),x) * K(x,y),(K(y,x) / T(x,z)) * x)
    ]]></literal>
    <justification jstring="[para(7788(a,1),13039(a,2,1))].">
      <j1 rule="para" parents="7788 13039"/>
    </justification>
  </clause>

  <clause id="13041">
    <literal><![CDATA[
      K(((x \ 1) \ K(y,x)) \ T(x,z),T(x,z) \ ((x \ 1) \ K(y,x))) = K(K(x,z) * K(x,y),(K(y,x) / T(x,z)) * x)
    ]]></literal>
    <justification jstring="[para(3569(a,1),13040(a,2,1,1))].">
      <j1 rule="para" parents="3569 13040"/>
    </justification>
  </clause>

  <clause id="13042">
    <literal><![CDATA[
      K(((x \ 1) \ K(y,x)) \ T(x,z),T(x,z) \ ((x \ 1) \ K(y,x))) = K(K(x,z) * K(x,y),K(y,x) * K(z,x))
    ]]></literal>
    <justification jstring="[para(7185(a,1),13041(a,2,2))].">
      <j1 rule="para" parents="7185 13041"/>
    </justification>
  </clause>

  <clause id="13043">
    <literal><![CDATA[
      (x * K(y,z * x)) / T(T(K(y,z),x * K(y,z * x)),x * K(y,z * x)) = (K(y,z * x) * x) / K(y,T(z,x))
    ]]></literal>
    <justification jstring="[para(8661(a,1),13036(a,2,2))].">
      <j1 rule="para" parents="8661 13036"/>
    </justification>
  </clause>

  <clause id="13044">
    <literal><![CDATA[
      (x * K(y,z * x)) / T(T(K(y,z),x * K(y,z * x)),x * K(y,z * x)) = (K(y,z * x) * x) * K(z,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(299,a,7583,a(flip),b,13043,a),flip(a)].">
      <j1 rule="hyper" parents="299 7583 13043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13046">
    <literal><![CDATA[
      (x * K(y,z * x)) / T(T(K(y,z),x * K(y,z * x)),x * K(y,z * x)) = K(y,z * x) * (x * K(z,T(y,x)))
    ]]></literal>
    <justification jstring="[hyper(299,a,7897,a(flip),b,13044,a),flip(a)].">
      <j1 rule="hyper" parents="299 7897 13044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13047">
    <literal><![CDATA[
      (x * K(y,z * x)) / T(T(K(y,z),x * K(y,z * x)),x * K(y,z * x)) = K(y,z * x) * (K(z,y) * x)
    ]]></literal>
    <justification jstring="[hyper(299,a,7601,a(flip),b,13046,a),flip(a)].">
      <j1 rule="hyper" parents="299 7601 13046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13048">
    <literal><![CDATA[
      (x * K(y,z * x)) / K(y,z) = K(y,z * x) * (K(z,y) * x)
    ]]></literal>
    <justification jstring="[para(8094(a,1),13047(a,1,2))].">
      <j1 rule="para" parents="8094 13047"/>
    </justification>
  </clause>

  <clause id="13049">
    <literal><![CDATA[
      (x * K(y,z * x)) * K(z,y) = K(y,z * x) * (K(z,y) * x)
    ]]></literal>
    <justification jstring="[hyper(7208,a,13048,a)].">
      <j1 rule="hyper" parents="7208 13048"/>
    </justification>
  </clause>

  <clause id="13051">
    <literal><![CDATA[
      K(x,y * z) * (K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      z * (K(x,y * z) * K(y,x)) = u
    ]]></literal>
    <justification jstring="[para(13049(a,1),9203(a,1))].">
      <j1 rule="para" parents="13049 9203"/>
    </justification>
  </clause>

  <clause id="13052">
    <literal><![CDATA[
      K(x * (y \ T(y * z,y)),K(y * z,L(y,z,x))) / ((x * z) / (x * (y \ T(y * z,y)))) = 1 / ((x * (y \ T(y * z,y))) \ (x * z))
    ]]></literal>
    <justification jstring="[para(9156(a,1),9408(a,1,1))].">
      <j1 rule="para" parents="9156 9408"/>
    </justification>
  </clause>

  <clause id="13053">
    <literal><![CDATA[
      R(x,T(K(y,z),x),T(K(z,K(u,w)),K(y,z) * x)) \ ((K(u,K(z,w)) * K(y,z)) * x) = T(K(y,z),x) * T(K(u,K(z,w)),K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(7983(a,1),10086(a,1,1,3,1))].">
      <j1 rule="para" parents="7983 10086"/>
    </justification>
  </clause>

  <clause id="13054">
    <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(7036(a,1),10194(a,1,2,1))].">
      <j1 rule="para" parents="7036 10194"/>
    </justification>
  </clause>

  <clause id="13055">
    <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(4250(a,1),13054(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4250 13054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13056">
    <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(9471(a,1),13055(a,2,2))].">
      <j1 rule="para" parents="9471 13055"/>
    </justification>
  </clause>

  <clause id="13057">
    <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),13056(a,2,2,1))].">
      <j1 rule="para" parents="9 13056"/>
    </justification>
  </clause>

  <clause id="13058">
    <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(6722(a,1),13057(a,1,1,2))].">
      <j1 rule="para" parents="6722 13057"/>
    </justification>
  </clause>

  <clause id="13059">
    <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(8911(a,1),13058(a,1,1))].">
      <j1 rule="para" parents="8911 13058"/>
    </justification>
  </clause>

  <clause id="13060">
    <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(6722(a,1),13059(a,1,2,1))].">
      <j1 rule="para" parents="6722 13059"/>
    </justification>
  </clause>

  <clause id="13062">
    <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(5652(a,1),13060(a,1,2))].">
      <j1 rule="para" parents="5652 13060"/>
    </justification>
  </clause>

  <clause id="13063">
    <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(7907(a,1),13062(a,1,2))].">
      <j1 rule="para" parents="7907 13062"/>
    </justification>
  </clause>

  <clause id="13064">
    <literal><![CDATA[
      (x * y) / (y * T(x,z)) = T(K(z,x),y) * K(x,y)
    ]]></literal>
    <justification jstring="[para(10723(a,1),13063(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10723 13063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13065">
    <literal><![CDATA[
      (x * y) / (y * T(x,z)) = T(K(z,x) * K(x,y),y)
    ]]></literal>
    <justification jstring="[hyper(299,a,7773,a,b,13064,a),flip(a)].">
      <j1 rule="hyper" parents="299 7773 13064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13067">
    <literal><![CDATA[
      K(x * (y \ T(y * z,y)),K(y * z,y)) / ((x * z) / (x * (y \ T(y * z,y)))) = 1 / ((x * (y \ T(y * z,y))) \ (x * z))
    ]]></literal>
    <justification jstring="[para(9188(a,1),13052(a,1,1,2))].">
      <j1 rule="para" parents="9188 13052"/>
    </justification>
  </clause>

  <clause id="13068">
    <literal><![CDATA[
      K(x * y,K(z * (x \ T(x * y,x)),x)) / ((z * y) / (z * (x \ T(x * y,x)))) = 1 / ((z * (x \ T(x * y,x))) \ (z * y))
    ]]></literal>
    <justification jstring="[para(7983(a,1),13067(a,1,1))].">
      <j1 rule="para" parents="7983 13067"/>
    </justification>
  </clause>

  <clause id="13070">
    <literal><![CDATA[
      K(x * y,K(z * (x \ (x * y)),x)) / ((z * y) / (z * (x \ T(x * y,x)))) = 1 / ((z * (x \ T(x * y,x))) \ (z * y))
    ]]></literal>
    <justification jstring="[para(9110(a,1),13068(a,1,1,2))].">
      <j1 rule="para" parents="9110 13068"/>
    </justification>
  </clause>

  <clause id="13071">
    <literal><![CDATA[
      K(x * y,K(z * y,x)) / ((z * y) / (z * (x \ T(x * y,x)))) = 1 / ((z * (x \ T(x * y,x))) \ (z * y))
    ]]></literal>
    <justification jstring="[para(9(a,1),13070(a,1,1,2,1,2))].">
      <j1 rule="para" parents="9 13070"/>
    </justification>
  </clause>

  <clause id="13072">
    <literal><![CDATA[
      K(x,K(x * y,z * y)) / ((z * y) / (z * (x \ T(x * y,x)))) = 1 / ((z * (x \ T(x * y,x))) \ (z * y))
    ]]></literal>
    <justification jstring="[para(7989(a,1),13071(a,1,1))].">
      <j1 rule="para" parents="7989 13071"/>
    </justification>
  </clause>

  <clause id="13073">
    <literal><![CDATA[
      K(x,K(y,z * y)) / ((z * y) / (z * (x \ T(x * y,x)))) = 1 / ((z * (x \ T(x * y,x))) \ (z * y))
    ]]></literal>
    <justification jstring="[para(8047(a,1),13072(a,1,1))].">
      <j1 rule="para" parents="8047 13072"/>
    </justification>
  </clause>

  <clause id="13074">
    <literal><![CDATA[
      K(x,K(y,z)) / ((y * z) / (y * (x \ T(x * z,x)))) = 1 / ((y * (x \ T(x * z,x))) \ (y * z))
    ]]></literal>
    <justification jstring="[para(8036(a,1),13073(a,1,1))].">
      <j1 rule="para" parents="8036 13073"/>
    </justification>
  </clause>

  <clause id="13075">
    <literal><![CDATA[
      K(x,K(y,z)) / ((x * z) / (x * (y \ T(y * z,y)))) = 1 / ((x * (y \ T(y * z,y))) \ (x * z))
    ]]></literal>
    <justification jstring="[para(7983(a,1),13074(a,1,1))].">
      <j1 rule="para" parents="7983 13074"/>
    </justification>
  </clause>

  <clause id="13076">
    <literal><![CDATA[
      K(x,K(y,z)) / L(K(y,T(z * y,x)),z,x) = 1 / ((x * (y \ T(y * z,y))) \ (x * z))
    ]]></literal>
    <justification jstring="[para(12056(a,1),13075(a,1,2))].">
      <j1 rule="para" parents="12056 13075"/>
    </justification>
  </clause>

  <clause id="13077">
    <literal><![CDATA[
      K(x,K(y,z)) * L(K(T(z * y,x),y),z,x) = 1 / ((x * (y \ T(y * z,y))) \ (x * z))
    ]]></literal>
    <justification jstring="[hyper(9101,a,13076,a)].">
      <j1 rule="hyper" parents="9101 13076"/>
    </justification>
  </clause>

  <clause id="13078">
    <literal><![CDATA[
      K(x,K(y,z)) * L(K(z * y,T(y,x)),z,x) = 1 / ((x * (y \ T(y * z,y))) \ (x * z))
    ]]></literal>
    <justification jstring="[para(7537(a,1),13077(a,1,2,1))].">
      <j1 rule="para" parents="7537 13077"/>
    </justification>
  </clause>

  <clause id="13079">
    <literal><![CDATA[
      L(K(x * y,T(y,z)),x,z) = K(y * x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(36,a,11414,a(flip),b,13078,a),flip(a)].">
      <j1 rule="hyper" parents="36 11414 13078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13080">
    <literal><![CDATA[
      K((x / (x * y)) \ z,z) = K(z * y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,12251,a(flip),b,13079,a)].">
      <j1 rule="hyper" parents="65 12251 13079"/>
    </justification>
  </clause>

  <clause id="13082">
    <literal><![CDATA[
      K(x * (y \ z),T(x,y)) = K((y / z) \ x,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),13080(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10 13080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13083">
    <literal><![CDATA[
      K((x \ y) * z,T(z,x)) = K((x / y) \ z,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,6293,a,b,13082,a)].">
      <j1 rule="hyper" parents="65 6293 13082"/>
    </justification>
  </clause>

  <clause id="13084">
    <literal><![CDATA[
      K(x / y,z) * a(z,y \ x,z) = K((y / x) \ z,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,9917,a,b,13083,a)].">
      <j1 rule="hyper" parents="65 9917 13083"/>
    </justification>
  </clause>

  <clause id="13085">
    <literal><![CDATA[
      K(x,y / z) * K((z / y) \ x,x) = a(x,z \ y,x)
    ]]></literal>
    <justification jstring="[hyper(5437,a,13084,a)].">
      <j1 rule="hyper" parents="5437 13084"/>
    </justification>
  </clause>

  <clause id="13086">
    <literal><![CDATA[
      T(x,(y / z) \ x) \ T(x,z / y) = a(x,y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,5720,a,b,13085,a)].">
      <j1 rule="hyper" parents="65 5720 13085"/>
    </justification>
  </clause>

  <clause id="13087">
    <literal><![CDATA[
      T(x,(y / z) \ x) \ T(x,(y / z) \ 1) = a(x,y \ z,x)
    ]]></literal>
    <justification jstring="[para(4641(a,2),13086(a,1,2))].">
      <j1 rule="para" parents="4641 13086"/>
    </justification>
  </clause>

  <clause id="13088">
    <literal><![CDATA[
      T(x,(y / z) \ x) \ ((x \ ((y / z) \ x)) \ ((y / z) \ x)) = a(x,y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,4645,a,b,13087,a)].">
      <j1 rule="hyper" parents="65 4645 13087"/>
    </justification>
  </clause>

  <clause id="13089">
    <literal><![CDATA[
      a(x,(y / z) \ 1,x) = a(x,y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,9726,a(flip),b,13088,a)].">
      <j1 rule="hyper" parents="65 9726 13088"/>
    </justification>
  </clause>

  <clause id="13090">
    <literal><![CDATA[
      a(x,(y * z) \ z,x) = a(x,y \ 1,x)
    ]]></literal>
    <justification jstring="[para(11(a,1),13089(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11 13089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13092">
    <literal><![CDATA[
      R(x,T(K(y,z),x),T(K(z,K(u,w)),x)) \ ((K(u,K(z,w)) * K(y,z)) * x) = T(K(y,z),x) * T(K(u,K(z,w)),K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(8667(a,1),13053(a,1,1,3))].">
      <j1 rule="para" parents="8667 13053"/>
    </justification>
  </clause>

  <clause id="13093">
    <literal><![CDATA[
      R(x,T(K(y,z),x),K(z,K(u,T(w,x)))) \ ((K(u,K(z,w)) * K(y,z)) * x) = T(K(y,z),x) * T(K(u,K(z,w)),K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(7528(a,2),13092(a,1,1,3))].">
      <j1 rule="para" parents="7528 13092"/>
    </justification>
  </clause>

  <clause id="13095">
    <literal><![CDATA[
      R(x,T(K(y,z),x),K(z,K(u,T(w,x)))) \ ((K(z,K(u,w)) * K(y,z)) * x) = T(K(y,z),x) * T(K(u,K(z,w)),K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(7983(a,1),13093(a,1,2,1,1))].">
      <j1 rule="para" parents="7983 13093"/>
    </justification>
  </clause>

  <clause id="13096">
    <literal><![CDATA[
      R(x,T(K(y,z),x),K(z,K(u,T(w,x)))) \ (K(y,z) * (K(z,K(u,w)) * x)) = T(K(y,z),x) * T(K(u,K(z,w)),K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(10037(a,1),13095(a,1,2))].">
      <j1 rule="para" parents="10037 13095"/>
    </justification>
  </clause>

  <clause id="13097">
    <literal><![CDATA[
      R(x,T(K(y,z),x),K(z,K(u,T(w,x)))) \ (K(y,z) * (K(z,K(u,w)) * x)) = T(K(y,z),x) * T(K(z,K(u,w)),K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(7983(a,1),13096(a,2,2,1))].">
      <j1 rule="para" parents="7983 13096"/>
    </justification>
  </clause>

  <clause id="13098">
    <literal><![CDATA[
      R(x,T(K(y,z),x),K(z,K(u,T(w,x)))) \ (K(y,z) * (K(z,K(u,w)) * x)) = T(K(y,z),x) * T(K(z,K(u,w)),x)
    ]]></literal>
    <justification jstring="[para(8667(a,1),13097(a,2,2))].">
      <j1 rule="para" parents="8667 13097"/>
    </justification>
  </clause>

  <clause id="13099">
    <literal><![CDATA[
      R(x,T(K(y,z),x),K(z,K(u,T(w,x)))) \ (K(y,z) * (K(z,K(u,w)) * x)) = T(K(y,z),x) * K(z,K(u,T(w,x)))
    ]]></literal>
    <justification jstring="[para(7528(a,2),13098(a,2,2))].">
      <j1 rule="para" parents="7528 13098"/>
    </justification>
  </clause>

  <clause id="13101">
    <literal><![CDATA[
      x \ (K(y,z) * (K(z,K(u,w)) * x)) = T(K(y,z),x) * K(z,K(u,T(w,x)))
    ]]></literal>
    <justification jstring="[para(9225(a,1),13099(a,1,1))].">
      <j1 rule="para" parents="9225 13099"/>
    </justification>
  </clause>

  <clause id="13102">
    <literal><![CDATA[
      T(K(x,y),z) * K(y,K(u,T(w,z))) = T(K(x,y) * K(y,K(u,w)),z)
    ]]></literal>
    <justification jstring="[hyper(10036,a,13101,a),flip(a)].">
      <j1 rule="hyper" parents="10036 13101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13104">
    <literal><![CDATA[
      L(T(T(x,y),x \ 1) * z,T(T(x,y),x \ 1),T(T(x,y),x \ 1)) = T(x,y) * L(z,T(T(x,y),x \ 1),T(T(x,y),x \ 1))
    ]]></literal>
    <justification jstring="[hyper(299,a,189,a(flip),b,3187,a),flip(a)].">
      <j1 rule="hyper" parents="299 189 3187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13106">
    <literal><![CDATA[
      L(x,y,z) * T(R(u,L(x,y,z),u),R(u,L(x,y,z),u) * x) = K(u,u * x) * T(u * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(10748(a,1),6474(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10748 6474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13107">
    <literal><![CDATA[
      L(x,y,z) * T(R(u,L(x,y,z),u),R(u,L(x,y,z),u) * x) = T(K(u,u * x) * (u * L(x,y,z)),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,7749,a,b,13106,a),flip(a)].">
      <j1 rule="hyper" parents="299 7749 13106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13109">
    <literal><![CDATA[
      L(x,y,z) * T(R(u,L(x,y,z),u),R(u,L(x,y,z),u) * x) = T(T(u,u * x) * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(5103(a,1),13107(a,2,1))].">
      <j1 rule="para" parents="5103 13107"/>
    </justification>
  </clause>

  <clause id="13110">
    <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(10748(a,1),6475(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10748 6475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13111">
    <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(299,a,7749,a,b,13110,a),flip(a)].">
      <j1 rule="hyper" parents="299 7749 13110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13113">
    <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(5103(a,1),13111(a,2,1))].">
      <j1 rule="para" parents="5103 13111"/>
    </justification>
  </clause>

  <clause id="13114">
    <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(299,a,10370,a(flip),b,13113,a),flip(a)].">
      <j1 rule="hyper" parents="299 10370 13113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13115">
    <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(4370(a,2),13114(a,1,2))].">
      <j1 rule="para" parents="4370 13114"/>
    </justification>
  </clause>

  <clause id="13116">
    <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(10744(a,1),13115(a,1,2,1))].">
      <j1 rule="para" parents="10744 13115"/>
    </justification>
  </clause>

  <clause id="13117">
    <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(4366(a,2),13116(a,1,2,1))].">
      <j1 rule="para" parents="4366 13116"/>
    </justification>
  </clause>

  <clause id="13119">
    <literal><![CDATA[
      (((x \ 1) \ K(y,x)) \ T(x,z)) \ K(((x \ 1) \ K(y,x)) \ T(x,z),T(x,z) \ ((x \ K(x,y)) \ 1)) = 1 / (((x \ K(x,y)) \ 1) \ T(x,z))
    ]]></literal>
    <justification jstring="[para(6605(a,1),12389(a,1,1,1))].">
      <j1 rule="para" parents="6605 12389"/>
    </justification>
  </clause>

  <clause id="13120">
    <literal><![CDATA[
      ((x \ K(x,y)) * T(x,z)) \ K(((x \ 1) \ K(y,x)) \ T(x,z),T(x,z) \ ((x \ K(x,y)) \ 1)) = 1 / (((x \ K(x,y)) \ 1) \ T(x,z))
    ]]></literal>
    <justification jstring="[para(12386(a,1),13119(a,1,1))].">
      <j1 rule="para" parents="12386 13119"/>
    </justification>
  </clause>

  <clause id="13121">
    <literal><![CDATA[
      ((x \ K(x,y)) * T(x,z)) \ K((x \ K(x,y)) * T(x,z),T(x,z) \ ((x \ K(x,y)) \ 1)) = 1 / (((x \ K(x,y)) \ 1) \ T(x,z))
    ]]></literal>
    <justification jstring="[para(12386(a,1),13120(a,1,2,1))].">
      <j1 rule="para" parents="12386 13120"/>
    </justification>
  </clause>

  <clause id="13122">
    <literal><![CDATA[
      ((x \ K(x,y)) * T(x,z)) \ K((x \ K(x,y)) * T(x,z),T(x,z) \ ((x \ 1) \ K(y,x))) = 1 / (((x \ K(x,y)) \ 1) \ T(x,z))
    ]]></literal>
    <justification jstring="[para(6605(a,1),13121(a,1,2,2,2))].">
      <j1 rule="para" parents="6605 13121"/>
    </justification>
  </clause>

  <clause id="13123">
    <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(11073(a,1),11074(a,2,2,1,1))].">
      <j1 rule="para" parents="11073 11074"/>
    </justification>
  </clause>

  <clause id="13124">
    <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(299,a,1877,a(flip),b,13123,a),flip(a)].">
      <j1 rule="hyper" parents="299 1877 13123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13125">
    <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(2064(a,1),13124(a,2,2))].">
      <j1 rule="para" parents="2064 13124"/>
    </justification>
  </clause>

  <clause id="13126">
    <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(1147(a,1),13125(a,2,2,1))].">
      <j1 rule="para" parents="1147 13125"/>
    </justification>
  </clause>

  <clause id="13127">
    <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(1455(a,1),13126(a,2,2,1,2))].">
      <j1 rule="para" parents="1455 13126"/>
    </justification>
  </clause>

  <clause id="13128">
    <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(1877(a,1),13127(a,1,1))].">
      <j1 rule="para" parents="1877 13127"/>
    </justification>
  </clause>

  <clause id="13129">
    <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(299,a,9602,a(flip),b,9938,a),flip(a)].">
      <j1 rule="hyper" parents="299 9602 9938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13130">
    <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(299,a,7989,a(flip),b,13129,a),flip(a)].">
      <j1 rule="hyper" parents="299 7989 13129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13132">
    <literal><![CDATA[
      K(R(T(x,y * (((y \ x) \ 1) \ 1)),x \ y,y \ (y / (((x \ y) \ 1) \ 1))),z) = K(((y \ (y / (x \ y))) * (x \ y)) \ (y / (((x \ y) \ 1) \ 1)),z)
    ]]></literal>
    <justification jstring="[para(3006(a,1),9853(a,1,1,1,2))].">
      <j1 rule="para" parents="3006 9853"/>
    </justification>
  </clause>

  <clause id="13133">
    <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(299,a,9,a(flip),b,12117,a),flip(a)].">
      <j1 rule="hyper" parents="299 9 12117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13135">
    <literal><![CDATA[
      L(x,K(y,z),K(u,y) * R(K(y,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[para(12115(a,1),13133(a,1,3))].">
      <j1 rule="para" parents="12115 13133"/>
    </justification>
  </clause>

  <clause id="13137">
    <literal><![CDATA[
      L(x,K(y,z),a(K(y,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[para(12882(a,1),13135(a,1,3))].">
      <j1 rule="para" parents="12882 13135"/>
    </justification>
  </clause>

  <clause id="13138">
    <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(1318,a,13137,a),flip(a)].">
      <j1 rule="hyper" parents="1318 13137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13139">
    <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(65,a,12910,a(flip),b,13138,a),flip(a)].">
      <j1 rule="hyper" parents="65 12910 13138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13140">
    <literal><![CDATA[
      a(K(x,T(y,z)),u,w) * z = z * a(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(5432(a,1),13139(a,1,2))].">
      <j1 rule="para" parents="5432 13139"/>
    </justification>
  </clause>

  <clause id="13141">
    <literal><![CDATA[
      x * a(K(y,T(z,x)),u,w) = a(K(y,z),u,w) * x
    ]]></literal>
    <justification jstring="[para(8104(a,1),13140(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="8104 13140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13142">
    <literal><![CDATA[
      a(K(x,T(y,z)),u,w) = T(a(K(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[hyper(236,a,13141,a),flip(a)].">
      <j1 rule="hyper" parents="236 13141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13143">
    <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(9160(a,1),12596(a,1,2))].">
      <j1 rule="para" parents="9160 12596"/>
    </justification>
  </clause>

  <clause id="13145">
    <literal><![CDATA[
      K(R(T(x,x),x \ y,y \ (y / (((x \ y) \ 1) \ 1))),z) = K(((y \ (y / (x \ y))) * (x \ y)) \ (y / (((x \ y) \ 1) \ 1)),z)
    ]]></literal>
    <justification jstring="[para(3887(a,1),13132(a,1,1,1))].">
      <j1 rule="para" parents="3887 13132"/>
    </justification>
  </clause>

  <clause id="13146">
    <literal><![CDATA[
      K(((x \ (x / (y \ x))) * (y \ x)) \ (x / (((y \ x) \ 1) \ 1)),z) = K(R(y,y \ x,x \ (x / (((y \ x) \ 1) \ 1))),z)
    ]]></literal>
    <justification jstring="[para(106(a,1),13145(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="106 13145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13150">
    <literal><![CDATA[
      K(((x \ (x / (y \ x))) * (y \ x)) \ (x / (((y \ x) \ 1) \ 1)),z) = K(R(y,y \ x,x \ (x * (((x \ y) \ 1) \ 1))),z)
    ]]></literal>
    <justification jstring="[para(3006(a,1),13146(a,2,1,3,2))].">
      <j1 rule="para" parents="3006 13146"/>
    </justification>
  </clause>

  <clause id="13151">
    <literal><![CDATA[
      K(((x \ (x / (y \ x))) * (y \ x)) \ (x / (((y \ x) \ 1) \ 1)),z) = K(R(y,y \ x,((x \ y) \ 1) \ 1),z)
    ]]></literal>
    <justification jstring="[para(9(a,1),13150(a,2,1,3))].">
      <j1 rule="para" parents="9 13150"/>
    </justification>
  </clause>

  <clause id="13155">
    <literal><![CDATA[
      K(((x \ (x / (y \ x))) * (y \ x)) \ (x / (((y \ x) \ 1) \ 1)),z) = K(R(y,y \ x,x \ y),z)
    ]]></literal>
    <justification jstring="[para(3387(a,1),13151(a,2,1))].">
      <j1 rule="para" parents="3387 13151"/>
    </justification>
  </clause>

  <clause id="13156">
    <literal><![CDATA[
      K(((x \ y) * (y \ x)) \ (x / (((y \ x) \ 1) \ 1)),z) = K(R(y,y \ x,x \ y),z)
    ]]></literal>
    <justification jstring="[para(76(a,1),13155(a,1,1,1,1,2))].">
      <j1 rule="para" parents="76 13155"/>
    </justification>
  </clause>

  <clause id="13158">
    <literal><![CDATA[
      K(((x \ y) * (y \ x)) \ (x * (((x \ y) \ 1) \ 1)),z) = K(R(y,y \ x,x \ y),z)
    ]]></literal>
    <justification jstring="[para(3006(a,1),13156(a,1,1,2))].">
      <j1 rule="para" parents="3006 13156"/>
    </justification>
  </clause>

  <clause id="13159">
    <literal><![CDATA[
      K(((x \ y) * (y \ x)) \ y,z) = K(R(y,y \ x,x \ y),z)
    ]]></literal>
    <justification jstring="[hyper(65,a,5891,a(flip),b,13158,a)].">
      <j1 rule="hyper" parents="65 5891 13158"/>
    </justification>
  </clause>

  <clause id="13161">
    <literal><![CDATA[
      K(R(x * y,(x * y) \ y,y \ (x * y)),z) = K((T(x,y) * ((x * y) \ y)) \ (x * y),z)
    ]]></literal>
    <justification jstring="[para(22(a,2),13159(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="22 13159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13162">
    <literal><![CDATA[
      K(R(x * y,(x * y) \ y,y \ (x * y)),z) = K((x * ((y * x) \ y)) \ (x * y),z)
    ]]></literal>
    <justification jstring="[para(9873(a,1),13161(a,2,1,1))].">
      <j1 rule="para" parents="9873 13161"/>
    </justification>
  </clause>

  <clause id="13163">
    <literal><![CDATA[
      K(R(x * y,(x * y) \ y,y \ (x * y)),z) = L(K(T(y * x,y),z),y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,7536,a(flip),b,13162,a),flip(a)].">
      <j1 rule="hyper" parents="299 7536 13162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13164">
    <literal><![CDATA[
      K(R(x * y,(x * y) \ y,T(x,y)),z) = L(K(T(y * x,y),z),y,x)
    ]]></literal>
    <justification jstring="[para(22(a,2),13163(a,1,1,3))].">
      <j1 rule="para" parents="22 13163"/>
    </justification>
  </clause>

  <clause id="13165">
    <literal><![CDATA[
      K(R(x * y,(x * y) \ y,T(x,y)),z) = L(K(y * x,T(z,y)),y,x)
    ]]></literal>
    <justification jstring="[para(7537(a,1),13164(a,2,1))].">
      <j1 rule="para" parents="7537 13164"/>
    </justification>
  </clause>

  <clause id="13166">
    <literal><![CDATA[
      R(K(x * y,z),y,T(x,y)) = L(K(y * x,T(z,y)),y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,10706,a(flip),b,13165,a)].">
      <j1 rule="hyper" parents="65 10706 13165"/>
    </justification>
  </clause>

  <clause id="13167">
    <literal><![CDATA[
      (K(x * y,z) * ((x * y) / x)) * x = (x * y) * L(K(y * x,T(z,y)),y,x)
    ]]></literal>
    <justification jstring="[para(13166(a,1),7135(a,2,2))].">
      <j1 rule="para" parents="13166 7135"/>
    </justification>
  </clause>

  <clause id="13168">
    <literal><![CDATA[
      K(x,T(y,K(y * T(x,y),z))) * ((K(y * T(x,y),z) * y) * x) = (x * y) * L(K(y * x,T(z,y)),y,x)
    ]]></literal>
    <justification jstring="[para(13166(a,1),9481(a,2,2))].">
      <j1 rule="para" parents="13166 9481"/>
    </justification>
  </clause>

  <clause id="13169">
    <literal><![CDATA[
      (K(x * y,z) * ((x * y) / x)) * x = x * (y * K(y * x,T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(299,a,94,a(flip),b,13167,a),flip(a)].">
      <j1 rule="hyper" parents="299 94 13167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13170">
    <literal><![CDATA[
      (K(x * y,z) * ((x * y) / x)) * x = x * (K(y * x,z) * y)
    ]]></literal>
    <justification jstring="[hyper(299,a,7601,a(flip),b,13169,a),flip(a)].">
      <j1 rule="hyper" parents="299 7601 13169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13171">
    <literal><![CDATA[
      (K(x * y,z) * y) * T(x,y) = x * (K(y * x,z) * y)
    ]]></literal>
    <justification jstring="[hyper(7101,a,13170,a)].">
      <j1 rule="hyper" parents="7101 13170"/>
    </justification>
  </clause>

  <clause id="13172">
    <literal><![CDATA[
      K(x * y,z) * x = x * K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(12138,a,13171,a),flip(a)].">
      <j1 rule="hyper" parents="12138 13171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13173">
    <literal><![CDATA[
      K(x * y,T(z,y)) = K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(8153,a,13172,a),flip(a)].">
      <j1 rule="hyper" parents="8153 13172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13174">
    <literal><![CDATA[
      K(x * y,T(z,x)) = K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(7606,a,13172,a)].">
      <j1 rule="hyper" parents="7606 13172"/>
    </justification>
  </clause>

  <clause id="13177">
    <literal><![CDATA[
      K(x * (y / x),z) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[para(12(a,1),13173(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12 13173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13178">
    <literal><![CDATA[
      K(x * T(x \ y,z),T(u,x)) = K(x * T(y / x,z),u)
    ]]></literal>
    <justification jstring="[para(432(a,1),13173(a,1,1))].">
      <j1 rule="para" parents="432 13173"/>
    </justification>
  </clause>

  <clause id="13179">
    <literal><![CDATA[
      K(x * ((x \ 1) \ (y * z)),T(u,z)) = K(z * (x * ((x \ 1) \ y)),u)
    ]]></literal>
    <justification jstring="[para(1174(a,1),13173(a,1,1))].">
      <j1 rule="para" parents="1174 13173"/>
    </justification>
  </clause>

  <clause id="13180">
    <literal><![CDATA[
      K(x * y,z) * (y * x) = T(y * x,T(z,x))
    ]]></literal>
    <justification jstring="[para(13173(a,1),5096(a,2,1)),flip(a)].">
      <j1 rule="para" parents="13173 5096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13181">
    <literal><![CDATA[
      K(x * y,z) * y = y * K(y * x,z)
    ]]></literal>
    <justification jstring="[para(13173(a,1),7507(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13173 7507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13182">
    <literal><![CDATA[
      K(x * y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * x,z) = u
    ]]></literal>
    <justification jstring="[para(13173(a,1),8171(a,1))].">
      <j1 rule="para" parents="13173 8171"/>
    </justification>
  </clause>

  <clause id="13183">
    <literal><![CDATA[
      x / ((y * z) * K(u,T(y * z,z))) = (x / (y * z)) * K(z * y,u)
    ]]></literal>
    <justification jstring="[para(13173(a,1),9048(a,2,2))].">
      <j1 rule="para" parents="13173 9048"/>
    </justification>
  </clause>

  <clause id="13184">
    <literal><![CDATA[
      K((x * y) * T(z,y),T(u,z * y)) = K((z * y) * R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(11279(a,1),13173(a,1,1))].">
      <j1 rule="para" parents="11279 13173"/>
    </justification>
  </clause>

  <clause id="13185">
    <literal><![CDATA[
      K((x \ 1) * y,T(z,x)) = K(y * (x \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(9450,a,13174,a)].">
      <j1 rule="hyper" parents="9450 13174"/>
    </justification>
  </clause>

  <clause id="13186">
    <literal><![CDATA[
      K((x \ y) * x,z) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[para(10(a,1),13174(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 13174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13187">
    <literal><![CDATA[
      K(x * y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * x,z) = u
    ]]></literal>
    <justification jstring="[para(13174(a,1),8171(a,1))].">
      <j1 rule="para" parents="13174 8171"/>
    </justification>
  </clause>

  <clause id="13188">
    <literal><![CDATA[
      K(x * y,z) * T(z,T(z * (y * x),y)) = L(z,y * x,z)
    ]]></literal>
    <justification jstring="[para(13174(a,1),12628(a,1,1))].">
      <j1 rule="para" parents="13174 12628"/>
    </justification>
  </clause>

  <clause id="13189">
    <literal><![CDATA[
      K(T(x,y) * y,z) = K(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[para(4263(a,2),13177(a,1,1))].">
      <j1 rule="para" parents="4263 13177"/>
    </justification>
  </clause>

  <clause id="13190">
    <literal><![CDATA[
      K(x * K((x \ y) \ 1,z),T(u,y)) = K(y * T(x / y,z),u)
    ]]></literal>
    <justification jstring="[para(5847(a,1),13177(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5847 13177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13191">
    <literal><![CDATA[
      T(x,(y \ z) * y) = x / K(z,T(x,y))
    ]]></literal>
    <justification jstring="[para(13186(a,1),5041(a,2,2))].">
      <j1 rule="para" parents="13186 5041"/>
    </justification>
  </clause>

  <clause id="13192">
    <literal><![CDATA[
      K(x,y) * (z * K(z * K(x,y),u)) = T(K(x,y) * z,T(u,K(x,y)))
    ]]></literal>
    <justification jstring="[para(13181(a,1),10403(a,1,2))].">
      <j1 rule="para" parents="13181 10403"/>
    </justification>
  </clause>

  <clause id="13193">
    <literal><![CDATA[
      T(x * K(x * y,z),T(y,x)) = T(x,y) * K(y * x,z)
    ]]></literal>
    <justification jstring="[para(13181(a,1),12137(a,1,1))].">
      <j1 rule="para" parents="13181 12137"/>
    </justification>
  </clause>

  <clause id="13194">
    <literal><![CDATA[
      K(T(x,y) * y,z) = K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,13174,a(flip),b,13189,a),flip(a)].">
      <j1 rule="hyper" parents="299 13174 13189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13195">
    <literal><![CDATA[
      T(x,(y \ z) * y) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,7561,a(flip),b,13191,a),flip(a)].">
      <j1 rule="hyper" parents="299 7561 13191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13196">
    <literal><![CDATA[
      T(x,(y \ z) * y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(13191(a,2),7566(a,1))].">
      <j1 rule="para" parents="13191 7566"/>
    </justification>
  </clause>

  <clause id="13197">
    <literal><![CDATA[
      T(x,T(y * z,y)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),13195(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 13195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13198">
    <literal><![CDATA[
      T(x,(x \ y) * x) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(13195(a,2),4462(a,1))].">
      <j1 rule="para" parents="13195 4462"/>
    </justification>
  </clause>

  <clause id="13199">
    <literal><![CDATA[
      T(x,T(y * z,y)) = x * K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(299,a,5083,a(flip),b,13197,a),flip(a)].">
      <j1 rule="hyper" parents="299 5083 13197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13200">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * y) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,8264,a,b,13197,a)].">
      <j1 rule="hyper" parents="65 8264 13197"/>
    </justification>
  </clause>

  <clause id="13201">
    <literal><![CDATA[
      K(T(x * y,x) / z,T(u,y * x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(z \ T(x * y,x),u) = w
    ]]></literal>
    <justification jstring="[para(13197(a,1),7526(a,1,2))].">
      <j1 rule="para" parents="13197 7526"/>
    </justification>
  </clause>

  <clause id="13202">
    <literal><![CDATA[
      T(x,T(y * x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(x * y,z)) = u
    ]]></literal>
    <justification jstring="[para(3479(a,1),13198(a,1,2))].">
      <j1 rule="para" parents="3479 13198"/>
    </justification>
  </clause>

  <clause id="13203">
    <literal><![CDATA[
      K(T(x,y),z * y) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(8274,a,13199,a),flip(a)].">
      <j1 rule="hyper" parents="8274 13199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13204">
    <literal><![CDATA[
      K(x / y,z * y) = K(y \ x,y * z)
    ]]></literal>
    <justification jstring="[hyper(7915,a,13199,a),flip(a)].">
      <j1 rule="hyper" parents="7915 13199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13205">
    <literal><![CDATA[
      K(x,T(y * z,y)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(5154,a,13199,a)].">
      <j1 rule="hyper" parents="5154 13199"/>
    </justification>
  </clause>

  <clause id="13206">
    <literal><![CDATA[
      T(x,T(y * z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(13199(a,2),5087(a,1))].">
      <j1 rule="para" parents="13199 5087"/>
    </justification>
  </clause>

  <clause id="13207">
    <literal><![CDATA[
      K(x,T(y * z,z)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(7709,a,13203,a)].">
      <j1 rule="hyper" parents="7709 13203"/>
    </justification>
  </clause>

  <clause id="13208">
    <literal><![CDATA[
      K(x / y,y * z) = K(y \ x,z * y)
    ]]></literal>
    <justification jstring="[para(109(a,1),13203(a,1,1)),flip(a)].">
      <j1 rule="para" parents="109 13203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13209">
    <literal><![CDATA[
      K(x,y * z) * z = z * K(x,z * y)
    ]]></literal>
    <justification jstring="[para(13203(a,1),7541(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13203 7541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13210">
    <literal><![CDATA[
      K(x,(y \ z) * y) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(10(a,1),13205(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 13205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13211">
    <literal><![CDATA[
      K(x,T(y * (z * u),y * z)) = K(x,L(u,z,y) * (y * z))
    ]]></literal>
    <justification jstring="[para(94(a,1),13205(a,1,2,1))].">
      <j1 rule="para" parents="94 13205"/>
    </justification>
  </clause>

  <clause id="13212">
    <literal><![CDATA[
      T(x * y,T(z,x)) \ 1 = (x * y) \ K(z,y * x)
    ]]></literal>
    <justification jstring="[para(13205(a,1),7550(a,2,2))].">
      <j1 rule="para" parents="13205 7550"/>
    </justification>
  </clause>

  <clause id="13213">
    <literal><![CDATA[
      K(x,y * z) * T(x,z) = T(T(x,z),z * y)
    ]]></literal>
    <justification jstring="[para(13205(a,1),7564(a,1,1))].">
      <j1 rule="para" parents="13205 7564"/>
    </justification>
  </clause>

  <clause id="13214">
    <literal><![CDATA[
      K(x,y * z) * ((z * y) \ u) = T(z * y,T(x,z)) \ u
    ]]></literal>
    <justification jstring="[para(13205(a,1),7574(a,1,1))].">
      <j1 rule="para" parents="13205 7574"/>
    </justification>
  </clause>

  <clause id="13215">
    <literal><![CDATA[
      K(x,y * (z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T((z \ 1) * y,z)) = u
    ]]></literal>
    <justification jstring="[para(13205(a,1),9450(a,1))].">
      <j1 rule="para" parents="13205 9450"/>
    </justification>
  </clause>

  <clause id="13216">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) \ u)) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(13205(a,1),12799(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13205 12799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13217">
    <literal><![CDATA[
      K(x,T(y * (z \ x),z)) = K(x,(z \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(8844,a,13207,a)].">
      <j1 rule="hyper" parents="8844 13207"/>
    </justification>
  </clause>

  <clause id="13218">
    <literal><![CDATA[
      K(x,y * (z / y)) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(12(a,1),13207(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 13207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13219">
    <literal><![CDATA[
      K(x,T((y * z) * u,z * u)) = K(x,(z * u) * R(y,z,u))
    ]]></literal>
    <justification jstring="[para(103(a,1),13207(a,1,2,1))].">
      <j1 rule="para" parents="103 13207"/>
    </justification>
  </clause>

  <clause id="13220">
    <literal><![CDATA[
      K(x,L(T(y * z,z),u,w)) = L(K(x,z * y),u,w)
    ]]></literal>
    <justification jstring="[para(13207(a,1),11889(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13207 11889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13221">
    <literal><![CDATA[
      K(x,T(T(y * z,u),y)) = K(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(3479(a,1),13210(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3479 13210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13222">
    <literal><![CDATA[
      K(x,T(y / (z \ 1),z)) = K(x,y / (T(z,y) \ 1))
    ]]></literal>
    <justification jstring="[para(7318(a,2),13218(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7318 13218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13223">
    <literal><![CDATA[
      T(x / (y * z),z * y) = T((y * z) \ x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(753,a,13200,a),flip(a)].">
      <j1 rule="hyper" parents="753 13200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13224">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * z) = T(x,z * y)
    ]]></literal>
    <justification jstring="[para(8050(a,1),13200(a,1,1))].">
      <j1 rule="para" parents="8050 13200"/>
    </justification>
  </clause>

  <clause id="13225">
    <literal><![CDATA[
      T(T(x,K(y,z)),(z \ 1) * y) = T(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[para(8812(a,1),13200(a,1,1))].">
      <j1 rule="para" parents="8812 13200"/>
    </justification>
  </clause>

  <clause id="13226">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * (z \ 1)) = T(x,(z \ 1) * y)
    ]]></literal>
    <justification jstring="[para(8814(a,1),13200(a,1,1))].">
      <j1 rule="para" parents="8814 13200"/>
    </justification>
  </clause>

  <clause id="13229">
    <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(5632(a,2),13182(a,1,1))].">
      <j1 rule="para" parents="5632 13182"/>
    </justification>
  </clause>

  <clause id="13231">
    <literal><![CDATA[
      K(T(x,y) * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * x,z) = u
    ]]></literal>
    <justification jstring="[para(13189(a,2),13182(a,1))].">
      <j1 rule="para" parents="13189 13182"/>
    </justification>
  </clause>

  <clause id="13232">
    <literal><![CDATA[
      K((x * x) * (y * z),T(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(z * ((x * x) * y),u) = w
    ]]></literal>
    <justification jstring="[para(33(a,1),13187(a,1,1))].">
      <j1 rule="para" parents="33 13187"/>
    </justification>
  </clause>

  <clause id="13233">
    <literal><![CDATA[
      K(x * T(y,z),T(u,K(y,z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(y,z) * (x * y),u) = w
    ]]></literal>
    <justification jstring="[para(6832(a,1),13187(a,1,1))].">
      <j1 rule="para" parents="6832 13187"/>
    </justification>
  </clause>

  <clause id="13234">
    <literal><![CDATA[
      K((x * y) * T(z,y),T(u,z * y)) != w
    ]]></literal>
    <literal><![CDATA[
      K((z * y) * R(x,y,z),u) = w
    ]]></literal>
    <justification jstring="[para(11279(a,1),13187(a,1,1))].">
      <j1 rule="para" parents="11279 13187"/>
    </justification>
  </clause>

  <clause id="13236">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(8264(a,2),13206(a,1))].">
      <j1 rule="para" parents="8264 13206"/>
    </justification>
  </clause>

  <clause id="13237">
    <literal><![CDATA[
      K(L(T(x,y),z,u) * y,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(y * L(x,z,u),w) = v5
    ]]></literal>
    <justification jstring="[para(25(a,2),13231(a,1,1,1))].">
      <j1 rule="para" parents="25 13231"/>
    </justification>
  </clause>

  <clause id="13239">
    <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(2093(a,1),13185(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2093 13185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13240">
    <literal><![CDATA[
      K(x,K(y,z \ (u \ 1))) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(8823,a,13216,a)].">
      <j1 rule="hyper" parents="8823 13216"/>
    </justification>
  </clause>

  <clause id="13241">
    <literal><![CDATA[
      K(x,K(y,((z / u) \ 1) \ u)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(12(a,1),13216(a,2,2,2))].">
      <j1 rule="para" parents="12 13216"/>
    </justification>
  </clause>

  <clause id="13242">
    <literal><![CDATA[
      K(x,(y \ x) * R(y,z,u)) = K(x,x * (y \ R(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,10950,a(flip),b,13217,a),flip(a)].">
      <j1 rule="hyper" parents="65 10950 13217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13243">
    <literal><![CDATA[
      K(x,T(T(y * z,y),u)) = K(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[hyper(7715,a,13221,a)].">
      <j1 rule="hyper" parents="7715 13221"/>
    </justification>
  </clause>

  <clause id="13244">
    <literal><![CDATA[
      K(x,T(y * x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(x * y,z)) = u
    ]]></literal>
    <justification jstring="[para(13221(a,1),5196(a,1))].">
      <j1 rule="para" parents="13221 5196"/>
    </justification>
  </clause>

  <clause id="13245">
    <literal><![CDATA[
      K(x,T(y * z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(13221(a,1),8171(a,1))].">
      <j1 rule="para" parents="13221 8171"/>
    </justification>
  </clause>

  <clause id="13247">
    <literal><![CDATA[
      K(x,T(y * z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(8974(a,1),13245(a,1))].">
      <j1 rule="para" parents="8974 13245"/>
    </justification>
  </clause>

  <clause id="13248">
    <literal><![CDATA[
      K(x,T(y * (z * u),y * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(u,z,y) * (y * z)) = w
    ]]></literal>
    <justification jstring="[para(94(a,1),13247(a,1,2,1))].">
      <j1 rule="para" parents="94 13247"/>
    </justification>
  </clause>

  <clause id="13249">
    <literal><![CDATA[
      K(x,(y \ 1) \ (z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,((y \ 1) \ z) * y) = u
    ]]></literal>
    <justification jstring="[para(1175(a,1),13247(a,1,2))].">
      <j1 rule="para" parents="1175 13247"/>
    </justification>
  </clause>

  <clause id="13250">
    <literal><![CDATA[
      K(x,y * ((y * z) / y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(13218(a,2),13247(a,1))].">
      <j1 rule="para" parents="13218 13247"/>
    </justification>
  </clause>

  <clause id="13251">
    <literal><![CDATA[
      K(x,K(y \ (z * u),z * u)) = K(x,K(z * u,(z \ y) \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,9554,a(flip),b,13240,a),flip(a)].">
      <j1 rule="hyper" parents="65 9554 13240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13252">
    <literal><![CDATA[
      (x / y) \ T(x,K(z,u)) = y * K(z,K(u,x))
    ]]></literal>
    <justification jstring="[para(13241(a,1),9161(a,2,2))].">
      <j1 rule="para" parents="13241 9161"/>
    </justification>
  </clause>

  <clause id="13254">
    <literal><![CDATA[
      T(x,y * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(T(x,K(y,z)),z * y) = u
    ]]></literal>
    <justification jstring="[para(6256(a,1),13236(a,1,1))].">
      <j1 rule="para" parents="6256 13236"/>
    </justification>
  </clause>

  <clause id="13255">
    <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(8004(a,1),13236(a,1,1,2))].">
      <j1 rule="para" parents="8004 13236"/>
    </justification>
  </clause>

  <clause id="13256">
    <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(7980(a,1),13236(a,1,1,2))].">
      <j1 rule="para" parents="7980 13236"/>
    </justification>
  </clause>

  <clause id="13257">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(8050(a,1),13236(a,1,1))].">
      <j1 rule="para" parents="8050 13236"/>
    </justification>
  </clause>

  <clause id="13258">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(T(z,u),u) * y) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * T(T(z,u),u)) = w
    ]]></literal>
    <justification jstring="[para(8104(a,1),13236(a,1,1,2))].">
      <j1 rule="para" parents="8104 13236"/>
    </justification>
  </clause>

  <clause id="13259">
    <literal><![CDATA[
      T(T(x,y * z),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(8060(a,1),13236(a,1))].">
      <j1 rule="para" parents="8060 13236"/>
    </justification>
  </clause>

  <clause id="13260">
    <literal><![CDATA[
      K(x,y * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y) * y) = u
    ]]></literal>
    <justification jstring="[para(223(a,1),13250(a,1,2,2))].">
      <j1 rule="para" parents="223 13250"/>
    </justification>
  </clause>

  <clause id="13261">
    <literal><![CDATA[
      K(x,T(y,z) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(4263(a,2),13250(a,1,2))].">
      <j1 rule="para" parents="4263 13250"/>
    </justification>
  </clause>

  <clause id="13262">
    <literal><![CDATA[
      K(x,T(y,z) * z) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(13260,a,xx)].">
      <j1 rule="hyper" parents="13260"/>
    </justification>
  </clause>

  <clause id="13263">
    <literal><![CDATA[
      K(x,T(y,z * (1 / u)) * (z * (u \ 1))) = K(x,(z * (1 / u)) * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,5659,a(flip),b,13262,a)].">
      <j1 rule="hyper" parents="65 5659 13262"/>
    </justification>
  </clause>

  <clause id="13264">
    <literal><![CDATA[
      K(x,T(y,(1 / z) \ u) * ((z \ 1) \ u)) = K(x,((1 / z) \ u) * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,5658,a(flip),b,13262,a)].">
      <j1 rule="hyper" parents="65 5658 13262"/>
    </justification>
  </clause>

  <clause id="13265">
    <literal><![CDATA[
      T(x,T(y,z) * z) = x * K(x,z * y)
    ]]></literal>
    <justification jstring="[para(13262(a,1),5083(a,2,2))].">
      <j1 rule="para" parents="13262 5083"/>
    </justification>
  </clause>

  <clause id="13266">
    <literal><![CDATA[
      T(x,T(y,z) * z) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(299,a,5083,a,b,13265,a),flip(a)].">
      <j1 rule="hyper" parents="299 5083 13265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13267">
    <literal><![CDATA[
      T(x,T(y,z) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(13265(a,2),5087(a,1))].">
      <j1 rule="para" parents="13265 5087"/>
    </justification>
  </clause>

  <clause id="13268">
    <literal><![CDATA[
      (T(x,y) * y) * T(z,y * x) = z * (T(x,y) * y)
    ]]></literal>
    <justification jstring="[para(13266(a,1),107(a,1,2))].">
      <j1 rule="para" parents="13266 107"/>
    </justification>
  </clause>

  <clause id="13269">
    <literal><![CDATA[
      T(x,(y \ z) * y) = T(x,y * (z / y))
    ]]></literal>
    <justification jstring="[para(109(a,1),13266(a,1,2,1))].">
      <j1 rule="para" parents="109 13266"/>
    </justification>
  </clause>

  <clause id="13270">
    <literal><![CDATA[
      T(x,T(y,z * u) * (u * z)) = T(x,(u * z) * T(y,K(z,u)))
    ]]></literal>
    <justification jstring="[para(13200(a,1),13266(a,1,2,1))].">
      <j1 rule="para" parents="13200 13266"/>
    </justification>
  </clause>

  <clause id="13271">
    <literal><![CDATA[
      T(x,y * (z / y)) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(13196,a,13269,a),flip(a)].">
      <j1 rule="hyper" parents="13196 13269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13272">
    <literal><![CDATA[
      T(x,T(y * z,z)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[para(11(a,1),13271(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 13271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13273">
    <literal><![CDATA[
      T(x,y * ((z * z) \ (u / y))) = T(x,T((z * z) \ u,y))
    ]]></literal>
    <justification jstring="[para(763(a,1),13271(a,1,2,2))].">
      <j1 rule="para" parents="763 13271"/>
    </justification>
  </clause>

  <clause id="13274">
    <literal><![CDATA[
      T(x,T(y,z * u) * (T(u,z) * z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(T(u,z) * z) * y) = w
    ]]></literal>
    <justification jstring="[para(13266(a,1),13267(a,1,2,1))].">
      <j1 rule="para" parents="13266 13267"/>
    </justification>
  </clause>

  <clause id="13276">
    <literal><![CDATA[
      T(K(x,y) * K(z,x),T(u,K(x,y))) \ 1 = K(x,T(z,u)) * K(y,T(x,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,12607,a(flip),b,13212,a),flip(a)].">
      <j1 rule="hyper" parents="299 12607 13212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13277">
    <literal><![CDATA[
      K(x,L(T(y * z,z),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(z * y,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(13220(a,2),11995(a,1))].">
      <j1 rule="para" parents="13220 11995"/>
    </justification>
  </clause>

  <clause id="13278">
    <literal><![CDATA[
      K(x,y / (T(z,y) \ 1)) = K(x,(z \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,8837,a(flip),b,13222,a),flip(a)].">
      <j1 rule="hyper" parents="65 8837 13222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13279">
    <literal><![CDATA[
      K(x,(y / z) / (z \ 1)) = K(x,(z \ 1) \ (z \ y))
    ]]></literal>
    <justification jstring="[para(10183(a,1),13278(a,1,2))].">
      <j1 rule="para" parents="10183 13278"/>
    </justification>
  </clause>

  <clause id="13280">
    <literal><![CDATA[
      T((x * y) \ z,K(y,x)) = (y * x) \ (z * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(11317,a,13223,a),flip(a)].">
      <j1 rule="hyper" parents="11317 13223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13281">
    <literal><![CDATA[
      T(T(x,K((y \ 1) \ z,y)),z) = T(x,((y \ 1) \ z) * (y \ 1))
    ]]></literal>
    <justification jstring="[para(10(a,1),13225(a,1,2))].">
      <j1 rule="para" parents="10 13225"/>
    </justification>
  </clause>

  <clause id="13282">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(y,z) * (z \ 1)) = T(x,(z \ 1) * T(y,z))
    ]]></literal>
    <justification jstring="[para(5188(a,1),13226(a,1,1,2))].">
      <j1 rule="para" parents="5188 13226"/>
    </justification>
  </clause>

  <clause id="13283">
    <literal><![CDATA[
      (x * ((x * y) / x)) * T(z,y * x) = z * (T(x,y) * y)
    ]]></literal>
    <justification jstring="[para(4263(a,1),13268(a,1,1))].">
      <j1 rule="para" parents="4263 13268"/>
    </justification>
  </clause>

  <clause id="13284">
    <literal><![CDATA[
      K(x,T((y \ 1) * (z * y),y)) = R(K(x,z),y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(13215,a,12834,a)].">
      <j1 rule="hyper" parents="13215 12834"/>
    </justification>
  </clause>

  <clause id="13285">
    <literal><![CDATA[
      R(K(x,y),z,z \ 1) = K(x,L(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(65,a,9488,a(flip),b,13284,a),flip(a)].">
      <j1 rule="hyper" parents="65 9488 13284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13286">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1)) = K(x,L(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(65,a,12833,a(flip),b,13285,a)].">
      <j1 rule="hyper" parents="65 12833 13285"/>
    </justification>
  </clause>

  <clause id="13287">
    <literal><![CDATA[
      K(x,R(y,z,(K(x,u) * z) \ 1)) = K(x,L(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(65,a,12187,a,b,13286,a)].">
      <j1 rule="hyper" parents="65 12187 13286"/>
    </justification>
  </clause>

  <clause id="13288">
    <literal><![CDATA[
      K(x,L(y / z,z,z \ 1)) = K(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[para(565(a,1),13286(a,1,2)),flip(a)].">
      <j1 rule="para" parents="565 13286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13289">
    <literal><![CDATA[
      (R(x,y,y \ 1) \ (x * y)) * R(x,y,y \ 1) = (x * y) * K((y \ 1) \ 1,L(x,y,y \ 1))
    ]]></literal>
    <justification jstring="[para(13286(a,1),12227(a,2,2))].">
      <j1 rule="para" parents="13286 12227"/>
    </justification>
  </clause>

  <clause id="13290">
    <literal><![CDATA[
      L(K(x,y / z),z,z \ 1) = K(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(11890,a,13288,a)].">
      <j1 rule="hyper" parents="11890 13288"/>
    </justification>
  </clause>

  <clause id="13291">
    <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(9450,a,13178,a)].">
      <j1 rule="hyper" parents="9450 13178"/>
    </justification>
  </clause>

  <clause id="13292">
    <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(10958(a,1),13188(a,1,1,1))].">
      <j1 rule="para" parents="10958 13188"/>
    </justification>
  </clause>

  <clause id="13293">
    <literal><![CDATA[
      K(x,T(T((y * z) * (u / (y * z)),y * z),z * (u / T(y * z,u)))) = K(x,(z * (u / T(y * z,u))) * R(y,z,u / T(y * z,u)))
    ]]></literal>
    <justification jstring="[para(4417(a,2),13219(a,1,2,1))].">
      <j1 rule="para" parents="4417 13219"/>
    </justification>
  </clause>

  <clause id="13294">
    <literal><![CDATA[
      K(x,K(y * z,(y \ u) \ z)) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(8776,a,13251,a),flip(a)].">
      <j1 rule="hyper" parents="8776 13251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13295">
    <literal><![CDATA[
      K(x,K(y * z,z \ (y \ u))) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(8823,a,13294,a)].">
      <j1 rule="hyper" parents="8823 13294"/>
    </justification>
  </clause>

  <clause id="13296">
    <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(5688(a,2),13295(a,2,2))].">
      <j1 rule="para" parents="5688 13295"/>
    </justification>
  </clause>

  <clause id="13297">
    <literal><![CDATA[
      T(T(x,y),K(z,(z \ 1) \ y)) = T(x,((z \ 1) \ y) * (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(8064,a,13281,a)].">
      <j1 rule="hyper" parents="8064 13281"/>
    </justification>
  </clause>

  <clause id="13298">
    <literal><![CDATA[
      T(T(x,K((y \ 1) \ (y \ z),y)),T((y \ 1) \ (y \ z),y) * (y \ 1)) = T(x,y \ (1 * T(1 \ z,y)))
    ]]></literal>
    <justification jstring="[para(1464(a,1),13282(a,2,2))].">
      <j1 rule="para" parents="1464 13282"/>
    </justification>
  </clause>

  <clause id="13299">
    <literal><![CDATA[
      T(T(x,y),K(z,(z \ 1) \ y)) = T(x,T(y,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(299,a,13195,a(flip),b,13297,a),flip(a)].">
      <j1 rule="hyper" parents="299 13195 13297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13300">
    <literal><![CDATA[
      T(T(x,y),K(z,(z \ 1) \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(13299(a,2),8840(a,1))].">
      <j1 rule="para" parents="13299 8840"/>
    </justification>
  </clause>

  <clause id="13301">
    <literal><![CDATA[
      K((x * x) * (y * z),T(u,z)) = K(z * (x * ((x \ 1) \ y)),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,6033,a(flip),b,13179,a)].">
      <j1 rule="hyper" parents="65 6033 13179"/>
    </justification>
  </clause>

  <clause id="13302">
    <literal><![CDATA[
      K(x * (y * ((y \ 1) \ z)),u) = K(x * ((y * y) * z),u)
    ]]></literal>
    <justification jstring="[hyper(13232,a,13301,a),flip(a)].">
      <j1 rule="hyper" parents="13232 13301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13303">
    <literal><![CDATA[
      x / ((y * z) * K(u,z * y)) = (x / (y * z)) * K(z * y,u)
    ]]></literal>
    <justification jstring="[para(13207(a,1),13183(a,1,2,2))].">
      <j1 rule="para" parents="13207 13183"/>
    </justification>
  </clause>

  <clause id="13304">
    <literal><![CDATA[
      x / y != (x / (z * u)) * K(u * z,w)
    ]]></literal>
    <literal><![CDATA[
      (z * u) * K(w,u * z) = y
    ]]></literal>
    <justification jstring="[para(13303(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="13303 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13305">
    <literal><![CDATA[
      T(K(x,y) * K(z,x),T(u,K(x,y))) = T(K(z,x) * K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(10046,a,13192,a),flip(a)].">
      <j1 rule="hyper" parents="10046 13192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13306">
    <literal><![CDATA[
      T(K(x,y) * K(y,z),u) \ 1 = K(y,T(x,u)) * K(z,T(y,u))
    ]]></literal>
    <justification jstring="[para(13305(a,1),13276(a,1,1))].">
      <j1 rule="para" parents="13305 13276"/>
    </justification>
  </clause>

  <clause id="13307">
    <literal><![CDATA[
      K(x,T(y,z)) * K(u,T(x,z)) = T(K(x,y) * K(u,x),z)
    ]]></literal>
    <justification jstring="[hyper(12372,a,13306,a),flip(a)].">
      <j1 rule="hyper" parents="12372 13306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13308">
    <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(13307(a,1),10033(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13307 10033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13309">
    <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(65,a,11819,a(flip),b,13308,a),flip(a)].">
      <j1 rule="hyper" parents="65 11819 13308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13310">
    <literal><![CDATA[
      K(x \ T(x * y,z),T(u,x)) = K((x \ 1) * T(y / (x \ 1),z),u)
    ]]></literal>
    <justification jstring="[para(1012(a,1),13291(a,1,1))].">
      <j1 rule="para" parents="1012 13291"/>
    </justification>
  </clause>

  <clause id="13311">
    <literal><![CDATA[
      K((x \ 1) * T(y / (x \ 1),z),u) = K(x \ T(y * x,z),u)
    ]]></literal>
    <justification jstring="[hyper(7809,a,13310,a),flip(a)].">
      <j1 rule="hyper" parents="7809 13310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13313">
    <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(11110(a,1),13309(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11110 13309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13315">
    <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(13313(a,1),12959(a,2,1))].">
      <j1 rule="para" parents="13313 12959"/>
    </justification>
  </clause>

  <clause id="13316">
    <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(12950(a,1),13315(a,2,1,1))].">
      <j1 rule="para" parents="12950 13315"/>
    </justification>
  </clause>

  <clause id="13318">
    <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(10278(a,1),13316(a,1,1,1))].">
      <j1 rule="para" parents="10278 13316"/>
    </justification>
  </clause>

  <clause id="13320">
    <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(11539(a,1),13318(a,1,1))].">
      <j1 rule="para" parents="11539 13318"/>
    </justification>
  </clause>

  <clause id="13321">
    <literal><![CDATA[
      (R(a(x,y,x),z,u) * z) * u = (z * a(x,y,x)) * u
    ]]></literal>
    <justification jstring="[para(9720(a,1),13320(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9720 13320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13322">
    <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(119,a,13321,a(flip),b,776,a)].">
      <j1 rule="hyper" parents="119 13321 776"/>
    </justification>
  </clause>

  <clause id="13324">
    <literal><![CDATA[
      a(R(a(x,y,x),z,u),z,u) = K(z,T(a(x,y,x),u))
    ]]></literal>
    <justification jstring="[hyper(11574,a,13322,a),flip(a)].">
      <j1 rule="hyper" parents="11574 13322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13325">
    <literal><![CDATA[
      a(R(a(x,y,x),z,u),z,u) = K(z,a(x,y,x))
    ]]></literal>
    <justification jstring="[para(10114(a,1),13324(a,2,2))].">
      <j1 rule="para" parents="10114 13324"/>
    </justification>
  </clause>

  <clause id="13326">
    <literal><![CDATA[
      a(R(a(x,y,x),z,u),z,u) = 1
    ]]></literal>
    <justification jstring="[hyper(299,a,10123,a(flip),b,13325,a),flip(a)].">
      <j1 rule="hyper" parents="299 10123 13325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13329">
    <literal><![CDATA[
      L(x,y,R(a(z,u,z),y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(54,a,13326,a)].">
      <j1 rule="hyper" parents="54 13326"/>
    </justification>
  </clause>

  <clause id="13330">
    <literal><![CDATA[
      (R(a(x,y,x),z,u) * (T(z,R(a(x,y,x),z,u)) * u)) / u = z * R(a(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(13329(a,1),11647(a,1,2))].">
      <j1 rule="para" parents="13329 11647"/>
    </justification>
  </clause>

  <clause id="13331">
    <literal><![CDATA[
      (R(a(x,y,x),z,u) * (z * u)) / u = z * R(a(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(10159(a,1),13330(a,1,1,2,1))].">
      <j1 rule="para" parents="10159 13330"/>
    </justification>
  </clause>

  <clause id="13332">
    <literal><![CDATA[
      x * R(a(y,z,y),x,u) = a(y,z,y) * x
    ]]></literal>
    <justification jstring="[hyper(550,a,13331,a),flip(a)].">
      <j1 rule="hyper" parents="550 13331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13334">
    <literal><![CDATA[
      R(a(x,y,x),z,u) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(36,a,10116,a(flip),b,13332,a),flip(a)].">
      <j1 rule="hyper" parents="36 10116 13332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13337">
    <literal><![CDATA[
      a(x,y,R(x,z,u)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,12948,a(flip),b,13334,a)].">
      <j1 rule="hyper" parents="65 12948 13334"/>
    </justification>
  </clause>

  <clause id="13338">
    <literal><![CDATA[
      a(x,y * K(z,y),x) = L(a(x,y,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,10630,a(flip),b,13334,a),flip(a)].">
      <j1 rule="hyper" parents="65 10630 13334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13339">
    <literal><![CDATA[
      (a(x,y,x) * z) * u = a(x,y,x) * (z * u)
    ]]></literal>
    <justification jstring="[para(13334(a,1),103(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13334 103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13341">
    <literal><![CDATA[
      L(x,y,a(z,u,z)) = x
    ]]></literal>
    <justification jstring="[para(13334(a,1),13329(a,1,3))].">
      <j1 rule="para" parents="13334 13329"/>
    </justification>
  </clause>

  <clause id="13342">
    <literal><![CDATA[
      a(x,y,x) * ((a(x,y,x) \ z) * u) = z * u
    ]]></literal>
    <justification jstring="[hyper(1164,a,13341,a)].">
      <j1 rule="hyper" parents="1164 13341"/>
    </justification>
  </clause>

  <clause id="13343">
    <literal><![CDATA[
      (a(x,y,x) * z) \ u = z \ (a(x,y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,281,a(flip),b,13341,a)].">
      <j1 rule="hyper" parents="65 281 13341"/>
    </justification>
  </clause>

  <clause id="13344">
    <literal><![CDATA[
      L(x,y,a(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      w = x
    ]]></literal>
    <justification jstring="[para(13341(a,1),52(a,1)),flip(a)].">
      <j1 rule="para" parents="13341 52"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13345">
    <literal><![CDATA[
      L(x,y,a(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(13341(a,1),52(a,2))].">
      <j1 rule="para" parents="13341 52"/>
    </justification>
  </clause>

  <clause id="13346">
    <literal><![CDATA[
      (a(x,y,x) * z) / u = a(x,y,x) * (z / u)
    ]]></literal>
    <justification jstring="[para(13341(a,1),585(a,1,2))].">
      <j1 rule="para" parents="13341 585"/>
    </justification>
  </clause>

  <clause id="13347">
    <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(13341(a,1),485(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13341 485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13350">
    <literal><![CDATA[
      a(x,y,R(x,z,u)) = a(x,y,L(x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(299,a,12938,a,b,13337,a),flip(a)].">
      <j1 rule="hyper" parents="299 12938 13337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13351">
    <literal><![CDATA[
      K(x,R(x,y,z) \ u) = K(x,u) * a(x,x \ u,x)
    ]]></literal>
    <justification jstring="[para(13337(a,1),12955(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13337 12955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13352">
    <literal><![CDATA[
      L(x,y,R(x,z,u)) = a(x,y,L(x,w,v5)) \ x
    ]]></literal>
    <justification jstring="[para(13350(a,1),12674(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13350 12674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13354">
    <literal><![CDATA[
      L(a(x,L(y,z,u),x),L(y,z,u),w) = a(x,L(y * K(w,y),z,u),x)
    ]]></literal>
    <justification jstring="[para(5809(a,1),13338(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5809 13338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13355">
    <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(13339(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="13339 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13356">
    <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(13339(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="13339 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13357">
    <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(13339(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="13339 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13358">
    <literal><![CDATA[
      a(x,y,x) * ((a(x,y,x) \ z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      z * u = w
    ]]></literal>
    <justification jstring="[para(13339(a,1),606(a,1))].">
      <j1 rule="para" parents="13339 606"/>
    </justification>
  </clause>

  <clause id="13359">
    <literal><![CDATA[
      (x * a(y,z,y)) * u = a(y,z,y) * (x * u)
    ]]></literal>
    <justification jstring="[para(10116(a,1),13339(a,1,1))].">
      <j1 rule="para" parents="10116 13339"/>
    </justification>
  </clause>

  <clause id="13360">
    <literal><![CDATA[
      L(x,y,R(x,z,u)) = L(x,y,L(x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(299,a,12943,a(flip),b,13352,a),flip(a)].">
      <j1 rule="hyper" parents="299 12943 13352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13363">
    <literal><![CDATA[
      L(x,y,L(x,z,u)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(535(a,1),13360(a,1,3)),flip(a)].">
      <j1 rule="para" parents="535 13360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13364">
    <literal><![CDATA[
      L(L(x,y,z),u,L(x,w,v5)) = L(L(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[para(13363(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13363 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13366">
    <literal><![CDATA[
      a(x,y,x) \ T(z * a(x,y,x),u) = z * K(z * a(x,y,x),u)
    ]]></literal>
    <justification jstring="[hyper(5090,a,13359,a)].">
      <j1 rule="hyper" parents="5090 13359"/>
    </justification>
  </clause>

  <clause id="13367">
    <literal><![CDATA[
      (x * a(y,x,y)) * z = x * (a(y,x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(299,a,12100,a(flip),b,13359,a),flip(a)].">
      <j1 rule="hyper" parents="299 12100 13359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13368">
    <literal><![CDATA[
      L(x,a(y,z,y),z) = x
    ]]></literal>
    <justification jstring="[hyper(490,a,13367,a)].">
      <j1 rule="hyper" parents="490 13367"/>
    </justification>
  </clause>

  <clause id="13369">
    <literal><![CDATA[
      L(x,K(y,z),z \ y) = x
    ]]></literal>
    <justification jstring="[hyper(12305,a,13368,a)].">
      <j1 rule="hyper" parents="12305 13368"/>
    </justification>
  </clause>

  <clause id="13370">
    <literal><![CDATA[
      L(x,K(y,z),y \ z) = x
    ]]></literal>
    <justification jstring="[hyper(7213,a,13369,a)].">
      <j1 rule="hyper" parents="7213 13369"/>
    </justification>
  </clause>

  <clause id="13371">
    <literal><![CDATA[
      (K(x,y) * (x \ y)) \ z = K(y,x) * ((x \ y) \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,7072,a(flip),b,13370,a)].">
      <j1 rule="hyper" parents="65 7072 13370"/>
    </justification>
  </clause>

  <clause id="13372">
    <literal><![CDATA[
      (L(x,y,z) \ L(L(x,u,x),y,z)) \ w = w * a(L(x,y,z),u,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(13364(a,1),10141(a,1,1,2))].">
      <j1 rule="para" parents="13364 10141"/>
    </justification>
  </clause>

  <clause id="13373">
    <literal><![CDATA[
      K(x,R(x,y,z) \ u) = K(x,x \ u)
    ]]></literal>
    <justification jstring="[hyper(299,a,9703,a(flip),b,13351,a),flip(a)].">
      <j1 rule="hyper" parents="299 9703 13351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13375">
    <literal><![CDATA[
      K(x,x \ ((x * R(T(x,y),z,u)) / w)) = K(x,w \ x)
    ]]></literal>
    <justification jstring="[hyper(10672,a,13373,a),flip(a)].">
      <j1 rule="hyper" parents="10672 13373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13377">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) / w) = K(x,w \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,11582,a(flip),b,13375,a)].">
      <j1 rule="hyper" parents="65 11582 13375"/>
    </justification>
  </clause>

  <clause id="13378">
    <literal><![CDATA[
      K(x,y \ R(x,z,u)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,12728,a(flip),b,13377,a)].">
      <j1 rule="hyper" parents="65 12728 13377"/>
    </justification>
  </clause>

  <clause id="13382">
    <literal><![CDATA[
      K(R(x,y,z),u \ x) = K(x,R(u,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,12868,a(flip),b,13378,a)].">
      <j1 rule="hyper" parents="65 12868 13378"/>
    </justification>
  </clause>

  <clause id="13384">
    <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(65,a,12488,a(flip),b,13382,a),flip(a)].">
      <j1 rule="hyper" parents="65 12488 13382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13385">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * (T(u * z,u) / u))) = a(u,L(z * K(x * y,z),y,x),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,12280,a(flip),b,13354,a)].">
      <j1 rule="hyper" parents="65 12280 13354"/>
    </justification>
  </clause>

  <clause id="13386">
    <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(65,a,12559,a(flip),b,13384,a)].">
      <j1 rule="hyper" parents="65 12559 13384"/>
    </justification>
  </clause>

  <clause id="13387">
    <literal><![CDATA[
      R(K(x,y),z,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(4778(a,1),13386(a,1,1))].">
      <j1 rule="para" parents="4778 13386"/>
    </justification>
  </clause>

  <clause id="13392">
    <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(13387(a,1),10771(a,1,1,1,2))].">
      <j1 rule="para" parents="13387 10771"/>
    </justification>
  </clause>

  <clause id="13395">
    <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(12460,a,13392,a)].">
      <j1 rule="hyper" parents="12460 13392"/>
    </justification>
  </clause>

  <clause id="13396">
    <literal><![CDATA[
      R(K(x,y),z,u) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(207,a,13395,a),flip(a)].">
      <j1 rule="hyper" parents="207 13395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13397">
    <literal><![CDATA[
      R(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,R(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(13395(a,1),207(a,1))].">
      <j1 rule="para" parents="13395 207"/>
    </justification>
  </clause>

  <clause id="13398">
    <literal><![CDATA[
      R(K(x,y),z,(K(x,u) * z) \ 1) = K(x,L(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(299,a,13287,a(flip),b,13396,a),flip(a)].">
      <j1 rule="hyper" parents="299 13287 13396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13399">
    <literal><![CDATA[
      K(R(x,y,z),u) = K(x,R(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,13387,a(flip),b,13396,a)].">
      <j1 rule="hyper" parents="65 13387 13396"/>
    </justification>
  </clause>

  <clause id="13404">
    <literal><![CDATA[
      K(x,y) * K(y,R(x,z,u)) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(13396(a,1),12882(a,1,2))].">
      <j1 rule="para" parents="13396 12882"/>
    </justification>
  </clause>

  <clause id="13405">
    <literal><![CDATA[
      T(x,x * y) * a(K(x,y),z,u) = L(x * K(x,R(y,z,u)),y,x)
    ]]></literal>
    <justification jstring="[para(13396(a,1),12909(a,2,1,2))].">
      <j1 rule="para" parents="13396 12909"/>
    </justification>
  </clause>

  <clause id="13406">
    <literal><![CDATA[
      K(R(x,y,z),R(x * y,y * z,u)) = K(x,R(x * y,z,u))
    ]]></literal>
    <justification jstring="[hyper(10829,a,13399,a),flip(a)].">
      <j1 rule="hyper" parents="10829 13399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13410">
    <literal><![CDATA[
      K(R(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,R(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(13387(a,1),13397(a,1))].">
      <j1 rule="para" parents="13387 13397"/>
    </justification>
  </clause>

  <clause id="13411">
    <literal><![CDATA[
      a(K(x,y),z * y,u) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,12889,a(flip),b,13404,a)].">
      <j1 rule="hyper" parents="65 12889 13404"/>
    </justification>
  </clause>

  <clause id="13412">
    <literal><![CDATA[
      K(a(K(x,y),z * y,u),w) = a(K(y,K(x,w)),z,u)
    ]]></literal>
    <justification jstring="[para(13411(a,2),12924(a,2,1)),flip(a)].">
      <j1 rule="para" parents="13411 12924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13413">
    <literal><![CDATA[
      a(K(x,K(y,z)),u * y,w) = a(K(y,K(x,z)),u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,12926,a,b,13412,a)].">
      <j1 rule="hyper" parents="65 12926 13412"/>
    </justification>
  </clause>

  <clause id="13415">
    <literal><![CDATA[
      x / (K(y,L(z,u,u \ 1)) * x) = u * ((K(y,z) * u) \ 1)
    ]]></literal>
    <justification jstring="[para(13398(a,1),6402(a,1,2,1))].">
      <j1 rule="para" parents="13398 6402"/>
    </justification>
  </clause>

  <clause id="13416">
    <literal><![CDATA[
      K(x,R(R(x * y,y * z,u),y,z)) = K(x,R(x * y,z,u))
    ]]></literal>
    <justification jstring="[hyper(13410,a,13406,a)].">
      <j1 rule="hyper" parents="13410 13406"/>
    </justification>
  </clause>

  <clause id="13417">
    <literal><![CDATA[
      x * ((K(y,z) * x) \ 1) = K(L(z,x,x \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(5440,a,13415,a),flip(a)].">
      <j1 rule="hyper" parents="5440 13415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13419">
    <literal><![CDATA[
      x \ K(y,L(z,x,x \ 1)) = (K(z,y) * x) \ 1
    ]]></literal>
    <justification jstring="[hyper(119,a,11929,a(flip),b,13417,a)].">
      <j1 rule="hyper" parents="119 11929 13417"/>
    </justification>
  </clause>

  <clause id="13420">
    <literal><![CDATA[
      K(x,((K(y,x) * (z \ 1)) \ 1) \ u) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(13419(a,1),9520(a,1,2,1))].">
      <j1 rule="para" parents="13419 9520"/>
    </justification>
  </clause>

  <clause id="13421">
    <literal><![CDATA[
      K(x,(((y \ 1) * K(z,x)) \ 1) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(7621(a,1),13420(a,1,2,1,1))].">
      <j1 rule="para" parents="7621 13420"/>
    </justification>
  </clause>

  <clause id="13422">
    <literal><![CDATA[
      K(x,((y * K(z,x)) \ 1) \ u) = K(x,(y \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,5910,a(flip),b,13421,a)].">
      <j1 rule="hyper" parents="65 5910 13421"/>
    </justification>
  </clause>

  <clause id="13423">
    <literal><![CDATA[
      K(x,((T(y,x) / z) \ 1) \ u) = K(x,((y / z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(1394(a,1),13422(a,1,2,1,1))].">
      <j1 rule="para" parents="1394 13422"/>
    </justification>
  </clause>

  <clause id="13424">
    <literal><![CDATA[
      K(x,((y / z) \ 1) \ z) = z \ ((T(y,x) / z) \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,10302,a(flip),b,13423,a),flip(a)].">
      <j1 rule="hyper" parents="65 10302 13423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13425">
    <literal><![CDATA[
      (T(x,y) / z) \ x = z * K(y,((x / z) \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(144,a,13424,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="144 13424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13426">
    <literal><![CDATA[
      x * K(y,((z / x) \ 1) \ x) != u
    ]]></literal>
    <literal><![CDATA[
      (T(z,y) / x) \ z = u
    ]]></literal>
    <justification jstring="[para(13424(a,2),250(a,1,2)),flip(b)].">
      <j1 rule="para" parents="13424 250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13427">
    <literal><![CDATA[
      (T(x,y) / z) \ x = (1 / z) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,12436,a(flip),b,13425,a),flip(a)].">
      <j1 rule="hyper" parents="299 12436 13425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13428">
    <literal><![CDATA[
      (1 / (x \ T(y,z))) \ K(z,y) = x \ y
    ]]></literal>
    <justification jstring="[para(76(a,1),13427(a,1,1)),flip(a)].">
      <j1 rule="para" parents="76 13427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13430">
    <literal><![CDATA[
      K(x,(1 / (y \ T(L(L(x,z,u),w,v5),v6))) \ K(v6,L(L(x,z,u),w,v5))) = K(x,L(L(x,z,u),w,v5) / y)
    ]]></literal>
    <justification jstring="[para(13428(a,2),7617(a,2,2)),flip(a)].">
      <j1 rule="para" parents="13428 7617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13431">
    <literal><![CDATA[
      (1 / x) \ K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      (T(z,y) / x) \ z = u
    ]]></literal>
    <justification jstring="[para(12436(a,1),13426(a,1))].">
      <j1 rule="para" parents="12436 13426"/>
    </justification>
  </clause>

  <clause id="13432">
    <literal><![CDATA[
      T(x,x * y) * a(K(x,y),z,u) = L(T(x,R(y,z,u)),y,x)
    ]]></literal>
    <justification jstring="[para(5083(a,2),13405(a,2,1))].">
      <j1 rule="para" parents="5083 13405"/>
    </justification>
  </clause>

  <clause id="13433">
    <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(13339(a,1),13357(a,1,2))].">
      <j1 rule="para" parents="13339 13357"/>
    </justification>
  </clause>

  <clause id="13434">
    <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(911,a,13433,a)].">
      <j1 rule="hyper" parents="911 13433"/>
    </justification>
  </clause>

  <clause id="13435">
    <literal><![CDATA[
      L(x,y,a(z,u,z) * w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(13345,a,13434,a),flip(a)].">
      <j1 rule="hyper" parents="13345 13434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13436">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),K(z,u) * y,a(u,z,u)) = L(x,y,K(u * z,u))
    ]]></literal>
    <justification jstring="[para(9684(a,1),13434(a,2,3))].">
      <j1 rule="para" parents="9684 13434"/>
    </justification>
  </clause>

  <clause id="13438">
    <literal><![CDATA[
      L(x,y,K(z * u,z)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(9684(a,1),13435(a,1,3))].">
      <j1 rule="para" parents="9684 13435"/>
    </justification>
  </clause>

  <clause id="13439">
    <literal><![CDATA[
      L(x,y,T(z * u,z)) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[para(9690(a,1),13435(a,1,3))].">
      <j1 rule="para" parents="9690 13435"/>
    </justification>
  </clause>

  <clause id="13440">
    <literal><![CDATA[
      L(x,y,K(z,z \ u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(9706(a,1),13435(a,1,3))].">
      <j1 rule="para" parents="9706 13435"/>
    </justification>
  </clause>

  <clause id="13441">
    <literal><![CDATA[
      L(x,y,R(z,u,z)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(10137(a,1),13435(a,1,3))].">
      <j1 rule="para" parents="10137 13435"/>
    </justification>
  </clause>

  <clause id="13442">
    <literal><![CDATA[
      L(x,y,L(z,u,z) \ w) = L(x,y,z \ w)
    ]]></literal>
    <justification jstring="[para(12040(a,1),13435(a,1,3))].">
      <j1 rule="para" parents="12040 13435"/>
    </justification>
  </clause>

  <clause id="13444">
    <literal><![CDATA[
      L(x,y,L(z,u,z)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,6003,a(flip),b,13441,a)].">
      <j1 rule="hyper" parents="65 6003 13441"/>
    </justification>
  </clause>

  <clause id="13445">
    <literal><![CDATA[
      L(x,y,L(z,u,z)) = L(x,y,L(z,w,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,13444,a,b,13444,a)].">
      <j1 rule="hyper" parents="299 13444 13444"/>
    </justification>
  </clause>

  <clause id="13447">
    <literal><![CDATA[
      L(x,y,T(z / u,z)) = L(x,y,u \ z)
    ]]></literal>
    <justification jstring="[para(4521(a,1),13444(a,1,3))].">
      <j1 rule="para" parents="4521 13444"/>
    </justification>
  </clause>

  <clause id="13449">
    <literal><![CDATA[
      L(x,y,K(z * y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(299,a,4570,a(flip),b,13438,a),flip(a)].">
      <j1 rule="hyper" parents="299 4570 13438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13450">
    <literal><![CDATA[
      L(x,y / z,K(y,z)) = x
    ]]></literal>
    <justification jstring="[para(5982(a,1),13449(a,1,3))].">
      <j1 rule="para" parents="5982 13449"/>
    </justification>
  </clause>

  <clause id="13451">
    <literal><![CDATA[
      K(x,y) * ((x / y) * z) = (x / T(y,x)) * z
    ]]></literal>
    <justification jstring="[para(13450(a,1),5550(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13450 5550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13452">
    <literal><![CDATA[
      L(x,y,(z \ u) * z) = L(x,y,T(u,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),13439(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="10 13439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13453">
    <literal><![CDATA[
      L(x,y \ z,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(4775,a,13440,a)].">
      <j1 rule="hyper" parents="4775 13440"/>
    </justification>
  </clause>

  <clause id="13454">
    <literal><![CDATA[
      (K(x,y) * (x \ y)) \ z = (x \ y) \ (K(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,5442,a(flip),b,13453,a)].">
      <j1 rule="hyper" parents="65 5442 13453"/>
    </justification>
  </clause>

  <clause id="13457">
    <literal><![CDATA[
      L(x,y,L(z,u,z)) = L(x,y,w / (T(w,z) / z))
    ]]></literal>
    <justification jstring="[para(9764(a,1),13445(a,1,3)),flip(a)].">
      <j1 rule="para" parents="9764 13445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13458">
    <literal><![CDATA[
      L(x,y,y / z) = L(x,y,z \ y)
    ]]></literal>
    <justification jstring="[hyper(11639,a,13447,a)].">
      <j1 rule="hyper" parents="11639 13447"/>
    </justification>
  </clause>

  <clause id="13459">
    <literal><![CDATA[
      L(x,y,z * (u / z)) = L(x,y,T(u,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,6047,a(flip),b,13452,a)].">
      <j1 rule="hyper" parents="65 6047 13452"/>
    </justification>
  </clause>

  <clause id="13460">
    <literal><![CDATA[
      L(x,y,T(T(z,u \ 1) / u,z)) = L(x,y,z / u)
    ]]></literal>
    <justification jstring="[hyper(65,a,6617,a(flip),b,13459,a),flip(a)].">
      <j1 rule="hyper" parents="65 6617 13459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13461">
    <literal><![CDATA[
      ((x \ y) * x) \ (L(x,x,x) \ y) = L(1 / x,L(x,x,x),x \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,12037,a(flip),b,13442,a)].">
      <j1 rule="hyper" parents="65 12037 13442"/>
    </justification>
  </clause>

  <clause id="13462">
    <literal><![CDATA[
      K(x,y) * ((y / T(x,y)) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[hyper(5437,a,13451,a)].">
      <j1 rule="hyper" parents="5437 13451"/>
    </justification>
  </clause>

  <clause id="13463">
    <literal><![CDATA[
      R(K(x,y),x \ y,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10820,a,13462,a)].">
      <j1 rule="hyper" parents="10820 13462"/>
    </justification>
  </clause>

  <clause id="13464">
    <literal><![CDATA[
      R(K(x,x * y),y,z) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),13463(a,1,2))].">
      <j1 rule="para" parents="9 13463"/>
    </justification>
  </clause>

  <clause id="13466">
    <literal><![CDATA[
      K(x,R(y \ 1,y,z) \ x) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,12554,a,b,13464,a)].">
      <j1 rule="hyper" parents="65 12554 13464"/>
    </justification>
  </clause>

  <clause id="13467">
    <literal><![CDATA[
      T(x,R(y \ 1,y,z) \ x) = x * K(x,x * y)
    ]]></literal>
    <justification jstring="[para(13464(a,1),12558(a,2,2))].">
      <j1 rule="para" parents="13464 12558"/>
    </justification>
  </clause>

  <clause id="13468">
    <literal><![CDATA[
      R(K(x,x * y),y * z,u) = K(x,((z * u) / ((y * z) * u)) \ x)
    ]]></literal>
    <justification jstring="[para(13466(a,1),12560(a,1,1))].">
      <j1 rule="para" parents="13466 12560"/>
    </justification>
  </clause>

  <clause id="13469">
    <literal><![CDATA[
      T(x,R(y \ 1,y,z) \ x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(299,a,5083,a,b,13467,a),flip(a)].">
      <j1 rule="hyper" parents="299 5083 13467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13470">
    <literal><![CDATA[
      T(x,(y / (z * y)) \ x) = T(x,x * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,3893,a(flip),b,13469,a)].">
      <j1 rule="hyper" parents="65 3893 13469"/>
    </justification>
  </clause>

  <clause id="13471">
    <literal><![CDATA[
      T(x,(y / z) \ x) = T(x,x * (z / y))
    ]]></literal>
    <justification jstring="[para(12(a,1),13470(a,1,2,1,2))].">
      <j1 rule="para" parents="12 13470"/>
    </justification>
  </clause>

  <clause id="13472">
    <literal><![CDATA[
      T(x,(y * x) / z) = T(x,x * (y / z))
    ]]></literal>
    <justification jstring="[hyper(65,a,8716,a,b,13471,a)].">
      <j1 rule="hyper" parents="65 8716 13471"/>
    </justification>
  </clause>

  <clause id="13473">
    <literal><![CDATA[
      x * K(x,x * (y / z)) = T(x,(y * x) / z)
    ]]></literal>
    <justification jstring="[hyper(299,a,5083,a(flip),b,13472,a)].">
      <j1 rule="hyper" parents="299 5083 13472"/>
    </justification>
  </clause>

  <clause id="13474">
    <literal><![CDATA[
      K(x,(y * x) / z) = K(x,x * (y / z))
    ]]></literal>
    <justification jstring="[hyper(36,a,5083,a(flip),b,13473,a)].">
      <j1 rule="hyper" parents="36 5083 13473"/>
    </justification>
  </clause>

  <clause id="13475">
    <literal><![CDATA[
      K(x,(y / z) \ x) = K(x,x * (z / y))
    ]]></literal>
    <justification jstring="[hyper(9067,a,13474,a)].">
      <j1 rule="hyper" parents="9067 13474"/>
    </justification>
  </clause>

  <clause id="13476">
    <literal><![CDATA[
      (x * K(y,y * (z / u))) / (y \ x) = T(y,T((z * y) / u,x))
    ]]></literal>
    <justification jstring="[para(13474(a,1),8152(a,1,1,2))].">
      <j1 rule="para" parents="13474 8152"/>
    </justification>
  </clause>

  <clause id="13477">
    <literal><![CDATA[
      (x * K(y,y * (z / u))) \ x = K((u / z) \ y,y)
    ]]></literal>
    <justification jstring="[para(13475(a,1),7200(a,1,1,2))].">
      <j1 rule="para" parents="13475 7200"/>
    </justification>
  </clause>

  <clause id="13478">
    <literal><![CDATA[
      R(K(x,x * (y / z)),x * u,w) = K(R(x,u,w),(z / y) \ x)
    ]]></literal>
    <justification jstring="[para(13475(a,1),10698(a,1,1))].">
      <j1 rule="para" parents="13475 10698"/>
    </justification>
  </clause>

  <clause id="13479">
    <literal><![CDATA[
      K((x / y) \ z,z) = K(z * (y / x),z)
    ]]></literal>
    <justification jstring="[hyper(7209,a,13477,a),flip(a)].">
      <j1 rule="hyper" parents="7209 13477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13480">
    <literal><![CDATA[
      K(x * (y \ z),T(x,y)) = K(x * (z / y),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,13082,a,b,13479,a)].">
      <j1 rule="hyper" parents="65 13082 13479"/>
    </justification>
  </clause>

  <clause id="13481">
    <literal><![CDATA[
      K(x * (y \ z),T(x,z)) = K(x * (z / y),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,9890,a,b,13480,a)].">
      <j1 rule="hyper" parents="65 9890 13480"/>
    </justification>
  </clause>

  <clause id="13482">
    <literal><![CDATA[
      K(x * (y / z),x) * K(x,T(z \ y,y)) = a(x,z \ y,x)
    ]]></literal>
    <justification jstring="[para(13481(a,1),11131(a,1,1))].">
      <j1 rule="para" parents="13481 11131"/>
    </justification>
  </clause>

  <clause id="13483">
    <literal><![CDATA[
      K(x * (y / z),x) * K(x,y / z) = a(x,z \ y,x)
    ]]></literal>
    <justification jstring="[para(8108(a,1),13482(a,1,2))].">
      <j1 rule="para" parents="8108 13482"/>
    </justification>
  </clause>

  <clause id="13484">
    <literal><![CDATA[
      a(x,y / z,x) = a(x,z \ y,x)
    ]]></literal>
    <justification jstring="[hyper(9700,a,13483,a)].">
      <j1 rule="hyper" parents="9700 13483"/>
    </justification>
  </clause>

  <clause id="13486">
    <literal><![CDATA[
      a(x,y / (z * y),x) = a(x,z \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,13090,a(flip),b,13484,a),flip(a)].">
      <j1 rule="hyper" parents="299 13090 13484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13487">
    <literal><![CDATA[
      a(x,(y \ z) \ z,x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[para(76(a,1),13484(a,1,2)),flip(a)].">
      <j1 rule="para" parents="76 13484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13488">
    <literal><![CDATA[
      a(x,R(y / z,z,u),x) = a(x,(z * u) \ (y * u),x)
    ]]></literal>
    <justification jstring="[para(104(a,2),13484(a,1,2))].">
      <j1 rule="para" parents="104 13484"/>
    </justification>
  </clause>

  <clause id="13489">
    <literal><![CDATA[
      a(x,T(y,z),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[para(4452(a,2),13487(a,1,2))].">
      <j1 rule="para" parents="4452 13487"/>
    </justification>
  </clause>

  <clause id="13490">
    <literal><![CDATA[
      a(x,y * K(z,y),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[para(5968(a,1),13487(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5968 13487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13491">
    <literal><![CDATA[
      a(x,R(y / z,u,w),x) = a(x,R(z \ y,u,w),x)
    ]]></literal>
    <justification jstring="[para(11696(a,1),13487(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11696 13487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13493">
    <literal><![CDATA[
      a(x,T(y,z),x) = K(x * y,T(T(x,u),w)) * K(x,T(T(y,u),w))
    ]]></literal>
    <justification jstring="[hyper(299,a,12276,a,b,13489,a),flip(a)].">
      <j1 rule="hyper" parents="299 12276 13489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13494">
    <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(13489(a,1),9701(a,1,1))].">
      <j1 rule="para" parents="13489 9701"/>
    </justification>
  </clause>

  <clause id="13495">
    <literal><![CDATA[
      L(a(x,y,x),y,z) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,13338,a(flip),b,13490,a)].">
      <j1 rule="hyper" parents="65 13338 13490"/>
    </justification>
  </clause>

  <clause id="13497">
    <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(4009(a,1),13486(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4009 13486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13498">
    <literal><![CDATA[
      a(x,R(y \ z,y,u),x) = a(x,(y * u) \ (z * u),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,13491,a(flip),b,13488,a)].">
      <j1 rule="hyper" parents="65 13491 13488"/>
    </justification>
  </clause>

  <clause id="13499">
    <literal><![CDATA[
      T(x,T((y * x) / z,u)) = T(x,T(x * (y / z),u))
    ]]></literal>
    <justification jstring="[hyper(8280,a,13476,a),flip(a)].">
      <j1 rule="hyper" parents="8280 13476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13500">
    <literal><![CDATA[
      T(x,T(y / (x \ z),u)) = T(x,T(x * (y / z),u))
    ]]></literal>
    <justification jstring="[hyper(65,a,9485,a(flip),b,13499,a)].">
      <j1 rule="hyper" parents="65 9485 13499"/>
    </justification>
  </clause>

  <clause id="13501">
    <literal><![CDATA[
      T(x,T((y / z) \ x,u)) = T(x,T(x * (z / y),u))
    ]]></literal>
    <justification jstring="[hyper(10227,a,13500,a)].">
      <j1 rule="hyper" parents="10227 13500"/>
    </justification>
  </clause>

  <clause id="13502">
    <literal><![CDATA[
      K(R(x,y,z),(u / w) \ x) != v5
    ]]></literal>
    <literal><![CDATA[
      K(R(x,y,z),x * (w / u)) = v5
    ]]></literal>
    <justification jstring="[para(13478(a,1),10812(a,1))].">
      <j1 rule="para" parents="13478 10812"/>
    </justification>
  </clause>

  <clause id="13504">
    <literal><![CDATA[
      R(K(x,x * y),y * z,u) = K(x,x * (((y * z) * u) / (z * u)))
    ]]></literal>
    <justification jstring="[hyper(299,a,13475,a(flip),b,13468,a),flip(a)].">
      <j1 rule="hyper" parents="299 13475 13468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13506">
    <literal><![CDATA[
      K(x * T(y,z),T(x,u)) = K(x * y,T(T(x,u),z))
    ]]></literal>
    <justification jstring="[hyper(11136,a,13493,a)].">
      <j1 rule="hyper" parents="11136 13493"/>
    </justification>
  </clause>

  <clause id="13507">
    <literal><![CDATA[
      K(x * T(y,z),T(x,u)) = T(K(x * y,T(x,u)),z)
    ]]></literal>
    <justification jstring="[hyper(299,a,7489,a(flip),b,13506,a),flip(a)].">
      <j1 rule="hyper" parents="299 7489 13506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13509">
    <literal><![CDATA[
      T(K(x * y,x) * K(x,K(y,z)),u) = K(x * T(y,u),T(x,z))
    ]]></literal>
    <justification jstring="[para(8487(a,2),13507(a,2,1)),flip(a)].">
      <j1 rule="para" parents="8487 13507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13510">
    <literal><![CDATA[
      T(K(x * y,y) * K(y,K(x,z)),u) = K(y * T(x,u),T(y,z))
    ]]></literal>
    <justification jstring="[para(5980(a,2),13509(a,1,1,1))].">
      <j1 rule="para" parents="5980 13509"/>
    </justification>
  </clause>

  <clause id="13511">
    <literal><![CDATA[
      R(K(x,x * y),y * z,u) = K(x,x * R(y,z,u))
    ]]></literal>
    <justification jstring="[para(20(a,2),13504(a,2,2,2))].">
      <j1 rule="para" parents="20 13504"/>
    </justification>
  </clause>

  <clause id="13512">
    <literal><![CDATA[
      K(x,R(x * y,y * z,u)) = K(x,x * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(13397,a,13511,a)].">
      <j1 rule="hyper" parents="13397 13511"/>
    </justification>
  </clause>

  <clause id="13513">
    <literal><![CDATA[
      L(x,y,K(z * u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(13436(a,1),13344(a,1)),flip(b)].">
      <j1 rule="para" parents="13436 13344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13514">
    <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(13339(a,1),13347(a,2,1))].">
      <j1 rule="para" parents="13339 13347"/>
    </justification>
  </clause>

  <clause id="13515">
    <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(299,a,13346,a(flip),b,13514,a),flip(a)].">
      <j1 rule="hyper" parents="299 13346 13514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13516">
    <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),13515(a,2,2))].">
      <j1 rule="para" parents="20 13515"/>
    </justification>
  </clause>

  <clause id="13517">
    <literal><![CDATA[
      R(a(x,y,x) * z,u,w) = a(x,y,x) * R(z,u,w)
    ]]></literal>
    <justification jstring="[para(13341(a,1),13516(a,1,2))].">
      <j1 rule="para" parents="13341 13516"/>
    </justification>
  </clause>

  <clause id="13518">
    <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(13517(a,2),13128(a,1,1,2))].">
      <j1 rule="para" parents="13517 13128"/>
    </justification>
  </clause>

  <clause id="13519">
    <literal><![CDATA[
      R(a(x,y,x) * z,u,w) * v5 = a(x,y,x) * (R(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(13517(a,2),13339(a,1,1))].">
      <j1 rule="para" parents="13517 13339"/>
    </justification>
  </clause>

  <clause id="13520">
    <literal><![CDATA[
      R(x * a(y,z,y),u,w) * v5 = a(y,z,y) * (R(x,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(10116(a,1),13519(a,1,1,1))].">
      <j1 rule="para" parents="10116 13519"/>
    </justification>
  </clause>

  <clause id="13521">
    <literal><![CDATA[
      a(x,y,x) * (R(y,z,u) * x) = T(x * R(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,9855,a(flip),b,13520,a),flip(a)].">
      <j1 rule="hyper" parents="65 9855 13520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13522">
    <literal><![CDATA[
      R(x,y,z) * R(u,x,u) = T(u * R(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(10461,a,13521,a)].">
      <j1 rule="hyper" parents="10461 13521"/>
    </justification>
  </clause>

  <clause id="13523">
    <literal><![CDATA[
      a(x,R(y,z,u),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(37,a,9690,a,b,13521,a)].">
      <j1 rule="hyper" parents="37 9690 13521"/>
    </justification>
  </clause>

  <clause id="13524">
    <literal><![CDATA[
      a(x,(y * z) \ (u * z),x) = a(x,y \ u,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,13498,a(flip),b,13523,a)].">
      <j1 rule="hyper" parents="65 13498 13523"/>
    </justification>
  </clause>

  <clause id="13525">
    <literal><![CDATA[
      R(T(x,y),R(z,u,w),x) = a(x,z,x) * T(x,y)
    ]]></literal>
    <justification jstring="[para(13523(a,1),10881(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13523 10881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13527">
    <literal><![CDATA[
      L(x,(y * z) \ (u * z),x) = (w / x) \ (a(x,y \ u,x) \ w)
    ]]></literal>
    <justification jstring="[para(13524(a,1),12647(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13524 12647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13528">
    <literal><![CDATA[
      (R(x,y,z) * R(u,x,u)) \ ((u * R(x,y,z)) * u) = T(u,u * R(x,y,z))
    ]]></literal>
    <justification jstring="[para(13522(a,2),4419(a,1,1))].">
      <j1 rule="para" parents="13522 4419"/>
    </justification>
  </clause>

  <clause id="13529">
    <literal><![CDATA[
      R(T(x,y),R(z,u,w),x) = R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,10881,a(flip),b,13525,a),flip(a)].">
      <j1 rule="hyper" parents="299 10881 13525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13530">
    <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(13529(a,1),13117(a,1,2))].">
      <j1 rule="para" parents="13529 13117"/>
    </justification>
  </clause>

  <clause id="13531">
    <literal><![CDATA[
      L(x,(y * z) \ (u * z),x) = L(x,y \ u,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,12647,a(flip),b,13527,a),flip(a)].">
      <j1 rule="hyper" parents="299 12647 13527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13532">
    <literal><![CDATA[
      T(x * R(y,z,u),x * y) = R(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(877(a,1),13530(a,1,2)),flip(a)].">
      <j1 rule="para" parents="877 13530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13534">
    <literal><![CDATA[
      (x * R(y,z,u)) / (R(y,z,u) * T(x,y)) = K(x * y,x * R(y,z,u))
    ]]></literal>
    <justification jstring="[para(13532(a,1),5033(a,2,2)),flip(a)].">
      <j1 rule="para" parents="13532 5033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13535">
    <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(65,a,13065,a(flip),b,13534,a)].">
      <j1 rule="hyper" parents="65 13065 13534"/>
    </justification>
  </clause>

  <clause id="13536">
    <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(12889(a,1),13535(a,1,1))].">
      <j1 rule="para" parents="12889 13535"/>
    </justification>
  </clause>

  <clause id="13537">
    <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(65,a,13142,a,b,13536,a),flip(a)].">
      <j1 rule="hyper" parents="65 13142 13536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13538">
    <literal><![CDATA[
      K(x * y,x * R(y,z,u)) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[para(172(a,1),13537(a,2,1,2))].">
      <j1 rule="para" parents="172 13537"/>
    </justification>
  </clause>

  <clause id="13539">
    <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(65,a,4778,a,b,13538,a)].">
      <j1 rule="hyper" parents="65 4778 13538"/>
    </justification>
  </clause>

  <clause id="13540">
    <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),13538(a,1,1))].">
      <j1 rule="para" parents="12 13538"/>
    </justification>
  </clause>

  <clause id="13541">
    <literal><![CDATA[
      K(x,(y \ x) * R(y,z,u)) = a(K(x / y,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,10507,a(flip),b,13540,a)].">
      <j1 rule="hyper" parents="65 10507 13540"/>
    </justification>
  </clause>

  <clause id="13542">
    <literal><![CDATA[
      K(x,x * (y \ R(y,z,u))) = a(K(x / y,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,13242,a(flip),b,13541,a)].">
      <j1 rule="hyper" parents="65 13242 13541"/>
    </justification>
  </clause>

  <clause id="13543">
    <literal><![CDATA[
      K(x,x * (y \ R(y,z,u))) = a(K(y \ x,y),z * y,u)
    ]]></literal>
    <justification jstring="[para(5192(a,1),13542(a,2,1))].">
      <j1 rule="para" parents="5192 13542"/>
    </justification>
  </clause>

  <clause id="13544">
    <literal><![CDATA[
      L(T(x,R(y,z,u)),y,T(x,R(y,z,u))) = T(x,x * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,10467,a(flip),b,13528,a)].">
      <j1 rule="hyper" parents="65 10467 13528"/>
    </justification>
  </clause>

  <clause id="13545">
    <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(13538(a,1),13539(a,1,1))].">
      <j1 rule="para" parents="13538 13539"/>
    </justification>
  </clause>

  <clause id="13546">
    <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(13339(a,1),13356(a,1,2,1))].">
      <j1 rule="para" parents="13339 13356"/>
    </justification>
  </clause>

  <clause id="13547">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * (T(u * z,u) / u))) = a(u,(x * (y * z)) / (x * y),u)
    ]]></literal>
    <justification jstring="[para(5254(a,1),13385(a,2,2))].">
      <j1 rule="para" parents="5254 13385"/>
    </justification>
  </clause>

  <clause id="13548">
    <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(9698,a,13547,a)].">
      <j1 rule="hyper" parents="9698 13547"/>
    </justification>
  </clause>

  <clause id="13549">
    <literal><![CDATA[
      L(a(x,y,x),z * y,u) = a(x,(u * (z * y)) / (u * z),x)
    ]]></literal>
    <justification jstring="[para(13495(a,1),13548(a,1,1))].">
      <j1 rule="para" parents="13495 13548"/>
    </justification>
  </clause>

  <clause id="13550">
    <literal><![CDATA[
      L(a(x,y,x),z * y,u) = a(x,(u * z) \ (u * (z * y)),x)
    ]]></literal>
    <justification jstring="[hyper(299,a,13484,a(flip),b,13549,a),flip(a)].">
      <j1 rule="hyper" parents="299 13484 13549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13552">
    <literal><![CDATA[
      L(a(x,y,x),z * y,u) = a(x,L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(18(a,2),13550(a,2,2))].">
      <j1 rule="para" parents="18 13550"/>
    </justification>
  </clause>

  <clause id="13553">
    <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(13339(a,1),13546(a,1,2))].">
      <j1 rule="para" parents="13339 13546"/>
    </justification>
  </clause>

  <clause id="13554">
    <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(913,a,13553,a)].">
      <j1 rule="hyper" parents="913 13553"/>
    </justification>
  </clause>

  <clause id="13555">
    <literal><![CDATA[
      a(a(x,y,x) * z,u,w) = a(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(13345,a,13554,a),flip(a)].">
      <j1 rule="hyper" parents="13345 13554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13556">
    <literal><![CDATA[
      a(a(x,y,x) * z,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(z,u,w) = v5
    ]]></literal>
    <justification jstring="[para(13554(a,1),13344(a,1)),flip(b)].">
      <j1 rule="para" parents="13554 13344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13558">
    <literal><![CDATA[
      a(a(x,y,x) \ z,u,w) = a(z,u,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),13555(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 13555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13559">
    <literal><![CDATA[
      a(K(x,x \ y),z,u) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(9706(a,1),13555(a,1,1))].">
      <j1 rule="para" parents="9706 13555"/>
    </justification>
  </clause>

  <clause id="13560">
    <literal><![CDATA[
      a(L(x,y,x) * z,u,w) = a(x * z,u,w)
    ]]></literal>
    <justification jstring="[para(12645(a,1),13555(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12645 13555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13561">
    <literal><![CDATA[
      a(K(x \ y,x),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(9668(a,1),13558(a,1,1))].">
      <j1 rule="para" parents="9668 13558"/>
    </justification>
  </clause>

  <clause id="13562">
    <literal><![CDATA[
      a(K(x \ 1,y),z,u) = a(K(x \ y,y),z,u)
    ]]></literal>
    <justification jstring="[para(9692(a,1),13558(a,1,1))].">
      <j1 rule="para" parents="9692 13558"/>
    </justification>
  </clause>

  <clause id="13563">
    <literal><![CDATA[
      K(x,x * (y \ R(y,z,u))) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,13543,a,b,13561,a)].">
      <j1 rule="hyper" parents="65 13543 13561"/>
    </justification>
  </clause>

  <clause id="13564">
    <literal><![CDATA[
      a(K(x,y \ x),z,u) = a(K(y,y \ x),z,u)
    ]]></literal>
    <justification jstring="[para(5193(a,1),13561(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5193 13561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13566">
    <literal><![CDATA[
      a(K(x,y \ x),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,13559,a(flip),b,13564,a),flip(a)].">
      <j1 rule="hyper" parents="299 13559 13564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13567">
    <literal><![CDATA[
      a(K(x \ y,y),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(6891(a,1),13566(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6891 13566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13568">
    <literal><![CDATA[
      a(K(x \ 1,y),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,13562,a,b,13567,a)].">
      <j1 rule="hyper" parents="65 13562 13567"/>
    </justification>
  </clause>

  <clause id="13569">
    <literal><![CDATA[
      a(K(x,y \ 1),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(3567(a,1),13568(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3567 13568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13570">
    <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(11599(a,2),13568(a,2,1)),flip(a)].">
      <j1 rule="para" parents="11599 13568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13571">
    <literal><![CDATA[
      K(x \ 1,y) * K(y,R(x,z,u) \ 1) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,12886,a,b,13569,a)].">
      <j1 rule="hyper" parents="65 12886 13569"/>
    </justification>
  </clause>

  <clause id="13572">
    <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(13399(a,1),13569(a,2,1))].">
      <j1 rule="para" parents="13399 13569"/>
    </justification>
  </clause>

  <clause id="13573">
    <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(65,a,5954,a,b,13563,a)].">
      <j1 rule="hyper" parents="65 5954 13563"/>
    </justification>
  </clause>

  <clause id="13574">
    <literal><![CDATA[
      (x \ T(x * (y \ R(y,z,u)),x)) \ (x \ (x * (y \ R(y,z,u)))) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,6954,a(flip),b,13563,a)].">
      <j1 rule="hyper" parents="65 6954 13563"/>
    </justification>
  </clause>

  <clause id="13575">
    <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(65,a,12991,a,b,13572,a)].">
      <j1 rule="hyper" parents="65 12991 13572"/>
    </justification>
  </clause>

  <clause id="13576">
    <literal><![CDATA[
      a(K(R(x,y,z),u),w,v5) = a(K(x,R(u,y,z)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,13569,a(flip),b,13572,a)].">
      <j1 rule="hyper" parents="65 13569 13572"/>
    </justification>
  </clause>

  <clause id="13577">
    <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(6443(a,1),13570(a,2,1))].">
      <j1 rule="para" parents="6443 13570"/>
    </justification>
  </clause>

  <clause id="13578">
    <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(299,a,13568,a(flip),b,13577,a),flip(a)].">
      <j1 rule="hyper" parents="299 13568 13577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13579">
    <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(11599(a,1),13578(a,1,1))].">
      <j1 rule="para" parents="11599 13578"/>
    </justification>
  </clause>

  <clause id="13580">
    <literal><![CDATA[
      a(K(x,R(y,x * z,u)),w,v5) = a(K(x,R(y,z,u)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(299,a,13576,a(flip),b,13579,a),flip(a)].">
      <j1 rule="hyper" parents="299 13576 13579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13581">
    <literal><![CDATA[
      a(K(x,R(y,z,u)),w,v5) = R(a(K(x,y),w,v5),z,u)
    ]]></literal>
    <justification jstring="[para(13571(a,1),13575(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13571 13575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13582">
    <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(299,a,13545,a(flip),b,13581,a),flip(a)].">
      <j1 rule="hyper" parents="299 13545 13581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13583">
    <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(65,a,13580,a(flip),b,13582,a)].">
      <j1 rule="hyper" parents="65 13580 13582"/>
    </justification>
  </clause>

  <clause id="13584">
    <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(67(a,1),13239(a,2,1,2,2,1,2))].">
      <j1 rule="para" parents="67 13239"/>
    </justification>
  </clause>

  <clause id="13585">
    <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),13584(a,2,1,2))].">
      <j1 rule="para" parents="7 13584"/>
    </justification>
  </clause>

  <clause id="13586">
    <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(13585(a,2),8220(a,1))].">
      <j1 rule="para" parents="13585 8220"/>
    </justification>
  </clause>

  <clause id="13587">
    <literal><![CDATA[
      (R(x,y,y \ 1) \ (x * y)) * R(x,y,y \ 1) = (x * y) * K(y,L(x,y,y \ 1))
    ]]></literal>
    <justification jstring="[para(3567(a,1),13289(a,2,2))].">
      <j1 rule="para" parents="3567 13289"/>
    </justification>
  </clause>

  <clause id="13588">
    <literal><![CDATA[
      (R(x,y,y \ 1) \ (x * y)) * R(x,y,y \ 1) = (x * y) * K(y,x)
    ]]></literal>
    <justification jstring="[para(6121(a,1),13587(a,2,2))].">
      <j1 rule="para" parents="6121 13587"/>
    </justification>
  </clause>

  <clause id="13589">
    <literal><![CDATA[
      (R(x,y,y \ 1) \ (x * y)) * R(x,y,y \ 1) = y * x
    ]]></literal>
    <justification jstring="[hyper(299,a,88,a(flip),b,13588,a),flip(a)].">
      <j1 rule="hyper" parents="299 88 13588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13591">
    <literal><![CDATA[
      (R(x,y,y) \ (x * y)) * R(x,y,y \ 1) = y * x
    ]]></literal>
    <justification jstring="[para(1249(a,1),13589(a,1,1,1))].">
      <j1 rule="para" parents="1249 13589"/>
    </justification>
  </clause>

  <clause id="13592">
    <literal><![CDATA[
      (R(x,y,y) \ (x * y)) * R(x,y,y) = y * x
    ]]></literal>
    <justification jstring="[para(1249(a,1),13591(a,1,2))].">
      <j1 rule="para" parents="1249 13591"/>
    </justification>
  </clause>

  <clause id="13593">
    <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),13518(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 13518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13594">
    <literal><![CDATA[
      T(x \ R(x,y,z),u) \ (u \ (u * (x \ R(x,y,z)))) = a(K(u,x),y * x,z)
    ]]></literal>
    <justification jstring="[para(13593(a,1),13574(a,1,1))].">
      <j1 rule="para" parents="13593 13574"/>
    </justification>
  </clause>

  <clause id="13595">
    <literal><![CDATA[
      T(x \ R(x,y,z),u) \ (x \ R(x,y,z)) = a(K(u,x),y * x,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),13594(a,1,2))].">
      <j1 rule="para" parents="9 13594"/>
    </justification>
  </clause>

  <clause id="13596">
    <literal><![CDATA[
      a(K(x,y),z * y,u) = K(x,y \ R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(5109,a,13595,a),flip(a)].">
      <j1 rule="hyper" parents="5109 13595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13598">
    <literal><![CDATA[
      a(K(x,K(y,z)),u * y,w) = K(x,K(z,y \ R(y,u,w)))
    ]]></literal>
    <justification jstring="[para(13596(a,1),12925(a,2,2))].">
      <j1 rule="para" parents="13596 12925"/>
    </justification>
  </clause>

  <clause id="13599">
    <literal><![CDATA[
      K(x,K(y,z \ R(z,u,w))) = a(K(z,K(x,y)),u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,13413,a(flip),b,13598,a),flip(a)].">
      <j1 rule="hyper" parents="65 13413 13598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13600">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w) * (z \ y))) = a(K(z,K(x,y)),u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,9573,a,b,13599,a)].">
      <j1 rule="hyper" parents="65 9573 13599"/>
    </justification>
  </clause>

  <clause id="13601">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w) * (z \ y))) = a(K(x,K(y,z)),u,w)
    ]]></literal>
    <justification jstring="[para(7989(a,2),13600(a,2,1))].">
      <j1 rule="para" parents="7989 13600"/>
    </justification>
  </clause>

  <clause id="13602">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w) \ z)) = a(K(x,K(y,z)),u,w)
    ]]></literal>
    <justification jstring="[hyper(9648,a,13601,a)].">
      <j1 rule="hyper" parents="9648 13601"/>
    </justification>
  </clause>

  <clause id="13603">
    <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(65,a,10949,a(flip),b,13602,a)].">
      <j1 rule="hyper" parents="65 10949 13602"/>
    </justification>
  </clause>

  <clause id="13604">
    <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(8004(a,1),13603(a,2,1))].">
      <j1 rule="para" parents="8004 13603"/>
    </justification>
  </clause>

  <clause id="13605">
    <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(11556(a,1),13604(a,2,1,2))].">
      <j1 rule="para" parents="11556 13604"/>
    </justification>
  </clause>

  <clause id="13606">
    <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(10951,a,13605,a)].">
      <j1 rule="hyper" parents="10951 13605"/>
    </justification>
  </clause>

  <clause id="13609">
    <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(65,a,11172,a(flip),b,13606,a)].">
      <j1 rule="hyper" parents="65 11172 13606"/>
    </justification>
  </clause>

  <clause id="13611">
    <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(11412,a,13497,a)].">
      <j1 rule="hyper" parents="11412 13497"/>
    </justification>
  </clause>

  <clause id="13612">
    <literal><![CDATA[
      T(T(x,K(y,(y \ 1) \ (y \ z))),T((y \ 1) \ (y \ z),y) * (y \ 1)) = T(x,y \ (1 * T(1 \ z,y)))
    ]]></literal>
    <justification jstring="[para(8050(a,1),13298(a,1,1))].">
      <j1 rule="para" parents="8050 13298"/>
    </justification>
  </clause>

  <clause id="13613">
    <literal><![CDATA[
      K(x,(1 / (y \ T(L(L(x,z,u),w,v5),v6))) \ K(v6,L(L(x,z,u),w,v5))) = K(x,y \ L(L(x,z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(299,a,7617,a(flip),b,13430,a),flip(a)].">
      <j1 rule="hyper" parents="299 7617 13430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13614">
    <literal><![CDATA[
      K(x,(1 / (y \ L(T(L(x,z,u),w),v5,v6))) \ K(w,L(L(x,z,u),v5,v6))) = K(x,y \ L(L(x,z,u),v5,v6))
    ]]></literal>
    <justification jstring="[para(25(a,2),13613(a,1,2,1,2,2))].">
      <j1 rule="para" parents="25 13613"/>
    </justification>
  </clause>

  <clause id="13615">
    <literal><![CDATA[
      K(x,(1 / (y \ L(L(T(x,z),u,w),v5,v6))) \ K(z,L(L(x,u,w),v5,v6))) = K(x,y \ L(L(x,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(25(a,2),13614(a,1,2,1,2,2,1))].">
      <j1 rule="para" parents="25 13614"/>
    </justification>
  </clause>

  <clause id="13616">
    <literal><![CDATA[
      K(x,(1 / (y \ L(L(T(x,z),u,w),v5,v6))) \ 1) = K(x,y \ L(L(x,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(65,a,11099,a(flip),b,13615,a)].">
      <j1 rule="hyper" parents="65 11099 13615"/>
    </justification>
  </clause>

  <clause id="13618">
    <literal><![CDATA[
      K(x,y \ L(L(T(x,z),u,w),v5,v6)) = K(x,y \ L(L(x,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(79(a,1),13616(a,1,2))].">
      <j1 rule="para" parents="79 13616"/>
    </justification>
  </clause>

  <clause id="13619">
    <literal><![CDATA[
      K((x \ y) \ T(y,x),z \ L((x \ y) \ T(y,x),u,w)) = K(x,z \ L(L(x,y,x),u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,12730,a,b,13618,a)].">
      <j1 rule="hyper" parents="65 12730 13618"/>
    </justification>
  </clause>

  <clause id="13622">
    <literal><![CDATA[
      K(x,y \ L(L(x,z,x),u,w)) = K(x,y \ L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,12531,a(flip),b,13619,a),flip(a)].">
      <j1 rule="hyper" parents="65 12531 13619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13624">
    <literal><![CDATA[
      K(x,(y \ 1) \ L(x,z,u)) * (y \ (T(y,x) * L(x,z,u))) = L(L(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(13622(a,1),12225(a,1,1))].">
      <j1 rule="para" parents="13622 12225"/>
    </justification>
  </clause>

  <clause id="13625">
    <literal><![CDATA[
      K(x,1 \ (y * L(x,z,u))) * (y \ (T(y,x) * L(x,z,u))) = L(L(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(12030(a,1),13624(a,1,1))].">
      <j1 rule="para" parents="12030 13624"/>
    </justification>
  </clause>

  <clause id="13627">
    <literal><![CDATA[
      K(x,y * L(x,z,u)) * (y \ (T(y,x) * L(x,z,u))) = L(L(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(67(a,1),13625(a,1,1,2))].">
      <j1 rule="para" parents="67 13625"/>
    </justification>
  </clause>

  <clause id="13628">
    <literal><![CDATA[
      K(x,y * L(x,z,u)) * (K(y,x) * L(x,z,u)) = L(L(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(5350(a,1),13627(a,1,2))].">
      <j1 rule="para" parents="5350 13627"/>
    </justification>
  </clause>

  <clause id="13629">
    <literal><![CDATA[
      L(x,y,z) * (K(x,u * L(x,y,z)) * K(u,x)) = L(L(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(13051,a,13628,a)].">
      <j1 rule="hyper" parents="13051 13628"/>
    </justification>
  </clause>

  <clause id="13630">
    <literal><![CDATA[
      L(x,y,z) * (K(u,x) * K(x,u * L(x,y,z))) = L(L(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[para(2278(a,1),13629(a,1,2))].">
      <j1 rule="para" parents="2278 13629"/>
    </justification>
  </clause>

  <clause id="13631">
    <literal><![CDATA[
      L(x,y,z) * (a(x,u,L(x,y,z)) \ 1) = L(L(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[para(12944(a,1),13630(a,1,2))].">
      <j1 rule="para" parents="12944 13630"/>
    </justification>
  </clause>

  <clause id="13632">
    <literal><![CDATA[
      L(x,y,z) \ L(L(x,u,x),y,z) = a(x,u,L(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(125,a,13631,a)].">
      <j1 rule="hyper" parents="125 13631"/>
    </justification>
  </clause>

  <clause id="13633">
    <literal><![CDATA[
      x * a(L(y,z,u),w,L(y,z,u)) = (a(y,w,L(y,z,u)) \ 1) \ x
    ]]></literal>
    <justification jstring="[para(13632(a,1),13372(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13632 13372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13634">
    <literal><![CDATA[
      a(L(x,y,z),u,L(x,y,z)) = a(x,u,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,13633,a,b,12517,a(flip))].">
      <j1 rule="hyper" parents="118 13633 12517"/>
    </justification>
  </clause>

  <clause id="13636">
    <literal><![CDATA[
      a(L(x,y,z),u,L(x,y,z)) = a(x,u,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,12938,a(flip),b,13634,a),flip(a)].">
      <j1 rule="hyper" parents="299 12938 13634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13638">
    <literal><![CDATA[
      L(a(x,y,x),z,u) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,11456,a(flip),b,13636,a)].">
      <j1 rule="hyper" parents="65 11456 13636"/>
    </justification>
  </clause>

  <clause id="13643">
    <literal><![CDATA[
      a(x,L(y,z,u),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,13552,a(flip),b,13638,a)].">
      <j1 rule="hyper" parents="65 13552 13638"/>
    </justification>
  </clause>

  <clause id="13645">
    <literal><![CDATA[
      (x * y) * a(z,u,z) = x * (y * a(z,u,z))
    ]]></literal>
    <justification jstring="[para(13638(a,1),94(a,1,2))].">
      <j1 rule="para" parents="13638 94"/>
    </justification>
  </clause>

  <clause id="13647">
    <literal><![CDATA[
      (x * (a(y,z,y) * u)) / a(y,z,y) = x * u
    ]]></literal>
    <justification jstring="[para(13638(a,1),10135(a,1,2))].">
      <j1 rule="para" parents="13638 10135"/>
    </justification>
  </clause>

  <clause id="13650">
    <literal><![CDATA[
      a(x,(y * z) \ u,x) = a(x,z \ (y \ u),x)
    ]]></literal>
    <justification jstring="[para(281(a,1),13643(a,1,2))].">
      <j1 rule="para" parents="281 13643"/>
    </justification>
  </clause>

  <clause id="13651">
    <literal><![CDATA[
      R(x,L(y,z,u),x) = x * a(x,y,x)
    ]]></literal>
    <justification jstring="[para(13643(a,1),9674(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13643 9674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13652">
    <literal><![CDATA[
      L(x,L(y,z,u),x) = a(x,y,x) \ x
    ]]></literal>
    <justification jstring="[para(13643(a,1),9715(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13643 9715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13653">
    <literal><![CDATA[
      R(x,L(y,z,u),x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,9674,a(flip),b,13651,a),flip(a)].">
      <j1 rule="hyper" parents="299 9674 13651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13654">
    <literal><![CDATA[
      L(x,y,z) * T(R(u,x,u),R(u,L(x,y,z),u) * x) = T(T(u,u * x) * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(13653(a,1),13109(a,1,2,1))].">
      <j1 rule="para" parents="13653 13109"/>
    </justification>
  </clause>

  <clause id="13655">
    <literal><![CDATA[
      L(x,L(y,z,u),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,9715,a(flip),b,13652,a),flip(a)].">
      <j1 rule="hyper" parents="299 9715 13652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13656">
    <literal><![CDATA[
      L(x,(y \ z) \ 1,x) = L(x,z \ y,x)
    ]]></literal>
    <justification jstring="[para(366(a,1),13655(a,1,2)),flip(a)].">
      <j1 rule="para" parents="366 13655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13657">
    <literal><![CDATA[
      L(x,L(y,z,u) \ y,x) = L(x,a(u,z,y),x)
    ]]></literal>
    <justification jstring="[para(1985(a,2),13655(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1985 13655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13658">
    <literal><![CDATA[
      L(x,(y / z) \ 1,x) = L(x,y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,10689,a,b,13656,a)].">
      <j1 rule="hyper" parents="65 10689 13656"/>
    </justification>
  </clause>

  <clause id="13659">
    <literal><![CDATA[
      L(x,y * (y \ ((z / u) \ 1)),x) = L(x,z \ u,x)
    ]]></literal>
    <justification jstring="[para(10(a,2),13658(a,1,2))].">
      <j1 rule="para" parents="10 13658"/>
    </justification>
  </clause>

  <clause id="13660">
    <literal><![CDATA[
      R(x,y,a(z,u,z)) = x
    ]]></literal>
    <justification jstring="[hyper(3985,a,13645,a)].">
      <j1 rule="hyper" parents="3985 13645"/>
    </justification>
  </clause>

  <clause id="13661">
    <literal><![CDATA[
      x \ (y * a(z,u,z)) = (x \ y) * a(z,u,z)
    ]]></literal>
    <justification jstring="[hyper(1020,a,13645,a)].">
      <j1 rule="hyper" parents="1020 13645"/>
    </justification>
  </clause>

  <clause id="13662">
    <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(13645(a,1),539(a,1,1))].">
      <j1 rule="para" parents="13645 539"/>
    </justification>
  </clause>

  <clause id="13663">
    <literal><![CDATA[
      L(T(x,y),y,a(z,u,z)) = T(x,y * a(z,u,z))
    ]]></literal>
    <justification jstring="[hyper(10673,a,13660,a)].">
      <j1 rule="hyper" parents="10673 13660"/>
    </justification>
  </clause>

  <clause id="13664">
    <literal><![CDATA[
      R(x,y,a(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(13660(a,1),53(a,2))].">
      <j1 rule="para" parents="13660 53"/>
    </justification>
  </clause>

  <clause id="13665">
    <literal><![CDATA[
      (x * y) \ ((x * (y * z)) * a(u,w,u)) = L(z,y,x) * a(u,w,u)
    ]]></literal>
    <justification jstring="[para(13660(a,1),584(a,1,1))].">
      <j1 rule="para" parents="13660 584"/>
    </justification>
  </clause>

  <clause id="13667">
    <literal><![CDATA[
      a(x,y,x) * (z * u) = z * (a(x,y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(10147,a,13647,a)].">
      <j1 rule="hyper" parents="10147 13647"/>
    </justification>
  </clause>

  <clause id="13668">
    <literal><![CDATA[
      a(x,y,x) \ (z * (a(x,y,x) * u)) = z * u
    ]]></literal>
    <justification jstring="[hyper(10126,a,13647,a)].">
      <j1 rule="hyper" parents="10126 13647"/>
    </justification>
  </clause>

  <clause id="13670">
    <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(65,a,13611,a(flip),b,13650,a),flip(a)].">
      <j1 rule="hyper" parents="65 13611 13650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13671">
    <literal><![CDATA[
      x \ (a(y,z,y) * u) = (x \ u) * a(y,z,y)
    ]]></literal>
    <justification jstring="[para(10116(a,2),13661(a,1,2))].">
      <j1 rule="para" parents="10116 13661"/>
    </justification>
  </clause>

  <clause id="13672">
    <literal><![CDATA[
      (x \ (a(y,z,y) \ u)) * a(y,z,y) = x \ u
    ]]></literal>
    <justification jstring="[para(10122(a,1),13661(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10122 13661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13673">
    <literal><![CDATA[
      a(x,y,x) * (z * (a(x,y,x) \ u)) = z * u
    ]]></literal>
    <justification jstring="[hyper(299,a,155,a(flip),b,13667,a),flip(a)].">
      <j1 rule="hyper" parents="299 155 13667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13674">
    <literal><![CDATA[
      a(x,y,x) \ (z * u) = z * (a(x,y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(119,a,155,a(flip),b,13667,a)].">
      <j1 rule="hyper" parents="119 155 13667"/>
    </justification>
  </clause>

  <clause id="13675">
    <literal><![CDATA[
      (x * a(y,z,y)) * u = x * (a(y,z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,13359,a,b,13667,a)].">
      <j1 rule="hyper" parents="65 13359 13667"/>
    </justification>
  </clause>

  <clause id="13677">
    <literal><![CDATA[
      (x * (a(y,z,y) * u)) * w = a(y,z,y) * ((x * u) * w)
    ]]></literal>
    <justification jstring="[para(13667(a,1),13339(a,1,1))].">
      <j1 rule="para" parents="13667 13339"/>
    </justification>
  </clause>

  <clause id="13678">
    <literal><![CDATA[
      (x * (a(y,z,y) * u)) \ w = (x * u) \ (a(y,z,y) \ w)
    ]]></literal>
    <justification jstring="[para(13667(a,1),13343(a,1,1))].">
      <j1 rule="para" parents="13667 13343"/>
    </justification>
  </clause>

  <clause id="13679">
    <literal><![CDATA[
      L(x,y,z * (a(u,w,u) * v5)) = L(x,y,z * v5)
    ]]></literal>
    <justification jstring="[para(13667(a,1),13435(a,1,3))].">
      <j1 rule="para" parents="13667 13435"/>
    </justification>
  </clause>

  <clause id="13681">
    <literal><![CDATA[
      (a(x,y,x) \ z) * u = z * (a(x,y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(13358,a,13673,a),flip(a)].">
      <j1 rule="hyper" parents="13358 13673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13682">
    <literal><![CDATA[
      x * (a(x,y,x) \ L(x \ a(x,y,x),z,u)) = L(x \ L(x,z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(10979,a,13674,a),flip(a)].">
      <j1 rule="hyper" parents="10979 13674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13683">
    <literal><![CDATA[
      a(x,y,x) \ (z \ a(x,y,x)) = z \ 1
    ]]></literal>
    <justification jstring="[hyper(576,a,13674,a),flip(a)].">
      <j1 rule="hyper" parents="576 13674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13685">
    <literal><![CDATA[
      L(x,a(y,z,y),u) = x
    ]]></literal>
    <justification jstring="[hyper(490,a,13675,a)].">
      <j1 rule="hyper" parents="490 13675"/>
    </justification>
  </clause>

  <clause id="13686">
    <literal><![CDATA[
      (x / y) * (a(y,z,y) * u) = (x / L(y,z,y)) * u
    ]]></literal>
    <justification jstring="[para(9689(a,1),13675(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9689 13675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13687">
    <literal><![CDATA[
      x / (a(y,z,y) \ u) = (x / u) * a(y,z,y)
    ]]></literal>
    <justification jstring="[para(13685(a,1),529(a,1,2))].">
      <j1 rule="para" parents="13685 529"/>
    </justification>
  </clause>

  <clause id="13688">
    <literal><![CDATA[
      x / ((1 / a(y,z,y)) * u) = (x / u) * a(y,z,y)
    ]]></literal>
    <justification jstring="[para(10079(a,2),13687(a,1,2))].">
      <j1 rule="para" parents="10079 13687"/>
    </justification>
  </clause>

  <clause id="13689">
    <literal><![CDATA[
      T(x,y * a(z,u,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(13345,a,13663,a),flip(a)].">
      <j1 rule="hyper" parents="13345 13663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13690">
    <literal><![CDATA[
      T(x,y * a(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = w
    ]]></literal>
    <justification jstring="[para(13663(a,1),13344(a,1)),flip(b)].">
      <j1 rule="para" parents="13663 13344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13692">
    <literal><![CDATA[
      K(x,y * a(z,u,z)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,13689,a(flip),b,5083,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 13689 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13693">
    <literal><![CDATA[
      T(x,(y * z) * y) = T(x,y * (z * y))
    ]]></literal>
    <justification jstring="[para(84(a,1),13689(a,1,2))].">
      <j1 rule="para" parents="84 13689"/>
    </justification>
  </clause>

  <clause id="13694">
    <literal><![CDATA[
      T(x,y * L(z,u,z)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(9714(a,1),13689(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9714 13689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13695">
    <literal><![CDATA[
      T(x,T(y,z) / z) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[para(9693(a,1),13689(a,1,2))].">
      <j1 rule="para" parents="9693 13689"/>
    </justification>
  </clause>

  <clause id="13696">
    <literal><![CDATA[
      T(x,a(y,z,y) * u) = T(x,u)
    ]]></literal>
    <justification jstring="[para(10116(a,2),13689(a,1,2))].">
      <j1 rule="para" parents="10116 13689"/>
    </justification>
  </clause>

  <clause id="13697">
    <literal><![CDATA[
      T(x,R(y,z,y) \ u) = T(x,y \ u)
    ]]></literal>
    <justification jstring="[para(10478(a,1),13689(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10478 13689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13698">
    <literal><![CDATA[
      T(x,y * (z * a(u,w,u))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(13645(a,1),13689(a,1,2))].">
      <j1 rule="para" parents="13645 13689"/>
    </justification>
  </clause>

  <clause id="13699">
    <literal><![CDATA[
      T(x,y \ (z * a(u,w,u))) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(13661(a,2),13689(a,1,2))].">
      <j1 rule="para" parents="13661 13689"/>
    </justification>
  </clause>

  <clause id="13700">
    <literal><![CDATA[
      K(a(x,y,x) * z,u) = u / T(u,z)
    ]]></literal>
    <justification jstring="[para(13696(a,1),5033(a,2,2))].">
      <j1 rule="para" parents="13696 5033"/>
    </justification>
  </clause>

  <clause id="13701">
    <literal><![CDATA[
      T(x,(y \ R(y,z,y)) * u) = T(x,u)
    ]]></literal>
    <justification jstring="[para(9669(a,1),13696(a,1,2,1))].">
      <j1 rule="para" parents="9669 13696"/>
    </justification>
  </clause>

  <clause id="13702">
    <literal><![CDATA[
      T(x,K(y,y * z) * u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(10065(a,1),13696(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10065 13696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13704">
    <literal><![CDATA[
      T(x,y / T(z,y)) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[para(4382(a,1),13695(a,1,2))].">
      <j1 rule="para" parents="4382 13695"/>
    </justification>
  </clause>

  <clause id="13705">
    <literal><![CDATA[
      T(x,y / (y \ z)) = T(x,(z / y) \ y)
    ]]></literal>
    <justification jstring="[para(4416(a,1),13695(a,1,2))].">
      <j1 rule="para" parents="4416 13695"/>
    </justification>
  </clause>

  <clause id="13706">
    <literal><![CDATA[
      K(T(x,y) / y,z) = z / T(z,y \ x)
    ]]></literal>
    <justification jstring="[para(13695(a,1),5033(a,2,2))].">
      <j1 rule="para" parents="13695 5033"/>
    </justification>
  </clause>

  <clause id="13707">
    <literal><![CDATA[
      T(x,T(y,z \ u) / ((u \ z) \ 1)) = T(x,((u \ z) \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(7037(a,1),13695(a,1,2,1))].">
      <j1 rule="para" parents="7037 13695"/>
    </justification>
  </clause>

  <clause id="13708">
    <literal><![CDATA[
      K(x,T(T(y,z) / z,u)) = (u * T(x,z \ y)) / (u * x)
    ]]></literal>
    <justification jstring="[para(13695(a,1),9466(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="13695 9466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13709">
    <literal><![CDATA[
      K(x,y * a(z,u,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,5036,a,b,13692,a),flip(a)].">
      <j1 rule="hyper" parents="299 5036 13692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13710">
    <literal><![CDATA[
      K(x,y * a(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(13692(a,2),5155(a,1))].">
      <j1 rule="para" parents="13692 5155"/>
    </justification>
  </clause>

  <clause id="13711">
    <literal><![CDATA[
      K(x,y * (z \ R(z,u,z))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(9669(a,1),13709(a,1,2,2))].">
      <j1 rule="para" parents="9669 13709"/>
    </justification>
  </clause>

  <clause id="13712">
    <literal><![CDATA[
      K(x,T(y,z) / z) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(9693(a,1),13709(a,1,2))].">
      <j1 rule="para" parents="9693 13709"/>
    </justification>
  </clause>

  <clause id="13713">
    <literal><![CDATA[
      K(x,a(y,z,y) * u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(10116(a,2),13709(a,1,2))].">
      <j1 rule="para" parents="10116 13709"/>
    </justification>
  </clause>

  <clause id="13714">
    <literal><![CDATA[
      K(x,y * R(z,u,z)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(10456(a,1),13709(a,1,2))].">
      <j1 rule="para" parents="10456 13709"/>
    </justification>
  </clause>

  <clause id="13715">
    <literal><![CDATA[
      K(x,R(y,z,y) * u) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(10474(a,1),13709(a,1,2))].">
      <j1 rule="para" parents="10474 13709"/>
    </justification>
  </clause>

  <clause id="13716">
    <literal><![CDATA[
      K(x,R(y,z,y) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(10478(a,1),13709(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10478 13709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13717">
    <literal><![CDATA[
      K(x,y \ (a(z,u,z) * w)) = K(x,y \ w)
    ]]></literal>
    <justification jstring="[para(13671(a,2),13709(a,1,2))].">
      <j1 rule="para" parents="13671 13709"/>
    </justification>
  </clause>

  <clause id="13718">
    <literal><![CDATA[
      a((a(x,x,x) * y) * K(x \ 1,y),z,u) = a((x \ 1) \ (y * (1 / x)),z,u)
    ]]></literal>
    <justification jstring="[para(13713(a,1),6385(a,1,1,2))].">
      <j1 rule="para" parents="13713 6385"/>
    </justification>
  </clause>

  <clause id="13719">
    <literal><![CDATA[
      K(x,(a(y,z,y) \ u) * w) = K(x,u * w)
    ]]></literal>
    <justification jstring="[para(13342(a,1),13713(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13342 13713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13720">
    <literal><![CDATA[
      K(x,y * (a(z,u,z) * w)) = K(x,y * w)
    ]]></literal>
    <justification jstring="[para(13667(a,1),13713(a,1,2))].">
      <j1 rule="para" parents="13667 13713"/>
    </justification>
  </clause>

  <clause id="13721">
    <literal><![CDATA[
      K(x,y / T(z,y)) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(4382(a,1),13712(a,1,2))].">
      <j1 rule="para" parents="4382 13712"/>
    </justification>
  </clause>

  <clause id="13722">
    <literal><![CDATA[
      K(T(x,y),x \ y) * (((T(y,x) / x) \ y) \ z) = (y / (T(y,x) / x)) \ z
    ]]></literal>
    <justification jstring="[para(13712(a,1),5921(a,1,1))].">
      <j1 rule="para" parents="13712 5921"/>
    </justification>
  </clause>

  <clause id="13723">
    <literal><![CDATA[
      K(x,T(y * z,T(y,u) * (1 / u)) / (T(y,u) * (1 / u))) = K(x,L((1 / T(u,y)) \ z,u,y))
    ]]></literal>
    <justification jstring="[para(11628(a,1),13712(a,2,2))].">
      <j1 rule="para" parents="11628 13712"/>
    </justification>
  </clause>

  <clause id="13724">
    <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(13712(a,1),13224(a,1,1,2))].">
      <j1 rule="para" parents="13712 13224"/>
    </justification>
  </clause>

  <clause id="13725">
    <literal><![CDATA[
      K(x,L(y / T(z,y),u,w)) = L(K(x,z \ y),u,w)
    ]]></literal>
    <justification jstring="[para(13721(a,1),11889(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13721 11889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13726">
    <literal><![CDATA[
      T(x,y * ((z \ u) \ u)) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(12708(a,1),13694(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12708 13694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13727">
    <literal><![CDATA[
      T(x,T(y,y * z) \ u) = T(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(4479(a,1),13697(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4479 13697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13728">
    <literal><![CDATA[
      K(a(x,y,x) * z,u) = K(z,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,5033,a,b,13700,a),flip(a)].">
      <j1 rule="hyper" parents="299 5033 13700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13729">
    <literal><![CDATA[
      K(K(x,x * y) * z,u) = K(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(10065(a,1),13728(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10065 13728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13730">
    <literal><![CDATA[
      K(x * a(y,z,y),u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(10116(a,1),13728(a,1,1))].">
      <j1 rule="para" parents="10116 13728"/>
    </justification>
  </clause>

  <clause id="13731">
    <literal><![CDATA[
      K(R(x,y,x) * z,u) = K(x * z,u)
    ]]></literal>
    <justification jstring="[para(10476(a,1),13728(a,1,1))].">
      <j1 rule="para" parents="10476 13728"/>
    </justification>
  </clause>

  <clause id="13733">
    <literal><![CDATA[
      K(L(x,y,x) * z,u) = K(x * z,u)
    ]]></literal>
    <justification jstring="[para(12645(a,1),13728(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12645 13728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13734">
    <literal><![CDATA[
      K(T(x,y) / y,z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(9693(a,1),13730(a,1,1))].">
      <j1 rule="para" parents="9693 13730"/>
    </justification>
  </clause>

  <clause id="13736">
    <literal><![CDATA[
      a(x,y,x) \ T(z * a(x,y,x),u) = z * K(z,u)
    ]]></literal>
    <justification jstring="[para(13730(a,1),13366(a,2,2))].">
      <j1 rule="para" parents="13730 13366"/>
    </justification>
  </clause>

  <clause id="13737">
    <literal><![CDATA[
      K(x \ (a(y,z,y) \ u),w) = K(x \ u,w)
    ]]></literal>
    <justification jstring="[para(13672(a,1),13730(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13672 13730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13738">
    <literal><![CDATA[
      K(x / T(y,x),z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,10381,a(flip),b,13734,a)].">
      <j1 rule="hyper" parents="65 10381 13734"/>
    </justification>
  </clause>

  <clause id="13739">
    <literal><![CDATA[
      K(L(T(x,y),z,u) / y,w) = K(y \ L(x,z,u),w)
    ]]></literal>
    <justification jstring="[para(25(a,2),13734(a,1,1,1))].">
      <j1 rule="para" parents="25 13734"/>
    </justification>
  </clause>

  <clause id="13740">
    <literal><![CDATA[
      K(x \ T(y * K(x,y),z),u) = K(T(y,z) / x,u)
    ]]></literal>
    <justification jstring="[para(5125(a,1),13734(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5125 13734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13741">
    <literal><![CDATA[
      T(x * K(x / y,z),x) = x * K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(13734(a,1),10380(a,2,2))].">
      <j1 rule="para" parents="13734 10380"/>
    </justification>
  </clause>

  <clause id="13742">
    <literal><![CDATA[
      K(x / L(T(y,x),z,u),w) = K(L(y,z,u) \ x,w)
    ]]></literal>
    <justification jstring="[para(25(a,2),13738(a,1,1,2))].">
      <j1 rule="para" parents="25 13738"/>
    </justification>
  </clause>

  <clause id="13743">
    <literal><![CDATA[
      K(x,y / (z \ R(z,u,z))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(12(a,1),13711(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 13711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13744">
    <literal><![CDATA[
      K(x,y * T(z,z * u)) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(4479(a,1),13714(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4479 13714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13745">
    <literal><![CDATA[
      K(x,y * ((z \ u) \ u)) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(10283(a,1),13714(a,1,2,2))].">
      <j1 rule="para" parents="10283 13714"/>
    </justification>
  </clause>

  <clause id="13747">
    <literal><![CDATA[
      K(x,((y \ z) \ z) * u) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(10283(a,1),13715(a,1,2,1))].">
      <j1 rule="para" parents="10283 13715"/>
    </justification>
  </clause>

  <clause id="13748">
    <literal><![CDATA[
      K(x,T(y,y \ z) \ u) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(4538(a,1),13716(a,1,2,1))].">
      <j1 rule="para" parents="4538 13716"/>
    </justification>
  </clause>

  <clause id="13749">
    <literal><![CDATA[
      L(K(x,y \ (z \ u)),z \ u,z) = K(x,T(y * z,y) \ u)
    ]]></literal>
    <justification jstring="[para(13716(a,1),8980(a,1,1))].">
      <j1 rule="para" parents="13716 8980"/>
    </justification>
  </clause>

  <clause id="13750">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ u) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(10283(a,1),13716(a,1,2,1))].">
      <j1 rule="para" parents="10283 13716"/>
    </justification>
  </clause>

  <clause id="13751">
    <literal><![CDATA[
      K(x,L(R(y,z,y),u,w) \ v5) = K(x,L(y,u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(11438(a,1),13716(a,1,2,1))].">
      <j1 rule="para" parents="11438 13716"/>
    </justification>
  </clause>

  <clause id="13753">
    <literal><![CDATA[
      K(T(x,x \ y) * z,u) = K(T(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(4538(a,1),13731(a,1,1,1))].">
      <j1 rule="para" parents="4538 13731"/>
    </justification>
  </clause>

  <clause id="13754">
    <literal><![CDATA[
      K(((x \ y) \ y) * z,u) = K(T(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(10283(a,1),13731(a,1,1,1))].">
      <j1 rule="para" parents="10283 13731"/>
    </justification>
  </clause>

  <clause id="13755">
    <literal><![CDATA[
      K(x,(y \ R(y,z,y)) \ u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(10130(a,1),13743(a,1,2))].">
      <j1 rule="para" parents="10130 13743"/>
    </justification>
  </clause>

  <clause id="13756">
    <literal><![CDATA[
      L(K(x,y \ z),y \ z,y) = K(x,(y * (u \ R(u,w,u))) \ z)
    ]]></literal>
    <justification jstring="[para(13755(a,1),7943(a,1,1))].">
      <j1 rule="para" parents="13755 7943"/>
    </justification>
  </clause>

  <clause id="13758">
    <literal><![CDATA[
      T(x,T(y,z) / z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(9693(a,1),13690(a,1,2))].">
      <j1 rule="para" parents="9693 13690"/>
    </justification>
  </clause>

  <clause id="13759">
    <literal><![CDATA[
      T(x,L(y,z,y) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ u) = w
    ]]></literal>
    <justification jstring="[para(12039(a,1),13690(a,1,2))].">
      <j1 rule="para" parents="12039 13690"/>
    </justification>
  </clause>

  <clause id="13760">
    <literal><![CDATA[
      T(x,((y \ z) * T(y,y \ z)) * (y \ z)) = T(x,(z / y) * (y * (y \ z)))
    ]]></literal>
    <justification jstring="[para(5929(a,1),13693(a,2,2))].">
      <j1 rule="para" parents="5929 13693"/>
    </justification>
  </clause>

  <clause id="13761">
    <literal><![CDATA[
      T(x / (x \ y),T(z,(y / x) \ x)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x / (x \ y),z) = u
    ]]></literal>
    <justification jstring="[para(13705(a,1),4462(a,1,2))].">
      <j1 rule="para" parents="13705 4462"/>
    </justification>
  </clause>

  <clause id="13762">
    <literal><![CDATA[
      K(T(x,y) / y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(13706(a,2),5118(a,1))].">
      <j1 rule="para" parents="13706 5118"/>
    </justification>
  </clause>

  <clause id="13763">
    <literal><![CDATA[
      K(x,y * K(z \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(3253(a,1),13710(a,1,2,2))].">
      <j1 rule="para" parents="3253 13710"/>
    </justification>
  </clause>

  <clause id="13764">
    <literal><![CDATA[
      K(x,T(y,z) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(9693(a,1),13710(a,1,2))].">
      <j1 rule="para" parents="9693 13710"/>
    </justification>
  </clause>

  <clause id="13765">
    <literal><![CDATA[
      T(x,y * ((z * u) * z)) = T(x,y * (z * (u * z)))
    ]]></literal>
    <justification jstring="[para(84(a,1),13698(a,1,2,2))].">
      <j1 rule="para" parents="84 13698"/>
    </justification>
  </clause>

  <clause id="13766">
    <literal><![CDATA[
      T(x,y * T(z * u,z)) = T(x,y * (u * z))
    ]]></literal>
    <justification jstring="[para(9691(a,1),13698(a,1,2,2))].">
      <j1 rule="para" parents="9691 13698"/>
    </justification>
  </clause>

  <clause id="13767">
    <literal><![CDATA[
      T(x,y * (z * L(u,w,u))) = T(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(9714(a,1),13698(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9714 13698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13768">
    <literal><![CDATA[
      T(x,y * (T(z,u) / u)) = T(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[para(9693(a,1),13698(a,1,2,2))].">
      <j1 rule="para" parents="9693 13698"/>
    </justification>
  </clause>

  <clause id="13769">
    <literal><![CDATA[
      T(x,y \ R(z,u,z)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(9674(a,1),13699(a,1,2,2))].">
      <j1 rule="para" parents="9674 13699"/>
    </justification>
  </clause>

  <clause id="13770">
    <literal><![CDATA[
      T(x,y \ T(z * u,z)) = T(x,y \ (u * z))
    ]]></literal>
    <justification jstring="[para(9691(a,1),13699(a,1,2,2))].">
      <j1 rule="para" parents="9691 13699"/>
    </justification>
  </clause>

  <clause id="13771">
    <literal><![CDATA[
      T(x,y \ (T(z,u) / u)) = T(x,y \ (u \ z))
    ]]></literal>
    <justification jstring="[para(9693(a,1),13699(a,1,2,2))].">
      <j1 rule="para" parents="9693 13699"/>
    </justification>
  </clause>

  <clause id="13772">
    <literal><![CDATA[
      T(x,y \ (R(z,u,z) \ w)) = T(x,y \ (z \ w))
    ]]></literal>
    <justification jstring="[para(10478(a,1),13699(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10478 13699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13773">
    <literal><![CDATA[
      T(x,y \ ((z \ u) \ u)) = T(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(10283(a,1),13769(a,1,2,2))].">
      <j1 rule="para" parents="10283 13769"/>
    </justification>
  </clause>

  <clause id="13774">
    <literal><![CDATA[
      K(x,y \ T(z * u,z)) = K(x,y \ (u * z))
    ]]></literal>
    <justification jstring="[para(9690(a,1),13717(a,1,2,2))].">
      <j1 rule="para" parents="9690 13717"/>
    </justification>
  </clause>

  <clause id="13775">
    <literal><![CDATA[
      K(x,y \ (z * R(u,w,u))) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[para(10452(a,1),13717(a,1,2,2))].">
      <j1 rule="para" parents="10452 13717"/>
    </justification>
  </clause>

  <clause id="13776">
    <literal><![CDATA[
      K(x,K(y * z,y) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(9680(a,1),13719(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9680 13719"/>
      <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="[para(9668(a,1),13719(a,1,2,1))].">
      <j1 rule="para" parents="9668 13719"/>
    </justification>
  </clause>

  <clause id="13778">
    <literal><![CDATA[
      K(x,(y * L(z,u,z)) * w) = K(x,(y * z) * w)
    ]]></literal>
    <justification jstring="[para(10138(a,1),13719(a,1,2,1))].">
      <j1 rule="para" parents="10138 13719"/>
    </justification>
  </clause>

  <clause id="13779">
    <literal><![CDATA[
      K(x,y * T(z * u,z)) = K(x,y * (u * z))
    ]]></literal>
    <justification jstring="[para(9690(a,1),13720(a,1,2,2))].">
      <j1 rule="para" parents="9690 13720"/>
    </justification>
  </clause>

  <clause id="13780">
    <literal><![CDATA[
      K(x,y * (z * R(u,w,u))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(10452(a,1),13720(a,1,2,2))].">
      <j1 rule="para" parents="10452 13720"/>
    </justification>
  </clause>

  <clause id="13781">
    <literal><![CDATA[
      K(x,y * (L(z,u,z) * w)) = K(x,y * (z * w))
    ]]></literal>
    <justification jstring="[para(12645(a,1),13720(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12645 13720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13782">
    <literal><![CDATA[
      K(x \ R(y,z,y),u) = K(x \ y,u)
    ]]></literal>
    <justification jstring="[para(10139(a,1),13737(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10139 13737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13783">
    <literal><![CDATA[
      K(x \ T(y,y * z),u) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[para(4479(a,1),13782(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4479 13782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13784">
    <literal><![CDATA[
      K(x \ ((y \ z) \ z),u) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[para(10283(a,1),13782(a,1,1,2))].">
      <j1 rule="para" parents="10283 13782"/>
    </justification>
  </clause>

  <clause id="13785">
    <literal><![CDATA[
      T(x,y / T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(4382(a,1),13758(a,1,2))].">
      <j1 rule="para" parents="4382 13758"/>
    </justification>
  </clause>

  <clause id="13787">
    <literal><![CDATA[
      K(x / T(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(4382(a,1),13762(a,1,1))].">
      <j1 rule="para" parents="4382 13762"/>
    </justification>
  </clause>

  <clause id="13788">
    <literal><![CDATA[
      K(T(x,y / z) / T(z \ y,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(T(z \ y,y) \ x,u) = w
    ]]></literal>
    <justification jstring="[para(8196(a,1),13762(a,1,1,1))].">
      <j1 rule="para" parents="8196 13762"/>
    </justification>
  </clause>

  <clause id="13789">
    <literal><![CDATA[
      K(x,y * (z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (1 / z)) = u
    ]]></literal>
    <justification jstring="[para(2677(a,1),13763(a,1,2))].">
      <j1 rule="para" parents="2677 13763"/>
    </justification>
  </clause>

  <clause id="13790">
    <literal><![CDATA[
      K(x,K(y \ 1,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(3205(a,2),13763(a,1,2))].">
      <j1 rule="para" parents="3205 13763"/>
    </justification>
  </clause>

  <clause id="13791">
    <literal><![CDATA[
      K(x,(1 / (1 / y)) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(3243(a,1),13763(a,1,2))].">
      <j1 rule="para" parents="3243 13763"/>
    </justification>
  </clause>

  <clause id="13792">
    <literal><![CDATA[
      K(x,((y \ 1) \ 1) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(3244(a,1),13763(a,1,2))].">
      <j1 rule="para" parents="3244 13763"/>
    </justification>
  </clause>

  <clause id="13793">
    <literal><![CDATA[
      K(x,(1 / y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(y \ 1) \ z) = u
    ]]></literal>
    <justification jstring="[para(3245(a,1),13763(a,1,2))].">
      <j1 rule="para" parents="3245 13763"/>
    </justification>
  </clause>

  <clause id="13798">
    <literal><![CDATA[
      K(x,K(y,y \ 1) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(2596(a,1),13790(a,1,2,1))].">
      <j1 rule="para" parents="2596 13790"/>
    </justification>
  </clause>

  <clause id="13799">
    <literal><![CDATA[
      K(x,((1 / y) * z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ u) = w
    ]]></literal>
    <justification jstring="[para(3265(a,1),13790(a,1,2))].">
      <j1 rule="para" parents="3265 13790"/>
    </justification>
  </clause>

  <clause id="13803">
    <literal><![CDATA[
      K(x,(y * (1 / z)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ u) = w
    ]]></literal>
    <justification jstring="[para(2797(a,1),13798(a,1,2))].">
      <j1 rule="para" parents="2797 13798"/>
    </justification>
  </clause>

  <clause id="13804">
    <literal><![CDATA[
      K(x,y * ((z \ 1) \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(3216(a,1),13798(a,1,2))].">
      <j1 rule="para" parents="3216 13798"/>
    </justification>
  </clause>

  <clause id="13806">
    <literal><![CDATA[
      K(x,y * (1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z \ 1)) = u
    ]]></literal>
    <justification jstring="[para(3218(a,1),13798(a,1,2))].">
      <j1 rule="para" parents="3218 13798"/>
    </justification>
  </clause>

  <clause id="13807">
    <literal><![CDATA[
      K(x,y * (z * (1 / u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * (u \ 1))) = w
    ]]></literal>
    <justification jstring="[para(3340(a,1),13798(a,1,2))].">
      <j1 rule="para" parents="3340 13798"/>
    </justification>
  </clause>

  <clause id="13810">
    <literal><![CDATA[
      T(x,y * T(z,z \ u)) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(108(a,2),13726(a,1,2,2))].">
      <j1 rule="para" parents="108 13726"/>
    </justification>
  </clause>

  <clause id="13811">
    <literal><![CDATA[
      T(x,K(y * z,y) * (y \ u)) = T(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(5383(a,2),13727(a,1,2))].">
      <j1 rule="para" parents="5383 13727"/>
    </justification>
  </clause>

  <clause id="13812">
    <literal><![CDATA[
      (x \ (x * K(y \ x,z))) \ (x * K(x / y,z)) = L(x,K(y \ x,z),x)
    ]]></literal>
    <justification jstring="[para(13741(a,1),10531(a,1,1,2))].">
      <j1 rule="para" parents="13741 10531"/>
    </justification>
  </clause>

  <clause id="13813">
    <literal><![CDATA[
      K(x,y * T(z,z * u)) = x \ T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,5036,a(flip),b,13744,a),flip(a)].">
      <j1 rule="hyper" parents="299 5036 13744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13815">
    <literal><![CDATA[
      K(x,K(y,z * T(u,w))) * K(x,y / (z * ((u \ w) \ w))) = K(x,(z * ((u \ w) \ w)) \ y)
    ]]></literal>
    <justification jstring="[para(13745(a,1),8507(a,1,1,2))].">
      <j1 rule="para" parents="13745 8507"/>
    </justification>
  </clause>

  <clause id="13816">
    <literal><![CDATA[
      K((x * y) / x,T(z,u) * w) = K(y,T(((z \ u) \ u) * w,x))
    ]]></literal>
    <justification jstring="[hyper(8121,a,13747,a),flip(a)].">
      <j1 rule="hyper" parents="8121 13747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13817">
    <literal><![CDATA[
      K(x,((y \ z) \ z) * u) = x \ T(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(299,a,5036,a(flip),b,13747,a),flip(a)].">
      <j1 rule="hyper" parents="299 5036 13747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13818">
    <literal><![CDATA[
      K(x,T(y / z,y) * u) = K(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[para(79(a,1),13747(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="79 13747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13819">
    <literal><![CDATA[
      K(x,T(y,y \ z) \ u) = K(x,((y \ z) \ z) \ u)
    ]]></literal>
    <justification jstring="[hyper(299,a,13748,a,b,13750,a)].">
      <j1 rule="hyper" parents="299 13748 13750"/>
    </justification>
  </clause>

  <clause id="13820">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ u) = (w * K(T(y,z) \ u,x)) \ w
    ]]></literal>
    <justification jstring="[hyper(299,a,7200,a,b,13750,a),flip(a)].">
      <j1 rule="hyper" parents="299 7200 13750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13821">
    <literal><![CDATA[
      K(x,T(y / z,y) \ u) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(79(a,1),13750(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="79 13750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13822">
    <literal><![CDATA[
      L(K(x,T(y,z) \ u),y,y \ z) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[para(13750(a,1),11916(a,1,1))].">
      <j1 rule="para" parents="13750 11916"/>
    </justification>
  </clause>

  <clause id="13823">
    <literal><![CDATA[
      T(x,((y \ 1) \ 1) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(2806(a,1),13759(a,1,2,1))].">
      <j1 rule="para" parents="2806 13759"/>
    </justification>
  </clause>

  <clause id="13824">
    <literal><![CDATA[
      T(x,y * (T(z,u) / u)) = x * K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(299,a,5083,a(flip),b,13768,a),flip(a)].">
      <j1 rule="hyper" parents="299 5083 13768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13825">
    <literal><![CDATA[
      T(x,y * (z / T(u,z))) = T(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[para(4382(a,1),13768(a,1,2,2))].">
      <j1 rule="para" parents="4382 13768"/>
    </justification>
  </clause>

  <clause id="13826">
    <literal><![CDATA[
      T(x,T(y,z * (u \ w)) * (z * (T(w,u) / u))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,(z * (T(w,u) / u)) * y) = v5
    ]]></literal>
    <justification jstring="[para(13768(a,1),13267(a,1,2,1))].">
      <j1 rule="para" parents="13768 13267"/>
    </justification>
  </clause>

  <clause id="13827">
    <literal><![CDATA[
      T(x,y \ T(z * u,u)) = T(x,y \ (T(z,u) * u))
    ]]></literal>
    <justification jstring="[para(107(a,1),13770(a,1,2,2,1))].">
      <j1 rule="para" parents="107 13770"/>
    </justification>
  </clause>

  <clause id="13828">
    <literal><![CDATA[
      T(x,y \ (z / T(u,z))) = T(x,y \ (u \ z))
    ]]></literal>
    <justification jstring="[para(4382(a,1),13771(a,1,2,2))].">
      <j1 rule="para" parents="4382 13771"/>
    </justification>
  </clause>

  <clause id="13829">
    <literal><![CDATA[
      T(x,y \ T(z \ 1,u * z)) = T(x,y \ T(z \ 1,u))
    ]]></literal>
    <justification jstring="[para(6191(a,2),13773(a,1,2,2))].">
      <j1 rule="para" parents="6191 13773"/>
    </justification>
  </clause>

  <clause id="13830">
    <literal><![CDATA[
      T(x,y \ T((z * u) * (1 / z),z * u)) = T(x,y \ ((u * z) * (1 / z)))
    ]]></literal>
    <justification jstring="[para(7138(a,1),13773(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7138 13773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13831">
    <literal><![CDATA[
      K(x,y \ ((z \ u) * z)) = K(x,y \ T(u,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),13774(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 13774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13832">
    <literal><![CDATA[
      K(x,K(y * z,y) * u) = x \ T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(299,a,5036,a(flip),b,13776,a),flip(a)].">
      <j1 rule="hyper" parents="299 5036 13776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13833">
    <literal><![CDATA[
      K(x,K(y \ z,y) * (z * u)) = K(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[para(5103(a,1),13777(a,2,2))].">
      <j1 rule="para" parents="5103 13777"/>
    </justification>
  </clause>

  <clause id="13834">
    <literal><![CDATA[
      K(x,K(y,z) * ((z \ y) \ u)) = K(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[para(5692(a,1),13777(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5692 13777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13835">
    <literal><![CDATA[
      K(x \ T(y / z,y),u) = K(x \ (z \ y),u)
    ]]></literal>
    <justification jstring="[para(79(a,1),13784(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 13784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13836">
    <literal><![CDATA[
      T(T(x,y),K(y,(z \ u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,T(u / z,u) * w)) = v5
    ]]></literal>
    <justification jstring="[para(13818(a,1),7154(a,1,2))].">
      <j1 rule="para" parents="13818 7154"/>
    </justification>
  </clause>

  <clause id="13837">
    <literal><![CDATA[
      K(T(x / y,x) \ z,u) = (w * K(u,(y \ x) \ z)) \ w
    ]]></literal>
    <justification jstring="[para(13821(a,1),7200(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="13821 7200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13838">
    <literal><![CDATA[
      T(x,y \ (z / T(T(u,u \ z),z))) = T(x,y \ T(u \ z,u))
    ]]></literal>
    <justification jstring="[para(4426(a,1),13828(a,2,2,2))].">
      <j1 rule="para" parents="4426 13828"/>
    </justification>
  </clause>

  <clause id="13839">
    <literal><![CDATA[
      K(x,y \ T((z \ 1) \ u,z)) = K(x,y \ ((z \ 1) \ T(u,z)))
    ]]></literal>
    <justification jstring="[para(2045(a,1),13831(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2045 13831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13840">
    <literal><![CDATA[
      T(x,y * (z * L(1 / u,w,v5))) = T(x,y * (z * L(u \ 1,w,v5)))
    ]]></literal>
    <justification jstring="[para(6755(a,1),13767(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6755 13767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13841">
    <literal><![CDATA[
      T(x,y \ ((z \ T(u * z,u)) \ w)) = T(x,y \ (u \ w))
    ]]></literal>
    <justification jstring="[para(4338(a,2),13772(a,1,2,2,1))].">
      <j1 rule="para" parents="4338 13772"/>
    </justification>
  </clause>

  <clause id="13842">
    <literal><![CDATA[
      T(x,y \ (T(z,z * u) \ w)) = T(x,y \ (T(z,u) \ w))
    ]]></literal>
    <justification jstring="[para(4479(a,1),13772(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4479 13772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13843">
    <literal><![CDATA[
      K(x,y \ (z * T(u,u * w))) = K(x,y \ (z * T(u,w)))
    ]]></literal>
    <justification jstring="[para(4479(a,1),13775(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4479 13775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13844">
    <literal><![CDATA[
      K(x,((y * z) * y) * u) = K(x,(y * (z * y)) * u)
    ]]></literal>
    <justification jstring="[para(94(a,1),13778(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="94 13778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13845">
    <literal><![CDATA[
      K(x,(y * R(z,u,z)) * w) = K(x,(y * z) * w)
    ]]></literal>
    <justification jstring="[para(4760(a,1),13778(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="4760 13778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13846">
    <literal><![CDATA[
      K(x,(y * L(1 / z,u,w)) * v5) = K(x,(y * L(z \ 1,u,w)) * v5)
    ]]></literal>
    <justification jstring="[para(6755(a,1),13778(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="6755 13778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13847">
    <literal><![CDATA[
      K(x,(y * ((z \ u) \ u)) * w) = K(x,(y * T(z,u)) * w)
    ]]></literal>
    <justification jstring="[para(12708(a,1),13778(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="12708 13778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13848">
    <literal><![CDATA[
      K(x,y * (z * ((u \ w) \ w))) = K(x,y * (z * T(u,w)))
    ]]></literal>
    <justification jstring="[para(10283(a,1),13780(a,1,2,2,2))].">
      <j1 rule="para" parents="10283 13780"/>
    </justification>
  </clause>

  <clause id="13849">
    <literal><![CDATA[
      K(x,y * (T(z / u,z) * w)) = K(x,y * ((u \ z) * w))
    ]]></literal>
    <justification jstring="[para(4521(a,1),13781(a,1,2,2,1))].">
      <j1 rule="para" parents="4521 13781"/>
    </justification>
  </clause>

  <clause id="13850">
    <literal><![CDATA[
      K(x,y * (((z \ u) \ u) * w)) = K(x,y * (T(z,u) * w))
    ]]></literal>
    <justification jstring="[para(12708(a,1),13781(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="12708 13781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13851">
    <literal><![CDATA[
      K(x,L(1 / y,z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y \ 1,z,u) * w) = v5
    ]]></literal>
    <justification jstring="[para(4141(a,1),13791(a,1,2,1))].">
      <j1 rule="para" parents="4141 13791"/>
    </justification>
  </clause>

  <clause id="13855">
    <literal><![CDATA[
      T(x,((y * z) \ y) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(y \ (y / z)) \ u) = w
    ]]></literal>
    <justification jstring="[para(10410(a,1),13823(a,1,2,1))].">
      <j1 rule="para" parents="10410 13823"/>
    </justification>
  </clause>

  <clause id="13856">
    <literal><![CDATA[
      K(x,T(y * z,y) * u) = K(x,(z * y) * u)
    ]]></literal>
    <justification jstring="[para(4341(a,1),13845(a,1,2,1))].">
      <j1 rule="para" parents="4341 13845"/>
    </justification>
  </clause>

  <clause id="13857">
    <literal><![CDATA[
      K(x,(y * L(z \ 1,u,z)) * w) = K(x,(y * (1 / z)) * w)
    ]]></literal>
    <justification jstring="[para(4706(a,1),13845(a,1,2,1,2))].">
      <j1 rule="para" parents="4706 13845"/>
    </justification>
  </clause>

  <clause id="13858">
    <literal><![CDATA[
      K(x,(y * z) * z) = K(x,z * (z * y))
    ]]></literal>
    <justification jstring="[hyper(13261,a,13856,a),flip(a)].">
      <j1 rule="hyper" parents="13261 13856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13859">
    <literal><![CDATA[
      K(x,((y \ z) * y) * u) = K(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[para(10(a,1),13856(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 13856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13860">
    <literal><![CDATA[
      K(x,(y \ (z * (y \ 1))) * u) = K(x,((y \ z) * (y \ 1)) * u)
    ]]></literal>
    <justification jstring="[para(1741(a,1),13856(a,1,2,1))].">
      <j1 rule="para" parents="1741 13856"/>
    </justification>
  </clause>

  <clause id="13861">
    <literal><![CDATA[
      K(x,T(y / (y \ z),y) * u) = K(x,((((z \ y) \ 1) \ 1) * y) * u)
    ]]></literal>
    <justification jstring="[para(10418(a,1),13856(a,1,2,1,1))].">
      <j1 rule="para" parents="10418 13856"/>
    </justification>
  </clause>

  <clause id="13862">
    <literal><![CDATA[
      K(x,(y * z) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * (z * y)) = u
    ]]></literal>
    <justification jstring="[para(13856(a,1),13261(a,1))].">
      <j1 rule="para" parents="13856 13261"/>
    </justification>
  </clause>

  <clause id="13863">
    <literal><![CDATA[
      K(x,(y \ z) * ((y \ z) * y)) = K(x,z * (y \ z))
    ]]></literal>
    <justification jstring="[para(10(a,1),13858(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 13858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13864">
    <literal><![CDATA[
      L(x,y,(z / L(u,w,u)) * v5) = L(x,y,(z / u) * v5)
    ]]></literal>
    <justification jstring="[para(13686(a,1),13679(a,1,3))].">
      <j1 rule="para" parents="13686 13679"/>
    </justification>
  </clause>

  <clause id="13865">
    <literal><![CDATA[
      (x / y) * (z \ (z * a(u,w,u))) = x / ((1 / a(u,w,u)) * y)
    ]]></literal>
    <justification jstring="[para(9(a,2),13688(a,2,2)),flip(a)].">
      <j1 rule="para" parents="9 13688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13866">
    <literal><![CDATA[
      K(x,L(y / T(z,y),u,w)) = K(x,L(z \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(299,a,11889,a(flip),b,13725,a),flip(a)].">
      <j1 rule="hyper" parents="299 11889 13725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13867">
    <literal><![CDATA[
      a(x,y,x) \ T(z * a(x,y,x),u) = T(z,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,5083,a,b,13736,a),flip(a)].">
      <j1 rule="hyper" parents="299 5083 13736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13869">
    <literal><![CDATA[
      T(x * a(y,z,y),u) = a(y,z,y) * T(x,u)
    ]]></literal>
    <justification jstring="[hyper(144,a,13867,a),flip(a)].">
      <j1 rule="hyper" parents="144 13867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13870">
    <literal><![CDATA[
      T(a(x,y,x) * z,u) = a(x,y,x) * T(z,u)
    ]]></literal>
    <justification jstring="[para(10116(a,2),13869(a,1,1))].">
      <j1 rule="para" parents="10116 13869"/>
    </justification>
  </clause>

  <clause id="13871">
    <literal><![CDATA[
      (x * (y * T(a(z,u,z) * (a(z,u,z) \ (y \ (x \ w))),v5))) \ w = K(v5,(x * (y * a(z,u,z))) \ w)
    ]]></literal>
    <justification jstring="[para(13870(a,2),9124(a,1,1,2,2))].">
      <j1 rule="para" parents="13870 9124"/>
    </justification>
  </clause>

  <clause id="13872">
    <literal><![CDATA[
      T(x,y * (T(z,u) * (z \ (w * K(z,u))))) = T(x,y * ((K(z,u) * w) * K(z,u)))
    ]]></literal>
    <justification jstring="[para(5056(a,2),13765(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5056 13765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13873">
    <literal><![CDATA[
      K(x,y * T(z,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(13813(a,2),5155(a,1))].">
      <j1 rule="para" parents="13813 5155"/>
    </justification>
  </clause>

  <clause id="13874">
    <literal><![CDATA[
      T(x,((y \ z) \ z) * u) = T(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(5086,a,13817,a)].">
      <j1 rule="hyper" parents="5086 13817"/>
    </justification>
  </clause>

  <clause id="13875">
    <literal><![CDATA[
      K(x,((y \ z) \ z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(13817(a,2),5155(a,1))].">
      <j1 rule="para" parents="13817 5155"/>
    </justification>
  </clause>

  <clause id="13876">
    <literal><![CDATA[
      T(x,T(y / z,y) * u) = T(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[para(79(a,1),13874(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="79 13874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13877">
    <literal><![CDATA[
      T(x,(y \ z) * z) = T(x,z * (z / y))
    ]]></literal>
    <justification jstring="[hyper(13267,a,13876,a),flip(a)].">
      <j1 rule="hyper" parents="13267 13876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13878">
    <literal><![CDATA[
      T(x,(y \ z) * (K(T(z / y,z),u) * w)) = T(x,T(T(z / y,z),u) * w)
    ]]></literal>
    <justification jstring="[para(5055(a,1),13876(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5055 13876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13880">
    <literal><![CDATA[
      ((x \ y) * y) * T(z,y * (y / x)) = z * ((x \ y) * y)
    ]]></literal>
    <justification jstring="[para(13877(a,1),107(a,1,2))].">
      <j1 rule="para" parents="13877 107"/>
    </justification>
  </clause>

  <clause id="13881">
    <literal><![CDATA[
      K(x,y * (T(z,u) / u)) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(5154,a,13824,a)].">
      <j1 rule="hyper" parents="5154 13824"/>
    </justification>
  </clause>

  <clause id="13882">
    <literal><![CDATA[
      T(x,y * (T(z,u) / u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (u \ z)) = w
    ]]></literal>
    <justification jstring="[para(13824(a,2),5087(a,1))].">
      <j1 rule="para" parents="13824 5087"/>
    </justification>
  </clause>

  <clause id="13883">
    <literal><![CDATA[
      K(x,y * ((z \ u) / z)) = K(x,y * (z \ (u / z)))
    ]]></literal>
    <justification jstring="[para(109(a,1),13881(a,1,2,2,1))].">
      <j1 rule="para" parents="109 13881"/>
    </justification>
  </clause>

  <clause id="13884">
    <literal><![CDATA[
      K(x,y * (z / T(u,z))) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[para(4382(a,1),13881(a,1,2,2))].">
      <j1 rule="para" parents="4382 13881"/>
    </justification>
  </clause>

  <clause id="13885">
    <literal><![CDATA[
      K(x,y * (z \ T(u * K(z,u),w))) = K(x,y * (T(u,w) / z))
    ]]></literal>
    <justification jstring="[para(5125(a,1),13881(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5125 13881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13886">
    <literal><![CDATA[
      K(x,K(y,z * (u \ w))) * K(y,(z * (w / T(u,w))) / x) = K(y,x \ (z * (w / T(u,w))))
    ]]></literal>
    <justification jstring="[para(13884(a,1),8505(a,1,1,2))].">
      <j1 rule="para" parents="13884 8505"/>
    </justification>
  </clause>

  <clause id="13887">
    <literal><![CDATA[
      T(x,K(y * z,y) * u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(5086,a,13832,a)].">
      <j1 rule="hyper" parents="5086 13832"/>
    </justification>
  </clause>

  <clause id="13888">
    <literal><![CDATA[
      K(x,K(y * z,y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(13832(a,2),5155(a,1))].">
      <j1 rule="para" parents="13832 5155"/>
    </justification>
  </clause>

  <clause id="13889">
    <literal><![CDATA[
      T(x,K(y \ z,y) * u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(10(a,1),13887(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 13887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13890">
    <literal><![CDATA[
      K(K(x * y,x) * z,u) = u / T(u,K(y,x) * z)
    ]]></literal>
    <justification jstring="[para(13887(a,1),5033(a,2,2))].">
      <j1 rule="para" parents="13887 5033"/>
    </justification>
  </clause>

  <clause id="13891">
    <literal><![CDATA[
      K(x,(((y \ z) * y) * (y \ z)) * u) = K(x,((y \ z) * z) * u)
    ]]></literal>
    <justification jstring="[para(10(a,1),13844(a,2,2,1,2))].">
      <j1 rule="para" parents="10 13844"/>
    </justification>
  </clause>

  <clause id="13892">
    <literal><![CDATA[
      K(x,L(T(y,z) / z,u,w)) = K(x,L(z \ y,u,w))
    ]]></literal>
    <justification jstring="[para(4382(a,2),13866(a,1,2,1))].">
      <j1 rule="para" parents="4382 13866"/>
    </justification>
  </clause>

  <clause id="13893">
    <literal><![CDATA[
      K(K(x * y,x) * z,u) = K(K(y,x) * z,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,5033,a,b,13890,a),flip(a)].">
      <j1 rule="hyper" parents="299 5033 13890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13894">
    <literal><![CDATA[
      K(K(x \ y,x) * z,u) = K(K(y,x) * z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),13893(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 13893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13895">
    <literal><![CDATA[
      K(K(x * y,y) * z,u) = K(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(5980(a,2),13893(a,1,1,1))].">
      <j1 rule="para" parents="5980 13893"/>
    </justification>
  </clause>

  <clause id="13896">
    <literal><![CDATA[
      K((x * (y / x)) \ z,u) = K(K(y,x) * (y \ z),u)
    ]]></literal>
    <justification jstring="[para(11653(a,1),13894(a,1,1))].">
      <j1 rule="para" parents="11653 13894"/>
    </justification>
  </clause>

  <clause id="13897">
    <literal><![CDATA[
      K(K(x,y) * (((x * y) * y) \ z),u) = K((y * (x * y)) \ z,u)
    ]]></literal>
    <justification jstring="[para(11606(a,1),13895(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11606 13895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13898">
    <literal><![CDATA[
      L(x,y,((z * u) / z) * w) = L(x,y,(z * (u / z)) * w)
    ]]></literal>
    <justification jstring="[para(585(a,1),13864(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="585 13864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13899">
    <literal><![CDATA[
      K(x,T(y,y \ z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(108(a,2),13875(a,1,2,1))].">
      <j1 rule="para" parents="108 13875"/>
    </justification>
  </clause>

  <clause id="13900">
    <literal><![CDATA[
      K(x,L((y \ 1) \ 1,z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(L(y,z,u),1) * w) = v5
    ]]></literal>
    <justification jstring="[para(4149(a,2),13875(a,1,2,1))].">
      <j1 rule="para" parents="4149 13875"/>
    </justification>
  </clause>

  <clause id="13901">
    <literal><![CDATA[
      T(x,y * (1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (z \ 1)) = u
    ]]></literal>
    <justification jstring="[para(195(a,1),13882(a,1,2,2,1))].">
      <j1 rule="para" parents="195 13882"/>
    </justification>
  </clause>

  <clause id="13902">
    <literal><![CDATA[
      K(x,K(y * z,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(5980(a,2),13888(a,1,2,1))].">
      <j1 rule="para" parents="5980 13888"/>
    </justification>
  </clause>

  <clause id="13903">
    <literal><![CDATA[
      (x * (a(y,z,y) * (u * w))) \ (a(y,z,y) * ((x * u) * w)) = a(x,a(y,z,y) * u,w)
    ]]></literal>
    <justification jstring="[para(13677(a,1),13355(a,1,2))].">
      <j1 rule="para" parents="13677 13355"/>
    </justification>
  </clause>

  <clause id="13904">
    <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="[hyper(911,a,13678,a),flip(a)].">
      <j1 rule="hyper" parents="911 13678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13905">
    <literal><![CDATA[
      K(x,T(T(y,z) / z,u)) = K(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,9466,a(flip),b,13708,a),flip(a)].">
      <j1 rule="hyper" parents="299 9466 13708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13906">
    <literal><![CDATA[
      K(x,T(y / T(z,y),u)) = K(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[para(4382(a,1),13905(a,1,2,1))].">
      <j1 rule="para" parents="4382 13905"/>
    </justification>
  </clause>

  <clause id="13907">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(13820(a,2),7209(a,1))].">
      <j1 rule="para" parents="13820 7209"/>
    </justification>
  </clause>

  <clause id="13909">
    <literal><![CDATA[
      K(T(x / y,x) \ z,u) = K((y \ x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,7200,a(flip),b,13837,a),flip(a)].">
      <j1 rule="hyper" parents="299 7200 13837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13910">
    <literal><![CDATA[
      K(((x \ y) \ y) \ z,u) = K(T(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[para(76(a,1),13909(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="76 13909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13911">
    <literal><![CDATA[
      K(T(x,x \ y) \ z,u) = K(T(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[para(108(a,2),13910(a,1,1,1))].">
      <j1 rule="para" parents="108 13910"/>
    </justification>
  </clause>

  <clause id="13912">
    <literal><![CDATA[
      K(T(x,y) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(13910(a,1),8322(a,1))].">
      <j1 rule="para" parents="13910 8322"/>
    </justification>
  </clause>

  <clause id="13913">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ u) * a(w,v5,K(T(y,z) \ u,x)) = K(x,L(((y \ z) \ z) \ u,v5,w))
    ]]></literal>
    <justification jstring="[para(13910(a,1),11896(a,1,2,3))].">
      <j1 rule="para" parents="13910 11896"/>
    </justification>
  </clause>

  <clause id="13914">
    <literal><![CDATA[
      K(x \ T(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(4396(a,1),13912(a,1,1))].">
      <j1 rule="para" parents="4396 13912"/>
    </justification>
  </clause>

  <clause id="13915">
    <literal><![CDATA[
      K(x,(y * T((z * u) * (1 / z),z * u)) * w) = K(x,(y * ((u * z) * (1 / z))) * w)
    ]]></literal>
    <justification jstring="[para(7138(a,1),13847(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="7138 13847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13916">
    <literal><![CDATA[
      K(x,y * (z * T(u / w,u))) = K(x,y * (z * (w \ u)))
    ]]></literal>
    <justification jstring="[para(79(a,1),13848(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="79 13848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13917">
    <literal><![CDATA[
      K(x,y * (z * T((u * w) * (1 / u),u * w))) = K(x,y * (z * ((w * u) * (1 / u))))
    ]]></literal>
    <justification jstring="[para(7138(a,1),13848(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="7138 13848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13918">
    <literal><![CDATA[
      K(x,y * (T(z,z \ u) * w)) = K(x,y * (T(z,u) * w))
    ]]></literal>
    <justification jstring="[para(108(a,2),13850(a,1,2,2,1))].">
      <j1 rule="para" parents="108 13850"/>
    </justification>
  </clause>

  <clause id="13919">
    <literal><![CDATA[
      K(x,T(y * z,y) \ u) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(10251,a,13749,a),flip(a)].">
      <j1 rule="hyper" parents="10251 13749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13920">
    <literal><![CDATA[
      K(x,T(y * z,y) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * y) \ u) = w
    ]]></literal>
    <justification jstring="[para(13749(a,1),10251(a,1))].">
      <j1 rule="para" parents="13749 10251"/>
    </justification>
  </clause>

  <clause id="13922">
    <literal><![CDATA[
      K(x,((y \ z) * y) \ u) = K(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(10(a,1),13919(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 13919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13923">
    <literal><![CDATA[
      K(x,T(y,z) \ z) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(8435,a,13922,a),flip(a)].">
      <j1 rule="hyper" parents="8435 13922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13924">
    <literal><![CDATA[
      K(x,T(y,z) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(13922(a,1),8435(a,1))].">
      <j1 rule="para" parents="13922 8435"/>
    </justification>
  </clause>

  <clause id="13925">
    <literal><![CDATA[
      K(x,y \ T(z,y)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(4396(a,1),13923(a,1,2))].">
      <j1 rule="para" parents="4396 13923"/>
    </justification>
  </clause>

  <clause id="13926">
    <literal><![CDATA[
      K(x,L(y \ T(z,y),u,w)) = L(K(x,z / y),u,w)
    ]]></literal>
    <justification jstring="[para(13925(a,1),11889(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13925 11889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13927">
    <literal><![CDATA[
      K(x,T(y * z,y) \ T(u,z * y)) = K(x,u / T(y * z,y))
    ]]></literal>
    <justification jstring="[para(13197(a,1),13925(a,1,2,2))].">
      <j1 rule="para" parents="13197 13925"/>
    </justification>
  </clause>

  <clause id="13928">
    <literal><![CDATA[
      K(x,L(T(y,z),u,w) \ z) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,z / L(y,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(25(a,2),13924(a,1,2,1))].">
      <j1 rule="para" parents="25 13924"/>
    </justification>
  </clause>

  <clause id="13929">
    <literal><![CDATA[
      K(x,y \ T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(4396(a,1),13924(a,1,2))].">
      <j1 rule="para" parents="4396 13924"/>
    </justification>
  </clause>

  <clause id="13930">
    <literal><![CDATA[
      K(x,L(y \ T(z,y),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(z / y,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(13926(a,2),11995(a,1))].">
      <j1 rule="para" parents="13926 11995"/>
    </justification>
  </clause>

  <clause id="13932">
    <literal><![CDATA[
      K(x,(y * z) \ ((y * y) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ u) = w
    ]]></literal>
    <justification jstring="[para(1068(a,2),13799(a,1,2))].">
      <j1 rule="para" parents="1068 13799"/>
    </justification>
  </clause>

  <clause id="13933">
    <literal><![CDATA[
      K(x,L(T(y,z) \ u,y,y \ z)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(11995,a,13822,a)].">
      <j1 rule="hyper" parents="11995 13822"/>
    </justification>
  </clause>

  <clause id="13934">
    <literal><![CDATA[
      K(x,(y * (z \ R(z,u,z))) \ w) = K(x,y \ w)
    ]]></literal>
    <justification jstring="[hyper(6838,a,13756,a),flip(a)].">
      <j1 rule="hyper" parents="6838 13756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13936">
    <literal><![CDATA[
      K(x,(a(y,z,y) * u) \ w) = K(x,u \ w)
    ]]></literal>
    <justification jstring="[para(10146(a,1),13934(a,1,2,1))].">
      <j1 rule="para" parents="10146 13934"/>
    </justification>
  </clause>

  <clause id="13937">
    <literal><![CDATA[
      K(x,K(y * z,y) \ u) = K(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(9684(a,1),13936(a,1,2,1))].">
      <j1 rule="para" parents="9684 13936"/>
    </justification>
  </clause>

  <clause id="13938">
    <literal><![CDATA[
      K(x,(L(y,z,y) * u) \ w) = K(x,(y * u) \ w)
    ]]></literal>
    <justification jstring="[para(12645(a,1),13936(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12645 13936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13939">
    <literal><![CDATA[
      K(x,K(y \ z,y) \ u) = K(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(10(a,1),13937(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 13937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13940">
    <literal><![CDATA[
      K(x,T(((y \ z) \ z) * u,w)) = K(x,T(T(y,z) * u,w))
    ]]></literal>
    <justification jstring="[hyper(8121,a,13816,a),flip(a)].">
      <j1 rule="hyper" parents="8121 13816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13941">
    <literal><![CDATA[
      K(x,T(T(y,y \ z) * u,w)) = K(x,T(T(y,z) * u,w))
    ]]></literal>
    <justification jstring="[para(108(a,2),13940(a,1,2,1,1))].">
      <j1 rule="para" parents="108 13940"/>
    </justification>
  </clause>

  <clause id="13942">
    <literal><![CDATA[
      K(x,T(T(y,y * z) * u,w)) = K(x,T(T(y,z) * u,w))
    ]]></literal>
    <justification jstring="[para(9(a,1),13941(a,1,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 13941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13943">
    <literal><![CDATA[
      K(x,T(T(T(y,T(y,z) * u),T(z,y)) * w,v5)) = K(x,T(T(T(y,z),u) * w,v5))
    ]]></literal>
    <justification jstring="[para(4397(a,2),13942(a,1,2,1,1))].">
      <j1 rule="para" parents="4397 13942"/>
    </justification>
  </clause>

  <clause id="13944">
    <literal><![CDATA[
      T(x,y \ T(z \ u,z)) = T(x,y \ (T(z,u) \ u))
    ]]></literal>
    <justification jstring="[para(9736(a,1),13838(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9736 13838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13945">
    <literal><![CDATA[
      (a(x,y,x) \ (z / u)) * (a(x,y,x) * a(w,v5,w)) = z / ((1 / a(w,v5,w)) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,13681,a,b,13865,a)].">
      <j1 rule="hyper" parents="65 13681 13865"/>
    </justification>
  </clause>

  <clause id="13946">
    <literal><![CDATA[
      K(x,(y * T(z \ y,z)) * u) = K(x,((z \ y) * y) * u)
    ]]></literal>
    <justification jstring="[para(888(a,1),13891(a,1,2,1))].">
      <j1 rule="para" parents="888 13891"/>
    </justification>
  </clause>

  <clause id="13947">
    <literal><![CDATA[
      K(x,(y * z) \ T(u,y * z)) = K(x,u / T(z * y,z))
    ]]></literal>
    <justification jstring="[hyper(13920,a,13927,a)].">
      <j1 rule="hyper" parents="13920 13927"/>
    </justification>
  </clause>

  <clause id="13948">
    <literal><![CDATA[
      K(x,y / T(z * u,z)) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[hyper(13929,a,13947,a),flip(a)].">
      <j1 rule="hyper" parents="13929 13947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13949">
    <literal><![CDATA[
      K(x,y / T(z * u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (u * z)) = w
    ]]></literal>
    <justification jstring="[para(13947(a,1),13929(a,1))].">
      <j1 rule="para" parents="13947 13929"/>
    </justification>
  </clause>

  <clause id="13950">
    <literal><![CDATA[
      K(x,y / ((z \ u) * z)) = K(x,y / T(u,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),13948(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 13948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13951">
    <literal><![CDATA[
      K(x / T(y * z,y),u) = (w * K(u,x / (z * y))) \ w
    ]]></literal>
    <justification jstring="[para(13948(a,1),7200(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="13948 7200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13952">
    <literal><![CDATA[
      T(x,y / ((z \ u) * z)) = x * K(x,y / T(u,z))
    ]]></literal>
    <justification jstring="[para(13950(a,1),5083(a,2,2))].">
      <j1 rule="para" parents="13950 5083"/>
    </justification>
  </clause>

  <clause id="13953">
    <literal><![CDATA[
      T(x,y / ((z \ u) * z)) = T(x,y / T(u,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,5083,a,b,13952,a),flip(a)].">
      <j1 rule="hyper" parents="299 5083 13952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13954">
    <literal><![CDATA[
      T(x,y / T(z * u,z)) = T(x,y / (u * z))
    ]]></literal>
    <justification jstring="[para(9(a,1),13953(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="9 13953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13955">
    <literal><![CDATA[
      K(x / T(y * z,y),u) = K(x / (z * y),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,7200,a(flip),b,13951,a),flip(a)].">
      <j1 rule="hyper" parents="299 7200 13951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13956">
    <literal><![CDATA[
      K(x / T(y * z,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x / (z * y),u) = w
    ]]></literal>
    <justification jstring="[para(13951(a,2),7209(a,1))].">
      <j1 rule="para" parents="13951 7209"/>
    </justification>
  </clause>

  <clause id="13957">
    <literal><![CDATA[
      K(x / ((y \ z) * y),u) = K(x / T(z,y),u)
    ]]></literal>
    <justification jstring="[para(10(a,1),13955(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 13955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13958">
    <literal><![CDATA[
      (x * y) \ (x * ((y * z) * a(u,w,u))) = L(z,y,x) * a(u,w,u)
    ]]></literal>
    <justification jstring="[para(13645(a,1),13665(a,1,2))].">
      <j1 rule="para" parents="13645 13665"/>
    </justification>
  </clause>

  <clause id="13960">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z * a(u,w,u)))) = L(z,y,x) * a(u,w,u)
    ]]></literal>
    <justification jstring="[para(13645(a,1),13958(a,1,2,2))].">
      <j1 rule="para" parents="13645 13958"/>
    </justification>
  </clause>

  <clause id="13961">
    <literal><![CDATA[
      L(x * a(y,z,y),u,w) = L(x,u,w) * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(493,a,13960,a)].">
      <j1 rule="hyper" parents="493 13960"/>
    </justification>
  </clause>

  <clause id="13962">
    <literal><![CDATA[
      L(a(x,y,x) \ z,u,w) = a(x,y,x) \ L(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(3931,a,13961,a),flip(a)].">
      <j1 rule="hyper" parents="3931 13961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13963">
    <literal><![CDATA[
      T(x,y * (z * L(1 / z,u,w))) = T(x,y * (z \ L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(6499(a,1),13840(a,2,2,2))].">
      <j1 rule="para" parents="6499 13840"/>
    </justification>
  </clause>

  <clause id="13964">
    <literal><![CDATA[
      K(x,((((y \ z) \ 1) \ 1) * z) * u) = K(x,((z \ y) \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,13818,a(flip),b,13861,a),flip(a)].">
      <j1 rule="hyper" parents="65 13818 13861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13965">
    <literal><![CDATA[
      x * L(a(x,y,x) \ (x \ a(x,y,x)),z,u) = L(x \ L(x,z,u),y,x)
    ]]></literal>
    <justification jstring="[para(13962(a,2),13682(a,1,2))].">
      <j1 rule="para" parents="13962 13682"/>
    </justification>
  </clause>

  <clause id="13966">
    <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),13812(a,1,1))].">
      <j1 rule="para" parents="9 13812"/>
    </justification>
  </clause>

  <clause id="13967">
    <literal><![CDATA[
      L(x,K(y \ x,z),x) = x
    ]]></literal>
    <justification jstring="[hyper(8148,a,13966,a),flip(a)].">
      <j1 rule="hyper" parents="8148 13966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13969">
    <literal><![CDATA[
      L(x,K(y,z),x) = x
    ]]></literal>
    <justification jstring="[para(79(a,1),13967(a,1,2,1))].">
      <j1 rule="para" parents="79 13967"/>
    </justification>
  </clause>

  <clause id="13971">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,x) = x * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(13683(a,1),13965(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13683 13965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13972">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,x) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,6499,a(flip),b,13971,a),flip(a)].">
      <j1 rule="hyper" parents="299 6499 13971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13974">
    <literal><![CDATA[
      L(T(x \ L(x,y,z),u),w,x) = T(x \ L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(13972(a,1),25(a,2,1))].">
      <j1 rule="para" parents="13972 25"/>
    </justification>
  </clause>

  <clause id="13977">
    <literal><![CDATA[
      K(x,y / x) * (((T(y,x) / x) \ y) \ z) = (y / (T(y,x) / x)) \ z
    ]]></literal>
    <justification jstring="[para(8122(a,1),13722(a,1,1))].">
      <j1 rule="para" parents="8122 13722"/>
    </justification>
  </clause>

  <clause id="13978">
    <literal><![CDATA[
      K(x,x \ y) * (((T(y,x) / x) \ y) \ z) = (y / (T(y,x) / x)) \ z
    ]]></literal>
    <justification jstring="[para(5205(a,1),13977(a,1,1))].">
      <j1 rule="para" parents="5205 13977"/>
    </justification>
  </clause>

  <clause id="13979">
    <literal><![CDATA[
      K(x,x \ y) * (T(x,y) \ z) = (y / (T(y,x) / x)) \ z
    ]]></literal>
    <justification jstring="[para(4415(a,1),13978(a,1,2,1))].">
      <j1 rule="para" parents="4415 13978"/>
    </justification>
  </clause>

  <clause id="13980">
    <literal><![CDATA[
      T(x,y) \ K(x,x \ y) = (y / (T(y,x) / x)) \ 1
    ]]></literal>
    <justification jstring="[hyper(10110,a,13979,a)].">
      <j1 rule="hyper" parents="10110 13979"/>
    </justification>
  </clause>

  <clause id="13981">
    <literal><![CDATA[
      T(x,(y / z) * (z * (z \ y))) = T(x,y * (z \ y))
    ]]></literal>
    <justification jstring="[para(220(a,1),13760(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="220 13760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13982">
    <literal><![CDATA[
      T(x,(y / z) * y) = T(x,y * (z \ y))
    ]]></literal>
    <justification jstring="[para(10(a,1),13981(a,1,2,2))].">
      <j1 rule="para" parents="10 13981"/>
    </justification>
  </clause>

  <clause id="13984">
    <literal><![CDATA[
      T(x,(T(y,z \ y) / T(z,y)) * (y * (T(y,z) / z))) = T(x,(y * (T(y,z) / z)) * (y \ (y * (T(y,z) / z))))
    ]]></literal>
    <justification jstring="[para(8608(a,1),13982(a,1,2,1))].">
      <j1 rule="para" parents="8608 13982"/>
    </justification>
  </clause>

  <clause id="13985">
    <literal><![CDATA[
      T(x,(y \ z) * (K(y \ z,u) * w)) = T(x,T(T(z / y,z),u) * w)
    ]]></literal>
    <justification jstring="[para(7440(a,1),13878(a,1,2,2,1))].">
      <j1 rule="para" parents="7440 13878"/>
    </justification>
  </clause>

  <clause id="13986">
    <literal><![CDATA[
      T(x,T(T(y / z,y),u) * w) = T(x,T(z \ y,u) * w)
    ]]></literal>
    <justification jstring="[para(5055(a,1),13985(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5055 13985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13987">
    <literal><![CDATA[
      a(a(x,x,x) * (y * K(x \ 1,y)),z,u) = a((x \ 1) \ (y * (1 / x)),z,u)
    ]]></literal>
    <justification jstring="[para(6816(a,1),13718(a,1,1))].">
      <j1 rule="para" parents="6816 13718"/>
    </justification>
  </clause>

  <clause id="13989">
    <literal><![CDATA[
      T(x,y * (T(z,u) * (z \ (w * K(z,u))))) = T(x,y * (K(z,u) * (w * K(z,u))))
    ]]></literal>
    <justification jstring="[hyper(299,a,13765,a(flip),b,13872,a),flip(a)].">
      <j1 rule="hyper" parents="299 13765 13872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13990">
    <literal><![CDATA[
      K(x,T(T(T(y,y * z),T(u,y)) * w,v5)) = K(x,T(T(T(y,u),z) * w,v5))
    ]]></literal>
    <justification jstring="[para(8549(a,1),13943(a,1,2,1,1,1))].">
      <j1 rule="para" parents="8549 13943"/>
    </justification>
  </clause>

  <clause id="13991">
    <literal><![CDATA[
      K(x,T(T(T(y,z),y * u) * w,v5)) = K(x,T(T(T(y,z),u) * w,v5))
    ]]></literal>
    <justification jstring="[para(4397(a,1),13990(a,1,2,1,1))].">
      <j1 rule="para" parents="4397 13990"/>
    </justification>
  </clause>

  <clause id="13993">
    <literal><![CDATA[
      K(x,T(T(T(y \ 1,z),y) * u,w)) = K(x,T(T(y \ 1,z) * u,w))
    ]]></literal>
    <justification jstring="[para(3203(a,1),13991(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="3203 13991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13994">
    <literal><![CDATA[
      x / (y * a(z,u,z)) = a(z,u,z) \ (x / y)
    ]]></literal>
    <justification jstring="[hyper(37,a,10144,a,b,13945,a)].">
      <j1 rule="hyper" parents="37 10144 13945"/>
    </justification>
  </clause>

  <clause id="13995">
    <literal><![CDATA[
      a(x,y,x) \ (z / x) = z / R(x,y,x)
    ]]></literal>
    <justification jstring="[para(9674(a,1),13994(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9674 13994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13997">
    <literal><![CDATA[
      K(x,(y / R(z,u,z)) * w) = K(x,(y / z) * w)
    ]]></literal>
    <justification jstring="[para(13995(a,1),13719(a,1,2,1))].">
      <j1 rule="para" parents="13995 13719"/>
    </justification>
  </clause>

  <clause id="13998">
    <literal><![CDATA[
      T(x,y * (T(z,u) * ((z \ w) * K(z,u)))) = T(x,y * (K(z,u) * (w * K(z,u))))
    ]]></literal>
    <justification jstring="[para(7029(a,1),13989(a,1,2,2,2))].">
      <j1 rule="para" parents="7029 13989"/>
    </justification>
  </clause>

  <clause id="13999">
    <literal><![CDATA[
      L((a(x,y,x) \ (z * (a(x,y,x) * (u * w)))) \ ((z * u) * w),a(x,y,x) \ (z * (a(x,y,x) * (u * w))),a(x,y,x)) = a(z,a(x,y,x) * u,w)
    ]]></literal>
    <justification jstring="[hyper(960,a,13903,a)].">
      <j1 rule="hyper" parents="960 13903"/>
    </justification>
  </clause>

  <clause id="14000">
    <literal><![CDATA[
      K(x,y * (z * T((u * w) * (1 / u),u * w))) = K(x,y * (z * ((w * u) * (u \ 1))))
    ]]></literal>
    <justification jstring="[hyper(299,a,5906,a(flip),b,13917,a),flip(a)].">
      <j1 rule="hyper" parents="299 5906 13917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14001">
    <literal><![CDATA[
      K(x,y * (z * T((u * w) * (1 / u),u * w))) = K(x,y * (z * R(w,u,u)))
    ]]></literal>
    <justification jstring="[para(1246(a,1),14000(a,2,2,2,2))].">
      <j1 rule="para" parents="1246 14000"/>
    </justification>
  </clause>

  <clause id="14002">
    <literal><![CDATA[
      L(x,y,z) * T(R(u,x,u),R(u,x,u) * x) = T(T(u,u * x) * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(13653(a,1),13654(a,1,2,2,1))].">
      <j1 rule="para" parents="13653 13654"/>
    </justification>
  </clause>

  <clause id="14004">
    <literal><![CDATA[
      L(x,y,z) * T(R(u,x,u),x * R(u,x,u)) = T(T(u,u * x) * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(4366(a,2),14002(a,1,2))].">
      <j1 rule="para" parents="4366 14002"/>
    </justification>
  </clause>

  <clause id="14006">
    <literal><![CDATA[
      L(x,y,z) * T(R(u,x,u),T(u * x,u)) = T(T(u,u * x) * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(4341(a,1),14004(a,1,2,2))].">
      <j1 rule="para" parents="4341 14004"/>
    </justification>
  </clause>

  <clause id="14007">
    <literal><![CDATA[
      L(x,y,z) * T(R(u,x,u),x * u) = T(T(u,u * x) * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(13197(a,1),14006(a,1,2))].">
      <j1 rule="para" parents="13197 14006"/>
    </justification>
  </clause>

  <clause id="14008">
    <literal><![CDATA[
      T(T(x,x * y) * L(y,z,u),x) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(875(a,1),14007(a,1,2)),flip(a)].">
      <j1 rule="para" parents="875 14007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14009">
    <literal><![CDATA[
      T(x * L(y,z,u),x * y) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,10369,a(flip),b,14008,a)].">
      <j1 rule="hyper" parents="65 10369 14008"/>
    </justification>
  </clause>

  <clause id="14010">
    <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(119,a,14009,a(flip),b,5083,a(flip))].">
      <j1 rule="hyper" parents="119 14009 5083"/>
    </justification>
  </clause>

  <clause id="14012">
    <literal><![CDATA[
      K(x * L(y,z,u),x * y) = K(x,y) * K(L(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(9665,a,14010,a),flip(a)].">
      <j1 rule="hyper" parents="9665 14010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14013">
    <literal><![CDATA[
      K(x * L(y,z,u),x * y) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(11953,a,14012,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="11953 14012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14014">
    <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),14013(a,1,1))].">
      <j1 rule="para" parents="12 14013"/>
    </justification>
  </clause>

  <clause id="14015">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ x)) = a(u,z,K(x / L(y,z,u),y))
    ]]></literal>
    <justification jstring="[hyper(65,a,9339,a(flip),b,14014,a)].">
      <j1 rule="hyper" parents="65 9339 14014"/>
    </justification>
  </clause>

  <clause id="14016">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ x)) = a(u,z,K(y \ x,y))
    ]]></literal>
    <justification jstring="[para(11451(a,1),14015(a,2,3))].">
      <j1 rule="para" parents="11451 14015"/>
    </justification>
  </clause>

  <clause id="14017">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ x)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,12080,a(flip),b,14016,a),flip(a)].">
      <j1 rule="hyper" parents="299 12080 14016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14019">
    <literal><![CDATA[
      K(x,x * (L(y,z,u) \ y)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,11394,a(flip),b,14017,a)].">
      <j1 rule="hyper" parents="65 11394 14017"/>
    </justification>
  </clause>

  <clause id="14020">
    <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(65,a,5954,a,b,14019,a)].">
      <j1 rule="hyper" parents="65 5954 14019"/>
    </justification>
  </clause>

  <clause id="14021">
    <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),14019(a,1,2))].">
      <j1 rule="para" parents="12 14019"/>
    </justification>
  </clause>

  <clause id="14022">
    <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(7176,a,14021,a)].">
      <j1 rule="hyper" parents="7176 14021"/>
    </justification>
  </clause>

  <clause id="14023">
    <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(65,a,11405,a(flip),b,14022,a)].">
      <j1 rule="hyper" parents="65 11405 14022"/>
    </justification>
  </clause>

  <clause id="14024">
    <literal><![CDATA[
      K(x * (y \ L(y,z,u)),x) = a(u,z,K((y / x) \ y,y))
    ]]></literal>
    <justification jstring="[para(12198(a,1),14023(a,2,3))].">
      <j1 rule="para" parents="12198 14023"/>
    </justification>
  </clause>

  <clause id="14025">
    <literal><![CDATA[
      K(x * (y \ L(y,z,u)),x) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(79(a,1),14024(a,2,3,1))].">
      <j1 rule="para" parents="79 14024"/>
    </justification>
  </clause>

  <clause id="14028">
    <literal><![CDATA[
      K(x,x * (y \ L(y,z,u))) = w / (a(u,z,K(x,y)) * w)
    ]]></literal>
    <justification jstring="[para(14025(a,1),5430(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14025 5430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14029">
    <literal><![CDATA[
      K(x,x * (y \ L(y,z,u))) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(299,a,10571,a(flip),b,14028,a),flip(a)].">
      <j1 rule="hyper" parents="299 10571 14028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14030">
    <literal><![CDATA[
      T(x,x * (y \ L(y,z,u))) = x * a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[para(14029(a,1),5083(a,2,2))].">
      <j1 rule="para" parents="14029 5083"/>
    </justification>
  </clause>

  <clause id="14031">
    <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(14029(a,1),12091(a,1,3)),flip(a)].">
      <j1 rule="para" parents="14029 12091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14032">
    <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(65,a,12096,a,b,14031,a)].">
      <j1 rule="hyper" parents="65 12096 14031"/>
    </justification>
  </clause>

  <clause id="14033">
    <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(14031(a,1),12466(a,1,1))].">
      <j1 rule="para" parents="14031 12466"/>
    </justification>
  </clause>

  <clause id="14034">
    <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(14032(a,1),10560(a,1,2))].">
      <j1 rule="para" parents="14032 10560"/>
    </justification>
  </clause>

  <clause id="14035">
    <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(13657(a,1),14020(a,1,2))].">
      <j1 rule="para" parents="13657 14020"/>
    </justification>
  </clause>

  <clause id="14036">
    <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(6086,a,14035,a)].">
      <j1 rule="hyper" parents="6086 14035"/>
    </justification>
  </clause>

  <clause id="14037">
    <literal><![CDATA[
      x \ L(T(x,L(y,z,u) \ y),a(u,z,y),x) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(7923,a,14036,a)].">
      <j1 rule="hyper" parents="7923 14036"/>
    </justification>
  </clause>

  <clause id="14038">
    <literal><![CDATA[
      K(L(x,y,z) \ x,u) = K(a(z,y,x),u) * 1
    ]]></literal>
    <justification jstring="[para(10583(a,1),14034(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10583 14034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14039">
    <literal><![CDATA[
      K(L(x,y,z) \ x,u) = K(a(z,y,x),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,8,a(flip),b,14038,a),flip(a)].">
      <j1 rule="hyper" parents="299 8 14038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14041">
    <literal><![CDATA[
      K(x,L(y,z,u) \ y) = w / (K(a(u,z,y),x) * w)
    ]]></literal>
    <justification jstring="[para(14039(a,1),5430(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14039 5430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14042">
    <literal><![CDATA[
      K(x,L(y,z,u) \ y) = K(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,5430,a(flip),b,14041,a),flip(a)].">
      <j1 rule="hyper" parents="299 5430 14041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14043">
    <literal><![CDATA[
      T(x,L(y,z,u) \ y) = x * K(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[para(14042(a,1),5083(a,2,2))].">
      <j1 rule="para" parents="14042 5083"/>
    </justification>
  </clause>

  <clause id="14044">
    <literal><![CDATA[
      T(x,L(y,z,u) \ y) = T(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,5083,a,b,14043,a),flip(a)].">
      <j1 rule="hyper" parents="299 5083 14043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14045">
    <literal><![CDATA[
      x \ L(T(x,a(y,z,u)),a(y,z,u),x) = a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[para(14044(a,1),14037(a,1,2,1))].">
      <j1 rule="para" parents="14044 14037"/>
    </justification>
  </clause>

  <clause id="14046">
    <literal><![CDATA[
      K(x,x * a(y,z,u)) = a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(5303,a,14045,a)].">
      <j1 rule="hyper" parents="5303 14045"/>
    </justification>
  </clause>

  <clause id="14047">
    <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(13645(a,1),13662(a,1,2))].">
      <j1 rule="para" parents="13645 13662"/>
    </justification>
  </clause>

  <clause id="14048">
    <literal><![CDATA[
      1 * K(x,L(y \ L(y,z,u),y,w)) = K(x,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(10584(a,1),14033(a,1,1))].">
      <j1 rule="para" parents="10584 14033"/>
    </justification>
  </clause>

  <clause id="14049">
    <literal><![CDATA[
      K(x,L(y \ L(y,z,u),y,w)) = K(x,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(122,a,14048,a)].">
      <j1 rule="hyper" parents="122 14048"/>
    </justification>
  </clause>

  <clause id="14051">
    <literal><![CDATA[
      K(x,a(y,z,u) \ 1) = K(x,u \ L(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,9346,a(flip),b,14049,a)].">
      <j1 rule="hyper" parents="65 9346 14049"/>
    </justification>
  </clause>

  <clause id="14053">
    <literal><![CDATA[
      x * K(x,y \ L(y,z,u)) = T(x,a(u,z,y) \ 1)
    ]]></literal>
    <justification jstring="[para(14051(a,1),5083(a,2,2)),flip(a)].">
      <j1 rule="para" parents="14051 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14056">
    <literal><![CDATA[
      T(x,a(y,z,u) \ 1) = T(x,u \ L(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(5087,a,14053,a),flip(a)].">
      <j1 rule="hyper" parents="5087 14053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14057">
    <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(14056(a,2),784(a,1,1))].">
      <j1 rule="para" parents="14056 784"/>
    </justification>
  </clause>

  <clause id="14059">
    <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(299,a,14030,a(flip),b,14057,a),flip(a)].">
      <j1 rule="hyper" parents="299 14030 14057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14060">
    <literal><![CDATA[
      R(R(x,y,z),y * z,a(u,w,u)) = R(x,y,z * a(u,w,u))
    ]]></literal>
    <justification jstring="[hyper(549,a,14047,a),flip(a)].">
      <j1 rule="hyper" parents="549 14047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14061">
    <literal><![CDATA[
      R(x,y,z * a(u,w,u)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(13664,a,14060,a),flip(a)].">
      <j1 rule="hyper" parents="13664 14060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14063">
    <literal><![CDATA[
      R(x,y,T(z,u) / u) = R(x,y,u \ z)
    ]]></literal>
    <justification jstring="[para(9693(a,1),14061(a,1,3))].">
      <j1 rule="para" parents="9693 14061"/>
    </justification>
  </clause>

  <clause id="14064">
    <literal><![CDATA[
      R(x,y,z / T(u,z)) = R(x,y,u \ z)
    ]]></literal>
    <justification jstring="[para(4382(a,1),14063(a,1,3))].">
      <j1 rule="para" parents="4382 14063"/>
    </justification>
  </clause>

  <clause id="14065">
    <literal><![CDATA[
      K(x,T(y,z) \ u) * a(w,v5,K(T(y,z) \ u,x)) = K(x,L(((y \ z) \ z) \ u,v5,w))
    ]]></literal>
    <justification jstring="[para(13750(a,1),13913(a,1,1))].">
      <j1 rule="para" parents="13750 13913"/>
    </justification>
  </clause>

  <clause id="14066">
    <literal><![CDATA[
      K(x,L(((y \ z) \ z) \ u,w,v5)) = K(x,L(T(y,z) \ u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(11950,a,14065,a),flip(a)].">
      <j1 rule="hyper" parents="11950 14065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14067">
    <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(14065(a,1),11950(a,1))].">
      <j1 rule="para" parents="14065 11950"/>
    </justification>
  </clause>

  <clause id="14068">
    <literal><![CDATA[
      K(x,L(T((y * z) * (1 / y),y * z) \ u,w,v5)) = K(x,L(((z * y) * (1 / y)) \ u,w,v5))
    ]]></literal>
    <justification jstring="[para(7138(a,1),14066(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="7138 14066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14069">
    <literal><![CDATA[
      K(x,L(T((y * z) * (1 / y),y * z) \ u,w,v5)) = K(x,L(((z * y) * (y \ 1)) \ u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(299,a,12043,a(flip),b,14068,a),flip(a)].">
      <j1 rule="hyper" parents="299 12043 14068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14070">
    <literal><![CDATA[
      K(x,L(T((y * z) * (1 / y),y * z) \ u,w,v5)) = K(x,L(R(z,y,y) \ u,w,v5))
    ]]></literal>
    <justification jstring="[para(1246(a,1),14069(a,2,2,1,1))].">
      <j1 rule="para" parents="1246 14069"/>
    </justification>
  </clause>

  <clause id="14071">
    <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),13670(a,1,2,2))].">
      <j1 rule="para" parents="18 13670"/>
    </justification>
  </clause>

  <clause id="14072">
    <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(3807(a,1),14071(a,1,2))].">
      <j1 rule="para" parents="3807 14071"/>
    </justification>
  </clause>

  <clause id="14073">
    <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(6416,a,14072,a)].">
      <j1 rule="hyper" parents="6416 14072"/>
    </justification>
  </clause>

  <clause id="14074">
    <literal><![CDATA[
      a(x,a(y,z,u) \ 1,x) = a(x,u \ L(u,z,y),x)
    ]]></literal>
    <justification jstring="[para(2613(a,1),14073(a,2,2)),flip(a)].">
      <j1 rule="para" parents="2613 14073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14075">
    <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(14074(a,1),10667(a,1,1,2))].">
      <j1 rule="para" parents="14074 10667"/>
    </justification>
  </clause>

  <clause id="14076">
    <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(13341(a,1),13904(a,2,1))].">
      <j1 rule="para" parents="13341 13904"/>
    </justification>
  </clause>

  <clause id="14077">
    <literal><![CDATA[
      L(x,a(y,z,y) * u,w) = (w * u) \ (w * (u * x))
    ]]></literal>
    <justification jstring="[para(13668(a,1),14076(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13668 14076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14078">
    <literal><![CDATA[
      L(x,a(y,z,y) * u,w) = L(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(299,a,18,a,b,14077,a),flip(a)].">
      <j1 rule="hyper" parents="299 18 14077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14080">
    <literal><![CDATA[
      L(x,T(y * z,y),u) = L(x,z * y,u)
    ]]></literal>
    <justification jstring="[para(9690(a,1),14078(a,1,2))].">
      <j1 rule="para" parents="9690 14078"/>
    </justification>
  </clause>

  <clause id="14081">
    <literal><![CDATA[
      L(x,y * a(z,u,z),w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[para(10116(a,1),14078(a,1,2))].">
      <j1 rule="para" parents="10116 14078"/>
    </justification>
  </clause>

  <clause id="14082">
    <literal><![CDATA[
      L(x,R(y,z,y),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(10137(a,1),14078(a,1,2))].">
      <j1 rule="para" parents="10137 14078"/>
    </justification>
  </clause>

  <clause id="14083">
    <literal><![CDATA[
      L(x,R(y,z,y),u) = L(x,R(y,w,y),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,14082,a,b,14082,a)].">
      <j1 rule="hyper" parents="299 14082 14082"/>
    </justification>
  </clause>

  <clause id="14084">
    <literal><![CDATA[
      L(x,R(y,z,y),R(u,w,u)) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,13441,a(flip),b,14082,a),flip(a)].">
      <j1 rule="hyper" parents="299 13441 14082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14085">
    <literal><![CDATA[
      L(x,((y \ z) * y) * (y \ z),u) = L(x,(y \ z) * z,u)
    ]]></literal>
    <justification jstring="[para(772(a,1),14081(a,1,2))].">
      <j1 rule="para" parents="772 14081"/>
    </justification>
  </clause>

  <clause id="14086">
    <literal><![CDATA[
      L(x,y * z,z) = L(x,z * y,z)
    ]]></literal>
    <justification jstring="[hyper(11643,a,14080,a),flip(a)].">
      <j1 rule="hyper" parents="11643 14080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14087">
    <literal><![CDATA[
      1 / L(R(x,y,x),x,x) = R(x,y,x) \ 1
    ]]></literal>
    <justification jstring="[para(14084(a,1),2808(a,1,2))].">
      <j1 rule="para" parents="14084 2808"/>
    </justification>
  </clause>

  <clause id="14088">
    <literal><![CDATA[
      L(x,y * T(z \ y,z),u) = L(x,(z \ y) * y,u)
    ]]></literal>
    <justification jstring="[para(888(a,1),14085(a,1,2))].">
      <j1 rule="para" parents="888 14085"/>
    </justification>
  </clause>

  <clause id="14089">
    <literal><![CDATA[
      K(x,(y * (z * a(u,w,u))) \ v5) = (y * (z * T(z \ (y \ v5),x))) \ v5
    ]]></literal>
    <justification jstring="[para(10(a,1),13871(a,1,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 13871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14090">
    <literal><![CDATA[
      K(x,(y * (z * a(u,w,u))) \ v5) = K(x,(y * z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(299,a,7287,a(flip),b,14089,a),flip(a)].">
      <j1 rule="hyper" parents="299 7287 14089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14092">
    <literal><![CDATA[
      K(x,(y * K(z * u,u)) \ w) = K(x,(y * K(z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(9705(a,1),14090(a,1,2,1,2))].">
      <j1 rule="para" parents="9705 14090"/>
    </justification>
  </clause>

  <clause id="14093">
    <literal><![CDATA[
      K(x,T(y,K(y * T(x,y),z))) * ((K(y * T(x,y),z) * y) * x) = x * (y * K(y * x,T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(299,a,94,a(flip),b,13168,a),flip(a)].">
      <j1 rule="hyper" parents="299 94 13168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14094">
    <literal><![CDATA[
      K(x,T(y,K(y * T(x,y),z))) * ((K(y * T(x,y),z) * y) * x) = x * (K(y * x,z) * y)
    ]]></literal>
    <justification jstring="[hyper(299,a,7601,a(flip),b,14093,a),flip(a)].">
      <j1 rule="hyper" parents="299 7601 14093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14095">
    <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),13296(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="18 13296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14096">
    <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(299,a,13035,a(flip),b,14095,a),flip(a)].">
      <j1 rule="hyper" parents="299 13035 14095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14097">
    <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(299,a,12580,a(flip),b,14096,a),flip(a)].">
      <j1 rule="hyper" parents="299 12580 14096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14098">
    <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(8206,a,14097,a)].">
      <j1 rule="hyper" parents="8206 14097"/>
    </justification>
  </clause>

  <clause id="14099">
    <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(14097(a,1),8206(a,1))].">
      <j1 rule="para" parents="14097 8206"/>
    </justification>
  </clause>

  <clause id="14100">
    <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(65,a,7979,a,b,14098,a)].">
      <j1 rule="hyper" parents="65 7979 14098"/>
    </justification>
  </clause>

  <clause id="14101">
    <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(65,a,13130,a,b,14100,a)].">
      <j1 rule="hyper" parents="65 13130 14100"/>
    </justification>
  </clause>

  <clause id="14102">
    <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(9513,a,14101,a)].">
      <j1 rule="hyper" parents="9513 14101"/>
    </justification>
  </clause>

  <clause id="14103">
    <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(65,a,13609,a(flip),b,14102,a)].">
      <j1 rule="hyper" parents="65 13609 14102"/>
    </justification>
  </clause>

  <clause id="14104">
    <literal><![CDATA[
      K(x,K(y * z,a(y,z,u))) = a(K(y,K(x,z * u)),z,u)
    ]]></literal>
    <justification jstring="[para(10782(a,1),14103(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10782 14103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14105">
    <literal><![CDATA[
      K(x,K(y * z,a(y,z,u))) = 1
    ]]></literal>
    <justification jstring="[hyper(299,a,12794,a(flip),b,14104,a),flip(a)].">
      <j1 rule="hyper" parents="299 12794 14104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14106">
    <literal><![CDATA[
      K(x,K(a(y,z,u),y * (z * u))) = 1
    ]]></literal>
    <justification jstring="[hyper(14099,a,14105,a)].">
      <j1 rule="hyper" parents="14099 14105"/>
    </justification>
  </clause>

  <clause id="14109">
    <literal><![CDATA[
      (1 / K(x,a(y,z,u))) * ((y * (z * u)) / (K(x,a(y,z,u)) \ 1)) = 1 * (y * (z * u))
    ]]></literal>
    <justification jstring="[para(14106(a,1),8082(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14106 8082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14110">
    <literal><![CDATA[
      (1 / K(x,a(y,z,u))) * ((y * (z * u)) / (K(x,a(y,z,u)) \ 1)) = y * (z * u)
    ]]></literal>
    <justification jstring="[hyper(299,a,7,a(flip),b,14109,a),flip(a)].">
      <j1 rule="hyper" parents="299 7 14109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14111">
    <literal><![CDATA[
      K(x,a(y,z,u)) * (y * (z * u)) = (y * (z * u)) * K(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(14110(a,1),8255(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14110 8255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14112">
    <literal><![CDATA[
      K(x,T(a(y,z,u),y * (z * u))) = K(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(7606,a,14111,a)].">
      <j1 rule="hyper" parents="7606 14111"/>
    </justification>
  </clause>

  <clause id="14113">
    <literal><![CDATA[
      K(x,((y * z) * u) / (y * (z * u))) = K(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(8317,a,14112,a)].">
      <j1 rule="hyper" parents="8317 14112"/>
    </justification>
  </clause>

  <clause id="14114">
    <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(65,a,10937,a,b,14113,a)].">
      <j1 rule="hyper" parents="65 10937 14113"/>
    </justification>
  </clause>

  <clause id="14115">
    <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(13596(a,2),14114(a,1,1))].">
      <j1 rule="para" parents="13596 14114"/>
    </justification>
  </clause>

  <clause id="14116">
    <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(65,a,13581,a,b,14115,a)].">
      <j1 rule="hyper" parents="65 13581 14115"/>
    </justification>
  </clause>

  <clause id="14117">
    <literal><![CDATA[
      a(K(x,y),z * y,u) = K(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,13583,a(flip),b,14116,a)].">
      <j1 rule="hyper" parents="65 13583 14116"/>
    </justification>
  </clause>

  <clause id="14119">
    <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(5852(a,1),13292(a,1,1))].">
      <j1 rule="para" parents="5852 13292"/>
    </justification>
  </clause>

  <clause id="14120">
    <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),14119(a,1,2,2,1,2))].">
      <j1 rule="para" parents="10 14119"/>
    </justification>
  </clause>

  <clause id="14122">
    <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(9486(a,1),14120(a,1,2))].">
      <j1 rule="para" parents="9486 14120"/>
    </justification>
  </clause>

  <clause id="14123">
    <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(13501(a,1),14122(a,1,2))].">
      <j1 rule="para" parents="13501 14122"/>
    </justification>
  </clause>

  <clause id="14124">
    <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(7733(a,1),14123(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7733 14123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14125">
    <literal><![CDATA[
      L(x,(y / z) * ((y / z) \ ((z / y) \ 1)),x) = L(x,y / z,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,5355,a(flip),b,14124,a),flip(a)].">
      <j1 rule="hyper" parents="299 5355 14124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14126">
    <literal><![CDATA[
      L(x,y / z,x) = L(x,z \ y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,13659,a(flip),b,14125,a),flip(a)].">
      <j1 rule="hyper" parents="65 13659 14125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14128">
    <literal><![CDATA[
      L(x \ y,y / x,x \ y) = T(x \ y,(y / x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,8732,a(flip),b,14126,a),flip(a)].">
      <j1 rule="hyper" parents="299 8732 14126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14129">
    <literal><![CDATA[
      L(x,(y \ z) \ z,x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(76(a,1),14126(a,1,2)),flip(a)].">
      <j1 rule="para" parents="76 14126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14130">
    <literal><![CDATA[
      L(x,R(y * K(z,y),z,u),x) = L(x,(z * u) \ ((z * y) * u),x)
    ]]></literal>
    <justification jstring="[para(5242(a,2),14126(a,1,2))].">
      <j1 rule="para" parents="5242 14126"/>
    </justification>
  </clause>

  <clause id="14131">
    <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(10874(a,2),14126(a,1,2))].">
      <j1 rule="para" parents="10874 14126"/>
    </justification>
  </clause>

  <clause id="14133">
    <literal><![CDATA[
      L(x,y * K(z,y),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(5968(a,1),14129(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5968 14129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14134">
    <literal><![CDATA[
      L(x,R(y * K(z,y),u,w),x) = L(x,R(y,u,w),x)
    ]]></literal>
    <justification jstring="[para(5813(a,1),14133(a,1,2))].">
      <j1 rule="para" parents="5813 14133"/>
    </justification>
  </clause>

  <clause id="14135">
    <literal><![CDATA[
      L(x \ y,y / x,x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      T(x \ y,y \ x) = z
    ]]></literal>
    <justification jstring="[para(14128(a,2),8734(a,1))].">
      <j1 rule="para" parents="14128 8734"/>
    </justification>
  </clause>

  <clause id="14136">
    <literal><![CDATA[
      L(x,(y * z) \ ((y * u) * z),x) = L(x,R(u,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,14134,a(flip),b,14130,a),flip(a)].">
      <j1 rule="hyper" parents="65 14134 14130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14138">
    <literal><![CDATA[
      L(x,R(y,z,u),x) = L(x,z \ (z * y),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,13531,a(flip),b,14136,a),flip(a)].">
      <j1 rule="hyper" parents="65 13531 14136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14140">
    <literal><![CDATA[
      L(x,R(y,z,u),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),14138(a,2,2))].">
      <j1 rule="para" parents="9 14138"/>
    </justification>
  </clause>

  <clause id="14141">
    <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),14131(a,2,2))].">
      <j1 rule="para" parents="14 14131"/>
    </justification>
  </clause>

  <clause id="14142">
    <literal><![CDATA[
      L(x,y \ R(y,z,u),x) = L(x,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,14140,a(flip),b,14141,a)].">
      <j1 rule="hyper" parents="65 14140 14141"/>
    </justification>
  </clause>

  <clause id="14144">
    <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(14142(a,1),13573(a,1,2))].">
      <j1 rule="para" parents="14142 13573"/>
    </justification>
  </clause>

  <clause id="14145">
    <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(6086,a,14144,a)].">
      <j1 rule="hyper" parents="6086 14144"/>
    </justification>
  </clause>

  <clause id="14146">
    <literal><![CDATA[
      a(K(x,y),z * y,u) * (x \ L(x,a(y,z,u),x)) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[para(13596(a,2),14145(a,1,1))].">
      <j1 rule="para" parents="13596 14145"/>
    </justification>
  </clause>

  <clause id="14147">
    <literal><![CDATA[
      a(x,a(y,z,u),x) \ a(K(x,y),z * y,u) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(10455,a,14146,a)].">
      <j1 rule="hyper" parents="10455 14146"/>
    </justification>
  </clause>

  <clause id="14148">
    <literal><![CDATA[
      a(x,a(y,z,u),x) = 1
    ]]></literal>
    <justification jstring="[hyper(167,a,14147,a),flip(a)].">
      <j1 rule="hyper" parents="167 14147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14149">
    <literal><![CDATA[
      a(x,a(y,z,u),x) \ K(x,a(y,z,u)) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[para(14117(a,1),14147(a,1,2))].">
      <j1 rule="para" parents="14117 14147"/>
    </justification>
  </clause>

  <clause id="14150">
    <literal><![CDATA[
      L(x,a(y,z,u),x) = x
    ]]></literal>
    <justification jstring="[hyper(54,a,14148,a)].">
      <j1 rule="hyper" parents="54 14148"/>
    </justification>
  </clause>

  <clause id="14152">
    <literal><![CDATA[
      a(x,a(y,z,u),x) \ w != v5
    ]]></literal>
    <literal><![CDATA[
      v5 = w
    ]]></literal>
    <justification jstring="[para(14148(a,2),166(a,1,1))].">
      <j1 rule="para" parents="14148 166"/>
    </justification>
  </clause>

  <clause id="14153">
    <literal><![CDATA[
      T(x * a(y,z,u),x) = a(y,z,u) * x
    ]]></literal>
    <justification jstring="[para(14150(a,1),4351(a,1,1,1))].">
      <j1 rule="para" parents="14150 4351"/>
    </justification>
  </clause>

  <clause id="14155">
    <literal><![CDATA[
      L(x,a(y,z,u),x) != w
    ]]></literal>
    <literal><![CDATA[
      w = x
    ]]></literal>
    <justification jstring="[para(9715(a,1),14152(a,1))].">
      <j1 rule="para" parents="9715 14152"/>
    </justification>
  </clause>

  <clause id="14156">
    <literal><![CDATA[
      L(T(x,y),a(z,u,w),x) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = v5
    ]]></literal>
    <justification jstring="[para(7770(a,1),14155(a,1)),flip(b)].">
      <j1 rule="para" parents="7770 14155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14157">
    <literal><![CDATA[
      x \ L(T(x,a(y,z,u)),a(y,z,u),x) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(10451,a,14149,a)].">
      <j1 rule="hyper" parents="10451 14149"/>
    </justification>
  </clause>

  <clause id="14159">
    <literal><![CDATA[
      K(x,x * a(y,z,u)) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(5303,a,14157,a)].">
      <j1 rule="hyper" parents="5303 14157"/>
    </justification>
  </clause>

  <clause id="14160">
    <literal><![CDATA[
      K(x,x * a(y,z,u)) = K(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,14117,a(flip),b,14159,a),flip(a)].">
      <j1 rule="hyper" parents="299 14117 14159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14161">
    <literal><![CDATA[
      K(x,x * a(y,z,u)) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,13411,a(flip),b,14159,a),flip(a)].">
      <j1 rule="hyper" parents="299 13411 14159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14162">
    <literal><![CDATA[
      a(x,y,K(z,u)) = K(z,a(x,y,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,14046,a(flip),b,14160,a)].">
      <j1 rule="hyper" parents="65 14046 14160"/>
    </justification>
  </clause>

  <clause id="14163">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ w = K(u,a(x,y,z)) * w
    ]]></literal>
    <justification jstring="[para(14162(a,1),10570(a,2,1))].">
      <j1 rule="para" parents="14162 10570"/>
    </justification>
  </clause>

  <clause id="14164">
    <literal><![CDATA[
      a(K(x,y),z,u) = a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,14046,a(flip),b,14161,a),flip(a)].">
      <j1 rule="hyper" parents="65 14046 14161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14165">
    <literal><![CDATA[
      a(K(x,y),z,z) = 1
    ]]></literal>
    <justification jstring="[hyper(299,a,6815,a(flip),b,14164,a),flip(a)].">
      <j1 rule="hyper" parents="299 6815 14164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14166">
    <literal><![CDATA[
      a(x,x,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(65,a,4774,a(flip),b,14164,a),flip(a)].">
      <j1 rule="hyper" parents="65 4774 14164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14167">
    <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(14164(a,1),12901(a,1,1,2))].">
      <j1 rule="para" parents="14164 12901"/>
    </justification>
  </clause>

  <clause id="14168">
    <literal><![CDATA[
      L(x,x,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(54,a,14165,a)].">
      <j1 rule="hyper" parents="54 14165"/>
    </justification>
  </clause>

  <clause id="14169">
    <literal><![CDATA[
      K(x \ L(x,y,y),z) = 1
    ]]></literal>
    <justification jstring="[hyper(65,a,11962,a,b,14166,a)].">
      <j1 rule="hyper" parents="65 11962 14166"/>
    </justification>
  </clause>

  <clause id="14170">
    <literal><![CDATA[
      L(K(x,y),z,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(54,a,14166,a)].">
      <j1 rule="hyper" parents="54 14166"/>
    </justification>
  </clause>

  <clause id="14171">
    <literal><![CDATA[
      L(L(x,y,z),x,K(u,w)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(14168(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14168 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14172">
    <literal><![CDATA[
      (K(x,y) * z) * z != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (z * z) = u
    ]]></literal>
    <justification jstring="[para(14168(a,1),279(a,1,2))].">
      <j1 rule="para" parents="14168 279"/>
    </justification>
  </clause>

  <clause id="14173">
    <literal><![CDATA[
      (K(x,y) * z) * z != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (K(x,y) * (z * z)) = w
    ]]></literal>
    <justification jstring="[para(14168(a,1),636(a,1,2))].">
      <j1 rule="para" parents="14168 636"/>
    </justification>
  </clause>

  <clause id="14174">
    <literal><![CDATA[
      T(x \ L(x,y,y),z) = x \ L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,14169,a)].">
      <j1 rule="hyper" parents="58 14169"/>
    </justification>
  </clause>

  <clause id="14175">
    <literal><![CDATA[
      K(L(x,y,y),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(12009,a,14170,a)].">
      <j1 rule="hyper" parents="12009 14170"/>
    </justification>
  </clause>

  <clause id="14176">
    <literal><![CDATA[
      K(x,L(y,z,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(11995,a,14170,a)].">
      <j1 rule="hyper" parents="11995 14170"/>
    </justification>
  </clause>

  <clause id="14177">
    <literal><![CDATA[
      K(x,(y * z) \ (y * y)) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(9506,a,14170,a)].">
      <j1 rule="hyper" parents="9506 14170"/>
    </justification>
  </clause>

  <clause id="14178">
    <literal><![CDATA[
      L(K(x,y),z \ 1,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2641,a,14170,a)].">
      <j1 rule="hyper" parents="2641 14170"/>
    </justification>
  </clause>

  <clause id="14180">
    <literal><![CDATA[
      L(K(x,y),z,z \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2502,a,14170,a)].">
      <j1 rule="hyper" parents="2502 14170"/>
    </justification>
  </clause>

  <clause id="14181">
    <literal><![CDATA[
      (1 / x) * (x * K(y,z)) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(758,a,14170,a)].">
      <j1 rule="hyper" parents="758 14170"/>
    </justification>
  </clause>

  <clause id="14182">
    <literal><![CDATA[
      K((x * x) \ y,z) = K(x \ (x \ y),z)
    ]]></literal>
    <justification jstring="[hyper(65,a,11931,a(flip),b,14170,a)].">
      <j1 rule="hyper" parents="65 11931 14170"/>
    </justification>
  </clause>

  <clause id="14183">
    <literal><![CDATA[
      K(x,(y * y) \ z) = K(x,y \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,11904,a(flip),b,14170,a)].">
      <j1 rule="hyper" parents="65 11904 14170"/>
    </justification>
  </clause>

  <clause id="14185">
    <literal><![CDATA[
      (x \ 1) * K(y,z) = x \ K(y,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,14170,a(flip),b,1673,a),flip(a)].">
      <j1 rule="hyper" parents="119 14170 1673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14186">
    <literal><![CDATA[
      (1 / x) \ K(y,z) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,14170,a(flip),b,475,a)].">
      <j1 rule="hyper" parents="119 14170 475"/>
    </justification>
  </clause>

  <clause id="14187">
    <literal><![CDATA[
      L(x * K(y,z),x,x) = L(x,x,x) * K(y,z)
    ]]></literal>
    <justification jstring="[para(14170(a,1),948(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14170 948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14189">
    <literal><![CDATA[
      L(x,x,x) * K(y,z) = (x \ 1) \ K(y,z)
    ]]></literal>
    <justification jstring="[para(14170(a,1),2816(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14170 2816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14190">
    <literal><![CDATA[
      T(x,L(y,z,z)) = x * K(x,y)
    ]]></literal>
    <justification jstring="[para(14170(a,1),11907(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14170 11907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14191">
    <literal><![CDATA[
      K((1 / x) * y,z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(511(a,1),14175(a,1,1))].">
      <j1 rule="para" parents="511 14175"/>
    </justification>
  </clause>

  <clause id="14194">
    <literal><![CDATA[
      K((x \ 1) \ y,z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(1670(a,1),14175(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1670 14175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14196">
    <literal><![CDATA[
      K(L(x,y,y \ 1),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(2470(a,2),14175(a,1,1))].">
      <j1 rule="para" parents="2470 14175"/>
    </justification>
  </clause>

  <clause id="14197">
    <literal><![CDATA[
      T(L(x,y,y),z) * a(y,y,x) = K(x,z) * x
    ]]></literal>
    <justification jstring="[para(14175(a,1),5378(a,2,1))].">
      <j1 rule="para" parents="14175 5378"/>
    </justification>
  </clause>

  <clause id="14199">
    <literal><![CDATA[
      K(x,(1 / y) * z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(511(a,1),14176(a,1,2))].">
      <j1 rule="para" parents="511 14176"/>
    </justification>
  </clause>

  <clause id="14200">
    <literal><![CDATA[
      K(x,(y \ 1) \ z) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(1670(a,1),14176(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1670 14176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14201">
    <literal><![CDATA[
      K(x,(y * y) * z) = K(x,y * (y * z))
    ]]></literal>
    <justification jstring="[para(1675(a,1),14176(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1675 14176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14203">
    <literal><![CDATA[
      K((x * y) \ 1,z) = K(y \ (x \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(10211,a,14178,a)].">
      <j1 rule="hyper" parents="10211 14178"/>
    </justification>
  </clause>

  <clause id="14205">
    <literal><![CDATA[
      K(x,y * (z \ 1)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(65,a,13290,a(flip),b,14180,a)].">
      <j1 rule="hyper" parents="65 13290 14180"/>
    </justification>
  </clause>

  <clause id="14206">
    <literal><![CDATA[
      T(x,L(y,z,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,5083,a,b,14190,a),flip(a)].">
      <j1 rule="hyper" parents="299 5083 14190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14207">
    <literal><![CDATA[
      T(x,L(y,z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(14190(a,2),5087(a,1))].">
      <j1 rule="para" parents="14190 5087"/>
    </justification>
  </clause>

  <clause id="14208">
    <literal><![CDATA[
      T(T(x,x \ 1) * y,L(x,z,z)) = x * ((x \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(299,a,2809,a(flip),b,14206,a),flip(a)].">
      <j1 rule="hyper" parents="299 2809 14206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14209">
    <literal><![CDATA[
      T(x,((y \ 1) * z) \ 1) = T(x,(y \ z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,12023,a(flip),b,14206,a)].">
      <j1 rule="hyper" parents="65 12023 14206"/>
    </justification>
  </clause>

  <clause id="14210">
    <literal><![CDATA[
      L(x,y,y) * T(z,x) = z * L(x,y,y)
    ]]></literal>
    <justification jstring="[para(14206(a,1),107(a,1,2))].">
      <j1 rule="para" parents="14206 107"/>
    </justification>
  </clause>

  <clause id="14211">
    <literal><![CDATA[
      T(x,(1 / y) * z) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(511(a,1),14206(a,1,2))].">
      <j1 rule="para" parents="511 14206"/>
    </justification>
  </clause>

  <clause id="14212">
    <literal><![CDATA[
      T(x,(y * y) \ z) = T(x,y \ (y \ z))
    ]]></literal>
    <justification jstring="[para(281(a,1),14206(a,1,2))].">
      <j1 rule="para" parents="281 14206"/>
    </justification>
  </clause>

  <clause id="14213">
    <literal><![CDATA[
      T(x,T((1 / y) * z,u)) = T(x,T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(515(a,1),14206(a,1,2))].">
      <j1 rule="para" parents="515 14206"/>
    </justification>
  </clause>

  <clause id="14215">
    <literal><![CDATA[
      T(x,(y \ 1) \ z) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(1670(a,1),14206(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1670 14206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14216">
    <literal><![CDATA[
      T(x,(y * y) * z) = T(x,y * (y * z))
    ]]></literal>
    <justification jstring="[para(1675(a,1),14206(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1675 14206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14218">
    <literal><![CDATA[
      (K(x,y) * z) \ 1 = z \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,14196,a(flip),b,13417,a),flip(a)].">
      <j1 rule="hyper" parents="119 14196 13417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14219">
    <literal><![CDATA[
      (x / y) \ T(x,z) = y * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,12422,a,b,14181,a)].">
      <j1 rule="hyper" parents="36 12422 14181"/>
    </justification>
  </clause>

  <clause id="14220">
    <literal><![CDATA[
      (x \ y) * K(y,z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,12419,a,b,14181,a),flip(a)].">
      <j1 rule="hyper" parents="36 12419 14181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14221">
    <literal><![CDATA[
      L(x \ (y * K(z,u)),x,1 / y) = ((1 / y) * x) \ K(z,u)
    ]]></literal>
    <justification jstring="[para(14181(a,1),96(a,2,2))].">
      <j1 rule="para" parents="14181 96"/>
    </justification>
  </clause>

  <clause id="14222">
    <literal><![CDATA[
      (1 / x) \ K(y,z) != x * u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(14181(a,1),124(a,1,2)),flip(b)].">
      <j1 rule="para" parents="14181 124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14223">
    <literal><![CDATA[
      (x \ K(y,z)) * K(z,y) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(7207,a,14185,a)].">
      <j1 rule="hyper" parents="7207 14185"/>
    </justification>
  </clause>

  <clause id="14225">
    <literal><![CDATA[
      (((x * x) \ y) \ 1) * K(z,u) = y \ ((x * x) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,666,a(flip),b,14185,a),flip(a)].">
      <j1 rule="hyper" parents="299 666 14185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14226">
    <literal><![CDATA[
      (x \ K(y,z)) / K(y,z) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(137,a,14185,a)].">
      <j1 rule="hyper" parents="137 14185"/>
    </justification>
  </clause>

  <clause id="14228">
    <literal><![CDATA[
      (x * x) \ K(y,z) = x \ (x \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,14185,a(flip),b,738,a),flip(a)].">
      <j1 rule="hyper" parents="119 14185 738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14232">
    <literal><![CDATA[
      L(x,y,z \ K(u,w)) = L(x,y,z * K(u,w))
    ]]></literal>
    <justification jstring="[para(14185(a,1),2489(a,1,3))].">
      <j1 rule="para" parents="14185 2489"/>
    </justification>
  </clause>

  <clause id="14233">
    <literal><![CDATA[
      L(x,y \ K(z,u),w) = L(x,y * K(z,u),w)
    ]]></literal>
    <justification jstring="[para(14185(a,1),2565(a,1,2))].">
      <j1 rule="para" parents="14185 2565"/>
    </justification>
  </clause>

  <clause id="14237">
    <literal><![CDATA[
      ((x \ 1) \ K(y,x)) * K(z,u) = (x \ K(x,y)) \ K(z,u)
    ]]></literal>
    <justification jstring="[para(6605(a,1),14185(a,1,1))].">
      <j1 rule="para" parents="6605 14185"/>
    </justification>
  </clause>

  <clause id="14240">
    <literal><![CDATA[
      (x \ K(y,z)) \ (x \ 1) = K(z,y)
    ]]></literal>
    <justification jstring="[para(14185(a,1),7200(a,1,1))].">
      <j1 rule="para" parents="14185 7200"/>
    </justification>
  </clause>

  <clause id="14241">
    <literal><![CDATA[
      (x \ K(y,z)) \ (x \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = u
    ]]></literal>
    <justification jstring="[para(14185(a,1),7209(a,1,1))].">
      <j1 rule="para" parents="14185 7209"/>
    </justification>
  </clause>

  <clause id="14242">
    <literal><![CDATA[
      T(x \ K(y,z),K(y,z)) = K(y,z) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(14185(a,1),8053(a,1,1))].">
      <j1 rule="para" parents="14185 8053"/>
    </justification>
  </clause>

  <clause id="14243">
    <literal><![CDATA[
      T(x \ K(y,z),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * (x \ 1) = u
    ]]></literal>
    <justification jstring="[para(14185(a,1),8074(a,1,1))].">
      <j1 rule="para" parents="14185 8074"/>
    </justification>
  </clause>

  <clause id="14244">
    <literal><![CDATA[
      (K(x,T(y,z \ 1)) * z) * (1 / z) = (z \ K(x,y)) * z
    ]]></literal>
    <justification jstring="[para(14185(a,1),8155(a,2,1))].">
      <j1 rule="para" parents="14185 8155"/>
    </justification>
  </clause>

  <clause id="14245">
    <literal><![CDATA[
      (T(x,y) / z) \ x = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(13431,a,14186,a)].">
      <j1 rule="hyper" parents="13431 14186"/>
    </justification>
  </clause>

  <clause id="14246">
    <literal><![CDATA[
      K(x,(y \ 1) * z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(12214,a,14186,a),flip(a)].">
      <j1 rule="hyper" parents="12214 14186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14247">
    <literal><![CDATA[
      (1 / (x / ((y * z) / y))) \ K(y,z) = x / z
    ]]></literal>
    <justification jstring="[hyper(299,a,9049,a(flip),b,14186,a),flip(a)].">
      <j1 rule="hyper" parents="299 9049 14186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14249">
    <literal><![CDATA[
      (x \ T(y,z)) * K(z,y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(65,a,13428,a(flip),b,14186,a),flip(a)].">
      <j1 rule="hyper" parents="65 13428 14186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14251">
    <literal><![CDATA[
      L(x,y * (z \ K(u,w)),v5) = L(x,y * (z * K(u,w)),v5)
    ]]></literal>
    <justification jstring="[para(14186(a,1),2887(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14186 2887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14252">
    <literal><![CDATA[
      K((x \ 1) * y,z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(9804,a,14191,a)].">
      <j1 rule="hyper" parents="9804 14191"/>
    </justification>
  </clause>

  <clause id="14256">
    <literal><![CDATA[
      K(x \ ((1 / x) \ y),z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),14191(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 14191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14258">
    <literal><![CDATA[
      ((x \ 1) * ((x \ 1) * y)) * K(x \ y,z) = (1 / x) * T((1 / x) * y,z)
    ]]></literal>
    <justification jstring="[para(14191(a,1),6879(a,1,2))].">
      <j1 rule="para" parents="14191 6879"/>
    </justification>
  </clause>

  <clause id="14259">
    <literal><![CDATA[
      K(x \ y,x * x) = K(x * y,x * x)
    ]]></literal>
    <justification jstring="[hyper(65,a,6545,a(flip),b,14194,a)].">
      <j1 rule="hyper" parents="65 6545 14194"/>
    </justification>
  </clause>

  <clause id="14260">
    <literal><![CDATA[
      K(T((x \ 1) \ 1,y) * z,u) = K((1 / T(x,y)) \ z,u)
    ]]></literal>
    <justification jstring="[para(3178(a,1),14194(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3178 14194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14261">
    <literal><![CDATA[
      K(x * ((x \ 1) \ T(y,(x \ 1) \ ((x \ 1) \ 1))),z) = K(T(((x \ 1) \ y) / (x \ 1),(x \ 1) \ 1),z)
    ]]></literal>
    <justification jstring="[para(4734(a,1),14194(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4734 14194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14264">
    <literal><![CDATA[
      x * (y * K(x * y,z)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(14194(a,1),7016(a,1,2,2))].">
      <j1 rule="para" parents="14194 7016"/>
    </justification>
  </clause>

  <clause id="14265">
    <literal><![CDATA[
      T(x * K(y * x,z),y) = y \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(14194(a,1),7132(a,1,1,2))].">
      <j1 rule="para" parents="14194 7132"/>
    </justification>
  </clause>

  <clause id="14266">
    <literal><![CDATA[
      K((x \ 1) * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(14194(a,1),7406(a,1))].">
      <j1 rule="para" parents="14194 7406"/>
    </justification>
  </clause>

  <clause id="14269">
    <literal><![CDATA[
      T(x * K(y * z,x),z \ (y \ 1)) = T(x,(z \ (y \ 1)) * (z \ (y \ 1)))
    ]]></literal>
    <justification jstring="[para(14194(a,1),7019(a,1,1,2))].">
      <j1 rule="para" parents="14194 7019"/>
    </justification>
  </clause>

  <clause id="14270">
    <literal><![CDATA[
      (x * K(y * (z \ x),z)) * y = (z \ (x * y)) * z
    ]]></literal>
    <justification jstring="[para(14194(a,1),9968(a,1,1,2))].">
      <j1 rule="para" parents="14194 9968"/>
    </justification>
  </clause>

  <clause id="14271">
    <literal><![CDATA[
      K(x,(1 / y) \ z) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(13791,a,14199,a),flip(a)].">
      <j1 rule="hyper" parents="13791 14199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14272">
    <literal><![CDATA[
      K(x,y \ ((1 / y) \ z)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),14199(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 14199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14273">
    <literal><![CDATA[
      K(x,(K(y,z) / z) * u) = K(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(5038(a,2),14199(a,1,2,1))].">
      <j1 rule="para" parents="5038 14199"/>
    </justification>
  </clause>

  <clause id="14274">
    <literal><![CDATA[
      K(x,(1 / y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(14199(a,1),13791(a,1))].">
      <j1 rule="para" parents="14199 13791"/>
    </justification>
  </clause>

  <clause id="14275">
    <literal><![CDATA[
      K(x,((y \ 1) \ z) * y) = K(x,y * (z * y))
    ]]></literal>
    <justification jstring="[hyper(13249,a,14200,a)].">
      <j1 rule="hyper" parents="13249 14200"/>
    </justification>
  </clause>

  <clause id="14277">
    <literal><![CDATA[
      (1 / x) \ K(y,z * u) = x * K(y,(z \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(119,a,14200,a(flip),b,14181,a)].">
      <j1 rule="hyper" parents="119 14200 14181"/>
    </justification>
  </clause>

  <clause id="14278">
    <literal><![CDATA[
      (x * y) * K(z,x * y) = x * (y * K(z,x * y))
    ]]></literal>
    <justification jstring="[para(14200(a,1),9555(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14200 9555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14279">
    <literal><![CDATA[
      L(K(x,y * (z \ u)),z \ u,z) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * (y \ 1)) \ u) = w
    ]]></literal>
    <justification jstring="[para(14200(a,1),10251(a,1,1))].">
      <j1 rule="para" parents="14200 10251"/>
    </justification>
  </clause>

  <clause id="14280">
    <literal><![CDATA[
      K(x,L((y \ 1) \ z,u,w)) = L(K(x,y * z),u,w)
    ]]></literal>
    <justification jstring="[para(14200(a,1),11889(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14200 11889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14281">
    <literal><![CDATA[
      K(x,(y \ 1) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(14200(a,1),13792(a,1))].">
      <j1 rule="para" parents="14200 13792"/>
    </justification>
  </clause>

  <clause id="14282">
    <literal><![CDATA[
      K(x,y / (z \ 1)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(13804,a,14205,a),flip(a)].">
      <j1 rule="hyper" parents="13804 14205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14283">
    <literal><![CDATA[
      K(x,y * (1 / z)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(13789,a,14205,a)].">
      <j1 rule="hyper" parents="13789 14205"/>
    </justification>
  </clause>

  <clause id="14284">
    <literal><![CDATA[
      L(K(x,y / z),u,u \ 1) = K(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(299,a,14180,a,b,14205,a)].">
      <j1 rule="hyper" parents="299 14180 14205"/>
    </justification>
  </clause>

  <clause id="14285">
    <literal><![CDATA[
      K(x,y / (1 / z)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(79(a,1),14205(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="79 14205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14286">
    <literal><![CDATA[
      K(x,y / ((z * z) \ u)) = K(x,y * (u \ (z * z)))
    ]]></literal>
    <justification jstring="[para(464(a,1),14205(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="464 14205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14287">
    <literal><![CDATA[
      K(x,y * (L(z,u,w) \ (z * z))) = K(x,y / L(1 / z,u,w))
    ]]></literal>
    <justification jstring="[para(6520(a,1),14205(a,1,2,2))].">
      <j1 rule="para" parents="6520 14205"/>
    </justification>
  </clause>

  <clause id="14289">
    <literal><![CDATA[
      K(x,L(y * (z \ 1),u,w)) = L(K(x,y / z),u,w)
    ]]></literal>
    <justification jstring="[para(14205(a,1),11889(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14205 11889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14290">
    <literal><![CDATA[
      K(x,y / (z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(14205(a,1),13804(a,1))].">
      <j1 rule="para" parents="14205 13804"/>
    </justification>
  </clause>

  <clause id="14291">
    <literal><![CDATA[
      T(x,(1 / y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(511(a,1),14207(a,1,2))].">
      <j1 rule="para" parents="511 14207"/>
    </justification>
  </clause>

  <clause id="14292">
    <literal><![CDATA[
      T(x,(y * y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (y \ z)) = u
    ]]></literal>
    <justification jstring="[para(281(a,1),14207(a,1,2))].">
      <j1 rule="para" parents="281 14207"/>
    </justification>
  </clause>

  <clause id="14293">
    <literal><![CDATA[
      T(x,T((y * y) \ z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y \ (y \ z),u)) = w
    ]]></literal>
    <justification jstring="[para(600(a,1),14207(a,1,2))].">
      <j1 rule="para" parents="600 14207"/>
    </justification>
  </clause>

  <clause id="14296">
    <literal><![CDATA[
      T(x,(1 / y) \ z) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,3871,a(flip),b,14211,a),flip(a)].">
      <j1 rule="hyper" parents="65 3871 14211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14297">
    <literal><![CDATA[
      T(x,(y \ 1) * z) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,3868,a(flip),b,14211,a)].">
      <j1 rule="hyper" parents="65 3868 14211"/>
    </justification>
  </clause>

  <clause id="14298">
    <literal><![CDATA[
      T(x,(1 / (y / (z * z))) * u) = T(x,(z * z) * (y \ u))
    ]]></literal>
    <justification jstring="[para(416(a,1),14211(a,2,2))].">
      <j1 rule="para" parents="416 14211"/>
    </justification>
  </clause>

  <clause id="14299">
    <literal><![CDATA[
      T(x,y * (((z \ 1) * u) * T(w,z \ u))) = T(x,y * (w * ((1 / z) * u)))
    ]]></literal>
    <justification jstring="[para(14211(a,1),3911(a,1,2,2,2))].">
      <j1 rule="para" parents="14211 3911"/>
    </justification>
  </clause>

  <clause id="14300">
    <literal><![CDATA[
      T(x,T(y,z \ u) / ((u \ z) \ 1)) = T(x,(u \ z) * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,13707,a,b,14215,a)].">
      <j1 rule="hyper" parents="65 13707 14215"/>
    </justification>
  </clause>

  <clause id="14301">
    <literal><![CDATA[
      T(x,(y * y) / z) = T(x,y * (y / z))
    ]]></literal>
    <justification jstring="[hyper(65,a,7355,a(flip),b,14215,a)].">
      <j1 rule="hyper" parents="65 7355 14215"/>
    </justification>
  </clause>

  <clause id="14302">
    <literal><![CDATA[
      K(x,T(y,z * u) * ((z \ 1) \ u)) = K(x,((z \ 1) \ u) * y)
    ]]></literal>
    <justification jstring="[para(14215(a,1),13262(a,1,2,1))].">
      <j1 rule="para" parents="14215 13262"/>
    </justification>
  </clause>

  <clause id="14304">
    <literal><![CDATA[
      T(x,(y \ 1) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(14215(a,1),13823(a,1))].">
      <j1 rule="para" parents="14215 13823"/>
    </justification>
  </clause>

  <clause id="14305">
    <literal><![CDATA[
      (K(x,y) * K(z,u)) \ 1 = K(u,z) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,5426,a(flip),b,14218,a),flip(a)].">
      <j1 rule="hyper" parents="299 5426 14218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14306">
    <literal><![CDATA[
      1 / (x \ K(y,z)) = K(z,y) * x
    ]]></literal>
    <justification jstring="[hyper(192,a,14218,a)].">
      <j1 rule="hyper" parents="192 14218"/>
    </justification>
  </clause>

  <clause id="14307">
    <literal><![CDATA[
      a(x \ K(y,z),u,w) = a(K(z,y) * x,u,w)
    ]]></literal>
    <justification jstring="[para(14218(a,1),2138(a,1,1))].">
      <j1 rule="para" parents="14218 2138"/>
    </justification>
  </clause>

  <clause id="14309">
    <literal><![CDATA[
      (K(x,y) * z) \ K(x,y) = z \ 1
    ]]></literal>
    <justification jstring="[para(5432(a,1),14218(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5432 14218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14312">
    <literal><![CDATA[
      (K(x,y) * z) \ K(u,w) = (z \ K(y,x)) * K(u,w)
    ]]></literal>
    <justification jstring="[para(14218(a,1),14185(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14218 14185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14313">
    <literal><![CDATA[
      K(x,y / (K(z,u) * w)) = K(x,y * (w \ K(u,z)))
    ]]></literal>
    <justification jstring="[para(14218(a,1),14205(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14218 14205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14316">
    <literal><![CDATA[
      T(x,y) / (z * K(x,y)) = x / z
    ]]></literal>
    <justification jstring="[hyper(192,a,14219,a)].">
      <j1 rule="hyper" parents="192 14219"/>
    </justification>
  </clause>

  <clause id="14317">
    <literal><![CDATA[
      T(x,y) * K(x * y,z) = y \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(185(a,1),14219(a,1,1)),flip(a)].">
      <j1 rule="para" parents="185 14219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14319">
    <literal><![CDATA[
      (x \ T(y,z)) / T(y,z) = (x \ y) / y
    ]]></literal>
    <justification jstring="[hyper(120,a,14220,a(flip),b,6869,a)].">
      <j1 rule="hyper" parents="120 14220 6869"/>
    </justification>
  </clause>

  <clause id="14324">
    <literal><![CDATA[
      T(x \ T(y,z),K(z,y)) = K(y,z) * (x \ y)
    ]]></literal>
    <justification jstring="[para(14220(a,1),7199(a,1,1))].">
      <j1 rule="para" parents="14220 7199"/>
    </justification>
  </clause>

  <clause id="14326">
    <literal><![CDATA[
      (K(x,y) / z) \ 1 = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(657,a,14223,a),flip(a)].">
      <j1 rule="hyper" parents="657 14223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14330">
    <literal><![CDATA[
      x / (y * K(z,x)) = T(x,z) / y
    ]]></literal>
    <justification jstring="[hyper(192,a,14245,a)].">
      <j1 rule="hyper" parents="192 14245"/>
    </justification>
  </clause>

  <clause id="14331">
    <literal><![CDATA[
      ((1 / x) \ y) * K(z,y) = (K(y,z) / x) \ y
    ]]></literal>
    <justification jstring="[para(12426(a,1),14245(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12426 14245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14332">
    <literal><![CDATA[
      K((x * y) / x,z \ u) = K(y,T((z \ 1) * u,x))
    ]]></literal>
    <justification jstring="[hyper(8121,a,14246,a),flip(a)].">
      <j1 rule="hyper" parents="8121 14246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14333">
    <literal><![CDATA[
      (x * K(y \ z,u)) \ x = K(u,(y \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(299,a,7200,a,b,14246,a)].">
      <j1 rule="hyper" parents="299 7200 14246"/>
    </justification>
  </clause>

  <clause id="14336">
    <literal><![CDATA[
      K(x,y \ (T(z,z \ u) * w)) = K(x,(y \ 1) * (T(z,u) * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,13918,a(flip),b,14246,a),flip(a)].">
      <j1 rule="hyper" parents="65 13918 14246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14337">
    <literal><![CDATA[
      K(x,y \ (z * T(u / w,u))) = K(x,(y \ 1) * (z * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,13916,a(flip),b,14246,a),flip(a)].">
      <j1 rule="hyper" parents="65 13916 14246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14338">
    <literal><![CDATA[
      K(x,y \ (T(z / u,z) * w)) = K(x,(y \ 1) * ((u \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,13849,a(flip),b,14246,a),flip(a)].">
      <j1 rule="hyper" parents="65 13849 14246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14339">
    <literal><![CDATA[
      K(x,((y * y) * (z \ 1)) * u) = K(x,(z / (y * y)) \ u)
    ]]></literal>
    <justification jstring="[para(416(a,1),14246(a,1,2,1))].">
      <j1 rule="para" parents="416 14246"/>
    </justification>
  </clause>

  <clause id="14340">
    <literal><![CDATA[
      K(x,y * (((1 / y) * z) * u)) = K(x,y \ ((y * z) * u))
    ]]></literal>
    <justification jstring="[para(2910(a,1),14246(a,1,2))].">
      <j1 rule="para" parents="2910 14246"/>
    </justification>
  </clause>

  <clause id="14342">
    <literal><![CDATA[
      (x \ T(y * x,z)) \ T(y,x) = K(z,y * x)
    ]]></literal>
    <justification jstring="[hyper(119,a,22,a,b,14249,a)].">
      <j1 rule="hyper" parents="119 22 14249"/>
    </justification>
  </clause>

  <clause id="14344">
    <literal><![CDATA[
      (x \ y) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ T(y,z) = u
    ]]></literal>
    <justification jstring="[para(14249(a,1),7216(a,1,1)),flip(b)].">
      <j1 rule="para" parents="14249 7216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14347">
    <literal><![CDATA[
      K(x \ y,T(z,y)) = K(y * (x \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(13187,a,14252,a),flip(a)].">
      <j1 rule="hyper" parents="13187 14252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14350">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),14252(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 14252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14351">
    <literal><![CDATA[
      K(((x * x) * (y \ 1)) * z,u) = K((y / (x * x)) \ z,u)
    ]]></literal>
    <justification jstring="[para(416(a,1),14252(a,1,1,1))].">
      <j1 rule="para" parents="416 14252"/>
    </justification>
  </clause>

  <clause id="14353">
    <literal><![CDATA[
      (x * ((y \ 1) * z)) * K(y \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      x * T((y \ 1) * z,u) = w
    ]]></literal>
    <justification jstring="[para(14252(a,1),6862(a,1,2))].">
      <j1 rule="para" parents="14252 6862"/>
    </justification>
  </clause>

  <clause id="14355">
    <literal><![CDATA[
      K(x,y * ((y \ 1) \ z)) = K(x,y * (y * z))
    ]]></literal>
    <justification jstring="[para(1668(a,1),14271(a,1,2))].">
      <j1 rule="para" parents="1668 14271"/>
    </justification>
  </clause>

  <clause id="14356">
    <literal><![CDATA[
      K(x,y * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(y \ 1) \ z) = u
    ]]></literal>
    <justification jstring="[para(14271(a,1),13793(a,1))].">
      <j1 rule="para" parents="14271 13793"/>
    </justification>
  </clause>

  <clause id="14358">
    <literal><![CDATA[
      (x \ ((1 / x) \ y)) * K(z,x \ ((1 / x) \ y)) = x \ (((1 / x) \ y) * K(z,y))
    ]]></literal>
    <justification jstring="[para(14272(a,1),6966(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14272 6966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14359">
    <literal><![CDATA[
      K(x,L(y / (z \ 1),u,w)) = L(K(x,y * z),u,w)
    ]]></literal>
    <justification jstring="[para(14282(a,1),11889(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14282 11889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14360">
    <literal><![CDATA[
      K(x,((y \ z) \ z) / u) = K(x,T(y,z) * (1 / u))
    ]]></literal>
    <justification jstring="[hyper(13875,a,14283,a),flip(a)].">
      <j1 rule="hyper" parents="13875 14283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14361">
    <literal><![CDATA[
      K(x,y / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z \ 1)) = u
    ]]></literal>
    <justification jstring="[para(14283(a,1),13806(a,1))].">
      <j1 rule="para" parents="14283 13806"/>
    </justification>
  </clause>

  <clause id="14362">
    <literal><![CDATA[
      K(x,(y * z) * z) = K(x,y * (z * z))
    ]]></literal>
    <justification jstring="[para(672(a,1),14285(a,1,2)),flip(a)].">
      <j1 rule="para" parents="672 14285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14364">
    <literal><![CDATA[
      T(x * ((x \ 1) \ y),x * x) = y * ((1 / x) \ x)
    ]]></literal>
    <justification jstring="[hyper(3094,a,14296,a),flip(a)].">
      <j1 rule="hyper" parents="3094 14296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14365">
    <literal><![CDATA[
      T(((x \ 1) \ y) * (1 / x),x * x) = (x \ y) * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,11478,a(flip),b,14296,a),flip(a)].">
      <j1 rule="hyper" parents="65 11478 14296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14366">
    <literal><![CDATA[
      T(x / ((1 / y) \ z),y * y) = (y \ 1) * (y \ (x / (y \ z)))
    ]]></literal>
    <justification jstring="[hyper(65,a,5958,a(flip),b,14296,a),flip(a)].">
      <j1 rule="hyper" parents="65 5958 14296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14367">
    <literal><![CDATA[
      T(((1 / x) \ y) * z,x * x) = (x \ y) * (z * ((1 / x) \ x))
    ]]></literal>
    <justification jstring="[hyper(65,a,3096,a(flip),b,14296,a),flip(a)].">
      <j1 rule="hyper" parents="65 3096 14296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14368">
    <literal><![CDATA[
      ((1 / x) \ y) * T(z,x * y) = z * ((1 / x) \ y)
    ]]></literal>
    <justification jstring="[para(14296(a,1),107(a,1,2))].">
      <j1 rule="para" parents="14296 107"/>
    </justification>
  </clause>

  <clause id="14369">
    <literal><![CDATA[
      T(x,y * ((y \ 1) \ z)) = T(x,y * (y * z))
    ]]></literal>
    <justification jstring="[para(1668(a,1),14296(a,1,2))].">
      <j1 rule="para" parents="1668 14296"/>
    </justification>
  </clause>

  <clause id="14370">
    <literal><![CDATA[
      (x \ 1) * (x \ (y / (z * (1 / x)))) = T(y,x * x) / (z * x)
    ]]></literal>
    <justification jstring="[para(14296(a,1),2453(a,2,1))].">
      <j1 rule="para" parents="14296 2453"/>
    </justification>
  </clause>

  <clause id="14371">
    <literal><![CDATA[
      T(1 / x,x * y) \ (y / (1 / x)) = x \ ((x * x) * ((1 / x) \ y))
    ]]></literal>
    <justification jstring="[para(14296(a,1),4331(a,1,1))].">
      <j1 rule="para" parents="14296 4331"/>
    </justification>
  </clause>

  <clause id="14372">
    <literal><![CDATA[
      ((1 / x) \ y) \ (z * ((x \ 1) \ 1)) = (x \ y) \ T(z * (x \ 1),x * x)
    ]]></literal>
    <justification jstring="[para(14296(a,1),5959(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14296 5959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14373">
    <literal><![CDATA[
      K(x,T(y,z * u) * ((z \ 1) \ u)) = K(x,((1 / z) \ u) * y)
    ]]></literal>
    <justification jstring="[para(14296(a,1),13264(a,1,2,1))].">
      <j1 rule="para" parents="14296 13264"/>
    </justification>
  </clause>

  <clause id="14375">
    <literal><![CDATA[
      x * (((x \ 1) \ y) * (x \ (1 / x))) = T(y,x \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(65,a,1780,a,b,14297,a)].">
      <j1 rule="hyper" parents="65 1780 14297"/>
    </justification>
  </clause>

  <clause id="14376">
    <literal><![CDATA[
      T(x * K(y,x),x \ y) = R(x,x \ L(y,x,x),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,7832,a(flip),b,14297,a),flip(a)].">
      <j1 rule="hyper" parents="65 7832 14297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14377">
    <literal><![CDATA[
      T(x,y \ ((y \ 1) \ z)) = T(x,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),14297(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 14297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14378">
    <literal><![CDATA[
      ((x \ 1) * y) * T(z,x \ y) = z * ((x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(14297(a,1),107(a,1,2))].">
      <j1 rule="para" parents="14297 107"/>
    </justification>
  </clause>

  <clause id="14379">
    <literal><![CDATA[
      ((x \ 1) * y) * L(T(z,x \ y),u,w) = L(z,u,w) * ((x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(14297(a,1),233(a,1,2,1))].">
      <j1 rule="para" parents="14297 233"/>
    </justification>
  </clause>

  <clause id="14380">
    <literal><![CDATA[
      T(x,y \ ((z * z) * u)) = T(x,(y \ (z * z)) * u)
    ]]></literal>
    <justification jstring="[para(462(a,1),14297(a,1,2)),flip(a)].">
      <j1 rule="para" parents="462 14297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14382">
    <literal><![CDATA[
      T(x,(y \ 1) * z) != x * u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(14297(a,2),5154(a,1))].">
      <j1 rule="para" parents="14297 5154"/>
    </justification>
  </clause>

  <clause id="14383">
    <literal><![CDATA[
      T(x,(y \ 1) * z) != u
    ]]></literal>
    <literal><![CDATA[
      x * K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(14297(a,2),5176(a,1))].">
      <j1 rule="para" parents="14297 5176"/>
    </justification>
  </clause>

  <clause id="14384">
    <literal><![CDATA[
      T(x,((1 / L(y,z,u)) * y) * w) = T(x,(y \ L(y,z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(6655(a,1),14297(a,1,2,1))].">
      <j1 rule="para" parents="6655 14297"/>
    </justification>
  </clause>

  <clause id="14385">
    <literal><![CDATA[
      K(x,T(y,z \ u) / ((z \ 1) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,((z \ 1) * u) \ y) = w
    ]]></literal>
    <justification jstring="[para(14297(a,1),13764(a,1,2,1))].">
      <j1 rule="para" parents="14297 13764"/>
    </justification>
  </clause>

  <clause id="14386">
    <literal><![CDATA[
      T(x,(K(y,z) * u) \ w) = T(x,(u \ K(z,y)) * w)
    ]]></literal>
    <justification jstring="[para(14218(a,1),14297(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14218 14297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14388">
    <literal><![CDATA[
      K(x,y) * (K(y,x) / z) = 1 / z
    ]]></literal>
    <justification jstring="[para(79(a,1),14306(a,1,2)),flip(a)].">
      <j1 rule="para" parents="79 14306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14389">
    <literal><![CDATA[
      (K(x,y) * z) \ y = z \ T(y,x)
    ]]></literal>
    <justification jstring="[para(14306(a,1),12428(a,1,1))].">
      <j1 rule="para" parents="14306 12428"/>
    </justification>
  </clause>

  <clause id="14390">
    <literal><![CDATA[
      T(x,K(y,z)) \ K(y,z) = (x / K(y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(8247(a,1),14309(a,1,1))].">
      <j1 rule="para" parents="8247 14309"/>
    </justification>
  </clause>

  <clause id="14391">
    <literal><![CDATA[
      x / (y * K(x * K(z,x),z)) = (x * K(z,x)) / y
    ]]></literal>
    <justification jstring="[para(5053(a,1),14316(a,1,1))].">
      <j1 rule="para" parents="5053 14316"/>
    </justification>
  </clause>

  <clause id="14392">
    <literal><![CDATA[
      T(x,y) / (z / T(y,x)) = x / (z / y)
    ]]></literal>
    <justification jstring="[para(7189(a,1),14316(a,1,2))].">
      <j1 rule="para" parents="7189 14316"/>
    </justification>
  </clause>

  <clause id="14394">
    <literal><![CDATA[
      1 / (x * K(y,z)) = K(z,y) / x
    ]]></literal>
    <justification jstring="[hyper(192,a,14326,a)].">
      <j1 rule="hyper" parents="192 14326"/>
    </justification>
  </clause>

  <clause id="14398">
    <literal><![CDATA[
      K(x,(y / (1 / (K(z,u) / w))) * v5) = K(x,(y / (w * K(u,z))) * v5)
    ]]></literal>
    <justification jstring="[para(14326(a,1),5665(a,2,2,1,2))].">
      <j1 rule="para" parents="14326 5665"/>
    </justification>
  </clause>

  <clause id="14400">
    <literal><![CDATA[
      ((x * ((x \ y) * K(x / y,y))) / x) \ 1 = x / (x * ((((x / (1 / (x \ y))) / x) \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(14326(a,1),11159(a,1,1,1,2))].">
      <j1 rule="para" parents="14326 11159"/>
    </justification>
  </clause>

  <clause id="14401">
    <literal><![CDATA[
      T(x,y) / (1 / y) = x / (K(y,x) / y)
    ]]></literal>
    <justification jstring="[para(4569(a,1),14330(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4569 14330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14404">
    <literal><![CDATA[
      (x \ y) * K(y,z) = (1 / x) * T(x \ ((x \ 1) \ y),z)
    ]]></literal>
    <justification jstring="[para(14350(a,1),10300(a,1,2))].">
      <j1 rule="para" parents="14350 10300"/>
    </justification>
  </clause>

  <clause id="14405">
    <literal><![CDATA[
      T(x,y \ (y \ L(y,z,u))) = T(x,L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(6503(a,1),14377(a,1,2,2))].">
      <j1 rule="para" parents="6503 14377"/>
    </justification>
  </clause>

  <clause id="14406">
    <literal><![CDATA[
      T(x,(y \ (z \ ((1 / z) \ y))) \ (((z \ ((1 / z) \ y)) \ y) \ u)) = T(x,u)
    ]]></literal>
    <justification jstring="[para(13027(a,1),14377(a,1,2,2,1))].">
      <j1 rule="para" parents="13027 14377"/>
    </justification>
  </clause>

  <clause id="14407">
    <literal><![CDATA[
      K(T(x,y) * (z \ ((z \ 1) \ y)),u) != w
    ]]></literal>
    <literal><![CDATA[
      K((z \ ((z \ 1) \ y)) * x,u) = w
    ]]></literal>
    <justification jstring="[para(14377(a,1),13231(a,1,1,1))].">
      <j1 rule="para" parents="14377 13231"/>
    </justification>
  </clause>

  <clause id="14408">
    <literal><![CDATA[
      K(x,T(y,z) * (u \ ((u \ 1) \ z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u \ ((u \ 1) \ z)) * y) = w
    ]]></literal>
    <justification jstring="[para(14377(a,1),13261(a,1,2,1))].">
      <j1 rule="para" parents="14377 13261"/>
    </justification>
  </clause>

  <clause id="14409">
    <literal><![CDATA[
      K(x,T(y,z) \ (u \ ((u \ 1) \ z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u \ ((u \ 1) \ z)) / y) = w
    ]]></literal>
    <justification jstring="[para(14377(a,1),13924(a,1,2,1))].">
      <j1 rule="para" parents="14377 13924"/>
    </justification>
  </clause>

  <clause id="14410">
    <literal><![CDATA[
      K(x,y) * (1 / z) = K(x,y) / z
    ]]></literal>
    <justification jstring="[hyper(5437,a,14388,a)].">
      <j1 rule="hyper" parents="5437 14388"/>
    </justification>
  </clause>

  <clause id="14411">
    <literal><![CDATA[
      K(x,y) * (1 / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) / z = u
    ]]></literal>
    <justification jstring="[para(14388(a,1),5438(a,1,2)),flip(b)].">
      <j1 rule="para" parents="14388 5438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14412">
    <literal><![CDATA[
      T(K(x,y) / z,K(x,y)) = (1 / z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(14388(a,1),7203(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14388 7203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14413">
    <literal><![CDATA[
      (K(x,y) / z) * K(y,x) = T(1 / z,K(x,y))
    ]]></literal>
    <justification jstring="[para(14388(a,1),8054(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14388 8054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14414">
    <literal><![CDATA[
      (K(x,y) * z) \ T(x,y) = z \ x
    ]]></literal>
    <justification jstring="[para(5432(a,1),14389(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5432 14389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14415">
    <literal><![CDATA[
      (T(x,y) \ z) \ x = (x \ z) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(5383(a,1),14389(a,1,1))].">
      <j1 rule="para" parents="5383 14389"/>
    </justification>
  </clause>

  <clause id="14416">
    <literal><![CDATA[
      (((x * y) / x) * z) \ T(x,y) = (y * z) \ x
    ]]></literal>
    <justification jstring="[para(5515(a,1),14389(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5515 14389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14418">
    <literal><![CDATA[
      T(x \ T(y,z),K(z,y)) = (x * K(z,y)) \ y
    ]]></literal>
    <justification jstring="[para(14389(a,1),8989(a,1,1))].">
      <j1 rule="para" parents="14389 8989"/>
    </justification>
  </clause>

  <clause id="14419">
    <literal><![CDATA[
      a(x * (K(y,z) / u),w,v5) = a(x * (u * K(z,y)),w,v5)
    ]]></literal>
    <justification jstring="[para(14394(a,1),3128(a,1,1,2))].">
      <j1 rule="para" parents="14394 3128"/>
    </justification>
  </clause>

  <clause id="14421">
    <literal><![CDATA[
      K(x,y) / T(x,x * y) = 1 / L(x,y,x)
    ]]></literal>
    <justification jstring="[para(5561(a,1),14394(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5561 14394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14424">
    <literal><![CDATA[
      L(x,K(y,z) / u,w) = L(x,K(y,z) * u,w)
    ]]></literal>
    <justification jstring="[para(14410(a,1),2886(a,1,2))].">
      <j1 rule="para" parents="14410 2886"/>
    </justification>
  </clause>

  <clause id="14425">
    <literal><![CDATA[
      a(K(x,y) / z,u,w) = a(K(x,y) * z,u,w)
    ]]></literal>
    <justification jstring="[para(14410(a,1),3128(a,1,1))].">
      <j1 rule="para" parents="14410 3128"/>
    </justification>
  </clause>

  <clause id="14426">
    <literal><![CDATA[
      K(x,y) * ((1 / z) * x) = (K(x,y) / z) * x
    ]]></literal>
    <justification jstring="[para(14410(a,1),7680(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14410 7680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14427">
    <literal><![CDATA[
      T(K(x * y,x) / z,K(x,y)) = (1 / z) * K(x * y,x)
    ]]></literal>
    <justification jstring="[para(14410(a,1),8262(a,1,1))].">
      <j1 rule="para" parents="14410 8262"/>
    </justification>
  </clause>

  <clause id="14429">
    <literal><![CDATA[
      T(x,y) / (z \ x) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(192,a,14414,a)].">
      <j1 rule="hyper" parents="192 14414"/>
    </justification>
  </clause>

  <clause id="14430">
    <literal><![CDATA[
      K(x,y) * (x / z) = T(x,y) / z
    ]]></literal>
    <justification jstring="[para(79(a,1),14429(a,1,2)),flip(a)].">
      <j1 rule="para" parents="79 14429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14431">
    <literal><![CDATA[
      K(x,y) * (T(y,x) / z) = y / z
    ]]></literal>
    <justification jstring="[hyper(5437,a,14430,a)].">
      <j1 rule="hyper" parents="5437 14430"/>
    </justification>
  </clause>

  <clause id="14432">
    <literal><![CDATA[
      T(x,y) * (x / z) = x * (T(x,y) / z)
    ]]></literal>
    <justification jstring="[para(14430(a,1),5055(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14430 5055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14434">
    <literal><![CDATA[
      x / (y * K(x,z)) = K(z,x) * (x / y)
    ]]></literal>
    <justification jstring="[para(14316(a,1),14431(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14316 14431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14435">
    <literal><![CDATA[
      R(K(x,y),z,L(L(z,u,w),z,K(x,y))) = (K(x,y) * (z * L(z,u,w))) / (z * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(14171(a,1),486(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14171 486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14436">
    <literal><![CDATA[
      T(x,y \ L(y,z,z)) = x
    ]]></literal>
    <justification jstring="[hyper(56,a,14174,a)].">
      <j1 rule="hyper" parents="56 14174"/>
    </justification>
  </clause>

  <clause id="14437">
    <literal><![CDATA[
      x / (y \ L(y,z,z)) = (y \ L(y,z,z)) \ x
    ]]></literal>
    <justification jstring="[para(14174(a,1),262(a,1,2))].">
      <j1 rule="para" parents="14174 262"/>
    </justification>
  </clause>

  <clause id="14438">
    <literal><![CDATA[
      T(x,a(y,y,z) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(65,a,14056,a,b,14436,a)].">
      <j1 rule="hyper" parents="65 14056 14436"/>
    </justification>
  </clause>

  <clause id="14439">
    <literal><![CDATA[
      K(x,y * ((z \ L(z,u,u)) * w)) = K(x,y * (w * (z \ L(z,u,u))))
    ]]></literal>
    <justification jstring="[para(14436(a,1),13779(a,1,2,2))].">
      <j1 rule="para" parents="14436 13779"/>
    </justification>
  </clause>

  <clause id="14440">
    <literal><![CDATA[
      K(x,K(y,z \ (z \ u))) * x = T(x,K((z * z) \ u,y))
    ]]></literal>
    <justification jstring="[para(14182(a,2),8023(a,2,2))].">
      <j1 rule="para" parents="14182 8023"/>
    </justification>
  </clause>

  <clause id="14441">
    <literal><![CDATA[
      1 / (x \ K(y \ (z \ 1),x)) = T(x,(z * y) \ 1)
    ]]></literal>
    <justification jstring="[para(14203(a,1),5119(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="14203 5119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14442">
    <literal><![CDATA[
      L(x,y,y) * (x \ T(z,x)) = x \ (z * L(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,14210,a(flip),b,1350,a),flip(a)].">
      <j1 rule="hyper" parents="119 14210 1350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14443">
    <literal><![CDATA[
      x \ ((y * y) * (z * ((y * y) \ x))) = T(z,y \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(1051,a,14212,a)].">
      <j1 rule="hyper" parents="1051 14212"/>
    </justification>
  </clause>

  <clause id="14444">
    <literal><![CDATA[
      T(x,y \ ((y \ 1) * z)) = T(x,y \ (y \ z))
    ]]></literal>
    <justification jstring="[para(728(a,2),14212(a,1,2))].">
      <j1 rule="para" parents="728 14212"/>
    </justification>
  </clause>

  <clause id="14445">
    <literal><![CDATA[
      T(x,y \ (y \ (z * u))) = T(x,((y * y) \ z) * u)
    ]]></literal>
    <justification jstring="[para(664(a,1),14212(a,1,2)),flip(a)].">
      <j1 rule="para" parents="664 14212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14446">
    <literal><![CDATA[
      T(T(x,y * y),z) = T(x,y * (y * z))
    ]]></literal>
    <justification jstring="[hyper(1281,a,14216,a)].">
      <j1 rule="hyper" parents="1281 14216"/>
    </justification>
  </clause>

  <clause id="14448">
    <literal><![CDATA[
      x * (y \ (y \ K(y \ 1,z))) = (x / y) * T(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(14228(a,1),9033(a,1,2))].">
      <j1 rule="para" parents="14228 9033"/>
    </justification>
  </clause>

  <clause id="14449">
    <literal><![CDATA[
      K(x * 1,x * x) * (y * K(x \ 1,y)) = ((1 / x) * y) / (x \ 1)
    ]]></literal>
    <justification jstring="[para(14259(a,1),8336(a,1,1))].">
      <j1 rule="para" parents="14259 8336"/>
    </justification>
  </clause>

  <clause id="14453">
    <literal><![CDATA[
      K(x * (y \ 1),z) = K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(8219,a,14347,a),flip(a)].">
      <j1 rule="hyper" parents="8219 14347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14454">
    <literal><![CDATA[
      K(x * (y \ 1),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x / y,z) = u
    ]]></literal>
    <justification jstring="[para(14347(a,1),8219(a,1))].">
      <j1 rule="para" parents="14347 8219"/>
    </justification>
  </clause>

  <clause id="14455">
    <literal><![CDATA[
      K(x * (1 / y),z) = K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(7409,a,14453,a)].">
      <j1 rule="hyper" parents="7409 14453"/>
    </justification>
  </clause>

  <clause id="14456">
    <literal><![CDATA[
      K((1 / x) / y,z) = K(x \ (y \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(65,a,14191,a(flip),b,14453,a),flip(a)].">
      <j1 rule="hyper" parents="65 14191 14453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14457">
    <literal><![CDATA[
      K(x / (1 / y),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(79(a,1),14453(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="79 14453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14458">
    <literal><![CDATA[
      1 / (x \ K(y / z,x)) = T(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[para(14453(a,1),5119(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="14453 5119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14459">
    <literal><![CDATA[
      K(x / (K(y,z) * u),w) = K(x * (u \ K(z,y)),w)
    ]]></literal>
    <justification jstring="[para(14218(a,1),14453(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="14218 14453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14460">
    <literal><![CDATA[
      K(x * (1 / y),z) = z / T(z,x / y)
    ]]></literal>
    <justification jstring="[hyper(299,a,5033,a(flip),b,14455,a),flip(a)].">
      <j1 rule="hyper" parents="299 5033 14455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14461">
    <literal><![CDATA[
      K(x / (1 / y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(14455(a,1),7408(a,1))].">
      <j1 rule="para" parents="14455 7408"/>
    </justification>
  </clause>

  <clause id="14462">
    <literal><![CDATA[
      ((x * y) / x) / ((x * (y * K(z / u,y))) / x) = K(y,T(z * (1 / u),x))
    ]]></literal>
    <justification jstring="[para(14455(a,1),9341(a,1,2,1,2,2))].">
      <j1 rule="para" parents="14455 9341"/>
    </justification>
  </clause>

  <clause id="14463">
    <literal><![CDATA[
      K(x / (1 / y),z) = K((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,14194,a,b,14457,a),flip(a)].">
      <j1 rule="hyper" parents="299 14194 14457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14464">
    <literal><![CDATA[
      K(x,y * (z * z)) = K(x,z * (z * y))
    ]]></literal>
    <justification jstring="[hyper(13862,a,14362,a),flip(a)].">
      <j1 rule="hyper" parents="13862 14362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14466">
    <literal><![CDATA[
      T(x,x \ 1) / (y / (1 / x)) = x / (y / (x \ 1))
    ]]></literal>
    <justification jstring="[para(1692(a,1),14392(a,1,2,2))].">
      <j1 rule="para" parents="1692 14392"/>
    </justification>
  </clause>

  <clause id="14467">
    <literal><![CDATA[
      K((x / y) \ (T(x,z) \ u),L(w,x / y,T(x,z))) = K((x * (T(x,z) / y)) \ u,w)
    ]]></literal>
    <justification jstring="[para(14432(a,1),11935(a,2,1,1))].">
      <j1 rule="para" parents="14432 11935"/>
    </justification>
  </clause>

  <clause id="14468">
    <literal><![CDATA[
      T(T(x,y),z * z) = T(x,z * (z * y))
    ]]></literal>
    <justification jstring="[hyper(861,a,14446,a)].">
      <j1 rule="hyper" parents="861 14446"/>
    </justification>
  </clause>

