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<!DOCTYPE proofs SYSTEM "proof3.dtd">

<?xml-stylesheet type="text/xsl" href="proof3.xsl"?>

<proofs number_of_proofs="1">

<source>MOL-M.out</source>

<heading><![CDATA[
Prover9 (32) version Aug-2007, Aug 2007.
Process 17639 was started by mccune on cleo,
Tue Aug  7 10:07:58 2007
The command was "/home/mccune/LADR/bin/prover9 -f MOL-M.in MOL-M-interp.outx".
]]></heading>

<proof number="1" length="546" max_count="59">

<comments><![CDATA[
% Proof 1 at 786.63 (+ 1.38) seconds: MOD_SS.
% Length of proof is 546.
% Level of proof is 73.
% Maximum clause weight is 59.
% Given clauses 1801.
]]></comments>

  <clause id="1" type="goal">
    <literal><![CDATA[
      f(x,f(y,f(x,f(z,z)))) = f(x,f(z,f(x,f(y,y))))
    ]]></literal>
    <attribute><![CDATA[
      answer(MOD_SS)
    ]]></attribute>
    <attribute><![CDATA[
      label(non_clause)
    ]]></attribute>
    <attribute><![CDATA[
      label(goal)
    ]]></attribute>
    <justification jstring="[goal].">
      <j1 rule="goal"/>
    </justification>
  </clause>

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

  <clause id="3" type="deny">
    <literal><![CDATA[
      f(c1,f(c3,f(c1,f(c2,c2)))) != f(c1,f(c2,f(c1,f(c3,c3))))
    ]]></literal>
    <attribute><![CDATA[
      answer(MOD_SS)
    ]]></attribute>
    <justification jstring="[deny(1)].">
      <j1 rule="deny" parents="1"/>
    </justification>
  </clause>

  <clause id="4">
    <literal><![CDATA[
      f(f(x,y),f(y,f(f(f(f(f(y,x),f(f(f(y,y),z),f(f(f(f(f(y,y),z),z),y),f(y,u)))),f(f(f(y,y),z),f(f(f(f(f(y,y),z),z),y),f(y,u)))),y),f(y,w)))) = y
    ]]></literal>
    <justification jstring="[para(2(a,1),2(a,1,2,1))].">
      <j1 rule="para" parents="2 2"/>
    </justification>
  </clause>

  <clause id="5">
    <literal><![CDATA[
      f(f(f(f(f(x,x),y),f(f(f(f(f(x,z),y),y),x),f(x,u))),f(z,x)),f(f(f(f(z,x),f(z,x)),w),f(f(f(f(x,w),w),f(z,x)),f(f(z,x),v5)))) = f(z,x)
    ]]></literal>
    <justification jstring="[para(2(a,1),2(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="2 2"/>
    </justification>
  </clause>

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

  <clause id="8">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),z),y)) = y
    ]]></literal>
    <justification jstring="[para(4(a,1),2(a,1,2,2))].">
      <j1 rule="para" parents="4 2"/>
    </justification>
  </clause>

  <clause id="11">
    <literal><![CDATA[
      f(f(x,y),f(y,y)) = y
    ]]></literal>
    <justification jstring="[para(4(a,1),4(a,1,2,2))].">
      <j1 rule="para" parents="4 4"/>
    </justification>
  </clause>

  <clause id="12">
    <literal><![CDATA[
      f(x,f(f(x,y),f(f(f(f(f(f(x,x),f(z,x)),y),y),f(x,x)),f(f(x,x),u)))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(11(a,1),2(a,1,1)),rewrite([11(3)])].">
      <j1 rule="para" parents="11 2"/>
      <j2 rule="rewrite" parents="11"/>
    </justification>
  </clause>

  <clause id="13">
    <literal><![CDATA[
      f(f(x,f(y,y)),f(f(y,z),f(f(f(f(f(f(y,y),x),z),z),f(y,y)),f(f(y,y),u)))) = f(y,y)
    ]]></literal>
    <justification jstring="[para(11(a,1),2(a,1,2,1,1))].">
      <j1 rule="para" parents="11 2"/>
    </justification>
  </clause>

  <clause id="14">
    <literal><![CDATA[
      f(f(x,y),f(y,f(f(f(f(f(y,x),f(y,y)),f(y,y)),y),f(y,z)))) = y
    ]]></literal>
    <justification jstring="[para(11(a,1),2(a,1,2,1))].">
      <j1 rule="para" parents="11 2"/>
    </justification>
  </clause>

  <clause id="16">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),f(x,x)),f(f(f(x,f(x,x)),y),f(y,z)))) = y
    ]]></literal>
    <justification jstring="[para(11(a,1),2(a,1,2,2,1,1,1))].">
      <j1 rule="para" parents="11 2"/>
    </justification>
  </clause>

  <clause id="20">
    <literal><![CDATA[
      f(f(x,f(y,y)),y) = f(y,y)
    ]]></literal>
    <justification jstring="[para(11(a,1),11(a,1,2))].">
      <j1 rule="para" parents="11 11"/>
    </justification>
  </clause>

  <clause id="22">
    <literal><![CDATA[
      f(f(x,y),f(y,f(f(y,y),f(y,z)))) = y
    ]]></literal>
    <justification jstring="[back_rewrite(14),rewrite([20(7)])].">
      <j1 rule="back_rewrite" parents="14"/>
      <j2 rule="rewrite" parents="20"/>
    </justification>
  </clause>

  <clause id="25">
    <literal><![CDATA[
      f(f(f(x,x),y),f(f(f(y,y),x),f(f(f(f(x,x),x),y),f(y,z)))) = y
    ]]></literal>
    <justification jstring="[para(20(a,1),2(a,1,2,2,1,1,1))].">
      <j1 rule="para" parents="20 2"/>
    </justification>
  </clause>

  <clause id="32">
    <literal><![CDATA[
      f(f(f(x,x),y),x) = f(x,x)
    ]]></literal>
    <justification jstring="[para(8(a,1),11(a,1,1)),rewrite([8(7)]),flip(a)].">
      <j1 rule="para" parents="8 11"/>
      <j2 rule="rewrite" parents="8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36">
    <literal><![CDATA[
      f(f(x,f(f(x,x),y)),f(f(f(f(f(x,x),y),f(f(x,x),y)),z),f(f(f(f(f(x,x),z),z),f(f(x,x),y)),f(f(f(x,x),y),u)))) = f(f(x,x),y)
    ]]></literal>
    <justification jstring="[para(32(a,1),2(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="32 2"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      f(f(x,x),f(f(f(x,x),x),f(f(f(x,x),x),f(x,y)))) = x
    ]]></literal>
    <justification jstring="[para(32(a,1),2(a,1,2,2,1,1))].">
      <j1 rule="para" parents="32 2"/>
    </justification>
  </clause>

  <clause id="40">
    <literal><![CDATA[
      f(f(x,y),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(11(a,1),32(a,1,1,1)),rewrite([11(6)])].">
      <j1 rule="para" parents="11 32"/>
      <j2 rule="rewrite" parents="11"/>
    </justification>
  </clause>

  <clause id="41">
    <literal><![CDATA[
      f(f(f(f(f(x,x),y),f(f(f(f(f(x,z),y),y),x),f(x,u))),f(z,x)),f(f(f(f(z,x),f(z,x)),w),f(f(f(f(x,w),w),f(z,x)),x))) = f(z,x)
    ]]></literal>
    <justification jstring="[para(2(a,1),5(a,1,2,2,2))].">
      <j1 rule="para" parents="2 5"/>
    </justification>
  </clause>

  <clause id="50">
    <literal><![CDATA[
      f(x,f(f(x,y),f(f(f(f(x,y),y),f(x,x)),f(f(x,x),z)))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(32(a,1),5(a,1,1)),rewrite([40(3),40(3)])].">
      <j1 rule="para" parents="32 5"/>
      <j2 rule="rewrite" parents="40 40"/>
    </justification>
  </clause>

  <clause id="53">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),f(f(y,x),f(y,x))),f(f(f(y,x),y),f(y,z)))) = y
    ]]></literal>
    <justification jstring="[para(40(a,1),2(a,1,2,2,1,1))].">
      <j1 rule="para" parents="40 2"/>
    </justification>
  </clause>

  <clause id="54">
    <literal><![CDATA[
      f(f(x,f(y,z)),f(f(f(f(y,z),f(y,z)),u),f(f(f(f(f(f(y,z),x),u),u),f(y,z)),y))) = f(y,z)
    ]]></literal>
    <justification jstring="[para(40(a,1),2(a,1,2,2,2))].">
      <j1 rule="para" parents="40 2"/>
    </justification>
  </clause>

  <clause id="55">
    <literal><![CDATA[
      f(x,f(f(y,x),f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(2(a,1),40(a,1,1))].">
      <j1 rule="para" parents="2 40"/>
    </justification>
  </clause>

  <clause id="61">
    <literal><![CDATA[
      f(x,f(f(x,y),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(40(a,1),40(a,1,1))].">
      <j1 rule="para" parents="40 40"/>
    </justification>
  </clause>

  <clause id="63">
    <literal><![CDATA[
      f(f(x,y),f(f(z,f(y,y)),f(f(f(f(f(y,x),f(f(z,f(y,y)),f(z,f(y,y)))),f(f(z,f(y,y)),f(z,f(y,y)))),y),f(y,u)))) = y
    ]]></literal>
    <justification jstring="[para(55(a,1),2(a,1,2,1))].">
      <j1 rule="para" parents="55 2"/>
    </justification>
  </clause>

