<?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>lraa2a.out</source>

<heading><![CDATA[
Prover9 (64) version 2026-3T, March 2026.
Process 872321 was started by veroff on b146-03,
Wed Apr 15 19:22:42 2026
The command was "prover9 -f lraa2a.in".
]]></heading>

<proof number="1" length="3591" max_count="49">

<comments><![CDATA[
% Proof 1 at 177.59 (+ 0.03) seconds: "aK1".
% Length of proof: 3591 (0 new hints)
% Level of proof: 304
% Maximum clause weight: 49.000
% Given clauses in run: 4085
% Given clauses in proof: 3573 (0 new hints)
]]></comments>

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  <clause id="35" type="assumption">
    <literal><![CDATA[
      a(a(x,y,z),u,w) = 1
    ]]></literal>
    <attribute><![CDATA[
      label("aa1")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="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="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="81">
    <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="82">
    <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="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="86">
    <literal><![CDATA[
      x \ (((x / (y * z)) * y) * z) = a(x / (y * z),y,z)
    ]]></literal>
    <justification jstring="[para(12(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="12 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="87">
    <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="88">
    <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="89">
    <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="90">
    <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="91">
    <literal><![CDATA[
      (x * (y / x)) \ y = K(y / x,x)
    ]]></literal>
    <justification jstring="[para(12(a,1),16(a,2,2)),flip(a)].">
      <j1 rule="para" parents="12 16"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="92">
    <literal><![CDATA[
      (x * 1) \ (x * y) = L(y,1,x)
    ]]></literal>
    <justification jstring="[para(7(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="7 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="93">
    <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="94">
    <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="95">
    <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="96">
    <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="97">
    <literal><![CDATA[
      ((x * 1) * y) / y = R(x,1,y)
    ]]></literal>
    <justification jstring="[para(7(a,1),20(a,2,2)),flip(a)].">
      <j1 rule="para" parents="7 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="98">
    <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="99">
    <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="100">
    <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="101">
    <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="102">
    <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="103">
    <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="104">
    <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="105">
    <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="106">
    <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="107">
    <literal><![CDATA[
      x \ (T(y,z) * x) = T(T(y,x),z)
    ]]></literal>
    <justification jstring="[para(23(a,1),22(a,1)),flip(a)].">
      <j1 rule="para" parents="23 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="108">
    <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="110">
    <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="111">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      x * z != y
    ]]></literal>
    <literal><![CDATA[
      1 = z
    ]]></literal>
    <justification jstring="[para(8(a,1),36(a,1))].">
      <j1 rule="para" parents="8 36"/>
    </justification>
  </clause>

  <clause id="112">
    <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="113">
    <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="114">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      (x * z) / u != y
    ]]></literal>
    <literal><![CDATA[
      z = u
    ]]></literal>
    <justification jstring="[para(11(a,1),38(a,1))].">
      <j1 rule="para" parents="11 38"/>
    </justification>
  </clause>

  <clause id="115">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z / u != y
    ]]></literal>
    <literal><![CDATA[
      x * u = z
    ]]></literal>
    <justification jstring="[para(11(a,1),39(a,1))].">
      <j1 rule="para" parents="11 39"/>
    </justification>
  </clause>

  <clause id="116">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z \ u != y
    ]]></literal>
    <literal><![CDATA[
      z * x = u
    ]]></literal>
    <justification jstring="[para(9(a,1),40(a,1))].">
      <j1 rule="para" parents="9 40"/>
    </justification>
  </clause>

  <clause id="117">
    <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="118">
    <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="119">
    <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="120">
    <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="121">
    <literal><![CDATA[
      x \ (x * (y * z)) != u * z
    ]]></literal>
    <literal><![CDATA[
      u = y
    ]]></literal>
    <justification jstring="[para(9(a,2),46(a,2)),flip(a)].">
      <j1 rule="para" parents="9 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="123">
    <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="124">
    <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="125">
    <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="127">
    <literal><![CDATA[
      T(T(x,y),z) != T(u,y)
    ]]></literal>
    <literal><![CDATA[
      T(x,z) = u
    ]]></literal>
    <justification jstring="[para(23(a,1),51(a,1))].">
      <j1 rule="para" parents="23 51"/>
    </justification>
  </clause>

  <clause id="128">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(54,a,35,a)].">
      <j1 rule="hyper" parents="54 35"/>
    </justification>
  </clause>

  <clause id="129">
    <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="130">
    <literal><![CDATA[
      (x * (x \ y)) * z = y * z
    ]]></literal>
    <justification jstring="[hyper(59,a,10,a)].">
      <j1 rule="hyper" parents="59 10"/>
    </justification>
  </clause>

  <clause id="131">
    <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="132">
    <literal><![CDATA[
      x * (y \ (y * z)) = x * z
    ]]></literal>
    <justification jstring="[hyper(60,a,9,a)].">
      <j1 rule="hyper" parents="60 9"/>
    </justification>
  </clause>

  <clause id="133">
    <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="134">
    <literal><![CDATA[
      (x * (x \ y)) / z = y / z
    ]]></literal>
    <justification jstring="[hyper(61,a,10,a)].">
      <j1 rule="hyper" parents="61 10"/>
    </justification>
  </clause>

  <clause id="136">
    <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="137">
    <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="138">
    <literal><![CDATA[
      (x / y) * y = z * (z \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,12,a,b,10,a(flip))].">
      <j1 rule="hyper" parents="65 12 10"/>
    </justification>
  </clause>

  <clause id="139">
    <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="140">
    <literal><![CDATA[
      (x * y) / y = x * 1
    ]]></literal>
    <justification jstring="[hyper(65,a,11,a,b,8,a(flip))].">
      <j1 rule="hyper" parents="65 11 8"/>
    </justification>
  </clause>

  <clause id="141">
    <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="142">
    <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="143">
    <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="144">
    <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="145">
    <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="146">
    <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="148">
    <literal><![CDATA[
      (x \ x) * y = y
    ]]></literal>
    <justification jstring="[para(68(a,2),7(a,1,1))].">
      <j1 rule="para" parents="68 7"/>
    </justification>
  </clause>

  <clause id="149">
    <literal><![CDATA[
      x * (y \ y) = x
    ]]></literal>
    <justification jstring="[para(68(a,2),8(a,1,2))].">
      <j1 rule="para" parents="68 8"/>
    </justification>
  </clause>

  <clause id="150">
    <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="151">
    <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="152">
    <literal><![CDATA[
      x / 1 != y
    ]]></literal>
    <literal><![CDATA[
      x = y
    ]]></literal>
    <justification jstring="[para(74(a,1),48(a,2))].">
      <j1 rule="para" parents="74 48"/>
    </justification>
  </clause>

  <clause id="153">
    <literal><![CDATA[
      T(x,R(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(44,a,27,a,b,103,a(flip))].">
      <j1 rule="hyper" parents="44 27 103"/>
    </justification>
  </clause>

  <clause id="155">
    <literal><![CDATA[
      T(x,T(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(42,a,23,a,b,103,a(flip))].">
      <j1 rule="hyper" parents="42 23 103"/>
    </justification>
  </clause>

  <clause id="156">
    <literal><![CDATA[
      T(L(x,y,z),x) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(103(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="103 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="157">
    <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="158">
    <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="159">
    <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="161">
    <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="162">
    <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="163">
    <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="164">
    <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="165">
    <literal><![CDATA[
      (x / y) \ x = y / 1
    ]]></literal>
    <justification jstring="[hyper(65,a,79,a,b,74,a(flip))].">
      <j1 rule="hyper" parents="65 79 74"/>
    </justification>
  </clause>

  <clause id="166">
    <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="167">
    <literal><![CDATA[
      x * ((y / z) \ y) = x * z
    ]]></literal>
    <justification jstring="[hyper(60,a,79,a)].">
      <j1 rule="hyper" parents="60 79"/>
    </justification>
  </clause>

  <clause id="168">
    <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="169">
    <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="170">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z \ u != y
    ]]></literal>
    <literal><![CDATA[
      u / x = z
    ]]></literal>
    <justification jstring="[para(79(a,1),41(a,1))].">
      <j1 rule="para" parents="79 41"/>
    </justification>
  </clause>

  <clause id="171">
    <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="172">
    <literal><![CDATA[
      T(x,1) = x
    ]]></literal>
    <justification jstring="[hyper(65,a,22,a,b,143,a)].">
      <j1 rule="hyper" parents="65 22 143"/>
    </justification>
  </clause>

  <clause id="174">
    <literal><![CDATA[
      T(1,x) = 1
    ]]></literal>
    <justification jstring="[hyper(56,a,172,a)].">
      <j1 rule="hyper" parents="56 172"/>
    </justification>
  </clause>

  <clause id="175">
    <literal><![CDATA[
      T(x,y * (y \ 1)) = x
    ]]></literal>
    <justification jstring="[para(10(a,2),172(a,1,2))].">
      <j1 rule="para" parents="10 172"/>
    </justification>
  </clause>

  <clause id="177">
    <literal><![CDATA[
      x * (y \ y) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(149(a,1),46(a,2))].">
      <j1 rule="para" parents="149 46"/>
    </justification>
  </clause>

  <clause id="178">
    <literal><![CDATA[
      T(x,R(T(x,y),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(42,a,23,a,b,153,a(flip))].">
      <j1 rule="hyper" parents="42 23 153"/>
    </justification>
  </clause>

  <clause id="179">
    <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="180">
    <literal><![CDATA[
      x \ ((x * y) * (y \ 1)) = a(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(71(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="71 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="181">
    <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="182">
    <literal><![CDATA[
      x * ((1 / x) * (1 / x)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(36,a,34,a(flip),b,77,a(flip))].">
      <j1 rule="hyper" parents="36 34 77"/>
    </justification>
  </clause>

  <clause id="183">
    <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="184">
    <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="185">
    <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="186">
    <literal><![CDATA[
      L(x,1 / x,y) = (y * (1 / x)) \ y
    ]]></literal>
    <justification jstring="[para(78(a,1),18(a,2,2))].">
      <j1 rule="para" parents="78 18"/>
    </justification>
  </clause>

  <clause id="187">
    <literal><![CDATA[
      (x \ y) * T(x,x \ y) = y
    ]]></literal>
    <justification jstring="[hyper(65,a,104,a,b,10,a)].">
      <j1 rule="hyper" parents="65 104 10"/>
    </justification>
  </clause>

  <clause id="188">
    <literal><![CDATA[
      x * (y * T(z,y)) = x * (z * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,104,a)].">
      <j1 rule="hyper" parents="60 104"/>
    </justification>
  </clause>

  <clause id="189">
    <literal><![CDATA[
      (x * T(y,x)) * z = (y * x) * z
    ]]></literal>
    <justification jstring="[hyper(59,a,104,a)].">
      <j1 rule="hyper" parents="59 104"/>
    </justification>
  </clause>

  <clause id="190">
    <literal><![CDATA[
      T((x * y) / x,x) = y
    ]]></literal>
    <justification jstring="[hyper(36,a,12,a(flip),b,104,a),flip(a)].">
      <j1 rule="hyper" parents="36 12 104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="191">
    <literal><![CDATA[
      (x * T(y,x)) / x = y
    ]]></literal>
    <justification jstring="[hyper(37,a,12,a,b,104,a(flip))].">
      <j1 rule="hyper" parents="37 12 104"/>
    </justification>
  </clause>

  <clause id="192">
    <literal><![CDATA[
      x * (y * (y \ T(z,x))) = z * x
    ]]></literal>
    <justification jstring="[para(10(a,2),104(a,1,2))].">
      <j1 rule="para" parents="10 104"/>
    </justification>
  </clause>

  <clause id="193">
    <literal><![CDATA[
      (x * (T(y,x) * z)) \ ((y * x) * z) = a(x,T(y,x),z)
    ]]></literal>
    <justification jstring="[para(104(a,1),14(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="104 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="194">
    <literal><![CDATA[
      (x * y) \ (y * (T(x,y) * z)) = L(z,T(x,y),y)
    ]]></literal>
    <justification jstring="[para(104(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="104 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="195">
    <literal><![CDATA[
      (x * y) \ (x * (z * y)) = L(T(z,y),y,x)
    ]]></literal>
    <justification jstring="[para(104(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="104 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="196">
    <literal><![CDATA[
      T(x,y) \ (x * y) = T(y,T(x,y))
    ]]></literal>
    <justification jstring="[para(104(a,1),22(a,2,2)),flip(a)].">
      <j1 rule="para" parents="104 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="197">
    <literal><![CDATA[
      x * T(T(y,x),z) = T(y,z) * x
    ]]></literal>
    <justification jstring="[para(23(a,1),104(a,1,2))].">
      <j1 rule="para" parents="23 104"/>
    </justification>
  </clause>

  <clause id="198">
    <literal><![CDATA[
      x * L(T(y,x),z,u) = L(y,z,u) * x
    ]]></literal>
    <justification jstring="[para(25(a,2),104(a,1,2))].">
      <j1 rule="para" parents="25 104"/>
    </justification>
  </clause>

  <clause id="199">
    <literal><![CDATA[
      x * R(T(y,x),z,u) = R(y,z,u) * x
    ]]></literal>
    <justification jstring="[para(27(a,2),104(a,1,2))].">
      <j1 rule="para" parents="27 104"/>
    </justification>
  </clause>

  <clause id="200">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      y * u != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(104(a,1),36(a,1))].">
      <j1 rule="para" parents="104 36"/>
    </justification>
  </clause>

  <clause id="201">
    <literal><![CDATA[
      x * y != z * x
    ]]></literal>
    <literal><![CDATA[
      T(z,x) = y
    ]]></literal>
    <justification jstring="[para(104(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="104 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="202">
    <literal><![CDATA[
      x * T(y,x) != z * x
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(104(a,2),46(a,1))].">
      <j1 rule="para" parents="104 46"/>
    </justification>
  </clause>

  <clause id="203">
    <literal><![CDATA[
      x * T(y,x) != z * x
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(104(a,2),46(a,2)),flip(a)].">
      <j1 rule="para" parents="104 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="204">
    <literal><![CDATA[
      T(x,y) * x = x * T(x,y)
    ]]></literal>
    <justification jstring="[para(155(a,1),104(a,1,2))].">
      <j1 rule="para" parents="155 104"/>
    </justification>
  </clause>

  <clause id="205">
    <literal><![CDATA[
      T(x / (x / y),x / y) = y
    ]]></literal>
    <justification jstring="[hyper(65,a,106,a,b,79,a)].">
      <j1 rule="hyper" parents="65 106 79"/>
    </justification>
  </clause>

  <clause id="206">
    <literal><![CDATA[
      T(T(x / y,z),y) = T(y \ x,z)
    ]]></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="207">
    <literal><![CDATA[
      T(L(x / y,z,u),y) = L(y \ x,z,u)
    ]]></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="208">
    <literal><![CDATA[
      T(R(x / y,z,u),y) = R(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(106(a,1),27(a,1,1)),flip(a)].">
      <j1 rule="para" parents="106 27"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="210">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x = v5
    ]]></literal>
    <justification jstring="[para(128(a,1),52(a,2))].">
      <j1 rule="para" parents="128 52"/>
    </justification>
  </clause>

  <clause id="211">
    <literal><![CDATA[
      (x / y) * y != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(139(a,2),119(a,1))].">
      <j1 rule="para" parents="139 119"/>
    </justification>
  </clause>

  <clause id="212">
    <literal><![CDATA[
      (x * y) / y != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(140(a,2),119(a,1))].">
      <j1 rule="para" parents="140 119"/>
    </justification>
  </clause>

  <clause id="213">
    <literal><![CDATA[
      (x * y) / y != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(140(a,2),120(a,1))].">
      <j1 rule="para" parents="140 120"/>
    </justification>
  </clause>

  <clause id="214">
    <literal><![CDATA[
      x * (x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(142(a,2),120(a,1))].">
      <j1 rule="para" parents="142 120"/>
    </justification>
  </clause>

  <clause id="215">
    <literal><![CDATA[
      x * ((x \ 1) * y) = L(y,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,18,a,b,144,a),flip(a)].">
      <j1 rule="hyper" parents="65 18 144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="216">
    <literal><![CDATA[
      K(x \ 1,x) = (x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(65,a,16,a,b,144,a)].">
      <j1 rule="hyper" parents="65 16 144"/>
    </justification>
  </clause>

  <clause id="217">
    <literal><![CDATA[
      (1 / x) * (x * y) = L(y,x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(65,a,18,a,b,145,a),flip(a)].">
      <j1 rule="hyper" parents="65 18 145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="218">
    <literal><![CDATA[
      K(x,1 / x) = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(65,a,16,a,b,145,a)].">
      <j1 rule="hyper" parents="65 16 145"/>
    </justification>
  </clause>

  <clause id="219">
    <literal><![CDATA[
      (x * y) * (y \ 1) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,20,a,b,150,a),flip(a)].">
      <j1 rule="hyper" parents="65 20 150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="220">
    <literal><![CDATA[
      (x * (1 / y)) * y = R(x,1 / y,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,20,a,b,151,a),flip(a)].">
      <j1 rule="hyper" parents="65 20 151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="221">
    <literal><![CDATA[
      x / T(y,y \ x) = y \ x
    ]]></literal>
    <justification jstring="[para(10(a,1),162(a,1,1))].">
      <j1 rule="para" parents="10 162"/>
    </justification>
  </clause>

  <clause id="222">
    <literal><![CDATA[
      (x * y) / z != y
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(162(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="162 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="223">
    <literal><![CDATA[
      (x / y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(165(a,2),152(a,1))].">
      <j1 rule="para" parents="165 152"/>
    </justification>
  </clause>

  <clause id="224">
    <literal><![CDATA[
      (x * x) * ((1 / x) * y) = x * y
    ]]></literal>
    <justification jstring="[para(184(a,1),33(a,1,1)),flip(a)].">
      <j1 rule="para" parents="184 33"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="225">
    <literal><![CDATA[
      (x * T(T(y,x),z)) / x = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(42,a,23,a,b,190,a),flip(a)].">
      <j1 rule="hyper" parents="42 23 190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="226">
    <literal><![CDATA[
      T(T((x * y) / x,z),x) = T(y,z)
    ]]></literal>
    <justification jstring="[para(190(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="190 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="227">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (y * z) / y = x
    ]]></literal>
    <justification jstring="[para(190(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="190 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="228">
    <literal><![CDATA[
      T((x * y) / x,y) = (x * y) / x
    ]]></literal>
    <justification jstring="[para(190(a,1),155(a,1,2))].">
      <j1 rule="para" parents="190 155"/>
    </justification>
  </clause>

  <clause id="229">
    <literal><![CDATA[
      (x * y) * T(R(z,x,y),x * y) = (z * x) * y
    ]]></literal>
    <justification jstring="[hyper(39,a,20,a(flip),b,191,a),flip(a)].">
      <j1 rule="hyper" parents="39 20 191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="230">
    <literal><![CDATA[
      R(x,y,z) * (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      (x * y) * z = u
    ]]></literal>
    <justification jstring="[para(20(a,2),211(a,1,1)),flip(b)].">
      <j1 rule="para" parents="20 211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="231">
    <literal><![CDATA[
      x * T(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      y * x = z
    ]]></literal>
    <justification jstring="[para(162(a,1),211(a,1,1)),flip(b)].">
      <j1 rule="para" parents="162 211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="232">
    <literal><![CDATA[
      x / (y \ x) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(10(a,1),212(a,1,1))].">
      <j1 rule="para" parents="10 212"/>
    </justification>
  </clause>

  <clause id="233">
    <literal><![CDATA[
      (x * T(y,x)) / x != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(104(a,2),212(a,1,1))].">
      <j1 rule="para" parents="104 212"/>
    </justification>
  </clause>

  <clause id="234">
    <literal><![CDATA[
      (x * y) * L(z,y,x) != u
    ]]></literal>
    <literal><![CDATA[
      x * (y * z) = u
    ]]></literal>
    <justification jstring="[para(18(a,2),214(a,1,2))].">
      <j1 rule="para" parents="18 214"/>
    </justification>
  </clause>

  <clause id="235">
    <literal><![CDATA[
      x \ (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(11(a,1),223(a,1,1))].">
      <j1 rule="para" parents="11 223"/>
    </justification>
  </clause>

  <clause id="236">
    <literal><![CDATA[
      x \ (y * x) != z
    ]]></literal>
    <literal><![CDATA[
      T(y,x) = z
    ]]></literal>
    <justification jstring="[para(162(a,1),223(a,1,1))].">
      <j1 rule="para" parents="162 223"/>
    </justification>
  </clause>

  <clause id="237">
    <literal><![CDATA[
      T((x * y) / x,x) != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(106(a,2),235(a,1))].">
      <j1 rule="para" parents="106 235"/>
    </justification>
  </clause>

  <clause id="238">
    <literal><![CDATA[
      x \ (y * 1) != z
    ]]></literal>
    <literal><![CDATA[
      x \ y = z
    ]]></literal>
    <justification jstring="[para(142(a,1),235(a,1,2))].">
      <j1 rule="para" parents="142 235"/>
    </justification>
  </clause>

  <clause id="239">
    <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="240">
    <literal><![CDATA[
      ((x * (x \ y)) / z) \ y = z
    ]]></literal>
    <justification jstring="[hyper(118,a,82,a)].">
      <j1 rule="hyper" parents="118 82"/>
    </justification>
  </clause>

  <clause id="241">
    <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="242">
    <literal><![CDATA[
      x * K(y \ x,y) = (y \ x) * y
    ]]></literal>
    <justification jstring="[para(10(a,1),87(a,1,1))].">
      <j1 rule="para" parents="10 87"/>
    </justification>
  </clause>

  <clause id="243">
    <literal><![CDATA[
      x * K(y,x / y) = y * (x / y)
    ]]></literal>
    <justification jstring="[para(12(a,1),87(a,1,1))].">
      <j1 rule="para" parents="12 87"/>
    </justification>
  </clause>

  <clause id="244">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (z * y)) = L(K(z,y),y * z,x)
    ]]></literal>
    <justification jstring="[para(87(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="87 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="245">
    <literal><![CDATA[
      T(x * y,K(y,x)) = K(y,x) \ (y * x)
    ]]></literal>
    <justification jstring="[para(87(a,1),22(a,2,2))].">
      <j1 rule="para" parents="87 22"/>
    </justification>
  </clause>

  <clause id="246">
    <literal><![CDATA[
      (x * y) \ (y * x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(87(a,1),235(a,1,2))].">
      <j1 rule="para" parents="87 235"/>
    </justification>
  </clause>

  <clause id="247">
    <literal><![CDATA[
      L(T(x,L(x,y,z) \ u),y,z) = (L(x,y,z) \ u) \ u
    ]]></literal>
    <justification jstring="[hyper(65,a,25,a,b,105,a)].">
      <j1 rule="hyper" parents="65 25 105"/>
    </justification>
  </clause>

  <clause id="248">
    <literal><![CDATA[
      x \ T(y,y \ z) = x \ ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,105,a)].">
      <j1 rule="hyper" parents="64 105"/>
    </justification>
  </clause>

  <clause id="249">
    <literal><![CDATA[
      x * T(y,y \ z) = x * ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(60,a,105,a)].">
      <j1 rule="hyper" parents="60 105"/>
    </justification>
  </clause>

  <clause id="250">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z != y
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(7(a,1),110(a,1))].">
      <j1 rule="para" parents="7 110"/>
    </justification>
  </clause>

  <clause id="252">
    <literal><![CDATA[
      (x * y) / y != z * u
    ]]></literal>
    <literal><![CDATA[
      x / u = z
    ]]></literal>
    <justification jstring="[para(137(a,2),46(a,1))].">
      <j1 rule="para" parents="137 46"/>
    </justification>
  </clause>

  <clause id="253">
    <literal><![CDATA[
      ((x / y) * y) * z != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(137(a,1),211(a,1,1)),flip(b)].">
      <j1 rule="para" parents="137 211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="254">
    <literal><![CDATA[
      (x / y) * y != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ x = u
    ]]></literal>
    <justification jstring="[para(138(a,2),45(a,1))].">
      <j1 rule="para" parents="138 45"/>
    </justification>
  </clause>

  <clause id="255">
    <literal><![CDATA[
      x * (x \ y) != z * u
    ]]></literal>
    <literal><![CDATA[
      y / u = z
    ]]></literal>
    <justification jstring="[para(138(a,1),46(a,1))].">
      <j1 rule="para" parents="138 46"/>
    </justification>
  </clause>

  <clause id="256">
    <literal><![CDATA[
      (x * (x \ y)) / z != u
    ]]></literal>
    <literal><![CDATA[
      y / z = u
    ]]></literal>
    <justification jstring="[para(138(a,1),212(a,1,1)),flip(b)].">
      <j1 rule="para" parents="138 212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="258">
    <literal><![CDATA[
      x \ y != z * (z \ u)
    ]]></literal>
    <literal><![CDATA[
      x * u = y
    ]]></literal>
    <justification jstring="[para(141(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="141 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="259">
    <literal><![CDATA[
      x * (y * (y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(141(a,1),214(a,1,2))].">
      <j1 rule="para" parents="141 214"/>
    </justification>
  </clause>

  <clause id="260">
    <literal><![CDATA[
      (x / (y \ x)) * z != u
    ]]></literal>
    <literal><![CDATA[
      y * z = u
    ]]></literal>
    <justification jstring="[para(157(a,1),211(a,1,1)),flip(b)].">
      <j1 rule="para" parents="157 211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="261">
    <literal><![CDATA[
      (x / y) * ((z / y) \ z) = x
    ]]></literal>
    <justification jstring="[hyper(250,a,12,a(flip),b,167,a),flip(a)].">
      <j1 rule="hyper" parents="250 12 167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="262">
    <literal><![CDATA[
      ((x / y) \ x) * (y \ z) = z
    ]]></literal>
    <justification jstring="[hyper(250,a,10,a(flip),b,168,a),flip(a)].">
      <j1 rule="hyper" parents="250 10 168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="263">
    <literal><![CDATA[
      (x \ y) * z != y
    ]]></literal>
    <literal><![CDATA[
      T(x,x \ y) = z
    ]]></literal>
    <justification jstring="[para(187(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="187 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="264">
    <literal><![CDATA[
      T(x / (x / y),(z / (x / y)) \ z) = y
    ]]></literal>
    <justification jstring="[para(79(a,2),205(a,1,2))].">
      <j1 rule="para" parents="79 205"/>
    </justification>
  </clause>

  <clause id="265">
    <literal><![CDATA[
      x * T(x \ 1,x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(250,a,104,a,b,216,a)].">
      <j1 rule="hyper" parents="250 104 216"/>
    </justification>
  </clause>

  <clause id="266">
    <literal><![CDATA[
      x \ (x * y) = L(y,1,x)
    ]]></literal>
    <justification jstring="[para(8(a,1),92(a,1,1))].">
      <j1 rule="para" parents="8 92"/>
    </justification>
  </clause>

  <clause id="267">
    <literal><![CDATA[
      L(x,1,y) = x
    ]]></literal>
    <justification jstring="[hyper(235,a,266,a),flip(a)].">
      <j1 rule="hyper" parents="235 266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="269">
    <literal><![CDATA[
      L(x,1,y) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(267(a,1),52(a,1)),flip(a)].">
      <j1 rule="para" parents="267 52"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="270">
    <literal><![CDATA[
      x \ (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(266(a,2),269(a,1))].">
      <j1 rule="para" parents="266 269"/>
    </justification>
  </clause>

  <clause id="271">
    <literal><![CDATA[
      (x * y) / y = R(x,1,y)
    ]]></literal>
    <justification jstring="[para(8(a,1),97(a,1,1,1))].">
      <j1 rule="para" parents="8 97"/>
    </justification>
  </clause>

  <clause id="272">
    <literal><![CDATA[
      R(x,1,y) = x
    ]]></literal>
    <justification jstring="[hyper(213,a,271,a),flip(a)].">
      <j1 rule="hyper" parents="213 271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="274">
    <literal><![CDATA[
      L(x \ 1,x,1 / x) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(250,a,145,a(flip),b,181,a),flip(a)].">
      <j1 rule="hyper" parents="250 145 181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="275">
    <literal><![CDATA[
      L((x \ y) \ 1,x \ y,x) = y \ x
    ]]></literal>
    <justification jstring="[hyper(250,a,136,a(flip),b,181,a),flip(a)].">
      <j1 rule="hyper" parents="250 136 181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="276">
    <literal><![CDATA[
      x * L(y \ 1,y,z) = x * ((z * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(60,a,181,a)].">
      <j1 rule="hyper" parents="60 181"/>
    </justification>
  </clause>

  <clause id="277">
    <literal><![CDATA[
      L(x \ 1,x,y) * z = ((y * x) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(59,a,181,a)].">
      <j1 rule="hyper" parents="59 181"/>
    </justification>
  </clause>

  <clause id="278">
    <literal><![CDATA[
      x / L(y \ 1,y,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(171,a,181,a(flip))].">
      <j1 rule="hyper" parents="171 181"/>
    </justification>
  </clause>

  <clause id="279">
    <literal><![CDATA[
      (x * y) * L(y \ 1,y,x) = x
    ]]></literal>
    <justification jstring="[hyper(125,a,181,a(flip))].">
      <j1 rule="hyper" parents="125 181"/>
    </justification>
  </clause>

  <clause id="280">
    <literal><![CDATA[
      L(x \ 1,x,y / x) = y \ (y / x)
    ]]></literal>
    <justification jstring="[para(12(a,1),181(a,2,1))].">
      <j1 rule="para" parents="12 181"/>
    </justification>
  </clause>

  <clause id="281">
    <literal><![CDATA[
      T((x * y) \ x,z) = L(T(y \ 1,z),y,x)
    ]]></literal>
    <justification jstring="[para(181(a,1),25(a,2,1)),flip(a)].">
      <j1 rule="para" parents="181 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="282">
    <literal><![CDATA[
      L(L(x \ 1,y,z),x,u) = L((u * x) \ u,y,z)
    ]]></literal>
    <justification jstring="[para(181(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="181 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="283">
    <literal><![CDATA[
      x * R(1 / y,y,z) = x * (z / (y * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,183,a)].">
      <j1 rule="hyper" parents="60 183"/>
    </justification>
  </clause>

  <clause id="284">
    <literal><![CDATA[
      R(1 / x,x,y) \ y = x * y
    ]]></literal>
    <justification jstring="[hyper(163,a,183,a(flip))].">
      <j1 rule="hyper" parents="163 183"/>
    </justification>
  </clause>

  <clause id="285">
    <literal><![CDATA[
      R(1 / x,x,x \ y) = (x \ y) / y
    ]]></literal>
    <justification jstring="[para(10(a,1),183(a,2,2))].">
      <j1 rule="para" parents="10 183"/>
    </justification>
  </clause>

  <clause id="286">
    <literal><![CDATA[
      R(1 / (x / y),x / y,y) = y / x
    ]]></literal>
    <justification jstring="[para(12(a,1),183(a,2,2))].">
      <j1 rule="para" parents="12 183"/>
    </justification>
  </clause>

  <clause id="287">
    <literal><![CDATA[
      T(x / (y * x),z) = R(T(1 / y,z),y,x)
    ]]></literal>
    <justification jstring="[para(183(a,1),27(a,2,1)),flip(a)].">
      <j1 rule="para" parents="183 27"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="288">
    <literal><![CDATA[
      R(R(1 / x,y,z),x,u) = R(u / (x * u),y,z)
    ]]></literal>
    <justification jstring="[para(183(a,1),31(a,1,1)),flip(a)].">
      <j1 rule="para" parents="183 31"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="289">
    <literal><![CDATA[
      x * T(T(y,x),z) != u * x
    ]]></literal>
    <literal><![CDATA[
      T(y,z) = u
    ]]></literal>
    <justification jstring="[para(23(a,1),202(a,1,2))].">
      <j1 rule="para" parents="23 202"/>
    </justification>
  </clause>

  <clause id="290">
    <literal><![CDATA[
      x * T(T(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(23(a,1),231(a,1,2))].">
      <j1 rule="para" parents="23 231"/>
    </justification>
  </clause>

  <clause id="291">
    <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),231(a,1,2))].">
      <j1 rule="para" parents="25 231"/>
    </justification>
  </clause>

  <clause id="292">
    <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),231(a,1,2))].">
      <j1 rule="para" parents="27 231"/>
    </justification>
  </clause>

  <clause id="293">
    <literal><![CDATA[
      T(x / y,y) != z
    ]]></literal>
    <literal><![CDATA[
      y \ x = z
    ]]></literal>
    <justification jstring="[para(10(a,1),237(a,1,1,1))].">
      <j1 rule="para" parents="10 237"/>
    </justification>
  </clause>

  <clause id="294">
    <literal><![CDATA[
      T((x * y) / (y * x),y * x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(87(a,1),237(a,1,1,1))].">
      <j1 rule="para" parents="87 237"/>
    </justification>
  </clause>

  <clause id="295">
    <literal><![CDATA[
      L(T(x \ 1,y),x,1 / x) = T(1 / x,y)
    ]]></literal>
    <justification jstring="[para(274(a,1),25(a,2,1))].">
      <j1 rule="para" parents="274 25"/>
    </justification>
  </clause>

  <clause id="296">
    <literal><![CDATA[
      (x * y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      L(y \ 1,y,x) = z
    ]]></literal>
    <justification jstring="[para(278(a,1),223(a,1,1))].">
      <j1 rule="para" parents="278 223"/>
    </justification>
  </clause>

  <clause id="299">
    <literal><![CDATA[
      R(x,x \ 1,y) \ y = (x \ 1) * y
    ]]></literal>
    <justification jstring="[para(76(a,1),284(a,1,1,1))].">
      <j1 rule="para" parents="76 284"/>
    </justification>
  </clause>

  <clause id="300">
    <literal><![CDATA[
      x / (y * x) != z
    ]]></literal>
    <literal><![CDATA[
      R(1 / y,y,x) = z
    ]]></literal>
    <justification jstring="[para(284(a,1),232(a,1,2)),flip(b)].">
      <j1 rule="para" parents="284 232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="301">
    <literal><![CDATA[
      T(x,x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) \ y = z
    ]]></literal>
    <justification jstring="[para(76(a,1),293(a,1,1))].">
      <j1 rule="para" parents="76 293"/>
    </justification>
  </clause>

  <clause id="302">
    <literal><![CDATA[
      K(x \ 1,x) \ 1 = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(216(a,2),89(a,1,1))].">
      <j1 rule="para" parents="216 89"/>
    </justification>
  </clause>

  <clause id="303">
    <literal><![CDATA[
      K(x,1 / x) \ 1 = K(1 / x,x)
    ]]></literal>
    <justification jstring="[para(218(a,2),91(a,1,1))].">
      <j1 rule="para" parents="218 91"/>
    </justification>
  </clause>

  <clause id="304">
    <literal><![CDATA[
      T(T(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(107(a,1),236(a,1))].">
      <j1 rule="para" parents="107 236"/>
    </justification>
  </clause>

  <clause id="305">
    <literal><![CDATA[
      (x * y) \ R(x,y,y \ 1) = y \ 1
    ]]></literal>
    <justification jstring="[hyper(112,a,20,a,b,150,a(flip))].">
      <j1 rule="hyper" parents="112 20 150"/>
    </justification>
  </clause>

  <clause id="307">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z * u != y
    ]]></literal>
    <literal><![CDATA[
      T(z,u) = u \ x
    ]]></literal>
    <justification jstring="[para(104(a,1),112(b,1)),flip(c)].">
      <j1 rule="para" parents="104 112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="308">
    <literal><![CDATA[
      R(x,y,y \ 1) / (y \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(113,a,20,a,b,150,a(flip))].">
      <j1 rule="hyper" parents="113 20 150"/>
    </justification>
  </clause>

  <clause id="309">
    <literal><![CDATA[
      R(R(x,y,z),u,w) * (y * z) = (R(x,u,w) * y) * z
    ]]></literal>
    <justification jstring="[hyper(115,a,31,a,b,20,a(flip))].">
      <j1 rule="hyper" parents="115 31 20"/>
    </justification>
  </clause>

  <clause id="310">
    <literal><![CDATA[
      L(R(x,y,z),u,w) * (y * z) = (L(x,u,w) * y) * z
    ]]></literal>
    <justification jstring="[hyper(115,a,29,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="115 29 20"/>
    </justification>
  </clause>

  <clause id="311">
    <literal><![CDATA[
      T(R(x,y,z),u) * (y * z) = (T(x,u) * y) * z
    ]]></literal>
    <justification jstring="[hyper(115,a,27,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="115 27 20"/>
    </justification>
  </clause>

  <clause id="312">
    <literal><![CDATA[
      (x * y) * L(L(z,y,x),u,w) = x * (y * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(116,a,30,a,b,18,a(flip))].">
      <j1 rule="hyper" parents="116 30 18"/>
    </justification>
  </clause>

  <clause id="313">
    <literal><![CDATA[
      (x * y) * R(L(z,y,x),u,w) = x * (y * R(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(116,a,29,a,b,18,a(flip))].">
      <j1 rule="hyper" parents="116 29 18"/>
    </justification>
  </clause>

  <clause id="314">
    <literal><![CDATA[
      x * L(y,z \ x,z) = z * ((z \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(116,a,18,a,b,136,a(flip))].">
      <j1 rule="hyper" parents="116 18 136"/>
    </justification>
  </clause>

  <clause id="315">
    <literal><![CDATA[
      (a(x,y,z) * u) * w = a(x,y,z) * (u * w)
    ]]></literal>
    <justification jstring="[hyper(116,a,128,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="116 128 18"/>
    </justification>
  </clause>

  <clause id="316">
    <literal><![CDATA[
      (x * y) * T(L(z,y,x),u) = x * (y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(116,a,25,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="116 25 18"/>
    </justification>
  </clause>

  <clause id="317">
    <literal><![CDATA[
      (x * y) * ((1 / y) * (1 / y)) = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(182(a,1),34(a,2,2))].">
      <j1 rule="para" parents="182 34"/>
    </justification>
  </clause>

  <clause id="318">
    <literal><![CDATA[
      (x * R(T(y,x),z,u)) * w = (R(y,z,u) * x) * w
    ]]></literal>
    <justification jstring="[para(27(a,2),189(a,1,1,2))].">
      <j1 rule="para" parents="27 189"/>
    </justification>
  </clause>

  <clause id="319">
    <literal><![CDATA[
      L(x \ T(y,z),x,z) = (z * x) \ (y * z)
    ]]></literal>
    <justification jstring="[para(192(a,1),18(a,2,2))].">
      <j1 rule="para" parents="192 18"/>
    </justification>
  </clause>

  <clause id="320">
    <literal><![CDATA[
      x * T(x \ (y * x),z) = T(y,z) * x
    ]]></literal>
    <justification jstring="[para(22(a,1),197(a,1,2,1))].">
      <j1 rule="para" parents="22 197"/>
    </justification>
  </clause>

  <clause id="321">
    <literal><![CDATA[
      T(x / y,z) * y = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(106(a,1),197(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="106 197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="322">
    <literal><![CDATA[
      T((x * y) / x,z) * x = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(190(a,1),197(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="190 197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="323">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ y,z) = T(x,z) * (x \ y)
    ]]></literal>
    <justification jstring="[para(105(a,1),197(a,1,2,1))].">
      <j1 rule="para" parents="105 197"/>
    </justification>
  </clause>

  <clause id="325">
    <literal><![CDATA[
      (x * T(x \ y,z)) / x = T(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(227,a,206,a)].">
      <j1 rule="hyper" parents="227 206"/>
    </justification>
  </clause>

  <clause id="326">
    <literal><![CDATA[
      (x * x) \ (x * y) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(118,a,224,a)].">
      <j1 rule="hyper" parents="118 224"/>
    </justification>
  </clause>

  <clause id="327">
    <literal><![CDATA[
      (x * T(y,z)) / x = T((x * y) / x,z)
    ]]></literal>
    <justification jstring="[para(190(a,1),225(a,1,1,2,1))].">
      <j1 rule="para" parents="190 225"/>
    </justification>
  </clause>

  <clause id="328">
    <literal><![CDATA[
      T(x,(y * x) / y) = x
    ]]></literal>
    <justification jstring="[hyper(56,a,228,a)].">
      <j1 rule="hyper" parents="56 228"/>
    </justification>
  </clause>

  <clause id="329">
    <literal><![CDATA[
      K(x \ y,x) * z != (x \ y) * x
    ]]></literal>
    <literal><![CDATA[
      T(y,K(x \ y,x)) = z
    ]]></literal>
    <justification jstring="[para(242(a,1),201(a,2))].">
      <j1 rule="para" parents="242 201"/>
    </justification>
  </clause>

  <clause id="330">
    <literal><![CDATA[
      x \ (y * (x / y)) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x / y) = z
    ]]></literal>
    <justification jstring="[para(243(a,1),235(a,1,2))].">
      <j1 rule="para" parents="243 235"/>
    </justification>
  </clause>

  <clause id="331">
    <literal><![CDATA[
      (x * (y * z)) / L(T(y,z),z,x) = x * z
    ]]></literal>
    <justification jstring="[hyper(113,a,188,a(flip),b,93,a)].">
      <j1 rule="hyper" parents="113 188 93"/>
    </justification>
  </clause>

  <clause id="332">
    <literal><![CDATA[
      x \ ((x * y) * L(z,y,x)) = y * z
    ]]></literal>
    <justification jstring="[hyper(112,a,93,a,b,xx)].">
      <j1 rule="hyper" parents="112 93"/>
    </justification>
  </clause>

  <clause id="333">
    <literal><![CDATA[
      (x * y) * L(z,T(x,y),y) = y * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,189,a(flip),b,93,a)].">
      <j1 rule="hyper" parents="65 189 93"/>
    </justification>
  </clause>

  <clause id="334">
    <literal><![CDATA[
      x * L(y,z,x / z) = (x / z) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,129,a(flip),b,93,a)].">
      <j1 rule="hyper" parents="65 129 93"/>
    </justification>
  </clause>

  <clause id="336">
    <literal><![CDATA[
      L(x \ T(y * x,y),x,y) = y
    ]]></literal>
    <justification jstring="[hyper(36,a,192,a(flip),b,93,a),flip(a)].">
      <j1 rule="hyper" parents="36 192 93"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="337">
    <literal><![CDATA[
      x \ (y * L(z,x \ y,x)) = (x \ y) * z
    ]]></literal>
    <justification jstring="[hyper(112,a,130,a(flip),b,93,a(flip))].">
      <j1 rule="hyper" parents="112 130 93"/>
    </justification>
  </clause>

  <clause id="339">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * (z * u))) = L(L(u,z,y),y * z,x)
    ]]></literal>
    <justification jstring="[para(93(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="93 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="340">
    <literal><![CDATA[
      ((x * (y * z)) * u) / (L(z,y,x) * u) = R(x * y,L(z,y,x),u)
    ]]></literal>
    <justification jstring="[para(93(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="93 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="341">
    <literal><![CDATA[
      (x * y) * z != x * (y * u)
    ]]></literal>
    <literal><![CDATA[
      L(u,y,x) = z
    ]]></literal>
    <justification jstring="[para(93(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="93 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="342">
    <literal><![CDATA[
      (x * y) \ (x * (y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,y,x) = u
    ]]></literal>
    <justification jstring="[para(93(a,1),235(a,1,2))].">
      <j1 rule="para" parents="93 235"/>
    </justification>
  </clause>

  <clause id="343">
    <literal><![CDATA[
      K(x \ 1,x) * L(y,x,x \ 1) = (x \ 1) * (x * y)
    ]]></literal>
    <justification jstring="[para(216(a,2),93(a,1,1))].">
      <j1 rule="para" parents="216 93"/>
    </justification>
  </clause>

  <clause id="344">
    <literal><![CDATA[
      (x * y) * L(K(z \ y,z),y,x) = x * ((z \ y) * z)
    ]]></literal>
    <justification jstring="[para(242(a,1),93(a,2,2))].">
      <j1 rule="para" parents="242 93"/>
    </justification>
  </clause>

  <clause id="345">
    <literal><![CDATA[
      T(a(x,y,z) * u,a(x,y,z)) = u * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,336,a(flip),b,128,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 336 128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="346">
    <literal><![CDATA[
      L(x,y,z) != z
    ]]></literal>
    <literal><![CDATA[
      y \ T(z * y,z) = x
    ]]></literal>
    <justification jstring="[para(336(a,1),52(a,1)),flip(a)].">
      <j1 rule="para" parents="336 52"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="347">
    <literal><![CDATA[
      L(x \ y,x,1 / x) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(250,a,145,a(flip),b,95,a),flip(a)].">
      <j1 rule="hyper" parents="250 145 95"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="348">
    <literal><![CDATA[
      L((x \ 1) \ y,x \ 1,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(250,a,144,a(flip),b,95,a),flip(a)].">
      <j1 rule="hyper" parents="250 144 95"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="349">
    <literal><![CDATA[
      L((x \ y) \ z,x \ y,x) = y \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(250,a,136,a(flip),b,95,a),flip(a)].">
      <j1 rule="hyper" parents="250 136 95"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="350">
    <literal><![CDATA[
      (a(x,y,z) * u) \ (a(x,y,z) * w) = u \ w
    ]]></literal>
    <justification jstring="[hyper(210,a,95,a),flip(a)].">
      <j1 rule="hyper" parents="210 95"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="352">
    <literal><![CDATA[
      L(x \ y,x,z / y) = ((z / y) * x) \ z
    ]]></literal>
    <justification jstring="[para(12(a,1),95(a,2,2))].">
      <j1 rule="para" parents="12 95"/>
    </justification>
  </clause>

  <clause id="353">
    <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),95(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14 95"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="354">
    <literal><![CDATA[
      T((x * y) \ (x * z),u) = L(T(y \ z,u),y,x)
    ]]></literal>
    <justification jstring="[para(95(a,1),25(a,2,1)),flip(a)].">
      <j1 rule="para" parents="95 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="355">
    <literal><![CDATA[
      L(T(x,y) \ z,T(x,y),y) = (x * y) \ (y * z)
    ]]></literal>
    <justification jstring="[para(104(a,1),95(a,2,1))].">
      <j1 rule="para" parents="104 95"/>
    </justification>
  </clause>

  <clause id="356">
    <literal><![CDATA[
      L(x \ 1,x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (y * x) \ y = z
    ]]></literal>
    <justification jstring="[para(95(a,2),238(a,1))].">
      <j1 rule="para" parents="95 238"/>
    </justification>
  </clause>

  <clause id="358">
    <literal><![CDATA[
      L(x \ L(y,z,u),x,u * z) = ((u * z) * x) \ (u * (z * y))
    ]]></literal>
    <justification jstring="[para(93(a,1),95(a,2,2))].">
      <j1 rule="para" parents="93 95"/>
    </justification>
  </clause>

  <clause id="359">
    <literal><![CDATA[
      (R(x,y,z) * (y * z)) / z = x * y
    ]]></literal>
    <justification jstring="[hyper(113,a,100,a,b,xx)].">
      <j1 rule="hyper" parents="113 100"/>
    </justification>
  </clause>

  <clause id="360">
    <literal><![CDATA[
      R(x,x \ y,z) \ (y * z) = (x \ y) * z
    ]]></literal>
    <justification jstring="[hyper(112,a,130,a(flip),b,100,a)].">
      <j1 rule="hyper" parents="112 130 100"/>
    </justification>
  </clause>

  <clause id="361">
    <literal><![CDATA[
      R(x / y,y,z) \ (x * z) = y * z
    ]]></literal>
    <justification jstring="[hyper(112,a,129,a(flip),b,100,a)].">
      <j1 rule="hyper" parents="112 129 100"/>
    </justification>
  </clause>

  <clause id="362">
    <literal><![CDATA[
      R(x,y,T(z,x * y)) \ (z * (x * y)) = y * T(z,x * y)
    ]]></literal>
    <justification jstring="[hyper(112,a,104,a(flip),b,100,a)].">
      <j1 rule="hyper" parents="112 104 100"/>
    </justification>
  </clause>

  <clause id="364">
    <literal><![CDATA[
      R(x,y,y \ z) * z = (x * y) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,131,a(flip),b,100,a)].">
      <j1 rule="hyper" parents="65 131 100"/>
    </justification>
  </clause>

  <clause id="365">
    <literal><![CDATA[
      R(x,y,z * z) = x
    ]]></literal>
    <justification jstring="[hyper(37,a,34,a(flip),b,100,a),flip(a)].">
      <j1 rule="hyper" parents="37 34 100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="366">
    <literal><![CDATA[
      ((x * y) * z) / L(z,y,R(x,y,z)) = R(x,y,z) * y
    ]]></literal>
    <justification jstring="[hyper(113,a,100,a(flip),b,93,a)].">
      <j1 rule="hyper" parents="113 100 93"/>
    </justification>
  </clause>

  <clause id="367">
    <literal><![CDATA[
      (R(x,y,z) * y) \ ((x * y) * z) = L(z,y,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(112,a,100,a(flip),b,93,a)].">
      <j1 rule="hyper" parents="112 100 93"/>
    </justification>
  </clause>

  <clause id="368">
    <literal><![CDATA[
      (((x * y) * z) * u) / ((y * z) * u) = R(R(x,y,z),y * z,u)
    ]]></literal>
    <justification jstring="[para(100(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="100 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="369">
    <literal><![CDATA[
      ((x * R(y,z,u)) * (z * u)) / ((y * z) * u) = R(x,R(y,z,u),z * u)
    ]]></literal>
    <justification jstring="[para(100(a,1),20(a,2,2)),flip(a)].">
      <j1 rule="para" parents="100 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="370">
    <literal><![CDATA[
      (x * y) * z != u * (y * z)
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(100(a,1),46(a,1))].">
      <j1 rule="para" parents="100 46"/>
    </justification>
  </clause>

  <clause id="371">
    <literal><![CDATA[
      ((x * y) * z) / (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(100(a,1),212(a,1,1)),flip(b)].">
      <j1 rule="para" parents="100 212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="372">
    <literal><![CDATA[
      R(x,y \ 1,y) * K(y \ 1,y) = (x * (y \ 1)) * y
    ]]></literal>
    <justification jstring="[para(216(a,2),100(a,1,2))].">
      <j1 rule="para" parents="216 100"/>
    </justification>
  </clause>

  <clause id="374">
    <literal><![CDATA[
      R(x,y,1) = x
    ]]></literal>
    <justification jstring="[para(7(a,1),365(a,1,3))].">
      <j1 rule="para" parents="7 365"/>
    </justification>
  </clause>

  <clause id="375">
    <literal><![CDATA[
      R(x,y,1) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(374(a,1),53(a,1)),flip(a)].">
      <j1 rule="para" parents="374 53"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="376">
    <literal><![CDATA[
      R(x / (1 / y),1 / y,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(250,a,151,a(flip),b,101,a),flip(a)].">
      <j1 rule="hyper" parents="250 151 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="377">
    <literal><![CDATA[
      R(x / y,y,y \ 1) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(250,a,150,a(flip),b,101,a),flip(a)].">
      <j1 rule="hyper" parents="250 150 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="378">
    <literal><![CDATA[
      R(x / y,y,x \ z) = z / (y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(250,a,134,a(flip),b,101,a),flip(a)].">
      <j1 rule="hyper" parents="250 134 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="379">
    <literal><![CDATA[
      R(x / (y / z),y / z,z) = (x * z) / y
    ]]></literal>
    <justification jstring="[para(12(a,1),101(a,2,2))].">
      <j1 rule="para" parents="12 101"/>
    </justification>
  </clause>

  <clause id="380">
    <literal><![CDATA[
      T((x * y) / (z * y),u) = R(T(x / z,u),z,y)
    ]]></literal>
    <justification jstring="[para(101(a,1),27(a,2,1)),flip(a)].">
      <j1 rule="para" parents="101 27"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="381">
    <literal><![CDATA[
      R(x / T(y,z),T(y,z),y) = (x * y) / (y * T(y,z))
    ]]></literal>
    <justification jstring="[para(204(a,1),101(a,2,2))].">
      <j1 rule="para" parents="204 101"/>
    </justification>
  </clause>

  <clause id="382">
    <literal><![CDATA[
      R(x / y,y,x \ z) \ z = y * (x \ z)
    ]]></literal>
    <justification jstring="[para(101(a,2),240(a,1,1))].">
      <j1 rule="para" parents="101 240"/>
    </justification>
  </clause>

  <clause id="383">
    <literal><![CDATA[
      R(R(x,y,z) / u,u,y * z) = ((x * y) * z) / (u * (y * z))
    ]]></literal>
    <justification jstring="[para(100(a,1),101(a,2,1))].">
      <j1 rule="para" parents="100 101"/>
    </justification>
  </clause>

  <clause id="384">
    <literal><![CDATA[
      R(x / R(y,z,u),R(y,z,u),z * u) = (x * (z * u)) / ((y * z) * u)
    ]]></literal>
    <justification jstring="[para(100(a,1),101(a,2,2))].">
      <j1 rule="para" parents="100 101"/>
    </justification>
  </clause>

  <clause id="385">
    <literal><![CDATA[
      R(R(x / y,y,z),y * z,u) = ((x * z) * u) / ((y * z) * u)
    ]]></literal>
    <justification jstring="[para(101(a,2),101(a,1,1))].">
      <j1 rule="para" parents="101 101"/>
    </justification>
  </clause>

  <clause id="386">
    <literal><![CDATA[
      x \ (x * y) != z * u
    ]]></literal>
    <literal><![CDATA[
      y / u = z
    ]]></literal>
    <justification jstring="[para(12(a,1),121(a,1,2,2)),flip(b)].">
      <j1 rule="para" parents="12 121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="387">
    <literal><![CDATA[
      R(x * y,K(y,x),z) \ ((y * x) * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[para(87(a,1),159(a,1,2,1))].">
      <j1 rule="para" parents="87 159"/>
    </justification>
  </clause>

  <clause id="388">
    <literal><![CDATA[
      x / K(x \ 1,x) = R(x,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(216(a,2),179(a,2,2)),flip(a)].">
      <j1 rule="para" parents="216 179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="389">
    <literal><![CDATA[
      x \ L(L(y,x \ 1,x),z,u) = (x \ 1) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(112,a,30,a,b,215,a)].">
      <j1 rule="hyper" parents="112 30 215"/>
    </justification>
  </clause>

  <clause id="390">
    <literal><![CDATA[
      x \ R(L(y,x \ 1,x),z,u) = (x \ 1) * R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(112,a,29,a,b,215,a)].">
      <j1 rule="hyper" parents="112 29 215"/>
    </justification>
  </clause>

  <clause id="391">
    <literal><![CDATA[
      x \ T(L(y,x \ 1,x),z) = (x \ 1) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(112,a,25,a(flip),b,215,a)].">
      <j1 rule="hyper" parents="112 25 215"/>
    </justification>
  </clause>

  <clause id="392">
    <literal><![CDATA[
      L(T(x,y),y,1 / y) = (1 / y) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,188,a(flip),b,217,a),flip(a)].">
      <j1 rule="hyper" parents="65 188 217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="393">
    <literal><![CDATA[
      T(R(x,y,y \ 1),z) / (y \ 1) = T(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(113,a,27,a(flip),b,219,a)].">
      <j1 rule="hyper" parents="113 27 219"/>
    </justification>
  </clause>

  <clause id="394">
    <literal><![CDATA[
      R(x,y,y \ 1) * L(z,y \ 1,x * y) = (x * y) * ((y \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(115,a,219,a(flip),b,161,a)].">
      <j1 rule="hyper" parents="115 219 161"/>
    </justification>
  </clause>

  <clause id="395">
    <literal><![CDATA[
      ((x \ 1) * (y * x)) \ R(y,x,x \ 1) = K(y * x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(112,a,219,a(flip),b,87,a)].">
      <j1 rule="hyper" parents="112 219 87"/>
    </justification>
  </clause>

  <clause id="396">
    <literal><![CDATA[
      L((x \ 1) \ 1,x \ 1,y * x) = R(y,x,x \ 1) \ (y * x)
    ]]></literal>
    <justification jstring="[para(219(a,1),181(a,2,1))].">
      <j1 rule="para" parents="219 181"/>
    </justification>
  </clause>

  <clause id="397">
    <literal><![CDATA[
      R(R(x,1 / y,y),z,u) / y = R(x,z,u) * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(113,a,31,a,b,220,a)].">
      <j1 rule="hyper" parents="113 31 220"/>
    </justification>
  </clause>

  <clause id="398">
    <literal><![CDATA[
      L(R(x,1 / y,y),z,u) / y = L(x,z,u) * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(113,a,29,a(flip),b,220,a)].">
      <j1 rule="hyper" parents="113 29 220"/>
    </justification>
  </clause>

  <clause id="399">
    <literal><![CDATA[
      T(R(x,1 / y,y),z) / y = T(x,z) * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(113,a,27,a(flip),b,220,a)].">
      <j1 rule="hyper" parents="113 27 220"/>
    </justification>
  </clause>

  <clause id="401">
    <literal><![CDATA[
      x * ((a(y,z,u) * x) \ w) = a(y,z,u) \ w
    ]]></literal>
    <justification jstring="[hyper(116,a,239,a(flip),b,128,a(flip))].">
      <j1 rule="hyper" parents="116 239 128"/>
    </justification>
  </clause>

  <clause id="402">
    <literal><![CDATA[
      L(L(x \ (y \ z),u,w),x,y) = L((y * x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(239(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="239 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="404">
    <literal><![CDATA[
      (x / y) * y != z * u
    ]]></literal>
    <literal><![CDATA[
      x / u = z
    ]]></literal>
    <justification jstring="[para(137(a,1),252(a,1))].">
      <j1 rule="para" parents="137 252"/>
    </justification>
  </clause>

  <clause id="405">
    <literal><![CDATA[
      (x * (x \ y)) * z != u
    ]]></literal>
    <literal><![CDATA[
      y * z = u
    ]]></literal>
    <justification jstring="[para(76(a,1),253(a,1,1,1))].">
      <j1 rule="para" parents="76 253"/>
    </justification>
  </clause>

  <clause id="406">
    <literal><![CDATA[
      (x * T(y,x)) * z != u
    ]]></literal>
    <literal><![CDATA[
      (y * x) * z = u
    ]]></literal>
    <justification jstring="[para(162(a,1),253(a,1,1,1))].">
      <j1 rule="para" parents="162 253"/>
    </justification>
  </clause>

  <clause id="407">
    <literal><![CDATA[
      x * (x \ y) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ y = u
    ]]></literal>
    <justification jstring="[para(76(a,1),254(a,1,1))].">
      <j1 rule="para" parents="76 254"/>
    </justification>
  </clause>

  <clause id="408">
    <literal><![CDATA[
      x * (y * (y \ 1)) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ x = u
    ]]></literal>
    <justification jstring="[para(150(a,1),254(a,1,1))].">
      <j1 rule="para" parents="150 254"/>
    </justification>
  </clause>

  <clause id="409">
    <literal><![CDATA[
      (x * y) / y != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ x = u
    ]]></literal>
    <justification jstring="[para(137(a,2),254(a,1))].">
      <j1 rule="para" parents="137 254"/>
    </justification>
  </clause>

  <clause id="410">
    <literal><![CDATA[
      x * T(y,x) != z * u
    ]]></literal>
    <literal><![CDATA[
      (y * x) / u = z
    ]]></literal>
    <justification jstring="[para(22(a,2),255(a,1,2))].">
      <j1 rule="para" parents="22 255"/>
    </justification>
  </clause>

  <clause id="411">
    <literal><![CDATA[
      ((1 / x) * x) * y != z * u
    ]]></literal>
    <literal><![CDATA[
      y / u = z
    ]]></literal>
    <justification jstring="[para(145(a,1),255(a,1,2))].">
      <j1 rule="para" parents="145 255"/>
    </justification>
  </clause>

  <clause id="412">
    <literal><![CDATA[
      ((x / y) * y) / z != u
    ]]></literal>
    <literal><![CDATA[
      x / z = u
    ]]></literal>
    <justification jstring="[para(79(a,1),256(a,1,1,2))].">
      <j1 rule="para" parents="79 256"/>
    </justification>
  </clause>

  <clause id="413">
    <literal><![CDATA[
      x \ y != z * T(u,z)
    ]]></literal>
    <literal><![CDATA[
      x * (u * z) = y
    ]]></literal>
    <justification jstring="[para(22(a,2),258(a,2,2))].">
      <j1 rule="para" parents="22 258"/>
    </justification>
  </clause>

  <clause id="414">
    <literal><![CDATA[
      x * (y * 1) != z
    ]]></literal>
    <literal><![CDATA[
      x * y = z
    ]]></literal>
    <justification jstring="[para(68(a,1),259(a,1,2,2))].">
      <j1 rule="para" parents="68 259"/>
    </justification>
  </clause>

  <clause id="415">
    <literal><![CDATA[
      x * (y \ (y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(141(a,2),259(a,1,2))].">
      <j1 rule="para" parents="141 259"/>
    </justification>
  </clause>

  <clause id="416">
    <literal><![CDATA[
      x * ((y / z) \ y) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(166(a,2),259(a,1,2))].">
      <j1 rule="para" parents="166 259"/>
    </justification>
  </clause>

  <clause id="417">
    <literal><![CDATA[
      T(x \ (x / y),z) = L(T(y \ 1,z),y,x / y)
    ]]></literal>
    <justification jstring="[para(280(a,1),25(a,2,1)),flip(a)].">
      <j1 rule="para" parents="280 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="418">
    <literal><![CDATA[
      ((x \ y) / y) * (R(1 / x,x,x \ y) \ z) = z
    ]]></literal>
    <justification jstring="[hyper(115,a,285,a(flip),b,76,a)].">
      <j1 rule="hyper" parents="115 285 76"/>
    </justification>
  </clause>

  <clause id="419">
    <literal><![CDATA[
      T((x \ y) / y,z) = R(T(1 / x,z),x,x \ y)
    ]]></literal>
    <justification jstring="[para(285(a,1),27(a,2,1)),flip(a)].">
      <j1 rule="para" parents="285 27"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="420">
    <literal><![CDATA[
      R(T(1 / (x / y),z),x / y,y) = T(y / x,z)
    ]]></literal>
    <justification jstring="[para(286(a,1),27(a,2,1))].">
      <j1 rule="para" parents="286 27"/>
    </justification>
  </clause>

  <clause id="421">
    <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),301(a,1))].">
      <j1 rule="para" parents="27 301"/>
    </justification>
  </clause>

  <clause id="422">
    <literal><![CDATA[
      ((x / y) * y) * z != u * w
    ]]></literal>
    <literal><![CDATA[
      (x * z) / w = u
    ]]></literal>
    <justification jstring="[para(137(a,1),404(a,1,1))].">
      <j1 rule="para" parents="137 404"/>
    </justification>
  </clause>

  <clause id="423">
    <literal><![CDATA[
      x * (y * (y \ (x \ z))) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ z = w
    ]]></literal>
    <justification jstring="[para(10(a,2),407(a,1,2))].">
      <j1 rule="para" parents="10 407"/>
    </justification>
  </clause>

  <clause id="424">
    <literal><![CDATA[
      x * (y * (y \ z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * z) = w
    ]]></literal>
    <justification jstring="[para(141(a,1),407(a,1,2))].">
      <j1 rule="para" parents="141 407"/>
    </justification>
  </clause>

  <clause id="425">
    <literal><![CDATA[
      R((x / y) / z,z,y) != u
    ]]></literal>
    <literal><![CDATA[
      x / (z * y) = u
    ]]></literal>
    <justification jstring="[para(101(a,2),412(a,1))].">
      <j1 rule="para" parents="101 412"/>
    </justification>
  </clause>

  <clause id="426">
    <literal><![CDATA[
      x * (y * T(z,x * y)) = L(z,y,x) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,93,a(flip),b,198,a)].">
      <j1 rule="hyper" parents="65 93 198"/>
    </justification>
  </clause>

  <clause id="427">
    <literal><![CDATA[
      x * L(x \ (y * x),z,u) = L(y,z,u) * x
    ]]></literal>
    <justification jstring="[para(22(a,1),198(a,1,2,1))].">
      <j1 rule="para" parents="22 198"/>
    </justification>
  </clause>

  <clause id="428">
    <literal><![CDATA[
      L(x / y,z,u) * y = y * L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(106(a,1),198(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="106 198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="429">
    <literal><![CDATA[
      L((x * y) / x,z,u) * x = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(190(a,1),198(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="190 198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="430">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ y,z,u) = L(x,z,u) * (x \ y)
    ]]></literal>
    <justification jstring="[para(105(a,1),198(a,1,2,1))].">
      <j1 rule="para" parents="105 198"/>
    </justification>
  </clause>

  <clause id="431">
    <literal><![CDATA[
      (x * y) * R(T(z,x * y),x,y) = (z * x) * y
    ]]></literal>
    <justification jstring="[hyper(250,a,100,a(flip),b,199,a),flip(a)].">
      <j1 rule="hyper" parents="250 100 199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="432">
    <literal><![CDATA[
      (x * y) \ ((z * x) * y) = R(T(z,x * y),x,y)
    ]]></literal>
    <justification jstring="[hyper(112,a,100,a(flip),b,199,a)].">
      <j1 rule="hyper" parents="112 100 199"/>
    </justification>
  </clause>

  <clause id="433">
    <literal><![CDATA[
      R(x / y,z,u) * y = y * R(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(106(a,1),199(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="106 199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="434">
    <literal><![CDATA[
      R((x * y) / x,z,u) * x = x * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(190(a,1),199(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="190 199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="435">
    <literal><![CDATA[
      (x \ y) * R((x \ y) \ y,z,u) = R(x,z,u) * (x \ y)
    ]]></literal>
    <justification jstring="[para(105(a,1),199(a,1,2,1))].">
      <j1 rule="para" parents="105 199"/>
    </justification>
  </clause>

  <clause id="436">
    <literal><![CDATA[
      T(x / y,(z / y) \ z) = y \ x
    ]]></literal>
    <justification jstring="[hyper(200,a,261,a,b,262,a)].">
      <j1 rule="hyper" parents="200 261 262"/>
    </justification>
  </clause>

  <clause id="437">
    <literal><![CDATA[
      L(T(x,y),y,x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(200,a,188,a(flip),b,93,a),flip(a)].">
      <j1 rule="hyper" parents="200 188 93"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="438">
    <literal><![CDATA[
      T(R(x,y,T(x,y)),x * y) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(200,a,188,a(flip),b,100,a(flip))].">
      <j1 rule="hyper" parents="200 188 100"/>
    </justification>
  </clause>

  <clause id="439">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * (u * a(x,y,z)) = T(u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(200,a,128,a(flip),b,215,a),flip(a)].">
      <j1 rule="hyper" parents="200 128 215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="440">
    <literal><![CDATA[
      T(L(x,y,x),y) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,25,a(flip),b,437,a)].">
      <j1 rule="hyper" parents="65 25 437"/>
    </justification>
  </clause>

  <clause id="441">
    <literal><![CDATA[
      L(R(T(x,y),z,u),y,x) = R(T(x,x * y),z,u)
    ]]></literal>
    <justification jstring="[para(437(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="437 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="442">
    <literal><![CDATA[
      x * T(y,y * x) = L(y,x,y) * x
    ]]></literal>
    <justification jstring="[para(437(a,1),198(a,1,2))].">
      <j1 rule="para" parents="437 198"/>
    </justification>
  </clause>

  <clause id="443">
    <literal><![CDATA[
      (x * y) * R(L(T(x,y),y,x),z,u) = R(x,z,u) * (x * y)
    ]]></literal>
    <justification jstring="[para(437(a,2),199(a,1,2,1))].">
      <j1 rule="para" parents="437 199"/>
    </justification>
  </clause>

  <clause id="444">
    <literal><![CDATA[
      T(L(x,x \ 1,x),x \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(250,a,175,a(flip),b,440,a),flip(a)].">
      <j1 rule="hyper" parents="250 175 440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="445">
    <literal><![CDATA[
      (x * T(y,y * x)) / x = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(227,a,440,a)].">
      <j1 rule="hyper" parents="227 440"/>
    </justification>
  </clause>

  <clause id="446">
    <literal><![CDATA[
      T((x * y) / x,y * x) = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(42,a,226,a,b,440,a)].">
      <j1 rule="hyper" parents="42 226 440"/>
    </justification>
  </clause>

  <clause id="447">
    <literal><![CDATA[
      T(((x * y) * x) / (x * y),y) = R(x,y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(42,a,226,a,b,438,a)].">
      <j1 rule="hyper" parents="42 226 438"/>
    </justification>
  </clause>

  <clause id="448">
    <literal><![CDATA[
      T(R(x,y,T(x,y)),z) * (x * y) = (x * y) * T(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(438(a,1),197(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="438 197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="449">
    <literal><![CDATA[
      L(x,x \ y,x) * (x \ y) = (x \ y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),442(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="450">
    <literal><![CDATA[
      T(((x \ y) * x) / (x \ y),y) = L(x,x \ y,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),446(a,1,2))].">
      <j1 rule="para" parents="10 446"/>
    </justification>
  </clause>

  <clause id="451">
    <literal><![CDATA[
      (x * L(x \ y,z,u)) / x = L(y / x,z,u)
    ]]></literal>
    <justification jstring="[hyper(227,a,207,a)].">
      <j1 rule="hyper" parents="227 207"/>
    </justification>
  </clause>

  <clause id="452">
    <literal><![CDATA[
      T(L(R(x / y,y,z),u,w),y * z) = L((y * z) \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[para(101(a,2),207(a,1,1,1))].">
      <j1 rule="para" parents="101 207"/>
    </justification>
  </clause>

  <clause id="453">
    <literal><![CDATA[
      (x * R(x \ y,z,u)) / x = R(y / x,z,u)
    ]]></literal>
    <justification jstring="[hyper(227,a,208,a)].">
      <j1 rule="hyper" parents="227 208"/>
    </justification>
  </clause>

  <clause id="454">
    <literal><![CDATA[
      T(x / (y * x),y) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(183(a,1),208(a,1,1))].">
      <j1 rule="para" parents="183 208"/>
    </justification>
  </clause>

  <clause id="455">
    <literal><![CDATA[
      T((x * y) / (z * y),z) = R(z \ x,z,y)
    ]]></literal>
    <justification jstring="[para(101(a,1),208(a,1,1))].">
      <j1 rule="para" parents="101 208"/>
    </justification>
  </clause>

  <clause id="456">
    <literal><![CDATA[
      T((x \ y) / y,x) = R(x \ 1,x,x \ y)
    ]]></literal>
    <justification jstring="[para(285(a,1),208(a,1,1))].">
      <j1 rule="para" parents="285 208"/>
    </justification>
  </clause>

  <clause id="457">
    <literal><![CDATA[
      R((1 / x) \ y,1 / x,x) = T(y * x,1 / x)
    ]]></literal>
    <justification jstring="[para(376(a,1),208(a,1,1)),flip(a)].">
      <j1 rule="para" parents="376 208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="458">
    <literal><![CDATA[
      (x / (y * x)) * y = y * R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,454,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 454 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="459">
    <literal><![CDATA[
      x \ ((y \ z) \ z) != x \ u
    ]]></literal>
    <literal><![CDATA[
      T(y,y \ z) = u
    ]]></literal>
    <justification jstring="[para(248(a,1),49(a,1))].">
      <j1 rule="para" parents="248 49"/>
    </justification>
  </clause>

  <clause id="460">
    <literal><![CDATA[
      (T(x,x \ y) * z) \ (z * ((x \ y) \ y)) = K(z,T(x,x \ y))
    ]]></literal>
    <justification jstring="[hyper(112,a,249,a(flip),b,87,a)].">
      <j1 rule="hyper" parents="112 249 87"/>
    </justification>
  </clause>

  <clause id="461">
    <literal><![CDATA[
      T(x,y) / (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      R(1 / y,y,T(x,y)) = z
    ]]></literal>
    <justification jstring="[para(104(a,1),300(a,1,2))].">
      <j1 rule="para" parents="104 300"/>
    </justification>
  </clause>

  <clause id="462">
    <literal><![CDATA[
      T(x / y,z) * y != u
    ]]></literal>
    <literal><![CDATA[
      y * T(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(325(a,1),211(a,1,1)),flip(b)].">
      <j1 rule="para" parents="325 211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="463">
    <literal><![CDATA[
      T(T(x / y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      T(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(325(a,1),237(a,1,1))].">
      <j1 rule="para" parents="325 237"/>
    </justification>
  </clause>

  <clause id="464">
    <literal><![CDATA[
      x * ((y * T(z,x)) / y) = ((y * z) / y) * x
    ]]></literal>
    <justification jstring="[hyper(116,a,327,a,b,22,a(flip))].">
      <j1 rule="hyper" parents="116 327 22"/>
    </justification>
  </clause>

  <clause id="465">
    <literal><![CDATA[
      T((x * (y / z)) / x,z) = (x * (z \ y)) / x
    ]]></literal>
    <justification jstring="[para(106(a,1),327(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="106 327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="466">
    <literal><![CDATA[
      T((x * y) / x,z) * x != u
    ]]></literal>
    <literal><![CDATA[
      x * T(y,z) = u
    ]]></literal>
    <justification jstring="[para(327(a,1),211(a,1,1)),flip(b)].">
      <j1 rule="para" parents="327 211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="467">
    <literal><![CDATA[
      (x * y) / a(z,z \ x,y) = z * ((z \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(113,a,130,a(flip),b,84,a)].">
      <j1 rule="hyper" parents="113 130 84"/>
    </justification>
  </clause>

  <clause id="469">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(84(a,1),235(a,1,2))].">
      <j1 rule="para" parents="84 235"/>
    </justification>
  </clause>

  <clause id="470">
    <literal><![CDATA[
      x * T(L(y,z \ x,z),u) = z * ((z \ x) * T(y,u))
    ]]></literal>
    <justification jstring="[hyper(116,a,25,a(flip),b,94,a)].">
      <j1 rule="hyper" parents="116 25 94"/>
    </justification>
  </clause>

  <clause id="472">
    <literal><![CDATA[
      (a(x,y,z) * u) / w = a(x,y,z) * (u / w)
    ]]></literal>
    <justification jstring="[hyper(170,a,128,a(flip),b,96,a(flip))].">
      <j1 rule="hyper" parents="170 128 96"/>
    </justification>
  </clause>

  <clause id="473">
    <literal><![CDATA[
      R((x * (y / z)) \ (x * y),u,w) = L(R(z,u,w),y / z,x)
    ]]></literal>
    <justification jstring="[para(96(a,1),29(a,1,1))].">
      <j1 rule="para" parents="96 29"/>
    </justification>
  </clause>

  <clause id="474">
    <literal><![CDATA[
      L(R(x,y,y \ z),u,w) * z = (L(x,u,w) * y) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(115,a,29,a(flip),b,99,a)].">
      <j1 rule="hyper" parents="115 29 99"/>
    </justification>
  </clause>

  <clause id="475">
    <literal><![CDATA[
      x \ R(x,y,y \ 1) = a(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(219(a,1),180(a,1,2))].">
      <j1 rule="para" parents="219 180"/>
    </justification>
  </clause>

  <clause id="476">
    <literal><![CDATA[
      x \ R(x,1 / y,y) = a(x,1 / y,y)
    ]]></literal>
    <justification jstring="[para(220(a,1),185(a,1,2))].">
      <j1 rule="para" parents="220 185"/>
    </justification>
  </clause>

  <clause id="477">
    <literal><![CDATA[
      L(T(x,y),y,z / y) = z \ ((z / y) * (x * y))
    ]]></literal>
    <justification jstring="[para(12(a,1),195(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12 195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="478">
    <literal><![CDATA[
      (x * y) * T((x * y) \ x,z) = x * (y * T(y \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(116,a,281,a,b,18,a(flip))].">
      <j1 rule="hyper" parents="116 281 18"/>
    </justification>
  </clause>

  <clause id="479">
    <literal><![CDATA[
      T(x / (y * x),z) * (y * x) = (T(1 / y,z) * y) * x
    ]]></literal>
    <justification jstring="[hyper(115,a,287,a,b,20,a(flip))].">
      <j1 rule="hyper" parents="115 287 20"/>
    </justification>
  </clause>

  <clause id="480">
    <literal><![CDATA[
      x * ((T(y,x) \ z) \ z) != u * x
    ]]></literal>
    <literal><![CDATA[
      T(y,T(y,x) \ z) = u
    ]]></literal>
    <justification jstring="[para(105(a,1),289(a,1,2))].">
      <j1 rule="para" parents="105 289"/>
    </justification>
  </clause>

  <clause id="481">
    <literal><![CDATA[
      (x / y) * T(y,z) != u * (x / y)
    ]]></literal>
    <literal><![CDATA[
      T(x / (x / y),z) = u
    ]]></literal>
    <justification jstring="[para(205(a,1),289(a,1,2,1))].">
      <j1 rule="para" parents="205 289"/>
    </justification>
  </clause>

  <clause id="482">
    <literal><![CDATA[
      x * T(x \ (y * x),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(22(a,1),290(a,1,2,1))].">
      <j1 rule="para" parents="22 290"/>
    </justification>
  </clause>

  <clause id="484">
    <literal><![CDATA[
      L(T(x \ 1,x),x,1 / x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(250,a,106,a(flip),b,295,a),flip(a)].">
      <j1 rule="hyper" parents="250 106 295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="485">
    <literal><![CDATA[
      x * ((x \ y) * T(z,y)) = L(z,x \ y,x) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,198,a(flip),b,314,a),flip(a)].">
      <j1 rule="hyper" parents="65 198 314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="486">
    <literal><![CDATA[
      x \ (L(y,x \ z,x) * z) = (x \ z) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(112,a,198,a(flip),b,314,a(flip))].">
      <j1 rule="hyper" parents="112 198 314"/>
    </justification>
  </clause>

  <clause id="488">
    <literal><![CDATA[
      x \ (y * ((y \ x) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,y \ x,y) = u
    ]]></literal>
    <justification jstring="[para(314(a,1),235(a,1,2))].">
      <j1 rule="para" parents="314 235"/>
    </justification>
  </clause>

  <clause id="489">
    <literal><![CDATA[
      x \ (y * L(z,x \ y,x)) != (x \ y) * u
    ]]></literal>
    <literal><![CDATA[
      u = z
    ]]></literal>
    <justification jstring="[para(314(a,2),117(a,1,2))].">
      <j1 rule="para" parents="314 117"/>
    </justification>
  </clause>

  <clause id="490">
    <literal><![CDATA[
      K(x,y) = L(x \ T(x,y),x,y)
    ]]></literal>
    <justification jstring="[hyper(250,a,16,a,b,319,a)].">
      <j1 rule="hyper" parents="250 16 319"/>
    </justification>
  </clause>

  <clause id="491">
    <literal><![CDATA[
      L(T(x \ T(y,z),u),x,z) = T((z * x) \ (y * z),u)
    ]]></literal>
    <justification jstring="[para(319(a,1),25(a,2,1))].">
      <j1 rule="para" parents="319 25"/>
    </justification>
  </clause>

  <clause id="492">
    <literal><![CDATA[
      (x * y) \ (x * (z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      L(T(z,y),y,x) = u
    ]]></literal>
    <justification jstring="[para(331(a,1),223(a,1,1))].">
      <j1 rule="para" parents="331 223"/>
    </justification>
  </clause>

  <clause id="493">
    <literal><![CDATA[
      L(x \ y,x,y / x) = T(y / x,y)
    ]]></literal>
    <justification jstring="[hyper(200,a,131,a(flip),b,334,a),flip(a)].">
      <j1 rule="hyper" parents="200 131 334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="494">
    <literal><![CDATA[
      (x / y) \ (L(z,y,x / y) * x) = y * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(112,a,198,a(flip),b,334,a(flip))].">
      <j1 rule="hyper" parents="112 198 334"/>
    </justification>
  </clause>

  <clause id="495">
    <literal><![CDATA[
      L(T((x \ y) \ z,u),x \ y,x) = T(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[para(349(a,1),25(a,2,1))].">
      <j1 rule="para" parents="349 25"/>
    </justification>
  </clause>

  <clause id="496">
    <literal><![CDATA[
      L(R((x \ y) \ z,u,w),x \ y,x) = R(y \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[para(349(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="349 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="497">
    <literal><![CDATA[
      L(L((x \ y) \ z,u,w),x \ y,x) = L(y \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[para(349(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="349 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="498">
    <literal><![CDATA[
      x * R(T(y,x),z,z \ x) = (y * z) * (z \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,199,a,b,364,a)].">
      <j1 rule="hyper" parents="65 199 364"/>
    </justification>
  </clause>

  <clause id="499">
    <literal><![CDATA[
      R(T(x / (y / z),u),y / z,z) = T((x * z) / y,u)
    ]]></literal>
    <justification jstring="[para(379(a,1),27(a,2,1))].">
      <j1 rule="para" parents="379 27"/>
    </justification>
  </clause>

  <clause id="500">
    <literal><![CDATA[
      (1 / x) * ((x \ 1) * x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,484,a(flip),b,392,a),flip(a)].">
      <j1 rule="hyper" parents="65 484 392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="501">
    <literal><![CDATA[
      (1 / x) \ T(L(y,x,1 / x),x) = y * x
    ]]></literal>
    <justification jstring="[hyper(112,a,25,a(flip),b,392,a(flip))].">
      <j1 rule="hyper" parents="112 25 392"/>
    </justification>
  </clause>

  <clause id="502">
    <literal><![CDATA[
      (1 / (1 / x)) * (x * (1 / x)) = (1 / x) \ 1
    ]]></literal>
    <justification jstring="[para(79(a,1),500(a,1,2,1))].">
      <j1 rule="para" parents="79 500"/>
    </justification>
  </clause>

  <clause id="503">
    <literal><![CDATA[
      (1 / x) * K(x \ 1,x) = x \ 1
    ]]></literal>
    <justification jstring="[para(216(a,2),500(a,1,2))].">
      <j1 rule="para" parents="216 500"/>
    </justification>
  </clause>

  <clause id="504">
    <literal><![CDATA[
      K((x \ 1) \ 1,x \ 1) = x \ ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(112,a,503,a(flip),b,158,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="112 503 158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="505">
    <literal><![CDATA[
      R(x,y,z) = T(((y * x) * z) / (y * z),y)
    ]]></literal>
    <justification jstring="[para(9(a,1),455(a,2,1)),flip(a)].">
      <j1 rule="para" parents="9 455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="506">
    <literal><![CDATA[
      T((x \ y) / y,x) * y = ((x \ 1) * x) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(115,a,456,a,b,99,a)].">
      <j1 rule="hyper" parents="115 456 99"/>
    </justification>
  </clause>

  <clause id="507">
    <literal><![CDATA[
      (x / y) * R((x / y) \ 1,x / y,y) = (y / x) * (x / y)
    ]]></literal>
    <justification jstring="[para(12(a,1),458(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12 458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="508">
    <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(455(a,1),463(a,1,1))].">
      <j1 rule="para" parents="455 463"/>
    </justification>
  </clause>

  <clause id="509">
    <literal><![CDATA[
      (1 / x) \ T((1 / x) * y,x) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(347(a,1),501(a,1,2,1))].">
      <j1 rule="para" parents="347 501"/>
    </justification>
  </clause>

  <clause id="511">
    <literal><![CDATA[
      T((x * y) \ ((x * z) * y),x) = T(R(z,x,y),x * y)
    ]]></literal>
    <justification jstring="[para(505(a,2),206(a,1,1)),flip(a)].">
      <j1 rule="para" parents="505 206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="512">
    <literal><![CDATA[
      T(R(x,y,x),y * x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(505(a,2),226(a,1,1))].">
      <j1 rule="para" parents="505 226"/>
    </justification>
  </clause>

  <clause id="513">
    <literal><![CDATA[
      R(T(x,y * x),y,x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,27,a,b,512,a)].">
      <j1 rule="hyper" parents="65 27 512"/>
    </justification>
  </clause>

  <clause id="514">
    <literal><![CDATA[
      R(T(x,(x \ y) * x),x \ y,x) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(250,a,105,a(flip),b,513,a),flip(a)].">
      <j1 rule="hyper" parents="250 105 513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="515">
    <literal><![CDATA[
      R(T(x,y),y / x,x) = T(x,y / x)
    ]]></literal>
    <justification jstring="[para(12(a,1),513(a,1,1,2))].">
      <j1 rule="para" parents="12 513"/>
    </justification>
  </clause>

  <clause id="516">
    <literal><![CDATA[
      R(x,y,z) != T(z,y)
    ]]></literal>
    <literal><![CDATA[
      T(z,y * z) = x
    ]]></literal>
    <justification jstring="[para(513(a,1),53(a,1)),flip(a)].">
      <j1 rule="para" parents="513 53"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="517">
    <literal><![CDATA[
      R(x,y / z,z) != T(z,y / z)
    ]]></literal>
    <literal><![CDATA[
      T(z,y) = x
    ]]></literal>
    <justification jstring="[para(515(a,1),53(a,1)),flip(a)].">
      <j1 rule="para" parents="515 53"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="518">
    <literal><![CDATA[
      R(x,1 / x,x) = T(x,1 / x)
    ]]></literal>
    <justification jstring="[para(172(a,1),515(a,1,1))].">
      <j1 rule="para" parents="172 515"/>
    </justification>
  </clause>

  <clause id="519">
    <literal><![CDATA[
      (x * y) * T(L(z,y,x),u) != w
    ]]></literal>
    <literal><![CDATA[
      x * (y * T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(25(a,1),234(a,1,2))].">
      <j1 rule="para" parents="25 234"/>
    </justification>
  </clause>

  <clause id="520">
    <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),234(a,1,2))].">
      <j1 rule="para" parents="29 234"/>
    </justification>
  </clause>

  <clause id="523">
    <literal><![CDATA[
      R(a(x,y,z),u,w) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(37,a,100,a,b,315,a(flip))].">
      <j1 rule="hyper" parents="37 100 315"/>
    </justification>
  </clause>

  <clause id="524">
    <literal><![CDATA[
      (a(x,y,z) * (u * (w * v5))) \ (((a(x,y,z) * u) * w) * v5) = a(a(x,y,z) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(315(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="315 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="525">
    <literal><![CDATA[
      (a(x,y,z) * (u * w)) \ ((a(x,y,z) * u) * (w * v5)) = L(v5,w,a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(315(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="315 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="526">
    <literal><![CDATA[
      R(a(x,y,z),u,w) = (a(x,y,z) * v5) / v5
    ]]></literal>
    <justification jstring="[hyper(250,a,11,a,b,523,a),flip(a)].">
      <j1 rule="hyper" parents="250 11 523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="527">
    <literal><![CDATA[
      R(a(x,y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = v5
    ]]></literal>
    <justification jstring="[para(526(a,2),212(a,1)),flip(b)].">
      <j1 rule="para" parents="526 212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="529">
    <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(93(a,1),342(a,1,2,2))].">
      <j1 rule="para" parents="93 342"/>
    </justification>
  </clause>

  <clause id="530">
    <literal><![CDATA[
      (a(x,y,z) * u) \ ((a(x,y,z) * w) * v5) = u \ (w * v5)
    ]]></literal>
    <justification jstring="[para(315(a,2),350(a,1,2))].">
      <j1 rule="para" parents="315 350"/>
    </justification>
  </clause>

  <clause id="531">
    <literal><![CDATA[
      (x * (y * z)) * K(z,y) != u * (z * y)
    ]]></literal>
    <literal><![CDATA[
      R(x,y * z,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(87(a,1),370(a,2,2))].">
      <j1 rule="para" parents="87 370"/>
    </justification>
  </clause>

  <clause id="532">
    <literal><![CDATA[
      x / (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      R((x / z) / y,y,z) = u
    ]]></literal>
    <justification jstring="[para(83(a,1),371(a,1,1))].">
      <j1 rule="para" parents="83 371"/>
    </justification>
  </clause>

  <clause id="533">
    <literal><![CDATA[
      L(1 / (x \ y),x \ y,x) * (x \ y) = (x \ y) * (y \ x)
    ]]></literal>
    <justification jstring="[para(275(a,1),428(a,2,2))].">
      <j1 rule="para" parents="275 428"/>
    </justification>
  </clause>

  <clause id="534">
    <literal><![CDATA[
      L((x * y) / x,z,u) = (x * L(y,z,u)) / x
    ]]></literal>
    <justification jstring="[hyper(123,a,429,a),flip(a)].">
      <j1 rule="hyper" parents="123 429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="535">
    <literal><![CDATA[
      L(((x * y) * z) / (x * y),y,x) = (x * (y * z)) / (x * y)
    ]]></literal>
    <justification jstring="[hyper(113,a,93,a(flip),b,429,a),flip(a)].">
      <j1 rule="hyper" parents="113 93 429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="536">
    <literal><![CDATA[
      ((((x * y) * z) / (x * y)) * x) * y = (x * y) * R(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(230,a,434,a)].">
      <j1 rule="hyper" parents="230 434"/>
    </justification>
  </clause>

  <clause id="537">
    <literal><![CDATA[
      R((x * y) / x,z,u) = (x * R(y,z,u)) / x
    ]]></literal>
    <justification jstring="[hyper(123,a,434,a),flip(a)].">
      <j1 rule="hyper" parents="123 434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="538">
    <literal><![CDATA[
      T(L(x / y,z,u),y) != w
    ]]></literal>
    <literal><![CDATA[
      L(y \ x,z,u) = w
    ]]></literal>
    <justification jstring="[para(451(a,1),237(a,1,1))].">
      <j1 rule="para" parents="451 237"/>
    </justification>
  </clause>

  <clause id="539">
    <literal><![CDATA[
      L((x \ y) / z,z,x) = (z * ((x * z) \ y)) / z
    ]]></literal>
    <justification jstring="[para(239(a,1),451(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="239 451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="540">
    <literal><![CDATA[
      L(T(x,y) / x,x,y) = (x * K(x,y)) / x
    ]]></literal>
    <justification jstring="[para(490(a,2),451(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="490 451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="541">
    <literal><![CDATA[
      ((x * (y / z)) / x) * z = z * ((x * (z \ y)) / x)
    ]]></literal>
    <justification jstring="[para(106(a,1),464(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="106 464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="542">
    <literal><![CDATA[
      (x \ y) * ((z * ((x \ y) \ y)) / z) = ((z * x) / z) * (x \ y)
    ]]></literal>
    <justification jstring="[para(105(a,1),464(a,1,2,1,2))].">
      <j1 rule="para" parents="105 464"/>
    </justification>
  </clause>

  <clause id="543">
    <literal><![CDATA[
      (1 / (1 / x)) * (x * (1 / x)) = x
    ]]></literal>
    <justification jstring="[hyper(250,a,79,a(flip),b,502,a),flip(a)].">
      <j1 rule="hyper" parents="250 79 502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="545">
    <literal><![CDATA[
      (1 / (1 / x)) * K(x,1 / x) = x
    ]]></literal>
    <justification jstring="[para(218(a,2),543(a,1,2))].">
      <j1 rule="para" parents="218 543"/>
    </justification>
  </clause>

  <clause id="546">
    <literal><![CDATA[
      (1 / x) * ((x \ y) * x) = T((1 / x) * y,x)
    ]]></literal>
    <justification jstring="[hyper(125,a,509,a)].">
      <j1 rule="hyper" parents="125 509"/>
    </justification>
  </clause>

  <clause id="547">
    <literal><![CDATA[
      L((x * y) / x,z,u) * x != w
    ]]></literal>
    <literal><![CDATA[
      x * L(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(534(a,2),211(a,1,1)),flip(b)].">
      <j1 rule="para" parents="534 211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="548">
    <literal><![CDATA[
      L((x * (y \ z)) / x,y,u) = (x * ((u * y) \ (u * z))) / x
    ]]></literal>
    <justification jstring="[para(95(a,1),534(a,2,1,2))].">
      <j1 rule="para" parents="95 534"/>
    </justification>
  </clause>

  <clause id="549">
    <literal><![CDATA[
      L((x * (y \ 1)) / x,y,z / y) = (x * (z \ (z / y))) / x
    ]]></literal>
    <justification jstring="[para(280(a,1),534(a,2,1,2))].">
      <j1 rule="para" parents="280 534"/>
    </justification>
  </clause>

  <clause id="550">
    <literal><![CDATA[
      L((x * ((y \ z) \ u)) / x,y \ z,y) = (x * (z \ (y * u))) / x
    ]]></literal>
    <justification jstring="[para(349(a,1),534(a,2,1,2))].">
      <j1 rule="para" parents="349 534"/>
    </justification>
  </clause>

  <clause id="551">
    <literal><![CDATA[
      ((x * R(y,z,u)) / x) * (z * u) = (((x * y) / x) * z) * u
    ]]></literal>
    <justification jstring="[hyper(115,a,537,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="115 537 20"/>
    </justification>
  </clause>

  <clause id="552">
    <literal><![CDATA[
      R((x * ((y / z) / u)) / x,u,z) = (x * (y / (u * z))) / x
    ]]></literal>
    <justification jstring="[para(241(a,1),537(a,2,1,2))].">
      <j1 rule="para" parents="241 537"/>
    </justification>
  </clause>

  <clause id="553">
    <literal><![CDATA[
      R((x * (y / (1 / z))) / x,1 / z,z) = (x * (y * z)) / x
    ]]></literal>
    <justification jstring="[para(376(a,1),537(a,2,1,2))].">
      <j1 rule="para" parents="376 537"/>
    </justification>
  </clause>

  <clause id="554">
    <literal><![CDATA[
      ((x * R(y,z,u)) / x) * (z * u) != w
    ]]></literal>
    <literal><![CDATA[
      (((x * y) / x) * z) * u = w
    ]]></literal>
    <justification jstring="[para(537(a,1),230(a,1,1))].">
      <j1 rule="para" parents="537 230"/>
    </justification>
  </clause>

  <clause id="555">
    <literal><![CDATA[
      (x * y) * L((y * T(x,y)) \ y,z,u) = y * (T(x,y) * L(T(x,y) \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(116,a,282,a(flip),b,194,a)].">
      <j1 rule="hyper" parents="116 282 194"/>
    </justification>
  </clause>

  <clause id="556">
    <literal><![CDATA[
      (x * y) * L((x * y) \ x,z,u) = x * (y * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(116,a,282,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="116 282 18"/>
    </justification>
  </clause>

  <clause id="558">
    <literal><![CDATA[
      R(x / (y * x),z,u) != R(w,y,x)
    ]]></literal>
    <literal><![CDATA[
      R(1 / y,z,u) = w
    ]]></literal>
    <justification jstring="[para(288(a,1),53(a,1))].">
      <j1 rule="para" parents="288 53"/>
    </justification>
  </clause>

  <clause id="559">
    <literal><![CDATA[
      T(R(x,y,T(z,y)),u) * (z * y) = (T(x,u) * y) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,188,a(flip),b,311,a)].">
      <j1 rule="hyper" parents="65 188 311"/>
    </justification>
  </clause>

  <clause id="560">
    <literal><![CDATA[
      (T((x / y) / z,u) * z) * y = T(x / (z * y),u) * (z * y)
    ]]></literal>
    <justification jstring="[para(241(a,1),311(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="241 311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="561">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (x * z),u) = x * (y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(95(a,1),316(a,1,2,1))].">
      <j1 rule="para" parents="95 316"/>
    </justification>
  </clause>

  <clause id="562">
    <literal><![CDATA[
      (x * y) * T((x * y) \ z,u) = x * (y * T(y \ (x \ z),u))
    ]]></literal>
    <justification jstring="[para(239(a,1),316(a,1,2,1))].">
      <j1 rule="para" parents="239 316"/>
    </justification>
  </clause>

  <clause id="563">
    <literal><![CDATA[
      (x * y) * T(T(x,x * y),z) = x * (y * T(T(x,y),z))
    ]]></literal>
    <justification jstring="[para(437(a,1),316(a,1,2,1))].">
      <j1 rule="para" parents="437 316"/>
    </justification>
  </clause>

  <clause id="564">
    <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(354(a,2),234(a,1,2))].">
      <j1 rule="para" parents="354 234"/>
    </justification>
  </clause>

  <clause id="565">
    <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(355(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="355 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="567">
    <literal><![CDATA[
      R(T((x * y) / x,z),x,y) * (x * y) = (x * y) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(115,a,380,a(flip),b,327,a)].">
      <j1 rule="hyper" parents="115 380 327"/>
    </justification>
  </clause>

  <clause id="568">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ y,z) = x \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(348(a,1),391(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="348 391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="569">
    <literal><![CDATA[
      T(x / (1 / y),z) * (1 / y) = T(x * y,z) / y
    ]]></literal>
    <justification jstring="[para(376(a,1),399(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="376 399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="570">
    <literal><![CDATA[
      T((x \ y) / y,z) * y = (T(1 / x,z) * x) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(115,a,419,a,b,99,a)].">
      <j1 rule="hyper" parents="115 419 99"/>
    </justification>
  </clause>

  <clause id="571">
    <literal><![CDATA[
      x * (y \ (y * z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * z) = w
    ]]></literal>
    <justification jstring="[para(141(a,2),424(a,1,2))].">
      <j1 rule="para" parents="141 424"/>
    </justification>
  </clause>

  <clause id="572">
    <literal><![CDATA[
      L(T(R(x,y,z),u),u,x) = R(T(x,x * u),y,z)
    ]]></literal>
    <justification jstring="[para(27(a,1),441(a,1,1))].">
      <j1 rule="para" parents="27 441"/>
    </justification>
  </clause>

  <clause id="573">
    <literal><![CDATA[
      T(x * y,1 / y) / y = ((1 / y) \ x) * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(113,a,457,a(flip),b,220,a)].">
      <j1 rule="hyper" parents="113 457 220"/>
    </justification>
  </clause>

  <clause id="574">
    <literal><![CDATA[
      T(x / (x / y),z) * (x / y) != u
    ]]></literal>
    <literal><![CDATA[
      (x / y) * T(y,z) = u
    ]]></literal>
    <justification jstring="[para(12(a,1),466(a,1,1,1,1))].">
      <j1 rule="para" parents="12 466"/>
    </justification>
  </clause>

  <clause id="575">
    <literal><![CDATA[
      (x * y) / a(z,z \ y,T(x,y)) = z * ((z \ y) * T(x,y))
    ]]></literal>
    <justification jstring="[para(104(a,1),467(a,1,1))].">
      <j1 rule="para" parents="104 467"/>
    </justification>
  </clause>

  <clause id="576">
    <literal><![CDATA[
      (x / y) * ((y \ 1) * y) = x * T(x \ (x / y),y)
    ]]></literal>
    <justification jstring="[hyper(116,a,417,a,b,477,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 417 477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="577">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ 1,y) = x \ ((y \ x) * y)
    ]]></literal>
    <justification jstring="[para(275(a,1),486(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="275 486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="578">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ z,y) = x \ ((y \ (x * z)) * y)
    ]]></literal>
    <justification jstring="[para(349(a,1),486(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="349 486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="579">
    <literal><![CDATA[
      (x / y) \ ((x \ (x / y)) * x) = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[para(280(a,1),494(a,1,2,1))].">
      <j1 rule="para" parents="280 494"/>
    </justification>
  </clause>

  <clause id="580">
    <literal><![CDATA[
      R(T(x / y,z),y,y \ z) = z \ (x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(112,a,129,a(flip),b,498,a),flip(a)].">
      <j1 rule="hyper" parents="112 129 498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="581">
    <literal><![CDATA[
      x * R(T(y,y * x),z,u) = L(R(y,z,u),x,y) * x
    ]]></literal>
    <justification jstring="[para(572(a,1),198(a,1,2))].">
      <j1 rule="para" parents="572 198"/>
    </justification>
  </clause>

  <clause id="582">
    <literal><![CDATA[
      (x \ (y * (z \ x))) * x = (T(y / z,x) * z) * (z \ x)
    ]]></literal>
    <justification jstring="[hyper(115,a,580,a(flip),b,99,a)].">
      <j1 rule="hyper" parents="115 580 99"/>
    </justification>
  </clause>

  <clause id="584">
    <literal><![CDATA[
      ((x \ 1) * x) * (x \ y) = y * T(y \ (x \ y),x)
    ]]></literal>
    <justification jstring="[hyper(462,a,506,a),flip(a)].">
      <j1 rule="hyper" parents="462 506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="585">
    <literal><![CDATA[
      x \ T(x * (y * (x \ 1)),z) = T(y,z) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(482,a,568,a),flip(a)].">
      <j1 rule="hyper" parents="482 568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="586">
    <literal><![CDATA[
      (x \ 1) \ (x \ T(x * y,z)) = T((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(118,a,568,a)].">
      <j1 rule="hyper" parents="118 568"/>
    </justification>
  </clause>

  <clause id="587">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ 1,y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[para(8(a,1),568(a,2,2,1))].">
      <j1 rule="para" parents="8 568"/>
    </justification>
  </clause>

  <clause id="588">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ (x \ y),z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),568(a,2,2,1))].">
      <j1 rule="para" parents="10 568"/>
    </justification>
  </clause>

  <clause id="589">
    <literal><![CDATA[
      T(x,y) * (x \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,323,a(flip),b,587,a)].">
      <j1 rule="hyper" parents="65 323 587"/>
    </justification>
  </clause>

  <clause id="590">
    <literal><![CDATA[
      (x \ T(x,y)) / (x \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(113,a,587,a(flip),b,323,a(flip))].">
      <j1 rule="hyper" parents="113 587 323"/>
    </justification>
  </clause>

  <clause id="591">
    <literal><![CDATA[
      T(x,y) * (x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x \ T(x,y) = z
    ]]></literal>
    <justification jstring="[para(590(a,1),211(a,1,1)),flip(b)].">
      <j1 rule="para" parents="590 211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="592">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      x \ T(x,y) = z
    ]]></literal>
    <justification jstring="[para(323(a,2),591(a,1))].">
      <j1 rule="para" parents="323 591"/>
    </justification>
  </clause>

  <clause id="594">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ y,z) = T(y * x,z) / x
    ]]></literal>
    <justification jstring="[hyper(462,a,569,a)].">
      <j1 rule="hyper" parents="462 569"/>
    </justification>
  </clause>

  <clause id="596">
    <literal><![CDATA[
      T(1 / (1 / x),y) * (1 / x) = T(x,y) / x
    ]]></literal>
    <justification jstring="[para(7(a,1),569(a,2,1,1))].">
      <j1 rule="para" parents="7 569"/>
    </justification>
  </clause>

  <clause id="597">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ 1,y) = T(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(462,a,596,a)].">
      <j1 rule="hyper" parents="462 596"/>
    </justification>
  </clause>

  <clause id="598">
    <literal><![CDATA[
      T(x,y) / x != z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(596(a,1),462(a,1))].">
      <j1 rule="para" parents="596 462"/>
    </justification>
  </clause>