  <clause id="14469">
    <literal><![CDATA[
      T(x \ 1,x * (x * y)) = T(1 / x,y)
    ]]></literal>
    <justification jstring="[para(469(a,1),14446(a,1,1)),flip(a)].">
      <j1 rule="para" parents="469 14446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14471">
    <literal><![CDATA[
      K((x / (y \ 1)) * T((x / (1 / y)) \ 1,z),u) = K(K(y \ (x \ 1),z),u)
    ]]></literal>
    <justification jstring="[para(14456(a,1),6767(a,2,1))].">
      <j1 rule="para" parents="14456 6767"/>
    </justification>
  </clause>

  <clause id="14472">
    <literal><![CDATA[
      T(x,y * (1 / z)) = T(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(5062,a,14460,a)].">
      <j1 rule="hyper" parents="5062 14460"/>
    </justification>
  </clause>

  <clause id="14473">
    <literal><![CDATA[
      K(x * (1 / y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x / y,z) = u
    ]]></literal>
    <justification jstring="[para(14460(a,2),5118(a,1))].">
      <j1 rule="para" parents="14460 5118"/>
    </justification>
  </clause>

  <clause id="14474">
    <literal><![CDATA[
      T(x,y * (z \ 1)) = T(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(13901,a,14472,a)].">
      <j1 rule="hyper" parents="13901 14472"/>
    </justification>
  </clause>

  <clause id="14475">
    <literal><![CDATA[
      L(T(x,y \ 1),y,x) = T(x,T(x,y) / y)
    ]]></literal>
    <justification jstring="[hyper(65,a,11681,a(flip),b,14472,a)].">
      <j1 rule="hyper" parents="65 11681 14472"/>
    </justification>
  </clause>

  <clause id="14476">
    <literal><![CDATA[
      T(x,(y / (z \ 1)) * (1 / u)) = T(x,(y / (1 / z)) / u)
    ]]></literal>
    <justification jstring="[hyper(65,a,3878,a(flip),b,14472,a)].">
      <j1 rule="hyper" parents="65 3878 14472"/>
    </justification>
  </clause>

  <clause id="14478">
    <literal><![CDATA[
      T(x,y / (z \ 1)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(76(a,1),14472(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="76 14472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14479">
    <literal><![CDATA[
      K(x,T(y,z / u) * (z * (u \ 1))) = K(x,(z * (1 / u)) * y)
    ]]></literal>
    <justification jstring="[para(14472(a,1),13263(a,1,2,1))].">
      <j1 rule="para" parents="14472 13263"/>
    </justification>
  </clause>

  <clause id="14480">
    <literal><![CDATA[
      K(x,T(y * z,T(y,u) / u) / (T(y,u) * (1 / u))) = K(x,L((1 / T(u,y)) \ z,u,y))
    ]]></literal>
    <justification jstring="[para(14472(a,1),13723(a,1,2,1))].">
      <j1 rule="para" parents="14472 13723"/>
    </justification>
  </clause>

  <clause id="14481">
    <literal><![CDATA[
      T(x,(y \ 1) / z) = T(x,y \ (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(65,a,14297,a(flip),b,14474,a),flip(a)].">
      <j1 rule="hyper" parents="65 14297 14474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14482">
    <literal><![CDATA[
      T(x,(1 / y) / z) = T(x,y \ (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(65,a,14211,a(flip),b,14474,a),flip(a)].">
      <j1 rule="hyper" parents="65 14211 14474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14483">
    <literal><![CDATA[
      T(x,T(y / z,y) / u) = T(x,(z \ y) * (u \ 1))
    ]]></literal>
    <justification jstring="[hyper(65,a,13876,a(flip),b,14474,a),flip(a)].">
      <j1 rule="hyper" parents="65 13876 14474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14484">
    <literal><![CDATA[
      T(x,y / (1 / z)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(79(a,1),14474(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="79 14474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14485">
    <literal><![CDATA[
      T(x,y / ((z * z) \ u)) = T(x,y * (u \ (z * z)))
    ]]></literal>
    <justification jstring="[para(464(a,1),14474(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="464 14474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14486">
    <literal><![CDATA[
      T(x,y / (z \ (u \ ((1 / u) \ z)))) = T(x,y * ((u \ ((1 / u) \ z)) \ z))
    ]]></literal>
    <justification jstring="[para(13027(a,1),14474(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13027 14474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14487">
    <literal><![CDATA[
      K(x,T(y,z / u) * (z * (u \ 1))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * (u \ 1)) * y) = w
    ]]></literal>
    <justification jstring="[para(14474(a,1),13261(a,1,2,1))].">
      <j1 rule="para" parents="14474 13261"/>
    </justification>
  </clause>

  <clause id="14488">
    <literal><![CDATA[
      T(x,y / (z \ L(z,u,u))) = T(x,y * a(u,u,z))
    ]]></literal>
    <justification jstring="[para(13006(a,1),14478(a,1,2,2))].">
      <j1 rule="para" parents="13006 14478"/>
    </justification>
  </clause>

  <clause id="14490">
    <literal><![CDATA[
      T(x,T(y * z,y * y) * y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(z * (y * y),y)) = u
    ]]></literal>
    <justification jstring="[para(14484(a,1),9982(a,1))].">
      <j1 rule="para" parents="14484 9982"/>
    </justification>
  </clause>

  <clause id="14491">
    <literal><![CDATA[
      K(x,(y \ z) * (y * y)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(10(a,1),14464(a,2,2,2))].">
      <j1 rule="para" parents="10 14464"/>
    </justification>
  </clause>

  <clause id="14492">
    <literal><![CDATA[
      T(x,x * (x * y)) = L(T(x,y),x,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,599,a(flip),b,14468,a),flip(a)].">
      <j1 rule="hyper" parents="65 599 14468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14493">
    <literal><![CDATA[
      (1 / x) * T(y,x * (x * (x \ 1))) = T(y * (x \ 1),x * x)
    ]]></literal>
    <justification jstring="[para(14468(a,1),1179(a,1,2))].">
      <j1 rule="para" parents="14468 1179"/>
    </justification>
  </clause>

  <clause id="14494">
    <literal><![CDATA[
      T(x,(x * x) * y) = L(T(x,y),x,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,14216,a,b,14492,a)].">
      <j1 rule="hyper" parents="65 14216 14492"/>
    </justification>
  </clause>

  <clause id="14495">
    <literal><![CDATA[
      L(T(x,x \ y),x,x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[para(10(a,1),14492(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 14492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14496">
    <literal><![CDATA[
      T((x \ 1) \ 1,x \ y) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2811,a,b,14495,a)].">
      <j1 rule="hyper" parents="65 2811 14495"/>
    </justification>
  </clause>

  <clause id="14497">
    <literal><![CDATA[
      (x \ 1) * T(x,x \ y) = x \ T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(119,a,14495,a(flip),b,1673,a),flip(a)].">
      <j1 rule="hyper" parents="119 14495 1673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14498">
    <literal><![CDATA[
      L((x \ y) \ y,x,x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[para(108(a,1),14495(a,1,1))].">
      <j1 rule="para" parents="108 14495"/>
    </justification>
  </clause>

  <clause id="14499">
    <literal><![CDATA[
      L(T(x,x \ y) \ L(T(x,x \ y),z,u),x,x) = T(x,x * y) \ L(L(T(x,x \ y),x,x),z,u)
    ]]></literal>
    <justification jstring="[para(14495(a,1),6776(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14495 6776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14500">
    <literal><![CDATA[
      L(x \ y,y / x,y / x) = T(y / x,(y / x) * y)
    ]]></literal>
    <justification jstring="[para(79(a,1),14498(a,1,1,1))].">
      <j1 rule="para" parents="79 14498"/>
    </justification>
  </clause>

  <clause id="14501">
    <literal><![CDATA[
      T(1 / x,x \ y) = T(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[para(10(a,1),14469(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 14469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14502">
    <literal><![CDATA[
      T(1 / x,x \ (x \ y)) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(72(a,1),14469(a,1,2)),flip(a)].">
      <j1 rule="para" parents="72 14469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14503">
    <literal><![CDATA[
      T(x,((y * y) * ((z \ 1) \ 1)) / u) = T(x,(z \ (y \ (y \ 1))) \ (u \ 1))
    ]]></literal>
    <justification jstring="[para(1774(a,1),14481(a,1,2,1))].">
      <j1 rule="para" parents="1774 14481"/>
    </justification>
  </clause>

  <clause id="14504">
    <literal><![CDATA[
      K(x,(y \ z) * (y * y)) = x \ T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(299,a,5036,a(flip),b,14491,a),flip(a)].">
      <j1 rule="hyper" parents="299 5036 14491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14505">
    <literal><![CDATA[
      T(x,x * y) = (((x \ y) \ y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,9751,a(flip),b,14496,a),flip(a)].">
      <j1 rule="hyper" parents="65 9751 14496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14506">
    <literal><![CDATA[
      1 / T(x,x \ y) = T(x,x * y) \ 1
    ]]></literal>
    <justification jstring="[para(14496(a,1),3178(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14496 3178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14507">
    <literal><![CDATA[
      T(((x \ 1) \ 1) * K(y,(x \ 1) \ 1),x \ z) = T(x,x * z) * K(y,T((x \ 1) \ 1,x \ z))
    ]]></literal>
    <justification jstring="[para(14496(a,1),5468(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14496 5468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14508">
    <literal><![CDATA[
      T(1 / x,y / x) = T(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(8329,a,14501,a)].">
      <j1 rule="hyper" parents="8329 14501"/>
    </justification>
  </clause>

  <clause id="14509">
    <literal><![CDATA[
      T(1 / x,x \ y) = T(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(299,a,6192,a,b,14501,a),flip(a)].">
      <j1 rule="hyper" parents="299 6192 14501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14510">
    <literal><![CDATA[
      L(T(x \ 1,y),x \ 1,x) = T(x \ 1,x \ (x \ y))
    ]]></literal>
    <justification jstring="[para(14502(a,1),1736(a,1,1))].">
      <j1 rule="para" parents="14502 1736"/>
    </justification>
  </clause>

  <clause id="14512">
    <literal><![CDATA[
      L(x,T(y,y * z),u) = L(x,(y \ z) \ z,u)
    ]]></literal>
    <justification jstring="[para(14505(a,2),2529(a,1,2))].">
      <j1 rule="para" parents="14505 2529"/>
    </justification>
  </clause>

  <clause id="14513">
    <literal><![CDATA[
      T(x,y * (z * (u * T(w,w * v5)))) = T(x,y * (z * (u * (1 / (((w \ v5) \ v5) \ 1)))))
    ]]></literal>
    <justification jstring="[para(14505(a,2),3902(a,2,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="14505 3902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14514">
    <literal><![CDATA[
      a(x,T(y,y * z),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,(y \ z) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(14505(a,2),6417(a,1,2))].">
      <j1 rule="para" parents="14505 6417"/>
    </justification>
  </clause>

  <clause id="14515">
    <literal><![CDATA[
      T((x \ 1) \ 1,x * y) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(38,a,9738,a,b,14506,a)].">
      <j1 rule="hyper" parents="38 9738 14506"/>
    </justification>
  </clause>

  <clause id="14516">
    <literal><![CDATA[
      x * (1 / T(x,x \ y)) = K(x * y,x)
    ]]></literal>
    <justification jstring="[para(14506(a,2),5034(a,2,2)),flip(a)].">
      <j1 rule="para" parents="14506 5034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14517">
    <literal><![CDATA[
      (x / y) * T(y \ 1,y * x) = (1 / y) * (x / y)
    ]]></literal>
    <justification jstring="[para(14508(a,1),107(a,1,2))].">
      <j1 rule="para" parents="14508 107"/>
    </justification>
  </clause>

  <clause id="14519">
    <literal><![CDATA[
      K(x * (x * y),x) = x * (1 / T(x,y))
    ]]></literal>
    <justification jstring="[para(9(a,1),14516(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="9 14516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14520">
    <literal><![CDATA[
      (x \ 1) \ K(x \ y,x) = K(x * y,x) * x
    ]]></literal>
    <justification jstring="[para(14516(a,1),7399(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14516 7399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14521">
    <literal><![CDATA[
      K(K((x / (1 / y)) * ((x / (1 / y)) * z),x / (1 / y)),u) = K((x / (y \ 1)) * (1 / T(x / (1 / y),z)),u)
    ]]></literal>
    <justification jstring="[para(14519(a,2),5624(a,1,1))].">
      <j1 rule="para" parents="14519 5624"/>
    </justification>
  </clause>

  <clause id="14523">
    <literal><![CDATA[
      K((1 / x) * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(5608(a,2),14266(a,1))].">
      <j1 rule="para" parents="5608 14266"/>
    </justification>
  </clause>

  <clause id="14525">
    <literal><![CDATA[
      K(x * (((y * z) \ y) \ 1),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(((y * z) \ y) \ x,z) = u
    ]]></literal>
    <justification jstring="[para(9658(a,1),14266(a,1))].">
      <j1 rule="para" parents="9658 14266"/>
    </justification>
  </clause>

  <clause id="14526">
    <literal><![CDATA[
      K(x,((y * y) \ z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z \ (y * y)) * u) = w
    ]]></literal>
    <justification jstring="[para(471(a,1),14274(a,1,2,1))].">
      <j1 rule="para" parents="471 14274"/>
    </justification>
  </clause>

  <clause id="14527">
    <literal><![CDATA[
      K(x,(y \ 1) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(5647(a,1),14274(a,1))].">
      <j1 rule="para" parents="5647 14274"/>
    </justification>
  </clause>

  <clause id="14528">
    <literal><![CDATA[
      K(x,(L(y,z,u) \ y) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(y \ L(y,z,u)) * w) = v5
    ]]></literal>
    <justification jstring="[para(13003(a,1),14274(a,1,2,1))].">
      <j1 rule="para" parents="13003 14274"/>
    </justification>
  </clause>

  <clause id="14529">
    <literal><![CDATA[
      K(x,(y \ (z * z)) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ ((z * z) * u)) = w
    ]]></literal>
    <justification jstring="[para(462(a,1),14281(a,1,2))].">
      <j1 rule="para" parents="462 14281"/>
    </justification>
  </clause>

  <clause id="14530">
    <literal><![CDATA[
      K(x,(1 / y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(5648(a,2),14281(a,1))].">
      <j1 rule="para" parents="5648 14281"/>
    </justification>
  </clause>

  <clause id="14531">
    <literal><![CDATA[
      K(x,(y \ L(y,z,z)) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,a(z,z,y) \ u) = w
    ]]></literal>
    <justification jstring="[para(13006(a,1),14281(a,1,2,1))].">
      <j1 rule="para" parents="13006 14281"/>
    </justification>
  </clause>

  <clause id="14534">
    <literal><![CDATA[
      T(x,(y \ 1) / z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (z \ 1)) = u
    ]]></literal>
    <justification jstring="[para(14474(a,1),14304(a,1))].">
      <j1 rule="para" parents="14474 14304"/>
    </justification>
  </clause>

  <clause id="14537">
    <literal><![CDATA[
      K(x,y) * (K(z,u) / u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) / T(u,z) = w
    ]]></literal>
    <justification jstring="[para(5038(a,2),14411(a,1,2))].">
      <j1 rule="para" parents="5038 14411"/>
    </justification>
  </clause>

  <clause id="14538">
    <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(14394(a,1),14411(a,1,2))].">
      <j1 rule="para" parents="14394 14411"/>
    </justification>
  </clause>

  <clause id="14539">
    <literal><![CDATA[
      K(x / (y * K(z,y)),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x * (y \ K(y,z)),u) = w
    ]]></literal>
    <justification jstring="[para(5492(a,1),14461(a,1,1,2))].">
      <j1 rule="para" parents="5492 14461"/>
    </justification>
  </clause>

  <clause id="14540">
    <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(14306(a,1),14461(a,1,1,2))].">
      <j1 rule="para" parents="14306 14461"/>
    </justification>
  </clause>

  <clause id="14541">
    <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(14394(a,1),14461(a,1,1,2))].">
      <j1 rule="para" parents="14394 14461"/>
    </justification>
  </clause>

  <clause id="14542">
    <literal><![CDATA[
      K((x \ 1) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(14463(a,1),14461(a,1))].">
      <j1 rule="para" parents="14463 14461"/>
    </justification>
  </clause>

  <clause id="14543">
    <literal><![CDATA[
      L(T(x,y \ 1),y,x) = T(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(299,a,13695,a(flip),b,14475,a),flip(a)].">
      <j1 rule="hyper" parents="299 13695 14475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14545">
    <literal><![CDATA[
      T(x,a(y,z,u) \ x) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,a(y,z,u) \ 1) = w
    ]]></literal>
    <justification jstring="[para(14543(a,1),14156(a,1))].">
      <j1 rule="para" parents="14543 14156"/>
    </justification>
  </clause>

  <clause id="14546">
    <literal><![CDATA[
      K((x * x) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ (x \ y),z) = u
    ]]></literal>
    <justification jstring="[para(441(a,1),14523(a,1,1))].">
      <j1 rule="para" parents="441 14523"/>
    </justification>
  </clause>

  <clause id="14547">
    <literal><![CDATA[
      K(x,(y * y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (y * z)) = u
    ]]></literal>
    <justification jstring="[para(730(a,1),14527(a,1,2))].">
      <j1 rule="para" parents="730 14527"/>
    </justification>
  </clause>

  <clause id="14549">
    <literal><![CDATA[
      K(x,y / T(z \ 1,z * (x * y))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(11678(a,2),14527(a,1))].">
      <j1 rule="para" parents="11678 14527"/>
    </justification>
  </clause>

  <clause id="14550">
    <literal><![CDATA[
      K(x,(K(y,z) / z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y) \ u) = w
    ]]></literal>
    <justification jstring="[para(5038(a,2),14530(a,1,2,1))].">
      <j1 rule="para" parents="5038 14530"/>
    </justification>
  </clause>

  <clause id="14553">
    <literal><![CDATA[
      K((x * x) * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * (x * y),z) = u
    ]]></literal>
    <justification jstring="[para(730(a,1),14542(a,1,1))].">
      <j1 rule="para" parents="730 14542"/>
    </justification>
  </clause>

  <clause id="14554">
    <literal><![CDATA[
      K((1 / x) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(5607(a,2),14542(a,1))].">
      <j1 rule="para" parents="5607 14542"/>
    </justification>
  </clause>

  <clause id="14556">
    <literal><![CDATA[
      a(x,y,K(z,u)) = K(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(6281,a,14163,a),flip(a)].">
      <j1 rule="hyper" parents="6281 14163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14557">
    <literal><![CDATA[
      T(x,a(y,z,u)) \ x = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(299,a,5024,a(flip),b,14556,a)].">
      <j1 rule="hyper" parents="299 5024 14556"/>
    </justification>
  </clause>

  <clause id="14558">
    <literal><![CDATA[
      K(a(x,x,y),z) = 1
    ]]></literal>
    <justification jstring="[hyper(65,a,14166,a(flip),b,14556,a),flip(a)].">
      <j1 rule="hyper" parents="65 14166 14556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14559">
    <literal><![CDATA[
      K(a(x,y,z),y) = 1
    ]]></literal>
    <justification jstring="[hyper(65,a,6815,a(flip),b,14556,a),flip(a)].">
      <j1 rule="hyper" parents="65 6815 14556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14560">
    <literal><![CDATA[
      T(x * a(y,z,K(u,x)),a(y,z,u)) = x
    ]]></literal>
    <justification jstring="[para(14556(a,2),5053(a,1,1,2))].">
      <j1 rule="para" parents="14556 5053"/>
    </justification>
  </clause>

  <clause id="14561">
    <literal><![CDATA[
      a(x,y,z) * a(x,y,K(z,u)) = T(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(14556(a,2),5083(a,2,2)),flip(a)].">
      <j1 rule="para" parents="14556 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14562">
    <literal><![CDATA[
      a(x,y,z) * a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(a(x,y,z),u) = w
    ]]></literal>
    <justification jstring="[para(14556(a,2),5087(a,1,2))].">
      <j1 rule="para" parents="14556 5087"/>
    </justification>
  </clause>

  <clause id="14563">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) != w
    ]]></literal>
    <literal><![CDATA[
      (a(y,z,u) * x) / a(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(14556(a,2),5268(a,1,2))].">
      <j1 rule="para" parents="14556 5268"/>
    </justification>
  </clause>

  <clause id="14564">
    <literal><![CDATA[
      x * ((x \ y) * a(z,u,K(w,x \ y))) = y * K(a(z,u,w),x \ y)
    ]]></literal>
    <justification jstring="[para(14556(a,2),6817(a,1,2,2))].">
      <j1 rule="para" parents="14556 6817"/>
    </justification>
  </clause>

  <clause id="14565">
    <literal><![CDATA[
      (x / y) * a(z,u,K(w,y)) = x / T(y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(14556(a,2),7189(a,1,2))].">
      <j1 rule="para" parents="14556 7189"/>
    </justification>
  </clause>

  <clause id="14566">
    <literal><![CDATA[
      (T(a(x,y,z),u) * w) / T(a(x,y,z),u) = w * a(x,y,K(z,T(w,u)))
    ]]></literal>
    <justification jstring="[para(14556(a,2),7565(a,2,2))].">
      <j1 rule="para" parents="14556 7565"/>
    </justification>
  </clause>

  <clause id="14567">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (1 / w) = K(a(x,y,z),u) / w
    ]]></literal>
    <justification jstring="[para(14556(a,2),14410(a,1,1))].">
      <j1 rule="para" parents="14556 14410"/>
    </justification>
  </clause>

  <clause id="14568">
    <literal><![CDATA[
      T(a(x,y,z),y) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,14559,a)].">
      <j1 rule="hyper" parents="58 14559"/>
    </justification>
  </clause>

  <clause id="14569">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(a(x,y,z),u) = w
    ]]></literal>
    <justification jstring="[para(14557(a,1),5109(a,1))].">
      <j1 rule="para" parents="14557 5109"/>
    </justification>
  </clause>

  <clause id="14570">
    <literal><![CDATA[
      L(x * K(y,z),x,x) = (x \ 1) \ K(y,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,14189,a(flip),b,14187,a),flip(a)].">
      <j1 rule="hyper" parents="299 14189 14187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14571">
    <literal><![CDATA[
      L(T(x * K(y,z),u),x,x) = T((x \ 1) \ K(y,z),u)
    ]]></literal>
    <justification jstring="[para(14570(a,1),25(a,2,1))].">
      <j1 rule="para" parents="14570 25"/>
    </justification>
  </clause>

  <clause id="14572">
    <literal><![CDATA[
      T(L(x,y,y),z) * a(y,y,x) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,5096,a,b,14197,a),flip(a)].">
      <j1 rule="hyper" parents="299 5096 14197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14574">
    <literal><![CDATA[
      L(T(x,y),z,z) * a(z,z,x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(25(a,2),14572(a,1,1))].">
      <j1 rule="para" parents="25 14572"/>
    </justification>
  </clause>

  <clause id="14575">
    <literal><![CDATA[
      a(x,x,T(y,z)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(1988,a,14574,a)].">
      <j1 rule="hyper" parents="1988 14574"/>
    </justification>
  </clause>

  <clause id="14577">
    <literal><![CDATA[
      T(x,((y \ 1) * z) \ 1) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(299,a,7037,a(flip),b,14209,a),flip(a)].">
      <j1 rule="hyper" parents="299 7037 14209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14578">
    <literal><![CDATA[
      T(x,(y * z) \ (y * y)) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,3909,a(flip),b,14577,a)].">
      <j1 rule="hyper" parents="65 3909 14577"/>
    </justification>
  </clause>

  <clause id="14579">
    <literal><![CDATA[
      T(x,T((y \ 1) \ z,u)) = T(x,T(y * z,u))
    ]]></literal>
    <justification jstring="[para(76(a,1),14213(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="76 14213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14580">
    <literal><![CDATA[
      L(T(x,x \ 1) \ y,x,x * K(x,z)) = K(x,z) \ ((((z * x) / z) \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,11759,a(flip),b,14232,a),flip(a)].">
      <j1 rule="hyper" parents="65 11759 14232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14581">
    <literal><![CDATA[
      (x / ((y * z) / y)) \ T(x / z,1 / (x / ((y * z) / y))) = (x / z) * (1 / (x / ((y * z) / y)))
    ]]></literal>
    <justification jstring="[para(14247(a,1),9054(a,2,1))].">
      <j1 rule="para" parents="14247 9054"/>
    </justification>
  </clause>

  <clause id="14582">
    <literal><![CDATA[
      T(K(x,y) * K(x,z),K(z,x) * K(y,x)) = K(x,y) * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,9427,a,b,14305,a)].">
      <j1 rule="hyper" parents="65 9427 14305"/>
    </justification>
  </clause>

  <clause id="14583">
    <literal><![CDATA[
      T(T(x,x \ 1),y) * K(L(x,x,x) * y,z) = y \ T(T(x,x \ 1) * y,z)
    ]]></literal>
    <justification jstring="[para(2807(a,1),14317(a,1,2,1))].">
      <j1 rule="para" parents="2807 14317"/>
    </justification>
  </clause>

  <clause id="14585">
    <literal><![CDATA[
      T(x \ K(y,z),K(y,z)) = (x / K(y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,9570,a,b,14390,a)].">
      <j1 rule="hyper" parents="65 9570 14390"/>
    </justification>
  </clause>

  <clause id="14586">
    <literal><![CDATA[
      ((1 / x) * K(y,z)) * K(u,x) = K(y,T(z,x)) / T(x,u)
    ]]></literal>
    <justification jstring="[para(14412(a,1),9820(a,1,1))].">
      <j1 rule="para" parents="14412 9820"/>
    </justification>
  </clause>

  <clause id="14587">
    <literal><![CDATA[
      T(1 / (x * K(y,z)),K(z,y)) = (1 / x) * K(z,y)
    ]]></literal>
    <justification jstring="[para(14394(a,2),14412(a,1,1))].">
      <j1 rule="para" parents="14394 14412"/>
    </justification>
  </clause>

  <clause id="14588">
    <literal><![CDATA[
      (x * K(y,z)) \ z = K(z,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,14324,a(flip),b,14418,a),flip(a)].">
      <j1 rule="hyper" parents="65 14324 14418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14589">
    <literal><![CDATA[
      a(K(x,y) / ((K(x,y) \ 1) \ z),u,w) = a((K(x,y) \ (1 / K(x,y))) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(1709(a,2),14425(a,2,1))].">
      <j1 rule="para" parents="1709 14425"/>
    </justification>
  </clause>

  <clause id="14590">
    <literal><![CDATA[
      ((x * x) \ y) * x = (K(y,x) / x) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,7160,a(flip),b,14426,a)].">
      <j1 rule="hyper" parents="65 7160 14426"/>
    </justification>
  </clause>

  <clause id="14591">
    <literal><![CDATA[
      K(x,T(y,z) \ z) = K(x,((y * y) \ z) * y)
    ]]></literal>
    <justification jstring="[para(14590(a,2),14273(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14590 14273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14592">
    <literal><![CDATA[
      T(x,(y \ 1) * ((y \ 1) * z)) = T(x,y \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,14297,a,b,14444,a)].">
      <j1 rule="hyper" parents="65 14297 14444"/>
    </justification>
  </clause>

  <clause id="14593">
    <literal><![CDATA[
      T(x,y * (z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(14458(a,1),5226(a,1))].">
      <j1 rule="para" parents="14458 5226"/>
    </justification>
  </clause>

  <clause id="14594">
    <literal><![CDATA[
      T(x,y * (1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(3874(a,2),14593(a,1))].">
      <j1 rule="para" parents="3874 14593"/>
    </justification>
  </clause>

  <clause id="14595">
    <literal><![CDATA[
      T(x,y * (z \ K(u,z))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y / T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(5039(a,1),14593(a,1,2,2))].">
      <j1 rule="para" parents="5039 14593"/>
    </justification>
  </clause>

  <clause id="14596">
    <literal><![CDATA[
      T(x,y \ (z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,(y \ 1) / z) = u
    ]]></literal>
    <justification jstring="[para(14297(a,1),14593(a,1))].">
      <j1 rule="para" parents="14297 14593"/>
    </justification>
  </clause>

  <clause id="14597">
    <literal><![CDATA[
      (x \ 1) * T(x,x \ y) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(299,a,5036,a,b,14497,a),flip(a)].">
      <j1 rule="hyper" parents="299 5036 14497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14598">
    <literal><![CDATA[
      K(x,x * y) / x = x \ K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(120,a,14597,a(flip),b,6467,a)].">
      <j1 rule="hyper" parents="120 14597 6467"/>
    </justification>
  </clause>

  <clause id="14599">
    <literal><![CDATA[
      (x \ K(x,x \ y)) * K(z,x) = K(x,x * y) / T(x,z)
    ]]></literal>
    <justification jstring="[para(14598(a,1),7189(a,1,1))].">
      <j1 rule="para" parents="14598 7189"/>
    </justification>
  </clause>

  <clause id="14600">
    <literal><![CDATA[
      T(x,(y \ z) * (y * y)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(5086,a,14504,a)].">
      <j1 rule="hyper" parents="5086 14504"/>
    </justification>
  </clause>

  <clause id="14601">
    <literal><![CDATA[
      T(x,y * (z * z)) = T(x,z * (z * y))
    ]]></literal>
    <justification jstring="[para(9(a,1),14600(a,1,2,1))].">
      <j1 rule="para" parents="9 14600"/>
    </justification>
  </clause>

  <clause id="14602">
    <literal><![CDATA[
      T(T(x,y),z * z) = T(x,y * (z * z))
    ]]></literal>
    <justification jstring="[hyper(299,a,14468,a,b,14601,a)].">
      <j1 rule="hyper" parents="299 14468 14601"/>
    </justification>
  </clause>

  <clause id="14603">
    <literal><![CDATA[
      T(T(x,y * y),z) = T(x,z * (y * y))
    ]]></literal>
    <justification jstring="[hyper(299,a,14446,a,b,14601,a)].">
      <j1 rule="hyper" parents="299 14446 14601"/>
    </justification>
  </clause>

  <clause id="14604">
    <literal><![CDATA[
      T(x,y * ((y \ 1) \ z)) = T(x,z * (y * y))
    ]]></literal>
    <justification jstring="[hyper(299,a,14369,a,b,14601,a)].">
      <j1 rule="hyper" parents="299 14369 14601"/>
    </justification>
  </clause>

  <clause id="14605">
    <literal><![CDATA[
      T(x,y \ (z * (u * u))) = T(x,u * (u * (y \ z)))
    ]]></literal>
    <justification jstring="[para(847(a,2),14601(a,1,2))].">
      <j1 rule="para" parents="847 14601"/>
    </justification>
  </clause>

  <clause id="14606">
    <literal><![CDATA[
      T(x,T(y,z) * ((1 / z) * (1 / z))) = T(x,(1 / z) * (((z * z) \ y) * z))
    ]]></literal>
    <justification jstring="[para(983(a,2),14601(a,2,2,2))].">
      <j1 rule="para" parents="983 14601"/>
    </justification>
  </clause>

  <clause id="14607">
    <literal><![CDATA[
      T(x,(y \ 1) * ((y \ 1) * z)) = T(x,z * (y \ (1 / y)))
    ]]></literal>
    <justification jstring="[para(1705(a,1),14601(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1705 14601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14609">
    <literal><![CDATA[
      L(x,((y \ 1) \ (z * ((y \ 1) \ 1))) \ (z * ((y \ 1) \ 1)),u) = L(x,T(y \ 1,(1 / y) * (z * y)),u)
    ]]></literal>
    <justification jstring="[para(3268(a,1),14512(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3268 14512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14610">
    <literal><![CDATA[
      (x \ 1) \ K(x \ y,x) = x * K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,3618,a(flip),b,14520,a),flip(a)].">
      <j1 rule="hyper" parents="299 3618 14520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14611">
    <literal><![CDATA[
      (x / K(y,z)) \ 1 = K(y,z) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,14242,a(flip),b,14585,a),flip(a)].">
      <j1 rule="hyper" parents="65 14242 14585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14612">
    <literal><![CDATA[
      (x * K(y,z)) \ 1 = K(z,y) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(7196(a,1),14611(a,1,1))].">
      <j1 rule="para" parents="7196 14611"/>
    </justification>
  </clause>

  <clause id="14613">
    <literal><![CDATA[
      L(x,y,z * (K(u,w) * (v5 \ 1))) = L(x,y,z * (v5 * K(w,u)))
    ]]></literal>
    <justification jstring="[para(14612(a,1),2627(a,1,3,2))].">
      <j1 rule="para" parents="14612 2627"/>
    </justification>
  </clause>

  <clause id="14614">
    <literal><![CDATA[
      K(x,y) * ((z \ 1) \ 1) = (z \ K(y,x)) \ 1
    ]]></literal>
    <justification jstring="[para(14185(a,1),14612(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14185 14612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14616">
    <literal><![CDATA[
      K((K(x,y) * (z \ 1)) \ u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K((z * K(y,x)) * u,w) = v5
    ]]></literal>
    <justification jstring="[para(14612(a,1),14542(a,1,1,1))].">
      <j1 rule="para" parents="14612 14542"/>
    </justification>
  </clause>

  <clause id="14617">
    <literal><![CDATA[
      K(x,((y * y) \ z) * y) = K(x,(K(z,y) / y) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,14273,a,b,14591,a),flip(a)].">
      <j1 rule="hyper" parents="65 14273 14591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14618">
    <literal><![CDATA[
      K(x,T(((y \ 1) * z) \ u,u * (y * y))) = K(x,(y * ((y \ 1) \ u)) / (y * z))
    ]]></literal>
    <justification jstring="[para(14604(a,1),8163(a,1,2))].">
      <j1 rule="para" parents="14604 8163"/>
    </justification>
  </clause>

  <clause id="14619">
    <literal><![CDATA[
      x * K(x * (x * y),x) = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),14610(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 14610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14620">
    <literal><![CDATA[
      K(x,y) * T(T(z,z \ 1),u) = (T(z,u) \ K(y,x)) \ 1
    ]]></literal>
    <justification jstring="[para(3171(a,2),14614(a,1,2))].">
      <j1 rule="para" parents="3171 14614"/>
    </justification>
  </clause>

  <clause id="14621">
    <literal><![CDATA[
      K(x,y) * T((z \ 1) \ 1,u) = (T(z,u) \ K(y,x)) \ 1
    ]]></literal>
    <justification jstring="[para(3174(a,2),14614(a,1,2))].">
      <j1 rule="para" parents="3174 14614"/>
    </justification>
  </clause>

  <clause id="14623">
    <literal><![CDATA[
      T((x \ 1) \ K(y,x),x * y) = R(x,x * y,x)
    ]]></literal>
    <justification jstring="[para(14619(a,1),5674(a,1,1))].">
      <j1 rule="para" parents="14619 5674"/>
    </justification>
  </clause>

  <clause id="14624">
    <literal><![CDATA[
      T(x,y) \ T((x \ 1) \ K(z,x),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * (x * z),T(x,y)) = u
    ]]></literal>
    <justification jstring="[para(14619(a,1),5878(a,1,2,1))].">
      <j1 rule="para" parents="14619 5878"/>
    </justification>
  </clause>

  <clause id="14626">
    <literal><![CDATA[
      K(x,y * (z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(14284(a,1),500(a,1)),flip(b)].">
      <j1 rule="para" parents="14284 500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14627">
    <literal><![CDATA[
      K(x,K(y,z * (u \ 1))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z / u)) = w
    ]]></literal>
    <justification jstring="[para(14284(a,1),7864(a,1,2))].">
      <j1 rule="para" parents="14284 7864"/>
    </justification>
  </clause>

  <clause id="14628">
    <literal><![CDATA[
      K(x,y * ((z * z) * ((u * w) \ 1))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (u * (w / (z * z)))) = v5
    ]]></literal>
    <justification jstring="[para(852(a,1),14626(a,1,2,2))].">
      <j1 rule="para" parents="852 14626"/>
    </justification>
  </clause>

  <clause id="14629">
    <literal><![CDATA[
      K(x,y * (1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(5639(a,2),14626(a,1))].">
      <j1 rule="para" parents="5639 14626"/>
    </justification>
  </clause>

  <clause id="14630">
    <literal><![CDATA[
      K(x,y * ((y \ 1) \ (z * (1 / u)))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * ((y \ 1) \ z)) / u) = w
    ]]></literal>
    <justification jstring="[para(1174(a,1),14629(a,1,2))].">
      <j1 rule="para" parents="1174 14629"/>
    </justification>
  </clause>

  <clause id="14631">
    <literal><![CDATA[
      T(x,((y * y) \ z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (y \ (z * u))) = w
    ]]></literal>
    <justification jstring="[para(664(a,1),14292(a,1,2))].">
      <j1 rule="para" parents="664 14292"/>
    </justification>
  </clause>

  <clause id="14632">
    <literal><![CDATA[
      T(x,(y \ L(y,z,u)) / w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,(L(y,z,u) \ y) \ (w \ 1)) = v5
    ]]></literal>
    <justification jstring="[para(13004(a,1),14534(a,1,2,1))].">
      <j1 rule="para" parents="13004 14534"/>
    </justification>
  </clause>

  <clause id="14633">
    <literal><![CDATA[
      K(((x * x) \ y) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ (x \ (y * z)),u) = w
    ]]></literal>
    <justification jstring="[para(664(a,1),14546(a,1,1))].">
      <j1 rule="para" parents="664 14546"/>
    </justification>
  </clause>

  <clause id="14634">
    <literal><![CDATA[
      L(x,((y \ 1) \ K(z,y)) * K(y * z,(y \ 1) \ K(z,y)),u) = L(x,R(y,y * z,y),u)
    ]]></literal>
    <justification jstring="[para(14623(a,1),5538(a,2,2))].">
      <j1 rule="para" parents="14623 5538"/>
    </justification>
  </clause>

  <clause id="14635">
    <literal><![CDATA[
      (x \ (y * z)) * K(x * (y \ (x \ (y * z))),y) = x \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(37,a,3940,a(flip),b,14270,a),flip(a)].">
      <j1 rule="hyper" parents="37 3940 14270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14637">
    <literal><![CDATA[
      x * K(y,(z \ 1) \ (z \ u)) = (1 / x) \ K(y,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),14277(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 14277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14639">
    <literal><![CDATA[
      K(x,L(y * z,z,y)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(11964,a,14278,a)].">
      <j1 rule="hyper" parents="11964 14278"/>
    </justification>
  </clause>

  <clause id="14640">
    <literal><![CDATA[
      K(x,K(y * z,L(u,z,y))) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[para(14639(a,1),8919(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14639 8919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14641">
    <literal><![CDATA[
      (x * (y * z)) * K(z,x * y) = L(z,y,x) * (x * y)
    ]]></literal>
    <justification jstring="[para(14639(a,1),11938(a,1,2))].">
      <j1 rule="para" parents="14639 11938"/>
    </justification>
  </clause>

  <clause id="14642">
    <literal><![CDATA[
      K(x,L((y \ 1) \ z,u,w)) = K(x,L(y * z,u,w))
    ]]></literal>
    <justification jstring="[hyper(299,a,11889,a(flip),b,14280,a),flip(a)].">
      <j1 rule="hyper" parents="299 11889 14280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14643">
    <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(14280(a,2),11995(a,1))].">
      <j1 rule="para" parents="14280 11995"/>
    </justification>
  </clause>

  <clause id="14644">
    <literal><![CDATA[
      K(x,(y / z) * (u * u)) = K(x,y * (z \ (u * u)))
    ]]></literal>
    <justification jstring="[para(827(a,1),14286(a,1,2))].">
      <j1 rule="para" parents="827 14286"/>
    </justification>
  </clause>

  <clause id="14645">
    <literal><![CDATA[
      K(x,L(y * (z \ 1),u,w)) = K(x,L(y / z,u,w))
    ]]></literal>
    <justification jstring="[hyper(299,a,11889,a(flip),b,14289,a),flip(a)].">
      <j1 rule="hyper" parents="299 11889 14289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14646">
    <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(14289(a,2),11995(a,1))].">
      <j1 rule="para" parents="14289 11995"/>
    </justification>
  </clause>

  <clause id="14647">
    <literal><![CDATA[
      K(x,y * ((z \ u) \ K(z,w))) = K(x,y / (T(z,w) \ u))
    ]]></literal>
    <justification jstring="[para(5383(a,1),14313(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5383 14313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14648">
    <literal><![CDATA[
      K(x,T((y \ 1) * z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y \ z,u)) = w
    ]]></literal>
    <justification jstring="[para(14332(a,1),8121(a,1))].">
      <j1 rule="para" parents="14332 8121"/>
    </justification>
  </clause>

  <clause id="14649">
    <literal><![CDATA[
      K(x,L(y / (z \ 1),u,w)) = K(x,L(y * z,u,w))
    ]]></literal>
    <justification jstring="[hyper(299,a,11889,a(flip),b,14359,a),flip(a)].">
      <j1 rule="hyper" parents="299 11889 14359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14650">
    <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(14359(a,2),11995(a,1))].">
      <j1 rule="para" parents="14359 11995"/>
    </justification>
  </clause>

  <clause id="14651">
    <literal><![CDATA[
      K(x,((y \ z) \ z) / u) = K(x,T(y,z) / u)
    ]]></literal>
    <justification jstring="[hyper(299,a,14283,a(flip),b,14360,a),flip(a)].">
      <j1 rule="hyper" parents="299 14283 14360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14652">
    <literal><![CDATA[
      T((1 / x) \ y,x * x) = (x \ y) * ((1 / x) \ x)
    ]]></literal>
    <justification jstring="[para(1664(a,1),14364(a,1,1))].">
      <j1 rule="para" parents="1664 14364"/>
    </justification>
  </clause>

  <clause id="14653">
    <literal><![CDATA[
      ((1 / x) \ y) \ ((x * x) * y) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(119,a,442,a(flip),b,14368,a)].">
      <j1 rule="hyper" parents="119 442 14368"/>
    </justification>
  </clause>

  <clause id="14654">
    <literal><![CDATA[
      R(x,x \ L(y,x,x),x) = R(x,x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,5677,a(flip),b,14376,a),flip(a)].">
      <j1 rule="hyper" parents="65 5677 14376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14655">
    <literal><![CDATA[
      R(x,(x \ 1) * y,x) = R(x,x \ y,x)
    ]]></literal>
    <justification jstring="[para(1679(a,1),14654(a,1,2))].">
      <j1 rule="para" parents="1679 14654"/>
    </justification>
  </clause>

  <clause id="14656">
    <literal><![CDATA[
      ((x \ 1) * y) \ L(y,x,x) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(119,a,1673,a(flip),b,14378,a)].">
      <j1 rule="hyper" parents="119 1673 14378"/>
    </justification>
  </clause>

  <clause id="14657">
    <literal><![CDATA[
      (x \ 1) * (y * L(y \ ((x \ 1) \ L(y,x,x)),z,u)) = ((x \ 1) * y) * L(T(x,x \ y),z,u)
    ]]></literal>
    <justification jstring="[para(14656(a,1),1150(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14656 1150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14658">
    <literal><![CDATA[
      (x * K(y,x)) / z = x / (z * K(x,y))
    ]]></literal>
    <justification jstring="[para(5201(a,1),14391(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5201 14391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14659">
    <literal><![CDATA[
      (x * K(y,x)) / z = K(y,x) * (x / z)
    ]]></literal>
    <justification jstring="[hyper(299,a,14434,a(flip),b,14658,a),flip(a)].">
      <j1 rule="hyper" parents="299 14434 14658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14661">
    <literal><![CDATA[
      ((x * y) * K(T(z,y),x * y)) / u = (x * y) / (u * K(y * x,z))
    ]]></literal>
    <justification jstring="[para(13173(a,1),14658(a,2,2,2))].">
      <j1 rule="para" parents="13173 14658"/>
    </justification>
  </clause>

  <clause id="14662">
    <literal><![CDATA[
      ((x * y) / x) / z = K(x,y) * (y / z)
    ]]></literal>
    <justification jstring="[para(5054(a,2),14659(a,1,1))].">
      <j1 rule="para" parents="5054 14659"/>
    </justification>
  </clause>

  <clause id="14664">
    <literal><![CDATA[
      T(x,(y * z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ (y \ 1)) = u
    ]]></literal>
    <justification jstring="[para(14441(a,1),5226(a,1))].">
      <j1 rule="para" parents="14441 5226"/>
    </justification>
  </clause>

  <clause id="14665">
    <literal><![CDATA[
      T(x,y \ (L(z,y,z) \ 1)) = T(x,z / (z * (y * z)))
    ]]></literal>
    <justification jstring="[hyper(14664,a,4649,a)].">
      <j1 rule="hyper" parents="14664 4649"/>
    </justification>
  </clause>

  <clause id="14666">
    <literal><![CDATA[
      T(x,(y * y) * ((z * u) \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(u / (y * y)) \ (z \ 1)) = w
    ]]></literal>
    <justification jstring="[para(852(a,1),14664(a,1,2))].">
      <j1 rule="para" parents="852 14664"/>
    </justification>
  </clause>

  <clause id="14667">
    <literal><![CDATA[
      T(x,y \ (L(y,z,u) * (y \ w))) = T(x,((y * y) \ L(y,z,u)) * w)
    ]]></literal>
    <justification jstring="[para(1348(a,1),14445(a,1,2,2))].">
      <j1 rule="para" parents="1348 14445"/>
    </justification>
  </clause>

  <clause id="14668">
    <literal><![CDATA[
      K(x * ((y / z) \ K(u,y)),w) = K(x / (T(y,u) / z),w)
    ]]></literal>
    <justification jstring="[para(14430(a,1),14459(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="14430 14459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14669">
    <literal><![CDATA[
      T(x \ 1,(x \ 1) \ 1) / (y / (1 / (x \ 1))) = x / ((y / ((x \ 1) \ 1)) * (x * x))
    ]]></literal>
    <justification jstring="[hyper(299,a,749,a,b,14466,a),flip(a)].">
      <j1 rule="hyper" parents="299 749 14466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14670">
    <literal><![CDATA[
      T(x,T(y / z,y) / u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z \ y) / u) = w
    ]]></literal>
    <justification jstring="[para(14483(a,2),14593(a,1))].">
      <j1 rule="para" parents="14483 14593"/>
    </justification>
  </clause>

  <clause id="14671">
    <literal><![CDATA[
      T(x,(y / z) * (u * u)) = T(x,y * (z \ (u * u)))
    ]]></literal>
    <justification jstring="[para(827(a,1),14485(a,1,2))].">
      <j1 rule="para" parents="827 14485"/>
    </justification>
  </clause>

  <clause id="14672">
    <literal><![CDATA[
      T(x,(y \ L(y,z,z)) \ u) = T(x,u * a(z,z,y))
    ]]></literal>
    <justification jstring="[para(14437(a,1),14488(a,1,2))].">
      <j1 rule="para" parents="14437 14488"/>
    </justification>
  </clause>

  <clause id="14673">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (1 / w) = a(x,y,K(z,u)) / w
    ]]></literal>
    <justification jstring="[para(14556(a,2),14567(a,2,1))].">
      <j1 rule="para" parents="14556 14567"/>
    </justification>
  </clause>

  <clause id="14674">
    <literal><![CDATA[
      1 / (K(x,y) * z) = (1 / z) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,8992,a(flip),b,14587,a)].">
      <j1 rule="hyper" parents="65 8992 14587"/>
    </justification>
  </clause>

  <clause id="14675">
    <literal><![CDATA[
      K(x,y * z) * (z * y) = (z * y) * K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(13304,a,14674,a),flip(a)].">
      <j1 rule="hyper" parents="13304 14674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14676">
    <literal><![CDATA[
      K(x,y) * ((1 / z) * K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) / (K(w,u) * z) = v5
    ]]></literal>
    <justification jstring="[para(14674(a,1),14411(a,1,2))].">
      <j1 rule="para" parents="14674 14411"/>
    </justification>
  </clause>

  <clause id="14677">
    <literal><![CDATA[
      T(x,y \ ((z * z) * T(u,z * z))) = T(x,z * (z * (y \ u)))
    ]]></literal>
    <justification jstring="[para(107(a,2),14605(a,1,2,2))].">
      <j1 rule="para" parents="107 14605"/>
    </justification>
  </clause>

  <clause id="14678">
    <literal><![CDATA[
      K(x,(K(y * z,u) / u) * (y * z)) = K(x,(((u * u) \ y) * z) * u)
    ]]></literal>
    <justification jstring="[para(664(a,1),14617(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="664 14617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14681">
    <literal><![CDATA[
      (1 / x) \ K(y,T(z * u,w)) = x * K(y,T((z \ 1) \ u,w))
    ]]></literal>
    <justification jstring="[para(1107(a,1),14637(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1107 14637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14683">
    <literal><![CDATA[
      K((x \ y) \ y,L(z * u,w,v5)) = K(x,T(L((z \ 1) \ u,w,v5),y))
    ]]></literal>
    <justification jstring="[hyper(7713,a,14642,a),flip(a)].">
      <j1 rule="hyper" parents="7713 14642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14684">
    <literal><![CDATA[
      K(x,y * ((z * u) \ (z * z))) = K(x,y / ((1 / z) * u))
    ]]></literal>
    <justification jstring="[para(1076(a,1),14644(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1076 14644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14685">
    <literal><![CDATA[
      K(x,L(y / (1 / z),u,w)) = K(x,L(y * z,u,w))
    ]]></literal>
    <justification jstring="[para(79(a,1),14645(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="79 14645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14686">
    <literal><![CDATA[
      K(x,L(((y \ 1) \ (z * ((y \ 1) \ 1))) / y,u,w)) = K(x,L(T(z,y \ 1) * (1 / (y \ 1)),u,w))
    ]]></literal>
    <justification jstring="[para(3735(a,1),14645(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3735 14645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14687">
    <literal><![CDATA[
      K(x,L(y * (1 / z),u,w)) = K(x,L(y / z,u,w))
    ]]></literal>
    <justification jstring="[para(79(a,1),14649(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="79 14649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14688">
    <literal><![CDATA[
      ((x * y) * z) / (y * (z * T((1 / u) \ (1 / u),u * u))) = R(x,y,z * (u \ (1 / u)))
    ]]></literal>
    <justification jstring="[para(14652(a,2),3102(a,1,2,2,2))].">
      <j1 rule="para" parents="14652 3102"/>
    </justification>
  </clause>

  <clause id="14689">
    <literal><![CDATA[
      K(x,L(T(y,1 / z) * z,u,w)) = K(x,L((1 / z) \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,13892,a(flip),b,14685,a),flip(a)].">
      <j1 rule="hyper" parents="65 13892 14685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14690">
    <literal><![CDATA[
      T(x \ a(y,z,K(u,w)),K(a(y,z,u),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(a(y,z,u),w) * (x \ 1) = v5
    ]]></literal>
    <justification jstring="[para(14556(a,2),14243(a,1,1,2))].">
      <j1 rule="para" parents="14556 14243"/>
    </justification>
  </clause>

  <clause id="14691">
    <literal><![CDATA[
      L(x \ y,y / x,x \ y) = T(y / x,(y / x) * y)
    ]]></literal>
    <justification jstring="[hyper(11644,a,14500,a)].">
      <j1 rule="hyper" parents="11644 14500"/>
    </justification>
  </clause>

  <clause id="14692">
    <literal><![CDATA[
      T(x \ 1,x \ (x \ y)) = T(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,1714,a(flip),b,14510,a),flip(a)].">
      <j1 rule="hyper" parents="65 1714 14510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14693">
    <literal><![CDATA[
      T(1 / x,x * y) = T(x \ 1,x \ y)
    ]]></literal>
    <justification jstring="[para(9(a,1),14692(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 14692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14694">
    <literal><![CDATA[
      T(x \ 1,x \ T(y,x)) = T(1 / x,y * x)
    ]]></literal>
    <justification jstring="[para(22(a,2),14692(a,1,2,2))].">
      <j1 rule="para" parents="22 14692"/>
    </justification>
  </clause>

  <clause id="14695">
    <literal><![CDATA[
      ((x \ 1) * T(x \ 1,x \ (x \ y))) * z = T(1 / x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[para(14692(a,1),6026(a,2,1))].">
      <j1 rule="para" parents="14692 6026"/>
    </justification>
  </clause>

  <clause id="14696">
    <literal><![CDATA[
      L(T(x * K(y,x),x * y),x,x) = R(x,x * y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,14623,a(flip),b,14571,a),flip(a)].">
      <j1 rule="hyper" parents="299 14623 14571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14697">
    <literal><![CDATA[
      T((x \ 1) \ K(x * y,x),y) = L(R(x,y,x),x,x)
    ]]></literal>
    <justification jstring="[para(5674(a,1),14571(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5674 14571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14698">
    <literal><![CDATA[
      L(L(x,y,x),x,x) = R(x,x * y,x)
    ]]></literal>
    <justification jstring="[para(5246(a,1),14696(a,1,1))].">
      <j1 rule="para" parents="5246 14696"/>
    </justification>
  </clause>

  <clause id="14699">
    <literal><![CDATA[
      L(L(x,x,x),y,x) = R(x,x * y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,30,a,b,14698,a)].">
      <j1 rule="hyper" parents="65 30 14698"/>
    </justification>
  </clause>

  <clause id="14700">
    <literal><![CDATA[
      R(x,(x \ 1) * y,x) = R(x,x * y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,9509,a,b,14699,a)].">
      <j1 rule="hyper" parents="65 9509 14699"/>
    </justification>
  </clause>

  <clause id="14701">
    <literal><![CDATA[
      R(x,x \ y,x) = R(x,x * y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,14655,a(flip),b,14700,a)].">
      <j1 rule="hyper" parents="65 14655 14700"/>
    </justification>
  </clause>

  <clause id="14702">
    <literal><![CDATA[
      R(x,x * y,x) = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,4343,a(flip),b,14701,a),flip(a)].">
      <j1 rule="hyper" parents="65 4343 14701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14703">
    <literal><![CDATA[
      K(x,K(y,z * (1 / u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z / u)) = w
    ]]></literal>
    <justification jstring="[para(5639(a,2),14627(a,1,2))].">
      <j1 rule="para" parents="5639 14627"/>
    </justification>
  </clause>

  <clause id="14704">
    <literal><![CDATA[
      L(x,y,z) = (z * (y * x)) / T(z * y,x)
    ]]></literal>
    <justification jstring="[hyper(7232,a,14641,a),flip(a)].">
      <j1 rule="hyper" parents="7232 14641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14705">
    <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(8101(a,1),14704(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="8101 14704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14706">
    <literal><![CDATA[
      T(x / y,(x / y) * x) = T(y \ x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(14135,a,14691,a),flip(a)].">
      <j1 rule="hyper" parents="14135 14691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14707">
    <literal><![CDATA[
      L(x / y,x,x / y) * x = x * T(y \ x,x \ y)
    ]]></literal>
    <justification jstring="[para(14706(a,1),788(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14706 788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14708">
    <literal><![CDATA[
      T(x * T(y \ x,x \ y),x / y) = x * (x / y)
    ]]></literal>
    <justification jstring="[para(14707(a,1),4351(a,1,1))].">
      <j1 rule="para" parents="14707 4351"/>
    </justification>
  </clause>

  <clause id="14709">
    <literal><![CDATA[
      T(x / (x \ y),x / y) = x * (x / y)
    ]]></literal>
    <justification jstring="[para(10420(a,1),14708(a,1,1))].">
      <j1 rule="para" parents="10420 14708"/>
    </justification>
  </clause>

  <clause id="14710">
    <literal><![CDATA[
      x \ ((y * y) * K(z,u)) = (x \ (y * y)) * K(z,u)
    ]]></literal>
    <justification jstring="[para(464(a,1),14225(a,1,1)),flip(a)].">
      <j1 rule="para" parents="464 14225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14711">
    <literal><![CDATA[
      (x * x) \ ((y \ (x * x)) * K(z,u)) = T(y,x * x) \ K(z,u)
    ]]></literal>
    <justification jstring="[para(14710(a,1),2127(a,1,2))].">
      <j1 rule="para" parents="14710 2127"/>
    </justification>
  </clause>

  <clause id="14712">
    <literal><![CDATA[
      (K(x,T(y,z)) * z) * (1 / z) = (z \ K(x,y)) * z
    ]]></literal>
    <justification jstring="[para(8832(a,1),14244(a,1,1,1))].">
      <j1 rule="para" parents="8832 14244"/>
    </justification>
  </clause>

  <clause id="14713">
    <literal><![CDATA[
      K(x,T(y,z)) * (z \ 1) = z \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(1090,a,14712,a)].">
      <j1 rule="hyper" parents="1090 14712"/>
    </justification>
  </clause>

  <clause id="14714">
    <literal><![CDATA[
      L(x,y * ((z * u) / z),w) = L(x,y * (u * K(u,z)),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,5479,a(flip),b,14251,a)].">
      <j1 rule="hyper" parents="65 5479 14251"/>
    </justification>
  </clause>

  <clause id="14715">
    <literal><![CDATA[
      K(T((x \ 1) \ 1,y) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(T(x,y) * z,u) = w
    ]]></literal>
    <justification jstring="[para(14260(a,2),14554(a,1))].">
      <j1 rule="para" parents="14260 14554"/>
    </justification>
  </clause>

  <clause id="14716">
    <literal><![CDATA[
      T(x,((y * y) / z) * u) = T(x,(y * y) * (z \ u))
    ]]></literal>
    <justification jstring="[para(623(a,1),14298(a,1,2,1))].">
      <j1 rule="para" parents="623 14298"/>
    </justification>
  </clause>

  <clause id="14717">
    <literal><![CDATA[
      T(x,((y * y) / z) * u) = T(x,y * (y * (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(299,a,14216,a(flip),b,14716,a),flip(a)].">
      <j1 rule="hyper" parents="299 14216 14716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14718">
    <literal><![CDATA[
      T(x,T(y,z \ u) * (u \ z)) = T(x,(u \ z) * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,14478,a(flip),b,14300,a)].">
      <j1 rule="hyper" parents="65 14478 14300"/>
    </justification>
  </clause>

  <clause id="14719">
    <literal><![CDATA[
      T(x,T(y,z) * ((u * z) \ u)) = T(x,((u * z) \ u) * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),14718(a,1,2,1,2))].">
      <j1 rule="para" parents="9 14718"/>
    </justification>
  </clause>

  <clause id="14720">
    <literal><![CDATA[
      T(x,T(y,z) * (z \ 1)) = T(x,(z \ 1) * y)
    ]]></literal>
    <justification jstring="[para(67(a,1),14718(a,1,2,1,2))].">
      <j1 rule="para" parents="67 14718"/>
    </justification>
  </clause>

  <clause id="14721">
    <literal><![CDATA[
      T(T(x,K(y,(y \ 1) \ (y \ z))),(y \ 1) * ((y \ 1) \ (y \ z))) = T(x,y \ (1 * T(1 \ z,y)))
    ]]></literal>
    <justification jstring="[hyper(65,a,13612,a(flip),b,14720,a),flip(a)].">
      <j1 rule="hyper" parents="65 13612 14720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14722">
    <literal><![CDATA[
      K(x,(y * y) * ((z \ 1) * u)) = K(x,(z / (y * y)) \ u)
    ]]></literal>
    <justification jstring="[para(33(a,1),14339(a,1,2))].">
      <j1 rule="para" parents="33 14339"/>
    </justification>
  </clause>

  <clause id="14723">
    <literal><![CDATA[
      K(x,y \ ((y * (y * z)) * u)) = K(x,y * (L(z,y,y) * u))
    ]]></literal>
    <justification jstring="[para(475(a,1),14340(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="475 14340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14724">
    <literal><![CDATA[
      K(x,y * (((1 / y) * y) * (z * ((y * y) \ u)))) = K(x,y \ (T(z,y \ (y \ 1)) * u))
    ]]></literal>
    <justification jstring="[para(1238(a,1),14340(a,2,2,2))].">
      <j1 rule="para" parents="1238 14340"/>
    </justification>
  </clause>

  <clause id="14725">
    <literal><![CDATA[
      K((x * x) * ((y \ 1) * z),u) = K((y / (x * x)) \ z,u)
    ]]></literal>
    <justification jstring="[para(33(a,1),14351(a,1,1))].">
      <j1 rule="para" parents="33 14351"/>
    </justification>
  </clause>

  <clause id="14726">
    <literal><![CDATA[
      T((x \ 1) * y,x \ (x \ 1)) = x * (y * (x \ (1 / x)))
    ]]></literal>
    <justification jstring="[para(9(a,1),14375(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 14375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14727">
    <literal><![CDATA[
      (1 / x) * T(x \ ((x \ 1) \ y),z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(14344,a,14404,a),flip(a)].">
      <j1 rule="hyper" parents="14344 14404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14729">
    <literal><![CDATA[
      (x \ (x \ y)) * ((x \ 1) \ 1) = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,4093,a(flip),b,14727,a)].">
      <j1 rule="hyper" parents="65 4093 14727"/>
    </justification>
  </clause>

  <clause id="14730">
    <literal><![CDATA[
      x \ (T(y,z \ (z \ 1)) * x) = T(y,z \ (z \ x))
    ]]></literal>
    <justification jstring="[para(1238(a,1),14443(a,1,2))].">
      <j1 rule="para" parents="1238 14443"/>
    </justification>
  </clause>

  <clause id="14731">
    <literal><![CDATA[
      T(T(x,y \ (y \ 1)),z) = T(x,y \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(318,a,14730,a)].">
      <j1 rule="hyper" parents="318 14730"/>
    </justification>
  </clause>

  <clause id="14732">
    <literal><![CDATA[
      T(T(x,y),z \ (z \ 1)) = T(x,z \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(861,a,14731,a)].">
      <j1 rule="hyper" parents="861 14731"/>
    </justification>
  </clause>

  <clause id="14733">
    <literal><![CDATA[
      T(x,y \ (y \ 1)) = T(x,y \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(860,a,14731,a)].">
      <j1 rule="hyper" parents="860 14731"/>
    </justification>
  </clause>

  <clause id="14734">
    <literal><![CDATA[
      T((x * y) / x,z \ (z \ x)) = T(y,z \ (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(757,a,14731,a),flip(a)].">
      <j1 rule="hyper" parents="757 14731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14735">
    <literal><![CDATA[
      T((x * y) / x,z \ (z \ x)) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z \ (z \ 1)) = u
    ]]></literal>
    <justification jstring="[para(14731(a,1),757(a,1))].">
      <j1 rule="para" parents="14731 757"/>
    </justification>
  </clause>

  <clause id="14736">
    <literal><![CDATA[
      T(x,y \ (y \ x)) = x * K(y * y,x)
    ]]></literal>
    <justification jstring="[hyper(6088,a,14733,a),flip(a)].">
      <j1 rule="hyper" parents="6088 14733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14737">
    <literal><![CDATA[
      K(x \ (x \ 1),y) * (y \ z) = T(y,x \ (x \ y)) \ z
    ]]></literal>
    <justification jstring="[para(14733(a,1),5383(a,2,1))].">
      <j1 rule="para" parents="14733 5383"/>
    </justification>
  </clause>

  <clause id="14738">
    <literal><![CDATA[
      T(T(x,y \ (y \ x)),z) = T(x,y \ (y \ z))
    ]]></literal>
    <justification jstring="[para(14733(a,1),14731(a,1,1))].">
      <j1 rule="para" parents="14733 14731"/>
    </justification>
  </clause>

  <clause id="14739">
    <literal><![CDATA[
      K(x,y \ (y \ x)) = K(y * y,x)
    ]]></literal>
    <justification jstring="[hyper(5154,a,14736,a)].">
      <j1 rule="hyper" parents="5154 14736"/>
    </justification>
  </clause>

  <clause id="14740">
    <literal><![CDATA[
      T(x,y \ (y \ x)) \ z = K(x,y * y) * (x \ z)
    ]]></literal>
    <justification jstring="[para(14736(a,2),5695(a,1,1))].">
      <j1 rule="para" parents="14736 5695"/>
    </justification>
  </clause>

  <clause id="14741">
    <literal><![CDATA[
      L(x,y,T(T(z,u \ (u \ z)),w)) = L(x,y,T(z,w))
    ]]></literal>
    <justification jstring="[para(14736(a,2),5473(a,1,3,1))].">
      <j1 rule="para" parents="14736 5473"/>
    </justification>
  </clause>

  <clause id="14742">
    <literal><![CDATA[
      T(T(x,y),z \ (u \ ((u * z) \ 1))) = T(x,(u * z) \ ((u * z) \ y))
    ]]></literal>
    <justification jstring="[para(956(a,1),14732(a,1,2))].">
      <j1 rule="para" parents="956 14732"/>
    </justification>
  </clause>

  <clause id="14743">
    <literal><![CDATA[
      T(T(x,y \ (y \ z)),u) = T(T(x,z),y \ (y \ u))
    ]]></literal>
    <justification jstring="[para(14732(a,1),14731(a,1,1))].">
      <j1 rule="para" parents="14732 14731"/>
    </justification>
  </clause>

  <clause id="14744">
    <literal><![CDATA[
      T((x * y) / x,x \ 1) = T(y,x \ (x \ 1))
    ]]></literal>
    <justification jstring="[para(68(a,1),14734(a,1,2,2))].">
      <j1 rule="para" parents="68 14734"/>
    </justification>
  </clause>

  <clause id="14745">
    <literal><![CDATA[
      K(x \ (x \ y),y) = K(y,x * x)
    ]]></literal>
    <justification jstring="[hyper(5525,a,14740,a)].">
      <j1 rule="hyper" parents="5525 14740"/>
    </justification>
  </clause>

  <clause id="14747">
    <literal><![CDATA[
      L(x,y,T(z,u \ (u \ w))) = L(x,y,T(z,w))
    ]]></literal>
    <justification jstring="[para(14738(a,1),14741(a,1,3))].">
      <j1 rule="para" parents="14738 14741"/>
    </justification>
  </clause>

  <clause id="14748">
    <literal><![CDATA[
      L(x,y,T(z,u \ w)) = L(x,y,T(z,u * w))
    ]]></literal>
    <justification jstring="[para(9(a,1),14747(a,1,3,2,2))].">
      <j1 rule="para" parents="9 14747"/>
    </justification>
  </clause>

  <clause id="14749">
    <literal><![CDATA[
      L(x,y,(z \ 1) * ((((z \ 1) \ 1) \ u) / (z \ 1))) = L(x,y,T(T(u,z) / z,z * 1))
    ]]></literal>
    <justification jstring="[hyper(65,a,6616,a,b,14748,a)].">
      <j1 rule="hyper" parents="65 6616 14748"/>
    </justification>
  </clause>

  <clause id="14750">
    <literal><![CDATA[
      T(T(x,y * z),y \ (y \ u)) = T(T(x,y \ z),u)
    ]]></literal>
    <justification jstring="[para(9(a,1),14743(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 14743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14751">
    <literal><![CDATA[
      T(T(x,y),y \ (y \ z)) = T(T(x,y \ 1),z)
    ]]></literal>
    <justification jstring="[para(68(a,1),14743(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="68 14743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14752">
    <literal><![CDATA[
      T(T(x,y),z \ (z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ (z \ y)) = u
    ]]></literal>
    <justification jstring="[para(14743(a,1),196(a,1)),flip(b)].">
      <j1 rule="para" parents="14743 196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14753">
    <literal><![CDATA[
      T(T(x,a(y,y,z)),a(y,y,z) \ (a(y,y,z) \ u)) = T(x,u)
    ]]></literal>
    <justification jstring="[para(14438(a,1),14751(a,2,1))].">
      <j1 rule="para" parents="14438 14751"/>
    </justification>
  </clause>

  <clause id="14755">
    <literal><![CDATA[
      T(T(x,L(1 / y,z,u) * w),L(1 / y,z,u) \ (y * (L(y,z,u) \ y))) = T(T(x,L(1 / y,z,u) \ w),1)
    ]]></literal>
    <justification jstring="[para(6527(a,1),14750(a,1,2,2))].">
      <j1 rule="para" parents="6527 14750"/>
    </justification>
  </clause>

  <clause id="14756">
    <literal><![CDATA[
      T(T(x,T(y \ z,z \ y) * (z / y)),T(y \ z,z \ y) \ (T(y \ z,z \ y) \ u)) = T(T(x,(z / y) * (1 / (y \ z))),u)
    ]]></literal>
    <justification jstring="[para(11795(a,1),14750(a,2,1,2))].">
      <j1 rule="para" parents="11795 14750"/>
    </justification>
  </clause>

  <clause id="14757">
    <literal><![CDATA[
      T(T(x,(L(y,z,u) \ y) * w),(L(y,z,u) \ y) \ (y \ L(y,z,u))) = T(T(x,(L(y,z,u) \ y) \ w),1)
    ]]></literal>
    <justification jstring="[para(13004(a,1),14750(a,1,2,2))].">
      <j1 rule="para" parents="13004 14750"/>
    </justification>
  </clause>

  <clause id="14758">
    <literal><![CDATA[
      (x / y) * T(y \ 1,z) = x * (y \ T(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(5040(a,1),14448(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5040 14448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14759">
    <literal><![CDATA[
      x * (y \ T(y \ 1,y * x)) = (1 / y) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(65,a,14517,a(flip),b,14758,a),flip(a)].">
      <j1 rule="hyper" parents="65 14517 14758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14760">
    <literal><![CDATA[
      x * (y \ T(y \ 1,x * y)) = (1 / y) * (x / y)
    ]]></literal>
    <justification jstring="[para(6192(a,2),14759(a,1,2,2))].">
      <j1 rule="para" parents="6192 14759"/>
    </justification>
  </clause>

  <clause id="14761">
    <literal><![CDATA[
      (x \ T(x \ 1,y * x)) * R(y,x \ T(x \ 1,y * x),y) = T((1 / x) * (y / x),y)
    ]]></literal>
    <justification jstring="[para(14760(a,1),4341(a,2,1))].">
      <j1 rule="para" parents="14760 4341"/>
    </justification>
  </clause>

  <clause id="14762">
    <literal><![CDATA[
      T(x * K((1 / y) * (x / y),x),y \ T(y \ 1,x * y)) = R(x,y \ T(y \ 1,x * y),x)
    ]]></literal>
    <justification jstring="[para(14760(a,1),5674(a,1,1,2,1))].">
      <j1 rule="para" parents="14760 5674"/>
    </justification>
  </clause>

  <clause id="14763">
    <literal><![CDATA[
      T(x,(y / (1 / z)) / u) = T(x,(y / (z \ 1)) / u)
    ]]></literal>
    <justification jstring="[hyper(14594,a,14476,a),flip(a)].">
      <j1 rule="hyper" parents="14594 14476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14765">
    <literal><![CDATA[
      T(K(x,x \ y) / T(x,z),x) = K(x,x * y) / T(x,z)
    ]]></literal>
    <justification jstring="[hyper(7890,a,14599,a)].">
      <j1 rule="hyper" parents="7890 14599"/>
    </justification>
  </clause>

  <clause id="14766">
    <literal><![CDATA[
      T(x,y * (z \ (1 / z))) = T(x,z \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(65,a,14592,a(flip),b,14607,a),flip(a)].">
      <j1 rule="hyper" parents="65 14592 14607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14767">
    <literal><![CDATA[
      T(x,y * (z * (u \ (1 / u)))) = T(x,u \ (u \ (y * z)))
    ]]></literal>
    <justification jstring="[para(563(a,1),14766(a,1,2))].">
      <j1 rule="para" parents="563 14766"/>
    </justification>
  </clause>

  <clause id="14768">
    <literal><![CDATA[
      K(x,y * (((z * K(z * u,z)) \ w) \ K(z * K(z * u,z),u))) = K(x,y / (R(z,u,z) \ w))
    ]]></literal>
    <justification jstring="[para(5674(a,1),14647(a,2,2,2,1))].">
      <j1 rule="para" parents="5674 14647"/>
    </justification>
  </clause>

  <clause id="14769">
    <literal><![CDATA[
      K(x,y * ((z * u) \ (z * z))) = K(x,y / ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[hyper(299,a,5913,a(flip),b,14684,a),flip(a)].">
      <j1 rule="hyper" parents="299 5913 14684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14770">
    <literal><![CDATA[
      L(x,y * ((z * u) / z),w) = L(x,y * T(u,z),w)
    ]]></literal>
    <justification jstring="[para(5083(a,2),14714(a,2,2,2))].">
      <j1 rule="para" parents="5083 14714"/>
    </justification>
  </clause>

  <clause id="14771">
    <literal><![CDATA[
      L(x,y * T(z \ u,z),w) = L(x,y * (u / z),w)
    ]]></literal>
    <justification jstring="[para(10(a,1),14770(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 14770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14772">
    <literal><![CDATA[
      L(x,(y \ z) * z,u) = L(x,z * (z / y),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,14088,a(flip),b,14771,a)].">
      <j1 rule="hyper" parents="65 14088 14771"/>
    </justification>
  </clause>

  <clause id="14773">
    <literal><![CDATA[
      L(x,L(T(y \ z,y),(y \ z) \ z,(y \ z) \ z),u) = L(x,z * (z / (y \ z)),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,4471,a,b,14772,a)].">
      <j1 rule="hyper" parents="65 4471 14772"/>
    </justification>
  </clause>

  <clause id="14774">
    <literal><![CDATA[
      T(x,T(y,z) * ((y * z) \ y)) = T(x,y * (y / (y * z)))
    ]]></literal>
    <justification jstring="[hyper(299,a,13877,a(flip),b,14719,a),flip(a)].">
      <j1 rule="hyper" parents="299 13877 14719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14775">
    <literal><![CDATA[
      K(x,y * (y * ((z \ 1) * u))) = K(x,(z / (y * y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(14547,a,14722,a)].">
      <j1 rule="hyper" parents="14547 14722"/>
    </justification>
  </clause>

  <clause id="14776">
    <literal><![CDATA[
      K(x * (x * ((y \ 1) * z)),u) = K((y / (x * x)) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(14553,a,14725,a)].">
      <j1 rule="hyper" parents="14553 14725"/>
    </justification>
  </clause>

  <clause id="14777">
    <literal><![CDATA[
      K(x,x \ 1) * (y / (x * x)) = x * ((x \ y) * (x \ (1 / x)))
    ]]></literal>
    <justification jstring="[hyper(65,a,6586,a(flip),b,14726,a)].">
      <j1 rule="hyper" parents="65 6586 14726"/>
    </justification>
  </clause>

  <clause id="14778">
    <literal><![CDATA[
      T(R((x \ 1) * (((x \ 1) \ 1) \ y),z,u),x \ (x \ 1)) = x * ((((x \ 1) \ 1) \ R(y,z,u)) * (x \ (1 / x)))
    ]]></literal>
    <justification jstring="[para(2026(a,2),14726(a,1,1))].">
      <j1 rule="para" parents="2026 14726"/>
    </justification>
  </clause>

  <clause id="14779">
    <literal><![CDATA[
      K(x \ (x \ 1),y) = K(y,x * x)
    ]]></literal>
    <justification jstring="[hyper(37,a,14740,a(flip),b,14737,a),flip(a)].">
      <j1 rule="hyper" parents="37 14740 14737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14780">
    <literal><![CDATA[
      K(x,((y * z) \ (y * y)) * T(u,(y * z) \ (y * y))) = K(x,u / ((y \ 1) * z))
    ]]></literal>
    <justification jstring="[para(107(a,2),14769(a,1,2))].">
      <j1 rule="para" parents="107 14769"/>
    </justification>
  </clause>

  <clause id="14781">
    <literal><![CDATA[
      T(x,y * (y / (y * z))) = T(x,y * ((z * y) \ y))
    ]]></literal>
    <justification jstring="[para(11611(a,1),14774(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11611 14774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14782">
    <literal><![CDATA[
      K(x,y * (y * ((z \ 1) * u))) = K(x,(y * y) * (z \ u))
    ]]></literal>
    <justification jstring="[para(416(a,1),14775(a,2,2))].">
      <j1 rule="para" parents="416 14775"/>
    </justification>
  </clause>

  <clause id="14783">
    <literal><![CDATA[
      K(x * (x * ((y \ 1) * z)),u) = K((x * x) * (y \ z),u)
    ]]></literal>
    <justification jstring="[para(416(a,1),14776(a,2,1))].">
      <j1 rule="para" parents="416 14776"/>
    </justification>
  </clause>

  <clause id="14784">
    <literal><![CDATA[
      K(x * (x * ((L(x,y,z) \ 1) * u)),w) = K(L(x \ 1,y,z) \ u,w)
    ]]></literal>
    <justification jstring="[para(6493(a,1),14776(a,2,1,1))].">
      <j1 rule="para" parents="6493 14776"/>
    </justification>
  </clause>

  <clause id="14785">
    <literal><![CDATA[
      K(x,y * (y * ((z \ 1) * u))) = K(x,y * (y * (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(299,a,14201,a(flip),b,14782,a),flip(a)].">
      <j1 rule="hyper" parents="299 14201 14782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14787">
    <literal><![CDATA[
      K(x * (x * ((y \ 1) * z)),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x * (x * (y \ z)),u) = w
    ]]></literal>
    <justification jstring="[para(14783(a,2),14553(a,1))].">
      <j1 rule="para" parents="14783 14553"/>
    </justification>
  </clause>

  <clause id="14788">
    <literal><![CDATA[
      K(x,y * (y * ((1 / z) \ u))) = K(x,y * (y * (z * u)))
    ]]></literal>
    <justification jstring="[para(79(a,1),14785(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="79 14785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14789">
    <literal><![CDATA[
      L(x \ (y * K(z,u)),x,y) = ((1 / y) * x) \ K(z,u)
    ]]></literal>
    <justification jstring="[hyper(2501,a,14221,a)].">
      <j1 rule="hyper" parents="2501 14221"/>
    </justification>
  </clause>

  <clause id="14790">
    <literal><![CDATA[
      T(x,y * ((z * z) \ (u / y))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(z \ (z \ u),y)) = w
    ]]></literal>
    <justification jstring="[para(13273(a,2),14293(a,1))].">
      <j1 rule="para" parents="13273 14293"/>
    </justification>
  </clause>

  <clause id="14791">
    <literal><![CDATA[
      K(x,L(y \ T(y * z,y \ 1),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(((y \ 1) \ z) / y,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(1106(a,2),14646(a,1,2,1))].">
      <j1 rule="para" parents="1106 14646"/>
    </justification>
  </clause>

  <clause id="14792">
    <literal><![CDATA[
      K(x,L(y * (z \ K(z,u)),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y / ((u * z) / u),w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(5182(a,1),14646(a,1,2,1,2))].">
      <j1 rule="para" parents="5182 14646"/>
    </justification>
  </clause>

  <clause id="14793">
    <literal><![CDATA[
      K(x,L(y * (K(z,y) * (u \ 1)),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L((y * K(z,y)) / u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(5488(a,1),14646(a,1,2,1))].">
      <j1 rule="para" parents="5488 14646"/>
    </justification>
  </clause>

  <clause id="14794">
    <literal><![CDATA[
      K(x,L(((y \ 1) \ z) * (1 / y),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(((1 / y) \ z) / y,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(11470(a,1),14646(a,1,2,1))].">
      <j1 rule="para" parents="11470 14646"/>
    </justification>
  </clause>

  <clause id="14795">
    <literal><![CDATA[
      K(x,L(y / (z \ K(u,w)),v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y * (K(w,u) * z),v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(14218(a,1),14650(a,1,2,1,2))].">
      <j1 rule="para" parents="14218 14650"/>
    </justification>
  </clause>

  <clause id="14796">
    <literal><![CDATA[
      T((x * y) / x,(z \ x) \ T(z,z \ x)) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,(z \ x) \ ((z \ x) \ 1)) = u
    ]]></literal>
    <justification jstring="[para(108(a,2),14735(a,1,2,2))].">
      <j1 rule="para" parents="108 14735"/>
    </justification>
  </clause>

  <clause id="14797">
    <literal><![CDATA[
      T(((x \ 1) * y) / (x \ 1),(z * (1 / x)) \ ((z * (x \ 1)) \ (1 / x))) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,(z * (1 / x)) \ ((z * (1 / x)) \ 1)) = u
    ]]></literal>
    <justification jstring="[para(3374(a,1),14735(a,1,2,2))].">
      <j1 rule="para" parents="3374 14735"/>
    </justification>
  </clause>

  <clause id="14798">
    <literal><![CDATA[
      K(x,y * (L(z,u,w) \ (z * z))) = K(x,y / L(z \ 1,u,w))
    ]]></literal>
    <justification jstring="[hyper(299,a,5752,a(flip),b,14287,a),flip(a)].">
      <j1 rule="hyper" parents="299 5752 14287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14799">
    <literal><![CDATA[
      K(x,y \ (T(z,z \ u) * w)) = K(x,y \ (T(z,u) * w))
    ]]></literal>
    <justification jstring="[hyper(299,a,14246,a(flip),b,14336,a),flip(a)].">
      <j1 rule="hyper" parents="299 14246 14336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14801">
    <literal><![CDATA[
      K(x,y \ (z * T(u / w,u))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (z * (w \ u))) = v5
    ]]></literal>
    <justification jstring="[para(14337(a,2),14281(a,1))].">
      <j1 rule="para" parents="14337 14281"/>
    </justification>
  </clause>

  <clause id="14802">
    <literal><![CDATA[
      K(x,y \ (T(z / u,z) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ ((u \ z) * w)) = v5
    ]]></literal>
    <justification jstring="[para(14338(a,2),14281(a,1))].">
      <j1 rule="para" parents="14338 14281"/>
    </justification>
  </clause>

  <clause id="14803">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ y,x) = (x \ y) * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,7105,a(flip),b,14365,a)].">
      <j1 rule="hyper" parents="65 7105 14365"/>
    </justification>
  </clause>

  <clause id="14804">
    <literal><![CDATA[
      (x \ y) * T(x,x \ 1) = x \ T(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(1140,a,14803,a),flip(a)].">
      <j1 rule="hyper" parents="1140 14803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14805">
    <literal><![CDATA[
      x \ T(x * ((1 / x) \ y),x) = ((1 / x) \ (x \ y)) * x
    ]]></literal>
    <justification jstring="[hyper(65,a,6065,a(flip),b,14804,a),flip(a)].">
      <j1 rule="hyper" parents="65 6065 14804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14806">
    <literal><![CDATA[
      x \ T((x * x) * y,x) = ((1 / x) \ (x \ y)) * x
    ]]></literal>
    <justification jstring="[para(442(a,1),14805(a,1,2,1))].">
      <j1 rule="para" parents="442 14805"/>
    </justification>
  </clause>

  <clause id="14807">
    <literal><![CDATA[
      x \ T((x * x) * y,x) = (x \ ((x \ 1) \ y)) * x
    ]]></literal>
    <justification jstring="[para(729(a,1),14806(a,2,1))].">
      <j1 rule="para" parents="729 14806"/>
    </justification>
  </clause>

  <clause id="14808">
    <literal><![CDATA[
      x \ T((x * x) * y,x) = (x \ 1) \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,2045,a(flip),b,14807,a),flip(a)].">
      <j1 rule="hyper" parents="299 2045 14807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14809">
    <literal><![CDATA[
      (x \ (1 / x)) * T(((1 / x) \ 1) * (x \ y),x * x) = T((1 / ((1 / x) \ x)) * y,(1 / x) \ x)
    ]]></literal>
    <justification jstring="[para(14367(a,2),3139(a,1,2))].">
      <j1 rule="para" parents="14367 3139"/>
    </justification>
  </clause>

  <clause id="14810">
    <literal><![CDATA[
      K(x,((1 / y) \ z) * u) = K(x,((y \ 1) \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,14302,a(flip),b,14373,a),flip(a)].">
      <j1 rule="hyper" parents="65 14302 14373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14811">
    <literal><![CDATA[
      T(x,((L(y,z,u) \ 1) * y) * w) = T(x,(y \ L(y,z,u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,3879,a(flip),b,14384,a)].">
      <j1 rule="hyper" parents="65 3879 14384"/>
    </justification>
  </clause>

  <clause id="14812">
    <literal><![CDATA[
      T(x * (y \ 1),y * y) = (1 / y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(71(a,1),14493(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="71 14493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14813">
    <literal><![CDATA[
      K(K(x,y) * K(x,z),K(z,x) * K(y,x)) = 1
    ]]></literal>
    <justification jstring="[hyper(57,a,14582,a)].">
      <j1 rule="hyper" parents="57 14582"/>
    </justification>
  </clause>

  <clause id="14814">
    <literal><![CDATA[
      K(((x \ 1) \ K(y,x)) \ T(x,z),T(x,z) \ ((x \ 1) \ K(y,x))) = 1
    ]]></literal>
    <justification jstring="[hyper(65,a,13042,a,b,14813,a)].">
      <j1 rule="hyper" parents="65 13042 14813"/>
    </justification>
  </clause>

  <clause id="14815">
    <literal><![CDATA[
      K(K(x,y) * K(x,z),(K(x,y) * K(x,z)) \ 1) = 1
    ]]></literal>
    <justification jstring="[para(9426(a,2),14813(a,1,2))].">
      <j1 rule="para" parents="9426 14813"/>
    </justification>
  </clause>

  <clause id="14816">
    <literal><![CDATA[
      K((K(x,y) * K(x,z)) \ 1,K(x,y) * K(x,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(2606,a,14815,a)].">
      <j1 rule="hyper" parents="2606 14815"/>
    </justification>
  </clause>

  <clause id="14817">
    <literal><![CDATA[
      L(x * 1,K(y,z) * K(y,u),(K(y,z) * K(y,u)) \ 1) = ((K(y,z) * K(y,u)) \ 1) * ((K(y,z) * K(y,u)) * x)
    ]]></literal>
    <justification jstring="[para(14816(a,1),3800(a,1,1,2))].">
      <j1 rule="para" parents="14816 3800"/>
    </justification>
  </clause>

  <clause id="14818">
    <literal><![CDATA[
      L(x,y,(z * K(u,z)) * w) = L(x,y,z * (w * K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,5712,a(flip),b,14613,a)].">
      <j1 rule="hyper" parents="65 5712 14613"/>
    </justification>
  </clause>

  <clause id="14819">
    <literal><![CDATA[
      L(x,y,z * (K(u,z) * w)) = L(x,y,z * (w * K(z,u)))
    ]]></literal>
    <justification jstring="[para(5488(a,1),14818(a,1,3))].">
      <j1 rule="para" parents="5488 14818"/>
    </justification>
  </clause>

  <clause id="14820">
    <literal><![CDATA[
      (x \ (y * z)) * K(y \ (y * z),y) = x \ (z * y)
    ]]></literal>
    <justification jstring="[para(11346(a,1),14635(a,1,2))].">
      <j1 rule="para" parents="11346 14635"/>
    </justification>
  </clause>

  <clause id="14821">
    <literal><![CDATA[
      (x \ (y * z)) * K(z,y) = x \ (z * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),14820(a,1,2,1))].">
      <j1 rule="para" parents="9 14820"/>
    </justification>
  </clause>

  <clause id="14823">
    <literal><![CDATA[
      R(x,y,z) \ (z * (x * y)) = (y * z) * K(z,x * y)
    ]]></literal>
    <justification jstring="[para(182(a,1),14821(a,1,1)),flip(a)].">
      <j1 rule="para" parents="182 14821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14824">
    <literal><![CDATA[
      ((x * y) / z) \ (y * x) != u
    ]]></literal>
    <literal><![CDATA[
      z * K(y,x) = u
    ]]></literal>
    <justification jstring="[para(14821(a,1),657(a,1))].">
      <j1 rule="para" parents="14821 657"/>
    </justification>
  </clause>

  <clause id="14827">
    <literal><![CDATA[
      R(x,y,z) \ (z * (x * y)) = y * T(z,x * y)
    ]]></literal>
    <justification jstring="[hyper(299,a,6832,a(flip),b,14823,a),flip(a)].">
      <j1 rule="hyper" parents="299 6832 14823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14828">
    <literal><![CDATA[
      R(x,y,z) = (z * (x * y)) / (y * T(z,x * y))
    ]]></literal>
    <justification jstring="[hyper(192,a,14827,a),flip(a)].">
      <j1 rule="hyper" parents="192 14827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14829">
    <literal><![CDATA[
      K(x,T((y \ 1) \ z,u)) = K(x,T(y * z,u))
    ]]></literal>
    <justification jstring="[hyper(14222,a,14681,a),flip(a)].">
      <j1 rule="hyper" parents="14222 14681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14830">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ x) = K(x,T(y * x,z))
    ]]></literal>
    <justification jstring="[hyper(8968,a,14829,a)].">
      <j1 rule="hyper" parents="8968 14829"/>
    </justification>
  </clause>

  <clause id="14831">
    <literal><![CDATA[
      K(x,1 \ (((y * T(z,u)) \ y) * x)) = K(x,T(((y * z) \ y) * x,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,13029,a(flip),b,14829,a)].">
      <j1 rule="hyper" parents="65 13029 14829"/>
    </justification>
  </clause>

  <clause id="14832">
    <literal><![CDATA[
      K(x,L(T(y,z \ 1) * z,u,w)) = K(x,L((1 / z) \ y,u,w))
    ]]></literal>
    <justification jstring="[para(3733(a,1),14689(a,1,2,1,1))].">
      <j1 rule="para" parents="3733 14689"/>
    </justification>
  </clause>

  <clause id="14833">
    <literal><![CDATA[
      ((x * x) \ (y \ (x * x))) * K(z,u) = T(y,x * x) \ K(z,u)
    ]]></literal>
    <justification jstring="[hyper(668,a,14711,a)].">
      <j1 rule="hyper" parents="668 14711"/>
    </justification>
  </clause>

  <clause id="14834">
    <literal><![CDATA[
      K(x,x \ 1) * (y / (x * x)) = y * (x \ (1 / x))
    ]]></literal>
    <justification jstring="[hyper(299,a,1046,a(flip),b,14777,a),flip(a)].">
      <j1 rule="hyper" parents="299 1046 14777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14835">
    <literal><![CDATA[
      (K(x \ 1,x) * y) * (x \ (1 / x)) = y / (x * x)
    ]]></literal>
    <justification jstring="[hyper(2792,a,14834,a)].">
      <j1 rule="hyper" parents="2792 14834"/>
    </justification>
  </clause>

  <clause id="14837">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (x \ (1 / x))) = y / (x * x)
    ]]></literal>
    <justification jstring="[hyper(2842,a,14835,a)].">
      <j1 rule="hyper" parents="2842 14835"/>
    </justification>
  </clause>

  <clause id="14838">
    <literal><![CDATA[
      K(x,x \ 1) * ((y \ z) * (x \ (1 / x))) = y \ (z / (x * x))
    ]]></literal>
    <justification jstring="[hyper(299,a,1771,a(flip),b,14837,a),flip(a)].">
      <j1 rule="hyper" parents="299 1771 14837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14839">
    <literal><![CDATA[
      K(x,y * (z * (L(z,u,w) \ z))) = K(x,y / L(z \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(1352(a,1),14798(a,1,2,2))].">
      <j1 rule="para" parents="1352 14798"/>
    </justification>
  </clause>

  <clause id="14840">
    <literal><![CDATA[
      T(x,(y * (L(y,z,u) \ 1)) * w) = T(x,(y \ L(y,z,u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,12054,a(flip),b,14811,a)].">
      <j1 rule="hyper" parents="65 12054 14811"/>
    </justification>
  </clause>

  <clause id="14841">
    <literal><![CDATA[
      T(x \ 1,y * y) * K(z,u) = T(x,y * y) \ K(z,u)
    ]]></literal>
    <justification jstring="[para(461(a,1),14833(a,1,1))].">
      <j1 rule="para" parents="461 14833"/>
    </justification>
  </clause>

  <clause id="14842">
    <literal><![CDATA[
      T(x \ 1,y * y) = T(x,y * y) \ 1
    ]]></literal>
    <justification jstring="[hyper(37,a,14185,a,b,14841,a),flip(a)].">
      <j1 rule="hyper" parents="37 14185 14841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14843">
    <literal><![CDATA[
      L(x,y,T(z,u * u) * (T(z \ 1,u * u) \ w)) = L(x,y,w)
    ]]></literal>
    <justification jstring="[para(14842(a,2),2468(a,1,3,2,1))].">
      <j1 rule="para" parents="14842 2468"/>
    </justification>
  </clause>

  <clause id="14844">
    <literal><![CDATA[
      x * T(x \ 1,y * y) = K(y * y,x)
    ]]></literal>
    <justification jstring="[para(14842(a,2),5034(a,2,2)),flip(a)].">
      <j1 rule="para" parents="14842 5034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14845">
    <literal><![CDATA[
      K(x \ 1,y * y) = K(y * y,x)
    ]]></literal>
    <justification jstring="[hyper(5300,a,14844,a)].">
      <j1 rule="hyper" parents="5300 14844"/>
    </justification>
  </clause>

  <clause id="14846">
    <literal><![CDATA[
      K(x * x,y \ 1) = K(y,x * x)
    ]]></literal>
    <justification jstring="[hyper(5318,a,14845,a),flip(a)].">
      <j1 rule="hyper" parents="5318 14845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14847">
    <literal><![CDATA[
      a(x,y,z * K(z,u * u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(14846(a,1),6611(a,1,3,2))].">
      <j1 rule="para" parents="14846 6611"/>
    </justification>
  </clause>

  <clause id="14848">
    <literal><![CDATA[
      a(x,y,T(z,u * u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(5083(a,2),14847(a,1,3))].">
      <j1 rule="para" parents="5083 14847"/>
    </justification>
  </clause>

  <clause id="14849">
    <literal><![CDATA[
      a(x,y,(z \ 1) * T(u,z)) = a(x,y,u * (1 / z))
    ]]></literal>
    <justification jstring="[para(7105(a,1),14848(a,1,3))].">
      <j1 rule="para" parents="7105 14848"/>
    </justification>
  </clause>

  <clause id="14850">
    <literal><![CDATA[
      a(x,y,z * T(u,z)) = a(x,y,u * (1 / z))
    ]]></literal>
    <justification jstring="[hyper(65,a,2369,a(flip),b,14849,a)].">
      <j1 rule="hyper" parents="65 2369 14849"/>
    </justification>
  </clause>

  <clause id="14851">
    <literal><![CDATA[
      a(x,y,z * (1 / u)) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(107(a,1),14850(a,1,3)),flip(a)].">
      <j1 rule="para" parents="107 14850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14852">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ y) * (x \ (1 / x)) = x \ (y / (x * x))
    ]]></literal>
    <justification jstring="[hyper(36,a,2706,a,b,14838,a),flip(a)].">
      <j1 rule="hyper" parents="36 2706 14838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14853">
    <literal><![CDATA[
      K(x,y / L(z \ 1,u,u)) = K(x,y * (z * a(u,u,z)))
    ]]></literal>
    <justification jstring="[para(1986(a,1),14839(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="1986 14839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14854">
    <literal><![CDATA[
      L(x,y,z * (T(z \ 1,u * u) \ w)) = L(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,2897,a(flip),b,14843,a)].">
      <j1 rule="hyper" parents="65 2897 14843"/>
    </justification>
  </clause>

  <clause id="14856">
    <literal><![CDATA[
      L(x,y,K(z * z,u \ 1) * w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,5390,a(flip),b,14854,a)].">
      <j1 rule="hyper" parents="65 5390 14854"/>
    </justification>
  </clause>

  <clause id="14858">
    <literal><![CDATA[
      L(x,y,K(z,u * u) * w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[para(14846(a,1),14856(a,1,3,1))].">
      <j1 rule="para" parents="14846 14856"/>
    </justification>
  </clause>

  <clause id="14859">
    <literal><![CDATA[
      K(x,y \ ((1 / z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ ((z \ 1) * u)) = w
    ]]></literal>
    <justification jstring="[para(193(a,1),14802(a,1,2,2,1))].">
      <j1 rule="para" parents="193 14802"/>
    </justification>
  </clause>

  <clause id="14860">
    <literal><![CDATA[
      a(K(x,y),z,u) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,10567,a(flip),b,14167,a),flip(a)].">
      <j1 rule="hyper" parents="65 10567 14167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14861">
    <literal><![CDATA[
      K(x,x * a(y,z,u)) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,14161,a,b,14860,a)].">
      <j1 rule="hyper" parents="65 14161 14860"/>
    </justification>
  </clause>

  <clause id="14862">
    <literal><![CDATA[
      a(L(K(x,y),K(y,x),K(y,x)),z,u) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,5294,a,b,14860,a)].">
      <j1 rule="hyper" parents="65 5294 14860"/>
    </justification>
  </clause>

  <clause id="14863">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,14164,a(flip),b,14860,a),flip(a)].">
      <j1 rule="hyper" parents="65 14164 14860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14864">
    <literal><![CDATA[
      (K(x,y) * (z * u)) * a(x,z,K(u,y)) = (K(x,y) * z) * u
    ]]></literal>
    <justification jstring="[para(14860(a,1),84(a,1,2))].">
      <j1 rule="para" parents="14860 84"/>
    </justification>
  </clause>

  <clause id="14865">
    <literal><![CDATA[
      a(K(x,T(y,z)),u,w) = a(T(x,z),u,K(w,y))
    ]]></literal>
    <justification jstring="[para(7537(a,1),14860(a,1,1))].">
      <j1 rule="para" parents="7537 14860"/>
    </justification>
  </clause>

  <clause id="14866">
    <literal><![CDATA[
      a(x,y,K(z,L(u,w,x))) = a(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(7843(a,1),14860(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7843 14860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14867">
    <literal><![CDATA[
      a(K(x,x \ (y \ z)),u,w) = a(x,u,K(w,(y * x) \ z))
    ]]></literal>
    <justification jstring="[para(11253(a,1),14860(a,1,1))].">
      <j1 rule="para" parents="11253 14860"/>
    </justification>
  </clause>

  <clause id="14868">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(y,x) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(11949,a,14863,a)].">
      <j1 rule="hyper" parents="11949 14863"/>
    </justification>
  </clause>

  <clause id="14869">
    <literal><![CDATA[
      a(K(x,y),z,u) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(299,a,14860,a,b,14863,a)].">
      <j1 rule="hyper" parents="299 14860 14863"/>
    </justification>
  </clause>

  <clause id="14870">
    <literal><![CDATA[
      L(K(x,y),z,u) * K(y,x) = a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,10541,a,b,14863,a)].">
      <j1 rule="hyper" parents="299 10541 14863"/>
    </justification>
  </clause>

  <clause id="14871">
    <literal><![CDATA[
      a(x,y,K(z,u)) = K(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,14162,a(flip),b,14863,a),flip(a)].">
      <j1 rule="hyper" parents="299 14162 14863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14872">
    <literal><![CDATA[
      a(x,y,K(y * x,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(299,a,11946,a(flip),b,14863,a),flip(a)].">
      <j1 rule="hyper" parents="299 11946 14863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14873">
    <literal><![CDATA[
      a(x,y,K(z * u,u)) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,12083,a,b,14863,a)].">
      <j1 rule="hyper" parents="65 12083 14863"/>
    </justification>
  </clause>

  <clause id="14874">
    <literal><![CDATA[
      K(x,y) * L(K(y,x),z,u) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,10536,a,b,14863,a)].">
      <j1 rule="hyper" parents="65 10536 14863"/>
    </justification>
  </clause>

  <clause id="14875">
    <literal><![CDATA[
      x * a(y,z,K(u,w)) = x * a(w,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,14863,a)].">
      <j1 rule="hyper" parents="60 14863"/>
    </justification>
  </clause>

  <clause id="14876">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = a(u,y,K(x,K(w,z)))
    ]]></literal>
    <justification jstring="[para(7984(a,1),14863(a,1,3))].">
      <j1 rule="para" parents="7984 14863"/>
    </justification>
  </clause>

  <clause id="14877">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = a(u,y,K(x,K(z,w)))
    ]]></literal>
    <justification jstring="[para(8001(a,1),14863(a,1,3))].">
      <j1 rule="para" parents="8001 14863"/>
    </justification>
  </clause>

  <clause id="14878">
    <literal><![CDATA[
      a(x,y,K(z,T(u,x) * w)) = a(z,y,K(u * w,x))
    ]]></literal>
    <justification jstring="[para(8584(a,1),14863(a,1,3)),flip(a)].">
      <j1 rule="para" parents="8584 14863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14879">
    <literal><![CDATA[
      K(x,y) * (L(K(y,x),z,u) * w) = a(y,z,K(u,x)) * w
    ]]></literal>
    <justification jstring="[para(14863(a,1),10548(a,2,1))].">
      <j1 rule="para" parents="14863 10548"/>
    </justification>
  </clause>

  <clause id="14880">
    <literal><![CDATA[
      x / a(y,z,K(u,w)) = x * a(w,z,K(u,y))
    ]]></literal>
    <justification jstring="[para(14863(a,2),10565(a,1,2))].">
      <j1 rule="para" parents="14863 10565"/>
    </justification>
  </clause>

  <clause id="14881">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ w = a(u,y,K(z,x)) * w
    ]]></literal>
    <justification jstring="[para(14863(a,2),10570(a,1,1))].">
      <j1 rule="para" parents="14863 10570"/>
    </justification>
  </clause>

  <clause id="14882">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u,y)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(14863(a,1),11896(a,1,2))].">
      <j1 rule="para" parents="14863 11896"/>
    </justification>
  </clause>

  <clause id="14883">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(u,y,z)) * K(u,x) = w
    ]]></literal>
    <justification jstring="[para(14863(a,1),11949(a,1))].">
      <j1 rule="para" parents="14863 11949"/>
    </justification>
  </clause>

  <clause id="14884">
    <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(14863(a,1),11950(a,1,2))].">
      <j1 rule="para" parents="14863 11950"/>
    </justification>
  </clause>

  <clause id="14885">
    <literal><![CDATA[
      L(K(x * y,z),x,y) = K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(54,a,14872,a)].">
      <j1 rule="hyper" parents="54 14872"/>
    </justification>
  </clause>

  <clause id="14886">
    <literal><![CDATA[
      L(K(x,y),z,u) \ K(x,y) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,10543,a,b,14869,a)].">
      <j1 rule="hyper" parents="299 10543 14869"/>
    </justification>
  </clause>

  <clause id="14887">
    <literal><![CDATA[
      x * a(K(y,z),u,w) = x * a(w,u,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,14869,a)].">
      <j1 rule="hyper" parents="60 14869"/>
    </justification>
  </clause>

  <clause id="14888">
    <literal><![CDATA[
      a(x,y,z) \ a(u,y,K(z,x)) = T(a(x,y,z),u) \ 1
    ]]></literal>
    <justification jstring="[hyper(119,a,14871,a,b,5034,a(flip))].">
      <j1 rule="hyper" parents="119 14871 5034"/>
    </justification>
  </clause>

  <clause id="14889">
    <literal><![CDATA[
      K(x,a(y,z,z \ 1)) = 1
    ]]></literal>
    <justification jstring="[hyper(65,a,6835,a(flip),b,14871,a),flip(a)].">
      <j1 rule="hyper" parents="65 6835 14871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14890">
    <literal><![CDATA[
      x * a(a(y,z,u) \ x,z,K(u,y)) = (a(y,z,u) \ x) * a(y,z,u)
    ]]></literal>
    <justification jstring="[para(14871(a,2),287(a,1,2))].">
      <j1 rule="para" parents="14871 287"/>
    </justification>
  </clause>

  <clause id="14891">
    <literal><![CDATA[
      a(x,y,K(z,u * (u * w))) = K(x,a(L(w,u,u),y,z))
    ]]></literal>
    <justification jstring="[para(2136(a,1),14871(a,2,2))].">
      <j1 rule="para" parents="2136 14871"/>
    </justification>
  </clause>

  <clause id="14892">
    <literal><![CDATA[
      L(x,y,a(y,z,K(u,w))) = x
    ]]></literal>
    <justification jstring="[para(14871(a,2),4570(a,1,3))].">
      <j1 rule="para" parents="14871 4570"/>
    </justification>
  </clause>

  <clause id="14893">
    <literal><![CDATA[
      x * a(x,y,K(z,u)) = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[para(14871(a,2),5083(a,2,2)),flip(a)].">
      <j1 rule="para" parents="14871 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14894">
    <literal><![CDATA[
      a(x,y,K(z,u)) * x = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[para(14871(a,2),5096(a,2,1)),flip(a)].">
      <j1 rule="para" parents="14871 5096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14895">
    <literal><![CDATA[
      (x * a(y,z,u)) / x = a(y,z,u) * a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[para(14871(a,2),5054(a,2,2))].">
      <j1 rule="para" parents="14871 5054"/>
    </justification>
  </clause>

  <clause id="14896">
    <literal><![CDATA[
      x * a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,a(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(14871(a,2),5087(a,1,2))].">
      <j1 rule="para" parents="14871 5087"/>
    </justification>
  </clause>

  <clause id="14898">
    <literal><![CDATA[
      (x * y) / ((a(z,u,w) * y) / a(z,u,w)) = x * a(y,u,K(w,z))
    ]]></literal>
    <justification jstring="[para(14871(a,2),9050(a,2,2))].">
      <j1 rule="para" parents="14871 9050"/>
    </justification>
  </clause>

  <clause id="14899">
    <literal><![CDATA[
      L(a(x,y,K(z,u)),w,v5) = K(x,L(a(u,y,z),w,v5))
    ]]></literal>
    <justification jstring="[para(14871(a,2),11889(a,1,1))].">
      <j1 rule="para" parents="14871 11889"/>
    </justification>
  </clause>

  <clause id="14900">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = K(z,K(x,a(w,y,u)))
    ]]></literal>
    <justification jstring="[para(14871(a,1),14162(a,2,2))].">
      <j1 rule="para" parents="14871 14162"/>
    </justification>
  </clause>

  <clause id="14901">
    <literal><![CDATA[
      T(x,a(y,z,z \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,14889,a)].">
      <j1 rule="hyper" parents="58 14889"/>
    </justification>
  </clause>

  <clause id="14902">
    <literal><![CDATA[
      T(x,a(y,z,z)) = x
    ]]></literal>
    <justification jstring="[para(2363(a,1),14901(a,1,2))].">
      <j1 rule="para" parents="2363 14901"/>
    </justification>
  </clause>

  <clause id="14904">
    <literal><![CDATA[
      a(x,y,y) * z = z * a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(2380,a,14902,a),flip(a)].">
      <j1 rule="hyper" parents="2380 14902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14905">
    <literal><![CDATA[
      T(a(x,y,y),z) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(56,a,14902,a)].">
      <j1 rule="hyper" parents="56 14902"/>
    </justification>
  </clause>

  <clause id="14906">
    <literal><![CDATA[
      T(x,a(y,z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(14902(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="14902 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14907">
    <literal><![CDATA[
      x / a(y,z,z) != u
    ]]></literal>
    <literal><![CDATA[
      a(y,z,z) \ x = u
    ]]></literal>
    <justification jstring="[para(14902(a,1),400(a,1))].">
      <j1 rule="para" parents="14902 400"/>
    </justification>
  </clause>

  <clause id="14908">
    <literal><![CDATA[
      L(a(x,y,y),z,u) * (u * z) = u * (z * a(x,y,y))
    ]]></literal>
    <justification jstring="[para(14905(a,1),681(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14905 681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14909">
    <literal><![CDATA[
      L(a(x,y,y),T(z,u),u) * (z * u) = u * (T(z,u) * a(x,y,y))
    ]]></literal>
    <justification jstring="[para(14905(a,1),1001(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14905 1001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14910">
    <literal><![CDATA[
      (x * a(y,z,z)) / (a(y,z,z) * T(x,u)) = K(u,x)
    ]]></literal>
    <justification jstring="[para(14904(a,2),5363(a,1,2))].">
      <j1 rule="para" parents="14904 5363"/>
    </justification>
  </clause>

  <clause id="14911">
    <literal><![CDATA[
      K(x * y,L(z,x,y)) = K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(11995,a,14885,a)].">
      <j1 rule="hyper" parents="11995 14885"/>
    </justification>
  </clause>

  <clause id="14912">
    <literal><![CDATA[
      a(x,y,K(z,u * x)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,14863,a(flip),b,14873,a)].">
      <j1 rule="hyper" parents="65 14863 14873"/>
    </justification>
  </clause>

  <clause id="14913">
    <literal><![CDATA[
      a(x,y,K(z,L(u,w,x))) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,14860,a(flip),b,14866,a),flip(a)].">
      <j1 rule="hyper" parents="299 14860 14866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14914">
    <literal><![CDATA[
      a(x,y,K(z,(x * u) \ w)) = a(x,y,K(z,u \ (x \ w)))
    ]]></literal>
    <justification jstring="[para(281(a,1),14913(a,1,3,2))].">
      <j1 rule="para" parents="281 14913"/>
    </justification>
  </clause>

  <clause id="14915">
    <literal><![CDATA[
      a(x,y,K(z,(x \ u) \ w)) = a(x,y,K(z,u \ (x * w)))
    ]]></literal>
    <justification jstring="[para(520(a,1),14913(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="520 14913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14916">
    <literal><![CDATA[
      a(x,y,K(z,(u * x) \ (x * w))) = a(x,y,K(z,T(u,x) \ w))
    ]]></literal>
    <justification jstring="[para(525(a,1),14913(a,1,3,2))].">
      <j1 rule="para" parents="525 14913"/>
    </justification>
  </clause>

  <clause id="14917">
    <literal><![CDATA[
      a(T(x,y),z,K(u,w)) = a(x,z,K(u,T(w,y)))
    ]]></literal>
    <justification jstring="[hyper(65,a,14860,a(flip),b,14865,a),flip(a)].">
      <j1 rule="hyper" parents="65 14860 14865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14918">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(z,y,K(u,x)) = w
    ]]></literal>
    <justification jstring="[para(14868(a,1),12004(a,1))].">
      <j1 rule="para" parents="14868 12004"/>
    </justification>
  </clause>

  <clause id="14920">
    <literal><![CDATA[
      a(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(14164(a,2),14918(a,1))].">
      <j1 rule="para" parents="14164 14918"/>
    </justification>
  </clause>

  <clause id="14921">
    <literal><![CDATA[
      a(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,z,K(y,x)) = w
    ]]></literal>
    <justification jstring="[para(14860(a,2),14918(a,1))].">
      <j1 rule="para" parents="14860 14918"/>
    </justification>
  </clause>

  <clause id="14922">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,y,K(x,z)) = w
    ]]></literal>
    <justification jstring="[para(14863(a,1),14918(a,1))].">
      <j1 rule="para" parents="14863 14918"/>
    </justification>
  </clause>

  <clause id="14925">
    <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(7984(a,1),14922(a,1,3))].">
      <j1 rule="para" parents="7984 14922"/>
    </justification>
  </clause>

  <clause id="14926">
    <literal><![CDATA[
      a(x,y,K(z \ (u / w),z)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(z,y,K(x,u / (z * w))) = v5
    ]]></literal>
    <justification jstring="[para(11575(a,1),14922(a,1,3))].">
      <j1 rule="para" parents="11575 14922"/>
    </justification>
  </clause>

  <clause id="14929">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(z,x) = L(K(z,x),y,u)
    ]]></literal>
    <justification jstring="[hyper(7207,a,14870,a)].">
      <j1 rule="hyper" parents="7207 14870"/>
    </justification>
  </clause>

  <clause id="14930">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = a(u,y,K(z,K(x,w)))
    ]]></literal>
    <justification jstring="[para(7989(a,1),14876(a,2,3))].">
      <j1 rule="para" parents="7989 14876"/>
    </justification>
  </clause>

  <clause id="14931">
    <literal><![CDATA[
      x \ (y * (a(z,u,K(w,v5)) * T(a(v5,u,K(w,z)) * (y \ x),v6))) = K((x \ (y * a(z,u,K(w,v5)))) \ 1,v6)
    ]]></literal>
    <justification jstring="[para(14881(a,1),5838(a,1,2,2,2,1))].">
      <j1 rule="para" parents="14881 5838"/>
    </justification>
  </clause>

  <clause id="14932">
    <literal><![CDATA[
      K(x,L(y,z * K(u,z),w)) = K(x,y) * a(x,T(z,u),K(w,y))
    ]]></literal>
    <justification jstring="[para(5538(a,2),14882(a,2,2)),flip(a)].">
      <j1 rule="para" parents="5538 14882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14933">
    <literal><![CDATA[
      K(x,T(y,z)) * a(x,u,K(y \ (w \ v5),T(y,z))) = K(x,L(T(y,z),u,(w * y) \ v5))
    ]]></literal>
    <justification jstring="[para(11971(a,1),14882(a,1,2,3))].">
      <j1 rule="para" parents="11971 14882"/>
    </justification>
  </clause>

  <clause id="14934">
    <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(14887(a,1),46(a,2))].">
      <j1 rule="para" parents="14887 46"/>
    </justification>
  </clause>

  <clause id="14935">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = K(u,K(x,a(w,y,z)))
    ]]></literal>
    <justification jstring="[para(7983(a,1),14900(a,1,3))].">
      <j1 rule="para" parents="7983 14900"/>
    </justification>
  </clause>

  <clause id="14936">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(z,x) = K(z,L(x,y,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,11889,a(flip),b,14929,a),flip(a)].">
      <j1 rule="hyper" parents="299 11889 14929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14937">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(z,x) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,L(x,y,u)) = w
    ]]></literal>
    <justification jstring="[para(14929(a,2),11995(a,1))].">
      <j1 rule="para" parents="14929 11995"/>
    </justification>
  </clause>

  <clause id="14938">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(x,u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(14863(a,2),14929(a,1,1))].">
      <j1 rule="para" parents="14863 14929"/>
    </justification>
  </clause>

  <clause id="14939">
    <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(10635,a,14930,a)].">
      <j1 rule="hyper" parents="10635 14930"/>
    </justification>
  </clause>

  <clause id="14940">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = K(x,K(z,a(u,y,w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,14876,a(flip),b,14935,a)].">
      <j1 rule="hyper" parents="65 14876 14935"/>
    </justification>
  </clause>

  <clause id="14941">
    <literal><![CDATA[
      K(x,L(y,z,L(u,u,w))) = a(y,z,K(x,u)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(7852(a,1),14936(a,1,1,3)),flip(a)].">
      <j1 rule="para" parents="7852 14936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14942">
    <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(299,a,8914,a(flip),b,14938,a),flip(a)].">
      <j1 rule="hyper" parents="299 8914 14938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14943">
    <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(14938(a,1),46(a,1))].">
      <j1 rule="para" parents="14938 46"/>
    </justification>
  </clause>

  <clause id="14944">
    <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(14938(a,2),9028(a,1))].">
      <j1 rule="para" parents="14938 9028"/>
    </justification>
  </clause>

  <clause id="14945">
    <literal><![CDATA[
      (1 / x) * a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(1 / x,a(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(2134(a,1),14896(a,1,2))].">
      <j1 rule="para" parents="2134 14896"/>
    </justification>
  </clause>

  <clause id="14946">
    <literal><![CDATA[
      a(x,y,K(z,L(u,w,v5))) = K(x,L(a(u,y,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,12737,a,b,14899,a)].">
      <j1 rule="hyper" parents="65 12737 14899"/>
    </justification>
  </clause>

  <clause id="14947">
    <literal><![CDATA[
      a(K(x,y),z,u) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[para(7677(a,1),14862(a,1,1))].">
      <j1 rule="para" parents="7677 14862"/>
    </justification>
  </clause>

  <clause id="14948">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(z,y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(14921,a,14947,a)].">
      <j1 rule="hyper" parents="14921 14947"/>
    </justification>
  </clause>

  <clause id="14949">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(u,y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(14920,a,14947,a)].">
      <j1 rule="hyper" parents="14920 14947"/>
    </justification>
  </clause>

  <clause id="14957">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,y,K(z,x)) = w
    ]]></literal>
    <justification jstring="[para(14947(a,1),14920(a,1))].">
      <j1 rule="para" parents="14947 14920"/>
    </justification>
  </clause>

  <clause id="14958">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(z,y,K(x,u)) = w
    ]]></literal>
    <justification jstring="[para(14947(a,1),14921(a,1))].">
      <j1 rule="para" parents="14947 14921"/>
    </justification>
  </clause>

  <clause id="14959">
    <literal><![CDATA[
      K(x,y) * a(y,z,K(u,x)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(14948(a,1),11896(a,1,2))].">
      <j1 rule="para" parents="14948 11896"/>
    </justification>
  </clause>

  <clause id="14960">
    <literal><![CDATA[
      a(x,y,z) * a(z,y,K(x,u)) = T(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(14948(a,1),14561(a,1,2))].">
      <j1 rule="para" parents="14948 14561"/>
    </justification>
  </clause>

  <clause id="14962">
    <literal><![CDATA[
      K(x,y) * a(z,u,K(x,y)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[para(14948(a,1),14882(a,1,2))].">
      <j1 rule="para" parents="14948 14882"/>
    </justification>
  </clause>

  <clause id="14963">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(y,u)) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(14949(a,1),10540(a,1,2))].">
      <j1 rule="para" parents="14949 10540"/>
    </justification>
  </clause>

  <clause id="14964">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(y,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(14949(a,1),11896(a,1,2))].">
      <j1 rule="para" parents="14949 11896"/>
    </justification>
  </clause>

  <clause id="14965">
    <literal><![CDATA[
      a(x,y,z) * a(u,y,K(z,x)) = T(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(14949(a,1),14561(a,1,2))].">
      <j1 rule="para" parents="14949 14561"/>
    </justification>
  </clause>

  <clause id="14966">
    <literal><![CDATA[
      (x / y) * a(y,z,K(u,w)) = x / T(y,a(w,z,u))
    ]]></literal>
    <justification jstring="[para(14949(a,1),14565(a,1,2))].">
      <j1 rule="para" parents="14949 14565"/>
    </justification>
  </clause>

  <clause id="14967">
    <literal><![CDATA[
      a(x,y,z) * a(u,y,K(z,x)) != w
    ]]></literal>
    <literal><![CDATA[
      T(a(x,y,z),u) = w
    ]]></literal>
    <justification jstring="[para(14949(a,1),14562(a,1,2))].">
      <j1 rule="para" parents="14949 14562"/>
    </justification>
  </clause>

  <clause id="14968">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(14949(a,1),14893(a,1,2))].">
      <j1 rule="para" parents="14949 14893"/>
    </justification>
  </clause>

  <clause id="14969">
    <literal><![CDATA[
      T(T(x,a(y,z,u)),a(y,z,u)) = x
    ]]></literal>
    <justification jstring="[para(14968(a,1),14560(a,1,1))].">
      <j1 rule="para" parents="14968 14560"/>
    </justification>
  </clause>

  <clause id="14970">
    <literal><![CDATA[
      T(x,a(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      (a(y,z,u) * x) / a(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(14968(a,1),14563(a,1))].">
      <j1 rule="para" parents="14968 14563"/>
    </justification>
  </clause>

  <clause id="14972">
    <literal><![CDATA[
      a(x \ 1,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,y,K(z,x)) = w
    ]]></literal>
    <justification jstring="[para(2138(a,2),14957(a,1))].">
      <j1 rule="para" parents="2138 14957"/>
    </justification>
  </clause>

  <clause id="14973">
    <literal><![CDATA[
      a(x,y,K(z,T(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      a(w * (u / w),y,K(z,x)) = v5
    ]]></literal>
    <justification jstring="[para(13218(a,1),14957(a,1,3))].">
      <j1 rule="para" parents="13218 14957"/>
    </justification>
  </clause>

  <clause id="14974">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      a(u,y,K(z,K(x,w))) = v5
    ]]></literal>
    <justification jstring="[para(14877(a,1),14958(a,1))].">
      <j1 rule="para" parents="14877 14958"/>
    </justification>
  </clause>

  <clause id="14976">
    <literal><![CDATA[
      K(x,y) * K(y,L(x,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,z,K(y,x)) = w
    ]]></literal>
    <justification jstring="[para(14962(a,1),5438(a,1,2)),flip(b)].">
      <j1 rule="para" parents="14962 5438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14978">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(y,u)) = L(K(x,y),y * z,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,9185,a,b,14964,a),flip(a)].">
      <j1 rule="hyper" parents="299 9185 14964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14979">
    <literal><![CDATA[
      a(x,y,z) * a(z,y,K(x,u)) = T(a(x,y,z),u * z)
    ]]></literal>
    <justification jstring="[para(14912(a,1),14960(a,1,2))].">
      <j1 rule="para" parents="14912 14960"/>
    </justification>
  </clause>

  <clause id="14980">
    <literal><![CDATA[
      a(x,y * z,K(y,u)) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(36,a,14963,a,b,14978,a)].">
      <j1 rule="hyper" parents="36 14963 14978"/>
    </justification>
  </clause>

  <clause id="14981">
    <literal><![CDATA[
      a(x,y \ z,K(y,u)) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),14980(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 14980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14982">
    <literal><![CDATA[
      a(x,y * z,K(u,K(w,y))) = a(x,z,K(y,K(u,w)))
    ]]></literal>
    <justification jstring="[para(7989(a,2),14980(a,1,3))].">
      <j1 rule="para" parents="7989 14980"/>
    </justification>
  </clause>

  <clause id="14983">
    <literal><![CDATA[
      a(x,y \ z,K(u,y)) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(14922,a,14981,a)].">
      <j1 rule="hyper" parents="14922 14981"/>
    </justification>
  </clause>

  <clause id="14984">
    <literal><![CDATA[
      a(x,x \ y,K(z,u)) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(14918,a,14981,a)].">
      <j1 rule="hyper" parents="14918 14981"/>
    </justification>
  </clause>

  <clause id="14985">
    <literal><![CDATA[
      K(x,L(y,z \ u,z)) = K(x,y) * a(x,u,K(z,y))
    ]]></literal>
    <justification jstring="[para(14981(a,1),14882(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14981 14882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14986">
    <literal><![CDATA[
      a(T(x,y) \ z,T((x \ z) \ z,y),K(u,w)) = a(w,z,K(T(x,y) \ z,u))
    ]]></literal>
    <justification jstring="[para(9741(a,2),14984(a,1,2))].">
      <j1 rule="para" parents="9741 14984"/>
    </justification>
  </clause>

  <clause id="14987">
    <literal><![CDATA[
      a(x,y * z,K(u,K(w,y))) = a(x,z,K(u,K(w,y)))
    ]]></literal>
    <justification jstring="[para(7989(a,2),14982(a,2,3))].">
      <j1 rule="para" parents="7989 14982"/>
    </justification>
  </clause>

  <clause id="14988">
    <literal><![CDATA[
      K(x,L(y,z \ u,z)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,14882,a(flip),b,14985,a),flip(a)].">
      <j1 rule="hyper" parents="299 14882 14985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14989">
    <literal><![CDATA[
      K((x \ y) \ z,L(u,y,x)) = K(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,11937,a(flip),b,14988,a),flip(a)].">
      <j1 rule="hyper" parents="65 11937 14988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14990">
    <literal><![CDATA[
      K(x,L(y,z * u,z)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),14988(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 14988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14991">
    <literal><![CDATA[
      K(x,L(y,T(z * u,u \ 1),u \ 1)) = K(x,L(y,R(z,u,u),u \ 1))
    ]]></literal>
    <justification jstring="[para(1250(a,1),14988(a,1,2,2))].">
      <j1 rule="para" parents="1250 14988"/>
    </justification>
  </clause>

  <clause id="14992">
    <literal><![CDATA[
      K(x,L(y,T(1 / (z / u),z),(1 / (z / u)) \ u)) = K(x,L(y,u,(1 / (z / u)) \ u))
    ]]></literal>
    <justification jstring="[para(4756(a,2),14988(a,1,2,2))].">
      <j1 rule="para" parents="4756 14988"/>
    </justification>
  </clause>

  <clause id="14993">
    <literal><![CDATA[
      K(x,L((y \ z) \ (y * u),u,y)) = K(x,z \ (y * (y * u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,11899,a(flip),b,14990,a),flip(a)].">
      <j1 rule="hyper" parents="65 11899 14990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14994">
    <literal><![CDATA[
      K(x,L((y * z) \ (y \ u),z,y)) = K(x,(y * (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(281(a,1),14990(a,1,2)),flip(a)].">
      <j1 rule="para" parents="281 14990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14995">
    <literal><![CDATA[
      K(x,L((y * z) \ ((y \ 1) \ u),z,y)) = K(x,((y \ 1) * (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(2476(a,1),14990(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2476 14990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14996">
    <literal><![CDATA[
      K(x,L(y,z * u,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(14086(a,2),14990(a,1,2))].">
      <j1 rule="para" parents="14086 14990"/>
    </justification>
  </clause>

  <clause id="14997">
    <literal><![CDATA[
      K(T(x,x \ y) \ z,L(u,y,x \ y)) = K(y \ ((x \ y) * z),u)
    ]]></literal>
    <justification jstring="[para(108(a,2),14989(a,1,1,1))].">
      <j1 rule="para" parents="108 14989"/>
    </justification>
  </clause>

  <clause id="14998">
    <literal><![CDATA[
      K((x \ (y \ ((1 / z) \ u))) \ w,L(v5,y \ (z \ u),x)) = K((y \ ((1 / z) \ u)) \ (x * w),v5)
    ]]></literal>
    <justification jstring="[para(2952(a,1),14989(a,1,2))].">
      <j1 rule="para" parents="2952 14989"/>
    </justification>
  </clause>

  <clause id="15000">
    <literal><![CDATA[
      K(x,L(y,z \ u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u,z)) = w
    ]]></literal>
    <justification jstring="[para(14985(a,2),14884(a,1))].">
      <j1 rule="para" parents="14985 14884"/>
    </justification>
  </clause>

  <clause id="15001">
    <literal><![CDATA[
      a(x,y,K(z,u * (u * w))) = a(x,y,K(z,L(w,u,u)))
    ]]></literal>
    <justification jstring="[hyper(299,a,14871,a,b,14891,a),flip(a)].">
      <j1 rule="hyper" parents="299 14871 14891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15002">
    <literal><![CDATA[
      a(x,y,z) * a(x * (y * z),y,K(z,x)) = ((x * y) * z) / (x * (y * z))
    ]]></literal>
    <justification jstring="[para(84(a,1),14895(a,1,1)),flip(a)].">
      <j1 rule="para" parents="84 14895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15003">
    <literal><![CDATA[
      ((x * (y * a(z,u,u))) / y) \ (L(a(z,u,u),y,x) * (y * x)) = T(y,x)
    ]]></literal>
    <justification jstring="[para(14908(a,1),11291(a,1,1,1))].">
      <j1 rule="para" parents="14908 11291"/>
    </justification>
  </clause>

  <clause id="15004">
    <literal><![CDATA[
      ((L(a(x,y,y),z,u) * (z * u)) / u) \ (u * (z * a(x,y,y))) = T(u,z)
    ]]></literal>
    <justification jstring="[para(14908(a,1),11291(a,1,2))].">
      <j1 rule="para" parents="14908 11291"/>
    </justification>
  </clause>

  <clause id="15006">
    <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(14948(a,1),14925(a,1))].">
      <j1 rule="para" parents="14948 14925"/>
    </justification>
  </clause>

  <clause id="15007">
    <literal><![CDATA[
      K(x,L(y,z,L(u,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(14941(a,2),14937(a,1))].">
      <j1 rule="para" parents="14941 14937"/>
    </justification>
  </clause>

  <clause id="15008">
    <literal><![CDATA[
      a(x,y,K(z * u,z)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(14976,a,12085,a),flip(a)].">
      <j1 rule="hyper" parents="14976 12085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15009">
    <literal><![CDATA[
      a(x,y,K(z * u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(12085(a,1),14976(a,1))].">
      <j1 rule="para" parents="12085 14976"/>
    </justification>
  </clause>

  <clause id="15010">
    <literal><![CDATA[
      T(a(x,y,z),u * z) = T(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,14960,a(flip),b,14979,a),flip(a)].">
      <j1 rule="hyper" parents="65 14960 14979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15011">
    <literal><![CDATA[
      a(x,y,K(z,u * (u * w))) = a(x,y,K(z,w))
    ]]></literal>
    <justification jstring="[para(14176(a,1),15001(a,2,3))].">
      <j1 rule="para" parents="14176 15001"/>
    </justification>
  </clause>

  <clause id="15012">
    <literal><![CDATA[
      a(x,y,K(z,u \ w)) = a(x,y,K(z,u * w))
    ]]></literal>
    <justification jstring="[para(10(a,1),15011(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="10 15011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15014">
    <literal><![CDATA[
      (x \ y) * a(z,u,K(w,x * y)) = T(x \ y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(15012(a,1),14968(a,1,2))].">
      <j1 rule="para" parents="15012 14968"/>
    </justification>
  </clause>

  <clause id="15015">
    <literal><![CDATA[
      a(x,y,K(z,(u * x) \ w)) = a(x,y,K(z,x \ (u \ w)))
    ]]></literal>
    <justification jstring="[hyper(14920,a,14867,a),flip(a)].">
      <j1 rule="hyper" parents="14920 14867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15016">
    <literal><![CDATA[
      a(x,y,K(z,u \ (x \ w))) = a(x,y,K(z,(x * u) * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,15012,a(flip),b,14914,a),flip(a)].">
      <j1 rule="hyper" parents="65 15012 14914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15017">
    <literal><![CDATA[
      a(x,y,K(z,(x \ u) \ w)) = a(x,y,K(z,u * (x * w)))
    ]]></literal>
    <justification jstring="[hyper(299,a,15012,a(flip),b,14915,a),flip(a)].">
      <j1 rule="hyper" parents="299 15012 14915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15019">
    <literal><![CDATA[
      a(x,y,K(z,(u * x) \ w)) = a(x,y,K(z,x * (u \ w)))
    ]]></literal>
    <justification jstring="[hyper(299,a,15012,a(flip),b,15015,a),flip(a)].">
      <j1 rule="hyper" parents="299 15012 15015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15020">
    <literal><![CDATA[
      a(x,y,K(z,(x * u) * w)) = a(x,y,K(z,u * (x \ w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,15012,a(flip),b,15016,a),flip(a)].">
      <j1 rule="hyper" parents="65 15012 15016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15021">
    <literal><![CDATA[
      a(x,y,K(z,(x \ u) * w)) = a(x,y,K(z,u * (x * w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,15012,a(flip),b,15017,a)].">
      <j1 rule="hyper" parents="65 15012 15017"/>
    </justification>
  </clause>

  <clause id="15022">
    <literal><![CDATA[
      ((K(x,y) * z) * u) / a(x,z,K(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (z * u) = w
    ]]></literal>
    <justification jstring="[para(14864(a,1),307(a,1,1)),flip(b)].">
      <j1 rule="para" parents="14864 307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15023">
    <literal><![CDATA[
      1 / T(x,a(y,z,u)) = T(1 / x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(14945,a,14966,a),flip(a)].">
      <j1 rule="hyper" parents="14945 14966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15024">
    <literal><![CDATA[
      a(x,y,K(z,x * (u \ (x * w)))) = a(x,y,K(z,T(u,x) \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,15019,a(flip),b,14916,a)].">
      <j1 rule="hyper" parents="65 15019 14916"/>
    </justification>
  </clause>

  <clause id="15025">
    <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(8004(a,1),14939(a,1,2))].">
      <j1 rule="para" parents="8004 14939"/>
    </justification>
  </clause>

  <clause id="15026">
    <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),14942(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="95 14942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15027">
    <literal><![CDATA[
      a(x,y,K(z,x * (u \ (x * w)))) = a(x,y,K(z,T(u,x) * w))
    ]]></literal>
    <justification jstring="[hyper(299,a,15012,a(flip),b,15024,a),flip(a)].">
      <j1 rule="hyper" parents="299 15012 15024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15028">
    <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(65,a,12347,a(flip),b,15025,a)].">
      <j1 rule="hyper" parents="65 12347 15025"/>
    </justification>
  </clause>

  <clause id="15029">
    <literal><![CDATA[
      K(a(x,y * z,K(z,u)),w) = a(z,y,K(w,K(x,u)))
    ]]></literal>
    <justification jstring="[para(10558(a,1),15028(a,1,1))].">
      <j1 rule="para" parents="10558 15028"/>
    </justification>
  </clause>

  <clause id="15030">
    <literal><![CDATA[
      K(a(x,y * z,K(z,u)),w) = a(z,y,K(w,K(u,x)))
    ]]></literal>
    <justification jstring="[para(8004(a,1),15029(a,2,3))].">
      <j1 rule="para" parents="8004 15029"/>
    </justification>
  </clause>

  <clause id="15031">
    <literal><![CDATA[
      a(x,y,K(z,x * (u \ (x * w)))) = a(z,y,K(u * w,x))
    ]]></literal>
    <justification jstring="[hyper(299,a,14878,a(flip),b,15027,a),flip(a)].">
      <j1 rule="hyper" parents="299 14878 15027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15032">
    <literal><![CDATA[
      L(a(x,y,y),z,u) * (z * u) = u * (T(z,u) * a(x,y,y))
    ]]></literal>
    <justification jstring="[para(11621(a,1),14909(a,1,1))].">
      <j1 rule="para" parents="11621 14909"/>
    </justification>
  </clause>

  <clause id="15033">
    <literal><![CDATA[
      K(x,L(y * (z \ u),z \ u,z)) = K(x,(z * (y \ 1)) \ u)
    ]]></literal>
    <justification jstring="[hyper(14279,a,11889,a),flip(a)].">
      <j1 rule="hyper" parents="14279 11889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15034">
    <literal><![CDATA[
      K(x,L(y * (z \ u),u,z)) = K(x,(z * (y \ 1)) \ u)
    ]]></literal>
    <justification jstring="[hyper(15000,a,15033,a)].">
      <j1 rule="hyper" parents="15000 15033"/>
    </justification>
  </clause>

  <clause id="15035">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ (y \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(z * (y \ (y \ u)),u,y)) = w
    ]]></literal>
    <justification jstring="[para(15034(a,1),15000(a,1))].">
      <j1 rule="para" parents="15034 15000"/>
    </justification>
  </clause>

  <clause id="15036">
    <literal><![CDATA[
      T(x \ 1,x \ y) \ (y / (1 / x)) = x \ ((x * x) * ((1 / x) \ y))
    ]]></literal>
    <justification jstring="[para(14693(a,1),14371(a,1,1))].">
      <j1 rule="para" parents="14693 14371"/>
    </justification>
  </clause>

  <clause id="15037">
    <literal><![CDATA[
      K(x,x * x) * (y * K(x \ 1,y)) = ((1 / x) * y) / (x \ 1)
    ]]></literal>
    <justification jstring="[para(8(a,1),14449(a,1,1,1))].">
      <j1 rule="para" parents="8 14449"/>
    </justification>
  </clause>

  <clause id="15038">
    <literal><![CDATA[
      a(x,x,x) * (y * K(x \ 1,y)) = ((1 / x) * y) / (x \ 1)
    ]]></literal>
    <justification jstring="[para(6383(a,1),15037(a,1,1))].">
      <j1 rule="para" parents="6383 15037"/>
    </justification>
  </clause>

  <clause id="15039">
    <literal><![CDATA[
      a(x,x,x) * (y * K(x \ 1,y)) = ((x \ 1) * y) / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(299,a,4703,a(flip),b,15038,a),flip(a)].">
      <j1 rule="hyper" parents="299 4703 15038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15040">
    <literal><![CDATA[
      a(((x \ 1) * y) / (1 / x),z,u) = a((x \ 1) \ (y * (1 / x)),z,u)
    ]]></literal>
    <justification jstring="[para(15039(a,1),13987(a,1,1))].">
      <j1 rule="para" parents="15039 13987"/>
    </justification>
  </clause>

  <clause id="15041">
    <literal><![CDATA[
      x * ((x \ y) * a(z,u,K(w,x \ y))) = y * a(z,u,K(w,x \ y))
    ]]></literal>
    <justification jstring="[para(14556(a,2),14564(a,2,2))].">
      <j1 rule="para" parents="14556 14564"/>
    </justification>
  </clause>

  <clause id="15042">
    <literal><![CDATA[
      ((x * y) * K(z,y * x)) / u = (x * y) / (u * K(y * x,z))
    ]]></literal>
    <justification jstring="[para(13203(a,1),14661(a,1,1,2))].">
      <j1 rule="para" parents="13203 14661"/>
    </justification>
  </clause>

  <clause id="15043">
    <literal><![CDATA[
      T(x,y \ (L(y,z,u) * (y \ w))) = T(x,L(1 / y,z,u) * w)
    ]]></literal>
    <justification jstring="[para(6518(a,1),14667(a,2,2,1))].">
      <j1 rule="para" parents="6518 14667"/>
    </justification>
  </clause>

  <clause id="15044">
    <literal><![CDATA[
      T(x,y \ (L(y,z,u) * (y \ w))) = T(x,L(y \ 1,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(299,a,4148,a(flip),b,15043,a),flip(a)].">
      <j1 rule="hyper" parents="299 4148 15043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15045">
    <literal><![CDATA[
      T(x,L(y,z,u) * (y \ (y \ w))) = T(x,L(y \ 1,z,u) * w)
    ]]></literal>
    <justification jstring="[para(1348(a,1),15044(a,1,2))].">
      <j1 rule="para" parents="1348 15044"/>
    </justification>
  </clause>

  <clause id="15046">
    <literal><![CDATA[
      K(x,(K(((y \ z) \ z) * u,w) / w) * (T(y,z) * u)) = K(x,(((w * w) \ ((y \ z) \ z)) * u) * w)
    ]]></literal>
    <justification jstring="[hyper(65,a,13850,a(flip),b,14678,a)].">
      <j1 rule="hyper" parents="65 13850 14678"/>
    </justification>
  </clause>

  <clause id="15047">
    <literal><![CDATA[
      K((x \ y) \ y,L(z * u,w,v5)) = K(x,L(T((z \ 1) \ u,y),w,v5))
    ]]></literal>
    <justification jstring="[para(25(a,2),14683(a,2,2))].">
      <j1 rule="para" parents="25 14683"/>
    </justification>
  </clause>

  <clause id="15048">
    <literal><![CDATA[
      ((x \ 1) * T(1 / x,y)) * z = T(1 / x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[para(14692(a,1),14695(a,1,1,2))].">
      <j1 rule="para" parents="14692 14695"/>
    </justification>
  </clause>

  <clause id="15049">
    <literal><![CDATA[
      (x \ T(x \ 1,y)) * z = T(1 / x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[para(1680(a,1),15048(a,1,1))].">
      <j1 rule="para" parents="1680 15048"/>
    </justification>
  </clause>

  <clause id="15050">
    <literal><![CDATA[
      K(x * (x * (L(x,y,z) \ u)),w) = K(L(x \ 1,y,z) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(14787,a,14784,a)].">
      <j1 rule="hyper" parents="14787 14784"/>
    </justification>
  </clause>

  <clause id="15052">
    <literal><![CDATA[
      K((x \ K(x,y)) * T(x,z),T(x,z) \ ((x \ 1) \ K(y,x))) = 1
    ]]></literal>
    <justification jstring="[para(12386(a,1),14814(a,1,1))].">
      <j1 rule="para" parents="12386 14814"/>
    </justification>
  </clause>

  <clause id="15053">
    <literal><![CDATA[
      1 / (((x \ K(x,y)) \ 1) \ T(x,z)) = ((x \ K(x,y)) * T(x,z)) \ 1
    ]]></literal>
    <justification jstring="[para(15052(a,1),13122(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15052 13122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15054">
    <literal><![CDATA[
      K(x,T(((y * z) \ y) * x,u)) = K(x,((y * T(z,u)) \ y) * x)
    ]]></literal>
    <justification jstring="[para(67(a,1),14831(a,1,2)),flip(a)].">
      <j1 rule="para" parents="67 14831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15055">
    <literal><![CDATA[
      K(x,T(((y * z) \ y) * x,u)) = K(x,x * ((y * T(z,u)) \ y))
    ]]></literal>
    <justification jstring="[hyper(299,a,5685,a(flip),b,15054,a),flip(a)].">
      <j1 rule="hyper" parents="299 5685 15054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15056">
    <literal><![CDATA[
      K(x,T(((y * z) \ y) * x,u)) = K(x,T(z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(11395,a,15055,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="11395 15055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15057">
    <literal><![CDATA[
      K(x,T(((y * z) \ y) * x,u)) = K(x,T(z \ x,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,8962,a,b,15056,a),flip(a)].">
      <j1 rule="hyper" parents="299 8962 15056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15058">
    <literal><![CDATA[
      K(x,T((y \ z) \ x,u)) = K(x,T((z \ y) * x,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),15057(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 15057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15059">
    <literal><![CDATA[
      K(x,T((y \ z) * x,z)) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(9492,a,15058,a),flip(a)].">
      <j1 rule="hyper" parents="9492 15058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15060">
    <literal><![CDATA[
      K(x,T(x * (y \ z),z)) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(13244,a,15059,a)].">
      <j1 rule="hyper" parents="13244 15059"/>
    </justification>
  </clause>

  <clause id="15061">
    <literal><![CDATA[
      K(x,T((y \ z) * x,y)) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,10187,a(flip),b,15059,a)].">
      <j1 rule="hyper" parents="65 10187 15059"/>
    </justification>
  </clause>

  <clause id="15062">
    <literal><![CDATA[
      K(x,T(x * T(y,z),z)) = K(x,((y \ z) / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,12310,a(flip),b,15060,a)].">
      <j1 rule="hyper" parents="65 12310 15060"/>
    </justification>
  </clause>

  <clause id="15063">
    <literal><![CDATA[
      K(x,(y / (y * z)) \ x) = K(x,T(z * x,y))
    ]]></literal>
    <justification jstring="[para(9(a,1),15061(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="9 15061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15064">
    <literal><![CDATA[
      K(x,T((y / (y * z)) \ T(T(x,u),w),w)) = K(T(x,w),T(z * T(x,w),y))
    ]]></literal>
    <justification jstring="[hyper(65,a,9297,a,b,15063,a)].">
      <j1 rule="hyper" parents="65 9297 15063"/>
    </justification>
  </clause>

  <clause id="15065">
    <literal><![CDATA[
      R(K(x,T(x * T(y,z),z)),x * u,w) = K(R(x,u,w),((y \ z) / z) \ x)
    ]]></literal>
    <justification jstring="[para(15062(a,2),10698(a,1,1))].">
      <j1 rule="para" parents="15062 10698"/>
    </justification>
  </clause>

  <clause id="15066">
    <literal><![CDATA[
      ((K(x,y) * z) * u) * a(x,z,K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (z * u) = w
    ]]></literal>
    <justification jstring="[para(10565(a,1),15022(a,1))].">
      <j1 rule="para" parents="10565 15022"/>
    </justification>
  </clause>

  <clause id="15067">
    <literal><![CDATA[
      ((K(x,y) * z) * u) * a(y,z,K(u,x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (z * u) = w
    ]]></literal>
    <justification jstring="[para(14880(a,1),15022(a,1))].">
      <j1 rule="para" parents="14880 15022"/>
    </justification>
  </clause>

  <clause id="15068">
    <literal><![CDATA[
      T(x \ 1,x \ y) \ (y / (1 / x)) = (x \ 1) \ ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(299,a,6622,a(flip),b,15036,a),flip(a)].">
      <j1 rule="hyper" parents="299 6622 15036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15069">
    <literal><![CDATA[
      (x / (1 / y)) * K((y \ 1) \ ((y \ 1) \ x),T(y \ 1,y \ x)) = (T(y \ 1,y \ x) \ (x / (1 / y))) * T(y \ 1,y \ x)
    ]]></literal>
    <justification jstring="[para(15068(a,1),287(a,1,2,1))].">
      <j1 rule="para" parents="15068 287"/>
    </justification>
  </clause>

  <clause id="15070">
    <literal><![CDATA[
      a((x \ 1) \ (y * (1 / x)),z,u) = a(((x \ 1) * y) / x,z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,2145,a(flip),b,15040,a),flip(a)].">
      <j1 rule="hyper" parents="65 2145 15040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15071">
    <literal><![CDATA[
      a(((x \ 1) * y) / x,z,u) = a((x \ 1) \ (y * x),z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,2146,a(flip),b,15070,a),flip(a)].">
      <j1 rule="hyper" parents="65 2146 15070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15072">
    <literal><![CDATA[
      a(((x \ 1) * y) / x,z,u) = a(x \ (y * x),z,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,2137,a(flip),b,15071,a),flip(a)].">
      <j1 rule="hyper" parents="299 2137 15071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15073">
    <literal><![CDATA[
      a(((x \ 1) * y) / x,z,u) = a(T(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(22(a,2),15072(a,2,1))].">
      <j1 rule="para" parents="22 15072"/>
    </justification>
  </clause>

  <clause id="15074">
    <literal><![CDATA[
      x * ((x \ y) * a(z,u,K(w,x * y))) = y * a(z,u,K(w,x \ y))
    ]]></literal>
    <justification jstring="[para(15012(a,1),15041(a,1,2,2))].">
      <j1 rule="para" parents="15012 15041"/>
    </justification>
  </clause>

  <clause id="15075">
    <literal><![CDATA[
      K(x,L(T((y \ 1) \ z,u),w,v5)) = K(x,T(L(y * z,w,v5),u))
    ]]></literal>
    <justification jstring="[hyper(7713,a,15047,a),flip(a)].">
      <j1 rule="hyper" parents="7713 15047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15076">
    <literal><![CDATA[
      K(x,L(T((y \ 1) \ z,u),w,v5)) = K(x,L(T(y * z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(25(a,2),15075(a,2,2))].">
      <j1 rule="para" parents="25 15075"/>
    </justification>
  </clause>

  <clause id="15077">
    <literal><![CDATA[
      1 / (((x \ K(x,y)) \ 1) \ T(x,z)) = x * (K(y,x) / T(x,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,10191,a(flip),b,15053,a),flip(a)].">
      <j1 rule="hyper" parents="299 10191 15053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15079">
    <literal><![CDATA[
      1 / (((x \ 1) \ K(y,x)) \ T(x,z)) = x * (K(y,x) / T(x,z))
    ]]></literal>
    <justification jstring="[para(6605(a,1),15077(a,1,2,1))].">
      <j1 rule="para" parents="6605 15077"/>
    </justification>
  </clause>

  <clause id="15080">
    <literal><![CDATA[
      1 / ((x \ K(x,y)) * T(x,z)) = x * (K(y,x) / T(x,z))
    ]]></literal>
    <justification jstring="[para(12386(a,1),15079(a,1,2))].">
      <j1 rule="para" parents="12386 15079"/>
    </justification>
  </clause>

  <clause id="15081">
    <literal><![CDATA[
      (x * (K(y,x) / T(x,z))) \ 1 = (x \ K(x,y)) * T(x,z)
    ]]></literal>
    <justification jstring="[hyper(186,a,15080,a)].">
      <j1 rule="hyper" parents="186 15080"/>
    </justification>
  </clause>

  <clause id="15082">
    <literal><![CDATA[
      (((x \ K(x,y)) * T(x,z)) \ 1) \ L(u,(x * (K(y,x) / T(x,z))) \ 1,x * (K(y,x) / T(x,z))) = ((((x * (K(y,x) / T(x,z))) \ 1) \ 1) \ 1) * u
    ]]></literal>
    <justification jstring="[para(15081(a,1),2480(a,1,1,1))].">
      <j1 rule="para" parents="15081 2480"/>
    </justification>
  </clause>

  <clause id="15083">
    <literal><![CDATA[
      x * ((x \ y) * a(z,u,K(w,x * y))) = y * a(z,u,K(w,x * y))
    ]]></literal>
    <justification jstring="[para(15012(a,1),15074(a,2,2))].">
      <j1 rule="para" parents="15012 15074"/>
    </justification>
  </clause>

  <clause id="15084">
    <literal><![CDATA[
      x * T(x \ y,a(z,u,w)) = y * a(z,u,K(w,x * y))
    ]]></literal>
    <justification jstring="[para(15014(a,1),15083(a,1,2))].">
      <j1 rule="para" parents="15014 15083"/>
    </justification>
  </clause>

  <clause id="15085">
    <literal><![CDATA[
      K(x,(y * (1 / z)) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * (z \ 1)) * u) = w
    ]]></literal>
    <justification jstring="[para(14479(a,1),14487(a,1))].">
      <j1 rule="para" parents="14479 14487"/>
    </justification>
  </clause>

  <clause id="15086">
    <literal><![CDATA[
      K(x,(y * L(z \ 1,u,z)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * (z \ 1)) * w) = v5
    ]]></literal>
    <justification jstring="[para(13857(a,2),15085(a,1))].">
      <j1 rule="para" parents="13857 15085"/>
    </justification>
  </clause>

  <clause id="15087">
    <literal><![CDATA[
      T(x,(y * y) / (z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(u / (y * y)) \ (z \ 1)) = w
    ]]></literal>
    <justification jstring="[para(14474(a,1),14666(a,1))].">
      <j1 rule="para" parents="14474 14666"/>
    </justification>
  </clause>

  <clause id="15088">
    <literal><![CDATA[
      T(x,(y / (z * z)) \ (u \ 1)) = T(x,z * (z / (u * y)))
    ]]></literal>
    <justification jstring="[hyper(15087,a,14301,a)].">
      <j1 rule="hyper" parents="15087 14301"/>
    </justification>
  </clause>

  <clause id="15089">
    <literal><![CDATA[
      T(x,(y * y) * (z \ (u \ 1))) = T(x,y * (y / (u * z)))
    ]]></literal>
    <justification jstring="[para(416(a,1),15088(a,1,2))].">
      <j1 rule="para" parents="416 15088"/>
    </justification>
  </clause>

  <clause id="15090">
    <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(7983(a,1),14944(a,1,1,3))].">
      <j1 rule="para" parents="7983 14944"/>
    </justification>
  </clause>

  <clause id="15091">
    <literal><![CDATA[
      K(x,L(y,T(z * u,u \ 1),u)) = K(x,L(y,R(z,u,u),u \ 1))
    ]]></literal>
    <justification jstring="[para(2470(a,1),14991(a,1,2))].">
      <j1 rule="para" parents="2470 14991"/>
    </justification>
  </clause>

  <clause id="15092">
    <literal><![CDATA[
      K(x,L((y * z) \ ((y \ 1) \ u),z,y)) = K(x,(y * ((1 / y) * z)) \ u)
    ]]></literal>
    <justification jstring="[para(944(a,1),14995(a,2,2,1))].">
      <j1 rule="para" parents="944 14995"/>
    </justification>
  </clause>

  <clause id="15093">
    <literal><![CDATA[
      ((x * (y * a(z,u,u))) / y) \ (x * (T(y,x) * a(z,u,u))) = T(y,x)
    ]]></literal>
    <justification jstring="[para(15032(a,1),15003(a,1,2))].">
      <j1 rule="para" parents="15032 15003"/>
    </justification>
  </clause>

  <clause id="15094">
    <literal><![CDATA[
      ((x * (T(y,x) * a(z,u,u))) / x) \ (x * (y * a(z,u,u))) = T(x,y)
    ]]></literal>
    <justification jstring="[para(15032(a,1),15004(a,1,1,1))].">
      <j1 rule="para" parents="15032 15004"/>
    </justification>
  </clause>

  <clause id="15095">
    <literal><![CDATA[
      ((x * (T(y,x) * a(z,u,u))) / x) \ (x * (a(z,u,u) * y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(14904(a,2),15094(a,1,2,2))].">
      <j1 rule="para" parents="14904 15094"/>
    </justification>
  </clause>

  <clause id="15096">
    <literal><![CDATA[
      (1 / x) * T((1 / x) * y,z) = (x \ 1) * T((x \ 1) * y,z)
    ]]></literal>
    <justification jstring="[hyper(14353,a,14258,a),flip(a)].">
      <j1 rule="hyper" parents="14353 14258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15097">
    <literal><![CDATA[
      T(x,y * (z * ((1 / u) * w))) = T(x,y * (z * ((u \ 1) * w)))
    ]]></literal>
    <justification jstring="[para(14378(a,1),14299(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14378 14299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15098">
    <literal><![CDATA[
      T(x,T(y,z * ((1 / u) * w)) * (z * ((u \ 1) * w))) = T(x,(z * ((1 / u) * w)) * y)
    ]]></literal>
    <justification jstring="[hyper(13267,a,15097,a),flip(a)].">
      <j1 rule="hyper" parents="13267 15097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15099">
    <literal><![CDATA[
      ((1 / x) \ y) \ (z * ((x \ 1) \ 1)) = (x \ y) \ ((1 / x) * T(z,x))
    ]]></literal>
    <justification jstring="[para(14812(a,1),14372(a,2,2))].">
      <j1 rule="para" parents="14812 14372"/>
    </justification>
  </clause>

  <clause id="15100">
    <literal><![CDATA[
      ((1 / x) \ y) \ (z * ((x \ 1) \ 1)) = ((x \ 1) \ y) \ (z * x)
    ]]></literal>
    <justification jstring="[hyper(299,a,1182,a(flip),b,15099,a),flip(a)].">
      <j1 rule="hyper" parents="299 1182 15099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15101">
    <literal><![CDATA[
      K(x,T(y * (1 / z),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y / z,u)) = w
    ]]></literal>
    <justification jstring="[para(14462(a,1),9342(a,1))].">
      <j1 rule="para" parents="14462 9342"/>
    </justification>
  </clause>

  <clause id="15102">
    <literal><![CDATA[
      K((x / (y \ 1)) * T((x / (1 / y)) \ 1,z),u) = K(z,K(y \ (x \ 1),u))
    ]]></literal>
    <justification jstring="[hyper(299,a,7988,a(flip),b,14471,a),flip(a)].">
      <j1 rule="hyper" parents="299 7988 14471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15103">
    <literal><![CDATA[
      T(x,(y \ (z \ (z \ 1))) \ (u \ 1)) = T(x,((z * z) / (1 / y)) / u)
    ]]></literal>
    <justification jstring="[para(1695(a,1),14503(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1695 14503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15104">
    <literal><![CDATA[
      T(x,(y \ (z \ (z \ 1))) \ (u \ 1)) = T(x,((z * z) / (y \ 1)) / u)
    ]]></literal>
    <justification jstring="[hyper(299,a,14763,a(flip),b,15103,a),flip(a)].">
      <j1 rule="hyper" parents="299 14763 15103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15105">
    <literal><![CDATA[
      T(x,(y \ (z \ (z \ 1))) \ (u \ 1)) = T(x,((z * z) * y) / u)
    ]]></literal>
    <justification jstring="[para(426(a,1),15104(a,2,2,1))].">
      <j1 rule="para" parents="426 15104"/>
    </justification>
  </clause>

  <clause id="15106">
    <literal><![CDATA[
      T(x,(y \ (z \ (z \ 1))) \ (u \ 1)) = T(x,(z * z) * (y / u))
    ]]></literal>
    <justification jstring="[para(670(a,1),15105(a,2,2))].">
      <j1 rule="para" parents="670 15105"/>
    </justification>
  </clause>

  <clause id="15107">
    <literal><![CDATA[
      T(x,(y \ (z \ (z \ 1))) \ (u \ 1)) = T(x,z * (z * (y / u)))
    ]]></literal>
    <justification jstring="[hyper(299,a,14216,a(flip),b,15106,a),flip(a)].">
      <j1 rule="hyper" parents="299 14216 15106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15108">
    <literal><![CDATA[
      T(x,(y * y) * ((z \ 1) \ (u \ 1))) = T(x,y * (y * (z / u)))
    ]]></literal>
    <justification jstring="[para(1774(a,1),15107(a,1,2))].">
      <j1 rule="para" parents="1774 15107"/>
    </justification>
  </clause>

  <clause id="15109">
    <literal><![CDATA[
      T(x,y * (y / (z * (u \ 1)))) = T(x,y * (y * (u / z)))
    ]]></literal>
    <justification jstring="[hyper(65,a,15089,a(flip),b,15108,a)].">
      <j1 rule="hyper" parents="65 15089 15108"/>
    </justification>
  </clause>

  <clause id="15110">
    <literal><![CDATA[
      T(x,T(y,z) * ((1 / z) * (z \ 1))) = T(x,(1 / z) * (((z * z) \ y) * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,3885,a(flip),b,14606,a)].">
      <j1 rule="hyper" parents="65 3885 14606"/>
    </justification>
  </clause>

  <clause id="15111">
    <literal><![CDATA[
      ((x * y) * z) / (x * (y * z)) = T(a(x,y,z),x * (y * z))
    ]]></literal>
    <justification jstring="[hyper(14967,a,15002,a),flip(a)].">
      <j1 rule="hyper" parents="14967 15002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15112">
    <literal><![CDATA[
      K(T(x,y),T(z * T(x,y),u)) = K(x,T((u / (u * z)) \ x,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,9298,a(flip),b,15064,a),flip(a)].">
      <j1 rule="hyper" parents="65 9298 15064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15113">
    <literal><![CDATA[
      K(x,T(T(y * T(x,z),u),z)) = K(x,T((u / (u * y)) \ x,z))
    ]]></literal>
    <justification jstring="[hyper(7709,a,15112,a)].">
      <j1 rule="hyper" parents="7709 15112"/>
    </justification>
  </clause>

  <clause id="15115">
    <literal><![CDATA[
      K(x,T((y / (y * z)) \ x,u)) = K(x,T(T(x * z,y),u))
    ]]></literal>
    <justification jstring="[hyper(65,a,10977,a(flip),b,15113,a),flip(a)].">
      <j1 rule="hyper" parents="65 10977 15113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15117">
    <literal><![CDATA[
      K(x,T(T(x * T(y,z),z),u)) = K(x,T((z / (y * z)) \ x,u))
    ]]></literal>
    <justification jstring="[para(107(a,1),15115(a,1,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="107 15115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15118">
    <literal><![CDATA[
      K(x,T(T(x * T(y,z),z),y)) = K(x,R(1 / (1 / (1 / y)),y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(299,a,9495,a(flip),b,15117,a),flip(a)].">
      <j1 rule="hyper" parents="299 9495 15117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15119">
    <literal><![CDATA[
      K(x,T(x * T(y,z),z)) = K(x,R(1 / (1 / (1 / y)),y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(9260,a,15118,a)].">
      <j1 rule="hyper" parents="9260 15118"/>
    </justification>
  </clause>

  <clause id="15120">
    <literal><![CDATA[
      K(x,T(x * T(y,z),z)) = K(x,R((1 / (1 / y)) \ 1,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(299,a,5666,a(flip),b,15119,a),flip(a)].">
      <j1 rule="hyper" parents="299 5666 15119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15121">
    <literal><![CDATA[
      K(x,T(x * T(y,z),z)) = K(x,R(1 / y,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(79(a,1),15120(a,2,2,1,1))].">
      <j1 rule="para" parents="79 15120"/>
    </justification>
  </clause>

  <clause id="15122">
    <literal><![CDATA[
      R(K(x,x * y),y,z) = K(x,T(x * T(y,z),z))
    ]]></literal>
    <justification jstring="[hyper(299,a,12557,a(flip),b,15121,a)].">
      <j1 rule="hyper" parents="299 12557 15121"/>
    </justification>
  </clause>

  <clause id="15124">
    <literal><![CDATA[
      R(R(K(x,x * y),y,z),x * u,w) = K(R(x,u,w),T(x * T(y,z),z))
    ]]></literal>
    <justification jstring="[para(15122(a,2),10698(a,1,1))].">
      <j1 rule="para" parents="15122 10698"/>
    </justification>
  </clause>

  <clause id="15125">
    <literal><![CDATA[
      R(K(R(x,y,z),x * u),u,w) = K(R(x,y,z),T(x * T(u,w),w))
    ]]></literal>
    <justification jstring="[hyper(65,a,10707,a(flip),b,15124,a)].">
      <j1 rule="hyper" parents="65 10707 15124"/>
    </justification>
  </clause>

  <clause id="15126">
    <literal><![CDATA[
      K(R(x,y,z),T(x * T(u,w),w)) = K(R(x,y,z),((u \ w) / w) \ x)
    ]]></literal>
    <justification jstring="[hyper(10812,a,15065,a)].">
      <j1 rule="hyper" parents="10812 15065"/>
    </justification>
  </clause>

  <clause id="15127">
    <literal><![CDATA[
      K(R(x,y,z),T(x * T(u,w),w)) = K(R(x,y,z),x * (w / (u \ w)))
    ]]></literal>
    <justification jstring="[hyper(13502,a,15126,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="13502 15126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15128">
    <literal><![CDATA[
      K(R(x,y,z),T(x * T(u,w),w)) = K(R(x,y,z),x * u)
    ]]></literal>
    <justification jstring="[para(76(a,1),15127(a,2,2,2))].">
      <j1 rule="para" parents="76 15127"/>
    </justification>
  </clause>

  <clause id="15130">
    <literal><![CDATA[
      R(K(R(x,y,z),x * u),u,w) = K(R(x,y,z),x * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,15125,a,b,15128,a)].">
      <j1 rule="hyper" parents="65 15125 15128"/>
    </justification>
  </clause>

  <clause id="15132">
    <literal><![CDATA[
      R(K(x,R(x * y,z,u)),y,w) = K(R(x,z,u),x * y)
    ]]></literal>
    <justification jstring="[para(13399(a,1),15130(a,1,1))].">
      <j1 rule="para" parents="13399 15130"/>
    </justification>
  </clause>

  <clause id="15133">
    <literal><![CDATA[
      K(x,R(R(x * y,z,u),y,w)) = K(R(x,z,u),x * y)
    ]]></literal>
    <justification jstring="[hyper(13397,a,15132,a)].">
      <j1 rule="hyper" parents="13397 15132"/>
    </justification>
  </clause>

  <clause id="15134">
    <literal><![CDATA[
      K(x,R(R(x * y,z,u),y,w)) = K(x,R(x * y,z,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,13399,a(flip),b,15133,a),flip(a)].">
      <j1 rule="hyper" parents="299 13399 15133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15135">
    <literal><![CDATA[
      K(x,R(x * y,y * z,u)) = K(x,R(x * y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,13416,a(flip),b,15134,a),flip(a)].">
      <j1 rule="hyper" parents="65 13416 15134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15137">
    <literal><![CDATA[
      K(x,R(x * y,z,u)) = K(x,x * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,13512,a(flip),b,15135,a),flip(a)].">
      <j1 rule="hyper" parents="65 13512 15135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15138">
    <literal><![CDATA[
      K(x,R(x * y,z,u)) * x = T(x,x * R(y,z,u))
    ]]></literal>
    <justification jstring="[para(15137(a,2),5096(a,2,1)),flip(a)].">
      <j1 rule="para" parents="15137 5096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15139">
    <literal><![CDATA[
      T(x,R(x * y,z,u)) = T(x,x * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(5097,a,15138,a)].">
      <j1 rule="hyper" parents="5097 15138"/>
    </justification>
  </clause>

  <clause id="15140">
    <literal><![CDATA[
      L(T(x,R(y,z,u)),y,T(x,R(y,z,u))) = T(x,R(x * y,z,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,13544,a,b,15139,a)].">
      <j1 rule="hyper" parents="299 13544 15139"/>
    </justification>
  </clause>

  <clause id="15141">
    <literal><![CDATA[
      L(T(x,R(y,z,u)),y,x) = T(x,R(x * y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,7770,a(flip),b,15140,a)].">
      <j1 rule="hyper" parents="65 7770 15140"/>
    </justification>
  </clause>

  <clause id="15142">
    <literal><![CDATA[
      T(x,x * y) * a(K(x,y),z,u) = T(x,R(x * y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,13432,a,b,15141,a)].">
      <j1 rule="hyper" parents="65 13432 15141"/>
    </justification>
  </clause>

  <clause id="15144">
    <literal><![CDATA[
      L(T(x,R(y / T(1 / (1 / x),z),u,w)),y / T(1 / (1 / x),z),x) = T(x,R(((x \ 1) \ 1) * (y / T(x,z)),u,w))
    ]]></literal>
    <justification jstring="[para(3991(a,2),15141(a,2,2,1))].">
      <j1 rule="para" parents="3991 15141"/>
    </justification>
  </clause>

  <clause id="15145">
    <literal><![CDATA[
      T(x,x * y) * a(x,z,K(u,y)) = T(x,R(x * y,z,u))
    ]]></literal>
    <justification jstring="[para(14860(a,1),15142(a,1,2))].">
      <j1 rule="para" parents="14860 15142"/>
    </justification>
  </clause>

  <clause id="15146">
    <literal><![CDATA[
      T(x,(1 / y) * (((y * y) \ z) * y)) = T(x,T(z,y) * ((y * y) \ 1))
    ]]></literal>
    <justification jstring="[para(441(a,1),15110(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="441 15110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15147">
    <literal><![CDATA[
      T(x,(1 / y) * (((y * y) \ z) * y)) = T(x,T(z,y) / (y * y))
    ]]></literal>
    <justification jstring="[hyper(299,a,14474,a(flip),b,15146,a),flip(a)].">
      <j1 rule="hyper" parents="299 14474 15146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15148">
    <literal><![CDATA[
      L(T(x,x \ 1) \ y,x,T(x,z)) = K(x,z) \ ((((z * x) / z) \ 1) * y)
    ]]></literal>
    <justification jstring="[para(5083(a,2),14580(a,1,3))].">
      <j1 rule="para" parents="5083 14580"/>
    </justification>
  </clause>

  <clause id="15149">
    <literal><![CDATA[
      L(T(x,x \ 1) \ y,x,x) = K(x,z) \ ((((z * x) / z) \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(6691,a,15148,a)].">
      <j1 rule="hyper" parents="6691 15148"/>
    </justification>
  </clause>

  <clause id="15151">
    <literal><![CDATA[
      T(T(x,x \ 1),y) * K(x * y,z) = y \ T(T(x,x \ 1) * y,z)
    ]]></literal>
    <justification jstring="[para(13733(a,1),14583(a,1,2))].">
      <j1 rule="para" parents="13733 14583"/>
    </justification>
  </clause>

  <clause id="15153">
    <literal><![CDATA[
      K(x,(y * ((y \ 1) \ z)) / u) = K(x,y * (y * (z * (1 / u))))
    ]]></literal>
    <justification jstring="[hyper(14630,a,14355,a)].">
      <j1 rule="hyper" parents="14630 14355"/>
    </justification>
  </clause>

  <clause id="15154">
    <literal><![CDATA[
      K(x,(y * ((y \ 1) \ z)) / u) = K(x,y * (y * (z * (u \ 1))))
    ]]></literal>
    <justification jstring="[hyper(299,a,5906,a(flip),b,15153,a),flip(a)].">
      <j1 rule="hyper" parents="299 5906 15153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15155">
    <literal><![CDATA[
      (x \ ((1 / x) \ y)) * K(z,x \ ((1 / x) \ y)) = x \ ((K(y,z) / x) \ y)
    ]]></literal>
    <justification jstring="[para(14331(a,1),14358(a,2,2))].">
      <j1 rule="para" parents="14331 14358"/>
    </justification>
  </clause>

  <clause id="15156">
    <literal><![CDATA[
      T(x \ ((K(y,z) / x) \ y),z) = x \ ((1 / x) \ y)
    ]]></literal>
    <justification jstring="[para(15155(a,1),5053(a,1,1))].">
      <j1 rule="para" parents="15155 5053"/>
    </justification>
  </clause>

  <clause id="15157">
    <literal><![CDATA[
      T(x \ ((1 / x) \ y),y) = x \ ((1 / x) \ y)
    ]]></literal>
    <justification jstring="[para(168(a,1),15156(a,1,1,2,1,1))].">
      <j1 rule="para" parents="168 15156"/>
    </justification>
  </clause>

  <clause id="15158">
    <literal><![CDATA[
      T(x * (y \ ((1 / y) \ z)),K(y \ ((1 / y) \ z),z)) = (y \ ((1 / y) \ z)) * T(x,y \ ((1 / y) \ z))
    ]]></literal>
    <justification jstring="[para(15157(a,1),7400(a,2,2,2))].">
      <j1 rule="para" parents="15157 7400"/>
    </justification>
  </clause>

  <clause id="15159">
    <literal><![CDATA[
      a((K(x,y) \ (1 / K(x,y))) \ z,u,w) = a(K(x,y) / (K(x,y) * z),u,w)
    ]]></literal>
    <justification jstring="[para(5447(a,1),14589(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5447 14589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15160">
    <literal><![CDATA[
      K(x,((y * z) \ (y * y)) * T(u,z \ y)) = K(x,u / ((y \ 1) * z))
    ]]></literal>
    <justification jstring="[para(14578(a,1),14780(a,1,2,2))].">
      <j1 rule="para" parents="14578 14780"/>
    </justification>
  </clause>

  <clause id="15161">
    <literal><![CDATA[
      L(x,L(T(y \ z,y),(y \ z) \ z,(y \ z) \ z),u) = L(x,z * y,u)
    ]]></literal>
    <justification jstring="[para(76(a,1),14773(a,2,2,2))].">
      <j1 rule="para" parents="76 14773"/>
    </justification>
  </clause>

  <clause id="15163">
    <literal><![CDATA[
      K(x,L(((y \ 1) \ z) / y,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(((1 / y) \ z) / y,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(14687(a,1),14794(a,1))].">
      <j1 rule="para" parents="14687 14794"/>
    </justification>
  </clause>

  <clause id="15164">
    <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(14981(a,1),15026(a,2,1))].">
      <j1 rule="para" parents="14981 15026"/>
    </justification>
  </clause>

  <clause id="15165">
    <literal><![CDATA[
      K(x,K(y,z \ (u * ((u \ z) * w)))) = K(x,K(y,L(w,z,u)))
    ]]></literal>
    <justification jstring="[hyper(299,a,14942,a(flip),b,15164,a),flip(a)].">
      <j1 rule="hyper" parents="299 14942 15164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15166">
    <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),15165(a,1,2,2))].">
      <j1 rule="para" parents="95 15165"/>
    </justification>
  </clause>

  <clause id="15167">
    <literal><![CDATA[
      K(x,K(y,L(z,u / w,w))) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(11629(a,2),15166(a,1,2,2))].">
      <j1 rule="para" parents="11629 15166"/>
    </justification>
  </clause>

  <clause id="15168">
    <literal><![CDATA[
      T(x,y * (z * (u * T(w,w * v5)))) = T(x,y * (z * (u * ((w \ v5) \ v5))))
    ]]></literal>
    <justification jstring="[para(76(a,1),14513(a,2,2,2,2,2))].">
      <j1 rule="para" parents="76 14513"/>
    </justification>
  </clause>

  <clause id="15171">
    <literal><![CDATA[
      T(x \ 1,(x \ 1) \ 1) / (y / (1 / (x \ 1))) = x / (y / ((x \ (x * x)) \ 1))
    ]]></literal>
    <justification jstring="[para(937(a,1),14669(a,2,2))].">
      <j1 rule="para" parents="937 14669"/>
    </justification>
  </clause>

  <clause id="15172">
    <literal><![CDATA[
      T(x \ 1,(x \ 1) \ 1) / (y / (1 / (x \ 1))) = x / (y / (x \ 1))
    ]]></literal>
    <justification jstring="[para(9(a,1),15171(a,2,2,2,1))].">
      <j1 rule="para" parents="9 15171"/>
    </justification>
  </clause>

  <clause id="15175">
    <literal><![CDATA[
      (1 / x) / (y / (1 / (x \ 1))) = x / (y / (x \ 1))
    ]]></literal>
    <justification jstring="[para(1690(a,1),15172(a,1,1))].">
      <j1 rule="para" parents="1690 15172"/>
    </justification>
  </clause>

  <clause id="15176">
    <literal><![CDATA[
      (1 / x) / (y / x) = x / (y / (x \ 1))
    ]]></literal>
    <justification jstring="[para(76(a,1),15175(a,1,2,2))].">
      <j1 rule="para" parents="76 15175"/>
    </justification>
  </clause>

  <clause id="15178">
    <literal><![CDATA[
      K(x,y \ (T(z,y \ (y \ 1)) * u)) = K(x,y * (z * ((y * y) \ u)))
    ]]></literal>
    <justification jstring="[para(77(a,1),14724(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="77 14724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15180">
    <literal><![CDATA[
      L(x,y,(z \ 1) * ((((z \ 1) \ 1) \ u) / (z \ 1))) = L(x,y,T(T(u,z) / z,z))
    ]]></literal>
    <justification jstring="[para(8(a,1),14749(a,2,3,2))].">
      <j1 rule="para" parents="8 14749"/>
    </justification>
  </clause>

  <clause id="15181">
    <literal><![CDATA[
      L(x,y,(z \ 1) * ((((z \ 1) \ 1) \ u) / (z \ 1))) = L(x,y,z \ T(u,z))
    ]]></literal>
    <justification jstring="[para(109(a,1),15180(a,2,3))].">
      <j1 rule="para" parents="109 15180"/>
    </justification>
  </clause>

  <clause id="15182">
    <literal><![CDATA[
      L(x,y,(z \ 1) \ T(u,z \ 1)) = L(x,y,z \ T(u,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,6455,a(flip),b,15181,a)].">
      <j1 rule="hyper" parents="65 6455 15181"/>
    </justification>
  </clause>

  <clause id="15183">
    <literal><![CDATA[
      L(x,y,z \ T(u,z \ 1)) = L(x,y,z \ T(u,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,2482,a(flip),b,15182,a)].">
      <j1 rule="hyper" parents="65 2482 15182"/>
    </justification>
  </clause>

  <clause id="15184">
    <literal><![CDATA[
      K(x,L(y,T(1 / (z / u),z),(z / u) \ u)) = K(x,L(y,u,(1 / (z / u)) \ u))
    ]]></literal>
    <justification jstring="[para(2483(a,1),14992(a,1,2))].">
      <j1 rule="para" parents="2483 14992"/>
    </justification>
  </clause>

  <clause id="15185">
    <literal><![CDATA[
      T(x,T(y,z * ((u \ 1) * w)) * (z * ((u \ 1) * w))) = T(x,(z * ((1 / u) * w)) * y)
    ]]></literal>
    <justification jstring="[para(3899(a,1),15098(a,1,2,1))].">
      <j1 rule="para" parents="3899 15098"/>
    </justification>
  </clause>

  <clause id="15186">
    <literal><![CDATA[
      T(x,(y * ((1 / z) * u)) * w) = T(x,(y * ((z \ 1) * u)) * w)
    ]]></literal>
    <justification jstring="[hyper(13267,a,15185,a),flip(a)].">
      <j1 rule="hyper" parents="13267 15185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15187">
    <literal><![CDATA[
      x \ T(x,(y * ((z \ 1) * u)) * w) = K(x,(y * ((1 / z) * u)) * w)
    ]]></literal>
    <justification jstring="[hyper(119,a,15186,a(flip),b,5083,a(flip))].">
      <j1 rule="hyper" parents="119 15186 5083"/>
    </justification>
  </clause>

  <clause id="15188">
    <literal><![CDATA[
      K(x,(y * ((1 / z) * u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * ((z \ 1) * u)) * w) = v5
    ]]></literal>
    <justification jstring="[para(15187(a,1),5155(a,1))].">
      <j1 rule="para" parents="15187 5155"/>
    </justification>
  </clause>

  <clause id="15189">
    <literal><![CDATA[
      R(K(x,y),z,L(L(z,u,w),z,K(x,y))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,11,a(flip),b,14435,a),flip(a)].">
      <j1 rule="hyper" parents="299 11 14435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15191">
    <literal><![CDATA[
      R(K(x,y),z,L(z,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(14171(a,1),15189(a,1,3))].">
      <j1 rule="para" parents="14171 15189"/>
    </justification>
  </clause>

  <clause id="15193">
    <literal><![CDATA[
      K(x,T(y * z,u \ y) / (T(y,u) * (1 / u))) = K(x,L((1 / T(u,y)) \ z,u,y))
    ]]></literal>
    <justification jstring="[para(13695(a,1),14480(a,1,2,1))].">
      <j1 rule="para" parents="13695 14480"/>
    </justification>
  </clause>

  <clause id="15194">
    <literal><![CDATA[
      K(x,T(y * z,u \ y) / (T(y,u) * (u \ 1))) = K(x,L((1 / T(u,y)) \ z,u,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,5915,a(flip),b,15193,a)].">
      <j1 rule="hyper" parents="65 5915 15193"/>
    </justification>
  </clause>

  <clause id="15196">
    <literal><![CDATA[
      ((x * y) * z) / (y * (z * T(1,u * u))) = R(x,y,z * (u \ (1 / u)))
    ]]></literal>
    <justification jstring="[para(68(a,1),14688(a,1,2,2,2,1))].">
      <j1 rule="para" parents="68 14688"/>
    </justification>
  </clause>

  <clause id="15198">
    <literal><![CDATA[
      R(x,y,z * (u \ (1 / u))) = ((x * y) * z) / (y * (z * 1))
    ]]></literal>
    <justification jstring="[para(195(a,1),15196(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="195 15196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15199">
    <literal><![CDATA[
      R(x,y,z * (u \ (1 / u))) = ((x * y) * z) / (y * z)
    ]]></literal>
    <justification jstring="[para(8(a,1),15198(a,2,2,2))].">
      <j1 rule="para" parents="8 15198"/>
    </justification>
  </clause>

  <clause id="15201">
    <literal><![CDATA[
      R(x,y,z * (u \ (1 / u))) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,20,a,b,15199,a),flip(a)].">
      <j1 rule="hyper" parents="299 20 15199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15202">
    <literal><![CDATA[
      R(x,y,1 / z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),15201(a,1,3))].">
      <j1 rule="para" parents="10 15201"/>
    </justification>
  </clause>

  <clause id="15203">
    <literal><![CDATA[
      R(x,y,z \ 1) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(3442,a,15202,a)].">
      <j1 rule="hyper" parents="3442 15202"/>
    </justification>
  </clause>

  <clause id="15205">
    <literal><![CDATA[
      R(1 / x,x,L(x,y,z)) \ (L(x,y,z) \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[para(15203(a,1),1359(a,1,1))].">
      <j1 rule="para" parents="15203 1359"/>
    </justification>
  </clause>

  <clause id="15206">
    <literal><![CDATA[
      T(x,y \ R(z \ 1,u,z)) = T(x,y \ (z \ 1))
    ]]></literal>
    <justification jstring="[para(15203(a,1),13769(a,1,2,2))].">
      <j1 rule="para" parents="15203 13769"/>
    </justification>
  </clause>

  <clause id="15207">
    <literal><![CDATA[
      R(1 / x,x,L(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(41,a,6649,a,b,15205,a),flip(a)].">
      <j1 rule="hyper" parents="41 6649 15205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15208">
    <literal><![CDATA[
      (x \ 1) \ L(x,y,z) = x * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(15207(a,1),374(a,1,1))].">
      <j1 rule="para" parents="15207 374"/>
    </justification>
  </clause>

  <clause id="15210">
    <literal><![CDATA[
      (x * x) * ((x \ L(x,y,z)) * u) = (x * L(x,y,z)) * u
    ]]></literal>
    <justification jstring="[para(15208(a,1),731(a,2,1))].">
      <j1 rule="para" parents="15208 731"/>
    </justification>
  </clause>

  <clause id="15211">
    <literal><![CDATA[
      (x \ L(x,y,z)) * ((x * x) * u) = (x * L(x,y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(65,a,12294,a,b,15210,a)].">
      <j1 rule="hyper" parents="65 12294 15210"/>
    </justification>
  </clause>

  <clause id="15212">
    <literal><![CDATA[
      ((x * ((y * (x / y)) \ y)) / x) \ 1 = x / (x * ((((x / (1 / (x \ y))) / x) \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(8517(a,1),14400(a,1,1,1,2))].">
      <j1 rule="para" parents="8517 14400"/>
    </justification>
  </clause>

  <clause id="15213">
    <literal><![CDATA[
      x / (x * ((((x / (1 / (x \ y))) / x) \ 1) \ 1)) = ((x / (x / y)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(5707(a,1),15212(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5707 15212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15214">
    <literal><![CDATA[
      x / (x * ((1 / ((x / ((x \ y) \ 1)) / x)) \ 1)) = ((x / (x / y)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(9776(a,2),15213(a,1,2,2,1))].">
      <j1 rule="para" parents="9776 15213"/>
    </justification>
  </clause>

  <clause id="15215">
    <literal><![CDATA[
      x / (x * ((x / ((x \ y) \ 1)) / x)) = ((x / (x / y)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(79(a,1),15214(a,1,2,2))].">
      <j1 rule="para" parents="79 15214"/>
    </justification>
  </clause>

  <clause id="15217">
    <literal><![CDATA[
      x / (x / ((y / x) \ 1)) = ((x / (x / y)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(11770(a,1),15215(a,1,2))].">
      <j1 rule="para" parents="11770 15215"/>
    </justification>
  </clause>

  <clause id="15218">
    <literal><![CDATA[
      1 / (x / (x / ((y / x) \ 1))) = (x / (x / y)) / x
    ]]></literal>
    <justification jstring="[hyper(192,a,15217,a(flip))].">
      <j1 rule="hyper" parents="192 15217"/>
    </justification>
  </clause>

  <clause id="15219">
    <literal><![CDATA[
      (x \ 1) * (y * L(y \ ((x \ 1) \ L(y,x,x)),z,u)) = L(x,z,u) * ((x \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(299,a,14379,a(flip),b,14657,a),flip(a)].">
      <j1 rule="hyper" parents="299 14379 14657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15220">
    <literal><![CDATA[
      (x \ 1) * (y * L(y \ (L(x,x,x) * y),z,u)) = L(x,z,u) * ((x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(2816(a,1),15219(a,1,2,2,1,2))].">
      <j1 rule="para" parents="2816 15219"/>
    </justification>
  </clause>

  <clause id="15221">
    <literal><![CDATA[
      (x \ 1) * (L(L(x,x,x),y,z) * u) = L(x,y,z) * ((x \ 1) * u)
    ]]></literal>
    <justification jstring="[para(682(a,1),15220(a,1,2))].">
      <j1 rule="para" parents="682 15220"/>
    </justification>
  </clause>

  <clause id="15222">
    <literal><![CDATA[
      L(x,y,z) * ((x \ 1) * u) = (1 / x) * (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,6756,a(flip),b,15221,a),flip(a)].">
      <j1 rule="hyper" parents="65 6756 15221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15223">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ ((1 / x) * (L(x,y,z) * u)) = L(u,x \ 1,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(15222(a,1),1275(a,1,2))].">
      <j1 rule="para" parents="15222 1275"/>
    </justification>
  </clause>

  <clause id="15224">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ ((1 / x) * (L(x,y,z) * u)) = L(u,x,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,2526,a(flip),b,15223,a),flip(a)].">
      <j1 rule="hyper" parents="299 2526 15223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15225">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (x * (L(x \ 1,y,z) * u)) = L(u,x,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(6645(a,1),15224(a,1,2))].">
      <j1 rule="para" parents="6645 15224"/>
    </justification>
  </clause>

  <clause id="15226">
    <literal><![CDATA[
      L(x,L(y,z,u),y) = L(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,6646,a(flip),b,15225,a)].">
      <j1 rule="hyper" parents="65 6646 15225"/>
    </justification>
  </clause>

  <clause id="15227">
    <literal><![CDATA[
      T(x * K((1 / y) * (y \ x),x),y \ T(y \ 1,x * y)) = R(x,y \ T(y \ 1,x * y),x)
    ]]></literal>
    <justification jstring="[para(10516(a,1),14762(a,1,1,2))].">
      <j1 rule="para" parents="10516 14762"/>
    </justification>
  </clause>

  <clause id="15228">
    <literal><![CDATA[
      K(x,y * ((K(z,z * u) * (z \ w)) \ K(z * K(z * u,z),u))) = K(x,y / (R(z,u,z) \ w))
    ]]></literal>
    <justification jstring="[para(5695(a,1),14768(a,1,2,2,1))].">
      <j1 rule="para" parents="5695 14768"/>
    </justification>
  </clause>

  <clause id="15229">
    <literal><![CDATA[
      T(x * K(y \ (y \ x),x),y \ T(y \ 1,x * y)) = R(x,y \ T(y \ 1,x * y),x)
    ]]></literal>
    <justification jstring="[para(14191(a,1),15227(a,1,1,2))].">
      <j1 rule="para" parents="14191 15227"/>
    </justification>
  </clause>

  <clause id="15230">
    <literal><![CDATA[
      T(x * K(x,y * y),y \ T(y \ 1,x * y)) = R(x,y \ T(y \ 1,x * y),x)
    ]]></literal>
    <justification jstring="[para(14745(a,1),15229(a,1,1,2))].">
      <j1 rule="para" parents="14745 15229"/>
    </justification>
  </clause>

  <clause id="15231">
    <literal><![CDATA[
      T(T(x,y * y),y \ T(y \ 1,x * y)) = R(x,y \ T(y \ 1,x * y),x)
    ]]></literal>
    <justification jstring="[para(5083(a,2),15230(a,1,1))].">
      <j1 rule="para" parents="5083 15230"/>
    </justification>
  </clause>

  <clause id="15232">
    <literal><![CDATA[
      T(T(x,y * y),y \ T(y \ 1,x)) = R(x,y \ T(y \ 1,x * y),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,13829,a(flip),b,15231,a)].">
      <j1 rule="hyper" parents="65 13829 15231"/>
    </justification>
  </clause>

  <clause id="15233">
    <literal><![CDATA[
      T(x,y * (y * (y \ T(y \ 1,x)))) = R(x,y \ T(y \ 1,x * y),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,14446,a(flip),b,15232,a)].">
      <j1 rule="hyper" parents="65 14446 15232"/>
    </justification>
  </clause>

  <clause id="15234">
    <literal><![CDATA[
      R(x,y \ T(y \ 1,x * y),x) = T(x,y * T(y \ 1,x))
    ]]></literal>
    <justification jstring="[para(10(a,1),15233(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 15233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15235">
    <literal><![CDATA[
      R(x,y \ T(y \ 1,x * y),x) = x
    ]]></literal>
    <justification jstring="[hyper(299,a,3609,a(flip),b,15234,a),flip(a)].">
      <j1 rule="hyper" parents="299 3609 15234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15238">
    <literal><![CDATA[
      (x \ T(x \ 1,y * x)) * y = T((1 / x) * (y / x),y)
    ]]></literal>
    <justification jstring="[para(15235(a,1),14761(a,1,2))].">
      <j1 rule="para" parents="15235 14761"/>
    </justification>
  </clause>

  <clause id="15239">
    <literal><![CDATA[
      T(1 / x,y * x) * (x \ y) = T((1 / x) * (y / x),y)
    ]]></literal>
    <justification jstring="[hyper(65,a,15049,a(flip),b,15238,a)].">
      <j1 rule="hyper" parents="65 15049 15238"/>
    </justification>
  </clause>

  <clause id="15240">
    <literal><![CDATA[
      K(x,y * ((K(z,z * u) * (z \ w)) \ K(z,T(u,z * u)))) = K(x,y / (R(z,u,z) \ w))
    ]]></literal>
    <justification jstring="[para(8132(a,1),15228(a,1,2,2,2))].">
      <j1 rule="para" parents="8132 15228"/>
    </justification>
  </clause>

  <clause id="15241">
    <literal><![CDATA[
      K(x,y * ((K(z,z * u) * (z \ w)) \ K(z,u))) = K(x,y / (R(z,u,z) \ w))
    ]]></literal>
    <justification jstring="[para(4619(a,1),15240(a,1,2,2,2))].">
      <j1 rule="para" parents="4619 15240"/>
    </justification>
  </clause>

  <clause id="15242">
    <literal><![CDATA[
      K(x,y * (((z \ u) \ K(z * w,z)) * K(z,w))) = K(x,y / (R(z,w,z) \ u))
    ]]></literal>
    <justification jstring="[para(14312(a,1),15241(a,1,2,2))].">
      <j1 rule="para" parents="14312 15241"/>
    </justification>
  </clause>

  <clause id="15243">
    <literal><![CDATA[
      L(T(x,x \ y) \ L(T(x,x \ y),z,u),x,x) = T(x,x * y) \ L(T(x,x * y),z,u)
    ]]></literal>
    <justification jstring="[para(14495(a,1),14499(a,2,2,1))].">
      <j1 rule="para" parents="14495 14499"/>
    </justification>
  </clause>

  <clause id="15244">
    <literal><![CDATA[
      L(T(x,x \ y) \ L(T(x,x \ y),z,u),x,x) = T(x \ L(x,z,u),x * y)
    ]]></literal>
    <justification jstring="[hyper(299,a,6731,a(flip),b,15243,a),flip(a)].">
      <j1 rule="hyper" parents="299 6731 15243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15245">
    <literal><![CDATA[
      L(T(x \ L(x,y,z),x \ u),x,x) = T(x \ L(x,y,z),x * u)
    ]]></literal>
    <justification jstring="[para(6731(a,1),15244(a,1,1))].">
      <j1 rule="para" parents="6731 15244"/>
    </justification>
  </clause>

  <clause id="15246">
    <literal><![CDATA[
      T(x \ L(x,y,z),x \ u) = T(x \ L(x,y,z),x * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,13974,a(flip),b,15245,a)].">
      <j1 rule="hyper" parents="65 13974 15245"/>
    </justification>
  </clause>

  <clause id="15247">
    <literal><![CDATA[
      (x * y) \ ((x \ L(x,z,u)) * (x * y)) = T(x \ L(x,z,u),x \ y)
    ]]></literal>
    <justification jstring="[hyper(299,a,22,a(flip),b,15246,a)].">
      <j1 rule="hyper" parents="299 22 15246"/>
    </justification>
  </clause>

  <clause id="15249">
    <literal><![CDATA[
      (x * y) \ (x * ((x \ L(x,z,u)) * y)) = T(x \ L(x,z,u),x \ y)
    ]]></literal>
    <justification jstring="[para(6538(a,1),15247(a,1,2))].">
      <j1 rule="para" parents="6538 15247"/>
    </justification>
  </clause>

  <clause id="15250">
    <literal><![CDATA[
      L(T(x \ L(x,y,z),u),u,x) = T(x \ L(x,y,z),x \ u)
    ]]></literal>
    <justification jstring="[hyper(855,a,15249,a)].">
      <j1 rule="hyper" parents="855 15249"/>
    </justification>
  </clause>

  <clause id="15251">
    <literal><![CDATA[
      T(x \ L(x,y,z),x \ u) = T(x \ L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,13974,a(flip),b,15250,a),flip(a)].">
      <j1 rule="hyper" parents="65 13974 15250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15253">
    <literal><![CDATA[
      T(((x \ 1) \ 1) * K(y,(x \ 1) \ 1),x \ z) = T(x,x * z) * K(y,T(x,x * z))
    ]]></literal>
    <justification jstring="[para(14496(a,1),14507(a,2,2,2))].">
      <j1 rule="para" parents="14496 14507"/>
    </justification>
  </clause>

  <clause id="15254">
    <literal><![CDATA[
      T(((x \ 1) \ 1) * K(y,(x \ 1) \ 1),x \ z) = T(x,x * z) * K(y,T(x,z))
    ]]></literal>
    <justification jstring="[para(7469(a,1),15253(a,2,2))].">
      <j1 rule="para" parents="7469 15253"/>
    </justification>
  </clause>

  <clause id="15255">
    <literal><![CDATA[
      T(((x \ 1) \ 1) * K(y,(x \ 1) \ 1),x \ z) = T(x * K(y,x),z * x)
    ]]></literal>
    <justification jstring="[hyper(299,a,12541,a(flip),b,15254,a),flip(a)].">
      <j1 rule="hyper" parents="299 12541 15254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15256">
    <literal><![CDATA[
      T((x \ 1) \ K(y,x),x \ z) = T(x * K(y,x),z * x)
    ]]></literal>
    <justification jstring="[para(4804(a,1),15255(a,1,1))].">
      <j1 rule="para" parents="4804 15255"/>
    </justification>
  </clause>

  <clause id="15257">
    <literal><![CDATA[
      T((T(x,y) \ 1) \ K(x * y,T(x,y)),T(x,y) \ z) = T(y \ T(x * y,T(x,y)),z * T(x,y))
    ]]></literal>
    <justification jstring="[para(14317(a,1),15256(a,2,1))].">
      <j1 rule="para" parents="14317 15256"/>
    </justification>
  </clause>

  <clause id="15258">
    <literal><![CDATA[
      (1 / ((x * y) / x)) \ T(1 / y,(x * y) / x) = (1 / y) * (1 / (1 / ((x * y) / x)))
    ]]></literal>
    <justification jstring="[para(3740(a,1),14581(a,1,2))].">
      <j1 rule="para" parents="3740 14581"/>
    </justification>
  </clause>

  <clause id="15260">
    <literal><![CDATA[
      (1 / x) * (1 / (1 / ((y * x) / y))) = (1 / ((y * x) / y)) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(5494(a,1),15258(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5494 15258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15261">
    <literal><![CDATA[
      (1 / x) * (1 / (1 / ((y * x) / y))) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(299,a,12301,a(flip),b,15260,a),flip(a)].">
      <j1 rule="hyper" parents="299 12301 15260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15263">
    <literal><![CDATA[
      K(x,L(((y \ 1) \ (z * ((y \ 1) \ 1))) / y,u,w)) = K(x,L(T(z,y \ 1) * y,u,w))
    ]]></literal>
    <justification jstring="[para(76(a,1),14686(a,2,2,1,2))].">
      <j1 rule="para" parents="76 14686"/>
    </justification>
  </clause>

  <clause id="15265">
    <literal><![CDATA[
      K(x,L(((y \ 1) \ (z * ((y \ 1) \ 1))) / y,u,w)) = K(x,L((1 / y) \ z,u,w))
    ]]></literal>
    <justification jstring="[hyper(299,a,14832,a(flip),b,15263,a),flip(a)].">
      <j1 rule="hyper" parents="299 14832 15263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15266">
    <literal><![CDATA[
      K(x,L(((1 / y) \ (z * y)) / y,u,w)) = K(x,L((1 / y) \ z,u,w))
    ]]></literal>
    <justification jstring="[para(6598(a,1),15265(a,1,2,1,1))].">
      <j1 rule="para" parents="6598 15265"/>
    </justification>
  </clause>

  <clause id="15267">
    <literal><![CDATA[
      T(T(x,K(y,(y \ 1) \ (y \ z))),y \ z) = T(x,y \ (1 * T(1 \ z,y)))
    ]]></literal>
    <justification jstring="[para(10(a,1),14721(a,1,2))].">
      <j1 rule="para" parents="10 14721"/>
    </justification>
  </clause>

  <clause id="15268">
    <literal><![CDATA[
      T(T(x,y \ z),K(y,(y \ 1) \ (y \ z))) = T(x,y \ (1 * T(1 \ z,y)))
    ]]></literal>
    <justification jstring="[hyper(861,a,15267,a)].">
      <j1 rule="hyper" parents="861 15267"/>
    </justification>
  </clause>

  <clause id="15270">
    <literal><![CDATA[
      T(x,y \ (1 * T(1 \ z,y))) = T(x,T(y \ z,y))
    ]]></literal>
    <justification jstring="[hyper(13300,a,15268,a),flip(a)].">
      <j1 rule="hyper" parents="13300 15268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15271">
    <literal><![CDATA[
      T(x,y \ (1 * T(1 \ z,y))) = T(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(299,a,8181,a(flip),b,15270,a),flip(a)].">
      <j1 rule="hyper" parents="299 8181 15270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15272">
    <literal><![CDATA[
      T(x,y \ (1 * T(z,y))) = T(x,z / y)
    ]]></literal>
    <justification jstring="[para(67(a,1),15271(a,1,2,2,2,1))].">
      <j1 rule="para" parents="67 15271"/>
    </justification>
  </clause>

  <clause id="15273">
    <literal><![CDATA[
      T(x,y \ T(z,y)) = T(x,z / y)
    ]]></literal>
    <justification jstring="[para(7(a,1),15272(a,1,2,2))].">
      <j1 rule="para" parents="7 15272"/>
    </justification>
  </clause>

  <clause id="15274">
    <literal><![CDATA[
      T(1 / x,y * x) = T(x \ 1,y / x)
    ]]></literal>
    <justification jstring="[hyper(65,a,14694,a(flip),b,15273,a)].">
      <j1 rule="hyper" parents="65 14694 15273"/>
    </justification>
  </clause>

  <clause id="15275">
    <literal><![CDATA[
      T(x,T(y,z) \ z) = T(x,z / y)
    ]]></literal>
    <justification jstring="[para(4396(a,2),15273(a,1,2))].">
      <j1 rule="para" parents="4396 15273"/>
    </justification>
  </clause>

  <clause id="15276">
    <literal><![CDATA[
      T((x * y) / x,z / (z \ x)) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,(z \ x) \ ((z \ x) \ 1)) = u
    ]]></literal>
    <justification jstring="[para(15273(a,1),14796(a,1))].">
      <j1 rule="para" parents="15273 14796"/>
    </justification>
  </clause>

  <clause id="15277">
    <literal><![CDATA[
      T(x,y / (z / y)) = T(x,(y \ z) \ y)
    ]]></literal>
    <justification jstring="[para(109(a,1),15275(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="109 15275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15278">
    <literal><![CDATA[
      K((T(x,y) \ y) \ T(z,y / x),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(z / (T(x,y) \ y),u) = w
    ]]></literal>
    <justification jstring="[para(15275(a,1),13914(a,1,1,2))].">
      <j1 rule="para" parents="15275 13914"/>
    </justification>
  </clause>

  <clause id="15279">
    <literal><![CDATA[
      T(1 / x,y * x) = T(x \ 1,x \ y)
    ]]></literal>
    <justification jstring="[hyper(299,a,7153,a(flip),b,15274,a),flip(a)].">
      <j1 rule="hyper" parents="299 7153 15274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15280">
    <literal><![CDATA[
      T(x * y,1 / y) / (1 / y) = (x * y) / T(y \ 1,y \ x)
    ]]></literal>
    <justification jstring="[para(15279(a,1),4382(a,2,2))].">
      <j1 rule="para" parents="15279 4382"/>
    </justification>
  </clause>

  <clause id="15281">
    <literal><![CDATA[
      T(x \ 1,x \ y) * (x \ y) = T((1 / x) * (y / x),y)
    ]]></literal>
    <justification jstring="[para(15279(a,1),15239(a,1,1))].">
      <j1 rule="para" parents="15279 15239"/>
    </justification>
  </clause>

  <clause id="15282">
    <literal><![CDATA[
      T(x * y,y \ 1) / (1 / y) = (x * y) / T(y \ 1,y \ x)
    ]]></literal>
    <justification jstring="[para(3733(a,1),15280(a,1,1))].">
      <j1 rule="para" parents="3733 15280"/>
    </justification>
  </clause>

  <clause id="15283">
    <literal><![CDATA[
      T((1 / ((1 / x) \ x)) * y,(1 / x) \ x) = (x \ (1 / x)) * T(y,x * x)
    ]]></literal>
    <justification jstring="[para(332(a,1),14809(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="332 14809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15284">
    <literal><![CDATA[
      T((1 / ((1 / x) \ x)) * y,(1 / x) \ x) = (x \ 1) * (x \ T(y,x * x))
    ]]></literal>
    <justification jstring="[hyper(299,a,1710,a(flip),b,15283,a),flip(a)].">
      <j1 rule="hyper" parents="299 1710 15283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15285">
    <literal><![CDATA[
      T((x \ (1 / x)) * y,(1 / x) \ x) = (x \ 1) * (x \ T(y,x * x))
    ]]></literal>
    <justification jstring="[para(1081(a,1),15284(a,1,1,1))].">
      <j1 rule="para" parents="1081 15284"/>
    </justification>
  </clause>

  <clause id="15286">
    <literal><![CDATA[
      T((x \ 1) * (x \ y),(1 / x) \ x) = (x \ 1) * (x \ T(y,x * x))
    ]]></literal>
    <justification jstring="[para(1710(a,1),15285(a,1,1))].">
      <j1 rule="para" parents="1710 15285"/>
    </justification>
  </clause>

  <clause id="15287">
    <literal><![CDATA[
      T((x \ 1) * (x \ y),x * x) = (x \ 1) * (x \ T(y,x * x))
    ]]></literal>
    <justification jstring="[hyper(65,a,14296,a(flip),b,15286,a)].">
      <j1 rule="hyper" parents="65 14296 15286"/>
    </justification>
  </clause>

  <clause id="15288">
    <literal><![CDATA[
      T((T(x,y) \ 1) \ K(x * y,x),T(x,y) \ z) = T(y \ T(x * y,T(x,y)),z * T(x,y))
    ]]></literal>
    <justification jstring="[para(6895(a,1),15257(a,1,1,2))].">
      <j1 rule="para" parents="6895 15257"/>
    </justification>
  </clause>

  <clause id="15289">
    <literal><![CDATA[
      K(x * ((x \ 1) \ T(y,(x \ 1) \ ((x \ 1) \ 1))),x \ 1) = K(((x \ 1) \ y) / (x \ 1),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,7539,a(flip),b,14261,a),flip(a)].">
      <j1 rule="hyper" parents="299 7539 14261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15290">
    <literal><![CDATA[
      K(x * ((x \ 1) \ T(y,(x \ 1) \ ((x \ 1) \ 1))),x \ 1) = K((x \ 1) \ ((x \ 1) \ y),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,5192,a(flip),b,15289,a),flip(a)].">
      <j1 rule="hyper" parents="299 5192 15289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15291">
    <literal><![CDATA[
      L(x,((y \ 1) \ (z * ((y \ 1) \ 1))) \ (z * ((y \ 1) \ 1)),u) = L(x,T(y \ 1,y \ (z * y)),u)
    ]]></literal>
    <justification jstring="[para(14211(a,1),14609(a,2,2))].">
      <j1 rule="para" parents="14211 14609"/>
    </justification>
  </clause>

  <clause id="15292">
    <literal><![CDATA[
      L(x,((y \ 1) \ (z * ((y \ 1) \ 1))) \ (z * ((y \ 1) \ 1)),u) = L(x,T(y \ 1,T(z,y)),u)
    ]]></literal>
    <justification jstring="[para(22(a,2),15291(a,2,2,2))].">
      <j1 rule="para" parents="22 15291"/>
    </justification>
  </clause>

  <clause id="15293">
    <literal><![CDATA[
      L(x,((y \ 1) \ (z * ((y \ 1) \ 1))) \ (z * ((y \ 1) \ 1)),u) = L(x,T(y \ 1,z),u)
    ]]></literal>
    <justification jstring="[para(7149(a,1),15292(a,2,2))].">
      <j1 rule="para" parents="7149 15292"/>
    </justification>
  </clause>

  <clause id="15294">
    <literal><![CDATA[
      L(x,((1 / y) \ (z * y)) \ (z * ((y \ 1) \ 1)),u) = L(x,T(y \ 1,z),u)
    ]]></literal>
    <justification jstring="[para(6598(a,1),15293(a,1,2,1))].">
      <j1 rule="para" parents="6598 15293"/>
    </justification>
  </clause>

  <clause id="15295">
    <literal><![CDATA[
      L(x,((y \ 1) \ (z * y)) \ (z * y),u) = L(x,T(y \ 1,z),u)
    ]]></literal>
    <justification jstring="[para(15100(a,1),15294(a,1,2))].">
      <j1 rule="para" parents="15100 15294"/>
    </justification>
  </clause>

  <clause id="15296">
    <literal><![CDATA[
      L(x,(y \ (z * y)) \ (z * y),u) = L(x,T(y \ 1,z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,2858,a(flip),b,15295,a)].">
      <j1 rule="hyper" parents="65 2858 15295"/>
    </justification>
  </clause>

  <clause id="15297">
    <literal><![CDATA[
      L(x,T(y \ 1,z),u) = L(x,T(y,z),u)
    ]]></literal>
    <justification jstring="[para(4452(a,2),15296(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4452 15296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15298">
    <literal><![CDATA[
      L(x,T(y,z),y) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(6676,a,15297,a),flip(a)].">
      <j1 rule="hyper" parents="6676 15297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15299">
    <literal><![CDATA[
      L(x,T(y,z),T(y,z)) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(6692,a,15298,a)].">
      <j1 rule="hyper" parents="6692 15298"/>
    </justification>
  </clause>

  <clause id="15300">
    <literal><![CDATA[
      L(x,(y \ z) \ z,y) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,14512,a(flip),b,15298,a)].">
      <j1 rule="hyper" parents="65 14512 15298"/>
    </justification>
  </clause>

  <clause id="15301">
    <literal><![CDATA[
      L(T(x,y) \ z,x,x) = (1 / T(x,y)) * z
    ]]></literal>
    <justification jstring="[hyper(613,a,15299,a),flip(a)].">
      <j1 rule="hyper" parents="613 15299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15302">
    <literal><![CDATA[
      (T(x,y) \ 1) \ L(z,x,x) = T((x \ 1) \ 1,y) * z
    ]]></literal>
    <justification jstring="[para(15299(a,1),3182(a,1,2))].">
      <j1 rule="para" parents="15299 3182"/>
    </justification>
  </clause>

  <clause id="15303">
    <literal><![CDATA[
      L(T(T(x,y),x \ 1) * z,T(T(x,y),x \ 1),T(T(x,y),x \ 1)) = T(x,y) * L(z,T(x,y),T(x,y))
    ]]></literal>
    <justification jstring="[para(15299(a,1),13104(a,2,2))].">
      <j1 rule="para" parents="15299 13104"/>
    </justification>
  </clause>

  <clause id="15304">
    <literal><![CDATA[
      L(x,(y \ z) \ z,(y \ z) \ z) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,6689,a,b,15300,a)].">
      <j1 rule="hyper" parents="65 6689 15300"/>
    </justification>
  </clause>

  <clause id="15305">
    <literal><![CDATA[
      K(x,y) \ ((((y * x) / y) \ 1) * z) = (1 / T(x,x \ 1)) * z
    ]]></literal>
    <justification jstring="[hyper(65,a,15149,a(flip),b,15301,a)].">
      <j1 rule="hyper" parents="65 15149 15301"/>
    </justification>
  </clause>

  <clause id="15307">
    <literal><![CDATA[
      L(x,L(T(y \ z,y),y,y),u) = L(x,z * y,u)
    ]]></literal>
    <justification jstring="[para(15304(a,1),15161(a,1,2))].">
      <j1 rule="para" parents="15304 15161"/>
    </justification>
  </clause>

  <clause id="15308">
    <literal><![CDATA[
      L(x,T((1 / y) * z,y),u) = L(x,z * y,u)
    ]]></literal>
    <justification jstring="[para(515(a,1),15307(a,1,2))].">
      <j1 rule="para" parents="515 15307"/>
    </justification>
  </clause>

  <clause id="15310">
    <literal><![CDATA[
      L(x,T((1 / y) * z,y),u) = L(x,T(y * z,y),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,14080,a,b,15308,a),flip(a)].">
      <j1 rule="hyper" parents="299 14080 15308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15311">
    <literal><![CDATA[
      L(x,y * ((y \ z) * y),u) = L(x,T(y * z,y),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,2568,a(flip),b,15310,a)].">
      <j1 rule="hyper" parents="65 2568 15310"/>
    </justification>
  </clause>

  <clause id="15312">
    <literal><![CDATA[
      L(x,y * (y * (z / y)),u) = L(x,T(y * z,y),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,11360,a(flip),b,15311,a)].">
      <j1 rule="hyper" parents="65 11360 15311"/>
    </justification>
  </clause>

  <clause id="15313">
    <literal><![CDATA[
      L(x,T(y * (T(y,z) * z),y),u) = L(x,L(z,T(y,z),T(y,z)),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,8482,a,b,15312,a),flip(a)].">
      <j1 rule="hyper" parents="65 8482 15312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15315">
    <literal><![CDATA[
      K(x,y) \ ((((y * x) / y) \ 1) * z) = (x \ 1) * z
    ]]></literal>
    <justification jstring="[para(262(a,1),15305(a,2,1))].">
      <j1 rule="para" parents="262 15305"/>
    </justification>
  </clause>

  <clause id="15316">
    <literal><![CDATA[
      K(x,y) * ((((x * y) / x) \ 1) * z) = (y \ 1) * z
    ]]></literal>
    <justification jstring="[hyper(5452,a,15315,a)].">
      <j1 rule="hyper" parents="5452 15315"/>
    </justification>
  </clause>

  <clause id="15317">
    <literal><![CDATA[
      K(x,L(((((y * z) / y) \ 1) * u) \ w,(((y * z) / y) \ 1) * u,K(y,z))) = K(x,((z \ 1) * u) \ (K(y,z) * w))
    ]]></literal>
    <justification jstring="[para(15316(a,1),8404(a,2,2,1))].">
      <j1 rule="para" parents="15316 8404"/>
    </justification>
  </clause>

  <clause id="15318">
    <literal><![CDATA[
      L(x,T(y * (T(y,z) * z),y),u) = L(x,L(z,y,y),u)
    ]]></literal>
    <justification jstring="[para(15299(a,1),15313(a,2,2))].">
      <j1 rule="para" parents="15299 15313"/>
    </justification>
  </clause>

  <clause id="15319">
    <literal><![CDATA[
      L(x,(T(y,z) * z) * y,u) = L(x,L(z,y,y),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,14080,a(flip),b,15318,a)].">
      <j1 rule="hyper" parents="65 14080 15318"/>
    </justification>
  </clause>

  <clause id="15321">
    <literal><![CDATA[
      L(x,(y * z) * T(y,z),u) = L(x,L(z,y,y),u)
    ]]></literal>
    <justification jstring="[para(7127(a,1),15319(a,1,2))].">
      <j1 rule="para" parents="7127 15319"/>
    </justification>
  </clause>

  <clause id="15322">
    <literal><![CDATA[
      L(x,R(y,z,z),u) = L(x,L(y,z,z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,8949,a(flip),b,15321,a)].">
      <j1 rule="hyper" parents="65 8949 15321"/>
    </justification>
  </clause>

  <clause id="15323">
    <literal><![CDATA[
      L(T(T(x,y),x \ 1) * z,T(T(x,y),x \ 1),T(T(x,y),x \ 1)) = T(x,y) * L(z,x,x)
    ]]></literal>
    <justification jstring="[para(15299(a,1),15303(a,2,2))].">
      <j1 rule="para" parents="15299 15303"/>
    </justification>
  </clause>

  <clause id="15326">
    <literal><![CDATA[
      K(K((x / (1 / y)) * ((x / (1 / y)) * z),x * y),u) = K((x / (y \ 1)) * (1 / T(x / (1 / y),z)),u)
    ]]></literal>
    <justification jstring="[para(14285(a,1),14521(a,1,1))].">
      <j1 rule="para" parents="14285 14521"/>
    </justification>
  </clause>

  <clause id="15327">
    <literal><![CDATA[
      K(K((x / (y \ 1)) * ((x / (1 / y)) * z),x * y),u) = K((x / (y \ 1)) * (1 / T(x / (1 / y),z)),u)
    ]]></literal>
    <justification jstring="[para(5624(a,1),15326(a,1,1))].">
      <j1 rule="para" parents="5624 15326"/>
    </justification>
  </clause>

  <clause id="15328">
    <literal><![CDATA[
      K(x,K(y * z,(y / (z \ 1)) * ((y / (1 / z)) * u))) = K((y / (z \ 1)) * (1 / T(y / (1 / z),u)),x)
    ]]></literal>
    <justification jstring="[hyper(6285,a,15327,a)].">
      <j1 rule="hyper" parents="6285 15327"/>
    </justification>
  </clause>

  <clause id="15329">
    <literal><![CDATA[
      x * ((((x \ 1) \ 1) \ R(y,z,u)) * (x \ (1 / x))) = T(R((x * x) \ y,z,u),x \ (x \ 1))
    ]]></literal>
    <justification jstring="[para(936(a,1),14778(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="936 14778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15330">
    <literal><![CDATA[
      x * ((((x \ 1) \ 1) \ R(y,z,u)) * (x \ (1 / x))) = R(T((x * x) \ y,x \ (x \ 1)),z,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,27,a,b,15329,a),flip(a)].">
      <j1 rule="hyper" parents="299 27 15329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15332">
    <literal><![CDATA[
      x * ((((x \ 1) \ 1) \ R(y,z,u)) * (x \ (1 / x))) = R(y / (x * x),z,u)
    ]]></literal>
    <justification jstring="[para(1057(a,1),15330(a,2,1))].">
      <j1 rule="para" parents="1057 15330"/>
    </justification>
  </clause>

  <clause id="15333">
    <literal><![CDATA[
      x * (x \ (R(y,z,u) / (x * x))) = R(y / (x * x),z,u)
    ]]></literal>
    <justification jstring="[para(14852(a,1),15332(a,1,2))].">
      <j1 rule="para" parents="14852 15332"/>
    </justification>
  </clause>

  <clause id="15334">
    <literal><![CDATA[
      R(x / (y * y),z,u) = R(x,z,u) / (y * y)
    ]]></literal>
    <justification jstring="[hyper(251,a,15333,a),flip(a)].">
      <j1 rule="hyper" parents="251 15333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15335">
    <literal><![CDATA[
      R((x * x) * y,z,u) = (x * x) * R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(975,a,15334,a),flip(a)].">
      <j1 rule="hyper" parents="975 15334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15337">
    <literal><![CDATA[
      R(x / (y * y),z,u) * (y * y) = R(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(143,a,15334,a(flip))].">
      <j1 rule="hyper" parents="143 15334"/>
    </justification>
  </clause>

  <clause id="15339">
    <literal><![CDATA[
      (x \ R((x * x) * (1 / x),y,z)) * (1 / x) = R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(15335(a,2),10879(a,1,1,2))].">
      <j1 rule="para" parents="15335 10879"/>
    </justification>
  </clause>

  <clause id="15340">
    <literal><![CDATA[
      R((x * x) \ y,z,u) = (x * x) \ R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(119,a,15337,a(flip),b,692,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 15337 692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15341">
    <literal><![CDATA[
      x * R((x * x) \ y,z,u) = (x \ 1) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(15340(a,2),738(a,1,2))].">
      <j1 rule="para" parents="15340 738"/>
    </justification>
  </clause>

  <clause id="15342">
    <literal><![CDATA[
      (x \ 1) * R(x,y,z) = x * R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(264(a,1),15341(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="264 15341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15343">
    <literal><![CDATA[
      (x \ 1) * R((y \ 1) \ z,u,w) = x * R((y \ (x * x)) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(745(a,1),15341(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="745 15341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15344">
    <literal><![CDATA[
      (x \ R(x,y,z)) * (1 / x) = R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(217(a,1),15339(a,1,1,2,1))].">
      <j1 rule="para" parents="217 15339"/>
    </justification>
  </clause>

  <clause id="15345">
    <literal><![CDATA[
      (x \ 1) \ R(1 / x,y,z) = (x \ 1) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(15344(a,1),10947(a,1,2))].">
      <j1 rule="para" parents="15344 10947"/>
    </justification>
  </clause>

  <clause id="15346">
    <literal><![CDATA[
      (x \ 1) \ R(1 / x,y,z) = x * R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,15342,a(flip),b,15345,a),flip(a)].">
      <j1 rule="hyper" parents="299 15342 15345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15347">
    <literal><![CDATA[
      (x \ 1) * R((x \ 1) \ y,z,u) = x * R(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),15343(a,2,2,1,1))].">
      <j1 rule="para" parents="9 15343"/>
    </justification>
  </clause>

  <clause id="15348">
    <literal><![CDATA[
      x * R(x \ 1,y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,1455,a(flip),b,15347,a),flip(a)].">
      <j1 rule="hyper" parents="65 1455 15347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15349">
    <literal><![CDATA[
      R(1 / x,y,z) * x = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(701,a,15348,a)].">
      <j1 rule="hyper" parents="701 15348"/>
    </justification>
  </clause>

  <clause id="15350">
    <literal><![CDATA[
      (x * y) \ ((x * (y * z)) * R((x * (y * z)) \ (x * y),u,w)) = L(z,y,x) \ R(L(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,4029,a,b,15348,a)].">
      <j1 rule="hyper" parents="65 4029 15348"/>
    </justification>
  </clause>

  <clause id="15351">
    <literal><![CDATA[
      (x \ y) \ R(x \ y,z,u) = x \ (y * R(y \ x,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,1877,a(flip),b,15348,a),flip(a)].">
      <j1 rule="hyper" parents="65 1877 15348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15352">
    <literal><![CDATA[
      x * (y * R(y \ (x \ y),z,u)) = (x \ R(x,z,u)) * y
    ]]></literal>
    <justification jstring="[para(15348(a,1),1945(a,2,1))].">
      <j1 rule="para" parents="15348 1945"/>
    </justification>
  </clause>

  <clause id="15353">
    <literal><![CDATA[
      K(x,y) / T(x,x * y) = R(1 / x,y,x)
    ]]></literal>
    <justification jstring="[hyper(37,a,7230,a,b,15349,a)].">
      <j1 rule="hyper" parents="37 7230 15349"/>
    </justification>
  </clause>

  <clause id="15354">
    <literal><![CDATA[
      R(1 / x,y,x) = 1 / L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,14421,a(flip),b,15353,a),flip(a)].">
      <j1 rule="hyper" parents="65 14421 15353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15355">
    <literal><![CDATA[
      1 / L(x \ 1,y,x \ 1) = R(x,y,x \ 1)
    ]]></literal>
    <justification jstring="[para(76(a,1),15354(a,1,1)),flip(a)].">
      <j1 rule="para" parents="76 15354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15356">
    <literal><![CDATA[
      R(T(x \ 1,T(x,y)),z,x) = 1 / L(x,z,x)
    ]]></literal>
    <justification jstring="[para(3537(a,2),15354(a,1,1))].">
      <j1 rule="para" parents="3537 15354"/>
    </justification>
  </clause>

  <clause id="15357">
    <literal><![CDATA[
      L(1 / x,y,x) \ 1 = R(x,y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,4145,a(flip),b,15355,a)].">
      <j1 rule="hyper" parents="65 4145 15355"/>
    </justification>
  </clause>

  <clause id="15358">
    <literal><![CDATA[
      L(1 / x,y,x) \ 1 = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,15203,a(flip),b,15357,a),flip(a)].">
      <j1 rule="hyper" parents="299 15203 15357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15359">
    <literal><![CDATA[
      L(1 / x,y,x) = 1 / R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(192,a,15358,a),flip(a)].">
      <j1 rule="hyper" parents="192 15358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15361">
    <literal><![CDATA[
      T(R(x \ 1,y,x),T(x,z)) = 1 / L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,27,a(flip),b,15356,a)].">
      <j1 rule="hyper" parents="65 27 15356"/>
    </justification>
  </clause>

  <clause id="15362">
    <literal><![CDATA[
      R(x \ 1,y,x) = L(x,y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(7939,a,15361,a),flip(a)].">
      <j1 rule="hyper" parents="7939 15361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15363">
    <literal><![CDATA[
      R(x \ 1,x,x) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(299,a,2814,a(flip),b,15362,a),flip(a)].">
      <j1 rule="hyper" parents="299 2814 15362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15364">
    <literal><![CDATA[
      T(x,y \ R(z \ 1,y,z)) = T(x,z / (z * (y * z)))
    ]]></literal>
    <justification jstring="[para(15362(a,2),14665(a,1,2,2))].">
      <j1 rule="para" parents="15362 14665"/>
    </justification>
  </clause>

  <clause id="15365">
    <literal><![CDATA[
      T(x,y / (y * (z * y))) = T(x,z \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(65,a,15206,a(flip),b,15364,a),flip(a)].">
      <j1 rule="hyper" parents="65 15206 15364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15367">
    <literal><![CDATA[
      (x * y) \ ((x * (y * z)) * R((x * (y * z)) \ (x * y),u,w)) = L(z,y,x) \ L(R(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[para(29(a,1),15350(a,2,2))].">
      <j1 rule="para" parents="29 15350"/>
    </justification>
  </clause>

  <clause id="15368">
    <literal><![CDATA[
      (x * y) \ (x * ((y * z) * R((y * z) \ y,u,w))) = L(z,y,x) \ L(R(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[para(1148(a,1),15367(a,1,2))].">
      <j1 rule="para" parents="1148 15367"/>
    </justification>
  </clause>

  <clause id="15369">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z * R(z \ 1,u,w)))) = L(z,y,x) \ L(R(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[para(1147(a,1),15368(a,1,2,2))].">
      <j1 rule="para" parents="1147 15368"/>
    </justification>
  </clause>

  <clause id="15370">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z \ R(z,u,w)))) = L(z,y,x) \ L(R(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[para(15348(a,1),15369(a,1,2,2,2))].">
      <j1 rule="para" parents="15348 15369"/>
    </justification>
  </clause>

  <clause id="15371">
    <literal><![CDATA[
      L(x,y,z) \ L(R(x,u,w),y,z) = L(x \ R(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(493,a,15370,a),flip(a)].">
      <j1 rule="hyper" parents="493 15370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15372">
    <literal><![CDATA[
      ((K(x,y) * K(x,z)) \ 1) * ((K(x,y) * K(x,z)) * u) = L(u,K(x,y) * K(x,z),(K(x,y) * K(x,z)) \ 1)
    ]]></literal>
    <justification jstring="[para(8(a,1),14817(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8 14817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15373">
    <literal><![CDATA[
      ((K(x,y) * K(x,z)) \ 1) * ((K(x,y) * K(x,z)) * u) = L(u,K(x,y) * K(x,z),K(y,x) * K(z,x))
    ]]></literal>
    <justification jstring="[para(9424(a,1),15372(a,2,3))].">
      <j1 rule="para" parents="9424 15372"/>
    </justification>
  </clause>

  <clause id="15374">
    <literal><![CDATA[
      (K(x,y) * K(z,y)) * ((K(y,x) * K(y,z)) * u) = L(u,K(y,x) * K(y,z),K(x,y) * K(z,y))
    ]]></literal>
    <justification jstring="[para(9424(a,1),15373(a,1,1))].">
      <j1 rule="para" parents="9424 15373"/>
    </justification>
  </clause>

  <clause id="15375">
    <literal><![CDATA[
      (K(x,y) * K(z,y)) * (K(y,x) * (K(y,z) * u)) = L(u,K(y,x) * K(y,z),K(x,y) * K(z,y))
    ]]></literal>
    <justification jstring="[para(10029(a,1),15374(a,1,2))].">
      <j1 rule="para" parents="10029 15374"/>
    </justification>
  </clause>

  <clause id="15376">
    <literal><![CDATA[
      K(x,y) * (K(z,y) * (K(y,z) * (K(y,x) * u))) = L(u,K(y,z) * K(y,x),K(z,y) * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,12257,a(flip),b,15375,a)].">
      <j1 rule="hyper" parents="65 12257 15375"/>
    </justification>
  </clause>

  <clause id="15377">
    <literal><![CDATA[
      L(x,K(y,z) * K(y,u),K(z,y) * K(u,y)) = K(u,y) * (K(y,u) * x)
    ]]></literal>
    <justification jstring="[para(5432(a,1),15376(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5432 15376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15378">
    <literal><![CDATA[
      L(x,K(y,z) * K(y,u),K(z,y) * K(u,y)) = x
    ]]></literal>
    <justification jstring="[hyper(299,a,5432,a(flip),b,15377,a),flip(a)].">
      <j1 rule="hyper" parents="299 5432 15377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15381">
    <literal><![CDATA[
      L(T(x,R(y / T((1 / x) \ 1,z),u,w)),y / T(1 / (1 / x),z),x) = T(x,R(((x \ 1) \ 1) * (y / T(x,z)),u,w))
    ]]></literal>
    <justification jstring="[para(12503(a,1),15144(a,1,1))].">
      <j1 rule="para" parents="12503 15144"/>
    </justification>
  </clause>

  <clause id="15382">
    <literal><![CDATA[
      L(T(x,R(y / T(x,z),u,w)),y / T(1 / (1 / x),z),x) = T(x,R(((x \ 1) \ 1) * (y / T(x,z)),u,w))
    ]]></literal>
    <justification jstring="[para(79(a,1),15381(a,1,1,2,1,2,1))].">
      <j1 rule="para" parents="79 15381"/>
    </justification>
  </clause>

  <clause id="15383">
    <literal><![CDATA[
      L(T(x,R(x \ y,z,u)),y / T(1 / (1 / x),w),x) = T(x,R(((x \ 1) \ 1) * (y / T(x,w)),z,u))
    ]]></literal>
    <justification jstring="[para(11518(a,1),15382(a,1,1))].">
      <j1 rule="para" parents="11518 15382"/>
    </justification>
  </clause>

  <clause id="15384">
    <literal><![CDATA[
      L(T(x,R(x \ y,z,u)),y / T((1 / x) \ 1,w),x) = T(x,R(((x \ 1) \ 1) * (y / T(x,w)),z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,9301,a(flip),b,15383,a)].">
      <j1 rule="hyper" parents="65 9301 15383"/>
    </justification>
  </clause>

  <clause id="15386">
    <literal><![CDATA[
      T(x,R(((x \ 1) \ 1) * (y / T(x,z)),u,w)) = L(T(x,R(x \ y,u,w)),y / T(x,z),x)
    ]]></literal>
    <justification jstring="[para(79(a,1),15384(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="79 15384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15387">
    <literal><![CDATA[
      T(x,R(((x \ 1) \ 1) * (y / T(x,z)),u,w)) = L(T(x,R(x \ y,u,w)),x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,11068,a(flip),b,15386,a),flip(a)].">
      <j1 rule="hyper" parents="299 11068 15386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15389">
    <literal><![CDATA[
      T(x,R(((x \ 1) \ 1) * (y / T(x,z)),u,w)) = T(x,R(x * (x \ y),u,w))
    ]]></literal>
    <justification jstring="[hyper(299,a,15141,a(flip),b,15387,a),flip(a)].">
      <j1 rule="hyper" parents="299 15141 15387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15390">
    <literal><![CDATA[
      T(x,R(((x \ 1) \ 1) * (y / T(x,z)),u,w)) = T(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(10(a,1),15389(a,2,2,1))].">
      <j1 rule="para" parents="10 15389"/>
    </justification>
  </clause>

  <clause id="15391">
    <literal><![CDATA[
      T(x,R(x * (y / T(1 / (1 / x),z)),u,w)) = T(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(3991(a,1),15390(a,1,2,1))].">
      <j1 rule="para" parents="3991 15390"/>
    </justification>
  </clause>

  <clause id="15392">
    <literal><![CDATA[
      T(((x \ 1) * y) / (x \ 1),(z * (x \ 1)) \ ((z * (x \ 1)) \ (1 / x))) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,(z * (1 / x)) \ ((z * (1 / x)) \ 1)) = u
    ]]></literal>
    <justification jstring="[para(3880(a,1),14797(a,1))].">
      <j1 rule="para" parents="3880 14797"/>
    </justification>
  </clause>

  <clause id="15393">
    <literal><![CDATA[
      T(T(x,(y / z) * T(z \ y,y \ z)),T(z \ y,y \ z) \ (T(z \ y,y \ z) \ u)) = T(T(x,(y / z) * (1 / (z \ y))),u)
    ]]></literal>
    <justification jstring="[para(451(a,1),14756(a,1,1,2))].">
      <j1 rule="para" parents="451 14756"/>
    </justification>
  </clause>

  <clause id="15394">
    <literal><![CDATA[
      (T(x \ 1,x \ y) \ (y / (1 / x))) * T(x \ 1,x \ y) = (y / (1 / x)) * K((x \ 1) \ ((x \ 1) \ y),T(x \ 1,y))
    ]]></literal>
    <justification jstring="[para(7912(a,1),15069(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7912 15069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15395">
    <literal><![CDATA[
      T(T(x,(y \ z) * T(z / y,y / z)),T(y \ z,z \ y) \ (T(y \ z,z \ y) \ u)) = T(T(x,(z / y) * (1 / (y \ z))),u)
    ]]></literal>
    <justification jstring="[para(9384(a,1),15393(a,1,1,2))].">
      <j1 rule="para" parents="9384 15393"/>
    </justification>
  </clause>

  <clause id="15396">
    <literal><![CDATA[
      T(T(x,(y \ z) * T(z / y,z \ y)),T(y \ z,z \ y) \ (T(y \ z,z \ y) \ u)) = T(T(x,(z / y) * (1 / (y \ z))),u)
    ]]></literal>
    <justification jstring="[para(3356(a,1),15395(a,1,1,2,2))].">
      <j1 rule="para" parents="3356 15395"/>
    </justification>
  </clause>

  <clause id="15397">
    <literal><![CDATA[
      T(T(x,(1 / (y \ z)) \ (z / y)),T(y \ z,z \ y) \ (T(y \ z,z \ y) \ u)) = T(T(x,(z / y) * (1 / (y \ z))),u)
    ]]></literal>
    <justification jstring="[para(12439(a,1),15396(a,1,1,2))].">
      <j1 rule="para" parents="12439 15396"/>
    </justification>
  </clause>

  <clause id="15398">
    <literal><![CDATA[
      T(T(x,(y \ z) * (z / y)),T(y \ z,z \ y) \ (T(y \ z,z \ y) \ u)) = T(T(x,(z / y) * (1 / (y \ z))),u)
    ]]></literal>
    <justification jstring="[para(14296(a,1),15397(a,1,1))].">
      <j1 rule="para" parents="14296 15397"/>
    </justification>
  </clause>

  <clause id="15399">
    <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(11020(a,1),13494(a,1,1))].">
      <j1 rule="para" parents="11020 13494"/>
    </justification>
  </clause>

  <clause id="15401">
    <literal><![CDATA[
      K(x,T(T((y * z) * (u / (y * z)),y * z),z * ((y * z) \ u))) = K(x,(z * (u / T(y * z,u))) * R(y,z,u / T(y * z,u)))
    ]]></literal>
    <justification jstring="[para(13825(a,1),13293(a,1,2))].">
      <j1 rule="para" parents="13825 13293"/>
    </justification>
  </clause>

  <clause id="15402">
    <literal><![CDATA[
      L((x * (y * z)) \ ((x * y) * z),a(u,w,u) \ (x * (a(u,w,u) * (y * z))),a(u,w,u)) = a(x,a(u,w,u) * y,z)
    ]]></literal>
    <justification jstring="[para(13668(a,1),13999(a,1,1,1))].">
      <j1 rule="para" parents="13668 13999"/>
    </justification>
  </clause>

  <clause id="15403">
    <literal><![CDATA[
      L(a(x,y,z),a(u,w,u) \ (x * (a(u,w,u) * (y * z))),a(u,w,u)) = a(x,a(u,w,u) * y,z)
    ]]></literal>
    <justification jstring="[para(14(a,2),15402(a,1,1))].">
      <j1 rule="para" parents="14 15402"/>
    </justification>
  </clause>

  <clause id="15405">
    <literal><![CDATA[
      a(x,a(y,z,y) * u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(13345,a,15403,a),flip(a)].">
      <j1 rule="hyper" parents="13345 15403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15407">
    <literal><![CDATA[
      a(x,y * a(z,u,z),w) = a(x,y,w)
    ]]></literal>
    <justification jstring="[para(10116(a,1),15405(a,1,2))].">
      <j1 rule="para" parents="10116 15405"/>
    </justification>
  </clause>

  <clause id="15408">
    <literal><![CDATA[
      a(x,y / L(z,u,z),w) = a(x,y / z,w)
    ]]></literal>
    <justification jstring="[para(9689(a,1),15407(a,1,2))].">
      <j1 rule="para" parents="9689 15407"/>
    </justification>
  </clause>

  <clause id="15409">
    <literal><![CDATA[
      a(x,(y * z) / y,u) = a(x,y * (z / y),u)
    ]]></literal>
    <justification jstring="[para(585(a,1),15408(a,1,2)),flip(a)].">
      <j1 rule="para" parents="585 15408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15410">
    <literal><![CDATA[
      a(x,y * (z / y),u) = a(x,T(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,10657,a(flip),b,15409,a),flip(a)].">
      <j1 rule="hyper" parents="65 10657 15409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15411">
    <literal><![CDATA[
      a(x,T(y,y * z),u) = a(x,z * (y / z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,6624,a(flip),b,15410,a),flip(a)].">
      <j1 rule="hyper" parents="65 6624 15410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15412">
    <literal><![CDATA[
      a(x,T(y,y * z),u) = a(x,T(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,15410,a(flip),b,15411,a),flip(a)].">
      <j1 rule="hyper" parents="299 15410 15411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15413">
    <literal><![CDATA[
      a(x,(y \ z) \ z,u) = a(x,T(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(14514,a,15412,a)].">
      <j1 rule="hyper" parents="14514 15412"/>
    </justification>
  </clause>

  <clause id="15414">
    <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(65,a,13252,a(flip),b,13143,a)].">
      <j1 rule="hyper" parents="65 13252 13143"/>
    </justification>
  </clause>

  <clause id="15415">
    <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(10437(a,1),15414(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10437 15414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15416">
    <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(8004(a,1),15415(a,2,2))].">
      <j1 rule="para" parents="8004 15415"/>
    </justification>
  </clause>

  <clause id="15418">
    <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(14640(a,1),15416(a,2,2))].">
      <j1 rule="para" parents="14640 15416"/>
    </justification>
  </clause>

  <clause id="15419">
    <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(7983(a,1),15418(a,2,2))].">
      <j1 rule="para" parents="7983 15418"/>
    </justification>
  </clause>

  <clause id="15420">
    <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(9160(a,1),15419(a,1,1))].">
      <j1 rule="para" parents="9160 15419"/>
    </justification>
  </clause>

  <clause id="15421">
    <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(65,a,11167,a,b,15420,a)].">
      <j1 rule="hyper" parents="65 11167 15420"/>
    </justification>
  </clause>

  <clause id="15422">
    <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(12595(a,1),15421(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12595 15421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15423">
    <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(15422(a,1),631(a,1))].">
      <j1 rule="para" parents="15422 631"/>
    </justification>
  </clause>

  <clause id="15424">
    <literal><![CDATA[
      (x * (K(y,x) / T(x,z))) \ L(u,(x * (K(y,x) / T(x,z))) \ 1,x * (K(y,x) / T(x,z))) = ((((x * (K(y,x) / T(x,z))) \ 1) \ 1) \ 1) * u
    ]]></literal>
    <justification jstring="[para(10191(a,1),15082(a,1,1))].">
      <j1 rule="para" parents="10191 15082"/>
    </justification>
  </clause>

  <clause id="15425">
    <literal><![CDATA[
      (x * (K(y,x) / T(x,z))) \ L(u,(x \ K(x,y)) * T(x,z),x * (K(y,x) / T(x,z))) = ((((x * (K(y,x) / T(x,z))) \ 1) \ 1) \ 1) * u
    ]]></literal>
    <justification jstring="[para(15081(a,1),15424(a,1,2,2))].">
      <j1 rule="para" parents="15081 15424"/>
    </justification>
  </clause>

  <clause id="15426">
    <literal><![CDATA[
      (x * (K(y,x) / T(x,z))) \ L(u,(x \ K(x,y)) * T(x,z),K(y,x) * K(z,x)) = ((((x * (K(y,x) / T(x,z))) \ 1) \ 1) \ 1) * u
    ]]></literal>
    <justification jstring="[para(9770(a,1),15425(a,1,2))].">
      <j1 rule="para" parents="9770 15425"/>
    </justification>
  </clause>

  <clause id="15427">
    <literal><![CDATA[
      (x * (K(y,x) / T(x,z))) \ L(u,K(x,y) * K(x,z),K(y,x) * K(z,x)) = ((((x * (K(y,x) / T(x,z))) \ 1) \ 1) \ 1) * u
    ]]></literal>
    <justification jstring="[para(6484(a,1),15426(a,1,2))].">
      <j1 rule="para" parents="6484 15426"/>
    </justification>
  </clause>

  <clause id="15428">
    <literal><![CDATA[
      ((((x * (K(y,x) / T(x,z))) \ 1) \ 1) \ 1) * u = (x * (K(y,x) / T(x,z))) \ u
    ]]></literal>
    <justification jstring="[para(15378(a,1),15427(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15378 15427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15429">
    <literal><![CDATA[
      ((((x \ K(x,y)) * T(x,z)) \ 1) \ 1) * u = (x * (K(y,x) / T(x,z))) \ u
    ]]></literal>
    <justification jstring="[para(15081(a,1),15428(a,1,1,1,1))].">
      <j1 rule="para" parents="15081 15428"/>
    </justification>
  </clause>

  <clause id="15430">
    <literal><![CDATA[
      ((x * (K(y,x) / T(x,z))) \ 1) * u = (x * (K(y,x) / T(x,z))) \ u
    ]]></literal>
    <justification jstring="[para(10191(a,1),15429(a,1,1,1))].">
      <j1 rule="para" parents="10191 15429"/>
    </justification>
  </clause>

  <clause id="15431">
    <literal><![CDATA[
      (x * (K(y,x) / T(x,z))) \ u = ((x \ K(x,y)) * T(x,z)) * u
    ]]></literal>
    <justification jstring="[para(15081(a,1),15430(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15081 15430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15432">
    <literal><![CDATA[
      L(((x \ K(x,y)) * T(x,z)) * u,T(x,z) \ ((x \ 1) \ K(y,x)),T(x,z)) = ((x \ 1) \ K(y,x)) \ (T(x,z) * u)
    ]]></literal>
    <justification jstring="[para(15431(a,1),9285(a,1,1))].">
      <j1 rule="para" parents="15431 9285"/>
    </justification>
  </clause>

  <clause id="15433">
    <literal><![CDATA[
      L(((x \ K(x,y)) * T(x,z)) * u,x * (K(y,x) / T(x,z)),T(x,z)) = ((x \ 1) \ K(y,x)) \ (T(x,z) * u)
    ]]></literal>
    <justification jstring="[para(8709(a,1),15432(a,1,2))].">
      <j1 rule="para" parents="8709 15432"/>
    </justification>
  </clause>

  <clause id="15434">
    <literal><![CDATA[
      L(((x \ K(x,y)) * T(x,z)) * u,x * (T(x,y) \ K(z,x)),T(x,z)) = ((x \ 1) \ K(y,x)) \ (T(x,z) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,10344,a(flip),b,15433,a)].">
      <j1 rule="hyper" parents="65 10344 15433"/>
    </justification>
  </clause>

  <clause id="15435">
    <literal><![CDATA[
      L(((x \ K(x,y)) * T(x,z)) * u,K(y,x) * K(z,x),T(x,z)) = ((x \ 1) \ K(y,x)) \ (T(x,z) * u)
    ]]></literal>
    <justification jstring="[para(5060(a,1),15434(a,1,2))].">
      <j1 rule="para" parents="5060 15434"/>
    </justification>
  </clause>

  <clause id="15436">
    <literal><![CDATA[
      ((x \ 1) \ K(y,x)) \ (T(x,z) * u) = ((x \ K(x,y)) * T(x,z)) * u
    ]]></literal>
    <justification jstring="[hyper(12266,a,15435,a),flip(a)].">
      <j1 rule="hyper" parents="12266 15435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15438">
    <literal><![CDATA[
      (((x \ 1) \ K(y,x)) \ (T(x,x \ 1) * z)) * K((K(x,y) / x) * (x * z),T(x,x \ 1) * z) = T(((x \ K(x,y)) \ 1) \ (T(x,x \ 1) * z),T(x,x \ 1) * z)
    ]]></literal>
    <justification jstring="[para(6605(a,1),9597(a,1,1,1))].">
      <j1 rule="para" parents="6605 9597"/>
    </justification>
  </clause>

  <clause id="15439">
    <literal><![CDATA[
      (((x \ K(x,y)) * T(x,x \ 1)) * z) * K((K(x,y) / x) * (x * z),T(x,x \ 1) * z) = T(((x \ K(x,y)) \ 1) \ (T(x,x \ 1) * z),T(x,x \ 1) * z)
    ]]></literal>
    <justification jstring="[para(15436(a,1),15438(a,1,1))].">
      <j1 rule="para" parents="15436 15438"/>
    </justification>
  </clause>

  <clause id="15440">
    <literal><![CDATA[
      T(((x \ K(x,y)) \ 1) \ (T(x,x \ 1) * z),T(x,x \ 1) * z) = (K(x,y) * z) * K((K(x,y) / x) * (x * z),T(x,x \ 1) * z)
    ]]></literal>
    <justification jstring="[para(4577(a,1),15439(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4577 15439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15441">
    <literal><![CDATA[
      T(((x \ K(x,y)) \ 1) \ (T(x,x \ 1) * z),T(x,x \ 1) * z) = (K(x,y) * z) * K((K(x,y) / x) * (x * z),x * z)
    ]]></literal>
    <justification jstring="[para(5646(a,1),15440(a,2,2))].">
      <j1 rule="para" parents="5646 15440"/>
    </justification>
  </clause>

  <clause id="15442">
    <literal><![CDATA[
      T(((x \ K(x,y)) \ 1) \ (T(x,x \ 1) * z),T(x,x \ 1) * z) = (K(x,y) * z) * K((x \ K(x,y)) * (x * z),x * z)
    ]]></literal>
    <justification jstring="[para(6227(a,1),15441(a,2,2))].">
      <j1 rule="para" parents="6227 15441"/>
    </justification>
  </clause>

  <clause id="15443">
    <literal><![CDATA[
      T(((x \ K(x,y)) \ 1) \ (T(x,x \ 1) * z),T(x,x \ 1) * z) = (K(x,y) * z) * K(x \ (x * z),T(x * z,y))
    ]]></literal>
    <justification jstring="[para(10763(a,1),15442(a,2,2))].">
      <j1 rule="para" parents="10763 15442"/>
    </justification>
  </clause>

  <clause id="15444">
    <literal><![CDATA[
      T(((x \ K(x,y)) \ 1) \ (T(x,x \ 1) * z),T(x,x \ 1) * z) = (K(x,y) * z) * K(z,T(x * z,y))
    ]]></literal>
    <justification jstring="[para(9(a,1),15443(a,2,2,1))].">
      <j1 rule="para" parents="9 15443"/>
    </justification>
  </clause>

  <clause id="15445">
    <literal><![CDATA[
      T(((x \ K(x,y)) \ 1) \ (T(x,x \ 1) * z),T(x,x \ 1) * z) = K(x,y) * T(z,T(x * z,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,6832,a(flip),b,15444,a),flip(a)].">
      <j1 rule="hyper" parents="299 6832 15444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15447">
    <literal><![CDATA[
      T(((x \ K(x,y)) \ 1) \ (T(x,x \ 1) * z),T(x,x \ 1) * z) = T(z,x * z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,9296,a(flip),b,15445,a),flip(a)].">
      <j1 rule="hyper" parents="299 9296 15445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15448">
    <literal><![CDATA[
      T(((x \ 1) \ K(y,x)) \ (T(x,x \ 1) * z),T(x,x \ 1) * z) = T(z,x * z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(6605(a,1),15447(a,1,1,1))].">
      <j1 rule="para" parents="6605 15447"/>
    </justification>
  </clause>

  <clause id="15449">
    <literal><![CDATA[
      T(((x \ K(x,y)) * T(x,x \ 1)) * z,T(x,x \ 1) * z) = T(z,x * z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(15436(a,1),15448(a,1,1))].">
      <j1 rule="para" parents="15436 15448"/>
    </justification>
  </clause>

  <clause id="15450">
    <literal><![CDATA[
      T(K(x,y) * z,T(x,x \ 1) * z) = T(z,x * z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(4577(a,1),15449(a,1,1,1))].">
      <j1 rule="para" parents="4577 15449"/>
    </justification>
  </clause>

  <clause id="15451">
    <literal><![CDATA[
      T(K(x,y) * z,x * z) = T(z,x * z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,3866,a(flip),b,15450,a)].">
      <j1 rule="hyper" parents="65 3866 15450"/>
    </justification>
  </clause>

  <clause id="15452">
    <literal><![CDATA[
      T(K(x,y) * z,x * z) = T(z,z * x) * K(x,y)
    ]]></literal>
    <justification jstring="[para(4366(a,1),15451(a,2,1))].">
      <j1 rule="para" parents="4366 15451"/>
    </justification>
  </clause>

  <clause id="15453">
    <literal><![CDATA[
      T(K(x,x * (y \ L(y,z,u))) * w,x * w) = T(w,w * x) * a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[para(14029(a,1),15452(a,2,2))].">
      <j1 rule="para" parents="14029 15452"/>
    </justification>
  </clause>

  <clause id="15454">
    <literal><![CDATA[
      T(a(x,y,K(z,u)) * w,u * w) = T(w,w * u) * a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(14029(a,1),15453(a,1,1,1))].">
      <j1 rule="para" parents="14029 15453"/>
    </justification>
  </clause>

  <clause id="15455">
    <literal><![CDATA[
      T(a(x,y,K(z,u)) * x,u * x) = T(x,R(x * u,y,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,15145,a(flip),b,15454,a),flip(a)].">
      <j1 rule="hyper" parents="299 15145 15454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15456">
    <literal><![CDATA[
      T(x * a(x,y,K(z,u)),u * x) = T(x,R(x * u,y,z))
    ]]></literal>
    <justification jstring="[para(11010(a,1),15455(a,1,1))].">
      <j1 rule="para" parents="11010 15455"/>
    </justification>
  </clause>

  <clause id="15457">
    <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(2009(a,1),14075(a,2,1))].">
      <j1 rule="para" parents="2009 14075"/>
    </justification>
  </clause>

  <clause id="15458">
    <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(299,a,13660,a(flip),b,15457,a),flip(a)].">
      <j1 rule="hyper" parents="299 13660 15457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15460">
    <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(10456(a,1),15458(a,1,1))].">
      <j1 rule="para" parents="10456 15458"/>
    </justification>
  </clause>

  <clause id="15461">
    <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(65,a,10487,a(flip),b,15460,a)].">
      <j1 rule="hyper" parents="65 10487 15460"/>
    </justification>
  </clause>

  <clause id="15462">
    <literal><![CDATA[
      T(x,a(y,z,u) \ x) = x * a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,14059,a(flip),b,15461,a),flip(a)].">
      <j1 rule="hyper" parents="65 14059 15461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15463">
    <literal><![CDATA[
      T(x,a(y,z,u) \ x) = x * a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,14875,a(flip),b,15462,a),flip(a)].">
      <j1 rule="hyper" parents="299 14875 15462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15464">
    <literal><![CDATA[
      T(T(x,a(y,z,u) \ x),u) = T(x,L(u,z,y))
    ]]></literal>
    <justification jstring="[para(15462(a,2),12572(a,1,1))].">
      <j1 rule="para" parents="15462 12572"/>
    </justification>
  </clause>

  <clause id="15465">
    <literal><![CDATA[
      T(T(x,a(y,z,u) \ x),x * u) = T(x,L(u * x,z,y))
    ]]></literal>
    <justification jstring="[para(15462(a,2),12574(a,1,1))].">
      <j1 rule="para" parents="15462 12574"/>
    </justification>
  </clause>

  <clause id="15466">
    <literal><![CDATA[
      T(T(x,a(y,z,u) \ x),u * x) = T(x,R(x * u,z,y))
    ]]></literal>
    <justification jstring="[para(15463(a,2),15456(a,1,1))].">
      <j1 rule="para" parents="15463 15456"/>
    </justification>
  </clause>

  <clause id="15467">
    <literal><![CDATA[
      T(T(x,y),a(z,u,y) \ x) = T(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(861,a,15464,a)].">
      <j1 rule="hyper" parents="861 15464"/>
    </justification>
  </clause>

  <clause id="15468">
    <literal><![CDATA[
      T(T(x,y * (z * (u \ 1))),a(w,v5,y * (z * (1 / u))) \ x) = T(x,L(y * (z * (1 / u)),v5,w))
    ]]></literal>
    <justification jstring="[para(3885(a,1),15467(a,1,1))].">
      <j1 rule="para" parents="3885 15467"/>
    </justification>
  </clause>

  <clause id="15469">
    <literal><![CDATA[
      T(T(x,x * y),a(z,u,y) \ x) = T(x,L(y * x,u,z))
    ]]></literal>
    <justification jstring="[hyper(861,a,15465,a)].">
      <j1 rule="hyper" parents="861 15465"/>
    </justification>
  </clause>

  <clause id="15470">
    <literal><![CDATA[
      T(T(x,x * y),a(z,u,y) \ x) = T(x,R(x * y,u,z))
    ]]></literal>
    <justification jstring="[hyper(4514,a,15466,a)].">
      <j1 rule="hyper" parents="4514 15466"/>
    </justification>
  </clause>

  <clause id="15471">
    <literal><![CDATA[
      T(x,R(x * y,z,u)) = T(x,L(y * x,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,15469,a(flip),b,15470,a),flip(a)].">
      <j1 rule="hyper" parents="65 15469 15470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15472">
    <literal><![CDATA[
      T(x,L((y / T(1 / (1 / x),z)) * x,u,w)) = T(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,15391,a(flip),b,15471,a),flip(a)].">
      <j1 rule="hyper" parents="65 15391 15471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15473">
    <literal><![CDATA[
      T(x,L(y * (x * (1 / T(x,z))),u,w)) = T(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(10319(a,1),15472(a,1,2,1))].">
      <j1 rule="para" parents="10319 15472"/>
    </justification>
  </clause>

  <clause id="15474">
    <literal><![CDATA[
      T(T(x,y * (z * (u \ 1))),a(w,v5,y * (z * (u \ 1))) \ x) = T(x,L(y * (z * (1 / u)),v5,w))
    ]]></literal>
    <justification jstring="[para(4007(a,1),15468(a,1,2,1))].">
      <j1 rule="para" parents="4007 15468"/>
    </justification>
  </clause>

  <clause id="15475">
    <literal><![CDATA[
      T(x,L(y * (z * (1 / u)),w,v5)) = T(x,L(y * (z * (u \ 1)),w,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,15467,a(flip),b,15474,a),flip(a)].">
      <j1 rule="hyper" parents="65 15467 15474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15476">
    <literal><![CDATA[
      T(x,L(y * (x * (T(x,z) \ 1)),u,w)) = T(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,15473,a(flip),b,15475,a),flip(a)].">
      <j1 rule="hyper" parents="65 15473 15475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15477">
    <literal><![CDATA[
      T(x,L(y * K(z,x),u,w)) = T(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(5034(a,2),15476(a,1,2,1,2))].">
      <j1 rule="para" parents="5034 15476"/>
    </justification>
  </clause>

  <clause id="15478">
    <literal><![CDATA[
      T(x,R(y,z,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(177(a,1),15477(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="177 15477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15480">
    <literal><![CDATA[
      x \ T(x,L(y,z,u)) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,15478,a(flip),b,5083,a(flip))].">
      <j1 rule="hyper" parents="119 15478 5083"/>
    </justification>
  </clause>

  <clause id="15481">
    <literal><![CDATA[
      R(x,y,z) * T(u,L(x,y,z)) = u * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(15478(a,1),107(a,1,2))].">
      <j1 rule="para" parents="15478 107"/>
    </justification>
  </clause>

  <clause id="15482">
    <literal><![CDATA[
      K(x,R(y,z,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(5155,a,15480,a),flip(a)].">
      <j1 rule="hyper" parents="5155 15480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15483">
    <literal><![CDATA[
      K(x,R(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(15480(a,1),5155(a,1))].">
      <j1 rule="para" parents="15480 5155"/>
    </justification>
  </clause>

  <clause id="15484">
    <literal><![CDATA[
      K(R(x,y,z),u) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,13399,a,b,15482,a)].">
      <j1 rule="hyper" parents="65 13399 15482"/>
    </justification>
  </clause>

  <clause id="15485">
    <literal><![CDATA[
      R(K(x,y),z,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,13396,a,b,15482,a)].">
      <j1 rule="hyper" parents="65 13396 15482"/>
    </justification>
  </clause>

  <clause id="15486">
    <literal><![CDATA[
      K(x,L((y / z) / u,u,z)) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[para(285(a,1),15482(a,1,2)),flip(a)].">
      <j1 rule="para" parents="285 15482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15487">
    <literal><![CDATA[
      K(x,L(y \ (z / u),y,u)) = K(x,T(z / (y * u),y))
    ]]></literal>
    <justification jstring="[para(703(a,1),15482(a,1,2)),flip(a)].">
      <j1 rule="para" parents="703 15482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15488">
    <literal><![CDATA[
      ((x * y) * z) * K(y * z,L(x,y,z)) = (y * z) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(15482(a,1),547(a,1,2))].">
      <j1 rule="para" parents="15482 547"/>
    </justification>
  </clause>

  <clause id="15490">
    <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(15482(a,1),10314(a,1,2))].">
      <j1 rule="para" parents="15482 10314"/>
    </justification>
  </clause>

  <clause id="15491">
    <literal><![CDATA[
      K(R(x,y,z),u) = K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,11929,a,b,15484,a),flip(a)].">
      <j1 rule="hyper" parents="299 11929 15484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15492">
    <literal><![CDATA[
      R(K(x,y),z,u) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,11889,a,b,15485,a),flip(a)].">
      <j1 rule="hyper" parents="299 11889 15485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15493">
    <literal><![CDATA[
      K(x,L(y,z,L(z,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,15191,a(flip),b,15485,a),flip(a)].">
      <j1 rule="hyper" parents="65 15191 15485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15494">
    <literal><![CDATA[
      K(x,L((y / z) / u,z \ y,z)) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,11285,a(flip),b,15485,a),flip(a)].">
      <j1 rule="hyper" parents="65 11285 15485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15495">
    <literal><![CDATA[
      K((x * y) / (z * y),u) = K(x / z,L(u,x,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,10743,a(flip),b,15485,a)].">
      <j1 rule="hyper" parents="65 10743 15485"/>
    </justification>
  </clause>

  <clause id="15496">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (z * u) = (K(x,y) * z) * u
    ]]></literal>
    <justification jstring="[para(15485(a,1),103(a,1,1))].">
      <j1 rule="para" parents="15485 103"/>
    </justification>
  </clause>

  <clause id="15497">
    <literal><![CDATA[
      K(x,L(y,z,z \ u)) * u = (K(x,y) * z) * (z \ u)
    ]]></literal>
    <justification jstring="[para(15485(a,1),347(a,1,1))].">
      <j1 rule="para" parents="15485 347"/>
    </justification>
  </clause>

  <clause id="15499">
    <literal><![CDATA[
      K(x,L(y,z \ u,z)) * u = (K(x,y) * (u / z)) * z
    ]]></literal>
    <justification jstring="[para(15485(a,1),11287(a,1,1))].">
      <j1 rule="para" parents="15485 11287"/>
    </justification>
  </clause>

  <clause id="15500">
    <literal><![CDATA[
      ((K(x,y) * z) * u) * K(u,z) = K(x,L(y,z,u)) * (u * z)
    ]]></literal>
    <justification jstring="[para(15485(a,1),11293(a,2,1))].">
      <j1 rule="para" parents="15485 11293"/>
    </justification>
  </clause>

  <clause id="15501">
    <literal><![CDATA[
      K(L(x / y,y,z),u) = K((x * z) / (y * z),u)
    ]]></literal>
    <justification jstring="[para(104(a,1),15491(a,1,1)),flip(a)].">
      <j1 rule="para" parents="104 15491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15502">
    <literal><![CDATA[
      K(L((x / y) / z,z,y),u) = K(x / (z * y),u)
    ]]></literal>
    <justification jstring="[para(285(a,1),15491(a,1,1)),flip(a)].">
      <j1 rule="para" parents="285 15491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15503">
    <literal><![CDATA[
      x * (K(L(y,z,u),x) * R(y,z,u)) = R(y,z,u) * x
    ]]></literal>
    <justification jstring="[para(15491(a,1),5166(a,1,2,1))].">
      <j1 rule="para" parents="15491 5166"/>
    </justification>
  </clause>

  <clause id="15504">
    <literal><![CDATA[
      K(R(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(15491(a,2),11999(a,1))].">
      <j1 rule="para" parents="15491 11999"/>
    </justification>
  </clause>

  <clause id="15505">
    <literal><![CDATA[
      L(K(x / (y / z),u),x,z) = K((x * z) / y,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,10750,a(flip),b,15492,a),flip(a)].">
      <j1 rule="hyper" parents="65 10750 15492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15506">
    <literal><![CDATA[
      L(K(x \ 1,y),z,u) = K(R(x,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,6008,a(flip),b,15492,a),flip(a)].">
      <j1 rule="hyper" parents="65 6008 15492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15507">
    <literal><![CDATA[
      L(K(x,y),z,u) * (z * u) = (K(x,y) * z) * u
    ]]></literal>
    <justification jstring="[para(15492(a,1),103(a,1,1))].">
      <j1 rule="para" parents="15492 103"/>
    </justification>
  </clause>

  <clause id="15508">
    <literal><![CDATA[
      L(K(x,y),z,u) \ ((K(x,y) * z) * u) = z * u
    ]]></literal>
    <justification jstring="[para(15492(a,1),182(a,1,1))].">
      <j1 rule="para" parents="15492 182"/>
    </justification>
  </clause>

  <clause id="15512">
    <literal><![CDATA[
      R(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(15492(a,2),11995(a,1))].">
      <j1 rule="para" parents="15492 11995"/>
    </justification>
  </clause>

  <clause id="15513">
    <literal><![CDATA[
      L(K(x,y),z,u) \ (u * (K(x,y) * z)) = z * T(u,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(15492(a,1),14827(a,1,1))].">
      <j1 rule="para" parents="15492 14827"/>
    </justification>
  </clause>

  <clause id="15514">
    <literal><![CDATA[
      K(x,L(y,z,L(z,u,w))) = 1 * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,7,a,b,15493,a),flip(a)].">
      <j1 rule="hyper" parents="299 7 15493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15515">
    <literal><![CDATA[
      K(x,L(y,z,L(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(15514(a,2),121(a,1)),flip(b)].">
      <j1 rule="para" parents="15514 121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15516">
    <literal><![CDATA[
      K(x,(y * z) / (u * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y / u,u,z)) = w
    ]]></literal>
    <justification jstring="[para(104(a,1),15483(a,1,2))].">
      <j1 rule="para" parents="104 15483"/>
    </justification>
  </clause>

  <clause id="15519">
    <literal><![CDATA[
      K(x,L(y,z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(477(a,1),15515(a,1,2,3))].">
      <j1 rule="para" parents="477 15515"/>
    </justification>
  </clause>

  <clause id="15520">
    <literal><![CDATA[
      K(x,L(y,L(z,u,w),z)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(15226(a,2),15515(a,1,2))].">
      <j1 rule="para" parents="15226 15515"/>
    </justification>
  </clause>

  <clause id="15523">
    <literal><![CDATA[
      L(K(x,y),z,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(11889(a,2),15519(a,1))].">
      <j1 rule="para" parents="11889 15519"/>
    </justification>
  </clause>

  <clause id="15525">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,u) = K(L(x,y,z) \ 1,u)
    ]]></literal>
    <justification jstring="[hyper(6335,a,15506,a),flip(a)].">
      <j1 rule="hyper" parents="6335 15506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15526">
    <literal><![CDATA[
      (x \ K(L(y,z,u) \ 1,w)) \ (x \ 1) = K(w,R(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(15525(a,1),14240(a,1,1,2))].">
      <j1 rule="para" parents="15525 14240"/>
    </justification>
  </clause>

  <clause id="15527">
    <literal><![CDATA[
      R(x,y,y) * T(z,x) = z * R(x,y,y)
    ]]></literal>
    <justification jstring="[para(14206(a,1),15481(a,1,2))].">
      <j1 rule="para" parents="14206 15481"/>
    </justification>
  </clause>

  <clause id="15528">
    <literal><![CDATA[
      R(x,y,y) * (x \ z) = (z / x) * R(x,y,y)
    ]]></literal>
    <justification jstring="[para(109(a,1),15527(a,1,2))].">
      <j1 rule="para" parents="109 15527"/>
    </justification>
  </clause>

  <clause id="15529">
    <literal><![CDATA[
      (x / y) * ((y * y) * R(1 / y,z,z)) = R(1 / y,z,z) * ((1 / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(299,a,680,a,b,15528,a)].">
      <j1 rule="hyper" parents="299 680 15528"/>
    </justification>
  </clause>

  <clause id="15530">
    <literal><![CDATA[
      K(x,R(1 / y,z,z) * ((1 / y) \ u)) = K(x,(u / (y \ 1)) * R(1 / y,z,z))
    ]]></literal>
    <justification jstring="[para(15528(a,2),5665(a,1,2))].">
      <j1 rule="para" parents="15528 5665"/>
    </justification>
  </clause>

  <clause id="15531">
    <literal><![CDATA[
      K(x,L((y * K(z,y)) / u,u,z)) = K(x,(z * y) / (u * z))
    ]]></literal>
    <justification jstring="[para(5054(a,1),15486(a,1,2,1,1))].">
      <j1 rule="para" parents="5054 15486"/>
    </justification>
  </clause>

  <clause id="15532">
    <literal><![CDATA[
      T(x,K(y,L((z / u) / w,w,u))) = x * K(y,K(x,z / (w * u)))
    ]]></literal>
    <justification jstring="[para(15486(a,1),7990(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="15486 7990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15533">
    <literal><![CDATA[
      K(x,K((y / z) / u,L(w,y / z,z))) = K(x,K(w,y / (u * z)))
    ]]></literal>
    <justification jstring="[para(15486(a,1),9195(a,2,2))].">
      <j1 rule="para" parents="15486 9195"/>
    </justification>
  </clause>

  <clause id="15534">
    <literal><![CDATA[
      K((L(x,y,z) * u) / (x * u),w) = a(z,y,K(L(w,L(x,y,z),u),x))
    ]]></literal>
    <justification jstring="[hyper(299,a,11961,a(flip),b,15495,a),flip(a)].">
      <j1 rule="hyper" parents="299 11961 15495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15535">
    <literal><![CDATA[
      (K(x,y) * z) * u != w * (z * u)
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(15496(a,1),46(a,1))].">
      <j1 rule="para" parents="15496 46"/>
    </justification>
  </clause>

  <clause id="15536">
    <literal><![CDATA[
      ((K(x,y) * z) * u) \ (z * u) = K(L(y,z,u),T(x,z * u))
    ]]></literal>
    <justification jstring="[para(15496(a,1),7492(a,1,1))].">
      <j1 rule="para" parents="15496 7492"/>
    </justification>
  </clause>

  <clause id="15537">
    <literal><![CDATA[
      (K(x,y * z) * z) * y = K(x,y * z) * (z * y)
    ]]></literal>
    <justification jstring="[para(14639(a,1),15496(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14639 15496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15538">
    <literal><![CDATA[
      ((K(x,y) * z) * u) * a(x,z,K(u,L(y,z,u))) = (K(x,L(y,z,u)) * z) * u
    ]]></literal>
    <justification jstring="[para(15496(a,1),14864(a,1,1))].">
      <j1 rule="para" parents="15496 14864"/>
    </justification>
  </clause>

  <clause id="15539">
    <literal><![CDATA[
      K((x * y) \ z,T(u,y)) = K(((x \ z) * x) / (y * x),u)
    ]]></literal>
    <justification jstring="[hyper(8307,a,15501,a)].">
      <j1 rule="hyper" parents="8307 15501"/>
    </justification>
  </clause>

  <clause id="15540">
    <literal><![CDATA[
      K(L(x / y,y,z),T(u,y * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K((y * z) \ (x * z),u) = w
    ]]></literal>
    <justification jstring="[para(15501(a,2),7801(a,1))].">
      <j1 rule="para" parents="15501 7801"/>
    </justification>
  </clause>

  <clause id="15541">
    <literal><![CDATA[
      K(((x \ y) * x) / (z * x),u) != w
    ]]></literal>
    <literal><![CDATA[
      K((x * z) \ y,T(u,z)) = w
    ]]></literal>
    <justification jstring="[para(15501(a,1),8307(a,1))].">
      <j1 rule="para" parents="15501 8307"/>
    </justification>
  </clause>

  <clause id="15542">
    <literal><![CDATA[
      K(L((x / y) / K(z,T(u,y)),K(z,T(u,y)),y),w) = K(x / (y * K(z,u)),w)
    ]]></literal>
    <justification jstring="[para(8101(a,1),15502(a,2,1,2))].">
      <j1 rule="para" parents="8101 15502"/>
    </justification>
  </clause>

  <clause id="15543">
    <literal><![CDATA[
      x \ (y * (K((y \ x) / (z / y),u) * (y \ x))) = K(((y \ x) * y) / z,T(u,y \ x))
    ]]></literal>
    <justification jstring="[hyper(65,a,7513,a(flip),b,15505,a)].">
      <j1 rule="hyper" parents="65 7513 15505"/>
    </justification>
  </clause>

  <clause id="15544">
    <literal><![CDATA[
      ((K(x,y) * K(x,y)) * (z * u)) / u = L(K(x,y),K(x,y),z) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(299,a,113,a,b,15507,a)].">
      <j1 rule="hyper" parents="299 113 15507"/>
    </justification>
  </clause>

  <clause id="15545">
    <literal><![CDATA[
      K(L(x,y,z),u) * ((x * y) * z) = (K(x,u) * (x * y)) * z
    ]]></literal>
    <justification jstring="[para(9164(a,1),15507(a,1,1))].">
      <j1 rule="para" parents="9164 15507"/>
    </justification>
  </clause>

  <clause id="15546">
    <literal><![CDATA[
      L(x,y,K(z,x * y)) = x
    ]]></literal>
    <justification jstring="[hyper(490,a,15537,a)].">
      <j1 rule="hyper" parents="490 15537"/>
    </justification>
  </clause>

  <clause id="15547">
    <literal><![CDATA[
      (x * K(y,x * z)) * z = K(y,z * x) * (x * z)
    ]]></literal>
    <justification jstring="[para(13209(a,1),15537(a,1,1))].">
      <j1 rule="para" parents="13209 15537"/>
    </justification>
  </clause>

  <clause id="15548">
    <literal><![CDATA[
      L(x,x \ y,K(z,y)) = x
    ]]></literal>
    <justification jstring="[para(10(a,1),15546(a,1,3,2))].">
      <j1 rule="para" parents="10 15546"/>
    </justification>
  </clause>

  <clause id="15549">
    <literal><![CDATA[
      L(x / y,y,K(z,x)) = x / y
    ]]></literal>
    <justification jstring="[para(12(a,1),15546(a,1,3,2))].">
      <j1 rule="para" parents="12 15546"/>
    </justification>
  </clause>

  <clause id="15550">
    <literal><![CDATA[
      L(x,y,K(z,y * x)) = x
    ]]></literal>
    <justification jstring="[para(13203(a,1),15546(a,1,3))].">
      <j1 rule="para" parents="13203 15546"/>
    </justification>
  </clause>

  <clause id="15551">
    <literal><![CDATA[
      L(x / y,y,K(x,z)) = x / y
    ]]></literal>
    <justification jstring="[hyper(5219,a,15549,a)].">
      <j1 rule="hyper" parents="5219 15549"/>
    </justification>
  </clause>

  <clause id="15552">
    <literal><![CDATA[
      L((x * y) / z,z,K(y,x)) = (x * y) / z
    ]]></literal>
    <justification jstring="[hyper(13513,a,15551,a)].">
      <j1 rule="hyper" parents="13513 15551"/>
    </justification>
  </clause>

  <clause id="15553">
    <literal><![CDATA[
      (x * K(y,x * z)) * z = (x * z) * K(y,z * x)
    ]]></literal>
    <justification jstring="[hyper(299,a,14675,a(flip),b,15547,a),flip(a)].">
      <j1 rule="hyper" parents="299 14675 15547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15554">
    <literal><![CDATA[
      K(x,T(1 / (y * z),y)) = K(x,(z * y) \ K(z,1 / z))
    ]]></literal>
    <justification jstring="[para(528(a,1),15487(a,1,2)),flip(a)].">
      <j1 rule="para" parents="528 15487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15555">
    <literal><![CDATA[
      K(x,L((y / z) / u,y,z)) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[hyper(15000,a,15494,a)].">
      <j1 rule="hyper" parents="15000 15494"/>
    </justification>
  </clause>

  <clause id="15556">
    <literal><![CDATA[
      K(x,L((y / z) * u,z \ y,z)) = K(x,y / ((u \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(14650,a,15494,a)].">
      <j1 rule="hyper" parents="14650 15494"/>
    </justification>
  </clause>

  <clause id="15557">
    <literal><![CDATA[
      K(x,L(y / z,u,y \ u)) = K(x,u / (z * (y \ u)))
    ]]></literal>
    <justification jstring="[para(76(a,1),15555(a,1,2,1,1))].">
      <j1 rule="para" parents="76 15555"/>
    </justification>
  </clause>

  <clause id="15558">
    <literal><![CDATA[
      K(x,L((y * z) / u,R(y,z,z),z \ 1)) = K(x,R(y,z,z) / (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[para(1251(a,1),15555(a,1,2,1,1))].">
      <j1 rule="para" parents="1251 15555"/>
    </justification>
  </clause>

  <clause id="15559">
    <literal><![CDATA[
      K(x,L((y / z) / (u \ w),y,z)) = K(x,y / ((u \ 1) * (u \ (((1 / u) \ w) * z))))
    ]]></literal>
    <justification jstring="[para(1783(a,2),15555(a,2,2,2))].">
      <j1 rule="para" parents="1783 15555"/>
    </justification>
  </clause>

  <clause id="15560">
    <literal><![CDATA[
      K(x,y / ((z \ 1) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L((y / u) * z,y,u)) = w
    ]]></literal>
    <justification jstring="[para(15555(a,1),14650(a,1))].">
      <j1 rule="para" parents="15555 14650"/>
    </justification>
  </clause>

  <clause id="15561">
    <literal><![CDATA[
      T(K(x,L(y,z * z,(z * z) \ u)) * u,z * z) = ((z * z) \ (K(x,y) * (z * z))) * T(u,z * z)
    ]]></literal>
    <justification jstring="[para(15497(a,2),1055(a,1,1))].">
      <j1 rule="para" parents="15497 1055"/>
    </justification>
  </clause>

  <clause id="15562">
    <literal><![CDATA[
      x \ (K(y,L(z,K(y,z),K(y,z) \ u)) * u) = (K(z,y) * (K(z,y) * x)) \ (K(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(15497(a,2),10051(a,2,2)),flip(a)].">
      <j1 rule="para" parents="15497 10051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15563">
    <literal><![CDATA[
      K(x,y \ (z * (u * (z \ y)))) * y = (K(x,T(u,z \ y)) * (y / z)) * z
    ]]></literal>
    <justification jstring="[para(777(a,1),15499(a,1,1,2))].">
      <j1 rule="para" parents="777 15499"/>
    </justification>
  </clause>

  <clause id="15564">
    <literal><![CDATA[
      K(L(x,y,z),u) * R(x,y,z) = R(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,234,a,b,15503,a),flip(a)].">
      <j1 rule="hyper" parents="36 234 15503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15565">
    <literal><![CDATA[
      K(x,L(y / (z \ u),z \ u,z)) = K(x,(y * z) / T(u,z))
    ]]></literal>
    <justification jstring="[hyper(15516,a,13950,a)].">
      <j1 rule="hyper" parents="15516 13950"/>
    </justification>
  </clause>

  <clause id="15566">
    <literal><![CDATA[
      K(((x \ y) * x) \ z,T(u,T((x \ 1) \ y,x))) = K((((1 / x) \ z) * (1 / x)) / (T((x \ 1) \ y,x) * (1 / x)),u)
    ]]></literal>
    <justification jstring="[para(1759(a,1),15539(a,1,1,1))].">
      <j1 rule="para" parents="1759 15539"/>
    </justification>
  </clause>

  <clause id="15567">
    <literal><![CDATA[
      K((x * T(y,z)) \ u,T(w,K(y,z))) = K((((x * y) \ u) * (x * y)) / (K(y,z) * (x * y)),w)
    ]]></literal>
    <justification jstring="[para(6832(a,1),15539(a,1,1,1))].">
      <j1 rule="para" parents="6832 15539"/>
    </justification>
  </clause>

  <clause id="15568">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (u * z) != w
    ]]></literal>
    <literal><![CDATA[
      (K(x,y) * z) * T(u,z) = w
    ]]></literal>
    <justification jstring="[para(15500(a,1),6862(a,1))].">
      <j1 rule="para" parents="15500 6862"/>
    </justification>
  </clause>

  <clause id="15569">
    <literal><![CDATA[
      ((K(x,(y \ z) \ u) * (y \ z)) * y) \ ((y \ z) * y) = K(z \ (y * u),T(x,(y \ z) * y))
    ]]></literal>
    <justification jstring="[para(520(a,1),15536(a,2,1))].">
      <j1 rule="para" parents="520 15536"/>
    </justification>
  </clause>

  <clause id="15570">
    <literal><![CDATA[
      K(L(x,y,z),u) * ((x * y) * z) = (T(x,u) * y) * z
    ]]></literal>
    <justification jstring="[para(5103(a,1),15545(a,2,1))].">
      <j1 rule="para" parents="5103 15545"/>
    </justification>
  </clause>

  <clause id="15571">
    <literal><![CDATA[
      K(x,y) * ((x * y) * z) = (T(x,y) * y) * z
    ]]></literal>
    <justification jstring="[para(11288(a,1),15570(a,1,1))].">
      <j1 rule="para" parents="11288 15570"/>
    </justification>
  </clause>

  <clause id="15572">
    <literal><![CDATA[
      K(x \ 1,x \ y) * ((x \ 1) * (x \ (y * z))) = (T(x \ 1,x \ y) * (x \ y)) * z
    ]]></literal>
    <justification jstring="[para(1740(a,1),15571(a,1,2))].">
      <j1 rule="para" parents="1740 15571"/>
    </justification>
  </clause>

  <clause id="15573">
    <literal><![CDATA[
      K(x,L(((y / z) \ 1) \ u,z \ y,z)) = K(x,y / ((u \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,14642,a,b,15556,a)].">
      <j1 rule="hyper" parents="65 14642 15556"/>
    </justification>
  </clause>

  <clause id="15574">
    <literal><![CDATA[
      K(x,L(y / (z \ u),u,z)) = K(x,(y * z) / T(u,z))
    ]]></literal>
    <justification jstring="[hyper(15000,a,15565,a)].">
      <j1 rule="hyper" parents="15000 15565"/>
    </justification>
  </clause>

  <clause id="15575">
    <literal><![CDATA[
      K(x,L(y / ((z \ u) \ z),z,z \ u)) = K(x,(y * (z \ u)) / ((z \ u) \ u))
    ]]></literal>
    <justification jstring="[para(108(a,1),15574(a,2,2,2))].">
      <j1 rule="para" parents="108 15574"/>
    </justification>
  </clause>

  <clause id="15576">
    <literal><![CDATA[
      ((x * y) * z) * K(y * z,x) = (y * z) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(14911(a,1),15488(a,1,2))].">
      <j1 rule="para" parents="14911 15488"/>
    </justification>
  </clause>

  <clause id="15577">
    <literal><![CDATA[
      R(x,y,z) * T(y * z,x) = (y * z) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(7092,a,15576,a)].">
      <j1 rule="hyper" parents="7092 15576"/>
    </justification>
  </clause>

  <clause id="15578">
    <literal><![CDATA[
      ((x * y) * z) * a(z,x,y) = (x * y) * R(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(11680,a,15577,a)].">
      <j1 rule="hyper" parents="11680 15577"/>
    </justification>
  </clause>

  <clause id="15579">
    <literal><![CDATA[
      x * a(x,y,y) = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(128,a,15578,a)].">
      <j1 rule="hyper" parents="128 15578"/>
    </justification>
  </clause>

  <clause id="15580">
    <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(7507(a,1),15578(a,1,1,1))].">
      <j1 rule="para" parents="7507 15578"/>
    </justification>
  </clause>

  <clause id="15581">
    <literal><![CDATA[
      x \ R(x,y,y) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(125,a,15579,a)].">
      <j1 rule="hyper" parents="125 15579"/>
    </justification>
  </clause>

  <clause id="15582">
    <literal><![CDATA[
      (x * (y \ 1)) / a(x / y,y,y) = x / y
    ]]></literal>
    <justification jstring="[hyper(120,a,1243,a(flip),b,15579,a)].">
      <j1 rule="hyper" parents="120 1243 15579"/>
    </justification>
  </clause>

  <clause id="15583">
    <literal><![CDATA[
      x \ R(x,y,y) != z
    ]]></literal>
    <literal><![CDATA[
      a(x,y,y) = z
    ]]></literal>
    <justification jstring="[para(15579(a,1),314(a,1,2))].">
      <j1 rule="para" parents="15579 314"/>
    </justification>
  </clause>

  <clause id="15584">
    <literal><![CDATA[
      (x \ 1) * a(x,y,y) = R(x \ 1,y,y)
    ]]></literal>
    <justification jstring="[para(2138(a,1),15579(a,1,2))].">
      <j1 rule="para" parents="2138 15579"/>
    </justification>
  </clause>

  <clause id="15585">
    <literal><![CDATA[
      (K(x,y) / z) * a(K(x,y) * z,u,u) = R(K(x,y) / z,u,u)
    ]]></literal>
    <justification jstring="[para(14425(a,1),15579(a,1,2))].">
      <j1 rule="para" parents="14425 15579"/>
    </justification>
  </clause>

  <clause id="15586">
    <literal><![CDATA[
      K(x,L(y,a(z,u,u),z)) = K(x,L(y,R(z,u,u),z))
    ]]></literal>
    <justification jstring="[para(15579(a,1),14990(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="15579 14990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15587">
    <literal><![CDATA[
      (1 / x) * R(x,y,y) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,10869,a,b,15581,a)].">
      <j1 rule="hyper" parents="65 10869 15581"/>
    </justification>
  </clause>

  <clause id="15588">
    <literal><![CDATA[
      x \ (y * R(y \ x,z,z)) = a(x \ y,z,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,15351,a(flip),b,15581,a)].">
      <j1 rule="hyper" parents="65 15351 15581"/>
    </justification>
  </clause>

  <clause id="15589">
    <literal><![CDATA[
      K(x,y * (z * ((u \ 1) \ R(1 / u,w,w)))) = K(x,y * (z * a(1 / u,w,w)))
    ]]></literal>
    <justification jstring="[para(15581(a,1),5905(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="15581 5905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15590">
    <literal><![CDATA[
      K(x,((y \ 1) \ R(1 / y,z,z)) * u) = K(x,a(1 / y,z,z) * u)
    ]]></literal>
    <justification jstring="[para(15581(a,1),14810(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="15581 14810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15591">
    <literal><![CDATA[
      T(x,y * ((z \ 1) * R(z,u,u))) = T(x,y * a(z,u,u))
    ]]></literal>
    <justification jstring="[para(15587(a,1),3899(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="15587 3899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15592">
    <literal><![CDATA[
      L(x,y,z) \ L(R(x,u,u),y,z) != w
    ]]></literal>
    <literal><![CDATA[
      a(L(x,y,z),u,u) = w
    ]]></literal>
    <justification jstring="[para(29(a,1),15583(a,1,2))].">
      <j1 rule="para" parents="29 15583"/>
    </justification>
  </clause>

  <clause id="15593">
    <literal><![CDATA[
      (x \ 1) \ L(R(x \ 1,x,x),y,z) = (x \ 1) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(15584(a,1),6525(a,1,2,1))].">
      <j1 rule="para" parents="15584 6525"/>
    </justification>
  </clause>

  <clause id="15594">
    <literal><![CDATA[
      (x * y) \ (((z * x) * y) * R(((z * x) * y) \ (x * y),u,u)) = a(R(T(z,x * y),x,y),u,u)
    ]]></literal>
    <justification jstring="[para(689(a,1),15588(a,2,1))].">
      <j1 rule="para" parents="689 15588"/>
    </justification>
  </clause>

  <clause id="15595">
    <literal><![CDATA[
      K(x,L(y,a(z,u,u),z)) = K(x,L(y,L(z,u,u),z))
    ]]></literal>
    <justification jstring="[para(15322(a,1),15586(a,2,2))].">
      <j1 rule="para" parents="15322 15586"/>
    </justification>
  </clause>

  <clause id="15596">
    <literal><![CDATA[
      K(x,L(y,a(z,u,u),z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(15595(a,2),15520(a,1))].">
      <j1 rule="para" parents="15595 15520"/>
    </justification>
  </clause>

  <clause id="15597">
    <literal><![CDATA[
      T(x,y * (z * R(1 / z,u,u))) = T(x,y * a(z,u,u))
    ]]></literal>
    <justification jstring="[para(15342(a,1),15591(a,1,2,2))].">
      <j1 rule="para" parents="15342 15591"/>
    </justification>
  </clause>

  <clause id="15598">
    <literal><![CDATA[
      (x \ 1) \ L(1 / x,y,z) = (x \ 1) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(15363(a,1),15593(a,1,2,1))].">
      <j1 rule="para" parents="15363 15593"/>
    </justification>
  </clause>

  <clause id="15599">
    <literal><![CDATA[
      (x \ 1) \ L(1 / x,y,z) = x * L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,6521,a(flip),b,15598,a),flip(a)].">
      <j1 rule="hyper" parents="299 6521 15598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15600">
    <literal><![CDATA[
      K(x,y * (z * (u * L(1 / u,w,v5)))) = K(x,y * (z * (u \ L(u,w,v5))))
    ]]></literal>
    <justification jstring="[para(15599(a,1),6522(a,1,2,2,2))].">
      <j1 rule="para" parents="15599 6522"/>
    </justification>
  </clause>

  <clause id="15601">
    <literal><![CDATA[
      K(x,R(y,z,u) \ 1) = K(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(14241,a,15526,a),flip(a)].">
      <j1 rule="hyper" parents="14241 15526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15602">
    <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(844(a,1),15601(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="844 15601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15603">
    <literal><![CDATA[
      L(x \ R(x,y,y),z,u) = a(L(x,z,u),y,y)
    ]]></literal>
    <justification jstring="[hyper(15592,a,15371,a),flip(a)].">
      <j1 rule="hyper" parents="15592 15371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15604">
    <literal><![CDATA[
      a(L(x,y,z),u,u) = L(a(x,u,u),y,z)
    ]]></literal>
    <justification jstring="[para(15581(a,1),15603(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15581 15603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15605">
    <literal><![CDATA[
      a(L(x,y,z),u,u) * (y * z) = z * (T(y,z) * a(x,u,u))
    ]]></literal>
    <justification jstring="[para(15604(a,2),15032(a,1,1))].">
      <j1 rule="para" parents="15604 15032"/>
    </justification>
  </clause>

  <clause id="15606">
    <literal><![CDATA[
      L(K(x,y),z,u) * (u * (K(y,x) * z)) = z * T(u,K(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(6392,a,15513,a)].">
      <j1 rule="hyper" parents="6392 15513"/>
    </justification>
  </clause>

  <clause id="15607">
    <literal><![CDATA[
      T(x,K(y,L((z / u) / w,w,u))) = x * K(x,K(y,z / (w * u)))
    ]]></literal>
    <justification jstring="[para(7983(a,1),15532(a,2,2))].">
      <j1 rule="para" parents="7983 15532"/>
    </justification>
  </clause>

  <clause id="15608">
    <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(14457(a,1),15533(a,1,2))].">
      <j1 rule="para" parents="14457 15533"/>
    </justification>
  </clause>

  <clause id="15609">
    <literal><![CDATA[
      K(x,L(((y / z) \ 1) \ u,y / z,z)) = K(x,y / ((u \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,11662,a,b,15573,a)].">
      <j1 rule="hyper" parents="65 11662 15573"/>
    </justification>
  </clause>

  <clause id="15610">
    <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(65,a,10358,a,b,15606,a)].">
      <j1 rule="hyper" parents="65 10358 15606"/>
    </justification>
  </clause>

  <clause id="15611">
    <literal><![CDATA[
      K(x,(y * ((z / y) \ 1)) \ (y * u)) = K(x,z / ((u \ 1) * y))
    ]]></literal>
    <justification jstring="[para(2531(a,1),15609(a,1,2))].">
      <j1 rule="para" parents="2531 15609"/>
    </justification>
  </clause>

  <clause id="15612">
    <literal><![CDATA[
      K(x,y / (((z \ u) \ 1) * z)) = K(x,(z * ((y / z) \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(10(a,1),15611(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 15611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15613">
    <literal><![CDATA[
      K((L(x,y,z) * u) / (x * u),w) = a(z,y,K(w,L(x,L(x,y,z),u)))
    ]]></literal>
    <justification jstring="[para(11929(a,1),15534(a,2,3))].">
      <j1 rule="para" parents="11929 15534"/>
    </justification>
  </clause>

  <clause id="15614">
    <literal><![CDATA[
      K(L(x * K(y,x),y,z),T(u,y * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K((y * z) \ ((y * x) * z),u) = w
    ]]></literal>
    <justification jstring="[para(5054(a,1),15540(a,1,1,1))].">
      <j1 rule="para" parents="5054 15540"/>
    </justification>
  </clause>

  <clause id="15615">
    <literal><![CDATA[
      K(x,((y \ 1) \ R(1 / y,z,z)) * u) = K(x,a(y,z,z) * u)
    ]]></literal>
    <justification jstring="[para(2134(a,1),15590(a,2,2,1))].">
      <j1 rule="para" parents="2134 15590"/>
    </justification>
  </clause>

  <clause id="15616">
    <literal><![CDATA[
      K(x,(y * R(1 / y,z,z)) * u) = K(x,a(y,z,z) * u)
    ]]></literal>
    <justification jstring="[para(15346(a,1),15615(a,1,2,1))].">
      <j1 rule="para" parents="15346 15615"/>
    </justification>
  </clause>

  <clause id="15617">
    <literal><![CDATA[
      K((L(x,y,z) * u) / (x * u),w) = a(z,y,K(w,x))
    ]]></literal>
    <justification jstring="[para(11898(a,1),15613(a,2,3))].">
      <j1 rule="para" parents="11898 15613"/>
    </justification>
  </clause>

  <clause id="15619">
    <literal><![CDATA[
      (x / y) * R((y * y) * (1 / y),z,z) = R(1 / y,z,z) * ((1 / y) \ x)
    ]]></literal>
    <justification jstring="[para(15335(a,2),15529(a,1,2))].">
      <j1 rule="para" parents="15335 15529"/>
    </justification>
  </clause>

  <clause id="15620">
    <literal><![CDATA[
      (K(x,T(y,z \ u)) * (u / z)) * z = u * K(x,(z * (y * (z \ u))) / u)
    ]]></literal>
    <justification jstring="[hyper(65,a,8146,a(flip),b,15563,a),flip(a)].">
      <j1 rule="hyper" parents="65 8146 15563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15621">
    <literal><![CDATA[
      R(1 / x,y,y) * ((1 / x) \ z) = (z / x) * R(x,y,y)
    ]]></literal>
    <justification jstring="[para(217(a,1),15619(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="217 15619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15622">
    <literal><![CDATA[
      ((K(x,y) * z) * u) * a(x,z,K(u,y)) = (K(x,L(y,z,u)) * z) * u
    ]]></literal>
    <justification jstring="[para(7843(a,1),15538(a,1,2,3))].">
      <j1 rule="para" parents="7843 15538"/>
    </justification>
  </clause>

  <clause id="15624">
    <literal><![CDATA[
      ((K(x,y) * z) * u) * a(y,z,K(u,x)) = (K(x,L(y,z,u)) * z) * u
    ]]></literal>
    <justification jstring="[para(14949(a,1),15622(a,1,2))].">
      <j1 rule="para" parents="14949 15622"/>
    </justification>
  </clause>

  <clause id="15625">
    <literal><![CDATA[
      (K(x,L(y,z,u)) * z) * u = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(15067,a,15624,a),flip(a)].">
      <j1 rule="hyper" parents="15067 15624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15626">
    <literal><![CDATA[
      K(x,L(L(y,z,u),z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(15535,a,15625,a)].">
      <j1 rule="hyper" parents="15535 15625"/>
    </justification>
  </clause>

  <clause id="15627">
    <literal><![CDATA[
      x \ ((K(y,L(z,K(y,z) \ x,u)) * (K(y,z) \ x)) * u) = L(u,K(y,z) \ x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,15625,a,b,482,a)].">
      <j1 rule="hyper" parents="119 15625 482"/>
    </justification>
  </clause>

  <clause id="15629">
    <literal><![CDATA[
      (K(x,L(y,z,u)) * (z * u)) * u = K(x,y) * ((z * u) * u)
    ]]></literal>
    <justification jstring="[para(14996(a,1),15625(a,1,1,1))].">
      <j1 rule="para" parents="14996 15625"/>
    </justification>
  </clause>

  <clause id="15630">
    <literal><![CDATA[
      K(x \ (y * z),L(u,x,y)) = K((y \ x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,14989,a(flip),b,15626,a)].">
      <j1 rule="hyper" parents="65 14989 15626"/>
    </justification>
  </clause>

  <clause id="15631">
    <literal><![CDATA[
      K((x * y) \ z,L(u,y,x)) = K(y \ (x \ z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,11935,a(flip),b,15626,a)].">
      <j1 rule="hyper" parents="65 11935 15626"/>
    </justification>
  </clause>

  <clause id="15632">
    <literal><![CDATA[
      K(x,L((y * z) \ u,z,y)) = K(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[para(281(a,1),15626(a,1,2,1))].">
      <j1 rule="para" parents="281 15626"/>
    </justification>
  </clause>

  <clause id="15633">
    <literal><![CDATA[
      K(x,L(y \ (z * u),z \ y,z)) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(520(a,1),15626(a,1,2,1))].">
      <j1 rule="para" parents="520 15626"/>
    </justification>
  </clause>