  <clause id="64">
    <literal><![CDATA[
      f(f(f(f(x,y),f(x,y)),y),f(f(f(y,y),z),f(f(f(f(f(x,y),z),z),y),f(y,u)))) = y
    ]]></literal>
    <justification jstring="[para(55(a,1),2(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="55 2"/>
    </justification>
  </clause>

  <clause id="66">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),z),f(f(f(f(f(y,x),z),z),y),f(u,y)))) = y
    ]]></literal>
    <justification jstring="[para(55(a,1),2(a,1,2,2,2))].">
      <j1 rule="para" parents="55 2"/>
    </justification>
  </clause>

  <clause id="82">
    <literal><![CDATA[
      f(f(x,f(f(x,x),f(x,y))),f(x,f(f(x,x),f(x,y)))) = x
    ]]></literal>
    <justification jstring="[para(22(a,1),32(a,1)),flip(a)].">
      <j1 rule="para" parents="22 32"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="85">
    <literal><![CDATA[
      f(f(x,y),f(y,f(f(y,y),f(z,y)))) = y
    ]]></literal>
    <justification jstring="[para(55(a,1),22(a,1,2,2,2))].">
      <j1 rule="para" parents="55 22"/>
    </justification>
  </clause>

  <clause id="102">
    <literal><![CDATA[
      f(x,f(f(x,x),f(x,f(y,f(x,x))))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(11(a,1),85(a,1,1)),rewrite([40(4)])].">
      <j1 rule="para" parents="11 85"/>
      <j2 rule="rewrite" parents="40"/>
    </justification>
  </clause>

  <clause id="126">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),z),f(f(f(f(f(y,x),z),z),y),f(f(f(y,y),u),f(f(f(f(f(y,w),u),u),y),f(y,v5)))))) = y
    ]]></literal>
    <justification jstring="[para(2(a,1),7(a,1,1,2)),rewrite([2(12),2(12),2(14),2(17),2(30)])].">
      <j1 rule="para" parents="2 7"/>
      <j2 rule="rewrite" parents="2 2 2 2 2"/>
    </justification>
  </clause>

  <clause id="127">
    <literal><![CDATA[
      f(f(f(x,x),f(y,x)),f(f(f(f(y,x),f(y,x)),z),f(f(f(f(x,z),z),f(y,x)),x))) = f(y,x)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(11(a,1),7(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="11 7"/>
    </justification>
  </clause>

  <clause id="137">
    <literal><![CDATA[
      f(f(x,f(y,z)),f(f(f(f(y,z),f(y,z)),f(f(f(y,z),x),f(f(y,z),x))),f(f(f(f(y,z),x),f(y,z)),z))) = f(y,z)
    ]]></literal>
    <justification jstring="[para(40(a,1),7(a,1,2,2,1,1))].">
      <j1 rule="para" parents="40 7"/>
    </justification>
  </clause>

  <clause id="154">
    <literal><![CDATA[
      f(f(f(f(f(x,x),x),f(f(x,x),x)),x),f(f(f(f(x,x),x),f(f(x,x),x)),x)) = f(f(f(x,x),x),f(f(f(f(x,x),x),f(f(x,x),x)),x))
    ]]></literal>
    <justification jstring="[para(127(a,1),20(a,1,1)),flip(a)].">
      <j1 rule="para" parents="127 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="157">
    <literal><![CDATA[
      f(f(f(x,x),f(y,x)),f(f(f(f(y,x),f(y,x)),f(x,x)),f(f(x,f(y,x)),x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(40(a,1),127(a,1,2,2,1,1))].">
      <j1 rule="para" parents="40 127"/>
    </justification>
  </clause>

  <clause id="161">
    <literal><![CDATA[
      f(f(f(x,x),x),f(f(f(f(x,x),x),f(f(x,x),x)),x)) = f(f(f(x,x),x),f(f(x,x),x))
    ]]></literal>
    <justification jstring="[para(127(a,1),102(a,1,2,2,2)),rewrite([154(19),32(24),40(21),32(9),154(18)]),flip(a)].">
      <j1 rule="para" parents="127 102"/>
      <j2 rule="rewrite" parents="154 32 40 32 154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="165">
    <literal><![CDATA[
      f(f(f(f(f(x,x),x),f(f(x,x),x)),x),f(f(f(f(x,x),x),f(f(x,x),x)),x)) = f(f(f(x,x),x),f(f(x,x),x))
    ]]></literal>
    <justification jstring="[back_rewrite(154),rewrite([161(22)])].">
      <j1 rule="back_rewrite" parents="154"/>
      <j2 rule="rewrite" parents="161"/>
    </justification>
  </clause>

  <clause id="174">
    <literal><![CDATA[
      f(f(f(f(x,x),x),f(f(f(x,x),x),f(x,y))),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(37(a,1),55(a,1,2,1)),rewrite([37(16),37(18)])].">
      <j1 rule="para" parents="37 55"/>
      <j2 rule="rewrite" parents="37 37"/>
    </justification>
  </clause>

  <clause id="175">
    <literal><![CDATA[
      f(f(x,x),f(f(f(x,x),x),f(f(f(x,x),x),f(y,x)))) = x
    ]]></literal>
    <justification jstring="[para(55(a,1),37(a,1,2,2,2))].">
      <j1 rule="para" parents="55 37"/>
    </justification>
  </clause>

  <clause id="182">
    <literal><![CDATA[
      f(x,f(f(x,x),f(x,y))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(82(a,1),11(a,1,1)),rewrite([82(9)]),flip(a)].">
      <j1 rule="para" parents="82 11"/>
      <j2 rule="rewrite" parents="82"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="193">
    <literal><![CDATA[
      f(f(x,x),f(x,f(f(x,x),y))) = x
    ]]></literal>
    <justification jstring="[para(11(a,1),182(a,1,2,1)),rewrite([40(8)])].">
      <j1 rule="para" parents="11 182"/>
      <j2 rule="rewrite" parents="40"/>
    </justification>
  </clause>

  <clause id="196">
    <literal><![CDATA[
      f(x,f(f(x,x),f(y,x))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(55(a,1),182(a,1,2,2))].">
      <j1 rule="para" parents="55 182"/>
    </justification>
  </clause>

  <clause id="205">
    <literal><![CDATA[
      f(f(x,x),f(x,f(y,f(x,x)))) = x
    ]]></literal>
    <justification jstring="[para(55(a,1),193(a,1,2,2))].">
      <j1 rule="para" parents="55 193"/>
    </justification>
  </clause>

  <clause id="234">
    <literal><![CDATA[
      f(f(f(f(x,x),x),f(f(x,x),x)),x) = f(f(x,x),x)
    ]]></literal>
    <justification jstring="[para(127(a,1),205(a,1,2,2)),rewrite([165(13),32(14),40(11)]),flip(a)].">
      <j1 rule="para" parents="127 205"/>
      <j2 rule="rewrite" parents="165 32 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="246">
    <literal><![CDATA[
      f(f(f(f(x,x),x),f(f(f(x,x),x),f(y,x))),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(55(a,1),174(a,1,1,2,2))].">
      <j1 rule="para" parents="55 174"/>
    </justification>
  </clause>

  <clause id="255">
    <literal><![CDATA[
      f(x,f(f(x,y),f(f(f(f(f(f(x,x),f(z,x)),y),y),f(x,x)),f(u,f(x,x))))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(55(a,1),12(a,1,2,2,2))].">
      <j1 rule="para" parents="55 12"/>
    </justification>
  </clause>

  <clause id="270">
    <literal><![CDATA[
      f(x,f(f(x,f(x,x)),f(f(x,f(x,x)),f(y,f(x,x))))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(11(a,1),175(a,1,1)),rewrite([40(3),40(5)])].">
      <j1 rule="para" parents="11 175"/>
      <j2 rule="rewrite" parents="40 40"/>
    </justification>
  </clause>

  <clause id="294">
    <literal><![CDATA[
      f(f(x,f(y,y)),f(f(y,z),f(f(f(f(f(f(y,y),x),z),z),f(y,y)),f(u,f(y,y))))) = f(y,y)
    ]]></literal>
    <justification jstring="[para(55(a,1),13(a,1,2,2,2))].">
      <j1 rule="para" parents="55 13"/>
    </justification>
  </clause>

  <clause id="302">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),f(f(x,f(x,x)),f(y,f(x,x)))),x) = f(x,x)
    ]]></literal>
    <justification jstring="[para(11(a,1),246(a,1,1,1,1)),rewrite([40(5),40(11)])].">
      <j1 rule="para" parents="11 246"/>
      <j2 rule="rewrite" parents="40 40"/>
    </justification>
  </clause>

  <clause id="358">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),f(x,x)),f(f(f(x,f(x,x)),y),f(z,y)))) = y
    ]]></literal>
    <justification jstring="[para(55(a,1),16(a,1,2,2,2))].">
      <j1 rule="para" parents="55 16"/>
    </justification>
  </clause>

  <clause id="364">
    <literal><![CDATA[
      f(x,f(f(f(x,x),x),f(x,f(f(x,x),y)))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(246(a,1),16(a,1,2,2,1)),rewrite([11(4),40(3),55(6)])].">
      <j1 rule="para" parents="246 16"/>
      <j2 rule="rewrite" parents="11 40 55"/>
    </justification>
  </clause>

  <clause id="387">
    <literal><![CDATA[
      f(f(f(f(x,x),x),f(x,f(f(x,x),y))),x) = f(x,x)
    ]]></literal>
    <justification jstring="[para(364(a,1),55(a,1,2,1)),rewrite([364(14),40(9),364(14)])].">
      <j1 rule="para" parents="364 55"/>
      <j2 rule="rewrite" parents="364 40 364"/>
    </justification>
  </clause>