  <clause id="599">
    <literal><![CDATA[
      (1 / x) * T(x,y) = T(x,y) / x
    ]]></literal>
    <justification jstring="[para(79(a,1),597(a,1,2,1))].">
      <j1 rule="para" parents="79 597"/>
    </justification>
  </clause>

  <clause id="600">
    <literal><![CDATA[
      (T(x,y) / x) / T(x,y) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(123,a,599,a)].">
      <j1 rule="hyper" parents="123 599"/>
    </justification>
  </clause>

  <clause id="601">
    <literal><![CDATA[
      T(x,x \ y) / x = (1 / x) * ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,249,a(flip),b,599,a),flip(a)].">
      <j1 rule="hyper" parents="65 249 599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="602">
    <literal><![CDATA[
      T(x \ 1,y) / (x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x * T(x \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(599(a,1),260(a,1))].">
      <j1 rule="para" parents="599 260"/>
    </justification>
  </clause>

  <clause id="603">
    <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(599(a,1),446(a,1,2))].">
      <j1 rule="para" parents="599 446"/>
    </justification>
  </clause>

  <clause id="604">
    <literal><![CDATA[
      ((1 / x) \ (y / x)) * (1 / x) = T(y,1 / x) / x
    ]]></literal>
    <justification jstring="[para(12(a,1),573(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="12 573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="605">
    <literal><![CDATA[
      (x / y) * K(y \ 1,y) = x * T(x \ (x / y),y)
    ]]></literal>
    <justification jstring="[para(216(a,2),576(a,1,2))].">
      <j1 rule="para" parents="216 576"/>
    </justification>
  </clause>

  <clause id="606">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ 1,y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(250,a,88,a(flip),b,577,a),flip(a)].">
      <j1 rule="hyper" parents="250 88 577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="607">
    <literal><![CDATA[
      K(x,y) = ((y * x) \ y) * T(((y * x) \ y) \ 1,y)
    ]]></literal>
    <justification jstring="[para(9(a,1),606(a,2,1)),flip(a)].">
      <j1 rule="para" parents="9 606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="608">
    <literal><![CDATA[
      K(x \ (x / y),x) = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,88,a(flip),b,579,a)].">
      <j1 rule="hyper" parents="65 88 579"/>
    </justification>
  </clause>

  <clause id="609">
    <literal><![CDATA[
      K(x \ (x / (y \ 1)),x) = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(250,a,587,a(flip),b,608,a),flip(a)].">
      <j1 rule="hyper" parents="250 587 608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="610">
    <literal><![CDATA[
      K(x \ (x / y),x) / y = T(1 / y,x)
    ]]></literal>
    <justification jstring="[hyper(113,a,608,a,b,321,a)].">
      <j1 rule="hyper" parents="113 608 321"/>
    </justification>
  </clause>

  <clause id="611">
    <literal><![CDATA[
      K(x \ (x / (((x * y) / x) \ 1)),x) = ((x * y) / x) \ y
    ]]></literal>
    <justification jstring="[para(190(a,1),609(a,2,2))].">
      <j1 rule="para" parents="190 609"/>
    </justification>
  </clause>

  <clause id="612">
    <literal><![CDATA[
      K((x * y) \ x,x * y) / y = T(1 / y,x * y)
    ]]></literal>
    <justification jstring="[para(11(a,1),610(a,1,1,1,2))].">
      <j1 rule="para" parents="11 610"/>
    </justification>
  </clause>

  <clause id="613">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) = y * T(y \ (x \ y),x)
    ]]></literal>
    <justification jstring="[para(216(a,2),584(a,1,1))].">
      <j1 rule="para" parents="216 584"/>
    </justification>
  </clause>

  <clause id="614">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ T(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(586(a,1),214(a,1,2))].">
      <j1 rule="para" parents="586 214"/>
    </justification>
  </clause>

  <clause id="616">
    <literal><![CDATA[
      K(x \ (x * y),x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(250,a,606,a(flip),b,607,a)].">
      <j1 rule="hyper" parents="250 606 607"/>
    </justification>
  </clause>

  <clause id="617">
    <literal><![CDATA[
      K(x \ (x * y),z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(69(a,1),616(a,1,1)),flip(a)].">
      <j1 rule="para" parents="69 616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="618">
    <literal><![CDATA[
      K(L(x \ 1,x,y),z) = K((y * x) \ y,z)
    ]]></literal>
    <justification jstring="[para(279(a,1),617(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="279 617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="620">
    <literal><![CDATA[
      R((x * y) / (z * y),u,w) * (z * y) = (R(x / z,u,w) * z) * y
    ]]></literal>
    <justification jstring="[para(101(a,1),309(a,1,1,1))].">
      <j1 rule="para" parents="101 309"/>
    </justification>
  </clause>

  <clause id="621">
    <literal><![CDATA[
      (x * y) * L((x * y) \ z,u,w) = x * (y * L(y \ (x \ z),u,w))
    ]]></literal>
    <justification jstring="[para(239(a,1),312(a,1,2,1))].">
      <j1 rule="para" parents="239 312"/>
    </justification>
  </clause>

  <clause id="622">
    <literal><![CDATA[
      (x * y) * L(T(x,x * y),z,u) = x * (y * L(T(x,y),z,u))
    ]]></literal>
    <justification jstring="[para(437(a,1),312(a,1,2,1))].">
      <j1 rule="para" parents="437 312"/>
    </justification>
  </clause>

  <clause id="623">
    <literal><![CDATA[
      (x * y) * R((x * y) \ x,z,u) = x * (y * R(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(181(a,1),313(a,1,2,1))].">
      <j1 rule="para" parents="181 313"/>
    </justification>
  </clause>

  <clause id="624">
    <literal><![CDATA[
      (x * y) * R((x * y) \ z,u,w) = x * (y * R(y \ (x \ z),u,w))
    ]]></literal>
    <justification jstring="[para(239(a,1),313(a,1,2,1))].">
      <j1 rule="para" parents="239 313"/>
    </justification>
  </clause>

  <clause id="625">
    <literal><![CDATA[
      K(x \ 1,x) * L(x \ y,x,x \ 1) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(250,a,131,a(flip),b,343,a),flip(a)].">
      <j1 rule="hyper" parents="250 131 343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="626">
    <literal><![CDATA[
      (R(x / y,y,z) * y) \ (x * z) = L(z,y,R(x / y,y,z))
    ]]></literal>
    <justification jstring="[para(12(a,1),367(a,1,2,1))].">
      <j1 rule="para" parents="12 367"/>
    </justification>
  </clause>

  <clause id="627">
    <literal><![CDATA[
      (x \ 1) * L((x \ 1) \ y,z,u) = x \ L(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(348(a,1),389(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="348 389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="628">
    <literal><![CDATA[
      (x \ 1) * R((x \ 1) \ y,z,u) = x \ R(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(348(a,1),390(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="348 390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="629">
    <literal><![CDATA[
      R(R(x,1 / y,y),z,u) / y != w * (1 / y)
    ]]></literal>
    <literal><![CDATA[
      R(x,z,u) = w
    ]]></literal>
    <justification jstring="[para(397(a,2),46(a,1))].">
      <j1 rule="para" parents="397 46"/>
    </justification>
  </clause>

  <clause id="630">
    <literal><![CDATA[
      R(x / (1 / y),z,u) * (1 / y) = R(x * y,z,u) / y
    ]]></literal>
    <justification jstring="[para(376(a,1),397(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="376 397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="631">
    <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(287(a,2),398(a,1,1,1))].">
      <j1 rule="para" parents="287 398"/>
    </justification>
  </clause>

  <clause id="632">
    <literal><![CDATA[
      L(T(x,1 / x),y,z) / x = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[para(518(a,1),398(a,1,1,1))].">
      <j1 rule="para" parents="518 398"/>
    </justification>
  </clause>

  <clause id="634">
    <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(402(a,1),343(a,1,2))].">
      <j1 rule="para" parents="402 343"/>
    </justification>
  </clause>

  <clause id="635">
    <literal><![CDATA[
      x * ((x \ y) * T((x \ y) \ 1,z)) = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(275(a,1),470(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="275 470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="636">
    <literal><![CDATA[
      x \ (y * T(y \ (x * z),u)) = (x \ y) * T((x \ y) \ z,u)
    ]]></literal>
    <justification jstring="[para(495(a,1),337(a,1,2,2))].">
      <j1 rule="para" parents="495 337"/>
    </justification>
  </clause>

  <clause id="637">
    <literal><![CDATA[
      (T(x / (y / z),u) * (y / z)) * z = T((x * z) / y,u) * y
    ]]></literal>
    <justification jstring="[hyper(115,a,499,a(flip),b,102,a),flip(a)].">
      <j1 rule="hyper" parents="115 499 102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="638">
    <literal><![CDATA[
      T((x * y) \ ((x * z) * y),x) = R(T(z,x * y),x,y)
    ]]></literal>
    <justification jstring="[hyper(250,a,27,a,b,511,a),flip(a)].">
      <j1 rule="hyper" parents="250 27 511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="639">
    <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(325(a,1),547(a,1,1,1))].">
      <j1 rule="para" parents="325 547"/>
    </justification>
  </clause>

  <clause id="640">
    <literal><![CDATA[
      K(x \ 1,x) * y != (x \ 1) * z
    ]]></literal>
    <literal><![CDATA[
      L(x \ z,x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(625(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="625 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="641">
    <literal><![CDATA[
      (x * y) * T((x * y) \ y,z) = (T(1 / x,z) * x) * y
    ]]></literal>
    <justification jstring="[hyper(462,a,479,a)].">
      <j1 rule="hyper" parents="462 479"/>
    </justification>
  </clause>

  <clause id="642">
    <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(239(a,1),519(a,1,2,1))].">
      <j1 rule="para" parents="239 519"/>
    </justification>
  </clause>

  <clause id="643">
    <literal><![CDATA[
      x * (y * T(T(x,y),z)) = T(x,z) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(290,a,563,a),flip(a)].">
      <j1 rule="hyper" parents="290 563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="644">
    <literal><![CDATA[
      T(x,y) * (x * z) = x * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[para(197(a,1),643(a,1,2)),flip(a)].">
      <j1 rule="para" parents="197 643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="645">
    <literal><![CDATA[
      T(x,y) * (x \ (T(x,y) \ z)) = x \ z
    ]]></literal>
    <justification jstring="[hyper(423,a,644,a),flip(a)].">
      <j1 rule="hyper" parents="423 644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="646">
    <literal><![CDATA[
      x * (T(x,y) * (x \ z)) = T(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(259,a,644,a),flip(a)].">
      <j1 rule="hyper" parents="259 644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="647">
    <literal><![CDATA[
      T(x,y) * (x * (T(x,y) \ z)) = x * z
    ]]></literal>
    <justification jstring="[hyper(250,a,131,a(flip),b,644,a),flip(a)].">
      <j1 rule="hyper" parents="250 131 644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="648">
    <literal><![CDATA[
      x * (T(x,y) \ 1) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(112,a,71,a(flip),b,644,a),flip(a)].">
      <j1 rule="hyper" parents="112 71 644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="649">
    <literal><![CDATA[
      x * (T(x,y) * T(z,x)) = T(x,y) * (z * x)
    ]]></literal>
    <justification jstring="[hyper(65,a,188,a(flip),b,644,a),flip(a)].">
      <j1 rule="hyper" parents="65 188 644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="650">
    <literal><![CDATA[
      (x / y) * (T(x / y,z) * y) = T(x / y,z) * x
    ]]></literal>
    <justification jstring="[para(12(a,1),644(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="651">
    <literal><![CDATA[
      (x / y) * (T(x / y,y) * z) = (y \ x) * ((x / y) * z)
    ]]></literal>
    <justification jstring="[para(106(a,1),644(a,1,1)),flip(a)].">
      <j1 rule="para" parents="106 644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="652">
    <literal><![CDATA[
      x \ (T(x,y) \ x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(118,a,648,a)].">
      <j1 rule="hyper" parents="118 648"/>
    </justification>
  </clause>

  <clause id="653">
    <literal><![CDATA[
      L(T(x,y) \ 1,x,1 / x) = (1 / x) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[para(648(a,1),217(a,1,2)),flip(a)].">
      <j1 rule="para" parents="648 217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="654">
    <literal><![CDATA[
      T((1 / x) * (T(x,y) \ x),x) = (1 / x) * ((T(x,y) \ 1) * x)
    ]]></literal>
    <justification jstring="[para(652(a,1),546(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="652 546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="655">
    <literal><![CDATA[
      T(x,y) \ (x \ z) = x \ (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(118,a,645,a)].">
      <j1 rule="hyper" parents="118 645"/>
    </justification>
  </clause>

  <clause id="656">
    <literal><![CDATA[
      T(x,y) * z != x * u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * (x \ z) = u
    ]]></literal>
    <justification jstring="[para(646(a,1),45(a,1))].">
      <j1 rule="para" parents="646 45"/>
    </justification>
  </clause>

  <clause id="657">
    <literal><![CDATA[
      x * (T(x,y) \ y) = T(y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(200,a,104,a,b,647,a),flip(a)].">
      <j1 rule="hyper" parents="200 104 647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="658">
    <literal><![CDATA[
      x * (T(x,y) \ ((x \ T(x,y)) * z)) = L(z,x \ T(x,y),x)
    ]]></literal>
    <justification jstring="[hyper(36,a,314,a,b,647,a),flip(a)].">
      <j1 rule="hyper" parents="36 314 647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="660">
    <literal><![CDATA[
      x * (T(x,y) \ (x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) \ z = u
    ]]></literal>
    <justification jstring="[para(655(a,2),214(a,1,2))].">
      <j1 rule="para" parents="655 214"/>
    </justification>
  </clause>

  <clause id="661">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ 1) * x) = x * K(x \ (x / T(x,y)),x)
    ]]></literal>
    <justification jstring="[para(608(a,2),649(a,1,2)),flip(a)].">
      <j1 rule="para" parents="608 649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="663">
    <literal><![CDATA[
      x * (T(x,y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) \ (x * z) = u
    ]]></literal>
    <justification jstring="[para(9(a,1),660(a,1,2,2))].">
      <j1 rule="para" parents="9 660"/>
    </justification>
  </clause>

  <clause id="664">
    <literal><![CDATA[
      (x / y) * (y * T(y \ x,z)) = T(x / y,z) * x
    ]]></literal>
    <justification jstring="[para(321(a,1),650(a,1,2))].">
      <j1 rule="para" parents="321 650"/>
    </justification>
  </clause>

  <clause id="665">
    <literal><![CDATA[
      (x / y) \ (T(x / y,z) * x) != u * w
    ]]></literal>
    <literal><![CDATA[
      (y * T(y \ x,z)) / w = u
    ]]></literal>
    <justification jstring="[para(664(a,1),386(a,1,2))].">
      <j1 rule="para" parents="664 386"/>
    </justification>
  </clause>

  <clause id="666">
    <literal><![CDATA[
      (T(1 / x,y) * x) * (x \ z) = z * T(z \ (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(462,a,570,a),flip(a)].">
      <j1 rule="hyper" parents="462 570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="667">
    <literal><![CDATA[
      (x \ (y * (z \ x))) * x = (z * T(z \ y,x)) * (z \ x)
    ]]></literal>
    <justification jstring="[para(321(a,1),582(a,2,1))].">
      <j1 rule="para" parents="321 582"/>
    </justification>
  </clause>

  <clause id="668">
    <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(611(a,2),301(a,1,2))].">
      <j1 rule="para" parents="611 301"/>
    </justification>
  </clause>

  <clause id="669">
    <literal><![CDATA[
      (x \ 1) * R((x \ 1) \ 1,y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(8(a,1),628(a,2,2,1))].">
      <j1 rule="para" parents="8 628"/>
    </justification>
  </clause>

  <clause id="670">
    <literal><![CDATA[
      R(x,y,z) * (x \ 1) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,435,a(flip),b,669,a)].">
      <j1 rule="hyper" parents="65 435 669"/>
    </justification>
  </clause>

  <clause id="671">
    <literal><![CDATA[
      (1 / x) \ R(1 / x,y,z) = R(1 / x,y,z) * x
    ]]></literal>
    <justification jstring="[hyper(416,a,670,a),flip(a)].">
      <j1 rule="hyper" parents="416 670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="672">
    <literal><![CDATA[
      ((x \ R(x,y,z)) * u) / ((x \ 1) * u) = R(R(x,y,z),x \ 1,u)
    ]]></literal>
    <justification jstring="[para(670(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="670 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="673">
    <literal><![CDATA[
      (1 / x) \ R(1 / x,y,z) = x * R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(250,a,433,a(flip),b,671,a),flip(a)].">
      <j1 rule="hyper" parents="250 433 671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="674">
    <literal><![CDATA[
      (1 / x) * ((y / (x * y)) * x) = R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,458,a,b,673,a)].">
      <j1 rule="hyper" parents="116 458 673"/>
    </justification>
  </clause>

  <clause id="675">
    <literal><![CDATA[
      ((x / (y * x)) * y) \ (x / (y * x)) = T(1 / y,(x / (y * x)) * y)
    ]]></literal>
    <justification jstring="[hyper(307,a,183,a(flip),b,674,a),flip(a)].">
      <j1 rule="hyper" parents="307 183 674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="676">
    <literal><![CDATA[
      (1 / x) * R((1 / x) \ y,z,u) = R(y * x,z,u) / x
    ]]></literal>
    <justification jstring="[hyper(65,a,433,a(flip),b,630,a)].">
      <j1 rule="hyper" parents="65 433 630"/>
    </justification>
  </clause>

  <clause id="677">
    <literal><![CDATA[
      R(x * y,z,u) / y != w * (1 / y)
    ]]></literal>
    <literal><![CDATA[
      R(x / (1 / y),z,u) = w
    ]]></literal>
    <justification jstring="[para(630(a,1),46(a,1))].">
      <j1 rule="para" parents="630 46"/>
    </justification>
  </clause>

  <clause id="678">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ 1,z) = x \ (y * T(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,635,a),flip(a)].">
      <j1 rule="hyper" parents="118 635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="679">
    <literal><![CDATA[
      x * T(x \ y,y \ x) = y * K((y \ x) \ 1,y \ x)
    ]]></literal>
    <justification jstring="[para(265(a,1),635(a,1,2)),flip(a)].">
      <j1 rule="para" parents="265 635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="680">
    <literal><![CDATA[
      x * T(x \ y,z) = y * K(z \ (z / (y \ x)),z)
    ]]></literal>
    <justification jstring="[para(608(a,2),635(a,1,2)),flip(a)].">
      <j1 rule="para" parents="608 635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="681">
    <literal><![CDATA[
      K(x \ (x / (y \ z)),x) = y \ (z * T(z \ y,x))
    ]]></literal>
    <justification jstring="[hyper(112,a,680,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="112 680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="682">
    <literal><![CDATA[
      T(x * y,z) / y = x * K(z \ (z / (x \ (1 / y))),z)
    ]]></literal>
    <justification jstring="[hyper(65,a,594,a(flip),b,680,a)].">
      <j1 rule="hyper" parents="65 594 680"/>
    </justification>
  </clause>

  <clause id="683">
    <literal><![CDATA[
      (x \ y) * K(z \ (z / ((x \ y) \ (x \ 1))),z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,588,a(flip),b,680,a),flip(a)].">
      <j1 rule="hyper" parents="65 588 680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="684">
    <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),680(a,2,2,1,2,2))].">
      <j1 rule="para" parents="18 680"/>
    </justification>
  </clause>

  <clause id="685">
    <literal><![CDATA[
      K(x \ (x / T(y,z)),x) = z \ ((y * z) * T((y * z) \ z,x))
    ]]></literal>
    <justification jstring="[para(22(a,2),681(a,1,1,2,2))].">
      <j1 rule="para" parents="22 681"/>
    </justification>
  </clause>

  <clause id="686">
    <literal><![CDATA[
      (x * y) * T((x * y) \ y,z) = (x * T(x \ 1,z)) * y
    ]]></literal>
    <justification jstring="[para(321(a,1),641(a,2,1))].">
      <j1 rule="para" parents="321 641"/>
    </justification>
  </clause>

  <clause id="687">
    <literal><![CDATA[
      (x / y) * ((y \ x) * z) = (y \ x) * ((x / y) * z)
    ]]></literal>
    <justification jstring="[para(106(a,1),651(a,1,2,1))].">
      <j1 rule="para" parents="106 651"/>
    </justification>
  </clause>

  <clause id="688">
    <literal><![CDATA[
      (x \ (x * y)) * (((x * y) / x) * z) = ((x * y) / x) * (y * z)
    ]]></literal>
    <justification jstring="[para(190(a,1),651(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="190 651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="689">
    <literal><![CDATA[
      (x \ y) \ ((y / x) * z) = (y / x) * ((x \ y) \ z)
    ]]></literal>
    <justification jstring="[hyper(424,a,687,a)].">
      <j1 rule="hyper" parents="424 687"/>
    </justification>
  </clause>

  <clause id="692">
    <literal><![CDATA[
      (x * T(x \ 1,y)) * (x \ z) = z * T(z \ (x \ z),y)
    ]]></literal>
    <justification jstring="[para(321(a,1),666(a,1,1))].">
      <j1 rule="para" parents="321 666"/>
    </justification>
  </clause>

  <clause id="693">
    <literal><![CDATA[
      (x * y) * K(((x * y) \ x) \ 1,(x * y) \ x) = x * T(y,(x * y) \ x)
    ]]></literal>
    <justification jstring="[para(9(a,1),679(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="694">
    <literal><![CDATA[
      (x / y) * K(z \ (z / ((x / y) \ (1 / y))),z) = T(x,z) / y
    ]]></literal>
    <justification jstring="[para(12(a,1),682(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="12 682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="695">
    <literal><![CDATA[
      T(x,x * T(x \ 1,y)) = x
    ]]></literal>
    <justification jstring="[hyper(200,a,478,a(flip),b,686,a(flip))].">
      <j1 rule="hyper" parents="200 478 686"/>
    </justification>
  </clause>

  <clause id="696">
    <literal><![CDATA[
      T(x,(x \ 1) * x) = x
    ]]></literal>
    <justification jstring="[para(104(a,1),695(a,1,2))].">
      <j1 rule="para" parents="104 695"/>
    </justification>
  </clause>

  <clause id="697">
    <literal><![CDATA[
      T(x \ 1,T(x,y) * (x \ 1)) = x \ 1
    ]]></literal>
    <justification jstring="[para(323(a,1),695(a,1,2))].">
      <j1 rule="para" parents="323 695"/>
    </justification>
  </clause>

  <clause id="698">
    <literal><![CDATA[
      T(x \ 1,x \ T(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[para(587(a,1),695(a,1,2))].">
      <j1 rule="para" parents="587 695"/>
    </justification>
  </clause>

  <clause id="699">
    <literal><![CDATA[
      T(1 / x,T(x,y) / x) = 1 / x
    ]]></literal>
    <justification jstring="[para(597(a,1),695(a,1,2))].">
      <j1 rule="para" parents="597 695"/>
    </justification>
  </clause>

  <clause id="700">
    <literal><![CDATA[
      ((x \ 1) * x) * x = x * ((x \ 1) * x)
    ]]></literal>
    <justification jstring="[hyper(116,a,696,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="116 696 22"/>
    </justification>
  </clause>

  <clause id="701">
    <literal><![CDATA[
      R(x,x \ 1,x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(696(a,1),514(a,1,1))].">
      <j1 rule="para" parents="696 514"/>
    </justification>
  </clause>

  <clause id="702">
    <literal><![CDATA[
      x / K(x \ 1,x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,388,a,b,701,a)].">
      <j1 rule="hyper" parents="65 388 701"/>
    </justification>
  </clause>

  <clause id="703">
    <literal><![CDATA[
      ((x \ 1) \ 1) * K(x \ 1,x) = x
    ]]></literal>
    <justification jstring="[hyper(115,a,701,a(flip),b,388,a)].">
      <j1 rule="hyper" parents="115 701 388"/>
    </justification>
  </clause>

  <clause id="704">
    <literal><![CDATA[
      T(x \ T(x,y),x \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(56,a,698,a)].">
      <j1 rule="hyper" parents="56 698"/>
    </justification>
  </clause>

  <clause id="705">
    <literal><![CDATA[
      T((x * (1 / y)) / x,T(y,z) / y) = (x * (1 / y)) / x
    ]]></literal>
    <justification jstring="[para(699(a,1),327(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="699 327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="706">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ x = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(163,a,702,a)].">
      <j1 rule="hyper" parents="163 702"/>
    </justification>
  </clause>

  <clause id="707">
    <literal><![CDATA[
      R(x \ 1,T(x,y),x \ 1) = T(x \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[para(697(a,1),513(a,1,1))].">
      <j1 rule="para" parents="697 513"/>
    </justification>
  </clause>

  <clause id="708">
    <literal><![CDATA[
      ((x \ 1) * x) * x = L(x,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(250,a,215,a(flip),b,700,a),flip(a)].">
      <j1 rule="hyper" parents="250 215 700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="709">
    <literal><![CDATA[
      T((x * y) \ (y * x),y \ 1) = L(y \ T(y,x),y,x)
    ]]></literal>
    <justification jstring="[para(704(a,1),491(a,1,1)),flip(a)].">
      <j1 rule="para" parents="704 491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="710">
    <literal><![CDATA[
      K(x,y) = T((y * x) \ (x * y),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(250,a,490,a,b,709,a)].">
      <j1 rule="hyper" parents="250 490 709"/>
    </justification>
  </clause>

  <clause id="711">
    <literal><![CDATA[
      T(K(x,y),x \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[para(16(a,2),710(a,2,1)),flip(a)].">
      <j1 rule="para" parents="16 710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="712">
    <literal><![CDATA[
      T(x \ 1,K(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(56,a,711,a)].">
      <j1 rule="hyper" parents="56 711"/>
    </justification>
  </clause>

  <clause id="713">
    <literal><![CDATA[
      K(x,y) * (x \ 1) = (x \ 1) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,711,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 711 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="714">
    <literal><![CDATA[
      x * T(x \ 1,K(x,y)) != z * u
    ]]></literal>
    <literal><![CDATA[
      1 / u = z
    ]]></literal>
    <justification jstring="[para(712(a,2),255(a,1,2))].">
      <j1 rule="para" parents="712 255"/>
    </justification>
  </clause>

  <clause id="715">
    <literal><![CDATA[
      K(x \ 1,x) * ((x \ 1) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(250,a,703,a(flip),b,713,a),flip(a)].">
      <j1 rule="hyper" parents="250 703 713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="716">
    <literal><![CDATA[
      T(1 / x,K(x,y)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(714,a,321,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="714 321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="717">
    <literal><![CDATA[
      T(x / y,K(y / x,z)) = R(1 / (y / x),y / x,x)
    ]]></literal>
    <justification jstring="[para(716(a,1),420(a,1,1)),flip(a)].">
      <j1 rule="para" parents="716 420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="718">
    <literal><![CDATA[
      T(x / y,K(y / x,z)) = x / y
    ]]></literal>
    <justification jstring="[hyper(250,a,286,a(flip),b,717,a),flip(a)].">
      <j1 rule="hyper" parents="250 286 717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="719">
    <literal><![CDATA[
      T(x \ y,K(x / y,z)) = T(y / x,x)
    ]]></literal>
    <justification jstring="[para(718(a,1),206(a,1,1)),flip(a)].">
      <j1 rule="para" parents="718 206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="720">
    <literal><![CDATA[
      T(x \ y,K(x / y,z)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(250,a,106,a(flip),b,719,a),flip(a)].">
      <j1 rule="hyper" parents="250 106 719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="722">
    <literal><![CDATA[
      (x * T(x \ (y \ x),z)) / (y \ x) != u
    ]]></literal>
    <literal><![CDATA[
      y * T(y \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(692(a,1),212(a,1,1)),flip(b)].">
      <j1 rule="para" parents="692 212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="723">
    <literal><![CDATA[
      T(x,a(y,z,u)) \ R(x,a(y,z,u),a(y,z,u) \ 1) = K(x * a(y,z,u),a(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(439(a,1),395(a,1,1))].">
      <j1 rule="para" parents="439 395"/>
    </justification>
  </clause>

  <clause id="724">
    <literal><![CDATA[
      x * (y * R(T(x,y),z,u)) = R(x,z,u) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,313,a(flip),b,443,a)].">
      <j1 rule="hyper" parents="65 313 443"/>
    </justification>
  </clause>

  <clause id="725">
    <literal><![CDATA[
      R(x,y,z) * (x * u) = x * (R(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(199(a,1),724(a,1,2)),flip(a)].">
      <j1 rule="para" parents="199 724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="726">
    <literal><![CDATA[
      R(x,y,z) * (x \ (R(x,y,z) \ u)) = x \ u
    ]]></literal>
    <justification jstring="[hyper(423,a,725,a),flip(a)].">
      <j1 rule="hyper" parents="423 725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="728">
    <literal><![CDATA[
      R(x,y,z) \ (x * (R(x,y,z) * u)) = x * u
    ]]></literal>
    <justification jstring="[hyper(118,a,725,a)].">
      <j1 rule="hyper" parents="118 725"/>
    </justification>
  </clause>

  <clause id="729">
    <literal><![CDATA[
      (x * y) / (x * (R(x,z,u) \ y)) = R(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(113,a,131,a(flip),b,725,a)].">
      <j1 rule="hyper" parents="113 131 725"/>
    </justification>
  </clause>

  <clause id="731">
    <literal><![CDATA[
      x * (R(x,y,z) \ 1) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(112,a,71,a(flip),b,725,a),flip(a)].">
      <j1 rule="hyper" parents="112 71 725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="732">
    <literal><![CDATA[
      x * (R(x,y,z) * T(u,x)) = R(x,y,z) * (u * x)
    ]]></literal>
    <justification jstring="[hyper(65,a,188,a(flip),b,725,a),flip(a)].">
      <j1 rule="hyper" parents="65 188 725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="733">
    <literal><![CDATA[
      (R(x,y,z) * (x \ u)) \ (R(x,y,z) * u) = T(x,R(x,y,z) * (x \ u))
    ]]></literal>
    <justification jstring="[hyper(307,a,131,a(flip),b,725,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="307 131 725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="734">
    <literal><![CDATA[
      (R(x,y,z) * u) / (R(x,y,z) * (x \ u)) = x
    ]]></literal>
    <justification jstring="[hyper(113,a,131,a(flip),b,725,a(flip))].">
      <j1 rule="hyper" parents="113 131 725"/>
    </justification>
  </clause>

  <clause id="735">
    <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(731(a,1),585(a,1,2,1,2))].">
      <j1 rule="para" parents="731 585"/>
    </justification>
  </clause>

  <clause id="736">
    <literal><![CDATA[
      R(x,y,z) * (x \ (y * z)) = x \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(159(a,1),726(a,1,2,2))].">
      <j1 rule="para" parents="159 726"/>
    </justification>
  </clause>

  <clause id="737">
    <literal><![CDATA[
      ((1 / x) * y) / ((1 / x) * (x * y)) = R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[para(284(a,1),729(a,1,2,2))].">
      <j1 rule="para" parents="284 729"/>
    </justification>
  </clause>

  <clause id="738">
    <literal><![CDATA[
      (x * (y * (x * z))) / (x * (z * T(y,x * z))) = R(x,z,T(y,x * z))
    ]]></literal>
    <justification jstring="[para(362(a,1),729(a,1,2,2))].">
      <j1 rule="para" parents="362 729"/>
    </justification>
  </clause>

  <clause id="739">
    <literal><![CDATA[
      R(x,y,z) = (x \ ((x * y) * z)) / (x \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(123,a,736,a),flip(a)].">
      <j1 rule="hyper" parents="123 736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="740">
    <literal><![CDATA[
      R(x,y,x) * T(y,x) = T(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(200,a,100,a(flip),b,732,a),flip(a)].">
      <j1 rule="hyper" parents="200 100 732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="741">
    <literal><![CDATA[
      R(x,y,x) \ T(x * y,x) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(118,a,740,a)].">
      <j1 rule="hyper" parents="118 740"/>
    </justification>
  </clause>

  <clause id="742">
    <literal><![CDATA[
      L((x \ y) / y,z,u) * y = (L(1 / x,z,u) * x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(285(a,1),474(a,1,1,1))].">
      <j1 rule="para" parents="285 474"/>
    </justification>
  </clause>

  <clause id="744">
    <literal><![CDATA[
      x * ((x \ y) * R((x \ y) \ z,u,w)) = y * R(y \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[hyper(116,a,496,a(flip),b,94,a),flip(a)].">
      <j1 rule="hyper" parents="116 496 94"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="746">
    <literal><![CDATA[
      x \ (y * L(y \ (x * z),u,w)) = (x \ y) * L((x \ y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(497(a,1),337(a,1,2,2))].">
      <j1 rule="para" parents="497 337"/>
    </justification>
  </clause>

  <clause id="747">
    <literal><![CDATA[
      L(1 / (x \ (x / y)),x \ (x / y),x) = ((x \ (x / y)) * y) / (x \ (x / y))
    ]]></literal>
    <justification jstring="[hyper(113,a,167,a(flip),b,533,a),flip(a)].">
      <j1 rule="hyper" parents="113 167 533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="748">
    <literal><![CDATA[
      L(((x * y) * z) / (x * y),y,x) != u / (x * y)
    ]]></literal>
    <literal><![CDATA[
      x * (y * z) = u
    ]]></literal>
    <justification jstring="[para(535(a,2),48(a,1))].">
      <j1 rule="para" parents="535 48"/>
    </justification>
  </clause>

  <clause id="749">
    <literal><![CDATA[
      ((x * y) * z) \ ((x * y) * R(z,x,y)) = a(((x * y) * z) / (x * y),x,y)
    ]]></literal>
    <justification jstring="[para(536(a,1),86(a,1,2))].">
      <j1 rule="para" parents="536 86"/>
    </justification>
  </clause>

  <clause id="750">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ (x * u))) / z) != w
    ]]></literal>
    <literal><![CDATA[
      x * (y * ((z * (y \ u)) / z)) = w
    ]]></literal>
    <justification jstring="[para(548(a,1),234(a,1,2))].">
      <j1 rule="para" parents="548 234"/>
    </justification>
  </clause>

  <clause id="751">
    <literal><![CDATA[
      (x / y) * (y * ((z * (y \ 1)) / z)) = x * ((z * (x \ (x / y))) / z)
    ]]></literal>
    <justification jstring="[para(549(a,1),334(a,1,2)),flip(a)].">
      <j1 rule="para" parents="549 334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="752">
    <literal><![CDATA[
      ((x * (y / (z * y))) / x) * (z * y) = (((x * (1 / z)) / x) * z) * y
    ]]></literal>
    <justification jstring="[para(183(a,1),551(a,1,1,1,2))].">
      <j1 rule="para" parents="183 551"/>
    </justification>
  </clause>

  <clause id="753">
    <literal><![CDATA[
      ((x * ((y * z) / (u * z))) / x) * (u * z) = (((x * (y / u)) / x) * u) * z
    ]]></literal>
    <justification jstring="[para(101(a,1),551(a,1,1,1,2))].">
      <j1 rule="para" parents="101 551"/>
    </justification>
  </clause>

  <clause id="754">
    <literal><![CDATA[
      (((x * ((y / z) / u)) / x) * u) * z = ((x * (y / (u * z))) / x) * (u * z)
    ]]></literal>
    <justification jstring="[para(241(a,1),551(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="241 551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="755">
    <literal><![CDATA[
      ((x * (y / (1 / z))) / x) * (1 / z) = ((x * (y * z)) / x) / z
    ]]></literal>
    <justification jstring="[hyper(113,a,553,a(flip),b,220,a),flip(a)].">
      <j1 rule="hyper" parents="113 553 220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="756">
    <literal><![CDATA[
      (T(x,y) * z) * T(x,z) = (x * z) * T(T(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(65,a,448,a(flip),b,559,a),flip(a)].">
      <j1 rule="hyper" parents="65 448 559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="757">
    <literal><![CDATA[
      T(T(x,x * y) * y,T(x,y)) = x * y
    ]]></literal>
    <justification jstring="[hyper(200,a,756,a,b,104,a(flip))].">
      <j1 rule="hyper" parents="200 756 104"/>
    </justification>
  </clause>

  <clause id="758">
    <literal><![CDATA[
      T(T(x,x \ 1),y) / T(x,x \ 1) = T(x,y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(113,a,70,a(flip),b,756,a)].">
      <j1 rule="hyper" parents="113 70 756"/>
    </justification>
  </clause>

  <clause id="759">
    <literal><![CDATA[
      T(T(x / y,(x / y) * y) * y,T(x / y,y)) = x
    ]]></literal>
    <justification jstring="[hyper(250,a,12,a(flip),b,757,a),flip(a)].">
      <j1 rule="hyper" parents="250 12 757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="761">
    <literal><![CDATA[
      T(T(x,x \ 1),y) / T(x,x \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(250,a,589,a(flip),b,758,a),flip(a)].">
      <j1 rule="hyper" parents="250 589 758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="762">
    <literal><![CDATA[
      (T((x * y) / x,z) * x) * y = (x * y) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(230,a,567,a)].">
      <j1 rule="hyper" parents="230 567"/>
    </justification>
  </clause>

  <clause id="763">
    <literal><![CDATA[
      (x * T(y,z)) * y = (x * y) * T(y,z)
    ]]></literal>
    <justification jstring="[para(322(a,1),762(a,1,1))].">
      <j1 rule="para" parents="322 762"/>
    </justification>
  </clause>

  <clause id="764">
    <literal><![CDATA[
      (x * y) / T(y,z) = (x / T(y,z)) * y
    ]]></literal>
    <justification jstring="[hyper(422,a,763,a)].">
      <j1 rule="hyper" parents="422 763"/>
    </justification>
  </clause>

  <clause id="765">
    <literal><![CDATA[
      (1 / T(x,y)) * x = x / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(411,a,763,a),flip(a)].">
      <j1 rule="hyper" parents="411 763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="766">
    <literal><![CDATA[
      ((x / T(y,z)) * y) * T(y,z) = x * y
    ]]></literal>
    <justification jstring="[hyper(253,a,763,a),flip(a)].">
      <j1 rule="hyper" parents="253 763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="767">
    <literal><![CDATA[
      ((x / y) * T(y,z)) * y = x * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(250,a,129,a(flip),b,763,a),flip(a)].">
      <j1 rule="hyper" parents="250 129 763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="768">
    <literal><![CDATA[
      (x * T(y,z)) \ ((x * y) * T(y,z)) = y
    ]]></literal>
    <justification jstring="[hyper(118,a,763,a)].">
      <j1 rule="hyper" parents="118 763"/>
    </justification>
  </clause>

  <clause id="769">
    <literal><![CDATA[
      (x * (y * x)) / x = y * T(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(113,a,104,a(flip),b,763,a)].">
      <j1 rule="hyper" parents="113 104 763"/>
    </justification>
  </clause>

  <clause id="770">
    <literal><![CDATA[
      ((x / T(y,z)) / y) * T(y,z) = x / y
    ]]></literal>
    <justification jstring="[hyper(113,a,83,a(flip),b,763,a),flip(a)].">
      <j1 rule="hyper" parents="113 83 763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="771">
    <literal><![CDATA[
      (x * (y / z)) * T(y / z,z) = (x * (z \ y)) * (y / z)
    ]]></literal>
    <justification jstring="[para(106(a,1),763(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="106 763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="772">
    <literal><![CDATA[
      (1 / T(x,y)) \ (x / T(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(118,a,765,a)].">
      <j1 rule="hyper" parents="118 765"/>
    </justification>
  </clause>

  <clause id="773">
    <literal><![CDATA[
      T(x,1 / T(x,y)) / T(x,y) = x * (1 / T(x,y))
    ]]></literal>
    <justification jstring="[para(772(a,1),604(a,1,1)),flip(a)].">
      <j1 rule="para" parents="772 604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="774">
    <literal><![CDATA[
      T((x / y) * T(y,x),y) = x
    ]]></literal>
    <justification jstring="[hyper(200,a,767,a,b,104,a(flip))].">
      <j1 rule="hyper" parents="200 767 104"/>
    </justification>
  </clause>

  <clause id="775">
    <literal><![CDATA[
      (x / y) * T(y,x) = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(113,a,104,a(flip),b,767,a),flip(a)].">
      <j1 rule="hyper" parents="113 104 767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="776">
    <literal><![CDATA[
      T(x * T(x \ y,y),x \ y) = y
    ]]></literal>
    <justification jstring="[para(76(a,1),774(a,1,1,1))].">
      <j1 rule="para" parents="76 774"/>
    </justification>
  </clause>

  <clause id="777">
    <literal><![CDATA[
      T(a(x,y,z),u / a(x,y,z)) = T(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(200,a,472,a(flip),b,775,a)].">
      <j1 rule="hyper" parents="200 472 775"/>
    </justification>
  </clause>

  <clause id="778">
    <literal><![CDATA[
      (T(x,y) / y) \ x = T(y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(112,a,191,a(flip),b,775,a)].">
      <j1 rule="hyper" parents="112 191 775"/>
    </justification>
  </clause>

  <clause id="779">
    <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(278(a,1),775(a,1,1)),flip(a)].">
      <j1 rule="para" parents="278 775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="780">
    <literal><![CDATA[
      R(T(x,y * T(x,z)),y,T(x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(768(a,1),638(a,1,1)),flip(a)].">
      <j1 rule="para" parents="768 638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="781">
    <literal><![CDATA[
      (x * (y / z)) * (z \ y) = (x * (z \ y)) * (y / z)
    ]]></literal>
    <justification jstring="[para(106(a,1),771(a,1,2))].">
      <j1 rule="para" parents="106 771"/>
    </justification>
  </clause>

  <clause id="782">
    <literal><![CDATA[
      (x * (y \ (y * z))) * ((y * z) / y) = (x * ((y * z) / y)) * z
    ]]></literal>
    <justification jstring="[para(190(a,1),771(a,1,2)),flip(a)].">
      <j1 rule="para" parents="190 771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="783">
    <literal><![CDATA[
      (x * (y \ z)) / (z / y) = (x / (z / y)) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(422,a,781,a)].">
      <j1 rule="hyper" parents="422 781"/>
    </justification>
  </clause>

  <clause id="784">
    <literal><![CDATA[
      (1 / (x / y)) * (y \ x) = (y \ x) / (x / y)
    ]]></literal>
    <justification jstring="[hyper(411,a,781,a),flip(a)].">
      <j1 rule="hyper" parents="411 781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="785">
    <literal><![CDATA[
      (x * (1 / x)) * (x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(250,a,70,a(flip),b,781,a),flip(a)].">
      <j1 rule="hyper" parents="250 70 781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="786">
    <literal><![CDATA[
      (x \ y) / (y / x) != (x \ y) * z
    ]]></literal>
    <literal><![CDATA[
      T(1 / (y / x),x \ y) = z
    ]]></literal>
    <justification jstring="[para(784(a,1),201(a,2)),flip(a)].">
      <j1 rule="para" parents="784 201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="787">
    <literal><![CDATA[
      ((x / (y \ z)) / (z / y)) * (y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      x / (z / y) = u
    ]]></literal>
    <justification jstring="[para(783(a,1),412(a,1))].">
      <j1 rule="para" parents="783 412"/>
    </justification>
  </clause>

  <clause id="788">
    <literal><![CDATA[
      T(x,y) / x != z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) * T(x,y) = z
    ]]></literal>
    <justification jstring="[para(596(a,1),574(a,1))].">
      <j1 rule="para" parents="596 574"/>
    </justification>
  </clause>

  <clause id="789">
    <literal><![CDATA[
      (x * y) / a(z,z \ y,T(x,y)) = L(x,z \ y,z) * y
    ]]></literal>
    <justification jstring="[hyper(250,a,485,a(flip),b,575,a),flip(a)].">
      <j1 rule="hyper" parents="250 485 575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="790">
    <literal><![CDATA[
      (L(x,y \ z,y) * z) \ (x * z) = a(y,y \ z,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(163,a,789,a)].">
      <j1 rule="hyper" parents="163 789"/>
    </justification>
  </clause>

  <clause id="791">
    <literal><![CDATA[
      L(x,y,R((y * z) / y,y,x)) = (y * R(z,y,x)) \ ((y * z) * x)
    ]]></literal>
    <justification jstring="[para(434(a,1),626(a,1,1)),flip(a)].">
      <j1 rule="para" parents="434 626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="792">
    <literal><![CDATA[
      (x / (y / z)) * (z \ y) != u
    ]]></literal>
    <literal><![CDATA[
      (x * (z \ y)) / (y / z) = u
    ]]></literal>
    <justification jstring="[para(11(a,1),787(a,1,1,1))].">
      <j1 rule="para" parents="11 787"/>
    </justification>
  </clause>

  <clause id="793">
    <literal><![CDATA[
      L(T(x,x \ 1),x \ 1,y * x) = R(y,x,x \ 1) \ (y * x)
    ]]></literal>
    <justification jstring="[para(105(a,2),396(a,1,1))].">
      <j1 rule="para" parents="105 396"/>
    </justification>
  </clause>

  <clause id="794">
    <literal><![CDATA[
      R(T(x \ y,x * z),x,z) != u
    ]]></literal>
    <literal><![CDATA[
      T((x * z) \ (y * z),x) = u
    ]]></literal>
    <justification jstring="[para(27(a,2),508(a,1))].">
      <j1 rule="para" parents="27 508"/>
    </justification>
  </clause>

  <clause id="795">
    <literal><![CDATA[
      (x * y) * R((x * y) \ z,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      x * (y * R(y \ (x \ z),u,w)) = v5
    ]]></literal>
    <justification jstring="[para(239(a,1),520(a,1,2,1))].">
      <j1 rule="para" parents="239 520"/>
    </justification>
  </clause>

  <clause id="797">
    <literal><![CDATA[
      (T((x / y) / z,u) * z) * y = (z * y) * T((z * y) \ x,u)
    ]]></literal>
    <justification jstring="[hyper(250,a,321,a(flip),b,560,a),flip(a)].">
      <j1 rule="hyper" parents="250 321 560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="798">
    <literal><![CDATA[
      T(x / (y * z),y) * (y * z) = ((y \ (x / z)) * y) * z
    ]]></literal>
    <justification jstring="[para(106(a,1),560(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="106 560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="799">
    <literal><![CDATA[
      (x * y) * T((x * y) \ z,x) = ((x \ (z / y)) * x) * y
    ]]></literal>
    <justification jstring="[hyper(462,a,798,a)].">
      <j1 rule="hyper" parents="462 798"/>
    </justification>
  </clause>

  <clause id="800">
    <literal><![CDATA[
      ((x \ (y / z)) * x) * z != u
    ]]></literal>
    <literal><![CDATA[
      (x * z) * T((x * z) \ y,x) = u
    ]]></literal>
    <justification jstring="[para(798(a,1),462(a,1))].">
      <j1 rule="para" parents="798 462"/>
    </justification>
  </clause>

  <clause id="801">
    <literal><![CDATA[
      ((x \ (x / y)) * x) * y = x * (y * T(y \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,478,a(flip),b,799,a),flip(a)].">
      <j1 rule="hyper" parents="65 478 799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="802">
    <literal><![CDATA[
      ((x \ ((x * y) / z)) * x) * z = x * (z * T(z \ y,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,799,a(flip),b,561,a)].">
      <j1 rule="hyper" parents="65 799 561"/>
    </justification>
  </clause>

  <clause id="803">
    <literal><![CDATA[
      x * (y * T(y \ (x \ z),x)) = ((x \ (z / y)) * x) * y
    ]]></literal>
    <justification jstring="[para(10(a,1),802(a,1,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="804">
    <literal><![CDATA[
      x * (x * T(x \ T(y,x),x)) = ((x \ y) * x) * x
    ]]></literal>
    <justification jstring="[para(191(a,1),802(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="191 802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="806">
    <literal><![CDATA[
      T((x \ y) * x,x) = (x \ T(y,x)) * x
    ]]></literal>
    <justification jstring="[hyper(200,a,804,a(flip),b,188,a(flip))].">
      <j1 rule="hyper" parents="200 804 188"/>
    </justification>
  </clause>

  <clause id="807">
    <literal><![CDATA[
      T((x \ y) * x,x) / x = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(113,a,806,a,b,xx)].">
      <j1 rule="hyper" parents="113 806"/>
    </justification>
  </clause>

  <clause id="808">
    <literal><![CDATA[
      x * (T((x \ y) * x,x) / x) = T(y,x)
    ]]></literal>
    <justification jstring="[para(806(a,2),75(a,1,2,1))].">
      <j1 rule="para" parents="806 75"/>
    </justification>
  </clause>

  <clause id="809">
    <literal><![CDATA[
      (x \ T(y,x)) * x != z
    ]]></literal>
    <literal><![CDATA[
      T((x \ y) * x,x) = z
    ]]></literal>
    <justification jstring="[para(807(a,1),211(a,1,1)),flip(b)].">
      <j1 rule="para" parents="807 211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="812">
    <literal><![CDATA[
      T(x * (y / x),x) = x * (T(y,x) / x)
    ]]></literal>
    <justification jstring="[para(81(a,1),808(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="81 808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="816">
    <literal><![CDATA[
      x * (y * T(y \ (x \ y),x)) = ((x \ 1) * x) * y
    ]]></literal>
    <justification jstring="[para(73(a,1),803(a,2,1,1,2))].">
      <j1 rule="para" parents="73 803"/>
    </justification>
  </clause>

  <clause id="817">
    <literal><![CDATA[
      ((x \ (y / (1 / z))) * x) * (1 / z) = x * (T((x \ y) * z,x) / z)
    ]]></literal>
    <justification jstring="[para(594(a,1),803(a,1,2)),flip(a)].">
      <j1 rule="para" parents="594 803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="818">
    <literal><![CDATA[
      x * (K(x \ 1,x) * (x \ y)) = ((x \ 1) * x) * y
    ]]></literal>
    <justification jstring="[para(613(a,2),816(a,1,2))].">
      <j1 rule="para" parents="613 816"/>
    </justification>
  </clause>

  <clause id="819">
    <literal><![CDATA[
      x * (K(x \ 1,x) * (x \ y)) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[para(216(a,2),818(a,2,1))].">
      <j1 rule="para" parents="216 818"/>
    </justification>
  </clause>

  <clause id="820">
    <literal><![CDATA[
      K(x \ 1,x) * (x * y) = x * (K(x \ 1,x) * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),819(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="821">
    <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(820(a,1),195(a,1,2))].">
      <j1 rule="para" parents="820 195"/>
    </justification>
  </clause>

  <clause id="822">
    <literal><![CDATA[
      x * (y * T(y \ (x \ y),z)) = (x * T(x \ 1,z)) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,686,a(flip),b,562,a),flip(a)].">
      <j1 rule="hyper" parents="65 686 562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="823">
    <literal><![CDATA[
      x * (y * L(T(x,y),z,u)) = L(x,z,u) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(291,a,622,a),flip(a)].">
      <j1 rule="hyper" parents="291 622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="824">
    <literal><![CDATA[
      L(x,y,z) * (x * u) = x * (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(198(a,1),823(a,1,2)),flip(a)].">
      <j1 rule="para" parents="198 823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="826">
    <literal><![CDATA[
      x * (L(x,y,z) \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(112,a,71,a(flip),b,824,a),flip(a)].">
      <j1 rule="hyper" parents="112 71 824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="827">
    <literal><![CDATA[
      x * (L(x,y,z) * T(u,x)) = L(x,y,z) * (u * x)
    ]]></literal>
    <justification jstring="[hyper(65,a,188,a(flip),b,824,a),flip(a)].">
      <j1 rule="hyper" parents="65 188 824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="828">
    <literal><![CDATA[
      (x * (L(x,y,z) * T(T(u,L(x,y,z)),x))) \ ((u * L(x,y,z)) * x) = a(L(x,y,z),T(u,L(x,y,z)),x)
    ]]></literal>
    <justification jstring="[para(827(a,2),193(a,1,1))].">
      <j1 rule="para" parents="827 193"/>
    </justification>
  </clause>

  <clause id="829">
    <literal><![CDATA[
      (x * y) * R((y * T(x,y)) \ y,z,u) = y * (T(x,y) * R(T(x,y) \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(406,a,623,a)].">
      <j1 rule="hyper" parents="406 623"/>
    </justification>
  </clause>

  <clause id="830">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ (x \ z),u) = x \ (y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),636(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="10 636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="831">
    <literal><![CDATA[
      (T(x / (y / z),u) * (y / z)) * z = y * T(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[hyper(250,a,321,a(flip),b,637,a),flip(a)].">
      <j1 rule="hyper" parents="250 321 637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="832">
    <literal><![CDATA[
      K(x \ (x / T(y,z)),x) = z \ ((y * T(y \ 1,x)) * z)
    ]]></literal>
    <justification jstring="[para(686(a,1),685(a,2,2))].">
      <j1 rule="para" parents="686 685"/>
    </justification>
  </clause>

  <clause id="833">
    <literal><![CDATA[
      T(x * T(x \ 1,y),z) = K(y \ (y / T(x,z)),y)
    ]]></literal>
    <justification jstring="[hyper(250,a,22,a,b,832,a)].">
      <j1 rule="hyper" parents="250 22 832"/>
    </justification>
  </clause>

  <clause id="834">
    <literal><![CDATA[
      (x * T(x \ 1,y)) * z = z * K(y \ (y / T(x,z)),y)
    ]]></literal>
    <justification jstring="[hyper(116,a,832,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="116 832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="835">
    <literal><![CDATA[
      T(x,y) \ T(x * T(x \ 1,z),y) = T(T(x,y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(112,a,833,a,b,608,a(flip))].">
      <j1 rule="hyper" parents="112 833 608"/>
    </justification>
  </clause>

  <clause id="836">
    <literal><![CDATA[
      K(x \ (x / T(x,y)),x) = T(K(x \ 1,x),y)
    ]]></literal>
    <justification jstring="[para(265(a,1),833(a,1,1)),flip(a)].">
      <j1 rule="para" parents="265 833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="837">
    <literal><![CDATA[
      T(x * T(x \ 1,T(x,y)),y) = (T(x,y) \ 1) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(40,a,22,a(flip),b,835,a),flip(a)].">
      <j1 rule="hyper" parents="40 22 835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="838">
    <literal><![CDATA[
      T(T(x,y) \ 1,x \ T(x,z)) = T(x,y) \ T(x * (x \ 1),y)
    ]]></literal>
    <justification jstring="[para(698(a,1),835(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="698 835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="839">
    <literal><![CDATA[
      ((x * y) / x) * (y * z) = y * (((x * y) / x) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),688(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="840">
    <literal><![CDATA[
      x \ (((y * x) / y) * z) = ((y * x) / y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(424,a,839,a)].">
      <j1 rule="hyper" parents="424 839"/>
    </justification>
  </clause>

  <clause id="841">
    <literal><![CDATA[
      ((x * y) / x) * (y \ 1) = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(408,a,839,a),flip(a)].">
      <j1 rule="hyper" parents="408 839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="842">
    <literal><![CDATA[
      ((x * y) / x) \ (y * z) = y * (((x * y) / x) \ z)
    ]]></literal>
    <justification jstring="[hyper(112,a,131,a(flip),b,839,a)].">
      <j1 rule="hyper" parents="112 131 839"/>
    </justification>
  </clause>

  <clause id="843">
    <literal><![CDATA[
      x * (((y * x) / y) \ 1) = ((y * x) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(112,a,71,a(flip),b,839,a),flip(a)].">
      <j1 rule="hyper" parents="112 71 839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="844">
    <literal><![CDATA[
      (((x * y) * x) / (x * y)) * y = T(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(200,a,12,a(flip),b,839,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="200 12 839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="845">
    <literal><![CDATA[
      (x \ 1) * ((y * ((x \ 1) \ 1)) / y) = x \ ((y * x) / y)
    ]]></literal>
    <justification jstring="[hyper(65,a,542,a,b,841,a)].">
      <j1 rule="hyper" parents="65 542 841"/>
    </justification>
  </clause>

  <clause id="846">
    <literal><![CDATA[
      ((x * y) * x) / (x * y) = T(x * y,x) / y
    ]]></literal>
    <justification jstring="[hyper(123,a,844,a),flip(a)].">
      <j1 rule="hyper" parents="123 844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="847">
    <literal><![CDATA[
      T(T(x * y,x) / y,x * y) = x
    ]]></literal>
    <justification jstring="[para(846(a,1),190(a,1,1))].">
      <j1 rule="para" parents="846 190"/>
    </justification>
  </clause>

  <clause id="848">
    <literal><![CDATA[
      T(T(x * y,x) / y,y) = R(x,y,T(x,y))
    ]]></literal>
    <justification jstring="[para(846(a,1),447(a,1,1))].">
      <j1 rule="para" parents="846 447"/>
    </justification>
  </clause>

  <clause id="849">
    <literal><![CDATA[
      T(T(x,x / y) / y,(x / y) * y) = x / y
    ]]></literal>
    <justification jstring="[para(12(a,1),847(a,1,1,1,1))].">
      <j1 rule="para" parents="12 847"/>
    </justification>
  </clause>

  <clause id="850">
    <literal><![CDATA[
      x \ T(y * x,y) = R(y,x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(293,a,848,a)].">
      <j1 rule="hyper" parents="293 848"/>
    </justification>
  </clause>

  <clause id="851">
    <literal><![CDATA[
      L(R(x,y,T(x,y)),y,x) = x
    ]]></literal>
    <justification jstring="[para(850(a,1),336(a,1,1))].">
      <j1 rule="para" parents="850 336"/>
    </justification>
  </clause>

  <clause id="852">
    <literal><![CDATA[
      R(L(x,y,x),y,T(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(65,a,29,a,b,851,a)].">
      <j1 rule="hyper" parents="65 29 851"/>
    </justification>
  </clause>

  <clause id="853">
    <literal><![CDATA[
      T(T(x,x / y) / y,x) = x / y
    ]]></literal>
    <justification jstring="[para(12(a,1),849(a,1,2))].">
      <j1 rule="para" parents="12 849"/>
    </justification>
  </clause>

  <clause id="854">
    <literal><![CDATA[
      T(T(x,x / (y \ x)) / (y \ x),x) = y
    ]]></literal>
    <justification jstring="[hyper(250,a,76,a(flip),b,853,a),flip(a)].">
      <j1 rule="hyper" parents="250 76 853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="855">
    <literal><![CDATA[
      T(x \ T(y,y / x),y) = T(y / x,x)
    ]]></literal>
    <justification jstring="[para(853(a,1),206(a,1,1)),flip(a)].">
      <j1 rule="para" parents="853 206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="856">
    <literal><![CDATA[
      T(T(x,y) / (y \ x),x) = y
    ]]></literal>
    <justification jstring="[para(76(a,1),854(a,1,1,1,2))].">
      <j1 rule="para" parents="76 854"/>
    </justification>
  </clause>

  <clause id="857">
    <literal><![CDATA[
      T(x,y) / (y \ x) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(227,a,856,a),flip(a)].">
      <j1 rule="hyper" parents="227 856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="858">
    <literal><![CDATA[
      T(T(R(x,y,y \ 1),x * y) / (y \ 1),R(x,y,y \ 1)) = x * y
    ]]></literal>
    <justification jstring="[para(305(a,1),856(a,1,1,2))].">
      <j1 rule="para" parents="305 856"/>
    </justification>
  </clause>

  <clause id="859">
    <literal><![CDATA[
      ((x * y) / x) \ T(x,y) = y \ x
    ]]></literal>
    <justification jstring="[hyper(163,a,857,a)].">
      <j1 rule="hyper" parents="163 857"/>
    </justification>
  </clause>

  <clause id="860">
    <literal><![CDATA[
      ((x * R(y,y \ 1,x)) / x) * ((y \ 1) * x) = T(x,R(y,y \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(116,a,299,a(flip),b,859,a)].">
      <j1 rule="hyper" parents="116 299 859"/>
    </justification>
  </clause>

  <clause id="861">
    <literal><![CDATA[
      ((x * R(1 / y,y,x)) / x) * (y * x) = T(x,R(1 / y,y,x))
    ]]></literal>
    <justification jstring="[hyper(116,a,284,a(flip),b,859,a)].">
      <j1 rule="hyper" parents="116 284 859"/>
    </justification>
  </clause>

  <clause id="862">
    <literal><![CDATA[
      T(x \ T(y,y / x),y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(250,a,106,a(flip),b,855,a),flip(a)].">
      <j1 rule="hyper" parents="250 106 855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="863">
    <literal><![CDATA[
      x \ T(y,y / x) = (y * (x \ y)) / y
    ]]></literal>
    <justification jstring="[hyper(227,a,862,a),flip(a)].">
      <j1 rule="hyper" parents="227 862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="864">
    <literal><![CDATA[
      x * ((y * (x \ y)) / y) = T(y,y / x)
    ]]></literal>
    <justification jstring="[hyper(125,a,863,a)].">
      <j1 rule="hyper" parents="125 863"/>
    </justification>
  </clause>

  <clause id="865">
    <literal><![CDATA[
      (x * y) * L((x \ y) / y,y,x) = T(y,y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(116,a,539,a,b,863,a)].">
      <j1 rule="hyper" parents="116 539 863"/>
    </justification>
  </clause>

  <clause id="866">
    <literal><![CDATA[
      x * ((y * (x \ y)) / y) != z
    ]]></literal>
    <literal><![CDATA[
      T(y,y / x) = z
    ]]></literal>
    <justification jstring="[para(863(a,1),214(a,1,2))].">
      <j1 rule="para" parents="863 214"/>
    </justification>
  </clause>

  <clause id="867">
    <literal><![CDATA[
      (x / y) * ((x * y) / x) = T(x,x / (x / y))
    ]]></literal>
    <justification jstring="[para(79(a,1),864(a,1,2,1,2))].">
      <j1 rule="para" parents="79 864"/>
    </justification>
  </clause>

  <clause id="868">
    <literal><![CDATA[
      T(x,x / (x / T(y,x))) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[para(191(a,1),867(a,1,2)),flip(a)].">
      <j1 rule="para" parents="191 867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="869">
    <literal><![CDATA[
      T(x,x / (x / T(y,x))) * T(y,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(115,a,868,a,b,764,a)].">
      <j1 rule="hyper" parents="115 868 764"/>
    </justification>
  </clause>

  <clause id="870">
    <literal><![CDATA[
      T(x,x / (x / T(y,x))) * (y * x) = x * (x * y)
    ]]></literal>
    <justification jstring="[para(869(a,1),649(a,1,2)),flip(a)].">
      <j1 rule="para" parents="869 649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="871">
    <literal><![CDATA[
      ((x * (x / y)) / x) * y != z
    ]]></literal>
    <literal><![CDATA[
      T(x,x / y) = z
    ]]></literal>
    <justification jstring="[para(541(a,2),866(a,1))].">
      <j1 rule="para" parents="541 866"/>
    </justification>
  </clause>

  <clause id="872">
    <literal><![CDATA[
      ((x * y) / x) * (y \ ((((x * y) / x) \ y) * z)) = L(z,((x * y) / x) \ y,(x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(488,a,840,a),flip(a)].">
      <j1 rule="hyper" parents="488 840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="873">
    <literal><![CDATA[
      T(x,x / (x / T(y,x))) = (x * (x * y)) / (y * x)
    ]]></literal>
    <justification jstring="[hyper(123,a,870,a),flip(a)].">
      <j1 rule="hyper" parents="123 870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="874">
    <literal><![CDATA[
      (x * (x * y)) / (y * x) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,868,a(flip),b,873,a),flip(a)].">
      <j1 rule="hyper" parents="65 868 873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="875">
    <literal><![CDATA[
      R(((x * (x * y)) / x) / y,y,x) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[hyper(532,a,874,a)].">
      <j1 rule="hyper" parents="532 874"/>
    </justification>
  </clause>

  <clause id="876">
    <literal><![CDATA[
      x * (y * ((x \ y) / y)) = T(y,y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(234,a,865,a)].">
      <j1 rule="hyper" parents="234 865"/>
    </justification>
  </clause>

  <clause id="877">
    <literal><![CDATA[
      T(x,x / (y * x)) != z
    ]]></literal>
    <literal><![CDATA[
      y * (x * ((y \ x) / x)) = z
    ]]></literal>
    <justification jstring="[para(865(a,1),234(a,1))].">
      <j1 rule="para" parents="865 234"/>
    </justification>
  </clause>

  <clause id="878">
    <literal><![CDATA[
      (L(1 / x,y,z) * x) * (x \ u) = u * L(u \ (x \ u),y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,428,a(flip),b,742,a),flip(a)].">
      <j1 rule="hyper" parents="65 428 742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="879">
    <literal><![CDATA[
      ((x * (x * y)) / x) / y = T(x,x / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(871,a,755,a),flip(a)].">
      <j1 rule="hyper" parents="871 755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="880">
    <literal><![CDATA[
      T(x,x / (1 / (x \ y))) = ((x * y) / x) / (x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),879(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10 879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="881">
    <literal><![CDATA[
      R(T(x,x / (1 / y)),y,x) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[para(879(a,1),875(a,1,1))].">
      <j1 rule="para" parents="879 875"/>
    </justification>
  </clause>

  <clause id="882">
    <literal><![CDATA[
      (x * ((y * z) / y)) * z = (x * z) * ((y * z) / y)
    ]]></literal>
    <justification jstring="[para(9(a,1),782(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="883">
    <literal><![CDATA[
      (x * y) / ((z * y) / z) = (x / ((z * y) / z)) * y
    ]]></literal>
    <justification jstring="[hyper(422,a,882,a)].">
      <j1 rule="hyper" parents="422 882"/>
    </justification>
  </clause>

  <clause id="884">
    <literal><![CDATA[
      (1 / x) * ((y * x) / y) = ((y * x) / y) / x
    ]]></literal>
    <justification jstring="[hyper(113,a,77,a(flip),b,882,a),flip(a)].">
      <j1 rule="hyper" parents="113 77 882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="886">
    <literal><![CDATA[
      ((x / y) * y) * ((x * y) / x) = T(x,x / (x / y)) * y
    ]]></literal>
    <justification jstring="[para(867(a,1),882(a,1,1)),flip(a)].">
      <j1 rule="para" parents="867 882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="887">
    <literal><![CDATA[
      (1 / x) * ((y * ((z / x) \ z)) / y) = ((y * x) / y) / x
    ]]></literal>
    <justification jstring="[para(167(a,2),884(a,1,2,1))].">
      <j1 rule="para" parents="167 884"/>
    </justification>
  </clause>

  <clause id="888">
    <literal><![CDATA[
      T(x,x / (x / y)) * y = x * ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(253,a,886,a),flip(a)].">
      <j1 rule="hyper" parents="253 886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="889">
    <literal><![CDATA[
      T(x,x / (x / y)) * (x \ y) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(656,a,888,a)].">
      <j1 rule="hyper" parents="656 888"/>
    </justification>
  </clause>

  <clause id="891">
    <literal><![CDATA[
      ((x * y) / x) / (x \ y) = T(x,x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(123,a,889,a)].">
      <j1 rule="hyper" parents="123 889"/>
    </justification>
  </clause>

  <clause id="892">
    <literal><![CDATA[
      T(x,x / (1 / (x \ y))) = T(x,x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(65,a,880,a,b,891,a)].">
      <j1 rule="hyper" parents="65 880 891"/>
    </justification>
  </clause>

  <clause id="893">
    <literal><![CDATA[
      T(x,x / (x / (x * y))) = T(x,x / (1 / y))
    ]]></literal>
    <justification jstring="[para(9(a,1),892(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="9 892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="894">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (z * y),u) = (T(z / x,u) * x) * y
    ]]></literal>
    <justification jstring="[para(11(a,1),797(a,1,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11 797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="895">
    <literal><![CDATA[
      (x * T(x \ (y / z),u)) * z = (x * z) * T((x * z) \ y,u)
    ]]></literal>
    <justification jstring="[para(321(a,1),797(a,1,1))].">
      <j1 rule="para" parents="321 797"/>
    </justification>
  </clause>

  <clause id="896">
    <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),830(a,1,1))].">
      <j1 rule="para" parents="22 830"/>
    </justification>
  </clause>

  <clause id="897">
    <literal><![CDATA[
      ((x / y) * T((x / y) \ z,u)) * y = x * T(x \ (z * y),u)
    ]]></literal>
    <justification jstring="[para(321(a,1),831(a,1,1))].">
      <j1 rule="para" parents="321 831"/>
    </justification>
  </clause>

  <clause id="898">
    <literal><![CDATA[
      T(T(x,y) \ 1,x \ T(x,z)) = T(x,y) \ T(1,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),838(a,2,2,1))].">
      <j1 rule="para" parents="10 838"/>
    </justification>
  </clause>

  <clause id="900">
    <literal><![CDATA[
      T(T(x,y) \ 1,x \ T(x,z)) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[para(174(a,1),898(a,2,2))].">
      <j1 rule="para" parents="174 898"/>
    </justification>
  </clause>

  <clause id="902">
    <literal><![CDATA[
      (((x * (1 / y)) / x) * y) * x = T(x,R(1 / y,y,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,551,a(flip),b,861,a)].">
      <j1 rule="hyper" parents="65 551 861"/>
    </justification>
  </clause>

  <clause id="903">
    <literal><![CDATA[
      (x * ((y * (x \ 1)) / y)) * y = T(y,R(1 / x,x,y))
    ]]></literal>
    <justification jstring="[para(541(a,1),902(a,1,1))].">
      <j1 rule="para" parents="541 902"/>
    </justification>
  </clause>

  <clause id="904">
    <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(648(a,1),903(a,1,1,2,1))].">
      <j1 rule="para" parents="648 903"/>
    </justification>
  </clause>

  <clause id="905">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) * (x \ u) = u * L(u \ (x \ u),y,z)
    ]]></literal>
    <justification jstring="[para(428(a,1),878(a,1,1))].">
      <j1 rule="para" parents="428 878"/>
    </justification>
  </clause>

  <clause id="906">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (z * y),u) = (x * T(x \ z,u)) * y
    ]]></literal>
    <justification jstring="[para(321(a,1),894(a,2,1))].">
      <j1 rule="para" parents="321 894"/>
    </justification>
  </clause>

  <clause id="907">
    <literal><![CDATA[
      (x * T(x \ (y / z),u)) * z = x * (z * T(z \ (x \ y),u))
    ]]></literal>
    <justification jstring="[hyper(250,a,562,a(flip),b,895,a),flip(a)].">
      <j1 rule="hyper" parents="250 562 895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="908">
    <literal><![CDATA[
      (x * y) * T((x * y) \ z,x) != u
    ]]></literal>
    <literal><![CDATA[
      ((x \ (z / y)) * x) * y = u
    ]]></literal>
    <justification jstring="[para(895(a,1),406(a,1))].">
      <j1 rule="para" parents="895 406"/>
    </justification>
  </clause>

  <clause id="909">
    <literal><![CDATA[
      (x * (y * T(y \ (x \ (z * u)),w))) / u = ((x * y) / u) * T(((x * y) / u) \ z,w)
    ]]></literal>
    <justification jstring="[hyper(113,a,562,a(flip),b,897,a)].">
      <j1 rule="hyper" parents="113 562 897"/>
    </justification>
  </clause>

  <clause id="910">
    <literal><![CDATA[
      (x / y) * T((x / y) \ z,x) = ((x \ (z * y)) * x) / y
    ]]></literal>
    <justification jstring="[hyper(113,a,104,a(flip),b,897,a),flip(a)].">
      <j1 rule="hyper" parents="113 104 897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="911">
    <literal><![CDATA[
      ((x / y) * T((x / y) \ 1,z)) * y = x * T(x \ y,z)
    ]]></literal>
    <justification jstring="[para(7(a,1),897(a,2,2,1,2))].">
      <j1 rule="para" parents="7 897"/>
    </justification>
  </clause>

  <clause id="912">
    <literal><![CDATA[
      (x / y) * T((x / y) \ 1,z) = (x * T(x \ y,z)) / y
    ]]></literal>
    <justification jstring="[hyper(123,a,911,a),flip(a)].">
      <j1 rule="hyper" parents="123 911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="913">
    <literal><![CDATA[
      K((x / y) \ 1,x / y) * y = x * T(x \ y,x / y)
    ]]></literal>
    <justification jstring="[para(265(a,1),911(a,1,1))].">
      <j1 rule="para" parents="265 911"/>
    </justification>
  </clause>

  <clause id="914">
    <literal><![CDATA[
      K(x \ (x / (y / z)),x) = (y * T(y \ z,x)) / z
    ]]></literal>
    <justification jstring="[hyper(65,a,608,a,b,912,a)].">
      <j1 rule="hyper" parents="65 608 912"/>
    </justification>
  </clause>

  <clause id="915">
    <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),914(a,1,1,2))].">
      <j1 rule="para" parents="11 914"/>
    </justification>
  </clause>

  <clause id="916">
    <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),914(a,1,1,2,2))].">
      <j1 rule="para" parents="20 914"/>
    </justification>
  </clause>

  <clause id="917">
    <literal><![CDATA[
      K((x / (y * x)) \ 1,x / (y * x)) * (y * x) = T(y,x / (y * x)) * x
    ]]></literal>
    <justification jstring="[hyper(250,a,320,a(flip),b,913,a),flip(a)].">
      <j1 rule="hyper" parents="250 320 913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="918">
    <literal><![CDATA[
      x * (y * T(y \ (x \ (z * y)),u)) = (x * T(x \ z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,562,a(flip),b,906,a)].">
      <j1 rule="hyper" parents="65 562 906"/>
    </justification>
  </clause>

  <clause id="925">
    <literal><![CDATA[
      x * ((y \ z) * T((y \ z) \ (x \ z),u)) = (x * T(x \ y,u)) * (y \ z)
    ]]></literal>
    <justification jstring="[para(76(a,1),907(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="76 907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="926">
    <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(907(a,1),236(a,1,2))].">
      <j1 rule="para" parents="907 236"/>
    </justification>
  </clause>

  <clause id="927">
    <literal><![CDATA[
      x * (y * T(y \ (x \ z),x)) != u
    ]]></literal>
    <literal><![CDATA[
      ((x \ (z / y)) * x) * y = u
    ]]></literal>
    <justification jstring="[para(907(a,1),406(a,1))].">
      <j1 rule="para" parents="907 406"/>
    </justification>
  </clause>

  <clause id="928">
    <literal><![CDATA[
      (x \ 1) * (y * T(y \ ((x \ 1) \ z),u)) = (x \ T(x * (z / y),u)) * y
    ]]></literal>
    <justification jstring="[para(568(a,1),907(a,1,1)),flip(a)].">
      <j1 rule="para" parents="568 907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="929">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,y)) * y = x * (y * T(y \ (x \ x),y))
    ]]></literal>
    <justification jstring="[para(605(a,2),907(a,1,1))].">
      <j1 rule="para" parents="605 907"/>
    </justification>
  </clause>

  <clause id="931">
    <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(95(a,2),918(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="95 918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="932">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,y)) * y = x * (y * T(y \ 1,y))
    ]]></literal>
    <justification jstring="[para(68(a,1),929(a,2,2,2,1,2))].">
      <j1 rule="para" parents="68 929"/>
    </justification>
  </clause>

  <clause id="934">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,y)) * y = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(265(a,1),932(a,2,2))].">
      <j1 rule="para" parents="265 932"/>
    </justification>
  </clause>

  <clause id="935">
    <literal><![CDATA[
      (R(x,y \ 1,y) / y) * K(y \ 1,y) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(37,a,372,a(flip),b,934,a),flip(a)].">
      <j1 rule="hyper" parents="37 372 934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="936">
    <literal><![CDATA[
      R(a(x,y,z) * u,L(w,u,a(x,y,z)),v5) = ((a(x,y,z) * (u * w)) * v5) / (w * v5)
    ]]></literal>
    <justification jstring="[para(128(a,1),340(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="128 340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="937">
    <literal><![CDATA[
      T(R(L(x / y,z,u),y,w),y * w) = L((y * w) \ (x * w),z,u)
    ]]></literal>
    <justification jstring="[para(29(a,2),452(a,1,1))].">
      <j1 rule="para" parents="29 452"/>
    </justification>
  </clause>

  <clause id="938">
    <literal><![CDATA[
      x * ((x \ y) * ((z * ((x \ y) \ u)) / z)) = y * ((z * (y \ (x * u))) / z)
    ]]></literal>
    <justification jstring="[hyper(116,a,550,a(flip),b,94,a),flip(a)].">
      <j1 rule="hyper" parents="116 550 94"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="940">
    <literal><![CDATA[
      x * (y \ T(y * (x \ z),x)) != u
    ]]></literal>
    <literal><![CDATA[
      ((x \ (z / (y \ 1))) * x) * (y \ 1) = u
    ]]></literal>
    <justification jstring="[para(568(a,1),927(a,1,2))].">
      <j1 rule="para" parents="568 927"/>
    </justification>
  </clause>

  <clause id="941">
    <literal><![CDATA[
      (x * y) * L((x * y) \ (z * y),u,w) = (L(z / x,u,w) * x) * y
    ]]></literal>
    <justification jstring="[para(937(a,1),229(a,1,2))].">
      <j1 rule="para" parents="937 229"/>
    </justification>
  </clause>

  <clause id="942">
    <literal><![CDATA[
      (x * y) * R((x * y) \ (z * y),u,w) = (R(z / x,u,w) * x) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,433,a(flip),b,620,a)].">
      <j1 rule="hyper" parents="65 433 620"/>
    </justification>
  </clause>

  <clause id="943">
    <literal><![CDATA[
      (x * (y * z)) * (a(x,y,z) * R(a(x,y,z) \ ((x * (y * z)) \ u),w,v5)) = ((x * y) * z) * R(((x * (y * z)) * a(x,y,z)) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(84(a,1),624(a,1,1)),flip(a)].">
      <j1 rule="para" parents="84 624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="944">
    <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(675(a,1),296(a,1))].">
      <j1 rule="para" parents="675 296"/>
    </justification>
  </clause>

  <clause id="945">
    <literal><![CDATA[
      R(x,y,y \ 1) * R(L(T(y,y \ 1),y \ 1,x * y),z,u) = x * ((x \ R(x,y,y \ 1)) * R((x \ R(x,y,y \ 1)) \ y,z,u))
    ]]></literal>
    <justification jstring="[para(793(a,2),744(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="793 744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="946">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ 1,z,u) = x \ (y * L(y \ x,z,u))
    ]]></literal>
    <justification jstring="[para(8(a,1),746(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="8 746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="947">
    <literal><![CDATA[
      (x / y) \ (x * ((z * (x \ (x / y))) / z)) = y * ((z * (y \ 1)) / z)
    ]]></literal>
    <justification jstring="[hyper(118,a,751,a)].">
      <j1 rule="hyper" parents="118 751"/>
    </justification>
  </clause>

  <clause id="948">
    <literal><![CDATA[
      ((x * ((y \ z) / (y * (y \ z)))) / x) * z = (((x * (1 / y)) / x) * y) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(259,a,752,a)].">
      <j1 rule="hyper" parents="259 752"/>
    </justification>
  </clause>

  <clause id="949">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ y)) / z) = (((z * (1 / x)) / z) * x) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,541,a(flip),b,752,a)].">
      <j1 rule="hyper" parents="65 541 752"/>
    </justification>
  </clause>

  <clause id="950">
    <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(100(a,1),752(a,1,2))].">
      <j1 rule="para" parents="100 752"/>
    </justification>
  </clause>

  <clause id="951">
    <literal><![CDATA[
      T(T(x,x * y) * y,R(x,y,y \ 1)) = x * y
    ]]></literal>
    <justification jstring="[para(393(a,1),858(a,1,1))].">
      <j1 rule="para" parents="393 858"/>
    </justification>
  </clause>

  <clause id="952">
    <literal><![CDATA[
      T(T(T(x,x * y) * y,z),R(x,y,y \ 1)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(951(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="951 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="953">
    <literal><![CDATA[
      T((x / y) * y,T(x / y,y)) = T(x,R(x / y,y,y \ 1))
    ]]></literal>
    <justification jstring="[para(759(a,1),952(a,1,1)),flip(a)].">
      <j1 rule="para" parents="759 952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="954">
    <literal><![CDATA[
      T((x / y) * y,T(x / y,y)) = T(x,x * (y \ 1))
    ]]></literal>
    <justification jstring="[para(377(a,1),953(a,2,2))].">
      <j1 rule="para" parents="377 953"/>
    </justification>
  </clause>

  <clause id="955">
    <literal><![CDATA[
      T(x,T(x / y,y)) = T(x,x * (y \ 1))
    ]]></literal>
    <justification jstring="[para(12(a,1),954(a,1,1))].">
      <j1 rule="para" parents="12 954"/>
    </justification>
  </clause>

  <clause id="956">
    <literal><![CDATA[
      T(x,x * (y \ 1)) = T(x,y \ x)
    ]]></literal>
    <justification jstring="[para(106(a,1),955(a,1,2)),flip(a)].">
      <j1 rule="para" parents="106 955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="957">
    <literal><![CDATA[
      (((x * y) / x) * (y \ 1)) * x = T(x,R(y,y \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(554,a,860,a)].">
      <j1 rule="hyper" parents="554 860"/>
    </justification>
  </clause>

  <clause id="958">
    <literal><![CDATA[
      (x \ ((y * x) / y)) * y = T(y,R(x,x \ 1,y))
    ]]></literal>
    <justification jstring="[para(841(a,1),957(a,1,1))].">
      <j1 rule="para" parents="841 957"/>
    </justification>
  </clause>

  <clause id="959">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) / x != z
    ]]></literal>
    <literal><![CDATA[
      y \ ((x * y) / x) = z
    ]]></literal>
    <justification jstring="[para(958(a,1),212(a,1,1)),flip(b)].">
      <j1 rule="para" parents="958 212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="960">
    <literal><![CDATA[
      (x * y) * L((x * y) \ y,z,u) = (L(1 / x,z,u) * x) * y
    ]]></literal>
    <justification jstring="[para(7(a,1),941(a,1,2,1,2))].">
      <j1 rule="para" parents="7 941"/>
    </justification>
  </clause>

  <clause id="961">
    <literal><![CDATA[
      (L((x * y) / x,z,u) * x) * y = (x * y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),941(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="963">
    <literal><![CDATA[
      (x * y) * L((x * y) \ (z * y),u,w) = (x * L(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[para(428(a,1),941(a,2,1))].">
      <j1 rule="para" parents="428 941"/>
    </justification>
  </clause>

  <clause id="964">
    <literal><![CDATA[
      (x * L(y,z,u)) * y = (x * y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(429(a,1),961(a,1,1))].">
      <j1 rule="para" parents="429 961"/>
    </justification>
  </clause>

  <clause id="965">
    <literal><![CDATA[
      (x * y) / L(y,z,u) = (x / L(y,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(422,a,964,a)].">
      <j1 rule="hyper" parents="422 964"/>
    </justification>
  </clause>

  <clause id="968">
    <literal><![CDATA[
      (1 / x) * L(x,y,z) = L(x,y,z) / x
    ]]></literal>
    <justification jstring="[hyper(113,a,77,a(flip),b,964,a),flip(a)].">
      <j1 rule="hyper" parents="113 77 964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="970">
    <literal><![CDATA[
      ((x * y) * z) * L(z,y,x) = (x * (y * z)) * z
    ]]></literal>
    <justification jstring="[para(93(a,1),964(a,1,1)),flip(a)].">
      <j1 rule="para" parents="93 964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="971">
    <literal><![CDATA[
      (L(x,y,z) / x) / L(x,y,z) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(123,a,968,a)].">
      <j1 rule="hyper" parents="123 968"/>
    </justification>
  </clause>

  <clause id="974">
    <literal><![CDATA[
      (x * y) * L((x * y) \ y,z,u) = (x * L(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[para(428(a,1),960(a,2,1))].">
      <j1 rule="para" parents="428 960"/>
    </justification>
  </clause>

  <clause id="975">
    <literal><![CDATA[
      x * (y * L(y \ (x \ y),z,u)) = (x * L(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,621,a(flip),b,974,a)].">
      <j1 rule="hyper" parents="65 621 974"/>
    </justification>
  </clause>

  <clause id="976">
    <literal><![CDATA[
      T(x,x * L(x \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(200,a,556,a(flip),b,974,a(flip))].">
      <j1 rule="hyper" parents="200 556 974"/>
    </justification>
  </clause>

  <clause id="977">
    <literal><![CDATA[
      T(x \ y,(x \ y) * (y \ x)) = x \ y
    ]]></literal>
    <justification jstring="[para(275(a,1),976(a,1,2,2))].">
      <j1 rule="para" parents="275 976"/>
    </justification>
  </clause>

  <clause id="978">
    <literal><![CDATA[
      T(x,x * (y \ (y / x))) = x
    ]]></literal>
    <justification jstring="[para(280(a,1),976(a,1,2,2))].">
      <j1 rule="para" parents="280 976"/>
    </justification>
  </clause>

  <clause id="979">
    <literal><![CDATA[
      (L(x \ 1,y,z) * x) / L(x \ 1,y,z) = L(x,L(x \ 1,y,z),x)
    ]]></literal>
    <justification jstring="[para(976(a,1),445(a,1,1,2))].">
      <j1 rule="para" parents="976 445"/>
    </justification>
  </clause>

  <clause id="980">
    <literal><![CDATA[
      ((x \ (x / y)) * y) / (x \ (x / y)) = L(y,x \ (x / y),y)
    ]]></literal>
    <justification jstring="[para(978(a,1),445(a,1,1,2))].">
      <j1 rule="para" parents="978 445"/>
    </justification>
  </clause>

  <clause id="981">
    <literal><![CDATA[
      L(x \ y,y \ x,x \ y) * (y \ x) = (y \ x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(977(a,1),442(a,1,2)),flip(a)].">
      <j1 rule="para" parents="977 442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="982">
    <literal><![CDATA[
      L(x \ y,y \ x,x \ y) = L(1 / (y \ x),y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(37,a,533,a,b,981,a),flip(a)].">
      <j1 rule="hyper" parents="37 533 981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="983">
    <literal><![CDATA[
      x \ (y * L(y \ x,x \ y,y \ x)) != (x \ y) * z
    ]]></literal>
    <literal><![CDATA[
      1 / (x \ y) = z
    ]]></literal>
    <justification jstring="[para(982(a,2),489(a,1,2,2)),flip(b)].">
      <j1 rule="para" parents="982 489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="984">
    <literal><![CDATA[
      (x * y) * R((x * y) \ (z * y),u,w) = (x * R(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[para(433(a,1),942(a,2,1))].">
      <j1 rule="para" parents="433 942"/>
    </justification>
  </clause>

  <clause id="985">
    <literal><![CDATA[
      (x * y) * R((x * y) \ ((x * z) * y),u,w) = (x * R(z,u,w)) * y
    ]]></literal>
    <justification jstring="[para(434(a,1),942(a,2,1))].">
      <j1 rule="para" parents="434 942"/>
    </justification>
  </clause>

  <clause id="986">
    <literal><![CDATA[
      (x / y) \ (x * ((x / y) / x)) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[para(10(a,1),947(a,1,2,2,1))].">
      <j1 rule="para" parents="10 947"/>
    </justification>
  </clause>

  <clause id="987">
    <literal><![CDATA[
      K(x,(x / y) / x) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(330,a,986,a)].">
      <j1 rule="hyper" parents="330 986"/>
    </justification>
  </clause>

  <clause id="988">
    <literal><![CDATA[
      K(x,(x / (y \ 1)) / x) = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(250,a,845,a(flip),b,987,a),flip(a)].">
      <j1 rule="hyper" parents="250 845 987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="989">
    <literal><![CDATA[
      (x \ y) * ((y * ((x \ y) \ 1)) / y) = K(y,x / y)
    ]]></literal>
    <justification jstring="[para(76(a,1),987(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="76 987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="990">
    <literal><![CDATA[
      x * ((T(x,y) * (x \ 1)) / T(x,y)) = K(T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[para(600(a,1),987(a,1,2)),flip(a)].">
      <j1 rule="para" parents="600 987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="991">
    <literal><![CDATA[
      x \ ((L(x \ 1,y,z) * x) / L(x \ 1,y,z)) = K(L(x \ 1,y,z),1 / (x \ 1))
    ]]></literal>
    <justification jstring="[para(971(a,1),988(a,1,2)),flip(a)].">
      <j1 rule="para" parents="971 988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="992">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ y)) / z) = (x * ((z * (x \ 1)) / z)) * y
    ]]></literal>
    <justification jstring="[para(541(a,1),949(a,2,1))].">
      <j1 rule="para" parents="541 949"/>
    </justification>
  </clause>

  <clause id="994">
    <literal><![CDATA[
      x * (y * L(y \ (x \ (z * y)),u,w)) = (x * L(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,621,a(flip),b,963,a)].">
      <j1 rule="hyper" parents="65 621 963"/>
    </justification>
  </clause>

  <clause id="995">
    <literal><![CDATA[
      ((x * y) * L((x * y) \ x,z,u)) * y = (x * y) * (y * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,556,a(flip),b,963,a),flip(a)].">
      <j1 rule="hyper" parents="65 556 963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="996">
    <literal><![CDATA[
      x * L(x \ (x \ (y * x)),z,u) = T(x * L(x \ y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(200,a,963,a(flip),b,621,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="200 963 621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="997">
    <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),996(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="22 996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="998">
    <literal><![CDATA[
      x \ T(x * L(x \ y,z,u),x) = L(x \ T(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(112,a,997,a,b,xx)].">
      <j1 rule="hyper" parents="112 997"/>
    </justification>
  </clause>

  <clause id="999">
    <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),998(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1002">
    <literal><![CDATA[
      x * (y * R(y \ (x \ (z * y)),u,w)) = (x * R(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,624,a(flip),b,984,a)].">
      <j1 rule="hyper" parents="65 624 984"/>
    </justification>
  </clause>

  <clause id="1003">
    <literal><![CDATA[
      (x \ (y * x)) * R((x \ (y * x)) \ x,z,u) = T(y * R(y \ x,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(200,a,984,a(flip),b,744,a),flip(a)].">
      <j1 rule="hyper" parents="200 984 744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1004">
    <literal><![CDATA[
      x * R(x \ (x \ (y * x)),z,u) = T(x * R(x \ y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(200,a,984,a(flip),b,624,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="200 984 624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1006">
    <literal><![CDATA[
      (x * y) * R((x * y) \ y,z,u) = (x * R(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[para(7(a,1),984(a,1,2,1,2))].">
      <j1 rule="para" parents="7 984"/>
    </justification>
  </clause>

  <clause id="1007">
    <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),1004(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="22 1004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1008">
    <literal><![CDATA[
      T(x * R(x \ y,z,u),x) / x = R(T(y,x) / x,z,u)
    ]]></literal>
    <justification jstring="[hyper(113,a,1007,a,b,433,a)].">
      <j1 rule="hyper" parents="113 1007 433"/>
    </justification>
  </clause>

  <clause id="1009">
    <literal><![CDATA[
      x \ T(x * R(x \ y,z,u),x) = R(x \ T(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(112,a,1007,a,b,xx)].">
      <j1 rule="hyper" parents="112 1007"/>
    </justification>
  </clause>

  <clause id="1010">
    <literal><![CDATA[
      T(x * R(x \ 1,y,z),x) = x * R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(174(a,1),1007(a,2,2,1,2))].">
      <j1 rule="para" parents="174 1007"/>
    </justification>
  </clause>

  <clause id="1011">
    <literal><![CDATA[
      T(x,x * R(x \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(56,a,1010,a)].">
      <j1 rule="hyper" parents="56 1010"/>
    </justification>
  </clause>

  <clause id="1012">
    <literal><![CDATA[
      T(x * ((x * R(x \ 1,y,z)) / x),x) = x * ((x * R(x \ 1,y,z)) / x)
    ]]></literal>
    <justification jstring="[para(1010(a,1),812(a,2,2,1))].">
      <j1 rule="para" parents="1010 812"/>
    </justification>
  </clause>

  <clause id="1013">
    <literal><![CDATA[
      T(x / y,(y / x) * (x / y)) = x / y
    ]]></literal>
    <justification jstring="[para(507(a,1),1011(a,1,2))].">
      <j1 rule="para" parents="507 1011"/>
    </justification>
  </clause>

  <clause id="1014">
    <literal><![CDATA[
      T(x / (y * x),y * (x / (y * x))) = x / (y * x)
    ]]></literal>
    <justification jstring="[para(11(a,1),1013(a,1,2,1))].">
      <j1 rule="para" parents="11 1013"/>
    </justification>
  </clause>

  <clause id="1015">
    <literal><![CDATA[
      R(x / (y * x),y,x / (y * x)) = T(x / (y * x),y)
    ]]></literal>
    <justification jstring="[para(1014(a,1),513(a,1,1))].">
      <j1 rule="para" parents="1014 513"/>
    </justification>
  </clause>

  <clause id="1016">
    <literal><![CDATA[
      R(x / (y * x),y,x / (y * x)) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(250,a,454,a(flip),b,1015,a),flip(a)].">
      <j1 rule="hyper" parents="250 454 1015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1017">
    <literal><![CDATA[
      R(1 / x,x,y / (x * y)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(558,a,1016,a)].">
      <j1 rule="hyper" parents="558 1016"/>
    </justification>
  </clause>

  <clause id="1018">
    <literal><![CDATA[
      R(1 / x,x,1 / x) = x \ 1
    ]]></literal>
    <justification jstring="[para(8(a,1),1017(a,1,3,2))].">
      <j1 rule="para" parents="8 1017"/>
    </justification>
  </clause>

  <clause id="1020">
    <literal><![CDATA[
      R(x / (y * x),y,1 / y) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(1018(a,1),288(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1018 288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1021">
    <literal><![CDATA[
      R(x \ 1,x,y) \ (((y / (x * y)) * x) * (1 / x)) = x * (1 / x)
    ]]></literal>
    <justification jstring="[para(1020(a,1),159(a,1,1))].">
      <j1 rule="para" parents="1020 159"/>
    </justification>
  </clause>

  <clause id="1022">
    <literal><![CDATA[
      R(T(x * y,x) / x,z,u) = T(x * R(y,z,u),x) / x
    ]]></literal>
    <justification jstring="[para(9(a,1),1008(a,1,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 1008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1023">
    <literal><![CDATA[
      x * (y * R(y \ (x \ y),z,u)) = (x * R(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,624,a(flip),b,1006,a)].">
      <j1 rule="hyper" parents="65 624 1006"/>
    </justification>
  </clause>

  <clause id="1024">
    <literal><![CDATA[
      (x * R(y,z,u)) * y = (x * y) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),985(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1025">
    <literal><![CDATA[
      ((x / R(y,z,u)) * y) * R(y,z,u) = x * y
    ]]></literal>
    <justification jstring="[hyper(253,a,1024,a),flip(a)].">
      <j1 rule="hyper" parents="253 1024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1026">
    <literal><![CDATA[
      (x * R(y,z,u)) \ ((x * y) * R(y,z,u)) = y
    ]]></literal>
    <justification jstring="[hyper(118,a,1024,a)].">
      <j1 rule="hyper" parents="118 1024"/>
    </justification>
  </clause>

  <clause id="1027">
    <literal><![CDATA[
      (1 / x) * R(x,y,z) = R(x,y,z) / x
    ]]></literal>
    <justification jstring="[hyper(113,a,77,a(flip),b,1024,a),flip(a)].">
      <j1 rule="hyper" parents="113 77 1024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1028">
    <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(1027(a,1),201(a,2)),flip(a)].">
      <j1 rule="para" parents="1027 201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1029">
    <literal><![CDATA[
      (x * y) / R(y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      (x / R(y,z,u)) * y = w
    ]]></literal>
    <justification jstring="[para(1025(a,1),212(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1025 212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1030">
    <literal><![CDATA[
      T(R(x,y,R(x,z,u)),y * R(x,z,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1026(a,1),511(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1026 511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1031">
    <literal><![CDATA[
      (x * R(y,z,u)) * T(y,x) = (y * x) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(1030(a,1),229(a,1,2))].">
      <j1 rule="para" parents="1030 229"/>
    </justification>
  </clause>

  <clause id="1032">
    <literal><![CDATA[
      (x * (((x * y) * (x \ 1)) / (x * y))) * y = (x * y) * (y / (x * y))
    ]]></literal>
    <justification jstring="[para(10(a,1),992(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1034">
    <literal><![CDATA[
      ((x * (1 / y)) * R(L(y,1 / y,x),z,u)) * w = (x * (1 / y)) * (w * R(w \ ((x * (1 / y)) \ (x * w)),z,u))
    ]]></literal>
    <justification jstring="[para(186(a,2),1002(a,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="186 1002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1037">
    <literal><![CDATA[
      ((a(x,y,z) * R(u,w,v5)) * (w * v5)) / ((u * w) * v5) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(250,a,523,a(flip),b,369,a),flip(a)].">
      <j1 rule="hyper" parents="250 523 369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1038">
    <literal><![CDATA[
      (x * (y * (x * z))) / (L(y,z,x) * (x * z)) = R(x,z,T(y,x * z))
    ]]></literal>
    <justification jstring="[para(426(a,1),738(a,1,2))].">
      <j1 rule="para" parents="426 738"/>
    </justification>
  </clause>

  <clause id="1039">
    <literal><![CDATA[
      (T(x,y) * ((T(x,y) \ x) / x)) * x = T(x,(1 * x) / (x * T(x,y)))
    ]]></literal>
    <justification jstring="[para(381(a,1),904(a,2,2))].">
      <j1 rule="para" parents="381 904"/>
    </justification>
  </clause>

  <clause id="1040">
    <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),1039(a,2,2,1))].">
      <j1 rule="para" parents="7 1039"/>
    </justification>
  </clause>

  <clause id="1041">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ (u * y))) / z) = (((z * (u / x)) / z) * x) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,541,a(flip),b,753,a)].">
      <j1 rule="hyper" parents="65 541 753"/>
    </justification>
  </clause>

  <clause id="1042">
    <literal><![CDATA[
      ((x * ((y * z) / (u * z))) / x) * (u * z) = (u * ((x * (u \ y)) / x)) * z
    ]]></literal>
    <justification jstring="[para(541(a,1),753(a,2,1))].">
      <j1 rule="para" parents="541 753"/>
    </justification>
  </clause>

  <clause id="1043">
    <literal><![CDATA[
      (((x * ((y / z) / u)) / x) * u) * z = (u * z) * ((x * ((u * z) \ y)) / x)
    ]]></literal>
    <justification jstring="[hyper(250,a,541,a(flip),b,754,a),flip(a)].">
      <j1 rule="hyper" parents="250 541 754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1044">
    <literal><![CDATA[
      (x \ T(x * (y / z),z)) * z = (x \ 1) * ((z \ ((x \ 1) \ y)) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,188,a(flip),b,928,a),flip(a)].">
      <j1 rule="hyper" parents="65 188 928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1045">
    <literal><![CDATA[
      T((x \ (x * (y / x))) * x,x) = (x \ 1) * ((x \ ((x \ 1) \ y)) * x)
    ]]></literal>
    <justification jstring="[hyper(809,a,1044,a)].">
      <j1 rule="hyper" parents="809 1044"/>
    </justification>
  </clause>

  <clause id="1046">
    <literal><![CDATA[
      T(x,y) = (y \ 1) * ((y \ ((y \ 1) \ x)) * y)
    ]]></literal>
    <justification jstring="[para(81(a,1),1045(a,1,1))].">
      <j1 rule="para" parents="81 1045"/>
    </justification>
  </clause>

  <clause id="1047">
    <literal><![CDATA[
      (x \ 1) * ((x \ y) * x) = T((x \ 1) * y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),1046(a,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9 1046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1048">
    <literal><![CDATA[
      ((x \ 1) * y) \ T((x \ 1) * y,x) = L(K(x \ y,x),y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(112,a,1047,a(flip),b,344,a)].">
      <j1 rule="hyper" parents="112 1047 344"/>
    </justification>
  </clause>

  <clause id="1049">
    <literal><![CDATA[
      x * K(y,(y / (x \ z)) / y) = z * ((y * (z \ (x * 1))) / y)
    ]]></literal>
    <justification jstring="[para(987(a,2),938(a,1,2))].">
      <j1 rule="para" parents="987 938"/>
    </justification>
  </clause>

  <clause id="1050">
    <literal><![CDATA[
      x * K(y,(y / (x \ z)) / y) = z * ((y * (z \ x)) / y)
    ]]></literal>
    <justification jstring="[para(8(a,1),1049(a,2,2,1,2,2))].">
      <j1 rule="para" parents="8 1049"/>
    </justification>
  </clause>

  <clause id="1051">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ y)) / z) = y * K(z,(z / T(x,y)) / z)
    ]]></literal>
    <justification jstring="[para(22(a,2),1050(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="22 1050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1052">
    <literal><![CDATA[
      T(x * ((y * (x \ 1)) / y),z) = K(y,(y / T(x,z)) / y)
    ]]></literal>
    <justification jstring="[hyper(200,a,992,a(flip),b,1051,a(flip))].">
      <j1 rule="hyper" parents="200 992 1051"/>
    </justification>
  </clause>

  <clause id="1053">
    <literal><![CDATA[
      T(x,y) * ((z * (T(x,y) \ 1)) / z) = T(x * ((z * (x \ 1)) / z),y)
    ]]></literal>
    <justification jstring="[hyper(250,a,987,a(flip),b,1052,a)].">
      <j1 rule="hyper" parents="250 987 1052"/>
    </justification>
  </clause>

  <clause id="1054">
    <literal><![CDATA[
      K(x,(x / T(y \ x,z)) / x) = T(K(x,y / x),z)
    ]]></literal>
    <justification jstring="[para(989(a,1),1052(a,1,1)),flip(a)].">
      <j1 rule="para" parents="989 1052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1055">
    <literal><![CDATA[
      T(K(x,y / x),K(y / x,z)) = K(x,(x / (y \ x)) / x)
    ]]></literal>
    <justification jstring="[para(720(a,1),1054(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="720 1054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1056">
    <literal><![CDATA[
      T(K(x,y / x),K(y / x,z)) = K(x,y / x)
    ]]></literal>
    <justification jstring="[para(76(a,1),1055(a,2,2,1))].">
      <j1 rule="para" parents="76 1055"/>
    </justification>
  </clause>

  <clause id="1057">
    <literal><![CDATA[
      T(K(x,y),K((y * x) / x,z)) = K(x,(y * x) / x)
    ]]></literal>
    <justification jstring="[para(11(a,1),1056(a,1,1,2))].">
      <j1 rule="para" parents="11 1056"/>
    </justification>
  </clause>