  <clause id="15634">
    <literal><![CDATA[
      K((x \ y) \ ((1 / x) * z),L(u,(x \ 1) \ y,x)) = K((x \ ((x \ 1) \ y)) \ z,u)
    ]]></literal>
    <justification jstring="[para(1181(a,1),15630(a,1,1))].">
      <j1 rule="para" parents="1181 15630"/>
    </justification>
  </clause>

  <clause id="15635">
    <literal><![CDATA[
      K(x \ ((y \ 1) * z),L(u,x,y)) = K(((y \ 1) \ x) \ z,u)
    ]]></literal>
    <justification jstring="[para(2470(a,1),15630(a,1,2))].">
      <j1 rule="para" parents="2470 15630"/>
    </justification>
  </clause>

  <clause id="15636">
    <literal><![CDATA[
      K((x * y) \ ((z \ 1) \ u),L(w,y,x)) = K(y \ (x \ ((1 / z) \ u)),w)
    ]]></literal>
    <justification jstring="[hyper(6313,a,15631,a)].">
      <j1 rule="hyper" parents="6313 15631"/>
    </justification>
  </clause>

  <clause id="15637">
    <literal><![CDATA[
      K((x * (y / x)) \ z,L(u,x \ y,x)) = K((y / x) \ (x \ z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,11662,a(flip),b,15631,a)].">
      <j1 rule="hyper" parents="65 11662 15631"/>
    </justification>
  </clause>

  <clause id="15638">
    <literal><![CDATA[
      K(((x * (y / x)) * x) \ z,L(u,T(x,x \ y),y)) = K(T(x,x \ y) \ (y \ z),u)
    ]]></literal>
    <justification jstring="[para(4445(a,2),15631(a,1,1,1))].">
      <j1 rule="para" parents="4445 15631"/>
    </justification>
  </clause>

  <clause id="15639">
    <literal><![CDATA[
      K(x,(y * (y * z)) \ u) = K(x,z \ (y \ (y \ u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,14994,a(flip),b,15632,a)].">
      <j1 rule="hyper" parents="65 14994 15632"/>
    </justification>
  </clause>

  <clause id="15640">
    <literal><![CDATA[
      K(x,L(y \ z,u,y / u)) = K(x,u \ ((y / u) \ z))
    ]]></literal>
    <justification jstring="[para(12(a,1),15632(a,1,2,1,1))].">
      <j1 rule="para" parents="12 15632"/>
    </justification>
  </clause>

  <clause id="15641">
    <literal><![CDATA[
      K(x,L((y * z) \ u,T(y,z),z)) = K(x,T(y,z) \ (z \ u))
    ]]></literal>
    <justification jstring="[para(107(a,1),15632(a,1,2,1,1))].">
      <j1 rule="para" parents="107 15632"/>
    </justification>
  </clause>

  <clause id="15642">
    <literal><![CDATA[
      K(x,L(a(y,y \ z,u),(y \ z) * u,y)) = K(x,((y \ z) * u) \ (y \ (z * u)))
    ]]></literal>
    <justification jstring="[para(85(a,1),15632(a,1,2,1))].">
      <j1 rule="para" parents="85 15632"/>
    </justification>
  </clause>

  <clause id="15643">
    <literal><![CDATA[
      K(x,L((y * (z \ 1)) \ u,z \ 1,y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,z * (y \ u)) = w
    ]]></literal>
    <justification jstring="[para(15632(a,2),14527(a,1))].">
      <j1 rule="para" parents="15632 14527"/>
    </justification>
  </clause>

  <clause id="15644">
    <literal><![CDATA[
      K(x,L(R(y,z,z) \ u,a(y,z,z),y)) = K(x,a(y,z,z) \ (y \ u))
    ]]></literal>
    <justification jstring="[para(15579(a,1),15632(a,1,2,1,1))].">
      <j1 rule="para" parents="15579 15632"/>
    </justification>
  </clause>

  <clause id="15645">
    <literal><![CDATA[
      K(x,L(y * (y * z),u,w) \ v5) = K(x,L(z,u,w) \ (y \ (y \ v5)))
    ]]></literal>
    <justification jstring="[para(6491(a,2),15639(a,1,2,1))].">
      <j1 rule="para" parents="6491 15639"/>
    </justification>
  </clause>

  <clause id="15646">
    <literal><![CDATA[
      K(x,L(y \ (z * u),y,z)) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(15000,a,15633,a)].">
      <j1 rule="hyper" parents="15000 15633"/>
    </justification>
  </clause>

  <clause id="15648">
    <literal><![CDATA[
      K(x,(L(y,z,u) \ y) \ w) = K(x,y \ (L(y,z,u) * w))
    ]]></literal>
    <justification jstring="[hyper(15515,a,15646,a),flip(a)].">
      <j1 rule="hyper" parents="15515 15646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15649">
    <literal><![CDATA[
      K(x,(y \ (y \ z)) \ u) = K(x,z \ (y * (y * u)))
    ]]></literal>
    <justification jstring="[para(520(a,1),15646(a,1,2)),flip(a)].">
      <j1 rule="para" parents="520 15646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15650">
    <literal><![CDATA[
      K(x,L((y * (z \ 1)) \ (z * u),y * (z \ 1),z)) = K(x,T(y * (z \ (1 / z)),z) \ u)
    ]]></literal>
    <justification jstring="[para(1730(a,2),15646(a,2,2,1))].">
      <j1 rule="para" parents="1730 15646"/>
    </justification>
  </clause>

  <clause id="15651">
    <literal><![CDATA[
      K(x,L((1 / y) \ (z * u),y,z)) = K(x,(z \ (1 / y)) \ u)
    ]]></literal>
    <justification jstring="[para(2521(a,1),15646(a,1,2))].">
      <j1 rule="para" parents="2521 15646"/>
    </justification>
  </clause>

  <clause id="15652">
    <literal><![CDATA[
      K(x,L(T(y,z) \ (z * u),T(y,z),z)) = K(x,(T(z,y) \ y) \ u)
    ]]></literal>
    <justification jstring="[para(4396(a,2),15646(a,2,2,1))].">
      <j1 rule="para" parents="4396 15646"/>
    </justification>
  </clause>

  <clause id="15653">
    <literal><![CDATA[
      T(x,L(y \ (z * u),y,z)) = x * K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(15646(a,1),5083(a,2,2))].">
      <j1 rule="para" parents="15646 5083"/>
    </justification>
  </clause>

  <clause id="15654">
    <literal><![CDATA[
      K(x,L(y \ (z * u),y,R(u,z,z) \ (u * z))) = K(x,((R(u,z,z) \ (u * z)) \ y) \ R(u,z,z))
    ]]></literal>
    <justification jstring="[para(13592(a,1),15646(a,1,2,1,2))].">
      <j1 rule="para" parents="13592 15646"/>
    </justification>
  </clause>

  <clause id="15655">
    <literal><![CDATA[
      T(x,L(y \ (z * u),y,z)) = T(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(299,a,5083,a,b,15653,a),flip(a)].">
      <j1 rule="hyper" parents="299 5083 15653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15656">
    <literal><![CDATA[
      T(x,((1 / y) * z) \ (y * u)) = T(x,(y \ z) \ ((y \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(2469(a,1),15655(a,1,2))].">
      <j1 rule="para" parents="2469 15655"/>
    </justification>
  </clause>

  <clause id="15657">
    <literal><![CDATA[
      T(x,L(T(y,z) \ (z * u),T(y,z),z)) = T(x,(T(z,y) \ y) \ u)
    ]]></literal>
    <justification jstring="[para(4396(a,2),15655(a,2,2,1))].">
      <j1 rule="para" parents="4396 15655"/>
    </justification>
  </clause>

  <clause id="15658">
    <literal><![CDATA[
      K(x,(L(y,z,u) \ y) \ w) = K(x,L(y,z,u) * (y \ w))
    ]]></literal>
    <justification jstring="[para(1348(a,1),15648(a,2,2))].">
      <j1 rule="para" parents="1348 15648"/>
    </justification>
  </clause>

  <clause id="15659">
    <literal><![CDATA[
      K(x,(y \ L(y,z,u)) * w) = K(x,L(y,z,u) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(14528,a,15658,a)].">
      <j1 rule="hyper" parents="14528 15658"/>
    </justification>
  </clause>

  <clause id="15660">
    <literal><![CDATA[
      K(x,(L(y,z,u) \ y) \ ((y * y) * w)) = K(x,L(y,z,u) * ((1 / y) \ w))
    ]]></literal>
    <justification jstring="[para(443(a,1),15658(a,2,2,2))].">
      <j1 rule="para" parents="443 15658"/>
    </justification>
  </clause>

  <clause id="15661">
    <literal><![CDATA[
      K(x,L(y,z,z) * (y \ u)) = K(x,a(z,z,y) \ u)
    ]]></literal>
    <justification jstring="[para(1986(a,1),15658(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1986 15658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15662">
    <literal><![CDATA[
      x * K(x,L(y,z,u) * (y \ w)) = T(x,(L(y,z,u) \ y) \ w)
    ]]></literal>
    <justification jstring="[para(15658(a,1),5083(a,2,2)),flip(a)].">
      <j1 rule="para" parents="15658 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15663">
    <literal><![CDATA[
      K(L(x,y,y) * (x \ z),u) = (w \ K(u,a(y,y,x) \ z)) \ (w \ 1)
    ]]></literal>
    <justification jstring="[para(15661(a,1),14240(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="15661 14240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15664">
    <literal><![CDATA[
      K(x,(y \ L(y,z,u)) * ((y * y) * w)) = K(x,L(y,z,u) * ((1 / y) \ w))
    ]]></literal>
    <justification jstring="[para(443(a,1),15659(a,2,2,2))].">
      <j1 rule="para" parents="443 15659"/>
    </justification>
  </clause>

  <clause id="15665">
    <literal><![CDATA[
      x * K(x,L(y,z,u) * (y \ w)) = T(x,(y \ L(y,z,u)) * w)
    ]]></literal>
    <justification jstring="[para(15659(a,1),5083(a,2,2)),flip(a)].">
      <j1 rule="para" parents="15659 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15666">
    <literal><![CDATA[
      K(x,L(y,z,z) * (y \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,a(z,z,y) \ u) = w
    ]]></literal>
    <justification jstring="[para(15659(a,1),14531(a,1))].">
      <j1 rule="para" parents="15659 14531"/>
    </justification>
  </clause>

  <clause id="15667">
    <literal><![CDATA[
      ((K(x,y) * z) * u) * u = K(x,y) * ((z * u) * u)
    ]]></literal>
    <justification jstring="[para(15496(a,1),15629(a,1,1))].">
      <j1 rule="para" parents="15496 15629"/>
    </justification>
  </clause>

  <clause id="15668">
    <literal><![CDATA[
      (K(x,K(y,z * u)) * z) * u = T(z * u,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(37,a,8014,a(flip),b,15667,a),flip(a)].">
      <j1 rule="hyper" parents="37 8014 15667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15669">
    <literal><![CDATA[
      ((K(x,y) * z) * (u * u)) \ (K(x,y) * ((z * u) * u)) = a(K(x,y) * z,u,u)
    ]]></literal>
    <justification jstring="[hyper(119,a,15667,a(flip),b,84,a)].">
      <j1 rule="hyper" parents="119 15667 84"/>
    </justification>
  </clause>

  <clause id="15671">
    <literal><![CDATA[
      (T(K(x,y),(x \ R(x,y,x)) * z) * K(x * y,x)) * z = T((x \ R(x,y,x)) * z,K(x,y))
    ]]></literal>
    <justification jstring="[para(8484(a,1),15668(a,1,1))].">
      <j1 rule="para" parents="8484 15668"/>
    </justification>
  </clause>

  <clause id="15672">
    <literal><![CDATA[
      K(x,L((y * z) \ u,y,z)) = K(x,T(y,z) \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,11661,a(flip),b,15641,a)].">
      <j1 rule="hyper" parents="65 11661 15641"/>
    </justification>
  </clause>

  <clause id="15673">
    <literal><![CDATA[
      K(x,L((((y * z) / y) * (z \ y)) \ u,(y * z) / y,z \ y)) = K(x,((z \ y) \ T(y,z)) \ ((z \ y) \ u))
    ]]></literal>
    <justification jstring="[para(1430(a,1),15672(a,2,2,1))].">
      <j1 rule="para" parents="1430 15672"/>
    </justification>
  </clause>

  <clause id="15674">
    <literal><![CDATA[
      K(x,L((y * L(1 / y,z,u)) \ w,y \ 1,L(y,z,u))) = K(x,T(y \ 1,L(y,z,u)) \ (L(y,z,u) \ w))
    ]]></literal>
    <justification jstring="[para(6521(a,1),15672(a,1,2,1,1))].">
      <j1 rule="para" parents="6521 15672"/>
    </justification>
  </clause>

  <clause id="15675">
    <literal><![CDATA[
      K(x,L((y * (z * (u * K(w,u)))) \ v5,y * (z * u),K(w,L(u,z,y)))) = K(x,T(y * (z * u),K(w,L(u,z,y))) \ (K(w,L(u,z,y)) \ v5))
    ]]></literal>
    <justification jstring="[para(12027(a,1),15672(a,1,2,1,1))].">
      <j1 rule="para" parents="12027 15672"/>
    </justification>
  </clause>

  <clause id="15676">
    <literal><![CDATA[
      T(x,((y \ 1) * z) \ (y * u)) = T(x,(y \ z) \ ((y \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,3876,a(flip),b,15656,a)].">
      <j1 rule="hyper" parents="65 3876 15656"/>
    </justification>
  </clause>

  <clause id="15677">
    <literal><![CDATA[
      T(x,(y \ (y * z)) \ ((y \ 1) \ u)) = T(x,L(z,y,y) \ (y * u))
    ]]></literal>
    <justification jstring="[para(475(a,1),15656(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="475 15656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15678">
    <literal><![CDATA[
      T(x,(L(y,z,u) \ y) \ w) = T(x,L(y,z,u) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(5087,a,15662,a),flip(a)].">
      <j1 rule="hyper" parents="5087 15662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15679">
    <literal><![CDATA[
      T(x,(L(y,z,u) \ y) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,L(y,z,u) * (y \ w)) = v5
    ]]></literal>
    <justification jstring="[para(15662(a,1),5087(a,1))].">
      <j1 rule="para" parents="15662 5087"/>
    </justification>
  </clause>

  <clause id="15680">
    <literal><![CDATA[
      T(x,(y \ L(y,z,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,L(y,z,u) * (y \ w)) = v5
    ]]></literal>
    <justification jstring="[para(15665(a,1),5087(a,1))].">
      <j1 rule="para" parents="15665 5087"/>
    </justification>
  </clause>

  <clause id="15681">
    <literal><![CDATA[
      K((x * (y / x)) \ z,L(u,y,x)) = K((y / x) \ (x \ z),u)
    ]]></literal>
    <justification jstring="[hyper(15000,a,15637,a)].">
      <j1 rule="hyper" parents="15000 15637"/>
    </justification>
  </clause>

  <clause id="15682">
    <literal><![CDATA[
      K(x,(T(y,z) \ z) \ u) = K(x,(z * y) \ (y * (y * u)))
    ]]></literal>
    <justification jstring="[para(525(a,1),15652(a,1,2)),flip(a)].">
      <j1 rule="para" parents="525 15652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15683">
    <literal><![CDATA[
      T(x,(T(y,z) \ z) \ u) = T(x,(z * y) \ (y * (y * u)))
    ]]></literal>
    <justification jstring="[para(525(a,1),15657(a,1,2)),flip(a)].">
      <j1 rule="para" parents="525 15657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15684">
    <literal><![CDATA[
      T(x,L(y,z,z) \ (z * u)) = T(x,y \ ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(9(a,1),15677(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 15677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15685">
    <literal><![CDATA[
      K(x,L((y * (z \ 1)) \ u,z,y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,z * (y \ u)) = w
    ]]></literal>
    <justification jstring="[para(2526(a,1),15643(a,1,2))].">
      <j1 rule="para" parents="2526 15643"/>
    </justification>
  </clause>

  <clause id="15686">
    <literal><![CDATA[
      K(L(x,y,y) * (x \ z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(a(y,y,x) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(15663(a,2),7262(a,1))].">
      <j1 rule="para" parents="15663 7262"/>
    </justification>
  </clause>

  <clause id="15687">
    <literal><![CDATA[
      K(x \ (y \ ((1 / z) \ u)),w) = K(x \ (y \ ((z \ 1) \ u)),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,15631,a(flip),b,15636,a),flip(a)].">
      <j1 rule="hyper" parents="65 15631 15636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15688">
    <literal><![CDATA[
      K((1 / x) \ (y \ ((z \ 1) \ u)),w) = K(x * (y \ ((1 / z) \ u)),w)
    ]]></literal>
    <justification jstring="[hyper(14554,a,15687,a),flip(a)].">
      <j1 rule="hyper" parents="14554 15687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15689">
    <literal><![CDATA[
      (x * y) / (K(z \ (u \ ((w \ 1) \ v5)),x) * y) = T(x,z \ (u \ ((1 / w) \ v5)))
    ]]></literal>
    <justification jstring="[para(15687(a,1),5517(a,1,2,1))].">
      <j1 rule="para" parents="15687 5517"/>
    </justification>
  </clause>

  <clause id="15690">
    <literal><![CDATA[
      K(x * (y \ ((1 / z) \ u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x * (y \ ((z \ 1) \ u)),w) = v5
    ]]></literal>
    <justification jstring="[para(15688(a,1),14554(a,1))].">
      <j1 rule="para" parents="15688 14554"/>
    </justification>
  </clause>

  <clause id="15691">
    <literal><![CDATA[
      K(x,L(y,z,u) * ((1 / y) \ w)) = K(x,(y * L(y,z,u)) * w)
    ]]></literal>
    <justification jstring="[para(15211(a,1),15664(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15211 15664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15692">
    <literal><![CDATA[
      K(L((x / y) * K(z,T(u,y)),K(u,T(z,y)),y),w) = K(x / (y * K(u,z)),w)
    ]]></literal>
    <justification jstring="[para(7583(a,1),15542(a,1,1,1))].">
      <j1 rule="para" parents="7583 15542"/>
    </justification>
  </clause>

  <clause id="15693">
    <literal><![CDATA[
      (K(x,y) * (K(x,y) * (z * u))) / u = L(K(x,y),K(x,y),z) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(10029(a,1),15544(a,1,1))].">
      <j1 rule="para" parents="10029 15544"/>
    </justification>
  </clause>

  <clause id="15694">
    <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(299,a,7498,a,b,15602,a),flip(a)].">
      <j1 rule="hyper" parents="299 7498 15602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15695">
    <literal><![CDATA[
      (x * x) \ ((K(y,z) * u) \ (K(y,z) * ((u * x) * x))) = a(K(y,z) * u,x,x)
    ]]></literal>
    <justification jstring="[hyper(603,a,15669,a)].">
      <j1 rule="hyper" parents="603 15669"/>
    </justification>
  </clause>

  <clause id="15696">
    <literal><![CDATA[
      (K(x,y) * (K(x,y) * (z * u))) / u = K(x,y) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(9200(a,1),15693(a,2,1))].">
      <j1 rule="para" parents="9200 15693"/>
    </justification>
  </clause>

  <clause id="15697">
    <literal><![CDATA[
      (K(x,y) * (K(x,y) * z)) * u = K(x,y) * (K(x,y) * (z * u))
    ]]></literal>
    <justification jstring="[hyper(143,a,15696,a)].">
      <j1 rule="hyper" parents="143 15696"/>
    </justification>
  </clause>

  <clause id="15699">
    <literal><![CDATA[
      (x * (T(T(x,y),y) \ z)) * u = K(y,x) * (K(y,x) * (z * u))
    ]]></literal>
    <justification jstring="[para(6199(a,1),15697(a,1,1))].">
      <j1 rule="para" parents="6199 15697"/>
    </justification>
  </clause>

  <clause id="15700">
    <literal><![CDATA[
      (x * (T(T(x,y),y) \ z)) * u = x * (T(T(x,y),y) \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(299,a,6199,a(flip),b,15699,a),flip(a)].">
      <j1 rule="hyper" parents="299 6199 15699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15701">
    <literal><![CDATA[
      K(x,L((y / z) \ u,y / z,z) \ 1) = K(x,T(y / (u * z),y / z))
    ]]></literal>
    <justification jstring="[hyper(299,a,10353,a(flip),b,15694,a),flip(a)].">
      <j1 rule="hyper" parents="299 10353 15694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15702">
    <literal><![CDATA[
      K(x,T(y / (z * u),y / u)) = K(x,(u * z) \ (u * (y / u)))
    ]]></literal>
    <justification jstring="[hyper(7095,a,15701,a),flip(a)].">
      <j1 rule="hyper" parents="7095 15701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15703">
    <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(299,a,13922,a(flip),b,15702,a),flip(a)].">
      <j1 rule="hyper" parents="299 13922 15702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15704">
    <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(6222(a,1),15702(a,2,2,1))].">
      <j1 rule="para" parents="6222 15702"/>
    </justification>
  </clause>

  <clause id="15705">
    <literal><![CDATA[
      L(a(x,y,y),x,K(z,u)) = a(K(z,u) * x,y,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2891,a(flip),b,15695,a)].">
      <j1 rule="hyper" parents="65 2891 15695"/>
    </justification>
  </clause>

  <clause id="15706">
    <literal><![CDATA[
      K(x,(y / (z \ 1)) * R(1 / z,u,u)) = K(x,(y / z) * R(z,u,u))
    ]]></literal>
    <justification jstring="[para(15621(a,1),15530(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15621 15530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15707">
    <literal><![CDATA[
      K(x,y * (z * ((u \ 1) \ R(1 / u,w,w)))) = K(x,y * (z * a(u,w,w)))
    ]]></literal>
    <justification jstring="[para(2134(a,1),15589(a,2,2,2,2))].">
      <j1 rule="para" parents="2134 15589"/>
    </justification>
  </clause>

  <clause id="15708">
    <literal><![CDATA[
      K(x,y * (z * (u * R(1 / u,w,w)))) = K(x,y * (z * a(u,w,w)))
    ]]></literal>
    <justification jstring="[para(15346(a,1),15707(a,1,2,2,2))].">
      <j1 rule="para" parents="15346 15707"/>
    </justification>
  </clause>

  <clause id="15709">
    <literal><![CDATA[
      a(x,y \ z,K(u,L(y,(y \ z) * u,y))) = K(x,((y \ z) * u) \ (y \ (z * u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,14946,a,b,15642,a)].">
      <j1 rule="hyper" parents="65 14946 15642"/>
    </justification>
  </clause>

  <clause id="15710">
    <literal><![CDATA[
      T(x,y \ (z \ ((1 / u) \ w))) = T(x,y \ (z \ ((u \ 1) \ w)))
    ]]></literal>
    <justification jstring="[hyper(5519,a,15689,a),flip(a)].">
      <j1 rule="hyper" parents="5519 15689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15711">
    <literal><![CDATA[
      T(x,y \ (z \ ((u \ 1) \ 1))) = T(x,y \ (z \ u))
    ]]></literal>
    <justification jstring="[para(79(a,1),15710(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="79 15710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15712">
    <literal><![CDATA[
      T(x,y \ (z \ T(a(u,u,u) * w,u \ 1))) = T(x,y \ (z \ ((1 / u) \ (w * (1 / u)))))
    ]]></literal>
    <justification jstring="[para(6379(a,2),15710(a,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6379 15710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15713">
    <literal><![CDATA[
      T(x,(y \ 1) \ (z \ ((u \ 1) \ 1))) = T(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(299,a,14215,a(flip),b,15711,a),flip(a)].">
      <j1 rule="hyper" parents="299 14215 15711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15714">
    <literal><![CDATA[
      T(x,y \ (z \ (1 / u))) = T(x,y \ (z \ (u \ 1)))
    ]]></literal>
    <justification jstring="[para(79(a,1),15711(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="79 15711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15715">
    <literal><![CDATA[
      T(((x \ 1) * y) / (x \ 1),(z * (x \ 1)) \ ((z * (x \ 1)) \ (x \ 1))) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,(z * (1 / x)) \ ((z * (1 / x)) \ 1)) = u
    ]]></literal>
    <justification jstring="[para(15714(a,1),15392(a,1))].">
      <j1 rule="para" parents="15714 15392"/>
    </justification>
  </clause>

  <clause id="15716">
    <literal><![CDATA[
      T(x,((y \ 1) \ 1) * (z \ ((u \ 1) \ 1))) = T(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,14297,a,b,15713,a)].">
      <j1 rule="hyper" parents="65 14297 15713"/>
    </justification>
  </clause>

  <clause id="15717">
    <literal><![CDATA[
      K(x,((y \ z) * u) \ (y \ (z * u))) = a(x,y \ z,K(u,y))
    ]]></literal>
    <justification jstring="[para(7473(a,1),15709(a,1,3)),flip(a)].">
      <j1 rule="para" parents="7473 15709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15718">
    <literal><![CDATA[
      K(x,((y \ z) * u) \ (y \ (z * u))) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(299,a,14983,a(flip),b,15717,a),flip(a)].">
      <j1 rule="hyper" parents="299 14983 15717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15720">
    <literal><![CDATA[
      K((x \ y) \ ((1 / x) * z),L(u,x \ y,x)) = K((x \ ((x \ 1) \ y)) \ z,u)
    ]]></literal>
    <justification jstring="[para(2538(a,1),15634(a,1,2))].">
      <j1 rule="para" parents="2538 15634"/>
    </justification>
  </clause>

  <clause id="15721">
    <literal><![CDATA[
      K((x \ y) \ ((1 / x) * z),L(u,y,x)) = K((x \ ((x \ 1) \ y)) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(15000,a,15720,a)].">
      <j1 rule="hyper" parents="15000 15720"/>
    </justification>
  </clause>

  <clause id="15722">
    <literal><![CDATA[
      K((x \ y) \ ((x \ 1) * z),L(u,y,x)) = K((x \ ((x \ 1) \ y)) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,5890,a(flip),b,15721,a)].">
      <j1 rule="hyper" parents="65 5890 15721"/>
    </justification>
  </clause>

  <clause id="15723">
    <literal><![CDATA[
      K((x \ ((x \ 1) \ y)) \ z,u) = K(y \ (x * ((x \ 1) * z)),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,14989,a(flip),b,15722,a),flip(a)].">
      <j1 rule="hyper" parents="65 14989 15722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15724">
    <literal><![CDATA[
      K((x \ ((x \ 1) \ y)) \ z,u) = K(y \ L(z,x,x),u)
    ]]></literal>
    <justification jstring="[para(1673(a,1),15723(a,2,1,2))].">
      <j1 rule="para" parents="1673 15723"/>
    </justification>
  </clause>

  <clause id="15725">
    <literal><![CDATA[
      K((x \ ((1 / x) \ y)) \ z,u) = K(y \ L(z,x,x),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,6058,a,b,15724,a)].">
      <j1 rule="hyper" parents="65 6058 15724"/>
    </justification>
  </clause>

  <clause id="15726">
    <literal><![CDATA[
      (T(x \ 1,x \ y) * (x \ y)) * z = T(x \ 1,x \ y) * (x \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(5398,a,15572,a),flip(a)].">
      <j1 rule="hyper" parents="5398 15572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15727">
    <literal><![CDATA[
      T(x \ 1,x \ y) * (x \ (y * z)) = T((1 / x) * (y / x),y) * z
    ]]></literal>
    <justification jstring="[para(15281(a,1),15726(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15281 15726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15728">
    <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(12595(a,1),15610(a,1,1))].">
      <j1 rule="para" parents="12595 15610"/>
    </justification>
  </clause>

  <clause id="15729">
    <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(8050(a,1),15728(a,1,1,2))].">
      <j1 rule="para" parents="8050 15728"/>
    </justification>
  </clause>

  <clause id="15730">
    <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(15423,a,15729,a)].">
      <j1 rule="hyper" parents="15423 15729"/>
    </justification>
  </clause>

  <clause id="15731">
    <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(8241(a,2),15730(a,1,2,2))].">
      <j1 rule="para" parents="8241 15730"/>
    </justification>
  </clause>

  <clause id="15732">
    <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(9224(a,2),15731(a,1,2))].">
      <j1 rule="para" parents="9224 15731"/>
    </justification>
  </clause>

  <clause id="15733">
    <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(8656(a,2),15732(a,1,2,2,2))].">
      <j1 rule="para" parents="8656 15732"/>
    </justification>
  </clause>

  <clause id="15734">
    <literal><![CDATA[
      x \ ((K(y,L(z,x,u)) * (K(y,z) \ x)) * u) = L(u,K(y,z) \ x,K(y,z))
    ]]></literal>
    <justification jstring="[para(11739(a,1),15627(a,1,2,1,1))].">
      <j1 rule="para" parents="11739 15627"/>
    </justification>
  </clause>

  <clause id="15735">
    <literal><![CDATA[
      x \ ((K(y,L(z,x,u)) * (K(z,y) * x)) * u) = L(u,K(y,z) \ x,K(y,z))
    ]]></literal>
    <justification jstring="[para(5426(a,1),15734(a,1,2,1,2))].">
      <j1 rule="para" parents="5426 15734"/>
    </justification>
  </clause>

  <clause id="15737">
    <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),15703(a,1,2,1,2))].">
      <j1 rule="para" parents="10 15703"/>
    </justification>
  </clause>

  <clause id="15738">
    <literal><![CDATA[
      x \ (K(y,L(z,K(y,z),K(y,z) \ u)) * u) = (K(z,y) * (K(z,y) * x)) \ (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(5426(a,1),15562(a,2,2))].">
      <j1 rule="para" parents="5426 15562"/>
    </justification>
  </clause>

  <clause id="15739">
    <literal><![CDATA[
      K(x,L((y * (z \ 1)) \ (z * u),y * z,z)) = K(x,T(y * (z \ (1 / z)),z) \ u)
    ]]></literal>
    <justification jstring="[para(2888(a,1),15650(a,1,2))].">
      <j1 rule="para" parents="2888 15650"/>
    </justification>
  </clause>

  <clause id="15740">
    <literal><![CDATA[
      T(x,y \ (z \ T(a(u,u,u) * w,u \ 1))) = T(x,y \ (z \ T(w,1 / u)))
    ]]></literal>
    <justification jstring="[para(22(a,2),15712(a,2,2,2,2))].">
      <j1 rule="para" parents="22 15712"/>
    </justification>
  </clause>

  <clause id="15741">
    <literal><![CDATA[
      T(x,y \ (z \ T(a(u,u,u) * w,u \ 1))) = T(x,y \ (z \ T(w,u \ 1)))
    ]]></literal>
    <justification jstring="[para(3733(a,1),15740(a,2,2,2,2))].">
      <j1 rule="para" parents="3733 15740"/>
    </justification>
  </clause>

  <clause id="15742">
    <literal><![CDATA[
      (((x \ y) * K(z,u / (x \ y))) * x) \ ((x \ y) * x) = K(y \ (x * u),T(z,(x \ y) * x))
    ]]></literal>
    <justification jstring="[para(8146(a,1),15569(a,1,1,1))].">
      <j1 rule="para" parents="8146 15569"/>
    </justification>
  </clause>

  <clause id="15743">
    <literal><![CDATA[
      T((x \ R(x,y,x)) * z,K(x,y)) = (T(K(x,y),z) * K(x * y,x)) * z
    ]]></literal>
    <justification jstring="[para(13701(a,1),15671(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="13701 15671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15744">
    <literal><![CDATA[
      T((x \ R(x,y,x)) * z,K(x,y)) = (T(x,K(y,z)) \ R(x,y,x)) * z
    ]]></literal>
    <justification jstring="[para(9806(a,1),15743(a,2,1))].">
      <j1 rule="para" parents="9806 15743"/>
    </justification>
  </clause>

  <clause id="15746">
    <literal><![CDATA[
      T((x \ R(x,y,x)) * z,K(x,y)) = (x \ R(T(x,K(y,z)),y,x)) * z
    ]]></literal>
    <justification jstring="[para(8710(a,1),15744(a,2,1))].">
      <j1 rule="para" parents="8710 15744"/>
    </justification>
  </clause>

  <clause id="15747">
    <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(7492(a,2),15733(a,1,2,2))].">
      <j1 rule="para" parents="7492 15733"/>
    </justification>
  </clause>

  <clause id="15748">
    <literal><![CDATA[
      (x * y) \ (((z * x) * R((z * x) \ x,u,u)) * y) = a(R(T(z,x * y),x,y),u,u)
    ]]></literal>
    <justification jstring="[para(1871(a,1),15594(a,1,2))].">
      <j1 rule="para" parents="1871 15594"/>
    </justification>
  </clause>

  <clause id="15749">
    <literal><![CDATA[
      (x * y) \ ((z * (x * R(x \ (z \ x),u,u))) * y) = a(R(T(z,x * y),x,y),u,u)
    ]]></literal>
    <justification jstring="[para(1149(a,1),15748(a,1,2,1))].">
      <j1 rule="para" parents="1149 15748"/>
    </justification>
  </clause>

  <clause id="15750">
    <literal><![CDATA[
      (x * y) \ (((z \ R(z,u,u)) * x) * y) = a(R(T(z,x * y),x,y),u,u)
    ]]></literal>
    <justification jstring="[para(15352(a,1),15749(a,1,2,1))].">
      <j1 rule="para" parents="15352 15749"/>
    </justification>
  </clause>

  <clause id="15751">
    <literal><![CDATA[
      (x * y) \ ((a(z,u,u) * x) * y) = a(R(T(z,x * y),x,y),u,u)
    ]]></literal>
    <justification jstring="[para(15581(a,1),15750(a,1,2,1,1))].">
      <j1 rule="para" parents="15581 15750"/>
    </justification>
  </clause>

  <clause id="15752">
    <literal><![CDATA[
      a(R(T(x,y * z),y,z),u,u) = R(T(a(x,u,u),y * z),y,z)
    ]]></literal>
    <justification jstring="[hyper(1025,a,15751,a),flip(a)].">
      <j1 rule="hyper" parents="1025 15751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15753">
    <literal><![CDATA[
      a(R(T(x,y * z),y,z),u,u) = R(a(x,u,u),y,z)
    ]]></literal>
    <justification jstring="[para(14905(a,1),15752(a,2,1))].">
      <j1 rule="para" parents="14905 15752"/>
    </justification>
  </clause>

  <clause id="15755">
    <literal><![CDATA[
      K(x,L(y \ (z * u),y,L(z,z,u * z))) = K(x,((R(u,z,z) \ (u * z)) \ y) \ R(u,z,z))
    ]]></literal>
    <justification jstring="[para(6539(a,1),15654(a,1,2))].">
      <j1 rule="para" parents="6539 15654"/>
    </justification>
  </clause>

  <clause id="15756">
    <literal><![CDATA[
      K(x,L(y \ (z * u),y,z)) = K(x,((R(u,z,z) \ (u * z)) \ y) \ R(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(15007,a,15755,a)].">
      <j1 rule="hyper" parents="15007 15755"/>
    </justification>
  </clause>

  <clause id="15757">
    <literal><![CDATA[
      K(x,((R(y,z,z) \ (y * z)) \ u) \ R(y,z,z)) = K(x,(z \ u) \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,15646,a(flip),b,15756,a),flip(a)].">
      <j1 rule="hyper" parents="65 15646 15756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15758">
    <literal><![CDATA[
      T(K(x,L(y,z * z,(z * z) \ u)) * u,z * z) = T(K(x,y),z * z) * T(u,z * z)
    ]]></literal>
    <justification jstring="[para(22(a,2),15561(a,2,1))].">
      <j1 rule="para" parents="22 15561"/>
    </justification>
  </clause>

  <clause id="15759">
    <literal><![CDATA[
      K(x,L(T(y,z) \ u,(y * z) / y,z \ y)) = K(x,((z \ y) \ T(y,z)) \ ((z \ y) \ u))
    ]]></literal>
    <justification jstring="[para(1426(a,2),15673(a,1,2,1,1))].">
      <j1 rule="para" parents="1426 15673"/>
    </justification>
  </clause>

  <clause id="15760">
    <literal><![CDATA[
      K(x,((y \ z) \ T(z,y)) \ ((y \ z) \ u)) = K(x,L(T(z,y) \ u,T(y,z),y \ z))
    ]]></literal>
    <justification jstring="[para(5734(a,1),15759(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5734 15759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15761">
    <literal><![CDATA[
      K(x,L((y * L(1 / y,z,u)) \ w,y,L(y,z,u))) = K(x,T(y \ 1,L(y,z,u)) \ (L(y,z,u) \ w))
    ]]></literal>
    <justification jstring="[para(2526(a,1),15674(a,1,2))].">
      <j1 rule="para" parents="2526 15674"/>
    </justification>
  </clause>

  <clause id="15762">
    <literal><![CDATA[
      K(x,T(y \ 1,L(y,z,u)) \ (L(y,z,u) \ w)) = K(x,(y * L(1 / y,z,u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(15515,a,15761,a),flip(a)].">
      <j1 rule="hyper" parents="15515 15761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15764">
    <literal><![CDATA[
      K(x,T(y \ 1,L(y,z,u)) \ (L(y,z,u) \ w)) = K(x,(y * L(y \ 1,z,u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(299,a,6043,a(flip),b,15762,a),flip(a)].">
      <j1 rule="hyper" parents="299 6043 15762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15765">
    <literal><![CDATA[
      K(x,T(y \ 1,L(y,z,u)) \ (L(y,z,u) \ w)) = K(x,(y \ L(y,z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(6499(a,1),15764(a,2,2,1))].">
      <j1 rule="para" parents="6499 15764"/>
    </justification>
  </clause>

  <clause id="15766">
    <literal><![CDATA[
      K(((x \ y) * x) \ z,T(u,T(x * y,x))) = K((((1 / x) \ z) * (1 / x)) / (T((x \ 1) \ y,x) * (1 / x)),u)
    ]]></literal>
    <justification jstring="[para(14579(a,1),15566(a,1,2))].">
      <j1 rule="para" parents="14579 15566"/>
    </justification>
  </clause>

  <clause id="15767">
    <literal><![CDATA[
      K(((x \ y) * x) \ z,T(u,y * x)) = K((((1 / x) \ z) * (1 / x)) / (T((x \ 1) \ y,x) * (1 / x)),u)
    ]]></literal>
    <justification jstring="[para(13197(a,1),15766(a,1,2))].">
      <j1 rule="para" parents="13197 15766"/>
    </justification>
  </clause>

  <clause id="15768">
    <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),15704(a,1,2,1,2))].">
      <j1 rule="para" parents="12 15704"/>
    </justification>
  </clause>

  <clause id="15769">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u)) = T(y,K(u,z) * x)
    ]]></literal>
    <justification jstring="[para(6097(a,2),15747(a,1,2))].">
      <j1 rule="para" parents="6097 15747"/>
    </justification>
  </clause>

  <clause id="15770">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u)) = T(y,K(z \ u,z) * x)
    ]]></literal>
    <justification jstring="[hyper(299,a,13889,a,b,15769,a),flip(a)].">
      <j1 rule="hyper" parents="299 13889 15769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15771">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u)) = T(y,K(z * u,z) * x)
    ]]></literal>
    <justification jstring="[hyper(299,a,13887,a,b,15769,a),flip(a)].">
      <j1 rule="hyper" parents="299 13887 15769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15772">
    <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(4263(a,2),15769(a,2,2))].">
      <j1 rule="para" parents="4263 15769"/>
    </justification>
  </clause>

  <clause id="15773">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(u,z)) = T(y,K(z,u) * x)
    ]]></literal>
    <justification jstring="[para(8050(a,1),15769(a,1,2,1,2))].">
      <j1 rule="para" parents="8050 15769"/>
    </justification>
  </clause>

  <clause id="15774">
    <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(8812(a,1),15769(a,1,2,1,2))].">
      <j1 rule="para" parents="8812 15769"/>
    </justification>
  </clause>

  <clause id="15775">
    <literal><![CDATA[
      x \ T(T(y,K(z,u)) * T(x,K(z,u)),K(u,z)) = K(y,x * K(z,u)) * T(y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,13213,a,b,15773,a),flip(a)].">
      <j1 rule="hyper" parents="299 13213 15773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15776">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u)) = T(y,K(z,u) * x)
    ]]></literal>
    <justification jstring="[para(8050(a,1),15773(a,1,2))].">
      <j1 rule="para" parents="8050 15773"/>
    </justification>
  </clause>

  <clause id="15777">
    <literal><![CDATA[
      T(x * T(y,K(z,u)),K(z,u)) = y * T(x,K(z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(144,a,15776,a),flip(a)].">
      <j1 rule="hyper" parents="144 15776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15778">
    <literal><![CDATA[
      T(x,K(y,z) * u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,15769,a(flip),b,15776,a)].">
      <j1 rule="hyper" parents="65 15769 15776"/>
    </justification>
  </clause>

  <clause id="15779">
    <literal><![CDATA[
      T(x,K(y,y * z) * u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(299,a,13702,a,b,15778,a)].">
      <j1 rule="hyper" parents="299 13702 15778"/>
    </justification>
  </clause>

  <clause id="15780">
    <literal><![CDATA[
      x \ T(x,K(y,z) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(119,a,15778,a,b,5083,a(flip))].">
      <j1 rule="hyper" parents="119 15778 5083"/>
    </justification>
  </clause>

  <clause id="15781">
    <literal><![CDATA[
      T(x,K(y,z) * (z * u)) = T(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[para(5103(a,1),15778(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5103 15778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15782">
    <literal><![CDATA[
      T(x,K(y,z) * (K(y,z) * u)) = T(x,u)
    ]]></literal>
    <justification jstring="[para(5432(a,1),15778(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5432 15778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15783">
    <literal><![CDATA[
      T(x,K(y,z) * (y \ u)) = T(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(5383(a,1),15778(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5383 15778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15784">
    <literal><![CDATA[
      T(x,K(y,z) * (z / u)) = T(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[para(14430(a,1),15778(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14430 15778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15785">
    <literal><![CDATA[
      T(x,y * (K(z,u) * K(z,u))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,14601,a,b,15782,a)].">
      <j1 rule="hyper" parents="65 14601 15782"/>
    </justification>
  </clause>

  <clause id="15786">
    <literal><![CDATA[
      T(x,K(y,z) * K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(42,a,14603,a(flip),b,15782,a),flip(a)].">
      <j1 rule="hyper" parents="42 14603 15782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15787">
    <literal><![CDATA[
      T(x,y * (T(T(y,z),z) \ u)) = T(x,u)
    ]]></literal>
    <justification jstring="[para(6199(a,1),15782(a,1,2))].">
      <j1 rule="para" parents="6199 15782"/>
    </justification>
  </clause>

  <clause id="15788">
    <literal><![CDATA[
      T(x,T(T(y,z),z) / u) = T(x,y / u)
    ]]></literal>
    <justification jstring="[para(6585(a,1),15782(a,1,2))].">
      <j1 rule="para" parents="6585 15782"/>
    </justification>
  </clause>

  <clause id="15789">
    <literal><![CDATA[
      T(x,K(y,z) * K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(15786(a,1),51(a,2))].">
      <j1 rule="para" parents="15786 51"/>
    </justification>
  </clause>

  <clause id="15791">
    <literal><![CDATA[
      T(x,K(y,z) * (K(y,z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u) = w
    ]]></literal>
    <justification jstring="[para(14468(a,1),15789(a,1))].">
      <j1 rule="para" parents="14468 15789"/>
    </justification>
  </clause>

  <clause id="15792">
    <literal><![CDATA[
      T(x,y * (K(z,u) * K(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = w
    ]]></literal>
    <justification jstring="[para(14602(a,1),15789(a,1))].">
      <j1 rule="para" parents="14602 15789"/>
    </justification>
  </clause>

  <clause id="15796">
    <literal><![CDATA[
      T(x,y * (z \ (K(u,w) * K(u,w)))) = T(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(65,a,14671,a(flip),b,15785,a)].">
      <j1 rule="hyper" parents="65 14671 15785"/>
    </justification>
  </clause>

  <clause id="15797">
    <literal><![CDATA[
      T(x,y * (z * (K(u,w) * K(u,w)))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(35(a,1),15785(a,1,2))].">
      <j1 rule="para" parents="35 15785"/>
    </justification>
  </clause>

  <clause id="15798">
    <literal><![CDATA[
      T(x,T(T(y,z),z) * u) = T(x,y * u)
    ]]></literal>
    <justification jstring="[para(9(a,1),15787(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 15787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15799">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * y) = T(x,y * T(T(z,u),u))
    ]]></literal>
    <justification jstring="[hyper(13258,a,15798,a),flip(a)].">
      <j1 rule="hyper" parents="13258 15798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15800">
    <literal><![CDATA[
      T(x,T(y \ z,z) * u) = T(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,13986,a(flip),b,15798,a)].">
      <j1 rule="hyper" parents="65 13986 15798"/>
    </justification>
  </clause>

  <clause id="15801">
    <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(13256,a,15779,a),flip(a)].">
      <j1 rule="hyper" parents="13256 15779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15802">
    <literal><![CDATA[
      K(x,K(y,z) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(5155,a,15780,a)].">
      <j1 rule="hyper" parents="5155 15780"/>
    </justification>
  </clause>

  <clause id="15803">
    <literal><![CDATA[
      K(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(15780(a,1),5155(a,1))].">
      <j1 rule="para" parents="15780 5155"/>
    </justification>
  </clause>

  <clause id="15804">
    <literal><![CDATA[
      K(x,K(y,y \ z) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(299,a,13777,a(flip),b,15802,a),flip(a)].">
      <j1 rule="hyper" parents="299 13777 15802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15805">
    <literal><![CDATA[
      K(x,K(y,z) \ u) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(5426(a,2),15802(a,1,2))].">
      <j1 rule="para" parents="5426 15802"/>
    </justification>
  </clause>

  <clause id="15806">
    <literal><![CDATA[
      K(x,K(y,z) * (T(z,y) \ u)) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(5351(a,1),15802(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5351 15802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15807">
    <literal><![CDATA[
      K(x,K(y,z) * (y \ u)) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(5383(a,1),15802(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5383 15802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15808">
    <literal><![CDATA[
      K(x,K(y,z \ u) * (u / z)) = K(x,T(u / z,T(y,z)))
    ]]></literal>
    <justification jstring="[para(7628(a,1),15802(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7628 15802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15809">
    <literal><![CDATA[
      K(x,K(y / (z \ u),z) * w) = K(x,K(z,(y * z) / u) * w)
    ]]></literal>
    <justification jstring="[para(9064(a,2),15802(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9064 15802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15810">
    <literal><![CDATA[
      K(x,K(y,z) \ u) = K(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(5426(a,2),15805(a,2,2))].">
      <j1 rule="para" parents="5426 15805"/>
    </justification>
  </clause>

  <clause id="15811">
    <literal><![CDATA[
      K(x,K(y,z) \ ((y \ 1) \ u)) = K(x,u * T(u \ ((y \ 1) \ u),z))
    ]]></literal>
    <justification jstring="[para(5093(a,1),15805(a,2,2))].">
      <j1 rule="para" parents="5093 15805"/>
    </justification>
  </clause>

  <clause id="15812">
    <literal><![CDATA[
      K(x,K(y,z) \ (y / u)) = K(x,T(y,z) / u)
    ]]></literal>
    <justification jstring="[para(14430(a,1),15805(a,2,2))].">
      <j1 rule="para" parents="14430 15805"/>
    </justification>
  </clause>

  <clause id="15813">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w) \ v5) = K(x,K(L(z,u,w),y) \ v5)
    ]]></literal>
    <justification jstring="[para(11889(a,2),15810(a,1,2,1))].">
      <j1 rule="para" parents="11889 15810"/>
    </justification>
  </clause>

  <clause id="15814">
    <literal><![CDATA[
      T(x,y * (K(z,y) * u)) = T(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(5524(a,1),15781(a,1,2))].">
      <j1 rule="para" parents="5524 15781"/>
    </justification>
  </clause>

  <clause id="15815">
    <literal><![CDATA[
      T(x,((y * z) / y) \ u) = T(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(5352(a,2),15783(a,1,2))].">
      <j1 rule="para" parents="5352 15783"/>
    </justification>
  </clause>

  <clause id="15816">
    <literal><![CDATA[
      T(x,y \ (K(y,z) * u)) = T(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(5371(a,2),15783(a,1,2))].">
      <j1 rule="para" parents="5371 15783"/>
    </justification>
  </clause>

  <clause id="15817">
    <literal><![CDATA[
      T(x,T(y \ z,y) \ u) = T(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[para(5692(a,1),15783(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5692 15783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15818">
    <literal><![CDATA[
      T(x,T(y,z) \ (z \ u)) = T(x,y \ (T(z,y) \ u))
    ]]></literal>
    <justification jstring="[para(5698(a,1),15783(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5698 15783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15819">
    <literal><![CDATA[
      T(x,K(y,y * a(z,u,w)) * ((y * a(z,u,w)) / v5)) = T(x,(a(z,u,w) * y) / v5)
    ]]></literal>
    <justification jstring="[para(14153(a,1),15784(a,2,2,1))].">
      <j1 rule="para" parents="14153 15784"/>
    </justification>
  </clause>

  <clause id="15820">
    <literal><![CDATA[
      T(x,(y / (y / z)) * u) = T(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[para(79(a,1),15800(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="79 15800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15821">
    <literal><![CDATA[
      K(x,K(y,y \ z) * u) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(299,a,15802,a,b,15804,a),flip(a)].">
      <j1 rule="hyper" parents="299 15802 15804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15822">
    <literal><![CDATA[
      K(x,T(T(y,z),z) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(5527(a,1),15806(a,1,2))].">
      <j1 rule="para" parents="5527 15806"/>
    </justification>
  </clause>

  <clause id="15823">
    <literal><![CDATA[
      K(x,T(y \ z,y) \ u) = K(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[para(109(a,1),15822(a,1,2,1,1))].">
      <j1 rule="para" parents="109 15822"/>
    </justification>
  </clause>

  <clause id="15824">
    <literal><![CDATA[
      K(x,((y * z) / y) \ u) = K(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(222(a,1),15822(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="222 15822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15825">
    <literal><![CDATA[
      K(x,(L(y,z,y) * z) \ u) = K(x,T(z * y,y) \ u)
    ]]></literal>
    <justification jstring="[para(4351(a,1),15822(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4351 15822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15826">
    <literal><![CDATA[
      T(x,T(y,y \ z) * ((y \ z) \ u)) = T(x,y * ((z / y) \ u))
    ]]></literal>
    <justification jstring="[para(5692(a,1),15814(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5692 15814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15827">
    <literal><![CDATA[
      T(x,T(T(y,z),z) \ u) = T(x,y \ u)
    ]]></literal>
    <justification jstring="[para(223(a,1),15815(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="223 15815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15828">
    <literal><![CDATA[
      T(x,T(y,y \ z) \ u) = T(x,(z / (z / y)) \ u)
    ]]></literal>
    <justification jstring="[para(4504(a,1),15815(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4504 15815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15829">
    <literal><![CDATA[
      T(x,T(y,z) \ (T(y,z) \ u)) = T(x,y \ (y \ u))
    ]]></literal>
    <justification jstring="[para(5351(a,1),15816(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5351 15816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15830">
    <literal><![CDATA[
      T(x,((y \ 1) * K((1 / y) \ z,1 / y)) * u) = T(x,T(1 / y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,5010,a(flip),b,15820,a)].">
      <j1 rule="hyper" parents="65 5010 15820"/>
    </justification>
  </clause>

  <clause id="15831">
    <literal><![CDATA[
      K(x,(((y \ z) \ z) \ z) \ u) = K(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[para(4391(a,1),15823(a,1,2,1))].">
      <j1 rule="para" parents="4391 15823"/>
    </justification>
  </clause>

  <clause id="15832">
    <literal><![CDATA[
      K(x,L(((y \ ((z * u) / z)) \ ((z * u) / z)) \ w,y,y \ ((z * u) / z))) = K(x,T(u,z) \ ((y \ ((z * u) / z)) * w))
    ]]></literal>
    <justification jstring="[para(11655(a,2),15824(a,1,2))].">
      <j1 rule="para" parents="11655 15824"/>
    </justification>
  </clause>

  <clause id="15833">
    <literal><![CDATA[
      T(x,K(y,z) * (z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(5061(a,1),15791(a,1,2,2))].">
      <j1 rule="para" parents="5061 15791"/>
    </justification>
  </clause>

  <clause id="15834">
    <literal><![CDATA[
      T(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(5432(a,1),15791(a,1,2,2))].">
      <j1 rule="para" parents="5432 15791"/>
    </justification>
  </clause>

  <clause id="15835">
    <literal><![CDATA[
      T(x,K(y,z) * (y \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(5351(a,1),15791(a,1,2,2))].">
      <j1 rule="para" parents="5351 15791"/>
    </justification>
  </clause>

  <clause id="15836">
    <literal><![CDATA[
      T(x,K(y,z) * (z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(z,y) / u) = w
    ]]></literal>
    <justification jstring="[para(14431(a,1),15791(a,1,2,2))].">
      <j1 rule="para" parents="14431 15791"/>
    </justification>
  </clause>

  <clause id="15838">
    <literal><![CDATA[
      T(x,y \ T(T(z,u),u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ z) = w
    ]]></literal>
    <justification jstring="[para(6316(a,1),15792(a,1,2))].">
      <j1 rule="para" parents="6316 15792"/>
    </justification>
  </clause>

  <clause id="15839">
    <literal><![CDATA[
      T(x,y * (z \ (K(u,w) * K(u,w)))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y / z) = v5
    ]]></literal>
    <justification jstring="[para(14671(a,1),15792(a,1))].">
      <j1 rule="para" parents="14671 15792"/>
    </justification>
  </clause>

  <clause id="15840">
    <literal><![CDATA[
      K(x,K(y,y \ z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(15804(a,2),15803(a,1))].">
      <j1 rule="para" parents="15804 15803"/>
    </justification>
  </clause>

  <clause id="15841">
    <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(15776(a,2),15834(a,1))].">
      <j1 rule="para" parents="15776 15834"/>
    </justification>
  </clause>

  <clause id="15842">
    <literal><![CDATA[
      T(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z * y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(15779(a,1),15834(a,1))].">
      <j1 rule="para" parents="15779 15834"/>
    </justification>
  </clause>

  <clause id="15843">
    <literal><![CDATA[
      T(x,K(y,y * z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(15779(a,2),15834(a,1))].">
      <j1 rule="para" parents="15779 15834"/>
    </justification>
  </clause>

  <clause id="15844">
    <literal><![CDATA[
      T(x,y \ T(z \ u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (u / z)) = w
    ]]></literal>
    <justification jstring="[para(109(a,1),15838(a,1,2,2,1))].">
      <j1 rule="para" parents="109 15838"/>
    </justification>
  </clause>

  <clause id="15845">
    <literal><![CDATA[
      T(x,y * (z \ K(z,u))) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(5366(a,1),15796(a,1,2,2))].">
      <j1 rule="para" parents="5366 15796"/>
    </justification>
  </clause>

  <clause id="15846">
    <literal><![CDATA[
      T(x,y * (z * (u * (K(w,v5) * K(w,v5))))) = T(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(35(a,1),15797(a,1,2,2))].">
      <j1 rule="para" parents="35 15797"/>
    </justification>
  </clause>

  <clause id="15847">
    <literal><![CDATA[
      T(x,y * (z \ T(T(u,w),w))) = T(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[para(6316(a,1),15797(a,1,2,2))].">
      <j1 rule="para" parents="6316 15797"/>
    </justification>
  </clause>

  <clause id="15848">
    <literal><![CDATA[
      T(x,y * T(T(z,u),u)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(13236,a,15799,a),flip(a)].">
      <j1 rule="hyper" parents="13236 15799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15849">
    <literal><![CDATA[
      T(x,y * T(z \ u,z)) = T(x,y * (u / z))
    ]]></literal>
    <justification jstring="[para(109(a,1),15848(a,1,2,2,1))].">
      <j1 rule="para" parents="109 15848"/>
    </justification>
  </clause>

  <clause id="15850">
    <literal><![CDATA[
      T(x,y * ((z * u) / z)) = T(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[para(222(a,1),15848(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="222 15848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15851">
    <literal><![CDATA[
      T(x,y * T(z,z \ u)) = T(x,y * (u / (u / z)))
    ]]></literal>
    <justification jstring="[para(4502(a,1),15848(a,1,2,2,1))].">
      <j1 rule="para" parents="4502 15848"/>
    </justification>
  </clause>

  <clause id="15852">
    <literal><![CDATA[
      T(x,(y / z) * (y / z)) = T(x,(z \ y) * (z \ y))
    ]]></literal>
    <justification jstring="[para(5928(a,1),15849(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5928 15849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15853">
    <literal><![CDATA[
      K(x * ((y * z) / y),u) = u / T(u,x * T(z,y))
    ]]></literal>
    <justification jstring="[para(15850(a,1),5033(a,2,2))].">
      <j1 rule="para" parents="15850 5033"/>
    </justification>
  </clause>

  <clause id="15854">
    <literal><![CDATA[
      T(x,T(y,z) \ (T(y,z) \ u)) = T(T(x,u),y \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(14752,a,15829,a)].">
      <j1 rule="hyper" parents="14752 15829"/>
    </justification>
  </clause>

  <clause id="15855">
    <literal><![CDATA[
      K(x,T(y \ z,z) \ u) = K(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(13907,a,15831,a)].">
      <j1 rule="hyper" parents="13907 15831"/>
    </justification>
  </clause>

  <clause id="15856">
    <literal><![CDATA[
      T(x,y * (z / (z / u))) = T(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,13810,a(flip),b,15851,a),flip(a)].">
      <j1 rule="hyper" parents="65 13810 15851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15857">
    <literal><![CDATA[
      T(x,y * T(z \ u,u)) = T(x,y * (u / z))
    ]]></literal>
    <justification jstring="[para(76(a,1),15856(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="76 15856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15858">
    <literal><![CDATA[
      T(x * K(y / z,x),z / y) = T(x,(y \ z) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,6326,a,b,15852,a)].">
      <j1 rule="hyper" parents="65 6326 15852"/>
    </justification>
  </clause>

  <clause id="15859">
    <literal><![CDATA[
      K(x * ((y * z) / y),u) = K(x * T(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,5033,a,b,15853,a),flip(a)].">
      <j1 rule="hyper" parents="299 5033 15853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15860">
    <literal><![CDATA[
      K(x * T(y \ z,y),u) = K(x * (z / y),u)
    ]]></literal>
    <justification jstring="[para(10(a,1),15859(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 15859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15861">
    <literal><![CDATA[
      K((x \ y) * ((z * ((x \ y) \ (x \ u))) / z),w) = K(x \ (y * T(y \ u,z)),w)
    ]]></literal>
    <justification jstring="[para(1464(a,1),15859(a,2,1))].">
      <j1 rule="para" parents="1464 15859"/>
    </justification>
  </clause>

  <clause id="15862">
    <literal><![CDATA[
      K(x,T(y * z,z) \ u) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,13938,a(flip),b,15825,a),flip(a)].">
      <j1 rule="hyper" parents="65 13938 15825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15864">
    <literal><![CDATA[
      K(x,(y * (z / y)) \ u) = K(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(12(a,1),15862(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="12 15862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15865">
    <literal><![CDATA[
      K(x,L((y / z) \ u,u,z)) = K(x,T(y,z) \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(11997,a,15864,a)].">
      <j1 rule="hyper" parents="11997 15864"/>
    </justification>
  </clause>

  <clause id="15866">
    <literal><![CDATA[
      K(x,((y \ z) * y) \ u) = K(x,(y * (z / y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(299,a,13922,a,b,15864,a)].">
      <j1 rule="hyper" parents="299 13922 15864"/>
    </justification>
  </clause>

  <clause id="15867">
    <literal><![CDATA[
      K(x,(y * ((y * z) / y)) \ u) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(299,a,13919,a(flip),b,15864,a),flip(a)].">
      <j1 rule="hyper" parents="299 13919 15864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15868">
    <literal><![CDATA[
      K(x,T(y,z) \ ((y / z) * u)) = K(x,y \ ((z \ y) * u))
    ]]></literal>
    <justification jstring="[para(11676(a,1),15864(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11676 15864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15869">
    <literal><![CDATA[
      K(x,(y * (z / y)) \ u) \ 1 = K(((y \ z) * y) \ u,x)
    ]]></literal>
    <justification jstring="[para(15866(a,1),5197(a,1,1))].">
      <j1 rule="para" parents="15866 5197"/>
    </justification>
  </clause>

  <clause id="15870">
    <literal><![CDATA[
      K(x,(T(y,z) * z) \ u) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[para(223(a,1),15867(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="223 15867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15871">
    <literal><![CDATA[
      K(x,(T(T(y,z * z),1 / z) * (1 / z)) \ u) = K(x,T((z \ 1) * y,z * z) \ u)
    ]]></literal>
    <justification jstring="[para(1178(a,2),15870(a,2,2,1))].">
      <j1 rule="para" parents="1178 15870"/>
    </justification>
  </clause>

  <clause id="15872">
    <literal><![CDATA[
      T(x,y * (K(z,y) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(5524(a,1),15833(a,1,2))].">
      <j1 rule="para" parents="5524 15833"/>
    </justification>
  </clause>

  <clause id="15873">
    <literal><![CDATA[
      T(x,y \ (T(z,u) \ u)) = T(x,y \ (u / z))
    ]]></literal>
    <justification jstring="[hyper(15844,a,13944,a),flip(a)].">
      <j1 rule="hyper" parents="15844 13944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15874">
    <literal><![CDATA[
      T(x,y \ (T(z,u) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (u / z)) = w
    ]]></literal>
    <justification jstring="[para(13944(a,1),15844(a,1))].">
      <j1 rule="para" parents="13944 15844"/>
    </justification>
  </clause>

  <clause id="15875">
    <literal><![CDATA[
      T(x,y \ (z \ T(u,z))) = T(x,y \ (u / z))
    ]]></literal>
    <justification jstring="[para(4396(a,1),15873(a,1,2,2))].">
      <j1 rule="para" parents="4396 15873"/>
    </justification>
  </clause>

  <clause id="15876">
    <literal><![CDATA[
      K(x,L((y / R(z,u,z)) \ T(w,z),T(w,z),R(z,u,z))) = K(x,T(y,R(z,u,z)) \ (w * R(z,u,z)))
    ]]></literal>
    <justification jstring="[para(7461(a,1),15865(a,2,2,2))].">
      <j1 rule="para" parents="7461 15865"/>
    </justification>
  </clause>

  <clause id="15878">
    <literal><![CDATA[
      T(x,T(y,z) \ (T(y,z) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (y \ u)) = w
    ]]></literal>
    <justification jstring="[para(15854(a,2),14752(a,1))].">
      <j1 rule="para" parents="15854 14752"/>
    </justification>
  </clause>

  <clause id="15879">
    <literal><![CDATA[
      T(x * K(T(y \ z,z \ y) / 1,x),(y \ z) \ 1) = T(x,(T(y \ z,z \ y) \ 1) * (T(y \ z,z \ y) \ 1))
    ]]></literal>
    <justification jstring="[para(2997(a,1),15858(a,1,2))].">
      <j1 rule="para" parents="2997 15858"/>
    </justification>
  </clause>

  <clause id="15880">
    <literal><![CDATA[
      T(x * K(L(y,z,y) * z,x),y / (y * (z * y))) = T(x,((y * (z * y)) \ y) * ((y * (z * y)) \ y))
    ]]></literal>
    <justification jstring="[para(4352(a,1),15858(a,1,1,2,1))].">
      <j1 rule="para" parents="4352 15858"/>
    </justification>
  </clause>

  <clause id="15881">
    <literal><![CDATA[
      K(x,T(y * (y * z),y) \ ((T(y,y * z) * z) * u)) = K(x,(y * (y * z)) \ ((y \ (y * (y * z))) * u))
    ]]></literal>
    <justification jstring="[para(4270(a,1),15868(a,1,2,2,1))].">
      <j1 rule="para" parents="4270 15868"/>
    </justification>
  </clause>

  <clause id="15882">
    <literal><![CDATA[
      K(((x \ y) * x) \ z,u) = K((x * (y / x)) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(5200,a,15869,a),flip(a)].">
      <j1 rule="hyper" parents="5200 15869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15883">
    <literal><![CDATA[
      K((x * ((x * y) / x)) \ z,u) = K((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),15882(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 15882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15884">
    <literal><![CDATA[
      K((T(x,y) * y) \ z,u) = K((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[para(223(a,1),15883(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="223 15883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15885">
    <literal><![CDATA[
      T(x,y * K(z,z * u)) = T(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(13255,a,15801,a),flip(a)].">
      <j1 rule="hyper" parents="13255 15801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15886">
    <literal><![CDATA[
      T(x,y * (z * (u * K(w,u)))) = T(x,y * (z * T(u,w)))
    ]]></literal>
    <justification jstring="[para(5387(a,1),15846(a,1,2,2,2))].">
      <j1 rule="para" parents="5387 15846"/>
    </justification>
  </clause>

  <clause id="15887">
    <literal><![CDATA[
      K(x,y * (z * (u * K(w,u)))) = x \ T(x,y * (z * T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(119,a,15886,a(flip),b,5083,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 15886 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15888">
    <literal><![CDATA[
      T(x,y * (z * T(T(u,w),w))) = T(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(5100(a,1),15886(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5100 15886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15889">
    <literal><![CDATA[
      T(x,y * (T(z,u) * u)) = T(x,y * (u * z))
    ]]></literal>
    <justification jstring="[para(107(a,1),15888(a,1,2,2))].">
      <j1 rule="para" parents="107 15888"/>
    </justification>
  </clause>

  <clause id="15890">
    <literal><![CDATA[
      T(x,y \ (T(z,u) * u)) = T(x,(y \ 1) * (u * z))
    ]]></literal>
    <justification jstring="[hyper(14304,a,15889,a)].">
      <j1 rule="hyper" parents="14304 15889"/>
    </justification>
  </clause>

  <clause id="15891">
    <literal><![CDATA[
      T(x,T(y,z * u) * (z * u)) = T(x,(T(u,z) * z) * y)
    ]]></literal>
    <justification jstring="[hyper(13274,a,15889,a),flip(a)].">
      <j1 rule="hyper" parents="13274 15889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15892">
    <literal><![CDATA[
      T(x,y * (T(z,u) * u)) = x * K(x,y * (u * z))
    ]]></literal>
    <justification jstring="[hyper(299,a,5083,a(flip),b,15889,a),flip(a)].">
      <j1 rule="hyper" parents="299 5083 15889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15893">
    <literal><![CDATA[
      T(x,y * T(z * T(u,z),z)) = T(x,y * (z * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,13766,a,b,15889,a)].">
      <j1 rule="hyper" parents="65 13766 15889"/>
    </justification>
  </clause>

  <clause id="15895">
    <literal><![CDATA[
      K(x,T(y,z * (u * w)) * (z * (T(w,u) * u))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * (T(w,u) * u)) * y) = v5
    ]]></literal>
    <justification jstring="[para(15889(a,1),13261(a,1,2,1))].">
      <j1 rule="para" parents="15889 13261"/>
    </justification>
  </clause>

  <clause id="15896">
    <literal><![CDATA[
      T(x,T(y,z * (u * w)) * (z * (T(w,u) * u))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,(z * (T(w,u) * u)) * y) = v5
    ]]></literal>
    <justification jstring="[para(15889(a,1),13267(a,1,2,1))].">
      <j1 rule="para" parents="15889 13267"/>
    </justification>
  </clause>

  <clause id="15897">
    <literal><![CDATA[
      T(x,y \ (T(z,u) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (u * z)) = w
    ]]></literal>
    <justification jstring="[para(15890(a,2),14304(a,1))].">
      <j1 rule="para" parents="15890 14304"/>
    </justification>
  </clause>

  <clause id="15898">
    <literal><![CDATA[
      K(x,y \ (T(z,u) * u)) = K(x,(y \ 1) * (u * z))
    ]]></literal>
    <justification jstring="[hyper(14382,a,15892,a)].">
      <j1 rule="hyper" parents="14382 15892"/>
    </justification>
  </clause>

  <clause id="15899">
    <literal><![CDATA[
      K(x,y * (T(z,u) * u)) = K(x,y * (u * z))
    ]]></literal>
    <justification jstring="[hyper(5154,a,15892,a)].">
      <j1 rule="hyper" parents="5154 15892"/>
    </justification>
  </clause>

  <clause id="15900">
    <literal><![CDATA[
      T(x,y * (T(z,u) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (u * z)) = w
    ]]></literal>
    <justification jstring="[para(15892(a,2),5087(a,1))].">
      <j1 rule="para" parents="15892 5087"/>
    </justification>
  </clause>

  <clause id="15901">
    <literal><![CDATA[
      K(x,y * (T(z \ u,w) * z)) = K(x,y * (z * T(u / z,w)))
    ]]></literal>
    <justification jstring="[para(242(a,1),15899(a,1,2,2,1))].">
      <j1 rule="para" parents="242 15899"/>
    </justification>
  </clause>

  <clause id="15902">
    <literal><![CDATA[
      K(x,y * (T(z,u) * T(u,w))) = K(x,y * (u * (z * K(u,w))))
    ]]></literal>
    <justification jstring="[para(7792(a,1),15899(a,1,2,2))].">
      <j1 rule="para" parents="7792 15899"/>
    </justification>
  </clause>

  <clause id="15903">
    <literal><![CDATA[
      K(x,y * (T(z,T(u,w)) * ((w * u) / w))) = K(x,y * (((w * u) / w) * z))
    ]]></literal>
    <justification jstring="[para(8182(a,1),15899(a,1,2,2,1))].">
      <j1 rule="para" parents="8182 15899"/>
    </justification>
  </clause>

  <clause id="15904">
    <literal><![CDATA[
      K(x,y * (T(z,u) * (u * K(w,u)))) = K(x,y * (u * (z * K(w,u))))
    ]]></literal>
    <justification jstring="[para(7782(a,1),15899(a,1,2,2))].">
      <j1 rule="para" parents="7782 15899"/>
    </justification>
  </clause>

  <clause id="15905">
    <literal><![CDATA[
      K(x,y * (T(z,(u \ w) * (u \ w)) * (w / u))) = K(x,y * ((w / u) * (z * K(u / w,z))))
    ]]></literal>
    <justification jstring="[para(15858(a,1),15899(a,1,2,2,1))].">
      <j1 rule="para" parents="15858 15899"/>
    </justification>
  </clause>

  <clause id="15906">
    <literal><![CDATA[
      T(x,y * T(z * u,u)) = T(x,y * (u * z))
    ]]></literal>
    <justification jstring="[para(107(a,1),15893(a,1,2,2,1))].">
      <j1 rule="para" parents="107 15893"/>
    </justification>
  </clause>

  <clause id="15907">
    <literal><![CDATA[
      T(x,y * (z * (u / z))) = T(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[para(219(a,1),15893(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="219 15893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15908">
    <literal><![CDATA[
      T(x,(y * z) * z) = T(x,z * (z * y))
    ]]></literal>
    <justification jstring="[para(107(a,1),15906(a,1,2))].">
      <j1 rule="para" parents="107 15906"/>
    </justification>
  </clause>

  <clause id="15909">
    <literal><![CDATA[
      K(x * T(y * z,z),u) = u / T(u,x * (z * y))
    ]]></literal>
    <justification jstring="[para(15906(a,1),5033(a,2,2))].">
      <j1 rule="para" parents="15906 5033"/>
    </justification>
  </clause>

  <clause id="15910">
    <literal><![CDATA[
      K(x,y \ (T(z,u) * u)) = K(x,y \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(299,a,14246,a(flip),b,15898,a),flip(a)].">
      <j1 rule="hyper" parents="299 14246 15898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15911">
    <literal><![CDATA[
      K(x,y \ (T(z,u) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (u * z)) = w
    ]]></literal>
    <justification jstring="[para(15898(a,2),14281(a,1))].">
      <j1 rule="para" parents="15898 14281"/>
    </justification>
  </clause>

  <clause id="15912">
    <literal><![CDATA[
      K(x,y \ (T(z,T(u,w) / w) * (T(u,w) / w))) = K(x,y \ ((u / T(w,u)) * z))
    ]]></literal>
    <justification jstring="[para(4414(a,1),15910(a,2,2,2))].">
      <j1 rule="para" parents="4414 15910"/>
    </justification>
  </clause>

  <clause id="15913">
    <literal><![CDATA[
      K(x * T(y * z,z),u) = K(x * (z * y),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,5033,a,b,15909,a),flip(a)].">
      <j1 rule="hyper" parents="299 5033 15909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15914">
    <literal><![CDATA[
      K(x * T(y * z,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x * (z * y),u) = w
    ]]></literal>
    <justification jstring="[para(15909(a,2),5118(a,1))].">
      <j1 rule="para" parents="15909 5118"/>
    </justification>
  </clause>

  <clause id="15915">
    <literal><![CDATA[
      K(x * (y * (z / y)),u) = K(x * T(z,y),u)
    ]]></literal>
    <justification jstring="[para(12(a,1),15913(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 15913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15916">
    <literal><![CDATA[
      K(x * T(T(y,z),u \ y),w) = K(x * T((u \ y) * u,z),w)
    ]]></literal>
    <justification jstring="[para(3470(a,1),15915(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3470 15915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15917">
    <literal><![CDATA[
      T(x,y \ T(z * u,u)) = T(x,y \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(15897,a,13827,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="15897 13827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15918">
    <literal><![CDATA[
      T(x,y \ (a(z,u,u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (w * a(z,u,u))) = v5
    ]]></literal>
    <justification jstring="[para(14905(a,1),15897(a,1,2,2,1))].">
      <j1 rule="para" parents="14905 15897"/>
    </justification>
  </clause>

  <clause id="15919">
    <literal><![CDATA[
      T(x,y \ (z * (u / z))) = T(x,y \ T(u,z))
    ]]></literal>
    <justification jstring="[para(12(a,1),15917(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="12 15917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15920">
    <literal><![CDATA[
      T(x,((y * y) \ z) * (u / z)) = T(x,(y * y) \ T(u,z))
    ]]></literal>
    <justification jstring="[para(664(a,1),15919(a,1,2))].">
      <j1 rule="para" parents="664 15919"/>
    </justification>
  </clause>

  <clause id="15921">
    <literal><![CDATA[
      T(x,y * (T(z,u) * L(u,w,u))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (L(u,w,u) * z)) = v5
    ]]></literal>
    <justification jstring="[para(7449(a,1),15900(a,1,2,2,1))].">
      <j1 rule="para" parents="7449 15900"/>
    </justification>
  </clause>

  <clause id="15922">
    <literal><![CDATA[
      K(x,y \ (T(z,u * w) * (T(w,u) * u))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ ((T(w,u) * u) * z)) = v5
    ]]></literal>
    <justification jstring="[para(13266(a,1),15911(a,1,2,2,1))].">
      <j1 rule="para" parents="13266 15911"/>
    </justification>
  </clause>

  <clause id="15923">
    <literal><![CDATA[
      K(x,y \ (T(z,u * (u / w)) * ((w \ u) * u))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (((w \ u) * u) * z)) = v5
    ]]></literal>
    <justification jstring="[para(13877(a,1),15911(a,1,2,2,1))].">
      <j1 rule="para" parents="13877 15911"/>
    </justification>
  </clause>

  <clause id="15924">
    <literal><![CDATA[
      T(x,(T(y,z) * z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z * y) * u) = w
    ]]></literal>
    <justification jstring="[para(15891(a,1),13267(a,1))].">
      <j1 rule="para" parents="15891 13267"/>
    </justification>
  </clause>

  <clause id="15925">
    <literal><![CDATA[
      T(x,((y * y) \ z) * (u / z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (y \ T(u,z))) = w
    ]]></literal>
    <justification jstring="[para(15920(a,2),14292(a,1))].">
      <j1 rule="para" parents="15920 14292"/>
    </justification>
  </clause>

  <clause id="15926">
    <literal><![CDATA[
      K(x,y * (z * (u * K(w,u)))) = K(x,y * (z * T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(299,a,5036,a,b,15887,a),flip(a)].">
      <j1 rule="hyper" parents="299 5036 15887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15927">
    <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(15887(a,2),5155(a,1))].">
      <j1 rule="para" parents="15887 5155"/>
    </justification>
  </clause>

  <clause id="15928">
    <literal><![CDATA[
      K(x,y * (z * T(T(u,w),w))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(5100(a,1),15926(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5100 15926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15929">
    <literal><![CDATA[
      K(x,y * (z * (T(u,u * w) * w))) = K(x,y * (z * T(u * w,u)))
    ]]></literal>
    <justification jstring="[para(4316(a,1),15928(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4316 15928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15930">
    <literal><![CDATA[
      T(x,K(y \ z,y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(15770(a,1),15841(a,1))].">
      <j1 rule="para" parents="15770 15841"/>
    </justification>
  </clause>

  <clause id="15931">
    <literal><![CDATA[
      T(x,K(y * z,y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(15771(a,1),15841(a,1))].">
      <j1 rule="para" parents="15771 15841"/>
    </justification>
  </clause>

  <clause id="15933">
    <literal><![CDATA[
      T(x,K(y * z,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(5980(a,2),15931(a,1,2,1))].">
      <j1 rule="para" parents="5980 15931"/>
    </justification>
  </clause>

  <clause id="15934">
    <literal><![CDATA[
      K(x,y * (z * ((u * w) / u))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * T(w,u))) = v5
    ]]></literal>
    <justification jstring="[para(5054(a,2),15927(a,1,2,2,2))].">
      <j1 rule="para" parents="5054 15927"/>
    </justification>
  </clause>

  <clause id="15935">
    <literal><![CDATA[
      K(x,y \ (z * ((u * w) / u))) = K(x,(y \ 1) * (z * T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(15934,a,14246,a),flip(a)].">
      <j1 rule="hyper" parents="15934 14246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15936">
    <literal><![CDATA[
      K(x,T(y,z * ((u * w) / u)) * (z * T(w,u))) = K(x,(z * ((u * w) / u)) * y)
    ]]></literal>
    <justification jstring="[hyper(15934,a,13262,a)].">
      <j1 rule="hyper" parents="15934 13262"/>
    </justification>
  </clause>

  <clause id="15938">
    <literal><![CDATA[
      K(x,y \ (z * ((u * w) / u))) = K(x,y \ (z * T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(299,a,14246,a(flip),b,15935,a),flip(a)].">
      <j1 rule="hyper" parents="299 14246 15935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15939">
    <literal><![CDATA[
      K(x,y \ (z * ((T(u,w) * T(w,v5)) / T(u,w)))) = K(x,y \ (z * T(T(w,u),v5)))
    ]]></literal>
    <justification jstring="[para(4397(a,1),15938(a,2,2,2,2))].">
      <j1 rule="para" parents="4397 15938"/>
    </justification>
  </clause>

  <clause id="15940">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u)) = T(y,K(u \ 1,z) * x)
    ]]></literal>
    <justification jstring="[para(8812(a,1),15774(a,1,2))].">
      <j1 rule="para" parents="8812 15774"/>
    </justification>
  </clause>

  <clause id="15941">
    <literal><![CDATA[
      T(x,K(y \ 1,z) * u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(15841,a,15940,a),flip(a)].">
      <j1 rule="hyper" parents="15841 15940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15942">
    <literal><![CDATA[
      K(x,K(y \ 1,z) * u) = x \ T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(119,a,15941,a(flip),b,5083,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 15941 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15943">
    <literal><![CDATA[
      T(x,K(y,z) * T(u,K(z,y \ 1))) = T(x,u * K(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(8063(a,1),15941(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8063 15941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15944">
    <literal><![CDATA[
      K(x,K(y \ 1,z) * u) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(299,a,5036,a,b,15942,a),flip(a)].">
      <j1 rule="hyper" parents="299 5036 15942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15945">
    <literal><![CDATA[
      K(x,K(y,z \ 1) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(15803,a,15944,a)].">
      <j1 rule="hyper" parents="15803 15944"/>
    </justification>
  </clause>

  <clause id="15946">
    <literal><![CDATA[
      K(x,K(y,z) * (y \ u)) = K(x,u * T(u \ (y \ u),z))
    ]]></literal>
    <justification jstring="[para(5339(a,1),15944(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5339 15944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15947">
    <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(15944(a,1),9837(a,1,1))].">
      <j1 rule="para" parents="15944 9837"/>
    </justification>
  </clause>

  <clause id="15948">
    <literal><![CDATA[
      K(x,K(y \ z,u) * w) = K(x,K(u,z \ y) * w)
    ]]></literal>
    <justification jstring="[para(6814(a,1),15945(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6814 15945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15949">
    <literal><![CDATA[
      K(x,K(y,z) * T(u,K(z,y))) = K(x,u * K(z,y \ 1))
    ]]></literal>
    <justification jstring="[para(8815(a,1),15945(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8815 15945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15950">
    <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(15945(a,1),9838(a,1,1))].">
      <j1 rule="para" parents="15945 9838"/>
    </justification>
  </clause>

  <clause id="15951">
    <literal><![CDATA[
      K(x,K(y,z \ y) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,13777,a(flip),b,15948,a),flip(a)].">
      <j1 rule="hyper" parents="65 13777 15948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15952">
    <literal><![CDATA[
      K(x,T(y,z \ y) \ u) = K(x,K(z,y) * (y \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,15807,a(flip),b,15951,a)].">
      <j1 rule="hyper" parents="65 15807 15951"/>
    </justification>
  </clause>

  <clause id="15953">
    <literal><![CDATA[
      K(x,T(y / z,T(u \ (z \ y),z))) = K(x,K(u,z \ y) * (y / z))
    ]]></literal>
    <justification jstring="[para(7628(a,1),15951(a,1,2))].">
      <j1 rule="para" parents="7628 15951"/>
    </justification>
  </clause>

  <clause id="15954">
    <literal><![CDATA[
      K(x,T(y,z \ y) \ u) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(5383(a,1),15952(a,2,2))].">
      <j1 rule="para" parents="5383 15952"/>
    </justification>
  </clause>

  <clause id="15955">
    <literal><![CDATA[
      K(x,y * T(y \ (z \ y),u)) = K(x,T(z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,15807,a(flip),b,15946,a),flip(a)].">
      <j1 rule="hyper" parents="65 15807 15946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15956">
    <literal><![CDATA[
      K(x,(y * z) * T((y * z) \ ((z * K(y,z)) \ (y * z)),u)) = K(x,K(z * K(y,z),u) * y)
    ]]></literal>
    <justification jstring="[para(5127(a,1),15946(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5127 15946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15957">
    <literal><![CDATA[
      K(x,y * K(z,u \ 1)) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[para(8063(a,1),15949(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8063 15949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15958">
    <literal><![CDATA[
      K(x * K(y,z \ 1),u) = 1 / K(u,x * K(z,y))
    ]]></literal>
    <justification jstring="[para(15957(a,1),5209(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15957 5209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15959">
    <literal><![CDATA[
      K(x * K(y,z \ 1),u) = K(x * K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,5209,a(flip),b,15958,a),flip(a)].">
      <j1 rule="hyper" parents="299 5209 15958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15960">
    <literal><![CDATA[
      K(x * K(x \ y,z),T(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(((z * (y \ x)) / z) * y,u) = w
    ]]></literal>
    <justification jstring="[para(15959(a,1),13229(a,1))].">
      <j1 rule="para" parents="15959 13229"/>
    </justification>
  </clause>

  <clause id="15961">
    <literal><![CDATA[
      T(x,K(y,z) * T(u,K(y,z))) = T(x,u * K(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(8813(a,1),15943(a,1,2,2))].">
      <j1 rule="para" parents="8813 15943"/>
    </justification>
  </clause>

  <clause id="15962">
    <literal><![CDATA[
      T(x,y * K(z \ 1,u)) = T(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[para(107(a,1),15961(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 15961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15963">
    <literal><![CDATA[
      K(x,K(y,z) \ ((y \ 1) \ u)) = K(x,T(y \ 1,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(299,a,15955,a(flip),b,15811,a),flip(a)].">
      <j1 rule="hyper" parents="299 15955 15811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15964">
    <literal><![CDATA[
      K(x,y * (T(z,u) * T(u,w))) = K(x,y * (u * (z * K(w,u))))
    ]]></literal>
    <justification jstring="[hyper(15927,a,15904,a)].">
      <j1 rule="hyper" parents="15927 15904"/>
    </justification>
  </clause>

  <clause id="15965">
    <literal><![CDATA[
      K(x,y * (z * (u * K(w,z)))) = K(x,y * (z * (u * K(z,w))))
    ]]></literal>
    <justification jstring="[hyper(65,a,15902,a(flip),b,15964,a),flip(a)].">
      <j1 rule="hyper" parents="65 15902 15964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15966">
    <literal><![CDATA[
      K(x,T(y / z,T(u \ (z \ y),z))) = K(x,T(y / z,T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(299,a,15808,a(flip),b,15953,a),flip(a)].">
      <j1 rule="hyper" parents="299 15808 15953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15967">
    <literal><![CDATA[
      K(x,T(y / z,y / (z * u))) = K(x,T(y / z,T(u,z)))
    ]]></literal>
    <justification jstring="[para(10598(a,1),15966(a,1,2))].">
      <j1 rule="para" parents="10598 15966"/>
    </justification>
  </clause>

  <clause id="15968">
    <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(65,a,15768,a(flip),b,15967,a)].">
      <j1 rule="hyper" parents="65 15768 15967"/>
    </justification>
  </clause>

  <clause id="15969">
    <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(6309(a,1),15967(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6309 15967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15970">
    <literal><![CDATA[
      T(x,y * (L(z,u,z) * w)) = T(x,y * (T(w,z) * z))
    ]]></literal>
    <justification jstring="[hyper(15921,a,13767,a)].">
      <j1 rule="hyper" parents="15921 13767"/>
    </justification>
  </clause>

  <clause id="15971">
    <literal><![CDATA[
      T(x,y * (L(z,u,z) * w)) = T(x,y * (z * w))
    ]]></literal>
    <justification jstring="[hyper(299,a,15889,a(flip),b,15970,a),flip(a)].">
      <j1 rule="hyper" parents="299 15889 15970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15972">
    <literal><![CDATA[
      T(x,y * L(z * u,z,z)) = T(x,y * (z * L(u,z,z)))
    ]]></literal>
    <justification jstring="[para(948(a,1),15971(a,1,2,2))].">
      <j1 rule="para" parents="948 15971"/>
    </justification>
  </clause>

  <clause id="15973">
    <literal><![CDATA[
      K(x,y * (T(z,T(u,w)) * T(u,w))) = K(x,y * (((w * u) / w) * z))
    ]]></literal>
    <justification jstring="[hyper(15934,a,15903,a)].">
      <j1 rule="hyper" parents="15934 15903"/>
    </justification>
  </clause>

  <clause id="15974">
    <literal><![CDATA[
      K(x,y * (((z * u) / z) * w)) = K(x,y * (T(u,z) * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,15899,a(flip),b,15973,a),flip(a)].">
      <j1 rule="hyper" parents="65 15899 15973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15975">
    <literal><![CDATA[
      K(x,y * (T(z \ u,z) * w)) = K(x,y * ((u / z) * w))
    ]]></literal>
    <justification jstring="[para(10(a,1),15974(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 15974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15976">
    <literal><![CDATA[
      K(x,y * (T(T(z,u),u) * w)) = K(x,y * (z * w))
    ]]></literal>
    <justification jstring="[para(223(a,1),15974(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="223 15974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15977">
    <literal><![CDATA[
      K(x,y * (z * (K(u,z) * w))) = K(x,y * (T(z,u) * w))
    ]]></literal>
    <justification jstring="[para(5705(a,1),15974(a,1,2,2))].">
      <j1 rule="para" parents="5705 15974"/>
    </justification>
  </clause>

  <clause id="15978">
    <literal><![CDATA[
      K(x,(y \ z) * (T(T(y \ z,y),y) * u)) = K(x,T(y \ z,y) * ((z / y) * u))
    ]]></literal>
    <justification jstring="[para(5736(a,1),15975(a,1,2))].">
      <j1 rule="para" parents="5736 15975"/>
    </justification>
  </clause>

  <clause id="15979">
    <literal><![CDATA[
      K(x,y \ (z * (K(u,z) * w))) = K(x,(y \ 1) * (T(z,u) * w))
    ]]></literal>
    <justification jstring="[hyper(14281,a,15977,a)].">
      <j1 rule="hyper" parents="14281 15977"/>
    </justification>
  </clause>

  <clause id="15980">
    <literal><![CDATA[
      K(x,y \ (z * (K(u,z) * w))) = K(x,y \ (T(z,u) * w))
    ]]></literal>
    <justification jstring="[hyper(299,a,14246,a(flip),b,15979,a),flip(a)].">
      <j1 rule="hyper" parents="299 14246 15979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15982">
    <literal><![CDATA[
      K(x,y \ (T(z \ u,z) * w)) = K(x,y \ ((u / z) * w))
    ]]></literal>
    <justification jstring="[para(5714(a,1),15980(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5714 15980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15983">
    <literal><![CDATA[
      K(x,(K(y,z \ K(z,u)) * u) \ w) = K(x,(u * K(y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(10253,a,15947,a),flip(a)].">
      <j1 rule="hyper" parents="10253 15947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15984">
    <literal><![CDATA[
      K(x,(y * K(z,u \ 1)) \ w) = K(x,(y * K(z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(6315(a,1),15983(a,1,2,1))].">
      <j1 rule="para" parents="6315 15983"/>
    </justification>
  </clause>

  <clause id="15985">
    <literal><![CDATA[
      K(x,(K(y \ K(y,z),u) * z) \ w) = K(x,(z * K(u,y)) \ w)
    ]]></literal>
    <justification jstring="[hyper(10253,a,15950,a),flip(a)].">
      <j1 rule="hyper" parents="10253 15950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15986">
    <literal><![CDATA[
      K(x,(y * K(z \ 1,u)) \ w) = K(x,(y * K(u,z)) \ w)
    ]]></literal>
    <justification jstring="[para(9093(a,1),15985(a,1,2,1))].">
      <j1 rule="para" parents="9093 15985"/>
    </justification>
  </clause>

  <clause id="15987">
    <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(7995(a,1),15986(a,2,2))].">
      <j1 rule="para" parents="7995 15986"/>
    </justification>
  </clause>

  <clause id="15988">
    <literal><![CDATA[
      K(x \ (y * ((z * (y \ u)) / z)),w) = K(x \ (y * T(y \ u,z)),w)
    ]]></literal>
    <justification jstring="[para(2093(a,1),15861(a,1,1))].">
      <j1 rule="para" parents="2093 15861"/>
    </justification>
  </clause>

  <clause id="15989">
    <literal><![CDATA[
      K(x \ (y * T(y \ 1,z)),u) = K(x \ K(z,y \ 1),u)
    ]]></literal>
    <justification jstring="[para(5072(a,1),15988(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5072 15988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15990">
    <literal><![CDATA[
      K(x \ K(y \ 1,z),u) = K(x \ K(z,y \ 1),u)
    ]]></literal>
    <justification jstring="[para(5035(a,1),15989(a,1,1,2))].">
      <j1 rule="para" parents="5035 15989"/>
    </justification>
  </clause>

  <clause id="15991">
    <literal><![CDATA[
      (x \ K(y \ K(z,u \ 1),w)) \ (x \ 1) = K(w,y \ K(u \ 1,z))
    ]]></literal>
    <justification jstring="[para(15990(a,1),14240(a,1,1,2))].">
      <j1 rule="para" parents="15990 14240"/>
    </justification>
  </clause>

  <clause id="15992">
    <literal><![CDATA[
      K(x,y \ K(z \ 1,u)) = K(x,y \ K(u,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(14241,a,15991,a),flip(a)].">
      <j1 rule="hyper" parents="14241 15991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15993">
    <literal><![CDATA[
      K(x,y \ (T(z,u \ w) * (T(w,u) / u))) = K(x,y \ ((w / T(u,w)) * z))
    ]]></literal>
    <justification jstring="[para(13695(a,1),15912(a,1,2,2,1))].">
      <j1 rule="para" parents="13695 15912"/>
    </justification>
  </clause>

  <clause id="15994">
    <literal><![CDATA[
      K(x,T(y,z * T(u,w)) * (z * T(u,w))) = K(x,(z * ((w * u) / w)) * y)
    ]]></literal>
    <justification jstring="[para(15850(a,1),15936(a,1,2,1))].">
      <j1 rule="para" parents="15850 15936"/>
    </justification>
  </clause>

  <clause id="15995">
    <literal><![CDATA[
      K(x,(y * ((z * u) / z)) * w) = K(x,(y * T(u,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(13261,a,15994,a),flip(a)].">
      <j1 rule="hyper" parents="13261 15994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15996">
    <literal><![CDATA[
      K(x,(y * T(z \ u,z)) * w) = K(x,(y * (u / z)) * w)
    ]]></literal>
    <justification jstring="[para(10(a,1),15995(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 15995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15997">
    <literal><![CDATA[
      K(x,(y * T(T(z,u),u)) * w) = K(x,(y * z) * w)
    ]]></literal>
    <justification jstring="[para(223(a,1),15995(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="223 15995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15998">
    <literal><![CDATA[
      K(x,(T(y,z) * z) * u) = K(x,(z * y) * u)
    ]]></literal>
    <justification jstring="[para(107(a,1),15997(a,1,2,1))].">
      <j1 rule="para" parents="107 15997"/>
    </justification>
  </clause>

  <clause id="15999">
    <literal><![CDATA[
      K(x,T(y,z * u) * (z * u)) = K(x,(T(u,z) * z) * y)
    ]]></literal>
    <justification jstring="[hyper(299,a,13262,a,b,15998,a)].">
      <j1 rule="hyper" parents="299 13262 15998"/>
    </justification>
  </clause>

  <clause id="16000">
    <literal><![CDATA[
      K(x,((y \ z) * y) * u) = K(x,(y * (z / y)) * u)
    ]]></literal>
    <justification jstring="[para(109(a,1),15998(a,1,2,1,1))].">
      <j1 rule="para" parents="109 15998"/>
    </justification>
  </clause>

  <clause id="16001">
    <literal><![CDATA[
      K(x,(T(y,z) * T(z,u)) * w) = K(x,(z * (y * K(z,u))) * w)
    ]]></literal>
    <justification jstring="[para(7792(a,1),15998(a,1,2,1))].">
      <j1 rule="para" parents="7792 15998"/>
    </justification>
  </clause>

  <clause id="16002">
    <literal><![CDATA[
      K(x,(y * (z / y)) * u) = K(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,13859,a(flip),b,16000,a),flip(a)].">
      <j1 rule="hyper" parents="65 13859 16000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16003">
    <literal><![CDATA[
      K(x,T(y * z,z) * u) = K(x,(z * y) * u)
    ]]></literal>
    <justification jstring="[para(11(a,1),16002(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="11 16002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16004">
    <literal><![CDATA[
      K(x,((y \ z) * z) * u) = K(x,(z * (z / y)) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,13946,a(flip),b,15996,a)].">
      <j1 rule="hyper" parents="65 13946 15996"/>
    </justification>
  </clause>

  <clause id="16005">
    <literal><![CDATA[
      K(x,(T(y,z) * z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * y) * u) = w
    ]]></literal>
    <justification jstring="[para(15999(a,1),13261(a,1))].">
      <j1 rule="para" parents="15999 13261"/>
    </justification>
  </clause>

  <clause id="16006">
    <literal><![CDATA[
      K(x,(T(y,z) * L(z,u,z)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(L(z,u,z) * y) * w) = v5
    ]]></literal>
    <justification jstring="[para(7449(a,1),16005(a,1,2,1,1))].">
      <j1 rule="para" parents="7449 16005"/>
    </justification>
  </clause>

  <clause id="16007">
    <literal><![CDATA[
      K(x,(L(y,z,y) * u) * w) = K(x,(T(u,y) * y) * w)
    ]]></literal>
    <justification jstring="[hyper(16006,a,13778,a)].">
      <j1 rule="hyper" parents="16006 13778"/>
    </justification>
  </clause>

  <clause id="16008">
    <literal><![CDATA[
      K(x,(L(y,z,y) * u) * w) = K(x,(y * u) * w)
    ]]></literal>
    <justification jstring="[hyper(299,a,15998,a(flip),b,16007,a),flip(a)].">
      <j1 rule="hyper" parents="299 15998 16007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16009">
    <literal><![CDATA[
      K(x,(((y \ z) \ z) * u) * w) = K(x,(T(y,z) * u) * w)
    ]]></literal>
    <justification jstring="[para(12708(a,1),16008(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="12708 16008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16010">
    <literal><![CDATA[
      K(x,(T(y \ z,1) * z) * u) = K(x,((z \ y) \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,13964,a(flip),b,16009,a),flip(a)].">
      <j1 rule="hyper" parents="65 13964 16009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16011">
    <literal><![CDATA[
      K(x,((y \ z) \ y) * u) = K(x,((z \ y) * y) * u)
    ]]></literal>
    <justification jstring="[para(193(a,1),16010(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="193 16010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16012">
    <literal><![CDATA[
      K(x,((y \ z) \ y) * u) = K(x,(y * (y / z)) * u)
    ]]></literal>
    <justification jstring="[hyper(299,a,16004,a(flip),b,16011,a),flip(a)].">
      <j1 rule="hyper" parents="299 16004 16011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16013">
    <literal><![CDATA[
      K(x,y \ (z * T((T(u,w) * w) / T(u,w),v5))) = K(x,y \ (z * T(T(w,u),v5)))
    ]]></literal>
    <justification jstring="[para(445(a,1),15939(a,1,2,2,2))].">
      <j1 rule="para" parents="445 15939"/>
    </justification>
  </clause>

  <clause id="16014">
    <literal><![CDATA[
      K(x,T(y \ z,y) * ((z / y) * u)) = K(x,(y \ z) * ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,15976,a(flip),b,15978,a),flip(a)].">
      <j1 rule="hyper" parents="65 15976 15978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16016">
    <literal><![CDATA[
      K(x,y \ (z * T(u * K(w,u),v5))) = K(x,y \ (z * T(T(u,w),v5)))
    ]]></literal>
    <justification jstring="[para(5122(a,1),16013(a,1,2,2,2,1))].">
      <j1 rule="para" parents="5122 16013"/>
    </justification>
  </clause>

  <clause id="16017">
    <literal><![CDATA[
      T(x,a(y,z,K(u,w)) * ((y * a(w,z,u)) / v5)) = T(x,(a(w,z,u) * y) / v5)
    ]]></literal>
    <justification jstring="[para(14861(a,1),15819(a,1,2,1))].">
      <j1 rule="para" parents="14861 15819"/>
    </justification>
  </clause>

  <clause id="16018">
    <literal><![CDATA[
      K(x,(T(T(y,z * z),z \ 1) * (1 / z)) \ u) = K(x,T((z \ 1) * y,z * z) \ u)
    ]]></literal>
    <justification jstring="[para(3733(a,1),15871(a,1,2,1,1))].">
      <j1 rule="para" parents="3733 15871"/>
    </justification>
  </clause>

  <clause id="16019">
    <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(65,a,15984,a(flip),b,15968,a)].">
      <j1 rule="hyper" parents="65 15984 15968"/>
    </justification>
  </clause>

  <clause id="16020">
    <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(65,a,14092,a(flip),b,16019,a)].">
      <j1 rule="hyper" parents="65 14092 16019"/>
    </justification>
  </clause>

  <clause id="16021">
    <literal><![CDATA[
      K(x,T(y,z) \ ((y * z) * (u / (y * z)))) = K(x,T(u / y,T(z,y)))
    ]]></literal>
    <justification jstring="[para(5083(a,2),16020(a,1,2,1))].">
      <j1 rule="para" parents="5083 16020"/>
    </justification>
  </clause>

  <clause id="16022">
    <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(4386(a,1),16021(a,1,2,1))].">
      <j1 rule="para" parents="4386 16021"/>
    </justification>
  </clause>

  <clause id="16023">
    <literal><![CDATA[
      K(x,(T(y,(z \ 1) * (z * z)) * (1 / z)) \ u) = K(x,T((z \ 1) * y,z * z) \ u)
    ]]></literal>
    <justification jstring="[para(14603(a,1),16018(a,1,2,1,1))].">
      <j1 rule="para" parents="14603 16018"/>
    </justification>
  </clause>

  <clause id="16024">
    <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(107(a,1),16022(a,1,2,2,1))].">
      <j1 rule="para" parents="107 16022"/>
    </justification>
  </clause>

  <clause id="16025">
    <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(107(a,1),16024(a,1,2,2,2,2))].">
      <j1 rule="para" parents="107 16024"/>
    </justification>
  </clause>

  <clause id="16026">
    <literal><![CDATA[
      K(x,T(y,z) \ ((z * y) * (u / (z * y)))) = K(x,T(u / y,z))
    ]]></literal>
    <justification jstring="[para(8179(a,1),16025(a,2,2))].">
      <j1 rule="para" parents="8179 16025"/>
    </justification>
  </clause>

  <clause id="16028">
    <literal><![CDATA[
      K(x,T((y \ 1) * z,y * y) \ u) = K(x,(T(z,y * 1) * (1 / y)) \ u)
    ]]></literal>
    <justification jstring="[para(14600(a,1),16023(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="14600 16023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16029">
    <literal><![CDATA[
      K(x,T((y \ 1) * z,y * y) \ u) = K(x,(T(z,y) * (1 / y)) \ u)
    ]]></literal>
    <justification jstring="[para(8(a,1),16028(a,2,2,1,1,2))].">
      <j1 rule="para" parents="8 16028"/>
    </justification>
  </clause>

  <clause id="16030">
    <literal><![CDATA[
      K(x,T((y \ 1) * z,y * y) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(T(z,y) * (y \ 1)) \ u) = w
    ]]></literal>
    <justification jstring="[para(16029(a,2),13803(a,1))].">
      <j1 rule="para" parents="16029 13803"/>
    </justification>
  </clause>

  <clause id="16031">
    <literal><![CDATA[
      K(x,(y * z) * T((y * z) \ ((z * K(y,z)) \ (y * z)),u)) = K(x,K(z,T(u,y)) * y)
    ]]></literal>
    <justification jstring="[para(8132(a,1),15956(a,2,2,1))].">
      <j1 rule="para" parents="8132 15956"/>
    </justification>
  </clause>

  <clause id="16032">
    <literal><![CDATA[
      K(x,(y * z) * T((y * z) \ ((z * K(y,z)) \ (y * z)),u)) = K(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[para(8101(a,1),16031(a,2,2))].">
      <j1 rule="para" parents="8101 16031"/>
    </justification>
  </clause>

  <clause id="16033">
    <literal><![CDATA[
      K(x,(y * z) * T((y * z) \ y,u)) = K(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[para(5127(a,1),16032(a,1,2,2,1,2))].">
      <j1 rule="para" parents="5127 16032"/>
    </justification>
  </clause>

  <clause id="16034">
    <literal><![CDATA[
      K(x,y * K(z \ 1,u)) = K(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[para(5336(a,1),16033(a,1,2))].">
      <j1 rule="para" parents="5336 16033"/>
    </justification>
  </clause>

  <clause id="16035">
    <literal><![CDATA[
      K(x * K(y \ 1,z),u) = 1 / K(u,x * K(y,z))
    ]]></literal>
    <justification jstring="[para(16034(a,1),5209(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16034 5209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16036">
    <literal><![CDATA[
      K(x * K(y \ 1,z),u) = K(x * K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,5209,a(flip),b,16035,a),flip(a)].">
      <j1 rule="hyper" parents="299 5209 16035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16037">
    <literal><![CDATA[
      K(x * K(x \ y,z),T(u,y)) = K(y * T(x / y,z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,13190,a(flip),b,16036,a),flip(a)].">
      <j1 rule="hyper" parents="65 13190 16036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16038">
    <literal><![CDATA[
      K(((x * (y \ z)) / x) * y,u) = K(y * T(z / y,x),u)
    ]]></literal>
    <justification jstring="[hyper(15960,a,16037,a)].">
      <j1 rule="hyper" parents="15960 16037"/>
    </justification>
  </clause>

  <clause id="16039">
    <literal><![CDATA[
      K(((x * y) / x) / z,u) = K((z \ 1) * T((z \ y) / (z \ 1),x),u)
    ]]></literal>
    <justification jstring="[hyper(13586,a,16038,a)].">
      <j1 rule="hyper" parents="13586 16038"/>
    </justification>
  </clause>

  <clause id="16040">
    <literal><![CDATA[
      K(x \ T((x \ y) * x,z),u) = K(((z * y) / z) / x,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,13311,a(flip),b,16039,a)].">
      <j1 rule="hyper" parents="299 13311 16039"/>
    </justification>
  </clause>

  <clause id="16041">
    <literal><![CDATA[
      K(T(x \ T(y,z),x),u) = K(((z * y) / z) / x,u)
    ]]></literal>
    <justification jstring="[para(3485(a,1),16040(a,1,1))].">
      <j1 rule="para" parents="3485 16040"/>
    </justification>
  </clause>

  <clause id="16042">
    <literal><![CDATA[
      K(((x * y) / x) / z,u) = K(T(y,x) / z,u)
    ]]></literal>
    <justification jstring="[hyper(8324,a,16041,a),flip(a)].">
      <j1 rule="hyper" parents="8324 16041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16043">
    <literal><![CDATA[
      K(((x * y) / x) / z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(T(y,x) / z,u) = w
    ]]></literal>
    <justification jstring="[para(16041(a,1),8324(a,1))].">
      <j1 rule="para" parents="16041 8324"/>
    </justification>
  </clause>

  <clause id="16044">
    <literal><![CDATA[
      K(T(x * K(y,x),z) / z,u) = K(T(x,y) / T(z,T(x,y)),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,10398,a,b,16042,a)].">
      <j1 rule="hyper" parents="65 10398 16042"/>
    </justification>
  </clause>

  <clause id="16045">
    <literal><![CDATA[
      K(T(T(x,y),y) / z,u) = K(x / z,u)
    ]]></literal>
    <justification jstring="[para(223(a,1),16042(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="223 16042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16046">
    <literal><![CDATA[
      K((x * K(y,x)) / z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(T(x,y) / z,u) = w
    ]]></literal>
    <justification jstring="[para(5054(a,1),16043(a,1,1,1))].">
      <j1 rule="para" parents="5054 16043"/>
    </justification>
  </clause>

  <clause id="16047">
    <literal><![CDATA[
      K(T(x,y) / T(z,T(x,y)),u) = K(z \ (x * K(y,x)),u)
    ]]></literal>
    <justification jstring="[hyper(13762,a,16044,a),flip(a)].">
      <j1 rule="hyper" parents="13762 16044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16048">
    <literal><![CDATA[
      K(x \ (y * K(z,y)),u) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(13787,a,16047,a),flip(a)].">
      <j1 rule="hyper" parents="13787 16047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16049">
    <literal><![CDATA[
      K(x \ T(y,y \ z),u) = K(x \ (z / (z / y)),u)
    ]]></literal>
    <justification jstring="[para(5002(a,2),16048(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5002 16048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16050">
    <literal><![CDATA[
      K(x \ ((y * z) / y),u) = K(x \ T(z,y),u)
    ]]></literal>
    <justification jstring="[para(5054(a,2),16048(a,1,1,2))].">
      <j1 rule="para" parents="5054 16048"/>
    </justification>
  </clause>

  <clause id="16051">
    <literal><![CDATA[
      K(x \ T(T(y,z),z),u) = K(x \ y,u)
    ]]></literal>
    <justification jstring="[para(5100(a,1),16048(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5100 16048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16052">
    <literal><![CDATA[
      K(x,y \ T(T(z,u),u)) = 1 / K(y \ z,x)
    ]]></literal>
    <justification jstring="[para(16051(a,1),5209(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16051 5209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16054">
    <literal><![CDATA[
      K(x \ (((y * y) * ((y \ 1) * (y \ z))) / (y * y)),u) = K(x \ ((y \ 1) * (y \ T(z,y * y))),u)
    ]]></literal>
    <justification jstring="[para(15287(a,1),16050(a,2,1,2))].">
      <j1 rule="para" parents="15287 16050"/>
    </justification>
  </clause>

  <clause id="16055">
    <literal><![CDATA[
      K(x,y \ T(T(z,u),u)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(299,a,5209,a(flip),b,16052,a),flip(a)].">
      <j1 rule="hyper" parents="299 5209 16052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16056">
    <literal><![CDATA[
      K(x,y \ T(T(z,u),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = w
    ]]></literal>
    <justification jstring="[para(16052(a,2),5211(a,1))].">
      <j1 rule="para" parents="16052 5211"/>
    </justification>
  </clause>

  <clause id="16057">
    <literal><![CDATA[
      K(x,y \ ((z * u) / z)) = K(x,y \ T(u,z))
    ]]></literal>
    <justification jstring="[para(222(a,1),16055(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="222 16055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16058">
    <literal><![CDATA[
      K(x,y \ T(z * (u / T(z,u)),z)) = K(x,y \ (z * (u / z)))
    ]]></literal>
    <justification jstring="[para(4417(a,1),16055(a,1,2,2,1))].">
      <j1 rule="para" parents="4417 16055"/>
    </justification>
  </clause>

  <clause id="16059">
    <literal><![CDATA[
      K(x,y \ (z * K(u,z))) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(5053(a,1),16055(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5053 16055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16060">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u,y)) = K(x,z \ T(y,u))
    ]]></literal>
    <justification jstring="[hyper(8411,a,16059,a)].">
      <j1 rule="hyper" parents="8411 16059"/>
    </justification>
  </clause>

  <clause id="16061">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u \ 1,y)) = K(x,z \ T(y,1 / u))
    ]]></literal>
    <justification jstring="[para(3565(a,1),16060(a,1,2,2))].">
      <j1 rule="para" parents="3565 16060"/>
    </justification>
  </clause>

  <clause id="16062">
    <literal><![CDATA[
      L(x,((y \ 1) \ K(z,y)) * K(y * z,1 \ T(y,z)),u) = L(x,R(y,y * z,y),u)
    ]]></literal>
    <justification jstring="[para(16060(a,1),14634(a,1,2,2))].">
      <j1 rule="para" parents="16060 14634"/>
    </justification>
  </clause>

  <clause id="16064">
    <literal><![CDATA[
      K(x,y \ ((z / T(u,z)) * u)) = K(x,y \ (u * (z / u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,13774,a(flip),b,16058,a)].">
      <j1 rule="hyper" parents="65 13774 16058"/>
    </justification>
  </clause>

  <clause id="16065">
    <literal><![CDATA[
      K(x,y \ (z * (u / z))) = K(x,y \ T(u,z))
    ]]></literal>
    <justification jstring="[para(4381(a,1),16064(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4381 16064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16066">
    <literal><![CDATA[
      K(x,T(y,z) \ T(u,z * y)) = K(x,T(u / y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,16026,a(flip),b,16065,a),flip(a)].">
      <j1 rule="hyper" parents="65 16026 16065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16067">
    <literal><![CDATA[
      K(x,y \ T(z * u,u)) = K(x,y \ (u * z))
    ]]></literal>
    <justification jstring="[para(11(a,1),16065(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="11 16065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16068">
    <literal><![CDATA[
      K(x,y \ T((z / (1 / u)) * w,(u * u) * w)) = K(x,y \ (((u * u) * w) * (z / u)))
    ]]></literal>
    <justification jstring="[para(680(a,1),16067(a,1,2,2,1))].">
      <j1 rule="para" parents="680 16067"/>
    </justification>
  </clause>

  <clause id="16069">
    <literal><![CDATA[
      K(x,y \ T((z * u) * (z \ 1),z \ 1)) = K(x,y \ (z * ((1 / z) * u)))
    ]]></literal>
    <justification jstring="[para(944(a,1),16067(a,2,2,2))].">
      <j1 rule="para" parents="944 16067"/>
    </justification>
  </clause>

  <clause id="16070">
    <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(6167(a,1),16066(a,1,2,2,2))].">
      <j1 rule="para" parents="6167 16066"/>
    </justification>
  </clause>

  <clause id="16072">
    <literal><![CDATA[
      L(x,((y \ 1) \ K(z,y)) * K(y * z,T(y,z)),u) = L(x,R(y,y * z,y),u)
    ]]></literal>
    <justification jstring="[para(67(a,1),16062(a,1,2,2,2))].">
      <j1 rule="para" parents="67 16062"/>
    </justification>
  </clause>

  <clause id="16074">
    <literal><![CDATA[
      L(x,((y \ 1) \ K(z,y)) * K(y * z,y),u) = L(x,R(y,y * z,y),u)
    ]]></literal>
    <justification jstring="[para(6895(a,1),16072(a,1,2,2))].">
      <j1 rule="para" parents="6895 16072"/>
    </justification>
  </clause>

  <clause id="16076">
    <literal><![CDATA[
      L(x,(y \ K(y,z)) \ K(y * z,y),u) = L(x,R(y,y * z,y),u)
    ]]></literal>
    <justification jstring="[para(14237(a,1),16074(a,1,2))].">
      <j1 rule="para" parents="14237 16074"/>
    </justification>
  </clause>

  <clause id="16078">
    <literal><![CDATA[
      L(x,(y \ K(y,z)) * K(y * z,y),u) = L(x,R(y,y * z,y),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,14233,a(flip),b,16076,a)].">
      <j1 rule="hyper" parents="65 14233 16076"/>
    </justification>
  </clause>

  <clause id="16080">
    <literal><![CDATA[
      L(x,T(K(y,z) / T(y,y * z),y),u) = L(x,R(y,y * z,y),u)
    ]]></literal>
    <justification jstring="[para(7889(a,2),16078(a,1,2))].">
      <j1 rule="para" parents="7889 16078"/>
    </justification>
  </clause>

  <clause id="16082">
    <literal><![CDATA[
      K(x,y \ T((z / (1 / u)) * w,u * (u * w))) = K(x,y \ (((u * u) * w) * (z / u)))
    ]]></literal>
    <justification jstring="[para(14216(a,1),16068(a,1,2,2))].">
      <j1 rule="para" parents="14216 16068"/>
    </justification>
  </clause>

  <clause id="16083">
    <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(10600(a,1),15969(a,2,2))].">
      <j1 rule="para" parents="10600 15969"/>
    </justification>
  </clause>

  <clause id="16084">
    <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(8183(a,1),16083(a,1,2))].">
      <j1 rule="para" parents="8183 16083"/>
    </justification>
  </clause>

  <clause id="16085">
    <literal><![CDATA[
      K(x,T(y / z,y / (u \ z))) = K(x,T(y / z,u \ 1))
    ]]></literal>
    <justification jstring="[para(9905(a,1),16084(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9905 16084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16086">
    <literal><![CDATA[
      K(x,T(y / z,y / (u \ z))) = K(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,8832,a(flip),b,16085,a),flip(a)].">
      <j1 rule="hyper" parents="299 8832 16085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16088">
    <literal><![CDATA[
      K(x,T(y,z) \ ((z \ y) * (u / (z \ y)))) = K(x,T(u / y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,15737,a(flip),b,16086,a)].">
      <j1 rule="hyper" parents="65 15737 16086"/>
    </justification>
  </clause>

  <clause id="16089">
    <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(4415(a,1),16088(a,1,2,2,1))].">
      <j1 rule="para" parents="4415 16088"/>
    </justification>
  </clause>

  <clause id="16090">
    <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(8578(a,1),15987(a,1,2,2,2))].">
      <j1 rule="para" parents="8578 15987"/>
    </justification>
  </clause>

  <clause id="16091">
    <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(7989(a,2),16090(a,1,2,2))].">
      <j1 rule="para" parents="7989 16090"/>
    </justification>
  </clause>

  <clause id="16093">
    <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(8803(a,1),16091(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8803 16091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16094">
    <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(299,a,6851,a(flip),b,16093,a),flip(a)].">
      <j1 rule="hyper" parents="299 6851 16093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16095">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ 1) = K(x,u \ K(y,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(65,a,13938,a(flip),b,16094,a)].">
      <j1 rule="hyper" parents="65 13938 16094"/>
    </justification>
  </clause>

  <clause id="16096">
    <literal><![CDATA[
      K(x,y \ K(z,u \ 1)) = K(x,y \ K(u,z))
    ]]></literal>
    <justification jstring="[hyper(7097,a,16095,a),flip(a)].">
      <j1 rule="hyper" parents="7097 16095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16100">
    <literal><![CDATA[
      K(x,y \ K(z \ 1,u)) = K(x,y \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,15992,a,b,16096,a)].">
      <j1 rule="hyper" parents="65 15992 16096"/>
    </justification>
  </clause>

  <clause id="16101">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u,y)) = K(x,z \ T(y,1 / u))
    ]]></literal>
    <justification jstring="[hyper(65,a,16061,a(flip),b,16100,a),flip(a)].">
      <j1 rule="hyper" parents="65 16061 16100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16102">
    <literal><![CDATA[
      K(x,y \ T(z,1 / u)) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,16060,a(flip),b,16101,a),flip(a)].">
      <j1 rule="hyper" parents="65 16060 16101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16103">
    <literal><![CDATA[
      K(x,y \ T(z,u \ 1)) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(76(a,1),16102(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="76 16102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16104">
    <literal><![CDATA[
      K(x,y \ T((z * u) * (z \ 1),z)) = K(x,y \ (z * ((1 / z) * u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,16069,a(flip),b,16103,a),flip(a)].">
      <j1 rule="hyper" parents="65 16069 16103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16105">
    <literal><![CDATA[
      K(x,y \ T(z,u \ (w \ u))) = K(x,y \ T(z,T(w,u)))
    ]]></literal>
    <justification jstring="[para(7594(a,1),16103(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7594 16103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16106">
    <literal><![CDATA[
      K(x,y \ (z * ((1 / z) * u))) = K(x,y \ R(u,z,z))
    ]]></literal>
    <justification jstring="[para(1258(a,1),16104(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1258 16104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16107">
    <literal><![CDATA[
      K(x,y \ R(z,u,u)) = K(x,y \ L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,6456,a(flip),b,16106,a),flip(a)].">
      <j1 rule="hyper" parents="65 6456 16106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16108">
    <literal><![CDATA[
      K(x,T(y,R(z,u,u)) \ L(z,u,u)) = K(x,R(z,u,u) / y)
    ]]></literal>
    <justification jstring="[hyper(13924,a,16107,a),flip(a)].">
      <j1 rule="hyper" parents="13924 16107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16109">
    <literal><![CDATA[
      K(x,((R(y,z,z) \ (y * z)) \ u) \ L(y,z,z)) = K(x,(z \ u) \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,15757,a(flip),b,16107,a),flip(a)].">
      <j1 rule="hyper" parents="65 15757 16107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16110">
    <literal><![CDATA[
      K(x,T(y,L(z,u,u)) \ L(z,u,u)) = K(x,R(z,u,u) / y)
    ]]></literal>
    <justification jstring="[para(15478(a,1),16108(a,1,2,1))].">
      <j1 rule="para" parents="15478 16108"/>
    </justification>
  </clause>

  <clause id="16111">
    <literal><![CDATA[
      K(x,R(y,z,z) / u) = K(x,L(y,z,z) / u)
    ]]></literal>
    <justification jstring="[hyper(13924,a,16110,a),flip(a)].">
      <j1 rule="hyper" parents="13924 16110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16113">
    <literal><![CDATA[
      K(x,(L(y,y,z) \ u) \ L(z,y,y)) = K(x,(y \ u) \ z)
    ]]></literal>
    <justification jstring="[para(10422(a,1),16109(a,1,2,1,1))].">
      <j1 rule="para" parents="10422 16109"/>
    </justification>
  </clause>

  <clause id="16114">
    <literal><![CDATA[
      K(x \ ((((y \ 1) \ 1) * (y \ z)) / (y * y)),u) = K(x \ ((y \ 1) * (y \ T(z,y * y))),u)
    ]]></literal>
    <justification jstring="[para(731(a,1),16054(a,1,1,2,1))].">
      <j1 rule="para" parents="731 16054"/>
    </justification>
  </clause>

  <clause id="16115">
    <literal><![CDATA[
      K(x \ ((K(y,y \ 1) * z) / (y * y)),u) = K(x \ ((y \ 1) * (y \ T(z,y * y))),u)
    ]]></literal>
    <justification jstring="[para(2730(a,1),16114(a,1,1,2,1))].">
      <j1 rule="para" parents="2730 16114"/>
    </justification>
  </clause>

  <clause id="16116">
    <literal><![CDATA[
      K(x \ (K(y,y \ 1) * (z / (y * y))),u) = K(x \ ((y \ 1) * (y \ T(z,y * y))),u)
    ]]></literal>
    <justification jstring="[para(849(a,1),16115(a,1,1,2))].">
      <j1 rule="para" parents="849 16115"/>
    </justification>
  </clause>

  <clause id="16117">
    <literal><![CDATA[
      K(x \ ((y \ 1) * (y \ T(z,y * y))),u) = K(x \ (z * (y \ (1 / y))),u)
    ]]></literal>
    <justification jstring="[para(14834(a,1),16116(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="14834 16116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16118">
    <literal><![CDATA[
      K(x \ ((y \ 1) * (y \ T(z,y * y))),u) = K((x \ z) * (y \ (1 / y)),u)
    ]]></literal>
    <justification jstring="[para(848(a,1),16117(a,2,1))].">
      <j1 rule="para" parents="848 16117"/>
    </justification>
  </clause>

  <clause id="16119">
    <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(8892(a,1),16089(a,1,2,1))].">
      <j1 rule="para" parents="8892 16089"/>
    </justification>
  </clause>

  <clause id="16120">
    <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(4415(a,1),16119(a,1,2,2,2,2))].">
      <j1 rule="para" parents="4415 16119"/>
    </justification>
  </clause>

  <clause id="16122">
    <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(65,a,15954,a(flip),b,16120,a)].">
      <j1 rule="hyper" parents="65 15954 16120"/>
    </justification>
  </clause>

  <clause id="16123">
    <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(13695(a,1),16122(a,2,2))].">
      <j1 rule="para" parents="13695 16122"/>
    </justification>
  </clause>

  <clause id="16124">
    <literal><![CDATA[
      K(x,T(y,z) \ T(u,T(z,y))) = K(x,T(u / y,z \ y))
    ]]></literal>
    <justification jstring="[hyper(65,a,16065,a(flip),b,16123,a)].">
      <j1 rule="hyper" parents="65 16065 16123"/>
    </justification>
  </clause>

  <clause id="16125">
    <literal><![CDATA[
      K(x,L((y / R(z,u,z)) \ T(w,z),T(w,z),L(z,u,z))) = K(x,T(y,R(z,u,z)) \ (w * R(z,u,z)))
    ]]></literal>
    <justification jstring="[para(6003(a,1),15876(a,1,2))].">
      <j1 rule="para" parents="6003 15876"/>
    </justification>
  </clause>

  <clause id="16126">
    <literal><![CDATA[
      T(x * K(y * z,x),y / (y * (z * y))) = T(x,((y * (z * y)) \ y) * ((y * (z * y)) \ y))
    ]]></literal>
    <justification jstring="[para(13733(a,1),15880(a,1,1,2))].">
      <j1 rule="para" parents="13733 15880"/>
    </justification>
  </clause>

  <clause id="16127">
    <literal><![CDATA[
      T(x * K(y * z,x),z \ (y \ 1)) = T(x,((y * (z * y)) \ y) * ((y * (z * y)) \ y))
    ]]></literal>
    <justification jstring="[hyper(65,a,15365,a(flip),b,16126,a)].">
      <j1 rule="hyper" parents="65 15365 16126"/>
    </justification>
  </clause>

  <clause id="16130">
    <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(65,a,13819,a(flip),b,16070,a)].">
      <j1 rule="hyper" parents="65 13819 16070"/>
    </justification>
  </clause>

  <clause id="16131">
    <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(15962(a,1),16130(a,1,2,2))].">
      <j1 rule="para" parents="15962 16130"/>
    </justification>
  </clause>

  <clause id="16132">
    <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(5685(a,1),16131(a,1,2,2,2,2))].">
      <j1 rule="para" parents="5685 16131"/>
    </justification>
  </clause>

  <clause id="16133">
    <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(15885(a,1),16132(a,1,2,2))].">
      <j1 rule="para" parents="15885 16132"/>
    </justification>
  </clause>

  <clause id="16134">
    <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(5083(a,2),16133(a,1,2,2,2))].">
      <j1 rule="para" parents="5083 16133"/>
    </justification>
  </clause>

  <clause id="16135">
    <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(13907,a,16134,a),flip(a)].">
      <j1 rule="hyper" parents="13907 16134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16136">
    <literal><![CDATA[
      K(x,T(y / (z * u),(z * u) \ u)) = K(x,(u * z) \ T(y,T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(299,a,15862,a(flip),b,16135,a),flip(a)].">
      <j1 rule="hyper" parents="299 15862 16135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16137">
    <literal><![CDATA[
      K(x,T(y / (z * u),u \ (z \ u))) = K(x,(u * z) \ T(y,T(u,z)))
    ]]></literal>
    <justification jstring="[para(8332(a,1),16136(a,1,2))].">
      <j1 rule="para" parents="8332 16136"/>
    </justification>
  </clause>

  <clause id="16138">
    <literal><![CDATA[
      K(x,T(y / (z * u),T(z,u))) = K(x,(u * z) \ T(y,T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(9455,a,16137,a)].">
      <j1 rule="hyper" parents="9455 16137"/>
    </justification>
  </clause>

  <clause id="16139">
    <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(5338(a,1),16138(a,2,2,1))].">
      <j1 rule="para" parents="5338 16138"/>
    </justification>
  </clause>

  <clause id="16140">
    <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(8058(a,1),15772(a,1,1))].">
      <j1 rule="para" parents="8058 15772"/>
    </justification>
  </clause>

  <clause id="16141">
    <literal><![CDATA[
      T(x,K(y,z)) \ T(u * T(T(x,K(z,y)),K(z,y)),K(z,y)) = T(u,T(K(y,z),x) * x)
    ]]></literal>
    <justification jstring="[para(6255(a,1),16140(a,1,2,1,2,1))].">
      <j1 rule="para" parents="6255 16140"/>
    </justification>
  </clause>

  <clause id="16142">
    <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(8057(a,1),16141(a,1,2,1,2))].">
      <j1 rule="para" parents="8057 16141"/>
    </justification>
  </clause>

  <clause id="16143">
    <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(8050(a,1),16142(a,1,2))].">
      <j1 rule="para" parents="8050 16142"/>
    </justification>
  </clause>

  <clause id="16144">
    <literal><![CDATA[
      T(x,K(y,z)) \ T(u * x,K(y,z)) = T(u,x * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,13266,a(flip),b,16143,a),flip(a)].">
      <j1 rule="hyper" parents="299 13266 16143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16145">
    <literal><![CDATA[
      T(x * K(T(y \ z,z \ y),x),(y \ z) \ 1) = T(x,(T(y \ z,z \ y) \ 1) * (T(y \ z,z \ y) \ 1))
    ]]></literal>
    <justification jstring="[para(74(a,1),15879(a,1,1,2,1))].">
      <j1 rule="para" parents="74 15879"/>
    </justification>
  </clause>

  <clause id="16146">
    <literal><![CDATA[
      T(x * K(y \ z,x),(y \ z) \ 1) = T(x,(T(y \ z,z \ y) \ 1) * (T(y \ z,z \ y) \ 1))
    ]]></literal>
    <justification jstring="[para(3570(a,1),16145(a,1,1,2))].">
      <j1 rule="para" parents="3570 16145"/>
    </justification>
  </clause>

  <clause id="16147">
    <literal><![CDATA[
      T(x * K(y \ z,x),z \ y) = T(x,(T(y \ z,z \ y) \ 1) * (T(y \ z,z \ y) \ 1))
    ]]></literal>
    <justification jstring="[hyper(7059,a,16146,a)].">
      <j1 rule="hyper" parents="7059 16146"/>
    </justification>
  </clause>

  <clause id="16148">
    <literal><![CDATA[
      T(x,(T(y \ z,z \ y) \ 1) * (T(y \ z,z \ y) \ 1)) = T(x,(z \ y) * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(65,a,7019,a(flip),b,16147,a),flip(a)].">
      <j1 rule="hyper" parents="65 7019 16147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16149">
    <literal><![CDATA[
      T(x,(1 / (y \ z)) * (T(y \ z,z \ y) \ 1)) = T(x,(z \ y) * (z \ y))
    ]]></literal>
    <justification jstring="[para(3000(a,1),16148(a,1,2,1))].">
      <j1 rule="para" parents="3000 16148"/>
    </justification>
  </clause>

  <clause id="16150">
    <literal><![CDATA[
      T(x,(1 / (y \ z)) * (1 / (y \ z))) = T(x,(z \ y) * (z \ y))
    ]]></literal>
    <justification jstring="[para(3000(a,1),16149(a,1,2,2))].">
      <j1 rule="para" parents="3000 16149"/>
    </justification>
  </clause>

  <clause id="16151">
    <literal><![CDATA[
      T(x,(y \ z) \ (1 / (y \ z))) = T(x,(z \ y) * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(14291,a,16150,a)].">
      <j1 rule="hyper" parents="14291 16150"/>
    </justification>
  </clause>

  <clause id="16152">
    <literal><![CDATA[
      T(x,(y \ z) \ ((y \ z) \ 1)) = T(x,(z \ y) * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(65,a,3875,a(flip),b,16151,a)].">
      <j1 rule="hyper" parents="65 3875 16151"/>
    </justification>
  </clause>

  <clause id="16153">
    <literal><![CDATA[
      T(T(x,y),(z \ u) * (z \ u)) = T(x,(u \ z) \ ((u \ z) \ y))
    ]]></literal>
    <justification jstring="[hyper(14752,a,16152,a),flip(a)].">
      <j1 rule="hyper" parents="14752 16152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16154">
    <literal><![CDATA[
      T(x,y \ (z * ((z \ y) \ 1))) = T(x,(y \ z) * (y \ z))
    ]]></literal>
    <justification jstring="[para(1092(a,1),16152(a,1,2))].">
      <j1 rule="para" parents="1092 16152"/>
    </justification>
  </clause>

  <clause id="16155">
    <literal><![CDATA[
      T(x,((y * z) \ y) * ((y * z) \ y)) = T(x,(y * z) \ (y * (z \ 1)))
    ]]></literal>
    <justification jstring="[para(9(a,1),16154(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="9 16154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16156">
    <literal><![CDATA[
      T(x,(y \ z) \ ((y \ z) \ u)) = T(x,(z \ y) * ((z \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,14468,a(flip),b,16153,a),flip(a)].">
      <j1 rule="hyper" parents="65 14468 16153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16157">
    <literal><![CDATA[
      T(x,(y \ z) * ((y \ z) * ((y / z) * u))) = T(x,(z \ y) \ (K(z,z \ y) * u))
    ]]></literal>
    <justification jstring="[para(5873(a,1),16156(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5873 16156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16158">
    <literal><![CDATA[
      T(x,((y * z) \ y) * ((y * z) \ y)) = T(x,z \ (z \ 1))
    ]]></literal>
    <justification jstring="[para(1089(a,1),16155(a,2,2))].">
      <j1 rule="para" parents="1089 16155"/>
    </justification>
  </clause>

  <clause id="16159">
    <literal><![CDATA[
      T(x * K(y * z,x),z \ (y \ 1)) = T(x,(z * y) \ ((z * y) \ 1))
    ]]></literal>
    <justification jstring="[hyper(65,a,16127,a,b,16158,a)].">
      <j1 rule="hyper" parents="65 16127 16158"/>
    </justification>
  </clause>

  <clause id="16162">
    <literal><![CDATA[
      T(x * K(y * z,x),z \ (y \ 1)) = T(x,y \ (z \ ((z * y) \ 1)))
    ]]></literal>
    <justification jstring="[para(956(a,1),16159(a,2,2))].">
      <j1 rule="para" parents="956 16159"/>
    </justification>
  </clause>

  <clause id="16163">
    <literal><![CDATA[
      T(x,(y \ (z \ 1)) * (y \ (z \ 1))) = T(x,z \ (y \ ((y * z) \ 1)))
    ]]></literal>
    <justification jstring="[hyper(65,a,14269,a(flip),b,16162,a)].">
      <j1 rule="hyper" parents="65 14269 16162"/>
    </justification>
  </clause>

  <clause id="16164">
    <literal><![CDATA[
      T(x,(y \ z) * ((y \ z) * ((y / z) * u))) = T(x,T(z \ y,z) \ u)
    ]]></literal>
    <justification jstring="[para(5372(a,1),16157(a,2,2))].">
      <j1 rule="para" parents="5372 16157"/>
    </justification>
  </clause>

  <clause id="16165">
    <literal><![CDATA[
      T(x,(y \ z) * ((y \ z) * ((y / z) * u))) = T(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[hyper(299,a,15817,a(flip),b,16164,a),flip(a)].">
      <j1 rule="hyper" parents="299 15817 16164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16166">
    <literal><![CDATA[
      T(x,a(y,y,z) * ((L(z,y,y) \ z) * ((L(z,y,y) / z) * u))) = T(x,(L(z,y,y) / z) \ u)
    ]]></literal>
    <justification jstring="[para(1986(a,1),16165(a,1,2,1))].">
      <j1 rule="para" parents="1986 16165"/>
    </justification>
  </clause>

  <clause id="16167">
    <literal><![CDATA[
      T(x,a(y,y,z) * (a(y,y,z) * ((L(z,y,y) / z) * u))) = T(x,(L(z,y,y) / z) \ u)
    ]]></literal>
    <justification jstring="[para(1986(a,1),16166(a,1,2,2,1))].">
      <j1 rule="para" parents="1986 16166"/>
    </justification>
  </clause>

  <clause id="16168">
    <literal><![CDATA[
      T(x,a(y,y,z) * (a(y,y,z) * ((z \ L(z,y,y)) * u))) = T(x,(L(z,y,y) / z) \ u)
    ]]></literal>
    <justification jstring="[para(3819(a,1),16167(a,1,2,2,2,1))].">
      <j1 rule="para" parents="3819 16167"/>
    </justification>
  </clause>

  <clause id="16169">
    <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(8181(a,1),16139(a,2,2,2))].">
      <j1 rule="para" parents="8181 16139"/>
    </justification>
  </clause>

  <clause id="16170">
    <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(9294(a,1),16169(a,2,2,2))].">
      <j1 rule="para" parents="9294 16169"/>
    </justification>
  </clause>

  <clause id="16171">
    <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(299,a,16105,a(flip),b,16170,a),flip(a)].">
      <j1 rule="hyper" parents="299 16105 16170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16172">
    <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(299,a,15986,a(flip),b,16171,a),flip(a)].">
      <j1 rule="hyper" parents="299 15986 16171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16173">
    <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(299,a,14092,a(flip),b,16172,a),flip(a)].">
      <j1 rule="hyper" parents="299 14092 16172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16174">
    <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(5083(a,2),16173(a,2,2,1))].">
      <j1 rule="para" parents="5083 16173"/>
    </justification>
  </clause>

  <clause id="16175">
    <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(299,a,16124,a(flip),b,16174,a),flip(a)].">
      <j1 rule="hyper" parents="299 16124 16174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16176">
    <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),16175(a,1,2,1,2))].">
      <j1 rule="para" parents="10 16175"/>
    </justification>
  </clause>

  <clause id="16177">
    <literal><![CDATA[
      K(x,T(y / z,T(z * u,z))) = K(x,T(y / z,u \ z))
    ]]></literal>
    <justification jstring="[para(7463(a,1),16176(a,1,2))].">
      <j1 rule="para" parents="7463 16176"/>
    </justification>
  </clause>

  <clause id="16178">
    <literal><![CDATA[
      K(x,T(y / z,u \ z)) = K(x,T(y / z,u * z))
    ]]></literal>
    <justification jstring="[para(13197(a,1),16177(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13197 16177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16179">
    <literal><![CDATA[
      K(x,T((y * z) / z,u * z)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[para(11(a,1),16178(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11 16178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16180">
    <literal><![CDATA[
      K(x,T(y / z,(z / u) * z)) = K(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[para(79(a,1),16178(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="79 16178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16181">
    <literal><![CDATA[
      K(x,T(y,z \ u)) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(11(a,1),16179(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11 16179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16182">
    <literal><![CDATA[
      K(x,T(y,z * (u \ z))) = K(x,T(y,T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(9455,a,16181,a),flip(a)].">
      <j1 rule="hyper" parents="9455 16181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16183">
    <literal><![CDATA[
      K(x,T(y,z \ u)) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(9454,a,16181,a)].">
      <j1 rule="hyper" parents="9454 16181"/>
    </justification>
  </clause>

  <clause id="16184">
    <literal><![CDATA[
      K(x,T(y,z * (z * u))) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),16181(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 16181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16185">
    <literal><![CDATA[
      K(x,L(T(y,z * u),w,v5)) = K(x,T(L(y,w,v5),z \ u))
    ]]></literal>
    <justification jstring="[para(25(a,2),16181(a,2,2)),flip(a)].">
      <j1 rule="para" parents="25 16181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16187">
    <literal><![CDATA[
      K(x,T(y,z * z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(198(a,1),16181(a,1,2)),flip(a)].">
      <j1 rule="para" parents="198 16181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16189">
    <literal><![CDATA[
      K(x,T(y,z * u)) * K(y,x) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(16181(a,1),8236(a,1,1))].">
      <j1 rule="para" parents="16181 8236"/>
    </justification>
  </clause>

  <clause id="16192">
    <literal><![CDATA[
      T(K(x,y),z * z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8419,a,16187,a)].">
      <j1 rule="hyper" parents="8419 16187"/>
    </justification>
  </clause>

  <clause id="16193">
    <literal><![CDATA[
      K(x / (y * y),z) = K((y * y) \ x,z)
    ]]></literal>
    <justification jstring="[hyper(8220,a,16187,a)].">
      <j1 rule="hyper" parents="8220 16187"/>
    </justification>
  </clause>

  <clause id="16194">
    <literal><![CDATA[
      K(x,L(T(y,z * z),u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(8214,a,16187,a),flip(a)].">
      <j1 rule="hyper" parents="8214 16187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16195">
    <literal><![CDATA[
      K(x,((y * y) \ z) * u) = K(x,z * (u / (y * y)))
    ]]></literal>
    <justification jstring="[para(1053(a,1),16187(a,1,2))].">
      <j1 rule="para" parents="1053 16187"/>
    </justification>
  </clause>

  <clause id="16196">
    <literal><![CDATA[
      K(x,T(y,z * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(16187(a,1),8171(a,1))].">
      <j1 rule="para" parents="16187 8171"/>
    </justification>
  </clause>

  <clause id="16197">
    <literal><![CDATA[
      K(x,T(T(y,z * z),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(16187(a,1),8213(a,1))].">
      <j1 rule="para" parents="16187 8213"/>
    </justification>
  </clause>

  <clause id="16198">
    <literal><![CDATA[
      K(x,T(y,z \ (z \ 1))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(14297(a,1),16187(a,1,2))].">
      <j1 rule="para" parents="14297 16187"/>
    </justification>
  </clause>

  <clause id="16199">
    <literal><![CDATA[
      T(x * x,K(y,z)) = x * x
    ]]></literal>
    <justification jstring="[hyper(56,a,16192,a)].">
      <j1 rule="hyper" parents="56 16192"/>
    </justification>
  </clause>

  <clause id="16200">
    <literal><![CDATA[
      T(K(x,L(y,z * z,(z * z) \ u)) * u,z * z) = K(x,y) * T(u,z * z)
    ]]></literal>
    <justification jstring="[para(16192(a,1),15758(a,2,1))].">
      <j1 rule="para" parents="16192 15758"/>
    </justification>
  </clause>

  <clause id="16201">
    <literal><![CDATA[
      T(x * x,K(y,z)) = 1 * (x * x)
    ]]></literal>
    <justification jstring="[hyper(299,a,7,a,b,16199,a),flip(a)].">
      <j1 rule="hyper" parents="299 7 16199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16202">
    <literal><![CDATA[
      K(x,T(y,z \ (z \ 1))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(16198(a,1),8171(a,1))].">
      <j1 rule="para" parents="16198 8171"/>
    </justification>
  </clause>

  <clause id="16203">
    <literal><![CDATA[
      K(x,K(y,z * z)) = 1
    ]]></literal>
    <justification jstring="[hyper(7982,a,16201,a)].">
      <j1 rule="hyper" parents="7982 16201"/>
    </justification>
  </clause>

  <clause id="16204">
    <literal><![CDATA[
      T(x,K(y,z * z)) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,16203,a)].">
      <j1 rule="hyper" parents="58 16203"/>
    </justification>
  </clause>

  <clause id="16205">
    <literal><![CDATA[
      K(x,T(y * y,z)) = K(x,y * y)
    ]]></literal>
    <justification jstring="[hyper(9819,a,16204,a)].">
      <j1 rule="hyper" parents="9819 16204"/>
    </justification>
  </clause>

  <clause id="16206">
    <literal><![CDATA[
      K(x * x,T(y,z)) = K(x * x,y)
    ]]></literal>
    <justification jstring="[hyper(8387,a,16204,a)].">
      <j1 rule="hyper" parents="8387 16204"/>
    </justification>
  </clause>

  <clause id="16207">
    <literal><![CDATA[
      T(x,T(y * y,z)) = T(x,y * y)
    ]]></literal>
    <justification jstring="[hyper(8072,a,16204,a)].">
      <j1 rule="hyper" parents="8072 16204"/>
    </justification>
  </clause>

  <clause id="16208">
    <literal><![CDATA[
      K(x * x,y) * (z * (x * x)) = z * T(x * x,y)
    ]]></literal>
    <justification jstring="[hyper(7325,a,16204,a)].">
      <j1 rule="hyper" parents="7325 16204"/>
    </justification>
  </clause>

  <clause id="16209">
    <literal><![CDATA[
      T(x,T(y,z * z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(7154,a,16204,a)].">
      <j1 rule="hyper" parents="7154 16204"/>
    </justification>
  </clause>

  <clause id="16210">
    <literal><![CDATA[
      T(x,T(y,z * z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(16204(a,1),7145(a,2))].">
      <j1 rule="para" parents="16204 7145"/>
    </justification>
  </clause>

  <clause id="16211">
    <literal><![CDATA[
      x * K(y,z * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z * z) * x = u
    ]]></literal>
    <justification jstring="[para(16204(a,1),8074(a,1))].">
      <j1 rule="para" parents="16204 8074"/>
    </justification>
  </clause>

  <clause id="16212">
    <literal><![CDATA[
      T(x,(y * y) / z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ (y * y)) = u
    ]]></literal>
    <justification jstring="[para(16204(a,1),8996(a,1))].">
      <j1 rule="para" parents="16204 8996"/>
    </justification>
  </clause>

  <clause id="16213">
    <literal><![CDATA[
      (((x \ 1) * (y * x)) / (x \ 1)) / T(1 / x,x * y) = y * (x * x)
    ]]></literal>
    <justification jstring="[para(16209(a,1),4885(a,1,2))].">
      <j1 rule="para" parents="16209 4885"/>
    </justification>
  </clause>

  <clause id="16214">
    <literal><![CDATA[
      T(x,T(y,z * (z * u))) = T(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(14468(a,1),16209(a,1,2))].">
      <j1 rule="para" parents="14468 16209"/>
    </justification>
  </clause>

  <clause id="16215">
    <literal><![CDATA[
      T(T(x,y),z \ (z \ 1)) = T(x,y) * K(z * z,x)
    ]]></literal>
    <justification jstring="[para(16206(a,1),5823(a,2,2))].">
      <j1 rule="para" parents="16206 5823"/>
    </justification>
  </clause>

  <clause id="16216">
    <literal><![CDATA[
      L(x \ T(y,z * z),x,T(z * z,u)) = (T(z * z,u) * x) \ (y * T(z * z,u))
    ]]></literal>
    <justification jstring="[para(16207(a,1),526(a,1,1,2))].">
      <j1 rule="para" parents="16207 526"/>
    </justification>
  </clause>

  <clause id="16217">
    <literal><![CDATA[
      K(x,T(y,z * (z * u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(14468(a,1),16196(a,1,2))].">
      <j1 rule="para" parents="14468 16196"/>
    </justification>
  </clause>

  <clause id="16218">
    <literal><![CDATA[
      K(x,T(y,z * (u * u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(14602(a,1),16196(a,1,2))].">
      <j1 rule="para" parents="14602 16196"/>
    </justification>
  </clause>

  <clause id="16219">
    <literal><![CDATA[
      T(x,T(y,z * (z * u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(14468(a,1),16210(a,1,2))].">
      <j1 rule="para" parents="14468 16210"/>
    </justification>
  </clause>

  <clause id="16220">
    <literal><![CDATA[
      K(x,T(y,z * u)) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,16181,a(flip),b,16183,a)].">
      <j1 rule="hyper" parents="65 16181 16183"/>
    </justification>
  </clause>

  <clause id="16222">
    <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(16144(a,2),16183(a,2,2)),flip(a)].">
      <j1 rule="para" parents="16144 16183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16223">
    <literal><![CDATA[
      K(x * (x * y),T(z,y)) = K(x * (x * y),z)
    ]]></literal>
    <justification jstring="[hyper(5196,a,16184,a),flip(a)].">
      <j1 rule="hyper" parents="5196 16184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16224">
    <literal><![CDATA[
      K(x / ((y * y) * z),u) = K((y * y) \ (x / z),u)
    ]]></literal>
    <justification jstring="[para(425(a,1),16193(a,1,1))].">
      <j1 rule="para" parents="425 16193"/>
    </justification>
  </clause>

  <clause id="16225">
    <literal><![CDATA[
      T(x,T(y,z \ u)) = T(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(10(a,1),16214(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10 16214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16226">
    <literal><![CDATA[
      (x * y) * K(z,T(u,y * x)) = K(z,u) * (x * y)
    ]]></literal>
    <justification jstring="[para(16220(a,1),7507(a,1,2))].">
      <j1 rule="para" parents="16220 7507"/>
    </justification>
  </clause>

  <clause id="16228">
    <literal><![CDATA[
      K(x,T(y * (z * u),z * y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(u,z,y) * (y * z)) = w
    ]]></literal>
    <justification jstring="[para(16220(a,1),13248(a,1))].">
      <j1 rule="para" parents="16220 13248"/>
    </justification>
  </clause>

  <clause id="16229">
    <literal><![CDATA[
      T(x / (x \ y),T(z,(y / x) * x)) = T(x / (x \ y),z)
    ]]></literal>
    <justification jstring="[hyper(13761,a,16225,a),flip(a)].">
      <j1 rule="hyper" parents="13761 16225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16230">
    <literal><![CDATA[
      T(x / (y / z),T(z \ y,y * (z * x))) = T((y / z) \ x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,11350,a(flip),b,16225,a),flip(a)].">
      <j1 rule="hyper" parents="65 11350 16225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16231">
    <literal><![CDATA[
      K(x,((y \ 1) \ z) * (u * (y \ 1))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y \ z) * (u * y)) = w
    ]]></literal>
    <justification jstring="[para(1655(a,1),16202(a,1,2))].">
      <j1 rule="para" parents="1655 16202"/>
    </justification>
  </clause>

  <clause id="16234">
    <literal><![CDATA[
      K(x,L(y \ T(y * z,y \ 1),u,w)) = K(x,L((y \ z) * y,u,w))
    ]]></literal>
    <justification jstring="[para(11198(a,1),16194(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11198 16194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16235">
    <literal><![CDATA[
      T(x,y \ (z * z)) = T(x,z * (z / y))
    ]]></literal>
    <justification jstring="[hyper(16212,a,14301,a)].">
      <j1 rule="hyper" parents="16212 14301"/>
    </justification>
  </clause>

  <clause id="16236">
    <literal><![CDATA[
      T(x,y * (y / (y * z))) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,14578,a(flip),b,16235,a),flip(a)].">
      <j1 rule="hyper" parents="65 14578 16235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16237">
    <literal><![CDATA[
      T(x,y * ((z * y) \ y)) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,14781,a(flip),b,16236,a)].">
      <j1 rule="hyper" parents="65 14781 16236"/>
    </justification>
  </clause>

  <clause id="16238">
    <literal><![CDATA[
      T(x,(y \ z) \ y) = T(x,y * (y / z))
    ]]></literal>
    <justification jstring="[para(10(a,1),16236(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10 16236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16239">
    <literal><![CDATA[
      T(x,(y / z) \ z) = T(x,z * (y \ z))
    ]]></literal>
    <justification jstring="[para(12(a,1),16237(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="12 16237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16240">
    <literal><![CDATA[
      T(x,y / (z / y)) = T(x,y * (y / z))
    ]]></literal>
    <justification jstring="[hyper(65,a,15277,a,b,16238,a)].">
      <j1 rule="hyper" parents="65 15277 16238"/>
    </justification>
  </clause>

  <clause id="16241">
    <literal><![CDATA[
      T(x,y * (y / (z * ((z \ y) \ 1)))) = T(x,((z \ y) * (z \ y)) * y)
    ]]></literal>
    <justification jstring="[para(1133(a,1),16238(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1133 16238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16242">
    <literal><![CDATA[
      T(x,y / (y \ z)) = T(x,y * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(65,a,13705,a,b,16239,a)].">
      <j1 rule="hyper" parents="65 13705 16239"/>
    </justification>
  </clause>

  <clause id="16243">
    <literal><![CDATA[
      K(((x / y) \ y) \ z,T(u,y * (x \ y))) != w
    ]]></literal>
    <literal><![CDATA[
      K(z / ((x / y) \ y),u) = w
    ]]></literal>
    <justification jstring="[para(16239(a,1),8220(a,1,2))].">
      <j1 rule="para" parents="16239 8220"/>
    </justification>
  </clause>

  <clause id="16244">
    <literal><![CDATA[
      T((x * y) / x,z * (x \ z)) = T(y,(z \ x) \ ((z \ x) \ 1))
    ]]></literal>
    <justification jstring="[hyper(15276,a,16242,a),flip(a)].">
      <j1 rule="hyper" parents="15276 16242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16245">
    <literal><![CDATA[
      K(x,T(((y \ 1) * z) \ u,u)) = K(x,(y * ((y \ 1) \ u)) / (y * z))
    ]]></literal>
    <justification jstring="[hyper(16218,a,14618,a)].">
      <j1 rule="hyper" parents="16218 14618"/>
    </justification>
  </clause>

  <clause id="16246">
    <literal><![CDATA[
      K(x,T(y,(z * z) \ u)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(16218,a,16183,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="16218 16183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16247">
    <literal><![CDATA[
      K(x,T(((y * y) \ z) \ u,z)) = K(x,u / ((y * y) \ z))
    ]]></literal>
    <justification jstring="[hyper(8215,a,16246,a),flip(a)].">
      <j1 rule="hyper" parents="8215 16246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16248">
    <literal><![CDATA[
      T(x,T(y,y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7462(a,1),16219(a,1))].">
      <j1 rule="para" parents="7462 16219"/>
    </justification>
  </clause>

  <clause id="16250">
    <literal><![CDATA[
      K(x,T(y / z,z * (u \ z))) = K(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[para(13982(a,1),16180(a,1,2))].">
      <j1 rule="para" parents="13982 16180"/>
    </justification>
  </clause>

  <clause id="16251">
    <literal><![CDATA[
      K(x,K(y,z \ u)) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(8295,a,16189,a),flip(a)].">
      <j1 rule="hyper" parents="8295 16189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16252">
    <literal><![CDATA[
      K(x,K(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z * u)) = w
    ]]></literal>
    <justification jstring="[para(16189(a,1),8295(a,1))].">
      <j1 rule="para" parents="16189 8295"/>
    </justification>
  </clause>

  <clause id="16253">
    <literal><![CDATA[
      K(x,K(y * (z \ u),z * u)) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(8211,a,16251,a),flip(a)].">
      <j1 rule="hyper" parents="8211 16251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16254">
    <literal><![CDATA[
      K(x,K(y \ z,u)) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(8035,a,16251,a)].">
      <j1 rule="hyper" parents="8035 16251"/>
    </justification>
  </clause>

  <clause id="16255">
    <literal><![CDATA[
      K(x,K(y,z * (z * u))) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),16251(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 16251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16256">
    <literal><![CDATA[
      K(x,K(y,z \ (z \ u))) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),16251(a,2,2,2))].">
      <j1 rule="para" parents="10 16251"/>
    </justification>
  </clause>

  <clause id="16257">
    <literal><![CDATA[
      x * K(x,K(y,z * u)) = T(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(16251(a,1),5083(a,2,2)),flip(a)].">
      <j1 rule="para" parents="16251 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16258">
    <literal><![CDATA[
      K(x,K(y,z * u)) * K(x,y / (z \ u)) = K(x,(z \ u) \ y)
    ]]></literal>
    <justification jstring="[para(16251(a,1),8507(a,1,1))].">
      <j1 rule="para" parents="16251 8507"/>
    </justification>
  </clause>

  <clause id="16259">
    <literal><![CDATA[
      K(x,K(y \ z,u)) = K(x,K(y * z,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,8004,a,b,16254,a),flip(a)].">
      <j1 rule="hyper" parents="299 8004 16254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16260">
    <literal><![CDATA[
      K((x / (y \ 1)) * T((x / (1 / y)) \ 1,z),u) = K(z,K(u,y * (x \ 1)))
    ]]></literal>
    <justification jstring="[hyper(65,a,15102,a,b,16254,a)].">
      <j1 rule="hyper" parents="65 15102 16254"/>
    </justification>
  </clause>

  <clause id="16261">
    <literal><![CDATA[
      K(x,K(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z \ u)) = w
    ]]></literal>
    <justification jstring="[para(16254(a,1),8035(a,1))].">
      <j1 rule="para" parents="16254 8035"/>
    </justification>
  </clause>

  <clause id="16263">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,x \ (u * (u * z))) = K(y,(u * (u * z)) / x)
    ]]></literal>
    <justification jstring="[para(16255(a,1),8502(a,1,1))].">
      <j1 rule="para" parents="16255 8502"/>
    </justification>
  </clause>

  <clause id="16264">
    <literal><![CDATA[
      K(x,K(y,z * (u \ z))) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(13863(a,1),16255(a,1,2))].">
      <j1 rule="para" parents="13863 16255"/>
    </justification>
  </clause>

  <clause id="16265">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,(u \ (u \ z)) \ x) = K(y,x / (u \ (u \ z)))
    ]]></literal>
    <justification jstring="[para(16256(a,1),8503(a,1,1))].">
      <j1 rule="para" parents="16256 8503"/>
    </justification>
  </clause>

  <clause id="16266">
    <literal><![CDATA[
      T(x,K((y * y) \ z,u)) = K(x,K(u,z)) * x
    ]]></literal>
    <justification jstring="[para(16256(a,1),14440(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16256 14440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16268">
    <literal><![CDATA[
      T(x,K(y,z \ u)) = T(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(5087,a,16257,a),flip(a)].">
      <j1 rule="hyper" parents="5087 16257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16269">
    <literal><![CDATA[
      T(x,K(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z * u)) = w
    ]]></literal>
    <justification jstring="[para(16257(a,1),5087(a,1))].">
      <j1 rule="para" parents="16257 5087"/>
    </justification>
  </clause>

  <clause id="16270">
    <literal><![CDATA[
      T(x,K(y,z \ u)) = T(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(8825,a,16268,a)].">
      <j1 rule="hyper" parents="8825 16268"/>
    </justification>
  </clause>

  <clause id="16271">
    <literal><![CDATA[
      T(x,K(y,z * (z * u))) = T(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),16268(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 16268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16272">
    <literal><![CDATA[
      T(T(x,y \ z),K(u,y * z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y \ z,u)) = w
    ]]></literal>
    <justification jstring="[para(16268(a,1),8072(a,1))].">
      <j1 rule="para" parents="16268 8072"/>
    </justification>
  </clause>

  <clause id="16273">
    <literal><![CDATA[
      T(x,K(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(16268(a,1),8825(a,1))].">
      <j1 rule="para" parents="16268 8825"/>
    </justification>
  </clause>

  <clause id="16274">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y / (z \ u)) = T(x,(z \ u) \ y)
    ]]></literal>
    <justification jstring="[para(16268(a,1),8997(a,1,1))].">
      <j1 rule="para" parents="16268 8997"/>
    </justification>
  </clause>

  <clause id="16275">
    <literal><![CDATA[
      T(T(x,K(y,z * (y * u))),y \ ((y \ z) \ u)) = T(x,((y \ z) \ u) / y)
    ]]></literal>
    <justification jstring="[para(16268(a,1),9003(a,1,1))].">
      <j1 rule="para" parents="16268 9003"/>
    </justification>
  </clause>

  <clause id="16276">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y * (z \ u)) = T(x,(z \ u) * y)
    ]]></literal>
    <justification jstring="[para(16268(a,1),13224(a,1,1))].">
      <j1 rule="para" parents="16268 13224"/>
    </justification>
  </clause>

  <clause id="16277">
    <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(16268(a,1),13257(a,1,1))].">
      <j1 rule="para" parents="16268 13257"/>
    </justification>
  </clause>

  <clause id="16278">
    <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(16268(a,1),13724(a,1,1))].">
      <j1 rule="para" parents="16268 13724"/>
    </justification>
  </clause>

  <clause id="16279">
    <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(16268(a,1),15769(a,1,2,1,2))].">
      <j1 rule="para" parents="16268 15769"/>
    </justification>
  </clause>

  <clause id="16280">
    <literal><![CDATA[
      T(x,K(y,z * u)) = T(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,16268,a(flip),b,16270,a)].">
      <j1 rule="hyper" parents="65 16268 16270"/>
    </justification>
  </clause>

  <clause id="16281">
    <literal><![CDATA[
      T(x,K(y,z * (z / u))) = T(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(79(a,1),16270(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="79 16270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16282">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y / (u \ z)) = T(x,(u \ z) \ y)
    ]]></literal>
    <justification jstring="[para(16270(a,1),8997(a,1,1))].">
      <j1 rule="para" parents="16270 8997"/>
    </justification>
  </clause>

  <clause id="16283">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),(u \ z) * y) = T(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[para(16270(a,1),13200(a,1,1))].">
      <j1 rule="para" parents="16270 13200"/>
    </justification>
  </clause>

  <clause id="16284">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y * (u \ z)) = T(x,(u \ z) * y)
    ]]></literal>
    <justification jstring="[para(16270(a,1),13224(a,1,1))].">
      <j1 rule="para" parents="16270 13224"/>
    </justification>
  </clause>

  <clause id="16285">
    <literal><![CDATA[
      T(x,K(y,z * (u \ z))) = T(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(13863(a,1),16271(a,1,2))].">
      <j1 rule="para" parents="13863 16271"/>
    </justification>
  </clause>

  <clause id="16286">
    <literal><![CDATA[
      T(x,K(y,z * (u * u))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(14464(a,2),16271(a,1,2))].">
      <j1 rule="para" parents="14464 16271"/>
    </justification>
  </clause>

  <clause id="16287">
    <literal><![CDATA[
      T(x,K(y * z,u)) = T(x,K(u,z * y))
    ]]></literal>
    <justification jstring="[hyper(8081,a,16280,a)].">
      <j1 rule="hyper" parents="8081 16280"/>
    </justification>
  </clause>

  <clause id="16291">
    <literal><![CDATA[
      T(T(x,K(y,z)),(u * (u / z)) \ y) = T(x,y / (u * (u / z)))
    ]]></literal>
    <justification jstring="[para(16281(a,1),9002(a,1,1))].">
      <j1 rule="para" parents="16281 9002"/>
    </justification>
  </clause>

  <clause id="16292">
    <literal><![CDATA[
      T(T(x,K(y,z)),y / (u * (z \ u))) = T(x,(u * (z \ u)) \ y)
    ]]></literal>
    <justification jstring="[para(16285(a,1),8997(a,1,1))].">
      <j1 rule="para" parents="16285 8997"/>
    </justification>
  </clause>

  <clause id="16293">
    <literal><![CDATA[
      T(x,K(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,u * z)) = w
    ]]></literal>
    <justification jstring="[para(16287(a,1),8081(a,1))].">
      <j1 rule="para" parents="16287 8081"/>
    </justification>
  </clause>

  <clause id="16294">
    <literal><![CDATA[
      T(x,K((y * y) \ z,u)) = T(x,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,8023,a(flip),b,16266,a),flip(a)].">
      <j1 rule="hyper" parents="299 8023 16266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16296">
    <literal><![CDATA[
      T(x,K(y \ (y \ z),u)) = T(x,K(z,u))
    ]]></literal>
    <justification jstring="[para(14182(a,1),16294(a,1,2))].">
      <j1 rule="para" parents="14182 16294"/>
    </justification>
  </clause>

  <clause id="16297">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K((w * w) \ z,u)) = T(y,K(u,(w * w) \ z) * x)
    ]]></literal>
    <justification jstring="[para(16294(a,1),15769(a,1,2,1,2))].">
      <j1 rule="para" parents="16294 15769"/>
    </justification>
  </clause>

  <clause id="16298">
    <literal><![CDATA[
      T(T(x,K(y,z)),(u \ (u \ y)) * z) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,z * (u \ (u \ y))) = w
    ]]></literal>
    <justification jstring="[para(16296(a,1),13257(a,1,1))].">
      <j1 rule="para" parents="16296 13257"/>
    </justification>
  </clause>

  <clause id="16299">
    <literal><![CDATA[
      K(x,T(y * y,z)) * (((x * T(y * y,z)) \ u) * T(y * y,z)) = K(y * y,z) * (((T(y * y,z) * x) \ u) * (y * y))
    ]]></literal>
    <justification jstring="[hyper(299,a,11612,a,b,16208,a)].">
      <j1 rule="hyper" parents="299 11612 16208"/>
    </justification>
  </clause>

  <clause id="16300">
    <literal><![CDATA[
      T(x,y) * K(z * z,x) = T(x,z \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(14752,a,16215,a),flip(a)].">
      <j1 rule="hyper" parents="14752 16215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16301">
    <literal><![CDATA[
      L(x,T(y,z \ (z \ u)),w) = L(x,T(y,u),w)
    ]]></literal>
    <justification jstring="[para(16300(a,1),9503(a,1,2))].">
      <j1 rule="para" parents="16300 9503"/>
    </justification>
  </clause>

  <clause id="16302">
    <literal><![CDATA[
      L(x,T(y,z \ u),w) = L(x,T(y,z * u),w)
    ]]></literal>
    <justification jstring="[para(9(a,1),16301(a,1,2,2,2))].">
      <j1 rule="para" parents="9 16301"/>
    </justification>
  </clause>

  <clause id="16303">
    <literal><![CDATA[
      L(x,T(y,z * u),z \ u) = L(x,y,z \ u)
    ]]></literal>
    <justification jstring="[hyper(11643,a,16302,a),flip(a)].">
      <j1 rule="hyper" parents="11643 16302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16304">
    <literal><![CDATA[
      L(x,T(y,z),(z / u) \ u) = L(x,y,(z / u) \ u)
    ]]></literal>
    <justification jstring="[para(12(a,1),16303(a,1,2,2))].">
      <j1 rule="para" parents="12 16303"/>
    </justification>
  </clause>

  <clause id="16305">
    <literal><![CDATA[
      K(x / ((y * y) * z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(y \ (y \ (x / z)),u) = w
    ]]></literal>
    <justification jstring="[para(16224(a,2),14546(a,1))].">
      <j1 rule="para" parents="16224 14546"/>
    </justification>
  </clause>

  <clause id="16307">
    <literal><![CDATA[
      (x * y) * K(z,L(T(u,y * x),w,v5)) = K(z,L(u,w,v5)) * (x * y)
    ]]></literal>
    <justification jstring="[para(25(a,2),16226(a,1,2,2))].">
      <j1 rule="para" parents="25 16226"/>
    </justification>
  </clause>

  <clause id="16308">
    <literal><![CDATA[
      K(x,T(y / z,T(u,z))) = K(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,16182,a(flip),b,16250,a)].">
      <j1 rule="hyper" parents="65 16182 16250"/>
    </justification>
  </clause>

  <clause id="16310">
    <literal><![CDATA[
      K(x,T(y / z,u)) * K(z \ y,T(x,u)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(16308(a,1),12585(a,1,1))].">
      <j1 rule="para" parents="16308 12585"/>
    </justification>
  </clause>

  <clause id="16311">
    <literal><![CDATA[
      K(x,K(y * (z \ u),z * u)) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(299,a,16251,a(flip),b,16253,a),flip(a)].">
      <j1 rule="hyper" parents="299 16251 16253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16312">
    <literal><![CDATA[
      K(x,L(y,1 / (z / u),(z / u) \ u)) = K(x,L(y,u,(1 / (z / u)) \ u))
    ]]></literal>
    <justification jstring="[para(16304(a,1),15184(a,1,2))].">
      <j1 rule="para" parents="16304 15184"/>
    </justification>
  </clause>

  <clause id="16313">
    <literal><![CDATA[
      K(x,K(y * z,u * (y \ z))) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(8035,a,16311,a)].">
      <j1 rule="hyper" parents="8035 16311"/>
    </justification>
  </clause>

  <clause id="16314">
    <literal><![CDATA[
      K(x,L(T(y,z \ u),w,v5)) = K(x,L(T(y,z * u),w,v5))
    ]]></literal>
    <justification jstring="[para(25(a,2),16185(a,2,2)),flip(a)].">
      <j1 rule="para" parents="25 16185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16315">
    <literal><![CDATA[
      K(x,L(T(y,z * u),z \ u,z)) = K(x,u \ (z * (y * (z \ u))))
    ]]></literal>
    <justification jstring="[para(869(a,1),16185(a,2,2))].">
      <j1 rule="para" parents="869 16185"/>
    </justification>
  </clause>

  <clause id="16316">
    <literal><![CDATA[
      T(x / (x \ y),T(z,y)) = T(x / (x \ y),z)
    ]]></literal>
    <justification jstring="[para(12(a,1),16229(a,1,2,2))].">
      <j1 rule="para" parents="12 16229"/>
    </justification>
  </clause>

  <clause id="16317">
    <literal><![CDATA[
      T(x / (x \ y),z / y) = T(x / (x \ y),y \ z)
    ]]></literal>
    <justification jstring="[hyper(8311,a,16316,a)].">
      <j1 rule="hyper" parents="8311 16316"/>
    </justification>
  </clause>

  <clause id="16318">
    <literal><![CDATA[
      T(x / (x \ y),y \ x) = x * (x / y)
    ]]></literal>
    <justification jstring="[hyper(65,a,14709,a(flip),b,16317,a),flip(a)].">
      <j1 rule="hyper" parents="65 14709 16317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16319">
    <literal><![CDATA[
      (x / (x \ y)) * (y \ x) = (y \ x) * (x * (x / y))
    ]]></literal>
    <justification jstring="[para(16318(a,1),107(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16318 107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16320">
    <literal><![CDATA[
      K(x,y \ (z * T(u / (u \ w),(u / (u \ w)) * (w \ u)))) = K(x,y \ (z * (u * (u / w))))
    ]]></literal>
    <justification jstring="[para(16318(a,1),13843(a,2,2,2,2))].">
      <j1 rule="para" parents="16318 13843"/>
    </justification>
  </clause>

  <clause id="16321">
    <literal><![CDATA[
      K(x,T(y \ ((z * z) * u),y)) = K(x,u / ((z * z) \ y))
    ]]></literal>
    <justification jstring="[para(666(a,1),16247(a,1,2,1))].">
      <j1 rule="para" parents="666 16247"/>
    </justification>
  </clause>

  <clause id="16322">
    <literal><![CDATA[
      T(T(x,K(y,z)),y / ((z / u) \ u)) = T(x,((z / u) \ u) \ y)
    ]]></literal>
    <justification jstring="[para(12(a,1),16274(a,1,1,2,2))].">
      <j1 rule="para" parents="12 16274"/>
    </justification>
  </clause>

  <clause id="16323">
    <literal><![CDATA[
      T(T(x,K(y,z)),y / ((u \ z) \ u)) = T(x,((u \ z) \ u) \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),16282(a,1,1,2,2))].">
      <j1 rule="para" parents="10 16282"/>
    </justification>
  </clause>

  <clause id="16324">
    <literal><![CDATA[
      T(T(x,K(y,z)),(u \ (z / u)) * y) = T(x,y * (u \ (z / u)))
    ]]></literal>
    <justification jstring="[para(12(a,1),16283(a,1,1,2,2))].">
      <j1 rule="para" parents="12 16283"/>
    </justification>
  </clause>

  <clause id="16326">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(12127,a,16310,a)].">
      <j1 rule="hyper" parents="12127 16310"/>
    </justification>
  </clause>

  <clause id="16327">
    <literal><![CDATA[
      K(x,K(T(y,z),u)) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(8240,a,16326,a)].">
      <j1 rule="hyper" parents="8240 16326"/>
    </justification>
  </clause>

  <clause id="16328">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,7989,a,b,16326,a),flip(a)].">
      <j1 rule="hyper" parents="299 7989 16326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16329">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,7983,a,b,16326,a),flip(a)].">
      <j1 rule="hyper" parents="299 7983 16326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16330">
    <literal><![CDATA[
      K(x,K(y,z)) * u = u * K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(16326(a,1),7611(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16326 7611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16331">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(16326(a,2),8025(a,1))].">
      <j1 rule="para" parents="16326 8025"/>
    </justification>
  </clause>

  <clause id="16333">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(z,K(x,T(y,w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,16326,a(flip),b,16327,a),flip(a)].">
      <j1 rule="hyper" parents="65 16326 16327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16334">
    <literal><![CDATA[
      K(x,K(y / z,u)) = K(x,K(z \ y,u))
    ]]></literal>
    <justification jstring="[para(109(a,1),16327(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="109 16327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16335">
    <literal><![CDATA[
      K(x,K(y,z / u)) = K(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[para(7538(a,1),16327(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7538 16327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16336">
    <literal><![CDATA[
      K(x,T(y,z)) * K(x,K(y,u)) = K(x,T(T(y,z),u))
    ]]></literal>
    <justification jstring="[para(16327(a,1),7967(a,1,2))].">
      <j1 rule="para" parents="16327 7967"/>
    </justification>
  </clause>

  <clause id="16337">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,T(y,u) / z) = K(x,z \ T(y,u))
    ]]></literal>
    <justification jstring="[para(16327(a,1),8507(a,1,1))].">
      <j1 rule="para" parents="16327 8507"/>
    </justification>
  </clause>

  <clause id="16338">
    <literal><![CDATA[
      K(x,K(y,z * u)) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[para(13203(a,1),16327(a,1,2))].">
      <j1 rule="para" parents="13203 16327"/>
    </justification>
  </clause>

  <clause id="16339">
    <literal><![CDATA[
      T(K(x,K(y,z)),u) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8422,a,16328,a)].">
      <j1 rule="hyper" parents="8422 16328"/>
    </justification>
  </clause>

  <clause id="16341">
    <literal><![CDATA[
      K(x,K(y,z)) * u = u * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(16328(a,1),7611(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16328 7611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16345">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,y \ T(z,u)) = K(x,T(z,u) / y)
    ]]></literal>
    <justification jstring="[para(16328(a,1),8497(a,1,1))].">
      <j1 rule="para" parents="16328 8497"/>
    </justification>
  </clause>

  <clause id="16346">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,y / T(z,u)) = K(x,T(z,u) \ y)
    ]]></literal>
    <justification jstring="[para(16328(a,1),8507(a,1,1))].">
      <j1 rule="para" parents="16328 8507"/>
    </justification>
  </clause>

  <clause id="16347">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,y \ T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,u) / y) = w
    ]]></literal>
    <justification jstring="[para(16328(a,1),8498(a,1,1))].">
      <j1 rule="para" parents="16328 8498"/>
    </justification>
  </clause>

  <clause id="16348">
    <literal><![CDATA[
      K(x,K(y,L(z / u,u,w))) = K(x,K(y,(w * u) \ (w * z)))
    ]]></literal>
    <justification jstring="[para(8708(a,1),16328(a,1,2))].">
      <j1 rule="para" parents="8708 16328"/>
    </justification>
  </clause>

  <clause id="16349">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,((y \ u) \ u) / z) = K(x,z \ ((y \ u) \ u))
    ]]></literal>
    <justification jstring="[para(16328(a,1),8514(a,1,1))].">
      <j1 rule="para" parents="16328 8514"/>
    </justification>
  </clause>

  <clause id="16350">
    <literal><![CDATA[
      K(x,K(y \ z,u)) = K(x,K(u,z / y))
    ]]></literal>
    <justification jstring="[para(7499(a,1),16329(a,1,2))].">
      <j1 rule="para" parents="7499 16329"/>
    </justification>
  </clause>

  <clause id="16351">
    <literal><![CDATA[
      K(x,K(y,z)) * u = u * K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(16329(a,1),7611(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16329 7611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16352">
    <literal><![CDATA[
      K(x,K(y,(z \ u) * z)) = K(x,K(u,y))
    ]]></literal>
    <justification jstring="[para(13210(a,2),16329(a,1,2))].">
      <j1 rule="para" parents="13210 16329"/>
    </justification>
  </clause>

  <clause id="16354">
    <literal><![CDATA[
      T(x,K(y,K(z,u))) = x
    ]]></literal>
    <justification jstring="[hyper(56,a,16339,a)].">
      <j1 rule="hyper" parents="56 16339"/>
    </justification>
  </clause>

  <clause id="16355">
    <literal><![CDATA[
      x * K(y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,u)) * x = w
    ]]></literal>
    <justification jstring="[para(16339(a,1),276(a,1,2))].">
      <j1 rule="para" parents="16339 276"/>
    </justification>
  </clause>

  <clause id="16356">
    <literal><![CDATA[
      x * R(K(y,K(z,u)),w,w \ x) = (K(y,K(z,u)) * w) * (w \ x)
    ]]></literal>
    <justification jstring="[para(16339(a,1),798(a,1,2,1))].">
      <j1 rule="para" parents="16339 798"/>
    </justification>
  </clause>

  <clause id="16357">
    <literal><![CDATA[
      T(x,K(y,z) * u) = T(x,u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(13259,a,16354,a)].">
      <j1 rule="hyper" parents="13259 16354"/>
    </justification>
  </clause>

  <clause id="16358">
    <literal><![CDATA[
      T(x,K(y,z) / u) = T(x,u \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8996,a,16354,a),flip(a)].">
      <j1 rule="hyper" parents="8996 16354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16359">
    <literal><![CDATA[
      K(x,T(y,K(z,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8373,a,16354,a)].">
      <j1 rule="hyper" parents="8373 16354"/>
    </justification>
  </clause>

  <clause id="16360">
    <literal><![CDATA[
      T(x,T(y,K(z,u))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(7154,a,16354,a)].">
      <j1 rule="hyper" parents="7154 16354"/>
    </justification>
  </clause>

  <clause id="16362">
    <literal><![CDATA[
      K(x,K(y,K(z,u))) = 1
    ]]></literal>
    <justification jstring="[hyper(57,a,16354,a)].">
      <j1 rule="hyper" parents="57 16354"/>
    </justification>
  </clause>

  <clause id="16363">
    <literal><![CDATA[
      T(x,K(y,K(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      w = x
    ]]></literal>
    <justification jstring="[para(16354(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="16354 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16364">
    <literal><![CDATA[
      K(x,K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      u * K(x,K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(16354(a,1),276(a,1,2))].">
      <j1 rule="para" parents="16354 276"/>
    </justification>
  </clause>

  <clause id="16365">
    <literal><![CDATA[
      T(x,T(y,K(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = w
    ]]></literal>
    <justification jstring="[para(16354(a,1),7145(a,2))].">
      <j1 rule="para" parents="16354 7145"/>
    </justification>
  </clause>

  <clause id="16367">
    <literal><![CDATA[
      T(x,K(y,z) / u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u \ K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(16354(a,1),8996(a,1))].">
      <j1 rule="para" parents="16354 8996"/>
    </justification>
  </clause>

  <clause id="16368">
    <literal><![CDATA[
      T(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u * K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(16354(a,1),13236(a,1,1))].">
      <j1 rule="para" parents="16354 13236"/>
    </justification>
  </clause>

  <clause id="16369">
    <literal><![CDATA[
      x \ T(y * x,K(z,K(u,w))) = T(y,K(K(u,w),z) * x)
    ]]></literal>
    <justification jstring="[para(16354(a,1),15769(a,1,2,1,2))].">
      <j1 rule="para" parents="16354 15769"/>
    </justification>
  </clause>

  <clause id="16370">
    <literal><![CDATA[
      K(K(x,y),K(z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(8198,a,16362,a)].">
      <j1 rule="hyper" parents="8198 16362"/>
    </justification>
  </clause>

  <clause id="16372">
    <literal><![CDATA[
      T(K(x,y),K(z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,16370,a)].">
      <j1 rule="hyper" parents="58 16370"/>
    </justification>
  </clause>

  <clause id="16374">
    <literal><![CDATA[
      K(x,K(y,z) * u) = K(x,u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(13247,a,16359,a),flip(a)].">
      <j1 rule="hyper" parents="13247 16359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16375">
    <literal><![CDATA[
      K(K(x,y) * (z * x),u) = K(z * T(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(13233,a,16359,a)].">
      <j1 rule="hyper" parents="13233 16359"/>
    </justification>
  </clause>

  <clause id="16376">
    <literal><![CDATA[
      K(K(x,y) * z,u) = K(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(13187,a,16359,a)].">
      <j1 rule="hyper" parents="13187 16359"/>
    </justification>
  </clause>

  <clause id="16379">
    <literal><![CDATA[
      K(x,K(y,z) / u) = K(x,u \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8327,a,16359,a)].">
      <j1 rule="hyper" parents="8327 16359"/>
    </justification>
  </clause>

  <clause id="16380">
    <literal><![CDATA[
      K(T(x,K(y,z)),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(8218,a,16359,a),flip(a)].">
      <j1 rule="hyper" parents="8218 16359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16382">
    <literal><![CDATA[
      K(((x \ y) * x) / (K(z,u) * x),w) = K((x * K(z,u)) \ y,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,15539,a(flip),b,16359,a)].">
      <j1 rule="hyper" parents="65 15539 16359"/>
    </justification>
  </clause>

  <clause id="16384">
    <literal><![CDATA[
      K(x,T(y,T(z,u))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7140(a,1),16359(a,1,2))].">
      <j1 rule="para" parents="7140 16359"/>
    </justification>
  </clause>

  <clause id="16385">
    <literal><![CDATA[
      K(x,y) * K(z,u) = K(z,u) * K(x,y)
    ]]></literal>
    <justification jstring="[para(16359(a,1),7507(a,1,2))].">
      <j1 rule="para" parents="16359 7507"/>
    </justification>
  </clause>

  <clause id="16386">
    <literal><![CDATA[
      (K(x,y) * K(z,u)) * K(y,x) = K(z,u)
    ]]></literal>
    <justification jstring="[para(16359(a,1),7527(a,1,2))].">
      <j1 rule="para" parents="16359 7527"/>
    </justification>
  </clause>

  <clause id="16388">
    <literal><![CDATA[
      K(x,y) * T(x,K(z,u)) = T(T(x,K(z,u)),y)
    ]]></literal>
    <justification jstring="[para(16359(a,1),7564(a,1,1))].">
      <j1 rule="para" parents="16359 7564"/>
    </justification>
  </clause>

  <clause id="16391">
    <literal><![CDATA[
      K(x,T(y,K(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(16359(a,1),8171(a,1))].">
      <j1 rule="para" parents="16359 8171"/>
    </justification>
  </clause>

  <clause id="16393">
    <literal><![CDATA[
      K(T(x,K(y,z)),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u) = w
    ]]></literal>
    <justification jstring="[para(16359(a,1),8218(a,1))].">
      <j1 rule="para" parents="16359 8218"/>
    </justification>
  </clause>

  <clause id="16394">
    <literal><![CDATA[
      K(x,K(y,z) \ u) = K(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[para(8252(a,1),16359(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8252 16359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16397">
    <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(16359(a,1),8213(a,1))].">
      <j1 rule="para" parents="16359 8213"/>
    </justification>
  </clause>

  <clause id="16400">
    <literal><![CDATA[
      K(x,T(y,z / u)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[para(8995(a,1),16359(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8995 16359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16402">
    <literal><![CDATA[
      K(x,y) * (K(z,u) * x) = K(z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(16359(a,1),9465(a,1,1))].">
      <j1 rule="para" parents="16359 9465"/>
    </justification>
  </clause>

  <clause id="16403">
    <literal><![CDATA[
      L(K(x,y),x,z) = (x * K(u,w)) \ (T(x,y) * K(u,w))
    ]]></literal>
    <justification jstring="[para(16359(a,1),9505(a,1,1))].">
      <j1 rule="para" parents="16359 9505"/>
    </justification>
  </clause>

  <clause id="16405">
    <literal><![CDATA[
      K(K(x,y) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(z * K(x,y),u) = w
    ]]></literal>
    <justification jstring="[para(16359(a,1),13182(a,1))].">
      <j1 rule="para" parents="16359 13182"/>
    </justification>
  </clause>

  <clause id="16406">
    <literal><![CDATA[
      K(x * K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(y,z) * x,u) = w
    ]]></literal>
    <justification jstring="[para(16359(a,1),13187(a,1))].">
      <j1 rule="para" parents="16359 13187"/>
    </justification>
  </clause>

  <clause id="16407">
    <literal><![CDATA[
      K(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,u) * y) = w
    ]]></literal>
    <justification jstring="[para(16359(a,1),13245(a,1))].">
      <j1 rule="para" parents="16359 13245"/>
    </justification>
  </clause>

  <clause id="16408">
    <literal><![CDATA[
      K(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(16359(a,1),13247(a,1))].">
      <j1 rule="para" parents="16359 13247"/>
    </justification>
  </clause>

  <clause id="16409">
    <literal><![CDATA[
      K(x,y) * ((K(y * T(x,y),z) * y) * x) = x * (K(y * x,z) * y)
    ]]></literal>
    <justification jstring="[para(16359(a,1),14094(a,1,1))].">
      <j1 rule="para" parents="16359 14094"/>
    </justification>
  </clause>

  <clause id="16411">
    <literal><![CDATA[
      T(x,K(y,z) * (u / z)) = T(x,u / T(z,y))
    ]]></literal>
    <justification jstring="[para(6925(a,1),16360(a,1,2))].">
      <j1 rule="para" parents="6925 16360"/>
    </justification>
  </clause>

  <clause id="16412">
    <literal><![CDATA[
      T(x,T(y,T(z,u))) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7140(a,1),16360(a,1,2))].">
      <j1 rule="para" parents="7140 16360"/>
    </justification>
  </clause>

  <clause id="16420">
    <literal><![CDATA[
      K(x,y) \ K(z,u) = K(z,u) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,16372,a(flip),b,8059,a)].">
      <j1 rule="hyper" parents="119 16372 8059"/>
    </justification>
  </clause>

  <clause id="16423">
    <literal><![CDATA[
      (x * K(y,z)) * K(x,u) = T(x,u) * K(y,z)
    ]]></literal>
    <justification jstring="[para(16372(a,1),7077(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16372 7077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16424">
    <literal><![CDATA[
      T(K(x,y),T(z,u)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(16372(a,1),7141(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16372 7141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16431">
    <literal><![CDATA[
      K(K(x,y) \ z,u) = K(z * K(y,x),u)
    ]]></literal>
    <justification jstring="[para(8252(a,1),16380(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8252 16380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16432">
    <literal><![CDATA[
      K(x,T(T(y,z) * u,y)) = K(x,u * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(13247,a,16384,a),flip(a)].">
      <j1 rule="hyper" parents="13247 16384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16433">
    <literal><![CDATA[
      K(x * T(y,z),T(u,y)) = K(T(y,z) * x,u)
    ]]></literal>
    <justification jstring="[hyper(13187,a,16384,a),flip(a)].">
      <j1 rule="hyper" parents="13187 16384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16434">
    <literal><![CDATA[
      K(T(x,y) * z,T(u,x)) = K(z * T(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(13182,a,16384,a),flip(a)].">
      <j1 rule="hyper" parents="13182 16384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16436">
    <literal><![CDATA[
      K(T(x,y) / z,T(u,x)) = K(z \ T(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(7526,a,16384,a),flip(a)].">
      <j1 rule="hyper" parents="7526 16384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16438">
    <literal><![CDATA[
      K(x * y,T(z,T(x,u))) = K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,13174,a(flip),b,16384,a),flip(a)].">
      <j1 rule="hyper" parents="299 13174 16384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16440">
    <literal><![CDATA[
      K(x \ y,T(z,T(y,u))) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,8107,a(flip),b,16384,a),flip(a)].">
      <j1 rule="hyper" parents="299 8107 16384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16442">
    <literal><![CDATA[
      K(x,T(y,z * (u \ z))) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,16182,a,b,16384,a)].">
      <j1 rule="hyper" parents="65 16182 16384"/>
    </justification>
  </clause>

  <clause id="16444">
    <literal><![CDATA[
      K(x,T(y,z)) * T(z,u) = T(z,u) * K(x,y)
    ]]></literal>
    <justification jstring="[para(16384(a,1),8101(a,1,1))].">
      <j1 rule="para" parents="16384 8101"/>
    </justification>
  </clause>

  <clause id="16445">
    <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(16384(a,1),8220(a,1))].">
      <j1 rule="para" parents="16384 8220"/>
    </justification>
  </clause>

  <clause id="16446">
    <literal><![CDATA[
      K(x \ y,T(z,T(x,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = w
    ]]></literal>
    <justification jstring="[para(16384(a,2),8220(a,1))].">
      <j1 rule="para" parents="16384 8220"/>
    </justification>
  </clause>

  <clause id="16447">
    <literal><![CDATA[
      K(x * y,T(x,z)) * K(x,T(y,T(z,u))) = a(x,y,x)
    ]]></literal>
    <justification jstring="[para(16384(a,1),11131(a,1,1))].">
      <j1 rule="para" parents="16384 11131"/>
    </justification>
  </clause>

  <clause id="16449">
    <literal><![CDATA[
      K(x * T(y,z),T(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(T(y,z) * x,u) = w
    ]]></literal>
    <justification jstring="[para(16384(a,1),13187(a,1))].">
      <j1 rule="para" parents="16384 13187"/>
    </justification>
  </clause>

  <clause id="16453">
    <literal><![CDATA[
      T(x,T(y,z * u)) = T(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[para(13197(a,1),16412(a,1,2))].">
      <j1 rule="para" parents="13197 16412"/>
    </justification>
  </clause>

  <clause id="16454">
    <literal><![CDATA[
      T(K(x,y),T(z,u)) = T(K(x,y),T(z,w))
    ]]></literal>
    <justification jstring="[hyper(299,a,16424,a,b,16424,a)].">
      <j1 rule="hyper" parents="299 16424 16424"/>
    </justification>
  </clause>

  <clause id="16461">
    <literal><![CDATA[
      T(x,K(y,z) * (u / z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u / T(z,y)) = w
    ]]></literal>
    <justification jstring="[para(6925(a,1),16365(a,1,2))].">
      <j1 rule="para" parents="6925 16365"/>
    </justification>
  </clause>

  <clause id="16462">
    <literal><![CDATA[
      T(x,y * (z * K(y,u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,u) * z) = w
    ]]></literal>
    <justification jstring="[para(8370(a,1),16365(a,1,2))].">
      <j1 rule="para" parents="8370 16365"/>
    </justification>
  </clause>

  <clause id="16463">
    <literal><![CDATA[
      T(x * K(y,z),T(u,x)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x * K(y,z),u) = w
    ]]></literal>
    <justification jstring="[para(8975(a,1),16365(a,1))].">
      <j1 rule="para" parents="8975 16365"/>
    </justification>
  </clause>

  <clause id="16464">
    <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(10645(a,2),16365(a,1))].">
      <j1 rule="para" parents="10645 16365"/>
    </justification>
  </clause>

  <clause id="16465">
    <literal><![CDATA[
      T(x,K(y,y \ z) * (u * (y \ z))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u * (z / y)) = w
    ]]></literal>
    <justification jstring="[para(11213(a,2),16365(a,1,2))].">
      <j1 rule="para" parents="11213 16365"/>
    </justification>
  </clause>

  <clause id="16466">
    <literal><![CDATA[
      T(x,K(y,z) * (u \ y)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u \ T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(14324(a,1),16365(a,1,2))].">
      <j1 rule="para" parents="14324 16365"/>
    </justification>
  </clause>

  <clause id="16467">
    <literal><![CDATA[
      K(x,T(y,L(K(z,u),w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v6
    ]]></literal>
    <justification jstring="[para(6131(a,1),16391(a,1,2,2))].">
      <j1 rule="para" parents="6131 16391"/>
    </justification>
  </clause>

  <clause id="16468">
    <literal><![CDATA[
      K(x,y / K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,u) \ y) = w
    ]]></literal>
    <justification jstring="[para(6254(a,1),16391(a,1,2))].">
      <j1 rule="para" parents="6254 16391"/>
    </justification>
  </clause>

  <clause id="16469">
    <literal><![CDATA[
      K(x,T(y,T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(7140(a,1),16391(a,1,2))].">
      <j1 rule="para" parents="7140 16391"/>
    </justification>
  </clause>

  <clause id="16470">
    <literal><![CDATA[
      K(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,z) \ y) = w
    ]]></literal>
    <justification jstring="[para(8252(a,1),16391(a,1,2))].">
      <j1 rule="para" parents="8252 16391"/>
    </justification>
  </clause>

  <clause id="16471">
    <literal><![CDATA[
      K(x,T(y / T(z,u),z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,u) \ y) = w
    ]]></literal>
    <justification jstring="[para(8092(a,1),16391(a,1,2))].">
      <j1 rule="para" parents="8092 16391"/>
    </justification>
  </clause>

  <clause id="16472">
    <literal><![CDATA[
      K(x,K(y,z) * (u * y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(8249(a,1),16391(a,1,2))].">
      <j1 rule="para" parents="8249 16391"/>
    </justification>
  </clause>

  <clause id="16473">
    <literal><![CDATA[
      K(x,y * (z * K(y,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u) * z) = w
    ]]></literal>
    <justification jstring="[para(8370(a,1),16391(a,1,2))].">
      <j1 rule="para" parents="8370 16391"/>
    </justification>
  </clause>

  <clause id="16475">
    <literal><![CDATA[
      K(L((x \ y) / K(z,u),K(z,u),x),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K((x * K(z,u)) \ y,w) = v5
    ]]></literal>
    <justification jstring="[para(8169(a,2),16391(a,1))].">
      <j1 rule="para" parents="8169 16391"/>
    </justification>
  </clause>

  <clause id="16476">
    <literal><![CDATA[
      K(K(x,y) * (z * x),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(z * T(x,y),u) = w
    ]]></literal>
    <justification jstring="[para(8368(a,1),16391(a,1))].">
      <j1 rule="para" parents="8368 16391"/>
    </justification>
  </clause>

  <clause id="16477">
    <literal><![CDATA[
      K((((x * y) \ z) * (x * y)) / (K(y,u) * (x * y)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K((x * T(y,u)) \ z,w) = v5
    ]]></literal>
    <justification jstring="[para(15567(a,1),16391(a,1))].">
      <j1 rule="para" parents="15567 16391"/>
    </justification>
  </clause>

  <clause id="16478">
    <literal><![CDATA[
      K(x * K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(z,y) \ x,u) = w
    ]]></literal>
    <justification jstring="[para(8252(a,1),16393(a,1,1))].">
      <j1 rule="para" parents="8252 16393"/>
    </justification>
  </clause>

  <clause id="16479">
    <literal><![CDATA[
      K((x \ y) * K(z,x),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(T(x,z) \ y,u) = w
    ]]></literal>
    <justification jstring="[para(8253(a,1),16393(a,1,1))].">
      <j1 rule="para" parents="8253 16393"/>
    </justification>
  </clause>

  <clause id="16480">
    <literal><![CDATA[
      (K(x,y) * z) * K(x,K(y,u)) = K(x,T(y,u)) * z
    ]]></literal>
    <justification jstring="[hyper(9388,a,16330,a),flip(a)].">
      <j1 rule="hyper" parents="9388 16330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16481">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * z) = u * T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,6832,a(flip),b,16330,a),flip(a)].">
      <j1 rule="hyper" parents="299 6832 16330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16482">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * z) != w
    ]]></literal>
    <literal><![CDATA[
      u * T(z,K(x,y)) = w
    ]]></literal>
    <justification jstring="[para(16330(a,2),6862(a,1))].">
      <j1 rule="para" parents="16330 6862"/>
    </justification>
  </clause>

  <clause id="16483">
    <literal><![CDATA[
      K(x,K(y,z)) * u = u * K(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(7952(a,1),16330(a,2,2))].">
      <j1 rule="para" parents="7952 16330"/>
    </justification>
  </clause>

  <clause id="16484">
    <literal><![CDATA[
      K(x,K(y,z)) * u = u * K(K(y,z),x)
    ]]></literal>
    <justification jstring="[para(7984(a,2),16330(a,2,2))].">
      <j1 rule="para" parents="7984 16330"/>
    </justification>
  </clause>

  <clause id="16485">
    <literal><![CDATA[
      K(x,K(y,z)) * u = u * K(y,K(z,x))
    ]]></literal>
    <justification jstring="[para(7989(a,1),16330(a,2,2))].">
      <j1 rule="para" parents="7989 16330"/>
    </justification>
  </clause>

  <clause id="16486">
    <literal><![CDATA[
      (K(x,y) * z) * K(x,K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u)) * z = w
    ]]></literal>
    <justification jstring="[para(16330(a,1),9388(a,1))].">
      <j1 rule="para" parents="16330 9388"/>
    </justification>
  </clause>

  <clause id="16493">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) * K(x * T(y,w),x) = K(x * T(y,w),T(x,z))
    ]]></literal>
    <justification jstring="[para(16333(a,2),8045(a,1,1))].">
      <j1 rule="para" parents="16333 8045"/>
    </justification>
  </clause>

  <clause id="16494">
    <literal><![CDATA[
      K(x,K(y / z,u)) = K(x,K(u,z * y))
    ]]></literal>
    <justification jstring="[hyper(299,a,16254,a(flip),b,16334,a),flip(a)].">
      <j1 rule="hyper" parents="299 16254 16334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16495">
    <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(299,a,9336,a,b,16335,a)].">
      <j1 rule="hyper" parents="299 9336 16335"/>
    </justification>
  </clause>

  <clause id="16496">
    <literal><![CDATA[
      K(x,K(y,z / u)) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(299,a,16251,a(flip),b,16335,a),flip(a)].">
      <j1 rule="hyper" parents="299 16251 16335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16497">
    <literal><![CDATA[
      K(x,K(y,(1 / z) * u)) = K(x,K(y,u / z))
    ]]></literal>
    <justification jstring="[para(14199(a,2),16335(a,2,2)),flip(a)].">
      <j1 rule="para" parents="14199 16335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16498">
    <literal><![CDATA[
      T(x,K(y,L((z / u) / w,w,u))) = x * K(x,K(y,(w * u) \ z))
    ]]></literal>
    <justification jstring="[para(16335(a,1),15607(a,2,2))].">
      <j1 rule="para" parents="16335 15607"/>
    </justification>
  </clause>

  <clause id="16499">
    <literal><![CDATA[
      K(x,K(y,z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u * z)) = w
    ]]></literal>
    <justification jstring="[para(16335(a,2),16252(a,1))].">
      <j1 rule="para" parents="16335 16252"/>
    </justification>
  </clause>

  <clause id="16500">
    <literal><![CDATA[
      K(x,K(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,K(x,u * z)) = w
    ]]></literal>
    <justification jstring="[para(16338(a,1),7985(a,1))].">
      <j1 rule="para" parents="16338 7985"/>
    </justification>
  </clause>

  <clause id="16501">
    <literal><![CDATA[
      K(x,K(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u * z,y)) = w
    ]]></literal>
    <justification jstring="[para(16338(a,1),8035(a,1))].">
      <j1 rule="para" parents="16338 8035"/>
    </justification>
  </clause>

  <clause id="16502">
    <literal><![CDATA[
      K(x,K(y,(1 / z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u / z)) = w
    ]]></literal>
    <justification jstring="[para(16338(a,1),14703(a,1))].">
      <j1 rule="para" parents="16338 14703"/>
    </justification>
  </clause>

  <clause id="16503">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) * T(K(w,x),u) = T(K(w,x) * K(x,K(y,z)),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,13102,a(flip),b,16341,a),flip(a)].">
      <j1 rule="hyper" parents="299 13102 16341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16504">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) * (w * u) = w * (u * K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(299,a,8915,a(flip),b,16341,a),flip(a)].">
      <j1 rule="hyper" parents="299 8915 16341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16505">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(x,y)) = u * T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(299,a,7977,a(flip),b,16341,a),flip(a)].">
      <j1 rule="hyper" parents="299 7977 16341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16507">
    <literal><![CDATA[
      K(x,y) * (z * K(x,K(y,u))) = K(x,T(y,u)) * z
    ]]></literal>
    <justification jstring="[para(16341(a,1),10049(a,1,2))].">
      <j1 rule="para" parents="16341 10049"/>
    </justification>
  </clause>

  <clause id="16508">
    <literal><![CDATA[
      K(x,K(y \ z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z / y,u)) = w
    ]]></literal>
    <justification jstring="[para(16350(a,2),8035(a,1))].">
      <j1 rule="para" parents="16350 8035"/>
    </justification>
  </clause>

  <clause id="16509">
    <literal><![CDATA[
      K(x,K(y \ (z \ u),L(w,y,z))) = K(x,K(w,u / (z * y)))
    ]]></literal>
    <justification jstring="[para(11935(a,2),16350(a,1,2))].">
      <j1 rule="para" parents="11935 16350"/>
    </justification>
  </clause>

  <clause id="16510">
    <literal><![CDATA[
      K(x,y \ z) * K(x,K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(16351(a,1),8498(a,1))].">
      <j1 rule="para" parents="16351 8498"/>
    </justification>
  </clause>

  <clause id="16511">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,((u \ y) * u) / z) = K(x,z \ ((u \ y) * u))
    ]]></literal>
    <justification jstring="[para(16352(a,1),8499(a,1,1))].">
      <j1 rule="para" parents="16352 8499"/>
    </justification>
  </clause>

  <clause id="16512">
    <literal><![CDATA[
      T(x,(y \ z) * K(y,u)) = T(x,T(y,u) \ z)
    ]]></literal>
    <justification jstring="[hyper(15835,a,16357,a),flip(a)].">
      <j1 rule="hyper" parents="15835 16357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16513">
    <literal><![CDATA[
      T(x,K(y,z) * u) = T(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(15834,a,16357,a)].">
      <j1 rule="hyper" parents="15834 16357"/>
    </justification>
  </clause>

  <clause id="16514">
    <literal><![CDATA[
      T(x,(y * z) * K(u,y)) = T(x,T(y,u) * z)
    ]]></literal>
    <justification jstring="[hyper(15833,a,16357,a),flip(a)].">
      <j1 rule="hyper" parents="15833 16357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16515">
    <literal><![CDATA[
      T(x,K(y,z) * (u * (w \ (w \ 1)))) = T(x,u * ((w * w) \ K(y,z)))
    ]]></literal>
    <justification jstring="[para(954(a,1),16357(a,2,2))].">
      <j1 rule="para" parents="954 16357"/>
    </justification>
  </clause>

  <clause id="16516">
    <literal><![CDATA[
      T(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(u,z) * y) = w
    ]]></literal>
    <justification jstring="[para(16357(a,1),15834(a,1))].">
      <j1 rule="para" parents="16357 15834"/>
    </justification>
  </clause>

  <clause id="16517">
    <literal><![CDATA[
      T(x,(y \ z) * K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,u) \ z) = w
    ]]></literal>
    <justification jstring="[para(16357(a,1),15835(a,1))].">
      <j1 rule="para" parents="16357 15835"/>
    </justification>
  </clause>

  <clause id="16518">
    <literal><![CDATA[
      T(x * T(y,K(z,u)),K(z,u)) = y * T(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[para(16357(a,1),15777(a,2,2))].">
      <j1 rule="para" parents="16357 15777"/>
    </justification>
  </clause>

  <clause id="16519">
    <literal><![CDATA[
      K(x,K(y,z) * u) = K(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(15803,a,16374,a)].">
      <j1 rule="hyper" parents="15803 16374"/>
    </justification>
  </clause>

  <clause id="16520">
    <literal><![CDATA[
      K(x,y * K(z \ 1,u)) = K(x,K(z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(299,a,16034,a,b,16374,a)].">
      <j1 rule="hyper" parents="299 16034 16374"/>
    </justification>
  </clause>

  <clause id="16521">
    <literal><![CDATA[
      K(x,K(y,z) \ u) = K(x,u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,15805,a,b,16374,a)].">
      <j1 rule="hyper" parents="65 15805 16374"/>
    </justification>
  </clause>

  <clause id="16522">
    <literal><![CDATA[
      K(x,(y \ z) * K(y,u)) = K(x,T(y,u) \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,15807,a(flip),b,16374,a),flip(a)].">
      <j1 rule="hyper" parents="65 15807 16374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16523">
    <literal><![CDATA[
      K(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,z) * y) = w
    ]]></literal>
    <justification jstring="[para(16374(a,1),15803(a,1))].">
      <j1 rule="para" parents="16374 15803"/>
    </justification>
  </clause>

  <clause id="16524">
    <literal><![CDATA[
      K(T(x \ y,x) * K(z,u),w) = K(K(z,u) * (y / x),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,15860,a(flip),b,16376,a),flip(a)].">
      <j1 rule="hyper" parents="65 15860 16376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16525">
    <literal><![CDATA[
      K(x * K(y \ z,y),u) = K(K(z,y) * x,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,13894,a(flip),b,16376,a),flip(a)].">
      <j1 rule="hyper" parents="65 13894 16376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16526">
    <literal><![CDATA[
      K(x / (y * K(z,y)),u) = K(K(y,z) * (x / y),u)
    ]]></literal>
    <justification jstring="[para(9044(a,2),16376(a,2,1)),flip(a)].">
      <j1 rule="para" parents="9044 16376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16527">
    <literal><![CDATA[
      K(K(x,L(y,z,u)) * (u * (z * y)),w) = K(u * (z * (y * K(x,y))),w)
    ]]></literal>
    <justification jstring="[para(12027(a,1),16376(a,2,1))].">
      <j1 rule="para" parents="12027 16376"/>
    </justification>
  </clause>

  <clause id="16528">
    <literal><![CDATA[
      K(x,T(1 / (y * z),y)) = K(x,K(z,1 / z) / (z * y))
    ]]></literal>
    <justification jstring="[hyper(299,a,15554,a,b,16379,a)].">
      <j1 rule="hyper" parents="299 15554 16379"/>
    </justification>
  </clause>

  <clause id="16529">
    <literal><![CDATA[
      x * (T(x,y) \ K(z,u)) = K(z,u) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(5521,a,16385,a)].">
      <j1 rule="hyper" parents="5521 16385"/>
    </justification>
  </clause>

  <clause id="16534">
    <literal><![CDATA[
      K(x,K(y \ z,y) \ (u * (y \ z))) = K(x,u * (z / y))
    ]]></literal>
    <justification jstring="[para(6970(a,1),16394(a,2,2))].">
      <j1 rule="para" parents="6970 16394"/>
    </justification>
  </clause>

  <clause id="16535">
    <literal><![CDATA[
      K(x,K(y,K(z,u) \ w)) \ (w * K(u,z)) = T(w * K(u,z),K(x,y))
    ]]></literal>
    <justification jstring="[para(16394(a,2),7973(a,1,1,2))].">
      <j1 rule="para" parents="16394 7973"/>
    </justification>
  </clause>

  <clause id="16536">
    <literal><![CDATA[
      K(x,K(y,z) \ (u / z)) = K(x,u / ((y * z) / y))
    ]]></literal>
    <justification jstring="[para(9046(a,2),16394(a,2,2))].">
      <j1 rule="para" parents="9046 16394"/>
    </justification>
  </clause>

  <clause id="16537">
    <literal><![CDATA[
      K(x,K(y \ z,y) \ (u * z)) = K(x,u * (y * (z / y)))
    ]]></literal>
    <justification jstring="[para(11333(a,1),16394(a,2,2))].">
      <j1 rule="para" parents="11333 16394"/>
    </justification>
  </clause>

  <clause id="16538">
    <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(299,a,15543,a,b,16400,a)].">
      <j1 rule="hyper" parents="299 15543 16400"/>
    </justification>
  </clause>

  <clause id="16539">
    <literal><![CDATA[
      K(x,T(y,z / u)) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(299,a,16181,a(flip),b,16400,a),flip(a)].">
      <j1 rule="hyper" parents="299 16181 16400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16540">
    <literal><![CDATA[
      K(x,T(y,z \ u)) * (u / z) = (u / z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(16400(a,1),8101(a,1,1))].">
      <j1 rule="para" parents="16400 8101"/>
    </justification>
  </clause>

  <clause id="16541">
    <literal><![CDATA[
      L(K(x,T(y,z \ u)),w,v5) = K(x,L(T(y,u / z),w,v5))
    ]]></literal>
    <justification jstring="[para(16400(a,1),11889(a,1,1))].">
      <j1 rule="para" parents="16400 11889"/>
    </justification>
  </clause>

  <clause id="16542">
    <literal><![CDATA[
      K(x,y) \ K(z,u) = K(u,z) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,5426,a,b,16420,a)].">
      <j1 rule="hyper" parents="299 5426 16420"/>
    </justification>
  </clause>

  <clause id="16544">
    <literal><![CDATA[
      T(x,y) * K(z * x,u) = K(x * z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(16438(a,1),7507(a,1,2))].">
      <j1 rule="para" parents="16438 7507"/>
    </justification>
  </clause>

  <clause id="16545">
    <literal><![CDATA[
      T(x,y) * K(x * z,u) = K(z * x,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(16438(a,1),8101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16438 8101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16547">
    <literal><![CDATA[
      K((x * (y \ x)) \ z,T(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(z / (x * (y \ x)),u) = w
    ]]></literal>
    <justification jstring="[para(16442(a,1),8220(a,1))].">
      <j1 rule="para" parents="16442 8220"/>
    </justification>
  </clause>

  <clause id="16548">
    <literal><![CDATA[
      T(x,y) \ T(T(x,z * u),T(y,u * z)) = K(x,z * u)
    ]]></literal>
    <justification jstring="[para(16453(a,1),8272(a,1,2))].">
      <j1 rule="para" parents="16453 8272"/>
    </justification>
  </clause>

  <clause id="16557">
    <literal><![CDATA[
      T(K(x,y) * z,u) * T(K(y,x),T(w,v5)) = K(y,T(x,w)) * T(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[para(16454(a,1),12542(a,1,2))].">
      <j1 rule="para" parents="16454 12542"/>
    </justification>
  </clause>

  <clause id="16558">
    <literal><![CDATA[
      K(x,K(y,z)) * (u / x) = u / T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8026,a,16483,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="8026 16483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16559">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(x,K(y,z))) != w
    ]]></literal>
    <literal><![CDATA[
      u = w
    ]]></literal>
    <justification jstring="[para(16484(a,2),7217(a,1))].">
      <j1 rule="para" parents="16484 7217"/>
    </justification>
  </clause>

  <clause id="16560">
    <literal><![CDATA[
      K(x,K(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u / z)) = w
    ]]></literal>
    <justification jstring="[para(16494(a,1),8035(a,1))].">
      <j1 rule="para" parents="16494 8035"/>
    </justification>
  </clause>

  <clause id="16562">
    <literal><![CDATA[
      T(x,K(y,z) * (u * z)) = T(x,u * T(z,y))
    ]]></literal>
    <justification jstring="[para(6832(a,1),16513(a,2,2))].">
      <j1 rule="para" parents="6832 16513"/>
    </justification>
  </clause>

  <clause id="16563">
    <literal><![CDATA[
      T(x,K(y,z) * (u / y)) = T(x,u / T(y,z))
    ]]></literal>
    <justification jstring="[para(7189(a,1),16513(a,2,2))].">
      <j1 rule="para" parents="7189 16513"/>
    </justification>
  </clause>

  <clause id="16566">
    <literal><![CDATA[
      K(x,K(y,z) * (u * z)) = K(x,u * T(z,y))
    ]]></literal>
    <justification jstring="[para(6832(a,1),16519(a,2,2))].">
      <j1 rule="para" parents="6832 16519"/>
    </justification>
  </clause>

  <clause id="16567">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ z)) = K(x,u \ T(z,y))
    ]]></literal>
    <justification jstring="[para(14220(a,1),16519(a,2,2))].">
      <j1 rule="para" parents="14220 16519"/>
    </justification>
  </clause>

  <clause id="16568">
    <literal><![CDATA[
      a(x,y,K(z,u * K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      a(K(v5,w) * u,y,K(z,x)) = v6
    ]]></literal>
    <justification jstring="[para(16519(a,1),14957(a,1,3))].">
      <j1 rule="para" parents="16519 14957"/>
    </justification>
  </clause>

  <clause id="16569">
    <literal><![CDATA[
      K(x,K(y,z) \ (u / z)) = K(x,u / T(z,y))
    ]]></literal>
    <justification jstring="[para(7189(a,1),16521(a,2,2))].">
      <j1 rule="para" parents="7189 16521"/>
    </justification>
  </clause>

  <clause id="16570">
    <literal><![CDATA[
      L(K(x,y),z,u) \ K(w,v5) = K(v5,w) \ K(L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(11889(a,2),16542(a,1,1))].">
      <j1 rule="para" parents="11889 16542"/>
    </justification>
  </clause>

  <clause id="16572">
    <literal><![CDATA[
      K(x,K(T(y,z),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(7537(a,2),16331(a,1,2))].">
      <j1 rule="para" parents="7537 16331"/>
    </justification>
  </clause>

  <clause id="16573">
    <literal><![CDATA[
      K(x,K(y * z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z * y,u)) = w
    ]]></literal>
    <justification jstring="[para(13173(a,1),16331(a,1,2))].">
      <j1 rule="para" parents="13173 16331"/>
    </justification>
  </clause>

  <clause id="16574">
    <literal><![CDATA[
      K(x,K(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u * z)) = w
    ]]></literal>
    <justification jstring="[para(13205(a,1),16331(a,1,2))].">
      <j1 rule="para" parents="13205 16331"/>
    </justification>
  </clause>

  <clause id="16576">
    <literal><![CDATA[
      K(x,T(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u * z)) = w
    ]]></literal>
    <justification jstring="[para(13197(a,1),16469(a,1,2))].">
      <j1 rule="para" parents="13197 16469"/>
    </justification>
  </clause>

  <clause id="16577">
    <literal><![CDATA[
      K(x,T(y,z * (u \ z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(16182(a,2),16469(a,1))].">
      <j1 rule="para" parents="16182 16469"/>
    </justification>
  </clause>

  <clause id="16579">
    <literal><![CDATA[
      K(K(x * (1 / y),y) * (z * (x * (1 / y))),u) = K(z * (y \ R(x,1 / y,y)),u)
    ]]></literal>
    <justification jstring="[para(598(a,2),16375(a,2,1,2))].">
      <j1 rule="para" parents="598 16375"/>
    </justification>
  </clause>

  <clause id="16581">
    <literal><![CDATA[
      K(x,y * z) * T(x,K(y,z)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(299,a,13224,a(flip),b,16388,a),flip(a)].">
      <j1 rule="hyper" parents="299 13224 16388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16582">
    <literal><![CDATA[
      T(x,(y / z) * K(z,u)) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,16513,a(flip),b,16411,a)].">
      <j1 rule="hyper" parents="65 16513 16411"/>
    </justification>
  </clause>

  <clause id="16583">
    <literal><![CDATA[
      T(x,K(y,T(y \ z,u)) * (w / (y \ T(z,u)))) = T(x,w / T(y \ T(z,u),y))
    ]]></literal>
    <justification jstring="[para(11779(a,2),16411(a,1,2,1))].">
      <j1 rule="para" parents="11779 16411"/>
    </justification>
  </clause>

  <clause id="16584">
    <literal><![CDATA[
      T(x,K(y \ (y \ 1),(y \ 1) * z) * (u / ((y \ 1) * z))) = T(x,u / (y * (z * (y \ (1 / y)))))
    ]]></literal>
    <justification jstring="[para(14726(a,1),16411(a,2,2,2))].">
      <j1 rule="para" parents="14726 16411"/>
    </justification>
  </clause>

  <clause id="16585">
    <literal><![CDATA[
      K(x,T(K(y,z) * u,y)) = K(x,(y \ u) * T(y,z))
    ]]></literal>
    <justification jstring="[para(5056(a,1),16432(a,1,2,1))].">
      <j1 rule="para" parents="5056 16432"/>
    </justification>
  </clause>

  <clause id="16586">
    <literal><![CDATA[
      K(x * T(T(y,z),u),T(w,y)) = K(T(T(y,z),u) * x,w)
    ]]></literal>
    <justification jstring="[hyper(16469,a,16433,a)].">
      <j1 rule="hyper" parents="16469 16433"/>
    </justification>
  </clause>

  <clause id="16587">
    <literal><![CDATA[
      K(x \ T(y,z),T(T(u,y),w)) = K(T(y,z) / x,T(u,w))
    ]]></literal>
    <justification jstring="[hyper(8213,a,16436,a),flip(a)].">
      <j1 rule="hyper" parents="8213 16436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16589">
    <literal><![CDATA[
      T(x,y) * K(z,x * u) = K(z,u * x) * T(x,y)
    ]]></literal>
    <justification jstring="[para(13205(a,1),16444(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13205 16444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16590">
    <literal><![CDATA[
      T(T(x,y),z) * K(x * u,w) = K(u * x,w) * T(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(16438(a,1),16444(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16438 16444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16591">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u * z) = u * T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(8032,a,16481,a)].">
      <j1 rule="hyper" parents="8032 16481"/>
    </justification>
  </clause>

  <clause id="16592">
    <literal><![CDATA[
      T(x,T((y \ z) * K(y,u),w)) = K(x,w) * T(x * K(w,x),T(y,u) \ z)
    ]]></literal>
    <justification jstring="[para(16512(a,1),9376(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16512 9376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16593">
    <literal><![CDATA[
      T(x,y * (z * K(u,y))) = T(x,T(y,u) * z)
    ]]></literal>
    <justification jstring="[para(7822(a,1),16514(a,1,2))].">
      <j1 rule="para" parents="7822 16514"/>
    </justification>
  </clause>

  <clause id="16594">
    <literal><![CDATA[
      K(x,(y \ z) * K(y,u * ((w \ 1) \ v5))) = K(x,T(y,u * ((1 / w) \ v5)) \ z)
    ]]></literal>
    <justification jstring="[para(3884(a,2),16522(a,2,2,1))].">
      <j1 rule="para" parents="3884 16522"/>
    </justification>
  </clause>

  <clause id="16595">
    <literal><![CDATA[
      K(x,(y \ z) * K(y,u * ((w \ 1) * v5))) = K(x,T(y,u * ((1 / w) * v5)) \ z)
    ]]></literal>
    <justification jstring="[para(3899(a,2),16522(a,2,2,1))].">
      <j1 rule="para" parents="3899 16522"/>
    </justification>
  </clause>

  <clause id="16596">
    <literal><![CDATA[
      x \ (K(y,z) * K(u,x)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u) \ K(y,z) = w
    ]]></literal>
    <justification jstring="[para(16529(a,1),314(a,1,2))].">
      <j1 rule="para" parents="16529 314"/>
    </justification>
  </clause>

  <clause id="16598">
    <literal><![CDATA[
      K(x,(y \ z) * K(u,z)) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,16374,a(flip),b,16567,a)].">
      <j1 rule="hyper" parents="65 16374 16567"/>
    </justification>
  </clause>

  <clause id="16599">
    <literal><![CDATA[
      K(x,y * z) * T(x,K(y,z)) = K(x,z * y) * x
    ]]></literal>
    <justification jstring="[hyper(299,a,5096,a(flip),b,16581,a),flip(a)].">
      <j1 rule="hyper" parents="299 5096 16581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16600">
    <literal><![CDATA[
      T(x,y / (z * K(u,z))) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(9044(a,2),16582(a,1,2))].">
      <j1 rule="para" parents="9044 16582"/>
    </justification>
  </clause>

  <clause id="16601">
    <literal><![CDATA[
      T(x,y / ((z * u) / z)) = T(x,y / T(u,z))
    ]]></literal>
    <justification jstring="[para(9046(a,2),16582(a,1,2))].">
      <j1 rule="para" parents="9046 16582"/>
    </justification>
  </clause>

  <clause id="16603">
    <literal><![CDATA[
      T(x,T(y,z) * (u \ T(y,z))) = T(x,y * (u \ y))
    ]]></literal>
    <justification jstring="[para(14249(a,1),16593(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14249 16593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16604">
    <literal><![CDATA[
      T(x,y / T(T(z,u),u)) = T(x,y / z)
    ]]></literal>
    <justification jstring="[para(5100(a,1),16600(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5100 16600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16605">
    <literal><![CDATA[
      T(x,y / T(T(z,u),u)) = x / K(y / z,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,5041,a(flip),b,16604,a),flip(a)].">
      <j1 rule="hyper" parents="299 5041 16604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16606">
    <literal><![CDATA[
      T(x,T(y / ((z * u) / z),w)) = K(x,w) * T(x * K(w,x),y / T(u,z))
    ]]></literal>
    <justification jstring="[para(16601(a,1),9376(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16601 9376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16607">
    <literal><![CDATA[
      T(x,y / T(T(z \ ((z \ 1) \ u),w),1 / z)) = T(x,y / ((z \ T(u,w)) / (1 / z)))
    ]]></literal>
    <justification jstring="[para(14727(a,1),16601(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="14727 16601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16610">
    <literal><![CDATA[
      T(x,y / T(T(z,u),u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y / z) = w
    ]]></literal>
    <justification jstring="[para(16605(a,2),5046(a,1))].">
      <j1 rule="para" parents="16605 5046"/>
    </justification>
  </clause>

  <clause id="16612">
    <literal><![CDATA[
      x * K(y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,K(y,u)) * x = w
    ]]></literal>
    <justification jstring="[para(7983(a,1),16355(a,1,2))].">
      <j1 rule="para" parents="7983 16355"/>
    </justification>
  </clause>

  <clause id="16613">
    <literal><![CDATA[
      x * K(y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,K(u,y)) * x = w
    ]]></literal>
    <justification jstring="[para(7989(a,1),16355(a,1,2))].">
      <j1 rule="para" parents="7989 16355"/>
    </justification>
  </clause>

  <clause id="16614">
    <literal><![CDATA[
      x * K(y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,K(u,z)) * x = w
    ]]></literal>
    <justification jstring="[para(8004(a,1),16355(a,1,2))].">
      <j1 rule="para" parents="8004 16355"/>
    </justification>
  </clause>

  <clause id="16616">
    <literal><![CDATA[
      K(x,K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      u * K(z,K(x,y)) = w
    ]]></literal>
    <justification jstring="[para(7989(a,2),16364(a,1,1))].">
      <j1 rule="para" parents="7989 16364"/>
    </justification>
  </clause>

  <clause id="16617">
    <literal><![CDATA[
      x * T(y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      (x * y) * K(z,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(16481(a,1),16364(a,1))].">
      <j1 rule="para" parents="16481 16364"/>
    </justification>
  </clause>

  <clause id="16620">
    <literal><![CDATA[
      T(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u * K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(15778(a,1),16368(a,1))].">
      <j1 rule="para" parents="15778 16368"/>
    </justification>
  </clause>

  <clause id="16621">
    <literal><![CDATA[
      K(x,T(K(y,z) * (u * y),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(u * T(y,z),w)) = v5
    ]]></literal>
    <justification jstring="[para(8249(a,1),16397(a,1,2,1))].">
      <j1 rule="para" parents="8249 16397"/>
    </justification>
  </clause>

  <clause id="16622">
    <literal><![CDATA[
      K(x * (y * (z / y)),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(y,y \ z) * (x * z),u) = w
    ]]></literal>
    <justification jstring="[para(11333(a,1),16406(a,1,1))].">
      <j1 rule="para" parents="11333 16406"/>
    </justification>
  </clause>

  <clause id="16623">
    <literal><![CDATA[
      K(x,K(y * z,y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(13776(a,2),16408(a,1))].">
      <j1 rule="para" parents="13776 16408"/>
    </justification>
  </clause>

  <clause id="16624">
    <literal><![CDATA[
      K(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(15802(a,1),16408(a,1))].">
      <j1 rule="para" parents="15802 16408"/>
    </justification>
  </clause>

  <clause id="16625">
    <literal><![CDATA[
      K(x,y * K(z \ 1,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(16520(a,2),16408(a,1))].">
      <j1 rule="para" parents="16520 16408"/>
    </justification>
  </clause>

  <clause id="16626">
    <literal><![CDATA[
      K(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(16519(a,2),16470(a,1))].">
      <j1 rule="para" parents="16519 16470"/>
    </justification>
  </clause>

  <clause id="16627">
    <literal><![CDATA[
      K(x,K(y,z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y) \ u) = w
    ]]></literal>
    <justification jstring="[para(16521(a,2),16470(a,1))].">
      <j1 rule="para" parents="16521 16470"/>
    </justification>
  </clause>

  <clause id="16630">
    <literal><![CDATA[
      K(x,K(y / z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y * z,u)) = w
    ]]></literal>
    <justification jstring="[para(16494(a,2),16501(a,1))].">
      <j1 rule="para" parents="16494 16501"/>
    </justification>
  </clause>

  <clause id="16633">
    <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(103(a,1),16574(a,1,2,2))].">
      <j1 rule="para" parents="103 16574"/>
    </justification>
  </clause>

  <clause id="16634">
    <literal><![CDATA[
      K(x,L(y,z,u) * (u * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(u * (z * y),z * u)) = w
    ]]></literal>
    <justification jstring="[para(13211(a,1),16576(a,1))].">
      <j1 rule="para" parents="13211 16576"/>
    </justification>
  </clause>

  <clause id="16635">
    <literal><![CDATA[
      K(x,T(y,z / (1 / u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u * z)) = w
    ]]></literal>
    <justification jstring="[para(14484(a,2),16576(a,1,2))].">
      <j1 rule="para" parents="14484 16576"/>
    </justification>
  </clause>

  <clause id="16636">
    <literal><![CDATA[
      K(x,T(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u * z)) = w
    ]]></literal>
    <justification jstring="[para(16181(a,2),16576(a,1))].">
      <j1 rule="para" parents="16181 16576"/>
    </justification>
  </clause>

  <clause id="16637">
    <literal><![CDATA[
      K(x,T(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z * u)) = w
    ]]></literal>
    <justification jstring="[para(16183(a,2),16576(a,1))].">
      <j1 rule="para" parents="16183 16576"/>
    </justification>
  </clause>

  <clause id="16638">
    <literal><![CDATA[
      T(x,y / T(z \ u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y / (u / z)) = w
    ]]></literal>
    <justification jstring="[para(109(a,1),16610(a,1,2,2,1))].">
      <j1 rule="para" parents="109 16610"/>
    </justification>
  </clause>

  <clause id="16639">
    <literal><![CDATA[
      T(x,T(y,z) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(13704(a,1),16610(a,1))].">
      <j1 rule="para" parents="13704 16610"/>
    </justification>
  </clause>

  <clause id="16641">
    <literal><![CDATA[
      T(x,y \ T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(4396(a,1),16639(a,1,2))].">
      <j1 rule="para" parents="4396 16639"/>
    </justification>
  </clause>

  <clause id="16642">
    <literal><![CDATA[
      T(x,K(y,z) * (y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(15783(a,2),16639(a,1))].">
      <j1 rule="para" parents="15783 16639"/>
    </justification>
  </clause>

  <clause id="16644">
    <literal><![CDATA[
      T(x,y \ L(T(z,y),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,L(z,u,w) / y) = v5
    ]]></literal>
    <justification jstring="[para(25(a,2),16641(a,1,2,2))].">
      <j1 rule="para" parents="25 16641"/>
    </justification>
  </clause>

  <clause id="16645">
    <literal><![CDATA[
      T(x,T(y \ z,z) \ T(u,z / y)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u / T(y \ z,z)) = w
    ]]></literal>
    <justification jstring="[para(8196(a,1),16641(a,1,2,2))].">
      <j1 rule="para" parents="8196 16641"/>
    </justification>
  </clause>

  <clause id="16646">
    <literal><![CDATA[
      T(x,T(y * z,z) \ T(u,z * y)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u / T(y * z,z)) = w
    ]]></literal>
    <justification jstring="[para(13272(a,1),16641(a,1,2,2))].">
      <j1 rule="para" parents="13272 16641"/>
    </justification>
  </clause>

  <clause id="16647">
    <literal><![CDATA[
      T(x,(y \ ((y \ 1) \ z)) \ T(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u / (y \ ((y \ 1) \ z))) = w
    ]]></literal>
    <justification jstring="[para(14377(a,1),16641(a,1,2,2))].">
      <j1 rule="para" parents="14377 16641"/>
    </justification>
  </clause>

  <clause id="16648">
    <literal><![CDATA[
      T(x,(y * (z \ 1)) \ T(u,y / z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u / (y * (z \ 1))) = w
    ]]></literal>
    <justification jstring="[para(14474(a,1),16641(a,1,2,2))].">
      <j1 rule="para" parents="14474 16641"/>
    </justification>
  </clause>

  <clause id="16649">
    <literal><![CDATA[
      T(x,T(y,z \ u) \ T(w,T(y,z * u))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,w / T(y,z \ u)) = v5
    ]]></literal>
    <justification jstring="[para(16225(a,1),16641(a,1,2,2))].">
      <j1 rule="para" parents="16225 16641"/>
    </justification>
  </clause>

  <clause id="16651">
    <literal><![CDATA[
      K((x \ y) / z,L(u,z,x)) != w
    ]]></literal>
    <literal><![CDATA[
      K((x * z) \ y,T(u,x * y)) = w
    ]]></literal>
    <justification jstring="[para(11972(a,1),16637(a,1))].">
      <j1 rule="para" parents="11972 16637"/>
    </justification>
  </clause>

  <clause id="16652">
    <literal><![CDATA[
      K(x,T(y,z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u * z)) = w
    ]]></literal>
    <justification jstring="[para(16400(a,2),16637(a,1))].">
      <j1 rule="para" parents="16400 16637"/>
    </justification>
  </clause>

  <clause id="16653">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(x,y)) = u * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,7503,a,b,16505,a),flip(a)].">
      <j1 rule="hyper" parents="299 7503 16505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16654">
    <literal><![CDATA[
      K(x,T(y,z)) * K(x,T(y,z)) = K(x,y) * K(x,y)
    ]]></literal>
    <justification jstring="[para(8292(a,1),16507(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8292 16507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16655">
    <literal><![CDATA[
      K(x,y / ((z * u) / z)) = K(x,y / T(u,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,16569,a(flip),b,16536,a),flip(a)].">
      <j1 rule="hyper" parents="65 16569 16536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16656">
    <literal><![CDATA[
      K(x,T(y,z) \ T(u,T(y,z))) = K(x,u / ((z * y) / z))
    ]]></literal>
    <justification jstring="[hyper(299,a,13925,a,b,16655,a)].">
      <j1 rule="hyper" parents="299 13925 16655"/>
    </justification>
  </clause>

  <clause id="16659">
    <literal><![CDATA[
      x * K(y,(z * (u * (z \ x))) / x) = ((x / z) * K(y,u)) * z
    ]]></literal>
    <justification jstring="[para(16540(a,1),15620(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16540 15620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16660">
    <literal><![CDATA[
      T(x * K(K(x * y,z),x),u) * K(x * y,z) = T(x,u) * K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,5130,a,b,16544,a)].">
      <j1 rule="hyper" parents="299 5130 16544"/>
    </justification>
  </clause>

  <clause id="16661">
    <literal><![CDATA[
      (T(x,y) \ 1) \ L(K(((x \ 1) \ 1) * z,u),x,x) = K(z * ((x \ 1) \ 1),u) * T((x \ 1) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,15302,a,b,16545,a)].">
      <j1 rule="hyper" parents="65 15302 16545"/>
    </justification>
  </clause>

  <clause id="16662">
    <literal><![CDATA[
      K(x,T(K(y * (z / y),y) * u,y * (z / y))) = K(x,((y * (z / y)) \ u) * (y * (z / T(y,z))))
    ]]></literal>
    <justification jstring="[para(4417(a,1),16585(a,2,2,2))].">
      <j1 rule="para" parents="4417 16585"/>
    </justification>
  </clause>

  <clause id="16663">
    <literal><![CDATA[
      K(x,y * z) * K(x,K(y,z)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(6928,a,16599,a)].">
      <j1 rule="hyper" parents="6928 16599"/>
    </justification>
  </clause>

  <clause id="16664">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,z * y) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(16614,a,16663,a)].">
      <j1 rule="hyper" parents="16614 16663"/>
    </justification>
  </clause>

  <clause id="16665">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z,x * y) = K(z,y * x)
    ]]></literal>
    <justification jstring="[hyper(16613,a,16663,a)].">
      <j1 rule="hyper" parents="16613 16663"/>
    </justification>
  </clause>

  <clause id="16666">
    <literal><![CDATA[
      K(x,y * (z * (u * (1 / w)))) * K(x,K(y,z * (u * (w \ 1)))) = K(x,(z * (u * (1 / w))) * y)
    ]]></literal>
    <justification jstring="[para(5659(a,1),16663(a,1,2,2))].">
      <j1 rule="para" parents="5659 16663"/>
    </justification>
  </clause>

  <clause id="16667">
    <literal><![CDATA[
      K(x,y * z) * K(x,K(z,y)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[para(8004(a,1),16663(a,1,2))].">
      <j1 rule="para" parents="8004 16663"/>
    </justification>
  </clause>

  <clause id="16668">
    <literal><![CDATA[
      K(x,(y / z) * u) * K(x,K(u,z * y)) = K(x,u * (y / z))
    ]]></literal>
    <justification jstring="[para(16494(a,1),16663(a,1,2))].">
      <j1 rule="para" parents="16494 16663"/>
    </justification>
  </clause>

  <clause id="16669">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,z * y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(16663(a,1),16559(a,1,2))].">
      <j1 rule="para" parents="16663 16559"/>
    </justification>
  </clause>

  <clause id="16670">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z,y * x) = K(z,x * y)
    ]]></literal>
    <justification jstring="[para(7989(a,2),16664(a,1,1))].">
      <j1 rule="para" parents="7989 16664"/>
    </justification>
  </clause>

  <clause id="16671">
    <literal><![CDATA[
      K(x * y,z) * K(z,y * x) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(37,a,16386,a,b,16665,a)].">
      <j1 rule="hyper" parents="37 16386 16665"/>
    </justification>
  </clause>

  <clause id="16672">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z,x * T(y,u)) = K(z,T(y,u) * x)
    ]]></literal>
    <justification jstring="[para(16327(a,1),16665(a,1,1))].">
      <j1 rule="para" parents="16327 16665"/>
    </justification>
  </clause>

  <clause id="16673">
    <literal><![CDATA[
      K(x,y * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) * K(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(16665(a,1),16616(a,1))].">
      <j1 rule="para" parents="16665 16616"/>
    </justification>
  </clause>

  <clause id="16674">
    <literal><![CDATA[
      K(x,((y \ 1) * z) * u) * K(x,K(u,y \ z)) = K(x,u * ((y \ 1) * z))
    ]]></literal>
    <justification jstring="[para(14246(a,1),16667(a,1,2,2))].">
      <j1 rule="para" parents="14246 16667"/>
    </justification>
  </clause>

  <clause id="16675">
    <literal><![CDATA[
      K(x,K(y \ T(z * K(y,z),u),w)) * K(w,(y \ T(z * K(y,z),u)) * x) = K(w,x * (T(z,u) / y))
    ]]></literal>
    <justification jstring="[hyper(299,a,13885,a(flip),b,16670,a),flip(a)].">
      <j1 rule="hyper" parents="299 13885 16670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16676">
    <literal><![CDATA[
      K(x,K(y,z)) * u != K(z,x * y)
    ]]></literal>
    <literal><![CDATA[
      K(z,y * x) = u
    ]]></literal>
    <justification jstring="[para(16670(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="16670 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16677">
    <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(16653(a,2),45(a,1))].">
      <j1 rule="para" parents="16653 45"/>
    </justification>
  </clause>

  <clause id="16678">
    <literal><![CDATA[
      L(K(x,y * K(z,u)),x,w) = (x * K(v5,v6)) \ (T(x,K(z,u) * y) * K(v5,v6))
    ]]></literal>
    <justification jstring="[para(16357(a,2),16403(a,2,2,1))].">
      <j1 rule="para" parents="16357 16403"/>
    </justification>
  </clause>

  <clause id="16679">
    <literal><![CDATA[
      K(x / T(y * y,z),u) = K(T(y * y,z) \ x,u)
    ]]></literal>
    <justification jstring="[hyper(16445,a,16187,a)].">
      <j1 rule="hyper" parents="16445 16187"/>
    </justification>
  </clause>

  <clause id="16680">
    <literal><![CDATA[
      K(T(x \ 1,y) \ z,T(u,x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(z / T(x \ 1,y),u) = w
    ]]></literal>
    <justification jstring="[para(8832(a,1),16445(a,1))].">
      <j1 rule="para" parents="8832 16445"/>
    </justification>
  </clause>

  <clause id="16681">
    <literal><![CDATA[
      K(T(x * x,x) \ y,z) = K(y / ((1 / x) \ x),z)
    ]]></literal>
    <justification jstring="[para(466(a,1),16679(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="466 16679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16682">
    <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(8109(a,1),16447(a,1,1))].">
      <j1 rule="para" parents="8109 16447"/>
    </justification>
  </clause>

  <clause id="16683">
    <literal><![CDATA[
      K(x * T(y * z,u),T(w,z * y)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(T(y * z,u) * x,w) = v5
    ]]></literal>
    <justification jstring="[para(16220(a,1),16449(a,1))].">
      <j1 rule="para" parents="16220 16449"/>
    </justification>
  </clause>

  <clause id="16685">
    <literal><![CDATA[
      T(x * K(x * y,z),y) = T(x,y) * K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(16463,a,13193,a)].">
      <j1 rule="hyper" parents="16463 13193"/>
    </justification>
  </clause>

  <clause id="16687">
    <literal><![CDATA[
      T(x * K(y,z),L(T(u,x),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x * K(y,z),L(u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(25(a,2),16463(a,1,2))].">
      <j1 rule="para" parents="25 16463"/>
    </justification>
  </clause>

  <clause id="16689">
    <literal><![CDATA[
      T(x,(y \ z) * K(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(16513(a,1),16466(a,1))].">
      <j1 rule="para" parents="16513 16466"/>
    </justification>
  </clause>

  <clause id="16690">
    <literal><![CDATA[
      K(x,L(K(y,z) * (u * y),w,v5)) = K(L(x,w,v5),u * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(16472,a,11929,a),flip(a)].">
      <j1 rule="hyper" parents="16472 11929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16691">
    <literal><![CDATA[
      K(x,K(y,z) * (u * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * T(z,y)) = w
    ]]></literal>
    <justification jstring="[para(15802(a,1),16472(a,1))].">
      <j1 rule="para" parents="15802 16472"/>
    </justification>
  </clause>

  <clause id="16692">
    <literal><![CDATA[
      K(x,K(y,z) \ (u * y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(15805(a,2),16472(a,1))].">
      <j1 rule="para" parents="15805 16472"/>
    </justification>
  </clause>

  <clause id="16694">
    <literal><![CDATA[
      K(x,T(y,z) \ u) * K(x,K(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(16328(a,1),16510(a,1,2))].">
      <j1 rule="para" parents="16328 16510"/>
    </justification>
  </clause>

  <clause id="16695">
    <literal><![CDATA[
      T(x,(y \ z) * K(y,K(u,w) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,v5 * K(u,w)) \ z) = v6
    ]]></literal>
    <justification jstring="[para(16374(a,2),16517(a,1,2,2))].">
      <j1 rule="para" parents="16374 16517"/>
    </justification>
  </clause>

  <clause id="16696">
    <literal><![CDATA[
      T(K(x,y) / T(z,u),z) != w
    ]]></literal>
    <literal><![CDATA[
      T(z,u) \ K(x,y) = w
    ]]></literal>
    <justification jstring="[para(7231(a,2),16596(a,1))].">
      <j1 rule="para" parents="7231 16596"/>
    </justification>
  </clause>

  <clause id="16697">
    <literal><![CDATA[
      (L(x,y,z) * u) * K(x,K(w,u)) = T(L(x,y,z) * u,K(x,w))
    ]]></literal>
    <justification jstring="[hyper(16617,a,10623,a(flip))].">
      <j1 rule="hyper" parents="16617 10623"/>
    </justification>
  </clause>

  <clause id="16698">
    <literal><![CDATA[
      K(x,y * K(z,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(16519(a,1),16623(a,1))].">
      <j1 rule="para" parents="16519 16623"/>
    </justification>
  </clause>

  <clause id="16701">
    <literal><![CDATA[
      K(x,y * z) * K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(16351(a,1),16669(a,1))].">
      <j1 rule="para" parents="16351 16669"/>
    </justification>
  </clause>

  <clause id="16702">
    <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(14556(a,2),16691(a,1,2,1))].">
      <j1 rule="para" parents="14556 16691"/>
    </justification>
  </clause>

  <clause id="16703">
    <literal><![CDATA[
      K(x,x * y) / T(x,z) = T(x,z) \ K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(16696,a,14765,a),flip(a)].">
      <j1 rule="hyper" parents="16696 14765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16704">
    <literal><![CDATA[
      T(x,y) \ K(x,x \ y) = 1 / R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,12652,a(flip),b,16703,a),flip(a)].">
      <j1 rule="hyper" parents="65 12652 16703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16705">
    <literal><![CDATA[
      (x / (T(x,y) / y)) \ 1 = 1 / R(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,13980,a(flip),b,16704,a)].">
      <j1 rule="hyper" parents="65 13980 16704"/>
    </justification>
  </clause>

  <clause id="16706">
    <literal><![CDATA[
      (x / (T(x,y) / y)) \ 1 = L(1 / y,x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,15359,a,b,16705,a),flip(a)].">
      <j1 rule="hyper" parents="299 15359 16705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16707">
    <literal><![CDATA[
      K(x,(y / z) * u) * K(x,K(u,z * y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * (y / z)) = w
    ]]></literal>
    <justification jstring="[para(16494(a,1),16701(a,1,2))].">
      <j1 rule="para" parents="16494 16701"/>
    </justification>
  </clause>

  <clause id="16708">
    <literal><![CDATA[
      K(x,((y * y) * z) / u) = K(x,z / ((y * y) \ u))
    ]]></literal>
    <justification jstring="[hyper(8215,a,16321,a)].">
      <j1 rule="hyper" parents="8215 16321"/>
    </justification>
  </clause>

  <clause id="16709">
    <literal><![CDATA[
      K(x,((y * y) * z) / u) = K(x,z * (u \ (y * y)))
    ]]></literal>
    <justification jstring="[hyper(299,a,14286,a(flip),b,16708,a),flip(a)].">
      <j1 rule="hyper" parents="299 14286 16708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16710">
    <literal><![CDATA[
      K(x,((y * y) * z) * (u \ 1)) = K(x,z * (u \ (y * y)))
    ]]></literal>
    <justification jstring="[hyper(14361,a,16709,a)].">
      <j1 rule="hyper" parents="14361 16709"/>
    </justification>
  </clause>

  <clause id="16711">
    <literal><![CDATA[
      K(x,y \ ((z * u) / z)) = K(x,K(u,y)) * K(x,T(u,z) / y)
    ]]></literal>
    <justification jstring="[hyper(299,a,16057,a,b,16337,a)].">
      <j1 rule="hyper" parents="299 16057 16337"/>
    </justification>
  </clause>

  <clause id="16712">
    <literal><![CDATA[
      K(x,y \ ((z \ u) * z)) = K(x,K(u,y)) * K(x,T(u,z) / y)
    ]]></literal>
    <justification jstring="[hyper(299,a,13831,a,b,16337,a)].">
      <j1 rule="hyper" parents="299 13831 16337"/>
    </justification>
  </clause>

  <clause id="16713">
    <literal><![CDATA[
      K(x,K(y,z * u)) * K(x,y / T(u / z,w)) = K(x,T(u / z,w) \ y)
    ]]></literal>
    <justification jstring="[para(16496(a,1),16346(a,1,1))].">
      <j1 rule="para" parents="16496 16346"/>
    </justification>
  </clause>

  <clause id="16714">
    <literal><![CDATA[
      T(x,K(K(y,z),u) * w) = w \ (x * w)
    ]]></literal>
    <justification jstring="[para(16354(a,1),16369(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16354 16369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16715">
    <literal><![CDATA[
      T(x,K(K(y,z),u) * w) = T(x,w)
    ]]></literal>
    <justification jstring="[hyper(299,a,22,a,b,16714,a),flip(a)].">
      <j1 rule="hyper" parents="299 22 16714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16716">
    <literal><![CDATA[
      T(x,K(K(y,z),u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,w) = v5
    ]]></literal>
    <justification jstring="[para(16714(a,2),318(a,1))].">
      <j1 rule="para" parents="16714 318"/>
    </justification>
  </clause>

  <clause id="16718">
    <literal><![CDATA[
      T(x,y * K(z,K(u,w))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(16620,a,16715,a)].">
      <j1 rule="hyper" parents="16620 16715"/>
    </justification>
  </clause>

  <clause id="16719">
    <literal><![CDATA[
      T(x,y / T(z,K(u,w))) = T(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(16461,a,16715,a)].">
      <j1 rule="hyper" parents="16461 16715"/>
    </justification>
  </clause>

  <clause id="16720">
    <literal><![CDATA[
      T(x,K(y,K(z,u)) * w) = T(x,w)
    ]]></literal>
    <justification jstring="[hyper(15834,a,16715,a)].">
      <j1 rule="hyper" parents="15834 16715"/>
    </justification>
  </clause>

  <clause id="16721">
    <literal><![CDATA[
      T(x,y * T(z,K(u,w))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,16562,a(flip),b,16715,a)].">
      <j1 rule="hyper" parents="65 16562 16715"/>
    </justification>
  </clause>

  <clause id="16722">
    <literal><![CDATA[
      T(x,K(y,K(z,u)) \ w) = T(x,w)
    ]]></literal>
    <justification jstring="[para(5426(a,2),16715(a,1,2))].">
      <j1 rule="para" parents="5426 16715"/>
    </justification>
  </clause>

  <clause id="16723">
    <literal><![CDATA[
      T(x,y * (K(z,K(u,w)) * v5)) = T(x,y * v5)
    ]]></literal>
    <justification jstring="[para(11484(a,1),16715(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11484 16715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16724">
    <literal><![CDATA[
      K(x,K(y,K(z,u)) * w) = x \ T(x,w)
    ]]></literal>
    <justification jstring="[para(16715(a,1),15780(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16715 15780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16725">
    <literal><![CDATA[
      T(x,K(y,T(z,u))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(7496(a,1),16718(a,1,2))].">
      <j1 rule="para" parents="7496 16718"/>
    </justification>
  </clause>

  <clause id="16726">
    <literal><![CDATA[
      T(x,K(y,z / u)) = T(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[para(8513(a,1),16718(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8513 16718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16727">
    <literal><![CDATA[
      T(x,y * (z * T(u,K(w,v5)))) = T(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(9496(a,1),16718(a,1,2))].">
      <j1 rule="para" parents="9496 16718"/>
    </justification>
  </clause>

  <clause id="16728">
    <literal><![CDATA[
      T(x,K(y,T(z,u)) * w) = T(x,K(y,z) * w)
    ]]></literal>
    <justification jstring="[para(16480(a,1),16718(a,1,2))].">
      <j1 rule="para" parents="16480 16718"/>
    </justification>
  </clause>

  <clause id="16729">
    <literal><![CDATA[
      K(K(x,K(y,z)) * u,w) = w / T(w,u)
    ]]></literal>
    <justification jstring="[para(16720(a,1),5033(a,2,2))].">
      <j1 rule="para" parents="16720 5033"/>
    </justification>
  </clause>

  <clause id="16730">
    <literal><![CDATA[
      T(x,K(y,K(z,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,w) = v5
    ]]></literal>
    <justification jstring="[para(16720(a,1),15791(a,1))].">
      <j1 rule="para" parents="16720 15791"/>
    </justification>
  </clause>

  <clause id="16731">
    <literal><![CDATA[
      T(x,y * K(z,T(u,w))) = T(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[para(16653(a,1),16720(a,1,2))].">
      <j1 rule="para" parents="16653 16720"/>
    </justification>
  </clause>

  <clause id="16732">
    <literal><![CDATA[
      T(x,K(y,T(z,u))) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,8050,a,b,16725,a),flip(a)].">
      <j1 rule="hyper" parents="299 8050 16725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16733">
    <literal><![CDATA[
      T(x,K(T(y,z),u)) = T(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(7537(a,2),16725(a,1,2))].">
      <j1 rule="para" parents="7537 16725"/>
    </justification>
  </clause>

  <clause id="16734">
    <literal><![CDATA[
      T(x,K(y,(z / u) \ 1)) = T(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(7930(a,1),16725(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7930 16725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16735">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(z,u) \ y) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(16725(a,1),9002(a,1,1))].">
      <j1 rule="para" parents="16725 9002"/>
    </justification>
  </clause>

  <clause id="16736">
    <literal><![CDATA[
      T(K(x,T(y,z)) * u,K(y,x)) = u * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(7280,a,16732,a),flip(a)].">
      <j1 rule="hyper" parents="7280 16732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16737">
    <literal><![CDATA[
      T(x,K(y / z,u)) = T(x,K(u,z \ y))
    ]]></literal>
    <justification jstring="[para(109(a,1),16732(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="109 16732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16739">
    <literal><![CDATA[
      T(T(x,T(y,z)),K(y,u)) = T(x,T(T(y,u),z))
    ]]></literal>
    <justification jstring="[hyper(65,a,7144,a(flip),b,16733,a),flip(a)].">
      <j1 rule="hyper" parents="65 7144 16733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16741">
    <literal><![CDATA[
      T(x,y / T(z,T(u,w))) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(7140(a,1),16719(a,1,2,2))].">
      <j1 rule="para" parents="7140 16719"/>
    </justification>
  </clause>

  <clause id="16742">
    <literal><![CDATA[
      T(x,y / T(z,u / w)) = T(x,y / T(z,w \ u))
    ]]></literal>
    <justification jstring="[para(8995(a,1),16719(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8995 16719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16743">
    <literal><![CDATA[
      T(x,T(y,z * u) * (u * z)) = T(x,(u * z) * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,13270,a,b,16721,a)].">
      <j1 rule="hyper" parents="65 13270 16721"/>
    </justification>
  </clause>

  <clause id="16744">
    <literal><![CDATA[
      T(x,y * (K(z,u) * (w * z))) = T(x,y * (w * T(z,u)))
    ]]></literal>
    <justification jstring="[para(8249(a,1),16721(a,1,2,2))].">
      <j1 rule="para" parents="8249 16721"/>
    </justification>
  </clause>

  <clause id="16745">
    <literal><![CDATA[
      T(x,y * ((z \ u) * K(w,z))) = T(x,y * (T(z,w) \ u))
    ]]></literal>
    <justification jstring="[para(8253(a,1),16721(a,1,2,2))].">
      <j1 rule="para" parents="8253 16721"/>
    </justification>
  </clause>

  <clause id="16748">
    <literal><![CDATA[
      K(x,K(y,K(z,u)) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(299,a,5036,a,b,16724,a),flip(a)].">
      <j1 rule="hyper" parents="299 5036 16724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16749">
    <literal><![CDATA[
      K(x,K(y,K(z,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w) = v5
    ]]></literal>
    <justification jstring="[para(16724(a,2),5155(a,1))].">
      <j1 rule="para" parents="16724 5155"/>
    </justification>
  </clause>

  <clause id="16750">
    <literal><![CDATA[
      K(x,K(y,K(z,u)) \ w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(16626,a,16748,a)].">
      <j1 rule="hyper" parents="16626 16748"/>
    </justification>
  </clause>

  <clause id="16751">
    <literal><![CDATA[
      K(x,y * K(z,K(u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(16623,a,16748,a)].">
      <j1 rule="hyper" parents="16623 16748"/>
    </justification>
  </clause>

  <clause id="16752">
    <literal><![CDATA[
      K(x,y * T(z,K(u,w))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(16472,a,16748,a)].">
      <j1 rule="hyper" parents="16472 16748"/>
    </justification>
  </clause>

  <clause id="16753">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) \ w) = K(x,y \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,15807,a(flip),b,16748,a)].">
      <j1 rule="hyper" parents="65 15807 16748"/>
    </justification>
  </clause>

  <clause id="16754">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) / w) = K(x,y / w)
    ]]></literal>
    <justification jstring="[para(6323(a,1),16748(a,1,2))].">
      <j1 rule="para" parents="6323 16748"/>
    </justification>
  </clause>

  <clause id="16755">
    <literal><![CDATA[
      K(x,K(y,T(z,u)) * w) = K(x,K(y,z) * w)
    ]]></literal>
    <justification jstring="[para(7521(a,1),16748(a,1,2))].">
      <j1 rule="para" parents="7521 16748"/>
    </justification>
  </clause>

  <clause id="16757">
    <literal><![CDATA[
      K(x,y / T(z,K(u,w))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(16558(a,1),16748(a,1,2))].">
      <j1 rule="para" parents="16558 16748"/>
    </justification>
  </clause>

  <clause id="16758">
    <literal><![CDATA[
      K(x,y * K(z,T(u,w))) = K(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[para(16653(a,1),16748(a,1,2))].">
      <j1 rule="para" parents="16653 16748"/>
    </justification>
  </clause>

  <clause id="16759">
    <literal><![CDATA[
      K(x,y * (K(z,u) * w)) = K(x,y * (w * K(z,u)))
    ]]></literal>
    <justification jstring="[para(9412(a,1),16751(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9412 16751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16760">
    <literal><![CDATA[
      K(x,y * (z * T(u,K(w,v5)))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(9496(a,1),16751(a,1,2))].">
      <j1 rule="para" parents="9496 16751"/>
    </justification>
  </clause>

  <clause id="16761">
    <literal><![CDATA[
      T(x,K(y,z / u)) = T(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(299,a,16268,a(flip),b,16726,a),flip(a)].">
      <j1 rule="hyper" parents="299 16268 16726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16762">
    <literal><![CDATA[
      T(x / y,K(((x / y) \ (1 / y)) \ 1,z)) = T(x,K(z,y \ x)) / y
    ]]></literal>
    <justification jstring="[para(16726(a,1),8051(a,2,1))].">
      <j1 rule="para" parents="16726 8051"/>
    </justification>
  </clause>

  <clause id="16763">
    <literal><![CDATA[
      K(K(x,K(y,z)) * u,w) = K(u,w)
    ]]></literal>
    <justification jstring="[hyper(299,a,5033,a,b,16729,a),flip(a)].">
      <j1 rule="hyper" parents="299 5033 16729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16764">
    <literal><![CDATA[
      K(K(x,K(y,z)) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(u,w) = v5
    ]]></literal>
    <justification jstring="[para(16729(a,2),5118(a,1))].">
      <j1 rule="para" parents="16729 5118"/>
    </justification>
  </clause>

  <clause id="16765">
    <literal><![CDATA[
      K(x * T(y,K(z,u)),w) = K(x * y,w)
    ]]></literal>
    <justification jstring="[hyper(16476,a,16763,a)].">
      <j1 rule="hyper" parents="16476 16763"/>
    </justification>
  </clause>

  <clause id="16766">
    <literal><![CDATA[
      K(x * K(y,K(z,u)),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(16405,a,16763,a)].">
      <j1 rule="hyper" parents="16405 16763"/>
    </justification>
  </clause>

  <clause id="16767">
    <literal><![CDATA[
      K(T(x,K(y,z)) / u,w) = K(x / u,w)
    ]]></literal>
    <justification jstring="[para(6323(a,1),16763(a,1,1))].">
      <j1 rule="para" parents="6323 16763"/>
    </justification>
  </clause>

  <clause id="16768">
    <literal><![CDATA[
      K(K(x,T(y,z)) * u,w) = K(K(x,y) * u,w)
    ]]></literal>
    <justification jstring="[para(7521(a,1),16763(a,1,1))].">
      <j1 rule="para" parents="7521 16763"/>
    </justification>
  </clause>

  <clause id="16769">
    <literal><![CDATA[
      K((K(x,y) * z) \ u,w) = K((z * K(x,y)) \ u,w)
    ]]></literal>
    <justification jstring="[para(11606(a,1),16763(a,1,1))].">
      <j1 rule="para" parents="11606 16763"/>
    </justification>
  </clause>

  <clause id="16770">
    <literal><![CDATA[
      K(x / T(y,K(z,u)),w) = K(x / y,w)
    ]]></literal>
    <justification jstring="[para(16558(a,1),16763(a,1,1))].">
      <j1 rule="para" parents="16558 16763"/>
    </justification>
  </clause>

  <clause id="16771">
    <literal><![CDATA[
      K(x * K(y,T(z,u)),w) = K(x * K(y,z),w)
    ]]></literal>
    <justification jstring="[para(16653(a,1),16763(a,1,1))].">
      <j1 rule="para" parents="16653 16763"/>
    </justification>
  </clause>

  <clause id="16772">
    <literal><![CDATA[
      K(x,y) * (x * K(z,K(u,w))) = T(x * K(z,K(u,w)),y)
    ]]></literal>
    <justification jstring="[para(16766(a,1),5096(a,2,1)),flip(a)].">
      <j1 rule="para" parents="16766 5096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16773">
    <literal><![CDATA[
      K(x * (K(y,z) * u),w) = K(x * (u * K(y,z)),w)
    ]]></literal>
    <justification jstring="[para(9412(a,1),16766(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9412 16766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16774">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u \ w)),K(w / u,z)) = T(y,K(z,u \ w) * x)
    ]]></literal>
    <justification jstring="[hyper(119,a,16737,a,b,15777,a(flip))].">
      <j1 rule="hyper" parents="119 16737 15777"/>
    </justification>
  </clause>

  <clause id="16775">
    <literal><![CDATA[
      K(x,y * T(z,T(u,w))) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(7140(a,1),16752(a,1,2,2))].">
      <j1 rule="para" parents="7140 16752"/>
    </justification>
  </clause>

  <clause id="16776">
    <literal><![CDATA[
      K(x,T(y,T(z,u)) \ w) = K(x,T(y,z) \ w)
    ]]></literal>
    <justification jstring="[para(7140(a,1),16753(a,1,2,1))].">
      <j1 rule="para" parents="7140 16753"/>
    </justification>
  </clause>

  <clause id="16778">
    <literal><![CDATA[
      K(x,L(T(y,K(z,u)) \ w,v5,v6)) = L(K(x,y \ w),v5,v6)
    ]]></literal>
    <justification jstring="[para(16753(a,1),11889(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16753 11889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16779">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * K(y,z)) \ w) = v5
    ]]></literal>
    <justification jstring="[para(16753(a,1),13920(a,1))].">
      <j1 rule="para" parents="16753 13920"/>
    </justification>
  </clause>

  <clause id="16780">
    <literal><![CDATA[
      K(x,L(T(y,K(z,u)) / w,v5,v6)) = L(K(x,y / w),v5,v6)
    ]]></literal>
    <justification jstring="[para(16754(a,1),11889(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16754 11889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16781">
    <literal><![CDATA[
      K(x,y / T(z,u / w)) = K(x,y / T(z,w \ u))
    ]]></literal>
    <justification jstring="[para(8995(a,1),16757(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8995 16757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16782">
    <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(16757(a,1),13949(a,1))].">
      <j1 rule="para" parents="16757 13949"/>
    </justification>
  </clause>

  <clause id="16783">
    <literal><![CDATA[
      T(T(x,y / z),K(u,z * y)) = T(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(8072,a,16761,a),flip(a)].">
      <j1 rule="hyper" parents="8072 16761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16784">
    <literal><![CDATA[
      T(T(x,y / z),K(u,z * y)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y / z,u)) = w
    ]]></literal>
    <justification jstring="[para(16761(a,1),8072(a,1))].">
      <j1 rule="para" parents="16761 8072"/>
    </justification>
  </clause>

  <clause id="16785">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),(u / z) * y) = T(x,y * (u / z))
    ]]></literal>
    <justification jstring="[para(16761(a,1),13200(a,1,1))].">
      <j1 rule="para" parents="16761 13200"/>
    </justification>
  </clause>

  <clause id="16786">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),(u / z) * y) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (u / z)) = w
    ]]></literal>
    <justification jstring="[para(16761(a,1),13236(a,1,1))].">
      <j1 rule="para" parents="16761 13236"/>
    </justification>
  </clause>

  <clause id="16787">
    <literal><![CDATA[
      K(x * T(y,T(z,u)),w) = K(x * T(y,z),w)
    ]]></literal>
    <justification jstring="[para(7140(a,1),16765(a,1,1,2))].">
      <j1 rule="para" parents="7140 16765"/>
    </justification>
  </clause>

  <clause id="16788">
    <literal><![CDATA[
      K(T(x,y / z) / u,w) = K(T(x,z \ y) / u,w)
    ]]></literal>
    <justification jstring="[para(8995(a,1),16767(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="8995 16767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16789">
    <literal><![CDATA[
      K((x * y) \ z,T(u,y)) = K(((x \ z) * x) / T(y * x,K(w,v5)),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,15539,a,b,16770,a)].">
      <j1 rule="hyper" parents="299 15539 16770"/>
    </justification>
  </clause>

  <clause id="16790">
    <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(11606(a,1),16716(a,1,2))].">
      <j1 rule="para" parents="11606 16716"/>
    </justification>
  </clause>

  <clause id="16791">
    <literal><![CDATA[
      T(x,y * T(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y * z) = v5
    ]]></literal>
    <justification jstring="[para(16562(a,1),16716(a,1))].">
      <j1 rule="para" parents="16562 16716"/>
    </justification>
  </clause>

  <clause id="16792">
    <literal><![CDATA[
      T(x,y \ T(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ z) = v5
    ]]></literal>
    <justification jstring="[para(5850(a,1),16730(a,1,2))].">
      <j1 rule="para" parents="5850 16730"/>
    </justification>
  </clause>

  <clause id="16793">
    <literal><![CDATA[
      T(x,K(y,T(z,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z) * w) = v5
    ]]></literal>
    <justification jstring="[para(7521(a,1),16730(a,1,2))].">
      <j1 rule="para" parents="7521 16730"/>
    </justification>
  </clause>

  <clause id="16794">
    <literal><![CDATA[
      T(x,(K(y,z) * u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,(u * K(y,z)) \ w) = v5
    ]]></literal>
    <justification jstring="[para(11606(a,1),16730(a,1,2))].">
      <j1 rule="para" parents="11606 16730"/>
    </justification>
  </clause>

  <clause id="16795">
    <literal><![CDATA[
      T(x,(T(y,K(z,u)) * w) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,(y * w) * v5) = v6
    ]]></literal>
    <justification jstring="[para(15570(a,1),16730(a,1,2))].">
      <j1 rule="para" parents="15570 16730"/>
    </justification>
  </clause>

  <clause id="16796">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * w) = v5
    ]]></literal>
    <justification jstring="[para(5103(a,1),16749(a,1,2))].">
      <j1 rule="para" parents="5103 16749"/>
    </justification>
  </clause>

  <clause id="16797">
    <literal><![CDATA[
      K(x,y * T(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = v5
    ]]></literal>
    <justification jstring="[para(5853(a,1),16749(a,1,2))].">
      <j1 rule="para" parents="5853 16749"/>
    </justification>
  </clause>

  <clause id="16798">
    <literal><![CDATA[
      K(x,K(K(y,z),u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w) = v5
    ]]></literal>
    <justification jstring="[para(6247(a,2),16749(a,1,2,1))].">
      <j1 rule="para" parents="6247 16749"/>
    </justification>
  </clause>

  <clause id="16799">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) / w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y / w) = v5
    ]]></literal>
    <justification jstring="[para(6323(a,1),16749(a,1,2))].">
      <j1 rule="para" parents="6323 16749"/>
    </justification>
  </clause>

  <clause id="16800">
    <literal><![CDATA[
      K(x,y * K(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(7621(a,1),16749(a,1,2))].">
      <j1 rule="para" parents="7621 16749"/>
    </justification>
  </clause>

  <clause id="16801">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ w) = v5
    ]]></literal>
    <justification jstring="[para(8029(a,1),16749(a,1,2))].">
      <j1 rule="para" parents="8029 16749"/>
    </justification>
  </clause>

  <clause id="16802">
    <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(9181(a,1),16749(a,1,2))].">
      <j1 rule="para" parents="9181 16749"/>
    </justification>
  </clause>

  <clause id="16803">
    <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(11613(a,1),16749(a,1,2))].">
      <j1 rule="para" parents="11613 16749"/>
    </justification>
  </clause>

  <clause id="16804">
    <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(16653(a,1),16749(a,1,2))].">
      <j1 rule="para" parents="16653 16749"/>
    </justification>
  </clause>

  <clause id="16805">
    <literal><![CDATA[
      K(x * K(y,K(z,u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w) = v5
    ]]></literal>
    <justification jstring="[para(7621(a,1),16764(a,1,1))].">
      <j1 rule="para" parents="7621 16764"/>
    </justification>
  </clause>

  <clause id="16806">
    <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(11606(a,1),16764(a,1,1))].">
      <j1 rule="para" parents="11606 16764"/>
    </justification>
  </clause>

  <clause id="16807">
    <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(11613(a,1),16764(a,1,1))].">
      <j1 rule="para" parents="11613 16764"/>
    </justification>
  </clause>

  <clause id="16808">
    <literal><![CDATA[
      K(x / T(y,K(z,u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x / y,w) = v5
    ]]></literal>
    <justification jstring="[para(16558(a,1),16764(a,1,1))].">
      <j1 rule="para" parents="16558 16764"/>
    </justification>
  </clause>

  <clause id="16809">
    <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(16653(a,1),16764(a,1,1))].">
      <j1 rule="para" parents="16653 16764"/>
    </justification>
  </clause>

  <clause id="16810">
    <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(9412(a,1),16800(a,1,2))].">
      <j1 rule="para" parents="9412 16800"/>
    </justification>
  </clause>

  <clause id="16811">
    <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(9496(a,1),16800(a,1,2))].">
      <j1 rule="para" parents="9496 16800"/>
    </justification>
  </clause>

  <clause id="16812">
    <literal><![CDATA[
      K(x * (y * K(z,K(u,w))),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x * y,v5) = v6
    ]]></literal>
    <justification jstring="[para(8915(a,1),16805(a,1,1))].">
      <j1 rule="para" parents="8915 16805"/>
    </justification>
  </clause>

  <clause id="16813">
    <literal><![CDATA[
      T(x,y * (K(z,T(u,w)) * v5)) = T(x,y * (K(z,u) * v5))
    ]]></literal>
    <justification jstring="[para(7521(a,1),16723(a,1,2,2))].">
      <j1 rule="para" parents="7521 16723"/>
    </justification>
  </clause>

  <clause id="16814">
    <literal><![CDATA[
      T(x,y * (z * K(u,T(w,v5)))) = T(x,y * (z * K(u,w)))
    ]]></literal>
    <justification jstring="[para(16653(a,1),16723(a,1,2,2))].">
      <j1 rule="para" parents="16653 16723"/>
    </justification>
  </clause>

  <clause id="16815">
    <literal><![CDATA[
      T(x,K(y,T(z,u)) * w) = T(x,K(z,y) * w)
    ]]></literal>
    <justification jstring="[hyper(299,a,15778,a,b,16728,a),flip(a)].">
      <j1 rule="hyper" parents="299 15778 16728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16816">
    <literal><![CDATA[
      T(x,K(y,T(z,u)) * (y \ w)) = T(x,T(y,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(299,a,15783,a(flip),b,16728,a),flip(a)].">
      <j1 rule="hyper" parents="299 15783 16728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16817">
    <literal><![CDATA[
      T(x,K(y,T(z,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y) * w) = v5
    ]]></literal>
    <justification jstring="[para(16728(a,2),15834(a,1))].">
      <j1 rule="para" parents="16728 15834"/>
    </justification>
  </clause>

  <clause id="16818">
    <literal><![CDATA[
      T(x,y * K(z * u,w)) = T(x,y * K(u * z,w))
    ]]></literal>
    <justification jstring="[para(13173(a,1),16731(a,1,2,2))].">
      <j1 rule="para" parents="13173 16731"/>
    </justification>
  </clause>

  <clause id="16819">
    <literal><![CDATA[
      (x * T(x \ y,z)) / K((x / y) \ 1,z) = T(y,K(z,x \ y))
    ]]></literal>
    <justification jstring="[hyper(65,a,6276,a,b,16734,a)].">
      <j1 rule="hyper" parents="65 6276 16734"/>
    </justification>
  </clause>

  <clause id="16820">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(y,u)) = T(x,T(T(y,z),u))
    ]]></literal>
    <justification jstring="[hyper(861,a,16739,a)].">
      <j1 rule="hyper" parents="861 16739"/>
    </justification>
  </clause>

  <clause id="16822">
    <literal><![CDATA[
      T(x,T(y,z) / T(u,y)) = T(x,u \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(13785,a,16741,a),flip(a)].">
      <j1 rule="hyper" parents="13785 16741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16823">
    <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(16755(a,2),15803(a,1))].">
      <j1 rule="para" parents="16755 15803"/>
    </justification>
  </clause>

  <clause id="16824">
    <literal><![CDATA[
      K(x,y * K(z * u,w)) = K(x,y * K(u * z,w))
    ]]></literal>
    <justification jstring="[para(13173(a,1),16758(a,1,2,2))].">
      <j1 rule="para" parents="13173 16758"/>
    </justification>
  </clause>

  <clause id="16825">
    <literal><![CDATA[
      K(K(x,y / z) * u,w) = K(K(x,z \ y) * u,w)
    ]]></literal>
    <justification jstring="[para(109(a,1),16768(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="109 16768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16826">
    <literal><![CDATA[
      K(x * K(x \ y,x),z) * (x * T(x \ y,u)) = (x * T(x \ y,u)) * K(x,z)
    ]]></literal>
    <justification jstring="[para(16771(a,1),11853(a,1,1))].">
      <j1 rule="para" parents="16771 11853"/>
    </justification>
  </clause>

  <clause id="16827">
    <literal><![CDATA[
      K(x,L(y * T(z,T(u,w)),v5,v6)) = K(L(x,v5,v6),y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(11999,a,16775,a)].">
      <j1 rule="hyper" parents="11999 16775"/>
    </justification>
  </clause>

  <clause id="16829">
    <literal><![CDATA[
      K(x,T(T(y,z) * u,y) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * T(y,z)) \ w) = v5
    ]]></literal>
    <justification jstring="[para(16776(a,1),13920(a,1))].">
      <j1 rule="para" parents="16776 13920"/>
    </justification>
  </clause>

  <clause id="16830">
    <literal><![CDATA[
      T(x,K(y,z) * (T(y,u) \ w)) = T(x,T(T(y,u),z) \ w)
    ]]></literal>
    <justification jstring="[para(5383(a,1),16815(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5383 16815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16831">
    <literal><![CDATA[
      T(T(x,T(T(y,z),u)),w \ (w \ 1)) = T(T(x,K(y,z)),w \ (w \ T(y,u)))
    ]]></literal>
    <justification jstring="[para(16820(a,1),14732(a,1,1))].">
      <j1 rule="para" parents="16820 14732"/>
    </justification>
  </clause>

  <clause id="16832">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(u \ (u \ y),w)) = T(x,T(T(u \ (u \ y),z),w))
    ]]></literal>
    <justification jstring="[para(16296(a,1),16820(a,1,1))].">
      <j1 rule="para" parents="16296 16820"/>
    </justification>
  </clause>

  <clause id="16833">
    <literal><![CDATA[
      T(x,y * ((z \ u) * K(w,z))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (T(z,w) \ u)) = v5
    ]]></literal>
    <justification jstring="[para(8253(a,1),16791(a,1,2,2))].">
      <j1 rule="para" parents="8253 16791"/>
    </justification>
  </clause>

  <clause id="16834">
    <literal><![CDATA[
      T(x,y * (K(z,u) / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (w \ K(z,u))) = v5
    ]]></literal>
    <justification jstring="[para(15857(a,1),16791(a,1))].">
      <j1 rule="para" parents="15857 16791"/>
    </justification>
  </clause>

  <clause id="16835">
    <literal><![CDATA[
      T(x,y \ (K(z,u) * (w * z))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (w * T(z,u))) = v5
    ]]></literal>
    <justification jstring="[para(8249(a,1),16792(a,1,2,2))].">
      <j1 rule="para" parents="8249 16792"/>
    </justification>
  </clause>

  <clause id="16836">
    <literal><![CDATA[
      K(x,(y * (z * K(y,u))) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(T(y,u) * z) * w) = v5
    ]]></literal>
    <justification jstring="[para(8370(a,1),16796(a,1,2,1))].">
      <j1 rule="para" parents="8370 16796"/>
    </justification>
  </clause>

  <clause id="16837">
    <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(13818(a,1),16796(a,1))].">
      <j1 rule="para" parents="13818 16796"/>
    </justification>
  </clause>

  <clause id="16838">
    <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(8249(a,1),16797(a,1,2,2))].">
      <j1 rule="para" parents="8249 16797"/>
    </justification>
  </clause>

  <clause id="16839">
    <literal><![CDATA[
      K(x,y * ((z \ u) * K(w,z))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (T(z,w) \ u)) = v5
    ]]></literal>
    <justification jstring="[para(8253(a,1),16797(a,1,2,2))].">
      <j1 rule="para" parents="8253 16797"/>
    </justification>
  </clause>

  <clause id="16840">
    <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(8370(a,1),16797(a,1,2,2))].">
      <j1 rule="para" parents="8370 16797"/>
    </justification>
  </clause>

  <clause id="16841">
    <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(7279(a,1),16799(a,1,2,1))].">
      <j1 rule="para" parents="7279 16799"/>
    </justification>
  </clause>

  <clause id="16842">
    <literal><![CDATA[
      K(x,(L(K(y,z),u,w) * v5) \ v6) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,(v5 * L(K(y,z),u,w)) \ v6) = v7
    ]]></literal>
    <justification jstring="[para(10358(a,1),16801(a,1,2,1))].">
      <j1 rule="para" parents="10358 16801"/>
    </justification>
  </clause>

  <clause id="16843">
    <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(8252(a,1),16808(a,1,1,2))].">
      <j1 rule="para" parents="8252 16808"/>
    </justification>
  </clause>

  <clause id="16844">
    <literal><![CDATA[
      T(x,y * (z * (u * (w * K(u,v5))))) = T(x,y * (z * (T(u,v5) * w)))
    ]]></literal>
    <justification jstring="[para(8370(a,1),16727(a,1,2,2,2))].">
      <j1 rule="para" parents="8370 16727"/>
    </justification>
  </clause>

  <clause id="16845">
    <literal><![CDATA[
      T(T(x,K(y,(z \ 1) * u)),(z * (u * (z \ (1 / z)))) \ y) = T(x,y / T((z \ 1) * u,z \ (z \ 1)))
    ]]></literal>
    <justification jstring="[para(14726(a,1),16735(a,1,2,1))].">
      <j1 rule="para" parents="14726 16735"/>
    </justification>
  </clause>

  <clause id="16846">
    <literal><![CDATA[
      (K(x,T(y,z)) * u) * K(y,T(x,z)) = T(u,K(x,y))
    ]]></literal>
    <justification jstring="[para(7571(a,1),16736(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7571 16736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16848">
    <literal><![CDATA[
      T(x,T(y,z * (u * z)) * (z * (z * u))) = T(x,(z * (z * u)) * y)
    ]]></literal>
    <justification jstring="[para(13693(a,1),16743(a,1,2,1))].">
      <j1 rule="para" parents="13693 16743"/>
    </justification>
  </clause>

  <clause id="16849">
    <literal><![CDATA[
      K(x,y * (z * T(u,w / v5))) = K(x,y * (z * T(u,v5 \ w)))
    ]]></literal>
    <justification jstring="[para(8995(a,1),16760(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="8995 16760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16850">
    <literal><![CDATA[
      K((K(x,y) * (z / y)) \ u,w) = K((z / T(y,x)) \ u,w)
    ]]></literal>
    <justification jstring="[para(7189(a,1),16769(a,2,1,1))].">
      <j1 rule="para" parents="7189 16769"/>
    </justification>
  </clause>

  <clause id="16851">
    <literal><![CDATA[
      T(T(x,y / T(z * u,z)),K(w,(u * z) * y)) = T(x,T(y / T(z * u,z),w))
    ]]></literal>
    <justification jstring="[para(13856(a,1),16783(a,1,2))].">
      <j1 rule="para" parents="13856 16783"/>
    </justification>
  </clause>

  <clause id="16852">
    <literal><![CDATA[
      K(x,y * K(z * u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u * z,w) * y) = v5
    ]]></literal>
    <justification jstring="[para(16824(a,1),16407(a,1))].">
      <j1 rule="para" parents="16824 16407"/>
    </justification>
  </clause>

  <clause id="16853">
    <literal><![CDATA[
      T(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,T(z,v5)) * u) = w
    ]]></literal>
    <justification jstring="[para(8104(a,1),16793(a,1,2,1))].">
      <j1 rule="para" parents="8104 16793"/>
    </justification>
  </clause>

  <clause id="16854">
    <literal><![CDATA[
      K(x,T(T(y,z) * u,y) * w) = K(x,(u * T(y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(16802,a,13856,a)].">
      <j1 rule="hyper" parents="16802 13856"/>
    </justification>
  </clause>

  <clause id="16855">
    <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(13197(a,1),16802(a,1,2,1))].">
      <j1 rule="para" parents="13197 16802"/>
    </justification>
  </clause>

  <clause id="16856">
    <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(13173(a,1),16804(a,1,2,2))].">
      <j1 rule="para" parents="13173 16804"/>
    </justification>
  </clause>

  <clause id="16857">
    <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(109(a,1),16809(a,1,1,2,2))].">
      <j1 rule="para" parents="109 16809"/>
    </justification>
  </clause>

  <clause id="16858">
    <literal><![CDATA[
      K(x * (T(y,K(z,u)) * w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x * (y * w),v5) = v6
    ]]></literal>
    <justification jstring="[para(5843(a,1),16812(a,1,1,2))].">
      <j1 rule="para" parents="5843 16812"/>
    </justification>
  </clause>

  <clause id="16859">
    <literal><![CDATA[
      T(x * T(y,x * K(z,u)),K(z,u)) = y * T(x,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(8068,a,16518,a)].">
      <j1 rule="hyper" parents="8068 16518"/>
    </justification>
  </clause>

  <clause id="16861">
    <literal><![CDATA[
      K(x,T(1 / (y * z),y)) = K(x,1 / (z * y))
    ]]></literal>
    <justification jstring="[hyper(299,a,5668,a(flip),b,16528,a),flip(a)].">
      <j1 rule="hyper" parents="299 5668 16528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16862">
    <literal><![CDATA[
      K(x,y / (y * (y * z))) = K(x,1 / (z * y))
    ]]></literal>
    <justification jstring="[hyper(8442,a,16861,a)].">
      <j1 rule="hyper" parents="8442 16861"/>
    </justification>
  </clause>

  <clause id="16864">
    <literal><![CDATA[
      K(x,y * T(z \ u,z)) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[hyper(16692,a,16534,a)].">
      <j1 rule="hyper" parents="16692 16534"/>
    </justification>
  </clause>

  <clause id="16865">
    <literal><![CDATA[
      K(x,K(y,z) \ (u * y)) = K(x,u * (z * (y / z)))
    ]]></literal>
    <justification jstring="[hyper(65,a,13939,a(flip),b,16537,a)].">
      <j1 rule="hyper" parents="65 13939 16537"/>
    </justification>
  </clause>

  <clause id="16866">
    <literal><![CDATA[
      K(x,y * (z * (u / z))) = K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[hyper(16692,a,16865,a),flip(a)].">
      <j1 rule="hyper" parents="16692 16865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16867">
    <literal><![CDATA[
      K(x,y * (z * (u / z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(u,z)) = w
    ]]></literal>
    <justification jstring="[para(16865(a,1),16692(a,1))].">
      <j1 rule="para" parents="16865 16692"/>
    </justification>
  </clause>

  <clause id="16868">
    <literal><![CDATA[
      K(x,L(T(y,z / u),w,v5)) = K(x,L(T(y,u \ z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(11995,a,16541,a),flip(a)].">
      <j1 rule="hyper" parents="11995 16541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16869">
    <literal><![CDATA[
      K(x,y) \ K(L(x,z,u),y) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,14886,a(flip),b,16570,a),flip(a)].">
      <j1 rule="hyper" parents="65 14886 16570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16870">
    <literal><![CDATA[
      K(x,y / ((z * u) / z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / T(u,z)) = w
    ]]></literal>
    <justification jstring="[para(16656(a,1),13929(a,1))].">
      <j1 rule="para" parents="16656 13929"/>
    </justification>
  </clause>

  <clause id="16872">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z,x * T(y,u * (w * u))) = K(z,T(y,(u * w) * u) * x)
    ]]></literal>
    <justification jstring="[para(13693(a,1),16672(a,1,2,2,2))].">
      <j1 rule="para" parents="13693 16672"/>
    </justification>
  </clause>

  <clause id="16873">
    <literal><![CDATA[
      K(x,(y * y) * (z * (u \ 1))) = K(x,z * (u \ (y * y)))
    ]]></literal>
    <justification jstring="[para(33(a,1),16710(a,1,2))].">
      <j1 rule="para" parents="33 16710"/>
    </justification>
  </clause>

  <clause id="16874">
    <literal><![CDATA[
      T(x,y * (K(z / u,u) * (w * (z / u)))) = T(x,y * (w * (u \ z)))
    ]]></literal>
    <justification jstring="[para(109(a,1),16744(a,2,2,2,2))].">
      <j1 rule="para" parents="109 16744"/>
    </justification>
  </clause>

  <clause id="16875">
    <literal><![CDATA[
      T(x,T(y,z) * (z \ u)) = T(x,y * (T(z,y) \ u))
    ]]></literal>
    <justification jstring="[hyper(16462,a,16745,a)].">
      <j1 rule="hyper" parents="16462 16745"/>
    </justification>
  </clause>

  <clause id="16876">
    <literal><![CDATA[
      T(x,y * (T(z,y) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z) * (z \ u)) = w
    ]]></literal>
    <justification jstring="[para(16745(a,1),16462(a,1))].">
      <j1 rule="para" parents="16745 16462"/>
    </justification>
  </clause>

  <clause id="16877">
    <literal><![CDATA[
      T(x,T((y \ z) \ 1,u) * (u \ w)) = T(x,((y \ z) \ 1) * (T(u,z \ y) \ w))
    ]]></literal>
    <justification jstring="[para(7037(a,1),16875(a,2,2,2,1))].">
      <j1 rule="para" parents="7037 16875"/>
    </justification>
  </clause>

  <clause id="16878">
    <literal><![CDATA[
      T(x,((1 / y) * (z / y)) * (T(z,(1 / y) * (z / y)) \ u)) = T(x,T(y \ 1,y \ z) * (y \ (z * (z \ u))))
    ]]></literal>
    <justification jstring="[para(15727(a,2),16875(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15727 16875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16879">
    <literal><![CDATA[
      T(x,(y * K(z / u,y)) * (T(u / z,y * K(z / u,y)) \ w)) = T(x,T(y,(z \ u) * (z \ u)) * ((u / z) \ w))
    ]]></literal>
    <justification jstring="[para(15858(a,1),16875(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="15858 16875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16880">
    <literal><![CDATA[
      T(x * K(y,K(z,u)),w) = T(x,w) * K(y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(5398,a,16772,a),flip(a)].">
      <j1 rule="hyper" parents="5398 16772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16881">
    <literal><![CDATA[
      T(K(x,y) * K(z,K(u,w)),v5) = K(x,T(y,v5)) * K(z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(8394,a,16880,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="8394 16880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16882">
    <literal><![CDATA[
      T(K(x,L(y,z,u)) * K(w,K(v5,v6)),v7) = K(x,L(T(y,v7),z,u)) * K(w,K(v5,v6))
    ]]></literal>
    <justification jstring="[para(7506(a,2),16880(a,2,1))].">
      <j1 rule="para" parents="7506 16880"/>
    </justification>
  </clause>

  <clause id="16883">
    <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(16880(a,2),8018(a,1,1))].">
      <j1 rule="para" parents="16880 8018"/>
    </justification>
  </clause>

  <clause id="16885">
    <literal><![CDATA[
      K(x,L(T(y,K(z,u)) \ w,v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y \ w,v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(16778(a,2),11995(a,1))].">
      <j1 rule="para" parents="16778 11995"/>
    </justification>
  </clause>

  <clause id="16886">
    <literal><![CDATA[
      K(x,L(T(y,K(z,u)) / w,v5,v6)) = K(x,L(y / w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(299,a,11889,a(flip),b,16780,a),flip(a)].">
      <j1 rule="hyper" parents="299 11889 16780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16887">
    <literal><![CDATA[
      K(x,L(T(y,K(z,u)) / w,v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y / w,v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(16780(a,2),11995(a,1))].">
      <j1 rule="para" parents="16780 11995"/>
    </justification>
  </clause>

  <clause id="16888">
    <literal><![CDATA[
      T(x,y * (K(z,T(u,w)) * (u \ v5))) = T(x,y * (T(u,z) \ v5))
    ]]></literal>
    <justification jstring="[para(5383(a,1),16813(a,2,2,2))].">
      <j1 rule="para" parents="5383 16813"/>
    </justification>
  </clause>

  <clause id="16889">
    <literal><![CDATA[
      T(T(x,K(y,z * K(u,T(w,v5)))),(z * K(u,T(w,v5))) * y) = T(x,y * (z * K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(13254,a,16814,a)].">
      <j1 rule="hyper" parents="13254 16814"/>
    </justification>
  </clause>

  <clause id="16890">
    <literal><![CDATA[
      T(x,K(y,z) * (T(z * y,u) \ w)) = T(x,T(T(z * y,u),z) \ w)
    ]]></literal>
    <justification jstring="[hyper(15931,a,16830,a)].">
      <j1 rule="hyper" parents="15931 16830"/>
    </justification>
  </clause>

  <clause id="16891">
    <literal><![CDATA[
      K((T(x,y) / y) \ z,u) = K((x / T(y,x)) \ z,u)
    ]]></literal>
    <justification jstring="[para(5531(a,1),16850(a,1,1,1))].">
      <j1 rule="para" parents="5531 16850"/>
    </justification>
  </clause>

  <clause id="16892">
    <literal><![CDATA[
      K(x,L(T(y,z / u),w,v5)) = K(x,L(T(y,u * z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(299,a,16314,a(flip),b,16868,a),flip(a)].">
      <j1 rule="hyper" parents="299 16314 16868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16893">
    <literal><![CDATA[
      K(x,y * (y * (z * (u \ 1)))) = K(x,z * (u \ (y * y)))
    ]]></literal>
    <justification jstring="[hyper(14547,a,16873,a)].">
      <j1 rule="hyper" parents="14547 16873"/>
    </justification>
  </clause>

  <clause id="16894">
    <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(7140(a,1),16886(a,1,2,1,1))].">
      <j1 rule="para" parents="7140 16886"/>
    </justification>
  </clause>

  <clause id="16895">
    <literal><![CDATA[
      K(x,L(T(((y / z) \ 1) \ u,y * z),w,v5)) = K(x,L(u / ((y / z) \ 1),w,v5))
    ]]></literal>
    <justification jstring="[hyper(12018,a,16892,a),flip(a)].">
      <j1 rule="hyper" parents="12018 16892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16896">
    <literal><![CDATA[
      K(x,L(T((y / z) \ u,z * y),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(u / (y / z),w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(16892(a,1),12001(a,1))].">
      <j1 rule="para" parents="16892 12001"/>
    </justification>
  </clause>

  <clause id="16897">
    <literal><![CDATA[
      K(x,(y * ((y \ 1) \ z)) / u) = K(x,z * (u \ (y * y)))
    ]]></literal>
    <justification jstring="[hyper(65,a,15154,a,b,16893,a)].">
      <j1 rule="hyper" parents="65 15154 16893"/>
    </justification>
  </clause>

  <clause id="16898">
    <literal><![CDATA[
      K(x,K(y,L(z / u,u,w))) = K(x,K(y,(w * z) / (w * u)))
    ]]></literal>
    <justification jstring="[hyper(299,a,16335,a,b,16348,a),flip(a)].">
      <j1 rule="hyper" parents="299 16335 16348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16899">
    <literal><![CDATA[
      K(x,K((y \ z) / u,L(w,u,y))) = K(x,K(w,z / (y * u)))
    ]]></literal>
    <justification jstring="[hyper(16508,a,16509,a)].">
      <j1 rule="hyper" parents="16508 16509"/>
    </justification>
  </clause>

  <clause id="16902">
    <literal><![CDATA[
      K(x,y / (z * K(u,w))) = K(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(16782,a,14313,a)].">
      <j1 rule="hyper" parents="16782 14313"/>
    </justification>
  </clause>

  <clause id="16903">
    <literal><![CDATA[
      x * K(x,y * (z \ K(u,w))) = T(x,y / (z * K(w,u)))
    ]]></literal>
    <justification jstring="[para(16902(a,1),5083(a,2,2)),flip(a)].">
      <j1 rule="para" parents="16902 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16904">
    <literal><![CDATA[
      K(x,y * ((z * u) \ K(w,u))) = K(x,y / (z * T(u,w)))
    ]]></literal>
    <justification jstring="[para(6832(a,1),16902(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6832 16902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16905">
    <literal><![CDATA[
      K(x,y / (z * (u * K(w,u)))) = K(x,y * ((z * u) \ K(u,w)))
    ]]></literal>
    <justification jstring="[para(6816(a,1),16902(a,1,2,2))].">
      <j1 rule="para" parents="6816 16902"/>
    </justification>
  </clause>

  <clause id="16906">
    <literal><![CDATA[
      K(x,y * ((z / u) \ K(u,w))) = K(x,y / (z / T(u,w)))
    ]]></literal>
    <justification jstring="[para(7189(a,1),16902(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7189 16902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16907">
    <literal><![CDATA[
      T(x,y / (z * K(u,w))) = T(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(5087,a,16903,a),flip(a)].">
      <j1 rule="hyper" parents="5087 16903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16908">
    <literal><![CDATA[
      T(x,y / (z * K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (z \ K(w,u))) = v5
    ]]></literal>
    <justification jstring="[para(16903(a,1),5087(a,1))].">
      <j1 rule="para" parents="16903 5087"/>
    </justification>
  </clause>

  <clause id="16909">
    <literal><![CDATA[
      T(x,(y * K(z,u)) \ w) = T(x,(y \ K(u,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(16794,a,14386,a)].">
      <j1 rule="hyper" parents="16794 14386"/>
    </justification>
  </clause>

  <clause id="16912">
    <literal><![CDATA[
      K(x * (T(T(y,K(z,u)),w) * v5),v6) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x * (T(y,w) * v5),v6) = v7
    ]]></literal>
    <justification jstring="[para(23(a,1),16858(a,1,1,2,1))].">
      <j1 rule="para" parents="23 16858"/>
    </justification>
  </clause>

  <clause id="16913">
    <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),16898(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="11 16898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16914">
    <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),16899(a,1,2,1,1))].">
      <j1 rule="para" parents="22 16899"/>
    </justification>
  </clause>

  <clause id="16917">
    <literal><![CDATA[
      T((x * y) / x,z * (x \ z)) = T(y,(x \ z) * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(299,a,16152,a(flip),b,16244,a),flip(a)].">
      <j1 rule="hyper" parents="299 16152 16244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16918">
    <literal><![CDATA[
      T((x * y) / x,z * (x \ z)) = T(y,(x \ T(z,u)) * (x \ T(z,u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,16603,a(flip),b,16917,a)].">
      <j1 rule="hyper" parents="65 16603 16917"/>
    </justification>
  </clause>

  <clause id="16919">
    <literal><![CDATA[
      K(x,K(y,z * u)) * K(x,y / (z \ u)) = K(x,T(u / z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(299,a,13821,a,b,16258,a),flip(a)].">
      <j1 rule="hyper" parents="299 13821 16258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16920">
    <literal><![CDATA[
      T(T(x,K(y,z)),(u * (u / y)) \ z) = T(x,z / (u * (u / y)))
    ]]></literal>
    <justification jstring="[para(8050(a,1),16291(a,1,1))].">
      <j1 rule="para" parents="8050 16291"/>
    </justification>
  </clause>

  <clause id="16921">
    <literal><![CDATA[
      T(T(x,K(y,z)),(u \ (y / u)) * z) = T(x,z * (u \ (y / u)))
    ]]></literal>
    <justification jstring="[para(8050(a,1),16324(a,1,1))].">
      <j1 rule="para" parents="8050 16324"/>
    </justification>
  </clause>