  <clause id="414">
    <literal><![CDATA[
      f(f(f(f(x,x),x),f(x,f(y,f(x,x)))),x) = f(x,x)
    ]]></literal>
    <justification jstring="[para(55(a,1),387(a,1,1,2,2))].">
      <j1 rule="para" parents="55 387"/>
    </justification>
  </clause>

  <clause id="459">
    <literal><![CDATA[
      f(f(f(f(x,x),y),f(f(f(f(y,y),y),x),f(x,z))),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(25(a,1),55(a,1,2,1)),rewrite([25(19),25(21)])].">
      <j1 rule="para" parents="25 55"/>
      <j2 rule="rewrite" parents="25 25"/>
    </justification>
  </clause>

  <clause id="529">
    <literal><![CDATA[
      f(f(x,f(f(x,x),y)),f(f(f(f(f(x,x),y),f(f(x,x),y)),z),f(f(f(f(f(x,x),z),z),f(f(x,x),y)),f(x,x)))) = f(f(x,x),y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(32(a,1),36(a,1,2,2,2))].">
      <j1 rule="para" parents="32 36"/>
    </justification>
  </clause>

  <clause id="534">
    <literal><![CDATA[
      f(f(x,f(f(x,x),x)),f(f(f(x,x),x),f(f(f(x,x),f(f(x,x),x)),f(f(f(x,x),x),y)))) = f(f(x,x),x)
    ]]></literal>
    <justification jstring="[para(234(a,1),36(a,1,2,1)),rewrite([32(8)])].">
      <j1 rule="para" parents="234 36"/>
      <j2 rule="rewrite" parents="32"/>
    </justification>
  </clause>

  <clause id="535">
    <literal><![CDATA[
      f(f(f(x,x),f(x,y)),f(f(f(f(x,y),f(x,y)),z),f(f(f(f(x,z),z),f(x,y)),x))) = f(x,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(11(a,1),529(a,1,1,2,1)),rewrite([40(6),40(7),40(10),40(12),40(14),40(17)])].">
      <j1 rule="para" parents="11 529"/>
      <j2 rule="rewrite" parents="40 40 40 40 40 40"/>
    </justification>
  </clause>

  <clause id="543">
    <literal><![CDATA[
      f(f(x,x),f(x,y)) = x
    ]]></literal>
    <justification jstring="[para(387(a,1),529(a,1,2,2)),rewrite([40(4),182(4),40(5),40(8),40(13),20(11),40(3),40(4)]),flip(a)].">
      <j1 rule="para" parents="387 529"/>
      <j2 rule="rewrite" parents="40 182 40 40 40 20 40 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="544">
    <literal><![CDATA[
      f(f(x,x),f(y,x)) = x
    ]]></literal>
    <justification jstring="[para(414(a,1),529(a,1,2,2)),rewrite([543(4),196(4),543(5),543(8),543(13),20(11),543(3),543(4)]),flip(a)].">
      <j1 rule="para" parents="414 529"/>
      <j2 rule="rewrite" parents="543 196 543 543 543 20 543 543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="546">
    <literal><![CDATA[
      f(x,f(f(f(f(x,y),f(x,y)),z),f(f(f(f(x,z),z),f(x,y)),x))) = f(x,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(535),rewrite([543(3)])].">
      <j1 rule="back_rewrite" parents="535"/>
      <j2 rule="rewrite" parents="543"/>
    </justification>
  </clause>

  <clause id="555">
    <literal><![CDATA[
      f(f(x,f(f(x,x),x)),f(f(f(x,x),x),f(x,f(f(f(x,x),x),y)))) = f(f(x,x),x)
    ]]></literal>
    <justification jstring="[back_rewrite(534),rewrite([544(9)])].">
      <j1 rule="back_rewrite" parents="534"/>
      <j2 rule="rewrite" parents="544"/>
    </justification>
  </clause>

  <clause id="568">
    <literal><![CDATA[
      f(x,f(f(x,y),f(f(f(f(x,y),y),f(x,x)),f(z,f(x,x))))) = f(x,x)
    ]]></literal>
    <justification jstring="[back_rewrite(255),rewrite([544(4)])].">
      <j1 rule="back_rewrite" parents="255"/>
      <j2 rule="rewrite" parents="544"/>
    </justification>
  </clause>

  <clause id="573">
    <literal><![CDATA[
      f(x,f(f(f(f(y,x),f(y,x)),f(x,x)),f(f(x,f(y,x)),x))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(157),rewrite([544(3)])].">
      <j1 rule="back_rewrite" parents="157"/>
      <j2 rule="rewrite" parents="544"/>
    </justification>
  </clause>

  <clause id="576">
    <literal><![CDATA[
      f(x,f(f(f(f(y,x),f(y,x)),z),f(f(f(f(x,z),z),f(y,x)),x))) = f(y,x)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(127),rewrite([544(3)])].">
      <j1 rule="back_rewrite" parents="127"/>
      <j2 rule="rewrite" parents="544"/>
    </justification>
  </clause>

  <clause id="579">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),z),f(f(f(f(f(x,y),z),z),y),f(x,y)))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(2(a,1),546(a,1,2,1,1,1)),rewrite([2(12),2(17),2(22)])].">
      <j1 rule="para" parents="2 546"/>
      <j2 rule="rewrite" parents="2 2 2"/>
    </justification>
  </clause>

  <clause id="582">
    <literal><![CDATA[
      f(f(x,f(y,y)),f(f(y,z),f(f(f(f(f(x,f(y,y)),z),z),f(y,y)),f(x,f(y,y))))) = f(y,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(20(a,1),546(a,1,2,1,1,1)),rewrite([20(6),543(5),20(10),20(17)])].">
      <j1 rule="para" parents="20 546"/>
      <j2 rule="rewrite" parents="20 543 20 20"/>
    </justification>
  </clause>

  <clause id="587">
    <literal><![CDATA[
      f(f(x,y),f(f(f(x,x),z),f(f(f(f(f(x,y),z),z),x),f(x,y)))) = x
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(40(a,1),546(a,1,2,1,1,1)),rewrite([40(4),40(9),40(14)])].">
      <j1 rule="para" parents="40 546"/>
      <j2 rule="rewrite" parents="40 40 40"/>
    </justification>
  </clause>

  <clause id="589">
    <literal><![CDATA[
      f(x,f(f(f(f(x,y),f(x,y)),f(x,x)),f(f(x,f(x,y)),x))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(40(a,1),546(a,1,2,2,1,1))].">
      <j1 rule="para" parents="40 546"/>
    </justification>
  </clause>

  <clause id="599">
    <literal><![CDATA[
      f(f(x,y),f(f(f(f(f(f(x,x),x),y),y),f(x,x)),f(f(x,x),z))) = x
    ]]></literal>
    <justification jstring="[para(13(a,1),546(a,1,2,2,1)),rewrite([40(6),40(17),543(29),20(27),40(3),40(5)]),flip(a)].">
      <j1 rule="para" parents="13 546"/>
      <j2 rule="rewrite" parents="40 40 543 20 40 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="604">
    <literal><![CDATA[
      f(x,f(f(x,x),y)) = f(x,x)
    ]]></literal>
    <justification jstring="[para(387(a,1),546(a,1,2,2)),rewrite([11(10)]),flip(a)].">
      <j1 rule="para" parents="387 546"/>
      <j2 rule="rewrite" parents="11"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="607">
    <literal><![CDATA[
      f(x,f(y,f(x,x))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(414(a,1),546(a,1,2,2)),rewrite([11(10)]),flip(a)].">
      <j1 rule="para" parents="414 546"/>
      <j2 rule="rewrite" parents="11"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="609">
    <literal><![CDATA[
      f(f(x,x),f(f(f(x,x),x),f(x,f(f(f(x,x),x),y)))) = f(f(x,x),x)
    ]]></literal>
    <justification jstring="[back_rewrite(555),rewrite([604(3)])].">
      <j1 rule="back_rewrite" parents="555"/>
      <j2 rule="rewrite" parents="604"/>
    </justification>
  </clause>

  <clause id="635">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),f(f(f(y,y),z),f(f(f(f(f(x,y),z),z),y),f(x,y)))),f(f(f(y,f(f(f(y,y),z),f(f(f(f(f(x,y),z),z),y),f(x,y)))),y),f(x,y)))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(579(a,1),579(a,1,2,2,1,1,1))].">
      <j1 rule="para" parents="579 579"/>
    </justification>
  </clause>

  <clause id="640">
    <literal><![CDATA[
      f(f(x,y),f(f(f(x,x),f(y,y)),f(f(f(y,f(y,y)),x),f(x,y)))) = x
    ]]></literal>
    <justification jstring="[para(11(a,1),587(a,1,2,2,1,1,1))].">
      <j1 rule="para" parents="11 587"/>
    </justification>
  </clause>

  <clause id="655">
    <literal><![CDATA[
      f(f(x,y),f(f(f(x,x),f(f(f(x,x),z),f(f(f(f(f(x,y),z),z),x),f(x,y)))),f(f(f(x,f(f(f(x,x),z),f(f(f(f(f(x,y),z),z),x),f(x,y)))),x),f(x,y)))) = x
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(587(a,1),587(a,1,2,2,1,1,1))].">
      <j1 rule="para" parents="587 587"/>
    </justification>
  </clause>

  <clause id="656">
    <literal><![CDATA[
      f(f(x,y),f(y,f(f(f(f(f(y,x),f(y,z)),f(y,z)),y),f(y,u)))) = y
    ]]></literal>
    <justification jstring="[para(543(a,1),2(a,1,2,1))].">
      <j1 rule="para" parents="543 2"/>
    </justification>
  </clause>