  <clause id="1058">
    <literal><![CDATA[
      T(K(x,y),K(y,z)) = K(x,(y * x) / x)
    ]]></literal>
    <justification jstring="[para(11(a,1),1057(a,1,2,1))].">
      <j1 rule="para" parents="11 1057"/>
    </justification>
  </clause>

  <clause id="1059">
    <literal><![CDATA[
      T(K(x,y),K(y,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(11(a,1),1058(a,2,2))].">
      <j1 rule="para" parents="11 1058"/>
    </justification>
  </clause>

  <clause id="1060">
    <literal><![CDATA[
      T(K(x,y),K(z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(56,a,1059,a)].">
      <j1 rule="hyper" parents="56 1059"/>
    </justification>
  </clause>

  <clause id="1061">
    <literal><![CDATA[
      K(x,y) * K(z,x) = K(z,x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,1059,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="116 1059 22"/>
    </justification>
  </clause>

  <clause id="1063">
    <literal><![CDATA[
      K(x,y) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(1060(a,1),231(a,1,2))].">
      <j1 rule="para" parents="1060 231"/>
    </justification>
  </clause>

  <clause id="1065">
    <literal><![CDATA[
      x \ y != K(z,u) * K(u,w)
    ]]></literal>
    <literal><![CDATA[
      x * (K(u,w) * K(z,u)) = y
    ]]></literal>
    <justification jstring="[para(1060(a,1),413(a,2,2))].">
      <j1 rule="para" parents="1060 413"/>
    </justification>
  </clause>

  <clause id="1066">
    <literal><![CDATA[
      T(x * ((T(x,y) * (x \ 1)) / T(x,y)),y) = T(x,y) * (1 / T(x,y))
    ]]></literal>
    <justification jstring="[para(10(a,1),1053(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 1053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1067">
    <literal><![CDATA[
      T(x,y) * ((x * (T(x,y) \ 1)) / x) = T(x * (1 / x),y)
    ]]></literal>
    <justification jstring="[para(10(a,1),1053(a,2,1,2,1))].">
      <j1 rule="para" parents="10 1053"/>
    </justification>
  </clause>

  <clause id="1068">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ x) / x) = T(x * (1 / x),y)
    ]]></literal>
    <justification jstring="[para(648(a,1),1067(a,1,2,1))].">
      <j1 rule="para" parents="648 1067"/>
    </justification>
  </clause>

  <clause id="1069">
    <literal><![CDATA[
      L((x \ y) \ 1,x \ y,y \ x) = 1 / (x \ y)
    ]]></literal>
    <justification jstring="[hyper(983,a,946,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="983 946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1070">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ (x \ y) = 1 / (y \ x)
    ]]></literal>
    <justification jstring="[hyper(356,a,1069,a)].">
      <j1 rule="hyper" parents="356 1069"/>
    </justification>
  </clause>

  <clause id="1071">
    <literal><![CDATA[
      (x \ y) / (1 / (y \ x)) = (x \ y) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(170,a,1069,a(flip),b,181,a(flip))].">
      <j1 rule="hyper" parents="170 1069 181"/>
    </justification>
  </clause>

  <clause id="1072">
    <literal><![CDATA[
      (((x * y) \ x) * y) \ ((x * y) \ x) = 1 / (x \ (x * y))
    ]]></literal>
    <justification jstring="[para(9(a,1),1070(a,1,1,2))].">
      <j1 rule="para" parents="9 1070"/>
    </justification>
  </clause>

  <clause id="1073">
    <literal><![CDATA[
      (((x * y) \ x) * y) \ ((x * y) \ x) = 1 / y
    ]]></literal>
    <justification jstring="[para(9(a,1),1072(a,2,2))].">
      <j1 rule="para" parents="9 1072"/>
    </justification>
  </clause>

  <clause id="1074">
    <literal><![CDATA[
      L(x \ 1,x,(y * x) \ y) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(296,a,1073,a)].">
      <j1 rule="hyper" parents="296 1073"/>
    </justification>
  </clause>

  <clause id="1075">
    <literal><![CDATA[
      (((x * y) \ x) * y) * (1 / y) = (x * y) \ x
    ]]></literal>
    <justification jstring="[hyper(125,a,1073,a)].">
      <j1 rule="hyper" parents="125 1073"/>
    </justification>
  </clause>

  <clause id="1076">
    <literal><![CDATA[
      L(x \ 1,x,x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[para(7(a,1),1074(a,1,3,1))].">
      <j1 rule="para" parents="7 1074"/>
    </justification>
  </clause>

  <clause id="1077">
    <literal><![CDATA[
      L((x * y) \ x,y,(z * y) \ z) = L(1 / y,y,x)
    ]]></literal>
    <justification jstring="[para(1074(a,1),282(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1074 282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1078">
    <literal><![CDATA[
      (x \ 1) / (1 / x) = (x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(170,a,1076,a(flip),b,181,a(flip))].">
      <j1 rule="hyper" parents="170 1076 181"/>
    </justification>
  </clause>

  <clause id="1079">
    <literal><![CDATA[
      x * L(x \ (y \ x),y,y \ 1) = (y * (1 / y)) * (y \ x)
    ]]></literal>
    <justification jstring="[para(1076(a,1),905(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1076 905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1080">
    <literal><![CDATA[
      x * (y * L(y \ (x \ y),x,x \ 1)) = (x * (1 / x)) * y
    ]]></literal>
    <justification jstring="[para(1076(a,1),975(a,2,1,2))].">
      <j1 rule="para" parents="1076 975"/>
    </justification>
  </clause>

  <clause id="1081">
    <literal><![CDATA[
      T(1 / (1 / x),x \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(786,a,1078,a)].">
      <j1 rule="hyper" parents="786 1078"/>
    </justification>
  </clause>

  <clause id="1083">
    <literal><![CDATA[
      K(x \ 1,x) * (1 / x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(115,a,216,a,b,1078,a)].">
      <j1 rule="hyper" parents="115 216 1078"/>
    </justification>
  </clause>

  <clause id="1085">
    <literal><![CDATA[
      L(x,x \ 1,x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(42,a,444,a,b,1081,a)].">
      <j1 rule="hyper" parents="42 444 1081"/>
    </justification>
  </clause>

  <clause id="1086">
    <literal><![CDATA[
      T(T(1 / (1 / x),y),x \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1081(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1081 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1087">
    <literal><![CDATA[
      T(x,x \ 1) / x = x * (1 / x)
    ]]></literal>
    <justification jstring="[para(1081(a,1),596(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1081 596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1088">
    <literal><![CDATA[
      (1 / (1 / x)) / x = (x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(113,a,1085,a(flip),b,708,a)].">
      <j1 rule="hyper" parents="113 1085 708"/>
    </justification>
  </clause>

  <clause id="1089">
    <literal><![CDATA[
      x \ (1 / (1 / x)) = (x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(112,a,1085,a(flip),b,215,a)].">
      <j1 rule="hyper" parents="112 1085 215"/>
    </justification>
  </clause>

  <clause id="1090">
    <literal><![CDATA[
      (x \ 1) * L(y,1 / x,K(x \ 1,x)) = K(x \ 1,x) * ((1 / x) * y)
    ]]></literal>
    <justification jstring="[hyper(115,a,1083,a(flip),b,161,a)].">
      <j1 rule="hyper" parents="115 1083 161"/>
    </justification>
  </clause>

  <clause id="1091">
    <literal><![CDATA[
      T(x,1 / x) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(200,a,1087,a(flip),b,599,a)].">
      <j1 rule="hyper" parents="200 1087 599"/>
    </justification>
  </clause>

  <clause id="1092">
    <literal><![CDATA[
      T(x,1 / x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(200,a,1087,a(flip),b,601,a(flip))].">
      <j1 rule="hyper" parents="200 1087 601"/>
    </justification>
  </clause>

  <clause id="1093">
    <literal><![CDATA[
      T(1 / x,1 / (1 / x)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(250,a,436,a(flip),b,1091,a),flip(a)].">
      <j1 rule="hyper" parents="250 436 1091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1094">
    <literal><![CDATA[
      (x * T(y,y \ 1)) / x = T((x * y) / x,1 / y)
    ]]></literal>
    <justification jstring="[para(1091(a,1),327(a,1,1,2))].">
      <j1 rule="para" parents="1091 327"/>
    </justification>
  </clause>

  <clause id="1095">
    <literal><![CDATA[
      R(x,1 / x,x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,518,a,b,1092,a)].">
      <j1 rule="hyper" parents="65 518 1092"/>
    </justification>
  </clause>

  <clause id="1096">
    <literal><![CDATA[
      a(x,1 / x,x) = x \ ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(1095(a,1),476(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1095 476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1097">
    <literal><![CDATA[
      K(x \ 1,x) * x = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(115,a,216,a,b,1088,a)].">
      <j1 rule="hyper" parents="115 216 1088"/>
    </justification>
  </clause>

  <clause id="1098">
    <literal><![CDATA[
      x \ (1 / (1 / x)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(250,a,216,a,b,1089,a),flip(a)].">
      <j1 rule="hyper" parents="250 216 1089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1099">
    <literal><![CDATA[
      x * K(x \ 1,x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(116,a,216,a,b,1089,a)].">
      <j1 rule="hyper" parents="116 216 1089"/>
    </justification>
  </clause>

  <clause id="1100">
    <literal><![CDATA[
      L(1 / x,y,z) * (1 / (1 / x)) = (1 / (1 / x)) * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(1093(a,1),198(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1093 198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1101">
    <literal><![CDATA[
      L(1 / x,y,z) * (1 / (1 / x)) = L(x \ 1,y,z) / (1 / x)
    ]]></literal>
    <justification jstring="[para(1093(a,1),632(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1093 632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1102">
    <literal><![CDATA[
      (x * y) \ x = (L(y \ 1,y,x) * y) * (1 / y)
    ]]></literal>
    <justification jstring="[para(181(a,2),1075(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="181 1075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1103">
    <literal><![CDATA[
      L(x \ 1,x,y) / (1 / x) = L(x \ 1,x,y) * x
    ]]></literal>
    <justification jstring="[hyper(113,a,181,a,b,1102,a(flip))].">
      <j1 rule="hyper" parents="113 181 1102"/>
    </justification>
  </clause>

  <clause id="1104">
    <literal><![CDATA[
      T((x * y) / x,1 / y) = T((x * y) / x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,327,a(flip),b,1094,a),flip(a)].">
      <j1 rule="hyper" parents="65 327 1094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1105">
    <literal><![CDATA[
      T((x * T(y,x)) / x,T(y,x) \ 1) = T(y,1 / T(y,x))
    ]]></literal>
    <justification jstring="[para(191(a,1),1104(a,1,1)),flip(a)].">
      <j1 rule="para" parents="191 1104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1106">
    <literal><![CDATA[
      T(x,1 / T(x,y)) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(191(a,1),1105(a,1,1)),flip(a)].">
      <j1 rule="para" parents="191 1105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1107">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) / T(x,y) = x * (1 / T(x,y))
    ]]></literal>
    <justification jstring="[para(1106(a,1),773(a,1,1))].">
      <j1 rule="para" parents="1106 773"/>
    </justification>
  </clause>

  <clause id="1108">
    <literal><![CDATA[
      ((x * (1 / T(x,y))) / x) * T(x,y) = T(x,T(x,y) \ 1) / x
    ]]></literal>
    <justification jstring="[para(1107(a,1),770(a,1,1,1))].">
      <j1 rule="para" parents="1107 770"/>
    </justification>
  </clause>

  <clause id="1109">
    <literal><![CDATA[
      x * ((x * (1 / x)) * (x \ y)) = (x * (1 / x)) * y
    ]]></literal>
    <justification jstring="[para(1079(a,1),1080(a,1,2))].">
      <j1 rule="para" parents="1079 1080"/>
    </justification>
  </clause>

  <clause id="1110">
    <literal><![CDATA[
      T(x,y) * ((x * (T(x,y) \ 1)) / x) = T(x,T(x,y) \ 1) / x
    ]]></literal>
    <justification jstring="[hyper(65,a,541,a(flip),b,1108,a)].">
      <j1 rule="hyper" parents="65 541 1108"/>
    </justification>
  </clause>

  <clause id="1111">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ x) / x) = T(x,T(x,y) \ 1) / x
    ]]></literal>
    <justification jstring="[para(648(a,1),1110(a,1,2,1))].">
      <j1 rule="para" parents="648 1110"/>
    </justification>
  </clause>

  <clause id="1112">
    <literal><![CDATA[
      (T(x,T(x,y) \ 1) / x) * x = T(x,x / (x * T(x,y)))
    ]]></literal>
    <justification jstring="[para(1111(a,1),1040(a,1,1))].">
      <j1 rule="para" parents="1111 1040"/>
    </justification>
  </clause>

  <clause id="1113">
    <literal><![CDATA[
      T(x,x / (x * T(x,y))) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,T(x,y) \ 1) = z
    ]]></literal>
    <justification jstring="[para(1112(a,1),211(a,1)),flip(b)].">
      <j1 rule="para" parents="1112 211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1114">
    <literal><![CDATA[
      (1 / (1 / x)) * L(x \ 1,y,z) = L(x \ 1,y,z) / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(65,a,1101,a(flip),b,1100,a),flip(a)].">
      <j1 rule="hyper" parents="65 1101 1100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1115">
    <literal><![CDATA[
      L((x \ y) \ 1,x \ y,x) / (1 / (x \ y)) = (1 / (1 / (x \ y))) * (y \ x)
    ]]></literal>
    <justification jstring="[para(275(a,1),1114(a,1,2)),flip(a)].">
      <j1 rule="para" parents="275 1114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1116">
    <literal><![CDATA[
      L(x \ L(y,1 / x,K(x \ 1,x)),x,x \ 1) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(640,a,1090,a(flip))].">
      <j1 rule="hyper" parents="640 1090"/>
    </justification>
  </clause>

  <clause id="1117">
    <literal><![CDATA[
      (x * (y * L(y \ 1,z,u))) * y = (x * y) * (y * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(556(a,1),995(a,1,1))].">
      <j1 rule="para" parents="556 995"/>
    </justification>
  </clause>

  <clause id="1118">
    <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),1003(a,1,1))].">
      <j1 rule="para" parents="22 1003"/>
    </justification>
  </clause>

  <clause id="1119">
    <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),1118(a,1,2,1,1))].">
      <j1 rule="para" parents="22 1118"/>
    </justification>
  </clause>

  <clause id="1120">
    <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),1119(a,2,1,2,1))].">
      <j1 rule="para" parents="9 1119"/>
    </justification>
  </clause>

  <clause id="1121">
    <literal><![CDATA[
      T(x * ((x * R(x \ 1,y,z)) / x),x) = x * R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(453(a,1),1012(a,2,2))].">
      <j1 rule="para" parents="453 1012"/>
    </justification>
  </clause>

  <clause id="1122">
    <literal><![CDATA[
      T(x * R(1 / x,y,z),x) = x * R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(453(a,1),1121(a,1,1,2))].">
      <j1 rule="para" parents="453 1121"/>
    </justification>
  </clause>

  <clause id="1123">
    <literal><![CDATA[
      T(x * (y / (x * y)),x) = x * R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[para(183(a,1),1122(a,1,1,2))].">
      <j1 rule="para" parents="183 1122"/>
    </justification>
  </clause>

  <clause id="1124">
    <literal><![CDATA[
      T(x * (y / (x * y)),x) = x * (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(250,a,283,a(flip),b,1123,a),flip(a)].">
      <j1 rule="hyper" parents="250 283 1123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1125">
    <literal><![CDATA[
      T(x,x * (y / (x * y))) = x
    ]]></literal>
    <justification jstring="[hyper(56,a,1124,a)].">
      <j1 rule="hyper" parents="56 1124"/>
    </justification>
  </clause>

  <clause id="1126">
    <literal><![CDATA[
      T(x / y,(x / y) * (y / x)) = x / y
    ]]></literal>
    <justification jstring="[para(12(a,1),1125(a,1,2,2,2))].">
      <j1 rule="para" parents="12 1125"/>
    </justification>
  </clause>

  <clause id="1127">
    <literal><![CDATA[
      T(x \ y,(y / x) * (x / y)) = T(y / x,x)
    ]]></literal>
    <justification jstring="[para(1126(a,1),206(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1126 206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1128">
    <literal><![CDATA[
      T(x \ y,(y / x) * (x / y)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(250,a,106,a(flip),b,1127,a),flip(a)].">
      <j1 rule="hyper" parents="250 106 1127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1129">
    <literal><![CDATA[
      K(((x / y) * (y / x)) \ (x / y),(x / y) * (y / x)) = (y * (y \ x)) / x
    ]]></literal>
    <justification jstring="[para(1128(a,1),915(a,2,1,2))].">
      <j1 rule="para" parents="1128 915"/>
    </justification>
  </clause>

  <clause id="1130">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ (u * y))) / z) = (x * ((z * (x \ u)) / z)) * y
    ]]></literal>
    <justification jstring="[para(541(a,1),1041(a,2,1))].">
      <j1 rule="para" parents="541 1041"/>
    </justification>
  </clause>

  <clause id="1131">
    <literal><![CDATA[
      (x * y) * ((x * ((x * y) \ z)) / x) = (x * ((z / y) / x)) * y
    ]]></literal>
    <justification jstring="[hyper(253,a,1043,a),flip(a)].">
      <j1 rule="hyper" parents="253 1043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1132">
    <literal><![CDATA[
      (x * y) * ((x * ((x * y) \ z)) / x) != u
    ]]></literal>
    <literal><![CDATA[
      (x * ((z / y) / x)) * y = u
    ]]></literal>
    <justification jstring="[para(1043(a,1),253(a,1))].">
      <j1 rule="para" parents="1043 253"/>
    </justification>
  </clause>

  <clause id="1134">
    <literal><![CDATA[
      T(x,x / (x * y)) != z
    ]]></literal>
    <literal><![CDATA[
      (x * ((x / y) / x)) * y = z
    ]]></literal>
    <justification jstring="[para(864(a,1),1132(a,1))].">
      <j1 rule="para" parents="864 1132"/>
    </justification>
  </clause>

  <clause id="1135">
    <literal><![CDATA[
      K(((x / y) * (y / x)) \ (x / y),(x / y) * (y / x)) = x / x
    ]]></literal>
    <justification jstring="[hyper(250,a,134,a(flip),b,1129,a),flip(a)].">
      <j1 rule="hyper" parents="250 134 1129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1137">
    <literal><![CDATA[
      K(((x / y) * (y / x)) \ (x / y),(x / y) * (y / x)) = 1
    ]]></literal>
    <justification jstring="[hyper(250,a,73,a(flip),b,1135,a),flip(a)].">
      <j1 rule="hyper" parents="250 73 1135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1139">
    <literal><![CDATA[
      T(1 / (x / y),(y / x) * (x / y)) = 1 / (x / y)
    ]]></literal>
    <justification jstring="[para(1137(a,1),612(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1137 612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1140">
    <literal><![CDATA[
      K(1 / (x / y),(y / x) * (x / y)) = 1
    ]]></literal>
    <justification jstring="[hyper(57,a,1139,a)].">
      <j1 rule="hyper" parents="57 1139"/>
    </justification>
  </clause>

  <clause id="1141">
    <literal><![CDATA[
      K(1 / x,(y / (x * y)) * ((x * y) / y)) = 1
    ]]></literal>
    <justification jstring="[para(11(a,1),1140(a,1,1,2))].">
      <j1 rule="para" parents="11 1140"/>
    </justification>
  </clause>

  <clause id="1142">
    <literal><![CDATA[
      K(1 / x,(y / (x * y)) * x) = 1
    ]]></literal>
    <justification jstring="[para(11(a,1),1141(a,1,2,2))].">
      <j1 rule="para" parents="11 1141"/>
    </justification>
  </clause>

  <clause id="1143">
    <literal><![CDATA[
      T(1 / x,(y / (x * y)) * x) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(58,a,1142,a)].">
      <j1 rule="hyper" parents="58 1142"/>
    </justification>
  </clause>

  <clause id="1144">
    <literal><![CDATA[
      L(x \ 1,x,y / (x * y)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(944,a,1143,a)].">
      <j1 rule="hyper" parents="944 1143"/>
    </justification>
  </clause>

  <clause id="1145">
    <literal><![CDATA[
      ((x / (y * x)) * y) * (1 / y) = x / (y * x)
    ]]></literal>
    <justification jstring="[hyper(116,a,1143,a(flip),b,675,a)].">
      <j1 rule="hyper" parents="116 1143 675"/>
    </justification>
  </clause>

  <clause id="1146">
    <literal><![CDATA[
      L(x \ 1,x,R(1 / x,x,y)) = 1 / x
    ]]></literal>
    <justification jstring="[para(183(a,2),1144(a,1,3))].">
      <j1 rule="para" parents="183 1144"/>
    </justification>
  </clause>

  <clause id="1147">
    <literal><![CDATA[
      R(1 / x,x,y) / (1 / x) = R(1 / x,x,y) * x
    ]]></literal>
    <justification jstring="[hyper(170,a,1146,a(flip),b,181,a(flip))].">
      <j1 rule="hyper" parents="170 1146 181"/>
    </justification>
  </clause>

  <clause id="1148">
    <literal><![CDATA[
      T(1 / (1 / x),R(1 / x,x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(1028,a,1147,a)].">
      <j1 rule="hyper" parents="1028 1147"/>
    </justification>
  </clause>

  <clause id="1149">
    <literal><![CDATA[
      T(1 / (1 / x),y / (x * y)) = x
    ]]></literal>
    <justification jstring="[para(183(a,1),1148(a,1,2))].">
      <j1 rule="para" parents="183 1148"/>
    </justification>
  </clause>

  <clause id="1150">
    <literal><![CDATA[
      T(x,y / (x * y)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1149(a,1),1086(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1149 1086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1151">
    <literal><![CDATA[
      T(x,y / (x * y)) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(250,a,105,a(flip),b,1150,a),flip(a)].">
      <j1 rule="hyper" parents="250 105 1150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1152">
    <literal><![CDATA[
      K((x / (y * x)) \ 1,x / (y * x)) * (y * x) = T(y,y \ 1) * x
    ]]></literal>
    <justification jstring="[para(1150(a,1),917(a,2,1))].">
      <j1 rule="para" parents="1150 917"/>
    </justification>
  </clause>

  <clause id="1153">
    <literal><![CDATA[
      T(x / y,y / x) = ((x / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(12(a,1),1151(a,1,2,2))].">
      <j1 rule="para" parents="12 1151"/>
    </justification>
  </clause>

  <clause id="1155">
    <literal><![CDATA[
      ((x / y) * ((z * ((x / y) \ u)) / z)) * y = x * ((z * (((x / y) * y) \ (u * y))) / z)
    ]]></literal>
    <justification jstring="[hyper(253,a,1130,a),flip(a)].">
      <j1 rule="hyper" parents="253 1130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1156">
    <literal><![CDATA[
      (x \ (y * x)) * ((z * ((x \ (y * x)) \ x)) / z) = T(y * ((z * (y \ x)) / z),x)
    ]]></literal>
    <justification jstring="[hyper(200,a,1130,a(flip),b,938,a),flip(a)].">
      <j1 rule="hyper" parents="200 1130 938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1157">
    <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),108(a,1,2,1))].">
      <j1 rule="para" parents="33 108"/>
    </justification>
  </clause>

  <clause id="1158">
    <literal><![CDATA[
      (T(x,y) * (1 / x)) / T(x,y) = L(1 / x,T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[hyper(65,a,705,a(flip),b,603,a)].">
      <j1 rule="hyper" parents="65 705 603"/>
    </justification>
  </clause>

  <clause id="1160">
    <literal><![CDATA[
      T(L(1 / x,T(x,y),1 / x),x) = (T(x,y) * (x \ 1)) / T(x,y)
    ]]></literal>
    <justification jstring="[para(1158(a,1),465(a,1,1))].">
      <j1 rule="para" parents="1158 465"/>
    </justification>
  </clause>

  <clause id="1161">
    <literal><![CDATA[
      (T(x,y) * (x \ 1)) / T(x,y) = L(x \ 1,T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[hyper(538,a,1160,a),flip(a)].">
      <j1 rule="hyper" parents="538 1160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1162">
    <literal><![CDATA[
      x * L(x \ 1,T(x,y),1 / x) = K(T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[para(1161(a,1),990(a,1,2))].">
      <j1 rule="para" parents="1161 990"/>
    </justification>
  </clause>

  <clause id="1163">
    <literal><![CDATA[
      L(1 / (x \ (x / y)),x \ (x / y),x) = L(y,x \ (x / y),y)
    ]]></literal>
    <justification jstring="[hyper(250,a,980,a(flip),b,747,a),flip(a)].">
      <j1 rule="hyper" parents="250 980 747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1164">
    <literal><![CDATA[
      (L(x \ 1,x,y) * y) / L(x \ 1,x,y) = y * (x * T(x \ 1,y))
    ]]></literal>
    <justification jstring="[hyper(250,a,316,a(flip),b,779,a),flip(a)].">
      <j1 rule="hyper" parents="250 316 779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1165">
    <literal><![CDATA[
      T(x,x * (y * T(y \ 1,x))) = x
    ]]></literal>
    <justification jstring="[para(1164(a,1),328(a,1,2))].">
      <j1 rule="para" parents="1164 328"/>
    </justification>
  </clause>

  <clause id="1166">
    <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(1164(a,1),841(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1164 841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1167">
    <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(1164(a,1),884(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1164 884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1168">
    <literal><![CDATA[
      T(x,x * K(y,x)) = x
    ]]></literal>
    <justification jstring="[para(607(a,2),1165(a,1,2,2))].">
      <j1 rule="para" parents="607 1165"/>
    </justification>
  </clause>

  <clause id="1169">
    <literal><![CDATA[
      T(x * K(y,x),x) = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(56,a,1168,a)].">
      <j1 rule="hyper" parents="56 1168"/>
    </justification>
  </clause>

  <clause id="1170">
    <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(821(a,1),236(a,1))].">
      <j1 rule="para" parents="821 236"/>
    </justification>
  </clause>

  <clause id="1171">
    <literal><![CDATA[
      (1 / (1 / (x \ y))) * (y \ x) = (y \ x) / (1 / (x \ y))
    ]]></literal>
    <justification jstring="[para(275(a,1),1115(a,1,1)),flip(a)].">
      <j1 rule="para" parents="275 1115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1172">
    <literal><![CDATA[
      (1 / (1 / (x \ y))) * (y \ x) = (y \ x) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(250,a,1071,a(flip),b,1171,a),flip(a)].">
      <j1 rule="hyper" parents="250 1071 1171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1173">
    <literal><![CDATA[
      T(1 / (1 / (x \ y)),y \ x) = x \ y
    ]]></literal>
    <justification jstring="[hyper(200,a,1171,a,b,1071,a(flip))].">
      <j1 rule="hyper" parents="200 1171 1071"/>
    </justification>
  </clause>

  <clause id="1174">
    <literal><![CDATA[
      T(1 / (1 / x),(y * x) \ y) = y \ (y * x)
    ]]></literal>
    <justification jstring="[para(9(a,1),1173(a,1,1,2,2))].">
      <j1 rule="para" parents="9 1173"/>
    </justification>
  </clause>

  <clause id="1175">
    <literal><![CDATA[
      T(1 / (1 / K(x \ (x / (y \ 1)),x)),T(y,x) \ y) = y \ T(y,x)
    ]]></literal>
    <justification jstring="[para(609(a,2),1173(a,1,1,2,2))].">
      <j1 rule="para" parents="609 1173"/>
    </justification>
  </clause>

  <clause id="1176">
    <literal><![CDATA[
      T(1 / (1 / x),(y * x) \ y) = x
    ]]></literal>
    <justification jstring="[hyper(250,a,9,a(flip),b,1174,a),flip(a)].">
      <j1 rule="hyper" parents="250 9 1174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1178">
    <literal><![CDATA[
      T(x,(y * x) \ y) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1176(a,1),1086(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1176 1086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1179">
    <literal><![CDATA[
      T(x,(y * x) \ y) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(250,a,105,a(flip),b,1178,a),flip(a)].">
      <j1 rule="hyper" parents="250 105 1178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1180">
    <literal><![CDATA[
      T(K(x,y),(x * y) \ (y * x)) = T(K(x,y),K(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(87(a,1),1178(a,1,2,1))].">
      <j1 rule="para" parents="87 1178"/>
    </justification>
  </clause>

  <clause id="1181">
    <literal><![CDATA[
      T(x \ y,y \ x) = ((x \ y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(10(a,1),1179(a,1,2,1))].">
      <j1 rule="para" parents="10 1179"/>
    </justification>
  </clause>

  <clause id="1182">
    <literal><![CDATA[
      T(x \ (x / y),y) = ((x \ (x / y)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(79(a,1),1181(a,1,2))].">
      <j1 rule="para" parents="79 1181"/>
    </justification>
  </clause>

  <clause id="1183">
    <literal><![CDATA[
      T(K(x \ (x / (y \ 1)),x),T(y,x) \ y) = ((y \ T(y,x)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(609(a,2),1181(a,1,1))].">
      <j1 rule="para" parents="609 1181"/>
    </justification>
  </clause>

  <clause id="1184">
    <literal><![CDATA[
      L(x \ y,y \ x,x \ y) = 1 / (1 / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(37,a,981,a,b,1172,a)].">
      <j1 rule="hyper" parents="37 981 1172"/>
    </justification>
  </clause>

  <clause id="1185">
    <literal><![CDATA[
      L(1 / (x \ y),x \ y,x) = 1 / (1 / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(37,a,533,a,b,1172,a)].">
      <j1 rule="hyper" parents="37 533 1172"/>
    </justification>
  </clause>

  <clause id="1186">
    <literal><![CDATA[
      L((x * y) \ x,y,(x * y) \ x) = 1 / (1 / ((x * y) \ x))
    ]]></literal>
    <justification jstring="[para(9(a,1),1184(a,1,2))].">
      <j1 rule="para" parents="9 1184"/>
    </justification>
  </clause>

  <clause id="1187">
    <literal><![CDATA[
      L(x,y \ (y / x),x) = 1 / (1 / ((y / x) \ y))
    ]]></literal>
    <justification jstring="[hyper(65,a,1163,a(flip),b,1185,a)].">
      <j1 rule="hyper" parents="65 1163 1185"/>
    </justification>
  </clause>

  <clause id="1188">
    <literal><![CDATA[
      L(x,y \ (y / x),x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[para(79(a,1),1187(a,2,2,2))].">
      <j1 rule="para" parents="79 1187"/>
    </justification>
  </clause>

  <clause id="1189">
    <literal><![CDATA[
      L(x,(y * x) \ y,x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[para(11(a,1),1188(a,1,2,2))].">
      <j1 rule="para" parents="11 1188"/>
    </justification>
  </clause>

  <clause id="1190">
    <literal><![CDATA[
      T(K(x,y),K(x,y) \ 1) = T(K(x,y),K(y,x))
    ]]></literal>
    <justification jstring="[para(16(a,2),1180(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16 1180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1191">
    <literal><![CDATA[
      T(K(x,y),K(y,x)) = (K(x,y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(301,a,1190,a),flip(a)].">
      <j1 rule="hyper" parents="301 1190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1192">
    <literal><![CDATA[
      (K(x,y) \ 1) \ 1 = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,1060,a(flip),b,1191,a),flip(a)].">
      <j1 rule="hyper" parents="65 1060 1191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1195">
    <literal><![CDATA[
      K(x,x \ 1) \ 1 = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(41,a,302,a,b,1192,a),flip(a)].">
      <j1 rule="hyper" parents="41 302 1192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1196">
    <literal><![CDATA[
      1 / (1 / K(x,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(1192(a,1),164(a,1,2,2))].">
      <j1 rule="para" parents="1192 164"/>
    </justification>
  </clause>

  <clause id="1197">
    <literal><![CDATA[
      L(1 / x,x,y) = 1 / (1 / ((y * x) \ y))
    ]]></literal>
    <justification jstring="[hyper(65,a,1077,a(flip),b,1186,a)].">
      <j1 rule="hyper" parents="65 1077 1186"/>
    </justification>
  </clause>

  <clause id="1199">
    <literal><![CDATA[
      L(x,x \ 1,y) = 1 / (1 / ((y * (x \ 1)) \ y))
    ]]></literal>
    <justification jstring="[para(76(a,1),1197(a,1,1))].">
      <j1 rule="para" parents="76 1197"/>
    </justification>
  </clause>

  <clause id="1200">
    <literal><![CDATA[
      T(K(x \ (x / (y \ 1)),x),T(y,x) \ y) = y \ T(y,x)
    ]]></literal>
    <justification jstring="[para(1196(a,1),1175(a,1,1))].">
      <j1 rule="para" parents="1196 1175"/>
    </justification>
  </clause>

  <clause id="1201">
    <literal><![CDATA[
      1 / (x \ T(x,y)) = (x \ T(x,y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(170,a,1200,a(flip),b,1183,a(flip))].">
      <j1 rule="hyper" parents="170 1200 1183"/>
    </justification>
  </clause>

  <clause id="1202">
    <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),1157(a,1,2))].">
      <j1 rule="para" parents="33 1157"/>
    </justification>
  </clause>

  <clause id="1203">
    <literal><![CDATA[
      (a(x,y,z) * (u * w)) \ (a(x,y,z) * (u * (w * v5))) = L(v5,w,a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(315(a,1),525(a,1,2))].">
      <j1 rule="para" parents="315 525"/>
    </justification>
  </clause>

  <clause id="1204">
    <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(104(a,1),555(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="104 555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1205">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ 1,z,u) = T(x * L(x \ 1,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(200,a,974,a(flip),b,1204,a),flip(a)].">
      <j1 rule="hyper" parents="200 974 1204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1206">
    <literal><![CDATA[
      T(x,y) \ T(x * L(x \ 1,z,u),y) = L(T(x,y) \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(118,a,1205,a)].">
      <j1 rule="hyper" parents="118 1205"/>
    </justification>
  </clause>

  <clause id="1207">
    <literal><![CDATA[
      T(x * L(x \ 1,T(x,y),z),y) = T(x,y) * ((z * T(x,y)) \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,276,a(flip),b,1205,a),flip(a)].">
      <j1 rule="hyper" parents="65 276 1205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1208">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ 1,x,1 / x) = T(x * T(1 / x,1),y)
    ]]></literal>
    <justification jstring="[para(493(a,1),1205(a,2,1,2))].">
      <j1 rule="para" parents="493 1205"/>
    </justification>
  </clause>

  <clause id="1209">
    <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(275(a,1),1206(a,1,2,1,2))].">
      <j1 rule="para" parents="275 1206"/>
    </justification>
  </clause>

  <clause id="1210">
    <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(599(a,1),1207(a,2,2,1))].">
      <j1 rule="para" parents="599 1207"/>
    </justification>
  </clause>

  <clause id="1211">
    <literal><![CDATA[
      T(x,y) * ((1 / x) * (T(x,y) \ x)) = T(x * T(1 / x,1),y)
    ]]></literal>
    <justification jstring="[para(653(a,1),1208(a,1,2))].">
      <j1 rule="para" parents="653 1208"/>
    </justification>
  </clause>

  <clause id="1212">
    <literal><![CDATA[
      T(x,y) * ((1 / x) * (T(x,y) \ x)) = T(x * (1 / x),y)
    ]]></literal>
    <justification jstring="[para(172(a,1),1211(a,2,1,2))].">
      <j1 rule="para" parents="172 1211"/>
    </justification>
  </clause>

  <clause id="1213">
    <literal><![CDATA[
      (1 / x) * (T(x,y) \ x) = (T(x,y) \ x) / x
    ]]></literal>
    <justification jstring="[hyper(36,a,1068,a,b,1212,a),flip(a)].">
      <j1 rule="hyper" parents="36 1068 1212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1214">
    <literal><![CDATA[
      T((T(x,y) \ x) / x,x) = (1 / x) * ((T(x,y) \ 1) * x)
    ]]></literal>
    <justification jstring="[para(1213(a,1),654(a,1,1))].">
      <j1 rule="para" parents="1213 654"/>
    </justification>
  </clause>

  <clause id="1215">
    <literal><![CDATA[
      (1 / x) * ((T(x,y) \ 1) * x) = x \ (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(293,a,1214,a),flip(a)].">
      <j1 rule="hyper" parents="293 1214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1216">
    <literal><![CDATA[
      (1 / x) * ((T(x,y) \ 1) * x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(250,a,652,a(flip),b,1215,a),flip(a)].">
      <j1 rule="hyper" parents="250 652 1215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1217">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) / x) \ (1 / x)) = T(K(T(x,y),1 / x),y)
    ]]></literal>
    <justification jstring="[para(1162(a,1),1210(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1162 1210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1218">
    <literal><![CDATA[
      L(T(1 / (1 / x),y),z,u) * (1 / x) = L(T(x,y),z,u) / x
    ]]></literal>
    <justification jstring="[para(151(a,1),631(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="151 631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1219">
    <literal><![CDATA[
      (1 / x) * L(T((1 / x) \ 1,y),z,u) = L(T(x,y),z,u) / x
    ]]></literal>
    <justification jstring="[hyper(639,a,1218,a)].">
      <j1 rule="hyper" parents="639 1218"/>
    </justification>
  </clause>

  <clause id="1220">
    <literal><![CDATA[
      (1 / x) * L(T(x,y),z,u) = L(T(x,y),z,u) / x
    ]]></literal>
    <justification jstring="[para(79(a,1),1219(a,1,2,1,1))].">
      <j1 rule="para" parents="79 1219"/>
    </justification>
  </clause>

  <clause id="1221">
    <literal><![CDATA[
      T(x,y) * (R(x,z,u) \ 1) = R(x,z,u) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),735(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1222">
    <literal><![CDATA[
      R(x / y,z,u) \ T(x / y,y) = (y \ x) * (R(x / y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(106(a,1),1221(a,1,1)),flip(a)].">
      <j1 rule="para" parents="106 1221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1223">
    <literal><![CDATA[
      (x \ y) * (R(y / x,z,u) \ 1) = R(y / x,z,u) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(106(a,1),1222(a,1,2)),flip(a)].">
      <j1 rule="para" parents="106 1222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1224">
    <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),1223(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 1223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1225">
    <literal><![CDATA[
      x * (R((y * x) / y,z,u) \ 1) = R((y * x) / y,z,u) \ x
    ]]></literal>
    <justification jstring="[para(9(a,1),1224(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 1224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1226">
    <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(104(a,1),829(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="104 829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1227">
    <literal><![CDATA[
      T(x,y) * R(T(x,y) \ 1,z,u) = T(x * R(x \ 1,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(200,a,1006,a(flip),b,1226,a),flip(a)].">
      <j1 rule="hyper" parents="200 1006 1226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1228">
    <literal><![CDATA[
      T(x * R(x \ 1,T(x,y),z),y) = (z / (T(x,y) * z)) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,458,a,b,1227,a),flip(a)].">
      <j1 rule="hyper" parents="65 458 1227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1229">
    <literal><![CDATA[
      T(x * R(x \ 1,T(x,y),x \ 1),y) = ((x \ 1) / (x \ T(x,y))) * T(x,y)
    ]]></literal>
    <justification jstring="[para(589(a,1),1228(a,2,1,2))].">
      <j1 rule="para" parents="589 1228"/>
    </justification>
  </clause>

  <clause id="1230">
    <literal><![CDATA[
      ((x \ 1) / (x \ T(x,y))) * T(x,y) = T(x * T(x \ 1,T(x,y)),y)
    ]]></literal>
    <justification jstring="[para(707(a,1),1229(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="707 1229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1231">
    <literal><![CDATA[
      (x \ 1) / (x \ T(x,y)) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(37,a,837,a(flip),b,1230,a),flip(a)].">
      <j1 rule="hyper" parents="37 837 1230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1232">
    <literal><![CDATA[
      T(T(x,y) \ 1,x \ T(x,y)) = (x \ T(x,y)) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(1231(a,1),106(a,1,1))].">
      <j1 rule="para" parents="1231 106"/>
    </justification>
  </clause>

  <clause id="1233">
    <literal><![CDATA[
      (x \ T(x,y)) \ (x \ 1) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,900,a(flip),b,1232,a),flip(a)].">
      <j1 rule="hyper" parents="65 900 1232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1235">
    <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),896(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="22 896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1236">
    <literal><![CDATA[
      x \ (y * (x * T(x \ (y \ z),u))) = T(y,x) * T(T(y,x) \ (x \ z),u)
    ]]></literal>
    <justification jstring="[para(562(a,1),1235(a,1,2))].">
      <j1 rule="para" parents="562 1235"/>
    </justification>
  </clause>

  <clause id="1237">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ (y \ z),u) = T(x * T(x \ (z / y),u),y)
    ]]></literal>
    <justification jstring="[hyper(926,a,1236,a),flip(a)].">
      <j1 rule="hyper" parents="926 1236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1238">
    <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),1237(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9 1237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1239">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ y,z) = T(x * T(x \ y,z),y)
    ]]></literal>
    <justification jstring="[para(11(a,1),1238(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="11 1238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1242">
    <literal><![CDATA[
      ((x * ((y \ z) / z)) / x) * z = (((x * (1 / y)) / x) * y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),948(a,1,1,1,2,2))].">
      <j1 rule="para" parents="10 948"/>
    </justification>
  </clause>

  <clause id="1243">
    <literal><![CDATA[
      (x * ((y \ x) / x)) / (y \ x) = ((x * (1 / y)) / x) * y
    ]]></literal>
    <justification jstring="[hyper(404,a,1242,a)].">
      <j1 rule="hyper" parents="404 1242"/>
    </justification>
  </clause>

  <clause id="1244">
    <literal><![CDATA[
      (x * ((y \ x) / x)) / (y \ x) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(250,a,541,a(flip),b,1243,a),flip(a)].">
      <j1 rule="hyper" parents="250 541 1243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1245">
    <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),1156(a,1,1))].">
      <j1 rule="para" parents="22 1156"/>
    </justification>
  </clause>

  <clause id="1246">
    <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),1245(a,1,2,1,2,1))].">
      <j1 rule="para" parents="22 1245"/>
    </justification>
  </clause>

  <clause id="1247">
    <literal><![CDATA[
      L(L(x,y,z),z * y,a(u,w,v5)) = L(x,y,a(u,w,v5) * z)
    ]]></literal>
    <justification jstring="[hyper(529,a,1203,a)].">
      <j1 rule="hyper" parents="529 1203"/>
    </justification>
  </clause>

  <clause id="1248">
    <literal><![CDATA[
      L(x,y,a(z,u,w) * v5) = L(x,y,v5)
    ]]></literal>
    <justification jstring="[hyper(210,a,1247,a),flip(a)].">
      <j1 rule="hyper" parents="210 1247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1250">
    <literal><![CDATA[
      L(x,y,a(z,u,w) \ v5) = L(x,y,v5)
    ]]></literal>
    <justification jstring="[para(10(a,1),1248(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10 1248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1251">
    <literal><![CDATA[
      x * ((x * y) * ((z * ((x * y) \ y)) / z)) = (x * ((z * (x \ 1)) / z)) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(750,a,992,a)].">
      <j1 rule="hyper" parents="750 992"/>
    </justification>
  </clause>

  <clause id="1252">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ x)) / z) != u
    ]]></literal>
    <literal><![CDATA[
      x * (y * ((z * (y \ 1)) / z)) = u
    ]]></literal>
    <justification jstring="[para(8(a,1),750(a,1,2,1,2,2))].">
      <j1 rule="para" parents="8 750"/>
    </justification>
  </clause>

  <clause id="1253">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ u)) / z) != w
    ]]></literal>
    <literal><![CDATA[
      x * (y * ((z * (y \ (x \ u))) / z)) = w
    ]]></literal>
    <justification jstring="[para(10(a,1),750(a,1,2,1,2,2))].">
      <j1 rule="para" parents="10 750"/>
    </justification>
  </clause>

  <clause id="1254">
    <literal><![CDATA[
      (x * ((y * (x \ 1)) / y)) * x = x * (x * ((y * (x \ 1)) / y))
    ]]></literal>
    <justification jstring="[hyper(1252,a,992,a),flip(a)].">
      <j1 rule="hyper" parents="1252 992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1255">
    <literal><![CDATA[
      x * (y * ((x * (y \ 1)) / x)) = T(x,x / (x * y))
    ]]></literal>
    <justification jstring="[hyper(1252,a,864,a)].">
      <j1 rule="hyper" parents="1252 864"/>
    </justification>
  </clause>

  <clause id="1256">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ x)) / z) = x * (y * ((z * (y \ 1)) / z))
    ]]></literal>
    <justification jstring="[hyper(1252,a,xx),flip(a)].">
      <j1 rule="hyper" parents="1252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1257">
    <literal><![CDATA[
      x \ T(x,x / (x * y)) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(118,a,1255,a)].">
      <j1 rule="hyper" parents="118 1255"/>
    </justification>
  </clause>

  <clause id="1258">
    <literal><![CDATA[
      x * K(x,(x / y) / x) = T(x,x / (x * y))
    ]]></literal>
    <justification jstring="[para(987(a,2),1255(a,1,2))].">
      <j1 rule="para" parents="987 1255"/>
    </justification>
  </clause>

  <clause id="1259">
    <literal><![CDATA[
      x * (T(x,T(x,y) \ 1) / x) = T(x,x / (x * T(x,y)))
    ]]></literal>
    <justification jstring="[para(1110(a,1),1255(a,1,2))].">
      <j1 rule="para" parents="1110 1255"/>
    </justification>
  </clause>

  <clause id="1260">
    <literal><![CDATA[
      T(x,R(1 / y,y,x)) = (x \ T(x,x / (x * y))) * x
    ]]></literal>
    <justification jstring="[para(1257(a,2),903(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1257 903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1261">
    <literal><![CDATA[
      T(x \ T(x,x / (x * y)),z) = K(x,(x / T(y,z)) / x)
    ]]></literal>
    <justification jstring="[para(1257(a,2),1052(a,1,1))].">
      <j1 rule="para" parents="1257 1052"/>
    </justification>
  </clause>

  <clause id="1262">
    <literal><![CDATA[
      x * (T(x,T(x,y) \ 1) / x) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(1113,a,1259,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="1113 1259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1263">
    <literal><![CDATA[
      x * (T(x,y) * ((T(x,y) \ x) / x)) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(1111(a,2),1262(a,1,2))].">
      <j1 rule="para" parents="1111 1262"/>
    </justification>
  </clause>

  <clause id="1264">
    <literal><![CDATA[
      (1 / x) * ((1 / x) * ((y * ((1 / x) \ 1)) / y)) = (((y * x) / y) / x) * (1 / x)
    ]]></literal>
    <justification jstring="[para(887(a,1),1254(a,1,1)),flip(a)].">
      <j1 rule="para" parents="887 1254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1265">
    <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(93(a,1),1256(a,1,1))].">
      <j1 rule="para" parents="93 1256"/>
    </justification>
  </clause>

  <clause id="1266">
    <literal><![CDATA[
      (x * ((y * (x \ 1)) / y)) * (x * z) = x * ((x * ((y * (x \ 1)) / y)) * z)
    ]]></literal>
    <justification jstring="[para(992(a,1),1251(a,1,2)),flip(a)].">
      <j1 rule="para" parents="992 1251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1267">
    <literal><![CDATA[
      (((x * y) / x) / y) * (1 / y) = (1 / y) * (((x * y) / x) / y)
    ]]></literal>
    <justification jstring="[para(887(a,1),1264(a,1,2)),flip(a)].">
      <j1 rule="para" parents="887 1264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1268">
    <literal><![CDATA[
      ((1 / x) * (((y * x) / y) / x)) / (1 / x) = ((y * x) / y) / x
    ]]></literal>
    <justification jstring="[hyper(123,a,1267,a)].">
      <j1 rule="hyper" parents="123 1267"/>
    </justification>
  </clause>

  <clause id="1270">
    <literal><![CDATA[
      R(((x * y) / x) / y,y,x) = ((1 / y) * ((x * y) / (y * x))) / (1 / y)
    ]]></literal>
    <justification jstring="[para(1268(a,1),552(a,1,1))].">
      <j1 rule="para" parents="1268 552"/>
    </justification>
  </clause>

  <clause id="1271">
    <literal><![CDATA[
      ((1 / x) * ((y * x) / (x * y))) / (1 / x) = (y * x) / (x * y)
    ]]></literal>
    <justification jstring="[hyper(425,a,1270,a),flip(a)].">
      <j1 rule="hyper" parents="425 1270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1272">
    <literal><![CDATA[
      T((x * y) / (y * x),y * x) = ((1 / y) * ((y * x) \ (x * y))) / (1 / y)
    ]]></literal>
    <justification jstring="[para(1271(a,1),465(a,1,1))].">
      <j1 rule="para" parents="1271 465"/>
    </justification>
  </clause>

  <clause id="1273">
    <literal><![CDATA[
      K(x,y) = ((1 / y) * ((y * x) \ (x * y))) / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(294,a,1272,a)].">
      <j1 rule="hyper" parents="294 1272"/>
    </justification>
  </clause>

  <clause id="1274">
    <literal><![CDATA[
      ((1 / x) * K(y,x)) / (1 / x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(16(a,2),1273(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="16 1273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1275">
    <literal><![CDATA[
      T(1 / x,K(y,x)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(222,a,1274,a)].">
      <j1 rule="hyper" parents="222 1274"/>
    </justification>
  </clause>

  <clause id="1277">
    <literal><![CDATA[
      x / (1 / (1 / x)) = K(x,1 / x)
    ]]></literal>
    <justification jstring="[para(545(a,1),1274(a,1,1))].">
      <j1 rule="para" parents="545 1274"/>
    </justification>
  </clause>

  <clause id="1278">
    <literal><![CDATA[
      T(x \ 1,K(y,x)) = T(1 / x,x)
    ]]></literal>
    <justification jstring="[para(1275(a,1),206(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1275 206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1280">
    <literal><![CDATA[
      T(x \ 1,K(y,x)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(250,a,106,a(flip),b,1278,a),flip(a)].">
      <j1 rule="hyper" parents="250 106 1278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1281">
    <literal><![CDATA[
      T((x * y) \ x,K(z,y)) = L(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(1280(a,1),281(a,2,1))].">
      <j1 rule="para" parents="1280 281"/>
    </justification>
  </clause>

  <clause id="1282">
    <literal><![CDATA[
      T(x \ y,K(z,y \ x)) = L((y \ x) \ 1,y \ x,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),1281(a,1,1,1))].">
      <j1 rule="para" parents="10 1281"/>
    </justification>
  </clause>

  <clause id="1283">
    <literal><![CDATA[
      T(x \ y,K(z,y \ x)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(250,a,275,a(flip),b,1282,a),flip(a)].">
      <j1 rule="hyper" parents="250 275 1282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1284">
    <literal><![CDATA[
      K(x,y \ z) * (z \ y) = (z \ y) * K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(116,a,1283,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="116 1283 22"/>
    </justification>
  </clause>

  <clause id="1285">
    <literal><![CDATA[
      R(a(x,y,z) * u,L(w,u,a(x,y,z)),v5) = (a(x,y,z) * ((u * w) * v5)) / (w * v5)
    ]]></literal>
    <justification jstring="[para(315(a,1),936(a,2,1))].">
      <j1 rule="para" parents="315 936"/>
    </justification>
  </clause>

  <clause id="1286">
    <literal><![CDATA[
      x \ ((L(x \ 1,y,z) * x) / L(x \ 1,y,z)) = K(L(x \ 1,y,z),x)
    ]]></literal>
    <justification jstring="[para(76(a,1),991(a,2,2))].">
      <j1 rule="para" parents="76 991"/>
    </justification>
  </clause>

  <clause id="1287">
    <literal><![CDATA[
      x \ L(x,L(x \ 1,y,z),x) = K(L(x \ 1,y,z),x)
    ]]></literal>
    <justification jstring="[para(979(a,1),1286(a,1,2))].">
      <j1 rule="para" parents="979 1286"/>
    </justification>
  </clause>

  <clause id="1288">
    <literal><![CDATA[
      x \ L(x,(y * x) \ y,x) = K(L(x \ 1,x,y),x)
    ]]></literal>
    <justification jstring="[para(181(a,1),1287(a,1,2,2))].">
      <j1 rule="para" parents="181 1287"/>
    </justification>
  </clause>

  <clause id="1289">
    <literal><![CDATA[
      K(L(x \ 1,x,y),x) = x \ (1 / (1 / x))
    ]]></literal>
    <justification jstring="[para(1189(a,1),1288(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1189 1288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1290">
    <literal><![CDATA[
      K(L(x \ 1,x,y),x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(250,a,1098,a(flip),b,1289,a),flip(a)].">
      <j1 rule="hyper" parents="250 1098 1289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1293">
    <literal><![CDATA[
      K((x * y) \ x,y) = K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,618,a(flip),b,1290,a)].">
      <j1 rule="hyper" parents="65 618 1290"/>
    </justification>
  </clause>

  <clause id="1294">
    <literal><![CDATA[
      K(1 / x,x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(274(a,1),1290(a,1,1))].">
      <j1 rule="para" parents="274 1290"/>
    </justification>
  </clause>

  <clause id="1295">
    <literal><![CDATA[
      K((x \ y) \ 1,x \ y) = K(y \ x,x \ y)
    ]]></literal>
    <justification jstring="[para(275(a,1),1290(a,1,1)),flip(a)].">
      <j1 rule="para" parents="275 1290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1296">
    <literal><![CDATA[
      K(x,x \ 1) \ 1 = K(1 / x,x)
    ]]></literal>
    <justification jstring="[hyper(250,a,1195,a,b,1294,a)].">
      <j1 rule="hyper" parents="250 1195 1294"/>
    </justification>
  </clause>

  <clause id="1297">
    <literal><![CDATA[
      K((x \ 1) \ 1,x \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(76(a,1),1294(a,1,1)),flip(a)].">
      <j1 rule="para" parents="76 1294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1299">
    <literal><![CDATA[
      (x * ((y * x) \ y)) * K(x \ 1,x) = ((y * x) \ y) * x
    ]]></literal>
    <justification jstring="[hyper(116,a,1293,a(flip),b,16,a(flip))].">
      <j1 rule="hyper" parents="116 1293 16"/>
    </justification>
  </clause>

  <clause id="1300">
    <literal><![CDATA[
      K(x,1 / x) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(41,a,303,a,b,1296,a)].">
      <j1 rule="hyper" parents="41 303 1296"/>
    </justification>
  </clause>

  <clause id="1301">
    <literal><![CDATA[
      K(x,x \ 1) = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(41,a,91,a,b,1296,a),flip(a)].">
      <j1 rule="hyper" parents="41 91 1296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1302">
    <literal><![CDATA[
      K(x,x \ 1) * (1 / (1 / x)) = x
    ]]></literal>
    <justification jstring="[hyper(115,a,1300,a(flip),b,1277,a)].">
      <j1 rule="hyper" parents="115 1300 1277"/>
    </justification>
  </clause>

  <clause id="1303">
    <literal><![CDATA[
      K(x \ 1,(x \ 1) \ 1) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(76(a,1),1300(a,1,2)),flip(a)].">
      <j1 rule="para" parents="76 1300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1304">
    <literal><![CDATA[
      T(x * ((T(x,y) * (x \ 1)) / T(x,y)),y) = K(T(x,y),T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(250,a,1066,a,b,1301,a)].">
      <j1 rule="hyper" parents="250 1066 1301"/>
    </justification>
  </clause>

  <clause id="1305">
    <literal><![CDATA[
      R(x \ 1,x,y) \ (((y / (x * y)) * x) * (1 / x)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(250,a,1021,a,b,1301,a)].">
      <j1 rule="hyper" parents="250 1021 1301"/>
    </justification>
  </clause>

  <clause id="1306">
    <literal><![CDATA[
      K(x,x \ 1) * x = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(115,a,1301,a,b,1087,a)].">
      <j1 rule="hyper" parents="115 1301 1087"/>
    </justification>
  </clause>

  <clause id="1307">
    <literal><![CDATA[
      K(x,x \ 1) * (x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[para(1301(a,2),785(a,1,1))].">
      <j1 rule="para" parents="1301 785"/>
    </justification>
  </clause>

  <clause id="1308">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ x) / x) = T(K(x,x \ 1),y)
    ]]></literal>
    <justification jstring="[para(1301(a,2),1068(a,2,1))].">
      <j1 rule="para" parents="1301 1068"/>
    </justification>
  </clause>

  <clause id="1309">
    <literal><![CDATA[
      x * (K(x,x \ 1) * (x \ y)) = (x * (1 / x)) * y
    ]]></literal>
    <justification jstring="[para(1301(a,2),1109(a,1,2,1))].">
      <j1 rule="para" parents="1301 1109"/>
    </justification>
  </clause>

  <clause id="1310">
    <literal><![CDATA[
      x \ ((x \ 1) \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,504,a(flip),b,1297,a)].">
      <j1 rule="hyper" parents="65 504 1297"/>
    </justification>
  </clause>

  <clause id="1311">
    <literal><![CDATA[
      x * K(x,x \ 1) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,1297,a(flip),b,504,a(flip))].">
      <j1 rule="hyper" parents="116 1297 504"/>
    </justification>
  </clause>

  <clause id="1312">
    <literal><![CDATA[
      x \ ((x \ 1) \ 1) = K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(250,a,1300,a,b,1310,a),flip(a)].">
      <j1 rule="hyper" parents="250 1300 1310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1313">
    <literal><![CDATA[
      a(x,1 / x,x) = K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(65,a,1096,a,b,1312,a)].">
      <j1 rule="hyper" parents="65 1096 1312"/>
    </justification>
  </clause>

  <clause id="1314">
    <literal><![CDATA[
      L(x,y,K(z,1 / z)) = x
    ]]></literal>
    <justification jstring="[para(1313(a,1),128(a,1,3))].">
      <j1 rule="para" parents="1313 128"/>
    </justification>
  </clause>

  <clause id="1315">
    <literal><![CDATA[
      L(x,y,K(z \ 1,z)) = x
    ]]></literal>
    <justification jstring="[para(76(a,1),1314(a,1,3,2))].">
      <j1 rule="para" parents="76 1314"/>
    </justification>
  </clause>

  <clause id="1316">
    <literal><![CDATA[
      L(x,y,K(z,z \ 1)) = x
    ]]></literal>
    <justification jstring="[para(1300(a,1),1314(a,1,3))].">
      <j1 rule="para" parents="1300 1314"/>
    </justification>
  </clause>

  <clause id="1317">
    <literal><![CDATA[
      T(x,K(x \ 1,x) * y) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(1170,a,1315,a)].">
      <j1 rule="hyper" parents="1170 1315"/>
    </justification>
  </clause>

  <clause id="1318">
    <literal><![CDATA[
      (K(x \ 1,x) * y) * z = K(x \ 1,x) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(748,a,1315,a),flip(a)].">
      <j1 rule="hyper" parents="748 1315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1319">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ (K(x \ 1,x) * z) = y \ z
    ]]></literal>
    <justification jstring="[hyper(65,a,95,a(flip),b,1315,a)].">
      <j1 rule="hyper" parents="65 95 1315"/>
    </justification>
  </clause>

  <clause id="1320">
    <literal><![CDATA[
      (K(x \ 1,x) * y) / z = K(x \ 1,x) * (y / z)
    ]]></literal>
    <justification jstring="[hyper(170,a,1315,a(flip),b,96,a(flip))].">
      <j1 rule="hyper" parents="170 1315 96"/>
    </justification>
  </clause>

  <clause id="1321">
    <literal><![CDATA[
      K(x \ 1,x) * ((1 / x) * y) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[para(1315(a,1),1090(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1315 1090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1322">
    <literal><![CDATA[
      L(x \ y,x,x \ 1) = (1 / x) * y
    ]]></literal>
    <justification jstring="[para(1315(a,1),1116(a,1,1,2))].">
      <j1 rule="para" parents="1315 1116"/>
    </justification>
  </clause>

  <clause id="1323">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * z = K(x,x \ 1) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(748,a,1316,a),flip(a)].">
      <j1 rule="hyper" parents="748 1316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1324">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ (K(x,x \ 1) * z) = y \ z
    ]]></literal>
    <justification jstring="[hyper(65,a,95,a(flip),b,1316,a)].">
      <j1 rule="hyper" parents="65 95 1316"/>
    </justification>
  </clause>

  <clause id="1325">
    <literal><![CDATA[
      (1 / x) * (x * y) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),1322(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 1322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1326">
    <literal><![CDATA[
      L(T(x,y),y,y \ 1) = (1 / y) * (x * y)
    ]]></literal>
    <justification jstring="[para(22(a,2),1322(a,1,1))].">
      <j1 rule="para" parents="22 1322"/>
    </justification>
  </clause>

  <clause id="1327">
    <literal><![CDATA[
      x * ((1 / x) * (y * x)) = L(y,x,x \ 1) * x
    ]]></literal>
    <justification jstring="[para(1322(a,1),427(a,1,2))].">
      <j1 rule="para" parents="1322 427"/>
    </justification>
  </clause>

  <clause id="1328">
    <literal><![CDATA[
      (1 / x) \ L(y,x,x \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(118,a,1325,a)].">
      <j1 rule="hyper" parents="118 1325"/>
    </justification>
  </clause>

  <clause id="1329">
    <literal><![CDATA[
      L(x,y,y \ 1) \ ((1 / y) * (x * y)) = L(K(x,y),y * x,1 / y)
    ]]></literal>
    <justification jstring="[para(1325(a,1),244(a,1,1))].">
      <j1 rule="para" parents="1325 244"/>
    </justification>
  </clause>

  <clause id="1330">
    <literal><![CDATA[
      ((1 / x) * y) / L(y,x,x \ 1) = R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[para(1325(a,1),737(a,1,2))].">
      <j1 rule="para" parents="1325 737"/>
    </justification>
  </clause>

  <clause id="1331">
    <literal><![CDATA[
      K(((x * y) \ x) \ 1,(x * y) \ x) = K(y,(x * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(250,a,617,a(flip),b,1295,a),flip(a)].">
      <j1 rule="hyper" parents="250 617 1295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1332">
    <literal><![CDATA[
      ((x \ 1) * y) / L(T(1 / x,y),y,K(x \ 1,x)) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[para(1321(a,1),331(a,1,1))].">
      <j1 rule="para" parents="1321 331"/>
    </justification>
  </clause>

  <clause id="1333">
    <literal><![CDATA[
      ((x \ 1) * y) \ (K(x \ 1,x) * ((1 / x) * (y * z))) = L(L(z,y,1 / x),(1 / x) * y,K(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(1321(a,1),339(a,1,1))].">
      <j1 rule="para" parents="1321 339"/>
    </justification>
  </clause>

  <clause id="1334">
    <literal><![CDATA[
      T(x,(1 / x) * y) = T(x,(x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(1321(a,1),1317(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1321 1317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1335">
    <literal><![CDATA[
      x * T(K(x,x \ 1),y) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(1308(a,1),1263(a,1,2))].">
      <j1 rule="para" parents="1308 1263"/>
    </justification>
  </clause>

  <clause id="1336">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) != x * z
    ]]></literal>
    <literal><![CDATA[
      T(K(x,x \ 1),y) = z
    ]]></literal>
    <justification jstring="[para(1335(a,1),45(a,1))].">
      <j1 rule="para" parents="1335 45"/>
    </justification>
  </clause>

  <clause id="1337">
    <literal><![CDATA[
      x * (K(x,x \ 1) * (x \ y)) = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[para(1301(a,2),1309(a,2,1))].">
      <j1 rule="para" parents="1301 1309"/>
    </justification>
  </clause>

  <clause id="1338">
    <literal><![CDATA[
      ((K(x \ 1,x) * (y * z)) * u) / (z * u) = R(K(x \ 1,x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(1318(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="1318 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1339">
    <literal><![CDATA[
      K(x \ 1,x) * (((x \ 1) \ 1) * y) = x * y
    ]]></literal>
    <justification jstring="[para(715(a,1),1318(a,1,1)),flip(a)].">
      <j1 rule="para" parents="715 1318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1340">
    <literal><![CDATA[
      K(x \ 1,x) * (x * y) = (1 / (1 / x)) * y
    ]]></literal>
    <justification jstring="[para(1097(a,1),1318(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1097 1318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1341">
    <literal><![CDATA[
      ((x \ 1) \ 1) * (K(x \ 1,x) * y) = x * y
    ]]></literal>
    <justification jstring="[hyper(36,a,820,a,b,1339,a),flip(a)].">
      <j1 rule="hyper" parents="36 820 1339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1342">
    <literal><![CDATA[
      K(x \ 1,x) * (x * L(x \ 1,y,z)) = L(x \ 1,y,z) / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(250,a,1114,a(flip),b,1340,a),flip(a)].">
      <j1 rule="hyper" parents="250 1114 1340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1343">
    <literal><![CDATA[
      x * (K(x \ 1,x) * y) = (1 / (1 / x)) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,820,a(flip),b,1340,a)].">
      <j1 rule="hyper" parents="65 820 1340"/>
    </justification>
  </clause>

  <clause id="1344">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) = ((x \ 1) \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(112,a,10,a(flip),b,1341,a),flip(a)].">
      <j1 rule="hyper" parents="112 10 1341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1345">
    <literal><![CDATA[
      x * T(x \ (y \ x),y) = ((y \ 1) \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(65,a,613,a(flip),b,1344,a)].">
      <j1 rule="hyper" parents="65 613 1344"/>
    </justification>
  </clause>

  <clause id="1346">
    <literal><![CDATA[
      ((x \ 1) * y) \ (K(x \ 1,x) * z) = ((1 / x) * y) \ z
    ]]></literal>
    <justification jstring="[para(1321(a,1),1319(a,1,1))].">
      <j1 rule="para" parents="1321 1319"/>
    </justification>
  </clause>

  <clause id="1347">
    <literal><![CDATA[
      K(x,x \ 1) * ((1 / (1 / x)) * y) = x * y
    ]]></literal>
    <justification jstring="[para(1302(a,1),1323(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1302 1323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1348">
    <literal><![CDATA[
      K(x,x \ 1) * (x * y) = T(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[para(1306(a,1),1323(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1306 1323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1349">
    <literal><![CDATA[
      K(x,x \ 1) * ((x \ 1) * y) = (1 / x) * y
    ]]></literal>
    <justification jstring="[para(1307(a,1),1323(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1307 1323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1350">
    <literal><![CDATA[
      K(x,x \ 1) * ((y \ (1 / (1 / x))) * y) = x * K(y \ (1 / (1 / x)),y)
    ]]></literal>
    <justification jstring="[para(242(a,1),1347(a,1,2))].">
      <j1 rule="para" parents="242 1347"/>
    </justification>
  </clause>

  <clause id="1351">
    <literal><![CDATA[
      K((x / (y * x)) \ 1,x / (y * x)) = K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(37,a,1152,a,b,1348,a)].">
      <j1 rule="hyper" parents="37 1152 1348"/>
    </justification>
  </clause>

  <clause id="1352">
    <literal><![CDATA[
      (1 / x) * ((x \ 1) \ y) = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(259,a,1349,a),flip(a)].">
      <j1 rule="hyper" parents="259 1349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1353">
    <literal><![CDATA[
      (x \ 1) \ ((1 / x) * y) = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,689,a,b,1352,a)].">
      <j1 rule="hyper" parents="65 689 1352"/>
    </justification>
  </clause>

  <clause id="1354">
    <literal><![CDATA[
      (x \ 1) * (K(x,x \ 1) * y) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(116,a,1352,a(flip),b,689,a)].">
      <j1 rule="hyper" parents="116 1352 689"/>
    </justification>
  </clause>

  <clause id="1355">
    <literal><![CDATA[
      K(x,x \ 1) * ((1 / x) \ y) = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[para(10(a,1),1353(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 1353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1356">
    <literal><![CDATA[
      L(K(x,x \ 1) * y,x \ 1,x) = x * ((1 / x) * y)
    ]]></literal>
    <justification jstring="[para(1353(a,1),348(a,1,1))].">
      <j1 rule="para" parents="1353 348"/>
    </justification>
  </clause>

  <clause id="1357">
    <literal><![CDATA[
      (x \ 1) * ((x * (1 / x)) * y) = (1 / x) * y
    ]]></literal>
    <justification jstring="[para(1301(a,1),1354(a,1,2,1))].">
      <j1 rule="para" parents="1301 1354"/>
    </justification>
  </clause>

  <clause id="1358">
    <literal><![CDATA[
      (x * (1 / x)) * ((1 / x) \ y) = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[para(1301(a,1),1355(a,1,1))].">
      <j1 rule="para" parents="1301 1355"/>
    </justification>
  </clause>

  <clause id="1359">
    <literal><![CDATA[
      K(x,x \ 1) * (x * y) = x * (K(x,x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),1337(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 1337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1361">
    <literal><![CDATA[
      (1 / (1 / x)) * (K(x,x \ 1) * y) = x * y
    ]]></literal>
    <justification jstring="[hyper(36,a,1347,a,b,1359,a)].">
      <j1 rule="hyper" parents="36 1347 1359"/>
    </justification>
  </clause>

  <clause id="1362">
    <literal><![CDATA[
      K(x \ 1,x) * (K(x,x \ 1) * y) = y
    ]]></literal>
    <justification jstring="[hyper(36,a,1343,a,b,1361,a(flip))].">
      <j1 rule="hyper" parents="36 1343 1361"/>
    </justification>
  </clause>

  <clause id="1363">
    <literal><![CDATA[
      K(x \ 1,x) \ y = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(118,a,1362,a)].">
      <j1 rule="hyper" parents="118 1362"/>
    </justification>
  </clause>

  <clause id="1364">
    <literal><![CDATA[
      K(x,x \ 1) * ((K(x \ 1,x) * y) * z) = y * z
    ]]></literal>
    <justification jstring="[hyper(36,a,1318,a(flip),b,1362,a),flip(a)].">
      <j1 rule="hyper" parents="36 1318 1362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1365">
    <literal><![CDATA[
      K(x \ 1,x) * y != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) * z = y
    ]]></literal>
    <justification jstring="[para(1362(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="1362 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1366">
    <literal><![CDATA[
      K(x \ 1,x) * ((x * (1 / x)) * y) = y
    ]]></literal>
    <justification jstring="[para(1301(a,1),1362(a,1,2,1))].">
      <j1 rule="para" parents="1301 1362"/>
    </justification>
  </clause>

  <clause id="1367">
    <literal><![CDATA[
      K(x \ 1,x) * ((x \ 1) \ y) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[para(1355(a,1),1362(a,1,2))].">
      <j1 rule="para" parents="1355 1362"/>
    </justification>
  </clause>

  <clause id="1368">
    <literal><![CDATA[
      (1 / x) * (K(x \ 1,x) * y) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(116,a,132,a(flip),b,1367,a(flip))].">
      <j1 rule="hyper" parents="116 132 1367"/>
    </justification>
  </clause>

  <clause id="1369">
    <literal><![CDATA[
      (x * ((y * x) \ y)) * K(x \ 1,x) = L(x \ 1,x,y) * x
    ]]></literal>
    <justification jstring="[hyper(250,a,277,a,b,1299,a),flip(a)].">
      <j1 rule="hyper" parents="250 277 1299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1370">
    <literal><![CDATA[
      (x * y) * K(y,(x * y) \ x) = x * T(y,(x * y) \ x)
    ]]></literal>
    <justification jstring="[para(1331(a,1),693(a,1,2))].">
      <j1 rule="para" parents="1331 693"/>
    </justification>
  </clause>

  <clause id="1371">
    <literal><![CDATA[
      (x * ((y * x) \ y)) * K(x \ 1,x) = L(x \ 1,x,y) / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(250,a,1103,a,b,1369,a),flip(a)].">
      <j1 rule="hyper" parents="250 1103 1369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1372">
    <literal><![CDATA[
      R(x \ 1,x,y) \ (y / (x * y)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1145(a,1),1305(a,1,2))].">
      <j1 rule="para" parents="1145 1305"/>
    </justification>
  </clause>

  <clause id="1373">
    <literal><![CDATA[
      K((x / (y * x)) \ 1,x / (y * x)) = R(y \ 1,y,z) \ (z / (y * z))
    ]]></literal>
    <justification jstring="[hyper(250,a,1351,a,b,1372,a)].">
      <j1 rule="hyper" parents="250 1351 1372"/>
    </justification>
  </clause>

  <clause id="1374">
    <literal><![CDATA[
      K(T(x,y),T(x,y) \ 1) = T(K(T(x,y),1 / x),y)
    ]]></literal>
    <justification jstring="[para(990(a,1),1304(a,1,1)),flip(a)].">
      <j1 rule="para" parents="990 1304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1375">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) / x) \ (1 / x)) = K(T(x,y),T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(250,a,1217,a,b,1374,a)].">
      <j1 rule="hyper" parents="250 1217 1374"/>
    </justification>
  </clause>

  <clause id="1376">
    <literal><![CDATA[
      (T(x,y) / x) \ (1 / x) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,1301,a(flip),b,1375,a),flip(a)].">
      <j1 rule="hyper" parents="36 1301 1375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1377">
    <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(221(a,1),1376(a,1,2))].">
      <j1 rule="para" parents="221 1376"/>
    </justification>
  </clause>

  <clause id="1378">
    <literal><![CDATA[
      K(x \ 1,x) * (x * L(x \ 1,x,y)) = (x * ((y * x) \ y)) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(250,a,1371,a,b,1342,a),flip(a)].">
      <j1 rule="hyper" parents="250 1371 1342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1379">
    <literal><![CDATA[
      ((x \ 1) * y) / T(1 / x,y) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[para(1315(a,1),1332(a,1,2))].">
      <j1 rule="para" parents="1315 1332"/>
    </justification>
  </clause>

  <clause id="1380">
    <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(1379(a,1),834(a,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="1379 834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1382">
    <literal><![CDATA[
      (K(x \ 1,x) * ((y * z) * u)) / (z * u) = R(K(x \ 1,x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(1318(a,1),1338(a,1,1))].">
      <j1 rule="para" parents="1318 1338"/>
    </justification>
  </clause>

  <clause id="1383">
    <literal><![CDATA[
      R(x \ 1,x,y) = ((y / (x * y)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(41,a,706,a,b,1373,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="41 706 1373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1384">
    <literal><![CDATA[
      (R(1 / x,x,y) \ 1) \ 1 = R(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[para(183(a,2),1383(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="183 1383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1385">
    <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,1320,a(flip),b,1382,a)].">
      <j1 rule="hyper" parents="65 1320 1382"/>
    </justification>
  </clause>

  <clause id="1386">
    <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),1385(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20 1385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1387">
    <literal><![CDATA[
      K(x,x \ 1) * R(K(x \ 1,x) * y,z,u) = R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(1365,a,1386,a(flip))].">
      <j1 rule="hyper" parents="1365 1386"/>
    </justification>
  </clause>

  <clause id="1388">
    <literal><![CDATA[
      (x * (1 / x)) * R(K(x \ 1,x) * y,z,u) = R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(36,a,1366,a,b,1386,a(flip))].">
      <j1 rule="hyper" parents="36 1366 1386"/>
    </justification>
  </clause>

  <clause id="1389">
    <literal><![CDATA[
      R((x * (1 / x)) * y,z,u) = (x * (1 / x)) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(1366(a,1),1388(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1366 1388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1390">
    <literal><![CDATA[
      (x \ 1) * R((x * (1 / x)) * y,z,u) = (1 / x) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(1389(a,2),1357(a,1,2))].">
      <j1 rule="para" parents="1389 1357"/>
    </justification>
  </clause>

  <clause id="1391">
    <literal><![CDATA[
      (1 / x) * R((1 / x) \ y,z,u) = (x \ 1) * R((x \ 1) \ y,z,u)
    ]]></literal>
    <justification jstring="[para(1358(a,1),1390(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1358 1390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1392">
    <literal><![CDATA[
      (1 / x) * R((1 / x) \ y,z,u) = x \ R(x * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(250,a,628,a(flip),b,1391,a),flip(a)].">
      <j1 rule="hyper" parents="250 628 1391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1393">
    <literal><![CDATA[
      R(x * y,z,u) / y = y \ R(y * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,676,a(flip),b,1392,a)].">
      <j1 rule="hyper" parents="65 676 1392"/>
    </justification>
  </clause>

  <clause id="1394">
    <literal><![CDATA[
      x * (R(y * x,z,u) / x) = R(x * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(116,a,676,a(flip),b,1392,a(flip))].">
      <j1 rule="hyper" parents="116 676 1392"/>
    </justification>
  </clause>

  <clause id="1395">
    <literal><![CDATA[
      R((x \ y) * x,z,u) / x = x \ R(y,z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),1393(a,2,2,1))].">
      <j1 rule="para" parents="10 1393"/>
    </justification>
  </clause>

  <clause id="1396">
    <literal><![CDATA[
      R(x * (y / x),z,u) = x * (R(y,z,u) / x)
    ]]></literal>
    <justification jstring="[para(12(a,1),1394(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="12 1394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1397">
    <literal><![CDATA[
      R((x \ y) * x,z,u) = (x \ R(y,z,u)) * x
    ]]></literal>
    <justification jstring="[hyper(124,a,1395,a),flip(a)].">
      <j1 rule="hyper" parents="124 1395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1398">
    <literal><![CDATA[
      R(x,y,z) / x = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(148(a,1),1395(a,1,1,1))].">
      <j1 rule="para" parents="148 1395"/>
    </justification>
  </clause>

  <clause id="1402">
    <literal><![CDATA[
      (1 / x) * R(x,y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,1027,a,b,1398,a)].">
      <j1 rule="hyper" parents="65 1027 1398"/>
    </justification>
  </clause>

  <clause id="1403">
    <literal><![CDATA[
      T(x,x \ R(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(38,a,221,a,b,1398,a)].">
      <j1 rule="hyper" parents="38 221 1398"/>
    </justification>
  </clause>

  <clause id="1404">
    <literal><![CDATA[
      R(x \ R(x,y,z),x,y * z) = ((x * y) * z) / (x * (y * z))
    ]]></literal>
    <justification jstring="[para(1398(a,1),383(a,1,1))].">
      <j1 rule="para" parents="1398 383"/>
    </justification>
  </clause>

  <clause id="1405">
    <literal><![CDATA[
      R(R(x,y,z) \ R(R(x,y,z),u,w),R(x,y,z),y * z) = (R(R(x,y,z),u,w) * (y * z)) / ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(1398(a,1),384(a,1,1))].">
      <j1 rule="para" parents="1398 384"/>
    </justification>
  </clause>

  <clause id="1407">
    <literal><![CDATA[
      (R(x,y,z) \ x) * R(x,y,z) = x
    ]]></literal>
    <justification jstring="[hyper(44,a,148,a(flip),b,1397,a),flip(a)].">
      <j1 rule="hyper" parents="44 148 1397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1408">
    <literal><![CDATA[
      R((x \ (y / z)) * x,z,z \ 1) = (x \ (y * (z \ 1))) * x
    ]]></literal>
    <justification jstring="[para(377(a,1),1397(a,2,1,2))].">
      <j1 rule="para" parents="377 1397"/>
    </justification>
  </clause>

  <clause id="1410">
    <literal><![CDATA[
      ((x \ (y * (z \ 1))) * x) / (z \ 1) = ((x \ (y / z)) * x) * z
    ]]></literal>
    <justification jstring="[hyper(113,a,1408,a(flip),b,219,a)].">
      <j1 rule="hyper" parents="113 1408 219"/>
    </justification>
  </clause>

  <clause id="1411">
    <literal><![CDATA[
      (x \ T(x,y)) \ (x \ 1) = 1 / T(T(x,x \ 1),y)
    ]]></literal>
    <justification jstring="[para(761(a,1),1377(a,1,1))].">
      <j1 rule="para" parents="761 1377"/>
    </justification>
  </clause>

  <clause id="1412">
    <literal><![CDATA[
      1 / T(T(x,x \ 1),y) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,1233,a(flip),b,1411,a),flip(a)].">
      <j1 rule="hyper" parents="65 1233 1411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1413">
    <literal><![CDATA[
      T(T(x,x \ 1),y) = (T(x,y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(163,a,1412,a),flip(a)].">
      <j1 rule="hyper" parents="163 1412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1414">
    <literal><![CDATA[
      T(1 / (1 / x),y) \ 1 = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[para(264(a,1),1412(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="264 1412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1415">
    <literal><![CDATA[
      T((x \ 1) \ 1,y) = (T(x,y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(105(a,1),1413(a,1,1))].">
      <j1 rule="para" parents="105 1413"/>
    </justification>
  </clause>

  <clause id="1416">
    <literal><![CDATA[
      1 / (1 / T(x,y)) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[hyper(171,a,1414,a)].">
      <j1 rule="hyper" parents="171 1414"/>
    </justification>
  </clause>

  <clause id="1417">
    <literal><![CDATA[
      x * ((T(y,x) \ 1) \ 1) = ((y \ 1) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(116,a,1415,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="116 1415 22"/>
    </justification>
  </clause>

  <clause id="1418">
    <literal><![CDATA[
      T(((x / y) \ 1) \ 1,y) = ((y \ x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(106(a,1),1415(a,2,1,1))].">
      <j1 rule="para" parents="106 1415"/>
    </justification>
  </clause>

  <clause id="1419">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(480,a,1417,a)].">
      <j1 rule="hyper" parents="480 1417"/>
    </justification>
  </clause>

  <clause id="1420">
    <literal><![CDATA[
      (((x / y) \ 1) \ 1) * y = y * (((y \ x) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(106(a,1),1417(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="106 1417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1421">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) = x * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(250,a,1311,a,b,1419,a),flip(a)].">
      <j1 rule="hyper" parents="250 1311 1419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1422">
    <literal><![CDATA[
      T(K(x,x \ 1),y) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(1336,a,1421,a)].">
      <j1 rule="hyper" parents="1336 1421"/>
    </justification>
  </clause>

  <clause id="1423">
    <literal><![CDATA[
      T(x,K(y,y \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(56,a,1422,a)].">
      <j1 rule="hyper" parents="56 1422"/>
    </justification>
  </clause>

  <clause id="1424">
    <literal><![CDATA[
      K(x,x \ 1) * y = y * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,1422,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 1422 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1427">
    <literal><![CDATA[
      T(x,K(y \ 1,y)) = x
    ]]></literal>
    <justification jstring="[para(1303(a,1),1423(a,1,2))].">
      <j1 rule="para" parents="1303 1423"/>
    </justification>
  </clause>

  <clause id="1428">
    <literal><![CDATA[
      T(K(x \ 1,x),y) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(56,a,1427,a)].">
      <j1 rule="hyper" parents="56 1427"/>
    </justification>
  </clause>

  <clause id="1429">
    <literal><![CDATA[
      K(x \ 1,x) * y = y * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,1427,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="116 1427 22"/>
    </justification>
  </clause>

  <clause id="1431">
    <literal><![CDATA[
      K(x \ (x / T(x,y)),x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,836,a,b,1428,a)].">
      <j1 rule="hyper" parents="65 836 1428"/>
    </justification>
  </clause>

  <clause id="1432">
    <literal><![CDATA[
      x * K(y \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ 1,y) * x = z
    ]]></literal>
    <justification jstring="[para(1428(a,1),231(a,1,2))].">
      <j1 rule="para" parents="1428 231"/>
    </justification>
  </clause>

  <clause id="1433">
    <literal><![CDATA[
      (K(x \ 1,x) * y) * K(x,x \ 1) = y
    ]]></literal>
    <justification jstring="[hyper(36,a,1364,a,b,1424,a)].">
      <j1 rule="hyper" parents="36 1364 1424"/>
    </justification>
  </clause>

  <clause id="1434">
    <literal><![CDATA[
      K(x \ 1,x) * (y * K(x,x \ 1)) = y
    ]]></literal>
    <justification jstring="[hyper(116,a,1424,a(flip),b,1363,a)].">
      <j1 rule="hyper" parents="116 1424 1363"/>
    </justification>
  </clause>

  <clause id="1435">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * z = K(y,y \ 1) * (x * z)
    ]]></literal>
    <justification jstring="[para(1424(a,1),1323(a,1,1))].">
      <j1 rule="para" parents="1424 1323"/>
    </justification>
  </clause>

  <clause id="1436">
    <literal><![CDATA[
      K(x,x \ 1) * (y * K(x \ 1,x)) = y
    ]]></literal>
    <justification jstring="[hyper(1365,a,1429,a)].">
      <j1 rule="hyper" parents="1365 1429"/>
    </justification>
  </clause>

  <clause id="1438">
    <literal><![CDATA[
      (x * y) * K(x \ 1,x) = (1 / (1 / x)) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,1340,a(flip),b,1429,a),flip(a)].">
      <j1 rule="hyper" parents="65 1340 1429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1440">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ ((z * y) * K(x \ 1,x)) = R(T(z,y * K(x \ 1,x)),y,K(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(1429(a,2),432(a,1,1))].">
      <j1 rule="para" parents="1429 432"/>
    </justification>
  </clause>

  <clause id="1441">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ ((z * y) * K(x \ 1,x)) != u
    ]]></literal>
    <literal><![CDATA[
      L(T(z,y),y,K(x \ 1,x)) = u
    ]]></literal>
    <justification jstring="[para(1429(a,1),492(a,1,2))].">
      <j1 rule="para" parents="1429 492"/>
    </justification>
  </clause>

  <clause id="1442">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * z = K(y \ 1,y) * (x * z)
    ]]></literal>
    <justification jstring="[para(1429(a,1),1318(a,1,1))].">
      <j1 rule="para" parents="1429 1318"/>
    </justification>
  </clause>

  <clause id="1444">
    <literal><![CDATA[
      x * K(x \ (x / T(x,y)),x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(116,a,1431,a,b,1098,a)].">
      <j1 rule="hyper" parents="116 1431 1098"/>
    </justification>
  </clause>

  <clause id="1445">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * K(y,y \ 1) = x
    ]]></literal>
    <justification jstring="[para(1429(a,1),1433(a,1,1))].">
      <j1 rule="para" parents="1429 1433"/>
    </justification>
  </clause>

  <clause id="1446">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ z = y \ (z * K(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(1436(a,1),1324(a,1,2))].">
      <j1 rule="para" parents="1436 1324"/>
    </justification>
  </clause>

  <clause id="1447">
    <literal><![CDATA[
      T(T(x / y,y / x),y) = ((y \ x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(1153(a,2),1418(a,1,1))].">
      <j1 rule="para" parents="1153 1418"/>
    </justification>
  </clause>

  <clause id="1448">
    <literal><![CDATA[
      ((x \ y) * z) * K(y \ x,x \ y) = (1 / (1 / (x \ y))) * z
    ]]></literal>
    <justification jstring="[para(1295(a,1),1438(a,1,2))].">
      <j1 rule="para" parents="1295 1438"/>
    </justification>
  </clause>

  <clause id="1449">
    <literal><![CDATA[
      T(x,y) \ (1 / (1 / x)) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(112,a,1444,a(flip),b,661,a)].">
      <j1 rule="hyper" parents="112 1444 661"/>
    </justification>
  </clause>

  <clause id="1450">
    <literal><![CDATA[
      T(x \ y,x / y) = ((x \ y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(463,a,1447,a)].">
      <j1 rule="hyper" parents="463 1447"/>
    </justification>
  </clause>

  <clause id="1451">
    <literal><![CDATA[
      T(x \ (y \ x),y) = ((x \ (y \ x)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(76(a,1),1450(a,1,2))].">
      <j1 rule="para" parents="76 1450"/>
    </justification>
  </clause>

  <clause id="1452">
    <literal><![CDATA[
      x * (((x \ (y \ x)) \ 1) \ 1) = ((y \ 1) \ 1) \ x
    ]]></literal>
    <justification jstring="[para(1451(a,1),1345(a,1,2))].">
      <j1 rule="para" parents="1451 1345"/>
    </justification>
  </clause>

  <clause id="1453">
    <literal><![CDATA[
      (x * (y * K(z \ 1,z))) \ (K(z \ 1,z) * (y * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * K(z \ 1,z),x) = u
    ]]></literal>
    <justification jstring="[para(1442(a,1),246(a,1,2))].">
      <j1 rule="para" parents="1442 246"/>
    </justification>
  </clause>

  <clause id="1454">
    <literal><![CDATA[
      (x * (y * K(z \ 1,z))) \ (x * (K(z \ 1,z) * (y * u))) != w
    ]]></literal>
    <literal><![CDATA[
      L(u,y * K(z \ 1,z),x) = w
    ]]></literal>
    <justification jstring="[para(1442(a,1),342(a,1,2,2))].">
      <j1 rule="para" parents="1442 342"/>
    </justification>
  </clause>

  <clause id="1455">
    <literal><![CDATA[
      (((x / y) \ 1) \ 1) \ x = x * (((x \ y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(79(a,1),1452(a,1,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="79 1452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1456">
    <literal><![CDATA[
      x / ((((y / x) \ 1) \ 1) * x) = ((x / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(170,a,1420,a,b,1455,a)].">
      <j1 rule="hyper" parents="170 1420 1455"/>
    </justification>
  </clause>

  <clause id="1457">
    <literal><![CDATA[
      x / (((y \ 1) \ 1) * x) = ((x / (y * x)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(11(a,1),1456(a,1,2,1,1,1))].">
      <j1 rule="para" parents="11 1456"/>
    </justification>
  </clause>

  <clause id="1458">
    <literal><![CDATA[
      R(x \ 1,x,y) = y / (((x \ 1) \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(250,a,1383,a,b,1457,a)].">
      <j1 rule="hyper" parents="250 1383 1457"/>
    </justification>
  </clause>

  <clause id="1459">
    <literal><![CDATA[
      R(x \ 1,(x \ 1) \ 1,y) = R(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(250,a,179,a,b,1458,a)].">
      <j1 rule="hyper" parents="250 179 1458"/>
    </justification>
  </clause>

  <clause id="1460">
    <literal><![CDATA[
      ((x \ (x / y)) * z) * K(y,x \ (x / y)) = (1 / (1 / (x \ (x / y)))) * z
    ]]></literal>
    <justification jstring="[para(79(a,1),1448(a,1,2,1))].">
      <j1 rule="para" parents="79 1448"/>
    </justification>
  </clause>

  <clause id="1461">
    <literal><![CDATA[
      ((x \ 1) * x) * (x * L(x \ 1,x,y)) = (x * ((y * x) \ y)) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(216(a,1),1378(a,1,1))].">
      <j1 rule="para" parents="216 1378"/>
    </justification>
  </clause>

  <clause id="1462">
    <literal><![CDATA[
      ((x \ 1) * (x * L(x \ 1,x,y))) * x = (x * ((y * x) \ y)) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,1117,a,b,1461,a)].">
      <j1 rule="hyper" parents="65 1117 1461"/>
    </justification>
  </clause>

  <clause id="1463">
    <literal><![CDATA[
      (x * y) \ x = (y \ 1) * (y * L(y \ 1,y,x))
    ]]></literal>
    <justification jstring="[hyper(37,a,1299,a(flip),b,1462,a)].">
      <j1 rule="hyper" parents="37 1299 1462"/>
    </justification>
  </clause>

  <clause id="1464">
    <literal><![CDATA[
      (x \ 1) * (x * ((y * x) \ y)) = (y * x) \ y
    ]]></literal>
    <justification jstring="[para(181(a,1),1463(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="181 1463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1465">
    <literal><![CDATA[
      (x \ 1) \ ((y * x) \ y) = x * ((y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(118,a,1464,a)].">
      <j1 rule="hyper" parents="118 1464"/>
    </justification>
  </clause>

  <clause id="1466">
    <literal><![CDATA[
      L(x * ((y * x) \ y),x \ 1,y * x) = ((y * x) * (x \ 1)) \ y
    ]]></literal>
    <justification jstring="[para(1465(a,1),239(a,1,1))].">
      <j1 rule="para" parents="1465 239"/>
    </justification>
  </clause>

  <clause id="1467">
    <literal><![CDATA[
      L(x * ((y * x) \ y),x \ 1,y * x) = R(y,x,x \ 1) \ y
    ]]></literal>
    <justification jstring="[para(219(a,1),1466(a,2,1))].">
      <j1 rule="para" parents="219 1466"/>
    </justification>
  </clause>

  <clause id="1468">
    <literal><![CDATA[
      x * (y * ((x * (y \ (x \ z))) / x)) = (x * ((z / y) / x)) * y
    ]]></literal>
    <justification jstring="[hyper(1253,a,1131,a)].">
      <j1 rule="hyper" parents="1253 1131"/>
    </justification>
  </clause>

  <clause id="1469">
    <literal><![CDATA[
      x * (y * ((z * (y \ (x \ (u * y)))) / z)) = (x * ((z * (x \ u)) / z)) * y
    ]]></literal>
    <justification jstring="[hyper(1253,a,1130,a)].">
      <j1 rule="hyper" parents="1253 1130"/>
    </justification>
  </clause>

  <clause id="1470">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ u)) / z) = x * (y * ((z * (y \ (x \ u))) / z))
    ]]></literal>
    <justification jstring="[hyper(1253,a,xx),flip(a)].">
      <j1 rule="hyper" parents="1253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1471">
    <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(378(a,2),1468(a,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="378 1468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1472">
    <literal><![CDATA[
      (x * ((y / (z * (x \ y))) / x)) * (z * (x \ y)) = x * ((z * ((x * (z \ 1)) / x)) * (x \ y))
    ]]></literal>
    <justification jstring="[para(992(a,1),1468(a,1,2)),flip(a)].">
      <j1 rule="para" parents="992 1468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1473">
    <literal><![CDATA[
      (x * ((y * (x \ z)) / y)) * y = x * (y * ((x \ (z * y)) / y))
    ]]></literal>
    <justification jstring="[para(10(a,1),1469(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 1469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1474">
    <literal><![CDATA[
      ((x * y) * ((z * ((x * y) \ x)) / z)) * z = (x * y) * (z * (L(y \ z,y,x) / z))
    ]]></literal>
    <justification jstring="[para(95(a,2),1473(a,2,2,2,1))].">
      <j1 rule="para" parents="95 1473"/>
    </justification>
  </clause>

  <clause id="1475">
    <literal><![CDATA[
      R(a(x,y,z) * u,L(w,u,a(x,y,z)),v5) = a(x,y,z) * (((u * w) * v5) / (w * v5))
    ]]></literal>
    <justification jstring="[hyper(250,a,472,a(flip),b,1285,a),flip(a)].">
      <j1 rule="hyper" parents="250 472 1285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1476">
    <literal><![CDATA[
      R(a(x,y,z) * u,L(w,u,a(x,y,z)),v5) = a(x,y,z) * R(u,w,v5)
    ]]></literal>
    <justification jstring="[para(20(a,2),1475(a,2,2))].">
      <j1 rule="para" parents="20 1475"/>
    </justification>
  </clause>

  <clause id="1477">
    <literal><![CDATA[
      R(a(x,y,z) * u,w,v5) = a(x,y,z) * R(u,w,v5)
    ]]></literal>
    <justification jstring="[para(128(a,1),1476(a,1,2))].">
      <j1 rule="para" parents="128 1476"/>
    </justification>
  </clause>

  <clause id="1478">
    <literal><![CDATA[
      (a(x,y,z) * (u * (w * v5))) \ ((a(x,y,z) * (u * w)) * v5) = a(a(x,y,z) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(315(a,1),524(a,1,2,1))].">
      <j1 rule="para" parents="315 524"/>
    </justification>
  </clause>

  <clause id="1479">
    <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),909(a,1,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="22 909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1485">
    <literal><![CDATA[
      ((x / y) * ((z * ((x / y) \ u)) / z)) * y = x * ((z * (x \ (u * y))) / z)
    ]]></literal>
    <justification jstring="[para(12(a,1),1155(a,2,2,1,2,1))].">
      <j1 rule="para" parents="12 1155"/>
    </justification>
  </clause>

  <clause id="1486">
    <literal><![CDATA[
      (x * ((y * (x \ (z * u))) / y)) / u = (x / u) * ((y * ((x / u) \ z)) / y)
    ]]></literal>
    <justification jstring="[hyper(123,a,1485,a)].">
      <j1 rule="hyper" parents="123 1485"/>
    </justification>
  </clause>

  <clause id="1487">
    <literal><![CDATA[
      (x / y) * ((z * ((x / y) \ 1)) / z) = (x * ((z * (x \ y)) / z)) / y
    ]]></literal>
    <justification jstring="[para(7(a,1),1486(a,1,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 1486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1488">
    <literal><![CDATA[
      (x * (y * T(y \ 1,x))) * (x \ 1) = x \ (x * (y * T(y \ 1,x)))
    ]]></literal>
    <justification jstring="[para(1164(a,1),1166(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1164 1166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1489">
    <literal><![CDATA[
      (x * (y * T(y \ 1,x))) * (x \ 1) = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(250,a,9,a(flip),b,1488,a),flip(a)].">
      <j1 rule="hyper" parents="250 9 1488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1491">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ 1,y) = (y * (x \ T(x,y))) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(587(a,1),1489(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="587 1489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1492">
    <literal><![CDATA[
      (x * (y \ T(y,x))) * (x \ 1) = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(592,a,1491,a),flip(a)].">
      <j1 rule="hyper" parents="592 1491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1493">
    <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(250,a,217,a(flip),b,1167,a),flip(a)].">
      <j1 rule="hyper" parents="250 217 1167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1494">
    <literal><![CDATA[
      L(x * T(x \ 1,y),y,1 / y) = (y * (x * T(x \ 1,y))) / y
    ]]></literal>
    <justification jstring="[para(1164(a,1),1493(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1164 1493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1495">
    <literal><![CDATA[
      (x * (((x * y) \ x) * T(((x * y) \ x) \ 1,x))) / x = L(K(y,x),x,1 / x)
    ]]></literal>
    <justification jstring="[para(607(a,2),1494(a,1,1)),flip(a)].">
      <j1 rule="para" parents="607 1494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1496">
    <literal><![CDATA[
      L(K(x,y),y,1 / y) = (y * K(x,y)) / y
    ]]></literal>
    <justification jstring="[para(607(a,2),1495(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="607 1495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1497">
    <literal><![CDATA[
      a(a(x,y,z) * u,w,v5) = (u * (w * v5)) \ ((u * w) * v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,530,a(flip),b,1478,a),flip(a)].">
      <j1 rule="hyper" parents="65 530 1478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1499">
    <literal><![CDATA[
      a(a(x,y,z) * u,w,v5) = a(u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(250,a,14,a,b,1497,a),flip(a)].">
      <j1 rule="hyper" parents="250 14 1497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1500">
    <literal><![CDATA[
      a(a(x,y,z) \ u,w,v5) = a(u,w,v5)
    ]]></literal>
    <justification jstring="[para(10(a,1),1499(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 1499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1501">
    <literal><![CDATA[
      (x * y) * K(z \ (z / L(u,y,x)),z) = x * ((y * u) * T((y * u) \ y,z))
    ]]></literal>
    <justification jstring="[hyper(564,a,684,a),flip(a)].">
      <j1 rule="hyper" parents="564 684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1502">
    <literal><![CDATA[
      (x * y) * K(z \ (z / L(u,y,x)),z) = x * (y * (u * T(u \ 1,z)))
    ]]></literal>
    <justification jstring="[para(478(a,1),1501(a,2,2))].">
      <j1 rule="para" parents="478 1501"/>
    </justification>
  </clause>

  <clause id="1503">
    <literal><![CDATA[
      L(x * T(x \ 1,y),z,u) = K(y \ (y / L(x,z,u)),y)
    ]]></literal>
    <justification jstring="[hyper(341,a,1502,a)].">
      <j1 rule="hyper" parents="341 1502"/>
    </justification>
  </clause>

  <clause id="1504">
    <literal><![CDATA[
      K(x \ (x / R(y,z,u)),x) = (((y * z) * T((y * z) \ z,x)) * u) / (z * u)
    ]]></literal>
    <justification jstring="[para(906(a,1),916(a,2,1))].">
      <j1 rule="para" parents="906 916"/>
    </justification>
  </clause>

  <clause id="1505">
    <literal><![CDATA[
      K(x \ (x / R(y,z,u)),x) = (((y * T(y \ 1,x)) * z) * u) / (z * u)
    ]]></literal>
    <justification jstring="[para(686(a,1),1504(a,2,1,1))].">
      <j1 rule="para" parents="686 1504"/>
    </justification>
  </clause>

  <clause id="1506">
    <literal><![CDATA[
      R(x * T(x \ 1,y),z,u) = K(y \ (y / R(x,z,u)),y)
    ]]></literal>
    <justification jstring="[hyper(250,a,20,a,b,1505,a)].">
      <j1 rule="hyper" parents="250 20 1505"/>
    </justification>
  </clause>

  <clause id="1507">
    <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(250,a,608,a(flip),b,1506,a)].">
      <j1 rule="hyper" parents="250 608 1506"/>
    </justification>
  </clause>

  <clause id="1508">
    <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(216(a,2),634(a,1,2,1,1))].">
      <j1 rule="para" parents="216 634"/>
    </justification>
  </clause>

  <clause id="1509">
    <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(250,a,994,a(flip),b,1508,a),flip(a)].">
      <j1 rule="hyper" parents="250 994 1508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1510">
    <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(627(a,1),1509(a,2,1))].">
      <j1 rule="para" parents="627 1509"/>
    </justification>
  </clause>

  <clause id="1511">
    <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(1363(a,1),1510(a,1,2,1))].">
      <j1 rule="para" parents="1363 1510"/>
    </justification>
  </clause>

  <clause id="1512">
    <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),1511(a,1,2,1,2))].">
      <j1 rule="para" parents="12 1511"/>
    </justification>
  </clause>

  <clause id="1513">
    <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(1424(a,1),1512(a,1,2,1))].">
      <j1 rule="para" parents="1424 1512"/>
    </justification>
  </clause>

  <clause id="1514">
    <literal><![CDATA[
      R(T(x,y * K(z \ 1,z)),y,K(z \ 1,z)) = L(T(x,y),y,K(z \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(1441,a,1440,a),flip(a)].">
      <j1 rule="hyper" parents="1441 1440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1515">
    <literal><![CDATA[
      R(T(x,y * K(z \ 1,z)),y,K(z \ 1,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(250,a,1315,a(flip),b,1514,a),flip(a)].">
      <j1 rule="hyper" parents="250 1315 1514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1517">
    <literal><![CDATA[
      (x * (T(y,x) * L(x,z,u))) \ ((y * L(x,z,u)) * x) = a(L(x,z,u),T(y,L(x,z,u)),x)
    ]]></literal>
    <justification jstring="[para(197(a,1),828(a,1,1,2))].">
      <j1 rule="para" parents="197 828"/>
    </justification>
  </clause>