  <clause id="16922">
    <literal><![CDATA[
      K((x * y) / (K(z,u) * y),w) = K((y * K(z,u)) \ (y * x),w)
    ]]></literal>
    <justification jstring="[para(9(a,1),16382(a,1,1,1,1))].">
      <j1 rule="para" parents="9 16382"/>
    </justification>
  </clause>

  <clause id="16923">
    <literal><![CDATA[
      T(T(x,x \ 1),y) * K(x * z,u) = (T(x,y) \ K(u,z * x)) \ 1
    ]]></literal>
    <justification jstring="[hyper(299,a,14620,a(flip),b,16590,a),flip(a)].">
      <j1 rule="hyper" parents="299 14620 16590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16924">
    <literal><![CDATA[
      K(x,L(K(y,z) * (u * y),w,v5)) = K(x,L(u * T(y,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(299,a,11929,a(flip),b,16690,a),flip(a)].">
      <j1 rule="hyper" parents="299 11929 16690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16926">
    <literal><![CDATA[
      K(x,K(y,L(y,z,u) * w)) = K(y,K(x,w))
    ]]></literal>
    <justification jstring="[hyper(36,a,7958,a,b,16697,a)].">
      <j1 rule="hyper" parents="36 7958 16697"/>
    </justification>
  </clause>

  <clause id="16927">
    <literal><![CDATA[
      K(x,K(y,L(y,z,u) * w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(299,a,7983,a,b,16926,a),flip(a)].">
      <j1 rule="hyper" parents="299 7983 16926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16928">
    <literal><![CDATA[
      K(x,K(y,z * L(y,u,w))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(16574,a,16927,a)].">
      <j1 rule="hyper" parents="16574 16927"/>
    </justification>
  </clause>

  <clause id="16929">
    <literal><![CDATA[
      K(x,K(y,z * (u * y))) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(94(a,1),16928(a,1,2,2))].">
      <j1 rule="para" parents="94 16928"/>
    </justification>
  </clause>

  <clause id="16930">
    <literal><![CDATA[
      K(x,K(y / z,u * z)) = K(x,K(y / z,u * y))
    ]]></literal>
    <justification jstring="[para(11334(a,1),16929(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11334 16929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16931">
    <literal><![CDATA[
      K(x,K(y / z,(z \ u) * y)) = K(x,K(u,y / z))
    ]]></literal>
    <justification jstring="[hyper(65,a,16352,a(flip),b,16930,a),flip(a)].">
      <j1 rule="hyper" parents="65 16352 16930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16933">
    <literal><![CDATA[
      (x * K((x \ y) \ 1,z)) / K((y / x) \ 1,z) = T(x,K(z,y \ x))
    ]]></literal>
    <justification jstring="[para(5328(a,1),16819(a,1,1))].">
      <j1 rule="para" parents="5328 16819"/>
    </justification>
  </clause>

  <clause id="16934">
    <literal><![CDATA[
      K(x,L(y * T(z,T(u,w)),v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y * T(z,u),v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(16827(a,2),11999(a,1))].">
      <j1 rule="para" parents="16827 11999"/>
    </justification>
  </clause>

  <clause id="16935">
    <literal><![CDATA[
      T(K(x,y) * K(z,K(u,w)),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(z,K(u,w)) * K(x,T(y,v5)) = v6
    ]]></literal>
    <justification jstring="[para(16881(a,2),16355(a,1))].">
      <j1 rule="para" parents="16881 16355"/>
    </justification>
  </clause>

  <clause id="16936">
    <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(16480(a,1),16883(a,1,1,1))].">
      <j1 rule="para" parents="16480 16883"/>
    </justification>
  </clause>

  <clause id="16937">
    <literal><![CDATA[
      T(x,y * (T(z,T(u,w)) \ v5)) = T(x,y * (T(z,u) \ v5))
    ]]></literal>
    <justification jstring="[para(7574(a,1),16888(a,1,2,2))].">
      <j1 rule="para" parents="7574 16888"/>
    </justification>
  </clause>

  <clause id="16938">
    <literal><![CDATA[
      T(x,y * (T(z,u * w) \ v5)) = T(x,y * (T(z,w * u) \ v5))
    ]]></literal>
    <justification jstring="[para(13197(a,1),16937(a,1,2,2,1))].">
      <j1 rule="para" parents="13197 16937"/>
    </justification>
  </clause>

  <clause id="16939">
    <literal><![CDATA[
      T(T(x,K(y,K(z,z \ (y / z)) * u)),((y / z) / z) * u) = T(x,(K(z,z \ (y / z)) * u) * (z \ (y / z)))
    ]]></literal>
    <justification jstring="[para(5714(a,1),16921(a,1,2))].">
      <j1 rule="para" parents="5714 16921"/>
    </justification>
  </clause>

  <clause id="16940">
    <literal><![CDATA[
      K(x,y \ (z * (u * (z \ y)))) = K(x,L(T(u,z * y),y,z))
    ]]></literal>
    <justification jstring="[hyper(15000,a,16315,a),flip(a)].">
      <j1 rule="hyper" parents="15000 16315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16941">
    <literal><![CDATA[
      x * R(K(y,K(z,u)),w,w \ x) = (K(u,K(y,z)) * w) * (w \ x)
    ]]></literal>
    <justification jstring="[para(7989(a,1),16356(a,2,1,1))].">
      <j1 rule="para" parents="7989 16356"/>
    </justification>
  </clause>

  <clause id="16943">
    <literal><![CDATA[
      T(x,K(y,L((z / u) / w,w,u))) != x * v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,(w * u) \ z)) = v5
    ]]></literal>
    <justification jstring="[para(16498(a,2),45(a,1))].">
      <j1 rule="para" parents="16498 45"/>
    </justification>
  </clause>

  <clause id="16944">
    <literal><![CDATA[
      K(K(x,x \ y) * (z * y),u) = K(z * T(y,x),u)
    ]]></literal>
    <justification jstring="[hyper(16622,a,15915,a)].">
      <j1 rule="hyper" parents="16622 15915"/>
    </justification>
  </clause>

  <clause id="16945">
    <literal><![CDATA[
      T(T(x,K(y,z)),((u * u) / z) * y) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * ((u * u) / z)) = w
    ]]></literal>
    <justification jstring="[para(16286(a,1),16786(a,1,1))].">
      <j1 rule="para" parents="16286 16786"/>
    </justification>
  </clause>

  <clause id="16946">
    <literal><![CDATA[
      K(x,(T(y,z) * T(z,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(T(z,u) * y) * w) = v5
    ]]></literal>
    <justification jstring="[para(16001(a,2),16836(a,1))].">
      <j1 rule="para" parents="16001 16836"/>
    </justification>
  </clause>

  <clause id="16947">
    <literal><![CDATA[
      K(x,K(y,z) * T(u * y,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(w,u * y) * (u * T(y,z))) = v5
    ]]></literal>
    <justification jstring="[para(16566(a,1),16838(a,1))].">
      <j1 rule="para" parents="16566 16838"/>
    </justification>
  </clause>

  <clause id="16948">
    <literal><![CDATA[
      K(x,y * (z * (u * K(w,z)))) = K(x,y * (T(z,w) * u))
    ]]></literal>
    <justification jstring="[hyper(16840,a,15965,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="16840 15965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16949">
    <literal><![CDATA[
      K(x,y * (z * (u * K(w,z)))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (T(z,w) * u)) = v5
    ]]></literal>
    <justification jstring="[para(15965(a,2),16840(a,1))].">
      <j1 rule="para" parents="15965 16840"/>
    </justification>
  </clause>

  <clause id="16950">
    <literal><![CDATA[
      K(x,y * (T(z,u) * (w / z))) = K(x,y * (z * (w / T(z,u))))
    ]]></literal>
    <justification jstring="[para(7189(a,1),16948(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="7189 16948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16951">
    <literal><![CDATA[
      K(x,L(T(y,T(z,u)) \ w,v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(y,z) \ w,v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(7140(a,1),16885(a,1,2,1,1))].">
      <j1 rule="para" parents="7140 16885"/>
    </justification>
  </clause>

  <clause id="16955">
    <literal><![CDATA[
      x * K(y,K(z,R(u,w,w \ x))) = (K(z,K(u,y)) * w) * (w \ x)
    ]]></literal>
    <justification jstring="[para(9323(a,1),16941(a,1,2))].">
      <j1 rule="para" parents="9323 16941"/>
    </justification>
  </clause>

  <clause id="16956">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * (u \ K(w,z)) = K(w,z) * K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(12761(a,1),16955(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12761 16955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16957">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * (u \ K(y,z)) = T(K(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(299,a,7996,a(flip),b,16956,a),flip(a)].">
      <j1 rule="hyper" parents="299 7996 16956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16958">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * (u \ K(x,y)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(7989(a,2),16957(a,1,1,1))].">
      <j1 rule="para" parents="7989 16957"/>
    </justification>
  </clause>

  <clause id="16959">
    <literal><![CDATA[
      K(x,T(y,z)) / (u \ K(x,y)) = K(x,K(y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(120,a,7489,a,b,16958,a)].">
      <j1 rule="hyper" parents="120 7489 16958"/>
    </justification>
  </clause>

  <clause id="16960">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,y) / u) = K(x,T(y,z)) / u
    ]]></literal>
    <justification jstring="[para(79(a,1),16959(a,1,2)),flip(a)].">
      <j1 rule="para" parents="79 16959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16961">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,T(y,z)) / u) = K(x,y) / u
    ]]></literal>
    <justification jstring="[hyper(8030,a,16960,a)].">
      <j1 rule="hyper" parents="8030 16960"/>
    </justification>
  </clause>

  <clause id="16962">
    <literal><![CDATA[
      (K(x,T(y,z)) / u) * K(x,K(y,z)) = T(K(x,y) / u,K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(16961(a,1),7279(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16961 7279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16963">
    <literal><![CDATA[
      (T(x,K(y,z)) / (K(y,z) \ 1)) / T(1 / K(y,z),K(y,z) * x) = x * (K(y,z) * K(y,z))
    ]]></literal>
    <justification jstring="[para(5545(a,1),16213(a,1,1,1))].">
      <j1 rule="para" parents="5545 16213"/>
    </justification>
  </clause>

  <clause id="16965">
    <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(5426(a,1),16222(a,2,2,2))].">
      <j1 rule="para" parents="5426 16222"/>
    </justification>
  </clause>

  <clause id="16966">
    <literal><![CDATA[
      K(x,L(((y \ 1) \ z) / y,u,w)) = K(x,L((y \ z) * y,u,w))
    ]]></literal>
    <justification jstring="[hyper(14791,a,16234,a)].">
      <j1 rule="hyper" parents="14791 16234"/>
    </justification>
  </clause>

  <clause id="16967">
    <literal><![CDATA[
      K(x,L((y \ z) * y,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(((1 / y) \ z) / y,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(16966(a,1),15163(a,1))].">
      <j1 rule="para" parents="16966 15163"/>
    </justification>
  </clause>

  <clause id="16968">
    <literal><![CDATA[
      T(x,y * (y / (z * ((z \ y) \ 1)))) = T(x,(z \ y) * ((z \ y) * y))
    ]]></literal>
    <justification jstring="[hyper(299,a,14216,a(flip),b,16241,a),flip(a)].">
      <j1 rule="hyper" parents="299 14216 16241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16969">
    <literal><![CDATA[
      K(x,(y * ((y \ 1) \ z)) / (y * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,z / ((y \ 1) * u)) = w
    ]]></literal>
    <justification jstring="[para(16245(a,1),8327(a,1))].">
      <j1 rule="para" parents="16245 8327"/>
    </justification>
  </clause>

  <clause id="16970">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z,x \ (u * (u * y))) = K(z,(u * (u * y)) / x)
    ]]></literal>
    <justification jstring="[para(8004(a,1),16263(a,1,1))].">
      <j1 rule="para" parents="8004 16263"/>
    </justification>
  </clause>

  <clause id="16971">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z,(u \ (u \ x)) \ y) = K(z,y / (u \ (u \ x)))
    ]]></literal>
    <justification jstring="[para(7989(a,1),16265(a,1,1))].">
      <j1 rule="para" parents="7989 16265"/>
    </justification>
  </clause>

  <clause id="16972">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y * (z \ u)) = T(x,(T(u,z) / z) * y)
    ]]></literal>
    <justification jstring="[hyper(13882,a,16278,a)].">
      <j1 rule="hyper" parents="13882 16278"/>
    </justification>
  </clause>

  <clause id="16973">
    <literal><![CDATA[
      T(x,(T(y,z) / z) * u) = T(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(16277,a,16972,a),flip(a)].">
      <j1 rule="hyper" parents="16277 16972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16974">
    <literal><![CDATA[
      T(x,(T(y,z) / z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z \ y) * u) = w
    ]]></literal>
    <justification jstring="[para(16972(a,1),16277(a,1))].">
      <j1 rule="para" parents="16972 16277"/>
    </justification>
  </clause>

  <clause id="16975">
    <literal><![CDATA[
      T(x,((y \ z) / y) * u) = T(x,(y \ (z / y)) * u)
    ]]></literal>
    <justification jstring="[para(109(a,1),16973(a,1,2,1,1))].">
      <j1 rule="para" parents="109 16973"/>
    </justification>
  </clause>

  <clause id="16979">
    <literal><![CDATA[
      (x * y) * K(z,L(T(u,y * x),x,y)) = (K(z,u) * x) * y
    ]]></literal>
    <justification jstring="[hyper(299,a,15496,a(flip),b,16307,a),flip(a)].">
      <j1 rule="hyper" parents="299 15496 16307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16980">
    <literal><![CDATA[
      T(x,y) * K(z,T(u,y * x)) = T(K(z,u) * x,y)
    ]]></literal>
    <justification jstring="[hyper(235,a,16979,a(flip),b,11915,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="235 16979 11915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16983">
    <literal><![CDATA[
      T(K(x,y * y) * z,u) = T(z,u) * K(x,y * y)
    ]]></literal>
    <justification jstring="[para(16205(a,1),16980(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16205 16980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16984">
    <literal><![CDATA[
      T(K(x,y * y) * z,u) = K(x,y * y) * T(z,u)
    ]]></literal>
    <justification jstring="[hyper(16211,a,16983,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="16211 16983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16985">
    <literal><![CDATA[
      x * T(K(y,z * z) * T(u,x),w) = T(u,w) * (x * K(y,z * z))
    ]]></literal>
    <justification jstring="[para(16983(a,2),12045(a,1,2))].">
      <j1 rule="para" parents="16983 12045"/>
    </justification>
  </clause>

  <clause id="16986">
    <literal><![CDATA[
      K(x,y \ ((z \ u) \ u)) = K(x,K(z,y)) * K(x,T(z,u) / y)
    ]]></literal>
    <justification jstring="[para(14651(a,1),16349(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14651 16349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16988">
    <literal><![CDATA[
      K(x,y) * ((K(x * y,z) * y) * x) = x * (K(y * x,z) * y)
    ]]></literal>
    <justification jstring="[para(107(a,1),16409(a,1,2,1,1,1))].">
      <j1 rule="para" parents="107 16409"/>
    </justification>
  </clause>

  <clause id="16990">
    <literal><![CDATA[
      L(T(K(x * y,z) * y,x),x,K(x,y)) = T(x,y) \ (x * (K(y * x,z) * y))
    ]]></literal>
    <justification jstring="[para(16988(a,1),5170(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16988 5170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16991">
    <literal><![CDATA[
      T(K(x,y) * z,z) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(16464,a,13969,a)].">
      <j1 rule="hyper" parents="16464 13969"/>
    </justification>
  </clause>

  <clause id="16992">
    <literal><![CDATA[
      (K(x,y) * z) * z = z * (z * K(x,y))
    ]]></literal>
    <justification jstring="[para(16991(a,1),107(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16991 107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16993">
    <literal><![CDATA[
      T(x * T(x \ y,z),y) = y * K((x / y) \ 1,z)
    ]]></literal>
    <justification jstring="[para(5329(a,1),16991(a,1,1))].">
      <j1 rule="para" parents="5329 16991"/>
    </justification>
  </clause>

  <clause id="16994">
    <literal><![CDATA[
      x \ (K(y,z) * (x * x)) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(14173,a,16992,a)].">
      <j1 rule="hyper" parents="14173 16992"/>
    </justification>
  </clause>

  <clause id="16995">
    <literal><![CDATA[
      K(x,y) * (z * z) = z * (z * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(14172,a,16992,a)].">
      <j1 rule="hyper" parents="14172 16992"/>
    </justification>
  </clause>

  <clause id="16996">
    <literal><![CDATA[
      T(x * K(y,z),x * x) = L(x * K(y,z),x,x)
    ]]></literal>
    <justification jstring="[para(16994(a,1),933(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16994 933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16997">
    <literal><![CDATA[
      x * (x * K(y,x \ 1)) = T(x \ 1,y) \ x
    ]]></literal>
    <justification jstring="[hyper(5770,a,16995,a),flip(a)].">
      <j1 rule="hyper" parents="5770 16995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16998">
    <literal><![CDATA[
      (x * y) / T(1 / y,z) = x * (T(y \ 1,z) \ y)
    ]]></literal>
    <justification jstring="[para(16997(a,1),9340(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16997 9340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16999">
    <literal><![CDATA[
      T(x * K(y,z),x * x) = (x \ 1) \ K(y,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,14570,a(flip),b,16996,a),flip(a)].">
      <j1 rule="hyper" parents="299 14570 16996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17000">
    <literal><![CDATA[
      T(x * K(y,z),x * (x * u)) = T((x \ 1) \ K(y,z),u)
    ]]></literal>
    <justification jstring="[para(16999(a,1),14446(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16999 14446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17001">
    <literal><![CDATA[
      K((T(x,y) \ y) \ 1,z) = K((y / x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(6426,a,16993,a)].">
      <j1 rule="hyper" parents="6426 16993"/>
    </justification>
  </clause>

  <clause id="17002">
    <literal><![CDATA[
      x * (T(y \ 1,y \ (y \ z)) \ y) = (x * y) / T(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(14502(a,1),16998(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14502 16998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17003">
    <literal><![CDATA[
      T((x \ 1) \ K(x * y,x),y) = L(x,x * y,x)
    ]]></literal>
    <justification jstring="[hyper(9835,a,17000,a),flip(a)].">
      <j1 rule="hyper" parents="9835 17000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17004">
    <literal><![CDATA[
      L(R(x,y,x),x,x) = L(x,x * y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,14697,a(flip),b,17003,a)].">
      <j1 rule="hyper" parents="65 14697 17003"/>
    </justification>
  </clause>

  <clause id="17005">
    <literal><![CDATA[
      T(x,y) != L(z,z * y,z)
    ]]></literal>
    <literal><![CDATA[
      (z \ 1) \ K(z * y,z) = x
    ]]></literal>
    <justification jstring="[para(17003(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="17003 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17006">
    <literal><![CDATA[
      L(R(x,y,L(x,x,x)),x,x) = L(x,x * y,x)
    ]]></literal>
    <justification jstring="[para(3405(a,2),17004(a,1,1))].">
      <j1 rule="para" parents="3405 17004"/>
    </justification>
  </clause>

  <clause id="17008">
    <literal><![CDATA[
      1 / L(x,x * y,x) = R(x,y,x) \ 1
    ]]></literal>
    <justification jstring="[para(17004(a,1),14087(a,1,2))].">
      <j1 rule="para" parents="17004 14087"/>
    </justification>
  </clause>

  <clause id="17009">
    <literal><![CDATA[
      T(T(x,x \ 1) * y,L(x,x,x)) = y * L(x,x * y,x)
    ]]></literal>
    <justification jstring="[para(17006(a,1),4719(a,2,2))].">
      <j1 rule="para" parents="17006 4719"/>
    </justification>
  </clause>

  <clause id="17010">
    <literal><![CDATA[
      x * L(y,y * x,y) = y * ((y \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,14208,a(flip),b,17009,a),flip(a)].">
      <j1 rule="hyper" parents="65 14208 17009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17012">
    <literal><![CDATA[
      T(x * K(x \ y,x),y) = L(x,x * y,x)
    ]]></literal>
    <justification jstring="[hyper(235,a,11149,a,b,17010,a)].">
      <j1 rule="hyper" parents="235 11149 17010"/>
    </justification>
  </clause>

  <clause id="17013">
    <literal><![CDATA[
      L(x,x \ y,x) = L(x,x * y,x)
    ]]></literal>
    <justification jstring="[hyper(36,a,482,a,b,17010,a)].">
      <j1 rule="hyper" parents="36 482 17010"/>
    </justification>
  </clause>

  <clause id="17014">
    <literal><![CDATA[
      L(x,x * y,x) = y / (T(y,x) / x)
    ]]></literal>
    <justification jstring="[hyper(65,a,9764,a(flip),b,17013,a),flip(a)].">
      <j1 rule="hyper" parents="65 9764 17013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17015">
    <literal><![CDATA[
      x / L(y,y * z,y) = x / (z / (T(z,y) / y))
    ]]></literal>
    <justification jstring="[hyper(62,a,17014,a)].">
      <j1 rule="hyper" parents="62 17014"/>
    </justification>
  </clause>

  <clause id="17016">
    <literal><![CDATA[
      1 / (x / (T(x,y) / y)) = R(y,x,y) \ 1
    ]]></literal>
    <justification jstring="[para(17014(a,1),17008(a,1,2))].">
      <j1 rule="para" parents="17014 17008"/>
    </justification>
  </clause>

  <clause id="17017">
    <literal><![CDATA[
      (x \ 1) \ K(x * y,x) = x * K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(17005,a,17012,a)].">
      <j1 rule="hyper" parents="17005 17012"/>
    </justification>
  </clause>

  <clause id="17018">
    <literal><![CDATA[
      R(x,x * y,x) \ 1 = 1 / L(x,y,x)
    ]]></literal>
    <justification jstring="[para(9766(a,1),17016(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9766 17016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17019">
    <literal><![CDATA[
      K(x,y) / T(x,x * y) = R(x,x * y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(299,a,14421,a,b,17018,a)].">
      <j1 rule="hyper" parents="299 14421 17018"/>
    </justification>
  </clause>

  <clause id="17020">
    <literal><![CDATA[
      x * K(x \ (x \ y),x) = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),17017(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 17017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17021">
    <literal><![CDATA[
      L(x \ (y * K(y \ z,y)),x,y) = ((y \ 1) * x) \ K(y * z,y)
    ]]></literal>
    <justification jstring="[para(17017(a,1),2476(a,1,1,2))].">
      <j1 rule="para" parents="17017 2476"/>
    </justification>
  </clause>

  <clause id="17022">
    <literal><![CDATA[
      K(x \ (x \ y),x) = K(x * (x * y),x)
    ]]></literal>
    <justification jstring="[hyper(36,a,14619,a,b,17020,a),flip(a)].">
      <j1 rule="hyper" parents="36 14619 17020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17023">
    <literal><![CDATA[
      T(x,y) \ T((x \ 1) \ K(z,x),y) = K(x \ (x \ z),T(x,y))
    ]]></literal>
    <justification jstring="[para(17020(a,1),5682(a,1,2,1))].">
      <j1 rule="para" parents="17020 5682"/>
    </justification>
  </clause>

  <clause id="17024">
    <literal><![CDATA[
      (x \ y) / ((((x \ y) \ y) \ y) / x) = T((x \ 1) \ K(y,x),x \ y)
    ]]></literal>
    <justification jstring="[para(17020(a,1),9765(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17020 9765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17025">
    <literal><![CDATA[
      K(x * ((x \ 1) \ T(y,(x \ 1) \ ((x \ 1) \ 1))),x \ 1) = K((x \ 1) * ((x \ 1) * y),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,15290,a,b,17022,a)].">
      <j1 rule="hyper" parents="65 15290 17022"/>
    </justification>
  </clause>

  <clause id="17026">
    <literal><![CDATA[
      L(x,T(R(y,y * z,y) \ 1,y),u) = L(x,R(y,y * z,y),u)
    ]]></literal>
    <justification jstring="[para(17019(a,1),16080(a,1,2,1))].">
      <j1 rule="para" parents="17019 16080"/>
    </justification>
  </clause>

  <clause id="17027">
    <literal><![CDATA[
      (x * y) / T(y \ 1,z) = x * (T(1 / y,z) \ y)
    ]]></literal>
    <justification jstring="[para(14692(a,1),17002(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14692 17002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17028">
    <literal><![CDATA[
      T(x * y,y \ 1) / (1 / y) = x * (T(1 / y,y \ x) \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,15282,a,b,17027,a)].">
      <j1 rule="hyper" parents="65 15282 17027"/>
    </justification>
  </clause>

  <clause id="17029">
    <literal><![CDATA[
      K(x \ (x \ y),T(x,z)) = K(x * (x * y),T(x,z))
    ]]></literal>
    <justification jstring="[hyper(14624,a,17023,a),flip(a)].">
      <j1 rule="hyper" parents="14624 17023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17030">
    <literal><![CDATA[
      (T(x \ 1,x \ y) \ (y / (1 / x))) * T(x \ 1,x \ y) = (y / (1 / x)) * K((x \ 1) * ((x \ 1) * y),T(x \ 1,y))
    ]]></literal>
    <justification jstring="[para(17029(a,1),15394(a,2,2))].">
      <j1 rule="para" parents="17029 15394"/>
    </justification>
  </clause>

  <clause id="17031">
    <literal><![CDATA[
      L(x,T(R(y,y * z,y) \ 1,y),u) = L(x,R(y,w,y),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,14083,a,b,17026,a),flip(a)].">
      <j1 rule="hyper" parents="299 14083 17026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17033">
    <literal><![CDATA[
      L(x,T(1 / L(y,z,y),y),u) = L(x,R(y,w,y),u)
    ]]></literal>
    <justification jstring="[para(17018(a,1),17031(a,1,2,1))].">
      <j1 rule="para" parents="17018 17031"/>
    </justification>
  </clause>

  <clause id="17034">
    <literal><![CDATA[
      L(x,R(y,z,y),u) = L(x,L(y,w,y) \ 1,u)
    ]]></literal>
    <justification jstring="[para(6369(a,1),17033(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6369 17033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17035">
    <literal><![CDATA[
      L(x,R(y,z,y),u) = L(x,L(y,w,y),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,2526,a(flip),b,17034,a),flip(a)].">
      <j1 rule="hyper" parents="299 2526 17034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17036">
    <literal><![CDATA[
      L(x,L(y,z,y),u) = L(x,L(y,w,y),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,17035,a(flip),b,17035,a)].">
      <j1 rule="hyper" parents="65 17035 17035"/>
    </justification>
  </clause>

  <clause id="17037">
    <literal><![CDATA[
      L(x,L(y,z,y),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,14082,a(flip),b,17035,a),flip(a)].">
      <j1 rule="hyper" parents="65 14082 17035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17038">
    <literal><![CDATA[
      L(T(R(x,y,x),z) \ u,L(x,w,x),z) = (R(x,y,x) * z) \ (z * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,11630,a(flip),b,17035,a),flip(a)].">
      <j1 rule="hyper" parents="65 11630 17035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17039">
    <literal><![CDATA[
      L(x,L(y,z,y),L(u,w,u)) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,13444,a(flip),b,17037,a),flip(a)].">
      <j1 rule="hyper" parents="299 13444 17037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17040">
    <literal><![CDATA[
      ((x \ y) * x) \ (L(x,x,x) \ y) = L(1 / x,x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,13461,a,b,17037,a)].">
      <j1 rule="hyper" parents="65 13461 17037"/>
    </justification>
  </clause>

  <clause id="17041">
    <literal><![CDATA[
      L(x,T(y / z,y),u) = L(x,z \ y,u)
    ]]></literal>
    <justification jstring="[para(4521(a,1),17037(a,1,2))].">
      <j1 rule="para" parents="4521 17037"/>
    </justification>
  </clause>

  <clause id="17046">
    <literal><![CDATA[
      L(x,L(y,z,y),u) = L(x,w / (T(w,y) / y),u)
    ]]></literal>
    <justification jstring="[para(9764(a,1),17036(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9764 17036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17047">
    <literal><![CDATA[
      L(x,y / z,y) = L(x,z \ y,y)
    ]]></literal>
    <justification jstring="[hyper(11643,a,17041,a)].">
      <j1 rule="hyper" parents="11643 17041"/>
    </justification>
  </clause>

  <clause id="17048">
    <literal><![CDATA[
      L(x,y / z,(y / u) \ u) = L(x,z \ y,(y / u) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,16304,a(flip),b,17041,a)].">
      <j1 rule="hyper" parents="65 16304 17041"/>
    </justification>
  </clause>

  <clause id="17049">
    <literal><![CDATA[
      (x / (T(x,y) / y)) \ L(z,L(y,u,y),x / (T(x,y) / y)) = ((x / (T(x,y) / y)) \ 1) * z
    ]]></literal>
    <justification jstring="[hyper(119,a,17046,a,b,1673,a)].">
      <j1 rule="hyper" parents="119 17046 1673"/>
    </justification>
  </clause>

  <clause id="17050">
    <literal><![CDATA[
      L(1 / x,x,x \ y) = y \ (y / L(x,x,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,12038,a(flip),b,17040,a),flip(a)].">
      <j1 rule="hyper" parents="65 12038 17040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17051">
    <literal><![CDATA[
      T(x \ (x / y),y) = L(1 / y,y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(299,a,2810,a(flip),b,17050,a)].">
      <j1 rule="hyper" parents="299 2810 17050"/>
    </justification>
  </clause>

  <clause id="17052">
    <literal><![CDATA[
      L(1 / x,x,x \ y) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(10417,a,17051,a),flip(a)].">
      <j1 rule="hyper" parents="10417 17051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17053">
    <literal><![CDATA[
      L((x \ y) \ 1,x \ y,y) = L(1 / (x \ y),x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(11641,a,17052,a),flip(a)].">
      <j1 rule="hyper" parents="11641 17052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17054">
    <literal><![CDATA[
      L((x \ y) \ 1,x \ y,y) = ((y \ x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(299,a,4151,a(flip),b,17053,a),flip(a)].">
      <j1 rule="hyper" parents="299 4151 17053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17055">
    <literal><![CDATA[
      x / (((x \ y) \ 1) \ 1) = x * (y \ x)
    ]]></literal>
    <justification jstring="[para(17054(a,1),368(a,1,2))].">
      <j1 rule="para" parents="17054 368"/>
    </justification>
  </clause>

  <clause id="17056">
    <literal><![CDATA[
      T(x * y,y \ 1) / (1 / y) = x * (T(y \ 1,y * x) \ y)
    ]]></literal>
    <justification jstring="[para(14501(a,1),17028(a,2,2,1))].">
      <j1 rule="para" parents="14501 17028"/>
    </justification>
  </clause>

  <clause id="17057">
    <literal><![CDATA[
      x * (T((y \ 1) \ 1,(y \ 1) * x) \ (y \ 1)) = T(x * (y \ 1),y) / (1 / (y \ 1))
    ]]></literal>
    <justification jstring="[para(3739(a,1),17056(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3739 17056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17058">
    <literal><![CDATA[
      T(x,(y * (T(z \ 1,z * y) \ z)) \ 1) = T(x,(1 / z) / T(y * z,z \ 1))
    ]]></literal>
    <justification jstring="[para(17056(a,1),4641(a,1,2,1))].">
      <j1 rule="para" parents="17056 4641"/>
    </justification>
  </clause>

  <clause id="17059">
    <literal><![CDATA[
      ((1 / x) * y) \ K(x \ z,x) = ((x \ 1) * y) \ K(x * z,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,14789,a(flip),b,17021,a)].">
      <j1 rule="hyper" parents="65 14789 17021"/>
    </justification>
  </clause>

  <clause id="17060">
    <literal><![CDATA[
      ((x \ 1) * y) \ K(x * y,x) = L(y / x,x,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,6331,a(flip),b,17059,a),flip(a)].">
      <j1 rule="hyper" parents="65 6331 17059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17061">
    <literal><![CDATA[
      L(x,y,((z \ 1) * u) * K(z * u,z)) = L(x,y,L(u / z,z,z) \ 1)
    ]]></literal>
    <justification jstring="[para(17060(a,1),14232(a,1,3)),flip(a)].">
      <j1 rule="para" parents="17060 14232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17063">
    <literal><![CDATA[
      T(K(x,y) * K(y,K(z,u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,T(u,w))) * K(x,T(y,w)) = v5
    ]]></literal>
    <justification jstring="[para(16503(a,1),8437(a,1))].">
      <j1 rule="para" parents="16503 8437"/>
    </justification>
  </clause>

  <clause id="17064">
    <literal><![CDATA[
      K(x,((y \ z) * y) / u) = K(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[hyper(36,a,16712,a(flip),b,16511,a),flip(a)].">
      <j1 rule="hyper" parents="36 16712 16511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17065">
    <literal><![CDATA[
      K(x,T(y * z,y) / u) = K(x,(z * y) / u)
    ]]></literal>
    <justification jstring="[para(9(a,1),17064(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="9 17064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17066">
    <literal><![CDATA[
      K(T(x * y,x) / z,u) = (w * K(u,(y * x) / z)) \ w
    ]]></literal>
    <justification jstring="[para(17065(a,1),7200(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="17065 7200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17067">
    <literal><![CDATA[
      K(T(x * y,x) / z,u) = K((y * x) / z,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,7200,a(flip),b,17066,a),flip(a)].">
      <j1 rule="hyper" parents="299 7200 17066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17068">
    <literal><![CDATA[
      K((x * y) / z,T(u,x * y)) = K(z \ T(y * x,y),u)
    ]]></literal>
    <justification jstring="[hyper(13201,a,17067,a),flip(a)].">
      <j1 rule="hyper" parents="13201 17067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17069">
    <literal><![CDATA[
      K(((x \ y) * x) / z,u) = K(T(y,x) / z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),17067(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 17067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17070">
    <literal><![CDATA[
      K((x * y) \ z,T(u,y)) = K(T(z,x) / (y * x),u)
    ]]></literal>
    <justification jstring="[hyper(15541,a,17069,a)].">
      <j1 rule="hyper" parents="15541 17069"/>
    </justification>
  </clause>

  <clause id="17071">
    <literal><![CDATA[
      K(x \ T(y * z,y),u) = K(x \ (z * y),u)
    ]]></literal>
    <justification jstring="[hyper(7526,a,17068,a),flip(a)].">
      <j1 rule="hyper" parents="7526 17068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17072">
    <literal><![CDATA[
      K(x \ ((y \ z) * y),u) = K(x \ T(z,y),u)
    ]]></literal>
    <justification jstring="[para(10(a,1),17071(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 17071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17077">
    <literal><![CDATA[
      T(x,K(y,z) * (u * (w \ (w \ 1)))) = T(x,u * (w \ (w \ K(y,z))))
    ]]></literal>
    <justification jstring="[para(14228(a,1),16515(a,2,2,2))].">
      <j1 rule="para" parents="14228 16515"/>
    </justification>
  </clause>

  <clause id="17078">
    <literal><![CDATA[
      K((x * y) \ z,T(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      K((x * y) \ z,T(u,x * z)) = w
    ]]></literal>
    <justification jstring="[para(11933(a,1),16651(a,1))].">
      <j1 rule="para" parents="11933 16651"/>
    </justification>
  </clause>

  <clause id="17079">
    <literal><![CDATA[
      T(x / y,K(((x / y) \ (1 / y)) \ 1,z)) = T(x / y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,8706,a(flip),b,16762,a),flip(a)].">
      <j1 rule="hyper" parents="299 8706 16762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17080">
    <literal><![CDATA[
      T(x / y,K(z,((x / y) \ (1 / y)) \ 1)) = T(x / y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(8081,a,17079,a)].">
      <j1 rule="hyper" parents="8081 17079"/>
    </justification>
  </clause>

  <clause id="17081">
    <literal><![CDATA[
      T(x / y,K(z,(1 / y) \ (x / y))) = T(x / y,K(x,z))
    ]]></literal>
    <justification jstring="[para(6814(a,1),17080(a,1,2))].">
      <j1 rule="para" parents="6814 17080"/>
    </justification>
  </clause>

  <clause id="17082">
    <literal><![CDATA[
      K(((x \ y) * x) / T(L(K(z,u),w,v5) * x,K(v6,v7)),v8) = K((x * L(K(z,u),w,v5)) \ y,v8)
    ]]></literal>
    <justification jstring="[hyper(16467,a,16789,a),flip(a)].">
      <j1 rule="hyper" parents="16467 16789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17084">
    <literal><![CDATA[
      T(x,(y / z) * (u * (z \ y))) = T(x,(z \ y) * (u * (y / z)))
    ]]></literal>
    <justification jstring="[para(5359(a,1),16874(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5359 16874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17085">
    <literal><![CDATA[
      T(x,K(y,z) * (T(y * z,u) \ w)) = T(x,T(T(y * z,u),y) \ w)
    ]]></literal>
    <justification jstring="[hyper(15834,a,16890,a)].">
      <j1 rule="hyper" parents="15834 16890"/>
    </justification>
  </clause>

  <clause id="17086">
    <literal><![CDATA[
      T(x,(y \ T(z,u)) * (y \ T(z,u))) = T(x,(y \ z) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,16917,a(flip),b,16918,a),flip(a)].">
      <j1 rule="hyper" parents="65 16917 16918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17087">
    <literal><![CDATA[
      T((x * y) / x,z * (x \ z)) = T(y,(x \ T((z \ 1) \ 1,u)) * (x \ T((z \ 1) \ 1,u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,15716,a(flip),b,16918,a)].">
      <j1 rule="hyper" parents="65 15716 16918"/>
    </justification>
  </clause>

  <clause id="17089">
    <literal><![CDATA[
      (T(x,y) \ K(z,y * x)) \ 1 = y \ T(T(x,x \ 1) * y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,15151,a(flip),b,16923,a),flip(a)].">
      <j1 rule="hyper" parents="65 15151 16923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17090">
    <literal><![CDATA[
      (T(x,y) / z) / K(((1 / z) / (x / z)) \ 1,y) = T(x / z,K(y,(1 / z) \ (x / z)))
    ]]></literal>
    <justification jstring="[para(5331(a,1),16933(a,1,1))].">
      <j1 rule="para" parents="5331 16933"/>
    </justification>
  </clause>

  <clause id="17091">
    <literal><![CDATA[
      (K(x,T(y,z)) / u) * K(x,K(y,z)) = T(K(x,y) / u,K(K(x,y),z))
    ]]></literal>
    <justification jstring="[para(7954(a,2),16962(a,2,2))].">
      <j1 rule="para" parents="7954 16962"/>
    </justification>
  </clause>

  <clause id="17092">
    <literal><![CDATA[
      K(x,y \ T(z * y,K(u,w))) = K(x,T(z,K(w,u) * y))
    ]]></literal>
    <justification jstring="[hyper(16801,a,16965,a)].">
      <j1 rule="hyper" parents="16801 16965"/>
    </justification>
  </clause>

  <clause id="17093">
    <literal><![CDATA[
      K(x,T(y * z,K(u,w)) / y) = K(x,T(z,K(w,u) * y))
    ]]></literal>
    <justification jstring="[hyper(8319,a,17092,a)].">
      <j1 rule="hyper" parents="8319 17092"/>
    </justification>
  </clause>

  <clause id="17095">
    <literal><![CDATA[
      K(x,T(y,K(z,u) * w)) = K(x,(w * y) / w)
    ]]></literal>
    <justification jstring="[hyper(16799,a,17093,a),flip(a)].">
      <j1 rule="hyper" parents="16799 17093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17098">
    <literal><![CDATA[
      K(x,T(y,K(z,u) * w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(299,a,8120,a(flip),b,17095,a),flip(a)].">
      <j1 rule="hyper" parents="299 8120 17095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17099">
    <literal><![CDATA[
      K(x,T(y,K(z,u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,w)) = v5
    ]]></literal>
    <justification jstring="[para(17095(a,2),8176(a,1))].">
      <j1 rule="para" parents="17095 8176"/>
    </justification>
  </clause>

  <clause id="17100">
    <literal><![CDATA[
      K(x,T(y,z \ K(u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(16577,a,17098,a),flip(a)].">
      <j1 rule="hyper" parents="16577 17098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17101">
    <literal><![CDATA[
      K(x,T(y,z * K(u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(16576,a,17098,a)].">
      <j1 rule="hyper" parents="16576 17098"/>
    </justification>
  </clause>

  <clause id="17102">
    <literal><![CDATA[
      T(K(x,y),K(z,u) * w) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(8419,a,17098,a)].">
      <j1 rule="hyper" parents="8419 17098"/>
    </justification>
  </clause>

  <clause id="17104">
    <literal><![CDATA[
      K(x,T(y,z * T(u,w))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(5853(a,1),17098(a,1,2,2))].">
      <j1 rule="para" parents="5853 17098"/>
    </justification>
  </clause>

  <clause id="17105">
    <literal><![CDATA[
      (K(x,y) * z) * K(u,T(w,z)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(u,w) * (K(x,y) * z) = v5
    ]]></literal>
    <justification jstring="[para(17098(a,1),7509(a,1,2))].">
      <j1 rule="para" parents="17098 7509"/>
    </justification>
  </clause>

  <clause id="17106">
    <literal><![CDATA[
      K(x,K(y,K(z,u) * w)) = K(x,T(y,w)) * K(y,x)
    ]]></literal>
    <justification jstring="[para(17098(a,1),8236(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17098 8236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17109">
    <literal><![CDATA[
      K(x,T(y,z * (K(u,w) * v5))) = K(x,T(y,z * v5))
    ]]></literal>
    <justification jstring="[para(11484(a,1),17098(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11484 17098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17111">
    <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(17100(a,1),13182(a,1))].">
      <j1 rule="para" parents="17100 13182"/>
    </justification>
  </clause>

  <clause id="17112">
    <literal><![CDATA[
      K(x,T(y,z)) * (K(u,w) / z) = (K(u,w) / z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(17100(a,1),16540(a,1,1))].">
      <j1 rule="para" parents="17100 16540"/>
    </justification>
  </clause>

  <clause id="17113">
    <literal><![CDATA[
      K(x * (y * K(z,u)),T(w,y)) = K((y * K(z,u)) * x,w)
    ]]></literal>
    <justification jstring="[hyper(13187,a,17101,a),flip(a)].">
      <j1 rule="hyper" parents="13187 17101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17115">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * K(u,w)) = (z * K(u,w)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(17101(a,1),8101(a,1,1))].">
      <j1 rule="para" parents="17101 8101"/>
    </justification>
  </clause>

  <clause id="17117">
    <literal><![CDATA[
      K(x,T(y,z / (u / w))) = K(x,T(y,z / (w \ u)))
    ]]></literal>
    <justification jstring="[para(9047(a,1),17101(a,1,2,2))].">
      <j1 rule="para" parents="9047 17101"/>
    </justification>
  </clause>

  <clause id="17121">
    <literal><![CDATA[
      K(L(x * K(y,x),y,K(z,u)),T(w,y)) != v5
    ]]></literal>
    <literal><![CDATA[
      K((y * K(z,u)) \ ((y * x) * K(z,u)),w) = v5
    ]]></literal>
    <justification jstring="[para(17101(a,1),15614(a,1))].">
      <j1 rule="para" parents="17101 15614"/>
    </justification>
  </clause>

  <clause id="17122">
    <literal><![CDATA[
      (K(x,y) * z) \ (z * (x \ R(x,y,x))) = K(x * y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(10161,a,17102,a)].">
      <j1 rule="hyper" parents="10161 17102"/>
    </justification>
  </clause>

  <clause id="17125">
    <literal><![CDATA[
      K(x,T(y,z * L(T(u,w),v5,v6))) = K(x,T(y,z * L(u,v5,v6)))
    ]]></literal>
    <justification jstring="[para(25(a,2),17104(a,1,2,2,2))].">
      <j1 rule="para" parents="25 17104"/>
    </justification>
  </clause>

  <clause id="17127">
    <literal><![CDATA[
      K(x,T(y,z * T(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u * z)) = v5
    ]]></literal>
    <justification jstring="[para(17104(a,2),16576(a,1))].">
      <j1 rule="para" parents="17104 16576"/>
    </justification>
  </clause>

  <clause id="17128">
    <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(5103(a,1),17099(a,1,2,2))].">
      <j1 rule="para" parents="5103 17099"/>
    </justification>
  </clause>

  <clause id="17129">
    <literal><![CDATA[
      K(x,T(y,K(z,u) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,w)) = v5
    ]]></literal>
    <justification jstring="[para(5426(a,2),17099(a,1,2,2))].">
      <j1 rule="para" parents="5426 17099"/>
    </justification>
  </clause>

  <clause id="17132">
    <literal><![CDATA[
      K(x,K(y,K(z,u) * w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(299,a,8236,a(flip),b,17106,a),flip(a)].">
      <j1 rule="hyper" parents="299 8236 17106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17133">
    <literal><![CDATA[
      K(x,K(y,z * K(u,w))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(16574,a,17132,a)].">
      <j1 rule="hyper" parents="16574 17132"/>
    </justification>
  </clause>

  <clause id="17136">
    <literal><![CDATA[
      K(x,K(y,T(z,u) * w)) = K(x,K(y,z * w))
    ]]></literal>
    <justification jstring="[para(5061(a,1),17132(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5061 17132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17137">
    <literal><![CDATA[
      K(x,K(y,((z * u) / z) * w)) = K(x,K(y,u * w))
    ]]></literal>
    <justification jstring="[para(5515(a,1),17132(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5515 17132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17139">
    <literal><![CDATA[
      K(x,K(y,z * T(u,w))) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(5853(a,1),17132(a,1,2,2))].">
      <j1 rule="para" parents="5853 17132"/>
    </justification>
  </clause>

  <clause id="17140">
    <literal><![CDATA[
      K(x,K(y,z / T(u,w))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[para(8360(a,1),17132(a,1,2,2))].">
      <j1 rule="para" parents="8360 17132"/>
    </justification>
  </clause>

  <clause id="17141">
    <literal><![CDATA[
      K(x,K(y,z * (K(u,w) * v5))) = K(x,K(y,z * v5))
    ]]></literal>
    <justification jstring="[para(11484(a,1),17132(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11484 17132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17142">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,(K(u,w) * z) * y) = K(x,y * (K(u,w) * z))
    ]]></literal>
    <justification jstring="[para(17132(a,1),16664(a,1,1))].">
      <j1 rule="para" parents="17132 16664"/>
    </justification>
  </clause>

  <clause id="17143">
    <literal><![CDATA[
      K(x,K(y,K(z,u) / w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(16560,a,17133,a)].">
      <j1 rule="hyper" parents="16560 17133"/>
    </justification>
  </clause>

  <clause id="17144">
    <literal><![CDATA[
      T(x,K(y,z * K(u,w))) = x * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(17133(a,1),5083(a,2,2))].">
      <j1 rule="para" parents="17133 5083"/>
    </justification>
  </clause>

  <clause id="17145">
    <literal><![CDATA[
      K(x,K(y,z * (u / w))) = K(x,K(y,z * (w \ u)))
    ]]></literal>
    <justification jstring="[para(6970(a,1),17133(a,1,2,2))].">
      <j1 rule="para" parents="6970 17133"/>
    </justification>
  </clause>

  <clause id="17146">
    <literal><![CDATA[
      K(x,K(y,z / ((u * w) / u))) = K(x,K(y,z / w))
    ]]></literal>
    <justification jstring="[para(9046(a,2),17133(a,1,2,2))].">
      <j1 rule="para" parents="9046 17133"/>
    </justification>
  </clause>

  <clause id="17147">
    <literal><![CDATA[
      K(x,K(y,z / (u / (u / w)))) = K(x,K(y,z / w))
    ]]></literal>
    <justification jstring="[para(9045(a,2),17133(a,1,2,2))].">
      <j1 rule="para" parents="9045 17133"/>
    </justification>
  </clause>

  <clause id="17148">
    <literal><![CDATA[
      K(x,K(y,z / (u / w))) = K(x,K(y,z / (w \ u)))
    ]]></literal>
    <justification jstring="[para(9047(a,1),17133(a,1,2,2))].">
      <j1 rule="para" parents="9047 17133"/>
    </justification>
  </clause>

  <clause id="17149">
    <literal><![CDATA[
      K(x,K(y,(z * K(u,w)) * v5)) = K(x,K(y,z * v5))
    ]]></literal>
    <justification jstring="[para(9940(a,1),17133(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9940 17133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17150">
    <literal><![CDATA[
      K(x,K(y,z / (u * w))) = K(x,K(y,z / (w * u)))
    ]]></literal>
    <justification jstring="[para(11147(a,1),17133(a,1,2,2))].">
      <j1 rule="para" parents="11147 17133"/>
    </justification>
  </clause>

  <clause id="17151">
    <literal><![CDATA[
      K(x,K(y,K(z,u) / w)) = K(x,K(w,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,8004,a,b,17143,a),flip(a)].">
      <j1 rule="hyper" parents="299 8004 17143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17153">
    <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(9020,a,17151,a)].">
      <j1 rule="hyper" parents="9020 17151"/>
    </justification>
  </clause>

  <clause id="17154">
    <literal><![CDATA[
      K(x,K(y * K(z,u),w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(8822,a,17151,a),flip(a)].">
      <j1 rule="hyper" parents="8822 17151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17155">
    <literal><![CDATA[
      K(x,K(K(y,z) / u,w)) = K(x,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(8035,a,17151,a)].">
      <j1 rule="hyper" parents="8035 17151"/>
    </justification>
  </clause>

  <clause id="17156">
    <literal><![CDATA[
      K(x,K(y * K(z,u),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,w)) = v5
    ]]></literal>
    <justification jstring="[para(17151(a,1),8822(a,1))].">
      <j1 rule="para" parents="17151 8822"/>
    </justification>
  </clause>

  <clause id="17157">
    <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(8921,a,17154,a)].">
      <j1 rule="hyper" parents="8921 17154"/>
    </justification>
  </clause>

  <clause id="17158">
    <literal><![CDATA[
      K(x,K(T(y,z) / u,w)) = K(x,K(y / u,w))
    ]]></literal>
    <justification jstring="[para(1394(a,1),17154(a,1,2,1))].">
      <j1 rule="para" parents="1394 17154"/>
    </justification>
  </clause>

  <clause id="17161">
    <literal><![CDATA[
      K(x,K(K(y,z) / u,w)) = K(x,K(u * K(v5,v6),w))
    ]]></literal>
    <justification jstring="[hyper(299,a,17154,a,b,17155,a),flip(a)].">
      <j1 rule="hyper" parents="299 17154 17155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17162">
    <literal><![CDATA[
      K(x,K(y,z * T(u,w))) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(16574,a,17136,a)].">
      <j1 rule="hyper" parents="16574 17136"/>
    </justification>
  </clause>

  <clause id="17163">
    <literal><![CDATA[
      K(x,K(y,z * u)) * K(x,y \ (T(z,w) * u)) = K(x,(T(z,w) * u) / y)
    ]]></literal>
    <justification jstring="[para(17136(a,1),8497(a,1,1))].">
      <j1 rule="para" parents="17136 8497"/>
    </justification>
  </clause>

  <clause id="17165">
    <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(17136(a,2),16261(a,1))].">
      <j1 rule="para" parents="17136 16261"/>
    </justification>
  </clause>

  <clause id="17166">
    <literal><![CDATA[
      K(x,(y / T(z,u)) * w) * K(x,K(w,z * y)) = K(x,w * (y / T(z,u)))
    ]]></literal>
    <justification jstring="[para(17136(a,1),16668(a,1,2))].">
      <j1 rule="para" parents="17136 16668"/>
    </justification>
  </clause>

  <clause id="17167">
    <literal><![CDATA[
      K(x,K(y,z * u)) * K(x,y / (z * T(u,w))) = K(x,(z * T(u,w)) \ y)
    ]]></literal>
    <justification jstring="[para(17139(a,1),8507(a,1,1))].">
      <j1 rule="para" parents="17139 8507"/>
    </justification>
  </clause>

  <clause id="17168">
    <literal><![CDATA[
      K(x,K(y,z * u)) * K(x,y / (z * ((u \ w) \ w))) = K(x,(z * ((u \ w) \ w)) \ y)
    ]]></literal>
    <justification jstring="[para(17139(a,1),13815(a,1,1))].">
      <j1 rule="para" parents="17139 13815"/>
    </justification>
  </clause>

  <clause id="17169">
    <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(17139(a,2),16574(a,1))].">
      <j1 rule="para" parents="17139 16574"/>
    </justification>
  </clause>

  <clause id="17170">
    <literal><![CDATA[
      T(x,K(y,z * K(u,w))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,5083,a,b,17144,a),flip(a)].">
      <j1 rule="hyper" parents="299 5083 17144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17171">
    <literal><![CDATA[
      T(x,K(y,K(z,u) * w)) = T(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(16293,a,17170,a)].">
      <j1 rule="hyper" parents="16293 17170"/>
    </justification>
  </clause>

  <clause id="17172">
    <literal><![CDATA[
      T(x,K(y,K(z,u) \ w)) = T(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(16273,a,17170,a)].">
      <j1 rule="hyper" parents="16273 17170"/>
    </justification>
  </clause>

  <clause id="17173">
    <literal><![CDATA[
      T(x,K(y,z * T(u,w))) = T(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(1389(a,1),17170(a,1,2,2))].">
      <j1 rule="para" parents="1389 17170"/>
    </justification>
  </clause>

  <clause id="17174">
    <literal><![CDATA[
      T(x,K(y,T(z,u) * w)) = T(x,K(y,z * w))
    ]]></literal>
    <justification jstring="[para(5843(a,1),17170(a,1,2,2))].">
      <j1 rule="para" parents="5843 17170"/>
    </justification>
  </clause>

  <clause id="17175">
    <literal><![CDATA[
      T(x,K(y,((z \ u) \ u) * w)) = T(x,K(y,z * w))
    ]]></literal>
    <justification jstring="[para(7031(a,2),17170(a,1,2,2))].">
      <j1 rule="para" parents="7031 17170"/>
    </justification>
  </clause>

  <clause id="17176">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u * K(w,v5))) = T(y,K(u * K(w,v5),z) * x)
    ]]></literal>
    <justification jstring="[para(17170(a,1),15769(a,1,2,1,2))].">
      <j1 rule="para" parents="17170 15769"/>
    </justification>
  </clause>

  <clause id="17177">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * (z \ K(u,w))) = T(x,(z \ K(u,w)) * y)
    ]]></literal>
    <justification jstring="[para(17170(a,1),16276(a,1,1))].">
      <j1 rule="para" parents="17170 16276"/>
    </justification>
  </clause>

  <clause id="17178">
    <literal><![CDATA[
      T(T(x,K(y,z)),(K(u,w) / z) * y) = T(x,y * (K(u,w) / z))
    ]]></literal>
    <justification jstring="[para(17170(a,1),16785(a,1,1))].">
      <j1 rule="para" parents="17170 16785"/>
    </justification>
  </clause>

  <clause id="17179">
    <literal><![CDATA[
      T(T(x,K(y,z)),(K(u,w) * z) / y) = T(x,y \ (K(u,w) * z))
    ]]></literal>
    <justification jstring="[para(17171(a,1),8998(a,1,1))].">
      <j1 rule="para" parents="17171 8998"/>
    </justification>
  </clause>

  <clause id="17180">
    <literal><![CDATA[
      T(x,K(y,K(z,u) \ w)) = K(y,K(w,x)) \ x
    ]]></literal>
    <justification jstring="[hyper(299,a,7973,a,b,17172,a),flip(a)].">
      <j1 rule="hyper" parents="299 7973 17172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17181">
    <literal><![CDATA[
      K(x,K(y / z,L(u,z,w))) = K(x,K(u,(y * w) / (w * z)))
    ]]></literal>
    <justification jstring="[hyper(65,a,16914,a(flip),b,17158,a),flip(a)].">
      <j1 rule="hyper" parents="65 16914 17158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17182">
    <literal><![CDATA[
      K(x,K(y,(z / u) * w)) = K(x,K(y,w * (u \ z)))
    ]]></literal>
    <justification jstring="[para(109(a,1),17162(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="109 17162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17183">
    <literal><![CDATA[
      K(x,K(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,T(z,v5) * u)) = w
    ]]></literal>
    <justification jstring="[para(17162(a,1),16574(a,1))].">
      <j1 rule="para" parents="17162 16574"/>
    </justification>
  </clause>

  <clause id="17184">
    <literal><![CDATA[
      T(T(x,y \ T(z,u)),K(w,y * z)) = T(x,T(y \ T(z,u),w))
    ]]></literal>
    <justification jstring="[hyper(16272,a,17173,a),flip(a)].">
      <j1 rule="hyper" parents="16272 17173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17185">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y / (u \ T(z,w))) = T(x,(u \ T(z,w)) \ y)
    ]]></literal>
    <justification jstring="[para(17174(a,1),16282(a,1,1))].">
      <j1 rule="para" parents="17174 16282"/>
    </justification>
  </clause>

  <clause id="17186">
    <literal><![CDATA[
      T(x,K(y,K(z,u) \ w)) = K(w,K(y,x)) \ x
    ]]></literal>
    <justification jstring="[para(7983(a,1),17180(a,2,1))].">
      <j1 rule="para" parents="7983 17180"/>
    </justification>
  </clause>

  <clause id="17187">
    <literal><![CDATA[
      K(x,K(y,K(z,u) \ w)) = K(w,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(8084,a,17186,a)].">
      <j1 rule="hyper" parents="8084 17186"/>
    </justification>
  </clause>

  <clause id="17188">
    <literal><![CDATA[
      K(x,K(y,z)) \ (x * K(u,w)) = T(x * K(u,w),K(y,z))
    ]]></literal>
    <justification jstring="[para(17187(a,1),16535(a,1,1))].">
      <j1 rule="para" parents="17187 16535"/>
    </justification>
  </clause>

  <clause id="17190">
    <literal><![CDATA[
      K(x,T(y,z * ((u / w) \ v5))) = K(x,T(y,z * ((w \ u) \ v5)))
    ]]></literal>
    <justification jstring="[para(5692(a,1),17109(a,1,2,2,2))].">
      <j1 rule="para" parents="5692 17109"/>
    </justification>
  </clause>

  <clause id="17193">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z / (u / w))) = K(x,T(y,z / (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,7967,a,b,17117,a)].">
      <j1 rule="hyper" parents="65 7967 17117"/>
    </justification>
  </clause>

  <clause id="17195">
    <literal><![CDATA[
      K(x,K(y,(K(z,u) * w) / v5)) = K(x,K(y,(1 / v5) * w))
    ]]></literal>
    <justification jstring="[hyper(16502,a,17141,a)].">
      <j1 rule="hyper" parents="16502 17141"/>
    </justification>
  </clause>

  <clause id="17196">
    <literal><![CDATA[
      K(x,K(y,z * (K(u,w) * v5))) = K(x,K(y,v5 * z))
    ]]></literal>
    <justification jstring="[hyper(299,a,16338,a,b,17141,a),flip(a)].">
      <j1 rule="hyper" parents="299 16338 17141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17200">
    <literal><![CDATA[
      K(x,K(y,z * (u \ w))) * K(y,x / (z * (w / u))) = K(y,(z * (w / u)) \ x)
    ]]></literal>
    <justification jstring="[para(17145(a,1),8506(a,1,1))].">
      <j1 rule="para" parents="17145 8506"/>
    </justification>
  </clause>

  <clause id="17202">
    <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(17148(a,2),8914(a,1,1))].">
      <j1 rule="para" parents="17148 8914"/>
    </justification>
  </clause>

  <clause id="17203">
    <literal><![CDATA[
      K(x,K(y,(T(z,u) / w) * v5)) = K(x,K(y,(z / w) * v5))
    ]]></literal>
    <justification jstring="[para(1394(a,1),17149(a,1,2,2,1))].">
      <j1 rule="para" parents="1394 17149"/>
    </justification>
  </clause>

  <clause id="17204">
    <literal><![CDATA[
      K(x,K(y,((z / u) * w) * v5)) = K(x,K(y,((u \ z) * w) * v5))
    ]]></literal>
    <justification jstring="[para(7123(a,1),17149(a,1,2,2,1))].">
      <j1 rule="para" parents="7123 17149"/>
    </justification>
  </clause>

  <clause id="17205">
    <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(17149(a,2),16574(a,1))].">
      <j1 rule="para" parents="17149 16574"/>
    </justification>
  </clause>

  <clause id="17206">
    <literal><![CDATA[
      K(x,K(y,(z * u) / w)) = K(x,K(y,w / (u * z)))
    ]]></literal>
    <justification jstring="[hyper(8828,a,17150,a)].">
      <j1 rule="hyper" parents="8828 17150"/>
    </justification>
  </clause>

  <clause id="17207">
    <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(65,a,9195,a(flip),b,17161,a),flip(a)].">
      <j1 rule="hyper" parents="65 9195 17161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17208">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y / (u \ ((z \ w) \ w))) = T(x,(u \ ((z \ w) \ w)) \ y)
    ]]></literal>
    <justification jstring="[para(17175(a,1),16282(a,1,1))].">
      <j1 rule="para" parents="17175 16282"/>
    </justification>
  </clause>

  <clause id="17209">
    <literal><![CDATA[
      K(x,K((y / z) \ 1,u * (w \ v5))) = K(x,K(z / y,(v5 / w) * u))
    ]]></literal>
    <justification jstring="[para(5852(a,1),17182(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5852 17182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17210">
    <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(17196(a,2),16574(a,1))].">
      <j1 rule="para" parents="17196 16574"/>
    </justification>
  </clause>

  <clause id="17211">
    <literal><![CDATA[
      K(x,K(y,(z * u) / w)) = K(x,K(y,(u * z) / w))
    ]]></literal>
    <justification jstring="[hyper(299,a,8791,a,b,17206,a)].">
      <j1 rule="hyper" parents="299 8791 17206"/>
    </justification>
  </clause>

  <clause id="17212">
    <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(17206(a,1),8828(a,1))].">
      <j1 rule="para" parents="17206 8828"/>
    </justification>
  </clause>

  <clause id="17213">
    <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(17206(a,2),8828(a,1))].">
      <j1 rule="para" parents="17206 8828"/>
    </justification>
  </clause>

  <clause id="17214">
    <literal><![CDATA[
      K(x,K(y,((z * u) * w) / (w * u))) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(299,a,16913,a(flip),b,17211,a),flip(a)].">
      <j1 rule="hyper" parents="299 16913 17211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17215">
    <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(1029(a,1),17211(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1029 17211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17216">
    <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(17211(a,1),8828(a,1))].">
      <j1 rule="para" parents="17211 8828"/>
    </justification>
  </clause>

  <clause id="17217">
    <literal><![CDATA[
      K(x,T(y,z)) / (z * K(u,w)) = (K(w,u) / z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(14538,a,17112,a)].">
      <j1 rule="hyper" parents="14538 17112"/>
    </justification>
  </clause>

  <clause id="17218">
    <literal><![CDATA[
      K(x,T(y,z)) / T(z,u) = (K(u,z) / z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(14537,a,17112,a)].">
      <j1 rule="hyper" parents="14537 17112"/>
    </justification>
  </clause>

  <clause id="17219">
    <literal><![CDATA[
      ((1 / x) * K(y,z)) * K(u,x) = (K(u,x) / x) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,14586,a,b,17218,a)].">
      <j1 rule="hyper" parents="65 14586 17218"/>
    </justification>
  </clause>

  <clause id="17220">
    <literal><![CDATA[
      K(x,y) * ((1 / y) * K(z,u)) = ((1 / y) * K(z,u)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(4799(a,1),17115(a,1,1))].">
      <j1 rule="para" parents="4799 17115"/>
    </justification>
  </clause>

  <clause id="17221">
    <literal><![CDATA[
      K(x,K(y,L(K(z,u) / w,v5,v6))) = K(x,K(y,L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(299,a,8919,a,b,17153,a),flip(a)].">
      <j1 rule="hyper" parents="299 8919 17153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17223">
    <literal><![CDATA[
      K(x,K(y,L(K(z,u) * w,v5,v6))) = K(x,K(w,L(y,v5,v6)))
    ]]></literal>
    <justification jstring="[para(7507(a,1),17157(a,1,2,2,1))].">
      <j1 rule="para" parents="7507 17157"/>
    </justification>
  </clause>

  <clause id="17224">
    <literal><![CDATA[
      T(x * K(y,z),K(u,w)) = T(x,K(u,w)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(8034,a,17188,a),flip(a)].">
      <j1 rule="hyper" parents="8034 17188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17226">
    <literal><![CDATA[
      T(K(x,y) * z,K(u,w)) = K(x,y) * T(z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(6544,a,17224,a),flip(a)].">
      <j1 rule="hyper" parents="6544 17224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17233">
    <literal><![CDATA[
      K(x,K(y,(K(z,u) * w) / v5)) = K(x,K(y,w / v5))
    ]]></literal>
    <justification jstring="[hyper(299,a,16497,a(flip),b,17195,a),flip(a)].">
      <j1 rule="hyper" parents="299 16497 17195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17234">
    <literal><![CDATA[
      K(x,K(y,z / (K(u,w) * v5))) = K(x,K(y,v5 / z))
    ]]></literal>
    <justification jstring="[hyper(8828,a,17233,a)].">
      <j1 rule="hyper" parents="8828 17233"/>
    </justification>
  </clause>

  <clause id="17236">
    <literal><![CDATA[
      K(x,K(y,(z * T(u,w)) / v5)) = K(x,K(y,(z * u) / v5))
    ]]></literal>
    <justification jstring="[para(5853(a,1),17233(a,1,2,2,1))].">
      <j1 rule="para" parents="5853 17233"/>
    </justification>
  </clause>

  <clause id="17237">
    <literal><![CDATA[
      K(x,K(y,(z * K(u,w)) / v5)) = K(x,K(y,v5 / z))
    ]]></literal>
    <justification jstring="[para(8140(a,1),17234(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="8140 17234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17238">
    <literal><![CDATA[
      K(x,K(y,z / ((K(u,w) * v5) * v6))) = K(x,K(y,(v5 * v6) / z))
    ]]></literal>
    <justification jstring="[para(10720(a,1),17234(a,1,2,2,2))].">
      <j1 rule="para" parents="10720 17234"/>
    </justification>
  </clause>

  <clause id="17240">
    <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(17237(a,1),16653(a,1,1))].">
      <j1 rule="para" parents="17237 16653"/>
    </justification>
  </clause>

  <clause id="17241">
    <literal><![CDATA[
      K(x,K(y,((z / (z / u)) / w) * v5)) = K(x,K(y,(u / w) * v5))
    ]]></literal>
    <justification jstring="[para(241(a,1),17203(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="241 17203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17242">
    <literal><![CDATA[
      K(x,K(y,z / (T(u,w) * v5))) = K(x,K(y,(v5 * u) / z))
    ]]></literal>
    <justification jstring="[hyper(65,a,17206,a(flip),b,17236,a)].">
      <j1 rule="hyper" parents="65 17206 17236"/>
    </justification>
  </clause>

  <clause id="17243">
    <literal><![CDATA[
      K(x,K(y,(z * (u / w)) / v5)) = K(x,K(y,v5 / ((w \ u) * z)))
    ]]></literal>
    <justification jstring="[para(109(a,1),17242(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="109 17242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17244">
    <literal><![CDATA[
      K(x * y,T(x,z)) / ((z * (x \ R(x,y,x))) / K(x * y,x)) = ((z * (x \ R(x,y,x))) / (K(x,y) * z)) / (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(17122(a,1),10162(a,1,1))].">
      <j1 rule="para" parents="17122 10162"/>
    </justification>
  </clause>

  <clause id="17246">
    <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(65,a,15166,a(flip),b,17181,a)].">
      <j1 rule="hyper" parents="65 15166 17181"/>
    </justification>
  </clause>

  <clause id="17247">
    <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(8075(a,1),17181(a,1,2,1))].">
      <j1 rule="para" parents="8075 17181"/>
    </justification>
  </clause>

  <clause id="17248">
    <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(7189(a,1),17205(a,1,2,2,1))].">
      <j1 rule="para" parents="7189 17205"/>
    </justification>
  </clause>

  <clause id="17249">
    <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(5020(a,1),17210(a,1,2,2,2))].">
      <j1 rule="para" parents="5020 17210"/>
    </justification>
  </clause>

  <clause id="17250">
    <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(5117(a,1),17210(a,1,2,2,2))].">
      <j1 rule="para" parents="5117 17210"/>
    </justification>
  </clause>

  <clause id="17252">
    <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(5359(a,1),17210(a,1,2,2))].">
      <j1 rule="para" parents="5359 17210"/>
    </justification>
  </clause>

  <clause id="17253">
    <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(11603(a,1),17210(a,1,2,2))].">
      <j1 rule="para" parents="11603 17210"/>
    </justification>
  </clause>

  <clause id="17254">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * (y \ K(u,w))) = T(x,(y \ K(u,w)) * z)
    ]]></literal>
    <justification jstring="[para(8050(a,1),17177(a,1,1))].">
      <j1 rule="para" parents="8050 17177"/>
    </justification>
  </clause>

  <clause id="17255">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * (K(u,w) / y)) = T(x,(K(u,w) / y) * z)
    ]]></literal>
    <justification jstring="[para(6256(a,1),17178(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6256 17178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17256">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),z \ T(u,w)) = T(x,T(z \ T(u,w),y))
    ]]></literal>
    <justification jstring="[hyper(861,a,17184,a)].">
      <j1 rule="hyper" parents="861 17184"/>
    </justification>
  </clause>

  <clause id="17258">
    <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(969(a,1),17204(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="969 17204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17259">
    <literal><![CDATA[
      ((1 / x) * K(y,z)) * K(u,x) = K(u,x) / (K(z,y) * x)
    ]]></literal>
    <justification jstring="[hyper(14676,a,17220,a),flip(a)].">
      <j1 rule="hyper" parents="14676 17220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17260">
    <literal><![CDATA[
      K(x,y) / (K(z,u) * y) = (K(x,y) / y) * K(u,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,17219,a(flip),b,17259,a),flip(a)].">
      <j1 rule="hyper" parents="65 17219 17259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17261">
    <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(17260(a,2),10558(a,2,2))].">
      <j1 rule="para" parents="17260 10558"/>
    </justification>
  </clause>

  <clause id="17262">
    <literal><![CDATA[
      K(x,K(y,z / ((K(u,w) * v5) * v6))) = K(x,K(y,z / (v5 * v6)))
    ]]></literal>
    <justification jstring="[hyper(299,a,8791,a,b,17238,a),flip(a)].">
      <j1 rule="hyper" parents="299 8791 17238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17263">
    <literal><![CDATA[
      K(x,K(y,z * ((u / (u / w)) / v5))) = K(x,K(y,(w / v5) * z))
    ]]></literal>
    <justification jstring="[hyper(16574,a,17241,a)].">
      <j1 rule="hyper" parents="16574 17241"/>
    </justification>
  </clause>

  <clause id="17264">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * (y \ K(u,w))) = T(x,(y * K(w,u)) \ z)
    ]]></literal>
    <justification jstring="[hyper(299,a,16909,a,b,17254,a),flip(a)].">
      <j1 rule="hyper" parents="299 16909 17254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17265">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * (y \ K(u,w))) = T(x,(K(u,w) / y) * z)
    ]]></literal>
    <justification jstring="[hyper(16834,a,17255,a)].">
      <j1 rule="hyper" parents="16834 17255"/>
    </justification>
  </clause>

  <clause id="17266">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),u \ T(z,w)) = T(x,T(u \ T(z,w),y))
    ]]></literal>
    <justification jstring="[para(16280(a,1),17256(a,1,1))].">
      <j1 rule="para" parents="16280 17256"/>
    </justification>
  </clause>

  <clause id="17267">
    <literal><![CDATA[
      K(x,K(y,z / (u * (K(w,v5) * v6)))) = K(x,K(y,z / (v6 * u)))
    ]]></literal>
    <justification jstring="[hyper(17212,a,17262,a)].">
      <j1 rule="hyper" parents="17212 17262"/>
    </justification>
  </clause>

  <clause id="17268">
    <literal><![CDATA[
      K(x,K(y,((z \ u) / w) * v5)) = K(x,K(y,v5 * ((u / z) / w)))
    ]]></literal>
    <justification jstring="[para(76(a,1),17263(a,1,2,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="76 17263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17269">
    <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(17263(a,1),16574(a,1))].">
      <j1 rule="para" parents="17263 16574"/>
    </justification>
  </clause>

  <clause id="17270">
    <literal><![CDATA[
      T(T(x,K(y,z)),z / (y * K(u,w))) = T(x,(y * K(u,w)) \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,16907,a,b,17264,a)].">
      <j1 rule="hyper" parents="65 16907 17264"/>
    </justification>
  </clause>

  <clause id="17271">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),T(u \ T(z,w),y)) = T(x,u \ T(z,w))
    ]]></literal>
    <justification jstring="[para(8057(a,1),17266(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8057 17266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17272">
    <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(17267(a,2),17212(a,1))].">
      <j1 rule="para" parents="17267 17212"/>
    </justification>
  </clause>

  <clause id="17273">
    <literal><![CDATA[
      T(x,K(y * K(z,u),w)) = T(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(42,a,8998,a,b,17270,a)].">
      <j1 rule="hyper" parents="42 8998 17270"/>
    </justification>
  </clause>

  <clause id="17274">
    <literal><![CDATA[
      T(x,(y * K(z,u)) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(T(x,K(y,w)),w * (y \ K(u,z))) = v5
    ]]></literal>
    <justification jstring="[para(17270(a,1),16908(a,1))].">
      <j1 rule="para" parents="17270 16908"/>
    </justification>
  </clause>

  <clause id="17275">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * (y * K(u,w))) = T(x,(y * K(u,w)) * z)
    ]]></literal>
    <justification jstring="[para(17273(a,1),13200(a,1,1))].">
      <j1 rule="para" parents="17273 13200"/>
    </justification>
  </clause>

  <clause id="17276">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z,x \ (u * (u * y))) = K(z,y / (u \ (u \ x)))
    ]]></literal>
    <justification jstring="[para(15649(a,1),16971(a,1,2))].">
      <j1 rule="para" parents="15649 16971"/>
    </justification>
  </clause>

  <clause id="17277">
    <literal><![CDATA[
      x * T(T(K(y,z * z) * u,x),w) = T(u,w) * (x * K(y,z * z))
    ]]></literal>
    <justification jstring="[para(16984(a,2),16985(a,1,2,1))].">
      <j1 rule="para" parents="16984 16985"/>
    </justification>
  </clause>

  <clause id="17278">
    <literal><![CDATA[
      (x \ y) / ((((x \ y) \ y) \ y) / x) = T(x * K(y,x),y * x)
    ]]></literal>
    <justification jstring="[hyper(299,a,15256,a(flip),b,17024,a),flip(a)].">
      <j1 rule="hyper" parents="299 15256 17024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17279">
    <literal><![CDATA[
      (x \ y) / ((((x \ y) \ y) \ y) / x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,5470,a(flip),b,17278,a),flip(a)].">
      <j1 rule="hyper" parents="299 5470 17278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17280">
    <literal><![CDATA[
      (x / y) / ((y \ x) / y) = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,10368,a(flip),b,17279,a)].">
      <j1 rule="hyper" parents="65 10368 17279"/>
    </justification>
  </clause>

  <clause id="17281">
    <literal><![CDATA[
      L(x,y,x) * ((x \ y) / x) = y / x
    ]]></literal>
    <justification jstring="[hyper(143,a,17280,a)].">
      <j1 rule="hyper" parents="143 17280"/>
    </justification>
  </clause>

  <clause id="17282">
    <literal><![CDATA[
      a(L((x \ y) / x,L(x,y,x),L(x,y,x)),z,u) = a(L(x,y,x) * (y / x),z,u)
    ]]></literal>
    <justification jstring="[para(17281(a,1),2136(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="17281 2136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17283">
    <literal><![CDATA[
      L(R(T(x,y),z,x) \ u,L(x,w,x),y) = (R(x,z,x) * y) \ (y * u)
    ]]></literal>
    <justification jstring="[para(27(a,2),17038(a,1,1,1))].">
      <j1 rule="para" parents="27 17038"/>
    </justification>
  </clause>

  <clause id="17284">
    <literal><![CDATA[
      T(x,K(y,z) * (T(y * z,y) \ u)) = T(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(299,a,15827,a(flip),b,17085,a),flip(a)].">
      <j1 rule="hyper" parents="299 15827 17085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17286">
    <literal><![CDATA[
      K(x,(y * (y * z)) / u) = K(x,z / (y \ (y \ u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,16970,a(flip),b,17276,a)].">
      <j1 rule="hyper" parents="65 16970 17276"/>
    </justification>
  </clause>

  <clause id="17287">
    <literal><![CDATA[
      K(x,(y * (y * z)) / (y * u)) = K(x,z / (y \ u))
    ]]></literal>
    <justification jstring="[para(9(a,1),17286(a,2,2,2,2))].">
      <j1 rule="para" parents="9 17286"/>
    </justification>
  </clause>

  <clause id="17288">
    <literal><![CDATA[
      K(x,(y \ z) / (y \ u)) = K(x,(y * z) / (y * u))
    ]]></literal>
    <justification jstring="[para(10(a,1),17287(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="10 17287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17289">
    <literal><![CDATA[
      K(x,K(y * z,y * u)) * K(x,(y * z) \ (y * u)) = K(x,(y \ u) / (y \ z))
    ]]></literal>
    <justification jstring="[hyper(299,a,8497,a,b,17288,a)].">
      <j1 rule="hyper" parents="299 8497 17288"/>
    </justification>
  </clause>

  <clause id="17290">
    <literal><![CDATA[
      K(x,(y \ ((1 / y) * z)) / (y \ u)) = K(x,((y \ 1) * (y * z)) / (y * u))
    ]]></literal>
    <justification jstring="[para(944(a,2),17288(a,2,2,1))].">
      <j1 rule="para" parents="944 17288"/>
    </justification>
  </clause>

  <clause id="17291">
    <literal><![CDATA[
      T(K(x,y * y) * z,u) * w = T(z,u) * (w * K(x,y * y))
    ]]></literal>
    <justification jstring="[hyper(395,a,17277,a)].">
      <j1 rule="hyper" parents="395 17277"/>
    </justification>
  </clause>

  <clause id="17292">
    <literal><![CDATA[
      L(R(T(x,y),x \ y,x) \ z,L(x,u,x),y) = ((x * (y / x)) * x) \ (y * z)
    ]]></literal>
    <justification jstring="[para(11287(a,1),17283(a,2,1))].">
      <j1 rule="para" parents="11287 17283"/>
    </justification>
  </clause>

  <clause id="17293">
    <literal><![CDATA[
      K(x * (y * z),T(u,y * z)) = K(T(z * y,y) * x,u)
    ]]></literal>
    <justification jstring="[hyper(16683,a,15913,a),flip(a)].">
      <j1 rule="hyper" parents="16683 15913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17294">
    <literal><![CDATA[
      K(T(x * y,y) * z,u) = K((y * x) * z,u)
    ]]></literal>
    <justification jstring="[hyper(13187,a,17293,a),flip(a)].">
      <j1 rule="hyper" parents="13187 17293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17295">
    <literal><![CDATA[
      K(x,T(y * z,z) * u) * a(w,v5,K((z * y) * u,x)) = K(x,L(T(y * z,z) * u,v5,w))
    ]]></literal>
    <justification jstring="[para(17294(a,1),11896(a,1,2,3))].">
      <j1 rule="para" parents="17294 11896"/>
    </justification>
  </clause>

  <clause id="17297">
    <literal><![CDATA[
      T(x,L(y,z,u)) * K(y,w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x * K(y,w),L(y,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(12568(a,1),16687(a,1))].">
      <j1 rule="para" parents="12568 16687"/>
    </justification>
  </clause>

  <clause id="17298">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x * K(u,x),L(u,z,y)) = w
    ]]></literal>
    <justification jstring="[para(11952(a,1),17297(a,1))].">
      <j1 rule="para" parents="11952 17297"/>
    </justification>
  </clause>

  <clause id="17300">
    <literal><![CDATA[
      T(T(x,K(y,z)),u * (u * (z \ y))) = T(x,y * ((u * u) / z))
    ]]></literal>
    <justification jstring="[hyper(16945,a,14717,a),flip(a)].">
      <j1 rule="hyper" parents="16945 14717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17301">
    <literal><![CDATA[
      K(x,y * ((z * u) \ (z * z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / ((z \ 1) * u)) = w
    ]]></literal>
    <justification jstring="[para(16897(a,1),16969(a,1))].">
      <j1 rule="para" parents="16897 16969"/>
    </justification>
  </clause>

  <clause id="17302">
    <literal><![CDATA[
      K(x,y / ((1 / z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / ((z \ 1) * u)) = w
    ]]></literal>
    <justification jstring="[para(14684(a,1),17301(a,1))].">
      <j1 rule="para" parents="14684 17301"/>
    </justification>
  </clause>

  <clause id="17303">
    <literal><![CDATA[
      L(x,y,((z \ 1) * u) * K(z * u,z)) = L(x,y,L(u / z,z,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,2470,a(flip),b,17061,a),flip(a)].">
      <j1 rule="hyper" parents="299 2470 17061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17304">
    <literal><![CDATA[
      L(x,y,((z \ 1) * u) * K(u * z,z)) = L(x,y,L(u / z,z,z))
    ]]></literal>
    <justification jstring="[para(5980(a,2),17303(a,1,3,2))].">
      <j1 rule="para" parents="5980 17303"/>
    </justification>
  </clause>

  <clause id="17305">
    <literal><![CDATA[
      L(x,y,(z \ 1) * (u * K(u * z,z))) = L(x,y,L(u / z,z,z))
    ]]></literal>
    <justification jstring="[para(11401(a,1),17304(a,1,3))].">
      <j1 rule="para" parents="11401 17304"/>
    </justification>
  </clause>

  <clause id="17306">
    <literal><![CDATA[
      L(x,y,z * (u * K(u * z,z))) = L(x,y,L(u / z,z,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,2489,a(flip),b,17305,a)].">
      <j1 rule="hyper" parents="65 2489 17305"/>
    </justification>
  </clause>

  <clause id="17307">
    <literal><![CDATA[
      L(x,y,L(z / u,u,u)) = L(x,y,T(u * z,u))
    ]]></literal>
    <justification jstring="[para(7299(a,1),17306(a,1,3)),flip(a)].">
      <j1 rule="para" parents="7299 17306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17308">
    <literal><![CDATA[
      L(x,y,T(z * (u * z),z)) = L(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[para(11(a,1),17307(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="11 17307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17309">
    <literal><![CDATA[
      L(x,y,(z * u) * u) = L(x,y,L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,13439,a(flip),b,17308,a)].">
      <j1 rule="hyper" parents="65 13439 17308"/>
    </justification>
  </clause>

  <clause id="17310">
    <literal><![CDATA[
      L(x,y,R(z,u,u)) = L(x,y,L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(2624,a,17309,a)].">
      <j1 rule="hyper" parents="2624 17309"/>
    </justification>
  </clause>

  <clause id="17311">
    <literal><![CDATA[
      L(x,x,L(y,x,x)) = R(y,x,x) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(65,a,1816,a(flip),b,17310,a),flip(a)].">
      <j1 rule="hyper" parents="65 1816 17310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17312">
    <literal><![CDATA[
      L(x,x,L(y,x,x)) = L(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,10422,a(flip),b,17311,a),flip(a)].">
      <j1 rule="hyper" parents="299 10422 17311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17313">
    <literal><![CDATA[
      K((x / (y \ 1)) * T((x / (1 / y)) \ 1,z),u) = K(z,K(u,y / x))
    ]]></literal>
    <justification jstring="[hyper(299,a,12763,a(flip),b,16260,a),flip(a)].">
      <j1 rule="hyper" parents="299 12763 16260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17314">
    <literal><![CDATA[
      K((x / (y \ 1)) * T((x / (1 / y)) \ 1,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,K(u,x * y)) = w
    ]]></literal>
    <justification jstring="[para(17313(a,2),16499(a,1))].">
      <j1 rule="para" parents="17313 16499"/>
    </justification>
  </clause>

  <clause id="17315">
    <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(16268(a,1),16279(a,1,2))].">
      <j1 rule="para" parents="16268 16279"/>
    </justification>
  </clause>

  <clause id="17316">
    <literal><![CDATA[
      K(x,L(y,z / u,(z / u) \ u)) = K(x,L(y,u,(1 / (z / u)) \ u))
    ]]></literal>
    <justification jstring="[para(2521(a,1),16312(a,1,2))].">
      <j1 rule="para" parents="2521 16312"/>
    </justification>
  </clause>

  <clause id="17317">
    <literal><![CDATA[
      K(x,L(y,z \ u,(u / z) \ z)) = K(x,L(y,z,(1 / (u / z)) \ z))
    ]]></literal>
    <justification jstring="[para(17048(a,1),17316(a,1,2))].">
      <j1 rule="para" parents="17048 17316"/>
    </justification>
  </clause>

  <clause id="17318">
    <literal><![CDATA[
      K(L((x \ y) * K(z,u),K(u,z),x),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K((x * K(u,z)) \ y,w) = v5
    ]]></literal>
    <justification jstring="[para(7196(a,1),16475(a,1,1,1))].">
      <j1 rule="para" parents="7196 16475"/>
    </justification>
  </clause>

  <clause id="17319">
    <literal><![CDATA[
      T(x,T((y \ z) * K(y,u),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,T(T(y,u) \ z,w)) = v5
    ]]></literal>
    <justification jstring="[para(16592(a,2),9377(a,1))].">
      <j1 rule="para" parents="16592 9377"/>
    </justification>
  </clause>

  <clause id="17320">
    <literal><![CDATA[
      T(x,T(y / ((z * u) / z),w)) = T(x,T(y / T(u,z),w))
    ]]></literal>
    <justification jstring="[hyper(299,a,9376,a(flip),b,16606,a),flip(a)].">
      <j1 rule="hyper" parents="299 9376 16606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17322">
    <literal><![CDATA[
      T(T(x,K(y,z)),u) * K(x * y,z) = T(x,u) * K(y * x,z)
    ]]></literal>
    <justification jstring="[para(8852(a,1),16660(a,1,1,1))].">
      <j1 rule="para" parents="8852 16660"/>
    </justification>
  </clause>

  <clause id="17323">
    <literal><![CDATA[
      T(x,T(y,z)) * K(x * y,z) = T(x,y) * K(y * x,z)
    ]]></literal>
    <justification jstring="[para(7141(a,1),17322(a,1,1))].">
      <j1 rule="para" parents="7141 17322"/>
    </justification>
  </clause>

  <clause id="17324">
    <literal><![CDATA[
      T(K(x * y,z) * y,T(x,y)) = T(y,T(x,z)) * K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,12137,a,b,17323,a)].">
      <j1 rule="hyper" parents="299 12137 17323"/>
    </justification>
  </clause>

  <clause id="17325">
    <literal><![CDATA[
      K(x,T(y,z)) * (x * K(x * y,z)) = T(K(y * x,z) * x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(299,a,5103,a,b,17324,a)].">
      <j1 rule="hyper" parents="299 5103 17324"/>
    </justification>
  </clause>

  <clause id="17326">
    <literal><![CDATA[
      K(x,T(y,z)) * (K(y * x,z) * x) = T(K(y * x,z) * x,T(y,x))
    ]]></literal>
    <justification jstring="[para(13181(a,2),17325(a,1,2))].">
      <j1 rule="para" parents="13181 17325"/>
    </justification>
  </clause>

  <clause id="17327">
    <literal><![CDATA[
      K(x * K(y * x,z),y) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(37,a,13180,a,b,17326,a)].">
      <j1 rule="hyper" parents="37 13180 17326"/>
    </justification>
  </clause>

  <clause id="17328">
    <literal><![CDATA[
      K(x,((y \ 1) * z) * u) * K(x,K(u,y * z)) = K(x,u * ((y \ 1) * z))
    ]]></literal>
    <justification jstring="[para(16251(a,1),16674(a,1,2))].">
      <j1 rule="para" parents="16251 16674"/>
    </justification>
  </clause>

  <clause id="17329">
    <literal><![CDATA[
      K(x,y / T(z / u,z)) = K(x,y / (u \ z))
    ]]></literal>
    <justification jstring="[hyper(36,a,16919,a,b,16713,a),flip(a)].">
      <j1 rule="hyper" parents="36 16919 16713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17330">
    <literal><![CDATA[
      K(x,L(y / T(z / u,z),w,v5)) = K(L(x,w,v5),y / (u \ z))
    ]]></literal>
    <justification jstring="[hyper(11999,a,17329,a)].">
      <j1 rule="hyper" parents="11999 17329"/>
    </justification>
  </clause>

  <clause id="17331">
    <literal><![CDATA[
      K(x,y / ((z \ u) \ u)) = K(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(76(a,1),17329(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="76 17329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17332">
    <literal><![CDATA[
      K(x,y / T(z,u * z)) = K(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(4452(a,2),17331(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4452 17331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17333">
    <literal><![CDATA[
      K(x,L(y / T(z / u,z),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y / (u \ z),w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(17330(a,2),11999(a,1))].">
      <j1 rule="para" parents="17330 11999"/>
    </justification>
  </clause>

  <clause id="17334">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u * w)),K(w / u,z)) = T(y,K(z,u \ w) * x)
    ]]></literal>
    <justification jstring="[para(16268(a,1),16774(a,1,2,1,2))].">
      <j1 rule="para" parents="16268 16774"/>
    </justification>
  </clause>

  <clause id="17335">
    <literal><![CDATA[
      T(T(x,K(y,z)),u \ (u \ T(y,w))) = T(x,u \ (u \ T(T(y,z),w)))
    ]]></literal>
    <justification jstring="[hyper(14752,a,16831,a),flip(a)].">
      <j1 rule="hyper" parents="14752 16831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17336">
    <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(7208,a,16936,a),flip(a)].">
      <j1 rule="hyper" parents="7208 16936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17337">
    <literal><![CDATA[
      K(x,(y / L(T(z,u),z,z)) * w) * K(x,K(w,T(z,u) * y)) = K(x,w * (y / T(T(z,u),z \ 1)))
    ]]></literal>
    <justification jstring="[para(2821(a,1),17166(a,1,1,2,1,2))].">
      <j1 rule="para" parents="2821 17166"/>
    </justification>
  </clause>

  <clause id="17338">
    <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(299,a,17221,a(flip),b,17207,a),flip(a)].">
      <j1 rule="hyper" parents="299 17221 17207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17340">
    <literal><![CDATA[
      K(x,K(y * K(z,u),L(w,K(v5,v6),v7))) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(299,a,8041,a(flip),b,17338,a),flip(a)].">
      <j1 rule="hyper" parents="299 8041 17338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17341">
    <literal><![CDATA[
      K(x,K(y,L(z,K(u,w),v5))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(17156,a,17340,a)].">
      <j1 rule="hyper" parents="17156 17340"/>
    </justification>
  </clause>

  <clause id="17343">
    <literal><![CDATA[
      K(x,T(y,(z * K(u,w)) / v5)) = K(x,T(y,v5 / z))
    ]]></literal>
    <justification jstring="[hyper(16677,a,17240,a),flip(a)].">
      <j1 rule="hyper" parents="16677 17240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17344">
    <literal><![CDATA[
      K(x,T(y,(z / T(u,w)) / v5)) = K(x,T(y,v5 / (z / u)))
    ]]></literal>
    <justification jstring="[para(7189(a,1),17343(a,1,2,2,1))].">
      <j1 rule="para" parents="7189 17343"/>
    </justification>
  </clause>

  <clause id="17345">
    <literal><![CDATA[
      K(x,T(y,z / (u / T(w,v5)))) = K(x,T(y,z / (u / w)))
    ]]></literal>
    <justification jstring="[hyper(9453,a,17344,a)].">
      <j1 rule="hyper" parents="9453 17344"/>
    </justification>
  </clause>

  <clause id="17346">
    <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(299,a,7859,a(flip),b,17345,a),flip(a)].">
      <j1 rule="hyper" parents="299 7859 17345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17347">
    <literal><![CDATA[
      K(x,T(y,z / (u / (w / v5)))) = K(x,T(y,z / (u / (v5 \ w))))
    ]]></literal>
    <justification jstring="[para(109(a,1),17345(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="109 17345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17348">
    <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(17345(a,1),5272(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17345 5272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17349">
    <literal><![CDATA[
      K(x,((y \ 1) * (y \ z)) / (y \ u)) = K(x,((y \ 1) * (y * z)) / (y * u))
    ]]></literal>
    <justification jstring="[para(1683(a,1),17290(a,1,2,1))].">
      <j1 rule="para" parents="1683 17290"/>
    </justification>
  </clause>

  <clause id="17350">
    <literal><![CDATA[
      T(x,K(y \ z,u) * w) = T(x,K(y * z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(15841,a,17315,a),flip(a)].">
      <j1 rule="hyper" parents="15841 17315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17351">
    <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(17315(a,1),15841(a,1))].">
      <j1 rule="para" parents="17315 15841"/>
    </justification>
  </clause>

  <clause id="17352">
    <literal><![CDATA[
      K(L((x \ y) * K(z,u),K(u,z),x),w) = K((x * K(u,z)) \ y,w)
    ]]></literal>
    <justification jstring="[hyper(17318,a,xx),flip(a)].">
      <j1 rule="hyper" parents="17318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17353">
    <literal><![CDATA[
      K(K(x,y),((z \ 1) * u) * w) * K(K(x,y),K(w,z * u)) = K(x,K(y,w * ((z \ 1) * u)))
    ]]></literal>
    <justification jstring="[hyper(299,a,7954,a(flip),b,17328,a),flip(a)].">
      <j1 rule="hyper" parents="299 7954 17328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17354">
    <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(7489(a,2),17336(a,1,2))].">
      <j1 rule="para" parents="7489 17336"/>
    </justification>
  </clause>

  <clause id="17355">
    <literal><![CDATA[
      K(x,((y \ 1) * (y * z)) / (y * u)) = K(x,(y \ 1) * (y \ (z / (y \ u))))
    ]]></literal>
    <justification jstring="[para(1770(a,1),17349(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1770 17349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17356">
    <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(7586,a,17354,a),flip(a)].">
      <j1 rule="hyper" parents="7586 17354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17357">
    <literal><![CDATA[
      K(x,((y \ 1) * (y * z)) / (y * u)) = K(x,T(z / ((1 / y) \ u),y * y))
    ]]></literal>
    <justification jstring="[para(14366(a,2),17355(a,2,2))].">
      <j1 rule="para" parents="14366 17355"/>
    </justification>
  </clause>

  <clause id="17358">
    <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(12467,a,17356,a)].">
      <j1 rule="hyper" parents="12467 17356"/>
    </justification>
  </clause>

  <clause id="17359">
    <literal><![CDATA[
      K(x,((y \ 1) * (y * z)) / (y * u)) = K(x,z / ((1 / y) \ u))
    ]]></literal>
    <justification jstring="[hyper(299,a,16187,a(flip),b,17357,a),flip(a)].">
      <j1 rule="hyper" parents="299 16187 17357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17361">
    <literal><![CDATA[
      K(x,((y \ 1) * (y * z)) / (y * u)) = K(x,z / ((y \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(299,a,5914,a(flip),b,17359,a),flip(a)].">
      <j1 rule="hyper" parents="299 5914 17359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17362">
    <literal><![CDATA[
      K(x,(y * ((1 / y) * z)) / (y * u)) = K(x,z / ((y \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(944(a,1),17361(a,1,2,1))].">
      <j1 rule="para" parents="944 17361"/>
    </justification>
  </clause>

  <clause id="17363">
    <literal><![CDATA[
      T(K(x,y) * z,u * u) = K(x,y) * T(z,u * u)
    ]]></literal>
    <justification jstring="[para(477(a,1),16200(a,1,1,1,2))].">
      <j1 rule="para" parents="477 16200"/>
    </justification>
  </clause>

  <clause id="17365">
    <literal><![CDATA[
      T((1 / K(x,y)) * L(K(x,y),z,u),w * w) = K(x,y) * T(L(K(x,y) \ 1,z,u),w * w)
    ]]></literal>
    <justification jstring="[para(6500(a,2),17363(a,1,1))].">
      <j1 rule="para" parents="6500 17363"/>
    </justification>
  </clause>

  <clause id="17366">
    <literal><![CDATA[
      T(K(x,y) * T(z,u),w * w) = K(x,y) * T(z,w * (w * u))
    ]]></literal>
    <justification jstring="[para(14468(a,1),17363(a,2,2))].">
      <j1 rule="para" parents="14468 17363"/>
    </justification>
  </clause>

  <clause id="17367">
    <literal><![CDATA[
      T(K(x,y) * K(z,u),w * w) = K(z,u) * T(K(x,y),w * w)
    ]]></literal>
    <justification jstring="[para(16385(a,1),17363(a,1,1))].">
      <j1 rule="para" parents="16385 17363"/>
    </justification>
  </clause>

  <clause id="17368">
    <literal><![CDATA[
      (((x * x) * y) / (x * x)) / (((x * x) * (y * K(K(z,u) * T(w,v5),y))) / (x * x)) = K(y,K(z,u) * T(w,x * (x * v5)))
    ]]></literal>
    <justification jstring="[para(17366(a,1),9341(a,2,2))].">
      <j1 rule="para" parents="17366 9341"/>
    </justification>
  </clause>

  <clause id="17369">
    <literal><![CDATA[
      T(K(x,y) * K(z,u),w * w) = K(z,u) * K(x,y)
    ]]></literal>
    <justification jstring="[para(16192(a,1),17367(a,2,2))].">
      <j1 rule="para" parents="16192 17367"/>
    </justification>
  </clause>

  <clause id="17371">
    <literal><![CDATA[
      K(((x / y) \ y) \ z,T(u,x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(z / ((x / y) \ y),u) = w
    ]]></literal>
    <justification jstring="[para(16442(a,1),16243(a,1))].">
      <j1 rule="para" parents="16442 16243"/>
    </justification>
  </clause>

  <clause id="17374">
    <literal><![CDATA[
      L(K(x,y * K(z,T(u,w))),x,v5) = (x * K(v6,v7)) \ (T(x,K(u,z) * y) * K(v6,v7))
    ]]></literal>
    <justification jstring="[para(16815(a,1),16678(a,2,2,1))].">
      <j1 rule="para" parents="16815 16678"/>
    </justification>
  </clause>

  <clause id="17375">
    <literal><![CDATA[
      L(T(K(x * y,z) * y,x),x,K(x,y)) = K(y,x) * (K(y * x,z) * y)
    ]]></literal>
    <justification jstring="[hyper(299,a,5382,a(flip),b,16990,a),flip(a)].">
      <j1 rule="hyper" parents="299 5382 16990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17376">
    <literal><![CDATA[
      K(x,y) * (K(x * y,z) * x) = T(K(y * x,z) * x,y)
    ]]></literal>
    <justification jstring="[hyper(4572,a,17375,a),flip(a)].">
      <j1 rule="hyper" parents="4572 17375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17378">
    <literal><![CDATA[
      T(K(x * y,z) * y,x) = K(y * x,z) * T(y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,16402,a(flip),b,17376,a),flip(a)].">
      <j1 rule="hyper" parents="65 16402 17376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17379">
    <literal><![CDATA[
      T(K(x * y,z) * y,x) \ T(y,T(x,z)) = K(z,y * x)
    ]]></literal>
    <justification jstring="[para(17378(a,2),12207(a,1,1))].">
      <j1 rule="para" parents="17378 12207"/>
    </justification>
  </clause>

  <clause id="17380">
    <literal><![CDATA[
      T(x * K(x * y,z),y) \ T(x,T(y,z)) = K(z,x * y)
    ]]></literal>
    <justification jstring="[para(13181(a,1),17379(a,1,1,1))].">
      <j1 rule="para" parents="13181 17379"/>
    </justification>
  </clause>

  <clause id="17381">
    <literal><![CDATA[
      T(x * K(x * ((y * z) \ z),y),(y * z) \ z) \ T(x,T((y * z) \ z,T(y,u))) = K(y,x * ((y * z) \ z))
    ]]></literal>
    <justification jstring="[para(6314(a,2),17380(a,1,2,2))].">
      <j1 rule="para" parents="6314 17380"/>
    </justification>
  </clause>

  <clause id="17383">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) * K(y * x,T(x,u)) = K(x * T(y,u),T(x,z))
    ]]></literal>
    <justification jstring="[hyper(17063,a,13510,a)].">
      <j1 rule="hyper" parents="17063 13510"/>
    </justification>
  </clause>

  <clause id="17384">
    <literal><![CDATA[
      K(x * T(y,z),x) = K(y * x,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(36,a,16493,a,b,17383,a)].">
      <j1 rule="hyper" parents="36 16493 17383"/>
    </justification>
  </clause>

  <clause id="17385">
    <literal><![CDATA[
      1 / (x \ K(y * x,T(x,z))) = T(x,x * T(y,z))
    ]]></literal>
    <justification jstring="[para(17384(a,1),5119(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="17384 5119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17387">
    <literal><![CDATA[
      T(x,T(y * x,z)) = T(x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(7575,a,17385,a)].">
      <j1 rule="hyper" parents="7575 17385"/>
    </justification>
  </clause>

  <clause id="17388">
    <literal><![CDATA[
      T(x,T(x * y,z)) = T(x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(13202,a,17387,a)].">
      <j1 rule="hyper" parents="13202 17387"/>
    </justification>
  </clause>

  <clause id="17389">
    <literal><![CDATA[
      L(T(x,x \ y) \ z,L(x,u,x),y) = ((x * (y / x)) * x) \ (y * z)
    ]]></literal>
    <justification jstring="[para(4377(a,1),17292(a,1,1,1))].">
      <j1 rule="para" parents="4377 17292"/>
    </justification>
  </clause>

  <clause id="17390">
    <literal><![CDATA[
      ((x * (y / x)) * x) \ (y * z) = L(T(x,x \ y) \ z,x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,17037,a(flip),b,17389,a),flip(a)].">
      <j1 rule="hyper" parents="65 17037 17389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17391">
    <literal><![CDATA[
      L(T(x,x \ y) \ L(T(x,x \ y),z,u),x,y) = y \ ((y / T(x,x \ y)) * L(T(x,x \ y),z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,12703,a(flip),b,17390,a),flip(a)].">
      <j1 rule="hyper" parents="65 12703 17390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17392">
    <literal><![CDATA[
      T(x,K(y,(z * z) \ u) * w) = w \ T(x * T(w,K(u,y)),K(u,y))
    ]]></literal>
    <justification jstring="[para(16294(a,1),16297(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16294 16297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17393">
    <literal><![CDATA[
      T(x,K(y,(z * z) \ u) * w) = T(x,K(y,u) * w)
    ]]></literal>
    <justification jstring="[hyper(299,a,15769,a(flip),b,17392,a),flip(a)].">
      <j1 rule="hyper" parents="299 15769 17392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17395">
    <literal><![CDATA[
      T(x,K(y,z \ 1) * u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(6842(a,1),17393(a,1,2,1))].">
      <j1 rule="para" parents="6842 17393"/>
    </justification>
  </clause>

  <clause id="17396">
    <literal><![CDATA[
      T(x,K(y,z \ (z \ u)) * w) = T(x,K(y,u) * w)
    ]]></literal>
    <justification jstring="[para(14183(a,1),17393(a,1,2,1))].">
      <j1 rule="para" parents="14183 17393"/>
    </justification>
  </clause>

  <clause id="17397">
    <literal><![CDATA[
      T(x,K(y * z,y \ 1) * (y \ u)) = T(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(299,a,13811,a(flip),b,17395,a),flip(a)].">
      <j1 rule="hyper" parents="299 13811 17395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17398">
    <literal><![CDATA[
      T(x,K(y,z \ u) * w) = T(x,K(y,z * u) * w)
    ]]></literal>
    <justification jstring="[para(9(a,1),17396(a,1,2,1,2,2))].">
      <j1 rule="para" parents="9 17396"/>
    </justification>
  </clause>

  <clause id="17399">
    <literal><![CDATA[
      T(x,K(y * y,z) * u) = T(x,K(z,z) * u)
    ]]></literal>
    <justification jstring="[para(14739(a,1),17396(a,1,2,1))].">
      <j1 rule="para" parents="14739 17396"/>
    </justification>
  </clause>

  <clause id="17400">
    <literal><![CDATA[
      T(x,K(y * y,z) * u) = T(x,1 * u)
    ]]></literal>
    <justification jstring="[para(168(a,1),17399(a,2,2,1))].">
      <j1 rule="para" parents="168 17399"/>
    </justification>
  </clause>

  <clause id="17401">
    <literal><![CDATA[
      T(x,K(y * y,z) * u) = T(x,u)
    ]]></literal>
    <justification jstring="[para(7(a,1),17400(a,2,2))].">
      <j1 rule="para" parents="7 17400"/>
    </justification>
  </clause>

  <clause id="17403">
    <literal><![CDATA[
      T(x,y * (z / (u * u))) = T(x,y * ((u * u) \ z))
    ]]></literal>
    <justification jstring="[hyper(16465,a,17401,a)].">
      <j1 rule="hyper" parents="16465 17401"/>
    </justification>
  </clause>

  <clause id="17404">
    <literal><![CDATA[
      T(x,T(y,z * z) / u) = T(x,y / u)
    ]]></literal>
    <justification jstring="[hyper(15836,a,17401,a)].">
      <j1 rule="hyper" parents="15836 17401"/>
    </justification>
  </clause>

  <clause id="17405">
    <literal><![CDATA[
      T(x,T(y,z * z) * u) = T(x,y * u)
    ]]></literal>
    <justification jstring="[hyper(15833,a,17401,a)].">
      <j1 rule="hyper" parents="15833 17401"/>
    </justification>
  </clause>

  <clause id="17406">
    <literal><![CDATA[
      T(x,y * T(z,u * u)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,16562,a(flip),b,17401,a)].">
      <j1 rule="hyper" parents="65 16562 17401"/>
    </justification>
  </clause>

  <clause id="17407">
    <literal><![CDATA[
      T(x,y * (K(z * z,u) * w)) = T(x,y * w)
    ]]></literal>
    <justification jstring="[para(11541(a,1),17401(a,1,2))].">
      <j1 rule="para" parents="11541 17401"/>
    </justification>
  </clause>

  <clause id="17408">
    <literal><![CDATA[
      T(x,K(y * y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u) = w
    ]]></literal>
    <justification jstring="[para(17401(a,1),15791(a,1))].">
      <j1 rule="para" parents="17401 15791"/>
    </justification>
  </clause>

  <clause id="17409">
    <literal><![CDATA[
      T(x,T(y * (z * z),z)) = T(x,(z * y) * z)
    ]]></literal>
    <justification jstring="[hyper(14490,a,17405,a)].">
      <j1 rule="hyper" parents="14490 17405"/>
    </justification>
  </clause>

  <clause id="17410">
    <literal><![CDATA[
      T(x,((y * y) \ z) * u) = T(x,z * ((y * y) \ u))
    ]]></literal>
    <justification jstring="[para(1066(a,1),17405(a,1,2))].">
      <j1 rule="para" parents="1066 17405"/>
    </justification>
  </clause>

  <clause id="17411">
    <literal><![CDATA[
      T(x,T(y,z * (u * u)) * w) = T(x,T(y,z) * w)
    ]]></literal>
    <justification jstring="[para(14602(a,1),17405(a,1,2,1))].">
      <j1 rule="para" parents="14602 17405"/>
    </justification>
  </clause>

  <clause id="17412">
    <literal><![CDATA[
      T(x,y * T(z,u * (u * w))) = T(x,y * T(z,w))
    ]]></literal>
    <justification jstring="[para(14468(a,1),17406(a,1,2,2))].">
      <j1 rule="para" parents="14468 17406"/>
    </justification>
  </clause>

  <clause id="17413">
    <literal><![CDATA[
      T(x,y * K(z * z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = w
    ]]></literal>
    <justification jstring="[para(8101(a,1),17408(a,1,2))].">
      <j1 rule="para" parents="8101 17408"/>
    </justification>
  </clause>

  <clause id="17414">
    <literal><![CDATA[
      T(x,K(y,z * z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u) = w
    ]]></literal>
    <justification jstring="[para(14846(a,1),17408(a,1,2,1))].">
      <j1 rule="para" parents="14846 17408"/>
    </justification>
  </clause>

  <clause id="17415">
    <literal><![CDATA[
      T(x,T(y,z * z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * u) = w
    ]]></literal>
    <justification jstring="[para(15781(a,1),17408(a,1))].">
      <j1 rule="para" parents="15781 17408"/>
    </justification>
  </clause>

  <clause id="17417">
    <literal><![CDATA[
      T(x,y * T(z,u * u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * z) = w
    ]]></literal>
    <justification jstring="[para(16562(a,1),17408(a,1))].">
      <j1 rule="para" parents="16562 17408"/>
    </justification>
  </clause>

  <clause id="17418">
    <literal><![CDATA[
      T(x,y * (T(z,u * u) \ w)) = T(x,y * (z \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,16888,a(flip),b,17407,a)].">
      <j1 rule="hyper" parents="65 16888 17407"/>
    </justification>
  </clause>

  <clause id="17419">
    <literal><![CDATA[
      T(x,y * (z * K(u,w * w))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(8140(a,1),17407(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8140 17407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17420">
    <literal><![CDATA[
      T(x,T(y * (z * z),z)) = T(x,z * (y * z))
    ]]></literal>
    <justification jstring="[hyper(299,a,13693,a(flip),b,17409,a),flip(a)].">
      <j1 rule="hyper" parents="299 13693 17409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17421">
    <literal><![CDATA[
      T(x,y * (z * T(u,w * w))) = T(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(1389(a,1),17419(a,1,2,2))].">
      <j1 rule="para" parents="1389 17419"/>
    </justification>
  </clause>

  <clause id="17422">
    <literal><![CDATA[
      T(x,y * (z * (u * T(w,v5 * v5)))) = T(x,y * (z * (u * w)))
    ]]></literal>
    <justification jstring="[para(9496(a,1),17419(a,1,2,2))].">
      <j1 rule="para" parents="9496 17419"/>
    </justification>
  </clause>

  <clause id="17423">
    <literal><![CDATA[
      T(x,T(1 / y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y \ 1,z) * u) = w
    ]]></literal>
    <justification jstring="[para(470(a,1),17415(a,1,2,1))].">
      <j1 rule="para" parents="470 17415"/>
    </justification>
  </clause>

  <clause id="17424">
    <literal><![CDATA[
      T(x,T(y,z * (u * u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z) * w) = v5
    ]]></literal>
    <justification jstring="[para(14602(a,1),17415(a,1,2,1))].">
      <j1 rule="para" parents="14602 17415"/>
    </justification>
  </clause>

  <clause id="17425">
    <literal><![CDATA[
      T(x,y * ((z * z) / u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (u \ (z * z))) = w
    ]]></literal>
    <justification jstring="[para(15857(a,1),17417(a,1))].">
      <j1 rule="para" parents="15857 17417"/>
    </justification>
  </clause>

  <clause id="17426">
    <literal><![CDATA[
      T(x,K(y,z \ u) * w) = T(x,w * K(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(299,a,16357,a(flip),b,17398,a),flip(a)].">
      <j1 rule="hyper" parents="299 16357 17398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17427">
    <literal><![CDATA[
      x / T(x,K(y,z * u) * w) = K(K(y,z \ u) * w,x)
    ]]></literal>
    <justification jstring="[para(17398(a,1),5033(a,2,2)),flip(a)].">
      <j1 rule="para" parents="17398 5033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17428">
    <literal><![CDATA[
      T(x,K(y,z \ u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,w * K(y,z * u)) = v5
    ]]></literal>
    <justification jstring="[para(17398(a,2),16368(a,1))].">
      <j1 rule="para" parents="17398 16368"/>
    </justification>
  </clause>

  <clause id="17429">
    <literal><![CDATA[
      T(x,y * (z * (u \ (u \ 1)))) = T(x,y * ((u * u) \ z))
    ]]></literal>
    <justification jstring="[para(951(a,2),17403(a,1,2,2))].">
      <j1 rule="para" parents="951 17403"/>
    </justification>
  </clause>

  <clause id="17430">
    <literal><![CDATA[
      T(x,y * ((z * z) \ (u / y))) = T(x,z \ (z \ T(u,y)))
    ]]></literal>
    <justification jstring="[hyper(15925,a,17410,a),flip(a)].">
      <j1 rule="hyper" parents="15925 17410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17431">
    <literal><![CDATA[
      T(x,y \ (y \ (z * u))) = T(x,z * ((y * y) \ u))
    ]]></literal>
    <justification jstring="[hyper(14631,a,17410,a)].">
      <j1 rule="hyper" parents="14631 17410"/>
    </justification>
  </clause>

  <clause id="17432">
    <literal><![CDATA[
      T(x,T(y,z \ u) * w) = T(x,T(y,z * u) * w)
    ]]></literal>
    <justification jstring="[para(14600(a,1),17411(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14600 17411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17433">
    <literal><![CDATA[
      T(x,y * T(z,u \ w)) = T(x,y * T(z,u * w))
    ]]></literal>
    <justification jstring="[para(10(a,1),17412(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10 17412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17434">
    <literal><![CDATA[
      T(x,y * T(z,u \ 1)) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(71(a,1),17412(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="71 17412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17435">
    <literal><![CDATA[
      T(x,y * (T(z,u \ (u \ 1)) \ w)) = T(x,y * (z \ w))
    ]]></literal>
    <justification jstring="[para(14297(a,1),17418(a,1,2,2,1))].">
      <j1 rule="para" parents="14297 17418"/>
    </justification>
  </clause>

  <clause id="17436">
    <literal><![CDATA[
      T(x,y * T(z * ((u * u) \ w),u * u)) = T(x,y * (((u * u) \ z) * w))
    ]]></literal>
    <justification jstring="[para(1055(a,2),17421(a,1,2,2))].">
      <j1 rule="para" parents="1055 17421"/>
    </justification>
  </clause>

  <clause id="17437">
    <literal><![CDATA[
      T(x,y * K(z,u \ w)) = T(x,y * K(z,u * w))
    ]]></literal>
    <justification jstring="[hyper(16368,a,17426,a)].">
      <j1 rule="hyper" parents="16368 17426"/>
    </justification>
  </clause>

  <clause id="17438">
    <literal><![CDATA[
      T(x,(y \ z) * K(y,u * w)) = T(x,T(y,u \ w) \ z)
    ]]></literal>
    <justification jstring="[hyper(15835,a,17426,a),flip(a)].">
      <j1 rule="hyper" parents="15835 17426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17439">
    <literal><![CDATA[
      T(x,y * (z * (u \ (1 / u)))) = T(x,y * ((u * u) \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,14767,a,b,17431,a)].">
      <j1 rule="hyper" parents="65 14767 17431"/>
    </justification>
  </clause>

  <clause id="17440">
    <literal><![CDATA[
      T(T(x,y * ((z * z) \ u)),w) = T(T(x,y * u),z \ (z \ w))
    ]]></literal>
    <justification jstring="[para(17431(a,1),14743(a,1,1))].">
      <j1 rule="para" parents="17431 14743"/>
    </justification>
  </clause>

  <clause id="17441">
    <literal><![CDATA[
      T(x,(y \ 1) * T(z,u * w)) = T(x,y \ T(z,u \ w))
    ]]></literal>
    <justification jstring="[hyper(14304,a,17433,a),flip(a)].">
      <j1 rule="hyper" parents="14304 17433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17442">
    <literal><![CDATA[
      x \ T(x,y * T(z,u * w)) = K(x,y * T(z,u \ w))
    ]]></literal>
    <justification jstring="[hyper(119,a,17433,a(flip),b,5083,a(flip))].">
      <j1 rule="hyper" parents="119 17433 5083"/>
    </justification>
  </clause>

  <clause id="17443">
    <literal><![CDATA[
      x \ T(x,y * K(z,u * w)) = K(x,y * K(z,u \ w))
    ]]></literal>
    <justification jstring="[hyper(119,a,17437,a(flip),b,5083,a(flip))].">
      <j1 rule="hyper" parents="119 17437 5083"/>
    </justification>
  </clause>

  <clause id="17444">
    <literal><![CDATA[
      K(x,y) * T(x * K(y,x),z * K(u,w * v5)) = T(x,T(z * K(u,w \ v5),y))
    ]]></literal>
    <justification jstring="[para(17437(a,1),9376(a,1,2))].">
      <j1 rule="para" parents="17437 9376"/>
    </justification>
  </clause>

  <clause id="17445">
    <literal><![CDATA[
      T(x,(y * (z * u)) * K(L(u,z,y),w * v5)) = T(x,y * (z * T(u,w \ v5)))
    ]]></literal>
    <justification jstring="[para(9496(a,1),17437(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9496 17437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17446">
    <literal><![CDATA[
      K(K(x,y \ z) * u,w) = K(K(x,y * z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(5118,a,17427,a),flip(a)].">
      <j1 rule="hyper" parents="5118 17427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17447">
    <literal><![CDATA[
      K(K(x,y \ z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(K(x,y * z) * u,w) = v5
    ]]></literal>
    <justification jstring="[para(17427(a,1),5118(a,1))].">
      <j1 rule="para" parents="17427 5118"/>
    </justification>
  </clause>

  <clause id="17449">
    <literal><![CDATA[
      K(K(x,y * (y * z)) * u,w) = K(K(x,z) * u,w)
    ]]></literal>
    <justification jstring="[para(9(a,1),17446(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 17446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17450">
    <literal><![CDATA[
      K(K(x,y * (z * z)) * u,w) = K(K(x,y) * u,w)
    ]]></literal>
    <justification jstring="[para(14464(a,2),17449(a,1,1,1))].">
      <j1 rule="para" parents="14464 17449"/>
    </justification>
  </clause>

  <clause id="17451">
    <literal><![CDATA[
      T(x,T(y \ (y \ z),u)) = T(x,y \ (y \ T(z,u)))
    ]]></literal>
    <justification jstring="[hyper(14790,a,17430,a)].">
      <j1 rule="hyper" parents="14790 17430"/>
    </justification>
  </clause>

  <clause id="17452">
    <literal><![CDATA[
      T(x,y \ (y \ T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y \ (y \ z),u)) = w
    ]]></literal>
    <justification jstring="[para(17430(a,1),14790(a,1))].">
      <j1 rule="para" parents="17430 14790"/>
    </justification>
  </clause>

  <clause id="17453">
    <literal><![CDATA[
      T(T(x,K(y,z)),u \ (u \ T(y,w))) = T(x,T(u \ (u \ T(y,z)),w))
    ]]></literal>
    <justification jstring="[hyper(299,a,17335,a,b,17451,a)].">
      <j1 rule="hyper" parents="299 17335 17451"/>
    </justification>
  </clause>

  <clause id="17454">
    <literal><![CDATA[
      T(x,y * ((z * (u \ 1)) \ ((u * u) \ w))) = T(x,y * ((z * u) \ w))
    ]]></literal>
    <justification jstring="[para(1244(a,1),17435(a,1,2,2))].">
      <j1 rule="para" parents="1244 17435"/>
    </justification>
  </clause>

  <clause id="17455">
    <literal><![CDATA[
      T(x,T(y,z \ u) \ w) = T(x,T(y,z * u) \ w)
    ]]></literal>
    <justification jstring="[hyper(16517,a,17438,a),flip(a)].">
      <j1 rule="hyper" parents="16517 17438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17456">
    <literal><![CDATA[
      T(x,T(y,z * u) \ T(w,T(y,z * u))) = T(x,w / T(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(16649,a,17455,a),flip(a)].">
      <j1 rule="hyper" parents="16649 17455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17457">
    <literal><![CDATA[
      T(x,T(y,y * z) \ u) = T(x,(z / (z / y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,15828,a(flip),b,17455,a),flip(a)].">
      <j1 rule="hyper" parents="65 15828 17455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17458">
    <literal><![CDATA[
      T(x,T(y,z \ 1) \ u) = T(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(8(a,1),17455(a,2,2,1,2))].">
      <j1 rule="para" parents="8 17455"/>
    </justification>
  </clause>

  <clause id="17459">
    <literal><![CDATA[
      K(x,T(y,T(z,u * w) \ v5) * (T(z,u \ w) \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,(T(z,u \ w) \ v5) * y) = v6
    ]]></literal>
    <justification jstring="[para(17455(a,1),13261(a,1,2,1))].">
      <j1 rule="para" parents="17455 13261"/>
    </justification>
  </clause>

  <clause id="17460">
    <literal><![CDATA[
      T(x,(y / (y / z)) \ u) = T(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,13727,a(flip),b,17457,a),flip(a)].">
      <j1 rule="hyper" parents="65 13727 17457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17461">
    <literal><![CDATA[
      T(x,T(y \ z,z) \ u) = T(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[para(76(a,1),17460(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="76 17460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17462">
    <literal><![CDATA[
      T(x,(y / z) \ T(u,y / z)) = T(x,u / T(z \ y,y))
    ]]></literal>
    <justification jstring="[hyper(16645,a,17461,a),flip(a)].">
      <j1 rule="hyper" parents="16645 17461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17463">
    <literal><![CDATA[
      T(x,y * (z * (u \ (1 / u)))) = T(x,y * (z * (u \ (u \ 1))))
    ]]></literal>
    <justification jstring="[hyper(299,a,17429,a,b,17439,a),flip(a)].">
      <j1 rule="hyper" parents="299 17429 17439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17464">
    <literal><![CDATA[
      T(x,y \ T(z,u \ w)) = T(x,y \ T(z,u * w))
    ]]></literal>
    <justification jstring="[hyper(14304,a,17441,a),flip(a)].">
      <j1 rule="hyper" parents="14304 17441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17465">
    <literal><![CDATA[
      T(x,(y \ z) \ T(u,y * z)) = T(x,u / (y \ z))
    ]]></literal>
    <justification jstring="[hyper(16641,a,17464,a),flip(a)].">
      <j1 rule="hyper" parents="16641 17464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17466">
    <literal><![CDATA[
      x / T(x,y \ T(z,u * w)) = K(y \ T(z,u \ w),x)
    ]]></literal>
    <justification jstring="[para(17464(a,1),5033(a,2,2)),flip(a)].">
      <j1 rule="para" parents="17464 5033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17467">
    <literal><![CDATA[
      T(x,T(y,z * u) / (z \ u)) = T(x,(z \ u) \ y)
    ]]></literal>
    <justification jstring="[hyper(15838,a,17465,a),flip(a)].">
      <j1 rule="hyper" parents="15838 17465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17468">
    <literal><![CDATA[
      T(x,T(y,(z / u) * z) / u) = T(x,((z / u) \ z) \ y)
    ]]></literal>
    <justification jstring="[para(79(a,1),17467(a,1,2,2))].">
      <j1 rule="para" parents="79 17467"/>
    </justification>
  </clause>

  <clause id="17469">
    <literal><![CDATA[
      T(x,T(y,z * T(u,z \ 1)) / (u * ((z \ u) / u))) = T(x,(z \ T(u,z \ 1)) \ y)
    ]]></literal>
    <justification jstring="[para(4229(a,1),17467(a,1,2,2))].">
      <j1 rule="para" parents="4229 17467"/>
    </justification>
  </clause>

  <clause id="17470">
    <literal><![CDATA[
      K(x,y * T(z,u \ w)) = K(x,y * T(z,u * w))
    ]]></literal>
    <justification jstring="[hyper(5155,a,17442,a),flip(a)].">
      <j1 rule="hyper" parents="5155 17442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17471">
    <literal><![CDATA[
      K(L(x,y,z),u * T(w,v5 * v6)) = K(x,L(u * T(w,v5 \ v6),y,z))
    ]]></literal>
    <justification jstring="[hyper(11999,a,17470,a),flip(a)].">
      <j1 rule="hyper" parents="11999 17470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17472">
    <literal><![CDATA[
      K(x,((y * z) \ (y * y)) * T(u,z * y)) = K(x,u / ((y \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,15160,a(flip),b,17470,a),flip(a)].">
      <j1 rule="hyper" parents="65 15160 17470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17473">
    <literal><![CDATA[
      K(x,y * T(z,u \ 1)) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(8(a,1),17470(a,2,2,2,2))].">
      <j1 rule="para" parents="8 17470"/>
    </justification>
  </clause>

  <clause id="17474">
    <literal><![CDATA[
      K(x,y * T(z,u * u)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(198(a,1),17470(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="198 17470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17475">
    <literal><![CDATA[
      K(x,(y \ z) * T(u,y * z)) = K(x,u * (y \ z))
    ]]></literal>
    <justification jstring="[para(107(a,1),17470(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 17470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17476">
    <literal><![CDATA[
      (x * K(y,z * T(u,w * v5))) \ x = K(z * T(u,w \ v5),y)
    ]]></literal>
    <justification jstring="[para(17470(a,1),7200(a,1,1,2))].">
      <j1 rule="para" parents="17470 7200"/>
    </justification>
  </clause>

  <clause id="17477">
    <literal><![CDATA[
      K(x,y * (z / (u * u))) = K(x,y * ((u * u) \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,16864,a(flip),b,17474,a)].">
      <j1 rule="hyper" parents="65 16864 17474"/>
    </justification>
  </clause>

  <clause id="17478">
    <literal><![CDATA[
      K(x,y * ((z * z) * u)) = K(x,y * (u * (z * z)))
    ]]></literal>
    <justification jstring="[hyper(65,a,13779,a(flip),b,17474,a),flip(a)].">
      <j1 rule="hyper" parents="65 13779 17474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17479">
    <literal><![CDATA[
      K(x,y * T((z \ 1) \ u,z)) = K(x,y * (u / (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(65,a,16864,a(flip),b,17473,a),flip(a)].">
      <j1 rule="hyper" parents="65 16864 17473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17480">
    <literal><![CDATA[
      K(x,((y * y) \ z) * u) = K(x,z * ((y * y) \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,16195,a,b,17477,a)].">
      <j1 rule="hyper" parents="65 16195 17477"/>
    </justification>
  </clause>

  <clause id="17481">
    <literal><![CDATA[
      K(x,y * ((z * z) * (u \ 1))) = K(x,y * (u \ (z * z)))
    ]]></literal>
    <justification jstring="[para(421(a,1),17478(a,2,2,2))].">
      <j1 rule="para" parents="421 17478"/>
    </justification>
  </clause>

  <clause id="17482">
    <literal><![CDATA[
      K(x,(((y * y) \ z) * u) * w) = K(x,(z * u) * ((y * y) \ w))
    ]]></literal>
    <justification jstring="[para(664(a,1),17480(a,1,2,1))].">
      <j1 rule="para" parents="664 17480"/>
    </justification>
  </clause>

  <clause id="17483">
    <literal><![CDATA[
      K(x,y * K(z,u \ w)) = K(x,y * K(z,u * w))
    ]]></literal>
    <justification jstring="[hyper(5155,a,17443,a),flip(a)].">
      <j1 rule="hyper" parents="5155 17443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17484">
    <literal><![CDATA[
      K(x,y * K(z,z \ u)) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(16698,a,17483,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="16698 17483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17485">
    <literal><![CDATA[
      K(x,y * K(z * u,u)) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[para(5203(a,1),17484(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5203 17484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17486">
    <literal><![CDATA[
      T(x,y / T(z \ u,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y / (u / z)) = w
    ]]></literal>
    <justification jstring="[para(17462(a,1),16641(a,1))].">
      <j1 rule="para" parents="17462 16641"/>
    </justification>
  </clause>

  <clause id="17487">
    <literal><![CDATA[
      K(x \ T(y,z \ u),w) = K(x \ T(y,z * u),w)
    ]]></literal>
    <justification jstring="[hyper(5118,a,17466,a),flip(a)].">
      <j1 rule="hyper" parents="5118 17466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17488">
    <literal><![CDATA[
      K(x \ T(y,y * z),u) = K(x \ (z / (z / y)),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,16049,a(flip),b,17487,a),flip(a)].">
      <j1 rule="hyper" parents="65 16049 17487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17489">
    <literal><![CDATA[
      K((x * y) \ T(z,u * w),L(v5,y,x)) = K(y \ (x \ T(z,u \ w)),v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,15631,a(flip),b,17487,a),flip(a)].">
      <j1 rule="hyper" parents="65 15631 17487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17490">
    <literal><![CDATA[
      K(x \ T(y,z * z),u) = K(x \ y,u)
    ]]></literal>
    <justification jstring="[para(198(a,1),17487(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="198 17487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17491">
    <literal><![CDATA[
      K(x \ T(y,z * z),u) = K(T(y,x) / x,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,13734,a,b,17490,a),flip(a)].">
      <j1 rule="hyper" parents="299 13734 17490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17492">
    <literal><![CDATA[
      K(x \ T((y \ 1) * z,u * u),w) = K(x \ ((1 / y) * z),w)
    ]]></literal>
    <justification jstring="[hyper(299,a,5890,a,b,17490,a),flip(a)].">
      <j1 rule="hyper" parents="299 5890 17490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17493">
    <literal><![CDATA[
      K(x \ T(y,z * z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,u) = w
    ]]></literal>
    <justification jstring="[para(17491(a,2),13762(a,1))].">
      <j1 rule="para" parents="17491 13762"/>
    </justification>
  </clause>

  <clause id="17494">
    <literal><![CDATA[
      K(x \ (y / (y / z)),u) = K(x \ T(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,13783,a(flip),b,17488,a),flip(a)].">
      <j1 rule="hyper" parents="65 13783 17488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17495">
    <literal><![CDATA[
      K((x \ y) \ T(z,u),L(w,y,x)) = K(y \ (x * (u / (u / z))),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,14989,a(flip),b,17494,a),flip(a)].">
      <j1 rule="hyper" parents="65 14989 17494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17496">
    <literal><![CDATA[
      K(x \ T(y \ z,z),u) = K(x \ (z / y),u)
    ]]></literal>
    <justification jstring="[para(76(a,1),17494(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="76 17494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17497">
    <literal><![CDATA[
      T(x,T(y,z * (u \ z)) / u) = T(x,((z / u) \ z) \ y)
    ]]></literal>
    <justification jstring="[para(13982(a,1),17468(a,1,2,1))].">
      <j1 rule="para" parents="13982 17468"/>
    </justification>
  </clause>

  <clause id="17498">
    <literal><![CDATA[
      K(x,y \ T((z \ 1) \ u,z)) = K(x,(y \ 1) * (u / (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(14281,a,17479,a)].">
      <j1 rule="hyper" parents="14281 17479"/>
    </justification>
  </clause>

  <clause id="17499">
    <literal><![CDATA[
      K(x,y / (z * (u / (w * w)))) = K(x,y * ((z * u) \ (w * w)))
    ]]></literal>
    <justification jstring="[hyper(14628,a,17481,a)].">
      <j1 rule="hyper" parents="14628 17481"/>
    </justification>
  </clause>

  <clause id="17500">
    <literal><![CDATA[
      T(x,T(y,z * (u \ z)) / u) = T(x,u \ y)
    ]]></literal>
    <justification jstring="[para(79(a,1),17497(a,2,2,1))].">
      <j1 rule="para" parents="79 17497"/>
    </justification>
  </clause>

  <clause id="17501">
    <literal><![CDATA[
      T(x,T(y,z * u) / (z / u)) = T(x,(z / u) \ y)
    ]]></literal>
    <justification jstring="[para(79(a,1),17500(a,1,2,1,2,2))].">
      <j1 rule="para" parents="79 17500"/>
    </justification>
  </clause>

  <clause id="17502">
    <literal><![CDATA[
      T(T(x,K(y,z)),u * (u * (z \ y))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (z \ (u * u))) = w
    ]]></literal>
    <justification jstring="[para(17300(a,2),17425(a,1))].">
      <j1 rule="para" parents="17300 17425"/>
    </justification>
  </clause>

  <clause id="17503">
    <literal><![CDATA[
      K(K(x,y / z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(K(x,z * y) * u,w) = v5
    ]]></literal>
    <justification jstring="[para(16825(a,2),17447(a,1))].">
      <j1 rule="para" parents="16825 17447"/>
    </justification>
  </clause>

  <clause id="17504">
    <literal><![CDATA[
      T(x,y * (z * ((u \ 1) * (w * (u * u))))) = T(x,y * (z * (u * w)))
    ]]></literal>
    <justification jstring="[para(742(a,2),17422(a,1,2,2,2))].">
      <j1 rule="para" parents="742 17422"/>
    </justification>
  </clause>

  <clause id="17505">
    <literal><![CDATA[
      T(x,K(y,K(z,u)) * (w * (v5 \ (v5 \ 1)))) = T(x,w * (v5 \ (1 / v5)))
    ]]></literal>
    <justification jstring="[hyper(16730,a,17463,a),flip(a)].">
      <j1 rule="hyper" parents="16730 17463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17506">
    <literal><![CDATA[
      K(x * T(y,z \ u),w) = K(x * T(y,z * u),w)
    ]]></literal>
    <justification jstring="[hyper(7209,a,17476,a),flip(a)].">
      <j1 rule="hyper" parents="7209 17476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17507">
    <literal><![CDATA[
      K(x * T(y,z \ u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x * T(y,z * u),w) = v5
    ]]></literal>
    <justification jstring="[para(17476(a,1),7209(a,1))].">
      <j1 rule="para" parents="17476 7209"/>
    </justification>
  </clause>

  <clause id="17508">
    <literal><![CDATA[
      K(x * T(y,z * z),u) = K(x * y,u)
    ]]></literal>
    <justification jstring="[para(198(a,1),17506(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="198 17506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17509">
    <literal><![CDATA[
      K(x * T((y \ z) * y,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x * T(T(z,u),y * z),w) = v5
    ]]></literal>
    <justification jstring="[para(15916(a,1),17507(a,1))].">
      <j1 rule="para" parents="15916 17507"/>
    </justification>
  </clause>

  <clause id="17510">
    <literal><![CDATA[
      K(x,(K(((y \ z) \ z) * u,w) / w) * (T(y,z) * u)) = K(x,(((y \ z) \ z) * u) * ((w * w) \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,15046,a,b,17482,a)].">
      <j1 rule="hyper" parents="65 15046 17482"/>
    </justification>
  </clause>

  <clause id="17511">
    <literal><![CDATA[
      K(x \ ((1 / y) * z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ ((y \ 1) * z),u) = w
    ]]></literal>
    <justification jstring="[para(17492(a,1),17493(a,1))].">
      <j1 rule="para" parents="17492 17493"/>
    </justification>
  </clause>

  <clause id="17512">
    <literal><![CDATA[
      K(x,y \ T((z \ 1) \ u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (u / (z \ 1))) = w
    ]]></literal>
    <justification jstring="[para(17498(a,2),14281(a,1))].">
      <j1 rule="para" parents="17498 14281"/>
    </justification>
  </clause>

  <clause id="17513">
    <literal><![CDATA[
      K(x \ (y * (z / (z / u))),w) = K(x \ (y * T(u,z)),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,14989,a(flip),b,17495,a),flip(a)].">
      <j1 rule="hyper" parents="65 14989 17495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17514">
    <literal><![CDATA[
      K(x,y \ ((z \ 1) \ T(u,z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (u / (z \ 1))) = w
    ]]></literal>
    <justification jstring="[para(13839(a,1),17512(a,1))].">
      <j1 rule="para" parents="13839 17512"/>
    </justification>
  </clause>

  <clause id="17515">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(u \ (u \ y),w)) = T(x,T(u \ (u \ T(y,z)),w))
    ]]></literal>
    <justification jstring="[hyper(17452,a,17453,a)].">
      <j1 rule="hyper" parents="17452 17453"/>
    </justification>
  </clause>

  <clause id="17516">
    <literal><![CDATA[
      T(x,y / T(z,u \ w)) = T(x,y / T(z,u * w))
    ]]></literal>
    <justification jstring="[hyper(16641,a,17456,a),flip(a)].">
      <j1 rule="hyper" parents="16641 17456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17517">
    <literal><![CDATA[
      T(x,y / T(z,u / w)) = T(x,y / T(z,w * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,16742,a,b,17516,a)].">
      <j1 rule="hyper" parents="65 16742 17516"/>
    </justification>
  </clause>

  <clause id="17518">
    <literal><![CDATA[
      K(x,L(y * T(z,u \ w),v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y * T(z,u * w),v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(17471(a,1),11999(a,1))].">
      <j1 rule="para" parents="17471 11999"/>
    </justification>
  </clause>

  <clause id="17519">
    <literal><![CDATA[
      T(x,y * L(z * (u * u),u,u)) = T(x,y * (u * (u * z)))
    ]]></literal>
    <justification jstring="[para(1673(a,1),17504(a,1,2,2))].">
      <j1 rule="para" parents="1673 17504"/>
    </justification>
  </clause>

  <clause id="17520">
    <literal><![CDATA[
      T(x,T(y,L(z * (u * u),u,u)) * (u * (u * z))) = T(x,L(z * (u * u),u,u) * y)
    ]]></literal>
    <justification jstring="[hyper(13267,a,17519,a),flip(a)].">
      <j1 rule="hyper" parents="13267 17519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17521">
    <literal><![CDATA[
      ((x * L(y * (z * z),z,z)) * T(u,w)) / ((x * L(y * (z * z),z,z)) * u) = K(u,T(w,x * (z * (z * y))))
    ]]></literal>
    <justification jstring="[para(17519(a,1),9466(a,2,2))].">
      <j1 rule="para" parents="17519 9466"/>
    </justification>
  </clause>

  <clause id="17522">
    <literal><![CDATA[
      T(x,y * (z \ (z \ K(u,K(w,v5))))) = T(x,y * (z \ (1 / z)))
    ]]></literal>
    <justification jstring="[hyper(65,a,17077,a(flip),b,17505,a)].">
      <j1 rule="hyper" parents="65 17077 17505"/>
    </justification>
  </clause>

  <clause id="17523">
    <literal><![CDATA[
      T(x,y * (z \ (z \ K(u,K(w,v5))))) = T(x,z \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(299,a,14766,a(flip),b,17522,a),flip(a)].">
      <j1 rule="hyper" parents="299 14766 17522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17524">
    <literal><![CDATA[
      T(x,y * (z \ (z \ 1))) = T(x,z \ (z \ y))
    ]]></literal>
    <justification jstring="[para(168(a,1),17523(a,1,2,2,2,2))].">
      <j1 rule="para" parents="168 17523"/>
    </justification>
  </clause>

  <clause id="17525">
    <literal><![CDATA[
      T(x,y / (z * z)) = T(x,z \ (z \ y))
    ]]></literal>
    <justification jstring="[para(951(a,1),17524(a,1,2))].">
      <j1 rule="para" parents="951 17524"/>
    </justification>
  </clause>

  <clause id="17526">
    <literal><![CDATA[
      T(x,(1 / y) * (((y * y) \ z) * y)) = T(x,y \ (y \ T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(65,a,15147,a,b,17525,a)].">
      <j1 rule="hyper" parents="65 15147 17525"/>
    </justification>
  </clause>

  <clause id="17527">
    <literal><![CDATA[
      T(x,(y * z) \ ((y * z) \ z)) = T(x,y \ ((y * z) \ 1))
    ]]></literal>
    <justification jstring="[para(850(a,1),17525(a,1,2)),flip(a)].">
      <j1 rule="para" parents="850 17525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17528">
    <literal><![CDATA[
      T(x,(1 / y) * (((y * y) \ z) * y)) = T(x,y \ (z / y))
    ]]></literal>
    <justification jstring="[hyper(299,a,15875,a(flip),b,17526,a),flip(a)].">
      <j1 rule="hyper" parents="299 15875 17526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17529">
    <literal><![CDATA[
      T(x,T(T(y \ (y \ z),u),w)) = T(x,T(y \ (y \ T(z,u)),w))
    ]]></literal>
    <justification jstring="[hyper(65,a,16832,a(flip),b,17515,a)].">
      <j1 rule="hyper" parents="65 16832 17515"/>
    </justification>
  </clause>

  <clause id="17530">
    <literal><![CDATA[
      K(x \ (y \ T(z,u \ w)),v5) = K(x \ (y \ T(z,u * w)),v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,15631,a(flip),b,17489,a),flip(a)].">
      <j1 rule="hyper" parents="65 15631 17489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17531">
    <literal><![CDATA[
      T(x,y * (((z * z) \ u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (u * ((z * z) \ w))) = v5
    ]]></literal>
    <justification jstring="[para(17436(a,1),17417(a,1))].">
      <j1 rule="para" parents="17436 17417"/>
    </justification>
  </clause>

  <clause id="17532">
    <literal><![CDATA[
      T(x,(1 / y) * (z * ((y * y) \ y))) = T(x,y \ (z / y))
    ]]></literal>
    <justification jstring="[hyper(17531,a,17528,a)].">
      <j1 rule="hyper" parents="17531 17528"/>
    </justification>
  </clause>

  <clause id="17533">
    <literal><![CDATA[
      T(x,(1 / y) * (z * (1 / y))) = T(x,y \ (z / y))
    ]]></literal>
    <justification jstring="[para(264(a,1),17532(a,1,2,2,2))].">
      <j1 rule="para" parents="264 17532"/>
    </justification>
  </clause>

  <clause id="17534">
    <literal><![CDATA[
      T(x,(y \ 1) * (z * (y \ 1))) = T(x,y \ (z / y))
    ]]></literal>
    <justification jstring="[para(3296(a,1),17533(a,1,2))].">
      <j1 rule="para" parents="3296 17533"/>
    </justification>
  </clause>

  <clause id="17535">
    <literal><![CDATA[
      T(x,y \ (z * (y \ 1))) = T(x,y \ (z / y))
    ]]></literal>
    <justification jstring="[hyper(14304,a,17534,a)].">
      <j1 rule="hyper" parents="14304 17534"/>
    </justification>
  </clause>

  <clause id="17536">
    <literal><![CDATA[
      T(x,y * (z * T(u,w \ v5))) = T(x,y * (z * T(u,w * v5)))
    ]]></literal>
    <justification jstring="[para(9496(a,1),17445(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9496 17445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17537">
    <literal><![CDATA[
      T(x,y * (T(z,T(u,w \ v5)) * T(u,w * v5))) = T(x,y * (T(u,w \ v5) * z))
    ]]></literal>
    <justification jstring="[hyper(15900,a,17536,a),flip(a)].">
      <j1 rule="hyper" parents="15900 17536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17538">
    <literal><![CDATA[
      T(x,(y \ 1) * (z * T(u,w * v5))) = T(x,y \ (z * T(u,w \ v5)))
    ]]></literal>
    <justification jstring="[hyper(14304,a,17536,a),flip(a)].">
      <j1 rule="hyper" parents="14304 17536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17539">
    <literal><![CDATA[
      T(x,T(y,z * T(u,w \ v5)) * (z * T(u,w * v5))) = T(x,(z * T(u,w \ v5)) * y)
    ]]></literal>
    <justification jstring="[hyper(13267,a,17536,a),flip(a)].">
      <j1 rule="hyper" parents="13267 17536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17540">
    <literal><![CDATA[
      x \ T(x,y * (z * T(u,w * v5))) = K(x,y * (z * T(u,w \ v5)))
    ]]></literal>
    <justification jstring="[hyper(119,a,17536,a(flip),b,5083,a(flip))].">
      <j1 rule="hyper" parents="119 17536 5083"/>
    </justification>
  </clause>

  <clause id="17541">
    <literal><![CDATA[
      T(x,y * ((z \ u) * T(w,z * u))) = T(x,y * (w * (z \ u)))
    ]]></literal>
    <justification jstring="[para(107(a,1),17536(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 17536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17542">
    <literal><![CDATA[
      x / T(x,y * (z * T(u,w * v5))) = K(y * (z * T(u,w \ v5)),x)
    ]]></literal>
    <justification jstring="[para(17536(a,1),5033(a,2,2)),flip(a)].">
      <j1 rule="para" parents="17536 5033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17543">
    <literal><![CDATA[
      T(x,y \ (z * T(u,w \ v5))) = T(x,y \ (z * T(u,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(14304,a,17538,a),flip(a)].">
      <j1 rule="hyper" parents="14304 17538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17544">
    <literal><![CDATA[
      T(x,y \ (z * T(u,w * w))) = T(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[para(198(a,1),17543(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="198 17543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17545">
    <literal><![CDATA[
      T(x,y \ ((z * z) * u)) = T(x,z * (z * (y \ u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,14677,a(flip),b,17544,a),flip(a)].">
      <j1 rule="hyper" parents="65 14677 17544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17546">
    <literal><![CDATA[
      T(x,y \ (z * (1 / u))) = T(x,y \ (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(469(a,1),17544(a,1,2,2,2))].">
      <j1 rule="para" parents="469 17544"/>
    </justification>
  </clause>

  <clause id="17548">
    <literal><![CDATA[
      T(x,(y \ (z * z)) * u) = T(x,z * (z * (y \ u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,14380,a(flip),b,17545,a)].">
      <j1 rule="hyper" parents="65 14380 17545"/>
    </justification>
  </clause>

  <clause id="17549">
    <literal><![CDATA[
      T(x,y * (y * ((y * z) \ u))) = T(x,((y \ 1) * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,3903,a(flip),b,17545,a),flip(a)].">
      <j1 rule="hyper" parents="65 3903 17545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17550">
    <literal><![CDATA[
      T(x,y \ T((z * u) * (1 / z),z * u)) = T(x,y \ ((u * z) * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(65,a,13830,a,b,17546,a)].">
      <j1 rule="hyper" parents="65 13830 17546"/>
    </justification>
  </clause>

  <clause id="17551">
    <literal><![CDATA[
      K(x,y * (z * T(u,w \ v5))) = K(x,y * (z * T(u,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(5155,a,17540,a),flip(a)].">
      <j1 rule="hyper" parents="5155 17540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17552">
    <literal><![CDATA[
      K(x,y * (z * T(u,w \ v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * T(u,w * v5))) = v6
    ]]></literal>
    <justification jstring="[para(17540(a,1),5155(a,1))].">
      <j1 rule="para" parents="17540 5155"/>
    </justification>
  </clause>

  <clause id="17553">
    <literal><![CDATA[
      K(x,(y \ 1) * (z * T(u,w * v5))) = K(x,y \ (z * T(u,w \ v5)))
    ]]></literal>
    <justification jstring="[hyper(14281,a,17551,a),flip(a)].">
      <j1 rule="hyper" parents="14281 17551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17554">
    <literal><![CDATA[
      K(x,T(y,z * T(u,w \ v5)) * (z * T(u,w * v5))) = K(x,(z * T(u,w \ v5)) * y)
    ]]></literal>
    <justification jstring="[hyper(13261,a,17551,a),flip(a)].">
      <j1 rule="hyper" parents="13261 17551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17555">
    <literal><![CDATA[
      K(x,(y * ((z * T(u,w \ v5)) \ 1)) * (z * T(u,w * v5))) = K(x,(y * (z * T(u,w \ v5))) * (1 / (z * T(u,w \ v5))))
    ]]></literal>
    <justification jstring="[para(1088(a,1),17551(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1088 17551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17556">
    <literal><![CDATA[
      K(x,((y * T(z,u \ w)) \ (v5 * ((y * T(z,u \ w)) \ 1))) * (y * T(z,u * w))) = K(x,T(v5,y * T(z,u \ w)) * (1 / (y * T(z,u \ w))))
    ]]></literal>
    <justification jstring="[para(3735(a,1),17551(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3735 17551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17557">
    <literal><![CDATA[
      K(x,y * ((z / u) * T(u,w * v5))) = K(x,y * (z * K(u,w \ v5)))
    ]]></literal>
    <justification jstring="[para(6869(a,1),17551(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6869 17551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17558">
    <literal><![CDATA[
      K(x * (y * T(z,u \ w)),v5) = K(x * (y * T(z,u * w)),v5)
    ]]></literal>
    <justification jstring="[hyper(5118,a,17542,a),flip(a)].">
      <j1 rule="hyper" parents="5118 17542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17559">
    <literal><![CDATA[
      K((x \ 1) * (y * T(z,u * w)),v5) = K(x \ (y * T(z,u \ w)),v5)
    ]]></literal>
    <justification jstring="[hyper(14266,a,17558,a),flip(a)].">
      <j1 rule="hyper" parents="14266 17558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17560">
    <literal><![CDATA[
      K(x,y \ (z * T(u,w \ v5))) = K(x,y \ (z * T(u,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(14281,a,17553,a),flip(a)].">
      <j1 rule="hyper" parents="14281 17553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17561">
    <literal><![CDATA[
      K(x,y \ (z * T(u,w \ v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (z * T(u,w * v5))) = v6
    ]]></literal>
    <justification jstring="[para(17553(a,1),14281(a,1))].">
      <j1 rule="para" parents="17553 14281"/>
    </justification>
  </clause>

  <clause id="17562">
    <literal><![CDATA[
      K(x,y \ (z * T(u,w * (w * v5)))) = K(x,y \ (z * T(u,v5)))
    ]]></literal>
    <justification jstring="[para(9(a,1),17560(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="9 17560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17563">
    <literal><![CDATA[
      K(x,y \ (z * T(u,w * w))) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[para(198(a,1),17560(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="198 17560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17564">
    <literal><![CDATA[
      K(x,y \ (z * (u / (w * w)))) = K(x,y \ (z * ((w * w) \ u)))
    ]]></literal>
    <justification jstring="[para(109(a,1),17563(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="109 17563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17565">
    <literal><![CDATA[
      K(x,y * (z * K(u,w \ v5))) = K(x,y * (z * K(u,w * v5)))
    ]]></literal>
    <justification jstring="[para(6869(a,1),17557(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6869 17557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17566">
    <literal><![CDATA[
      K(x,y * (K(z,u \ w) * v5)) = K(x,y * (v5 * K(z,u * w)))
    ]]></literal>
    <justification jstring="[hyper(16810,a,17565,a)].">
      <j1 rule="hyper" parents="16810 17565"/>
    </justification>
  </clause>

  <clause id="17567">
    <literal><![CDATA[
      K(x,y * (K(z,u \ w) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (K(z,u * w) * v5)) = v6
    ]]></literal>
    <justification jstring="[para(17566(a,2),16810(a,1))].">
      <j1 rule="para" parents="17566 16810"/>
    </justification>
  </clause>

  <clause id="17568">
    <literal><![CDATA[
      K(x \ (y * T(z,u \ w)),v5) = K(x \ (y * T(z,u * w)),v5)
    ]]></literal>
    <justification jstring="[hyper(14266,a,17559,a),flip(a)].">
      <j1 rule="hyper" parents="14266 17559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17569">
    <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(17559(a,1),14266(a,1))].">
      <j1 rule="para" parents="17559 14266"/>
    </justification>
  </clause>

  <clause id="17570">
    <literal><![CDATA[
      K(x \ ((y \ z) * T(u,y * z)),w) = K(x \ (u * (y \ z)),w)
    ]]></literal>
    <justification jstring="[para(107(a,1),17568(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="107 17568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17571">
    <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(16849(a,2),17552(a,1))].">
      <j1 rule="para" parents="16849 17552"/>
    </justification>
  </clause>

  <clause id="17572">
    <literal><![CDATA[
      T(x,y \ T((z * u) * (1 / z),z * u)) = T(x,y \ R(u,z,z))
    ]]></literal>
    <justification jstring="[para(1246(a,1),17550(a,2,2,2))].">
      <j1 rule="para" parents="1246 17550"/>
    </justification>
  </clause>

  <clause id="17573">
    <literal><![CDATA[
      T(x,y \ ((1 / z) * (z * u))) = T(x,y \ R(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,13770,a(flip),b,17572,a)].">
      <j1 rule="hyper" parents="65 13770 17572"/>
    </justification>
  </clause>

  <clause id="17574">
    <literal><![CDATA[
      T(x,y \ R(z,u,u)) = T(x,y \ L(z,u,u))
    ]]></literal>
    <justification jstring="[para(475(a,1),17573(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="475 17573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17575">
    <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(8666(a,1),16557(a,1,2))].">
      <j1 rule="para" parents="8666 16557"/>
    </justification>
  </clause>

  <clause id="17576">
    <literal><![CDATA[
      T(x,K(y \ z,y) * (u / (y \ T(z,w)))) = T(x,u / T(y \ T(z,w),y))
    ]]></literal>
    <justification jstring="[hyper(16817,a,16583,a)].">
      <j1 rule="hyper" parents="16817 16583"/>
    </justification>
  </clause>

  <clause id="17577">
    <literal><![CDATA[
      T(x,K(y,z) * (u / (z \ T(y,w)))) = T(x,u / T(z \ T(y,w),z))
    ]]></literal>
    <justification jstring="[hyper(15930,a,17576,a)].">
      <j1 rule="hyper" parents="15930 17576"/>
    </justification>
  </clause>

  <clause id="17580">
    <literal><![CDATA[
      T(x,K(y,z) * (u / (z \ T(y,w)))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,u / (T(y,w) / z)) = v5
    ]]></literal>
    <justification jstring="[para(17577(a,2),16638(a,1))].">
      <j1 rule="para" parents="17577 16638"/>
    </justification>
  </clause>

  <clause id="17581">
    <literal><![CDATA[
      K(x,T(y,x \ z)) * (x * T(x \ z,u)) = (x * T(x \ z,u)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(8132(a,1),16826(a,1,1))].">
      <j1 rule="para" parents="8132 16826"/>
    </justification>
  </clause>

  <clause id="17583">
    <literal><![CDATA[
      K(x,T(y,z)) * (x * T(x \ z,u)) = (x * T(x \ z,u)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(7623(a,1),17581(a,1,1))].">
      <j1 rule="para" parents="7623 17581"/>
    </justification>
  </clause>

  <clause id="17584">
    <literal><![CDATA[
      T(x,T(y,z)) * T(x \ z,u) = (x * T(x \ z,u)) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5398,a,17583,a)].">
      <j1 rule="hyper" parents="5398 17583"/>
    </justification>
  </clause>

  <clause id="17585">
    <literal><![CDATA[
      (x * T(x \ y,z)) * K(x,T(y,u)) = T(x,T(y,u)) * T(x \ y,z)
    ]]></literal>
    <justification jstring="[para(175(a,1),17584(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="175 17584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17586">
    <literal><![CDATA[
      T(T(x,y / (z * u)),K(w,(z * u) * y)) = T(x,T(y / T(u * z,u),w))
    ]]></literal>
    <justification jstring="[para(13954(a,1),16851(a,1,1))].">
      <j1 rule="para" parents="13954 16851"/>
    </justification>
  </clause>

  <clause id="17587">
    <literal><![CDATA[
      T(x,T(y / T(z * u,z),w)) = T(x,T(y / (u * z),w))
    ]]></literal>
    <justification jstring="[hyper(16784,a,17586,a),flip(a)].">
      <j1 rule="hyper" parents="16784 17586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17589">
    <literal><![CDATA[
      K(x,T(y,(z * u) * z) * w) != K(w,K(y,x)) * v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w * T(y,z * (u * z))) = v5
    ]]></literal>
    <justification jstring="[para(16872(a,1),45(a,1))].">
      <j1 rule="para" parents="16872 45"/>
    </justification>
  </clause>

  <clause id="17590">
    <literal><![CDATA[
      K(x,L(T((y / z) * u,y * z),w,v5)) = K(x,L(u / ((y / z) \ 1),w,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,15076,a(flip),b,16895,a)].">
      <j1 rule="hyper" parents="65 15076 16895"/>
    </justification>
  </clause>

  <clause id="17591">
    <literal><![CDATA[
      K(x,L(T((y / z) * u,y * z),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(u * (y / z),w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(17590(a,2),14650(a,1))].">
      <j1 rule="para" parents="17590 14650"/>
    </justification>
  </clause>

  <clause id="17592">
    <literal><![CDATA[
      T(x,K(y * K(z,u),w) * v5) = v5 \ T(x * T(v5,K(w,y)),K(w,y))
    ]]></literal>
    <justification jstring="[para(17170(a,1),17176(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17170 17176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17593">
    <literal><![CDATA[
      T(x,K(y * K(z,u),w) * v5) = T(x,K(y,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(299,a,15769,a(flip),b,17592,a),flip(a)].">
      <j1 rule="hyper" parents="299 15769 17592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17595">
    <literal><![CDATA[
      T(x,y * K(z * K(u,w),v5)) = T(x,K(z,v5) * y)
    ]]></literal>
    <justification jstring="[hyper(16368,a,17593,a)].">
      <j1 rule="hyper" parents="16368 17593"/>
    </justification>
  </clause>

  <clause id="17597">
    <literal><![CDATA[
      T(x,K(K(y,z) * u,w) * v5) = T(x,K(u,w) * v5)
    ]]></literal>
    <justification jstring="[para(7507(a,1),17593(a,1,2,1,1))].">
      <j1 rule="para" parents="7507 17593"/>
    </justification>
  </clause>

  <clause id="17598">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,x / (u * (u / z))) = K(y,(u * (u / z)) \ x)
    ]]></literal>
    <justification jstring="[para(16264(a,1),17200(a,1,1))].">
      <j1 rule="para" parents="16264 17200"/>
    </justification>
  </clause>

  <clause id="17599">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z,y / (u * (u / x))) = K(z,(u * (u / x)) \ y)
    ]]></literal>
    <justification jstring="[para(7989(a,1),17598(a,1,1))].">
      <j1 rule="para" parents="7989 17598"/>
    </justification>
  </clause>

  <clause id="17600">
    <literal><![CDATA[
      K(K(x,y * (y * K(z,u))) * K(u,z / (w * (w / x))),v5) = K(K(u,(w * (w / x)) \ z),v5)
    ]]></literal>
    <justification jstring="[para(17599(a,1),17449(a,2,1))].">
      <j1 rule="para" parents="17599 17449"/>
    </justification>
  </clause>

  <clause id="17603">
    <literal><![CDATA[
      a(L((x \ y) / x,x,x),z,u) = a(L(x,y,x) * (y / x),z,u)
    ]]></literal>
    <justification jstring="[para(17039(a,1),17282(a,1,1))].">
      <j1 rule="para" parents="17039 17282"/>
    </justification>
  </clause>

  <clause id="17604">
    <literal><![CDATA[
      a(L(x,y,x) * (y / x),z,u) = a(((x \ 1) * y) / x,z,u)
    ]]></literal>
    <justification jstring="[para(1040(a,1),17603(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1040 17603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17606">
    <literal><![CDATA[
      a(L(x,y,x) * (y / x),z,u) = a(T(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,15073,a(flip),b,17604,a),flip(a)].">
      <j1 rule="hyper" parents="299 15073 17604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17607">
    <literal><![CDATA[
      a(x * (y / x),z,u) = a(T(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,13560,a(flip),b,17606,a)].">
      <j1 rule="hyper" parents="65 13560 17606"/>
    </justification>
  </clause>

  <clause id="17609">
    <literal><![CDATA[
      a(K(x,y) * ((K(x * y,x) / z) / K(x,y)),u,w) = a((1 / z) * K(x * y,x),u,w)
    ]]></literal>
    <justification jstring="[para(14427(a,1),17607(a,2,1))].">
      <j1 rule="para" parents="14427 17607"/>
    </justification>
  </clause>

  <clause id="17610">
    <literal><![CDATA[
      K(x,(y \ z) / (y \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * z) / (y * u)) = w
    ]]></literal>
    <justification jstring="[para(17289(a,1),8498(a,1))].">
      <j1 rule="para" parents="17289 8498"/>
    </justification>
  </clause>

  <clause id="17611">
    <literal><![CDATA[
      K(x,K(y \ z,y * u)) * K(x,(y * z) \ (y * u)) = K(x,(y \ u) / (y \ z))
    ]]></literal>
    <justification jstring="[para(16259(a,2),17289(a,1,1))].">
      <j1 rule="para" parents="16259 17289"/>
    </justification>
  </clause>

  <clause id="17612">
    <literal><![CDATA[
      T(x,T(y * K(z,u \ w),v5)) = T(x,T(y * K(z,u * w),v5))
    ]]></literal>
    <justification jstring="[hyper(9377,a,17444,a),flip(a)].">
      <j1 rule="hyper" parents="9377 17444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17613">
    <literal><![CDATA[
      T(x,T((y \ z) * K(y,u * w),v5)) = T(x,T(T(y,u \ w) \ z,v5))
    ]]></literal>
    <justification jstring="[hyper(17319,a,17612,a),flip(a)].">
      <j1 rule="hyper" parents="17319 17612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17614">
    <literal><![CDATA[
      T(x,T(T(y,z \ u) \ w,v5)) = T(x,T(T(y,z * u) \ w,v5))
    ]]></literal>
    <justification jstring="[hyper(17319,a,17613,a),flip(a)].">
      <j1 rule="hyper" parents="17319 17613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17616">
    <literal><![CDATA[
      T(x,y * (T(z,T(u,w * v5)) * T(u,w * v5))) = T(x,y * (T(u,w \ v5) * z))
    ]]></literal>
    <justification jstring="[para(16225(a,1),17537(a,1,2,2,1))].">
      <j1 rule="para" parents="16225 17537"/>
    </justification>
  </clause>

  <clause id="17617">
    <literal><![CDATA[
      K(x,K(y \ z,y \ u)) * K(x,(y * z) \ (y * u)) = K(x,(y \ u) / (y \ z))
    ]]></literal>
    <justification jstring="[para(16251(a,2),17611(a,1,1))].">
      <j1 rule="para" parents="16251 17611"/>
    </justification>
  </clause>

  <clause id="17618">
    <literal><![CDATA[
      T(x,y * (T(z,u \ w) * v5)) = T(x,y * (T(z,u * w) * v5))
    ]]></literal>
    <justification jstring="[hyper(15900,a,17616,a),flip(a)].">
      <j1 rule="hyper" parents="15900 17616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17619">
    <literal><![CDATA[
      T(x,(y \ 1) * (T(z,u * w) * v5)) = T(x,y \ (T(z,u \ w) * v5))
    ]]></literal>
    <justification jstring="[hyper(14304,a,17618,a),flip(a)].">
      <j1 rule="hyper" parents="14304 17618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17620">
    <literal><![CDATA[
      x * K(x,y \ (T(z,u * w) * v5)) = T(x,y \ (T(z,u \ w) * v5))
    ]]></literal>
    <justification jstring="[hyper(14383,a,17619,a)].">
      <j1 rule="hyper" parents="14383 17619"/>
    </justification>
  </clause>

  <clause id="17621">
    <literal><![CDATA[
      T(x,y \ (T(z,u \ w) * v5)) = T(x,y \ (T(z,u * w) * v5))
    ]]></literal>
    <justification jstring="[hyper(14304,a,17619,a),flip(a)].">
      <j1 rule="hyper" parents="14304 17619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17622">
    <literal><![CDATA[
      T(x,y \ (T(z,u \ w) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (T(z,u * w) * v5)) = v6
    ]]></literal>
    <justification jstring="[para(17619(a,1),14304(a,1))].">
      <j1 rule="para" parents="17619 14304"/>
    </justification>
  </clause>

  <clause id="17623">
    <literal><![CDATA[
      T(x,y \ (T(z,T(u,w) * w) * v5)) = T(x,y \ (T(z,w / u) * v5))
    ]]></literal>
    <justification jstring="[para(15275(a,1),17621(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="15275 17621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17624">
    <literal><![CDATA[
      K(x,y \ (T(z,u \ w) * v5)) = K(x,y \ (T(z,u * w) * v5))
    ]]></literal>
    <justification jstring="[hyper(36,a,5083,a(flip),b,17620,a)].">
      <j1 rule="hyper" parents="36 5083 17620"/>
    </justification>
  </clause>

  <clause id="17625">
    <literal><![CDATA[
      K(x,y \ (T(z,y * (y \ 1)) * u)) = K(x,y * (z * ((y * y) \ u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,15178,a(flip),b,17624,a),flip(a)].">
      <j1 rule="hyper" parents="65 15178 17624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17626">
    <literal><![CDATA[
      T(x,y \ (T(z,u / w) * v5)) = T(x,y \ (T(z,u * w) * v5))
    ]]></literal>
    <justification jstring="[para(13266(a,1),17623(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="13266 17623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17627">
    <literal><![CDATA[
      K(x,y * (z * ((y * y) \ u))) = K(x,y \ (T(z,1) * u))
    ]]></literal>
    <justification jstring="[para(10(a,1),17625(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="10 17625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17629">
    <literal><![CDATA[
      K(x,y * (z * ((y * y) \ u))) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[para(193(a,1),17627(a,2,2,2,1))].">
      <j1 rule="para" parents="193 17627"/>
    </justification>
  </clause>

  <clause id="17630">
    <literal><![CDATA[
      K(x,(y \ z) \ (y \ u)) = K(x,(y * z) \ (y * u))
    ]]></literal>
    <justification jstring="[hyper(8500,a,17617,a)].">
      <j1 rule="hyper" parents="8500 17617"/>
    </justification>
  </clause>

  <clause id="17631">
    <literal><![CDATA[
      K(x,L((y \ (y * z)) \ (y * u),u,y)) = K(x,(y \ z) \ (y \ (y * u)))
    ]]></literal>
    <justification jstring="[hyper(299,a,14993,a,b,17630,a)].">
      <j1 rule="hyper" parents="299 14993 17630"/>
    </justification>
  </clause>

  <clause id="17632">
    <literal><![CDATA[
      K(x,L((y \ (y * z)) \ (y * u),u,y)) = K(x,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[para(9(a,1),17631(a,2,2,2))].">
      <j1 rule="para" parents="9 17631"/>
    </justification>
  </clause>

  <clause id="17633">
    <literal><![CDATA[
      K(x,L(y \ (z * u),u,z)) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(9(a,1),17632(a,1,2,1,1))].">
      <j1 rule="para" parents="9 17632"/>
    </justification>
  </clause>

  <clause id="17634">
    <literal><![CDATA[
      K(x,L(y \ z,u,z / u)) = K(x,((z / u) \ y) \ u)
    ]]></literal>
    <justification jstring="[para(12(a,1),17633(a,1,2,1,2))].">
      <j1 rule="para" parents="12 17633"/>
    </justification>
  </clause>

  <clause id="17637">
    <literal><![CDATA[
      K(x,K(y \ (1 / z),L(y / u,u,z))) = K(x,K(z * y,y / u))
    ]]></literal>
    <justification jstring="[hyper(299,a,17151,a(flip),b,16495,a),flip(a)].">
      <j1 rule="hyper" parents="299 17151 16495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17638">
    <literal><![CDATA[
      K(x,K((1 / y) / z,L(z / u,u,y))) = K(x,K(y * z,z / u))
    ]]></literal>
    <justification jstring="[hyper(16508,a,17637,a)].">
      <j1 rule="hyper" parents="16508 17637"/>
    </justification>
  </clause>

  <clause id="17640">
    <literal><![CDATA[
      K(x,K((y \ z) * u,u / y)) = K(x,K(z,(1 / (y \ z)) / u))
    ]]></literal>
    <justification jstring="[hyper(65,a,15490,a(flip),b,17638,a),flip(a)].">
      <j1 rule="hyper" parents="65 15490 17638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17641">
    <literal><![CDATA[
      K(x,K(y / z,(z \ u) * y)) = K(x,K(u,(1 / (z \ u)) / y))
    ]]></literal>
    <justification jstring="[hyper(8035,a,17640,a)].">
      <j1 rule="hyper" parents="8035 17640"/>
    </justification>
  </clause>

  <clause id="17642">
    <literal><![CDATA[
      K(x,K(y,(1 / (z \ y)) / u)) = K(x,K(y,u / z))
    ]]></literal>
    <justification jstring="[hyper(65,a,16931,a(flip),b,17641,a),flip(a)].">
      <j1 rule="hyper" parents="65 16931 17641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17643">
    <literal><![CDATA[
      K(x,K(y,(1 / z) / u)) = K(x,K(y,u / (y / z)))
    ]]></literal>
    <justification jstring="[para(79(a,1),17642(a,1,2,2,1,2))].">
      <j1 rule="para" parents="79 17642"/>
    </justification>
  </clause>

  <clause id="17644">
    <literal><![CDATA[
      K(x,K(y,z / (y / u))) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,12767,a(flip),b,17643,a),flip(a)].">
      <j1 rule="hyper" parents="65 12767 17643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17645">
    <literal><![CDATA[
      K(x,K(y,z * (y / u))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(65,a,17147,a(flip),b,17644,a),flip(a)].">
      <j1 rule="hyper" parents="65 17147 17644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17646">
    <literal><![CDATA[
      K(x,K(y,z * (x / u))) = K(y,K(x,z / u))
    ]]></literal>
    <justification jstring="[hyper(7985,a,17645,a)].">
      <j1 rule="hyper" parents="7985 17645"/>
    </justification>
  </clause>

  <clause id="17647">
    <literal><![CDATA[
      K(x,K(y,z * (x / u))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(299,a,7983,a,b,17646,a),flip(a)].">
      <j1 rule="hyper" parents="299 7983 17646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17648">
    <literal><![CDATA[
      K(K(x \ y,x) * (z * (y * (1 / x))),u) = K(z * (x \ R(y,1 / x,x)),u)
    ]]></literal>
    <justification jstring="[para(6180(a,1),16579(a,1,1,1))].">
      <j1 rule="para" parents="6180 16579"/>
    </justification>
  </clause>

  <clause id="17649">
    <literal><![CDATA[
      K(K(x,y) * (z * (x * (1 / y))),u) = K(z * (y \ R(x,1 / y,y)),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,13894,a(flip),b,17648,a)].">
      <j1 rule="hyper" parents="65 13894 17648"/>
    </justification>
  </clause>

  <clause id="17650">
    <literal><![CDATA[
      L(K(x,y * K(z,T(u * K(w,v5),v6))),x,v7) = (x * K(v8,v9)) \ (T(x,K(u,z) * y) * K(v8,v9))
    ]]></literal>
    <justification jstring="[para(17593(a,1),17374(a,2,2,1))].">
      <j1 rule="para" parents="17593 17374"/>
    </justification>
  </clause>

  <clause id="17651">
    <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(6978(a,1),16538(a,1,2,2))].">
      <j1 rule="para" parents="6978 16538"/>
    </justification>
  </clause>

  <clause id="17652">
    <literal><![CDATA[
      T(x,y / T(T(z \ ((z \ 1) \ u),w),1 / z)) = T(x,y / T((z \ u) / (1 / z),w))
    ]]></literal>
    <justification jstring="[para(3484(a,1),16607(a,2,2,2))].">
      <j1 rule="para" parents="3484 16607"/>
    </justification>
  </clause>

  <clause id="17653">
    <literal><![CDATA[
      T(T(x,K(y,z)),(z * K(u,T(w,v5))) * y) = T(x,y * (z * K(u,w)))
    ]]></literal>
    <justification jstring="[para(17170(a,1),16889(a,1,1))].">
      <j1 rule="para" parents="17170 16889"/>
    </justification>
  </clause>

  <clause id="17655">
    <literal><![CDATA[
      x * (T((y \ 1) \ 1,(y \ 1) * x) \ (y \ 1)) = T(x * (y \ 1),y) / y
    ]]></literal>
    <justification jstring="[para(76(a,1),17057(a,2,2))].">
      <j1 rule="para" parents="76 17057"/>
    </justification>
  </clause>

  <clause id="17657">
    <literal><![CDATA[
      x * (T((y \ 1) \ 1,(y \ 1) * x) \ (y \ 1)) = (y \ x) * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(299,a,1751,a(flip),b,17655,a),flip(a)].">
      <j1 rule="hyper" parents="299 1751 17655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17658">
    <literal><![CDATA[
      x * (T(((y \ 1) \ 1) \ 1,((y \ 1) \ 1) * x) \ ((y \ 1) \ 1)) = ((y \ 1) \ x) * y
    ]]></literal>
    <justification jstring="[para(76(a,1),17657(a,2,2))].">
      <j1 rule="para" parents="76 17657"/>
    </justification>
  </clause>

  <clause id="17659">
    <literal><![CDATA[
      (T(x,y) / z) / K(((1 / z) / (x / z)) \ 1,y) = T(x / z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,17081,a(flip),b,17090,a),flip(a)].">
      <j1 rule="hyper" parents="299 17081 17090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17660">
    <literal><![CDATA[
      (T(x,y) / z) / K(((z \ 1) / (x / z)) \ 1,y) = T(x / z,K(x,y))
    ]]></literal>
    <justification jstring="[para(5894(a,1),17659(a,1,2))].">
      <j1 rule="para" parents="5894 17659"/>
    </justification>
  </clause>

  <clause id="17661">
    <literal><![CDATA[
      (T(x,y) / z) * K(y,((z \ 1) / (x / z)) \ 1) = T(x / z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(7208,a,17660,a)].">
      <j1 rule="hyper" parents="7208 17660"/>
    </justification>
  </clause>

  <clause id="17662">
    <literal><![CDATA[
      (T(x,y) / z) * K(y,(x / z) / (z \ 1)) = T(x / z,K(x,y))
    ]]></literal>
    <justification jstring="[para(5937(a,1),17661(a,1,2))].">
      <j1 rule="para" parents="5937 17661"/>
    </justification>
  </clause>

  <clause id="17663">
    <literal><![CDATA[
      (K(x,T(y,z)) / u) * K(z,(K(x,y) / u) / (u \ 1)) = T(K(x,y) / u,K(K(x,y),z))
    ]]></literal>
    <justification jstring="[para(7489(a,2),17662(a,1,1,1))].">
      <j1 rule="para" parents="7489 17662"/>
    </justification>
  </clause>

  <clause id="17665">
    <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(7689(a,1),17358(a,1,2,1))].">
      <j1 rule="para" parents="7689 17358"/>
    </justification>
  </clause>

  <clause id="17666">
    <literal><![CDATA[
      T(x,T(y,z * T(u,z)) / (u * ((z \ u) / u))) = T(x,(z \ T(u,z \ 1)) \ y)
    ]]></literal>
    <justification jstring="[para(17434(a,1),17469(a,1,2,1))].">
      <j1 rule="para" parents="17434 17469"/>
    </justification>
  </clause>

  <clause id="17667">
    <literal><![CDATA[
      T(x,T(y,z * u) / (z * ((u \ z) / z))) = T(x,(u \ T(z,u \ 1)) \ y)
    ]]></literal>
    <justification jstring="[para(107(a,1),17666(a,1,2,1,2))].">
      <j1 rule="para" parents="107 17666"/>
    </justification>
  </clause>

  <clause id="17668">
    <literal><![CDATA[
      T(x,T(y,L(z * (u * u),u,u)) * (u * (u * z))) = T(x,L(z,u,u) * ((u * u) * y))
    ]]></literal>
    <justification jstring="[para(6516(a,1),17520(a,2,2))].">
      <j1 rule="para" parents="6516 17520"/>
    </justification>
  </clause>

  <clause id="17669">
    <literal><![CDATA[
      T(x,T(y,z * T(u,w * v5)) * (z * T(u,w * v5))) = T(x,(z * T(u,w \ v5)) * y)
    ]]></literal>
    <justification jstring="[para(17433(a,1),17539(a,1,2,1))].">
      <j1 rule="para" parents="17433 17539"/>
    </justification>
  </clause>

  <clause id="17670">
    <literal><![CDATA[
      K(x,T(y,z * T(u,w * v5)) * (z * T(u,w * v5))) = K(x,(z * T(u,w \ v5)) * y)
    ]]></literal>
    <justification jstring="[para(17433(a,1),17554(a,1,2,1))].">
      <j1 rule="para" parents="17433 17554"/>
    </justification>
  </clause>

  <clause id="17671">
    <literal><![CDATA[
      a(K(x,y) * ((K(x * y,x) / z) * K(y,x)),u,w) = a((1 / z) * K(x * y,x),u,w)
    ]]></literal>
    <justification jstring="[para(7196(a,1),17609(a,1,1,2))].">
      <j1 rule="para" parents="7196 17609"/>
    </justification>
  </clause>

  <clause id="17672">
    <literal><![CDATA[
      K(((x \ y) * x) / z,T(u,y / x)) = y \ (y * K((x * (z / x)) \ y,u))
    ]]></literal>
    <justification jstring="[para(8954(a,1),17651(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8954 17651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17673">
    <literal><![CDATA[
      K(((x \ y) * x) / z,T(u,y / x)) = K((x * (z / x)) \ y,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,9,a(flip),b,17672,a),flip(a)].">
      <j1 rule="hyper" parents="299 9 17672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17674">
    <literal><![CDATA[
      K((x * ((y * ((x \ z) * x)) / x)) \ z,u) = K(1 / y,T(u,z / x))
    ]]></literal>
    <justification jstring="[hyper(5863,a,17673,a),flip(a)].">
      <j1 rule="hyper" parents="5863 17673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17676">
    <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(17673(a,1),5863(a,1))].">
      <j1 rule="para" parents="17673 5863"/>
    </justification>
  </clause>

  <clause id="17677">
    <literal><![CDATA[
      x * (T(1 / y,((y \ 1) \ 1) * x) \ ((y \ 1) \ 1)) = ((y \ 1) \ x) * y
    ]]></literal>
    <justification jstring="[para(1689(a,1),17658(a,1,2,1,1))].">
      <j1 rule="para" parents="1689 17658"/>
    </justification>
  </clause>

  <clause id="17678">
    <literal><![CDATA[
      x * (T(1 / y,y * x) \ ((y \ 1) \ 1)) = ((y \ 1) \ x) * y
    ]]></literal>
    <justification jstring="[para(3867(a,1),17677(a,1,2,1))].">
      <j1 rule="para" parents="3867 17677"/>
    </justification>
  </clause>

  <clause id="17679">
    <literal><![CDATA[
      x * (T(y \ 1,y * x) \ y) = ((y \ 1) \ x) * y
    ]]></literal>
    <justification jstring="[para(3700(a,1),17678(a,1,2))].">
      <j1 rule="para" parents="3700 17678"/>
    </justification>
  </clause>

  <clause id="17680">
    <literal><![CDATA[
      T(x,(1 / y) / T(z * y,y \ 1)) = T(x,(((y \ 1) \ z) * y) \ 1)
    ]]></literal>
    <justification jstring="[para(17679(a,1),17058(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="17679 17058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17681">
    <literal><![CDATA[
      T(x,(1 / y) / T(z * y,y \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (((y \ 1) \ z) \ 1)) = u
    ]]></literal>
    <justification jstring="[para(17680(a,2),14664(a,1))].">
      <j1 rule="para" parents="17680 14664"/>
    </justification>
  </clause>

  <clause id="17682">
    <literal><![CDATA[
      T(x,(1 / y) / T(z * y,y * 1)) = T(x,y \ (((y \ 1) \ z) \ 1))
    ]]></literal>
    <justification jstring="[hyper(17681,a,17516,a),flip(a)].">
      <j1 rule="hyper" parents="17681 17516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17683">
    <literal><![CDATA[
      T(x,y \ (((y \ 1) \ z) \ 1)) = T(x,(1 / y) / T(z * y,y))
    ]]></literal>
    <justification jstring="[para(8(a,1),17682(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="8 17682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17684">
    <literal><![CDATA[
      K(x,(K(y,z) / u) / (u \ 1)) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(36,a,17091,a,b,17663,a),flip(a)].">
      <j1 rule="hyper" parents="36 17091 17663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17685">
    <literal><![CDATA[
      K(x,(y \ 1) \ (y \ K(z,u))) = K(z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,13279,a(flip),b,17684,a)].">
      <j1 rule="hyper" parents="65 13279 17684"/>
    </justification>
  </clause>

  <clause id="17687">
    <literal><![CDATA[
      (x \ K(y,z)) \ (x \ K(y,T(z,u))) = K(y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,12497,a,b,17685,a)].">
      <j1 rule="hyper" parents="65 12497 17685"/>
    </justification>
  </clause>

  <clause id="17689">
    <literal><![CDATA[
      (x \ K(y,z)) * K(y,K(z,u)) = x \ K(y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(144,a,17687,a)].">
      <j1 rule="hyper" parents="144 17687"/>
    </justification>
  </clause>

  <clause id="17690">
    <literal><![CDATA[
      K(x,K(y,z)) * (u \ K(x,y)) = u \ K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(16355,a,17689,a)].">
      <j1 rule="hyper" parents="16355 17689"/>
    </justification>
  </clause>

  <clause id="17691">
    <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(16653(a,1),17665(a,1,2,1))].">
      <j1 rule="para" parents="16653 17665"/>
    </justification>
  </clause>

  <clause id="17692">
    <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(5452,a,17691,a),flip(a)].">
      <j1 rule="hyper" parents="5452 17691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17693">
    <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(65,a,17575,a(flip),b,17692,a)].">
      <j1 rule="hyper" parents="65 17575 17692"/>
    </justification>
  </clause>

  <clause id="17694">
    <literal><![CDATA[
      T(x,T(y,z * (u * u)) * (u * (u * z))) = T(x,L(z,u,u) * ((u * u) * y))
    ]]></literal>
    <justification jstring="[para(14206(a,1),17668(a,1,2,1))].">
      <j1 rule="para" parents="14206 17668"/>
    </justification>
  </clause>

  <clause id="17695">
    <literal><![CDATA[
      T(x,T(y,z) * (u * (u * z))) = T(x,L(z,u,u) * ((u * u) * y))
    ]]></literal>
    <justification jstring="[hyper(17424,a,17694,a)].">
      <j1 rule="hyper" parents="17424 17694"/>
    </justification>
  </clause>

  <clause id="17698">
    <literal><![CDATA[
      T(x,(y * T(z,u \ w)) * v5) = T(x,(y * T(z,u * w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(13267,a,17669,a),flip(a)].">
      <j1 rule="hyper" parents="13267 17669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17699">
    <literal><![CDATA[
      T(x,(y * T(z,u \ w)) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,(y * T(z,u * w)) * v5) = v6
    ]]></literal>
    <justification jstring="[para(17669(a,1),13267(a,1))].">
      <j1 rule="para" parents="17669 13267"/>
    </justification>
  </clause>

  <clause id="17700">
    <literal><![CDATA[
      T(x,(y * T(z,u * u)) * w) = T(x,(y * z) * w)
    ]]></literal>
    <justification jstring="[para(198(a,1),17698(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="198 17698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17701">
    <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(17670(a,1),13261(a,1))].">
      <j1 rule="para" parents="17670 13261"/>
    </justification>
  </clause>

  <clause id="17703">
    <literal><![CDATA[
      K(x,y \ (z * T(u / (u \ w),(w \ u) * (u * (u / w))))) = K(x,y \ (z * (u * (u / w))))
    ]]></literal>
    <justification jstring="[para(16319(a,1),16320(a,1,2,2,2,2))].">
      <j1 rule="para" parents="16319 16320"/>
    </justification>
  </clause>

  <clause id="17704">
    <literal><![CDATA[
      (T(x,K(y,z)) * K(y,z)) / T(1 / K(y,z),K(y,z) * x) = x * (K(y,z) * K(y,z))
    ]]></literal>
    <justification jstring="[para(7221(a,1),16963(a,1,1))].">
      <j1 rule="para" parents="7221 16963"/>
    </justification>
  </clause>

  <clause id="17705">
    <literal><![CDATA[
      T(x * K(y,z),K(y,z)) / T(1 / K(y,z),K(y,z) * x) = x * (K(y,z) * K(y,z))
    ]]></literal>
    <justification jstring="[para(10096(a,2),17704(a,1,1))].">
      <j1 rule="para" parents="10096 17704"/>
    </justification>
  </clause>

  <clause id="17706">
    <literal><![CDATA[
      T(x * (y * K(x,z)),K(x,z)) / T(1 / K(x,z),K(x,z) * (x * y)) = (x * y) * (K(x,z) * K(x,z))
    ]]></literal>
    <justification jstring="[para(7074(a,1),17705(a,1,1,1))].">
      <j1 rule="para" parents="7074 17705"/>
    </justification>
  </clause>

  <clause id="17707">
    <literal><![CDATA[
      (x / (T(x,y) / y)) \ L(z,L(y,u,y),L(y,w,y)) = ((x / (T(x,y) / y)) \ 1) * z
    ]]></literal>
    <justification jstring="[para(13457(a,2),17049(a,1,2))].">
      <j1 rule="para" parents="13457 17049"/>
    </justification>
  </clause>

  <clause id="17709">
    <literal><![CDATA[
      (x / (T(x,y) / y)) \ L(z,y,y) = ((x / (T(x,y) / y)) \ 1) * z
    ]]></literal>
    <justification jstring="[para(17039(a,1),17707(a,1,2))].">
      <j1 rule="para" parents="17039 17707"/>
    </justification>
  </clause>

  <clause id="17710">
    <literal><![CDATA[
      (x / (T(x,y) / y)) \ L(z,y,y) = L(1 / y,x,y) * z
    ]]></literal>
    <justification jstring="[para(16706(a,1),17709(a,2,1))].">
      <j1 rule="para" parents="16706 17709"/>
    </justification>
  </clause>

  <clause id="17711">
    <literal><![CDATA[
      T(x,(y \ T((z \ 1) \ 1,u)) * (y \ T((z \ 1) \ 1,u))) = T(x,(y \ z) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,16917,a(flip),b,17087,a),flip(a)].">
      <j1 rule="hyper" parents="65 16917 17087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17712">
    <literal><![CDATA[
      T(x,(y \ ((z \ 1) \ 1)) * (y \ ((z \ 1) \ 1))) = T(x,(y \ z) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,17086,a(flip),b,17711,a)].">
      <j1 rule="hyper" parents="65 17086 17711"/>
    </justification>
  </clause>

  <clause id="17713">
    <literal><![CDATA[
      T(x,(y \ 1) \ (z \ ((z * (y \ 1)) \ 1))) = T(x,(z \ y) * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(65,a,16163,a(flip),b,17712,a)].">
      <j1 rule="hyper" parents="65 16163 17712"/>
    </justification>
  </clause>

  <clause id="17714">
    <literal><![CDATA[
      T(x,y * (z \ ((z * (y \ 1)) \ 1))) = T(x,(z \ y) * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(65,a,14215,a(flip),b,17713,a)].">
      <j1 rule="hyper" parents="65 14215 17713"/>
    </justification>
  </clause>

  <clause id="17715">
    <literal><![CDATA[
      T(x,(y \ ((z \ 1) \ 1)) * (y \ ((z \ 1) \ 1))) = T(x,((z \ 1) \ 1) * (y \ ((y * (1 / z)) \ 1)))
    ]]></literal>
    <justification jstring="[para(1689(a,1),17714(a,1,2,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="1689 17714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17716">
    <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(299,a,14900,a,b,17215,a),flip(a)].">
      <j1 rule="hyper" parents="299 14900 17215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17717">
    <literal><![CDATA[
      K(x,(y * z) * u) * a(w,v5,K((y * z) * u,x)) = K(x,L(T(z * y,y) * u,v5,w))
    ]]></literal>
    <justification jstring="[para(16003(a,1),17295(a,1,1))].">
      <j1 rule="para" parents="16003 17295"/>
    </justification>
  </clause>

  <clause id="17718">
    <literal><![CDATA[
      K(x,L(T(y * z,z) * u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L((z * y) * u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(17717(a,1),11950(a,1))].">
      <j1 rule="para" parents="17717 11950"/>
    </justification>
  </clause>

  <clause id="17719">
    <literal><![CDATA[
      K(x,K(y,((z \ 1) * u) * w)) * K(K(x,y),K(w,z * u)) = K(x,K(y,w * ((z \ 1) * u)))
    ]]></literal>
    <justification jstring="[para(7954(a,1),17353(a,1,1))].">
      <j1 rule="para" parents="7954 17353"/>
    </justification>
  </clause>

  <clause id="17720">
    <literal><![CDATA[
      T((1 / K(x,y)) * L(K(x,y),z,u),w * w) = K(x,y) * T(L(K(y,x),z,u),w * w)
    ]]></literal>
    <justification jstring="[para(5197(a,1),17365(a,2,2,1,1))].">
      <j1 rule="para" parents="5197 17365"/>
    </justification>
  </clause>

  <clause id="17721">
    <literal><![CDATA[
      T((1 / K(x,y)) * L(K(x,y),z,u),w * w) = K(x,y) * T(K(y,L(x,z,u)),w * w)
    ]]></literal>
    <justification jstring="[para(11889(a,1),17720(a,2,2,1))].">
      <j1 rule="para" parents="11889 17720"/>
    </justification>
  </clause>

  <clause id="17722">
    <literal><![CDATA[
      T((1 / K(x,y)) * L(K(x,y),z,u),w * w) = K(x,y) * K(y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(16192(a,1),17721(a,2,2))].">
      <j1 rule="para" parents="16192 17721"/>
    </justification>
  </clause>

  <clause id="17723">
    <literal><![CDATA[
      T(K(x,y) * L(K(y,x),z,u),w * w) = K(y,x) * K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(5209(a,1),17722(a,1,1,1))].">
      <j1 rule="para" parents="5209 17722"/>
    </justification>
  </clause>

  <clause id="17725">
    <literal><![CDATA[
      T(K(x,y) * K(y,L(x,z,u)),w * w) = K(y,x) * K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(11889(a,1),17723(a,1,1,2))].">
      <j1 rule="para" parents="11889 17723"/>
    </justification>
  </clause>

  <clause id="17726">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(y,x) = K(x,y) * K(y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,17369,a(flip),b,17725,a)].">
      <j1 rule="hyper" parents="65 17369 17725"/>
    </justification>
  </clause>

  <clause id="17727">
    <literal><![CDATA[
      x * (K(x,y) * K(y,L(x,z,u))) = T(x,L(y,z,u)) * K(y,x)
    ]]></literal>
    <justification jstring="[para(17726(a,1),5055(a,1,2))].">
      <j1 rule="para" parents="17726 5055"/>
    </justification>
  </clause>

  <clause id="17728">
    <literal><![CDATA[
      T(x,L(y,z,u)) * K(y,x) = T(x,y) * K(y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(5511,a,17727,a),flip(a)].">
      <j1 rule="hyper" parents="5511 17727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17729">
    <literal><![CDATA[
      T(x * K(y,L(x,z,u)),y) = T(x,L(y,z,u)) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,7785,a,b,17728,a)].">
      <j1 rule="hyper" parents="299 7785 17728"/>
    </justification>
  </clause>

  <clause id="17730">
    <literal><![CDATA[
      T(1 / x,L(x,y,z)) * K(x,1 / x) = T(K(x,L(1 / x,y,z)) / x,x)
    ]]></literal>
    <justification jstring="[para(4569(a,1),17729(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4569 17729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17731">
    <literal><![CDATA[
      T(1 / x,L(x,y,z)) * K(x,x \ 1) = T(K(x,L(1 / x,y,z)) / x,x)
    ]]></literal>
    <justification jstring="[para(2584(a,1),17730(a,1,2))].">
      <j1 rule="para" parents="2584 17730"/>
    </justification>
  </clause>

  <clause id="17732">
    <literal><![CDATA[
      T(K(x,L(1 / x,y,z)) / x,x) = T(x \ 1,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,3690,a(flip),b,17731,a),flip(a)].">
      <j1 rule="hyper" parents="65 3690 17731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17733">
    <literal><![CDATA[
      T(K(x,L(x \ 1,y,z)) / x,x) = T(x \ 1,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(4805(a,1),17732(a,1,1,1))].">
      <j1 rule="para" parents="4805 17732"/>
    </justification>
  </clause>

  <clause id="17734">
    <literal><![CDATA[
      T(x \ 1,L(x,y,z)) = T(K(x,x \ 1) / x,x)
    ]]></literal>
    <justification jstring="[para(6103(a,1),17733(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6103 17733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17735">
    <literal><![CDATA[
      T(x \ 1,L(x,y,z)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(299,a,5143,a(flip),b,17734,a),flip(a)].">
      <j1 rule="hyper" parents="299 5143 17734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17738">
    <literal><![CDATA[
      (L(x,y,z) \ T((x \ 1) * L(x,y,z),u)) \ (1 / x) = K(u,(x \ 1) * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(17735(a,1),14342(a,1,2))].">
      <j1 rule="para" parents="17735 14342"/>
    </justification>
  </clause>

  <clause id="17739">
    <literal><![CDATA[
      K(x,(1 / y) \ (L(y,z,u) \ w)) = K(x,(y \ L(y,z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(17735(a,1),15765(a,1,2,1))].">
      <j1 rule="para" parents="17735 15765"/>
    </justification>
  </clause>

  <clause id="17740">
    <literal><![CDATA[
      K(x,(y \ L(y,z,u)) \ w) = K(x,y * (L(y,z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(14274,a,17739,a),flip(a)].">
      <j1 rule="hyper" parents="14274 17739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17742">
    <literal><![CDATA[
      x * K(x,y * (L(y,z,u) \ w)) = T(x,(y \ L(y,z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(17740(a,1),5083(a,2,2)),flip(a)].">
      <j1 rule="para" parents="17740 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17743">
    <literal><![CDATA[
      T(x,(y \ L(y,z,u)) \ w) = T(x,y * (L(y,z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(5087,a,17742,a),flip(a)].">
      <j1 rule="hyper" parents="5087 17742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17744">
    <literal><![CDATA[
      T(x,(y * (L(y,z,u) \ 1)) * w) = T(x,y * (L(y,z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,14840,a,b,17743,a)].">
      <j1 rule="hyper" parents="65 14840 17743"/>
    </justification>
  </clause>

  <clause id="17745">
    <literal><![CDATA[
      T(x,(L(y,z,u) \ y) * w) = T(x,y * (L(y,z,u) \ w))
    ]]></literal>
    <justification jstring="[para(1353(a,1),17744(a,1,2,1))].">
      <j1 rule="para" parents="1353 17744"/>
    </justification>
  </clause>

  <clause id="17746">
    <literal><![CDATA[
      T(x,y * (L(y,z,u) \ (w \ 1))) = T(x,(L(y,z,u) \ y) / w)
    ]]></literal>
    <justification jstring="[hyper(14593,a,17745,a),flip(a)].">
      <j1 rule="hyper" parents="14593 17745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17747">
    <literal><![CDATA[
      T(T(x,y * (L(y,z,u) \ w)),(L(y,z,u) \ y) \ (y \ L(y,z,u))) = T(T(x,(L(y,z,u) \ y) \ w),1)
    ]]></literal>
    <justification jstring="[para(17745(a,1),14757(a,1,1))].">
      <j1 rule="para" parents="17745 14757"/>
    </justification>
  </clause>

  <clause id="17748">
    <literal><![CDATA[
      L(x,y,z) \ T((x \ 1) * L(x,y,z),u) = (1 / x) * K(x \ L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(41,a,14333,a,b,17738,a),flip(a)].">
      <j1 rule="hyper" parents="41 14333 17738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17749">
    <literal><![CDATA[
      L(x,y,z) \ T((x \ 1) * L(x,y,z),u) = (1 / x) * a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[para(11962(a,1),17748(a,2,2))].">
      <j1 rule="para" parents="11962 17748"/>
    </justification>
  </clause>

  <clause id="17750">
    <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(16350(a,1),17716(a,2,3))].">
      <j1 rule="para" parents="16350 17716"/>
    </justification>
  </clause>

  <clause id="17751">
    <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(65,a,17140,a(flip),b,17750,a)].">
      <j1 rule="hyper" parents="65 17140 17750"/>
    </justification>
  </clause>

  <clause id="17753">
    <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),17258(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="9 17258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17754">
    <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(16633,a,17753,a)].">
      <j1 rule="hyper" parents="16633 17753"/>
    </justification>
  </clause>

  <clause id="17756">
    <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),17754(a,1,2,2,2))].">
      <j1 rule="para" parents="29 17754"/>
    </justification>
  </clause>

  <clause id="17757">
    <literal><![CDATA[
      L(K(x,y * K(z,T(u * K(w,v5),v6))),x,v7) = L(K(x,y * K(u,z)),x,v8)
    ]]></literal>
    <justification jstring="[hyper(299,a,16678,a,b,17650,a),flip(a)].">
      <j1 rule="hyper" parents="299 16678 17650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17758">
    <literal><![CDATA[
      L(K(x,y * K(z,T(u * K(w,v5),v6))),x,v7) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,15550,a(flip),b,17757,a),flip(a)].">
      <j1 rule="hyper" parents="299 15550 17757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17759">
    <literal><![CDATA[
      L(K(x,y * K(z,u * K(w,v5))),x,v6) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[para(106(a,1),17758(a,1,1,2,2,2))].">
      <j1 rule="para" parents="106 17758"/>
    </justification>
  </clause>

  <clause id="17760">
    <literal><![CDATA[
      K(x,y * K(z,u * K(w,v5))) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(15523,a,17759,a)].">
      <j1 rule="hyper" parents="15523 17759"/>
    </justification>
  </clause>

  <clause id="17761">
    <literal><![CDATA[
      K(x,K(y,z * K(u,w)) * v5) = K(x,v5 * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(16407,a,17760,a)].">
      <j1 rule="hyper" parents="16407 17760"/>
    </justification>
  </clause>

  <clause id="17762">
    <literal><![CDATA[
      K(K(x,y * K(z,u)) * w,v5) = (v6 * K(v5,w * K(y,x))) \ v6
    ]]></literal>
    <justification jstring="[para(17761(a,1),7200(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="17761 7200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17763">
    <literal><![CDATA[
      K(K(x,y * K(z,u)) * w,v5) = K(w * K(y,x),v5)
    ]]></literal>
    <justification jstring="[hyper(299,a,7200,a(flip),b,17762,a),flip(a)].">
      <j1 rule="hyper" parents="299 7200 17762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17764">
    <literal><![CDATA[
      K((x * K(y,z)) * K(x,u),w) = K(x * K(y,z),T(w,u))
    ]]></literal>
    <justification jstring="[hyper(8309,a,17763,a),flip(a)].">
      <j1 rule="hyper" parents="8309 17763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17765">
    <literal><![CDATA[
      K(K(x,y) * z,u) = K(z * K(y,x),u)
    ]]></literal>
    <justification jstring="[para(177(a,1),17763(a,1,1,1,2))].">
      <j1 rule="para" parents="177 17763"/>
    </justification>
  </clause>

  <clause id="17766">
    <literal><![CDATA[
      K(K(x,T(y,z)) * u,w) = K(u * K(y,x),w)
    ]]></literal>
    <justification jstring="[para(5083(a,2),17763(a,1,1,1,2))].">
      <j1 rule="para" parents="5083 17763"/>
    </justification>
  </clause>

  <clause id="17767">
    <literal><![CDATA[
      K(K(x,y * z) * u,w) = K(u * K(y \ z,x),w)
    ]]></literal>
    <justification jstring="[hyper(17447,a,17765,a)].">
      <j1 rule="hyper" parents="17447 17765"/>
    </justification>
  </clause>

  <clause id="17768">
    <literal><![CDATA[
      K(x * K(y,z),u) = K(x * K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(16405,a,17765,a)].">
      <j1 rule="hyper" parents="16405 17765"/>
    </justification>
  </clause>

  <clause id="17769">
    <literal><![CDATA[
      K(K(x,y) * z,u) = K(K(y,x) * z,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,16376,a,b,17765,a)].">
      <j1 rule="hyper" parents="299 16376 17765"/>
    </justification>
  </clause>

  <clause id="17770">
    <literal><![CDATA[
      K(x * K(y * z,y),u) = K(K(y,z) * x,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,13729,a(flip),b,17765,a),flip(a)].">
      <j1 rule="hyper" parents="65 13729 17765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17771">
    <literal><![CDATA[
      K(K(x,y) * (x \ z),u) = K(T(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(16479,a,17765,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="16479 17765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17772">
    <literal><![CDATA[
      (K(x,y) * z) * K(z * K(y,x),u) = T(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(17765(a,1),5083(a,2,2)),flip(a)].">
      <j1 rule="para" parents="17765 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17773">
    <literal><![CDATA[
      K(K(x,y) \ z,u) = K(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[para(5426(a,2),17765(a,1,1))].">
      <j1 rule="para" parents="5426 17765"/>
    </justification>
  </clause>

  <clause id="17774">
    <literal><![CDATA[
      K(((x / y) \ z) * K(y \ x,y),u) = K((y \ x) \ z,u)
    ]]></literal>
    <justification jstring="[para(5918(a,1),17765(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5918 17765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17775">
    <literal><![CDATA[
      K(K(x,y) * (z / x),u) = K(z / T(x,y),u)
    ]]></literal>
    <justification jstring="[para(7189(a,1),17765(a,2,1))].">
      <j1 rule="para" parents="7189 17765"/>
    </justification>
  </clause>

  <clause id="17776">
    <literal><![CDATA[
      K(K(x,L(y,z,u)) * (u * (z * y)),w) = K(u * (z * T(y,x)),w)
    ]]></literal>
    <justification jstring="[para(9496(a,1),17765(a,2,1))].">
      <j1 rule="para" parents="9496 17765"/>
    </justification>
  </clause>

  <clause id="17777">
    <literal><![CDATA[
      K(K(x,x \ y) * (z * y),u) = K(z * ((x \ y) * x),u)
    ]]></literal>
    <justification jstring="[para(11265(a,1),17765(a,2,1))].">
      <j1 rule="para" parents="11265 17765"/>
    </justification>
  </clause>

  <clause id="17778">
    <literal><![CDATA[
      K(K(x,y) * (z * (x * y)),u) = K(z * (y * x),u)
    ]]></literal>
    <justification jstring="[para(11274(a,1),17765(a,2,1))].">
      <j1 rule="para" parents="11274 17765"/>
    </justification>
  </clause>

  <clause id="17779">
    <literal><![CDATA[
      K(x,y) * (z * K(z * K(y,x),u)) = T(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(17765(a,1),14264(a,1,2,2))].">
      <j1 rule="para" parents="17765 14264"/>
    </justification>
  </clause>

  <clause id="17780">
    <literal><![CDATA[
      K(K(K(x,y) * z,u) * w,v5) = K(w * K(u,K(y,x) * z),v5)
    ]]></literal>
    <justification jstring="[para(15802(a,1),17765(a,2,1,2))].">
      <j1 rule="para" parents="15802 17765"/>
    </justification>
  </clause>

  <clause id="17781">
    <literal><![CDATA[
      K(x * K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x * K(z,y),u) = w
    ]]></literal>
    <justification jstring="[para(17765(a,1),16405(a,1))].">
      <j1 rule="para" parents="17765 16405"/>
    </justification>
  </clause>

  <clause id="17782">
    <literal><![CDATA[
      K(x * (K(y,(z / T(u,w)) * v5) * K(y,K(v5,u * z))),v6) = K(K(v5 * (z / T(u,w)),y) * x,v6)
    ]]></literal>
    <justification jstring="[para(17166(a,2),17765(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="17166 17765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17783">
    <literal><![CDATA[
      x * (K(y,z) * K(x * K(z,y),u)) = T(x * K(y,z),u)
    ]]></literal>
    <justification jstring="[para(17768(a,1),14264(a,1,2,2))].">
      <j1 rule="para" parents="17768 14264"/>
    </justification>
  </clause>

  <clause id="17784">
    <literal><![CDATA[
      K(x * K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(z,y) * x,u) = w
    ]]></literal>
    <justification jstring="[para(17768(a,1),16406(a,1))].">
      <j1 rule="para" parents="17768 16406"/>
    </justification>
  </clause>

  <clause id="17785">
    <literal><![CDATA[
      K((x \ y) * K(x,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(T(x,z) \ y,u) = w
    ]]></literal>
    <justification jstring="[para(17768(a,1),16479(a,1))].">
      <j1 rule="para" parents="17768 16479"/>
    </justification>
  </clause>

  <clause id="17786">
    <literal><![CDATA[
      K(K(x,y) * (K(x,y) * z),u) = K(z,u)
    ]]></literal>
    <justification jstring="[para(5432(a,1),17769(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5432 17769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17787">
    <literal><![CDATA[
      K(K(x,y) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(z * K(y,x),u) = w
    ]]></literal>
    <justification jstring="[para(17769(a,1),16405(a,1))].">
      <j1 rule="para" parents="17769 16405"/>
    </justification>
  </clause>

  <clause id="17788">
    <literal><![CDATA[
      K(K(x,y) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(y,x) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(17773(a,2),16478(a,1))].">
      <j1 rule="para" parents="17773 16478"/>
    </justification>
  </clause>

  <clause id="17789">
    <literal><![CDATA[
      K(x * (T(T(x,y),y) \ z),u) = K(z,u)
    ]]></literal>
    <justification jstring="[para(6199(a,1),17786(a,1,1))].">
      <j1 rule="para" parents="6199 17786"/>
    </justification>
  </clause>

  <clause id="17790">
    <literal><![CDATA[
      K(T(T(x,y),y) * z,u) = K(x * z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),17789(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 17789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17791">
    <literal><![CDATA[
      K(T(x,x \ y) * z,u) = K((y / (y / x)) * z,u)
    ]]></literal>
    <justification jstring="[para(4502(a,1),17790(a,1,1,1,1))].">
      <j1 rule="para" parents="4502 17790"/>
    </justification>
  </clause>

  <clause id="17792">
    <literal><![CDATA[
      K((x * (y / x)) \ z,u) = K(T(y,x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,13896,a,b,17771,a)].">
      <j1 rule="hyper" parents="65 13896 17771"/>
    </justification>
  </clause>

  <clause id="17793">
    <literal><![CDATA[
      K(((x * y) / x) \ z,u) = K(T(y,x) \ z,u)
    ]]></literal>
    <justification jstring="[para(5352(a,2),17771(a,1,1))].">
      <j1 rule="para" parents="5352 17771"/>
    </justification>
  </clause>

  <clause id="17794">
    <literal><![CDATA[
      K(x / (y * K(z,y)),u) = K(x / T(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,16526,a,b,17775,a)].">
      <j1 rule="hyper" parents="65 16526 17775"/>
    </justification>
  </clause>

  <clause id="17795">
    <literal><![CDATA[
      K(((x \ y) * x) \ z,u) = K(T(y,x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,15882,a,b,17792,a)].">
      <j1 rule="hyper" parents="65 15882 17792"/>
    </justification>
  </clause>

  <clause id="17796">
    <literal><![CDATA[
      K(T(x * y,x) \ z,u) = K((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,15883,a(flip),b,17792,a),flip(a)].">
      <j1 rule="hyper" parents="65 15883 17792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17797">
    <literal><![CDATA[
      K(T(x,y) \ z,L(u,x,y)) = K((x / y) \ (y \ z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,15681,a(flip),b,17792,a),flip(a)].">
      <j1 rule="hyper" parents="65 15681 17792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17798">
    <literal><![CDATA[
      K(T(T(x,y),y) \ z,u) = K(x \ z,u)
    ]]></literal>
    <justification jstring="[para(223(a,1),17793(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="223 17793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17799">
    <literal><![CDATA[
      K(x * (y \ K(y,z)),u) = K(x / T(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(14539,a,17794,a)].">
      <j1 rule="hyper" parents="14539 17794"/>
    </justification>
  </clause>

  <clause id="17800">
    <literal><![CDATA[
      K(x / T(y,y \ z),u) = K(x / (z / (z / y)),u)
    ]]></literal>
    <justification jstring="[para(5002(a,2),17794(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5002 17794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17801">
    <literal><![CDATA[
      K(T(x,y) \ z,T(u,x * y)) = K((((1 / y) \ z) * (1 / y)) / (T((y \ 1) \ x,y) * (1 / y)),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,15767,a(flip),b,17795,a),flip(a)].">
      <j1 rule="hyper" parents="65 15767 17795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17802">
    <literal><![CDATA[
      1 / (x \ K(T(y,z) \ u,x)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,((z \ y) * z) \ u) = w
    ]]></literal>
    <justification jstring="[para(17795(a,1),5226(a,1,2,2))].">
      <j1 rule="para" parents="17795 5226"/>
    </justification>
  </clause>

  <clause id="17803">
    <literal><![CDATA[
      K(x / ((1 / y) \ y),z) = K((y * y) \ x,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,16681,a(flip),b,17796,a)].">
      <j1 rule="hyper" parents="65 16681 17796"/>
    </justification>
  </clause>

  <clause id="17804">
    <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(17796(a,1),11896(a,1,2,3))].">
      <j1 rule="para" parents="17796 11896"/>
    </justification>
  </clause>

  <clause id="17805">
    <literal><![CDATA[
      K(x * (((y \ 1) * z) \ K((y \ 1) * z,y)),u) = K(x / ((y \ 1) * ((y \ z) * y)),u)
    ]]></literal>
    <justification jstring="[para(2046(a,2),17799(a,2,1,2))].">
      <j1 rule="para" parents="2046 17799"/>
    </justification>
  </clause>

  <clause id="17806">
    <literal><![CDATA[
      K(x,y * (z \ K(z,u))) * a(w,v5,K(y / T(z,u),x)) = K(x,L(y * (z \ K(z,u)),v5,w))
    ]]></literal>
    <justification jstring="[para(17799(a,1),11896(a,1,2,3))].">
      <j1 rule="para" parents="17799 11896"/>
    </justification>
  </clause>

  <clause id="17807">
    <literal><![CDATA[
      K(x / ((1 / y) \ y),z) = K(y \ (y \ x),z)
    ]]></literal>
    <justification jstring="[hyper(299,a,14182,a(flip),b,17803,a),flip(a)].">
      <j1 rule="hyper" parents="299 14182 17803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17808">
    <literal><![CDATA[
      K(x * (y \ (1 / y)),z) = K(y \ (y \ x),z)
    ]]></literal>
    <justification jstring="[para(1185(a,1),17807(a,1,1))].">
      <j1 rule="para" parents="1185 17807"/>
    </justification>
  </clause>

  <clause id="17809">
    <literal><![CDATA[
      K(x \ ((y \ 1) * (y \ T(z,y * y))),u) = K(y \ (y \ (x \ z)),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,16118,a,b,17808,a)].">
      <j1 rule="hyper" parents="65 16118 17808"/>
    </justification>
  </clause>

  <clause id="17810">
    <literal><![CDATA[
      K(K(x,T(y,z)) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(u * K(y,x),w) = v5
    ]]></literal>
    <justification jstring="[para(16768(a,2),17787(a,1))].">
      <j1 rule="para" parents="16768 17787"/>
    </justification>
  </clause>

  <clause id="17811">
    <literal><![CDATA[
      K(x * K(y \ z,u),w) = K(x * K(y * z,u),w)
    ]]></literal>
    <justification jstring="[hyper(17787,a,17767,a),flip(a)].">
      <j1 rule="hyper" parents="17787 17767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17812">
    <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(17767(a,1),17787(a,1))].">
      <j1 rule="para" parents="17767 17787"/>
    </justification>
  </clause>

  <clause id="17813">
    <literal><![CDATA[
      K(K(x,y * z) * (u * (x * (z / y))),w) = K(u * ((z / y) * x),w)
    ]]></literal>
    <justification jstring="[hyper(17503,a,17778,a)].">
      <j1 rule="hyper" parents="17503 17778"/>
    </justification>
  </clause>

  <clause id="17814">
    <literal><![CDATA[
      K(K(x,y * y) * T(z * x,y * y),u) = K(((y * y) \ z) * ((y * y) * x),u)
    ]]></literal>
    <justification jstring="[para(696(a,1),17778(a,1,1,2))].">
      <j1 rule="para" parents="696 17778"/>
    </justification>
  </clause>

  <clause id="17815">
    <literal><![CDATA[
      K((x / (x / y)) * z,u) = K(T(y,x) * z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,13753,a(flip),b,17791,a),flip(a)].">
      <j1 rule="hyper" parents="65 13753 17791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17816">
    <literal><![CDATA[
      (x * K(y,z * K(u * w,v5))) \ x = K(z * K(u \ w,v5),y)
    ]]></literal>
    <justification jstring="[hyper(299,a,7200,a,b,17811,a)].">
      <j1 rule="hyper" parents="299 7200 17811"/>
    </justification>
  </clause>

  <clause id="17817">
    <literal><![CDATA[
      K((a(x,y,z) \ u) * a(x,y,K(z,w)),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(T(a(x,y,z),w) \ u,v5) = v6
    ]]></literal>
    <justification jstring="[para(14556(a,2),17785(a,1,1,2))].">
      <j1 rule="para" parents="14556 17785"/>
    </justification>
  </clause>

  <clause id="17818">
    <literal><![CDATA[
      K(T(x,y) * K(z,u),w) = K(x * K(z,u),T(w,y))
    ]]></literal>
    <justification jstring="[para(16423(a,1),17764(a,1,1))].">
      <j1 rule="para" parents="16423 17764"/>
    </justification>
  </clause>

  <clause id="17819">
    <literal><![CDATA[
      K((x \ y) * K(z,u),T(w,x)) = K(K(z,u) * (y / x),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,16524,a(flip),b,17818,a),flip(a)].">
      <j1 rule="hyper" parents="65 16524 17818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17820">
    <literal><![CDATA[
      K(((x / y) \ z) * K(y * x,y),u) = K((y \ x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,17811,a(flip),b,17774,a)].">
      <j1 rule="hyper" parents="65 17811 17774"/>
    </justification>
  </clause>

  <clause id="17821">
    <literal><![CDATA[
      K(x * ((y \ z) * y),u) = K(x * T(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,16944,a(flip),b,17777,a),flip(a)].">
      <j1 rule="hyper" parents="65 16944 17777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17822">
    <literal><![CDATA[
      K(x * T((y \ z) * y,u),w) = K(x * T(T(z,u),y),w)
    ]]></literal>
    <justification jstring="[para(3483(a,2),17821(a,1,1,2))].">
      <j1 rule="para" parents="3483 17821"/>
    </justification>
  </clause>

  <clause id="17823">
    <literal><![CDATA[
      K(x,T(y * ((z \ u) * z),w)) = ((w * x) / w) / ((w * (x * K(y * T(u,z),x))) / w)
    ]]></literal>
    <justification jstring="[para(17821(a,1),9341(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="17821 9341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17824">
    <literal><![CDATA[
      K(T(K(x,y) * z,u) * T(w,z * K(z * K(y,x),u)),T(v5,w * (z * K(z * K(y,x),u)))) = K((w * (z * K(z * K(y,x),u))) * R(K(x,y),z * K(z * K(y,x),u),w),v5)
    ]]></literal>
    <justification jstring="[para(17779(a,1),13184(a,1,1,1))].">
      <j1 rule="para" parents="17779 13184"/>
    </justification>
  </clause>

  <clause id="17825">
    <literal><![CDATA[
      K(K(x,y) * ((y / x) \ z),u) = K((x \ y) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,17770,a(flip),b,17820,a)].">
      <j1 rule="hyper" parents="65 17770 17820"/>
    </justification>
  </clause>

  <clause id="17826">
    <literal><![CDATA[
      K(x * T(T(y,z),u * y),w) = K(x * T(T(y,z),u),w)
    ]]></literal>
    <justification jstring="[hyper(17509,a,17822,a)].">
      <j1 rule="hyper" parents="17509 17822"/>
    </justification>
  </clause>

  <clause id="17827">
    <literal><![CDATA[
      x / T(x,K(K(y,z) * u,w) * v5) = K(v5 * K(w,K(z,y) * u),x)
    ]]></literal>
    <justification jstring="[hyper(5051,a,17780,a)].">
      <j1 rule="hyper" parents="5051 17780"/>
    </justification>
  </clause>

  <clause id="17828">
    <literal><![CDATA[
      x / T(x,y * K(z,K(u,w) * v5)) = K(K(K(w,u) * v5,z) * y,x)
    ]]></literal>
    <justification jstring="[hyper(299,a,5033,a(flip),b,17780,a)].">
      <j1 rule="hyper" parents="299 5033 17780"/>
    </justification>
  </clause>

  <clause id="17829">
    <literal><![CDATA[
      x * K(x,y * K(z * u,w)) = T(x,y * K(z \ u,w))
    ]]></literal>
    <justification jstring="[hyper(41,a,5024,a(flip),b,17816,a),flip(a)].">
      <j1 rule="hyper" parents="41 5024 17816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17830">
    <literal><![CDATA[
      K(x,y * K(z \ u,w)) = K(x,y * K(z * u,w))
    ]]></literal>
    <justification jstring="[hyper(36,a,5083,a(flip),b,17829,a)].">
      <j1 rule="hyper" parents="36 5083 17829"/>
    </justification>
  </clause>

  <clause id="17831">
    <literal><![CDATA[
      K(x,K(y * z,u) * w) = K(x,w * K(y \ z,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,16374,a,b,17830,a)].">
      <j1 rule="hyper" parents="299 16374 17830"/>
    </justification>
  </clause>

  <clause id="17832">
    <literal><![CDATA[
      K(x,y * K(z * (u * z),w)) = K(x,y * K(T(u,z),w))
    ]]></literal>
    <justification jstring="[para(22(a,2),17830(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="22 17830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17833">
    <literal><![CDATA[
      K(x,y * K((z * (u * u)) \ w,v5)) = K(x,y * K(z * ((u * u) * w),v5))
    ]]></literal>
    <justification jstring="[para(34(a,1),17830(a,2,2,2,1))].">
      <j1 rule="para" parents="34 17830"/>
    </justification>
  </clause>

  <clause id="17834">
    <literal><![CDATA[
      K(x,y * K((z / u) * z,w)) = K(x,y * K(u,w))
    ]]></literal>
    <justification jstring="[para(79(a,1),17830(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="79 17830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17835">
    <literal><![CDATA[
      K(x,y * K((z * u) * (z * ((z \ 1) \ w)),v5)) = K(x,y * K(((z \ 1) * u) \ w,v5))
    ]]></literal>
    <justification jstring="[para(2507(a,1),17830(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="2507 17830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17836">
    <literal><![CDATA[
      K(x,(y * z) * K(u * w,L(v5,z,y))) = K(x,y * (z * K(u \ w,v5)))
    ]]></literal>
    <justification jstring="[para(11903(a,1),17830(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11903 17830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17837">
    <literal><![CDATA[
      K(x,K(y \ z,u) * w) = K(x,K(y * z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(299,a,16374,a,b,17831,a)].">
      <j1 rule="hyper" parents="299 16374 17831"/>
    </justification>
  </clause>

  <clause id="17838">
    <literal><![CDATA[
      K(x,y * K(z \ u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * K(z * u,w)) = v5
    ]]></literal>
    <justification jstring="[para(17831(a,1),16408(a,1))].">
      <j1 rule="para" parents="17831 16408"/>
    </justification>
  </clause>

  <clause id="17839">
    <literal><![CDATA[
      K(x,K(y * z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,y \ z) * w) = v5
    ]]></literal>
    <justification jstring="[para(17831(a,2),16523(a,1))].">
      <j1 rule="para" parents="17831 16523"/>
    </justification>
  </clause>

  <clause id="17840">
    <literal><![CDATA[
      K(x,y * K(z * (z / u),w)) = K(x,y * K(u,w))
    ]]></literal>
    <justification jstring="[hyper(16856,a,17834,a)].">
      <j1 rule="hyper" parents="16856 17834"/>
    </justification>
  </clause>

  <clause id="17841">
    <literal><![CDATA[
      (x * K(y,K(z * u,w) * v5)) \ x = K(K(z \ u,w) * v5,y)
    ]]></literal>
    <justification jstring="[para(17837(a,1),7200(a,1,1,2))].">
      <j1 rule="para" parents="17837 7200"/>
    </justification>
  </clause>

  <clause id="17842">
    <literal><![CDATA[
      K(x,K(y \ z,T(u,z)) * w) = K(x,K(z * y,u) * w)
    ]]></literal>
    <justification jstring="[para(13173(a,1),17837(a,2,2,1))].">
      <j1 rule="para" parents="13173 17837"/>
    </justification>
  </clause>

  <clause id="17844">
    <literal><![CDATA[
      K(x,y * K(z * (u * z),w)) = K(x,y * K(u,T(w,z)))
    ]]></literal>
    <justification jstring="[para(7537(a,1),17832(a,2,2,2))].">
      <j1 rule="para" parents="7537 17832"/>
    </justification>
  </clause>

  <clause id="17845">
    <literal><![CDATA[
      K(x,K(y / z,u) * w) = K(x,K(y * z,u) * w)
    ]]></literal>
    <justification jstring="[para(8107(a,1),17842(a,1,2,1))].">
      <j1 rule="para" parents="8107 17842"/>
    </justification>
  </clause>

  <clause id="17846">
    <literal><![CDATA[
      K(x,K(y * (z \ u),z) * w) = K(x,K(z,(y * z) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(65,a,15809,a(flip),b,17845,a),flip(a)].">
      <j1 rule="hyper" parents="65 15809 17845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17847">
    <literal><![CDATA[
      K(x,y * K(z * (u * z),w)) = K(x,y * K(u,w))
    ]]></literal>
    <justification jstring="[hyper(299,a,16758,a(flip),b,17844,a),flip(a)].">
      <j1 rule="hyper" parents="299 16758 17844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17849">
    <literal><![CDATA[
      K(x,y \ T(z,u * (w * u))) = K(x,(y \ z) * K(w,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,16598,a(flip),b,17847,a)].">
      <j1 rule="hyper" parents="65 16598 17847"/>
    </justification>
  </clause>

  <clause id="17850">
    <literal><![CDATA[
      K(x,y \ T(z,u * (w * u))) = K(x,y \ T(z,w))
    ]]></literal>
    <justification jstring="[hyper(299,a,16598,a(flip),b,17849,a),flip(a)].">
      <j1 rule="hyper" parents="299 16598 17849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17851">
    <literal><![CDATA[
      K(x,y \ T(z,(u \ w) * w)) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),17850(a,1,2,2,2,2))].">
      <j1 rule="para" parents="10 17850"/>
    </justification>
  </clause>

  <clause id="17852">
    <literal><![CDATA[
      K(x,y \ T(z,u * (u / w))) = K(x,y \ T(z,w))
    ]]></literal>
    <justification jstring="[para(13877(a,1),17851(a,1,2,2))].">
      <j1 rule="para" parents="13877 17851"/>
    </justification>
  </clause>

  <clause id="17853">
    <literal><![CDATA[
      K(x,K(y,z \ u) * w) = K(x,K(y,z * u) * w)
    ]]></literal>
    <justification jstring="[hyper(17839,a,15802,a)].">
      <j1 rule="hyper" parents="17839 15802"/>
    </justification>
  </clause>

  <clause id="17854">
    <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(15802(a,1),17839(a,1))].">
      <j1 rule="para" parents="15802 17839"/>
    </justification>
  </clause>

  <clause id="17855">
    <literal><![CDATA[
      K(x,K(y,y \ (z \ u)) * w) = K(x,K(y,(z * y) * u) * w)
    ]]></literal>
    <justification jstring="[para(11253(a,1),17853(a,1,2,1))].">
      <j1 rule="para" parents="11253 17853"/>
    </justification>
  </clause>

  <clause id="17856">
    <literal><![CDATA[
      K(x,K(y,T(z,u) * u) * w) = K(x,K(y,u / z) * w)
    ]]></literal>
    <justification jstring="[para(13923(a,1),17853(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13923 17853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17857">
    <literal><![CDATA[
      K(x,K(y,z \ u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z * u,y) * w) = v5
    ]]></literal>
    <justification jstring="[para(17853(a,2),15803(a,1))].">
      <j1 rule="para" parents="17853 15803"/>
    </justification>
  </clause>

  <clause id="17858">
    <literal><![CDATA[
      K(x,K(y,z / u) * w) = K(x,K(y,z * u) * w)
    ]]></literal>
    <justification jstring="[para(13262(a,1),17856(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13262 17856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17859">
    <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(15802(a,1),17857(a,1))].">
      <j1 rule="para" parents="15802 17857"/>
    </justification>
  </clause>

  <clause id="17860">
    <literal><![CDATA[
      K(K(x \ y,z) * u,w) = K(K(x * y,z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(7209,a,17841,a),flip(a)].">
      <j1 rule="hyper" parents="7209 17841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17861">
    <literal><![CDATA[
      K(K(x \ y,z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(K(x * y,z) * u,w) = v5
    ]]></literal>
    <justification jstring="[para(17841(a,1),7209(a,1))].">
      <j1 rule="para" parents="17841 7209"/>
    </justification>
  </clause>

  <clause id="17862">
    <literal><![CDATA[
      K(K(x \ y,z) * u,w) = K(u * K(z,x * y),w)
    ]]></literal>
    <justification jstring="[hyper(299,a,17765,a(flip),b,17860,a),flip(a)].">
      <j1 rule="hyper" parents="299 17765 17860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17863">
    <literal><![CDATA[
      K(x * K(y,z \ u),w) = K(x * K(y,z * u),w)
    ]]></literal>
    <justification jstring="[hyper(17787,a,17862,a)].">
      <j1 rule="hyper" parents="17787 17862"/>
    </justification>
  </clause>

  <clause id="17864">
    <literal><![CDATA[
      K(x * K(y,z / u),w) = K(x * K(y,u * z),w)
    ]]></literal>
    <justification jstring="[hyper(16857,a,17863,a)].">
      <j1 rule="hyper" parents="16857 17863"/>
    </justification>
  </clause>

  <clause id="17865">
    <literal><![CDATA[
      K(K(x,y * (y * K(z,u))) * K(u,(w * (w / x)) * z),v5) = K(K(u,(w * (w / x)) \ z),v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,17600,a(flip),b,17864,a),flip(a)].">
      <j1 rule="hyper" parents="65 17600 17864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17866">
    <literal><![CDATA[
      K(x,K(y,(z * y) * u) * w) = K(x,K(y,z \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(15840,a,17855,a),flip(a)].">
      <j1 rule="hyper" parents="15840 17855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17867">
    <literal><![CDATA[
      K(x,K(y,(z * y) * u) * w) = K(x,K(y,z * u) * w)
    ]]></literal>
    <justification jstring="[hyper(299,a,17853,a(flip),b,17866,a),flip(a)].">
      <j1 rule="hyper" parents="299 17853 17866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17868">
    <literal><![CDATA[
      K(x,K(y,(z * y) / u) * w) = K(x,K(y,z * u) * w)
    ]]></literal>
    <justification jstring="[hyper(65,a,17858,a,b,17867,a)].">
      <j1 rule="hyper" parents="65 17858 17867"/>
    </justification>
  </clause>

  <clause id="17869">
    <literal><![CDATA[
      K(x,K(y * (z \ u),z) * w) = K(x,K(z,y * u) * w)
    ]]></literal>
    <justification jstring="[hyper(65,a,17846,a,b,17868,a)].">
      <j1 rule="hyper" parents="65 17846 17868"/>
    </justification>
  </clause>

  <clause id="17870">
    <literal><![CDATA[
      K(x,y * K(z,u * (z \ w))) = K(x,K(z,u * w) * y)
    ]]></literal>
    <justification jstring="[hyper(16624,a,17869,a)].">
      <j1 rule="hyper" parents="16624 17869"/>
    </justification>
  </clause>

  <clause id="17871">
    <literal><![CDATA[
      K(x * (y * (z * K(u,z))),w) = K(x * (y * T(z,u)),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,16527,a(flip),b,17776,a)].">
      <j1 rule="hyper" parents="65 16527 17776"/>
    </justification>
  </clause>

  <clause id="17872">
    <literal><![CDATA[
      K(x \ (y * (z * K(u,z))),w) = K((x \ 1) * (y * T(z,u)),w)
    ]]></literal>
    <justification jstring="[hyper(14266,a,17871,a)].">
      <j1 rule="hyper" parents="14266 17871"/>
    </justification>
  </clause>

  <clause id="17873">
    <literal><![CDATA[
      K(x \ (y * (z * K(u,z))),w) = K(x \ (y * T(z,u)),w)
    ]]></literal>
    <justification jstring="[hyper(299,a,14252,a(flip),b,17872,a),flip(a)].">
      <j1 rule="hyper" parents="299 14252 17872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17874">
    <literal><![CDATA[
      K(x \ (y * T(z,z \ u)),w) = K(x \ (y * (u / (u / z))),w)
    ]]></literal>
    <justification jstring="[para(5002(a,2),17873(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5002 17873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17876">
    <literal><![CDATA[
      K(x \ (y * (z / (z / u))),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x \ (y * T(u,u * z)),w) = v5
    ]]></literal>
    <justification jstring="[para(17874(a,1),17569(a,1))].">
      <j1 rule="para" parents="17874 17569"/>
    </justification>
  </clause>

  <clause id="17877">
    <literal><![CDATA[
      T(x,T(y,z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,((z \ y) * z) \ u) = w
    ]]></literal>
    <justification jstring="[para(5119(a,2),17802(a,1))].">
      <j1 rule="para" parents="5119 17802"/>
    </justification>
  </clause>

  <clause id="17878">
    <literal><![CDATA[
      K(x \ T((y \ 1) * (y \ z),y * y),u) = K(y \ (y \ (x \ z)),u)
    ]]></literal>
    <justification jstring="[para(15287(a,2),17809(a,1,1,2))].">
      <j1 rule="para" parents="15287 17809"/>
    </justification>
  </clause>

  <clause id="17879">
    <literal><![CDATA[
      K(K(x,y) * (z * (x * (1 / y))),u) = K(z * ((1 / y) * x),u)
    ]]></literal>
    <justification jstring="[para(8(a,1),17813(a,1,1,1,2))].">
      <j1 rule="para" parents="8 17813"/>
    </justification>
  </clause>

  <clause id="17880">
    <literal><![CDATA[
      K(x * (y \ R(z,1 / y,y)),u) = K(x * ((1 / y) * z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,17649,a(flip),b,17879,a)].">
      <j1 rule="hyper" parents="65 17649 17879"/>
    </justification>
  </clause>

  <clause id="17881">
    <literal><![CDATA[
      K(x * T(y * (1 / z),z),u) = K(x * ((1 / z) * y),u)
    ]]></literal>
    <justification jstring="[para(598(a,1),17880(a,1,1,2))].">
      <j1 rule="para" parents="598 17880"/>
    </justification>
  </clause>

  <clause id="17882">
    <literal><![CDATA[
      K(x * ((y \ 1) * (T(y,y \ 1) * z)),u) = K(x * T((y * z) * (1 / y),y),u)
    ]]></literal>
    <justification jstring="[para(5929(a,2),17881(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="5929 17881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17883">
    <literal><![CDATA[
      K(x * K(y,K(z,u) * w),v5) = v5 / T(v5,K(w,y) * x)
    ]]></literal>
    <justification jstring="[para(17597(a,1),17827(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17597 17827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17884">
    <literal><![CDATA[
      K(x * K(y,K(z,u) * w),v5) = K(K(w,y) * x,v5)
    ]]></literal>
    <justification jstring="[hyper(299,a,5033,a,b,17883,a),flip(a)].">
      <j1 rule="hyper" parents="299 5033 17883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17886">
    <literal><![CDATA[
      K(K(K(x,y) * z,u) * w,v5) = K(K(z,u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(17784,a,17884,a)].">
      <j1 rule="hyper" parents="17784 17884"/>
    </justification>
  </clause>

  <clause id="17887">
    <literal><![CDATA[
      K(x * K(K(y,z) * u,w),v5) = K(K(u,w) * x,v5)
    ]]></literal>
    <justification jstring="[hyper(17781,a,17884,a)].">
      <j1 rule="hyper" parents="17781 17884"/>
    </justification>
  </clause>

  <clause id="17888">
    <literal><![CDATA[
      K(K(x,K(y,z) * u) * w,v5) = K(K(u,x) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(16406,a,17884,a)].">
      <j1 rule="hyper" parents="16406 17884"/>
    </justification>
  </clause>

  <clause id="17889">
    <literal><![CDATA[
      K(K(K(x,y) * z,u) * w,v5) = K(w * K(u,z),v5)
    ]]></literal>
    <justification jstring="[para(5432(a,1),17884(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5432 17884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17891">
    <literal><![CDATA[
      K(K(x,y) * ((K(z,u) * x) * w),v5) = K(T(K(z,u) * x,y) * w,v5)
    ]]></literal>
    <justification jstring="[para(5103(a,1),17886(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5103 17886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17892">
    <literal><![CDATA[
      K(K((x / y) * z,u) * w,v5) = K(K((y \ x) * z,u) * w,v5)
    ]]></literal>
    <justification jstring="[para(5410(a,1),17886(a,1,1,1,1))].">
      <j1 rule="para" parents="5410 17886"/>
    </justification>
  </clause>

  <clause id="17893">
    <literal><![CDATA[
      K(K(T(x * (y / z),K(y,z)),u) * w,v5) = K(K(x * (z \ y),u) * w,v5)
    ]]></literal>
    <justification jstring="[para(11213(a,1),17886(a,1,1,1,1))].">
      <j1 rule="para" parents="11213 17886"/>
    </justification>
  </clause>

  <clause id="17894">
    <literal><![CDATA[
      K(K(K(x,y) * z,u) * w,v5) = v5 / T(v5,w * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,5033,a(flip),b,17889,a),flip(a)].">
      <j1 rule="hyper" parents="299 5033 17889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17896">
    <literal><![CDATA[
      T(x,y * K(z,K(u,w) * v5)) = T(x,y * K(z,v5))
    ]]></literal>
    <justification jstring="[hyper(38,a,17894,a(flip),b,17828,a),flip(a)].">
      <j1 rule="hyper" parents="38 17894 17828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17897">
    <literal><![CDATA[
      T(x,T(y,z * K(u,w)) \ v5) = T(x,(y \ v5) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(16695,a,17896,a)].">
      <j1 rule="hyper" parents="16695 17896"/>
    </justification>
  </clause>

  <clause id="17899">
    <literal><![CDATA[
      T(x,T(y,z * K(u,w)) \ v5) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z) \ v5) = v6
    ]]></literal>
    <justification jstring="[para(17897(a,2),16517(a,1))].">
      <j1 rule="para" parents="17897 16517"/>
    </justification>
  </clause>

  <clause id="17900">
    <literal><![CDATA[
      T(x,T(y,T(z,u)) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z) \ w) = v5
    ]]></literal>
    <justification jstring="[para(5083(a,2),17899(a,1,2,1,2))].">
      <j1 rule="para" parents="5083 17899"/>
    </justification>
  </clause>

  <clause id="17901">
    <literal><![CDATA[
      K(x \ ((y \ 1) * (y \ z)),u) = K(y \ (y \ (x \ z)),u)
    ]]></literal>
    <justification jstring="[hyper(17493,a,17878,a)].">
      <j1 rule="hyper" parents="17493 17878"/>
    </justification>
  </clause>

  <clause id="17903">
    <literal><![CDATA[
      K(x \ (x \ (y \ z)),L(u,y,x)) = K(((x \ 1) \ y) \ (x \ z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,15635,a(flip),b,17901,a),flip(a)].">
      <j1 rule="hyper" parents="65 15635 17901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17904">
    <literal><![CDATA[
      K(x \ (x \ (y \ z)),L(u,y,x)) = K((x * y) \ ((1 / x) * z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,11973,a(flip),b,17901,a),flip(a)].">
      <j1 rule="hyper" parents="65 11973 17901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17905">
    <literal><![CDATA[
      K(x \ (x \ (y \ (x * z))),u) = K(y \ ((x \ 1) * z),u)
    ]]></literal>
    <justification jstring="[para(9(a,1),17901(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 17901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17906">
    <literal><![CDATA[
      K(x \ (x \ (y \ z)),L(u,y,x)) = K((x * y) \ ((x \ 1) * z),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,5890,a(flip),b,17904,a),flip(a)].">
      <j1 rule="hyper" parents="299 5890 17904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17907">
    <literal><![CDATA[
      K(x,y * (z * K(u \ w,v5))) = K(x,y * (z * K(u * w,v5)))
    ]]></literal>
    <justification jstring="[para(11903(a,1),17836(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11903 17836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17908">
    <literal><![CDATA[
      K(x,y * (z * K(u \ 1,w))) = K(x,y * (z * K(u,w)))
    ]]></literal>
    <justification jstring="[para(8(a,1),17907(a,2,2,2,2,1))].">
      <j1 rule="para" parents="8 17907"/>
    </justification>
  </clause>

  <clause id="17909">
    <literal><![CDATA[
      K(x,y * (z * K(u * u,w))) = K(x,y * (z * K(1,w)))
    ]]></literal>
    <justification jstring="[para(68(a,1),17907(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="68 17907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17910">
    <literal><![CDATA[
      K(x,y * (T(z,K(u,w \ v5)) * K(w * v5,u))) = K(x,y * (K(w \ v5,u) * z))
    ]]></literal>
    <justification jstring="[para(6257(a,1),17907(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6257 17907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17911">
    <literal><![CDATA[
      (x * K(y,z * (u * K(w * v5,v6)))) \ x = K(z * (u * K(w \ v5,v6)),y)
    ]]></literal>
    <justification jstring="[para(17907(a,1),7200(a,1,1,2))].">
      <j1 rule="para" parents="17907 7200"/>
    </justification>
  </clause>

  <clause id="17912">
    <literal><![CDATA[
      K(x,y * ((z / u) * K(w * v5,u))) = K(x,y * (z / T(u,w \ v5)))
    ]]></literal>
    <justification jstring="[para(7189(a,1),17907(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7189 17907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17913">
    <literal><![CDATA[
      K(x,y * ((z * u) * K(w * v5,z))) = K(x,y * (z * (u * K(w \ v5,z))))
    ]]></literal>
    <justification jstring="[para(7822(a,1),17907(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7822 17907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17914">
    <literal><![CDATA[
      K(x,y * ((z \ 1) * K(u * w,v5))) = K(x,y * (z \ K(u \ w,v5)))
    ]]></literal>
    <justification jstring="[para(14185(a,1),17907(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14185 17907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17915">
    <literal><![CDATA[
      K(x,y * (((z * (u \ 1)) / z) \ 1)) = K(x,y * (u * K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(65,a,7117,a,b,17908,a)].">
      <j1 rule="hyper" parents="65 7117 17908"/>
    </justification>
  </clause>

  <clause id="17916">
    <literal><![CDATA[
      K(x,y * (z * K(u * u,w))) = K(x,y * (z * 1))
    ]]></literal>
    <justification jstring="[para(199(a,1),17909(a,2,2,2,2))].">
      <j1 rule="para" parents="199 17909"/>
    </justification>
  </clause>

  <clause id="17917">
    <literal><![CDATA[
      K(x,y * (z * K(u * u,w))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(8(a,1),17916(a,2,2,2))].">
      <j1 rule="para" parents="8 17916"/>
    </justification>
  </clause>

  <clause id="17919">
    <literal><![CDATA[
      K(x,y * (K(z * z,u) * w)) = K(x,y * w)
    ]]></literal>
    <justification jstring="[hyper(16810,a,17917,a)].">
      <j1 rule="hyper" parents="16810 17917"/>
    </justification>
  </clause>

  <clause id="17920">
    <literal><![CDATA[
      K(x,K(y,z * z) * u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(7603(a,1),17917(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7603 17917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17921">
    <literal><![CDATA[
      K(x,y * K(z * z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(16624,a,17920,a)].">
      <j1 rule="hyper" parents="16624 17920"/>
    </justification>
  </clause>

  <clause id="17922">
    <literal><![CDATA[
      K(x,T(y,z * z) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,15807,a(flip),b,17920,a)].">
      <j1 rule="hyper" parents="65 15807 17920"/>
    </justification>
  </clause>

  <clause id="17923">
    <literal><![CDATA[
      K(x,T(y,z * z) * u) = K(x,y * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,13833,a(flip),b,17920,a)].">
      <j1 rule="hyper" parents="65 13833 17920"/>
    </justification>
  </clause>

  <clause id="17924">
    <literal><![CDATA[
      K(x,y \ T(z,u * u)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(5850(a,1),17920(a,1,2))].">
      <j1 rule="para" parents="5850 17920"/>
    </justification>
  </clause>

  <clause id="17925">
    <literal><![CDATA[
      K(x,y / T(z,u * u)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(7189(a,1),17921(a,1,2))].">
      <j1 rule="para" parents="7189 17921"/>
    </justification>
  </clause>

  <clause id="17926">
    <literal><![CDATA[
      K(x,(T(y,z) * (z \ 1)) \ u) = K(x,((z \ 1) * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(16030,a,17922,a)].">
      <j1 rule="hyper" parents="16030 17922"/>
    </justification>
  </clause>

  <clause id="17927">
    <literal><![CDATA[
      K(x,((y \ 1) * T(z,y)) \ u) = K(x,(z * (1 / y)) \ u)
    ]]></literal>
    <justification jstring="[para(7105(a,1),17922(a,1,2,1))].">
      <j1 rule="para" parents="7105 17922"/>
    </justification>
  </clause>

  <clause id="17928">
    <literal><![CDATA[
      K(x,T(y,z * (z * u)) \ w) = K(x,T(y,u) \ w)
    ]]></literal>
    <justification jstring="[para(14468(a,1),17922(a,1,2,1))].">
      <j1 rule="para" parents="14468 17922"/>
    </justification>
  </clause>

  <clause id="17929">
    <literal><![CDATA[
      K(x,T(y,z * (z * u)) * w) = K(x,T(y,u) * w)
    ]]></literal>
    <justification jstring="[para(14468(a,1),17923(a,1,2,1))].">
      <j1 rule="para" parents="14468 17923"/>
    </justification>
  </clause>

  <clause id="17930">
    <literal><![CDATA[
      K(x,y \ (((z * z) \ u) * w)) = K(x,y \ (u * (w / (z * z))))
    ]]></literal>
    <justification jstring="[para(1053(a,1),17924(a,1,2,2))].">
      <j1 rule="para" parents="1053 17924"/>
    </justification>
  </clause>

  <clause id="17931">
    <literal><![CDATA[
      K(x,y \ T(z,u * (u * w))) = K(x,y \ T(z,w))
    ]]></literal>
    <justification jstring="[para(14468(a,1),17924(a,1,2,2))].">
      <j1 rule="para" parents="14468 17924"/>
    </justification>
  </clause>

  <clause id="17932">
    <literal><![CDATA[
      K(x,y \ T(z,u * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = w
    ]]></literal>
    <justification jstring="[para(17924(a,1),16056(a,1))].">
      <j1 rule="para" parents="17924 16056"/>
    </justification>
  </clause>

  <clause id="17933">
    <literal><![CDATA[
      K(x,y / T(z,u * (u * w))) = K(x,y / T(z,w))
    ]]></literal>
    <justification jstring="[para(14468(a,1),17925(a,1,2,2))].">
      <j1 rule="para" parents="14468 17925"/>
    </justification>
  </clause>

  <clause id="17934">
    <literal><![CDATA[
      K(x,y / ((1 / z) * T(u,z))) = K(x,y / (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[para(14812(a,1),17925(a,1,2,2))].">
      <j1 rule="para" parents="14812 17925"/>
    </justification>
  </clause>

  <clause id="17935">
    <literal><![CDATA[
      K(x,y * (T(z,u * u) * w)) = K(x,y * (z * w))
    ]]></literal>
    <justification jstring="[para(5061(a,1),17919(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5061 17919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17936">
    <literal><![CDATA[
      K(x,y \ T(z,u * (u * w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ T(z,w)) = v5
    ]]></literal>
    <justification jstring="[para(14468(a,1),17932(a,1,2,2))].">
      <j1 rule="para" parents="14468 17932"/>
    </justification>
  </clause>

  <clause id="17937">
    <literal><![CDATA[
      K(x,T(y,z \ u) \ w) = K(x,T(y,z * u) \ w)
    ]]></literal>
    <justification jstring="[para(10(a,1),17928(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 17928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17938">
    <literal><![CDATA[
      K(x,T(y,(z * u) * z) * w) = K(x,T(y,u) * w)
    ]]></literal>
    <justification jstring="[hyper(16855,a,17929,a)].">
      <j1 rule="hyper" parents="16855 17929"/>
    </justification>
  </clause>

  <clause id="17939">
    <literal><![CDATA[
      K(x,T(y,z \ u) * w) = K(x,T(y,z * u) * w)
    ]]></literal>
    <justification jstring="[para(10(a,1),17929(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 17929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17940">
    <literal><![CDATA[
      K(x,T(y,(z * z) * u) * w) = K(x,T(y,u) * w)
    ]]></literal>
    <justification jstring="[para(14216(a,2),17929(a,1,2,1))].">
      <j1 rule="para" parents="14216 17929"/>
    </justification>
  </clause>

  <clause id="17941">
    <literal><![CDATA[
      K(x,y \ T((z / (1 / u)) * w,w)) = K(x,y \ (((u * u) * w) * (z / u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,16082,a(flip),b,17931,a),flip(a)].">
      <j1 rule="hyper" parents="65 16082 17931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17942">
    <literal><![CDATA[
      K(x,y \ T(z,u \ w)) = K(x,y \ T(z,u * w))
    ]]></literal>
    <justification jstring="[para(10(a,1),17931(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10 17931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17943">
    <literal><![CDATA[
      K(x,y / T(z,u \ w)) = K(x,y / T(z,u * w))
    ]]></literal>
    <justification jstring="[para(10(a,1),17933(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10 17933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17944">
    <literal><![CDATA[
      K(x,y / T(z,(u / w) * u)) = K(x,y / T(z,w))
    ]]></literal>
    <justification jstring="[para(12(a,1),17933(a,1,2,2,2,2))].">
      <j1 rule="para" parents="12 17933"/>
    </justification>
  </clause>

  <clause id="17945">
    <literal><![CDATA[
      K(x,y * ((z / u) * (w * K(u / z,w)))) = K(x,y * (w * (z / u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,15905,a(flip),b,17935,a)].">
      <j1 rule="hyper" parents="65 15905 17935"/>
    </justification>
  </clause>

  <clause id="17946">
    <literal><![CDATA[
      K(L(x,y,z),T(u,w * v5) \ v6) = K(x,L(T(u,w \ v5) \ v6,y,z))
    ]]></literal>
    <justification jstring="[hyper(11999,a,17937,a),flip(a)].">
      <j1 rule="hyper" parents="11999 17937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17947">
    <literal><![CDATA[
      K(x,T(y,(z * (u * u)) \ w) \ v5) = K(x,T(y,z * ((u * u) * w)) \ v5)
    ]]></literal>
    <justification jstring="[para(34(a,1),17937(a,2,2,1,2))].">
      <j1 rule="para" parents="34 17937"/>
    </justification>
  </clause>

  <clause id="17948">
    <literal><![CDATA[
      K(x,T(y,T(z,u) * u) \ w) = K(x,T(y,u / z) \ w)
    ]]></literal>
    <justification jstring="[para(15275(a,1),17937(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="15275 17937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17949">
    <literal><![CDATA[
      K(x,T(y,(z * u) * z) * w) = K(w,K(y,x)) * K(x,w * T(y,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,16672,a,b,17938,a),flip(a)].">
      <j1 rule="hyper" parents="299 16672 17938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17950">
    <literal><![CDATA[
      K(x,T(y,z * (u * z)) * w) = K(x,T(y,u) * w)
    ]]></literal>
    <justification jstring="[para(13693(a,1),17938(a,1,2,1))].">
      <j1 rule="para" parents="13693 17938"/>
    </justification>
  </clause>

  <clause id="17951">
    <literal><![CDATA[
      K(x,T(y,z * u) * (z \ u)) = K(x,(z \ u) * y)
    ]]></literal>
    <justification jstring="[hyper(13261,a,17939,a),flip(a)].">
      <j1 rule="hyper" parents="13261 17939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17952">
    <literal><![CDATA[
      K(L(x,y,z),T(u,w * v5) * v6) = K(x,L(T(u,w \ v5) * v6,y,z))
    ]]></literal>
    <justification jstring="[hyper(11999,a,17939,a),flip(a)].">
      <j1 rule="hyper" parents="11999 17939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17953">
    <literal><![CDATA[
      K(x,T(y,((z \ 1) * u) \ ((z * z) * w)) * v5) = K(x,T(y,(z * T(u,z * z)) * w) * v5)
    ]]></literal>
    <justification jstring="[para(1045(a,1),17939(a,2,2,1,2))].">
      <j1 rule="para" parents="1045 17939"/>
    </justification>
  </clause>

  <clause id="17954">
    <literal><![CDATA[
      K(x,T(y,z * u) * (z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z \ u) * y) = w
    ]]></literal>
    <justification jstring="[para(17939(a,1),13261(a,1))].">
      <j1 rule="para" parents="17939 13261"/>
    </justification>
  </clause>

  <clause id="17955">
    <literal><![CDATA[
      K(x,T(y,((z \ 1) \ u) * w) * v5) = K(x,T(y,(z \ u) * w) * v5)
    ]]></literal>
    <justification jstring="[para(731(a,1),17940(a,1,2,1,2))].">
      <j1 rule="para" parents="731 17940"/>
    </justification>
  </clause>

  <clause id="17956">
    <literal><![CDATA[
      K(x,T(y,T(z,u \ w)) \ T(z,u * w)) = K(x,T(z,u \ w) / y)
    ]]></literal>
    <justification jstring="[hyper(13924,a,17942,a),flip(a)].">
      <j1 rule="hyper" parents="13924 17942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17957">
    <literal><![CDATA[
      L(K(x,y \ T(z,u * w)),v5,v6) = K(x,L(y \ T(z,u \ w),v5,v6))
    ]]></literal>
    <justification jstring="[para(17942(a,1),11889(a,1,1))].">
      <j1 rule="para" parents="17942 11889"/>
    </justification>
  </clause>

  <clause id="17958">
    <literal><![CDATA[
      K(x,y / T(z,u / w)) = K(x,y / T(z,w * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,16781,a,b,17943,a)].">
      <j1 rule="hyper" parents="65 16781 17943"/>
    </justification>
  </clause>

  <clause id="17959">
    <literal><![CDATA[
      (x * K(y,z / T(u,w * v5))) \ x = K(z / T(u,w \ v5),y)
    ]]></literal>
    <justification jstring="[para(17943(a,1),7200(a,1,1,2))].">
      <j1 rule="para" parents="17943 7200"/>
    </justification>
  </clause>

  <clause id="17960">
    <literal><![CDATA[
      K(x,T(y,z / u) * w) = K(x,T(y,u * z) * w)
    ]]></literal>
    <justification jstring="[para(12(a,1),17950(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 17950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17961">
    <literal><![CDATA[
      T(x,T(y,z * (u * z)) * w) = x * K(x,T(y,u) * w)
    ]]></literal>
    <justification jstring="[para(17950(a,1),5083(a,2,2))].">
      <j1 rule="para" parents="17950 5083"/>
    </justification>
  </clause>

  <clause id="17962">
    <literal><![CDATA[
      K(x,T(y,(z * z) * u) * (z \ ((1 / z) \ u))) = K(x,(z \ ((1 / z) \ u)) * y)
    ]]></literal>
    <justification jstring="[para(442(a,1),17951(a,1,2,1,2))].">
      <j1 rule="para" parents="442 17951"/>
    </justification>
  </clause>

  <clause id="17963">
    <literal><![CDATA[
      K(x,y / T((z / u) * w,u * z)) = K(x,y / (w * (z / u)))
    ]]></literal>
    <justification jstring="[hyper(13949,a,17958,a),flip(a)].">
      <j1 rule="hyper" parents="13949 17958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17964">
    <literal><![CDATA[
      K(x,(T(y,y \ z) * ((z / y) \ 1)) \ u) = K(x,(((z / y) \ 1) * y) \ u)
    ]]></literal>
    <justification jstring="[para(4400(a,1),17926(a,1,2,1,1))].">
      <j1 rule="para" parents="4400 17926"/>
    </justification>
  </clause>

  <clause id="17965">
    <literal><![CDATA[
      K(x,((y \ 1) * T(z,y)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * (y \ 1)) \ u) = w
    ]]></literal>
    <justification jstring="[para(17927(a,2),13803(a,1))].">
      <j1 rule="para" parents="17927 13803"/>
    </justification>
  </clause>

  <clause id="17966">
    <literal><![CDATA[
      K(x,y / ((z \ 1) * T(u,z))) = K(x,y / (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(17302,a,17934,a)].">
      <j1 rule="hyper" parents="17302 17934"/>
    </justification>
  </clause>

  <clause id="17967">
    <literal><![CDATA[
      K(x,T(y,z / u) \ w) = K(x,T(y,z * u) \ w)
    ]]></literal>
    <justification jstring="[para(13266(a,1),17948(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13266 17948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17968">
    <literal><![CDATA[
      T(x,T(y,z * (u * z)) * w) = T(x,T(y,u) * w)
    ]]></literal>
    <justification jstring="[hyper(299,a,5083,a,b,17961,a),flip(a)].">
      <j1 rule="hyper" parents="299 5083 17961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17969">
    <literal><![CDATA[
      T(x,T(y,z) * (u * (u * z))) = T(x,(u * (u * z)) * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,16848,a(flip),b,17968,a),flip(a)].">
      <j1 rule="hyper" parents="65 16848 17968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17970">
    <literal><![CDATA[
      T(x,T(y,z / u) * w) = T(x,T(y,u * z) * w)
    ]]></literal>
    <justification jstring="[para(12(a,1),17968(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 17968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17972">
    <literal><![CDATA[
      T(x,L(y,z,z) * ((z * z) * u)) = T(x,(z * (z * y)) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,17695,a(flip),b,17969,a)].">
      <j1 rule="hyper" parents="65 17695 17969"/>
    </justification>
  </clause>

  <clause id="17973">
    <literal><![CDATA[
      K(x,(y \ z) * K(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(17849(a,1),17936(a,1))].">
      <j1 rule="para" parents="17849 17936"/>
    </justification>
  </clause>

  <clause id="17974">
    <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(13874(a,1),17954(a,1,2,1))].">
      <j1 rule="para" parents="13874 17954"/>
    </justification>
  </clause>

  <clause id="17975">
    <literal><![CDATA[
      K(x,T(y,z * T(u,w * v5)) * (z \ T(u,w \ v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,(z \ T(u,w \ v5)) * y) = v6
    ]]></literal>
    <justification jstring="[para(17433(a,1),17954(a,1,2,1))].">
      <j1 rule="para" parents="17433 17954"/>
    </justification>
  </clause>

  <clause id="17976">
    <literal><![CDATA[
      K(x,y * (((z * (u \ 1)) / z) \ 1)) = K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[para(5083(a,2),17915(a,2,2,2))].">
      <j1 rule="para" parents="5083 17915"/>
    </justification>
  </clause>

  <clause id="17977">
    <literal><![CDATA[
      K(x,y / ((z * (u \ 1)) / z)) = K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[hyper(14626,a,17976,a)].">
      <j1 rule="hyper" parents="14626 17976"/>
    </justification>
  </clause>

  <clause id="17978">
    <literal><![CDATA[
      K(x,y / T(z \ 1,u)) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(16870,a,17977,a)].">
      <j1 rule="hyper" parents="16870 17977"/>
    </justification>
  </clause>

  <clause id="17979">
    <literal><![CDATA[
      K(x,y * T(z,z * (x * y))) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(14549,a,17978,a),flip(a)].">
      <j1 rule="hyper" parents="14549 17978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17980">
    <literal><![CDATA[
      K(x,y * T(z,x * y)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(13873,a,17979,a)].">
      <j1 rule="hyper" parents="13873 17979"/>
    </justification>
  </clause>

  <clause id="17981">
    <literal><![CDATA[
      T(x,y * T(z,x * y)) = K(x,z * y) * x
    ]]></literal>
    <justification jstring="[para(17980(a,1),5096(a,2,1))].">
      <j1 rule="para" parents="17980 5096"/>
    </justification>
  </clause>

  <clause id="17982">
    <literal><![CDATA[
      T(x,y * T(z,x * y)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(299,a,5096,a,b,17981,a),flip(a)].">
      <j1 rule="hyper" parents="299 5096 17981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17983">
    <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(65,a,15773,a,b,17982,a)].">
      <j1 rule="hyper" parents="65 15773 17982"/>
    </justification>
  </clause>

  <clause id="17984">
    <literal><![CDATA[
      K(x,y \ (((z * z) \ u) * w)) = K(x,y \ (u * ((z * z) \ w)))
    ]]></literal>
    <justification jstring="[hyper(299,a,17564,a(flip),b,17930,a),flip(a)].">
      <j1 rule="hyper" parents="299 17564 17930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17985">
    <literal><![CDATA[
      K(x / T(y,z \ u),w) = K(x / T(y,z * u),w)
    ]]></literal>
    <justification jstring="[hyper(7209,a,17959,a),flip(a)].">
      <j1 rule="hyper" parents="7209 17959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17986">
    <literal><![CDATA[
      K(x / T(y,z \ u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x / T(y,z * u),w) = v5
    ]]></literal>
    <justification jstring="[para(17959(a,1),7209(a,1))].">
      <j1 rule="para" parents="17959 7209"/>
    </justification>
  </clause>

  <clause id="17987">
    <literal><![CDATA[
      K(x / L(T(y,z \ u),w,v5),v6) = K(x / T(L(y,w,v5),z * u),v6)
    ]]></literal>
    <justification jstring="[para(25(a,2),17985(a,1,1,2))].">
      <j1 rule="para" parents="25 17985"/>
    </justification>
  </clause>

  <clause id="17988">
    <literal><![CDATA[
      K(x / T(y,z * z),u) = K(x / y,u)
    ]]></literal>
    <justification jstring="[para(198(a,1),17985(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="198 17985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17989">
    <literal><![CDATA[
      K(x / T(y,y * z),u) = K(x / ((y \ z) \ z),u)
    ]]></literal>
    <justification jstring="[para(108(a,1),17985(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="108 17985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17990">
    <literal><![CDATA[
      K(x / ((y * y) * z),u) = K(x / (z * (y * y)),u)
    ]]></literal>
    <justification jstring="[hyper(13956,a,17988,a),flip(a)].">
      <j1 rule="hyper" parents="13956 17988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17991">
    <literal><![CDATA[
      K(x / ((y \ 1) * T(z,y)),u) = K(x / (z * (1 / y)),u)
    ]]></literal>
    <justification jstring="[para(7105(a,1),17988(a,1,1,2))].">
      <j1 rule="para" parents="7105 17988"/>
    </justification>
  </clause>

  <clause id="17992">
    <literal><![CDATA[
      K(x / (y * (z * z)),u) = K(z \ (z \ (x / y)),u)
    ]]></literal>
    <justification jstring="[hyper(16305,a,17990,a),flip(a)].">
      <j1 rule="hyper" parents="16305 17990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17994">
    <literal><![CDATA[
      K(x / ((y \ 1) * T(z,y)),u) = K(x / (z * (y \ 1)),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,5898,a(flip),b,17991,a),flip(a)].">
      <j1 rule="hyper" parents="299 5898 17991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17995">
    <literal><![CDATA[
      K(x / (y / (y / z)),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x / T(z,z * y),u) = w
    ]]></literal>
    <justification jstring="[para(17800(a,1),17986(a,1))].">
      <j1 rule="para" parents="17800 17986"/>
    </justification>
  </clause>

  <clause id="17996">
    <literal><![CDATA[
      K(x,y / T((z / (z / u)) * w,u)) = K(x,y / (w * (z / (z / u))))
    ]]></literal>
    <justification jstring="[hyper(65,a,17944,a(flip),b,17963,a)].">
      <j1 rule="hyper" parents="65 17944 17963"/>
    </justification>
  </clause>

  <clause id="17997">
    <literal><![CDATA[
      K(x,((T(y,z) \ 1) * z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * (y \ 1)) \ u) = w
    ]]></literal>
    <justification jstring="[para(6950(a,2),17965(a,1,2,1))].">
      <j1 rule="para" parents="6950 17965"/>
    </justification>
  </clause>

  <clause id="17998">
    <literal><![CDATA[
      K(x,(((y \ z) \ 1) * y) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * ((z / y) \ 1)) \ u) = w
    ]]></literal>
    <justification jstring="[para(109(a,1),17997(a,1,2,1,1,1))].">
      <j1 rule="para" parents="109 17997"/>
    </justification>
  </clause>

  <clause id="17999">
    <literal><![CDATA[
      K(x,y * (z / T(u,w \ v5))) = K(x,y * (z / T(u,w * v5)))
    ]]></literal>
    <justification jstring="[para(7189(a,1),17912(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7189 17912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18000">
    <literal><![CDATA[
      K(x,y * (z / T(u,u * w))) = K(x,y * (z / ((u \ w) \ w)))
    ]]></literal>
    <justification jstring="[para(108(a,1),17999(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="108 17999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18001">
    <literal><![CDATA[
      K(x,y * (z \ K(u \ w,v5))) = K(x,y * (z \ K(u * w,v5)))
    ]]></literal>
    <justification jstring="[para(14185(a,1),17914(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14185 17914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18002">
    <literal><![CDATA[
      K(x,y * ((z / u) * T(w,u / z))) = K(x,y * (w * (z / u)))
    ]]></literal>
    <justification jstring="[hyper(15927,a,17945,a)].">
      <j1 rule="hyper" parents="15927 17945"/>
    </justification>
  </clause>

  <clause id="18004">
    <literal><![CDATA[
      K(x,y * ((z / u) * T(w,z * u))) = K(x,y * (w * (z / u)))
    ]]></literal>
    <justification jstring="[hyper(17571,a,18002,a)].">
      <j1 rule="hyper" parents="17571 18002"/>
    </justification>
  </clause>

  <clause id="18005">
    <literal><![CDATA[
      K(x,y * (z * (a(z,u,1 / u) * K(u,u \ 1)))) = K(x,y * ((1 / u) * T(z * u,1 * u)))
    ]]></literal>
    <justification jstring="[para(3341(a,2),18004(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="3341 18004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18006">
    <literal><![CDATA[
      K(x,L(T(y,z \ u) \ w,v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(y,z * u) \ w,v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(17946(a,1),11999(a,1))].">
      <j1 rule="para" parents="17946 11999"/>
    </justification>
  </clause>

  <clause id="18007">
    <literal><![CDATA[
      K(x,y * T(z,u * (w * u))) = K(x,y * T(z,w))
    ]]></literal>
    <justification jstring="[hyper(17589,a,17949,a)].">
      <j1 rule="hyper" parents="17589 17949"/>
    </justification>
  </clause>

  <clause id="18009">
    <literal><![CDATA[
      K(x,L(T(y,z \ u) * w,v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(y,z * u) * w,v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(17952(a,1),11999(a,1))].">
      <j1 rule="para" parents="17952 11999"/>
    </justification>
  </clause>

  <clause id="18010">
    <literal><![CDATA[
      K(x,T(y,z * ((u \ 1) \ w)) * v5) = K(x,T(y,(u \ w) * z) * v5)
    ]]></literal>
    <justification jstring="[hyper(16855,a,17955,a)].">
      <j1 rule="hyper" parents="16855 17955"/>
    </justification>
  </clause>

  <clause id="18011">
    <literal><![CDATA[
      K(x,T(y,T(z,u * w)) \ T(z,u * w)) = K(x,T(z,u \ w) / y)
    ]]></literal>
    <justification jstring="[para(16225(a,1),17956(a,1,2,1))].">
      <j1 rule="para" parents="16225 17956"/>
    </justification>
  </clause>

  <clause id="18012">
    <literal><![CDATA[
      K(x,L(y \ T(z,u \ w),v5,v6)) = K(x,L(y \ T(z,u * w),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(11995,a,17957,a),flip(a)].">
      <j1 rule="hyper" parents="11995 17957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18013">
    <literal><![CDATA[
      K(x / L(T(y,z \ u),w,v5),v6) = K(x / L(T(y,z * u),w,v5),v6)
    ]]></literal>
    <justification jstring="[para(25(a,2),17987(a,2,1,2))].">
      <j1 rule="para" parents="25 17987"/>
    </justification>
  </clause>

  <clause id="18014">
    <literal><![CDATA[
      K(x,y / T((z / (z / u)) * w,u)) = K(x,y / (w * (u * K(u \ z,u))))
    ]]></literal>
    <justification jstring="[para(5002(a,1),17996(a,2,2,2,2))].">
      <j1 rule="para" parents="5002 17996"/>
    </justification>
  </clause>

  <clause id="18015">
    <literal><![CDATA[
      K(x,T(y,z \ u) / w) = K(x,T(y,z * u) / w)
    ]]></literal>
    <justification jstring="[hyper(13924,a,18011,a),flip(a)].">
      <j1 rule="hyper" parents="13924 18011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18016">
    <literal><![CDATA[
      K(x,T(y,z \ u) / w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z * u) / w) = v5
    ]]></literal>
    <justification jstring="[para(18011(a,1),13924(a,1))].">
      <j1 rule="para" parents="18011 13924"/>
    </justification>
  </clause>

  <clause id="18017">
    <literal><![CDATA[
      K(L(x,y,z),T(u,w * v5) / v6) = K(x,L(T(u,w \ v5) / v6,y,z))
    ]]></literal>
    <justification jstring="[hyper(11999,a,18015,a),flip(a)].">
      <j1 rule="hyper" parents="11999 18015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18018">
    <literal><![CDATA[
      (x * K(y,T(z,u * w) / v5)) \ x = K(T(z,u \ w) / v5,y)
    ]]></literal>
    <justification jstring="[para(18015(a,1),7200(a,1,1,2))].">
      <j1 rule="para" parents="18015 7200"/>
    </justification>
  </clause>

  <clause id="18019">
    <literal><![CDATA[
      K(T(x,y \ z) / u,w) = K(T(x,y * z) / u,w)
    ]]></literal>
    <justification jstring="[hyper(7209,a,18018,a),flip(a)].">
      <j1 rule="hyper" parents="7209 18018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18020">
    <literal><![CDATA[
      K(T(x,y \ z) / u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(T(x,y * z) / u,w) = v5
    ]]></literal>
    <justification jstring="[para(18018(a,1),7209(a,1))].">
      <j1 rule="para" parents="18018 7209"/>
    </justification>
  </clause>

  <clause id="18021">
    <literal><![CDATA[
      K(T(x,(y / z) * y) / u,w) = K(T(x,z) / u,w)
    ]]></literal>
    <justification jstring="[para(79(a,1),18019(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="79 18019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18022">
    <literal><![CDATA[
      K(T(x,y * (z \ y)) / u,w) = K(T(x,z) / u,w)
    ]]></literal>
    <justification jstring="[para(13982(a,1),18021(a,1,1,1))].">
      <j1 rule="para" parents="13982 18021"/>
    </justification>
  </clause>

  <clause id="18023">
    <literal><![CDATA[
      K(T(x,y) / (z * (y \ z)),u) != w
    ]]></literal>
    <literal><![CDATA[
      K((z * (y \ z)) \ x,u) = w
    ]]></literal>
    <justification jstring="[para(18022(a,1),13762(a,1))].">
      <j1 rule="para" parents="18022 13762"/>
    </justification>
  </clause>

  <clause id="18024">
    <literal><![CDATA[
      K(T(x,y / z) / u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(T(x,z * y) / u,w) = v5
    ]]></literal>
    <justification jstring="[para(16788(a,2),18020(a,1))].">
      <j1 rule="para" parents="16788 18020"/>
    </justification>
  </clause>

  <clause id="18025">
    <literal><![CDATA[
      K((x * (y \ x)) \ T(z,y),u) = K(z / (x * (y \ x)),u)
    ]]></literal>
    <justification jstring="[hyper(18023,a,16045,a)].">
      <j1 rule="hyper" parents="18023 16045"/>
    </justification>
  </clause>

  <clause id="18026">
    <literal><![CDATA[
      K((x \ y) \ (y \ T(z,x)),L(u,x \ y,y)) = K(z / (y * (x \ y)),u)
    ]]></literal>
    <justification jstring="[hyper(12000,a,18025,a)].">
      <j1 rule="hyper" parents="12000 18025"/>
    </justification>
  </clause>

  <clause id="18027">
    <literal><![CDATA[
      K(x,L(y \ T(y * z,y * 1),u,w)) = K(x,L((y \ z) * y,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,16234,a(flip),b,18012,a),flip(a)].">
      <j1 rule="hyper" parents="65 16234 18012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18028">
    <literal><![CDATA[
      K(x,L(T(y,z \ u) / w,v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(y,z * u) / w,v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(18017(a,1),11999(a,1))].">
      <j1 rule="para" parents="18017 11999"/>
    </justification>
  </clause>

  <clause id="18029">
    <literal><![CDATA[
      K(x,L(y \ T(y * z,y),u,w)) = K(x,L((y \ z) * y,u,w))
    ]]></literal>
    <justification jstring="[para(8(a,1),18027(a,1,2,1,2,2))].">
      <j1 rule="para" parents="8 18027"/>
    </justification>
  </clause>

  <clause id="18030">
    <literal><![CDATA[
      K(x,L((y * z) / y,u,w)) = K(x,L((y \ z) * y,u,w))
    ]]></literal>
    <justification jstring="[hyper(13930,a,18029,a)].">
      <j1 rule="hyper" parents="13930 18029"/>
    </justification>
  </clause>

  <clause id="18031">
    <literal><![CDATA[
      K(x,L((y \ z) * y,u,w)) = K(x,L(T(z,y),u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,8380,a(flip),b,18030,a),flip(a)].">
      <j1 rule="hyper" parents="65 8380 18030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18032">
    <literal><![CDATA[
      K(x,L(((1 / y) \ z) / y,u,w)) = K(x,L(T(z,y),u,w))
    ]]></literal>
    <justification jstring="[hyper(16967,a,18031,a)].">
      <j1 rule="hyper" parents="16967 18031"/>
    </justification>
  </clause>

  <clause id="18033">
    <literal><![CDATA[
      K(x,L(T(y * z,z),u,w)) = K(x,L((1 / z) \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,15266,a(flip),b,18032,a),flip(a)].">
      <j1 rule="hyper" parents="65 15266 18032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18034">
    <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(18033(a,1),13277(a,1))].">
      <j1 rule="para" parents="18033 13277"/>
    </justification>
  </clause>

  <clause id="18035">
    <literal><![CDATA[
      K(x,L((K(y,z) * u) \ w,v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,L((u \ K(z,y)) * w,v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(14306(a,1),18034(a,1,2,1,1))].">
      <j1 rule="para" parents="14306 18034"/>
    </justification>
  </clause>

  <clause id="18036">
    <literal><![CDATA[
      K(x,(y \ (1 / z)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(z * (y * u),z,y)) = w
    ]]></literal>
    <justification jstring="[para(15651(a,1),18034(a,1))].">
      <j1 rule="para" parents="15651 18034"/>
    </justification>
  </clause>

  <clause id="18037">
    <literal><![CDATA[
      K(x,L(y * (z * u),y,z)) = K(x,(z \ (y \ 1)) \ u)
    ]]></literal>
    <justification jstring="[hyper(18036,a,5899,a)].">
      <j1 rule="hyper" parents="18036 5899"/>
    </justification>
  </clause>

  <clause id="18038">
    <literal><![CDATA[
      K(x,(L(y,z,u) \ (y \ 1)) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (L(y,z,u) * w)) = v5
    ]]></literal>
    <justification jstring="[para(18037(a,1),15515(a,1))].">
      <j1 rule="para" parents="18037 15515"/>
    </justification>
  </clause>

  <clause id="18039">
    <literal><![CDATA[
      K(x \ (y * T(z,z * u)),w) = K(x \ (y * T(z,u)),w)
    ]]></literal>
    <justification jstring="[hyper(17876,a,17513,a)].">
      <j1 rule="hyper" parents="17876 17513"/>
    </justification>
  </clause>

  <clause id="18040">
    <literal><![CDATA[
      K(x \ (y * T(z,z * T((u \ w) \ 1,v5))),v6) = K(x \ (y * T(z,T(w \ u,v5))),v6)
    ]]></literal>
    <justification jstring="[para(9542(a,1),18039(a,2,1,2,2))].">
      <j1 rule="para" parents="9542 18039"/>
    </justification>
  </clause>

  <clause id="18041">
    <literal><![CDATA[
      K(x,(y * ((z / y) \ 1)) \ T(u,((y \ z) \ 1) * y)) = K(x,u / (((y \ z) \ 1) * y))
    ]]></literal>
    <justification jstring="[hyper(17998,a,13925,a)].">
      <j1 rule="hyper" parents="17998 13925"/>
    </justification>
  </clause>

  <clause id="18042">
    <literal><![CDATA[
      K(x,(((y \ z) \ 1) * y) \ u) = K(x,(y * ((z / y) \ 1)) \ u)
    ]]></literal>
    <justification jstring="[hyper(17998,a,xx),flip(a)].">
      <j1 rule="hyper" parents="17998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18043">
    <literal><![CDATA[
      K(x,(((y \ z) \ 1) * y) \ T(u,y * ((z / y) \ 1))) = K(x,u / (y * ((z / y) \ 1)))
    ]]></literal>
    <justification jstring="[hyper(299,a,13925,a(flip),b,18042,a),flip(a)].">
      <j1 rule="hyper" parents="299 13925 18042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18044">
    <literal><![CDATA[
      K(x,y * K((z * z) \ (u \ w),v5)) = K(x,y * K(u * ((z * z) * w),v5))
    ]]></literal>
    <justification jstring="[para(419(a,1),17833(a,1,2,2,1))].">
      <j1 rule="para" parents="419 17833"/>
    </justification>
  </clause>

  <clause id="18045">
    <literal><![CDATA[
      K(K(x * (y / z),u) * w,v5) = K(K(x * (z \ y),u) * w,v5)
    ]]></literal>
    <justification jstring="[para(16380(a,1),17893(a,1,1,1))].">
      <j1 rule="para" parents="16380 17893"/>
    </justification>
  </clause>

  <clause id="18047">
    <literal><![CDATA[
      K(x * (y * K(z \ u,w)),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x * (y * K(z * u,w)),v5) = v6
    ]]></literal>
    <justification jstring="[para(17911(a,1),7209(a,1))].">
      <j1 rule="para" parents="17911 7209"/>
    </justification>
  </clause>

  <clause id="18048">
    <literal><![CDATA[
      K(x,y * ((z * u) * K(w * v5,z))) = K(x,y * (T(z,w \ v5) * u))
    ]]></literal>
    <justification jstring="[hyper(299,a,16948,a(flip),b,17913,a),flip(a)].">
      <j1 rule="hyper" parents="299 16948 17913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18049">
    <literal><![CDATA[
      K(x,y * (z * (u * K(w * v5,z)))) = K(x,y * (T(z,w \ v5) * u))
    ]]></literal>
    <justification jstring="[para(7822(a,1),18048(a,1,2,2))].">
      <j1 rule="para" parents="7822 18048"/>
    </justification>
  </clause>

  <clause id="18050">
    <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(18049(a,1),16949(a,1))].">
      <j1 rule="para" parents="18049 16949"/>
    </justification>
  </clause>

  <clause id="18052">
    <literal><![CDATA[
      K(x,y \ (((z * z) * u) * (w / z))) = K(x,y \ (u * (w / (1 / z))))
    ]]></literal>
    <justification jstring="[hyper(65,a,16067,a(flip),b,17941,a),flip(a)].">
      <j1 rule="hyper" parents="65 16067 17941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18053">
    <literal><![CDATA[
      K(x,y \ ((z * z) * (u * (w / z)))) = K(x,y \ (u * (w / (1 / z))))
    ]]></literal>
    <justification jstring="[para(33(a,1),18052(a,1,2,2))].">
      <j1 rule="para" parents="33 18052"/>
    </justification>
  </clause>

  <clause id="18054">
    <literal><![CDATA[
      K(x,T(y,(z * z) \ (u \ w)) \ v5) = K(x,T(y,u * ((z * z) * w)) \ v5)
    ]]></literal>
    <justification jstring="[para(419(a,1),17947(a,1,2,1,2))].">
      <j1 rule="para" parents="419 17947"/>
    </justification>
  </clause>

  <clause id="18055">
    <literal><![CDATA[
      K(x,(((y / z) \ 1) * z) \ u) = K(x,(z * ((z \ y) \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(5922(a,1),17964(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5922 17964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18056">
    <literal><![CDATA[
      K(x,y * K(z \ (z \ (u \ w)),v5)) = K(x,y * K(u * ((z * z) * w),v5))
    ]]></literal>
    <justification jstring="[para(14182(a,1),18044(a,1,2,2))].">
      <j1 rule="para" parents="14182 18044"/>
    </justification>
  </clause>

  <clause id="18057">
    <literal><![CDATA[
      K(x,T(y,z \ (z \ (u \ w))) \ v5) = K(x,T(y,u * ((z * z) * w)) \ v5)
    ]]></literal>
    <justification jstring="[para(14212(a,1),18054(a,1,2,1))].">
      <j1 rule="para" parents="14212 18054"/>
    </justification>
  </clause>

  <clause id="18058">
    <literal><![CDATA[
      K(x,y * K(z * (z \ (u \ w)),v5)) = K(x,y * K(u * ((z * z) * w),v5))
    ]]></literal>
    <justification jstring="[hyper(17838,a,18056,a)].">
      <j1 rule="hyper" parents="17838 18056"/>
    </justification>
  </clause>

  <clause id="18059">
    <literal><![CDATA[
      K(x,T(y,z * (z \ (u \ w))) \ v5) = K(x,T(y,u * ((z * z) * w)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,17937,a(flip),b,18057,a)].">
      <j1 rule="hyper" parents="65 17937 18057"/>
    </justification>
  </clause>

  <clause id="18060">
    <literal><![CDATA[
      K(x,y * K(z * ((u * u) * w),v5)) = K(x,y * K(z \ w,v5))
    ]]></literal>
    <justification jstring="[para(10(a,1),18058(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 18058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18063">
    <literal><![CDATA[
      K(x,y * K(z * ((u * u) * w),v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * K(z * w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(18060(a,2),17838(a,1))].">
      <j1 rule="para" parents="18060 17838"/>
    </justification>
  </clause>

  <clause id="18064">
    <literal><![CDATA[
      K(x,T(y,z * ((u * u) * w)) \ v5) = K(x,T(y,z \ w) \ v5)
    ]]></literal>
    <justification jstring="[para(10(a,1),18059(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="10 18059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18065">
    <literal><![CDATA[
      K(x,T(y,z * ((u * u) * w)) \ v5) = K(x,T(y,z * w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(299,a,17937,a(flip),b,18064,a),flip(a)].">
      <j1 rule="hyper" parents="299 17937 18064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18067">
    <literal><![CDATA[
      K(x,T(y,z * ((u \ 1) \ w)) \ v5) = K(x,T(y,z * (u \ w)) \ v5)
    ]]></literal>
    <justification jstring="[para(724(a,1),18065(a,1,2,1,2,2))].">
      <j1 rule="para" parents="724 18065"/>
    </justification>
  </clause>

  <clause id="18068">
    <literal><![CDATA[
      K(x,L(T(y,z * 1) \ u,y,z)) = K(x,(y * (z \ 1)) \ ((1 / z) * u))
    ]]></literal>
    <justification jstring="[hyper(18006,a,11686,a)].">
      <j1 rule="hyper" parents="18006 11686"/>
    </justification>
  </clause>

  <clause id="18069">
    <literal><![CDATA[
      K(x,L(T(y,z) \ u,y,z)) = K(x,(y * (z \ 1)) \ ((1 / z) * u))
    ]]></literal>
    <justification jstring="[para(8(a,1),18068(a,1,2,1,1,2))].">
      <j1 rule="para" parents="8 18068"/>
    </justification>
  </clause>

  <clause id="18070">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ ((1 / z) * u)) = K(x,(y * z) \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,11663,a(flip),b,18069,a),flip(a)].">
      <j1 rule="hyper" parents="65 11663 18069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18071">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ ((z \ 1) * u)) = K(x,(y * z) \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(14859,a,18070,a)].">
      <j1 rule="hyper" parents="14859 18070"/>
    </justification>
  </clause>

  <clause id="18072">
    <literal><![CDATA[
      K(x,L(T(y,z \ 1) \ u,y,z \ 1)) = K(x,(y * z) \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,11663,a,b,18071,a)].">
      <j1 rule="hyper" parents="65 11663 18071"/>
    </justification>
  </clause>

  <clause id="18073">
    <literal><![CDATA[
      K(x,L(T(y,(z / y) \ 1) \ u,y,(z / y) \ 1)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[para(11676(a,1),18072(a,2,2))].">
      <j1 rule="para" parents="11676 18072"/>
    </justification>
  </clause>

  <clause id="18074">
    <literal><![CDATA[
      K(x,L(T(y,z \ (y * 1)) \ u,y,(z / y) \ 1)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[para(8645(a,1),18073(a,1,2,1,1))].">
      <j1 rule="para" parents="8645 18073"/>
    </justification>
  </clause>

  <clause id="18075">
    <literal><![CDATA[
      K(x,L(T(y,z \ y) \ u,y,(z / y) \ 1)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[para(8(a,1),18074(a,1,2,1,1,2,2))].">
      <j1 rule="para" parents="8 18074"/>
    </justification>
  </clause>

  <clause id="18076">
    <literal><![CDATA[
      K(x,L(T(y,z \ y) \ u,y,z / y)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[para(2470(a,1),18075(a,1,2))].">
      <j1 rule="para" parents="2470 18075"/>
    </justification>
  </clause>

  <clause id="18077">
    <literal><![CDATA[
      K(K(x,y * y) * (z * x),u) = K(((y * y) \ z) * ((y * y) * x),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,17508,a(flip),b,17814,a)].">
      <j1 rule="hyper" parents="65 17508 17814"/>
    </justification>
  </clause>

  <clause id="18078">
    <literal><![CDATA[
      K(((x * x) \ y) * ((x * x) * z),u) = K(y * T(z,x * x),u)
    ]]></literal>
    <justification jstring="[hyper(16476,a,18077,a),flip(a)].">
      <j1 rule="hyper" parents="16476 18077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18080">
    <literal><![CDATA[
      K(T(x,y * y) * z,u) = K(x * T(z,y * y),u)
    ]]></literal>
    <justification jstring="[para(760(a,1),18078(a,1,1))].">
      <j1 rule="para" parents="760 18078"/>
    </justification>
  </clause>

  <clause id="18081">
    <literal><![CDATA[
      K(T(x,y * y) * z,u) = K(x * z,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,17508,a(flip),b,18080,a),flip(a)].">
      <j1 rule="hyper" parents="299 17508 18080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18083">
    <literal><![CDATA[
      K(((x * x) \ y) * z,u) = K(y * ((x * x) \ z),u)
    ]]></literal>
    <justification jstring="[para(1066(a,1),18081(a,1,1))].">
      <j1 rule="para" parents="1066 18081"/>
    </justification>
  </clause>

  <clause id="18084">
    <literal><![CDATA[
      K(x \ (x \ (y * z)),u) = K(y * ((x * x) \ z),u)
    ]]></literal>
    <justification jstring="[hyper(14633,a,18083,a)].">
      <j1 rule="hyper" parents="14633 18083"/>
    </justification>
  </clause>

  <clause id="18085">
    <literal><![CDATA[
      K(x * ((y \ 1) * (T(y,y \ 1) * z)),u) = K(x * ((z * y) * (1 / y)),u)
    ]]></literal>
    <justification jstring="[para(2378(a,1),17882(a,2,1,2))].">
      <j1 rule="para" parents="2378 17882"/>
    </justification>
  </clause>

  <clause id="18086">
    <literal><![CDATA[
      K(x * ((y \ 1) * (T(y,y \ 1) * z)),u) = K(x * ((z * y) * (y \ 1)),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,5619,a(flip),b,18085,a),flip(a)].">
      <j1 rule="hyper" parents="299 5619 18085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18087">
    <literal><![CDATA[
      K(x * ((y \ 1) * (T(y,y \ 1) * z)),u) = K(x * R(z,y,y),u)
    ]]></literal>
    <justification jstring="[para(1246(a,1),18086(a,2,1,2))].">
      <j1 rule="para" parents="1246 18086"/>
    </justification>
  </clause>

  <clause id="18088">
    <literal><![CDATA[
      K(x * ((1 / y) * (y * z)),u) = K(x * R(z,y,y),u)
    ]]></literal>
    <justification jstring="[para(5929(a,1),18087(a,1,1,2))].">
      <j1 rule="para" parents="5929 18087"/>
    </justification>
  </clause>

  <clause id="18089">
    <literal><![CDATA[
      K(x * R(y,z,z),u) = K(x * L(y,z,z),u)
    ]]></literal>
    <justification jstring="[para(475(a,1),18088(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="475 18088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18090">
    <literal><![CDATA[
      K(x,y * (T(z,K(u,w * v5)) * K(w * v5,u))) = K(x,y * (K(w \ v5,u) * z))
    ]]></literal>
    <justification jstring="[para(16268(a,1),17910(a,1,2,2,1))].">
      <j1 rule="para" parents="16268 17910"/>
    </justification>
  </clause>

  <clause id="18091">
    <literal><![CDATA[
      K(x,T(y,z * (z * u)) * (z \ ((1 / z) \ u))) = K(x,(z \ ((1 / z) \ u)) * y)
    ]]></literal>
    <justification jstring="[para(14216(a,1),17962(a,1,2,1))].">
      <j1 rule="para" parents="14216 17962"/>
    </justification>
  </clause>

  <clause id="18092">
    <literal><![CDATA[
      K(x,y * (K(z \ u,w) * v5)) = K(x,y * (K(z * u,w) * v5))
    ]]></literal>
    <justification jstring="[para(6257(a,1),18090(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6257 18090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18093">
    <literal><![CDATA[
      K(x,y * (K(z * u,w) * (w \ v5))) = K(x,y * (T(w,z \ u) \ v5))
    ]]></literal>
    <justification jstring="[para(5383(a,1),18092(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5383 18092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18094">
    <literal><![CDATA[
      K(x,y * (K(z * 1,u) * ((1 / z) \ w))) = K(x,y * ((K(u,z \ 1) / z) \ w))
    ]]></literal>
    <justification jstring="[para(7723(a,1),18092(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7723 18092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18095">
    <literal><![CDATA[
      K(x,y * (T(z,u \ w) \ v5)) = K(x,y * (T(z,u * w) \ v5))
    ]]></literal>
    <justification jstring="[para(5383(a,1),18093(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5383 18093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18096">
    <literal><![CDATA[
      K(x,T(y,T(z,u * w) \ v5) * (T(z,u * w) \ v5)) = K(x,(T(z,u \ w) \ v5) * y)
    ]]></literal>
    <justification jstring="[hyper(17459,a,18095,a),flip(a)].">
      <j1 rule="hyper" parents="17459 18095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18097">
    <literal><![CDATA[
      K(x,T(y,z * (z * u)) * (z \ ((z \ 1) \ u))) = K(x,(z \ ((1 / z) \ u)) * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,6061,a(flip),b,18091,a)].">
      <j1 rule="hyper" parents="65 6061 18091"/>
    </justification>
  </clause>

  <clause id="18098">
    <literal><![CDATA[
      K(x,T(y,z) * (u \ ((u \ 1) \ z))) = K(x,(u \ ((1 / u) \ z)) * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,17929,a(flip),b,18097,a)].">
      <j1 rule="hyper" parents="65 17929 18097"/>
    </justification>
  </clause>

  <clause id="18099">
    <literal><![CDATA[
      K(x,(y \ ((1 / y) \ z)) * u) = K(x,(y \ ((y \ 1) \ z)) * u)
    ]]></literal>
    <justification jstring="[hyper(14408,a,18098,a),flip(a)].">
      <j1 rule="hyper" parents="14408 18098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18101">
    <literal><![CDATA[
      K(x,T((y \ ((1 / (y \ 1)) \ z)) * u,y \ (y \ 1))) = K(x,((y \ 1) \ (((y \ 1) \ 1) \ z)) * (u / (y * y)))
    ]]></literal>
    <justification jstring="[para(1239(a,2),18099(a,1,2))].">
      <j1 rule="para" parents="1239 18099"/>
    </justification>
  </clause>

  <clause id="18102">
    <literal><![CDATA[
      K(x * (((y \ 1) * z) \ K(y \ z,y)),u) = K(x / ((y \ 1) * ((y \ z) * y)),u)
    ]]></literal>
    <justification jstring="[para(4857(a,1),17805(a,1,1,2,2))].">
      <j1 rule="para" parents="4857 17805"/>
    </justification>
  </clause>

  <clause id="18103">
    <literal><![CDATA[
      K(x,T(y * ((z \ u) * z),w)) = K(x,T(y * T(u,z),w))
    ]]></literal>
    <justification jstring="[hyper(299,a,9341,a(flip),b,17823,a),flip(a)].">
      <j1 rule="hyper" parents="299 9341 17823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18104">
    <literal><![CDATA[
      K(x,T(y * T(z * u,z),w)) = K(x,T(y * (u * z),w))
    ]]></literal>
    <justification jstring="[para(9(a,1),18103(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 18103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18105">
    <literal><![CDATA[
      K(x,T(y \ T(z * u,z),w)) = K(x,T((y \ 1) * (u * z),w))
    ]]></literal>
    <justification jstring="[hyper(14648,a,18104,a)].">
      <j1 rule="hyper" parents="14648 18104"/>
    </justification>
  </clause>

  <clause id="18106">
    <literal><![CDATA[
      K(x,T(y \ T(z * u,z),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y \ (u * z),w)) = v5
    ]]></literal>
    <justification jstring="[para(18105(a,2),14648(a,1))].">
      <j1 rule="para" parents="18105 14648"/>
    </justification>
  </clause>