  <clause id="657">
    <literal><![CDATA[
      f(f(f(x,y),f(x,y)),y) = f(x,y)
    ]]></literal>
    <justification jstring="[para(2(a,1),543(a,1,2))].">
      <j1 rule="para" parents="2 543"/>
    </justification>
  </clause>

  <clause id="662">
    <literal><![CDATA[
      f(f(f(x,y),f(x,y)),x) = f(x,y)
    ]]></literal>
    <justification jstring="[para(40(a,1),543(a,1,2))].">
      <j1 rule="para" parents="40 543"/>
    </justification>
  </clause>

  <clause id="679">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),z),f(f(f(f(f(x,y),z),z),y),f(y,u)))) = y
    ]]></literal>
    <justification jstring="[back_rewrite(64),rewrite([657(4)])].">
      <j1 rule="back_rewrite" parents="64"/>
      <j2 rule="rewrite" parents="657"/>
    </justification>
  </clause>

  <clause id="753">
    <literal><![CDATA[
      f(f(x,x),f(f(f(x,x),y),f(f(f(f(f(x,z),y),y),x),f(x,u)))) = x
    ]]></literal>
    <justification jstring="[para(2(a,1),657(a,1,1,1)),rewrite([2(11),2(22)])].">
      <j1 rule="para" parents="2 657"/>
      <j2 rule="rewrite" parents="2 2"/>
    </justification>
  </clause>

  <clause id="762">
    <literal><![CDATA[
      f(f(x,x),f(f(f(x,x),f(y,y)),f(f(f(y,f(y,y)),x),f(x,z)))) = x
    ]]></literal>
    <justification jstring="[para(16(a,1),657(a,1,1,1)),rewrite([16(11),16(22)])].">
      <j1 rule="para" parents="16 657"/>
      <j2 rule="rewrite" parents="16 16"/>
    </justification>
  </clause>

  <clause id="764">
    <literal><![CDATA[
      f(x,f(f(x,y),f(f(f(f(x,y),y),f(x,y)),x))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(657(a,1),546(a,1,2,1))].">
      <j1 rule="para" parents="657 546"/>
    </justification>
  </clause>

  <clause id="767">
    <literal><![CDATA[
      f(f(x,x),f(f(f(x,x),y),f(f(f(f(f(z,x),y),y),x),f(z,x)))) = x
    ]]></literal>
    <justification jstring="[para(579(a,1),657(a,1,1,1)),rewrite([579(11),579(22)])].">
      <j1 rule="para" parents="579 657"/>
      <j2 rule="rewrite" parents="579 579"/>
    </justification>
  </clause>

  <clause id="768">
    <literal><![CDATA[
      f(x,f(f(y,x),f(f(f(f(x,x),x),f(y,x)),x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(657(a,1),576(a,1,2,1))].">
      <j1 rule="para" parents="657 576"/>
    </justification>
  </clause>

  <clause id="771">
    <literal><![CDATA[
      f(f(x,y),f(y,f(f(f(y,f(f(f(y,y),z),f(f(f(f(f(x,y),z),z),y),f(x,y)))),y),f(x,y)))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(657(a,1),635(a,1,1)),rewrite([657(8),657(12),767(12),657(7),657(11),657(16)])].">
      <j1 rule="para" parents="657 635"/>
      <j2 rule="rewrite" parents="657 657 767 657 657 657"/>
    </justification>
  </clause>

  <clause id="774">
    <literal><![CDATA[
      f(f(x,y),f(x,f(f(f(x,f(f(f(x,x),z),f(f(f(f(f(x,y),z),z),x),f(x,y)))),x),f(x,y)))) = x
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(655(a,1),657(a,2)),rewrite([753(12),753(28),753(44),657(48)])].">
      <j1 rule="para" parents="655 657"/>
      <j2 rule="rewrite" parents="753 753 753 657"/>
    </justification>
  </clause>

  <clause id="783">
    <literal><![CDATA[
      f(f(f(f(f(x,x),y),f(f(f(f(f(x,z),y),y),x),f(x,u))),f(z,x)),f(f(z,x),f(f(f(f(x,z),z),f(z,x)),f(f(z,x),w)))) = f(z,x)
    ]]></literal>
    <justification jstring="[para(662(a,1),5(a,1,2,1))].">
      <j1 rule="para" parents="662 5"/>
    </justification>
  </clause>

  <clause id="825">
    <literal><![CDATA[
      f(x,f(f(x,y),f(f(f(f(x,y),f(f(f(f(x,y),f(x,y)),z),f(f(f(f(x,z),z),f(x,y)),x))),f(x,y)),x))) = f(x,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(543(a,1),771(a,1,1)),rewrite([543(9),543(13),543(18)])].">
      <j1 rule="para" parents="543 771"/>
      <j2 rule="rewrite" parents="543 543 543"/>
    </justification>
  </clause>

  <clause id="846">
    <literal><![CDATA[
      f(f(f(f(x,y),f(f(f(f(x,y),f(f(f(f(x,y),f(x,y)),z),f(f(f(f(x,z),z),f(x,y)),x))),f(x,y)),x)),x),f(f(f(x,x),u),f(f(f(f(f(x,y),u),u),x),f(x,w)))) = x
    ]]></literal>
    <justification jstring="[para(825(a,1),2(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="825 2"/>
    </justification>
  </clause>

  <clause id="1005">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),z),f(f(f(f(f(x,y),z),z),y),f(u,y)))) = y
    ]]></literal>
    <justification jstring="[para(55(a,1),66(a,1,2,2,1,1,1,1)),rewrite([657(4)])].">
      <j1 rule="para" parents="55 66"/>
      <j2 rule="rewrite" parents="657"/>
    </justification>
  </clause>

  <clause id="1008">
    <literal><![CDATA[
      f(f(x,y),f(f(f(x,x),z),f(f(f(f(f(x,y),z),z),x),f(u,x)))) = x
    ]]></literal>
    <justification jstring="[para(61(a,1),66(a,1,2,2,1,1,1,1)),rewrite([662(4)])].">
      <j1 rule="para" parents="61 66"/>
      <j2 rule="rewrite" parents="662"/>
    </justification>
  </clause>

  <clause id="1018">
    <literal><![CDATA[
      f(f(f(x,x),y),f(f(f(f(f(x,f(x,x)),y),y),x),f(z,x))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(66(a,1),546(a,1,2,2,1)),rewrite([32(7),32(17),604(27),11(26),32(3),32(6)]),flip(a)].">
      <j1 rule="para" parents="66 546"/>
      <j2 rule="rewrite" parents="32 32 604 11 32 32"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1156">
    <literal><![CDATA[
      f(f(f(f(f(f(x,y),f(x,y)),f(y,y)),f(f(y,f(x,y)),y)),y),f(f(f(y,y),f(f(x,y),f(x,y))),f(f(f(x,y),y),f(y,z)))) = y
    ]]></literal>
    <justification jstring="[para(573(a,1),53(a,1,2,1,2,1)),rewrite([573(22),573(25)])].">
      <j1 rule="para" parents="573 53"/>
      <j2 rule="rewrite" parents="573 573"/>
    </justification>
  </clause>

  <clause id="1181">
    <literal><![CDATA[
      f(f(f(x,f(f(f(x,f(f(f(x,x),y),f(f(f(f(f(x,z),y),y),x),f(x,z)))),x),f(x,z))),f(x,z)),f(f(f(f(x,z),f(x,z)),u),f(f(f(f(x,u),u),f(x,z)),x))) = f(x,z)
    ]]></literal>
    <justification jstring="[para(774(a,1),54(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="774 54"/>
    </justification>
  </clause>

  <clause id="1212">
    <literal><![CDATA[
      f(x,f(f(f(f(f(x,f(x,x)),f(x,y)),f(x,y)),x),f(x,z))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(543(a,1),599(a,1,1)),rewrite([543(3),543(9),543(10)])].">
      <j1 rule="para" parents="543 599"/>
      <j2 rule="rewrite" parents="543 543 543"/>
    </justification>
  </clause>

  <clause id="1213">
    <literal><![CDATA[
      f(x,f(f(f(f(f(x,f(x,x)),f(y,x)),f(y,x)),x),f(x,z))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(544(a,1),599(a,1,1)),rewrite([543(3),543(9),543(10)])].">
      <j1 rule="para" parents="544 599"/>
      <j2 rule="rewrite" parents="543 543 543"/>
    </justification>
  </clause>

  <clause id="1278">
    <literal><![CDATA[
      f(f(f(f(f(x,x),f(y,y)),f(f(f(y,f(y,y)),x),f(x,y))),f(x,y)),f(f(f(f(x,y),f(x,y)),z),f(f(f(f(x,z),z),f(x,y)),x))) = f(x,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(640(a,1),54(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="640 54"/>
    </justification>
  </clause>

  <clause id="1279">
    <literal><![CDATA[
      f(f(x,f(y,z)),f(f(y,z),f(f(f(f(y,z),f(f(f(f(y,z),f(y,z)),f(x,x)),f(f(f(x,f(x,x)),f(y,z)),f(f(y,z),x)))),f(y,z)),y))) = f(y,z)
    ]]></literal>
    <justification jstring="[para(640(a,1),54(a,1,2,2,1,1,1)),rewrite([762(19)])].">
      <j1 rule="para" parents="640 54"/>
      <j2 rule="rewrite" parents="762"/>
    </justification>
  </clause>