  <clause id="1518">
    <literal><![CDATA[
      (x * (T(y,x) * L(x,z,u))) \ ((y * x) * L(x,z,u)) = a(L(x,z,u),T(y,L(x,z,u)),x)
    ]]></literal>
    <justification jstring="[para(964(a,1),1517(a,1,2))].">
      <j1 rule="para" parents="964 1517"/>
    </justification>
  </clause>

  <clause id="1519">
    <literal><![CDATA[
      a(L(x,y,z),T(u,L(x,y,z)),x) = a(x,T(u,x),L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,193,a(flip),b,1518,a),flip(a)].">
      <j1 rule="hyper" parents="65 193 1518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1520">
    <literal><![CDATA[
      L(L(x,y,1 / z),(1 / z) * y,K(z \ 1,z)) = ((z \ 1) * y) \ ((z \ 1) * (y * x))
    ]]></literal>
    <justification jstring="[para(1321(a,1),1333(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1321 1333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1521">
    <literal><![CDATA[
      L(L(x,y,1 / z),(1 / z) * y,K(z \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(1520(a,2),342(a,1))].">
      <j1 rule="para" parents="1520 342"/>
    </justification>
  </clause>

  <clause id="1522">
    <literal><![CDATA[
      L(x,y,1 / z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(1315(a,1),1521(a,1))].">
      <j1 rule="para" parents="1315 1521"/>
    </justification>
  </clause>

  <clause id="1524">
    <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(1329(a,2),1522(a,1))].">
      <j1 rule="para" parents="1329 1522"/>
    </justification>
  </clause>

  <clause id="1525">
    <literal><![CDATA[
      R(R(x,y,z) \ R(R(x,y,z),u,w),R(x,y,z),y * z) = ((R(x,u,w) * y) * z) / ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(309(a,1),1405(a,2,1))].">
      <j1 rule="para" parents="309 1405"/>
    </justification>
  </clause>

  <clause id="1526">
    <literal><![CDATA[
      (x * (1 / y)) * (z * R(z \ L((1 / y) \ z,1 / y,x),u,w)) = ((x * (1 / y)) * R(L(y,1 / y,x),u,w)) * z
    ]]></literal>
    <justification jstring="[para(95(a,2),1034(a,2,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="95 1034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1527">
    <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(250,a,1468,a(flip),b,1471,a),flip(a)].">
      <j1 rule="hyper" parents="250 1468 1471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1528">
    <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(1396(a,2),1527(a,1,1))].">
      <j1 rule="para" parents="1396 1527"/>
    </justification>
  </clause>

  <clause id="1529">
    <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(1528(a,1),230(a,1))].">
      <j1 rule="para" parents="1528 230"/>
    </justification>
  </clause>

  <clause id="1530">
    <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(100(a,1),950(a,1,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="100 950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1531">
    <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(250,a,1042,a(flip),b,1530,a),flip(a)].">
      <j1 rule="hyper" parents="250 1042 1530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1532">
    <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(541(a,1),1531(a,1,1))].">
      <j1 rule="para" parents="541 1531"/>
    </justification>
  </clause>

  <clause id="1533">
    <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(992(a,1),1532(a,2,1))].">
      <j1 rule="para" parents="992 1532"/>
    </justification>
  </clause>

  <clause id="1534">
    <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,100,a,b,1533,a),flip(a)].">
      <j1 rule="hyper" parents="37 100 1533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1535">
    <literal><![CDATA[
      R(x * ((y * (x \ 1)) / y),z,u) = K(y,(y / R(x,z,u)) / y)
    ]]></literal>
    <justification jstring="[hyper(65,a,987,a,b,1534,a),flip(a)].">
      <j1 rule="hyper" parents="65 987 1534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1536">
    <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(93(a,1),1265(a,1,2,1,2,1))].">
      <j1 rule="para" parents="93 1265"/>
    </justification>
  </clause>

  <clause id="1537">
    <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(750,a,1536,a),flip(a)].">
      <j1 rule="hyper" parents="750 1536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1538">
    <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(1256(a,1),1537(a,2,2))].">
      <j1 rule="para" parents="1256 1537"/>
    </justification>
  </clause>

  <clause id="1539">
    <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(341,a,1538,a),flip(a)].">
      <j1 rule="hyper" parents="341 1538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1540">
    <literal><![CDATA[
      R(x,y,y \ 1) * R(L(T(y,y \ 1),y \ 1,x * y),z,u) = x * (a(x,y,y \ 1) * R((x \ R(x,y,y \ 1)) \ y,z,u))
    ]]></literal>
    <justification jstring="[para(475(a,1),945(a,2,2,1))].">
      <j1 rule="para" parents="475 945"/>
    </justification>
  </clause>

  <clause id="1541">
    <literal><![CDATA[
      R(x,y,y \ 1) * R(L(T(y,y \ 1),y \ 1,x * y),z,u) = x * (a(x,y,y \ 1) * R(a(x,y,y \ 1) \ y,z,u))
    ]]></literal>
    <justification jstring="[para(475(a,1),1540(a,2,2,2,1,1))].">
      <j1 rule="para" parents="475 1540"/>
    </justification>
  </clause>

  <clause id="1542">
    <literal><![CDATA[
      R(x,y,y \ 1) * R(L(T(y,y \ 1),y \ 1,x * y),z,u) = x * R(a(x,y,y \ 1) * (a(x,y,y \ 1) \ y),z,u)
    ]]></literal>
    <justification jstring="[para(1477(a,2),1541(a,2,2))].">
      <j1 rule="para" parents="1477 1541"/>
    </justification>
  </clause>

  <clause id="1543">
    <literal><![CDATA[
      R(x,y,y \ 1) * R(L(T(y,y \ 1),y \ 1,x * y),z,u) = x * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),1542(a,2,2,1))].">
      <j1 rule="para" parents="10 1542"/>
    </justification>
  </clause>

  <clause id="1544">
    <literal><![CDATA[
      R(x,y,y \ 1) * L(R(T(y,y \ 1),z,u),y \ 1,x * y) = x * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(29(a,1),1543(a,1,2))].">
      <j1 rule="para" parents="29 1543"/>
    </justification>
  </clause>

  <clause id="1545">
    <literal><![CDATA[
      (x * y) * ((y \ 1) * R(T(y,y \ 1),z,u)) = x * R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,394,a(flip),b,1544,a)].">
      <j1 rule="hyper" parents="65 394 1544"/>
    </justification>
  </clause>

  <clause id="1546">
    <literal><![CDATA[
      (x * y) * (R(y,z,u) * (y \ 1)) = x * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(199(a,1),1545(a,1,2))].">
      <j1 rule="para" parents="199 1545"/>
    </justification>
  </clause>

  <clause id="1547">
    <literal><![CDATA[
      (x * y) * (y \ R(y,z,u)) = x * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(670(a,1),1546(a,1,2))].">
      <j1 rule="para" parents="670 1546"/>
    </justification>
  </clause>

  <clause id="1548">
    <literal><![CDATA[
      (x / y) * R(y,z,u) = x * (y \ R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(253,a,1547,a),flip(a)].">
      <j1 rule="hyper" parents="253 1547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1549">
    <literal><![CDATA[
      (x * y) \ (x * R(y,z,u)) = y \ R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(118,a,1547,a)].">
      <j1 rule="hyper" parents="118 1547"/>
    </justification>
  </clause>

  <clause id="1550">
    <literal><![CDATA[
      (x * y) \ (y * R(T(x,y),z,u)) = T(x,y) \ R(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(112,a,1547,a(flip),b,189,a(flip))].">
      <j1 rule="hyper" parents="112 1547 189"/>
    </justification>
  </clause>

  <clause id="1551">
    <literal><![CDATA[
      (x \ y) \ R(x \ y,z,u) = y \ (x * R(x \ y,z,u))
    ]]></literal>
    <justification jstring="[hyper(112,a,1547,a(flip),b,130,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="112 1547 130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1552">
    <literal><![CDATA[
      T(x,y) \ R(T(x,y),z,u) = (x * y) \ (R(x,z,u) * y)
    ]]></literal>
    <justification jstring="[para(199(a,1),1550(a,1,2)),flip(a)].">
      <j1 rule="para" parents="199 1550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1553">
    <literal><![CDATA[
      T(x,y * z) \ R(T(x,y * z),y,z) = (x * (y * z)) \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(431(a,1),1550(a,1,2)),flip(a)].">
      <j1 rule="para" parents="431 1550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1554">
    <literal><![CDATA[
      a(x,y,z) = T(x,y * z) \ R(T(x,y * z),y,z)
    ]]></literal>
    <justification jstring="[hyper(250,a,14,a,b,1553,a)].">
      <j1 rule="hyper" parents="250 14 1553"/>
    </justification>
  </clause>

  <clause id="1555">
    <literal><![CDATA[
      (x * (y * z)) * (a(x,y,z) * R(a(x,y,z) \ ((x * (y * z)) \ u),w,v5)) = ((x * y) * z) * R(((x * y) * z) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(84(a,1),943(a,2,2,1,1))].">
      <j1 rule="para" parents="84 943"/>
    </justification>
  </clause>

  <clause id="1556">
    <literal><![CDATA[
      (x * (y * z)) * (a(x,y,z) * R(a(x,y,z) \ ((x * (y * z)) \ u),w,v5)) = (x * y) * (z * R(z \ ((x * y) \ u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(250,a,624,a(flip),b,1555,a),flip(a)].">
      <j1 rule="hyper" parents="250 624 1555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1557">
    <literal><![CDATA[
      (x * (y * z)) * R(a(x,y,z) * (a(x,y,z) \ ((x * (y * z)) \ u)),w,v5) = (x * y) * (z * R(z \ ((x * y) \ u),w,v5))
    ]]></literal>
    <justification jstring="[para(1477(a,2),1556(a,1,2))].">
      <j1 rule="para" parents="1477 1556"/>
    </justification>
  </clause>

  <clause id="1558">
    <literal><![CDATA[
      (x * (y * z)) * R((x * (y * z)) \ u,w,v5) = (x * y) * (z * R(z \ ((x * y) \ u),w,v5))
    ]]></literal>
    <justification jstring="[para(10(a,1),1557(a,1,2,1))].">
      <j1 rule="para" parents="10 1557"/>
    </justification>
  </clause>

  <clause id="1559">
    <literal><![CDATA[
      (x * y) * (z * R(z \ ((x * y) \ u),w,v5)) = x * ((y * z) * R((y * z) \ (x \ u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(795,a,1558,a),flip(a)].">
      <j1 rule="hyper" parents="795 1558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1561">
    <literal><![CDATA[
      (x * y) * (z * R(z \ ((x * y) \ u),w,v5)) = x * (y * (z * R(z \ (y \ (x \ u)),w,v5)))
    ]]></literal>
    <justification jstring="[para(624(a,1),1559(a,2,2))].">
      <j1 rule="para" parents="624 1559"/>
    </justification>
  </clause>

  <clause id="1562">
    <literal><![CDATA[
      (x * y) * (z * R(z \ L(y \ u,y,x),w,v5)) = x * (y * (z * R(z \ (y \ (x \ (x * u))),w,v5)))
    ]]></literal>
    <justification jstring="[para(95(a,2),1561(a,1,2,2,1,2))].">
      <j1 rule="para" parents="95 1561"/>
    </justification>
  </clause>

  <clause id="1563">
    <literal><![CDATA[
      (x * y) * (z * R(z \ L(y \ u,y,x),w,v5)) = x * (y * (z * R(z \ (y \ u),w,v5)))
    ]]></literal>
    <justification jstring="[para(9(a,1),1562(a,2,2,2,2,1,2,2))].">
      <j1 rule="para" parents="9 1562"/>
    </justification>
  </clause>

  <clause id="1564">
    <literal><![CDATA[
      ((x * (1 / y)) * R(L(y,1 / y,x),z,u)) * w = x * ((1 / y) * (w * R(w \ ((1 / y) \ w),z,u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,1526,a(flip),b,1563,a)].">
      <j1 rule="hyper" parents="65 1526 1563"/>
    </justification>
  </clause>

  <clause id="1565">
    <literal><![CDATA[
      ((x * (1 / y)) * R(L(y,1 / y,x),z,u)) * w = x * (((1 / y) * R((1 / y) \ 1,z,u)) * w)
    ]]></literal>
    <justification jstring="[para(1023(a,1),1564(a,2,2))].">
      <j1 rule="para" parents="1023 1564"/>
    </justification>
  </clause>

  <clause id="1566">
    <literal><![CDATA[
      ((x * (1 / y)) * R(L(y,1 / y,x),z,u)) * w = x * (((1 / y) * R(y,z,u)) * w)
    ]]></literal>
    <justification jstring="[para(79(a,1),1565(a,2,2,1,2,1))].">
      <j1 rule="para" parents="79 1565"/>
    </justification>
  </clause>

  <clause id="1567">
    <literal><![CDATA[
      ((x * (1 / y)) * R(L(y,1 / y,x),z,u)) * w = x * ((y \ R(y,z,u)) * w)
    ]]></literal>
    <justification jstring="[para(1402(a,1),1566(a,2,2,1))].">
      <j1 rule="para" parents="1402 1566"/>
    </justification>
  </clause>

  <clause id="1568">
    <literal><![CDATA[
      (x * ((1 / y) * R(y,z,u))) * w = x * ((y \ R(y,z,u)) * w)
    ]]></literal>
    <justification jstring="[para(313(a,1),1567(a,1,1))].">
      <j1 rule="para" parents="313 1567"/>
    </justification>
  </clause>

  <clause id="1569">
    <literal><![CDATA[
      (x * (y \ R(y,z,u))) * w = x * ((y \ R(y,z,u)) * w)
    ]]></literal>
    <justification jstring="[para(1402(a,1),1568(a,1,1,2))].">
      <j1 rule="para" parents="1402 1568"/>
    </justification>
  </clause>

  <clause id="1570">
    <literal><![CDATA[
      R(x,y \ R(y,z,u),w) = x
    ]]></literal>
    <justification jstring="[hyper(370,a,1569,a)].">
      <j1 rule="hyper" parents="370 1569"/>
    </justification>
  </clause>

  <clause id="1571">
    <literal><![CDATA[
      L(x,y \ R(y,z,u),w) = x
    ]]></literal>
    <justification jstring="[hyper(341,a,1569,a)].">
      <j1 rule="hyper" parents="341 1569"/>
    </justification>
  </clause>

  <clause id="1572">
    <literal><![CDATA[
      (x * (y \ R(y,z,u))) \ w = (y \ R(y,z,u)) \ (x \ w)
    ]]></literal>
    <justification jstring="[hyper(112,a,72,a(flip),b,1569,a)].">
      <j1 rule="hyper" parents="112 72 1569"/>
    </justification>
  </clause>

  <clause id="1574">
    <literal><![CDATA[
      R(x,a(y,z,u),w) = x
    ]]></literal>
    <justification jstring="[para(1554(a,2),1570(a,1,2))].">
      <j1 rule="para" parents="1554 1570"/>
    </justification>
  </clause>

  <clause id="1575">
    <literal><![CDATA[
      T((a(x,y,z) * u) \ (w * u),a(x,y,z)) = T(a(x,y,z) \ w,a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(794,a,1574,a)].">
      <j1 rule="hyper" parents="794 1574"/>
    </justification>
  </clause>

  <clause id="1576">
    <literal><![CDATA[
      (x * a(y,z,u)) * w = x * (a(y,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(115,a,1574,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="115 1574 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1577">
    <literal><![CDATA[
      x / (a(y,z,u) \ 1) = x * a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(113,a,1574,a(flip),b,219,a)].">
      <j1 rule="hyper" parents="113 1574 219"/>
    </justification>
  </clause>

  <clause id="1578">
    <literal><![CDATA[
      (x * (a(y,z,u) * w)) / w = x * a(y,z,u)
    ]]></literal>
    <justification jstring="[para(1574(a,1),359(a,1,1,1))].">
      <j1 rule="para" parents="1574 359"/>
    </justification>
  </clause>

  <clause id="1579">
    <literal><![CDATA[
      K(x * a(y,z,u),a(y,z,u) \ 1) = T(x,a(y,z,u)) \ x
    ]]></literal>
    <justification jstring="[para(1574(a,1),723(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1574 723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1581">
    <literal><![CDATA[
      L(x,a(y,z,u),w) = x
    ]]></literal>
    <justification jstring="[para(1554(a,2),1571(a,1,2))].">
      <j1 rule="para" parents="1554 1571"/>
    </justification>
  </clause>

  <clause id="1582">
    <literal><![CDATA[
      L(x,a(y,z,u),w) = L(x,v5 \ R(v5,v6,v7),v8)
    ]]></literal>
    <justification jstring="[hyper(250,a,1571,a,b,1581,a),flip(a)].">
      <j1 rule="hyper" parents="250 1571 1581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1583">
    <literal><![CDATA[
      (x * a(y,z,u)) \ w = a(y,z,u) \ (x \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,239,a(flip),b,1581,a)].">
      <j1 rule="hyper" parents="65 239 1581"/>
    </justification>
  </clause>

  <clause id="1585">
    <literal><![CDATA[
      a(x,a(y,z,u),w) = 1
    ]]></literal>
    <justification jstring="[hyper(55,a,1581,a)].">
      <j1 rule="hyper" parents="55 1581"/>
    </justification>
  </clause>

  <clause id="1586">
    <literal><![CDATA[
      x / (a(y,z,u) \ w) = (x / w) * a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(170,a,1581,a(flip),b,352,a(flip))].">
      <j1 rule="hyper" parents="170 1581 352"/>
    </justification>
  </clause>

  <clause id="1587">
    <literal><![CDATA[
      L(x,K(y,1 / y),z) = x
    ]]></literal>
    <justification jstring="[para(1313(a,1),1581(a,1,2))].">
      <j1 rule="para" parents="1313 1581"/>
    </justification>
  </clause>

  <clause id="1588">
    <literal><![CDATA[
      x * a(y,a(z,u,w),v5) = x
    ]]></literal>
    <justification jstring="[hyper(116,a,1585,a,b,68,a)].">
      <j1 rule="hyper" parents="116 1585 68"/>
    </justification>
  </clause>

  <clause id="1589">
    <literal><![CDATA[
      L(x,K(y \ 1,y),z) = x
    ]]></literal>
    <justification jstring="[para(76(a,1),1587(a,1,2,2))].">
      <j1 rule="para" parents="76 1587"/>
    </justification>
  </clause>

  <clause id="1591">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * z = x * (K(y \ 1,y) * z)
    ]]></literal>
    <justification jstring="[hyper(748,a,1589,a),flip(a)].">
      <j1 rule="hyper" parents="748 1589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1594">
    <literal><![CDATA[
      (x * (y * z)) * (a(x,y,z) * u) = ((x * y) * z) * u
    ]]></literal>
    <justification jstring="[para(84(a,1),1576(a,1,1)),flip(a)].">
      <j1 rule="para" parents="84 1576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1595">
    <literal><![CDATA[
      K(x \ 1,x) * (y * z) = y * (K(x \ 1,x) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,1442,a(flip),b,1591,a)].">
      <j1 rule="hyper" parents="65 1442 1591"/>
    </justification>
  </clause>

  <clause id="1596">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * ((y \ 1) \ 1) = x * y
    ]]></literal>
    <justification jstring="[para(715(a,1),1591(a,2,2))].">
      <j1 rule="para" parents="715 1591"/>
    </justification>
  </clause>

  <clause id="1597">
    <literal><![CDATA[
      (x / y) * K(y \ 1,y) = x / ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(113,a,12,a(flip),b,1596,a),flip(a)].">
      <j1 rule="hyper" parents="113 12 1596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1598">
    <literal><![CDATA[
      T(x \ (x / y),y) = x \ (x / ((y \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(112,a,1597,a(flip),b,605,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="112 1597 605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1599">
    <literal><![CDATA[
      1 / (x \ (x / ((y \ 1) \ 1))) = (x \ (x / y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(170,a,1598,a(flip),b,1182,a(flip))].">
      <j1 rule="hyper" parents="170 1598 1182"/>
    </justification>
  </clause>

  <clause id="1600">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (K(x \ 1,x) * z)) = y * z
    ]]></literal>
    <justification jstring="[hyper(1365,a,1595,a)].">
      <j1 rule="hyper" parents="1365 1595"/>
    </justification>
  </clause>

  <clause id="1603">
    <literal><![CDATA[
      (x * y) \ (x * (K(z \ 1,z) * (y * u))) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(z \ 1,z) * u,y,x) = w
    ]]></literal>
    <justification jstring="[para(1595(a,2),342(a,1,2,2))].">
      <j1 rule="para" parents="1595 342"/>
    </justification>
  </clause>

  <clause id="1604">
    <literal><![CDATA[
      K(x \ 1,x) * (y * z) = y * (z * K(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(1429(a,1),1595(a,2,2))].">
      <j1 rule="para" parents="1429 1595"/>
    </justification>
  </clause>

  <clause id="1605">
    <literal><![CDATA[
      (x \ (x / (1 / (1 / y)))) \ 1 = 1 / (x \ (x / y))
    ]]></literal>
    <justification jstring="[para(169(a,1),1599(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="169 1599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1607">
    <literal><![CDATA[
      x \ (K(y \ 1,y) * z) = (x \ z) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(424,a,1604,a)].">
      <j1 rule="hyper" parents="424 1604"/>
    </justification>
  </clause>

  <clause id="1608">
    <literal><![CDATA[
      (x * y) * K(z \ 1,z) = x * (y * K(z \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,1429,a(flip),b,1604,a)].">
      <j1 rule="hyper" parents="65 1429 1604"/>
    </justification>
  </clause>

  <clause id="1609">
    <literal><![CDATA[
      (x * (y * K(z \ 1,z))) * u = K(z \ 1,z) * ((x * y) * u)
    ]]></literal>
    <justification jstring="[para(1604(a,1),1318(a,1,1))].">
      <j1 rule="para" parents="1604 1318"/>
    </justification>
  </clause>

  <clause id="1610">
    <literal><![CDATA[
      (x * (y * K(z \ 1,z))) \ (K(z \ 1,z) * u) = (x * y) \ u
    ]]></literal>
    <justification jstring="[para(1604(a,1),1319(a,1,1))].">
      <j1 rule="para" parents="1604 1319"/>
    </justification>
  </clause>

  <clause id="1611">
    <literal><![CDATA[
      1 / (1 / (x \ (x / y))) = x \ (x / (1 / (1 / y)))
    ]]></literal>
    <justification jstring="[hyper(171,a,1605,a)].">
      <j1 rule="hyper" parents="171 1605"/>
    </justification>
  </clause>

  <clause id="1612">
    <literal><![CDATA[
      (x \ y) * K(y \ 1,y) = x \ (1 / (1 / y))
    ]]></literal>
    <justification jstring="[para(1097(a,1),1607(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1097 1607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1613">
    <literal><![CDATA[
      x \ (y * K(z \ 1,z)) = (x \ y) * K(z \ 1,z)
    ]]></literal>
    <justification jstring="[para(1429(a,1),1607(a,1,2))].">
      <j1 rule="para" parents="1429 1607"/>
    </justification>
  </clause>

  <clause id="1614">
    <literal><![CDATA[
      x \ (y * (K(z \ 1,z) * u)) = (x \ (y * u)) * K(z \ 1,z)
    ]]></literal>
    <justification jstring="[para(1595(a,1),1607(a,1,2))].">
      <j1 rule="para" parents="1595 1607"/>
    </justification>
  </clause>

  <clause id="1615">
    <literal><![CDATA[
      K(x \ 1,x) * (y \ x) = y \ (1 / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(1432,a,1612,a)].">
      <j1 rule="hyper" parents="1432 1612"/>
    </justification>
  </clause>

  <clause id="1616">
    <literal><![CDATA[
      (1 / x) * (y \ (1 / (1 / x))) = (x \ 1) * (y \ x)
    ]]></literal>
    <justification jstring="[para(1615(a,1),1368(a,1,2))].">
      <j1 rule="para" parents="1615 1368"/>
    </justification>
  </clause>

  <clause id="1617">
    <literal><![CDATA[
      K(x,x \ 1) * ((y \ (1 / (1 / x))) * z) = (y \ x) * z
    ]]></literal>
    <justification jstring="[para(1615(a,1),1364(a,1,2,1))].">
      <j1 rule="para" parents="1615 1364"/>
    </justification>
  </clause>

  <clause id="1618">
    <literal><![CDATA[
      R(x,y,K(z \ 1,z)) = x
    ]]></literal>
    <justification jstring="[hyper(370,a,1608,a)].">
      <j1 rule="hyper" parents="370 1608"/>
    </justification>
  </clause>

  <clause id="1619">
    <literal><![CDATA[
      (x * (1 / y)) * K(y \ 1,y) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[para(503(a,1),1608(a,2,2))].">
      <j1 rule="para" parents="503 1608"/>
    </justification>
  </clause>

  <clause id="1620">
    <literal><![CDATA[
      (x * ((y \ 1) \ 1)) * K(y \ 1,y) = x * y
    ]]></literal>
    <justification jstring="[para(703(a,1),1608(a,2,2))].">
      <j1 rule="para" parents="703 1608"/>
    </justification>
  </clause>

  <clause id="1621">
    <literal><![CDATA[
      T(x,y * K(z \ 1,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,1515,a(flip),b,1618,a),flip(a)].">
      <j1 rule="hyper" parents="65 1515 1618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1622">
    <literal><![CDATA[
      R(x,y,K(z,z \ 1)) = x
    ]]></literal>
    <justification jstring="[para(1297(a,1),1618(a,1,3))].">
      <j1 rule="para" parents="1297 1618"/>
    </justification>
  </clause>

  <clause id="1623">
    <literal><![CDATA[
      x \ (y * K(z,z \ 1)) = (x \ y) * K(z,z \ 1)
    ]]></literal>
    <justification jstring="[para(1622(a,1),360(a,1,1))].">
      <j1 rule="para" parents="1622 360"/>
    </justification>
  </clause>

  <clause id="1625">
    <literal><![CDATA[
      T(x,1 / y) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(503(a,1),1621(a,1,2)),flip(a)].">
      <j1 rule="para" parents="503 1621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1626">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[para(703(a,1),1621(a,1,2)),flip(a)].">
      <j1 rule="para" parents="703 1621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1627">
    <literal><![CDATA[
      T(x,y * K(z,z \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1297(a,1),1621(a,1,2,2))].">
      <j1 rule="para" parents="1297 1621"/>
    </justification>
  </clause>

  <clause id="1632">
    <literal><![CDATA[
      T((x \ 1) * y,(x \ 1) \ 1) = (x \ 1) * ((x \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(250,a,1047,a,b,1626,a),flip(a)].">
      <j1 rule="hyper" parents="250 1047 1626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1633">
    <literal><![CDATA[
      T(x,R(y \ 1,y,z)) = T(x,z / (y * z))
    ]]></literal>
    <justification jstring="[para(1383(a,2),1626(a,1,2))].">
      <j1 rule="para" parents="1383 1626"/>
    </justification>
  </clause>

  <clause id="1634">
    <literal><![CDATA[
      T(x,R(1 / y,y,z)) = T(x,R(y \ 1,y,z))
    ]]></literal>
    <justification jstring="[para(1384(a,1),1626(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1384 1626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1635">
    <literal><![CDATA[
      (x / (1 / y)) * (y \ 1) = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(253,a,1619,a),flip(a)].">
      <j1 rule="hyper" parents="253 1619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1636">
    <literal><![CDATA[
      R(x,y \ 1,y) / y = x * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(37,a,935,a,b,1619,a)].">
      <j1 rule="hyper" parents="37 935 1619"/>
    </justification>
  </clause>

  <clause id="1637">
    <literal><![CDATA[
      R(x / (1 / y),y \ 1,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(677,a,1636,a)].">
      <j1 rule="hyper" parents="677 1636"/>
    </justification>
  </clause>

  <clause id="1638">
    <literal><![CDATA[
      R(x,1 / y,y) = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(629,a,1636,a),flip(a)].">
      <j1 rule="hyper" parents="629 1636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1639">
    <literal><![CDATA[
      (x * (1 / y)) * y = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(124,a,1636,a)].">
      <j1 rule="hyper" parents="124 1636"/>
    </justification>
  </clause>

  <clause id="1640">
    <literal><![CDATA[
      R((x \ (y / (1 / z))) * x,z \ 1,z) = (x \ (y * z)) * x
    ]]></literal>
    <justification jstring="[para(1637(a,1),1397(a,2,1,2))].">
      <j1 rule="para" parents="1637 1397"/>
    </justification>
  </clause>

  <clause id="1641">
    <literal><![CDATA[
      (x * y) * K(y,y \ 1) = x * ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(1620(a,1),1445(a,1,1))].">
      <j1 rule="para" parents="1620 1445"/>
    </justification>
  </clause>

  <clause id="1642">
    <literal><![CDATA[
      (x * ((y * (x \ 1)) / y)) * y = T(y,R(x \ 1,x,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,903,a,b,1634,a)].">
      <j1 rule="hyper" parents="65 903 1634"/>
    </justification>
  </clause>

  <clause id="1643">
    <literal><![CDATA[
      (x * (y \ 1)) / (1 / y) = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(792,a,1635,a)].">
      <j1 rule="hyper" parents="792 1635"/>
    </justification>
  </clause>

  <clause id="1644">
    <literal><![CDATA[
      (x / (y \ 1)) * K(y \ 1,y) = x / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(787,a,1635,a),flip(a)].">
      <j1 rule="hyper" parents="787 1635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1645">
    <literal><![CDATA[
      (x * y) * K(y,y \ 1) = x * T(y,(z * y) \ z)
    ]]></literal>
    <justification jstring="[para(1179(a,2),1641(a,2,2))].">
      <j1 rule="para" parents="1179 1641"/>
    </justification>
  </clause>

  <clause id="1646">
    <literal><![CDATA[
      ((1 / (1 / x)) * y) * (1 / x) = (x * y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(115,a,1438,a(flip),b,1643,a)].">
      <j1 rule="hyper" parents="115 1438 1643"/>
    </justification>
  </clause>

  <clause id="1647">
    <literal><![CDATA[
      R(x * K(y \ 1,y),y \ 1,y) = (x * (y \ 1)) * y
    ]]></literal>
    <justification jstring="[para(1643(a,1),1637(a,1,1))].">
      <j1 rule="para" parents="1643 1637"/>
    </justification>
  </clause>

  <clause id="1648">
    <literal><![CDATA[
      T(x,y / (1 / z)) = T(x,y / (z \ 1))
    ]]></literal>
    <justification jstring="[para(1644(a,1),1621(a,1,2))].">
      <j1 rule="para" parents="1644 1621"/>
    </justification>
  </clause>

  <clause id="1649">
    <literal><![CDATA[
      x * (1 / (1 / (x \ (x / y)))) = x / (1 / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(116,a,1611,a,b,xx)].">
      <j1 rule="hyper" parents="116 1611"/>
    </justification>
  </clause>

  <clause id="1650">
    <literal><![CDATA[
      1 / (1 / (x \ (x / (y \ 1)))) = x \ (x / (1 / y))
    ]]></literal>
    <justification jstring="[para(76(a,1),1611(a,2,2,2,2))].">
      <j1 rule="para" parents="76 1611"/>
    </justification>
  </clause>

  <clause id="1651">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ z = (y \ z) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,1446,a,b,1613,a)].">
      <j1 rule="hyper" parents="65 1446 1613"/>
    </justification>
  </clause>

  <clause id="1652">
    <literal><![CDATA[
      (1 / x) * ((T(x,y) \ 1) * x) = (x \ 1) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[para(1449(a,1),1616(a,1,2))].">
      <j1 rule="para" parents="1449 1616"/>
    </justification>
  </clause>

  <clause id="1653">
    <literal><![CDATA[
      (x \ y) * K(y,y \ 1) = x \ ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(1311(a,1),1623(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1311 1623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1654">
    <literal><![CDATA[
      K(x,x \ 1) * ((y \ x) * z) = (y \ ((x \ 1) \ 1)) * z
    ]]></literal>
    <justification jstring="[para(1653(a,1),1435(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1653 1435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1655">
    <literal><![CDATA[
      K(x,(y * x) \ y) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(36,a,1370,a,b,1645,a)].">
      <j1 rule="hyper" parents="36 1370 1645"/>
    </justification>
  </clause>

  <clause id="1656">
    <literal><![CDATA[
      K(x,y \ (y / x)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(12(a,1),1655(a,1,2,1))].">
      <j1 rule="para" parents="12 1655"/>
    </justification>
  </clause>

  <clause id="1658">
    <literal><![CDATA[
      ((x \ (x / y)) * z) * K(y,y \ 1) = (1 / (1 / (x \ (x / y)))) * z
    ]]></literal>
    <justification jstring="[para(1656(a,1),1460(a,1,2))].">
      <j1 rule="para" parents="1656 1460"/>
    </justification>
  </clause>

  <clause id="1659">
    <literal><![CDATA[
      (x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ (1 / (1 / x))) * y) * (1 / x)
    ]]></literal>
    <justification jstring="[para(242(a,1),1646(a,1,1)),flip(a)].">
      <j1 rule="para" parents="242 1646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1660">
    <literal><![CDATA[
      x / (1 / (1 / (y \ x))) = x * (1 / (1 / (x \ y)))
    ]]></literal>
    <justification jstring="[para(76(a,1),1649(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="76 1649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1661">
    <literal><![CDATA[
      x / (y * K(z \ 1,z)) = K(z,z \ 1) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(170,a,168,a(flip),b,1651,a)].">
      <j1 rule="hyper" parents="170 168 1651"/>
    </justification>
  </clause>

  <clause id="1662">
    <literal><![CDATA[
      (x * (1 / (1 / (x \ y)))) \ x = 1 / (1 / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(163,a,1660,a)].">
      <j1 rule="hyper" parents="163 1660"/>
    </justification>
  </clause>

  <clause id="1663">
    <literal><![CDATA[
      x / (1 / (1 / ((x * y) \ x))) = x * (1 / (1 / y))
    ]]></literal>
    <justification jstring="[para(9(a,1),1660(a,2,2,2,2))].">
      <j1 rule="para" parents="9 1660"/>
    </justification>
  </clause>

  <clause id="1664">
    <literal><![CDATA[
      x / (K(y \ 1,y) * z) = K(y,y \ 1) * (x / z)
    ]]></literal>
    <justification jstring="[para(1429(a,2),1661(a,1,2))].">
      <j1 rule="para" parents="1429 1661"/>
    </justification>
  </clause>

  <clause id="1665">
    <literal><![CDATA[
      (x * (1 / (1 / T(y,x)))) \ x = 1 / (1 / ((y * x) \ x))
    ]]></literal>
    <justification jstring="[para(22(a,2),1662(a,1,1,2,2,2))].">
      <j1 rule="para" parents="22 1662"/>
    </justification>
  </clause>

  <clause id="1666">
    <literal><![CDATA[
      x / L(y,y \ 1,x) = x * (1 / (1 / (y \ 1)))
    ]]></literal>
    <justification jstring="[para(1199(a,2),1663(a,1,2))].">
      <j1 rule="para" parents="1199 1663"/>
    </justification>
  </clause>

  <clause id="1667">
    <literal><![CDATA[
      x / L(y,y \ 1,x) = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(76(a,1),1666(a,2,2,2))].">
      <j1 rule="para" parents="76 1666"/>
    </justification>
  </clause>

  <clause id="1668">
    <literal><![CDATA[
      K(x \ (x / L(y,y \ 1,x)),z) = K(1 / y,z)
    ]]></literal>
    <justification jstring="[para(1667(a,2),617(a,1,1,2))].">
      <j1 rule="para" parents="1667 617"/>
    </justification>
  </clause>

  <clause id="1669">
    <literal><![CDATA[
      L(x * T(x \ 1,y),x \ 1,y) = K(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,1503,a,b,1668,a)].">
      <j1 rule="hyper" parents="65 1503 1668"/>
    </justification>
  </clause>

  <clause id="1670">
    <literal><![CDATA[
      L((1 / x) * T((1 / x) \ 1,y),x,y) = K(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(79(a,1),1669(a,1,2))].">
      <j1 rule="para" parents="79 1669"/>
    </justification>
  </clause>

  <clause id="1671">
    <literal><![CDATA[
      a(x,y,z) * L(z,y,x) = z
    ]]></literal>
    <justification jstring="[hyper(36,a,970,a(flip),b,1594,a),flip(a)].">
      <j1 rule="hyper" parents="36 970 1594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1672">
    <literal><![CDATA[
      a(x,y,z) = z / L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(123,a,1671,a),flip(a)].">
      <j1 rule="hyper" parents="123 1671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1673">
    <literal><![CDATA[
      L(x,y,z) = a(z,y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(118,a,1671,a),flip(a)].">
      <j1 rule="hyper" parents="118 1671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1674">
    <literal><![CDATA[
      a(x,y,z) * (L(z,y,x) * u) = z * u
    ]]></literal>
    <justification jstring="[para(1671(a,1),315(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1671 315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1675">
    <literal><![CDATA[
      (a(x,y,z) * u) \ z = u \ L(z,y,x)
    ]]></literal>
    <justification jstring="[para(1671(a,1),350(a,1,2))].">
      <j1 rule="para" parents="1671 350"/>
    </justification>
  </clause>

  <clause id="1676">
    <literal><![CDATA[
      L(x,y,z) * (x \ u) = a(z,y,x) \ u
    ]]></literal>
    <justification jstring="[para(1671(a,1),401(a,1,2,1))].">
      <j1 rule="para" parents="1671 401"/>
    </justification>
  </clause>

  <clause id="1677">
    <literal><![CDATA[
      L(x,y,L(z,u,w)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1671(a,1),1248(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1671 1248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1678">
    <literal><![CDATA[
      a(L(x,y,z),u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[para(1671(a,1),1499(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1671 1499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1679">
    <literal><![CDATA[
      (x * y) / L(y,z,u) = x * a(u,z,y)
    ]]></literal>
    <justification jstring="[para(1671(a,1),1578(a,1,1,2))].">
      <j1 rule="para" parents="1671 1578"/>
    </justification>
  </clause>

  <clause id="1680">
    <literal><![CDATA[
      R(a(x,y,R(z,u,w)),L(R(z,u,w),y,x),u * w) = ((z * u) * w) / (L(R(z,u,w),y,x) * (u * w))
    ]]></literal>
    <justification jstring="[para(1672(a,2),383(a,1,1))].">
      <j1 rule="para" parents="1672 383"/>
    </justification>
  </clause>

  <clause id="1681">
    <literal><![CDATA[
      (x / y) * a(z,u,y) = x / L(y,u,z)
    ]]></literal>
    <justification jstring="[para(1673(a,2),1586(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1673 1586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1682">
    <literal><![CDATA[
      a(1 / x,y,z) = a(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(274(a,1),1678(a,1,1))].">
      <j1 rule="para" parents="274 1678"/>
    </justification>
  </clause>

  <clause id="1683">
    <literal><![CDATA[
      a((x * y) \ z,u,w) = a(y \ (x \ z),u,w)
    ]]></literal>
    <justification jstring="[para(239(a,1),1678(a,1,1))].">
      <j1 rule="para" parents="239 1678"/>
    </justification>
  </clause>

  <clause id="1684">
    <literal><![CDATA[
      a((x \ 1) \ 1,y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(76(a,1),1682(a,1,1)),flip(a)].">
      <j1 rule="para" parents="76 1682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1685">
    <literal><![CDATA[
      L(x,y,z) \ 1 = x \ a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(408,a,1674,a),flip(a)].">
      <j1 rule="hyper" parents="408 1674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1686">
    <literal><![CDATA[
      a(x,y,z) = z * (L(z,y,x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,71,a(flip),b,1674,a)].">
      <j1 rule="hyper" parents="65 71 1674"/>
    </justification>
  </clause>

  <clause id="1687">
    <literal><![CDATA[
      R(a(x,y,z),L(z,y,x) * u,w) = ((z * u) * w) / ((L(z,y,x) * u) * w)
    ]]></literal>
    <justification jstring="[para(1674(a,1),20(a,2,1,1))].">
      <j1 rule="para" parents="1674 20"/>
    </justification>
  </clause>

  <clause id="1688">
    <literal><![CDATA[
      (x * (y * z)) / (L(y,u,w) * z) = x * a(w,u,y)
    ]]></literal>
    <justification jstring="[para(1674(a,1),1578(a,1,1,2))].">
      <j1 rule="para" parents="1674 1578"/>
    </justification>
  </clause>

  <clause id="1689">
    <literal><![CDATA[
      a(x,y,z) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(250,a,826,a(flip),b,1686,a),flip(a)].">
      <j1 rule="hyper" parents="250 826 1686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1690">
    <literal><![CDATA[
      L(x,y,z) * a(z,y,x) = x
    ]]></literal>
    <justification jstring="[hyper(116,a,1686,a,b,826,a(flip))].">
      <j1 rule="hyper" parents="116 1686 826"/>
    </justification>
  </clause>

  <clause id="1693">
    <literal><![CDATA[
      L(a(x,y,z),L(z,y,x),u) = (u * L(z,y,x)) \ (u * z)
    ]]></literal>
    <justification jstring="[para(1689(a,2),95(a,1,1))].">
      <j1 rule="para" parents="1689 95"/>
    </justification>
  </clause>

  <clause id="1694">
    <literal><![CDATA[
      L(a(x,y,L(z,u,w)),L(L(z,u,w),y,x),w * u) = ((w * u) * L(L(z,u,w),y,x)) \ (w * (u * z))
    ]]></literal>
    <justification jstring="[para(1689(a,2),358(a,1,1))].">
      <j1 rule="para" parents="1689 358"/>
    </justification>
  </clause>

  <clause id="1695">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ x = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1689(a,1),1673(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1689 1673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1696">
    <literal><![CDATA[
      L(x,y,z) * (a(z,y,x) * u) = x * u
    ]]></literal>
    <justification jstring="[hyper(115,a,1690,a(flip),b,1578,a),flip(a)].">
      <j1 rule="hyper" parents="115 1690 1578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1697">
    <literal><![CDATA[
      T(x,L(x,y,z) \ x) = x
    ]]></literal>
    <justification jstring="[hyper(43,a,247,a,b,1695,a(flip))].">
      <j1 rule="hyper" parents="43 247 1695"/>
    </justification>
  </clause>

  <clause id="1698">
    <literal><![CDATA[
      T(x,a(y,z,x)) = x
    ]]></literal>
    <justification jstring="[para(1689(a,2),1697(a,1,2))].">
      <j1 rule="para" parents="1689 1697"/>
    </justification>
  </clause>

  <clause id="1699">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ y,z,u) = a(u,z,x) \ y
    ]]></literal>
    <justification jstring="[hyper(65,a,430,a,b,1676,a)].">
      <j1 rule="hyper" parents="65 430 1676"/>
    </justification>
  </clause>

  <clause id="1700">
    <literal><![CDATA[
      (1 / x) * a(x \ 1,x,y) = R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,1330,a(flip),b,1679,a),flip(a)].">
      <j1 rule="hyper" parents="65 1330 1679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1701">
    <literal><![CDATA[
      (x / L(y,z,u)) * y = x * a(u,z,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,965,a(flip),b,1679,a)].">
      <j1 rule="hyper" parents="65 965 1679"/>
    </justification>
  </clause>

  <clause id="1702">
    <literal><![CDATA[
      (x * y) * a(R(x,y,z),y,z) = R(x,y,z) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,366,a(flip),b,1679,a),flip(a)].">
      <j1 rule="hyper" parents="65 366 1679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1703">
    <literal><![CDATA[
      T((x * (y * z)) / z,a(x,y,z)) = a(x,y,z) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(307,a,161,a(flip),b,1681,a)].">
      <j1 rule="hyper" parents="307 161 1681"/>
    </justification>
  </clause>

  <clause id="1705">
    <literal><![CDATA[
      a(x,y,z) = ((x * (y * z)) / z) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(112,a,161,a(flip),b,1681,a),flip(a)].">
      <j1 rule="hyper" parents="112 161 1681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1706">
    <literal><![CDATA[
      a(x,y,z) \ 1 = z \ L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(408,a,1696,a),flip(a)].">
      <j1 rule="hyper" parents="408 1696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1708">
    <literal><![CDATA[
      a(x,y,z) * (z \ u) = L(z,y,x) \ u
    ]]></literal>
    <justification jstring="[hyper(112,a,10,a(flip),b,1696,a),flip(a)].">
      <j1 rule="hyper" parents="112 10 1696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1709">
    <literal><![CDATA[
      x / (y \ L(y,z,u)) = x * a(u,z,y)
    ]]></literal>
    <justification jstring="[para(1706(a,1),1577(a,1,2))].">
      <j1 rule="para" parents="1706 1577"/>
    </justification>
  </clause>

  <clause id="1710">
    <literal><![CDATA[
      (x * L(y,z,u)) * a(u,z,y) = x * y
    ]]></literal>
    <justification jstring="[para(11(a,1),1701(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 1701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1711">
    <literal><![CDATA[
      T(L(x,y,z) \ u,a(z,y,x)) = (x \ u) * a(z,y,x)
    ]]></literal>
    <justification jstring="[para(1708(a,1),345(a,1,1))].">
      <j1 rule="para" parents="1708 345"/>
    </justification>
  </clause>

  <clause id="1712">
    <literal><![CDATA[
      x * (y \ L(y,a(z,u,w),v5)) = x
    ]]></literal>
    <justification jstring="[hyper(115,a,1588,a(flip),b,1709,a)].">
      <j1 rule="hyper" parents="115 1588 1709"/>
    </justification>
  </clause>

  <clause id="1713">
    <literal><![CDATA[
      (x * L(y,z,u)) \ (x * y) = a(u,z,y)
    ]]></literal>
    <justification jstring="[hyper(118,a,1710,a)].">
      <j1 rule="hyper" parents="118 1710"/>
    </justification>
  </clause>

  <clause id="1714">
    <literal><![CDATA[
      (x * L(x \ y,z,u)) \ y = a(u,z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(112,a,10,a(flip),b,1710,a)].">
      <j1 rule="hyper" parents="112 10 1710"/>
    </justification>
  </clause>

  <clause id="1715">
    <literal><![CDATA[
      L(a(x,y,z),u * L(z,y,x),w) = (w * (u * L(z,y,x))) \ (w * (u * z))
    ]]></literal>
    <justification jstring="[para(1710(a,1),18(a,2,2,2))].">
      <j1 rule="para" parents="1710 18"/>
    </justification>
  </clause>

  <clause id="1716">
    <literal><![CDATA[
      a(1 / (x * y),z,u) = a(y \ (x \ 1),z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,1682,a,b,1683,a)].">
      <j1 rule="hyper" parents="65 1682 1683"/>
    </justification>
  </clause>

  <clause id="1717">
    <literal><![CDATA[
      (1 / x) * a(1 / x,x,y) = R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[para(1682(a,2),1700(a,1,2))].">
      <j1 rule="para" parents="1682 1700"/>
    </justification>
  </clause>

  <clause id="1718">
    <literal><![CDATA[
      (x / (y * x)) * y = a(1 / y,y,x)
    ]]></literal>
    <justification jstring="[hyper(36,a,674,a,b,1717,a)].">
      <j1 rule="hyper" parents="36 674 1717"/>
    </justification>
  </clause>

  <clause id="1719">
    <literal><![CDATA[
      a(1 / x,x,y) \ (y / (x * y)) = L(x \ 1,x,y / (x * y))
    ]]></literal>
    <justification jstring="[para(1718(a,1),181(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1718 181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1720">
    <literal><![CDATA[
      R(x,y,T(z,x * y)) = x * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,1038,a(flip),b,1688,a)].">
      <j1 rule="hyper" parents="65 1038 1688"/>
    </justification>
  </clause>

  <clause id="1722">
    <literal><![CDATA[
      a(x,y,(z \ u) \ u) = (a(x,y,z) \ u) \ u
    ]]></literal>
    <justification jstring="[para(1699(a,1),1714(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1699 1714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1723">
    <literal><![CDATA[
      a(x,y,T(z,z \ u)) = (a(x,y,z) \ u) \ u
    ]]></literal>
    <justification jstring="[para(105(a,2),1722(a,1,3))].">
      <j1 rule="para" parents="105 1722"/>
    </justification>
  </clause>

  <clause id="1724">
    <literal><![CDATA[
      x * ((x * (((x * y) * (x \ 1)) / (x * y))) * y) = T(x * y,R(x \ 1,x,x * y))
    ]]></literal>
    <justification jstring="[hyper(65,a,1266,a(flip),b,1642,a)].">
      <j1 rule="hyper" parents="65 1266 1642"/>
    </justification>
  </clause>

  <clause id="1725">
    <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(801(a,1),1647(a,2,1))].">
      <j1 rule="para" parents="801 1647"/>
    </justification>
  </clause>

  <clause id="1726">
    <literal><![CDATA[
      x * K(y \ (1 / (1 / x)),y) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,1350,a(flip),b,1617,a)].">
      <j1 rule="hyper" parents="65 1350 1617"/>
    </justification>
  </clause>

  <clause id="1727">
    <literal><![CDATA[
      (x \ 1) \ (T(x,y) \ 1) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(112,a,1216,a(flip),b,1652,a(flip))].">
      <j1 rule="hyper" parents="112 1216 1652"/>
    </justification>
  </clause>

  <clause id="1728">
    <literal><![CDATA[
      (x \ 1) * ((y \ ((x \ 1) \ 1)) * z) = (1 / x) * ((y \ x) * z)
    ]]></literal>
    <justification jstring="[hyper(116,a,1654,a(flip),b,1353,a)].">
      <j1 rule="hyper" parents="116 1654 1353"/>
    </justification>
  </clause>

  <clause id="1729">
    <literal><![CDATA[
      L((x \ ((y \ 1) \ 1)) * z,y \ 1,y) = y * ((1 / y) * ((x \ y) * z))
    ]]></literal>
    <justification jstring="[para(1654(a,1),1356(a,1,1))].">
      <j1 rule="para" parents="1654 1356"/>
    </justification>
  </clause>

  <clause id="1730">
    <literal><![CDATA[
      (x * T(1 / (1 / y),x)) \ x = 1 / (1 / ((y * x) \ x))
    ]]></literal>
    <justification jstring="[para(1416(a,1),1665(a,1,1,2))].">
      <j1 rule="para" parents="1416 1665"/>
    </justification>
  </clause>

  <clause id="1731">
    <literal><![CDATA[
      L(a(x,y,z),L(z,y,x),u) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(250,a,1713,a(flip),b,1693,a),flip(a)].">
      <j1 rule="hyper" parents="250 1713 1693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1733">
    <literal><![CDATA[
      1 / (1 / ((x * y) \ y)) = ((1 / (1 / x)) * y) \ y
    ]]></literal>
    <justification jstring="[para(104(a,1),1730(a,1,1)),flip(a)].">
      <j1 rule="para" parents="104 1730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1734">
    <literal><![CDATA[
      (((1 / (1 / x)) * y) \ y) \ 1 = 1 / ((x * y) \ y)
    ]]></literal>
    <justification jstring="[hyper(163,a,1733,a)].">
      <j1 rule="hyper" parents="163 1733"/>
    </justification>
  </clause>

  <clause id="1735">
    <literal><![CDATA[
      1 / (((x \ 1) * y) \ y) = (((1 / x) * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(76(a,1),1734(a,1,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="76 1734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1736">
    <literal><![CDATA[
      ((((1 / x) * y) \ y) \ 1) \ 1 = ((x \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[hyper(163,a,1735,a)].">
      <j1 rule="hyper" parents="163 1735"/>
    </justification>
  </clause>

  <clause id="1737">
    <literal><![CDATA[
      ((L(x,y,y \ 1) \ (y * x)) \ 1) \ 1 = ((y \ 1) * (y * x)) \ (y * x)
    ]]></literal>
    <justification jstring="[para(1325(a,1),1736(a,1,1,1,1))].">
      <j1 rule="para" parents="1325 1736"/>
    </justification>
  </clause>

  <clause id="1738">
    <literal><![CDATA[
      ((x \ (y / (1 / z))) * x) * (1 / z) = ((x \ (y * z)) * x) / z
    ]]></literal>
    <justification jstring="[hyper(113,a,1640,a(flip),b,1639,a),flip(a)].">
      <j1 rule="hyper" parents="113 1640 1639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1739">
    <literal><![CDATA[
      L(T(x,y) / x,x,y) = K(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(597(a,1),1670(a,1,1))].">
      <j1 rule="para" parents="597 1670"/>
    </justification>
  </clause>

  <clause id="1740">
    <literal><![CDATA[
      K(1 / (1 / x),y) = (x * K(x,y)) / x
    ]]></literal>
    <justification jstring="[hyper(65,a,540,a(flip),b,1739,a),flip(a)].">
      <j1 rule="hyper" parents="65 540 1739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1741">
    <literal><![CDATA[
      T(K(1 / (1 / x),y),x) = K(x,y)
    ]]></literal>
    <justification jstring="[para(1740(a,2),190(a,1,1))].">
      <j1 rule="para" parents="1740 190"/>
    </justification>
  </clause>

  <clause id="1742">
    <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(113,a,1609,a(flip),b,100,a)].">
      <j1 rule="hyper" parents="113 1609 100"/>
    </justification>
  </clause>

  <clause id="1743">
    <literal><![CDATA[
      K(x * K(y \ 1,y),z) = (z * x) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(1453,a,1610,a)].">
      <j1 rule="hyper" parents="1453 1610"/>
    </justification>
  </clause>

  <clause id="1744">
    <literal><![CDATA[
      (x * (y * K(z \ 1,z))) \ u = (x * y) \ (K(z,z \ 1) * u)
    ]]></literal>
    <justification jstring="[para(1362(a,1),1610(a,1,2))].">
      <j1 rule="para" parents="1362 1610"/>
    </justification>
  </clause>

  <clause id="1745">
    <literal><![CDATA[
      K(x * K(y \ 1,y),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(250,a,16,a,b,1743,a),flip(a)].">
      <j1 rule="hyper" parents="250 16 1743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1747">
    <literal><![CDATA[
      K((x \ 1) \ 1,y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(703(a,1),1745(a,1,1)),flip(a)].">
      <j1 rule="para" parents="703 1745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1748">
    <literal><![CDATA[
      K(1 / (1 / x),y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(1099(a,1),1745(a,1,1))].">
      <j1 rule="para" parents="1099 1745"/>
    </justification>
  </clause>

  <clause id="1751">
    <literal><![CDATA[
      K(x * ((y \ 1) \ 1),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(1620(a,1),1745(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1620 1745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1752">
    <literal><![CDATA[
      K((K(x,x \ 1) * y) \ z,u) = K(y \ z,u)
    ]]></literal>
    <justification jstring="[para(1651(a,2),1745(a,1,1))].">
      <j1 rule="para" parents="1651 1745"/>
    </justification>
  </clause>

  <clause id="1753">
    <literal><![CDATA[
      (x * K(x,y)) / x = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,1740,a(flip),b,1748,a)].">
      <j1 rule="hyper" parents="65 1740 1748"/>
    </justification>
  </clause>

  <clause id="1754">
    <literal><![CDATA[
      K(L(x,x \ 1,y),z) = K((y * (x \ 1)) \ y,z)
    ]]></literal>
    <justification jstring="[para(1199(a,2),1748(a,1,1))].">
      <j1 rule="para" parents="1199 1748"/>
    </justification>
  </clause>

  <clause id="1755">
    <literal><![CDATA[
      T(K(x,y),x) = K(x,y)
    ]]></literal>
    <justification jstring="[para(1748(a,1),1741(a,1,1))].">
      <j1 rule="para" parents="1748 1741"/>
    </justification>
  </clause>

  <clause id="1757">
    <literal><![CDATA[
      T(x,K(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(56,a,1755,a)].">
      <j1 rule="hyper" parents="56 1755"/>
    </justification>
  </clause>

  <clause id="1759">
    <literal><![CDATA[
      T(T(x,y),K(x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1757(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1757 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1760">
    <literal><![CDATA[
      L(x,y,z) * K(x,u) = K(x,u) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1757(a,1),198(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1757 198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1761">
    <literal><![CDATA[
      R(x,y,z) * K(x,u) = K(x,u) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(1757(a,1),199(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1757 199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1762">
    <literal><![CDATA[
      T(x,y \ ((x * y) / x)) = x
    ]]></literal>
    <justification jstring="[para(988(a,1),1757(a,1,2))].">
      <j1 rule="para" parents="988 1757"/>
    </justification>
  </clause>

  <clause id="1763">
    <literal><![CDATA[
      T(K(x,y),x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(1753(a,1),237(a,1,1))].">
      <j1 rule="para" parents="1753 237"/>
    </justification>
  </clause>

  <clause id="1764">
    <literal><![CDATA[
      T(K(x,y),T(x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(56,a,1759,a)].">
      <j1 rule="hyper" parents="56 1759"/>
    </justification>
  </clause>

  <clause id="1765">
    <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(1759(a,1),318(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1759 318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1766">
    <literal><![CDATA[
      T(x,y) * K(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * T(x,y) = u
    ]]></literal>
    <justification jstring="[para(1764(a,1),231(a,1,2))].">
      <j1 rule="para" parents="1764 231"/>
    </justification>
  </clause>

  <clause id="1767">
    <literal><![CDATA[
      T(x,y) * K(x,z) != u * w
    ]]></literal>
    <literal><![CDATA[
      (K(x,z) * T(x,y)) / w = u
    ]]></literal>
    <justification jstring="[para(1764(a,1),410(a,1,2))].">
      <j1 rule="para" parents="1764 410"/>
    </justification>
  </clause>

  <clause id="1769">
    <literal><![CDATA[
      K(((1 / x) * y) \ z,u) = K(((x \ 1) * y) \ z,u)
    ]]></literal>
    <justification jstring="[para(1349(a,1),1752(a,1,1,1))].">
      <j1 rule="para" parents="1349 1752"/>
    </justification>
  </clause>

  <clause id="1770">
    <literal><![CDATA[
      T(K(x,y),L(x,z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(201,a,1760,a)].">
      <j1 rule="hyper" parents="201 1760"/>
    </justification>
  </clause>

  <clause id="1771">
    <literal><![CDATA[
      L(x,y,z) * K(x,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u) * L(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(1770(a,1),231(a,1,2))].">
      <j1 rule="para" parents="1770 231"/>
    </justification>
  </clause>

  <clause id="1772">
    <literal><![CDATA[
      T(K(x,y),R(x,z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(201,a,1761,a)].">
      <j1 rule="hyper" parents="201 1761"/>
    </justification>
  </clause>

  <clause id="1773">
    <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),1614(a,2,1))].">
      <j1 rule="para" parents="18 1614"/>
    </justification>
  </clause>

  <clause id="1774">
    <literal><![CDATA[
      a(1 / x,x,y) \ (y / (x * y)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(250,a,1144,a(flip),b,1719,a),flip(a)].">
      <j1 rule="hyper" parents="250 1144 1719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1776">
    <literal><![CDATA[
      a(x / (y * x),z,u) = a(1 / y,z,u)
    ]]></literal>
    <justification jstring="[para(1774(a,1),1500(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1774 1500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1777">
    <literal><![CDATA[
      x * (T((x \ y) * z,x) / z) = ((x \ (y * z)) * x) / z
    ]]></literal>
    <justification jstring="[hyper(65,a,817,a(flip),b,1738,a)].">
      <j1 rule="hyper" parents="65 817 1738"/>
    </justification>
  </clause>

  <clause id="1778">
    <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(1454,a,1744,a),flip(a)].">
      <j1 rule="hyper" parents="1454 1744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1779">
    <literal><![CDATA[
      ((x \ (x / (y \ 1))) * z) * K(y \ 1,y) = (1 / (1 / (x \ (x / (y \ 1))))) * z
    ]]></literal>
    <justification jstring="[para(1303(a,1),1658(a,1,2))].">
      <j1 rule="para" parents="1303 1658"/>
    </justification>
  </clause>

  <clause id="1782">
    <literal><![CDATA[
      L(K(x \ 1,x) * y,z,u) = L(y,z,u) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(1603,a,1773,a)].">
      <j1 rule="hyper" parents="1603 1773"/>
    </justification>
  </clause>

  <clause id="1783">
    <literal><![CDATA[
      L(K(x \ 1,x) * y,z,u) = K(x \ 1,x) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(250,a,1429,a,b,1782,a),flip(a)].">
      <j1 rule="hyper" parents="250 1429 1782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1784">
    <literal><![CDATA[
      K(x \ 1,x) * L(y * K(x,x \ 1),z,u) = L(y,z,u)
    ]]></literal>
    <justification jstring="[para(1434(a,1),1783(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1434 1783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1785">
    <literal><![CDATA[
      (x \ L(x * (y / x),z,u)) * x = L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,1513,a(flip),b,1784,a)].">
      <j1 rule="hyper" parents="65 1513 1784"/>
    </justification>
  </clause>

  <clause id="1787">
    <literal><![CDATA[
      L(x * (y / x),z,u) = x * (L(y,z,u) / x)
    ]]></literal>
    <justification jstring="[para(1785(a,1),75(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1785 75"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1788">
    <literal><![CDATA[
      L((x \ y) * x,z,u) = (x \ L(y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(75(a,1),1785(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 1785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1789">
    <literal><![CDATA[
      (x * y) * ((z \ L(u,y,x)) * z) = x * (y * ((z \ u) * z))
    ]]></literal>
    <justification jstring="[hyper(116,a,1788,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="116 1788 18"/>
    </justification>
  </clause>

  <clause id="1790">
    <literal><![CDATA[
      (x \ L(x,y,z)) * x = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(148(a,1),1788(a,1,1)),flip(a)].">
      <j1 rule="para" parents="148 1788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1791">
    <literal><![CDATA[
      L((x \ ((y \ 1) \ z)) * x,y \ 1,y) = (x \ (y * z)) * x
    ]]></literal>
    <justification jstring="[para(348(a,1),1788(a,2,1,2))].">
      <j1 rule="para" parents="348 1788"/>
    </justification>
  </clause>

  <clause id="1792">
    <literal><![CDATA[
      L((x \ ((y \ z) \ u)) * x,y \ z,y) = (x \ (z \ (y * u))) * x
    ]]></literal>
    <justification jstring="[para(349(a,1),1788(a,2,1,2))].">
      <j1 rule="para" parents="349 1788"/>
    </justification>
  </clause>

  <clause id="1794">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ L(x,y,z) = x
    ]]></literal>
    <justification jstring="[hyper(118,a,1790,a)].">
      <j1 rule="hyper" parents="118 1790"/>
    </justification>
  </clause>

  <clause id="1795">
    <literal><![CDATA[
      T(x,y) * (x \ L(x,z,u)) = (x \ L(x,z,u)) * T(x,y)
    ]]></literal>
    <justification jstring="[para(1794(a,1),323(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1794 323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1796">
    <literal><![CDATA[
      x \ ((x \ L(x,y,z)) * T(x,u)) = T(x,u) * (x \ (x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(112,a,1795,a(flip),b,646,a)].">
      <j1 rule="hyper" parents="112 1795 646"/>
    </justification>
  </clause>

  <clause id="1797">
    <literal><![CDATA[
      (x * y) * ((z \ ((x * y) \ u)) * z) = x * (y * ((z \ (y \ (x \ u))) * z))
    ]]></literal>
    <justification jstring="[para(239(a,1),1789(a,1,2,1,2))].">
      <j1 rule="para" parents="239 1789"/>
    </justification>
  </clause>

  <clause id="1798">
    <literal><![CDATA[
      (x \ 1) * ((y \ ((x \ 1) \ z)) * y) = x \ ((y \ (x * z)) * y)
    ]]></literal>
    <justification jstring="[hyper(112,a,1791,a(flip),b,215,a),flip(a)].">
      <j1 rule="hyper" parents="112 1791 215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1799">
    <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(250,a,308,a,b,1659,a)].">
      <j1 rule="hyper" parents="250 308 1659"/>
    </justification>
  </clause>

  <clause id="1800">
    <literal><![CDATA[
      ((x \ (x / (y \ 1))) * z) * K(y \ 1,y) = (x \ (x / (1 / y))) * z
    ]]></literal>
    <justification jstring="[para(1650(a,1),1779(a,2,1))].">
      <j1 rule="para" parents="1650 1779"/>
    </justification>
  </clause>

  <clause id="1804">
    <literal><![CDATA[
      T(x * y,R(x \ 1,x,x * y)) = x * ((x * y) * (y / (x * y)))
    ]]></literal>
    <justification jstring="[para(1032(a,1),1724(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1032 1724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1805">
    <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(1442(a,1),1742(a,1,2))].">
      <j1 rule="para" parents="1442 1742"/>
    </justification>
  </clause>

  <clause id="1806">
    <literal><![CDATA[
      L(x,y * K(z \ 1,z),u) = (u * y) \ (u * (y * x))
    ]]></literal>
    <justification jstring="[para(1600(a,1),1778(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1600 1778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1807">
    <literal><![CDATA[
      L(x,y * K(z \ 1,z),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(250,a,18,a,b,1806,a),flip(a)].">
      <j1 rule="hyper" parents="250 18 1806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1809">
    <literal><![CDATA[
      L(x,1 / y,z) = L(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[para(503(a,1),1807(a,1,2)),flip(a)].">
      <j1 rule="para" parents="503 1807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1810">
    <literal><![CDATA[
      (x * (1 / y)) * L(z,y \ 1,x) = x * ((1 / y) * z)
    ]]></literal>
    <justification jstring="[hyper(116,a,1809,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="116 1809 18"/>
    </justification>
  </clause>

  <clause id="1811">
    <literal><![CDATA[
      (x * (1 / (1 / y))) * L(z,y,x) = x * ((1 / (1 / y)) * z)
    ]]></literal>
    <justification jstring="[para(79(a,1),1810(a,1,2,2))].">
      <j1 rule="para" parents="79 1810"/>
    </justification>
  </clause>

  <clause id="1812">
    <literal><![CDATA[
      (x * (1 / (1 / y))) * z != x * ((1 / (1 / y)) * u)
    ]]></literal>
    <literal><![CDATA[
      L(u,y,x) = z
    ]]></literal>
    <justification jstring="[para(1811(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="1811 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1813">
    <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,1664,a(flip),b,1805,a)].">
      <j1 rule="hyper" parents="65 1664 1805"/>
    </justification>
  </clause>

  <clause id="1814">
    <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(1382(a,1),1813(a,1,2))].">
      <j1 rule="para" parents="1382 1813"/>
    </justification>
  </clause>

  <clause id="1815">
    <literal><![CDATA[
      R(x,y * K(z \ 1,z),u) = R(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,1387,a(flip),b,1814,a),flip(a)].">
      <j1 rule="hyper" parents="65 1387 1814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1818">
    <literal><![CDATA[
      R(x,(y \ 1) \ 1,z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(703(a,1),1815(a,1,2)),flip(a)].">
      <j1 rule="para" parents="703 1815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1819">
    <literal><![CDATA[
      R(x,y,z) * (((y \ 1) \ 1) * z) = (x * ((y \ 1) \ 1)) * z
    ]]></literal>
    <justification jstring="[hyper(115,a,1818,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="115 1818 20"/>
    </justification>
  </clause>

  <clause id="1820">
    <literal><![CDATA[
      (x * ((y \ 1) \ 1)) * z != u * (((y \ 1) \ 1) * z)
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(1819(a,1),46(a,1))].">
      <j1 rule="para" parents="1819 46"/>
    </justification>
  </clause>

  <clause id="1821">
    <literal><![CDATA[
      R(a(x,y,R(z,u,w)),L(R(z,u,w),y,x),u * w) = ((z * u) * w) / ((L(z,y,x) * u) * w)
    ]]></literal>
    <justification jstring="[para(310(a,1),1680(a,2,2))].">
      <j1 rule="para" parents="310 1680"/>
    </justification>
  </clause>

  <clause id="1822">
    <literal><![CDATA[
      ((x * y) * z) / ((L(x,u,w) * y) * z) = a(w,u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(527,a,1821,a),flip(a)].">
      <j1 rule="hyper" parents="527 1821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1824">
    <literal><![CDATA[
      R(a(x,y,z),L(z,y,x) * u,w) = a(x,y,R(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,1687,a,b,1822,a)].">
      <j1 rule="hyper" parents="65 1687 1822"/>
    </justification>
  </clause>

  <clause id="1825">
    <literal><![CDATA[
      a(x,y,R(z,u,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(527,a,1824,a),flip(a)].">
      <j1 rule="hyper" parents="527 1824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1827">
    <literal><![CDATA[
      a(x,y,L(z,u,z)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(852(a,1),1825(a,1,3)),flip(a)].">
      <j1 rule="para" parents="852 1825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1828">
    <literal><![CDATA[
      L(a(x,y,L(z,u,w)),L(L(z,u,w),y,x),w * u) = (w * (u * L(z,y,x))) \ (w * (u * z))
    ]]></literal>
    <justification jstring="[para(312(a,1),1694(a,2,1))].">
      <j1 rule="para" parents="312 1694"/>
    </justification>
  </clause>

  <clause id="1829">
    <literal><![CDATA[
      (x * (y * L(z,u,w))) \ (x * (y * z)) = a(w,u,L(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,1731,a(flip),b,1828,a),flip(a)].">
      <j1 rule="hyper" parents="65 1731 1828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1831">
    <literal><![CDATA[
      L(a(x,y,z),u * L(z,y,x),w) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,1715,a,b,1829,a)].">
      <j1 rule="hyper" parents="65 1715 1829"/>
    </justification>
  </clause>

  <clause id="1832">
    <literal><![CDATA[
      a(x,y,L(z,u / L(z,y,x),w)) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(12(a,1),1831(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 1831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1833">
    <literal><![CDATA[
      L(a(x,y,z),u,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,1827,a(flip),b,1832,a),flip(a)].">
      <j1 rule="hyper" parents="65 1827 1832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1834">
    <literal><![CDATA[
      (x * y) * a(z,u,x) = x * (y * a(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(116,a,1833,a(flip),b,1806,a(flip))].">
      <j1 rule="hyper" parents="116 1833 1806"/>
    </justification>
  </clause>

  <clause id="1835">
    <literal><![CDATA[
      T((x * y) / L(x,z,u),x) = y * a(u,z,x)
    ]]></literal>
    <justification jstring="[hyper(200,a,1701,a,b,1834,a(flip))].">
      <j1 rule="hyper" parents="200 1701 1834"/>
    </justification>
  </clause>

  <clause id="1837">
    <literal><![CDATA[
      T(x / L(y,z,u),y) = (y \ x) * a(u,z,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),1835(a,1,1,1))].">
      <j1 rule="para" parents="10 1835"/>
    </justification>
  </clause>

  <clause id="1838">
    <literal><![CDATA[
      T(L(x,y,z) \ u,a(z,y,x)) = T(u / L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(250,a,1711,a,b,1837,a)].">
      <j1 rule="hyper" parents="250 1711 1837"/>
    </justification>
  </clause>

  <clause id="1839">
    <literal><![CDATA[
      T((L(x,y,z) * u) / L(x,y,z),x) = T(u,a(z,y,x))
    ]]></literal>
    <justification jstring="[para(9(a,1),1838(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 1838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1840">
    <literal><![CDATA[
      T(T(x,a(y,z,u)),L(u,z,y)) = T(x,u)
    ]]></literal>
    <justification jstring="[para(1839(a,1),226(a,1,1))].">
      <j1 rule="para" parents="1839 226"/>
    </justification>
  </clause>

  <clause id="1841">
    <literal><![CDATA[
      R((x \ (x / (1 / y))) * x,y \ 1,y) = (x * ((y \ 1) * T((y \ 1) \ 1,x))) * y
    ]]></literal>
    <justification jstring="[para(1800(a,1),1725(a,1,1))].">
      <j1 rule="para" parents="1800 1725"/>
    </justification>
  </clause>

  <clause id="1842">
    <literal><![CDATA[
      R((x \ (x / (1 / y))) * x,y \ 1,y) = (x * (y \ T(y,x))) * y
    ]]></literal>
    <justification jstring="[para(587(a,1),1841(a,2,1,2))].">
      <j1 rule="para" parents="587 1841"/>
    </justification>
  </clause>

  <clause id="1843">
    <literal><![CDATA[
      (x \ (x * y)) * x = (x * (y \ T(y,x))) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,1640,a(flip),b,1842,a)].">
      <j1 rule="hyper" parents="65 1640 1842"/>
    </justification>
  </clause>

  <clause id="1844">
    <literal><![CDATA[
      (x * (y \ T(y,x))) * y = y * x
    ]]></literal>
    <justification jstring="[para(9(a,1),1843(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 1843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1845">
    <literal><![CDATA[
      x * (y \ T(y,x)) = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(123,a,1844,a),flip(a)].">
      <j1 rule="hyper" parents="123 1844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1846">
    <literal><![CDATA[
      (x \ y) * (x \ T(x,x \ y)) = y / x
    ]]></literal>
    <justification jstring="[hyper(113,a,10,a(flip),b,1844,a),flip(a)].">
      <j1 rule="hyper" parents="113 10 1844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1847">
    <literal><![CDATA[
      x \ ((y * x) / y) = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(118,a,1845,a)].">
      <j1 rule="hyper" parents="118 1845"/>
    </justification>
  </clause>

  <clause id="1848">
    <literal><![CDATA[
      T(x,y) \ x = y \ T(y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(112,a,191,a(flip),b,1845,a)].">
      <j1 rule="hyper" parents="112 191 1845"/>
    </justification>
  </clause>

  <clause id="1849">
    <literal><![CDATA[
      (x / y) \ T(x / y,y) = y \ (x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(112,a,133,a(flip),b,1845,a),flip(a)].">
      <j1 rule="hyper" parents="112 133 1845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1850">
    <literal><![CDATA[
      ((x * y) / x) * (y \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[para(1845(a,1),1492(a,1,1))].">
      <j1 rule="para" parents="1845 1492"/>
    </justification>
  </clause>

  <clause id="1851">
    <literal><![CDATA[
      T(x,x \ T(x,y)) = x
    ]]></literal>
    <justification jstring="[para(1847(a,1),1762(a,1,2))].">
      <j1 rule="para" parents="1847 1762"/>
    </justification>
  </clause>

  <clause id="1852">
    <literal><![CDATA[
      T(x,y) / x = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(170,a,1851,a(flip),b,105,a(flip))].">
      <j1 rule="hyper" parents="170 1851 105"/>
    </justification>
  </clause>

  <clause id="1853">
    <literal><![CDATA[
      (x \ T(x,y)) * x = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,1851,a(flip),b,105,a(flip))].">
      <j1 rule="hyper" parents="116 1851 105"/>
    </justification>
  </clause>

  <clause id="1854">
    <literal><![CDATA[
      T(x,K(y \ (y / (x \ 1)),y)) = x
    ]]></literal>
    <justification jstring="[para(609(a,2),1851(a,1,2))].">
      <j1 rule="para" parents="609 1851"/>
    </justification>
  </clause>

  <clause id="1855">
    <literal><![CDATA[
      x \ T(x,R(y,y \ 1,x)) = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(959,a,1852,a),flip(a)].">
      <j1 rule="hyper" parents="959 1852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1856">
    <literal><![CDATA[
      (1 / x) * T(x,y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(788,a,1852,a)].">
      <j1 rule="hyper" parents="788 1852"/>
    </justification>
  </clause>

  <clause id="1857">
    <literal><![CDATA[
      (x \ 1) \ T(x \ 1,y) = x * T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(602,a,1852,a),flip(a)].">
      <j1 rule="hyper" parents="602 1852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1858">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ 1,y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(598,a,1852,a)].">
      <j1 rule="hyper" parents="598 1852"/>
    </justification>
  </clause>

  <clause id="1860">
    <literal><![CDATA[
      T(x,R(1 / y,y,x)) = T(x,x / (x * y))
    ]]></literal>
    <justification jstring="[hyper(65,a,1260,a,b,1853,a)].">
      <j1 rule="hyper" parents="65 1260 1853"/>
    </justification>
  </clause>

  <clause id="1862">
    <literal><![CDATA[
      T(x,y) \ ((x \ T(x,y)) * (x * z)) = L(z,x,x \ T(x,y))
    ]]></literal>
    <justification jstring="[para(1853(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1853 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1863">
    <literal><![CDATA[
      T(x,y) \ x = T(y,T(x,y)) / y
    ]]></literal>
    <justification jstring="[hyper(250,a,1852,a,b,1848,a),flip(a)].">
      <j1 rule="hyper" parents="250 1852 1848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1864">
    <literal><![CDATA[
      (((x * y) / x) \ y) \ y = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(668,a,1854,a)].">
      <j1 rule="hyper" parents="668 1854"/>
    </justification>
  </clause>

  <clause id="1865">
    <literal><![CDATA[
      T(1 / x,T(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(200,a,1856,a,b,589,a)].">
      <j1 rule="hyper" parents="200 1856 589"/>
    </justification>
  </clause>

  <clause id="1866">
    <literal><![CDATA[
      T(x / (y * x),T(y,z)) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(1865(a,1),287(a,2,1))].">
      <j1 rule="para" parents="1865 287"/>
    </justification>
  </clause>

  <clause id="1867">
    <literal><![CDATA[
      R(T(x,y) \ x,y,z) = (T(y,T(x,y)) * z) / (y * z)
    ]]></literal>
    <justification jstring="[para(1863(a,2),101(a,1,1))].">
      <j1 rule="para" parents="1863 101"/>
    </justification>
  </clause>

  <clause id="1868">
    <literal><![CDATA[
      (x \ y) * (x \ ((x \ y) \ y)) = y / x
    ]]></literal>
    <justification jstring="[para(105(a,1),1846(a,1,2,2))].">
      <j1 rule="para" parents="105 1846"/>
    </justification>
  </clause>

  <clause id="1869">
    <literal><![CDATA[
      (((x * y) / x) \ y) * ((x * y) / x) = y
    ]]></literal>
    <justification jstring="[hyper(125,a,1864,a)].">
      <j1 rule="hyper" parents="125 1864"/>
    </justification>
  </clause>

  <clause id="1870">
    <literal><![CDATA[
      (x \ y) \ (y / x) = x \ ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[hyper(118,a,1868,a)].">
      <j1 rule="hyper" parents="118 1868"/>
    </justification>
  </clause>

  <clause id="1871">
    <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(1327(a,1),1869(a,1,1,1,1))].">
      <j1 rule="para" parents="1327 1869"/>
    </justification>
  </clause>

  <clause id="1872">
    <literal><![CDATA[
      T(x,R(y \ 1,y,x)) = T(x,x / (x * y))
    ]]></literal>
    <justification jstring="[hyper(65,a,1634,a(flip),b,1860,a)].">
      <j1 rule="hyper" parents="65 1634 1860"/>
    </justification>
  </clause>

  <clause id="1874">
    <literal><![CDATA[
      (x / y) \ (y \ x) = y \ (x / (x / y))
    ]]></literal>
    <justification jstring="[para(106(a,1),1849(a,1,2))].">
      <j1 rule="para" parents="106 1849"/>
    </justification>
  </clause>

  <clause id="1875">
    <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(1858(a,1),1380(a,2,1))].">
      <j1 rule="para" parents="1858 1380"/>
    </justification>
  </clause>

  <clause id="1876">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(40,a,1847,a(flip),b,1855,a),flip(a)].">
      <j1 rule="hyper" parents="40 1847 1855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1877">
    <literal><![CDATA[
      T(x,R(y \ 1,y,x)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(1459(a,1),1876(a,1,2))].">
      <j1 rule="para" parents="1459 1876"/>
    </justification>
  </clause>

  <clause id="1878">
    <literal><![CDATA[
      T(x,x / (x * y)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,1872,a(flip),b,1877,a)].">
      <j1 rule="hyper" parents="65 1872 1877"/>
    </justification>
  </clause>

  <clause id="1879">
    <literal><![CDATA[
      x * ((x * y) * (y / (x * y))) = T(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,1804,a(flip),b,1877,a)].">
      <j1 rule="hyper" parents="65 1804 1877"/>
    </justification>
  </clause>

  <clause id="1880">
    <literal><![CDATA[
      T(x,x / (y * x)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,1633,a(flip),b,1877,a)].">
      <j1 rule="hyper" parents="65 1633 1877"/>
    </justification>
  </clause>

  <clause id="1882">
    <literal><![CDATA[
      (x * ((x / y) / x)) * y = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(1134,a,1878,a)].">
      <j1 rule="hyper" parents="1134 1878"/>
    </justification>
  </clause>

  <clause id="1885">
    <literal><![CDATA[
      K(x,(x / y) / x) = x \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(112,a,1878,a(flip),b,1258,a),flip(a)].">
      <j1 rule="hyper" parents="112 1878 1258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1886">
    <literal><![CDATA[
      x * ((y * (x \ 1)) / y) = y \ T(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(112,a,1878,a(flip),b,1255,a),flip(a)].">
      <j1 rule="hyper" parents="112 1878 1255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1887">
    <literal><![CDATA[
      T(x \ T(x,y \ 1),z) = K(x,(x / T(y,z)) / x)
    ]]></literal>
    <justification jstring="[para(1878(a,1),1261(a,1,1,2))].">
      <j1 rule="para" parents="1878 1261"/>
    </justification>
  </clause>

  <clause id="1888">
    <literal><![CDATA[
      x * (y * ((x \ y) / y)) = T(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(877,a,1880,a)].">
      <j1 rule="hyper" parents="877 1880"/>
    </justification>
  </clause>

  <clause id="1889">
    <literal><![CDATA[
      x \ T(y,x \ 1) = y * ((x \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(112,a,1880,a(flip),b,876,a)].">
      <j1 rule="hyper" parents="112 1880 876"/>
    </justification>
  </clause>

  <clause id="1891">
    <literal><![CDATA[
      (x / y) \ T(x,(x / y) \ 1) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(79(a,1),1889(a,2,2,1))].">
      <j1 rule="para" parents="79 1889"/>
    </justification>
  </clause>

  <clause id="1892">
    <literal><![CDATA[
      (x * ((y \ x) / x)) / (y \ x) = x \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,1244,a,b,1886,a)].">
      <j1 rule="hyper" parents="65 1244 1886"/>
    </justification>
  </clause>

  <clause id="1893">
    <literal><![CDATA[
      L(x * ((y * (x \ 1)) / y),z,u) = y \ T(y,L(x,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,1539,a(flip),b,1886,a)].">
      <j1 rule="hyper" parents="65 1539 1886"/>
    </justification>
  </clause>

  <clause id="1894">
    <literal><![CDATA[
      (x * ((y / (z * (x \ y))) / x)) * (z * (x \ y)) = x * ((x \ T(x,z \ 1)) * (x \ y))
    ]]></literal>
    <justification jstring="[para(1886(a,1),1472(a,2,2,1))].">
      <j1 rule="para" parents="1886 1472"/>
    </justification>
  </clause>

  <clause id="1895">
    <literal><![CDATA[
      R(x \ T(x,y \ 1),z,u) = K(x,(x / R(y,z,u)) / x)
    ]]></literal>
    <justification jstring="[para(1886(a,1),1535(a,1,1))].">
      <j1 rule="para" parents="1886 1535"/>
    </justification>
  </clause>

  <clause id="1896">
    <literal><![CDATA[
      ((x \ 1) * y) * (y / ((x \ 1) * y)) = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(36,a,1632,a(flip),b,1879,a),flip(a)].">
      <j1 rule="hyper" parents="36 1632 1879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1897">
    <literal><![CDATA[
      T(x \ T(x,y \ 1),z) = x \ T(x,T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(250,a,1885,a(flip),b,1887,a),flip(a)].">
      <j1 rule="hyper" parents="250 1885 1887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1898">
    <literal><![CDATA[
      ((x \ 1) * y) * R(x,x \ 1,y) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(179(a,2),1896(a,1,2))].">
      <j1 rule="para" parents="179 1896"/>
    </justification>
  </clause>

  <clause id="1899">
    <literal><![CDATA[
      ((((x \ 1) * y) * x) / ((x \ 1) * y)) * (x \ 1) = ((x \ y) * x) / y
    ]]></literal>
    <justification jstring="[hyper(113,a,1898,a(flip),b,536,a),flip(a)].">
      <j1 rule="hyper" parents="113 1898 536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1900">
    <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(1866(a,1),1897(a,2,2,2,1))].">
      <j1 rule="para" parents="1866 1897"/>
    </justification>
  </clause>

  <clause id="1901">
    <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(1867(a,1),565(a,1,1))].">
      <j1 rule="para" parents="1867 565"/>
    </justification>
  </clause>

  <clause id="1902">
    <literal><![CDATA[
      R(x \ T(x,y \ 1),z,u) = x \ T(x,R(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(250,a,1885,a(flip),b,1895,a),flip(a)].">
      <j1 rule="hyper" parents="250 1885 1895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1904">
    <literal><![CDATA[
      L(x * y,x \ T(x,z),x) = x * L(y,x,x \ T(x,z))
    ]]></literal>
    <justification jstring="[para(1862(a,1),658(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1862 658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1906">
    <literal><![CDATA[
      L(x \ T(x,y \ 1),z,u) = x \ T(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(1886(a,1),1893(a,1,1))].">
      <j1 rule="para" parents="1886 1893"/>
    </justification>
  </clause>

  <clause id="1907">
    <literal><![CDATA[
      ((x \ 1) * y) \ T((x \ 1) * y,x) = ((x \ y) * x) / y
    ]]></literal>
    <justification jstring="[hyper(65,a,1850,a(flip),b,1899,a)].">
      <j1 rule="hyper" parents="65 1850 1899"/>
    </justification>
  </clause>

  <clause id="1908">
    <literal><![CDATA[
      L(K(x \ y,x),y,x \ 1) = ((x \ y) * x) / y
    ]]></literal>
    <justification jstring="[hyper(65,a,1048,a(flip),b,1907,a)].">
      <j1 rule="hyper" parents="65 1048 1907"/>
    </justification>
  </clause>

  <clause id="1909">
    <literal><![CDATA[
      ((x \ (x * y)) * x) / (x * y) = L(K(y,x),x * y,x \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),1908(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 1908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1910">
    <literal><![CDATA[
      L(K(x,y),y * x,y \ 1) = (x * y) / (y * x)
    ]]></literal>
    <justification jstring="[para(9(a,1),1909(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 1909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1911">
    <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),1901(a,2,1))].">
      <j1 rule="para" parents="16 1901"/>
    </justification>
  </clause>

  <clause id="1912">
    <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(250,a,1902,a,b,1900,a),flip(a)].">
      <j1 rule="hyper" parents="250 1902 1900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1913">
    <literal><![CDATA[
      T(x \ T(x,(y / (z * y)) \ 1),T(z,u)) = R(x \ T(x,z),z,y)
    ]]></literal>
    <justification jstring="[para(1626(a,1),1912(a,2,1,2))].">
      <j1 rule="para" parents="1626 1912"/>
    </justification>
  </clause>

  <clause id="1914">
    <literal><![CDATA[
      ((x * ((x / y) / x)) * y) * (x \ z) = x * ((x \ T(x,y \ 1)) * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(1529,a,1894,a)].">
      <j1 rule="hyper" parents="1529 1894"/>
    </justification>
  </clause>

  <clause id="1915">
    <literal><![CDATA[
      x * ((x \ T(x,y \ 1)) * (x \ z)) = T(x,y \ 1) * (x \ z)
    ]]></literal>
    <justification jstring="[para(1882(a,1),1914(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1882 1914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1916">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) * (x \ z) = x * ((x \ T(x,y)) * (x \ z))
    ]]></literal>
    <justification jstring="[para(1626(a,1),1915(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="1626 1915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1917">
    <literal><![CDATA[
      x * ((x \ T(x,y)) * (x \ z)) = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[para(1626(a,1),1916(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1626 1916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1918">
    <literal><![CDATA[
      T(x,y) * (x \ (x * z)) = x * ((x \ T(x,y)) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),1917(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 1917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1919">
    <literal><![CDATA[
      x \ (T(x,y) * z) = (x \ T(x,y)) * z
    ]]></literal>
    <justification jstring="[hyper(571,a,1918,a)].">
      <j1 rule="hyper" parents="571 1918"/>
    </justification>
  </clause>

  <clause id="1920">
    <literal><![CDATA[
      x * ((x \ T(x,y)) * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(415,a,1918,a),flip(a)].">
      <j1 rule="hyper" parents="415 1918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1921">
    <literal><![CDATA[
      (x * T(x \ y,z)) / y = (y / x) \ T(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(665,a,1919,a)].">
      <j1 rule="hyper" parents="665 1919"/>
    </justification>
  </clause>

  <clause id="1922">
    <literal><![CDATA[
      L(x,y \ T(y,z),y) = x
    ]]></literal>
    <justification jstring="[hyper(489,a,1919,a)].">
      <j1 rule="hyper" parents="489 1919"/>
    </justification>
  </clause>

  <clause id="1924">
    <literal><![CDATA[
      R(x,x \ T(x,y),z) = x
    ]]></literal>
    <justification jstring="[hyper(41,a,360,a,b,1919,a)].">
      <j1 rule="hyper" parents="41 360 1919"/>
    </justification>
  </clause>

  <clause id="1925">
    <literal><![CDATA[
      (x \ T(x,y)) \ 1 = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(65,a,275,a(flip),b,1922,a),flip(a)].">
      <j1 rule="hyper" parents="65 275 1922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1926">
    <literal><![CDATA[
      L(x,y,y \ T(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(36,a,1904,a(flip),b,1922,a(flip))].">
      <j1 rule="hyper" parents="36 1904 1922"/>
    </justification>
  </clause>

  <clause id="1927">
    <literal><![CDATA[
      1 / (x \ T(x,y)) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(65,a,1201,a,b,1925,a)].">
      <j1 rule="hyper" parents="65 1201 1925"/>
    </justification>
  </clause>

  <clause id="1928">
    <literal><![CDATA[
      T(x / y,y) \ (x / y) = ((x / y) \ (y \ x)) \ 1
    ]]></literal>
    <justification jstring="[para(106(a,1),1925(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="106 1925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1929">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) \ x = 1 / (y \ ((x * y) / x))
    ]]></literal>
    <justification jstring="[para(1855(a,1),1927(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1855 1927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1931">
    <literal><![CDATA[
      (x \ T(x,y)) * z = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(36,a,646,a,b,1920,a),flip(a)].">
      <j1 rule="hyper" parents="36 646 1920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1933">
    <literal><![CDATA[
      x * ((T(y,x) \ y) * z) = T(x,T(y,x)) * z
    ]]></literal>
    <justification jstring="[para(1848(a,2),1920(a,1,2,1))].">
      <j1 rule="para" parents="1848 1920"/>
    </justification>
  </clause>

  <clause id="1935">
    <literal><![CDATA[
      (T(x,y) * z) / (x * z) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(113,a,132,a(flip),b,1931,a)].">
      <j1 rule="hyper" parents="113 132 1931"/>
    </justification>
  </clause>

  <clause id="1936">
    <literal><![CDATA[
      (x \ T(x,y)) \ (T(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(1935(a,1),223(a,1,1))].">
      <j1 rule="para" parents="1935 223"/>
    </justification>
  </clause>

  <clause id="1937">
    <literal><![CDATA[
      (x \ T(x,y)) \ z = x * (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[para(1935(a,1),240(a,1,1))].">
      <j1 rule="para" parents="1935 240"/>
    </justification>
  </clause>

  <clause id="1938">
    <literal><![CDATA[
      R(K(x,y),x,z) = L(x \ T(x,T(y,x)),T(y,x),x)
    ]]></literal>
    <justification jstring="[para(1935(a,1),1911(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1935 1911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1939">
    <literal><![CDATA[
      (x \ T(x,y)) \ y = T(y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(250,a,657,a(flip),b,1937,a),flip(a)].">
      <j1 rule="hyper" parents="250 657 1937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1940">
    <literal><![CDATA[
      (x * T(x \ 1,y)) \ y = T(y,T(x \ 1,y))
    ]]></literal>
    <justification jstring="[para(1857(a,1),1939(a,1,1))].">
      <j1 rule="para" parents="1857 1939"/>
    </justification>
  </clause>

  <clause id="1941">
    <literal><![CDATA[
      (x \ T(x,y)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      x * (T(x,y) \ z) = u
    ]]></literal>
    <justification jstring="[para(10(a,1),1936(a,1,2))].">
      <j1 rule="para" parents="10 1936"/>
    </justification>
  </clause>

  <clause id="1942">
    <literal><![CDATA[
      ((x \ y) / y) \ T((x \ y) / y,z) = x * T(x \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(722,a,1921,a),flip(a)].">
      <j1 rule="hyper" parents="722 1921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1943">
    <literal><![CDATA[
      ((x / y) \ (y \ x)) \ 1 = (y \ x) \ (x / y)
    ]]></literal>
    <justification jstring="[para(106(a,1),1928(a,1,1)),flip(a)].">
      <j1 rule="para" parents="106 1928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1944">
    <literal><![CDATA[
      (x \ (x * y)) \ ((x * y) / x) = (((x * y) / x) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(9(a,1),1943(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 1943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1945">
    <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(1938(a,1),375(a,1)),flip(b)].">
      <j1 rule="para" parents="1938 375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1947">
    <literal><![CDATA[
      R(K(x,y),x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(1938(a,2),1945(a,1))].">
      <j1 rule="para" parents="1938 1945"/>
    </justification>
  </clause>

  <clause id="1948">
    <literal><![CDATA[
      x \ ((y \ x) / ((y \ x) / x)) = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,1849,a(flip),b,1942,a)].">
      <j1 rule="hyper" parents="65 1849 1942"/>
    </justification>
  </clause>

  <clause id="1949">
    <literal><![CDATA[
      T(x,T((y \ z) / z,x)) = (y * T(y \ 1,x)) \ x
    ]]></literal>
    <justification jstring="[para(1942(a,1),1939(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1942 1939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1950">
    <literal><![CDATA[
      T(x,T((y \ z) / z,x)) = T(x,T(y \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(250,a,1940,a(flip),b,1949,a),flip(a)].">
      <j1 rule="hyper" parents="250 1940 1949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1951">
    <literal><![CDATA[
      (((x * y) / x) \ y) \ 1 = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[para(9(a,1),1944(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 1944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1952">
    <literal><![CDATA[
      1 / (x \ ((y * x) / y)) = ((y * x) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(171,a,1951,a)].">
      <j1 rule="hyper" parents="171 1951"/>
    </justification>
  </clause>

  <clause id="1953">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) \ x = ((x * y) / x) \ y
    ]]></literal>
    <justification jstring="[hyper(65,a,1929,a,b,1952,a)].">
      <j1 rule="hyper" parents="65 1929 1952"/>
    </justification>
  </clause>

  <clause id="1955">
    <literal><![CDATA[
      ((x * y) / x) \ y = T(x,y) \ x
    ]]></literal>
    <justification jstring="[para(1876(a,1),1953(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1876 1953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1956">
    <literal><![CDATA[
      T(x,x \ y) \ x = (y / x) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),1955(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 1955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1957">
    <literal><![CDATA[
      T(x,T(y,x)) \ x = y \ T(y,x)
    ]]></literal>
    <justification jstring="[para(191(a,1),1955(a,1,1)),flip(a)].">
      <j1 rule="para" parents="191 1955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1958">
    <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(1955(a,1),667(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1955 667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1959">
    <literal><![CDATA[
      ((x * y) / x) * (y \ ((T(x,y) \ x) * z)) = L(z,((x * y) / x) \ y,(x * y) / x)
    ]]></literal>
    <justification jstring="[para(1955(a,1),872(a,1,2,2,1))].">
      <j1 rule="para" parents="1955 872"/>
    </justification>
  </clause>

  <clause id="1960">
    <literal><![CDATA[
      (T(x,y) \ x) * ((x * y) / x) = y
    ]]></literal>
    <justification jstring="[para(1955(a,1),1869(a,1,1))].">
      <j1 rule="para" parents="1955 1869"/>
    </justification>
  </clause>

  <clause id="1961">
    <literal><![CDATA[
      L(x,T(y,T(z,y)) \ y,z) = x
    ]]></literal>
    <justification jstring="[para(1957(a,2),1922(a,1,2))].">
      <j1 rule="para" parents="1957 1922"/>
    </justification>
  </clause>

  <clause id="1962">
    <literal><![CDATA[
      L(x,T(y,z) \ y,(y * z) / y) = x
    ]]></literal>
    <justification jstring="[para(190(a,1),1961(a,1,2,1,2))].">
      <j1 rule="para" parents="190 1961"/>
    </justification>
  </clause>

  <clause id="1963">
    <literal><![CDATA[
      T(x,x \ y) \ x = x \ (y / (y / x))
    ]]></literal>
    <justification jstring="[hyper(250,a,1874,a(flip),b,1956,a),flip(a)].">
      <j1 rule="hyper" parents="250 1874 1956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1964">
    <literal><![CDATA[
      ((x * y) / x) * (y \ ((T(x,y) \ x) * z)) = L(z,T(x,y) \ x,(x * y) / x)
    ]]></literal>
    <justification jstring="[para(1955(a,1),1959(a,2,2))].">
      <j1 rule="para" parents="1955 1959"/>
    </justification>
  </clause>

  <clause id="1965">
    <literal><![CDATA[
      x \ ((T(y,x) \ y) * z) = ((y * x) / y) \ z
    ]]></literal>
    <justification jstring="[hyper(112,a,1962,a(flip),b,1964,a),flip(a)].">
      <j1 rule="hyper" parents="112 1962 1964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1966">
    <literal><![CDATA[
      x * (((y * x) / y) \ z) = (T(y,x) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(125,a,1965,a)].">
      <j1 rule="hyper" parents="125 1965"/>
    </justification>
  </clause>

  <clause id="1967">
    <literal><![CDATA[
      (T(x,y) \ x) * (x * y) = y * x
    ]]></literal>
    <justification jstring="[hyper(116,a,79,a(flip),b,1965,a),flip(a)].">
      <j1 rule="hyper" parents="116 79 1965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1968">
    <literal><![CDATA[
      (T(x,y) \ x) * T(x,y) = x
    ]]></literal>
    <justification jstring="[hyper(40,a,859,a(flip),b,1965,a),flip(a)].">
      <j1 rule="hyper" parents="40 859 1965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1969">
    <literal><![CDATA[
      T(T(x,y),T(x,y) \ x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(263,a,1968,a)].">
      <j1 rule="hyper" parents="263 1968"/>
    </justification>
  </clause>

  <clause id="1970">
    <literal><![CDATA[
      x / T(x,y) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(123,a,1968,a)].">
      <j1 rule="hyper" parents="123 1968"/>
    </justification>
  </clause>

  <clause id="1971">
    <literal><![CDATA[
      (T(x,y) \ x) \ x = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(118,a,1968,a)].">
      <j1 rule="hyper" parents="118 1968"/>
    </justification>
  </clause>

  <clause id="1972">
    <literal><![CDATA[
      T(x,T(y,x)) * T(y,x) = x * y
    ]]></literal>
    <justification jstring="[para(1968(a,1),1933(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1968 1933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1973">
    <literal><![CDATA[
      (T(x,y) \ x) / x = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(113,a,1970,a(flip),b,765,a)].">
      <j1 rule="hyper" parents="113 1970 765"/>
    </justification>
  </clause>

  <clause id="1974">
    <literal><![CDATA[
      K(x,y) = T(T(y,x) \ y,y * x)
    ]]></literal>
    <justification jstring="[hyper(200,a,1967,a,b,87,a),flip(a)].">
      <j1 rule="hyper" parents="200 1967 87"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1975">
    <literal><![CDATA[
      (x * y) / (y * x) = T(y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(123,a,1967,a)].">
      <j1 rule="hyper" parents="123 1967"/>
    </justification>
  </clause>

  <clause id="1976">
    <literal><![CDATA[
      T(x,T(x,y) \ x) = x
    ]]></literal>
    <justification jstring="[hyper(127,a,1969,a)].">
      <j1 rule="hyper" parents="127 1969"/>
    </justification>
  </clause>

  <clause id="1978">
    <literal><![CDATA[
      T(x,y \ T(y,x)) = x
    ]]></literal>
    <justification jstring="[para(1957(a,1),1976(a,1,2))].">
      <j1 rule="para" parents="1957 1976"/>
    </justification>
  </clause>

  <clause id="1979">
    <literal><![CDATA[
      T(x \ T(x,y),y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(56,a,1978,a)].">
      <j1 rule="hyper" parents="56 1978"/>
    </justification>
  </clause>

  <clause id="1980">
    <literal><![CDATA[
      T(x,y * T(y \ 1,x)) = x
    ]]></literal>
    <justification jstring="[para(1857(a,1),1978(a,1,2))].">
      <j1 rule="para" parents="1857 1978"/>
    </justification>
  </clause>

  <clause id="1981">
    <literal><![CDATA[
      T(x,K(y,x)) = x
    ]]></literal>
    <justification jstring="[para(607(a,2),1980(a,1,2))].">
      <j1 rule="para" parents="607 1980"/>
    </justification>
  </clause>

  <clause id="1983">
    <literal><![CDATA[
      K(x,K(y,x)) = 1
    ]]></literal>
    <justification jstring="[hyper(57,a,1981,a)].">
      <j1 rule="hyper" parents="57 1981"/>
    </justification>
  </clause>

  <clause id="1984">
    <literal><![CDATA[
      T(K(x,y),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(56,a,1981,a)].">
      <j1 rule="hyper" parents="56 1981"/>
    </justification>
  </clause>

  <clause id="1985">
    <literal><![CDATA[
      (x * K(y,x)) / x = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(170,a,1981,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="170 1981 22"/>
    </justification>
  </clause>

  <clause id="1986">
    <literal><![CDATA[
      K(x,y) * y = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,1981,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="116 1981 22"/>
    </justification>
  </clause>

  <clause id="1987">
    <literal><![CDATA[
      R(x,y,z) * K(u,x) = K(u,x) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(1981(a,1),199(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1981 199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1988">
    <literal><![CDATA[
      L(K(x,y),y,1 / y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,1496,a,b,1985,a)].">
      <j1 rule="hyper" parents="65 1496 1985"/>
    </justification>
  </clause>

  <clause id="1989">
    <literal><![CDATA[
      (1 / x) \ K(y,x) = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(112,a,1988,a(flip),b,217,a)].">
      <j1 rule="hyper" parents="112 1988 217"/>
    </justification>
  </clause>

  <clause id="1990">
    <literal><![CDATA[
      (x / T(y,x)) * y = T(x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(37,a,766,a,b,1972,a)].">
      <j1 rule="hyper" parents="37 766 1972"/>
    </justification>
  </clause>