  <clause id="18107">
    <literal><![CDATA[
      K(x,y * K((z * u) * (z * ((z \ 1) \ w)),v5)) = K(x,y * K(((z \ 1) * u) * w,v5))
    ]]></literal>
    <justification jstring="[hyper(299,a,17830,a(flip),b,17835,a),flip(a)].">
      <j1 rule="hyper" parents="299 17830 17835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18108">
    <literal><![CDATA[
      K(x \ (y * T(z,T(z * ((u \ w) \ 1),v5))),v6) = K(x \ (y * T(z,T(w \ u,v5))),v6)
    ]]></literal>
    <justification jstring="[para(17388(a,2),18040(a,1,1,2,2))].">
      <j1 rule="para" parents="17388 18040"/>
    </justification>
  </clause>

  <clause id="18109">
    <literal><![CDATA[
      K(x,(y * ((z / y) \ 1)) \ T(u,(y \ z) \ y)) = K(x,u / (((y \ z) \ 1) * y))
    ]]></literal>
    <justification jstring="[para(14297(a,1),18041(a,1,2,2))].">
      <j1 rule="para" parents="14297 18041"/>
    </justification>
  </clause>

  <clause id="18110">
    <literal><![CDATA[
      K(x,(y * ((z / y) \ 1)) \ T(u,y * (y / z))) = K(x,u / (((y \ z) \ 1) * y))
    ]]></literal>
    <justification jstring="[para(16238(a,1),18109(a,1,2,2))].">
      <j1 rule="para" parents="16238 18109"/>
    </justification>
  </clause>

  <clause id="18111">
    <literal><![CDATA[
      K(x,(y * ((z / y) \ 1)) \ T(u,z)) = K(x,u / (((y \ z) \ 1) * y))
    ]]></literal>
    <justification jstring="[hyper(65,a,17852,a(flip),b,18110,a)].">
      <j1 rule="hyper" parents="65 17852 18110"/>
    </justification>
  </clause>

  <clause id="18113">
    <literal><![CDATA[
      K(x,(((y \ z) \ 1) * y) \ T(u,y / (z / y))) = K(x,u / (y * ((z / y) \ 1)))
    ]]></literal>
    <justification jstring="[para(14474(a,1),18043(a,1,2,2))].">
      <j1 rule="para" parents="14474 18043"/>
    </justification>
  </clause>

  <clause id="18114">
    <literal><![CDATA[
      K(x,(((y \ z) \ 1) * y) \ T(u,y * (y / z))) = K(x,u / (y * ((z / y) \ 1)))
    ]]></literal>
    <justification jstring="[para(16240(a,1),18113(a,1,2,2))].">
      <j1 rule="para" parents="16240 18113"/>
    </justification>
  </clause>

  <clause id="18115">
    <literal><![CDATA[
      K(x,(((y \ z) \ 1) * y) \ T(u,z)) = K(x,u / (y * ((z / y) \ 1)))
    ]]></literal>
    <justification jstring="[hyper(65,a,17852,a(flip),b,18114,a)].">
      <j1 rule="hyper" parents="65 17852 18114"/>
    </justification>
  </clause>

  <clause id="18116">
    <literal><![CDATA[
      K(x,(y * ((z / y) \ 1)) \ T(u,z)) = K(x,u / (y * ((z / y) \ 1)))
    ]]></literal>
    <justification jstring="[hyper(17998,a,18115,a)].">
      <j1 rule="hyper" parents="17998 18115"/>
    </justification>
  </clause>

  <clause id="18118">
    <literal><![CDATA[
      K(x,y / (((z \ u) \ 1) * z)) = K(x,y / (z * ((u / z) \ 1)))
    ]]></literal>
    <justification jstring="[hyper(65,a,18111,a(flip),b,18116,a)].">
      <j1 rule="hyper" parents="65 18111 18116"/>
    </justification>
  </clause>

  <clause id="18119">
    <literal><![CDATA[
      K(x,y / (z * ((u / z) \ 1))) = K(x,(z * ((y / z) \ 1)) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,15612,a(flip),b,18118,a),flip(a)].">
      <j1 rule="hyper" parents="65 15612 18118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18120">
    <literal><![CDATA[
      K(x,(T(y,z \ u) \ w) * v5) = K(x,(T(y,z * u) \ w) * v5)
    ]]></literal>
    <justification jstring="[hyper(13261,a,18096,a),flip(a)].">
      <j1 rule="hyper" parents="13261 18096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18122">
    <literal><![CDATA[
      K(x,(T(y,z * z) \ u) * w) = K(x,(y \ u) * w)
    ]]></literal>
    <justification jstring="[para(198(a,1),18120(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="198 18120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18123">
    <literal><![CDATA[
      (x * K(y,(T(z,u * w) \ v5) * v6)) \ x = K((T(z,u \ w) \ v5) * v6,y)
    ]]></literal>
    <justification jstring="[para(18120(a,1),7200(a,1,1,2))].">
      <j1 rule="para" parents="18120 7200"/>
    </justification>
  </clause>

  <clause id="18124">
    <literal><![CDATA[
      K(x,(L(T(y,z),y,y) \ u) * w) = K(x,(T(y,z) \ u) * w)
    ]]></literal>
    <justification jstring="[para(599(a,1),18122(a,1,2,1,1))].">
      <j1 rule="para" parents="599 18122"/>
    </justification>
  </clause>

  <clause id="18125">
    <literal><![CDATA[
      K((T(x,y \ z) \ u) * w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K((T(x,y * z) \ u) * w,v5) = v6
    ]]></literal>
    <justification jstring="[para(18123(a,1),7209(a,1))].">
      <j1 rule="para" parents="18123 7209"/>
    </justification>
  </clause>

  <clause id="18126">
    <literal><![CDATA[
      K(x,y * K((z * u) * ((z * z) * w),v5)) = K(x,y * K(((z \ 1) * u) * w,v5))
    ]]></literal>
    <justification jstring="[para(13302(a,1),18107(a,1,2,2))].">
      <j1 rule="para" parents="13302 18107"/>
    </justification>
  </clause>

  <clause id="18127">
    <literal><![CDATA[
      K(x,y * K(((z \ 1) * u) * w,v5)) = K(x,y * K((z * u) * w,v5))
    ]]></literal>
    <justification jstring="[hyper(18063,a,18126,a),flip(a)].">
      <j1 rule="hyper" parents="18063 18126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18129">
    <literal><![CDATA[
      K(x,K(y * ((z \ 1) * u),w) * v5) = K(x,v5 * K((z * u) * y,w))
    ]]></literal>
    <justification jstring="[hyper(16852,a,18127,a)].">
      <j1 rule="hyper" parents="16852 18127"/>
    </justification>
  </clause>

  <clause id="18130">
    <literal><![CDATA[
      K(x,K(((y \ 1) * z) * u,w) * v5) = K(x,v5 * K((y * z) * u,w))
    ]]></literal>
    <justification jstring="[hyper(16407,a,18127,a)].">
      <j1 rule="hyper" parents="16407 18127"/>
    </justification>
  </clause>

  <clause id="18131">
    <literal><![CDATA[
      K(x,y * K(z,u * ((w \ 1) * v5))) = K(x,y * K((w * v5) * u,z))
    ]]></literal>
    <justification jstring="[hyper(16624,a,18129,a)].">
      <j1 rule="hyper" parents="16624 18129"/>
    </justification>
  </clause>

  <clause id="18132">
    <literal><![CDATA[
      K(x,T(y,z * ((1 / u) * w)) \ v5) = K(x,(y \ v5) * K((u * w) * z,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,16595,a(flip),b,18131,a)].">
      <j1 rule="hyper" parents="65 16595 18131"/>
    </justification>
  </clause>

  <clause id="18133">
    <literal><![CDATA[
      K(x,T(y / T(z,(u * w) * v5),z)) = K(x,T(z,v5 * ((1 / u) * w)) \ y)
    ]]></literal>
    <justification jstring="[para(7889(a,2),18132(a,2,2)),flip(a)].">
      <j1 rule="para" parents="7889 18132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18134">
    <literal><![CDATA[
      K(x,T(y,z * ((1 / u) * w)) \ v5) = K(x,T(y,(u * w) * z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(16471,a,18133,a),flip(a)].">
      <j1 rule="hyper" parents="16471 18133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18135">
    <literal><![CDATA[
      K(x,T(y,z * ((u \ 1) * w)) \ v5) = K(x,T(y,(u * w) * z) \ v5)
    ]]></literal>
    <justification jstring="[para(3899(a,1),18134(a,1,2,1))].">
      <j1 rule="para" parents="3899 18134"/>
    </justification>
  </clause>

  <clause id="18136">
    <literal><![CDATA[
      K(x \ (y * T(z,T((u \ w) \ z,v5))),v6) = K(x \ (y * T(z,T(w \ u,v5))),v6)
    ]]></literal>
    <justification jstring="[para(9486(a,1),18108(a,1,1,2,2))].">
      <j1 rule="para" parents="9486 18108"/>
    </justification>
  </clause>

  <clause id="18137">
    <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(13919(a,1),17804(a,1,1))].">
      <j1 rule="para" parents="13919 17804"/>
    </justification>
  </clause>

  <clause id="18138">
    <literal><![CDATA[
      K(x,L(T(y * z,y) \ u,w,v5)) = K(x,L((z * y) \ u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(11950,a,18137,a),flip(a)].">
      <j1 rule="hyper" parents="11950 18137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18139">
    <literal><![CDATA[
      K(x,L(((1 / y) * (y * z)) \ u,w,v5)) = K(x,L(R(z,y,y) \ u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,14070,a(flip),b,18138,a),flip(a)].">
      <j1 rule="hyper" parents="65 14070 18138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18140">
    <literal><![CDATA[
      K(x,L(R(y,z,z) \ u,w,v5)) = K(x,L(L(y,z,z) \ u,w,v5))
    ]]></literal>
    <justification jstring="[para(475(a,1),18139(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="475 18139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18141">
    <literal><![CDATA[
      K(x,L(L(y,z,z) \ u,a(y,z,z),y)) = K(x,a(y,z,z) \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,15644,a(flip),b,18140,a),flip(a)].">
      <j1 rule="hyper" parents="65 15644 18140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18142">
    <literal><![CDATA[
      K(x,T(y,z * (z * (((z \ 1) * u) \ w))) * v5) = K(x,T(y,(z * T(u,z * z)) * w) * v5)
    ]]></literal>
    <justification jstring="[para(17545(a,1),17953(a,1,2,1))].">
      <j1 rule="para" parents="17545 17953"/>
    </justification>
  </clause>

  <clause id="18143">
    <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),17983(a,1,2,1,2))].">
      <j1 rule="para" parents="23 17983"/>
    </justification>
  </clause>

  <clause id="18144">
    <literal><![CDATA[
      K(x,T(y,(z * T(u,z * z)) * w) * v5) = K(x,T(y,((z \ 1) * u) \ w) * v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,17929,a(flip),b,18142,a),flip(a)].">
      <j1 rule="hyper" parents="65 17929 18142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18146">
    <literal><![CDATA[
      K(x,T(y,(z * T(u,z * z)) * w) * v5) = K(x,T(y,((z \ 1) * u) * w) * v5)
    ]]></literal>
    <justification jstring="[hyper(299,a,17939,a(flip),b,18144,a),flip(a)].">
      <j1 rule="hyper" parents="299 17939 18144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18147">
    <literal><![CDATA[
      K(x,T(y,((z \ 1) * u) * w) * v5) = K(x,T(y,(z * u) * w) * v5)
    ]]></literal>
    <justification jstring="[para(17700(a,1),18146(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="17700 18146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18148">
    <literal><![CDATA[
      K(x,T(y,((z \ 1) * u) * w) * v5) = K(x,T(y,w * (z * u)) * v5)
    ]]></literal>
    <justification jstring="[hyper(16855,a,18147,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="16855 18147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18149">
    <literal><![CDATA[
      K(x,T(y,((z \ 1) * u) * w) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,w * (z * u)) * v5) = v6
    ]]></literal>
    <justification jstring="[para(18147(a,2),16855(a,1))].">
      <j1 rule="para" parents="18147 16855"/>
    </justification>
  </clause>

  <clause id="18151">
    <literal><![CDATA[
      K(x,T(y,((z \ 1) * u) * w) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,(z * u) * w) * v5) = v6
    ]]></literal>
    <justification jstring="[para(18148(a,2),16855(a,1))].">
      <j1 rule="para" parents="18148 16855"/>
    </justification>
  </clause>

  <clause id="18152">
    <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(8050(a,1),18143(a,1,2))].">
      <j1 rule="para" parents="8050 18143"/>
    </justification>
  </clause>

  <clause id="18153">
    <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(16859(a,1),18152(a,1,2))].">
      <j1 rule="para" parents="16859 18152"/>
    </justification>
  </clause>

  <clause id="18154">
    <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(65,a,10084,a(flip),b,18153,a)].">
      <j1 rule="hyper" parents="65 10084 18153"/>
    </justification>
  </clause>

  <clause id="18155">
    <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(17226(a,2),18154(a,1,2))].">
      <j1 rule="para" parents="17226 18154"/>
    </justification>
  </clause>

  <clause id="18156">
    <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(13172(a,1),18155(a,1,2,1))].">
      <j1 rule="para" parents="13172 18155"/>
    </justification>
  </clause>

  <clause id="18157">
    <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(14265(a,1),18156(a,1,2))].">
      <j1 rule="para" parents="14265 18156"/>
    </justification>
  </clause>

  <clause id="18158">
    <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(5426(a,1),18157(a,1,2))].">
      <j1 rule="para" parents="5426 18157"/>
    </justification>
  </clause>

  <clause id="18159">
    <literal><![CDATA[
      K(x,T(y,z)) * T(u * K(y,x),z) = T(u,z * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(8438,a,18158,a)].">
      <j1 rule="hyper" parents="8438 18158"/>
    </justification>
  </clause>

  <clause id="18160">
    <literal><![CDATA[
      K(x,y) * T(z * K(y,T(x,u)),u) = T(z,u * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,17693,a(flip),b,18159,a)].">
      <j1 rule="hyper" parents="65 17693 18159"/>
    </justification>
  </clause>

  <clause id="18161">
    <literal><![CDATA[
      T(x * K(y,T(z,u)),u) = K(y,z) * T(x,u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(5437,a,18160,a),flip(a)].">
      <j1 rule="hyper" parents="5437 18160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18162">
    <literal><![CDATA[
      (x * (y * K(z,u))) / T(x * K(z,T(u,y)),y) = R(y,K(z,u),x)
    ]]></literal>
    <justification jstring="[para(18161(a,2),14828(a,2,2)),flip(a)].">
      <j1 rule="para" parents="18161 14828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18163">
    <literal><![CDATA[
      L(x,K(y,T(z,x)),u) = R(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,14705,a(flip),b,18162,a)].">
      <j1 rule="hyper" parents="65 14705 18162"/>
    </justification>
  </clause>

  <clause id="18164">
    <literal><![CDATA[
      K(x,y * (z * (a(z,u,1 / u) * K(u,u \ 1)))) = K(x,y * ((1 / u) * T(z * u,u)))
    ]]></literal>
    <justification jstring="[para(7(a,1),18005(a,2,2,2,2,2))].">
      <j1 rule="para" parents="7 18005"/>
    </justification>
  </clause>

  <clause id="18165">
    <literal><![CDATA[
      T(x,K(y \ (y \ 1),y \ z) * (u / ((y \ 1) * z))) = T(x,u / (y * (z * (y \ (1 / y)))))
    ]]></literal>
    <justification jstring="[para(14246(a,1),16584(a,1,2,1))].">
      <j1 rule="para" parents="14246 16584"/>
    </justification>
  </clause>

  <clause id="18166">
    <literal><![CDATA[
      T(x,K(y \ z,y * y) * (u / ((y \ 1) * z))) = T(x,u / (y * (z * (y \ (1 / y)))))
    ]]></literal>
    <justification jstring="[para(14779(a,1),18165(a,1,2,1))].">
      <j1 rule="para" parents="14779 18165"/>
    </justification>
  </clause>

  <clause id="18167">
    <literal><![CDATA[
      T(x,y / (z * (u * (z \ (1 / z))))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y / ((z \ 1) * u)) = w
    ]]></literal>
    <justification jstring="[para(18166(a,1),17414(a,1))].">
      <j1 rule="para" parents="18166 17414"/>
    </justification>
  </clause>

  <clause id="18168">
    <literal><![CDATA[
      K(x,y * (z * (u * (w \ 1)))) * K(x,K(y,z * (u * (w \ 1)))) = K(x,(z * (u * (1 / w))) * y)
    ]]></literal>
    <justification jstring="[para(5906(a,1),16666(a,1,1))].">
      <j1 rule="para" parents="5906 16666"/>
    </justification>
  </clause>

  <clause id="18169">
    <literal><![CDATA[
      K(x * ((x \ 1) \ T(y,(x \ 1) \ ((x \ 1) \ 1))),x \ 1) = K(x \ ((x \ 1) * y),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,14252,a(flip),b,17025,a),flip(a)].">
      <j1 rule="hyper" parents="299 14252 17025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18170">
    <literal><![CDATA[
      K(x * ((x \ 1) \ T(y,(x \ 1) \ ((x \ 1) \ 1))),x \ 1) = K((x * x) \ y,x \ 1)
    ]]></literal>
    <justification jstring="[para(728(a,1),18169(a,2,1))].">
      <j1 rule="para" parents="728 18169"/>
    </justification>
  </clause>

  <clause id="18171">
    <literal><![CDATA[
      K(x * ((x \ 1) \ T(y,(x \ 1) \ ((x \ 1) \ 1))),x \ 1) = K(x \ (x \ y),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,14182,a(flip),b,18170,a),flip(a)].">
      <j1 rule="hyper" parents="299 14182 18170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18172">
    <literal><![CDATA[
      K(x * ((x \ 1) \ T(y,(1 / x) \ x)),x \ 1) = K(x \ (x \ y),x \ 1)
    ]]></literal>
    <justification jstring="[para(5957(a,1),18171(a,1,1,2,2,2))].">
      <j1 rule="para" parents="5957 18171"/>
    </justification>
  </clause>

  <clause id="18173">
    <literal><![CDATA[
      K(x * ((x \ 1) \ T(y,x * x)),x \ 1) = K(x \ (x \ y),x \ 1)
    ]]></literal>
    <justification jstring="[para(14296(a,1),18172(a,1,1,2,2))].">
      <j1 rule="para" parents="14296 18172"/>
    </justification>
  </clause>

  <clause id="18174">
    <literal><![CDATA[
      K(x * T(y / (1 / x),x),x \ 1) = K(x \ (x \ y),x \ 1)
    ]]></literal>
    <justification jstring="[para(9657(a,1),18173(a,1,1,2))].">
      <j1 rule="para" parents="9657 18173"/>
    </justification>
  </clause>

  <clause id="18175">
    <literal><![CDATA[
      K((x / (1 / y)) * y,y \ 1) = K(y \ (y \ x),y \ 1)
    ]]></literal>
    <justification jstring="[para(107(a,1),18174(a,1,1))].">
      <j1 rule="para" parents="107 18174"/>
    </justification>
  </clause>

  <clause id="18176">
    <literal><![CDATA[
      K(x * ((1 / y) \ y),y \ 1) = K(y \ (y \ x),y \ 1)
    ]]></literal>
    <justification jstring="[para(1263(a,1),18175(a,1,1))].">
      <j1 rule="para" parents="1263 18175"/>
    </justification>
  </clause>

  <clause id="18177">
    <literal><![CDATA[
      K(x * ((y \ 1) \ y),y \ 1) = K(y \ (y \ x),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,5618,a(flip),b,18176,a)].">
      <j1 rule="hyper" parents="65 5618 18176"/>
    </justification>
  </clause>

  <clause id="18178">
    <literal><![CDATA[
      K(x \ (x \ y),x \ 1) = K(y * (x * x),x \ 1)
    ]]></literal>
    <justification jstring="[para(460(a,1),18177(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="460 18177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18179">
    <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(9156(a,1),17261(a,1,1))].">
      <j1 rule="para" parents="9156 17261"/>
    </justification>
  </clause>

  <clause id="18180">
    <literal><![CDATA[
      K(x,(K(((y \ z) \ z) * u,w) / w) * (T(y,z) * u)) = K(x,(((y \ z) \ z) * u) * (1 / w))
    ]]></literal>
    <justification jstring="[para(264(a,1),17510(a,2,2,2))].">
      <j1 rule="para" parents="264 17510"/>
    </justification>
  </clause>

  <clause id="18181">
    <literal><![CDATA[
      K(x,(K(((y \ z) \ z) * u,w) / w) * (T(y,z) * u)) = K(x,(((y \ z) \ z) * u) / w)
    ]]></literal>
    <justification jstring="[hyper(299,a,14283,a(flip),b,18180,a),flip(a)].">
      <j1 rule="hyper" parents="299 14283 18180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18182">
    <literal><![CDATA[
      K(x,(K(T(y,z) * u,w) / w) * (T(y,z) * u)) = K(x,(((y \ z) \ z) * u) / w)
    ]]></literal>
    <justification jstring="[para(13754(a,1),18181(a,1,2,1,1))].">
      <j1 rule="para" parents="13754 18181"/>
    </justification>
  </clause>

  <clause id="18183">
    <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(14550,a,18182,a)].">
      <j1 rule="hyper" parents="14550 18182"/>
    </justification>
  </clause>

  <clause id="18184">
    <literal><![CDATA[
      K(x,(((y \ z) \ z) * u) / w) = K(x,(T(y,z) * u) / w)
    ]]></literal>
    <justification jstring="[hyper(13924,a,18183,a),flip(a)].">
      <j1 rule="hyper" parents="13924 18183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18185">
    <literal><![CDATA[
      K(x,(T(y,z) * ((y \ z) * u)) / w) = K(x,(y * ((z / y) * u)) / w)
    ]]></literal>
    <justification jstring="[para(6054(a,1),18184(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6054 18184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18186">
    <literal><![CDATA[
      K(x,(y * ((1 / y) * z)) / u) = K(x,(y * ((y \ 1) * z)) / u)
    ]]></literal>
    <justification jstring="[para(193(a,1),18185(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="193 18185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18187">
    <literal><![CDATA[
      K(x,(y * ((1 / y) * z)) / u) = K(x,L(z,y,y) / u)
    ]]></literal>
    <justification jstring="[para(1673(a,1),18186(a,2,2,1))].">
      <j1 rule="para" parents="1673 18186"/>
    </justification>
  </clause>

  <clause id="18188">
    <literal><![CDATA[
      K(x,L(y,z,z) / (z * u)) = K(x,y / ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,17362,a(flip),b,18187,a),flip(a)].">
      <j1 rule="hyper" parents="65 17362 18187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18189">
    <literal><![CDATA[
      T(x,(y \ ((z \ 1) \ 1)) * (y \ ((z \ 1) \ 1))) = T(x,z * (y \ ((y * (1 / z)) \ 1)))
    ]]></literal>
    <justification jstring="[hyper(299,a,3867,a(flip),b,17715,a),flip(a)].">
      <j1 rule="hyper" parents="299 3867 17715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18190">
    <literal><![CDATA[
      T(x,y * (z \ ((z * (1 / y)) \ 1))) = T(x,(z \ y) * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(65,a,17712,a(flip),b,18189,a),flip(a)].">
      <j1 rule="hyper" parents="65 17712 18189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18191">
    <literal><![CDATA[
      K(x * (K(y,(z / T(u,w)) * v5) * K(y,K(v5,u * z))),v6) = K(K(v5 * (T(u,w) \ z),y) * x,v6)
    ]]></literal>
    <justification jstring="[hyper(299,a,18045,a(flip),b,17782,a),flip(a)].">
      <j1 rule="hyper" parents="299 18045 17782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18192">
    <literal><![CDATA[
      K(T(x,y) \ z,T(u,x * y)) = K((((y \ 1) \ z) * (y \ 1)) / (T((y \ 1) \ x,y) * (1 / y)),u)
    ]]></literal>
    <justification jstring="[para(3278(a,1),17801(a,2,1,1))].">
      <j1 rule="para" parents="3278 17801"/>
    </justification>
  </clause>

  <clause id="18193">
    <literal><![CDATA[
      K(x,(y * (z * (1 / u))) * w) = K(x,(y * (z * (u \ 1))) * w)
    ]]></literal>
    <justification jstring="[hyper(16701,a,18168,a),flip(a)].">
      <j1 rule="hyper" parents="16701 18168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18194">
    <literal><![CDATA[
      K(x,(y * T((z * u) * (1 / z),z * u)) * w) = K(x,(y * ((u * z) * (z \ 1))) * w)
    ]]></literal>
    <justification jstring="[hyper(65,a,13915,a,b,18193,a)].">
      <j1 rule="hyper" parents="65 13915 18193"/>
    </justification>
  </clause>

  <clause id="18195">
    <literal><![CDATA[
      K(x,(y * T((z * u) * (1 / z),z * u)) * w) = K(x,(y * R(u,z,z)) * w)
    ]]></literal>
    <justification jstring="[para(1246(a,1),18194(a,2,2,1,2))].">
      <j1 rule="para" parents="1246 18194"/>
    </justification>
  </clause>

  <clause id="18196">
    <literal><![CDATA[
      K(K(x * (T(y,z) \ u),w) * v5,v6) = K(v5 * K(w,(u / T(y,z)) * x),v6)
    ]]></literal>
    <justification jstring="[hyper(16812,a,18191,a),flip(a)].">
      <j1 rule="hyper" parents="16812 18191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18197">
    <literal><![CDATA[
      K(T(x,y) \ z,T(u,x * y)) = K((((y \ 1) \ z) * (y \ 1)) / (T((y \ 1) \ x,y) * (y \ 1)),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,5898,a(flip),b,18192,a),flip(a)].">
      <j1 rule="hyper" parents="299 5898 18192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18198">
    <literal><![CDATA[
      (T(x,y) \ 1) \ L(K(x * z,u),x,x) = K(z * ((x \ 1) \ 1),u) * T((x \ 1) \ 1,y)
    ]]></literal>
    <justification jstring="[para(5609(a,1),16661(a,1,2,1))].">
      <j1 rule="para" parents="5609 16661"/>
    </justification>
  </clause>

  <clause id="18199">
    <literal><![CDATA[
      K(x * ((y \ 1) \ 1),z) * T((y \ 1) \ 1,u) = (T(y,u) \ 1) \ K(y * x,z)
    ]]></literal>
    <justification jstring="[para(14170(a,1),18198(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14170 18198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18200">
    <literal><![CDATA[
      K(x * y,z) * T((y \ 1) \ 1,u) = (T(y,u) \ 1) \ K(y * x,z)
    ]]></literal>
    <justification jstring="[para(5603(a,1),18199(a,1,1))].">
      <j1 rule="para" parents="5603 18199"/>
    </justification>
  </clause>

  <clause id="18202">
    <literal><![CDATA[
      (T(x,y) \ K(z,u * x)) \ 1 = (T(x,y) \ 1) \ K(x * u,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,14621,a(flip),b,18200,a)].">
      <j1 rule="hyper" parents="65 14621 18200"/>
    </justification>
  </clause>

  <clause id="18203">
    <literal><![CDATA[
      (T(x,y) \ 1) \ K(x * y,z) = y \ T(T(x,x \ 1) * y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,17089,a(flip),b,18202,a),flip(a)].">
      <j1 rule="hyper" parents="65 17089 18202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18204">
    <literal><![CDATA[
      T(x \ T(T(y,y \ 1) * x,y),T(y,x) \ z) = T(x \ T(y * x,T(y,x)),z * T(y,x))
    ]]></literal>
    <justification jstring="[para(18203(a,1),15288(a,1,1))].">
      <j1 rule="para" parents="18203 15288"/>
    </justification>
  </clause>

  <clause id="18205">
    <literal><![CDATA[
      T(x \ T(y * x,T(y,x)),z * T(y,x)) = T(x \ (y * ((y \ x) * y)),T(y,x) \ z)
    ]]></literal>
    <justification jstring="[para(2809(a,1),18204(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2809 18204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18206">
    <literal><![CDATA[
      T(L(x,x \ y,x),T(x,y) \ z) = T(y \ T(x * y,T(x,y)),z * T(x,y))
    ]]></literal>
    <justification jstring="[para(95(a,1),18205(a,2,1)),flip(a)].">
      <j1 rule="para" parents="95 18205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18207">
    <literal><![CDATA[
      T(L(x,x * y,x),T(x,y) \ z) = T(y \ T(x * y,T(x,y)),z * T(x,y))
    ]]></literal>
    <justification jstring="[para(17013(a,1),18206(a,1,1))].">
      <j1 rule="para" parents="17013 18206"/>
    </justification>
  </clause>

  <clause id="18208">
    <literal><![CDATA[
      T(x \ T(y * x,T(y,x)),z * T(y,x)) = L(T(y,T(y,x) \ z),y * x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,25,a,b,18207,a),flip(a)].">
      <j1 rule="hyper" parents="65 25 18207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18209">
    <literal><![CDATA[
      T(x \ T(y * x,T(y,x)),z * T(y,x)) = L(T(y,y \ z),y * x,y)
    ]]></literal>
    <justification jstring="[para(8552(a,1),18208(a,2,1))].">
      <j1 rule="para" parents="8552 18208"/>
    </justification>
  </clause>

  <clause id="18210">
    <literal><![CDATA[
      T(x \ T(y * x,y),z * T(y,x)) = L(T(y,y \ z),y * x,y)
    ]]></literal>
    <justification jstring="[para(4283(a,1),18209(a,1,1,2))].">
      <j1 rule="para" parents="4283 18209"/>
    </justification>
  </clause>

  <clause id="18212">
    <literal><![CDATA[
      T(R(x,y,x),z * T(x,y)) = L(T(x,x \ z),x * y,x)
    ]]></literal>
    <justification jstring="[para(4338(a,1),18210(a,1,1))].">
      <j1 rule="para" parents="4338 18210"/>
    </justification>
  </clause>

  <clause id="18213">
    <literal><![CDATA[
      R(T(x,y * T(x,z)),z,x) = L(T(x,x \ y),x * z,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,27,a,b,18212,a)].">
      <j1 rule="hyper" parents="65 27 18212"/>
    </justification>
  </clause>

  <clause id="18214">
    <literal><![CDATA[
      L(T(x,x \ y),x * z,x) = R(T(x,x * y),z,x)
    ]]></literal>
    <justification jstring="[para(8615(a,1),18213(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8615 18213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18216">
    <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(10607(a,1),16682(a,1,1))].">
      <j1 rule="para" parents="10607 16682"/>
    </justification>
  </clause>

  <clause id="18217">
    <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(6977(a,1),18216(a,1,2))].">
      <j1 rule="para" parents="6977 18216"/>
    </justification>
  </clause>

  <clause id="18218">
    <literal><![CDATA[
      K((x \ y) \ z,x / y) * K(x / y,z) = a((x \ y) \ 1,z,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(16440(a,1),18217(a,1,2))].">
      <j1 rule="para" parents="16440 18217"/>
    </justification>
  </clause>

  <clause id="18219">
    <literal><![CDATA[
      a((x \ y) \ 1,z,(x \ y) \ 1) = a(y \ x,z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,12984,a(flip),b,18218,a),flip(a)].">
      <j1 rule="hyper" parents="65 12984 18218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18220">
    <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(18219(a,1),15399(a,1,1))].">
      <j1 rule="para" parents="18219 15399"/>
    </justification>
  </clause>

  <clause id="18221">
    <literal><![CDATA[
      x \ ((x / T(y,y \ x)) * L(T(y,y \ x),z,u)) = L(T(y \ L(y,z,u),y \ x),y,x)
    ]]></literal>
    <justification jstring="[para(6731(a,1),17391(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6731 17391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18222">
    <literal><![CDATA[
      x \ ((x / T(y,y \ x)) * L(T(y,y \ x),z,u)) = L(T(y \ L(y,z,u),x),y,x)
    ]]></literal>
    <justification jstring="[para(15251(a,1),18221(a,2,1))].">
      <j1 rule="para" parents="15251 18221"/>
    </justification>
  </clause>

  <clause id="18223">
    <literal><![CDATA[
      x \ ((x / T(y,y \ x)) * L(T(y,y \ x),z,u)) = (y * x) \ (L(y,z,u) * x)
    ]]></literal>
    <justification jstring="[hyper(299,a,11674,a(flip),b,18222,a),flip(a)].">
      <j1 rule="hyper" parents="299 11674 18222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18224">
    <literal><![CDATA[
      x \ ((y \ x) * L(T(y,y \ x),z,u)) = (y * x) \ (L(y,z,u) * x)
    ]]></literal>
    <justification jstring="[para(262(a,1),18223(a,1,2,1))].">
      <j1 rule="para" parents="262 18223"/>
    </justification>
  </clause>

  <clause id="18225">
    <literal><![CDATA[
      (x * y) \ (L(x,z,u) * y) = y \ (L(x,z,u) * (x \ y))
    ]]></literal>
    <justification jstring="[para(233(a,1),18224(a,1,2)),flip(a)].">
      <j1 rule="para" parents="233 18224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18226">
    <literal><![CDATA[
      T(x,T(y,z)) \ (L(K(x,x \ z),u,w) * (K(x,x \ z) \ T(x,T(y,z)))) = T((x \ z) \ z,y) \ (L(K(x,x \ z),u,w) * T(x,T(y,z)))
    ]]></literal>
    <justification jstring="[para(10383(a,1),18225(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10383 18225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18227">
    <literal><![CDATA[
      K(x,K(T(y,z) / u,w)) * K(w,(u \ T(y * K(u,y),z)) * x) = K(w,x * (T(y,z) / u))
    ]]></literal>
    <justification jstring="[para(13740(a,1),16675(a,1,1,2))].">
      <j1 rule="para" parents="13740 16675"/>
    </justification>
  </clause>

  <clause id="18228">
    <literal><![CDATA[
      K(x,(y \ T(z * K(y,z),u)) * w) = K(x,(T(z,u) / y) * w)
    ]]></literal>
    <justification jstring="[hyper(16676,a,18227,a),flip(a)].">
      <j1 rule="hyper" parents="16676 18227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18229">
    <literal><![CDATA[
      K(x,(T(y,z) / z) * u) = K(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[para(5053(a,1),18228(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="5053 18228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18230">
    <literal><![CDATA[
      T(T(x,K(y,z \ u)),(z * (u * (z \ (1 / z)))) \ y) = T(x,y / T((z \ 1) * u,z \ (z \ 1)))
    ]]></literal>
    <justification jstring="[para(14246(a,1),16845(a,1,1,2))].">
      <j1 rule="para" parents="14246 16845"/>
    </justification>
  </clause>

  <clause id="18231">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),(z * (u * (z \ (1 / z)))) \ y) = T(x,y / T((z \ 1) * u,z \ (z \ 1)))
    ]]></literal>
    <justification jstring="[para(16268(a,1),18230(a,1,1))].">
      <j1 rule="para" parents="16268 18230"/>
    </justification>
  </clause>

  <clause id="18232">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),z * ((z \ 1) \ ((z * u) \ y))) = T(x,y / T((z \ 1) * u,z \ (z \ 1)))
    ]]></literal>
    <justification jstring="[para(2437(a,1),18231(a,1,2))].">
      <j1 rule="para" parents="2437 18231"/>
    </justification>
  </clause>

  <clause id="18233">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),z * (z * ((z * u) \ y))) = T(x,y / T((z \ 1) * u,z \ (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(65,a,14369,a(flip),b,18232,a)].">
      <j1 rule="hyper" parents="65 14369 18232"/>
    </justification>
  </clause>

  <clause id="18234">
    <literal><![CDATA[
      T(x,y / T((z \ 1) * u,z \ (z \ 1))) = T(x,y * ((z * u) \ (z * z)))
    ]]></literal>
    <justification jstring="[hyper(17502,a,18233,a),flip(a)].">
      <j1 rule="hyper" parents="17502 18233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18235">
    <literal><![CDATA[
      T(x,y / (z * (u * (z \ (1 / z))))) = T(x,y * ((z * u) \ (z * z)))
    ]]></literal>
    <justification jstring="[para(14726(a,1),18234(a,1,2,2))].">
      <j1 rule="para" parents="14726 18234"/>
    </justification>
  </clause>

  <clause id="18236">
    <literal><![CDATA[
      T(x,y * ((z * u) \ (z * z))) = T(x,y / ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[hyper(18167,a,18235,a),flip(a)].">
      <j1 rule="hyper" parents="18167 18235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18237">
    <literal><![CDATA[
      T(T(x,K(y,(z * u) \ (z * z))),((z * u) \ (z * z)) * y) = T(x,y / ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[hyper(13254,a,18236,a)].">
      <j1 rule="hyper" parents="13254 18236"/>
    </justification>
  </clause>

  <clause id="18238">
    <literal><![CDATA[
      T(x,y * (((z * (u / z)) \ w) \ (K(z \ u,z) * K(z \ u,z)))) = T(x,y / ((K(z \ u,z) \ 1) * (u \ w)))
    ]]></literal>
    <justification jstring="[para(11653(a,1),18236(a,1,2,2,1))].">
      <j1 rule="para" parents="11653 18236"/>
    </justification>
  </clause>

  <clause id="18239">
    <literal><![CDATA[
      T(T(x,K(y,z \ u)),((u * z) \ (u * u)) * y) = T(x,y / ((u \ 1) * z))
    ]]></literal>
    <justification jstring="[para(14177(a,1),18237(a,1,1,2))].">
      <j1 rule="para" parents="14177 18237"/>
    </justification>
  </clause>

  <clause id="18240">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),((u * z) \ (u * u)) * y) = T(x,y / ((u \ 1) * z))
    ]]></literal>
    <justification jstring="[para(16268(a,1),18239(a,1,1))].">
      <j1 rule="para" parents="16268 18239"/>
    </justification>
  </clause>

  <clause id="18241">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),u * (u * ((u * z) \ y))) = T(x,y / ((u \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,17548,a(flip),b,18240,a)].">
      <j1 rule="hyper" parents="65 17548 18240"/>
    </justification>
  </clause>

  <clause id="18242">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),((u \ 1) * z) \ y) = T(x,y / ((u \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,17549,a(flip),b,18241,a)].">
      <j1 rule="hyper" parents="65 17549 18241"/>
    </justification>
  </clause>

  <clause id="18243">
    <literal><![CDATA[
      T(T(x,K(y * K(z \ 1,u),u * z)),((z \ 1) * u) \ (y * K(z \ 1,u))) = T(x,y / (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[para(11290(a,1),18242(a,2,2))].">
      <j1 rule="para" parents="11290 18242"/>
    </justification>
  </clause>

  <clause id="18244">
    <literal><![CDATA[
      (T(x,y) * z) / T(1 / K(x,y),K(x,y) * (x * z)) = (x * z) * (K(x,y) * K(x,y))
    ]]></literal>
    <justification jstring="[para(8386(a,1),17706(a,1,1))].">
      <j1 rule="para" parents="8386 17706"/>
    </justification>
  </clause>

  <clause id="18245">
    <literal><![CDATA[
      (T(x,y) * z) / T(K(y,x),K(x,y) * (x * z)) = (x * z) * (K(x,y) * K(x,y))
    ]]></literal>
    <justification jstring="[para(5209(a,1),18244(a,1,2,1))].">
      <j1 rule="para" parents="5209 18244"/>
    </justification>
  </clause>

  <clause id="18246">
    <literal><![CDATA[
      (T(x,y) * z) / K(y,T(x,x * z)) = (x * z) * (K(x,y) * K(x,y))
    ]]></literal>
    <justification jstring="[para(17102(a,1),18245(a,1,2))].">
      <j1 rule="para" parents="17102 18245"/>
    </justification>
  </clause>

  <clause id="18247">
    <literal><![CDATA[
      (T(x,y) * z) / K(y,T(x,z)) = (x * z) * (K(x,y) * K(x,y))
    ]]></literal>
    <justification jstring="[para(7469(a,1),18246(a,1,2))].">
      <j1 rule="para" parents="7469 18246"/>
    </justification>
  </clause>

  <clause id="18249">
    <literal><![CDATA[
      (T(x,y) * z) * K(x,T(y,z)) = (x * z) * (K(x,y) * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(7586,a,18247,a)].">
      <j1 rule="hyper" parents="7586 18247"/>
    </justification>
  </clause>

  <clause id="18250">
    <literal><![CDATA[
      T(x,y) * (z * K(x,T(y,z))) = (x * z) * (K(x,y) * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(7358,a,18249,a)].">
      <j1 rule="hyper" parents="7358 18249"/>
    </justification>
  </clause>

  <clause id="18251">
    <literal><![CDATA[
      (x * y) * (K(x,z) * K(x,z)) = T(x,z) * (K(x,z) * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,7601,a(flip),b,18250,a),flip(a)].">
      <j1 rule="hyper" parents="65 7601 18250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18252">
    <literal><![CDATA[
      (x * y) * (K(x,z) * K(x,z)) = K(x,z) * (T(x,z) * y)
    ]]></literal>
    <justification jstring="[hyper(299,a,5425,a,b,18251,a),flip(a)].">
      <j1 rule="hyper" parents="299 5425 18251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18253">
    <literal><![CDATA[
      (x * y) * (K(x,z) * K(x,z)) = T(T(x,z),z) * y
    ]]></literal>
    <justification jstring="[hyper(299,a,5424,a(flip),b,18252,a),flip(a)].">
      <j1 rule="hyper" parents="299 5424 18252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18254">
    <literal><![CDATA[
      x * (y * (K(x,z) * K(x,z))) = T(T(x,z),z) * y
    ]]></literal>
    <justification jstring="[hyper(903,a,18253,a)].">
      <j1 rule="hyper" parents="903 18253"/>
    </justification>
  </clause>

  <clause id="18255">
    <literal><![CDATA[
      T(x,y * (T(T(z,u),u) * w)) = T(x,y * (z * w))
    ]]></literal>
    <justification jstring="[para(18253(a,1),15797(a,1,2,2))].">
      <j1 rule="para" parents="18253 15797"/>
    </justification>
  </clause>

  <clause id="18256">
    <literal><![CDATA[
      T(T(x,y * (L(y,z,u) \ w)),L(y,z,u) * (y \ (y \ L(y,z,u)))) = T(T(x,(L(y,z,u) \ y) \ w),1)
    ]]></literal>
    <justification jstring="[hyper(15679,a,17747,a)].">
      <j1 rule="hyper" parents="15679 17747"/>
    </justification>
  </clause>

  <clause id="18257">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),((u \ 1) * z) \ (y * K(u \ 1,z))) = T(x,y / (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(17273(a,1),18243(a,1,1))].">
      <j1 rule="para" parents="17273 18243"/>
    </justification>
  </clause>

  <clause id="18258">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),T((z * (u \ 1)) \ y,K(u \ 1,z))) = T(x,y / (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(13280(a,2),18257(a,1,2))].">
      <j1 rule="para" parents="13280 18257"/>
    </justification>
  </clause>

  <clause id="18260">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),(z * (u \ 1)) \ y) = T(x,y / (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(16365,a,18258,a)].">
      <j1 rule="hyper" parents="16365 18258"/>
    </justification>
  </clause>

  <clause id="18262">
    <literal><![CDATA[
      T(x,((1 / y) * (z / y)) * (T(z,(1 / y) * (z / y)) \ u)) = T(x,T(y \ 1,y \ z) * (y \ u))
    ]]></literal>
    <justification jstring="[para(10(a,1),16878(a,2,2,2,2))].">
      <j1 rule="para" parents="10 16878"/>
    </justification>
  </clause>

  <clause id="18263">
    <literal><![CDATA[
      T(x,((1 / y) * (z / y)) * (T(z,(1 / y) * (z / y)) \ u)) = T(x,T(y \ 1,y * z) * (y \ u))
    ]]></literal>
    <justification jstring="[hyper(299,a,17432,a(flip),b,18262,a),flip(a)].">
      <j1 rule="hyper" parents="299 17432 18262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18264">
    <literal><![CDATA[
      T(T(x,K(y,z)),((y / u) / u) * z) = T(x,(K(u,u \ (y / u)) * z) * (u \ (y / u)))
    ]]></literal>
    <justification jstring="[para(17171(a,1),16939(a,1,1))].">
      <j1 rule="para" parents="17171 16939"/>
    </justification>
  </clause>

  <clause id="18265">
    <literal><![CDATA[
      T(T(x,K(y,z)),((y / u) / u) * z) = T(x,K(u,u \ (y / u)) * (z * (u \ (y / u))))
    ]]></literal>
    <justification jstring="[para(7472(a,1),18264(a,2,2))].">
      <j1 rule="para" parents="7472 18264"/>
    </justification>
  </clause>

  <clause id="18267">
    <literal><![CDATA[
      T(T(x,K(y,z)),((y / u) / u) * z) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,z * ((y / u) / u)) = w
    ]]></literal>
    <justification jstring="[para(18265(a,2),16465(a,1))].">
      <j1 rule="para" parents="18265 16465"/>
    </justification>
  </clause>

  <clause id="18268">
    <literal><![CDATA[
      ((x * L(y,z,z)) * ((z * z) * T(u,w))) / ((x * L(y * (z * z),z,z)) * u) = K(u,T(w,x * (z * (z * y))))
    ]]></literal>
    <justification jstring="[para(6517(a,1),17521(a,1,1))].">
      <j1 rule="para" parents="6517 17521"/>
    </justification>
  </clause>

  <clause id="18269">
    <literal><![CDATA[
      K(x,((y \ 1) \ (((y \ 1) \ 1) \ z)) * (u / (y * y))) = K(x,T((y \ (y \ z)) * u,y \ (y \ 1)))
    ]]></literal>
    <justification jstring="[para(76(a,1),18101(a,1,2,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="76 18101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18271">
    <literal><![CDATA[
      K(x,((y \ 1) \ (((y \ 1) \ 1) \ z)) * (u / (y * y))) = K(x,(y \ (y \ z)) * u)
    ]]></literal>
    <justification jstring="[hyper(299,a,16198,a(flip),b,18269,a),flip(a)].">
      <j1 rule="hyper" parents="299 16198 18269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18273">
    <literal><![CDATA[
      K(x,(y \ ((y \ 1) \ z)) * (u / (y * y))) = K(x,(y \ (y \ z)) * u)
    ]]></literal>
    <justification jstring="[para(769(a,1),18271(a,1,2,1))].">
      <j1 rule="para" parents="769 18271"/>
    </justification>
  </clause>

  <clause id="18274">
    <literal><![CDATA[
      K(x,(y \ ((y \ 1) \ z)) * ((y * y) \ u)) = K(x,(y \ (y \ z)) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,17477,a(flip),b,18273,a)].">
      <j1 rule="hyper" parents="65 17477 18273"/>
    </justification>
  </clause>

  <clause id="18275">
    <literal><![CDATA[
      T(x,y / ((K(z \ u,z) \ 1) * (u \ w))) = T(x,y / ((z * (u / z)) \ w))
    ]]></literal>
    <justification jstring="[hyper(15839,a,18238,a),flip(a)].">
      <j1 rule="hyper" parents="15839 18238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18277">
    <literal><![CDATA[
      T(x,y / (K(z,z \ u) * (u \ w))) = T(x,y / ((z * (u / z)) \ w))
    ]]></literal>
    <justification jstring="[para(5197(a,1),18275(a,1,2,2,1))].">
      <j1 rule="para" parents="5197 18275"/>
    </justification>
  </clause>

  <clause id="18278">
    <literal><![CDATA[
      T(x,y / (((z \ u) * z) \ w)) = T(x,y / ((z * (u / z)) \ w))
    ]]></literal>
    <justification jstring="[para(11609(a,1),18277(a,1,2,2))].">
      <j1 rule="para" parents="11609 18277"/>
    </justification>
  </clause>

  <clause id="18279">
    <literal><![CDATA[
      ((x * L(y,z,z)) * ((z * z) * T(u,w))) / ((x * L(y,z,z)) * ((z * z) * u)) = K(u,T(w,x * (z * (z * y))))
    ]]></literal>
    <justification jstring="[para(6517(a,1),18268(a,1,2))].">
      <j1 rule="para" parents="6517 18268"/>
    </justification>
  </clause>

  <clause id="18280">
    <literal><![CDATA[
      T(x,(y * K(z / u,y)) * (T(u / z,y * K(z / u,y)) \ w)) = T(x,y * ((u / z) \ w))
    ]]></literal>
    <justification jstring="[hyper(299,a,17405,a(flip),b,16879,a),flip(a)].">
      <j1 rule="hyper" parents="299 17405 16879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18282">
    <literal><![CDATA[
      T(x,(y * K(z / u,y)) * (T(u / z,T(y,z / u)) \ w)) = T(x,y * ((u / z) \ w))
    ]]></literal>
    <justification jstring="[para(8184(a,1),18280(a,1,2,2,1))].">
      <j1 rule="para" parents="8184 18280"/>
    </justification>
  </clause>

  <clause id="18283">
    <literal><![CDATA[
      T(x,(y * K(z / u,y)) * (T(u / z,y) \ w)) = T(x,y * ((u / z) \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,16937,a(flip),b,18282,a)].">
      <j1 rule="hyper" parents="65 16937 18282"/>
    </justification>
  </clause>

  <clause id="18285">
    <literal><![CDATA[
      T(x,y * (K(z / u,y) * (T(u / z,y) \ w))) = T(x,y * ((u / z) \ w))
    ]]></literal>
    <justification jstring="[para(5488(a,1),18283(a,1,2))].">
      <j1 rule="para" parents="5488 18283"/>
    </justification>
  </clause>

  <clause id="18286">
    <literal><![CDATA[
      T(x,T(y,z / u) * (T(u / z,y) \ w)) = T(x,y * ((u / z) \ w))
    ]]></literal>
    <justification jstring="[hyper(15872,a,18285,a)].">
      <j1 rule="hyper" parents="15872 18285"/>
    </justification>
  </clause>

  <clause id="18287">
    <literal><![CDATA[
      T(x,T(y,z * u) * (T(z / u,y) \ w)) = T(x,y * ((z / u) \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,17970,a(flip),b,18286,a)].">
      <j1 rule="hyper" parents="65 17970 18286"/>
    </justification>
  </clause>

  <clause id="18288">
    <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),18220(a,1,1,1))].">
      <j1 rule="para" parents="9 18220"/>
    </justification>
  </clause>

  <clause id="18289">
    <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),18288(a,1,1,3)),flip(a)].">
      <j1 rule="para" parents="9 18288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18290">
    <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(6840(a,1),18289(a,2,2))].">
      <j1 rule="para" parents="6840 18289"/>
    </justification>
  </clause>

  <clause id="18291">
    <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),18290(a,2,2,2))].">
      <j1 rule="para" parents="9 18290"/>
    </justification>
  </clause>

  <clause id="18292">
    <literal><![CDATA[
      K(x * (1 / ((y * z) \ y)),1 / ((y * z) \ y)) = a(z,x,z) * K(x,z)
    ]]></literal>
    <justification jstring="[para(5188(a,1),18291(a,2,2))].">
      <j1 rule="para" parents="5188 18291"/>
    </justification>
  </clause>

  <clause id="18293">
    <literal><![CDATA[
      K(x * (1 / ((y * z) \ y)),1 / ((y * z) \ y)) = K(z * x,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,9684,a(flip),b,18292,a),flip(a)].">
      <j1 rule="hyper" parents="299 9684 18292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18294">
    <literal><![CDATA[
      K(x * (1 / ((y * z) \ y)),y \ (y * z)) = K(z * x,z)
    ]]></literal>
    <justification jstring="[hyper(7096,a,18293,a)].">
      <j1 rule="hyper" parents="7096 18293"/>
    </justification>
  </clause>

  <clause id="18295">
    <literal><![CDATA[
      K(x * (1 / ((y * z) \ y)),z) = K(z * x,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),18294(a,1,2))].">
      <j1 rule="para" parents="9 18294"/>
    </justification>
  </clause>

  <clause id="18296">
    <literal><![CDATA[
      K(x * (((y * z) \ y) \ 1),z) = K(z * x,z)
    ]]></literal>
    <justification jstring="[hyper(7416,a,18295,a)].">
      <j1 rule="hyper" parents="7416 18295"/>
    </justification>
  </clause>

  <clause id="18297">
    <literal><![CDATA[
      K(((x * y) \ x) \ z,y) = K(y * z,y)
    ]]></literal>
    <justification jstring="[hyper(14525,a,18296,a)].">
      <j1 rule="hyper" parents="14525 18296"/>
    </justification>
  </clause>

  <clause id="18298">
    <literal><![CDATA[
      K(((x * y) \ x) \ (y \ z),y) = K(z,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),18297(a,2,1))].">
      <j1 rule="para" parents="10 18297"/>
    </justification>
  </clause>

  <clause id="18299">
    <literal><![CDATA[
      K((1 / ((x * y) \ x)) \ z,y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,10994,a(flip),b,18298,a),flip(a)].">
      <j1 rule="hyper" parents="65 10994 18298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18300">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) \ z,y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[hyper(7405,a,18299,a)].">
      <j1 rule="hyper" parents="7405 18299"/>
    </justification>
  </clause>

  <clause id="18302">
    <literal><![CDATA[
      K(x * ((y * z) \ y),z) = K(z \ x,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,10298,a(flip),b,18300,a)].">
      <j1 rule="hyper" parents="65 10298 18300"/>
    </justification>
  </clause>

  <clause id="18304">
    <literal><![CDATA[
      K(x * ((y * z) \ z),y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,9117,a,b,18302,a)].">
      <j1 rule="hyper" parents="65 9117 18302"/>
    </justification>
  </clause>

  <clause id="18305">
    <literal><![CDATA[
      K((x \ y) \ z,x \ y) = K(z * (y \ x),x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),18302(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 18302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18307">
    <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(18304(a,1),17381(a,1,1,1,2))].">
      <j1 rule="para" parents="18304 17381"/>
    </justification>
  </clause>

  <clause id="18308">
    <literal><![CDATA[
      K((x \ y) \ z,x \ y) = K(z * (x / y),x \ y)
    ]]></literal>
    <justification jstring="[hyper(299,a,7933,a,b,18305,a),flip(a)].">
      <j1 rule="hyper" parents="299 7933 18305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18309">
    <literal><![CDATA[
      x * K(x * (y / z),y \ z) = ((y \ z) \ x) * (y \ z)
    ]]></literal>
    <justification jstring="[para(18308(a,1),287(a,1,2))].">
      <j1 rule="para" parents="18308 287"/>
    </justification>
  </clause>

  <clause id="18310">
    <literal><![CDATA[
      ((1 / (x \ y)) \ z) * (1 / (x \ y)) = ((y \ x) \ z) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,9856,a,b,18309,a)].">
      <j1 rule="hyper" parents="65 9856 18309"/>
    </justification>
  </clause>

  <clause id="18311">
    <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(18310(a,1),17674(a,1,1,1,2,1,2))].">
      <j1 rule="para" parents="18310 17674"/>
    </justification>
  </clause>

  <clause id="18312">
    <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(287(a,1),18307(a,1,1,1))].">
      <j1 rule="para" parents="287 18307"/>
    </justification>
  </clause>

  <clause id="18314">
    <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(8332(a,1),18312(a,1,1))].">
      <j1 rule="para" parents="8332 18312"/>
    </justification>
  </clause>

  <clause id="18315">
    <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(106(a,1),18314(a,1,2,2,2))].">
      <j1 rule="para" parents="106 18314"/>
    </justification>
  </clause>

  <clause id="18316">
    <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(9549(a,1),18315(a,1,2))].">
      <j1 rule="para" parents="9549 18315"/>
    </justification>
  </clause>

  <clause id="18317">
    <literal><![CDATA[
      T((x \ y) * x,z \ (x \ z)) \ T(y,z \ (x \ z)) = K(x,y * ((x * z) \ z))
    ]]></literal>
    <justification jstring="[para(3744(a,1),18316(a,1,2))].">
      <j1 rule="para" parents="3744 18316"/>
    </justification>
  </clause>

  <clause id="18318">
    <literal><![CDATA[
      K(x,T(x \ y,z \ (x \ z))) = K(x,y * ((x * z) \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,11782,a(flip),b,18317,a)].">
      <j1 rule="hyper" parents="65 11782 18317"/>
    </justification>
  </clause>

  <clause id="18319">
    <literal><![CDATA[
      K(x,T(x \ y,z \ z)) = K(x,y * ((x * z) \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,9586,a(flip),b,18318,a)].">
      <j1 rule="hyper" parents="65 9586 18318"/>
    </justification>
  </clause>

  <clause id="18320">
    <literal><![CDATA[
      K(x,y * ((x * z) \ z)) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(198(a,1),18319(a,1,2)),flip(a)].">
      <j1 rule="para" parents="198 18319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18321">
    <literal><![CDATA[
      K(x,R(x \ 1,x,y) * z) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,11533,a,b,18320,a)].">
      <j1 rule="hyper" parents="65 11533 18320"/>
    </justification>
  </clause>

  <clause id="18324">
    <literal><![CDATA[
      K(x,y * (z / (x * z))) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,11051,a(flip),b,18321,a)].">
      <j1 rule="hyper" parents="65 11051 18321"/>
    </justification>
  </clause>

  <clause id="18326">
    <literal><![CDATA[
      K(x \ y,(x \ y) \ z) = K(x \ y,z * (x / y))
    ]]></literal>
    <justification jstring="[hyper(65,a,11550,a(flip),b,18324,a),flip(a)].">
      <j1 rule="hyper" parents="65 11550 18324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18328">
    <literal><![CDATA[
      x * K(y \ z,x * (y / z)) = (y \ z) * (x / (y \ z))
    ]]></literal>
    <justification jstring="[para(18326(a,1),5293(a,1,2))].">
      <j1 rule="para" parents="18326 5293"/>
    </justification>
  </clause>

  <clause id="18329">
    <literal><![CDATA[
      (1 / (x \ y)) * (z / (1 / (x \ y))) = (y \ x) * (z / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(65,a,9857,a,b,18328,a)].">
      <j1 rule="hyper" parents="65 9857 18328"/>
    </justification>
  </clause>

  <clause id="18330">
    <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(18329(a,1),18311(a,1,1,1))].">
      <j1 rule="para" parents="18329 18311"/>
    </justification>
  </clause>

  <clause id="18331">
    <literal><![CDATA[
      K(1 / x,T(y,z / (1 / (u \ w)))) = K(1 / x,T(y,z / (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(17676,a,18330,a),flip(a)].">
      <j1 rule="hyper" parents="17676 18330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18332">
    <literal><![CDATA[
      K(1 / x,T(y,z / (1 / (u \ w)))) = K(1 / x,T(y,z / (u / w)))
    ]]></literal>
    <justification jstring="[hyper(299,a,17117,a,b,18331,a),flip(a)].">
      <j1 rule="hyper" parents="299 17117 18331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18333">
    <literal><![CDATA[
      K(1 / x,T(y,z / (1 / (u / w)))) = K(1 / x,T(y,z / (w / u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,17347,a,b,18332,a)].">
      <j1 rule="hyper" parents="65 17347 18332"/>
    </justification>
  </clause>

  <clause id="18334">
    <literal><![CDATA[
      K(1 / x,T(y,z / (u / w))) = K(1 / x,T(y,(w / u) * z))
    ]]></literal>
    <justification jstring="[hyper(16635,a,18333,a),flip(a)].">
      <j1 rule="hyper" parents="16635 18333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18335">
    <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(18334(a,1),17348(a,2,1))].">
      <j1 rule="para" parents="18334 17348"/>
    </justification>
  </clause>

  <clause id="18336">
    <literal><![CDATA[
      T(1 / x,T(y,z / (u / T(w,v5)))) = T(1 / x,T(y,(w / u) * z))
    ]]></literal>
    <justification jstring="[hyper(299,a,5272,a(flip),b,18335,a),flip(a)].">
      <j1 rule="hyper" parents="299 5272 18335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18337">
    <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(18336(a,1),6364(a,1,1))].">
      <j1 rule="para" parents="18336 6364"/>
    </justification>
  </clause>

  <clause id="18338">
    <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(65,a,6364,a(flip),b,18337,a),flip(a)].">
      <j1 rule="hyper" parents="65 6364 18337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18339">
    <literal><![CDATA[
      K(x,y * y) * (((x * T(y * y,z)) \ u) * T(y * y,z)) = K(y * y,z) * (((T(y * y,z) * x) \ u) * (y * y))
    ]]></literal>
    <justification jstring="[para(16205(a,1),16299(a,1,1))].">
      <j1 rule="para" parents="16205 16299"/>
    </justification>
  </clause>

  <clause id="18340">
    <literal><![CDATA[
      K(x,y * y) * ((T(y * y,z) \ (x \ u)) * T(y * y,z)) = K(y * y,z) * (((T(y * y,z) * x) \ u) * (y * y))
    ]]></literal>
    <justification jstring="[para(2670(a,1),18339(a,1,2,1))].">
      <j1 rule="para" parents="2670 18339"/>
    </justification>
  </clause>

  <clause id="18342">
    <literal><![CDATA[
      (T(x \ 1,x \ y) \ (y / (1 / x))) * T(x \ 1,x \ y) = (y / (1 / x)) * K((x \ 1) * ((x \ 1) * y),x \ 1)
    ]]></literal>
    <justification jstring="[para(16223(a,1),17030(a,2,2))].">
      <j1 rule="para" parents="16223 17030"/>
    </justification>
  </clause>

  <clause id="18343">
    <literal><![CDATA[
      (T(x \ 1,x \ y) \ (y / (1 / x))) * T(x \ 1,x \ y) = (y / (1 / x)) * K(x \ ((x \ 1) * y),x \ 1)
    ]]></literal>
    <justification jstring="[para(7294(a,1),18342(a,2,2))].">
      <j1 rule="para" parents="7294 18342"/>
    </justification>
  </clause>

  <clause id="18344">
    <literal><![CDATA[
      (T(x \ 1,x \ y) \ (y / (1 / x))) * T(x \ 1,x \ y) = (y / (1 / x)) * K((x * x) \ y,x \ 1)
    ]]></literal>
    <justification jstring="[para(728(a,1),18343(a,2,2,1))].">
      <j1 rule="para" parents="728 18343"/>
    </justification>
  </clause>

  <clause id="18345">
    <literal><![CDATA[
      (T(x \ 1,x \ y) \ (y / (1 / x))) * T(x \ 1,x \ y) = (y / (1 / x)) * K(x \ (x \ y),x \ 1)
    ]]></literal>
    <justification jstring="[para(14182(a,1),18344(a,2,2))].">
      <j1 rule="para" parents="14182 18344"/>
    </justification>
  </clause>

  <clause id="18346">
    <literal><![CDATA[
      (T(x \ 1,x \ y) \ (y / (1 / x))) * T(x \ 1,x \ y) = (y / (1 / x)) * K(y * (x * x),x \ 1)
    ]]></literal>
    <justification jstring="[para(18178(a,1),18345(a,2,2))].">
      <j1 rule="para" parents="18178 18345"/>
    </justification>
  </clause>

  <clause id="18347">
    <literal><![CDATA[
      (T(x \ 1,x \ y) \ (y / (1 / x))) * T(x \ 1,x \ y) = y / T(1 / x,T(y * (x * x),x))
    ]]></literal>
    <justification jstring="[hyper(299,a,7632,a(flip),b,18346,a),flip(a)].">
      <j1 rule="hyper" parents="299 7632 18346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18348">
    <literal><![CDATA[
      (T(x \ 1,x \ y) \ (y / (1 / x))) * T(x \ 1,x \ y) = y / T(1 / x,x * (y * x))
    ]]></literal>
    <justification jstring="[para(17420(a,1),18347(a,2,2))].">
      <j1 rule="para" parents="17420 18347"/>
    </justification>
  </clause>

  <clause id="18349">
    <literal><![CDATA[
      (T(x \ 1,x \ y) \ (y / (1 / x))) * T(x \ 1,x \ y) = y / T(x \ 1,x \ (y * x))
    ]]></literal>
    <justification jstring="[para(14693(a,1),18348(a,2,2))].">
      <j1 rule="para" parents="14693 18348"/>
    </justification>
  </clause>

  <clause id="18350">
    <literal><![CDATA[
      (T(x \ 1,x \ y) \ (y / (1 / x))) * T(x \ 1,x \ y) = y / T(x \ 1,T(y,x))
    ]]></literal>
    <justification jstring="[para(22(a,2),18349(a,2,2,2))].">
      <j1 rule="para" parents="22 18349"/>
    </justification>
  </clause>

  <clause id="18351">
    <literal><![CDATA[
      (T(x \ 1,x \ y) \ (y / (1 / x))) * T(x \ 1,x \ y) = y / T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(7149(a,1),18350(a,2,2))].">
      <j1 rule="para" parents="7149 18350"/>
    </justification>
  </clause>

  <clause id="18352">
    <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(16572,a,17247,a),flip(a)].">
      <j1 rule="hyper" parents="16572 17247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18354">
    <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(15484(a,1),18352(a,2,2))].">
      <j1 rule="para" parents="15484 18352"/>
    </justification>
  </clause>

  <clause id="18355">
    <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(299,a,17341,a(flip),b,18354,a),flip(a)].">
      <j1 rule="hyper" parents="299 17341 18354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18356">
    <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(17272,a,18355,a)].">
      <j1 rule="hyper" parents="17272 18355"/>
    </justification>
  </clause>

  <clause id="18358">
    <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(65,a,17214,a(flip),b,18356,a)].">
      <j1 rule="hyper" parents="65 17214 18356"/>
    </justification>
  </clause>

  <clause id="18359">
    <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(65,a,17223,a(flip),b,18358,a),flip(a)].">
      <j1 rule="hyper" parents="65 17223 18358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18360">
    <literal><![CDATA[
      L(K(x,K(y,z)),K(u,w) * v5,v6) = K(y,K(z,L(x,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(11947,a,18359,a)].">
      <j1 rule="hyper" parents="11947 18359"/>
    </justification>
  </clause>

  <clause id="18362">
    <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(14388(a,1),18359(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="14388 18359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18363">
    <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(299,a,14942,a,b,18360,a),flip(a)].">
      <j1 rule="hyper" parents="299 14942 18360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18364">
    <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(299,a,8923,a(flip),b,18362,a),flip(a)].">
      <j1 rule="hyper" parents="299 8923 18362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18365">
    <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(18364(a,1),18179(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18364 18179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18366">
    <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(14943,a,18363,a)].">
      <j1 rule="hyper" parents="14943 18363"/>
    </justification>
  </clause>

  <clause id="18367">
    <literal><![CDATA[
      a(x,y * (z / y),K(u,K(w,v5))) = a(x,z,K(u,K(w,v5)))
    ]]></literal>
    <justification jstring="[para(5026(a,1),18366(a,1,2))].">
      <j1 rule="para" parents="5026 18366"/>
    </justification>
  </clause>

  <clause id="18368">
    <literal><![CDATA[
      a(x,y / z,K(u,K(w,v5))) = a(x,z \ y,K(u,K(w,v5)))
    ]]></literal>
    <justification jstring="[para(5117(a,1),18366(a,1,2))].">
      <j1 rule="para" parents="5117 18366"/>
    </justification>
  </clause>

  <clause id="18369">
    <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(65,a,12771,a(flip),b,18367,a),flip(a)].">
      <j1 rule="hyper" parents="65 12771 18367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18370">
    <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(7989(a,2),18369(a,2,3))].">
      <j1 rule="para" parents="7989 18369"/>
    </justification>
  </clause>

  <clause id="18371">
    <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(12767(a,1),18370(a,2,3))].">
      <j1 rule="para" parents="12767 18370"/>
    </justification>
  </clause>

  <clause id="18372">
    <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),18371(a,1,3,2,2))].">
      <j1 rule="para" parents="10 18371"/>
    </justification>
  </clause>

  <clause id="18373">
    <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(7989(a,1),18372(a,1,3))].">
      <j1 rule="para" parents="7989 18372"/>
    </justification>
  </clause>

  <clause id="18374">
    <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),18373(a,2,3,2,2))].">
      <j1 rule="para" parents="10 18373"/>
    </justification>
  </clause>

  <clause id="18375">
    <literal><![CDATA[
      a(x,1 / (y \ z),K(z,K(u,w))) = a(x,y,K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(7989(a,1),18374(a,2,3))].">
      <j1 rule="para" parents="7989 18374"/>
    </justification>
  </clause>

  <clause id="18376">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(x,z / y,K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(79(a,1),18375(a,1,2,2))].">
      <j1 rule="para" parents="79 18375"/>
    </justification>
  </clause>

  <clause id="18377">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(x,w / y,K(w,K(z,u)))
    ]]></literal>
    <justification jstring="[para(7989(a,2),18376(a,1,3))].">
      <j1 rule="para" parents="7989 18376"/>
    </justification>
  </clause>

  <clause id="18378">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(x,w / y,K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(7989(a,2),18377(a,2,3))].">
      <j1 rule="para" parents="7989 18377"/>
    </justification>
  </clause>

  <clause id="18379">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(w,u / y,K(z,K(x,u)))
    ]]></literal>
    <justification jstring="[hyper(15006,a,18378,a)].">
      <j1 rule="hyper" parents="15006 18378"/>
    </justification>
  </clause>

  <clause id="18380">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(w,u / y,K(z,K(u,x)))
    ]]></literal>
    <justification jstring="[para(8004(a,1),18379(a,2,3))].">
      <j1 rule="para" parents="8004 18379"/>
    </justification>
  </clause>

  <clause id="18381">
    <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(8003(a,1),18365(a,2,2))].">
      <j1 rule="para" parents="8003 18365"/>
    </justification>
  </clause>

  <clause id="18383">
    <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(299,a,12347,a(flip),b,18381,a),flip(a)].">
      <j1 rule="hyper" parents="299 12347 18381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18384">
    <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(10558(a,1),18383(a,2,1))].">
      <j1 rule="para" parents="10558 18383"/>
    </justification>
  </clause>

  <clause id="18385">
    <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(299,a,15030,a(flip),b,18384,a),flip(a)].">
      <j1 rule="hyper" parents="299 15030 18384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18386">
    <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(17260(a,1),18385(a,1,2))].">
      <j1 rule="para" parents="17260 18385"/>
    </justification>
  </clause>

  <clause id="18387">
    <literal><![CDATA[
      a(x,(K(y,z) / z) * K(u,w),K(v5,K(u,w))) = a(w,z,K(v5,K(u,x)))
    ]]></literal>
    <justification jstring="[para(8003(a,1),18386(a,1,3))].">
      <j1 rule="para" parents="8003 18386"/>
    </justification>
  </clause>

  <clause id="18388">
    <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(12003,a,18387,a)].">
      <j1 rule="hyper" parents="12003 18387"/>
    </justification>
  </clause>

  <clause id="18389">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(w,y,K(z,K(u,x)))
    ]]></literal>
    <justification jstring="[para(168(a,1),18388(a,1,2,1))].">
      <j1 rule="para" parents="168 18388"/>
    </justification>
  </clause>

  <clause id="18390">
    <literal><![CDATA[
      a(x,y / z,K(u,K(y,w))) = a(x,z,K(u,K(y,w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,18380,a(flip),b,18389,a)].">
      <j1 rule="hyper" parents="65 18380 18389"/>
    </justification>
  </clause>

  <clause id="18391">
    <literal><![CDATA[
      a(x,y / z,K(u,K(y,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      a(y,z,K(u,K(x,w))) = v5
    ]]></literal>
    <justification jstring="[para(18390(a,2),14974(a,1))].">
      <j1 rule="para" parents="18390 14974"/>
    </justification>
  </clause>

  <clause id="18392">
    <literal><![CDATA[
      K(x,(y * ((z * T(u,w \ v5)) \ 1)) * (z * T(u,w * v5))) = K(x,(y * (z * T(u,w \ v5))) / (z * T(u,w \ v5)))
    ]]></literal>
    <justification jstring="[hyper(299,a,14283,a(flip),b,17555,a),flip(a)].">
      <j1 rule="hyper" parents="299 14283 17555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18393">
    <literal><![CDATA[
      K(x,(y * ((z * T(u,w \ v5)) \ 1)) * (z * T(u,w * v5))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(11(a,1),18392(a,2,2))].">
      <j1 rule="para" parents="11 18392"/>
    </justification>
  </clause>

  <clause id="18394">
    <literal><![CDATA[
      T(x,T(y,z)) \ (L(K(x,x \ z),u,w) * (K(x,x \ z) \ T(x,T(y,z)))) = T((x \ z) \ z,y) \ (K(x,L(x \ z,u,w)) * T(x,T(y,z)))
    ]]></literal>
    <justification jstring="[para(11889(a,1),18226(a,2,2,1))].">
      <j1 rule="para" parents="11889 18226"/>
    </justification>
  </clause>

  <clause id="18395">
    <literal><![CDATA[
      K(x,((y * T(z,u \ w)) \ (v5 * ((y * T(z,u \ w)) \ 1))) * (y * T(z,u * w))) = K(x,T(v5,y * T(z,u * w)) * (1 / (y * T(z,u \ w))))
    ]]></literal>
    <justification jstring="[para(17433(a,1),17556(a,2,2,1))].">
      <j1 rule="para" parents="17433 17556"/>
    </justification>
  </clause>

  <clause id="18396">
    <literal><![CDATA[
      K(x,((y * T(z,u \ w)) \ (v5 * ((y * T(z,u \ w)) \ 1))) * (y * T(z,u * w))) = K(x,T(v5,y * T(z,u * w)) / (y * T(z,u \ w)))
    ]]></literal>
    <justification jstring="[hyper(299,a,14283,a(flip),b,18395,a),flip(a)].">
      <j1 rule="hyper" parents="299 14283 18395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18397">
    <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(3392(a,1),6768(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3392 6768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18399">
    <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(9773(a,1),18397(a,2,2,2))].">
      <j1 rule="para" parents="9773 18397"/>
    </justification>
  </clause>

  <clause id="18400">
    <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(15261(a,1),18399(a,2,2))].">
      <j1 rule="para" parents="15261 18399"/>
    </justification>
  </clause>

  <clause id="18401">
    <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(299,a,5426,a(flip),b,18400,a),flip(a)].">
      <j1 rule="hyper" parents="299 5426 18400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18402">
    <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(299,a,7362,a(flip),b,18401,a),flip(a)].">
      <j1 rule="hyper" parents="299 7362 18401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18403">
    <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(3392(a,1),18402(a,1,2,2,2))].">
      <j1 rule="para" parents="3392 18402"/>
    </justification>
  </clause>

  <clause id="18405">
    <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(5426(a,1),18403(a,1,2,2))].">
      <j1 rule="para" parents="5426 18403"/>
    </justification>
  </clause>

  <clause id="18406">
    <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(11177(a,1),18405(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11177 18405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18407">
    <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(299,a,9314,a(flip),b,18406,a),flip(a)].">
      <j1 rule="hyper" parents="299 9314 18406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18408">
    <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(193(a,1),18407(a,2,2))].">
      <j1 rule="para" parents="193 18407"/>
    </justification>
  </clause>

  <clause id="18409">
    <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(18338(a,1),18408(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="18338 18408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18410">
    <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(299,a,18408,a(flip),b,18409,a),flip(a)].">
      <j1 rule="hyper" parents="299 18408 18409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18411">
    <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(299,a,7537,a(flip),b,18410,a),flip(a)].">
      <j1 rule="hyper" parents="299 7537 18410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18412">
    <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(7709,a,18411,a)].">
      <j1 rule="hyper" parents="7709 18411"/>
    </justification>
  </clause>

  <clause id="18413">
    <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(65,a,17345,a(flip),b,18412,a)].">
      <j1 rule="hyper" parents="65 17345 18412"/>
    </justification>
  </clause>

  <clause id="18414">
    <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(65,a,17346,a(flip),b,18413,a),flip(a)].">
      <j1 rule="hyper" parents="65 17346 18413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18415">
    <literal><![CDATA[
      K(x,T(y,(T(z,u) / w) * v5)) = K(x,T(y,v5 / (w / z)))
    ]]></literal>
    <justification jstring="[hyper(65,a,7859,a(flip),b,18414,a)].">
      <j1 rule="hyper" parents="65 7859 18414"/>
    </justification>
  </clause>

  <clause id="18416">
    <literal><![CDATA[
      K(x,T(y,z / (u / w))) = K(x,T(y,(w / u) * z))
    ]]></literal>
    <justification jstring="[para(106(a,1),18415(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="106 18415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18418">
    <literal><![CDATA[
      K(x,T(y,z / (u \ w))) = K(x,T(y,(u / w) * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,17117,a(flip),b,18416,a)].">
      <j1 rule="hyper" parents="65 17117 18416"/>
    </justification>
  </clause>

  <clause id="18419">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,(z / u) * w)) = K(x,T(y,w / (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(299,a,7967,a,b,18418,a)].">
      <j1 rule="hyper" parents="299 7967 18418"/>
    </justification>
  </clause>

  <clause id="18420">
    <literal><![CDATA[
      K(x,K(y,z / (u / w))) = K(x,K(y,(w / u) * z))
    ]]></literal>
    <justification jstring="[hyper(36,a,17193,a,b,18419,a)].">
      <j1 rule="hyper" parents="36 17193 18419"/>
    </justification>
  </clause>

  <clause id="18421">
    <literal><![CDATA[
      K(x,K(y,(z / u) / w)) = K(x,K(y,(u / z) * w))
    ]]></literal>
    <justification jstring="[hyper(8828,a,18420,a)].">
      <j1 rule="hyper" parents="8828 18420"/>
    </justification>
  </clause>

  <clause id="18422">
    <literal><![CDATA[
      K(x,K(y,((z / u) / z) * w)) = K(x,K(y,w / u))
    ]]></literal>
    <justification jstring="[hyper(65,a,17147,a(flip),b,18420,a),flip(a)].">
      <j1 rule="hyper" parents="65 17147 18420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18423">
    <literal><![CDATA[
      K(x,K(y,(z / (z * u)) * w)) = K(x,K(y,w / u))
    ]]></literal>
    <justification jstring="[hyper(65,a,17146,a(flip),b,18420,a),flip(a)].">
      <j1 rule="hyper" parents="65 17146 18420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18424">
    <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(18420(a,1),17202(a,1,1))].">
      <j1 rule="para" parents="18420 17202"/>
    </justification>
  </clause>

  <clause id="18425">
    <literal><![CDATA[
      K(x,K(y,z * (u / (u * w)))) = K(x,K(y,z / w))
    ]]></literal>
    <justification jstring="[hyper(16574,a,18423,a)].">
      <j1 rule="hyper" parents="16574 18423"/>
    </justification>
  </clause>

  <clause id="18426">
    <literal><![CDATA[
      K(x,K(y,z / (u \ w))) = K(x,K(y,z * (u / w)))
    ]]></literal>
    <justification jstring="[para(10(a,1),18425(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10 18425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18427">
    <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(9028,a,18424,a),flip(a)].">
      <j1 rule="hyper" parents="9028 18424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18428">
    <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(65,a,17246,a(flip),b,18427,a),flip(a)].">
      <j1 rule="hyper" parents="65 17246 18427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18429">
    <literal><![CDATA[
      K(x,K(((y / z) / y) * u,L(w,v5,v6))) = K(x,K(u / z,L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(79(a,1),18427(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="79 18427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18430">
    <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(16573,a,18429,a)].">
      <j1 rule="hyper" parents="16573 18429"/>
    </justification>
  </clause>

  <clause id="18431">
    <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),18428(a,2,2,2,2))].">
      <j1 rule="para" parents="10 18428"/>
    </justification>
  </clause>

  <clause id="18432">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,z,y))) = K(x,K(w,(y * u) / z))
    ]]></literal>
    <justification jstring="[hyper(299,a,17211,a,b,18431,a),flip(a)].">
      <j1 rule="hyper" parents="299 17211 18431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18433">
    <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(18431(a,2),17213(a,1))].">
      <j1 rule="para" parents="18431 17213"/>
    </justification>
  </clause>

  <clause id="18434">
    <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(65,a,18430,a(flip),b,18432,a)].">
      <j1 rule="hyper" parents="65 18430 18432"/>
    </justification>
  </clause>

  <clause id="18435">
    <literal><![CDATA[
      K(x,K((y / z) / u,L(w,z,y))) = K(x,K(w,(y * (1 / u)) / z))
    ]]></literal>
    <justification jstring="[para(14455(a,1),18432(a,1,2))].">
      <j1 rule="para" parents="14455 18432"/>
    </justification>
  </clause>

  <clause id="18436">
    <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(18432(a,2),17213(a,1))].">
      <j1 rule="para" parents="18432 17213"/>
    </justification>
  </clause>

  <clause id="18438">
    <literal><![CDATA[
      K(x,K(y,(z * ((u / w) / u)) / v5)) = K(x,K(y,(z * (1 / w)) / v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,18435,a(flip),b,18434,a),flip(a)].">
      <j1 rule="hyper" parents="65 18435 18434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18439">
    <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(4232(a,2),18434(a,2,2,2,1))].">
      <j1 rule="para" parents="4232 18434"/>
    </justification>
  </clause>

  <clause id="18440">
    <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(14457(a,1),18439(a,1,2))].">
      <j1 rule="para" parents="14457 18439"/>
    </justification>
  </clause>

  <clause id="18441">
    <literal><![CDATA[
      K(x,K(y,(T(z,u) / (1 / u)) / w)) = K(x,K(y,(z * u) / w))
    ]]></literal>
    <justification jstring="[hyper(18433,a,18440,a),flip(a)].">
      <j1 rule="hyper" parents="18433 18440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18442">
    <literal><![CDATA[
      K(x,K(y,((1 / z) / T(u,z)) * w)) = K(x,K(y,(u * z) / w))
    ]]></literal>
    <justification jstring="[hyper(65,a,18421,a(flip),b,18441,a)].">
      <j1 rule="hyper" parents="65 18421 18441"/>
    </justification>
  </clause>

  <clause id="18443">
    <literal><![CDATA[
      K(x,K(y,z * ((1 / u) / w))) = K(x,K(y,(w * u) / z))
    ]]></literal>
    <justification jstring="[hyper(17248,a,18442,a)].">
      <j1 rule="hyper" parents="17248 18442"/>
    </justification>
  </clause>

  <clause id="18444">
    <literal><![CDATA[
      K(x,K(y,((z \ 1) / u) * w)) = K(x,K(y,(u * z) / w))
    ]]></literal>
    <justification jstring="[hyper(65,a,17268,a,b,18443,a)].">
      <j1 rule="hyper" parents="65 17268 18443"/>
    </justification>
  </clause>

  <clause id="18445">
    <literal><![CDATA[
      K(x,K(y,(z * (1 / u)) / w)) = K(x,K(y,(u / z) * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,17263,a(flip),b,18443,a),flip(a)].">
      <j1 rule="hyper" parents="65 17263 18443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18446">
    <literal><![CDATA[
      K(x,K(y,((z / (z / (u \ 1))) / w) * v5)) = K(x,K(y,(w * u) / v5))
    ]]></literal>
    <justification jstring="[hyper(17269,a,18444,a)].">
      <j1 rule="hyper" parents="17269 18444"/>
    </justification>
  </clause>

  <clause id="18447">
    <literal><![CDATA[
      K(x,K(y,z / ((1 / u) * w))) = K(x,K(y,(u / w) * z))
    ]]></literal>
    <justification jstring="[hyper(17216,a,18445,a)].">
      <j1 rule="hyper" parents="17216 18445"/>
    </justification>
  </clause>

  <clause id="18448">
    <literal><![CDATA[
      K(x,K(y,(z * ((u / w) / u)) / v5)) = K(x,K(y,(w / z) * v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,18438,a,b,18445,a)].">
      <j1 rule="hyper" parents="65 18438 18445"/>
    </justification>
  </clause>

  <clause id="18449">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,y / z,z))) = K(x,K(w,(u / z) * y))
    ]]></literal>
    <justification jstring="[hyper(65,a,15608,a,b,18447,a)].">
      <j1 rule="hyper" parents="65 15608 18447"/>
    </justification>
  </clause>

  <clause id="18450">
    <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(11857(a,1),18447(a,1,2))].">
      <j1 rule="para" parents="11857 18447"/>
    </justification>
  </clause>

  <clause id="18451">
    <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(15218(a,1),18447(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="15218 18447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18452">
    <literal><![CDATA[
      K(x,K(y,z / (((u / w) / u) * v5))) = K(x,K(y,(w / v5) * z))
    ]]></literal>
    <justification jstring="[hyper(17216,a,18448,a)].">
      <j1 rule="hyper" parents="17216 18448"/>
    </justification>
  </clause>

  <clause id="18453">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,y,z))) = K(x,K(w,(u / z) * y))
    ]]></literal>
    <justification jstring="[hyper(65,a,15167,a(flip),b,18449,a)].">
      <j1 rule="hyper" parents="65 15167 18449"/>
    </justification>
  </clause>

  <clause id="18454">
    <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(16862(a,1),18450(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16862 18450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18455">
    <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(299,a,18452,a(flip),b,18451,a),flip(a)].">
      <j1 rule="hyper" parents="299 18452 18451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18457">
    <literal><![CDATA[
      K(x,K(y,(z * (u / w)) / v5)) = K(x,K(y,((w / u) / z) * v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,18446,a(flip),b,18455,a)].">
      <j1 rule="hyper" parents="65 18446 18455"/>
    </justification>
  </clause>

  <clause id="18458">
    <literal><![CDATA[
      K(x,K(y,((z / u) * w) / v5)) = K(x,K(y,((u / z) / w) * v5))
    ]]></literal>
    <justification jstring="[hyper(17213,a,18457,a)].">
      <j1 rule="hyper" parents="17213 18457"/>
    </justification>
  </clause>

  <clause id="18460">
    <literal><![CDATA[
      K(x,K(y,z / ((u \ w) * v5))) = K(x,K(y,((u / w) / v5) * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,17243,a(flip),b,18457,a)].">
      <j1 rule="hyper" parents="65 17243 18457"/>
    </justification>
  </clause>

  <clause id="18461">
    <literal><![CDATA[
      K(x,K(y,((z \ u) * w) / v5)) = K(x,K(y,((z / u) / w) * v5))
    ]]></literal>
    <justification jstring="[hyper(8828,a,18460,a)].">
      <j1 rule="hyper" parents="8828 18460"/>
    </justification>
  </clause>

  <clause id="18462">
    <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(65,a,17751,a(flip),b,18461,a),flip(a)].">
      <j1 rule="hyper" parents="65 17751 18461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18463">
    <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(16500,a,18462,a)].">
      <j1 rule="hyper" parents="16500 18462"/>
    </justification>
  </clause>

  <clause id="18464">
    <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(299,a,14987,a,b,18462,a),flip(a)].">
      <j1 rule="hyper" parents="299 14987 18462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18465">
    <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(18462(a,1),7985(a,1))].">
      <j1 rule="para" parents="18462 7985"/>
    </justification>
  </clause>

  <clause id="18466">
    <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),18463(a,1,2,2,2,2))].">
      <j1 rule="para" parents="12 18463"/>
    </justification>
  </clause>

  <clause id="18467">
    <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),18464(a,2,2))].">
      <j1 rule="para" parents="12 18464"/>
    </justification>
  </clause>

  <clause id="18468">
    <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(299,a,8789,a(flip),b,18454,a),flip(a)].">
      <j1 rule="hyper" parents="299 8789 18454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18469">
    <literal><![CDATA[
      K(x,K(y,z * ((1 / u) * w))) = K(x,K(y,(u / w) / z))
    ]]></literal>
    <justification jstring="[hyper(65,a,18425,a(flip),b,18468,a),flip(a)].">
      <j1 rule="hyper" parents="65 18425 18468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18471">
    <literal><![CDATA[
      K(x,K(y,z * ((1 / u) * w))) = K(x,K(y,(w / u) * z))
    ]]></literal>
    <justification jstring="[hyper(299,a,18421,a(flip),b,18469,a),flip(a)].">
      <j1 rule="hyper" parents="299 18421 18469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18472">
    <literal><![CDATA[
      K(x,K(y,z * L(u,w,1 / w))) = K(x,K(y,((w * u) / w) * z))
    ]]></literal>
    <justification jstring="[para(255(a,1),18471(a,1,2,2,2))].">
      <j1 rule="para" parents="255 18471"/>
    </justification>
  </clause>

  <clause id="18473">
    <literal><![CDATA[
      K(x,K(y,z * L(u,w,1 / w))) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(299,a,17137,a(flip),b,18472,a),flip(a)].">
      <j1 rule="hyper" parents="299 17137 18472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18475">
    <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(65,a,17756,a(flip),b,18473,a),flip(a)].">
      <j1 rule="hyper" parents="65 17756 18473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18477">
    <literal><![CDATA[
      K(x,K(y,(((1 / z) * u) * w) * v5)) = K(x,K(y,((u / z) * w) * v5))
    ]]></literal>
    <justification jstring="[para(103(a,1),18475(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="103 18475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18478">
    <literal><![CDATA[
      K(x,K(y,(z * ((1 / u) * w)) * v5)) = K(x,K(y,((w / u) * z) * v5))
    ]]></literal>
    <justification jstring="[hyper(17253,a,18477,a)].">
      <j1 rule="hyper" parents="17253 18477"/>
    </justification>
  </clause>

  <clause id="18479">
    <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(17169,a,18478,a),flip(a)].">
      <j1 rule="hyper" parents="17169 18478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18480">
    <literal><![CDATA[
      K(x,K(y,(z * ((1 / u) * w)) / v5)) = K(x,K(y,((w / u) * z) * (1 / v5)))
    ]]></literal>
    <justification jstring="[hyper(14703,a,18478,a)].">
      <j1 rule="hyper" parents="14703 18478"/>
    </justification>
  </clause>

  <clause id="18481">
    <literal><![CDATA[
      K(x,K(y,z * (u * ((1 / w) * v5)))) = K(x,K(y,z * ((v5 / w) * u)))
    ]]></literal>
    <justification jstring="[hyper(17169,a,18479,a),flip(a)].">
      <j1 rule="hyper" parents="17169 18479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18482">
    <literal><![CDATA[
      K(x,K(y,z * (((1 / u) * w) * v5))) = K(x,K(y,z * ((w / u) * v5)))
    ]]></literal>
    <justification jstring="[hyper(17249,a,18481,a)].">
      <j1 rule="hyper" parents="17249 18481"/>
    </justification>
  </clause>

  <clause id="18483">
    <literal><![CDATA[
      K(x,K(y,(z * ((1 / u) * w)) / v5)) = K(x,K(y,((w / u) * z) / v5))
    ]]></literal>
    <justification jstring="[hyper(299,a,12765,a(flip),b,18480,a),flip(a)].">
      <j1 rule="hyper" parents="299 12765 18480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18484">
    <literal><![CDATA[
      K(x,K(y,(z * ((1 / u) * w)) / v5)) = K(x,K(y,((u / w) / z) * v5))
    ]]></literal>
    <justification jstring="[hyper(299,a,18458,a(flip),b,18483,a),flip(a)].">
      <j1 rule="hyper" parents="299 18458 18483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18485">
    <literal><![CDATA[
      K(x,K(y,z / (u * ((1 / w) * v5)))) = K(x,K(y,((w / v5) / u) * z))
    ]]></literal>
    <justification jstring="[hyper(8828,a,18484,a)].">
      <j1 rule="hyper" parents="8828 18484"/>
    </justification>
  </clause>

  <clause id="18486">
    <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(14113(a,1),18485(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14113 18485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18487">
    <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(299,a,14940,a,b,18486,a),flip(a)].">
      <j1 rule="hyper" parents="299 14940 18486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18488">
    <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(299,a,18389,a(flip),b,18487,a),flip(a)].">
      <j1 rule="hyper" parents="299 18389 18487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18489">
    <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(7989(a,1),18488(a,2,3))].">
      <j1 rule="para" parents="7989 18488"/>
    </justification>
  </clause>

  <clause id="18490">
    <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(5816(a,1),18489(a,1,2,2,2,1))].">
      <j1 rule="para" parents="5816 18489"/>
    </justification>
  </clause>

  <clause id="18491">
    <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(6774(a,1),18490(a,1,2))].">
      <j1 rule="para" parents="6774 18490"/>
    </justification>
  </clause>

  <clause id="18492">
    <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(14398(a,1),18491(a,1,2))].">
      <j1 rule="para" parents="14398 18491"/>
    </justification>
  </clause>

  <clause id="18493">
    <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(9044(a,1),18492(a,1,2,2,1))].">
      <j1 rule="para" parents="9044 18492"/>
    </justification>
  </clause>

  <clause id="18494">
    <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(65,a,18482,a(flip),b,18493,a)].">
      <j1 rule="hyper" parents="65 18482 18493"/>
    </justification>
  </clause>

  <clause id="18495">
    <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(17205,a,18494,a)].">
      <j1 rule="hyper" parents="17205 18494"/>
    </justification>
  </clause>

  <clause id="18496">
    <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(7223(a,1),18495(a,2,3,2))].">
      <j1 rule="para" parents="7223 18495"/>
    </justification>
  </clause>

  <clause id="18497">
    <literal><![CDATA[
      K(x,K(y,((z / u) * w) * ((u / w) / z))) = a(w,u,K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(17133(a,1),18496(a,2,3))].">
      <j1 rule="para" parents="17133 18496"/>
    </justification>
  </clause>

  <clause id="18498">
    <literal><![CDATA[
      a(x,y,K(z,K(u / y,w / y))) = a(w,y,K(x,K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,18466,a(flip),b,18497,a)].">
      <j1 rule="hyper" parents="65 18466 18497"/>
    </justification>
  </clause>

  <clause id="18500">
    <literal><![CDATA[
      a(x,y \ z,K(u,K(y,w / (y \ z)))) = a(w,y \ z,K(x,K(u,z)))
    ]]></literal>
    <justification jstring="[para(76(a,1),18498(a,1,3,2,1))].">
      <j1 rule="para" parents="76 18498"/>
    </justification>
  </clause>

  <clause id="18501">
    <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(18426(a,1),18500(a,1,3))].">
      <j1 rule="para" parents="18426 18500"/>
    </justification>
  </clause>

  <clause id="18502">
    <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(7983(a,1),18501(a,1,3))].">
      <j1 rule="para" parents="7983 18501"/>
    </justification>
  </clause>

  <clause id="18503">
    <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(17647(a,1),18502(a,1,3))].">
      <j1 rule="para" parents="17647 18502"/>
    </justification>
  </clause>

  <clause id="18504">
    <literal><![CDATA[
      a(x,y \ z,K(u,K(w,z))) = a(u,z,K(y,K(w,x / z)))
    ]]></literal>
    <justification jstring="[hyper(65,a,14981,a(flip),b,18503,a),flip(a)].">
      <j1 rule="hyper" parents="65 14981 18503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18505">
    <literal><![CDATA[
      a(x,y \ z,K(u,K(z,w))) = a(u,z,K(y,K(w,x / z)))
    ]]></literal>
    <justification jstring="[para(8004(a,1),18504(a,1,3))].">
      <j1 rule="para" parents="8004 18504"/>
    </justification>
  </clause>

  <clause id="18506">
    <literal><![CDATA[
      a(x,y / z,K(u,K(y,w))) = a(u,y,K(z,K(w,x / y)))
    ]]></literal>
    <justification jstring="[hyper(65,a,18368,a,b,18505,a)].">
      <j1 rule="hyper" parents="65 18368 18505"/>
    </justification>
  </clause>

  <clause id="18507">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w / y))) = a(y,z,K(x,K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(18391,a,18506,a),flip(a)].">
      <j1 rule="hyper" parents="18391 18506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18508">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w / y))) = a(y,z,K(w,K(x,u)))
    ]]></literal>
    <justification jstring="[para(7983(a,1),18507(a,2,3))].">
      <j1 rule="para" parents="7983 18507"/>
    </justification>
  </clause>

  <clause id="18509">
    <literal><![CDATA[
      K(x,K(y,((z / u) / (w * z)) * (w * u))) = a(z,y,K(u,K(x,w)))
    ]]></literal>
    <justification jstring="[hyper(18465,a,18508,a)].">
      <j1 rule="hyper" parents="18465 18508"/>
    </justification>
  </clause>

  <clause id="18510">
    <literal><![CDATA[
      K(x,K(y,((z / u) / (w * z)) * (w * u))) = a(z,y,K(x,K(w,u)))
    ]]></literal>
    <justification jstring="[para(7989(a,2),18509(a,2,3))].">
      <j1 rule="para" parents="7989 18509"/>
    </justification>
  </clause>

  <clause id="18511">
    <literal><![CDATA[
      a(x,y,K(z,K(u,y / w))) = a(w,x,K(z,K(u,y)))
    ]]></literal>
    <justification jstring="[hyper(65,a,18467,a(flip),b,18510,a)].">
      <j1 rule="hyper" parents="65 18467 18510"/>
    </justification>
  </clause>

  <clause id="18512">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w / y))) = a(w,x,K(z,K(u,y)))
    ]]></literal>
    <justification jstring="[para(8791(a,1),18511(a,1,3))].">
      <j1 rule="para" parents="8791 18511"/>
    </justification>
  </clause>

  <clause id="18513">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w / y))) = a(w,x,K(z,K(y,u)))
    ]]></literal>
    <justification jstring="[para(8004(a,1),18512(a,2,3))].">
      <j1 rule="para" parents="8004 18512"/>
    </justification>
  </clause>

  <clause id="18514">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = a(u,z,K(x,K(y,w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,18508,a(flip),b,18513,a),flip(a)].">
      <j1 rule="hyper" parents="65 18508 18513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18515">
    <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(18514(a,1),14938(a,1,1))].">
      <j1 rule="para" parents="18514 14938"/>
    </justification>
  </clause>

  <clause id="18516">
    <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(7983(a,1),18515(a,1,2))].">
      <j1 rule="para" parents="7983 18515"/>
    </justification>
  </clause>

  <clause id="18517">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(x,K(z,L(y,w,u)))
    ]]></literal>
    <justification jstring="[hyper(15090,a,18516,a),flip(a)].">
      <j1 rule="hyper" parents="15090 18516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18518">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(x,K(y,L(z,w,u)))
    ]]></literal>
    <justification jstring="[hyper(9021,a,18517,a)].">
      <j1 rule="hyper" parents="9021 18517"/>
    </justification>
  </clause>

  <clause id="18519">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,z,y))) = K(x,K(w,(u / z) * y))
    ]]></literal>
    <justification jstring="[hyper(299,a,18453,a(flip),b,18518,a),flip(a)].">
      <j1 rule="hyper" parents="299 18453 18518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18520">
    <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(780(a,1),18518(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="780 18518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18521">
    <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(10261(a,1),18518(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10261 18518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18522">
    <literal><![CDATA[
      K(x,K(y,(z * u) / w)) = K(x,K(y,(z / w) * u))
    ]]></literal>
    <justification jstring="[hyper(18436,a,18519,a)].">
      <j1 rule="hyper" parents="18436 18519"/>
    </justification>
  </clause>

  <clause id="18523">
    <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(18521(a,2),8807(a,1))].">
      <j1 rule="para" parents="18521 8807"/>
    </justification>
  </clause>

  <clause id="18524">
    <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(299,a,16335,a,b,18520,a),flip(a)].">
      <j1 rule="hyper" parents="299 16335 18520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18525">
    <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(299,a,18522,a(flip),b,18524,a),flip(a)].">
      <j1 rule="hyper" parents="299 18522 18524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18526">
    <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(299,a,18422,a(flip),b,18525,a),flip(a)].">
      <j1 rule="hyper" parents="299 18422 18525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18529">
    <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(8172(a,1),18526(a,2,2))].">
      <j1 rule="para" parents="8172 18526"/>
    </justification>
  </clause>

  <clause id="18530">
    <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(299,a,16328,a(flip),b,18529,a),flip(a)].">
      <j1 rule="hyper" parents="299 16328 18529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18533">
    <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(65,a,15167,a(flip),b,18530,a)].">
      <j1 rule="hyper" parents="65 15167 18530"/>
    </justification>
  </clause>

  <clause id="18534">
    <literal><![CDATA[
      K(x,K(y,L(1 / z,z,u))) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(18523,a,18533,a),flip(a)].">
      <j1 rule="hyper" parents="18523 18533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18536">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(x,K(y,1 / z))
    ]]></literal>
    <justification jstring="[para(7851(a,1),18534(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7851 18534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18539">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,8789,a(flip),b,18536,a),flip(a)].">
      <j1 rule="hyper" parents="299 8789 18536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18543">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(11919,a,18539,a)].">
      <j1 rule="hyper" parents="11919 18539"/>
    </justification>
  </clause>

  <clause id="18544">
    <literal><![CDATA[
      K(x,K(L(y,z,u),w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(8922,a,18539,a)].">
      <j1 rule="hyper" parents="8922 18539"/>
    </justification>
  </clause>

  <clause id="18549">
    <literal><![CDATA[
      K(x,K(y,(z \ u) \ w)) = K(x,K(y,u \ (z * w)))
    ]]></literal>
    <justification jstring="[para(520(a,1),18539(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="520 18539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18550">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w))) = x * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(18539(a,1),5083(a,2,2))].">
      <j1 rule="para" parents="18539 5083"/>
    </justification>
  </clause>

  <clause id="18551">
    <literal><![CDATA[
      T(x / T(K(y,L(z,u,w)),v5),K(K(y,L(z,u,w)),v5)) = K(v5,K(y,z)) * (x / K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(18539(a,1),6925(a,2,1))].">
      <j1 rule="para" parents="18539 6925"/>
    </justification>
  </clause>

  <clause id="18554">
    <literal><![CDATA[
      (x * y) * K(z,K(u,w)) = x * (y * K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(18539(a,1),8915(a,1,2))].">
      <j1 rule="para" parents="18539 8915"/>
    </justification>
  </clause>

  <clause id="18555">
    <literal><![CDATA[
      (x * y) * K(z,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x * (y * K(z,K(u,w))) = v5
    ]]></literal>
    <justification jstring="[para(18539(a,1),8916(a,1,2))].">
      <j1 rule="para" parents="18539 8916"/>
    </justification>
  </clause>

  <clause id="18557">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(15482(a,2),18539(a,1,2))].">
      <j1 rule="para" parents="15482 18539"/>
    </justification>
  </clause>

  <clause id="18558">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * w) = u * (w * K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(18539(a,1),16504(a,1,1))].">
      <j1 rule="para" parents="18539 16504"/>
    </justification>
  </clause>

  <clause id="18561">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = 1
    ]]></literal>
    <justification jstring="[hyper(55,a,18543,a)].">
      <j1 rule="hyper" parents="55 18543"/>
    </justification>
  </clause>

  <clause id="18562">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * w = K(x,K(y,z)) * (u * w)
    ]]></literal>
    <justification jstring="[para(18543(a,1),15507(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18543 15507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18563">
    <literal><![CDATA[
      a(x,y,K(K(z,u),w)) = 1
    ]]></literal>
    <justification jstring="[hyper(15009,a,18561,a)].">
      <j1 rule="hyper" parents="15009 18561"/>
    </justification>
  </clause>

  <clause id="18564">
    <literal><![CDATA[
      a(K(x,y),z,K(u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(14972,a,18561,a)].">
      <j1 rule="hyper" parents="14972 18561"/>
    </justification>
  </clause>

  <clause id="18567">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,w) = 1
    ]]></literal>
    <justification jstring="[hyper(65,a,14860,a,b,18561,a)].">
      <j1 rule="hyper" parents="65 14860 18561"/>
    </justification>
  </clause>

  <clause id="18571">
    <literal><![CDATA[
      K(a(x,y,K(z,u)),w) = 1
    ]]></literal>
    <justification jstring="[hyper(14569,a,18563,a)].">
      <j1 rule="hyper" parents="14569 18563"/>
    </justification>
  </clause>

  <clause id="18574">
    <literal><![CDATA[
      L(K(x,y),z,K(u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(54,a,18564,a)].">
      <j1 rule="hyper" parents="54 18564"/>
    </justification>
  </clause>

  <clause id="18578">
    <literal><![CDATA[
      L(x,y,K(z,K(u,w))) = x
    ]]></literal>
    <justification jstring="[hyper(54,a,18567,a)].">
      <j1 rule="hyper" parents="54 18567"/>
    </justification>
  </clause>

  <clause id="18581">
    <literal><![CDATA[
      T(a(x,y,K(z,u)),w) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,18571,a)].">
      <j1 rule="hyper" parents="58 18571"/>
    </justification>
  </clause>

  <clause id="18582">
    <literal><![CDATA[
      L(x,y,T(z,K(u,w))) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(6684,a,18578,a)].">
      <j1 rule="hyper" parents="6684 18578"/>
    </justification>
  </clause>

  <clause id="18583">
    <literal><![CDATA[
      (K(x,K(y,z)) \ u) \ w = u \ (K(x,K(y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(615,a,18578,a),flip(a)].">
      <j1 rule="hyper" parents="615 18578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18584">
    <literal><![CDATA[
      L(x,y,K(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      x = v5
    ]]></literal>
    <justification jstring="[para(18578(a,1),52(a,2))].">
      <j1 rule="para" parents="18578 52"/>
    </justification>
  </clause>

  <clause id="18585">
    <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(18578(a,1),483(a,1,2,2,1))].">
      <j1 rule="para" parents="18578 483"/>
    </justification>
  </clause>

  <clause id="18586">
    <literal><![CDATA[
      K(L(x,y,K(z,u)),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(12009,a,18574,a)].">
      <j1 rule="hyper" parents="12009 18574"/>
    </justification>
  </clause>

  <clause id="18587">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(11995,a,18574,a)].">
      <j1 rule="hyper" parents="11995 18574"/>
    </justification>
  </clause>

  <clause id="18588">
    <literal><![CDATA[
      K(x,T(y \ z,K(u,w) \ y)) = K(x,(K(w,u) * z) / (K(w,u) * y))
    ]]></literal>
    <justification jstring="[hyper(65,a,12014,a(flip),b,18574,a),flip(a)].">
      <j1 rule="hyper" parents="65 12014 18574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18589">
    <literal><![CDATA[
      K(x,(K(y,z) \ u) \ w) = K(x,u \ (K(y,z) * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,11905,a(flip),b,18574,a),flip(a)].">
      <j1 rule="hyper" parents="65 11905 18574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18590">
    <literal><![CDATA[
      K((K(x,y) * z) \ u,w) = K(z \ (K(y,x) * u),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,7425,a(flip),b,18574,a),flip(a)].">
      <j1 rule="hyper" parents="65 7425 18574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18592">
    <literal><![CDATA[
      L(L(K(x,y),z,u),w,K(v5,v6)) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(18574(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18574 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18593">
    <literal><![CDATA[
      (K(x,y) * z) * K(u,w) = K(x,y) * (z * K(u,w))
    ]]></literal>
    <justification jstring="[para(18574(a,1),94(a,1,2))].">
      <j1 rule="para" parents="18574 94"/>
    </justification>
  </clause>

  <clause id="18595">
    <literal><![CDATA[
      L(K(x,y),z,L(K(u,w),v5,v6)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6131(a,1),18574(a,1,3))].">
      <j1 rule="para" parents="6131 18574"/>
    </justification>
  </clause>

  <clause id="18598">
    <literal><![CDATA[
      K((x * K(y,z)) \ ((x * u) * K(y,z)),w) = K(u * K(x,u),T(w,x))
    ]]></literal>
    <justification jstring="[hyper(17121,a,18586,a)].">
      <j1 rule="hyper" parents="17121 18586"/>
    </justification>
  </clause>

  <clause id="18600">
    <literal><![CDATA[
      K(x,T(y * (z * u),K(w,L(u,z,y))) \ (K(w,L(u,z,y)) \ v5)) = K(x,(y * (z * (u * K(w,u)))) \ v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,15675,a(flip),b,18587,a)].">
      <j1 rule="hyper" parents="65 15675 18587"/>
    </justification>
  </clause>

  <clause id="18602">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ w) = K(x,u \ (K(z,y) * w))
    ]]></literal>
    <justification jstring="[para(5442(a,1),18587(a,1,2))].">
      <j1 rule="para" parents="5442 18587"/>
    </justification>
  </clause>

  <clause id="18603">
    <literal><![CDATA[
      K(x,L(y,z,T(u,w))) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(6685(a,1),18587(a,1,2))].">
      <j1 rule="para" parents="6685 18587"/>
    </justification>
  </clause>

  <clause id="18604">
    <literal><![CDATA[
      L(x,y,K(z,u) * w) = L(x,y,w * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,13439,a(flip),b,18582,a),flip(a)].">
      <j1 rule="hyper" parents="65 13439 18582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18605">
    <literal><![CDATA[
      L(x,y,T(z,T(u,w))) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(7140(a,1),18582(a,1,3))].">
      <j1 rule="para" parents="7140 18582"/>
    </justification>
  </clause>

  <clause id="18606">
    <literal><![CDATA[
      L(x,y,z * (u * K(z,w))) = L(x,y,T(z,w) * u)
    ]]></literal>
    <justification jstring="[para(8370(a,1),18582(a,1,3))].">
      <j1 rule="para" parents="8370 18582"/>
    </justification>
  </clause>

  <clause id="18607">
    <literal><![CDATA[
      T(K(x,L(y,z,u)),w) * K(v5 / y,K(x,L(y,z,u))) = K(x,K(y,w)) * ((v5 / T(y,L(x,z,u))) / (v5 / y))
    ]]></literal>
    <justification jstring="[para(18544(a,1),12704(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18544 12704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18614">
    <literal><![CDATA[
      T(K(x,y),R(z,u,w)) = K(x,y) * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(18557(a,1),7964(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18557 7964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18618">
    <literal><![CDATA[
      T(x,a(y,z,K(u,w))) = x
    ]]></literal>
    <justification jstring="[hyper(56,a,18581,a)].">
      <j1 rule="hyper" parents="56 18581"/>
    </justification>
  </clause>

  <clause id="18619">
    <literal><![CDATA[
      a(x,y,K(z,u)) * w = w * a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(18581(a,1),107(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18581 107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18620">
    <literal><![CDATA[
      x * a(y,z,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(y,z,K(u,w)) * x = v5
    ]]></literal>
    <justification jstring="[para(18581(a,1),276(a,1,2))].">
      <j1 rule="para" parents="18581 276"/>
    </justification>
  </clause>

  <clause id="18623">
    <literal><![CDATA[
      T(x,a(K(y,z),u,w)) = x
    ]]></literal>
    <justification jstring="[para(14164(a,2),18618(a,1,2))].">
      <j1 rule="para" parents="14164 18618"/>
    </justification>
  </clause>

  <clause id="18624">
    <literal><![CDATA[
      T(x,K(a(y,z,u),w)) = x
    ]]></literal>
    <justification jstring="[para(14556(a,1),18618(a,1,2))].">
      <j1 rule="para" parents="14556 18618"/>
    </justification>
  </clause>

  <clause id="18626">
    <literal><![CDATA[
      (a(K(x,y),z,u) \ w) * a(K(x,y),z,u) = w
    ]]></literal>
    <justification jstring="[hyper(2379,a,18623,a)].">
      <j1 rule="hyper" parents="2379 18623"/>
    </justification>
  </clause>

  <clause id="18629">
    <literal><![CDATA[
      K(a(x,y,z),u) * (w \ 1) = w \ a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(14690,a,18624,a)].">
      <j1 rule="hyper" parents="14690 18624"/>
    </justification>
  </clause>

  <clause id="18631">
    <literal><![CDATA[
      T(x,a(y,z,u) * w) = T(x,w * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(13259,a,18624,a),flip(a)].">
      <j1 rule="hyper" parents="13259 18624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18633">
    <literal><![CDATA[
      T(x,y / a(z,u,w)) = T(x,a(z,u,w) \ y)
    ]]></literal>
    <justification jstring="[hyper(8996,a,18624,a),flip(a)].">
      <j1 rule="hyper" parents="8996 18624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18634">
    <literal><![CDATA[
      K(x,T(y,a(z,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8387,a,18624,a)].">
      <j1 rule="hyper" parents="8387 18624"/>
    </justification>
  </clause>

  <clause id="18635">
    <literal><![CDATA[
      T(x,a(y,z,u) / w) = T(x,w \ a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(8091,a,18624,a),flip(a)].">
      <j1 rule="hyper" parents="8091 18624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18638">
    <literal><![CDATA[
      T(x,T(a(y,z,u),w)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(7154,a,18624,a)].">
      <j1 rule="hyper" parents="7154 18624"/>
    </justification>
  </clause>

  <clause id="18640">
    <literal><![CDATA[
      T(x,K(a(y,z,u),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x = v5
    ]]></literal>
    <justification jstring="[para(18624(a,1),51(a,2))].">
      <j1 rule="para" parents="18624 51"/>
    </justification>
  </clause>

  <clause id="18644">
    <literal><![CDATA[
      T(x,y * a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,a(z,u,w) * y) = v5
    ]]></literal>
    <justification jstring="[para(18624(a,1),13236(a,1,1))].">
      <j1 rule="para" parents="18624 13236"/>
    </justification>
  </clause>

  <clause id="18645">
    <literal><![CDATA[
      T(x,a(y,z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,w * a(y,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(18624(a,1),13257(a,1,1))].">
      <j1 rule="para" parents="18624 13257"/>
    </justification>
  </clause>

  <clause id="18646">
    <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(18624(a,1),15769(a,1,2,1,2))].">
      <j1 rule="para" parents="18624 15769"/>
    </justification>
  </clause>

  <clause id="18650">
    <literal><![CDATA[
      K(x,y) * a(z,u,w) = a(z,u,w) * K(x,y)
    ]]></literal>
    <justification jstring="[para(18634(a,1),7507(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18634 7507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18652">
    <literal><![CDATA[
      K(x / a(y,z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(a(y,z,u) \ x,w) = v5
    ]]></literal>
    <justification jstring="[para(18634(a,1),7801(a,1))].">
      <j1 rule="para" parents="18634 7801"/>
    </justification>
  </clause>

  <clause id="18653">
    <literal><![CDATA[
      K(x,T(y,a(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(18634(a,1),8171(a,1))].">
      <j1 rule="para" parents="18634 8171"/>
    </justification>
  </clause>

  <clause id="18654">
    <literal><![CDATA[
      K(a(x,y,z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(u * a(x,y,z),w) = v5
    ]]></literal>
    <justification jstring="[para(18634(a,1),13182(a,1))].">
      <j1 rule="para" parents="18634 13182"/>
    </justification>
  </clause>

  <clause id="18655">
    <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(18634(a,1),13245(a,1))].">
      <j1 rule="para" parents="18634 13245"/>
    </justification>
  </clause>

  <clause id="18656">
    <literal><![CDATA[
      K(x,y) * (a(z,u,w) \ 1) = a(z,u,w) \ K(x,y)
    ]]></literal>
    <justification jstring="[para(18634(a,1),14713(a,1,1))].">
      <j1 rule="para" parents="18634 14713"/>
    </justification>
  </clause>

  <clause id="18657">
    <literal><![CDATA[
      T(x,T(y,a(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = v5
    ]]></literal>
    <justification jstring="[para(8056(a,1),18640(a,1))].">
      <j1 rule="para" parents="8056 18640"/>
    </justification>
  </clause>

  <clause id="18658">
    <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(65,a,11905,a(flip),b,18595,a),flip(a)].">
      <j1 rule="hyper" parents="65 11905 18595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18659">
    <literal><![CDATA[
      (L(K(x,y),z,u) * w) * K(v5,v6) = L(K(x,y),z,u) * (w * K(v5,v6))
    ]]></literal>
    <justification jstring="[para(18595(a,1),94(a,1,2))].">
      <j1 rule="para" parents="18595 94"/>
    </justification>
  </clause>

  <clause id="18660">
    <literal><![CDATA[
      K((T(x,y) * z) \ u,L(w,z,x)) = K(z \ (T(x,y) \ u),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,15631,a(flip),b,18603,a),flip(a)].">
      <j1 rule="hyper" parents="65 15631 18603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18661">
    <literal><![CDATA[
      K((T(x,y) \ z) \ u,L(w,z,x)) = K(z \ (T(x,y) * u),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,14989,a(flip),b,18603,a),flip(a)].">
      <j1 rule="hyper" parents="65 14989 18603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18662">
    <literal><![CDATA[
      K((x / y) \ (T(x,z) \ u),L(w,x / y,x)) = K((x * (T(x,z) / y)) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,14467,a(flip),b,18603,a),flip(a)].">
      <j1 rule="hyper" parents="65 14467 18603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18663">
    <literal><![CDATA[
      K(x,L(y,z,u / w)) = K(x,L(y,z,w \ u))
    ]]></literal>
    <justification jstring="[para(109(a,1),18603(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="109 18603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18664">
    <literal><![CDATA[
      K(x,L(y,1 / z,T(u,w))) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(2521(a,1),18603(a,2,2))].">
      <j1 rule="para" parents="2521 18603"/>
    </justification>
  </clause>

  <clause id="18665">
    <literal><![CDATA[
      L(x,y,T(T(z,u) / w,z)) = L(x,y,w \ T(z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,13447,a(flip),b,18605,a),flip(a)].">
      <j1 rule="hyper" parents="65 13447 18605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18666">
    <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(8119(a,1),18653(a,1))].">
      <j1 rule="para" parents="8119 18653"/>
    </justification>
  </clause>

  <clause id="18667">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,5083,a,b,18550,a),flip(a)].">
      <j1 rule="hyper" parents="299 5083 18550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18668">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = v5
    ]]></literal>
    <justification jstring="[para(18550(a,2),5087(a,1))].">
      <j1 rule="para" parents="18550 5087"/>
    </justification>
  </clause>

  <clause id="18669">
    <literal><![CDATA[
      T(x,K(y,L(z / u,w,v5))) = x * K(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[para(16335(a,1),18550(a,2,2))].">
      <j1 rule="para" parents="16335 18550"/>
    </justification>
  </clause>

  <clause id="18671">
    <literal><![CDATA[
      T(x,L(K(y,z),u,w)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,9160,a,b,18667,a)].">
      <j1 rule="hyper" parents="65 9160 18667"/>
    </justification>
  </clause>

  <clause id="18672">
    <literal><![CDATA[
      T(x * (y * K(z,u)),K(z,u)) = ((x * (y * K(z,u))) \ (x * y)) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,12075,a(flip),b,18667,a),flip(a)].">
      <j1 rule="hyper" parents="65 12075 18667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18673">
    <literal><![CDATA[
      T(x,K(y,(z \ u) \ w)) = T(x,K(y,u \ (z * w)))
    ]]></literal>
    <justification jstring="[para(520(a,1),18667(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="520 18667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18674">
    <literal><![CDATA[
      T(x / L(K(y,z),u,w),K(y,z)) = L(K(y,z),u,w) \ x
    ]]></literal>
    <justification jstring="[hyper(400,a,18671,a),flip(a)].">
      <j1 rule="hyper" parents="400 18671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18676">
    <literal><![CDATA[
      (T(x,K(y,z)) * K(u,z)) * (K(z,u) * L(K(y,z),w,v5)) = x * ((x * L(K(y,z),w,v5)) / x)
    ]]></literal>
    <justification jstring="[para(18671(a,1),10177(a,1,1,1))].">
      <j1 rule="para" parents="18671 10177"/>
    </justification>
  </clause>

  <clause id="18678">
    <literal><![CDATA[
      (x * (K(y,z) * u)) \ ((x * K(y,z)) * (L(u,K(y,z),x) * w)) = L(w,L(u,K(y,z),x),K(y,z) * x)
    ]]></literal>
    <justification jstring="[hyper(299,a,483,a,b,18604,a)].">
      <j1 rule="hyper" parents="299 483 18604"/>
    </justification>
  </clause>

  <clause id="18679">
    <literal><![CDATA[
      L(x,K(y,z),u * K(w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,K(z,y),K(w,v5) * u) = v6
    ]]></literal>
    <justification jstring="[para(18604(a,1),7213(a,1))].">
      <j1 rule="para" parents="18604 7213"/>
    </justification>
  </clause>

  <clause id="18680">
    <literal><![CDATA[
      L(x,y,K(z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,w * K(u,z)) = v5
    ]]></literal>
    <justification jstring="[para(18604(a,2),9425(a,1))].">
      <j1 rule="para" parents="18604 9425"/>
    </justification>
  </clause>

  <clause id="18681">
    <literal><![CDATA[
      L(x,y,K(z,u * u) * (w * v5)) = L(x,y,w * (v5 * K(z,u * u)))
    ]]></literal>
    <justification jstring="[para(11965(a,1),18604(a,2,3))].">
      <j1 rule="para" parents="11965 18604"/>
    </justification>
  </clause>

  <clause id="18682">
    <literal><![CDATA[
      x / a(y,z,K(u,w)) = a(w,z,K(u,y)) * x
    ]]></literal>
    <justification jstring="[hyper(299,a,14880,a,b,18619,a)].">
      <j1 rule="hyper" parents="299 14880 18619"/>
    </justification>
  </clause>

  <clause id="18683">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ w = w * a(u,y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,14881,a,b,18619,a)].">
      <j1 rule="hyper" parents="65 14881 18619"/>
    </justification>
  </clause>

  <clause id="18685">
    <literal><![CDATA[
      (1 / x) * a(y,z,K(u,w)) = a(y,z,K(u,w)) / x
    ]]></literal>
    <justification jstring="[hyper(65,a,14673,a(flip),b,18619,a),flip(a)].">
      <j1 rule="hyper" parents="65 14673 18619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18686">
    <literal><![CDATA[
      K(x,a(y,z,u)) * w = w * a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[para(14871(a,1),18619(a,1,1))].">
      <j1 rule="para" parents="14871 18619"/>
    </justification>
  </clause>

  <clause id="18687">
    <literal><![CDATA[
      a(K(x,y),z,u) \ (w * a(u,z,K(y,x))) = w
    ]]></literal>
    <justification jstring="[hyper(14934,a,18626,a)].">
      <j1 rule="hyper" parents="14934 18626"/>
    </justification>
  </clause>

  <clause id="18688">
    <literal><![CDATA[
      a(K(x,y),z,u) \ w = w * a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(12902,a,18626,a),flip(a)].">
      <j1 rule="hyper" parents="12902 18626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18689">
    <literal><![CDATA[
      T(x,a(y,z,u) \ w) / x = K(x,w / a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(120,a,18633,a(flip),b,5096,a(flip))].">
      <j1 rule="hyper" parents="120 18633 5096"/>
    </justification>
  </clause>

  <clause id="18690">
    <literal><![CDATA[
      T(x,a(y,z,u) \ w) \ x = K(w / a(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(18633(a,1),5024(a,2,1)),flip(a)].">
      <j1 rule="para" parents="18633 5024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18693">
    <literal><![CDATA[
      (K(x,y) * a(z,u,w)) \ y = K(y,x) * (a(z,u,w) \ y)
    ]]></literal>
    <justification jstring="[para(18650(a,2),14588(a,1,1))].">
      <j1 rule="para" parents="18650 14588"/>
    </justification>
  </clause>

  <clause id="18694">
    <literal><![CDATA[
      K(x,L(y,1 / z,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,18603,a(flip),b,18664,a)].">
      <j1 rule="hyper" parents="65 18603 18664"/>
    </justification>
  </clause>

  <clause id="18695">
    <literal><![CDATA[
      K(x,L(y,z \ 1,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(76(a,1),18694(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="76 18694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18696">
    <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(281(a,1),18668(a,1,2,2))].">
      <j1 rule="para" parents="281 18668"/>
    </justification>
  </clause>

  <clause id="18697">
    <literal><![CDATA[
      x / (x * a(y,z,K(u,w))) = a(w,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(304,a,18682,a)].">
      <j1 rule="hyper" parents="304 18682"/>
    </justification>
  </clause>

  <clause id="18698">
    <literal><![CDATA[
      (a(x,y,K(z,u)) * w) * a(u,y,K(z,x)) = w
    ]]></literal>
    <justification jstring="[hyper(143,a,18682,a)].">
      <j1 rule="hyper" parents="143 18682"/>
    </justification>
  </clause>

  <clause id="18700">
    <literal><![CDATA[
      x * (y * a(x,z,K(u,w))) = T(x,a(w,z,u)) * y
    ]]></literal>
    <justification jstring="[para(18686(a,1),5055(a,1,2))].">
      <j1 rule="para" parents="18686 5055"/>
    </justification>
  </clause>

  <clause id="18702">
    <literal><![CDATA[
      a(T(x \ y,y),z,K(u,w)) = v5 / (v5 * a(w,z,K(u,y / x)))
    ]]></literal>
    <justification jstring="[para(8108(a,1),18697(a,1,2,2,3)),flip(a)].">
      <j1 rule="para" parents="8108 18697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18703">
    <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(18592(a,1),6081(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18592 6081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18704">
    <literal><![CDATA[
      T(K(x,y),R(z,u,w)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(299,a,7964,a(flip),b,18614,a),flip(a)].">
      <j1 rule="hyper" parents="299 7964 18614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18705">
    <literal><![CDATA[
      T(K(x,y),L(z,u,w)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(65,a,15478,a(flip),b,18704,a)].">
      <j1 rule="hyper" parents="65 15478 18704"/>
    </justification>
  </clause>

  <clause id="18706">
    <literal><![CDATA[
      K(x,T(y,L(z,u,w))) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(7714,a,18705,a)].">
      <j1 rule="hyper" parents="7714 18705"/>
    </justification>
  </clause>

  <clause id="18707">
    <literal><![CDATA[
      K(x,T(y,L(z,u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,7489,a,b,18706,a),flip(a)].">
      <j1 rule="hyper" parents="299 7489 18706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18710">
    <literal><![CDATA[
      K(x,T(y,(z * u) \ w)) = K(x,T(y,u \ (z \ w)))
    ]]></literal>
    <justification jstring="[para(281(a,1),18707(a,1,2,2))].">
      <j1 rule="para" parents="281 18707"/>
    </justification>
  </clause>

  <clause id="18712">
    <literal><![CDATA[
      T(x,T(y,L(z,u,w))) = x * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(18707(a,1),5083(a,2,2))].">
      <j1 rule="para" parents="18707 5083"/>
    </justification>
  </clause>

  <clause id="18713">
    <literal><![CDATA[
      L(x,y,z) * K(u,T(w,x)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(u,w) * L(x,y,z) = v5
    ]]></literal>
    <justification jstring="[para(18707(a,1),7509(a,1,2))].">
      <j1 rule="para" parents="18707 7509"/>
    </justification>
  </clause>

  <clause id="18714">
    <literal><![CDATA[
      K(x * L(y,z,u),T(w,y)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(L(y,z,u) * x,w) = v5
    ]]></literal>
    <justification jstring="[para(18707(a,1),13187(a,1))].">
      <j1 rule="para" parents="18707 13187"/>
    </justification>
  </clause>

  <clause id="18715">
    <literal><![CDATA[
      K(x,T(y,R(z,u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(15478(a,2),18707(a,1,2))].">
      <j1 rule="para" parents="15478 18707"/>
    </justification>
  </clause>

  <clause id="18716">
    <literal><![CDATA[
      K(x * R(y,z,u),T(w,y)) = K(R(y,z,u) * x,w)
    ]]></literal>
    <justification jstring="[hyper(13187,a,18715,a),flip(a)].">
      <j1 rule="hyper" parents="13187 18715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18717">
    <literal><![CDATA[
      K(x * R(y,z,u),T(w,y)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(R(y,z,u) * x,w) = v5
    ]]></literal>
    <justification jstring="[para(18715(a,1),13187(a,1))].">
      <j1 rule="para" parents="18715 13187"/>
    </justification>
  </clause>

  <clause id="18718">
    <literal><![CDATA[
      T(x,T(y,L(z,u,w))) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,5083,a,b,18712,a),flip(a)].">
      <j1 rule="hyper" parents="299 5083 18712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18719">
    <literal><![CDATA[
      T(x,T(y,L(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = v5
    ]]></literal>
    <justification jstring="[para(18712(a,2),5087(a,1))].">
      <j1 rule="para" parents="18712 5087"/>
    </justification>
  </clause>

  <clause id="18720">
    <literal><![CDATA[
      K(x,L(y,z,u)) * T(x,T(w,y)) = T(T(x,w),L(y,z,u))
    ]]></literal>
    <justification jstring="[para(18718(a,1),7718(a,1,2))].">
      <j1 rule="para" parents="18718 7718"/>
    </justification>
  </clause>

  <clause id="18722">
    <literal><![CDATA[
      K(x,K(y,z \ (u * w))) = K(x,K(y,(u \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(16252,a,18549,a),flip(a)].">
      <j1 rule="hyper" parents="16252 18549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18724">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * w) = u * (w * K(y,K(x,z)))
    ]]></literal>
    <justification jstring="[hyper(16612,a,18554,a)].">
      <j1 rule="hyper" parents="16612 18554"/>
    </justification>
  </clause>

  <clause id="18726">
    <literal><![CDATA[
      x \ (y * K(z,K(u,w))) = (x \ y) * K(z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(1020,a,18554,a)].">
      <j1 rule="hyper" parents="1020 18554"/>
    </justification>
  </clause>

  <clause id="18728">
    <literal><![CDATA[
      (x * (K(y,K(z,u)) * (w * v5))) \ ((x * w) * (v5 * K(y,K(z,u)))) = a(x,w,v5 * K(y,K(z,u)))
    ]]></literal>
    <justification jstring="[para(18558(a,2),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="18558 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18729">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * w) = u * (K(x,K(y,z)) * w)
    ]]></literal>
    <justification jstring="[para(16341(a,2),18558(a,2,2))].">
      <j1 rule="para" parents="16341 18558"/>
    </justification>
  </clause>

  <clause id="18732">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * (w * v5)) = u * (w * (v5 * K(x,K(y,z))))
    ]]></literal>
    <justification jstring="[para(18554(a,1),18558(a,2,2))].">
      <j1 rule="para" parents="18554 18558"/>
    </justification>
  </clause>

  <clause id="18733">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * w = u * (w * K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(299,a,18558,a(flip),b,18562,a),flip(a)].">
      <j1 rule="hyper" parents="299 18558 18562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18735">
    <literal><![CDATA[
      K(x,K(y,z)) * ((x \ u) * w) = (T(x,K(y,z)) \ u) * w
    ]]></literal>
    <justification jstring="[para(8029(a,1),18562(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8029 18562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18736">
    <literal><![CDATA[
      (x * K(y,K(z,u))) * w = K(y,K(z,u)) * (x * w)
    ]]></literal>
    <justification jstring="[para(16341(a,1),18562(a,1,1))].">
      <j1 rule="para" parents="16341 18562"/>
    </justification>
  </clause>

  <clause id="18737">
    <literal><![CDATA[
      (K(x,K(y,z)) \ u) \ w = u \ (K(x,K(y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(8028(a,2),18583(a,2,2))].">
      <j1 rule="para" parents="8028 18583"/>
    </justification>
  </clause>

  <clause id="18738">
    <literal><![CDATA[
      K(x,(K(y,z) \ u) \ w) = K(x,u \ (K(z,y) \ w))
    ]]></literal>
    <justification jstring="[para(5426(a,2),18589(a,2,2,2))].">
      <j1 rule="para" parents="5426 18589"/>
    </justification>
  </clause>

  <clause id="18739">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,w) = K(x \ (K(z,y) * u),w)
    ]]></literal>
    <justification jstring="[hyper(16806,a,18590,a)].">
      <j1 rule="hyper" parents="16806 18590"/>
    </justification>
  </clause>

  <clause id="18741">
    <literal><![CDATA[
      K((x / y) \ (K(z,x) * u),w) = K((T(x,z) / y) \ u,w)
    ]]></literal>
    <justification jstring="[para(14430(a,1),18590(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="14430 18590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18742">
    <literal><![CDATA[
      (K(x,y) * z) * K(u,T(w,z)) = K(x,y) * (K(u,w) * z)
    ]]></literal>
    <justification jstring="[hyper(299,a,7601,a(flip),b,18593,a),flip(a)].">
      <j1 rule="hyper" parents="299 7601 18593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18744">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * K(u,w)) = (z * K(x,y)) * K(u,w)
    ]]></literal>
    <justification jstring="[para(8101(a,1),18593(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8101 18593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18747">
    <literal><![CDATA[
      K(x,y) * ((1 / z) * K(u,w)) = (K(x,y) / z) * K(u,w)
    ]]></literal>
    <justification jstring="[para(14410(a,1),18593(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14410 18593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18748">
    <literal><![CDATA[
      K(x,(y * K(z,u)) \ w) = K(x,y \ (K(u,z) * w))
    ]]></literal>
    <justification jstring="[hyper(16779,a,18602,a)].">
      <j1 rule="hyper" parents="16779 18602"/>
    </justification>
  </clause>

  <clause id="18749">
    <literal><![CDATA[
      L(x,y,z * (K(u,z) * w)) = L(x,y,T(z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(65,a,14819,a,b,18606,a)].">
      <j1 rule="hyper" parents="65 14819 18606"/>
    </justification>
  </clause>

  <clause id="18750">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w \ 1) = w \ a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(14556(a,2),18629(a,1,1))].">
      <j1 rule="para" parents="14556 18629"/>
    </justification>
  </clause>

  <clause id="18751">
    <literal><![CDATA[
      K(x,y) * (z \ L(z,u,u)) = a(u,u,z) \ K(x,y)
    ]]></literal>
    <justification jstring="[para(13006(a,1),18656(a,1,2))].">
      <j1 rule="para" parents="13006 18656"/>
    </justification>
  </clause>

  <clause id="18752">
    <literal><![CDATA[
      L(x,y,z \ T(u,z \ 1)) = L(x,y,u / z)
    ]]></literal>
    <justification jstring="[hyper(65,a,13460,a(flip),b,18665,a),flip(a)].">
      <j1 rule="hyper" parents="65 13460 18665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18753">
    <literal><![CDATA[
      L(x,y,z \ T(u,z)) = L(x,y,u / z)
    ]]></literal>
    <justification jstring="[hyper(65,a,15183,a(flip),b,18752,a)].">
      <j1 rule="hyper" parents="65 15183 18752"/>
    </justification>
  </clause>

  <clause id="18754">
    <literal><![CDATA[
      L(x,y,T(z,u) \ u) = L(x,y,u / z)
    ]]></literal>
    <justification jstring="[para(4396(a,2),18753(a,1,3))].">
      <j1 rule="para" parents="4396 18753"/>
    </justification>
  </clause>

  <clause id="18755">
    <literal><![CDATA[
      L(x,y,z / (u / z)) = L(x,y,(z \ u) \ z)
    ]]></literal>
    <justification jstring="[para(109(a,1),18754(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="109 18754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18756">
    <literal><![CDATA[
      L(x,y,(z / y) \ y) = L(x,y,(y \ z) \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,13458,a(flip),b,18755,a)].">
      <j1 rule="hyper" parents="65 13458 18755"/>
    </justification>
  </clause>

  <clause id="18757">
    <literal><![CDATA[
      L(x,y \ z,(z / y) \ y) = L(x,y \ z,(y \ z) \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,11679,a(flip),b,18755,a)].">
      <j1 rule="hyper" parents="65 11679 18755"/>
    </justification>
  </clause>

  <clause id="18758">
    <literal><![CDATA[
      T(x,K(y,z \ (u * w))) = T(x,K(y,(u \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(16269,a,18673,a),flip(a)].">
      <j1 rule="hyper" parents="16269 18673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18760">
    <literal><![CDATA[
      K(x,(L(1 / y,z,1 / y) * a(u,w,K(v5,v6))) * v7) = K(x,(a(u,w,K(v5,v6)) / y) * v7)
    ]]></literal>
    <justification jstring="[para(18685(a,1),16008(a,2,2,1))].">
      <j1 rule="para" parents="18685 16008"/>
    </justification>
  </clause>

  <clause id="18761">
    <literal><![CDATA[
      x * (y * a(z,u,K(x,w))) = T(x,a(z,u,w)) * y
    ]]></literal>
    <justification jstring="[para(14863(a,1),18700(a,1,2,2))].">
      <j1 rule="para" parents="14863 18700"/>
    </justification>
  </clause>

  <clause id="18762">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ w))) = K(x,T(y,(u * z) * w))
    ]]></literal>
    <justification jstring="[hyper(16637,a,18710,a),flip(a)].">
      <j1 rule="hyper" parents="16637 18710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18765">
    <literal><![CDATA[
      K(K(x,R(y,z,u)) * R(y,z,u),T(w,y)) = K(R(y,z,u),T(w,x))
    ]]></literal>
    <justification jstring="[hyper(299,a,8132,a(flip),b,18716,a),flip(a)].">
      <j1 rule="hyper" parents="299 8132 18716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18766">
    <literal><![CDATA[
      K((x \ y) * R(x,z,z),T(u,x)) = K((y / x) * R(x,z,z),u)
    ]]></literal>
    <justification jstring="[para(15528(a,1),18716(a,2,1))].">
      <j1 rule="para" parents="15528 18716"/>
    </justification>
  </clause>

  <clause id="18767">
    <literal><![CDATA[
      K(x,K(y,(z \ u) * w)) = K(x,K(y,u * (z * w)))
    ]]></literal>
    <justification jstring="[hyper(16252,a,18722,a),flip(a)].">
      <j1 rule="hyper" parents="16252 18722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18768">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * w) != u * v5
    ]]></literal>
    <literal><![CDATA[
      w * K(y,K(x,z)) = v5
    ]]></literal>
    <justification jstring="[para(18724(a,2),45(a,1))].">
      <j1 rule="para" parents="18724 45"/>
    </justification>
  </clause>

  <clause id="18769">
    <literal><![CDATA[
      x \ (y * (z * K(u,K(w,v5)))) = (x \ (y * z)) * K(u,K(w,v5))
    ]]></literal>
    <justification jstring="[para(18554(a,1),18726(a,1,2))].">
      <j1 rule="para" parents="18554 18726"/>
    </justification>
  </clause>

  <clause id="18771">
    <literal><![CDATA[
      K(x,y * (K(z,K(u,w)) * v5)) = K(x,y * v5)
    ]]></literal>
    <justification jstring="[para(18729(a,1),16748(a,1,2))].">
      <j1 rule="para" parents="18729 16748"/>
    </justification>
  </clause>

  <clause id="18772">
    <literal><![CDATA[
      K(x,y * (K(z,K(u,w)) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * v5) = v6
    ]]></literal>
    <justification jstring="[para(18729(a,1),16749(a,1,2))].">
      <j1 rule="para" parents="18729 16749"/>
    </justification>
  </clause>

  <clause id="18773">
    <literal><![CDATA[
      K(x,y * (T(z,T(u,w)) * v5)) = K(x,y * (T(z,u) * v5))
    ]]></literal>
    <justification jstring="[para(9181(a,1),18771(a,1,2,2))].">
      <j1 rule="para" parents="9181 18771"/>
    </justification>
  </clause>

  <clause id="18775">
    <literal><![CDATA[
      K(x,y * (z / T(u,K(w,v5)))) = K(x,y * (z / u))
    ]]></literal>
    <justification jstring="[para(16558(a,1),18771(a,1,2,2))].">
      <j1 rule="para" parents="16558 18771"/>
    </justification>
  </clause>

  <clause id="18776">
    <literal><![CDATA[
      (x * K(y,K(z,u))) * w = x * (K(y,K(z,u)) * w)
    ]]></literal>
    <justification jstring="[hyper(299,a,18729,a(flip),b,18736,a),flip(a)].">
      <j1 rule="hyper" parents="299 18729 18736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18777">
    <literal><![CDATA[
      K(x,(y \ z) \ (K(u,y) \ w)) = K(x,(T(y,u) \ z) \ w)
    ]]></literal>
    <justification jstring="[para(5348(a,1),18738(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5348 18738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18778">
    <literal><![CDATA[
      K(L((x \ y) * K(z,u),K(u,z),x),w) = K(x \ (K(z,u) * y),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,17352,a,b,18739,a)].">
      <j1 rule="hyper" parents="65 17352 18739"/>
    </justification>
  </clause>

  <clause id="18779">
    <literal><![CDATA[
      K((x * y) / (K(z,u) * y),w) = K(y \ (K(u,z) * (y * x)),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,16922,a,b,18739,a)].">
      <j1 rule="hyper" parents="65 16922 18739"/>
    </justification>
  </clause>

  <clause id="18780">
    <literal><![CDATA[
      K(x \ ((K(y,z) * L(K(y,u) \ 1,w,v5)) * v6),v7) = K((x * K(z,y)) \ (L(K(u,y),w,v5) * v6),v7)
    ]]></literal>
    <justification jstring="[para(10188(a,2),18739(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="10188 18739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18782">
    <literal><![CDATA[
      K(x,(y * K(z,u)) \ w) = K(x,y \ (K(z,u) \ w))
    ]]></literal>
    <justification jstring="[para(5426(a,2),18748(a,2,2,2))].">
      <j1 rule="para" parents="5426 18748"/>
    </justification>
  </clause>

  <clause id="18783">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ (K(z \ u,z) * w)) = K(x,(y * (u / z)) \ w)
    ]]></literal>
    <justification jstring="[para(6970(a,1),18748(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6970 18748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18784">
    <literal><![CDATA[
      L(x,y,((z * u) / z) * w) = L(x,y,T(u,z) * w)
    ]]></literal>
    <justification jstring="[para(5705(a,2),18749(a,1,3))].">
      <j1 rule="para" parents="5705 18749"/>
    </justification>
  </clause>

  <clause id="18785">
    <literal><![CDATA[
      (K(x,y) * L(z \ L(z,u,u),w,v5)) / K(x,y) = L((a(u,u,z) \ K(x,y)) / K(x,y),w,v5)
    ]]></literal>
    <justification jstring="[para(18751(a,1),925(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="18751 925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18786">
    <literal><![CDATA[
      K(x,y) * L(z \ L(z,u,u),w,v5) = a(u,u,L(z,w,v5)) \ K(x,y)
    ]]></literal>
    <justification jstring="[para(6776(a,1),18751(a,1,2))].">
      <j1 rule="para" parents="6776 18751"/>
    </justification>
  </clause>

  <clause id="18787">
    <literal><![CDATA[
      T(x,K(y,(z \ u) * w)) = T(x,K(y,u * (z * w)))
    ]]></literal>
    <justification jstring="[hyper(16269,a,18758,a),flip(a)].">
      <j1 rule="hyper" parents="16269 18758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18788">
    <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(18762(a,1),16637(a,1))].">
      <j1 rule="para" parents="18762 16637"/>
    </justification>
  </clause>

  <clause id="18789">
    <literal><![CDATA[
      K(x,K(y,(z / u) * w)) = K(x,K(y,z * (u * w)))
    ]]></literal>
    <justification jstring="[hyper(17252,a,18767,a)].">
      <j1 rule="hyper" parents="17252 18767"/>
    </justification>
  </clause>

  <clause id="18791">
    <literal><![CDATA[
      K(x,y * (z / T(u,T(w,v5)))) = K(x,y * (z / T(u,w)))
    ]]></literal>
    <justification jstring="[para(7140(a,1),18775(a,1,2,2,2))].">
      <j1 rule="para" parents="7140 18775"/>
    </justification>
  </clause>

  <clause id="18792">
    <literal><![CDATA[
      L(x,K(y,K(z,u)),w) = x
    ]]></literal>
    <justification jstring="[hyper(490,a,18776,a)].">
      <j1 rule="hyper" parents="490 18776"/>
    </justification>
  </clause>

  <clause id="18793">
    <literal><![CDATA[
      (x * (K(y,K(z,u)) * w)) \ ((x * K(y,K(z,u))) * (w * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      L(v5,w,x * K(y,K(z,u))) = v6
    ]]></literal>
    <justification jstring="[para(18776(a,1),493(a,1,1))].">
      <j1 rule="para" parents="18776 493"/>
    </justification>
  </clause>

  <clause id="18794">
    <literal><![CDATA[
      (x * K(y,K(z,u))) \ w = K(K(z,u),y) * (x \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,5443,a(flip),b,18792,a)].">
      <j1 rule="hyper" parents="65 5443 18792"/>
    </justification>
  </clause>

  <clause id="18795">
    <literal><![CDATA[
      L(x,y,(z * (u / z)) * w) = L(x,y,T(u,z) * w)
    ]]></literal>
    <justification jstring="[hyper(65,a,13898,a(flip),b,18784,a)].">
      <j1 rule="hyper" parents="65 13898 18784"/>
    </justification>
  </clause>

  <clause id="18796">
    <literal><![CDATA[
      L(x,y,(((((z * z) \ u) * w) / u) * (z * z)) * v5) = L(x,y,T(w,(z * z) \ u) * v5)
    ]]></literal>
    <justification jstring="[para(827(a,1),18784(a,1,3,1))].">
      <j1 rule="para" parents="827 18784"/>
    </justification>
  </clause>

  <clause id="18797">
    <literal><![CDATA[
      L(x,y,((T(z,u) * w) / z) * v5) = L(x,y,T(K(z,u) * w,z) * v5)
    ]]></literal>
    <justification jstring="[para(5055(a,1),18784(a,1,3,1,1))].">
      <j1 rule="para" parents="5055 18784"/>
    </justification>
  </clause>

  <clause id="18798">
    <literal><![CDATA[
      T(T(x,y),K(y,z * (u * w))) = T(x,T(y,T(z / u,z) * w))
    ]]></literal>
    <justification jstring="[hyper(13836,a,18787,a),flip(a)].">
      <j1 rule="hyper" parents="13836 18787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18799">
    <literal><![CDATA[
      T(x,K(y,z * ((u \ z) * w))) = T(x,K(y,u * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,17175,a(flip),b,18787,a),flip(a)].">
      <j1 rule="hyper" parents="65 17175 18787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18800">
    <literal><![CDATA[
      T(T(x,K(y,z * (u * w))),y \ ((u \ z) * w)) = T(x,((u \ z) * w) / y)
    ]]></literal>
    <justification jstring="[para(18787(a,1),9001(a,1,1))].">
      <j1 rule="para" parents="18787 9001"/>
    </justification>
  </clause>

  <clause id="18801">
    <literal><![CDATA[
      K(x,K((y / z) \ 1,u * (w \ v5))) = K(x,K(z / y,v5 * (w * u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,17209,a,b,18789,a)].">
      <j1 rule="hyper" parents="65 17209 18789"/>
    </justification>
  </clause>

  <clause id="18802">
    <literal><![CDATA[
      K(x,K(y * z,y * ((z \ 1) * ((y / (1 / z)) * u)))) = K((y / (z \ 1)) * (1 / T(y / (1 / z),u)),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,15328,a(flip),b,18789,a),flip(a)].">
      <j1 rule="hyper" parents="65 15328 18789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18803">
    <literal><![CDATA[
      K(x,K(y,z * ((u \ z) * w))) = K(x,K(y,u * w))
    ]]></literal>
    <justification jstring="[para(76(a,1),18789(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="76 18789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18804">
    <literal><![CDATA[
      (x * K(y,K(z,u))) \ w = K(y,K(z,u)) * (x \ w)
    ]]></literal>
    <justification jstring="[para(8003(a,1),18794(a,2,1))].">
      <j1 rule="para" parents="8003 18794"/>
    </justification>
  </clause>

  <clause id="18805">
    <literal><![CDATA[
      T(x,K(y,(z / u) * w)) = T(x,K(y,z * (u * w)))
    ]]></literal>
    <justification jstring="[para(79(a,1),18799(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="79 18799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18806">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) \ w = K(x,K(y,z)) * (u \ w)
    ]]></literal>
    <justification jstring="[para(16341(a,2),18804(a,1,1))].">
      <j1 rule="para" parents="16341 18804"/>
    </justification>
  </clause>

  <clause id="18807">
    <literal><![CDATA[
      T(T(x,y / (z / u)),K(w,z * (u * y))) = T(x,T(y / (z / u),w))
    ]]></literal>
    <justification jstring="[hyper(16784,a,18805,a),flip(a)].">
      <j1 rule="hyper" parents="16784 18805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18808">
    <literal><![CDATA[
      (K(x,K(y,z)) \ u) \ w = K(x,K(y,z)) \ (u \ w)
    ]]></literal>
    <justification jstring="[hyper(616,a,18806,a),flip(a)].">
      <j1 rule="hyper" parents="616 18806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18809">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) \ w = (u \ w) * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,16341,a(flip),b,18806,a),flip(a)].">
      <j1 rule="hyper" parents="299 16341 18806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18810">
    <literal><![CDATA[
      L(K(x,K(y,z)) * (u \ (y * w)),K(x,K(y,z)) \ u,K(x,K(y,z))) = u \ (T(y,K(x,z)) * w)
    ]]></literal>
    <justification jstring="[para(18806(a,1),11774(a,1,1))].">
      <j1 rule="para" parents="18806 11774"/>
    </justification>
  </clause>

  <clause id="18811">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u \ w) = u \ (K(x,K(y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,18737,a(flip),b,18808,a),flip(a)].">
      <j1 rule="hyper" parents="65 18737 18808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18812">
    <literal><![CDATA[
      K(x,(K(y,K(z,u)) \ w) \ v5) = K(x,w \ v5)
    ]]></literal>
    <justification jstring="[para(18808(a,2),16750(a,1,2))].">
      <j1 rule="para" parents="18808 16750"/>
    </justification>
  </clause>

  <clause id="18813">
    <literal><![CDATA[
      K(x,y \ (K(z,K(u,w)) * v5)) = K(x,y \ v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,18589,a(flip),b,18812,a)].">
      <j1 rule="hyper" parents="65 18589 18812"/>
    </justification>
  </clause>

  <clause id="18814">
    <literal><![CDATA[
      K(x,(y * T(z,K(u,w))) \ v5) = K(x,(y * z) \ v5)
    ]]></literal>
    <justification jstring="[para(16591(a,1),18812(a,1,2,1))].">
      <j1 rule="para" parents="16591 18812"/>
    </justification>
  </clause>

  <clause id="18815">
    <literal><![CDATA[
      K(x,y \ (T(z,K(u,w)) \ v5)) = K(x,y \ (z \ v5))
    ]]></literal>
    <justification jstring="[para(5351(a,1),18813(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5351 18813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18816">
    <literal><![CDATA[
      K(x,y \ (z * T(u,K(w,v5)))) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[para(5853(a,1),18813(a,1,2,2))].">
      <j1 rule="para" parents="5853 18813"/>
    </justification>
  </clause>

  <clause id="18817">
    <literal><![CDATA[
      (x * (K(y,K(z,u)) * w)) \ v5 = ((x * w) \ v5) * K(y,K(z,u))
    ]]></literal>
    <justification jstring="[para(18729(a,1),18809(a,1,1))].">
      <j1 rule="para" parents="18729 18809"/>
    </justification>
  </clause>

  <clause id="18818">
    <literal><![CDATA[
      T(x,y \ (K(z,K(u,w)) \ v5)) = T(x,y \ v5)
    ]]></literal>
    <justification jstring="[para(18811(a,1),16722(a,1,2))].">
      <j1 rule="para" parents="18811 16722"/>
    </justification>
  </clause>

  <clause id="18819">
    <literal><![CDATA[
      T(x,y \ (T(z,K(u,w)) \ v5)) = T(x,y \ (z \ v5))
    ]]></literal>
    <justification jstring="[para(5348(a,1),18818(a,1,2,2))].">
      <j1 rule="para" parents="5348 18818"/>
    </justification>
  </clause>

  <clause id="18820">
    <literal><![CDATA[
      K(x,(y * T(z,T(u,w))) \ v5) = K(x,(y * T(z,u)) \ v5)
    ]]></literal>
    <justification jstring="[para(7140(a,1),18814(a,1,2,1,2))].">
      <j1 rule="para" parents="7140 18814"/>
    </justification>
  </clause>

  <clause id="18821">
    <literal><![CDATA[
      K(x,y \ (z * T(u,T(w,v5)))) = K(x,y \ (z * T(u,w)))
    ]]></literal>
    <justification jstring="[para(7140(a,1),18816(a,1,2,2,2))].">
      <j1 rule="para" parents="7140 18816"/>
    </justification>
  </clause>

  <clause id="18822">
    <literal><![CDATA[
      T(x,y \ ((K(z,u) * (w \ 1)) \ v5)) = T(x,y \ ((w \ K(z,u)) \ v5))
    ]]></literal>
    <justification jstring="[para(14242(a,1),18819(a,1,2,2,1))].">
      <j1 rule="para" parents="14242 18819"/>
    </justification>
  </clause>

  <clause id="18824">
    <literal><![CDATA[
      K(x,K(y,(z * u) \ w)) = K(x,K(y,z \ (w / u)))
    ]]></literal>
    <justification jstring="[hyper(16943,a,18669,a)].">
      <j1 rule="hyper" parents="16943 18669"/>
    </justification>
  </clause>

  <clause id="18825">
    <literal><![CDATA[
      K(x,K(y,z \ (u / w))) = K(x,K(y,(z * w) * u))
    ]]></literal>
    <justification jstring="[hyper(16252,a,18824,a),flip(a)].">
      <j1 rule="hyper" parents="16252 18824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18827">
    <literal><![CDATA[
      K(x,K(y,(z * u) * w)) = K(x,K(y,z * (w / u)))
    ]]></literal>
    <justification jstring="[hyper(16252,a,18825,a),flip(a)].">
      <j1 rule="hyper" parents="16252 18825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18828">
    <literal><![CDATA[
      K(x,K(y,(z * u) * w)) = K(x,K(y,z * (u \ w)))
    ]]></literal>
    <justification jstring="[hyper(299,a,17145,a(flip),b,18827,a),flip(a)].">
      <j1 rule="hyper" parents="299 17145 18827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18829">
    <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(18827(a,2),17250(a,1))].">
      <j1 rule="para" parents="18827 17250"/>
    </justification>
  </clause>

  <clause id="18830">
    <literal><![CDATA[
      K(x,K(y,T(z * u,w) * v5)) = K(x,K(y,z * (u \ v5)))
    ]]></literal>
    <justification jstring="[hyper(17183,a,18828,a)].">
      <j1 rule="hyper" parents="17183 18828"/>
    </justification>
  </clause>

  <clause id="18831">
    <literal><![CDATA[
      K(x,K(y * z,y * (u \ z))) * K(x,R(u * K(y,u),y,z)) = K(x,(y * z) \ ((y * u) * z))
    ]]></literal>
    <justification jstring="[para(18828(a,1),8504(a,1,1))].">
      <j1 rule="para" parents="18828 8504"/>
    </justification>
  </clause>

  <clause id="18832">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) * (u \ w))) * K(K(x,y),K(w,z * u)) = K(x,K(y,w * ((z \ 1) * u)))
    ]]></literal>
    <justification jstring="[para(18828(a,1),17719(a,1,1))].">
      <j1 rule="para" parents="18828 17719"/>
    </justification>
  </clause>

  <clause id="18833">
    <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(5103(a,1),18772(a,1,2,2))].">
      <j1 rule="para" parents="5103 18772"/>
    </justification>
  </clause>

  <clause id="18834">
    <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(8029(a,1),18772(a,1,2,2))].">
      <j1 rule="para" parents="8029 18772"/>
    </justification>
  </clause>

  <clause id="18837">
    <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(17690(a,1),18772(a,1,2,2))].">
      <j1 rule="para" parents="17690 18772"/>
    </justification>
  </clause>

  <clause id="18838">
    <literal><![CDATA[
      T(x * K(L(y,z,u),w),K(w,y)) = L(K(w,y),z,u) \ x
    ]]></literal>
    <justification jstring="[para(11909(a,1),18674(a,1,1))].">
      <j1 rule="para" parents="11909 18674"/>
    </justification>
  </clause>

  <clause id="18839">
    <literal><![CDATA[
      K(x,L(x \ y,z,u)) * T(x,T(w,y)) = T(T(x,w),L(x \ y,z,u))
    ]]></literal>
    <justification jstring="[para(7729(a,1),18720(a,1,2))].">
      <j1 rule="para" parents="7729 18720"/>
    </justification>
  </clause>

  <clause id="18840">
    <literal><![CDATA[
      (T(x,K(y,z)) \ u) * z = (x \ u) * T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(16482,a,18735,a),flip(a)].">
      <j1 rule="hyper" parents="16482 18735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18841">
    <literal><![CDATA[
      (x \ R(T(x,K(y,z)),u,x)) * z = (x \ R(x,u,x)) * T(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(8710(a,1),18840(a,1,1))].">
      <j1 rule="para" parents="8710 18840"/>
    </justification>
  </clause>

  <clause id="18842">
    <literal><![CDATA[
      K(x,y) * (K(z,u) * w) = K(z,u) * (K(x,y) * w)
    ]]></literal>
    <justification jstring="[hyper(17105,a,18742,a)].">
      <j1 rule="hyper" parents="17105 18742"/>
    </justification>
  </clause>

  <clause id="18850">
    <literal><![CDATA[
      K(x,y) * (K(z,u) * (x * w)) = K(z,u) * (T(x,y) * w)
    ]]></literal>
    <justification jstring="[para(5103(a,1),18842(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5103 18842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18851">
    <literal><![CDATA[
      K(x,y) * (K(z,u) * (y \ w)) = K(z,u) * (T(y,x) \ w)
    ]]></literal>
    <justification jstring="[para(5383(a,1),18842(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5383 18842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18853">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,w) = (x * K(u,w)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,17115,a(flip),b,18744,a)].">
      <j1 rule="hyper" parents="65 17115 18744"/>
    </justification>
  </clause>

  <clause id="18855">
    <literal><![CDATA[
      ((x * K(y,z)) * K(u,w)) * K(z,y) = x * K(u,w)
    ]]></literal>
    <justification jstring="[hyper(7207,a,18853,a)].">
      <j1 rule="hyper" parents="7207 18853"/>
    </justification>
  </clause>

  <clause id="18856">
    <literal><![CDATA[
      ((x * K(y,z)) * K(u,w)) \ (x * K(u,w)) = K(z,y)
    ]]></literal>
    <justification jstring="[para(18853(a,1),7200(a,1,1))].">
      <j1 rule="para" parents="18853 7200"/>
    </justification>
  </clause>

  <clause id="18857">
    <literal><![CDATA[
      ((x * K(y,z)) * K(u,w)) \ (x * K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = v5
    ]]></literal>
    <justification jstring="[para(18853(a,1),7209(a,1,1))].">
      <j1 rule="para" parents="18853 7209"/>
    </justification>
  </clause>

  <clause id="18860">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      (x * K(u,w)) * K(y,z) = v5
    ]]></literal>
    <justification jstring="[para(18855(a,1),7216(a,1,1)),flip(b)].">
      <j1 rule="para" parents="18855 7216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18861">
    <literal><![CDATA[
      K(x,y) / (K(z,u) * w) = (K(x,y) / w) * K(u,z)
    ]]></literal>
    <justification jstring="[hyper(14676,a,18747,a)].">
      <j1 rule="hyper" parents="14676 18747"/>
    </justification>
  </clause>

  <clause id="18863">
    <literal><![CDATA[
      a((K(x,y) \ (1 / K(x,y))) \ z,u,w) = a((K(x,y) / z) * K(y,x),u,w)
    ]]></literal>
    <justification jstring="[para(18861(a,1),15159(a,2,1))].">
      <j1 rule="para" parents="18861 15159"/>
    </justification>
  </clause>

  <clause id="18864">
    <literal><![CDATA[
      K(x,L(y,z \ u,(z \ u) \ z)) = K(x,L(y,z,(1 / (u / z)) \ z))
    ]]></literal>
    <justification jstring="[para(18757(a,1),17317(a,1,2))].">
      <j1 rule="para" parents="18757 17317"/>
    </justification>
  </clause>

  <clause id="18865">
    <literal><![CDATA[
      K(x,y * (T(z,u) / T(w,z))) = K(x,y * (w \ T(z,u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,13884,a(flip),b,18791,a),flip(a)].">
      <j1 rule="hyper" parents="65 13884 18791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18866">
    <literal><![CDATA[
      K(x,y * (z / T(T(u,w),u \ v5))) = K(x,y * (z / T((u \ v5) \ v5,w)))
    ]]></literal>
    <justification jstring="[para(4404(a,1),18791(a,1,2,2,2))].">
      <j1 rule="para" parents="4404 18791"/>
    </justification>
  </clause>

  <clause id="18867">
    <literal><![CDATA[
      K(x,((T(y,z) \ 1) * T(u,y)) \ w) = K(x,(u * (T(y,z) \ 1)) \ w)
    ]]></literal>
    <justification jstring="[hyper(17965,a,18820,a),flip(a)].">
      <j1 rule="hyper" parents="17965 18820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18869">
    <literal><![CDATA[
      K(x,K(y,T(z * u,w) * v5)) = K(x,y) * K(y,T(x,z * (u \ v5)))
    ]]></literal>
    <justification jstring="[hyper(299,a,8010,a,b,18830,a),flip(a)].">
      <j1 rule="hyper" parents="299 8010 18830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18870">
    <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(119,a,18838,a(flip),b,5431,a)].">
      <j1 rule="hyper" parents="119 18838 5431"/>
    </justification>
  </clause>

  <clause id="18871">
    <literal><![CDATA[
      (K(x,y) * (K(z,u) * x)) \ (K(z,u) * (T(x,y) * w)) = L(L(w,x,K(z,u)),K(z,u) * x,K(x,y))
    ]]></literal>
    <justification jstring="[para(18850(a,1),484(a,1,2))].">
      <j1 rule="para" parents="18850 484"/>
    </justification>
  </clause>

  <clause id="18872">
    <literal><![CDATA[
      K(x,y * z) * ((z * y) \ u) = K(y,z) * (T(y * z,x) \ u)
    ]]></literal>
    <justification jstring="[para(11606(a,1),18851(a,1,2))].">
      <j1 rule="para" parents="11606 18851"/>
    </justification>
  </clause>

  <clause id="18873">
    <literal><![CDATA[
      K(x,T(y,T(z,u) / T(w,z)) * (w \ T(z,u))) = K(x,(T(z,u) / T(w,z)) * y)
    ]]></literal>
    <justification jstring="[hyper(13261,a,18865,a),flip(a)].">
      <j1 rule="hyper" parents="13261 18865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18876">
    <literal><![CDATA[
      K((x * y) \ z,L(u,x,y)) = K(x \ (T(y,x) \ z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,15884,a(flip),b,18660,a)].">
      <j1 rule="hyper" parents="65 15884 18660"/>
    </justification>
  </clause>

  <clause id="18877">
    <literal><![CDATA[
      T(x,K(y,z \ (u \ w))) = T(x,K(y,(u * z) * w))
    ]]></literal>
    <justification jstring="[hyper(18696,a,16268,a)].">
      <j1 rule="hyper" parents="18696 16268"/>
    </justification>
  </clause>

  <clause id="18878">
    <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(18877(a,1),16269(a,1))].">
      <j1 rule="para" parents="18877 16269"/>
    </justification>
  </clause>

  <clause id="18881">
    <literal><![CDATA[
      K(x,y * ((K(z,u) / w) * v5)) = K(x,y * ((w \ K(z,u)) * v5))
    ]]></literal>
    <justification jstring="[hyper(18833,a,13849,a)].">
      <j1 rule="hyper" parents="18833 13849"/>
    </justification>
  </clause>

  <clause id="18882">
    <literal><![CDATA[
      K(x,y * ((K(z,u) * w) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * ((w * K(z,u)) * v5)) = v6
    ]]></literal>
    <justification jstring="[para(7199(a,1),18833(a,1,2,2,1))].">
      <j1 rule="para" parents="7199 18833"/>
    </justification>
  </clause>

  <clause id="18884">
    <literal><![CDATA[
      T(x,K(y,a(z,u,w)) * v5) = v5 \ (x * v5)
    ]]></literal>
    <justification jstring="[para(18624(a,1),18646(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18624 18646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18885">
    <literal><![CDATA[
      T(x,K(y,a(z,u,w)) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,v5) = v6
    ]]></literal>
    <justification jstring="[para(18884(a,2),318(a,1))].">
      <j1 rule="para" parents="18884 318"/>
    </justification>
  </clause>

  <clause id="18887">
    <literal><![CDATA[
      T(x,a(y,z,K(u,w)) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,v5) = v6
    ]]></literal>
    <justification jstring="[para(14162(a,2),18885(a,1,2,1))].">
      <j1 rule="para" parents="14162 18885"/>
    </justification>
  </clause>

  <clause id="18888">
    <literal><![CDATA[
      T(x,y * T(a(z,u,w),v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,y * a(z,u,w)) = v6
    ]]></literal>
    <justification jstring="[para(16562(a,1),18885(a,1))].">
      <j1 rule="para" parents="16562 18885"/>
    </justification>
  </clause>

  <clause id="18889">
    <literal><![CDATA[
      T(x,y / T(z,a(u,w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,y / z) = v6
    ]]></literal>
    <justification jstring="[para(16563(a,1),18885(a,1))].">
      <j1 rule="para" parents="16563 18885"/>
    </justification>
  </clause>

  <clause id="18890">
    <literal><![CDATA[
      T(x,y * a(z,u,K(w,v5))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(18887,a,18631,a),flip(a)].">
      <j1 rule="hyper" parents="18887 18631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18891">
    <literal><![CDATA[
      T(x,(a(y,z,u) * w) / v5) = T(x,(w * a(y,z,u)) / v5)
    ]]></literal>
    <justification jstring="[hyper(18887,a,16017,a),flip(a)].">
      <j1 rule="hyper" parents="18887 16017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18892">
    <literal><![CDATA[
      T(x,a(y,z,K(u,w)) * v5) = T(x,v5)
    ]]></literal>
    <justification jstring="[hyper(18887,a,xx),flip(a)].">
      <j1 rule="hyper" parents="18887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18893">
    <literal><![CDATA[
      T(x,y) \ T(T(x,z),T(y,a(u,w,K(v5,v6)) * z)) = K(x,z * a(u,w,K(v5,v6)))
    ]]></literal>
    <justification jstring="[para(18890(a,1),16548(a,1,2,1))].">
      <j1 rule="para" parents="18890 16548"/>
    </justification>
  </clause>

  <clause id="18894">
    <literal><![CDATA[
      K((T(x,y) \ (y * a(z,u,K(w,v5)))) \ 1,v6) = K(((y * a(z,u,K(w,v5))) / x) \ 1,v6)
    ]]></literal>
    <justification jstring="[para(18890(a,1),17001(a,1,1,1,1))].">
      <j1 rule="para" parents="18890 17001"/>
    </justification>
  </clause>

  <clause id="18896">
    <literal><![CDATA[
      (K(x,K(y,z)) * (u * w)) \ (u * (w * (v5 * K(x,K(y,z))))) != v6
    ]]></literal>
    <literal><![CDATA[
      L(L(v5,w,u),u * w,K(x,K(y,z))) = v6
    ]]></literal>
    <justification jstring="[para(18732(a,1),911(a,1,2))].">
      <j1 rule="para" parents="18732 911"/>
    </justification>
  </clause>

  <clause id="18897">
    <literal><![CDATA[
      K((x \ y) * L(x,z,z),T(u,x)) = K((y / x) * R(x,z,z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,18089,a(flip),b,18766,a)].">
      <j1 rule="hyper" parents="65 18089 18766"/>
    </justification>
  </clause>

  <clause id="18898">
    <literal><![CDATA[
      T(x,T(y,T(z / u,z) * w)) = T(x,T(y,z * (u * w)))
    ]]></literal>
    <justification jstring="[hyper(7154,a,18798,a),flip(a)].">
      <j1 rule="hyper" parents="7154 18798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18899">
    <literal><![CDATA[
      T(x,T(y,(z \ u) * w)) = T(x,T(y,u * (z * w)))
    ]]></literal>
    <justification jstring="[para(13876(a,1),18898(a,1,2))].">
      <j1 rule="para" parents="13876 18898"/>
    </justification>
  </clause>

  <clause id="18900">
    <literal><![CDATA[
      T(x,T(y \ z,z * (y * u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y \ z,u)) = w
    ]]></literal>
    <justification jstring="[para(18899(a,1),16248(a,1))].">
      <j1 rule="para" parents="18899 16248"/>
    </justification>
  </clause>

  <clause id="18901">
    <literal><![CDATA[
      T(x / (y / z),T(z \ y,x)) = T((y / z) \ x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(18900,a,16230,a)].">
      <j1 rule="hyper" parents="18900 16230"/>
    </justification>
  </clause>

  <clause id="18902">
    <literal><![CDATA[
      K(x,y) * (T(x * y,z) \ u) = T(y * x,T(z,y)) \ u
    ]]></literal>
    <justification jstring="[hyper(65,a,13214,a(flip),b,18872,a),flip(a)].">
      <j1 rule="hyper" parents="65 13214 18872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18903">
    <literal><![CDATA[
      T(x,T(y * z,T(z,y)) \ u) = T(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[para(18902(a,1),17284(a,1,2))].">
      <j1 rule="para" parents="18902 17284"/>
    </justification>
  </clause>

  <clause id="18904">
    <literal><![CDATA[
      T(x,T(y * z,z) \ u) = T(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(17900,a,18903,a)].">
      <j1 rule="hyper" parents="17900 18903"/>
    </justification>
  </clause>

  <clause id="18905">
    <literal><![CDATA[
      T(x,(y * z) \ T(u,y * z)) = T(x,u / T(z * y,y))
    ]]></literal>
    <justification jstring="[hyper(16646,a,18904,a),flip(a)].">
      <j1 rule="hyper" parents="16646 18904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18906">
    <literal><![CDATA[
      T(x,T(y * (z \ 1),z) \ u) = T(x,((z \ 1) * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,17458,a(flip),b,18904,a)].">
      <j1 rule="hyper" parents="65 17458 18904"/>
    </justification>
  </clause>

  <clause id="18907">
    <literal><![CDATA[
      T(x,y / T(z * u,u)) = T(x,y / (u * z))
    ]]></literal>
    <justification jstring="[hyper(16641,a,18905,a),flip(a)].">
      <j1 rule="hyper" parents="16641 18905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18908">
    <literal><![CDATA[
      T(x,y \ (((y \ 1) \ z) \ 1)) = T(x,(1 / y) / (y * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,17683,a,b,18907,a)].">
      <j1 rule="hyper" parents="65 17683 18907"/>
    </justification>
  </clause>

  <clause id="18909">
    <literal><![CDATA[
      T(x,y / (z * (u / z))) = T(x,y / T(u,z))
    ]]></literal>
    <justification jstring="[para(12(a,1),18907(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="12 18907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18910">
    <literal><![CDATA[
      T(x,T(y,z * u) / T(u \ z,z)) = T(x,(u \ T(z,u \ 1)) \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,17667,a(flip),b,18909,a),flip(a)].">
      <j1 rule="hyper" parents="65 17667 18909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18911">
    <literal><![CDATA[
      T(x,T(T(y * (z \ 1),z) \ u,w)) = K(x,w) * T(x * K(w,x),((z \ 1) * y) \ u)
    ]]></literal>
    <justification jstring="[para(18906(a,1),9376(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18906 9376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18912">
    <literal><![CDATA[
      T(x,y \ (((y \ 1) \ z) \ 1)) = T(x,y \ ((y * z) \ 1))
    ]]></literal>
    <justification jstring="[hyper(299,a,14482,a(flip),b,18908,a),flip(a)].">
      <j1 rule="hyper" parents="299 14482 18908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18913">
    <literal><![CDATA[
      T(x,(y \ 1) / ((y \ 1) \ z)) = T(x,y \ ((y * z) \ 1))
    ]]></literal>
    <justification jstring="[hyper(14596,a,18912,a)].">
      <j1 rule="hyper" parents="14596 18912"/>
    </justification>
  </clause>

  <clause id="18914">
    <literal><![CDATA[
      T(x,(y \ 1) * (z \ (y \ 1))) = T(x,y \ ((y * z) \ 1))
    ]]></literal>
    <justification jstring="[hyper(65,a,16242,a(flip),b,18913,a)].">
      <j1 rule="hyper" parents="65 16242 18913"/>
    </justification>
  </clause>

  <clause id="18915">
    <literal><![CDATA[
      T(x,y \ ((y * z) \ 1)) = T(x,y \ (z \ (y \ 1)))
    ]]></literal>
    <justification jstring="[hyper(14304,a,18914,a),flip(a)].">
      <j1 rule="hyper" parents="14304 18914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18916">
    <literal><![CDATA[
      T(x,(y * z) \ ((y * z) \ z)) = T(x,y \ (z \ (y \ 1)))
    ]]></literal>
    <justification jstring="[hyper(65,a,17527,a,b,18915,a)].">
      <j1 rule="hyper" parents="65 17527 18915"/>
    </justification>
  </clause>

  <clause id="18917">
    <literal><![CDATA[
      T((x * y) / x,z \ (x \ (z \ 1))) = T(y,(z * x) \ ((z * x) \ 1))
    ]]></literal>
    <justification jstring="[hyper(14735,a,18916,a),flip(a)].">
      <j1 rule="hyper" parents="14735 18916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18918">
    <literal><![CDATA[
      T(((x \ 1) * y) / (x \ 1),z \ ((x \ 1) \ (z \ 1))) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,(z * (1 / x)) \ ((z * (1 / x)) \ 1)) = u
    ]]></literal>
    <justification jstring="[para(18916(a,1),15715(a,1))].">
      <j1 rule="para" parents="18916 15715"/>
    </justification>
  </clause>

  <clause id="18919">
    <literal><![CDATA[
      K(x,y * ((K(z,u) / w) * a(w \ K(z,u),v5,v5))) = K(x,y * R(w \ K(z,u),v5,v5))
    ]]></literal>
    <justification jstring="[para(15579(a,1),18881(a,2,2,2))].">
      <j1 rule="para" parents="15579 18881"/>
    </justification>
  </clause>

  <clause id="18920">
    <literal><![CDATA[
      K(L(x,y,y) * (x \ z),u) = K((z / x) * R(x,y,y),u)
    ]]></literal>
    <justification jstring="[hyper(18714,a,18897,a)].">
      <j1 rule="hyper" parents="18714 18897"/>
    </justification>
  </clause>

  <clause id="18921">
    <literal><![CDATA[
      K(L(x,y,y) * (x \ z),u) = K((z / x) * L(x,y,y),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,18089,a(flip),b,18920,a),flip(a)].">
      <j1 rule="hyper" parents="299 18089 18920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18922">
    <literal><![CDATA[
      K(K(x,L(y,z,u)) * R(y,z,u),T(w,y)) = K(R(y,z,u),T(w,x))
    ]]></literal>
    <justification jstring="[para(15482(a,1),18765(a,1,1,1))].">
      <j1 rule="para" parents="15482 18765"/>
    </justification>
  </clause>

  <clause id="18923">
    <literal><![CDATA[
      K(x,y / (z / T(u,T(w,v5)))) = K(x,y * ((z / u) \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(18837,a,16906,a),flip(a)].">
      <j1 rule="hyper" parents="18837 16906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18924">
    <literal><![CDATA[
      K(x,y / (z / T(u,T(w,v5)))) = K(x,y / (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(299,a,16906,a(flip),b,18923,a),flip(a)].">
      <j1 rule="hyper" parents="299 16906 18923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18927">
    <literal><![CDATA[
      K(x,T(y \ z,K(u,w) \ y)) = K(x,(K(u,w) \ z) / (K(w,u) * y))
    ]]></literal>
    <justification jstring="[para(5426(a,2),18588(a,2,2,1))].">
      <j1 rule="para" parents="5426 18588"/>
    </justification>
  </clause>

  <clause id="18928">
    <literal><![CDATA[
      K((x * K(y,z)) \ ((x * u) * K(y,z)),w) = K(u,T(T(w,x),x))
    ]]></literal>
    <justification jstring="[hyper(299,a,8132,a(flip),b,18598,a),flip(a)].">
      <j1 rule="hyper" parents="299 8132 18598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18929">
    <literal><![CDATA[
      K((x * K(y,z)) \ ((x * u) * K(y,z)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(u,w) = v5
    ]]></literal>
    <justification jstring="[para(18928(a,2),8171(a,1))].">
      <j1 rule="para" parents="18928 8171"/>
    </justification>
  </clause>

  <clause id="18931">
    <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),18658(a,2,2,2))].">
      <j1 rule="para" parents="10 18658"/>
    </justification>
  </clause>

  <clause id="18932">
    <literal><![CDATA[
      K(x,(L(K(y,z),u,w) * v5) \ v6) = K(x,v5 \ (L(K(z,y),u,w) * v6))
    ]]></literal>
    <justification jstring="[para(6387(a,1),18658(a,1,2,1))].">
      <j1 rule="para" parents="6387 18658"/>
    </justification>
  </clause>

  <clause id="18933">
    <literal><![CDATA[
      L(x,y,z * (u * K(w,v5 * v5))) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,14858,a(flip),b,18681,a),flip(a)].">
      <j1 rule="hyper" parents="65 14858 18681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18935">
    <literal><![CDATA[
      K(x,K((y / z) \ 1,u * (w \ y))) = K(x,K(y \ z,(w * u) * y))
    ]]></literal>
    <justification jstring="[para(13208(a,1),18801(a,2,2))].">
      <j1 rule="para" parents="13208 18801"/>
    </justification>
  </clause>

  <clause id="18936">
    <literal><![CDATA[
      T(T(x,y / ((z * (z * u)) / z)),K(w,(z * (z * u)) * (z * y))) = T(x,T(y / (T(z,z * u) * u),w))
    ]]></literal>
    <justification jstring="[para(4270(a,1),18807(a,2,2,1,2))].">
      <j1 rule="para" parents="4270 18807"/>
    </justification>
  </clause>

  <clause id="18937">
    <literal><![CDATA[
      T(x,T(y,z)) \ (L(K(x,x \ z),u,w) * (K(x,x \ z) \ T(x,T(y,z)))) = T((x \ z) \ z,y) \ T(T(x,y),L(x \ z,u,w))
    ]]></literal>
    <justification jstring="[para(18839(a,1),18394(a,2,2))].">
      <j1 rule="para" parents="18839 18394"/>
    </justification>
  </clause>

  <clause id="18938">
    <literal><![CDATA[
      (x \ R(T(x,K(y,z)),y,x)) * z = K(x,y) * (z * K(x * y,x))
    ]]></literal>
    <justification jstring="[hyper(299,a,10263,a(flip),b,18841,a),flip(a)].">
      <j1 rule="hyper" parents="299 10263 18841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18939">
    <literal><![CDATA[
      T((x \ R(x,y,x)) * z,K(x,y)) = K(x,y) * (z * K(x * y,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,15746,a,b,18938,a)].">
      <j1 rule="hyper" parents="65 15746 18938"/>
    </justification>
  </clause>

  <clause id="18940">
    <literal><![CDATA[
      K(x,y) * (z * K(x * y,x)) = T(a(x,y,x) * z,K(x,y))
    ]]></literal>
    <justification jstring="[para(9671(a,1),18939(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9671 18939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18941">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z * (u \ w))) = K(x,K(y,(z * u) \ w))
    ]]></literal>
    <justification jstring="[hyper(17165,a,18869,a),flip(a)].">
      <j1 rule="hyper" parents="17165 18869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18942">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z * ((u \ w) \ v5))) = K(x,K(y,(z * (w / u)) \ v5))
    ]]></literal>
    <justification jstring="[para(17190(a,1),18941(a,1,2))].">
      <j1 rule="para" parents="17190 18941"/>
    </justification>
  </clause>

  <clause id="18943">
    <literal><![CDATA[
      T(x,(y \ T(z,y \ 1)) \ u) = T(x,T(u,z * y) / (z / y))
    ]]></literal>
    <justification jstring="[hyper(17486,a,18910,a),flip(a)].">
      <j1 rule="hyper" parents="17486 18910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18944">
    <literal><![CDATA[
      T(x,(y \ T(z,y \ 1)) \ u) = T(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(299,a,17501,a(flip),b,18943,a),flip(a)].">
      <j1 rule="hyper" parents="299 17501 18943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18945">
    <literal><![CDATA[
      T((x * y) / x,z \ (x \ (z \ 1))) = T(y,x \ (z \ ((z * x) \ 1)))
    ]]></literal>
    <justification jstring="[para(956(a,1),18917(a,2,2))].">
      <j1 rule="para" parents="956 18917"/>
    </justification>
  </clause>

  <clause id="18946">
    <literal><![CDATA[
      K(x,T(y \ z,K(u,w) \ y)) = K(x,(K(u,w) \ z) / (K(u,w) \ y))
    ]]></literal>
    <justification jstring="[para(5426(a,2),18927(a,2,2,2))].">
      <j1 rule="para" parents="5426 18927"/>
    </justification>
  </clause>

  <clause id="18947">
    <literal><![CDATA[
      K(x,(y * L(K(z,u),w,v5)) \ v6) = K(x,y \ (L(K(u,z),w,v5) * v6))
    ]]></literal>
    <justification jstring="[hyper(16842,a,18932,a)].">
      <j1 rule="hyper" parents="16842 18932"/>
    </justification>
  </clause>

  <clause id="18948">
    <literal><![CDATA[
      K(x,K((y / z) \ 1,u * (w \ y))) = K(x,K(y \ z,w * (u \ y)))
    ]]></literal>
    <justification jstring="[hyper(299,a,18828,a(flip),b,18935,a),flip(a)].">
      <j1 rule="hyper" parents="299 18828 18935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18949">
    <literal><![CDATA[
      (x * K(y,z \ (L(K(u,w),v5,v6) * v7))) \ x = K((z * L(K(w,u),v5,v6)) \ v7,y)
    ]]></literal>
    <justification jstring="[para(18947(a,1),7200(a,1,1,2))].">
      <j1 rule="para" parents="18947 7200"/>
    </justification>
  </clause>

  <clause id="18950">
    <literal><![CDATA[
      K(x,K((y / z) \ 1,u * (w \ y))) = K(x,K(y * z,w * (u \ y)))
    ]]></literal>
    <justification jstring="[hyper(299,a,16259,a(flip),b,18948,a),flip(a)].">
      <j1 rule="hyper" parents="299 16259 18948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18951">
    <literal><![CDATA[
      K(x,K(y / z,u * (w \ z))) = K(x,K(z * y,w * (u \ z)))
    ]]></literal>
    <justification jstring="[para(5852(a,1),18950(a,1,2))].">
      <j1 rule="para" parents="5852 18950"/>
    </justification>
  </clause>

  <clause id="18952">
    <literal><![CDATA[
      K(x,K(y * z,u * (w \ z))) = K(x,K(z * y,w * (u \ z)))
    ]]></literal>
    <justification jstring="[hyper(16630,a,18951,a)].">
      <j1 rule="hyper" parents="16630 18951"/>
    </justification>
  </clause>

  <clause id="18953">
    <literal><![CDATA[
      K(x,K(y * z,z * (u \ y))) = K(x,K(u,z * y))
    ]]></literal>
    <justification jstring="[hyper(65,a,16313,a(flip),b,18952,a),flip(a)].">
      <j1 rule="hyper" parents="65 16313 18952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18956">
    <literal><![CDATA[
      T(x * (y * K(z,u)),K(z,u)) = K(L(u,y,x),z) \ (x * y)
    ]]></literal>
    <justification jstring="[para(11927(a,1),18672(a,2,1))].">
      <j1 rule="para" parents="11927 18672"/>
    </justification>
  </clause>

  <clause id="18957">
    <literal><![CDATA[
      T(x * (y * K(z,u)),K(z,u)) = K(z,L(u,y,x)) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(299,a,5426,a(flip),b,18956,a),flip(a)].">
      <j1 rule="hyper" parents="299 5426 18956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18958">
    <literal><![CDATA[
      T(x * (y * K(z,u)),K(z,u)) = (K(z,u) * y) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(15568,a,18957,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="15568 18957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18959">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * (w * u)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w * (u * K(y,z))) = v5
    ]]></literal>
    <justification jstring="[para(18957(a,1),16391(a,1,2))].">
      <j1 rule="para" parents="18957 16391"/>
    </justification>
  </clause>

  <clause id="18960">
    <literal><![CDATA[
      T((K(x,y) * z) * T(u,z),K(x,y)) = u * (z * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(8068,a,18958,a)].">
      <j1 rule="hyper" parents="8068 18958"/>
    </justification>
  </clause>

  <clause id="18961">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y \ ((z \ y) * u)) = T(x,((z \ y) * u) / y)
    ]]></literal>
    <justification jstring="[para(8259(a,1),18800(a,1,1))].">
      <j1 rule="para" parents="8259 18800"/>
    </justification>
  </clause>

  <clause id="18962">
    <literal><![CDATA[
      a((K(x,y) \ (1 / K(x,y))) \ z,u,w) = a(T(1 / z,K(x,y)),u,w)
    ]]></literal>
    <justification jstring="[para(14413(a,1),18863(a,2,1))].">
      <j1 rule="para" parents="14413 18863"/>
    </justification>
  </clause>

  <clause id="18963">
    <literal><![CDATA[
      a((K(x,y) \ K(y,x)) \ z,u,w) = a(T(1 / z,K(x,y)),u,w)
    ]]></literal>
    <justification jstring="[para(5209(a,1),18962(a,1,1,1,2))].">
      <j1 rule="para" parents="5209 18962"/>
    </justification>
  </clause>

  <clause id="18964">
    <literal><![CDATA[
      a((K(x,y) * K(x,y)) \ z,u,w) = a(T(1 / z,K(y,x)),u,w)
    ]]></literal>
    <justification jstring="[para(5426(a,1),18963(a,1,1,1))].">
      <j1 rule="para" parents="5426 18963"/>
    </justification>
  </clause>

  <clause id="18965">
    <literal><![CDATA[
      a(T(1 / x,K(y,z)),u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,2133,a(flip),b,18964,a),flip(a)].">
      <j1 rule="hyper" parents="65 2133 18964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18967">
    <literal><![CDATA[
      a(T(x \ 1,K(y,z)),u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,4001,a(flip),b,18965,a)].">
      <j1 rule="hyper" parents="65 4001 18965"/>
    </justification>
  </clause>

  <clause id="18968">
    <literal><![CDATA[
      a(T(x,K(y,z)),u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,8994,a(flip),b,18967,a)].">
      <j1 rule="hyper" parents="65 8994 18967"/>
    </justification>
  </clause>

  <clause id="18970">
    <literal><![CDATA[
      K(x,K(y,(z * (u / w)) \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z * ((w \ u) \ v5))) = v6
    ]]></literal>
    <justification jstring="[para(18942(a,1),8205(a,1))].">
      <j1 rule="para" parents="18942 8205"/>
    </justification>
  </clause>

  <clause id="18972">
    <literal><![CDATA[
      K(x,T(y,z \ T(u,w)) * (z \ T(u,w))) = K(x,(T(u,w) / T(z,u)) * y)
    ]]></literal>
    <justification jstring="[para(16822(a,1),18873(a,1,2,1))].">
      <j1 rule="para" parents="16822 18873"/>
    </justification>
  </clause>

  <clause id="18973">
    <literal><![CDATA[
      K(x,(T(y,z) / T(u,y)) * w) = K(x,(u \ T(y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(13261,a,18972,a),flip(a)].">
      <j1 rule="hyper" parents="13261 18972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18974">
    <literal><![CDATA[
      K(x,(T(y,z) / T(u,y)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(u \ T(y,z)) * w) = v5
    ]]></literal>
    <justification jstring="[para(18972(a,1),13261(a,1))].">
      <j1 rule="para" parents="18972 13261"/>
    </justification>
  </clause>

  <clause id="18975">
    <literal><![CDATA[
      T(x,(T(y,z) / T(u,y)) * w) = x * K(x,(u \ T(y,z)) * w)
    ]]></literal>
    <justification jstring="[para(18973(a,1),5083(a,2,2))].">
      <j1 rule="para" parents="18973 5083"/>
    </justification>
  </clause>

  <clause id="18976">
    <literal><![CDATA[
      T(x,(T(y,z) / T(u,y)) * w) = T(x,(u \ T(y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(299,a,5083,a,b,18975,a),flip(a)].">
      <j1 rule="hyper" parents="299 5083 18975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18978">
    <literal><![CDATA[
      K(x,y * a(z,u,K(w,v5))) = T(x,v6) \ T(T(x,y),T(v6,y))
    ]]></literal>
    <justification jstring="[para(18892(a,1),18893(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="18892 18893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18979">
    <literal><![CDATA[
      K(x,y * a(z,u,K(w,v5))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,8272,a(flip),b,18978,a),flip(a)].">
      <j1 rule="hyper" parents="299 8272 18978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18982">
    <literal><![CDATA[
      K(x,a(y,z,K(u,w)) * v5) = K(x,v5)
    ]]></literal>
    <justification jstring="[hyper(18655,a,18979,a)].">
      <j1 rule="hyper" parents="18655 18979"/>
    </justification>
  </clause>

  <clause id="18983">
    <literal><![CDATA[
      K(x * a(y,z,K(u,w)),v5) = (v6 * K(v5,x)) \ v6
    ]]></literal>
    <justification jstring="[para(18979(a,1),7200(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="18979 7200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18985">
    <literal><![CDATA[
      K(x,(K(y,z) * u) * w) = K(x,K(y,z) * (u * w))
    ]]></literal>
    <justification jstring="[para(14864(a,1),18979(a,1,2))].">
      <j1 rule="para" parents="14864 18979"/>
    </justification>
  </clause>

  <clause id="18986">
    <literal><![CDATA[
      K(x,y * T(z,a(u,w,v5))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(16702,a,18982,a)].">
      <j1 rule="hyper" parents="16702 18982"/>
    </justification>
  </clause>

  <clause id="18987">
    <literal><![CDATA[
      K(x * a(y,z,K(u,w)),v5) = K(x,v5)
    ]]></literal>
    <justification jstring="[hyper(299,a,18856,a(flip),b,18983,a),flip(a)].">
      <j1 rule="hyper" parents="299 18856 18983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18988">
    <literal><![CDATA[
      K(T(a(x,y,z),u) \ w,v5) = K(a(x,y,z) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(17817,a,18987,a)].">
      <j1 rule="hyper" parents="17817 18987"/>
    </justification>
  </clause>

  <clause id="18989">
    <literal><![CDATA[
      K((x * y) * K(z,u),w) = K(x * (y * K(z,u)),w)
    ]]></literal>
    <justification jstring="[para(84(a,1),18987(a,1,1))].">
      <j1 rule="para" parents="84 18987"/>
    </justification>
  </clause>

  <clause id="18990">
    <literal><![CDATA[
      K(x / T(y,a(z,u,w)),v5) = K(x / y,v5)
    ]]></literal>
    <justification jstring="[para(14565(a,1),18987(a,1,1))].">
      <j1 rule="para" parents="14565 18987"/>
    </justification>
  </clause>

  <clause id="18991">
    <literal><![CDATA[
      K((K(x,y) * z) * u,w) = K(K(x,y) * (z * u),w)
    ]]></literal>
    <justification jstring="[para(14864(a,1),18987(a,1,1))].">
      <j1 rule="para" parents="14864 18987"/>
    </justification>
  </clause>

  <clause id="18992">
    <literal><![CDATA[
      K(a(x,y,K(z,u)) * w,v5) = K(w,v5)
    ]]></literal>
    <justification jstring="[para(18619(a,2),18987(a,1,1))].">
      <j1 rule="para" parents="18619 18987"/>
    </justification>
  </clause>

  <clause id="18993">
    <literal><![CDATA[
      (K(x,y) * a(z,u,K(w,v5))) * K(K(y,x),v6) = T(K(x,y) * a(z,u,K(w,v5)),v6)
    ]]></literal>
    <justification jstring="[para(18992(a,1),17772(a,1,2))].">
      <j1 rule="para" parents="18992 17772"/>
    </justification>
  </clause>

  <clause id="18994">
    <literal><![CDATA[
      K(x / (a(y,z,u) * w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x / (w * a(y,z,u)),v5) = v6
    ]]></literal>
    <justification jstring="[para(18990(a,1),13956(a,1))].">
      <j1 rule="para" parents="18990 13956"/>
    </justification>
  </clause>

  <clause id="18995">
    <literal><![CDATA[
      K(x,K(y,z) * (T(u,K(y,z)) * w)) = K(x,(u * K(y,z)) * w)
    ]]></literal>
    <justification jstring="[para(107(a,1),18985(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="107 18985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18996">
    <literal><![CDATA[
      K(x,(a(y,z,K(u,w)) * v5) * v6) = K(x,K(a(y,z,u),w) * (v5 * v6))
    ]]></literal>
    <justification jstring="[para(14556(a,2),18985(a,1,2,1,1))].">
      <j1 rule="para" parents="14556 18985"/>
    </justification>
  </clause>

  <clause id="18997">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * ((u * w) * v5)) = K(x,((K(y,z) * u) * w) * v5)
    ]]></literal>
    <justification jstring="[para(15496(a,1),18985(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="15496 18985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18998">
    <literal><![CDATA[
      K(x,K(y,K(z,u) * (w * v5))) * K(x,((K(z,u) * w) * v5) * y) = K(x,y * ((K(z,u) * w) * v5))
    ]]></literal>
    <justification jstring="[para(18985(a,1),16664(a,1,1,2))].">
      <j1 rule="para" parents="18985 16664"/>
    </justification>
  </clause>

  <clause id="18999">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(u,w) * (z * y)) = K(x,y * (K(u,w) * z))
    ]]></literal>
    <justification jstring="[para(18985(a,1),17142(a,1,2))].">
      <j1 rule="para" parents="18985 17142"/>
    </justification>
  </clause>

  <clause id="19000">
    <literal><![CDATA[
      K((x * y) * K(z,u),w) = K(x * (y * K(u,z)),w)
    ]]></literal>
    <justification jstring="[hyper(17781,a,18989,a)].">
      <j1 rule="hyper" parents="17781 18989"/>
    </justification>
  </clause>

  <clause id="19001">
    <literal><![CDATA[
      K(K(x,y) * (T(z,K(x,y)) * u),w) = K((z * K(x,y)) * u,w)
    ]]></literal>
    <justification jstring="[para(107(a,1),18991(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="107 18991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19002">
    <literal><![CDATA[
      K(x,(y * K(z,u)) * w) = K(x,K(z,u) * (y * w))
    ]]></literal>
    <justification jstring="[hyper(18833,a,18995,a),flip(a)].">
      <j1 rule="hyper" parents="18833 18995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19004">
    <literal><![CDATA[
      K(x,K(y,z) * ((u / z) * w)) = K(x,(u / T(z,y)) * w)
    ]]></literal>
    <justification jstring="[para(7189(a,1),19002(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7189 19002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19005">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * ((w * u) * v5)) = K(x,(w * (u * K(y,z))) * v5)
    ]]></literal>
    <justification jstring="[para(11903(a,1),19002(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11903 19002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19006">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (w \ 1))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * K(y,z)) / w) = v5
    ]]></literal>
    <justification jstring="[para(19002(a,1),14626(a,1))].">
      <j1 rule="para" parents="19002 14626"/>
    </justification>
  </clause>

  <clause id="19007">
    <literal><![CDATA[
      K(x,K(y \ 1,T(y,z)) * ((u / T(y,z)) * w)) = K(x,(u / L(T(y,z),y,y)) * w)
    ]]></literal>
    <justification jstring="[para(2821(a,1),19004(a,2,2,1,2))].">
      <j1 rule="para" parents="2821 19004"/>
    </justification>
  </clause>

  <clause id="19008">
    <literal><![CDATA[
      K(x * K(y * x,(z / T(u,w)) * v5),y) = K(x,T(y,K(w,u) * ((z / u) * v5)))
    ]]></literal>
    <justification jstring="[para(19004(a,1),17327(a,1,1,2))].">
      <j1 rule="para" parents="19004 17327"/>
    </justification>
  </clause>

  <clause id="19009">
    <literal><![CDATA[
      K(x * K(y,(z / T(u,w)) * v5),v6) = K(K((z / u) * v5,y) * x,v6)
    ]]></literal>
    <justification jstring="[para(19004(a,1),17884(a,1,1,2))].">
      <j1 rule="para" parents="19004 17884"/>
    </justification>
  </clause>

  <clause id="19010">
    <literal><![CDATA[
      K((x * K(y,z)) * u,w) = K(K(y,z) * (x * u),w)
    ]]></literal>
    <justification jstring="[hyper(16858,a,19001,a),flip(a)].">
      <j1 rule="hyper" parents="16858 19001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19011">
    <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(19001(a,1),16858(a,1))].">
      <j1 rule="para" parents="19001 16858"/>
    </justification>
  </clause>

  <clause id="19012">
    <literal><![CDATA[
      1 / (x \ K(K(y,z) * (u * w),x)) = T(x,(u * K(y,z)) * w)
    ]]></literal>
    <justification jstring="[para(19010(a,1),5119(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="19010 5119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19013">
    <literal><![CDATA[
      K(K(x,y) * ((z * x) * u),w) = K((z * T(x,y)) * u,w)
    ]]></literal>
    <justification jstring="[para(6832(a,1),19010(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6832 19010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19014">
    <literal><![CDATA[
      K(K(x,y) * ((z \ 1) * u),w) = K((z \ K(x,y)) * u,w)
    ]]></literal>
    <justification jstring="[para(14185(a,1),19010(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="14185 19010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19015">
    <literal><![CDATA[
      K(T(K(x,y) * z,u) * w,v5) = K((K(x,y) * T(z,u)) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,17891,a(flip),b,19013,a)].">
      <j1 rule="hyper" parents="65 17891 19013"/>
    </justification>
  </clause>

  <clause id="19016">
    <literal><![CDATA[
      K(x * (y * K(z,u)),T(w,y)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(K(z,u) * (y * x),w) = v5
    ]]></literal>
    <justification jstring="[para(17113(a,2),19011(a,1))].">
      <j1 rule="para" parents="17113 19011"/>
    </justification>
  </clause>

  <clause id="19017">
    <literal><![CDATA[
      T(x,(y * K(z,u)) * w) = T(x,K(z,u) * (y * w))
    ]]></literal>
    <justification jstring="[hyper(5226,a,19012,a),flip(a)].">
      <j1 rule="hyper" parents="5226 19012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19018">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * (y * K(u,w))) = T(x,K(u,w) * (y * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,17275,a,b,19017,a)].">
      <j1 rule="hyper" parents="65 17275 19017"/>
    </justification>
  </clause>

  <clause id="19019">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(u,T(w,v5)) * (z * y)) = T(x,y * (z * K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,17653,a(flip),b,19017,a),flip(a)].">
      <j1 rule="hyper" parents="65 17653 19017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19020">
    <literal><![CDATA[
      T(x,K(y,z) * ((u \ y) * w)) = T(x,(u \ T(y,z)) * w)
    ]]></literal>
    <justification jstring="[para(14220(a,1),19017(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14220 19017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19021">
    <literal><![CDATA[
      T(x,K(y,z) * ((u \ z) * w)) = T(x,(u \ T(z,y)) * w)
    ]]></literal>
    <justification jstring="[hyper(15834,a,19020,a)].">
      <j1 rule="hyper" parents="15834 19020"/>
    </justification>
  </clause>

  <clause id="19022">
    <literal><![CDATA[
      T(x,K(y * z,y) * ((u \ y) * w)) = T(x,(u \ T(y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(15842,a,19021,a)].">
      <j1 rule="hyper" parents="15842 19021"/>
    </justification>
  </clause>

  <clause id="19023">
    <literal><![CDATA[
      T(x,K(y \ z,u) * ((w \ u) * v5)) = T(x,(w \ T(u,y * z)) * v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,17350,a,b,19021,a)].">
      <j1 rule="hyper" parents="65 17350 19021"/>
    </justification>
  </clause>

  <clause id="19024">
    <literal><![CDATA[
      K(T(K(x,y) * z,u) * w,v5) = K(K(x,y) * (T(z,u) * w),v5)
    ]]></literal>
    <justification jstring="[hyper(299,a,18991,a(flip),b,19015,a),flip(a)].">
      <j1 rule="hyper" parents="299 18991 19015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19025">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(u,w) * (y * z)) = T(x,z * (y * K(u,w)))
    ]]></literal>
    <justification jstring="[para(8057(a,1),19018(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8057 19018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19026">
    <literal><![CDATA[
      T(x,(y \ T(z,z * u)) * w) = T(x,(y \ T(z,u)) * w)
    ]]></literal>
    <justification jstring="[hyper(65,a,19021,a(flip),b,19022,a)].">
      <j1 rule="hyper" parents="65 19021 19022"/>
    </justification>
  </clause>

  <clause id="19027">
    <literal><![CDATA[
      K(K(x,y) * (T(T(z,K(x,y)),u) * w),v5) = K(T(z * K(x,y),u) * w,v5)
    ]]></literal>
    <justification jstring="[para(107(a,1),19024(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="107 19024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19028">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(u * w,u) * (y * z)) = T(x,z * T(K(u * w,u) * y,K(u,w)))
    ]]></literal>
    <justification jstring="[para(8262(a,2),19025(a,2,2,2))].">
      <j1 rule="para" parents="8262 19025"/>
    </justification>
  </clause>

  <clause id="19029">
    <literal><![CDATA[
      K(x * (K(y,z) * u),T(w,u)) = K(K(y,z) * (u * x),w)
    ]]></literal>
    <justification jstring="[hyper(19016,a,16773,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="19016 16773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19030">
    <literal><![CDATA[
      K(x * (T(y,z) * K(u,w)),T(v5,y)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(K(u,w) * (T(y,z) * x),v5) = v6
    ]]></literal>
    <justification jstring="[para(16384(a,1),19016(a,1))].">
      <j1 rule="para" parents="16384 19016"/>
    </justification>
  </clause>

  <clause id="19032">
    <literal><![CDATA[
      K(x,(a(y,z,K(u,w)) * v5) * v6) = K(x,a(y,z,K(u,w)) * (v5 * v6))
    ]]></literal>
    <justification jstring="[para(14556(a,2),18996(a,2,2,1))].">
      <j1 rule="para" parents="14556 18996"/>
    </justification>
  </clause>

  <clause id="19033">
    <literal><![CDATA[
      K(x * K(y,(z / T(u,w)) * v5),v6) = K(K((u \ z) * v5,y) * x,v6)
    ]]></literal>
    <justification jstring="[hyper(299,a,17892,a(flip),b,19009,a),flip(a)].">
      <j1 rule="hyper" parents="299 17892 19009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19034">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(u,w) * (z * y)) = T(x,y * (z * K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(16817,a,19019,a)].">
      <j1 rule="hyper" parents="16817 19019"/>
    </justification>
  </clause>

  <clause id="19036">
    <literal><![CDATA[
      T(x,(y \ T(z,u \ w)) * v5) = T(x,(y \ T(z,u * w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,19021,a(flip),b,19023,a)].">
      <j1 rule="hyper" parents="65 19021 19023"/>
    </justification>
  </clause>

  <clause id="19037">
    <literal><![CDATA[
      K(x,(a(y,z,K(u,w)) * v5) * v6) = K(x,v5 * v6)
    ]]></literal>
    <justification jstring="[hyper(299,a,18982,a(flip),b,19032,a),flip(a)].">
      <j1 rule="hyper" parents="299 18982 19032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19039">
    <literal><![CDATA[
      K(x,(a(y,z,K(u,w)) * (v5 \ 1)) * v6) = K(x,v5 \ v6)
    ]]></literal>
    <justification jstring="[hyper(299,a,14246,a(flip),b,19037,a),flip(a)].">
      <j1 rule="hyper" parents="299 14246 19037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19040">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * v5) = K(x,K(y,z) * v5)
    ]]></literal>
    <justification jstring="[para(11912(a,1),19037(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11912 19037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19041">
    <literal><![CDATA[
      K(x,(y * a(z,u,K(w,v5))) * v6) = K(x,y * v6)
    ]]></literal>
    <justification jstring="[para(18619(a,1),19037(a,1,2,1))].">
      <j1 rule="para" parents="18619 19037"/>
    </justification>
  </clause>

  <clause id="19042">
    <literal><![CDATA[
      K(x,K(y,z) * (u * w)) = K(x,u * (w * K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(18959,a,19040,a),flip(a)].">
      <j1 rule="hyper" parents="18959 19040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19043">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * v5) = x \ T(x,K(y,z) * v5)
    ]]></literal>
    <justification jstring="[hyper(299,a,5036,a(flip),b,19040,a),flip(a)].">
      <j1 rule="hyper" parents="299 5036 19040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19044">
    <literal><![CDATA[
      K(x,K((y * z) \ u,w) * v5) = K(x,K(z \ (y \ u),w) * v5)
    ]]></literal>
    <justification jstring="[para(11935(a,1),19040(a,1,2,1))].">
      <j1 rule="para" parents="11935 19040"/>
    </justification>
  </clause>

  <clause id="19045">
    <literal><![CDATA[
      K(x,K(y,z) * (u * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,u * (w * K(y,z))) = v5
    ]]></literal>
    <justification jstring="[para(19040(a,1),18959(a,1))].">
      <j1 rule="para" parents="19040 18959"/>
    </justification>
  </clause>

  <clause id="19046">
    <literal><![CDATA[
      K(x,y * (z * K(u,z))) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(16691,a,19042,a),flip(a)].">
      <j1 rule="hyper" parents="16691 19042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19047">
    <literal><![CDATA[
      K(x,K(y,z) * (u * w)) = K(x,u * (w * K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(15803,a,19042,a)].">
      <j1 rule="hyper" parents="15803 19042"/>
    </justification>
  </clause>

  <clause id="19048">
    <literal><![CDATA[
      K(x,K(y,z) * (u * w)) = K(x,u * (K(y,z) * w))
    ]]></literal>
    <justification jstring="[hyper(299,a,16759,a,b,19042,a),flip(a)].">
      <j1 rule="hyper" parents="299 16759 19042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19049">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (w * y))) = K(x,u * (w * T(y,z)))
    ]]></literal>
    <justification jstring="[para(6832(a,1),19042(a,2,2,2))].">
      <j1 rule="para" parents="6832 19042"/>
    </justification>
  </clause>

  <clause id="19050">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (w / z))) = K(x,u * (w / T(z,y)))
    ]]></literal>
    <justification jstring="[para(7189(a,1),19042(a,2,2,2))].">
      <j1 rule="para" parents="7189 19042"/>
    </justification>
  </clause>

  <clause id="19051">
    <literal><![CDATA[
      K(x,K(y \ z,y) * (u * (w * (z / y)))) = K(x,u * (w * (y \ z)))
    ]]></literal>
    <justification jstring="[para(7202(a,1),19042(a,2,2,2))].">
      <j1 rule="para" parents="7202 19042"/>
    </justification>
  </clause>

  <clause id="19052">
    <literal><![CDATA[
      K(x,y * (z * K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(w,u) * (y * z)) = v5
    ]]></literal>
    <justification jstring="[para(19042(a,1),15803(a,1))].">
      <j1 rule="para" parents="19042 15803"/>
    </justification>
  </clause>

  <clause id="19054">
    <literal><![CDATA[
      K(x,((y \ 1) * K(z,y \ 1)) * u) * K(x,K(u,y * K(z,y \ 1))) = K(x,u * T(y \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,17328,a,b,19046,a)].">
      <j1 rule="hyper" parents="65 17328 19046"/>
    </justification>
  </clause>

  <clause id="19055">
    <literal><![CDATA[
      K(x,y * T(T(z,u),u)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(5100(a,1),19046(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5100 19046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19056">
    <literal><![CDATA[
      K(x,y * (z * (u * K(w,z * u)))) = K(x,y * T(z * u,w))
    ]]></literal>
    <justification jstring="[para(14278(a,1),19046(a,1,2,2))].">
      <j1 rule="para" parents="14278 19046"/>
    </justification>
  </clause>

  <clause id="19057">
    <literal><![CDATA[
      K(x,K(y,z) * (u * w)) = K(x,u * (K(z,y) * w))
    ]]></literal>
    <justification jstring="[hyper(299,a,16759,a,b,19047,a),flip(a)].">
      <j1 rule="hyper" parents="299 16759 19047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19058">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (w * z))) = K(x,u * (w * T(z,y)))
    ]]></literal>
    <justification jstring="[para(6832(a,1),19047(a,2,2,2))].">
      <j1 rule="para" parents="6832 19047"/>
    </justification>
  </clause>

  <clause id="19059">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (w * (y * z)))) = K(x,u * (w * (z * y)))
    ]]></literal>
    <justification jstring="[para(11274(a,1),19047(a,2,2,2))].">
      <j1 rule="para" parents="11274 19047"/>
    </justification>
  </clause>

  <clause id="19060">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (w \ 1))) = K(x,u * (w \ K(z,y)))
    ]]></literal>
    <justification jstring="[para(14185(a,1),19047(a,2,2,2))].">
      <j1 rule="para" parents="14185 19047"/>
    </justification>
  </clause>

  <clause id="19061">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (w \ K(y,z)))) = K(x,u * (w \ 1))
    ]]></literal>
    <justification jstring="[para(14223(a,1),19047(a,2,2,2))].">
      <j1 rule="para" parents="14223 19047"/>
    </justification>
  </clause>

  <clause id="19062">
    <literal><![CDATA[
      K(x,y * (K(z,u) * w)) = K(x,y * (w * K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(65,a,19047,a(flip),b,19048,a),flip(a)].">
      <j1 rule="hyper" parents="65 19047 19048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19063">
    <literal><![CDATA[
      K(x,y * (K(z * u,z) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,z) * (y * w)) = v5
    ]]></literal>
    <justification jstring="[para(19048(a,1),13888(a,1))].">
      <j1 rule="para" parents="19048 13888"/>
    </justification>
  </clause>

  <clause id="19064">
    <literal><![CDATA[
      K(x,y * (K(z,u) * w)) = K(x,y * (K(u,z) * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,19048,a(flip),b,19057,a)].">
      <j1 rule="hyper" parents="65 19048 19057"/>
    </justification>
  </clause>

  <clause id="19065">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (z * w))) = K(x,u * (T(z,y) * w))
    ]]></literal>
    <justification jstring="[para(5103(a,1),19057(a,2,2,2))].">
      <j1 rule="para" parents="5103 19057"/>
    </justification>
  </clause>

  <clause id="19066">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (z \ w))) = K(x,y * (T(z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(16839,a,19062,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="16839 19062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19067">
    <literal><![CDATA[
      K(x,y * (K(z,u) * K(z,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5210(a,1),19062(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5210 19062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19068">
    <literal><![CDATA[
      K(x,y * (K(z,u \ w) * ((u * w) / u))) = K(x,y * (T(u,w) * T(u \ w,z)))
    ]]></literal>
    <justification jstring="[para(6880(a,1),19062(a,2,2,2))].">
      <j1 rule="para" parents="6880 19062"/>
    </justification>
  </clause>

  <clause id="19069">
    <literal><![CDATA[
      K(x,y * (K(z,y) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(19062(a,2),16473(a,1))].">
      <j1 rule="para" parents="19062 16473"/>
    </justification>
  </clause>

  <clause id="19070">
    <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(19062(a,2),16810(a,1))].">
      <j1 rule="para" parents="19062 16810"/>
    </justification>
  </clause>

  <clause id="19071">
    <literal><![CDATA[
      K(x,T(T(y,z),z) * u) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(18253(a,1),19067(a,1,2))].">
      <j1 rule="para" parents="18253 19067"/>
    </justification>
  </clause>

  <clause id="19072">
    <literal><![CDATA[
      K((x * y) / x,z * u) = K(y,T(T(T(z,w),w) * u,x))
    ]]></literal>
    <justification jstring="[hyper(8121,a,19071,a),flip(a)].">
      <j1 rule="hyper" parents="8121 19071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19073">
    <literal><![CDATA[
      K(x,T(y \ z,y) * u) = K(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[para(109(a,1),19071(a,1,2,1,1))].">
      <j1 rule="para" parents="109 19071"/>
    </justification>
  </clause>

  <clause id="19074">
    <literal><![CDATA[
      K(x,((y * z) / y) * u) = K(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[para(222(a,1),19071(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="222 19071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19075">
    <literal><![CDATA[
      K(x,T(y,y \ z) * u) = K(x,(z / (z / y)) * u)
    ]]></literal>
    <justification jstring="[para(4502(a,1),19071(a,1,2,1,1))].">
      <j1 rule="para" parents="4502 19071"/>
    </justification>
  </clause>

  <clause id="19076">
    <literal><![CDATA[
      K(x,(y / z) * ((y / z) * u)) = K(x,(z \ y) * ((z \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,16014,a(flip),b,19073,a),flip(a)].">
      <j1 rule="hyper" parents="65 16014 19073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19077">
    <literal><![CDATA[
      K(x,L(((y * z) / y) * u,w,v5)) = L(K(x,T(z,y) * u),w,v5)
    ]]></literal>
    <justification jstring="[para(19074(a,1),11889(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19074 11889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19078">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (u / w))) = K(x,y * (T(u,z) / w))
    ]]></literal>
    <justification jstring="[para(14430(a,1),19064(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14430 19064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19079">
    <literal><![CDATA[
      K(x,(y / (y / z)) * u) = K(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(13899,a,19075,a),flip(a)].">
      <j1 rule="hyper" parents="13899 19075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19080">
    <literal><![CDATA[
      K(x,T(y \ z,z) * u) = K(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[para(76(a,1),19079(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="76 19079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19081">
    <literal><![CDATA[
      K(x,K(y,T(z,u) * w)) * K(x,y \ ((u / (u / z)) * w)) = K(x,((u / (u / z)) * w) / y)
    ]]></literal>
    <justification jstring="[para(19079(a,1),8497(a,1,1,2))].">
      <j1 rule="para" parents="19079 8497"/>
    </justification>
  </clause>

  <clause id="19082">
    <literal><![CDATA[
      K(x,(y \ a(z,u,K(w,v5))) * v6) = K(x,y \ v6)
    ]]></literal>
    <justification jstring="[para(18750(a,1),19039(a,1,2,1))].">
      <j1 rule="para" parents="18750 19039"/>
    </justification>
  </clause>

  <clause id="19083">
    <literal><![CDATA[
      K(x,(T(a(y,z,u),w) \ 1) * v5) = K(x,a(y,z,u) \ v5)
    ]]></literal>
    <justification jstring="[para(14888(a,1),19082(a,1,2,1))].">
      <j1 rule="para" parents="14888 19082"/>
    </justification>
  </clause>

  <clause id="19084">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w)) * v5) = T(x,K(y,z) * v5)
    ]]></literal>
    <justification jstring="[hyper(5086,a,19043,a)].">
      <j1 rule="hyper" parents="5086 19043"/>
    </justification>
  </clause>

  <clause id="19085">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) * v5) = v6
    ]]></literal>
    <justification jstring="[para(19043(a,2),5155(a,1))].">
      <j1 rule="para" parents="19043 5155"/>
    </justification>
  </clause>

  <clause id="19086">
    <literal><![CDATA[
      T(x,K(y,z) * (y \ L(z,u,w))) = T(x,L(z,u,w) / y)
    ]]></literal>
    <justification jstring="[hyper(16642,a,19084,a),flip(a)].">
      <j1 rule="hyper" parents="16642 19084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19087">
    <literal><![CDATA[
      T(x,y * K(z,L(u,w,v5))) = T(x,K(z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(16368,a,19084,a)].">
      <j1 rule="hyper" parents="16368 19084"/>
    </justification>
  </clause>

  <clause id="19088">
    <literal><![CDATA[
      K(K(x,L(y,z,u)) * w,v5) = v5 / T(v5,K(x,y) * w)
    ]]></literal>
    <justification jstring="[para(19084(a,1),5033(a,2,2))].">
      <j1 rule="para" parents="19084 5033"/>
    </justification>
  </clause>

  <clause id="19089">
    <literal><![CDATA[
      T(x,K(L(y,z,u),w) * v5) = T(x,K(y,w) * v5)
    ]]></literal>
    <justification jstring="[para(11929(a,2),19084(a,1,2,1))].">
      <j1 rule="para" parents="11929 19084"/>
    </justification>
  </clause>

  <clause id="19090">
    <literal><![CDATA[
      T(x,K(y,z) * (u * w)) = T(x,u * (w * K(y,z)))
    ]]></literal>
    <justification jstring="[para(11903(a,1),19087(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11903 19087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19091">
    <literal><![CDATA[
      T(x,K(y,z) * (u * (w * K(z,y)))) = T(x,u * w)
    ]]></literal>
    <justification jstring="[para(11910(a,1),19087(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11910 19087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19092">
    <literal><![CDATA[
      T(x,K(y,z) * (u * (w * y))) = T(x,u * (w * T(y,z)))
    ]]></literal>
    <justification jstring="[para(11942(a,1),19087(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11942 19087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19093">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w)) \ v5) = T(x,K(z,y) * v5)
    ]]></literal>
    <justification jstring="[para(5426(a,2),19089(a,1,2))].">
      <j1 rule="para" parents="5426 19089"/>
    </justification>
  </clause>

  <clause id="19094">
    <literal><![CDATA[
      T(x,L(K(y,z),u,w) \ v5) = T(x,K(z,y) * v5)
    ]]></literal>
    <justification jstring="[para(7810(a,1),19093(a,1,2,1))].">
      <j1 rule="para" parents="7810 19093"/>
    </justification>
  </clause>

  <clause id="19095">
    <literal><![CDATA[
      T(x,L(K(y,z),u,w) \ v5) = T(x,K(y,z) \ v5)
    ]]></literal>
    <justification jstring="[para(5426(a,2),19094(a,2,2))].">
      <j1 rule="para" parents="5426 19094"/>
    </justification>
  </clause>

  <clause id="19096">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w) \ v5) = x \ T(x,K(y,z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(119,a,19095,a(flip),b,5083,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 19095 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19097">
    <literal><![CDATA[
      T(x,K(L(y,z,u),w) * (v5 * (u * (z * y)))) = T(x,v5 * ((u * z) * T(L(y,z,u),w)))
    ]]></literal>
    <justification jstring="[para(6873(a,1),19090(a,2,2,2))].">
      <j1 rule="para" parents="6873 19090"/>
    </justification>
  </clause>

  <clause id="19098">
    <literal><![CDATA[
      K(x,T(y,z * (u * K(w,v5)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z * u)) = v6
    ]]></literal>
    <justification jstring="[para(19090(a,1),17099(a,1,2))].">
      <j1 rule="para" parents="19090 17099"/>
    </justification>
  </clause>

  <clause id="19099">
    <literal><![CDATA[
      K(x,((y * z) / y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(5705(a,2),19069(a,1,2))].">
      <j1 rule="para" parents="5705 19069"/>
    </justification>
  </clause>

  <clause id="19100">
    <literal><![CDATA[
      K(K(x,L(y,z,u)) * w,v5) = K(K(x,y) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(299,a,5033,a,b,19088,a),flip(a)].">
      <j1 rule="hyper" parents="299 5033 19088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19101">
    <literal><![CDATA[
      K(K(x,y) * R(y,z,u),T(w,y)) = K(R(y,z,u),T(w,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,18922,a(flip),b,19100,a),flip(a)].">
      <j1 rule="hyper" parents="65 18922 19100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19102">
    <literal><![CDATA[
      K(K(x,T((y * z) \ u,w)) * v5,v6) = K(K(x,T(z \ (y \ u),w)) * v5,v6)
    ]]></literal>
    <justification jstring="[para(600(a,1),19100(a,1,1,1,2))].">
      <j1 rule="para" parents="600 19100"/>
    </justification>
  </clause>

  <clause id="19103">
    <literal><![CDATA[
      K(K(L(x,y,z),u) * w,v5) = K(K(x,u) * w,v5)
    ]]></literal>
    <justification jstring="[para(11929(a,2),19100(a,1,1,1))].">
      <j1 rule="para" parents="11929 19100"/>
    </justification>
  </clause>

  <clause id="19104">
    <literal><![CDATA[
      K(K((x * y) \ z,u) * w,v5) = K(K(y \ (x \ z),u) * w,v5)
    ]]></literal>
    <justification jstring="[para(11935(a,1),19100(a,1,1,1))].">
      <j1 rule="para" parents="11935 19100"/>
    </justification>
  </clause>

  <clause id="19105">
    <literal><![CDATA[
      K(x * K(L(y,z,u),w),v5) = K(K(y,w) * x,v5)
    ]]></literal>
    <justification jstring="[hyper(16405,a,19103,a)].">
      <j1 rule="hyper" parents="16405 19103"/>
    </justification>
  </clause>

  <clause id="19106">
    <literal><![CDATA[
      K(x * L(K(y,z),u,w),v5) = K(K(y,z) * x,v5)
    ]]></literal>
    <justification jstring="[para(7431(a,1),19105(a,1,1,2))].">
      <j1 rule="para" parents="7431 19105"/>
    </justification>
  </clause>

  <clause id="19107">
    <literal><![CDATA[
      K(x * ((x \ y) * K(z,u)),w) = K(K(z,u) * y,w)
    ]]></literal>
    <justification jstring="[para(482(a,1),19106(a,1,1))].">
      <j1 rule="para" parents="482 19106"/>
    </justification>
  </clause>

  <clause id="19108">
    <literal><![CDATA[
      K(((x \ y) * K(z,u)) * x,w) = K(K(z,u) * y,T(w,x))
    ]]></literal>
    <justification jstring="[hyper(13182,a,19107,a)].">
      <j1 rule="hyper" parents="13182 19107"/>
    </justification>
  </clause>

  <clause id="19109">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w) \ v5) = K(x,K(y,z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(299,a,5036,a,b,19096,a),flip(a)].">
      <j1 rule="hyper" parents="299 5036 19096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19110">
    <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(19096(a,2),5155(a,1))].">
      <j1 rule="para" parents="19096 5155"/>
    </justification>
  </clause>

  <clause id="19111">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (w * (y * z)))) = K(x,u * (w * T(y * z,z)))
    ]]></literal>
    <justification jstring="[hyper(13902,a,19049,a)].">
      <j1 rule="hyper" parents="13902 19049"/>
    </justification>
  </clause>

  <clause id="19112">
    <literal><![CDATA[
      K(x,K(y * z,(y \ 1) \ 1) * (u * (w / ((y \ 1) \ 1)))) = K(x,u * (w / T(y,y \ z)))
    ]]></literal>
    <justification jstring="[para(14515(a,1),19050(a,2,2,2,2))].">
      <j1 rule="para" parents="14515 19050"/>
    </justification>
  </clause>

  <clause id="19113">
    <literal><![CDATA[
      a(K(x,y) * (z * (u * y)),w,K(v5,v6)) = v7 / (v7 * a(v6,w,K(v5,z * (u * T(y,x)))))
    ]]></literal>
    <justification jstring="[para(19058(a,1),18697(a,1,2,2,3)),flip(a)].">
      <j1 rule="para" parents="19058 18697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19114">
    <literal><![CDATA[
      K(x,(y * K(z,u)) / w) = K(x,y * (w \ K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(19006,a,19060,a)].">
      <j1 rule="hyper" parents="19006 19060"/>
    </justification>
  </clause>

  <clause id="19115">
    <literal><![CDATA[
      K(x,y * (z \ K(z,u))) = K(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(7206(a,1),19114(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7206 19114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19116">
    <literal><![CDATA[
      K(x,y / T(z,u)) * a(w,v5,K(y / T(z,u),x)) = K(x,L(y * (z \ K(z,u)),v5,w))
    ]]></literal>
    <justification jstring="[para(19115(a,1),17806(a,1,1))].">
      <j1 rule="para" parents="19115 17806"/>
    </justification>
  </clause>

  <clause id="19117">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (w \ K(y,z)))) = K(x,u / w)
    ]]></literal>
    <justification jstring="[hyper(299,a,14205,a(flip),b,19061,a),flip(a)].">
      <j1 rule="hyper" parents="299 14205 19061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19118">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (w \ K(z,y)))) = K(x,u / w)
    ]]></literal>
    <justification jstring="[hyper(15803,a,19117,a)].">
      <j1 rule="hyper" parents="15803 19117"/>
    </justification>
  </clause>

  <clause id="19119">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (z * w))) = x \ T(x,u * (T(z,y) * w))
    ]]></literal>
    <justification jstring="[hyper(299,a,5036,a(flip),b,19065,a),flip(a)].">
      <j1 rule="hyper" parents="299 5036 19065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19120">
    <literal><![CDATA[
      K(x * K(y,z * (T(u,w) * v5)),v6) = K(K(z * (u * v5),y) * x,v6)
    ]]></literal>
    <justification jstring="[para(19065(a,1),17884(a,1,1,2))].">
      <j1 rule="para" parents="19065 17884"/>
    </justification>
  </clause>

  <clause id="19121">
    <literal><![CDATA[
      K(x,y * ((z \ K(u,z \ 1)) \ w)) = K(x,y * (T(z \ 1,u) \ w))
    ]]></literal>
    <justification jstring="[para(5696(a,1),19066(a,1,2,2))].">
      <j1 rule="para" parents="5696 19066"/>
    </justification>
  </clause>

  <clause id="19122">
    <literal><![CDATA[
      K(x,T(T(T(y,z),z) * u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y * u,w)) = v5
    ]]></literal>
    <justification jstring="[para(19072(a,1),8121(a,1))].">
      <j1 rule="para" parents="19072 8121"/>
    </justification>
  </clause>

  <clause id="19123">
    <literal><![CDATA[
      K(x,y * (K(z * u,w) * (w / v5))) = K(x,y * (T(w,z \ u) / v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,18092,a(flip),b,19078,a)].">
      <j1 rule="hyper" parents="65 18092 19078"/>
    </justification>
  </clause>

  <clause id="19124">
    <literal><![CDATA[
      K(x,y * (((z * u) / z) / w)) = K(x,y * (T(u,z) / w))
    ]]></literal>
    <justification jstring="[para(14662(a,2),19078(a,1,2,2))].">
      <j1 rule="para" parents="14662 19078"/>
    </justification>
  </clause>

  <clause id="19125">
    <literal><![CDATA[
      K(x,T(a(y,z,u),w) \ v5) = K(x,a(y,z,u) \ v5)
    ]]></literal>
    <justification jstring="[hyper(14281,a,19083,a)].">
      <j1 rule="hyper" parents="14281 19083"/>
    </justification>
  </clause>

  <clause id="19126">
    <literal><![CDATA[
      T(x,T(y,z) \ L(z,u,w)) = T(x,L(z,u,w) / y)
    ]]></literal>
    <justification jstring="[hyper(15835,a,19086,a)].">
      <j1 rule="hyper" parents="15835 19086"/>
    </justification>
  </clause>

  <clause id="19127">
    <literal><![CDATA[
      T(x,K(y,z) * (u * (w * (y * z)))) = T(x,u * (w * T(y * z,z)))
    ]]></literal>
    <justification jstring="[hyper(15933,a,19092,a)].">
      <j1 rule="hyper" parents="15933 19092"/>
    </justification>
  </clause>

  <clause id="19128">
    <literal><![CDATA[
      T(x,K(y,z) * (u * (w * z))) = T(x,u * (w * T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(15834,a,19092,a)].">
      <j1 rule="hyper" parents="15834 19092"/>
    </justification>
  </clause>

  <clause id="19129">
    <literal><![CDATA[
      K(R(x,y,z) * K(u,x),w) = K(R(x,y,z),T(w,u))
    ]]></literal>
    <justification jstring="[hyper(18717,a,19101,a)].">
      <j1 rule="hyper" parents="18717 19101"/>
    </justification>
  </clause>

  <clause id="19131">
    <literal><![CDATA[
      K(R(x,y,z) * K(u,x),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(w,u),y,z)) = v5
    ]]></literal>
    <justification jstring="[para(19129(a,2),15504(a,1))].">
      <j1 rule="para" parents="19129 15504"/>
    </justification>
  </clause>

  <clause id="19132">
    <literal><![CDATA[
      K(K(x,y) * ((z \ u) * z),w) = K(K(x,y) * u,T(w,z))
    ]]></literal>
    <justification jstring="[hyper(19011,a,19108,a)].">
      <j1 rule="hyper" parents="19011 19108"/>
    </justification>
  </clause>

  <clause id="19133">
    <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(15813(a,1),19110(a,1))].">
      <j1 rule="para" parents="15813 19110"/>
    </justification>
  </clause>

  <clause id="19134">
    <literal><![CDATA[
      K(x,y * (T(T(z,u),u) / w)) = K(x,y * (z / w))
    ]]></literal>
    <justification jstring="[para(223(a,1),19124(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="223 19124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19135">
    <literal><![CDATA[
      K(x,K(((y * z) / y) / u,w) * (T(z,y) / u)) = K(x,T(((y * z) / y) / u,w))
    ]]></literal>
    <justification jstring="[para(5096(a,2),19124(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5096 19124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19136">
    <literal><![CDATA[
      K(x,T(y,T(T(z,u),u) / w) * (z / w)) = K(x,(T(T(z,u),u) / w) * y)
    ]]></literal>
    <justification jstring="[hyper(13261,a,19134,a),flip(a)].">
      <j1 rule="hyper" parents="13261 19134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19137">
    <literal><![CDATA[
      K(x,y * (z \ T(u,z))) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[hyper(65,a,13881,a(flip),b,19134,a)].">
      <j1 rule="hyper" parents="65 13881 19134"/>
    </justification>
  </clause>

  <clause id="19138">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) * (u / (z \ 1))) = K(x,(y * z) * (z \ T(u,z \ 1)))
    ]]></literal>
    <justification jstring="[para(1993(a,1),19137(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1993 19137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19139">
    <literal><![CDATA[
      K(K(x,y) * T(z,u),w) = K(K(x,y) * z,T(w,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,17821,a(flip),b,19132,a)].">
      <j1 rule="hyper" parents="65 17821 19132"/>
    </justification>
  </clause>

  <clause id="19140">
    <literal><![CDATA[
      (((x * x) * y) / (x * x)) / (((x * x) * (y * K(K(z,u) * w,T(y,v5)))) / (x * x)) = K(y,K(z,u) * T(w,x * (x * v5)))
    ]]></literal>
    <justification jstring="[para(19139(a,1),17368(a,1,2,1,2,2))].">
      <j1 rule="para" parents="19139 17368"/>
    </justification>
  </clause>

  <clause id="19142">
    <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(16374(a,1),19045(a,1))].">
      <j1 rule="para" parents="16374 19045"/>
    </justification>
  </clause>

  <clause id="19145">
    <literal><![CDATA[
      K(x,(y * z) * K(u * w,v5)) = K(x,y * (z * K(u \ w,v5)))
    ]]></literal>
    <justification jstring="[hyper(19142,a,17830,a),flip(a)].">
      <j1 rule="hyper" parents="19142 17830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19146">
    <literal><![CDATA[
      K(x,K((y * z) \ u,w) * v5) = K(x,K(z * (y \ u),w) * v5)
    ]]></literal>
    <justification jstring="[hyper(299,a,17837,a(flip),b,19044,a),flip(a)].">
      <j1 rule="hyper" parents="299 17837 19044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19147">
    <literal><![CDATA[
      K(x,y * L(z / (u \ 1),u,u)) = K(x,y * T(u * z,u \ 1))
    ]]></literal>
    <justification jstring="[para(6197(a,1),19056(a,1,2,2))].">
      <j1 rule="para" parents="6197 19056"/>
    </justification>
  </clause>

  <clause id="19148">
    <literal><![CDATA[
      K(x,L(((y * z) / y) * u,w,v5)) = K(x,L(T(z,y) * u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(299,a,11889,a(flip),b,19077,a),flip(a)].">
      <j1 rule="hyper" parents="299 11889 19077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19149">
    <literal><![CDATA[
      K(K(x \ (y \ z),u) * w,v5) = K(K((y * x) * z,u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(17861,a,19104,a),flip(a)].">
      <j1 rule="hyper" parents="17861 19104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19150">
    <literal><![CDATA[
      T(x,K(y,z) * (u * (z * w))) = T(x,u * (T(z,y) * w))
    ]]></literal>
    <justification jstring="[hyper(5086,a,19119,a)].">
      <j1 rule="hyper" parents="5086 19119"/>
    </justification>
  </clause>

  <clause id="19151">
    <literal><![CDATA[
      T(x,K(y,z) * (u * (T(z,w) * v5))) = T(x,u * (T(T(z,w),y) * v5))
    ]]></literal>
    <justification jstring="[hyper(16793,a,19150,a)].">
      <j1 rule="hyper" parents="16793 19150"/>
    </justification>
  </clause>

  <clause id="19152">
    <literal><![CDATA[
      T(x,K(y,z) * (u * (T(z,w) * v5))) = T(x,u * (T(z,y) * (v5 * K(z,w))))
    ]]></literal>
    <justification jstring="[hyper(65,a,16844,a(flip),b,19150,a)].">
      <j1 rule="hyper" parents="65 16844 19150"/>
    </justification>
  </clause>

  <clause id="19153">
    <literal><![CDATA[
      K(x,(y * (z / (u \ w))) * K(u * w,u)) = K(x,y * (z / (w / u)))
    ]]></literal>
    <justification jstring="[para(9047(a,1),19145(a,2,2,2))].">
      <j1 rule="para" parents="9047 19145"/>
    </justification>
  </clause>

  <clause id="19154">
    <literal><![CDATA[
      K(x,K((y * z) * u,w) * v5) = K(x,K(z * (y \ u),w) * v5)
    ]]></literal>
    <justification jstring="[hyper(17859,a,19146,a)].">
      <j1 rule="hyper" parents="17859 19146"/>
    </justification>
  </clause>

  <clause id="19155">
    <literal><![CDATA[
      K(x,L(y * (K(z,y) * u),w,v5)) = K(x,L(T(y,z) * u,w,v5))
    ]]></literal>
    <justification jstring="[para(5705(a,1),19148(a,1,2,1))].">
      <j1 rule="para" parents="5705 19148"/>
    </justification>
  </clause>

  <clause id="19156">
    <literal><![CDATA[
      K(K((x * y) * z,u) * w,v5) = K(K(y * (x \ z),u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(17861,a,19149,a),flip(a)].">
      <j1 rule="hyper" parents="17861 19149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19158">
    <literal><![CDATA[
      K(x,K(y * ((z \ 1) \ u),w) * v5) = K(x,v5 * K((z * y) * u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,18130,a(flip),b,19154,a),flip(a)].">
      <j1 rule="hyper" parents="65 18130 19154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19159">
    <literal><![CDATA[
      K(x,L((y * K(z,y)) / u,w,v5)) = K(x,L(T(y,z) * (u \ 1),w,v5))
    ]]></literal>
    <justification jstring="[hyper(14793,a,19155,a)].">
      <j1 rule="hyper" parents="14793 19155"/>
    </justification>
  </clause>

  <clause id="19160">
    <literal><![CDATA[
      K(K(x * (y \ z),T(u,w)) * v5,v6) = K(v5 * K(u,(y * x) * z),v6)
    ]]></literal>
    <justification jstring="[hyper(17810,a,19156,a),flip(a)].">
      <j1 rule="hyper" parents="17810 19156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19161">
    <literal><![CDATA[
      K(x,y * L(z / (u \ 1),u,u)) = K(x,y * T(u * z,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,17473,a(flip),b,19147,a),flip(a)].">
      <j1 rule="hyper" parents="299 17473 19147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19162">
    <literal><![CDATA[
      K(x,y * L(z / (u \ 1),u,u)) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[hyper(299,a,13779,a(flip),b,19161,a),flip(a)].">
      <j1 rule="hyper" parents="299 13779 19161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19163">
    <literal><![CDATA[
      K(K(x * (T(y,z) \ u),w) * v5,v6) = K(K((y \ u) * x,w) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,18196,a,b,19033,a)].">
      <j1 rule="hyper" parents="65 18196 19033"/>
    </justification>
  </clause>

  <clause id="19164">
    <literal><![CDATA[
      K(x,K(y * z,y) * (u * (w * (z / y)))) = K(x,u * (w * (y \ z)))
    ]]></literal>
    <justification jstring="[hyper(17859,a,19051,a)].">
      <j1 rule="hyper" parents="17859 19051"/>
    </justification>
  </clause>

  <clause id="19165">
    <literal><![CDATA[
      K(x,y * (z * T(u * w,w))) = K(x,y * (z * (w * u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,19059,a(flip),b,19111,a),flip(a)].">
      <j1 rule="hyper" parents="65 19059 19111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19166">
    <literal><![CDATA[
      K(x,y * (z * (a(z,u,1 / u) * K(u,u \ 1)))) = K(x,y * ((1 / u) * (u * z)))
    ]]></literal>
    <justification jstring="[hyper(65,a,18164,a,b,19165,a)].">
      <j1 rule="hyper" parents="65 18164 19165"/>
    </justification>
  </clause>

  <clause id="19167">
    <literal><![CDATA[
      K(x,y * (z * (u * (w / u)))) = K(x,y * (z * T(w,u)))
    ]]></literal>
    <justification jstring="[para(12(a,1),19165(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="12 19165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19168">
    <literal><![CDATA[
      K(x,y * ((z * u) * u)) = K(x,y * (u * (u * z)))
    ]]></literal>
    <justification jstring="[para(107(a,1),19165(a,1,2,2))].">
      <j1 rule="para" parents="107 19165"/>
    </justification>
  </clause>

  <clause id="19169">
    <literal><![CDATA[
      K(x,y * (z * T((u * (w * u)) / u,T(u,u * w)))) = K(x,y * (z * (T(u,u * w) * w)))
    ]]></literal>
    <justification jstring="[para(4356(a,2),19165(a,1,2,2,2,1))].">
      <j1 rule="para" parents="4356 19165"/>
    </justification>
  </clause>

  <clause id="19170">
    <literal><![CDATA[
      K(x,y * (z * (u * (w / u)))) = x \ T(x,y * (z * T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(299,a,5036,a(flip),b,19167,a),flip(a)].">
      <j1 rule="hyper" parents="299 5036 19167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19171">
    <literal><![CDATA[
      K(x,y * (z * T(u * w,u))) = K(x,y * (z * (T(u,w) * w)))
    ]]></literal>
    <justification jstring="[para(4263(a,2),19167(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4263 19167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19172">
    <literal><![CDATA[
      K(x,y * (K(z,u) * T(w,z))) = K(x,y * (T(z,u) * (w / z)))
    ]]></literal>
    <justification jstring="[para(5103(a,1),19167(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5103 19167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19173">
    <literal><![CDATA[
      T(x,y * (z * (u * (w / u)))) = T(x,y * (z * T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(5086,a,19170,a)].">
      <j1 rule="hyper" parents="5086 19170"/>
    </justification>
  </clause>

  <clause id="19174">
    <literal><![CDATA[
      K(x,y * (z * (u * (w / u)))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * T(w,u))) = v5
    ]]></literal>
    <justification jstring="[para(19170(a,2),5155(a,1))].">
      <j1 rule="para" parents="19170 5155"/>
    </justification>
  </clause>

  <clause id="19175">
    <literal><![CDATA[
      T(x,y * (T(z,u * (w / u)) * T(w,u))) = T(x,y * ((u * (w / u)) * z))
    ]]></literal>
    <justification jstring="[hyper(15900,a,19173,a),flip(a)].">
      <j1 rule="hyper" parents="15900 19173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19176">
    <literal><![CDATA[
      T(x,T(y,z * (u * (w / u))) * (z * T(w,u))) = T(x,(z * (u * (w / u))) * y)
    ]]></literal>
    <justification jstring="[hyper(13267,a,19173,a),flip(a)].">
      <j1 rule="hyper" parents="13267 19173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19177">
    <literal><![CDATA[
      T(x,y * (z * T(u * w,w))) = T(x,y * (z * (w * u)))
    ]]></literal>
    <justification jstring="[para(11(a,1),19173(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="11 19173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19178">
    <literal><![CDATA[
      T(x,y * (z * T(u * w,u))) = T(x,y * (z * (T(u,w) * w)))
    ]]></literal>
    <justification jstring="[para(4263(a,2),19173(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4263 19173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19179">
    <literal><![CDATA[
      T(x,y * (z * T(u * (1 / z),1 / z))) = T(x,y * ((z \ 1) * (z * u)))
    ]]></literal>
    <justification jstring="[para(944(a,2),19177(a,2,2,2))].">
      <j1 rule="para" parents="944 19177"/>
    </justification>
  </clause>

  <clause id="19180">
    <literal><![CDATA[
      T(x,y * (z * T((u * w) * (1 / u),u \ 1))) = T(x,y * (z * ((u \ 1) * (T(u,u \ 1) * w))))
    ]]></literal>
    <justification jstring="[para(3267(a,1),19177(a,1,2,2,2,1))].">
      <j1 rule="para" parents="3267 19177"/>
    </justification>
  </clause>

  <clause id="19181">
    <literal><![CDATA[
      K(x,y * (K(z,u) * T(w,z))) = K(x,y * (z * (w / T(z,u))))
    ]]></literal>
    <justification jstring="[hyper(299,a,16950,a(flip),b,19172,a),flip(a)].">
      <j1 rule="hyper" parents="299 16950 19172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19182">
    <literal><![CDATA[
      K(x,y * T(K(z,u) * w,z)) = K(x,y * (z * (w / T(z,u))))
    ]]></literal>
    <justification jstring="[para(7749(a,2),19181(a,1,2,2))].">
      <j1 rule="para" parents="7749 19181"/>
    </justification>
  </clause>

  <clause id="19183">
    <literal><![CDATA[
      K(x,T(K(y * (z / y),y) * u,y * (z / y))) = K(x,((y * (z / y)) \ u) * T(K(y,z) * z,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,16662,a,b,19182,a)].">
      <j1 rule="hyper" parents="299 16662 19182"/>
    </justification>
  </clause>

  <clause id="19184">
    <literal><![CDATA[
      K(K(x * (T(y,z) * u),w) * v5,v6) = K(K(x * (y * u),w) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(17784,a,19120,a)].">
      <j1 rule="hyper" parents="17784 19120"/>
    </justification>
  </clause>

  <clause id="19185">
    <literal><![CDATA[
      K(x,y * (T(z,u \ w) / v5)) = K(x,y * (T(z,u * w) / v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,19078,a(flip),b,19123,a),flip(a)].">
      <j1 rule="hyper" parents="65 19078 19123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19186">
    <literal><![CDATA[
      K(x,y * (T(z,u * w) / T(v5,T(z,u \ w)))) = K(x,y * (v5 \ T(z,u \ w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,13884,a(flip),b,19185,a),flip(a)].">
      <j1 rule="hyper" parents="65 13884 19185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19187">
    <literal><![CDATA[
      T(x,K(y,y * z) * (u * (w * (y * z)))) = T(x,u * (w * T(y * z,z)))
    ]]></literal>
    <justification jstring="[hyper(65,a,13702,a,b,19127,a)].">
      <j1 rule="hyper" parents="65 13702 19127"/>
    </justification>
  </clause>

  <clause id="19188">
    <literal><![CDATA[
      K(x,(y * (z / (u \ w))) * K(w * u,u)) = K(x,y * (z / (w / u)))
    ]]></literal>
    <justification jstring="[hyper(16856,a,19153,a)].">
      <j1 rule="hyper" parents="16856 19153"/>
    </justification>
  </clause>

  <clause id="19189">
    <literal><![CDATA[
      K(x,y * K(z,u * ((w \ 1) \ v5))) = K(x,y * K((w * u) * v5,z))
    ]]></literal>
    <justification jstring="[hyper(16624,a,19158,a)].">
      <j1 rule="hyper" parents="16624 19158"/>
    </justification>
  </clause>

  <clause id="19190">
    <literal><![CDATA[
      K(x,L((y * K(z,y)) / u,w,v5)) = K(x,L(T(y,z) / u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(299,a,14645,a(flip),b,19159,a),flip(a)].">
      <j1 rule="hyper" parents="299 14645 19159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19191">
    <literal><![CDATA[
      K(x,L(T(y,z) / u,u,z)) = K(x,(z * y) / (u * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,15531,a(flip),b,19190,a),flip(a)].">
      <j1 rule="hyper" parents="65 15531 19190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19192">
    <literal><![CDATA[
      K(x,L(T(y * z,y \ 1) / u,u,y \ 1)) = K(x,(y * ((1 / y) * z)) / (u * (y \ 1)))
    ]]></literal>
    <justification jstring="[para(944(a,1),19191(a,2,2,1))].">
      <j1 rule="para" parents="944 19191"/>
    </justification>
  </clause>

  <clause id="19193">
    <literal><![CDATA[
      K(x * K(y,(z * u) * w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x * K(y,u * (z \ w)),v5) = v6
    ]]></literal>
    <justification jstring="[para(19160(a,1),17810(a,1))].">
      <j1 rule="para" parents="19160 17810"/>
    </justification>
  </clause>

  <clause id="19195">
    <literal><![CDATA[
      K(x,(y * (z * (u / w))) * K(u,w)) = K(x,y * (z * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(16623,a,19164,a)].">
      <j1 rule="hyper" parents="16623 19164"/>
    </justification>
  </clause>

  <clause id="19196">
    <literal><![CDATA[
      K(x,y * ((z * (u / w)) * K(u,w))) = K(x,y * (z * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(19142,a,19195,a)].">
      <j1 rule="hyper" parents="19142 19195"/>
    </justification>
  </clause>

  <clause id="19197">
    <literal><![CDATA[
      K(x,(y * (z / (u \ w))) * K(u,w)) = K(x,y * (z / (w / u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,17485,a(flip),b,19188,a)].">
      <j1 rule="hyper" parents="65 17485 19188"/>
    </justification>
  </clause>

  <clause id="19198">
    <literal><![CDATA[
      K(x,y * (z / (K(u,w) / v5))) = K(x,y * (z / (v5 \ K(u,w))))
    ]]></literal>
    <justification jstring="[hyper(16800,a,19197,a),flip(a)].">
      <j1 rule="hyper" parents="16800 19197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19199">
    <literal><![CDATA[
      K(x,y * (T(z,K(u,w) / v5) / (v5 \ K(u,w)))) = K(x,y * ((K(u,w) / v5) \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,13881,a(flip),b,19198,a),flip(a)].">
      <j1 rule="hyper" parents="65 13881 19198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19200">
    <literal><![CDATA[
      K(x,T(y,z * ((1 / u) \ w)) \ v5) = K(x,(y \ v5) * K((u * z) * w,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,16594,a(flip),b,19189,a)].">
      <j1 rule="hyper" parents="65 16594 19189"/>
    </justification>
  </clause>

  <clause id="19201">
    <literal><![CDATA[
      K(x,((K(y,z) * u) * w) * v5) = K(x,K(y,z) * ((u * w) * v5))
    ]]></literal>
    <justification jstring="[hyper(19085,a,18997,a),flip(a)].">
      <j1 rule="hyper" parents="19085 18997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19203">
    <literal><![CDATA[
      K(x,(y * (z * K(u,w))) * v5) = K(x,K(u,w) * ((y * z) * v5))
    ]]></literal>
    <justification jstring="[hyper(19085,a,19005,a),flip(a)].">
      <j1 rule="hyper" parents="19085 19005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19205">
    <literal><![CDATA[
      K(x,(y * (z * K(u,w))) * v5) = K(x,(y * z) * (v5 * K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(299,a,19042,a(flip),b,19203,a),flip(a)].">
      <j1 rule="hyper" parents="299 19042 19203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19206">
    <literal><![CDATA[
      K(x,(y * z) * (u * K(z,w))) = K(x,(y * T(z,w)) * u)
    ]]></literal>
    <justification jstring="[para(5083(a,2),19205(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="5083 19205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19207">
    <literal><![CDATA[
      K(x,K(y,z) * ((u * z) * w)) = K(x,(u * T(z,y)) * w)
    ]]></literal>
    <justification jstring="[hyper(19052,a,19206,a)].">
      <j1 rule="hyper" parents="19052 19206"/>
    </justification>
  </clause>

  <clause id="19208">
    <literal><![CDATA[
      K(x,(y * z) * (u * K(w,z))) = K(x,(y * T(z,w)) * u)
    ]]></literal>
    <justification jstring="[hyper(19045,a,19207,a)].">
      <j1 rule="hyper" parents="19045 19207"/>
    </justification>
  </clause>

  <clause id="19209">
    <literal><![CDATA[
      K(x,(T(y,z) * T(z,u)) * w) = K(x,(z * y) * (w * K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(16005,a,19208,a),flip(a)].">
      <j1 rule="hyper" parents="16005 19208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19210">
    <literal><![CDATA[
      K(x,(y * z) * (u * K(w,y))) = K(x,(T(y,w) * z) * u)
    ]]></literal>
    <justification jstring="[hyper(16946,a,19209,a),flip(a)].">
      <j1 rule="hyper" parents="16946 19209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19211">
    <literal><![CDATA[
      K(x,(T(y,z) * u) * (y \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * u) * (T(y,z) \ w)) = v5
    ]]></literal>
    <justification jstring="[para(19210(a,1),16839(a,1))].">
      <j1 rule="para" parents="19210 16839"/>
    </justification>
  </clause>

  <clause id="19212">
    <literal><![CDATA[
      K(K(x,y * (y * K(z,u))) * K(u,(w / x) * (w \ z)),v5) = K(K(u,(w * (w / x)) \ z),v5)
    ]]></literal>
    <justification jstring="[hyper(19193,a,17865,a)].">
      <j1 rule="hyper" parents="19193 17865"/>
    </justification>
  </clause>

  <clause id="19213">
    <literal><![CDATA[
      K(T(x * K(y,z),u) * w,v5) = K(K(y,z) * (T(x,u) * w),v5)
    ]]></literal>
    <justification jstring="[hyper(16912,a,19027,a),flip(a)].">
      <j1 rule="hyper" parents="16912 19027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19214">
    <literal><![CDATA[
      K(T(x * K(y,z),u) * w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(K(y,z) * (T(x,u) * w),v5) = v6
    ]]></literal>
    <justification jstring="[para(19027(a,1),16912(a,1))].">
      <j1 rule="para" parents="19027 16912"/>
    </justification>
  </clause>

  <clause id="19215">
    <literal><![CDATA[
      K(K(x,T(y \ (z \ u),w)) * v5,v6) = K(v5 * K((z * y) \ u,x),v6)
    ]]></literal>
    <justification jstring="[hyper(17810,a,19102,a),flip(a)].">
      <j1 rule="hyper" parents="17810 19102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19217">
    <literal><![CDATA[
      K(K(x,T(y \ (z \ u),w)) * v5,v6) = K(v5 * K((z * y) * u,x),v6)
    ]]></literal>
    <justification jstring="[hyper(299,a,17811,a(flip),b,19215,a),flip(a)].">
      <j1 rule="hyper" parents="299 17811 19215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19218">
    <literal><![CDATA[
      K(x * K(y \ (z \ u),w),v5) = K(x * K((z * y) * u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(17810,a,19217,a)].">
      <j1 rule="hyper" parents="17810 19217"/>
    </justification>
  </clause>

  <clause id="19219">
    <literal><![CDATA[
      K(x * K((y * z) * u,w),v5) = K(x * K(z * (y \ u),w),v5)
    ]]></literal>
    <justification jstring="[hyper(17812,a,19218,a),flip(a)].">
      <j1 rule="hyper" parents="17812 19218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19220">
    <literal><![CDATA[
      K(x * K(K(y,z) * (u * w),v5),v6) = K(x * K(u * (K(y,z) \ w),v5),v6)
    ]]></literal>
    <justification jstring="[para(18991(a,1),19219(a,1,1,2))].">
      <j1 rule="para" parents="18991 19219"/>
    </justification>
  </clause>

  <clause id="19221">
    <literal><![CDATA[
      K(x,T(y,z / u) * (z / u)) = K(x,(T(T(z,w),w) / u) * y)
    ]]></literal>
    <justification jstring="[para(15788(a,1),19136(a,1,2,1))].">
      <j1 rule="para" parents="15788 19136"/>
    </justification>
  </clause>

  <clause id="19222">
    <literal><![CDATA[
      K(x,(T(T(y,z),z) / u) * w) = K(x,(y / u) * w)
    ]]></literal>
    <justification jstring="[hyper(13261,a,19221,a),flip(a)].">
      <j1 rule="hyper" parents="13261 19221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19224">
    <literal><![CDATA[
      K(x,(y \ T(T(z,u),u)) * w) = K(x,(z / T(y,T(z,u))) * w)
    ]]></literal>
    <justification jstring="[hyper(18974,a,19222,a)].">
      <j1 rule="hyper" parents="18974 19222"/>
    </justification>
  </clause>

  <clause id="19225">
    <literal><![CDATA[
      K(x,(y \ T(z,y)) * u) = K(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,18229,a(flip),b,19222,a)].">
      <j1 rule="hyper" parents="65 18229 19222"/>
    </justification>
  </clause>

  <clause id="19226">
    <literal><![CDATA[
      K(x,((y / z) / z) * u) = K(x,(z \ (z \ y)) * u)
    ]]></literal>
    <justification jstring="[para(109(a,1),19225(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="109 19225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19227">
    <literal><![CDATA[
      K(x,(T(y,z) \ z) * u) = K(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[para(4396(a,2),19225(a,1,2,1))].">
      <j1 rule="para" parents="4396 19225"/>
    </justification>
  </clause>

  <clause id="19228">
    <literal><![CDATA[
      T(x,(T(y,z) \ z) * u) = x * K(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[para(19227(a,1),5083(a,2,2))].">
      <j1 rule="para" parents="19227 5083"/>
    </justification>
  </clause>

  <clause id="19229">
    <literal><![CDATA[
      K((T(x,y) \ y) * z,u) = (w * K(u,(y / x) * z)) \ w
    ]]></literal>
    <justification jstring="[para(19227(a,1),7200(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="19227 7200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19230">
    <literal><![CDATA[
      T(x,(T(y,z) \ z) * u) = T(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[hyper(299,a,5083,a,b,19228,a),flip(a)].">
      <j1 rule="hyper" parents="299 5083 19228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19231">
    <literal><![CDATA[
      T(x,(y \ T(z,y)) * u) = T(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[para(4396(a,1),19230(a,1,2,1))].">
      <j1 rule="para" parents="4396 19230"/>
    </justification>
  </clause>

  <clause id="19232">
    <literal><![CDATA[
      T(x,((y / z) / z) * u) = T(x,(z \ (z \ y)) * u)
    ]]></literal>
    <justification jstring="[para(109(a,1),19231(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="109 19231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19233">
    <literal><![CDATA[
      T(T(x,K(y,z)),(u \ (u \ y)) * z) = T(x,z * ((y / u) / u))
    ]]></literal>
    <justification jstring="[hyper(18267,a,19232,a),flip(a)].">
      <j1 rule="hyper" parents="18267 19232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19234">
    <literal><![CDATA[
      K((T(x,y) \ y) * z,u) = K((y / x) * z,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,18856,a(flip),b,19229,a),flip(a)].">
      <j1 rule="hyper" parents="299 18856 19229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19235">
    <literal><![CDATA[
      K((x \ T(y,x)) * z,u) = K((y / x) * z,u)
    ]]></literal>
    <justification jstring="[para(4396(a,1),19234(a,1,1,1))].">
      <j1 rule="para" parents="4396 19234"/>
    </justification>
  </clause>

  <clause id="19236">
    <literal><![CDATA[
      K((T(x,y * z) \ T(u,T(x,y \ z))) * w,v5) = K((u / T(x,y \ z)) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(18125,a,19235,a)].">
      <j1 rule="hyper" parents="18125 19235"/>
    </justification>
  </clause>

  <clause id="19237">
    <literal><![CDATA[
      T(x,y * ((z / u) / u)) = T(x,y * (u \ (u \ z)))
    ]]></literal>
    <justification jstring="[hyper(16298,a,19233,a),flip(a)].">
      <j1 rule="hyper" parents="16298 19233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19238">
    <literal><![CDATA[
      T(x,y * (T(z,u) * (w * K(z,v5)))) = T(x,y * (T(T(z,v5),u) * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,19151,a(flip),b,19152,a),flip(a)].">
      <j1 rule="hyper" parents="65 19151 19152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19239">
    <literal><![CDATA[
      T(x,y * (T(T(z,u),u) * (z \ w))) = T(x,y * (K(z,u) * (w * K(z,u))))
    ]]></literal>
    <justification jstring="[hyper(65,a,13998,a(flip),b,19238,a),flip(a)].">
      <j1 rule="hyper" parents="65 13998 19238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19240">
    <literal><![CDATA[
      T(x,y * (T(z,T(u,w)) * T(u,w))) = T(x,y * ((w * (u / w)) * z))
    ]]></literal>
    <justification jstring="[para(13271(a,1),19175(a,1,2,2,1))].">
      <j1 rule="para" parents="13271 19175"/>
    </justification>
  </clause>

  <clause id="19241">
    <literal><![CDATA[
      T(x,y * ((z * (u / z)) * w)) = T(x,y * (T(u,z) * w))
    ]]></literal>
    <justification jstring="[hyper(15900,a,19240,a),flip(a)].">
      <j1 rule="hyper" parents="15900 19240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19242">
    <literal><![CDATA[
      T(x,(y * (z / y)) * u) = T(x,1 * (T(z,y) * u))
    ]]></literal>
    <justification jstring="[para(7(a,1),19241(a,1,2))].">
      <j1 rule="para" parents="7 19241"/>
    </justification>
  </clause>

  <clause id="19243">
    <literal><![CDATA[
      T(x,(y * (z / y)) * u) = T(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[para(7(a,1),19242(a,2,2))].">
      <j1 rule="para" parents="7 19242"/>
    </justification>
  </clause>

  <clause id="19244">
    <literal><![CDATA[
      T(x,T(y * z,y) * u) = T(x,(T(y,z) * z) * u)
    ]]></literal>
    <justification jstring="[para(4263(a,2),19243(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4263 19243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19245">
    <literal><![CDATA[
      T(x,T(y * z,y) * u) = T(x,(z * y) * u)
    ]]></literal>
    <justification jstring="[hyper(15924,a,19244,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="15924 19244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19246">
    <literal><![CDATA[
      T(x,T(y * z,y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z * y) * u) = w
    ]]></literal>
    <justification jstring="[para(19244(a,2),15924(a,1))].">
      <j1 rule="para" parents="19244 15924"/>
    </justification>
  </clause>

  <clause id="19247">
    <literal><![CDATA[
      T(x,(y * z) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z * (z * y)) = u
    ]]></literal>
    <justification jstring="[para(19245(a,1),13267(a,1))].">
      <j1 rule="para" parents="19245 13267"/>
    </justification>
  </clause>

  <clause id="19248">
    <literal><![CDATA[
      T(x,y * (z * T(u * (1 / z),z \ 1))) = T(x,y * ((z \ 1) * (z * u)))
    ]]></literal>
    <justification jstring="[para(3733(a,1),19179(a,1,2,2,2))].">
      <j1 rule="para" parents="3733 19179"/>
    </justification>
  </clause>

  <clause id="19249">
    <literal><![CDATA[
      T(x,y * (z * T(u * w,w))) = T(x,y * (z * T(u * w,u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,19128,a(flip),b,19187,a),flip(a)].">
      <j1 rule="hyper" parents="65 19128 19187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19250">
    <literal><![CDATA[
      T(x,y * (z * T(u * w,u))) = T(x,y * (z * (w * u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,19177,a(flip),b,19249,a),flip(a)].">
      <j1 rule="hyper" parents="65 19177 19249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19251">
    <literal><![CDATA[
      T(x,y \ (z * T(u * w,u))) = T(x,(y \ 1) * (z * (w * u)))
    ]]></literal>
    <justification jstring="[hyper(14304,a,19250,a)].">
      <j1 rule="hyper" parents="14304 19250"/>
    </justification>
  </clause>

  <clause id="19252">
    <literal><![CDATA[
      T(x,y * (z * (T(u,w) * w))) = T(x,y * (z * (w * u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,19178,a(flip),b,19250,a)].">
      <j1 rule="hyper" parents="65 19178 19250"/>
    </justification>
  </clause>

  <clause id="19253">
    <literal><![CDATA[
      T(x,T(y,z * (u * w)) * (z * (u * w))) = T(x,(z * (T(w,u) * u)) * y)
    ]]></literal>
    <justification jstring="[hyper(15896,a,19252,a),flip(a)].">
      <j1 rule="hyper" parents="15896 19252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19254">
    <literal><![CDATA[
      T(x,y * (z * (T(u,(w \ v5) \ v5) * ((w \ v5) \ v5)))) = T(x,y * (z * (T(w,w \ v5) * u)))
    ]]></literal>
    <justification jstring="[para(296(a,2),19252(a,2,2,2,2))].">
      <j1 rule="para" parents="296 19252"/>
    </justification>
  </clause>

  <clause id="19255">
    <literal><![CDATA[
      T(x,y \ (z * T(u * w,u))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (z * (w * u))) = v5
    ]]></literal>
    <justification jstring="[para(19251(a,2),14304(a,1))].">
      <j1 rule="para" parents="19251 14304"/>
    </justification>
  </clause>

  <clause id="19256">
    <literal><![CDATA[
      K(x,T(y / T(z,(u * w) * v5),z)) = K(x,T(z,w * ((1 / u) \ v5)) \ y)
    ]]></literal>
    <justification jstring="[para(7889(a,2),19200(a,2,2)),flip(a)].">
      <j1 rule="para" parents="7889 19200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19257">
    <literal><![CDATA[
      K(x * K(y * (K(z,u) \ w),v5),v6) = K(K(y * w,v5) * x,v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,17887,a(flip),b,19220,a),flip(a)].">
      <j1 rule="hyper" parents="65 17887 19220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19259">
    <literal><![CDATA[
      K(x * K((y * z) * (K(u,w) \ v5),v6),v7) = K(K(z * (y \ v5),v6) * x,v7)
    ]]></literal>
    <justification jstring="[hyper(299,a,19156,a(flip),b,19257,a),flip(a)].">
      <j1 rule="hyper" parents="299 19156 19257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19260">
    <literal><![CDATA[
      T(x,y * (K(z,u) * (w * K(z,u)))) = T(x,y * (z * (z \ w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,18255,a(flip),b,19239,a),flip(a)].">
      <j1 rule="hyper" parents="65 18255 19239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19262">
    <literal><![CDATA[
      T(x,y * (K(z,u) * (w * K(z,u)))) = T(x,y * w)
    ]]></literal>
    <justification jstring="[para(10(a,1),19260(a,2,2,2))].">
      <j1 rule="para" parents="10 19260"/>
    </justification>
  </clause>

  <clause id="19264">
    <literal><![CDATA[
      T(x,y * (K(z,u) * w)) = T(x,y * (w * K(u,z)))
    ]]></literal>
    <justification jstring="[para(7184(a,1),19262(a,1,2,2,2))].">
      <j1 rule="para" parents="7184 19262"/>
    </justification>
  </clause>

  <clause id="19265">
    <literal><![CDATA[
      T(x,(y \ 1) * (z * K(u,w))) = T(x,y \ (K(w,u) * z))
    ]]></literal>
    <justification jstring="[hyper(14304,a,19264,a),flip(a)].">
      <j1 rule="hyper" parents="14304 19264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19266">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(u,w) * (z * y)) = T(x,y * (K(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(299,a,19034,a,b,19264,a)].">
      <j1 rule="hyper" parents="299 19034 19264"/>
    </justification>
  </clause>

  <clause id="19267">
    <literal><![CDATA[
      T(x,y * (K(z,u) * (z \ w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (T(z,u) \ w)) = v5
    ]]></literal>
    <justification jstring="[para(19264(a,2),16833(a,1))].">
      <j1 rule="para" parents="19264 16833"/>
    </justification>
  </clause>

  <clause id="19268">
    <literal><![CDATA[
      T(x,y \ (K(z,u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (w * K(u,z))) = v5
    ]]></literal>
    <justification jstring="[para(19265(a,1),14304(a,1))].">
      <j1 rule="para" parents="19265 14304"/>
    </justification>
  </clause>

  <clause id="19269">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(u * w,v5) * (z * y)) = T(x,y * (K(u \ w,v5) * z))
    ]]></literal>
    <justification jstring="[hyper(17351,a,19266,a)].">
      <j1 rule="hyper" parents="17351 19266"/>
    </justification>
  </clause>

  <clause id="19270">
    <literal><![CDATA[
      T(x,y * (z * T(u * (1 / z),z * 1))) = T(x,y * ((z \ 1) * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,17536,a(flip),b,19248,a)].">
      <j1 rule="hyper" parents="65 17536 19248"/>
    </justification>
  </clause>

  <clause id="19271">
    <literal><![CDATA[
      T(x,(y * (T(z,u) * u)) * w) = T(x,(y * (u * z)) * w)
    ]]></literal>
    <justification jstring="[hyper(13267,a,19253,a),flip(a)].">
      <j1 rule="hyper" parents="13267 19253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19273">
    <literal><![CDATA[
      K(x,T(y,z * ((1 / u) \ w)) \ v5) = K(x,T(y,(u * z) * w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(16471,a,19256,a),flip(a)].">
      <j1 rule="hyper" parents="16471 19256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19274">
    <literal><![CDATA[
      K(x,T(y,z * ((u \ 1) \ w)) \ v5) = K(x,T(y,(u * z) * w) \ v5)
    ]]></literal>
    <justification jstring="[para(3884(a,1),19273(a,1,2,1))].">
      <j1 rule="para" parents="3884 19273"/>
    </justification>
  </clause>

  <clause id="19275">
    <literal><![CDATA[
      K(x,T(y,(z * u) * w) \ v5) = K(x,T(y,u * (z \ w)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,18067,a(flip),b,19274,a),flip(a)].">
      <j1 rule="hyper" parents="65 18067 19274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19276">
    <literal><![CDATA[
      K(x,T(y,z * ((u \ 1) * w)) \ v5) = K(x,T(y,w * (u \ z)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,18135,a,b,19275,a)].">
      <j1 rule="hyper" parents="65 18135 19275"/>
    </justification>
  </clause>

  <clause id="19277">
    <literal><![CDATA[
      K(x * K((T(y,z) * u) * (K(w,v5) \ v6),v7),v8) = K(K((y \ v6) * u,v7) * x,v8)
    ]]></literal>
    <justification jstring="[hyper(299,a,19163,a(flip),b,19259,a),flip(a)].">
      <j1 rule="hyper" parents="299 19163 19259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19278">
    <literal><![CDATA[
      T(x,y * (K(z \ u,w) * v5)) = T(x,y * (K(z * u,w) * v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,19266,a(flip),b,19269,a),flip(a)].">
      <j1 rule="hyper" parents="65 19266 19269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19279">
    <literal><![CDATA[
      T(x,y * (K(z * u,w) * (w \ v5))) = T(x,y * (T(w,z \ u) \ v5))
    ]]></literal>
    <justification jstring="[para(5383(a,1),19278(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5383 19278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19280">
    <literal><![CDATA[
      T(x,y * (T(z,u \ w) \ v5)) = T(x,y * (T(z,u * w) \ v5))
    ]]></literal>
    <justification jstring="[para(5383(a,1),19279(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5383 19279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19281">
    <literal><![CDATA[
      T(x,T(y \ z,u) * (u \ w)) = T(x,(y \ z) * (T(u,y * z) \ w))
    ]]></literal>
    <justification jstring="[hyper(16876,a,19280,a)].">
      <j1 rule="hyper" parents="16876 19280"/>
    </justification>
  </clause>

  <clause id="19282">
    <literal><![CDATA[
      T(x,(y \ 1) * (T(z,u * w) \ v5)) = T(x,y \ (T(z,u \ w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(14304,a,19280,a),flip(a)].">
      <j1 rule="hyper" parents="14304 19280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19283">
    <literal><![CDATA[
      T(x,T(y \ z,u) * (u \ w)) = T(x,(y \ z) * (T(u,z * y) \ w))
    ]]></literal>
    <justification jstring="[hyper(299,a,16938,a,b,19281,a),flip(a)].">
      <j1 rule="hyper" parents="299 16938 19281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19284">
    <literal><![CDATA[
      T(x,y \ (T(z,u \ w) \ v5)) = T(x,y \ (T(z,u * w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(14304,a,19282,a),flip(a)].">
      <j1 rule="hyper" parents="14304 19282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19285">
    <literal><![CDATA[
      T(x,y \ (T(z,u \ w) \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (T(z,u * w) \ v5)) = v6
    ]]></literal>
    <justification jstring="[para(19282(a,1),14304(a,1))].">
      <j1 rule="para" parents="19282 14304"/>
    </justification>
  </clause>

  <clause id="19286">
    <literal><![CDATA[
      T(x,y \ (T(z,u * u) \ w)) = T(x,y \ (z \ w))
    ]]></literal>
    <justification jstring="[para(198(a,1),19284(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="198 19284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19287">
    <literal><![CDATA[
      T(x,y \ (T(z,u \ (u \ 1)) \ w)) = T(x,y \ (z \ w))
    ]]></literal>
    <justification jstring="[para(14297(a,1),19286(a,1,2,2,1))].">
      <j1 rule="para" parents="14297 19286"/>
    </justification>
  </clause>

  <clause id="19288">
    <literal><![CDATA[
      T(x,y \ ((z * (u * (z \ (1 / z)))) \ w)) = T(x,y \ (((z \ 1) * u) \ w))
    ]]></literal>
    <justification jstring="[para(14726(a,1),19287(a,1,2,2,1))].">
      <j1 rule="para" parents="14726 19287"/>
    </justification>
  </clause>

  <clause id="19289">
    <literal><![CDATA[
      T(x,y * (z * T(u * (1 / z),z))) = T(x,y * ((z \ 1) * (z * u)))
    ]]></literal>
    <justification jstring="[para(8(a,1),19270(a,1,2,2,2,2))].">
      <j1 rule="para" parents="8 19270"/>
    </justification>
  </clause>

  <clause id="19290">
    <literal><![CDATA[
      T(x,y * ((z \ 1) * (z * u))) = T(x,y * R(u,z,z))
    ]]></literal>
    <justification jstring="[para(1753(a,1),19289(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1753 19289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19291">
    <literal><![CDATA[
      T(x,y * (z * ((1 / z) * u))) = T(x,y * R(u,z,z))
    ]]></literal>
    <justification jstring="[para(944(a,1),19290(a,1,2,2))].">
      <j1 rule="para" parents="944 19290"/>
    </justification>
  </clause>

  <clause id="19292">
    <literal><![CDATA[
      T(x,y * (z * ((z \ 1) * u))) = T(x,y * R(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,15097,a(flip),b,19291,a)].">
      <j1 rule="hyper" parents="65 15097 19291"/>
    </justification>
  </clause>

  <clause id="19293">
    <literal><![CDATA[
      T(x,y * R(z,u,u)) = T(x,y * L(z,u,u))
    ]]></literal>
    <justification jstring="[para(1673(a,1),19292(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1673 19292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19294">
    <literal><![CDATA[
      K(x,T(y,z * L(T(u,w),v5,v5))) = K(x,T(y,z * R(u,v5,v5)))
    ]]></literal>
    <justification jstring="[para(19293(a,2),17125(a,2,2))].">
      <j1 rule="para" parents="19293 17125"/>
    </justification>
  </clause>

  <clause id="19295">
    <literal><![CDATA[
      K(x,T(y,z * R(u,w,w))) = K(x,T(y,z * L(u,w,w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,17125,a(flip),b,19294,a),flip(a)].">
      <j1 rule="hyper" parents="65 17125 19294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19296">
    <literal><![CDATA[
      T(x,y \ (z * ((z \ 1) \ ((z * u) \ w)))) = T(x,y \ (((z \ 1) * u) \ w))
    ]]></literal>
    <justification jstring="[para(2437(a,1),19288(a,1,2,2))].">
      <j1 rule="para" parents="2437 19288"/>
    </justification>
  </clause>

  <clause id="19297">
    <literal><![CDATA[
      T(x,(y \ 1) \ ((y * z) \ u)) = T(x,y \ (((y \ 1) * z) \ u))
    ]]></literal>
    <justification jstring="[para(9(a,1),19296(a,1,2))].">
      <j1 rule="para" parents="9 19296"/>
    </justification>
  </clause>

  <clause id="19298">
    <literal><![CDATA[
      T(x,y \ (((y \ 1) * z) \ u)) = T(x,y * ((y * z) \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,14215,a(flip),b,19297,a),flip(a)].">
      <j1 rule="hyper" parents="65 14215 19297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19299">
    <literal><![CDATA[
      T(T(x,K((y * z) \ u,y)),y \ (((y \ 1) * z) \ u)) = T(x,((y * z) \ u) * y)
    ]]></literal>
    <justification jstring="[hyper(299,a,13200,a(flip),b,19298,a),flip(a)].">
      <j1 rule="hyper" parents="299 13200 19298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19300">
    <literal><![CDATA[
      T(x,y \ (((y \ 1) * ((y \ z) * (y \ z))) \ u)) = T(x,y * ((z / (1 / (y \ z))) \ u))
    ]]></literal>
    <justification jstring="[para(676(a,1),19298(a,2,2,2,1))].">
      <j1 rule="para" parents="676 19298"/>
    </justification>
  </clause>

  <clause id="19301">
    <literal><![CDATA[
      K((x * L(K(y,z),u,w)) \ v5,v6) = K(x \ (L(K(z,y),u,w) * v5),v6)
    ]]></literal>
    <justification jstring="[hyper(18857,a,18949,a),flip(a)].">
      <j1 rule="hyper" parents="18857 18949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19302">
    <literal><![CDATA[
      K(((x \ y) * x) / T(L(K(z,u),w,v5) * x,K(v6,v7)),v8) = K(x \ (L(K(u,z),w,v5) * y),v8)
    ]]></literal>
    <justification jstring="[hyper(65,a,17082,a,b,19301,a)].">
      <j1 rule="hyper" parents="65 17082 19301"/>
    </justification>
  </clause>

  <clause id="19303">
    <literal><![CDATA[
      (K(x,y) * a(z,u,K(w,v5))) * K(x,K(y,v6)) = T(K(x,y) * a(z,u,K(w,v5)),v6)
    ]]></literal>
    <justification jstring="[para(7988(a,1),18993(a,1,2))].">
      <j1 rule="para" parents="7988 18993"/>
    </justification>
  </clause>

  <clause id="19304">
    <literal><![CDATA[
      K(x,y * (K(z,u \ w) * T(w,u))) = K(x,y * (T(u,w) * T(u \ w,z)))
    ]]></literal>
    <justification jstring="[hyper(15934,a,19068,a)].">
      <j1 rule="hyper" parents="15934 19068"/>
    </justification>
  </clause>

  <clause id="19305">
    <literal><![CDATA[
      K(x,y * (T(z,u) * T(z \ u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (K(w,z * u) * T(u,z))) = v5
    ]]></literal>
    <justification jstring="[para(19304(a,1),17567(a,1))].">
      <j1 rule="para" parents="19304 17567"/>
    </justification>
  </clause>

  <clause id="19306">
    <literal><![CDATA[
      K(x,K(T(y,z) / u,w) * (T(y,z) / u)) = K(x,T(((z * y) / z) / u,w))
    ]]></literal>
    <justification jstring="[para(16042(a,1),19135(a,1,2,1))].">
      <j1 rule="para" parents="16042 19135"/>
    </justification>
  </clause>

  <clause id="19307">
    <literal><![CDATA[
      K(x,T(((y * z) / y) / u,w)) = K(x,T(T(z,y) / u,w))
    ]]></literal>
    <justification jstring="[para(5096(a,2),19306(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5096 19306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19308">
    <literal><![CDATA[
      T(x,T(y,z * T(u,w)) * (z * T(u,w))) = T(x,(z * (w * (u / w))) * y)
    ]]></literal>
    <justification jstring="[para(15907(a,1),19176(a,1,2,1))].">
      <j1 rule="para" parents="15907 19176"/>
    </justification>
  </clause>

  <clause id="19309">
    <literal><![CDATA[
      T(x,(y * (z * (u / z))) * w) = T(x,(y * T(u,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(13267,a,19308,a),flip(a)].">
      <j1 rule="hyper" parents="13267 19308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19310">
    <literal><![CDATA[
      K(x,(y * (z * (u / z))) * w) = x \ T(x,(y * T(u,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(119,a,19309,a(flip),b,5083,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 19309 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19311">
    <literal><![CDATA[
      T(x,(y * T(z * u,z)) * w) = T(x,(y * (T(z,u) * u)) * w)
    ]]></literal>
    <justification jstring="[para(4263(a,2),19309(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="4263 19309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19312">
    <literal><![CDATA[
      K(x,(y * (z * (u / z))) * w) = K(x,(y * T(u,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(299,a,5036,a,b,19310,a),flip(a)].">
      <j1 rule="hyper" parents="299 5036 19310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19313">
    <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(19310(a,2),5155(a,1))].">
      <j1 rule="para" parents="19310 5155"/>
    </justification>
  </clause>

  <clause id="19314">
    <literal><![CDATA[
      K(x,(y * T(z * u,u)) * w) = K(x,(y * (u * z)) * w)
    ]]></literal>
    <justification jstring="[para(11(a,1),19312(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 19312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19315">
    <literal><![CDATA[
      K(x,(y * T(z * (1 / y),1 / y)) * u) = K(x,((y \ 1) * (y * z)) * u)
    ]]></literal>
    <justification jstring="[para(944(a,2),19314(a,2,2,1))].">
      <j1 rule="para" parents="944 19314"/>
    </justification>
  </clause>

  <clause id="19316">
    <literal><![CDATA[
      T(x,(y * T((z \ u) * w,z * u)) * v5) = T(x,(y * (T(z \ u,w) * w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(17699,a,19311,a)].">
      <j1 rule="hyper" parents="17699 19311"/>
    </justification>
  </clause>

  <clause id="19317">
    <literal><![CDATA[
      K(x,(y * T(z * (1 / y),y \ 1)) * u) = K(x,((y \ 1) * (y * z)) * u)
    ]]></literal>
    <justification jstring="[para(3733(a,1),19315(a,1,2,1,2))].">
      <j1 rule="para" parents="3733 19315"/>
    </justification>
  </clause>

  <clause id="19318">
    <literal><![CDATA[
      K(x,(y * T(z * (1 / y),y * 1)) * u) = K(x,((y \ 1) * (y * z)) * u)
    ]]></literal>
    <justification jstring="[hyper(17701,a,19317,a)].">
      <j1 rule="hyper" parents="17701 19317"/>
    </justification>
  </clause>

  <clause id="19319">
    <literal><![CDATA[
      K(x,(y * T(z * (1 / y),y)) * u) = K(x,((y \ 1) * (y * z)) * u)
    ]]></literal>
    <justification jstring="[para(8(a,1),19318(a,1,2,1,2,2))].">
      <j1 rule="para" parents="8 19318"/>
    </justification>
  </clause>

  <clause id="19320">
    <literal><![CDATA[
      K(x,((y \ 1) * (y * z)) * u) = K(x,R(z,y,y) * u)
    ]]></literal>
    <justification jstring="[para(1753(a,1),19319(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1753 19319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19321">
    <literal><![CDATA[
      K(x,(y * ((1 / y) * z)) * u) = K(x,R(z,y,y) * u)
    ]]></literal>
    <justification jstring="[para(944(a,1),19320(a,1,2,1))].">
      <j1 rule="para" parents="944 19320"/>
    </justification>
  </clause>

  <clause id="19322">
    <literal><![CDATA[
      K(x,(y * ((y \ 1) * z)) * u) = K(x,R(z,y,y) * u)
    ]]></literal>
    <justification jstring="[hyper(15188,a,19321,a)].">
      <j1 rule="hyper" parents="15188 19321"/>
    </justification>
  </clause>

  <clause id="19323">
    <literal><![CDATA[
      K(x,R(y,z,z) * u) = K(x,L(y,z,z) * u)
    ]]></literal>
    <justification jstring="[para(1673(a,1),19322(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1673 19322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19324">
    <literal><![CDATA[
      K(x,y * (T(z,u * w) / T(v5,T(z,u * w)))) = K(x,y * (v5 \ T(z,u \ w)))
    ]]></literal>
    <justification jstring="[para(16225(a,1),19186(a,1,2,2,2))].">
      <j1 rule="para" parents="16225 19186"/>
    </justification>
  </clause>

  <clause id="19325">
    <literal><![CDATA[
      K(x,y * (T(z,u \ K(w,v5)) / (u \ K(w,v5)))) = K(x,y * ((K(w,v5) / u) \ z))
    ]]></literal>
    <justification jstring="[para(16358(a,1),19199(a,1,2,2,1))].">
      <j1 rule="para" parents="16358 19199"/>
    </justification>
  </clause>

  <clause id="19326">
    <literal><![CDATA[
      K((T(x,y * z) \ T(u,T(x,y * z))) * w,v5) = K((u / T(x,y \ z)) * w,v5)
    ]]></literal>
    <justification jstring="[para(16225(a,1),19236(a,1,1,1,2))].">
      <j1 rule="para" parents="16225 19236"/>
    </justification>
  </clause>

  <clause id="19327">
    <literal><![CDATA[
      K(x * K((T(y,z) * u) * (K(w,v5) * v6),v7),v8) = K(K((y \ v6) * u,v7) * x,v8)
    ]]></literal>
    <justification jstring="[para(5426(a,1),19277(a,1,1,2,1,2))].">
      <j1 rule="para" parents="5426 19277"/>
    </justification>
  </clause>

  <clause id="19328">
    <literal><![CDATA[
      T(T(x,K(y \ (z \ u),z)),z \ (((z \ 1) * y) \ u)) = T(x,((z * y) \ u) * z)
    ]]></literal>
    <justification jstring="[para(7827(a,1),19299(a,1,1,2))].">
      <j1 rule="para" parents="7827 19299"/>
    </justification>
  </clause>

  <clause id="19329">
    <literal><![CDATA[
      T(K(x,y) * a(z,u,K(w,v5)),v6) = K(x,T(y,v6)) * a(z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(16486,a,19303,a),flip(a)].">
      <j1 rule="hyper" parents="16486 19303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19330">
    <literal><![CDATA[
      T(x,(y * T((z \ 1) * u,z)) * w) = T(x,(y * (T(z \ 1,u) * u)) * w)
    ]]></literal>
    <justification jstring="[para(8(a,1),19316(a,1,2,1,2,2))].">
      <j1 rule="para" parents="8 19316"/>
    </justification>
  </clause>

  <clause id="19331">
    <literal><![CDATA[
      T(x,(y * T((z \ 1) * u,z)) * w) = T(x,(y * (u * (z \ 1))) * w)
    ]]></literal>
    <justification jstring="[hyper(299,a,19271,a(flip),b,19330,a),flip(a)].">
      <j1 rule="hyper" parents="299 19271 19330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19333">
    <literal><![CDATA[
      K(x,y * (z \ T(u,w \ v5))) = K(x,y * (z \ T(u,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(65,a,13884,a(flip),b,19324,a),flip(a)].">
      <j1 rule="hyper" parents="65 13884 19324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19334">
    <literal><![CDATA[
      K(x,T(y,z * T(u,w * v5)) * (z \ T(u,w * v5))) = K(x,(z \ T(u,w \ v5)) * y)
    ]]></literal>
    <justification jstring="[hyper(17975,a,19333,a),flip(a)].">
      <j1 rule="hyper" parents="17975 19333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19335">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) * (u / (z \ 1))) = K(x,(y * z) * (z \ T(u,z * 1)))
    ]]></literal>
    <justification jstring="[hyper(65,a,19138,a,b,19333,a)].">
      <j1 rule="hyper" parents="65 19138 19333"/>
    </justification>
  </clause>

  <clause id="19336">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) * (u / (z \ 1))) = K(x,(y * z) * (z \ T(u,z)))
    ]]></literal>
    <justification jstring="[para(8(a,1),19335(a,2,2,2,2,2))].">
      <j1 rule="para" parents="8 19335"/>
    </justification>
  </clause>

  <clause id="19337">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) * (u / (z \ 1))) = K(x,(y * z) * (u / z))
    ]]></literal>
    <justification jstring="[hyper(299,a,19137,a(flip),b,19336,a),flip(a)].">
      <j1 rule="hyper" parents="299 19137 19336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19338">
    <literal><![CDATA[
      K(x,y * ((K(z,u) / w) \ v5)) = K(x,y * ((w \ K(z,u)) \ v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,13881,a(flip),b,19325,a),flip(a)].">
      <j1 rule="hyper" parents="65 13881 19325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19339">
    <literal><![CDATA[
      K(x,y * (K(z * 1,u) * ((1 / z) \ w))) = K(x,y * ((z \ K(u,z \ 1)) \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,18094,a,b,19338,a)].">
      <j1 rule="hyper" parents="65 18094 19338"/>
    </justification>
  </clause>

  <clause id="19340">
    <literal><![CDATA[
      K((x / T(y,z \ u)) * w,v5) = K((x / T(y,z * u)) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,19235,a(flip),b,19326,a),flip(a)].">
      <j1 rule="hyper" parents="65 19235 19326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19341">
    <literal><![CDATA[
      K((x / T(y,z * u)) * (w \ 1),v5) = K((x / T(y,z \ u)) / w,v5)
    ]]></literal>
    <justification jstring="[hyper(14454,a,19340,a),flip(a)].">
      <j1 rule="hyper" parents="14454 19340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19342">
    <literal><![CDATA[
      K((x / T(y,z \ u)) / w,v5) = K((x / T(y,z * u)) / w,v5)
    ]]></literal>
    <justification jstring="[hyper(14454,a,19341,a),flip(a)].">
      <j1 rule="hyper" parents="14454 19341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19343">
    <literal><![CDATA[
      K((x / T(y,y * z)) / u,w) = K((x / ((y \ z) \ z)) / u,w)
    ]]></literal>
    <justification jstring="[para(108(a,1),19342(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="108 19342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19344">
    <literal><![CDATA[
      K((x / T((y * y) * z,y \ y)) / u,w) = K((x / (z * (y * y))) / u,w)
    ]]></literal>
    <justification jstring="[para(221(a,1),19342(a,2,1,1,2))].">
      <j1 rule="para" parents="221 19342"/>
    </justification>
  </clause>

  <clause id="19345">
    <literal><![CDATA[
      K((x / ((y * y) * z)) / u,w) = K((x / (z * (y * y))) / u,w)
    ]]></literal>
    <justification jstring="[para(198(a,1),19344(a,1,1,1,2))].">
      <j1 rule="para" parents="198 19344"/>
    </justification>
  </clause>

  <clause id="19347">
    <literal><![CDATA[
      K((x / ((y \ z) * (y * y))) / u,w) = K((x / ((y \ 1) \ z)) / u,w)
    ]]></literal>
    <justification jstring="[para(724(a,1),19345(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="724 19345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19348">
    <literal><![CDATA[
      K((x / (y * (z * z))) / u,w) = K((x / y) / (u * (z * z)),w)
    ]]></literal>
    <justification jstring="[para(750(a,1),19345(a,1,1)),flip(a)].">
      <j1 rule="para" parents="750 19345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19349">
    <literal><![CDATA[
      K((x / (y * (z * z))) / u,w) = K(z \ (z \ ((x / y) / u)),w)
    ]]></literal>
    <justification jstring="[hyper(299,a,17992,a(flip),b,19348,a),flip(a)].">
      <j1 rule="hyper" parents="299 17992 19348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19351">
    <literal><![CDATA[
      K(x \ (x \ ((y / (x \ z)) / u)),w) = K((y / ((x \ 1) \ z)) / u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,19349,a(flip),b,19347,a)].">
      <j1 rule="hyper" parents="65 19349 19347"/>
    </justification>
  </clause>

  <clause id="19352">
    <literal><![CDATA[
      T(T(x,K(y,z \ (y \ u))),y \ (((y \ 1) * z) \ u)) = T(x,((y * z) \ u) * y)
    ]]></literal>
    <justification jstring="[para(8050(a,1),19328(a,1,1))].">
      <j1 rule="para" parents="8050 19328"/>
    </justification>
  </clause>

  <clause id="19353">
    <literal><![CDATA[
      K(x,y * (K(z * 1,u) * ((1 / z) \ w))) = K(x,y * (T(z \ 1,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(299,a,19121,a(flip),b,19339,a),flip(a)].">
      <j1 rule="hyper" parents="299 19121 19339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19354">
    <literal><![CDATA[
      K(x,y * (K(z,u) * ((1 / z) \ w))) = K(x,y * (T(z \ 1,u) \ w))
    ]]></literal>
    <justification jstring="[para(8(a,1),19353(a,1,2,2,1,1))].">
      <j1 rule="para" parents="8 19353"/>
    </justification>
  </clause>

  <clause id="19355">
    <literal><![CDATA[
      K(x,y * ((1 / T(z,u)) \ w)) = K(x,y * (T(z \ 1,u) \ w))
    ]]></literal>
    <justification jstring="[para(7246(a,1),19354(a,1,2,2))].">
      <j1 rule="para" parents="7246 19354"/>
    </justification>
  </clause>

  <clause id="19356">
    <literal><![CDATA[
      T(T(x,K(y,z * (y \ u))),y \ (((y \ 1) * z) \ u)) = T(x,((y * z) \ u) * y)
    ]]></literal>
    <justification jstring="[para(16268(a,1),19352(a,1,1))].">
      <j1 rule="para" parents="16268 19352"/>
    </justification>
  </clause>

  <clause id="19357">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y \ (((y \ 1) * z) \ u)) = T(x,((y * z) \ u) * y)
    ]]></literal>
    <justification jstring="[para(11249(a,1),19356(a,1,1))].">
      <j1 rule="para" parents="11249 19356"/>
    </justification>
  </clause>

  <clause id="19358">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y * ((y * z) \ u)) = T(x,((y * z) \ u) * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,19298,a(flip),b,19357,a)].">
      <j1 rule="hyper" parents="65 19298 19357"/>
    </justification>
  </clause>

  <clause id="19359">
    <literal><![CDATA[
      T(x,K(y,z * (y * u))) = T(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(42,a,16284,a,b,19358,a)].">
      <j1 rule="hyper" parents="42 16284 19358"/>
    </justification>
  </clause>