  <clause id="1294">
    <literal><![CDATA[
      f(f(f(x,f(f(f(f(f(x,y),f(x,y)),f(x,y)),x),f(x,y))),f(x,y)),f(f(f(f(x,y),f(x,y)),z),f(f(f(f(x,z),z),f(x,y)),x))) = f(x,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(61(a,1),1278(a,1,1,1,2,2)),rewrite([543(8),543(3),543(10),61(13),61(15),61(16),61(21),61(26)])].">
      <j1 rule="para" parents="61 1278"/>
      <j2 rule="rewrite" parents="543 543 543 61 61 61 61 61"/>
    </justification>
  </clause>

  <clause id="1330">
    <literal><![CDATA[
      f(f(x,y),f(f(f(f(y,x),f(y,z)),f(y,z)),y)) = y
    ]]></literal>
    <justification jstring="[para(607(a,1),656(a,1,2,2)),rewrite([55(15)])].">
      <j1 rule="para" parents="607 656"/>
      <j2 rule="rewrite" parents="55"/>
    </justification>
  </clause>

  <clause id="1360">
    <literal><![CDATA[
      f(f(x,f(y,z)),f(f(f(f(f(y,z),x),z),z),f(y,z))) = f(y,z)
    ]]></literal>
    <justification jstring="[para(2(a,1),1330(a,1,2,1,1,2)),rewrite([2(16)])].">
      <j1 rule="para" parents="2 1330"/>
      <j2 rule="rewrite" parents="2"/>
    </justification>
  </clause>

  <clause id="1362">
    <literal><![CDATA[
      f(x,f(f(f(x,f(f(y,x),z)),f(f(y,x),z)),f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(11(a,1),1330(a,1,2,1,1,1)),rewrite([544(3)])].">
      <j1 rule="para" parents="11 1330"/>
      <j2 rule="rewrite" parents="544"/>
    </justification>
  </clause>

  <clause id="1366">
    <literal><![CDATA[
      f(x,f(f(f(x,f(f(x,y),z)),f(f(x,y),z)),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(40(a,1),1330(a,1,2,1,1,1)),rewrite([543(3)])].">
      <j1 rule="para" parents="40 1330"/>
      <j2 rule="rewrite" parents="543"/>
    </justification>
  </clause>

  <clause id="1367">
    <literal><![CDATA[
      f(f(x,f(y,z)),f(f(f(f(f(y,z),x),y),y),f(y,z))) = f(y,z)
    ]]></literal>
    <justification jstring="[para(40(a,1),1330(a,1,2,1,1,2)),rewrite([40(8)])].">
      <j1 rule="para" parents="40 1330"/>
      <j2 rule="rewrite" parents="40"/>
    </justification>
  </clause>

  <clause id="1368">
    <literal><![CDATA[
      f(f(x,y),f(f(f(f(x,y),f(y,z)),f(y,z)),y)) = y
    ]]></literal>
    <justification jstring="[para(55(a,1),1330(a,1,2,1,1,1)),rewrite([657(4)])].">
      <j1 rule="para" parents="55 1330"/>
      <j2 rule="rewrite" parents="657"/>
    </justification>
  </clause>

  <clause id="1369">
    <literal><![CDATA[
      f(f(x,y),f(f(f(f(y,x),f(z,y)),f(z,y)),y)) = y
    ]]></literal>
    <justification jstring="[para(55(a,1),1330(a,1,2,1,1,2)),rewrite([55(8)])].">
      <j1 rule="para" parents="55 1330"/>
      <j2 rule="rewrite" parents="55"/>
    </justification>
  </clause>

  <clause id="1370">
    <literal><![CDATA[
      f(f(x,y),f(f(f(f(x,y),f(x,z)),f(x,z)),x)) = x
    ]]></literal>
    <justification jstring="[para(61(a,1),1330(a,1,2,1,1,1)),rewrite([662(4)])].">
      <j1 rule="para" parents="61 1330"/>
      <j2 rule="rewrite" parents="662"/>
    </justification>
  </clause>

  <clause id="1378">
    <literal><![CDATA[
      f(f(f(f(x,f(x,x)),f(x,y)),f(x,y)),x) = f(x,x)
    ]]></literal>
    <justification jstring="[para(1330(a,1),25(a,1,2,2,1)),rewrite([544(9),657(16),1212(18)]),flip(a)].">
      <j1 rule="para" parents="1330 25"/>
      <j2 rule="rewrite" parents="544 657 1212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1383">
    <literal><![CDATA[
      f(x,f(f(f(x,x),x),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(582(a,1),1330(a,1,2,1,1)),rewrite([543(3),40(5),40(9),20(7),40(4)])].">
      <j1 rule="para" parents="582 1330"/>
      <j2 rule="rewrite" parents="543 40 40 20 40"/>
    </justification>
  </clause>

  <clause id="1388">
    <literal><![CDATA[
      f(f(x,y),f(f(y,f(y,f(f(f(y,f(f(f(y,y),z),f(f(f(f(f(y,x),z),z),y),f(y,x)))),y),f(y,x)))),y)) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(774(a,1),1330(a,1,2,1,1))].">
      <j1 rule="para" parents="774 1330"/>
    </justification>
  </clause>

  <clause id="1427">
    <literal><![CDATA[
      f(x,f(f(f(x,x),x),f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(55(a,1),1383(a,1,2,2)),rewrite([55(9)])].">
      <j1 rule="para" parents="55 1383"/>
      <j2 rule="rewrite" parents="55"/>
    </justification>
  </clause>

  <clause id="1455">
    <literal><![CDATA[
      f(f(x,x),f(f(f(x,x),x),f(x,y))) = f(f(x,x),x)
    ]]></literal>
    <justification jstring="[para(1383(a,1),609(a,1,2,2))].">
      <j1 rule="para" parents="1383 609"/>
    </justification>
  </clause>

  <clause id="1464">
    <literal><![CDATA[
      f(f(x,x),f(f(x,f(x,x)),f(y,f(x,x)))) = f(y,f(x,x))
    ]]></literal>
    <justification jstring="[para(11(a,1),1427(a,1,2,1,1))].">
      <j1 rule="para" parents="11 1427"/>
    </justification>
  </clause>

  <clause id="1613">
    <literal><![CDATA[
      f(f(x,f(y,z)),f(f(f(f(x,f(y,z)),y),y),f(y,z))) = f(y,z)
    ]]></literal>
    <justification jstring="[para(40(a,1),1368(a,1,2,1,1,2)),rewrite([40(8)])].">
      <j1 rule="para" parents="40 1368"/>
      <j2 rule="rewrite" parents="40"/>
    </justification>
  </clause>

  <clause id="1614">
    <literal><![CDATA[
      f(f(x,y),f(f(f(f(x,y),f(z,y)),f(z,y)),y)) = y
    ]]></literal>
    <justification jstring="[para(55(a,1),1368(a,1,2,1,1,2)),rewrite([55(8)])].">
      <j1 rule="para" parents="55 1368"/>
      <j2 rule="rewrite" parents="55"/>
    </justification>
  </clause>

  <clause id="1646">
    <literal><![CDATA[
      f(x,f(f(f(x,f(y,f(z,x))),f(y,f(z,x))),f(z,x))) = f(z,x)
    ]]></literal>
    <justification jstring="[para(11(a,1),1369(a,1,2,1,1,1)),rewrite([544(3)])].">
      <j1 rule="para" parents="11 1369"/>
      <j2 rule="rewrite" parents="544"/>
    </justification>
  </clause>

  <clause id="1648">
    <literal><![CDATA[
      f(x,f(f(f(x,f(y,f(x,z))),f(y,f(x,z))),f(x,z))) = f(x,z)
    ]]></literal>
    <justification jstring="[para(40(a,1),1369(a,1,2,1,1,1)),rewrite([543(3)])].">
      <j1 rule="para" parents="40 1369"/>
      <j2 rule="rewrite" parents="543"/>
    </justification>
  </clause>

  <clause id="1649">
    <literal><![CDATA[
      f(f(x,y),f(f(f(f(x,y),f(z,x)),f(z,x)),x)) = x
    ]]></literal>
    <justification jstring="[para(61(a,1),1369(a,1,2,1,1,1)),rewrite([662(4)])].">
      <j1 rule="para" parents="61 1369"/>
      <j2 rule="rewrite" parents="662"/>
    </justification>
  </clause>

  <clause id="1655">
    <literal><![CDATA[
      f(f(f(f(x,f(x,x)),f(y,x)),f(y,x)),x) = f(x,x)
    ]]></literal>
    <justification jstring="[para(1369(a,1),25(a,1,2,2,1)),rewrite([544(9),657(16),1213(18)]),flip(a)].">
      <j1 rule="para" parents="1369 25"/>
      <j2 rule="rewrite" parents="544 657 1213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1708">
    <literal><![CDATA[
      f(f(f(x,y),z),f(f(f(f(f(x,y),z),y),y),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(2(a,1),1370(a,1,2,1,1,2)),rewrite([2(16)])].">
      <j1 rule="para" parents="2 1370"/>
      <j2 rule="rewrite" parents="2"/>
    </justification>
  </clause>

  <clause id="1745">
    <literal><![CDATA[
      f(x,f(f(f(x,f(x,x)),f(x,y)),f(x,y))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(1378(a,1),662(a,1,1,1)),rewrite([1378(8),543(3),1378(14)])].">
      <j1 rule="para" parents="1378 662"/>
      <j2 rule="rewrite" parents="1378 543 1378"/>
    </justification>
  </clause>

  <clause id="1831">
    <literal><![CDATA[
      f(f(f(x,y),f(x,y)),f(f(f(f(x,y),f(x,y)),f(x,y)),y)) = f(f(f(x,y),f(x,y)),f(x,y))
    ]]></literal>
    <justification jstring="[para(2(a,1),1455(a,1,2,2))].">
      <j1 rule="para" parents="2 1455"/>
    </justification>
  </clause>