  <clause id="1991">
    <literal><![CDATA[
      ((T(x,y) \ x) / x) \ 1 = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(114,a,1973,a,b,134,a)].">
      <j1 rule="hyper" parents="114 1973 134"/>
    </justification>
  </clause>

  <clause id="1992">
    <literal><![CDATA[
      T(x / y,y) \ (x / y) = (y * (x / y)) / x
    ]]></literal>
    <justification jstring="[para(12(a,1),1975(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 1975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1993">
    <literal><![CDATA[
      T(x,y / x) \ x != z
    ]]></literal>
    <literal><![CDATA[
      y / (x * (y / x)) = z
    ]]></literal>
    <justification jstring="[para(1975(a,1),412(a,1))].">
      <j1 rule="para" parents="1975 412"/>
    </justification>
  </clause>

  <clause id="1994">
    <literal><![CDATA[
      x * (y \ T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      (y \ T(y,x)) * x = z
    ]]></literal>
    <justification jstring="[para(1979(a,1),231(a,1,2))].">
      <j1 rule="para" parents="1979 231"/>
    </justification>
  </clause>

  <clause id="1995">
    <literal><![CDATA[
      (x * (y / x)) / y = (x \ y) \ (y / x)
    ]]></literal>
    <justification jstring="[para(106(a,1),1992(a,1,1)),flip(a)].">
      <j1 rule="para" parents="106 1992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1996">
    <literal><![CDATA[
      (x * (y / x)) / y = x \ ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[hyper(250,a,1870,a(flip),b,1995,a),flip(a)].">
      <j1 rule="hyper" parents="250 1870 1995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1997">
    <literal><![CDATA[
      (x \ T(x,x \ y)) * y = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(115,a,248,a,b,1996,a)].">
      <j1 rule="hyper" parents="115 248 1996"/>
    </justification>
  </clause>

  <clause id="1998">
    <literal><![CDATA[
      x \ ((x \ (y \ x)) \ (y \ x)) = x \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,1892,a(flip),b,1996,a),flip(a)].">
      <j1 rule="hyper" parents="65 1892 1996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1999">
    <literal><![CDATA[
      T(x,x \ y) * (x \ y) = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(65,a,1931,a(flip),b,1997,a)].">
      <j1 rule="hyper" parents="65 1931 1997"/>
    </justification>
  </clause>

  <clause id="2000">
    <literal><![CDATA[
      T(x,x \ (y \ x)) \ (y \ T(x,y \ 1)) = x \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(112,a,1889,a,b,1999,a)].">
      <j1 rule="hyper" parents="112 1889 1999"/>
    </justification>
  </clause>

  <clause id="2001">
    <literal><![CDATA[
      (x \ T(x,y)) * y = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(1994,a,1845,a)].">
      <j1 rule="hyper" parents="1994 1845"/>
    </justification>
  </clause>

  <clause id="2002">
    <literal><![CDATA[
      ((x * y) / x) / y = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(123,a,2001,a)].">
      <j1 rule="hyper" parents="123 2001"/>
    </justification>
  </clause>

  <clause id="2003">
    <literal><![CDATA[
      T(x,y) * (x \ y) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(65,a,1931,a(flip),b,2001,a)].">
      <j1 rule="hyper" parents="65 1931 2001"/>
    </justification>
  </clause>

  <clause id="2004">
    <literal><![CDATA[
      R(x \ T(x,y),y,z) \ (((x * y) / x) * z) = y * z
    ]]></literal>
    <justification jstring="[para(2001(a,1),159(a,1,2,1))].">
      <j1 rule="para" parents="2001 159"/>
    </justification>
  </clause>

  <clause id="2005">
    <literal><![CDATA[
      R(x \ T(x,y),y,((x * y) / x) \ z) \ z = y * (((x * y) / x) \ z)
    ]]></literal>
    <justification jstring="[para(2002(a,1),382(a,1,1,1))].">
      <j1 rule="para" parents="2002 382"/>
    </justification>
  </clause>

  <clause id="2006">
    <literal><![CDATA[
      T(x,T(y,x * y)) = y \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(200,a,769,a(flip),b,2003,a)].">
      <j1 rule="hyper" parents="200 769 2003"/>
    </justification>
  </clause>

  <clause id="2007">
    <literal><![CDATA[
      T(x,x / (x / y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(37,a,889,a,b,2003,a)].">
      <j1 rule="hyper" parents="37 889 2003"/>
    </justification>
  </clause>

  <clause id="2008">
    <literal><![CDATA[
      T(x,x / (1 / y)) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,893,a(flip),b,2007,a)].">
      <j1 rule="hyper" parents="65 893 2007"/>
    </justification>
  </clause>

  <clause id="2009">
    <literal><![CDATA[
      T(x,x / y) = T(x,y \ x)
    ]]></literal>
    <justification jstring="[para(76(a,1),2007(a,1,2,2))].">
      <j1 rule="para" parents="76 2007"/>
    </justification>
  </clause>

  <clause id="2010">
    <literal><![CDATA[
      T(x,T(y,x * y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(250,a,22,a,b,2006,a),flip(a)].">
      <j1 rule="hyper" parents="250 22 2006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2011">
    <literal><![CDATA[
      R(T(x,x * y),y,x) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[para(2008(a,1),881(a,1,1))].">
      <j1 rule="para" parents="2008 881"/>
    </justification>
  </clause>

  <clause id="2012">
    <literal><![CDATA[
      R(T(x,x * y),y,x) = T(x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(250,a,1990,a(flip),b,2011,a),flip(a)].">
      <j1 rule="hyper" parents="250 1990 2011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2013">
    <literal><![CDATA[
      L(R(x,y,x),y,x) * y = y * T(x,T(y,x))
    ]]></literal>
    <justification jstring="[para(2012(a,1),581(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2012 581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2014">
    <literal><![CDATA[
      T(x,x \ (y \ x)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(459,a,1998,a)].">
      <j1 rule="hyper" parents="459 1998"/>
    </justification>
  </clause>

  <clause id="2015">
    <literal><![CDATA[
      T(x,(x / y) \ 1) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(79(a,1),2014(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="79 2014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2017">
    <literal><![CDATA[
      x \ ((y \ x) / ((y \ x) / x)) = T(x,y \ 1) \ x
    ]]></literal>
    <justification jstring="[para(2014(a,1),1963(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2014 1963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2018">
    <literal><![CDATA[
      (x / y) \ T(x,x \ y) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(2015(a,1),1891(a,1,2))].">
      <j1 rule="para" parents="2015 1891"/>
    </justification>
  </clause>

  <clause id="2019">
    <literal><![CDATA[
      (x / (y * x)) \ T(x,x \ (y * x)) = x * y
    ]]></literal>
    <justification jstring="[para(11(a,1),2018(a,2,2))].">
      <j1 rule="para" parents="11 2018"/>
    </justification>
  </clause>

  <clause id="2020">
    <literal><![CDATA[
      (x / (y * x)) \ T(x,T(y,x)) = x * y
    ]]></literal>
    <justification jstring="[para(22(a,2),2019(a,1,2,2))].">
      <j1 rule="para" parents="22 2019"/>
    </justification>
  </clause>

  <clause id="2021">
    <literal><![CDATA[
      T(x,y \ 1) \ x = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,1948,a(flip),b,2017,a),flip(a)].">
      <j1 rule="hyper" parents="65 1948 2017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2022">
    <literal><![CDATA[
      K(x \ (x / y),x) = T(x,y \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(250,a,608,a,b,2021,a)].">
      <j1 rule="hyper" parents="250 608 2021"/>
    </justification>
  </clause>

  <clause id="2023">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) \ x = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(250,a,587,a(flip),b,2021,a),flip(a)].">
      <j1 rule="hyper" parents="250 587 2021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2025">
    <literal><![CDATA[
      T(x,y) \ x = y \ T(y,x)
    ]]></literal>
    <justification jstring="[para(1626(a,1),2023(a,1,1))].">
      <j1 rule="para" parents="1626 2023"/>
    </justification>
  </clause>

  <clause id="2026">
    <literal><![CDATA[
      T(x,y) \ x = T(y,x) / y
    ]]></literal>
    <justification jstring="[hyper(250,a,1852,a,b,2025,a),flip(a)].">
      <j1 rule="hyper" parents="250 1852 2025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2027">
    <literal><![CDATA[
      T(x,y / x) \ x = x \ (y / (y / x))
    ]]></literal>
    <justification jstring="[hyper(250,a,1849,a(flip),b,2025,a),flip(a)].">
      <j1 rule="hyper" parents="250 1849 2025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2028">
    <literal><![CDATA[
      (T(x,y / z) \ x) * y = z * T(z \ y,x)
    ]]></literal>
    <justification jstring="[hyper(115,a,2025,a,b,1921,a)].">
      <j1 rule="hyper" parents="115 2025 1921"/>
    </justification>
  </clause>

  <clause id="2029">
    <literal><![CDATA[
      T(x,T(y,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(41,a,1957,a,b,2025,a)].">
      <j1 rule="hyper" parents="41 1957 2025"/>
    </justification>
  </clause>

  <clause id="2031">
    <literal><![CDATA[
      x * ((T(y,x) \ y) * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[para(2025(a,2),1920(a,1,2,1))].">
      <j1 rule="para" parents="2025 1920"/>
    </justification>
  </clause>

  <clause id="2032">
    <literal><![CDATA[
      T(x,y) * (x \ z) = (T(y,x) \ y) * z
    ]]></literal>
    <justification jstring="[para(2025(a,2),1931(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2025 1931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2033">
    <literal><![CDATA[
      K(x,y) = T(x \ T(x,y),y * x)
    ]]></literal>
    <justification jstring="[para(2025(a,1),1974(a,2,1))].">
      <j1 rule="para" parents="2025 1974"/>
    </justification>
  </clause>

  <clause id="2034">
    <literal><![CDATA[
      x * T(y,T(x,y)) = y * x
    ]]></literal>
    <justification jstring="[hyper(116,a,2029,a,b,22,a(flip))].">
      <j1 rule="hyper" parents="116 2029 22"/>
    </justification>
  </clause>

  <clause id="2035">
    <literal><![CDATA[
      R(T(x,x * y),y,x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2012,a,b,2029,a)].">
      <j1 rule="hyper" parents="65 2012 2029"/>
    </justification>
  </clause>

  <clause id="2036">
    <literal><![CDATA[
      (x / T(y,x)) * y = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,1990,a,b,2029,a)].">
      <j1 rule="hyper" parents="65 1990 2029"/>
    </justification>
  </clause>

  <clause id="2037">
    <literal><![CDATA[
      T(x,T(y \ 1,x)) = T(x,(y \ z) / z)
    ]]></literal>
    <justification jstring="[hyper(65,a,1950,a(flip),b,2029,a)].">
      <j1 rule="hyper" parents="65 1950 2029"/>
    </justification>
  </clause>

  <clause id="2038">
    <literal><![CDATA[
      T(x,y) / y = x / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(170,a,2029,a(flip),b,778,a),flip(a)].">
      <j1 rule="hyper" parents="170 2029 778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2039">
    <literal><![CDATA[
      T(x,y) * T(y,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(116,a,2029,a(flip),b,196,a)].">
      <j1 rule="hyper" parents="116 2029 196"/>
    </justification>
  </clause>

  <clause id="2040">
    <literal><![CDATA[
      T(x,y) \ y = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(112,a,2029,a(flip),b,657,a),flip(a)].">
      <j1 rule="hyper" parents="112 2029 657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2042">
    <literal><![CDATA[
      T(x,y / x) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(106(a,1),2029(a,1,2)),flip(a)].">
      <j1 rule="para" parents="106 2029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2043">
    <literal><![CDATA[
      T(x,(x * y) / x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(190(a,1),2029(a,1,2)),flip(a)].">
      <j1 rule="para" parents="190 2029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2044">
    <literal><![CDATA[
      (x / (y * x)) \ T(x,y) = x * y
    ]]></literal>
    <justification jstring="[para(2029(a,1),2020(a,1,2))].">
      <j1 rule="para" parents="2029 2020"/>
    </justification>
  </clause>

  <clause id="2045">
    <literal><![CDATA[
      (x * y) / (y * x) = T(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(65,a,1975,a,b,2026,a)].">
      <j1 rule="hyper" parents="65 1975 2026"/>
    </justification>
  </clause>

  <clause id="2047">
    <literal><![CDATA[
      L(R(x,y,x),y,x) = x
    ]]></literal>
    <justification jstring="[hyper(37,a,2013,a,b,2034,a(flip))].">
      <j1 rule="hyper" parents="37 2013 2034"/>
    </justification>
  </clause>

  <clause id="2048">
    <literal><![CDATA[
      (x / y) * T(y,y \ x) = y * (x / y)
    ]]></literal>
    <justification jstring="[para(106(a,1),2034(a,1,2,2))].">
      <j1 rule="para" parents="106 2034"/>
    </justification>
  </clause>

  <clause id="2049">
    <literal><![CDATA[
      x \ T(y * x,y) = R(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(346,a,2047,a)].">
      <j1 rule="hyper" parents="346 2047"/>
    </justification>
  </clause>

  <clause id="2050">
    <literal><![CDATA[
      R(L(x,y,x),y,x) = x
    ]]></literal>
    <justification jstring="[hyper(65,a,29,a,b,2047,a)].">
      <j1 rule="hyper" parents="65 29 2047"/>
    </justification>
  </clause>

  <clause id="2051">
    <literal><![CDATA[
      (x * (y * x)) / x = L(x,y,x) * y
    ]]></literal>
    <justification jstring="[para(2050(a,1),359(a,1,1,1))].">
      <j1 rule="para" parents="2050 359"/>
    </justification>
  </clause>

  <clause id="2052">
    <literal><![CDATA[
      (x / T(y,x)) * y != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(2038(a,1),211(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2038 211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2053">
    <literal><![CDATA[
      (T(x,y) * T(y,x)) / y = x
    ]]></literal>
    <justification jstring="[hyper(113,a,2039,a,b,xx)].">
      <j1 rule="hyper" parents="113 2039"/>
    </justification>
  </clause>

  <clause id="2054">
    <literal><![CDATA[
      (T(x,y) * (T(y,x) * z)) \ ((x * y) * z) = a(T(x,y),T(y,x),z)
    ]]></literal>
    <justification jstring="[para(2039(a,1),14(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="2039 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2056">
    <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(2040(a,1),1120(a,1,2,1))].">
      <j1 rule="para" parents="2040 1120"/>
    </justification>
  </clause>

  <clause id="2058">
    <literal><![CDATA[
      T(x,y / x) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(250,a,105,a(flip),b,2042,a),flip(a)].">
      <j1 rule="hyper" parents="250 105 2042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2060">
    <literal><![CDATA[
      (a(x,y,z) \ u) \ u = T(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,777,a(flip),b,2058,a),flip(a)].">
      <j1 rule="hyper" parents="65 777 2058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2061">
    <literal><![CDATA[
      T(x,x * (y / x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(517,a,2035,a),flip(a)].">
      <j1 rule="hyper" parents="517 2035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2062">
    <literal><![CDATA[
      T(x,y * x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(516,a,2035,a)].">
      <j1 rule="hyper" parents="516 2035"/>
    </justification>
  </clause>

  <clause id="2063">
    <literal><![CDATA[
      T(R(x,y,x),x * y) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,27,a(flip),b,2035,a)].">
      <j1 rule="hyper" parents="65 27 2035"/>
    </justification>
  </clause>

  <clause id="2064">
    <literal><![CDATA[
      T(x,(x \ y) * x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(75(a,1),2061(a,1,2)),flip(a)].">
      <j1 rule="para" parents="75 2061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2065">
    <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,2062,a)].">
      <j1 rule="hyper" parents="65 27 2062"/>
    </justification>
  </clause>

  <clause id="2066">
    <literal><![CDATA[
      T(x,T(y,y * x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2062(a,1),2010(a,1,2))].">
      <j1 rule="para" parents="2062 2010"/>
    </justification>
  </clause>

  <clause id="2067">
    <literal><![CDATA[
      ((x \ y) * x) * T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      x * ((x \ y) * x) = z
    ]]></literal>
    <justification jstring="[para(2064(a,1),231(a,1,2))].">
      <j1 rule="para" parents="2064 231"/>
    </justification>
  </clause>

  <clause id="2068">
    <literal><![CDATA[
      (((x \ y) * x) / T(x,y)) * x = T((x \ y) * x,x)
    ]]></literal>
    <justification jstring="[para(2064(a,1),2036(a,1,1,2))].">
      <j1 rule="para" parents="2064 2036"/>
    </justification>
  </clause>

  <clause id="2070">
    <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(2066(a,1),292(a,1,2,1))].">
      <j1 rule="para" parents="2066 292"/>
    </justification>
  </clause>

  <clause id="2071">
    <literal><![CDATA[
      x * R(y,x,y) = T(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(125,a,2049,a)].">
      <j1 rule="hyper" parents="125 2049"/>
    </justification>
  </clause>

  <clause id="2074">
    <literal><![CDATA[
      x \ T(x,T(y,(y \ 1) * x) \ 1) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(250,a,1897,a(flip),b,2033,a)].">
      <j1 rule="hyper" parents="250 1897 2033"/>
    </justification>
  </clause>

  <clause id="2075">
    <literal><![CDATA[
      R(1 / x,x,y) \ T(y,x) = y * x
    ]]></literal>
    <justification jstring="[para(183(a,2),2044(a,1,1))].">
      <j1 rule="para" parents="183 2044"/>
    </justification>
  </clause>

  <clause id="2076">
    <literal><![CDATA[
      T(x,L(x,y,x) * y) = T(x,y * x)
    ]]></literal>
    <justification jstring="[para(2051(a,1),2043(a,1,2))].">
      <j1 rule="para" parents="2051 2043"/>
    </justification>
  </clause>

  <clause id="2077">
    <literal><![CDATA[
      T(x,T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(1990(a,1),2052(a,1))].">
      <j1 rule="para" parents="1990 2052"/>
    </justification>
  </clause>

  <clause id="2078">
    <literal><![CDATA[
      T(x,y) / (x * y) = R(1 / y,y,x)
    ]]></literal>
    <justification jstring="[hyper(171,a,2075,a)].">
      <j1 rule="hyper" parents="171 2075"/>
    </justification>
  </clause>

  <clause id="2079">
    <literal><![CDATA[
      T(x,(x \ y) * T(x,y)) = T(x,(x \ y) * x)
    ]]></literal>
    <justification jstring="[para(449(a,1),2076(a,1,2))].">
      <j1 rule="para" parents="449 2076"/>
    </justification>
  </clause>

  <clause id="2080">
    <literal><![CDATA[
      R(1 / x,x,T(y,x)) = R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(461,a,2078,a)].">
      <j1 rule="hyper" parents="461 2078"/>
    </justification>
  </clause>

  <clause id="2082">
    <literal><![CDATA[
      x / (y * (x / y)) = y \ (x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(1993,a,2027,a)].">
      <j1 rule="hyper" parents="1993 2027"/>
    </justification>
  </clause>

  <clause id="2083">
    <literal><![CDATA[
      x * (((y * x) / y) \ z) = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(250,a,1966,a,b,2032,a)].">
      <j1 rule="hyper" parents="250 1966 2032"/>
    </justification>
  </clause>

  <clause id="2084">
    <literal><![CDATA[
      T(x,(y \ z) / z) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(2077,a,2037,a),flip(a)].">
      <j1 rule="hyper" parents="2077 2037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2086">
    <literal><![CDATA[
      T(x,(y / z) \ 1) = T(x,z / y)
    ]]></literal>
    <justification jstring="[para(79(a,1),2084(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 2084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2087">
    <literal><![CDATA[
      T(x \ T(x,(y * z) / z),T(y,u)) = R(x \ T(x,y),y,z)
    ]]></literal>
    <justification jstring="[para(2086(a,1),1913(a,1,1,2))].">
      <j1 rule="para" parents="2086 1913"/>
    </justification>
  </clause>

  <clause id="2088">
    <literal><![CDATA[
      T(x / (x / y),y \ x) = y
    ]]></literal>
    <justification jstring="[hyper(481,a,2048,a)].">
      <j1 rule="hyper" parents="481 2048"/>
    </justification>
  </clause>

  <clause id="2089">
    <literal><![CDATA[
      ((x \ y) * x) / (x \ y) = y / (y / x)
    ]]></literal>
    <justification jstring="[hyper(227,a,2088,a)].">
      <j1 rule="hyper" parents="227 2088"/>
    </justification>
  </clause>

  <clause id="2090">
    <literal><![CDATA[
      (x / (x / y)) * (y \ x) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(116,a,2088,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 2088 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2092">
    <literal><![CDATA[
      T(x / (x / (x / y)),y) = x / y
    ]]></literal>
    <justification jstring="[para(79(a,1),2088(a,1,2))].">
      <j1 rule="para" parents="79 2088"/>
    </justification>
  </clause>

  <clause id="2093">
    <literal><![CDATA[
      (x * (y / x)) / x = y / (y / (y / x))
    ]]></literal>
    <justification jstring="[hyper(227,a,2092,a)].">
      <j1 rule="hyper" parents="227 2092"/>
    </justification>
  </clause>

  <clause id="2094">
    <literal><![CDATA[
      R(x / y,x / (x / y),x / y) = T((x * (x / y)) / x,y)
    ]]></literal>
    <justification jstring="[para(2092(a,1),499(a,1,1))].">
      <j1 rule="para" parents="2092 499"/>
    </justification>
  </clause>

  <clause id="2095">
    <literal><![CDATA[
      R(1 / x,x,y / x) = R(1 / x,x,x \ y)
    ]]></literal>
    <justification jstring="[para(106(a,1),2080(a,1,3)),flip(a)].">
      <j1 rule="para" parents="106 2080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2096">
    <literal><![CDATA[
      T(x / (x / y),x) = L(y,y \ x,y)
    ]]></literal>
    <justification jstring="[para(2089(a,1),450(a,1,1))].">
      <j1 rule="para" parents="2089 450"/>
    </justification>
  </clause>

  <clause id="2097">
    <literal><![CDATA[
      x * T(x / (x / y),x) = y * ((y \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(116,a,2096,a,b,94,a)].">
      <j1 rule="hyper" parents="116 2096 94"/>
    </justification>
  </clause>

  <clause id="2098">
    <literal><![CDATA[
      L(x \ y,(x \ y) \ y,x \ y) = T(y / x,y)
    ]]></literal>
    <justification jstring="[para(76(a,1),2096(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="76 2096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2099">
    <literal><![CDATA[
      ((x \ y) * x) * (y / x) = y * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(115,a,2090,a(flip),b,783,a)].">
      <j1 rule="hyper" parents="115 2090 783"/>
    </justification>
  </clause>

  <clause id="2100">
    <literal><![CDATA[
      (x * (y / x)) * (y / (y / x)) = y * ((y / x) \ y)
    ]]></literal>
    <justification jstring="[para(79(a,1),2099(a,1,1,1))].">
      <j1 rule="para" parents="79 2099"/>
    </justification>
  </clause>

  <clause id="2101">
    <literal><![CDATA[
      x * K(y \ (y / (x \ z)),y) = (T(y,x / z) \ y) * x
    ]]></literal>
    <justification jstring="[hyper(250,a,680,a(flip),b,2028,a)].">
      <j1 rule="hyper" parents="250 680 2028"/>
    </justification>
  </clause>

  <clause id="2102">
    <literal><![CDATA[
      T(x,(x \ y) * T(x,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(250,a,2064,a(flip),b,2079,a),flip(a)].">
      <j1 rule="hyper" parents="250 2064 2079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2103">
    <literal><![CDATA[
      R(T(x,y),x \ y,T(x,y)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(2102(a,1),780(a,1,1))].">
      <j1 rule="para" parents="2102 780"/>
    </justification>
  </clause>

  <clause id="2104">
    <literal><![CDATA[
      a(x,y,T(z,z \ u)) = a(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(2103(a,1),1825(a,1,3))].">
      <j1 rule="para" parents="2103 1825"/>
    </justification>
  </clause>

  <clause id="2105">
    <literal><![CDATA[
      (a(x,y,z) \ u) \ u = a(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,1723,a(flip),b,2104,a)].">
      <j1 rule="hyper" parents="65 1723 2104"/>
    </justification>
  </clause>

  <clause id="2106">
    <literal><![CDATA[
      a(x,y,T(z,u)) = T(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,2060,a(flip),b,2105,a),flip(a)].">
      <j1 rule="hyper" parents="65 2060 2105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2107">
    <literal><![CDATA[
      ((x * y) / x) \ (y * z) = T(y,x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,842,a,b,2083,a)].">
      <j1 rule="hyper" parents="65 842 2083"/>
    </justification>
  </clause>

  <clause id="2108">
    <literal><![CDATA[
      R(1 / x,x,x \ y) \ (y / x) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(2095(a,1),284(a,1,1))].">
      <j1 rule="para" parents="2095 284"/>
    </justification>
  </clause>

  <clause id="2109">
    <literal><![CDATA[
      ((x \ y) / y) * (x * (y / x)) = y / x
    ]]></literal>
    <justification jstring="[para(2108(a,1),418(a,1,2))].">
      <j1 rule="para" parents="2108 418"/>
    </justification>
  </clause>

  <clause id="2110">
    <literal><![CDATA[
      ((x \ y) * x) / T(x,y) = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(37,a,806,a(flip),b,2068,a),flip(a)].">
      <j1 rule="hyper" parents="37 806 2068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2111">
    <literal><![CDATA[
      (x \ T(y,x)) * T(x,y) = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(124,a,2110,a)].">
      <j1 rule="hyper" parents="124 2110"/>
    </justification>
  </clause>

  <clause id="2112">
    <literal><![CDATA[
      L(x,K(y,z \ 1),y) = x
    ]]></literal>
    <justification jstring="[para(2074(a,1),1922(a,1,2))].">
      <j1 rule="para" parents="2074 1922"/>
    </justification>
  </clause>

  <clause id="2113">
    <literal><![CDATA[
      R(x,K(x,y \ 1),z) = x
    ]]></literal>
    <justification jstring="[para(2074(a,1),1924(a,1,2))].">
      <j1 rule="para" parents="2074 1924"/>
    </justification>
  </clause>

  <clause id="2114">
    <literal><![CDATA[
      L(x,y,K(y,z \ 1)) = x
    ]]></literal>
    <justification jstring="[para(2074(a,1),1926(a,1,3))].">
      <j1 rule="para" parents="2074 1926"/>
    </justification>
  </clause>

  <clause id="2115">
    <literal><![CDATA[
      L(x,K(y,z),y) = x
    ]]></literal>
    <justification jstring="[para(79(a,1),2112(a,1,2,2))].">
      <j1 rule="para" parents="79 2112"/>
    </justification>
  </clause>

  <clause id="2116">
    <literal><![CDATA[
      L(x,K(y,z),L(y,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(65,a,1677,a,b,2115,a)].">
      <j1 rule="hyper" parents="65 1677 2115"/>
    </justification>
  </clause>

  <clause id="2117">
    <literal><![CDATA[
      R(x,K(x,y),z) = x
    ]]></literal>
    <justification jstring="[para(79(a,1),2113(a,1,2,2))].">
      <j1 rule="para" parents="79 2113"/>
    </justification>
  </clause>

  <clause id="2118">
    <literal><![CDATA[
      R(T(x,y),K(x,z),u) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2117(a,1),27(a,2,1))].">
      <j1 rule="para" parents="2117 27"/>
    </justification>
  </clause>

  <clause id="2119">
    <literal><![CDATA[
      L(x,y,K(y,z)) = x
    ]]></literal>
    <justification jstring="[para(79(a,1),2114(a,1,3,2))].">
      <j1 rule="para" parents="79 2114"/>
    </justification>
  </clause>

  <clause id="2120">
    <literal><![CDATA[
      (K(x,y) * x) * z = K(x,y) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(748,a,2119,a),flip(a)].">
      <j1 rule="hyper" parents="748 2119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2121">
    <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(2118(a,1),309(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2118 309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2122">
    <literal><![CDATA[
      (x * (y / x)) * (y / (y / x)) = y * x
    ]]></literal>
    <justification jstring="[hyper(250,a,167,a(flip),b,2100,a),flip(a)].">
      <j1 rule="hyper" parents="250 167 2100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2124">
    <literal><![CDATA[
      (x * y) * ((y * x) / ((y * x) / x)) = (y * x) * x
    ]]></literal>
    <justification jstring="[para(11(a,1),2122(a,1,1,2))].">
      <j1 rule="para" parents="11 2122"/>
    </justification>
  </clause>

  <clause id="2125">
    <literal><![CDATA[
      (x * y) * ((y * x) / y) = (y * x) * x
    ]]></literal>
    <justification jstring="[para(11(a,1),2124(a,1,2,2))].">
      <j1 rule="para" parents="11 2124"/>
    </justification>
  </clause>

  <clause id="2126">
    <literal><![CDATA[
      x * (((y \ x) * y) / (y \ x)) = ((y \ x) * y) * y
    ]]></literal>
    <justification jstring="[hyper(405,a,2125,a)].">
      <j1 rule="hyper" parents="405 2125"/>
    </justification>
  </clause>

  <clause id="2127">
    <literal><![CDATA[
      ((x \ y) * x) * x = y * (y / (y / x))
    ]]></literal>
    <justification jstring="[para(2089(a,1),2126(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2089 2126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2128">
    <literal><![CDATA[
      ((x \ T(y,x)) * T(x,y)) * T(x,y) = y * (y / (y / T(x,y)))
    ]]></literal>
    <justification jstring="[para(2040(a,1),2127(a,1,1,1))].">
      <j1 rule="para" parents="2040 2127"/>
    </justification>
  </clause>

  <clause id="2129">
    <literal><![CDATA[
      T(x,y \ 1) \ (y \ T(x,y \ 1)) = x \ (y \ x)
    ]]></literal>
    <justification jstring="[para(2014(a,1),2000(a,1,1))].">
      <j1 rule="para" parents="2014 2000"/>
    </justification>
  </clause>

  <clause id="2130">
    <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(1328(a,1),2129(a,2,2))].">
      <j1 rule="para" parents="1328 2129"/>
    </justification>
  </clause>

  <clause id="2131">
    <literal><![CDATA[
      (T(x,(y / z) / (1 / z)) \ x) * (y / z) = T(y,x) / z
    ]]></literal>
    <justification jstring="[hyper(65,a,694,a(flip),b,2101,a),flip(a)].">
      <j1 rule="hyper" parents="65 694 2101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2132">
    <literal><![CDATA[
      T(x \ T(x,y),T(y,z)) = R(x \ T(x,y),y,u)
    ]]></literal>
    <justification jstring="[para(11(a,1),2087(a,1,1,2,2))].">
      <j1 rule="para" parents="11 2087"/>
    </justification>
  </clause>

  <clause id="2133">
    <literal><![CDATA[
      T(x \ T(x,y),T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x \ T(x,y) = u
    ]]></literal>
    <justification jstring="[para(2132(a,2),375(a,1)),flip(b)].">
      <j1 rule="para" parents="2132 375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2134">
    <literal><![CDATA[
      R(x \ T(x,y),y,z) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(2133,a,2132,a),flip(a)].">
      <j1 rule="hyper" parents="2133 2132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2135">
    <literal><![CDATA[
      (x \ T(x,y)) \ (((x * y) / x) * z) = y * z
    ]]></literal>
    <justification jstring="[para(2134(a,1),2004(a,1,1))].">
      <j1 rule="para" parents="2134 2004"/>
    </justification>
  </clause>

  <clause id="2136">
    <literal><![CDATA[
      (x \ T(x,x \ y)) \ y = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(82(a,1),2135(a,1,2))].">
      <j1 rule="para" parents="82 2135"/>
    </justification>
  </clause>

  <clause id="2138">
    <literal><![CDATA[
      (x \ ((x \ y) \ y)) \ y = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(105(a,1),2136(a,1,1,2))].">
      <j1 rule="para" parents="105 2136"/>
    </justification>
  </clause>

  <clause id="2139">
    <literal><![CDATA[
      x / ((y \ x) * y) = y \ ((y \ x) \ x)
    ]]></literal>
    <justification jstring="[hyper(171,a,2138,a)].">
      <j1 rule="hyper" parents="171 2138"/>
    </justification>
  </clause>

  <clause id="2140">
    <literal><![CDATA[
      (x * (y / x)) / y = y / ((x \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(250,a,1996,a,b,2139,a)].">
      <j1 rule="hyper" parents="250 1996 2139"/>
    </justification>
  </clause>

  <clause id="2141">
    <literal><![CDATA[
      R(x / y,x / (x / y),x / y) = (x * (y \ x)) / x
    ]]></literal>
    <justification jstring="[hyper(250,a,465,a(flip),b,2094,a),flip(a)].">
      <j1 rule="hyper" parents="250 465 2094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2142">
    <literal><![CDATA[
      R(x / (x / y),(y * (x / y)) / y,x / (x / y)) = (x * ((x / y) \ x)) / x
    ]]></literal>
    <justification jstring="[para(2093(a,2),2141(a,1,2))].">
      <j1 rule="para" parents="2093 2141"/>
    </justification>
  </clause>

  <clause id="2143">
    <literal><![CDATA[
      R(T(x,R(x,y,z) * u),y,z) = R(T(x,u * R(x,y,z)),y,z)
    ]]></literal>
    <justification jstring="[hyper(250,a,27,a,b,2065,a)].">
      <j1 rule="hyper" parents="250 27 2065"/>
    </justification>
  </clause>

  <clause id="2144">
    <literal><![CDATA[
      ((x \ y) * x) * T(x,y) = y * (y / (y / T(x,y)))
    ]]></literal>
    <justification jstring="[para(2111(a,1),2128(a,1,1))].">
      <j1 rule="para" parents="2111 2128"/>
    </justification>
  </clause>

  <clause id="2145">
    <literal><![CDATA[
      x * (x / (x / T(y,x))) = y * ((y \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(2067,a,2144,a),flip(a)].">
      <j1 rule="hyper" parents="2067 2144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2146">
    <literal><![CDATA[
      x / (x / T(y,x)) = T(x / (x / y),x)
    ]]></literal>
    <justification jstring="[hyper(36,a,2097,a,b,2145,a),flip(a)].">
      <j1 rule="hyper" parents="36 2097 2145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2147">
    <literal><![CDATA[
      T(x / (x / y),x) \ x = x / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(163,a,2146,a)].">
      <j1 rule="hyper" parents="163 2146"/>
    </justification>
  </clause>

  <clause id="2148">
    <literal><![CDATA[
      x / T(y \ x,x) = T(x / y,x) \ x
    ]]></literal>
    <justification jstring="[para(76(a,1),2147(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="76 2147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2149">
    <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,1765,a(flip),b,2121,a)].">
      <j1 rule="hyper" parents="65 1765 2121"/>
    </justification>
  </clause>

  <clause id="2150">
    <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(2149(a,1),739(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="2149 739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2151">
    <literal><![CDATA[
      R(x \ T(x,y),y,((x * y) / x) \ z) \ z = (T(x,y) \ x) * z
    ]]></literal>
    <justification jstring="[hyper(250,a,1966,a(flip),b,2005,a),flip(a)].">
      <j1 rule="hyper" parents="250 1966 2005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2152">
    <literal><![CDATA[
      (x \ T(x,y)) \ z = (T(x,y) \ x) * z
    ]]></literal>
    <justification jstring="[para(2134(a,1),2151(a,1,1))].">
      <j1 rule="para" parents="2134 2151"/>
    </justification>
  </clause>

  <clause id="2153">
    <literal><![CDATA[
      (T(x,y) \ x) * z = x * (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(1941,a,2152,a),flip(a)].">
      <j1 rule="hyper" parents="1941 2152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2154">
    <literal><![CDATA[
      (T(x,y) \ x) * (T(x,y) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(1936,a,2152,a),flip(a)].">
      <j1 rule="hyper" parents="1936 2152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2156">
    <literal><![CDATA[
      x * (T(x,(y / z) / (1 / z)) \ (y / z)) = T(y,x) / z
    ]]></literal>
    <justification jstring="[hyper(65,a,2131,a(flip),b,2153,a),flip(a)].">
      <j1 rule="hyper" parents="65 2131 2153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2157">
    <literal><![CDATA[
      x * T(x \ y,z) = z * (T(z,y / x) \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2028,a(flip),b,2153,a)].">
      <j1 rule="hyper" parents="65 2028 2153"/>
    </justification>
  </clause>

  <clause id="2158">
    <literal><![CDATA[
      T(x,y) * (x \ (T(y,x) * z)) = y * z
    ]]></literal>
    <justification jstring="[hyper(65,a,2032,a,b,2154,a)].">
      <j1 rule="hyper" parents="65 2032 2154"/>
    </justification>
  </clause>

  <clause id="2159">
    <literal><![CDATA[
      T(x,y) * (T(y,x) * z) = x * (y * z)
    ]]></literal>
    <justification jstring="[para(2154(a,1),2031(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2154 2031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2160">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) = a(T(x,y),T(y,x),z)
    ]]></literal>
    <justification jstring="[para(2159(a,1),2054(a,1,1))].">
      <j1 rule="para" parents="2159 2054"/>
    </justification>
  </clause>

  <clause id="2161">
    <literal><![CDATA[
      x * (T(x,y / (z \ 1)) \ y) != u
    ]]></literal>
    <literal><![CDATA[
      z \ T(z * y,x) = u
    ]]></literal>
    <justification jstring="[para(2157(a,1),614(a,1))].">
      <j1 rule="para" parents="2157 614"/>
    </justification>
  </clause>

  <clause id="2162">
    <literal><![CDATA[
      a(T(x,y),T(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(2160(a,1),469(a,1))].">
      <j1 rule="para" parents="2160 469"/>
    </justification>
  </clause>

  <clause id="2163">
    <literal><![CDATA[
      a(T(x * (y / x),x),T(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x * (y / x),x,z) = u
    ]]></literal>
    <justification jstring="[para(2061(a,1),2162(a,1,2))].">
      <j1 rule="para" parents="2061 2162"/>
    </justification>
  </clause>

  <clause id="2164">
    <literal><![CDATA[
      x * (T(x,(y / z) / (z \ 1)) \ (y / z)) = T(y,x) / z
    ]]></literal>
    <justification jstring="[para(1648(a,1),2156(a,1,2,1))].">
      <j1 rule="para" parents="1648 2156"/>
    </justification>
  </clause>

  <clause id="2165">
    <literal><![CDATA[
      x \ T(x * (y / x),z) = T(y,z) / x
    ]]></literal>
    <justification jstring="[hyper(2161,a,2164,a)].">
      <j1 rule="hyper" parents="2161 2164"/>
    </justification>
  </clause>

  <clause id="2166">
    <literal><![CDATA[
      T(x * (y / x),z) = x * (T(y,z) / x)
    ]]></literal>
    <justification jstring="[hyper(125,a,2165,a),flip(a)].">
      <j1 rule="hyper" parents="125 2165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2167">
    <literal><![CDATA[
      (x \ T(x * (y / x),z)) * x = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(115,a,2165,a,b,xx)].">
      <j1 rule="hyper" parents="115 2165"/>
    </justification>
  </clause>

  <clause id="2168">
    <literal><![CDATA[
      T(x * y,z) / y = y \ T(y * x,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),2165(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="11 2165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2169">
    <literal><![CDATA[
      T((x \ y) * x,z) / x = x \ T(y,z)
    ]]></literal>
    <justification jstring="[para(75(a,1),2165(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 2165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2170">
    <literal><![CDATA[
      x * (y * (T(z,x) / y)) = (y * (z / y)) * x
    ]]></literal>
    <justification jstring="[para(2165(a,1),192(a,1,2,2))].">
      <j1 rule="para" parents="2165 192"/>
    </justification>
  </clause>

  <clause id="2174">
    <literal><![CDATA[
      T(x * (y / x),y) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(103(a,1),2166(a,2,2,1))].">
      <j1 rule="para" parents="103 2166"/>
    </justification>
  </clause>

  <clause id="2177">
    <literal><![CDATA[
      T(x * (y / x),y) / y = y / ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(2174(a,2),2140(a,1,1))].">
      <j1 rule="para" parents="2174 2140"/>
    </justification>
  </clause>

  <clause id="2178">
    <literal><![CDATA[
      (x \ T(x * y,z)) * x = T(y * x,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),2167(a,1,1,2,1,2))].">
      <j1 rule="para" parents="11 2167"/>
    </justification>
  </clause>

  <clause id="2179">
    <literal><![CDATA[
      T((x \ y) * x,z) = (x \ T(y,z)) * x
    ]]></literal>
    <justification jstring="[para(75(a,1),2167(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 2167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2181">
    <literal><![CDATA[
      x * (y \ T(y * (x \ z),x)) = ((x \ (z * y)) * x) / y
    ]]></literal>
    <justification jstring="[para(2168(a,1),1777(a,1,2))].">
      <j1 rule="para" parents="2168 1777"/>
    </justification>
  </clause>

  <clause id="2183">
    <literal><![CDATA[
      T(x,y) / R(x,z,u) = R(x,z,u) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(1407(a,1),2169(a,1,1,1))].">
      <j1 rule="para" parents="1407 2169"/>
    </justification>
  </clause>

  <clause id="2184">
    <literal><![CDATA[
      T(x * y,z) / y != u
    ]]></literal>
    <literal><![CDATA[
      y \ T(y * x,z) = u
    ]]></literal>
    <justification jstring="[para(2178(a,1),212(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2178 212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2185">
    <literal><![CDATA[
      x * ((y \ T(z,x)) * y) = ((y \ z) * y) * x
    ]]></literal>
    <justification jstring="[hyper(116,a,2179,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="116 2179 22"/>
    </justification>
  </clause>

  <clause id="2186">
    <literal><![CDATA[
      T((x \ y) * x,y) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(103(a,1),2179(a,2,1,2))].">
      <j1 rule="para" parents="103 2179"/>
    </justification>
  </clause>

  <clause id="2187">
    <literal><![CDATA[
      (x * ((y / z) / x)) * z = z * (x * ((z \ y) / x))
    ]]></literal>
    <justification jstring="[para(106(a,1),2170(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="106 2170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2188">
    <literal><![CDATA[
      x / ((((y \ 1) * x) \ x) * ((y \ 1) * x)) = T((y \ x) * y,x) / x
    ]]></literal>
    <justification jstring="[para(1896(a,1),2177(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1896 2177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2191">
    <literal><![CDATA[
      ((x \ (y / z)) * x) * z = z * ((x \ (z \ y)) * x)
    ]]></literal>
    <justification jstring="[para(106(a,1),2185(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="106 2185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2192">
    <literal><![CDATA[
      (x \ y) * ((z \ ((x \ y) \ y)) * z) = ((z \ x) * z) * (x \ y)
    ]]></literal>
    <justification jstring="[para(105(a,1),2185(a,1,2,1,2))].">
      <j1 rule="para" parents="105 2185"/>
    </justification>
  </clause>

  <clause id="2193">
    <literal><![CDATA[
      T(x,y) / (z \ x) != u
    ]]></literal>
    <literal><![CDATA[
      (z \ x) \ T((z \ x) * z,y) = u
    ]]></literal>
    <justification jstring="[para(10(a,1),2184(a,1,1,1))].">
      <j1 rule="para" parents="10 2184"/>
    </justification>
  </clause>

  <clause id="2194">
    <literal><![CDATA[
      (x * (y \ z)) * (u * (((x * (y \ z)) \ z) / u)) = ((u * ((y / x) / u)) * x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(1529,a,2187,a),flip(a)].">
      <j1 rule="hyper" parents="1529 2187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2195">
    <literal><![CDATA[
      (x * y) * T((x * y) \ z,x) = y * ((x \ (y \ z)) * x)
    ]]></literal>
    <justification jstring="[hyper(800,a,2191,a)].">
      <j1 rule="hyper" parents="800 2191"/>
    </justification>
  </clause>

  <clause id="2196">
    <literal><![CDATA[
      ((x \ (y * (z \ 1))) * x) / (z \ 1) = z * ((x \ (z \ y)) * x)
    ]]></literal>
    <justification jstring="[hyper(65,a,1410,a,b,2191,a)].">
      <j1 rule="hyper" parents="65 1410 2191"/>
    </justification>
  </clause>

  <clause id="2197">
    <literal><![CDATA[
      ((x \ R(1 / y,y,z)) * x) * (y * z) = (y * z) * ((x \ ((y * z) \ z)) * x)
    ]]></literal>
    <justification jstring="[para(183(a,2),2191(a,1,1,1,2))].">
      <j1 rule="para" parents="183 2191"/>
    </justification>
  </clause>

  <clause id="2198">
    <literal><![CDATA[
      ((x \ (y / (z \ 1))) * x) * (z \ 1) = ((x \ (y * z)) * x) / z
    ]]></literal>
    <justification jstring="[hyper(940,a,2181,a)].">
      <j1 rule="hyper" parents="940 2181"/>
    </justification>
  </clause>

  <clause id="2199">
    <literal><![CDATA[
      (x \ y) \ T((x \ y) * x,x) = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(2193,a,857,a)].">
      <j1 rule="hyper" parents="2193 857"/>
    </justification>
  </clause>

  <clause id="2200">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ 1) = (1 / y) * ((x \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(65,a,1728,a(flip),b,2192,a),flip(a)].">
      <j1 rule="hyper" parents="65 1728 2192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2201">
    <literal><![CDATA[
      (x \ 1) * ((y \ ((x \ 1) \ z)) * y) = ((y \ (z * x)) * y) / x
    ]]></literal>
    <justification jstring="[hyper(65,a,2191,a(flip),b,2198,a)].">
      <j1 rule="hyper" parents="65 2191 2198"/>
    </justification>
  </clause>

  <clause id="2202">
    <literal><![CDATA[
      ((x \ (y * z)) * x) / z = z \ ((x \ (z * y)) * x)
    ]]></literal>
    <justification jstring="[hyper(65,a,1798,a(flip),b,2201,a),flip(a)].">
      <j1 rule="hyper" parents="65 1798 2201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2203">
    <literal><![CDATA[
      R(x / (x / y),(y * (x / y)) / y,x / (x / y)) = (x * y) / x
    ]]></literal>
    <justification jstring="[para(79(a,1),2142(a,2,1,2))].">
      <j1 rule="para" parents="79 2142"/>
    </justification>
  </clause>

  <clause id="2205">
    <literal><![CDATA[
      R((x \ (1 / y)) * x,y,z) * (y * z) = (y * z) * ((x \ ((y * z) \ z)) * x)
    ]]></literal>
    <justification jstring="[para(1397(a,2),2197(a,1,1))].">
      <j1 rule="para" parents="1397 2197"/>
    </justification>
  </clause>

  <clause id="2206">
    <literal><![CDATA[
      (x * y) * ((z \ ((x * y) \ y)) * z) = (((z \ (1 / x)) * z) * x) * y
    ]]></literal>
    <justification jstring="[hyper(230,a,2205,a),flip(a)].">
      <j1 rule="hyper" parents="230 2205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2207">
    <literal><![CDATA[
      (x * (y \ z)) * (u * (((x * (y \ z)) \ z) / u)) = (x * (u * ((x \ y) / u))) * (y \ z)
    ]]></literal>
    <justification jstring="[para(2187(a,1),2194(a,2,1))].">
      <j1 rule="para" parents="2187 2194"/>
    </justification>
  </clause>

  <clause id="2208">
    <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),2207(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="79 2207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2213">
    <literal><![CDATA[
      (x \ T(x,(x \ 1) * y)) * y = y * K(((1 / x) * y) \ y,(x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(1346(a,1),1875(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1346 1875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2214">
    <literal><![CDATA[
      (x \ T(x,(x \ 1) * y)) * y = y * K(((x \ 1) * y) \ y,(x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(1769(a,1),2213(a,2,2))].">
      <j1 rule="para" parents="1769 2213"/>
    </justification>
  </clause>

  <clause id="2215">
    <literal><![CDATA[
      (((x \ 1) * y) \ y) * ((x \ 1) * y) = (x \ T(x,(x \ 1) * y)) * y
    ]]></literal>
    <justification jstring="[hyper(250,a,242,a(flip),b,2214,a)].">
      <j1 rule="hyper" parents="250 242 2214"/>
    </justification>
  </clause>

  <clause id="2216">
    <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(1479(a,1),1958(a,1,1))].">
      <j1 rule="para" parents="1479 1958"/>
    </justification>
  </clause>

  <clause id="2217">
    <literal><![CDATA[
      ((x * ((y \ T(z,x)) * y)) / x) * (((x * y) / x) \ y) = (y \ (z * (T(x,y) \ x))) * y
    ]]></literal>
    <justification jstring="[para(104(a,1),2216(a,1,1,1,2))].">
      <j1 rule="para" parents="104 2216"/>
    </justification>
  </clause>

  <clause id="2218">
    <literal><![CDATA[
      ((x * ((y \ T(z,x)) * y)) / x) * (T(x,y) \ x) = (y \ (z * (T(x,y) \ x))) * y
    ]]></literal>
    <justification jstring="[para(1955(a,1),2217(a,1,2))].">
      <j1 rule="para" parents="1955 2217"/>
    </justification>
  </clause>

  <clause id="2219">
    <literal><![CDATA[
      ((x * T((y \ z) * y,x)) / x) * (T(x,y) \ x) = (y \ (z * (T(x,y) \ x))) * y
    ]]></literal>
    <justification jstring="[para(2179(a,2),2218(a,1,1,1,2))].">
      <j1 rule="para" parents="2179 2218"/>
    </justification>
  </clause>

  <clause id="2220">
    <literal><![CDATA[
      (x \ (y * (T(z,x) \ z))) * x = ((x \ y) * x) * (T(z,x) \ z)
    ]]></literal>
    <justification jstring="[para(191(a,1),2219(a,1,1)),flip(a)].">
      <j1 rule="para" parents="191 2219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2222">
    <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),2208(a,2,2,2,1,1,2))].">
      <j1 rule="para" parents="79 2208"/>
    </justification>
  </clause>

  <clause id="2223">
    <literal><![CDATA[
      (x * (y * ((x \ (z / u)) / y))) * u = (x * u) * (y * (((x * u) \ z) / y))
    ]]></literal>
    <justification jstring="[hyper(416,a,2222,a)].">
      <j1 rule="hyper" parents="416 2222"/>
    </justification>
  </clause>

  <clause id="2226">
    <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),1871(a,1,1,1))].">
      <j1 rule="para" parents="11 1871"/>
    </justification>
  </clause>

  <clause id="2227">
    <literal><![CDATA[
      L(x,y,y \ 1) \ ((1 / y) * (x * y)) = T(y,(1 / y) * (x * y)) \ y
    ]]></literal>
    <justification jstring="[hyper(37,a,1960,a,b,2226,a),flip(a)].">
      <j1 rule="hyper" parents="37 1960 2226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2230">
    <literal><![CDATA[
      L(K(x,y),y * x,y \ 1) = T(y,(1 / y) * (x * y)) \ y
    ]]></literal>
    <justification jstring="[hyper(1524,a,2227,a)].">
      <j1 rule="hyper" parents="1524 2227"/>
    </justification>
  </clause>

  <clause id="2231">
    <literal><![CDATA[
      L(K(x,y),y * x,y \ 1) = T(y,(y \ 1) * (x * y)) \ y
    ]]></literal>
    <justification jstring="[para(1334(a,1),2230(a,2,1))].">
      <j1 rule="para" parents="1334 2230"/>
    </justification>
  </clause>

  <clause id="2232">
    <literal><![CDATA[
      T(x,(x \ 1) * (y * x)) \ x = (y * x) / (x * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,1910,a(flip),b,2231,a),flip(a)].">
      <j1 rule="hyper" parents="65 1910 2231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2233">
    <literal><![CDATA[
      T(x,(x \ 1) * (y * x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(41,a,1975,a(flip),b,2232,a),flip(a)].">
      <j1 rule="hyper" parents="41 1975 2232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2234">
    <literal><![CDATA[
      T(x,T((x \ 1) * y,x)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(1047(a,1),2233(a,1,2))].">
      <j1 rule="para" parents="1047 2233"/>
    </justification>
  </clause>

  <clause id="2235">
    <literal><![CDATA[
      T(x,(x \ 1) * y) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(2077,a,2234,a)].">
      <j1 rule="hyper" parents="2077 2234"/>
    </justification>
  </clause>

  <clause id="2236">
    <literal><![CDATA[
      (((x \ 1) * y) \ y) * ((x \ 1) * y) = (x \ T(x,x \ y)) * y
    ]]></literal>
    <justification jstring="[para(2235(a,1),2215(a,2,1,2))].">
      <j1 rule="para" parents="2235 2215"/>
    </justification>
  </clause>

  <clause id="2237">
    <literal><![CDATA[
      (((x \ 1) * y) \ y) * ((x \ 1) * y) = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(250,a,1997,a(flip),b,2236,a),flip(a)].">
      <j1 rule="hyper" parents="250 1997 2236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2238">
    <literal><![CDATA[
      T((x \ y) * x,y) / y = y / (x * (y / x))
    ]]></literal>
    <justification jstring="[para(2237(a,1),2188(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2237 2188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2239">
    <literal><![CDATA[
      ((x \ y) * x) / y = y / (x * (y / x))
    ]]></literal>
    <justification jstring="[para(2186(a,1),2238(a,1,1))].">
      <j1 rule="para" parents="2186 2238"/>
    </justification>
  </clause>

  <clause id="2240">
    <literal><![CDATA[
      ((x \ y) * x) / y = x \ (y / (y / x))
    ]]></literal>
    <justification jstring="[hyper(250,a,2082,a(flip),b,2239,a),flip(a)].">
      <j1 rule="hyper" parents="250 2082 2239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2241">
    <literal><![CDATA[
      R((x \ (1 / (1 / y))) * x,1 / y,y) / ((1 / y) \ 1) = (y * K(x \ (1 / (1 / y)),x)) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(79(a,1),1799(a,1,1,3))].">
      <j1 rule="para" parents="79 1799"/>
    </justification>
  </clause>

  <clause id="2242">
    <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(1638(a,1),2241(a,1,1))].">
      <j1 rule="para" parents="1638 2241"/>
    </justification>
  </clause>

  <clause id="2243">
    <literal><![CDATA[
      (x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ (1 * x)) * y) / ((1 / x) \ 1)
    ]]></literal>
    <justification jstring="[para(1640(a,1),2242(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1640 2242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2244">
    <literal><![CDATA[
      (x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ x) * y) / ((1 / x) \ 1)
    ]]></literal>
    <justification jstring="[para(7(a,1),2243(a,2,1,1,2))].">
      <j1 rule="para" parents="7 2243"/>
    </justification>
  </clause>

  <clause id="2245">
    <literal><![CDATA[
      (x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ x) * y) / x
    ]]></literal>
    <justification jstring="[para(79(a,1),2244(a,2,2))].">
      <j1 rule="para" parents="79 2244"/>
    </justification>
  </clause>

  <clause id="2246">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ 1) = ((x \ y) * x) / y
    ]]></literal>
    <justification jstring="[para(1726(a,1),2245(a,1,1))].">
      <j1 rule="para" parents="1726 2245"/>
    </justification>
  </clause>

  <clause id="2247">
    <literal><![CDATA[
      (1 / x) * ((y \ x) * y) = ((y \ x) * y) / x
    ]]></literal>
    <justification jstring="[hyper(65,a,2200,a(flip),b,2246,a)].">
      <j1 rule="hyper" parents="65 2200 2246"/>
    </justification>
  </clause>

  <clause id="2248">
    <literal><![CDATA[
      (1 / x) * ((y \ x) * y) = y \ (x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(250,a,2240,a(flip),b,2247,a),flip(a)].">
      <j1 rule="hyper" parents="250 2240 2247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2249">
    <literal><![CDATA[
      L((x \ ((y \ 1) \ 1)) * x,y \ 1,y) = y * (x \ (y / (y / x)))
    ]]></literal>
    <justification jstring="[para(2248(a,1),1729(a,2,2))].">
      <j1 rule="para" parents="2248 1729"/>
    </justification>
  </clause>

  <clause id="2250">
    <literal><![CDATA[
      (x \ (1 \ (y * 1))) * x = y * (x \ (y / (y / x)))
    ]]></literal>
    <justification jstring="[hyper(65,a,1792,a(flip),b,2249,a)].">
      <j1 rule="hyper" parents="65 1792 2249"/>
    </justification>
  </clause>

  <clause id="2251">
    <literal><![CDATA[
      x * (y \ (x / (x / y))) = (y \ x) * y
    ]]></literal>
    <justification jstring="[para(143(a,1),2250(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="143 2250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2252">
    <literal><![CDATA[
      x \ (y / (y / x)) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(36,a,242,a,b,2251,a),flip(a)].">
      <j1 rule="hyper" parents="36 242 2251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2253">
    <literal><![CDATA[
      x / (x / y) = y * K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(125,a,2252,a),flip(a)].">
      <j1 rule="hyper" parents="125 2252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2254">
    <literal><![CDATA[
      (x / y) * K(y \ x,y) = y \ x
    ]]></literal>
    <justification jstring="[hyper(116,a,2252,a(flip),b,1874,a)].">
      <j1 rule="hyper" parents="116 2252 1874"/>
    </justification>
  </clause>

  <clause id="2255">
    <literal><![CDATA[
      K(x \ y,x) * y = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(115,a,2252,a(flip),b,2240,a)].">
      <j1 rule="hyper" parents="115 2252 2240"/>
    </justification>
  </clause>

  <clause id="2256">
    <literal><![CDATA[
      K(x \ y,x) * (x * (y / x)) = y
    ]]></literal>
    <justification jstring="[hyper(115,a,2252,a(flip),b,2082,a)].">
      <j1 rule="hyper" parents="115 2252 2082"/>
    </justification>
  </clause>

  <clause id="2258">
    <literal><![CDATA[
      T(x * K(x \ y,x),y) = L(x,x \ y,x)
    ]]></literal>
    <justification jstring="[para(2253(a,1),2096(a,1,1))].">
      <j1 rule="para" parents="2253 2096"/>
    </justification>
  </clause>

  <clause id="2260">
    <literal><![CDATA[
      T(x,K(y \ x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(329,a,2255,a)].">
      <j1 rule="hyper" parents="329 2255"/>
    </justification>
  </clause>

  <clause id="2261">
    <literal><![CDATA[
      (((x * (y * z)) / z) \ (x * y)) * ((x * (y * z)) / z) = K(a(x,y,z),(x * (y * z)) / z) * (x * y)
    ]]></literal>
    <justification jstring="[para(1705(a,2),2255(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1705 2255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2262">
    <literal><![CDATA[
      T(x * y,K(y,x)) = x * y
    ]]></literal>
    <justification jstring="[para(9(a,1),2260(a,1,2,1))].">
      <j1 rule="para" parents="9 2260"/>
    </justification>
  </clause>

  <clause id="2263">
    <literal><![CDATA[
      K(x,y) = (x * y) / (y * x)
    ]]></literal>
    <justification jstring="[hyper(170,a,2262,a(flip),b,245,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="170 2262 245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2264">
    <literal><![CDATA[
      K(x,y) * (y * x) = x * y
    ]]></literal>
    <justification jstring="[hyper(116,a,2262,a(flip),b,245,a(flip))].">
      <j1 rule="hyper" parents="116 2262 245"/>
    </justification>
  </clause>

  <clause id="2265">
    <literal><![CDATA[
      K(x,y) = T(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(250,a,2045,a(flip),b,2263,a),flip(a)].">
      <j1 rule="hyper" parents="250 2045 2263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2266">
    <literal><![CDATA[
      K(x,y) = T(y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(250,a,1975,a(flip),b,2263,a),flip(a)].">
      <j1 rule="hyper" parents="250 1975 2263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2267">
    <literal><![CDATA[
      T(x,y) = x / K(y,x)
    ]]></literal>
    <justification jstring="[hyper(170,a,2263,a,b,1975,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="170 2263 1975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2268">
    <literal><![CDATA[
      T(x,y) * K(y,x) = x
    ]]></literal>
    <justification jstring="[hyper(116,a,2263,a,b,1975,a(flip))].">
      <j1 rule="hyper" parents="116 2263 1975"/>
    </justification>
  </clause>

  <clause id="2269">
    <literal><![CDATA[
      T(x,y) = K(x,y) * x
    ]]></literal>
    <justification jstring="[hyper(115,a,2263,a,b,2045,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="115 2263 2045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2270">
    <literal><![CDATA[
      K(x,T(y,x)) = T(y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(250,a,1863,a,b,2265,a),flip(a)].">
      <j1 rule="hyper" parents="250 1863 2265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2271">
    <literal><![CDATA[
      K(x,y) = (1 / x) * T((1 / x) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(250,a,597,a,b,2265,a),flip(a)].">
      <j1 rule="hyper" parents="250 597 2265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2272">
    <literal><![CDATA[
      K(x,y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(250,a,1852,a(flip),b,2265,a),flip(a)].">
      <j1 rule="hyper" parents="250 1852 2265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2274">
    <literal><![CDATA[
      T(x,y) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,2265,a,b,1852,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 2265 1852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2276">
    <literal><![CDATA[
      K(x,y) / T(x,y) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(113,a,2265,a,b,599,a)].">
      <j1 rule="hyper" parents="113 2265 599"/>
    </justification>
  </clause>

  <clause id="2277">
    <literal><![CDATA[
      x * T(x \ 1,y) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(602,a,2265,a(flip))].">
      <j1 rule="hyper" parents="602 2265"/>
    </justification>
  </clause>

  <clause id="2278">
    <literal><![CDATA[
      (T(R(x,y,z),u) * (y * z)) / ((x * y) * z) = R(K(R(x,y,z),u),R(x,y,z),y * z)
    ]]></literal>
    <justification jstring="[para(2265(a,2),384(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2265 384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2279">
    <literal><![CDATA[
      K(x \ (x / y),x) = K(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(250,a,2022,a,b,2266,a)].">
      <j1 rule="hyper" parents="250 2022 2266"/>
    </justification>
  </clause>

  <clause id="2280">
    <literal><![CDATA[
      K(x,y) = ((y * x) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(250,a,1955,a,b,2266,a),flip(a)].">
      <j1 rule="hyper" parents="250 1955 2266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2281">
    <literal><![CDATA[
      K(x * a(y,z,u),a(y,z,u) \ 1) = K(a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(250,a,1579,a,b,2266,a)].">
      <j1 rule="hyper" parents="250 1579 2266"/>
    </justification>
  </clause>

  <clause id="2282">
    <literal><![CDATA[
      K(x,y) = y * (T(y,x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(250,a,648,a,b,2266,a),flip(a)].">
      <j1 rule="hyper" parents="250 648 2266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2283">
    <literal><![CDATA[
      K(T(x,y),y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(250,a,1957,a(flip),b,2266,a),flip(a)].">
      <j1 rule="hyper" parents="250 1957 2266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2284">
    <literal><![CDATA[
      (x \ 1) * K(y,x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,2266,a,b,1727,a)].">
      <j1 rule="hyper" parents="116 2266 1727"/>
    </justification>
  </clause>

  <clause id="2285">
    <literal><![CDATA[
      T(x,y) \ 1 = x \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(112,a,2266,a,b,648,a),flip(a)].">
      <j1 rule="hyper" parents="112 2266 648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2287">
    <literal><![CDATA[
      T(x,y) = K(y,x) \ x
    ]]></literal>
    <justification jstring="[para(2266(a,2),1971(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2266 1971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2288">
    <literal><![CDATA[
      T(x,y) = (K(y,x) / x) \ 1
    ]]></literal>
    <justification jstring="[para(2266(a,2),1991(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2266 1991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2289">
    <literal><![CDATA[
      x * (K(x,y) * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[para(2266(a,2),2031(a,1,2,1))].">
      <j1 rule="para" parents="2266 2031"/>
    </justification>
  </clause>

  <clause id="2290">
    <literal><![CDATA[
      T(x,y) * (x \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(2266(a,2),2032(a,2,1))].">
      <j1 rule="para" parents="2266 2032"/>
    </justification>
  </clause>

  <clause id="2291">
    <literal><![CDATA[
      K(x / y,z) * x = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(2266(a,2),2028(a,1,1))].">
      <j1 rule="para" parents="2266 2028"/>
    </justification>
  </clause>

  <clause id="2292">
    <literal><![CDATA[
      x * (T(x,y) \ z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[para(2266(a,2),2153(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2266 2153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2293">
    <literal><![CDATA[
      K(x,y) * (T(y,x) * z) = y * z
    ]]></literal>
    <justification jstring="[para(2266(a,2),2154(a,1,1))].">
      <j1 rule="para" parents="2266 2154"/>
    </justification>
  </clause>

  <clause id="2294">
    <literal><![CDATA[
      ((x \ y) * x) * (T(z,x) \ z) = (x \ (y * K(x,z))) * x
    ]]></literal>
    <justification jstring="[para(2266(a,2),2220(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2266 2220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2297">
    <literal><![CDATA[
      T(x,y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(2267(a,2),223(a,1,1))].">
      <j1 rule="para" parents="2267 223"/>
    </justification>
  </clause>

  <clause id="2299">
    <literal><![CDATA[
      K(a(x,y,z),u) * a(x,y,z) = a(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,2106,a,b,2269,a),flip(a)].">
      <j1 rule="hyper" parents="65 2106 2269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2301">
    <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(2269(a,2),1029(a,1,1))].">
      <j1 rule="para" parents="2269 1029"/>
    </justification>
  </clause>

  <clause id="2302">
    <literal><![CDATA[
      K(x,y) * (x * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[para(2269(a,2),2120(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2269 2120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2303">
    <literal><![CDATA[
      L(x \ T(x,y \ 1),z,u) = K(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(250,a,1906,a,b,2272,a)].">
      <j1 rule="hyper" parents="250 1906 2272"/>
    </justification>
  </clause>

  <clause id="2304">
    <literal><![CDATA[
      T(x \ T(x,y \ 1),z) = K(x,T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(250,a,1897,a,b,2272,a)].">
      <j1 rule="hyper" parents="250 1897 2272"/>
    </justification>
  </clause>

  <clause id="2305">
    <literal><![CDATA[
      x * ((y * (x \ 1)) / y) = K(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(250,a,1886,a,b,2272,a)].">
      <j1 rule="hyper" parents="250 1886 2272"/>
    </justification>
  </clause>

  <clause id="2306">
    <literal><![CDATA[
      K(x,y) = T(x,y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(250,a,589,a,b,2272,a),flip(a)].">
      <j1 rule="hyper" parents="250 589 2272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2308">
    <literal><![CDATA[
      (x * y) / x = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,2272,a,b,1847,a),flip(a)].">
      <j1 rule="hyper" parents="116 2272 1847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2310">
    <literal><![CDATA[
      (x * y) / x = K(x,y) * y
    ]]></literal>
    <justification jstring="[hyper(115,a,2272,a,b,2002,a),flip(a)].">
      <j1 rule="hyper" parents="115 2272 2002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2312">
    <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),2272(a,2,2)),flip(a)].">
      <j1 rule="para" parents="25 2272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2313">
    <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),2272(a,2,2)),flip(a)].">
      <j1 rule="para" parents="27 2272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2314">
    <literal><![CDATA[
      x * K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(2272(a,2),214(a,1,2))].">
      <j1 rule="para" parents="2272 214"/>
    </justification>
  </clause>

  <clause id="2315">
    <literal><![CDATA[
      x * K(x,y) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ T(x,y) = u
    ]]></literal>
    <justification jstring="[para(2272(a,2),407(a,1,2))].">
      <j1 rule="para" parents="2272 407"/>
    </justification>
  </clause>

  <clause id="2316">
    <literal><![CDATA[
      K(x,x * (y \ 1)) = x \ T(x,y \ x)
    ]]></literal>
    <justification jstring="[para(956(a,1),2272(a,2,2))].">
      <j1 rule="para" parents="956 2272"/>
    </justification>
  </clause>

  <clause id="2317">
    <literal><![CDATA[
      x \ T(x,y \ 1) = K(x,1 / y)
    ]]></literal>
    <justification jstring="[para(1625(a,1),2272(a,2,2)),flip(a)].">
      <j1 rule="para" parents="1625 2272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2318">
    <literal><![CDATA[
      K(x,y * K(z,z \ 1)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[para(1627(a,1),2272(a,2,2))].">
      <j1 rule="para" parents="1627 2272"/>
    </justification>
  </clause>

  <clause id="2320">
    <literal><![CDATA[
      (x \ y) * K(x,x \ y) = y / x
    ]]></literal>
    <justification jstring="[para(2272(a,2),1846(a,1,2))].">
      <j1 rule="para" parents="2272 1846"/>
    </justification>
  </clause>

  <clause id="2321">
    <literal><![CDATA[
      x \ (T(x,y) * z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(2272(a,2),1919(a,2,1))].">
      <j1 rule="para" parents="2272 1919"/>
    </justification>
  </clause>

  <clause id="2322">
    <literal><![CDATA[
      T(x,y) \ x = K(x,y) \ 1
    ]]></literal>
    <justification jstring="[para(2272(a,2),1925(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2272 1925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2323">
    <literal><![CDATA[
      x * (T(x,y) \ z) = K(x,y) \ z
    ]]></literal>
    <justification jstring="[para(2272(a,2),1937(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2272 1937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2325">
    <literal><![CDATA[
      K(x,(y \ z) / z) = x \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(2084(a,1),2272(a,2,2))].">
      <j1 rule="para" parents="2084 2272"/>
    </justification>
  </clause>

  <clause id="2326">
    <literal><![CDATA[
      (x * y) * L(K(y,z),y,x) = x * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,2274,a,b,332,a),flip(a)].">
      <j1 rule="hyper" parents="116 2274 332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2327">
    <literal><![CDATA[
      T(x,y) != x * z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(2274(a,2),45(a,1))].">
      <j1 rule="para" parents="2274 45"/>
    </justification>
  </clause>

  <clause id="2328">
    <literal><![CDATA[
      x \ T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(2274(a,2),235(a,1,2))].">
      <j1 rule="para" parents="2274 235"/>
    </justification>
  </clause>

  <clause id="2332">
    <literal><![CDATA[
      K(x,T(y,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(250,a,2266,a,b,2270,a),flip(a)].">
      <j1 rule="hyper" parents="250 2266 2270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2333">
    <literal><![CDATA[
      K(x,x \ (y * x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(22(a,1),2332(a,1,2))].">
      <j1 rule="para" parents="22 2332"/>
    </justification>
  </clause>

  <clause id="2334">
    <literal><![CDATA[
      K(x,L(T(y,x),z,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(25(a,2),2332(a,1,2))].">
      <j1 rule="para" parents="25 2332"/>
    </justification>
  </clause>

  <clause id="2335">
    <literal><![CDATA[
      K(x,y / x) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(106(a,1),2332(a,1,2)),flip(a)].">
      <j1 rule="para" parents="106 2332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2337">
    <literal><![CDATA[
      K(x,R(y / x,z,u)) = K(x,R(x \ y,z,u))
    ]]></literal>
    <justification jstring="[para(208(a,1),2332(a,1,2)),flip(a)].">
      <j1 rule="para" parents="208 2332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2338">
    <literal><![CDATA[
      K(a(x,y,z),a(x,y,z) \ (x * y)) = K(a(x,y,z),(x * (y * z)) / z)
    ]]></literal>
    <justification jstring="[para(1703(a,1),2332(a,1,2))].">
      <j1 rule="para" parents="1703 2332"/>
    </justification>
  </clause>

  <clause id="2339">
    <literal><![CDATA[
      K(x,y) = x * (((y * x) / y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(250,a,843,a,b,2280,a),flip(a)].">
      <j1 rule="hyper" parents="250 843 2280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2340">
    <literal><![CDATA[
      (x * y) \ (x * K(z,y)) = L(T(y,z) \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(2282(a,2),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="2282 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2341">
    <literal><![CDATA[
      L(T(x \ y,z) \ 1,x \ y,x) = y \ (x * K(z,x \ y))
    ]]></literal>
    <justification jstring="[para(2282(a,2),94(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2282 94"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2342">
    <literal><![CDATA[
      K(T(x,y),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(250,a,2272,a,b,2283,a),flip(a)].">
      <j1 rule="hyper" parents="250 2272 2283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2343">
    <literal><![CDATA[
      K(x \ (y * x),x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(22(a,1),2342(a,1,1))].">
      <j1 rule="para" parents="22 2342"/>
    </justification>
  </clause>

  <clause id="2344">
    <literal><![CDATA[
      K(x / y,y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(106(a,1),2342(a,1,1)),flip(a)].">
      <j1 rule="para" parents="106 2342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2346">
    <literal><![CDATA[
      K(x,y) = (1 / y) * ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(116,a,2308,a,b,1989,a),flip(a)].">
      <j1 rule="hyper" parents="116 2308 1989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2347">
    <literal><![CDATA[
      T(x * K(y,x),y) = x
    ]]></literal>
    <justification jstring="[para(2308(a,1),190(a,1,1))].">
      <j1 rule="para" parents="2308 190"/>
    </justification>
  </clause>

  <clause id="2348">
    <literal><![CDATA[
      T(x,y) * K(y,T(x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(2308(a,1),233(a,1))].">
      <j1 rule="para" parents="2308 233"/>
    </justification>
  </clause>

  <clause id="2350">
    <literal><![CDATA[
      T(T(x * K(y,x),z),y) = T(x,z)
    ]]></literal>
    <justification jstring="[para(2308(a,1),226(a,1,1,1))].">
      <j1 rule="para" parents="2308 226"/>
    </justification>
  </clause>

  <clause id="2351">
    <literal><![CDATA[
      R(x / y,y,K(z,x)) \ ((z * x) / z) = y * K(z,x)
    ]]></literal>
    <justification jstring="[para(2308(a,2),361(a,1,2))].">
      <j1 rule="para" parents="2308 361"/>
    </justification>
  </clause>

  <clause id="2354">
    <literal><![CDATA[
      R(x * K(y,x),z,u) = (y * R(x,z,u)) / y
    ]]></literal>
    <justification jstring="[para(2308(a,1),537(a,1,1))].">
      <j1 rule="para" parents="2308 537"/>
    </justification>
  </clause>

  <clause id="2356">
    <literal><![CDATA[
      (x * y) / ((z * y) / z) = (x / (y * K(z,y))) * y
    ]]></literal>
    <justification jstring="[para(2308(a,1),883(a,2,1,2))].">
      <j1 rule="para" parents="2308 883"/>
    </justification>
  </clause>

  <clause id="2358">
    <literal><![CDATA[
      ((x * y) * z) \ ((x * y) * R(z,x,y)) = a(z * K(x * y,z),x,y)
    ]]></literal>
    <justification jstring="[para(2308(a,1),749(a,2,1))].">
      <j1 rule="para" parents="2308 749"/>
    </justification>
  </clause>

  <clause id="2359">
    <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(42,a,1030,a,b,2347,a),flip(a)].">
      <j1 rule="hyper" parents="42 1030 2347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2361">
    <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(2347(a,1),1220(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2347 1220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2362">
    <literal><![CDATA[
      R(x,y,z) = x * a(x,y,z * K(x * y,z))
    ]]></literal>
    <justification jstring="[para(2347(a,1),1720(a,1,3))].">
      <j1 rule="para" parents="2347 1720"/>
    </justification>
  </clause>

  <clause id="2365">
    <literal><![CDATA[
      (x * ((y * z) / y)) / L(z,K(y,z),x) = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(2310(a,2),161(a,1,1,2))].">
      <j1 rule="para" parents="2310 161"/>
    </justification>
  </clause>

  <clause id="2366">
    <literal><![CDATA[
      K(x,y) \ 1 = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,2266,a,b,2322,a),flip(a)].">
      <j1 rule="hyper" parents="65 2266 2322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2367">
    <literal><![CDATA[
      1 / K(x,y) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(170,a,2266,a,b,2322,a(flip))].">
      <j1 rule="hyper" parents="170 2266 2322"/>
    </justification>
  </clause>

  <clause id="2368">
    <literal><![CDATA[
      K(x,y) * K(y,x) = 1
    ]]></literal>
    <justification jstring="[hyper(116,a,2266,a,b,2322,a(flip))].">
      <j1 rule="hyper" parents="116 2266 2322"/>
    </justification>
  </clause>

  <clause id="2369">
    <literal><![CDATA[
      K(x,y) != z \ 1
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(2366(a,1),50(a,1))].">
      <j1 rule="para" parents="2366 50"/>
    </justification>
  </clause>

  <clause id="2370">
    <literal><![CDATA[
      1 / K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(2366(a,1),232(a,1,2)),flip(b)].">
      <j1 rule="para" parents="2366 232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2373">
    <literal><![CDATA[
      K(x,y) * T(K(y,x),z) = K(K(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(115,a,2367,a(flip),b,2276,a)].">
      <j1 rule="hyper" parents="115 2367 2276"/>
    </justification>
  </clause>

  <clause id="2374">
    <literal><![CDATA[
      K(x,y) != 1 / z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(2367(a,1),47(a,1))].">
      <j1 rule="para" parents="2367 47"/>
    </justification>
  </clause>

  <clause id="2375">
    <literal><![CDATA[
      K(x,y) \ 1 != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(2367(a,1),223(a,1,1))].">
      <j1 rule="para" parents="2367 223"/>
    </justification>
  </clause>

  <clause id="2376">
    <literal><![CDATA[
      K(x,y) * z != 1
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(2368(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="2368 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2377">
    <literal><![CDATA[
      x * K(y,y \ x) = y * (x / y)
    ]]></literal>
    <justification jstring="[hyper(116,a,2335,a(flip),b,90,a)].">
      <j1 rule="hyper" parents="116 2335 90"/>
    </justification>
  </clause>

  <clause id="2379">
    <literal><![CDATA[
      K(x,T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(2270(a,2),2297(a,1))].">
      <j1 rule="para" parents="2270 2297"/>
    </justification>
  </clause>

  <clause id="2380">
    <literal><![CDATA[
      K(x,L(T(y,x),z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(25(a,2),2379(a,1,2))].">
      <j1 rule="para" parents="25 2379"/>
    </justification>
  </clause>

  <clause id="2381">
    <literal><![CDATA[
      x * (y * T(y \ (x \ 1),z)) = K((x * y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(642,a,2277,a)].">
      <j1 rule="hyper" parents="642 2277"/>
    </justification>
  </clause>

  <clause id="2382">
    <literal><![CDATA[
      R(x * T(x \ 1,y),z,u) = K(R(x,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,1507,a(flip),b,2277,a)].">
      <j1 rule="hyper" parents="65 1507 2277"/>
    </justification>
  </clause>

  <clause id="2383">
    <literal><![CDATA[
      x \ (y * T(y \ x,z)) = K((x \ y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,678,a(flip),b,2277,a)].">
      <j1 rule="hyper" parents="65 678 2277"/>
    </justification>
  </clause>

  <clause id="2384">
    <literal><![CDATA[
      x * T(x \ y,z) = y * K((y \ x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,2277,a(flip),b,678,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 2277 678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2386">
    <literal><![CDATA[
      (x * y) * T((x * y) \ x,z) = x * K(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(2277(a,1),478(a,2,2))].">
      <j1 rule="para" parents="2277 478"/>
    </justification>
  </clause>

  <clause id="2388">
    <literal><![CDATA[
      x * (y * T(y \ (x \ y),z)) = K(x \ 1,z) * y
    ]]></literal>
    <justification jstring="[para(2277(a,1),822(a,2,1))].">
      <j1 rule="para" parents="2277 822"/>
    </justification>
  </clause>

  <clause id="2389">
    <literal><![CDATA[
      K(x \ (x / T(y,z)),x) = T(K(y \ 1,x),z)
    ]]></literal>
    <justification jstring="[para(2277(a,1),833(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2277 833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2390">
    <literal><![CDATA[
      K((x * y) \ 1,x) != z
    ]]></literal>
    <literal><![CDATA[
      ((x \ (1 / y)) * x) * y = z
    ]]></literal>
    <justification jstring="[para(2277(a,1),908(a,1))].">
      <j1 rule="para" parents="2277 908"/>
    </justification>
  </clause>

  <clause id="2391">
    <literal><![CDATA[
      K(x \ (x / L(y,z,u)),x) = L(K(y \ 1,x),z,u)
    ]]></literal>
    <justification jstring="[para(2277(a,1),1503(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2277 1503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2393">
    <literal><![CDATA[
      (x \ 1) * K(y,x) = x \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(250,a,2285,a(flip),b,2284,a),flip(a)].">
      <j1 rule="hyper" parents="250 2285 2284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2394">
    <literal><![CDATA[
      K(x,y) * (x \ 1) = x \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(112,a,2306,a,b,2289,a),flip(a)].">
      <j1 rule="hyper" parents="112 2306 2289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2395">
    <literal><![CDATA[
      K(x,y) * (T(x,y) \ z) = x \ z
    ]]></literal>
    <justification jstring="[hyper(112,a,10,a(flip),b,2289,a),flip(a)].">
      <j1 rule="hyper" parents="112 10 2289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2396">
    <literal><![CDATA[
      T(x,y) * T(z,K(x,y)) = x * (z * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,188,a(flip),b,2289,a),flip(a)].">
      <j1 rule="hyper" parents="65 188 2289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2397">
    <literal><![CDATA[
      K(x,y) * (z * x) = T(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(36,a,649,a,b,2289,a),flip(a)].">
      <j1 rule="hyper" parents="36 649 2289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2398">
    <literal><![CDATA[
      (K(x,y) * z) \ (T(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(x,y) * z) = u
    ]]></literal>
    <justification jstring="[para(2289(a,1),236(a,1,2))].">
      <j1 rule="para" parents="2289 236"/>
    </justification>
  </clause>

  <clause id="2399">
    <literal><![CDATA[
      x * (K(y,x) * K(x,z)) = T(x,z) * K(y,x)
    ]]></literal>
    <justification jstring="[para(1061(a,1),2289(a,1,2))].">
      <j1 rule="para" parents="1061 2289"/>
    </justification>
  </clause>

  <clause id="2400">
    <literal><![CDATA[
      T(x,y) * (x \ R(x,z,u)) = R(x,z,u) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(250,a,1761,a,b,2290,a),flip(a)].">
      <j1 rule="hyper" parents="250 1761 2290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2402">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ y,z) = K(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,323,a,b,2290,a)].">
      <j1 rule="hyper" parents="65 323 2290"/>
    </justification>
  </clause>

  <clause id="2403">
    <literal><![CDATA[
      (x \ L(x,y,z)) * T(x,u) = K(x,u) * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,1795,a(flip),b,2290,a)].">
      <j1 rule="hyper" parents="65 1795 2290"/>
    </justification>
  </clause>

  <clause id="2404">
    <literal><![CDATA[
      (x * y) / (T(x,z) * y) = K(z,x)
    ]]></literal>
    <justification jstring="[hyper(113,a,2158,a(flip),b,2290,a(flip))].">
      <j1 rule="hyper" parents="113 2158 2290"/>
    </justification>
  </clause>

  <clause id="2405">
    <literal><![CDATA[
      K(x,y) * (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(2290(a,1),415(a,1))].">
      <j1 rule="para" parents="2290 415"/>
    </justification>
  </clause>

  <clause id="2406">
    <literal><![CDATA[
      K(x,y) * T(x,z) = T(x,y) * K(x,z)
    ]]></literal>
    <justification jstring="[para(2272(a,2),2290(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2272 2290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2407">
    <literal><![CDATA[
      T(x,y) \ (x * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(663,a,2292,a)].">
      <j1 rule="hyper" parents="663 2292"/>
    </justification>
  </clause>

  <clause id="2408">
    <literal><![CDATA[
      K(x,y) * (y \ z) = T(y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(660,a,2292,a),flip(a)].">
      <j1 rule="hyper" parents="660 2292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2410">
    <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(2293(a,1),339(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2293 339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2412">
    <literal><![CDATA[
      ((T(x,y) * z) * u) / ((x * z) * u) = R(K(x,y),x * z,u)
    ]]></literal>
    <justification jstring="[para(2302(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="2302 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2413">
    <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),2302(a,2,1))].">
      <j1 rule="para" parents="27 2302"/>
    </justification>
  </clause>

  <clause id="2414">
    <literal><![CDATA[
      T(x,y) * (x \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(2302(a,1),259(a,1))].">
      <j1 rule="para" parents="2302 259"/>
    </justification>
  </clause>

  <clause id="2416">
    <literal><![CDATA[
      K(x,y) * (R(z,u,w) * x) = T(x,y) * R(T(z,x),u,w)
    ]]></literal>
    <justification jstring="[para(199(a,1),2302(a,1,2))].">
      <j1 rule="para" parents="199 2302"/>
    </justification>
  </clause>

  <clause id="2417">
    <literal><![CDATA[
      K(x,1 / y) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(2328,a,2317,a),flip(a)].">
      <j1 rule="hyper" parents="2328 2317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2419">
    <literal><![CDATA[
      K(x,(y \ 1) \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[para(76(a,1),2417(a,1,2)),flip(a)].">
      <j1 rule="para" parents="76 2417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2421">
    <literal><![CDATA[
      x * (K(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(2321(a,1),214(a,1,2))].">
      <j1 rule="para" parents="2321 214"/>
    </justification>
  </clause>

  <clause id="2422">
    <literal><![CDATA[
      K(x,y) \ z = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(65,a,2292,a(flip),b,2323,a),flip(a)].">
      <j1 rule="hyper" parents="65 2292 2323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2423">
    <literal><![CDATA[
      x \ (K(y,z) \ x) = T(K(z,y),x)
    ]]></literal>
    <justification jstring="[hyper(307,a,2323,a(flip),b,2292,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="307 2323 2292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2424">
    <literal><![CDATA[
      x / (y * T(y \ x,z)) = K(z,x / y)
    ]]></literal>
    <justification jstring="[hyper(170,a,2157,a,b,2323,a(flip))].">
      <j1 rule="hyper" parents="170 2157 2323"/>
    </justification>
  </clause>

  <clause id="2425">
    <literal><![CDATA[
      x / (K(y,z) * x) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(170,a,2292,a(flip),b,2323,a(flip))].">
      <j1 rule="hyper" parents="170 2292 2323"/>
    </justification>
  </clause>

  <clause id="2426">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * z) = z
    ]]></literal>
    <justification jstring="[hyper(116,a,2292,a(flip),b,2323,a(flip))].">
      <j1 rule="hyper" parents="116 2292 2323"/>
    </justification>
  </clause>

  <clause id="2427">
    <literal><![CDATA[
      K(x,y) * (K(x,z) * K(y,x)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(1065,a,2422,a)].">
      <j1 rule="hyper" parents="1065 2422"/>
    </justification>
  </clause>

  <clause id="2430">
    <literal><![CDATA[
      K(x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * u = z
    ]]></literal>
    <justification jstring="[para(2422(a,1),125(a,1))].">
      <j1 rule="para" parents="2422 125"/>
    </justification>
  </clause>

  <clause id="2431">
    <literal><![CDATA[
      x / (K(y,z) * x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = u
    ]]></literal>
    <justification jstring="[para(2422(a,1),232(a,1,2)),flip(b)].">
      <j1 rule="para" parents="2422 232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2432">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      u = z
    ]]></literal>
    <justification jstring="[para(2422(a,1),270(a,1))].">
      <j1 rule="para" parents="2422 270"/>
    </justification>
  </clause>

  <clause id="2433">
    <literal><![CDATA[
      L(x \ (K(y,z) * u),x,K(z,y)) = (K(z,y) * x) \ u
    ]]></literal>
    <justification jstring="[para(2422(a,1),239(a,1,1,2))].">
      <j1 rule="para" parents="2422 239"/>
    </justification>
  </clause>

  <clause id="2434">
    <literal><![CDATA[
      L(K(x,y) * (z \ u),K(y,x),z) = (z * K(y,x)) \ u
    ]]></literal>
    <justification jstring="[para(2422(a,1),239(a,1,1))].">
      <j1 rule="para" parents="2422 239"/>
    </justification>
  </clause>

  <clause id="2437">
    <literal><![CDATA[
      K(x,y) \ z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * z = u
    ]]></literal>
    <justification jstring="[para(2425(a,1),223(a,1,1))].">
      <j1 rule="para" parents="2425 223"/>
    </justification>
  </clause>

  <clause id="2441">
    <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(2339(a,2),725(a,2,2))].">
      <j1 rule="para" parents="2339 725"/>
    </justification>
  </clause>

  <clause id="2443">
    <literal><![CDATA[
      T(x * K(x * y,x),y) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(42,a,2063,a,b,2350,a),flip(a)].">
      <j1 rule="hyper" parents="42 2063 2350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2444">
    <literal><![CDATA[
      (x * (y / x)) \ (y * (K(x,x \ y) * z)) = L(z,K(x,x \ y),y)
    ]]></literal>
    <justification jstring="[para(2377(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="2377 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2445">
    <literal><![CDATA[
      ((x * (y \ 1)) * K(z,y)) / (y \ K(z,y)) = R(x,y \ 1,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(170,a,2393,a(flip),b,159,a)].">
      <j1 rule="hyper" parents="170 2393 159"/>
    </justification>
  </clause>

  <clause id="2446">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,y)) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(170,a,2394,a(flip),b,2422,a)].">
      <j1 rule="hyper" parents="170 2394 2422"/>
    </justification>
  </clause>

  <clause id="2447">
    <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),2404(a,1,2,1))].">
      <j1 rule="para" parents="27 2404"/>
    </justification>
  </clause>

  <clause id="2448">
    <literal><![CDATA[
      T(x,y) * (K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(2407(a,1),214(a,1,2))].">
      <j1 rule="para" parents="2407 214"/>
    </justification>
  </clause>

  <clause id="2450">
    <literal><![CDATA[
      K(x,y) * (y * z) = y * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(2407(a,1),2292(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2407 2292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2452">
    <literal><![CDATA[
      T(x,y) \ (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * z = u
    ]]></literal>
    <justification jstring="[para(2408(a,1),415(a,1))].">
      <j1 rule="para" parents="2408 415"/>
    </justification>
  </clause>

  <clause id="2454">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(2394(a,1),2431(a,1,2))].">
      <j1 rule="para" parents="2394 2431"/>
    </justification>
  </clause>

  <clause id="2455">
    <literal><![CDATA[
      T(T(x * K(x * y,x),z),y) = T(R(x,y,x),z)
    ]]></literal>
    <justification jstring="[para(2443(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2443 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2456">
    <literal><![CDATA[
      ((1 / x) * y) * T(((1 / x) * y) \ y,z) = K(x,z) * y
    ]]></literal>
    <justification jstring="[para(2271(a,2),686(a,2,1))].">
      <j1 rule="para" parents="2271 686"/>
    </justification>
  </clause>

  <clause id="2457">
    <literal><![CDATA[
      (x * (y * T(y \ z,u))) / (x * z) = K((x * z) / (x * y),u)
    ]]></literal>
    <justification jstring="[hyper(113,a,561,a(flip),b,2291,a)].">
      <j1 rule="hyper" parents="113 561 2291"/>
    </justification>
  </clause>

  <clause id="2458">
    <literal><![CDATA[
      R(x * ((y * (x \ 1)) / y),z,u) = K(y,R(x,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,1534,a(flip),b,2305,a)].">
      <j1 rule="hyper" parents="65 1534 2305"/>
    </justification>
  </clause>

  <clause id="2459">
    <literal><![CDATA[
      (x * ((y * (x \ z)) / y)) / z = K(y,(x / z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,1487,a(flip),b,2305,a)].">
      <j1 rule="hyper" parents="65 1487 2305"/>
    </justification>
  </clause>

  <clause id="2461">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ x)) / z) = x * K(z,y \ 1)
    ]]></literal>
    <justification jstring="[para(2305(a,1),1256(a,2,2))].">
      <j1 rule="para" parents="2305 1256"/>
    </justification>
  </clause>

  <clause id="2462">
    <literal><![CDATA[
      K(x,x * (y \ 1)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(250,a,2272,a,b,2316,a),flip(a)].">
      <j1 rule="hyper" parents="250 2272 2316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2463">
    <literal><![CDATA[
      K(x,y * K(z,z \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(250,a,2272,a,b,2318,a),flip(a)].">
      <j1 rule="hyper" parents="250 2272 2318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2464">
    <literal><![CDATA[
      K(x,K(y \ 1,y) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(1433(a,1),2463(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1433 2463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2465">
    <literal><![CDATA[
      K(x,(y \ 1) * (y * z)) = K(x,L(z,y,y \ 1))
    ]]></literal>
    <justification jstring="[para(343(a,1),2464(a,1,2))].">
      <j1 rule="para" parents="343 2464"/>
    </justification>
  </clause>

  <clause id="2466">
    <literal><![CDATA[
      K(x,(y \ z) / z) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(250,a,2272,a,b,2325,a),flip(a)].">
      <j1 rule="hyper" parents="250 2272 2325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2467">
    <literal><![CDATA[
      K(x,(y \ z) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ 1) = u
    ]]></literal>
    <justification jstring="[para(2325(a,2),2328(a,1))].">
      <j1 rule="para" parents="2325 2328"/>
    </justification>
  </clause>

  <clause id="2468">
    <literal><![CDATA[
      K(x,(y / z) \ 1) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(79(a,1),2466(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 2466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2469">
    <literal><![CDATA[
      K(x,R(y / z,z,u) \ 1) = K(x,(z * u) / (y * u))
    ]]></literal>
    <justification jstring="[para(361(a,1),2466(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="361 2466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2470">
    <literal><![CDATA[
      (K(x,y) * T(x,z)) / T(x,y) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(1767,a,2406,a(flip))].">
      <j1 rule="hyper" parents="1767 2406"/>
    </justification>
  </clause>

  <clause id="2471">
    <literal><![CDATA[
      K(x,y) * T(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * T(x,y) = u
    ]]></literal>
    <justification jstring="[para(2406(a,2),1766(a,1))].">
      <j1 rule="para" parents="2406 1766"/>
    </justification>
  </clause>

  <clause id="2472">
    <literal><![CDATA[
      x / (((y \ (x * z)) * y) / z) = K(y,x / (y / z))
    ]]></literal>
    <justification jstring="[para(910(a,1),2424(a,1,2))].">
      <j1 rule="para" parents="910 2424"/>
    </justification>
  </clause>

  <clause id="2473">
    <literal><![CDATA[
      x / (y * ((z \ (y \ x)) * z)) = K(z,x / (z * y))
    ]]></literal>
    <justification jstring="[para(2195(a,1),2424(a,1,2))].">
      <j1 rule="para" parents="2195 2424"/>
    </justification>
  </clause>

  <clause id="2478">
    <literal><![CDATA[
      K(x,y) * T(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * K(x,z) = u
    ]]></literal>
    <justification jstring="[para(2274(a,2),2405(a,1,2))].">
      <j1 rule="para" parents="2274 2405"/>
    </justification>
  </clause>

  <clause id="2479">
    <literal><![CDATA[
      x * T(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * K(K(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(2274(a,2),2421(a,1,2))].">
      <j1 rule="para" parents="2274 2421"/>
    </justification>
  </clause>

  <clause id="2480">
    <literal><![CDATA[
      T(x \ y,z) * ((y \ x) * K(z,x \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      (x \ y) * (y \ x) = u
    ]]></literal>
    <justification jstring="[para(1284(a,1),2448(a,1,2))].">
      <j1 rule="para" parents="1284 2448"/>
    </justification>
  </clause>

  <clause id="2481">
    <literal><![CDATA[
      T(x,y) \ T(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * K(x,z) = u
    ]]></literal>
    <justification jstring="[para(2274(a,2),2452(a,1,2))].">
      <j1 rule="para" parents="2274 2452"/>
    </justification>
  </clause>

  <clause id="2482">
    <literal><![CDATA[
      K(x,T(y,z) \ 1) = T(K(x,y \ 1),z)
    ]]></literal>
    <justification jstring="[para(2272(a,2),2304(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2272 2304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2484">
    <literal><![CDATA[
      x * K(y,T(z,x) \ 1) = K(y,z \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(116,a,2482,a,b,22,a(flip))].">
      <j1 rule="hyper" parents="116 2482 22"/>
    </justification>
  </clause>

  <clause id="2486">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ 1) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(2419(a,1),2482(a,2,1))].">
      <j1 rule="para" parents="2419 2482"/>
    </justification>
  </clause>

  <clause id="2488">
    <literal><![CDATA[
      R(x,y,z) * K(u,R(x,y,z)) = R(x * K(u,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(250,a,2308,a(flip),b,2354,a)].">
      <j1 rule="hyper" parents="250 2308 2354"/>
    </justification>
  </clause>

  <clause id="2490">
    <literal><![CDATA[
      R(x * K(y,x),z,u) \ R(x,z,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(2354(a,2),2280(a,2,1)),flip(a)].">
      <j1 rule="para" parents="2354 2280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2491">
    <literal><![CDATA[
      a(x,y,z * K(x * y,z)) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(112,a,2362,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="112 2362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2492">
    <literal><![CDATA[
      (x * y) * K(((x * y) \ y) \ 1,z) = T(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(482,a,2384,a),flip(a)].">
      <j1 rule="hyper" parents="482 2384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2493">
    <literal><![CDATA[
      T(K(x / y,z),x) = K((x \ y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(200,a,2291,a,b,2384,a(flip))].">
      <j1 rule="hyper" parents="200 2291 2384"/>
    </justification>
  </clause>

  <clause id="2494">
    <literal><![CDATA[
      x * (y * K((y \ (x \ 1)) \ 1,z)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,2384,a(flip),b,568,a(flip))].">
      <j1 rule="hyper" parents="116 2384 568"/>
    </justification>
  </clause>

  <clause id="2497">
    <literal><![CDATA[
      T(K(x / y,z),x) \ 1 = K(z,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(2493(a,2),2366(a,1,1))].">
      <j1 rule="para" parents="2493 2366"/>
    </justification>
  </clause>

  <clause id="2498">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) = T(K(x \ 1,z),y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2279,a(flip),b,2389,a)].">
      <j1 rule="hyper" parents="65 2279 2389"/>
    </justification>
  </clause>

  <clause id="2499">
    <literal><![CDATA[
      K(T(x \ 1,y) \ 1,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[para(1747(a,1),2498(a,2,1))].">
      <j1 rule="para" parents="1747 2498"/>
    </justification>
  </clause>

  <clause id="2500">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ 1) = T(K(y,x),z) \ 1
    ]]></literal>
    <justification jstring="[para(2499(a,1),2366(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2499 2366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2505">
    <literal><![CDATA[
      K(x,(y / z) \ 1) * z = z * K(x,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(106(a,1),2484(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="106 2484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2506">
    <literal><![CDATA[
      R(x \ R(x,y,z),u,w) = a(x,y,z * K(x * y,z))
    ]]></literal>
    <justification jstring="[para(2491(a,1),523(a,1,1))].">
      <j1 rule="para" parents="2491 523"/>
    </justification>
  </clause>

  <clause id="2507">
    <literal><![CDATA[
      a(x,y,T(z * K(x * y,z),u)) = T(x \ R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(2491(a,1),2106(a,2,1))].">
      <j1 rule="para" parents="2491 2106"/>
    </justification>
  </clause>

  <clause id="2508">
    <literal><![CDATA[
      T(K(x,y),z) \ 1 = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(65,a,2486,a(flip),b,2500,a),flip(a)].">
      <j1 rule="hyper" parents="65 2486 2500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2509">
    <literal><![CDATA[
      1 / T(K(x,y),z) = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(170,a,2486,a(flip),b,2500,a(flip))].">
      <j1 rule="hyper" parents="170 2486 2500"/>
    </justification>
  </clause>

  <clause id="2510">
    <literal><![CDATA[
      K(x,y) * T(K(y,x),z) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(116,a,2508,a(flip),b,2285,a(flip))].">
      <j1 rule="hyper" parents="116 2508 2285"/>
    </justification>
  </clause>

  <clause id="2512">
    <literal><![CDATA[
      T(K(x,y),z) \ 1 != u
    ]]></literal>
    <literal><![CDATA[
      T(K(y,x),z) = u
    ]]></literal>
    <justification jstring="[para(2509(a,1),223(a,1,1))].">
      <j1 rule="para" parents="2509 223"/>
    </justification>
  </clause>

  <clause id="2513">
    <literal><![CDATA[
      K(K(x,y),z) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,2373,a(flip),b,2510,a)].">
      <j1 rule="hyper" parents="65 2373 2510"/>
    </justification>
  </clause>

  <clause id="2514">
    <literal><![CDATA[
      x * K(K(y,z),x) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(116,a,2513,a,b,2272,a(flip))].">
      <j1 rule="hyper" parents="116 2513 2272"/>
    </justification>
  </clause>

  <clause id="2515">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z,y) = T(K(z,y),x)
    ]]></literal>
    <justification jstring="[hyper(115,a,2513,a(flip),b,2265,a(flip))].">
      <j1 rule="hyper" parents="115 2513 2265"/>
    </justification>
  </clause>

  <clause id="2516">
    <literal><![CDATA[
      K(x,K(y,z)) \ 1 != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(2513(a,1),2375(a,1,1))].">
      <j1 rule="para" parents="2513 2375"/>
    </justification>
  </clause>

  <clause id="2517">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(2348,a,2514,a)].">
      <j1 rule="hyper" parents="2348 2514"/>
    </justification>
  </clause>

  <clause id="2518">
    <literal><![CDATA[
      T(K(x,y) \ z,K(y,x)) = z / K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2320,a(flip),b,2514,a),flip(a)].">
      <j1 rule="hyper" parents="65 2320 2514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2519">
    <literal><![CDATA[
      T(x,K(y,z)) * K(z,y) = K(z,y) * x
    ]]></literal>
    <justification jstring="[hyper(115,a,2514,a(flip),b,2308,a)].">
      <j1 rule="hyper" parents="115 2514 2308"/>
    </justification>
  </clause>

  <clause id="2521">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(2514(a,1),2348(a,1))].">
      <j1 rule="para" parents="2514 2348"/>
    </justification>
  </clause>

  <clause id="2522">
    <literal><![CDATA[
      T(K(x,y),K(x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(42,a,1060,a,b,2517,a),flip(a)].">
      <j1 rule="hyper" parents="42 1060 2517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2526">
    <literal><![CDATA[
      T(K(x,y) * z,K(x,y)) = z / K(y,x)
    ]]></literal>
    <justification jstring="[para(2422(a,1),2518(a,1,1))].">
      <j1 rule="para" parents="2422 2518"/>
    </justification>
  </clause>

  <clause id="2527">
    <literal><![CDATA[
      K(x,(y \ z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y / z),y) = u
    ]]></literal>
    <justification jstring="[para(2497(a,1),2512(a,1))].">
      <j1 rule="para" parents="2497 2512"/>
    </justification>
  </clause>