  <clause id="19360">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y / (u \ (y * z))) = T(x,(u \ (y * z)) \ y)
    ]]></literal>
    <justification jstring="[para(19359(a,1),16274(a,1,1))].">
      <j1 rule="para" parents="19359 16274"/>
    </justification>
  </clause>

  <clause id="19361">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y \ ((y \ u) \ z)) = T(x,((y \ u) \ z) / y)
    ]]></literal>
    <justification jstring="[para(19359(a,1),16275(a,1,1))].">
      <j1 rule="para" parents="19359 16275"/>
    </justification>
  </clause>

  <clause id="19362">
    <literal><![CDATA[
      K(x,K(y,y \ 1) * ((z / T(y,u)) * w)) = K(x,(z / L(T(y,u),y,y)) * w)
    ]]></literal>
    <justification jstring="[hyper(16823,a,19007,a)].">
      <j1 rule="hyper" parents="16823 19007"/>
    </justification>
  </clause>

  <clause id="19363">
    <literal><![CDATA[
      K(x,(y / L(T(z,u),z,z)) * w) = K(x,(y / T(z,u)) * w)
    ]]></literal>
    <justification jstring="[hyper(13798,a,19362,a),flip(a)].">
      <j1 rule="hyper" parents="13798 19362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19365">
    <literal><![CDATA[
      K(x,(y / T(z,u)) * w) * K(x,K(w,T(z,u) * y)) = K(x,w * (y / T(T(z,u),z \ 1)))
    ]]></literal>
    <justification jstring="[para(19363(a,1),17337(a,1,1))].">
      <j1 rule="para" parents="19363 17337"/>
    </justification>
  </clause>

  <clause id="19366">
    <literal><![CDATA[
      K(x,y * (z * (a(z,u,1 / u) * K(u,u \ 1)))) = K(x,y * L(z,u,u))
    ]]></literal>
    <justification jstring="[para(475(a,1),19166(a,2,2,2))].">
      <j1 rule="para" parents="475 19166"/>
    </justification>
  </clause>

  <clause id="19367">
    <literal><![CDATA[
      K(x,y * ((z * u) * (1 / u))) = K(x,y * L(z,u,u))
    ]]></literal>
    <justification jstring="[para(3341(a,1),19366(a,1,2,2))].">
      <j1 rule="para" parents="3341 19366"/>
    </justification>
  </clause>

  <clause id="19368">
    <literal><![CDATA[
      K(x,y * ((z * u) * (u \ 1))) = K(x,y * L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(13807,a,19367,a)].">
      <j1 rule="hyper" parents="13807 19367"/>
    </justification>
  </clause>

  <clause id="19369">
    <literal><![CDATA[
      K(x,((y \ 1) \ z) * L(u,y,y)) = K(x,(y \ z) * ((u * y) * y))
    ]]></literal>
    <justification jstring="[hyper(16231,a,19368,a),flip(a)].">
      <j1 rule="hyper" parents="16231 19368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19370">
    <literal><![CDATA[
      K(x,y * R(z,u,u)) = K(x,y * L(z,u,u))
    ]]></literal>
    <justification jstring="[para(1246(a,1),19368(a,1,2,2))].">
      <j1 rule="para" parents="1246 19368"/>
    </justification>
  </clause>

  <clause id="19371">
    <literal><![CDATA[
      K(x,(y / (z \ 1)) * R(1 / z,u,u)) = K(x,(y / z) * L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,15706,a,b,19370,a)].">
      <j1 rule="hyper" parents="65 15706 19370"/>
    </justification>
  </clause>

  <clause id="19372">
    <literal><![CDATA[
      K(x,R(y,z,z) * (y \ u)) = K(x,(u / y) * L(y,z,z))
    ]]></literal>
    <justification jstring="[para(15528(a,2),19370(a,1,2))].">
      <j1 rule="para" parents="15528 19370"/>
    </justification>
  </clause>

  <clause id="19373">
    <literal><![CDATA[
      K(x,((y \ 1) \ z) * L(u,y,y)) = K(x,(y \ z) * (y * (y * u)))
    ]]></literal>
    <justification jstring="[hyper(299,a,19168,a(flip),b,19369,a),flip(a)].">
      <j1 rule="hyper" parents="299 19168 19369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19374">
    <literal><![CDATA[
      K(x,(y / (z \ 1)) * L(1 / z,u,u)) = K(x,(y / z) * L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,19370,a(flip),b,19371,a)].">
      <j1 rule="hyper" parents="65 19370 19371"/>
    </justification>
  </clause>

  <clause id="19375">
    <literal><![CDATA[
      K(x,(y / (z \ 1)) * L(z \ 1,u,u)) = K(x,(y / z) * L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,5750,a(flip),b,19374,a)].">
      <j1 rule="hyper" parents="65 5750 19374"/>
    </justification>
  </clause>

  <clause id="19376">
    <literal><![CDATA[
      K(x,R(y \ 1,z,z) * ((y \ 1) \ u)) = K(x,(u / y) * L(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,19372,a,b,19375,a)].">
      <j1 rule="hyper" parents="65 19372 19375"/>
    </justification>
  </clause>

  <clause id="19377">
    <literal><![CDATA[
      K(x,L(y \ 1,z,z) * ((y \ 1) \ u)) = K(x,(u / y) * L(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,19323,a(flip),b,19376,a)].">
      <j1 rule="hyper" parents="65 19323 19376"/>
    </justification>
  </clause>

  <clause id="19378">
    <literal><![CDATA[
      K(x,a(y,y,z \ 1) \ u) = K(x,(u / z) * L(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(15666,a,19377,a)].">
      <j1 rule="hyper" parents="15666 19377"/>
    </justification>
  </clause>

  <clause id="19379">
    <literal><![CDATA[
      K(x,(y / z) * L(z,u,u)) = K(x,a(u,u,z) \ y)
    ]]></literal>
    <justification jstring="[para(2363(a,1),19378(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2363 19378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19380">
    <literal><![CDATA[
      L(x,y,(((T(z,u * u) * w) / z) * (u * u)) * v5) = L(x,y,T((u * u) * w,(u * u) \ z) * v5)
    ]]></literal>
    <justification jstring="[para(760(a,1),18796(a,1,3,1,1,1))].">
      <j1 rule="para" parents="760 18796"/>
    </justification>
  </clause>

  <clause id="19381">
    <literal><![CDATA[
      L(x,y,(((z * z) \ ((u * w) / u)) * (z * z)) * v5) = L(x,y,T(w,(z * z) \ u) * v5)
    ]]></literal>
    <justification jstring="[para(764(a,1),18796(a,1,3,1,1))].">
      <j1 rule="para" parents="764 18796"/>
    </justification>
  </clause>

  <clause id="19382">
    <literal><![CDATA[
      T(x,T(T(y * (z \ 1),z) \ u,w)) = T(x,T(((z \ 1) * y) \ u,w))
    ]]></literal>
    <justification jstring="[hyper(299,a,9376,a(flip),b,18911,a),flip(a)].">
      <j1 rule="hyper" parents="299 9376 18911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19384">
    <literal><![CDATA[
      K(x,y * ((K(z,u) / w) * a(K(u,z) * w,v5,v5))) = K(x,y * R(w \ K(z,u),v5,v5))
    ]]></literal>
    <justification jstring="[para(14307(a,1),18919(a,1,2,2,2))].">
      <j1 rule="para" parents="14307 18919"/>
    </justification>
  </clause>

  <clause id="19385">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(u,w) * (y * z)) = T(x,z * T(K(w * u,w) * y,K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(15931,a,19028,a)].">
      <j1 rule="hyper" parents="15931 19028"/>
    </justification>
  </clause>

  <clause id="19386">
    <literal><![CDATA[
      T(x,y * T(K(z * u,z) * w,K(z,u))) = T(x,y * (w * K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(65,a,19025,a(flip),b,19385,a),flip(a)].">
      <j1 rule="hyper" parents="65 19025 19385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19387">
    <literal><![CDATA[
      T(x,y * (K(z * u,z) * w)) = T(x,y * (w * K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(16791,a,19386,a)].">
      <j1 rule="hyper" parents="16791 19386"/>
    </justification>
  </clause>

  <clause id="19388">
    <literal><![CDATA[
      T(x,y * (K(z \ u,z) * w)) = T(x,y * (w * K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(65,a,19278,a,b,19387,a)].">
      <j1 rule="hyper" parents="65 19278 19387"/>
    </justification>
  </clause>

  <clause id="19390">
    <literal><![CDATA[
      T(x,y * (((z \ u) \ w) * K(u,z))) = T(x,y * ((u / z) \ w))
    ]]></literal>
    <justification jstring="[para(5692(a,1),19388(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5692 19388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19391">
    <literal><![CDATA[
      T(x,K(y,z) * (u * (w * (v5 * y)))) = T(x,u * ((w * v5) * T(L(y,v5,w),z)))
    ]]></literal>
    <justification jstring="[hyper(65,a,19089,a(flip),b,19097,a)].">
      <j1 rule="hyper" parents="65 19089 19097"/>
    </justification>
  </clause>

  <clause id="19393">
    <literal><![CDATA[
      T(x,K(y,z) * (u * (w * (v5 * y)))) = T(x,u * (w * (v5 * T(y,z))))
    ]]></literal>
    <justification jstring="[para(487(a,1),19391(a,2,2,2))].">
      <j1 rule="para" parents="487 19391"/>
    </justification>
  </clause>

  <clause id="19394">
    <literal><![CDATA[
      T(x,K(y,z) * (u * (w * (v5 * y)))) = T(x,u * (w * (v5 * T(y,y * z))))
    ]]></literal>
    <justification jstring="[hyper(15843,a,19393,a)].">
      <j1 rule="hyper" parents="15843 19393"/>
    </justification>
  </clause>

  <clause id="19395">
    <literal><![CDATA[
      T(x,y * (z * (u * T(w,w * v5)))) = T(x,y * (z * (u * T(w,v5))))
    ]]></literal>
    <justification jstring="[hyper(65,a,19393,a(flip),b,19394,a),flip(a)].">
      <j1 rule="hyper" parents="65 19393 19394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19396">
    <literal><![CDATA[
      T(x,y * (z * (u * ((w \ v5) \ v5)))) = T(x,y * (z * (u * T(w,v5))))
    ]]></literal>
    <justification jstring="[hyper(65,a,15168,a(flip),b,19395,a)].">
      <j1 rule="hyper" parents="65 15168 19395"/>
    </justification>
  </clause>

  <clause id="19397">
    <literal><![CDATA[
      a(K(x,y) * (z * (u * y)),w,K(v5,v6)) = a(z * (u * T(y,x)),w,K(v5,v6))
    ]]></literal>
    <justification jstring="[hyper(299,a,18697,a(flip),b,19113,a),flip(a)].">
      <j1 rule="hyper" parents="299 18697 19113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19398">
    <literal><![CDATA[
      a(K(x,y) * (z * T(x,y)),u,K(w,v5)) = a(z * x,u,K(w,v5))
    ]]></literal>
    <justification jstring="[para(5432(a,1),19397(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5432 19397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19399">
    <literal><![CDATA[
      K(x,L(y * (z \ K(z,u)),w,v5)) = K(x,L(y / T(z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(11950,a,19116,a),flip(a)].">
      <j1 rule="hyper" parents="11950 19116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19400">
    <literal><![CDATA[
      K(x,L(y / ((z * u) / z),w,v5)) = K(x,L(y / T(u,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(14792,a,19399,a)].">
      <j1 rule="hyper" parents="14792 19399"/>
    </justification>
  </clause>

  <clause id="19401">
    <literal><![CDATA[
      K(x,L(y / (T(z,u \ z) / u),w,v5)) = K(x,L(y / T(z / u,z),w,v5))
    ]]></literal>
    <justification jstring="[para(4279(a,2),19400(a,1,2,1,2))].">
      <j1 rule="para" parents="4279 19400"/>
    </justification>
  </clause>

  <clause id="19402">
    <literal><![CDATA[
      K(x,L(y / (z \ K(u,z \ 1)),w,v5)) = K(x,L(y / T(z \ 1,u),w,v5))
    ]]></literal>
    <justification jstring="[para(5079(a,2),19400(a,1,2,1,2))].">
      <j1 rule="para" parents="5079 19400"/>
    </justification>
  </clause>

  <clause id="19403">
    <literal><![CDATA[
      K(x,L(y / (T(z,u \ z) / u),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y / (u \ z),w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(19401(a,2),17333(a,1))].">
      <j1 rule="para" parents="19401 17333"/>
    </justification>
  </clause>

  <clause id="19404">
    <literal><![CDATA[
      T(x,y \ ((y \ ((y \ z) * (y \ z))) \ u)) = T(x,y * ((z / (1 / (y \ z))) \ u))
    ]]></literal>
    <justification jstring="[para(421(a,1),19300(a,1,2,2,1))].">
      <j1 rule="para" parents="421 19300"/>
    </justification>
  </clause>

  <clause id="19405">
    <literal><![CDATA[
      K(x,(y \ T(z,u \ w)) * v5) = K(x,(y \ T(z,u * w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(17954,a,19334,a),flip(a)].">
      <j1 rule="hyper" parents="17954 19334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19406">
    <literal><![CDATA[
      (x * K(y,(z \ T(u,w * v5)) * v6)) \ x = K((z \ T(u,w \ v5)) * v6,y)
    ]]></literal>
    <justification jstring="[para(19405(a,1),7200(a,1,1,2))].">
      <j1 rule="para" parents="19405 7200"/>
    </justification>
  </clause>

  <clause id="19407">
    <literal><![CDATA[
      K((x \ T(y,z \ u)) * w,v5) = K((x \ T(y,z * u)) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(18857,a,19406,a),flip(a)].">
      <j1 rule="hyper" parents="18857 19406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19409">
    <literal><![CDATA[
      L(x,y,T((z * u) / z,w * w) * v5) = L(x,y,T(u,(w * w) \ z) * v5)
    ]]></literal>
    <justification jstring="[para(663(a,1),19381(a,1,3,1))].">
      <j1 rule="para" parents="663 19381"/>
    </justification>
  </clause>

  <clause id="19410">
    <literal><![CDATA[
      L(x,y,T(z,(u * u) \ w) * v5) = L(x,y,((w * z) / w) * v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,2897,a(flip),b,19409,a),flip(a)].">
      <j1 rule="hyper" parents="65 2897 19409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19412">
    <literal><![CDATA[
      L(x,y,T(z,(u * u) \ w) * v5) = L(x,y,T(z,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(299,a,18784,a(flip),b,19410,a),flip(a)].">
      <j1 rule="hyper" parents="299 18784 19410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19413">
    <literal><![CDATA[
      K(x,(L(1 / y,z,y) * a(u,w,K(v5,v6))) * v7) = K(x,(a(u,w,K(v5,v6)) / y) * v7)
    ]]></literal>
    <justification jstring="[para(2467(a,1),18760(a,1,2,1,1))].">
      <j1 rule="para" parents="2467 18760"/>
    </justification>
  </clause>

  <clause id="19414">
    <literal><![CDATA[
      K(x,L(1 / y,z,y) * u) = K(x,(a(w,v5,K(v6,v7)) / y) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,19041,a(flip),b,19413,a)].">
      <j1 rule="hyper" parents="65 19041 19413"/>
    </justification>
  </clause>

  <clause id="19416">
    <literal><![CDATA[
      K(x,(a(y,z,K(u,w)) / v5) * v6) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,L(v5 \ 1,v8,v5) * v6) = v7
    ]]></literal>
    <justification jstring="[para(19414(a,1),13851(a,1))].">
      <j1 rule="para" parents="19414 13851"/>
    </justification>
  </clause>

  <clause id="19417">
    <literal><![CDATA[
      K(x,L(T(y * z,y \ 1) / u,u,y)) = K(x,(y * ((1 / y) * z)) / (u * (y \ 1)))
    ]]></literal>
    <justification jstring="[para(2470(a,1),19192(a,1,2))].">
      <j1 rule="para" parents="2470 19192"/>
    </justification>
  </clause>

  <clause id="19418">
    <literal><![CDATA[
      K(x,L(T(y * z,y * 1) / u,u,y)) = K(x,(y * ((1 / y) * z)) / (u * (y \ 1)))
    ]]></literal>
    <justification jstring="[hyper(18028,a,19417,a)].">
      <j1 rule="hyper" parents="18028 19417"/>
    </justification>
  </clause>

  <clause id="19419">
    <literal><![CDATA[
      K(x,L(T(y * z,y) / u,u,y)) = K(x,(y * ((1 / y) * z)) / (u * (y \ 1)))
    ]]></literal>
    <justification jstring="[para(8(a,1),19418(a,1,2,1,1,2))].">
      <j1 rule="para" parents="8 19418"/>
    </justification>
  </clause>

  <clause id="19420">
    <literal><![CDATA[
      K(x,(y * ((1 / y) * z)) / (u * (y \ 1))) = K(x,(y * (y * z)) / (u * y))
    ]]></literal>
    <justification jstring="[hyper(65,a,19191,a(flip),b,19419,a),flip(a)].">
      <j1 rule="hyper" parents="65 19191 19419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19421">
    <literal><![CDATA[
      K(x,L(y,z,z) / (u * (z \ 1))) = K(x,(z * (z * y)) / (u * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,18187,a(flip),b,19420,a)].">
      <j1 rule="hyper" parents="65 18187 19420"/>
    </justification>
  </clause>

  <clause id="19422">
    <literal><![CDATA[
      (K(x,y) * z) * (K(y,x) * L(K(x,y),u,w)) = z * ((z * L(K(x,y),u,w)) / z)
    ]]></literal>
    <justification jstring="[para(8069(a,1),18676(a,1,1))].">
      <j1 rule="para" parents="8069 18676"/>
    </justification>
  </clause>

  <clause id="19424">
    <literal><![CDATA[
      (K(x,y) * z) * (K(y,x) * L(K(x,y),u,w)) = z * L(K(x,T(y,z)),u,w)
    ]]></literal>
    <justification jstring="[para(8244(a,1),19422(a,2,2))].">
      <j1 rule="para" parents="8244 19422"/>
    </justification>
  </clause>

  <clause id="19425">
    <literal><![CDATA[
      (K(x,y) * z) * (K(y,x) * L(K(x,y),u,w)) = L(K(x,y),u,w) * z
    ]]></literal>
    <justification jstring="[hyper(299,a,7510,a(flip),b,19424,a),flip(a)].">
      <j1 rule="hyper" parents="299 7510 19424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19426">
    <literal><![CDATA[
      (K(x,y) * (z * (K(y,x) * L(K(x,y),u,w)))) * a(x,z,K(K(y,x) * L(K(x,y),u,w),y)) = L(K(x,y),u,w) * z
    ]]></literal>
    <justification jstring="[hyper(65,a,14864,a,b,19425,a)].">
      <j1 rule="hyper" parents="65 14864 19425"/>
    </justification>
  </clause>

  <clause id="19427">
    <literal><![CDATA[
      (K(x,y) * z) * a(x,u,K(w,y)) = L(K(x,y),u,w) * z
    ]]></literal>
    <justification jstring="[para(14874(a,1),19425(a,1,2))].">
      <j1 rule="para" parents="14874 19425"/>
    </justification>
  </clause>

  <clause id="19428">
    <literal><![CDATA[
      L((a(x,x,y) \ K(z,u)) / K(z,u),w,v5) = (a(x,x,L(y,w,v5)) \ K(z,u)) / K(z,u)
    ]]></literal>
    <justification jstring="[para(18786(a,1),18785(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18786 18785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19429">
    <literal><![CDATA[
      L((a(x,x,y) \ K(z,u)) / K(z,u),w,v5) = a(x,x,L(y,w,v5)) \ 1
    ]]></literal>
    <justification jstring="[hyper(299,a,14226,a(flip),b,19428,a),flip(a)].">
      <j1 rule="hyper" parents="299 14226 19428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19431">
    <literal><![CDATA[
      L(a(x,x,y) \ 1,z,u) = a(x,x,L(y,z,u)) \ 1
    ]]></literal>
    <justification jstring="[para(14226(a,1),19429(a,1,1))].">
      <j1 rule="para" parents="14226 19429"/>
    </justification>
  </clause>

  <clause id="19432">
    <literal><![CDATA[
      L(a(x,x,y) \ 1,z,u) != w \ 1
    ]]></literal>
    <literal><![CDATA[
      a(x,x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(19431(a,2),50(a,1))].">
      <j1 rule="para" parents="19431 50"/>
    </justification>
  </clause>

  <clause id="19433">
    <literal><![CDATA[
      K(x,K(y,z \ (u \ w))) * K(K(x,y),K(w,z * u)) = K(x,K(y,w * ((z \ 1) * u)))
    ]]></literal>
    <justification jstring="[para(14246(a,1),18832(a,1,1,2))].">
      <j1 rule="para" parents="14246 18832"/>
    </justification>
  </clause>

  <clause id="19434">
    <literal><![CDATA[
      K(x,K(y,z * (u \ w))) * K(K(x,y),K(w,z * u)) = K(x,K(y,w * ((z \ 1) * u)))
    ]]></literal>
    <justification jstring="[para(16251(a,1),19433(a,1,1))].">
      <j1 rule="para" parents="16251 19433"/>
    </justification>
  </clause>

  <clause id="19435">
    <literal><![CDATA[
      K(x,K(y,z * ((u \ 1) * w))) = K(x,K(y,u * (w \ z))) * 1
    ]]></literal>
    <justification jstring="[para(16370(a,1),19434(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16370 19434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19436">
    <literal><![CDATA[
      K(x,K(y,z * ((u \ 1) * w))) = K(x,K(y,u * (w \ z)))
    ]]></literal>
    <justification jstring="[hyper(299,a,8,a(flip),b,19435,a),flip(a)].">
      <j1 rule="hyper" parents="299 8 19435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19437">
    <literal><![CDATA[
      K(x,K(y,z * ((u \ 1) * w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u * (w \ z))) = v5
    ]]></literal>
    <justification jstring="[para(19435(a,2),132(a,1)),flip(b)].">
      <j1 rule="para" parents="19435 132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19439">
    <literal><![CDATA[
      K(x,K(y,z * u)) * K(x,y \ ((w / (w / z)) * u)) = K(x,((w / (w / z)) * u) / y)
    ]]></literal>
    <justification jstring="[para(17136(a,1),19081(a,1,1))].">
      <j1 rule="para" parents="17136 19081"/>
    </justification>
  </clause>

  <clause id="19441">
    <literal><![CDATA[
      K(x,K(y * z,y) * (u * (w / ((y \ 1) \ 1)))) = K(x,u * (w / T(y,y \ z)))
    ]]></literal>
    <justification jstring="[para(4793(a,1),19112(a,1,2,1))].">
      <j1 rule="para" parents="4793 19112"/>
    </justification>
  </clause>

  <clause id="19442">
    <literal><![CDATA[
      K(x,(y * (z / ((u \ 1) \ 1))) * K(w,u)) = K(x,y * (z / T(u,u \ w)))
    ]]></literal>
    <justification jstring="[hyper(16623,a,19441,a)].">
      <j1 rule="hyper" parents="16623 19441"/>
    </justification>
  </clause>

  <clause id="19443">
    <literal><![CDATA[
      K(x,y * ((z / ((u \ 1) \ 1)) * K(w,u))) = K(x,y * (z / T(u,u \ w)))
    ]]></literal>
    <justification jstring="[hyper(19142,a,19442,a)].">
      <j1 rule="hyper" parents="19142 19442"/>
    </justification>
  </clause>

  <clause id="19444">
    <literal><![CDATA[
      K(x,y * (z / T((u \ 1) \ 1,w))) = K(x,y * (z / T(u,u \ w)))
    ]]></literal>
    <justification jstring="[para(7245(a,1),19443(a,1,2,2))].">
      <j1 rule="para" parents="7245 19443"/>
    </justification>
  </clause>

  <clause id="19445">
    <literal><![CDATA[
      K(x,y * (z / T((u \ 1) \ 1,w))) = K(x,y * (z / T(u,u * w)))
    ]]></literal>
    <justification jstring="[hyper(299,a,17999,a(flip),b,19444,a),flip(a)].">
      <j1 rule="hyper" parents="299 17999 19444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19446">
    <literal><![CDATA[
      K(x,y * (z * T((u * (w * u)) / u,T(u,u * w)))) = K(x,y * (z * T(u * w,u)))
    ]]></literal>
    <justification jstring="[hyper(299,a,15929,a(flip),b,19169,a),flip(a)].">
      <j1 rule="hyper" parents="299 15929 19169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19447">
    <literal><![CDATA[
      K(x,y * (z * T((u * (w * u)) / u,T(u,w)))) = K(x,y * (z * T(u * w,u)))
    ]]></literal>
    <justification jstring="[para(7462(a,1),19446(a,1,2,2,2))].">
      <j1 rule="para" parents="7462 19446"/>
    </justification>
  </clause>

  <clause id="19448">
    <literal><![CDATA[
      K(x,y * (z * T(u * w,K(w,u)))) = K(x,y * (z * T(w * u,w)))
    ]]></literal>
    <justification jstring="[para(7139(a,1),19447(a,1,2,2,2))].">
      <j1 rule="para" parents="7139 19447"/>
    </justification>
  </clause>

  <clause id="19449">
    <literal><![CDATA[
      K(x,y * (z * T(u * w,u))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * (w * u))) = v5
    ]]></literal>
    <justification jstring="[para(19448(a,1),16811(a,1))].">
      <j1 rule="para" parents="19448 16811"/>
    </justification>
  </clause>

  <clause id="19450">
    <literal><![CDATA[
      K(x,y * (z * (T(u,w) * w))) = K(x,y * (z * (w * u)))
    ]]></literal>
    <justification jstring="[hyper(19449,a,19171,a),flip(a)].">
      <j1 rule="hyper" parents="19449 19171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19451">
    <literal><![CDATA[
      K(x,y * (z * ((1 / u) * (u * w)))) = K(x,y * (z * R(w,u,u)))
    ]]></literal>
    <justification jstring="[hyper(19449,a,14001,a)].">
      <j1 rule="hyper" parents="19449 14001"/>
    </justification>
  </clause>

  <clause id="19452">
    <literal><![CDATA[
      K(x,T(y,z * (u * w)) * (z * (u * w))) = K(x,(z * (T(w,u) * u)) * y)
    ]]></literal>
    <justification jstring="[hyper(15895,a,19450,a),flip(a)].">
      <j1 rule="hyper" parents="15895 19450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19453">
    <literal><![CDATA[
      K(x,y \ (z * (T(u,w) * w))) = K(x,(y \ 1) * (z * (w * u)))
    ]]></literal>
    <justification jstring="[hyper(14281,a,19450,a)].">
      <j1 rule="hyper" parents="14281 19450"/>
    </justification>
  </clause>

  <clause id="19454">
    <literal><![CDATA[
      K(x,y \ (z * (T(u,w) * w))) = K(x,y \ (z * (w * u)))
    ]]></literal>
    <justification jstring="[hyper(299,a,14246,a(flip),b,19453,a),flip(a)].">
      <j1 rule="hyper" parents="299 14246 19453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19455">
    <literal><![CDATA[
      K(x,y \ (T(z,u * w) * (u * w))) = K(x,y \ ((T(w,u) * u) * z))
    ]]></literal>
    <justification jstring="[hyper(15922,a,19454,a),flip(a)].">
      <j1 rule="hyper" parents="15922 19454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19456">
    <literal><![CDATA[
      K(x,y * (z * R(u,w,w))) = K(x,y * (z * L(u,w,w)))
    ]]></literal>
    <justification jstring="[para(475(a,1),19451(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="475 19451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19457">
    <literal><![CDATA[
      K(x,y * ((z * u) * R(L(w,u,z),v5,v5))) = K(x,y * (z * (u * L(w,v5,v5))))
    ]]></literal>
    <justification jstring="[para(489(a,1),19456(a,2,2,2))].">
      <j1 rule="para" parents="489 19456"/>
    </justification>
  </clause>

  <clause id="19458">
    <literal><![CDATA[
      K(x,y \ ((T(z,u) * u) * w)) = K(x,y \ ((u * z) * w))
    ]]></literal>
    <justification jstring="[hyper(15911,a,19455,a),flip(a)].">
      <j1 rule="hyper" parents="15911 19455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19460">
    <literal><![CDATA[
      K(x,y \ ((T(z,u * z) * u) * w)) = K(x,y \ ((u * L(z,u,z)) * w))
    ]]></literal>
    <justification jstring="[para(4360(a,1),19458(a,1,2,2,1,1))].">
      <j1 rule="para" parents="4360 19458"/>
    </justification>
  </clause>

  <clause id="19461">
    <literal><![CDATA[
      K(x,y \ (((K(z,u) * K(z,u)) * w) * v5)) = K(x,y \ ((w * (K(z,u) * K(z,u))) * v5))
    ]]></literal>
    <justification jstring="[para(15786(a,1),19458(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="15786 19458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19462">
    <literal><![CDATA[
      K(x,(y * (T(z,u) * u)) * w) = K(x,(y * (u * z)) * w)
    ]]></literal>
    <justification jstring="[hyper(13261,a,19452,a),flip(a)].">
      <j1 rule="hyper" parents="13261 19452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19463">
    <literal><![CDATA[
      K(x,(y * (z * ((z * u) / z))) * w) = K(x,(y * (u * z)) * w)
    ]]></literal>
    <justification jstring="[para(222(a,1),19462(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="222 19462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19464">
    <literal><![CDATA[
      K(x,(y * T(z * u,z)) * w) = K(x,(y * (u * z)) * w)
    ]]></literal>
    <justification jstring="[hyper(19313,a,19463,a)].">
      <j1 rule="hyper" parents="19313 19463"/>
    </justification>
  </clause>

  <clause id="19465">
    <literal><![CDATA[
      K(x,(y * ((1 / z) * (z * u))) * w) = K(x,(y * R(u,z,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(65,a,18195,a(flip),b,19464,a),flip(a)].">
      <j1 rule="hyper" parents="65 18195 19464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19466">
    <literal><![CDATA[
      K(x,(y * ((z \ u) * z)) * w) = K(x,(y * T(u,z)) * w)
    ]]></literal>
    <justification jstring="[para(10(a,1),19464(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 19464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19467">
    <literal><![CDATA[
      K(x,(y * T(z,u)) * K(u,y * (u \ z))) = K(x,L(u,u \ z,y) * (y * (u \ z)))
    ]]></literal>
    <justification jstring="[para(14641(a,1),19466(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14641 19466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19468">
    <literal><![CDATA[
      K(x,(y * R(z,u,u)) * w) = K(x,(y * L(z,u,u)) * w)
    ]]></literal>
    <justification jstring="[para(475(a,1),19465(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="475 19465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19469">
    <literal><![CDATA[
      K(x,(y * L(1 / y,z,z)) * u) = K(x,a(y,z,z) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,15616,a(flip),b,19468,a),flip(a)].">
      <j1 rule="hyper" parents="65 15616 19468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19470">
    <literal><![CDATA[
      K(x,(y * L(y \ 1,z,z)) * u) = K(x,a(y,z,z) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,13846,a(flip),b,19469,a)].">
      <j1 rule="hyper" parents="65 13846 19469"/>
    </justification>
  </clause>

  <clause id="19471">
    <literal><![CDATA[
      K(x,(y \ L(y,z,z)) * u) = K(x,a(y,z,z) * u)
    ]]></literal>
    <justification jstring="[para(6499(a,1),19470(a,1,2,1))].">
      <j1 rule="para" parents="6499 19470"/>
    </justification>
  </clause>

  <clause id="19472">
    <literal><![CDATA[
      K(x,a(y,y,z) \ u) = K(x,a(z,y,y) * u)
    ]]></literal>
    <justification jstring="[hyper(14531,a,19471,a)].">
      <j1 rule="hyper" parents="14531 19471"/>
    </justification>
  </clause>

  <clause id="19473">
    <literal><![CDATA[
      K(x,L(y,z,z) * (y \ u)) = K(x,a(y,z,z) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,15659,a(flip),b,19471,a)].">
      <j1 rule="hyper" parents="65 15659 19471"/>
    </justification>
  </clause>

  <clause id="19474">
    <literal><![CDATA[
      K(x,(y / z) * L(z,u,u)) = K(x,a(z,u,u) * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,19379,a,b,19472,a)].">
      <j1 rule="hyper" parents="65 19379 19472"/>
    </justification>
  </clause>

  <clause id="19475">
    <literal><![CDATA[
      K(x,a(y,z,z) * (u * y)) = K(x,u * L(y,z,z))
    ]]></literal>
    <justification jstring="[para(11(a,1),19474(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11 19474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19476">
    <literal><![CDATA[
      K(x,y * (z * (u * R(w,v5,v5)))) = K(x,y * (z * (u * L(w,v5,v5))))
    ]]></literal>
    <justification jstring="[para(488(a,1),19457(a,1,2,2))].">
      <j1 rule="para" parents="488 19457"/>
    </justification>
  </clause>

  <clause id="19477">
    <literal><![CDATA[
      K(x,y * (z * (u * L(1 / u,w,w)))) = K(x,y * (z * a(u,w,w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,15708,a(flip),b,19476,a),flip(a)].">
      <j1 rule="hyper" parents="65 15708 19476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19478">
    <literal><![CDATA[
      K(x,y * (z * (u \ L(u,w,w)))) = K(x,y * (z * a(u,w,w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,15600,a(flip),b,19477,a)].">
      <j1 rule="hyper" parents="65 15600 19477"/>
    </justification>
  </clause>

  <clause id="19479">
    <literal><![CDATA[
      K(x,y * ((z \ L(z,u,u)) * w)) = K(x,y * (w * a(z,u,u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,14439,a,b,19478,a)].">
      <j1 rule="hyper" parents="65 14439 19478"/>
    </justification>
  </clause>

  <clause id="19480">
    <literal><![CDATA[
      K(x,L(y,y \ z,u) * (u * (y \ z))) = K(x,K(y,u * z) * (u * T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(65,a,17870,a(flip),b,19467,a),flip(a)].">
      <j1 rule="hyper" parents="65 17870 19467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19481">
    <literal><![CDATA[
      K(x,y \ ((z * (T(T(z,u),u) \ w)) * v5)) = K(x,y \ ((w * (K(u,z) * K(u,z))) * v5))
    ]]></literal>
    <justification jstring="[para(10048(a,1),19461(a,1,2,2,1))].">
      <j1 rule="para" parents="10048 19461"/>
    </justification>
  </clause>

  <clause id="19482">
    <literal><![CDATA[
      K(x,y \ ((z * (K(u,w) * K(u,w))) * v5)) = K(x,y \ (w * (T(T(w,u),u) \ (z * v5))))
    ]]></literal>
    <justification jstring="[para(15700(a,1),19481(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="15700 19481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19483">
    <literal><![CDATA[
      K(K(x,K(y,z)) * K(z,(u / x) * (u \ y)),w) = K(K(z,(u * (u / x)) \ y),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,17450,a(flip),b,19212,a)].">
      <j1 rule="hyper" parents="65 17450 19212"/>
    </justification>
  </clause>

  <clause id="19484">
    <literal><![CDATA[
      K(K(x,(y * (y / z)) \ u),w) = K(K(x,(y / z) * (y \ u)),w)
    ]]></literal>
    <justification jstring="[hyper(16764,a,19483,a),flip(a)].">
      <j1 rule="hyper" parents="16764 19483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19486">
    <literal><![CDATA[
      K(K(x,(y * (y / z)) \ u),w) = K(x,K(w,(y / z) * (y \ u)))
    ]]></literal>
    <justification jstring="[hyper(299,a,8001,a(flip),b,19484,a),flip(a)].">
      <j1 rule="hyper" parents="299 8001 19484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19487">
    <literal><![CDATA[
      K(K(x,(y * (y / z)) \ u),w) = K(x,K(w,y * (z * (y \ u))))
    ]]></literal>
    <justification jstring="[hyper(299,a,18789,a(flip),b,19486,a),flip(a)].">
      <j1 rule="hyper" parents="299 18789 19486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19488">
    <literal><![CDATA[
      K(x,K(y,(z * (z / u)) \ w)) = K(x,K(y,z * (u * (z \ w))))
    ]]></literal>
    <justification jstring="[hyper(8200,a,19487,a)].">
      <j1 rule="hyper" parents="8200 19487"/>
    </justification>
  </clause>

  <clause id="19489">
    <literal><![CDATA[
      K(x,K(y,z * ((u \ z) \ w))) = K(x,K(y,z * (u * (z \ w))))
    ]]></literal>
    <justification jstring="[hyper(18970,a,19488,a)].">
      <j1 rule="hyper" parents="18970 19488"/>
    </justification>
  </clause>

  <clause id="19490">
    <literal><![CDATA[
      T(x,y * (z * (T(u,T(w,v5)) * ((w \ v5) \ v5)))) = T(x,y * (z * (T(w,w \ v5) * u)))
    ]]></literal>
    <justification jstring="[para(7482(a,1),19254(a,1,2,2,2,1))].">
      <j1 rule="para" parents="7482 19254"/>
    </justification>
  </clause>

  <clause id="19491">
    <literal><![CDATA[
      T(x,y * (z * (T(u,T(w,v5)) * T(w,v5)))) = T(x,y * (z * (T(w,w \ v5) * u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,19396,a(flip),b,19490,a)].">
      <j1 rule="hyper" parents="65 19396 19490"/>
    </justification>
  </clause>

  <clause id="19492">
    <literal><![CDATA[
      T(x,y * (z * (T(u,u \ w) * v5))) = T(x,y * (z * (T(u,w) * v5)))
    ]]></literal>
    <justification jstring="[hyper(65,a,19252,a(flip),b,19491,a),flip(a)].">
      <j1 rule="hyper" parents="65 19252 19491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19493">
    <literal><![CDATA[
      K(((x \ y) * x) / (L(K(z,u),w,v5) * x),v6) = K(x \ (L(K(u,z),w,v5) * y),v6)
    ]]></literal>
    <justification jstring="[hyper(16808,a,19302,a)].">
      <j1 rule="hyper" parents="16808 19302"/>
    </justification>
  </clause>

  <clause id="19494">
    <literal><![CDATA[
      K(x,y * (z / T(T(u,w),u \ 1))) = K(x,y * (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(16707,a,19365,a),flip(a)].">
      <j1 rule="hyper" parents="16707 19365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19495">
    <literal><![CDATA[
      K(x,y * (z / T((u \ 1) \ 1,w))) = K(x,y * (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,18866,a(flip),b,19494,a)].">
      <j1 rule="hyper" parents="65 18866 19494"/>
    </justification>
  </clause>

  <clause id="19496">
    <literal><![CDATA[
      K(x,y * (z / T(u,u * w))) = K(x,y * (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,19445,a(flip),b,19495,a)].">
      <j1 rule="hyper" parents="65 19445 19495"/>
    </justification>
  </clause>

  <clause id="19497">
    <literal><![CDATA[
      K(x,y * (z / ((u \ w) \ w))) = K(x,y * (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,18000,a(flip),b,19496,a)].">
      <j1 rule="hyper" parents="65 18000 19496"/>
    </justification>
  </clause>

  <clause id="19498">
    <literal><![CDATA[
      K(x,y * (T(z,(u \ w) \ w) / T(u,w))) = K(x,y * (((u \ w) \ w) \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,13881,a(flip),b,19497,a),flip(a)].">
      <j1 rule="hyper" parents="65 13881 19497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19499">
    <literal><![CDATA[
      K(x,y * (T(z,T(u,w)) / T(u,w))) = K(x,y * (((u \ w) \ w) \ z))
    ]]></literal>
    <justification jstring="[para(7482(a,1),19498(a,1,2,2,1))].">
      <j1 rule="para" parents="7482 19498"/>
    </justification>
  </clause>

  <clause id="19500">
    <literal><![CDATA[
      K(x,y * (((z \ u) \ u) \ w)) = K(x,y * (T(z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,13881,a(flip),b,19499,a),flip(a)].">
      <j1 rule="hyper" parents="65 13881 19499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19501">
    <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(17974,a,19500,a),flip(a)].">
      <j1 rule="hyper" parents="17974 19500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19502">
    <literal><![CDATA[
      K(x,(((y \ z) \ z) \ u) * w) = K(x,(T(y,z) \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(17954,a,19501,a),flip(a)].">
      <j1 rule="hyper" parents="17954 19501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19503">
    <literal><![CDATA[
      K(x,((((1 / y) \ z) \ ((y * y) * z)) \ u) * w) = K(x,(T(y,(y * y) * z) \ u) * w)
    ]]></literal>
    <justification jstring="[para(443(a,1),19502(a,1,2,1,1,1))].">
      <j1 rule="para" parents="443 19502"/>
    </justification>
  </clause>

  <clause id="19504">
    <literal><![CDATA[
      K(x,(T(y,(y * y) * z) \ u) * w) = K(x,(T(y,y * z) \ u) * w)
    ]]></literal>
    <justification jstring="[para(14653(a,1),19503(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="14653 19503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19505">
    <literal><![CDATA[
      K(x,(L(T(y,z),y,y) \ u) * w) = K(x,(T(y,y * z) \ u) * w)
    ]]></literal>
    <justification jstring="[para(14494(a,1),19504(a,1,2,1,1))].">
      <j1 rule="para" parents="14494 19504"/>
    </justification>
  </clause>

  <clause id="19506">
    <literal><![CDATA[
      K(x,(T(y,y * z) \ u) * w) = K(x,(T(y,z) \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(65,a,18124,a(flip),b,19505,a),flip(a)].">
      <j1 rule="hyper" parents="65 18124 19505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19507">
    <literal><![CDATA[
      K(x,(T(y,y * z) \ u) / w) = K(x,(T(y,z) \ u) * (1 / w))
    ]]></literal>
    <justification jstring="[hyper(14629,a,19506,a)].">
      <j1 rule="hyper" parents="14629 19506"/>
    </justification>
  </clause>

  <clause id="19508">
    <literal><![CDATA[
      K(x,(T(y,y * z) \ u) / w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(T(y,z) \ u) / w) = v5
    ]]></literal>
    <justification jstring="[para(19507(a,2),14629(a,1))].">
      <j1 rule="para" parents="19507 14629"/>
    </justification>
  </clause>

  <clause id="19509">
    <literal><![CDATA[
      T(x / K(y,L(T(z,u),w,v5)),K(K(y,L(z,w,v5)),u)) = K(u,K(y,z)) * (x / K(y,L(z,w,v5)))
    ]]></literal>
    <justification jstring="[para(7506(a,2),18551(a,1,1,2))].">
      <j1 rule="para" parents="7506 18551"/>
    </justification>
  </clause>

  <clause id="19510">
    <literal><![CDATA[
      ((x * (K(y,K(z,u)) * (w * v5))) \ ((x * w) * v5)) * K(y,K(z,u)) = a(x,w,v5 * K(y,K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,18769,a(flip),b,18728,a)].">
      <j1 rule="hyper" parents="65 18769 18728"/>
    </justification>
  </clause>

  <clause id="19511">
    <literal><![CDATA[
      K(x,K(y,z)) * (u \ (y * w)) = u \ (T(y,K(x,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(18584,a,18810,a)].">
      <j1 rule="hyper" parents="18584 18810"/>
    </justification>
  </clause>

  <clause id="19513">
    <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(19511(a,1),16749(a,1,2))].">
      <j1 rule="para" parents="19511 16749"/>
    </justification>
  </clause>

  <clause id="19514">
    <literal><![CDATA[
      K(x,K(y * z,y * (u \ z))) * K(x,L(u * K(y,u),y,z)) = K(x,(y * z) \ ((y * u) * z))
    ]]></literal>
    <justification jstring="[para(15482(a,1),18831(a,1,2))].">
      <j1 rule="para" parents="15482 18831"/>
    </justification>
  </clause>

  <clause id="19515">
    <literal><![CDATA[
      T(x * K(L(T(y,z),u,w),v5),K(K(v5,L(y,u,w)),z)) = K(z,K(v5,y)) * (x / K(v5,L(y,u,w)))
    ]]></literal>
    <justification jstring="[para(7196(a,1),19509(a,1,1))].">
      <j1 rule="para" parents="7196 19509"/>
    </justification>
  </clause>

  <clause id="19516">
    <literal><![CDATA[
      (((x * (y * z)) \ ((x * y) * z)) * K(u,K(w,v5))) * K(u,K(w,v5)) = a(x,y,z * K(u,K(w,v5)))
    ]]></literal>
    <justification jstring="[para(18817(a,1),19510(a,1,1))].">
      <j1 rule="para" parents="18817 19510"/>
    </justification>
  </clause>

  <clause id="19517">
    <literal><![CDATA[
      K(x,K(y * z,y * (u \ z))) * K(x,L(T(u,y),y,z)) = K(x,(y * z) \ ((y * u) * z))
    ]]></literal>
    <justification jstring="[para(8381(a,1),19514(a,1,2))].">
      <j1 rule="para" parents="8381 19514"/>
    </justification>
  </clause>

  <clause id="19518">
    <literal><![CDATA[
      T(x * K(T(y,z),L(u,w,v5)),K(K(u,L(y,w,v5)),z)) = K(z,K(u,y)) * (x / K(u,L(y,w,v5)))
    ]]></literal>
    <justification jstring="[para(11929(a,1),19515(a,1,1,2))].">
      <j1 rule="para" parents="11929 19515"/>
    </justification>
  </clause>

  <clause id="19519">
    <literal><![CDATA[
      (a(x,y,z) * K(u,K(w,v5))) * K(u,K(w,v5)) = a(x,y,z * K(u,K(w,v5)))
    ]]></literal>
    <justification jstring="[para(14(a,2),19516(a,1,1,1))].">
      <j1 rule="para" parents="14 19516"/>
    </justification>
  </clause>

  <clause id="19520">
    <literal><![CDATA[
      a(x,y,z) * (K(u,K(w,v5)) * K(u,K(w,v5))) = a(x,y,z * K(u,K(w,v5)))
    ]]></literal>
    <justification jstring="[hyper(18555,a,19519,a)].">
      <j1 rule="hyper" parents="18555 19519"/>
    </justification>
  </clause>

  <clause id="19521">
    <literal><![CDATA[
      a(x,y,z * K(u,K(w,v5))) = a(x,y,z) * 1
    ]]></literal>
    <justification jstring="[para(8027(a,1),19520(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8027 19520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19522">
    <literal><![CDATA[
      a(x,y,z * K(u,K(w,v5))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(299,a,8,a(flip),b,19521,a),flip(a)].">
      <j1 rule="hyper" parents="299 8 19521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19524">
    <literal><![CDATA[
      a(x,y,K(z,T(u,w))) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(7496(a,1),19522(a,1,3))].">
      <j1 rule="para" parents="7496 19522"/>
    </justification>
  </clause>

  <clause id="19525">
    <literal><![CDATA[
      a(x,y,K(z,u / w)) = a(x,y,K(z,w \ u))
    ]]></literal>
    <justification jstring="[para(8513(a,1),19522(a,1,3)),flip(a)].">
      <j1 rule="para" parents="8513 19522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19526">
    <literal><![CDATA[
      a(x * (y / x),z,K(u,w)) = a(w,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(14973,a,19524,a)].">
      <j1 rule="hyper" parents="14973 19524"/>
    </justification>
  </clause>

  <clause id="19527">
    <literal><![CDATA[
      a(x,y,K(z,T(u,w))) = a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(299,a,14863,a,b,19524,a),flip(a)].">
      <j1 rule="hyper" parents="299 14863 19524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19528">
    <literal><![CDATA[
      a(x,y,K(z * (u / w),z)) = a(x,y,K(z * (w \ u),z))
    ]]></literal>
    <justification jstring="[para(13480(a,1),19524(a,1,3))].">
      <j1 rule="para" parents="13480 19524"/>
    </justification>
  </clause>

  <clause id="19529">
    <literal><![CDATA[
      (T(a(x,y,z),u) * w) / T(a(x,y,z),u) = w * a(x,y,K(z,w))
    ]]></literal>
    <justification jstring="[para(19524(a,1),14566(a,2,2))].">
      <j1 rule="para" parents="19524 14566"/>
    </justification>
  </clause>

  <clause id="19530">
    <literal><![CDATA[
      K(x,T(y,z)) * a(x,u,K(y \ (w \ v5),y)) = K(x,L(T(y,z),u,(w * y) \ v5))
    ]]></literal>
    <justification jstring="[para(19524(a,1),14933(a,1,2))].">
      <j1 rule="para" parents="19524 14933"/>
    </justification>
  </clause>

  <clause id="19531">
    <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(19527(a,2),14922(a,1))].">
      <j1 rule="para" parents="19527 14922"/>
    </justification>
  </clause>

  <clause id="19532">
    <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(19527(a,1),15580(a,1,2))].">
      <j1 rule="para" parents="19527 15580"/>
    </justification>
  </clause>

  <clause id="19533">
    <literal><![CDATA[
      a(x,y,K(z,u / w)) = a(x,y,K(z,w * u))
    ]]></literal>
    <justification jstring="[hyper(299,a,15012,a(flip),b,19525,a),flip(a)].">
      <j1 rule="hyper" parents="299 15012 19525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19534">
    <literal><![CDATA[
      a(x * y,z,K(u,w)) = a(w,z,K(u,y * x))
    ]]></literal>
    <justification jstring="[para(11(a,1),19526(a,1,1,2))].">
      <j1 rule="para" parents="11 19526"/>
    </justification>
  </clause>

  <clause id="19535">
    <literal><![CDATA[
      a(T(x \ y,y),z,K(u,w)) = v5 / (v5 * a(w,z,K(u,x * y)))
    ]]></literal>
    <justification jstring="[para(19533(a,1),18702(a,2,2,2))].">
      <j1 rule="para" parents="19533 18702"/>
    </justification>
  </clause>

  <clause id="19536">
    <literal><![CDATA[
      a(x * y,z,K(u,x)) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,14912,a(flip),b,19534,a),flip(a)].">
      <j1 rule="hyper" parents="299 14912 19534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19537">
    <literal><![CDATA[
      a(x,y,K(z,u * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(z,w * u)) = v5
    ]]></literal>
    <justification jstring="[para(19534(a,1),14957(a,1))].">
      <j1 rule="para" parents="19534 14957"/>
    </justification>
  </clause>

  <clause id="19538">
    <literal><![CDATA[
      a(x,y,K(z,x * u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(14957,a,19536,a)].">
      <j1 rule="hyper" parents="14957 19536"/>
    </justification>
  </clause>

  <clause id="19539">
    <literal><![CDATA[
      a(x,y,z) * a(x,y,K(z,u)) = T(a(x,y,z),x * u)
    ]]></literal>
    <justification jstring="[para(19536(a,1),14965(a,1,2))].">
      <j1 rule="para" parents="19536 14965"/>
    </justification>
  </clause>

  <clause id="19540">
    <literal><![CDATA[
      a(x,y,K(z,u \ (x * w))) = a(z,y,K(u * w,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,15031,a(flip),b,19538,a),flip(a)].">
      <j1 rule="hyper" parents="65 15031 19538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19541">
    <literal><![CDATA[
      a(x,y,K(z \ u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(u / z,w)) = v5
    ]]></literal>
    <justification jstring="[para(7499(a,1),19531(a,1,3))].">
      <j1 rule="para" parents="7499 19531"/>
    </justification>
  </clause>

  <clause id="19543">
    <literal><![CDATA[
      a(T(x,y),z,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,z,K(u,w)) = v5
    ]]></literal>
    <justification jstring="[para(14917(a,2),19531(a,1))].">
      <j1 rule="para" parents="14917 19531"/>
    </justification>
  </clause>

  <clause id="19546">
    <literal><![CDATA[
      a(x,y,K(z,u * (x * w))) = a(z,y,K(u * w,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,15012,a(flip),b,19540,a)].">
      <j1 rule="hyper" parents="65 15012 19540"/>
    </justification>
  </clause>

  <clause id="19547">
    <literal><![CDATA[
      a(x,y,K(z,(x \ u) * w)) = a(z,y,K(u * w,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,15021,a,b,19546,a)].">
      <j1 rule="hyper" parents="65 15021 19546"/>
    </justification>
  </clause>

  <clause id="19548">
    <literal><![CDATA[
      a(x,y,K(T(z * K(u * w,z),v5) * w,u)) = a(u,y,K(x,(u * w) * T(z,v5)))
    ]]></literal>
    <justification jstring="[para(5130(a,1),19546(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="5130 19546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19549">
    <literal><![CDATA[
      a(x * y,z,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(w,z,K(u,y * x)) = v5
    ]]></literal>
    <justification jstring="[para(14949(a,1),19537(a,1))].">
      <j1 rule="para" parents="14949 19537"/>
    </justification>
  </clause>

  <clause id="19550">
    <literal><![CDATA[
      T(a(x,y,z),x * u) = T(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(14562,a,19539,a),flip(a)].">
      <j1 rule="hyper" parents="14562 19539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19551">
    <literal><![CDATA[
      ((x * y) * z) / (x * (y * z)) = T(a(x,y,z),y * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,15111,a,b,19550,a)].">
      <j1 rule="hyper" parents="65 15111 19550"/>
    </justification>
  </clause>

  <clause id="19552">
    <literal><![CDATA[
      ((x * y) * z) / (x * (y * z)) = T(a(x,y,z),y)
    ]]></literal>
    <justification jstring="[hyper(299,a,15010,a(flip),b,19551,a),flip(a)].">
      <j1 rule="hyper" parents="299 15010 19551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19553">
    <literal><![CDATA[
      a(x,y,z) = ((x * y) * z) / (x * (y * z))
    ]]></literal>
    <justification jstring="[hyper(299,a,14568,a(flip),b,19552,a)].">
      <j1 rule="hyper" parents="299 14568 19552"/>
    </justification>
  </clause>

  <clause id="19554">
    <literal><![CDATA[
      ((x * y) * K(z,T(u,w))) / (x * (y * K(z,T(u,w)))) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(19531,a,19553,a),flip(a)].">
      <j1 rule="hyper" parents="19531 19553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19555">
    <literal><![CDATA[
      a(x,y,z) = R(x \ R(x,y,z),x,y * z)
    ]]></literal>
    <justification jstring="[hyper(299,a,10874,a,b,19553,a),flip(a)].">
      <j1 rule="hyper" parents="299 10874 19553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19556">
    <literal><![CDATA[
      a(x,y,z) * (x * (y * z)) = (x * y) * z
    ]]></literal>
    <justification jstring="[hyper(143,a,19553,a(flip))].">
      <j1 rule="hyper" parents="143 19553"/>
    </justification>
  </clause>

  <clause id="19557">
    <literal><![CDATA[
      R((1 / x) * R(x,y,z),x,y * z) = L(a(x,y,z),x,x)
    ]]></literal>
    <justification jstring="[para(19555(a,2),516(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19555 516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19558">
    <literal><![CDATA[
      ((x * y) * z) / (x * (y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(19556(a,1),307(a,1,1)),flip(b)].">
      <j1 rule="para" parents="19556 307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19560">
    <literal><![CDATA[
      K(x,((y * z) * y) \ u) = K(x,(y * (z * y)) \ u)
    ]]></literal>
    <justification jstring="[para(19556(a,1),13936(a,1,2,1))].">
      <j1 rule="para" parents="19556 13936"/>
    </justification>
  </clause>

  <clause id="19561">
    <literal><![CDATA[
      R(x \ R(x,y,z),x,y * z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(10874(a,2),19558(a,1))].">
      <j1 rule="para" parents="10874 19558"/>
    </justification>
  </clause>

  <clause id="19563">
    <literal><![CDATA[
      K(x,(y * (z * y)) \ ((z * y) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(y,z) \ u,u,z * y)) = w
    ]]></literal>
    <justification jstring="[para(19560(a,1),12012(a,1))].">
      <j1 rule="para" parents="19560 12012"/>
    </justification>
  </clause>

  <clause id="19564">
    <literal><![CDATA[
      R(x \ R(x,y,z),x,y * z) = L(a(x,y,z),x,x)
    ]]></literal>
    <justification jstring="[para(10869(a,1),19557(a,1,1))].">
      <j1 rule="para" parents="10869 19557"/>
    </justification>
  </clause>

  <clause id="19565">
    <literal><![CDATA[
      L(a(x,y,z),x,x) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(19561,a,19564,a),flip(a)].">
      <j1 rule="hyper" parents="19561 19564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19567">
    <literal><![CDATA[
      (a(x,y,z) \ a(x,y,z)) * (a(x,y,z) \ 1) = L(a(x,y,z) \ 1,x,x)
    ]]></literal>
    <justification jstring="[para(19565(a,1),6506(a,1,1,2))].">
      <j1 rule="para" parents="19565 6506"/>
    </justification>
  </clause>

  <clause id="19568">
    <literal><![CDATA[
      a(T(x \ y,y),z,K(u,w)) = a(x * y,z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(299,a,18697,a(flip),b,19535,a),flip(a)].">
      <j1 rule="hyper" parents="299 18697 19535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19569">
    <literal><![CDATA[
      a(x \ y,z,K(u,w)) = a(x * y,z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(19543,a,19568,a)].">
      <j1 rule="hyper" parents="19543 19568"/>
    </justification>
  </clause>

  <clause id="19570">
    <literal><![CDATA[
      K(x,y) * a(z * u,w,K(y,x)) = K(x,L(y,w,z \ u))
    ]]></literal>
    <justification jstring="[para(19569(a,1),11896(a,1,2))].">
      <j1 rule="para" parents="19569 11896"/>
    </justification>
  </clause>

  <clause id="19571">
    <literal><![CDATA[
      x * a(a(y,z,u) * x,z,K(u,y)) = (a(y,z,u) \ x) * a(y,z,u)
    ]]></literal>
    <justification jstring="[para(19569(a,1),14890(a,1,2))].">
      <j1 rule="para" parents="19569 14890"/>
    </justification>
  </clause>

  <clause id="19572">
    <literal><![CDATA[
      K(x,L(y,z,u \ w)) = K(x,L(y,z,u * w))
    ]]></literal>
    <justification jstring="[hyper(11950,a,19570,a),flip(a)].">
      <j1 rule="hyper" parents="11950 19570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19573">
    <literal><![CDATA[
      K(x,L(y,z,u \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u * w)) = v5
    ]]></literal>
    <justification jstring="[para(19570(a,1),11950(a,1))].">
      <j1 rule="para" parents="19570 11950"/>
    </justification>
  </clause>

  <clause id="19574">
    <literal><![CDATA[
      K(x,y) * a(y,z,K(u * w,x)) = K(x,L(y,z,u \ w))
    ]]></literal>
    <justification jstring="[para(14948(a,1),19570(a,1,2))].">
      <j1 rule="para" parents="14948 19570"/>
    </justification>
  </clause>

  <clause id="19575">
    <literal><![CDATA[
      K(x,L(y,z \ u,(z \ u) * z)) = K(x,L(y,z,(1 / (u / z)) \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,18864,a(flip),b,19572,a),flip(a)].">
      <j1 rule="hyper" parents="65 18864 19572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19576">
    <literal><![CDATA[
      K(x,L(y / z,u,y * u)) = K(x,u / (z * (y \ u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,15557,a(flip),b,19572,a),flip(a)].">
      <j1 rule="hyper" parents="65 15557 19572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19577">
    <literal><![CDATA[
      K(x,L(y,z,u * (u * w))) = K(x,L(y,z,w))
    ]]></literal>
    <justification jstring="[para(9(a,1),19572(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="9 19572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19578">
    <literal><![CDATA[
      K(x,L(y,z,L(u,w,w))) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(2465(a,1),19577(a,1,2))].">
      <j1 rule="para" parents="2465 19577"/>
    </justification>
  </clause>

  <clause id="19579">
    <literal><![CDATA[
      K(x,(y * (z \ u)) / ((z \ u) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y / ((z \ u) \ z),z,z * u)) = w
    ]]></literal>
    <justification jstring="[para(15575(a,1),19573(a,1))].">
      <j1 rule="para" parents="15575 19573"/>
    </justification>
  </clause>

  <clause id="19580">
    <literal><![CDATA[
      K(x,((y \ z) \ T(z,y)) \ ((y \ z) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(z,y) \ u,T(y,z),y * z)) = w
    ]]></literal>
    <justification jstring="[para(15760(a,2),19573(a,1))].">
      <j1 rule="para" parents="15760 19573"/>
    </justification>
  </clause>

  <clause id="19581">
    <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(18663(a,2),19573(a,1))].">
      <j1 rule="para" parents="18663 19573"/>
    </justification>
  </clause>

  <clause id="19582">
    <literal><![CDATA[
      K(x,L(T(y,z),u,(z * y) * u)) = K(x,u / (z * ((z * y) \ u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,8380,a(flip),b,19576,a)].">
      <j1 rule="hyper" parents="65 8380 19576"/>
    </justification>
  </clause>

  <clause id="19583">
    <literal><![CDATA[
      K(x,L((y * (z / y)) / u,w,T(z,y) * w)) = K(x,w / (u * ((y * (z / y)) \ w)))
    ]]></literal>
    <justification jstring="[para(18795(a,1),19576(a,1,2))].">
      <j1 rule="para" parents="18795 19576"/>
    </justification>
  </clause>

  <clause id="19584">
    <literal><![CDATA[
      K(x,L(T(y,z \ y) \ u,y,y * z)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(19581,a,18076,a)].">
      <j1 rule="hyper" parents="19581 18076"/>
    </justification>
  </clause>

  <clause id="19585">
    <literal><![CDATA[
      K(x,L(y \ z,u,u * z)) = K(x,((z / u) \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(19581,a,17634,a)].">
      <j1 rule="hyper" parents="19581 17634"/>
    </justification>
  </clause>

  <clause id="19586">
    <literal><![CDATA[
      K(x,L(y \ z,u,u * y)) = K(x,u \ ((y / u) \ z))
    ]]></literal>
    <justification jstring="[hyper(19581,a,15640,a)].">
      <j1 rule="hyper" parents="19581 15640"/>
    </justification>
  </clause>

  <clause id="19587">
    <literal><![CDATA[
      a(x,y,K(z \ u,w)) = a(x,y,K(z * u,w))
    ]]></literal>
    <justification jstring="[hyper(36,a,14959,a,b,19574,a)].">
      <j1 rule="hyper" parents="36 14959 19574"/>
    </justification>
  </clause>

  <clause id="19588">
    <literal><![CDATA[
      a(x,y,K(z / u,w)) = a(x,y,K(u * z,w))
    ]]></literal>
    <justification jstring="[hyper(19541,a,19587,a)].">
      <j1 rule="hyper" parents="19541 19587"/>
    </justification>
  </clause>

  <clause id="19589">
    <literal><![CDATA[
      a(x,y,K(z * (u / w),z)) = a(z,y,K(x,u / (z * w)))
    ]]></literal>
    <justification jstring="[hyper(14926,a,19587,a),flip(a)].">
      <j1 rule="hyper" parents="14926 19587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19590">
    <literal><![CDATA[
      a(x,y,K(z * (u \ w),z)) = a(z,y,K(x,w / (z * u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,19528,a(flip),b,19589,a)].">
      <j1 rule="hyper" parents="65 19528 19589"/>
    </justification>
  </clause>

  <clause id="19591">
    <literal><![CDATA[
      a(x,y,K(z * (u \ w),z)) = a(z,y,K(x,(z * u) * w))
    ]]></literal>
    <justification jstring="[hyper(299,a,19533,a(flip),b,19590,a),flip(a)].">
      <j1 rule="hyper" parents="299 19533 19590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19592">
    <literal><![CDATA[
      a(x,y,K(z * (u \ w),z)) = a(z,y,K(x,u * (z \ w)))
    ]]></literal>
    <justification jstring="[hyper(299,a,15020,a(flip),b,19591,a),flip(a)].">
      <j1 rule="hyper" parents="299 15020 19591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19593">
    <literal><![CDATA[
      a(x,y,K(z,u * (x \ w))) = a(z,y,K(x,u \ w))
    ]]></literal>
    <justification jstring="[hyper(15009,a,19592,a),flip(a)].">
      <j1 rule="hyper" parents="15009 19592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19594">
    <literal><![CDATA[
      a(x,y,K(z,u * (x \ w))) = a(z,y,K(x,u * w))
    ]]></literal>
    <justification jstring="[hyper(299,a,15012,a(flip),b,19593,a),flip(a)].">
      <j1 rule="hyper" parents="299 15012 19593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19595">
    <literal><![CDATA[
      a(x,y,K(z,(x * u) * w)) = a(z,y,K(x,u * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,15020,a,b,19594,a)].">
      <j1 rule="hyper" parents="65 15020 19594"/>
    </justification>
  </clause>

  <clause id="19597">
    <literal><![CDATA[
      K(x,L(T(y,z * y) \ u,y,y * z)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(18006,a,19584,a)].">
      <j1 rule="hyper" parents="18006 19584"/>
    </justification>
  </clause>

  <clause id="19598">
    <literal><![CDATA[
      K(x,L(T(y,y * z) \ u,y,y * z)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[para(4366(a,1),19597(a,1,2,1,1))].">
      <j1 rule="para" parents="4366 19597"/>
    </justification>
  </clause>

  <clause id="19599">
    <literal><![CDATA[
      K(x,(y * (y * z)) \ ((y * z) * u)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,11663,a(flip),b,19598,a)].">
      <j1 rule="hyper" parents="65 11663 19598"/>
    </justification>
  </clause>

  <clause id="19600">
    <literal><![CDATA[
      K(x,(y * ((y \ 1) * z)) \ ((y * z) * u)) = K(x,z \ (((y \ 1) \ z) * u))
    ]]></literal>
    <justification jstring="[para(3066(a,1),19599(a,1,2))].">
      <j1 rule="para" parents="3066 19599"/>
    </justification>
  </clause>

  <clause id="19601">
    <literal><![CDATA[
      K(x,L(y,z \ u,T(u,z))) = K(x,L(y,z,(1 / (u / z)) \ z))
    ]]></literal>
    <justification jstring="[para(13452(a,1),19575(a,1,2))].">
      <j1 rule="para" parents="13452 19575"/>
    </justification>
  </clause>

  <clause id="19602">
    <literal><![CDATA[
      K(x,L(y,z \ u,u)) = K(x,L(y,z,(1 / (u / z)) \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,18603,a(flip),b,19601,a)].">
      <j1 rule="hyper" parents="65 18603 19601"/>
    </justification>
  </clause>

  <clause id="19604">
    <literal><![CDATA[
      K(x,L(y,z \ u,u)) = K(x,L(y,z,(u / z) \ z))
    ]]></literal>
    <justification jstring="[para(2483(a,1),19602(a,2,2))].">
      <j1 rule="para" parents="2483 19602"/>
    </justification>
  </clause>

  <clause id="19605">
    <literal><![CDATA[
      K(x,L(y,z \ u,u)) = K(x,L(y,z,(z \ u) \ z))
    ]]></literal>
    <justification jstring="[para(18756(a,1),19604(a,2,2))].">
      <j1 rule="para" parents="18756 19604"/>
    </justification>
  </clause>

  <clause id="19606">
    <literal><![CDATA[
      K(x,L(y,z \ u,u)) = K(x,L(y,z,(z \ u) * z))
    ]]></literal>
    <justification jstring="[hyper(299,a,19572,a(flip),b,19605,a),flip(a)].">
      <j1 rule="hyper" parents="299 19572 19605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19607">
    <literal><![CDATA[
      K(x,L(y,z \ u,u)) = K(x,L(y,z,T(u,z)))
    ]]></literal>
    <justification jstring="[para(13452(a,1),19606(a,2,2))].">
      <j1 rule="para" parents="13452 19606"/>
    </justification>
  </clause>

  <clause id="19608">
    <literal><![CDATA[
      K(x,L(y,z \ u,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,18603,a(flip),b,19607,a),flip(a)].">
      <j1 rule="hyper" parents="299 18603 19607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19610">
    <literal><![CDATA[
      ((x * y) * K(z,T(u,y))) / (x * (K(z,u) * y)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(7507(a,1),19554(a,1,2,2))].">
      <j1 rule="para" parents="7507 19554"/>
    </justification>
  </clause>

  <clause id="19611">
    <literal><![CDATA[
      ((x * y) * K(z,T(u,y))) / L(K(z,u) * y,x,a(x,y,K(z,u))) = (((x * y) * K(z,T(u,y))) / (x * (K(z,u) * y))) * x
    ]]></literal>
    <justification jstring="[para(19610(a,1),349(a,1,2,3))].">
      <j1 rule="para" parents="19610 349"/>
    </justification>
  </clause>

  <clause id="19612">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,x,x) = 1 * (a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(68(a,1),19567(a,1,1)),flip(a)].">
      <j1 rule="para" parents="68 19567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19613">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,x,x) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(299,a,7,a(flip),b,19612,a),flip(a)].">
      <j1 rule="hyper" parents="299 7 19612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19615">
    <literal><![CDATA[
      a(x,x,L(y,x,x)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(19432,a,19613,a)].">
      <j1 rule="hyper" parents="19432 19613"/>
    </justification>
  </clause>

  <clause id="19616">
    <literal><![CDATA[
      (x * y) * a(x,x,L(x \ y,x,x)) = (x * x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(19615(a,2),772(a,1,2))].">
      <j1 rule="para" parents="19615 772"/>
    </justification>
  </clause>

  <clause id="19617">
    <literal><![CDATA[
      (x * y) * a(x,x,(1 / x) * y) = (x * x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(511(a,1),19616(a,1,2,3))].">
      <j1 rule="para" parents="511 19616"/>
    </justification>
  </clause>

  <clause id="19618">
    <literal><![CDATA[
      (x * y) * a(x,x,x * y) = (x * x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(2360(a,1),19617(a,1,2))].">
      <j1 rule="para" parents="2360 19617"/>
    </justification>
  </clause>

  <clause id="19619">
    <literal><![CDATA[
      (x * y) * a(x,x,x * y) = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(299,a,724,a(flip),b,19618,a),flip(a)].">
      <j1 rule="hyper" parents="299 724 19618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19620">
    <literal><![CDATA[
      K(x,L(y,z,z) \ ((z * y) * u)) = K(x,y \ (((z \ 1) \ y) * u))
    ]]></literal>
    <justification jstring="[para(1673(a,1),19600(a,1,2,1))].">
      <j1 rule="para" parents="1673 19600"/>
    </justification>
  </clause>

  <clause id="19621">
    <literal><![CDATA[
      K(x,L(y \ z,1 / y,1 / y) \ (((y * y) \ z) * u)) = K(x,(y \ z) \ ((((1 / y) \ 1) \ (y \ z)) * u))
    ]]></literal>
    <justification jstring="[para(441(a,1),19620(a,1,2,2,1))].">
      <j1 rule="para" parents="441 19620"/>
    </justification>
  </clause>

  <clause id="19623">
    <literal><![CDATA[
      K(x,T(y,z)) * a(x,u,K(y * (w \ v5),y)) = K(x,L(T(y,z),u,(w * y) \ v5))
    ]]></literal>
    <justification jstring="[para(19587(a,1),19530(a,1,2))].">
      <j1 rule="para" parents="19587 19530"/>
    </justification>
  </clause>

  <clause id="19624">
    <literal><![CDATA[
      a(x,y,K(T(z * K(u * w,z),v5) * w,u)) = a(x,y,K(u,w * T(z,v5)))
    ]]></literal>
    <justification jstring="[hyper(299,a,19595,a(flip),b,19548,a),flip(a)].">
      <j1 rule="hyper" parents="299 19595 19548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19625">
    <literal><![CDATA[
      a(x,y,K(K(z * u,w) * (T(w,v5) * u),z)) = a(x,y,K(z,u * T(w,v5)))
    ]]></literal>
    <justification jstring="[para(19213(a,1),19624(a,1,3))].">
      <j1 rule="para" parents="19213 19624"/>
    </justification>
  </clause>

  <clause id="19626">
    <literal><![CDATA[
      K(x,T(y,z)) * a(x,u,K(y,w \ v5)) = K(x,L(T(y,z),u,(w * y) \ v5))
    ]]></literal>
    <justification jstring="[para(15008(a,1),19623(a,1,2))].">
      <j1 rule="para" parents="15008 19623"/>
    </justification>
  </clause>

  <clause id="19627">
    <literal><![CDATA[
      K(x,T(y,z)) * a(x,u,K(y,w * v5)) = K(x,L(T(y,z),u,(w * y) \ v5))
    ]]></literal>
    <justification jstring="[para(15012(a,1),19626(a,1,2))].">
      <j1 rule="para" parents="15012 19626"/>
    </justification>
  </clause>

  <clause id="19628">
    <literal><![CDATA[
      T(K(x,y) * a(x,z,K(y,u * w)),v5) = K(x,L(T(y,v5),z,(u * y) \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,19329,a,b,19627,a)].">
      <j1 rule="hyper" parents="65 19329 19627"/>
    </justification>
  </clause>

  <clause id="19629">
    <literal><![CDATA[
      K(x,L(T(y,z),u,(w * y) \ v5)) = T(K(x,L(y,u,w * v5)),z)
    ]]></literal>
    <justification jstring="[para(14964(a,1),19628(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14964 19628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19630">
    <literal><![CDATA[
      K(x,L(T(y,z),u,(w * y) \ v5)) = K(x,L(T(y,z),u,w * v5))
    ]]></literal>
    <justification jstring="[hyper(299,a,7506,a,b,19629,a),flip(a)].">
      <j1 rule="hyper" parents="299 7506 19629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19631">
    <literal><![CDATA[
      K(x,L(T(y,z),u,(w * y) * v5)) = K(x,L(T(y,z),u,w * v5))
    ]]></literal>
    <justification jstring="[hyper(19573,a,19630,a)].">
      <j1 rule="hyper" parents="19573 19630"/>
    </justification>
  </clause>

  <clause id="19632">
    <literal><![CDATA[
      K(x,y / (z * ((z * u) \ y))) = K(x,L(T(u,z),y,z * y))
    ]]></literal>
    <justification jstring="[hyper(65,a,19582,a(flip),b,19631,a)].">
      <j1 rule="hyper" parents="65 19582 19631"/>
    </justification>
  </clause>

  <clause id="19633">
    <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(15066,a,19532,a),flip(a)].">
      <j1 rule="hyper" parents="15066 19532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19635">
    <literal><![CDATA[
      (K(x,y) * z) * R(u,z,K(x,T(y,z))) = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[para(7507(a,1),19633(a,1,1))].">
      <j1 rule="para" parents="7507 19633"/>
    </justification>
  </clause>

  <clause id="19636">
    <literal><![CDATA[
      (K(x,y) * z) * R(u,z,K(x,y)) = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[para(11281(a,1),19635(a,1,2))].">
      <j1 rule="para" parents="11281 19635"/>
    </justification>
  </clause>

  <clause id="19637">
    <literal><![CDATA[
      R(x,y,K(z,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(490,a,19636,a),flip(a)].">
      <j1 rule="hyper" parents="490 19636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19638">
    <literal><![CDATA[
      ((x * y) * K(z,T(u,y))) / (K(z,u) * y) = L(x,y,K(z,T(u,y)))
    ]]></literal>
    <justification jstring="[hyper(65,a,7604,a,b,19637,a)].">
      <j1 rule="hyper" parents="65 7604 19637"/>
    </justification>
  </clause>

  <clause id="19639">
    <literal><![CDATA[
      L((x * K(y,z)) / u,u,K(z,y)) = x / (u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,7211,a(flip),b,19637,a),flip(a)].">
      <j1 rule="hyper" parents="65 7211 19637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19640">
    <literal><![CDATA[
      L((x * y) / z,z,K(y,x)) = (y * x) / (z * ((x * y) \ (y * x)))
    ]]></literal>
    <justification jstring="[hyper(65,a,797,a(flip),b,19637,a),flip(a)].">
      <j1 rule="hyper" parents="65 797 19637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19641">
    <literal><![CDATA[
      L(x,y,K(z,u)) * (y * K(z,u)) = (x * y) * K(z,u)
    ]]></literal>
    <justification jstring="[para(19637(a,1),103(a,1,1))].">
      <j1 rule="para" parents="19637 103"/>
    </justification>
  </clause>

  <clause id="19642">
    <literal><![CDATA[
      L(x,x \ y,K(z,u)) \ (y * K(z,u)) = (x \ y) * K(z,u)
    ]]></literal>
    <justification jstring="[para(19637(a,1),580(a,1,1))].">
      <j1 rule="para" parents="19637 580"/>
    </justification>
  </clause>

  <clause id="19643">
    <literal><![CDATA[
      L(x,x \ y,K(z,z \ y)) \ (z * (y / z)) = (x \ y) * K(z,z \ y)
    ]]></literal>
    <justification jstring="[para(19637(a,1),5507(a,1,1))].">
      <j1 rule="para" parents="19637 5507"/>
    </justification>
  </clause>

  <clause id="19644">
    <literal><![CDATA[
      L(x,y,K(z,u)) * (K(z,u) * y) = (x * y) * T(K(z,u),y)
    ]]></literal>
    <justification jstring="[para(19637(a,1),11279(a,1,1))].">
      <j1 rule="para" parents="19637 11279"/>
    </justification>
  </clause>

  <clause id="19645">
    <literal><![CDATA[
      K(x,(y * K(z,u)) / w) = K(x,y / (w * K(u,z)))
    ]]></literal>
    <justification jstring="[para(19639(a,1),18587(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19639 18587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19646">
    <literal><![CDATA[
      K(x,(K(y,z) * u) / w) = K(x,u / (w * K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(16841,a,19645,a)].">
      <j1 rule="hyper" parents="16841 19645"/>
    </justification>
  </clause>

  <clause id="19647">
    <literal><![CDATA[
      K(x,y / (z * K(u,w))) = K(x,y * (z \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,19114,a(flip),b,19645,a),flip(a)].">
      <j1 rule="hyper" parents="65 19114 19645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19648">
    <literal><![CDATA[
      K(x,(K(y,z) * u) / w) = K(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(299,a,16902,a(flip),b,19646,a),flip(a)].">
      <j1 rule="hyper" parents="299 16902 19646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19649">
    <literal><![CDATA[
      K(x,y * (z \ K(u,w))) = K(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,16902,a(flip),b,19647,a)].">
      <j1 rule="hyper" parents="65 16902 19647"/>
    </justification>
  </clause>

  <clause id="19650">
    <literal><![CDATA[
      K(x,y * ((z * u) \ K(u,w))) = K(x,y / (z * T(u,w)))
    ]]></literal>
    <justification jstring="[para(6832(a,1),19647(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6832 19647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19651">
    <literal><![CDATA[
      K(x,y / (z * (u * K(w,u)))) = K(x,y * ((z * u) \ K(w,u)))
    ]]></literal>
    <justification jstring="[para(6816(a,1),19647(a,1,2,2))].">
      <j1 rule="para" parents="6816 19647"/>
    </justification>
  </clause>

  <clause id="19652">
    <literal><![CDATA[
      K(x,y / L(z * K(u,w),u,u)) = K(x,y * (L(z,u,u) \ K(u,w)))
    ]]></literal>
    <justification jstring="[para(9599(a,2),19647(a,1,2,2))].">
      <j1 rule="para" parents="9599 19647"/>
    </justification>
  </clause>

  <clause id="19653">
    <literal><![CDATA[
      x * K(x,y * (z \ K(u,w))) = T(x,(K(u,w) * y) / z)
    ]]></literal>
    <justification jstring="[para(19648(a,1),5083(a,2,2)),flip(a)].">
      <j1 rule="para" parents="19648 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19654">
    <literal><![CDATA[
      K(x,((y / (y / z)) * u) / w) = K(x,(z * u) * (w \ K(z \ y,z)))
    ]]></literal>
    <justification jstring="[para(5012(a,1),19648(a,1,2,1))].">
      <j1 rule="para" parents="5012 19648"/>
    </justification>
  </clause>

  <clause id="19655">
    <literal><![CDATA[
      K(x,(y \ K(z,u)) * w) * K(x,K(y \ K(z,u),w)) = K(x,w * (y \ K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(16673,a,19649,a)].">
      <j1 rule="hyper" parents="16673 19649"/>
    </justification>
  </clause>

  <clause id="19656">
    <literal><![CDATA[
      K(x,y * (z \ K(u * w,v5))) = K(x,y * (z \ K(v5,u \ w)))
    ]]></literal>
    <justification jstring="[hyper(299,a,18001,a(flip),b,19649,a)].">
      <j1 rule="hyper" parents="299 18001 19649"/>
    </justification>
  </clause>

  <clause id="19657">
    <literal><![CDATA[
      K(x,y * ((z \ u) \ K(w,z))) = K(x,y / (T(z,w) \ u))
    ]]></literal>
    <justification jstring="[hyper(299,a,14647,a(flip),b,19649,a),flip(a)].">
      <j1 rule="hyper" parents="299 14647 19649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19658">
    <literal><![CDATA[
      K(x,T(y,z * K(u,w)) * (z \ K(w,u))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(z \ K(u,w)) * y) = v5
    ]]></literal>
    <justification jstring="[para(19649(a,1),17954(a,1))].">
      <j1 rule="para" parents="19649 17954"/>
    </justification>
  </clause>

  <clause id="19659">
    <literal><![CDATA[
      L(x,y,K(z * z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(37,a,11969,a(flip),b,19641,a),flip(a)].">
      <j1 rule="hyper" parents="37 11969 19641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19661">
    <literal><![CDATA[
      (x * y) * K(z \ 1,y * z) = x * (y * K(z \ 1,y * z))
    ]]></literal>
    <justification jstring="[para(11626(a,1),19641(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11626 19641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19662">
    <literal><![CDATA[
      (x * (y / z)) * K(y,z) = x * ((y / z) * K(y,z))
    ]]></literal>
    <justification jstring="[para(13450(a,1),19641(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13450 19641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19663">
    <literal><![CDATA[
      (x * y) * K(z,y * x) = x * (y * K(z,y * x))
    ]]></literal>
    <justification jstring="[para(15550(a,1),19641(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15550 19641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19664">
    <literal><![CDATA[
      L(x,y,T(z * z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(5095,a,19659,a)].">
      <j1 rule="hyper" parents="5095 19659"/>
    </justification>
  </clause>

  <clause id="19665">
    <literal><![CDATA[
      (T(x * x,y) * z) \ (u * T(x * x,y)) = z \ T(u,x * x)
    ]]></literal>
    <justification jstring="[hyper(65,a,16216,a(flip),b,19664,a)].">
      <j1 rule="hyper" parents="65 16216 19664"/>
    </justification>
  </clause>

  <clause id="19666">
    <literal><![CDATA[
      (T(x * x,y) * z) \ u = z \ (T(x * x,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,281,a(flip),b,19664,a)].">
      <j1 rule="hyper" parents="65 281 19664"/>
    </justification>
  </clause>

  <clause id="19667">
    <literal><![CDATA[
      (x * (y / z)) * K(y,z) = x * (y / T(z,y))
    ]]></literal>
    <justification jstring="[para(7189(a,1),19662(a,2,2))].">
      <j1 rule="para" parents="7189 19662"/>
    </justification>
  </clause>

  <clause id="19668">
    <literal><![CDATA[
      K(x,y * (z * (u / T(w,u)))) = K(x,y * (z * (w \ u)))
    ]]></literal>
    <justification jstring="[para(19667(a,1),19196(a,1,2,2))].">
      <j1 rule="para" parents="19667 19196"/>
    </justification>
  </clause>

  <clause id="19669">
    <literal><![CDATA[
      (x * K(y,x * z)) * z = x * (z * K(y,z * x))
    ]]></literal>
    <justification jstring="[hyper(65,a,15553,a,b,19663,a)].">
      <j1 rule="hyper" parents="65 15553 19663"/>
    </justification>
  </clause>

  <clause id="19670">
    <literal><![CDATA[
      x / (y * (z * K(u,z * y))) = (x / (y * z)) * K(z * y,u)
    ]]></literal>
    <justification jstring="[para(19663(a,1),13303(a,1,2))].">
      <j1 rule="para" parents="19663 13303"/>
    </justification>
  </clause>

  <clause id="19671">
    <literal><![CDATA[
      (x * (y * K(z,y * x))) / u = (x * y) / (u * K(y * x,z))
    ]]></literal>
    <justification jstring="[para(19663(a,1),15042(a,1,1))].">
      <j1 rule="para" parents="19663 15042"/>
    </justification>
  </clause>

  <clause id="19672">
    <literal><![CDATA[
      (x * (y * K(z,y * x))) / (y * (x * K(z,x * y))) = K(x * K(z,x * y),y)
    ]]></literal>
    <justification jstring="[hyper(120,a,19669,a(flip),b,5020,a)].">
      <j1 rule="hyper" parents="120 19669 5020"/>
    </justification>
  </clause>

  <clause id="19673">
    <literal><![CDATA[
      K(x,y / (z * (u * K(w,u)))) = K(x,y / (z * T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,16905,a,b,19650,a)].">
      <j1 rule="hyper" parents="65 16905 19650"/>
    </justification>
  </clause>

  <clause id="19674">
    <literal><![CDATA[
      T(x,(K(y,z) * u) / w) = T(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(5087,a,19653,a),flip(a)].">
      <j1 rule="hyper" parents="5087 19653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19676">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * (y \ K(u,w))) = T(x,y \ (K(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,17179,a(flip),b,19674,a),flip(a)].">
      <j1 rule="hyper" parents="65 17179 19674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19677">
    <literal><![CDATA[
      T(x,y * ((z \ u) \ K(w,z))) = x * K(x,y / (T(z,w) \ u))
    ]]></literal>
    <justification jstring="[para(19657(a,1),5083(a,2,2))].">
      <j1 rule="para" parents="19657 5083"/>
    </justification>
  </clause>

  <clause id="19678">
    <literal><![CDATA[
      K(x,T(y,z * (u / T(w,u))) * (z * (w \ u))) = K(x,(z * (u / T(w,u))) * y)
    ]]></literal>
    <justification jstring="[hyper(13261,a,19668,a),flip(a)].">
      <j1 rule="hyper" parents="13261 19668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19679">
    <literal><![CDATA[
      K(x,y * (z * (u / T(w,u)))) = x \ T(x,y * (z * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(299,a,5036,a(flip),b,19668,a),flip(a)].">
      <j1 rule="hyper" parents="299 5036 19668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19680">
    <literal><![CDATA[
      K(x,y / (z * ((u \ w) \ w))) = K(x,y / (z * (u * K(u \ w,u))))
    ]]></literal>
    <justification jstring="[para(108(a,1),19673(a,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="108 19673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19681">
    <literal><![CDATA[
      K(x,y / (z * T(T(u,w),w))) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[para(5100(a,1),19673(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5100 19673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19682">
    <literal><![CDATA[
      K(x,y / (T(z,u) * (u \ 1))) = K(x,y / ((u \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,17966,a(flip),b,19681,a)].">
      <j1 rule="hyper" parents="65 17966 19681"/>
    </justification>
  </clause>

  <clause id="19683">
    <literal><![CDATA[
      K(x,y / (T(z,u) * u)) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[para(107(a,1),19681(a,1,2,2))].">
      <j1 rule="para" parents="107 19681"/>
    </justification>
  </clause>

  <clause id="19684">
    <literal><![CDATA[
      K(x,(y * z) \ T(u,y * z)) = K(x,u / (T(z,y) * y))
    ]]></literal>
    <justification jstring="[hyper(299,a,13925,a,b,19683,a)].">
      <j1 rule="hyper" parents="299 13925 19683"/>
    </justification>
  </clause>

  <clause id="19685">
    <literal><![CDATA[
      K(x,(T(y,z) \ u) / (T(y,z) \ z)) = K(x,(T(y,z) * u) / (z * y))
    ]]></literal>
    <justification jstring="[hyper(65,a,17288,a,b,19683,a)].">
      <j1 rule="hyper" parents="65 17288 19683"/>
    </justification>
  </clause>

  <clause id="19686">
    <literal><![CDATA[
      K(x,T(y * z,u \ y) / ((u \ 1) * y)) = K(x,L((1 / T(u,y)) \ z,u,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,15194,a(flip),b,19682,a),flip(a)].">
      <j1 rule="hyper" parents="65 15194 19682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19687">
    <literal><![CDATA[
      K(x,y / (T(z,u) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (u * z)) = w
    ]]></literal>
    <justification jstring="[para(19684(a,1),13929(a,1))].">
      <j1 rule="para" parents="19684 13929"/>
    </justification>
  </clause>

  <clause id="19688">
    <literal><![CDATA[
      x \ (y * K(z,y)) = (x \ y) * K(z,y)
    ]]></literal>
    <justification jstring="[para(15548(a,1),19642(a,1,1))].">
      <j1 rule="para" parents="15548 19642"/>
    </justification>
  </clause>

  <clause id="19689">
    <literal><![CDATA[
      x \ (y / (y / z)) = (x \ z) * K(z \ y,z)
    ]]></literal>
    <justification jstring="[para(5002(a,2),19688(a,1,2))].">
      <j1 rule="para" parents="5002 19688"/>
    </justification>
  </clause>

  <clause id="19690">
    <literal><![CDATA[
      x \ ((y * z) / y) = (x \ z) * K(y,z)
    ]]></literal>
    <justification jstring="[para(5054(a,2),19688(a,1,2))].">
      <j1 rule="para" parents="5054 19688"/>
    </justification>
  </clause>

  <clause id="19692">
    <literal><![CDATA[
      L(x,y,z \ ((u * w) / u)) = L(x,y,(z \ w) * K(w,u))
    ]]></literal>
    <justification jstring="[para(19690(a,2),5221(a,1,3))].">
      <j1 rule="para" parents="19690 5221"/>
    </justification>
  </clause>

  <clause id="19694">
    <literal><![CDATA[
      K(x,y \ ((z * u) / z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ T(u,z)) = w
    ]]></literal>
    <justification jstring="[para(19690(a,2),17973(a,1,2))].">
      <j1 rule="para" parents="19690 17973"/>
    </justification>
  </clause>

  <clause id="19696">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,T(y,u) / z) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(16711(a,1),19694(a,1))].">
      <j1 rule="para" parents="16711 19694"/>
    </justification>
  </clause>

  <clause id="19697">
    <literal><![CDATA[
      L(x,y,z \ ((u * w) / u)) = L(x,y,z \ T(w,u))
    ]]></literal>
    <justification jstring="[para(14220(a,1),19692(a,2,3))].">
      <j1 rule="para" parents="14220 19692"/>
    </justification>
  </clause>

  <clause id="19698">
    <literal><![CDATA[
      K(x,L(((y \ ((z * u) / z)) \ ((z * u) / z)) \ w,y,y \ T(u,z))) = K(x,T(u,z) \ ((y \ ((z * u) / z)) * w))
    ]]></literal>
    <justification jstring="[para(19697(a,1),15832(a,1,2))].">
      <j1 rule="para" parents="19697 15832"/>
    </justification>
  </clause>

  <clause id="19699">
    <literal><![CDATA[
      L(x,y,K(z,u)) * (K(z,u) * y) = (x * y) * K(z,T(u,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,7503,a,b,19644,a),flip(a)].">
      <j1 rule="hyper" parents="299 7503 19644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19700">
    <literal><![CDATA[
      K(x,y / T((z / (z / u)) * w,u)) = K(x,y * ((w * u) \ K(u \ z,u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,18014,a,b,19651,a)].">
      <j1 rule="hyper" parents="65 18014 19651"/>
    </justification>
  </clause>

  <clause id="19701">
    <literal><![CDATA[
      K(x,y * (z \ K(u,w \ v5))) = K(x,y * (z \ K(u,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(65,a,19649,a,b,19656,a),flip(a)].">
      <j1 rule="hyper" parents="65 19649 19656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19702">
    <literal><![CDATA[
      (x * y) * K(z \ 1,z * y) = x * (y * K(z \ 1,y * z))
    ]]></literal>
    <justification jstring="[para(6163(a,1),19661(a,1,2))].">
      <j1 rule="para" parents="6163 19661"/>
    </justification>
  </clause>

  <clause id="19704">
    <literal><![CDATA[
      ((T(x * x,y) * z) \ u) * T(x * x,y) = z \ T(u,x * x)
    ]]></literal>
    <justification jstring="[hyper(65,a,1102,a(flip),b,19665,a)].">
      <j1 rule="hyper" parents="65 1102 19665"/>
    </justification>
  </clause>

  <clause id="19705">
    <literal><![CDATA[
      T(x,y * ((z \ u) \ K(w,z))) = T(x,y / (T(z,w) \ u))
    ]]></literal>
    <justification jstring="[hyper(299,a,5083,a,b,19677,a),flip(a)].">
      <j1 rule="hyper" parents="299 5083 19677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19707">
    <literal><![CDATA[
      T(x,y * (z * (u / T(w,u)))) = T(x,y * (z * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(5086,a,19679,a)].">
      <j1 rule="hyper" parents="5086 19679"/>
    </justification>
  </clause>

  <clause id="19708">
    <literal><![CDATA[
      T(x,y * (T(z,u / T(w,u)) * (w \ u))) = T(x,y * ((u / T(w,u)) * z))
    ]]></literal>
    <justification jstring="[hyper(15900,a,19707,a),flip(a)].">
      <j1 rule="hyper" parents="15900 19707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19709">
    <literal><![CDATA[
      T(x,y * (z * (T(u,w) / w))) = T(x,y * (z * (w \ u)))
    ]]></literal>
    <justification jstring="[para(4382(a,2),19707(a,1,2,2,2))].">
      <j1 rule="para" parents="4382 19707"/>
    </justification>
  </clause>

  <clause id="19710">
    <literal><![CDATA[
      T(x,y * (z * ((u \ w) / u))) = T(x,y * (z * (u \ (w / u))))
    ]]></literal>
    <justification jstring="[para(4384(a,1),19707(a,1,2,2,2))].">
      <j1 rule="para" parents="4384 19707"/>
    </justification>
  </clause>

  <clause id="19711">
    <literal><![CDATA[
      T(x,T(y,z * (u \ w)) * (z * (u \ w))) = T(x,(z * (T(w,u) / u)) * y)
    ]]></literal>
    <justification jstring="[hyper(13826,a,19709,a),flip(a)].">
      <j1 rule="hyper" parents="13826 19709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19712">
    <literal><![CDATA[
      T(x,(y * (T(y,z) / z)) * (y \ (y * (T(y,z) / z)))) = T(x,(T(y,z \ y) / T(z,y)) * (y * (z \ y)))
    ]]></literal>
    <justification jstring="[hyper(65,a,13984,a(flip),b,19709,a)].">
      <j1 rule="hyper" parents="65 13984 19709"/>
    </justification>
  </clause>

  <clause id="19713">
    <literal><![CDATA[
      K(x,y * (z \ K(u,T(w / v5,w)))) = K(x,y * (z \ K(u,v5 * w)))
    ]]></literal>
    <justification jstring="[para(7474(a,2),19701(a,1,2,2,2))].">
      <j1 rule="para" parents="7474 19701"/>
    </justification>
  </clause>

  <clause id="19714">
    <literal><![CDATA[
      x * (y * K(x \ 1,y * x)) = L(y,x,x \ 1) / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(65,a,5235,a(flip),b,19702,a),flip(a)].">
      <j1 rule="hyper" parents="65 5235 19702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19715">
    <literal><![CDATA[
      x * (y * K(x \ 1,y * x)) = L(y,x,x) / (1 / x)
    ]]></literal>
    <justification jstring="[para(2470(a,1),19714(a,2,1))].">
      <j1 rule="para" parents="2470 19714"/>
    </justification>
  </clause>

  <clause id="19716">
    <literal><![CDATA[
      L(x / (y \ 1),y,y) = L(x,y,y) / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(6171,a,19715,a)].">
      <j1 rule="hyper" parents="6171 19715"/>
    </justification>
  </clause>

  <clause id="19717">
    <literal><![CDATA[
      L(x / T(y,y \ 1),y \ 1,y \ 1) = L(x,y \ 1,y \ 1) / (1 / (y \ 1))
    ]]></literal>
    <justification jstring="[para(108(a,2),19716(a,1,1,2))].">
      <j1 rule="para" parents="108 19716"/>
    </justification>
  </clause>

  <clause id="19718">
    <literal><![CDATA[
      L(x / (T(y,y \ 1) \ 1),T(y,y \ 1),T(y,y \ 1)) = L(x,T(y,y \ 1),T(y,y \ 1)) / (y \ 1)
    ]]></literal>
    <justification jstring="[para(262(a,1),19716(a,2,2))].">
      <j1 rule="para" parents="262 19716"/>
    </justification>
  </clause>

  <clause id="19719">
    <literal><![CDATA[
      (x \ (T(y * y,z) \ u)) * T(y * y,z) = x \ T(u,y * y)
    ]]></literal>
    <justification jstring="[para(19666(a,1),19704(a,1,1))].">
      <j1 rule="para" parents="19666 19704"/>
    </justification>
  </clause>

  <clause id="19720">
    <literal><![CDATA[
      (T(x * x,y) \ z) * T(x * x,y) = T(z,x * x)
    ]]></literal>
    <justification jstring="[hyper(1134,a,19719,a(flip))].">
      <j1 rule="hyper" parents="1134 19719"/>
    </justification>
  </clause>

  <clause id="19721">
    <literal><![CDATA[
      K(x * x,y) * (((T(x * x,y) * z) \ u) * (x * x)) = K(z,x * x) * T(z \ u,x * x)
    ]]></literal>
    <justification jstring="[para(19720(a,1),18340(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19720 18340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19722">
    <literal><![CDATA[
      (x * y) / (z * ((y * x) \ (x * y))) = (y * x) / z
    ]]></literal>
    <justification jstring="[hyper(65,a,15552,a(flip),b,19640,a),flip(a)].">
      <j1 rule="hyper" parents="65 15552 19640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19723">
    <literal><![CDATA[
      (x * y) / (z * K(x,y)) = (y * x) / z
    ]]></literal>
    <justification jstring="[para(16(a,2),19722(a,1,2,2))].">
      <j1 rule="para" parents="16 19722"/>
    </justification>
  </clause>

  <clause id="19724">
    <literal><![CDATA[
      (x * (y * z)) / (L(x,z,y) * (y * z)) = ((y * z) * x) / (y * (z * x))
    ]]></literal>
    <justification jstring="[para(14641(a,1),19723(a,1,2))].">
      <j1 rule="para" parents="14641 19723"/>
    </justification>
  </clause>

  <clause id="19725">
    <literal><![CDATA[
      K(x,y \ ((z \ u) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(16986(a,2),19696(a,1))].">
      <j1 rule="para" parents="16986 19696"/>
    </justification>
  </clause>

  <clause id="19726">
    <literal><![CDATA[
      K(x,((y / (y / z)) * u) / w) = K(x,(z * u) * (w \ K(z * y,z)))
    ]]></literal>
    <justification jstring="[hyper(299,a,18001,a(flip),b,19654,a),flip(a)].">
      <j1 rule="hyper" parents="299 18001 19654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19727">
    <literal><![CDATA[
      K(x,y / (z * T(u,T(w / v5,w)))) = K(x,y * ((z * u) \ K(u,v5 * w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,19650,a(flip),b,19713,a)].">
      <j1 rule="hyper" parents="65 19650 19713"/>
    </justification>
  </clause>

  <clause id="19728">
    <literal><![CDATA[
      L(x,x \ y,K(z,y)) \ (z * (y / z)) = (x \ y) * K(z,z \ y)
    ]]></literal>
    <justification jstring="[para(13440(a,1),19643(a,1,1))].">
      <j1 rule="para" parents="13440 19643"/>
    </justification>
  </clause>

  <clause id="19729">
    <literal><![CDATA[
      (x \ y) * K(z,z \ y) = x \ (z * (y / z))
    ]]></literal>
    <justification jstring="[para(15548(a,1),19728(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15548 19728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19730">
    <literal><![CDATA[
      a(x,y,z) = (z * (x * y)) / (L(z,y,x) * (x * y))
    ]]></literal>
    <justification jstring="[hyper(299,a,19553,a,b,19724,a)].">
      <j1 rule="hyper" parents="299 19553 19724"/>
    </justification>
  </clause>

  <clause id="19731">
    <literal><![CDATA[
      K((L(x,y,z) * (z * y)) / (x * (z * y)),u) = K(a(z,y,x) \ 1,u)
    ]]></literal>
    <justification jstring="[para(19730(a,2),5852(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="19730 5852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19732">
    <literal><![CDATA[
      K(a(x,y,z) \ 1,u) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,15617,a(flip),b,19731,a),flip(a)].">
      <j1 rule="hyper" parents="65 15617 19731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19734">
    <literal><![CDATA[
      K(x,((a(y,z,u) \ 1) \ w) * T(a(y,z,u) \ 1,v5)) = K(x,T(a(y,z,K(v5,u)) * w,a(y,z,u) \ 1))
    ]]></literal>
    <justification jstring="[para(19732(a,1),16585(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="19732 16585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19735">
    <literal><![CDATA[
      K(x,y / T((z / (z / u)) * w,u)) = K(x,y * ((w * u) \ K(u * z,u)))
    ]]></literal>
    <justification jstring="[hyper(299,a,18001,a(flip),b,19700,a),flip(a)].">
      <j1 rule="hyper" parents="299 18001 19700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19736">
    <literal><![CDATA[
      T(x,y * (T(z,u \ w) * (u \ w))) = T(x,y * ((w / T(u,w)) * z))
    ]]></literal>
    <justification jstring="[para(13704(a,1),19708(a,1,2,2,1))].">
      <j1 rule="para" parents="13704 19708"/>
    </justification>
  </clause>

  <clause id="19737">
    <literal><![CDATA[
      T(x,y * ((z / T(u,z)) * w)) = T(x,y * ((u \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(15900,a,19736,a),flip(a)].">
      <j1 rule="hyper" parents="15900 19736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19738">
    <literal><![CDATA[
      T(x,y * (((z \ u) / z) * w)) = T(x,y * ((z \ (u / z)) * w))
    ]]></literal>
    <justification jstring="[para(4384(a,1),19737(a,1,2,2,1))].">
      <j1 rule="para" parents="4384 19737"/>
    </justification>
  </clause>

  <clause id="19739">
    <literal><![CDATA[
      T(x,(y * (T(z,u) / u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,(y * (u \ z)) * w) = v5
    ]]></literal>
    <justification jstring="[para(19711(a,1),13267(a,1))].">
      <j1 rule="para" parents="19711 13267"/>
    </justification>
  </clause>

  <clause id="19740">
    <literal><![CDATA[
      T(x,(y * (1 / z)) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(y * (z \ 1)) * u) = w
    ]]></literal>
    <justification jstring="[para(195(a,1),19739(a,1,2,1,2,1))].">
      <j1 rule="para" parents="195 19739"/>
    </justification>
  </clause>

  <clause id="19742">
    <literal><![CDATA[
      K(x,y / (z * T(u,T(w / v5,w)))) = K(x,y / (z * T(u,v5 * w)))
    ]]></literal>
    <justification jstring="[hyper(299,a,19650,a(flip),b,19727,a),flip(a)].">
      <j1 rule="hyper" parents="299 19650 19727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19743">
    <literal><![CDATA[
      K(x,y / (z * T(u,w \ v5))) = K(x,y / (z * T(u,w * v5)))
    ]]></literal>
    <justification jstring="[para(7456(a,1),19742(a,1,2,2,2))].">
      <j1 rule="para" parents="7456 19742"/>
    </justification>
  </clause>

  <clause id="19744">
    <literal><![CDATA[
      K(x,((y * T(z,u \ w)) \ (v5 * ((y * T(z,u \ w)) \ 1))) * (y * T(z,u * w))) = K(x,T(v5,y * T(z,u * w)) / (y * T(z,u * w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,18396,a,b,19743,a)].">
      <j1 rule="hyper" parents="65 18396 19743"/>
    </justification>
  </clause>

  <clause id="19745">
    <literal><![CDATA[
      K(x,L((1 / T(y,z)) \ u,y,z)) = K(x,((y \ 1) * z) \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(14385,a,19686,a),flip(a)].">
      <j1 rule="hyper" parents="14385 19686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19746">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,y,z)) = K(x,((y \ 1) * z) \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(18034,a,19745,a)].">
      <j1 rule="hyper" parents="18034 19745"/>
    </justification>
  </clause>

  <clause id="19747">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ (z * ((y * y) \ u))) = K(x,L((y \ K(y,z)) * u,y,z))
    ]]></literal>
    <justification jstring="[para(6395(a,1),19746(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6395 19746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19749">
    <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(19655(a,1),16701(a,1))].">
      <j1 rule="para" parents="19655 16701"/>
    </justification>
  </clause>

  <clause id="19750">
    <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(14313(a,2),19749(a,1))].">
      <j1 rule="para" parents="14313 19749"/>
    </justification>
  </clause>

  <clause id="19751">
    <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(19647(a,2),19749(a,1))].">
      <j1 rule="para" parents="19647 19749"/>
    </justification>
  </clause>

  <clause id="19752">
    <literal><![CDATA[
      K(x,y * (z \ K(u,w \ v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z \ K(w * v5,u))) = v6
    ]]></literal>
    <justification jstring="[para(19701(a,2),19749(a,1))].">
      <j1 rule="para" parents="19701 19749"/>
    </justification>
  </clause>

  <clause id="19753">
    <literal><![CDATA[
      K(x,y / L(K(z,u) * w,z,z)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (L(w,z,z) \ K(z,u))) = v5
    ]]></literal>
    <justification jstring="[para(9598(a,2),19750(a,1,2,2))].">
      <j1 rule="para" parents="9598 19750"/>
    </justification>
  </clause>

  <clause id="19754">
    <literal><![CDATA[
      K(x,(y * K(z,u)) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(w,y * K(z,u)) * (y \ K(u,z))) = v5
    ]]></literal>
    <justification jstring="[para(13712(a,1),19751(a,1))].">
      <j1 rule="para" parents="13712 19751"/>
    </justification>
  </clause>

  <clause id="19756">
    <literal><![CDATA[
      ((x * (y * K(z,y * x))) / (y * x)) * K(x * y,z) = K(x * K(z,x * y),y)
    ]]></literal>
    <justification jstring="[hyper(65,a,19670,a(flip),b,19672,a)].">
      <j1 rule="hyper" parents="65 19670 19672"/>
    </justification>
  </clause>

  <clause id="19757">
    <literal><![CDATA[
      K(x,T(y,z * (u \ w)) * (z * (u \ w))) = K(x,(z * (w / T(u,w))) * y)
    ]]></literal>
    <justification jstring="[para(13825(a,1),19678(a,1,2,1))].">
      <j1 rule="para" parents="13825 19678"/>
    </justification>
  </clause>

  <clause id="19758">
    <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(19757(a,1),13261(a,1))].">
      <j1 rule="para" parents="19757 13261"/>
    </justification>
  </clause>

  <clause id="19759">
    <literal><![CDATA[
      K(x,(y * (z / T(u,z))) / w) = K(x,(y * (u \ z)) * (w \ 1))
    ]]></literal>
    <justification jstring="[hyper(19758,a,14205,a),flip(a)].">
      <j1 rule="hyper" parents="19758 14205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19760">
    <literal><![CDATA[
      K(x,(y * (z / T(u,z))) / w) = K(x,(y * (u \ z)) / w)
    ]]></literal>
    <justification jstring="[hyper(299,a,14205,a(flip),b,19759,a),flip(a)].">
      <j1 rule="hyper" parents="299 14205 19759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19761">
    <literal><![CDATA[
      K(x,K(y,z * (u \ w))) * K(y,(z * (u \ w)) / x) = K(y,x \ (z * (w / T(u,w))))
    ]]></literal>
    <justification jstring="[para(19760(a,1),13886(a,1,2))].">
      <j1 rule="para" parents="19760 13886"/>
    </justification>
  </clause>

  <clause id="19763">
    <literal><![CDATA[
      L(x / T(y,y \ 1),y \ 1,y \ 1) = L(x,y \ 1,y) / (1 / (y \ 1))
    ]]></literal>
    <justification jstring="[para(2470(a,1),19717(a,2,1))].">
      <j1 rule="para" parents="2470 19717"/>
    </justification>
  </clause>

  <clause id="19765">
    <literal><![CDATA[
      L(x / T(y,y \ 1),y \ 1,y \ 1) = L(x,y,y) / (1 / (y \ 1))
    ]]></literal>
    <justification jstring="[para(2526(a,1),19763(a,2,1))].">
      <j1 rule="para" parents="2526 19763"/>
    </justification>
  </clause>

  <clause id="19766">
    <literal><![CDATA[
      L(x / T(y,y \ 1),y \ 1,y \ 1) = L(x,y,y) / y
    ]]></literal>
    <justification jstring="[para(76(a,1),19765(a,2,2))].">
      <j1 rule="para" parents="76 19765"/>
    </justification>
  </clause>

  <clause id="19768">
    <literal><![CDATA[
      L(x / T(y,y \ 1),y \ 1,y) = L(x,y,y) / y
    ]]></literal>
    <justification jstring="[hyper(2503,a,19766,a)].">
      <j1 rule="hyper" parents="2503 19766"/>
    </justification>
  </clause>

  <clause id="19769">
    <literal><![CDATA[
      L(x / T(y,y \ 1),y,y) = L(x,y,y) / y
    ]]></literal>
    <justification jstring="[hyper(65,a,2526,a(flip),b,19768,a)].">
      <j1 rule="hyper" parents="65 2526 19768"/>
    </justification>
  </clause>

  <clause id="19770">
    <literal><![CDATA[
      L(x / T(L(y,y * z,y),L(y,y * z,y) \ 1),L(y,y * z,y),L(y,y * z,y)) = L(x,L(y,y * z,y),L(y,y * z,y)) / (z / (T(z,y) / y))
    ]]></literal>
    <justification jstring="[hyper(299,a,17015,a(flip),b,19769,a),flip(a)].">
      <j1 rule="hyper" parents="299 17015 19769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19771">
    <literal><![CDATA[
      ((x * y) / ((y * x) * K(y * x,z))) * K(x * y,z) = K(x * K(z,x * y),y)
    ]]></literal>
    <justification jstring="[para(19671(a,1),19756(a,1,1))].">
      <j1 rule="para" parents="19671 19756"/>
    </justification>
  </clause>

  <clause id="19772">
    <literal><![CDATA[
      ((x * y) / T(y * x,z)) * K(x * y,z) = K(x * K(z,x * y),y)
    ]]></literal>
    <justification jstring="[para(5083(a,2),19771(a,1,1,2))].">
      <j1 rule="para" parents="5083 19771"/>
    </justification>
  </clause>

  <clause id="19773">
    <literal><![CDATA[
      (K(x,y) * K(z,y * x)) * K(x * y,z) = K(x * K(z,x * y),y)
    ]]></literal>
    <justification jstring="[para(7188(a,1),19772(a,1,1))].">
      <j1 rule="para" parents="7188 19772"/>
    </justification>
  </clause>

  <clause id="19774">
    <literal><![CDATA[
      K(x,y) * (K(x * y,z) * K(z,y * x)) = K(x * K(z,x * y),y)
    ]]></literal>
    <justification jstring="[hyper(9422,a,19773,a)].">
      <j1 rule="hyper" parents="9422 19773"/>
    </justification>
  </clause>

  <clause id="19775">
    <literal><![CDATA[
      K(x * K(y,x * z),z) = K(x,z) * K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(16671(a,1),19774(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16671 19774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19776">
    <literal><![CDATA[
      K(x * K(y,x * z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(19775(a,2),8234(a,1))].">
      <j1 rule="para" parents="19775 8234"/>
    </justification>
  </clause>

  <clause id="19777">
    <literal><![CDATA[
      K(x,(y * (z \ u)) / T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y / ((z \ u) \ z),z,z * u)) = w
    ]]></literal>
    <justification jstring="[para(17331(a,1),19579(a,1))].">
      <j1 rule="para" parents="17331 19579"/>
    </justification>
  </clause>

  <clause id="19778">
    <literal><![CDATA[
      K(x,y \ (z * (u / T(w,u)))) = K(x,y \ (z * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(8509,a,19761,a),flip(a)].">
      <j1 rule="hyper" parents="8509 19761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19779">
    <literal><![CDATA[
      K(x,y \ (z * (T(u,w) / w))) = K(x,y \ (z * (w \ u)))
    ]]></literal>
    <justification jstring="[para(4382(a,2),19778(a,1,2,2,2))].">
      <j1 rule="para" parents="4382 19778"/>
    </justification>
  </clause>

  <clause id="19780">
    <literal><![CDATA[
      K(x,y \ (T(z,u \ w) * (u \ w))) = K(x,y \ ((w / T(u,w)) * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,15993,a(flip),b,19779,a),flip(a)].">
      <j1 rule="hyper" parents="65 15993 19779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19781">
    <literal><![CDATA[
      K(x,y \ ((z / T(u,z)) * w)) = K(x,y \ ((u \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(15911,a,19780,a),flip(a)].">
      <j1 rule="hyper" parents="15911 19780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19784">
    <literal><![CDATA[
      T(K(x,y * y) * (x \ z),y * y) = K(y * y,u) * (((T(y * y,u) * x) \ z) * (y * y))
    ]]></literal>
    <justification jstring="[hyper(299,a,17363,a,b,19721,a)].">
      <j1 rule="hyper" parents="299 17363 19721"/>
    </justification>
  </clause>

  <clause id="19786">
    <literal><![CDATA[
      T(K(x,y * y) * (x \ z),y * y) = K(y * y,u) * ((x \ (T(y * y,u) \ z)) * (y * y))
    ]]></literal>
    <justification jstring="[para(19666(a,1),19784(a,2,2,1))].">
      <j1 rule="para" parents="19666 19784"/>
    </justification>
  </clause>

  <clause id="19787">
    <literal><![CDATA[
      T(K(x,y * y) * (x \ z),y * y) = (x \ (T(y * y,u) \ z)) * T(y * y,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,16208,a(flip),b,19786,a),flip(a)].">
      <j1 rule="hyper" parents="299 16208 19786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19788">
    <literal><![CDATA[
      T(K(x,y * y) * (x \ z),y * y) = x \ T(z,y * y)
    ]]></literal>
    <justification jstring="[hyper(299,a,19719,a(flip),b,19787,a),flip(a)].">
      <j1 rule="hyper" parents="299 19719 19787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19789">
    <literal><![CDATA[
      (((x * x) * y) \ z) * ((x * x) * u) = (y \ T(z,x * x)) * u
    ]]></literal>
    <justification jstring="[para(19788(a,1),11772(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19788 11772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19790">
    <literal><![CDATA[
      (x \ ((y * y) \ z)) * ((y * y) * u) = (x \ T(z,y * y)) * u
    ]]></literal>
    <justification jstring="[para(420(a,1),19789(a,1,1))].">
      <j1 rule="para" parents="420 19789"/>
    </justification>
  </clause>

  <clause id="19791">
    <literal><![CDATA[
      T(x * K(y,T(L(z,u,w),v5)),K(K(z,L(y,u,w)),v5)) = K(v5,K(z,y)) * (x / K(z,L(y,u,w)))
    ]]></literal>
    <justification jstring="[para(7537(a,1),19518(a,1,1,2))].">
      <j1 rule="para" parents="7537 19518"/>
    </justification>
  </clause>

  <clause id="19792">
    <literal><![CDATA[
      T(x * K(y,L(T(z,u),w,v5)),K(K(z,L(y,w,v5)),u)) = K(u,K(z,y)) * (x / K(z,L(y,w,v5)))
    ]]></literal>
    <justification jstring="[para(25(a,2),19791(a,1,1,2,2))].">
      <j1 rule="para" parents="25 19791"/>
    </justification>
  </clause>

  <clause id="19793">
    <literal><![CDATA[
      T(x * K(y,L(T(z,u),w,v5)),K(z,K(L(y,w,v5),u))) = K(u,K(z,y)) * (x / K(z,L(y,w,v5)))
    ]]></literal>
    <justification jstring="[para(7954(a,1),19792(a,1,2))].">
      <j1 rule="para" parents="7954 19792"/>
    </justification>
  </clause>

  <clause id="19794">
    <literal><![CDATA[
      K(x,K(y,z)) * (u / K(y,L(z,w,v5))) = u * K(z,L(T(y,x),w,v5))
    ]]></literal>
    <justification jstring="[hyper(16363,a,19793,a)].">
      <j1 rule="hyper" parents="16363 19793"/>
    </justification>
  </clause>

  <clause id="19796">
    <literal><![CDATA[
      K(x,K(y,z)) * (u / K(x,L(y,w,v5))) = u * K(y,L(T(x,z),w,v5))
    ]]></literal>
    <justification jstring="[para(7989(a,2),19794(a,1,1))].">
      <j1 rule="para" parents="7989 19794"/>
    </justification>
  </clause>

  <clause id="19797">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(L(y,w,v5),x)) = u * K(y,L(T(x,z),w,v5))
    ]]></literal>
    <justification jstring="[para(7196(a,1),19796(a,1,2))].">
      <j1 rule="para" parents="7196 19796"/>
    </justification>
  </clause>

  <clause id="19798">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(y,L(x,w,v5))) = u * K(y,L(T(x,z),w,v5))
    ]]></literal>
    <justification jstring="[para(11929(a,1),19797(a,1,2,2))].">
      <j1 rule="para" parents="11929 19797"/>
    </justification>
  </clause>

  <clause id="19799">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(x,K(y,w)) = K(x,L(T(y,w),z,u))
    ]]></literal>
    <justification jstring="[hyper(18768,a,19798,a)].">
      <j1 rule="hyper" parents="18768 19798"/>
    </justification>
  </clause>

  <clause id="19800">
    <literal><![CDATA[
      K(K(x,y),z) * (u * K(x,L(T(z,y),w,v5))) = u * K(x,L(z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(5437,a,19798,a)].">
      <j1 rule="hyper" parents="5437 19798"/>
    </justification>
  </clause>

  <clause id="19801">
    <literal><![CDATA[
      K(x,L(T(y,z),u,w)) * K(x,K(y,v5)) = T(K(x,L(T(y,v5),u,w)),z)
    ]]></literal>
    <justification jstring="[para(19799(a,1),16882(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19799 16882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19802">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(x,L(T(z,y),w,v5))) = u * K(x,L(z,w,v5))
    ]]></literal>
    <justification jstring="[para(7954(a,1),19800(a,1,1))].">
      <j1 rule="para" parents="7954 19800"/>
    </justification>
  </clause>

  <clause id="19803">
    <literal><![CDATA[
      K(x,L(T(y,z),u,w)) * K(x,K(y,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(T(y,v5),z),u,w)) = v6
    ]]></literal>
    <justification jstring="[para(19801(a,2),8349(a,1))].">
      <j1 rule="para" parents="19801 8349"/>
    </justification>
  </clause>

  <clause id="19804">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,L(T(z,y),u,w)) = K(x,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(10068,a,19802,a)].">
      <j1 rule="hyper" parents="10068 19802"/>
    </justification>
  </clause>

  <clause id="19806">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,L(T(z,u),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(y,L(T(T(z,x),u),w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(16485(a,2),19803(a,1))].">
      <j1 rule="para" parents="16485 19803"/>
    </justification>
  </clause>

  <clause id="19807">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),K(z,u) * y,K(y,w)) = (K(z,u) * T(y,w)) \ (K(z,u) * (T(y,w) * x))
    ]]></literal>
    <justification jstring="[para(16402(a,1),18871(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16402 18871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19808">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),K(z,u) * y,K(y,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,T(y,w),K(z,u)) = v5
    ]]></literal>
    <justification jstring="[para(19807(a,2),493(a,1))].">
      <j1 rule="para" parents="19807 493"/>
    </justification>
  </clause>

  <clause id="19809">
    <literal><![CDATA[
      K(x,K(y,z * u)) * K(x,((K(w,v5) * z) * u) * y) = K(x,y * ((K(w,v5) * z) * u))
    ]]></literal>
    <justification jstring="[para(17132(a,1),18998(a,1,1))].">
      <j1 rule="para" parents="17132 18998"/>
    </justification>
  </clause>

  <clause id="19811">
    <literal><![CDATA[
      K(x,K(y,z * u)) * K(x,K(w,v5) * ((z * u) * y)) = K(x,y * ((K(w,v5) * z) * u))
    ]]></literal>
    <justification jstring="[para(19201(a,1),19809(a,1,2))].">
      <j1 rule="para" parents="19201 19809"/>
    </justification>
  </clause>

  <clause id="19812">
    <literal><![CDATA[
      K(x,y * ((K(z,u) * w) * v5)) = K(x,y * (K(z,u) * (w * v5)))
    ]]></literal>
    <justification jstring="[hyper(65,a,18999,a(flip),b,19811,a),flip(a)].">
      <j1 rule="hyper" parents="65 18999 19811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19813">
    <literal><![CDATA[
      K(x,y * ((z * K(u,w)) * v5)) = K(x,y * (K(u,w) * (z * v5)))
    ]]></literal>
    <justification jstring="[hyper(18882,a,19812,a)].">
      <j1 rule="hyper" parents="18882 19812"/>
    </justification>
  </clause>

  <clause id="19814">
    <literal><![CDATA[
      K(x,(y \ 1) * (K(z,u) * (w * v5))) = K(x,y \ ((w * K(z,u)) * v5))
    ]]></literal>
    <justification jstring="[hyper(14281,a,19813,a),flip(a)].">
      <j1 rule="hyper" parents="14281 19813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19815">
    <literal><![CDATA[
      K(x,y * (((z \ 1) * K(u,w)) * K(v5,v6))) = K(x,y * (K(u,w) * (z \ K(v5,v6))))
    ]]></literal>
    <justification jstring="[para(14185(a,1),19813(a,2,2,2,2))].">
      <j1 rule="para" parents="14185 19813"/>
    </justification>
  </clause>

  <clause id="19816">
    <literal><![CDATA[
      K(x,y * (K(z,u) * ((w \ z) * v5))) = K(x,y * ((w \ T(z,u)) * v5))
    ]]></literal>
    <justification jstring="[para(14220(a,1),19813(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="14220 19813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19817">
    <literal><![CDATA[
      K(x,y \ ((z * K(u,w)) * v5)) = K(x,y \ (K(u,w) * (z * v5)))
    ]]></literal>
    <justification jstring="[hyper(14281,a,19814,a),flip(a)].">
      <j1 rule="hyper" parents="14281 19814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19818">
    <literal><![CDATA[
      K(x,y * (K(z,u) * ((w \ u) * v5))) = K(x,y * ((w \ T(u,z)) * v5))
    ]]></literal>
    <justification jstring="[hyper(19070,a,19816,a)].">
      <j1 rule="hyper" parents="19070 19816"/>
    </justification>
  </clause>

  <clause id="19819">
    <literal><![CDATA[
      K(x,y * ((z \ T(u,w * w)) * v5)) = K(x,y * ((z \ u) * v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,17919,a(flip),b,19818,a),flip(a)].">
      <j1 rule="hyper" parents="65 17919 19818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19820">
    <literal><![CDATA[
      K(x,y * ((z \ K(u,w)) * K(v5,v6))) = K(x,y * (K(u,w) * (z \ K(v5,v6))))
    ]]></literal>
    <justification jstring="[para(14185(a,1),19815(a,1,2,2,1))].">
      <j1 rule="para" parents="14185 19815"/>
    </justification>
  </clause>

  <clause id="19821">
    <literal><![CDATA[
      K(x,y * (K(z * u,z) * ((z \ w) \ K(z,u)))) = K(x,y / (R(z,u,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,15242,a(flip),b,19820,a),flip(a)].">
      <j1 rule="hyper" parents="65 15242 19820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19822">
    <literal><![CDATA[
      K(x,K(y,z) * (u * ((z \ w) \ K(z,y)))) = K(x,u / (R(z,y,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(19063,a,19821,a)].">
      <j1 rule="hyper" parents="19063 19821"/>
    </justification>
  </clause>

  <clause id="19823">
    <literal><![CDATA[
      K(x,y / (R(z,u,z) \ w)) = K(x,y / (z \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,19118,a(flip),b,19822,a),flip(a)].">
      <j1 rule="hyper" parents="65 19118 19822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19825">
    <literal><![CDATA[
      K(x,y / (((z \ u) \ u) \ w)) = K(x,y / (T(z,u) \ w))
    ]]></literal>
    <justification jstring="[para(10283(a,1),19823(a,1,2,2,1))].">
      <j1 rule="para" parents="10283 19823"/>
    </justification>
  </clause>

  <clause id="19826">
    <literal><![CDATA[
      K(x,y / T(z \ u,u)) = K(x,y / (T(z,u) \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,17331,a(flip),b,19825,a)].">
      <j1 rule="hyper" parents="65 17331 19825"/>
    </justification>
  </clause>

  <clause id="19827">
    <literal><![CDATA[
      K(x,(y \ K(z,y \ 1)) * u) * K(x,K(u,y * K(z,y \ 1))) = K(x,u * T(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(3661(a,1),19054(a,1,1,2,1))].">
      <j1 rule="para" parents="3661 19054"/>
    </justification>
  </clause>

  <clause id="19828">
    <literal><![CDATA[
      T(x,y * (z * T((u * w) * (1 / u),u * 1))) = T(x,y * (z * ((u \ 1) * (T(u,u \ 1) * w))))
    ]]></literal>
    <justification jstring="[hyper(65,a,17536,a(flip),b,19180,a)].">
      <j1 rule="hyper" parents="65 17536 19180"/>
    </justification>
  </clause>

  <clause id="19829">
    <literal><![CDATA[
      K(x,T(K(y * (z / y),y) * u,y * (z / y))) = K(x,((y * (z / y)) \ u) * z)
    ]]></literal>
    <justification jstring="[para(5138(a,1),19183(a,2,2,2))].">
      <j1 rule="para" parents="5138 19183"/>
    </justification>
  </clause>

  <clause id="19830">
    <literal><![CDATA[
      K(x,T(K(y,z) * u,z * (y / z))) = K(x,((z * (y / z)) \ u) * y)
    ]]></literal>
    <justification jstring="[para(5982(a,1),19829(a,1,2,1,1))].">
      <j1 rule="para" parents="5982 19829"/>
    </justification>
  </clause>

  <clause id="19831">
    <literal><![CDATA[
      K(x,T(K(y,z) * u,T(y,z))) = K(x,((z * (y / z)) \ u) * y)
    ]]></literal>
    <justification jstring="[para(13271(a,1),19830(a,1,2))].">
      <j1 rule="para" parents="13271 19830"/>
    </justification>
  </clause>

  <clause id="19832">
    <literal><![CDATA[
      K(x,((y * (z / y)) \ u) * z) = K(x,T(u * K(z,y),z))
    ]]></literal>
    <justification jstring="[para(7296(a,1),19831(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7296 19831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19833">
    <literal><![CDATA[
      L(x,y,((T(z,u * u) * w) / z) * ((u * u) * v5)) = L(x,y,T((u * u) * w,(u * u) \ z) * v5)
    ]]></literal>
    <justification jstring="[para(34(a,1),19380(a,1,3))].">
      <j1 rule="para" parents="34 19380"/>
    </justification>
  </clause>

  <clause id="19834">
    <literal><![CDATA[
      T(x,y * (z * ((u \ 1) * (T(u,u \ 1) * w)))) = T(x,y * (z * T((u * w) * (1 / u),u)))
    ]]></literal>
    <justification jstring="[para(8(a,1),19828(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="8 19828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19835">
    <literal><![CDATA[
      T(x,y * (z * ((u \ 1) * (T(u,u \ 1) * w)))) = T(x,y * (z * ((w * u) * (1 / u))))
    ]]></literal>
    <justification jstring="[para(2378(a,1),19834(a,2,2,2,2))].">
      <j1 rule="para" parents="2378 19834"/>
    </justification>
  </clause>

  <clause id="19836">
    <literal><![CDATA[
      T(x,y * (z * ((u \ 1) * (T(u,u \ 1) * w)))) = T(x,y * (z * ((w * u) * (u \ 1))))
    ]]></literal>
    <justification jstring="[hyper(299,a,3902,a(flip),b,19835,a),flip(a)].">
      <j1 rule="hyper" parents="299 3902 19835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19837">
    <literal><![CDATA[
      T(x,y * (z * ((u \ 1) * (T(u,u \ 1) * w)))) = T(x,y * (z * R(w,u,u)))
    ]]></literal>
    <justification jstring="[para(1246(a,1),19836(a,2,2,2,2))].">
      <j1 rule="para" parents="1246 19836"/>
    </justification>
  </clause>

  <clause id="19838">
    <literal><![CDATA[
      T(x,y * (z * ((1 / u) * (u * w)))) = T(x,y * (z * R(w,u,u)))
    ]]></literal>
    <justification jstring="[para(5929(a,1),19837(a,1,2,2,2))].">
      <j1 rule="para" parents="5929 19837"/>
    </justification>
  </clause>

  <clause id="19839">
    <literal><![CDATA[
      T(x,y * (z * R(u,w,w))) = T(x,y * (z * L(u,w,w)))
    ]]></literal>
    <justification jstring="[para(475(a,1),19838(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="475 19838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19840">
    <literal><![CDATA[
      T(x,y * (z * L(1 / z,u,u))) = T(x,y * a(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,15597,a(flip),b,19839,a),flip(a)].">
      <j1 rule="hyper" parents="65 15597 19839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19841">
    <literal><![CDATA[
      T(x,y * ((z * u) * R(L(w,u,z),v5,v5))) = T(x,y * (z * (u * L(w,v5,v5))))
    ]]></literal>
    <justification jstring="[para(489(a,1),19839(a,2,2,2))].">
      <j1 rule="para" parents="489 19839"/>
    </justification>
  </clause>

  <clause id="19842">
    <literal><![CDATA[
      T(x,y * (z \ L(z,u,u))) = T(x,y * a(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,13963,a(flip),b,19840,a)].">
      <j1 rule="hyper" parents="65 13963 19840"/>
    </justification>
  </clause>

  <clause id="19843">
    <literal><![CDATA[
      T(x,y * (z \ L(z,u,u))) = T(x,a(z,u,u) * y)
    ]]></literal>
    <justification jstring="[hyper(299,a,18631,a,b,19842,a),flip(a)].">
      <j1 rule="hyper" parents="299 18631 19842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19844">
    <literal><![CDATA[
      T(x,y * (a(z,z,u) \ 1)) = T(x,y * a(u,z,z))
    ]]></literal>
    <justification jstring="[para(13006(a,2),19842(a,1,2,2))].">
      <j1 rule="para" parents="13006 19842"/>
    </justification>
  </clause>

  <clause id="19846">
    <literal><![CDATA[
      T(x,y * a(z \ (z \ u),z,z)) = T(x,y * ((z \ ((1 / z) \ u)) \ u))
    ]]></literal>
    <justification jstring="[para(13028(a,1),19844(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13028 19844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19847">
    <literal><![CDATA[
      T(x,y * (z * (u * R(w,v5,v5)))) = T(x,y * (z * (u * L(w,v5,v5))))
    ]]></literal>
    <justification jstring="[para(488(a,1),19841(a,1,2,2))].">
      <j1 rule="para" parents="488 19841"/>
    </justification>
  </clause>

  <clause id="19848">
    <literal><![CDATA[
      L(x,y,T((z * z) * u,(z * z) \ w) * v5) = L(x,y,((T(w,z * z) * u) / w) * v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,2895,a(flip),b,19833,a),flip(a)].">
      <j1 rule="hyper" parents="65 2895 19833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19850">
    <literal><![CDATA[
      L(x,y,T(K(z,u * u) * w,z) * v5) = L(x,y,T((u * u) * w,(u * u) \ z) * v5)
    ]]></literal>
    <justification jstring="[hyper(299,a,18797,a(flip),b,19848,a)].">
      <j1 rule="hyper" parents="299 18797 19848"/>
    </justification>
  </clause>

  <clause id="19851">
    <literal><![CDATA[
      L(x,y,T((z * z) * u,(z * z) \ w) * v5) = L(x,y,T(u,w) * (v5 * K(w,z * z)))
    ]]></literal>
    <justification jstring="[para(17291(a,1),19850(a,1,3)),flip(a)].">
      <j1 rule="para" parents="17291 19850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19852">
    <literal><![CDATA[
      L(x,y,T((z * z) * u,(z * z) \ w) * v5) = L(x,y,T(u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(299,a,18933,a(flip),b,19851,a),flip(a)].">
      <j1 rule="hyper" parents="299 18933 19851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19854">
    <literal><![CDATA[
      L(x,y,T((z * z) * u,w) * v5) = L(x,y,T(u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,19412,a(flip),b,19852,a)].">
      <j1 rule="hyper" parents="65 19412 19852"/>
    </justification>
  </clause>

  <clause id="19856">
    <literal><![CDATA[
      L(x,y,T(((z \ 1) * z) * (1 / z),u) * w) = L(x,y,T(z,u) * w)
    ]]></literal>
    <justification jstring="[para(1088(a,1),19854(a,1,3,1,1))].">
      <j1 rule="para" parents="1088 19854"/>
    </justification>
  </clause>

  <clause id="19857">
    <literal><![CDATA[
      L(x,y,T(z \ 1,u) * w) = L(x,y,T(z,u) * w)
    ]]></literal>
    <justification jstring="[para(2222(a,1),19856(a,1,3,1,1))].">
      <j1 rule="para" parents="2222 19856"/>
    </justification>
  </clause>

  <clause id="19858">
    <literal><![CDATA[
      L(x,y,T(z,u) * (z \ w)) = L(x,y,K(z \ 1,u) * w)
    ]]></literal>
    <justification jstring="[hyper(65,a,6310,a(flip),b,19857,a),flip(a)].">
      <j1 rule="hyper" parents="65 6310 19857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19860">
    <literal><![CDATA[
      L(x,y,K(z \ 1,u) * w) = L(x,y,K(z,u) * w)
    ]]></literal>
    <justification jstring="[para(5056(a,1),19858(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5056 19858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19861">
    <literal><![CDATA[
      (x * (K(y,K(z,u)) * w)) \ ((x * K(y,K(z,u))) * (w * v5)) = L(v5,L(w,K(y,K(z,u)),x),K(y,K(z,u)) * x)
    ]]></literal>
    <justification jstring="[para(18792(a,1),18678(a,1,2,2,1))].">
      <j1 rule="para" parents="18792 18678"/>
    </justification>
  </clause>

  <clause id="19863">
    <literal><![CDATA[
      K(x,T(y * (z * u),K(w,u)) \ (K(w,L(u,z,y)) \ v5)) = K(x,(y * (z * (u * K(w,u)))) \ v5)
    ]]></literal>
    <justification jstring="[para(18667(a,1),18600(a,1,2,1))].">
      <j1 rule="para" parents="18667 18600"/>
    </justification>
  </clause>

  <clause id="19864">
    <literal><![CDATA[
      K(x,T(y * (z * u),K(u,w)) \ (K(w,L(u,z,y)) \ v5)) = K(x,(y * (z * (u * K(w,u)))) \ v5)
    ]]></literal>
    <justification jstring="[para(8050(a,1),19863(a,1,2,1))].">
      <j1 rule="para" parents="8050 19863"/>
    </justification>
  </clause>

  <clause id="19866">
    <literal><![CDATA[
      K(x,T(y * (z * u),K(u,w)) \ (K(L(u,z,y),w) * v5)) = K(x,(y * (z * (u * K(w,u)))) \ v5)
    ]]></literal>
    <justification jstring="[para(5426(a,1),19864(a,1,2,2))].">
      <j1 rule="para" parents="5426 19864"/>
    </justification>
  </clause>

  <clause id="19867">
    <literal><![CDATA[
      K((x / (y \ 1)) * (1 / T(x / (1 / y),z)),u) = K(u,K(x * y,y * (((x / (1 / y)) * z) \ x)))
    ]]></literal>
    <justification jstring="[hyper(19437,a,18802,a),flip(a)].">
      <j1 rule="hyper" parents="19437 18802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19868">
    <literal><![CDATA[
      K((x / (y \ 1)) * (1 / T(x / (1 / y),z)),u) = K(u,K((x / (1 / y)) * z,y * x))
    ]]></literal>
    <justification jstring="[hyper(299,a,18953,a(flip),b,19867,a),flip(a)].">
      <j1 rule="hyper" parents="299 18953 19867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19869">
    <literal><![CDATA[
      K((x / (y \ 1)) * (1 / T(x / (1 / y),z)),u) = K(u,K((x / (y \ 1)) * z,y * x))
    ]]></literal>
    <justification jstring="[para(5624(a,1),19868(a,2,2))].">
      <j1 rule="para" parents="5624 19868"/>
    </justification>
  </clause>

  <clause id="19870">
    <literal><![CDATA[
      K((x / (y \ 1)) * (1 / T(x / (1 / y),z)),u) = K(u,K(y * x,(x / (y \ 1)) * z))
    ]]></literal>
    <justification jstring="[hyper(299,a,8004,a,b,19869,a),flip(a)].">
      <j1 rule="hyper" parents="299 8004 19869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19871">
    <literal><![CDATA[
      K((x / (y \ 1)) * (1 / T(x / (1 / y),z)),u) = K(u,K(y * x,x * ((y \ 1) * z)))
    ]]></literal>
    <justification jstring="[hyper(299,a,18789,a(flip),b,19870,a),flip(a)].">
      <j1 rule="hyper" parents="299 18789 19870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19872">
    <literal><![CDATA[
      K((x / (y \ 1)) * (1 / T(x / (1 / y),z)),u) = K(u,K(y * x,y * (z \ x)))
    ]]></literal>
    <justification jstring="[hyper(299,a,19436,a(flip),b,19871,a),flip(a)].">
      <j1 rule="hyper" parents="299 19436 19871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19873">
    <literal><![CDATA[
      K((x / (y \ 1)) / T(x / (1 / y),z),u) = K(u,K(y * x,y * (z \ x)))
    ]]></literal>
    <justification jstring="[hyper(14473,a,19872,a)].">
      <j1 rule="hyper" parents="14473 19872"/>
    </justification>
  </clause>

  <clause id="19874">
    <literal><![CDATA[
      T(T(x,y / T(z * u,z)),K(w,(z * (z * u)) * (z * y))) = T(x,T(y / (T(z,z * u) * u),w))
    ]]></literal>
    <justification jstring="[para(16601(a,1),18936(a,1,1))].">
      <j1 rule="para" parents="16601 18936"/>
    </justification>
  </clause>

  <clause id="19875">
    <literal><![CDATA[
      T(T(x,y / (z * u)),K(w,(u * (u * z)) * (u * y))) = T(x,T(y / (T(u,u * z) * z),w))
    ]]></literal>
    <justification jstring="[para(13954(a,1),19874(a,1,1))].">
      <j1 rule="para" parents="13954 19874"/>
    </justification>
  </clause>

  <clause id="19876">
    <literal><![CDATA[
      T(T(x,y / (z * u)),K(w,(u * z) * (u \ (u * y)))) = T(x,T(y / (T(u,u * z) * z),w))
    ]]></literal>
    <justification jstring="[hyper(18878,a,19875,a)].">
      <j1 rule="hyper" parents="18878 19875"/>
    </justification>
  </clause>

  <clause id="19877">
    <literal><![CDATA[
      T(T(x,y / (z * u)),K(w,(u * z) * y)) = T(x,T(y / (T(u,u * z) * z),w))
    ]]></literal>
    <justification jstring="[para(9(a,1),19876(a,1,2,2,2))].">
      <j1 rule="para" parents="9 19876"/>
    </justification>
  </clause>

  <clause id="19878">
    <literal><![CDATA[
      T(T(x,y / (z * u)),K(w,z * (u \ y))) = T(x,T(y / (T(u,u * z) * z),w))
    ]]></literal>
    <justification jstring="[hyper(18878,a,19877,a)].">
      <j1 rule="hyper" parents="18878 19877"/>
    </justification>
  </clause>

  <clause id="19879">
    <literal><![CDATA[
      T(T(x,y / (z * u)),K(w,z * (u \ y))) = T(x,T(y / ((u * (u * z)) / u),w))
    ]]></literal>
    <justification jstring="[para(4270(a,2),19878(a,2,2,1,2))].">
      <j1 rule="para" parents="4270 19878"/>
    </justification>
  </clause>

  <clause id="19880">
    <literal><![CDATA[
      T(T(x,y / (z * u)),K(w,z * (u \ y))) = T(x,T(y / T(u * z,u),w))
    ]]></literal>
    <justification jstring="[hyper(299,a,17320,a(flip),b,19879,a),flip(a)].">
      <j1 rule="hyper" parents="299 17320 19879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19881">
    <literal><![CDATA[
      T(T(x,y / (z * u)),K(w,z * (u \ y))) = T(x,T(y / (z * u),w))
    ]]></literal>
    <justification jstring="[hyper(299,a,17587,a(flip),b,19880,a),flip(a)].">
      <j1 rule="hyper" parents="299 17587 19880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19882">
    <literal><![CDATA[
      T(x,T(y / (T(z,z * u) * u),w)) = T(x,T(y / (u * z),w))
    ]]></literal>
    <justification jstring="[hyper(65,a,19878,a(flip),b,19881,a)].">
      <j1 rule="hyper" parents="65 19878 19881"/>
    </justification>
  </clause>

  <clause id="19883">
    <literal><![CDATA[
      T(x,(y * (T(y,z) / z)) * (y \ (y * (T(y,z) / z)))) = T(x,(z \ T(y,z \ y)) * (y * (z \ y)))
    ]]></literal>
    <justification jstring="[hyper(299,a,18976,a(flip),b,19712,a),flip(a)].">
      <j1 rule="hyper" parents="299 18976 19712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19884">
    <literal><![CDATA[
      T(x,(y * (T(y,z) / z)) * (y \ (y * (T(y,z) / z)))) = T(x,(z \ T(y,z * y)) * (y * (z \ y)))
    ]]></literal>
    <justification jstring="[hyper(299,a,19036,a(flip),b,19883,a),flip(a)].">
      <j1 rule="hyper" parents="299 19036 19883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19885">
    <literal><![CDATA[
      T(x,(y * (T(y,z) / z)) * (y \ (y * (T(y,z) / z)))) = T(x,(z \ T(y,y * z)) * (y * (z \ y)))
    ]]></literal>
    <justification jstring="[para(4366(a,1),19884(a,2,2,1,2))].">
      <j1 rule="para" parents="4366 19884"/>
    </justification>
  </clause>

  <clause id="19886">
    <literal><![CDATA[
      T(x,(y * (T(y,z) / z)) * (y \ (y * (T(y,z) / z)))) = T(x,(z \ T(y,z)) * (y * (z \ y)))
    ]]></literal>
    <justification jstring="[hyper(299,a,19026,a(flip),b,19885,a),flip(a)].">
      <j1 rule="hyper" parents="299 19026 19885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19887">
    <literal><![CDATA[
      T(x,(y * (T(y,z) / z)) * (y \ (y * (T(y,z) / z)))) = T(x,(y / z) * (y * (z \ y)))
    ]]></literal>
    <justification jstring="[hyper(299,a,19231,a(flip),b,19886,a),flip(a)].">
      <j1 rule="hyper" parents="299 19231 19886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19888">
    <literal><![CDATA[
      T(x,(y * (T(y,z) / z)) * (y \ (y * (T(y,z) / z)))) = T(x,(z \ y) * (y * (y / z)))
    ]]></literal>
    <justification jstring="[hyper(299,a,17084,a(flip),b,19887,a),flip(a)].">
      <j1 rule="hyper" parents="299 17084 19887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19889">
    <literal><![CDATA[
      T(x,(y * (T(y,z) / z)) * (T(y,z) / z)) = T(x,(z \ y) * (y * (y / z)))
    ]]></literal>
    <justification jstring="[para(9(a,1),19888(a,1,2,2))].">
      <j1 rule="para" parents="9 19888"/>
    </justification>
  </clause>

  <clause id="19890">
    <literal><![CDATA[
      T(x,(y * (T(y,z) / z)) * (z \ y)) = T(x,(z \ y) * (y * (y / z)))
    ]]></literal>
    <justification jstring="[hyper(13882,a,19889,a)].">
      <j1 rule="hyper" parents="13882 19889"/>
    </justification>
  </clause>

  <clause id="19892">
    <literal><![CDATA[
      T(x,(y * (z \ y)) * (z \ y)) = T(x,(z \ y) * (y * (y / z)))
    ]]></literal>
    <justification jstring="[hyper(19739,a,19890,a)].">
      <j1 rule="hyper" parents="19739 19890"/>
    </justification>
  </clause>

  <clause id="19893">
    <literal><![CDATA[
      T(x,(y \ z) * ((y \ z) * z)) = T(x,(y \ z) * (z * (z / y)))
    ]]></literal>
    <justification jstring="[hyper(19247,a,19892,a)].">
      <j1 rule="hyper" parents="19247 19892"/>
    </justification>
  </clause>

  <clause id="19894">
    <literal><![CDATA[
      T(x,y * (y / (z * ((z \ y) \ 1)))) = T(x,(z \ y) * (y * (y / z)))
    ]]></literal>
    <justification jstring="[hyper(65,a,16968,a,b,19893,a)].">
      <j1 rule="hyper" parents="65 16968 19893"/>
    </justification>
  </clause>

  <clause id="19895">
    <literal><![CDATA[
      T(x,(y \ z) * (z * (z / y))) = T(x,z * (z * ((y \ z) / y)))
    ]]></literal>
    <justification jstring="[hyper(65,a,15109,a(flip),b,19894,a),flip(a)].">
      <j1 rule="hyper" parents="65 15109 19894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19896">
    <literal><![CDATA[
      T(x,(y \ z) * (z * (z / y))) = T(x,z * (z * (y \ (z / y))))
    ]]></literal>
    <justification jstring="[hyper(299,a,19710,a(flip),b,19895,a),flip(a)].">
      <j1 rule="hyper" parents="299 19710 19895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19897">
    <literal><![CDATA[
      K(x,y \ (z * T(u / (u \ w),u * (u * (w \ (u / w)))))) = K(x,y \ (z * (u * (u / w))))
    ]]></literal>
    <justification jstring="[para(19896(a,1),17703(a,1,2,2,2))].">
      <j1 rule="para" parents="19896 17703"/>
    </justification>
  </clause>

  <clause id="19898">
    <literal><![CDATA[
      K(x,y \ (z * T(u / (u \ w),w \ (u / w)))) = K(x,y \ (z * (u * (u / w))))
    ]]></literal>
    <justification jstring="[hyper(65,a,17562,a(flip),b,19897,a)].">
      <j1 rule="hyper" parents="65 17562 19897"/>
    </justification>
  </clause>

  <clause id="19899">
    <literal><![CDATA[
      K(x,y \ (z * T(u / (u \ w),w * (u / w)))) = K(x,y \ (z * (u * (u / w))))
    ]]></literal>
    <justification jstring="[hyper(17561,a,19898,a)].">
      <j1 rule="hyper" parents="17561 19898"/>
    </justification>
  </clause>

  <clause id="19901">
    <literal><![CDATA[
      K(x,y \ (z * T(u / (u \ w),T(u,w)))) = K(x,y \ (z * (u * (u / w))))
    ]]></literal>
    <justification jstring="[para(13271(a,1),19899(a,1,2,2,2))].">
      <j1 rule="para" parents="13271 19899"/>
    </justification>
  </clause>

  <clause id="19902">
    <literal><![CDATA[
      K(x,y \ (z * T(u / (u \ w),u))) = K(x,y \ (z * (u * (u / w))))
    ]]></literal>
    <justification jstring="[hyper(65,a,18821,a(flip),b,19901,a)].">
      <j1 rule="hyper" parents="65 18821 19901"/>
    </justification>
  </clause>

  <clause id="19903">
    <literal><![CDATA[
      K(x,y \ (z * ((u \ w) \ u))) = K(x,y \ (z * (u * (u / w))))
    ]]></literal>
    <justification jstring="[hyper(14801,a,19902,a)].">
      <j1 rule="hyper" parents="14801 19902"/>
    </justification>
  </clause>

  <clause id="19905">
    <literal><![CDATA[
      L(x / (T(y,y \ 1) \ 1),T(y,y \ 1),T(y,y \ 1)) = L(x,y,y) / (y \ 1)
    ]]></literal>
    <justification jstring="[para(15299(a,1),19718(a,2,1))].">
      <j1 rule="para" parents="15299 19718"/>
    </justification>
  </clause>

  <clause id="19906">
    <literal><![CDATA[
      L(x / T(y \ 1,y),T(y,y \ 1),T(y,y \ 1)) = L(x,y,y) / (y \ 1)
    ]]></literal>
    <justification jstring="[para(1490(a,1),19905(a,1,1,2))].">
      <j1 rule="para" parents="1490 19905"/>
    </justification>
  </clause>

  <clause id="19908">
    <literal><![CDATA[
      L(x / (1 / y),T(y,y \ 1),T(y,y \ 1)) = L(x,y,y) / (y \ 1)
    ]]></literal>
    <justification jstring="[para(1692(a,1),19906(a,1,1,2))].">
      <j1 rule="para" parents="1692 19906"/>
    </justification>
  </clause>

  <clause id="19909">
    <literal><![CDATA[
      L(x / (1 / y),y,y) = L(x,y,y) / (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,15299,a(flip),b,19908,a)].">
      <j1 rule="hyper" parents="65 15299 19908"/>
    </justification>
  </clause>

  <clause id="19911">
    <literal><![CDATA[
      T(K(x,L(y,z,u)),w) * K(v5 / y,K(x,L(y,z,u))) = K(x,K(y,w)) * K(L(x,z,u),T(y,v5))
    ]]></literal>
    <justification jstring="[para(8361(a,1),18607(a,2,2))].">
      <j1 rule="para" parents="8361 18607"/>
    </justification>
  </clause>

  <clause id="19913">
    <literal><![CDATA[
      T(K(x,L(y,z,u)),w) * K(v5 / y,K(x,L(y,z,u))) = K(x,K(y,w)) * K(x,L(T(y,v5),z,u))
    ]]></literal>
    <justification jstring="[para(11929(a,1),19911(a,2,2))].">
      <j1 rule="para" parents="11929 19911"/>
    </justification>
  </clause>

  <clause id="19914">
    <literal><![CDATA[
      K(x,L(T(y,z),u,w)) * K(v5 / y,K(x,L(y,u,w))) = K(x,K(y,z)) * K(x,L(T(y,v5),u,w))
    ]]></literal>
    <justification jstring="[para(7506(a,2),19913(a,1,1))].">
      <j1 rule="para" parents="7506 19913"/>
    </justification>
  </clause>

  <clause id="19915">
    <literal><![CDATA[
      K(x,L(T(y,z),u,w)) * K(x,K(v5 / y,L(y,u,w))) = K(x,K(y,z)) * K(x,L(T(y,v5),u,w))
    ]]></literal>
    <justification jstring="[para(7983(a,1),19914(a,1,2))].">
      <j1 rule="para" parents="7983 19914"/>
    </justification>
  </clause>

  <clause id="19916">
    <literal><![CDATA[
      K(x,L(T(y,z),u,w)) * K(x,K(y \ v5,L(y,u,w))) = K(x,K(y,z)) * K(x,L(T(y,v5),u,w))
    ]]></literal>
    <justification jstring="[para(7626(a,1),19915(a,1,2,2))].">
      <j1 rule="para" parents="7626 19915"/>
    </justification>
  </clause>

  <clause id="19917">
    <literal><![CDATA[
      K(x,L(T(y,z),u,w)) * K(x,K(y \ v5,y)) = K(x,K(y,z)) * K(x,L(T(y,v5),u,w))
    ]]></literal>
    <justification jstring="[para(18539(a,1),19916(a,1,2))].">
      <j1 rule="para" parents="18539 19916"/>
    </justification>
  </clause>

  <clause id="19918">
    <literal><![CDATA[
      K(x,L(T(y,z),u,w)) * K(x,K(y,y * v5)) = K(x,K(y,z)) * K(x,L(T(y,v5),u,w))
    ]]></literal>
    <justification jstring="[para(16254(a,1),19917(a,1,2))].">
      <j1 rule="para" parents="16254 19917"/>
    </justification>
  </clause>

  <clause id="19920">
    <literal><![CDATA[
      K(x,L(T(y,z),u,w)) * K(x,K(y,v5)) = K(x,K(y,z)) * K(x,L(T(y,v5),u,w))
    ]]></literal>
    <justification jstring="[para(7980(a,1),19918(a,1,2))].">
      <j1 rule="para" parents="7980 19918"/>
    </justification>
  </clause>

  <clause id="19921">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,L(T(y,u),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(T(y,u),z),w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(19920(a,1),19803(a,1))].">
      <j1 rule="para" parents="19920 19803"/>
    </justification>
  </clause>

  <clause id="19922">
    <literal><![CDATA[
      K(x,L(y \ z,1 / y,y) \ (((y * y) \ z) * u)) = K(x,(y \ z) \ ((((1 / y) \ 1) \ (y \ z)) * u))
    ]]></literal>
    <justification jstring="[para(2467(a,1),19621(a,1,2,1))].">
      <j1 rule="para" parents="2467 19621"/>
    </justification>
  </clause>

  <clause id="19923">
    <literal><![CDATA[
      K(x,L(y \ z,y,y) \ (((y * y) \ z) * u)) = K(x,(y \ z) \ ((((1 / y) \ 1) \ (y \ z)) * u))
    ]]></literal>
    <justification jstring="[para(2521(a,1),19922(a,1,2,1))].">
      <j1 rule="para" parents="2521 19922"/>
    </justification>
  </clause>

  <clause id="19924">
    <literal><![CDATA[
      K(x,(y \ z) \ ((((1 / y) \ 1) \ (y \ z)) * u)) = K(x,((1 / y) * z) \ (((y * y) \ z) * u))
    ]]></literal>
    <justification jstring="[para(511(a,1),19923(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="511 19923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19925">
    <literal><![CDATA[
      K(x,(y \ z) \ ((((1 / y) \ 1) \ (y \ z)) * u)) = K(x,((1 / y) * z) \ (z * ((y * y) \ u)))
    ]]></literal>
    <justification jstring="[hyper(299,a,17984,a(flip),b,19924,a),flip(a)].">
      <j1 rule="hyper" parents="299 17984 19924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19926">
    <literal><![CDATA[
      K(x,(y \ z) \ ((((1 / y) \ 1) \ (y \ z)) * u)) = K(x,((y \ 1) * z) \ (z * ((y * y) \ u)))
    ]]></literal>
    <justification jstring="[hyper(299,a,5664,a(flip),b,19925,a),flip(a)].">
      <j1 rule="hyper" parents="299 5664 19925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19927">
    <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))),u * K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(299,a,18604,a(flip),b,18585,a),flip(a)].">
      <j1 rule="hyper" parents="299 18604 18585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19928">
    <literal><![CDATA[
      (x * (K(y,K(z,u)) * w)) \ (x * (K(y,K(z,u)) * (w * v5))) = L(v5,L(w,K(y,K(z,u)),x),K(y,K(z,u)) * x)
    ]]></literal>
    <justification jstring="[para(18776(a,1),19861(a,1,2))].">
      <j1 rule="para" parents="18776 19861"/>
    </justification>
  </clause>

  <clause id="19929">
    <literal><![CDATA[
      L(x,L(y,K(z,K(u,w)),v5),K(z,K(u,w)) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y,v5 * K(z,K(u,w))) = v6
    ]]></literal>
    <justification jstring="[para(19861(a,1),18793(a,1))].">
      <j1 rule="para" parents="19861 18793"/>
    </justification>
  </clause>

  <clause id="19930">
    <literal><![CDATA[
      (K(x,K(y,z)) * (u * w)) \ (u * ((w * v5) * K(x,K(y,z)))) = L(v5,L(w,u,K(x,K(y,z))),u * K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(18733(a,1),19927(a,1,2))].">
      <j1 rule="para" parents="18733 19927"/>
    </justification>
  </clause>

  <clause id="19931">
    <literal><![CDATA[
      L(L(x,y,K(z,K(u,w))),K(z,K(u,w)) * y,v5) = L(x,L(y,K(z,K(u,w)),v5),K(z,K(u,w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(911,a,19928,a)].">
      <j1 rule="hyper" parents="911 19928"/>
    </justification>
  </clause>

  <clause id="19932">
    <literal><![CDATA[
      L(x,L(y,K(z,K(u,w)),v5),K(z,K(u,w)) * v5) = L(x,K(z,K(u,w)) * y,v5)
    ]]></literal>
    <justification jstring="[para(18578(a,1),19931(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18578 19931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19933">
    <literal><![CDATA[
      L(x,K(y,K(z,u)) * w,v5) = L(x,w,v5 * K(y,K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(19929,a,19932,a),flip(a)].">
      <j1 rule="hyper" parents="19929 19932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19934">
    <literal><![CDATA[
      (K(x,K(y,z)) * (u * w)) \ (u * (w * (v5 * K(x,K(y,z))))) = L(v5,L(w,u,K(x,K(y,z))),u * K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(18554(a,1),19930(a,1,2,2))].">
      <j1 rule="para" parents="18554 19930"/>
    </justification>
  </clause>

  <clause id="19935">
    <literal><![CDATA[
      (K(x,K(y,z)) * (u * w)) \ (u * (w * (v5 * K(x,K(y,z))))) = L(v5,w,u * K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(18578(a,1),19934(a,2,2))].">
      <j1 rule="para" parents="18578 19934"/>
    </justification>
  </clause>

  <clause id="19936">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(u,K(w,v5))) = L(x,y,z * K(u,K(w,v5)))
    ]]></literal>
    <justification jstring="[hyper(18896,a,19935,a)].">
      <j1 rule="hyper" parents="18896 19935"/>
    </justification>
  </clause>

  <clause id="19937">
    <literal><![CDATA[
      L(x,y,z * K(u,K(w,v5))) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(18584,a,19936,a),flip(a)].">
      <j1 rule="hyper" parents="18584 19936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19938">
    <literal><![CDATA[
      L(x,y,z * K(u,K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = v6
    ]]></literal>
    <justification jstring="[para(19936(a,1),18584(a,1))].">
      <j1 rule="para" parents="19936 18584"/>
    </justification>
  </clause>

  <clause id="19940">
    <literal><![CDATA[
      L(x,K(y,K(z,u)) * w,v5) = L(x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,19933,a,b,19937,a)].">
      <j1 rule="hyper" parents="65 19933 19937"/>
    </justification>
  </clause>

  <clause id="19943">
    <literal><![CDATA[
      L(x,K(y,T(z,u)),w) = L(x,K(y,z),w)
    ]]></literal>
    <justification jstring="[para(7495(a,1),19940(a,1,2))].">
      <j1 rule="para" parents="7495 19940"/>
    </justification>
  </clause>

  <clause id="19944">
    <literal><![CDATA[
      L(x,K(y,T(z,u)),w) = L(x,K(z,y),w)
    ]]></literal>
    <justification jstring="[hyper(299,a,5220,a,b,19943,a),flip(a)].">
      <j1 rule="hyper" parents="299 5220 19943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19945">
    <literal><![CDATA[
      R(x,K(y,z),u) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,18163,a(flip),b,19943,a)].">
      <j1 rule="hyper" parents="65 18163 19943"/>
    </justification>
  </clause>

  <clause id="19947">
    <literal><![CDATA[
      L((x / y) * K(z,u),K(u,z),y) = x / (K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,7218,a(flip),b,19945,a),flip(a)].">
      <j1 rule="hyper" parents="65 7218 19945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19948">
    <literal><![CDATA[
      L(x,K(y,z),u) * (K(y,z) * u) = (x * K(y,z)) * u
    ]]></literal>
    <justification jstring="[para(19945(a,1),103(a,1,1))].">
      <j1 rule="para" parents="19945 103"/>
    </justification>
  </clause>

  <clause id="19949">
    <literal><![CDATA[
      L(x,K(y,z),K(z,y) * u) * u = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(19945(a,1),5459(a,1,1))].">
      <j1 rule="para" parents="19945 5459"/>
    </justification>
  </clause>

  <clause id="19950">
    <literal><![CDATA[
      L(x,K(y,z),u) * (u * K(y,z)) = (x * K(y,z)) * T(u,K(y,z))
    ]]></literal>
    <justification jstring="[para(19945(a,1),11279(a,1,1))].">
      <j1 rule="para" parents="19945 11279"/>
    </justification>
  </clause>

  <clause id="19951">
    <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(19944(a,2),7213(a,1))].">
      <j1 rule="para" parents="19944 7213"/>
    </justification>
  </clause>

  <clause id="19952">
    <literal><![CDATA[
      L(x,y,K(z,T(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(z,u)) = v5
    ]]></literal>
    <justification jstring="[para(7496(a,1),19938(a,1,3))].">
      <j1 rule="para" parents="7496 19938"/>
    </justification>
  </clause>

  <clause id="19954">
    <literal><![CDATA[
      R(x,K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,K(y,z),u) = w
    ]]></literal>
    <justification jstring="[para(18163(a,1),19951(a,1))].">
      <j1 rule="para" parents="18163 19951"/>
    </justification>
  </clause>

  <clause id="19956">
    <literal><![CDATA[
      T(x,L(((y / z) * K(u,w)) \ 1,K(w,u),z)) = T(x,(y / (K(w,u) * z)) \ 1)
    ]]></literal>
    <justification jstring="[para(19947(a,1),12020(a,2,2,1))].">
      <j1 rule="para" parents="19947 12020"/>
    </justification>
  </clause>

  <clause id="19957">
    <literal><![CDATA[
      (x * K(y,z)) * u != w * (K(y,z) * u)
    ]]></literal>
    <literal><![CDATA[
      L(x,K(y,z),u) = w
    ]]></literal>
    <justification jstring="[para(19948(a,1),46(a,1))].">
      <j1 rule="para" parents="19948 46"/>
    </justification>
  </clause>

  <clause id="19958">
    <literal><![CDATA[
      L(x,K(y,T(z,u)),u) * (u * K(y,z)) = (x * K(y,T(z,u))) * u
    ]]></literal>
    <justification jstring="[para(8101(a,1),19948(a,1,2))].">
      <j1 rule="para" parents="8101 19948"/>
    </justification>
  </clause>

  <clause id="19959">
    <literal><![CDATA[
      x \ (L(K(y,z),K(y,z),K(z,y) * u) * u) = (K(z,y) * (K(z,y) * x)) \ (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(19949(a,2),10051(a,2,2)),flip(a)].">
      <j1 rule="para" parents="19949 10051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19960">
    <literal><![CDATA[
      L(x,K(y,z),u) * (u * K(z,y)) = (x * K(z,T(y,u))) * u
    ]]></literal>
    <justification jstring="[para(19944(a,1),19958(a,1,1))].">
      <j1 rule="para" parents="19944 19958"/>
    </justification>
  </clause>

  <clause id="19961">
    <literal><![CDATA[
      x \ (L(K(y,T(z,u)),K(z,y),u) * (u * K(y,z))) = ((K(y,T(z,u)) * K(y,T(z,u))) \ x) \ u
    ]]></literal>
    <justification jstring="[para(19960(a,2),666(a,2,2)),flip(a)].">
      <j1 rule="para" parents="19960 666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19963">
    <literal><![CDATA[
      T(x,L(((y / z) * K(u,w)) \ 1,K(w,u),z)) = T(x,(K(w,u) * z) / y)
    ]]></literal>
    <justification jstring="[hyper(299,a,4641,a(flip),b,19956,a),flip(a)].">
      <j1 rule="hyper" parents="299 4641 19956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19964">
    <literal><![CDATA[
      T(x,L(((y / z) * K(u,w)) \ 1,K(w,u),z)) = T(x,z * (y \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(299,a,19674,a(flip),b,19963,a),flip(a)].">
      <j1 rule="hyper" parents="299 19674 19963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19965">
    <literal><![CDATA[
      T(x,L(K(y,z) * ((u / w) \ 1),K(y,z),w)) = T(x,w * (u \ K(y,z)))
    ]]></literal>
    <justification jstring="[para(14612(a,1),19964(a,1,2,1))].">
      <j1 rule="para" parents="14612 19964"/>
    </justification>
  </clause>

  <clause id="19966">
    <literal><![CDATA[
      x \ (L(K(y,z),K(y,z),K(z,y) * u) * u) = (y * (T(T(y,z),z) \ x)) \ (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(6199(a,1),19959(a,2,1))].">
      <j1 rule="para" parents="6199 19959"/>
    </justification>
  </clause>

  <clause id="19967">
    <literal><![CDATA[
      x \ (L(K(y,T(z,u)),K(z,y),u) * (u * K(y,z))) = ((K(y,z) * K(y,z)) \ x) \ u
    ]]></literal>
    <justification jstring="[para(16654(a,1),19961(a,2,1,1))].">
      <j1 rule="para" parents="16654 19961"/>
    </justification>
  </clause>

  <clause id="19968">
    <literal><![CDATA[
      x \ (L(K(y,T(z,u)),K(z,y),u) * (u * K(y,z))) = (K(z,y) * (K(z,y) * x)) \ u
    ]]></literal>
    <justification jstring="[para(10030(a,1),19967(a,2,1))].">
      <j1 rule="para" parents="10030 19967"/>
    </justification>
  </clause>

  <clause id="19970">
    <literal><![CDATA[
      x \ (L(K(y,T(z,u)),K(z,y),u) * (u * K(y,z))) = (y * (T(T(y,z),z) \ x)) \ u
    ]]></literal>
    <justification jstring="[para(6199(a,1),19968(a,2,1))].">
      <j1 rule="para" parents="6199 19968"/>
    </justification>
  </clause>

  <clause id="19971">
    <literal><![CDATA[
      x \ (L(K(y,T(z,u)),K(z,y),u) * (u * K(y,z))) = x \ (z * (T(T(z,y),y) \ u))
    ]]></literal>
    <justification jstring="[hyper(299,a,10112,a(flip),b,19970,a),flip(a)].">
      <j1 rule="hyper" parents="299 10112 19970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19972">
    <literal><![CDATA[
      x \ (K(y,T(z,u)) * (u * K(y,z))) = x \ (z * (T(T(z,y),y) \ u))
    ]]></literal>
    <justification jstring="[para(9205(a,1),19971(a,1,2,1))].">
      <j1 rule="para" parents="9205 19971"/>
    </justification>
  </clause>

  <clause id="19975">
    <literal><![CDATA[
      (K(x,y) * (z * (K(y,x) * L(K(x,y),u,w)))) * a(x,z,K(K(x,y) * K(y,x),y)) = L(K(x,y),u,w) * z
    ]]></literal>
    <justification jstring="[para(19106(a,1),19426(a,1,2,3))].">
      <j1 rule="para" parents="19106 19426"/>
    </justification>
  </clause>

  <clause id="19976">
    <literal><![CDATA[
      (K(x,y) * (z * (K(y,x) * L(K(x,y),u,w)))) * a(x,z,K(1,y)) = L(K(x,y),u,w) * z
    ]]></literal>
    <justification jstring="[para(5198(a,1),19975(a,1,2,3,1))].">
      <j1 rule="para" parents="5198 19975"/>
    </justification>
  </clause>

  <clause id="19978">
    <literal><![CDATA[
      (K(x,y) * (z * (K(y,x) * L(K(x,y),u,w)))) * 1 = L(K(x,y),u,w) * z
    ]]></literal>
    <justification jstring="[para(359(a,1),19976(a,1,2))].">
      <j1 rule="para" parents="359 19976"/>
    </justification>
  </clause>

  <clause id="19980">
    <literal><![CDATA[
      K(x,y) * (z * (K(y,x) * L(K(x,y),u,w))) = L(K(x,y),u,w) * z
    ]]></literal>
    <justification jstring="[hyper(133,a,19978,a)].">
      <j1 rule="hyper" parents="133 19978"/>
    </justification>
  </clause>

  <clause id="19982">
    <literal><![CDATA[
      K(x,y) * (z * a(x,u,K(w,y))) = L(K(x,y),u,w) * z
    ]]></literal>
    <justification jstring="[para(14874(a,1),19980(a,1,2,2))].">
      <j1 rule="para" parents="14874 19980"/>
    </justification>
  </clause>

  <clause id="19983">
    <literal><![CDATA[
      L(K(x,y),z * a(x,u,K(w,y)),v5) \ ((L(K(x,y),u,w) * z) * v5) = (z * a(x,u,K(w,y))) * v5
    ]]></literal>
    <justification jstring="[para(19982(a,1),15508(a,1,2,1))].">
      <j1 rule="para" parents="19982 15508"/>
    </justification>
  </clause>

  <clause id="19984">
    <literal><![CDATA[
      K(x,y) \ ((L(K(x,y),z,u) * w) * K(v5,v6)) = (w * a(x,z,K(u,y))) * K(v5,v6)
    ]]></literal>
    <justification jstring="[para(18574(a,1),19983(a,1,1))].">
      <j1 rule="para" parents="18574 19983"/>
    </justification>
  </clause>

  <clause id="19985">
    <literal><![CDATA[
      K(x,y) \ (L(K(x,y),z,u) * (w * K(v5,v6))) = (w * a(x,z,K(u,y))) * K(v5,v6)
    ]]></literal>
    <justification jstring="[para(18659(a,1),19984(a,1,2))].">
      <j1 rule="para" parents="18659 19984"/>
    </justification>
  </clause>

  <clause id="19986">
    <literal><![CDATA[
      K(x,y) * (L(K(y,x),z,u) * (w * K(v5,v6))) = (w * a(y,z,K(u,x))) * K(v5,v6)
    ]]></literal>
    <justification jstring="[hyper(5452,a,19985,a)].">
      <j1 rule="hyper" parents="5452 19985"/>
    </justification>
  </clause>

  <clause id="19987">
    <literal><![CDATA[
      (x * a(y,z,K(u,w))) * K(v5,v6) = a(y,z,K(u,w)) * (x * K(v5,v6))
    ]]></literal>
    <justification jstring="[hyper(65,a,14879,a(flip),b,19986,a),flip(a)].">
      <j1 rule="hyper" parents="65 14879 19986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19988">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w * K(w * a(x,y,K(z,u)),v5)) = T(w * a(x,y,K(z,u)),v5)
    ]]></literal>
    <justification jstring="[hyper(5087,a,19987,a),flip(a)].">
      <j1 rule="hyper" parents="5087 19987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19989">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w * K(w,v5)) = T(w * a(x,y,K(z,u)),v5)
    ]]></literal>
    <justification jstring="[para(18987(a,1),19988(a,1,2,2))].">
      <j1 rule="para" parents="18987 19988"/>
    </justification>
  </clause>

  <clause id="19990">
    <literal><![CDATA[
      T(x * a(y,z,K(u,w)),v5) = a(y,z,K(u,w)) * T(x,v5)
    ]]></literal>
    <justification jstring="[para(5083(a,2),19989(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5083 19989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19992">
    <literal><![CDATA[
      x \ (y * T((a(z,u,K(w,v5)) * (y \ x)) * a(v5,u,K(w,z)),v6)) = K((x \ (y * a(v5,u,K(w,z)))) \ 1,v6)
    ]]></literal>
    <justification jstring="[para(19990(a,2),14931(a,1,2,2))].">
      <j1 rule="para" parents="19990 14931"/>
    </justification>
  </clause>

  <clause id="19993">
    <literal><![CDATA[
      K((x \ (y * a(z,u,K(w,v5)))) \ 1,v6) = x \ (y * T(y \ x,v6))
    ]]></literal>
    <justification jstring="[para(18698(a,1),19992(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="18698 19992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19994">
    <literal><![CDATA[
      K((x \ (y * a(z,u,K(w,v5)))) \ 1,v6) = K((x \ y) \ 1,v6)
    ]]></literal>
    <justification jstring="[hyper(299,a,5326,a(flip),b,19993,a),flip(a)].">
      <j1 rule="hyper" parents="299 5326 19993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19996">
    <literal><![CDATA[
      K((T(x,y) \ y) \ 1,z) = K(((y * a(u,w,K(v5,v6))) / x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,18894,a(flip),b,19994,a),flip(a)].">
      <j1 rule="hyper" parents="65 18894 19994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19998">
    <literal><![CDATA[
      K(((x * a(y,z,K(u,w))) / v5) \ 1,v6) = K((x / v5) \ 1,v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,17001,a(flip),b,19996,a),flip(a)].">
      <j1 rule="hyper" parents="65 17001 19996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19999">
    <literal><![CDATA[
      K(x / (y * a(z,u,K(w,v5))),v6) = K((y / x) \ 1,v6)
    ]]></literal>
    <justification jstring="[hyper(6001,a,19998,a)].">
      <j1 rule="hyper" parents="6001 19998"/>
    </justification>
  </clause>

  <clause id="20000">
    <literal><![CDATA[
      K(x / (y * a(z,u,K(w,v5))),v6) = K(x / y,v6)
    ]]></literal>
    <justification jstring="[hyper(299,a,5852,a(flip),b,19999,a),flip(a)].">
      <j1 rule="hyper" parents="299 5852 19999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20001">
    <literal><![CDATA[
      K(x / (L(K(y,z),u,w) * v5),v6) = K(x / (K(y,z) * v5),v6)
    ]]></literal>
    <justification jstring="[para(19427(a,1),20000(a,1,1,2))].">
      <j1 rule="para" parents="19427 20000"/>
    </justification>
  </clause>

  <clause id="20002">
    <literal><![CDATA[
      K(x \ (L(K(y,z),u,w) * v5),v6) = K(((x \ v5) * x) / (K(z,y) * x),v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,19493,a(flip),b,20001,a)].">
      <j1 rule="hyper" parents="65 19493 20001"/>
    </justification>
  </clause>

  <clause id="20004">
    <literal><![CDATA[
      K(x \ (L(K(y,z),u,w) * v5),v6) = K(x \ (K(y,z) * (x * (x \ v5))),v6)
    ]]></literal>
    <justification jstring="[hyper(299,a,18779,a(flip),b,20002,a),flip(a)].">
      <j1 rule="hyper" parents="299 18779 20002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20005">
    <literal><![CDATA[
      K(x \ (L(K(y,z),u,w) * v5),v6) = K(x \ (K(y,z) * v5),v6)
    ]]></literal>
    <justification jstring="[para(10(a,1),20004(a,2,1,2,2))].">
      <j1 rule="para" parents="10 20004"/>
    </justification>
  </clause>

  <clause id="20006">
    <literal><![CDATA[
      K(x \ ((K(y,z) * L(K(y,u) \ 1,w,v5)) * v6),v7) = K((x * K(z,y)) \ (K(u,y) * v6),v7)
    ]]></literal>
    <justification jstring="[hyper(65,a,18780,a,b,20005,a)].">
      <j1 rule="hyper" parents="65 18780 20005"/>
    </justification>
  </clause>

  <clause id="20009">
    <literal><![CDATA[
      K(x \ ((K(y,z) * L(K(y,u) \ 1,w,v5)) * v6),v7) = K(x \ (K(y,z) * (K(u,y) * v6)),v7)
    ]]></literal>
    <justification jstring="[hyper(299,a,18739,a(flip),b,20006,a),flip(a)].">
      <j1 rule="hyper" parents="299 18739 20006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20010">
    <literal><![CDATA[
      K(x \ ((K(y,z) * L(K(y,z) \ 1,u,w)) * v5),v6) = K(x \ v5,v6)
    ]]></literal>
    <justification jstring="[para(5432(a,1),20009(a,2,1,2))].">
      <j1 rule="para" parents="5432 20009"/>
    </justification>
  </clause>

  <clause id="20011">
    <literal><![CDATA[
      K(x \ ((K(y,z) * L(K(z,y),u,w)) * v5),v6) = K(x \ v5,v6)
    ]]></literal>
    <justification jstring="[para(5197(a,1),20010(a,1,1,2,1,2,1))].">
      <j1 rule="para" parents="5197 20010"/>
    </justification>
  </clause>

  <clause id="20012">
    <literal><![CDATA[
      K(x \ (a(y,z,K(u,w)) * v5),v6) = K(x \ v5,v6)
    ]]></literal>
    <justification jstring="[para(10534(a,1),20011(a,1,1,2,1))].">
      <j1 rule="para" parents="10534 20011"/>
    </justification>
  </clause>

  <clause id="20013">
    <literal><![CDATA[
      K(x \ ((y * z) * K(u,w)),v5) = K(x \ (y * (z * K(u,w))),v5)
    ]]></literal>
    <justification jstring="[para(19556(a,1),20012(a,1,1,2))].">
      <j1 rule="para" parents="19556 20012"/>
    </justification>
  </clause>

  <clause id="20014">
    <literal><![CDATA[
      K((x * K(y,z)) \ (x * (u * K(y,z))),w) = K(u,w)
    ]]></literal>
    <justification jstring="[hyper(18929,a,20013,a),flip(a)].">
      <j1 rule="hyper" parents="18929 20013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20015">
    <literal><![CDATA[
      K(L(T(x,K(y,z)),K(y,z),u),w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(230(a,1),20014(a,1,1))].">
      <j1 rule="para" parents="230 20014"/>
    </justification>
  </clause>

  <clause id="20016">
    <literal><![CDATA[
      K(L(x,K(y,z),u),T(w,K(y,z))) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(7711,a,20015,a)].">
      <j1 rule="hyper" parents="7711 20015"/>
    </justification>
  </clause>

  <clause id="20017">
    <literal><![CDATA[
      K(L(x,K(y,z),u),w) = K(T(x,K(z,y)),w)
    ]]></literal>
    <justification jstring="[para(6256(a,1),20015(a,1,1,1))].">
      <j1 rule="para" parents="6256 20015"/>
    </justification>
  </clause>

  <clause id="20018">
    <literal><![CDATA[
      K(L(x,K(y,z),u),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(16391,a,20016,a)].">
      <j1 rule="hyper" parents="16391 20016"/>
    </justification>
  </clause>

  <clause id="20019">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,w) = K((x \ u) * K(z,y),w)
    ]]></literal>
    <justification jstring="[hyper(17318,a,20018,a)].">
      <j1 rule="hyper" parents="17318 20018"/>
    </justification>
  </clause>

  <clause id="20020">
    <literal><![CDATA[
      K(x,L(y,K(z,u),w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(11999,a,20018,a)].">
      <j1 rule="hyper" parents="11999 20018"/>
    </justification>
  </clause>

  <clause id="20021">
    <literal><![CDATA[
      L(K(x,y),K(z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(11945,a,20018,a)].">
      <j1 rule="hyper" parents="11945 20018"/>
    </justification>
  </clause>

  <clause id="20027">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),w) = K((x \ u) * K(y,z),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,18778,a(flip),b,20018,a)].">
      <j1 rule="hyper" parents="65 18778 20018"/>
    </justification>
  </clause>

  <clause id="20028">
    <literal><![CDATA[
      K((x / y) * K(z,T(u,y)),w) = K(x / (y * K(u,z)),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,15692,a(flip),b,20018,a),flip(a)].">
      <j1 rule="hyper" parents="65 15692 20018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20031">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,w) = x * (K(y,z) * K(u,w))
    ]]></literal>
    <justification jstring="[para(20018(a,1),11930(a,1,2))].">
      <j1 rule="para" parents="20018 11930"/>
    </justification>
  </clause>

  <clause id="20032">
    <literal><![CDATA[
      K(x / (K(y,z) * u),w) = K((x / u) * K(z,y),w)
    ]]></literal>
    <justification jstring="[para(19947(a,1),20018(a,1,1))].">
      <j1 rule="para" parents="19947 20018"/>
    </justification>
  </clause>

  <clause id="20035">
    <literal><![CDATA[
      K(x,(y * K(z,u)) \ w) = K(x,K(z,u) \ (y \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,15632,a(flip),b,20020,a),flip(a)].">
      <j1 rule="hyper" parents="65 15632 20020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20036">
    <literal><![CDATA[
      K(x,(y / z) / K(u,w)) = K(x,y / (K(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,15486,a(flip),b,20020,a),flip(a)].">
      <j1 rule="hyper" parents="65 15486 20020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20037">
    <literal><![CDATA[
      K(x,(y * K(z,u)) \ w) = K(x,K(u,z) * (y \ w))
    ]]></literal>
    <justification jstring="[para(5443(a,1),20020(a,1,2))].">
      <j1 rule="para" parents="5443 20020"/>
    </justification>
  </clause>

  <clause id="20039">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,w))) * K(w,u) = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(20020(a,1),11910(a,1,2))].">
      <j1 rule="para" parents="20020 11910"/>
    </justification>
  </clause>

  <clause id="20041">
    <literal><![CDATA[
      K(x,y / (K(z,u) * w)) = K(x,(y / w) * K(u,z))
    ]]></literal>
    <justification jstring="[para(19947(a,1),20020(a,1,2))].">
      <j1 rule="para" parents="19947 20020"/>
    </justification>
  </clause>

  <clause id="20047">
    <literal><![CDATA[
      L(K(x,y),L(K(z,u),w,v5),v6) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6131(a,1),20021(a,1,2))].">
      <j1 rule="para" parents="6131 20021"/>
    </justification>
  </clause>

  <clause id="20051">
    <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(65,a,11904,a(flip),b,20047,a)].">
      <j1 rule="hyper" parents="65 11904 20047"/>
    </justification>
  </clause>

  <clause id="20054">
    <literal><![CDATA[
      K(L(x,K(y,z),u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w) = v5
    ]]></literal>
    <justification jstring="[para(20017(a,2),16393(a,1))].">
      <j1 rule="para" parents="20017 16393"/>
    </justification>
  </clause>

  <clause id="20057">
    <literal><![CDATA[
      K(x,L(y,K(z,u),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(11929(a,1),20054(a,1))].">
      <j1 rule="para" parents="11929 20054"/>
    </justification>
  </clause>

  <clause id="20060">
    <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(5443(a,1),20057(a,1,2))].">
      <j1 rule="para" parents="5443 20057"/>
    </justification>
  </clause>

  <clause id="20062">
    <literal><![CDATA[
      K((K(x,y) * z) \ u,w) = K((z \ u) * K(y,x),w)
    ]]></literal>
    <justification jstring="[hyper(16807,a,20019,a)].">
      <j1 rule="hyper" parents="16807 20019"/>
    </justification>
  </clause>

  <clause id="20064">
    <literal><![CDATA[
      K(((x \ 1) \ y) * K(z,u),w) = K((x \ K(u,z)) \ y,w)
    ]]></literal>
    <justification jstring="[para(14185(a,1),20019(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="14185 20019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20066">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),w) = K(K(y,z) * (x \ u),w)
    ]]></literal>
    <justification jstring="[hyper(299,a,16376,a,b,20027,a),flip(a)].">
      <j1 rule="hyper" parents="299 16376 20027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20067">
    <literal><![CDATA[
      K(x \ (K(y,K(z,u)) * w),v5) = K(x \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(299,a,16766,a(flip),b,20027,a),flip(a)].">
      <j1 rule="hyper" parents="299 16766 20027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20068">
    <literal><![CDATA[
      K(x \ (y * T(z,K(u,w))),v5) = K(x \ (y * z),v5)
    ]]></literal>
    <justification jstring="[para(5853(a,1),20067(a,1,1,2))].">
      <j1 rule="para" parents="5853 20067"/>
    </justification>
  </clause>

  <clause id="20069">
    <literal><![CDATA[
      K(x \ (T(y,T(z,u)) * w),v5) = K(x \ (T(y,z) * w),v5)
    ]]></literal>
    <justification jstring="[para(9181(a,1),20067(a,1,1,2))].">
      <j1 rule="para" parents="9181 20067"/>
    </justification>
  </clause>

  <clause id="20070">
    <literal><![CDATA[
      L(x,K(y,z),K(u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(19957,a,20031,a)].">
      <j1 rule="hyper" parents="19957 20031"/>
    </justification>
  </clause>

  <clause id="20071">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,w) = x * (K(u,w) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(18860,a,20031,a)].">
      <j1 rule="hyper" parents="18860 20031"/>
    </justification>
  </clause>

  <clause id="20073">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * K(u,w)) = z * (K(u,w) * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,17115,a,b,20031,a)].">
      <j1 rule="hyper" parents="65 17115 20031"/>
    </justification>
  </clause>

  <clause id="20079">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,w) = x * (K(w,u) \ K(y,z))
    ]]></literal>
    <justification jstring="[para(16420(a,2),20031(a,2,2))].">
      <j1 rule="para" parents="16420 20031"/>
    </justification>
  </clause>

  <clause id="20082">
    <literal><![CDATA[
      (K(x,y) * K(z,u)) \ w = K(u,z) * (K(y,x) * w)
    ]]></literal>
    <justification jstring="[hyper(65,a,6082,a(flip),b,20070,a)].">
      <j1 rule="hyper" parents="65 6082 20070"/>
    </justification>
  </clause>

  <clause id="20083">
    <literal><![CDATA[
      L(x,K(y,z),K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x = v5
    ]]></literal>
    <justification jstring="[para(20070(a,1),52(a,2))].">
      <j1 rule="para" parents="20070 52"/>
    </justification>
  </clause>

  <clause id="20091">
    <literal><![CDATA[
      K((x / y) * K(z,u),w) = K(x * (y \ K(z,u)),w)
    ]]></literal>
    <justification jstring="[hyper(14540,a,20032,a),flip(a)].">
      <j1 rule="hyper" parents="14540 20032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20092">
    <literal><![CDATA[
      K(x / (K(y,z) * u),w) = K(K(z,y) * (x / u),w)
    ]]></literal>
    <justification jstring="[hyper(299,a,16376,a,b,20032,a),flip(a)].">
      <j1 rule="hyper" parents="299 16376 20032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20094">
    <literal><![CDATA[
      K(x,K(y,z) \ (u \ w)) = K(x,u \ (K(y,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,18782,a(flip),b,20035,a),flip(a)].">
      <j1 rule="hyper" parents="65 18782 20035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20095">
    <literal><![CDATA[
      K(x,(y / z) / K(u,w)) = K(x,y / (K(w,u) \ z))
    ]]></literal>
    <justification jstring="[para(5426(a,2),20036(a,2,2,2))].">
      <j1 rule="para" parents="5426 20036"/>
    </justification>
  </clause>

  <clause id="20096">
    <literal><![CDATA[
      K(x,T(y,z * K(u,w)) * (z \ K(w,u))) = K(x,K(w,u) * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(19754,a,20037,a)].">
      <j1 rule="hyper" parents="19754 20037"/>
    </justification>
  </clause>

  <clause id="20097">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ w) = K(x,K(z,y) * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(16803,a,20037,a)].">
      <j1 rule="hyper" parents="16803 20037"/>
    </justification>
  </clause>

  <clause id="20098">
    <literal><![CDATA[
      K(x,y \ (K(z,u) * w)) = K(x,K(z,u) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,18748,a(flip),b,20037,a)].">
      <j1 rule="hyper" parents="65 18748 20037"/>
    </justification>
  </clause>

  <clause id="20099">
    <literal><![CDATA[
      K(x,K(y,z) * ((u * z) \ w)) = K(x,(u * T(z,y)) \ w)
    ]]></literal>
    <justification jstring="[para(6832(a,1),20037(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6832 20037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20100">
    <literal><![CDATA[
      K(x,K(y,z) * ((u / y) \ w)) = K(x,(u / T(y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(7189(a,1),20037(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7189 20037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20101">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * ((w * (u * z)) \ v5)) = K(x,(w * (u * T(z,y))) \ v5)
    ]]></literal>
    <justification jstring="[para(9496(a,1),20037(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9496 20037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20102">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * ((w * u) \ v5)) = K(x,(w * (u * K(z,y))) \ v5)
    ]]></literal>
    <justification jstring="[para(11930(a,1),20037(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11930 20037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20103">
    <literal><![CDATA[
      K(x,K(y,z) * ((u \ z) \ w)) = K(x,(u \ T(z,y)) \ w)
    ]]></literal>
    <justification jstring="[para(14220(a,1),20037(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14220 20037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20105">
    <literal><![CDATA[
      (x * (y \ R(y,z,y))) * K(y,y * z) = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(5587(a,1),20039(a,1,1,2))].">
      <j1 rule="para" parents="5587 20039"/>
    </justification>
  </clause>

  <clause id="20106">
    <literal><![CDATA[
      K(x,(y / z) * K(u,w)) = K(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(19750,a,20041,a),flip(a)].">
      <j1 rule="hyper" parents="19750 20041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20107">
    <literal><![CDATA[
      K(((x \ 1) \ y) * K(z,u),w) = K((x * K(z,u)) * y,w)
    ]]></literal>
    <justification jstring="[hyper(14616,a,20062,a),flip(a)].">
      <j1 rule="hyper" parents="14616 20062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20108">
    <literal><![CDATA[
      K(K(x,y) * ((y / z) \ u),w) = K((T(y,x) / z) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,18741,a(flip),b,20066,a),flip(a)].">
      <j1 rule="hyper" parents="65 18741 20066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20109">
    <literal><![CDATA[
      K(x \ (y * T(z,T(u,w))),v5) = K(x \ (y * T(z,u)),v5)
    ]]></literal>
    <justification jstring="[para(7140(a,1),20068(a,1,1,2,2))].">
      <j1 rule="para" parents="7140 20068"/>
    </justification>
  </clause>

  <clause id="20114">
    <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(65,a,18870,a,b,20079,a)].">
      <j1 rule="hyper" parents="65 18870 20079"/>
    </justification>
  </clause>

  <clause id="20117">
    <literal><![CDATA[
      K(x * (y \ K(z,u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(K(u,z) * (x / y),w) = v5
    ]]></literal>
    <justification jstring="[para(20091(a,1),17784(a,1))].">
      <j1 rule="para" parents="20091 17784"/>
    </justification>
  </clause>

  <clause id="20118">
    <literal><![CDATA[
      K(K(x,y) * ((((z * y) \ u) * (z * y)) / (z * y)),w) = K((z * T(y,x)) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(16477,a,20092,a),flip(a)].">
      <j1 rule="hyper" parents="16477 20092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20119">
    <literal><![CDATA[
      K((x \ y) * K(z,u),T(w,x)) = K(y / (K(u,z) * x),w)
    ]]></literal>
    <justification jstring="[hyper(299,a,17819,a,b,20092,a)].">
      <j1 rule="hyper" parents="299 17819 20092"/>
    </justification>
  </clause>

  <clause id="20120">
    <literal><![CDATA[
      K(x,K(y,z) \ (u \ w)) = K(x,u \ (K(z,y) \ w))
    ]]></literal>
    <justification jstring="[hyper(16627,a,20094,a)].">
      <j1 rule="hyper" parents="16627 20094"/>
    </justification>
  </clause>

  <clause id="20121">
    <literal><![CDATA[
      K(x,y / (K(z,u) \ w)) = K(x,K(u,z) \ (y / w))
    ]]></literal>
    <justification jstring="[hyper(16468,a,20095,a),flip(a)].">
      <j1 rule="hyper" parents="16468 20095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20122">
    <literal><![CDATA[
      K(L(x,y,z),K(u,w) * (v5 \ v6)) = K(x,L((K(w,u) * v5) \ v6,y,z))
    ]]></literal>
    <justification jstring="[hyper(11999,a,20097,a),flip(a)].">
      <j1 rule="hyper" parents="11999 20097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20123">
    <literal><![CDATA[
      x * K(x,K(y,z) * (u \ w)) = T(x,(K(z,y) * u) \ w)
    ]]></literal>
    <justification jstring="[para(20097(a,1),5083(a,2,2)),flip(a)].">
      <j1 rule="para" parents="20097 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20124">
    <literal><![CDATA[
      K(x,K(y,z) * ((z * u) \ w)) = K(x,(T(z,y) * u) \ w)
    ]]></literal>
    <justification jstring="[para(5103(a,1),20097(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5103 20097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20125">
    <literal><![CDATA[
      K(x,(y * (K(z,y) * u)) \ w) = K(x,K(y,z) * ((y * u) \ w))
    ]]></literal>
    <justification jstring="[para(5524(a,1),20097(a,1,2,1))].">
      <j1 rule="para" parents="5524 20097"/>
    </justification>
  </clause>

  <clause id="20126">
    <literal><![CDATA[
      K(x,K(L(y,z,u),w) * ((z * u) \ v5)) = K(x,((K(w,y) * z) * u) \ v5)
    ]]></literal>
    <justification jstring="[para(15496(a,1),20097(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="15496 20097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20127">
    <literal><![CDATA[
      K(x,y \ (K(z,u) * w)) = K(x,K(u,z) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(299,a,15802,a,b,20098,a),flip(a)].">
      <j1 rule="hyper" parents="299 15802 20098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20128">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (y * w))) = K(x,u \ (T(y,z) * w))
    ]]></literal>
    <justification jstring="[para(5103(a,1),20098(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5103 20098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20129">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (T(z,y) \ w))) = K(x,u \ (T(T(z,y),y) \ w))
    ]]></literal>
    <justification jstring="[para(5527(a,1),20098(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5527 20098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20130">
    <literal><![CDATA[
      K(x,K(y,T(z,u)) * (w \ (T(y,z) \ v5))) = K(x,w \ (T(y,K(z,u)) \ v5))
    ]]></literal>
    <justification jstring="[para(9286(a,1),20098(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9286 20098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20131">
    <literal><![CDATA[
      K(x,y \ L(K(z,u) * w,z,z)) = K(x,K(z,u) * (y \ L(w,z,z)))
    ]]></literal>
    <justification jstring="[para(9598(a,2),20098(a,1,2,2))].">
      <j1 rule="para" parents="9598 20098"/>
    </justification>
  </clause>

  <clause id="20132">
    <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(20098(a,2),15803(a,1))].">
      <j1 rule="para" parents="20098 15803"/>
    </justification>
  </clause>

  <clause id="20133">
    <literal><![CDATA[
      x * K(x,y * (z \ K(u,w))) = T(x,(y / z) * K(w,u))
    ]]></literal>
    <justification jstring="[para(20106(a,1),5083(a,2,2)),flip(a)].">
      <j1 rule="para" parents="20106 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20134">
    <literal><![CDATA[
      K(x,y \ (K(z,L(u,w,v5)) \ v6)) = K(x,K(z,u) \ (y \ v6))
    ]]></literal>
    <justification jstring="[hyper(19133,a,20120,a),flip(a)].">
      <j1 rule="hyper" parents="19133 20120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20135">
    <literal><![CDATA[
      K(x,K(y,z) \ ((y \ u) \ w)) = K(x,(T(y,z) \ u) \ w)
    ]]></literal>
    <justification jstring="[hyper(299,a,18777,a(flip),b,20120,a),flip(a)].">
      <j1 rule="hyper" parents="299 18777 20120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20136">
    <literal><![CDATA[
      K(x,T(y \ z,K(u,w) \ y)) = K(x,K(w,u) \ ((K(u,w) \ z) / y))
    ]]></literal>
    <justification jstring="[hyper(65,a,18946,a,b,20121,a)].">
      <j1 rule="hyper" parents="65 18946 20121"/>
    </justification>
  </clause>

  <clause id="20137">
    <literal><![CDATA[
      K(x,y \ ((z * K(u,w)) * v5)) = K(x,K(w,u) * (y \ (z * v5)))
    ]]></literal>
    <justification jstring="[hyper(65,a,19817,a,b,20127,a)].">
      <j1 rule="hyper" parents="65 19817 20127"/>
    </justification>
  </clause>

  <clause id="20138">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * (T(w * (u * z),K(z,y)) \ v5)) = K(x,(w * (u * (z * K(y,z)))) \ v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,19866,a(flip),b,20127,a),flip(a)].">
      <j1 rule="hyper" parents="65 19866 20127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20139">
    <literal><![CDATA[
      K(x,K(y,y \ z) * ((u * (y \ z)) \ w)) = K(x,(u * (z / y)) \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,18783,a(flip),b,20127,a),flip(a)].">
      <j1 rule="hyper" parents="65 18783 20127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20140">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (y \ w))) = K(x,u \ (T(y,z) \ w))
    ]]></literal>
    <justification jstring="[para(5383(a,1),20127(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5383 20127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20141">
    <literal><![CDATA[
      (x * (y \ R(y,z,y))) / K(y * z,y) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(7265,a,20105,a)].">
      <j1 rule="hyper" parents="7265 20105"/>
    </justification>
  </clause>

  <clause id="20142">
    <literal><![CDATA[
      ((x * (y \ R(y,z,y))) / (K(y,z) * x)) / (K(y,z) * x) = K(y * z,T(y,x)) / (x * K(y,z))
    ]]></literal>
    <justification jstring="[para(20141(a,1),17244(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20141 17244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20143">
    <literal><![CDATA[
      K(x / (y * K(z,u)),w) = K((x / y) * K(u,z),w)
    ]]></literal>
    <justification jstring="[hyper(16809,a,20028,a),flip(a)].">
      <j1 rule="hyper" parents="16809 20028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20146">
    <literal><![CDATA[
      K(x / (y * K(z,u)),w) = K(K(z,u) \ (x / y),w)
    ]]></literal>
    <justification jstring="[hyper(299,a,16431,a,b,20143,a),flip(a)].">
      <j1 rule="hyper" parents="299 16431 20143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20148">
    <literal><![CDATA[
      K(x / (y * K(z,u)),w) = K(x * (y \ K(u,z)),w)
    ]]></literal>
    <justification jstring="[hyper(299,a,20091,a(flip),b,20143,a),flip(a)].">
      <j1 rule="hyper" parents="299 20091 20143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20149">
    <literal><![CDATA[
      K(x / (K(y,z) \ u),w) = K(K(z,y) \ (x / u),w)
    ]]></literal>
    <justification jstring="[hyper(16843,a,20146,a)].">
      <j1 rule="hyper" parents="16843 20146"/>
    </justification>
  </clause>

  <clause id="20151">
    <literal><![CDATA[
      K(x * ((y * z) \ K(u,z)),w) = K(x / (y * T(z,u)),w)
    ]]></literal>
    <justification jstring="[para(6832(a,1),20148(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6832 20148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20152">
    <literal><![CDATA[
      K(K(x,y) \ (z / (x * u)),w) = K(z / (T(x,y) * u),w)
    ]]></literal>
    <justification jstring="[para(5364(a,1),20149(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5364 20149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20153">
    <literal><![CDATA[
      K(K(x,y) * ((z \ 1) \ u),w) = K((z \ K(x,y)) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(17784,a,20064,a)].">
      <j1 rule="hyper" parents="17784 20064"/>
    </justification>
  </clause>

  <clause id="20154">
    <literal><![CDATA[
      x \ (y * (T(T(y,z),z) \ u)) = x \ (u * (K(z,y) * K(z,y)))
    ]]></literal>
    <justification jstring="[para(20073(a,1),19972(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20073 19972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20155">
    <literal><![CDATA[
      K(x,((y * z) \ u) * K(w,z)) = K(x,(y * T(z,w)) \ u)
    ]]></literal>
    <justification jstring="[hyper(16408,a,20099,a)].">
      <j1 rule="hyper" parents="16408 20099"/>
    </justification>
  </clause>

  <clause id="20156">
    <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(20099(a,1),16798(a,1))].">
      <j1 rule="para" parents="20099 16798"/>
    </justification>
  </clause>

  <clause id="20157">
    <literal><![CDATA[
      K(x,K(y,z) * ((u \ y) \ w)) = K(x,(u \ T(y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(15803,a,20103,a)].">
      <j1 rule="hyper" parents="15803 20103"/>
    </justification>
  </clause>

  <clause id="20158">
    <literal><![CDATA[
      K((x \ K(y,z)) \ u,w) = K((x * K(z,y)) * u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,20064,a(flip),b,20107,a)].">
      <j1 rule="hyper" parents="65 20064 20107"/>
    </justification>
  </clause>

  <clause id="20159">
    <literal><![CDATA[
      K((x \ K(y,z)) \ u,w) = K(K(z,y) * (x * u),w)
    ]]></literal>
    <justification jstring="[hyper(299,a,19010,a(flip),b,20158,a),flip(a)].">
      <j1 rule="hyper" parents="299 19010 20158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20161">
    <literal><![CDATA[
      K((T(x,y) / y) \ z,u) = K((y \ x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,17825,a(flip),b,20108,a),flip(a)].">
      <j1 rule="hyper" parents="65 17825 20108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20162">
    <literal><![CDATA[
      K((x / T(y,x)) \ z,u) = K((y \ x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,16891,a(flip),b,20161,a)].">
      <j1 rule="hyper" parents="65 16891 20161"/>
    </justification>
  </clause>

  <clause id="20163">
    <literal><![CDATA[
      K((x / (x \ y)) \ z,u) = K(((y / x) \ x) \ z,u)
    ]]></literal>
    <justification jstring="[para(4416(a,1),20161(a,1,1,1))].">
      <j1 rule="para" parents="4416 20161"/>
    </justification>
  </clause>

  <clause id="20164">
    <literal><![CDATA[
      K(x \ (y * T(z,T(u \ w,v5))),v6) = K(x \ (y * T(z,(w \ u) \ z)),v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,18136,a(flip),b,20109,a)].">
      <j1 rule="hyper" parents="65 18136 20109"/>
    </justification>
  </clause>

  <clause id="20165">
    <literal><![CDATA[
      K(x / (K(y,y \ z) * u),w) = K(K(z,y) * (u \ x),T(w,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,16525,a(flip),b,20119,a),flip(a)].">
      <j1 rule="hyper" parents="65 16525 20119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20166">
    <literal><![CDATA[
      T(x,(K(y,z) * u) \ w) = T(x,K(z,y) * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(5087,a,20123,a),flip(a)].">
      <j1 rule="hyper" parents="5087 20123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20167">
    <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(20123(a,1),5087(a,1))].">
      <j1 rule="para" parents="20123 5087"/>
    </justification>
  </clause>

  <clause id="20168">
    <literal><![CDATA[
      T(x,(y * K(z,u)) \ w) = T(x,K(u,z) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(16794,a,20166,a)].">
      <j1 rule="hyper" parents="16794 20166"/>
    </justification>
  </clause>

  <clause id="20169">
    <literal><![CDATA[
      T(x,(y \ K(z,u)) * w) = T(x,K(z,u) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,14386,a(flip),b,20166,a)].">
      <j1 rule="hyper" parents="65 14386 20166"/>
    </justification>
  </clause>

  <clause id="20170">
    <literal><![CDATA[
      T(x,K(y,z) * ((z * u) \ w)) = T(x,(T(z,y) * u) \ w)
    ]]></literal>
    <justification jstring="[para(5103(a,1),20166(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5103 20166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20172">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * (y \ K(u,w))) = T(x,K(u,w) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(17274,a,20168,a)].">
      <j1 rule="hyper" parents="17274 20168"/>
    </justification>
  </clause>

  <clause id="20173">
    <literal><![CDATA[
      T(x,K(y,z) * ((u / y) \ w)) = T(x,(u / T(y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(7189(a,1),20168(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7189 20168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20174">
    <literal><![CDATA[
      T(x,K(y,z) * ((u \ z) \ w)) = T(x,(u \ T(z,y)) \ w)
    ]]></literal>
    <justification jstring="[para(14220(a,1),20168(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14220 20168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20175">
    <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(20168(a,1),16790(a,1))].">
      <j1 rule="para" parents="20168 16790"/>
    </justification>
  </clause>

  <clause id="20176">
    <literal><![CDATA[
      T(x,(y \ K(y * z,y \ 1)) * u) = T(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(299,a,17397,a(flip),b,20169,a),flip(a)].">
      <j1 rule="hyper" parents="299 17397 20169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20177">
    <literal><![CDATA[
      K(x,((y * z) \ u) * K(y,w)) = K(x,(T(y,w) * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(16624,a,20124,a)].">
      <j1 rule="hyper" parents="16624 20124"/>
    </justification>
  </clause>

  <clause id="20178">
    <literal><![CDATA[
      K(x,(T(y,y * z) * u) \ w) = K(x,((y * u) \ w) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(16623,a,20124,a),flip(a)].">
      <j1 rule="hyper" parents="16623 20124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20179">
    <literal><![CDATA[
      K(x,((y * z) \ u) * K(w,y)) = K(x,(T(y,w) * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(16408,a,20124,a)].">
      <j1 rule="hyper" parents="16408 20124"/>
    </justification>
  </clause>

  <clause id="20180">
    <literal><![CDATA[
      K(x,K(y,z) * ((y * u) \ w)) = K(x,(T(y,z) * u) \ w)
    ]]></literal>
    <justification jstring="[hyper(15803,a,20124,a)].">
      <j1 rule="hyper" parents="15803 20124"/>
    </justification>
  </clause>

  <clause id="20181">
    <literal><![CDATA[
      K(x,(y \ (z * u)) * K(w,z)) = K(x,y \ (T(z,w) * u))
    ]]></literal>
    <justification jstring="[hyper(16624,a,20128,a)].">
      <j1 rule="hyper" parents="16624 20128"/>
    </justification>
  </clause>

  <clause id="20182">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ ((y * z) * w))) = K(x,u \ (T(y * z,z) * w))
    ]]></literal>
    <justification jstring="[hyper(13902,a,20128,a)].">
      <j1 rule="hyper" parents="13902 20128"/>
    </justification>
  </clause>

  <clause id="20183">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ ((z * y) * w))) = K(x,u \ (T(z * y,z) * w))
    ]]></literal>
    <justification jstring="[hyper(13888,a,20128,a)].">
      <j1 rule="hyper" parents="13888 20128"/>
    </justification>
  </clause>

  <clause id="20184">
    <literal><![CDATA[
      K(x,K(R(y,z,u),w) * (v5 \ ((y * z) * u))) = K(x,v5 \ (T(R(y,z,u),w) * (z * u)))
    ]]></literal>
    <justification jstring="[para(103(a,1),20128(a,1,2,2,2))].">
      <j1 rule="para" parents="103 20128"/>
    </justification>
  </clause>

  <clause id="20185">
    <literal><![CDATA[
      T(x,(y / z) * K(u,w)) = T(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(5087,a,20133,a),flip(a)].">
      <j1 rule="hyper" parents="5087 20133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20186">
    <literal><![CDATA[
      T(x,y * (z \ K(u,w * w))) = T(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(17413,a,20185,a),flip(a)].">
      <j1 rule="hyper" parents="17413 20185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20187">
    <literal><![CDATA[
      T(x,K(y,z) * (u / w)) = T(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(16516,a,20185,a)].">
      <j1 rule="hyper" parents="16516 20185"/>
    </justification>
  </clause>

  <clause id="20188">
    <literal><![CDATA[
      T(x,y / (z * K(u * u,w))) = T(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(65,a,16907,a,b,20186,a)].">
      <j1 rule="hyper" parents="65 16907 20186"/>
    </justification>
  </clause>

  <clause id="20189">
    <literal><![CDATA[
      T(x,y / (z \ T(u,w * w))) = T(x,y / (z \ u))
    ]]></literal>
    <justification jstring="[para(7335(a,1),20188(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7335 20188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20190">
    <literal><![CDATA[
      T(x,K(y,z) * (u / (z \ w))) = T(x,u / (T(z,y) \ w))
    ]]></literal>
    <justification jstring="[hyper(299,a,19705,a(flip),b,20187,a),flip(a)].">
      <j1 rule="hyper" parents="299 19705 20187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20191">
    <literal><![CDATA[
      T(x,y / T(z / (1 / u),u)) = T(x,y / ((u \ 1) \ z))
    ]]></literal>
    <justification jstring="[para(9657(a,1),20189(a,1,2,2))].">
      <j1 rule="para" parents="9657 20189"/>
    </justification>
  </clause>

  <clause id="20192">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ u) = K(x,(T(y,z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,15963,a(flip),b,20135,a)].">
      <j1 rule="hyper" parents="65 15963 20135"/>
    </justification>
  </clause>

  <clause id="20193">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ u) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(299,a,14200,a(flip),b,20192,a),flip(a)].">
      <j1 rule="hyper" parents="299 14200 20192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20194">
    <literal><![CDATA[
      K(x,(T(y,z) \ 1) \ x) = K(x,T(y * x,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,14830,a(flip),b,20192,a),flip(a)].">
      <j1 rule="hyper" parents="65 14830 20192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20195">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(20192(a,2),14527(a,1))].">
      <j1 rule="para" parents="20192 14527"/>
    </justification>
  </clause>

  <clause id="20196">
    <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(11999,a,20193,a)].">
      <j1 rule="hyper" parents="11999 20193"/>
    </justification>
  </clause>

  <clause id="20197">
    <literal><![CDATA[
      K(x,T(y \ 1,z * u) \ w) = K(x,T(y,z / u) * w)
    ]]></literal>
    <justification jstring="[hyper(65,a,17967,a(flip),b,20193,a)].">
      <j1 rule="hyper" parents="65 17967 20193"/>
    </justification>
  </clause>

  <clause id="20198">
    <literal><![CDATA[
      K(x,T(1 / y,z) * u) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(79(a,1),20193(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="79 20193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20199">
    <literal><![CDATA[
      K(x,T(y * x,z)) = K(x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(8685,a,20194,a),flip(a)].">
      <j1 rule="hyper" parents="8685 20194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20200">
    <literal><![CDATA[
      K(x,T(x * y,z)) = K(x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(13244,a,20199,a)].">
      <j1 rule="hyper" parents="13244 20199"/>
    </justification>
  </clause>

  <clause id="20201">
    <literal><![CDATA[
      K(x,x * T(x \ y,z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),20200(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 20200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20202">
    <literal><![CDATA[
      K(x,y * ((z * T(z \ u,w)) * K(z,T(u,w)))) = K(x,y * T(z * T(z \ u,w),z))
    ]]></literal>
    <justification jstring="[para(20201(a,1),19046(a,1,2,2,2))].">
      <j1 rule="para" parents="20201 19046"/>
    </justification>
  </clause>

  <clause id="20203">
    <literal><![CDATA[
      K(x,K(y,z \ u) * (w \ (y \ v5))) = K(x,w \ (T(y,z * u) \ v5))
    ]]></literal>
    <justification jstring="[hyper(17854,a,20140,a)].">
      <j1 rule="hyper" parents="17854 20140"/>
    </justification>
  </clause>

  <clause id="20204">
    <literal><![CDATA[
      K(x,y \ (T(z,u * u) \ w)) = K(x,y \ (z \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,17920,a(flip),b,20140,a),flip(a)].">
      <j1 rule="hyper" parents="65 17920 20140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20206">
    <literal><![CDATA[
      K(K(x,y) \ (z / (y * u)),w) = K(z / (T(y,x) * u),w)
    ]]></literal>
    <justification jstring="[hyper(17788,a,20152,a)].">
      <j1 rule="hyper" parents="17788 20152"/>
    </justification>
  </clause>

  <clause id="20207">
    <literal><![CDATA[
      K(((x \ 1) \ K(y,z)) \ u,w) = K(K(y,z) * (x \ u),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,6032,a(flip),b,20153,a),flip(a)].">
      <j1 rule="hyper" parents="65 6032 20153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20208">
    <literal><![CDATA[
      K(x,(((1 / y) * T(z,y)) \ u) * K(w,y)) = K(x,(((y * y) \ z) * T(y,w)) \ u)
    ]]></literal>
    <justification jstring="[para(983(a,1),20155(a,1,2,1,1))].">
      <j1 rule="para" parents="983 20155"/>
    </justification>
  </clause>

  <clause id="20209">
    <literal><![CDATA[
      K(x,((y \ z) \ T(z,u)) \ w) = K(x,K(z,u) * (T(y,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,19500,a(flip),b,20157,a),flip(a)].">
      <j1 rule="hyper" parents="65 19500 20157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20210">
    <literal><![CDATA[
      K(x,(y \ T(z,y)) \ u) = K(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,13834,a(flip),b,20157,a),flip(a)].">
      <j1 rule="hyper" parents="65 13834 20157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20211">
    <literal><![CDATA[
      K(x,(T(y,z * z) \ (z * z)) * u) = K(x,(y / (z * z)) \ u)
    ]]></literal>
    <justification jstring="[hyper(14526,a,20210,a)].">
      <j1 rule="hyper" parents="14526 20210"/>
    </justification>
  </clause>

  <clause id="20212">
    <literal><![CDATA[
      K(x,((y * (z / y)) / y) \ u) = K(x,(T(z,y) / y) \ u)
    ]]></literal>
    <justification jstring="[para(1610(a,1),20210(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1610 20210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20213">
    <literal><![CDATA[
      K(x,(T(y,z) \ z) \ u) = K(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[para(4396(a,2),20210(a,1,2,1))].">
      <j1 rule="para" parents="4396 20210"/>
    </justification>
  </clause>

  <clause id="20214">
    <literal><![CDATA[
      T(x,(y \ T(z,y)) \ u) = x * K(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[para(20210(a,1),5083(a,2,2))].">
      <j1 rule="para" parents="20210 5083"/>
    </justification>
  </clause>

  <clause id="20215">
    <literal><![CDATA[
      K(x,(L(y,y,z) \ T(u,y)) \ w) = K(x,(u / L(y,y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(7103(a,1),20210(a,1,2,1,2))].">
      <j1 rule="para" parents="7103 20210"/>
    </justification>
  </clause>

  <clause id="20216">
    <literal><![CDATA[
      K((x \ T(y,x)) \ z,u) = (w * K(u,(y / x) \ z)) \ w
    ]]></literal>
    <justification jstring="[para(20210(a,1),7200(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="20210 7200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20217">
    <literal><![CDATA[
      K(x,(y / z) \ T(u,T(z,y) \ y)) = K(x,u / (T(z,y) \ y))
    ]]></literal>
    <justification jstring="[hyper(13929,a,20213,a),flip(a)].">
      <j1 rule="hyper" parents="13929 20213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20218">
    <literal><![CDATA[
      T(x,(y \ T(z,y)) \ u) = T(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(299,a,5083,a,b,20214,a),flip(a)].">
      <j1 rule="hyper" parents="299 5083 20214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20219">
    <literal><![CDATA[
      T(x,(y \ T(z,y)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z / y) \ u) = w
    ]]></literal>
    <justification jstring="[para(20214(a,2),5087(a,1))].">
      <j1 rule="para" parents="20214 5087"/>
    </justification>
  </clause>

  <clause id="20220">
    <literal><![CDATA[
      T(x,(T(y,z) \ z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z / y) \ u) = w
    ]]></literal>
    <justification jstring="[para(4396(a,2),20219(a,1,2,1))].">
      <j1 rule="para" parents="4396 20219"/>
    </justification>
  </clause>

  <clause id="20221">
    <literal><![CDATA[
      T(x,(T(y,z) * u) \ z) = T(x,(y * u) \ T(z,y))
    ]]></literal>
    <justification jstring="[hyper(16466,a,20170,a),flip(a)].">
      <j1 rule="hyper" parents="16466 20170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20222">
    <literal><![CDATA[
      T(x,K(y,T(z,u)) * ((w / y) \ v5)) = T(x,(w / T(y,z)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(16853,a,20173,a)].">
      <j1 rule="hyper" parents="16853 20173"/>
    </justification>
  </clause>

  <clause id="20223">
    <literal><![CDATA[
      T(x,K(y,z) * ((u \ y) \ w)) = T(x,(u \ T(y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(15834,a,20174,a)].">
      <j1 rule="hyper" parents="15834 20174"/>
    </justification>
  </clause>

  <clause id="20224">
    <literal><![CDATA[
      T(x,((y \ 1) * K(y * z,y \ 1)) * u) = T(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(3661(a,2),20176(a,1,2,1))].">
      <j1 rule="para" parents="3661 20176"/>
    </justification>
  </clause>

  <clause id="20225">
    <literal><![CDATA[
      K(x,(((1 / y) * z) \ u) * K(1 / y,w * y)) = K(x,(T(y \ 1,y \ w) * z) \ u)
    ]]></literal>
    <justification jstring="[para(15279(a,1),20177(a,2,2,1,1))].">
      <j1 rule="para" parents="15279 20177"/>
    </justification>
  </clause>

  <clause id="20226">
    <literal><![CDATA[
      K(x,y \ (T(z,u * (u / w)) * v5)) = K(x,(y \ (z * v5)) * K(w,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,17840,a(flip),b,20181,a),flip(a)].">
      <j1 rule="hyper" parents="65 17840 20181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20227">
    <literal><![CDATA[
      T(x,y / (T(z,u) \ T(u,w))) = T(x,y / (T(u,w) / z))
    ]]></literal>
    <justification jstring="[hyper(17580,a,20190,a),flip(a)].">
      <j1 rule="hyper" parents="17580 20190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20228">
    <literal><![CDATA[
      T(x,y / (T(z,u * u) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y / (z \ w)) = v5
    ]]></literal>
    <justification jstring="[para(20190(a,1),17408(a,1))].">
      <j1 rule="para" parents="20190 17408"/>
    </justification>
  </clause>

  <clause id="20229">
    <literal><![CDATA[
      T(x,y / T(T(z \ ((z \ 1) \ u),z),1 / z)) = T(x,y / ((z \ 1) \ (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,17652,a,b,20191,a)].">
      <j1 rule="hyper" parents="65 17652 20191"/>
    </justification>
  </clause>

  <clause id="20230">
    <literal><![CDATA[
      K(x,T(y \ 1,z * (u \ w)) \ v5) = K(x,T(y,w / ((u \ 1) * z)) * v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,19276,a(flip),b,20197,a)].">
      <j1 rule="hyper" parents="65 19276 20197"/>
    </justification>
  </clause>

  <clause id="20231">
    <literal><![CDATA[
      K(x / (K(y,z) \ (y * u)),w) = K(x / (T(y,z) * u),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,20149,a,b,20206,a)].">
      <j1 rule="hyper" parents="65 20149 20206"/>
    </justification>
  </clause>

  <clause id="20232">
    <literal><![CDATA[
      K(K(x,y) * ((z \ 1) * u),w) = K(K(y,x) * (z \ u),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,20159,a(flip),b,20207,a)].">
      <j1 rule="hyper" parents="65 20159 20207"/>
    </justification>
  </clause>

  <clause id="20233">
    <literal><![CDATA[
      K(x,(T(y,z) / z) \ u) = K(x,T(y / z,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,15824,a(flip),b,20212,a),flip(a)].">
      <j1 rule="hyper" parents="65 15824 20212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20234">
    <literal><![CDATA[
      K(x,(T(y,z) / z) \ u) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(109(a,1),20233(a,2,2,1))].">
      <j1 rule="para" parents="109 20233"/>
    </justification>
  </clause>

  <clause id="20235">
    <literal><![CDATA[
      K(x,(y / T(z,y)) \ u) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(4382(a,1),20234(a,1,2,1))].">
      <j1 rule="para" parents="4382 20234"/>
    </justification>
  </clause>

  <clause id="20236">
    <literal><![CDATA[
      K((x \ T(y,x)) \ z,u) = K((y / x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,18856,a(flip),b,20216,a),flip(a)].">
      <j1 rule="hyper" parents="299 18856 20216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20237">
    <literal><![CDATA[
      K((T(x,y) \ y) \ z,u) = K((y / x) \ z,u)
    ]]></literal>
    <justification jstring="[para(4396(a,2),20236(a,1,1,1))].">
      <j1 rule="para" parents="4396 20236"/>
    </justification>
  </clause>

  <clause id="20238">
    <literal><![CDATA[
      K((x / y) \ T(z,x / y),u) = K(z / (T(y,x) \ x),u)
    ]]></literal>
    <justification jstring="[hyper(15278,a,20237,a),flip(a)].">
      <j1 rule="hyper" parents="15278 20237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20239">
    <literal><![CDATA[
      K((x / y) \ z,L(u,x,y)) = K(x \ (T(y,x) * z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,18661,a(flip),b,20237,a),flip(a)].">
      <j1 rule="hyper" parents="65 18661 20237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20241">
    <literal><![CDATA[
      T(x,(y \ T(z,u \ (u \ w))) \ v5) = T(x,K(z,w) * ((y \ z) \ v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,17396,a(flip),b,20223,a),flip(a)].">
      <j1 rule="hyper" parents="65 17396 20223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20242">
    <literal><![CDATA[
      T(x,K(y,z) * ((z \ y) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(y / z) \ u) = w
    ]]></literal>
    <justification jstring="[para(20223(a,2),20219(a,1))].">
      <j1 rule="para" parents="20223 20219"/>
    </justification>
  </clause>

  <clause id="20243">
    <literal><![CDATA[
      T(x,y / (T(z,u / w) \ (w \ u))) = T(x,y / (T(u / w,w) / z))
    ]]></literal>
    <justification jstring="[para(109(a,1),20227(a,1,2,2,2))].">
      <j1 rule="para" parents="109 20227"/>
    </justification>
  </clause>

  <clause id="20244">
    <literal><![CDATA[
      K(x / (T(y,z) * z),u) = K(x / (z * y),u)
    ]]></literal>
    <justification jstring="[para(5018(a,1),20231(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5018 20231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20245">
    <literal><![CDATA[
      K(x / ((y \ z) * y),u) = K(x / (y * (z / y)),u)
    ]]></literal>
    <justification jstring="[para(109(a,1),20244(a,1,1,2,1))].">
      <j1 rule="para" parents="109 20244"/>
    </justification>
  </clause>

  <clause id="20246">
    <literal><![CDATA[
      K(x / (y * (z / y)),u) = K(x / T(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,13957,a(flip),b,20245,a),flip(a)].">
      <j1 rule="hyper" parents="65 13957 20245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20247">
    <literal><![CDATA[
      K(x / T(y * z,z),u) = K(x / (z * y),u)
    ]]></literal>
    <justification jstring="[para(11(a,1),20246(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 20246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20248">
    <literal><![CDATA[
      K(x / T((y \ 1) * T(z,y),T(y,y \ 1)),u) = K(x / (T(y,y \ 1) * ((y * y) \ z)),u)
    ]]></literal>
    <justification jstring="[para(10856(a,1),20247(a,1,1,2,1))].">
      <j1 rule="para" parents="10856 20247"/>
    </justification>
  </clause>

  <clause id="20249">
    <literal><![CDATA[
      K((x \ K(y,z)) * u,w) = K(K(z,y) * (x \ u),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,19014,a(flip),b,20232,a)].">
      <j1 rule="hyper" parents="65 19014 20232"/>
    </justification>
  </clause>

  <clause id="20250">
    <literal><![CDATA[
      K(K(x,y) * (z \ u),T(w,z)) = K(u * (z \ K(y,x)),w)
    ]]></literal>
    <justification jstring="[hyper(17111,a,20249,a),flip(a)].">
      <j1 rule="hyper" parents="17111 20249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20252">
    <literal><![CDATA[
      K(x / (T(y,z) \ z),u) = K(x / (z / y),u)
    ]]></literal>
    <justification jstring="[hyper(13914,a,20238,a),flip(a)].">
      <j1 rule="hyper" parents="13914 20238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20253">
    <literal><![CDATA[
      K(x / (y / (z / y)),u) = K(x / ((y \ z) \ y),u)
    ]]></literal>
    <justification jstring="[para(109(a,1),20252(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="109 20252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20254">
    <literal><![CDATA[
      K(x / (y \ T(z,y)),u) = K(x / (z / y),u)
    ]]></literal>
    <justification jstring="[para(4396(a,1),20252(a,1,1,2))].">
      <j1 rule="para" parents="4396 20252"/>
    </justification>
  </clause>

  <clause id="20255">
    <literal><![CDATA[
      K(x / ((y \ z) \ ((y \ z) \ z)),u) = K(x / (y / (y \ z)),u)
    ]]></literal>
    <justification jstring="[para(108(a,1),20254(a,1,1,2,2))].">
      <j1 rule="para" parents="108 20254"/>
    </justification>
  </clause>

  <clause id="20257">
    <literal><![CDATA[
      K(K(x,y) * (z / (x / u)),w) = K(z / (T(x,y) / u),w)
    ]]></literal>
    <justification jstring="[hyper(20117,a,14668,a)].">
      <j1 rule="hyper" parents="20117 14668"/>
    </justification>
  </clause>

  <clause id="20258">
    <literal><![CDATA[
      K(x / (K(y,z) * (z / u)),w) = K(x / (T(z,y) / u),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,20092,a,b,20257,a)].">
      <j1 rule="hyper" parents="65 20092 20257"/>
    </justification>
  </clause>

  <clause id="20259">
    <literal><![CDATA[
      K(x / (((y * z) / y) / u),w) = K(x / (T(z,y) / u),w)
    ]]></literal>
    <justification jstring="[para(14662(a,2),20258(a,1,1,2))].">
      <j1 rule="para" parents="14662 20258"/>
    </justification>
  </clause>

  <clause id="20260">
    <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(19817(a,2),20132(a,1))].">
      <j1 rule="para" parents="19817 20132"/>
    </justification>
  </clause>

  <clause id="20261">
    <literal><![CDATA[
      K(x,y \ (L(K(z,u),w,v5) \ v6)) = K(x,K(z,u) \ (y \ v6))
    ]]></literal>
    <justification jstring="[para(7810(a,1),20134(a,1,2,2,1))].">
      <j1 rule="para" parents="7810 20134"/>
    </justification>
  </clause>

  <clause id="20262">
    <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(7140(a,1),20156(a,1,2,1,2))].">
      <j1 rule="para" parents="7140 20156"/>
    </justification>
  </clause>

  <clause id="20263">
    <literal><![CDATA[
      T(x,K(y,z) * ((T(z,u) \ y) \ w)) = T(x,(y / T(z,u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(20242,a,16728,a),flip(a)].">
      <j1 rule="hyper" parents="20242 16728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20264">
    <literal><![CDATA[
      K(x,K(y,z) \ ((L(K(y,z),u,w) \ v5) \ v6)) = K(x,v5 \ v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,18931,a(flip),b,20261,a),flip(a)].">
      <j1 rule="hyper" parents="65 18931 20261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20266">
    <literal><![CDATA[
      K(x,K(y,z) \ ((K(L(y,u,w),z) \ v5) \ v6)) = K(x,v5 \ v6)
    ]]></literal>
    <justification jstring="[para(7433(a,1),20264(a,1,2,2,1,1))].">
      <j1 rule="para" parents="7433 20264"/>
    </justification>
  </clause>

  <clause id="20267">
    <literal><![CDATA[
      K(x,(y * (K(z,y) * u)) \ w) = K(x,(T(y,z) * u) \ w)
    ]]></literal>
    <justification jstring="[hyper(299,a,20180,a(flip),b,20125,a),flip(a)].">
      <j1 rule="hyper" parents="299 20180 20125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20268">
    <literal><![CDATA[
      K(x,(((y * z) / y) * u) \ w) = K(x,(T(z,y) * u) \ w)
    ]]></literal>
    <justification jstring="[para(5705(a,2),20267(a,1,2,1))].">
      <j1 rule="para" parents="5705 20267"/>
    </justification>
  </clause>

  <clause id="20269">
    <literal><![CDATA[
      K(x,y \ ((z \ ((u * w) / u)) * v5)) = K(x,K(w,u) * (y \ ((z \ w) * v5)))
    ]]></literal>
    <justification jstring="[para(19690(a,2),20137(a,1,2,2,1))].">
      <j1 rule="para" parents="19690 20137"/>
    </justification>
  </clause>

  <clause id="20270">
    <literal><![CDATA[
      x \ (y * (T(T(y,z),z) \ u)) = (x \ u) * (K(z,y) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,847,a(flip),b,20154,a),flip(a)].">
      <j1 rule="hyper" parents="299 847 20154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20271">
    <literal><![CDATA[
      K(x / (K(y,y \ z) * u),w) = K(x * (u \ K(y,z)),w)
    ]]></literal>
    <justification jstring="[hyper(299,a,20250,a(flip),b,20165,a),flip(a)].">
      <j1 rule="hyper" parents="299 20250 20165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20272">
    <literal><![CDATA[
      K(x / (K(y,y \ z) * (u * z)),w) = K(x / (u * T(z,y)),w)
    ]]></literal>
    <justification jstring="[hyper(299,a,20151,a(flip),b,20271,a),flip(a)].">
      <j1 rule="hyper" parents="299 20151 20271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20273">
    <literal><![CDATA[
      T(x,y \ (K(z,u) * w)) = T(x,K(z,u) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,19676,a(flip),b,20172,a)].">
      <j1 rule="hyper" parents="65 19676 20172"/>
    </justification>
  </clause>

  <clause id="20274">
    <literal><![CDATA[
      T(x,(K(y,z) / u) * w) = T(x,K(y,z) * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,17265,a(flip),b,20172,a)].">
      <j1 rule="hyper" parents="65 17265 20172"/>
    </justification>
  </clause>

  <clause id="20275">
    <literal><![CDATA[
      T(x,y \ (z * K(u,w))) = T(x,K(w,u) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(19268,a,20273,a)].">
      <j1 rule="hyper" parents="19268 20273"/>
    </justification>
  </clause>

  <clause id="20276">
    <literal><![CDATA[
      T(x,y \ (K(z,u) * w)) = T(x,K(u,z) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(299,a,15778,a,b,20273,a),flip(a)].">
      <j1 rule="hyper" parents="299 15778 20273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20277">
    <literal><![CDATA[
      T(x,K(y,z) * (u \ (w \ z))) = T(x,u \ (w \ T(z,y)))
    ]]></literal>
    <justification jstring="[para(14220(a,1),20275(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14220 20275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20278">
    <literal><![CDATA[
      T(x,K(y,z) * (u \ (y \ w))) = T(x,u \ (T(y,z) \ w))
    ]]></literal>
    <justification jstring="[para(5383(a,1),20276(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5383 20276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20279">
    <literal><![CDATA[
      T(x,K(y,z) * (u \ (w * z))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,u \ (w * T(z,y))) = v5
    ]]></literal>
    <justification jstring="[para(20276(a,1),16835(a,1))].">
      <j1 rule="para" parents="20276 16835"/>
    </justification>
  </clause>

  <clause id="20280">
    <literal><![CDATA[
      T(x,K(y * z,u) * (w \ (v5 \ u))) = T(x,w \ (v5 \ T(u,y \ z)))
    ]]></literal>
    <justification jstring="[hyper(17351,a,20277,a)].">
      <j1 rule="hyper" parents="17351 20277"/>
    </justification>
  </clause>

  <clause id="20281">
    <literal><![CDATA[
      T(x,y \ (K(z,u) * (z \ w))) = T(x,y \ (T(z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,20273,a,b,20278,a)].">
      <j1 rule="hyper" parents="65 20273 20278"/>
    </justification>
  </clause>

  <clause id="20282">
    <literal><![CDATA[
      T(x,y \ (((z * u) / z) \ w)) = T(x,y \ (T(u,z) \ w))
    ]]></literal>
    <justification jstring="[para(5352(a,2),20281(a,1,2,2))].">
      <j1 rule="para" parents="5352 20281"/>
    </justification>
  </clause>

  <clause id="20283">
    <literal><![CDATA[
      T(x,y \ (T(T(z,u),u) \ w)) = T(x,y \ (z \ w))
    ]]></literal>
    <justification jstring="[para(223(a,1),20282(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="223 20282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20284">
    <literal><![CDATA[
      T(x,y \ (T(T(z,u \ (w \ ((w * u) \ 1))),w \ (u \ (w \ 1))) \ v5)) = T(x,y \ (((u * z) / u) \ v5))
    ]]></literal>
    <justification jstring="[para(18945(a,1),20283(a,1,2,2,1,1))].">
      <j1 rule="para" parents="18945 20283"/>
    </justification>
  </clause>

  <clause id="20285">
    <literal><![CDATA[
      K(x,(T(y,y * z) * u) \ w) = K(x,(T(y,z) * u) \ w)
    ]]></literal>
    <justification jstring="[hyper(299,a,20179,a(flip),b,20178,a),flip(a)].">
      <j1 rule="hyper" parents="299 20179 20178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20286">
    <literal><![CDATA[
      K(x,(T(y \ 1,y \ z) * u) \ w) = K(x,(T(y \ 1,z) * u) \ w)
    ]]></literal>
    <justification jstring="[para(14297(a,1),20285(a,1,2,1,1))].">
      <j1 rule="para" parents="14297 20285"/>
    </justification>
  </clause>

  <clause id="20287">
    <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(299,a,11929,a(flip),b,20196,a),flip(a)].">
      <j1 rule="hyper" parents="299 11929 20196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20288">
    <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(20196(a,2),11999(a,1))].">
      <j1 rule="para" parents="20196 11999"/>
    </justification>
  </clause>

  <clause id="20289">
    <literal><![CDATA[
      K(x,K(y,z) * (T(z,y) \ ((z \ y) \ u))) = K(x,L(T(y,z) \ u,T(z,y),z * y))
    ]]></literal>
    <justification jstring="[hyper(19580,a,20209,a),flip(a)].">
      <j1 rule="hyper" parents="19580 20209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20290">
    <literal><![CDATA[
      K(x,(y / (z * z)) \ u) = K(x,(y \ (z * z)) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,18122,a(flip),b,20211,a),flip(a)].">
      <j1 rule="hyper" parents="65 18122 20211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20292">
    <literal><![CDATA[
      K(x,(y \ (z * z)) * u) = K(x,(z * z) * (y \ u))
    ]]></literal>
    <justification jstring="[para(416(a,1),20290(a,1,2)),flip(a)].">
      <j1 rule="para" parents="416 20290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20293">
    <literal><![CDATA[
      K(x,(y \ (z * z)) * u) = K(x,z * (z * (y \ u)))
    ]]></literal>
    <justification jstring="[hyper(299,a,14201,a(flip),b,20292,a),flip(a)].">
      <j1 rule="hyper" parents="299 14201 20292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20294">
    <literal><![CDATA[
      K(x,y \ ((z * z) * u)) = K(x,z * (z * (y \ u)))
    ]]></literal>
    <justification jstring="[hyper(14529,a,20293,a)].">
      <j1 rule="hyper" parents="14529 20293"/>
    </justification>
  </clause>

  <clause id="20295">
    <literal><![CDATA[
      K(x,y * (y * ((y * z) \ T(u,z * y)))) = K(x,u / ((y \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,17472,a(flip),b,20293,a),flip(a)].">
      <j1 rule="hyper" parents="65 17472 20293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20296">
    <literal><![CDATA[
      K(x,y * (y * ((y * z) \ u))) = K(x,((y \ 1) * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(13932,a,20294,a),flip(a)].">
      <j1 rule="hyper" parents="13932 20294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20297">
    <literal><![CDATA[
      K(x,y * (y * (z \ (u * (w / y))))) = K(x,z \ (u * (w / (1 / y))))
    ]]></literal>
    <justification jstring="[hyper(65,a,18053,a(flip),b,20294,a),flip(a)].">
      <j1 rule="hyper" parents="65 18053 20294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20298">
    <literal><![CDATA[
      K(x,y * (y * ((y * z) \ u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ u) = w
    ]]></literal>
    <justification jstring="[para(20294(a,1),13932(a,1))].">
      <j1 rule="para" parents="20294 13932"/>
    </justification>
  </clause>

  <clause id="20299">
    <literal><![CDATA[
      K(x,(y / z) * ((y / z) * (y \ u))) = K(x,(((y / z) \ 1) * z) \ u)
    ]]></literal>
    <justification jstring="[para(12(a,1),20296(a,1,2,2,2,1))].">
      <j1 rule="para" parents="12 20296"/>
    </justification>
  </clause>

  <clause id="20300">
    <literal><![CDATA[
      K(x,(1 / y) * ((1 / y) * ((1 / L(y,z,z)) \ u))) = K(x,(((1 / y) \ 1) * a(z,z,y)) \ u)
    ]]></literal>
    <justification jstring="[para(6554(a,1),20296(a,1,2,2,2,1))].">
      <j1 rule="para" parents="6554 20296"/>
    </justification>
  </clause>

  <clause id="20301">
    <literal><![CDATA[
      K(x,(y / z) \ T(u,y / z)) = K(x,u / (T(z,y) \ y))
    ]]></literal>
    <justification jstring="[para(15275(a,1),20217(a,1,2,2))].">
      <j1 rule="para" parents="15275 20217"/>
    </justification>
  </clause>

  <clause id="20302">
    <literal><![CDATA[
      K(x,y / (T(z,u) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (u / z)) = w
    ]]></literal>
    <justification jstring="[para(20301(a,1),13929(a,1))].">
      <j1 rule="para" parents="20301 13929"/>
    </justification>
  </clause>

  <clause id="20303">
    <literal><![CDATA[
      K(x,y / T(z \ u,u)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(20302,a,19826,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="20302 19826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20304">
    <literal><![CDATA[
      K(x,y / (z \ T(u,z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (u / z)) = w
    ]]></literal>
    <justification jstring="[para(4396(a,1),20302(a,1,2,2))].">
      <j1 rule="para" parents="4396 20302"/>
    </justification>
  </clause>

  <clause id="20305">
    <literal><![CDATA[
      K(x,(T(y,z) * u) / (z * y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(T(y,z) \ u) / (z / y)) = w
    ]]></literal>
    <justification jstring="[para(19685(a,1),20302(a,1))].">
      <j1 rule="para" parents="19685 20302"/>
    </justification>
  </clause>

  <clause id="20306">
    <literal><![CDATA[
      K(x / T(y \ z,z),u) = (w * K(u,x / (z / y))) \ w
    ]]></literal>
    <justification jstring="[para(20303(a,1),7200(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="20303 7200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20307">
    <literal><![CDATA[
      K(x / T(y \ z,z),u) = K(x / (z / y),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,18856,a(flip),b,20306,a),flip(a)].">
      <j1 rule="hyper" parents="299 18856 20306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20308">
    <literal><![CDATA[
      K(T(x,y / z) / (y / z),u) = K(T(z \ y,y) \ x,u)
    ]]></literal>
    <justification jstring="[hyper(13788,a,20307,a),flip(a)].">
      <j1 rule="hyper" parents="13788 20307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20309">
    <literal><![CDATA[
      K(x / (y / (y / z)),u) = K(x / T(z,y),u)
    ]]></literal>
    <justification jstring="[para(79(a,1),20307(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 20307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20310">
    <literal><![CDATA[
      K(x / T(y,y * z),u) = K(x / T(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(17995,a,20309,a)].">
      <j1 rule="hyper" parents="17995 20309"/>
    </justification>
  </clause>

  <clause id="20311">
    <literal><![CDATA[
      K(x / ((y \ z) \ z),u) = K(x / T(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,17989,a(flip),b,20310,a)].">
      <j1 rule="hyper" parents="65 17989 20310"/>
    </justification>
  </clause>

  <clause id="20312">
    <literal><![CDATA[
      K(T(x \ y,y) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K((y / x) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(20308(a,1),13762(a,1))].">
      <j1 rule="para" parents="20308 13762"/>
    </justification>
  </clause>

  <clause id="20313">
    <literal><![CDATA[
      T(x,(y / T(z,T(u,w))) \ v5) = T(x,(y / T(z,u)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,20173,a(flip),b,20222,a)].">
      <j1 rule="hyper" parents="65 20173 20222"/>
    </justification>
  </clause>

  <clause id="20314">
    <literal><![CDATA[
      T(x,((y \ 1) * K((1 / y) \ z,1 / y)) * u) = T(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(6046(a,2),20224(a,1,2,1,2))].">
      <j1 rule="para" parents="6046 20224"/>
    </justification>
  </clause>

  <clause id="20315">
    <literal><![CDATA[
      T(x,(K(y,z) * (T(y,u) \ z)) \ w) = T(x,(z / T(y,u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(20175,a,20263,a)].">
      <j1 rule="hyper" parents="20175 20263"/>
    </justification>
  </clause>

  <clause id="20316">
    <literal><![CDATA[
      (x * (T(T(x,y),y) \ z)) \ u = (z \ u) * (K(x,y) * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,10112,a,b,20270,a)].">
      <j1 rule="hyper" parents="65 10112 20270"/>
    </justification>
  </clause>

  <clause id="20317">
    <literal><![CDATA[
      ((K(x,y) * z) \ u) * (K(x,y) * K(x,y)) = ((K(x,y) \ 1) * z) \ u
    ]]></literal>
    <justification jstring="[hyper(65,a,6587,a(flip),b,20270,a),flip(a)].">
      <j1 rule="hyper" parents="65 6587 20270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20318">
    <literal><![CDATA[
      K(x,y \ ((z * (K(u,w) * K(u,w))) * v5)) = K(x,(y \ (z * v5)) * (K(u,w) * K(u,w)))
    ]]></literal>
    <justification jstring="[para(20270(a,1),19482(a,2,2))].">
      <j1 rule="para" parents="20270 19482"/>
    </justification>
  </clause>

  <clause id="20319">
    <literal><![CDATA[
      K(x * ((y * z) \ K(u \ z,u)),w) = K(x / (y * T(z,u)),w)
    ]]></literal>
    <justification jstring="[hyper(14540,a,20272,a)].">
      <j1 rule="hyper" parents="14540 20272"/>
    </justification>
  </clause>

  <clause id="20320">
    <literal><![CDATA[
      K(x,L(T(y,z) * T(u,T(y \ 1,z)),w,v5)) = K(x,L(u / T(y \ 1,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(13930,a,20287,a),flip(a)].">
      <j1 rule="hyper" parents="13930 20287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20321">
    <literal><![CDATA[
      T(x,(y / T(z,y)) \ u) = T(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(5351(a,1),20315(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5351 20315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20322">
    <literal><![CDATA[
      T(x,(((y \ z) \ z) / T(u,T(y,z))) \ w) = T(x,(u \ ((y \ z) \ z)) \ w)
    ]]></literal>
    <justification jstring="[para(7482(a,1),20321(a,1,2,1,2))].">
      <j1 rule="para" parents="7482 20321"/>
    </justification>
  </clause>

  <clause id="20323">
    <literal><![CDATA[
      x \ (L(K(y,z),K(y,z),K(z,y) * u) * u) = (x \ (K(z,y) * u)) * (K(y,z) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,19966,a,b,20316,a)].">
      <j1 rule="hyper" parents="65 19966 20316"/>
    </justification>
  </clause>

  <clause id="20324">
    <literal><![CDATA[
      K(x,y * (y * ((z \ u) * (K(y,w) * K(y,w))))) = K(x,((y \ 1) * (T(T(y,w),w) \ z)) \ u)
    ]]></literal>
    <justification jstring="[para(20316(a,1),20296(a,1,2,2,2))].">
      <j1 rule="para" parents="20316 20296"/>
    </justification>
  </clause>

  <clause id="20325">
    <literal><![CDATA[
      K(x / ((y \ 1) * ((y \ z) * y)),u) = K(x / ((y \ 1) * T(z,y)),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,18102,a(flip),b,20319,a)].">
      <j1 rule="hyper" parents="65 18102 20319"/>
    </justification>
  </clause>

  <clause id="20326">
    <literal><![CDATA[
      K(x,(y * L(K(z,u),w,v5)) \ v6) = K(x,K(z,u) \ (y \ v6))
    ]]></literal>
    <justification jstring="[hyper(299,a,19109,a(flip),b,20051,a),flip(a)].">
      <j1 rule="hyper" parents="299 19109 20051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20327">
    <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(20051(a,2),19110(a,1))].">
      <j1 rule="para" parents="20051 19110"/>
    </justification>
  </clause>

  <clause id="20329">
    <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(18703(a,2),20326(a,1,2,1))].">
      <j1 rule="para" parents="18703 20326"/>
    </justification>
  </clause>

  <clause id="20330">
    <literal><![CDATA[
      K(x,(y \ K(z,u)) * w) = K(x,K(u,z) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(19658,a,20096,a)].">
      <j1 rule="hyper" parents="19658 20096"/>
    </justification>
  </clause>

  <clause id="20331">
    <literal><![CDATA[
      K(x,(K(y,z) / u) * w) = K(x,K(z,y) * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(16837,a,20330,a)].">
      <j1 rule="hyper" parents="16837 20330"/>
    </justification>
  </clause>

  <clause id="20332">
    <literal><![CDATA[
      K(x,y \ (K(z,u) * w)) = K(x,(y \ K(z,u)) * w)
    ]]></literal>
    <justification jstring="[hyper(299,a,20127,a,b,20330,a)].">
      <j1 rule="hyper" parents="299 20127 20330"/>
    </justification>
  </clause>

  <clause id="20333">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ w)) * K(x,K(u \ K(z,y),w)) = K(x,w * (u \ K(y,z)))
    ]]></literal>
    <justification jstring="[para(20330(a,1),19655(a,1,1))].">
      <j1 rule="para" parents="20330 19655"/>
    </justification>
  </clause>

  <clause id="20334">
    <literal><![CDATA[
      K(x,K(y \ 1,z) * (y \ u)) * K(x,K(u,y * K(z,y \ 1))) = K(x,u * T(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(20330(a,1),19827(a,1,1))].">
      <j1 rule="para" parents="20330 19827"/>
    </justification>
  </clause>

  <clause id="20335">
    <literal><![CDATA[
      K(x,K(y,z) * (y \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(20331(a,1),14550(a,1))].">
      <j1 rule="para" parents="20331 14550"/>
    </justification>
  </clause>

  <clause id="20336">
    <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(20332(a,1),20132(a,1))].">
      <j1 rule="para" parents="20332 20132"/>
    </justification>
  </clause>

  <clause id="20340">
    <literal><![CDATA[
      K(x,y) \ (L(K(y,x),z,u) \ w) = w * a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(16869(a,1),20114(a,2,2))].">
      <j1 rule="para" parents="16869 20114"/>
    </justification>
  </clause>

  <clause id="20341">
    <literal><![CDATA[
      K(x,y) \ (L(K(y,x),z,u) \ w) = a(K(y,x),z,u) \ w
    ]]></literal>
    <justification jstring="[hyper(299,a,18688,a,b,20340,a),flip(a)].">
      <j1 rule="hyper" parents="299 18688 20340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20342">
    <literal><![CDATA[
      K(x,L((K(y,z) * u) \ w,v5,v6)) = K(x,L(K(z,y) * (u \ w),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(11999,a,20122,a),flip(a)].">
      <j1 rule="hyper" parents="11999 20122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20343">
    <literal><![CDATA[
      K(x,T(y \ z,y)) = K(x,K(u,w) \ ((K(w,u) \ z) / y))
    ]]></literal>
    <justification jstring="[hyper(17129,a,20136,a)].">
      <j1 rule="hyper" parents="17129 20136"/>
    </justification>
  </clause>

  <clause id="20344">
    <literal><![CDATA[
      K(x,K(y,z) \ ((K(z,y) \ u) / w)) = K(x,u / w)
    ]]></literal>
    <justification jstring="[hyper(8215,a,20343,a),flip(a)].">
      <j1 rule="hyper" parents="8215 20343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20345">
    <literal><![CDATA[
      K(x,(K(y,z) \ u) / w) = K(x,K(y,z) \ (u / w))
    ]]></literal>
    <justification jstring="[para(5427(a,1),20344(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5427 20344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20346">
    <literal><![CDATA[
      K(x,K(y \ z,y) \ (z / u)) = K(x,(y * (z / y)) / u)
    ]]></literal>
    <justification jstring="[para(5461(a,1),20345(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5461 20345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20347">
    <literal><![CDATA[
      K(x,K(y,z) \ (y / u)) = K(x,(z * (y / z)) / u)
    ]]></literal>
    <justification jstring="[hyper(65,a,13939,a(flip),b,20346,a)].">
      <j1 rule="hyper" parents="65 13939 20346"/>
    </justification>
  </clause>

  <clause id="20348">
    <literal><![CDATA[
      K(x,(y * (z / y)) / u) = K(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[hyper(65,a,15812,a(flip),b,20347,a),flip(a)].">
      <j1 rule="hyper" parents="65 15812 20347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20349">
    <literal><![CDATA[
      K(x,(y * ((y * z) / y)) / u) = K(x,(z * y) / u)
    ]]></literal>
    <justification jstring="[hyper(299,a,17065,a(flip),b,20348,a),flip(a)].">
      <j1 rule="hyper" parents="299 17065 20348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20350">
    <literal><![CDATA[
      K(x,(T(y,z) * z) / u) = K(x,(z * y) / u)
    ]]></literal>
    <justification jstring="[para(223(a,1),20349(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="223 20349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20351">
    <literal><![CDATA[
      K(x,(y * z) / (u * y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(z,y) / u,u,y)) = w
    ]]></literal>
    <justification jstring="[para(20350(a,1),15516(a,1))].">
      <j1 rule="para" parents="20350 15516"/>
    </justification>
  </clause>

  <clause id="20352">
    <literal><![CDATA[
      K(x,(y * T(z \ u,z)) \ w) = K(x,(y * (u / z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,20099,a(flip),b,20139,a)].">
      <j1 rule="hyper" parents="65 20099 20139"/>
    </justification>
  </clause>

  <clause id="20353">
    <literal><![CDATA[
      K(x,(y * ((z * u) / z)) \ w) = K(x,(y * T(u,z)) \ w)
    ]]></literal>
    <justification jstring="[para(9(a,1),20352(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 20352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20354">
    <literal><![CDATA[
      K(x,(((((y * z) / y) * ((y * z) / y)) \ u) * T(z,y)) \ w) = K(x,((1 / ((y * z) / y)) * T(u,(y * z) / y)) \ w)
    ]]></literal>
    <justification jstring="[para(983(a,1),20353(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="983 20353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20355">
    <literal><![CDATA[
      K(x,(((((y * z) / y) * ((y * z) / y)) \ u) * T(z,y)) \ w) = K(x,((K(u,(y * z) / y) / ((y * z) / y)) * u) \ w)
    ]]></literal>
    <justification jstring="[para(14590(a,1),20353(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14590 20353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20356">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ ((z * y) * w))) = K(x,u \ (T(z * y,y) * w))
    ]]></literal>
    <justification jstring="[hyper(15803,a,20182,a)].">
      <j1 rule="hyper" parents="15803 20182"/>
    </justification>
  </clause>

  <clause id="20357">
    <literal><![CDATA[
      K(x,y \ (T(z,u \ w) \ v5)) = K(x,y \ (T(z,u * w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,20140,a(flip),b,20203,a)].">
      <j1 rule="hyper" parents="65 20140 20203"/>
    </justification>
  </clause>

  <clause id="20358">
    <literal><![CDATA[
      K(x,T(y,T(z,u \ w) \ v5) \ (T(z,u * w) \ v5)) = K(x,(T(z,u \ w) \ v5) / y)
    ]]></literal>
    <justification jstring="[hyper(13924,a,20357,a),flip(a)].">
      <j1 rule="hyper" parents="13924 20357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20359">
    <literal><![CDATA[
      K(x,y \ (T(z,u * (u / w)) * v5)) = K(x,y \ (T(z,w) * v5))
    ]]></literal>
    <justification jstring="[hyper(299,a,20181,a(flip),b,20226,a),flip(a)].">
      <j1 rule="hyper" parents="299 20181 20226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20360">
    <literal><![CDATA[
      K(x,y \ (T(z,u) * (w * (w / u)))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ ((w * (w / u)) * z)) = v5
    ]]></literal>
    <justification jstring="[para(20359(a,1),15911(a,1))].">
      <j1 rule="para" parents="20359 15911"/>
    </justification>
  </clause>

  <clause id="20361">
    <literal><![CDATA[
      K(x,y \ (T(z,u) * ((u \ w) * w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (((u \ w) * w) * z)) = v5
    ]]></literal>
    <justification jstring="[para(20359(a,1),15923(a,1))].">
      <j1 rule="para" parents="20359 15923"/>
    </justification>
  </clause>

  <clause id="20362">
    <literal><![CDATA[
      T(x,(y \ T(z,u \ (u \ w))) \ v5) = T(x,((y \ z) * K(w,z)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(299,a,20168,a,b,20241,a),flip(a)].">
      <j1 rule="hyper" parents="299 20168 20241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20363">
    <literal><![CDATA[
      T(x,y \ (z \ T(u,w \ v5))) = T(x,y \ (z \ T(u,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(65,a,20277,a(flip),b,20280,a),flip(a)].">
      <j1 rule="hyper" parents="65 20277 20280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20364">
    <literal><![CDATA[
      T(x,y \ (z \ T(a(u,u,u) * w,u \ 1))) = T(x,y \ (z \ T(w,u * 1)))
    ]]></literal>
    <justification jstring="[hyper(65,a,15741,a,b,20363,a)].">
      <j1 rule="hyper" parents="65 15741 20363"/>
    </justification>
  </clause>

  <clause id="20365">
    <literal><![CDATA[
      K(x,(T(y \ 1,z / y) * u) \ w) = K(x,(T(y \ 1,z) * u) \ w)
    ]]></literal>
    <justification jstring="[para(7153(a,2),20286(a,1,2,1,1))].">
      <j1 rule="para" parents="7153 20286"/>
    </justification>
  </clause>

  <clause id="20366">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ T(u,z * y)) = K(x,u / ((y \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(20298,a,20295,a)].">
      <j1 rule="hyper" parents="20298 20295"/>
    </justification>
  </clause>

  <clause id="20367">
    <literal><![CDATA[
      K(x,T(y,z * u) / ((u \ 1) * z)) = K(x,((u \ 1) * z) \ y)
    ]]></literal>
    <justification jstring="[hyper(16056,a,20366,a),flip(a)].">
      <j1 rule="hyper" parents="16056 20366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20369">
    <literal><![CDATA[
      K(x,(y \ z) * ((y \ z) * (z \ u))) = K(x,(((z / y) \ 1) * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,19076,a(flip),b,20299,a)].">
      <j1 rule="hyper" parents="65 19076 20299"/>
    </justification>
  </clause>

  <clause id="20370">
    <literal><![CDATA[
      T(x,T(1 / y,z) * u) = T(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,15830,a(flip),b,20314,a)].">
      <j1 rule="hyper" parents="65 15830 20314"/>
    </justification>
  </clause>

  <clause id="20371">
    <literal><![CDATA[
      T(x,T(y \ 1,z) * u) = T(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(17423,a,20370,a)].">
      <j1 rule="hyper" parents="17423 20370"/>
    </justification>
  </clause>

  <clause id="20372">
    <literal><![CDATA[
      T(x,T(y \ 1,z) \ u) = T(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(76(a,1),20370(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="76 20370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20373">
    <literal><![CDATA[
      T(x,((1 / y) * (z / y)) * (T(z,(1 / y) * (z / y)) \ u)) = T(x,T(y,y * z) \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,18263,a,b,20371,a)].">
      <j1 rule="hyper" parents="65 18263 20371"/>
    </justification>
  </clause>

  <clause id="20374">
    <literal><![CDATA[
      T(x,T(y \ z,u) \ (u \ w)) = T(x,((y \ z) \ 1) * (T(u,z \ y) \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,16877,a(flip),b,20371,a),flip(a)].">
      <j1 rule="hyper" parents="65 16877 20371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20375">
    <literal><![CDATA[
      K(T(x \ 1,y) * z,u) = u / T(u,T(x,y) \ z)
    ]]></literal>
    <justification jstring="[para(20371(a,1),5033(a,2,2))].">
      <j1 rule="para" parents="20371 5033"/>
    </justification>
  </clause>

  <clause id="20376">
    <literal><![CDATA[
      (x * T(y,T(z,u) \ w)) / (x * y) = K(y,T(T(z \ 1,u) * w,x))
    ]]></literal>
    <justification jstring="[para(20371(a,1),9466(a,1,1,2))].">
      <j1 rule="para" parents="20371 9466"/>
    </justification>
  </clause>

  <clause id="20377">
    <literal><![CDATA[
      K(T(x \ 1,y) * z,u) = K(T(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,5033,a,b,20375,a),flip(a)].">
      <j1 rule="hyper" parents="299 5033 20375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20378">
    <literal><![CDATA[
      K(T(x \ 1,y) \ z,u) = K(T(x,y) * z,u)
    ]]></literal>
    <justification jstring="[hyper(14715,a,20377,a),flip(a)].">
      <j1 rule="hyper" parents="14715 20377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20379">
    <literal><![CDATA[
      K(T(K(x,y) / z,u) \ w,v5) = K(T(z * K(y,x),u) * w,v5)
    ]]></literal>
    <justification jstring="[para(14326(a,1),20377(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="14326 20377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20380">
    <literal><![CDATA[
      K(x / T(y \ 1,z),u) = K(T(y,z) * x,T(u,y))
    ]]></literal>
    <justification jstring="[hyper(16680,a,20378,a)].">
      <j1 rule="hyper" parents="16680 20378"/>
    </justification>
  </clause>

  <clause id="20381">
    <literal><![CDATA[
      K(x / T(y \ 1,z),u) = K(x * T(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,16434,a(flip),b,20380,a),flip(a)].">
      <j1 rule="hyper" parents="299 16434 20380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20382">
    <literal><![CDATA[
      K(x * T(1 / y,z),u) = K(x / T(y,z),u)
    ]]></literal>
    <justification jstring="[para(79(a,1),20381(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 20381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20383">
    <literal><![CDATA[
      K(x * T(y \ 1,z),u) = K(x / T(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,5742,a(flip),b,20382,a)].">
      <j1 rule="hyper" parents="65 5742 20382"/>
    </justification>
  </clause>

  <clause id="20384">
    <literal><![CDATA[
      K((x / (y \ 1)) / T(x / (1 / y),z),u) = K(z,K(u,x * y))
    ]]></literal>
    <justification jstring="[hyper(17314,a,20383,a),flip(a)].">
      <j1 rule="hyper" parents="17314 20383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20385">
    <literal><![CDATA[
      K(x * T(y \ 1,z),u) = u / T(u,x / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,5033,a(flip),b,20383,a),flip(a)].">
      <j1 rule="hyper" parents="299 5033 20383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20386">
    <literal><![CDATA[
      T(x,y * T(z \ 1,u)) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[hyper(5062,a,20385,a)].">
      <j1 rule="hyper" parents="5062 20385"/>
    </justification>
  </clause>

  <clause id="20387">
    <literal><![CDATA[
      K(T(K(x,y) / z,u) \ w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(K(y,x) * (T(z,u) * w),v5) = v6
    ]]></literal>
    <justification jstring="[para(20379(a,2),19214(a,1))].">
      <j1 rule="para" parents="20379 19214"/>
    </justification>
  </clause>

  <clause id="20388">
    <literal><![CDATA[
      K(x,K(y * z,y * (u \ z))) = K(u,K(x,z * y))
    ]]></literal>
    <justification jstring="[hyper(65,a,19873,a(flip),b,20384,a)].">
      <j1 rule="hyper" parents="65 19873 20384"/>
    </justification>
  </clause>

  <clause id="20389">
    <literal><![CDATA[
      K(x,K(y,z * u)) * K(y,L(T(x,u),u,z)) = K(y,(u * z) \ ((u * x) * z))
    ]]></literal>
    <justification jstring="[para(20388(a,1),19517(a,1,1))].">
      <j1 rule="para" parents="20388 19517"/>
    </justification>
  </clause>

  <clause id="20390">
    <literal><![CDATA[
      ((x \ y) \ (K(y,x) * z)) * (K(x,y) * K(x,y)) = ((K(x,y) \ 1) * (x \ y)) \ z
    ]]></literal>
    <justification jstring="[para(13454(a,1),20317(a,1,1))].">
      <j1 rule="para" parents="13454 20317"/>
    </justification>
  </clause>

  <clause id="20391">
    <literal><![CDATA[
      K(x / T((y \ 1) * z,y),u) = K(x / ((y \ 1) * T(z,y)),u)
    ]]></literal>
    <justification jstring="[para(2046(a,1),20325(a,1,1,2))].">
      <j1 rule="para" parents="2046 20325"/>
    </justification>
  </clause>

  <clause id="20392">
    <literal><![CDATA[
      K(x / T((y \ 1) * z,y),u) = K(x / (z * (y \ 1)),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,17994,a(flip),b,20391,a),flip(a)].">
      <j1 rule="hyper" parents="299 17994 20391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20393">
    <literal><![CDATA[
      K(x,L((y \ K(z,u)) * w,v5,v6)) = K(x,L(K(z,u) * (y \ w),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(18035,a,20342,a)].">
      <j1 rule="hyper" parents="18035 20342"/>
    </justification>
  </clause>

  <clause id="20394">
    <literal><![CDATA[
      K(x,y \ (T(z * u,u) * w)) = K(x,y \ (T(z * u,z) * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,20183,a(flip),b,20356,a),flip(a)].">
      <j1 rule="hyper" parents="65 20183 20356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20395">
    <literal><![CDATA[
      T(x,(y \ T(z,u \ (u \ w))) \ v5) = T(x,(y \ (z * K(w,z))) \ v5)
    ]]></literal>
    <justification jstring="[para(19688(a,2),20362(a,2,2,1))].">
      <j1 rule="para" parents="19688 20362"/>
    </justification>
  </clause>

  <clause id="20396">
    <literal><![CDATA[
      T(x,(y \ T(z,u \ (u \ (z \ w)))) \ v5) = T(x,(y \ (w / (w / z))) \ v5)
    ]]></literal>
    <justification jstring="[para(19689(a,2),20362(a,2,2,1))].">
      <j1 rule="para" parents="19689 20362"/>
    </justification>
  </clause>

  <clause id="20397">
    <literal><![CDATA[
      K(x,(T(y \ 1,z * y) * u) \ w) = K(x,(T(y \ 1,z) * u) \ w)
    ]]></literal>
    <justification jstring="[para(11(a,1),20365(a,1,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11 20365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20398">
    <literal><![CDATA[
      K(x,(y \ z) * ((y \ z) * (z \ u))) = K(x,(y * ((y \ z) \ 1)) \ u)
    ]]></literal>
    <justification jstring="[hyper(299,a,18055,a(flip),b,20369,a),flip(a)].">
      <j1 rule="hyper" parents="299 18055 20369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20399">
    <literal><![CDATA[
      K(x,T(T(y \ 1,z) * u,w)) = K(x,T(T(y,z) \ u,w))
    ]]></literal>
    <justification jstring="[hyper(9469,a,20376,a),flip(a)].">
      <j1 rule="hyper" parents="9469 20376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20400">
    <literal><![CDATA[
      K(x,T(T(T(y \ 1,z),y) * u,w)) = K(x,T(T(y,z) \ u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,13993,a,b,20399,a)].">
      <j1 rule="hyper" parents="65 13993 20399"/>
    </justification>
  </clause>

  <clause id="20401">
    <literal><![CDATA[
      K(x,T(T(1 / y,z) * u,w)) = K(x,T(T(y,z) \ u,w))
    ]]></literal>
    <justification jstring="[para(1698(a,1),20400(a,1,2,1,1))].">
      <j1 rule="para" parents="1698 20400"/>
    </justification>
  </clause>

  <clause id="20402">
    <literal><![CDATA[
      K(x,T(T(y \ 1,z) \ u,w)) = K(x,T(T(y,z) * u,w))
    ]]></literal>
    <justification jstring="[para(76(a,1),20401(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="76 20401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20403">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ (z * ((y * y) \ u))) = K(x,L(K(y,z) * (y \ u),y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,19747,a,b,20393,a)].">
      <j1 rule="hyper" parents="65 19747 20393"/>
    </justification>
  </clause>

  <clause id="20404">
    <literal><![CDATA[
      K(x,(y \ z) * ((y \ z) * (z \ u))) = K(x,(y * (1 / (y \ z))) \ u)
    ]]></literal>
    <justification jstring="[hyper(299,a,5656,a,b,20398,a),flip(a)].">
      <j1 rule="hyper" parents="299 5656 20398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20405">
    <literal><![CDATA[
      K(x,(y \ L(y,z,z)) * ((L(y,z,z) \ u) * a(y,z,z))) = K(x,(y * (1 / (y \ L(y,z,z)))) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,19479,a(flip),b,20404,a)].">
      <j1 rule="hyper" parents="65 19479 20404"/>
    </justification>
  </clause>

  <clause id="20406">
    <literal><![CDATA[
      K(x,(y * (z * K(u,w))) \ v5) = K(x,K(w,u) * ((y * z) \ v5))
    ]]></literal>
    <justification jstring="[hyper(19085,a,20102,a),flip(a)].">
      <j1 rule="hyper" parents="19085 20102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20408">
    <literal><![CDATA[
      K(x,(y * T((z / u) * w,K(u,u \ z))) \ v5) = K(x,K(u \ z,u) * ((y * ((u \ z) * w)) \ v5))
    ]]></literal>
    <justification jstring="[para(7283(a,2),20406(a,1,2,1,2))].">
      <j1 rule="para" parents="7283 20406"/>
    </justification>
  </clause>

  <clause id="20409">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * ((u * w) \ v5)) = K(x,((K(z,y) * u) * w) \ v5)
    ]]></literal>
    <justification jstring="[para(11929(a,1),20126(a,1,2,1))].">
      <j1 rule="para" parents="11929 20126"/>
    </justification>
  </clause>

  <clause id="20410">
    <literal><![CDATA[
      K(x,((K(y,z) * u) * w) \ v5) = K(x,K(z,y) * ((u * w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(19085,a,20409,a),flip(a)].">
      <j1 rule="hyper" parents="19085 20409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20412">
    <literal><![CDATA[
      K(x,K(y,z) * (((y \ u) * w) \ v5)) = K(x,((T(y,z) \ u) * w) \ v5)
    ]]></literal>
    <justification jstring="[para(5383(a,1),20410(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5383 20410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20413">
    <literal><![CDATA[
      K(x,y \ (T(z,K(u,w)) \ v5)) = K(x,K(u,z) * (y \ (T(z,u) \ v5)))
    ]]></literal>
    <justification jstring="[hyper(16823,a,20130,a),flip(a)].">
      <j1 rule="hyper" parents="16823 20130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20414">
    <literal><![CDATA[
      K(x,y \ (T(T(z,u),u) \ w)) = K(x,y \ (T(z,K(u,v5)) \ w))
    ]]></literal>
    <justification jstring="[hyper(299,a,20129,a(flip),b,20413,a)].">
      <j1 rule="hyper" parents="299 20129 20413"/>
    </justification>
  </clause>

  <clause id="20415">
    <literal><![CDATA[
      K(x,y \ (T(T(z,u),u) \ w)) = K(x,y \ (z \ w))
    ]]></literal>
    <justification jstring="[hyper(299,a,18815,a(flip),b,20414,a),flip(a)].">
      <j1 rule="hyper" parents="299 18815 20414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20417">
    <literal><![CDATA[
      K(x,y \ (T(z \ u,z) \ w)) = K(x,y \ ((u / z) \ w))
    ]]></literal>
    <justification jstring="[para(109(a,1),20415(a,1,2,2,1,1))].">
      <j1 rule="para" parents="109 20415"/>
    </justification>
  </clause>

  <clause id="20418">
    <literal><![CDATA[
      K(x,y \ (T((1 / z) / u,z * z) \ w)) = K(x,y \ (((z / u) / (z * z)) \ w))
    ]]></literal>
    <justification jstring="[para(765(a,1),20417(a,1,2,2,1,1))].">
      <j1 rule="para" parents="765 20417"/>
    </justification>
  </clause>

  <clause id="20420">
    <literal><![CDATA[
      K(x \ (y * T(z,T(u \ w,v5))),v6) = K(x \ (y * T(z,u \ (w * z))),v6)
    ]]></literal>
    <justification jstring="[para(8415(a,1),20164(a,2,1,2,2))].">
      <j1 rule="para" parents="8415 20164"/>
    </justification>
  </clause>

  <clause id="20421">
    <literal><![CDATA[
      K(x,T(y,z / ((u \ 1) * w)) * v5) = K(x,T(y,w * (u \ z)) * v5)
    ]]></literal>
    <justification jstring="[hyper(20195,a,20230,a),flip(a)].">
      <j1 rule="hyper" parents="20195 20230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20422">
    <literal><![CDATA[
      K(x,T(y,((z \ 1) * u) * w) * v5) = K(x,T(y,u * (z \ w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,17960,a(flip),b,20421,a)].">
      <j1 rule="hyper" parents="65 17960 20421"/>
    </justification>
  </clause>

  <clause id="20423">
    <literal><![CDATA[
      K(x,T(y,(z * u) * w) * v5) = K(x,T(y,u * (z \ w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(18151,a,20422,a)].">
      <j1 rule="hyper" parents="18151 20422"/>
    </justification>
  </clause>

  <clause id="20424">
    <literal><![CDATA[
      K(x,T(y,z * ((u \ 1) \ w)) * v5) = K(x,T(y,w * (u * z)) * v5)
    ]]></literal>
    <justification jstring="[hyper(18149,a,20423,a),flip(a)].">
      <j1 rule="hyper" parents="18149 20423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20425">
    <literal><![CDATA[
      K(x,T(y,(z \ u) * w) * v5) = K(x,T(y,u * (z * w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,18010,a(flip),b,20424,a)].">
      <j1 rule="hyper" parents="65 18010 20424"/>
    </justification>
  </clause>

  <clause id="20426">
    <literal><![CDATA[
      K(x,T(y,z) \ ((u \ ((z * y) / z)) * w)) = K(x,y \ ((u \ y) * w))
    ]]></literal>
    <justification jstring="[para(5351(a,1),20269(a,2,2))].">
      <j1 rule="para" parents="5351 20269"/>
    </justification>
  </clause>

  <clause id="20427">
    <literal><![CDATA[
      T(x,(((y \ z) \ z) / T(u,y)) \ w) = T(x,(u \ ((y \ z) \ z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,20313,a(flip),b,20322,a)].">
      <j1 rule="hyper" parents="65 20313 20322"/>
    </justification>
  </clause>

  <clause id="20429">
    <literal><![CDATA[
      T(x,(((y \ z) \ z) / T(u,y)) \ w) = T(x,(u \ T(y,y \ z)) \ w)
    ]]></literal>
    <justification jstring="[para(108(a,2),20427(a,2,2,1,2))].">
      <j1 rule="para" parents="108 20427"/>
    </justification>
  </clause>

  <clause id="20430">
    <literal><![CDATA[
      T(x,(y \ T(z,z \ u)) \ w) = T(x,(y \ ((z \ u) \ u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,20427,a(flip),b,20429,a),flip(a)].">
      <j1 rule="hyper" parents="65 20427 20429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20431">
    <literal><![CDATA[
      T(x,T(y \ z,u) \ (u \ w)) = T(x,((y \ z) \ 1) * (T(u,z * y) \ w))
    ]]></literal>
    <justification jstring="[hyper(299,a,19280,a(flip),b,20374,a),flip(a)].">
      <j1 rule="hyper" parents="299 19280 20374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20432">
    <literal><![CDATA[
      T(x,(y \ (z / (z / u))) \ w) = T(x,(y \ (u * K(u \ z,u))) \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,20395,a(flip),b,20396,a),flip(a)].">
      <j1 rule="hyper" parents="65 20395 20396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20433">
    <literal><![CDATA[
      T(x,(y \ T(z,z \ u)) \ w) = T(x,(y \ (u / (u / z))) \ w)
    ]]></literal>
    <justification jstring="[para(5427(a,1),20396(a,1,2,1,2,2))].">
      <j1 rule="para" parents="5427 20396"/>
    </justification>
  </clause>

  <clause id="20434">
    <literal><![CDATA[
      K(x \ (y * T(z,T(u \ w,v5))),v6) = K(x \ (y * T(z,u * (w * z))),v6)
    ]]></literal>
    <justification jstring="[hyper(299,a,17568,a(flip),b,20420,a),flip(a)].">
      <j1 rule="hyper" parents="299 17568 20420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20435">
    <literal><![CDATA[
      T(x,T(y \ z,u) \ (u \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,(y \ z) \ (T(u,z * y) \ w)) = v5
    ]]></literal>
    <justification jstring="[para(20431(a,2),14304(a,1))].">
      <j1 rule="para" parents="20431 14304"/>
    </justification>
  </clause>

  <clause id="20436">
    <literal><![CDATA[
      K(x \ (y * T(z,u * (w * z))),v5) = K(x \ (y * T(z,u \ w)),v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,20109,a(flip),b,20434,a),flip(a)].">
      <j1 rule="hyper" parents="65 20109 20434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20437">
    <literal><![CDATA[
      K(x \ (y * T(z,u * (w * z))),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x \ (y * T(z,u * w)),v5) = v6
    ]]></literal>
    <justification jstring="[para(20436(a,2),17569(a,1))].">
      <j1 rule="para" parents="20436 17569"/>
    </justification>
  </clause>

  <clause id="20439">
    <literal><![CDATA[
      T(x,y \ (z \ T(a(u,u,u) * w,u \ 1))) = T(x,y \ (z \ T(w,u)))
    ]]></literal>
    <justification jstring="[para(8(a,1),20364(a,2,2,2,2,2))].">
      <j1 rule="para" parents="8 20364"/>
    </justification>
  </clause>

  <clause id="20440">
    <literal><![CDATA[
      K(x,K(y,z * u)) * K(x,L(T(y,u),u,z)) = K(x,(u * z) \ ((u * y) * z))
    ]]></literal>
    <justification jstring="[para(7983(a,1),20389(a,1,1))].">
      <j1 rule="para" parents="7983 20389"/>
    </justification>
  </clause>

  <clause id="20441">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ (z * ((y * y) \ u))) = K(x,(T(z,y) * y) \ (z * u))
    ]]></literal>
    <justification jstring="[para(11636(a,1),20403(a,2,2))].">
      <j1 rule="para" parents="11636 20403"/>
    </justification>
  </clause>

  <clause id="20442">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ (z * ((y * y) \ u))) = K(x,(y * z) \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(299,a,15870,a(flip),b,20441,a),flip(a)].">
      <j1 rule="hyper" parents="299 15870 20441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20443">
    <literal><![CDATA[
      K(x,(y \ z) \ ((((1 / y) \ 1) \ (y \ z)) * u)) = K(x,(y * z) \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,19926,a,b,20442,a)].">
      <j1 rule="hyper" parents="65 19926 20442"/>
    </justification>
  </clause>

  <clause id="20444">
    <literal><![CDATA[
      K(x,(y \ z) \ ((y \ (y \ z)) * u)) = K(x,(y * z) \ (z * u))
    ]]></literal>
    <justification jstring="[para(79(a,1),20443(a,1,2,2,1,1))].">
      <j1 rule="para" parents="79 20443"/>
    </justification>
  </clause>

  <clause id="20445">
    <literal><![CDATA[
      K(x,T(y,T(z,u)) \ ((((u * z) / u) \ (((u * z) / u) \ (y * (z * K(u,z))))) * w)) = K(x,(((u * z) / u) * (y * (z * K(u,z)))) \ ((y * (z * K(u,z))) * w))
    ]]></literal>
    <justification jstring="[para(10209(a,1),20444(a,1,2,1))].">
      <j1 rule="para" parents="10209 20444"/>
    </justification>
  </clause>

  <clause id="20446">
    <literal><![CDATA[
      K(x,L(T(T(y,z),u * z),z,u)) = K(x,(z * u) \ ((z * y) * u))
    ]]></literal>
    <justification jstring="[hyper(19921,a,20440,a)].">
      <j1 rule="hyper" parents="19921 20440"/>
    </justification>
  </clause>

  <clause id="20447">
    <literal><![CDATA[
      K(x,(y * (z * u)) / (y * u)) = K(x,(u * y) \ ((u * z) * y))
    ]]></literal>
    <justification jstring="[hyper(9907,a,20446,a)].">
      <j1 rule="hyper" parents="9907 20446"/>
    </justification>
  </clause>

  <clause id="20448">
    <literal><![CDATA[
      K(x,((y \ z) * y) \ (((y \ z) * u) * y)) = K(x,(y * (u * (y \ z))) / z)
    ]]></literal>
    <justification jstring="[para(10(a,1),20447(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 20447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20449">
    <literal><![CDATA[
      K(x,(y * (z * (y \ u))) / u) = K(x,u \ (((u / y) * z) * y))
    ]]></literal>
    <justification jstring="[para(11717(a,1),20448(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11717 20448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20450">
    <literal><![CDATA[
      x * K(y,x \ (((x / z) * u) * z)) = ((x / z) * K(y,u)) * z
    ]]></literal>
    <justification jstring="[para(20449(a,1),16659(a,1,2))].">
      <j1 rule="para" parents="20449 16659"/>
    </justification>
  </clause>

  <clause id="20451">
    <literal><![CDATA[
      K(K(x,y) * ((z * y) \ u),w) = K((z * T(y,x)) \ u,w)
    ]]></literal>
    <justification jstring="[para(11(a,1),20118(a,1,1,2))].">
      <j1 rule="para" parents="11 20118"/>
    </justification>
  </clause>

  <clause id="20452">
    <literal><![CDATA[
      K(((x * y) * T(y,x)) \ z,u) = K((y * (x * y)) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,13897,a(flip),b,20451,a),flip(a)].">
      <j1 rule="hyper" parents="65 13897 20451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20454">
    <literal><![CDATA[
      K(((x * y) * x) \ z,u) = K((x * (y * x)) \ z,u)
    ]]></literal>
    <justification jstring="[para(886(a,1),20452(a,1,1,1))].">
      <j1 rule="para" parents="886 20452"/>
    </justification>
  </clause>

  <clause id="20455">
    <literal><![CDATA[
      T(x,y / T(T(z \ ((z \ 1) \ u),z),1 / z)) = T(x,y / (z \ ((1 / z) \ u)))
    ]]></literal>
    <justification jstring="[para(1663(a,1),20229(a,2,2,2))].">
      <j1 rule="para" parents="1663 20229"/>
    </justification>
  </clause>

  <clause id="20456">
    <literal><![CDATA[
      K(x,L(T(y,z) * T(u,y \ 1),w,v5)) = K(x,L(u / T(y \ 1,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(16934,a,20320,a)].">
      <j1 rule="hyper" parents="16934 20320"/>
    </justification>
  </clause>

  <clause id="20457">
    <literal><![CDATA[
      K(x,L(T(y,z) * T(u,y * 1),w,v5)) = K(x,L(u / T(y \ 1,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(17518,a,20456,a)].">
      <j1 rule="hyper" parents="17518 20456"/>
    </justification>
  </clause>

  <clause id="20458">
    <literal><![CDATA[
      K(x,L(y / T(z \ 1,u),w,v5)) = K(x,L(T(z,u) * T(y,z),w,v5))
    ]]></literal>
    <justification jstring="[para(8(a,1),20457(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8 20457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20459">
    <literal><![CDATA[
      K(x,L(y / T(z \ 1,u),w,v5)) = K(x,L(K(z,u) * (y * z),w,v5))
    ]]></literal>
    <justification jstring="[para(5353(a,2),20458(a,2,2,1))].">
      <j1 rule="para" parents="5353 20458"/>
    </justification>
  </clause>

  <clause id="20460">
    <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(299,a,16924,a(flip),b,20459,a),flip(a)].">
      <j1 rule="hyper" parents="299 16924 20459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20461">
    <literal><![CDATA[
      K(x,L(y / (z \ K(u,z \ 1)),w,v5)) = K(x,L(y * T(z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,19402,a,b,20460,a)].">
      <j1 rule="hyper" parents="65 19402 20460"/>
    </justification>
  </clause>

  <clause id="20462">
    <literal><![CDATA[
      K(x,L(y * (K(z \ 1,u) * z),w,v5)) = K(x,L(y * T(z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(14795,a,20461,a)].">
      <j1 rule="hyper" parents="14795 20461"/>
    </justification>
  </clause>

  <clause id="20463">
    <literal><![CDATA[
      K(x,L(y * (z * K(z \ 1,u)),w,v5)) = K(x,L(y * T(z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(1508(a,1),20462(a,1,2,1,2))].">
      <j1 rule="para" parents="1508 20462"/>
    </justification>
  </clause>

  <clause id="20464">
    <literal><![CDATA[
      K(x,L(y * ((z / u) * K((z / u) \ 1,u)),w,v5)) = K(x,L(y * (u \ z),w,v5))
    ]]></literal>
    <justification jstring="[para(109(a,1),20463(a,2,2,1,2))].">
      <j1 rule="para" parents="109 20463"/>
    </justification>
  </clause>

  <clause id="20465">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ w)) * K(x,K(w,u * K(z,y))) = K(x,w * (u \ K(y,z)))
    ]]></literal>
    <justification jstring="[para(16254(a,1),20333(a,1,2))].">
      <j1 rule="para" parents="16254 20333"/>
    </justification>
  </clause>

  <clause id="20466">
    <literal><![CDATA[
      K(x,y \ (((z / u) / (z * z)) \ w)) = K(x,y \ (((1 / z) / u) \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,20204,a(flip),b,20418,a),flip(a)].">
      <j1 rule="hyper" parents="65 20204 20418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20468">
    <literal><![CDATA[
      K(x,y \ ((z * z) * ((z / u) \ w))) = K(x,y \ (((1 / z) / u) \ w))
    ]]></literal>
    <justification jstring="[para(416(a,1),20466(a,1,2,2))].">
      <j1 rule="para" parents="416 20466"/>
    </justification>
  </clause>

  <clause id="20469">
    <literal><![CDATA[
      K(x,y * (y * (z \ ((y / u) \ w)))) = K(x,z \ (((1 / y) / u) \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,20294,a(flip),b,20468,a)].">
      <j1 rule="hyper" parents="65 20294 20468"/>
    </justification>
  </clause>

  <clause id="20470">
    <literal><![CDATA[
      T(x,y / T(T(z \ ((z \ 1) \ u),z),z * 1)) = T(x,y / (z \ ((1 / z) \ u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,17517,a(flip),b,20455,a)].">
      <j1 rule="hyper" parents="65 17517 20455"/>
    </justification>
  </clause>

  <clause id="20471">
    <literal><![CDATA[
      K(x,L(y * ((z / u) * K(z \ u,u)),w,v5)) = K(x,L(y * (u \ z),w,v5))
    ]]></literal>
    <justification jstring="[para(7002(a,1),20464(a,1,2,1,2,2))].">
      <j1 rule="para" parents="7002 20464"/>
    </justification>
  </clause>

  <clause id="20472">
    <literal><![CDATA[
      K(x,L(y * (z / T(u,z \ u)),w,v5)) = K(x,L(y * (u \ z),w,v5))
    ]]></literal>
    <justification jstring="[para(7189(a,1),20471(a,1,2,1,2))].">
      <j1 rule="para" parents="7189 20471"/>
    </justification>
  </clause>

  <clause id="20473">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ w)) * K(x,K(w,u)) = K(x,w * (u \ K(y,z)))
    ]]></literal>
    <justification jstring="[para(17133(a,1),20465(a,1,2))].">
      <j1 rule="para" parents="17133 20465"/>
    </justification>
  </clause>

  <clause id="20474">
    <literal><![CDATA[
      K(x,y * (z \ K(u,u \ w))) = K(x,K(u,w) * (z \ y)) * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(15821(a,1),20473(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15821 20473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20476">
    <literal><![CDATA[
      K(x,y * (z \ K(u,u \ w))) = K(x,y * (z \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(299,a,20473,a(flip),b,20474,a),flip(a)].">
      <j1 rule="hyper" parents="299 20473 20474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20477">
    <literal><![CDATA[
      K(x,y * (z \ K(u * w,u))) = K(x,y * (z \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(19752,a,20476,a)].">
      <j1 rule="hyper" parents="19752 20476"/>
    </justification>
  </clause>

  <clause id="20478">
    <literal><![CDATA[
      K(x,y / (z / T(u,u \ w))) = K(x,y * ((z / u) \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,16906,a(flip),b,20476,a)].">
      <j1 rule="hyper" parents="65 16906 20476"/>
    </justification>
  </clause>

  <clause id="20479">
    <literal><![CDATA[
      K(x,y * (z \ K(u * w,u))) = K(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(299,a,19649,a,b,20477,a),flip(a)].">
      <j1 rule="hyper" parents="299 19649 20477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20480">
    <literal><![CDATA[
      K(x,y / T((z / (z / u)) * w,u)) = K(x,y * ((w * u) \ K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,19735,a,b,20479,a)].">
      <j1 rule="hyper" parents="65 19735 20479"/>
    </justification>
  </clause>

  <clause id="20481">
    <literal><![CDATA[
      K(x,((y / (y / z)) * u) / w) = K(x,(z * u) * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(65,a,19726,a,b,20479,a)].">
      <j1 rule="hyper" parents="65 19726 20479"/>
    </justification>
  </clause>

  <clause id="20482">
    <literal><![CDATA[
      K(x,y * (L(z / u,u,u) \ 1)) = K(x,y * (((u \ 1) * z) \ K(z,u)))
    ]]></literal>
    <justification jstring="[para(17060(a,1),20479(a,1,2,2))].">
      <j1 rule="para" parents="17060 20479"/>
    </justification>
  </clause>

  <clause id="20483">
    <literal><![CDATA[
      K(x,y / (z / T(u,u \ w))) = K(x,y / (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(299,a,16906,a(flip),b,20478,a),flip(a)].">
      <j1 rule="hyper" parents="299 16906 20478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20484">
    <literal><![CDATA[
      K(x,((y / (y / z)) * u) / (w * z)) = K(x,(z * u) / (w * T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(299,a,16904,a(flip),b,20481,a),flip(a)].">
      <j1 rule="hyper" parents="299 16904 20481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20485">
    <literal><![CDATA[
      K(x,y / T((z / (z / u)) * w,u)) = K(x,y / (w * T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(299,a,16904,a(flip),b,20480,a),flip(a)].">
      <j1 rule="hyper" parents="299 16904 20480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20486">
    <literal><![CDATA[
      K(x,y / (z * (u * K(u \ w,u)))) = K(x,y / (z * T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,18014,a(flip),b,20485,a)].">
      <j1 rule="hyper" parents="65 18014 20485"/>
    </justification>
  </clause>

  <clause id="20487">
    <literal><![CDATA[
      K(x,y / (z * ((u \ w) \ w))) = K(x,y / (z * T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,19680,a,b,20486,a)].">
      <j1 rule="hyper" parents="65 19680 20486"/>
    </justification>
  </clause>

  <clause id="20488">
    <literal><![CDATA[
      K(x,(y * ((z \ u) \ u)) \ w) = K(x,K(w,y * z)) * K(x,w / (y * T(z,u)))
    ]]></literal>
    <justification jstring="[para(20487(a,1),17168(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20487 17168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20489">
    <literal><![CDATA[
      K(x,y * (L(z / u,u,u) \ 1)) = K(x,y / ((u \ 1) * T(z,u)))
    ]]></literal>
    <justification jstring="[hyper(299,a,19650,a(flip),b,20482,a),flip(a)].">
      <j1 rule="hyper" parents="299 19650 20482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20490">
    <literal><![CDATA[
      K(x,y * (L(z / u,u,u) \ 1)) = K(x,y / (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(299,a,17966,a(flip),b,20489,a),flip(a)].">
      <j1 rule="hyper" parents="299 17966 20489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20491">
    <literal><![CDATA[
      K(x,y / L(z / u,u,u)) = K(x,y / (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(14626,a,20490,a)].">
      <j1 rule="hyper" parents="14626 20490"/>
    </justification>
  </clause>

  <clause id="20492">
    <literal><![CDATA[
      K(x,y / L(K(z,u) * (u / w),w,w)) = K(x,y / (((z * u) / z) * (w \ 1)))
    ]]></literal>
    <justification jstring="[para(14662(a,1),20491(a,1,2,2,1))].">
      <j1 rule="para" parents="14662 20491"/>
    </justification>
  </clause>

  <clause id="20493">
    <literal><![CDATA[
      K(x,y * (L(z / u,u,u) \ K(u,z))) = K(x,y / (((u * z) / u) * (u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(19753,a,20492,a)].">
      <j1 rule="hyper" parents="19753 20492"/>
    </justification>
  </clause>

  <clause id="20494">
    <literal><![CDATA[
      K(x,y * (L(z / u,u,u) \ K(u,z))) = K(x,y / ((u * z) / (u * u)))
    ]]></literal>
    <justification jstring="[para(1245(a,1),20493(a,2,2,2))].">
      <j1 rule="para" parents="1245 20493"/>
    </justification>
  </clause>

  <clause id="20495">
    <literal><![CDATA[
      K(x,y * (L(z / u,u,u) \ K(u,z))) = K(x,y / (u * (z / (u * u))))
    ]]></literal>
    <justification jstring="[para(849(a,1),20494(a,2,2,2))].">
      <j1 rule="para" parents="849 20494"/>
    </justification>
  </clause>

  <clause id="20496">
    <literal><![CDATA[
      K(x,y * (L(z / u,u,u) \ K(u,z))) = K(x,y * ((u * z) \ (u * u)))
    ]]></literal>
    <justification jstring="[hyper(299,a,17499,a(flip),b,20495,a),flip(a)].">
      <j1 rule="hyper" parents="299 17499 20495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20497">
    <literal><![CDATA[
      K(x,y * (L(z / u,u,u) \ K(u,z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / ((u \ 1) * z)) = w
    ]]></literal>
    <justification jstring="[para(20496(a,2),17301(a,1))].">
      <j1 rule="para" parents="20496 17301"/>
    </justification>
  </clause>

  <clause id="20498">
    <literal><![CDATA[
      T(x,y / T(T(z \ ((z \ 1) \ u),z),z)) = T(x,y / (z \ ((1 / z) \ u)))
    ]]></literal>
    <justification jstring="[para(8(a,1),20470(a,1,2,2,2))].">
      <j1 rule="para" parents="8 20470"/>
    </justification>
  </clause>

  <clause id="20499">
    <literal><![CDATA[
      T(x,y / (z \ ((1 / z) \ u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y / (z \ ((z \ 1) \ u))) = w
    ]]></literal>
    <justification jstring="[para(20498(a,1),16610(a,1))].">
      <j1 rule="para" parents="20498 16610"/>
    </justification>
  </clause>