  <clause id="1832">
    <literal><![CDATA[
      f(x,f(f(x,f(x,x)),f(f(x,x),y))) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(11(a,1),1455(a,1,1)),rewrite([543(3),543(9)])].">
      <j1 rule="para" parents="11 1455"/>
      <j2 rule="rewrite" parents="543 543"/>
    </justification>
  </clause>

  <clause id="1836">
    <literal><![CDATA[
      f(f(x,x),f(f(f(x,x),x),f(y,x))) = f(f(x,x),x)
    ]]></literal>
    <justification jstring="[para(55(a,1),1455(a,1,2,2))].">
      <j1 rule="para" parents="55 1455"/>
    </justification>
  </clause>

  <clause id="1885">
    <literal><![CDATA[
      f(f(f(f(x,f(x,x)),f(y,f(x,x))),f(y,f(x,x))),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(1614(a,1),640(a,1,2,2,1)),rewrite([20(11),657(24),20(23),543(14),20(12),543(3)]),flip(a)].">
      <j1 rule="para" parents="1614 640"/>
      <j2 rule="rewrite" parents="20 657 20 543 20 543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2012">
    <literal><![CDATA[
      f(x,f(f(f(x,f(x,x)),f(y,x)),f(y,x))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(1655(a,1),662(a,1,1,1)),rewrite([1655(8),543(3),1655(14)])].">
      <j1 rule="para" parents="1655 662"/>
      <j2 rule="rewrite" parents="1655 543 1655"/>
    </justification>
  </clause>

  <clause id="2026">
    <literal><![CDATA[
      f(x,f(f(x,f(x,x)),f(y,f(x,x)))) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(55(a,1),1832(a,1,2,2))].">
      <j1 rule="para" parents="55 1832"/>
    </justification>
  </clause>

  <clause id="2041">
    <literal><![CDATA[
      f(f(x,x),f(f(f(f(y,f(x,x)),f(y,f(x,x))),f(f(f(x,x),x),f(z,x))),f(f(f(f(f(x,x),x),f(f(f(x,x),x),f(z,x))),f(y,f(x,x))),f(x,x)))) = f(y,f(x,x))
    ]]></literal>
    <justification jstring="[para(1836(a,1),576(a,1,2,2,1,1,1))].">
      <j1 rule="para" parents="1836 576"/>
    </justification>
  </clause>

  <clause id="2158">
    <literal><![CDATA[
      f(x,f(f(x,f(x,x)),f(f(f(f(x,f(x,x)),f(f(x,f(x,x)),f(y,f(x,x)))),f(x,f(x,x))),x))) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(2026(a,1),764(a,1,2,1)),rewrite([2026(8),2026(16),2026(22)])].">
      <j1 rule="para" parents="2026 764"/>
      <j2 rule="rewrite" parents="2026 2026 2026"/>
    </justification>
  </clause>

  <clause id="2257">
    <literal><![CDATA[
      f(x,f(f(f(x,y),y),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(40(a,1),1360(a,1,2,1,1,1)),rewrite([543(3)])].">
      <j1 rule="para" parents="40 1360"/>
      <j2 rule="rewrite" parents="543"/>
    </justification>
  </clause>

  <clause id="2473">
    <literal><![CDATA[
      f(f(x,x),f(f(f(f(x,x),x),f(f(f(x,x),x),f(y,x))),f(f(x,x),x))) = f(f(x,x),x)
    ]]></literal>
    <justification jstring="[para(1836(a,1),2257(a,1,2,1,1)),rewrite([1836(14),1836(18)])].">
      <j1 rule="para" parents="1836 2257"/>
      <j2 rule="rewrite" parents="1836 1836"/>
    </justification>
  </clause>

  <clause id="2482">
    <literal><![CDATA[
      f(x,f(f(f(x,y),f(f(f(x,y),y),f(x,y))),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(2257(a,1),2257(a,1,2,1,1)),rewrite([2257(11),2257(14)])].">
      <j1 rule="para" parents="2257 2257"/>
      <j2 rule="rewrite" parents="2257 2257"/>
    </justification>
  </clause>

  <clause id="2487">
    <literal><![CDATA[
      f(x,f(f(f(x,y),y),f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(40(a,1),1362(a,1,2,1,1,2)),rewrite([40(4)])].">
      <j1 rule="para" parents="40 1362"/>
      <j2 rule="rewrite" parents="40"/>
    </justification>
  </clause>

  <clause id="2546">
    <literal><![CDATA[
      f(f(x,x),x) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(32(a,1),2487(a,1,2,1)),rewrite([543(5)])].">
      <j1 rule="para" parents="32 2487"/>
      <j2 rule="rewrite" parents="543"/>
    </justification>
  </clause>

  <clause id="2548">
    <literal><![CDATA[
      f(f(x,x),f(f(x,f(x,x)),f(f(x,f(x,x)),f(y,x)))) = x
    ]]></literal>
    <justification jstring="[para(2487(a,1),37(a,1,2,2,2)),rewrite([2546(3),2546(5)])].">
      <j1 rule="para" parents="2487 37"/>
      <j2 rule="rewrite" parents="2546 2546"/>
    </justification>
  </clause>

  <clause id="2550">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),f(f(x,f(x,x)),f(y,x))),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(2487(a,1),174(a,1,1,2,2)),rewrite([2546(2),2546(4)])].">
      <j1 rule="para" parents="2487 174"/>
      <j2 rule="rewrite" parents="2546 2546"/>
    </justification>
  </clause>

  <clause id="2575">
    <literal><![CDATA[
      f(x,f(f(y,x),f(f(f(x,f(x,x)),f(y,x)),x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(768(a,1),2487(a,1,2,2)),rewrite([2546(3),2546(10),1708(19),2546(4)]),flip(a)].">
      <j1 rule="para" parents="768 2487"/>
      <j2 rule="rewrite" parents="2546 2546 1708 2546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2581">
    <literal><![CDATA[
      f(f(f(f(x,x),y),f(f(f(y,f(y,y)),x),f(z,x))),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(2487(a,1),459(a,1,1,2,2)),rewrite([2546(4)])].">
      <j1 rule="para" parents="2487 459"/>
      <j2 rule="rewrite" parents="2546"/>
    </justification>
  </clause>

  <clause id="2582">
    <literal><![CDATA[
      f(f(f(f(x,x),y),f(f(f(y,f(y,y)),x),f(x,z))),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(459(a,1),2487(a,1,2,2)),rewrite([2546(6),2546(15),544(22),2546(4)]),flip(a)].">
      <j1 rule="para" parents="459 2487"/>
      <j2 rule="rewrite" parents="2546 2546 544 2546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2610">
    <literal><![CDATA[
      f(f(f(x,f(f(f(f(x,y),f(f(x,y),f(x,y))),x),f(x,y))),f(x,y)),f(f(f(f(x,y),f(x,y)),z),f(f(f(f(x,z),z),f(x,y)),x))) = f(x,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(1294(a,1),2487(a,2)),rewrite([2546(25),2546(37),2546(49),2487(68)])].">
      <j1 rule="para" parents="1294 2487"/>
      <j2 rule="rewrite" parents="2546 2546 2546 2487"/>
    </justification>
  </clause>

  <clause id="2615">
    <literal><![CDATA[
      f(x,f(f(x,f(x,x)),f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(2487(a,1),1383(a,1,2,2)),rewrite([2546(2),2487(10)])].">
      <j1 rule="para" parents="2487 1383"/>
      <j2 rule="rewrite" parents="2546 2487"/>
    </justification>
  </clause>

  <clause id="2617">
    <literal><![CDATA[
      f(x,f(f(x,f(x,x)),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(1383(a,1),2487(a,1,2,2)),rewrite([2546(2),2546(6),1613(13),2546(3)]),flip(a)].">
      <j1 rule="para" parents="1383 2487"/>
      <j2 rule="rewrite" parents="2546 2546 1613 2546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2629">
    <literal><![CDATA[
      f(f(x,x),f(f(x,f(x,x)),f(y,x))) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(2487(a,1),1455(a,1,2,2)),rewrite([2546(3),2546(8)])].">
      <j1 rule="para" parents="2487 1455"/>
      <j2 rule="rewrite" parents="2546 2546"/>
    </justification>
  </clause>

  <clause id="2631">
    <literal><![CDATA[
      f(f(x,x),f(f(x,f(x,x)),f(x,y))) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(1455(a,1),2487(a,1,2,2)),rewrite([2546(2),2546(6),2546(14),1708(16),2546(5)]),flip(a)].">
      <j1 rule="para" parents="1455 2487"/>
      <j2 rule="rewrite" parents="2546 2546 2546 1708 2546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2648">
    <literal><![CDATA[
      f(x,f(f(f(y,x),f(f(f(x,y),y),f(y,x))),f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(2487(a,1),2257(a,1,2,1,1)),rewrite([2487(11),2487(14)])].">
      <j1 rule="para" parents="2487 2257"/>
      <j2 rule="rewrite" parents="2487 2487"/>
    </justification>
  </clause>

  <clause id="2664">
    <literal><![CDATA[
      f(f(x,x),f(f(f(x,f(x,x)),f(f(x,f(x,x)),f(y,x))),f(x,f(x,x)))) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[back_rewrite(2473),rewrite([2546(3),2546(5),2546(10),2546(14)])].">
      <j1 rule="back_rewrite" parents="2473"/>
      <j2 rule="rewrite" parents="2546 2546 2546 2546"/>
    </justification>
  </clause>