  <clause id="2528">
    <literal><![CDATA[
      K(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(y,x)) = u
    ]]></literal>
    <justification jstring="[para(2366(a,1),2516(a,1))].">
      <j1 rule="para" parents="2366 2516"/>
    </justification>
  </clause>

  <clause id="2529">
    <literal><![CDATA[
      K(x,y) * T(K(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(2373(a,2),2528(a,1))].">
      <j1 rule="para" parents="2373 2528"/>
    </justification>
  </clause>

  <clause id="2530">
    <literal><![CDATA[
      K(R(x,y,z),x \ R(x,u,w)) = R(x,y,z) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(1403(a,1),2313(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1403 2313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2532">
    <literal><![CDATA[
      T(T(x * K(x * y,x),z),y) = R(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(250,a,27,a,b,2455,a),flip(a)].">
      <j1 rule="hyper" parents="250 27 2455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2533">
    <literal><![CDATA[
      L(K(x,y \ 1),z,u) = K(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(2272(a,2),2303(a,1,1))].">
      <j1 rule="para" parents="2272 2303"/>
    </justification>
  </clause>

  <clause id="2534">
    <literal><![CDATA[
      K(x,L(y \ 1,z,u) \ 1) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2419(a,1),2533(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2419 2533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2535">
    <literal><![CDATA[
      K(L(x \ 1,y,z) \ 1,u) = 1 / L(K(u,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(170,a,2534,a(flip),b,2366,a),flip(a)].">
      <j1 rule="hyper" parents="170 2534 2366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2536">
    <literal><![CDATA[
      L(K(x,y \ z),y \ z,y) = K(x,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(275(a,1),2534(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="275 2534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2537">
    <literal><![CDATA[
      L(T(K(x,y \ z),u),y \ z,y) = T(K(x,(z \ y) \ 1),u)
    ]]></literal>
    <justification jstring="[para(2536(a,1),25(a,2,1))].">
      <j1 rule="para" parents="2536 25"/>
    </justification>
  </clause>

  <clause id="2538">
    <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(2356(a,1),293(a,1,1))].">
      <j1 rule="para" parents="2356 293"/>
    </justification>
  </clause>

  <clause id="2539">
    <literal><![CDATA[
      (x * T(x \ y,z)) * (y \ 1) = K((x * (y \ 1)) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,925,a(flip),b,2381,a)].">
      <j1 rule="hyper" parents="65 925 2381"/>
    </justification>
  </clause>

  <clause id="2540">
    <literal><![CDATA[
      x * (y \ T(y * (x \ 1),z)) = K((x * (y \ 1)) \ 1,z)
    ]]></literal>
    <justification jstring="[para(568(a,1),2381(a,1,2))].">
      <j1 rule="para" parents="568 2381"/>
    </justification>
  </clause>

  <clause id="2541">
    <literal><![CDATA[
      R(K(x \ 1,y),z,u) = K(R(x,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[para(2277(a,1),2382(a,1,1))].">
      <j1 rule="para" parents="2277 2382"/>
    </justification>
  </clause>

  <clause id="2542">
    <literal><![CDATA[
      K(R(1 / x,y,z) \ 1,u) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(2271(a,2),2382(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2271 2382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2543">
    <literal><![CDATA[
      K(R(x \ 1,y,z) \ 1,u) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(1747(a,1),2541(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1747 2541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2544">
    <literal><![CDATA[
      K(x,R(1 / y,z,u) \ 1) = R(K(y,x),z,u) \ 1
    ]]></literal>
    <justification jstring="[para(2542(a,1),2366(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2542 2366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2545">
    <literal><![CDATA[
      (x * y) * (z * T(z \ L(y \ z,y,x),u)) = (x * K(y \ 1,u)) * z
    ]]></literal>
    <justification jstring="[para(2386(a,1),931(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2386 931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2546">
    <literal><![CDATA[
      x * (y \ T(y * (x \ (y \ 1)),z)) = K(x \ 1,z) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(568(a,1),2388(a,1,2))].">
      <j1 rule="para" parents="568 2388"/>
    </justification>
  </clause>

  <clause id="2547">
    <literal><![CDATA[
      L(K(x \ 1,y),z,u) = K(L(x,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2279,a(flip),b,2391,a),flip(a)].">
      <j1 rule="hyper" parents="65 2279 2391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2548">
    <literal><![CDATA[
      K(L(x \ 1,y,z) \ 1,u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(1747(a,1),2547(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1747 2547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2549">
    <literal><![CDATA[
      K(x,L(y \ 1,z,u) \ 1) * w = L(K(y,x),z,u) \ w
    ]]></literal>
    <justification jstring="[para(2548(a,1),2422(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2548 2422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2550">
    <literal><![CDATA[
      T(x * ((y * (x \ z)) / y),z) / z = K(y,(T(x,z) / z) \ 1)
    ]]></literal>
    <justification jstring="[para(1246(a,1),2459(a,1,1))].">
      <j1 rule="para" parents="1246 2459"/>
    </justification>
  </clause>

  <clause id="2551">
    <literal><![CDATA[
      (x * (y * ((z * (y \ (x \ u))) / z))) / u = K(z,((x * y) / u) \ 1)
    ]]></literal>
    <justification jstring="[para(1470(a,1),2459(a,1,1))].">
      <j1 rule="para" parents="1470 2459"/>
    </justification>
  </clause>

  <clause id="2552">
    <literal><![CDATA[
      x / (y * ((z \ (y \ x)) * z)) = K(z,x / (z / (y \ 1)))
    ]]></literal>
    <justification jstring="[para(2196(a,1),2472(a,1,2))].">
      <j1 rule="para" parents="2196 2472"/>
    </justification>
  </clause>

  <clause id="2553">
    <literal><![CDATA[
      K(x,y) * (z * K((z \ K(y,x)) \ 1,u)) = T(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(2366(a,1),2494(a,1,2,2,1,1,2))].">
      <j1 rule="para" parents="2366 2494"/>
    </justification>
  </clause>

  <clause id="2554">
    <literal><![CDATA[
      1 / L(K(x,y),z,u) = L(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,2548,a(flip),b,2535,a),flip(a)].">
      <j1 rule="hyper" parents="65 2548 2535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2555">
    <literal><![CDATA[
      L(K(x,y),z,u) \ 1 = L(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(163,a,2554,a)].">
      <j1 rule="hyper" parents="163 2554"/>
    </justification>
  </clause>

  <clause id="2556">
    <literal><![CDATA[
      K(x,y) * L(K(y,x),z,u) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(116,a,2555,a(flip),b,1685,a(flip))].">
      <j1 rule="hyper" parents="116 2555 1685"/>
    </justification>
  </clause>

  <clause id="2557">
    <literal><![CDATA[
      K(x,y) * a(z,u,K(y,x)) = L(K(x,y),u,z)
    ]]></literal>
    <justification jstring="[hyper(2430,a,2556,a)].">
      <j1 rule="hyper" parents="2430 2556"/>
    </justification>
  </clause>

  <clause id="2559">
    <literal><![CDATA[
      (L(x,y,z) * K(x,u)) \ w = K(u,x) * (L(x,y,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,2116,a(flip),b,2434,a),flip(a)].">
      <j1 rule="hyper" parents="65 2116 2434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2560">
    <literal><![CDATA[
      R(x \ R(x,y,z),u,w) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(250,a,2491,a(flip),b,2506,a),flip(a)].">
      <j1 rule="hyper" parents="250 2491 2506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2561">
    <literal><![CDATA[
      ((R(x,y,z) * u) * w) / ((x * u) * w) = R(x,u,w) \ R(R(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,1525,a(flip),b,2560,a)].">
      <j1 rule="hyper" parents="65 1525 2560"/>
    </justification>
  </clause>

  <clause id="2562">
    <literal><![CDATA[
      (x \ (y * K(x,z))) * x = ((x \ y) * x) * K(x,z)
    ]]></literal>
    <justification jstring="[para(2266(a,2),2294(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2266 2294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2565">
    <literal><![CDATA[
      K(x,x * y) * (R(y,z,u) * x) = R(y,z,u) * T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(2070,a,2416,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="2070 2416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2566">
    <literal><![CDATA[
      R(K(x,y \ 1),z,u) = K(x,R(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(2305(a,1),2458(a,1,1))].">
      <j1 rule="para" parents="2305 2458"/>
    </justification>
  </clause>

  <clause id="2567">
    <literal><![CDATA[
      K(x,R(y,x,z) \ 1) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(1947,a,2566,a),flip(a)].">
      <j1 rule="hyper" parents="1947 2566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2568">
    <literal><![CDATA[
      K(x,R(1 / y,z,u) \ 1) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(79(a,1),2566(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="79 2566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2569">
    <literal><![CDATA[
      K(x,R(y / z,u,w) \ 1) = R(K(x,z / y),u,w)
    ]]></literal>
    <justification jstring="[para(2468(a,1),2566(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2468 2566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2570">
    <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),2567(a,1,2,1))].">
      <j1 rule="para" parents="31 2567"/>
    </justification>
  </clause>

  <clause id="2571">
    <literal><![CDATA[
      R(K(x,y),z,u) \ 1 = R(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,2544,a(flip),b,2568,a)].">
      <j1 rule="hyper" parents="65 2544 2568"/>
    </justification>
  </clause>

  <clause id="2572">
    <literal><![CDATA[
      R(K(x,y / z),y,u) = K(x,(y * u) / (z * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,2469,a(flip),b,2569,a),flip(a)].">
      <j1 rule="hyper" parents="65 2469 2569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2573">
    <literal><![CDATA[
      R(K(x,y / z),y,z \ 1) = K(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[para(382(a,1),2569(a,1,2)),flip(a)].">
      <j1 rule="para" parents="382 2569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2574">
    <literal><![CDATA[
      R(K(x,(y / z) / u),y / z,z) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[para(12(a,1),2572(a,2,2,1))].">
      <j1 rule="para" parents="12 2572"/>
    </justification>
  </clause>

  <clause id="2575">
    <literal><![CDATA[
      R(K(x,y / (z / u)),y,u) = K(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[para(12(a,1),2572(a,2,2,2))].">
      <j1 rule="para" parents="12 2572"/>
    </justification>
  </clause>

  <clause id="2576">
    <literal><![CDATA[
      K(x,(y * z) / ((u \ y) * z)) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(76(a,1),2572(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="76 2572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2577">
    <literal><![CDATA[
      K(x,R(y,y \ z,u)) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(98(a,2),2576(a,1,2))].">
      <j1 rule="para" parents="98 2576"/>
    </justification>
  </clause>

  <clause id="2578">
    <literal><![CDATA[
      R(K(x,y),y * z,u) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),2577(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 2577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2579">
    <literal><![CDATA[
      R(K(x,y),z * y,u) = K(x,R(y,T(z,y),u))
    ]]></literal>
    <justification jstring="[para(22(a,2),2577(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="22 2577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2580">
    <literal><![CDATA[
      R(K(x,y),T(y,z),u) = K(x,y)
    ]]></literal>
    <justification jstring="[para(1924(a,1),2577(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1924 2577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2581">
    <literal><![CDATA[
      R(K(x,y),y,z) = K(x,y)
    ]]></literal>
    <justification jstring="[para(103(a,1),2580(a,1,2))].">
      <j1 rule="para" parents="103 2580"/>
    </justification>
  </clause>

  <clause id="2582">
    <literal><![CDATA[
      (K(x,y) * y) * z = K(x,y) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(115,a,2581,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="115 2581 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2583">
    <literal><![CDATA[
      R(T(K(x,y),z),y * u,w) = T(K(x,R(y,u,w)),z)
    ]]></literal>
    <justification jstring="[para(2578(a,1),27(a,2,1))].">
      <j1 rule="para" parents="2578 27"/>
    </justification>
  </clause>

  <clause id="2584">
    <literal><![CDATA[
      (x * K(y,x)) * z = K(y,x) * (x * z)
    ]]></literal>
    <justification jstring="[para(1986(a,1),2582(a,1,1))].">
      <j1 rule="para" parents="1986 2582"/>
    </justification>
  </clause>

  <clause id="2585">
    <literal><![CDATA[
      K(x,y) * (y * z) = ((x * y) / x) * z
    ]]></literal>
    <justification jstring="[para(2310(a,2),2582(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2310 2582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2586">
    <literal><![CDATA[
      (x * K(y,x)) * z = x * (K(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(250,a,2450,a(flip),b,2584,a),flip(a)].">
      <j1 rule="hyper" parents="250 2450 2584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2589">
    <literal><![CDATA[
      ((x * y) / x) * (y \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(259,a,2585,a),flip(a)].">
      <j1 rule="hyper" parents="259 2585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2590">
    <literal><![CDATA[
      ((x * y) / x) * z = y * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,2450,a(flip),b,2585,a),flip(a)].">
      <j1 rule="hyper" parents="65 2450 2585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2591">
    <literal><![CDATA[
      L(x,K(y,z),z) = x
    ]]></literal>
    <justification jstring="[hyper(341,a,2586,a)].">
      <j1 rule="hyper" parents="341 2586"/>
    </justification>
  </clause>

  <clause id="2592">
    <literal><![CDATA[
      (x * K(y,x)) \ (T(x,z) * K(y,x)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(112,a,2399,a(flip),b,2586,a)].">
      <j1 rule="hyper" parents="112 2399 2586"/>
    </justification>
  </clause>

  <clause id="2595">
    <literal><![CDATA[
      L(x,K(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(2591(a,1),52(a,1)),flip(a)].">
      <j1 rule="para" parents="2591 52"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2596">
    <literal><![CDATA[
      (x * K(y,x)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (x \ z) = u
    ]]></literal>
    <justification jstring="[para(2434(a,1),2595(a,1)),flip(b)].">
      <j1 rule="para" parents="2434 2595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2598">
    <literal><![CDATA[
      (x * (K(y * z,x) * y)) * z = (y * z) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(2590(a,1),536(a,1,1))].">
      <j1 rule="para" parents="2590 536"/>
    </justification>
  </clause>

  <clause id="2599">
    <literal><![CDATA[
      K(x,R(y / x,x * z,u) \ 1) = K(x,(((y * z) * u) / ((x * z) * u)) \ 1)
    ]]></literal>
    <justification jstring="[para(385(a,1),2570(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="385 2570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2600">
    <literal><![CDATA[
      ((x * y) * ((z * ((x * y) \ x)) / z)) * y = (x * y) * K(z,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,1130,a(flip),b,2461,a)].">
      <j1 rule="hyper" parents="65 1130 2461"/>
    </justification>
  </clause>

  <clause id="2601">
    <literal><![CDATA[
      (x * y) * (z * (L(y \ z,y,x) / z)) = (x * K(z,y \ 1)) * z
    ]]></literal>
    <justification jstring="[para(2461(a,1),1474(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2461 1474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2602">
    <literal><![CDATA[
      a(x,y,z) = T(x \ R(x,y,z),x * y)
    ]]></literal>
    <justification jstring="[para(2347(a,1),2507(a,1,3))].">
      <j1 rule="para" parents="2347 2507"/>
    </justification>
  </clause>

  <clause id="2603">
    <literal><![CDATA[
      K(R(x,y,z),x \ R(x,u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(250,a,68,a(flip),b,2530,a),flip(a)].">
      <j1 rule="hyper" parents="250 68 2530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2605">
    <literal><![CDATA[
      K(x \ R(x,y,z),R(x,u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(111,a,2603,a,b,2368,a),flip(a)].">
      <j1 rule="hyper" parents="111 2603 2368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2606">
    <literal><![CDATA[
      K(x \ R(x,y,z),R(x,u,w)) = v5 \ v5
    ]]></literal>
    <justification jstring="[hyper(250,a,68,a,b,2605,a),flip(a)].">
      <j1 rule="hyper" parents="250 68 2605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2607">
    <literal><![CDATA[
      K(x \ R(x,y,z),R(x,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      1 = v5
    ]]></literal>
    <justification jstring="[para(2606(a,2),146(a,1)),flip(b)].">
      <j1 rule="para" parents="2606 146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2608">
    <literal><![CDATA[
      K(((1 / x) * (y \ 1)) \ 1,z) = (1 / x) * (y \ T(y * x,z))
    ]]></literal>
    <justification jstring="[para(79(a,1),2540(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="79 2540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2609">
    <literal><![CDATA[
      L(K(x,y),z,u) \ w = L(K(y,x),z,u) * w
    ]]></literal>
    <justification jstring="[para(2534(a,1),2549(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2534 2549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2610">
    <literal><![CDATA[
      K(x,y / (x / (z \ 1))) = K(x,y / (x * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,2473,a(flip),b,2552,a),flip(a)].">
      <j1 rule="hyper" parents="65 2473 2552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2611">
    <literal><![CDATA[
      (K(x,y) / R(x,z,u)) * x = R(x,z,u) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(2301,a,2183,a)].">
      <j1 rule="hyper" parents="2301 2183"/>
    </justification>
  </clause>

  <clause id="2612">
    <literal><![CDATA[
      T(x \ y,z) \ T((x \ y) * (y \ x),z) = y \ (x * K(z,x \ y))
    ]]></literal>
    <justification jstring="[hyper(65,a,1209,a,b,2341,a)].">
      <j1 rule="hyper" parents="65 1209 2341"/>
    </justification>
  </clause>

  <clause id="2613">
    <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(2413(a,1),2431(a,1,2))].">
      <j1 rule="para" parents="2413 2431"/>
    </justification>
  </clause>

  <clause id="2614">
    <literal><![CDATA[
      L(T(K(x,y \ z),u),y \ z,y) = K(x,T(z \ y,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(250,a,2482,a,b,2537,a),flip(a)].">
      <j1 rule="hyper" parents="250 2482 2537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2615">
    <literal><![CDATA[
      K((x * y) / (x * (z \ y)),u) = (x * (K(z,u) * y)) / (x * y)
    ]]></literal>
    <justification jstring="[para(2402(a,1),2457(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2402 2457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2616">
    <literal><![CDATA[
      T(((x * y) / x) * (y \ z),z) / z = K(x,(T(y \ z,z) / z) \ 1)
    ]]></literal>
    <justification jstring="[para(542(a,1),2550(a,1,1,1))].">
      <j1 rule="para" parents="542 2550"/>
    </justification>
  </clause>

  <clause id="2617">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * T(K(y,x) \ z,u)) = T(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(2384(a,2),2553(a,1,2))].">
      <j1 rule="para" parents="2384 2553"/>
    </justification>
  </clause>

  <clause id="2618">
    <literal><![CDATA[
      T(K(x,y) * (z * K(y,x)),u) = K(x,y) * (T(z,u) * K(y,x))
    ]]></literal>
    <justification jstring="[para(2492(a,1),2553(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2492 2553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2620">
    <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(2071(a,1),2565(a,1,2))].">
      <j1 rule="para" parents="2071 2565"/>
    </justification>
  </clause>

  <clause id="2621">
    <literal><![CDATA[
      ((1 / x) * T((1 / x) \ y,z)) * (y \ 1) = (1 / x) * (y \ T(y * x,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,2539,a,b,2608,a)].">
      <j1 rule="hyper" parents="65 2539 2608"/>
    </justification>
  </clause>

  <clause id="2622">
    <literal><![CDATA[
      K(x,(y * z) / (y * (u \ z))) * (y * (K(u,x) * z)) = y * z
    ]]></literal>
    <justification jstring="[hyper(38,a,2425,a,b,2615,a(flip))].">
      <j1 rule="hyper" parents="38 2425 2615"/>
    </justification>
  </clause>

  <clause id="2623">
    <literal><![CDATA[
      K(x,y) \ T(K(x,y) * z,u) = K(y,x) * T(K(y,x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(118,a,2617,a)].">
      <j1 rule="hyper" parents="118 2617"/>
    </justification>
  </clause>

  <clause id="2624">
    <literal><![CDATA[
      K(x,y) * (R(y,z,u) * (K(y,x) * w)) = R(y,z,u) * w
    ]]></literal>
    <justification jstring="[para(734(a,1),2622(a,1,1,2))].">
      <j1 rule="para" parents="734 2622"/>
    </justification>
  </clause>

  <clause id="2625">
    <literal><![CDATA[
      (K(x,y) * T(K(x,y) \ z,u)) * K(y,x) = T(z * K(y,x),u)
    ]]></literal>
    <justification jstring="[hyper(115,a,2623,a(flip),b,2168,a)].">
      <j1 rule="hyper" parents="115 2623 2168"/>
    </justification>
  </clause>

  <clause id="2626">
    <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),2625(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 2625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2627">
    <literal><![CDATA[
      L(K(x \ y,x) * z,K(x,x \ y),y) = (x * (y / x)) \ (y * z)
    ]]></literal>
    <justification jstring="[para(2426(a,1),2444(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2426 2444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2628">
    <literal><![CDATA[
      (x * y) * L(z * ((y \ z) / z),y,x) = (x * K(z,y \ 1)) * z
    ]]></literal>
    <justification jstring="[para(1787(a,2),2601(a,1,2))].">
      <j1 rule="para" parents="1787 2601"/>
    </justification>
  </clause>

  <clause id="2629">
    <literal><![CDATA[
      x * (y * (z * ((y \ z) / z))) = (x * K(z,y \ 1)) * z
    ]]></literal>
    <justification jstring="[hyper(234,a,2628,a)].">
      <j1 rule="hyper" parents="234 2628"/>
    </justification>
  </clause>

  <clause id="2630">
    <literal><![CDATA[
      (x * K(y,z \ 1)) * y = x * T(y,z \ 1)
    ]]></literal>
    <justification jstring="[para(1888(a,1),2629(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1888 2629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2632">
    <literal><![CDATA[
      (x * K(y,z)) * y = x * T(y,(z \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2419(a,1),2630(a,1,1,2))].">
      <j1 rule="para" parents="2419 2630"/>
    </justification>
  </clause>

  <clause id="2633">
    <literal><![CDATA[
      (x * K(y,z)) * y = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(1626(a,1),2632(a,2,2))].">
      <j1 rule="para" parents="1626 2632"/>
    </justification>
  </clause>

  <clause id="2635">
    <literal><![CDATA[
      (x * K(T(y,x),z)) \ (T(y,z) * x) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(112,a,197,a(flip),b,2633,a)].">
      <j1 rule="hyper" parents="112 197 2633"/>
    </justification>
  </clause>

  <clause id="2636">
    <literal><![CDATA[
      (x / y) * T(y,z) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(37,a,767,a,b,2633,a)].">
      <j1 rule="hyper" parents="37 767 2633"/>
    </justification>
  </clause>

  <clause id="2637">
    <literal><![CDATA[
      (x * y) * K(y,z) = x * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(37,a,763,a,b,2633,a),flip(a)].">
      <j1 rule="hyper" parents="37 763 2633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2640">
    <literal><![CDATA[
      x * T(x \ y,z) = y * K(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(260,a,2636,a)].">
      <j1 rule="hyper" parents="260 2636"/>
    </justification>
  </clause>

  <clause id="2641">
    <literal><![CDATA[
      x \ (y * T(y \ x,z)) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(112,a,158,a(flip),b,2636,a(flip))].">
      <j1 rule="hyper" parents="112 158 2636"/>
    </justification>
  </clause>

  <clause id="2642">
    <literal><![CDATA[
      ((x / y) * K(y,z)) \ (x * K(y,z)) = y
    ]]></literal>
    <justification jstring="[hyper(112,a,2636,a(flip),b,2633,a)].">
      <j1 rule="hyper" parents="112 2636 2633"/>
    </justification>
  </clause>

  <clause id="2645">
    <literal><![CDATA[
      (x * y) \ (x * T(y,z)) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(118,a,2637,a)].">
      <j1 rule="hyper" parents="118 2637"/>
    </justification>
  </clause>

  <clause id="2646">
    <literal><![CDATA[
      ((x / T(y,z)) * y) \ x = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(112,a,12,a(flip),b,2637,a)].">
      <j1 rule="hyper" parents="112 12 2637"/>
    </justification>
  </clause>

  <clause id="2647">
    <literal><![CDATA[
      (x \ (y * K(x,z))) * x = (x \ y) * T(x,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,2562,a,b,2637,a)].">
      <j1 rule="hyper" parents="65 2562 2637"/>
    </justification>
  </clause>

  <clause id="2648">
    <literal><![CDATA[
      L(K(x,y),x,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,2326,a,b,2637,a)].">
      <j1 rule="hyper" parents="36 2326 2637"/>
    </justification>
  </clause>

  <clause id="2649">
    <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(2637(a,1),387(a,1,2))].">
      <j1 rule="para" parents="2637 387"/>
    </justification>
  </clause>

  <clause id="2650">
    <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(2637(a,1),368(a,1,1))].">
      <j1 rule="para" parents="2637 368"/>
    </justification>
  </clause>

  <clause id="2652">
    <literal><![CDATA[
      L(K(x,y),x,z) = K(y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(250,a,2366,a,b,2648,a),flip(a)].">
      <j1 rule="hyper" parents="250 2366 2648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2653">
    <literal><![CDATA[
      a(x,y,K(z,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(111,a,2648,a(flip),b,2557,a),flip(a)].">
      <j1 rule="hyper" parents="111 2648 2557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2655">
    <literal><![CDATA[
      L(K(x,y),y,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(54,a,2653,a)].">
      <j1 rule="hyper" parents="54 2653"/>
    </justification>
  </clause>

  <clause id="2658">
    <literal><![CDATA[
      K(x,(y \ z) \ 1) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2536,a(flip),b,2655,a)].">
      <j1 rule="hyper" parents="65 2536 2655"/>
    </justification>
  </clause>

  <clause id="2659">
    <literal><![CDATA[
      (x * y) * K(z,y) = x * (y * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(116,a,2655,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="116 2655 18"/>
    </justification>
  </clause>

  <clause id="2660">
    <literal><![CDATA[
      L(K(x,y),x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(2652(a,2),2375(a,1))].">
      <j1 rule="para" parents="2652 2375"/>
    </justification>
  </clause>

  <clause id="2661">
    <literal><![CDATA[
      (x * y) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * T(y,z) = u
    ]]></literal>
    <justification jstring="[para(2645(a,1),214(a,1,2))].">
      <j1 rule="para" parents="2645 214"/>
    </justification>
  </clause>

  <clause id="2662">
    <literal><![CDATA[
      T(K(x,y / z),y) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(2527,a,2658,a)].">
      <j1 rule="hyper" parents="2527 2658"/>
    </justification>
  </clause>

  <clause id="2664">
    <literal><![CDATA[
      K(x,(y \ z) \ 1) = K(z \ y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(250,a,2366,a,b,2658,a),flip(a)].">
      <j1 rule="hyper" parents="250 2366 2658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2665">
    <literal><![CDATA[
      T(x,(y \ z) \ 1) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(114,a,2658,a,b,2470,a),flip(a)].">
      <j1 rule="hyper" parents="114 2658 2470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2668">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1) \ y) = K(x,a(y,z,z \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(475(a,1),2658(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="475 2658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2669">
    <literal><![CDATA[
      K(x,L(y \ z,u,w) \ 1) = L(K(x,z \ y),u,w)
    ]]></literal>
    <justification jstring="[para(2658(a,1),2533(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2658 2533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2670">
    <literal><![CDATA[
      K(x,x / y) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(1763,a,2662,a)].">
      <j1 rule="hyper" parents="1763 2662"/>
    </justification>
  </clause>

  <clause id="2671">
    <literal><![CDATA[
      T(x,y) != K(z,u \ y)
    ]]></literal>
    <literal><![CDATA[
      K(z,y / u) = x
    ]]></literal>
    <justification jstring="[para(2662(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="2662 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2672">
    <literal><![CDATA[
      K(x,(y \ z) \ z) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(76(a,1),2662(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="76 2662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2673">
    <literal><![CDATA[
      K(x,(y \ x) \ x) = K(x,y)
    ]]></literal>
    <justification jstring="[para(76(a,1),2670(a,1,2)),flip(a)].">
      <j1 rule="para" parents="76 2670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2674">
    <literal><![CDATA[
      R(K(x,(y / z) \ x),x,z) = K(x,(x * z) / y)
    ]]></literal>
    <justification jstring="[para(2670(a,1),2575(a,1,1))].">
      <j1 rule="para" parents="2670 2575"/>
    </justification>
  </clause>

  <clause id="2679">
    <literal><![CDATA[
      K(x,T(y,y \ z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(105(a,2),2672(a,1,2))].">
      <j1 rule="para" parents="105 2672"/>
    </justification>
  </clause>

  <clause id="2680">
    <literal><![CDATA[
      T(K(x,y),y * z) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),2679(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 2679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2681">
    <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(2680(a,1),2529(a,1,2))].">
      <j1 rule="para" parents="2680 2529"/>
    </justification>
  </clause>

  <clause id="2682">
    <literal><![CDATA[
      x \ T(x * y,z) = y * K((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(614,a,2640,a)].">
      <j1 rule="hyper" parents="614 2640"/>
    </justification>
  </clause>

  <clause id="2683">
    <literal><![CDATA[
      T(K(x / y,z),x) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(200,a,2291,a,b,2640,a(flip))].">
      <j1 rule="hyper" parents="200 2291 2640"/>
    </justification>
  </clause>

  <clause id="2684">
    <literal><![CDATA[
      K((x \ y) \ y,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(200,a,2402,a(flip),b,2640,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="200 2402 2640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2685">
    <literal><![CDATA[
      x \ (((y \ (x * z)) * y) / z) = K((y / z) \ x,y)
    ]]></literal>
    <justification jstring="[hyper(112,a,910,a(flip),b,2640,a(flip))].">
      <j1 rule="hyper" parents="112 910 2640"/>
    </justification>
  </clause>

  <clause id="2687">
    <literal><![CDATA[
      K((x * y) \ x,z) = K(y \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,2386,a(flip),b,2640,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="36 2386 2640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2689">
    <literal><![CDATA[
      x \ (y * T(y \ x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(2640(a,2),235(a,1,2))].">
      <j1 rule="para" parents="2640 235"/>
    </justification>
  </clause>

  <clause id="2690">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ y,z) = T(y * K(x \ y,z),y)
    ]]></literal>
    <justification jstring="[para(2640(a,1),1239(a,2,1))].">
      <j1 rule="para" parents="2640 1239"/>
    </justification>
  </clause>

  <clause id="2691">
    <literal><![CDATA[
      K(x / y,x) = K(y \ x,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,1984,a(flip),b,2683,a)].">
      <j1 rule="hyper" parents="65 1984 2683"/>
    </justification>
  </clause>

  <clause id="2693">
    <literal><![CDATA[
      K((x \ y) \ y,y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(76(a,1),2691(a,1,1)),flip(a)].">
      <j1 rule="para" parents="76 2691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2694">
    <literal><![CDATA[
      K(T(x,x \ y),y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(105(a,2),2693(a,1,1))].">
      <j1 rule="para" parents="105 2693"/>
    </justification>
  </clause>

  <clause id="2696">
    <literal><![CDATA[
      K(T(x,x \ y),z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[para(105(a,2),2684(a,1,1))].">
      <j1 rule="para" parents="105 2684"/>
    </justification>
  </clause>

  <clause id="2697">
    <literal><![CDATA[
      K((x * (y \ 1)) \ x,z) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(250,a,1747,a(flip),b,2687,a),flip(a)].">
      <j1 rule="hyper" parents="250 1747 2687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2701">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) = K((x * y) \ y,z)
    ]]></literal>
    <justification jstring="[para(104(a,1),2687(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="104 2687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2702">
    <literal><![CDATA[
      T(K(x,y),x * z) = K(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(9(a,1),2696(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 2696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2703">
    <literal><![CDATA[
      K(L(x,x \ 1,y),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,1754,a,b,2697,a)].">
      <j1 rule="hyper" parents="65 1754 2697"/>
    </justification>
  </clause>

  <clause id="2705">
    <literal><![CDATA[
      (x * (y * K(z,y))) * z = (x * y) * T(z,y)
    ]]></literal>
    <justification jstring="[para(2659(a,1),2633(a,1,1))].">
      <j1 rule="para" parents="2659 2633"/>
    </justification>
  </clause>

  <clause id="2706">
    <literal><![CDATA[
      K(x,(y \ z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(2664(a,2),2375(a,1))].">
      <j1 rule="para" parents="2664 2375"/>
    </justification>
  </clause>

  <clause id="2707">
    <literal><![CDATA[
      K(((x \ 1) * y) \ y,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2499,a(flip),b,2701,a),flip(a)].">
      <j1 rule="hyper" parents="65 2499 2701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2708">
    <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(95(a,2),2706(a,1,2,1))].">
      <j1 rule="para" parents="95 2706"/>
    </justification>
  </clause>

  <clause id="2709">
    <literal><![CDATA[
      x \ (y * K(x,z)) = (x \ y) * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(37,a,2633,a,b,2647,a),flip(a)].">
      <j1 rule="hyper" parents="37 2633 2647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2710">
    <literal><![CDATA[
      x * ((x \ y) * K(x,z)) = y * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,2709,a)].">
      <j1 rule="hyper" parents="125 2709"/>
    </justification>
  </clause>

  <clause id="2711">
    <literal><![CDATA[
      (x * y) * K(x,z) = x * (y * K(x,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),2710(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 2710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2712">
    <literal><![CDATA[
      R(x,y,K(x,z)) = x
    ]]></literal>
    <justification jstring="[hyper(1820,a,2711,a)].">
      <j1 rule="hyper" parents="1820 2711"/>
    </justification>
  </clause>

  <clause id="2713">
    <literal><![CDATA[
      L(K(x,y),z,x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(1812,a,2711,a)].">
      <j1 rule="hyper" parents="1812 2711"/>
    </justification>
  </clause>

  <clause id="2714">
    <literal><![CDATA[
      T(x,y) * T(z,K(x,y)) = (x * z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(250,a,2396,a,b,2711,a)].">
      <j1 rule="hyper" parents="250 2396 2711"/>
    </justification>
  </clause>

  <clause id="2715">
    <literal><![CDATA[
      R(T(x,y),z,K(x,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2712(a,1),27(a,2,1))].">
      <j1 rule="para" parents="2712 27"/>
    </justification>
  </clause>

  <clause id="2716">
    <literal><![CDATA[
      R(K(x,y),z,K(y,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2712(a,1),2577(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2712 2577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2717">
    <literal><![CDATA[
      L(K(x,y),z,x) = u \ (u * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(250,a,9,a,b,2713,a),flip(a)].">
      <j1 rule="hyper" parents="250 9 2713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2718">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,u) = K(x,y) * (z * K(y,u))
    ]]></literal>
    <justification jstring="[hyper(115,a,2716,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="115 2716 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2719">
    <literal><![CDATA[
      L(K(x,y),z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(2717(a,2),235(a,1))].">
      <j1 rule="para" parents="2717 235"/>
    </justification>
  </clause>

  <clause id="2720">
    <literal><![CDATA[
      ((x * y) * T(z,y)) / ((y * K(z,y)) * z) = R(x,y * K(z,y),z)
    ]]></literal>
    <justification jstring="[hyper(113,a,2705,a(flip),b,100,a)].">
      <j1 rule="hyper" parents="113 2705 100"/>
    </justification>
  </clause>

  <clause id="2721">
    <literal><![CDATA[
      T((x * y) / x,T(x,z)) = T(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(200,a,2636,a,b,2714,a)].">
      <j1 rule="hyper" parents="200 2636 2714"/>
    </justification>
  </clause>

  <clause id="2722">
    <literal><![CDATA[
      T(T(x,y),K(y,z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(191(a,1),2721(a,1,1)),flip(a)].">
      <j1 rule="para" parents="191 2721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2723">
    <literal><![CDATA[
      T(T(x,K(y,z)),y) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(2721(a,1),226(a,1,1))].">
      <j1 rule="para" parents="2721 226"/>
    </justification>
  </clause>

  <clause id="2728">
    <literal><![CDATA[
      K(x,(x * y) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) \ x) = u
    ]]></literal>
    <justification jstring="[para(2674(a,1),1947(a,1))].">
      <j1 rule="para" parents="2674 1947"/>
    </justification>
  </clause>

  <clause id="2730">
    <literal><![CDATA[
      x \ (y \ ((z \ (y * x)) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K((y \ z) \ x,z) = u
    ]]></literal>
    <justification jstring="[para(578(a,1),2689(a,1,2))].">
      <j1 rule="para" parents="578 2689"/>
    </justification>
  </clause>

  <clause id="2732">
    <literal><![CDATA[
      K((x \ y) \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(2383(a,1),2689(a,1))].">
      <j1 rule="para" parents="2383 2689"/>
    </justification>
  </clause>

  <clause id="2733">
    <literal><![CDATA[
      T(K(x / y,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(2493(a,2),2732(a,1))].">
      <j1 rule="para" parents="2493 2732"/>
    </justification>
  </clause>

  <clause id="2734">
    <literal><![CDATA[
      x \ (y \ ((z \ (y * x)) * z)) = K((z / y) \ x,z)
    ]]></literal>
    <justification jstring="[para(2202(a,1),2685(a,1,2))].">
      <j1 rule="para" parents="2202 2685"/>
    </justification>
  </clause>

  <clause id="2735">
    <literal><![CDATA[
      L(K(x,y),z,K(u,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(1812,a,2718,a)].">
      <j1 rule="hyper" parents="1812 2718"/>
    </justification>
  </clause>

  <clause id="2736">
    <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(1467(a,2),2668(a,1,2))].">
      <j1 rule="para" parents="1467 2668"/>
    </justification>
  </clause>

  <clause id="2737">
    <literal><![CDATA[
      x \ T(x * K(y \ x,z),x) = K(T(y,x) \ x,z)
    ]]></literal>
    <justification jstring="[hyper(112,a,2690,a(flip),b,2640,a(flip))].">
      <j1 rule="hyper" parents="112 2690 2640"/>
    </justification>
  </clause>

  <clause id="2738">
    <literal><![CDATA[
      K(T(x / y,x) \ x,z) = x \ T(x * K(y,z),x)
    ]]></literal>
    <justification jstring="[para(79(a,1),2737(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 2737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2740">
    <literal><![CDATA[
      K((x / y) \ z,x) = K((y \ x) \ z,x)
    ]]></literal>
    <justification jstring="[hyper(2730,a,2734,a),flip(a)].">
      <j1 rule="hyper" parents="2730 2734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2741">
    <literal><![CDATA[
      L(K(x,y \ z),z,u) = K(x,(u * y) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(2708,a,2669,a),flip(a)].">
      <j1 rule="hyper" parents="2708 2669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2742">
    <literal><![CDATA[
      K(x,(y * z) \ (y * x)) = K(x,z \ x)
    ]]></literal>
    <justification jstring="[hyper(2660,a,2741,a),flip(a)].">
      <j1 rule="hyper" parents="2660 2741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2743">
    <literal><![CDATA[
      L(K(x,(y \ z) \ u),u,y) = K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[para(10(a,1),2741(a,2,2,1))].">
      <j1 rule="para" parents="10 2741"/>
    </justification>
  </clause>

  <clause id="2744">
    <literal><![CDATA[
      L(K(x,y \ (z \ u)),z \ u,z) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[para(10(a,1),2741(a,2,2,2))].">
      <j1 rule="para" parents="10 2741"/>
    </justification>
  </clause>

  <clause id="2745">
    <literal><![CDATA[
      K(x,(y * (z / u)) \ (y * z)) = L(K(x,u),z,y)
    ]]></literal>
    <justification jstring="[para(79(a,1),2741(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="79 2741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2746">
    <literal><![CDATA[
      K(x,(y \ z) \ x) = K(x,z \ (y * x))
    ]]></literal>
    <justification jstring="[para(10(a,1),2742(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 2742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2748">
    <literal><![CDATA[
      L(T(K(x,(y \ z) \ u),w),u,y) = T(K(x,z \ (y * u)),w)
    ]]></literal>
    <justification jstring="[para(2743(a,1),25(a,2,1))].">
      <j1 rule="para" parents="2743 25"/>
    </justification>
  </clause>

  <clause id="2749">
    <literal><![CDATA[
      K(x,L(y,z / y,u)) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(96(a,2),2745(a,1,2))].">
      <j1 rule="para" parents="96 2745"/>
    </justification>
  </clause>

  <clause id="2750">
    <literal><![CDATA[
      K(x,L(y,z / y,u)) = L(K(y,x),z,u) \ 1
    ]]></literal>
    <justification jstring="[hyper(250,a,2555,a,b,2749,a),flip(a)].">
      <j1 rule="hyper" parents="250 2555 2749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2751">
    <literal><![CDATA[
      L(K(x,y),z * y,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(11(a,1),2749(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 2749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2752">
    <literal><![CDATA[
      K(x,L(y,z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2719,a,2751,a),flip(a)].">
      <j1 rule="hyper" parents="2719 2751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2753">
    <literal><![CDATA[
      K(x,L(y,z,K(u,x))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2735,a(flip),b,2751,a),flip(a)].">
      <j1 rule="hyper" parents="65 2735 2751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2754">
    <literal><![CDATA[
      K(x,L(y,z,x)) = 1 / K(y,x)
    ]]></literal>
    <justification jstring="[hyper(250,a,2367,a,b,2752,a),flip(a)].">
      <j1 rule="hyper" parents="250 2367 2752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2755">
    <literal><![CDATA[
      K(x,L(L(y,z,x),u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(30(a,1),2752(a,1,2))].">
      <j1 rule="para" parents="30 2752"/>
    </justification>
  </clause>

  <clause id="2756">
    <literal><![CDATA[
      K(x,(x * y) \ z) = K(x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[para(239(a,1),2752(a,1,2))].">
      <j1 rule="para" parents="239 2752"/>
    </justification>
  </clause>

  <clause id="2757">
    <literal><![CDATA[
      K(x,T((x \ y) \ z,u)) = K(x,T(y \ (x * z),u))
    ]]></literal>
    <justification jstring="[para(495(a,1),2752(a,1,2)),flip(a)].">
      <j1 rule="para" parents="495 2752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2758">
    <literal><![CDATA[
      K(L(x,y,z),L(u,w,x)) = K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(1677(a,1),2752(a,1,2))].">
      <j1 rule="para" parents="1677 2752"/>
    </justification>
  </clause>

  <clause id="2760">
    <literal><![CDATA[
      K(x,(K(y,x) * z) \ u) = K(x,z \ (K(x,y) * u))
    ]]></literal>
    <justification jstring="[para(2433(a,1),2753(a,1,2))].">
      <j1 rule="para" parents="2433 2753"/>
    </justification>
  </clause>

  <clause id="2761">
    <literal><![CDATA[
      K(L(x,y,z),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(2374,a,2754,a)].">
      <j1 rule="hyper" parents="2374 2754"/>
    </justification>
  </clause>

  <clause id="2763">
    <literal><![CDATA[
      K((x * y) \ z,x) = K(y \ (x \ z),x)
    ]]></literal>
    <justification jstring="[para(239(a,1),2761(a,1,1))].">
      <j1 rule="para" parents="239 2761"/>
    </justification>
  </clause>

  <clause id="2764">
    <literal><![CDATA[
      K((x \ 1) \ y,x) = K(x * y,x)
    ]]></literal>
    <justification jstring="[para(348(a,1),2761(a,1,1)),flip(a)].">
      <j1 rule="para" parents="348 2761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2766">
    <literal><![CDATA[
      K((x * (y / x)) \ (y * z),y) = K(K(x \ y,x) * z,y)
    ]]></literal>
    <justification jstring="[para(2627(a,1),2761(a,1,1))].">
      <j1 rule="para" parents="2627 2761"/>
    </justification>
  </clause>

  <clause id="2767">
    <literal><![CDATA[
      x \ T(x * y,x) = y * K(x * y,x)
    ]]></literal>
    <justification jstring="[para(2764(a,1),2682(a,2,2))].">
      <j1 rule="para" parents="2764 2682"/>
    </justification>
  </clause>

  <clause id="2768">
    <literal><![CDATA[
      ((x \ (1 / y)) * x) * y = K(y \ (x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(2390,a,2763,a)].">
      <j1 rule="hyper" parents="2390 2763"/>
    </justification>
  </clause>

  <clause id="2770">
    <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(2767(a,2),2340(a,1,1))].">
      <j1 rule="para" parents="2767 2340"/>
    </justification>
  </clause>

  <clause id="2771">
    <literal><![CDATA[
      K(L(x,y / x,z),u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(2369,a,2750,a)].">
      <j1 rule="hyper" parents="2369 2750"/>
    </justification>
  </clause>

  <clause id="2773">
    <literal><![CDATA[
      L(K(x,y),z,y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2761,a(flip),b,2771,a),flip(a)].">
      <j1 rule="hyper" parents="65 2761 2771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2774">
    <literal><![CDATA[
      L(K(x,y),z * x,u) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(11(a,1),2771(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11 2771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2775">
    <literal><![CDATA[
      L(K(x \ y,z),y,u) = K(L(x \ y,x,u),z)
    ]]></literal>
    <justification jstring="[para(76(a,1),2771(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="76 2771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2776">
    <literal><![CDATA[
      K(x,L(y,z,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2751,a(flip),b,2773,a)].">
      <j1 rule="hyper" parents="65 2751 2773"/>
    </justification>
  </clause>

  <clause id="2777">
    <literal><![CDATA[
      T(L(x,y,x),z) * K(z,x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,2776,a(flip),b,2266,a(flip))].">
      <j1 rule="hyper" parents="116 2776 2266"/>
    </justification>
  </clause>

  <clause id="2778">
    <literal><![CDATA[
      K(x,T(y / z,y)) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(2098(a,1),2776(a,1,2))].">
      <j1 rule="para" parents="2098 2776"/>
    </justification>
  </clause>

  <clause id="2779">
    <literal><![CDATA[
      K(x,(y \ z) \ z) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(76(a,1),2778(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="76 2778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2780">
    <literal><![CDATA[
      T(x,(y \ z) \ z) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(114,a,2779,a,b,2470,a),flip(a)].">
      <j1 rule="hyper" parents="114 2779 2470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2781">
    <literal><![CDATA[
      K(x,T(y,z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(65,a,2672,a(flip),b,2779,a),flip(a)].">
      <j1 rule="hyper" parents="65 2672 2779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2782">
    <literal><![CDATA[
      K(x,T(y,y \ z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(105(a,2),2779(a,1,2))].">
      <j1 rule="para" parents="105 2779"/>
    </justification>
  </clause>

  <clause id="2783">
    <literal><![CDATA[
      K((x \ y) \ y,z) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(250,a,2684,a,b,2781,a)].">
      <j1 rule="hyper" parents="250 2684 2781"/>
    </justification>
  </clause>

  <clause id="2784">
    <literal><![CDATA[
      R(T(K(x,y),z),y * u,w) = K(x,T(R(y,u,w),z))
    ]]></literal>
    <justification jstring="[hyper(250,a,2583,a,b,2781,a)].">
      <j1 rule="hyper" parents="250 2583 2781"/>
    </justification>
  </clause>

  <clause id="2785">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z,y) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(250,a,2515,a,b,2781,a)].">
      <j1 rule="hyper" parents="250 2515 2781"/>
    </justification>
  </clause>

  <clause id="2786">
    <literal><![CDATA[
      T(K(x,y),z) \ 1 = K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(250,a,2508,a,b,2781,a)].">
      <j1 rule="hyper" parents="250 2508 2781"/>
    </justification>
  </clause>

  <clause id="2787">
    <literal><![CDATA[
      K(x,T(y,x * z)) = K(T(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(250,a,2702,a(flip),b,2781,a),flip(a)].">
      <j1 rule="hyper" parents="250 2702 2781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2788">
    <literal><![CDATA[
      K(x / y,T(z,x)) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(250,a,2683,a(flip),b,2781,a),flip(a)].">
      <j1 rule="hyper" parents="250 2683 2781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2789">
    <literal><![CDATA[
      K(x,T(y,K(x,z))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(250,a,2522,a(flip),b,2781,a),flip(a)].">
      <j1 rule="hyper" parents="250 2522 2781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2790">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(250,a,1772,a(flip),b,2781,a),flip(a)].">
      <j1 rule="hyper" parents="250 1772 2781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2791">
    <literal><![CDATA[
      K(x,T(y,K(z,x))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(250,a,1060,a(flip),b,2781,a),flip(a)].">
      <j1 rule="hyper" parents="250 1060 2781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2792">
    <literal><![CDATA[
      x * K(y,T(z,x)) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(116,a,2781,a,b,22,a(flip))].">
      <j1 rule="hyper" parents="116 2781 22"/>
    </justification>
  </clause>

  <clause id="2793">
    <literal><![CDATA[
      x * T(K(x,y),z) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(116,a,2781,a(flip),b,2272,a(flip))].">
      <j1 rule="hyper" parents="116 2781 2272"/>
    </justification>
  </clause>

  <clause id="2794">
    <literal><![CDATA[
      K(x,T(T(y,z),u)) = T(K(x,T(y,u)),z)
    ]]></literal>
    <justification jstring="[para(23(a,1),2781(a,1,2))].">
      <j1 rule="para" parents="23 2781"/>
    </justification>
  </clause>

  <clause id="2795">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(2781(a,2),2510(a,1,2))].">
      <j1 rule="para" parents="2781 2510"/>
    </justification>
  </clause>

  <clause id="2796">
    <literal><![CDATA[
      L(K(x,T(y \ z,u)),y \ z,y) = K(x,T(z \ y,u) \ 1)
    ]]></literal>
    <justification jstring="[para(2781(a,2),2614(a,1,1))].">
      <j1 rule="para" parents="2781 2614"/>
    </justification>
  </clause>

  <clause id="2797">
    <literal><![CDATA[
      K(x,T(y,T(z,x))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(2722(a,1),2791(a,1,2))].">
      <j1 rule="para" parents="2722 2791"/>
    </justification>
  </clause>

  <clause id="2798">
    <literal><![CDATA[
      K(x,y / R(x,z,u)) = K(x,R(x,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(106(a,1),2790(a,1,2)),flip(a)].">
      <j1 rule="para" parents="106 2790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2799">
    <literal><![CDATA[
      T(x / ((y \ z) \ z),T(y,z)) = ((y \ z) \ z) \ x
    ]]></literal>
    <justification jstring="[hyper(293,a,2780,a),flip(a)].">
      <j1 rule="hyper" parents="293 2780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2800">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) = K(x,T(y,z \ y))
    ]]></literal>
    <justification jstring="[para(2014(a,1),2782(a,1,2))].">
      <j1 rule="para" parents="2014 2782"/>
    </justification>
  </clause>

  <clause id="2801">
    <literal><![CDATA[
      a(x,y,K(z,T(y,u))) = 1
    ]]></literal>
    <justification jstring="[para(2783(a,1),2653(a,1,3))].">
      <j1 rule="para" parents="2783 2653"/>
    </justification>
  </clause>

  <clause id="2802">
    <literal><![CDATA[
      L(K(x,T(y,z)),y,u) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(54,a,2801,a)].">
      <j1 rule="hyper" parents="54 2801"/>
    </justification>
  </clause>

  <clause id="2803">
    <literal><![CDATA[
      K(T(x,y),z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(41,a,2366,a,b,2786,a)].">
      <j1 rule="hyper" parents="41 2366 2786"/>
    </justification>
  </clause>

  <clause id="2804">
    <literal><![CDATA[
      K(x,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(2786(a,1),2512(a,1))].">
      <j1 rule="para" parents="2786 2512"/>
    </justification>
  </clause>

  <clause id="2805">
    <literal><![CDATA[
      K(T(x,y),z) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(250,a,2781,a,b,2803,a),flip(a)].">
      <j1 rule="hyper" parents="250 2781 2803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2807">
    <literal><![CDATA[
      K(T(x,K(y,z)),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(250,a,1059,a(flip),b,2803,a),flip(a)].">
      <j1 rule="hyper" parents="250 1059 2803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2808">
    <literal><![CDATA[
      x * K(T(y,x),z) = K(z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(116,a,2803,a,b,2423,a)].">
      <j1 rule="hyper" parents="116 2803 2423"/>
    </justification>
  </clause>

  <clause id="2809">
    <literal><![CDATA[
      x * K(T(y,x),z) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(116,a,2803,a,b,22,a(flip))].">
      <j1 rule="hyper" parents="116 2803 22"/>
    </justification>
  </clause>

  <clause id="2810">
    <literal><![CDATA[
      x * K(T(x,y),z) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(116,a,2805,a,b,2272,a(flip))].">
      <j1 rule="hyper" parents="116 2805 2272"/>
    </justification>
  </clause>

  <clause id="2811">
    <literal><![CDATA[
      K(x,T(y,x \ z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(65,a,2696,a(flip),b,2805,a),flip(a)].">
      <j1 rule="hyper" parents="65 2696 2805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2812">
    <literal><![CDATA[
      K(x,T(y,x \ y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2694,a(flip),b,2805,a),flip(a)].">
      <j1 rule="hyper" parents="65 2694 2805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2813">
    <literal><![CDATA[
      K(T(x,y),T(z,u)) = K(x,T(T(z,y),u))
    ]]></literal>
    <justification jstring="[para(23(a,1),2805(a,2,2))].">
      <j1 rule="para" parents="23 2805"/>
    </justification>
  </clause>

  <clause id="2814">
    <literal><![CDATA[
      K(T(x,y),z / y) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(106(a,1),2805(a,2,2))].">
      <j1 rule="para" parents="106 2805"/>
    </justification>
  </clause>

  <clause id="2815">
    <literal><![CDATA[
      K((x * y) / x,T(z,x)) = K(y,z)
    ]]></literal>
    <justification jstring="[para(190(a,1),2805(a,1,1)),flip(a)].">
      <j1 rule="para" parents="190 2805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2816">
    <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(1030(a,1),2805(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1030 2805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2817">
    <literal><![CDATA[
      K(x,y) * T(x,K(y,z)) = T(T(x,K(y,z)),y)
    ]]></literal>
    <justification jstring="[hyper(115,a,2807,a(flip),b,2265,a(flip))].">
      <j1 rule="hyper" parents="115 2807 2265"/>
    </justification>
  </clause>

  <clause id="2818">
    <literal><![CDATA[
      T(x,T(y,x \ y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(114,a,2812,a,b,2470,a),flip(a)].">
      <j1 rule="hyper" parents="114 2812 2470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2819">
    <literal><![CDATA[
      T(x,T(y,y / x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2009(a,2),2818(a,1,2))].">
      <j1 rule="para" parents="2009 2818"/>
    </justification>
  </clause>

  <clause id="2820">
    <literal><![CDATA[
      T(K(x,y) * z,T(z,K(y,x))) = T(K(x,y) * z,z)
    ]]></literal>
    <justification jstring="[para(2425(a,1),2819(a,1,2,2))].">
      <j1 rule="para" parents="2425 2819"/>
    </justification>
  </clause>

  <clause id="2821">
    <literal><![CDATA[
      K(x,T(y,x * z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(250,a,2805,a(flip),b,2787,a),flip(a)].">
      <j1 rule="hyper" parents="250 2805 2787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2822">
    <literal><![CDATA[
      K(x,y) * (z * K(y,T(x,z))) = z
    ]]></literal>
    <justification jstring="[hyper(116,a,2792,a,b,2422,a)].">
      <j1 rule="hyper" parents="116 2792 2422"/>
    </justification>
  </clause>

  <clause id="2823">
    <literal><![CDATA[
      K(x,T((y / z) \ 1,z)) = K(x,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(36,a,2505,a(flip),b,2792,a),flip(a)].">
      <j1 rule="hyper" parents="36 2505 2792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2824">
    <literal><![CDATA[
      T(x,y) * K(K(x,y),z) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(2479,a,2793,a)].">
      <j1 rule="hyper" parents="2479 2793"/>
    </justification>
  </clause>

  <clause id="2826">
    <literal><![CDATA[
      K((x * y) / x,z) * x = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(190(a,1),2809(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="190 2809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2827">
    <literal><![CDATA[
      (K(x,y) * z) \ (T(x,y) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(2809(a,1),2635(a,1,1))].">
      <j1 rule="para" parents="2809 2635"/>
    </justification>
  </clause>

  <clause id="2828">
    <literal><![CDATA[
      K(x,T(y,x \ z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(250,a,2781,a,b,2811,a),flip(a)].">
      <j1 rule="hyper" parents="250 2781 2811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2829">
    <literal><![CDATA[
      K(T(x,y),z \ 1) = K(x,y \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(2467,a,2814,a)].">
      <j1 rule="hyper" parents="2467 2814"/>
    </justification>
  </clause>

  <clause id="2830">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,T(x,z)) = z
    ]]></literal>
    <justification jstring="[hyper(65,a,2718,a,b,2822,a)].">
      <j1 rule="hyper" parents="65 2718 2822"/>
    </justification>
  </clause>

  <clause id="2831">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) * K(y,x) = K(y,z)
    ]]></literal>
    <justification jstring="[para(2789(a,1),2830(a,1,2))].">
      <j1 rule="para" parents="2789 2830"/>
    </justification>
  </clause>

  <clause id="2832">
    <literal><![CDATA[
      (K(x,y) * z) * K(T(y,z),x) = z
    ]]></literal>
    <justification jstring="[para(2805(a,2),2830(a,1,2))].">
      <j1 rule="para" parents="2805 2830"/>
    </justification>
  </clause>

  <clause id="2833">
    <literal><![CDATA[
      K(L(x,y,x),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(2719,a,2774,a),flip(a)].">
      <j1 rule="hyper" parents="2719 2774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2835">
    <literal><![CDATA[
      (x * (y * z)) / K(L(y,z,x),z) = x * (z * y)
    ]]></literal>
    <justification jstring="[hyper(170,a,2774,a(flip),b,244,a)].">
      <j1 rule="hyper" parents="170 2774 244"/>
    </justification>
  </clause>

  <clause id="2836">
    <literal><![CDATA[
      K(L(x,y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(2774(a,1),2719(a,1))].">
      <j1 rule="para" parents="2774 2719"/>
    </justification>
  </clause>

  <clause id="2837">
    <literal><![CDATA[
      L(x,y,x) * K(x,z) = L(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,2833,a(flip),b,2312,a)].">
      <j1 rule="hyper" parents="116 2833 2312"/>
    </justification>
  </clause>

  <clause id="2838">
    <literal><![CDATA[
      T(x,x * y) * K(y,x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(440(a,1),2777(a,1,1))].">
      <j1 rule="para" parents="440 2777"/>
    </justification>
  </clause>

  <clause id="2840">
    <literal><![CDATA[
      (x * K(y,x)) \ L(x,y,x) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(2838(a,1),2592(a,1,2))].">
      <j1 rule="para" parents="2838 2592"/>
    </justification>
  </clause>

  <clause id="2841">
    <literal><![CDATA[
      K(x * y,K(x,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(2681,a,2795,a)].">
      <j1 rule="hyper" parents="2681 2795"/>
    </justification>
  </clause>

  <clause id="2842">
    <literal><![CDATA[
      K(x * y,K(x,z)) = K(K(z,x),y)
    ]]></literal>
    <justification jstring="[hyper(250,a,2513,a,b,2841,a),flip(a)].">
      <j1 rule="hyper" parents="250 2513 2841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2843">
    <literal><![CDATA[
      K(x \ y,K(x,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),2841(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 2841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2844">
    <literal><![CDATA[
      K(x,T(y,(z \ u) \ y)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[para(2665(a,1),2800(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2665 2800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2845">
    <literal><![CDATA[
      T(x,K(x,y) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(2398,a,2827,a)].">
      <j1 rule="hyper" parents="2398 2827"/>
    </justification>
  </clause>

  <clause id="2846">
    <literal><![CDATA[
      (T(x,y) * (x \ z)) \ (T(x,y) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(2290(a,2),2827(a,1,1))].">
      <j1 rule="para" parents="2290 2827"/>
    </justification>
  </clause>

  <clause id="2847">
    <literal><![CDATA[
      T(x,K(y,x) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(2426(a,1),2845(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2426 2845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2848">
    <literal><![CDATA[
      T(x,y * K(z,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2826(a,1),2847(a,1,2))].">
      <j1 rule="para" parents="2826 2847"/>
    </justification>
  </clause>

  <clause id="2849">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) = K(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,2805,a(flip),b,2829,a)].">
      <j1 rule="hyper" parents="65 2805 2829"/>
    </justification>
  </clause>

  <clause id="2850">
    <literal><![CDATA[
      K(x,y) * L(x,z,x) = L(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(1771,a,2837,a)].">
      <j1 rule="hyper" parents="1771 2837"/>
    </justification>
  </clause>

  <clause id="2851">
    <literal><![CDATA[
      K(x,y) * (L(y,z,y) \ u) = L(T(y,x),z,y) \ u
    ]]></literal>
    <justification jstring="[para(2837(a,1),2559(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2837 2559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2852">
    <literal><![CDATA[
      (x * y) * ((z \ ((x * y) \ y)) * z) = K(x \ (z \ 1),z) * y
    ]]></literal>
    <justification jstring="[para(2768(a,1),2206(a,2,1))].">
      <j1 rule="para" parents="2768 2206"/>
    </justification>
  </clause>

  <clause id="2853">
    <literal><![CDATA[
      K(L(x \ y,x,z),y) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2655,a(flip),b,2775,a),flip(a)].">
      <j1 rule="hyper" parents="65 2655 2775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2854">
    <literal><![CDATA[
      L(K(x \ y,z),y,u) = K((u * x) \ (u * y),z)
    ]]></literal>
    <justification jstring="[para(95(a,1),2775(a,2,1))].">
      <j1 rule="para" parents="95 2775"/>
    </justification>
  </clause>

  <clause id="2855">
    <literal><![CDATA[
      L(K(x \ (y \ z),u),y \ z,y) = K((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[para(239(a,1),2775(a,2,1))].">
      <j1 rule="para" parents="239 2775"/>
    </justification>
  </clause>

  <clause id="2856">
    <literal><![CDATA[
      L(K((x \ y) \ z,u),z,x) = K(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[para(349(a,1),2775(a,2,1))].">
      <j1 rule="para" parents="349 2775"/>
    </justification>
  </clause>

  <clause id="2859">
    <literal><![CDATA[
      K((x \ y) \ z,z) = K(y \ (x * z),z)
    ]]></literal>
    <justification jstring="[para(349(a,1),2853(a,1,1)),flip(a)].">
      <j1 rule="para" parents="349 2853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2860">
    <literal><![CDATA[
      K(x,y) * T(x,K(y,z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(250,a,2723,a(flip),b,2817,a),flip(a)].">
      <j1 rule="hyper" parents="250 2723 2817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2861">
    <literal><![CDATA[
      T(x,y) * K(x,K(y,z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(2478,a,2860,a)].">
      <j1 rule="hyper" parents="2478 2860"/>
    </justification>
  </clause>

  <clause id="2862">
    <literal><![CDATA[
      K(x,K(y,z)) * T(x,y) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(2471,a,2860,a)].">
      <j1 rule="hyper" parents="2471 2860"/>
    </justification>
  </clause>

  <clause id="2863">
    <literal><![CDATA[
      K(K(x,y),z) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(36,a,2824,a,b,2861,a)].">
      <j1 rule="hyper" parents="36 2824 2861"/>
    </justification>
  </clause>

  <clause id="2864">
    <literal><![CDATA[
      K(x,K(y,z)) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(2528,a,2863,a)].">
      <j1 rule="hyper" parents="2528 2863"/>
    </justification>
  </clause>

  <clause id="2865">
    <literal><![CDATA[
      K(x * y,K(x,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,2842,a,b,2863,a)].">
      <j1 rule="hyper" parents="65 2842 2863"/>
    </justification>
  </clause>

  <clause id="2866">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(116,a,2863,a(flip),b,2272,a(flip))].">
      <j1 rule="hyper" parents="116 2863 2272"/>
    </justification>
  </clause>

  <clause id="2868">
    <literal><![CDATA[
      K(x,K(y,z)) \ 1 = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(2863(a,1),2366(a,1,1))].">
      <j1 rule="para" parents="2863 2366"/>
    </justification>
  </clause>

  <clause id="2870">
    <literal><![CDATA[
      x * K(y,K(z,x)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(2863(a,1),2514(a,1,2))].">
      <j1 rule="para" parents="2863 2514"/>
    </justification>
  </clause>

  <clause id="2873">
    <literal><![CDATA[
      K(x,K(y,y * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,2864,a,b,2865,a)].">
      <j1 rule="hyper" parents="65 2864 2865"/>
    </justification>
  </clause>

  <clause id="2874">
    <literal><![CDATA[
      K(x,K(y,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(2516,a,2868,a)].">
      <j1 rule="hyper" parents="2516 2868"/>
    </justification>
  </clause>

  <clause id="2876">
    <literal><![CDATA[
      K(x,K(y,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(250,a,2864,a,b,2874,a),flip(a)].">
      <j1 rule="hyper" parents="250 2864 2874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2877">
    <literal><![CDATA[
      K(K(x,y),z) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(250,a,2863,a,b,2874,a)].">
      <j1 rule="hyper" parents="250 2863 2874"/>
    </justification>
  </clause>

  <clause id="2878">
    <literal><![CDATA[
      K(x,K(x \ y,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(250,a,2843,a(flip),b,2874,a),flip(a)].">
      <j1 rule="hyper" parents="250 2843 2874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2879">
    <literal><![CDATA[
      K(x,K(y,z)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(250,a,2874,a,b,2876,a)].">
      <j1 rule="hyper" parents="250 2874 2876"/>
    </justification>
  </clause>

  <clause id="2881">
    <literal><![CDATA[
      K(x,K(y,z)) * z = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(115,a,2876,a,b,2265,a(flip))].">
      <j1 rule="hyper" parents="115 2876 2265"/>
    </justification>
  </clause>

  <clause id="2882">
    <literal><![CDATA[
      K(x,K(y,z)) * (z * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(z,K(x,y)) * u = w
    ]]></literal>
    <justification jstring="[para(2876(a,2),2405(a,1,1))].">
      <j1 rule="para" parents="2876 2405"/>
    </justification>
  </clause>

  <clause id="2883">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,x) = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[para(2876(a,2),2515(a,1,1))].">
      <j1 rule="para" parents="2876 2515"/>
    </justification>
  </clause>

  <clause id="2884">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,x) = K(y,T(x,z))
    ]]></literal>
    <justification jstring="[para(2876(a,2),2785(a,1,1))].">
      <j1 rule="para" parents="2876 2785"/>
    </justification>
  </clause>

  <clause id="2885">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(2877(a,1),2528(a,1))].">
      <j1 rule="para" parents="2877 2528"/>
    </justification>
  </clause>

  <clause id="2886">
    <literal><![CDATA[
      T(x,K(y,z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(114,a,2879,a,b,2470,a)].">
      <j1 rule="hyper" parents="114 2879 2470"/>
    </justification>
  </clause>

  <clause id="2887">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(2521,a,2886,a)].">
      <j1 rule="hyper" parents="2521 2886"/>
    </justification>
  </clause>

  <clause id="2888">
    <literal><![CDATA[
      K(x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      T(z,K(x,y)) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(2887(a,1),231(a,1,2))].">
      <j1 rule="para" parents="2887 231"/>
    </justification>
  </clause>

  <clause id="2889">
    <literal><![CDATA[
      T(x,K(y,y * z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(114,a,2873,a,b,2470,a),flip(a)].">
      <j1 rule="hyper" parents="114 2873 2470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2890">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = K(x,K(y,z \ y))
    ]]></literal>
    <justification jstring="[para(2462(a,1),2873(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2462 2873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2891">
    <literal><![CDATA[
      K(x,K(x \ y,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(250,a,2864,a,b,2878,a),flip(a)].">
      <j1 rule="hyper" parents="250 2864 2878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2892">
    <literal><![CDATA[
      K(x,K(y,z)) * T(z,y) = T(z,T(y,x))
    ]]></literal>
    <justification jstring="[para(2864(a,1),2862(a,1,1))].">
      <j1 rule="para" parents="2864 2862"/>
    </justification>
  </clause>

  <clause id="2893">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(250,a,2781,a,b,2866,a),flip(a)].">
      <j1 rule="hyper" parents="250 2781 2866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2897">
    <literal><![CDATA[
      K(x,T(y,z)) != K(x,y) * u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(2893(a,1),45(a,1))].">
      <j1 rule="para" parents="2893 45"/>
    </justification>
  </clause>

  <clause id="2898">
    <literal><![CDATA[
      K(x,y) * K(z,K(x,y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(2876(a,1),2893(a,1,2))].">
      <j1 rule="para" parents="2876 2893"/>
    </justification>
  </clause>

  <clause id="2899">
    <literal><![CDATA[
      K(x,y) * K(x,K(z,y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(2879(a,1),2893(a,1,2))].">
      <j1 rule="para" parents="2879 2893"/>
    </justification>
  </clause>

  <clause id="2902">
    <literal><![CDATA[
      K(x,T(y,z)) * z = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(115,a,2898,a(flip),b,2308,a)].">
      <j1 rule="hyper" parents="115 2898 2308"/>
    </justification>
  </clause>

  <clause id="2903">
    <literal><![CDATA[
      T(K(x,T(y,z)),z) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2898(a,1),2347(a,1,1))].">
      <j1 rule="para" parents="2898 2347"/>
    </justification>
  </clause>

  <clause id="2904">
    <literal><![CDATA[
      K(x \ y,T(z,y)) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(2733,a,2903,a)].">
      <j1 rule="hyper" parents="2733 2903"/>
    </justification>
  </clause>

  <clause id="2905">
    <literal><![CDATA[
      K(x,T(y \ z,z)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(2671,a,2903,a),flip(a)].">
      <j1 rule="hyper" parents="2671 2903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2906">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,2803,a,b,2903,a)].">
      <j1 rule="hyper" parents="65 2803 2903"/>
    </justification>
  </clause>

  <clause id="2907">
    <literal><![CDATA[
      K(x,T(T(y,z),z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2794,a,b,2903,a)].">
      <j1 rule="hyper" parents="65 2794 2903"/>
    </justification>
  </clause>

  <clause id="2909">
    <literal><![CDATA[
      x * K(T(x,y),T(z,y)) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,2906,a,b,2272,a(flip))].">
      <j1 rule="hyper" parents="116 2906 2272"/>
    </justification>
  </clause>

  <clause id="2910">
    <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),2906(a,1,1))].">
      <j1 rule="para" parents="25 2906"/>
    </justification>
  </clause>

  <clause id="2911">
    <literal><![CDATA[
      K(R(T(x,y),z,u),T(w,y)) = K(R(x,z,u),w)
    ]]></literal>
    <justification jstring="[para(27(a,2),2906(a,1,1))].">
      <j1 rule="para" parents="27 2906"/>
    </justification>
  </clause>

  <clause id="2912">
    <literal><![CDATA[
      K(x \ y,T(z,x)) = K(y / x,z)
    ]]></literal>
    <justification jstring="[para(106(a,1),2906(a,1,1))].">
      <j1 rule="para" parents="106 2906"/>
    </justification>
  </clause>

  <clause id="2913">
    <literal><![CDATA[
      K(T(x,y),y \ z) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(106(a,1),2906(a,1,2))].">
      <j1 rule="para" parents="106 2906"/>
    </justification>
  </clause>

  <clause id="2914">
    <literal><![CDATA[
      K(x * T(x \ y,y),z) = K(y,T(z,x \ y))
    ]]></literal>
    <justification jstring="[para(776(a,1),2906(a,1,1)),flip(a)].">
      <j1 rule="para" parents="776 2906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2915">
    <literal><![CDATA[
      K(x * K(y,x),z) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(2347(a,1),2906(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2347 2906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2916">
    <literal><![CDATA[
      R(K(x,y),T(y,z) * u,w) = K(T(x,z),R(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(2906(a,1),2578(a,1,1))].">
      <j1 rule="para" parents="2906 2578"/>
    </justification>
  </clause>

  <clause id="2917">
    <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(2906(a,1),2624(a,1,1))].">
      <j1 rule="para" parents="2906 2624"/>
    </justification>
  </clause>

  <clause id="2918">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * K(y,x)) = z
    ]]></literal>
    <justification jstring="[para(2906(a,1),2822(a,1,2,2))].">
      <j1 rule="para" parents="2906 2822"/>
    </justification>
  </clause>

  <clause id="2919">
    <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(2906(a,1),2774(a,1,1))].">
      <j1 rule="para" parents="2906 2774"/>
    </justification>
  </clause>

  <clause id="2920">
    <literal><![CDATA[
      T(x,T(T(y,z),z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(114,a,2907,a,b,2470,a),flip(a)].">
      <j1 rule="hyper" parents="114 2907 2470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2921">
    <literal><![CDATA[
      T(x,(y * z) / y) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(190(a,1),2920(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="190 2920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2922">
    <literal><![CDATA[
      x * T(x \ y,T(z,y)) = y * K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,2291,a(flip),b,2902,a)].">
      <j1 rule="hyper" parents="65 2291 2902"/>
    </justification>
  </clause>

  <clause id="2923">
    <literal><![CDATA[
      K(x,T((y \ z) \ 1,y)) = K(x,(z / y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(37,a,2505,a,b,2902,a),flip(a)].">
      <j1 rule="hyper" parents="37 2505 2902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2924">
    <literal><![CDATA[
      T(x,T(y,z)) * z = x * (z * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(116,a,2902,a(flip),b,2321,a),flip(a)].">
      <j1 rule="hyper" parents="116 2902 2321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2925">
    <literal><![CDATA[
      R(T(K(x,T(y,z)),z * u),z,u) = (z * u) \ ((z * K(x,y)) * u)
    ]]></literal>
    <justification jstring="[para(2902(a,1),432(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2902 432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2927">
    <literal><![CDATA[
      T(x,y * K(x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2902(a,1),2845(a,1,2))].">
      <j1 rule="para" parents="2902 2845"/>
    </justification>
  </clause>

  <clause id="2928">
    <literal><![CDATA[
      K(x,y * K(x,z)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(112,a,2927,a(flip),b,2274,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="112 2927 2274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2930">
    <literal><![CDATA[
      K(x,T(y,z * K(x,u))) = K(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(2927(a,1),2805(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2927 2805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2931">
    <literal><![CDATA[
      K(x,T(y \ (x * z),z)) = K(x,(x * z) / y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2821,a(flip),b,2905,a)].">
      <j1 rule="hyper" parents="65 2821 2905"/>
    </justification>
  </clause>

  <clause id="2932">
    <literal><![CDATA[
      x * T(x \ y,T(z,x)) = y * K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,2912,a(flip),b,2641,a),flip(a)].">
      <j1 rule="hyper" parents="116 2912 2641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2933">
    <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),2912(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14 2912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2934">
    <literal><![CDATA[
      K(T(x,y),(y * K(z,x)) \ u) = K(x,u / (y * K(z,x)))
    ]]></literal>
    <justification jstring="[para(2848(a,1),2913(a,1,1))].">
      <j1 rule="para" parents="2848 2913"/>
    </justification>
  </clause>

  <clause id="2935">
    <literal><![CDATA[
      T(x,R((y * z) / y,u,w)) = T(x,T(R(z,u,w),y))
    ]]></literal>
    <justification jstring="[para(537(a,2),2921(a,1,2))].">
      <j1 rule="para" parents="537 2921"/>
    </justification>
  </clause>

  <clause id="2936">
    <literal><![CDATA[
      K(x,y * K(x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(250,a,2272,a,b,2928,a),flip(a)].">
      <j1 rule="hyper" parents="250 2272 2928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2940">
    <literal><![CDATA[
      K(x,K(y,x * K(y,z))) = 1
    ]]></literal>
    <justification jstring="[para(2936(a,2),1983(a,1,2))].">
      <j1 rule="para" parents="2936 1983"/>
    </justification>
  </clause>

  <clause id="2941">
    <literal><![CDATA[
      K(x,K(x,y) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(2792(a,1),2936(a,1,2))].">
      <j1 rule="para" parents="2792 2936"/>
    </justification>
  </clause>

  <clause id="2944">
    <literal><![CDATA[
      K(x,T(x,y) * z) = K(x,x * z)
    ]]></literal>
    <justification jstring="[para(2302(a,1),2941(a,1,2))].">
      <j1 rule="para" parents="2302 2941"/>
    </justification>
  </clause>

  <clause id="2946">
    <literal><![CDATA[
      K(x,T(y,x) \ z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(2408(a,1),2941(a,1,2))].">
      <j1 rule="para" parents="2408 2941"/>
    </justification>
  </clause>

  <clause id="2947">
    <literal><![CDATA[
      K(x,R(K(x,y),z,u) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(2568(a,1),2941(a,1,2,1))].">
      <j1 rule="para" parents="2568 2941"/>
    </justification>
  </clause>

  <clause id="2948">
    <literal><![CDATA[
      K(x,K(y,K(x,z) * u)) = K(y,K(x,u))
    ]]></literal>
    <justification jstring="[para(2941(a,1),2874(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2941 2874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2949">
    <literal><![CDATA[
      K(x,y * K(z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2918(a,1),2941(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2918 2941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2951">
    <literal><![CDATA[
      K(x * K(y,z),z) = 1 / K(z,x)
    ]]></literal>
    <justification jstring="[hyper(170,a,2949,a(flip),b,2366,a),flip(a)].">
      <j1 rule="hyper" parents="170 2949 2366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2952">
    <literal><![CDATA[
      R(K(x,y),y * K(z,x),u) = K(x,y * K(z,x))
    ]]></literal>
    <justification jstring="[para(2949(a,1),2581(a,1,1))].">
      <j1 rule="para" parents="2949 2581"/>
    </justification>
  </clause>

  <clause id="2953">
    <literal><![CDATA[
      K(x * K(y,z),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(250,a,2367,a(flip),b,2951,a),flip(a)].">
      <j1 rule="hyper" parents="250 2367 2951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2954">
    <literal><![CDATA[
      K(x * K(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(2951(a,2),2370(a,1))].">
      <j1 rule="para" parents="2951 2370"/>
    </justification>
  </clause>

  <clause id="2956">
    <literal><![CDATA[
      K(K(x,y) \ z,x) = K(z,x)
    ]]></literal>
    <justification jstring="[para(2808(a,1),2953(a,1,1))].">
      <j1 rule="para" parents="2808 2953"/>
    </justification>
  </clause>

  <clause id="2957">
    <literal><![CDATA[
      K(K(x,y) * z,x) = K(z,x)
    ]]></literal>
    <justification jstring="[para(2832(a,1),2953(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2832 2953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2959">
    <literal><![CDATA[
      K(R(K(x,y),z,u) * w,x) = K(w,x)
    ]]></literal>
    <justification jstring="[para(2568(a,1),2957(a,1,1,1))].">
      <j1 rule="para" parents="2568 2957"/>
    </justification>
  </clause>

  <clause id="2960">
    <literal><![CDATA[
      L(K(x,y),K(y,z) * x,u) = K(K(y,z) * x,y)
    ]]></literal>
    <justification jstring="[para(2957(a,1),2648(a,1,1))].">
      <j1 rule="para" parents="2957 2648"/>
    </justification>
  </clause>

  <clause id="2961">
    <literal><![CDATA[
      K(K(x,y) * z,K(x,u)) = K(K(z,x),u)
    ]]></literal>
    <justification jstring="[para(2957(a,1),2863(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2957 2863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2962">
    <literal><![CDATA[
      K(x * K(y,z),y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2902(a,1),2957(a,1,1))].">
      <j1 rule="para" parents="2902 2957"/>
    </justification>
  </clause>

  <clause id="2963">
    <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(2962(a,1),2490(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2962 2490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2967">
    <literal><![CDATA[
      K(x \ T(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(683(a,1),2954(a,1,1))].">
      <j1 rule="para" parents="683 2954"/>
    </justification>
  </clause>

  <clause id="2968">
    <literal><![CDATA[
      R(K(x,y),T(y,T(z,u)) * u,w) = K(x,R(y,u * K(y,z),w))
    ]]></literal>
    <justification jstring="[para(2924(a,2),2578(a,1,2))].">
      <j1 rule="para" parents="2924 2578"/>
    </justification>
  </clause>

  <clause id="2969">
    <literal><![CDATA[
      K(x,T(y,z * K(x,u))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(250,a,2805,a(flip),b,2930,a),flip(a)].">
      <j1 rule="hyper" parents="250 2805 2930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2970">
    <literal><![CDATA[
      K(x,K(y,K(x,z) * u)) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(250,a,2874,a,b,2948,a),flip(a)].">
      <j1 rule="hyper" parents="250 2874 2948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2971">
    <literal><![CDATA[
      K(K(x,y) * z,K(x,u)) = K(z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(250,a,2863,a(flip),b,2961,a),flip(a)].">
      <j1 rule="hyper" parents="250 2863 2961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2972">
    <literal><![CDATA[
      K(x,T(y,K(x,z) * u)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(2792(a,1),2969(a,1,2,2))].">
      <j1 rule="para" parents="2792 2969"/>
    </justification>
  </clause>

  <clause id="2973">
    <literal><![CDATA[
      K(x,T(y,T(z,K(u,x)))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(2870(a,1),2969(a,1,2,2))].">
      <j1 rule="para" parents="2870 2969"/>
    </justification>
  </clause>

  <clause id="2974">
    <literal><![CDATA[
      K(x,K(y,z * K(u,x))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(2918(a,1),2970(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2918 2970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2975">
    <literal><![CDATA[
      K(x * y,K(y,z)) = K(y * x,K(y,z))
    ]]></literal>
    <justification jstring="[para(2264(a,1),2971(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2264 2971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2977">
    <literal><![CDATA[
      K(x,T(y,T(z,x) \ u)) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(2408(a,1),2972(a,1,2,2))].">
      <j1 rule="para" parents="2408 2972"/>
    </justification>
  </clause>

  <clause id="2978">
    <literal><![CDATA[
      T(K(x,y),T(z,K(u,x))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(2804,a,2973,a)].">
      <j1 rule="hyper" parents="2804 2973"/>
    </justification>
  </clause>

  <clause id="2979">
    <literal><![CDATA[
      K(x,K(y,z)) * (z * K(u,x)) = T(z * K(u,x),K(x,y))
    ]]></literal>
    <justification jstring="[para(2974(a,1),2881(a,1,1))].">
      <j1 rule="para" parents="2974 2881"/>
    </justification>
  </clause>

  <clause id="2980">
    <literal><![CDATA[
      K(x * y,K(y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(250,a,2841,a(flip),b,2975,a),flip(a)].">
      <j1 rule="hyper" parents="250 2841 2975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2981">
    <literal><![CDATA[
      K(x,K(y \ x,z)) = K(y,K(y \ x,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),2980(a,1,1))].">
      <j1 rule="para" parents="10 2980"/>
    </justification>
  </clause>

  <clause id="2982">
    <literal><![CDATA[
      K(x,K(y \ x,z)) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(250,a,2891,a(flip),b,2981,a),flip(a)].">
      <j1 rule="hyper" parents="250 2891 2981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2983">
    <literal><![CDATA[
      K(x,K(y,z \ y)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(2885,a,2982,a)].">
      <j1 rule="hyper" parents="2885 2982"/>
    </justification>
  </clause>

  <clause id="2984">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,2890,a,b,2983,a)].">
      <j1 rule="hyper" parents="65 2890 2983"/>
    </justification>
  </clause>

  <clause id="2985">
    <literal><![CDATA[
      K(x,K(y,z \ (u * y))) = K(x,K(u \ z,y))
    ]]></literal>
    <justification jstring="[para(2746(a,1),2983(a,1,2))].">
      <j1 rule="para" parents="2746 2983"/>
    </justification>
  </clause>

  <clause id="2986">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(250,a,2879,a,b,2984,a),flip(a)].">
      <j1 rule="hyper" parents="250 2879 2984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2987">
    <literal><![CDATA[
      K(x,K(y \ z,u)) = K(x,K(u,z \ y))
    ]]></literal>
    <justification jstring="[para(2658(a,1),2984(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2658 2984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2988">
    <literal><![CDATA[
      T(x,K(y,z \ 1)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(114,a,2986,a,b,2470,a),flip(a)].">
      <j1 rule="hyper" parents="114 2986 2470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2989">
    <literal><![CDATA[
      T(T(x,y),K(y,z)) = T(x,T(y,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(65,a,2722,a(flip),b,2988,a),flip(a)].">
      <j1 rule="hyper" parents="65 2722 2988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2990">
    <literal><![CDATA[
      T(x,T(y,z \ 1)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,2722,a(flip),b,2989,a),flip(a)].">
      <j1 rule="hyper" parents="65 2722 2989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2991">
    <literal><![CDATA[
      T(x,T(y,z \ 1)) = x * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(250,a,2274,a(flip),b,2990,a),flip(a)].">
      <j1 rule="hyper" parents="250 2274 2990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2992">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(2327,a,2991,a)].">
      <j1 rule="hyper" parents="2327 2991"/>
    </justification>
  </clause>

  <clause id="2993">
    <literal><![CDATA[
      K(x,T(y,z \ u)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[para(2665(a,1),2992(a,1,2))].">
      <j1 rule="para" parents="2665 2992"/>
    </justification>
  </clause>

  <clause id="2994">
    <literal><![CDATA[
      K(x,T(y,z \ x)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(250,a,2828,a(flip),b,2993,a),flip(a)].">
      <j1 rule="hyper" parents="250 2828 2993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2995">
    <literal><![CDATA[
      K(x * y,T(z,y)) = K(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[para(9(a,1),2994(a,1,2,2))].">
      <j1 rule="para" parents="9 2994"/>
    </justification>
  </clause>

  <clause id="2996">
    <literal><![CDATA[
      K(x * R(y,z,u),T(y,x)) = K(x * R(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(153(a,1),2995(a,1,2)),flip(a)].">
      <j1 rule="para" parents="153 2995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2998">
    <literal><![CDATA[
      K(x \ (y \ (z * y)),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ z,y) = u
    ]]></literal>
    <justification jstring="[para(22(a,1),2967(a,1,1,2))].">
      <j1 rule="para" parents="22 2967"/>
    </justification>
  </clause>

  <clause id="2999">
    <literal><![CDATA[
      K(x,T((y / z) \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(2823(a,2),2706(a,1))].">
      <j1 rule="para" parents="2823 2706"/>
    </justification>
  </clause>

  <clause id="3000">
    <literal><![CDATA[
      (T(x,y) * z) / T(x,z) = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(171,a,2846,a)].">
      <j1 rule="hyper" parents="171 2846"/>
    </justification>
  </clause>

  <clause id="3002">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) = K(L(x,T(x,y) \ 1,u),z)
    ]]></literal>
    <justification jstring="[hyper(65,a,2703,a(flip),b,2910,a)].">
      <j1 rule="hyper" parents="65 2703 2910"/>
    </justification>
  </clause>

  <clause id="3003">
    <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(156(a,1),2911(a,1,2))].">
      <j1 rule="para" parents="156 2911"/>
    </justification>
  </clause>

  <clause id="3004">
    <literal><![CDATA[
      K(R(x / (x / y),z,u),w) = K(R(y,z,u),T(w,y \ x))
    ]]></literal>
    <justification jstring="[para(2088(a,1),2911(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2088 2911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3005">
    <literal><![CDATA[
      K(T(x * K(y \ x,x),x),z) = K(x,T(z,T(y,x) \ x))
    ]]></literal>
    <justification jstring="[para(2690(a,1),2914(a,1,1))].">
      <j1 rule="para" parents="2690 2914"/>
    </justification>
  </clause>

  <clause id="3006">
    <literal><![CDATA[
      T(x \ y,T(z,y)) = T(x \ y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(36,a,2922,a,b,2932,a)].">
      <j1 rule="hyper" parents="36 2922 2932"/>
    </justification>
  </clause>

  <clause id="3007">
    <literal><![CDATA[
      K(x,T(y \ x,T(z,y))) = K(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[para(3006(a,1),2797(a,1,2))].">
      <j1 rule="para" parents="3006 2797"/>
    </justification>
  </clause>

  <clause id="3008">
    <literal><![CDATA[
      K(x,K(y,z \ (u * y))) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(250,a,2987,a(flip),b,2985,a),flip(a)].">
      <j1 rule="hyper" parents="250 2987 2985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3009">
    <literal><![CDATA[
      K(x,T(y \ x,z / y)) = K(x,T(y \ x,y \ z))
    ]]></literal>
    <justification jstring="[para(106(a,1),3007(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="106 3007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3010">
    <literal><![CDATA[
      L(K(x \ y,T(z,u * y)),y,u) = K((u * y) / (u * x),z)
    ]]></literal>
    <justification jstring="[hyper(250,a,2904,a(flip),b,2854,a),flip(a)].">
      <j1 rule="hyper" parents="250 2904 2854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3012">
    <literal><![CDATA[
      K((x \ y) \ z,u \ (x * z)) = K(y \ (x * z),(x \ u) \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,2743,a(flip),b,2856,a)].">
      <j1 rule="hyper" parents="65 2743 2856"/>
    </justification>
  </clause>

  <clause id="3015">
    <literal><![CDATA[
      K(x,y * K(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(2952(a,1),375(a,1)),flip(b)].">
      <j1 rule="para" parents="2952 375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3016">
    <literal><![CDATA[
      K(x,y \ T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(683(a,1),3015(a,1,2))].">
      <j1 rule="para" parents="683 3015"/>
    </justification>
  </clause>

  <clause id="3017">
    <literal><![CDATA[
      K(x,y \ (x \ (z * x))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(22(a,1),3016(a,1,2,2))].">
      <j1 rule="para" parents="22 3016"/>
    </justification>
  </clause>

  <clause id="3018">
    <literal><![CDATA[
      K(x,y \ R(T(z,x),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ R(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(27(a,2),3016(a,1,2,2))].">
      <j1 rule="para" parents="27 3016"/>
    </justification>
  </clause>

  <clause id="3019">
    <literal><![CDATA[
      K(L(x,K(y,z),u),y) = K(K(y,z) * x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2774,a(flip),b,2960,a)].">
      <j1 rule="hyper" parents="65 2774 2960"/>
    </justification>
  </clause>

  <clause id="3020">
    <literal><![CDATA[
      K(L(x,K(y,z),u),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(250,a,2957,a(flip),b,3019,a),flip(a)].">
      <j1 rule="hyper" parents="250 2957 3019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3022">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,y) = K(K(y,z) \ (x \ u),y)
    ]]></literal>
    <justification jstring="[para(239(a,1),3020(a,1,1))].">
      <j1 rule="para" parents="239 3020"/>
    </justification>
  </clause>

  <clause id="3024">
    <literal><![CDATA[
      K(x \ (y \ (z * y)),y) = K(x \ z,y)
    ]]></literal>
    <justification jstring="[hyper(2998,a,xx),flip(a)].">
      <j1 rule="hyper" parents="2998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3026">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * z) \ z) = u
    ]]></literal>
    <justification jstring="[para(11(a,1),2999(a,1,2,1,1))].">
      <j1 rule="para" parents="11 2999"/>
    </justification>
  </clause>

  <clause id="3028">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(3002(a,2),2836(a,1))].">
      <j1 rule="para" parents="3002 2836"/>
    </justification>
  </clause>

  <clause id="3029">
    <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),3028(a,1,1))].">
      <j1 rule="para" parents="25 3028"/>
    </justification>
  </clause>

  <clause id="3030">
    <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),3028(a,1,2))].">
      <j1 rule="para" parents="27 3028"/>
    </justification>
  </clause>

  <clause id="3031">
    <literal><![CDATA[
      K(T(x,y),y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(106(a,1),3028(a,1,2))].">
      <j1 rule="para" parents="106 3028"/>
    </justification>
  </clause>

  <clause id="3032">
    <literal><![CDATA[
      K(x,T(y,R(T(x,z),u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(178(a,1),3028(a,1,1))].">
      <j1 rule="para" parents="178 3028"/>
    </justification>
  </clause>

  <clause id="3033">
    <literal><![CDATA[
      K(x,T(T(y,z),z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(2805(a,1),3028(a,1))].">
      <j1 rule="para" parents="2805 3028"/>
    </justification>
  </clause>

  <clause id="3034">
    <literal><![CDATA[
      K(T(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(2907(a,1),3028(a,1))].">
      <j1 rule="para" parents="2907 3028"/>
    </justification>
  </clause>

  <clause id="3035">
    <literal><![CDATA[
      K(L(x,T(x,y) \ 1,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u) = w
    ]]></literal>
    <justification jstring="[para(3002(a,1),3028(a,1))].">
      <j1 rule="para" parents="3002 3028"/>
    </justification>
  </clause>

  <clause id="3036">
    <literal><![CDATA[
      K(x,T(y \ z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(106(a,1),3033(a,1,2,1))].">
      <j1 rule="para" parents="106 3033"/>
    </justification>
  </clause>

  <clause id="3037">
    <literal><![CDATA[
      K(x \ y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(2788(a,1),3033(a,1))].">
      <j1 rule="para" parents="2788 3033"/>
    </justification>
  </clause>

  <clause id="3038">
    <literal><![CDATA[
      T(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(2803(a,1),3034(a,1))].">
      <j1 rule="para" parents="2803 3034"/>
    </justification>
  </clause>

  <clause id="3039">
    <literal><![CDATA[
      K(x,T(y,x * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(2787(a,2),3034(a,1))].">
      <j1 rule="para" parents="2787 3034"/>
    </justification>
  </clause>

  <clause id="3040">
    <literal><![CDATA[
      K(x,y \ (z \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z \ 1,y)) = u
    ]]></literal>
    <justification jstring="[para(2829(a,1),3034(a,1))].">
      <j1 rule="para" parents="2829 3034"/>
    </justification>
  </clause>

  <clause id="3041">
    <literal><![CDATA[
      K(x,T(y,z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y \ 1,z)) = u
    ]]></literal>
    <justification jstring="[para(2482(a,2),3038(a,1))].">
      <j1 rule="para" parents="2482 3038"/>
    </justification>
  </clause>

  <clause id="3042">
    <literal><![CDATA[
      K(x,T(y,y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(2679(a,2),3038(a,1))].">
      <j1 rule="para" parents="2679 3038"/>
    </justification>
  </clause>

  <clause id="3043">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(2866(a,2),3038(a,1))].">
      <j1 rule="para" parents="2866 3038"/>
    </justification>
  </clause>

  <clause id="3044">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(x,z)) = u
    ]]></literal>
    <justification jstring="[para(2883(a,2),3038(a,1))].">
      <j1 rule="para" parents="2883 3038"/>
    </justification>
  </clause>

  <clause id="3045">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w / R(T(x,y),z,u)) = v5
    ]]></literal>
    <justification jstring="[para(178(a,1),3031(a,1,1))].">
      <j1 rule="para" parents="178 3031"/>
    </justification>
  </clause>

  <clause id="3046">
    <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(2845(a,1),3037(a,1,2))].">
      <j1 rule="para" parents="2845 3037"/>
    </justification>
  </clause>

  <clause id="3047">
    <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(460(a,2),3042(a,1))].">
      <j1 rule="para" parents="460 3042"/>
    </justification>
  </clause>

  <clause id="3048">
    <literal><![CDATA[
      K(x,T(y,z \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(2993(a,1),3042(a,1))].">
      <j1 rule="para" parents="2993 3042"/>
    </justification>
  </clause>

  <clause id="3049">
    <literal><![CDATA[
      K(x,T(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(2844(a,1),3048(a,1))].">
      <j1 rule="para" parents="2844 3048"/>
    </justification>
  </clause>

  <clause id="3050">
    <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(2778(a,1),3032(a,1))].">
      <j1 rule="para" parents="2778 3032"/>
    </justification>
  </clause>

  <clause id="3051">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) / w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w \ R(T(x,y),z,u)) = v5
    ]]></literal>
    <justification jstring="[para(2905(a,1),3032(a,1))].">
      <j1 rule="para" parents="2905 3032"/>
    </justification>
  </clause>

  <clause id="3054">
    <literal><![CDATA[
      K(x,(x * y) \ (z * x)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(3017,a,2756,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="3017 2756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3055">
    <literal><![CDATA[
      K(x,(x \ y) \ z) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[para(10(a,1),3054(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 3054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3056">
    <literal><![CDATA[
      K(x,y \ (((x \ y) * z) * x)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),3055(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 3055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3057">
    <literal><![CDATA[
      K(x,(y * z) \ z) = K(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(3026,a,2849,a)].">
      <j1 rule="hyper" parents="3026 2849"/>
    </justification>
  </clause>

  <clause id="3058">
    <literal><![CDATA[
      K(x,T(y,(z \ u) \ x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(2994(a,2),3049(a,1))].">
      <j1 rule="para" parents="2994 3049"/>
    </justification>
  </clause>

  <clause id="3059">
    <literal><![CDATA[
      K(x,T(y \ (x * z),z)) = K(x,z / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(65,a,2905,a(flip),b,2757,a),flip(a)].">
      <j1 rule="hyper" parents="65 2905 2757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3060">
    <literal><![CDATA[
      K(x,(x * y) / z) = K(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,2931,a(flip),b,3059,a)].">
      <j1 rule="hyper" parents="65 2931 3059"/>
    </justification>
  </clause>

  <clause id="3061">
    <literal><![CDATA[
      K(x,y / (x \ z)) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(2728,a,3060,a),flip(a)].">
      <j1 rule="hyper" parents="2728 3060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3062">
    <literal><![CDATA[
      K(x,(x \ y) / (x \ z)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(10(a,1),3060(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 3060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3063">
    <literal><![CDATA[
      K(x,((x * y) / z) \ x) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(9(a,1),3061(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 3061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3064">
    <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),2784(a,2,2))].">
      <j1 rule="para" parents="27 2784"/>
    </justification>
  </clause>

  <clause id="3066">
    <literal><![CDATA[
      T(x,y) * (L(T(x,y),z,x) \ u) = x * (L(x,z,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(116,a,2851,a(flip),b,2407,a)].">
      <j1 rule="hyper" parents="116 2851 2407"/>
    </justification>
  </clause>

  <clause id="3070">
    <literal><![CDATA[
      T(x,R((y * z) / y,u,w)) = x * K(T(x,y),R(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(250,a,2810,a,b,2935,a),flip(a)].">
      <j1 rule="hyper" parents="250 2810 2935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3072">
    <literal><![CDATA[
      T(x,y) * K(y * R(x,z,u),x) = R(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(2996(a,1),2359(a,1,2))].">
      <j1 rule="para" parents="2996 2359"/>
    </justification>
  </clause>

  <clause id="3073">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,y) = K(x \ u,y)
    ]]></literal>
    <justification jstring="[hyper(250,a,2956,a(flip),b,3022,a),flip(a)].">
      <j1 rule="hyper" parents="250 2956 3022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3075">
    <literal><![CDATA[
      K((x * y) \ z,y) = K((y * x) \ z,y)
    ]]></literal>
    <justification jstring="[para(87(a,1),3073(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="87 3073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3076">
    <literal><![CDATA[
      K((K(x,y) * z) \ u,y) = K(z \ u,y)
    ]]></literal>
    <justification jstring="[para(2830(a,1),3073(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2830 3073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3078">
    <literal><![CDATA[
      1 / K((x * y) \ z,x) = K(x,(y * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(170,a,3075,a(flip),b,2366,a)].">
      <j1 rule="hyper" parents="170 3075 2366"/>
    </justification>
  </clause>

  <clause id="3081">
    <literal><![CDATA[
      K(x,(y * x) \ z) = K(x,(x * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(2370,a,3078,a),flip(a)].">
      <j1 rule="hyper" parents="2370 3078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3082">
    <literal><![CDATA[
      K(x,(y * x) \ (z * x)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(250,a,3054,a(flip),b,3081,a),flip(a)].">
      <j1 rule="hyper" parents="250 3054 3081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3083">
    <literal><![CDATA[
      K(x,(y * x) \ z) = K(x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(250,a,2756,a(flip),b,3081,a),flip(a)].">
      <j1 rule="hyper" parents="250 2756 3081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3084">
    <literal><![CDATA[
      K(x,(y / x) \ z) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[para(12(a,1),3082(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 3082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3085">
    <literal><![CDATA[
      K(x,y \ (x \ (y * (z * x)))) = K(x,L(T(z,x),x,y))
    ]]></literal>
    <justification jstring="[para(195(a,1),3083(a,1,2)),flip(a)].">
      <j1 rule="para" parents="195 3083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3087">
    <literal><![CDATA[
      R(K(x,T(y,z)),y * u,w) = K(x,R(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(2781(a,2),3064(a,1,1))].">
      <j1 rule="para" parents="2781 3064"/>
    </justification>
  </clause>

  <clause id="3089">
    <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),3087(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 3087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3090">
    <literal><![CDATA[
      K(x,R(T(y,z),y \ 1,u)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(250,a,272,a(flip),b,3089,a),flip(a)].">
      <j1 rule="hyper" parents="250 272 3089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3091">
    <literal><![CDATA[
      K(x,R(T(y,z),y \ 1,u)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(250,a,2781,a(flip),b,3090,a),flip(a)].">
      <j1 rule="hyper" parents="250 2781 3090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3092">
    <literal><![CDATA[
      K(x,(x * y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(2744(a,1),2719(a,1))].">
      <j1 rule="para" parents="2744 2719"/>
    </justification>
  </clause>

  <clause id="3093">
    <literal><![CDATA[
      L(K(x,y \ ((z \ u) * x)),z \ u,z) = K(x,(z * (y / x)) \ u)
    ]]></literal>
    <justification jstring="[para(3084(a,1),2744(a,1,1))].">
      <j1 rule="para" parents="3084 2744"/>
    </justification>
  </clause>

  <clause id="3097">
    <literal><![CDATA[
      L(K((x \ y) \ (z \ u),y),z \ u,z) = K((z * (y / x)) \ u,y)
    ]]></literal>
    <justification jstring="[para(2740(a,1),2855(a,1,1))].">
      <j1 rule="para" parents="2740 2855"/>
    </justification>
  </clause>

  <clause id="3099">
    <literal><![CDATA[
      K(x * R(y,z,u),y) * K(y,x) = y \ R(y,x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(112,a,3072,a(flip),b,2399,a),flip(a)].">
      <j1 rule="hyper" parents="112 3072 2399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3100">
    <literal><![CDATA[
      K(x,y \ (x \ (y * (z * x)))) = K(x,L(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(250,a,2334,a(flip),b,3085,a),flip(a)].">
      <j1 rule="hyper" parents="250 2334 3085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3101">
    <literal><![CDATA[
      K(x,y \ (x \ (y * (z * x)))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,L(z,x,y)) = u
    ]]></literal>
    <justification jstring="[para(3085(a,2),2380(a,1))].">
      <j1 rule="para" parents="3085 2380"/>
    </justification>
  </clause>

  <clause id="3104">
    <literal><![CDATA[
      R(K(x,y),T(y,z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,R(y,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(2916(a,2),3030(a,1))].">
      <j1 rule="para" parents="2916 3030"/>
    </justification>
  </clause>

  <clause id="3105">
    <literal><![CDATA[
      R(K(x,y),y * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,R(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(103(a,1),3104(a,1,2,1))].">
      <j1 rule="para" parents="103 3104"/>
    </justification>
  </clause>