  <clause id="20500">
    <literal><![CDATA[
      K(x,(y * ((z \ u) \ u)) \ w) = K(x,(y * T(z,u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(299,a,17167,a(flip),b,20488,a),flip(a)].">
      <j1 rule="hyper" parents="299 17167 20488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20501">
    <literal><![CDATA[
      K(x,(y * T(z,u * z)) \ w) = K(x,(y * T(z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(4452(a,2),20500(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="4452 20500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20502">
    <literal><![CDATA[
      K(x,(y * T(z \ 1,u * z)) \ w) = K(x,(y * T(z \ 1,u)) \ w)
    ]]></literal>
    <justification jstring="[para(6191(a,2),20500(a,1,2,1,2))].">
      <j1 rule="para" parents="6191 20500"/>
    </justification>
  </clause>

  <clause id="20503">
    <literal><![CDATA[
      K(x,T(T(y,y * T(z \ 1,u * z)) * T(z \ 1,u * z),y) \ w) = K(x,(y * T(z \ 1,u)) \ w)
    ]]></literal>
    <justification jstring="[para(4316(a,2),20502(a,1,2,1))].">
      <j1 rule="para" parents="4316 20502"/>
    </justification>
  </clause>

  <clause id="20504">
    <literal><![CDATA[
      K(x,L(T(y,z) \ u,T(z,y),z * y)) = K(x,z \ ((z \ y) \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,15806,a(flip),b,20289,a),flip(a)].">
      <j1 rule="hyper" parents="65 15806 20289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20506">
    <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(65,a,18738,a(flip),b,20329,a)].">
      <j1 rule="hyper" parents="65 18738 20329"/>
    </justification>
  </clause>

  <clause id="20507">
    <literal><![CDATA[
      K(x,K(y,z) \ ((K(u,w) \ v5) \ v6)) = K(x,K(y,z) \ (v5 \ (K(w,u) \ v6)))
    ]]></literal>
    <justification jstring="[hyper(20327,a,20506,a),flip(a)].">
      <j1 rule="hyper" parents="20327 20506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20508">
    <literal><![CDATA[
      K(x,K(y,z) \ (u \ (K(z,L(y,w,v5)) \ v6))) = K(x,u \ v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,20266,a(flip),b,20507,a),flip(a)].">
      <j1 rule="hyper" parents="65 20266 20507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20509">
    <literal><![CDATA[
      K(x,K(y,z) \ (u \ (L(K(z,y),w,v5) \ v6))) = K(x,u \ v6)
    ]]></literal>
    <justification jstring="[para(7810(a,1),20508(a,1,2,2,2,1))].">
      <j1 rule="para" parents="7810 20508"/>
    </justification>
  </clause>

  <clause id="20510">
    <literal><![CDATA[
      K(x,y \ (K(z,u) \ (L(K(u,z),w,v5) \ v6))) = K(x,y \ v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,20094,a(flip),b,20509,a)].">
      <j1 rule="hyper" parents="65 20094 20509"/>
    </justification>
  </clause>

  <clause id="20511">
    <literal><![CDATA[
      K(x,y \ (a(K(z,u),w,v5) \ v6)) = K(x,y \ v6)
    ]]></literal>
    <justification jstring="[para(20341(a,1),20510(a,1,2,2))].">
      <j1 rule="para" parents="20341 20510"/>
    </justification>
  </clause>

  <clause id="20512">
    <literal><![CDATA[
      K(x,y \ (z * a(u,w,K(v5,v6)))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(18687(a,1),20511(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="18687 20511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20513">
    <literal><![CDATA[
      K(x,(y * (a(z,u,K(w,v5)) / v6)) \ y) = L(K(x,v6),a(z,u,K(w,v5)),y)
    ]]></literal>
    <justification jstring="[hyper(8397,a,20512,a),flip(a)].">
      <j1 rule="hyper" parents="8397 20512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20514">
    <literal><![CDATA[
      L(K(x,y),a(z,u,K(w,v5)),v6) = K(x,y / a(z,u,K(w,v5)))
    ]]></literal>
    <justification jstring="[hyper(6897,a,20513,a),flip(a)].">
      <j1 rule="hyper" parents="6897 20513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20515">
    <literal><![CDATA[
      K(x,y / a(z,u,K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v6
    ]]></literal>
    <justification jstring="[para(20514(a,1),505(a,1))].">
      <j1 rule="para" parents="20514 505"/>
    </justification>
  </clause>

  <clause id="20516">
    <literal><![CDATA[
      K(x,a(y,z,K(u,w)) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,v5) = v6
    ]]></literal>
    <justification jstring="[para(18682(a,1),20515(a,1,2))].">
      <j1 rule="para" parents="18682 20515"/>
    </justification>
  </clause>

  <clause id="20517">
    <literal><![CDATA[
      K(x,T(y * a(z,u,K(w,v5)),v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,v6)) = v7
    ]]></literal>
    <justification jstring="[para(19990(a,2),20516(a,1,2))].">
      <j1 rule="para" parents="19990 20516"/>
    </justification>
  </clause>

  <clause id="20518">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * (v5 \ ((y * u) * w))) = K(x,v5 \ (T(R(y,u,w),z) * (u * w)))
    ]]></literal>
    <justification jstring="[para(15484(a,1),20184(a,1,2,1))].">
      <j1 rule="para" parents="15484 20184"/>
    </justification>
  </clause>

  <clause id="20519">
    <literal><![CDATA[
      K(x,y * T(z * T(z \ u,w),z)) = K(x,y * (T(z,T(u,w)) * T(z \ u,w)))
    ]]></literal>
    <justification jstring="[para(17585(a,1),20202(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="17585 20202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20520">
    <literal><![CDATA[
      K(x,y * T(z * T(z \ u,w),z)) = K(x,y * (T(z,u) * T(z \ u,w)))
    ]]></literal>
    <justification jstring="[hyper(299,a,18773,a(flip),b,20519,a),flip(a)].">
      <j1 rule="hyper" parents="299 18773 20519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20522">
    <literal><![CDATA[
      K(x,y * (T(z,u) * T(z \ u,w))) = K(x,y * (T(z \ u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,13779,a(flip),b,20520,a),flip(a)].">
      <j1 rule="hyper" parents="65 13779 20520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20523">
    <literal><![CDATA[
      K(x,y * (T(z,u) * T(z \ u,w))) = K(x,y * (z * T(u / z,w)))
    ]]></literal>
    <justification jstring="[hyper(299,a,15901,a(flip),b,20522,a),flip(a)].">
      <j1 rule="hyper" parents="299 15901 20522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20524">
    <literal><![CDATA[
      K(x,y * (K(z,u * w) * T(w,u))) = K(x,y * (u * T(w / u,z)))
    ]]></literal>
    <justification jstring="[hyper(19305,a,20523,a)].">
      <j1 rule="hyper" parents="19305 20523"/>
    </justification>
  </clause>

  <clause id="20525">
    <literal><![CDATA[
      K(x,y * (T(z,u) * K(w,z * u))) = K(x,y * (u * T(z / u,w)))
    ]]></literal>
    <justification jstring="[para(16589(a,2),20524(a,1,2,2))].">
      <j1 rule="para" parents="16589 20524"/>
    </justification>
  </clause>

  <clause id="20526">
    <literal><![CDATA[
      K(x,T(y,z * u) * T(z,u)) = K(x,y * (u * T(z / u,y)))
    ]]></literal>
    <justification jstring="[hyper(16473,a,20525,a)].">
      <j1 rule="hyper" parents="16473 20525"/>
    </justification>
  </clause>

  <clause id="20527">
    <literal><![CDATA[
      K(x,T(y / z,u * w) * T(u,w)) = K(x,(y / z) * (w * T(u / w,z \ y)))
    ]]></literal>
    <justification jstring="[hyper(299,a,16849,a(flip),b,20526,a),flip(a)].">
      <j1 rule="hyper" parents="299 16849 20526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20528">
    <literal><![CDATA[
      K(x,T(y,z * u) \ T(z,u)) = K(x,(1 / y) * (u * T(z / u,y \ 1)))
    ]]></literal>
    <justification jstring="[hyper(65,a,20198,a(flip),b,20527,a)].">
      <j1 rule="hyper" parents="65 20198 20527"/>
    </justification>
  </clause>

  <clause id="20529">
    <literal><![CDATA[
      K(x,T(y,z * u) \ T(z,u)) = K(x,(1 / y) * (u * T(z / u,y * 1)))
    ]]></literal>
    <justification jstring="[hyper(299,a,17551,a(flip),b,20528,a),flip(a)].">
      <j1 rule="hyper" parents="299 17551 20528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20530">
    <literal><![CDATA[
      K(x,T(y,z * u) \ T(z,u)) = K(x,(1 / y) * (u * T(z / u,y)))
    ]]></literal>
    <justification jstring="[para(8(a,1),20529(a,2,2,2,2,2))].">
      <j1 rule="para" parents="8 20529"/>
    </justification>
  </clause>

  <clause id="20531">
    <literal><![CDATA[
      K(x,T(y,z * u) \ T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (u * T(z / u,y))) = w
    ]]></literal>
    <justification jstring="[para(20530(a,2),14530(a,1))].">
      <j1 rule="para" parents="20530 14530"/>
    </justification>
  </clause>

  <clause id="20532">
    <literal><![CDATA[
      K(x,(((1 / y) * z) \ u) * K(y \ 1,y * w)) = K(x,(T(y \ 1,y \ w) * z) \ u)
    ]]></literal>
    <justification jstring="[para(13204(a,1),20225(a,1,2,2))].">
      <j1 rule="para" parents="13204 20225"/>
    </justification>
  </clause>

  <clause id="20533">
    <literal><![CDATA[
      K(x,y \ ((z * (K(u,w) * K(u,w))) * v5)) = K(x,y \ (z * v5))
    ]]></literal>
    <justification jstring="[hyper(299,a,19067,a(flip),b,20318,a),flip(a)].">
      <j1 rule="hyper" parents="299 19067 20318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20535">
    <literal><![CDATA[
      K(x,y \ (z * ((K(u,w) * K(u,w)) * v5))) = K(x,y \ (z * v5))
    ]]></literal>
    <justification jstring="[para(34(a,1),20533(a,1,2,2))].">
      <j1 rule="para" parents="34 20533"/>
    </justification>
  </clause>

  <clause id="20536">
    <literal><![CDATA[
      K(x,y \ ((z * (u * K(w,u))) * v5)) = K(x,y \ ((z * T(u,w)) * v5))
    ]]></literal>
    <justification jstring="[para(5534(a,1),20535(a,1,2,2))].">
      <j1 rule="para" parents="5534 20535"/>
    </justification>
  </clause>

  <clause id="20537">
    <literal><![CDATA[
      K(x,T(y,T(z,u * w) \ v5) \ (T(z,u * w) \ v5)) = K(x,(T(z,u \ w) \ v5) / y)
    ]]></literal>
    <justification jstring="[para(17455(a,1),20358(a,1,2,1))].">
      <j1 rule="para" parents="17455 20358"/>
    </justification>
  </clause>

  <clause id="20538">
    <literal><![CDATA[
      K(x,y \ (T(R(z,u,w),v5) * (u * w))) = K(x,K(z,v5) * (y \ ((z * u) * w)))
    ]]></literal>
    <justification jstring="[hyper(19085,a,20518,a),flip(a)].">
      <j1 rule="hyper" parents="19085 20518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20540">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ ((y * w) * v5))) = K(x,u \ ((T(y,z) * w) * v5))
    ]]></literal>
    <justification jstring="[para(541(a,1),20538(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="541 20538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20541">
    <literal><![CDATA[
      K(x,y \ (T(z * u,u) * w)) = K(x,y \ ((T(z,u) * u) * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,20182,a(flip),b,20540,a)].">
      <j1 rule="hyper" parents="65 20182 20540"/>
    </justification>
  </clause>

  <clause id="20542">
    <literal><![CDATA[
      K(x,y \ (T(z * u,u) * w)) = K(x,y \ ((u * z) * w))
    ]]></literal>
    <justification jstring="[hyper(299,a,19458,a(flip),b,20541,a),flip(a)].">
      <j1 rule="hyper" parents="299 19458 20541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20543">
    <literal><![CDATA[
      K(x,y \ (T(z * u,z) * w)) = K(x,y \ ((u * z) * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,20394,a(flip),b,20542,a)].">
      <j1 rule="hyper" parents="65 20394 20542"/>
    </justification>
  </clause>

  <clause id="20544">
    <literal><![CDATA[
      K(x,y \ (T(z / (z / u),u) * w)) = K(x,y \ ((u * K(u \ z,u)) * w))
    ]]></literal>
    <justification jstring="[para(5007(a,2),20542(a,1,2,2,1,1))].">
      <j1 rule="para" parents="5007 20542"/>
    </justification>
  </clause>

  <clause id="20545">
    <literal><![CDATA[
      K(x,y \ (((z \ u) * z) * w)) = K(x,y \ (T(u,z) * w))
    ]]></literal>
    <justification jstring="[para(10(a,1),20543(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 20543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20546">
    <literal><![CDATA[
      K(x,y \ (T(z / (z \ u),z) * w)) = K(x,y \ (((((u \ z) \ 1) \ 1) * z) * w))
    ]]></literal>
    <justification jstring="[para(10418(a,1),20543(a,1,2,2,1,1))].">
      <j1 rule="para" parents="10418 20543"/>
    </justification>
  </clause>

  <clause id="20547">
    <literal><![CDATA[
      K(x,y \ (T(z \ u,z \ 1) * w)) = K(x,y \ ((z \ T(u,z \ 1)) * w))
    ]]></literal>
    <justification jstring="[para(1137(a,1),20545(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="1137 20545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20548">
    <literal><![CDATA[
      K(x,y \ (((z \ (L(z,u,z) * u)) * z) * w)) = K(x,y \ ((u * z) * w))
    ]]></literal>
    <justification jstring="[para(4351(a,1),20545(a,2,2,2,1))].">
      <j1 rule="para" parents="4351 20545"/>
    </justification>
  </clause>

  <clause id="20549">
    <literal><![CDATA[
      K(x,y \ (T(z / (1 / u),T(u \ 1,u \ z)) * w)) = K(x,y \ ((z / T(u \ 1,z)) * w))
    ]]></literal>
    <justification jstring="[para(18351(a,1),20545(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="18351 20545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20550">
    <literal><![CDATA[
      K(x,y \ ((z * L(u,z,u)) * w)) = K(x,y \ ((z * u) * w))
    ]]></literal>
    <justification jstring="[para(12033(a,1),20548(a,1,2,2,1))].">
      <j1 rule="para" parents="12033 20548"/>
    </justification>
  </clause>

  <clause id="20551">
    <literal><![CDATA[
      K(x,y \ ((T(z,u * z) * u) * w)) = K(x,y \ ((u * z) * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,19460,a,b,20550,a)].">
      <j1 rule="hyper" parents="65 19460 20550"/>
    </justification>
  </clause>

  <clause id="20552">
    <literal><![CDATA[
      K(x,y \ ((T(z,z * u) * u) * w)) = K(x,y \ ((u * z) * w))
    ]]></literal>
    <justification jstring="[para(4366(a,1),20551(a,1,2,2,1,1))].">
      <j1 rule="para" parents="4366 20551"/>
    </justification>
  </clause>

  <clause id="20553">
    <literal><![CDATA[
      K(x,(y * (y * z)) \ ((y \ (y * (y * z))) * u)) = K(x,T(y * (y * z),y) \ ((z * y) * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,15881,a(flip),b,20552,a)].">
      <j1 rule="hyper" parents="65 15881 20552"/>
    </justification>
  </clause>

  <clause id="20554">
    <literal><![CDATA[
      K(x,y \ (T(z / (z / u),u) * w)) = K(x,y \ (u * (K(u \ z,u) * w)))
    ]]></literal>
    <justification jstring="[para(5488(a,1),20544(a,2,2,2))].">
      <j1 rule="para" parents="5488 20544"/>
    </justification>
  </clause>

  <clause id="20555">
    <literal><![CDATA[
      K(x,y \ (T(z \ u,z * 1) * w)) = K(x,y \ ((z \ T(u,z \ 1)) * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,17624,a(flip),b,20547,a)].">
      <j1 rule="hyper" parents="65 17624 20547"/>
    </justification>
  </clause>

  <clause id="20556">
    <literal><![CDATA[
      K(x,y \ (T(z / (z / u),u) * w)) = K(x,y \ (T(u,u \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(299,a,15980,a(flip),b,20554,a),flip(a)].">
      <j1 rule="hyper" parents="299 15980 20554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20557">
    <literal><![CDATA[
      K(x,y \ (T(z / (z / u),u) * w)) = K(x,y \ (T(u,z) * w))
    ]]></literal>
    <justification jstring="[hyper(299,a,14799,a(flip),b,20556,a),flip(a)].">
      <j1 rule="hyper" parents="299 14799 20556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20558">
    <literal><![CDATA[
      K(x,y \ ((z / (z / u)) * w)) = K(x,y \ (T(u,z) * w))
    ]]></literal>
    <justification jstring="[para(341(a,1),20557(a,1,2,2,1))].">
      <j1 rule="para" parents="341 20557"/>
    </justification>
  </clause>

  <clause id="20559">
    <literal><![CDATA[
      K(x,((y / (y / z)) * u) / w) = K(x,K(w,z * u)) * K(x,w \ (T(z,y) * u))
    ]]></literal>
    <justification jstring="[para(20558(a,1),19439(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20558 19439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20560">
    <literal><![CDATA[
      K(x,y \ ((z \ T(u,z \ 1)) * w)) = K(x,y \ (T(z \ u,z) * w))
    ]]></literal>
    <justification jstring="[para(8(a,1),20555(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="8 20555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20561">
    <literal><![CDATA[
      K(x,y \ ((z \ T(u,z \ 1)) * w)) = K(x,y \ ((u / z) * w))
    ]]></literal>
    <justification jstring="[hyper(299,a,15982,a(flip),b,20560,a),flip(a)].">
      <j1 rule="hyper" parents="299 15982 20560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20563">
    <literal><![CDATA[
      K(x,y \ (((((z \ u) \ 1) \ 1) * u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (((u \ z) \ u) * w)) = v5
    ]]></literal>
    <justification jstring="[para(20546(a,1),14802(a,1))].">
      <j1 rule="para" parents="20546 14802"/>
    </justification>
  </clause>

  <clause id="20564">
    <literal><![CDATA[
      K(x,((y / (y / z)) * u) / w) = K(x,(T(z,y) * u) / w)
    ]]></literal>
    <justification jstring="[hyper(299,a,17163,a(flip),b,20559,a),flip(a)].">
      <j1 rule="hyper" parents="299 17163 20559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20565">
    <literal><![CDATA[
      K(x,(T(y,z) * u) / (w * y)) = K(x,(y * u) / (w * T(y,z)))
    ]]></literal>
    <justification jstring="[hyper(65,a,20484,a(flip),b,20564,a),flip(a)].">
      <j1 rule="hyper" parents="65 20484 20564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20566">
    <literal><![CDATA[
      K(x,(T(y,z) \ u) / (z / y)) = K(x,(y * u) / (z * T(y,z)))
    ]]></literal>
    <justification jstring="[hyper(20305,a,20565,a)].">
      <j1 rule="hyper" parents="20305 20565"/>
    </justification>
  </clause>

  <clause id="20567">
    <literal><![CDATA[
      K(x,(T(y,z) \ u) / (z / y)) = K(x,(y * u) / (y * z))
    ]]></literal>
    <justification jstring="[para(107(a,1),20566(a,2,2,2))].">
      <j1 rule="para" parents="107 20566"/>
    </justification>
  </clause>

  <clause id="20568">
    <literal><![CDATA[
      K(x,(T(y,(z / y) \ 1) \ u) / (((z / y) \ 1) / y)) = K(x,(y * (((y * u) / y) \ 1)) \ z)
    ]]></literal>
    <justification jstring="[hyper(299,a,18119,a(flip),b,20567,a),flip(a)].">
      <j1 rule="hyper" parents="299 18119 20567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20569">
    <literal><![CDATA[
      K(x,(((1 / y) * z) \ u) * K(y,y * w)) = K(x,(T(y \ 1,y \ w) * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(16625,a,20532,a)].">
      <j1 rule="hyper" parents="16625 20532"/>
    </justification>
  </clause>

  <clause id="20570">
    <literal><![CDATA[
      K(x,(T(y \ 1,y \ z) * u) \ w) = K(x,(((1 / y) * u) \ w) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(16698,a,20569,a),flip(a)].">
      <j1 rule="hyper" parents="16698 20569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20571">
    <literal><![CDATA[
      K(x,(((1 / y) * z) \ u) * K(w,y)) = K(x,(T(y \ 1,w) * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,20286,a(flip),b,20570,a),flip(a)].">
      <j1 rule="hyper" parents="65 20286 20570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20572">
    <literal><![CDATA[
      K(x,(T(y \ 1,z) * T(u,y)) \ w) = K(x,(((y * y) \ u) * T(y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,20208,a(flip),b,20571,a),flip(a)].">
      <j1 rule="hyper" parents="65 20208 20571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20573">
    <literal><![CDATA[
      K(x,(T(y,z \ u) \ w) / v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,(T(y,z * u) \ w) / v5) = v6
    ]]></literal>
    <justification jstring="[para(20537(a,1),13924(a,1))].">
      <j1 rule="para" parents="20537 13924"/>
    </justification>
  </clause>

  <clause id="20574">
    <literal><![CDATA[
      (x \ (K(y,z) * u)) * (K(z,y) * K(z,y)) = x \ (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(9200(a,1),20323(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9200 20323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20575">
    <literal><![CDATA[
      ((K(x,y) \ 1) * (x \ y)) \ z = (x \ y) \ (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,20390,a(flip),b,20574,a)].">
      <j1 rule="hyper" parents="65 20390 20574"/>
    </justification>
  </clause>

  <clause id="20578">
    <literal><![CDATA[
      (K(x,y) * (y \ x)) \ z = (y \ x) \ (K(y,x) * z)
    ]]></literal>
    <justification jstring="[para(5197(a,1),20575(a,1,1,1))].">
      <j1 rule="para" parents="5197 20575"/>
    </justification>
  </clause>

  <clause id="20579">
    <literal><![CDATA[
      (x \ y) \ (K(x,y) * z) = (T(x,y) \ y) \ z
    ]]></literal>
    <justification jstring="[para(5383(a,1),20578(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5383 20578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20580">
    <literal><![CDATA[
      K(x,(L(y,y,K(y,z) * u) \ z) \ L(K(y,z) * u,y,y)) = K(x,(T(y,z) \ z) \ u)
    ]]></literal>
    <justification jstring="[para(20579(a,1),16113(a,2,2))].">
      <j1 rule="para" parents="20579 16113"/>
    </justification>
  </clause>

  <clause id="20581">
    <literal><![CDATA[
      K(x,K(y,z) * ((L(y,y,K(y,z) * u) \ z) \ L(u,y,y))) = K(x,(T(y,z) \ z) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,20131,a(flip),b,20580,a)].">
      <j1 rule="hyper" parents="65 20131 20580"/>
    </justification>
  </clause>

  <clause id="20582">
    <literal><![CDATA[
      K(x,(L(y,y,K(y,z) * u) \ T(z,y)) \ L(u,y,y)) = K(x,(T(y,z) \ z) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,20103,a(flip),b,20581,a)].">
      <j1 rule="hyper" parents="65 20103 20581"/>
    </justification>
  </clause>

  <clause id="20583">
    <literal><![CDATA[
      K(x,(y / L(z,z,K(z,y) * u)) \ L(u,z,z)) = K(x,(T(z,y) \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,20215,a(flip),b,20582,a)].">
      <j1 rule="hyper" parents="65 20215 20582"/>
    </justification>
  </clause>

  <clause id="20584">
    <literal><![CDATA[
      K(x,(y / L(z,z,K(z,y) * u)) \ L(u,z,z)) = K(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[hyper(299,a,20213,a(flip),b,20583,a),flip(a)].">
      <j1 rule="hyper" parents="299 20213 20583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20585">
    <literal><![CDATA[
      K(x / (T(y,y \ 1) * ((y * y) \ z)),u) = K(x / T((y \ 1) * T(z,y),y),u)
    ]]></literal>
    <justification jstring="[para(3743(a,1),20248(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3743 20248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20586">
    <literal><![CDATA[
      K(x / (T(y,y \ 1) * ((y * y) \ z)),u) = K(x / (T(z,y) * (y \ 1)),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,20392,a(flip),b,20585,a),flip(a)].">
      <j1 rule="hyper" parents="299 20392 20585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20587">
    <literal><![CDATA[
      K(x / (T(y,z) * (z \ 1)),u) = K(x / ((1 / z) * y),u)
    ]]></literal>
    <justification jstring="[para(6394(a,1),20586(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6394 20586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20588">
    <literal><![CDATA[
      K(x / (T(y,z) * (z \ 1)),u) = K(x / ((z \ 1) * y),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,5897,a(flip),b,20587,a),flip(a)].">
      <j1 rule="hyper" parents="299 5897 20587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20589">
    <literal><![CDATA[
      K(T(x,y) \ z,T(u,x * y)) = K((((y \ 1) \ z) * (y \ 1)) / ((y \ 1) * ((y \ 1) \ x)),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,18197,a,b,20588,a)].">
      <j1 rule="hyper" parents="65 18197 20588"/>
    </justification>
  </clause>

  <clause id="20590">
    <literal><![CDATA[
      K(x,(y \ 1) * ((y \ 1) * ((1 / L(y,z,z)) \ u))) = K(x,(((1 / y) \ 1) * a(z,z,y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,19076,a(flip),b,20300,a)].">
      <j1 rule="hyper" parents="65 19076 20300"/>
    </justification>
  </clause>

  <clause id="20591">
    <literal><![CDATA[
      K(x,((y \ 1) * (T(T(y,z),z) \ u)) \ w) = K(x,y * (T(T(y,z),z) * (u \ w)))
    ]]></literal>
    <justification jstring="[para(18254(a,1),20324(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="18254 20324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20592">
    <literal><![CDATA[
      K(x,((y \ 1) * (T(T(y,z),z) \ u)) \ w) = K(x,y * (y * (u \ w)))
    ]]></literal>
    <justification jstring="[hyper(299,a,15976,a(flip),b,20591,a),flip(a)].">
      <j1 rule="hyper" parents="299 15976 20591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20594">
    <literal><![CDATA[
      K(x,K(y,z) * (y \ u)) * K(x,K(u,y * K(z,y \ 1))) = K(x,u * T(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(15944(a,1),20334(a,1,1))].">
      <j1 rule="para" parents="15944 20334"/>
    </justification>
  </clause>

  <clause id="20595">
    <literal><![CDATA[
      K(x,T(y,z) \ u) * K(x,K(u,y * K(z,y \ 1))) = K(x,u * T(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(15807(a,1),20594(a,1,1))].">
      <j1 rule="para" parents="15807 20594"/>
    </justification>
  </clause>

  <clause id="20596">
    <literal><![CDATA[
      K(x,T(y,z) \ u) * K(x,K(u,y)) = K(x,u * T(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(17133(a,1),20595(a,1,2))].">
      <j1 rule="para" parents="17133 20595"/>
    </justification>
  </clause>

  <clause id="20597">
    <literal><![CDATA[
      K(x,y * T(z \ 1,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(20596(a,1),16694(a,1))].">
      <j1 rule="para" parents="20596 16694"/>
    </justification>
  </clause>

  <clause id="20599">
    <literal><![CDATA[
      K(x,((a(y,z,u) \ 1) \ w) / T(a(y,z,u),v5)) = K(x,T(a(y,z,K(v5,u)) * w,a(y,z,u) \ 1))
    ]]></literal>
    <justification jstring="[hyper(20597,a,19734,a)].">
      <j1 rule="hyper" parents="20597 19734"/>
    </justification>
  </clause>

  <clause id="20600">
    <literal><![CDATA[
      T(x,((1 / y) * (z / y)) * (T(z,(1 / y) * (z / y)) \ u)) = T(x,y \ (T(y,y * z) \ u))
    ]]></literal>
    <justification jstring="[para(1203(a,1),20373(a,2,2))].">
      <j1 rule="para" parents="1203 20373"/>
    </justification>
  </clause>

  <clause id="20601">
    <literal><![CDATA[
      K(x,y \ (T(z / (1 / u),T(u \ 1,u \ z)) * w)) = K(x,y \ (((u \ 1) \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(299,a,19781,a(flip),b,20549,a),flip(a)].">
      <j1 rule="hyper" parents="299 19781 20549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20602">
    <literal><![CDATA[
      K(x,y \ (T(z / (1 / u),T(u \ 1,u * z)) * w)) = K(x,y \ (((u \ 1) \ z) * w))
    ]]></literal>
    <justification jstring="[para(16225(a,1),20601(a,1,2,2,1))].">
      <j1 rule="para" parents="16225 20601"/>
    </justification>
  </clause>

  <clause id="20603">
    <literal><![CDATA[
      K(x,y \ (T(z / (1 / u),T(u \ 1,z)) * w)) = K(x,y \ (((u \ 1) \ z) * w))
    ]]></literal>
    <justification jstring="[para(7596(a,1),20602(a,1,2,2,1))].">
      <j1 rule="para" parents="7596 20602"/>
    </justification>
  </clause>

  <clause id="20604">
    <literal><![CDATA[
      K(x,y \ (T((1 / z) \ u,K(1,z)) * w)) = K(x,y \ (((z \ 1) \ u) * w))
    ]]></literal>
    <justification jstring="[para(18901(a,1),20603(a,1,2,2,1))].">
      <j1 rule="para" parents="18901 20603"/>
    </justification>
  </clause>

  <clause id="20605">
    <literal><![CDATA[
      K(x,y \ (((1 / z) \ u) * w)) = K(x,y \ (((z \ 1) \ u) * w))
    ]]></literal>
    <justification jstring="[hyper(19513,a,20604,a)].">
      <j1 rule="hyper" parents="19513 20604"/>
    </justification>
  </clause>

  <clause id="20606">
    <literal><![CDATA[
      K(x,y \ ((((z \ 1) \ 1) \ u) * w)) = K(x,y \ ((z \ u) * w))
    ]]></literal>
    <justification jstring="[para(76(a,1),20605(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="76 20605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20607">
    <literal><![CDATA[
      K(x,y \ (((z \ 1) \ L(u,z,z)) * w)) = K(x,y \ ((z * u) * w))
    ]]></literal>
    <justification jstring="[para(481(a,1),20605(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="481 20605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20608">
    <literal><![CDATA[
      K(x,y \ (((z \ 1) \ T(((1 / z) * (1 / z)) * u,1 / z)) * w)) = K(x,y \ ((((1 / z) \ 1) \ T(u,1 / z)) * w))
    ]]></literal>
    <justification jstring="[para(14808(a,1),20605(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="14808 20605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20609">
    <literal><![CDATA[
      K(x,y \ ((((z \ 1) \ 1) * u) * w)) = K(x,y \ ((z * u) * w))
    ]]></literal>
    <justification jstring="[para(1761(a,1),20607(a,1,2,2,1))].">
      <j1 rule="para" parents="1761 20607"/>
    </justification>
  </clause>

  <clause id="20610">
    <literal><![CDATA[
      K(x,y \ (((z \ u) \ z) * w)) = K(x,y \ (((u \ z) * z) * w))
    ]]></literal>
    <justification jstring="[hyper(20563,a,20609,a)].">
      <j1 rule="hyper" parents="20563 20609"/>
    </justification>
  </clause>

  <clause id="20611">
    <literal><![CDATA[
      K(x,y \ (((z \ u) * u) * T(w,(u \ z) \ u))) = K(x,y \ (w * ((u \ z) \ u)))
    ]]></literal>
    <justification jstring="[para(107(a,1),20610(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 20610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20612">
    <literal><![CDATA[
      K(x,y \ (((z \ u) * u) * T(w,u * (u / z)))) = K(x,y \ (w * ((u \ z) \ u)))
    ]]></literal>
    <justification jstring="[para(16238(a,1),20611(a,1,2,2,2))].">
      <j1 rule="para" parents="16238 20611"/>
    </justification>
  </clause>

  <clause id="20613">
    <literal><![CDATA[
      K(x,y \ (z * ((u \ w) \ u))) = K(x,y \ (z * ((w \ u) * u)))
    ]]></literal>
    <justification jstring="[para(13880(a,1),20612(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13880 20612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20614">
    <literal><![CDATA[
      K(x,y \ (z * ((u \ w) * w))) = K(x,y \ (z * (w * (w / u))))
    ]]></literal>
    <justification jstring="[hyper(65,a,19903,a(flip),b,20613,a),flip(a)].">
      <j1 rule="hyper" parents="65 19903 20613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20615">
    <literal><![CDATA[
      K(x,y \ (T(z,u) * (w * (w / u)))) = K(x,y \ (((u \ w) * w) * z))
    ]]></literal>
    <justification jstring="[hyper(20361,a,20614,a),flip(a)].">
      <j1 rule="hyper" parents="20361 20614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20616">
    <literal><![CDATA[
      K(x,y \ (((z \ u) * u) * w)) = K(x,y \ ((u * (u / z)) * w))
    ]]></literal>
    <justification jstring="[hyper(20360,a,20615,a),flip(a)].">
      <j1 rule="hyper" parents="20360 20615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20617">
    <literal><![CDATA[
      K(x,y \ (((T(z,u) \ (z * u)) * (z * u)) * w)) = K(x,y \ (((z * u) * u) * w))
    ]]></literal>
    <justification jstring="[para(185(a,1),20616(a,2,2,2,1,2))].">
      <j1 rule="para" parents="185 20616"/>
    </justification>
  </clause>

  <clause id="20618">
    <literal><![CDATA[
      K(x,y \ ((T(z,u) * (u * z)) * w)) = K(x,y \ (((u * z) * z) * w))
    ]]></literal>
    <justification jstring="[para(4419(a,1),20617(a,1,2,2,1,1))].">
      <j1 rule="para" parents="4419 20617"/>
    </justification>
  </clause>

  <clause id="20619">
    <literal><![CDATA[
      K(x,y \ (((z * u) * u) * w)) = K(x,y \ ((u * (u * z)) * w))
    ]]></literal>
    <justification jstring="[para(4430(a,1),20618(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4430 20618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20620">
    <literal><![CDATA[
      K(x,(y * (y * z)) \ ((y \ (y * (y * z))) * u)) = K(x,((y * z) * y) \ ((z * y) * u))
    ]]></literal>
    <justification jstring="[hyper(299,a,13919,a(flip),b,20553,a),flip(a)].">
      <j1 rule="hyper" parents="299 13919 20553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20621">
    <literal><![CDATA[
      K(x,(y * (y * z)) \ ((y \ (y * (y * z))) * u)) = K(x,(y * (z * y)) \ ((z * y) * u))
    ]]></literal>
    <justification jstring="[hyper(299,a,19560,a(flip),b,20620,a),flip(a)].">
      <j1 rule="hyper" parents="299 19560 20620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20622">
    <literal><![CDATA[
      K(x,(y * (z * y)) \ ((z * y) * u)) = K(x,(y * (y * z)) \ ((y * z) * u))
    ]]></literal>
    <justification jstring="[para(9(a,1),20621(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="9 20621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20623">
    <literal><![CDATA[
      K(x,(y * (z * y)) \ ((z * y) * u)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(299,a,19599,a(flip),b,20622,a),flip(a)].">
      <j1 rule="hyper" parents="299 19599 20622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20625">
    <literal><![CDATA[
      K(x,L(T(y,z) \ u,u,z * y)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(19563,a,20623,a)].">
      <j1 rule="hyper" parents="19563 20623"/>
    </justification>
  </clause>

  <clause id="20626">
    <literal><![CDATA[
      K(x,L(T(y,z \ 1) \ u,u,(z \ 1) * y)) = K(x,z * ((y \ (z \ 1)) * u))
    ]]></literal>
    <justification jstring="[hyper(299,a,14200,a(flip),b,20625,a),flip(a)].">
      <j1 rule="hyper" parents="299 14200 20625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20627">
    <literal><![CDATA[
      K(x,L(T(y,T(z,u)) \ w,w,(z * K(u,z)) * y)) = K(x,(z * K(u,z)) \ ((y \ (z * K(u,z))) * w))
    ]]></literal>
    <justification jstring="[para(8184(a,1),20625(a,1,2,1,1))].">
      <j1 rule="para" parents="8184 20625"/>
    </justification>
  </clause>

  <clause id="20628">
    <literal><![CDATA[
      K(x,L(T(y,z \ 1) \ u,u,z * y)) = K(x,z * ((y \ (z \ 1)) * u))
    ]]></literal>
    <justification jstring="[para(2489(a,1),20626(a,1,2))].">
      <j1 rule="para" parents="2489 20626"/>
    </justification>
  </clause>

  <clause id="20629">
    <literal><![CDATA[
      K(x,L(T(y,z * 1) \ u,u,z * y)) = K(x,z * ((y \ (z \ 1)) * u))
    ]]></literal>
    <justification jstring="[hyper(18006,a,20628,a)].">
      <j1 rule="hyper" parents="18006 20628"/>
    </justification>
  </clause>

  <clause id="20630">
    <literal><![CDATA[
      K(x,L(T(y,z) \ u,u,z * y)) = K(x,z * ((y \ (z \ 1)) * u))
    ]]></literal>
    <justification jstring="[para(8(a,1),20629(a,1,2,1,1,2))].">
      <j1 rule="para" parents="8 20629"/>
    </justification>
  </clause>

  <clause id="20631">
    <literal><![CDATA[
      K(x,y * ((z \ (y \ 1)) * u)) = K(x,y \ ((z \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,20625,a(flip),b,20630,a),flip(a)].">
      <j1 rule="hyper" parents="65 20625 20630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20632">
    <literal><![CDATA[
      K(x,(y \ 1) \ ((z \ (y \ 1)) * u)) = K(x,y \ ((z \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(14356,a,20631,a)].">
      <j1 rule="hyper" parents="14356 20631"/>
    </justification>
  </clause>

  <clause id="20633">
    <literal><![CDATA[
      K(x,(T(y,z \ (y * 1)) \ u) / (((z / y) \ 1) / y)) = K(x,(y * (((y * u) / y) \ 1)) \ z)
    ]]></literal>
    <justification jstring="[para(8645(a,1),20568(a,1,2,1,1))].">
      <j1 rule="para" parents="8645 20568"/>
    </justification>
  </clause>

  <clause id="20634">
    <literal><![CDATA[
      K(T(x,y) \ z,T(u,x * y)) = K((((y \ 1) \ z) * (y \ 1)) / x,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),20589(a,2,1,2))].">
      <j1 rule="para" parents="10 20589"/>
    </justification>
  </clause>

  <clause id="20635">
    <literal><![CDATA[
      K(T(x,y) \ z,T(u,x * y)) = K(T(z,y \ 1) / x,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,17069,a(flip),b,20634,a),flip(a)].">
      <j1 rule="hyper" parents="299 17069 20634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20636">
    <literal><![CDATA[
      K(T(x,y) \ z,T(u,x * y)) = K(T(z,y * 1) / x,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,18019,a(flip),b,20635,a),flip(a)].">
      <j1 rule="hyper" parents="299 18019 20635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20637">
    <literal><![CDATA[
      K(T(x,y) \ z,T(u,x * y)) = K(T(z,y) / x,u)
    ]]></literal>
    <justification jstring="[para(8(a,1),20636(a,2,1,1,2))].">
      <j1 rule="para" parents="8 20636"/>
    </justification>
  </clause>

  <clause id="20638">
    <literal><![CDATA[
      K(T(K(x,T(y,z)) / x,z) \ y,T(u,(K(x,T(y,z)) / x) * z)) = K(T(T(y,z),x) / (1 / x),u)
    ]]></literal>
    <justification jstring="[para(14401(a,2),20637(a,2,1))].">
      <j1 rule="para" parents="14401 20637"/>
    </justification>
  </clause>

  <clause id="20639">
    <literal><![CDATA[
      a(x,y,K(T(z,u) / w,v5)) = a(x,y,K(T(w,u) \ z,v5))
    ]]></literal>
    <justification jstring="[para(20637(a,1),19524(a,1,3))].">
      <j1 rule="para" parents="20637 19524"/>
    </justification>
  </clause>

  <clause id="20640">
    <literal><![CDATA[
      a(x,y,K(T(z,u) \ w,v5)) = a(x,y,K(z * T(w,u),v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,19588,a(flip),b,20639,a),flip(a)].">
      <j1 rule="hyper" parents="65 19588 20639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20641">
    <literal><![CDATA[
      a(x,y,K(T(z,u) * w,v5)) = a(x,y,K(z * T(w,u),v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,19587,a(flip),b,20640,a)].">
      <j1 rule="hyper" parents="65 19587 20640"/>
    </justification>
  </clause>

  <clause id="20642">
    <literal><![CDATA[
      K(x,(y \ 1) * ((y \ 1) * (L(y,z,z) * u))) = K(x,(((1 / y) \ 1) * a(z,z,y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,14788,a(flip),b,20590,a)].">
      <j1 rule="hyper" parents="65 14788 20590"/>
    </justification>
  </clause>

  <clause id="20643">
    <literal><![CDATA[
      K(x,(((1 / y) \ 1) * a(z,z,y)) \ u) = K(x,y \ ((y \ 1) * (L(y,z,z) * u)))
    ]]></literal>
    <justification jstring="[hyper(14281,a,20642,a),flip(a)].">
      <j1 rule="hyper" parents="14281 20642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20644">
    <literal><![CDATA[
      K(x,(((1 / y) \ 1) * a(z,z,y)) \ u) = K(x,(y * y) \ (L(y,z,z) * u))
    ]]></literal>
    <justification jstring="[para(728(a,1),20643(a,2,2))].">
      <j1 rule="para" parents="728 20643"/>
    </justification>
  </clause>

  <clause id="20645">
    <literal><![CDATA[
      K(x,(((1 / y) \ 1) * a(z,z,y)) \ u) = K(x,((y * y) \ L(y,z,z)) * u)
    ]]></literal>
    <justification jstring="[para(664(a,1),20644(a,2,2))].">
      <j1 rule="para" parents="664 20644"/>
    </justification>
  </clause>

  <clause id="20646">
    <literal><![CDATA[
      K(x,(((1 / y) \ 1) * a(z,z,y)) \ u) = K(x,L(1 / y,z,z) * u)
    ]]></literal>
    <justification jstring="[para(6518(a,1),20645(a,2,2,1))].">
      <j1 rule="para" parents="6518 20645"/>
    </justification>
  </clause>

  <clause id="20647">
    <literal><![CDATA[
      K(x,(((1 / y) \ 1) * a(z,z,y)) \ u) = K(x,L(y \ 1,z,z) * u)
    ]]></literal>
    <justification jstring="[hyper(299,a,5754,a(flip),b,20646,a),flip(a)].">
      <j1 rule="hyper" parents="299 5754 20646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20648">
    <literal><![CDATA[
      K(x,(y * a(z,z,y)) \ u) = K(x,L(y \ 1,z,z) * u)
    ]]></literal>
    <justification jstring="[para(79(a,1),20647(a,1,2,1,1))].">
      <j1 rule="para" parents="79 20647"/>
    </justification>
  </clause>

  <clause id="20650">
    <literal><![CDATA[
      T(x,((1 / y) * (z / y)) * (T(z,(1 / y) * (z / y)) \ u)) = T(x,y \ (T(y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(299,a,13842,a(flip),b,20600,a),flip(a)].">
      <j1 rule="hyper" parents="299 13842 20600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20651">
    <literal><![CDATA[
      T(x,((1 / y) * (z / y)) * (T(z,(1 / y) * (y \ z)) \ u)) = T(x,y \ (T(y,z) \ u))
    ]]></literal>
    <justification jstring="[para(10514(a,1),20650(a,1,2,2,1))].">
      <j1 rule="para" parents="10514 20650"/>
    </justification>
  </clause>

  <clause id="20652">
    <literal><![CDATA[
      T(x,((1 / y) * (z / y)) * (T(z,y \ (y \ z)) \ u)) = T(x,y \ (T(y,z) \ u))
    ]]></literal>
    <justification jstring="[para(14211(a,1),20651(a,1,2,2,1))].">
      <j1 rule="para" parents="14211 20651"/>
    </justification>
  </clause>

  <clause id="20653">
    <literal><![CDATA[
      T(x,((1 / y) * (z / y)) * (K(z,y * y) * (z \ u))) = T(x,y \ (T(y,z) \ u))
    ]]></literal>
    <justification jstring="[para(14740(a,1),20652(a,1,2,2))].">
      <j1 rule="para" parents="14740 20652"/>
    </justification>
  </clause>

  <clause id="20654">
    <literal><![CDATA[
      T(x,((1 / y) * (z / y)) * (T(z,y * y) \ u)) = T(x,y \ (T(y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(19267,a,20653,a)].">
      <j1 rule="hyper" parents="19267 20653"/>
    </justification>
  </clause>

  <clause id="20655">
    <literal><![CDATA[
      T(x,((1 / y) * (z / y)) * (z \ u)) = T(x,y \ (T(y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,17418,a(flip),b,20654,a)].">
      <j1 rule="hyper" parents="65 17418 20654"/>
    </justification>
  </clause>

  <clause id="20657">
    <literal><![CDATA[
      T(x,((y \ 1) * (z / y)) * (z \ u)) = T(x,y \ (T(y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,3879,a(flip),b,20655,a)].">
      <j1 rule="hyper" parents="65 3879 20655"/>
    </justification>
  </clause>

  <clause id="20658">
    <literal><![CDATA[
      K(x,(T(y,z \ y) \ u) / (((z / y) \ 1) / y)) = K(x,(y * (((y * u) / y) \ 1)) \ z)
    ]]></literal>
    <justification jstring="[para(8(a,1),20633(a,1,2,1,1,2,2))].">
      <j1 rule="para" parents="8 20633"/>
    </justification>
  </clause>

  <clause id="20659">
    <literal><![CDATA[
      K(x,(T(y,z * y) \ u) / (((z / y) \ 1) / y)) = K(x,(y * (((y * u) / y) \ 1)) \ z)
    ]]></literal>
    <justification jstring="[hyper(20573,a,20658,a)].">
      <j1 rule="hyper" parents="20573 20658"/>
    </justification>
  </clause>

  <clause id="20660">
    <literal><![CDATA[
      K(x,(T(y,y * z) \ u) / (((z / y) \ 1) / y)) = K(x,(y * (((y * u) / y) \ 1)) \ z)
    ]]></literal>
    <justification jstring="[para(4366(a,1),20659(a,1,2,1,1))].">
      <j1 rule="para" parents="4366 20659"/>
    </justification>
  </clause>

  <clause id="20662">
    <literal><![CDATA[
      K(x,(y * (((y * z) / y) \ 1)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(T(y,u) \ z) / (((u / y) \ 1) / y)) = w
    ]]></literal>
    <justification jstring="[para(20660(a,1),19508(a,1))].">
      <j1 rule="para" parents="20660 19508"/>
    </justification>
  </clause>

  <clause id="20663">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * ((w * (u * z)) \ v5)) = K(x,(w * (u * (z * K(y,z)))) \ v5)
    ]]></literal>
    <justification jstring="[hyper(18834,a,20138,a)].">
      <j1 rule="hyper" parents="18834 20138"/>
    </justification>
  </clause>

  <clause id="20664">
    <literal><![CDATA[
      K(x,(y * (z * (u * K(w,u)))) \ v5) = K(x,(y * (z * T(u,w))) \ v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,20101,a(flip),b,20663,a),flip(a)].">
      <j1 rule="hyper" parents="65 20101 20663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20665">
    <literal><![CDATA[
      ((x * (y \ R(y,z,y))) / (K(y,z) * x)) / (K(y,z) * x) = (K(z,y) / x) * K(y * z,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,17217,a(flip),b,20142,a),flip(a)].">
      <j1 rule="hyper" parents="299 17217 20142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20666">
    <literal><![CDATA[
      K(x * y,x) / (K(x,y) * z) = (K(y,x) / z) * K(x * y,x)
    ]]></literal>
    <justification jstring="[para(10149(a,1),20665(a,1,1))].">
      <j1 rule="para" parents="10149 20665"/>
    </justification>
  </clause>

  <clause id="20667">
    <literal><![CDATA[
      (K(x * y,x) / z) * K(y,x) = (K(y,x) / z) * K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,18861,a(flip),b,20666,a)].">
      <j1 rule="hyper" parents="65 18861 20666"/>
    </justification>
  </clause>

  <clause id="20669">
    <literal><![CDATA[
      a(K(x,y) * ((K(y,x) / z) * K(x * y,x)),u,w) = a((1 / z) * K(x * y,x),u,w)
    ]]></literal>
    <justification jstring="[para(20667(a,1),17671(a,1,1,2))].">
      <j1 rule="para" parents="20667 17671"/>
    </justification>
  </clause>

  <clause id="20670">
    <literal><![CDATA[
      a(T(a(x,y,x) * (K(y,x) / z),K(x,y)),u,w) = a((1 / z) * K(x * y,x),u,w)
    ]]></literal>
    <justification jstring="[para(18940(a,1),20669(a,1,1))].">
      <j1 rule="para" parents="18940 20669"/>
    </justification>
  </clause>

  <clause id="20671">
    <literal><![CDATA[
      a(a(x,y,x) * (K(y,x) / z),u,w) = a((1 / z) * K(x * y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,18968,a(flip),b,20670,a)].">
      <j1 rule="hyper" parents="65 18968 20670"/>
    </justification>
  </clause>

  <clause id="20673">
    <literal><![CDATA[
      a(a(x,y,x) * (z * K(x,y)),u,w) = a((1 / z) * K(x * y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,14419,a(flip),b,20671,a)].">
      <j1 rule="hyper" parents="65 14419 20671"/>
    </justification>
  </clause>

  <clause id="20674">
    <literal><![CDATA[
      a((1 / x) * K(y * z,y),u,w) = a(x * K(y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(13556,a,20673,a),flip(a)].">
      <j1 rule="hyper" parents="13556 20673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20676">
    <literal><![CDATA[
      a(x * K(y * z,y),u,w) = a(x * K(y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,2135,a(flip),b,20674,a)].">
      <j1 rule="hyper" parents="65 2135 20674"/>
    </justification>
  </clause>

  <clause id="20677">
    <literal><![CDATA[
      a((x \ y) * K(z * (z \ y),z),u,w) = a(x \ (z * (y / z)),u,w)
    ]]></literal>
    <justification jstring="[para(19729(a,1),20676(a,2,1))].">
      <j1 rule="para" parents="19729 20676"/>
    </justification>
  </clause>

  <clause id="20678">
    <literal><![CDATA[
      a(x \ (y * (z / y)),u,w) = a((x \ z) * K(z,y),u,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),20677(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 20677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20679">
    <literal><![CDATA[
      a(x \ (y * (z / y)),u,w) = a(x \ T(z,y),u,w)
    ]]></literal>
    <justification jstring="[para(14220(a,1),20678(a,2,1))].">
      <j1 rule="para" parents="14220 20678"/>
    </justification>
  </clause>

  <clause id="20680">
    <literal><![CDATA[
      a(x \ T((y * (z * y)) / y,T(y,y * z)),u,w) = a(x \ (T(y,y * z) * z),u,w)
    ]]></literal>
    <justification jstring="[para(4357(a,1),20679(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4357 20679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20681">
    <literal><![CDATA[
      a(x \ T((y * (z * y)) / y,T(y,z)),u,w) = a(x \ (T(y,y * z) * z),u,w)
    ]]></literal>
    <justification jstring="[para(7462(a,1),20680(a,1,1,2))].">
      <j1 rule="para" parents="7462 20680"/>
    </justification>
  </clause>

  <clause id="20682">
    <literal><![CDATA[
      a(x \ T(y * z,K(z,y)),u,w) = a(x \ (T(z,z * y) * y),u,w)
    ]]></literal>
    <justification jstring="[para(7139(a,1),20681(a,1,1,2))].">
      <j1 rule="para" parents="7139 20681"/>
    </justification>
  </clause>

  <clause id="20683">
    <literal><![CDATA[
      a(x \ (T(y,y * z) * z),u,w) = a(x \ (z * y),u,w)
    ]]></literal>
    <justification jstring="[para(5017(a,1),20682(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5017 20682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20684">
    <literal><![CDATA[
      K(x,a(y,z,z) * ((L(y,z,z) \ u) * a(y,z,z))) = K(x,(y * (1 / (y \ L(y,z,z)))) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,19471,a(flip),b,20405,a)].">
      <j1 rule="hyper" parents="65 19471 20405"/>
    </justification>
  </clause>

  <clause id="20685">
    <literal><![CDATA[
      K(x,(y * T((1 / z) * u,K(z,z \ 1))) \ w) = K(x,(y * ((z \ 1) * u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(299,a,5645,a(flip),b,20408,a),flip(a)].">
      <j1 rule="hyper" parents="299 5645 20408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20686">
    <literal><![CDATA[
      K(x,(y * ((1 / z) * u)) \ w) = K(x,(y * ((z \ 1) * u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(20156,a,20685,a)].">
      <j1 rule="hyper" parents="20156 20685"/>
    </justification>
  </clause>

  <clause id="20688">
    <literal><![CDATA[
      K(x,L((y * z) \ ((y \ 1) \ u),z,y)) = K(x,(y * ((y \ 1) * z)) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,15092,a,b,20686,a)].">
      <j1 rule="hyper" parents="65 15092 20686"/>
    </justification>
  </clause>

  <clause id="20689">
    <literal><![CDATA[
      K(x,L((y * z) \ ((y \ 1) \ u),z,y)) = K(x,L(z,y,y) \ u)
    ]]></literal>
    <justification jstring="[para(1673(a,1),20688(a,2,2,1))].">
      <j1 rule="para" parents="1673 20688"/>
    </justification>
  </clause>

  <clause id="20690">
    <literal><![CDATA[
      K(x,y * (z \ ((z \ 1) \ u))) = K(x,L(y \ 1,z,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(15643,a,20689,a)].">
      <j1 rule="hyper" parents="15643 20689"/>
    </justification>
  </clause>

  <clause id="20691">
    <literal><![CDATA[
      K(x,y \ (z \ ((z \ 1) \ u))) = K(x,L(y,z,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,15632,a(flip),b,20689,a)].">
      <j1 rule="hyper" parents="65 15632 20689"/>
    </justification>
  </clause>

  <clause id="20692">
    <literal><![CDATA[
      K(x,L(T(y,z),u,u) \ z) = K(x,(u \ ((u \ 1) \ z)) / y)
    ]]></literal>
    <justification jstring="[hyper(14409,a,20691,a),flip(a)].">
      <j1 rule="hyper" parents="14409 20691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20693">
    <literal><![CDATA[
      K(x,L(y,z,z) \ R(u,z,z)) = K(x,y \ (z \ T(u * z,z \ 1)))
    ]]></literal>
    <justification jstring="[para(1250(a,1),20691(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="1250 20691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20694">
    <literal><![CDATA[
      K(x,y * (z \ ((1 / z) \ u))) = K(x,L(y \ 1,z,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,6061,a,b,20690,a)].">
      <j1 rule="hyper" parents="65 6061 20690"/>
    </justification>
  </clause>

  <clause id="20695">
    <literal><![CDATA[
      K(x,L((y \ K(z \ ((z \ 1) \ u),y \ 1)) \ 1,z,z) \ u) = K(x,(z \ ((z \ 1) \ u)) * (y \ 1))
    ]]></literal>
    <justification jstring="[para(5279(a,1),20690(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5279 20690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20696">
    <literal><![CDATA[
      K(x,(y \ ((y \ 1) \ z)) / u) = K(x,z / L(u,y,y))
    ]]></literal>
    <justification jstring="[hyper(13928,a,20692,a),flip(a)].">
      <j1 rule="hyper" parents="13928 20692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20698">
    <literal><![CDATA[
      K(x,(y \ ((y \ 1) \ z)) * u) = K(x,z / L(u \ 1,y,y))
    ]]></literal>
    <justification jstring="[hyper(14290,a,20696,a)].">
      <j1 rule="hyper" parents="14290 20696"/>
    </justification>
  </clause>

  <clause id="20699">
    <literal><![CDATA[
      K(x,y / L(((z * z) \ u) \ 1,z,z)) = K(x,(z \ (z \ y)) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,18274,a(flip),b,20698,a),flip(a)].">
      <j1 rule="hyper" parents="65 18274 20698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20700">
    <literal><![CDATA[
      K(x,L(y,z,z) \ R(u,z,z)) = K(x,y \ T((z \ u) * z,z \ 1))
    ]]></literal>
    <justification jstring="[para(3757(a,2),20693(a,2,2,2))].">
      <j1 rule="para" parents="3757 20693"/>
    </justification>
  </clause>

  <clause id="20701">
    <literal><![CDATA[
      K(x,L(y,z,z) \ R(u,z,z)) = K(x,y \ T((z \ u) * z,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,16103,a(flip),b,20700,a),flip(a)].">
      <j1 rule="hyper" parents="299 16103 20700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20702">
    <literal><![CDATA[
      K(x,L(y,z,z) \ R(u,z,z)) = K(x,y \ (z * (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(299,a,16067,a(flip),b,20701,a),flip(a)].">
      <j1 rule="hyper" parents="299 16067 20701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20703">
    <literal><![CDATA[
      K(x,L(y,z,z) \ R(u,z,z)) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(10(a,1),20702(a,2,2,2))].">
      <j1 rule="para" parents="10 20702"/>
    </justification>
  </clause>

  <clause id="20704">
    <literal><![CDATA[
      K(x,L(y,z,z) \ L(u,z,z)) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,16107,a(flip),b,20703,a)].">
      <j1 rule="hyper" parents="65 16107 20703"/>
    </justification>
  </clause>

  <clause id="20705">
    <literal><![CDATA[
      K(T(K(x,T(y,z)) / x,z) \ y,T(u,K(x,T(y,z)) * (x \ z))) = K(T(T(y,z),x) / (1 / x),u)
    ]]></literal>
    <justification jstring="[para(20274(a,1),20638(a,1,2))].">
      <j1 rule="para" parents="20274 20638"/>
    </justification>
  </clause>

  <clause id="20706">
    <literal><![CDATA[
      K(T(K(x,T(y,z)) / x,z) \ y,T(u,T(x,y) \ z)) = K(T(T(y,z),x) / (1 / x),u)
    ]]></literal>
    <justification jstring="[para(16816(a,1),20705(a,1,2))].">
      <j1 rule="para" parents="16816 20705"/>
    </justification>
  </clause>

  <clause id="20707">
    <literal><![CDATA[
      K(T(K(x,T(y,z)) / x,z) \ y,T(u,T(x,y) * z)) = K(T(T(y,z),x) / (1 / x),u)
    ]]></literal>
    <justification jstring="[hyper(16637,a,20706,a)].">
      <j1 rule="hyper" parents="16637 20706"/>
    </justification>
  </clause>

  <clause id="20709">
    <literal><![CDATA[
      K(T(K(x,T(y,z)) / x,z) \ y,T(u,x * z)) = K(T(T(y,z),x) / (1 / x),u)
    ]]></literal>
    <justification jstring="[hyper(17128,a,20707,a)].">
      <j1 rule="hyper" parents="17128 20707"/>
    </justification>
  </clause>

  <clause id="20710">
    <literal><![CDATA[
      K(K(T(x,y),z) * (T(z,y) * x),T(u,z * y)) = K(T(T(x,y),z) / (1 / z),u)
    ]]></literal>
    <justification jstring="[hyper(20387,a,20709,a)].">
      <j1 rule="hyper" parents="20387 20709"/>
    </justification>
  </clause>

  <clause id="20711">
    <literal><![CDATA[
      K(K(x,T(y,z)) * (T(y,z) * x),T(u,y * z)) = K(T(T(x,z),y) / (1 / y),u)
    ]]></literal>
    <justification jstring="[para(7537(a,1),20710(a,1,1,1))].">
      <j1 rule="para" parents="7537 20710"/>
    </justification>
  </clause>

  <clause id="20712">
    <literal><![CDATA[
      K(T(T(x,y),z) / (1 / z),u) = K(x * T(z,y),T(u,z * y))
    ]]></literal>
    <justification jstring="[para(5020(a,1),20711(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5020 20711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20713">
    <literal><![CDATA[
      K(x * T(y,z),T(u,y * z)) = K(T(T(x,z),y) * y,u)
    ]]></literal>
    <justification jstring="[hyper(14461,a,20712,a),flip(a)].">
      <j1 rule="hyper" parents="14461 20712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20714">
    <literal><![CDATA[
      K(x * T(y,z),T(u,y * z)) = K(y * T(x,z),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,13194,a(flip),b,20713,a),flip(a)].">
      <j1 rule="hyper" parents="299 13194 20713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20715">
    <literal><![CDATA[
      K((x * y) * R(z,y,x),u) = K(x * T(z * y,y),u)
    ]]></literal>
    <justification jstring="[hyper(13234,a,20714,a)].">
      <j1 rule="hyper" parents="13234 20714"/>
    </justification>
  </clause>

  <clause id="20716">
    <literal><![CDATA[
      K((x * y) * R(z,y,x),u) = K(x * (y * z),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,15913,a(flip),b,20715,a),flip(a)].">
      <j1 rule="hyper" parents="299 15913 20715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20717">
    <literal><![CDATA[
      K((x * y) * R(z,y,x),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x * (y * z),u) = w
    ]]></literal>
    <justification jstring="[para(20715(a,2),15914(a,1))].">
      <j1 rule="para" parents="20715 15914"/>
    </justification>
  </clause>

  <clause id="20718">
    <literal><![CDATA[
      K(x,(y * z) * R(u,z,y)) = (w * K(y * (z * u),x)) \ w
    ]]></literal>
    <justification jstring="[para(20716(a,1),7200(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="20716 7200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20719">
    <literal><![CDATA[
      K(x,(y * z) * R(u,z,y)) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[hyper(299,a,18856,a(flip),b,20718,a),flip(a)].">
      <j1 rule="hyper" parents="299 18856 20718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20720">
    <literal><![CDATA[
      K(x,(y * z) * R(u,y,T(z,y))) = K(x,T(z,y) * (y * u))
    ]]></literal>
    <justification jstring="[hyper(16005,a,20719,a)].">
      <j1 rule="hyper" parents="16005 20719"/>
    </justification>
  </clause>

  <clause id="20721">
    <literal><![CDATA[
      K(x,(y * z) * R(T(u,y * z),z,y)) = K(x,L(u,z,y) * (y * z))
    ]]></literal>
    <justification jstring="[para(681(a,1),20719(a,2,2))].">
      <j1 rule="para" parents="681 20719"/>
    </justification>
  </clause>

  <clause id="20722">
    <literal><![CDATA[
      K(x,(y * z) * R(u,y,z)) = K(x,T(z,y) * (y * u))
    ]]></literal>
    <justification jstring="[para(11273(a,1),20720(a,1,2,2))].">
      <j1 rule="para" parents="11273 20720"/>
    </justification>
  </clause>

  <clause id="20723">
    <literal><![CDATA[
      K(x,R(y,z,u) * (u * z)) = K(x,L(y,z,u) * (u * z))
    ]]></literal>
    <justification jstring="[para(234(a,1),20721(a,1,2))].">
      <j1 rule="para" parents="234 20721"/>
    </justification>
  </clause>

  <clause id="20724">
    <literal><![CDATA[
      K(x,L(y,z,u) * (u * z)) = K(x,(y * z) * T(u,z))
    ]]></literal>
    <justification jstring="[para(11279(a,1),20723(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11279 20723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20725">
    <literal><![CDATA[
      K(x,L(y,z \ u,1 / z) * ((z * z) \ u)) = K(x,(y * (z \ u)) * T(1 / z,z \ u))
    ]]></literal>
    <justification jstring="[para(441(a,1),20724(a,1,2,2))].">
      <j1 rule="para" parents="441 20724"/>
    </justification>
  </clause>

  <clause id="20726">
    <literal><![CDATA[
      K(x,L(y,z,u) * (T(u,z) * z)) = K(x,(y * z) * T(T(u,z),z))
    ]]></literal>
    <justification jstring="[para(11622(a,1),20724(a,1,2,1))].">
      <j1 rule="para" parents="11622 20724"/>
    </justification>
  </clause>

  <clause id="20727">
    <literal><![CDATA[
      K(x,L(y,z,u) * (T(u,z) * z)) = K(x,(y * z) * u)
    ]]></literal>
    <justification jstring="[hyper(299,a,19055,a(flip),b,20726,a),flip(a)].">
      <j1 rule="hyper" parents="299 19055 20726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20729">
    <literal><![CDATA[
      K(x,L(y,z,u) * (z * u)) = K(x,(y * z) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,15899,a(flip),b,20727,a)].">
      <j1 rule="hyper" parents="65 15899 20727"/>
    </justification>
  </clause>

  <clause id="20730">
    <literal><![CDATA[
      K(x,L(y,z / u,u \ 1) * (z / (u * u))) = K(x,(y * (z / u)) * (u \ 1))
    ]]></literal>
    <justification jstring="[para(1245(a,1),20729(a,1,2,2))].">
      <j1 rule="para" parents="1245 20729"/>
    </justification>
  </clause>

  <clause id="20731">
    <literal><![CDATA[
      K(x,L(y,(z \ 1) \ (u * z),1 / z) * (T(u,z \ 1) * z)) = K(x,(y * ((z \ 1) \ (u * z))) * (1 / z))
    ]]></literal>
    <justification jstring="[para(11472(a,1),20729(a,1,2,2))].">
      <j1 rule="para" parents="11472 20729"/>
    </justification>
  </clause>

  <clause id="20732">
    <literal><![CDATA[
      K(x,L(y,z / u,u) * (z / (u * u))) = K(x,(y * (z / u)) * (u \ 1))
    ]]></literal>
    <justification jstring="[para(2470(a,1),20730(a,1,2,1))].">
      <j1 rule="para" parents="2470 20730"/>
    </justification>
  </clause>

  <clause id="20733">
    <literal><![CDATA[
      K(x,L(y,z \ u,z) * (u / (z * z))) = K(x,(y * (u / z)) * (z \ 1))
    ]]></literal>
    <justification jstring="[para(11629(a,1),20732(a,1,2,1))].">
      <j1 rule="para" parents="11629 20732"/>
    </justification>
  </clause>

  <clause id="20734">
    <literal><![CDATA[
      K(x,L(y,z \ u,z) * ((z * z) \ u)) = K(x,(y * (u / z)) * (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(65,a,17477,a(flip),b,20733,a)].">
      <j1 rule="hyper" parents="65 17477 20733"/>
    </justification>
  </clause>

  <clause id="20736">
    <literal><![CDATA[
      K(x,L(y,z \ u,z) * ((z * z) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * (u / z)) / z) = w
    ]]></literal>
    <justification jstring="[para(20734(a,2),14626(a,1))].">
      <j1 rule="para" parents="20734 14626"/>
    </justification>
  </clause>

  <clause id="20737">
    <literal><![CDATA[
      K(x,L(y,z \ u,z) * ((z * z) \ u)) = K(x,(y * (z \ u)) * T(1 / z,z \ u))
    ]]></literal>
    <justification jstring="[para(2467(a,1),20725(a,1,2,1))].">
      <j1 rule="para" parents="2467 20725"/>
    </justification>
  </clause>

  <clause id="20738">
    <literal><![CDATA[
      K(x,(y * (z \ u)) * T(1 / z,z \ u)) = K(x,(y * (u / z)) / z)
    ]]></literal>
    <justification jstring="[hyper(20736,a,20737,a),flip(a)].">
      <j1 rule="hyper" parents="20736 20737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20739">
    <literal><![CDATA[
      K(x,(y * (z \ u)) * T(z \ 1,u * z)) = K(x,(y * (u / z)) / z)
    ]]></literal>
    <justification jstring="[para(14509(a,1),20738(a,1,2,2))].">
      <j1 rule="para" parents="14509 20738"/>
    </justification>
  </clause>

  <clause id="20740">
    <literal><![CDATA[
      K(x,(y * (z \ u)) / T(z,u * z)) = K(x,(y * (u / z)) / z)
    ]]></literal>
    <justification jstring="[hyper(20597,a,20739,a)].">
      <j1 rule="hyper" parents="20597 20739"/>
    </justification>
  </clause>

  <clause id="20741">
    <literal><![CDATA[
      K(x,(y * (z \ u)) / T(z,u)) = K(x,(y * (u / z)) / z)
    ]]></literal>
    <justification jstring="[hyper(65,a,17332,a(flip),b,20740,a)].">
      <j1 rule="hyper" parents="65 17332 20740"/>
    </justification>
  </clause>

  <clause id="20742">
    <literal><![CDATA[
      K(x,L(y / ((z \ u) \ z),z,z * u)) = K(x,(y * (u / z)) / z)
    ]]></literal>
    <justification jstring="[hyper(19777,a,20741,a)].">
      <j1 rule="hyper" parents="19777 20741"/>
    </justification>
  </clause>

  <clause id="20743">
    <literal><![CDATA[
      K(x,L(T(y,T(z,u)) \ w,w,z * (K(u,z) * y))) = K(x,(z * K(u,z)) \ ((y \ (z * K(u,z))) * w))
    ]]></literal>
    <justification jstring="[para(5488(a,1),20627(a,1,2,3))].">
      <j1 rule="para" parents="5488 20627"/>
    </justification>
  </clause>

  <clause id="20744">
    <literal><![CDATA[
      K(x,L((y \ K(z \ ((z \ 1) \ u),y \ 1)) \ 1,z,z) \ u) = K(x,(z \ ((z \ 1) \ u)) / y)
    ]]></literal>
    <justification jstring="[hyper(299,a,14205,a(flip),b,20695,a),flip(a)].">
      <j1 rule="hyper" parents="299 14205 20695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20745">
    <literal><![CDATA[
      K(x,L((y \ K(z \ ((z \ 1) \ u),y \ 1)) \ 1,z,z) \ u) = K(x,u / L(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,20696,a(flip),b,20744,a),flip(a)].">
      <j1 rule="hyper" parents="299 20696 20744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20746">
    <literal><![CDATA[
      K(x,L((y \ K(z,y \ 1)) \ 1,u,u) \ z) = K(x,z / L(y,u,u))
    ]]></literal>
    <justification jstring="[para(14350(a,1),20745(a,1,2,1,1,1,2))].">
      <j1 rule="para" parents="14350 20745"/>
    </justification>
  </clause>

  <clause id="20747">
    <literal><![CDATA[
      K(x,L(((y * (z \ 1)) / y) \ 1,u,u) \ y) = K(x,y / L(z,u,u))
    ]]></literal>
    <justification jstring="[para(5079(a,1),20746(a,1,2,1,1,1))].">
      <j1 rule="para" parents="5079 20746"/>
    </justification>
  </clause>

  <clause id="20749">
    <literal><![CDATA[
      K(x,L((y \ 1) \ K(y \ 1,z),u,u) \ z) = K(x,z / L(y,u,u))
    ]]></literal>
    <justification jstring="[para(5182(a,1),20747(a,1,2,1,1))].">
      <j1 rule="para" parents="5182 20747"/>
    </justification>
  </clause>

  <clause id="20750">
    <literal><![CDATA[
      K(x,L((y * y) * (y \ K(y \ 1,z)),u,u) \ z) = K(x,z / L(y,u,u))
    ]]></literal>
    <justification jstring="[para(724(a,2),20749(a,1,2,1,1))].">
      <j1 rule="para" parents="724 20749"/>
    </justification>
  </clause>

  <clause id="20751">
    <literal><![CDATA[
      K(x,L((y * y) * T(y \ 1,z),u,u) \ z) = K(x,z / L(y,u,u))
    ]]></literal>
    <justification jstring="[para(5040(a,1),20750(a,1,2,1,1,2))].">
      <j1 rule="para" parents="5040 20750"/>
    </justification>
  </clause>

  <clause id="20752">
    <literal><![CDATA[
      K(x,L(y * (y * T(1 / y,z)),u,u) \ z) = K(x,z / L(y,u,u))
    ]]></literal>
    <justification jstring="[para(924(a,1),20751(a,1,2,1,1))].">
      <j1 rule="para" parents="924 20751"/>
    </justification>
  </clause>

  <clause id="20753">
    <literal><![CDATA[
      K(x,L(T(1 / y,z),u,u) \ (y \ (y \ z))) = K(x,z / L(y,u,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,15645,a(flip),b,20752,a)].">
      <j1 rule="hyper" parents="65 15645 20752"/>
    </justification>
  </clause>

  <clause id="20754">
    <literal><![CDATA[
      K(x,L(T(y \ 1,z),u,u) \ (y \ (y \ z))) = K(x,z / L(y,u,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,11183,a(flip),b,20753,a)].">
      <j1 rule="hyper" parents="65 11183 20753"/>
    </justification>
  </clause>

  <clause id="20755">
    <literal><![CDATA[
      K(x,L(T(y,T(z,u)) \ w,w,T(z,u) * y)) = K(x,(z * K(u,z)) \ ((y \ (z * K(u,z))) * w))
    ]]></literal>
    <justification jstring="[para(18749(a,1),20743(a,1,2))].">
      <j1 rule="para" parents="18749 20743"/>
    </justification>
  </clause>

  <clause id="20756">
    <literal><![CDATA[
      K(x,(y * K(z,y)) \ ((u \ (y * K(z,y))) * w)) = K(x,T(y,z) \ ((u \ T(y,z)) * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,20625,a(flip),b,20755,a),flip(a)].">
      <j1 rule="hyper" parents="65 20625 20755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20757">
    <literal><![CDATA[
      K(x,(y * K(z,y)) \ (((u \ y) * K(z,y)) * w)) = K(x,T(y,z) \ ((u \ T(y,z)) * w))
    ]]></literal>
    <justification jstring="[para(19688(a,1),20756(a,1,2,2,1))].">
      <j1 rule="para" parents="19688 20756"/>
    </justification>
  </clause>

  <clause id="20758">
    <literal><![CDATA[
      K(x,K(y,z) * (y \ (((u \ y) * K(z,y)) * w))) = K(x,T(y,z) \ ((u \ T(y,z)) * w))
    ]]></literal>
    <justification jstring="[hyper(20060,a,20757,a)].">
      <j1 rule="hyper" parents="20060 20757"/>
    </justification>
  </clause>

  <clause id="20759">
    <literal><![CDATA[
      K(x,T(y,z) \ (((u \ y) * K(z,y)) * w)) = K(x,T(y,z) \ ((u \ T(y,z)) * w))
    ]]></literal>
    <justification jstring="[hyper(20335,a,20758,a)].">
      <j1 rule="hyper" parents="20335 20758"/>
    </justification>
  </clause>

  <clause id="20760">
    <literal><![CDATA[
      K(x,K(y,z) * (T(y,z) \ ((u \ y) * w))) = K(x,T(y,z) \ ((u \ T(y,z)) * w))
    ]]></literal>
    <justification jstring="[hyper(20260,a,20759,a)].">
      <j1 rule="hyper" parents="20260 20759"/>
    </justification>
  </clause>

  <clause id="20761">
    <literal><![CDATA[
      K(x,T(y,z) \ ((u \ T(y,z)) * w)) = K(x,y \ ((u \ y) * w))
    ]]></literal>
    <justification jstring="[para(5351(a,1),20760(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5351 20760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20763">
    <literal><![CDATA[
      T(x,y \ (T(T(z,u \ (w \ (u \ 1))),w \ (u \ ((u * w) \ 1))) \ v5)) = T(x,y \ (((w * z) / w) \ v5))
    ]]></literal>
    <justification jstring="[para(23(a,1),20284(a,1,2,2,1))].">
      <j1 rule="para" parents="23 20284"/>
    </justification>
  </clause>

  <clause id="20764">
    <literal><![CDATA[
      K(x,T(T(y,y / T(z,u * z)) * T(z \ 1,u * z),y) \ w) = K(x,(y * T(z \ 1,u)) \ w)
    ]]></literal>
    <justification jstring="[para(20386(a,1),20503(a,1,2,1,1,1))].">
      <j1 rule="para" parents="20386 20503"/>
    </justification>
  </clause>

  <clause id="20765">
    <literal><![CDATA[
      K(x,T(T(y,y / T(z,z * u)) * T(z \ 1,u * z),y) \ w) = K(x,(y * T(z \ 1,u)) \ w)
    ]]></literal>
    <justification jstring="[para(4366(a,1),20764(a,1,2,1,1,1,2,2))].">
      <j1 rule="para" parents="4366 20764"/>
    </justification>
  </clause>

  <clause id="20766">
    <literal><![CDATA[
      K(x,T(T(y,T(z,z * u) \ y) * T(z \ 1,u * z),y) \ w) = K(x,(y * T(z \ 1,u)) \ w)
    ]]></literal>
    <justification jstring="[para(4277(a,1),20765(a,1,2,1,1,1))].">
      <j1 rule="para" parents="4277 20765"/>
    </justification>
  </clause>

  <clause id="20767">
    <literal><![CDATA[
      K(x,T(T(y,T(z,u) \ y) * T(z \ 1,u * z),y) \ w) = K(x,(y * T(z \ 1,u)) \ w)
    ]]></literal>
    <justification jstring="[para(13727(a,1),20766(a,1,2,1,1,1))].">
      <j1 rule="para" parents="13727 20766"/>
    </justification>
  </clause>

  <clause id="20768">
    <literal><![CDATA[
      K(x,(T(y \ 1,z * y) * T(u,T(y,z) \ u)) \ w) = K(x,(u * T(y \ 1,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(16829,a,20767,a)].">
      <j1 rule="hyper" parents="16829 20767"/>
    </justification>
  </clause>

  <clause id="20769">
    <literal><![CDATA[
      T(x,y \ (T(z,(u * w) \ ((u * w) \ (u \ (w \ (u \ 1))))) \ v5)) = T(x,y \ (((w * z) / w) \ v5))
    ]]></literal>
    <justification jstring="[para(14742(a,1),20763(a,1,2,2,1))].">
      <j1 rule="para" parents="14742 20763"/>
    </justification>
  </clause>

  <clause id="20770">
    <literal><![CDATA[
      T(x,y \ (T(z,(u * w) * ((u * w) \ (u \ (w \ (u \ 1))))) \ v5)) = T(x,y \ (((w * z) / w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(19285,a,20769,a)].">
      <j1 rule="hyper" parents="19285 20769"/>
    </justification>
  </clause>

  <clause id="20771">
    <literal><![CDATA[
      T(x,y \ (T(z,u \ (w \ (u \ 1))) \ v5)) = T(x,y \ (((w * z) / w) \ v5))
    ]]></literal>
    <justification jstring="[para(10(a,1),20770(a,1,2,2,1,2))].">
      <j1 rule="para" parents="10 20770"/>
    </justification>
  </clause>

  <clause id="20773">
    <literal><![CDATA[
      T(x,y \ (T(z,u * (w \ u)) \ v5)) = T(x,y \ (((w * z) / w) \ v5))
    ]]></literal>
    <justification jstring="[para(15713(a,1),20771(a,1,2,2,1))].">
      <j1 rule="para" parents="15713 20771"/>
    </justification>
  </clause>

  <clause id="20774">
    <literal><![CDATA[
      T(x,y \ (T(z,u * (w \ u)) \ v5)) = T(x,y \ (T(z,w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(299,a,20282,a(flip),b,20773,a),flip(a)].">
      <j1 rule="hyper" parents="299 20282 20773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20775">
    <literal><![CDATA[
      K(x,L(y,(z \ 1) \ (u * z),z) * (T(u,z \ 1) * z)) = K(x,(y * ((z \ 1) \ (u * z))) * (1 / z))
    ]]></literal>
    <justification jstring="[para(2467(a,1),20731(a,1,2,1))].">
      <j1 rule="para" parents="2467 20731"/>
    </justification>
  </clause>

  <clause id="20776">
    <literal><![CDATA[
      K(x,L(y,z \ (u * z),z) * (T(u,z \ 1) * z)) = K(x,(y * ((z \ 1) \ (u * z))) * (1 / z))
    ]]></literal>
    <justification jstring="[para(2538(a,1),20775(a,1,2,1))].">
      <j1 rule="para" parents="2538 20775"/>
    </justification>
  </clause>

  <clause id="20777">
    <literal><![CDATA[
      K(x,L(y,T(z,u),u) * (T(z,u \ 1) * u)) = K(x,(y * ((u \ 1) \ (z * u))) * (1 / u))
    ]]></literal>
    <justification jstring="[para(22(a,2),20776(a,1,2,1,2))].">
      <j1 rule="para" parents="22 20776"/>
    </justification>
  </clause>

  <clause id="20778">
    <literal><![CDATA[
      K(x,L(y,z,u) * (T(z,u \ 1) * u)) = K(x,(y * ((u \ 1) \ (z * u))) * (1 / u))
    ]]></literal>
    <justification jstring="[para(11621(a,1),20777(a,1,2,1))].">
      <j1 rule="para" parents="11621 20777"/>
    </justification>
  </clause>

  <clause id="20779">
    <literal><![CDATA[
      K(x,L(y,z,u) * (T(z,u * 1) * u)) = K(x,(y * ((u \ 1) \ (z * u))) * (1 / u))
    ]]></literal>
    <justification jstring="[hyper(18050,a,20778,a)].">
      <j1 rule="hyper" parents="18050 20778"/>
    </justification>
  </clause>

  <clause id="20780">
    <literal><![CDATA[
      K(x,L(y,z,u) * (T(z,u) * u)) = K(x,(y * ((u \ 1) \ (z * u))) * (1 / u))
    ]]></literal>
    <justification jstring="[para(8(a,1),20779(a,1,2,2,1,2))].">
      <j1 rule="para" parents="8 20779"/>
    </justification>
  </clause>

  <clause id="20781">
    <literal><![CDATA[
      K(x,L(y,z,u) * (u * z)) = K(x,(y * ((u \ 1) \ (z * u))) * (1 / u))
    ]]></literal>
    <justification jstring="[hyper(65,a,15899,a(flip),b,20780,a)].">
      <j1 rule="hyper" parents="65 15899 20780"/>
    </justification>
  </clause>

  <clause id="20782">
    <literal><![CDATA[
      K(x,(((((y * z) / y) * ((y * z) / y)) \ u) * T(z,y)) \ w) = K(x,((1 / ((y * z) / y)) * T(u,T(z,y))) \ w)
    ]]></literal>
    <justification jstring="[para(8182(a,1),20354(a,2,2,1,2))].">
      <j1 rule="para" parents="8182 20354"/>
    </justification>
  </clause>

  <clause id="20783">
    <literal><![CDATA[
      K(x,(((((y * z) / y) * ((y * z) / y)) \ u) * T(z,y)) \ w) = K(x,((1 / ((y * z) / y)) * T(u,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(299,a,18820,a(flip),b,20782,a),flip(a)].">
      <j1 rule="hyper" parents="299 18820 20782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20785">
    <literal><![CDATA[
      K(x,(((((y * z) / y) * ((y * z) / y)) \ u) * T(z,y)) \ w) = K(x,((((y * z) / y) \ 1) * T(u,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(299,a,5664,a(flip),b,20783,a),flip(a)].">
      <j1 rule="hyper" parents="299 5664 20783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20786">
    <literal><![CDATA[
      K(x,(((((y * z) / y) * ((y * z) / y)) \ u) * T(z,y)) \ w) = K(x,((1 / T((y * z) / y,u)) * u) \ w)
    ]]></literal>
    <justification jstring="[para(5038(a,1),20355(a,2,2,1,1))].">
      <j1 rule="para" parents="5038 20355"/>
    </justification>
  </clause>

  <clause id="20787">
    <literal><![CDATA[
      K(x,((T((y * z) / y,u) \ 1) * u) \ w) = K(x,(((((y * z) / y) * ((y * z) / y)) \ u) * T(z,y)) \ w)
    ]]></literal>
    <justification jstring="[hyper(299,a,5664,a(flip),b,20786,a)].">
      <j1 rule="hyper" parents="299 5664 20786"/>
    </justification>
  </clause>

  <clause id="20788">
    <literal><![CDATA[
      K(x,(((((y * z) / y) * ((y * z) / y)) \ u) * T(z,y)) \ w) = K(x,(u * (((y * z) / y) \ 1)) \ w)
    ]]></literal>
    <justification jstring="[hyper(17997,a,20787,a),flip(a)].">
      <j1 rule="hyper" parents="17997 20787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20789">
    <literal><![CDATA[
      K(x,(((((y * z) / y) * ((y * z) / y)) \ u) * T(z,y)) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * (((y * z) / y) \ 1)) \ w) = v5
    ]]></literal>
    <justification jstring="[para(20787(a,1),17997(a,1))].">
      <j1 rule="para" parents="20787 17997"/>
    </justification>
  </clause>

  <clause id="20790">
    <literal><![CDATA[
      K(x,(y * T(z,u)) \ ((((u * z) / u) * ((u * z) / u)) * w)) = K(x,(y * (((u * z) / u) \ 1)) \ w)
    ]]></literal>
    <justification jstring="[para(767(a,1),20788(a,1,2))].">
      <j1 rule="para" parents="767 20788"/>
    </justification>
  </clause>

  <clause id="20791">
    <literal><![CDATA[
      K(x,((y * z) / y) * (((y * z) / y) * ((u * T(z,y)) \ w))) = K(x,(u * (((y * z) / y) \ 1)) \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,20294,a(flip),b,20790,a)].">
      <j1 rule="hyper" parents="65 20294 20790"/>
    </justification>
  </clause>

  <clause id="20792">
    <literal><![CDATA[
      K(x,((y * z) / y) * (T(z,y) * ((u * T(z,y)) \ w))) = K(x,(u * (((y * z) / y) \ 1)) \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,15974,a(flip),b,20791,a)].">
      <j1 rule="hyper" parents="65 15974 20791"/>
    </justification>
  </clause>

  <clause id="20793">
    <literal><![CDATA[
      K(x,T(y,z) * (T(y,z) * ((u * T(y,z)) \ w))) = K(x,(u * (((z * y) / z) \ 1)) \ w)
    ]]></literal>
    <justification jstring="[hyper(19099,a,20792,a)].">
      <j1 rule="hyper" parents="19099 20792"/>
    </justification>
  </clause>

  <clause id="20794">
    <literal><![CDATA[
      K(x,y * (T(T(y,z),z) * ((u * T(y,z)) \ w))) = K(x,(u * (((z * y) / z) \ 1)) \ w)
    ]]></literal>
    <justification jstring="[para(5736(a,1),20793(a,1,2))].">
      <j1 rule="para" parents="5736 20793"/>
    </justification>
  </clause>

  <clause id="20795">
    <literal><![CDATA[
      K(x,(y * (((z * u) / z) \ 1)) \ w) = K(x,u * (u * ((y * T(u,z)) \ w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,15976,a(flip),b,20794,a),flip(a)].">
      <j1 rule="hyper" parents="65 15976 20794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20797">
    <literal><![CDATA[
      K(x,y \ (((z \ 1) \ T(((1 / z) * (1 / z)) * u,1 / z)) * w)) = K(x,y \ ((z \ T(u,1 / z)) * w))
    ]]></literal>
    <justification jstring="[para(79(a,1),20608(a,2,2,2,1,1))].">
      <j1 rule="para" parents="79 20608"/>
    </justification>
  </clause>

  <clause id="20798">
    <literal><![CDATA[
      K(x,y \ (((z \ 1) \ T(((1 / z) * (1 / z)) * u,1 / z)) * w)) = K(x,y \ ((z \ T(u,z \ 1)) * w))
    ]]></literal>
    <justification jstring="[para(3733(a,1),20797(a,2,2,2,1,2))].">
      <j1 rule="para" parents="3733 20797"/>
    </justification>
  </clause>

  <clause id="20799">
    <literal><![CDATA[
      K(x,y \ (((z \ 1) \ T(((1 / z) * (1 / z)) * u,1 / z)) * w)) = K(x,y \ ((u / z) * w))
    ]]></literal>
    <justification jstring="[hyper(299,a,20561,a(flip),b,20798,a),flip(a)].">
      <j1 rule="hyper" parents="299 20561 20798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20800">
    <literal><![CDATA[
      K(x,y \ (((z \ 1) \ T((z \ (1 / z)) * u,1 / z)) * w)) = K(x,y \ ((u / z) * w))
    ]]></literal>
    <justification jstring="[para(428(a,1),20799(a,1,2,2,1,2,1,1))].">
      <j1 rule="para" parents="428 20799"/>
    </justification>
  </clause>

  <clause id="20801">
    <literal><![CDATA[
      K(x,y \ (((z \ 1) \ T((z \ 1) * (z \ u),1 / z)) * w)) = K(x,y \ ((u / z) * w))
    ]]></literal>
    <justification jstring="[para(1710(a,1),20800(a,1,2,2,1,2,1))].">
      <j1 rule="para" parents="1710 20800"/>
    </justification>
  </clause>

  <clause id="20802">
    <literal><![CDATA[
      K(x,y \ (((z \ 1) \ T((z \ 1) * (z \ u),z \ 1)) * w)) = K(x,y \ ((u / z) * w))
    ]]></literal>
    <justification jstring="[para(3733(a,1),20801(a,1,2,2,1,2))].">
      <j1 rule="para" parents="3733 20801"/>
    </justification>
  </clause>

  <clause id="20803">
    <literal><![CDATA[
      K(x,y \ (((z \ 1) \ (z \ (u * (z \ 1)))) * w)) = K(x,y \ ((u / z) * w))
    ]]></literal>
    <justification jstring="[para(1741(a,1),20802(a,1,2,2,1,2))].">
      <j1 rule="para" parents="1741 20802"/>
    </justification>
  </clause>

  <clause id="20804">
    <literal><![CDATA[
      K(x,y \ ((z \ ((1 / z) \ (u * (z \ 1)))) * w)) = K(x,y \ ((u / z) * w))
    ]]></literal>
    <justification jstring="[para(1663(a,1),20803(a,1,2,2,1))].">
      <j1 rule="para" parents="1663 20803"/>
    </justification>
  </clause>

  <clause id="20805">
    <literal><![CDATA[
      K(x,y \ ((z \ ((z \ 1) \ (u * (1 / z)))) * w)) = K(x,y \ ((u / z) * w))
    ]]></literal>
    <justification jstring="[para(3294(a,1),20804(a,1,2,2,1,2))].">
      <j1 rule="para" parents="3294 20804"/>
    </justification>
  </clause>

  <clause id="20806">
    <literal><![CDATA[
      K(x,y \ (T(T(z,u) / u,u \ 1) * w)) = K(x,y \ ((z / u) * w))
    ]]></literal>
    <justification jstring="[para(4736(a,1),20805(a,1,2,2,1))].">
      <j1 rule="para" parents="4736 20805"/>
    </justification>
  </clause>

  <clause id="20807">
    <literal><![CDATA[
      K(x,y \ (T(T(z,u) / u,u * 1) * w)) = K(x,y \ ((z / u) * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,17624,a(flip),b,20806,a)].">
      <j1 rule="hyper" parents="65 17624 20806"/>
    </justification>
  </clause>

  <clause id="20808">
    <literal><![CDATA[
      K(x,y \ (T(T(z,u) / u,u) * w)) = K(x,y \ ((z / u) * w))
    ]]></literal>
    <justification jstring="[para(8(a,1),20807(a,1,2,2,1,2))].">
      <j1 rule="para" parents="8 20807"/>
    </justification>
  </clause>

  <clause id="20809">
    <literal><![CDATA[
      K(x,y \ ((z \ T(u,z)) * w)) = K(x,y \ ((u / z) * w))
    ]]></literal>
    <justification jstring="[para(109(a,1),20808(a,1,2,2,1))].">
      <j1 rule="para" parents="109 20808"/>
    </justification>
  </clause>

  <clause id="20810">
    <literal><![CDATA[
      K(x,y \ ((T(z,u) \ u) * w)) = K(x,y \ ((u / z) * w))
    ]]></literal>
    <justification jstring="[para(4396(a,2),20809(a,1,2,2,1))].">
      <j1 rule="para" parents="4396 20809"/>
    </justification>
  </clause>

  <clause id="20811">
    <literal><![CDATA[
      K(x,T(T(K(y,z) * u,w * w),v5)) = K(x,K(y,z) * T(u,w * (w * v5)))
    ]]></literal>
    <justification jstring="[hyper(10354,a,19140,a)].">
      <j1 rule="hyper" parents="10354 19140"/>
    </justification>
  </clause>

  <clause id="20812">
    <literal><![CDATA[
      K(x,K(y,z) * T(u,w * (w * v5))) = K(x,T(K(y,z) * u,v5))
    ]]></literal>
    <justification jstring="[hyper(16197,a,20811,a),flip(a)].">
      <j1 rule="hyper" parents="16197 20811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20813">
    <literal><![CDATA[
      K(x,T(K(y,z) * u,w)) = K(x,K(y,z) * T(u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,18007,a(flip),b,20812,a),flip(a)].">
      <j1 rule="hyper" parents="65 18007 20812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20814">
    <literal><![CDATA[
      K(x,T(K(y \ z,u) * w,v5)) = K(x,K(y * z,u) * T(w,v5))
    ]]></literal>
    <justification jstring="[hyper(299,a,17837,a(flip),b,20813,a),flip(a)].">
      <j1 rule="hyper" parents="299 17837 20813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20815">
    <literal><![CDATA[
      K(x,K(y,z * u) * (z * T(u,w))) = K(x,T(K(u,w) * (z * u),y))
    ]]></literal>
    <justification jstring="[hyper(16947,a,20813,a(flip))].">
      <j1 rule="hyper" parents="16947 20813"/>
    </justification>
  </clause>

  <clause id="20816">
    <literal><![CDATA[
      K(x,K(y * z,u) * T(u \ w,v5)) = K(x,T(T(u,y \ z) \ w,v5))
    ]]></literal>
    <justification jstring="[para(5383(a,1),20814(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5383 20814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20817">
    <literal><![CDATA[
      K(x,K(y,z * u) * (z * T(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z * T(u,w),y)) = v5
    ]]></literal>
    <justification jstring="[para(20815(a,2),16621(a,1))].">
      <j1 rule="para" parents="20815 16621"/>
    </justification>
  </clause>

  <clause id="20818">
    <literal><![CDATA[
      K(x,T(K(y * z,u) * (u \ w),v5)) = K(x,T(T(u,y \ z) \ w,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,20813,a,b,20816,a)].">
      <j1 rule="hyper" parents="65 20813 20816"/>
    </justification>
  </clause>

  <clause id="20819">
    <literal><![CDATA[
      K(x,T(T(y,z \ u) \ w,v5)) = K(x,T(T(y,z * u) \ w,v5))
    ]]></literal>
    <justification jstring="[para(5383(a,1),20818(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5383 20818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20820">
    <literal><![CDATA[
      K(x,L(y,y \ z,u) * (u * (y \ z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(u * T(z,y),y)) = w
    ]]></literal>
    <justification jstring="[para(19480(a,2),20817(a,1))].">
      <j1 rule="para" parents="19480 20817"/>
    </justification>
  </clause>

  <clause id="20821">
    <literal><![CDATA[
      (((x * y) * K(z,T(u,y))) / (x * (K(z,u) * y))) * x = ((x * y) * K(z,T(u,y))) / (K(z,u) * y)
    ]]></literal>
    <justification jstring="[para(14892(a,1),19611(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14892 19611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20822">
    <literal><![CDATA[
      (((x * y) * K(z,T(u,y))) / (x * (K(z,u) * y))) * x = L(x,y,K(z,T(u,y)))
    ]]></literal>
    <justification jstring="[hyper(299,a,19638,a(flip),b,20821,a),flip(a)].">
      <j1 rule="hyper" parents="299 19638 20821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20824">
    <literal><![CDATA[
      L(x,y,K(z,T(u,y))) = a(x,y,K(z,u)) * x
    ]]></literal>
    <justification jstring="[para(19610(a,1),20822(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19610 20822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20825">
    <literal><![CDATA[
      L(x,y,K(z,T(u,y))) = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,14894,a(flip),b,20824,a),flip(a)].">
      <j1 rule="hyper" parents="299 14894 20824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20826">
    <literal><![CDATA[
      L(x,y,K(z,u)) = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(19952,a,20825,a)].">
      <j1 rule="hyper" parents="19952 20825"/>
    </justification>
  </clause>

  <clause id="20827">
    <literal><![CDATA[
      T(x,a(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(20825(a,1),19952(a,1))].">
      <j1 rule="para" parents="20825 19952"/>
    </justification>
  </clause>

  <clause id="20828">
    <literal><![CDATA[
      L(x,y,K(z,u)) = T(x,a(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(5219,a,20826,a)].">
      <j1 rule="hyper" parents="5219 20826"/>
    </justification>
  </clause>

  <clause id="20829">
    <literal><![CDATA[
      T(x,a(y,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(4775,a,20826,a)].">
      <j1 rule="hyper" parents="4775 20826"/>
    </justification>
  </clause>

  <clause id="20830">
    <literal><![CDATA[
      T(x,T(a(y,z,u),w)) = L(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,18638,a,b,20826,a)].">
      <j1 rule="hyper" parents="299 18638 20826"/>
    </justification>
  </clause>

  <clause id="20831">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) = L(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,14968,a,b,20826,a)].">
      <j1 rule="hyper" parents="299 14968 20826"/>
    </justification>
  </clause>

  <clause id="20832">
    <literal><![CDATA[
      x * a(x,y,K(z,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,14893,a,b,20826,a)].">
      <j1 rule="hyper" parents="299 14893 20826"/>
    </justification>
  </clause>

  <clause id="20833">
    <literal><![CDATA[
      L(a(x,y,y),z,K(u,w)) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,14905,a(flip),b,20826,a),flip(a)].">
      <j1 rule="hyper" parents="299 14905 20826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20834">
    <literal><![CDATA[
      x \ L(x,y,K(z,u)) = a(u,y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(119,a,20826,a,b,14968,a)].">
      <j1 rule="hyper" parents="119 20826 14968"/>
    </justification>
  </clause>

  <clause id="20835">
    <literal><![CDATA[
      (a(x,y,z) * u) / a(x,y,z) = L(u,y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(14970,a,20826,a(flip))].">
      <j1 rule="hyper" parents="14970 20826"/>
    </justification>
  </clause>

  <clause id="20837">
    <literal><![CDATA[
      L(x,y,K(z,u)) \ x = a(u,y,K(z,x))
    ]]></literal>
    <justification jstring="[para(20826(a,2),14557(a,1,1))].">
      <j1 rule="para" parents="20826 14557"/>
    </justification>
  </clause>

  <clause id="20838">
    <literal><![CDATA[
      (x / y) * a(z,u,K(w,y)) = x / L(y,u,K(w,z))
    ]]></literal>
    <justification jstring="[para(20826(a,2),14565(a,2,2))].">
      <j1 rule="para" parents="20826 14565"/>
    </justification>
  </clause>

  <clause id="20839">
    <literal><![CDATA[
      1 / L(x,y,K(z,u)) = T(1 / x,a(u,y,z))
    ]]></literal>
    <justification jstring="[para(20826(a,2),15023(a,1,2))].">
      <j1 rule="para" parents="20826 15023"/>
    </justification>
  </clause>

  <clause id="20840">
    <literal><![CDATA[
      x * L(x \ y,z,K(u,w)) = y * a(w,z,K(u,x * y))
    ]]></literal>
    <justification jstring="[para(20826(a,2),15084(a,1,2))].">
      <j1 rule="para" parents="20826 15084"/>
    </justification>
  </clause>

  <clause id="20841">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(20826(a,2),18653(a,1,2))].">
      <j1 rule="para" parents="20826 18653"/>
    </justification>
  </clause>

  <clause id="20842">
    <literal><![CDATA[
      x * (y * a(z,u,K(x,w))) = L(x,u,K(w,z)) * y
    ]]></literal>
    <justification jstring="[para(20826(a,2),18761(a,2,1))].">
      <j1 rule="para" parents="20826 18761"/>
    </justification>
  </clause>

  <clause id="20843">
    <literal><![CDATA[
      K(x,y * L(z,u,K(w,v5))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(20826(a,2),18986(a,1,2,2))].">
      <j1 rule="para" parents="20826 18986"/>
    </justification>
  </clause>

  <clause id="20844">
    <literal><![CDATA[
      (x \ ((1 / x) \ y)) / y = y \ (x \ ((1 / x) \ y))
    ]]></literal>
    <justification jstring="[para(20829(a,1),1737(a,1,2))].">
      <j1 rule="para" parents="20829 1737"/>
    </justification>
  </clause>

  <clause id="20845">
    <literal><![CDATA[
      T(x,a(y,y,z) \ (a(y,y,z) \ u)) = T(x,u)
    ]]></literal>
    <justification jstring="[para(20829(a,1),14753(a,1,1))].">
      <j1 rule="para" parents="20829 14753"/>
    </justification>
  </clause>

  <clause id="20846">
    <literal><![CDATA[
      x * a(x,y,K(z,u)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,14893,a,b,20828,a)].">
      <j1 rule="hyper" parents="299 14893 20828"/>
    </justification>
  </clause>

  <clause id="20847">
    <literal><![CDATA[
      T(L(x,y,K(z,u)),a(z,y,u)) = x
    ]]></literal>
    <justification jstring="[hyper(43,a,14969,a(flip),b,20828,a),flip(a)].">
      <j1 rule="hyper" parents="43 14969 20828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20848">
    <literal><![CDATA[
      (a(x,y,z) * u) / a(x,y,z) = L(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(14970,a,20828,a(flip))].">
      <j1 rule="hyper" parents="14970 20828"/>
    </justification>
  </clause>

  <clause id="20849">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),y,K(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(65,a,20828,a,b,20847,a)].">
      <j1 rule="hyper" parents="65 20828 20847"/>
    </justification>
  </clause>

  <clause id="20850">
    <literal><![CDATA[
      a(K(x,y) * z,u,u) = a(z,u,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,15705,a(flip),b,20833,a)].">
      <j1 rule="hyper" parents="65 15705 20833"/>
    </justification>
  </clause>

  <clause id="20852">
    <literal><![CDATA[
      a(x / y,z,z) = a(y \ x,z,z)
    ]]></literal>
    <justification jstring="[para(5117(a,1),20850(a,1,1))].">
      <j1 rule="para" parents="5117 20850"/>
    </justification>
  </clause>

  <clause id="20853">
    <literal><![CDATA[
      a(L(T(x,y),z,u),w,w) = a(L(x,z,u),w,w)
    ]]></literal>
    <justification jstring="[para(5165(a,1),20850(a,1,1))].">
      <j1 rule="para" parents="5165 20850"/>
    </justification>
  </clause>

  <clause id="20854">
    <literal><![CDATA[
      a(x \ T(y,z),u,u) = a(x \ y,u,u)
    ]]></literal>
    <justification jstring="[para(5728(a,1),20850(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5728 20850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20855">
    <literal><![CDATA[
      a((x * y) \ z,u,u) = a((y * x) \ z,u,u)
    ]]></literal>
    <justification jstring="[para(11606(a,1),20850(a,1,1))].">
      <j1 rule="para" parents="11606 20850"/>
    </justification>
  </clause>

  <clause id="20856">
    <literal><![CDATA[
      a(R(T(x,y),z,u),w,w) = a(R(x,z,u),w,w)
    ]]></literal>
    <justification jstring="[para(15564(a,1),20850(a,1,1))].">
      <j1 rule="para" parents="15564 20850"/>
    </justification>
  </clause>

  <clause id="20857">
    <literal><![CDATA[
      (K(x,y) / z) * a(z,u,u) = R(K(x,y) / z,u,u)
    ]]></literal>
    <justification jstring="[para(20850(a,1),15585(a,1,2))].">
      <j1 rule="para" parents="20850 15585"/>
    </justification>
  </clause>

  <clause id="20858">
    <literal><![CDATA[
      K(x,y * ((K(z,u) / w) * a(w,v5,v5))) = K(x,y * R(w \ K(z,u),v5,v5))
    ]]></literal>
    <justification jstring="[para(20850(a,1),19384(a,1,2,2,2))].">
      <j1 rule="para" parents="20850 19384"/>
    </justification>
  </clause>

  <clause id="20859">
    <literal><![CDATA[
      (x * (y \ 1)) / a(y \ x,y,y) = x / y
    ]]></literal>
    <justification jstring="[para(20852(a,1),15582(a,1,2))].">
      <j1 rule="para" parents="20852 15582"/>
    </justification>
  </clause>

  <clause id="20860">
    <literal><![CDATA[
      K(x,(y \ T(T(a(z,u,w),v5),v5)) * v6) = K(x,(a(z,u,w) / L(y,u,K(w,z))) * v6)
    ]]></literal>
    <justification jstring="[para(20830(a,1),19224(a,2,2,1,2))].">
      <j1 rule="para" parents="20830 19224"/>
    </justification>
  </clause>

  <clause id="20861">
    <literal><![CDATA[
      T(x * K(y,x),L(y,z,u)) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(17298,a,20831,a)].">
      <j1 rule="hyper" parents="17298 20831"/>
    </justification>
  </clause>

  <clause id="20862">
    <literal><![CDATA[
      (T(a(x,y,z),u) * w) / T(a(x,y,z),u) = L(w,y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,19529,a,b,20831,a)].">
      <j1 rule="hyper" parents="65 19529 20831"/>
    </justification>
  </clause>

  <clause id="20863">
    <literal><![CDATA[
      x \ L(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,y,K(z,x)) = w
    ]]></literal>
    <justification jstring="[para(20831(a,1),314(a,1,2))].">
      <j1 rule="para" parents="20831 314"/>
    </justification>
  </clause>

  <clause id="20865">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w)) * v5) = K(x,y * v5)
    ]]></literal>
    <justification jstring="[para(20831(a,1),19041(a,1,2,1))].">
      <j1 rule="para" parents="20831 19041"/>
    </justification>
  </clause>

  <clause id="20866">
    <literal><![CDATA[
      K(x,y \ L(z,u,K(w,v5))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(20831(a,1),20512(a,1,2,2))].">
      <j1 rule="para" parents="20831 20512"/>
    </justification>
  </clause>

  <clause id="20867">
    <literal><![CDATA[
      T(x,a(y,z,u) \ x) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,15463,a,b,20832,a)].">
      <j1 rule="hyper" parents="65 15463 20832"/>
    </justification>
  </clause>

  <clause id="20868">
    <literal><![CDATA[
      x * a(y,z,K(x,u)) = L(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,14875,a(flip),b,20832,a)].">
      <j1 rule="hyper" parents="65 14875 20832"/>
    </justification>
  </clause>

  <clause id="20869">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(20834(a,1),250(a,1,2)),flip(b)].">
      <j1 rule="para" parents="20834 250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20873">
    <literal><![CDATA[
      K(x,L(y,z,T(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(6685(a,1),20841(a,1,2))].">
      <j1 rule="para" parents="6685 20841"/>
    </justification>
  </clause>

  <clause id="20874">
    <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(6780(a,1),20841(a,1,2))].">
      <j1 rule="para" parents="6780 20841"/>
    </justification>
  </clause>

  <clause id="20876">
    <literal><![CDATA[
      K(L(x,y,K(z,u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w) = v5
    ]]></literal>
    <justification jstring="[para(11929(a,2),20841(a,1))].">
      <j1 rule="para" parents="11929 20841"/>
    </justification>
  </clause>

  <clause id="20877">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ (K(u,y) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,((((u * y) / u) \ 1) * z) \ w) = v5
    ]]></literal>
    <justification jstring="[para(15317(a,1),20841(a,1))].">
      <j1 rule="para" parents="15317 20841"/>
    </justification>
  </clause>

  <clause id="20879">
    <literal><![CDATA[
      a(x \ (T(y,y * z) * z),u,u) = a(x \ (y * z),u,u)
    ]]></literal>
    <justification jstring="[para(1103(a,1),20854(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1103 20854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20880">
    <literal><![CDATA[
      T(x,a(y,z,u) \ 1) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(14545,a,20867,a)].">
      <j1 rule="hyper" parents="14545 20867"/>
    </justification>
  </clause>

  <clause id="20881">
    <literal><![CDATA[
      a(x,y,K(z,u)) * z = L(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(18620,a,20868,a)].">
      <j1 rule="hyper" parents="18620 20868"/>
    </justification>
  </clause>

  <clause id="20885">
    <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(19639(a,1),20876(a,1,1))].">
      <j1 rule="para" parents="19639 20876"/>
    </justification>
  </clause>

  <clause id="20886">
    <literal><![CDATA[
      T(x,a(y,z,u) \ 1) = L(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,5218,a,b,20880,a),flip(a)].">
      <j1 rule="hyper" parents="299 5218 20880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20887">
    <literal><![CDATA[
      T(x,a(y,z,u) \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(20886(a,2),5219(a,1))].">
      <j1 rule="para" parents="20886 5219"/>
    </justification>
  </clause>

  <clause id="20888">
    <literal><![CDATA[
      a(x \ y,x,x) \ (y * (x \ 1)) = y / x
    ]]></literal>
    <justification jstring="[hyper(14907,a,20859,a)].">
      <j1 rule="hyper" parents="14907 20859"/>
    </justification>
  </clause>

  <clause id="20889">
    <literal><![CDATA[
      K(x,T(K(y,z) * (u * w),u * K(y,z))) = K(x,w * (K(y,z) * u))
    ]]></literal>
    <justification jstring="[hyper(16634,a,20865,a)].">
      <j1 rule="hyper" parents="16634 20865"/>
    </justification>
  </clause>

  <clause id="20890">
    <literal><![CDATA[
      L(1 / x,y,K(z,u)) = 1 / L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,20826,a,b,20839,a)].">
      <j1 rule="hyper" parents="299 20826 20839"/>
    </justification>
  </clause>

  <clause id="20892">
    <literal><![CDATA[
      T(x,a(y,y,z) \ u) = T(x,a(y,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(42,a,14750,a,b,20845,a),flip(a)].">
      <j1 rule="hyper" parents="42 14750 20845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20893">
    <literal><![CDATA[
      a((x * y) \ (y * (z * x)),u,u) = a(L(T(z,x),x,y),u,u)
    ]]></literal>
    <justification jstring="[para(230(a,1),20855(a,1,1)),flip(a)].">
      <j1 rule="para" parents="230 20855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20894">
    <literal><![CDATA[
      L(T(x,y),z,K(y,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(5100(a,1),20861(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5100 20861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20895">
    <literal><![CDATA[
      T(x * K(y,x),L(y,y \ z,u)) = L(x,z / y,K(y,u))
    ]]></literal>
    <justification jstring="[para(11339(a,1),20861(a,1,2))].">
      <j1 rule="para" parents="11339 20861"/>
    </justification>
  </clause>

  <clause id="20896">
    <literal><![CDATA[
      T(x,L(y,K(z,u),w)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(20083,a,20894,a),flip(a)].">
      <j1 rule="hyper" parents="20083 20894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20897">
    <literal><![CDATA[
      K(x,y * T(z,L(u,w,v5))) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(20894(a,1),20843(a,1,2,2))].">
      <j1 rule="para" parents="20894 20843"/>
    </justification>
  </clause>

  <clause id="20898">
    <literal><![CDATA[
      K(x,y \ T(z,L(u,w,v5))) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(20894(a,1),20866(a,1,2,2))].">
      <j1 rule="para" parents="20894 20866"/>
    </justification>
  </clause>

  <clause id="20900">
    <literal><![CDATA[
      T(x,K(y,z) * ((u / w) \ 1)) = T(x,w * (u \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(65,a,19965,a(flip),b,20896,a),flip(a)].">
      <j1 rule="hyper" parents="65 19965 20896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20901">
    <literal><![CDATA[
      T(x,a(y,y,z) * (a(y,y,z) * u)) = T(x,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),20892(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 20892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20902">
    <literal><![CDATA[
      T(x,(L(y,z,z) / y) \ u) = T(x,(y \ L(y,z,z)) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,16168,a(flip),b,20901,a)].">
      <j1 rule="hyper" parents="65 16168 20901"/>
    </justification>
  </clause>

  <clause id="20903">
    <literal><![CDATA[
      L(a(x,y,z) \ u,y,K(z,x)) = u / a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(964,a,20835,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="964 20835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20904">
    <literal><![CDATA[
      (x * y) / L(y,z,K(u,w)) = x * a(y,z,K(u,w))
    ]]></literal>
    <justification jstring="[para(20835(a,1),14898(a,1,2))].">
      <j1 rule="para" parents="20835 14898"/>
    </justification>
  </clause>

  <clause id="20905">
    <literal><![CDATA[
      T(L(x,y,K(z,u)),a(z,y,u) \ 1) = T(x,a(z,y,u) \ (a(z,y,u) \ 1))
    ]]></literal>
    <justification jstring="[para(20848(a,1),14744(a,1,1))].">
      <j1 rule="para" parents="20848 14744"/>
    </justification>
  </clause>

  <clause id="20906">
    <literal><![CDATA[
      T(x * K(y,x),L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(12571(a,2),20869(a,1))].">
      <j1 rule="para" parents="12571 20869"/>
    </justification>
  </clause>

  <clause id="20908">
    <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(5731(a,1),20873(a,1,2))].">
      <j1 rule="para" parents="5731 20873"/>
    </justification>
  </clause>

  <clause id="20909">
    <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(13439(a,1),20873(a,1,2))].">
      <j1 rule="para" parents="13439 20873"/>
    </justification>
  </clause>

  <clause id="20910">
    <literal><![CDATA[
      K(x,L(y,z,L(u,w,K(v5,v6)))) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = v7
    ]]></literal>
    <justification jstring="[para(20826(a,2),20873(a,1,2,3))].">
      <j1 rule="para" parents="20826 20873"/>
    </justification>
  </clause>

  <clause id="20913">
    <literal><![CDATA[
      K(x,L(y,z,u) \ T(w,y)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w / L(y,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(20898(a,1),13929(a,1))].">
      <j1 rule="para" parents="20898 13929"/>
    </justification>
  </clause>

  <clause id="20914">
    <literal><![CDATA[
      K(x,T(y,L(z,u,w)) / v5) = K(x,K(v5,y)) * K(x,v5 \ T(y,z))
    ]]></literal>
    <justification jstring="[para(20898(a,1),16345(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20898 16345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20915">
    <literal><![CDATA[
      L(x,y,z) \ T((x \ 1) * L(x,y,z),u) = 1 / L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,17749,a,b,20838,a)].">
      <j1 rule="hyper" parents="65 17749 20838"/>
    </justification>
  </clause>

  <clause id="20916">
    <literal><![CDATA[
      K(x,(y / L(z,u,K(w,v5))) * v6) = K(x,(y / z) * v6)
    ]]></literal>
    <justification jstring="[para(20838(a,1),19041(a,1,2,1))].">
      <j1 rule="para" parents="20838 19041"/>
    </justification>
  </clause>

  <clause id="20917">
    <literal><![CDATA[
      (x * y) * a(z,u,K(x,w)) = L(x,u,K(w,z)) * y
    ]]></literal>
    <justification jstring="[hyper(36,a,1347,a(flip),b,20842,a),flip(a)].">
      <j1 rule="hyper" parents="36 1347 20842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20918">
    <literal><![CDATA[
      (x \ (y \ ((1 / y) \ x))) * x = y \ ((1 / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(143,a,20844,a)].">
      <j1 rule="hyper" parents="143 20844"/>
    </justification>
  </clause>

  <clause id="20919">
    <literal><![CDATA[
      (x \ (y \ ((1 / y) \ x))) * K(a(y,y,y \ (y \ x)),z) = T((y \ ((1 / y) \ x)) / x,T(z,x))
    ]]></literal>
    <justification jstring="[para(20844(a,1),7916(a,1,1))].">
      <j1 rule="para" parents="20844 7916"/>
    </justification>
  </clause>

  <clause id="20921">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (z * w) = L(z,y,K(u,x)) * w
    ]]></literal>
    <justification jstring="[hyper(18620,a,20917,a)].">
      <j1 rule="hyper" parents="18620 20917"/>
    </justification>
  </clause>

  <clause id="20922">
    <literal><![CDATA[
      (x \ ((1 / x) \ y)) \ (K((y \ (x \ ((1 / x) \ y))) \ 1,z) * y) = T(((y \ (x \ ((1 / x) \ y))) * y) \ y,z)
    ]]></literal>
    <justification jstring="[para(20918(a,1),6022(a,1,1))].">
      <j1 rule="para" parents="20918 6022"/>
    </justification>
  </clause>

  <clause id="20923">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w)) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * v5) = v6
    ]]></literal>
    <justification jstring="[para(20921(a,1),20516(a,1,2))].">
      <j1 rule="para" parents="20921 20516"/>
    </justification>
  </clause>

  <clause id="20924">
    <literal><![CDATA[
      K(x,L(y \ z,u,y * u)) = K(x,u \ ((y / u) \ z))
    ]]></literal>
    <justification jstring="[hyper(20909,a,19586,a)].">
      <j1 rule="hyper" parents="20909 19586"/>
    </justification>
  </clause>

  <clause id="20925">
    <literal><![CDATA[
      K(x,y \ ((z / y) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(z \ u,y,z * y)) = w
    ]]></literal>
    <justification jstring="[para(19586(a,1),20909(a,1))].">
      <j1 rule="para" parents="19586 20909"/>
    </justification>
  </clause>

  <clause id="20926">
    <literal><![CDATA[
      (K(x,y) * (z * (z \ u))) / (u * a(y,z,K(x,z * u))) = R(K(x,y),z,L(z \ u,z,K(x,y)))
    ]]></literal>
    <justification jstring="[para(20840(a,1),486(a,1,2))].">
      <j1 rule="para" parents="20840 486"/>
    </justification>
  </clause>

  <clause id="20927">
    <literal><![CDATA[
      x * a(y,z,K(u,a(y,z,u) * x)) = a(y,z,u) * (x / a(y,z,u))
    ]]></literal>
    <justification jstring="[para(20903(a,1),20840(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20903 20840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20928">
    <literal><![CDATA[
      a(x \ (y * z),u,u) = a(x \ (z * y),u,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,20683,a(flip),b,20879,a)].">
      <j1 rule="hyper" parents="65 20683 20879"/>
    </justification>
  </clause>

  <clause id="20929">
    <literal><![CDATA[
      a((x * y) \ (y * (z * x)),u,u) = a(R(T(z,x * y),x,y),u,u)
    ]]></literal>
    <justification jstring="[para(689(a,1),20928(a,1,1)),flip(a)].">
      <j1 rule="para" parents="689 20928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20930">
    <literal><![CDATA[
      T(x * K(y,x),L(y,z,u)) = L(x,z / y,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,11981,a(flip),b,20895,a)].">
      <j1 rule="hyper" parents="65 11981 20895"/>
    </justification>
  </clause>

  <clause id="20931">
    <literal><![CDATA[
      L(x,y / z,K(z,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(20906,a,20930,a),flip(a)].">
      <j1 rule="hyper" parents="20906 20930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20932">
    <literal><![CDATA[
      L(x,K(y,z) / u,K(u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(299,a,20070,a(flip),b,20931,a),flip(a)].">
      <j1 rule="hyper" parents="299 20070 20931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20933">
    <literal><![CDATA[
      L(x,K(y,z) * u,K(u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(65,a,14424,a(flip),b,20932,a)].">
      <j1 rule="hyper" parents="65 14424 20932"/>
    </justification>
  </clause>

  <clause id="20934">
    <literal><![CDATA[
      L(x,T(y,z),K(u,w)) = L(x,y,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(19808,a,20933,a)].">
      <j1 rule="hyper" parents="19808 20933"/>
    </justification>
  </clause>

  <clause id="20936">
    <literal><![CDATA[
      a(x,T(y,z),K(u,w)) = w \ L(w,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(119,a,20934,a(flip),b,20831,a),flip(a)].">
      <j1 rule="hyper" parents="119 20934 20831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20937">
    <literal><![CDATA[
      a(x,T(y,z),K(u,w)) = a(x,y,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(299,a,20834,a(flip),b,20936,a),flip(a)].">
      <j1 rule="hyper" parents="299 20834 20936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20938">
    <literal><![CDATA[
      a(x,T(y,z),K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(u,w)) = v5
    ]]></literal>
    <justification jstring="[para(20936(a,2),20863(a,1))].">
      <j1 rule="para" parents="20936 20863"/>
    </justification>
  </clause>

  <clause id="20940">
    <literal><![CDATA[
      a(T(x,y) \ z,(x \ z) \ z,K(u,w)) = a(w,z,K(T(x,y) \ z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,14986,a(flip),b,20937,a),flip(a)].">
      <j1 rule="hyper" parents="65 14986 20937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20943">
    <literal><![CDATA[
      K(x,L(y,z * K(u,z),w)) = K(x,y) * a(x,z,K(w,y))
    ]]></literal>
    <justification jstring="[para(20937(a,1),14932(a,2,2))].">
      <j1 rule="para" parents="20937 14932"/>
    </justification>
  </clause>

  <clause id="20945">
    <literal><![CDATA[
      T(x,K(y,z) / (u / w)) = T(x,w * (u \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(14593,a,20900,a)].">
      <j1 rule="hyper" parents="14593 20900"/>
    </justification>
  </clause>

  <clause id="20947">
    <literal><![CDATA[
      T(x,(y / z) \ K(u,w)) = T(x,z * (y \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(16367,a,20945,a)].">
      <j1 rule="hyper" parents="16367 20945"/>
    </justification>
  </clause>

  <clause id="20949">
    <literal><![CDATA[
      T(x,(y \ L(y,z,z)) \ u) = T(x,(y \ L(y,z,z)) * u)
    ]]></literal>
    <justification jstring="[para(3819(a,1),20902(a,1,2,1))].">
      <j1 rule="para" parents="3819 20902"/>
    </justification>
  </clause>

  <clause id="20950">
    <literal><![CDATA[
      K(x,L(y,z * K(u,z),w)) = K(x,L(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(299,a,14882,a(flip),b,20943,a),flip(a)].">
      <j1 rule="hyper" parents="299 14882 20943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20952">
    <literal><![CDATA[
      K(x,L(y,T(z,u),w)) = K(x,L(y,z,w))
    ]]></literal>
    <justification jstring="[para(5100(a,1),20950(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5100 20950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20956">
    <literal><![CDATA[
      K(x,L(T(y,z) \ u,z,z * y)) = K(x,z \ ((z \ y) \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,20504,a(flip),b,20952,a),flip(a)].">
      <j1 rule="hyper" parents="65 20504 20952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20957">
    <literal><![CDATA[
      K(x,L((y / R(z,u,z)) \ T(w,z),w,L(z,u,z))) = K(x,T(y,R(z,u,z)) \ (w * R(z,u,z)))
    ]]></literal>
    <justification jstring="[hyper(65,a,16125,a(flip),b,20952,a),flip(a)].">
      <j1 rule="hyper" parents="65 16125 20952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20958">
    <literal><![CDATA[
      K(x,L(y,R(z,u,u),u \ 1)) = K(x,L(y,z * u,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,15091,a(flip),b,20952,a)].">
      <j1 rule="hyper" parents="65 15091 20952"/>
    </justification>
  </clause>

  <clause id="20960">
    <literal><![CDATA[
      K(x,L(y,R(z,u,u),u \ 1)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,14996,a(flip),b,20958,a),flip(a)].">
      <j1 rule="hyper" parents="299 14996 20958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20961">
    <literal><![CDATA[
      K(x,L((y * z) / u,y,z)) = K(x,R(y,z,z) / (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(65,a,15558,a(flip),b,20960,a),flip(a)].">
      <j1 rule="hyper" parents="65 15558 20960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20962">
    <literal><![CDATA[
      K(T(a(x,y,z),u) \ (T(a(x,y,z),u) * w),v5 / T(a(x,y,z),u)) = K(L(w,y,K(z,x)),T(a(x,y,z),u) \ v5)
    ]]></literal>
    <justification jstring="[para(20862(a,1),7624(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20862 7624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20964">
    <literal><![CDATA[
      K((x * K(y,z)) / u,w) = K(x * (u \ K(y,z)),w)
    ]]></literal>
    <justification jstring="[hyper(20885,a,20148,a)].">
      <j1 rule="hyper" parents="20885 20148"/>
    </justification>
  </clause>

  <clause id="20965">
    <literal><![CDATA[
      K((x / y) * (z \ K(u,y)),w) = K((x / T(y,u)) / z,w)
    ]]></literal>
    <justification jstring="[para(7189(a,1),20964(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7189 20964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20966">
    <literal><![CDATA[
      K(K(x,y) * ((z / x) / u),w) = K((z / T(x,y)) / u,w)
    ]]></literal>
    <justification jstring="[hyper(20117,a,20965,a)].">
      <j1 rule="hyper" parents="20117 20965"/>
    </justification>
  </clause>

  <clause id="20967">
    <literal><![CDATA[
      K((x / T(y,y * z)) / u,w) = K(K(y,z) * ((x / y) / u),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,13729,a(flip),b,20966,a),flip(a)].">
      <j1 rule="hyper" parents="65 13729 20966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20968">
    <literal><![CDATA[
      a((x * y) \ (y * (z * x)),u,u) = a(L(z,x,y),u,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,20853,a(flip),b,20893,a),flip(a)].">
      <j1 rule="hyper" parents="299 20853 20893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20970">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,z,z * (y \ 1))) = K(x,z \ ((z \ (y \ 1)) \ u))
    ]]></literal>
    <justification jstring="[hyper(20288,a,20956,a)].">
      <j1 rule="hyper" parents="20288 20956"/>
    </justification>
  </clause>

  <clause id="20972">
    <literal><![CDATA[
      K(x,L(T((y * z) / y,y) \ u,y,T(y,z) * z)) = K(x,y \ ((y \ ((y * z) / y)) \ u))
    ]]></literal>
    <justification jstring="[para(4263(a,2),20956(a,1,2,3))].">
      <j1 rule="para" parents="4263 20956"/>
    </justification>
  </clause>

  <clause id="20973">
    <literal><![CDATA[
      K(x,L((y * z) / u,y,z)) = K(x,L(y,z,z) / (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(299,a,16111,a(flip),b,20961,a),flip(a)].">
      <j1 rule="hyper" parents="299 16111 20961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20974">
    <literal><![CDATA[
      K((x / ((y \ z) \ z)) / u,w) = K(K(y,z) * ((x / y) / u),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,19343,a(flip),b,20967,a)].">
      <j1 rule="hyper" parents="65 19343 20967"/>
    </justification>
  </clause>

  <clause id="20975">
    <literal><![CDATA[
      K(x,L((y * z) / u,y,z)) = K(x,(z * (z * y)) / (u * z))
    ]]></literal>
    <justification jstring="[hyper(299,a,19421,a(flip),b,20973,a),flip(a)].">
      <j1 rule="hyper" parents="299 19421 20973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20976">
    <literal><![CDATA[
      K(x,L((y * z) / u,y,z)) = K(x,y / (z \ (z \ (u * z))))
    ]]></literal>
    <justification jstring="[hyper(299,a,17286,a(flip),b,20975,a),flip(a)].">
      <j1 rule="hyper" parents="299 17286 20975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20977">
    <literal><![CDATA[
      K(x,L((y * z) / u,y,z)) = K(x,y / (z \ T(u,z)))
    ]]></literal>
    <justification jstring="[para(22(a,2),20976(a,2,2,2,2))].">
      <j1 rule="para" parents="22 20976"/>
    </justification>
  </clause>

  <clause id="20978">
    <literal><![CDATA[
      K(x,L((y * z) / u,y,z)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(20304,a,20977,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="20304 20977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20979">
    <literal><![CDATA[
      K(x,L((y * z) / u,y,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (u / z)) = w
    ]]></literal>
    <justification jstring="[para(20977(a,2),20304(a,1))].">
      <j1 rule="para" parents="20977 20304"/>
    </justification>
  </clause>

  <clause id="20980">
    <literal><![CDATA[
      K(x,L((y * T(z,u)) / w,y,z)) = K(x,y / (w / T(z,u)))
    ]]></literal>
    <justification jstring="[hyper(20873,a,20978,a)].">
      <j1 rule="hyper" parents="20873 20978"/>
    </justification>
  </clause>

  <clause id="20981">
    <literal><![CDATA[
      K(L((x * y) / z,x,y),u) = (w * K(u,x / (z / y))) \ w
    ]]></literal>
    <justification jstring="[para(20978(a,1),7200(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="20978 7200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20983">
    <literal><![CDATA[
      K(x,L((y * T(z,z \ y)) / u,z * (y / z),z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * (y / z)) / (u / z)) = w
    ]]></literal>
    <justification jstring="[para(4445(a,1),20979(a,1,2,1,1))].">
      <j1 rule="para" parents="4445 20979"/>
    </justification>
  </clause>

  <clause id="20984">
    <literal><![CDATA[
      K(x,L((y * z) * u,y,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / ((u \ 1) / z)) = w
    ]]></literal>
    <justification jstring="[para(14649(a,1),20979(a,1))].">
      <j1 rule="para" parents="14649 20979"/>
    </justification>
  </clause>

  <clause id="20985">
    <literal><![CDATA[
      K(x,L((y * T(z,u)) / w,y,z)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (w / T(z,u))) = v5
    ]]></literal>
    <justification jstring="[para(18603(a,1),20979(a,1))].">
      <j1 rule="para" parents="18603 20979"/>
    </justification>
  </clause>

  <clause id="20986">
    <literal><![CDATA[
      K(x,L(T(y * z,K(z,u)) / w,z,y)) = K(x,z / (w / T(y,T(z,u))))
    ]]></literal>
    <justification jstring="[para(7400(a,2),20980(a,1,2,1,1))].">
      <j1 rule="para" parents="7400 20980"/>
    </justification>
  </clause>

  <clause id="20987">
    <literal><![CDATA[
      K(L((x * y) / z,x,y),u) = K(x / (z / y),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,18856,a(flip),b,20981,a),flip(a)].">
      <j1 rule="hyper" parents="299 18856 20981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20988">
    <literal><![CDATA[
      K((x * y) / z,L(u,x,y)) = K(x / (z / y),u)
    ]]></literal>
    <justification jstring="[hyper(11999,a,20987,a)].">
      <j1 rule="hyper" parents="11999 20987"/>
    </justification>
  </clause>

  <clause id="20989">
    <literal><![CDATA[
      K((x * (y \ z)) / (z / (z / y)),L(u,x,y \ z)) = K(x / (y / (z / y)),u)
    ]]></literal>
    <justification jstring="[para(7317(a,1),20988(a,2,1,2))].">
      <j1 rule="para" parents="7317 20988"/>
    </justification>
  </clause>

  <clause id="20990">
    <literal><![CDATA[
      K((x / ((y \ z) \ z)) / u,w) = K((x / T(y,z)) / u,w)
    ]]></literal>
    <justification jstring="[hyper(299,a,20966,a(flip),b,20974,a),flip(a)].">
      <j1 rule="hyper" parents="299 20966 20974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20991">
    <literal><![CDATA[
      K(x,T(y,L(z,u,w)) / v5) = K(x,T(y,z) / v5)
    ]]></literal>
    <justification jstring="[hyper(299,a,16345,a(flip),b,20914,a),flip(a)].">
      <j1 rule="hyper" parents="299 16345 20914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20992">
    <literal><![CDATA[
      K(x,T(y,L(z,u,w)) / v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) / v5) = v6
    ]]></literal>
    <justification jstring="[para(20914(a,2),16347(a,1))].">
      <j1 rule="para" parents="20914 16347"/>
    </justification>
  </clause>

  <clause id="20993">
    <literal><![CDATA[
      K(x,T(y,(z \ u) \ w) / v5) = K(x,T(y,u \ (z * w)) / v5)
    ]]></literal>
    <justification jstring="[para(520(a,1),20991(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="520 20991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20994">
    <literal><![CDATA[
      K(x,T(y,(z \ u) \ w) / v5) = K(x,T(y,u * (z * w)) / v5)
    ]]></literal>
    <justification jstring="[hyper(299,a,18015,a(flip),b,20993,a),flip(a)].">
      <j1 rule="hyper" parents="299 18015 20993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20995">
    <literal><![CDATA[
      K(x,T(y,(z \ u) * w) / v5) = K(x,T(y,u * (z * w)) / v5)
    ]]></literal>
    <justification jstring="[hyper(18016,a,20994,a)].">
      <j1 rule="hyper" parents="18016 20994"/>
    </justification>
  </clause>

  <clause id="20996">
    <literal><![CDATA[
      K(x,T(y,z * (u * w)) / ((u \ z) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,((u \ z) * w) \ y) = v5
    ]]></literal>
    <justification jstring="[para(20995(a,1),13764(a,1))].">
      <j1 rule="para" parents="20995 13764"/>
    </justification>
  </clause>

  <clause id="20997">
    <literal><![CDATA[
      L(x,y,z) \ T((x \ 1) * L(x,y,z),u) = L(1 / x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,20890,a,b,20915,a),flip(a)].">
      <j1 rule="hyper" parents="299 20890 20915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20998">
    <literal><![CDATA[
      a((x * y) \ (y * (z * x)),u,u) = a(R(z,x,y),u,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,20856,a(flip),b,20929,a),flip(a)].">
      <j1 rule="hyper" parents="299 20856 20929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21000">
    <literal><![CDATA[
      a(R(x,y,z),u,u) = a(L(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,20968,a(flip),b,20998,a),flip(a)].">
      <j1 rule="hyper" parents="65 20968 20998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21001">
    <literal><![CDATA[
      a(L(T(x,y * z),y,z),u,u) = R(a(x,u,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,15753,a(flip),b,21000,a),flip(a)].">
      <j1 rule="hyper" parents="65 15753 21000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21002">
    <literal><![CDATA[
      a(L(x,y,z),u,u) = R(a(x,u,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,20853,a(flip),b,21001,a)].">
      <j1 rule="hyper" parents="65 20853 21001"/>
    </justification>
  </clause>

  <clause id="21004">
    <literal><![CDATA[
      a(L(x,y,z),u,u) * (y * z) = (a(x,u,u) * y) * z
    ]]></literal>
    <justification jstring="[para(21002(a,2),103(a,1,1))].">
      <j1 rule="para" parents="21002 103"/>
    </justification>
  </clause>

  <clause id="21005">
    <literal><![CDATA[
      x * (T(y,x) * a(z,u,u)) = (a(z,u,u) * y) * x
    ]]></literal>
    <justification jstring="[hyper(65,a,15605,a(flip),b,21004,a)].">
      <j1 rule="hyper" parents="65 15605 21004"/>
    </justification>
  </clause>

  <clause id="21006">
    <literal><![CDATA[
      x * (T(y,x) * a(z,u,u)) = (y * a(z,u,u)) * x
    ]]></literal>
    <justification jstring="[para(14904(a,1),21005(a,2,1))].">
      <j1 rule="para" parents="14904 21005"/>
    </justification>
  </clause>

  <clause id="21007">
    <literal><![CDATA[
      (((a(x,y,y) * z) * u) / u) \ (u * (a(x,y,y) * z)) = T(u,z)
    ]]></literal>
    <justification jstring="[para(21005(a,1),15095(a,1,1,1))].">
      <j1 rule="para" parents="21005 15095"/>
    </justification>
  </clause>

  <clause id="21008">
    <literal><![CDATA[
      ((x * (y * a(z,u,u))) / y) \ ((y * a(z,u,u)) * x) = T(y,x)
    ]]></literal>
    <justification jstring="[para(21006(a,1),15093(a,1,2))].">
      <j1 rule="para" parents="21006 15093"/>
    </justification>
  </clause>

  <clause id="21009">
    <literal><![CDATA[
      (a(x,y,y) * z) \ (u * (a(x,y,y) * z)) = T(u,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),21007(a,1,1))].">
      <j1 rule="para" parents="11 21007"/>
    </justification>
  </clause>

  <clause id="21010">
    <literal><![CDATA[
      T(x,a(y,z,z) * u) = T(x,u)
    ]]></literal>
    <justification jstring="[hyper(318,a,21009,a)].">
      <j1 rule="hyper" parents="318 21009"/>
    </justification>
  </clause>

  <clause id="21012">
    <literal><![CDATA[
      x * K(x * a(y,z,z),u) = T(x,u)
    ]]></literal>
    <justification jstring="[hyper(14824,a,21008,a)].">
      <j1 rule="hyper" parents="14824 21008"/>
    </justification>
  </clause>

  <clause id="21013">
    <literal><![CDATA[
      L(1 / x,y,K(z,u)) \ (1 / x) = K(z,(x \ 1) * L(x,y,u))
    ]]></literal>
    <justification jstring="[para(20997(a,1),17738(a,1,1))].">
      <j1 rule="para" parents="20997 17738"/>
    </justification>
  </clause>

  <clause id="21014">
    <literal><![CDATA[
      K(x,(y \ 1) * L(y,z,u)) = a(u,z,K(x,1 / y))
    ]]></literal>
    <justification jstring="[hyper(65,a,20837,a(flip),b,21013,a),flip(a)].">
      <j1 rule="hyper" parents="65 20837 21013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21015">
    <literal><![CDATA[
      K(x,(y \ 1) * L(y,z,u)) = a(u,z,K(x,y * 1))
    ]]></literal>
    <justification jstring="[hyper(299,a,19533,a(flip),b,21014,a),flip(a)].">
      <j1 rule="hyper" parents="299 19533 21014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21016">
    <literal><![CDATA[
      K(x,(y \ 1) * L(y,z,u)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(8(a,1),21015(a,2,3,2))].">
      <j1 rule="para" parents="8 21015"/>
    </justification>
  </clause>

  <clause id="21017">
    <literal><![CDATA[
      K(x,y \ L(y,z,u)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(14281,a,21016,a)].">
      <j1 rule="hyper" parents="14281 21016"/>
    </justification>
  </clause>

  <clause id="21018">
    <literal><![CDATA[
      K(x,((y \ z) \ u) \ (z \ (y * u))) = a(y,y \ z,K(x,(y \ z) \ u))
    ]]></literal>
    <justification jstring="[para(520(a,1),21017(a,1,2,2))].">
      <j1 rule="para" parents="520 21017"/>
    </justification>
  </clause>

  <clause id="21019">
    <literal><![CDATA[
      T(x,K(y,z \ L(z,u,w))) = x
    ]]></literal>
    <justification jstring="[para(21017(a,2),18618(a,1,2))].">
      <j1 rule="para" parents="21017 18618"/>
    </justification>
  </clause>

  <clause id="21020">
    <literal><![CDATA[
      T(x,(y \ L(y,z,u)) * w) = T(x,w * (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(13259,a,21019,a)].">
      <j1 rule="hyper" parents="13259 21019"/>
    </justification>
  </clause>

  <clause id="21021">
    <literal><![CDATA[
      T(x,(y \ L(y,z,u)) / w) = T(x,w \ (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(8996,a,21019,a),flip(a)].">
      <j1 rule="hyper" parents="8996 21019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21022">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w) \ z)) = x
    ]]></literal>
    <justification jstring="[hyper(8825,a,21019,a)].">
      <j1 rule="hyper" parents="8825 21019"/>
    </justification>
  </clause>

  <clause id="21023">
    <literal><![CDATA[
      T(x,(y \ L(y,z,u)) / w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,w \ (y \ L(y,z,u))) = v5
    ]]></literal>
    <justification jstring="[para(21019(a,1),8996(a,1))].">
      <j1 rule="para" parents="21019 8996"/>
    </justification>
  </clause>

  <clause id="21024">
    <literal><![CDATA[
      T(x,(L(y,z,u) \ y) / w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,w \ (L(y,z,u) \ y)) = v5
    ]]></literal>
    <justification jstring="[para(21022(a,1),8996(a,1))].">
      <j1 rule="para" parents="21022 8996"/>
    </justification>
  </clause>

  <clause id="21025">
    <literal><![CDATA[
      T(x,(y \ L(y,z,z)) * u) = T(x,a(y,z,z) * u)
    ]]></literal>
    <justification jstring="[hyper(299,a,19843,a(flip),b,21020,a),flip(a)].">
      <j1 rule="hyper" parents="299 19843 21020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21026">
    <literal><![CDATA[
      T(x,(y \ L(y,z,z)) \ u) = T(x,a(y,z,z) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,20949,a,b,21025,a)].">
      <j1 rule="hyper" parents="65 20949 21025"/>
    </justification>
  </clause>

  <clause id="21027">
    <literal><![CDATA[
      T(x,a(y,z,z) * u) = T(x,u * a(z,z,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,14672,a(flip),b,21026,a),flip(a)].">
      <j1 rule="hyper" parents="65 14672 21026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21028">
    <literal><![CDATA[
      T(x,y * a(z,z,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,21010,a(flip),b,21027,a),flip(a)].">
      <j1 rule="hyper" parents="65 21010 21027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21029">
    <literal><![CDATA[
      x / T(x,y * a(z,z,u)) = K(a(u,z,z) * y,x)
    ]]></literal>
    <justification jstring="[para(21027(a,1),5033(a,2,2)),flip(a)].">
      <j1 rule="para" parents="21027 5033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21030">
    <literal><![CDATA[
      T(x,y * a(z,z,u)) = T(x,y * a(w,w,v5))
    ]]></literal>
    <justification jstring="[hyper(299,a,21028,a,b,21028,a)].">
      <j1 rule="hyper" parents="299 21028 21028"/>
    </justification>
  </clause>

  <clause id="21032">
    <literal><![CDATA[
      T(x,a(y,y,z) * u) = T(x,u * a(w,w,v5))
    ]]></literal>
    <justification jstring="[hyper(18644,a,21030,a)].">
      <j1 rule="hyper" parents="18644 21030"/>
    </justification>
  </clause>

  <clause id="21035">
    <literal><![CDATA[
      T(x,y * a(z,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = w
    ]]></literal>
    <justification jstring="[para(21030(a,1),13690(a,1))].">
      <j1 rule="para" parents="21030 13690"/>
    </justification>
  </clause>

  <clause id="21036">
    <literal><![CDATA[
      T(x,(y * y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (y * z)) = u
    ]]></literal>
    <justification jstring="[para(84(a,1),21035(a,1,2))].">
      <j1 rule="para" parents="84 21035"/>
    </justification>
  </clause>

  <clause id="21037">
    <literal><![CDATA[
      T(x,(y \ 1) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(19619(a,1),21035(a,1,2))].">
      <j1 rule="para" parents="19619 21035"/>
    </justification>
  </clause>

  <clause id="21038">
    <literal><![CDATA[
      T(x,a(y,z,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u) = w
    ]]></literal>
    <justification jstring="[para(21027(a,2),21035(a,1))].">
      <j1 rule="para" parents="21027 21035"/>
    </justification>
  </clause>

  <clause id="21040">
    <literal><![CDATA[
      T(x,((y \ 1) \ 1) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(14297(a,2),21037(a,1))].">
      <j1 rule="para" parents="14297 21037"/>
    </justification>
  </clause>

  <clause id="21042">
    <literal><![CDATA[
      T(x,K(y,z) * ((u \ 1) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,u * (K(z,y) * w)) = v5
    ]]></literal>
    <justification jstring="[para(20276(a,1),21037(a,1))].">
      <j1 rule="para" parents="20276 21037"/>
    </justification>
  </clause>

  <clause id="21046">
    <literal><![CDATA[
      T(x,a(y,z,z) * u) = T(x,a(w,w,v5) * u)
    ]]></literal>
    <justification jstring="[hyper(299,a,21027,a,b,21032,a)].">
      <j1 rule="hyper" parents="299 21027 21032"/>
    </justification>
  </clause>

  <clause id="21047">
    <literal><![CDATA[
      T(x,a(y,y,z) * u) = T(x,u * a(w,v5,v5))
    ]]></literal>
    <justification jstring="[hyper(18645,a,21046,a),flip(a)].">
      <j1 rule="hyper" parents="18645 21046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21048">
    <literal><![CDATA[
      T(x,a(y,z,z) * u) = T(x,(w \ (v5 \ ((1 / v5) \ w))) * u)
    ]]></literal>
    <justification jstring="[para(1667(a,1),21046(a,2,2,1))].">
      <j1 rule="para" parents="1667 21046"/>
    </justification>
  </clause>

  <clause id="21049">
    <literal><![CDATA[
      T(x,a(y,z,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u * a(v5,v5,v6)) = w
    ]]></literal>
    <justification jstring="[para(21046(a,2),18645(a,1))].">
      <j1 rule="para" parents="21046 18645"/>
    </justification>
  </clause>

  <clause id="21050">
    <literal><![CDATA[
      T(x,a(y,z,z) * u) = T(x,u * a(w,v5,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,21046,a,b,21047,a)].">
      <j1 rule="hyper" parents="65 21046 21047"/>
    </justification>
  </clause>

  <clause id="21051">
    <literal><![CDATA[
      T(x,a(y,y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,a(v5,v6,v6) * u) = w
    ]]></literal>
    <justification jstring="[para(21047(a,2),18644(a,1))].">
      <j1 rule="para" parents="21047 18644"/>
    </justification>
  </clause>

  <clause id="21053">
    <literal><![CDATA[
      T(x,a(y,z,z) * u) = T(x,u * ((w \ ((1 / w) \ v5)) \ v5))
    ]]></literal>
    <justification jstring="[hyper(299,a,19846,a(flip),b,21050,a),flip(a)].">
      <j1 rule="hyper" parents="299 19846 21050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21055">
    <literal><![CDATA[
      T(T(x,y * y),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (y * z)) = u
    ]]></literal>
    <justification jstring="[para(1280(a,2),21036(a,1))].">
      <j1 rule="para" parents="1280 21036"/>
    </justification>
  </clause>

  <clause id="21058">
    <literal><![CDATA[
      T(x,L(y \ 1,z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,L(1 / y,z,u) * w) = v5
    ]]></literal>
    <justification jstring="[para(4143(a,1),21040(a,1,2,1))].">
      <j1 rule="para" parents="4143 21040"/>
    </justification>
  </clause>

  <clause id="21060">
    <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),21055(a,1))].">
      <j1 rule="para" parents="23 21055"/>
    </justification>
  </clause>

  <clause id="21061">
    <literal><![CDATA[
      T(x,(y \ z) \ ((y \ z) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z \ y) * ((z \ y) * u)) = w
    ]]></literal>
    <justification jstring="[para(16153(a,1),21060(a,1))].">
      <j1 rule="para" parents="16153 21060"/>
    </justification>
  </clause>

  <clause id="21062">
    <literal><![CDATA[
      K(a(x,y,y) * z,u) = K(z * a(y,y,x),u)
    ]]></literal>
    <justification jstring="[hyper(5118,a,21029,a),flip(a)].">
      <j1 rule="hyper" parents="5118 21029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21064">
    <literal><![CDATA[
      a(x,y,y) * (z * K(z * a(y,y,x),u)) = T(a(x,y,y) * z,u)
    ]]></literal>
    <justification jstring="[para(21062(a,1),14264(a,1,2,2))].">
      <j1 rule="para" parents="21062 14264"/>
    </justification>
  </clause>

  <clause id="21065">
    <literal><![CDATA[
      T(x * K(x * a(y,z,z),u),a(y,z,z)) = T(x,a(y,z,z)) * K(x * a(z,z,y),u)
    ]]></literal>
    <justification jstring="[para(21062(a,1),16685(a,2,2))].">
      <j1 rule="para" parents="21062 16685"/>
    </justification>
  </clause>

  <clause id="21068">
    <literal><![CDATA[
      T(x,a(y,y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u * a(v5,v5,v6)) = w
    ]]></literal>
    <justification jstring="[para(21046(a,1),21049(a,1))].">
      <j1 rule="para" parents="21046 21049"/>
    </justification>
  </clause>

  <clause id="21069">
    <literal><![CDATA[
      T(x,(y \ (z \ ((1 / z) \ y))) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,a(v5,v6,v6) * u) = w
    ]]></literal>
    <justification jstring="[para(1667(a,1),21051(a,1,2,1))].">
      <j1 rule="para" parents="1667 21051"/>
    </justification>
  </clause>

  <clause id="21072">
    <literal><![CDATA[
      T(x,(L(y,z,u) \ y) \ (w \ 1)) = T(x,w \ (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(14632,a,21021,a)].">
      <j1 rule="hyper" parents="14632 21021"/>
    </justification>
  </clause>

  <clause id="21073">
    <literal><![CDATA[
      T(x,a(y,y,z) * u) = T(x,(w \ (v5 \ ((1 / v5) \ w))) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,21046,a(flip),b,21048,a)].">
      <j1 rule="hyper" parents="65 21046 21048"/>
    </justification>
  </clause>

  <clause id="21076">
    <literal><![CDATA[
      T(x,L(y,z,u) * (y \ (w \ 1))) = T(x,w \ (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(15679,a,21072,a)].">
      <j1 rule="hyper" parents="15679 21072"/>
    </justification>
  </clause>

  <clause id="21077">
    <literal><![CDATA[
      T(x,y * (L(y,z,u) \ (w \ 1))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,w \ (L(y,z,u) \ y)) = v5
    ]]></literal>
    <justification jstring="[para(17746(a,2),21024(a,1))].">
      <j1 rule="para" parents="17746 21024"/>
    </justification>
  </clause>

  <clause id="21078">
    <literal><![CDATA[
      K(T(x,y * K(z,u)),w * (K(z,u) * y)) = K(x,K(z,u) * (y * w))
    ]]></literal>
    <justification jstring="[hyper(8218,a,20889,a),flip(a)].">
      <j1 rule="hyper" parents="8218 20889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21079">
    <literal><![CDATA[
      x * a(a(y,z,u) * x,z,K(u,y)) = a(y,z,u) * (x / a(y,z,u))
    ]]></literal>
    <justification jstring="[para(14949(a,1),20927(a,1,2))].">
      <j1 rule="para" parents="14949 20927"/>
    </justification>
  </clause>

  <clause id="21081">
    <literal><![CDATA[
      a(T(x,y) \ z,T(x,z),K(u,w)) = a(w,z,K(T(x,y) \ z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,15413,a(flip),b,20940,a)].">
      <j1 rule="hyper" parents="65 15413 20940"/>
    </justification>
  </clause>

  <clause id="21082">
    <literal><![CDATA[
      a(T(x,y) \ z,x,K(u,w)) = a(w,z,K(T(x,y) \ z,u))
    ]]></literal>
    <justification jstring="[hyper(20938,a,21081,a)].">
      <j1 rule="hyper" parents="20938 21081"/>
    </justification>
  </clause>

  <clause id="21084">
    <literal><![CDATA[
      a(T(x,y) * z,x,K(u,w)) = a(w,z,K(T(x,y) \ z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,19569,a(flip),b,21082,a)].">
      <j1 rule="hyper" parents="65 19569 21082"/>
    </justification>
  </clause>

  <clause id="21085">
    <literal><![CDATA[
      K(x,T(y * (K(z,u) * w),w * K(z,u))) = K(x,K(z,u) * (w * y))
    ]]></literal>
    <justification jstring="[hyper(7709,a,21078,a)].">
      <j1 rule="hyper" parents="7709 21078"/>
    </justification>
  </clause>

  <clause id="21086">
    <literal><![CDATA[
      (a(x,y,z) \ u) * a(x,y,z) = a(x,y,z) * (u / a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,19571,a(flip),b,21079,a)].">
      <j1 rule="hyper" parents="65 19571 21079"/>
    </justification>
  </clause>

  <clause id="21087">
    <literal><![CDATA[
      K(K(x,K(y,z) * (u * w)) * v5,v6) = K(v5 * K(w * (K(y,z) * u),x),v6)
    ]]></literal>
    <justification jstring="[para(21085(a,1),17766(a,1,1,1))].">
      <j1 rule="para" parents="21085 17766"/>
    </justification>
  </clause>

  <clause id="21088">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,z,z * y)) = K(x,z \ ((z \ (y \ 1)) \ u))
    ]]></literal>
    <justification jstring="[para(2627(a,1),20970(a,1,2))].">
      <j1 rule="para" parents="2627 20970"/>
    </justification>
  </clause>

  <clause id="21089">
    <literal><![CDATA[
      K(x,L((y * z) / u,z,y)) = K(x,z / (u / T(y,T(z,w))))
    ]]></literal>
    <justification jstring="[hyper(16887,a,20986,a)].">
      <j1 rule="hyper" parents="16887 20986"/>
    </justification>
  </clause>

  <clause id="21091">
    <literal><![CDATA[
      K(x,((y \ z) \ u) \ (z \ (y * u))) = a(y,y \ z,K(x,(y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(299,a,15012,a(flip),b,21018,a),flip(a)].">
      <j1 rule="hyper" parents="299 15012 21018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21092">
    <literal><![CDATA[
      K(x,((y \ z) \ u) \ (z \ (y * u))) = a(x,y \ z,K(z * u,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,19547,a(flip),b,21091,a),flip(a)].">
      <j1 rule="hyper" parents="299 19547 21091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21093">
    <literal><![CDATA[
      K(x,((y \ z) \ u) \ (z \ (y * u))) = a(z * u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(299,a,14983,a(flip),b,21092,a),flip(a)].">
      <j1 rule="hyper" parents="299 14983 21092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21095">
    <literal><![CDATA[
      K(x,y * R(K(z,u) / w,v5,v5)) = K(x,y * R(w \ K(z,u),v5,v5))
    ]]></literal>
    <justification jstring="[para(20857(a,1),20858(a,1,2,2))].">
      <j1 rule="para" parents="20857 20858"/>
    </justification>
  </clause>

  <clause id="21096">
    <literal><![CDATA[
      K(x,y * R(z \ K(u,w),v5,v5)) = K(x,y * L(K(u,w) / z,v5,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,19370,a(flip),b,21095,a),flip(a)].">
      <j1 rule="hyper" parents="65 19370 21095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21097">
    <literal><![CDATA[
      K(x,y * L(K(z,u) / w,v5,v5)) = K(x,y * L(w \ K(z,u),v5,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,19370,a(flip),b,21096,a),flip(a)].">
      <j1 rule="hyper" parents="65 19370 21096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21098">
    <literal><![CDATA[
      T(x,a(y,z,u) \ (a(y,z,u) \ 1)) = L(L(x,z,K(y,u)),z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(20887,a,20905,a),flip(a)].">
      <j1 rule="hyper" parents="20887 20905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21099">
    <literal><![CDATA[
      T(x,a(y,z,u) \ (a(y,z,u) \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(299,a,20849,a(flip),b,21098,a),flip(a)].">
      <j1 rule="hyper" parents="299 20849 21098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21100">
    <literal><![CDATA[
      T(x,a(y,z,u) \ (a(y,z,u) \ w)) = T(x,w)
    ]]></literal>
    <justification jstring="[hyper(14752,a,21099,a)].">
      <j1 rule="hyper" parents="14752 21099"/>
    </justification>
  </clause>

  <clause id="21102">
    <literal><![CDATA[
      T(x,a(y,z,u) \ w) = T(x,a(y,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(42,a,14750,a,b,21100,a),flip(a)].">
      <j1 rule="hyper" parents="42 14750 21100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21103">
    <literal><![CDATA[
      T(x,a(y,z,u) \ w) = T(x,w * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,18631,a(flip),b,21102,a),flip(a)].">
      <j1 rule="hyper" parents="299 18631 21102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21106">
    <literal><![CDATA[
      T(x,y * a(z,u,w)) / x = K(x,y / a(z,u,w))
    ]]></literal>
    <justification jstring="[para(21103(a,1),18689(a,1,1))].">
      <j1 rule="para" parents="21103 18689"/>
    </justification>
  </clause>

  <clause id="21107">
    <literal><![CDATA[
      T(x,y * a(z,u,w)) \ x = K(y / a(z,u,w),x)
    ]]></literal>
    <justification jstring="[para(21103(a,1),18690(a,1,1))].">
      <j1 rule="para" parents="21103 18690"/>
    </justification>
  </clause>

  <clause id="21108">
    <literal><![CDATA[
      K(x,y / a(z,u,w)) = K(x,y * a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(5167,a,21106,a),flip(a)].">
      <j1 rule="hyper" parents="5167 21106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21109">
    <literal><![CDATA[
      K(x,a(y,z,u) \ w) = K(x,w * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(18666,a,21108,a)].">
      <j1 rule="hyper" parents="18666 21108"/>
    </justification>
  </clause>

  <clause id="21110">
    <literal><![CDATA[
      K(x,L(L(y,z,z) \ u,a(y,z,z),y)) = K(x,(y \ u) * a(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,18141,a,b,21109,a)].">
      <j1 rule="hyper" parents="65 18141 21109"/>
    </justification>
  </clause>

  <clause id="21111">
    <literal><![CDATA[
      K(x,a(y,z,u) \ w) = K(x,a(y,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(18655,a,21109,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="18655 21109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21112">
    <literal><![CDATA[
      K(L(x,y,y) * (x \ z),u) = (w \ K(u,a(y,y,x) * z)) \ (w \ 1)
    ]]></literal>
    <justification jstring="[para(21111(a,1),15663(a,2,1,2))].">
      <j1 rule="para" parents="21111 15663"/>
    </justification>
  </clause>

  <clause id="21113">
    <literal><![CDATA[
      K(x / a(y,z,u),w) = K(x * a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(5109,a,21107,a),flip(a)].">
      <j1 rule="hyper" parents="5109 21107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21114">
    <literal><![CDATA[
      K(a(x,y,z) \ u,w) = K(u * a(x,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(18652,a,21113,a)].">
      <j1 rule="hyper" parents="18652 21113"/>
    </justification>
  </clause>

  <clause id="21115">
    <literal><![CDATA[
      K(x,(y \ z) * a(y,u,u)) = K(x,L(y,u,u) \ z)
    ]]></literal>
    <justification jstring="[hyper(15596,a,21110,a),flip(a)].">
      <j1 rule="hyper" parents="15596 21110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21116">
    <literal><![CDATA[
      K(L(x,y,y) * (x \ z),u) = K(a(y,y,x) * z,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,14240,a(flip),b,21112,a),flip(a)].">
      <j1 rule="hyper" parents="299 14240 21112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21117">
    <literal><![CDATA[
      K(a(x,x,y) \ z,u) = K(a(x,x,y) * z,u)
    ]]></literal>
    <justification jstring="[hyper(15686,a,21116,a)].">
      <j1 rule="hyper" parents="15686 21116"/>
    </justification>
  </clause>

  <clause id="21118">
    <literal><![CDATA[
      K((x / y) * L(y,z,z),u) = K(a(z,z,y) * x,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,18921,a(flip),b,21116,a)].">
      <j1 rule="hyper" parents="65 18921 21116"/>
    </justification>
  </clause>

  <clause id="21119">
    <literal><![CDATA[
      K(a(x,x,y) * (z * y),u) = K(z * L(y,x,x),u)
    ]]></literal>
    <justification jstring="[para(11(a,1),21118(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11 21118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21120">
    <literal><![CDATA[
      K(a(x,x,y) * (z * y),u) = u / T(u,z * L(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(299,a,5033,a(flip),b,21119,a),flip(a)].">
      <j1 rule="hyper" parents="299 5033 21119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21121">
    <literal><![CDATA[
      T(x,a(y,y,z) * (u * z)) = T(x,u * L(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(5062,a,21120,a)].">
      <j1 rule="hyper" parents="5062 21120"/>
    </justification>
  </clause>

  <clause id="21122">
    <literal><![CDATA[
      K(x * K(y * (K(z,u) * w),v5),v6) = K(K(w * y,v5) * x,v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,17888,a(flip),b,21087,a),flip(a)].">
      <j1 rule="hyper" parents="65 17888 21087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21124">
    <literal><![CDATA[
      K(K(x * (T(y,z) * u),w) * v5,v6) = K(K((y \ x) * u,w) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,19327,a(flip),b,21122,a),flip(a)].">
      <j1 rule="hyper" parents="65 19327 21122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21125">
    <literal><![CDATA[
      K(K((x \ y) * z,u) * w,v5) = K(K(y * (x * z),u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,19184,a(flip),b,21124,a),flip(a)].">
      <j1 rule="hyper" parents="65 19184 21124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21126">
    <literal><![CDATA[
      K(x * K(y,(z / T(u,w)) * v5),v6) = K(K(z * (u * v5),y) * x,v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,19033,a,b,21125,a)].">
      <j1 rule="hyper" parents="65 19033 21125"/>
    </justification>
  </clause>

  <clause id="21127">
    <literal><![CDATA[
      K(K(x * (y * z),u * w) * w,u) = K(w,T(u,K(v5,y) * ((x / y) * z)))
    ]]></literal>
    <justification jstring="[hyper(65,a,19008,a(flip),b,21126,a),flip(a)].">
      <j1 rule="hyper" parents="65 19008 21126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21129">
    <literal><![CDATA[
      K(x * K(y * (z * u),x * w),w) = K(x,T(w,K(v5,z) * ((y / z) * u)))
    ]]></literal>
    <justification jstring="[para(13209(a,1),21127(a,1,1))].">
      <j1 rule="para" parents="13209 21127"/>
    </justification>
  </clause>

  <clause id="21130">
    <literal><![CDATA[
      K(x,T(y,K(z,u) * ((w / u) * v5))) = K(x,T(y,w * (u * v5)))
    ]]></literal>
    <justification jstring="[hyper(19776,a,21129,a),flip(a)].">
      <j1 rule="hyper" parents="19776 21129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21131">
    <literal><![CDATA[
      K(x,T(y,(z \ u) * w)) = K(x,T(y,u * (z * w)))
    ]]></literal>
    <justification jstring="[para(5718(a,1),21130(a,1,2,2))].">
      <j1 rule="para" parents="5718 21130"/>
    </justification>
  </clause>

  <clause id="21132">
    <literal><![CDATA[
      K(x,T(y,((z * u) \ w) * (1 / u))) = K(x,T(y,w * ((z * (u \ 1)) * u)))
    ]]></literal>
    <justification jstring="[para(1088(a,2),21131(a,2,2,2,2))].">
      <j1 rule="para" parents="1088 21131"/>
    </justification>
  </clause>

  <clause id="21133">
    <literal><![CDATA[
      K(x,T(y,z * ((u * (w \ 1)) * w))) = K(x,T(y,((u * w) \ z) / w))
    ]]></literal>
    <justification jstring="[para(14472(a,1),21132(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14472 21132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21134">
    <literal><![CDATA[
      K(x,T(y,z * ((u * (w \ 1)) * w))) = K(x,T(y,w * ((u * w) \ z)))
    ]]></literal>
    <justification jstring="[hyper(299,a,16539,a(flip),b,21133,a),flip(a)].">
      <j1 rule="hyper" parents="299 16539 21133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21135">
    <literal><![CDATA[
      K(x,T(y,z * ((u * w) * (1 / w)))) = K(x,T(y,w * ((u * w) \ z)))
    ]]></literal>
    <justification jstring="[para(1088(a,1),21134(a,1,2,2,2))].">
      <j1 rule="para" parents="1088 21134"/>
    </justification>
  </clause>

  <clause id="21136">
    <literal><![CDATA[
      K(x,T(y,z * ((u * w) * (w \ 1)))) = K(x,T(y,w * ((u * w) \ z)))
    ]]></literal>
    <justification jstring="[para(3885(a,1),21135(a,1,2))].">
      <j1 rule="para" parents="3885 21135"/>
    </justification>
  </clause>

  <clause id="21137">
    <literal><![CDATA[
      K(x,T(y,z * ((u * z) \ w))) = K(x,T(y,w * R(u,z,z)))
    ]]></literal>
    <justification jstring="[para(1246(a,1),21136(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="1246 21136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21138">
    <literal><![CDATA[
      K(x,T(y,z * ((u * z) \ w))) = K(x,T(y,w * L(u,z,z)))
    ]]></literal>
    <justification jstring="[hyper(299,a,19295,a(flip),b,21137,a),flip(a)].">
      <j1 rule="hyper" parents="299 19295 21137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21139">
    <literal><![CDATA[
      K(x,T(T((y * z) * (u / (y * z)),y * z),u * L(y,z,z))) = K(x,(z * (u / T(y * z,u))) * R(y,z,u / T(y * z,u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,15401,a(flip),b,21138,a),flip(a)].">
      <j1 rule="hyper" parents="65 15401 21138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21140">
    <literal><![CDATA[
      K((x * (y \ z)) / T(y,z),L(u,x,y \ z)) = K(x / (y / (z / y)),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,20309,a(flip),b,20989,a)].">
      <j1 rule="hyper" parents="65 20309 20989"/>
    </justification>
  </clause>

  <clause id="21141">
    <literal><![CDATA[
      K(x / (T(y,z) / (y \ z)),u) = K(x / (y / (z / y)),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,20988,a(flip),b,21140,a)].">
      <j1 rule="hyper" parents="65 20988 21140"/>
    </justification>
  </clause>

  <clause id="21142">
    <literal><![CDATA[
      K(x / (T(y,z) / (y \ z)),u) = K(x / ((y \ z) \ y),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,20253,a(flip),b,21141,a),flip(a)].">
      <j1 rule="hyper" parents="299 20253 21141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21143">
    <literal><![CDATA[
      K(x,(y \ T(T(a(z,u,w),v5),v5)) * v6) = K(x,(a(z,u,w) / y) * v6)
    ]]></literal>
    <justification jstring="[hyper(299,a,20916,a(flip),b,20860,a),flip(a)].">
      <j1 rule="hyper" parents="299 20916 20860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21145">
    <literal><![CDATA[
      K(x,(a(y,z,u) / w) * v5) = K(x,(w \ a(y,z,u)) * v5)
    ]]></literal>
    <justification jstring="[para(6256(a,1),21143(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="6256 21143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21146">
    <literal><![CDATA[
      K(x,L(y \ 1,z,y) * u) = K(x,(y \ a(w,v5,K(v6,v7))) * u)
    ]]></literal>
    <justification jstring="[hyper(19416,a,21145,a)].">
      <j1 rule="hyper" parents="19416 21145"/>
    </justification>
  </clause>

  <clause id="21147">
    <literal><![CDATA[
      K(x,L(y \ 1,z,y) * u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(299,a,19082,a(flip),b,21146,a),flip(a)].">
      <j1 rule="hyper" parents="299 19082 21146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21148">
    <literal><![CDATA[
      K(x,((((y * z) / y) \ 1) * u) \ w) = K(x,K(z,y) * (((z \ 1) * u) \ w))
    ]]></literal>
    <justification jstring="[hyper(20877,a,20127,a)].">
      <j1 rule="hyper" parents="20877 20127"/>
    </justification>
  </clause>

  <clause id="21149">
    <literal><![CDATA[
      K(x,((((y * z) / y) \ 1) * u) \ w) = K(x,((T(z,y) \ 1) * u) \ w)
    ]]></literal>
    <justification jstring="[hyper(299,a,20412,a(flip),b,21148,a),flip(a)].">
      <j1 rule="hyper" parents="299 20412 21148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21150">
    <literal><![CDATA[
      K(x,(((((y * z) / y) * ((y * z) / y)) \ u) * T(z,y)) \ w) = K(x,((T(z,y) \ 1) * T(u,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,20785,a,b,21149,a)].">
      <j1 rule="hyper" parents="65 20785 21149"/>
    </justification>
  </clause>

  <clause id="21151">
    <literal><![CDATA[
      T(x * K(x * a(y,z,z),u),a(y,z,z)) = x * K(x * a(z,z,y),u)
    ]]></literal>
    <justification jstring="[para(14902(a,1),21065(a,2,1))].">
      <j1 rule="para" parents="14902 21065"/>
    </justification>
  </clause>

  <clause id="21152">
    <literal><![CDATA[
      x * K(x * a(y,z,z),u) = x * K(x * a(z,z,y),u)
    ]]></literal>
    <justification jstring="[hyper(14906,a,21151,a),flip(a)].">
      <j1 rule="hyper" parents="14906 21151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21154">
    <literal><![CDATA[
      x * K(x * a(y,y,z),u) = T(x,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,21012,a(flip),b,21152,a),flip(a)].">
      <j1 rule="hyper" parents="65 21012 21152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21156">
    <literal><![CDATA[
      K(x * a(y,y,z),u) = K(x * a(w,w,v5),u)
    ]]></literal>
    <justification jstring="[hyper(36,a,21154,a,b,21154,a)].">
      <j1 rule="hyper" parents="36 21154 21154"/>
    </justification>
  </clause>

  <clause id="21158">
    <literal><![CDATA[
      T(a(x,y,y) * z,u) = a(x,y,y) * T(z,u)
    ]]></literal>
    <justification jstring="[para(21154(a,1),21064(a,1,2)),flip(a)].">
      <j1 rule="para" parents="21154 21064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21163">
    <literal><![CDATA[
      (x * a(y,z,z)) / T(a(y,z,z) * x,u) = K(u,x)
    ]]></literal>
    <justification jstring="[para(21158(a,2),14910(a,1,2))].">
      <j1 rule="para" parents="21158 14910"/>
    </justification>
  </clause>

  <clause id="21164">
    <literal><![CDATA[
      K(x,a(y,z,z)) * K(u,a(y,z,z) * x) = K(u,x)
    ]]></literal>
    <justification jstring="[hyper(7361,a,21163,a)].">
      <j1 rule="hyper" parents="7361 21163"/>
    </justification>
  </clause>

  <clause id="21165">
    <literal><![CDATA[
      a(x,y,K(y,z)) * K(u,a(z,y,y) * x) = K(u,x)
    ]]></literal>
    <justification jstring="[para(14871(a,2),21164(a,1,1))].">
      <j1 rule="para" parents="14871 21164"/>
    </justification>
  </clause>

  <clause id="21166">
    <literal><![CDATA[
      1 * K(x,a(y,z,z) * u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(6828(a,1),21165(a,1,1))].">
      <j1 rule="para" parents="6828 21165"/>
    </justification>
  </clause>

  <clause id="21167">
    <literal><![CDATA[
      K(x,a(y,z,z) * u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(122,a,21166,a)].">
      <j1 rule="hyper" parents="122 21166"/>
    </justification>
  </clause>

  <clause id="21169">
    <literal><![CDATA[
      K(x,y * L(z,u,u)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,19475,a(flip),b,21167,a)].">
      <j1 rule="hyper" parents="65 19475 21167"/>
    </justification>
  </clause>

  <clause id="21171">
    <literal><![CDATA[
      K(x,y * a(z,u,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(14904(a,1),21167(a,1,2))].">
      <j1 rule="para" parents="14904 21167"/>
    </justification>
  </clause>

  <clause id="21174">
    <literal><![CDATA[
      K(x,L(y \ z,u,T(u,y) * y)) = K(x,u \ ((u \ ((u * y) / u)) \ z))
    ]]></literal>
    <justification jstring="[para(222(a,1),20972(a,1,2,1,1))].">
      <j1 rule="para" parents="222 20972"/>
    </justification>
  </clause>

  <clause id="21175">
    <literal><![CDATA[
      K(x,L(y \ z,u,y * u)) = K(x,u \ ((u \ ((u * y) / u)) \ z))
    ]]></literal>
    <justification jstring="[para(6051(a,1),21174(a,1,2))].">
      <j1 rule="para" parents="6051 21174"/>
    </justification>
  </clause>

  <clause id="21176">
    <literal><![CDATA[
      K(x,y \ ((y \ ((y * z) / y)) \ u)) = K(x,y \ ((z / y) \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,20924,a(flip),b,21175,a),flip(a)].">
      <j1 rule="hyper" parents="65 20924 21175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21177">
    <literal><![CDATA[
      T((x \ ((1 / x) \ y)) / y,T(z,y)) = (y \ (x \ ((1 / x) \ y))) * 1
    ]]></literal>
    <justification jstring="[para(14558(a,1),20919(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14558 20919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21179">
    <literal><![CDATA[
      T((x \ ((1 / x) \ y)) / y,T(z,y)) = y \ (x \ ((1 / x) \ y))
    ]]></literal>
    <justification jstring="[hyper(299,a,8,a(flip),b,21177,a),flip(a)].">
      <j1 rule="hyper" parents="299 8 21177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21182">
    <literal><![CDATA[
      T(x \ (y \ ((1 / y) \ x)),T(z,x)) = x \ (y \ ((1 / y) \ x))
    ]]></literal>
    <justification jstring="[para(20844(a,1),21179(a,1,1))].">
      <j1 rule="para" parents="20844 21179"/>
    </justification>
  </clause>

  <clause id="21183">
    <literal><![CDATA[
      T(x \ (y \ ((1 / y) \ x)),z) = x \ (y \ ((1 / y) \ x))
    ]]></literal>
    <justification jstring="[hyper(8310,a,21182,a)].">
      <j1 rule="hyper" parents="8310 21182"/>
    </justification>
  </clause>

  <clause id="21184">
    <literal><![CDATA[
      x / (y \ (z \ ((1 / z) \ y))) = (y \ (z \ ((1 / z) \ y))) \ x
    ]]></literal>
    <justification jstring="[para(21183(a,1),262(a,1,2))].">
      <j1 rule="para" parents="21183 262"/>
    </justification>
  </clause>

  <clause id="21185">
    <literal><![CDATA[
      T(x,(y \ (z \ ((1 / z) \ y))) \ u) = T(x,u * ((z \ ((1 / z) \ y)) \ y))
    ]]></literal>
    <justification jstring="[para(21184(a,1),14486(a,1,2))].">
      <j1 rule="para" parents="21184 14486"/>
    </justification>
  </clause>

  <clause id="21186">
    <literal><![CDATA[
      T(x,(y \ (z \ ((1 / z) \ y))) \ u) = T(x,a(w,v5,v5) * u)
    ]]></literal>
    <justification jstring="[hyper(299,a,21053,a,b,21185,a),flip(a)].">
      <j1 rule="hyper" parents="299 21053 21185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21188">
    <literal><![CDATA[
      T(x,a(y,z,z) * (((u \ ((1 / u) \ w)) \ w) \ v5)) = T(x,v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,14406,a(flip),b,21186,a),flip(a)].">
      <j1 rule="hyper" parents="65 14406 21186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21189">
    <literal><![CDATA[
      T(x,((y \ ((1 / y) \ z)) \ z) \ u) = T(x,u)
    ]]></literal>
    <justification jstring="[hyper(21038,a,21188,a)].">
      <j1 rule="hyper" parents="21038 21188"/>
    </justification>
  </clause>

  <clause id="21191">
    <literal><![CDATA[
      T(x,((y \ ((1 / y) \ z)) \ z) / u) = T(x,u \ 1)
    ]]></literal>
    <justification jstring="[hyper(7057,a,21189,a),flip(a)].">
      <j1 rule="hyper" parents="7057 21189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21193">
    <literal><![CDATA[
      R(K(x,y),z,L(z \ u,z,K(x,y))) = (K(x,y) * u) / (u * a(y,z,K(x,z * u)))
    ]]></literal>
    <justification jstring="[para(10(a,1),20926(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10 20926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21194">
    <literal><![CDATA[
      K(x,L(y,z,L(z \ u,z,K(x,y)))) = (K(x,y) * u) / (u * a(y,z,K(x,z * u)))
    ]]></literal>
    <justification jstring="[hyper(15512,a,21193,a)].">
      <j1 rule="hyper" parents="15512 21193"/>
    </justification>
  </clause>

  <clause id="21196">
    <literal><![CDATA[
      (K(x,y) * z) / (z * a(y,u,K(x,u * z))) = K(x,L(y,u,u \ z))
    ]]></literal>
    <justification jstring="[hyper(20910,a,21194,a),flip(a)].">
      <j1 rule="hyper" parents="20910 21194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21197">
    <literal><![CDATA[
      (K(x,y) * z) / (z * a(y,u,K(x,u * z))) = K(x,L(y,u,u * z))
    ]]></literal>
    <justification jstring="[hyper(299,a,19572,a(flip),b,21196,a),flip(a)].">
      <j1 rule="hyper" parents="299 19572 21196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21199">
    <literal><![CDATA[
      K(x,L((y / R(z,u,z)) \ T(w,z),w,z)) = K(x,T(y,R(z,u,z)) \ (w * R(z,u,z)))
    ]]></literal>
    <justification jstring="[para(13444(a,1),20957(a,1,2))].">
      <j1 rule="para" parents="13444 20957"/>
    </justification>
  </clause>

  <clause id="21201">
    <literal><![CDATA[
      K(x,T(y,R(z,u,z)) \ (w * R(z,u,z))) = K(x,(z * (y / R(z,u,z))) \ (w * z))
    ]]></literal>
    <justification jstring="[hyper(12046,a,21199,a),flip(a)].">
      <j1 rule="hyper" parents="12046 21199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21202">
    <literal><![CDATA[
      K(x,(y * (z / R(y,u,y))) \ (w * y)) = K(x,T(z,y) \ (w * R(y,u,y)))
    ]]></literal>
    <justification jstring="[para(7457(a,1),21201(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7457 21201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21203">
    <literal><![CDATA[
      K(x,(y * (z / R(y,u,y))) \ (w * y)) = K(x,T(z,y) \ (w * y))
    ]]></literal>
    <justification jstring="[hyper(299,a,13775,a(flip),b,21202,a),flip(a)].">
      <j1 rule="hyper" parents="299 13775 21202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21206">
    <literal><![CDATA[
      K(x,(((((y * z) / y) * ((y * z) / y)) \ u) * T(z,y)) \ w) = K(x,(u * (T(z,y) \ 1)) \ w)
    ]]></literal>
    <justification jstring="[hyper(299,a,18867,a(flip),b,21150,a),flip(a)].">
      <j1 rule="hyper" parents="299 18867 21150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21207">
    <literal><![CDATA[
      K(x,(y * (((z * u) / z) \ 1)) \ w) = K(x,(y * (T(u,z) \ 1)) \ w)
    ]]></literal>
    <justification jstring="[hyper(20789,a,21206,a)].">
      <j1 rule="hyper" parents="20789 21206"/>
    </justification>
  </clause>

  <clause id="21208">
    <literal><![CDATA[
      (x \ ((1 / x) \ y)) \ (K((x \ ((1 / x) \ y)) \ y,z) * y) = T(((y \ (x \ ((1 / x) \ y))) * y) \ y,z)
    ]]></literal>
    <justification jstring="[para(6977(a,1),20922(a,1,2,1))].">
      <j1 rule="para" parents="6977 20922"/>
    </justification>
  </clause>

  <clause id="21209">
    <literal><![CDATA[
      (x \ ((1 / x) \ y)) \ (K(y \ L(y,x,x),z) * y) = T(((y \ (x \ ((1 / x) \ y))) * y) \ y,z)
    ]]></literal>
    <justification jstring="[para(15725(a,1),21208(a,1,2,1))].">
      <j1 rule="para" parents="15725 21208"/>
    </justification>
  </clause>

  <clause id="21210">
    <literal><![CDATA[
      T(((x \ (y \ ((1 / y) \ x))) * x) \ x,z) = (y \ ((1 / y) \ x)) \ (1 * x)
    ]]></literal>
    <justification jstring="[para(14169(a,1),21209(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14169 21209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21211">
    <literal><![CDATA[
      T(((x \ (y \ ((1 / y) \ x))) * x) \ x,z) = (y \ ((1 / y) \ x)) \ x
    ]]></literal>
    <justification jstring="[para(7(a,1),21210(a,2,2))].">
      <j1 rule="para" parents="7 21210"/>
    </justification>
  </clause>

  <clause id="21213">
    <literal><![CDATA[
      T((x \ ((1 / x) \ y)) \ y,z) = (x \ ((1 / x) \ y)) \ y
    ]]></literal>
    <justification jstring="[para(20918(a,1),21211(a,1,1,1))].">
      <j1 rule="para" parents="20918 21211"/>
    </justification>
  </clause>

  <clause id="21214">
    <literal><![CDATA[
      K(T(a(x,y,z),u) \ (T(a(x,y,z),u) * w),v5 / T(a(x,y,z),u)) = K(L(w,y,K(z,x)),a(x,y,z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(299,a,19125,a(flip),b,20962,a),flip(a)].">
      <j1 rule="hyper" parents="299 19125 20962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21216">
    <literal><![CDATA[
      K(T(a(x,y,z),u) \ (T(a(x,y,z),u) * w),v5 / T(a(x,y,z),u)) = K(w,a(x,y,z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(299,a,18586,a(flip),b,21214,a),flip(a)].">
      <j1 rule="hyper" parents="299 18586 21214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21218">
    <literal><![CDATA[
      K(x,a(y,z,u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w / T(a(y,z,u),v6)) = v5
    ]]></literal>
    <justification jstring="[para(21216(a,1),7476(a,1))].">
      <j1 rule="para" parents="21216 7476"/>
    </justification>
  </clause>

  <clause id="21219">
    <literal><![CDATA[
      K(x,y / T(a(z,u,w),v5)) = K(x,y * a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(21218,a,21109,a)].">
      <j1 rule="hyper" parents="21218 21109"/>
    </justification>
  </clause>

  <clause id="21221">
    <literal><![CDATA[
      K(x,T(a(y,z,K(u,w)) * v5,a(y,z,w) \ 1)) = K(x,((a(y,z,w) \ 1) \ v5) * a(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,20599,a(flip),b,21219,a)].">
      <j1 rule="hyper" parents="65 20599 21219"/>
    </justification>
  </clause>

  <clause id="21223">
    <literal><![CDATA[
      K(x,T(a(y,z,K(u,w)) * v5,a(y,z,w) \ 1)) = K(x,a(y,z,w) * (v5 * a(y,z,w)))
    ]]></literal>
    <justification jstring="[hyper(299,a,14275,a(flip),b,21221,a),flip(a)].">
      <j1 rule="hyper" parents="299 14275 21221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21224">
    <literal><![CDATA[
      K(x,L(a(y,z,K(u,w)) * v5,z,K(w,y))) = K(x,a(y,z,w) * (v5 * a(y,z,w)))
    ]]></literal>
    <justification jstring="[para(20886(a,1),21223(a,1,2))].">
      <j1 rule="para" parents="20886 21223"/>
    </justification>
  </clause>

  <clause id="21225">
    <literal><![CDATA[
      K(x,a(y,z,K(u,w)) * v5) = K(x,a(y,z,w) * (v5 * a(y,z,w)))
    ]]></literal>
    <justification jstring="[hyper(20841,a,21224,a)].">
      <j1 rule="hyper" parents="20841 21224"/>
    </justification>
  </clause>

  <clause id="21226">
    <literal><![CDATA[
      K(x,a(y,z,u) * (w * a(y,z,u))) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(20516,a,21225,a),flip(a)].">
      <j1 rule="hyper" parents="20516 21225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21229">
    <literal><![CDATA[
      K(x,(y * (1 / (y \ L(y,z,z)))) \ u) = K(x,L(y,z,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,20684,a(flip),b,21226,a)].">
      <j1 rule="hyper" parents="65 20684 21226"/>
    </justification>
  </clause>

  <clause id="21231">
    <literal><![CDATA[
      K(x,(y * (L(y,z,z) \ y)) \ u) = K(x,L(y,z,z) \ u)
    ]]></literal>
    <justification jstring="[para(13003(a,1),21229(a,1,2,1,2))].">
      <j1 rule="para" parents="13003 21229"/>
    </justification>
  </clause>

  <clause id="21232">
    <literal><![CDATA[
      K(x,(y * a(z,z,y)) \ u) = K(x,L(y,z,z) \ u)
    ]]></literal>
    <justification jstring="[para(1986(a,1),21231(a,1,2,1,2))].">
      <j1 rule="para" parents="1986 21231"/>
    </justification>
  </clause>

  <clause id="21233">
    <literal><![CDATA[
      K(x,L(y \ 1,z,z) * u) = K(x,L(y,z,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,20648,a(flip),b,21232,a)].">
      <j1 rule="hyper" parents="65 20648 21232"/>
    </justification>
  </clause>

  <clause id="21234">
    <literal><![CDATA[
      K(x,L(y \ 1,z,z) \ u) = K(x,T(L(y,z,z),1) * u)
    ]]></literal>
    <justification jstring="[hyper(13900,a,21233,a),flip(a)].">
      <j1 rule="hyper" parents="13900 21233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21235">
    <literal><![CDATA[
      K(x,L(y \ 1,z,z) \ u) = K(x,L(y,z,z) * u)
    ]]></literal>
    <justification jstring="[para(193(a,1),21234(a,2,2,1))].">
      <j1 rule="para" parents="193 21234"/>
    </justification>
  </clause>

  <clause id="21236">
    <literal><![CDATA[
      K(x,L(y,z,z) * T(u,y \ 1)) = K(x,u / L(y \ 1,z,z))
    ]]></literal>
    <justification jstring="[hyper(20913,a,21235,a),flip(a)].">
      <j1 rule="hyper" parents="20913 21235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21237">
    <literal><![CDATA[
      K(x,y * (z \ ((1 / z) \ u))) = K(x,L(y,z,z) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,20694,a,b,21235,a)].">
      <j1 rule="hyper" parents="65 20694 21235"/>
    </justification>
  </clause>

  <clause id="21238">
    <literal><![CDATA[
      K(x,L((y * (z \ 1)) / y,u,u) * y) = K(x,y / L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,20747,a(flip),b,21235,a),flip(a)].">
      <j1 rule="hyper" parents="65 20747 21235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21239">
    <literal><![CDATA[
      K(x,L(L(1 / y,z,y),u,u) * w) = K(x,L(R(y,z,y),u,u) \ w)
    ]]></literal>
    <justification jstring="[para(15358(a,1),21235(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="15358 21235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21240">
    <literal><![CDATA[
      K(x,y / L(z \ 1,u,u)) = K(x,L(z,u,u) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,17473,a(flip),b,21236,a),flip(a)].">
      <j1 rule="hyper" parents="65 17473 21236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21241">
    <literal><![CDATA[
      K(x,y / L(z \ 1,u,u)) = K(x,y * L(z,u,u))
    ]]></literal>
    <justification jstring="[para(14210(a,1),21240(a,2,2))].">
      <j1 rule="para" parents="14210 21240"/>
    </justification>
  </clause>

  <clause id="21242">
    <literal><![CDATA[
      K(x,y / L(z \ 1,u,u)) = x \ T(x,y * L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,5036,a(flip),b,21241,a),flip(a)].">
      <j1 rule="hyper" parents="299 5036 21241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21243">
    <literal><![CDATA[
      K(x,y * L((z * z) \ u,z,z)) = K(x,(z \ (z \ y)) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,20699,a(flip),b,21241,a),flip(a)].">
      <j1 rule="hyper" parents="65 20699 21241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21244">
    <literal><![CDATA[
      K(x,y * (z * a(u,u,z))) = K(x,y * L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,14853,a(flip),b,21241,a)].">
      <j1 rule="hyper" parents="65 14853 21241"/>
    </justification>
  </clause>

  <clause id="21245">
    <literal><![CDATA[
      K(x,y / L(z * K(u,w),v5,v5)) = K(x,y * L(K(w,u) / z,v5,v5))
    ]]></literal>
    <justification jstring="[para(14326(a,1),21241(a,1,2,2,1))].">
      <j1 rule="para" parents="14326 21241"/>
    </justification>
  </clause>

  <clause id="21246">
    <literal><![CDATA[
      K(x,y * L(z * u,z,z)) = K(x,y * ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(19619(a,1),21244(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="19619 21244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21247">
    <literal><![CDATA[
      K(x,y * ((z \ 1) \ (z \ u))) = K(x,y * L(u,z,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),21246(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 21246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21248">
    <literal><![CDATA[
      K(x,y * L(T(T(z,u),z \ 1) * w,T(T(z,u),z \ 1),T(T(z,u),z \ 1))) = K(x,y * ((1 / T(z,u)) \ w))
    ]]></literal>
    <justification jstring="[para(3186(a,1),21246(a,2,2,2,1))].">
      <j1 rule="para" parents="3186 21246"/>
    </justification>
  </clause>

  <clause id="21249">
    <literal><![CDATA[
      K(x,y * (z \ ((1 / z) \ u))) = K(x,y * L(u,z,z))
    ]]></literal>
    <justification jstring="[para(1663(a,1),21247(a,1,2,2))].">
      <j1 rule="para" parents="1663 21247"/>
    </justification>
  </clause>

  <clause id="21250">
    <literal><![CDATA[
      K(x,L(y,z,z) * u) = K(x,y * L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,21237,a(flip),b,21249,a)].">
      <j1 rule="hyper" parents="65 21237 21249"/>
    </justification>
  </clause>

  <clause id="21251">
    <literal><![CDATA[
      x \ T(x,y * L(z,u,u)) = K(x,L(y,u,u) * z)
    ]]></literal>
    <justification jstring="[hyper(299,a,5036,a(flip),b,21250,a)].">
      <j1 rule="hyper" parents="299 5036 21250"/>
    </justification>
  </clause>

  <clause id="21252">
    <literal><![CDATA[
      K(x,y * L(y \ z,u,u)) = K(x,a(y,u,u) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,19473,a(flip),b,21250,a),flip(a)].">
      <j1 rule="hyper" parents="65 19473 21250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21253">
    <literal><![CDATA[
      K(x,((y \ 1) \ z) * L(u,y,y)) = K(x,(y * z) * u)
    ]]></literal>
    <justification jstring="[para(1670(a,1),21250(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1670 21250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21254">
    <literal><![CDATA[
      K(x,y * L(z \ 1,u,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u,u) / z) = w
    ]]></literal>
    <justification jstring="[para(21250(a,1),14626(a,1))].">
      <j1 rule="para" parents="21250 14626"/>
    </justification>
  </clause>

  <clause id="21255">
    <literal><![CDATA[
      T(x,L(y,z,z) * u) = T(x,y * L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(40,a,5036,a(flip),b,21251,a)].">
      <j1 rule="hyper" parents="40 5036 21251"/>
    </justification>
  </clause>

  <clause id="21256">
    <literal><![CDATA[
      K(x,L(y,z,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * L(u,z,z)) = w
    ]]></literal>
    <justification jstring="[para(21251(a,1),5155(a,1))].">
      <j1 rule="para" parents="21251 5155"/>
    </justification>
  </clause>

  <clause id="21257">
    <literal><![CDATA[
      T(x,y * L((z * z) * u,z,z)) = T(x,(z * (z * y)) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,17972,a(flip),b,21255,a),flip(a)].">
      <j1 rule="hyper" parents="65 17972 21255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21258">
    <literal><![CDATA[
      K(x,a(y * z,u,u) * (y * (z * w))) = K(x,(y * z) * L(L(w,z,y),u,u))
    ]]></literal>
    <justification jstring="[para(18(a,2),21252(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="18 21252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21259">
    <literal><![CDATA[
      K(x,((y \ z) \ z) * L(y \ (y \ z),u,u)) = K(x,a((y \ z) \ z,u,u) * (z / y))
    ]]></literal>
    <justification jstring="[para(4332(a,1),21252(a,1,2,2,1))].">
      <j1 rule="para" parents="4332 21252"/>
    </justification>
  </clause>

  <clause id="21260">
    <literal><![CDATA[
      K(x,((y \ 1) \ z) * u) = K(x,(y * z) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,21169,a(flip),b,21253,a)].">
      <j1 rule="hyper" parents="65 21169 21253"/>
    </justification>
  </clause>

  <clause id="21261">
    <literal><![CDATA[
      K(x,(y \ z) * (y * (y * u))) = K(x,(y * z) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,19373,a(flip),b,21253,a)].">
      <j1 rule="hyper" parents="65 19373 21253"/>
    </justification>
  </clause>

  <clause id="21263">
    <literal><![CDATA[
      K(x,((1 / y) \ z) * u) = K(x,(y * z) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,14810,a,b,21260,a)].">
      <j1 rule="hyper" parents="65 14810 21260"/>
    </justification>
  </clause>

  <clause id="21264">
    <literal><![CDATA[
      K(x,(y \ z) * (y * T(u,y))) = K(x,(y * z) * (u / y))
    ]]></literal>
    <justification jstring="[hyper(19174,a,21261,a)].">
      <j1 rule="hyper" parents="19174 21261"/>
    </justification>
  </clause>

  <clause id="21265">
    <literal><![CDATA[
      K(x,(y * z) * (y \ (y \ u))) = K(x,(y \ z) * u)
    ]]></literal>
    <justification jstring="[para(72(a,1),21261(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="72 21261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21266">
    <literal><![CDATA[
      K(x,(y \ (y \ z)) * u) = K(x,z * (y \ (y \ u)))
    ]]></literal>
    <justification jstring="[para(10(a,1),21265(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 21265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21267">
    <literal><![CDATA[
      K(x,((y / z) / z) * u) = K(x,y * (z \ (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,19226,a,b,21266,a)].">
      <j1 rule="hyper" parents="65 19226 21266"/>
    </justification>
  </clause>

  <clause id="21268">
    <literal><![CDATA[
      K(x,(y * z) * (z \ (z \ u))) = K(x,(y / z) * u)
    ]]></literal>
    <justification jstring="[para(11(a,1),21267(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="11 21267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21269">
    <literal><![CDATA[
      K(x,(y * (y / z)) * ((y / z) \ ((y / z) \ ((y / z) * u)))) = K(x,z * ((z \ y) * u))
    ]]></literal>
    <justification jstring="[para(5932(a,1),21268(a,2,2))].">
      <j1 rule="para" parents="5932 21268"/>
    </justification>
  </clause>

  <clause id="21270">
    <literal><![CDATA[
      T(x,y / L(z \ 1,u,u)) = T(x,y * L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(5086,a,21242,a)].">
      <j1 rule="hyper" parents="5086 21242"/>
    </justification>
  </clause>

  <clause id="21271">
    <literal><![CDATA[
      K(x / L(y \ 1,z,z),u) = u / T(u,x * L(y,z,z))
    ]]></literal>
    <justification jstring="[para(21270(a,1),5033(a,2,2))].">
      <j1 rule="para" parents="21270 5033"/>
    </justification>
  </clause>

  <clause id="21272">
    <literal><![CDATA[
      K(x,(y \ z) * (u * y)) = K(x,(y * z) * (u / y))
    ]]></literal>
    <justification jstring="[para(107(a,1),21264(a,1,2,2))].">
      <j1 rule="para" parents="107 21264"/>
    </justification>
  </clause>

  <clause id="21273">
    <literal><![CDATA[
      K(x,(y * (z * y)) * (u / y)) = K(x,T(z,y) * (u * y))
    ]]></literal>
    <justification jstring="[para(22(a,2),21272(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="22 21272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21274">
    <literal><![CDATA[
      K(x,(T(y,y \ z) \ u) * ((z / y) * T(y,y \ z))) = K(x,(T(y,y \ z) * u) * ((y \ z) / y))
    ]]></literal>
    <justification jstring="[para(4485(a,1),21272(a,2,2,2))].">
      <j1 rule="para" parents="4485 21272"/>
    </justification>
  </clause>

  <clause id="21275">
    <literal><![CDATA[
      K(x / L(y \ 1,z,z),u) = K(x * L(y,z,z),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,5033,a,b,21271,a),flip(a)].">
      <j1 rule="hyper" parents="299 5033 21271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21276">
    <literal><![CDATA[
      K(x / L(T(y,y \ 1),z,z),u) = K(x * L(y \ 1,z,z),u)
    ]]></literal>
    <justification jstring="[para(108(a,2),21275(a,1,1,2,1))].">
      <j1 rule="para" parents="108 21275"/>
    </justification>
  </clause>

  <clause id="21277">
    <literal><![CDATA[
      K(x,y * L(L(z \ u,z,z),z,z)) = K(x,(z \ (z \ y)) * (z * u))
    ]]></literal>
    <justification jstring="[para(96(a,2),21243(a,1,2,2,1))].">
      <j1 rule="para" parents="96 21243"/>
    </justification>
  </clause>

  <clause id="21278">
    <literal><![CDATA[
      T(x,(y * (y * z)) * u) = T(x,z * (y * (y * u)))
    ]]></literal>
    <justification jstring="[para(1675(a,1),21257(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1675 21257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21279">
    <literal><![CDATA[
      T(x,((y \ z) * y) * ((1 / y) * ((1 / y) * u))) = T(x,((1 / y) * T((1 / y) * z,y)) * u)
    ]]></literal>
    <justification jstring="[para(820(a,1),21278(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="820 21278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21280">
    <literal><![CDATA[
      K(x,y * L(z \ 1,u,u)) = K(x,y / L(z,u,u))
    ]]></literal>
    <justification jstring="[para(686(a,1),21238(a,1,2))].">
      <j1 rule="para" parents="686 21238"/>
    </justification>
  </clause>

  <clause id="21281">
    <literal><![CDATA[
      K(x,L(y,z,z) / u) = K(x,y / L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(21254,a,21280,a)].">
      <j1 rule="hyper" parents="21254 21280"/>
    </justification>
  </clause>

  <clause id="21282">
    <literal><![CDATA[
      K(x,y / L(z * u,z,z)) = K(x,y / ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,18188,a(flip),b,21281,a),flip(a)].">
      <j1 rule="hyper" parents="65 18188 21281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21283">
    <literal><![CDATA[
      K(x,y / L(L(1 / z,u,z) * w,L(1 / z,u,z),L(1 / z,u,z))) = K(x,y / (R(z,u,z) \ w))
    ]]></literal>
    <justification jstring="[para(15358(a,1),21282(a,2,2,2,1))].">
      <j1 rule="para" parents="15358 21282"/>
    </justification>
  </clause>

  <clause id="21284">
    <literal><![CDATA[
      K(x / L(T(y,y * 1),z,z),u) = K(x * L(y \ 1,z,z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,18013,a(flip),b,21276,a)].">
      <j1 rule="hyper" parents="65 18013 21276"/>
    </justification>
  </clause>

  <clause id="21285">
    <literal><![CDATA[
      K(x / L(T(y,y),z,z),u) = K(x * L(y \ 1,z,z),u)
    ]]></literal>
    <justification jstring="[para(8(a,1),21284(a,1,1,2,1,2))].">
      <j1 rule="para" parents="8 21284"/>
    </justification>
  </clause>

  <clause id="21286">
    <literal><![CDATA[
      K(x * L(y \ 1,z,z),u) = K(x / L(y,z,z),u)
    ]]></literal>
    <justification jstring="[para(106(a,1),21285(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="106 21285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21287">
    <literal><![CDATA[
      K(x,L(L(1 / y,z,y),u,u) * w) = K(x,L(y,u,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(299,a,13751,a(flip),b,21239,a),flip(a)].">
      <j1 rule="hyper" parents="299 13751 21239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21288">
    <literal><![CDATA[
      K(x,L(1 / y,z,y) * L(u,w,w)) = K(x,L(y,w,w) \ u)
    ]]></literal>
    <justification jstring="[hyper(21256,a,21287,a)].">
      <j1 rule="hyper" parents="21256 21287"/>
    </justification>
  </clause>

  <clause id="21290">
    <literal><![CDATA[
      K(x,L(y \ 1,z,y) * L(u,w,w)) = K(x,L(y,w,w) \ u)
    ]]></literal>
    <justification jstring="[hyper(13851,a,21288,a)].">
      <j1 rule="hyper" parents="13851 21288"/>
    </justification>
  </clause>

  <clause id="21291">
    <literal><![CDATA[
      K(x,L(y,z,z) \ u) = K(x,y \ L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,21147,a(flip),b,21290,a),flip(a)].">
      <j1 rule="hyper" parents="65 21147 21290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21292">
    <literal><![CDATA[
      K(x,(y \ z) * a(y,u,u)) = K(x,y \ L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,21115,a,b,21291,a)].">
      <j1 rule="hyper" parents="65 21115 21291"/>
    </justification>
  </clause>

  <clause id="21293">
    <literal><![CDATA[
      K(x,y \ L(L(z,u,u),u,u)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,20704,a(flip),b,21291,a),flip(a)].">
      <j1 rule="hyper" parents="65 20704 21291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21294">
    <literal><![CDATA[
      K(x,y \ L((z * y) * u,z,z)) = K(x,y \ (((z \ 1) \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,19620,a(flip),b,21291,a),flip(a)].">
      <j1 rule="hyper" parents="65 19620 21291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21295">
    <literal><![CDATA[
      K(x,y \ L(z,u,u)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,21171,a(flip),b,21292,a),flip(a)].">
      <j1 rule="hyper" parents="65 21171 21292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21298">
    <literal><![CDATA[
      K(x,(y / L(z,z,K(z,y) * u)) \ u) = K(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,20584,a(flip),b,21295,a),flip(a)].">
      <j1 rule="hyper" parents="65 20584 21295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21300">
    <literal><![CDATA[
      K(x,y \ (((z \ 1) \ y) * u)) = K(x,y \ ((z * y) * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,21295,a(flip),b,21294,a),flip(a)].">
      <j1 rule="hyper" parents="65 21295 21294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21302">
    <literal><![CDATA[
      K(x,y / L(z * K(u,w),v5,v5)) = K(x,y * L(z \ K(w,u),v5,v5))
    ]]></literal>
    <justification jstring="[hyper(299,a,21097,a(flip),b,21245,a),flip(a)].">
      <j1 rule="hyper" parents="299 21097 21245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21303">
    <literal><![CDATA[
      K(x,y * L((1 / z) * u,z,z)) = K(x,(z \ (z \ y)) * (z * u))
    ]]></literal>
    <justification jstring="[para(511(a,1),21277(a,1,2,2,1))].">
      <j1 rule="para" parents="511 21277"/>
    </justification>
  </clause>

  <clause id="21304">
    <literal><![CDATA[
      K(x,y * L((z \ 1) * u,z,z)) = K(x,(z \ (z \ y)) * (z * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,6125,a(flip),b,21303,a)].">
      <j1 rule="hyper" parents="65 6125 21303"/>
    </justification>
  </clause>

  <clause id="21305">
    <literal><![CDATA[
      K(x,y * L((z \ 1) * u,z,z)) = K(x,y * (z \ (z \ (z * u))))
    ]]></literal>
    <justification jstring="[hyper(299,a,21266,a(flip),b,21304,a),flip(a)].">
      <j1 rule="hyper" parents="299 21266 21304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21306">
    <literal><![CDATA[
      K(x,y * L((z \ 1) * u,z,z)) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[para(9(a,1),21305(a,2,2,2,2))].">
      <j1 rule="para" parents="9 21305"/>
    </justification>
  </clause>

  <clause id="21307">
    <literal><![CDATA[
      K(x,y * ((z \ 1) * u)) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,21169,a(flip),b,21306,a)].">
      <j1 rule="hyper" parents="65 21169 21306"/>
    </justification>
  </clause>

  <clause id="21310">
    <literal><![CDATA[
      K(x,y * L(z \ K(u,w),w,w)) = K(x,y * (L(z,w,w) \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,19652,a(flip),b,21302,a),flip(a)].">
      <j1 rule="hyper" parents="65 19652 21302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21311">
    <literal><![CDATA[
      K(x,y * L((z / u) \ K(z,u),u,u)) = K(x,y / ((u \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(20497,a,21310,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="20497 21310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21312">
    <literal><![CDATA[
      K(x,T(y,L((z / u) \ K(z,u),u,u)) / ((u \ 1) * z)) = K(x,L((z / u) \ K(z,u),u,u) * y)
    ]]></literal>
    <justification jstring="[hyper(13261,a,21311,a),flip(a)].">
      <j1 rule="hyper" parents="13261 21311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21313">
    <literal><![CDATA[
      K(x,a(y * z,u,u) * (y * (z * w))) = K(x,y * (z * L(w,u,u)))
    ]]></literal>
    <justification jstring="[para(489(a,1),21258(a,2,2))].">
      <j1 rule="para" parents="489 21258"/>
    </justification>
  </clause>

  <clause id="21314">
    <literal><![CDATA[
      K(x,y * (z * L(u,w,w))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,21167,a(flip),b,21313,a),flip(a)].">
      <j1 rule="hyper" parents="65 21167 21313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21315">
    <literal><![CDATA[
      K(x,a(y * z,u,u) * (y * (w * z))) = K(x,y * (z * L(T(w,z),u,u)))
    ]]></literal>
    <justification jstring="[para(107(a,1),21313(a,1,2,2,2))].">
      <j1 rule="para" parents="107 21313"/>
    </justification>
  </clause>

  <clause id="21317">
    <literal><![CDATA[
      K(x,y * (z * ((u * u) \ w))) = K(x,y * (z * (u \ (u \ w))))
    ]]></literal>
    <justification jstring="[para(281(a,1),21314(a,1,2,2,2))].">
      <j1 rule="para" parents="281 21314"/>
    </justification>
  </clause>

  <clause id="21318">
    <literal><![CDATA[
      K(x,y * (z * (y \ (y \ u)))) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,17629,a(flip),b,21317,a),flip(a)].">
      <j1 rule="hyper" parents="65 17629 21317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21319">
    <literal><![CDATA[
      K(x,a(y * z,u,u) * (y * (w * z))) = K(x,y * (L(w,u,u) * z))
    ]]></literal>
    <justification jstring="[para(233(a,1),21315(a,2,2,2))].">
      <j1 rule="para" parents="233 21315"/>
    </justification>
  </clause>

  <clause id="21320">
    <literal><![CDATA[
      K(x,y * (L(z,u,u) * w)) = K(x,y * (z * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,21167,a(flip),b,21319,a),flip(a)].">
      <j1 rule="hyper" parents="65 21167 21319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21322">
    <literal><![CDATA[
      K(x,y \ ((y * (y * z)) * u)) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,14723,a,b,21320,a)].">
      <j1 rule="hyper" parents="65 14723 21320"/>
    </justification>
  </clause>

  <clause id="21324">
    <literal><![CDATA[
      K(x,T(y,z) * L(y \ (y \ z),u,u)) = K(x,a((y \ z) \ z,u,u) * (z / y))
    ]]></literal>
    <justification jstring="[hyper(13875,a,21259,a)].">
      <j1 rule="hyper" parents="13875 21259"/>
    </justification>
  </clause>

  <clause id="21325">
    <literal><![CDATA[
      K(x,(y * (y / z)) * ((y / z) \ u)) = K(x,z * ((z \ y) * u))
    ]]></literal>
    <justification jstring="[para(9(a,1),21269(a,1,2,2,2))].">
      <j1 rule="para" parents="9 21269"/>
    </justification>
  </clause>

  <clause id="21326">
    <literal><![CDATA[
      T(x,((y \ z) * y) * ((1 / y) * ((1 / y) * u))) = T(x,((y \ 1) * T((y \ 1) * z,y)) * u)
    ]]></literal>
    <justification jstring="[para(15096(a,1),21279(a,2,2,1))].">
      <j1 rule="para" parents="15096 21279"/>
    </justification>
  </clause>

  <clause id="21327">
    <literal><![CDATA[
      T(x,((y \ z) * y) * ((1 / y) * ((1 / y) * u))) = T(x,((y \ 1) * (z * (y \ 1))) * u)
    ]]></literal>
    <justification jstring="[hyper(299,a,19331,a(flip),b,21326,a),flip(a)].">
      <j1 rule="hyper" parents="299 19331 21326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21328">
    <literal><![CDATA[
      T(x,((y \ z) * y) * ((y \ 1) * ((y \ 1) * u))) = T(x,((y \ 1) * (z * (y \ 1))) * u)
    ]]></literal>
    <justification jstring="[para(2838(a,1),21327(a,1,2,2))].">
      <j1 rule="para" parents="2838 21327"/>
    </justification>
  </clause>

  <clause id="21329">
    <literal><![CDATA[
      T(x,((y \ z) * (1 / y)) * L(u,y,y)) = T(x,((y \ 1) * (z * (y \ 1))) * u)
    ]]></literal>
    <justification jstring="[para(1749(a,1),21328(a,1,2))].">
      <j1 rule="para" parents="1749 21328"/>
    </justification>
  </clause>

  <clause id="21330">
    <literal><![CDATA[
      T(x,((y \ z) * (y \ 1)) * L(u,y,y)) = T(x,((y \ 1) * (z * (y \ 1))) * u)
    ]]></literal>
    <justification jstring="[hyper(19740,a,21329,a)].">
      <j1 rule="hyper" parents="19740 21329"/>
    </justification>
  </clause>

  <clause id="21331">
    <literal><![CDATA[
      K(x,(T(y,y \ z) \ u) * (y * (z / y))) = K(x,(T(y,y \ z) * u) * ((y \ z) / y))
    ]]></literal>
    <justification jstring="[para(4441(a,1),21274(a,1,2,2))].">
      <j1 rule="para" parents="4441 21274"/>
    </justification>
  </clause>

  <clause id="21332">
    <literal><![CDATA[
      K(x,(T(y,y \ z) * u) * ((y \ z) / y)) = K(x,(T(y,y \ z) \ u) * T(z,y))
    ]]></literal>
    <justification jstring="[hyper(16867,a,21331,a),flip(a)].">
      <j1 rule="hyper" parents="16867 21331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21333">
    <literal><![CDATA[
      K(x,(T(y,y \ z) * u) * ((y \ z) / y)) = K(x,(T(y,y * z) \ u) * T(z,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,18120,a(flip),b,21332,a),flip(a)].">
      <j1 rule="hyper" parents="299 18120 21332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21334">
    <literal><![CDATA[
      K(x,(T(y,y \ z) * u) * ((y \ z) / y)) = K(x,(T(y,z) \ u) * T(z,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,19506,a(flip),b,21333,a),flip(a)].">
      <j1 rule="hyper" parents="299 19506 21333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21335">
    <literal><![CDATA[
      K(x,(T(y,y \ z) * u) * (y \ (z / y))) = K(x,(T(y,z) \ u) * T(z,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,13883,a(flip),b,21334,a)].">
      <j1 rule="hyper" parents="65 13883 21334"/>
    </justification>
  </clause>

  <clause id="21336">
    <literal><![CDATA[
      K(x,(y * z) * (T(y,y \ u) \ (u / y))) = K(x,(T(y,u) \ z) * T(u,y))
    ]]></literal>
    <justification jstring="[hyper(19211,a,21335,a)].">
      <j1 rule="hyper" parents="19211 21335"/>
    </justification>
  </clause>

  <clause id="21337">
    <literal><![CDATA[
      K(x,(T(y,z) \ u) * T(z,y)) = K(x,(y * u) * (y \ (y \ z)))
    ]]></literal>
    <justification jstring="[para(4325(a,1),21336(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4325 21336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21338">
    <literal><![CDATA[
      K(x,(T(y,z) \ u) * T(z,y)) = K(x,(y \ u) * z)
    ]]></literal>
    <justification jstring="[hyper(299,a,21265,a(flip),b,21337,a),flip(a)].">
      <j1 rule="hyper" parents="299 21265 21337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21339">
    <literal><![CDATA[
      K(x,T(y,(z / u) \ K(z,u)) / ((u \ 1) * z)) = K(x,L((z / u) \ K(z,u),u,u) * y)
    ]]></literal>
    <justification jstring="[hyper(20992,a,21312,a)].">
      <j1 rule="hyper" parents="20992 21312"/>
    </justification>
  </clause>

  <clause id="21341">
    <literal><![CDATA[
      K(x,T(y,z * (u \ K(u,z))) / ((z \ 1) * u)) = K(x,L((u / z) \ K(u,z),z,z) * y)
    ]]></literal>
    <justification jstring="[para(20947(a,1),21339(a,1,2,1))].">
      <j1 rule="para" parents="20947 21339"/>
    </justification>
  </clause>

  <clause id="21342">
    <literal><![CDATA[
      K(x,T(y,z / T(u,z)) / ((z \ 1) * u)) = K(x,L((u / z) \ K(u,z),z,z) * y)
    ]]></literal>
    <justification jstring="[para(15845(a,1),21341(a,1,2,1))].">
      <j1 rule="para" parents="15845 21341"/>
    </justification>
  </clause>

  <clause id="21343">
    <literal><![CDATA[
      K(x,L((y / z) \ K(y,z),z,z) * u) = K(x,T(u,y \ z) / ((z \ 1) * y))
    ]]></literal>
    <justification jstring="[para(13704(a,1),21342(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13704 21342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21344">
    <literal><![CDATA[
      K(x,L((y / z) \ K(y,z),z,z) * u) = K(x,T(u,y * z) / ((z \ 1) * y))
    ]]></literal>
    <justification jstring="[hyper(299,a,18015,a(flip),b,21343,a),flip(a)].">
      <j1 rule="hyper" parents="299 18015 21343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21345">
    <literal><![CDATA[
      K(x,L((y / z) \ K(y,z),z,z) * u) = K(x,((z \ 1) * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(299,a,20367,a(flip),b,21344,a),flip(a)].">
      <j1 rule="hyper" parents="299 20367 21344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21346">
    <literal><![CDATA[
      K(x,((y / z) \ K(y,z)) * L(u,z,z)) = K(x,((z \ 1) * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(21256,a,21345,a)].">
      <j1 rule="hyper" parents="21256 21345"/>
    </justification>
  </clause>

  <clause id="21347">
    <literal><![CDATA[
      K(x,K(y,z) * ((z / y) \ L(u,y,y))) = K(x,((y \ 1) * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(20336,a,21346,a)].">
      <j1 rule="hyper" parents="20336 21346"/>
    </justification>
  </clause>

  <clause id="21348">
    <literal><![CDATA[
      K(x,(y / T(z,y)) \ L(u,z,z)) = K(x,((z \ 1) * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,20100,a(flip),b,21347,a)].">
      <j1 rule="hyper" parents="65 20100 21347"/>
    </justification>
  </clause>

  <clause id="21349">
    <literal><![CDATA[
      K(x,(y \ z) \ L(u,y,y)) = K(x,((y \ 1) * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,20235,a(flip),b,21348,a)].">
      <j1 rule="hyper" parents="65 20235 21348"/>
    </justification>
  </clause>

  <clause id="21350">
    <literal><![CDATA[
      K(x,(L(y,y,L(z,y,y)) \ u) \ L(L(z,y,y),y,y)) = K(x,((y \ 1) * u) \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,16113,a,b,21349,a)].">
      <j1 rule="hyper" parents="65 16113 21349"/>
    </justification>
  </clause>

  <clause id="21351">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ u) = K(x,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,21295,a(flip),b,21349,a),flip(a)].">
      <j1 rule="hyper" parents="65 21295 21349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21353">
    <literal><![CDATA[
      K(x,(L(y,y,z) \ u) \ L(L(z,y,y),y,y)) = K(x,((y \ 1) * u) \ z)
    ]]></literal>
    <justification jstring="[para(17312(a,1),21350(a,1,2,1,1))].">
      <j1 rule="para" parents="17312 21350"/>
    </justification>
  </clause>

  <clause id="21354">
    <literal><![CDATA[
      K(x,(L(y,y,z) \ u) \ z) = K(x,((y \ 1) * u) \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,21293,a(flip),b,21353,a)].">
      <j1 rule="hyper" parents="65 21293 21353"/>
    </justification>
  </clause>

  <clause id="21356">
    <literal><![CDATA[
      K(x,(L(y,y,K(y \ 1,z) * u) \ z) \ (K(y \ 1,z) * u)) = K(x,(z * (y \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(11616(a,1),21354(a,2,2))].">
      <j1 rule="para" parents="11616 21354"/>
    </justification>
  </clause>

  <clause id="21357">
    <literal><![CDATA[
      K(x,(L(y,y,K(y,z) * u) \ z) \ (K(y \ 1,z) * u)) = K(x,(z * (y \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(19860(a,1),21356(a,1,2,1,1))].">
      <j1 rule="para" parents="19860 21356"/>
    </justification>
  </clause>

  <clause id="21358">
    <literal><![CDATA[
      K(x,K(y,z \ 1) * ((L(z,z,K(z,y) * u) \ y) \ u)) = K(x,(y * (z \ 1)) \ u)
    ]]></literal>
    <justification jstring="[hyper(20132,a,21357,a)].">
      <j1 rule="hyper" parents="20132 21357"/>
    </justification>
  </clause>

  <clause id="21359">
    <literal><![CDATA[
      K(x,(L(y,y,K(y,z) * u) \ T(z,y \ 1)) \ u) = K(x,(z * (y \ 1)) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,20157,a(flip),b,21358,a)].">
      <j1 rule="hyper" parents="65 20157 21358"/>
    </justification>
  </clause>

  <clause id="21360">
    <literal><![CDATA[
      K(x,y / L(L(1 / z,u,z) * w,L(1 / z,u,z),L(z,u,z))) = K(x,y / (R(z,u,z) \ w))
    ]]></literal>
    <justification jstring="[para(6510(a,1),21283(a,1,2,2))].">
      <j1 rule="para" parents="6510 21283"/>
    </justification>
  </clause>

  <clause id="21361">
    <literal><![CDATA[
      K(x,y / L(L(1 / z,u,z) * w,L(1 / z,u,z),z)) = K(x,y / (R(z,u,z) \ w))
    ]]></literal>
    <justification jstring="[para(13444(a,1),21360(a,1,2,2))].">
      <j1 rule="para" parents="13444 21360"/>
    </justification>
  </clause>

  <clause id="21363">
    <literal><![CDATA[
      K(x,y / L(L(1 / z,u,z) * w,L(z,u,z),z)) = K(x,y / (R(z,u,z) \ w))
    ]]></literal>
    <justification jstring="[para(6512(a,1),21361(a,1,2,2))].">
      <j1 rule="para" parents="6512 21361"/>
    </justification>
  </clause>

  <clause id="21364">
    <literal><![CDATA[
      K(x,y / L(L(1 / z,u,z) * w,z,z)) = K(x,y / (R(z,u,z) \ w))
    ]]></literal>
    <justification jstring="[para(17037(a,1),21363(a,1,2,2))].">
      <j1 rule="para" parents="17037 21363"/>
    </justification>
  </clause>

  <clause id="21366">
    <literal><![CDATA[
      K(x,y / L(L(1 / z,u,z) * w,z,z)) = K(x,y / (z \ w))
    ]]></literal>
    <justification jstring="[hyper(299,a,19823,a(flip),b,21364,a),flip(a)].">
      <j1 rule="hyper" parents="299 19823 21364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21368">
    <literal><![CDATA[
      K(x,y * (T(z,u) * L(w,z,z))) = K(x,y * ((1 / T(z,u)) \ w))
    ]]></literal>
    <justification jstring="[para(15323(a,1),21248(a,1,2,2))].">
      <j1 rule="para" parents="15323 21248"/>
    </justification>
  </clause>

  <clause id="21369">
    <literal><![CDATA[
      K(x,y * (T(z,u) * L(w,z,z))) = K(x,y * (T(z \ 1,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(299,a,19355,a(flip),b,21368,a),flip(a)].">
      <j1 rule="hyper" parents="299 19355 21368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21370">
    <literal><![CDATA[
      K(x,y * (T(z \ 1,u) \ w)) = K(x,y * (T(z,u) * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,21314,a(flip),b,21369,a),flip(a)].">
      <j1 rule="hyper" parents="65 21314 21369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21372">
    <literal><![CDATA[
      K(x,y * (T(1 / z,u) \ w)) = K(x,y * (T(z,u) * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,5907,a,b,21370,a)].">
      <j1 rule="hyper" parents="65 5907 21370"/>
    </justification>
  </clause>

  <clause id="21373">
    <literal><![CDATA[
      T(x,T(y,z)) \ (K(x,L(x \ z,u,w)) * (K(x,x \ z) \ T(x,T(y,z)))) = T((x \ z) \ z,y) \ T(T(x,y),L(x \ z,u,w))
    ]]></literal>
    <justification jstring="[para(11889(a,1),18937(a,1,2,1))].">
      <j1 rule="para" parents="11889 18937"/>
    </justification>
  </clause>

  <clause id="21374">
    <literal><![CDATA[
      K(x,(y * (z / T(u * y,z))) * R(u,y,z / T(u * y,z))) = K(x,T((z / (u * y)) * (u * y),z * L(u,y,y)))
    ]]></literal>
    <justification jstring="[hyper(65,a,13243,a(flip),b,21139,a),flip(a)].">
      <j1 rule="hyper" parents="65 13243 21139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21375">
    <literal><![CDATA[
      K(x,(y * (z / T(u * y,z))) * R(u,y,z / T(u * y,z))) = K(x,T(z,z * L(u,y,y)))
    ]]></literal>
    <justification jstring="[para(12(a,1),21374(a,2,2,1))].">
      <j1 rule="para" parents="12 21374"/>
    </justification>
  </clause>

  <clause id="21376">
    <literal><![CDATA[
      K(x,(y * (z / T(u * y,z))) * R(u,y,z / T(u * y,z))) = K(x,T(z,L(u,y,y)))
    ]]></literal>
    <justification jstring="[hyper(299,a,7469,a(flip),b,21375,a),flip(a)].">
      <j1 rule="hyper" parents="299 7469 21375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21377">
    <literal><![CDATA[
      K(x,(y * (z / T(u * y,z))) * R(u,y,z / T(u * y,z))) = K(x,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,18707,a(flip),b,21376,a),flip(a)].">
      <j1 rule="hyper" parents="299 18707 21376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21379">
    <literal><![CDATA[
      K(x,(y * (z / T(u * y,z))) * R(u,y,(u * y) \ z)) = K(x,T(z,u))
    ]]></literal>
    <justification jstring="[para(14064(a,1),21377(a,1,2,2))].">
      <j1 rule="para" parents="14064 21377"/>
    </justification>
  </clause>

  <clause id="21380">
    <literal><![CDATA[
      K(x,(y * ((z * y) \ u)) * R(z,y,(z * y) \ u)) = K(x,T(u,z))
    ]]></literal>
    <justification jstring="[hyper(19758,a,21379,a)].">
      <j1 rule="hyper" parents="19758 21379"/>
    </justification>
  </clause>

  <clause id="21381">
    <literal><![CDATA[
      K(x,T((y * z) \ u,z) * (z * y)) = K(x,T(u,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,20722,a(flip),b,21380,a)].">
      <j1 rule="hyper" parents="65 20722 21380"/>
    </justification>
  </clause>

  <clause id="21382">
    <literal><![CDATA[
      K(x,T((y * (z \ u)) \ w,z * u) * ((z \ u) * y)) = K(x,T(w,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,17939,a(flip),b,21381,a)].">
      <j1 rule="hyper" parents="65 17939 21381"/>
    </justification>
  </clause>

  <clause id="21383">
    <literal><![CDATA[
      K(x,T((a(y,z,u) * (w / a(y,z,u))) \ v5,a(y,z,u)) * (a(y,z,u) * (a(y,z,u) \ w))) = K(x,T(v5,a(y,z,u) \ w))
    ]]></literal>
    <justification jstring="[para(21086(a,1),21381(a,1,2,1,1,1))].">
      <j1 rule="para" parents="21086 21381"/>
    </justification>
  </clause>

  <clause id="21384">
    <literal><![CDATA[
      K(x,T((y * (z \ 1)) \ u,z) * ((z \ 1) * y)) = K(x,T(u,y))
    ]]></literal>
    <justification jstring="[para(8(a,1),21382(a,1,2,1,2))].">
      <j1 rule="para" parents="8 21382"/>
    </justification>
  </clause>

  <clause id="21385">
    <literal><![CDATA[
      K(x,T((y * (z \ 1)) \ u,z) * (z \ y)) = K(x,T(u,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,21307,a(flip),b,21384,a)].">
      <j1 rule="hyper" parents="65 21307 21384"/>
    </justification>
  </clause>

  <clause id="21386">
    <literal><![CDATA[
      K(x,L((a(y,z,u) * (w / a(y,z,u))) \ v5,z,K(u,y)) * (a(y,z,u) * (a(y,z,u) \ w))) = K(x,T(v5,a(y,z,u) \ w))
    ]]></literal>
    <justification jstring="[para(20826(a,2),21383(a,1,2,1))].">
      <j1 rule="para" parents="20826 21383"/>
    </justification>
  </clause>

  <clause id="21387">
    <literal><![CDATA[
      K(x,L((a(y,z,u) * (w / a(y,z,u))) \ v5,z,K(u,y)) * w) = K(x,T(v5,a(y,z,u) \ w))
    ]]></literal>
    <justification jstring="[para(10(a,1),21386(a,1,2,2))].">
      <j1 rule="para" parents="10 21386"/>
    </justification>
  </clause>

  <clause id="21388">
    <literal><![CDATA[
      K(x,((a(y,z,u) * (w / a(y,z,u))) \ v5) * w) = K(x,T(v5,a(y,z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(20923,a,21387,a)].">
      <j1 rule="hyper" parents="20923 21387"/>
    </justification>
  </clause>

  <clause id="21391">
    <literal><![CDATA[
      K(x,T(y * K(z,a(u,w,v5)),z)) = K(x,T(y,a(u,w,v5) \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,19832,a(flip),b,21388,a)].">
      <j1 rule="hyper" parents="65 19832 21388"/>
    </justification>
  </clause>

  <clause id="21392">
    <literal><![CDATA[
      K(x,T(y * a(z,u,K(w,v5)),z)) = K(x,T(y,a(v5,u,w) \ z))
    ]]></literal>
    <justification jstring="[para(14871(a,2),21391(a,1,2,1,2))].">
      <j1 rule="para" parents="14871 21391"/>
    </justification>
  </clause>

  <clause id="21393">
    <literal><![CDATA[
      K(x,T(y,a(z,u,w) \ v5)) = K(x,T(y,v5))
    ]]></literal>
    <justification jstring="[hyper(20517,a,21392,a),flip(a)].">
      <j1 rule="hyper" parents="20517 21392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21395">
    <literal><![CDATA[
      K(x,T(y,a(z,u,w) * v5)) = K(x,T(y,v5))
    ]]></literal>
    <justification jstring="[hyper(16637,a,21393,a)].">
      <j1 rule="hyper" parents="16637 21393"/>
    </justification>
  </clause>

  <clause id="21396">
    <literal><![CDATA[
      K(x,T(y,z * a(u,w,v5))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(16636,a,21393,a)].">
      <j1 rule="hyper" parents="16636 21393"/>
    </justification>
  </clause>

  <clause id="21397">
    <literal><![CDATA[
      T(x * K(y,T(x,z)),y) = T(x,K(y,a(u,w,v5) * z))
    ]]></literal>
    <justification jstring="[para(21395(a,1),8093(a,1,1,2))].">
      <j1 rule="para" parents="21395 8093"/>
    </justification>
  </clause>

  <clause id="21398">
    <literal><![CDATA[
      K((a(x,y,z) * u) \ w,T(v5,u)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(w / (a(x,y,z) * u),v5) = v6
    ]]></literal>
    <justification jstring="[para(21395(a,1),8220(a,1))].">
      <j1 rule="para" parents="21395 8220"/>
    </justification>
  </clause>

  <clause id="21399">
    <literal><![CDATA[
      T(x,a(y,z,u)) * K(w,T(v5,x)) = T(K(w,v5) * x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(21395(a,1),16980(a,1,2))].">
      <j1 rule="para" parents="21395 16980"/>
    </justification>
  </clause>

  <clause id="21400">
    <literal><![CDATA[
      K(x,T(y,(z * u) * w)) = K(x,T(y,z * (u * w)))
    ]]></literal>
    <justification jstring="[para(19556(a,1),21395(a,1,2,2))].">
      <j1 rule="para" parents="19556 21395"/>
    </justification>
  </clause>

  <clause id="21401">
    <literal><![CDATA[
      K(x,T(y,z * L(u,w,w))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(21121(a,1),21395(a,1,2))].">
      <j1 rule="para" parents="21121 21395"/>
    </justification>
  </clause>

  <clause id="21402">
    <literal><![CDATA[
      T(K(x,y),z * a(u,w,v5)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(8419,a,21396,a)].">
      <j1 rule="hyper" parents="8419 21396"/>
    </justification>
  </clause>

  <clause id="21405">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z * (u * w))) = K(x,K(y,(z * u) * w))
    ]]></literal>
    <justification jstring="[para(21400(a,1),8010(a,1,2))].">
      <j1 rule="para" parents="21400 8010"/>
    </justification>
  </clause>

  <clause id="21406">
    <literal><![CDATA[
      T(x,K(y,a(z,u,w) * v5)) = T(x,K(y,v5))
    ]]></literal>
    <justification jstring="[hyper(8374,a,21397,a),flip(a)].">
      <j1 rule="hyper" parents="8374 21397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21407">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(u / a(w,v5,v6),z)) = T(y,K(z,a(w,v5,v6) \ u) * x)
    ]]></literal>
    <justification jstring="[para(21406(a,1),17334(a,1,2,1,2))].">
      <j1 rule="para" parents="21406 17334"/>
    </justification>
  </clause>

  <clause id="21408">
    <literal><![CDATA[
      L(x,y,K(z,u)) * K(w,T(v5,x)) = T(K(w,v5) * x,a(u,y,z))
    ]]></literal>
    <justification jstring="[para(20826(a,2),21399(a,1,1))].">
      <j1 rule="para" parents="20826 21399"/>
    </justification>
  </clause>

  <clause id="21409">
    <literal><![CDATA[
      K(x,K(y,(z * u) * w)) = K(x,K(y,z * (u * w)))
    ]]></literal>
    <justification jstring="[hyper(8205,a,21405,a),flip(a)].">
      <j1 rule="hyper" parents="8205 21405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21410">
    <literal><![CDATA[
      K(x,K(y,z * (u \ w))) = K(x,K(y,z * (u * w)))
    ]]></literal>
    <justification jstring="[hyper(18829,a,21409,a)].">
      <j1 rule="hyper" parents="18829 21409"/>
    </justification>
  </clause>

  <clause id="21411">
    <literal><![CDATA[
      K(x,K(y * z,y * (z * u))) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(8207,a,21409,a),flip(a)].">
      <j1 rule="hyper" parents="8207 21409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21413">
    <literal><![CDATA[
      K(x,K(y,z * ((u \ z) * w))) = K(x,K(y,z * (u * (z \ w))))
    ]]></literal>
    <justification jstring="[hyper(65,a,19489,a(flip),b,21410,a),flip(a)].">
      <j1 rule="hyper" parents="65 19489 21410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21416">
    <literal><![CDATA[
      T(K(x,y) * z,a(u,w,v5)) = K(x,y) * L(z,w,K(v5,u))
    ]]></literal>
    <justification jstring="[hyper(18713,a,21408,a),flip(a)].">
      <j1 rule="hyper" parents="18713 21408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21417">
    <literal><![CDATA[
      L(K(x,y) * z,u,K(w,v5)) = K(x,y) * L(z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(20827,a,21416,a)].">
      <j1 rule="hyper" parents="20827 21416"/>
    </justification>
  </clause>

  <clause id="21418">
    <literal><![CDATA[
      (x \ K(y,z)) \ L(x \ K(y,z),u,K(w,v5)) = x \ L(K(y,z) * (K(y,z) \ x),u,K(w,v5))
    ]]></literal>
    <justification jstring="[para(21417(a,2),6505(a,2,2))].">
      <j1 rule="para" parents="21417 6505"/>
    </justification>
  </clause>

  <clause id="21419">
    <literal><![CDATA[
      K(x,K(y,z * (u * (z \ w)))) = K(x,K(y,u * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,18803,a(flip),b,21413,a),flip(a)].">
      <j1 rule="hyper" parents="65 18803 21413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21421">
    <literal><![CDATA[
      K(x,K(y,z * x)) * K(y,L(T(z,u \ x),u \ x,u)) = K(y,(u * (z * (u \ x))) / x)
    ]]></literal>
    <justification jstring="[para(21419(a,1),8508(a,1,1))].">
      <j1 rule="para" parents="21419 8508"/>
    </justification>
  </clause>

  <clause id="21422">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z / a(w,v5,v6),u)) = T(y,K(u,a(w,v5,v6) \ z) * x)
    ]]></literal>
    <justification jstring="[para(8050(a,1),21407(a,1,2,1,2))].">
      <j1 rule="para" parents="8050 21407"/>
    </justification>
  </clause>

  <clause id="21423">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(u,a(w,v5,v6) \ z)) = T(y,K(u,a(w,v5,v6) \ z) * x)
    ]]></literal>
    <justification jstring="[para(16737(a,1),21422(a,1,2))].">
      <j1 rule="para" parents="16737 21422"/>
    </justification>
  </clause>

  <clause id="21424">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(u,a(w,v5,v6) * z)) = T(y,K(u,a(w,v5,v6) \ z) * x)
    ]]></literal>
    <justification jstring="[para(16268(a,1),21423(a,1,2))].">
      <j1 rule="para" parents="16268 21423"/>
    </justification>
  </clause>

  <clause id="21425">
    <literal><![CDATA[
      T(x,K(y,a(z,u,w) \ v5) * v6) = v6 \ T(x * T(v6,K(v5,y)),K(y,v5))
    ]]></literal>
    <justification jstring="[para(21406(a,1),21424(a,1,2)),flip(a)].">
      <j1 rule="para" parents="21406 21424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21426">
    <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(8050(a,1),21425(a,2,2))].">
      <j1 rule="para" parents="8050 21425"/>
    </justification>
  </clause>

  <clause id="21428">
    <literal><![CDATA[
      T(x,K(y,a(z,u,w) \ v5) * v6) = T(x,K(y,v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(299,a,15769,a(flip),b,21426,a),flip(a)].">
      <j1 rule="hyper" parents="299 15769 21426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21429">
    <literal><![CDATA[
      T(x,y * K(z,a(u,w,v5) * v6)) = T(x,K(z,v6) * y)
    ]]></literal>
    <justification jstring="[hyper(17428,a,21428,a)].">
      <j1 rule="hyper" parents="17428 21428"/>
    </justification>
  </clause>

  <clause id="21430">
    <literal><![CDATA[
      T(x,K(y,z) * (u \ (a(w,v5,v6) * z))) = T(x,u \ T(a(w,v5,v6) * z,y))
    ]]></literal>
    <justification jstring="[hyper(16689,a,21429,a),flip(a)].">
      <j1 rule="hyper" parents="16689 21429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21431">
    <literal><![CDATA[
      T(x,y \ T(a(z,u,w) * v5,v6)) = T(x,y \ (a(z,u,w) * T(v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(20279,a,21430,a),flip(a)].">
      <j1 rule="hyper" parents="20279 21430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21432">
    <literal><![CDATA[
      T(x,y \ T(a(z,u,u) * w,v5)) = T(x,y \ (T(w,v5) * a(z,u,u)))
    ]]></literal>
    <justification jstring="[hyper(15918,a,21431,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="15918 21431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21433">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,L(T(z,u \ x),u \ x,u)) = K(y,(u * (z * (u \ x))) / x)
    ]]></literal>
    <justification jstring="[para(8048(a,1),21421(a,1,1))].">
      <j1 rule="para" parents="8048 21421"/>
    </justification>
  </clause>

  <clause id="21435">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,x \ (u * (z * (u \ x)))) = K(y,(u * (z * (u \ x))) / x)
    ]]></literal>
    <justification jstring="[para(777(a,1),21433(a,1,2,2))].">
      <j1 rule="para" parents="777 21433"/>
    </justification>
  </clause>

  <clause id="21436">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,x \ (u * (z * (u \ x)))) = K(y,x \ (((x / u) * z) * u))
    ]]></literal>
    <justification jstring="[hyper(299,a,20449,a(flip),b,21435,a),flip(a)].">
      <j1 rule="hyper" parents="299 20449 21435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21437">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,L(T(z,u * x),x,u)) = K(y,x \ (((x / u) * z) * u))
    ]]></literal>
    <justification jstring="[para(16940(a,1),21436(a,1,2))].">
      <j1 rule="para" parents="16940 21436"/>
    </justification>
  </clause>

  <clause id="21438">
    <literal><![CDATA[
      K(x,L(T(T(y,z),u * z),z,u)) = K(x,z \ (((z / u) * y) * u))
    ]]></literal>
    <justification jstring="[hyper(19806,a,21437,a)].">
      <j1 rule="hyper" parents="19806 21437"/>
    </justification>
  </clause>

  <clause id="21439">
    <literal><![CDATA[
      K(x,(y * z) / (y * (u \ z))) = K(x,z \ (((z / y) * u) * y))
    ]]></literal>
    <justification jstring="[hyper(11914,a,21438,a)].">
      <j1 rule="hyper" parents="11914 21438"/>
    </justification>
  </clause>

  <clause id="21440">
    <literal><![CDATA[
      x \ L(K(y,z) * (K(y,z) \ x),u,K(w,v5)) = a(v5,u,K(w,x \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(20863,a,21418,a),flip(a)].">
      <j1 rule="hyper" parents="20863 21418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21441">
    <literal><![CDATA[
      x \ L(K(y,z) * (K(y,z) \ x),u,K(w,v5)) = a(v5,u,K(w,x * K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(299,a,15012,a(flip),b,21440,a),flip(a)].">
      <j1 rule="hyper" parents="299 15012 21440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21442">
    <literal><![CDATA[
      a(x,y,K(z,u * K(w,v5))) = u \ L(u,y,K(z,x))
    ]]></literal>
    <justification jstring="[para(10(a,1),21441(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 21441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21443">
    <literal><![CDATA[
      a(x,y,K(z,u * K(w,v5))) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,20834,a(flip),b,21442,a),flip(a)].">
      <j1 rule="hyper" parents="299 20834 21442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21444">
    <literal><![CDATA[
      a(K(x,y) * z,u,K(w,v5)) = a(v5,u,K(w,z))
    ]]></literal>
    <justification jstring="[hyper(16568,a,21443,a)].">
      <j1 rule="hyper" parents="16568 21443"/>
    </justification>
  </clause>

  <clause id="21445">
    <literal><![CDATA[
      a(x,y,K(z,u * T(w,v5))) = a(u * w,y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,19398,a(flip),b,21444,a),flip(a)].">
      <j1 rule="hyper" parents="65 19398 21444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21447">
    <literal><![CDATA[
      T(x,T(y,z)) \ (K(x,L(x \ z,u,w)) * (K(x \ z,x) * T(x,T(y,z)))) = T((x \ z) \ z,y) \ T(T(x,y),L(x \ z,u,w))
    ]]></literal>
    <justification jstring="[para(5426(a,1),21373(a,1,2,2))].">
      <j1 rule="para" parents="5426 21373"/>
    </justification>
  </clause>

  <clause id="21448">
    <literal><![CDATA[
      T(x,T(y,z)) \ (K(x,L(x \ z,u,w)) * T(z / (z / x),y)) = T((x \ z) \ z,y) \ T(T(x,y),L(x \ z,u,w))
    ]]></literal>
    <justification jstring="[para(9168(a,1),21447(a,1,2,2))].">
      <j1 rule="para" parents="9168 21447"/>
    </justification>
  </clause>

  <clause id="21449">
    <literal><![CDATA[
      K(x,L(x \ y,z,u)) * (T(x,T(w,y)) \ T(y / (y / x),w)) = T((x \ y) \ y,w) \ T(T(x,w),L(x \ y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,10107,a(flip),b,21448,a)].">
      <j1 rule="hyper" parents="65 10107 21448"/>
    </justification>
  </clause>

  <clause id="21450">
    <literal><![CDATA[
      T((x \ y) \ y,z) \ T(T(x,z),L(x \ y,u,w)) = K(x,L(x \ y,u,w)) * K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(9169(a,1),21449(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9169 21449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21451">
    <literal><![CDATA[
      T((x \ y) \ y,z) \ T(T(x,z),L(x \ y,u,w)) = a(x,u,K(w,x \ y))
    ]]></literal>
    <justification jstring="[hyper(299,a,14868,a(flip),b,21450,a),flip(a)].">
      <j1 rule="hyper" parents="299 14868 21450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21453">
    <literal><![CDATA[
      T((x \ y) \ y,z) \ T(T(x,z),L(x \ y,u,w)) = a(x,u,K(w,x * y))
    ]]></literal>
    <justification jstring="[hyper(299,a,15012,a(flip),b,21451,a),flip(a)].">
      <j1 rule="hyper" parents="299 15012 21451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21454">
    <literal><![CDATA[
      K(x,((y * T(z,u \ w)) \ (v5 * ((y * T(z,u \ w)) \ 1))) * (y * T(z,u * w))) = K(x,(y * T(z,u * w)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(299,a,13712,a(flip),b,19744,a),flip(a)].">
      <j1 rule="hyper" parents="299 13712 19744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21455">
    <literal><![CDATA[
      K(x,(((y * T(z,u \ w)) \ v5) * ((y * T(z,u \ w)) \ 1)) * (y * T(z,u * w))) = K(x,(y * T(z,u * w)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,13860,a(flip),b,21454,a)].">
      <j1 rule="hyper" parents="65 13860 21454"/>
    </justification>
  </clause>

  <clause id="21456">
    <literal><![CDATA[
      K(x,(y * T(z,u \ w)) \ v5) = K(x,(y * T(z,u * w)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,18393,a(flip),b,21455,a)].">
      <j1 rule="hyper" parents="65 18393 21455"/>
    </justification>
  </clause>

  <clause id="21458">
    <literal><![CDATA[
      K(x,(T(y \ 1,z * y) * T(u,T(y,z) * u)) \ w) = K(x,(u * T(y \ 1,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,20768,a(flip),b,21456,a),flip(a)].">
      <j1 rule="hyper" parents="65 20768 21456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21459">
    <literal><![CDATA[
      K(x,((1 / y) * T(y \ ((y \ 1) \ z),u * w)) \ v5) = K(x,(y \ T(z,u \ w)) \ v5)
    ]]></literal>
    <justification jstring="[para(14727(a,1),21456(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14727 21456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21460">
    <literal><![CDATA[
      K(x,(T(y \ 1,z * y) * T(u,T(y,z))) \ w) = K(x,(u * T(y \ 1,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,20501,a(flip),b,21458,a)].">
      <j1 rule="hyper" parents="65 20501 21458"/>
    </justification>
  </clause>

  <clause id="21461">
    <literal><![CDATA[
      K(x,(T(y \ 1,z * y) * T(u,y)) \ w) = K(x,(u * T(y \ 1,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(20262,a,21460,a)].">
      <j1 rule="hyper" parents="20262 21460"/>
    </justification>
  </clause>

  <clause id="21463">
    <literal><![CDATA[
      K(x,(T(y \ 1,z) * T(u,y)) \ w) = K(x,(u * T(y \ 1,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,20397,a(flip),b,21461,a)].">
      <j1 rule="hyper" parents="65 20397 21461"/>
    </justification>
  </clause>

  <clause id="21464">
    <literal><![CDATA[
      K(x,(((y * y) \ z) * T(y,u)) \ w) = K(x,(z * T(y \ 1,u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,20572,a(flip),b,21463,a)].">
      <j1 rule="hyper" parents="65 20572 21463"/>
    </justification>
  </clause>

  <clause id="21465">
    <literal><![CDATA[
      K(x,(y * T(z,u)) \ ((z * z) * w)) = K(x,(y * T(z \ 1,u)) \ w)
    ]]></literal>
    <justification jstring="[para(767(a,1),21464(a,1,2))].">
      <j1 rule="para" parents="767 21464"/>
    </justification>
  </clause>

  <clause id="21466">
    <literal><![CDATA[
      K(x,y * (y * ((z * T(y,u)) \ w))) = K(x,(z * T(y \ 1,u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,20294,a(flip),b,21465,a)].">
      <j1 rule="hyper" parents="65 20294 21465"/>
    </justification>
  </clause>

  <clause id="21467">
    <literal><![CDATA[
      K(x,(y * (((z * u) / z) \ 1)) \ w) = K(x,(y * T(u \ 1,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,20795,a,b,21466,a)].">
      <j1 rule="hyper" parents="65 20795 21466"/>
    </justification>
  </clause>

  <clause id="21468">
    <literal><![CDATA[
      K(x,(T(y,z) \ u) / (((z / y) \ 1) / y)) = K(x,(y * T(u \ 1,y)) \ z)
    ]]></literal>
    <justification jstring="[hyper(20662,a,21467,a)].">
      <j1 rule="hyper" parents="20662 21467"/>
    </justification>
  </clause>

  <clause id="21469">
    <literal><![CDATA[
      K(x,(y * T(z \ 1,u)) \ w) = K(x,(y * (T(z,u) \ 1)) \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,21207,a(flip),b,21467,a),flip(a)].">
      <j1 rule="hyper" parents="65 21207 21467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21470">
    <literal><![CDATA[
      K(x,((T(y \ 1,z) \ L(T(y \ 1,z),u,w)) * (T(y,z) \ 1)) \ v5) = K(x,L(T(y \ 1,z),u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(3815(a,1),21469(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3815 21469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21471">
    <literal><![CDATA[
      K(x,(T(y,z) \ u) / (((z / y) \ 1) / y)) = K(x,((u \ 1) * y) \ z)
    ]]></literal>
    <justification jstring="[para(107(a,1),21468(a,2,2,1))].">
      <j1 rule="para" parents="107 21468"/>
    </justification>
  </clause>

  <clause id="21472">
    <literal><![CDATA[
      K(x,(y \ T(z,u \ w)) \ v5) = K(x,(y \ T(z,u * w)) \ v5)
    ]]></literal>
    <justification jstring="[para(14727(a,1),21459(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14727 21459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21473">
    <literal><![CDATA[
      K(x,(L(y,y,K(y,z) * u) \ T(z,y * 1)) \ u) = K(x,(z * (y \ 1)) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,21359,a(flip),b,21472,a),flip(a)].">
      <j1 rule="hyper" parents="65 21359 21472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21474">
    <literal><![CDATA[
      K(x,(L(y,y,K(y,z) * u) \ T(z,y)) \ u) = K(x,(z * (y \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(8(a,1),21473(a,1,2,1,2,2))].">
      <j1 rule="para" parents="8 21473"/>
    </justification>
  </clause>

  <clause id="21475">
    <literal><![CDATA[
      K(x,(y / L(z,z,K(z,y) * u)) \ u) = K(x,(y * (z \ 1)) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,20215,a(flip),b,21474,a)].">
      <j1 rule="hyper" parents="65 20215 21474"/>
    </justification>
  </clause>

  <clause id="21476">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ u) = K(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,21298,a(flip),b,21475,a),flip(a)].">
      <j1 rule="hyper" parents="65 21298 21475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21477">
    <literal><![CDATA[
      K(x,(T((y \ 1) \ L(y \ 1,z,u),w) * (T(y,w) \ 1)) \ v5) = K(x,L(T(y \ 1,w),z,u) \ v5)
    ]]></literal>
    <justification jstring="[para(6731(a,1),21470(a,1,2,1,1))].">
      <j1 rule="para" parents="6731 21470"/>
    </justification>
  </clause>

  <clause id="21478">
    <literal><![CDATA[
      K(x,(T(y \ L(y,z,u),w) * (T(y,w) \ 1)) \ v5) = K(x,L(T(y \ 1,w),z,u) \ v5)
    ]]></literal>
    <justification jstring="[para(6503(a,1),21477(a,1,2,1,1,1))].">
      <j1 rule="para" parents="6503 21477"/>
    </justification>
  </clause>

  <clause id="21479">
    <literal><![CDATA[
      K(x,L(T(y \ 1,z),u,w) \ v5) = K(x,L(T(y,z) \ 1,u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(6735(a,1),21478(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6735 21478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21480">
    <literal><![CDATA[
      K(x,L(T(y \ 1,z),u,u) \ w) = K(x,L(T(y,z),u,u) * w)
    ]]></literal>
    <justification jstring="[hyper(299,a,21235,a(flip),b,21479,a),flip(a)].">
      <j1 rule="hyper" parents="299 21235 21479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21481">
    <literal><![CDATA[
      K(x,L(T(y,z),u,u) * (y \ (y \ z))) = K(x,z / L(y,u,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,20754,a(flip),b,21480,a),flip(a)].">
      <j1 rule="hyper" parents="65 20754 21480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21482">
    <literal><![CDATA[
      K(x,T(y,z) * L(y \ (y \ z),u,u)) = K(x,z / L(y,u,u))
    ]]></literal>
    <justification jstring="[hyper(21256,a,21481,a)].">
      <j1 rule="hyper" parents="21256 21481"/>
    </justification>
  </clause>

  <clause id="21483">
    <literal><![CDATA[
      K(x,a((y \ z) \ z,u,u) * (z / y)) = K(x,z / L(y,u,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,21324,a(flip),b,21482,a)].">
      <j1 rule="hyper" parents="65 21324 21482"/>
    </justification>
  </clause>

  <clause id="21484">
    <literal><![CDATA[
      K(x,y / L(z,u,u)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(65,a,21167,a(flip),b,21483,a),flip(a)].">
      <j1 rule="hyper" parents="65 21167 21483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21486">
    <literal><![CDATA[
      K(x,y / (L(1 / z,u,z) * w)) = K(x,y / (z \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,21366,a(flip),b,21484,a),flip(a)].">
      <j1 rule="hyper" parents="65 21366 21484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21488">
    <literal><![CDATA[
      K(x,y / ((z \ 1) * u)) = K(x,y / (z \ u))
    ]]></literal>
    <justification jstring="[para(921(a,1),21486(a,1,2,2,1))].">
      <j1 rule="para" parents="921 21486"/>
    </justification>
  </clause>

  <clause id="21491">
    <literal><![CDATA[
      L(x / L(T(y,y \ 1),y * z,y),L(y,y * z,y),L(y,y * z,y)) = L(x,L(y,y * z,y),L(y,y * z,y)) / (z / (T(z,y) / y))
    ]]></literal>
    <justification jstring="[para(11377(a,1),19770(a,1,1,2))].">
      <j1 rule="para" parents="11377 19770"/>
    </justification>
  </clause>

  <clause id="21498">
    <literal><![CDATA[
      L(x / R(T(y,y * 1),z,y),L(y,y * z,y),L(y,y * z,y)) = L(x,L(y,y * z,y),L(y,y * z,y)) / (z / (T(z,y) / y))
    ]]></literal>
    <justification jstring="[para(18214(a,1),21491(a,1,1,2))].">
      <j1 rule="para" parents="18214 21491"/>
    </justification>
  </clause>

  <clause id="21501">
    <literal><![CDATA[
      L(x / R(T(y,y),z,y),L(y,y * z,y),L(y,y * z,y)) = L(x,L(y,y * z,y),L(y,y * z,y)) / (z / (T(z,y) / y))
    ]]></literal>
    <justification jstring="[para(8(a,1),21498(a,1,1,2,1,2))].">
      <j1 rule="para" parents="8 21498"/>
    </justification>
  </clause>

  <clause id="21506">
    <literal><![CDATA[
      L(x,L(y,y * z,y),L(y,y * z,y)) / (z / (T(z,y) / y)) = L(x / R(y,z,y),L(y,y * z,y),L(y,y * z,y))
    ]]></literal>
    <justification jstring="[para(106(a,1),21501(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="106 21501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21511">
    <literal><![CDATA[
      L(x,L(y,y * z,y),L(y,y * z,y)) / (z / (T(z,y) / y)) = L(x / R(y,z,y),y,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,17039,a(flip),b,21506,a),flip(a)].">
      <j1 rule="hyper" parents="299 17039 21506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21517">
    <literal><![CDATA[
      L(x,y,y) / (z / (T(z,y) / y)) = L(x / R(y,z,y),y,y)
    ]]></literal>
    <justification jstring="[para(17039(a,1),21511(a,1,1))].">
      <j1 rule="para" parents="17039 21511"/>
    </justification>
  </clause>

  <clause id="21519">
    <literal><![CDATA[
      K(x,T((y / (T(y,z) / z)) \ L(u,z,z),L(u,z,z)) * w) = K(x,L(u / R(z,y,z),z,z) * w)
    ]]></literal>
    <justification jstring="[para(21517(a,1),19080(a,2,2,1))].">
      <j1 rule="para" parents="21517 19080"/>
    </justification>
  </clause>

  <clause id="21520">
    <literal><![CDATA[
      K(x,T(L(1 / y,z,y) * u,L(u,y,y)) * w) = K(x,L(u / R(y,z,y),y,y) * w)
    ]]></literal>
    <justification jstring="[para(17710(a,1),21519(a,1,2,1,1))].">
      <j1 rule="para" parents="17710 21519"/>
    </justification>
  </clause>

  <clause id="21521">
    <literal><![CDATA[
      K(x,T(L(1 / y,z,y) * u,u) * w) = K(x,L(u / R(y,z,y),y,y) * w)
    ]]></literal>
    <justification jstring="[para(14206(a,1),21520(a,1,2,1))].">
      <j1 rule="para" parents="14206 21520"/>
    </justification>
  </clause>

  <clause id="21522">
    <literal><![CDATA[
      K(x,L(y / R(z,u,z),z,z) * w) = K(x,(y * L(1 / z,u,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(65,a,16003,a(flip),b,21521,a),flip(a)].">
      <j1 rule="hyper" parents="65 16003 21521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21524">
    <literal><![CDATA[
      K(x,L(y / R(z,u,z),z,z) * w) = K(x,(y * L(z \ 1,u,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(299,a,13846,a(flip),b,21522,a),flip(a)].">
      <j1 rule="hyper" parents="299 13846 21522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21525">
    <literal><![CDATA[
      K(x,L(y / R(z,u,z),z,z) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * (z \ 1)) * w) = v5
    ]]></literal>
    <justification jstring="[para(21524(a,2),15086(a,1))].">
      <j1 rule="para" parents="21524 15086"/>
    </justification>
  </clause>

  <clause id="21526">
    <literal><![CDATA[
      K(x,(y / R(z,u,z)) * L(w,z,z)) = K(x,(y * (z \ 1)) * w)
    ]]></literal>
    <justification jstring="[hyper(21525,a,21250,a),flip(a)].">
      <j1 rule="hyper" parents="21525 21250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21527">
    <literal><![CDATA[
      K(x,(y / z) * L(u,z,z)) = K(x,(y * (z \ 1)) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,13997,a(flip),b,21526,a)].">
      <j1 rule="hyper" parents="65 13997 21526"/>
    </justification>
  </clause>

  <clause id="21528">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) * (u / (z \ 1))) = K(x,(y / z) * (u * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,19162,a(flip),b,21527,a),flip(a)].">
      <j1 rule="hyper" parents="65 19162 21527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21529">
    <literal><![CDATA[
      K(x,(y / z) * (u * z)) = K(x,(y * z) * (u / z))
    ]]></literal>
    <justification jstring="[hyper(65,a,19337,a(flip),b,21528,a),flip(a)].">
      <j1 rule="hyper" parents="65 19337 21528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21530">
    <literal><![CDATA[
      K(x,(y * (z \ y)) * (u / (z \ y))) = K(x,z * (u * (z \ y)))
    ]]></literal>
    <justification jstring="[para(76(a,1),21529(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="76 21529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21531">
    <literal><![CDATA[
      K(x,(y * L(y,z,z)) * (u / (a(z,z,y) \ y))) = K(x,a(z,z,y) * (u * (a(z,z,y) \ y)))
    ]]></literal>
    <justification jstring="[para(6374(a,1),21530(a,1,2,1,2))].">
      <j1 rule="para" parents="6374 21530"/>
    </justification>
  </clause>

  <clause id="21532">
    <literal><![CDATA[
      K(x,(y * L(y,z,z)) * (u / L(y,z,z))) = K(x,a(z,z,y) * (u * (a(z,z,y) \ y)))
    ]]></literal>
    <justification jstring="[para(6374(a,1),21531(a,1,2,2,2))].">
      <j1 rule="para" parents="6374 21531"/>
    </justification>
  </clause>

  <clause id="21533">
    <literal><![CDATA[
      K(x,(((y * z) / y) * (u * (z * K(y,z)))) \ ((u * (z * K(y,z))) * w)) = K(x,T(u,T(z,y)) \ ((((y * z) / y) \ T(u,T(z,y))) * w))
    ]]></literal>
    <justification jstring="[para(10209(a,1),20445(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="10209 20445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21534">
    <literal><![CDATA[
      K(x,(((y * z) / y) * (u * (z * K(y,z)))) \ ((u * (z * K(y,z))) * w)) = K(x,u \ ((((y * z) / y) \ u) * w))
    ]]></literal>
    <justification jstring="[hyper(299,a,20761,a(flip),b,21533,a),flip(a)].">
      <j1 rule="hyper" parents="299 20761 21533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21536">
    <literal><![CDATA[
      K(x,(((y * z) / y) * (u * (z * K(y,z)))) \ ((u * T(z,y)) * w)) = K(x,u \ ((((y * z) / y) \ u) * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,20536,a(flip),b,21534,a)].">
      <j1 rule="hyper" parents="65 20536 21534"/>
    </justification>
  </clause>

  <clause id="21537">
    <literal><![CDATA[
      K(x,(((y * z) / y) * (u * T(z,y))) \ ((u * T(z,y)) * w)) = K(x,u \ ((((y * z) / y) \ u) * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,20664,a(flip),b,21536,a)].">
      <j1 rule="hyper" parents="65 20664 21536"/>
    </justification>
  </clause>

  <clause id="21538">
    <literal><![CDATA[
      K(x,(T(y,z) * (u * T(y,z))) \ ((u * T(y,z)) * w)) = K(x,u \ ((((z * y) / z) \ u) * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,20268,a(flip),b,21537,a)].">
      <j1 rule="hyper" parents="65 20268 21537"/>
    </justification>
  </clause>

  <clause id="21539">
    <literal><![CDATA[
      K(x,y \ ((((z * u) / z) \ y) * w)) = K(x,y \ ((T(u,z) \ y) * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,20623,a(flip),b,21538,a),flip(a)].">
      <j1 rule="hyper" parents="65 20623 21538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21540">
    <literal><![CDATA[
      K(T(K(x,y) * z,u) * T(w,K(z,u) * z),T(v5,w * (z * K(z * K(y,x),u)))) = K((w * (z * K(z * K(y,x),u))) * R(K(x,y),z * K(z * K(y,x),u),w),v5)
    ]]></literal>
    <justification jstring="[para(17595(a,1),17824(a,1,1,2))].">
      <j1 rule="para" parents="17595 17824"/>
    </justification>
  </clause>

  <clause id="21541">
    <literal><![CDATA[
      K(T(K(x,y) * z,u) * T(w,T(z,u)),T(v5,w * (z * K(z * K(y,x),u)))) = K((w * (z * K(z * K(y,x),u))) * R(K(x,y),z * K(z * K(y,x),u),w),v5)
    ]]></literal>
    <justification jstring="[para(5096(a,2),21540(a,1,1,2,2))].">
      <j1 rule="para" parents="5096 21540"/>
    </justification>
  </clause>

  <clause id="21543">
    <literal><![CDATA[
      K((x * (y * K(y * K(z,u),w))) * R(K(u,z),y * K(y * K(z,u),w),x),v5) = K(T(K(u,z) * y,w) * T(x,T(y,w)),T(v5,x * y))
    ]]></literal>
    <justification jstring="[hyper(19098,a,21541,a),flip(a)].">
      <j1 rule="hyper" parents="19098 21541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21544">
    <literal><![CDATA[
      K((x * (y * K(y * K(z,u),w))) * R(K(u,z),y * K(y * K(z,u),w),x),v5) = K(T(K(u,z) * y,w) * T(x,y),T(v5,x * y))
    ]]></literal>
    <justification jstring="[hyper(299,a,16787,a(flip),b,21543,a),flip(a)].">
      <j1 rule="hyper" parents="299 16787 21543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21546">
    <literal><![CDATA[
      K((x * (y * K(y * K(z,u),w))) * R(K(u,z),y * K(y * K(z,u),w),x),v5) = K(K(u,z) * (T(y,w) * T(x,y)),T(v5,x * y))
    ]]></literal>
    <justification jstring="[hyper(299,a,19024,a(flip),b,21544,a),flip(a)].">
      <j1 rule="hyper" parents="299 19024 21544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21547">
    <literal><![CDATA[
      K((x * (y * K(y * K(z,u),w))) * R(K(u,z),y * K(y * K(z,u),w),x),v5) = K(K(u,z) * (K(y,w) * (x * y)),T(v5,x * y))
    ]]></literal>
    <justification jstring="[para(5353(a,2),21546(a,2,1,2))].">
      <j1 rule="para" parents="5353 21546"/>
    </justification>
  </clause>

  <clause id="21548">
    <literal><![CDATA[
      K((x * (y * K(y * K(z,u),w))) * R(K(u,z),y * K(y * K(z,u),w),x),v5) = K(K(y,w) * ((x * y) * K(u,z)),v5)
    ]]></literal>
    <justification jstring="[hyper(299,a,19029,a(flip),b,21547,a),flip(a)].">
      <j1 rule="hyper" parents="299 19029 21547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21549">
    <literal><![CDATA[
      K((x * (y * K(y * K(z,u),w))) * R(K(u,z),y * K(y * K(z,u),w),x),v5) = K((x * T(y,w)) * K(u,z),v5)
    ]]></literal>
    <justification jstring="[hyper(299,a,19013,a(flip),b,21548,a),flip(a)].">
      <j1 rule="hyper" parents="299 19013 21548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21550">
    <literal><![CDATA[
      K((x * (y * K(y * K(z,u),w))) * R(K(u,z),y * K(y * K(z,u),w),x),v5) = K(x * (T(y,w) * K(z,u)),v5)
    ]]></literal>
    <justification jstring="[hyper(299,a,19000,a(flip),b,21549,a),flip(a)].">
      <j1 rule="hyper" parents="299 19000 21549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21551">
    <literal><![CDATA[
      K(x * ((y * K(y * K(z,u),w)) * K(u,z)),v5) = K(x * (T(y,w) * K(z,u)),v5)
    ]]></literal>
    <justification jstring="[hyper(20717,a,21550,a)].">
      <j1 rule="hyper" parents="20717 21550"/>
    </justification>
  </clause>

  <clause id="21552">
    <literal><![CDATA[
      K(x * (y * (K(z,u) * K(y * K(u,z),w))),v5) = K(x * (T(y,w) * K(u,z)),v5)
    ]]></literal>
    <justification jstring="[para(20071(a,1),21551(a,1,1,2))].">
      <j1 rule="para" parents="20071 21551"/>
    </justification>
  </clause>

  <clause id="21553">
    <literal><![CDATA[
      K(x * T(y * K(z,u),w),v5) = K(x * (T(y,w) * K(u,z)),v5)
    ]]></literal>
    <justification jstring="[para(17783(a,1),21552(a,1,1,2))].">
      <j1 rule="para" parents="17783 21552"/>
    </justification>
  </clause>

  <clause id="21554">
    <literal><![CDATA[
      K(x * T(y * K(z,u),w),T(v5,y)) = K(K(u,z) * (T(y,w) * x),v5)
    ]]></literal>
    <justification jstring="[hyper(19030,a,21553,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="19030 21553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21555">
    <literal><![CDATA[
      K(K(x,y) * (T(y,z) * u),w) = K(u * T(T(y,x),z),T(w,y))
    ]]></literal>
    <justification jstring="[para(5083(a,2),21554(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5083 21554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21556">
    <literal><![CDATA[
      K(K(x,y) * (T(y,z) * u),w) = K(T(T(y,x),z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(299,a,16586,a(flip),b,21555,a),flip(a)].">
      <j1 rule="hyper" parents="299 16586 21555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21557">
    <literal><![CDATA[
      a(x,y,K(T(T(z,u * w),v5) * w,u)) = a(x,y,K(u,w * T(z,v5)))
    ]]></literal>
    <justification jstring="[para(21556(a,1),19625(a,1,3))].">
      <j1 rule="para" parents="21556 19625"/>
    </justification>
  </clause>

  <clause id="21558">
    <literal><![CDATA[
      a(x,y,K(T(z,u * w) * T(w,v5),u)) = a(x,y,K(u,w * T(z,v5)))
    ]]></literal>
    <justification jstring="[hyper(65,a,20641,a(flip),b,21557,a)].">
      <j1 rule="hyper" parents="65 20641 21557"/>
    </justification>
  </clause>

  <clause id="21559">
    <literal><![CDATA[
      a(x,y,K(z * T(T(u,w),v5 * u),v5)) = a(x,y,K(v5,u * T(z,w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,20641,a(flip),b,21558,a)].">
      <j1 rule="hyper" parents="65 20641 21558"/>
    </justification>
  </clause>

  <clause id="21560">
    <literal><![CDATA[
      a(x,y,K(z * T(T(u,w),v5),v5)) = a(x,y,K(v5,u * T(z,w)))
    ]]></literal>
    <justification jstring="[para(17826(a,1),21559(a,1,3))].">
      <j1 rule="para" parents="17826 21559"/>
    </justification>
  </clause>

  <clause id="21561">
    <literal><![CDATA[
      a(x,y,K(z * T(u,w),v5)) = a(x,y,K(v5,u * T(z,w)))
    ]]></literal>
    <justification jstring="[para(8580(a,1),21560(a,1,3))].">
      <j1 rule="para" parents="8580 21560"/>
    </justification>
  </clause>

  <clause id="21562">
    <literal><![CDATA[
      a(x,y,K(z * T(u,w),v5)) = a(u * z,y,K(v5,x))
    ]]></literal>
    <justification jstring="[hyper(299,a,21445,a(flip),b,21561,a),flip(a)].">
      <j1 rule="hyper" parents="299 21445 21561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21564">
    <literal><![CDATA[
      a(x,y,K(T(z,u) * w,v5)) = a(w * z,y,K(v5,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,20641,a,b,21562,a)].">
      <j1 rule="hyper" parents="65 20641 21562"/>
    </justification>
  </clause>

  <clause id="21565">
    <literal><![CDATA[
      K(x,L(y,z,u \ T(w,v5))) = K(x,y) * a(w * u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(21562(a,1),19574(a,1,2)),flip(a)].">
      <j1 rule="para" parents="21562 19574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21566">
    <literal><![CDATA[
      a(T(x,y) * z,u,K(w,v5)) = a(z * x,u,K(v5,w))
    ]]></literal>
    <justification jstring="[hyper(14958,a,21564,a)].">
      <j1 rule="hyper" parents="14958 21564"/>
    </justification>
  </clause>

  <clause id="21568">
    <literal><![CDATA[
      a(x * y,y,K(z,u)) = a(z,x,K(T(y,w) \ x,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,21084,a(flip),b,21566,a),flip(a)].">
      <j1 rule="hyper" parents="65 21084 21566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21569">
    <literal><![CDATA[
      a(x * y,y,K(z,u)) = a(z,x,K(T(y,w) * x,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,19587,a(flip),b,21568,a),flip(a)].">
      <j1 rule="hyper" parents="299 19587 21568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21571">
    <literal><![CDATA[
      a(x * y,y,K(z,u)) = a(x * y,x,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,21564,a(flip),b,21569,a),flip(a)].">
      <j1 rule="hyper" parents="299 21564 21569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21572">
    <literal><![CDATA[
      a(x * y,x,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(z,y,K(u,y * x)) = w
    ]]></literal>
    <justification jstring="[para(21571(a,1),19549(a,1))].">
      <j1 rule="para" parents="21571 19549"/>
    </justification>
  </clause>

  <clause id="21573">
    <literal><![CDATA[
      K(x,L(y,z,u \ T(w,v5))) = K(x,L(y,z,w * u))
    ]]></literal>
    <justification jstring="[hyper(299,a,14962,a(flip),b,21565,a),flip(a)].">
      <j1 rule="hyper" parents="299 14962 21565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21574">
    <literal><![CDATA[
      K(x,L(y,z,u * T(w,v5))) = K(x,L(y,z,w * u))
    ]]></literal>
    <justification jstring="[hyper(19573,a,21573,a)].">
      <j1 rule="hyper" parents="19573 21573"/>
    </justification>
  </clause>

  <clause id="21575">
    <literal><![CDATA[
      K(x,L(((y \ ((z * u) / z)) \ ((z * u) / z)) \ w,y,u * y)) = K(x,T(u,z) \ ((y \ ((z * u) / z)) * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,19698,a(flip),b,21573,a),flip(a)].">
      <j1 rule="hyper" parents="65 19698 21573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21576">
    <literal><![CDATA[
      K(x,L(y,z,T(u,w) * v5)) = K(x,L(y,z,u * v5))
    ]]></literal>
    <justification jstring="[hyper(20909,a,21574,a)].">
      <j1 rule="hyper" parents="20909 21574"/>
    </justification>
  </clause>

  <clause id="21577">
    <literal><![CDATA[
      K(x,L((y * (z / y)) / u,w,z * w)) = K(x,w / (u * ((y * (z / y)) \ w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,19583,a(flip),b,21576,a),flip(a)].">
      <j1 rule="hyper" parents="65 19583 21576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21579">
    <literal><![CDATA[
      K(x,L(T(y / z,z),u,y * u)) = K(x,u / (z * ((z * (y / z)) \ u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,8380,a(flip),b,21577,a)].">
      <j1 rule="hyper" parents="65 8380 21577"/>
    </justification>
  </clause>

  <clause id="21580">
    <literal><![CDATA[
      K(x,L(y \ z,u,z * u)) = K(x,u / (y * ((y * (z / y)) \ u)))
    ]]></literal>
    <justification jstring="[para(109(a,1),21579(a,1,2,1))].">
      <j1 rule="para" parents="109 21579"/>
    </justification>
  </clause>

  <clause id="21581">
    <literal><![CDATA[
      K(x,L(T(y / z,z),u,z * u)) = K(x,L(z \ y,u,y * u))
    ]]></literal>
    <justification jstring="[hyper(299,a,19632,a(flip),b,21580,a)].">
      <j1 rule="hyper" parents="299 19632 21580"/>
    </justification>
  </clause>

  <clause id="21582">
    <literal><![CDATA[
      K(x,L(y \ z,u,z * u)) = K(x,L(y \ z,u,y * u))
    ]]></literal>
    <justification jstring="[para(109(a,1),21581(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="109 21581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21583">
    <literal><![CDATA[
      K(x,L(T(y,(z * u) / z) \ w,y,u * y)) = K(x,T(u,z) \ ((y \ ((z * u) / z)) * w))
    ]]></literal>
    <justification jstring="[hyper(14067,a,21575,a)].">
      <j1 rule="hyper" parents="14067 21575"/>
    </justification>
  </clause>

  <clause id="21585">
    <literal><![CDATA[
      K(x,L(T(y,T(z,u)) \ w,y,z * y)) = K(x,T(z,u) \ ((y \ ((u * z) / u)) * w))
    ]]></literal>
    <justification jstring="[para(8182(a,1),21583(a,1,2,1,1))].">
      <j1 rule="para" parents="8182 21583"/>
    </justification>
  </clause>

  <clause id="21586">
    <literal><![CDATA[
      K(x,L(T(y,z) \ u,y,z * y)) = K(x,T(z,w) \ ((y \ ((w * z) / w)) * u))
    ]]></literal>
    <justification jstring="[hyper(16951,a,21585,a)].">
      <j1 rule="hyper" parents="16951 21585"/>
    </justification>
  </clause>

  <clause id="21587">
    <literal><![CDATA[
      K(x,L(T(y,z) \ u,y,z * y)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(299,a,20426,a(flip),b,21586,a),flip(a)].">
      <j1 rule="hyper" parents="299 20426 21586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21588">
    <literal><![CDATA[
      K(x,L(T(y,z) \ u,y \ (z * y),z * y)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,19608,a,b,21587,a)].">
      <j1 rule="hyper" parents="65 19608 21587"/>
    </justification>
  </clause>

  <clause id="21589">
    <literal><![CDATA[
      K(x,L(T(y,z) \ u,T(z,y),z * y)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[para(22(a,2),21588(a,1,2,2))].">
      <j1 rule="para" parents="22 21588"/>
    </justification>
  </clause>

  <clause id="21590">
    <literal><![CDATA[
      K(x,y \ ((y \ z) \ u)) = K(x,y \ ((z \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,20504,a(flip),b,21589,a)].">
      <j1 rule="hyper" parents="65 20504 21589"/>
    </justification>
  </clause>

  <clause id="21591">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,z,z * y)) = K(x,z \ (((y \ 1) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,21088,a,b,21590,a)].">
      <j1 rule="hyper" parents="65 21088 21590"/>
    </justification>
  </clause>

  <clause id="21592">
    <literal><![CDATA[
      K(x,y \ ((((y * z) / y) \ y) * u)) = K(x,y \ ((z / y) \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,21176,a(flip),b,21590,a),flip(a)].">
      <j1 rule="hyper" parents="65 21176 21590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21593">
    <literal><![CDATA[
      K(x,y \ (((y * z) \ y) * u)) = K(x,y \ (z \ u))
    ]]></literal>
    <justification jstring="[para(9(a,1),21590(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="9 21590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21594">
    <literal><![CDATA[
      K(x,y \ ((T(z,y) \ y) * u)) = K(x,y \ ((z / y) \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,21539,a(flip),b,21592,a)].">
      <j1 rule="hyper" parents="65 21539 21592"/>
    </justification>
  </clause>

  <clause id="21595">
    <literal><![CDATA[
      K(x,y \ ((z / y) \ u)) = K(x,y \ ((y / z) * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,20810,a(flip),b,21594,a),flip(a)].">
      <j1 rule="hyper" parents="65 20810 21594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21596">
    <literal><![CDATA[
      K(x,L(y \ z,u,y * u)) = K(x,u \ ((u / y) * z))
    ]]></literal>
    <justification jstring="[hyper(20925,a,21595,a)].">
      <j1 rule="hyper" parents="20925 21595"/>
    </justification>
  </clause>

  <clause id="21597">
    <literal><![CDATA[
      K(x,L(y \ z,u,z * u)) = K(x,u \ ((u / y) * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,21582,a,b,21596,a)].">
      <j1 rule="hyper" parents="65 21582 21596"/>
    </justification>
  </clause>

  <clause id="21598">
    <literal><![CDATA[
      K(x,L(y \ z,u,u * z)) = K(x,u \ ((u / y) * z))
    ]]></literal>
    <justification jstring="[hyper(20909,a,21597,a)].">
      <j1 rule="hyper" parents="20909 21597"/>
    </justification>
  </clause>

  <clause id="21599">
    <literal><![CDATA[
      K(x,y \ ((y / (z \ 1)) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(z * u,y,u * y)) = w
    ]]></literal>
    <justification jstring="[para(21597(a,1),14643(a,1))].">
      <j1 rule="para" parents="21597 14643"/>
    </justification>
  </clause>

  <clause id="21600">
    <literal><![CDATA[
      K(x,((y / z) \ u) \ z) = K(x,z \ ((z / u) * y))
    ]]></literal>
    <justification jstring="[hyper(65,a,19585,a(flip),b,21598,a)].">
      <j1 rule="hyper" parents="65 19585 21598"/>
    </justification>
  </clause>

  <clause id="21601">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,z,y * z)) = K(x,z \ (((y \ 1) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(20909,a,21591,a)].">
      <j1 rule="hyper" parents="20909 21591"/>
    </justification>
  </clause>

  <clause id="21602">
    <literal><![CDATA[
      K(x,L(T(y * z,z \ 1) * u,z \ 1,R(y,z,z))) = K(x,(z \ 1) \ ((((y * z) \ 1) \ (z \ 1)) * u))
    ]]></literal>
    <justification jstring="[para(1246(a,1),21601(a,1,2,3))].">
      <j1 rule="para" parents="1246 21601"/>
    </justification>
  </clause>

  <clause id="21603">
    <literal><![CDATA[
      K(x,L(T(y * z,z \ 1) * u,z \ 1,L(y,z,z))) = K(x,(z \ 1) \ ((((y * z) \ 1) \ (z \ 1)) * u))
    ]]></literal>
    <justification jstring="[para(17310(a,1),21602(a,1,2))].">
      <j1 rule="para" parents="17310 21602"/>
    </justification>
  </clause>

  <clause id="21604">
    <literal><![CDATA[
      K(x,L(T(y * z,z \ 1) * u,z,L(y,z,z))) = K(x,(z \ 1) \ ((((y * z) \ 1) \ (z \ 1)) * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,18695,a(flip),b,21603,a)].">
      <j1 rule="hyper" parents="65 18695 21603"/>
    </justification>
  </clause>

  <clause id="21605">
    <literal><![CDATA[
      K(x,L(T(y * z,z \ 1) * u,z,y)) = K(x,(z \ 1) \ ((((y * z) \ 1) \ (z \ 1)) * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,19578,a(flip),b,21604,a)].">
      <j1 rule="hyper" parents="65 19578 21604"/>
    </justification>
  </clause>

  <clause id="21606">
    <literal><![CDATA[
      K(x,L(T(y * z,z * 1) * u,z,y)) = K(x,(z \ 1) \ ((((y * z) \ 1) \ (z \ 1)) * u))
    ]]></literal>
    <justification jstring="[hyper(18009,a,21605,a)].">
      <j1 rule="hyper" parents="18009 21605"/>
    </justification>
  </clause>

  <clause id="21608">
    <literal><![CDATA[
      K(x,L(T(y * z,z) * u,z,y)) = K(x,(z \ 1) \ ((((y * z) \ 1) \ (z \ 1)) * u))
    ]]></literal>
    <justification jstring="[para(8(a,1),21606(a,1,2,1,1,2))].">
      <j1 rule="para" parents="8 21606"/>
    </justification>
  </clause>

  <clause id="21609">
    <literal><![CDATA[
      K(x,L((y * z) * u,y,z)) = K(x,(y \ 1) \ ((((z * y) \ 1) \ (y \ 1)) * u))
    ]]></literal>
    <justification jstring="[hyper(17718,a,21608,a)].">
      <j1 rule="hyper" parents="17718 21608"/>
    </justification>
  </clause>

  <clause id="21610">
    <literal><![CDATA[
      K(x,L((y * z) * u,y,z)) = K(x,y \ ((((z * y) \ 1) \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(299,a,20632,a(flip),b,21609,a),flip(a)].">
      <j1 rule="hyper" parents="299 20632 21609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21611">
    <literal><![CDATA[
      K(x,y \ ((((z * y) \ 1) \ y) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / ((u \ 1) / z)) = w
    ]]></literal>
    <justification jstring="[para(21610(a,1),20984(a,1))].">
      <j1 rule="para" parents="21610 20984"/>
    </justification>
  </clause>

  <clause id="21612">
    <literal><![CDATA[
      K(x,y \ (((z * y) * y) * u)) = K(x,y / ((u \ 1) / z))
    ]]></literal>
    <justification jstring="[hyper(21611,a,21300,a),flip(a)].">
      <j1 rule="hyper" parents="21611 21300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21613">
    <literal><![CDATA[
      K(x,y \ ((y * (y * z)) * u)) = K(x,y / ((u \ 1) / z))
    ]]></literal>
    <justification jstring="[hyper(65,a,20619,a(flip),b,21612,a)].">
      <j1 rule="hyper" parents="65 20619 21612"/>
    </justification>
  </clause>

  <clause id="21614">
    <literal><![CDATA[
      K(x,y / ((z \ 1) / u)) = K(x,y * (u * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,21322,a(flip),b,21613,a),flip(a)].">
      <j1 rule="hyper" parents="65 21322 21613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21615">
    <literal><![CDATA[
      K(x,(T(y,z) \ u) * (y * (z / y))) = K(x,((u \ 1) * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,21471,a(flip),b,21614,a),flip(a)].">
      <j1 rule="hyper" parents="65 21471 21614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21616">
    <literal><![CDATA[
      K(x,(T(y,z) \ u) * T(z,y)) = K(x,((u \ 1) * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(16867,a,21615,a)].">
      <j1 rule="hyper" parents="16867 21615"/>
    </justification>
  </clause>

  <clause id="21617">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ u) = K(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,21338,a(flip),b,21616,a),flip(a)].">
      <j1 rule="hyper" parents="65 21338 21616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21618">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ u) = K(x,(T(y,z) \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(17965,a,21617,a)].">
      <j1 rule="hyper" parents="17965 21617"/>
    </justification>
  </clause>

  <clause id="21619">
    <literal><![CDATA[
      K(x,(y \ z) \ u) = K(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,21351,a(flip),b,21617,a)].">
      <j1 rule="hyper" parents="65 21351 21617"/>
    </justification>
  </clause>

  <clause id="21620">
    <literal><![CDATA[
      K(x,((T(T(y,z),z) \ u) \ y) * w) = K(x,y * (y * (u \ w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,20592,a(flip),b,21617,a),flip(a)].">
      <j1 rule="hyper" parents="65 20592 21617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21621">
    <literal><![CDATA[
      K(x,(y \ z) * T(u,y * z)) = K(x,u / ((z \ 1) * y))
    ]]></literal>
    <justification jstring="[hyper(65,a,20366,a(flip),b,21617,a),flip(a)].">
      <j1 rule="hyper" parents="65 20366 21617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21622">
    <literal><![CDATA[
      K(x,y \ ((y / z) * u)) = K(x,(z \ (u / y)) * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,21600,a(flip),b,21619,a)].">
      <j1 rule="hyper" parents="65 21600 21619"/>
    </justification>
  </clause>

  <clause id="21623">
    <literal><![CDATA[
      K(x,(y \ (z \ u)) * (u \ (z * y))) = a(u * y,u,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,21093,a(flip),b,21619,a),flip(a)].">
      <j1 rule="hyper" parents="65 21093 21619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21626">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ u) = K(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[hyper(299,a,19227,a(flip),b,21618,a),flip(a)].">
      <j1 rule="hyper" parents="299 19227 21618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21627">
    <literal><![CDATA[
      K(x,L(y * (z \ (z \ u)),u,z)) = K(x,(y / z) * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(15035,a,21626,a)].">
      <j1 rule="hyper" parents="15035 21626"/>
    </justification>
  </clause>

  <clause id="21628">
    <literal><![CDATA[
      K(x,(y / z) \ u) = K(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,21476,a(flip),b,21626,a)].">
      <j1 rule="hyper" parents="65 21476 21626"/>
    </justification>
  </clause>

  <clause id="21629">
    <literal><![CDATA[
      K(R(x,y,z) * K(u,x),(w / v5) * v6) = K(x,L(T((v5 / w) \ v6,u),y,z))
    ]]></literal>
    <justification jstring="[hyper(19131,a,21628,a),flip(a)].">
      <j1 rule="hyper" parents="19131 21628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21631">
    <literal><![CDATA[
      x * K(x,(y / z) * u) = T(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[para(21628(a,1),5083(a,2,2)),flip(a)].">
      <j1 rule="para" parents="21628 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21633">
    <literal><![CDATA[
      T(x,(y / z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z / y) * u) = w
    ]]></literal>
    <justification jstring="[para(21631(a,1),5087(a,1))].">
      <j1 rule="para" parents="21631 5087"/>
    </justification>
  </clause>

  <clause id="21634">
    <literal><![CDATA[
      T(x,(T(y,z) / z) * u) = T(x,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[hyper(21633,a,20321,a)].">
      <j1 rule="hyper" parents="21633 20321"/>
    </justification>
  </clause>

  <clause id="21636">
    <literal><![CDATA[
      T(x,(y \ z) \ u) = T(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(16974,a,21634,a),flip(a)].">
      <j1 rule="hyper" parents="16974 21634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21637">
    <literal><![CDATA[
      T(x,(y \ z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z \ y) * u) = w
    ]]></literal>
    <justification jstring="[para(21634(a,1),16974(a,1))].">
      <j1 rule="para" parents="21634 16974"/>
    </justification>
  </clause>

  <clause id="21639">
    <literal><![CDATA[
      K(x,T(y,(z \ u) * w) / ((u \ z) \ w)) = K(x,((u \ z) \ w) \ y)
    ]]></literal>
    <justification jstring="[para(21636(a,1),13712(a,1,2,1))].">
      <j1 rule="para" parents="21636 13712"/>
    </justification>
  </clause>

  <clause id="21641">
    <literal><![CDATA[
      K(x,L(y * z,u,z * u)) = K(x,((y \ 1) \ (z / u)) * u)
    ]]></literal>
    <justification jstring="[hyper(21599,a,21622,a)].">
      <j1 rule="hyper" parents="21599 21622"/>
    </justification>
  </clause>

  <clause id="21643">
    <literal><![CDATA[
      K(x,y / ((z \ 1) * u)) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,17475,a(flip),b,21621,a),flip(a)].">
      <j1 rule="hyper" parents="65 17475 21621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21644">
    <literal><![CDATA[
      K(x,L((y / z) * u,y,z)) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(15560,a,21643,a)].">
      <j1 rule="hyper" parents="15560 21643"/>
    </justification>
  </clause>

  <clause id="21645">
    <literal><![CDATA[
      K(x,y / (z \ u)) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,21488,a(flip),b,21643,a)].">
      <j1 rule="hyper" parents="65 21488 21643"/>
    </justification>
  </clause>

  <clause id="21646">
    <literal><![CDATA[
      K(x,(y * z) / (y * u)) = K(x,(y \ z) * (u \ y))
    ]]></literal>
    <justification jstring="[hyper(17610,a,21645,a)].">
      <j1 rule="hyper" parents="17610 21645"/>
    </justification>
  </clause>

  <clause id="21647">
    <literal><![CDATA[
      K(x,y \ (((y / z) * u) * z)) = K(x,(z \ y) * ((u \ y) \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,21439,a(flip),b,21646,a)].">
      <j1 rule="hyper" parents="65 21439 21646"/>
    </justification>
  </clause>

  <clause id="21648">
    <literal><![CDATA[
      K(x,L(y * z,u,z * u)) = K(x,(y * (z / u)) * u)
    ]]></literal>
    <justification jstring="[hyper(299,a,21260,a(flip),b,21641,a),flip(a)].">
      <j1 rule="hyper" parents="299 21260 21641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21649">
    <literal><![CDATA[
      K(x,((y \ z) \ y) * u) = K(x,y * (y * (z \ u)))
    ]]></literal>
    <justification jstring="[para(6256(a,1),21620(a,1,2,1,1,1))].">
      <j1 rule="para" parents="6256 21620"/>
    </justification>
  </clause>

  <clause id="21650">
    <literal><![CDATA[
      K(x,(y * (y / z)) * u) = K(x,y * (y * (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,16012,a(flip),b,21649,a)].">
      <j1 rule="hyper" parents="65 16012 21649"/>
    </justification>
  </clause>

  <clause id="21651">
    <literal><![CDATA[
      K(x,y * (y * (z \ ((y / z) \ u)))) = K(x,z * ((z \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,21325,a(flip),b,21650,a),flip(a)].">
      <j1 rule="hyper" parents="65 21325 21650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21652">
    <literal><![CDATA[
      x * K(y,(z \ x) * ((u \ x) \ z)) = ((x / z) * K(y,u)) * z
    ]]></literal>
    <justification jstring="[para(21647(a,1),20450(a,1,2))].">
      <j1 rule="para" parents="21647 20450"/>
    </justification>
  </clause>

  <clause id="21653">
    <literal><![CDATA[
      K(x,y \ (((1 / z) / y) \ u)) = K(x,y * ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,20469,a(flip),b,21651,a)].">
      <j1 rule="hyper" parents="65 20469 21651"/>
    </justification>
  </clause>

  <clause id="21654">
    <literal><![CDATA[
      K(x,y \ ((y / (1 / z)) * u)) = K(x,y * ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,21595,a(flip),b,21653,a)].">
      <j1 rule="hyper" parents="65 21595 21653"/>
    </justification>
  </clause>

  <clause id="21655">
    <literal><![CDATA[
      K(x,((1 / y) \ (z / u)) * u) = K(x,u * ((u \ y) * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,21622,a(flip),b,21654,a)].">
      <j1 rule="hyper" parents="65 21622 21654"/>
    </justification>
  </clause>

  <clause id="21656">
    <literal><![CDATA[
      K(x,(y * (z / u)) * u) = K(x,u * ((u \ y) * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,21263,a(flip),b,21655,a)].">
      <j1 rule="hyper" parents="65 21263 21655"/>
    </justification>
  </clause>

  <clause id="21657">
    <literal><![CDATA[
      K(x,L(y * z,u,z * u)) = K(x,u * ((u \ y) * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,21648,a,b,21656,a)].">
      <j1 rule="hyper" parents="65 21648 21656"/>
    </justification>
  </clause>

  <clause id="21658">
    <literal><![CDATA[
      K(x,L(y * (z \ (z \ u)),(z \ 1) \ 1,z \ T(u,z))) = K(x,((z \ 1) \ 1) * ((((z \ 1) \ 1) \ y) * (z \ (z \ u))))
    ]]></literal>
    <justification jstring="[para(14729(a,1),21657(a,1,2,3))].">
      <j1 rule="para" parents="14729 21657"/>
    </justification>
  </clause>

  <clause id="21659">
    <literal><![CDATA[
      x * K(y,(z \ x) * (T(1 / (u / x),u) \ z)) = ((x / z) * K(y,(1 / (u / x)) \ x)) * z
    ]]></literal>
    <justification jstring="[para(4756(a,2),21652(a,1,2,2,2,1))].">
      <j1 rule="para" parents="4756 21652"/>
    </justification>
  </clause>

  <clause id="21660">
    <literal><![CDATA[
      K(x,T(y,(z \ u) * w) * (w \ (u \ z))) = K(x,((u \ z) \ w) \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,21645,a(flip),b,21639,a)].">
      <j1 rule="hyper" parents="65 21645 21639"/>
    </justification>
  </clause>

  <clause id="21661">
    <literal><![CDATA[
      K(x,T(y,z * (u * w)) * (w \ (z \ u))) = K(x,((z \ u) \ w) \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,20425,a(flip),b,21660,a)].">
      <j1 rule="hyper" parents="65 20425 21660"/>
    </justification>
  </clause>