  <clause id="2785">
    <literal><![CDATA[
      f(f(x,x),f(f(f(f(y,f(x,x)),f(y,f(x,x))),f(f(x,f(x,x)),f(z,x))),f(f(f(f(x,f(x,x)),f(f(x,f(x,x)),f(z,x))),f(y,f(x,x))),f(x,x)))) = f(y,f(x,x))
    ]]></literal>
    <justification jstring="[back_rewrite(2041),rewrite([2546(8),2546(13),2546(15)])].">
      <j1 rule="back_rewrite" parents="2041"/>
      <j2 rule="rewrite" parents="2546 2546 2546"/>
    </justification>
  </clause>

  <clause id="2834">
    <literal><![CDATA[
      f(f(f(x,y),f(x,y)),f(f(f(x,y),f(f(x,y),f(x,y))),y)) = f(f(x,y),f(f(x,y),f(x,y)))
    ]]></literal>
    <justification jstring="[back_rewrite(1831),rewrite([2546(8),2546(15)])].">
      <j1 rule="back_rewrite" parents="1831"/>
      <j2 rule="rewrite" parents="2546 2546"/>
    </justification>
  </clause>

  <clause id="3130">
    <literal><![CDATA[
      f(f(f(f(x,f(x,x)),f(f(x,f(x,x)),f(y,f(x,x)))),f(x,f(x,x))),x) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[back_rewrite(2158),rewrite([2615(16)])].">
      <j1 rule="back_rewrite" parents="2158"/>
      <j2 rule="rewrite" parents="2615"/>
    </justification>
  </clause>

  <clause id="3145">
    <literal><![CDATA[
      f(f(f(x,f(f(f(f(x,y),f(f(x,y),f(x,y))),x),f(x,z))),f(y,x)),f(f(f(f(y,x),f(y,x)),u),f(f(f(f(x,u),u),f(y,x)),x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(2546(a,1),41(a,1,1,1,2,1,1)),rewrite([543(3)])].">
      <j1 rule="para" parents="2546 41"/>
      <j2 rule="rewrite" parents="543"/>
    </justification>
  </clause>

  <clause id="3170">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,x),f(f(y,x),f(y,x))),y)) = y
    ]]></literal>
    <justification jstring="[para(2546(a,1),1330(a,1,2,1))].">
      <j1 rule="para" parents="2546 1330"/>
    </justification>
  </clause>

  <clause id="3660">
    <literal><![CDATA[
      f(f(x,x),f(f(x,f(x,x)),f(f(x,f(x,x)),f(f(x,f(x,x)),f(y,f(x,x)))))) = f(f(x,f(x,x)),f(f(x,f(x,x)),f(y,f(x,x))))
    ]]></literal>
    <justification jstring="[para(270(a,1),3170(a,1,1)),rewrite([302(10),302(11),302(12),543(5),2546(3)])].">
      <j1 rule="para" parents="270 3170"/>
      <j2 rule="rewrite" parents="302 302 302 543 2546"/>
    </justification>
  </clause>

  <clause id="3837">
    <literal><![CDATA[
      f(x,f(f(x,f(x,x)),f(f(x,f(x,x)),f(f(x,f(x,x)),f(y,x))))) = f(f(x,f(x,x)),f(f(x,f(x,x)),f(y,x)))
    ]]></literal>
    <justification jstring="[para(2548(a,1),3170(a,1,1)),rewrite([2550(9),2550(9),2550(9)])].">
      <j1 rule="para" parents="2548 3170"/>
      <j2 rule="rewrite" parents="2550 2550 2550"/>
    </justification>
  </clause>

  <clause id="4530">
    <literal><![CDATA[
      f(x,f(f(f(x,x),f(f(f(x,f(x,x)),f(y,x)),f(y,x))),f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(2012(a,1),1646(a,1,2,1,1))].">
      <j1 rule="para" parents="2012 1646"/>
    </justification>
  </clause>

  <clause id="4566">
    <literal><![CDATA[
      f(x,f(f(f(x,x),f(f(f(x,f(x,x)),f(x,y)),f(x,y))),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(1745(a,1),1648(a,1,2,1,1))].">
      <j1 rule="para" parents="1745 1648"/>
    </justification>
  </clause>

  <clause id="4650">
    <literal><![CDATA[
      f(f(x,y),f(f(f(f(x,y),f(f(f(x,x),f(z,z)),f(f(f(z,f(z,z)),x),f(u,x)))),f(f(f(x,x),f(z,z)),f(f(f(z,f(z,z)),x),f(u,x)))),x)) = x
    ]]></literal>
    <justification jstring="[para(358(a,1),1708(a,1,1,1)),rewrite([358(12),358(33),358(35)])].">
      <j1 rule="para" parents="358 1708"/>
      <j2 rule="rewrite" parents="358 358 358"/>
    </justification>
  </clause>

  <clause id="5400">
    <literal><![CDATA[
      f(f(f(x,x),y),f(f(x,f(x,x)),f(f(f(x,x),y),f(f(f(y,f(y,y)),x),f(z,x))))) = f(f(f(x,x),y),f(f(f(y,f(y,y)),x),f(z,x)))
    ]]></literal>
    <justification jstring="[para(2581(a,1),1366(a,1,2,1,1,2)),rewrite([32(5),2581(13),2546(4)])].">
      <j1 rule="para" parents="2581 1366"/>
      <j2 rule="rewrite" parents="32 2581 2546"/>
    </justification>
  </clause>

  <clause id="5408">
    <literal><![CDATA[
      f(f(f(x,x),y),f(f(x,f(x,x)),f(f(f(x,x),y),f(f(f(y,f(y,y)),x),f(x,z))))) = f(f(f(x,x),y),f(f(f(y,f(y,y)),x),f(x,z)))
    ]]></literal>
    <justification jstring="[para(2582(a,1),1366(a,1,2,1,1,2)),rewrite([32(5),2582(13),2546(4)])].">
      <j1 rule="para" parents="2582 1366"/>
      <j2 rule="rewrite" parents="32 2582 2546"/>
    </justification>
  </clause>

  <clause id="6230">
    <literal><![CDATA[
      f(f(f(f(x,f(x,x)),f(x,y)),f(x,y)),f(f(x,y),f(f(f(x,f(x,x)),f(x,y)),f(f(x,y),z)))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(1378(a,1),679(a,1,2,2,1,1,1)),rewrite([662(10),2546(9)])].">
      <j1 rule="para" parents="1378 679"/>
      <j2 rule="rewrite" parents="662 2546"/>
    </justification>
  </clause>

  <clause id="7510">
    <literal><![CDATA[
      f(f(f(f(f(x,f(x,x)),y),y),x),f(f(f(f(x,f(x,x)),y),y),x)) = x
    ]]></literal>
    <justification jstring="[para(1018(a,1),20(a,1,1)),rewrite([544(7)]),flip(a)].">
      <j1 rule="para" parents="1018 20"/>
      <j2 rule="rewrite" parents="544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7557">
    <literal><![CDATA[
      f(f(f(f(x,f(x,x)),y),y),x) = f(x,x)
    ]]></literal>
    <justification jstring="[para(1018(a,1),1885(a,1,1,1,2)),rewrite([7510(16),11(8),7510(13),32(3),7510(13),20(3)]),flip(a)].">
      <j1 rule="para" parents="1018 1885"/>
      <j2 rule="rewrite" parents="7510 11 7510 32 7510 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7559">
    <literal><![CDATA[
      f(f(f(f(x,f(x,x)),y),y),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(11(a,1),7557(a,1,1,1,1,2)),rewrite([2546(2),543(9)])].">
      <j1 rule="para" parents="11 7557"/>
      <j2 rule="rewrite" parents="2546 543"/>
    </justification>
  </clause>

  <clause id="7648">
    <literal><![CDATA[
      f(f(x,x),f(f(f(x,f(x,x)),y),y)) = x
    ]]></literal>
    <justification jstring="[para(7559(a,1),662(a,1,1,1)),rewrite([7559(6),7559(12)])].">
      <j1 rule="para" parents="7559 662"/>
      <j2 rule="rewrite" parents="7559 7559"/>
    </justification>
  </clause>

  <clause id="7663">
    <literal><![CDATA[
      f(x,f(f(f(x,y),y),f(f(f(x,f(x,x)),y),y))) = f(f(f(x,f(x,x)),y),y)
    ]]></literal>
    <justification jstring="[para(7559(a,1),1360(a,1,2,1,1,1)),rewrite([7648(6)])].">
      <j1 rule="para" parents="7559 1360"/>
      <j2 rule="rewrite" parents="7648"/>
    </justification>
  </clause>

  <clause id="7716">
    <literal><![CDATA[
      f(x,f(x,f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(4566),rewrite([7648(8)])].">
      <j1 rule="back_rewrite" parents="4566"/>
      <j2 rule="rewrite" parents="7648"/>
    </justification>
  </clause>

  <clause id="7717">
    <literal><![CDATA[
      f(x,f(x,f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(4530),rewrite([7648(8)])].">
      <j1 rule="back_rewrite" parents="4530"/>
      <j2 rule="rewrite" parents="7648"/>
    </justification>
  </clause>