  <clause id="3106">
    <literal><![CDATA[
      L(K(x,y),z * T(x,u),w) = K(L(x,z,w),y)
    ]]></literal>
    <justification jstring="[hyper(250,a,2910,a(flip),b,2919,a),flip(a)].">
      <j1 rule="hyper" parents="250 2910 2919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3108">
    <literal><![CDATA[
      L(K(x,y),x * z,u) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(104(a,1),3106(a,1,2))].">
      <j1 rule="para" parents="104 3106"/>
    </justification>
  </clause>

  <clause id="3109">
    <literal><![CDATA[
      K(L(x,y,z),(z \ u) \ (x * y)) = K(x,u \ (z * (x * y)))
    ]]></literal>
    <justification jstring="[hyper(65,a,2743,a(flip),b,3108,a),flip(a)].">
      <j1 rule="hyper" parents="65 2743 3108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3110">
    <literal><![CDATA[
      K(L(x,T(x,y) \ 1,z),u) = L(K(x,u),K(y,x),z)
    ]]></literal>
    <justification jstring="[para(2282(a,2),3108(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2282 3108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3111">
    <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(2906(a,1),3108(a,1,1))].">
      <j1 rule="para" parents="2906 3108"/>
    </justification>
  </clause>

  <clause id="3112">
    <literal><![CDATA[
      L(K(x,y),K(z,x),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3035,a,3110,a),flip(a)].">
      <j1 rule="hyper" parents="3035 3110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3113">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,u) = x * (K(y,z) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(116,a,3112,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="116 3112 18"/>
    </justification>
  </clause>

  <clause id="3115">
    <literal><![CDATA[
      R(x,K(y,z),K(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(370,a,3113,a)].">
      <j1 rule="hyper" parents="370 3113"/>
    </justification>
  </clause>

  <clause id="3116">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,u) = x * (K(z,u) * K(y,z))
    ]]></literal>
    <justification jstring="[para(1061(a,2),3113(a,2,2))].">
      <j1 rule="para" parents="1061 3113"/>
    </justification>
  </clause>

  <clause id="3117">
    <literal><![CDATA[
      T(x * K(y,z),K(z,u)) = T(x,K(z,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(2882,a,2979,a),flip(a)].">
      <j1 rule="hyper" parents="2882 2979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3118">
    <literal><![CDATA[
      T(x * K(y,z),K(z,y)) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(250,a,2519,a(flip),b,3117,a),flip(a)].">
      <j1 rule="hyper" parents="250 2519 3117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3119">
    <literal><![CDATA[
      T(x * K(y,z),K(y,z)) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(65,a,2886,a,b,3118,a)].">
      <j1 rule="hyper" parents="65 2886 3118"/>
    </justification>
  </clause>

  <clause id="3120">
    <literal><![CDATA[
      T(K(x,y) * z,K(y,x)) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(42,a,2887,a,b,3118,a)].">
      <j1 rule="hyper" parents="42 2887 3118"/>
    </justification>
  </clause>

  <clause id="3121">
    <literal><![CDATA[
      T(K(x,y) * z,K(x,y)) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(42,a,2517,a,b,3118,a)].">
      <j1 rule="hyper" parents="42 2517 3118"/>
    </justification>
  </clause>

  <clause id="3123">
    <literal><![CDATA[
      T(K(x,y) * (z * K(y,u)),K(y,u)) = K(y,u) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(2718(a,1),3119(a,1,1))].">
      <j1 rule="para" parents="2718 3119"/>
    </justification>
  </clause>

  <clause id="3124">
    <literal><![CDATA[
      T(K(x * y,x) * z,K(x,y)) = z * K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,2889,a(flip),b,3120,a)].">
      <j1 rule="hyper" parents="65 2889 3120"/>
    </justification>
  </clause>

  <clause id="3125">
    <literal><![CDATA[
      x / K(y,z) = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2526,a(flip),b,3121,a)].">
      <j1 rule="hyper" parents="65 2526 3121"/>
    </justification>
  </clause>

  <clause id="3126">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,y) = x
    ]]></literal>
    <justification jstring="[hyper(115,a,3121,a(flip),b,2526,a(flip))].">
      <j1 rule="hyper" parents="115 3121 2526"/>
    </justification>
  </clause>

  <clause id="3127">
    <literal><![CDATA[
      (K(x,y) \ z) * K(x,y) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(10(a,1),3121(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 3121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3129">
    <literal><![CDATA[
      (x * K(y,z)) \ x = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(409,a,3125,a)].">
      <j1 rule="hyper" parents="409 3125"/>
    </justification>
  </clause>

  <clause id="3130">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,y))) * K(z,y) = x * K(u,y)
    ]]></literal>
    <justification jstring="[hyper(115,a,3116,a(flip),b,3125,a)].">
      <j1 rule="hyper" parents="115 3116 3125"/>
    </justification>
  </clause>

  <clause id="3132">
    <literal><![CDATA[
      (x * T(y,z)) * K(z,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(115,a,2637,a(flip),b,3125,a)].">
      <j1 rule="hyper" parents="115 2637 3125"/>
    </justification>
  </clause>

  <clause id="3133">
    <literal><![CDATA[
      (x * (y * z)) * K(z,L(y,z,x)) = x * (z * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2835,a(flip),b,3125,a),flip(a)].">
      <j1 rule="hyper" parents="65 2835 3125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3134">
    <literal><![CDATA[
      x * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      u * K(z,y) = x
    ]]></literal>
    <justification jstring="[para(3125(a,1),124(a,1))].">
      <j1 rule="para" parents="3125 124"/>
    </justification>
  </clause>

  <clause id="3135">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,y) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(3125(a,1),211(a,1,1))].">
      <j1 rule="para" parents="3125 211"/>
    </justification>
  </clause>

  <clause id="3136">
    <literal><![CDATA[
      (x * K(y,z)) \ x != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = u
    ]]></literal>
    <justification jstring="[para(3125(a,1),223(a,1,1))].">
      <j1 rule="para" parents="3125 223"/>
    </justification>
  </clause>

  <clause id="3137">
    <literal><![CDATA[
      R((x / y) * K(z,u),K(u,z),y) != w
    ]]></literal>
    <literal><![CDATA[
      x / (K(u,z) * y) = w
    ]]></literal>
    <justification jstring="[para(3125(a,1),425(a,1,1))].">
      <j1 rule="para" parents="3125 425"/>
    </justification>
  </clause>

  <clause id="3139">
    <literal><![CDATA[
      (x * K(y,z)) * T(z,y) = x * z
    ]]></literal>
    <justification jstring="[para(3126(a,1),2633(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3126 2633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3142">
    <literal><![CDATA[
      (x * T(x \ y,z)) \ y = K(z,x \ y)
    ]]></literal>
    <justification jstring="[para(2640(a,2),3129(a,1,1))].">
      <j1 rule="para" parents="2640 3129"/>
    </justification>
  </clause>

  <clause id="3143">
    <literal><![CDATA[
      (x * (y * K(z,y))) \ (x * y) = K(y,z)
    ]]></literal>
    <justification jstring="[para(2659(a,1),3129(a,1,1))].">
      <j1 rule="para" parents="2659 3129"/>
    </justification>
  </clause>

  <clause id="3144">
    <literal><![CDATA[
      T(x * K(y,z),K(z,u)) \ T(x,K(z,u)) = K(z,y)
    ]]></literal>
    <justification jstring="[para(3117(a,2),3129(a,1,1))].">
      <j1 rule="para" parents="3117 3129"/>
    </justification>
  </clause>

  <clause id="3145">
    <literal><![CDATA[
      (x * (y \ z)) * K(y,z / y) = x * (z / y)
    ]]></literal>
    <justification jstring="[para(106(a,1),3132(a,1,1,2))].">
      <j1 rule="para" parents="106 3132"/>
    </justification>
  </clause>

  <clause id="3147">
    <literal><![CDATA[
      (x * T(y,z)) * T(z,y) = (x * y) * z
    ]]></literal>
    <justification jstring="[para(3132(a,1),2633(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3132 2633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3149">
    <literal><![CDATA[
      (x * K(y,z)) * z = (x * z) * K(y,z)
    ]]></literal>
    <justification jstring="[para(3139(a,1),3132(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3139 3132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3151">
    <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(2488(a,1),3136(a,1,1))].">
      <j1 rule="para" parents="2488 3136"/>
    </justification>
  </clause>

  <clause id="3152">
    <literal><![CDATA[
      (x * T(x \ y,z)) \ y != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x \ y) = u
    ]]></literal>
    <justification jstring="[para(2640(a,2),3136(a,1,1))].">
      <j1 rule="para" parents="2640 3136"/>
    </justification>
  </clause>

  <clause id="3154">
    <literal><![CDATA[
      (x * (y * T(y \ (x \ z),u))) \ z = K(u,(x * y) \ z)
    ]]></literal>
    <justification jstring="[para(562(a,1),3142(a,1,1))].">
      <j1 rule="para" parents="562 3142"/>
    </justification>
  </clause>

  <clause id="3155">
    <literal><![CDATA[
      ((x * T(x \ y,z)) * u) \ (y * u) = K(z,(x * u) \ (y * u))
    ]]></literal>
    <justification jstring="[para(906(a,1),3142(a,1,1))].">
      <j1 rule="para" parents="906 3142"/>
    </justification>
  </clause>

  <clause id="3156">
    <literal><![CDATA[
      (x * ((y \ (x \ z)) * y)) \ z = K(y,(y * x) \ z)
    ]]></literal>
    <justification jstring="[para(2195(a,1),3142(a,1,1))].">
      <j1 rule="para" parents="2195 3142"/>
    </justification>
  </clause>

  <clause id="3158">
    <literal><![CDATA[
      1 / (x * K(y,x)) = K(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(113,a,3143,a(flip),b,326,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="113 3143 326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3160">
    <literal><![CDATA[
      ((x * y) / T(z,y)) * z = x * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(37,a,766,a,b,3147,a)].">
      <j1 rule="hyper" parents="37 766 3147"/>
    </justification>
  </clause>

  <clause id="3162">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * (z * K(y,z))) = z
    ]]></literal>
    <justification jstring="[hyper(112,a,2659,a(flip),b,3149,a)].">
      <j1 rule="hyper" parents="112 2659 3149"/>
    </justification>
  </clause>

  <clause id="3163">
    <literal><![CDATA[
      (T(x,y) * (x \ z)) * x = T(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[para(3000(a,1),3160(a,1,1))].">
      <j1 rule="para" parents="3000 3160"/>
    </justification>
  </clause>

  <clause id="3164">
    <literal><![CDATA[
      L(T(x,K(y,x)),K(y,x),z) = x
    ]]></literal>
    <justification jstring="[hyper(492,a,3162,a)].">
      <j1 rule="hyper" parents="492 3162"/>
    </justification>
  </clause>

  <clause id="3165">
    <literal><![CDATA[
      L(x,K(y,x),z) = x
    ]]></literal>
    <justification jstring="[para(1981(a,1),3164(a,1,1))].">
      <j1 rule="para" parents="1981 3164"/>
    </justification>
  </clause>

  <clause id="3166">
    <literal><![CDATA[
      (x * K(y,z)) * R(z,u,w) = x * (K(y,z) * R(z,u,w))
    ]]></literal>
    <justification jstring="[para(3165(a,1),313(a,1,2,1))].">
      <j1 rule="para" parents="3165 313"/>
    </justification>
  </clause>

  <clause id="3167">
    <literal><![CDATA[
      (x * ((y * z) / y)) / z = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(3165(a,1),2365(a,1,2))].">
      <j1 rule="para" parents="3165 2365"/>
    </justification>
  </clause>

  <clause id="3168">
    <literal><![CDATA[
      (x / ((y * z) / y)) * K(y,z) = x / z
    ]]></literal>
    <justification jstring="[hyper(412,a,3167,a),flip(a)].">
      <j1 rule="hyper" parents="412 3167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3169">
    <literal><![CDATA[
      x / ((y * z) / y) = (x / z) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(3134,a,3168,a),flip(a)].">
      <j1 rule="hyper" parents="3134 3168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3170">
    <literal><![CDATA[
      (x / (y \ z)) * K(y \ z,y) = x / (z / y)
    ]]></literal>
    <justification jstring="[para(10(a,1),3169(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 3169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3171">
    <literal><![CDATA[
      (x * y) / ((z * y) / z) = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),3169(a,2,1))].">
      <j1 rule="para" parents="11 3169"/>
    </justification>
  </clause>

  <clause id="3172">
    <literal><![CDATA[
      (x / (y * K(z,y))) * y = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,2356,a(flip),b,3171,a)].">
      <j1 rule="hyper" parents="65 2356 3171"/>
    </justification>
  </clause>

  <clause id="3175">
    <literal><![CDATA[
      T(x,y * (z / x)) = T(x,y * (x \ z))
    ]]></literal>
    <justification jstring="[para(3145(a,1),2927(a,1,2))].">
      <j1 rule="para" parents="3145 2927"/>
    </justification>
  </clause>

  <clause id="3176">
    <literal><![CDATA[
      K(x,T(y,z * (u / x))) = K(x,T(y,z * (x \ u)))
    ]]></literal>
    <justification jstring="[para(3145(a,1),2969(a,1,2,2))].">
      <j1 rule="para" parents="3145 2969"/>
    </justification>
  </clause>

  <clause id="3177">
    <literal><![CDATA[
      T(T(x,y) * (x \ z),x) = T(x,y) * (x \ T(z,x))
    ]]></literal>
    <justification jstring="[hyper(200,a,3163,a,b,646,a)].">
      <j1 rule="hyper" parents="200 3163 646"/>
    </justification>
  </clause>

  <clause id="3178">
    <literal><![CDATA[
      (K(x,y) * z) * x = T(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[para(2290(a,1),3163(a,1,1))].">
      <j1 rule="para" parents="2290 3163"/>
    </justification>
  </clause>

  <clause id="3179">
    <literal><![CDATA[
      (K(x,y) * z) * x = K(x,y) * (z * x)
    ]]></literal>
    <justification jstring="[hyper(250,a,2397,a,b,3178,a),flip(a)].">
      <j1 rule="hyper" parents="250 2397 3178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3180">
    <literal><![CDATA[
      T(K(x,y) * z,x) = K(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(200,a,3178,a,b,2289,a)].">
      <j1 rule="hyper" parents="200 3178 2289"/>
    </justification>
  </clause>

  <clause id="3181">
    <literal><![CDATA[
      R(K(x,y),z,x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(1820,a,3179,a)].">
      <j1 rule="hyper" parents="1820 3179"/>
    </justification>
  </clause>

  <clause id="3182">
    <literal><![CDATA[
      L(x,y,K(x,z)) = x
    ]]></literal>
    <justification jstring="[hyper(1812,a,3179,a)].">
      <j1 rule="hyper" parents="1812 3179"/>
    </justification>
  </clause>

  <clause id="3183">
    <literal><![CDATA[
      (K(x,y) * z) * R(x,u,w) = K(x,y) * (z * R(x,u,w))
    ]]></literal>
    <justification jstring="[para(3182(a,1),313(a,1,2,1))].">
      <j1 rule="para" parents="3182 313"/>
    </justification>
  </clause>

  <clause id="3187">
    <literal><![CDATA[
      T(x * K(y,z),z) = T(x,z) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,2618,a(flip),b,3180,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="36 2618 3180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3188">
    <literal><![CDATA[
      K(x,y) * T(K(x,y) \ z,x) = T(z,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),3180(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 3180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3189">
    <literal><![CDATA[
      T(x * K(y,z),y) = T(x,y) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(482,a,3188,a),flip(a)].">
      <j1 rule="hyper" parents="482 3188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3190">
    <literal><![CDATA[
      K(x,y) * (z * T(z \ (K(x,y) \ u),x)) = T(u / z,x) * z
    ]]></literal>
    <justification jstring="[para(3188(a,1),907(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3188 907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3191">
    <literal><![CDATA[
      K(x,T(x * K(y,z),y)) = K(x,x * K(y,z))
    ]]></literal>
    <justification jstring="[para(3189(a,2),2944(a,1,2))].">
      <j1 rule="para" parents="3189 2944"/>
    </justification>
  </clause>

  <clause id="3192">
    <literal><![CDATA[
      K(x,y / (z / x)) = K(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[para(3170(a,1),2949(a,1,2))].">
      <j1 rule="para" parents="3170 2949"/>
    </justification>
  </clause>

  <clause id="3193">
    <literal><![CDATA[
      K(x,(x \ y) / (z / x)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(250,a,3062,a(flip),b,3192,a),flip(a)].">
      <j1 rule="hyper" parents="250 3062 3192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3194">
    <literal><![CDATA[
      K(x,(x \ y) / z) = K(x,y / (z * x))
    ]]></literal>
    <justification jstring="[para(11(a,1),3193(a,1,2,2))].">
      <j1 rule="para" parents="11 3193"/>
    </justification>
  </clause>

  <clause id="3196">
    <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(3130(a,1),3135(a,1,1)),flip(b)].">
      <j1 rule="para" parents="3130 3135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3197">
    <literal><![CDATA[
      T(x,K(y,z)) \ T(x * K(y,u),K(y,z)) = K(y,u)
    ]]></literal>
    <justification jstring="[para(3126(a,1),3144(a,1,1,1))].">
      <j1 rule="para" parents="3126 3144"/>
    </justification>
  </clause>

  <clause id="3198">
    <literal><![CDATA[
      (x * ((y \ (x \ z)) * y)) \ z = K(y,x \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(250,a,2756,a(flip),b,3156,a),flip(a)].">
      <j1 rule="hyper" parents="250 2756 3156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3199">
    <literal><![CDATA[
      T(x,y) * (x \ T(x * z,x)) = T(T(x,y) * z,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),3177(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 3177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3200">
    <literal><![CDATA[
      T(x * K(y,z),K(y,u)) = T(x,K(y,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,3197,a),flip(a)].">
      <j1 rule="hyper" parents="125 3197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3202">
    <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(1009(a,1),3199(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1009 3199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3203">
    <literal><![CDATA[
      T(K(x,y) * z,K(y,u)) = K(x,y) * T(z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(37,a,2626,a(flip),b,3200,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="37 2626 3200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3204">
    <literal><![CDATA[
      K(T(x * K(y \ (z * x),x),x),u) = K(x,T(u,T(z \ y,x) \ x))
    ]]></literal>
    <justification jstring="[para(2859(a,1),3005(a,1,1,1,2))].">
      <j1 rule="para" parents="2859 3005"/>
    </justification>
  </clause>

  <clause id="3205">
    <literal><![CDATA[
      T(x,R(y / (y / z),u,w)) = x * K(T(x,z \ y),R(z,u,w))
    ]]></literal>
    <justification jstring="[para(2089(a,1),3070(a,1,2,1))].">
      <j1 rule="para" parents="2089 3070"/>
    </justification>
  </clause>

  <clause id="3206">
    <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(3111(a,2),3029(a,1))].">
      <j1 rule="para" parents="3111 3029"/>
    </justification>
  </clause>

  <clause id="3211">
    <literal><![CDATA[
      (x * (y * (z * T(z \ (y \ (x \ u)),w)))) \ u = K(w,(x * (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(562(a,1),3154(a,1,1,2))].">
      <j1 rule="para" parents="562 3154"/>
    </justification>
  </clause>

  <clause id="3212">
    <literal><![CDATA[
      K(x,(y * K(x,z)) \ u) = (y * T(y \ u,x)) \ u
    ]]></literal>
    <justification jstring="[para(3188(a,1),3154(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3188 3154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3213">
    <literal><![CDATA[
      K(x,(y * K(x,z)) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(250,a,3142,a(flip),b,3212,a),flip(a)].">
      <j1 rule="hyper" parents="250 3142 3212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3214">
    <literal><![CDATA[
      T(x,(y * K(x,z)) \ u) = T(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(114,a,3213,a,b,2470,a),flip(a)].">
      <j1 rule="hyper" parents="114 3213 2470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3216">
    <literal><![CDATA[
      K(x,(K(y,x) * z) \ u) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(2830(a,1),3213(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2830 3213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3217">
    <literal><![CDATA[
      K(x,(y * K(z,x)) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(3126(a,1),3213(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3126 3213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3218">
    <literal><![CDATA[
      K(x,(y * (z * x)) \ u) = K(x,(y * (x * z)) \ u)
    ]]></literal>
    <justification jstring="[para(3133(a,1),3213(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3133 3213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3219">
    <literal><![CDATA[
      T(T(x,y),T(x,z) \ u) = T(T(x,y),x \ u)
    ]]></literal>
    <justification jstring="[para(2909(a,1),3214(a,1,2,1))].">
      <j1 rule="para" parents="2909 3214"/>
    </justification>
  </clause>

  <clause id="3221">
    <literal><![CDATA[
      K(x,y \ (K(x,z) * u)) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,2760,a(flip),b,3216,a)].">
      <j1 rule="hyper" parents="65 2760 3216"/>
    </justification>
  </clause>

  <clause id="3222">
    <literal><![CDATA[
      K(x,(y * K(z,x)) \ u) = (y * T(y \ u,x)) \ u
    ]]></literal>
    <justification jstring="[hyper(250,a,3142,a,b,3217,a),flip(a)].">
      <j1 rule="hyper" parents="250 3142 3217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3225">
    <literal><![CDATA[
      K(x,y \ (z * K(x,u))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(2902(a,1),3221(a,1,2,2))].">
      <j1 rule="para" parents="2902 3221"/>
    </justification>
  </clause>

  <clause id="3226">
    <literal><![CDATA[
      K(x,y \ (z * (u / x))) = K(x,y \ (z * (x \ u)))
    ]]></literal>
    <justification jstring="[para(3145(a,1),3225(a,1,2,2))].">
      <j1 rule="para" parents="3145 3225"/>
    </justification>
  </clause>

  <clause id="3227">
    <literal><![CDATA[
      T(T(x,y),x \ z) = (T(x,y) \ z) \ z
    ]]></literal>
    <justification jstring="[hyper(301,a,3219,a),flip(a)].">
      <j1 rule="hyper" parents="301 3219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3228">
    <literal><![CDATA[
      T(T(x,x \ y),z) = (T(x,z) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(304,a,3227,a)].">
      <j1 rule="hyper" parents="304 3227"/>
    </justification>
  </clause>

  <clause id="3231">
    <literal><![CDATA[
      (T(x / y,z) \ x) \ x = T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(436(a,1),3228(a,1,1)),flip(a)].">
      <j1 rule="para" parents="436 3228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3233">
    <literal><![CDATA[
      K(x,T(T(y / z,u),y)) = K(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[para(3231(a,1),2779(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3231 2779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3234">
    <literal><![CDATA[
      K(x,T(y \ z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(3233(a,1),3033(a,1))].">
      <j1 rule="para" parents="3233 3033"/>
    </justification>
  </clause>

  <clause id="3235">
    <literal><![CDATA[
      K(x,(y * K(z,x)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ u) = w
    ]]></literal>
    <justification jstring="[para(3222(a,2),3152(a,1))].">
      <j1 rule="para" parents="3222 3152"/>
    </justification>
  </clause>

  <clause id="3236">
    <literal><![CDATA[
      K(T(x,y),(z * K(u,x)) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(T(x,y),z \ w) = v5
    ]]></literal>
    <justification jstring="[para(2815(a,1),3235(a,1,2,1,2))].">
      <j1 rule="para" parents="2815 3235"/>
    </justification>
  </clause>

  <clause id="3238">
    <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,3057,a(flip),b,3226,a),flip(a)].">
      <j1 rule="hyper" parents="65 3057 3226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3240">
    <literal><![CDATA[
      R(x,K(y,z),R(z,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(370,a,3166,a)].">
      <j1 rule="hyper" parents="370 3166"/>
    </justification>
  </clause>

  <clause id="3241">
    <literal><![CDATA[
      R(K(x,y),z,R(x,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(1820,a,3183,a)].">
      <j1 rule="hyper" parents="1820 3183"/>
    </justification>
  </clause>

  <clause id="3242">
    <literal><![CDATA[
      K(x,(y * R(x,z,u)) / w) = K(x,y / (w / R(x,z,u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,2575,a(flip),b,3241,a)].">
      <j1 rule="hyper" parents="65 2575 3241"/>
    </justification>
  </clause>

  <clause id="3244">
    <literal><![CDATA[
      L(T(K(x,(y \ z) \ u),w),u,y) = K(x,T(z \ (y * u),w))
    ]]></literal>
    <justification jstring="[hyper(250,a,2781,a,b,2748,a),flip(a)].">
      <j1 rule="hyper" parents="250 2781 2748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3245">
    <literal><![CDATA[
      L(K(x,T(y \ z,u)),y \ z,y) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T((z \ y) \ 1,u)) = w
    ]]></literal>
    <justification jstring="[para(2796(a,2),3041(a,1))].">
      <j1 rule="para" parents="2796 3041"/>
    </justification>
  </clause>

  <clause id="3246">
    <literal><![CDATA[
      K(R(x,y,R(x,z,u)),T(w,y * R(x,z,u))) = K(x,T(w,y))
    ]]></literal>
    <justification jstring="[hyper(250,a,2805,a(flip),b,2816,a),flip(a)].">
      <j1 rule="hyper" parents="250 2805 2816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3247">
    <literal><![CDATA[
      L(K(x,T(T(y,z * u),u)),u,z) = K((z * u) / (z * (x \ u)),y)
    ]]></literal>
    <justification jstring="[para(2783(a,1),3010(a,1,1))].">
      <j1 rule="para" parents="2783 3010"/>
    </justification>
  </clause>

  <clause id="3248">
    <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(339(a,1),3109(a,2,2))].">
      <j1 rule="para" parents="339 3109"/>
    </justification>
  </clause>

  <clause id="3249">
    <literal><![CDATA[
      K(T(x,y),y \ z) = K(x,z / (y * K(u,x)))
    ]]></literal>
    <justification jstring="[hyper(3236,a,2934,a)].">
      <j1 rule="hyper" parents="3236 2934"/>
    </justification>
  </clause>

  <clause id="3250">
    <literal><![CDATA[
      K(x,y / (z * K(u,x))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(3031,a,3249,a),flip(a)].">
      <j1 rule="hyper" parents="3031 3249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3251">
    <literal><![CDATA[
      K(x,y / (z * x)) = K(x,y / (x * z))
    ]]></literal>
    <justification jstring="[para(87(a,1),3250(a,1,2,2))].">
      <j1 rule="para" parents="87 3250"/>
    </justification>
  </clause>

  <clause id="3252">
    <literal><![CDATA[
      K(x,y / (z * K(x,u))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(3126(a,1),3250(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3126 3250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3253">
    <literal><![CDATA[
      K(x,R(y / x,x,z)) = K(x,(y * z) / (z * x))
    ]]></literal>
    <justification jstring="[para(101(a,2),3251(a,2,2)),flip(a)].">
      <j1 rule="para" parents="101 3251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3254">
    <literal><![CDATA[
      K(x,R(x \ y,x,z)) = K(x,(y * z) / (z * x))
    ]]></literal>
    <justification jstring="[hyper(65,a,2337,a(flip),b,3253,a)].">
      <j1 rule="hyper" parents="65 2337 3253"/>
    </justification>
  </clause>

  <clause id="3255">
    <literal><![CDATA[
      L(K(x,T((y \ z) \ u,w)),u,y) = K(x,T(z \ (y * u),w))
    ]]></literal>
    <justification jstring="[para(2781(a,2),3244(a,1,1))].">
      <j1 rule="para" parents="2781 3244"/>
    </justification>
  </clause>

  <clause id="3256">
    <literal><![CDATA[
      K(x,T((y \ z) \ x,u)) = K(x,T(z \ (y * x),u))
    ]]></literal>
    <justification jstring="[hyper(2660,a,3255,a)].">
      <j1 rule="hyper" parents="2660 3255"/>
    </justification>
  </clause>

  <clause id="3257">
    <literal><![CDATA[
      K(x,y / (x / ((z * y) \ 1))) = y / (K(z \ (x \ 1),x) * y)
    ]]></literal>
    <justification jstring="[para(2852(a,1),2552(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2852 2552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3258">
    <literal><![CDATA[
      K(x,R(y,z * K(y,u),w)) = K(x,R(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(3104,a,2968,a),flip(a)].">
      <j1 rule="hyper" parents="3104 2968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3259">
    <literal><![CDATA[
      K(x,R(y,T(z,y),u)) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(2268(a,1),3258(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2268 3258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3260">
    <literal><![CDATA[
      K(x,R(y,K(y,z) * u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(2792(a,1),3258(a,1,2,2))].">
      <j1 rule="para" parents="2792 3258"/>
    </justification>
  </clause>

  <clause id="3261">
    <literal><![CDATA[
      R(K(x,y),z * y,u) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,2579,a,b,3259,a)].">
      <j1 rule="hyper" parents="65 2579 3259"/>
    </justification>
  </clause>

  <clause id="3262">
    <literal><![CDATA[
      K(R(x,K(x,y) * z,u),w) = (v5 * K(w,R(x,z,u))) \ v5
    ]]></literal>
    <justification jstring="[para(3260(a,1),3129(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3260 3129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3263">
    <literal><![CDATA[
      K(R(x,K(x,y) * z,u),w) = K(R(x,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(250,a,3129,a(flip),b,3262,a),flip(a)].">
      <j1 rule="hyper" parents="250 3129 3262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3264">
    <literal><![CDATA[
      K(R(x,K(y,x) * z,u),w) = K(R(x,z,u),w)
    ]]></literal>
    <justification jstring="[para(2426(a,1),3263(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2426 3263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3265">
    <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(733(a,1),3012(a,2,1))].">
      <j1 rule="para" parents="733 3012"/>
    </justification>
  </clause>

  <clause id="3266">
    <literal><![CDATA[
      T(K(x,y) * T(z,K(y,u)),K(y,u)) = K(y,u) * (K(x,y) * (K(y,u) \ z))
    ]]></literal>
    <justification jstring="[para(3127(a,1),3123(a,1,1,2))].">
      <j1 rule="para" parents="3127 3123"/>
    </justification>
  </clause>

  <clause id="3267">
    <literal><![CDATA[
      x / (K(y,z) * R(z,u,w)) = (x / R(z,u,w)) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(3137,a,3240,a)].">
      <j1 rule="hyper" parents="3137 3240"/>
    </justification>
  </clause>

  <clause id="3268">
    <literal><![CDATA[
      (((x / y) * T(y,z)) * u) \ (x * u) = K(z,((x / y) * u) \ (x * u))
    ]]></literal>
    <justification jstring="[para(79(a,1),3155(a,1,1,1,2,1))].">
      <j1 rule="para" parents="79 3155"/>
    </justification>
  </clause>

  <clause id="3269">
    <literal><![CDATA[
      K(x,y) * (z * T(z \ (K(x,y) \ u),x)) = z * T(z \ u,x)
    ]]></literal>
    <justification jstring="[hyper(250,a,321,a(flip),b,3190,a),flip(a)].">
      <j1 rule="hyper" parents="250 321 3190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3270">
    <literal><![CDATA[
      K(x,y / (x / ((z * y) \ 1))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ (x \ 1)) = u
    ]]></literal>
    <justification jstring="[para(3257(a,2),2431(a,1))].">
      <j1 rule="para" parents="3257 2431"/>
    </justification>
  </clause>

  <clause id="3271">
    <literal><![CDATA[
      K(x,y / (x * (z * y))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ (x \ 1)) = u
    ]]></literal>
    <justification jstring="[para(2610(a,1),3270(a,1))].">
      <j1 rule="para" parents="2610 3270"/>
    </justification>
  </clause>

  <clause id="3272">
    <literal><![CDATA[
      K(x,y / ((z * y) * x)) = K(x,z \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(3271,a,3251,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="3271 3251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3273">
    <literal><![CDATA[
      K(x,(y / z) \ (x \ 1)) = K(x,z / (y * x))
    ]]></literal>
    <justification jstring="[para(12(a,1),3272(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="12 3272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3274">
    <literal><![CDATA[
      K(x,(y * (z / y)) / ((z / y) * x)) = K(x,((y \ z) / z) \ (x \ 1))
    ]]></literal>
    <justification jstring="[para(2109(a,1),3272(a,1,2,2,1))].">
      <j1 rule="para" parents="2109 3272"/>
    </justification>
  </clause>

  <clause id="3275">
    <literal><![CDATA[
      K(x,y) * (z * T(z \ u,x)) = z * T(z \ (K(x,y) * u),x)
    ]]></literal>
    <justification jstring="[para(9(a,1),3269(a,1,2,2,1,2))].">
      <j1 rule="para" parents="9 3269"/>
    </justification>
  </clause>

  <clause id="3276">
    <literal><![CDATA[
      ((1 / x) * y) * T(((1 / x) * y) \ (K(z,u) * y),z) = K(z,u) * (K(x,z) * y)
    ]]></literal>
    <justification jstring="[para(2456(a,1),3275(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2456 3275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3277">
    <literal><![CDATA[
      (x * y) \ (y * T(x,z)) = K(y,x) * K(x,z)
    ]]></literal>
    <justification jstring="[para(3115(a,1),2649(a,1,1))].">
      <j1 rule="para" parents="3115 2649"/>
    </justification>
  </clause>

  <clause id="3278">
    <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(250,a,3099,a(flip),b,3277,a),flip(a)].">
      <j1 rule="hyper" parents="250 3099 3277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3281">
    <literal><![CDATA[
      ((x * y) * T(z,y)) / (y * T(z,y)) = R(x,y * K(z,y),z)
    ]]></literal>
    <justification jstring="[para(2633(a,1),2720(a,1,2))].">
      <j1 rule="para" parents="2633 2720"/>
    </justification>
  </clause>

  <clause id="3282">
    <literal><![CDATA[
      R(x,y * K(z,y),z) = R(x,y,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(371,a,3281,a),flip(a)].">
      <j1 rule="hyper" parents="371 3281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3283">
    <literal><![CDATA[
      R(x,y \ z,T(y,y \ z)) = R(x,z / y,y)
    ]]></literal>
    <justification jstring="[para(2320(a,1),3282(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2320 3282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3285">
    <literal><![CDATA[
      R(K(x,T(T(y,z),z * u)),z,u) = (z * u) \ ((z * K(x,y)) * u)
    ]]></literal>
    <justification jstring="[para(2781(a,2),2925(a,1,1))].">
      <j1 rule="para" parents="2781 2925"/>
    </justification>
  </clause>

  <clause id="3286">
    <literal><![CDATA[
      K(R(x,y,z),u * K(x,w)) = K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(250,a,2490,a(flip),b,2963,a),flip(a)].">
      <j1 rule="hyper" parents="250 2490 2963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3287">
    <literal><![CDATA[
      K(R(x,y,z),u * K(w,x)) = K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(3126(a,1),3286(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3126 3286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3288">
    <literal><![CDATA[
      K((x * (y / z)) \ u,y) = K((x * (z \ y)) \ u,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2855,a(flip),b,3097,a),flip(a)].">
      <j1 rule="hyper" parents="65 2855 3097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3289">
    <literal><![CDATA[
      K((x * (y / x)) \ z,y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),3288(a,2,1,1))].">
      <j1 rule="para" parents="10 3288"/>
    </justification>
  </clause>

  <clause id="3290">
    <literal><![CDATA[
      K(x \ (x * y),x) = K(K(z \ x,z) * y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,2766,a(flip),b,3289,a),flip(a)].">
      <j1 rule="hyper" parents="65 2766 3289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3292">
    <literal><![CDATA[
      K(K(x \ y,x) * z,y) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,617,a(flip),b,3290,a),flip(a)].">
      <j1 rule="hyper" parents="65 617 3290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3294">
    <literal><![CDATA[
      (K(x \ y,x) * z) * K(z,y) = T(K(x \ y,x) * z,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,3292,a(flip),b,2272,a(flip))].">
      <j1 rule="hyper" parents="116 3292 2272"/>
    </justification>
  </clause>

  <clause id="3295">
    <literal><![CDATA[
      T(K(x \ y,x) * z,y) = K(x \ y,x) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(2661,a,3294,a),flip(a)].">
      <j1 rule="hyper" parents="2661 3294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3296">
    <literal><![CDATA[
      T(K(x \ (y * x),x) * z,y * x) = K(y,x) * T(z,y * x)
    ]]></literal>
    <justification jstring="[para(2343(a,1),3295(a,2,1))].">
      <j1 rule="para" parents="2343 3295"/>
    </justification>
  </clause>

  <clause id="3297">
    <literal><![CDATA[
      T(K(x,y) * z,x * y) = K(x,y) * T(z,x * y)
    ]]></literal>
    <justification jstring="[para(2343(a,1),3296(a,1,1,1))].">
      <j1 rule="para" parents="2343 3296"/>
    </justification>
  </clause>

  <clause id="3298">
    <literal><![CDATA[
      T(x * K(y,z),z * y) = T(x,z * y) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,2618,a(flip),b,3297,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="36 2618 3297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3299">
    <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(3298(a,2),333(a,2,2))].">
      <j1 rule="para" parents="3298 333"/>
    </justification>
  </clause>

  <clause id="3300">
    <literal><![CDATA[
      L(K(x,T(T(y,z),u * z)),z,u) = K((u * z) / (u * (x \ z)),y)
    ]]></literal>
    <justification jstring="[para(23(a,1),3247(a,1,1,2))].">
      <j1 rule="para" parents="23 3247"/>
    </justification>
  </clause>

  <clause id="3301">
    <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(3285(a,1),2571(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3285 2571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3302">
    <literal><![CDATA[
      L(K(x,T(T(y,z),u * z)),z,u) = (u * (K(x,y) * z)) / (u * z)
    ]]></literal>
    <justification jstring="[hyper(250,a,2615,a(flip),b,3300,a),flip(a)].">
      <j1 rule="hyper" parents="250 2615 3300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3303">
    <literal><![CDATA[
      L(K(T(T(x,y),z * y),u),y,z) * w = K((z * y) / (z * (u \ y)),x) \ w
    ]]></literal>
    <justification jstring="[para(3300(a,1),2609(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3300 2609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3304">
    <literal><![CDATA[
      L(T(K(x,T(y,z * u)),u),u,z) = (z * (K(x,y) * u)) / (z * u)
    ]]></literal>
    <justification jstring="[para(2794(a,1),3302(a,1,1))].">
      <j1 rule="para" parents="2794 3302"/>
    </justification>
  </clause>

  <clause id="3305">
    <literal><![CDATA[
      a(x * K(y * z,x),y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,1549,a(flip),b,2358,a),flip(a)].">
      <j1 rule="hyper" parents="65 1549 2358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3307">
    <literal><![CDATA[
      T(x,y \ R(y,z,x)) = x
    ]]></literal>
    <justification jstring="[para(3305(a,1),1698(a,1,2))].">
      <j1 rule="para" parents="3305 1698"/>
    </justification>
  </clause>

  <clause id="3308">
    <literal><![CDATA[
      T(x \ R(x,y,z),z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(114,a,3307,a,b,2053,a)].">
      <j1 rule="hyper" parents="114 3307 2053"/>
    </justification>
  </clause>

  <clause id="3309">
    <literal><![CDATA[
      T(((x * (y / z)) \ (x * y)) \ R((x * (y / z)) \ (x * y),u,w),w) = ((x * (y / z)) \ (x * y)) \ L(R(z,u,w),y / z,x)
    ]]></literal>
    <justification jstring="[para(473(a,1),3308(a,2,2))].">
      <j1 rule="para" parents="473 3308"/>
    </justification>
  </clause>

  <clause id="3310">
    <literal><![CDATA[
      (x * (y * ((x \ z) / y))) / z = K(y,((x * y) / z) \ 1)
    ]]></literal>
    <justification jstring="[para(10(a,1),2551(a,1,1,2,2,1))].">
      <j1 rule="para" parents="10 2551"/>
    </justification>
  </clause>

  <clause id="3311">
    <literal><![CDATA[
      (x * (y * ((x \ z) / y))) / z = K(y,z / (x * y))
    ]]></literal>
    <justification jstring="[hyper(250,a,2468,a(flip),b,3310,a),flip(a)].">
      <j1 rule="hyper" parents="250 2468 3310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3312">
    <literal><![CDATA[
      R(K(x,(y / z) / (u * x)),y / z,z) = ((u * (x * ((u \ (y / z)) / x))) * z) / y
    ]]></literal>
    <justification jstring="[para(3311(a,1),379(a,1,1))].">
      <j1 rule="para" parents="3311 379"/>
    </justification>
  </clause>

  <clause id="3313">
    <literal><![CDATA[
      (x * K(y,z \ 1)) * z = (x * z) * K(y,z \ 1)
    ]]></literal>
    <justification jstring="[para(2461(a,1),2600(a,1,1))].">
      <j1 rule="para" parents="2461 2600"/>
    </justification>
  </clause>

  <clause id="3314">
    <literal><![CDATA[
      (x * (y \ 1)) * K(z,(y \ 1) \ 1) = (x * K(z,y)) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(2419(a,1),3313(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2419 3313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3315">
    <literal><![CDATA[
      (x * K(y,z)) * (z \ 1) = (x * (z \ 1)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(2419(a,1),3314(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2419 3314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3316">
    <literal><![CDATA[
      K(x,(T(y \ z,z) / z) \ 1) = T(K(x,y) * z,z) / z
    ]]></literal>
    <justification jstring="[para(2589(a,1),2616(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2589 2616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3317">
    <literal><![CDATA[
      K(x,(T(y \ z,z) / z) \ 1) = z \ T(z * K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(250,a,2168,a(flip),b,3316,a),flip(a)].">
      <j1 rule="hyper" parents="250 2168 3316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3318">
    <literal><![CDATA[
      K(x,y / T(z \ y,y)) = y \ T(y * K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2468,a(flip),b,3317,a)].">
      <j1 rule="hyper" parents="65 2468 3317"/>
    </justification>
  </clause>

  <clause id="3319">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) = y \ T(y * K(x,z),y)
    ]]></literal>
    <justification jstring="[para(2148(a,1),3318(a,1,2))].">
      <j1 rule="para" parents="2148 3318"/>
    </justification>
  </clause>

  <clause id="3320">
    <literal><![CDATA[
      K(T(x / y,x) \ x,z) = K(y,T(x / z,x) \ x)
    ]]></literal>
    <justification jstring="[hyper(250,a,2738,a,b,3319,a)].">
      <j1 rule="hyper" parents="250 2738 3319"/>
    </justification>
  </clause>

  <clause id="3324">
    <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(250,a,2056,a(flip),b,3202,a),flip(a)].">
      <j1 rule="hyper" parents="250 2056 3202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3325">
    <literal><![CDATA[
      K(T(x * K(y \ (x \ (z * x)),x),x),u) = K(x,T(u,T(z \ (x * y),x) \ x))
    ]]></literal>
    <justification jstring="[para(2763(a,1),3204(a,1,1,1,2))].">
      <j1 rule="para" parents="2763 3204"/>
    </justification>
  </clause>

  <clause id="3326">
    <literal><![CDATA[
      K(x,T((y \ z) \ 1,u)) = K(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[hyper(3245,a,2802,a)].">
      <j1 rule="hyper" parents="3245 2802"/>
    </justification>
  </clause>

  <clause id="3327">
    <literal><![CDATA[
      K(x,T((y \ z) \ 1,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(3326(a,2),3234(a,1))].">
      <j1 rule="para" parents="3326 3234"/>
    </justification>
  </clause>

  <clause id="3328">
    <literal><![CDATA[
      K(x,(y / z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(2923(a,1),3327(a,1))].">
      <j1 rule="para" parents="2923 3327"/>
    </justification>
  </clause>

  <clause id="3329">
    <literal><![CDATA[
      K(x,((y / z) * u) \ (y * u)) = ((y * K(z,x)) * u) \ (y * u)
    ]]></literal>
    <justification jstring="[para(2636(a,1),3268(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2636 3268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3330">
    <literal><![CDATA[
      ((x * K(y,z)) * u) * K(z,((x / y) * u) \ (x * u)) = x * u
    ]]></literal>
    <justification jstring="[hyper(116,a,3329,a,b,xx)].">
      <j1 rule="hyper" parents="116 3329"/>
    </justification>
  </clause>

  <clause id="3332">
    <literal><![CDATA[
      ((x * K(y,z)) * K(y,u)) * K(z,y) = x * K(y,u)
    ]]></literal>
    <justification jstring="[para(2642(a,1),3330(a,1,2,2))].">
      <j1 rule="para" parents="2642 3330"/>
    </justification>
  </clause>

  <clause id="3333">
    <literal><![CDATA[
      K(((x / y) * z) \ (x * z),u) = (x * z) \ ((x * K(y,u)) * z)
    ]]></literal>
    <justification jstring="[para(3330(a,1),3129(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3330 3129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3334">
    <literal><![CDATA[
      K(x,y / ((z * K(u,x)) * w)) = K(x,y / (z * w))
    ]]></literal>
    <justification jstring="[para(3330(a,1),3252(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3330 3252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3335">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,y) = (x * K(u,y)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(3126(a,1),3332(a,1,1,1))].">
      <j1 rule="para" parents="3126 3332"/>
    </justification>
  </clause>

  <clause id="3336">
    <literal><![CDATA[
      K(x,y / ((z * x) * u)) = K(x,y / ((x * z) * u))
    ]]></literal>
    <justification jstring="[para(87(a,1),3334(a,1,2,2,1))].">
      <j1 rule="para" parents="87 3334"/>
    </justification>
  </clause>

  <clause id="3337">
    <literal><![CDATA[
      K(x,y / (((x \ z) * x) * u)) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[para(242(a,1),3334(a,1,2,2,1))].">
      <j1 rule="para" parents="242 3334"/>
    </justification>
  </clause>

  <clause id="3338">
    <literal><![CDATA[
      K(x,y / ((K(x,z) * u) * w)) = K(x,y / (u * w))
    ]]></literal>
    <justification jstring="[para(2832(a,1),3334(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="2832 3334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3339">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,y) = x * (K(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[hyper(250,a,3116,a(flip),b,3335,a),flip(a)].">
      <j1 rule="hyper" parents="250 3116 3335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3340">
    <literal><![CDATA[
      K(x,y / ((z * (K(u,x) * w)) * v5)) = K(x,y / ((z * w) * v5))
    ]]></literal>
    <justification jstring="[para(2622(a,1),3338(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="2622 3338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3341">
    <literal><![CDATA[
      L(K(x,y),K(y,z),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(341,a,3339,a)].">
      <j1 rule="hyper" parents="341 3339"/>
    </justification>
  </clause>

  <clause id="3342">
    <literal><![CDATA[
      L(K(x,T(y,z)),K(y,u),w) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(2906(a,1),3341(a,1,2))].">
      <j1 rule="para" parents="2906 3341"/>
    </justification>
  </clause>

  <clause id="3345">
    <literal><![CDATA[
      K(x,(y * (z / y)) / ((z / y) * x)) = K(x,z / ((y \ z) * x))
    ]]></literal>
    <justification jstring="[hyper(250,a,3273,a(flip),b,3274,a),flip(a)].">
      <j1 rule="hyper" parents="250 3273 3274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3346">
    <literal><![CDATA[
      K(x,R(x \ y,x,z / y)) = K(x,z / ((y \ z) * x))
    ]]></literal>
    <justification jstring="[hyper(65,a,3254,a,b,3345,a)].">
      <j1 rule="hyper" parents="65 3254 3345"/>
    </justification>
  </clause>

  <clause id="3347">
    <literal><![CDATA[
      K(x,R(x \ (y / z),x,y / (y / z))) = K(x,y / (z * x))
    ]]></literal>
    <justification jstring="[para(79(a,1),3346(a,2,2,2,1))].">
      <j1 rule="para" parents="79 3346"/>
    </justification>
  </clause>

  <clause id="3354">
    <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(537(a,2),2441(a,1,2,2,1))].">
      <j1 rule="para" parents="537 2441"/>
    </justification>
  </clause>

  <clause id="3356">
    <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(568(a,1),2545(a,1,2))].">
      <j1 rule="para" parents="568 2545"/>
    </justification>
  </clause>

  <clause id="3357">
    <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(1404(a,2),2933(a,1,1))].">
      <j1 rule="para" parents="1404 2933"/>
    </justification>
  </clause>

  <clause id="3358">
    <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(2805(a,1),3301(a,1,1))].">
      <j1 rule="para" parents="2805 3301"/>
    </justification>
  </clause>

  <clause id="3359">
    <literal><![CDATA[
      R(x,y,z) * (R((u * x) / u,y,z) \ x) = x * K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(1225(a,1),3354(a,1,2))].">
      <j1 rule="para" parents="1225 3354"/>
    </justification>
  </clause>

  <clause id="3361">
    <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(2813(a,1),3358(a,1,1))].">
      <j1 rule="para" parents="2813 3358"/>
    </justification>
  </clause>

  <clause id="3362">
    <literal><![CDATA[
      ((x * y) \ ((x * K(z,u)) * y)) \ 1 = (x * y) \ ((x * K(u,z)) * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,3285,a(flip),b,3361,a),flip(a)].">
      <j1 rule="hyper" parents="65 3285 3361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3363">
    <literal><![CDATA[
      K(((x / y) * z) \ (x * z),u) \ 1 = (x * z) \ ((x * K(u,y)) * z)
    ]]></literal>
    <justification jstring="[para(3333(a,2),3362(a,1,1))].">
      <j1 rule="para" parents="3333 3362"/>
    </justification>
  </clause>

  <clause id="3364">
    <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(3363(a,1),2375(a,1))].">
      <j1 rule="para" parents="3363 2375"/>
    </justification>
  </clause>

  <clause id="3366">
    <literal><![CDATA[
      (T(x * y,z) / y) * (x \ 1) = (1 / y) * (x \ T(x * y,z))
    ]]></literal>
    <justification jstring="[para(594(a,1),2621(a,1,1))].">
      <j1 rule="para" parents="594 2621"/>
    </justification>
  </clause>

  <clause id="3367">
    <literal><![CDATA[
      (1 / x) * ((x \ y) \ T((x \ y) * x,x)) = (x \ T(y,x)) * ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(807(a,1),3366(a,1,1)),flip(a)].">
      <j1 rule="para" parents="807 3366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3369">
    <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(2637(a,1),2650(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2637 2650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3370">
    <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(3369(a,2),371(a,1))].">
      <j1 rule="para" parents="3369 371"/>
    </justification>
  </clause>

  <clause id="3372">
    <literal><![CDATA[
      R(R(x,y * z,K(z,u)),y,z) = R(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(3370,a,31,a),flip(a)].">
      <j1 rule="hyper" parents="3370 31"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3377">
    <literal><![CDATA[
      R(T(x,y),z,T(x,u)) = R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[para(2715(a,1),3372(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2715 3372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3378">
    <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(3377(a,1),741(a,1,1))].">
      <j1 rule="para" parents="3377 741"/>
    </justification>
  </clause>

  <clause id="3379">
    <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(2519(a,1),3378(a,1,2,1))].">
      <j1 rule="para" parents="2519 3378"/>
    </justification>
  </clause>

  <clause id="3382">
    <literal><![CDATA[
      (x * (y * ((z \ (y \ (x \ u))) * z))) \ u = K(z,(x * (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(104(a,1),3211(a,1,1,2,2))].">
      <j1 rule="para" parents="104 3211"/>
    </justification>
  </clause>

  <clause id="3383">
    <literal><![CDATA[
      ((x * y) * ((z \ ((x * y) \ u)) * z)) \ u = K(z,(x * (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(1797(a,2),3382(a,1,1))].">
      <j1 rule="para" parents="1797 3382"/>
    </justification>
  </clause>

  <clause id="3384">
    <literal><![CDATA[
      K(x,(y * (z * x)) \ u) = K(x,(y * z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,3198,a(flip),b,3383,a),flip(a)].">
      <j1 rule="hyper" parents="65 3198 3383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3385">
    <literal><![CDATA[
      K(x,(y * (x * z)) \ u) = K(x,(y * z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,3218,a(flip),b,3384,a)].">
      <j1 rule="hyper" parents="65 3218 3384"/>
    </justification>
  </clause>

  <clause id="3386">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ (x \ u)) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[para(12(a,1),3384(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="12 3384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3388">
    <literal><![CDATA[
      K(x,(y * (x \ z)) \ (x \ u)) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[para(10(a,1),3385(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="10 3385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3389">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ u) = K(x,(y * z) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(3017,a,3386,a)].">
      <j1 rule="hyper" parents="3017 3386"/>
    </justification>
  </clause>

  <clause id="3390">
    <literal><![CDATA[
      K(x,(y * (x \ z)) \ u) = K(x,(y * z) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(3017,a,3388,a)].">
      <j1 rule="hyper" parents="3017 3388"/>
    </justification>
  </clause>

  <clause id="3391">
    <literal><![CDATA[
      L(K(x,y \ ((z \ u) * x)),z \ u,z) = K(x,(z * y) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(65,a,3093,a,b,3389,a)].">
      <j1 rule="hyper" parents="65 3093 3389"/>
    </justification>
  </clause>

  <clause id="3392">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,(y * z) \ (u * x))) = K((y * (z / x)) \ u,x)
    ]]></literal>
    <justification jstring="[para(3389(a,1),2446(a,1,2,2))].">
      <j1 rule="para" parents="3389 2446"/>
    </justification>
  </clause>

  <clause id="3393">
    <literal><![CDATA[
      K(x,K(y,(z * u) \ (y * y))) = K(x,K(z * (u / y),y))
    ]]></literal>
    <justification jstring="[para(3389(a,1),2983(a,1,2))].">
      <j1 rule="para" parents="3389 2983"/>
    </justification>
  </clause>

  <clause id="3394">
    <literal><![CDATA[
      L(K(x,(y * z) \ ((u \ w) * x)),u \ w,u) = K(x,(u * (y * (z / x))) \ w)
    ]]></literal>
    <justification jstring="[para(3389(a,1),2744(a,1,1))].">
      <j1 rule="para" parents="3389 2744"/>
    </justification>
  </clause>

  <clause id="3395">
    <literal><![CDATA[
      K(x,K(y * (z / u),u)) = K(x,K(u,(y * z) \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,3008,a(flip),b,3393,a),flip(a)].">
      <j1 rule="hyper" parents="65 3008 3393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3396">
    <literal><![CDATA[
      K(x,K(y * (z / u),u)) = K(x,K(y * z,u))
    ]]></literal>
    <justification jstring="[hyper(250,a,2983,a(flip),b,3395,a),flip(a)].">
      <j1 rule="hyper" parents="250 2983 3395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3397">
    <literal><![CDATA[
      K(x,y) * K(x,K(z * u,y)) = K(x,T(y,z * (u / y)))
    ]]></literal>
    <justification jstring="[para(3396(a,1),2899(a,1,2))].">
      <j1 rule="para" parents="3396 2899"/>
    </justification>
  </clause>

  <clause id="3398">
    <literal><![CDATA[
      K(x,T(y,z * (u / y))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,2899,a(flip),b,3397,a),flip(a)].">
      <j1 rule="hyper" parents="65 2899 3397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3399">
    <literal><![CDATA[
      K(x,T(y \ z,u * z)) = K(x,T(y \ z,u * y))
    ]]></literal>
    <justification jstring="[para(76(a,1),3398(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="76 3398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3400">
    <literal><![CDATA[
      K(x,T(y,z * (y \ u))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(3175(a,1),3398(a,1,2))].">
      <j1 rule="para" parents="3175 3398"/>
    </justification>
  </clause>

  <clause id="3401">
    <literal><![CDATA[
      K(T(x,y * (x \ z)),u) = w / (K(u,T(x,y * z)) * w)
    ]]></literal>
    <justification jstring="[para(3400(a,1),2425(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3400 2425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3402">
    <literal><![CDATA[
      K(T(x,y * (x \ z)),u) = K(T(x,y * z),u)
    ]]></literal>
    <justification jstring="[hyper(250,a,2425,a(flip),b,3401,a),flip(a)].">
      <j1 rule="hyper" parents="250 2425 3401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3403">
    <literal><![CDATA[
      K(T(x,y * (x \ z)),u) = K(x,T(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(250,a,2805,a(flip),b,3402,a),flip(a)].">
      <j1 rule="hyper" parents="250 2805 3402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3404">
    <literal><![CDATA[
      K(x,T(y,z * (x \ u))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(3034,a,3403,a)].">
      <j1 rule="hyper" parents="3034 3403"/>
    </justification>
  </clause>

  <clause id="3405">
    <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(3403(a,1),3031(a,1))].">
      <j1 rule="para" parents="3403 3031"/>
    </justification>
  </clause>

  <clause id="3406">
    <literal><![CDATA[
      K(x,T(y,z * (u / x))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,3176,a,b,3404,a)].">
      <j1 rule="hyper" parents="65 3176 3404"/>
    </justification>
  </clause>

  <clause id="3407">
    <literal><![CDATA[
      K(x,T(y,z * x)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(149(a,1),3404(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="149 3404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3408">
    <literal><![CDATA[
      K(x,T(y \ (z * x),z)) = K(x,(z * x) / y)
    ]]></literal>
    <justification jstring="[hyper(3234,a,3407,a),flip(a)].">
      <j1 rule="hyper" parents="3234 3407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3409">
    <literal><![CDATA[
      K(x,T(y \ x,z * y)) = K(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,3399,a(flip),b,3407,a)].">
      <j1 rule="hyper" parents="65 3399 3407"/>
    </justification>
  </clause>

  <clause id="3410">
    <literal><![CDATA[
      (x * y) * K(y,T(z,x)) = K(y,z) * (x * y)
    ]]></literal>
    <justification jstring="[para(3407(a,1),2792(a,1,2))].">
      <j1 rule="para" parents="3407 2792"/>
    </justification>
  </clause>

  <clause id="3411">
    <literal><![CDATA[
      K(x,T(y \ x,z / y)) = K(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[para(12(a,1),3409(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 3409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3412">
    <literal><![CDATA[
      K(x,y) * (z * x) = z * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(2661,a,3410,a),flip(a)].">
      <j1 rule="hyper" parents="2661 3410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3413">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * x) = z * T(x,y)
    ]]></literal>
    <justification jstring="[para(2920(a,1),3412(a,2,2))].">
      <j1 rule="para" parents="2920 3412"/>
    </justification>
  </clause>

  <clause id="3414">
    <literal><![CDATA[
      (x * T(y,z)) / T(x,y) = T(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(113,a,3413,a(flip),b,2397,a(flip))].">
      <j1 rule="hyper" parents="113 3413 2397"/>
    </justification>
  </clause>

  <clause id="3415">
    <literal><![CDATA[
      T(K(x,y),z) * ((x \ z) * x) = (x \ z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(2811(a,1),3413(a,1,1))].">
      <j1 rule="para" parents="2811 3413"/>
    </justification>
  </clause>

  <clause id="3416">
    <literal><![CDATA[
      (x * ((y \ z) \ z)) / T(x,y) = T(y,T(y \ z,x))
    ]]></literal>
    <justification jstring="[para(105(a,1),3414(a,1,1,2))].">
      <j1 rule="para" parents="105 3414"/>
    </justification>
  </clause>

  <clause id="3417">
    <literal><![CDATA[
      K(x,T(y \ x,y \ z)) = K(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,3009,a(flip),b,3411,a)].">
      <j1 rule="hyper" parents="65 3009 3411"/>
    </justification>
  </clause>

  <clause id="3418">
    <literal><![CDATA[
      (T(x,T(x \ y,z)) * z) \ (z * ((x \ y) \ y)) = K(z,x)
    ]]></literal>
    <justification jstring="[para(3416(a,1),2646(a,1,1,1))].">
      <j1 rule="para" parents="3416 2646"/>
    </justification>
  </clause>

  <clause id="3421">
    <literal><![CDATA[
      K((x * (y / z)) \ u,z) = K((x * y) \ (u * z),z)
    ]]></literal>
    <justification jstring="[hyper(2454,a,3392,a),flip(a)].">
      <j1 rule="hyper" parents="2454 3392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3422">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,(y * (x \ z)) \ u)) = K((y * (z / x)) \ u,x)
    ]]></literal>
    <justification jstring="[para(3390(a,2),3392(a,1,2,2))].">
      <j1 rule="para" parents="3390 3392"/>
    </justification>
  </clause>

  <clause id="3423">
    <literal><![CDATA[
      K((x * (y / z)) \ u,z) != w
    ]]></literal>
    <literal><![CDATA[
      K((x * (z \ y)) \ u,z) = w
    ]]></literal>
    <justification jstring="[para(3422(a,1),2454(a,1))].">
      <j1 rule="para" parents="3422 2454"/>
    </justification>
  </clause>

  <clause id="3424">
    <literal><![CDATA[
      K((x * (y \ z)) \ u,y) = K((x * z) \ (u * y),y)
    ]]></literal>
    <justification jstring="[hyper(3423,a,3421,a)].">
      <j1 rule="hyper" parents="3423 3421"/>
    </justification>
  </clause>

  <clause id="3434">
    <literal><![CDATA[
      T(T(K(x,y) * z,K(y,u)),K(y,u)) = K(y,u) * (K(x,y) * (K(y,u) \ z))
    ]]></literal>
    <justification jstring="[para(3203(a,2),3266(a,1,1))].">
      <j1 rule="para" parents="3203 3266"/>
    </justification>
  </clause>

  <clause id="3436">
    <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),3324(a,1,1,2,1))].">
      <j1 rule="para" parents="9 3324"/>
    </justification>
  </clause>

  <clause id="3437">
    <literal><![CDATA[
      (x \ T(y,x)) * ((x \ y) \ 1) = (1 / x) * ((y * x) / y)
    ]]></literal>
    <justification jstring="[para(2199(a,1),3367(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2199 3367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3438">
    <literal><![CDATA[
      K(x,y) = (y \ T(x,y)) * ((y \ x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(250,a,2346,a,b,3437,a)].">
      <j1 rule="hyper" parents="250 2346 3437"/>
    </justification>
  </clause>

  <clause id="3439">
    <literal><![CDATA[
      (x \ T(x * y,x)) * (y \ 1) = K(x * y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),3438(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="9 3438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3440">
    <literal><![CDATA[
      (x \ T(x * K(y,z),x)) * (K(z,y) * 1) = K(x * K(y,z),x)
    ]]></literal>
    <justification jstring="[para(2422(a,1),3439(a,1,2))].">
      <j1 rule="para" parents="2422 3439"/>
    </justification>
  </clause>

  <clause id="3441">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) * (K(z,x) * 1) = K(y * K(x,z),y)
    ]]></literal>
    <justification jstring="[para(3319(a,2),3440(a,1,1))].">
      <j1 rule="para" parents="3319 3440"/>
    </justification>
  </clause>

  <clause id="3442">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) * K(z,x) = K(y * K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(414,a,3441,a)].">
      <j1 rule="hyper" parents="414 3441"/>
    </justification>
  </clause>

  <clause id="3443">
    <literal><![CDATA[
      K(x,y) * (K(z,x) * (K(x,y) \ u)) = K(z,x) * u
    ]]></literal>
    <justification jstring="[hyper(65,a,2887,a(flip),b,3434,a),flip(a)].">
      <j1 rule="hyper" parents="65 2887 3434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3445">
    <literal><![CDATA[
      K(x,y) * (K(z,x) * u) = K(z,x) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(9(a,1),3443(a,1,2,2))].">
      <j1 rule="para" parents="9 3443"/>
    </justification>
  </clause>

  <clause id="3446">
    <literal><![CDATA[
      T(K(x,y) * z,K(y,u)) * K(y,u) = K(x,y) * (K(y,u) * z)
    ]]></literal>
    <justification jstring="[hyper(2888,a,3445,a)].">
      <j1 rule="hyper" parents="2888 3445"/>
    </justification>
  </clause>

  <clause id="3447">
    <literal><![CDATA[
      K(x,y) * (K(y,z) * (K(y,x) * u)) = K(y,z) * u
    ]]></literal>
    <justification jstring="[para(2426(a,1),3445(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2426 3445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3448">
    <literal><![CDATA[
      (x * K(y * z,y)) * K(y,z) = K(y * z,y) * (K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(3124(a,1),3446(a,1,1))].">
      <j1 rule="para" parents="3124 3446"/>
    </justification>
  </clause>

  <clause id="3449">
    <literal><![CDATA[
      K(x * y,x) * (K(x,y) * z) = z * (K(x,y) * K(x * y,x))
    ]]></literal>
    <justification jstring="[hyper(3196,a,3448,a),flip(a)].">
      <j1 rule="hyper" parents="3196 3448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3450">
    <literal><![CDATA[
      K(x,R(y / x,x * z,u) \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,((x * z) * u) / ((y * z) * u)) = w
    ]]></literal>
    <justification jstring="[para(2599(a,2),3328(a,1))].">
      <j1 rule="para" parents="2599 3328"/>
    </justification>
  </clause>

  <clause id="3451">
    <literal><![CDATA[
      L(K(T(T(x,y),z * y),u),y,z) * w = K(x,(z * y) / (z * (u \ y))) * w
    ]]></literal>
    <justification jstring="[hyper(250,a,2422,a(flip),b,3303,a),flip(a)].">
      <j1 rule="hyper" parents="250 2422 3303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3454">
    <literal><![CDATA[
      K(x,(y * (z * (u / x))) \ w) = K(x,(y * (z * u)) \ (w * x))
    ]]></literal>
    <justification jstring="[hyper(65,a,3391,a(flip),b,3394,a),flip(a)].">
      <j1 rule="hyper" parents="65 3391 3394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3455">
    <literal><![CDATA[
      L(K(T(x,y),T(z,u * y)),y,u) * w = K(x,(u * y) / (u * (z \ y))) * w
    ]]></literal>
    <justification jstring="[para(2805(a,1),3451(a,1,1,1))].">
      <j1 rule="para" parents="2805 3451"/>
    </justification>
  </clause>

  <clause id="3456">
    <literal><![CDATA[
      L(K(x,T(T(y,z * u),u)),u,z) * w = K(x,(z * u) / (z * (y \ u))) * w
    ]]></literal>
    <justification jstring="[para(2805(a,1),3455(a,1,1,1))].">
      <j1 rule="para" parents="2805 3455"/>
    </justification>
  </clause>

  <clause id="3457">
    <literal><![CDATA[
      K((x * y) / (x * (z \ y)),u) * w = K(z,(x * y) / (x * (u \ y))) * w
    ]]></literal>
    <justification jstring="[para(3247(a,1),3456(a,1,1))].">
      <j1 rule="para" parents="3247 3456"/>
    </justification>
  </clause>

  <clause id="3458">
    <literal><![CDATA[
      K((x * y) / (x * (z \ y)),u) = K(z,(x * y) / (x * (u \ y)))
    ]]></literal>
    <justification jstring="[hyper(46,a,3457,a)].">
      <j1 rule="hyper" parents="46 3457"/>
    </justification>
  </clause>

  <clause id="3459">
    <literal><![CDATA[
      K(x,(y * z) / (y * (u \ z))) = (y * (K(x,u) * z)) / (y * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,2615,a(flip),b,3458,a),flip(a)].">
      <j1 rule="hyper" parents="65 2615 3458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3460">
    <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(3158(a,1),2361(a,2,1))].">
      <j1 rule="para" parents="3158 2361"/>
    </justification>
  </clause>

  <clause id="3461">
    <literal><![CDATA[
      L(x,y,z) / (x * K(u,x)) = (K(x,u) / x) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(2347(a,1),3460(a,1,1,1))].">
      <j1 rule="para" parents="2347 3460"/>
    </justification>
  </clause>

  <clause id="3462">
    <literal><![CDATA[
      ((K(x,y) / x) * L(x,z,u)) \ L(x,z,u) = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(163,a,3461,a)].">
      <j1 rule="hyper" parents="163 3461"/>
    </justification>
  </clause>

  <clause id="3463">
    <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(2047(a,1),3462(a,1,1,2))].">
      <j1 rule="para" parents="2047 3462"/>
    </justification>
  </clause>

  <clause id="3464">
    <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(2906(a,1),2917(a,1,2,2,1))].">
      <j1 rule="para" parents="2906 2917"/>
    </justification>
  </clause>

  <clause id="3466">
    <literal><![CDATA[
      ((1 / x) * T((1 / x) \ K(y,z),y)) * u = K(y,z) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,906,a(flip),b,3276,a)].">
      <j1 rule="hyper" parents="65 906 3276"/>
    </justification>
  </clause>

  <clause id="3467">
    <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(1031(a,1),3278(a,1,2))].">
      <j1 rule="para" parents="1031 3278"/>
    </justification>
  </clause>

  <clause id="3468">
    <literal><![CDATA[
      x \ R(x,y,R(x,z,u)) = a(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(469,a,3467,a),flip(a)].">
      <j1 rule="hyper" parents="469 3467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3469">
    <literal><![CDATA[
      K(x * R(y,z,u),y) * K(y,x) = a(y,x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,3099,a,b,3468,a)].">
      <j1 rule="hyper" parents="65 3099 3468"/>
    </justification>
  </clause>

  <clause id="3470">
    <literal><![CDATA[
      a(x,y,R(x,z,u)) * K(x,y * R(x,z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3469(a,1),2831(a,1,1))].">
      <j1 rule="para" parents="3469 2831"/>
    </justification>
  </clause>

  <clause id="3471">
    <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),3470(a,1,2,2))].">
      <j1 rule="para" parents="12 3470"/>
    </justification>
  </clause>

  <clause id="3472">
    <literal><![CDATA[
      K(x,T(y,T(z \ (x * u),x) \ x)) = K(T(x * K(u \ z,x),x),y)
    ]]></literal>
    <justification jstring="[para(3024(a,1),3325(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3024 3325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3473">
    <literal><![CDATA[
      K(x,T(y,T(z \ (x * u),x) \ x)) = K(x * K(u \ z,x),y)
    ]]></literal>
    <justification jstring="[para(1169(a,1),3472(a,2,1))].">
      <j1 rule="para" parents="1169 3472"/>
    </justification>
  </clause>

  <clause id="3474">
    <literal><![CDATA[
      K(x,T(y,T(z \ (x * u),x) \ x)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[hyper(250,a,2915,a(flip),b,3473,a),flip(a)].">
      <j1 rule="hyper" parents="250 2915 3473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3475">
    <literal><![CDATA[
      K(x,T(y,(z \ (x * u)) \ x)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,2977,a(flip),b,3474,a)].">
      <j1 rule="hyper" parents="65 2977 3474"/>
    </justification>
  </clause>

  <clause id="3476">
    <literal><![CDATA[
      K(x,T(y,(x * z) \ u)) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(3058,a,3475,a)].">
      <j1 rule="hyper" parents="3058 3475"/>
    </justification>
  </clause>

  <clause id="3477">
    <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),3476(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14 3476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3478">
    <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(432(a,1),3477(a,1,2,2))].">
      <j1 rule="para" parents="432 3477"/>
    </justification>
  </clause>

  <clause id="3479">
    <literal><![CDATA[
      K(x,T(y,a(x,z,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3032,a,3478,a),flip(a)].">
      <j1 rule="hyper" parents="3032 3478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3480">
    <literal><![CDATA[
      T(x,T(y,a(x,z,u))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(114,a,3479,a,b,2470,a),flip(a)].">
      <j1 rule="hyper" parents="114 3479 2470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3481">
    <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(3480(a,1),3418(a,1,1,1))].">
      <j1 rule="para" parents="3480 3418"/>
    </justification>
  </clause>

  <clause id="3482">
    <literal><![CDATA[
      K(a(x,y,z),T(x,u)) = K(a(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(3047,a,3481,a)].">
      <j1 rule="hyper" parents="3047 3481"/>
    </justification>
  </clause>

  <clause id="3487">
    <literal><![CDATA[
      R(K(x,x / y),x * z,u) = K(x,((x * z) * u) / ((y * z) * u))
    ]]></literal>
    <justification jstring="[hyper(3450,a,2569,a),flip(a)].">
      <j1 rule="hyper" parents="3450 2569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3488">
    <literal><![CDATA[
      R(K(x,y \ x),x * z,u) = K(x,((x * z) * u) / ((y * z) * u))
    ]]></literal>
    <justification jstring="[para(2670(a,1),3487(a,1,1))].">
      <j1 rule="para" parents="2670 3487"/>
    </justification>
  </clause>

  <clause id="3490">
    <literal><![CDATA[
      ((x * (y * ((x \ (z / u)) / y))) * u) / z = K(y,z / ((x * y) * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,2574,a(flip),b,3312,a),flip(a)].">
      <j1 rule="hyper" parents="65 2574 3312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3491">
    <literal><![CDATA[
      ((x * y) * (z * (((x * y) \ u) / z))) / u = K(z,u / ((x * z) * y))
    ]]></literal>
    <justification jstring="[para(2223(a,1),3490(a,1,1))].">
      <j1 rule="para" parents="2223 3490"/>
    </justification>
  </clause>

  <clause id="3492">
    <literal><![CDATA[
      K(x,y / ((z * u) * x)) = K(x,y / ((z * x) * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,3311,a(flip),b,3491,a)].">
      <j1 rule="hyper" parents="65 3311 3491"/>
    </justification>
  </clause>

  <clause id="3493">
    <literal><![CDATA[
      K(x,y / ((z * x) * u)) = K(x,y / (x * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,3251,a(flip),b,3492,a),flip(a)].">
      <j1 rule="hyper" parents="65 3251 3492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3494">
    <literal><![CDATA[
      K(x,y / ((x * z) * u)) = K(x,y / (x * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,3336,a(flip),b,3493,a)].">
      <j1 rule="hyper" parents="65 3336 3493"/>
    </justification>
  </clause>

  <clause id="3495">
    <literal><![CDATA[
      x * K(x,y / (x * (z * u))) = T(x,y / ((x * z) * u))
    ]]></literal>
    <justification jstring="[hyper(116,a,3494,a(flip),b,2272,a(flip))].">
      <j1 rule="hyper" parents="116 3494 2272"/>
    </justification>
  </clause>

  <clause id="3496">
    <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(999(a,2),3356(a,1,2))].">
      <j1 rule="para" parents="999 3356"/>
    </justification>
  </clause>

  <clause id="3501">
    <literal><![CDATA[
      x * (y * (z \ T(z * (y \ (z \ 1)),z))) = (x * K(y \ 1,z)) * (z \ 1)
    ]]></literal>
    <justification jstring="[hyper(234,a,3496,a)].">
      <j1 rule="hyper" parents="234 3496"/>
    </justification>
  </clause>

  <clause id="3502">
    <literal><![CDATA[
      (x * K(y \ 1,z)) * (z \ 1) = x * (K(y \ 1,z) * (z \ 1))
    ]]></literal>
    <justification jstring="[para(2546(a,1),3501(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2546 3501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3503">
    <literal><![CDATA[
      (x * K(y \ 1,z)) * (z \ 1) = x * (T(z,y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2408(a,1),3502(a,2,2))].">
      <j1 rule="para" parents="2408 3502"/>
    </justification>
  </clause>

  <clause id="3504">
    <literal><![CDATA[
      (x * K(y,z)) * (z \ 1) = x * (T(z,(1 / y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(79(a,1),3503(a,1,1,2,1))].">
      <j1 rule="para" parents="79 3503"/>
    </justification>
  </clause>

  <clause id="3505">
    <literal><![CDATA[
      (x * K(y,z)) * (z \ 1) = x * (T(z,y) \ 1)
    ]]></literal>
    <justification jstring="[para(79(a,1),3504(a,2,2,1,2))].">
      <j1 rule="para" parents="79 3504"/>
    </justification>
  </clause>

  <clause id="3506">
    <literal><![CDATA[
      (x * K(y,z)) * (z \ 1) = x * (z \ K(y,z))
    ]]></literal>
    <justification jstring="[para(2285(a,1),3505(a,2,2))].">
      <j1 rule="para" parents="2285 3505"/>
    </justification>
  </clause>

  <clause id="3508">
    <literal><![CDATA[
      (x * (y \ 1)) * K(z,y) = x * (y \ K(z,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,3315,a(flip),b,3506,a)].">
      <j1 rule="hyper" parents="65 3315 3506"/>
    </justification>
  </clause>

  <clause id="3509">
    <literal><![CDATA[
      (x * (y \ K(z,y))) / (y \ K(z,y)) = R(x,y \ 1,K(z,y))
    ]]></literal>
    <justification jstring="[para(3508(a,1),2445(a,1,1))].">
      <j1 rule="para" parents="3508 2445"/>
    </justification>
  </clause>

  <clause id="3510">
    <literal><![CDATA[
      R(x,y \ 1,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(213,a,3509,a),flip(a)].">
      <j1 rule="hyper" parents="213 3509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3512">
    <literal><![CDATA[
      R(x,y,K(z,y \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(65,a,1818,a(flip),b,3510,a)].">
      <j1 rule="hyper" parents="65 1818 3510"/>
    </justification>
  </clause>

  <clause id="3513">
    <literal><![CDATA[
      R(x,y \ z,K(u,z \ y)) = x
    ]]></literal>
    <justification jstring="[para(2658(a,1),3512(a,1,3))].">
      <j1 rule="para" parents="2658 3512"/>
    </justification>
  </clause>

  <clause id="3514">
    <literal><![CDATA[
      x \ (y * K(z,y \ x)) = (x \ y) * K(z,y \ x)
    ]]></literal>
    <justification jstring="[para(3513(a,1),360(a,1,1))].">
      <j1 rule="para" parents="3513 360"/>
    </justification>
  </clause>

  <clause id="3515">
    <literal><![CDATA[
      T(x \ y,z) * ((y \ x) * K(z,x \ y)) = T((x \ y) * (y \ x),z)
    ]]></literal>
    <justification jstring="[hyper(116,a,3514,a(flip),b,2612,a)].">
      <j1 rule="hyper" parents="116 3514 2612"/>
    </justification>
  </clause>

  <clause id="3516">
    <literal><![CDATA[
      T((x \ y) * (y \ x),z) = (x \ y) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(2480,a,3515,a),flip(a)].">
      <j1 rule="hyper" parents="2480 3515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3517">
    <literal><![CDATA[
      T(x,(y \ z) * (z \ y)) = x
    ]]></literal>
    <justification jstring="[hyper(114,a,3516,a,b,2053,a)].">
      <j1 rule="hyper" parents="114 3516 2053"/>
    </justification>
  </clause>

  <clause id="3518">
    <literal><![CDATA[
      T(x,y * ((z * y) \ z)) = x
    ]]></literal>
    <justification jstring="[para(9(a,1),3517(a,1,2,1))].">
      <j1 rule="para" parents="9 3517"/>
    </justification>
  </clause>

  <clause id="3520">
    <literal><![CDATA[
      K(x,y * ((z * y) \ z)) = 1
    ]]></literal>
    <justification jstring="[hyper(57,a,3518,a)].">
      <j1 rule="hyper" parents="57 3518"/>
    </justification>
  </clause>

  <clause id="3521">
    <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(311(a,1),2278(a,1,1)),flip(a)].">
      <j1 rule="para" parents="311 2278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3522">
    <literal><![CDATA[
      ((T(x,y) * z) * u) / ((x * z) * u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(1947,a,3521,a),flip(a)].">
      <j1 rule="hyper" parents="1947 3521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3523">
    <literal><![CDATA[
      R(K(x,y),x * z,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2412,a(flip),b,3522,a)].">
      <j1 rule="hyper" parents="65 2412 3522"/>
    </justification>
  </clause>

  <clause id="3524">
    <literal><![CDATA[
      K(x,((x * y) * z) / ((u * y) * z)) = K(R(x,y,z),u \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,3488,a(flip),b,3523,a)].">
      <j1 rule="hyper" parents="65 3488 3523"/>
    </justification>
  </clause>

  <clause id="3525">
    <literal><![CDATA[
      K(R(x,y,R(x,z,u)),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,3241,a(flip),b,3523,a),flip(a)].">
      <j1 rule="hyper" parents="65 3241 3523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3526">
    <literal><![CDATA[
      K(R(x,y,x),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,3181,a(flip),b,3523,a),flip(a)].">
      <j1 rule="hyper" parents="65 3181 3523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3527">
    <literal><![CDATA[
      K(R(x,x \ y,z),u) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),3523(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 3523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3528">
    <literal><![CDATA[
      R(K(x,T(y,z)),x * u,w) = K(R(x,u,w),T(y,x \ z))
    ]]></literal>
    <justification jstring="[para(2828(a,1),3523(a,1,1))].">
      <j1 rule="para" parents="2828 3523"/>
    </justification>
  </clause>

  <clause id="3529">
    <literal><![CDATA[
      K(x,K(R(x,y,z),u) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(3523(a,1),2947(a,1,2,1))].">
      <j1 rule="para" parents="3523 2947"/>
    </justification>
  </clause>

  <clause id="3530">
    <literal><![CDATA[
      K(K(R(x,y,z),u) * w,x) = K(w,x)
    ]]></literal>
    <justification jstring="[para(3523(a,1),2959(a,1,1,1))].">
      <j1 rule="para" parents="3523 2959"/>
    </justification>
  </clause>

  <clause id="3531">
    <literal><![CDATA[
      x * K(R(x,y,x),z) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,3526,a,b,2272,a(flip))].">
      <j1 rule="hyper" parents="116 3526 2272"/>
    </justification>
  </clause>

  <clause id="3532">
    <literal><![CDATA[
      K(x,R(y,z,y)) = 1 / K(y,x)
    ]]></literal>
    <justification jstring="[hyper(170,a,3526,a(flip),b,2366,a),flip(a)].">
      <j1 rule="hyper" parents="170 3526 2366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3533">
    <literal><![CDATA[
      R(x,y,x) * K(x,z) = R(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,3526,a(flip),b,2313,a)].">
      <j1 rule="hyper" parents="116 3526 2313"/>
    </justification>
  </clause>

  <clause id="3534">
    <literal><![CDATA[
      R((x * y) / x,z,y) \ y = R(y,z,y) \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(112,a,3531,a(flip),b,3359,a),flip(a)].">
      <j1 rule="hyper" parents="112 3531 3359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3535">
    <literal><![CDATA[
      K(x,R(y,z,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(250,a,2367,a(flip),b,3532,a),flip(a)].">
      <j1 rule="hyper" parents="250 2367 3532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3537">
    <literal><![CDATA[
      T(x,R(y,z,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(114,a,3535,a,b,2470,a),flip(a)].">
      <j1 rule="hyper" parents="114 3535 2470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3538">
    <literal><![CDATA[
      R(K(x,y),z,y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2577,a(flip),b,3535,a)].">
      <j1 rule="hyper" parents="65 2577 3535"/>
    </justification>
  </clause>

  <clause id="3539">
    <literal><![CDATA[
      R(x * K(y,x),z,x) = R(x,z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[para(3535(a,1),2488(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3535 2488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3540">
    <literal><![CDATA[
      T(x / R(y,z,y),y) = R(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(293,a,3537,a),flip(a)].">
      <j1 rule="hyper" parents="293 3537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3541">
    <literal><![CDATA[
      T(x,(y * z) / y) = T(x,y / (y / z))
    ]]></literal>
    <justification jstring="[para(2203(a,1),3537(a,1,2))].">
      <j1 rule="para" parents="2203 3537"/>
    </justification>
  </clause>

  <clause id="3542">
    <literal><![CDATA[
      (K(x,y) * z) * y = K(x,y) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(115,a,3538,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="115 3538 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3543">
    <literal><![CDATA[
      K(x,T(y,z * R(x,u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,3246,a(flip),b,3525,a),flip(a)].">
      <j1 rule="hyper" parents="65 3246 3525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3544">
    <literal><![CDATA[
      K(x,T(R(x,y,z),u) \ w) = K(x,R(x,y,z) \ w)
    ]]></literal>
    <justification jstring="[para(2395(a,1),3529(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2395 3529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3545">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) * w) = K(x,R(x,z,u) * w)
    ]]></literal>
    <justification jstring="[para(2413(a,1),3529(a,1,2))].">
      <j1 rule="para" parents="2413 3529"/>
    </justification>
  </clause>

  <clause id="3546">
    <literal><![CDATA[
      K(x,T(y,T(z,R(x,u,w)))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(2892(a,1),3529(a,1,2))].">
      <j1 rule="para" parents="2892 3529"/>
    </justification>
  </clause>

  <clause id="3547">
    <literal><![CDATA[
      K(x,y * K(z,R(x,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2918(a,1),3529(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2918 3529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3548">
    <literal><![CDATA[
      K(T(x,R(y,z,u)) * w,y) = K(x * w,y)
    ]]></literal>
    <justification jstring="[para(2293(a,1),3530(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2293 3530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3549">
    <literal><![CDATA[
      K(x,y / (z / R(x,u,w))) = K(x,y / (R(x,u,w) \ z))
    ]]></literal>
    <justification jstring="[para(3170(a,1),3547(a,1,2))].">
      <j1 rule="para" parents="3170 3547"/>
    </justification>
  </clause>

  <clause id="3550">
    <literal><![CDATA[
      K(R(x,x \ 1,y),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(250,a,272,a(flip),b,3527,a),flip(a)].">
      <j1 rule="hyper" parents="250 272 3527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3552">
    <literal><![CDATA[
      K((x * y) / ((z \ x) * y),u) = R(K(z,u),x,y)
    ]]></literal>
    <justification jstring="[para(98(a,1),3527(a,1,1))].">
      <j1 rule="para" parents="98 3527"/>
    </justification>
  </clause>

  <clause id="3553">
    <literal><![CDATA[
      R(K(x,y),R(x,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[para(1570(a,1),3527(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1570 3527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3554">
    <literal><![CDATA[
      K(x,R(y,y \ z,u)) = (w * R(K(y,x),z,u)) \ w
    ]]></literal>
    <justification jstring="[para(3527(a,1),3129(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3527 3129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3555">
    <literal><![CDATA[
      R(K(x,y),R(x,z,u),w) = (v5 * K(y,x)) \ v5
    ]]></literal>
    <justification jstring="[hyper(250,a,3129,a,b,3553,a),flip(a)].">
      <j1 rule="hyper" parents="250 3129 3553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3556">
    <literal><![CDATA[
      T(x,y) \ R(T(x,y),z,x) = x \ R(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(112,a,3533,a(flip),b,2400,a)].">
      <j1 rule="hyper" parents="112 3533 2400"/>
    </justification>
  </clause>

  <clause id="3557">
    <literal><![CDATA[
      (x / R(y,z,y)) * y = y * (R(y,z,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(116,a,3540,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 3540 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3558">
    <literal><![CDATA[
      T((x / (y * K(z,y))) * y,z / (z / y)) = ((z * y) / z) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(2538,a,3541,a),flip(a)].">
      <j1 rule="hyper" parents="2538 3541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3559">
    <literal><![CDATA[
      L(x,y,K(z,x)) = x
    ]]></literal>
    <justification jstring="[hyper(1812,a,3542,a)].">
      <j1 rule="hyper" parents="1812 3542"/>
    </justification>
  </clause>

  <clause id="3560">
    <literal><![CDATA[
      L(K(x,y),z,K(u,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3559(a,1),2749(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3559 2749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3561">
    <literal><![CDATA[
      K(L(x,y,K(z,u)),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(3206,a,3560,a)].">
      <j1 rule="hyper" parents="3206 3560"/>
    </justification>
  </clause>

  <clause id="3562">
    <literal><![CDATA[
      K((K(x,y) * z) \ u,y) = K(z \ (K(y,x) * u),y)
    ]]></literal>
    <justification jstring="[para(2433(a,1),3561(a,1,1))].">
      <j1 rule="para" parents="2433 3561"/>
    </justification>
  </clause>

  <clause id="3564">
    <literal><![CDATA[
      K(x,T(y,z / R(x,u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(12(a,1),3543(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 3543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3565">
    <literal><![CDATA[
      K(x,T(y,z / R(x,u,w))) = K(x,T(y,R(x,u,w) \ z))
    ]]></literal>
    <justification jstring="[para(106(a,1),3546(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="106 3546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3566">
    <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(3548(a,1),3469(a,1,1))].">
      <j1 rule="para" parents="3548 3469"/>
    </justification>
  </clause>

  <clause id="3567">
    <literal><![CDATA[
      R(x * K(y,x),z,x) = K(y,x) * R(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(250,a,1987,a(flip),b,3539,a),flip(a)].">
      <j1 rule="hyper" parents="250 1987 3539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3568">
    <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(2543(a,1),3539(a,2,2))].">
      <j1 rule="para" parents="2543 3539"/>
    </justification>
  </clause>

  <clause id="3569">
    <literal><![CDATA[
      R(K(x,y),R(x,z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(3555(a,2),3136(a,1))].">
      <j1 rule="para" parents="3555 3136"/>
    </justification>
  </clause>

  <clause id="3570">
    <literal><![CDATA[
      K(x,(R(x,y,z) * u) / w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,R(x,y,z) / (w / u)) = v5
    ]]></literal>
    <justification jstring="[para(2575(a,1),3569(a,1))].">
      <j1 rule="para" parents="2575 3569"/>
    </justification>
  </clause>

  <clause id="3571">
    <literal><![CDATA[
      x \ R(x,y,x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,1554,a,b,3556,a),flip(a)].">
      <j1 rule="hyper" parents="65 1554 3556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3572">
    <literal><![CDATA[
      x * a(x,y,x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,1554,a,b,3556,a(flip))].">
      <j1 rule="hyper" parents="116 1554 3556"/>
    </justification>
  </clause>

  <clause id="3573">
    <literal><![CDATA[
      T(x,x * y) \ T(x,y) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[para(2035(a,1),3556(a,1,2))].">
      <j1 rule="para" parents="2035 3556"/>
    </justification>
  </clause>

  <clause id="3574">
    <literal><![CDATA[
      T(x,y) \ R(T(x,y),z,x) = a(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,3556,a,b,3571,a)].">
      <j1 rule="hyper" parents="65 3556 3571"/>
    </justification>
  </clause>

  <clause id="3575">
    <literal><![CDATA[
      R(x,y,x) / x = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,1398,a,b,3571,a)].">
      <j1 rule="hyper" parents="65 1398 3571"/>
    </justification>
  </clause>

  <clause id="3577">
    <literal><![CDATA[
      a(x,y,x) * x = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(115,a,3571,a(flip),b,1398,a)].">
      <j1 rule="hyper" parents="115 3571 1398"/>
    </justification>
  </clause>

  <clause id="3578">
    <literal><![CDATA[
      x * (a(x,y,x) * z) = R(x,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(115,a,3572,a(flip),b,1578,a),flip(a)].">
      <j1 rule="hyper" parents="115 3572 1578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3579">
    <literal><![CDATA[
      x \ R(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(3572(a,1),235(a,1,2))].">
      <j1 rule="para" parents="3572 235"/>
    </justification>
  </clause>

  <clause id="3581">
    <literal><![CDATA[
      a(x,y,x) * (x * z) = R(x,y,x) * z
    ]]></literal>
    <justification jstring="[para(3577(a,1),315(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3577 315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3582">
    <literal><![CDATA[
      R(x,y,x) \ x = x \ L(x,y,x)
    ]]></literal>
    <justification jstring="[para(3577(a,1),1675(a,1,1))].">
      <j1 rule="para" parents="3577 1675"/>
    </justification>
  </clause>

  <clause id="3584">
    <literal><![CDATA[
      x \ (x \ L(x,y,x)) = R(x,y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(112,a,3582,a(flip),b,731,a)].">
      <j1 rule="hyper" parents="112 3582 731"/>
    </justification>
  </clause>

  <clause id="3585">
    <literal><![CDATA[
      a(x,y,x) * T(x,z) = R(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(115,a,3574,a(flip),b,1398,a)].">
      <j1 rule="hyper" parents="115 3574 1398"/>
    </justification>
  </clause>

  <clause id="3586">
    <literal><![CDATA[
      a(x,y,x) * (y * x) = T(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(200,a,100,a(flip),b,3578,a),flip(a)].">
      <j1 rule="hyper" parents="200 100 3578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3587">
    <literal><![CDATA[
      a(x,y,x) * (R(x,y,x) \ z) = x \ z
    ]]></literal>
    <justification jstring="[hyper(112,a,10,a(flip),b,3578,a),flip(a)].">
      <j1 rule="hyper" parents="112 10 3578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3588">
    <literal><![CDATA[
      a(T(x * y,x),z,u) = a(y * x,z,u)
    ]]></literal>
    <justification jstring="[para(3586(a,1),1499(a,1,1))].">
      <j1 rule="para" parents="3586 1499"/>
    </justification>
  </clause>

  <clause id="3589">
    <literal><![CDATA[
      x \ ((x \ L(x,y,x)) * T(x,z)) = T(x,z) * (R(x,y,x) \ 1)
    ]]></literal>
    <justification jstring="[para(3584(a,1),1796(a,2,2))].">
      <j1 rule="para" parents="3584 1796"/>
    </justification>
  </clause>

  <clause id="3590">
    <literal><![CDATA[
      a(T(x * (y / x),x),z,u) = a(y,z,u)
    ]]></literal>
    <justification jstring="[para(12(a,1),3588(a,2,1))].">
      <j1 rule="para" parents="12 3588"/>
    </justification>
  </clause>

  <clause id="3591">
    <literal><![CDATA[
      a(x * (y / x),x,z) = a(y,T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(2163,a,3590,a)].">
      <j1 rule="hyper" parents="2163 3590"/>
    </justification>
  </clause>

  <clause id="3592">
    <literal><![CDATA[
      K(x * y,x) * K(x,y) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(2481,a,3573,a)].">
      <j1 rule="hyper" parents="2481 3573"/>
    </justification>
  </clause>

  <clause id="3593">
    <literal><![CDATA[
      K(x * y,x) * K(x,y) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(250,a,3571,a(flip),b,3592,a),flip(a)].">
      <j1 rule="hyper" parents="250 3571 3592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3594">
    <literal><![CDATA[
      x \ R(x,x \ y,x) = K(y,x) * K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),3592(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 3592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3595">
    <literal><![CDATA[
      K(x,x * y) * a(x,y,x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2430,a,3593,a)].">
      <j1 rule="hyper" parents="2430 3593"/>
    </justification>
  </clause>

  <clause id="3596">
    <literal><![CDATA[
      K(x,y) * K(x * y,x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(1063,a,3593,a)].">
      <j1 rule="hyper" parents="1063 3593"/>
    </justification>
  </clause>

  <clause id="3599">
    <literal><![CDATA[
      K(x,x * y) * (a(x,y,x) * z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(115,a,3595,a(flip),b,1578,a),flip(a)].">
      <j1 rule="hyper" parents="115 3595 1578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3600">
    <literal><![CDATA[
      K(x,y) * a(x,x \ y,x) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),3595(a,1,1,2))].">
      <j1 rule="para" parents="10 3595"/>
    </justification>
  </clause>

  <clause id="3601">
    <literal><![CDATA[
      K(x * y,x) * (K(x,y) * z) = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[para(3596(a,1),3449(a,2,2))].">
      <j1 rule="para" parents="3596 3449"/>
    </justification>
  </clause>

  <clause id="3602">
    <literal><![CDATA[
      x / R(y * K(z,y),u,y) = (x / R(y,u,y)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(3567(a,2),3267(a,1,2))].">
      <j1 rule="para" parents="3567 3267"/>
    </justification>
  </clause>

  <clause id="3603">
    <literal><![CDATA[
      R(K(x / y,z),x,u) = K((x * u) / (y * u),z)
    ]]></literal>
    <justification jstring="[para(79(a,1),3552(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 3552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3605">
    <literal><![CDATA[
      K(x * y,x) * (K(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) * z = u
    ]]></literal>
    <justification jstring="[para(3599(a,1),2432(a,1,2)),flip(b)].">
      <j1 rule="para" parents="3599 2432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3606">
    <literal><![CDATA[
      K((x * y) / (z * y),T(u,x)) = R(K(z \ x,u),x,y)
    ]]></literal>
    <justification jstring="[para(2788(a,1),3603(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2788 3603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3609">
    <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),3544(a,1,2,1))].">
      <j1 rule="para" parents="27 3544"/>
    </justification>
  </clause>

  <clause id="3610">
    <literal><![CDATA[
      (x * R(K(y,z),u,w)) \ x = R(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,2577,a(flip),b,3554,a),flip(a)].">
      <j1 rule="hyper" parents="65 2577 3554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3611">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),y) = K(x \ u,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,3076,a(flip),b,3562,a),flip(a)].">
      <j1 rule="hyper" parents="65 3076 3562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3613">
    <literal><![CDATA[
      K(x \ K(y,z),y) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(8(a,1),3611(a,1,1,2))].">
      <j1 rule="para" parents="8 3611"/>
    </justification>
  </clause>

  <clause id="3614">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),T(y,w)) = K(x \ u,T(y,w))
    ]]></literal>
    <justification jstring="[para(2906(a,1),3611(a,1,1,2,1))].">
      <j1 rule="para" parents="2906 3611"/>
    </justification>
  </clause>

  <clause id="3615">
    <literal><![CDATA[
      K(x \ (y * K(z,u)),z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(2902(a,1),3611(a,1,1,2))].">
      <j1 rule="para" parents="2902 3611"/>
    </justification>
  </clause>

  <clause id="3616">
    <literal><![CDATA[
      K(x,y) * K(z \ 1,x) = z * T(z \ K(x,y),x)
    ]]></literal>
    <justification jstring="[hyper(116,a,3613,a(flip),b,2641,a)].">
      <j1 rule="hyper" parents="116 3613 2641"/>
    </justification>
  </clause>

  <clause id="3617">
    <literal><![CDATA[
      K(x \ (y / z),z \ y) = K(x \ (z \ y),z \ y)
    ]]></literal>
    <justification jstring="[para(2254(a,1),3615(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2254 3615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3619">
    <literal><![CDATA[
      K(x,y / R(T(x,z),u,w)) = K(x,R(x,u,w) \ y)
    ]]></literal>
    <justification jstring="[hyper(3045,a,3609,a)].">
      <j1 rule="hyper" parents="3045 3609"/>
    </justification>
  </clause>

  <clause id="3620">
    <literal><![CDATA[
      K(x \ y,T(z,y)) = K((K(z,u) * y) / x,z)
    ]]></literal>
    <justification jstring="[hyper(3046,a,3614,a),flip(a)].">
      <j1 rule="hyper" parents="3046 3614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3621">
    <literal><![CDATA[
      K((K(x,y) * z) / u,x) = K(z / u,x)
    ]]></literal>
    <justification jstring="[hyper(3037,a,3620,a),flip(a)].">
      <j1 rule="hyper" parents="3037 3620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3622">
    <literal><![CDATA[
      K(x,(K(x,y) * z) / u) = (w * K(z / u,x)) \ w
    ]]></literal>
    <justification jstring="[para(3621(a,1),3129(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3621 3129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3623">
    <literal><![CDATA[
      (K(x,y) * K((1 / z) \ 1,x)) * u = K(x,y) * (K(z,x) * u)
    ]]></literal>
    <justification jstring="[para(3616(a,2),3466(a,1,1))].">
      <j1 rule="para" parents="3616 3466"/>
    </justification>
  </clause>

  <clause id="3624">
    <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(3617(a,1),2490(a,1,1,1,2))].">
      <j1 rule="para" parents="3617 2490"/>
    </justification>
  </clause>

  <clause id="3626">
    <literal><![CDATA[
      K(x,(K(x,y) * z) / u) = K(x,z / u)
    ]]></literal>
    <justification jstring="[hyper(250,a,3129,a(flip),b,3622,a),flip(a)].">
      <j1 rule="hyper" parents="250 3129 3622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3627">
    <literal><![CDATA[
      K(x,(y * x) / z) = K(x,(x * y) / z)
    ]]></literal>
    <justification jstring="[para(2264(a,1),3626(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2264 3626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3628">
    <literal><![CDATA[
      K(x,(y * x) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) \ x) = u
    ]]></literal>
    <justification jstring="[para(3627(a,2),2728(a,1))].">
      <j1 rule="para" parents="3627 2728"/>
    </justification>
  </clause>

  <clause id="3629">
    <literal><![CDATA[
      K(x,T(y \ (z * x),z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(y / z) \ x) = u
    ]]></literal>
    <justification jstring="[para(3408(a,2),3628(a,1))].">
      <j1 rule="para" parents="3408 3628"/>
    </justification>
  </clause>

  <clause id="3630">
    <literal><![CDATA[
      K(x,T((y \ z) \ x,y)) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(3629,a,3256,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="3629 3256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3631">
    <literal><![CDATA[
      K(x,((y * z) / y) \ x) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[para(9(a,1),3630(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="9 3630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3632">
    <literal><![CDATA[
      K(x,T(y \ x,y \ z)) = K(x,(z / (z / y)) \ x)
    ]]></literal>
    <justification jstring="[para(2089(a,1),3631(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2089 3631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3633">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ x) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,3417,a(flip),b,3632,a),flip(a)].">
      <j1 rule="hyper" parents="65 3417 3632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3634">
    <literal><![CDATA[
      K(x,T(y \ x,x * z)) = K(x,((x * z) / y) / z)
    ]]></literal>
    <justification jstring="[hyper(65,a,3063,a(flip),b,3633,a),flip(a)].">
      <j1 rule="hyper" parents="65 3063 3633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3635">
    <literal><![CDATA[
      K(x,((x * y) / z) / y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z \ x,y)) = u
    ]]></literal>
    <justification jstring="[para(3634(a,1),3039(a,1))].">
      <j1 rule="para" parents="3634 3039"/>
    </justification>
  </clause>

  <clause id="3636">
    <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(3635,a,3619,a),flip(a)].">
      <j1 rule="hyper" parents="3635 3619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3637">
    <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,3523,a(flip),b,3528,a),flip(a)].">
      <j1 rule="hyper" parents="65 3523 3528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3638">
    <literal><![CDATA[
      K(R(x,y,z),T(u,w)) * K(T(u,x \ w),R(x,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(111,a,3637,a,b,2427,a),flip(a)].">
      <j1 rule="hyper" parents="111 3637 2427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3639">
    <literal><![CDATA[
      K(R(x / (x / y),z,u),w) = K(R(y,z,u),T(w,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,3004,a,b,3637,a)].">
      <j1 rule="hyper" parents="65 3004 3637"/>
    </justification>
  </clause>

  <clause id="3640">
    <literal><![CDATA[
      K(R(x,y / x,z),T(u,y)) = K((y * z) / ((y / x) * z),u)
    ]]></literal>
    <justification jstring="[para(101(a,1),3639(a,1,1)),flip(a)].">
      <j1 rule="para" parents="101 3639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3641">
    <literal><![CDATA[
      K(x,(y * R(x,z,u)) / w) = K(x,y / (R(x,z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,3242,a,b,3549,a)].">
      <j1 rule="hyper" parents="65 3242 3549"/>
    </justification>
  </clause>