  <clause id="21662">
    <literal><![CDATA[
      K(x,T(y,z * (u * w)) * (w \ (z \ u))) = K(x,(w \ (z \ u)) * y)
    ]]></literal>
    <justification jstring="[hyper(299,a,21619,a(flip),b,21661,a),flip(a)].">
      <j1 rule="hyper" parents="299 21619 21661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21663">
    <literal><![CDATA[
      K(x,L(T((y / z) \ u,w),v5,v6)) = K(x,L(T((z / y) * u,w),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(19131,a,21629,a),flip(a)].">
      <j1 rule="hyper" parents="19131 21629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21664">
    <literal><![CDATA[
      K(x,L(T((y / z) * u,y * z),w,v5)) = K(x,L(u / (z / y),w,v5))
    ]]></literal>
    <justification jstring="[hyper(16896,a,21663,a),flip(a)].">
      <j1 rule="hyper" parents="16896 21663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21665">
    <literal><![CDATA[
      K(x,L(y / (z / u),w,v5)) = K(x,L(y * (u / z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(17591,a,21664,a),flip(a)].">
      <j1 rule="hyper" parents="17591 21664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21666">
    <literal><![CDATA[
      K(x,L(y * (z / T(u,z \ u)),w,v5)) = K(x,L(y / (z \ u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(19403,a,21665,a),flip(a)].">
      <j1 rule="hyper" parents="19403 21665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21667">
    <literal><![CDATA[
      K(x,L(y / (z \ u),w,v5)) = K(x,L(y * (u \ z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,20472,a(flip),b,21666,a),flip(a)].">
      <j1 rule="hyper" parents="65 20472 21666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21668">
    <literal><![CDATA[
      K(x,L(y * (z \ (z \ u)),z,z * u)) = K(x,(y * (u / z)) / z)
    ]]></literal>
    <justification jstring="[hyper(65,a,20742,a(flip),b,21667,a),flip(a)].">
      <j1 rule="hyper" parents="65 20742 21667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21669">
    <literal><![CDATA[
      K(x,L((y / z) * (u \ w),y,z)) = K(x,y / ((w \ 1) * (w \ (((1 / w) \ u) * z))))
    ]]></literal>
    <justification jstring="[hyper(65,a,15559,a(flip),b,21667,a),flip(a)].">
      <j1 rule="hyper" parents="65 15559 21667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21670">
    <literal><![CDATA[
      K(x,y / ((z \ 1) * (z \ (((1 / z) \ u) * w)))) = K(x,y * (w \ (u \ z)))
    ]]></literal>
    <justification jstring="[hyper(65,a,21644,a(flip),b,21669,a),flip(a)].">
      <j1 rule="hyper" parents="65 21644 21669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21671">
    <literal><![CDATA[
      K(x,y / ((z \ u) * w)) = K(x,y * (w \ (u \ z)))
    ]]></literal>
    <justification jstring="[para(1783(a,1),21670(a,1,2,2))].">
      <j1 rule="para" parents="1783 21670"/>
    </justification>
  </clause>

  <clause id="21672">
    <literal><![CDATA[
      K(x,T(y,z * (u * w)) * (w \ (z \ u))) = K(x,((u \ z) * w) \ y)
    ]]></literal>
    <justification jstring="[hyper(20996,a,21671,a),flip(a)].">
      <j1 rule="hyper" parents="20996 21671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21673">
    <literal><![CDATA[
      K(x,((y \ z) * u) \ w) = K(x,(u \ (z \ y)) * w)
    ]]></literal>
    <justification jstring="[hyper(65,a,21662,a(flip),b,21672,a),flip(a)].">
      <j1 rule="hyper" parents="65 21662 21672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21675">
    <literal><![CDATA[
      K(x,(y \ (z \ u)) * (u \ (z * y))) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,15718,a(flip),b,21673,a),flip(a)].">
      <j1 rule="hyper" parents="65 15718 21673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21676">
    <literal><![CDATA[
      a(x * y,x,K(z,u)) = a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,21623,a(flip),b,21675,a)].">
      <j1 rule="hyper" parents="65 21623 21675"/>
    </justification>
  </clause>

  <clause id="21677">
    <literal><![CDATA[
      a(x,y,K(z,y * u)) = a(y,x,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(21572,a,21676,a)].">
      <j1 rule="hyper" parents="21572 21676"/>
    </justification>
  </clause>

  <clause id="21678">
    <literal><![CDATA[
      K(x,L(y,z,z * u)) = (K(x,y) * u) / (u * a(z,y,K(u,x)))
    ]]></literal>
    <justification jstring="[para(21677(a,1),21197(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="21677 21197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21679">
    <literal><![CDATA[
      K(x,L(y,z,z * u)) = (K(x,y) * u) / L(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[para(20868(a,1),21678(a,2,2))].">
      <j1 rule="para" parents="20868 21678"/>
    </justification>
  </clause>

  <clause id="21680">
    <literal><![CDATA[
      K(x,L(y,z,z * u)) = K(x,y) * a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,20904,a(flip),b,21679,a),flip(a)].">
      <j1 rule="hyper" parents="299 20904 21679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21681">
    <literal><![CDATA[
      K(x,y) * a(z * u,y,K(x,z)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,19577,a(flip),b,21680,a),flip(a)].">
      <j1 rule="hyper" parents="65 19577 21680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21682">
    <literal><![CDATA[
      K(x,y) * a(z,y,K(x,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(19536(a,1),21681(a,1,2))].">
      <j1 rule="para" parents="19536 21681"/>
    </justification>
  </clause>

  <clause id="21683">
    <literal><![CDATA[
      K(x,L(y,z * u,z)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,21681,a(flip),b,21682,a),flip(a)].">
      <j1 rule="hyper" parents="65 21681 21682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21684">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(u,x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(36,a,11896,a,b,21682,a),flip(a)].">
      <j1 rule="hyper" parents="36 11896 21682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21685">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(14958,a,21684,a)].">
      <j1 rule="hyper" parents="14958 21684"/>
    </justification>
  </clause>

  <clause id="21686">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(14922,a,21684,a)].">
      <j1 rule="hyper" parents="14922 21684"/>
    </justification>
  </clause>

  <clause id="21688">
    <literal><![CDATA[
      K(x,y) * a(z,x,K(u,y)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[para(21684(a,1),14964(a,1,2))].">
      <j1 rule="para" parents="21684 14964"/>
    </justification>
  </clause>

  <clause id="21689">
    <literal><![CDATA[
      a(x,y,K(z,u)) * y = L(y,x,K(z,u))
    ]]></literal>
    <justification jstring="[para(21684(a,2),20881(a,1,1))].">
      <j1 rule="para" parents="21684 20881"/>
    </justification>
  </clause>

  <clause id="21690">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(y,x) = a(y,u,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(14883,a,21685,a)].">
      <j1 rule="hyper" parents="14883 21685"/>
    </justification>
  </clause>

  <clause id="21691">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(x,u,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,21684,a(flip),b,21685,a)].">
      <j1 rule="hyper" parents="299 21684 21685"/>
    </justification>
  </clause>

  <clause id="21692">
    <literal><![CDATA[
      a(x,y,K(z * u,z)) = a(x,u,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,15008,a,b,21691,a)].">
      <j1 rule="hyper" parents="299 15008 21691"/>
    </justification>
  </clause>

  <clause id="21693">
    <literal><![CDATA[
      K(x,L((y * T(z,z \ y)) / u,z,y / z)) = K(x,(z * (y / z)) / (u / z))
    ]]></literal>
    <justification jstring="[hyper(20983,a,21683,a),flip(a)].">
      <j1 rule="hyper" parents="20983 21683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21694">
    <literal><![CDATA[
      K(x,L(y,z,u)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,14990,a(flip),b,21683,a)].">
      <j1 rule="hyper" parents="65 14990 21683"/>
    </justification>
  </clause>

  <clause id="21695">
    <literal><![CDATA[
      K((x * y) \ ((1 / x) \ z),L(u,x,y)) = K((x * ((x \ 1) * y)) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,12015,a(flip),b,21683,a),flip(a)].">
      <j1 rule="hyper" parents="65 12015 21683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21696">
    <literal><![CDATA[
      K(x,L(y,z,z \ u)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),21683(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 21683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21697">
    <literal><![CDATA[
      K(x,L(y,z * u,u)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[para(14086(a,2),21683(a,1,2))].">
      <j1 rule="para" parents="14086 21683"/>
    </justification>
  </clause>

  <clause id="21698">
    <literal><![CDATA[
      K(x,L((y * z) / u,z,y)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(20979,a,21694,a),flip(a)].">
      <j1 rule="hyper" parents="20979 21694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21699">
    <literal><![CDATA[
      K(x,L(y,T(z,u),w)) = K(x,L(y,w,z))
    ]]></literal>
    <justification jstring="[hyper(20873,a,21694,a),flip(a)].">
      <j1 rule="hyper" parents="20873 21694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21700">
    <literal><![CDATA[
      K(x,L(y,z \ u,u)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,19608,a,b,21694,a)].">
      <j1 rule="hyper" parents="299 19608 21694"/>
    </justification>
  </clause>

  <clause id="21701">
    <literal><![CDATA[
      K(x,L((y * z) \ u,y,z)) = K(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(299,a,15632,a(flip),b,21694,a),flip(a)].">
      <j1 rule="hyper" parents="299 15632 21694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21702">
    <literal><![CDATA[
      K((x \ y) \ z,L(u,x,y)) = K(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,14989,a(flip),b,21694,a),flip(a)].">
      <j1 rule="hyper" parents="299 14989 21694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21703">
    <literal><![CDATA[
      K(x,L(T(y,z) \ u,z,y)) = K(x,(y * z) \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(299,a,11663,a(flip),b,21694,a),flip(a)].">
      <j1 rule="hyper" parents="299 11663 21694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21704">
    <literal><![CDATA[
      K(x,L(y,z,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u,z)) = w
    ]]></literal>
    <justification jstring="[para(21694(a,1),15000(a,1))].">
      <j1 rule="para" parents="21694 15000"/>
    </justification>
  </clause>

  <clause id="21705">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (u * z) = (K(x,y) * u) * z
    ]]></literal>
    <justification jstring="[para(21694(a,1),15496(a,1,1))].">
      <j1 rule="para" parents="21694 15496"/>
    </justification>
  </clause>

  <clause id="21706">
    <literal><![CDATA[
      a(x,y,K(z,x * u)) = a(y,u,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,21684,a(flip),b,21692,a)].">
      <j1 rule="hyper" parents="65 21684 21692"/>
    </justification>
  </clause>

  <clause id="21707">
    <literal><![CDATA[
      K(((x \ y) * x) \ z,L(u,y,x)) = K(x \ ((x \ y) \ z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,15631,a(flip),b,21696,a),flip(a)].">
      <j1 rule="hyper" parents="65 15631 21696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21708">
    <literal><![CDATA[
      K(x,L(T(y,z) \ u,z,y)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,13933,a(flip),b,21696,a),flip(a)].">
      <j1 rule="hyper" parents="65 13933 21696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21709">
    <literal><![CDATA[
      K(x,L((y * (z \ 1)) \ (z * u),z,y)) = K(x,T(y * (z \ (1 / z)),z) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,15739,a(flip),b,21697,a),flip(a)].">
      <j1 rule="hyper" parents="65 15739 21697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21710">
    <literal><![CDATA[
      K(((x * (y / x)) * x) \ z,L(u,y,x)) = K(T(x,x \ y) \ (y \ z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,15638,a(flip),b,21699,a),flip(a)].">
      <j1 rule="hyper" parents="65 15638 21699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21711">
    <literal><![CDATA[
      K(x,L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u,z)) = w
    ]]></literal>
    <justification jstring="[para(21699(a,1),20874(a,1))].">
      <j1 rule="para" parents="21699 20874"/>
    </justification>
  </clause>

  <clause id="21712">
    <literal><![CDATA[
      K(x,L(y,z,u \ z)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,21694,a,b,21700,a)].">
      <j1 rule="hyper" parents="65 21694 21700"/>
    </justification>
  </clause>

  <clause id="21713">
    <literal><![CDATA[
      K((x \ y) \ (y \ T(z,x)),L(u,y,x)) = K(z / (y * (x \ y)),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,18026,a(flip),b,21700,a),flip(a)].">
      <j1 rule="hyper" parents="65 18026 21700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21714">
    <literal><![CDATA[
      K(x,L(y,z / u,z)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(17047(a,2),21700(a,1,2))].">
      <j1 rule="para" parents="17047 21700"/>
    </justification>
  </clause>

  <clause id="21715">
    <literal><![CDATA[
      T((x \ y) \ y,z) \ T(T(x,z),L(x \ y,u,w)) = a(u,y,K(x,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,21453,a,b,21706,a)].">
      <j1 rule="hyper" parents="65 21453 21706"/>
    </justification>
  </clause>

  <clause id="21716">
    <literal><![CDATA[
      K(T(x,x \ y) \ z,L(u,y,x)) = K(y \ ((x \ y) * z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,14997,a(flip),b,21712,a),flip(a)].">
      <j1 rule="hyper" parents="65 14997 21712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21717">
    <literal><![CDATA[
      K((x / y) \ (T(x,z) \ u),L(w,x,y)) = K((x * (T(x,z) / y)) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,18662,a(flip),b,21714,a),flip(a)].">
      <j1 rule="hyper" parents="65 18662 21714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21722">
    <literal><![CDATA[
      K(x,L(y,T(z,u),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,w)) = v5
    ]]></literal>
    <justification jstring="[para(21699(a,2),21711(a,1))].">
      <j1 rule="para" parents="21699 21711"/>
    </justification>
  </clause>

  <clause id="21723">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (K(y,x) * w) = a(y,u,K(z,x)) * w
    ]]></literal>
    <justification jstring="[para(21690(a,1),10014(a,1,1)),flip(a)].">
      <j1 rule="para" parents="21690 10014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21724">
    <literal><![CDATA[
      K(x,y / (z / T(u,T(y,w)))) = K(x,u / (z / y))
    ]]></literal>
    <justification jstring="[hyper(65,a,21089,a(flip),b,21698,a)].">
      <j1 rule="hyper" parents="65 21089 21698"/>
    </justification>
  </clause>

  <clause id="21725">
    <literal><![CDATA[
      K(x,T(y,z) \ (z \ u)) = K(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,15672,a(flip),b,21701,a)].">
      <j1 rule="hyper" parents="65 15672 21701"/>
    </justification>
  </clause>

  <clause id="21726">
    <literal><![CDATA[
      K(x,T(y,z \ u) \ T(z,u)) = K(x,(z \ u) \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(19725,a,21725,a)].">
      <j1 rule="hyper" parents="19725 21725"/>
    </justification>
  </clause>

  <clause id="21727">
    <literal><![CDATA[
      K(x,y \ (T(z,y) \ u)) = K(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,15822,a(flip),b,21725,a),flip(a)].">
      <j1 rule="hyper" parents="65 15822 21725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21728">
    <literal><![CDATA[
      T(x,T(y,z) \ (z \ u)) = x * K(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[para(21725(a,1),5083(a,2,2))].">
      <j1 rule="para" parents="21725 5083"/>
    </justification>
  </clause>

  <clause id="21730">
    <literal><![CDATA[
      K(x,(y \ (y \ 1)) \ ((z \ (y \ 1)) \ ((y * y) \ u))) = K(x,(z \ y) \ ((y \ (y \ 1)) \ u))
    ]]></literal>
    <justification jstring="[para(1777(a,1),21727(a,1,2,2))].">
      <j1 rule="para" parents="1777 21727"/>
    </justification>
  </clause>

  <clause id="21731">
    <literal><![CDATA[
      K(x,L(y,z,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u,z)) = w
    ]]></literal>
    <justification jstring="[para(19572(a,1),21704(a,1))].">
      <j1 rule="para" parents="19572 21704"/>
    </justification>
  </clause>

  <clause id="21732">
    <literal><![CDATA[
      (K(x,y) * z) * T(u,z) = (K(x,y) * u) * z
    ]]></literal>
    <justification jstring="[hyper(15568,a,21705,a)].">
      <j1 rule="hyper" parents="15568 21705"/>
    </justification>
  </clause>

  <clause id="21733">
    <literal><![CDATA[
      (K(x,y) * z) * u != w * (z * u)
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u,z)) = w
    ]]></literal>
    <justification jstring="[para(21705(a,1),46(a,1))].">
      <j1 rule="para" parents="21705 46"/>
    </justification>
  </clause>

  <clause id="21735">
    <literal><![CDATA[
      T((K(x,y) * z) * u,K(x,y)) = z * (u * K(x,y))
    ]]></literal>
    <justification jstring="[para(21732(a,1),18960(a,1,1))].">
      <j1 rule="para" parents="21732 18960"/>
    </justification>
  </clause>

  <clause id="21739">
    <literal><![CDATA[
      K(x,y / (z / T(u,y))) = K(x,u / (z / y))
    ]]></literal>
    <justification jstring="[hyper(65,a,18924,a(flip),b,21724,a)].">
      <j1 rule="hyper" parents="65 18924 21724"/>
    </justification>
  </clause>

  <clause id="21740">
    <literal><![CDATA[
      T(x,T(y,z) \ (z \ u)) = T(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(299,a,5083,a,b,21728,a),flip(a)].">
      <j1 rule="hyper" parents="299 5083 21728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21741">
    <literal><![CDATA[
      T(x,T(y,z) \ (z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ (y \ u)) = w
    ]]></literal>
    <justification jstring="[para(21728(a,2),5087(a,1))].">
      <j1 rule="para" parents="21728 5087"/>
    </justification>
  </clause>

  <clause id="21742">
    <literal><![CDATA[
      T(x,(y \ z) \ (T(u,z * y) \ w)) = T(x,u \ ((y \ z) \ w))
    ]]></literal>
    <justification jstring="[hyper(20435,a,21740,a)].">
      <j1 rule="hyper" parents="20435 21740"/>
    </justification>
  </clause>

  <clause id="21743">
    <literal><![CDATA[
      T(x,y \ ((z \ 1) \ u)) = T(x,T(z,y) * (y \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,20372,a(flip),b,21740,a),flip(a)].">
      <j1 rule="hyper" parents="65 20372 21740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21744">
    <literal><![CDATA[
      T(x,y \ (T(z,y) \ u)) = T(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,15827,a(flip),b,21740,a),flip(a)].">
      <j1 rule="hyper" parents="65 15827 21740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21745">
    <literal><![CDATA[
      T(x,L(y,z,z) \ (T(u,L(y,z,z)) \ y)) = T(x,u \ a(z,z,y))
    ]]></literal>
    <justification jstring="[para(1986(a,1),21744(a,2,2,2))].">
      <j1 rule="para" parents="1986 21744"/>
    </justification>
  </clause>

  <clause id="21746">
    <literal><![CDATA[
      T((K(x,y) * z) * K(x,y),K(x,y)) \ u = (K(x,y) * K(x,y)) \ (z \ u)
    ]]></literal>
    <justification jstring="[para(21735(a,2),419(a,1,1))].">
      <j1 rule="para" parents="21735 419"/>
    </justification>
  </clause>

  <clause id="21747">
    <literal><![CDATA[
      (x * (y * K(z,u))) * K(u,z) = K(u,z) * ((K(z,u) * x) * y)
    ]]></literal>
    <justification jstring="[para(21735(a,1),6257(a,1,1))].">
      <j1 rule="para" parents="21735 6257"/>
    </justification>
  </clause>

  <clause id="21748">
    <literal><![CDATA[
      T((a(x,y,K(z,u)) * w) * v5,K(a(x,y,z),u)) = w * (v5 * K(a(x,y,z),u))
    ]]></literal>
    <justification jstring="[para(14556(a,2),21735(a,1,1,1,1))].">
      <j1 rule="para" parents="14556 21735"/>
    </justification>
  </clause>

  <clause id="21749">
    <literal><![CDATA[
      T(x,(y \ z) * (T(u,z * y) \ w)) = T(x,u \ (((y \ z) \ 1) \ w))
    ]]></literal>
    <justification jstring="[hyper(299,a,19283,a(flip),b,21743,a)].">
      <j1 rule="hyper" parents="299 19283 21743"/>
    </justification>
  </clause>

  <clause id="21750">
    <literal><![CDATA[
      T(x,(y \ z) \ ((y \ 1) \ u)) = T(x,y * ((z / y) \ u))
    ]]></literal>
    <justification jstring="[hyper(299,a,15826,a(flip),b,21743,a),flip(a)].">
      <j1 rule="hyper" parents="299 15826 21743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21751">
    <literal><![CDATA[
      T(x,L(y,z,u) \ ((y \ 1) \ w)) = T(x,y * (L(y,z,u) \ w))
    ]]></literal>
    <justification jstring="[para(173(a,1),21743(a,2,2,1))].">
      <j1 rule="para" parents="173 21743"/>
    </justification>
  </clause>

  <clause id="21752">
    <literal><![CDATA[
      K(x,(y * z) \ (z * u)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,21703,a(flip),b,21708,a)].">
      <j1 rule="hyper" parents="65 21703 21708"/>
    </justification>
  </clause>

  <clause id="21753">
    <literal><![CDATA[
      K(x,(T(y,z) \ z) \ u) = K(x,y \ ((z \ y) * (y * u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,15682,a,b,21752,a)].">
      <j1 rule="hyper" parents="65 15682 21752"/>
    </justification>
  </clause>

  <clause id="21754">
    <literal><![CDATA[
      K(x,y \ ((T(z,y) \ y) * u)) = K(x,(y * z) \ (y * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,15870,a(flip),b,21752,a),flip(a)].">
      <j1 rule="hyper" parents="65 15870 21752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21755">
    <literal><![CDATA[
      K(x,y \ ((z \ y) * (y \ u))) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[para(10(a,1),21752(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 21752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21756">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ (z * ((1 / z) * u))) = K(x,(z \ 1) \ ((y \ (z \ 1)) * (z * u)))
    ]]></literal>
    <justification jstring="[para(944(a,1),21752(a,1,2,2))].">
      <j1 rule="para" parents="944 21752"/>
    </justification>
  </clause>

  <clause id="21757">
    <literal><![CDATA[
      x * K(x,y \ ((z \ y) * u)) = T(x,(z * y) \ (y * u))
    ]]></literal>
    <justification jstring="[para(21752(a,1),5083(a,2,2)),flip(a)].">
      <j1 rule="para" parents="21752 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21758">
    <literal><![CDATA[
      K(x,((y * z) * y) \ u) = K(x,y \ (z \ (y \ u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,21593,a(flip),b,21755,a),flip(a)].">
      <j1 rule="hyper" parents="65 21593 21755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21759">
    <literal><![CDATA[
      K(x,(y * (z * y)) \ u) = K(x,y \ (z \ (y \ u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,19560,a(flip),b,21758,a)].">
      <j1 rule="hyper" parents="65 19560 21758"/>
    </justification>
  </clause>

  <clause id="21760">
    <literal><![CDATA[
      x * K(x,y \ (z \ (y \ u))) = T(x,(y * (z * y)) \ u)
    ]]></literal>
    <justification jstring="[para(21759(a,1),5083(a,2,2)),flip(a)].">
      <j1 rule="para" parents="21759 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21761">
    <literal><![CDATA[
      T(x,(y \ z) \ (y \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ ((z / y) \ u)) = w
    ]]></literal>
    <justification jstring="[para(109(a,1),21741(a,1,2,1))].">
      <j1 rule="para" parents="109 21741"/>
    </justification>
  </clause>

  <clause id="21762">
    <literal><![CDATA[
      T(x,(y / z) \ (z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ ((z \ y) \ u)) = w
    ]]></literal>
    <justification jstring="[para(15817(a,1),21741(a,1))].">
      <j1 rule="para" parents="15817 21741"/>
    </justification>
  </clause>

  <clause id="21763">
    <literal><![CDATA[
      T(x,y \ (T(z,y) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ (y \ u)) = w
    ]]></literal>
    <justification jstring="[para(15818(a,1),21741(a,1))].">
      <j1 rule="para" parents="15818 21741"/>
    </justification>
  </clause>

  <clause id="21764">
    <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(19284(a,1),21763(a,1))].">
      <j1 rule="para" parents="19284 21763"/>
    </justification>
  </clause>

  <clause id="21765">
    <literal><![CDATA[
      T(x,(y * (z \ y)) \ (T(u,z) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,u \ ((y * (z \ y)) \ w)) = v5
    ]]></literal>
    <justification jstring="[para(20774(a,1),21763(a,1))].">
      <j1 rule="para" parents="20774 21763"/>
    </justification>
  </clause>

  <clause id="21766">
    <literal><![CDATA[
      L(x,K(y,z) \ u,K(y,z)) = u \ ((a(z,x,K(u,y)) * u) * x)
    ]]></literal>
    <justification jstring="[para(21723(a,1),15735(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="21723 15735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21767">
    <literal><![CDATA[
      K(x,T(y,z * u) \ T(z,u)) = K(x,(z \ u) \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,17937,a(flip),b,21726,a)].">
      <j1 rule="hyper" parents="65 17937 21726"/>
    </justification>
  </clause>

  <clause id="21768">
    <literal><![CDATA[
      T(x,((y \ 1) * z) \ (y * u)) = T(x,y * ((z / y) \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,15676,a,b,21750,a)].">
      <j1 rule="hyper" parents="65 15676 21750"/>
    </justification>
  </clause>

  <clause id="21769">
    <literal><![CDATA[
      T(x,y * ((z / y) \ ((y \ 1) * u))) = T(x,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[para(9(a,1),21750(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 21750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21770">
    <literal><![CDATA[
      K(x,y \ ((z \ y) * (y * u))) = K(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,20213,a(flip),b,21753,a),flip(a)].">
      <j1 rule="hyper" parents="65 20213 21753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21771">
    <literal><![CDATA[
      K(x,(y / z) \ (z \ u)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[para(10(a,1),21770(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10 21770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21772">
    <literal><![CDATA[
      K(x,(y / z) \ (z \ (u * ((1 / y) \ y)))) = K(x,z \ T(((1 / y) \ z) * u,y * y))
    ]]></literal>
    <justification jstring="[para(14367(a,2),21771(a,2,2,2))].">
      <j1 rule="para" parents="14367 21771"/>
    </justification>
  </clause>

  <clause id="21773">
    <literal><![CDATA[
      K(x,(y * z) \ (y * u)) = K(x,y \ ((y / z) * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,20810,a(flip),b,21754,a),flip(a)].">
      <j1 rule="hyper" parents="65 20810 21754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21774">
    <literal><![CDATA[
      x * K(x,y \ ((y / z) * u)) = T(x,(y * z) \ (y * u))
    ]]></literal>
    <justification jstring="[para(21773(a,1),5083(a,2,2)),flip(a)].">
      <j1 rule="para" parents="21773 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21775">
    <literal><![CDATA[
      (x * K(y,z \ ((z / u) * w))) \ x = K((z * u) \ (z * w),y)
    ]]></literal>
    <justification jstring="[para(21773(a,1),7200(a,1,1,2))].">
      <j1 rule="para" parents="21773 7200"/>
    </justification>
  </clause>

  <clause id="21776">
    <literal><![CDATA[
      T(x,(y * z) \ (z * u)) = T(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(5087,a,21757,a),flip(a)].">
      <j1 rule="hyper" parents="5087 21757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21777">
    <literal><![CDATA[
      T(x,(T(y,z) \ z) \ u) = T(x,y \ ((z \ y) * (y * u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,15683,a,b,21776,a)].">
      <j1 rule="hyper" parents="65 15683 21776"/>
    </justification>
  </clause>

  <clause id="21778">
    <literal><![CDATA[
      T(x,(y * (z * y)) \ u) = T(x,y \ (z \ (y \ u)))
    ]]></literal>
    <justification jstring="[hyper(5087,a,21760,a),flip(a)].">
      <j1 rule="hyper" parents="5087 21760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21779">
    <literal><![CDATA[
      T(x,(y \ 1) \ (z \ T(a(y,y,y) * u,y \ 1))) = T(x,((y \ 1) * (z * (y \ 1))) \ (u * (1 / y)))
    ]]></literal>
    <justification jstring="[para(6379(a,2),21778(a,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6379 21778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21780">
    <literal><![CDATA[
      K(x,y \ (z * T(u / z,y))) = K(x,(u \ z) \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(20531,a,21767,a)].">
      <j1 rule="hyper" parents="20531 21767"/>
    </justification>
  </clause>

  <clause id="21781">
    <literal><![CDATA[
      T(x,y * ((z / y) \ ((y \ 1) * u))) = T(x,((y \ 1) * z) \ L(u,y,y))
    ]]></literal>
    <justification jstring="[para(1673(a,1),21768(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1673 21768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21782">
    <literal><![CDATA[
      T(x,(y * z) \ (y * u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ ((y / z) * u)) = w
    ]]></literal>
    <justification jstring="[para(21774(a,1),5087(a,1))].">
      <j1 rule="para" parents="21774 5087"/>
    </justification>
  </clause>

  <clause id="21783">
    <literal><![CDATA[
      T(x,y \ ((z \ y) * (y * u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z / y) \ u) = w
    ]]></literal>
    <justification jstring="[para(21777(a,1),20220(a,1))].">
      <j1 rule="para" parents="21777 20220"/>
    </justification>
  </clause>

  <clause id="21784">
    <literal><![CDATA[
      K(x,((y * z) \ y) \ (u \ y)) = K(x,u \ (y * T(z * K(y,z),u)))
    ]]></literal>
    <justification jstring="[para(5054(a,1),21780(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5054 21780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21785">
    <literal><![CDATA[
      K(T(x,y) \ z,L(u,x,y)) = K(y \ ((y \ x) \ z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,17795,a(flip),b,21707,a)].">
      <j1 rule="hyper" parents="65 17795 21707"/>
    </justification>
  </clause>

  <clause id="21786">
    <literal><![CDATA[
      K(T(x,y) \ z,L(u,y,x)) = K(y \ ((x \ y) * z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,13911,a(flip),b,21716,a)].">
      <j1 rule="hyper" parents="65 13911 21716"/>
    </justification>
  </clause>

  <clause id="21787">
    <literal><![CDATA[
      K(T(x,y) \ z,L(u,x,y)) = K(y \ ((x \ y) * z),u)
    ]]></literal>
    <justification jstring="[hyper(21711,a,21786,a)].">
      <j1 rule="hyper" parents="21711 21786"/>
    </justification>
  </clause>

  <clause id="21788">
    <literal><![CDATA[
      K(x \ ((x \ y) \ z),u) = K(x \ ((y \ x) * z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,21785,a(flip),b,21787,a)].">
      <j1 rule="hyper" parents="65 21785 21787"/>
    </justification>
  </clause>

  <clause id="21789">
    <literal><![CDATA[
      K((x / y) \ (y \ z),u) = K(y \ ((x \ y) * z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,17797,a(flip),b,21787,a)].">
      <j1 rule="hyper" parents="65 17797 21787"/>
    </justification>
  </clause>

  <clause id="21790">
    <literal><![CDATA[
      K((x * y) \ (y * z),u) = K(y \ ((x \ y) * z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,11944,a(flip),b,21787,a)].">
      <j1 rule="hyper" parents="65 11944 21787"/>
    </justification>
  </clause>

  <clause id="21791">
    <literal><![CDATA[
      K(x \ (((K(y,x) * z) \ x) * u),w) = K(x \ ((T(x,y) \ z) \ u),w)
    ]]></literal>
    <justification jstring="[para(5372(a,1),21788(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5372 21788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21793">
    <literal><![CDATA[
      T(x,y \ ((z \ y) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z / y) \ (y \ u)) = w
    ]]></literal>
    <justification jstring="[para(10(a,1),21783(a,1,2,2,2))].">
      <j1 rule="para" parents="10 21783"/>
    </justification>
  </clause>

  <clause id="21794">
    <literal><![CDATA[
      T(x,(y / z) \ (z \ u)) = T(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(21793,a,xx)].">
      <j1 rule="hyper" parents="21793"/>
    </justification>
  </clause>

  <clause id="21795">
    <literal><![CDATA[
      T(x,y \ ((y \ z) \ u)) = T(x,y \ ((z \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(21762,a,21794,a)].">
      <j1 rule="hyper" parents="21762 21794"/>
    </justification>
  </clause>

  <clause id="21797">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y \ ((u \ y) * z)) = T(x,((y \ u) \ z) / y)
    ]]></literal>
    <justification jstring="[hyper(65,a,19361,a(flip),b,21795,a),flip(a)].">
      <j1 rule="hyper" parents="65 19361 21795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21798">
    <literal><![CDATA[
      T(x,R(y,z,y) \ (T(u,T(y * z,y) * z) \ w)) = T(x,u \ ((z \ T(y * z,y)) \ w))
    ]]></literal>
    <justification jstring="[para(4338(a,1),21742(a,1,2,1))].">
      <j1 rule="para" parents="4338 21742"/>
    </justification>
  </clause>

  <clause id="21799">
    <literal><![CDATA[
      T(x,(K(y,z) * u) \ (T(w,u * K(z,y)) \ v5)) = T(x,w \ ((K(z,y) \ u) \ v5))
    ]]></literal>
    <justification jstring="[para(5426(a,1),21742(a,1,2,1))].">
      <j1 rule="para" parents="5426 21742"/>
    </justification>
  </clause>

  <clause id="21800">
    <literal><![CDATA[
      T(x,T(y,z * K(u,w)) \ (T(v5,T(y * z,K(u,w)) * T(z,K(u,w))) \ v6)) = T(x,v5 \ ((T(z,K(u,w)) \ T(y * z,K(u,w))) \ v6))
    ]]></literal>
    <justification jstring="[para(16144(a,1),21742(a,1,2,1))].">
      <j1 rule="para" parents="16144 21742"/>
    </justification>
  </clause>

  <clause id="21801">
    <literal><![CDATA[
      K((x * y) \ (x * z),u) = K(x \ ((x / y) * z),u)
    ]]></literal>
    <justification jstring="[hyper(18857,a,21775,a),flip(a)].">
      <j1 rule="hyper" parents="18857 21775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21802">
    <literal><![CDATA[
      K((x * y) \ (x * z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ ((x / y) * z),u) = w
    ]]></literal>
    <justification jstring="[para(21775(a,1),7209(a,1))].">
      <j1 rule="para" parents="21775 7209"/>
    </justification>
  </clause>

  <clause id="21803">
    <literal><![CDATA[
      K((T(x,y) * y) \ (y * z),u) = K(y \ ((y / x) * z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,15884,a,b,21801,a)].">
      <j1 rule="hyper" parents="65 15884 21801"/>
    </justification>
  </clause>

  <clause id="21804">
    <literal><![CDATA[
      K((1 / x) \ (((1 / x) / y) * z),u) = K((x * y) \ (x * z),u)
    ]]></literal>
    <justification jstring="[para(1069(a,1),21801(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1069 21801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21805">
    <literal><![CDATA[
      K(x \ ((T(y,x) \ x) * z),u) = K(x \ ((x / y) * z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,21790,a(flip),b,21803,a)].">
      <j1 rule="hyper" parents="65 21790 21803"/>
    </justification>
  </clause>

  <clause id="21806">
    <literal><![CDATA[
      K(x \ ((y \ T(x,y)) * z),u) = K(x \ ((x / y) * z),u)
    ]]></literal>
    <justification jstring="[para(4396(a,1),21805(a,1,1,2,1))].">
      <j1 rule="para" parents="4396 21805"/>
    </justification>
  </clause>

  <clause id="21807">
    <literal><![CDATA[
      K((1 / x) \ (((1 / x) / (y * (z * z))) * u),w) = K((z * z) \ ((x * y) \ (x * u)),w)
    ]]></literal>
    <justification jstring="[para(744(a,1),21804(a,2,1))].">
      <j1 rule="para" parents="744 21804"/>
    </justification>
  </clause>

  <clause id="21808">
    <literal><![CDATA[
      K((1 / x) \ (((1 / x) / y) * z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ ((x / y) * z),u) = w
    ]]></literal>
    <justification jstring="[para(21804(a,2),21802(a,1))].">
      <j1 rule="para" parents="21804 21802"/>
    </justification>
  </clause>

  <clause id="21809">
    <literal><![CDATA[
      K(x \ (y * (x \ T(z,y))),u) = K(z / (x * (y \ x)),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,14989,a(flip),b,21713,a)].">
      <j1 rule="hyper" parents="65 14989 21713"/>
    </justification>
  </clause>

  <clause id="21810">
    <literal><![CDATA[
      K(x \ (L(x,y,y) * (x \ T(z,L(x,y,y)))),u) = K(z / (x * a(y,y,x)),u)
    ]]></literal>
    <justification jstring="[para(1986(a,1),21809(a,2,1,2,2))].">
      <j1 rule="para" parents="1986 21809"/>
    </justification>
  </clause>

  <clause id="21811">
    <literal><![CDATA[
      K((x * K(y,x)) / (z * (y \ z)),u) = K(z \ (y * (z \ x)),u)
    ]]></literal>
    <justification jstring="[para(5053(a,1),21809(a,1,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5053 21809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21812">
    <literal><![CDATA[
      K(T(x,y) / (z * (y \ z)),u) = K(z \ (y * (z \ x)),u)
    ]]></literal>
    <justification jstring="[hyper(16046,a,21811,a)].">
      <j1 rule="hyper" parents="16046 21811"/>
    </justification>
  </clause>

  <clause id="21813">
    <literal><![CDATA[
      K((x * (y \ x)) \ z,u) = K(x \ (y * (x \ z)),u)
    ]]></literal>
    <justification jstring="[hyper(18023,a,21812,a)].">
      <j1 rule="hyper" parents="18023 21812"/>
    </justification>
  </clause>

  <clause id="21814">
    <literal><![CDATA[
      K(x \ (y * (x \ z)),u) != w
    ]]></literal>
    <literal><![CDATA[
      K((x * (y \ x)) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(21812(a,1),18023(a,1))].">
      <j1 rule="para" parents="21812 18023"/>
    </justification>
  </clause>

  <clause id="21815">
    <literal><![CDATA[
      (x * y) / (K(z \ (u * (z \ w)),x) * y) = T(x,(z * (u \ z)) \ w)
    ]]></literal>
    <justification jstring="[para(21813(a,1),5517(a,1,2,1))].">
      <j1 rule="para" parents="21813 5517"/>
    </justification>
  </clause>

  <clause id="21816">
    <literal><![CDATA[
      K(x \ (y * (x \ z)),T(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(z / (x * (y \ x)),u) = w
    ]]></literal>
    <justification jstring="[para(21813(a,1),16547(a,1))].">
      <j1 rule="para" parents="21813 16547"/>
    </justification>
  </clause>

  <clause id="21817">
    <literal><![CDATA[
      T(x,L(y,z,z) \ (T(u,y) \ y)) = T(x,u \ a(z,z,y))
    ]]></literal>
    <justification jstring="[para(14206(a,1),21745(a,1,2,2,1))].">
      <j1 rule="para" parents="14206 21745"/>
    </justification>
  </clause>

  <clause id="21818">
    <literal><![CDATA[
      T(x,L(y,z,z) \ (y / u)) = T(x,u \ a(z,z,y))
    ]]></literal>
    <justification jstring="[hyper(15874,a,21817,a)].">
      <j1 rule="hyper" parents="15874 21817"/>
    </justification>
  </clause>

  <clause id="21820">
    <literal><![CDATA[
      K(x,((y * z) \ y) \ (u \ y)) = K(x,u \ (y * T(T(z,y),u)))
    ]]></literal>
    <justification jstring="[hyper(299,a,16016,a(flip),b,21784,a),flip(a)].">
      <j1 rule="hyper" parents="299 16016 21784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21821">
    <literal><![CDATA[
      K(x,((y * z) \ y) \ (u \ y)) = K(x,u \ (T(z,u) * y))
    ]]></literal>
    <justification jstring="[para(232(a,1),21820(a,2,2,2))].">
      <j1 rule="para" parents="232 21820"/>
    </justification>
  </clause>

  <clause id="21822">
    <literal><![CDATA[
      K(x \ ((T(x,y) \ z) \ u),w) = K(x \ ((z \ T(x,y)) * u),w)
    ]]></literal>
    <justification jstring="[para(14389(a,1),21791(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14389 21791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21823">
    <literal><![CDATA[
      T(x,(y * (z \ y)) \ u) = T(x,y \ (z * (y \ u)))
    ]]></literal>
    <justification jstring="[hyper(5519,a,21815,a),flip(a)].">
      <j1 rule="hyper" parents="5519 21815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21824">
    <literal><![CDATA[
      T(x,(y * (z \ y)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (z * (y \ u))) = w
    ]]></literal>
    <justification jstring="[para(21815(a,1),5519(a,1))].">
      <j1 rule="para" parents="21815 5519"/>
    </justification>
  </clause>

  <clause id="21825">
    <literal><![CDATA[
      T(T(x,K(y,z)),y / (u * (z \ u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u \ (z * (u \ y))) = w
    ]]></literal>
    <justification jstring="[para(16292(a,2),21824(a,1))].">
      <j1 rule="para" parents="16292 21824"/>
    </justification>
  </clause>

  <clause id="21826">
    <literal><![CDATA[
      K((x * y) \ ((x \ 1) \ z),L(u,x,y)) = K((x * ((x \ 1) * y)) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(6313,a,21695,a)].">
      <j1 rule="hyper" parents="6313 21695"/>
    </justification>
  </clause>

  <clause id="21828">
    <literal><![CDATA[
      K((x * ((y / x) * x)) \ z,L(u,y,x)) = K(T(x,x \ y) \ (y \ z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,20454,a(flip),b,21710,a)].">
      <j1 rule="hyper" parents="65 20454 21710"/>
    </justification>
  </clause>

  <clause id="21829">
    <literal><![CDATA[
      K(x \ (T(y,x) * (T(x,z) \ u)),w) = K((x * (T(x,z) / y)) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,20239,a(flip),b,21717,a)].">
      <j1 rule="hyper" parents="65 20239 21717"/>
    </justification>
  </clause>

  <clause id="21830">
    <literal><![CDATA[
      T(x,((y / z) \ z) \ (T(u,y) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,u \ (((y / z) \ z) \ w)) = v5
    ]]></literal>
    <justification jstring="[para(12(a,1),21764(a,1,2,2,1,2))].">
      <j1 rule="para" parents="12 21764"/>
    </justification>
  </clause>

  <clause id="21831">
    <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(21636(a,1),21764(a,1))].">
      <j1 rule="para" parents="21636 21764"/>
    </justification>
  </clause>

  <clause id="21832">
    <literal><![CDATA[
      T(x,((y \ 1) * z) \ L(u,y,y)) = T(x,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,21769,a(flip),b,21781,a),flip(a)].">
      <j1 rule="hyper" parents="65 21769 21781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21833">
    <literal><![CDATA[
      T(x,(y \ ((y \ 1) \ z)) \ u) = T(x,z \ L(u,y,y))
    ]]></literal>
    <justification jstring="[para(10(a,1),21832(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 21832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21834">
    <literal><![CDATA[
      T(x,y \ L(T(z,y),u,u)) = T(x,z / (u \ ((u \ 1) \ y)))
    ]]></literal>
    <justification jstring="[hyper(16647,a,21833,a),flip(a)].">
      <j1 rule="hyper" parents="16647 21833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21835">
    <literal><![CDATA[
      T(x,y / (z \ ((z \ 1) \ u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,L(y,z,z) / u) = w
    ]]></literal>
    <justification jstring="[para(21834(a,1),16644(a,1))].">
      <j1 rule="para" parents="21834 16644"/>
    </justification>
  </clause>

  <clause id="21836">
    <literal><![CDATA[
      K((x * y) \ ((x \ 1) \ z),L(u,x,y)) = K(L(y,x,x) \ z,u)
    ]]></literal>
    <justification jstring="[para(1673(a,1),21826(a,2,1,1))].">
      <j1 rule="para" parents="1673 21826"/>
    </justification>
  </clause>

  <clause id="21837">
    <literal><![CDATA[
      K(x \ (T(y,x) \ ((x \ 1) \ z)),u) = K(L(y,x,x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,18876,a(flip),b,21836,a)].">
      <j1 rule="hyper" parents="65 18876 21836"/>
    </justification>
  </clause>

  <clause id="21838">
    <literal><![CDATA[
      K(T(x,x \ y) \ (y \ z),u) = K((x * y) \ z,L(u,y,x))
    ]]></literal>
    <justification jstring="[para(12(a,1),21828(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12 21828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21839">
    <literal><![CDATA[
      K(T(x,x \ y) \ (y \ z),u) = K(y \ (x \ z),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,15631,a(flip),b,21838,a),flip(a)].">
      <j1 rule="hyper" parents="299 15631 21838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21840">
    <literal><![CDATA[
      K(T(x,y) \ (y \ z),u) = K(y \ (x \ z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,13911,a(flip),b,21839,a)].">
      <j1 rule="hyper" parents="65 13911 21839"/>
    </justification>
  </clause>

  <clause id="21841">
    <literal><![CDATA[
      K((x / y) \ (x \ z),u) = K(x \ ((y \ x) \ z),u)
    ]]></literal>
    <justification jstring="[hyper(20312,a,21840,a)].">
      <j1 rule="hyper" parents="20312 21840"/>
    </justification>
  </clause>

  <clause id="21842">
    <literal><![CDATA[
      K(x \ (T(y,x) \ z),u) = K(y \ (x \ z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,17798,a(flip),b,21840,a),flip(a)].">
      <j1 rule="hyper" parents="65 17798 21840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21843">
    <literal><![CDATA[
      K((x \ y) \ (x \ z),u) = K(x \ ((y / x) \ z),u)
    ]]></literal>
    <justification jstring="[para(109(a,1),21840(a,1,1,1))].">
      <j1 rule="para" parents="109 21840"/>
    </justification>
  </clause>

  <clause id="21844">
    <literal><![CDATA[
      K(x \ (y \ ((y \ 1) \ z)),u) = K(L(x,y,y) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,21837,a(flip),b,21842,a),flip(a)].">
      <j1 rule="hyper" parents="65 21837 21842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21845">
    <literal><![CDATA[
      K((x / T(y,x)) \ (y \ z),u) = K(y \ ((T(y,x) \ x) \ z),u)
    ]]></literal>
    <justification jstring="[para(4300(a,1),21842(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4300 21842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21846">
    <literal><![CDATA[
      K((x / y) \ (x \ T(z,(y \ x) \ z)),u) = K(x \ ((z * ((y \ x) \ z)) / z),u)
    ]]></literal>
    <justification jstring="[para(4280(a,1),21841(a,2,1,2))].">
      <j1 rule="para" parents="4280 21841"/>
    </justification>
  </clause>

  <clause id="21847">
    <literal><![CDATA[
      K((x / T(y,x)) \ (y \ z),u) = K(y \ ((x \ T(y,x)) * z),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,21822,a(flip),b,21845,a),flip(a)].">
      <j1 rule="hyper" parents="299 21822 21845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21848">
    <literal><![CDATA[
      K((x / T(y,x)) \ (y \ z),u) = K(y \ ((y / x) * z),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,21806,a(flip),b,21847,a),flip(a)].">
      <j1 rule="hyper" parents="299 21806 21847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21849">
    <literal><![CDATA[
      K((x \ y) \ (x \ z),u) = K(x \ ((x / y) * z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,20162,a(flip),b,21848,a)].">
      <j1 rule="hyper" parents="65 20162 21848"/>
    </justification>
  </clause>

  <clause id="21850">
    <literal><![CDATA[
      K(x \ ((y / x) \ z),u) = K(x \ ((x / y) * z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,21843,a(flip),b,21849,a)].">
      <j1 rule="hyper" parents="65 21843 21849"/>
    </justification>
  </clause>

  <clause id="21851">
    <literal><![CDATA[
      (x * y) / (K(z \ ((z / u) * w),x) * y) = T(x,(z \ u) \ (z \ w))
    ]]></literal>
    <justification jstring="[para(21849(a,1),5517(a,1,2,1))].">
      <j1 rule="para" parents="21849 5517"/>
    </justification>
  </clause>

  <clause id="21852">
    <literal><![CDATA[
      (K(x \ ((x / y) * z),u) * w) \ w = K(u,T((x \ y) \ (x \ z),w))
    ]]></literal>
    <justification jstring="[para(21849(a,1),7492(a,1,1,1))].">
      <j1 rule="para" parents="21849 7492"/>
    </justification>
  </clause>

  <clause id="21853">
    <literal><![CDATA[
      K(x \ ((x \ (y \ ((1 / y) \ x))) \ z),u) = K(x \ ((x / (y \ ((1 / y) \ x))) * z),u)
    ]]></literal>
    <justification jstring="[para(20844(a,1),21850(a,1,1,2,1))].">
      <j1 rule="para" parents="20844 21850"/>
    </justification>
  </clause>

  <clause id="21854">
    <literal><![CDATA[
      T(x,(y \ z) \ (y \ u)) = T(x,y \ ((y / z) * u))
    ]]></literal>
    <justification jstring="[hyper(5519,a,21851,a),flip(a)].">
      <j1 rule="hyper" parents="5519 21851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21855">
    <literal><![CDATA[
      T(x,y \ ((z / y) \ u)) = T(x,y \ ((y / z) * u))
    ]]></literal>
    <justification jstring="[hyper(21761,a,21854,a)].">
      <j1 rule="hyper" parents="21761 21854"/>
    </justification>
  </clause>

  <clause id="21856">
    <literal><![CDATA[
      T(x * (y \ ((1 / y) \ z)),K(y \ ((1 / y) \ z),z)) = (y \ ((1 / y) \ z)) * T(x,y \ ((y / 1) * z))
    ]]></literal>
    <justification jstring="[para(21855(a,1),15158(a,2,2))].">
      <j1 rule="para" parents="21855 15158"/>
    </justification>
  </clause>

  <clause id="21857">
    <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(21852(a,1),7614(a,1))].">
      <j1 rule="para" parents="21852 7614"/>
    </justification>
  </clause>

  <clause id="21858">
    <literal><![CDATA[
      (K(x,y) * (K(x,y) * z)) \ u = (K(x,y) * K(x,y)) \ (z \ u)
    ]]></literal>
    <justification jstring="[para(8053(a,1),21746(a,1,1))].">
      <j1 rule="para" parents="8053 21746"/>
    </justification>
  </clause>

  <clause id="21859">
    <literal><![CDATA[
      (K(x,y) * (K(x,y) * z)) \ u = K(y,x) * (K(y,x) * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(299,a,20082,a(flip),b,21858,a),flip(a)].">
      <j1 rule="hyper" parents="299 20082 21858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21860">
    <literal><![CDATA[
      x \ (K(y,L(z,K(y,z),K(y,z) \ u)) * u) = K(y,z) * (K(y,z) * (x \ (K(z,y) * u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,15738,a,b,21859,a)].">
      <j1 rule="hyper" parents="65 15738 21859"/>
    </justification>
  </clause>

  <clause id="21861">
    <literal><![CDATA[
      (x * (T(T(x,y),y) \ z)) \ u = K(x,y) * (K(x,y) * (z \ u))
    ]]></literal>
    <justification jstring="[para(6199(a,1),21859(a,1,1))].">
      <j1 rule="para" parents="6199 21859"/>
    </justification>
  </clause>

  <clause id="21862">
    <literal><![CDATA[
      (x * (T(T(x,y),y) \ z)) \ u = y * (T(T(y,x),x) \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(299,a,6199,a(flip),b,21861,a),flip(a)].">
      <j1 rule="hyper" parents="299 6199 21861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21863">
    <literal><![CDATA[
      x \ (y * (T(T(y,z),z) \ u)) = y * (T(T(y,z),z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,10112,a(flip),b,21862,a)].">
      <j1 rule="hyper" parents="65 10112 21862"/>
    </justification>
  </clause>

  <clause id="21864">
    <literal><![CDATA[
      x * (T(T(x,y),y) \ ((K(y,x) * z) \ u)) = ((K(y,x) \ 1) * z) \ u
    ]]></literal>
    <justification jstring="[hyper(65,a,6587,a(flip),b,21863,a),flip(a)].">
      <j1 rule="hyper" parents="65 6587 21863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21865">
    <literal><![CDATA[
      x * (T(T(x,y),y) \ (K(x,y) * ((y \ x) \ z))) = ((K(y,x) \ 1) * (y \ x)) \ z
    ]]></literal>
    <justification jstring="[para(13371(a,1),21864(a,1,2,2))].">
      <j1 rule="para" parents="13371 21864"/>
    </justification>
  </clause>

  <clause id="21866">
    <literal><![CDATA[
      K(x,L((y * T(z,z \ y)) / u,z,z \ y)) = K(x,(z * (y / z)) / (u / z))
    ]]></literal>
    <justification jstring="[hyper(20908,a,21693,a)].">
      <j1 rule="hyper" parents="20908 21693"/>
    </justification>
  </clause>

  <clause id="21867">
    <literal><![CDATA[
      K(x,T(y * (z \ (1 / z)),z) \ u) = K(x,z * (y \ (z * u)))
    ]]></literal>
    <justification jstring="[hyper(15685,a,21709,a),flip(a)].">
      <j1 rule="hyper" parents="15685 21709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21868">
    <literal><![CDATA[
      K(x,(y \ (z * (y \ 1))) \ u) = K(x,y * (z \ (y * u)))
    ]]></literal>
    <justification jstring="[para(1730(a,1),21867(a,1,2,1))].">
      <j1 rule="para" parents="1730 21867"/>
    </justification>
  </clause>

  <clause id="21869">
    <literal><![CDATA[
      (a(x,y,K(z,u)) * w) * v5 = w * (v5 * K(a(x,y,z),u))
    ]]></literal>
    <justification jstring="[hyper(18640,a,21748,a)].">
      <j1 rule="hyper" parents="18640 21748"/>
    </justification>
  </clause>

  <clause id="21871">
    <literal><![CDATA[
      (a(x,y,K(z,u)) * w) * v5 = w * (v5 * a(x,y,K(z,u)))
    ]]></literal>
    <justification jstring="[para(14556(a,2),21869(a,2,2,2))].">
      <j1 rule="para" parents="14556 21869"/>
    </justification>
  </clause>

  <clause id="21873">
    <literal><![CDATA[
      L(x,K(y,z) \ u,K(y,z)) = u \ (u * (x * a(z,x,K(u,y))))
    ]]></literal>
    <justification jstring="[para(21871(a,1),21766(a,2,2))].">
      <j1 rule="para" parents="21871 21766"/>
    </justification>
  </clause>

  <clause id="21874">
    <literal><![CDATA[
      L(x,K(y,z) \ u,K(y,z)) = u \ (T(u,a(z,x,y)) * x)
    ]]></literal>
    <justification jstring="[para(18761(a,1),21873(a,2,2))].">
      <j1 rule="para" parents="18761 21873"/>
    </justification>
  </clause>

  <clause id="21875">
    <literal><![CDATA[
      L(x,K(y,z) \ u,K(y,z)) = K(u,a(z,x,y)) * x
    ]]></literal>
    <justification jstring="[hyper(299,a,5350,a(flip),b,21874,a),flip(a)].">
      <j1 rule="hyper" parents="299 5350 21874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21876">
    <literal><![CDATA[
      L(x,K(y,z) \ u,K(y,z)) = a(u,x,K(y,z)) * x
    ]]></literal>
    <justification jstring="[para(14871(a,2),21875(a,2,1))].">
      <j1 rule="para" parents="14871 21875"/>
    </justification>
  </clause>

  <clause id="21877">
    <literal><![CDATA[
      L(x,K(y,z) * u,K(z,y)) = a(u,x,K(z,y)) * x
    ]]></literal>
    <justification jstring="[para(5426(a,1),21876(a,1,2))].">
      <j1 rule="para" parents="5426 21876"/>
    </justification>
  </clause>

  <clause id="21878">
    <literal><![CDATA[
      T(x,y \ (z * (y \ (T(u,z) \ w)))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,u \ ((y * (z \ y)) \ w)) = v5
    ]]></literal>
    <justification jstring="[para(21823(a,1),21765(a,1))].">
      <j1 rule="para" parents="21823 21765"/>
    </justification>
  </clause>

  <clause id="21879">
    <literal><![CDATA[
      K(x \ (L(x,y,y) * (x \ T(z,x))),u) = K(z / (x * a(y,y,x)),u)
    ]]></literal>
    <justification jstring="[para(14206(a,1),21810(a,1,1,2,2,2))].">
      <j1 rule="para" parents="14206 21810"/>
    </justification>
  </clause>

  <clause id="21881">
    <literal><![CDATA[
      K(x \ (x \ (y * L(x,z,z))),u) = K(y / (x * a(z,z,x)),u)
    ]]></literal>
    <justification jstring="[para(14442(a,1),21879(a,1,1,2))].">
      <j1 rule="para" parents="14442 21879"/>
    </justification>
  </clause>

  <clause id="21882">
    <literal><![CDATA[
      K(x * ((y * y) \ L(y,z,z)),u) = K(x / (y * a(z,z,y)),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,18084,a(flip),b,21881,a)].">
      <j1 rule="hyper" parents="65 18084 21881"/>
    </justification>
  </clause>

  <clause id="21883">
    <literal><![CDATA[
      K(x / (y * a(z,z,y)),u) = K(x * L(1 / y,z,z),u)
    ]]></literal>
    <justification jstring="[para(6518(a,1),21882(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6518 21882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21884">
    <literal><![CDATA[
      K(x / (y * a(z,z,y)),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x * L(y \ 1,z,z),u) = w
    ]]></literal>
    <justification jstring="[para(21883(a,2),7417(a,1))].">
      <j1 rule="para" parents="21883 7417"/>
    </justification>
  </clause>

  <clause id="21885">
    <literal><![CDATA[
      K(x,L((y * T(z,z \ y)) / u,y,z)) = K(x,(z * (y / z)) / (u / z))
    ]]></literal>
    <justification jstring="[hyper(21704,a,21866,a)].">
      <j1 rule="hyper" parents="21704 21866"/>
    </justification>
  </clause>

  <clause id="21886">
    <literal><![CDATA[
      K(x,(y * (z / y)) / (u / y)) = K(x,z / (u / T(y,y \ z)))
    ]]></literal>
    <justification jstring="[hyper(20985,a,21885,a),flip(a)].">
      <j1 rule="hyper" parents="20985 21885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21887">
    <literal><![CDATA[
      K(x,(y * (z / y)) / (u / y)) = K(x,z / (u / T(y,z)))
    ]]></literal>
    <justification jstring="[hyper(299,a,20483,a(flip),b,21886,a),flip(a)].">
      <j1 rule="hyper" parents="299 20483 21886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21888">
    <literal><![CDATA[
      K(x,(y * (z / y)) / (u / y)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(299,a,21739,a(flip),b,21887,a),flip(a)].">
      <j1 rule="hyper" parents="299 21739 21887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21889">
    <literal><![CDATA[
      K(x,T(y,z) / (u / z)) = K(x,z / (u / y))
    ]]></literal>
    <justification jstring="[hyper(65,a,20348,a(flip),b,21888,a)].">
      <j1 rule="hyper" parents="65 20348 21888"/>
    </justification>
  </clause>

  <clause id="21890">
    <literal><![CDATA[
      T(x,T(y,z) / (u / z)) = x * K(x,z / (u / y))
    ]]></literal>
    <justification jstring="[para(21889(a,1),5083(a,2,2))].">
      <j1 rule="para" parents="21889 5083"/>
    </justification>
  </clause>

  <clause id="21891">
    <literal><![CDATA[
      T(x,T(y,z) / (u / z)) = T(x,z / (u / y))
    ]]></literal>
    <justification jstring="[hyper(299,a,5083,a,b,21890,a),flip(a)].">
      <j1 rule="hyper" parents="299 5083 21890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21892">
    <literal><![CDATA[
      T(x,(y \ z) / (u / z)) = T(x,z / (u / (z / y)))
    ]]></literal>
    <justification jstring="[hyper(14670,a,21891,a)].">
      <j1 rule="hyper" parents="14670 21891"/>
    </justification>
  </clause>

  <clause id="21893">
    <literal><![CDATA[
      T(x,y \ (z * (y \ (z \ u)))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ ((y * (z \ y)) \ u)) = w
    ]]></literal>
    <justification jstring="[para(106(a,1),21878(a,1,2,2,2,2,1))].">
      <j1 rule="para" parents="106 21878"/>
    </justification>
  </clause>

  <clause id="21894">
    <literal><![CDATA[
      T(x,(K(y,z) * (u \ 1)) \ (T(w,u \ K(z,y)) \ v5)) = T(x,w \ ((K(z,y) \ (u \ 1)) \ v5))
    ]]></literal>
    <justification jstring="[para(14185(a,1),21799(a,1,2,2,1,2))].">
      <j1 rule="para" parents="14185 21799"/>
    </justification>
  </clause>

  <clause id="21895">
    <literal><![CDATA[
      K((x / y) \ (x \ T(z,x \ (y * z))),u) = K(x \ ((z * ((y \ x) \ z)) / z),u)
    ]]></literal>
    <justification jstring="[para(8415(a,1),21846(a,1,1,2,2))].">
      <j1 rule="para" parents="8415 21846"/>
    </justification>
  </clause>

  <clause id="21896">
    <literal><![CDATA[
      x * (T(x,T(y,y)) \ ((y \ x) \ z)) = ((K(y,x) \ 1) * (y \ x)) \ z
    ]]></literal>
    <justification jstring="[para(10427(a,1),21865(a,1,2))].">
      <j1 rule="para" parents="10427 21865"/>
    </justification>
  </clause>

  <clause id="21897">
    <literal><![CDATA[
      ((K(x,y) \ 1) * (x \ y)) \ z = y * (T(y,x) \ ((x \ y) \ z))
    ]]></literal>
    <justification jstring="[para(106(a,1),21896(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="106 21896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21898">
    <literal><![CDATA[
      ((K(x,y) \ 1) * (x \ y)) \ z = K(x,y) * ((x \ y) \ z)
    ]]></literal>
    <justification jstring="[hyper(299,a,5060,a(flip),b,21897,a),flip(a)].">
      <j1 rule="hyper" parents="299 5060 21897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21899">
    <literal><![CDATA[
      (K(x,y) * (y \ x)) \ z = K(y,x) * ((y \ x) \ z)
    ]]></literal>
    <justification jstring="[para(5197(a,1),21898(a,1,1,1))].">
      <j1 rule="para" parents="5197 21898"/>
    </justification>
  </clause>

  <clause id="21900">
    <literal><![CDATA[
      K(x,y) * ((x \ y) \ z) = (T(x,y) \ y) \ z
    ]]></literal>
    <justification jstring="[para(5383(a,1),21899(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5383 21899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21901">
    <literal><![CDATA[
      T(x,y * (((z \ u) \ w) * K(u,z))) = T(x,y * ((T(z,u) \ u) \ w))
    ]]></literal>
    <justification jstring="[para(21900(a,1),19264(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="21900 19264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21902">
    <literal><![CDATA[
      T(x,y * ((T(z,u) \ u) \ w)) = T(x,y * ((u / z) \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,19390,a(flip),b,21901,a),flip(a)].">
      <j1 rule="hyper" parents="65 19390 21901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21903">
    <literal><![CDATA[
      T(x,y * ((z \ T(u,z)) \ w)) = T(x,y * ((u / z) \ w))
    ]]></literal>
    <justification jstring="[para(4396(a,1),21902(a,1,2,2,1))].">
      <j1 rule="para" parents="4396 21902"/>
    </justification>
  </clause>

  <clause id="21904">
    <literal><![CDATA[
      T(x,y * (((((z \ u) \ 1) \ 1) \ T(z,((z \ u) \ 1) \ 1)) \ w)) = T(x,y * ((z * (u \ z)) \ w))
    ]]></literal>
    <justification jstring="[para(17055(a,1),21903(a,2,2,2,1))].">
      <j1 rule="para" parents="17055 21903"/>
    </justification>
  </clause>

  <clause id="21905">
    <literal><![CDATA[
      T(x,y * (((z \ 1) \ T(L(u,z,z),z \ 1)) \ w)) = T(x,y * (L(u / (1 / z),z,z) \ w))
    ]]></literal>
    <justification jstring="[para(19909(a,2),21903(a,2,2,2,1))].">
      <j1 rule="para" parents="19909 21903"/>
    </justification>
  </clause>

  <clause id="21906">
    <literal><![CDATA[
      K((x / y) \ (x \ T(z,x * (y * z))),u) = K(x \ ((z * ((y \ x) \ z)) / z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,17530,a(flip),b,21895,a)].">
      <j1 rule="hyper" parents="65 17530 21895"/>
    </justification>
  </clause>

  <clause id="21907">
    <literal><![CDATA[
      K(x \ ((y \ x) \ T(z,x * (y * z))),u) = K(x \ ((z * ((y \ x) \ z)) / z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,21841,a(flip),b,21906,a)].">
      <j1 rule="hyper" parents="65 21841 21906"/>
    </justification>
  </clause>

  <clause id="21908">
    <literal><![CDATA[
      K(x \ ((y \ x) \ T(z,x * (y * z))),u) = K(x \ T((y \ x) \ z,z),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,16050,a(flip),b,21907,a),flip(a)].">
      <j1 rule="hyper" parents="299 16050 21907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21909">
    <literal><![CDATA[
      K(x \ ((y \ x) \ T(z,x * (y * z))),u) = K(x \ (z / (y \ x)),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,17496,a(flip),b,21908,a),flip(a)].">
      <j1 rule="hyper" parents="299 17496 21908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21910">
    <literal><![CDATA[
      K(x,(y \ 1) \ ((z \ (y \ 1)) * (y * u))) = K(x,(z * (y \ 1)) \ L(u,y,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,6456,a(flip),b,21756,a),flip(a)].">
      <j1 rule="hyper" parents="65 6456 21756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21911">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ L(u,z,z)) = K(x,z \ ((y \ z) * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,20632,a(flip),b,21910,a),flip(a)].">
      <j1 rule="hyper" parents="65 20632 21910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21912">
    <literal><![CDATA[
      x * K(x,y \ ((z \ y) * (y * u))) = T(x,(z * (y \ 1)) \ L(u,y,y))
    ]]></literal>
    <justification jstring="[para(21911(a,1),5083(a,2,2)),flip(a)].">
      <j1 rule="para" parents="21911 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21913">
    <literal><![CDATA[
      T(x,(y * (z \ 1)) \ L(u,z,z)) = T(x,z \ ((y \ z) * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(5087,a,21912,a),flip(a)].">
      <j1 rule="hyper" parents="5087 21912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21914">
    <literal><![CDATA[
      T(x,(y * (z \ 1)) \ L(u,z,z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(y / z) \ u) = w
    ]]></literal>
    <justification jstring="[para(21913(a,2),21783(a,1))].">
      <j1 rule="para" parents="21913 21783"/>
    </justification>
  </clause>

  <clause id="21915">
    <literal><![CDATA[
      K(x,(y / z) \ ((z \ u) * ((1 / y) \ y))) = K(x,z \ T(((1 / y) \ z) * u,y * y))
    ]]></literal>
    <justification jstring="[para(3090(a,1),21772(a,1,2,2))].">
      <j1 rule="para" parents="3090 21772"/>
    </justification>
  </clause>

  <clause id="21916">
    <literal><![CDATA[
      K((1 / x) \ (((1 / x) / (y * (z * z))) * u),w) = K(z \ (z \ ((x * y) \ (x * u))),w)
    ]]></literal>
    <justification jstring="[hyper(299,a,14182,a(flip),b,21807,a),flip(a)].">
      <j1 rule="hyper" parents="299 14182 21807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21917">
    <literal><![CDATA[
      K(x,y \ T(((1 / z) \ y) * u,z * z)) = K(x,((z / y) \ (y \ u)) * ((1 / z) \ z))
    ]]></literal>
    <justification jstring="[para(3090(a,1),21915(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3090 21915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21918">
    <literal><![CDATA[
      K(x \ (x \ ((y * z) \ (y * u))),w) = K(y \ ((y / (z * (x * x))) * u),w)
    ]]></literal>
    <justification jstring="[hyper(21808,a,21916,a),flip(a)].">
      <j1 rule="hyper" parents="21808 21916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21919">
    <literal><![CDATA[
      K(x \ (x \ ((x * y) \ (x * z))),u) = K(x \ (((x \ 1) / y) * z),u)
    ]]></literal>
    <justification jstring="[para(749(a,1),21918(a,2,1,2,1))].">
      <j1 rule="para" parents="749 21918"/>
    </justification>
  </clause>

  <clause id="21920">
    <literal><![CDATA[
      K((x * y) \ ((x \ 1) * z),u) = K(x \ (((x \ 1) / y) * z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,17905,a(flip),b,21919,a)].">
      <j1 rule="hyper" parents="65 17905 21919"/>
    </justification>
  </clause>

  <clause id="21921">
    <literal><![CDATA[
      K(x \ (x \ (y \ z)),L(u,y,x)) = K(x \ (((x \ 1) / y) * z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,17906,a,b,21920,a)].">
      <j1 rule="hyper" parents="65 17906 21920"/>
    </justification>
  </clause>

  <clause id="21922">
    <literal><![CDATA[
      K(((x \ 1) \ y) \ (x \ z),u) = K(x \ (((x \ 1) / y) * z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,17903,a(flip),b,21921,a)].">
      <j1 rule="hyper" parents="65 17903 21921"/>
    </justification>
  </clause>

  <clause id="21923">
    <literal><![CDATA[
      K(x,y \ T(((1 / z) \ y) * u,z * z)) = K(x,((z / y) \ (y \ u)) * (z * z))
    ]]></literal>
    <justification jstring="[hyper(299,a,6040,a(flip),b,21917,a),flip(a)].">
      <j1 rule="hyper" parents="299 6040 21917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21924">
    <literal><![CDATA[
      K(x,((y / z) \ (z \ u)) * (y * y)) = K(x,z \ (((1 / y) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(17932,a,21923,a),flip(a)].">
      <j1 rule="hyper" parents="17932 21923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21926">
    <literal><![CDATA[
      K(x,((y / z) \ (z \ u)) * (y * y)) = K(x,z \ (((y \ 1) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(299,a,20605,a(flip),b,21924,a),flip(a)].">
      <j1 rule="hyper" parents="299 20605 21924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21927">
    <literal><![CDATA[
      T(x,R(y,z,y) \ (T(u,(z * y) * z) \ w)) = T(x,u \ ((z \ T(y * z,y)) \ w))
    ]]></literal>
    <justification jstring="[para(19245(a,1),21798(a,1,2,2,1))].">
      <j1 rule="para" parents="19245 21798"/>
    </justification>
  </clause>

  <clause id="21928">
    <literal><![CDATA[
      T(x,R(y,z,y) \ (T(u,z * (y * z)) \ w)) = T(x,u \ ((z \ T(y * z,y)) \ w))
    ]]></literal>
    <justification jstring="[para(13693(a,1),21927(a,1,2,2,1))].">
      <j1 rule="para" parents="13693 21927"/>
    </justification>
  </clause>

  <clause id="21929">
    <literal><![CDATA[
      T(x,y \ (T(z,u * (y * u)) \ w)) = T(x,z \ ((u \ T(y * u,y)) \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,13697,a(flip),b,21928,a)].">
      <j1 rule="hyper" parents="65 13697 21928"/>
    </justification>
  </clause>

  <clause id="21930">
    <literal><![CDATA[
      T(x,y \ (T(z,u * (y * u)) \ w)) = T(x,z \ (y \ w))
    ]]></literal>
    <justification jstring="[hyper(299,a,13841,a(flip),b,21929,a),flip(a)].">
      <j1 rule="hyper" parents="299 13841 21929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21933">
    <literal><![CDATA[
      T(x,T(y,z) \ (T(u,z * (z * y)) \ w)) = T(x,u \ (T(y,z) \ w))
    ]]></literal>
    <justification jstring="[para(15889(a,1),21930(a,1,2,2,1))].">
      <j1 rule="para" parents="15889 21930"/>
    </justification>
  </clause>

  <clause id="21934">
    <literal><![CDATA[
      K(x,y) * (K(x,y) * (z \ (K(y,x) * u))) = z \ (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(6930(a,1),21860(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="6930 21860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21935">
    <literal><![CDATA[
      x * (T(T(x,y),y) \ (z \ (K(x,y) * u))) = z \ (K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,6199,a(flip),b,21934,a)].">
      <j1 rule="hyper" parents="65 6199 21934"/>
    </justification>
  </clause>

  <clause id="21937">
    <literal><![CDATA[
      ((x / y) * K(z,(1 / (u / x)) \ x)) * y = x * K(z,(y \ x) * (T(u / x,u) * y))
    ]]></literal>
    <justification jstring="[para(21372(a,1),21659(a,1,2)),flip(a)].">
      <j1 rule="para" parents="21372 21659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21938">
    <literal><![CDATA[
      ((x / y) * K(z,(1 / (u / x)) \ x)) * y = x * K(z,(y \ x) * ((x \ u) * y))
    ]]></literal>
    <justification jstring="[para(13849(a,1),21937(a,2,2))].">
      <j1 rule="para" parents="13849 21937"/>
    </justification>
  </clause>

  <clause id="21939">
    <literal><![CDATA[
      ((x / y) * K(z,(1 / (u / x)) \ x)) * y = x * K(z,(y * x) * ((x \ u) / y))
    ]]></literal>
    <justification jstring="[para(21272(a,1),21938(a,2,2))].">
      <j1 rule="para" parents="21272 21938"/>
    </justification>
  </clause>

  <clause id="21940">
    <literal><![CDATA[
      ((x / y) * K(z,(u / x) * x)) * y = x * K(z,(y * x) * ((x \ u) / y))
    ]]></literal>
    <justification jstring="[para(14271(a,1),21939(a,1,1,2))].">
      <j1 rule="para" parents="14271 21939"/>
    </justification>
  </clause>

  <clause id="21941">
    <literal><![CDATA[
      x * K(y,(z * x) * ((x \ u) / z)) = ((x / z) * K(y,u)) * z
    ]]></literal>
    <justification jstring="[para(12(a,1),21940(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 21940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21942">
    <literal><![CDATA[
      (x * y) * K(z,(y * (x * y)) * (((x * y) \ u) / y)) = (x * K(z,u)) * y
    ]]></literal>
    <justification jstring="[para(11(a,1),21941(a,2,1,1))].">
      <j1 rule="para" parents="11 21941"/>
    </justification>
  </clause>

  <clause id="21943">
    <literal><![CDATA[
      (x * y) * K(z,T(x,y) * (((x * y) \ u) * y)) = (x * K(z,u)) * y
    ]]></literal>
    <justification jstring="[para(21273(a,1),21942(a,1,2))].">
      <j1 rule="para" parents="21273 21942"/>
    </justification>
  </clause>

  <clause id="21944">
    <literal><![CDATA[
      (x * y) * K(z,x * (((y * x) \ u) * y)) = (x * K(z,u)) * y
    ]]></literal>
    <justification jstring="[para(11664(a,1),21943(a,1,2,2))].">
      <j1 rule="para" parents="11664 21943"/>
    </justification>
  </clause>

  <clause id="21945">
    <literal><![CDATA[
      ((x \ 1) * ((x * x) * y)) * K(z,(x \ 1) * (((((x * x) * y) * (x \ 1)) \ u) * ((x * x) * y))) = (x * T(K(z,u),x * x)) * y
    ]]></literal>
    <justification jstring="[hyper(299,a,1045,a(flip),b,21944,a),flip(a)].">
      <j1 rule="hyper" parents="299 1045 21944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21946">
    <literal><![CDATA[
      K(x,(y * y) * ((z \ (y \ 1)) \ ((y * y) \ u))) = K(x,(z \ y) \ ((y \ (y \ 1)) \ u))
    ]]></literal>
    <justification jstring="[para(740(a,1),21730(a,1,2))].">
      <j1 rule="para" parents="740 21730"/>
    </justification>
  </clause>

  <clause id="21947">
    <literal><![CDATA[
      K(x,T(y \ (z \ 1),z \ (z \ 1)) \ u) = K(x,(y \ z) \ ((z \ (z \ 1)) \ u))
    ]]></literal>
    <justification jstring="[para(11733(a,1),21946(a,1,2))].">
      <j1 rule="para" parents="11733 21946"/>
    </justification>
  </clause>

  <clause id="21948">
    <literal><![CDATA[
      K(x,T(y \ (z \ 1),z * (z \ 1)) \ u) = K(x,(y \ z) \ ((z \ (z \ 1)) \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,17937,a(flip),b,21947,a)].">
      <j1 rule="hyper" parents="65 17937 21947"/>
    </justification>
  </clause>

  <clause id="21949">
    <literal><![CDATA[
      K(x,(y \ z) \ ((z \ (z \ 1)) \ u)) = K(x,T(y \ (z \ 1),1) \ u)
    ]]></literal>
    <justification jstring="[para(10(a,1),21948(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="10 21948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21951">
    <literal><![CDATA[
      K(x,(y \ z) \ ((z \ (z \ 1)) \ u)) = K(x,(y \ (z \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(193(a,1),21949(a,2,2,1))].">
      <j1 rule="para" parents="193 21949"/>
    </justification>
  </clause>

  <clause id="21952">
    <literal><![CDATA[
      K(x,(y \ z) \ ((z * z) * u)) = K(x,(y \ (z \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(740(a,1),21951(a,1,2,2))].">
      <j1 rule="para" parents="740 21951"/>
    </justification>
  </clause>

  <clause id="21953">
    <literal><![CDATA[
      K(x,(L(y,z,u) \ (y \ 1)) \ w) = K(x,L(y,z,u) * ((1 / y) \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,15660,a(flip),b,21952,a),flip(a)].">
      <j1 rule="hyper" parents="65 15660 21952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21954">
    <literal><![CDATA[
      K(x,L(y,z,u) * ((1 / y) \ w)) = K(x,y * (L(y,z,u) * w))
    ]]></literal>
    <justification jstring="[hyper(18038,a,21953,a),flip(a)].">
      <j1 rule="hyper" parents="18038 21953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21955">
    <literal><![CDATA[
      K(x,(y * L(y,z,u)) * w) = K(x,y * (L(y,z,u) * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,15691,a(flip),b,21954,a)].">
      <j1 rule="hyper" parents="65 15691 21954"/>
    </justification>
  </clause>

  <clause id="21956">
    <literal><![CDATA[
      K(x,a(y,y,z) * (u * (a(y,y,z) \ z))) = K(x,z * (L(z,y,y) * (u / L(z,y,y))))
    ]]></literal>
    <justification jstring="[hyper(65,a,21532,a(flip),b,21955,a)].">
      <j1 rule="hyper" parents="65 21532 21955"/>
    </justification>
  </clause>

  <clause id="21957">
    <literal><![CDATA[
      K(x,a(y,y,z) * (u * (a(y,y,z) \ z))) = K(x,z * T(u,L(z,y,y)))
    ]]></literal>
    <justification jstring="[hyper(299,a,16866,a(flip),b,21956,a),flip(a)].">
      <j1 rule="hyper" parents="299 16866 21956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21958">
    <literal><![CDATA[
      K(x,a(y,y,z) * (u * (a(y,y,z) \ z))) = K(x,z * T(u,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,20897,a(flip),b,21957,a),flip(a)].">
      <j1 rule="hyper" parents="299 20897 21957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21960">
    <literal><![CDATA[
      K(x,a(y,y,z) * (u * (a(y,y,z) \ z))) = K(x,u * z)
    ]]></literal>
    <justification jstring="[para(107(a,1),21958(a,2,2))].">
      <j1 rule="para" parents="107 21958"/>
    </justification>
  </clause>

  <clause id="21961">
    <literal><![CDATA[
      K(x,a(y,y,z) * (u * L(z,y,y))) = K(x,u * z)
    ]]></literal>
    <justification jstring="[para(6374(a,1),21960(a,1,2,2,2))].">
      <j1 rule="para" parents="6374 21960"/>
    </justification>
  </clause>

  <clause id="21962">
    <literal><![CDATA[
      T(x,a(y,y,z) * (u * L(z,y,y))) = x * K(x,u * z)
    ]]></literal>
    <justification jstring="[para(21961(a,1),5083(a,2,2))].">
      <j1 rule="para" parents="21961 5083"/>
    </justification>
  </clause>

  <clause id="21963">
    <literal><![CDATA[
      T(x,a(y,y,z) * (u * L(z,y,y))) = T(x,u * z)
    ]]></literal>
    <justification jstring="[hyper(299,a,5083,a,b,21962,a),flip(a)].">
      <j1 rule="hyper" parents="299 5083 21962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21964">
    <literal><![CDATA[
      T(x,(y \ (z \ ((1 / z) \ y))) * (u * L(w,v5,v5))) = T(x,u * w)
    ]]></literal>
    <justification jstring="[hyper(65,a,21073,a(flip),b,21963,a)].">
      <j1 rule="hyper" parents="65 21073 21963"/>
    </justification>
  </clause>

  <clause id="21965">
    <literal><![CDATA[
      T(x,a(y,y,y \ z) * (u * ((1 / y) * z))) = T(x,u * (y \ z))
    ]]></literal>
    <justification jstring="[para(511(a,1),21963(a,1,2,2,2))].">
      <j1 rule="para" parents="511 21963"/>
    </justification>
  </clause>

  <clause id="21966">
    <literal><![CDATA[
      T(x,a(y,y,(1 / T(y,y)) \ z) * (u * ((T(y,y) * (1 / y)) \ (y * z)))) = T(x,u * ((1 / T(y,y)) \ z))
    ]]></literal>
    <justification jstring="[para(11628(a,2),21963(a,1,2,2,2))].">
      <j1 rule="para" parents="11628 21963"/>
    </justification>
  </clause>

  <clause id="21968">
    <literal><![CDATA[
      T(x,(y \ (z \ ((1 / z) \ y))) * (u * ((w * w) \ v5))) = T(x,u * (w \ (w \ v5)))
    ]]></literal>
    <justification jstring="[para(281(a,1),21964(a,1,2,2,2))].">
      <j1 rule="para" parents="281 21964"/>
    </justification>
  </clause>

  <clause id="21969">
    <literal><![CDATA[
      T(x,a(y,y,y \ z) * (u * ((y \ 1) * z))) = T(x,u * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,15097,a(flip),b,21965,a)].">
      <j1 rule="hyper" parents="65 15097 21965"/>
    </justification>
  </clause>

  <clause id="21970">
    <literal><![CDATA[
      T(x,(y * ((y * ((z \ 1) * u)) / y)) * T(a(z,z,z \ u),((z \ 1) * u) * y)) = T(x,T(y,(z \ 1) * u) * (z \ u))
    ]]></literal>
    <justification jstring="[para(13283(a,2),21969(a,1,2))].">
      <j1 rule="para" parents="13283 21969"/>
    </justification>
  </clause>

  <clause id="21971">
    <literal><![CDATA[
      T(x,a(y,z,z) * (u * ((w * w) \ v5))) = T(x,u * (w \ (w \ v5)))
    ]]></literal>
    <justification jstring="[hyper(21069,a,21968,a)].">
      <j1 rule="hyper" parents="21069 21968"/>
    </justification>
  </clause>

  <clause id="21972">
    <literal><![CDATA[
      T(x,y * ((z * z) \ u)) = T(x,y * (z \ (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(21038,a,21971,a)].">
      <j1 rule="hyper" parents="21038 21971"/>
    </justification>
  </clause>

  <clause id="21973">
    <literal><![CDATA[
      T(T(x,y * (z \ (z \ u))),w) = T(T(x,y * u),z \ (z \ w))
    ]]></literal>
    <justification jstring="[para(21972(a,1),17440(a,1,1))].">
      <j1 rule="para" parents="21972 17440"/>
    </justification>
  </clause>

  <clause id="21974">
    <literal><![CDATA[
      T(x,(K(y,z) * (u \ 1)) \ (T(w,u * K(z,y)) \ v5)) = T(x,w \ ((K(z,y) \ (u \ 1)) \ v5))
    ]]></literal>
    <justification jstring="[hyper(19285,a,21894,a)].">
      <j1 rule="hyper" parents="19285 21894"/>
    </justification>
  </clause>

  <clause id="21975">
    <literal><![CDATA[
      T(x,y * (((z \ 1) \ (z * (u * (z \ 1)))) \ w)) = T(x,y * (L(u / (1 / z),z,z) \ w))
    ]]></literal>
    <justification jstring="[para(1733(a,1),21905(a,1,2,2,1,2))].">
      <j1 rule="para" parents="1733 21905"/>
    </justification>
  </clause>

  <clause id="21976">
    <literal><![CDATA[
      T(x,y * (((z * z) * (u * (z \ 1))) \ w)) = T(x,y * (L(u / (1 / z),z,z) \ w))
    ]]></literal>
    <justification jstring="[para(730(a,1),21975(a,1,2,2,1))].">
      <j1 rule="para" parents="730 21975"/>
    </justification>
  </clause>

  <clause id="21977">
    <literal><![CDATA[
      T(x,y * ((z * (u \ 1)) \ ((u * u) \ w))) = T(x,y * (L(z / (1 / u),u,u) \ w))
    ]]></literal>
    <justification jstring="[para(420(a,1),21976(a,1,2,2))].">
      <j1 rule="para" parents="420 21976"/>
    </justification>
  </clause>

  <clause id="21978">
    <literal><![CDATA[
      T(x,y * (L(z / (1 / u),u,u) \ w)) = T(x,y * ((z * u) \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,17454,a(flip),b,21977,a),flip(a)].">
      <j1 rule="hyper" parents="65 17454 21977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21979">
    <literal><![CDATA[
      T(x,y * (((((z \ u) \ 1) \ 1) \ T(z,z \ u)) \ w)) = T(x,y * ((z * (u \ z)) \ w))
    ]]></literal>
    <justification jstring="[para(3739(a,1),21904(a,1,2,2,1,2))].">
      <j1 rule="para" parents="3739 21904"/>
    </justification>
  </clause>

  <clause id="21980">
    <literal><![CDATA[
      T(x,y * (((z \ u) \ T(z,z \ u)) \ w)) = T(x,y * ((z * (u \ z)) \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,4844,a(flip),b,21979,a)].">
      <j1 rule="hyper" parents="65 4844 21979"/>
    </justification>
  </clause>

  <clause id="21981">
    <literal><![CDATA[
      T(x,y * ((z / (z \ u)) \ w)) = T(x,y * ((z * (u \ z)) \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,21903,a(flip),b,21980,a)].">
      <j1 rule="hyper" parents="65 21903 21980"/>
    </justification>
  </clause>

  <clause id="21982">
    <literal><![CDATA[
      T(x,(y \ 1) \ (z \ T(a(y,y,y) * u,y \ 1))) = T(x,((y \ 1) * (z * (y \ 1))) \ (u * (y \ 1)))
    ]]></literal>
    <justification jstring="[hyper(299,a,17546,a(flip),b,21779,a),flip(a)].">
      <j1 rule="hyper" parents="299 17546 21779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21983">
    <literal><![CDATA[
      T(x * (y \ ((1 / y) \ z)),K(y \ ((1 / y) \ z),z)) = (y \ ((1 / y) \ z)) * T(x,y \ (y * z))
    ]]></literal>
    <justification jstring="[para(74(a,1),21856(a,2,2,2,2,1))].">
      <j1 rule="para" parents="74 21856"/>
    </justification>
  </clause>

  <clause id="21984">
    <literal><![CDATA[
      T(x * (y \ ((1 / y) \ z)),K(y \ ((1 / y) \ z),z)) = (y \ ((1 / y) \ z)) * T(x,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),21983(a,2,2,2))].">
      <j1 rule="para" parents="9 21983"/>
    </justification>
  </clause>

  <clause id="21985">
    <literal><![CDATA[
      T(x * (y \ ((1 / y) \ z)),K(z,z)) = (y \ ((1 / y) \ z)) * T(x,z)
    ]]></literal>
    <justification jstring="[para(14256(a,1),21984(a,1,2))].">
      <j1 rule="para" parents="14256 21984"/>
    </justification>
  </clause>

  <clause id="21986">
    <literal><![CDATA[
      T(x * (y \ ((1 / y) \ z)),1) = (y \ ((1 / y) \ z)) * T(x,z)
    ]]></literal>
    <justification jstring="[para(168(a,1),21985(a,1,2))].">
      <j1 rule="para" parents="168 21985"/>
    </justification>
  </clause>

  <clause id="21988">
    <literal><![CDATA[
      (x \ ((1 / x) \ y)) * T(z,y) = z * (x \ ((1 / x) \ y))
    ]]></literal>
    <justification jstring="[hyper(197,a,21986,a),flip(a)].">
      <j1 rule="hyper" parents="197 21986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21990">
    <literal><![CDATA[
      T(x,a(y,y,(1 / y) \ z) * (u * ((T(y,y) * (1 / y)) \ (y * z)))) = T(x,u * ((1 / T(y,y)) \ z))
    ]]></literal>
    <justification jstring="[para(106(a,1),21966(a,1,2,1,3,1,2))].">
      <j1 rule="para" parents="106 21966"/>
    </justification>
  </clause>

  <clause id="21991">
    <literal><![CDATA[
      T(x,a(y,y,y \ z) * (u * ((T(y,y) * (1 / y)) \ (y * z)))) = T(x,u * ((1 / T(y,y)) \ z))
    ]]></literal>
    <justification jstring="[para(2361(a,1),21990(a,1,2,1))].">
      <j1 rule="para" parents="2361 21990"/>
    </justification>
  </clause>

  <clause id="21992">
    <literal><![CDATA[
      T(x,a(y,y,y \ z) * (u * ((y * (1 / y)) \ (y * z)))) = T(x,u * ((1 / T(y,y)) \ z))
    ]]></literal>
    <justification jstring="[para(106(a,1),21991(a,1,2,2,2,1,1))].">
      <j1 rule="para" parents="106 21991"/>
    </justification>
  </clause>

  <clause id="21993">
    <literal><![CDATA[
      T(x,a(y,y,y \ z) * (u * (K(y,y \ 1) \ (y * z)))) = T(x,u * ((1 / T(y,y)) \ z))
    ]]></literal>
    <justification jstring="[para(2585(a,2),21992(a,1,2,2,2,1))].">
      <j1 rule="para" parents="2585 21992"/>
    </justification>
  </clause>

  <clause id="21994">
    <literal><![CDATA[
      T(x,a(y,y,y \ z) * (u * (K(y \ 1,y) * (y * z)))) = T(x,u * ((1 / T(y,y)) \ z))
    ]]></literal>
    <justification jstring="[para(2741(a,1),21993(a,1,2,2,2))].">
      <j1 rule="para" parents="2741 21993"/>
    </justification>
  </clause>

  <clause id="21995">
    <literal><![CDATA[
      T(x,a(y,y,y \ z) * (u * (K(y,y \ 1) * (y * z)))) = T(x,u * ((1 / T(y,y)) \ z))
    ]]></literal>
    <justification jstring="[para(2596(a,1),21994(a,1,2,2,2,1))].">
      <j1 rule="para" parents="2596 21994"/>
    </justification>
  </clause>

  <clause id="21996">
    <literal><![CDATA[
      T(x,a(y,y,y \ z) * (u * (T(y,y \ 1) * z))) = T(x,u * ((1 / T(y,y)) \ z))
    ]]></literal>
    <justification jstring="[para(2724(a,1),21995(a,1,2,2,2))].">
      <j1 rule="para" parents="2724 21995"/>
    </justification>
  </clause>

  <clause id="21997">
    <literal><![CDATA[
      T(x,a(y,y,y \ z) * (u * (T(y,1) * z))) = T(x,u * ((1 / T(y,y)) \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,19492,a(flip),b,21996,a)].">
      <j1 rule="hyper" parents="65 19492 21996"/>
    </justification>
  </clause>

  <clause id="21998">
    <literal><![CDATA[
      T(x,a(y,y,y \ z) * (u * (y * z))) = T(x,u * ((1 / T(y,y)) \ z))
    ]]></literal>
    <justification jstring="[para(193(a,1),21997(a,1,2,2,2,1))].">
      <j1 rule="para" parents="193 21997"/>
    </justification>
  </clause>

  <clause id="21999">
    <literal><![CDATA[
      T(x,a(y,y,y \ z) * (u * (y * z))) = T(x,u * ((1 / y) \ z))
    ]]></literal>
    <justification jstring="[para(106(a,1),21998(a,2,2,2,1,2))].">
      <j1 rule="para" parents="106 21998"/>
    </justification>
  </clause>

  <clause id="22000">
    <literal><![CDATA[
      T(x,a(y,y,y \ z) * (u * (y * z))) = T(x,u * ((y \ 1) \ z))
    ]]></literal>
    <justification jstring="[hyper(299,a,3884,a(flip),b,21999,a),flip(a)].">
      <j1 rule="hyper" parents="299 3884 21999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22001">
    <literal><![CDATA[
      T(x,a(y,y,T(z * (1 / y),y)) * (u * (y * R(z,y,y)))) = T(x,u * ((y \ 1) \ R(z,y,y)))
    ]]></literal>
    <justification jstring="[para(1755(a,2),22000(a,1,2,1,3))].">
      <j1 rule="para" parents="1755 22000"/>
    </justification>
  </clause>

  <clause id="22002">
    <literal><![CDATA[
      T(x,a(y,y,z * (1 / y)) * (u * (y * R(z,y,y)))) = T(x,u * ((y \ 1) \ R(z,y,y)))
    ]]></literal>
    <justification jstring="[para(14575(a,1),22001(a,1,2,1))].">
      <j1 rule="para" parents="14575 22001"/>
    </justification>
  </clause>

  <clause id="22004">
    <literal><![CDATA[
      T(x,a(y,y,z * y) * (u * (y * R(z,y,y)))) = T(x,u * ((y \ 1) \ R(z,y,y)))
    ]]></literal>
    <justification jstring="[para(14851(a,1),22002(a,1,2,1))].">
      <j1 rule="para" parents="14851 22002"/>
    </justification>
  </clause>

  <clause id="22005">
    <literal><![CDATA[
      T(x,a(y,y,z * y) * (u * (y * L(z,y,y)))) = T(x,u * ((y \ 1) \ R(z,y,y)))
    ]]></literal>
    <justification jstring="[hyper(65,a,19847,a(flip),b,22004,a)].">
      <j1 rule="hyper" parents="65 19847 22004"/>
    </justification>
  </clause>

  <clause id="22006">
    <literal><![CDATA[
      T(x,a(y,y,z * y) * (u * (y * L(z,y,y)))) = T(x,u * T(z * y,y \ 1))
    ]]></literal>
    <justification jstring="[para(1250(a,1),22005(a,2,2,2))].">
      <j1 rule="para" parents="1250 22005"/>
    </justification>
  </clause>

  <clause id="22007">
    <literal><![CDATA[
      T(x,a(y,y,z * y) * (u * (y * L(z,y,y)))) = T(x,u * T(z * y,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,17434,a(flip),b,22006,a),flip(a)].">
      <j1 rule="hyper" parents="299 17434 22006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22008">
    <literal><![CDATA[
      T(x,a(y,y,z * y) * (u * (y * L(z,y,y)))) = T(x,u * (y * z))
    ]]></literal>
    <justification jstring="[hyper(299,a,15906,a(flip),b,22007,a),flip(a)].">
      <j1 rule="hyper" parents="299 15906 22007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22009">
    <literal><![CDATA[
      T(x,(y * (z * L(u,z,z))) * a(w,w,v5)) = T(x,y * (z * u))
    ]]></literal>
    <justification jstring="[hyper(21068,a,22008,a)].">
      <j1 rule="hyper" parents="21068 22008"/>
    </justification>
  </clause>

  <clause id="22010">
    <literal><![CDATA[
      T(x,y * (z * L(u,z,z))) = T(x,y * (z * u))
    ]]></literal>
    <justification jstring="[hyper(21035,a,22009,a)].">
      <j1 rule="hyper" parents="21035 22009"/>
    </justification>
  </clause>

  <clause id="22012">
    <literal><![CDATA[
      K(x,L(y * (z \ (z \ u)),(z \ 1) \ 1,u / z)) = K(x,((z \ 1) \ 1) * ((((z \ 1) \ 1) \ y) * (z \ (z \ u))))
    ]]></literal>
    <justification jstring="[para(18753(a,1),21658(a,1,2))].">
      <j1 rule="para" parents="18753 21658"/>
    </justification>
  </clause>

  <clause id="22013">
    <literal><![CDATA[
      K(x,L(y * (z \ (z \ u)),z,u / z)) = K(x,((z \ 1) \ 1) * ((((z \ 1) \ 1) \ y) * (z \ (z \ u))))
    ]]></literal>
    <justification jstring="[para(2529(a,1),22012(a,1,2))].">
      <j1 rule="para" parents="2529 22012"/>
    </justification>
  </clause>

  <clause id="22014">
    <literal><![CDATA[
      K(x,L(y * (z \ (z \ u)),z,z * u)) = K(x,((z \ 1) \ 1) * ((((z \ 1) \ 1) \ y) * (z \ (z \ u))))
    ]]></literal>
    <justification jstring="[hyper(19581,a,22013,a)].">
      <j1 rule="hyper" parents="19581 22013"/>
    </justification>
  </clause>

  <clause id="22015">
    <literal><![CDATA[
      K(x,((y \ 1) \ 1) * ((((y \ 1) \ 1) \ z) * (y \ (y \ u)))) = K(x,(z * (u / y)) / y)
    ]]></literal>
    <justification jstring="[hyper(65,a,21668,a(flip),b,22014,a),flip(a)].">
      <j1 rule="hyper" parents="65 21668 22014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22016">
    <literal><![CDATA[
      K(x,(y \ 1) * (((y \ 1) \ z) * (y \ (y \ u)))) = K(x,(z * (u / y)) / y)
    ]]></literal>
    <justification jstring="[para(1758(a,1),22015(a,1,2))].">
      <j1 rule="para" parents="1758 22015"/>
    </justification>
  </clause>

  <clause id="22017">
    <literal><![CDATA[
      K(x,y * ((y \ z) * (y \ (y \ u)))) = K(x,(z * (u / y)) / y)
    ]]></literal>
    <justification jstring="[para(1758(a,1),22016(a,1,2))].">
      <j1 rule="para" parents="1758 22016"/>
    </justification>
  </clause>

  <clause id="22018">
    <literal><![CDATA[
      K(x,(y * (z / u)) / u) = K(x,u \ ((u \ y) * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,21318,a(flip),b,22017,a),flip(a)].">
      <j1 rule="hyper" parents="65 21318 22017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22019">
    <literal><![CDATA[
      K(x,L(y * (z \ (z \ u)),z,z * u)) = K(x,z \ ((z \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,21668,a,b,22018,a)].">
      <j1 rule="hyper" parents="65 21668 22018"/>
    </justification>
  </clause>

  <clause id="22020">
    <literal><![CDATA[
      K(x,L(y * (z \ (z \ u)),u,z)) = K(x,z \ ((z \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(21731,a,22019,a)].">
      <j1 rule="hyper" parents="21731 22019"/>
    </justification>
  </clause>

  <clause id="22021">
    <literal><![CDATA[
      K(x,y \ ((y \ z) * u)) = K(x,(z / y) * (y \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,21627,a(flip),b,22020,a),flip(a)].">
      <j1 rule="hyper" parents="65 21627 22020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22022">
    <literal><![CDATA[
      K(x,((y * z) / y) * (y \ u)) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[para(9(a,1),22021(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="9 22021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22023">
    <literal><![CDATA[
      K(x,T(y,z) * (z \ u)) = K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[hyper(19099,a,22022,a)].">
      <j1 rule="hyper" parents="19099 22022"/>
    </justification>
  </clause>

  <clause id="22024">
    <literal><![CDATA[
      K(x,T(y,z) / (u \ z)) = K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,21645,a,b,22023,a)].">
      <j1 rule="hyper" parents="65 21645 22023"/>
    </justification>
  </clause>

  <clause id="22025">
    <literal><![CDATA[
      K(x,y \ (((z * (y \ 1)) \ u) * z)) = K(x,T(u,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,21385,a(flip),b,22023,a),flip(a)].">
      <j1 rule="hyper" parents="65 21385 22023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22026">
    <literal><![CDATA[
      K(x,y \ (z * (y / u))) = K(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[para(79(a,1),22024(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="79 22024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22027">
    <literal><![CDATA[
      T(x,(y * ((y * ((z \ 1) * u)) / y)) * a(z,z,z \ u)) = T(x,T(y,(z \ 1) * u) * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(18888,a,21970,a)].">
      <j1 rule="hyper" parents="18888 21970"/>
    </justification>
  </clause>

  <clause id="22029">
    <literal><![CDATA[
      T(x,T(y * ((z \ 1) * u),y) * a(z,z,z \ u)) = T(x,T(y,(z \ 1) * u) * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,19243,a(flip),b,22027,a)].">
      <j1 rule="hyper" parents="65 19243 22027"/>
    </justification>
  </clause>

  <clause id="22030">
    <literal><![CDATA[
      T(x,(((y \ 1) * z) * u) * a(y,y,y \ z)) = T(x,T(u,(y \ 1) * z) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(19246,a,22029,a)].">
      <j1 rule="hyper" parents="19246 22029"/>
    </justification>
  </clause>

  <clause id="22033">
    <literal><![CDATA[
      T(x,(((y \ 1) * z) * u) * a(y,y,y \ z)) = T(x,T(u,y \ z) * (y \ z))
    ]]></literal>
    <justification jstring="[para(14297(a,1),22030(a,2,2,1))].">
      <j1 rule="para" parents="14297 22030"/>
    </justification>
  </clause>

  <clause id="22034">
    <literal><![CDATA[
      T(x,(((y \ 1) * z) * u) * a(y,y,y \ z)) = T(x,(y \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(299,a,13266,a(flip),b,22033,a),flip(a)].">
      <j1 rule="hyper" parents="299 13266 22033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22036">
    <literal><![CDATA[
      T(x,((y \ 1) * z) * u) = T(x,(y \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(21035,a,22034,a)].">
      <j1 rule="hyper" parents="21035 22034"/>
    </justification>
  </clause>

  <clause id="22039">
    <literal><![CDATA[
      T(x,(y \ (z / y)) * (z \ u)) = T(x,y \ (T(y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,20657,a(flip),b,22036,a),flip(a)].">
      <j1 rule="hyper" parents="65 20657 22036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22040">
    <literal><![CDATA[
      (x * (((1 / x) * x) * y)) * K(z,(x \ 1) * (((((x * x) * y) * (x \ 1)) \ u) * ((x * x) * y))) = (x * T(K(z,u),x * x)) * y
    ]]></literal>
    <justification jstring="[para(2910(a,1),21945(a,1,1))].">
      <j1 rule="para" parents="2910 21945"/>
    </justification>
  </clause>

  <clause id="22041">
    <literal><![CDATA[
      (x * y) * K(z,(x \ 1) * (((((x * x) * y) * (x \ 1)) \ u) * ((x * x) * y))) = (x * T(K(z,u),x * x)) * y
    ]]></literal>
    <justification jstring="[para(77(a,1),22040(a,1,1,2))].">
      <j1 rule="para" parents="77 22040"/>
    </justification>
  </clause>

  <clause id="22042">
    <literal><![CDATA[
      (x * y) * K(z,(x \ 1) * (((y * (x \ 1)) \ ((x * x) \ u)) * ((x * x) * y))) = (x * T(K(z,u),x * x)) * y
    ]]></literal>
    <justification jstring="[para(747(a,1),22041(a,1,2,2,2,1))].">
      <j1 rule="para" parents="747 22041"/>
    </justification>
  </clause>

  <clause id="22043">
    <literal><![CDATA[
      (x * y) * K(z,(x \ 1) * (((y * (x \ 1)) \ T(u,x * x)) * y)) = (x * T(K(z,u),x * x)) * y
    ]]></literal>
    <justification jstring="[para(19790(a,1),22042(a,1,2,2,2))].">
      <j1 rule="para" parents="19790 22042"/>
    </justification>
  </clause>

  <clause id="22044">
    <literal><![CDATA[
      (x * y) * K(z,(x \ 1) * (((y * (x \ 1)) \ u) * y)) = (x * T(K(z,u),x * x)) * y
    ]]></literal>
    <justification jstring="[para(19819(a,1),22043(a,1,2))].">
      <j1 rule="para" parents="19819 22043"/>
    </justification>
  </clause>

  <clause id="22045">
    <literal><![CDATA[
      (x * y) * K(z,x \ (((y * (x \ 1)) \ u) * y)) = (x * T(K(z,u),x * x)) * y
    ]]></literal>
    <justification jstring="[para(14246(a,1),22044(a,1,2))].">
      <j1 rule="para" parents="14246 22044"/>
    </justification>
  </clause>

  <clause id="22047">
    <literal><![CDATA[
      (x * y) * K(z,x \ (((y * (x \ 1)) \ u) * y)) = (x * K(z,u)) * y
    ]]></literal>
    <justification jstring="[para(16192(a,1),22045(a,2,1,2))].">
      <j1 rule="para" parents="16192 22045"/>
    </justification>
  </clause>

  <clause id="22049">
    <literal><![CDATA[
      (x * y) * K(z,T(u,y)) = (x * K(z,u)) * y
    ]]></literal>
    <justification jstring="[para(22025(a,1),22047(a,1,2))].">
      <j1 rule="para" parents="22025 22047"/>
    </justification>
  </clause>

  <clause id="22051">
    <literal><![CDATA[
      L(x,y,K(z,u)) * (K(z,u) * y) = (x * K(z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,19699,a,b,22049,a)].">
      <j1 rule="hyper" parents="65 19699 22049"/>
    </justification>
  </clause>

  <clause id="22052">
    <literal><![CDATA[
      (x * T(y,K(z,u))) * K(z,u) = (x * K(z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,8246,a,b,22049,a)].">
      <j1 rule="hyper" parents="65 8246 22049"/>
    </justification>
  </clause>

  <clause id="22053">
    <literal><![CDATA[
      K((x * y) \ (z * y),u) = K(x \ z,T(u,y))
    ]]></literal>
    <justification jstring="[hyper(36,a,9966,a,b,22049,a)].">
      <j1 rule="hyper" parents="36 9966 22049"/>
    </justification>
  </clause>

  <clause id="22054">
    <literal><![CDATA[
      ((x * K(y,z)) * u) \ (x * u) = K(z,T(y,u))
    ]]></literal>
    <justification jstring="[para(22049(a,1),7546(a,1,1))].">
      <j1 rule="para" parents="22049 7546"/>
    </justification>
  </clause>

  <clause id="22057">
    <literal><![CDATA[
      (x * K(y,z)) * a(u,w,v5) = (x * a(u,w,v5)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(18634(a,1),22049(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18634 22049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22058">
    <literal><![CDATA[
      ((x * K(y,z)) * u) / (x * (K(y,z) * u)) = a(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[para(22049(a,1),19610(a,1,1))].">
      <j1 rule="para" parents="22049 19610"/>
    </justification>
  </clause>

  <clause id="22060">
    <literal><![CDATA[
      K(x \ (y / z),T(u,z)) = K((x * z) \ y,u)
    ]]></literal>
    <justification jstring="[para(12(a,1),22053(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12 22053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22062">
    <literal><![CDATA[
      K(x \ (y * z),T(u,(y \ x) * y)) = K(z / (y \ x),T(u,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,15742,a(flip),b,22054,a)].">
      <j1 rule="hyper" parents="65 15742 22054"/>
    </justification>
  </clause>

  <clause id="22063">
    <literal><![CDATA[
      K((x * y) \ z,T(u,y)) = K(x \ (z / y),u)
    ]]></literal>
    <justification jstring="[hyper(8171,a,22060,a),flip(a)].">
      <j1 rule="hyper" parents="8171 22060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22064">
    <literal><![CDATA[
      K(x / (a(y,z,u) * w),v5) = K(a(y,z,u) \ (x / w),v5)
    ]]></literal>
    <justification jstring="[hyper(21398,a,22063,a)].">
      <j1 rule="hyper" parents="21398 22063"/>
    </justification>
  </clause>

  <clause id="22065">
    <literal><![CDATA[
      K((x * y) \ z,T(u,x * z)) = K(x \ (z / y),u)
    ]]></literal>
    <justification jstring="[hyper(17078,a,22063,a)].">
      <j1 rule="hyper" parents="17078 22063"/>
    </justification>
  </clause>

  <clause id="22066">
    <literal><![CDATA[
      K(T(x,y) / (z * y),u) = K(y \ (x / z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,17070,a(flip),b,22063,a)].">
      <j1 rule="hyper" parents="65 17070 22063"/>
    </justification>
  </clause>

  <clause id="22067">
    <literal><![CDATA[
      K(T(x,y) / (z * y),u) = (w * K(u,y \ (x / z))) \ w
    ]]></literal>
    <justification jstring="[hyper(299,a,7200,a,b,22066,a),flip(a)].">
      <j1 rule="hyper" parents="299 7200 22066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22068">
    <literal><![CDATA[
      (x * K(y,z)) * T(u,K(y,z)) = (x * u) * K(y,z)
    ]]></literal>
    <justification jstring="[para(8057(a,1),22052(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="8057 22052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22069">
    <literal><![CDATA[
      L(x,K(y,z),u) * (u * K(y,z)) = (x * u) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,19950,a,b,22068,a)].">
      <j1 rule="hyper" parents="65 19950 22068"/>
    </justification>
  </clause>

  <clause id="22070">
    <literal><![CDATA[
      (x * K(y,z)) * u != w * (K(y,z) * u)
    ]]></literal>
    <literal><![CDATA[
      L(x,u,K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(22051(a,1),46(a,1))].">
      <j1 rule="para" parents="22051 46"/>
    </justification>
  </clause>

  <clause id="22071">
    <literal><![CDATA[
      L(x,K(y,z),u) * (u * K(z,y)) = (x * u) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,5485,a,b,22069,a)].">
      <j1 rule="hyper" parents="65 5485 22069"/>
    </justification>
  </clause>

  <clause id="22072">
    <literal><![CDATA[
      L(x,K(y,z),u) = L(x,u,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(37,a,19641,a,b,22071,a),flip(a)].">
      <j1 rule="hyper" parents="37 19641 22071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22073">
    <literal><![CDATA[
      L(x,K(y,z),u * K(w,v5)) = L(x,K(v5,w) * u,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(18680,a,22072,a)].">
      <j1 rule="hyper" parents="18680 22072"/>
    </justification>
  </clause>

  <clause id="22074">
    <literal><![CDATA[
      (K(x,y) * z) * L(u,K(y,x),z) = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[para(22072(a,2),94(a,1,2))].">
      <j1 rule="para" parents="22072 94"/>
    </justification>
  </clause>

  <clause id="22075">
    <literal><![CDATA[
      x * (K(y,T(z,x)) * u) = K(y,z) * (x * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,11668,a(flip),b,22074,a)].">
      <j1 rule="hyper" parents="65 11668 22074"/>
    </justification>
  </clause>

  <clause id="22077">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * u) = z * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(8104(a,1),22075(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8104 22075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22078">
    <literal><![CDATA[
      K(x,y * z) * (z * u) = z * (K(x,z * y) * u)
    ]]></literal>
    <justification jstring="[para(13207(a,1),22075(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13207 22075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22079">
    <literal><![CDATA[
      T(x,y) * (K(z,T(u,x)) * w) = K(z,u) * (T(x,y) * w)
    ]]></literal>
    <justification jstring="[para(16384(a,1),22075(a,1,2,1))].">
      <j1 rule="para" parents="16384 22075"/>
    </justification>
  </clause>

  <clause id="22081">
    <literal><![CDATA[
      (x * (K(y,z) * u)) / (x * u) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(137,a,22077,a)].">
      <j1 rule="hyper" parents="137 22077"/>
    </justification>
  </clause>

  <clause id="22082">
    <literal><![CDATA[
      (x * (K(y,z) * u)) * K(z,T(y,x)) = T(x * u,K(y,z))
    ]]></literal>
    <justification jstring="[para(22077(a,1),16846(a,1,1))].">
      <j1 rule="para" parents="22077 16846"/>
    </justification>
  </clause>

  <clause id="22084">
    <literal><![CDATA[
      (x * (y * K(z,u))) / (x * y) = K(z,T(T(u,y),x))
    ]]></literal>
    <justification jstring="[para(8101(a,1),22081(a,1,1,2))].">
      <j1 rule="para" parents="8101 22081"/>
    </justification>
  </clause>

  <clause id="22085">
    <literal><![CDATA[
      K(x,L(T(y,z * u),u,z)) = K(x,T(T(y,u),z))
    ]]></literal>
    <justification jstring="[hyper(11998,a,22084,a)].">
      <j1 rule="hyper" parents="11998 22084"/>
    </justification>
  </clause>

  <clause id="22086">
    <literal><![CDATA[
      K(x,L(T(y,z * u),z,u)) = K(x,T(T(y,u),z))
    ]]></literal>
    <justification jstring="[hyper(21711,a,22085,a)].">
      <j1 rule="hyper" parents="21711 22085"/>
    </justification>
  </clause>

  <clause id="22087">
    <literal><![CDATA[
      K(x,T(T(y \ z,y),u)) = K(x,(u * z) / (u * y))
    ]]></literal>
    <justification jstring="[hyper(8318,a,22085,a),flip(a)].">
      <j1 rule="hyper" parents="8318 22085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22088">
    <literal><![CDATA[
      K(L(x,y,z),T(u,y * z)) = K(x,T(T(u,z),y))
    ]]></literal>
    <justification jstring="[hyper(12010,a,22086,a)].">
      <j1 rule="hyper" parents="12010 22086"/>
    </justification>
  </clause>

  <clause id="22089">
    <literal><![CDATA[
      K(L(x,y,z),T(u,z * y)) = K(x,T(T(u,z),y))
    ]]></literal>
    <justification jstring="[hyper(16576,a,22088,a)].">
      <j1 rule="hyper" parents="16576 22088"/>
    </justification>
  </clause>

  <clause id="22090">
    <literal><![CDATA[
      (x * (y * T(z,u))) / (x * (y * z)) = K(z,T(T(u,x),y))
    ]]></literal>
    <justification jstring="[hyper(65,a,11199,a,b,22089,a)].">
      <j1 rule="hyper" parents="65 11199 22089"/>
    </justification>
  </clause>

  <clause id="22091">
    <literal><![CDATA[
      K(x,(y * z) / (y * u)) = K(x,T(z / u,y))
    ]]></literal>
    <justification jstring="[hyper(8431,a,22087,a),flip(a)].">
      <j1 rule="hyper" parents="8431 22087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22092">
    <literal><![CDATA[
      K(x,T(y,z) / (z * u)) = K(x,T((y / z) / u,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,20348,a(flip),b,22091,a)].">
      <j1 rule="hyper" parents="65 20348 22091"/>
    </justification>
  </clause>

  <clause id="22093">
    <literal><![CDATA[
      K(x,T((y * z) / u,y)) = K(x,z / (y \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,17287,a(flip),b,22091,a),flip(a)].">
      <j1 rule="hyper" parents="65 17287 22091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22094">
    <literal><![CDATA[
      K(x,(y * z) / (u * y)) = K(x,T(z / T(u,y),y))
    ]]></literal>
    <justification jstring="[para(107(a,1),22091(a,1,2,2))].">
      <j1 rule="para" parents="107 22091"/>
    </justification>
  </clause>

  <clause id="22095">
    <literal><![CDATA[
      T(x,(y * z) / (y * u)) = x * K(x,T(z / u,y))
    ]]></literal>
    <justification jstring="[para(22091(a,1),5083(a,2,2))].">
      <j1 rule="para" parents="22091 5083"/>
    </justification>
  </clause>

  <clause id="22096">
    <literal><![CDATA[
      K(x,T((y * z) / y,u)) * K(x,K(u * (y * z),u * y)) = K(x,L(z,y,u))
    ]]></literal>
    <justification jstring="[para(22091(a,1),8515(a,1,1))].">
      <j1 rule="para" parents="22091 8515"/>
    </justification>
  </clause>

  <clause id="22097">
    <literal><![CDATA[
      K(x,L(T(y,z) / u,u,z)) = K(x,T(y / T(u,z),z))
    ]]></literal>
    <justification jstring="[hyper(20351,a,22094,a)].">
      <j1 rule="hyper" parents="20351 22094"/>
    </justification>
  </clause>

  <clause id="22098">
    <literal><![CDATA[
      T(x,(y * z) / (y * u)) = T(x,T(z / u,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,5083,a,b,22095,a),flip(a)].">
      <j1 rule="hyper" parents="299 5083 22095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22099">
    <literal><![CDATA[
      T(x,(y * z) / (y * u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(z / u,y)) = w
    ]]></literal>
    <justification jstring="[para(22095(a,2),5087(a,1))].">
      <j1 rule="para" parents="22095 5087"/>
    </justification>
  </clause>

  <clause id="22100">
    <literal><![CDATA[
      T(x,T(y / L(z,u,u),a(u,u,z))) = T(x,(a(u,u,z) * y) / z)
    ]]></literal>
    <justification jstring="[para(6375(a,1),22098(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6375 22098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22101">
    <literal><![CDATA[
      K(x,T(y / T(T(z,u),y),u)) = K(x,L(T(T(y,T(z,u)),u) / z,z,u))
    ]]></literal>
    <justification jstring="[para(4382(a,1),22097(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4382 22097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22102">
    <literal><![CDATA[
      K(x / (y * a(z,u,w)),v5) = K(a(z,u,w) \ (x / y),v5)
    ]]></literal>
    <justification jstring="[hyper(18994,a,22064,a)].">
      <j1 rule="hyper" parents="18994 22064"/>
    </justification>
  </clause>

  <clause id="22103">
    <literal><![CDATA[
      T(x,T(y,z) / (u * z)) = x * K(x,z \ (y / u))
    ]]></literal>
    <justification jstring="[hyper(5028,a,22067,a)].">
      <j1 rule="hyper" parents="5028 22067"/>
    </justification>
  </clause>

  <clause id="22104">
    <literal><![CDATA[
      K(x,T(y,z) / (u * z)) = K(x,z \ (y / u))
    ]]></literal>
    <justification jstring="[hyper(5154,a,22103,a)].">
      <j1 rule="hyper" parents="5154 22103"/>
    </justification>
  </clause>

  <clause id="22105">
    <literal><![CDATA[
      K(x,T(y,z) / (z * u)) = K(x,z \ (y / T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(19687,a,22104,a)].">
      <j1 rule="hyper" parents="19687 22104"/>
    </justification>
  </clause>

  <clause id="22106">
    <literal><![CDATA[
      K(x,(y * z) / (u * z)) = K(x,z \ ((z * y) / u))
    ]]></literal>
    <justification jstring="[hyper(65,a,17065,a(flip),b,22104,a)].">
      <j1 rule="hyper" parents="65 17065 22104"/>
    </justification>
  </clause>

  <clause id="22107">
    <literal><![CDATA[
      K(x,T((y / z) / u,z)) = K(x,z \ (y / T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(65,a,22092,a(flip),b,22105,a)].">
      <j1 rule="hyper" parents="65 22092 22105"/>
    </justification>
  </clause>

  <clause id="22108">
    <literal><![CDATA[
      K(x,L(y / z,z,u)) = K(x,u \ ((u * y) / z))
    ]]></literal>
    <justification jstring="[hyper(15516,a,22106,a)].">
      <j1 rule="hyper" parents="15516 22106"/>
    </justification>
  </clause>

  <clause id="22109">
    <literal><![CDATA[
      K(x,L(y / T(z,u),z,w)) = K(x,w \ ((w * y) / T(z,u)))
    ]]></literal>
    <justification jstring="[hyper(21722,a,22108,a)].">
      <j1 rule="hyper" parents="21722 22108"/>
    </justification>
  </clause>

  <clause id="22111">
    <literal><![CDATA[
      L(x,K(y,z),u * K(z,y)) = a(u,x,K(z,y)) * x
    ]]></literal>
    <justification jstring="[hyper(299,a,21877,a(flip),b,22073,a),flip(a)].">
      <j1 rule="hyper" parents="299 21877 22073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22112">
    <literal><![CDATA[
      L(x,K(y,z),u * K(z,y)) = L(x,u,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,21689,a(flip),b,22111,a),flip(a)].">
      <j1 rule="hyper" parents="299 21689 22111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22113">
    <literal><![CDATA[
      L(x,K(y,z),K(y,z) * u) = L(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(18679,a,22112,a)].">
      <j1 rule="hyper" parents="18679 22112"/>
    </justification>
  </clause>

  <clause id="22114">
    <literal><![CDATA[
      K(x,y) * (T(z,K(x,y)) * u) = z * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,7515,a(flip),b,22079,a),flip(a)].">
      <j1 rule="hyper" parents="65 7515 22079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22116">
    <literal><![CDATA[
      T(x,K(y,z)) * (K(y,z) * u) = K(y,z) * (x * u)
    ]]></literal>
    <justification jstring="[para(8057(a,1),22114(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8057 22114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22117">
    <literal><![CDATA[
      (x * K(y,z)) * (K(y,z) * u) = K(y,z) * ((K(y,z) * x) * u)
    ]]></literal>
    <justification jstring="[para(8053(a,1),22114(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8053 22114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22118">
    <literal><![CDATA[
      T(x,(T(y,K(z,u)) * w) * (v5 \ K(z,u))) = T(x,(y * (K(z,u) * w)) / v5)
    ]]></literal>
    <justification jstring="[para(22114(a,1),19674(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="22114 19674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22119">
    <literal><![CDATA[
      T(x,K(y,z)) * T(u,K(y,z)) = K(y,z) * (x * (u * K(z,y)))
    ]]></literal>
    <justification jstring="[para(8059(a,1),22116(a,1,2))].">
      <j1 rule="para" parents="8059 22116"/>
    </justification>
  </clause>

  <clause id="22120">
    <literal><![CDATA[
      T(x * y,K(z,u)) \ (x * (K(z,u) * y)) = K(z,T(u,x))
    ]]></literal>
    <justification jstring="[para(22082(a,1),7546(a,1,1))].">
      <j1 rule="para" parents="22082 7546"/>
    </justification>
  </clause>

  <clause id="22121">
    <literal><![CDATA[
      K(x,T(T(y,z * L(u,w,w)),w * w)) = K(x,T(y,z * (w * (w * u))))
    ]]></literal>
    <justification jstring="[hyper(65,a,18279,a(flip),b,22090,a),flip(a)].">
      <j1 rule="hyper" parents="65 18279 22090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22122">
    <literal><![CDATA[
      K(a(x,x,y) \ (z / y),u) = K(z * L(y \ 1,x,x),u)
    ]]></literal>
    <justification jstring="[hyper(21884,a,22102,a),flip(a)].">
      <j1 rule="hyper" parents="21884 22102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22123">
    <literal><![CDATA[
      T(K(x,y),z * a(u,w,v5)) = T(z * v6,K(x,y)) \ (z * (K(x,y) * v6))
    ]]></literal>
    <justification jstring="[hyper(299,a,21402,a,b,22120,a)].">
      <j1 rule="hyper" parents="299 21402 22120"/>
    </justification>
  </clause>

  <clause id="22124">
    <literal><![CDATA[
      K(a(x,x,y) * (z / y),u) = K(z * L(y \ 1,x,x),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,21117,a(flip),b,22122,a)].">
      <j1 rule="hyper" parents="65 21117 22122"/>
    </justification>
  </clause>

  <clause id="22125">
    <literal><![CDATA[
      K(a(x,x,y) * (z / y),u) = K(z / L(y,x,x),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,21286,a(flip),b,22124,a),flip(a)].">
      <j1 rule="hyper" parents="299 21286 22124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22126">
    <literal><![CDATA[
      K((x / y) * a(z,z,y),u) = K(x / L(y,z,z),u)
    ]]></literal>
    <justification jstring="[hyper(18654,a,22125,a)].">
      <j1 rule="hyper" parents="18654 22125"/>
    </justification>
  </clause>

  <clause id="22128">
    <literal><![CDATA[
      a(x,K(y,z),u) = a(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(19558,a,22058,a)].">
      <j1 rule="hyper" parents="19558 22058"/>
    </justification>
  </clause>

  <clause id="22129">
    <literal><![CDATA[
      a(x,K(y,z),u) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,21686,a,b,22128,a),flip(a)].">
      <j1 rule="hyper" parents="299 21686 22128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22130">
    <literal><![CDATA[
      (K(x,y) * a(z,u,K(w,v5))) \ y = K(y,x) * (a(z,K(u,v5),w) \ y)
    ]]></literal>
    <justification jstring="[para(22129(a,1),18693(a,1,1,2))].">
      <j1 rule="para" parents="22129 18693"/>
    </justification>
  </clause>

  <clause id="22131">
    <literal><![CDATA[
      K(x,T(((y * z) / y) / u,y)) = K(x,L(z / T(u,y),u,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,22107,a,b,22109,a)].">
      <j1 rule="hyper" parents="299 22107 22109"/>
    </justification>
  </clause>

  <clause id="22132">
    <literal><![CDATA[
      K(x,L(y / T(z,u),z,u)) = K(x,T(T(y,u) / z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,19307,a(flip),b,22131,a),flip(a)].">
      <j1 rule="hyper" parents="65 19307 22131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22133">
    <literal><![CDATA[
      K(L(x / T(y,z),y,z),u) = (w * K(u,T(T(x,z) / y,z))) \ w
    ]]></literal>
    <justification jstring="[para(22132(a,1),7200(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="22132 7200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22135">
    <literal><![CDATA[
      K(x \ (y * z),T(u,T(x,y))) = K(z / (y \ x),T(u,y))
    ]]></literal>
    <justification jstring="[para(13195(a,1),22062(a,1,2))].">
      <j1 rule="para" parents="13195 22062"/>
    </justification>
  </clause>

  <clause id="22136">
    <literal><![CDATA[
      K(x / (y \ z),T(u,y)) = K((y * x) / z,u)
    ]]></literal>
    <justification jstring="[hyper(16446,a,22135,a),flip(a)].">
      <j1 rule="hyper" parents="16446 22135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22137">
    <literal><![CDATA[
      K((x * y) / (x * z),u) = K(y / z,T(u,x))
    ]]></literal>
    <justification jstring="[para(9(a,1),22136(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 22136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22138">
    <literal><![CDATA[
      K((x * y) / (y * z),u) = K(T(x,y) / z,T(u,y))
    ]]></literal>
    <justification jstring="[para(107(a,1),22137(a,1,1,1))].">
      <j1 rule="para" parents="107 22137"/>
    </justification>
  </clause>

  <clause id="22139">
    <literal><![CDATA[
      K(T(x,y / z) / z,T(u,y / z)) = K((x * (y / z)) / y,u)
    ]]></literal>
    <justification jstring="[para(12(a,1),22138(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12 22138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22140">
    <literal><![CDATA[
      (x * (T(T(x,y),y) \ z)) \ (K(y,x) * ((K(y,x) * u) * z)) = R(T(u,x * (T(T(x,y),y) \ z)),K(y,x),K(y,x) * z)
    ]]></literal>
    <justification jstring="[para(22117(a,1),12705(a,1,2))].">
      <j1 rule="para" parents="22117 12705"/>
    </justification>
  </clause>

  <clause id="22141">
    <literal><![CDATA[
      x \ T(K(y,z) * (u * (x * K(z,y))),K(z,y)) = K(u,x * K(y,z)) * T(u,K(y,z))
    ]]></literal>
    <justification jstring="[para(22119(a,1),15775(a,1,2,1))].">
      <j1 rule="para" parents="22119 15775"/>
    </justification>
  </clause>

  <clause id="22142">
    <literal><![CDATA[
      K(T(x,y / z) / z,T(u,z * y)) = K((x * (y / z)) / y,u)
    ]]></literal>
    <justification jstring="[hyper(16652,a,22139,a)].">
      <j1 rule="hyper" parents="16652 22139"/>
    </justification>
  </clause>

  <clause id="22143">
    <literal><![CDATA[
      K(T(x,y * z) / y,T(u,y * z)) = K((x * (z / y)) / z,u)
    ]]></literal>
    <justification jstring="[hyper(18024,a,22142,a)].">
      <j1 rule="hyper" parents="18024 22142"/>
    </justification>
  </clause>

  <clause id="22144">
    <literal><![CDATA[
      T(x,(a(y,y,z) * u) / z) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u / L(z,y,y)) = w
    ]]></literal>
    <justification jstring="[para(22100(a,1),18657(a,1))].">
      <j1 rule="para" parents="22100 18657"/>
    </justification>
  </clause>

  <clause id="22145">
    <literal><![CDATA[
      K(L(x / T(y,z),y,z),u) = K(T(x,z) / y,T(u,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,7546,a(flip),b,22133,a),flip(a)].">
      <j1 rule="hyper" parents="299 7546 22133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22146">
    <literal><![CDATA[
      K(x / T(y,z),L(u,y,z)) = K(T(x,z) / y,T(u,z))
    ]]></literal>
    <justification jstring="[hyper(11999,a,22145,a)].">
      <j1 rule="hyper" parents="11999 22145"/>
    </justification>
  </clause>

  <clause id="22147">
    <literal><![CDATA[
      K(x / T(y,z),L(u,z,y)) = K(T(x,z) / y,T(u,z))
    ]]></literal>
    <justification jstring="[hyper(21711,a,22146,a)].">
      <j1 rule="hyper" parents="21711 22146"/>
    </justification>
  </clause>

  <clause id="22148">
    <literal><![CDATA[
      K(x / ((y \ z) \ z),L(u,y,y \ z)) = K(T(x,y \ z) / y,T(u,y \ z))
    ]]></literal>
    <justification jstring="[para(108(a,1),22146(a,1,1,2))].">
      <j1 rule="para" parents="108 22146"/>
    </justification>
  </clause>

  <clause id="22149">
    <literal><![CDATA[
      K(x,y) * (a(z,K(y,x),u) \ x) = K(y,L(x,u,z)) \ x
    ]]></literal>
    <justification jstring="[para(21688(a,1),22130(a,1,1)),flip(a)].">
      <j1 rule="para" parents="21688 22130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22150">
    <literal><![CDATA[
      K(x,y) * (a(z,K(y,x),u) \ x) = K(L(x,u,z),y) * x
    ]]></literal>
    <justification jstring="[hyper(299,a,5426,a(flip),b,22149,a),flip(a)].">
      <j1 rule="hyper" parents="299 5426 22149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22151">
    <literal><![CDATA[
      K(x,y) * (a(z,K(y,x),u) \ x) = K(x,L(y,u,z)) * x
    ]]></literal>
    <justification jstring="[para(11929(a,1),22150(a,2,1))].">
      <j1 rule="para" parents="11929 22150"/>
    </justification>
  </clause>

  <clause id="22152">
    <literal><![CDATA[
      K(x,y) * (a(z,K(y,x),u) \ x) = T(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,5096,a,b,22151,a),flip(a)].">
      <j1 rule="hyper" parents="299 5096 22151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22153">
    <literal><![CDATA[
      K(x,y) * (a(z,y,K(u,x)) \ x) = T(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[para(22129(a,1),22152(a,1,2,1))].">
      <j1 rule="para" parents="22129 22152"/>
    </justification>
  </clause>

  <clause id="22154">
    <literal><![CDATA[
      K(x,y) * (x * a(x,y,K(z,u))) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(18683(a,1),22153(a,1,2))].">
      <j1 rule="para" parents="18683 22153"/>
    </justification>
  </clause>

  <clause id="22155">
    <literal><![CDATA[
      K(x,y) * L(x,y,K(z,u)) = T(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[para(20846(a,1),22154(a,1,2))].">
      <j1 rule="para" parents="20846 22154"/>
    </justification>
  </clause>

  <clause id="22156">
    <literal><![CDATA[
      L(T(x,y),y,K(z,u)) = T(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,11297,a(flip),b,22155,a)].">
      <j1 rule="hyper" parents="65 11297 22155"/>
    </justification>
  </clause>

  <clause id="22157">
    <literal><![CDATA[
      K(x,T(y / T(T(z,u),y),u)) = K(x,L(T(T(y,u),T(z,u)) / z,z,u))
    ]]></literal>
    <justification jstring="[para(23(a,1),22101(a,2,2,1,1))].">
      <j1 rule="para" parents="23 22101"/>
    </justification>
  </clause>

  <clause id="22158">
    <literal><![CDATA[
      K(x,T(y,z * (u * (u * w)))) = K(x,T(y,z * L(w,u,u)))
    ]]></literal>
    <justification jstring="[hyper(16196,a,22121,a),flip(a)].">
      <j1 rule="hyper" parents="16196 22121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22159">
    <literal><![CDATA[
      K(x,T(y,(z * (z * u)) * w)) = K(x,T(y,w * L(u,z,z)))
    ]]></literal>
    <justification jstring="[hyper(16576,a,22158,a)].">
      <j1 rule="hyper" parents="16576 22158"/>
    </justification>
  </clause>

  <clause id="22161">
    <literal><![CDATA[
      K(x,T(y,(z * u) * (z \ w))) = K(x,T(y,w * L(u,z,z)))
    ]]></literal>
    <justification jstring="[hyper(18788,a,22159,a)].">
      <j1 rule="hyper" parents="18788 22159"/>
    </justification>
  </clause>

  <clause id="22162">
    <literal><![CDATA[
      K(x,T(y,z * (u \ (u \ w)))) = K(x,T(y,w * L(z,u,u)))
    ]]></literal>
    <justification jstring="[hyper(18788,a,22161,a)].">
      <j1 rule="hyper" parents="18788 22161"/>
    </justification>
  </clause>

  <clause id="22163">
    <literal><![CDATA[
      (x * a(y,z,u)) * K(w,v5) = x * (K(w,v5) * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(4453,a,22123,a(flip))].">
      <j1 rule="hyper" parents="4453 22123"/>
    </justification>
  </clause>

  <clause id="22164">
    <literal><![CDATA[
      (x * K(y,z)) * a(u,w,v5) = x * (K(y,z) * a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,22057,a,b,22163,a)].">
      <j1 rule="hyper" parents="65 22057 22163"/>
    </justification>
  </clause>

  <clause id="22165">
    <literal><![CDATA[
      L(x,a(y,z,u),K(w,v5)) = x
    ]]></literal>
    <justification jstring="[hyper(22070,a,22164,a)].">
      <j1 rule="hyper" parents="22070 22164"/>
    </justification>
  </clause>

  <clause id="22169">
    <literal><![CDATA[
      (K(x,y) * a(z,u,w)) * v5 = K(x,y) * (a(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(1318,a,22165,a),flip(a)].">
      <j1 rule="hyper" parents="1318 22165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22170">
    <literal><![CDATA[
      K(x,L(y,z,a(u,w,v5))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(21733,a,22169,a)].">
      <j1 rule="hyper" parents="21733 22169"/>
    </justification>
  </clause>

  <clause id="22171">
    <literal><![CDATA[
      K((x \ a(y,z,u)) \ w,v5) = K(a(y,z,u) \ (x * w),v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,21702,a(flip),b,22170,a),flip(a)].">
      <j1 rule="hyper" parents="65 21702 22170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22172">
    <literal><![CDATA[
      K(x,T(y / T(T(z,u),y),u)) = K(x,L(T(T(y,u),z) / z,z,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,16894,a(flip),b,22157,a),flip(a)].">
      <j1 rule="hyper" parents="299 16894 22157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22174">
    <literal><![CDATA[
      K(x,T(y / T(T(z,u),y),u)) = K(x,L(z \ T(y,u),z,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,13892,a(flip),b,22172,a),flip(a)].">
      <j1 rule="hyper" parents="299 13892 22172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22175">
    <literal><![CDATA[
      K(x,T(y / T(T(z,u),y),u)) = K(x,(u * z) \ (y * u))
    ]]></literal>
    <justification jstring="[para(526(a,1),22174(a,2,2))].">
      <j1 rule="para" parents="526 22174"/>
    </justification>
  </clause>

  <clause id="22176">
    <literal><![CDATA[
      K(x,T(T(y,z) \ u,z)) = K(x,(z * y) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,13906,a(flip),b,22175,a)].">
      <j1 rule="hyper" parents="65 13906 22175"/>
    </justification>
  </clause>

  <clause id="22177">
    <literal><![CDATA[
      K(x,T(T(y / R(z,u,z),z) \ w,z)) = K(x,T(y,z) \ (w * z))
    ]]></literal>
    <justification jstring="[hyper(299,a,21203,a(flip),b,22176,a),flip(a)].">
      <j1 rule="hyper" parents="299 21203 22176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22178">
    <literal><![CDATA[
      K(x,T(T(y \ 1,z / y) \ u,z / y)) = K(x,(z / (y * y)) \ (u * (z / y)))
    ]]></literal>
    <justification jstring="[para(1245(a,1),22176(a,2,2,1))].">
      <j1 rule="para" parents="1245 22176"/>
    </justification>
  </clause>

  <clause id="22179">
    <literal><![CDATA[
      x * K(x,T(T(y,z) \ u,z)) = T(x,(z * y) \ (u * z))
    ]]></literal>
    <justification jstring="[para(22176(a,2),5083(a,2,2)),flip(a)].">
      <j1 rule="para" parents="22176 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22180">
    <literal><![CDATA[
      T(x,T(T(y,z) \ u,z)) = T(x,(z * y) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(5087,a,22179,a)].">
      <j1 rule="hyper" parents="5087 22179"/>
    </justification>
  </clause>

  <clause id="22181">
    <literal><![CDATA[
      T(x,(y \ 1) \ (z \ T(a(y,y,y) * u,y \ 1))) = T(x,T(T(z * (y \ 1),y \ 1) \ u,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(299,a,21982,a,b,22180,a)].">
      <j1 rule="hyper" parents="299 21982 22180"/>
    </justification>
  </clause>

  <clause id="22182">
    <literal><![CDATA[
      K(x,T((R(y,z,y) \ u) \ w,y)) = K(x,T(u,y) \ (w * y))
    ]]></literal>
    <justification jstring="[para(7459(a,1),22177(a,1,2,1,1))].">
      <j1 rule="para" parents="7459 22177"/>
    </justification>
  </clause>

  <clause id="22183">
    <literal><![CDATA[
      K(x,T((y \ z) \ u,y)) = K(x,T(z,y) \ (u * y))
    ]]></literal>
    <justification jstring="[para(536(a,1),22182(a,1,2,1,1,1))].">
      <j1 rule="para" parents="536 22182"/>
    </justification>
  </clause>

  <clause id="22184">
    <literal><![CDATA[
      K(x,T((y \ (z \ y)) \ u,y)) = K(x,(y / z) \ (u * y))
    ]]></literal>
    <justification jstring="[hyper(299,a,15855,a(flip),b,22183,a),flip(a)].">
      <j1 rule="hyper" parents="299 15855 22183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22185">
    <literal><![CDATA[
      K(x,T(T(y,z \ 1),z * z) \ (u * (z * z))) = K(x,T((z \ (y * (z \ 1))) \ u,z * z))
    ]]></literal>
    <justification jstring="[para(726(a,1),22183(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="726 22183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22186">
    <literal><![CDATA[
      K(x,T((y \ z) \ (u / (1 / y)),y)) = K(x,T(z,y) \ (u * ((1 / y) \ y)))
    ]]></literal>
    <justification jstring="[para(1263(a,1),22183(a,2,2,2))].">
      <j1 rule="para" parents="1263 22183"/>
    </justification>
  </clause>

  <clause id="22187">
    <literal><![CDATA[
      K(x,T((y \ (z \ y)) \ (u / (1 / y)),y)) = K(x,(y / z) \ (u * ((1 / y) \ y)))
    ]]></literal>
    <justification jstring="[para(1263(a,1),22184(a,2,2,2))].">
      <j1 rule="para" parents="1263 22184"/>
    </justification>
  </clause>

  <clause id="22188">
    <literal><![CDATA[
      K(x,T((y \ (z \ y)) \ (y \ ((y \ 1) \ u)),y)) = K(x,(y / z) \ ((y \ 1) \ T(u,y)))
    ]]></literal>
    <justification jstring="[para(2045(a,1),22184(a,2,2,2))].">
      <j1 rule="para" parents="2045 22184"/>
    </justification>
  </clause>

  <clause id="22189">
    <literal><![CDATA[
      T(x,(y * (K(z,u) * w)) / v5) = T(x,(y * w) * (v5 \ K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(16795,a,22118,a),flip(a)].">
      <j1 rule="hyper" parents="16795 22118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22190">
    <literal><![CDATA[
      T(x,(y * z) * (u \ K(z,w))) = T(x,(y * T(z,w)) / u)
    ]]></literal>
    <justification jstring="[para(5096(a,2),22189(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="5096 22189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22191">
    <literal><![CDATA[
      T(x,(y * T(z,u)) / u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(y * z) / T(u,z)) = w
    ]]></literal>
    <justification jstring="[para(22190(a,1),14595(a,1))].">
      <j1 rule="para" parents="22190 14595"/>
    </justification>
  </clause>

  <clause id="22192">
    <literal><![CDATA[
      K(x,T((y \ z) \ (u / (1 / y)),y)) = K(x,(T(z,y) \ u) * ((1 / y) \ y))
    ]]></literal>
    <justification jstring="[para(3090(a,1),22186(a,2,2))].">
      <j1 rule="para" parents="3090 22186"/>
    </justification>
  </clause>

  <clause id="22193">
    <literal><![CDATA[
      K(x,T((y \ z) \ (u / (1 / y)),y)) = K(x,(T(z,y) \ u) * (y * y))
    ]]></literal>
    <justification jstring="[hyper(299,a,6040,a(flip),b,22192,a),flip(a)].">
      <j1 rule="hyper" parents="299 6040 22192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22194">
    <literal><![CDATA[
      K(x,T(T(y,z),u)) * K(x,K(u * (z * y),u * z)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(9013(a,1),22096(a,1,1))].">
      <j1 rule="para" parents="9013 22096"/>
    </justification>
  </clause>

  <clause id="22195">
    <literal><![CDATA[
      K(x,T(T(y,z),u)) * K(x,K(u * z,u * (z * y))) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(8004(a,1),22194(a,1,2))].">
      <j1 rule="para" parents="8004 22194"/>
    </justification>
  </clause>

  <clause id="22196">
    <literal><![CDATA[
      K(x,T(T(y,z),u)) * K(x,K(y,u * z)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(21411(a,1),22195(a,1,2))].">
      <j1 rule="para" parents="21411 22195"/>
    </justification>
  </clause>

  <clause id="22197">
    <literal><![CDATA[
      T(K(x,T(y,z)) * K(x,K(y,u * z)),u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,16881,a,b,22196,a)].">
      <j1 rule="hyper" parents="65 16881 22196"/>
    </justification>
  </clause>

  <clause id="22198">
    <literal><![CDATA[
      T(K(x,T(T(y,z),u * z)),u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(16336(a,1),22197(a,1,1))].">
      <j1 rule="para" parents="16336 22197"/>
    </justification>
  </clause>

  <clause id="22199">
    <literal><![CDATA[
      K(x,T(T(T(y,z),u),u * z)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(8395,a,22198,a)].">
      <j1 rule="hyper" parents="8395 22198"/>
    </justification>
  </clause>

  <clause id="22200">
    <literal><![CDATA[
      K(x,T(T(T(y,z),u),z * u)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(7905,a,22198,a),flip(a)].">
      <j1 rule="hyper" parents="7905 22198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22201">
    <literal><![CDATA[
      K(x,T(T(T(y,z),u),u * z)) = K(x,L(y,u \ z,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,14988,a,b,22199,a),flip(a)].">
      <j1 rule="hyper" parents="299 14988 22199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22202">
    <literal><![CDATA[
      T(K(x,T(T(y,z),u)),u * z) = K(x,L(y,u \ z,u))
    ]]></literal>
    <justification jstring="[hyper(8419,a,22201,a)].">
      <j1 rule="hyper" parents="8419 22201"/>
    </justification>
  </clause>

  <clause id="22203">
    <literal><![CDATA[
      T(T(K(x,T(y,z)),u),u * z) = K(x,L(y,u \ z,u))
    ]]></literal>
    <justification jstring="[para(7489(a,1),22202(a,1,1))].">
      <j1 rule="para" parents="7489 22202"/>
    </justification>
  </clause>

  <clause id="22204">
    <literal><![CDATA[
      T(T(K(x,y) * K(x,K(z,y)),u),u * z) = K(x,L(y,u \ z,u))
    ]]></literal>
    <justification jstring="[para(8021(a,2),22203(a,1,1,1))].">
      <j1 rule="para" parents="8021 22203"/>
    </justification>
  </clause>

  <clause id="22205">
    <literal><![CDATA[
      T(K(x,T(y,z)) * K(x,K(u,y)),z * u) = K(x,L(y,z \ u,z))
    ]]></literal>
    <justification jstring="[para(16881(a,1),22204(a,1,1))].">
      <j1 rule="para" parents="16881 22204"/>
    </justification>
  </clause>

  <clause id="22206">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,T(T(z,u),u * y)) = K(x,L(z,u \ y,u))
    ]]></literal>
    <justification jstring="[hyper(16935,a,22205,a)].">
      <j1 rule="hyper" parents="16935 22205"/>
    </justification>
  </clause>

  <clause id="22207">
    <literal><![CDATA[
      K(x,L(T(y,z),u \ z,u)) = K(x,T(T(y,u),u * z))
    ]]></literal>
    <justification jstring="[hyper(36,a,19804,a,b,22206,a)].">
      <j1 rule="hyper" parents="36 19804 22206"/>
    </justification>
  </clause>

  <clause id="22208">
    <literal><![CDATA[
      K(x,T(T(y,z),z * u)) = K(x,L(T(y,u),u,z))
    ]]></literal>
    <justification jstring="[hyper(15000,a,22207,a),flip(a)].">
      <j1 rule="hyper" parents="15000 22207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22209">
    <literal><![CDATA[
      K(x,T(T((y * z) / y,u),u * (w \ (w \ y)))) = K(x,L(T(z,w \ (w \ 1)),w \ (w \ y),u))
    ]]></literal>
    <justification jstring="[para(14734(a,1),22208(a,2,2,1))].">
      <j1 rule="para" parents="14734 22208"/>
    </justification>
  </clause>

  <clause id="22210">
    <literal><![CDATA[
      K(T(x,y \ z) / y,T(u,y \ z)) = K(x / ((y \ z) \ z),L(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(21704,a,22148,a),flip(a)].">
      <j1 rule="hyper" parents="21704 22148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22211">
    <literal><![CDATA[
      K(T(x,y \ z) / y,T(u,y \ z)) = K(x / T(y,z),L(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,20311,a(flip),b,22210,a),flip(a)].">
      <j1 rule="hyper" parents="299 20311 22210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22212">
    <literal><![CDATA[
      K(T(x,y \ z) / y,T(u,y \ z)) = K(T(x,z) / y,T(u,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,22147,a(flip),b,22211,a),flip(a)].">
      <j1 rule="hyper" parents="299 22147 22211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22213">
    <literal><![CDATA[
      K(T(x,y \ z) / y,T(u,y * z)) = K(T(x,z) / y,T(u,z))
    ]]></literal>
    <justification jstring="[hyper(16637,a,22212,a)].">
      <j1 rule="hyper" parents="16637 22212"/>
    </justification>
  </clause>

  <clause id="22214">
    <literal><![CDATA[
      K(T(x,y * z) / y,T(u,y * z)) = K(T(x,z) / y,T(u,z))
    ]]></literal>
    <justification jstring="[hyper(18020,a,22213,a)].">
      <j1 rule="hyper" parents="18020 22213"/>
    </justification>
  </clause>

  <clause id="22215">
    <literal><![CDATA[
      K((x * (y / z)) / y,u) = K(T(x,y) / z,T(u,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,22143,a(flip),b,22214,a)].">
      <j1 rule="hyper" parents="65 22143 22214"/>
    </justification>
  </clause>

  <clause id="22216">
    <literal><![CDATA[
      K(T(x,y) / (z \ y),T(u,y)) = K((x * z) / y,u)
    ]]></literal>
    <justification jstring="[para(76(a,1),22215(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="76 22215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22217">
    <literal><![CDATA[
      K(x,T(T(y \ 1,z / y) \ u,z / y)) = K(x,(y * y) * (z \ (u * (z / y))))
    ]]></literal>
    <justification jstring="[para(416(a,1),22178(a,2,2))].">
      <j1 rule="para" parents="416 22178"/>
    </justification>
  </clause>

  <clause id="22218">
    <literal><![CDATA[
      K(x,T(T(y \ 1,z / y) \ u,z / y)) = K(x,y * (y * (z \ (u * (z / y)))))
    ]]></literal>
    <justification jstring="[hyper(299,a,14201,a(flip),b,22217,a),flip(a)].">
      <j1 rule="hyper" parents="299 14201 22217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22219">
    <literal><![CDATA[
      K(x,T(T(y \ 1,z / y) \ u,z / y)) = K(x,z \ (u * (z / (1 / y))))
    ]]></literal>
    <justification jstring="[hyper(299,a,20297,a(flip),b,22218,a),flip(a)].">
      <j1 rule="hyper" parents="299 20297 22218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22220">
    <literal><![CDATA[
      K(x,T(T(y \ 1,z / y) \ u,z / y)) = K(x,T(u,z) / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(299,a,22026,a(flip),b,22219,a),flip(a)].">
      <j1 rule="hyper" parents="299 22026 22219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22221">
    <literal><![CDATA[
      K(x,T(T(y \ 1,z / y) \ u,z / y)) = K(x,T(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(299,a,14285,a(flip),b,22220,a),flip(a)].">
      <j1 rule="hyper" parents="299 14285 22220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22222">
    <literal><![CDATA[
      K(x,T(T(y \ 1,y \ z) \ u,z / y)) = K(x,T(u,z) * y)
    ]]></literal>
    <justification jstring="[para(7153(a,1),22221(a,1,2,1,1))].">
      <j1 rule="para" parents="7153 22221"/>
    </justification>
  </clause>

  <clause id="22223">
    <literal><![CDATA[
      K(x,T(T(y \ 1,y \ z) \ u,y * z)) = K(x,T(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(16652,a,22222,a)].">
      <j1 rule="hyper" parents="16652 22222"/>
    </justification>
  </clause>

  <clause id="22224">
    <literal><![CDATA[
      K(x,T(T(y \ 1,y * z) \ u,y * z)) = K(x,T(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,20819,a(flip),b,22223,a)].">
      <j1 rule="hyper" parents="65 20819 22223"/>
    </justification>
  </clause>

  <clause id="22225">
    <literal><![CDATA[
      K(x,T(T(y,y * z) * u,y * z)) = K(x,T(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,20402,a(flip),b,22224,a)].">
      <j1 rule="hyper" parents="65 20402 22224"/>
    </justification>
  </clause>

  <clause id="22226">
    <literal><![CDATA[
      K(x,T(T(y,z) * u,y * z)) = K(x,T(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,13942,a(flip),b,22225,a)].">
      <j1 rule="hyper" parents="65 13942 22225"/>
    </justification>
  </clause>

  <clause id="22227">
    <literal><![CDATA[
      K(x,T(T(y,z) * u,z * y)) = K(x,T(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(16576,a,22226,a)].">
      <j1 rule="hyper" parents="16576 22226"/>
    </justification>
  </clause>

  <clause id="22228">
    <literal><![CDATA[
      K(x,T(T(T(y,z),y * z) * u,(y * z) * T(y,z))) = K(x,u * (z * T(y / z,u)))
    ]]></literal>
    <justification jstring="[hyper(299,a,20526,a(flip),b,22227,a),flip(a)].">
      <j1 rule="hyper" parents="299 20526 22227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22229">
    <literal><![CDATA[
      K(x,T(y * (z * u),z * y)) = K(x,T(T(z,y) * u,z) * y)
    ]]></literal>
    <justification jstring="[para(4961(a,1),22227(a,1,2,1))].">
      <j1 rule="para" parents="4961 22227"/>
    </justification>
  </clause>

  <clause id="22230">
    <literal><![CDATA[
      K(x,T(T(y,z) * u,y) * z) = K(x,L(u,y,z) * (z * y))
    ]]></literal>
    <justification jstring="[hyper(16228,a,22229,a),flip(a)].">
      <j1 rule="hyper" parents="16228 22229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22231">
    <literal><![CDATA[
      K(x,L(y,z,u) * (u * z)) = K(x,(y * T(z,u)) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,16854,a(flip),b,22230,a),flip(a)].">
      <j1 rule="hyper" parents="65 16854 22230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22232">
    <literal><![CDATA[
      K(x,(y * T(y \ z,u)) * u) = K(x,T(u * T(z,y),y))
    ]]></literal>
    <justification jstring="[hyper(20820,a,22231,a),flip(a)].">
      <j1 rule="hyper" parents="20820 22231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22233">
    <literal><![CDATA[
      K(x,(y * ((z \ 1) \ (u * z))) * (1 / z)) = K(x,(y * T(u,z)) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,20781,a(flip),b,22231,a)].">
      <j1 rule="hyper" parents="65 20781 22231"/>
    </justification>
  </clause>

  <clause id="22235">
    <literal><![CDATA[
      K(x,(y * ((z \ 1) \ (u * z))) / z) = K(x,(y * T(u,z)) * z)
    ]]></literal>
    <justification jstring="[hyper(14629,a,22233,a)].">
      <j1 rule="hyper" parents="14629 22233"/>
    </justification>
  </clause>

  <clause id="22236">
    <literal><![CDATA[
      x \ ((y * (x * K(z,u))) * K(u,z)) = K(y,x * K(u,z)) * T(y,K(u,z))
    ]]></literal>
    <justification jstring="[para(8054(a,1),22141(a,1,2))].">
      <j1 rule="para" parents="8054 22141"/>
    </justification>
  </clause>

  <clause id="22237">
    <literal><![CDATA[
      x \ (K(y,z) * ((K(z,y) * u) * x)) = K(u,x * K(y,z)) * T(u,K(y,z))
    ]]></literal>
    <justification jstring="[para(21747(a,1),22236(a,1,2))].">
      <j1 rule="para" parents="21747 22236"/>
    </justification>
  </clause>

  <clause id="22238">
    <literal><![CDATA[
      x \ (K(y,z) * ((K(z,y) * u) * x)) = T(T(u,K(y,z)),x * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,16388,a(flip),b,22237,a),flip(a)].">
      <j1 rule="hyper" parents="299 16388 22237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22240">
    <literal><![CDATA[
      K(x,T(y \ ((y / (z \ y)) * ((y \ 1) \ u)),y)) = K(x,(y / z) \ ((y \ 1) \ T(u,y)))
    ]]></literal>
    <justification jstring="[hyper(21857,a,22188,a)].">
      <j1 rule="hyper" parents="21857 22188"/>
    </justification>
  </clause>

  <clause id="22241">
    <literal><![CDATA[
      K(x,T(T(T(y,z),y * z) * u,y * (y * z))) = K(x,u * (z * T(y / z,u)))
    ]]></literal>
    <justification jstring="[hyper(17127,a,22228,a)].">
      <j1 rule="hyper" parents="17127 22228"/>
    </justification>
  </clause>

  <clause id="22242">
    <literal><![CDATA[
      K(x,T(T(T(y,z),y * z) * u,z)) = K(x,u * (z * T(y / z,u)))
    ]]></literal>
    <justification jstring="[hyper(16217,a,22241,a)].">
      <j1 rule="hyper" parents="16217 22241"/>
    </justification>
  </clause>

  <clause id="22244">
    <literal><![CDATA[
      K(x,T(T(T(y,z),z) * u,z)) = K(x,u * (z * T(y / z,u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,13991,a(flip),b,22242,a)].">
      <j1 rule="hyper" parents="65 13991 22242"/>
    </justification>
  </clause>

  <clause id="22245">
    <literal><![CDATA[
      K(x,y * (z * T(u / z,y))) = K(x,T(u * y,z))
    ]]></literal>
    <justification jstring="[hyper(19122,a,22244,a),flip(a)].">
      <j1 rule="hyper" parents="19122 22244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22246">
    <literal><![CDATA[
      K(x,(y / z) * (u * T(w / u,z * y))) = K(x,T(w * (y / z),u))
    ]]></literal>
    <justification jstring="[hyper(17571,a,22245,a)].">
      <j1 rule="hyper" parents="17571 22245"/>
    </justification>
  </clause>

  <clause id="22247">
    <literal><![CDATA[
      K(x,(1 / y) * (z * T(u / z,y))) = K(x,T(u * (1 / y),z))
    ]]></literal>
    <justification jstring="[para(8(a,1),22246(a,1,2,2,2,2))].">
      <j1 rule="para" parents="8 22246"/>
    </justification>
  </clause>

  <clause id="22248">
    <literal><![CDATA[
      K(x,y \ (z * T(u / z,y))) = K(x,T(u * (1 / y),z))
    ]]></literal>
    <justification jstring="[hyper(14530,a,22247,a)].">
      <j1 rule="hyper" parents="14530 22247"/>
    </justification>
  </clause>

  <clause id="22249">
    <literal><![CDATA[
      K(x,T(y * (1 / z),u)) = K(x,(y \ u) \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,21780,a(flip),b,22248,a),flip(a)].">
      <j1 rule="hyper" parents="65 21780 22248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22250">
    <literal><![CDATA[
      K(x,(y \ z) \ (u \ z)) = K(x,T(y / u,z))
    ]]></literal>
    <justification jstring="[hyper(15101,a,22249,a),flip(a)].">
      <j1 rule="hyper" parents="15101 22249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22251">
    <literal><![CDATA[
      K(x,T((y * z) / u,y)) = K(x,u \ (T(z,u) * y))
    ]]></literal>
    <justification jstring="[hyper(65,a,21821,a(flip),b,22250,a),flip(a)].">
      <j1 rule="hyper" parents="65 21821 22250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22252">
    <literal><![CDATA[
      K(x,y \ (T(z,y) * u)) = K(x,z / (u \ y))
    ]]></literal>
    <justification jstring="[hyper(65,a,22093,a(flip),b,22251,a),flip(a)].">
      <j1 rule="hyper" parents="65 22093 22251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22253">
    <literal><![CDATA[
      K(x,T(y,z) \ (T(u,(y \ z) \ z) * w)) = K(x,u / (w \ ((y \ z) \ z)))
    ]]></literal>
    <justification jstring="[hyper(13907,a,22252,a)].">
      <j1 rule="hyper" parents="13907 22252"/>
    </justification>
  </clause>

  <clause id="22254">
    <literal><![CDATA[
      K(x,T(y,z) \ (z * u)) = K(x,z / (u \ y))
    ]]></literal>
    <justification jstring="[para(4960(a,2),22252(a,1,2))].">
      <j1 rule="para" parents="4960 22252"/>
    </justification>
  </clause>

  <clause id="22255">
    <literal><![CDATA[
      T(x,T(y,z) \ (z * u)) = x * K(x,z / (u \ y))
    ]]></literal>
    <justification jstring="[para(22254(a,1),5083(a,2,2))].">
      <j1 rule="para" parents="22254 5083"/>
    </justification>
  </clause>

  <clause id="22256">
    <literal><![CDATA[
      K(T(x,y) \ (y * z),u) = (w * K(u,y / (z \ x))) \ w
    ]]></literal>
    <justification jstring="[para(22254(a,1),7200(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="22254 7200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22257">
    <literal><![CDATA[
      T(x,T(y,z) \ (z * u)) = T(x,z / (u \ y))
    ]]></literal>
    <justification jstring="[hyper(299,a,5083,a,b,22255,a),flip(a)].">
      <j1 rule="hyper" parents="299 5083 22255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22258">
    <literal><![CDATA[
      T(x,T(y,z) \ (z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,z / (u \ y)) = w
    ]]></literal>
    <justification jstring="[para(22255(a,2),5087(a,1))].">
      <j1 rule="para" parents="22255 5087"/>
    </justification>
  </clause>

  <clause id="22259">
    <literal><![CDATA[
      T(x,T(y,z) \ (z * (u * w))) = T(x,z / (T(w * u,w) \ y))
    ]]></literal>
    <justification jstring="[hyper(19255,a,22257,a)].">
      <j1 rule="hyper" parents="19255 22257"/>
    </justification>
  </clause>

  <clause id="22260">
    <literal><![CDATA[
      T(x,((y \ z) * y) \ (y * u)) = T(x,y / (u \ z))
    ]]></literal>
    <justification jstring="[hyper(17877,a,22257,a)].">
      <j1 rule="hyper" parents="17877 22257"/>
    </justification>
  </clause>

  <clause id="22261">
    <literal><![CDATA[
      T(x,y \ (T(z,y) * u)) = T(x,z / (u \ y))
    ]]></literal>
    <justification jstring="[para(4960(a,1),22257(a,1,2))].">
      <j1 rule="para" parents="4960 22257"/>
    </justification>
  </clause>

  <clause id="22262">
    <literal><![CDATA[
      T(x,y / (a(y,z,z) \ u)) = T(x,T(u,y) \ R(y,z,z))
    ]]></literal>
    <justification jstring="[para(15579(a,1),22257(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="15579 22257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22263">
    <literal><![CDATA[
      T(x,(y \ z) \ (T(u,y * z) * w)) = T(x,u / (w \ (y \ z)))
    ]]></literal>
    <justification jstring="[hyper(17622,a,22261,a)].">
      <j1 rule="hyper" parents="17622 22261"/>
    </justification>
  </clause>

  <clause id="22264">
    <literal><![CDATA[
      T(x,((y / z) \ 1) \ (T(u,z / y) * w)) = T(x,u / (w \ ((y / z) \ 1)))
    ]]></literal>
    <justification jstring="[para(4641(a,1),22261(a,1,2,2,1))].">
      <j1 rule="para" parents="4641 22261"/>
    </justification>
  </clause>

  <clause id="22265">
    <literal><![CDATA[
      T(x,((y \ z) \ 1) \ (T(u,z \ y) * w)) = T(x,u / (w \ ((y \ z) \ 1)))
    ]]></literal>
    <justification jstring="[para(7037(a,1),22261(a,1,2,2,1))].">
      <j1 rule="para" parents="7037 22261"/>
    </justification>
  </clause>

  <clause id="22266">
    <literal><![CDATA[
      T(x,(y * (z \ 1)) \ (T(u,y * (z \ 1)) * a(z \ y,z,z))) = T(x,u / (y / z))
    ]]></literal>
    <justification jstring="[para(20888(a,1),22261(a,2,2,2))].">
      <j1 rule="para" parents="20888 22261"/>
    </justification>
  </clause>

  <clause id="22267">
    <literal><![CDATA[
      T(x,y \ (T(z,y) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,z / (u \ y)) = w
    ]]></literal>
    <justification jstring="[para(4960(a,1),22258(a,1,2))].">
      <j1 rule="para" parents="4960 22258"/>
    </justification>
  </clause>

  <clause id="22268">
    <literal><![CDATA[
      T(x,L(y,z,z) \ (T(u,y) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,u / (w \ L(y,z,z))) = v5
    ]]></literal>
    <justification jstring="[para(14206(a,1),22267(a,1,2,2,1))].">
      <j1 rule="para" parents="14206 22267"/>
    </justification>
  </clause>

  <clause id="22269">
    <literal><![CDATA[
      K(T(x,y) \ (y * z),u) = K(y / (z \ x),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,18856,a(flip),b,22256,a),flip(a)].">
      <j1 rule="hyper" parents="299 18856 22256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22270">
    <literal><![CDATA[
      K(x \ (T(y,x) * z),u) = K(y / (z \ x),u)
    ]]></literal>
    <justification jstring="[hyper(7653,a,22269,a)].">
      <j1 rule="hyper" parents="7653 22269"/>
    </justification>
  </clause>

  <clause id="22271">
    <literal><![CDATA[
      K(x / ((x \ y) \ z),u) = K(T(z,x) \ y,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),22269(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10 22269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22272">
    <literal><![CDATA[
      K(x / ((T(y,z) \ u) \ y),w) = K((y * (T(y,z) / x)) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,21829,a(flip),b,22270,a),flip(a)].">
      <j1 rule="hyper" parents="65 21829 22270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22273">
    <literal><![CDATA[
      K(T(x,y) \ (T(z,x) * u),w) = K(z / (u \ T(x,y)),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,20069,a(flip),b,22270,a)].">
      <j1 rule="hyper" parents="65 20069 22270"/>
    </justification>
  </clause>

  <clause id="22274">
    <literal><![CDATA[
      K((x / y) / (z \ y),u) = K(y \ ((y \ x) * z),u)
    ]]></literal>
    <justification jstring="[para(109(a,1),22270(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="109 22270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22275">
    <literal><![CDATA[
      K(((x \ y) \ y) \ (T(z,T(x,y)) * u),w) = K(z / (u \ ((x \ y) \ y)),w)
    ]]></literal>
    <justification jstring="[para(7482(a,1),22270(a,1,1,2,1))].">
      <j1 rule="para" parents="7482 22270"/>
    </justification>
  </clause>

  <clause id="22276">
    <literal><![CDATA[
      K(((x \ y) \ z) \ x,u) = K(T(z,x) \ y,T(u,x))
    ]]></literal>
    <justification jstring="[hyper(7526,a,22271,a)].">
      <j1 rule="hyper" parents="7526 22271"/>
    </justification>
  </clause>

  <clause id="22277">
    <literal><![CDATA[
      K((a(x,y,z) * a(x,y,K(z,u))) \ w,T(v5,u)) = K(((u \ w) \ a(x,y,z)) \ u,v5)
    ]]></literal>
    <justification jstring="[para(14561(a,2),22276(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="14561 22276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22278">
    <literal><![CDATA[
      T(x,y / (a(y,z,z) \ u)) = T(x,T(u,y) \ L(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,17574,a(flip),b,22262,a),flip(a)].">
      <j1 rule="hyper" parents="299 17574 22262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22279">
    <literal><![CDATA[
      T(x,y / (a(y,z,z) \ u)) = T(x,L(y,z,z) / u)
    ]]></literal>
    <justification jstring="[hyper(299,a,19126,a(flip),b,22278,a),flip(a)].">
      <j1 rule="hyper" parents="299 19126 22278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22280">
    <literal><![CDATA[
      T(x,y / (T(z * u,z) \ w)) = T(x,y / ((u * z) \ w))
    ]]></literal>
    <justification jstring="[hyper(22258,a,22259,a),flip(a)].">
      <j1 rule="hyper" parents="22258 22259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22281">
    <literal><![CDATA[
      T(x,y / (((z \ u) * z) \ w)) = T(x,y / (T(u,z) \ w))
    ]]></literal>
    <justification jstring="[para(10(a,1),22280(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 22280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22282">
    <literal><![CDATA[
      T(x,y / ((z * (u / z)) \ w)) = T(x,y / (T(u,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,18278,a(flip),b,22281,a)].">
      <j1 rule="hyper" parents="65 18278 22281"/>
    </justification>
  </clause>

  <clause id="22283">
    <literal><![CDATA[
      T(x,y / (((z * u) * ((u \ 1) * (u \ (w / (z * (1 / u)))))) \ v5)) = T(x,y / (T(w,z * (1 / u)) \ v5))
    ]]></literal>
    <justification jstring="[para(1729(a,2),22282(a,1,2,2,1))].">
      <j1 rule="para" parents="1729 22282"/>
    </justification>
  </clause>

  <clause id="22284">
    <literal><![CDATA[
      T(x,(y \ z) * (T(u,z * y) * w)) = T(x,u / (w \ (z \ y)))
    ]]></literal>
    <justification jstring="[hyper(21637,a,22263,a)].">
      <j1 rule="hyper" parents="21637 22263"/>
    </justification>
  </clause>

  <clause id="22285">
    <literal><![CDATA[
      K(x / ((y \ z) \ T(y,u)),w) = K((y * (T(y,u) / x)) \ z,w)
    ]]></literal>
    <justification jstring="[para(14415(a,1),22272(a,1,1,2))].">
      <j1 rule="para" parents="14415 22272"/>
    </justification>
  </clause>

  <clause id="22286">
    <literal><![CDATA[
      K(x,T(y,z) \ (T(u,T(y,z)) * w)) = K(x,u / (w \ ((y \ z) \ z)))
    ]]></literal>
    <justification jstring="[para(7482(a,1),22253(a,1,2,2,1))].">
      <j1 rule="para" parents="7482 22253"/>
    </justification>
  </clause>

  <clause id="22287">
    <literal><![CDATA[
      K(x,y / (z \ ((u \ w) \ w))) = K(x,y / (z \ T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,22252,a(flip),b,22286,a),flip(a)].">
      <j1 rule="hyper" parents="65 22252 22286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22288">
    <literal><![CDATA[
      T(x,y / (z \ ((u \ w) \ w))) = x * K(x,y / (z \ T(u,w)))
    ]]></literal>
    <justification jstring="[para(22287(a,1),5083(a,2,2))].">
      <j1 rule="para" parents="22287 5083"/>
    </justification>
  </clause>

  <clause id="22289">
    <literal><![CDATA[
      T(x,y / (z \ ((u \ w) \ w))) = T(x,y / (z \ T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(299,a,5083,a,b,22288,a),flip(a)].">
      <j1 rule="hyper" parents="299 5083 22288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22290">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y / (u \ T(z,w))) = T(x,(u \ ((z \ w) \ w)) \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,17208,a(flip),b,22289,a),flip(a)].">
      <j1 rule="hyper" parents="65 17208 22289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22291">
    <literal><![CDATA[
      T(x,((y / z) \ 1) \ (T(u,z * y) * w)) = T(x,u / (w \ ((y / z) \ 1)))
    ]]></literal>
    <justification jstring="[hyper(65,a,17626,a(flip),b,22264,a)].">
      <j1 rule="hyper" parents="65 17626 22264"/>
    </justification>
  </clause>

  <clause id="22292">
    <literal><![CDATA[
      T(x,((y \ z) \ 1) \ (T(u,z * y) * w)) = T(x,u / (w \ ((y \ z) \ 1)))
    ]]></literal>
    <justification jstring="[hyper(17622,a,22265,a)].">
      <j1 rule="hyper" parents="17622 22265"/>
    </justification>
  </clause>

  <clause id="22293">
    <literal><![CDATA[
      K(((x \ y) \ y) \ (T(z,x) * u),w) = K(z / (u \ ((x \ y) \ y)),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,20069,a(flip),b,22275,a)].">
      <j1 rule="hyper" parents="65 20069 22275"/>
    </justification>
  </clause>

  <clause id="22295">
    <literal><![CDATA[
      K(T(x,y) \ (T(z,x) * u),w) = K(z / (u \ ((x \ y) \ y)),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,13910,a(flip),b,22293,a)].">
      <j1 rule="hyper" parents="65 13910 22293"/>
    </justification>
  </clause>

  <clause id="22296">
    <literal><![CDATA[
      K(x / (y \ ((z \ u) \ u)),w) = K(x / (y \ T(z,u)),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,22273,a(flip),b,22295,a),flip(a)].">
      <j1 rule="hyper" parents="65 22273 22295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22297">
    <literal><![CDATA[
      K(x / ((y \ z) \ T(y,z)),u) = K(x / (y / (y \ z)),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,20255,a(flip),b,22296,a),flip(a)].">
      <j1 rule="hyper" parents="65 20255 22296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22298">
    <literal><![CDATA[
      K((x * (T(x,y) / z)) \ y,u) = K(z / (x / (x \ y)),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,22285,a(flip),b,22297,a)].">
      <j1 rule="hyper" parents="65 22285 22297"/>
    </justification>
  </clause>

  <clause id="22299">
    <literal><![CDATA[
      K((((x * y) / x) * (T((x * y) / x,T(x,y)) / z)) \ T(x,y),u) = K(z / (((x * y) / x) / (y \ x)),u)
    ]]></literal>
    <justification jstring="[para(1431(a,1),22298(a,2,1,2,2))].">
      <j1 rule="para" parents="1431 22298"/>
    </justification>
  </clause>

  <clause id="22300">
    <literal><![CDATA[
      T(x,(y \ ((z \ u) \ u)) \ w) = T(x,(y \ T(z,u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,17185,a(flip),b,22290,a),flip(a)].">
      <j1 rule="hyper" parents="65 17185 22290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22301">
    <literal><![CDATA[
      T(x,(y \ T(z,z \ u)) \ w) = T(x,(y \ T(z,u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,20430,a,b,22300,a)].">
      <j1 rule="hyper" parents="65 20430 22300"/>
    </justification>
  </clause>

  <clause id="22302">
    <literal><![CDATA[
      T(x,(y \ (z / (z / u))) \ w) = T(x,(y \ T(u,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,20433,a(flip),b,22301,a)].">
      <j1 rule="hyper" parents="65 20433 22301"/>
    </justification>
  </clause>

  <clause id="22303">
    <literal><![CDATA[
      T(x,(y \ (z * K(z \ u,z))) \ w) = T(x,(y \ T(z,u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,20432,a(flip),b,22302,a)].">
      <j1 rule="hyper" parents="65 20432 22302"/>
    </justification>
  </clause>

  <clause id="22304">
    <literal><![CDATA[
      T(x,(y \ (z * K(z \ y,z))) \ u) = T(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(299,a,20218,a(flip),b,22303,a),flip(a)].">
      <j1 rule="hyper" parents="299 20218 22303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22305">
    <literal><![CDATA[
      T(x,((y * (z / y)) \ y) \ u) = T(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[para(5290(a,1),22304(a,1,2,1))].">
      <j1 rule="para" parents="5290 22304"/>
    </justification>
  </clause>

  <clause id="22306">
    <literal><![CDATA[
      T(x,(y \ (y / (z / y))) \ u) = T(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[hyper(13855,a,22305,a)].">
      <j1 rule="hyper" parents="13855 22305"/>
    </justification>
  </clause>

  <clause id="22307">
    <literal><![CDATA[
      T(x,((1 / y) \ ((1 / y) / (z / y))) \ u) = T(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[para(766(a,2),22306(a,1,2,1))].">
      <j1 rule="para" parents="766 22306"/>
    </justification>
  </clause>

  <clause id="22308">
    <literal><![CDATA[
      T(x,((1 / y) \ (y / (z / (y \ 1)))) \ u) = T(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[para(15176(a,1),22307(a,1,2,1,2))].">
      <j1 rule="para" parents="15176 22307"/>
    </justification>
  </clause>

  <clause id="22309">
    <literal><![CDATA[
      T(x,((y \ 1) \ (y / (z / (y \ 1)))) \ u) = T(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,3886,a(flip),b,22308,a)].">
      <j1 rule="hyper" parents="65 3886 22308"/>
    </justification>
  </clause>

  <clause id="22310">
    <literal><![CDATA[
      K(((x \ 1) \ (x / (y / (x \ 1)))) \ z,u) = u / T(u,(x / y) \ z)
    ]]></literal>
    <justification jstring="[para(22309(a,1),5033(a,2,2))].">
      <j1 rule="para" parents="22309 5033"/>
    </justification>
  </clause>

  <clause id="22311">
    <literal><![CDATA[
      K(((x \ 1) \ (x / (y / (x \ 1)))) \ z,u) = K((x / y) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,5033,a,b,22310,a),flip(a)].">
      <j1 rule="hyper" parents="299 5033 22310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22312">
    <literal><![CDATA[
      K(((x \ 1) \ (x / (y / (x \ 1)))) \ (x \ z),u) = K(x \ ((y \ x) \ z),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,21841,a(flip),b,22311,a),flip(a)].">
      <j1 rule="hyper" parents="299 21841 22311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22313">
    <literal><![CDATA[
      T(x,(y / z) * (T(u,z * y) * w)) = T(x,u / (w \ ((y / z) \ 1)))
    ]]></literal>
    <justification jstring="[hyper(21037,a,22291,a)].">
      <j1 rule="hyper" parents="21037 22291"/>
    </justification>
  </clause>

  <clause id="22314">
    <literal><![CDATA[
      T(x,(y \ z) * (T(u,z * y) * w)) = T(x,u / (w \ ((y \ z) \ 1)))
    ]]></literal>
    <justification jstring="[hyper(21037,a,22292,a)].">
      <j1 rule="hyper" parents="21037 22292"/>
    </justification>
  </clause>

  <clause id="22315">
    <literal><![CDATA[
      T(x,y / (z \ ((u \ w) \ 1))) = T(x,y / (z \ (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,22284,a(flip),b,22314,a),flip(a)].">
      <j1 rule="hyper" parents="65 22284 22314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22316">
    <literal><![CDATA[
      K(x \ (((x \ 1) / (x / (y / (x \ 1)))) * z),u) = K(x \ ((y \ x) \ z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,21922,a(flip),b,22312,a)].">
      <j1 rule="hyper" parents="65 21922 22312"/>
    </justification>
  </clause>

  <clause id="22317">
    <literal><![CDATA[
      T(x,(y * (z \ 1)) \ (T(u,y / z) * a(z \ y,z,z))) = T(x,u / (y / z))
    ]]></literal>
    <justification jstring="[para(14474(a,1),22266(a,1,2,2,1))].">
      <j1 rule="para" parents="14474 22266"/>
    </justification>
  </clause>

  <clause id="22318">
    <literal><![CDATA[
      T(x,(y * (z \ 1)) \ T(a(z \ y,z,z) * u,y / z)) = T(x,u / (y / z))
    ]]></literal>
    <justification jstring="[hyper(65,a,21432,a,b,22317,a)].">
      <j1 rule="hyper" parents="65 21432 22317"/>
    </justification>
  </clause>

  <clause id="22319">
    <literal><![CDATA[
      T(x,(a(y \ z,y,y) * u) / (z * (y \ 1))) = T(x,u / (z / y))
    ]]></literal>
    <justification jstring="[hyper(16648,a,22318,a)].">
      <j1 rule="hyper" parents="16648 22318"/>
    </justification>
  </clause>

  <clause id="22320">
    <literal><![CDATA[
      K((a(x,y,z) * a(x,y,K(z,u))) \ w,T(v5,u)) = K(a(x,y,z) \ ((u \ w) * u),v5)
    ]]></literal>
    <justification jstring="[hyper(299,a,22171,a(flip),b,22277,a),flip(a)].">
      <j1 rule="hyper" parents="299 22171 22277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22321">
    <literal><![CDATA[
      K((a(x,y,z) * a(x,y,K(z,u))) \ w,T(v5,u)) = K(a(x,y,z) \ T(w,u),v5)
    ]]></literal>
    <justification jstring="[hyper(299,a,17072,a(flip),b,22320,a),flip(a)].">
      <j1 rule="hyper" parents="299 17072 22320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22322">
    <literal><![CDATA[
      K(T(a(x,y,z),u) \ w,T(v5,u)) = K(a(x,y,z) \ T(w,u),v5)
    ]]></literal>
    <justification jstring="[para(14561(a,1),22321(a,1,1,1))].">
      <j1 rule="para" parents="14561 22321"/>
    </justification>
  </clause>

  <clause id="22323">
    <literal><![CDATA[
      K(a(x,y,z) \ T(u,w),v5) = K(a(x,y,z) \ u,T(v5,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,18988,a(flip),b,22322,a),flip(a)].">
      <j1 rule="hyper" parents="65 18988 22322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22325">
    <literal><![CDATA[
      K(T(x,y) * a(z,u,w),v5) = K(a(z,u,w) \ x,T(v5,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,21114,a(flip),b,22323,a)].">
      <j1 rule="hyper" parents="65 21114 22323"/>
    </justification>
  </clause>

  <clause id="22326">
    <literal><![CDATA[
      K(T(x,y) * a(z,u,w),v5) = K(x * a(z,u,w),T(v5,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,21114,a(flip),b,22325,a),flip(a)].">
      <j1 rule="hyper" parents="299 21114 22325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22327">
    <literal><![CDATA[
      K(x,T(y \ (z * ((y \ 1) \ u)),y)) = K(x,(y / z) \ ((y \ 1) \ T(u,y)))
    ]]></literal>
    <justification jstring="[para(76(a,1),22240(a,1,2,1,2,1))].">
      <j1 rule="para" parents="76 22240"/>
    </justification>
  </clause>

  <clause id="22329">
    <literal><![CDATA[
      K(x,(y / z) \ ((y \ 1) \ T(u,y))) = K(x,(z * ((y \ 1) \ u)) / y)
    ]]></literal>
    <justification jstring="[hyper(8215,a,22327,a),flip(a)].">
      <j1 rule="hyper" parents="8215 22327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22330">
    <literal><![CDATA[
      K(x,(y * ((z \ 1) \ u)) / z) = K(x,(z / y) \ (u / (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(17514,a,22329,a),flip(a)].">
      <j1 rule="hyper" parents="17514 22329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22331">
    <literal><![CDATA[
      K(x,(y / z) \ ((u * y) / (y \ 1))) = K(x,(z * T(u,y)) * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,22235,a(flip),b,22330,a),flip(a)].">
      <j1 rule="hyper" parents="65 22235 22330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22332">
    <literal><![CDATA[
      K(x,(y / z) \ (u * ((1 / y) \ y))) = K(x,(z * T(u,y)) * y)
    ]]></literal>
    <justification jstring="[para(3101(a,1),22331(a,1,2,2))].">
      <j1 rule="para" parents="3101 22331"/>
    </justification>
  </clause>

  <clause id="22333">
    <literal><![CDATA[
      K(x,T(y,z * (z * (z \ 1))) \ (u * (z * z))) = K(x,T((z \ (y * (z \ 1))) \ u,z * z))
    ]]></literal>
    <justification jstring="[para(14468(a,1),22185(a,1,2,1))].">
      <j1 rule="para" parents="14468 22185"/>
    </justification>
  </clause>

  <clause id="22334">
    <literal><![CDATA[
      K(x,T((y \ (z * (y \ 1))) \ u,y * y)) = K(x,T(z,y) \ (u * (y * y)))
    ]]></literal>
    <justification jstring="[para(71(a,1),22333(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="71 22333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22335">
    <literal><![CDATA[
      K(x,T((y \ (z * (y \ 1))) \ u,y * y)) = K(x,(T(z,y) \ u) * (y * y))
    ]]></literal>
    <justification jstring="[para(847(a,1),22334(a,2,2))].">
      <j1 rule="para" parents="847 22334"/>
    </justification>
  </clause>

  <clause id="22336">
    <literal><![CDATA[
      K(x,(y \ (z * (y \ 1))) \ u) = K(x,(T(z,y) \ u) * (y * y))
    ]]></literal>
    <justification jstring="[hyper(16196,a,22335,a)].">
      <j1 rule="hyper" parents="16196 22335"/>
    </justification>
  </clause>

  <clause id="22338">
    <literal><![CDATA[
      K(x,(T(y,z) \ u) * (z * z)) = K(x,z * (y \ (z * u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,21868,a(flip),b,22336,a),flip(a)].">
      <j1 rule="hyper" parents="65 21868 22336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22339">
    <literal><![CDATA[
      K(x,T((y \ z) \ (u / (1 / y)),y)) = K(x,y * (z \ (y * u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,22193,a,b,22338,a)].">
      <j1 rule="hyper" parents="65 22193 22338"/>
    </justification>
  </clause>

  <clause id="22340">
    <literal><![CDATA[
      K(x,(y / z) \ (u * ((1 / y) \ y))) = K(x,y * ((z \ y) \ (y * u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,22187,a(flip),b,22339,a)].">
      <j1 rule="hyper" parents="65 22187 22339"/>
    </justification>
  </clause>

  <clause id="22341">
    <literal><![CDATA[
      K(x,y * ((z \ y) \ (y * u))) = K(x,(z * T(u,y)) * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,22332,a(flip),b,22340,a),flip(a)].">
      <j1 rule="hyper" parents="65 22332 22340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22342">
    <literal><![CDATA[
      K(x,((y / z) \ u) * ((1 / y) \ y)) = K(x,y * ((z \ y) \ (y * u)))
    ]]></literal>
    <justification jstring="[para(3090(a,1),22340(a,1,2))].">
      <j1 rule="para" parents="3090 22340"/>
    </justification>
  </clause>

  <clause id="22343">
    <literal><![CDATA[
      K(x,((y / z) \ u) * (y * y)) = K(x,y * ((z \ y) \ (y * u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,6040,a(flip),b,22342,a)].">
      <j1 rule="hyper" parents="65 6040 22342"/>
    </justification>
  </clause>

  <clause id="22344">
    <literal><![CDATA[
      K(x,y * ((z \ y) \ (y * (z \ u)))) = K(x,z \ (((y \ 1) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,21926,a(flip),b,22343,a),flip(a)].">
      <j1 rule="hyper" parents="65 21926 22343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22345">
    <literal><![CDATA[
      K(x,y \ (((z \ 1) \ y) * u)) = K(x,(y * T(y \ u,z)) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,22341,a(flip),b,22344,a),flip(a)].">
      <j1 rule="hyper" parents="65 22341 22344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22346">
    <literal><![CDATA[
      K(x,y \ (((z \ 1) \ y) * u)) = K(x,T(z * T(u,y),y))
    ]]></literal>
    <justification jstring="[hyper(299,a,22232,a(flip),b,22345,a),flip(a)].">
      <j1 rule="hyper" parents="299 22232 22345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22347">
    <literal><![CDATA[
      K(x,T((y \ 1) * T(z,u),u)) = K(x,u \ ((y \ u) * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,20606,a(flip),b,22346,a),flip(a)].">
      <j1 rule="hyper" parents="65 20606 22346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22348">
    <literal><![CDATA[
      K(x,T(y \ T(z,u),u)) = K(x,u \ ((y \ u) * z))
    ]]></literal>
    <justification jstring="[hyper(14648,a,22347,a)].">
      <j1 rule="hyper" parents="14648 22347"/>
    </justification>
  </clause>

  <clause id="22349">
    <literal><![CDATA[
      K(x,T(y \ T(z * u,z),z)) = K(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[hyper(299,a,21770,a(flip),b,22348,a),flip(a)].">
      <j1 rule="hyper" parents="299 21770 22348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22350">
    <literal><![CDATA[
      K(x,T(y \ (z * u),u)) = K(x,(y / u) \ z)
    ]]></literal>
    <justification jstring="[hyper(18106,a,22349,a)].">
      <j1 rule="hyper" parents="18106 22349"/>
    </justification>
  </clause>

  <clause id="22351">
    <literal><![CDATA[
      K(T(x \ (y * z),z),u) = (w * K(u,(x / z) \ y)) \ w
    ]]></literal>
    <justification jstring="[para(22350(a,1),7200(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="22350 7200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22354">
    <literal><![CDATA[
      K(T(x \ (y * z),z),u) = K((x / z) \ y,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,18856,a(flip),b,22351,a),flip(a)].">
      <j1 rule="hyper" parents="299 18856 22351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22355">
    <literal><![CDATA[
      K(x \ (y * z),T(u,z)) = K((x / z) \ y,u)
    ]]></literal>
    <justification jstring="[hyper(7709,a,22354,a)].">
      <j1 rule="hyper" parents="7709 22354"/>
    </justification>
  </clause>

  <clause id="22356">
    <literal><![CDATA[
      K((x * (y \ x)) \ z,T(u,x \ z)) = K((x / (x \ z)) \ y,u)
    ]]></literal>
    <justification jstring="[hyper(21814,a,22355,a)].">
      <j1 rule="hyper" parents="21814 22355"/>
    </justification>
  </clause>

  <clause id="22357">
    <literal><![CDATA[
      K((x / y) \ (y \ z),u) = K(x \ T(z,y),T(u,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,17072,a(flip),b,22355,a),flip(a)].">
      <j1 rule="hyper" parents="65 17072 22355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22358">
    <literal><![CDATA[
      K(x \ ((y \ x) * z),u) = K(y \ T(z,x),T(u,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,21789,a(flip),b,22357,a)].">
      <j1 rule="hyper" parents="65 21789 22357"/>
    </justification>
  </clause>

  <clause id="22359">
    <literal><![CDATA[
      K(x \ ((y \ x) * z),T(u,z)) = K(T(z,x) / y,T(u,x))
    ]]></literal>
    <justification jstring="[hyper(299,a,16587,a(flip),b,22358,a),flip(a)].">
      <j1 rule="hyper" parents="299 16587 22358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22360">
    <literal><![CDATA[
      K(x \ ((x \ y) \ z),u) = K(y \ T(z,x),T(u,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,21788,a,b,22358,a)].">
      <j1 rule="hyper" parents="65 21788 22358"/>
    </justification>
  </clause>

  <clause id="22361">
    <literal><![CDATA[
      (x * y) / (K(z \ T(u,w),T(x,w)) * y) = T(x,w \ ((z \ w) * u))
    ]]></literal>
    <justification jstring="[para(22358(a,1),5517(a,1,2,1))].">
      <j1 rule="para" parents="22358 5517"/>
    </justification>
  </clause>

  <clause id="22362">
    <literal><![CDATA[
      K(x \ ((x / (y \ ((1 / y) \ x))) * z),u) = K((y \ ((1 / y) \ x)) \ T(z,x),T(u,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,21853,a(flip),b,22360,a)].">
      <j1 rule="hyper" parents="65 21853 22360"/>
    </justification>
  </clause>

  <clause id="22363">
    <literal><![CDATA[
      K((x / y) \ (z \ x),u) = K(T(y,x) / z,T(u,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,22355,a(flip),b,22359,a)].">
      <j1 rule="hyper" parents="65 22355 22359"/>
    </justification>
  </clause>

  <clause id="22364">
    <literal><![CDATA[
      K((T(x,y) / z) \ R(y,y * x,y),u) = K(T(z,T(x,y)) / (y \ x),T(u,T(x,y)))
    ]]></literal>
    <justification jstring="[para(14702(a,2),22363(a,1,1,2))].">
      <j1 rule="para" parents="14702 22363"/>
    </justification>
  </clause>

  <clause id="22365">
    <literal><![CDATA[
      K((x * (y \ x)) \ z,T(u,x * z)) = K((x / (x \ z)) \ y,u)
    ]]></literal>
    <justification jstring="[hyper(16637,a,22356,a)].">
      <j1 rule="hyper" parents="16637 22356"/>
    </justification>
  </clause>

  <clause id="22366">
    <literal><![CDATA[
      K((x / (x \ y)) \ z,u) = K(x \ (y / (z \ x)),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,22065,a(flip),b,22365,a),flip(a)].">
      <j1 rule="hyper" parents="65 22065 22365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22367">
    <literal><![CDATA[
      K(((x / y) \ y) \ z,u) = K(y \ (x / (z \ y)),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,20163,a(flip),b,22366,a)].">
      <j1 rule="hyper" parents="65 20163 22366"/>
    </justification>
  </clause>

  <clause id="22368">
    <literal><![CDATA[
      K(x \ (y / (z \ x)),T(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(z / ((y / x) \ x),u) = w
    ]]></literal>
    <justification jstring="[para(22367(a,1),17371(a,1))].">
      <j1 rule="para" parents="22367 17371"/>
    </justification>
  </clause>

  <clause id="22369">
    <literal><![CDATA[
      T(x,T(y \ T(z,u),u)) = T(x,u \ ((y \ u) * z))
    ]]></literal>
    <justification jstring="[hyper(7581,a,22361,a)].">
      <j1 rule="hyper" parents="7581 22361"/>
    </justification>
  </clause>

  <clause id="22370">
    <literal><![CDATA[
      T(x,T(y \ T(z,u),u)) = T(x,u \ ((u \ y) \ z))
    ]]></literal>
    <justification jstring="[hyper(299,a,21795,a,b,22369,a),flip(a)].">
      <j1 rule="hyper" parents="299 21795 22369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22371">
    <literal><![CDATA[
      T(x,T(y \ T(z,u),u)) = T(x,(y / u) \ (u \ z))
    ]]></literal>
    <justification jstring="[hyper(299,a,21794,a,b,22369,a),flip(a)].">
      <j1 rule="hyper" parents="299 21794 22369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22372">
    <literal><![CDATA[
      T(x,T(y \ T(z,u),u)) = T(x,(y * u) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(299,a,21776,a,b,22369,a),flip(a)].">
      <j1 rule="hyper" parents="299 21776 22369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22373">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),T(u \ T(z,y),y)) = T(x,((y \ u) \ z) / y)
    ]]></literal>
    <justification jstring="[hyper(299,a,21797,a(flip),b,22369,a),flip(a)].">
      <j1 rule="hyper" parents="299 21797 22369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22374">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),T(z \ T(u,y),y)) = T(x,((z \ y) * u) / y)
    ]]></literal>
    <justification jstring="[hyper(299,a,18961,a(flip),b,22369,a),flip(a)].">
      <j1 rule="hyper" parents="299 18961 22369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22375">
    <literal><![CDATA[
      T(x,T(((y \ z) * (y \ z)) \ T(u,y),y)) = T(x,y * ((z / (1 / (y \ z))) \ u))
    ]]></literal>
    <justification jstring="[hyper(299,a,19404,a(flip),b,22370,a),flip(a)].">
      <j1 rule="hyper" parents="299 19404 22370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22376">
    <literal><![CDATA[
      T(x,T(y \ T(z,u),u)) = T(x,(u / y) * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(21633,a,22371,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="21633 22371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22377">
    <literal><![CDATA[
      T(x,T((y \ z) \ T(u,y),y)) = T(x,y / (u \ z))
    ]]></literal>
    <justification jstring="[hyper(299,a,22260,a(flip),b,22372,a),flip(a)].">
      <j1 rule="hyper" parents="299 22260 22372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22378">
    <literal><![CDATA[
      T(x,y / (z \ (y * u))) = T(x,T(u \ T(z,y),y))
    ]]></literal>
    <justification jstring="[para(9(a,1),22377(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="9 22377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22379">
    <literal><![CDATA[
      T(x,T(((y \ 1) * z) \ T(u,y),y)) = T(x,y / (u \ L(z,y,y)))
    ]]></literal>
    <justification jstring="[para(1679(a,1),22377(a,1,2,1,1))].">
      <j1 rule="para" parents="1679 22377"/>
    </justification>
  </clause>

  <clause id="22380">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),T(z \ T(u,y),y)) = T(x,(u \ (y * z)) \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,19360,a(flip),b,22378,a),flip(a)].">
      <j1 rule="hyper" parents="65 19360 22378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22381">
    <literal><![CDATA[
      T(x,((y \ z) \ u) / y) = T(x,z \ T(u,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,17271,a(flip),b,22373,a),flip(a)].">
      <j1 rule="hyper" parents="65 17271 22373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22383">
    <literal><![CDATA[
      T(x,(y * z) \ T(u,y)) = T(x,(z \ u) / y)
    ]]></literal>
    <justification jstring="[para(9(a,1),22381(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="9 22381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22384">
    <literal><![CDATA[
      T(x,(y \ T(z,y \ 1)) \ T(u,z)) = T(x,(((y \ z) / z) \ u) / z)
    ]]></literal>
    <justification jstring="[para(4235(a,1),22381(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4235 22381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22385">
    <literal><![CDATA[
      T(x,(T(y,z) * u) \ z) = T(x,(u \ z) / y)
    ]]></literal>
    <justification jstring="[hyper(65,a,20221,a,b,22383,a)].">
      <j1 rule="hyper" parents="65 20221 22383"/>
    </justification>
  </clause>

  <clause id="22386">
    <literal><![CDATA[
      T(x,(y * z) \ L(T(u,y),w,v5)) = T(x,(z \ L(u,w,v5)) / y)
    ]]></literal>
    <justification jstring="[para(25(a,2),22383(a,1,2,2))].">
      <j1 rule="para" parents="25 22383"/>
    </justification>
  </clause>

  <clause id="22387">
    <literal><![CDATA[
      T(x,(y \ z) / L(z,u,w)) = T(x,(L(z,u,w) * y) \ z)
    ]]></literal>
    <justification jstring="[para(173(a,1),22383(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="173 22383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22388">
    <literal><![CDATA[
      T(x,(y * z) \ T(R(z,u,u),y)) = T(x,a(z,u,u) / y)
    ]]></literal>
    <justification jstring="[para(15581(a,1),22383(a,2,2,1))].">
      <j1 rule="para" parents="15581 22383"/>
    </justification>
  </clause>

  <clause id="22389">
    <literal><![CDATA[
      T(x,(T(y,L(z,u,u)) * (1 / u)) \ L(z,u,u)) = T(x,(u * z) / y)
    ]]></literal>
    <justification jstring="[para(481(a,1),22385(a,2,2,1))].">
      <j1 rule="para" parents="481 22385"/>
    </justification>
  </clause>

  <clause id="22390">
    <literal><![CDATA[
      T(x,(y \ T(T(z,u),y \ 1)) \ u) = T(x,(((y \ T(z,u)) / T(z,u)) \ u) / z)
    ]]></literal>
    <justification jstring="[para(4229(a,2),22385(a,1,2,1))].">
      <j1 rule="para" parents="4229 22385"/>
    </justification>
  </clause>

  <clause id="22391">
    <literal><![CDATA[
      T(x,(y \ z) / (u \ ((1 / u) \ z))) = T(x,((u \ ((1 / u) \ z)) * y) \ z)
    ]]></literal>
    <justification jstring="[para(15157(a,1),22385(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="15157 22385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22392">
    <literal><![CDATA[
      T(x,(y * z) \ R(T(z,y),u,u)) = T(x,a(z,u,u) / y)
    ]]></literal>
    <justification jstring="[para(27(a,2),22388(a,1,2,2))].">
      <j1 rule="para" parents="27 22388"/>
    </justification>
  </clause>

  <clause id="22393">
    <literal><![CDATA[
      T(x,(y * z) \ L(T(z,y),u,u)) = T(x,a(z,u,u) / y)
    ]]></literal>
    <justification jstring="[hyper(65,a,17574,a(flip),b,22392,a)].">
      <j1 rule="hyper" parents="65 17574 22392"/>
    </justification>
  </clause>

  <clause id="22394">
    <literal><![CDATA[
      T(x,(y \ L(y,z,z)) / u) = T(x,a(y,z,z) / u)
    ]]></literal>
    <justification jstring="[hyper(65,a,22393,a(flip),b,22386,a),flip(a)].">
      <j1 rule="hyper" parents="65 22393 22386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22395">
    <literal><![CDATA[
      T(x,y \ (z \ L(z,u,u))) = T(x,a(z,u,u) / y)
    ]]></literal>
    <justification jstring="[hyper(21023,a,22394,a)].">
      <j1 rule="hyper" parents="21023 22394"/>
    </justification>
  </clause>

  <clause id="22396">
    <literal><![CDATA[
      T(x,y \ (z \ L(z,u,u))) = T(x,y \ a(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,18635,a(flip),b,22395,a),flip(a)].">
      <j1 rule="hyper" parents="299 18635 22395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22398">
    <literal><![CDATA[
      T(x,((y \ z) * u) / z) = T(x,(u \ (z * y)) \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,22374,a(flip),b,22380,a)].">
      <j1 rule="hyper" parents="65 22374 22380"/>
    </justification>
  </clause>

  <clause id="22399">
    <literal><![CDATA[
      T(x,(((y \ z) / z) \ u) / z) = T(x,(z / y) \ T(u,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,18944,a(flip),b,22384,a),flip(a)].">
      <j1 rule="hyper" parents="65 18944 22384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22400">
    <literal><![CDATA[
      T(x,(T(y,z) * (1 / u)) \ L(z,u,u)) = T(x,(u * z) / y)
    ]]></literal>
    <justification jstring="[para(14206(a,1),22389(a,1,2,1,1))].">
      <j1 rule="para" parents="14206 22389"/>
    </justification>
  </clause>

  <clause id="22401">
    <literal><![CDATA[
      T(x,(T(y,z) * (u \ 1)) \ L(z,u,u)) = T(x,(u * z) / y)
    ]]></literal>
    <justification jstring="[hyper(65,a,3880,a(flip),b,22400,a)].">
      <j1 rule="hyper" parents="65 3880 22400"/>
    </justification>
  </clause>

  <clause id="22403">
    <literal><![CDATA[
      T(x,(T(y,z) / u) \ z) = T(x,(u * z) / y)
    ]]></literal>
    <justification jstring="[hyper(21914,a,22401,a)].">
      <j1 rule="hyper" parents="21914 22401"/>
    </justification>
  </clause>

  <clause id="22404">
    <literal><![CDATA[
      T(x,(y \ z) / (u \ ((u \ 1) \ z))) = T(x,((u \ ((1 / u) \ z)) * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(20499,a,22391,a)].">
      <j1 rule="hyper" parents="20499 22391"/>
    </justification>
  </clause>

  <clause id="22405">
    <literal><![CDATA[
      T(x,((y \ ((1 / y) \ z)) * u) \ z) = T(x,L(u \ z,y,y) / z)
    ]]></literal>
    <justification jstring="[hyper(21835,a,22404,a),flip(a)].">
      <j1 rule="hyper" parents="21835 22404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22406">
    <literal><![CDATA[
      T(x,T((y \ z) \ ((y \ z) \ T(u,y)),y)) = T(x,y * ((z / (1 / (y \ z))) \ u))
    ]]></literal>
    <justification jstring="[hyper(14293,a,22375,a)].">
      <j1 rule="hyper" parents="14293 22375"/>
    </justification>
  </clause>

  <clause id="22407">
    <literal><![CDATA[
      T(x,(((y \ T(z,u)) / T(z,u)) \ u) / z) = T(x,(T(z,u) / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,18944,a(flip),b,22390,a),flip(a)].">
      <j1 rule="hyper" parents="65 18944 22390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22408">
    <literal><![CDATA[
      T(x,(((y \ T(z,u)) / T(z,u)) \ u) / z) = T(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[hyper(299,a,22403,a(flip),b,22407,a),flip(a)].">
      <j1 rule="hyper" parents="299 22403 22407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22409">
    <literal><![CDATA[
      T(x,(((y \ z) / z) \ u) / z) = T(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[para(14319(a,1),22408(a,1,2,1,1))].">
      <j1 rule="para" parents="14319 22408"/>
    </justification>
  </clause>

  <clause id="22410">
    <literal><![CDATA[
      T(x,(y / z) \ T(u,y)) = T(x,(z * u) / y)
    ]]></literal>
    <justification jstring="[hyper(65,a,22399,a(flip),b,22409,a)].">
      <j1 rule="hyper" parents="65 22399 22409"/>
    </justification>
  </clause>

  <clause id="22412">
    <literal><![CDATA[
      T(x,(y * T(z,u)) / u) = T(x,(u / y) \ z)
    ]]></literal>
    <justification jstring="[hyper(15838,a,22410,a),flip(a)].">
      <j1 rule="hyper" parents="15838 22410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22413">
    <literal><![CDATA[
      T(x,((y \ z) * u) / z) = T(x,y \ T(u,z))
    ]]></literal>
    <justification jstring="[para(76(a,1),22410(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="76 22410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22414">
    <literal><![CDATA[
      T(x,(y * z) / T(u,z)) = T(x,(u / y) \ z)
    ]]></literal>
    <justification jstring="[hyper(22191,a,22412,a)].">
      <j1 rule="hyper" parents="22191 22412"/>
    </justification>
  </clause>

  <clause id="22415">
    <literal><![CDATA[
      T(x,(y \ (z * u)) \ z) = T(x,u \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,22398,a(flip),b,22413,a)].">
      <j1 rule="hyper" parents="65 22398 22413"/>
    </justification>
  </clause>

  <clause id="22416">
    <literal><![CDATA[
      T(x,(y * a(z,u,w)) / v5) = T(x,(v5 / y) \ a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(18889,a,22414,a)].">
      <j1 rule="hyper" parents="18889 22414"/>
    </justification>
  </clause>

  <clause id="22418">
    <literal><![CDATA[
      T(x,(a(y,z,u) * w) / v5) = T(x,(v5 / w) \ a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,18891,a,b,22416,a)].">
      <j1 rule="hyper" parents="65 18891 22416"/>
    </justification>
  </clause>

  <clause id="22419">
    <literal><![CDATA[
      T(x,((y * (z \ 1)) / u) \ a(z \ y,z,z)) = T(x,u / (y / z))
    ]]></literal>
    <justification jstring="[hyper(65,a,22319,a(flip),b,22418,a),flip(a)].">
      <j1 rule="hyper" parents="65 22319 22418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22420">
    <literal><![CDATA[
      T(x,(y / z) \ a(u,u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,z / L(y,u,u)) = w
    ]]></literal>
    <justification jstring="[para(22418(a,1),22144(a,1))].">
      <j1 rule="para" parents="22418 22144"/>
    </justification>
  </clause>

  <clause id="22421">
    <literal><![CDATA[
      T(x,T(T((y \ z) \ ((y \ z) \ u),y),y)) = T(x,y * ((z / (1 / (y \ z))) \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,17529,a,b,22406,a)].">
      <j1 rule="hyper" parents="65 17529 22406"/>
    </justification>
  </clause>

  <clause id="22422">
    <literal><![CDATA[
      T(x,y * ((z / (1 / (y \ z))) \ u)) = T(x,(y \ z) \ ((y \ z) \ u))
    ]]></literal>
    <justification jstring="[hyper(8310,a,22421,a),flip(a)].">
      <j1 rule="hyper" parents="8310 22421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22424">
    <literal><![CDATA[
      T(x,y * ((z / (1 / (y \ z))) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z \ y) * ((z \ y) * u)) = w
    ]]></literal>
    <justification jstring="[para(22422(a,2),21061(a,1))].">
      <j1 rule="para" parents="22422 21061"/>
    </justification>
  </clause>

  <clause id="22425">
    <literal><![CDATA[
      K(T(x,T(y,z)) / (z \ y),T(u,T(y,z))) = K((T(y,z) / x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,13782,a(flip),b,22364,a),flip(a)].">
      <j1 rule="hyper" parents="65 13782 22364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22426">
    <literal><![CDATA[
      K(T(x,T(y,z)) / (z \ y),T(u,y)) = K((T(y,z) / x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(16469,a,22425,a)].">
      <j1 rule="hyper" parents="16469 22425"/>
    </justification>
  </clause>

  <clause id="22429">
    <literal><![CDATA[
      K(x \ ((x / (y \ ((1 / y) \ x))) * z),u) = K(x \ L(T(z,x),y,y),T(u,x))
    ]]></literal>
    <justification jstring="[hyper(299,a,15725,a(flip),b,22362,a),flip(a)].">
      <j1 rule="hyper" parents="299 15725 22362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22430">
    <literal><![CDATA[
      K(x \ ((x / (y \ ((1 / y) \ x))) * z),u) = K(L(T(z,x),y,y) / x,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,8116,a(flip),b,22429,a),flip(a)].">
      <j1 rule="hyper" parents="299 8116 22429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22431">
    <literal><![CDATA[
      K(x \ ((x / (y \ ((1 / y) \ x))) * z),u) = K(x \ L(z,y,y),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,13739,a(flip),b,22430,a),flip(a)].">
      <j1 rule="hyper" parents="299 13739 22430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22433">
    <literal><![CDATA[
      K(x,T(T((y * z) / y,u),y * L(u,w,w))) = K(x,L(T(z,w \ (w \ 1)),w \ (w \ y),u))
    ]]></literal>
    <justification jstring="[hyper(65,a,22162,a(flip),b,22209,a)].">
      <j1 rule="hyper" parents="65 22162 22209"/>
    </justification>
  </clause>

  <clause id="22434">
    <literal><![CDATA[
      K(x,T(T(T(y,z),u),z * L(u,w,w))) = K(x,L(T(y,w \ (w \ 1)),w \ (w \ z),u))
    ]]></literal>
    <justification jstring="[hyper(65,a,9605,a(flip),b,22433,a)].">
      <j1 rule="hyper" parents="65 9605 22433"/>
    </justification>
  </clause>

  <clause id="22435">
    <literal><![CDATA[
      K(x,T(T(T(y,z),u),z * L(u,w,w))) = K(x,L(T(y,w * (w \ 1)),w \ (w \ z),u))
    ]]></literal>
    <justification jstring="[hyper(299,a,16314,a(flip),b,22434,a),flip(a)].">
      <j1 rule="hyper" parents="299 16314 22434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22436">
    <literal><![CDATA[
      K(x,T(T(T(y,z),u),z * L(u,w,w))) = K(x,L(T(y,1),w \ (w \ z),u))
    ]]></literal>
    <justification jstring="[para(10(a,1),22435(a,2,2,1,2))].">
      <j1 rule="para" parents="10 22435"/>
    </justification>
  </clause>

  <clause id="22438">
    <literal><![CDATA[
      K(x,T(T(T(y,z),u),z * L(u,w,w))) = K(x,L(y,w \ (w \ z),u))
    ]]></literal>
    <justification jstring="[para(193(a,1),22436(a,2,2,1))].">
      <j1 rule="para" parents="193 22436"/>
    </justification>
  </clause>

  <clause id="22439">
    <literal><![CDATA[
      K(x,T(T(T(y,z),u),z * u)) = K(x,L(y,w \ (w \ z),u))
    ]]></literal>
    <justification jstring="[hyper(65,a,21401,a(flip),b,22438,a)].">
      <j1 rule="hyper" parents="65 21401 22438"/>
    </justification>
  </clause>

  <clause id="22441">
    <literal><![CDATA[
      K(x,L(y,z \ (z \ u),w)) = K(x,L(y,w,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,22200,a(flip),b,22439,a),flip(a)].">
      <j1 rule="hyper" parents="65 22200 22439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22442">
    <literal><![CDATA[
      K((x \ (y \ ((1 / y) \ z))) \ u,L(w,x,z)) = K((y \ ((1 / y) \ z)) \ (x * u),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,14998,a(flip),b,22441,a),flip(a)].">
      <j1 rule="hyper" parents="65 14998 22441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22443">
    <literal><![CDATA[
      K((x \ (y \ ((1 / y) \ x))) \ z,u) = K((y \ ((1 / y) \ x)) \ (x * z),u)
    ]]></literal>
    <justification jstring="[hyper(15519,a,22442,a)].">
      <j1 rule="hyper" parents="15519 22442"/>
    </justification>
  </clause>

  <clause id="22444">
    <literal><![CDATA[
      K((x \ (y \ ((1 / y) \ x))) \ z,u) = K(x \ L(x * z,y,y),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,15725,a(flip),b,22443,a),flip(a)].">
      <j1 rule="hyper" parents="299 15725 22443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22445">
    <literal><![CDATA[
      K((x \ (y \ ((1 / y) \ x))) \ z,u) = K(x * L(x \ z,y,y),u)
    ]]></literal>
    <justification jstring="[para(6514(a,1),22444(a,2,1))].">
      <j1 rule="para" parents="6514 22444"/>
    </justification>
  </clause>

  <clause id="22446">
    <literal><![CDATA[
      K(a(x,x,x \ (x \ y)) \ z,u) = K(y * L(y \ z,x,x),u)
    ]]></literal>
    <justification jstring="[para(1667(a,2),22445(a,1,1,1))].">
      <j1 rule="para" parents="1667 22445"/>
    </justification>
  </clause>

  <clause id="22447">
    <literal><![CDATA[
      K((x \ (y \ ((1 / y) \ x))) \ (z / (z / (z / x))),u) = K(x * L((z / (z / x)) \ (z / x),y,y),u)
    ]]></literal>
    <justification jstring="[para(5956(a,2),22445(a,2,1,2,1))].">
      <j1 rule="para" parents="5956 22445"/>
    </justification>
  </clause>

  <clause id="22448">
    <literal><![CDATA[
      K(x * L(x \ y,z,z),u) = K(y * a(z,z,z \ (z \ x)),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,21114,a(flip),b,22446,a),flip(a)].">
      <j1 rule="hyper" parents="65 21114 22446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22449">
    <literal><![CDATA[
      K(x * L(x \ y,z,z),u) = K(y * a(w,w,v5),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,21156,a,b,22448,a),flip(a)].">
      <j1 rule="hyper" parents="299 21156 22448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22451">
    <literal><![CDATA[
      T(x,(y \ 1) \ (z \ T(a(y,y,y) * u,y \ 1))) = T(x,T(T(z * (y \ 1),y \ 1) \ u,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,8839,a(flip),b,22181,a),flip(a)].">
      <j1 rule="hyper" parents="299 8839 22181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22452">
    <literal><![CDATA[
      T(x,(y \ 1) \ (z \ T(a(y,y,y) * u,y \ 1))) = T(x,T(T(z * (y \ 1),y * 1) \ u,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,17614,a(flip),b,22451,a),flip(a)].">
      <j1 rule="hyper" parents="299 17614 22451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22453">
    <literal><![CDATA[
      T(x,(y \ 1) \ (z \ T(a(y,y,y) * u,y \ 1))) = T(x,T(T(z * (y \ 1),y) \ u,y))
    ]]></literal>
    <justification jstring="[para(8(a,1),22452(a,2,2,1,1,2))].">
      <j1 rule="para" parents="8 22452"/>
    </justification>
  </clause>

  <clause id="22454">
    <literal><![CDATA[
      T(x,(y \ 1) \ (z \ T(a(y,y,y) * u,y \ 1))) = T(x,T(((y \ 1) * z) \ u,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,19382,a(flip),b,22453,a),flip(a)].">
      <j1 rule="hyper" parents="299 19382 22453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22455">
    <literal><![CDATA[
      T(x,T(((y \ 1) * z) \ u,y)) = T(x,(y \ 1) \ (z \ T(u,y)))
    ]]></literal>
    <justification jstring="[hyper(65,a,20439,a(flip),b,22454,a),flip(a)].">
      <j1 rule="hyper" parents="65 20439 22454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22456">
    <literal><![CDATA[
      T(x,T(((y \ 1) * z) \ u,y)) = T(x,y * (z \ T(u,y)))
    ]]></literal>
    <justification jstring="[hyper(299,a,14215,a(flip),b,22455,a),flip(a)].">
      <j1 rule="hyper" parents="299 14215 22455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22457">
    <literal><![CDATA[
      T(x,y * (z \ T(T(u,y),y))) = T(x,y / (u \ L(z,y,y)))
    ]]></literal>
    <justification jstring="[hyper(65,a,22379,a(flip),b,22456,a),flip(a)].">
      <j1 rule="hyper" parents="65 22379 22456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22458">
    <literal><![CDATA[
      T(x,y / (z \ L(u,y,y))) = T(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,15847,a(flip),b,22457,a),flip(a)].">
      <j1 rule="hyper" parents="65 15847 22457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22460">
    <literal><![CDATA[
      K((x \ (y \ ((1 / y) \ x))) \ T(z / x,z),u) = K(x * L((z / (z / x)) \ (z / x),y,y),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,17494,a(flip),b,22447,a)].">
      <j1 rule="hyper" parents="65 17494 22447"/>
    </justification>
  </clause>

  <clause id="22461">
    <literal><![CDATA[
      K(x * L((y / (y / x)) \ (y / x),z,z),u) = K((x \ (z \ ((1 / z) \ x))) \ (x \ y),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,13835,a(flip),b,22460,a),flip(a)].">
      <j1 rule="hyper" parents="65 13835 22460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22462">
    <literal><![CDATA[
      K(x * L((y / (y / x)) \ (y / x),z,z),u) = K(x \ ((x / (z \ ((1 / z) \ x))) * y),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,21849,a(flip),b,22461,a),flip(a)].">
      <j1 rule="hyper" parents="299 21849 22461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22463">
    <literal><![CDATA[
      K(x * L((y / (y / x)) \ (y / x),z,z),u) = K(x \ L(y,z,z),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,22431,a(flip),b,22462,a),flip(a)].">
      <j1 rule="hyper" parents="299 22431 22462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22464">
    <literal><![CDATA[
      K(x * L(x \ (y / (y / (y / x))),z,z),u) = K(x \ L(y,z,z),u)
    ]]></literal>
    <justification jstring="[para(5956(a,1),22463(a,1,1,2,1))].">
      <j1 rule="para" parents="5956 22463"/>
    </justification>
  </clause>

  <clause id="22465">
    <literal><![CDATA[
      K(x \ L(y,z,z),u) = K((y / (y / (y / x))) * a(w,w,v5),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,22449,a(flip),b,22464,a),flip(a)].">
      <j1 rule="hyper" parents="65 22449 22464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22467">
    <literal><![CDATA[
      K(x \ L(y,z,z),u) = K(T(y / x,y) * a(w,w,v5),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,17815,a(flip),b,22465,a),flip(a)].">
      <j1 rule="hyper" parents="299 17815 22465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22468">
    <literal><![CDATA[
      K(x \ L(y,z,z),u) = K((y / x) * a(w,w,v5),T(u,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,22326,a(flip),b,22467,a),flip(a)].">
      <j1 rule="hyper" parents="299 22326 22467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22469">
    <literal><![CDATA[
      K(x \ L(y,z,z),u) = K(y / L(x,w,w),T(u,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,22126,a(flip),b,22468,a),flip(a)].">
      <j1 rule="hyper" parents="299 22126 22468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22470">
    <literal><![CDATA[
      K(L(x,y,y) \ z,u) = K(x \ L(z,w,w),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,7499,a(flip),b,22469,a)].">
      <j1 rule="hyper" parents="299 7499 22469"/>
    </justification>
  </clause>

  <clause id="22471">
    <literal><![CDATA[
      T(x,L(y,z,z) \ u) = (x * w) / (K(y \ L(u,v5,v5),x) * w)
    ]]></literal>
    <justification jstring="[para(22470(a,1),5517(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="22470 5517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22472">
    <literal><![CDATA[
      T(x,L(y,z,z) \ u) = T(x,y \ L(u,w,w))
    ]]></literal>
    <justification jstring="[hyper(299,a,5517,a(flip),b,22471,a),flip(a)].">
      <j1 rule="hyper" parents="299 5517 22471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22473">
    <literal><![CDATA[
      T(x,y \ L(T(z,y) * u,w,w)) = T(x,z / (u \ L(y,v5,v5)))
    ]]></literal>
    <justification jstring="[hyper(22268,a,22472,a),flip(a)].">
      <j1 rule="hyper" parents="22268 22472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22474">
    <literal><![CDATA[
      T(x,y \ L(z,u,u)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(13759,a,22472,a),flip(a)].">
      <j1 rule="hyper" parents="13759 22472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22475">
    <literal><![CDATA[
      T(x,y \ L(y / z,u,u)) = T(x,z \ a(w,w,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,21818,a(flip),b,22472,a),flip(a)].">
      <j1 rule="hyper" parents="65 21818 22472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22476">
    <literal><![CDATA[
      T(x,y \ L(z * u,w,w)) = T(x,y \ ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,15684,a(flip),b,22472,a),flip(a)].">
      <j1 rule="hyper" parents="65 15684 22472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22477">
    <literal><![CDATA[
      T(x,y \ L(z,u,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ z) = w
    ]]></literal>
    <justification jstring="[para(22472(a,1),13759(a,1))].">
      <j1 rule="para" parents="22472 13759"/>
    </justification>
  </clause>

  <clause id="22478">
    <literal><![CDATA[
      T(x,(y * (z \ 1)) \ u) = T(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[hyper(21914,a,22474,a),flip(a)].">
      <j1 rule="hyper" parents="21914 22474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22480">
    <literal><![CDATA[
      T(x,y \ ((z \ 1) \ u)) = T(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[para(1670(a,1),22474(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1670 22474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22481">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),(z / u) \ y) = T(x,y / (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(65,a,18260,a(flip),b,22478,a),flip(a)].">
      <j1 rule="hyper" parents="65 18260 22478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22483">
    <literal><![CDATA[
      T(x,y \ ((z \ 1) \ (y \ 1))) = T(x,y \ (z / y))
    ]]></literal>
    <justification jstring="[hyper(299,a,17535,a(flip),b,22480,a),flip(a)].">
      <j1 rule="hyper" parents="299 17535 22480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22484">
    <literal><![CDATA[
      T(x,(y \ z) * (T(u,z * y) \ w)) = T(x,u \ ((y \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,21749,a,b,22480,a)].">
      <j1 rule="hyper" parents="65 21749 22480"/>
    </justification>
  </clause>

  <clause id="22485">
    <literal><![CDATA[
      T(x,L(y,z,u) \ (y * w)) = T(x,y * (L(y,z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,21751,a(flip),b,22480,a),flip(a)].">
      <j1 rule="hyper" parents="65 21751 22480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22487">
    <literal><![CDATA[
      T(((x \ 1) * y) / (x \ 1),z \ (x / z)) = T(y,(z * (1 / x)) \ ((z * (1 / x)) \ 1))
    ]]></literal>
    <justification jstring="[hyper(18918,a,22483,a),flip(a)].">
      <j1 rule="hyper" parents="18918 22483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22489">
    <literal><![CDATA[
      T(x,y \ L(T(z,u) * w,v5,v5)) = T(x,y \ ((z \ K(u,z)) \ w))
    ]]></literal>
    <justification jstring="[para(5039(a,1),22476(a,2,2,2,1))].">
      <j1 rule="para" parents="5039 22476"/>
    </justification>
  </clause>

  <clause id="22490">
    <literal><![CDATA[
      T(x,y * (L(y,z,u) \ (y \ w))) = T(x,L(y,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(10(a,1),22485(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 22485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22491">
    <literal><![CDATA[
      T(x,y \ (T(z,y) * u)) = T(x,z / (u \ L(y,w,w)))
    ]]></literal>
    <justification jstring="[hyper(22477,a,22473,a)].">
      <j1 rule="hyper" parents="22477 22473"/>
    </justification>
  </clause>

  <clause id="22492">
    <literal><![CDATA[
      T(x,y / (z \ L(u,w,w))) = T(x,y / (z \ u))
    ]]></literal>
    <justification jstring="[hyper(22267,a,22491,a),flip(a)].">
      <j1 rule="hyper" parents="22267 22491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22493">
    <literal><![CDATA[
      T(x,y / (z \ u)) = T(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,22458,a(flip),b,22492,a),flip(a)].">
      <j1 rule="hyper" parents="65 22458 22492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22494">
    <literal><![CDATA[
      T(x,y / (z \ L(u,w,w))) = T(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,22492,a,b,22493,a)].">
      <j1 rule="hyper" parents="65 22492 22493"/>
    </justification>
  </clause>

  <clause id="22495">
    <literal><![CDATA[
      T(x,y * (((z \ u) \ 1) \ w)) = T(x,y / (w \ (u \ z)))
    ]]></literal>
    <justification jstring="[hyper(65,a,22315,a(flip),b,22493,a),flip(a)].">
      <j1 rule="hyper" parents="65 22315 22493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22497">
    <literal><![CDATA[
      T(x,y * (L(z,u,u) \ w)) = T(x,y * (z \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,22493,a(flip),b,22494,a)].">
      <j1 rule="hyper" parents="65 22493 22494"/>
    </justification>
  </clause>

  <clause id="22498">
    <literal><![CDATA[
      T(x,y * ((z / (1 / u)) \ w)) = T(x,y * ((z * u) \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,21978,a(flip),b,22497,a),flip(a)].">
      <j1 rule="hyper" parents="65 21978 22497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22500">
    <literal><![CDATA[
      T(x,y * ((z * (y \ z)) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z \ y) * ((z \ y) * u)) = w
    ]]></literal>
    <justification jstring="[para(22498(a,1),22424(a,1))].">
      <j1 rule="para" parents="22498 22424"/>
    </justification>
  </clause>

  <clause id="22501">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),(u / z) * y) = T(x,y / (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(21633,a,22481,a)].">
      <j1 rule="hyper" parents="21633 22481"/>
    </justification>
  </clause>

  <clause id="22502">
    <literal><![CDATA[
      T(x,y \ ((z \ u) \ w)) = T(x,y \ ((u \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(21831,a,22484,a)].">
      <j1 rule="hyper" parents="21831 22484"/>
    </justification>
  </clause>

  <clause id="22507">
    <literal><![CDATA[
      T(x,y / (z * (u \ 1))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (u / z)) = w
    ]]></literal>
    <justification jstring="[para(22501(a,1),16786(a,1))].">
      <j1 rule="para" parents="22501 16786"/>
    </justification>
  </clause>

  <clause id="22508">
    <literal><![CDATA[
      T(((x \ 1) * y) / (x \ 1),z \ (x / z)) = T(y,(1 / x) \ (z \ ((z * (1 / x)) \ 1)))
    ]]></literal>
    <justification jstring="[para(956(a,1),22487(a,2,2))].">
      <j1 rule="para" parents="956 22487"/>
    </justification>
  </clause>

  <clause id="22509">
    <literal><![CDATA[
      T(((x \ 1) * y) / (x \ 1),z \ (x / z)) = T(y,x * (z \ ((z * (1 / x)) \ 1)))
    ]]></literal>
    <justification jstring="[hyper(299,a,14296,a(flip),b,22508,a),flip(a)].">
      <j1 rule="hyper" parents="299 14296 22508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22510">
    <literal><![CDATA[
      T(((x \ 1) * y) / (x \ 1),z \ (x / z)) = T(y,(z \ x) * (z \ x))
    ]]></literal>
    <justification jstring="[hyper(299,a,18190,a(flip),b,22509,a),flip(a)].">
      <j1 rule="hyper" parents="299 18190 22509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22511">
    <literal><![CDATA[
      T(((L(x,y,z) \ 1) * u) / (L(x,y,z) \ 1),x \ (L(x,y,z) / x)) = T(u,T(x \ L(x,y,z),x) * (x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[para(3818(a,2),22510(a,2,2,1))].">
      <j1 rule="para" parents="3818 22510"/>
    </justification>
  </clause>

  <clause id="22512">
    <literal><![CDATA[
      T(x,y / (((z * u) * (T(w,u * u) / (z * u))) \ v5)) = T(x,y / (T(w,z * (1 / u)) \ v5))
    ]]></literal>
    <justification jstring="[para(14370(a,1),22283(a,1,2,2,1,2))].">
      <j1 rule="para" parents="14370 22283"/>
    </justification>
  </clause>

  <clause id="22513">
    <literal><![CDATA[
      T(x,y / (T((z * u) * (w / (z * u)),u * u) \ v5)) = T(x,y / (T(w,z * (1 / u)) \ v5))
    ]]></literal>
    <justification jstring="[para(3459(a,2),22512(a,1,2,2,1))].">
      <j1 rule="para" parents="3459 22512"/>
    </justification>
  </clause>

  <clause id="22514">
    <literal><![CDATA[
      T(x,y / (((z * u) * (w / (z * u))) \ v5)) = T(x,y / (T(w,z * (1 / u)) \ v5))
    ]]></literal>
    <justification jstring="[hyper(20228,a,22513,a)].">
      <j1 rule="hyper" parents="20228 22513"/>
    </justification>
  </clause>

  <clause id="22515">
    <literal><![CDATA[
      T(x,y / (T(z,u * (1 / w)) \ v5)) = T(x,y / (T(z,u * w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,22282,a(flip),b,22514,a),flip(a)].">
      <j1 rule="hyper" parents="65 22282 22514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22516">
    <literal><![CDATA[
      T(x,y / (T(z,u / w) \ v5)) = T(x,y / (T(z,u * w) \ v5))
    ]]></literal>
    <justification jstring="[para(14472(a,1),22515(a,1,2,2,1))].">
      <j1 rule="para" parents="14472 22515"/>
    </justification>
  </clause>

  <clause id="22517">
    <literal><![CDATA[
      T(x,y / (T(z,u * w) \ (w \ u))) = T(x,y / (T(u / w,w) / z))
    ]]></literal>
    <justification jstring="[hyper(65,a,20243,a(flip),b,22516,a),flip(a)].">
      <j1 rule="hyper" parents="65 20243 22516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22518">
    <literal><![CDATA[
      T(x,y / (T(z,u * w) \ (w \ u))) = T(x,y / ((w \ u) / z))
    ]]></literal>
    <justification jstring="[para(109(a,1),22517(a,2,2,2,1))].">
      <j1 rule="para" parents="109 22517"/>
    </justification>
  </clause>

  <clause id="22519">
    <literal><![CDATA[
      K((((x * y) / x) * (T(y,K(x,y)) / z)) \ T(x,y),u) = K(z / (((x * y) / x) / (y \ x)),u)
    ]]></literal>
    <justification jstring="[para(7139(a,1),22299(a,1,1,1,2,1))].">
      <j1 rule="para" parents="7139 22299"/>
    </justification>
  </clause>

  <clause id="22520">
    <literal><![CDATA[
      K((((x * y) / x) * (y / z)) \ T(x,y),u) = K(z / (((x * y) / x) / (y \ x)),u)
    ]]></literal>
    <justification jstring="[para(3612(a,1),22519(a,1,1,1,2,1))].">
      <j1 rule="para" parents="3612 22519"/>
    </justification>
  </clause>

  <clause id="22521">
    <literal><![CDATA[
      K(x / (((y * z) / y) / (z \ y)),u) = K((z * (z / x)) \ y,u)
    ]]></literal>
    <justification jstring="[para(14416(a,1),22520(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14416 22520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22522">
    <literal><![CDATA[
      K(x / (T(y,z) / (y \ z)),u) = K((y * (y / x)) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,20259,a(flip),b,22521,a)].">
      <j1 rule="hyper" parents="65 20259 22521"/>
    </justification>
  </clause>

  <clause id="22523">
    <literal><![CDATA[
      K(x / ((y \ z) \ y),u) = K((y * (y / x)) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,21142,a(flip),b,22522,a)].">
      <j1 rule="hyper" parents="65 21142 22522"/>
    </justification>
  </clause>

  <clause id="22524">
    <literal><![CDATA[
      K(x / (((y \ 1) * (y \ z)) \ y),u) = K((y * (y / x)) \ ((1 / y) * z),u)
    ]]></literal>
    <justification jstring="[para(1683(a,1),22523(a,1,1,2,1))].">
      <j1 rule="para" parents="1683 22523"/>
    </justification>
  </clause>

  <clause id="22525">
    <literal><![CDATA[
      (x * y) / (K((z * (z / u)) \ w,x) * y) = T(x,u / ((z \ w) \ z))
    ]]></literal>
    <justification jstring="[para(22523(a,1),5517(a,1,2,1))].">
      <j1 rule="para" parents="22523 5517"/>
    </justification>
  </clause>

  <clause id="22526">
    <literal><![CDATA[
      T(x,y / ((z \ u) \ z)) = T(x,(z * (z / y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(5519,a,22525,a),flip(a)].">
      <j1 rule="hyper" parents="5519 22525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22527">
    <literal><![CDATA[
      T(T(x,K(y,z)),(u * (u / y)) \ z) = T(x,((u \ z) \ u) \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,16323,a(flip),b,22526,a),flip(a)].">
      <j1 rule="hyper" parents="65 16323 22526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22528">
    <literal><![CDATA[
      T(x,(y * (y / z)) \ (y * u)) = T(x,z / (u \ y))
    ]]></literal>
    <justification jstring="[para(9(a,1),22526(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="9 22526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22529">
    <literal><![CDATA[
      T(x,y \ ((y / (y / z)) * u)) = T(x,z / (u \ y))
    ]]></literal>
    <justification jstring="[hyper(21782,a,22528,a)].">
      <j1 rule="hyper" parents="21782 22528"/>
    </justification>
  </clause>

  <clause id="22530">
    <literal><![CDATA[
      T(x,y / (a(z / (z / y),u,u) \ z)) = T(x,z \ R(z / (z / y),u,u))
    ]]></literal>
    <justification jstring="[para(15579(a,1),22529(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="15579 22529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22531">
    <literal><![CDATA[
      T(x,y / (z * (z / u))) = T(x,((z \ y) \ z) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,16920,a(flip),b,22527,a)].">
      <j1 rule="hyper" parents="65 16920 22527"/>
    </justification>
  </clause>

  <clause id="22532">
    <literal><![CDATA[
      T(x,((y \ (y * z)) \ y) \ u) = T(x,T(z / (y / u),y))
    ]]></literal>
    <justification jstring="[hyper(22099,a,22531,a),flip(a)].">
      <j1 rule="hyper" parents="22099 22531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22533">
    <literal><![CDATA[
      T(x,T(y / (z / u),z)) = T(x,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[para(9(a,1),22532(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="9 22532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22534">
    <literal><![CDATA[
      T(x,T(y / (T(z,z * u) * u),z * (z * u))) = T(x,(y \ (z * (z * u))) \ z)
    ]]></literal>
    <justification jstring="[para(4270(a,1),22533(a,1,2,1,2))].">
      <j1 rule="para" parents="4270 22533"/>
    </justification>
  </clause>

  <clause id="22535">
    <literal><![CDATA[
      K(x / (y \ (z * ((z \ 1) \ z))),u) = K((z * (z / x)) \ ((1 / z) * y),u)
    ]]></literal>
    <justification jstring="[para(2506(a,1),22524(a,1,1,2))].">
      <j1 rule="para" parents="2506 22524"/>
    </justification>
  </clause>

  <clause id="22536">
    <literal><![CDATA[
      T(x,y / (a(z / (z / y),u,u) \ z)) = T(x,z \ L(z / (z / y),u,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,17574,a(flip),b,22530,a),flip(a)].">
      <j1 rule="hyper" parents="299 17574 22530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22537">
    <literal><![CDATA[
      K((x * (x / y)) \ ((1 / x) * z),u) = K(y / (z \ (x * (x * x))),u)
    ]]></literal>
    <justification jstring="[para(460(a,1),22535(a,1,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="460 22535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22538">
    <literal><![CDATA[
      K((x * (x / y)) \ ((1 / x) * z),u) = K(y / ((z \ x) * (x * x)),u)
    ]]></literal>
    <justification jstring="[para(847(a,1),22537(a,2,1,2))].">
      <j1 rule="para" parents="847 22537"/>
    </justification>
  </clause>

  <clause id="22539">
    <literal><![CDATA[
      K((x * (x / y)) \ ((1 / x) * z),u) = K(x \ (x \ (y / (z \ x))),u)
    ]]></literal>
    <justification jstring="[hyper(299,a,17992,a(flip),b,22538,a),flip(a)].">
      <j1 rule="hyper" parents="299 17992 22538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22540">
    <literal><![CDATA[
      K((x * (x / y)) \ ((x \ 1) * z),u) = K(x \ (x \ (y / (z \ x))),u)
    ]]></literal>
    <justification jstring="[hyper(17511,a,22539,a)].">
      <j1 rule="hyper" parents="17511 22539"/>
    </justification>
  </clause>

  <clause id="22541">
    <literal><![CDATA[
      K(x \ (((x \ 1) / (x / y)) * z),u) = K(x \ (x \ (y / (z \ x))),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,21920,a(flip),b,22540,a)].">
      <j1 rule="hyper" parents="65 21920 22540"/>
    </justification>
  </clause>

  <clause id="22542">
    <literal><![CDATA[
      K(x \ (x \ ((y / (x \ 1)) / (z \ x))),u) = K(x \ ((y \ x) \ z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,22316,a(flip),b,22541,a),flip(a)].">
      <j1 rule="hyper" parents="65 22316 22541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22543">
    <literal><![CDATA[
      K((x / ((y \ 1) \ 1)) / (z \ y),u) = K(y \ ((x \ y) \ z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,19351,a(flip),b,22542,a)].">
      <j1 rule="hyper" parents="65 19351 22542"/>
    </justification>
  </clause>

  <clause id="22544">
    <literal><![CDATA[
      K((x / T(y,1)) / (z \ y),u) = K(y \ ((x \ y) \ z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,20990,a(flip),b,22543,a)].">
      <j1 rule="hyper" parents="65 20990 22543"/>
    </justification>
  </clause>

  <clause id="22545">
    <literal><![CDATA[
      K((x / y) / (z \ y),u) = K(y \ ((x \ y) \ z),u)
    ]]></literal>
    <justification jstring="[para(193(a,1),22544(a,1,1,1,2))].">
      <j1 rule="para" parents="193 22544"/>
    </justification>
  </clause>

  <clause id="22546">
    <literal><![CDATA[
      K(x \ ((y \ x) \ z),u) = K(x \ ((x \ y) * z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,22274,a(flip),b,22545,a),flip(a)].">
      <j1 rule="hyper" parents="65 22274 22545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22547">
    <literal><![CDATA[
      K(x \ ((x \ y) * T(z,x * (y * z))),u) = K(x \ (z / (y \ x)),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,21909,a(flip),b,22546,a),flip(a)].">
      <j1 rule="hyper" parents="65 21909 22546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22548">
    <literal><![CDATA[
      K(x \ ((x \ y) * T(z,x * y)),u) = K(x \ (z / (y \ x)),u)
    ]]></literal>
    <justification jstring="[hyper(20437,a,22547,a)].">
      <j1 rule="hyper" parents="20437 22547"/>
    </justification>
  </clause>

  <clause id="22549">
    <literal><![CDATA[
      K(x \ (y / (z \ x)),u) = K(x \ (y * (x \ z)),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,17570,a(flip),b,22548,a),flip(a)].">
      <j1 rule="hyper" parents="65 17570 22548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22550">
    <literal><![CDATA[
      K(x \ (y * (x \ z)),T(u,y)) = K(z / ((y / x) \ x),u)
    ]]></literal>
    <justification jstring="[hyper(22368,a,22549,a),flip(a)].">
      <j1 rule="hyper" parents="22368 22549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22551">
    <literal><![CDATA[
      K(x / ((y / z) \ z),u) = K(x / (z * (y \ z)),u)
    ]]></literal>
    <justification jstring="[hyper(21816,a,22550,a),flip(a)].">
      <j1 rule="hyper" parents="21816 22550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22552">
    <literal><![CDATA[
      (x * y) / (K(z / (u * (w \ u)),x) * y) = T(x,z / ((w / u) \ u))
    ]]></literal>
    <justification jstring="[para(22551(a,1),5517(a,1,2,1))].">
      <j1 rule="para" parents="22551 5517"/>
    </justification>
  </clause>

  <clause id="22553">
    <literal><![CDATA[
      T(x,y / ((z / u) \ u)) = T(x,y / (u * (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(5519,a,22552,a),flip(a)].">
      <j1 rule="hyper" parents="5519 22552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22554">
    <literal><![CDATA[
      T(T(x,K(y,z)),y / (u * (z \ u))) = T(x,((z / u) \ u) \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,16322,a(flip),b,22553,a),flip(a)].">
      <j1 rule="hyper" parents="65 16322 22553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22555">
    <literal><![CDATA[
      T(x,((y / z) \ z) \ u) = T(x,z \ (y * (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(21825,a,22554,a),flip(a)].">
      <j1 rule="hyper" parents="21825 22554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22556">
    <literal><![CDATA[
      T(x,y \ (z * (y \ (T(u,z) \ w)))) = T(x,u \ (((z / y) \ y) \ w))
    ]]></literal>
    <justification jstring="[hyper(21830,a,22555,a),flip(a)].">
      <j1 rule="hyper" parents="21830 22555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22557">
    <literal><![CDATA[
      T(x,y \ (z * (y \ u))) = T(x,(y \ (z / y)) * u)
    ]]></literal>
    <justification jstring="[hyper(21637,a,22555,a),flip(a)].">
      <j1 rule="hyper" parents="21637 22555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22559">
    <literal><![CDATA[
      T(x,y \ ((z * (y \ z)) \ u)) = T(x,(z \ (y / z)) * (y \ u))
    ]]></literal>
    <justification jstring="[hyper(21893,a,22557,a)].">
      <j1 rule="hyper" parents="21893 22557"/>
    </justification>
  </clause>

  <clause id="22560">
    <literal><![CDATA[
      T(x,y \ ((z * (y \ z)) \ u)) = T(x,z \ (T(z,y) \ u))
    ]]></literal>
    <justification jstring="[hyper(299,a,22039,a(flip),b,22559,a),flip(a)].">
      <j1 rule="hyper" parents="299 22039 22559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22561">
    <literal><![CDATA[
      T(x,y \ (((z / u) \ u) \ w)) = T(x,y \ ((u * (z \ u)) \ w))
    ]]></literal>
    <justification jstring="[hyper(21878,a,22556,a),flip(a)].">
      <j1 rule="hyper" parents="21878 22556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22562">
    <literal><![CDATA[
      T(x,y \ ((z * (u \ z)) \ w)) = T(x,y \ ((z \ (u / z)) * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,22502,a(flip),b,22561,a),flip(a)].">
      <j1 rule="hyper" parents="65 22502 22561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22563">
    <literal><![CDATA[
      T(x,y \ ((z \ (y / z)) * u)) = T(x,z \ (T(z,y) \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,22560,a(flip),b,22562,a),flip(a)].">
      <j1 rule="hyper" parents="65 22560 22562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22564">
    <literal><![CDATA[
      T(x,y / (a((z / y) \ z,u,u) \ z)) = T(x,z \ L(z / (z / y),u,u))
    ]]></literal>
    <justification jstring="[para(20852(a,1),22536(a,1,2,2,1))].">
      <j1 rule="para" parents="20852 22536"/>
    </justification>
  </clause>

  <clause id="22565">
    <literal><![CDATA[
      T(x,y \ L(y / (y / z),u,u)) = T(x,z / (a(z,u,u) \ y))
    ]]></literal>
    <justification jstring="[para(79(a,1),22564(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="79 22564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22566">
    <literal><![CDATA[
      T(x,y \ L(y / (y / z),u,u)) = T(x,L(z,u,u) / y)
    ]]></literal>
    <justification jstring="[hyper(299,a,22279,a(flip),b,22565,a),flip(a)].">
      <j1 rule="hyper" parents="299 22279 22565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22567">
    <literal><![CDATA[
      T(x,(y / z) \ a(u,u,y)) = T(x,L(z,w,w) / y)
    ]]></literal>
    <justification jstring="[hyper(65,a,22475,a(flip),b,22566,a)].">
      <j1 rule="hyper" parents="65 22475 22566"/>
    </justification>
  </clause>

  <clause id="22568">
    <literal><![CDATA[
      T(x,L(y,z,z) / u) = T(x,y / L(u,w,w))
    ]]></literal>
    <justification jstring="[hyper(22420,a,22567,a),flip(a)].">
      <j1 rule="hyper" parents="22420 22567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22570">
    <literal><![CDATA[
      T(x,((y \ ((1 / y) \ z)) * u) \ z) = T(x,(u \ z) / L(z,w,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,22405,a,b,22568,a)].">
      <j1 rule="hyper" parents="65 22405 22568"/>
    </justification>
  </clause>

  <clause id="22572">
    <literal><![CDATA[
      T(x,T(y / (T(z,z * u) * u),u)) = T(x,(y \ (z * (z * u))) \ z)
    ]]></literal>
    <justification jstring="[hyper(16219,a,22534,a)].">
      <j1 rule="hyper" parents="16219 22534"/>
    </justification>
  </clause>

  <clause id="22574">
    <literal><![CDATA[
      T(x,T(y / (z * u),z)) = T(x,(y \ (u * (u * z))) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,19882,a(flip),b,22572,a)].">
      <j1 rule="hyper" parents="65 19882 22572"/>
    </justification>
  </clause>

  <clause id="22575">
    <literal><![CDATA[
      T(x,T(y / (z * u),z)) = T(x,(u * z) \ T(y,u))
    ]]></literal>
    <justification jstring="[hyper(299,a,22415,a(flip),b,22574,a),flip(a)].">
      <j1 rule="hyper" parents="299 22415 22574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22576">
    <literal><![CDATA[
      T(x,T(y / (z * u),z)) = T(x,(z \ y) / u)
    ]]></literal>
    <justification jstring="[hyper(299,a,22383,a(flip),b,22575,a),flip(a)].">
      <j1 rule="hyper" parents="299 22383 22575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22577">
    <literal><![CDATA[
      T(x,T(y / (L(y,z,u) * w),L(y,z,u))) = T(x,(y / L(y,z,u)) / w)
    ]]></literal>
    <justification jstring="[para(6372(a,2),22576(a,2,2,1))].">
      <j1 rule="para" parents="6372 22576"/>
    </justification>
  </clause>

  <clause id="22578">
    <literal><![CDATA[
      T(x,T(y / ((z \ ((1 / z) \ y)) * u),z \ ((1 / z) \ y))) = T(x,T((z \ ((1 / z) \ y)) \ y,w) / u)
    ]]></literal>
    <justification jstring="[para(21213(a,2),22576(a,2,2,1))].">
      <j1 rule="para" parents="21213 22576"/>
    </justification>
  </clause>

  <clause id="22579">
    <literal><![CDATA[
      T(x,T(y / (L(y,z,u) * w),y)) = T(x,(y / L(y,z,u)) / w)
    ]]></literal>
    <justification jstring="[hyper(18719,a,22577,a)].">
      <j1 rule="hyper" parents="18719 22577"/>
    </justification>
  </clause>

  <clause id="22580">
    <literal><![CDATA[
      T(x,(y / L(y,z,u)) / w) = T(x,(L(y,z,u) * w) \ y)
    ]]></literal>
    <justification jstring="[hyper(7481,a,22579,a),flip(a)].">
      <j1 rule="hyper" parents="7481 22579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22582">
    <literal><![CDATA[
      T(x,(L(y,z,u) \ y) / w) = T(x,(L(y,z,u) * w) \ y)
    ]]></literal>
    <justification jstring="[para(6372(a,1),22580(a,1,2,1))].">
      <j1 rule="para" parents="6372 22580"/>
    </justification>
  </clause>

  <clause id="22583">
    <literal><![CDATA[
      T(x,(L(y,z,u) * w) \ y) = T(x,w \ (L(y,z,u) \ y))
    ]]></literal>
    <justification jstring="[hyper(21024,a,22582,a),flip(a)].">
      <j1 rule="hyper" parents="21024 22582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22584">
    <literal><![CDATA[
      T(x,(y \ z) / L(z,u,w)) = T(x,y \ (L(z,u,w) \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,22387,a,b,22583,a)].">
      <j1 rule="hyper" parents="65 22387 22583"/>
    </justification>
  </clause>

  <clause id="22585">
    <literal><![CDATA[
      T(x,T(y / ((z \ ((1 / z) \ y)) * u),z \ ((z / 1) * y))) = T(x,T((z \ ((1 / z) \ y)) \ y,w) / u)
    ]]></literal>
    <justification jstring="[para(21855(a,1),22578(a,1,2))].">
      <j1 rule="para" parents="21855 22578"/>
    </justification>
  </clause>

  <clause id="22586">
    <literal><![CDATA[
      T(x,T(y / ((z \ ((1 / z) \ y)) * u),z \ (z * y))) = T(x,T((z \ ((1 / z) \ y)) \ y,w) / u)
    ]]></literal>
    <justification jstring="[para(74(a,1),22585(a,1,2,2,2,1))].">
      <j1 rule="para" parents="74 22585"/>
    </justification>
  </clause>

  <clause id="22587">
    <literal><![CDATA[
      T(x,T(y / ((z \ ((1 / z) \ y)) * u),y)) = T(x,T((z \ ((1 / z) \ y)) \ y,w) / u)
    ]]></literal>
    <justification jstring="[para(9(a,1),22586(a,1,2,2))].">
      <j1 rule="para" parents="9 22586"/>
    </justification>
  </clause>

  <clause id="22588">
    <literal><![CDATA[
      T(x,T((y \ ((1 / y) \ z)) \ z,u) / w) = T(x,((y \ ((1 / y) \ z)) * w) \ z)
    ]]></literal>
    <justification jstring="[hyper(7481,a,22587,a),flip(a)].">
      <j1 rule="hyper" parents="7481 22587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22589">
    <literal><![CDATA[
      x * (T(T(x,y),y) \ (z \ (K(x,y) * ((K(x,y) * u) * z)))) = R(T(u,y * (T(T(y,x),x) \ z)),K(x,y),K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,21862,a(flip),b,22140,a)].">
      <j1 rule="hyper" parents="65 21862 22140"/>
    </justification>
  </clause>

  <clause id="22590">
    <literal><![CDATA[
      T(((L(x,y,z) \ 1) * u) / (L(x,y,z) \ 1),x \ (x \ L(x,y,z))) = T(u,T(x \ L(x,y,z),x) * (x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[para(3819(a,1),22511(a,1,2,2))].">
      <j1 rule="para" parents="3819 22511"/>
    </justification>
  </clause>

  <clause id="22591">
    <literal><![CDATA[
      R(T(x,y * (T(T(y,z),z) \ u)),K(z,y),K(z,y) * u) = u \ (K(y,z) * ((K(z,y) * x) * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,21935,a(flip),b,22589,a),flip(a)].">
      <j1 rule="hyper" parents="65 21935 22589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22592">
    <literal><![CDATA[
      R(T(x,y * (T(T(y,z),z) \ u)),K(z,y),K(z,y) * u) = T(T(x,K(y,z)),u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,22238,a(flip),b,22591,a),flip(a)].">
      <j1 rule="hyper" parents="299 22238 22591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22593">
    <literal><![CDATA[
      R(T(x,y * (T(T(y,z),z) \ u)),K(z,y),K(z,y) * u) = T(T(x,K(z,y)),u * K(y,z))
    ]]></literal>
    <justification jstring="[para(8050(a,1),22592(a,2,1))].">
      <j1 rule="para" parents="8050 22592"/>
    </justification>
  </clause>

  <clause id="22594">
    <literal><![CDATA[
      R(T(x,y),K(z,u),K(z,u) * y) = T(T(x,K(z,u)),y * K(u,z))
    ]]></literal>
    <justification jstring="[para(15787(a,1),22593(a,1,1))].">
      <j1 rule="para" parents="15787 22593"/>
    </justification>
  </clause>

  <clause id="22595">
    <literal><![CDATA[
      L(T(x,y),K(z,u),K(z,u) * y) = T(T(x,K(z,u)),y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(19954,a,22594,a)].">
      <j1 rule="hyper" parents="19954 22594"/>
    </justification>
  </clause>

  <clause id="22597">
    <literal><![CDATA[
      T(T(x,K(y,z)),u * K(z,y)) = L(T(x,u),u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,22113,a(flip),b,22595,a),flip(a)].">
      <j1 rule="hyper" parents="65 22113 22595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22598">
    <literal><![CDATA[
      T(T(x,K(y,z)),u * K(z,y)) = T(x,L(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(299,a,22156,a(flip),b,22597,a),flip(a)].">
      <j1 rule="hyper" parents="299 22156 22597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22599">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),w * K(u * z,y)) = T(x,L(w,z * u,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,16818,a,b,22598,a)].">
      <j1 rule="hyper" parents="65 16818 22598"/>
    </justification>
  </clause>

  <clause id="22600">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),u * K(u * z,y)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,L(u,z,y)) = w
    ]]></literal>
    <justification jstring="[para(22599(a,2),11957(a,1))].">
      <j1 rule="para" parents="22599 11957"/>
    </justification>
  </clause>

  <clause id="22601">
    <literal><![CDATA[
      T(((L(x,y,z) \ 1) * u) / (L(x,y,z) \ 1),L(x \ 1,y,z)) = T(u,T(x \ L(x,y,z),x) * (x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(65,a,14405,a(flip),b,22590,a)].">
      <j1 rule="hyper" parents="65 14405 22590"/>
    </justification>
  </clause>

  <clause id="22602">
    <literal><![CDATA[
      T(x,T(y \ L(y,z,u),y) * (y \ L(y,z,u))) = (L(y,z,u) \ 1) \ ((L(y,z,u) \ 1) * x)
    ]]></literal>
    <justification jstring="[hyper(12021,a,22601,a),flip(a)].">
      <j1 rule="hyper" parents="12021 22601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22603">
    <literal><![CDATA[
      T(x,T(y \ L(y,z,u),y) * (y \ L(y,z,u))) = x
    ]]></literal>
    <justification jstring="[hyper(299,a,9,a(flip),b,22602,a),flip(a)].">
      <j1 rule="hyper" parents="299 9 22602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22605">
    <literal><![CDATA[
      T(x,(y \ L(y,z,u)) * (y \ L(y,z,u))) = x
    ]]></literal>
    <justification jstring="[para(3818(a,1),22603(a,1,2,1))].">
      <j1 rule="para" parents="3818 22603"/>
    </justification>
  </clause>

  <clause id="22606">
    <literal><![CDATA[
      T(x,L(y,z,u) * (y \ (y \ L(y,z,u)))) = x
    ]]></literal>
    <justification jstring="[hyper(15680,a,22605,a)].">
      <j1 rule="hyper" parents="15680 22605"/>
    </justification>
  </clause>

  <clause id="22607">
    <literal><![CDATA[
      T(T(x,(L(y,z,u) \ y) \ w),1) = T(x,y * (L(y,z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,18256,a(flip),b,22606,a)].">
      <j1 rule="hyper" parents="65 18256 22606"/>
    </justification>
  </clause>

  <clause id="22609">
    <literal><![CDATA[
      T(T(x,L(y,z,u) * (y \ w)),1) = T(x,y * (L(y,z,u) \ w))
    ]]></literal>
    <justification jstring="[para(15678(a,1),22607(a,1,1))].">
      <j1 rule="para" parents="15678 22607"/>
    </justification>
  </clause>

  <clause id="22610">
    <literal><![CDATA[
      T(x,L(y,z,u) * (y \ w)) = T(x,y * (L(y,z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(197,a,22609,a)].">
      <j1 rule="hyper" parents="197 22609"/>
    </justification>
  </clause>

  <clause id="22611">
    <literal><![CDATA[
      T(x,y * (L(y,z,u) \ (w \ 1))) = T(x,w \ (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,21076,a(flip),b,22610,a),flip(a)].">
      <j1 rule="hyper" parents="65 21076 22610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22612">
    <literal><![CDATA[
      T(x,y * (L(y,z,u) \ (y \ w))) = T(x,L(y \ 1,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(65,a,15045,a(flip),b,22610,a),flip(a)].">
      <j1 rule="hyper" parents="65 15045 22610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22613">
    <literal><![CDATA[
      T(x,y \ (L(z,u,w) \ z)) = T(x,y \ (z \ L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(21077,a,22611,a)].">
      <j1 rule="hyper" parents="21077 22611"/>
    </justification>
  </clause>

  <clause id="22614">
    <literal><![CDATA[
      T(x,(y \ z) / L(z,u,w)) = T(x,y \ (z \ L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,22584,a,b,22613,a)].">
      <j1 rule="hyper" parents="65 22584 22613"/>
    </justification>
  </clause>

  <clause id="22615">
    <literal><![CDATA[
      T(x,((y \ ((1 / y) \ z)) * u) \ z) = T(x,u \ (z \ L(z,w,w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,22570,a,b,22614,a)].">
      <j1 rule="hyper" parents="65 22570 22614"/>
    </justification>
  </clause>

  <clause id="22616">
    <literal><![CDATA[
      T(x,L(y \ 1,z,u) * w) = T(x,L(y,z,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,22490,a(flip),b,22612,a),flip(a)].">
      <j1 rule="hyper" parents="65 22490 22612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22617">
    <literal><![CDATA[
      T(x,L(1 / y,z,u) * w) = T(x,L(y,z,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(21058,a,22616,a)].">
      <j1 rule="hyper" parents="21058 22616"/>
    </justification>
  </clause>

  <clause id="22618">
    <literal><![CDATA[
      T(x,L(1 / y,z,u) \ w) = T(x,L(y,z,u) * w)
    ]]></literal>
    <justification jstring="[para(79(a,1),22616(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="79 22616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22619">
    <literal><![CDATA[
      T(T(x,L(y,z,u) \ w),L(1 / y,z,u) \ (y * (L(y,z,u) \ y))) = T(T(x,L(1 / y,z,u) \ w),1)
    ]]></literal>
    <justification jstring="[para(22617(a,1),14755(a,1,1))].">
      <j1 rule="para" parents="22617 14755"/>
    </justification>
  </clause>

  <clause id="22620">
    <literal><![CDATA[
      T(x,((y \ ((1 / y) \ z)) * u) \ z) = T(x,u \ a(z,w,w))
    ]]></literal>
    <justification jstring="[hyper(299,a,22396,a(flip),b,22615,a),flip(a)].">
      <j1 rule="hyper" parents="299 22396 22615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22621">
    <literal><![CDATA[
      T(x,y \ a(z,u,u)) = T(x,T((w \ ((1 / w) \ z)) \ z,v5) / y)
    ]]></literal>
    <justification jstring="[hyper(65,a,22588,a,b,22620,a),flip(a)].">
      <j1 rule="hyper" parents="65 22588 22620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22623">
    <literal><![CDATA[
      T(x,y \ a(z,u,u)) = T(x,((w \ ((1 / w) \ z)) \ z) / y)
    ]]></literal>
    <justification jstring="[hyper(299,a,17404,a(flip),b,22621,a),flip(a)].">
      <j1 rule="hyper" parents="299 17404 22621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22625">
    <literal><![CDATA[
      T(x,y \ a(z,u,u)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(299,a,21191,a(flip),b,22623,a),flip(a)].">
      <j1 rule="hyper" parents="299 21191 22623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22627">
    <literal><![CDATA[
      T(x,((y * (z \ 1)) / u) \ 1) = T(x,u / (y / z))
    ]]></literal>
    <justification jstring="[hyper(65,a,22419,a(flip),b,22625,a),flip(a)].">
      <j1 rule="hyper" parents="65 22419 22625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22629">
    <literal><![CDATA[
      T(x,y / (z * (u \ 1))) = T(x,y / (z / u))
    ]]></literal>
    <justification jstring="[hyper(65,a,4641,a(flip),b,22627,a)].">
      <j1 rule="hyper" parents="65 4641 22627"/>
    </justification>
  </clause>

  <clause id="22630">
    <literal><![CDATA[
      T(x,y / (z / u)) = T(x,y * (u / z))
    ]]></literal>
    <justification jstring="[hyper(22507,a,22629,a),flip(a)].">
      <j1 rule="hyper" parents="22507 22629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22631">
    <literal><![CDATA[
      T(x,y / (z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (u / z)) = w
    ]]></literal>
    <justification jstring="[para(22629(a,1),22507(a,1))].">
      <j1 rule="para" parents="22629 22507"/>
    </justification>
  </clause>

  <clause id="22632">
    <literal><![CDATA[
      T(x,(y \ z) / (u / w)) = T(x,(z \ y) \ (w / u))
    ]]></literal>
    <justification jstring="[hyper(299,a,21636,a,b,22630,a),flip(a)].">
      <j1 rule="hyper" parents="299 21636 22630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22633">
    <literal><![CDATA[
      T(x,y / (z / (y / u))) = T(x,(y \ u) \ (y / z))
    ]]></literal>
    <justification jstring="[hyper(65,a,21892,a(flip),b,22632,a)].">
      <j1 rule="hyper" parents="65 21892 22632"/>
    </justification>
  </clause>

  <clause id="22634">
    <literal><![CDATA[
      T(x,(y \ z) \ (y / u)) = T(x,y * ((y / z) / u))
    ]]></literal>
    <justification jstring="[hyper(22631,a,22633,a),flip(a)].">
      <j1 rule="hyper" parents="22631 22633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22635">
    <literal><![CDATA[
      T(x,(y \ z) * (z / u)) = T(x,z * ((z / y) / u))
    ]]></literal>
    <justification jstring="[hyper(21637,a,22634,a)].">
      <j1 rule="hyper" parents="21637 22634"/>
    </justification>
  </clause>

  <clause id="22636">
    <literal><![CDATA[
      T(T(x,y * ((y / z) / z)),T(z \ y,y \ z) \ (T(z \ y,y \ z) \ u)) = T(T(x,(y / z) * (1 / (z \ y))),u)
    ]]></literal>
    <justification jstring="[para(22635(a,1),15398(a,1,1))].">
      <j1 rule="para" parents="22635 15398"/>
    </justification>
  </clause>

  <clause id="22637">
    <literal><![CDATA[
      T(T(x,L(y,z,u) \ w),L(y,z,u) * (y * (L(y,z,u) \ y))) = T(T(x,L(1 / y,z,u) \ w),1)
    ]]></literal>
    <justification jstring="[hyper(65,a,22618,a(flip),b,22619,a)].">
      <j1 rule="hyper" parents="65 22618 22619"/>
    </justification>
  </clause>

  <clause id="22638">
    <literal><![CDATA[
      T(T(x,L(y,z,u) \ w),y * (L(y,z,u) * (L(y,z,u) \ y))) = T(T(x,L(1 / y,z,u) \ w),1)
    ]]></literal>
    <justification jstring="[para(1347(a,1),22637(a,1,2))].">
      <j1 rule="para" parents="1347 22637"/>
    </justification>
  </clause>

  <clause id="22639">
    <literal><![CDATA[
      T(T(x,L(1 / y,z,u) \ w),1) = T(T(x,L(y,z,u) \ w),y * y)
    ]]></literal>
    <justification jstring="[para(10(a,1),22638(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 22638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22640">
    <literal><![CDATA[
      T(T(x,L(1 / y,z,u) \ w),1) = T(x,y * (y * (L(y,z,u) \ w)))
    ]]></literal>
    <justification jstring="[hyper(299,a,14468,a(flip),b,22639,a),flip(a)].">
      <j1 rule="hyper" parents="299 14468 22639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22642">
    <literal><![CDATA[
      T(x,y * (y * (L(y,z,u) \ w))) = T(T(x,L(y,z,u) * w),1)
    ]]></literal>
    <justification jstring="[para(22618(a,1),22640(a,1,1)),flip(a)].">
      <j1 rule="para" parents="22618 22640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22643">
    <literal><![CDATA[
      T(x,y * (y * (L(y,z,u) \ w))) = T(x,L(y,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(299,a,193,a(flip),b,22642,a),flip(a)].">
      <j1 rule="hyper" parents="299 193 22642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22644">
    <literal><![CDATA[
      K(x * (x * (L(x,y,z) \ u)),w) = w / T(w,L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(22643(a,1),5033(a,2,2))].">
      <j1 rule="para" parents="22643 5033"/>
    </justification>
  </clause>

  <clause id="22645">
    <literal><![CDATA[
      K(x * (x * (L(x,y,z) \ u)),w) = K(L(x,y,z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(299,a,5033,a,b,22644,a),flip(a)].">
      <j1 rule="hyper" parents="299 5033 22644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22646">
    <literal><![CDATA[
      K(L(x \ 1,y,z) \ u,w) = K(L(x,y,z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,15050,a(flip),b,22645,a)].">
      <j1 rule="hyper" parents="65 15050 22645"/>
    </justification>
  </clause>

  <clause id="22647">
    <literal><![CDATA[
      T(T(x,y * (z \ (z \ y))),T(z \ y,y \ z) \ (T(z \ y,y \ z) \ u)) = T(T(x,(y / z) * (1 / (z \ y))),u)
    ]]></literal>
    <justification jstring="[para(19237(a,1),22636(a,1,1))].">
      <j1 rule="para" parents="19237 22636"/>
    </justification>
  </clause>

  <clause id="22648">
    <literal><![CDATA[
      T(T(x,y * (z \ (z \ y))),(z \ y) \ ((z \ y) \ u)) = T(T(x,(y / z) * (1 / (z \ y))),u)
    ]]></literal>
    <justification jstring="[hyper(15878,a,22647,a)].">
      <j1 rule="hyper" parents="15878 22647"/>
    </justification>
  </clause>

  <clause id="22649">
    <literal><![CDATA[
      T(T(x,y * (z \ (z \ y))),(y \ z) * ((y \ z) * u)) = T(T(x,(y / z) * (1 / (z \ y))),u)
    ]]></literal>
    <justification jstring="[hyper(21061,a,22648,a)].">
      <j1 rule="hyper" parents="21061 22648"/>
    </justification>
  </clause>

  <clause id="22651">
    <literal><![CDATA[
      T(x,T(y,z * K(u,w)) \ (T(v5,K(u,w) * ((y * z) * (z * K(w,u)))) \ v6)) = T(x,v5 \ ((T(z,K(u,w)) \ T(y * z,K(u,w))) \ v6))
    ]]></literal>
    <justification jstring="[para(22119(a,1),21800(a,1,2,2,1,2))].">
      <j1 rule="para" parents="22119 21800"/>
    </justification>
  </clause>

  <clause id="22652">
    <literal><![CDATA[
      T(x,T(y,z * K(u,w)) \ (T(v5,(y * z) * z) \ v6)) = T(x,v5 \ ((T(z,K(u,w)) \ T(y * z,K(u,w))) \ v6))
    ]]></literal>
    <justification jstring="[para(19091(a,1),22651(a,1,2,2,1))].">
      <j1 rule="para" parents="19091 22651"/>
    </justification>
  </clause>

  <clause id="22653">
    <literal><![CDATA[
      T(x,T(y,z * K(u,w)) \ (T(v5,z * (z * y)) \ v6)) = T(x,v5 \ ((T(z,K(u,w)) \ T(y * z,K(u,w))) \ v6))
    ]]></literal>
    <justification jstring="[para(15908(a,1),22652(a,1,2,2,1))].">
      <j1 rule="para" parents="15908 22652"/>
    </justification>
  </clause>

  <clause id="22655">
    <literal><![CDATA[
      T(x,T(y,z) \ (T(u,z * (z * y)) \ w)) = T(x,u \ ((T(z,K(v5,v6)) \ T(y * z,K(v5,v6))) \ w))
    ]]></literal>
    <justification jstring="[hyper(17899,a,22653,a)].">
      <j1 rule="hyper" parents="17899 22653"/>
    </justification>
  </clause>

  <clause id="22656">
    <literal><![CDATA[
      T(x,y \ ((T(z,K(u,w)) \ T(v5 * z,K(u,w))) \ v6)) = T(x,y \ (T(v5,z) \ v6))
    ]]></literal>
    <justification jstring="[hyper(65,a,21933,a(flip),b,22655,a),flip(a)].">
      <j1 rule="hyper" parents="65 21933 22655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22657">
    <literal><![CDATA[
      T(x,y \ (T(z,u * K(w,v5)) \ v6)) = T(x,y \ (T(z,u) \ v6))
    ]]></literal>
    <justification jstring="[para(16144(a,1),22656(a,1,2,2,1))].">
      <j1 rule="para" parents="16144 22656"/>
    </justification>
  </clause>

  <clause id="22658">
    <literal><![CDATA[
      T(x,(K(y,z) * (u \ 1)) \ (T(w,u) \ v5)) = T(x,w \ ((K(z,y) \ (u \ 1)) \ v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,21974,a(flip),b,22657,a),flip(a)].">
      <j1 rule="hyper" parents="65 21974 22657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22659">
    <literal><![CDATA[
      T(x,K(y,z) * ((u \ 1) \ (T(w,u) \ v5))) = T(x,w \ ((K(y,z) \ (u \ 1)) \ v5))
    ]]></literal>
    <justification jstring="[hyper(20167,a,22658,a)].">
      <j1 rule="hyper" parents="20167 22658"/>
    </justification>
  </clause>

  <clause id="22661">
    <literal><![CDATA[
      T(x,y \ ((K(z,u) \ (w \ 1)) \ v5)) = T(x,w * (K(u,z) * (T(y,w) \ v5)))
    ]]></literal>
    <justification jstring="[hyper(21042,a,22659,a),flip(a)].">
      <j1 rule="hyper" parents="21042 22659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22662">
    <literal><![CDATA[
      T(x,y \ ((K(z,u) * (w \ 1)) \ v5)) = T(x,w * (K(z,u) * (T(y,w) \ v5)))
    ]]></literal>
    <justification jstring="[para(5426(a,1),22661(a,1,2,2,1))].">
      <j1 rule="para" parents="5426 22661"/>
    </justification>
  </clause>

  <clause id="22663">
    <literal><![CDATA[
      T(x,y * (K(z,u) * (T(w,y) \ v5))) = T(x,w \ ((y \ K(z,u)) \ v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,18822,a(flip),b,22662,a),flip(a)].">
      <j1 rule="hyper" parents="65 18822 22662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22664">
    <literal><![CDATA[
      T(x,y \ ((z \ K(u,z)) \ w)) = T(x,T(z,u) * (T(y,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(15872,a,22663,a),flip(a)].">
      <j1 rule="hyper" parents="15872 22663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22665">
    <literal><![CDATA[
      T(x,y \ L(T(z,u) * w,v5,v5)) = T(x,T(z,u) * (T(y,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,22489,a,b,22664,a)].">
      <j1 rule="hyper" parents="65 22489 22664"/>
    </justification>
  </clause>

  <clause id="22666">
    <literal><![CDATA[
      T(x,T(y,z) * (T(u,y) \ w)) = T(x,u \ (T(y,z) * w))
    ]]></literal>
    <justification jstring="[hyper(22477,a,22665,a),flip(a)].">
      <j1 rule="hyper" parents="22477 22665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22667">
    <literal><![CDATA[
      T(x,(y / z) \ (T(u,y * z) * w)) = T(x,u * ((y / z) \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,18287,a(flip),b,22666,a),flip(a)].">
      <j1 rule="hyper" parents="65 18287 22666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22668">
    <literal><![CDATA[
      T(x,(y / z) * (T(u,z * y) * w)) = T(x,u * ((z / y) \ w))
    ]]></literal>
    <justification jstring="[hyper(21633,a,22667,a)].">
      <j1 rule="hyper" parents="21633 22667"/>
    </justification>
  </clause>

  <clause id="22669">
    <literal><![CDATA[
      T(x,y / (z \ ((u / w) \ 1))) = T(x,y * ((w / u) \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,22313,a(flip),b,22668,a)].">
      <j1 rule="hyper" parents="65 22313 22668"/>
    </justification>
  </clause>

  <clause id="22670">
    <literal><![CDATA[
      T(x,y * (((z / u) \ 1) \ w)) = T(x,y * ((u / z) \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,22493,a(flip),b,22669,a)].">
      <j1 rule="hyper" parents="65 22493 22669"/>
    </justification>
  </clause>

  <clause id="22671">
    <literal><![CDATA[
      (((T(x,y) / z) / (x / z)) \ (T(x,y) / z)) * T(T((T(x,y) / z) / (x / z),T(x,y) / z),u) = K(x,K(y,u)) * ((((T(x,y) / z) / (x / z)) \ (T(x,y) / z)) * K((z \ 1) \ (x / z),y))
    ]]></literal>
    <justification jstring="[para(12787(a,1),11372(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12787 11372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22672">
    <literal><![CDATA[
      (((T(x,y) / z) / (x / z)) \ (T(x,y) / z)) * T(T((T(x,y) / z) / (x / z),T(x,y) / z),u) = K(x,K(y,u)) * ((x / z) * K((z \ 1) \ (x / z),y))
    ]]></literal>
    <justification jstring="[para(79(a,1),22671(a,2,2,1))].">
      <j1 rule="para" parents="79 22671"/>
    </justification>
  </clause>

  <clause id="22675">
    <literal><![CDATA[
      (((T(x,y) / z) / (x / z)) \ (T(x,y) / z)) * T(T((T(x,y) / z) / (x / z),T(x,y) / z),u) = K(x,K(y,u)) * (T(x,y) / z)
    ]]></literal>
    <justification jstring="[para(7130(a,1),22672(a,2,2))].">
      <j1 rule="para" parents="7130 22672"/>
    </justification>
  </clause>

  <clause id="22676">
    <literal><![CDATA[
      (x / y) * T(T((T(x,z) / y) / (x / y),T(x,z) / y),u) = K(x,K(z,u)) * (T(x,z) / y)
    ]]></literal>
    <justification jstring="[hyper(657,a,22675,a)].">
      <j1 rule="hyper" parents="657 22675"/>
    </justification>
  </clause>

  <clause id="22678">
    <literal><![CDATA[
      K(x,K(y,z)) * (T(x,y) / u) = (x / u) * T(K((u \ 1) \ (x / u),y),z)
    ]]></literal>
    <justification jstring="[para(7690(a,1),22676(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7690 22676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22679">
    <literal><![CDATA[
      K(x,K(y,z)) * (T(x,y) / u) = (x / u) * K((u \ 1) \ (x / u),T(y,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,7503,a,b,22678,a),flip(a)].">
      <j1 rule="hyper" parents="299 7503 22678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22680">
    <literal><![CDATA[
      K(x,K(y,z)) * (T(x,y) / u) = T(x,T(y,z)) / u
    ]]></literal>
    <justification jstring="[hyper(299,a,7130,a(flip),b,22679,a),flip(a)].">
      <j1 rule="hyper" parents="299 7130 22679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22681">
    <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(22680(a,1),16764(a,1,1))].">
      <j1 rule="para" parents="22680 16764"/>
    </justification>
  </clause>

  <clause id="22682">
    <literal><![CDATA[
      K((T(x,y) / z) \ y,u) = K(T(z,x) / (y \ x),T(u,x))
    ]]></literal>
    <justification jstring="[hyper(22681,a,22426,a),flip(a)].">
      <j1 rule="hyper" parents="22681 22426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22683">
    <literal><![CDATA[
      K((T(x,y) / z) \ y,u) = K((z * y) / x,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,22216,a(flip),b,22682,a),flip(a)].">
      <j1 rule="hyper" parents="299 22216 22682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22684">
    <literal><![CDATA[
      K((x * y) / (K(y,z \ 1) / z),u) = K(((1 / z) / x) \ y,u)
    ]]></literal>
    <justification jstring="[para(5143(a,1),22683(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5143 22683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22685">
    <literal><![CDATA[
      K((x * y) / (K(y,z \ 1) / z),u) = K(((z \ 1) / x) \ y,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,5894,a(flip),b,22684,a),flip(a)].">
      <j1 rule="hyper" parents="299 5894 22684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22686">
    <literal><![CDATA[
      K((x * y) * (z * K(z \ 1,y)),u) = K(((z \ 1) / x) \ y,u)
    ]]></literal>
    <justification jstring="[hyper(14541,a,22685,a)].">
      <j1 rule="hyper" parents="14541 22685"/>
    </justification>
  </clause>

  <clause id="22687">
    <literal><![CDATA[
      K((x * y) * (z * K(z * 1,y)),u) = K(((z \ 1) / x) \ y,u)
    ]]></literal>
    <justification jstring="[hyper(18047,a,22686,a)].">
      <j1 rule="hyper" parents="18047 22686"/>
    </justification>
  </clause>

  <clause id="22688">
    <literal><![CDATA[
      K((x * y) * (z * K(z,y)),u) = K(((z \ 1) / x) \ y,u)
    ]]></literal>
    <justification jstring="[para(8(a,1),22687(a,1,1,2,2,1))].">
      <j1 rule="para" parents="8 22687"/>
    </justification>
  </clause>

  <clause id="22689">
    <literal><![CDATA[
      K(((x \ 1) / y) \ z,u) = K((y * z) * T(x,z),u)
    ]]></literal>
    <justification jstring="[para(5083(a,2),22688(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5083 22688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22690">
    <literal><![CDATA[
      K(((x \ 1) / (y \ (z \ ((1 / z) \ y)))) \ y,u) = K((z \ ((1 / z) \ y)) * T(x,y),u)
    ]]></literal>
    <justification jstring="[para(20918(a,1),22689(a,2,1,1))].">
      <j1 rule="para" parents="20918 22689"/>
    </justification>
  </clause>

  <clause id="22691">
    <literal><![CDATA[
      K(((x \ (y \ ((1 / y) \ x))) \ (z \ 1)) \ x,u) = K((y \ ((1 / y) \ x)) * T(z,x),u)
    ]]></literal>
    <justification jstring="[para(21184(a,1),22690(a,1,1,1))].">
      <j1 rule="para" parents="21184 22690"/>
    </justification>
  </clause>

  <clause id="22692">
    <literal><![CDATA[
      K(T(x \ 1,y) \ (z \ ((1 / z) \ y)),T(u,y)) = K((z \ ((1 / z) \ y)) * T(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,22276,a(flip),b,22691,a)].">
      <j1 rule="hyper" parents="65 22276 22691"/>
    </justification>
  </clause>

  <clause id="22693">
    <literal><![CDATA[
      K(T(x \ 1,y) \ (z \ ((z \ 1) \ y)),T(u,y)) = K((z \ ((1 / z) \ y)) * T(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,15687,a(flip),b,22692,a)].">
      <j1 rule="hyper" parents="65 15687 22692"/>
    </justification>
  </clause>

  <clause id="22694">
    <literal><![CDATA[
      K(L(T(x \ 1,y),z,z) \ y,T(u,y)) = K((z \ ((1 / z) \ y)) * T(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,21844,a(flip),b,22693,a)].">
      <j1 rule="hyper" parents="65 21844 22693"/>
    </justification>
  </clause>

  <clause id="22695">
    <literal><![CDATA[
      K((x \ ((1 / x) \ y)) * T(z,y),u) = K(y / L(T(z \ 1,y),x,x),u)
    ]]></literal>
    <justification jstring="[hyper(8219,a,22694,a),flip(a)].">
      <j1 rule="hyper" parents="8219 22694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22696">
    <literal><![CDATA[
      K((x \ ((1 / x) \ y)) * T(z,y),u) = K(L(z \ 1,x,x) \ y,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,13742,a(flip),b,22695,a),flip(a)].">
      <j1 rule="hyper" parents="299 13742 22695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22697">
    <literal><![CDATA[
      K((x \ ((1 / x) \ y)) * T(z,y),u) = K(L(z,x,x) * y,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,22646,a(flip),b,22696,a),flip(a)].">
      <j1 rule="hyper" parents="299 22646 22696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22698">
    <literal><![CDATA[
      K(x * (y \ ((1 / y) \ z)),u) = K(L(x,y,y) * z,u)
    ]]></literal>
    <justification jstring="[para(21988(a,1),22697(a,1,1))].">
      <j1 rule="para" parents="21988 22697"/>
    </justification>
  </clause>

  <clause id="22699">
    <literal><![CDATA[
      K(x * (y \ ((y \ 1) \ z)),u) = K(L(x,y,y) * z,u)
    ]]></literal>
    <justification jstring="[hyper(15690,a,22698,a)].">
      <j1 rule="hyper" parents="15690 22698"/>
    </justification>
  </clause>

  <clause id="22700">
    <literal><![CDATA[
      K(L(T(x,y),z,z) * y,u) = K((z \ ((z \ 1) \ y)) * x,u)
    ]]></literal>
    <justification jstring="[hyper(14407,a,22699,a),flip(a)].">
      <j1 rule="hyper" parents="14407 22699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22701">
    <literal><![CDATA[
      K((x \ ((x \ 1) \ y)) * z,u) = K(y * L(z,x,x),u)
    ]]></literal>
    <justification jstring="[hyper(13237,a,22700,a),flip(a)].">
      <j1 rule="hyper" parents="13237 22700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22702">
    <literal><![CDATA[
      K((x * (y \ 1)) * L(z,y,y),u) = K((y \ T(x,y \ 1)) * z,u)
    ]]></literal>
    <justification jstring="[para(22(a,2),22701(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="22 22701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22703">
    <literal><![CDATA[
      K((x * (y \ 1)) * L(z,y,y),u) = K((y \ T(x,y * 1)) * z,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,19407,a(flip),b,22702,a),flip(a)].">
      <j1 rule="hyper" parents="299 19407 22702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22704">
    <literal><![CDATA[
      K((x * (y \ 1)) * L(z,y,y),u) = K((y \ T(x,y)) * z,u)
    ]]></literal>
    <justification jstring="[para(8(a,1),22703(a,2,1,1,2,2))].">
      <j1 rule="para" parents="8 22703"/>
    </justification>
  </clause>

  <clause id="22705">
    <literal><![CDATA[
      K((x * (y \ 1)) * L(z,y,y),u) = K((x / y) * z,u)
    ]]></literal>
    <justification jstring="[hyper(299,a,19235,a(flip),b,22704,a),flip(a)].">
      <j1 rule="hyper" parents="299 19235 22704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22706">
    <literal><![CDATA[
      T(x,(y * (z \ 1)) * L(u,z,z)) = (x * w) / (K((y / z) * u,x) * w)
    ]]></literal>
    <justification jstring="[para(22705(a,1),5517(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="22705 5517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22707">
    <literal><![CDATA[
      T(x,(y * (z \ 1)) * L(u,z,z)) = T(x,(y / z) * u)
    ]]></literal>
    <justification jstring="[hyper(299,a,5517,a(flip),b,22706,a),flip(a)].">
      <j1 rule="hyper" parents="299 5517 22706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22708">
    <literal><![CDATA[
      T(x,((y \ 1) * (z * (y \ 1))) * u) = T(x,((y \ z) / y) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,21330,a(flip),b,22707,a)].">
      <j1 rule="hyper" parents="65 21330 22707"/>
    </justification>
  </clause>

  <clause id="22709">
    <literal><![CDATA[
      T(x,((y \ 1) * (z * (y \ 1))) * u) = T(x,(y \ (z / y)) * u)
    ]]></literal>
    <justification jstring="[hyper(299,a,16975,a(flip),b,22708,a),flip(a)].">
      <j1 rule="hyper" parents="299 16975 22708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22710">
    <literal><![CDATA[
      T(x,(y \ (z / y)) * T(u,y \ (z * (y \ 1)))) = T(x,u * ((y \ 1) * (z * (y \ 1))))
    ]]></literal>
    <justification jstring="[para(14378(a,1),22709(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14378 22709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22711">
    <literal><![CDATA[
      T(x,(y \ (z / y)) * T(u,y \ (z / y))) = T(x,u * ((y \ 1) * (z * (y \ 1))))
    ]]></literal>
    <justification jstring="[para(17535(a,1),22710(a,1,2,2))].">
      <j1 rule="para" parents="17535 22710"/>
    </justification>
  </clause>

  <clause id="22712">
    <literal><![CDATA[
      T(x,y * ((z \ 1) * (u * (z \ 1)))) = T(x,y * (z \ (u / z)))
    ]]></literal>
    <justification jstring="[para(107(a,1),22711(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 22711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22713">
    <literal><![CDATA[
      T(x,y * ((z \ 1) \ ((u * (z \ 1)) / (z \ 1)))) = T(x,y * (((z \ 1) \ 1) * R(u,z,z)))
    ]]></literal>
    <justification jstring="[para(1994(a,1),22712(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="1994 22712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22714">
    <literal><![CDATA[
      T(x,y * ((z \ 1) \ ((u * (z \ 1)) / (z \ 1)))) = T(x,y * R(z * u,z,z))
    ]]></literal>
    <justification jstring="[para(3439(a,1),22713(a,2,2,2))].">
      <j1 rule="para" parents="3439 22713"/>
    </justification>
  </clause>

  <clause id="22715">
    <literal><![CDATA[
      T(x,y * ((z \ 1) \ ((u * (z \ 1)) / (z \ 1)))) = T(x,y * L(z * u,z,z))
    ]]></literal>
    <justification jstring="[hyper(299,a,19293,a(flip),b,22714,a),flip(a)].">
      <j1 rule="hyper" parents="299 19293 22714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22716">
    <literal><![CDATA[
      T(x,y * L(z * u,z,z)) = T(x,y * ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(11(a,1),22715(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="11 22715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22717">
    <literal><![CDATA[
      T(x,y * (z * L(u,z,z))) = T(x,y * ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,15972,a(flip),b,22716,a)].">
      <j1 rule="hyper" parents="65 15972 22716"/>
    </justification>
  </clause>

  <clause id="22718">
    <literal><![CDATA[
      T(x,y * ((z \ 1) \ u)) = T(x,y * (z * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,22010,a(flip),b,22717,a),flip(a)].">
      <j1 rule="hyper" parents="65 22010 22717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22719">
    <literal><![CDATA[
      T(x,y * ((z / u) \ w)) = T(x,y * ((u / z) * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,22670,a(flip),b,22718,a)].">
      <j1 rule="hyper" parents="65 22670 22718"/>
    </justification>
  </clause>

  <clause id="22720">
    <literal><![CDATA[
      T(x,y / (z \ (u \ w))) = T(x,y * ((w \ u) * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,22495,a(flip),b,22718,a)].">
      <j1 rule="hyper" parents="65 22495 22718"/>
    </justification>
  </clause>

  <clause id="22721">
    <literal><![CDATA[
      T(x,y * ((z * (u \ z)) \ w)) = T(x,y * (((z \ u) / z) * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,21981,a(flip),b,22719,a)].">
      <j1 rule="hyper" parents="65 21981 22719"/>
    </justification>
  </clause>

  <clause id="22722">
    <literal><![CDATA[
      T(x,y * ((z \ u) * T(w,z * u))) = T(x,y / ((u \ z) / w))
    ]]></literal>
    <justification jstring="[hyper(65,a,22518,a(flip),b,22720,a),flip(a)].">
      <j1 rule="hyper" parents="65 22518 22720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22723">
    <literal><![CDATA[
      T(x,y * ((z * (u \ z)) \ w)) = T(x,y * ((z \ (u / z)) * w))
    ]]></literal>
    <justification jstring="[hyper(299,a,19738,a(flip),b,22721,a),flip(a)].">
      <j1 rule="hyper" parents="299 19738 22721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22724">
    <literal><![CDATA[
      T(x,y / ((z \ u) / w)) = T(x,y * (w * (u \ z)))
    ]]></literal>
    <justification jstring="[hyper(65,a,17541,a(flip),b,22722,a),flip(a)].">
      <j1 rule="hyper" parents="65 17541 22722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22725">
    <literal><![CDATA[
      T(x,y * (z / (u \ w))) = T(x,y * (z * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(22631,a,22724,a)].">
      <j1 rule="hyper" parents="22631 22724"/>
    </justification>
  </clause>

  <clause id="22727">
    <literal><![CDATA[
      T(x,(y \ z) * ((y \ z) * u)) = T(x,z * ((y \ (z / y)) * u))
    ]]></literal>
    <justification jstring="[hyper(22500,a,22723,a)].">
      <j1 rule="hyper" parents="22500 22723"/>
    </justification>
  </clause>

  <clause id="22728">
    <literal><![CDATA[
      T(T(x,y * (z \ (z \ y))),z * ((y \ (z / y)) * u)) = T(T(x,(y / z) * (1 / (z \ y))),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,22649,a(flip),b,22727,a),flip(a)].">
      <j1 rule="hyper" parents="65 22649 22727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22729">
    <literal><![CDATA[
      T(T(x,y * y),z \ (z \ (z * ((y \ (z / y)) * u)))) = T(T(x,(y / z) * (1 / (z \ y))),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,21973,a(flip),b,22728,a)].">
      <j1 rule="hyper" parents="65 21973 22728"/>
    </justification>
  </clause>

  <clause id="22730">
    <literal><![CDATA[
      T(T(x,y * y),z \ ((y \ (z / y)) * u)) = T(T(x,(y / z) * (1 / (z \ y))),u)
    ]]></literal>
    <justification jstring="[para(9(a,1),22729(a,1,2,2))].">
      <j1 rule="para" parents="9 22729"/>
    </justification>
  </clause>

  <clause id="22731">
    <literal><![CDATA[
      T(T(x,(y / z) * (1 / (z \ y))),u) = T(T(x,y * y),y \ (T(y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,22563,a(flip),b,22730,a),flip(a)].">
      <j1 rule="hyper" parents="65 22563 22730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22733">
    <literal><![CDATA[
      T(T(x,(y / z) * (1 / (z \ y))),u) = T(x,y * (y * (y \ (T(y,z) \ u))))
    ]]></literal>
    <justification jstring="[hyper(299,a,14446,a(flip),b,22731,a),flip(a)].">
      <j1 rule="hyper" parents="299 14446 22731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22734">
    <literal><![CDATA[
      T(T(x,(y / z) * (1 / (z \ y))),u) = T(x,y * (T(y,z) \ u))
    ]]></literal>
    <justification jstring="[para(10(a,1),22733(a,2,2,2))].">
      <j1 rule="para" parents="10 22733"/>
    </justification>
  </clause>

  <clause id="22736">
    <literal><![CDATA[
      T(T(x,(y / z) * (1 / (z \ y))),u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(5060(a,1),22734(a,2,2))].">
      <j1 rule="para" parents="5060 22734"/>
    </justification>
  </clause>

  <clause id="22737">
    <literal><![CDATA[
      T(T(x,(y / z) * (1 * (y \ z))),u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(22725(a,1),22736(a,1,1))].">
      <j1 rule="para" parents="22725 22736"/>
    </justification>
  </clause>

  <clause id="22738">
    <literal><![CDATA[
      T(T(x,(y / z) * (y \ z)),u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(7(a,1),22737(a,1,1,2,2))].">
      <j1 rule="para" parents="7 22737"/>
    </justification>
  </clause>

  <clause id="22739">
    <literal><![CDATA[
      T(T(x,T(y \ T(y,z),z)),u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(22376(a,2),22738(a,1,1))].">
      <j1 rule="para" parents="22376 22738"/>
    </justification>
  </clause>

  <clause id="22740">
    <literal><![CDATA[
      T(T(x,T(K(y,z),z)),u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(5036(a,2),22739(a,1,1,2,1))].">
      <j1 rule="para" parents="5036 22739"/>
    </justification>
  </clause>

  <clause id="22741">
    <literal><![CDATA[
      T(T(x,K(y,z)),u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(3616(a,1),22740(a,1,1,2))].">
      <j1 rule="para" parents="3616 22740"/>
    </justification>
  </clause>

  <clause id="22742">
    <literal><![CDATA[
      T(x,K(y,z * u) * (u * K(u * z,y))) = T(x,L(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(22600,a,22741,a),flip(a)].">
      <j1 rule="hyper" parents="22600 22741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22750">
    <literal><![CDATA[
      T(x,y * (K(z,y * u) * K(y * u,z))) = T(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[para(22078(a,1),22742(a,1,2))].">
      <j1 rule="para" parents="22078 22742"/>
    </justification>
  </clause>

  <clause id="22751">
    <literal><![CDATA[
      T(x,L(y,z,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(5210(a,1),22750(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5210 22750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22772">
    <literal><![CDATA[
      T((x \ y) \ y,z) \ T(T(x,z),L(x \ y,u,w)) = 1
    ]]></literal>
    <justification jstring="[para(22751(a,2),716(a,1,2))].">
      <j1 rule="para" parents="22751 716"/>
    </justification>
  </clause>

  <clause id="22790">
    <literal><![CDATA[
      a(x,y,K(z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(65,a,21715,a(flip),b,22772,a)].">
      <j1 rule="hyper" parents="65 21715 22772"/>
    </justification>
  </clause>

  <clause id="22797">
    <literal><![CDATA[
      a(K(x,y),z,u) = 1
    ]]></literal>
    <justification jstring="[hyper(65,a,14947,a,b,22790,a)].">
      <j1 rule="hyper" parents="65 14947 22790"/>
    </justification>
  </clause>

  <clause id="22798">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer("aK1")
    ]]></attribute>
    <justification jstring="[resolve(22797,a,66,a)].">
      <j1 rule="resolve" parents="22797 66"/>
    </justification>
  </clause>

</proof>

</proofs>