  <clause id="3642">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u) \ w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,3564,a(flip),b,3565,a),flip(a)].">
      <j1 rule="hyper" parents="65 3564 3565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3644">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u) * w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(9(a,1),3642(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 3642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3645">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u) * w)) = K(x,y) * K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(250,a,2893,a,b,3644,a),flip(a)].">
      <j1 rule="hyper" parents="250 2893 3644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3646">
    <literal><![CDATA[
      K(x,T(y \ (R(x,z,u) * w),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(R(x,z,u) * w) / y) = v5
    ]]></literal>
    <justification jstring="[para(3644(a,1),3234(a,1))].">
      <j1 rule="para" parents="3644 3234"/>
    </justification>
  </clause>

  <clause id="3647">
    <literal><![CDATA[
      K(x,K(y,R(x,z,u) * w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(2897,a,3645,a)].">
      <j1 rule="hyper" parents="2897 3645"/>
    </justification>
  </clause>

  <clause id="3648">
    <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(3645(a,2),3043(a,1))].">
      <j1 rule="para" parents="3645 3043"/>
    </justification>
  </clause>

  <clause id="3649">
    <literal><![CDATA[
      K(x,K(y,(x * z) * u)) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(100(a,1),3647(a,1,2,2))].">
      <j1 rule="para" parents="100 3647"/>
    </justification>
  </clause>

  <clause id="3650">
    <literal><![CDATA[
      K(x,K(y,z * u)) * K(y,x) = K(y,T(x,(x * z) * u))
    ]]></literal>
    <justification jstring="[para(3649(a,1),2884(a,1,1))].">
      <j1 rule="para" parents="3649 2884"/>
    </justification>
  </clause>

  <clause id="3651">
    <literal><![CDATA[
      a(x,y,x) * z = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(3605,a,3601,a)].">
      <j1 rule="hyper" parents="3605 3601"/>
    </justification>
  </clause>

  <clause id="3652">
    <literal><![CDATA[
      x * a(y,z,y) != u
    ]]></literal>
    <literal><![CDATA[
      a(y,z,y) * x = u
    ]]></literal>
    <justification jstring="[para(3601(a,1),3605(a,1))].">
      <j1 rule="para" parents="3601 3605"/>
    </justification>
  </clause>

  <clause id="3653">
    <literal><![CDATA[
      T(x,a(y,z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(203,a,3651,a)].">
      <j1 rule="hyper" parents="203 3651"/>
    </justification>
  </clause>

  <clause id="3654">
    <literal><![CDATA[
      a(x,y,x) \ (z * a(x,y,x)) = z
    ]]></literal>
    <justification jstring="[hyper(118,a,3651,a)].">
      <j1 rule="hyper" parents="118 3651"/>
    </justification>
  </clause>

  <clause id="3655">
    <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(112,a,3651,a,b,431,a)].">
      <j1 rule="hyper" parents="112 3651 431"/>
    </justification>
  </clause>

  <clause id="3656">
    <literal><![CDATA[
      (L(x,y,x) * z) \ (x * z) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(112,a,1674,a(flip),b,3651,a(flip))].">
      <j1 rule="hyper" parents="112 1674 3651"/>
    </justification>
  </clause>

  <clause id="3658">
    <literal><![CDATA[
      (x * a(y,z,y)) * u = a(y,z,y) * (x * u)
    ]]></literal>
    <justification jstring="[para(3651(a,1),315(a,1,1))].">
      <j1 rule="para" parents="3651 315"/>
    </justification>
  </clause>

  <clause id="3660">
    <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(3651(a,1),492(a,1,1))].">
      <j1 rule="para" parents="3651 492"/>
    </justification>
  </clause>

  <clause id="3662">
    <literal><![CDATA[
      (a(x,y,x) * z) \ u = a(x,y,x) \ (z \ u)
    ]]></literal>
    <justification jstring="[para(3651(a,2),1583(a,1,1))].">
      <j1 rule="para" parents="3651 1583"/>
    </justification>
  </clause>

  <clause id="3663">
    <literal><![CDATA[
      T(a(x,y,x) \ z,a(x,y,x) * u) = (a(x,y,x) * u) \ (z * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,1575,a(flip),b,3653,a)].">
      <j1 rule="hyper" parents="65 1575 3653"/>
    </justification>
  </clause>

  <clause id="3668">
    <literal><![CDATA[
      x * (L(x,y,x) \ z) = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,3656,a(flip),b,136,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 3656 136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3669">
    <literal><![CDATA[
      T(x,y) * (L(T(x,y),z,x) \ u) = u * a(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,3066,a,b,3668,a)].">
      <j1 rule="hyper" parents="65 3066 3668"/>
    </justification>
  </clause>

  <clause id="3670">
    <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(2315,a,3658,a)].">
      <j1 rule="hyper" parents="2315 3658"/>
    </justification>
  </clause>

  <clause id="3671">
    <literal><![CDATA[
      T(x * y,x) / x = y * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(113,a,3586,a(flip),b,3658,a)].">
      <j1 rule="hyper" parents="113 3586 3658"/>
    </justification>
  </clause>

  <clause id="3673">
    <literal><![CDATA[
      a(x,y,x) * (z * u) = z * (a(x,y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,1576,a(flip),b,3658,a),flip(a)].">
      <j1 rule="hyper" parents="65 1576 3658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3674">
    <literal><![CDATA[
      R(T(x * y,x) / x,z,u) = R(y,z,u) * a(x,R(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,1022,a,b,3671,a)].">
      <j1 rule="hyper" parents="65 1022 3671"/>
    </justification>
  </clause>

  <clause id="3675">
    <literal><![CDATA[
      (x \ y) * a(x,x \ y,x) = T(y,x) / x
    ]]></literal>
    <justification jstring="[para(10(a,1),3671(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 3671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3680">
    <literal><![CDATA[
      x * (a(y,z,y) * (x \ u)) = a(y,z,y) * u
    ]]></literal>
    <justification jstring="[hyper(259,a,3673,a),flip(a)].">
      <j1 rule="hyper" parents="259 3673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3683">
    <literal><![CDATA[
      a(x,y,T(x,z)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(110,a,3669,a(flip),b,1686,a),flip(a)].">
      <j1 rule="hyper" parents="110 3669 1686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3684">
    <literal><![CDATA[
      a(x,y,T(x,z)) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(250,a,3571,a,b,3683,a),flip(a)].">
      <j1 rule="hyper" parents="250 3571 3683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3685">
    <literal><![CDATA[
      a(x,y,T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(3684(a,2),3579(a,1))].">
      <j1 rule="para" parents="3684 3579"/>
    </justification>
  </clause>

  <clause id="3687">
    <literal><![CDATA[
      K(T(x,y \ z),R(y,u,w)) = K(T(x,z),R(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(2376,a,3638,a),flip(a)].">
      <j1 rule="hyper" parents="2376 3638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3688">
    <literal><![CDATA[
      T(x,R(y / (y / z),u,w)) = x * K(T(x,y),R(z,u,w))
    ]]></literal>
    <justification jstring="[para(3687(a,1),3205(a,2,2))].">
      <j1 rule="para" parents="3687 3205"/>
    </justification>
  </clause>

  <clause id="3689">
    <literal><![CDATA[
      K(x,T(y,(y * z) * u)) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(3044,a,3650,a),flip(a)].">
      <j1 rule="hyper" parents="3044 3650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3690">
    <literal><![CDATA[
      K(x,T(y,(y \ z) * u)) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(10(a,1),3689(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 3689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3691">
    <literal><![CDATA[
      K(x \ y,T(x,y * z)) = K(x \ y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(3039,a,3690,a),flip(a)].">
      <j1 rule="hyper" parents="3039 3690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3692">
    <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(3691(a,1),3304(a,1,1,1))].">
      <j1 rule="para" parents="3691 3304"/>
    </justification>
  </clause>

  <clause id="3694">
    <literal><![CDATA[
      T(x,R((y * z) / y,u,w)) = T(x,R(y / (y / z),u,w))
    ]]></literal>
    <justification jstring="[hyper(250,a,3070,a,b,3688,a)].">
      <j1 rule="hyper" parents="250 3070 3688"/>
    </justification>
  </clause>

  <clause id="3695">
    <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),3524(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 3524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3696">
    <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(2598(a,1),3524(a,1,2,1))].">
      <j1 rule="para" parents="2598 3524"/>
    </justification>
  </clause>

  <clause id="3697">
    <literal><![CDATA[
      K(R(x,y / x,z),u) = K((y * z) / ((y / x) * z),T(u,y))
    ]]></literal>
    <justification jstring="[hyper(3033,a,3640,a)].">
      <j1 rule="hyper" parents="3033 3640"/>
    </justification>
  </clause>

  <clause id="3698">
    <literal><![CDATA[
      R(K((x / y) \ x,z),x,u) = K(R(y,x / y,u),z)
    ]]></literal>
    <justification jstring="[hyper(250,a,3606,a(flip),b,3697,a)].">
      <j1 rule="hyper" parents="250 3606 3697"/>
    </justification>
  </clause>

  <clause id="3699">
    <literal><![CDATA[
      K(R(x,y / x,z),u) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(79(a,1),3698(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 3698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3700">
    <literal><![CDATA[
      R(K(x,y),z * x,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(11(a,1),3699(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11 3699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3701">
    <literal><![CDATA[
      K(R(x,y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,R(y,x,z)) = u
    ]]></literal>
    <justification jstring="[para(3700(a,1),3105(a,1))].">
      <j1 rule="para" parents="3700 3105"/>
    </justification>
  </clause>

  <clause id="3702">
    <literal><![CDATA[
      K(a(x,y,z),T(x,x * (y * z))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ R(x,y,z),R(x,x \ R(x,y,z),y * z)) = u
    ]]></literal>
    <justification jstring="[para(3357(a,1),3701(a,1))].">
      <j1 rule="para" parents="3357 3701"/>
    </justification>
  </clause>

  <clause id="3703">
    <literal><![CDATA[
      x \ ((x \ L(x,y,x)) * T(x,z)) = R(x,y,x) \ T(x,z)
    ]]></literal>
    <justification jstring="[hyper(250,a,1221,a(flip),b,3589,a),flip(a)].">
      <j1 rule="hyper" parents="250 1221 3589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3704">
    <literal><![CDATA[
      x \ (K(x,y) * L(x,z,x)) = R(x,z,x) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(2403(a,1),3703(a,1,2))].">
      <j1 rule="para" parents="2403 3703"/>
    </justification>
  </clause>

  <clause id="3705">
    <literal><![CDATA[
      R(x,y,x) \ T(x,z) = x \ L(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[para(2850(a,1),3704(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2850 3704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3706">
    <literal><![CDATA[
      R((x * y) / x,z,y) \ y = y \ L(T(y,x),z,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,3534,a,b,3705,a)].">
      <j1 rule="hyper" parents="65 3534 3705"/>
    </justification>
  </clause>

  <clause id="3707">
    <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(3706(a,1),2799(a,1,1,2,1))].">
      <j1 rule="para" parents="3706 2799"/>
    </justification>
  </clause>

  <clause id="3708">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) * u = K(x,y) * (K(z,x) * u)
    ]]></literal>
    <justification jstring="[para(79(a,1),3623(a,1,1,2,1))].">
      <j1 rule="para" parents="79 3623"/>
    </justification>
  </clause>

  <clause id="3709">
    <literal><![CDATA[
      L(x,K(y,z),K(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(341,a,3708,a)].">
      <j1 rule="hyper" parents="341 3708"/>
    </justification>
  </clause>

  <clause id="3710">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) * u = K(y,z) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(1061(a,1),3708(a,1,1))].">
      <j1 rule="para" parents="1061 3708"/>
    </justification>
  </clause>

  <clause id="3711">
    <literal><![CDATA[
      L(T(x / (x / y),y \ x),K(z,u),K(u,w)) = y
    ]]></literal>
    <justification jstring="[hyper(250,a,2088,a(flip),b,3709,a),flip(a)].">
      <j1 rule="hyper" parents="250 2088 3709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3712">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) * u = K(x,y) * (K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(250,a,3445,a(flip),b,3710,a),flip(a)].">
      <j1 rule="hyper" parents="250 3445 3710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3713">
    <literal><![CDATA[
      (K(x,y) * z) / (K(x,u) * z) = K(u,x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(113,a,3447,a(flip),b,3712,a)].">
      <j1 rule="hyper" parents="113 3447 3712"/>
    </justification>
  </clause>

  <clause id="3715">
    <literal><![CDATA[
      x / (K(y \ x,z) * (y * (x / y))) = K(z,y \ x) * K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(2256(a,1),3713(a,1,1))].">
      <j1 rule="para" parents="2256 3713"/>
    </justification>
  </clause>

  <clause id="3717">
    <literal><![CDATA[
      R(x,y,z) * a(u,R(x,y,z),u) = R(x * a(u,x,u),y,z)
    ]]></literal>
    <justification jstring="[para(3671(a,1),3674(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3671 3674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3718">
    <literal><![CDATA[
      a(x,R(y,z,u),x) * R(y,z,u) = R(y * a(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(3652,a,3717,a)].">
      <j1 rule="hyper" parents="3652 3717"/>
    </justification>
  </clause>

  <clause id="3719">
    <literal><![CDATA[
      (R(x * a(y,x,y),z,u) * (z * u)) / ((x * z) * u) = a(y,R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(3718(a,1),1037(a,1,1,1))].">
      <j1 rule="para" parents="3718 1037"/>
    </justification>
  </clause>

  <clause id="3720">
    <literal><![CDATA[
      T(a(x,y,x) \ z,u * a(x,y,x)) = (a(x,y,x) * u) \ (z * u)
    ]]></literal>
    <justification jstring="[para(3651(a,1),3663(a,1,2))].">
      <j1 rule="para" parents="3651 3663"/>
    </justification>
  </clause>

  <clause id="3721">
    <literal><![CDATA[
      a(x,y,x) \ T(z * a(x,y,x),u) != z * w
    ]]></literal>
    <literal><![CDATA[
      K(z * a(x,y,x),u) = w
    ]]></literal>
    <justification jstring="[para(3670(a,2),45(a,1))].">
      <j1 rule="para" parents="3670 45"/>
    </justification>
  </clause>

  <clause id="3722">
    <literal><![CDATA[
      K(x,(y * z) / ((u * (x \ y)) * z)) = R(K(x,u \ x),y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,3527,a(flip),b,3695,a),flip(a)].">
      <j1 rule="hyper" parents="65 3527 3695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3723">
    <literal><![CDATA[
      T(a(x,y,x) \ z,u * a(x,y,x)) = a(x,y,x) \ (u \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(250,a,3662,a(flip),b,3720,a),flip(a)].">
      <j1 rule="hyper" parents="250 3662 3720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3724">
    <literal><![CDATA[
      T(a(x,y,x) \ z,u * a(x,y,x)) = a(x,y,x) \ T(z,u)
    ]]></literal>
    <justification jstring="[para(22(a,2),3723(a,2,2))].">
      <j1 rule="para" parents="22 3723"/>
    </justification>
  </clause>

  <clause id="3725">
    <literal><![CDATA[
      T(x * K(y,z),z / (z / y)) = ((z * y) / z) \ (x * y)
    ]]></literal>
    <justification jstring="[para(3172(a,1),3558(a,1,1))].">
      <j1 rule="para" parents="3172 3558"/>
    </justification>
  </clause>

  <clause id="3726">
    <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(179(a,2),3715(a,1,2,2,2))].">
      <j1 rule="para" parents="179 3715"/>
    </justification>
  </clause>

  <clause id="3727">
    <literal><![CDATA[
      (x * (K(y \ x,y) * z)) / (x * z) = L(K(y \ x,y),z,x)
    ]]></literal>
    <justification jstring="[para(2903(a,1),3692(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2903 3692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3728">
    <literal><![CDATA[
      L(K(x \ y,x),z,y) * (y * z) = y * (K(x \ y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(124,a,3727,a)].">
      <j1 rule="hyper" parents="124 3727"/>
    </justification>
  </clause>

  <clause id="3730">
    <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),3728(a,1,1,1,1))].">
      <j1 rule="para" parents="9 3728"/>
    </justification>
  </clause>

  <clause id="3731">
    <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(2543(a,1),3568(a,1,1,2))].">
      <j1 rule="para" parents="2543 3568"/>
    </justification>
  </clause>

  <clause id="3732">
    <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(3731(a,2),3610(a,1,1))].">
      <j1 rule="para" parents="3731 3610"/>
    </justification>
  </clause>

  <clause id="3737">
    <literal><![CDATA[
      (((x * a(y,x,y)) * z) * u) / ((x * z) * u) = a(y,R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(100(a,1),3719(a,1,1))].">
      <j1 rule="para" parents="100 3719"/>
    </justification>
  </clause>

  <clause id="3738">
    <literal><![CDATA[
      ((x * (a(y,x,y) * z)) * u) / ((x * z) * u) = a(y,R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(1576(a,1),3737(a,1,1,1))].">
      <j1 rule="para" parents="1576 3737"/>
    </justification>
  </clause>

  <clause id="3739">
    <literal><![CDATA[
      ((x * (a(y,x,y) * (x \ z))) * u) / (z * u) = a(y,R(x,x \ z,u),y)
    ]]></literal>
    <justification jstring="[para(10(a,1),3738(a,1,2,1))].">
      <j1 rule="para" parents="10 3738"/>
    </justification>
  </clause>

  <clause id="3740">
    <literal><![CDATA[
      a(x,R(y,y \ z,u),x) = ((a(x,y,x) * z) * u) / (z * u)
    ]]></literal>
    <justification jstring="[para(3680(a,1),3739(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3680 3739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3741">
    <literal><![CDATA[
      a(x,R(y,y \ z,u),x) = R(a(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(250,a,20,a,b,3740,a),flip(a)].">
      <j1 rule="hyper" parents="250 20 3740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3743">
    <literal><![CDATA[
      R(a(x,y,x),y * z,u) = a(x,R(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(9(a,1),3741(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 3741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3744">
    <literal><![CDATA[
      a(x,R(y,z,u),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(527,a,3743,a),flip(a)].">
      <j1 rule="hyper" parents="527 3743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3746">
    <literal><![CDATA[
      R(T(x,y),R(z,u,w),x) = a(x,z,x) * T(x,y)
    ]]></literal>
    <justification jstring="[para(3744(a,1),3585(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3744 3585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3747">
    <literal><![CDATA[
      R(T(x,y),R(z,u,w),x) = R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(250,a,3585,a(flip),b,3746,a),flip(a)].">
      <j1 rule="hyper" parents="250 3585 3746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3751">
    <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),3730(a,2,2,1,1))].">
      <j1 rule="para" parents="9 3730"/>
    </justification>
  </clause>

  <clause id="3752">
    <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(3751(a,1),212(a,1,1)),flip(b)].">
      <j1 rule="para" parents="3751 212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3754">
    <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(3459(a,2),3752(a,1))].">
      <j1 rule="para" parents="3459 3752"/>
    </justification>
  </clause>

  <clause id="3755">
    <literal><![CDATA[
      K(x,((y * x) * z) / (x * (y * (y \ z)))) = L(K(x,y),z,y * x)
    ]]></literal>
    <justification jstring="[hyper(3754,a,3493,a),flip(a)].">
      <j1 rule="hyper" parents="3754 3493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3756">
    <literal><![CDATA[
      L(K(x,y),z,y * x) = K(x,((y * x) * z) / (x * z))
    ]]></literal>
    <justification jstring="[para(10(a,1),3755(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10 3755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3757">
    <literal><![CDATA[
      L(K(x,y),z,y * x) = K(x,R(y,x,z))
    ]]></literal>
    <justification jstring="[para(20(a,2),3756(a,2,2))].">
      <j1 rule="para" parents="20 3756"/>
    </justification>
  </clause>

  <clause id="3759">
    <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(2790(a,1),3566(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2790 3566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3760">
    <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(250,a,3469,a(flip),b,3759,a),flip(a)].">
      <j1 rule="hyper" parents="250 3469 3759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3762">
    <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(106(a,1),3760(a,1,2)),flip(a)].">
      <j1 rule="para" parents="106 3760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3763">
    <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(3762(a,1),3471(a,1,1))].">
      <j1 rule="para" parents="3762 3471"/>
    </justification>
  </clause>

  <clause id="3764">
    <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(250,a,2798,a(flip),b,3763,a),flip(a)].">
      <j1 rule="hyper" parents="250 2798 3763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3765">
    <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(3636(a,2),3032(a,1))].">
      <j1 rule="para" parents="3636 3032"/>
    </justification>
  </clause>

  <clause id="3766">
    <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(3655(a,1),3660(a,1))].">
      <j1 rule="para" parents="3655 3660"/>
    </justification>
  </clause>

  <clause id="3767">
    <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(2293(a,1),2410(a,2,2))].">
      <j1 rule="para" parents="2293 2410"/>
    </justification>
  </clause>

  <clause id="3768">
    <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(3767(a,2),342(a,1))].">
      <j1 rule="para" parents="3767 342"/>
    </justification>
  </clause>

  <clause id="3779">
    <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,3454,a(flip),b,3238,a),flip(a)].">
      <j1 rule="hyper" parents="65 3454 3238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3780">
    <literal><![CDATA[
      K(x,(y * (z * u)) \ ((z * (x \ u)) * x)) = K(x,T(y \ 1,z * (u / x)))
    ]]></literal>
    <justification jstring="[hyper(3040,a,3779,a),flip(a)].">
      <j1 rule="hyper" parents="3040 3779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3781">
    <literal><![CDATA[
      K(x,(y * (z * u)) \ ((z * (x \ u)) * x)) = K(x,T(y \ 1,z * u))
    ]]></literal>
    <justification jstring="[hyper(250,a,3406,a(flip),b,3780,a),flip(a)].">
      <j1 rule="hyper" parents="250 3406 3780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3782">
    <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),3781(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 3781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3783">
    <literal><![CDATA[
      K(x,y \ ((z * (x \ u)) * x)) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(2999,a,3782,a),flip(a)].">
      <j1 rule="hyper" parents="2999 3782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3784">
    <literal><![CDATA[
      K(x,y \ ((x \ y) * z)) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,3056,a(flip),b,3783,a),flip(a)].">
      <j1 rule="hyper" parents="65 3056 3783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3785">
    <literal><![CDATA[
      K(x,x \ (y * z)) = K(x,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,2333,a(flip),b,3783,a),flip(a)].">
      <j1 rule="hyper" parents="65 2333 3783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3786">
    <literal><![CDATA[
      K(x,x \ ((x \ y) \ z)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),3784(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 3784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3787">
    <literal><![CDATA[
      (x * K(y,z * (y \ u))) \ x = K(y \ (z * u),y)
    ]]></literal>
    <justification jstring="[para(3785(a,1),3129(a,1,1,2))].">
      <j1 rule="para" parents="3785 3129"/>
    </justification>
  </clause>

  <clause id="3788">
    <literal><![CDATA[
      K(x,(x * y) \ z) = K(x,x \ (y \ z))
    ]]></literal>
    <justification jstring="[para(9(a,1),3786(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="9 3786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3789">
    <literal><![CDATA[
      K(x,y \ (x \ z)) = K(x,x \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(3092,a,3788,a)].">
      <j1 rule="hyper" parents="3092 3788"/>
    </justification>
  </clause>

  <clause id="3790">
    <literal><![CDATA[
      K(x,y \ (x \ (y * z))) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(9(a,1),3789(a,2,2,2))].">
      <j1 rule="para" parents="9 3789"/>
    </justification>
  </clause>

  <clause id="3791">
    <literal><![CDATA[
      K(x,y \ (x \ (y * (z * x)))) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(250,a,2333,a(flip),b,3790,a),flip(a)].">
      <j1 rule="hyper" parents="250 2333 3790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3792">
    <literal><![CDATA[
      K(x,L(y,x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3101,a,3791,a)].">
      <j1 rule="hyper" parents="3101 3791"/>
    </justification>
  </clause>

  <clause id="3794">
    <literal><![CDATA[
      T(x,L(y,x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(114,a,3792,a,b,2470,a),flip(a)].">
      <j1 rule="hyper" parents="114 3792 2470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3795">
    <literal><![CDATA[
      K(R(x,x \ 1,y),L(z,x,u)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,3550,a,b,3792,a)].">
      <j1 rule="hyper" parents="65 3550 3792"/>
    </justification>
  </clause>

  <clause id="3796">
    <literal><![CDATA[
      L(K(x,y),x * y,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2751,a,b,3792,a)].">
      <j1 rule="hyper" parents="65 2751 3792"/>
    </justification>
  </clause>

  <clause id="3797">
    <literal><![CDATA[
      (x * (y * z)) * K(z,y) = x * (z * y)
    ]]></literal>
    <justification jstring="[para(3792(a,1),3133(a,1,2))].">
      <j1 rule="para" parents="3792 3133"/>
    </justification>
  </clause>

  <clause id="3798">
    <literal><![CDATA[
      T(x,a(y,x,z)) = x
    ]]></literal>
    <justification jstring="[hyper(42,a,1840,a,b,3794,a)].">
      <j1 rule="hyper" parents="42 1840 3794"/>
    </justification>
  </clause>

  <clause id="3800">
    <literal><![CDATA[
      T(a(x,y,z),y) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(114,a,3798,a,b,2053,a)].">
      <j1 rule="hyper" parents="114 3798 2053"/>
    </justification>
  </clause>

  <clause id="3802">
    <literal><![CDATA[
      K(L(x,y,z),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,3108,a(flip),b,3796,a)].">
      <j1 rule="hyper" parents="65 3108 3796"/>
    </justification>
  </clause>

  <clause id="3804">
    <literal><![CDATA[
      K((x \ 1) \ y,x \ 1) = K(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[para(348(a,1),3802(a,1,1)),flip(a)].">
      <j1 rule="para" parents="348 3802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3805">
    <literal><![CDATA[
      R(x,y * z,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(531,a,3797,a)].">
      <j1 rule="hyper" parents="531 3797"/>
    </justification>
  </clause>

  <clause id="3807">
    <literal><![CDATA[
      R(x,y,T(z,y)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(3370,a,3805,a)].">
      <j1 rule="hyper" parents="3370 3805"/>
    </justification>
  </clause>

  <clause id="3808">
    <literal><![CDATA[
      R(x,y / z,z) = R(x,z \ y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,3283,a(flip),b,3807,a)].">
      <j1 rule="hyper" parents="65 3283 3807"/>
    </justification>
  </clause>

  <clause id="3810">
    <literal><![CDATA[
      R(K(x,(y / z) / u),z \ y,z) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,2574,a(flip),b,3808,a),flip(a)].">
      <j1 rule="hyper" parents="65 2574 3808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3811">
    <literal><![CDATA[
      x \ R(x,x \ y,x) = a(x,y / x,x)
    ]]></literal>
    <justification jstring="[hyper(112,a,3808,a(flip),b,3572,a)].">
      <j1 rule="hyper" parents="112 3808 3572"/>
    </justification>
  </clause>

  <clause id="3812">
    <literal><![CDATA[
      K(x,y) * K(y,y \ x) = a(y,x / y,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,3594,a(flip),b,3811,a)].">
      <j1 rule="hyper" parents="65 3594 3811"/>
    </justification>
  </clause>

  <clause id="3813">
    <literal><![CDATA[
      a(x,y / x,x) \ K(y,x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(3812(a,1),3129(a,1,1))].">
      <j1 rule="para" parents="3812 3129"/>
    </justification>
  </clause>

  <clause id="3814">
    <literal><![CDATA[
      L(x,y,K(z \ u,z)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(3813(a,1),1250(a,1,3))].">
      <j1 rule="para" parents="3813 1250"/>
    </justification>
  </clause>

  <clause id="3815">
    <literal><![CDATA[
      a(K(x \ y,x),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(3813(a,1),1500(a,1,1))].">
      <j1 rule="para" parents="3813 1500"/>
    </justification>
  </clause>

  <clause id="3816">
    <literal><![CDATA[
      L(x,y,K(z \ y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(250,a,2119,a(flip),b,3814,a),flip(a)].">
      <j1 rule="hyper" parents="250 2119 3814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3817">
    <literal><![CDATA[
      L(x,y * z,K(z,y)) = x
    ]]></literal>
    <justification jstring="[para(9(a,1),3816(a,1,3,1))].">
      <j1 rule="para" parents="9 3816"/>
    </justification>
  </clause>

  <clause id="3818">
    <literal><![CDATA[
      L(x,T(y,z) * z,K(z,y)) = x
    ]]></literal>
    <justification jstring="[para(2332(a,1),3817(a,1,3))].">
      <j1 rule="para" parents="2332 3817"/>
    </justification>
  </clause>

  <clause id="3819">
    <literal><![CDATA[
      L(x,y,T(z,y)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(3768,a,3818,a),flip(a)].">
      <j1 rule="hyper" parents="3768 3818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3820">
    <literal><![CDATA[
      L(x,y,(y * z) / y) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(190(a,1),3819(a,1,3)),flip(a)].">
      <j1 rule="para" parents="190 3819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3821">
    <literal><![CDATA[
      a(T(x,y),y,z) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[para(3819(a,1),1689(a,2,1))].">
      <j1 rule="para" parents="3819 1689"/>
    </justification>
  </clause>

  <clause id="3822">
    <literal><![CDATA[
      a(T(x,y),y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(250,a,1689,a,b,3821,a),flip(a)].">
      <j1 rule="hyper" parents="250 1689 3821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3823">
    <literal><![CDATA[
      a(x * (y / x),x,z) = a(y,x,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,3590,a(flip),b,3822,a),flip(a)].">
      <j1 rule="hyper" parents="65 3590 3822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3824">
    <literal><![CDATA[
      a(x,T(y,x),z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,3591,a(flip),b,3823,a)].">
      <j1 rule="hyper" parents="65 3591 3823"/>
    </justification>
  </clause>

  <clause id="3825">
    <literal><![CDATA[
      a(L(x,y,z),T(u,L(x,y,z)),x) = a(x,u,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,1519,a,b,3824,a)].">
      <j1 rule="hyper" parents="65 1519 3824"/>
    </justification>
  </clause>

  <clause id="3833">
    <literal><![CDATA[
      K(x \ (y * z),x) = K(y * (x \ z),x)
    ]]></literal>
    <justification jstring="[hyper(3136,a,3787,a),flip(a)].">
      <j1 rule="hyper" parents="3136 3787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3834">
    <literal><![CDATA[
      K(x * (y \ 1),y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(8(a,1),3833(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="8 3833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3835">
    <literal><![CDATA[
      K((x \ 1) \ y,x \ 1) = K(y * x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,1751,a(flip),b,3834,a),flip(a)].">
      <j1 rule="hyper" parents="65 1751 3834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3836">
    <literal><![CDATA[
      K(x * y,y \ 1) = K(y * x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,3804,a(flip),b,3835,a),flip(a)].">
      <j1 rule="hyper" parents="65 3804 3835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3837">
    <literal><![CDATA[
      K(a(x,y,z) * u,a(x,y,z) \ 1) = K(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,2281,a(flip),b,3836,a),flip(a)].">
      <j1 rule="hyper" parents="65 2281 3836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3838">
    <literal><![CDATA[
      R(K(x,(y / (z / u)) \ x),u \ z,u) = K(x,z / ((x \ y) * u))
    ]]></literal>
    <justification jstring="[para(3061(a,1),3810(a,1,1))].">
      <j1 rule="para" parents="3061 3810"/>
    </justification>
  </clause>

  <clause id="3839">
    <literal><![CDATA[
      a(L(x,y,z),u,x) = a(x,u,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,3824,a(flip),b,3825,a)].">
      <j1 rule="hyper" parents="65 3824 3825"/>
    </justification>
  </clause>

  <clause id="3840">
    <literal><![CDATA[
      a(x,y,L(x,z,u)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,1678,a(flip),b,3839,a),flip(a)].">
      <j1 rule="hyper" parents="65 1678 3839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3841">
    <literal><![CDATA[
      a(x,y,L(x,z,u)) = R(x,y,x) / x
    ]]></literal>
    <justification jstring="[hyper(250,a,3575,a,b,3840,a),flip(a)].">
      <j1 rule="hyper" parents="250 3575 3840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3843">
    <literal><![CDATA[
      L(a(x,y,x),z,u) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,1832,a(flip),b,3840,a)].">
      <j1 rule="hyper" parents="65 1832 3840"/>
    </justification>
  </clause>

  <clause id="3845">
    <literal><![CDATA[
      (x * y) * a(z,u,z) = x * (y * a(z,u,z))
    ]]></literal>
    <justification jstring="[hyper(116,a,3843,a(flip),b,1806,a(flip))].">
      <j1 rule="hyper" parents="116 3843 1806"/>
    </justification>
  </clause>

  <clause id="3848">
    <literal><![CDATA[
      R(x,y,a(z,u,z)) = x
    ]]></literal>
    <justification jstring="[hyper(1820,a,3845,a)].">
      <j1 rule="hyper" parents="1820 3845"/>
    </justification>
  </clause>

  <clause id="3850">
    <literal><![CDATA[
      L(T(x,y),y,a(z,u,z)) = T(x,y * a(z,u,z))
    ]]></literal>
    <justification jstring="[hyper(3766,a,3848,a)].">
      <j1 rule="hyper" parents="3766 3848"/>
    </justification>
  </clause>

  <clause id="3852">
    <literal><![CDATA[
      T(x,y * a(z,u,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(210,a,3850,a),flip(a)].">
      <j1 rule="hyper" parents="210 3850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3854">
    <literal><![CDATA[
      T(a(x,y,x) \ z,u) = a(x,y,x) \ T(z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,3724,a(flip),b,3852,a),flip(a)].">
      <j1 rule="hyper" parents="65 3724 3852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3855">
    <literal><![CDATA[
      K(x,y * a(z,u,z)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(112,a,3852,a(flip),b,2274,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="112 3852 2274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3857">
    <literal><![CDATA[
      K(x,y * a(z,u,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(250,a,2272,a,b,3855,a),flip(a)].">
      <j1 rule="hyper" parents="250 2272 3855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3858">
    <literal><![CDATA[
      K(x,y * a(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(3855(a,2),2328(a,1))].">
      <j1 rule="para" parents="3855 2328"/>
    </justification>
  </clause>

  <clause id="3859">
    <literal><![CDATA[
      K(x,a(y,z,y) * u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(3651(a,2),3857(a,1,2))].">
      <j1 rule="para" parents="3651 3857"/>
    </justification>
  </clause>

  <clause id="3860">
    <literal><![CDATA[
      K(x,T(y,z) / z) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(3675(a,1),3857(a,1,2))].">
      <j1 rule="para" parents="3675 3857"/>
    </justification>
  </clause>

  <clause id="3861">
    <literal><![CDATA[
      K(x,R(y,z,y) * u) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(3581(a,1),3859(a,1,2))].">
      <j1 rule="para" parents="3581 3859"/>
    </justification>
  </clause>

  <clause id="3862">
    <literal><![CDATA[
      K(x,y / T(z,y)) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(2038(a,1),3860(a,1,2))].">
      <j1 rule="para" parents="2038 3860"/>
    </justification>
  </clause>

  <clause id="3863">
    <literal><![CDATA[
      K(x,y / T(z,y)) = K(x,T(y / z,y))
    ]]></literal>
    <justification jstring="[hyper(250,a,2778,a,b,3862,a),flip(a)].">
      <j1 rule="hyper" parents="250 2778 3862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3864">
    <literal><![CDATA[
      K(R(x,y,x),R(z,u,z) * w) = K(x,z * w)
    ]]></literal>
    <justification jstring="[hyper(250,a,3526,a(flip),b,3861,a),flip(a)].">
      <j1 rule="hyper" parents="250 3526 3861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3865">
    <literal><![CDATA[
      K(x,T(y,z) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(3675(a,1),3858(a,1,2))].">
      <j1 rule="para" parents="3675 3858"/>
    </justification>
  </clause>

  <clause id="3866">
    <literal><![CDATA[
      K(x,y / T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(2038(a,1),3865(a,1,2))].">
      <j1 rule="para" parents="2038 3865"/>
    </justification>
  </clause>

  <clause id="3867">
    <literal><![CDATA[
      K(x,T(y / z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(3863(a,1),3866(a,1))].">
      <j1 rule="para" parents="3863 3866"/>
    </justification>
  </clause>

  <clause id="3868">
    <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(2790(a,1),3867(a,1))].">
      <j1 rule="para" parents="2790 3867"/>
    </justification>
  </clause>

  <clause id="3870">
    <literal><![CDATA[
      a(x,y,x) \ T(z * a(x,y,x),u) = T(z,u)
    ]]></literal>
    <justification jstring="[para(3654(a,1),3854(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3654 3854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3871">
    <literal><![CDATA[
      a(x,y,x) \ T(z * a(x,y,x),u) = z * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(250,a,2274,a(flip),b,3870,a),flip(a)].">
      <j1 rule="hyper" parents="250 2274 3870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3872">
    <literal><![CDATA[
      K(x * a(y,z,y),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(3721,a,3871,a)].">
      <j1 rule="hyper" parents="3721 3871"/>
    </justification>
  </clause>

  <clause id="3873">
    <literal><![CDATA[
      K(a(x,y,x) * z,u) = K(z,u)
    ]]></literal>
    <justification jstring="[para(3651(a,2),3872(a,1,1))].">
      <j1 rule="para" parents="3651 3872"/>
    </justification>
  </clause>

  <clause id="3875">
    <literal><![CDATA[
      K(R(x,y,x) \ z,u) = K(x \ z,u)
    ]]></literal>
    <justification jstring="[para(3587(a,1),3873(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3587 3873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3876">
    <literal><![CDATA[
      K(T(x,x \ y) \ z,u) = K(T(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[para(2103(a,1),3875(a,1,1,1))].">
      <j1 rule="para" parents="2103 3875"/>
    </justification>
  </clause>

  <clause id="3877">
    <literal><![CDATA[
      K(((x \ y) \ y) \ z,u) = K(T(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[para(105(a,1),3876(a,1,1,1))].">
      <j1 rule="para" parents="105 3876"/>
    </justification>
  </clause>

  <clause id="3878">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ u) = (w * K(T(y,z) \ u,x)) \ w
    ]]></literal>
    <justification jstring="[para(3877(a,1),3129(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3877 3129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3879">
    <literal><![CDATA[
      K(a(x,y,z),a(x,y,z) \ u) = K(u,a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(10(a,1),3837(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 3837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3880">
    <literal><![CDATA[
      K(a(x,y,z),(x * (y * z)) / z) = K(x * y,a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,2338,a(flip),b,3879,a)].">
      <j1 rule="hyper" parents="65 2338 3879"/>
    </justification>
  </clause>

  <clause id="3881">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ u) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(250,a,3129,a(flip),b,3878,a),flip(a)].">
      <j1 rule="hyper" parents="250 3129 3878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3882">
    <literal><![CDATA[
      K(x,((y \ x) \ x) \ z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(250,a,2946,a(flip),b,3881,a),flip(a)].">
      <j1 rule="hyper" parents="250 2946 3881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3893">
    <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),3248(a,1,2,1))].">
      <j1 rule="para" parents="9 3248"/>
    </justification>
  </clause>

  <clause id="3895">
    <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),3893(a,1,2))].">
      <j1 rule="para" parents="18 3893"/>
    </justification>
  </clause>

  <clause id="3896">
    <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,2758,a(flip),b,3895,a)].">
      <j1 rule="hyper" parents="65 2758 3895"/>
    </justification>
  </clause>

  <clause id="3897">
    <literal><![CDATA[
      K(L(x,y * z,u),z) = K(x,L(z,x * y,u))
    ]]></literal>
    <justification jstring="[hyper(250,a,2755,a(flip),b,3896,a),flip(a)].">
      <j1 rule="hyper" parents="250 2755 3896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3900">
    <literal><![CDATA[
      K(L(x,(x \ y) * z,u),z) = K(x,L(z,y,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),3897(a,2,2,2))].">
      <j1 rule="para" parents="10 3897"/>
    </justification>
  </clause>

  <clause id="3901">
    <literal><![CDATA[
      K(x,L(y * ((z * y) \ z),u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(65,a,3520,a(flip),b,3900,a),flip(a)].">
      <j1 rule="hyper" parents="65 3520 3900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3903">
    <literal><![CDATA[
      K(x,a(y,z,z \ 1) \ 1) = 1
    ]]></literal>
    <justification jstring="[hyper(65,a,2736,a(flip),b,3901,a)].">
      <j1 rule="hyper" parents="65 2736 3901"/>
    </justification>
  </clause>

  <clause id="3905">
    <literal><![CDATA[
      T(x,a(y,z,z \ 1) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,3903,a)].">
      <j1 rule="hyper" parents="58 3903"/>
    </justification>
  </clause>

  <clause id="3909">
    <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(112,a,104,a(flip),b,3299,a)].">
      <j1 rule="hyper" parents="112 104 3299"/>
    </justification>
  </clause>

  <clause id="3910">
    <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(3364,a,3909,a)].">
      <j1 rule="hyper" parents="3364 3909"/>
    </justification>
  </clause>

  <clause id="3911">
    <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(65,a,3384,a(flip),b,3910,a)].">
      <j1 rule="hyper" parents="65 3384 3910"/>
    </justification>
  </clause>

  <clause id="3912">
    <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),3911(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 3911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3913">
    <literal><![CDATA[
      L(K(x,y),T(z,y * x),y * x) = K(x,L(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(250,a,3100,a(flip),b,3912,a),flip(a)].">
      <j1 rule="hyper" parents="250 3100 3912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3914">
    <literal><![CDATA[
      K(x,L(y,x,((y * x) * z) / (y * x))) = L(K(x,y),z,y * x)
    ]]></literal>
    <justification jstring="[para(190(a,1),3913(a,1,2)),flip(a)].">
      <j1 rule="para" parents="190 3913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3916">
    <literal><![CDATA[
      L(K(x,y),z,y * x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,3792,a(flip),b,3914,a),flip(a)].">
      <j1 rule="hyper" parents="65 3792 3914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3919">
    <literal><![CDATA[
      K(x,R(y,x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,3757,a(flip),b,3916,a)].">
      <j1 rule="hyper" parents="65 3757 3916"/>
    </justification>
  </clause>

  <clause id="3921">
    <literal><![CDATA[
      K(x,R(y,x,z)) = K(x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(250,a,2332,a,b,3919,a),flip(a)].">
      <j1 rule="hyper" parents="250 2332 3919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3922">
    <literal><![CDATA[
      T(x,R(y,x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(114,a,3919,a,b,2470,a),flip(a)].">
      <j1 rule="hyper" parents="114 3919 2470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3923">
    <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(384(a,1),3922(a,1,2))].">
      <j1 rule="para" parents="384 3922"/>
    </justification>
  </clause>

  <clause id="3925">
    <literal><![CDATA[
      K(x,R(y,x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(3921(a,2),2379(a,1))].">
      <j1 rule="para" parents="3921 2379"/>
    </justification>
  </clause>

  <clause id="3926">
    <literal><![CDATA[
      K(x,y / (z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ (y / z)) = u
    ]]></literal>
    <justification jstring="[para(3347(a,1),3925(a,1))].">
      <j1 rule="para" parents="3347 3925"/>
    </justification>
  </clause>

  <clause id="3927">
    <literal><![CDATA[
      K(x,y / ((z * x) * u)) = K(x,x \ (y / (z * u)))
    ]]></literal>
    <justification jstring="[hyper(3926,a,3492,a),flip(a)].">
      <j1 rule="hyper" parents="3926 3492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3928">
    <literal><![CDATA[
      K(x,y / (x * z)) = K(x,x \ (y / z))
    ]]></literal>
    <justification jstring="[hyper(3926,a,3251,a),flip(a)].">
      <j1 rule="hyper" parents="3926 3251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3929">
    <literal><![CDATA[
      K(x,(x \ y) / z) = K(x,x \ (y / z))
    ]]></literal>
    <justification jstring="[hyper(3926,a,3194,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="3926 3194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3930">
    <literal><![CDATA[
      x * K(x,x \ (y / (z * u))) = T(x,y / ((x * z) * u))
    ]]></literal>
    <justification jstring="[para(3928(a,1),3495(a,1,2))].">
      <j1 rule="para" parents="3928 3495"/>
    </justification>
  </clause>

  <clause id="3931">
    <literal><![CDATA[
      K(x,x \ ((x * y) / z)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(9(a,1),3929(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 3929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3932">
    <literal><![CDATA[
      K(x,x \ (y / ((x \ z) * u))) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,3337,a(flip),b,3927,a),flip(a)].">
      <j1 rule="hyper" parents="65 3337 3927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3933">
    <literal><![CDATA[
      K(x,(x * y) / (z * u)) = K(x,y / ((x \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,3931,a(flip),b,3932,a),flip(a)].">
      <j1 rule="hyper" parents="65 3931 3932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3934">
    <literal><![CDATA[
      K(x,y / ((x \ z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,((z * u) / y) \ x) = w
    ]]></literal>
    <justification jstring="[para(3933(a,1),2728(a,1))].">
      <j1 rule="para" parents="3933 2728"/>
    </justification>
  </clause>

  <clause id="3935">
    <literal><![CDATA[
      T(x,y / ((x * z) * u)) = T(x,x \ (y / (z * u)))
    ]]></literal>
    <justification jstring="[hyper(2314,a,3930,a),flip(a)].">
      <j1 rule="hyper" parents="2314 3930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3939">
    <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,3923,a)].">
      <j1 rule="hyper" parents="65 27 3923"/>
    </justification>
  </clause>

  <clause id="3940">
    <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(250,a,2042,a(flip),b,3939,a),flip(a)].">
      <j1 rule="hyper" parents="250 2042 3939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3941">
    <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(250,a,27,a,b,3940,a),flip(a)].">
      <j1 rule="hyper" parents="250 27 3940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3942">
    <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(3935(a,1),3941(a,1,1))].">
      <j1 rule="para" parents="3935 3941"/>
    </justification>
  </clause>

  <clause id="3943">
    <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),3942(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 3942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3944">
    <literal><![CDATA[
      R(T(x,x \ y),z,u) = (R(x,z,u) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(421,a,3943,a),flip(a)].">
      <j1 rule="hyper" parents="421 3943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3945">
    <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(3943(a,1),2447(a,1,2,1))].">
      <j1 rule="para" parents="3943 2447"/>
    </justification>
  </clause>

  <clause id="3946">
    <literal><![CDATA[
      (R(x,y,z) \ (x * u)) \ (x * u) = R(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),3944(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 3944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3947">
    <literal><![CDATA[
      R(T(x,x \ y),x \ 1,y) = ((x \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[para(299(a,1),3944(a,2,1))].">
      <j1 rule="para" parents="299 3944"/>
    </justification>
  </clause>

  <clause id="3948">
    <literal><![CDATA[
      (R(x / y,z,u) \ x) \ x = R(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(436(a,1),3944(a,1,1)),flip(a)].">
      <j1 rule="para" parents="436 3944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3950">
    <literal><![CDATA[
      K(x,R(x / y,z,u) \ w) = K(x,R(y \ x,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(3948(a,1),3882(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3948 3882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3951">
    <literal><![CDATA[
      R(T(x,y / x),x \ 1,y) = ((x \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[para(2042(a,2),3947(a,1,1))].">
      <j1 rule="para" parents="2042 3947"/>
    </justification>
  </clause>

  <clause id="3952">
    <literal><![CDATA[
      ((x \ 1) * (y * x)) \ (y * x) = R(T(x,y),x \ 1,y * x)
    ]]></literal>
    <justification jstring="[para(11(a,1),3951(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11 3951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3953">
    <literal><![CDATA[
      R(T(x,R(x,y,z) * u),y,z) = (x * u) \ (x * (R(x,y,z) * u))
    ]]></literal>
    <justification jstring="[para(728(a,1),3946(a,1,1)),flip(a)].">
      <j1 rule="para" parents="728 3946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3954">
    <literal><![CDATA[
      (((1 / x) * (y * x)) \ (y * x)) \ 1 = 1 / R(T(x,y),x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(170,a,3952,a(flip),b,1736,a),flip(a)].">
      <j1 rule="hyper" parents="170 3952 1736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3955">
    <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(250,a,195,a(flip),b,3953,a),flip(a)].">
      <j1 rule="hyper" parents="250 195 3953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3956">
    <literal><![CDATA[
      R(T(x,R(x,y,z) * u),y,z) = R(T(x,x * u),y,z)
    ]]></literal>
    <justification jstring="[hyper(250,a,572,a(flip),b,3955,a),flip(a)].">
      <j1 rule="hyper" parents="250 572 3955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3957">
    <literal><![CDATA[
      T(x,y * R(x,z,u)) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(44,a,2143,a(flip),b,3956,a(flip))].">
      <j1 rule="hyper" parents="44 2143 3956"/>
    </justification>
  </clause>

  <clause id="3959">
    <literal><![CDATA[
      K(R(x,y,z) \ u,R(x,y,z)) = K(x \ u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(2613,a,3945,a),flip(a)].">
      <j1 rule="hyper" parents="2613 3945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3960">
    <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(3959(a,1),2258(a,1,1,2))].">
      <j1 rule="para" parents="3959 2258"/>
    </justification>
  </clause>

  <clause id="3961">
    <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(2488(a,1),3960(a,1,1))].">
      <j1 rule="para" parents="2488 3960"/>
    </justification>
  </clause>

  <clause id="3962">
    <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,3961,a)].">
      <j1 rule="hyper" parents="65 27 3961"/>
    </justification>
  </clause>

  <clause id="3963">
    <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(2258(a,1),3962(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2258 3962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3964">
    <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(250,a,29,a(flip),b,3963,a),flip(a)].">
      <j1 rule="hyper" parents="250 29 3963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3965">
    <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(3964(a,1),790(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3964 790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3966">
    <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(2820(a,1),3379(a,1,2))].">
      <j1 rule="para" parents="2820 3379"/>
    </justification>
  </clause>

  <clause id="3967">
    <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(250,a,2978,a(flip),b,3966,a),flip(a)].">
      <j1 rule="hyper" parents="250 2978 3966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3969">
    <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(2047(a,1),3463(a,1,2))].">
      <j1 rule="para" parents="2047 3463"/>
    </justification>
  </clause>

  <clause id="3970">
    <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(250,a,2488,a(flip),b,3969,a),flip(a)].">
      <j1 rule="hyper" parents="250 2488 3969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3971">
    <literal><![CDATA[
      ((K(x,y) / R(x,z,x)) * x) \ x = R(x * K(y,x),z,x)
    ]]></literal>
    <justification jstring="[para(3526(a,1),3970(a,1,1,1,1))].">
      <j1 rule="para" parents="3526 3970"/>
    </justification>
  </clause>

  <clause id="3972">
    <literal><![CDATA[
      (R(x,y,x) \ T(x,z)) \ x = R(x * K(z,x),y,x)
    ]]></literal>
    <justification jstring="[para(2611(a,1),3971(a,1,1))].">
      <j1 rule="para" parents="2611 3971"/>
    </justification>
  </clause>

  <clause id="3974">
    <literal><![CDATA[
      (x \ L(T(x,y),z,x)) \ x = R(x * K(y,x),z,x)
    ]]></literal>
    <justification jstring="[para(3705(a,1),3972(a,1,1))].">
      <j1 rule="para" parents="3705 3972"/>
    </justification>
  </clause>

  <clause id="3975">
    <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(2876(a,1),2770(a,1,2,2))].">
      <j1 rule="para" parents="2876 2770"/>
    </justification>
  </clause>

  <clause id="3976">
    <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(3702,a,3482,a)].">
      <j1 rule="hyper" parents="3702 3482"/>
    </justification>
  </clause>

  <clause id="3977">
    <literal><![CDATA[
      K(a(x,y,z),x) = 1
    ]]></literal>
    <justification jstring="[hyper(2607,a,3976,a),flip(a)].">
      <j1 rule="hyper" parents="2607 3976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3979">
    <literal><![CDATA[
      T(a(x,y,z),x) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3977,a)].">
      <j1 rule="hyper" parents="58 3977"/>
    </justification>
  </clause>

  <clause id="3980">
    <literal><![CDATA[
      a(x,y,z) * x = x * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,3979,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 3979 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3982">
    <literal><![CDATA[
      ((x * a(x,y,z)) * (x \ u)) / u = R(a(x,y,z),x,x \ u)
    ]]></literal>
    <justification jstring="[para(3980(a,1),99(a,1,1,1))].">
      <j1 rule="para" parents="3980 99"/>
    </justification>
  </clause>

  <clause id="3983">
    <literal><![CDATA[
      (x * a(x,y,z)) * (x \ u) = a(x,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(115,a,523,a(flip),b,3982,a),flip(a)].">
      <j1 rule="hyper" parents="115 523 3982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3986">
    <literal><![CDATA[
      R(1 / x,x,y) * ((1 / x) \ z) = a(1 / x,x,y) * z
    ]]></literal>
    <justification jstring="[para(1717(a,1),3983(a,1,1))].">
      <j1 rule="para" parents="1717 3983"/>
    </justification>
  </clause>

  <clause id="3987">
    <literal><![CDATA[
      R(x,y,T(z,x * y)) * (x \ u) = a(x,y,z) * u
    ]]></literal>
    <justification jstring="[para(1720(a,2),3983(a,1,1))].">
      <j1 rule="para" parents="1720 3983"/>
    </justification>
  </clause>

  <clause id="3988">
    <literal><![CDATA[
      R(x,x \ 1,y) * (x \ z) = a(x,x \ 1,y) * z
    ]]></literal>
    <justification jstring="[para(175(a,1),3987(a,1,1,3))].">
      <j1 rule="para" parents="175 3987"/>
    </justification>
  </clause>

  <clause id="3989">
    <literal><![CDATA[
      a(x,x \ 1,y) * (x * z) = R(x,x \ 1,y) * z
    ]]></literal>
    <justification jstring="[hyper(415,a,3988,a),flip(a)].">
      <j1 rule="hyper" parents="415 3988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3990">
    <literal><![CDATA[
      ((R(x,x \ 1,y) * z) * u) / ((x * z) * u) = R(a(x,x \ 1,y),x * z,u)
    ]]></literal>
    <justification jstring="[para(3989(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="3989 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3991">
    <literal><![CDATA[
      R(1 / x,x,y) * ((1 / x) \ z) = a(x \ 1,x,y) * z
    ]]></literal>
    <justification jstring="[para(1682(a,1),3986(a,2,1))].">
      <j1 rule="para" parents="1682 3986"/>
    </justification>
  </clause>

  <clause id="3992">
    <literal><![CDATA[
      a(x \ 1,x,y) * (R(1 / x,x,y) \ z) = (1 / x) \ z
    ]]></literal>
    <justification jstring="[hyper(65,a,726,a(flip),b,3991,a),flip(a)].">
      <j1 rule="hyper" parents="65 726 3991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3993">
    <literal><![CDATA[
      a(x \ 1,x,y) * (x * y) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[para(284(a,1),3992(a,1,2))].">
      <j1 rule="para" parents="284 3992"/>
    </justification>
  </clause>

  <clause id="3994">
    <literal><![CDATA[
      a((x \ 1) \ 1,x \ 1,y) * ((x \ 1) * y) = x \ y
    ]]></literal>
    <justification jstring="[para(76(a,1),3993(a,2,1))].">
      <j1 rule="para" parents="76 3993"/>
    </justification>
  </clause>

  <clause id="3995">
    <literal><![CDATA[
      a(x,x \ 1,y) * ((x \ 1) * y) = x \ y
    ]]></literal>
    <justification jstring="[para(1684(a,1),3994(a,1,1))].">
      <j1 rule="para" parents="1684 3994"/>
    </justification>
  </clause>

  <clause id="3996">
    <literal><![CDATA[
      (x * (y \ z)) / ((y \ 1) * z) = x * a(y,y \ 1,z)
    ]]></literal>
    <justification jstring="[para(3995(a,1),1578(a,1,1,2))].">
      <j1 rule="para" parents="3995 1578"/>
    </justification>
  </clause>

  <clause id="3997">
    <literal><![CDATA[
      R(x,y,z) \ R(R(x,y,z),x \ 1,u) = R(a(x,x \ 1,u),x * y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,2561,a(flip),b,3990,a)].">
      <j1 rule="hyper" parents="65 2561 3990"/>
    </justification>
  </clause>

  <clause id="3998">
    <literal><![CDATA[
      R(x,y,z) * a(x,x \ 1,u) = R(R(x,y,z),x \ 1,u)
    ]]></literal>
    <justification jstring="[hyper(116,a,523,a(flip),b,3997,a)].">
      <j1 rule="hyper" parents="116 523 3997"/>
    </justification>
  </clause>

  <clause id="3999">
    <literal><![CDATA[
      (R(x,y,z) * (x \ u)) / ((x \ 1) * u) = R(R(x,y,z),x \ 1,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,3996,a,b,3998,a)].">
      <j1 rule="hyper" parents="65 3996 3998"/>
    </justification>
  </clause>

  <clause id="4000">
    <literal><![CDATA[
      (x \ R(x,y,z)) * u = R(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(39,a,672,a,b,3999,a)].">
      <j1 rule="hyper" parents="39 672 3999"/>
    </justification>
  </clause>

  <clause id="4001">
    <literal><![CDATA[
      T(x \ R(x,y,z),x * u) = (x * u) \ (R(x,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(307,a,132,a(flip),b,4000,a)].">
      <j1 rule="hyper" parents="307 132 4000"/>
    </justification>
  </clause>

  <clause id="4002">
    <literal><![CDATA[
      (R(x,y,z) * u) / (x * u) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(113,a,132,a(flip),b,4000,a)].">
      <j1 rule="hyper" parents="113 132 4000"/>
    </justification>
  </clause>

  <clause id="4003">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ u = x * (R(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(4002(a,1),240(a,1,1))].">
      <j1 rule="para" parents="4002 240"/>
    </justification>
  </clause>

  <clause id="4004">
    <literal><![CDATA[
      (x * (y \ R(y,z,u))) \ w = y * (R(y,z,u) \ (x \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,1572,a,b,4003,a)].">
      <j1 rule="hyper" parents="65 1572 4003"/>
    </justification>
  </clause>

  <clause id="4005">
    <literal><![CDATA[
      (x * y) * a(x,y,z) = R(x,y,z) * y
    ]]></literal>
    <justification jstring="[hyper(116,a,2602,a,b,4001,a(flip))].">
      <j1 rule="hyper" parents="116 2602 4001"/>
    </justification>
  </clause>

  <clause id="4006">
    <literal><![CDATA[
      a(R(x,y,z),y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,1702,a,b,4005,a)].">
      <j1 rule="hyper" parents="36 1702 4005"/>
    </justification>
  </clause>

  <clause id="4007">
    <literal><![CDATA[
      L(x,y,R(z,y,x)) = a(z,y,x) \ x
    ]]></literal>
    <justification jstring="[para(4006(a,1),1673(a,2,1))].">
      <j1 rule="para" parents="4006 1673"/>
    </justification>
  </clause>

  <clause id="4008">
    <literal><![CDATA[
      L(x,y,R(z,y,x)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(250,a,1673,a,b,4007,a),flip(a)].">
      <j1 rule="hyper" parents="250 1673 4007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4010">
    <literal><![CDATA[
      x * (R(x,y,z) \ ((u * x) \ w)) = (u * R(x,y,z)) \ w
    ]]></literal>
    <justification jstring="[para(1547(a,1),4004(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1547 4004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4011">
    <literal><![CDATA[
      (x * R(y,z,u)) \ ((x * y) * w) = y * (R(y,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(9(a,1),4010(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 4010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4012">
    <literal><![CDATA[
      L(x,y,R((y * z) / y,y,x)) = z * (R(z,y,x) \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,791,a,b,4011,a)].">
      <j1 rule="hyper" parents="65 791 4011"/>
    </justification>
  </clause>

  <clause id="4014">
    <literal><![CDATA[
      L(x,y,(y * z) / y) = z * (R(z,y,x) \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,4008,a(flip),b,4012,a)].">
      <j1 rule="hyper" parents="65 4008 4012"/>
    </justification>
  </clause>

  <clause id="4016">
    <literal><![CDATA[
      R(x,y,z) \ z = x \ L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(112,a,3820,a(flip),b,4014,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="112 3820 4014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4018">
    <literal><![CDATA[
      R(x,y,z) = a(x,y,z) * x
    ]]></literal>
    <justification jstring="[hyper(41,a,1675,a,b,4016,a),flip(a)].">
      <j1 rule="hyper" parents="41 1675 4016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4019">
    <literal><![CDATA[
      R(x,y,z) = x * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(250,a,3980,a(flip),b,4018,a),flip(a)].">
      <j1 rule="hyper" parents="250 3980 4018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4022">
    <literal><![CDATA[
      a(x,y,z) = R(x,y,z) / x
    ]]></literal>
    <justification jstring="[hyper(113,a,4018,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="113 4018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4023">
    <literal><![CDATA[
      a(x,y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(112,a,4018,a,b,3980,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="112 4018 3980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4027">
    <literal><![CDATA[
      a(R(x,y,z),u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[para(4018(a,2),1499(a,1,1))].">
      <j1 rule="para" parents="4018 1499"/>
    </justification>
  </clause>

  <clause id="4029">
    <literal><![CDATA[
      K(x,y) * R(K(y,x),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(116,a,4019,a,b,2422,a)].">
      <j1 rule="hyper" parents="116 4019 2422"/>
    </justification>
  </clause>

  <clause id="4031">
    <literal><![CDATA[
      x * (a(x,y,z) * u) = R(x,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(115,a,4019,a,b,1578,a),flip(a)].">
      <j1 rule="hyper" parents="115 4019 1578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4035">
    <literal><![CDATA[
      R(x,y,L(x,z,u)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(39,a,3841,a(flip),b,4022,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="39 3841 4022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4037">
    <literal><![CDATA[
      (x * y) * a(T(x,y),z,u) = R(x,z,u) * y
    ]]></literal>
    <justification jstring="[hyper(116,a,4023,a,b,1552,a(flip))].">
      <j1 rule="hyper" parents="116 4023 1552"/>
    </justification>
  </clause>

  <clause id="4040">
    <literal><![CDATA[
      a(x,y,z) = T(x \ R(x,y,z),y)
    ]]></literal>
    <justification jstring="[para(4023(a,1),3800(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4023 3800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4044">
    <literal><![CDATA[
      K(R(x,y,L(x,z,u)),w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(4035(a,2),3526(a,1,1))].">
      <j1 rule="para" parents="4035 3526"/>
    </justification>
  </clause>

  <clause id="4046">
    <literal><![CDATA[
      T(((x * (y / z)) \ (x * y)) \ L(R(z,u,w),y / z,x),u) = a((x * (y / z)) \ (x * y),u,w)
    ]]></literal>
    <justification jstring="[para(473(a,1),4040(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="473 4040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4047">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) = K(R(x,u,L(T(x,y),w,v5)),z)
    ]]></literal>
    <justification jstring="[hyper(65,a,2911,a(flip),b,4044,a),flip(a)].">
      <j1 rule="hyper" parents="65 2911 4044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4065">
    <literal><![CDATA[
      K(x,y) * K(y,R(x,z,u)) = a(K(y,x),z * x,u)
    ]]></literal>
    <justification jstring="[para(3261(a,1),4029(a,1,2))].">
      <j1 rule="para" parents="3261 4029"/>
    </justification>
  </clause>

  <clause id="4066">
    <literal><![CDATA[
      K(R(x,y,L(T(x,z),u,w)),v5) = K(x,v5)
    ]]></literal>
    <justification jstring="[hyper(3028,a,4047,a),flip(a)].">
      <j1 rule="hyper" parents="3028 4047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4068">
    <literal><![CDATA[
      T(x,R(y,z,L(T(y,u),w,v5))) = (K(y,x) / x) \ 1
    ]]></literal>
    <justification jstring="[para(4066(a,1),2288(a,2,1,1))].">
      <j1 rule="para" parents="4066 2288"/>
    </justification>
  </clause>

  <clause id="4069">
    <literal><![CDATA[
      T(x,R(y,z,L(T(y,u),w,v5))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(250,a,2288,a,b,4068,a),flip(a)].">
      <j1 rule="hyper" parents="250 2288 4068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4070">
    <literal><![CDATA[
      T(x,R(y / (y / z),u,z)) = T(x,y / (y / z))
    ]]></literal>
    <justification jstring="[para(3711(a,1),4069(a,1,2,3))].">
      <j1 rule="para" parents="3711 4069"/>
    </justification>
  </clause>

  <clause id="4078">
    <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(2786(a,1),3975(a,2,1))].">
      <j1 rule="para" parents="2786 3975"/>
    </justification>
  </clause>

  <clause id="4079">
    <literal><![CDATA[
      (x \ T(x * y,x)) \ (y * K(x,K(z,x * y))) = K(x,T(x * y,z))
    ]]></literal>
    <justification jstring="[hyper(250,a,3342,a(flip),b,4078,a),flip(a)].">
      <j1 rule="hyper" parents="250 3342 4078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4082">
    <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(3319(a,2),4079(a,1,1))].">
      <j1 rule="para" parents="3319 4079"/>
    </justification>
  </clause>

  <clause id="4083">
    <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(2940(a,1),4082(a,1,2,2))].">
      <j1 rule="para" parents="2940 4082"/>
    </justification>
  </clause>

  <clause id="4084">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) \ K(x,z) = K(y,T(y * K(x,z),x))
    ]]></literal>
    <justification jstring="[hyper(238,a,4083,a)].">
      <j1 rule="hyper" parents="238 4083"/>
    </justification>
  </clause>

  <clause id="4085">
    <literal><![CDATA[
      K(T(x / y,x) \ x,z) * K(z,y) = K(x,T(x * K(z,y),z))
    ]]></literal>
    <justification jstring="[hyper(2437,a,4084,a)].">
      <j1 rule="hyper" parents="2437 4084"/>
    </justification>
  </clause>

  <clause id="4086">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) * K(z,x) = K(y,T(y * K(z,x),z))
    ]]></literal>
    <justification jstring="[para(3320(a,1),4085(a,1,1))].">
      <j1 rule="para" parents="3320 4085"/>
    </justification>
  </clause>

  <clause id="4087">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) * K(z,x) = K(y,y * K(z,x))
    ]]></literal>
    <justification jstring="[hyper(250,a,3191,a(flip),b,4086,a),flip(a)].">
      <j1 rule="hyper" parents="250 3191 4086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4088">
    <literal><![CDATA[
      K(x * K(y,z),x) = K(x,x * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,3442,a(flip),b,4087,a)].">
      <j1 rule="hyper" parents="65 3442 4087"/>
    </justification>
  </clause>

  <clause id="4089">
    <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(4088(a,1),2532(a,1,1,1,2))].">
      <j1 rule="para" parents="4088 2532"/>
    </justification>
  </clause>

  <clause id="4090">
    <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(2274(a,2),4089(a,1,1,1))].">
      <j1 rule="para" parents="2274 4089"/>
    </justification>
  </clause>

  <clause id="4091">
    <literal><![CDATA[
      R(T(x,K(y,z)),K(z,y),x) = T(x,x * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(2521,a,4090,a)].">
      <j1 rule="hyper" parents="2521 4090"/>
    </justification>
  </clause>

  <clause id="4092">
    <literal><![CDATA[
      T(x,x * K(y,z)) \ T(K(z,y) * x,x) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[para(4091(a,1),3967(a,1,1))].">
      <j1 rule="para" parents="4091 3967"/>
    </justification>
  </clause>

  <clause id="4093">
    <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(3424(a,1),4092(a,1,1,2,2))].">
      <j1 rule="para" parents="3424 4092"/>
    </justification>
  </clause>

  <clause id="4112">
    <literal><![CDATA[
      K(a(x,y,z),(x * (y * z)) / z) * (x * y) = a(x,y,z) * ((x * (y * z)) / z)
    ]]></literal>
    <justification jstring="[para(1705(a,2),2261(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1705 2261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4113">
    <literal><![CDATA[
      K(x * y,a(x,y,z) \ 1) * (x * y) = a(x,y,z) * ((x * (y * z)) / z)
    ]]></literal>
    <justification jstring="[para(3880(a,1),4112(a,1,1))].">
      <j1 rule="para" parents="3880 4112"/>
    </justification>
  </clause>

  <clause id="4114">
    <literal><![CDATA[
      a(x,y,z) * ((x * (y * z)) / z) = T(x * y,a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,2269,a,b,4113,a),flip(a)].">
      <j1 rule="hyper" parents="65 2269 4113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4115">
    <literal><![CDATA[
      T(x * y,a(x,y,y \ 1) \ 1) = a(x,y,y \ 1) * (x / (y \ 1))
    ]]></literal>
    <justification jstring="[para(71(a,1),4114(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="71 4114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4116">
    <literal><![CDATA[
      a(x,y,y \ 1) \ (x * y) = x / (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(112,a,3905,a(flip),b,4115,a(flip))].">
      <j1 rule="hyper" parents="112 3905 4115"/>
    </justification>
  </clause>

  <clause id="4117">
    <literal><![CDATA[
      a(x / (y \ 1),z,u) = a(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(4116(a,1),1500(a,1,1))].">
      <j1 rule="para" parents="4116 1500"/>
    </justification>
  </clause>

  <clause id="4118">
    <literal><![CDATA[
      a(x * (1 / y),z,u) = a(x / y,z,u)
    ]]></literal>
    <justification jstring="[para(79(a,1),4117(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="79 4117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4119">
    <literal><![CDATA[
      K(R(x \ y,z,u),w \ (y / x)) = K(R(x \ y,z,u),w \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(3151,a,3624,a),flip(a)].">
      <j1 rule="hyper" parents="3151 3624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4120">
    <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(2351(a,1),4119(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2351 4119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4122">
    <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(250,a,790,a(flip),b,3965,a),flip(a)].">
      <j1 rule="hyper" parents="250 790 3965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4124">
    <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,3340,a(flip),b,3696,a),flip(a)].">
      <j1 rule="hyper" parents="65 3340 3696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4126">
    <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(3974(a,1),3707(a,1,1,2))].">
      <j1 rule="para" parents="3974 3707"/>
    </justification>
  </clause>

  <clause id="4127">
    <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(3602(a,1),4126(a,1,1))].">
      <j1 rule="para" parents="3602 4126"/>
    </justification>
  </clause>

  <clause id="4128">
    <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),4127(a,1,2))].">
      <j1 rule="para" parents="27 4127"/>
    </justification>
  </clause>

  <clause id="4129">
    <literal><![CDATA[
      T((x / R(y,z,y)) * K(y,u),R((u * y) / u,z,y)) = ((R((u * y) / u,z,y) \ y) \ y) \ x
    ]]></literal>
    <justification jstring="[para(228(a,1),4128(a,1,2,1))].">
      <j1 rule="para" parents="228 4128"/>
    </justification>
  </clause>

  <clause id="4130">
    <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,3694,a(flip),b,4129,a)].">
      <j1 rule="hyper" parents="65 3694 4129"/>
    </justification>
  </clause>

  <clause id="4131">
    <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,4070,a(flip),b,4130,a)].">
      <j1 rule="hyper" parents="65 4070 4130"/>
    </justification>
  </clause>

  <clause id="4133">
    <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,3725,a(flip),b,4131,a),flip(a)].">
      <j1 rule="hyper" parents="65 3725 4131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4134">
    <literal><![CDATA[
      ((R((x * y) / x,z,y) \ y) \ y) \ u = ((x * y) / x) \ (y * (R(y,z,y) \ u))
    ]]></literal>
    <justification jstring="[para(3557(a,1),4133(a,2,2))].">
      <j1 rule="para" parents="3557 4133"/>
    </justification>
  </clause>

  <clause id="4135">
    <literal><![CDATA[
      ((R((x * y) / x,z,y) \ y) \ y) \ u = T(y,x) * (y \ (R(y,z,y) \ u))
    ]]></literal>
    <justification jstring="[hyper(250,a,2107,a(flip),b,4134,a),flip(a)].">
      <j1 rule="hyper" parents="250 2107 4134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4136">
    <literal><![CDATA[
      ((x \ L(T(x,y),z,x)) \ x) \ u = T(x,y) * (x \ (R(x,z,x) \ u))
    ]]></literal>
    <justification jstring="[para(3706(a,1),4135(a,1,1,1))].">
      <j1 rule="para" parents="3706 4135"/>
    </justification>
  </clause>

  <clause id="4137">
    <literal><![CDATA[
      T(x,y) * (x \ (R(x,z,x) \ u)) = R(x * K(y,x),z,x) \ u
    ]]></literal>
    <justification jstring="[para(3974(a,1),4136(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3974 4136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4138">
    <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(4137(a,1),2414(a,1))].">
      <j1 rule="para" parents="4137 2414"/>
    </justification>
  </clause>

  <clause id="4139">
    <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),4120(a,2,1,1))].">
      <j1 rule="para" parents="9 4120"/>
    </justification>
  </clause>

  <clause id="4140">
    <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(250,a,3287,a(flip),b,4139,a),flip(a)].">
      <j1 rule="hyper" parents="250 3287 4139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4142">
    <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),4140(a,1,1,1))].">
      <j1 rule="para" parents="9 4140"/>
    </justification>
  </clause>

  <clause id="4143">
    <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),4142(a,1,2,2))].">
      <j1 rule="para" parents="9 4142"/>
    </justification>
  </clause>

  <clause id="4144">
    <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(2548(a,1),4143(a,1,2,1,3))].">
      <j1 rule="para" parents="2548 4143"/>
    </justification>
  </clause>

  <clause id="4145">
    <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(3390(a,1),4093(a,1,2,1,1))].">
      <j1 rule="para" parents="3390 4093"/>
    </justification>
  </clause>

  <clause id="4146">
    <literal><![CDATA[
      K(x,T((y * (x \ z)) \ u,w)) = K(x,T((y * z) \ (u * x),w))
    ]]></literal>
    <justification jstring="[hyper(65,a,4092,a(flip),b,4145,a),flip(a)].">
      <j1 rule="hyper" parents="65 4092 4145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4147">
    <literal><![CDATA[
      K(x,T((y * z) \ (u * x),y * z)) = K(x,u / (y * (x \ z)))
    ]]></literal>
    <justification jstring="[hyper(3405,a,4146,a),flip(a)].">
      <j1 rule="hyper" parents="3405 4146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4148">
    <literal><![CDATA[
      K(x,(y * x) / (z * u)) = K(x,y / (z * (x \ u)))
    ]]></literal>
    <justification jstring="[hyper(3036,a,4147,a)].">
      <j1 rule="hyper" parents="3036 4147"/>
    </justification>
  </clause>

  <clause id="4149">
    <literal><![CDATA[
      K(x,y / (z * (x \ u))) = K(x,((z * u) / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(3628,a,4148,a),flip(a)].">
      <j1 rule="hyper" parents="3628 4148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4150">
    <literal><![CDATA[
      R(K(x,((y * z) / (u / w)) \ x),w \ u,w) = K(x,u / ((y * (x \ z)) * w))
    ]]></literal>
    <justification jstring="[para(4149(a,1),3810(a,1,1))].">
      <j1 rule="para" parents="4149 3810"/>
    </justification>
  </clause>

  <clause id="4151">
    <literal><![CDATA[
      K(x,y / ((x \ (z * u)) * w)) = K(x,y / ((z * (x \ u)) * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,3838,a(flip),b,4150,a)].">
      <j1 rule="hyper" parents="65 3838 4150"/>
    </justification>
  </clause>

  <clause id="4152">
    <literal><![CDATA[
      K(x,y / ((z * (x \ u)) * w)) = K(x,(((z * u) * w) / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(3934,a,4151,a),flip(a)].">
      <j1 rule="hyper" parents="3934 4151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4153">
    <literal><![CDATA[
      K(x,(((y * z) * u) / (z * u)) \ x) = R(K(x,y \ x),z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,3722,a(flip),b,4152,a),flip(a)].">
      <j1 rule="hyper" parents="65 3722 4152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4154">
    <literal><![CDATA[
      R(K(x,y \ x),z,u) = K(x,R(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[para(20(a,2),4153(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="20 4153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4155">
    <literal><![CDATA[
      K(x,R(y \ x,z,u) \ x) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2673(a,1),4154(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2673 4154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4156">
    <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(3950(a,1),4154(a,1,1))].">
      <j1 rule="para" parents="3950 4154"/>
    </justification>
  </clause>

  <clause id="4157">
    <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(4155(a,1),4156(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4155 4156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4158">
    <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),2130(a,1,1,2))].">
      <j1 rule="para" parents="79 2130"/>
    </justification>
  </clause>

  <clause id="4159">
    <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),4158(a,1,1))].">
      <j1 rule="para" parents="25 4158"/>
    </justification>
  </clause>

  <clause id="4160">
    <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(1326(a,1),4159(a,1,1))].">
      <j1 rule="para" parents="1326 4159"/>
    </justification>
  </clause>

  <clause id="4161">
    <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),4160(a,1,2,2,2))].">
      <j1 rule="para" parents="79 4160"/>
    </justification>
  </clause>

  <clause id="4162">
    <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),4161(a,1,2,2))].">
      <j1 rule="para" parents="25 4161"/>
    </justification>
  </clause>

  <clause id="4163">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ ((1 / x) \ ((1 / x) * (y * x))) = L(y,x,x \ 1) \ (x * y)
    ]]></literal>
    <justification jstring="[para(1326(a,1),4162(a,1,2,2))].">
      <j1 rule="para" parents="1326 4162"/>
    </justification>
  </clause>

  <clause id="4164">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ (y * x) = L(y,x,x \ 1) \ (x * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),4163(a,1,2))].">
      <j1 rule="para" parents="9 4163"/>
    </justification>
  </clause>

  <clause id="4166">
    <literal><![CDATA[
      1 / R(T(x,y),x \ 1,y * x) = (L(y,x,x \ 1) \ (x * y)) \ 1
    ]]></literal>
    <justification jstring="[para(4164(a,1),3954(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4164 3954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4167">
    <literal><![CDATA[
      ((L(x,y,y \ 1) \ (y * x)) \ 1) \ 1 = R(T(y,x),y \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(163,a,4166,a)].">
      <j1 rule="hyper" parents="163 4166"/>
    </justification>
  </clause>

  <clause id="4168">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) \ (x * y) = R(T(x,y),x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(65,a,1737,a(flip),b,4167,a)].">
      <j1 rule="hyper" parents="65 1737 4167"/>
    </justification>
  </clause>

  <clause id="4169">
    <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(2422(a,1),2150(a,1,1))].">
      <j1 rule="para" parents="2422 2150"/>
    </justification>
  </clause>

  <clause id="4170">
    <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(3464(a,1),4169(a,1,1))].">
      <j1 rule="para" parents="3464 4169"/>
    </justification>
  </clause>

  <clause id="4171">
    <literal><![CDATA[
      R(K(x,y),R(T(x,z),u,w),v5) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(232,a,4170,a)].">
      <j1 rule="hyper" parents="232 4170"/>
    </justification>
  </clause>

  <clause id="4174">
    <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,2573,a(flip),b,4171,a)].">
      <j1 rule="hyper" parents="65 2573 4171"/>
    </justification>
  </clause>

  <clause id="4175">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) * (w \ 1)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w \ R(T(x,y),z,u)) = v5
    ]]></literal>
    <justification jstring="[para(4174(a,2),3051(a,1))].">
      <j1 rule="para" parents="4174 3051"/>
    </justification>
  </clause>

  <clause id="4176">
    <literal><![CDATA[
      K(x,y \ R(T(x,z),u,w)) = K(x,R(x,u,w) * (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(4175,a,3545,a)].">
      <j1 rule="hyper" parents="4175 3545"/>
    </justification>
  </clause>

  <clause id="4178">
    <literal><![CDATA[
      K(x,R(x,y,z) * (u \ 1)) = K(x,u \ R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(3018,a,4176,a),flip(a)].">
      <j1 rule="hyper" parents="3018 4176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4179">
    <literal><![CDATA[
      K(x,y \ R(T(x,z),u,w)) = K(x,y \ R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,4176,a,b,4178,a)].">
      <j1 rule="hyper" parents="65 4176 4178"/>
    </justification>
  </clause>

  <clause id="4180">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) / w) = K(x,w \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(3050,a,4179,a)].">
      <j1 rule="hyper" parents="3050 4179"/>
    </justification>
  </clause>

  <clause id="4182">
    <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),3265(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 3265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4183">
    <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(250,a,2783,a(flip),b,4182,a),flip(a)].">
      <j1 rule="hyper" parents="250 2783 4182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4185">
    <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(3646,a,4183,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="3646 4183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4186">
    <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,3403,a(flip),b,4185,a)].">
      <j1 rule="hyper" parents="65 3403 4185"/>
    </justification>
  </clause>

  <clause id="4187">
    <literal><![CDATA[
      K(x,T((R(x,y,z) \ u) \ w,w)) = K(x,(R(x,y,z) * w) / u)
    ]]></literal>
    <justification jstring="[hyper(3648,a,4186,a)].">
      <j1 rule="hyper" parents="3648 4186"/>
    </justification>
  </clause>

  <clause id="4188">
    <literal><![CDATA[
      K(x,(R(x,y,z) * u) / w) = K(x,u / (R(x,y,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(3234,a,4187,a),flip(a)].">
      <j1 rule="hyper" parents="3234 4187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4190">
    <literal><![CDATA[
      K(x,R(x,y,z) / (u / w)) = K(x,w / (R(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(3570,a,4188,a)].">
      <j1 rule="hyper" parents="3570 4188"/>
    </justification>
  </clause>

  <clause id="4191">
    <literal><![CDATA[
      K(x,y / (R(x,z,u) \ w)) = K(x,(w / y) \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(3868,a,4190,a),flip(a)].">
      <j1 rule="hyper" parents="3868 4190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4192">
    <literal><![CDATA[
      K(x,(y * R(x,z,u)) / w) = K(x,(w / y) \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,3641,a,b,4191,a)].">
      <j1 rule="hyper" parents="65 3641 4191"/>
    </justification>
  </clause>

  <clause id="4193">
    <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,4124,a,b,4192,a)].">
      <j1 rule="hyper" parents="65 4124 4192"/>
    </justification>
  </clause>

  <clause id="4194">
    <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),4193(a,2,2,1))].">
      <j1 rule="para" parents="20 4193"/>
    </justification>
  </clause>

  <clause id="4195">
    <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,3264,a(flip),b,4194,a),flip(a)].">
      <j1 rule="hyper" parents="65 3264 4194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4197">
    <literal><![CDATA[
      T((x * y) \ ((x * (y / z)) * R((x * (y / z)) \ (x * y),u,w)),w) = ((x * (y / z)) \ (x * y)) \ L(R(z,u,w),y / z,x)
    ]]></literal>
    <justification jstring="[para(1551(a,1),3309(a,1,1))].">
      <j1 rule="para" parents="1551 3309"/>
    </justification>
  </clause>

  <clause id="4198">
    <literal><![CDATA[
      T((x * y) \ (x * ((y / z) * R((y / z) \ (x \ (x * y)),u,w))),w) = ((x * (y / z)) \ (x * y)) \ L(R(z,u,w),y / z,x)
    ]]></literal>
    <justification jstring="[para(624(a,1),4197(a,1,1,2))].">
      <j1 rule="para" parents="624 4197"/>
    </justification>
  </clause>

  <clause id="4199">
    <literal><![CDATA[
      T((x * y) \ (x * ((y / z) * R((y / z) \ y,u,w))),w) = ((x * (y / z)) \ (x * y)) \ L(R(z,u,w),y / z,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),4198(a,1,1,2,2,2,1,2))].">
      <j1 rule="para" parents="9 4198"/>
    </justification>
  </clause>

  <clause id="4200">
    <literal><![CDATA[
      T((x * y) \ (x * ((y / z) * R(z,u,w))),w) = ((x * (y / z)) \ (x * y)) \ L(R(z,u,w),y / z,x)
    ]]></literal>
    <justification jstring="[para(79(a,1),4199(a,1,1,2,2,2,1))].">
      <j1 rule="para" parents="79 4199"/>
    </justification>
  </clause>

  <clause id="4201">
    <literal><![CDATA[
      T((x * y) \ (x * (y * (z \ R(z,u,w)))),w) = ((x * (y / z)) \ (x * y)) \ L(R(z,u,w),y / z,x)
    ]]></literal>
    <justification jstring="[para(1548(a,1),4200(a,1,1,2,2))].">
      <j1 rule="para" parents="1548 4200"/>
    </justification>
  </clause>

  <clause id="4202">
    <literal><![CDATA[
      T(L(x \ R(x,y,z),u,w),z) = ((w * (u / x)) \ (w * u)) \ L(R(x,y,z),u / x,w)
    ]]></literal>
    <justification jstring="[para(18(a,2),4201(a,1,1))].">
      <j1 rule="para" parents="18 4201"/>
    </justification>
  </clause>

  <clause id="4203">
    <literal><![CDATA[
      L(T(x \ R(x,y,z),z),u,w) = ((w * (u / x)) \ (w * u)) \ L(R(x,y,z),u / x,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,25,a,b,4202,a)].">
      <j1 rule="hyper" parents="65 25 4202"/>
    </justification>
  </clause>

  <clause id="4204">
    <literal><![CDATA[
      ((x * (y / z)) \ (x * y)) \ L(R(z,u,w),y / z,x) = L(z \ R(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[para(3308(a,1),4203(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3308 4203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4205">
    <literal><![CDATA[
      T(L(x \ R(x,y,z),u,w),y) = a((w * (u / x)) \ (w * u),y,z)
    ]]></literal>
    <justification jstring="[para(4204(a,1),4046(a,1,1))].">
      <j1 rule="para" parents="4204 4046"/>
    </justification>
  </clause>

  <clause id="4206">
    <literal><![CDATA[
      L(T(x \ R(x,y,z),y),u,w) = a((w * (u / x)) \ (w * u),y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,25,a,b,4205,a)].">
      <j1 rule="hyper" parents="65 25 4205"/>
    </justification>
  </clause>

  <clause id="4207">
    <literal><![CDATA[
      a((x * (y / z)) \ (x * y),u,w) = L(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[para(4040(a,2),4206(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4040 4206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4208">
    <literal><![CDATA[
      a(L(x,y / x,z),u,w) = L(a(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(96(a,2),4207(a,1,1))].">
      <j1 rule="para" parents="96 4207"/>
    </justification>
  </clause>

  <clause id="4209">
    <literal><![CDATA[
      L(a(x,y,z),u,w) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,1678,a(flip),b,4208,a),flip(a)].">
      <j1 rule="hyper" parents="65 1678 4208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4215">
    <literal><![CDATA[
      (x * (y * (z * u))) \ (x * ((y * z) * u)) = a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,353,a,b,4209,a)].">
      <j1 rule="hyper" parents="65 353 4209"/>
    </justification>
  </clause>

  <clause id="4217">
    <literal><![CDATA[
      (x * y) * a(z,u,w) = x * (y * a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(116,a,4209,a(flip),b,1806,a(flip))].">
      <j1 rule="hyper" parents="116 4209 1806"/>
    </justification>
  </clause>

  <clause id="4229">
    <literal><![CDATA[
      x * (y * a(T(x,y),z,u)) = R(x,z,u) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,4037,a(flip),b,4217,a),flip(a)].">
      <j1 rule="hyper" parents="65 4037 4217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4232">
    <literal><![CDATA[
      x * a(T(y,x),z,u) = a(y,z,u) * x
    ]]></literal>
    <justification jstring="[hyper(36,a,4031,a,b,4229,a),flip(a)].">
      <j1 rule="hyper" parents="36 4031 4229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4233">
    <literal><![CDATA[
      a(T(x,y),z,u) = T(a(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(201,a,4232,a),flip(a)].">
      <j1 rule="hyper" parents="201 4232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4235">
    <literal><![CDATA[
      a((x * x) * y,z,u) = a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,1202,a(flip),b,4215,a)].">
      <j1 rule="hyper" parents="65 1202 4215"/>
    </justification>
  </clause>

  <clause id="4237">
    <literal><![CDATA[
      a((x * x) \ y,z,u) = a(y,z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),4235(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 4235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4238">
    <literal><![CDATA[
      a(1 / x,y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(184(a,1),4235(a,1,1)),flip(a)].">
      <j1 rule="para" parents="184 4235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4239">
    <literal><![CDATA[
      a(x * (x * y),z,u) = a(L(y,x,x),z,u)
    ]]></literal>
    <justification jstring="[para(93(a,1),4235(a,1,1))].">
      <j1 rule="para" parents="93 4235"/>
    </justification>
  </clause>

  <clause id="4240">
    <literal><![CDATA[
      a(x \ (y \ 1),z,u) = a(y * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,1716,a(flip),b,4238,a)].">
      <j1 rule="hyper" parents="65 1716 4238"/>
    </justification>
  </clause>

  <clause id="4241">
    <literal><![CDATA[
      a(x \ 1,y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,1682,a(flip),b,4238,a)].">
      <j1 rule="hyper" parents="65 1682 4238"/>
    </justification>
  </clause>

  <clause id="4242">
    <literal><![CDATA[
      a(x * (y * y),z,u) = a(x \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,4237,a(flip),b,4240,a),flip(a)].">
      <j1 rule="hyper" parents="65 4237 4240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4243">
    <literal><![CDATA[
      a(x * (y * y),z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(250,a,4241,a(flip),b,4242,a),flip(a)].">
      <j1 rule="hyper" parents="250 4241 4242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4244">
    <literal><![CDATA[
      a(x * (1 / y),z,u) = a(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(317(a,1),4243(a,1,1))].">
      <j1 rule="para" parents="317 4243"/>
    </justification>
  </clause>

  <clause id="4245">
    <literal><![CDATA[
      a(x / y,z,u) = a(x * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,4118,a(flip),b,4244,a)].">
      <j1 rule="hyper" parents="65 4118 4244"/>
    </justification>
  </clause>

  <clause id="4246">
    <literal><![CDATA[
      a(x * (y * x),z,u) = a(1 / y,z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,1776,a(flip),b,4245,a),flip(a)].">
      <j1 rule="hyper" parents="65 1776 4245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4247">
    <literal><![CDATA[
      a(x * (x * y),z,u) = a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(250,a,1678,a(flip),b,4239,a),flip(a)].">
      <j1 rule="hyper" parents="250 1678 4239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4249">
    <literal><![CDATA[
      a(x * (y * x),z,u) = a(T(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(104(a,1),4247(a,1,1,2))].">
      <j1 rule="para" parents="104 4247"/>
    </justification>
  </clause>

  <clause id="4250">
    <literal><![CDATA[
      a(T(x,y),z,u) = a(1 / x,z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,4246,a(flip),b,4249,a),flip(a)].">
      <j1 rule="hyper" parents="65 4246 4249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4252">
    <literal><![CDATA[
      a(T(x,y),z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(250,a,4238,a(flip),b,4250,a),flip(a)].">
      <j1 rule="hyper" parents="250 4238 4250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4254">
    <literal><![CDATA[
      T(a(x,y,z),u) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,4233,a(flip),b,4252,a)].">
      <j1 rule="hyper" parents="65 4233 4252"/>
    </justification>
  </clause>

  <clause id="4266">
    <literal><![CDATA[
      K(x,a(y,z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(111,a,4254,a,b,2268,a),flip(a)].">
      <j1 rule="hyper" parents="111 4254 2268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4268">
    <literal><![CDATA[
      K(a(x,y,z),u) = 1
    ]]></literal>
    <justification jstring="[hyper(57,a,4254,a)].">
      <j1 rule="hyper" parents="57 4254"/>
    </justification>
  </clause>

  <clause id="4271">
    <literal><![CDATA[
      K(x,y) * a(z,u,w) = a(z,u,w) * K(x,y)
    ]]></literal>
    <attribute><![CDATA[
      label(flip_matches_hint)
    ]]></attribute>
    <justification jstring="[para(4254(a,1),2519(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4254 2519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4279">
    <literal><![CDATA[
      a(x,y,T(z,u)) = 1 * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(4268(a,1),2299(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4268 2299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4281">
    <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(110,a,4279,a(flip),b,4122,a),flip(a)].">
      <j1 rule="hyper" parents="110 4279 4122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4286">
    <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(3685,a,4281,a)].">
      <j1 rule="hyper" parents="3685 4281"/>
    </justification>
  </clause>

  <clause id="4288">
    <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,4027,a(flip),b,4286,a)].">
      <j1 rule="hyper" parents="65 4027 4286"/>
    </justification>
  </clause>

  <clause id="4290">
    <literal><![CDATA[
      a(x,x \ y,R(x,z,u)) * K(x,y) = K(x,R(x,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(4288(a,1),3764(a,1,1))].">
      <j1 rule="para" parents="4288 3764"/>
    </justification>
  </clause>

  <clause id="4291">
    <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,4271,a,b,4290,a)].">
      <j1 rule="hyper" parents="65 4271 4290"/>
    </justification>
  </clause>

  <clause id="4292">
    <literal><![CDATA[
      K(x,R(x,y,z) \ u) = K(x,u) * a(x,x \ u,x)
    ]]></literal>
    <justification jstring="[para(1825(a,1),4291(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1825 4291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4293">
    <literal><![CDATA[
      K(x,R(x,y,z) \ u) = K(x,x \ u)
    ]]></literal>
    <justification jstring="[hyper(250,a,3600,a(flip),b,4292,a),flip(a)].">
      <j1 rule="hyper" parents="250 3600 4292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4295">
    <literal><![CDATA[
      K(x,x \ ((x * R(T(x,y),z,u)) / w)) = K(x,w \ x)
    ]]></literal>
    <justification jstring="[hyper(3765,a,4293,a),flip(a)].">
      <j1 rule="hyper" parents="3765 4293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4296">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) / w) = K(x,w \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,3931,a(flip),b,4295,a)].">
      <j1 rule="hyper" parents="65 3931 4295"/>
    </justification>
  </clause>

  <clause id="4297">
    <literal><![CDATA[
      K(x,y \ R(x,z,u)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,4180,a(flip),b,4296,a)].">
      <j1 rule="hyper" parents="65 4180 4296"/>
    </justification>
  </clause>

  <clause id="4299">
    <literal><![CDATA[
      K(R(x,y,z),u \ x) = K(x,R(u,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,4195,a(flip),b,4297,a)].">
      <j1 rule="hyper" parents="65 4195 4297"/>
    </justification>
  </clause>

  <clause id="4301">
    <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,4144,a(flip),b,4299,a),flip(a)].">
      <j1 rule="hyper" parents="65 4144 4299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4302">
    <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,4157,a(flip),b,4301,a)].">
      <j1 rule="hyper" parents="65 4157 4301"/>
    </justification>
  </clause>

  <clause id="4303">
    <literal><![CDATA[
      R(K(x,y),z,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(2581(a,1),4302(a,1,1))].">
      <j1 rule="para" parents="2581 4302"/>
    </justification>
  </clause>

  <clause id="4305">
    <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(4303(a,1),3732(a,1,1,1,2))].">
      <j1 rule="para" parents="4303 3732"/>
    </justification>
  </clause>

  <clause id="4306">
    <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(4138,a,4305,a)].">
      <j1 rule="hyper" parents="4138 4305"/>
    </justification>
  </clause>

  <clause id="4307">
    <literal><![CDATA[
      R(K(x,y),z,u) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(177,a,4306,a),flip(a)].">
      <j1 rule="hyper" parents="177 4306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4309">
    <literal><![CDATA[
      K(x,y) * K(y,R(x,z,u)) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(4307(a,1),4029(a,1,2))].">
      <j1 rule="para" parents="4307 4029"/>
    </justification>
  </clause>

  <clause id="4310">
    <literal><![CDATA[
      a(K(x,y),z * y,u) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,4065,a(flip),b,4309,a)].">
      <j1 rule="hyper" parents="65 4065 4309"/>
    </justification>
  </clause>

  <clause id="4342">
    <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(2707(a,1),3726(a,1,2,1))].">
      <j1 rule="para" parents="2707 3726"/>
    </justification>
  </clause>

  <clause id="4343">
    <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(1898(a,1),4342(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1898 4342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4344">
    <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(3415(a,1),4343(a,2,2))].">
      <j1 rule="para" parents="3415 4343"/>
    </justification>
  </clause>

  <clause id="4345">
    <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),4344(a,2,2,1))].">
      <j1 rule="para" parents="9 4344"/>
    </justification>
  </clause>

  <clause id="4346">
    <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(4168(a,1),4345(a,1,1,2))].">
      <j1 rule="para" parents="4168 4345"/>
    </justification>
  </clause>

  <clause id="4347">
    <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(3091(a,1),4346(a,1,1))].">
      <j1 rule="para" parents="3091 4346"/>
    </justification>
  </clause>

  <clause id="4349">
    <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(4168(a,1),4347(a,1,2,1))].">
      <j1 rule="para" parents="4168 4347"/>
    </justification>
  </clause>

  <clause id="4350">
    <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(2465(a,1),4349(a,1,2))].">
      <j1 rule="para" parents="2465 4349"/>
    </justification>
  </clause>

  <clause id="4351">
    <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(3003(a,1),4350(a,1,2))].">
      <j1 rule="para" parents="3003 4350"/>
    </justification>
  </clause>

  <clause id="4352">
    <literal><![CDATA[
      (x * y) / (y * T(x,z)) = T(K(z,x),y) * K(x,y)
    ]]></literal>
    <justification jstring="[para(3795(a,1),4351(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3795 4351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4353">
    <literal><![CDATA[
      (x * y) / (y * T(x,z)) = T(K(z,x) * K(x,y),y)
    ]]></literal>
    <justification jstring="[hyper(250,a,3187,a,b,4352,a),flip(a)].">
      <j1 rule="hyper" parents="250 3187 4352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4380">
    <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(3864(a,1),2620(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3864 2620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4381">
    <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(250,a,3180,a,b,4380,a),flip(a)].">
      <j1 rule="hyper" parents="250 3180 4380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4383">
    <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(2302(a,1),4381(a,2,1))].">
      <j1 rule="para" parents="2302 4381"/>
    </justification>
  </clause>

  <clause id="4384">
    <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(250,a,3436,a(flip),b,4383,a),flip(a)].">
      <j1 rule="hyper" parents="250 3436 4383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4385">
    <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(2065(a,2),4384(a,1,2))].">
      <j1 rule="para" parents="2065 4384"/>
    </justification>
  </clause>

  <clause id="4386">
    <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(3957(a,1),4385(a,1,2,1))].">
      <j1 rule="para" parents="3957 4385"/>
    </justification>
  </clause>

  <clause id="4387">
    <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(2062(a,2),4386(a,1,2,1))].">
      <j1 rule="para" parents="2062 4386"/>
    </justification>
  </clause>

  <clause id="4389">
    <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(3747(a,1),4387(a,1,2))].">
      <j1 rule="para" parents="3747 4387"/>
    </justification>
  </clause>

  <clause id="4390">
    <literal><![CDATA[
      T(x * R(y,z,u),x * y) = R(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(513(a,1),4389(a,1,2)),flip(a)].">
      <j1 rule="para" parents="513 4389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4392">
    <literal><![CDATA[
      (x * R(y,z,u)) / (R(y,z,u) * T(x,y)) = K(x * y,x * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(170,a,4390,a(flip),b,2287,a(flip))].">
      <j1 rule="hyper" parents="170 4390 2287"/>
    </justification>
  </clause>

  <clause id="4393">
    <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,4353,a(flip),b,4392,a)].">
      <j1 rule="hyper" parents="65 4353 4392"/>
    </justification>
  </clause>

  <clause id="4394">
    <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(4065(a,1),4393(a,1,1))].">
      <j1 rule="para" parents="4065 4393"/>
    </justification>
  </clause>

  <clause id="4396">
    <literal><![CDATA[
      K(x * y,x * R(y,z,u)) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,4254,a(flip),b,4394,a),flip(a)].">
      <j1 rule="hyper" parents="65 4254 4394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4398">
    <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),4396(a,1,1))].">
      <j1 rule="para" parents="12 4396"/>
    </justification>
  </clause>

  <clause id="4399">
    <literal><![CDATA[
      K(x,x * (y \ R(y,z,u))) = a(K(x / y,y),z * y,u)
    ]]></literal>
    <justification jstring="[para(1548(a,1),4398(a,1,2))].">
      <j1 rule="para" parents="1548 4398"/>
    </justification>
  </clause>

  <clause id="4400">
    <literal><![CDATA[
      K(x,x * (y \ R(y,z,u))) = a(K(y \ x,y),z * y,u)
    ]]></literal>
    <justification jstring="[para(2344(a,1),4399(a,2,1))].">
      <j1 rule="para" parents="2344 4399"/>
    </justification>
  </clause>

  <clause id="4401">
    <literal><![CDATA[
      K(x,x * (y \ R(y,z,u))) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(250,a,3815,a(flip),b,4400,a),flip(a)].">
      <j1 rule="hyper" parents="250 3815 4400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4402">
    <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,2840,a,b,4401,a)].">
      <j1 rule="hyper" parents="65 2840 4401"/>
    </justification>
  </clause>

  <clause id="4403">
    <literal><![CDATA[
      (x * K(y \ R(y,z,u),x)) \ L(x,a(w,v5,v6),v7) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[para(1582(a,2),4402(a,1,2))].">
      <j1 rule="para" parents="1582 4402"/>
    </justification>
  </clause>

  <clause id="4404">
    <literal><![CDATA[
      K(x,y \ R(y,z,u)) * (x \ L(x,a(w,v5,v6),v7)) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(2596,a,4403,a)].">
      <j1 rule="hyper" parents="2596 4403"/>
    </justification>
  </clause>

  <clause id="4406">
    <literal><![CDATA[
      a(K(x,y),z * y,u) = K(x,y \ R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,1712,a(flip),b,4404,a),flip(a)].">
      <j1 rule="hyper" parents="65 1712 4404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4408">
    <literal><![CDATA[
      a(K(x,y),z * y,u) = K(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(4023(a,2),4406(a,2,2))].">
      <j1 rule="para" parents="4023 4406"/>
    </justification>
  </clause>

  <clause id="4409">
    <literal><![CDATA[
      a(K(x,y),z,u) = K(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,4310,a(flip),b,4408,a)].">
      <j1 rule="hyper" parents="65 4310 4408"/>
    </justification>
  </clause>

  <clause id="4410">
    <literal><![CDATA[
      a(K(x,y),z,u) = 1
    ]]></literal>
    <justification jstring="[hyper(250,a,4266,a(flip),b,4409,a),flip(a)].">
      <j1 rule="hyper" parents="250 4266 4409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4411">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer("aK1")
    ]]></attribute>
    <justification jstring="[resolve(4410,a,66,a)].">
      <j1 rule="resolve" parents="4410 66"/>
    </justification>
  </clause>

</proof>

</proofs>