  <clause id="7727">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(x,f(x,x)),f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(3837),rewrite([7716(10),2615(5)]),flip(a)].">
      <j1 rule="back_rewrite" parents="3837"/>
      <j2 rule="rewrite" parents="7716 2615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7728">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(x,f(x,x)),f(y,f(x,x)))) = f(y,f(x,x))
    ]]></literal>
    <justification jstring="[back_rewrite(3660),rewrite([7716(12),1464(7)]),flip(a)].">
      <j1 rule="back_rewrite" parents="3660"/>
      <j2 rule="rewrite" parents="7716 1464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7758">
    <literal><![CDATA[
      f(f(x,x),f(f(f(f(y,f(x,x)),f(y,f(x,x))),f(f(x,f(x,x)),f(z,x))),f(f(f(z,x),f(y,f(x,x))),f(x,x)))) = f(y,f(x,x))
    ]]></literal>
    <justification jstring="[back_rewrite(2785),rewrite([7727(18)])].">
      <j1 rule="back_rewrite" parents="2785"/>
      <j2 rule="rewrite" parents="7727"/>
    </justification>
  </clause>

  <clause id="7763">
    <literal><![CDATA[
      f(f(x,x),f(f(y,x),f(x,f(x,x)))) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[back_rewrite(2664),rewrite([7727(8)])].">
      <j1 rule="back_rewrite" parents="2664"/>
      <j2 rule="rewrite" parents="7727"/>
    </justification>
  </clause>

  <clause id="7772">
    <literal><![CDATA[
      f(f(f(x,f(y,y)),f(y,f(y,y))),y) = f(y,f(y,y))
    ]]></literal>
    <justification jstring="[back_rewrite(3130),rewrite([7728(8)])].">
      <j1 rule="back_rewrite" parents="3130"/>
      <j2 rule="rewrite" parents="7728"/>
    </justification>
  </clause>

  <clause id="7848">
    <literal><![CDATA[
      f(f(x,y),f(f(x,y),y)) = y
    ]]></literal>
    <justification jstring="[para(2(a,1),7716(a,1,2,2)),rewrite([2(15)])].">
      <j1 rule="para" parents="2 7716"/>
      <j2 rule="rewrite" parents="2"/>
    </justification>
  </clause>

  <clause id="7850">
    <literal><![CDATA[
      f(f(x,y),f(f(x,y),x)) = x
    ]]></literal>
    <justification jstring="[para(40(a,1),7716(a,1,2,2)),rewrite([40(7)])].">
      <j1 rule="para" parents="40 7716"/>
      <j2 rule="rewrite" parents="40"/>
    </justification>
  </clause>

  <clause id="7880">
    <literal><![CDATA[
      f(x,f(f(x,y),f(f(f(f(x,y),f(x,f(x,y))),f(x,x)),f(z,f(x,x))))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(7716(a,1),568(a,1,2,1)),rewrite([7716(4)])].">
      <j1 rule="para" parents="7716 568"/>
      <j2 rule="rewrite" parents="7716"/>
    </justification>
  </clause>

  <clause id="7881">
    <literal><![CDATA[
      f(x,f(f(f(f(x,f(x,y)),f(x,f(x,y))),f(x,x)),f(f(x,y),x))) = f(x,f(x,y))
    ]]></literal>
    <justification jstring="[para(7716(a,1),589(a,1,2,2,1))].">
      <j1 rule="para" parents="7716 589"/>
    </justification>
  </clause>

  <clause id="8049">
    <literal><![CDATA[
      f(x,f(f(f(f(x,f(y,x)),f(x,f(y,x))),f(x,x)),f(f(y,x),x))) = f(x,f(y,x))
    ]]></literal>
    <justification jstring="[para(7717(a,1),589(a,1,2,2,1))].">
      <j1 rule="para" parents="7717 589"/>
    </justification>
  </clause>

  <clause id="8054">
    <literal><![CDATA[
      f(f(f(f(f(x,y),f(x,y)),z),f(f(f(f(f(f(x,y),u),z),z),f(x,y)),x)),f(f(f(f(f(x,y),f(x,y)),z),f(f(f(f(f(f(x,y),u),z),z),f(x,y)),x)),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(54(a,1),7717(a,1,2,2)),rewrite([54(42)])].">
      <j1 rule="para" parents="54 7717"/>
      <j2 rule="rewrite" parents="54"/>
    </justification>
  </clause>

  <clause id="8184">
    <literal><![CDATA[
      f(x,f(x,f(f(f(x,x),y),f(f(f(f(f(x,z),y),y),x),f(x,u))))) = f(f(f(x,x),y),f(f(f(f(f(x,z),y),y),x),f(x,u)))
    ]]></literal>
    <justification jstring="[para(2(a,1),7848(a,1,1)),rewrite([2(11)])].">
      <j1 rule="para" parents="2 7848"/>
      <j2 rule="rewrite" parents="2"/>
    </justification>
  </clause>

  <clause id="8196">
    <literal><![CDATA[
      f(f(x,y),f(f(x,y),f(f(f(f(x,y),f(x,y)),z),f(f(f(f(x,z),z),f(x,y)),x)))) = f(f(f(f(x,y),f(x,y)),z),f(f(f(f(x,z),z),f(x,y)),x))
    ]]></literal>
    <justification jstring="[para(546(a,1),7848(a,1,1)),rewrite([546(12)])].">
      <j1 rule="para" parents="546 7848"/>
      <j2 rule="rewrite" parents="546"/>
    </justification>
  </clause>

  <clause id="8223">
    <literal><![CDATA[
      f(f(x,y),f(f(x,y),f(f(f(f(x,y),f(x,y)),z),f(f(f(f(f(f(x,y),u),z),z),f(x,y)),x)))) = f(f(f(f(x,y),f(x,y)),z),f(f(f(f(f(f(x,y),u),z),z),f(x,y)),x))
    ]]></literal>
    <justification jstring="[para(54(a,1),7848(a,1,1)),rewrite([54(16)])].">
      <j1 rule="para" parents="54 7848"/>
      <j2 rule="rewrite" parents="54"/>
    </justification>
  </clause>

  <clause id="8239">
    <literal><![CDATA[
      f(f(x,y),f(f(y,f(f(x,y),y)),y)) = y
    ]]></literal>
    <justification jstring="[para(7848(a,1),1614(a,1,2,1,1))].">
      <j1 rule="para" parents="7848 1614"/>
    </justification>
  </clause>

  <clause id="8363">
    <literal><![CDATA[
      f(f(x,y),f(f(y,f(f(y,x),y)),y)) = y
    ]]></literal>
    <justification jstring="[para(7850(a,1),1369(a,1,2,1,1))].">
      <j1 rule="para" parents="7850 1369"/>
    </justification>
  </clause>

  <clause id="8366">
    <literal><![CDATA[
      f(f(x,y),f(f(x,f(f(x,y),x)),x)) = x
    ]]></literal>
    <justification jstring="[para(7850(a,1),1649(a,1,2,1,1))].">
      <j1 rule="para" parents="7850 1649"/>
    </justification>
  </clause>

  <clause id="8448">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),y),y) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(7557(a,1),7850(a,1,1)),rewrite([7557(6),7648(7),2546(2)]),flip(a)].">
      <j1 rule="para" parents="7557 7850"/>
      <j2 rule="rewrite" parents="7557 7648 2546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8457">
    <literal><![CDATA[
      f(x,f(f(f(x,y),y),f(x,f(x,x)))) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[back_rewrite(7663),rewrite([8448(6),8448(10)])].">
      <j1 rule="back_rewrite" parents="7663"/>
      <j2 rule="rewrite" parents="8448 8448"/>
    </justification>
  </clause>

  <clause id="8479">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(x,y),f(f(f(x,f(x,x)),f(x,y)),f(f(x,y),z)))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(6230),rewrite([8448(6)])].">
      <j1 rule="back_rewrite" parents="6230"/>
      <j2 rule="rewrite" parents="8448"/>
    </justification>
  </clause>

  <clause id="8653">
    <literal><![CDATA[
      f(f(x,y),f(y,f(f(f(y,f(f(y,f(f(x,y),y)),y)),f(f(x,y),f(x,y))),f(z,f(f(x,y),f(x,y)))))) = f(f(x,y),f(x,y))
    ]]></literal>
    <justification jstring="[para(8239(a,1),568(a,1,2,1)),rewrite([8239(7)])].">
      <j1 rule="para" parents="8239 568"/>
      <j2 rule="rewrite" parents="8239"/>
    </justification>
  </clause>

  <clause id="8676">
    <literal><![CDATA[
      f(f(f(f(x,f(f(y,x),x)),x),f(y,x)),f(f(f(x,y),y),f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(8239(a,1),1367(a,1,2,1,1,1))].">
      <j1 rule="para" parents="8239 1367"/>
    </justification>
  </clause>

  <clause id="8754">
    <literal><![CDATA[
      f(f(f(f(f(f(x,y),f(x,y)),f(y,y)),f(f(y,f(x,y)),y)),y),f(f(y,f(f(x,y),y)),y)) = y
    ]]></literal>
    <justification jstring="[para(573(a,1),8363(a,1,2,1,2,1))].">
      <j1 rule="para" parents="573 8363"/>
    </justification>
  </clause>

  <clause id="8755">
    <literal><![CDATA[
      f(f(f(f(f(f(x,y),f(x,y)),f(x,x)),f(f(x,f(x,y)),x)),x),f(f(x,f(f(x,y),x)),x)) = x
    ]]></literal>
    <justification jstring="[para(589(a,1),8363(a,1,2,1,2,1))].">
      <j1 rule="para" parents="589 8363"/>
    </justification>
  </clause>

  <clause id="8989">
    <literal><![CDATA[
      f(f(f(f(x,f(f(x,y),x)),x),f(x,y)),f(f(f(f(x,y),f(x,y)),f(x,x)),f(f(x,f(x,y)),y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(8366(a,1),137(a,1,2,1,2,1)),rewrite([8366(15),8366(17)])].">
      <j1 rule="para" parents="8366 137"/>
      <j2 rule="rewrite" parents="8366 8366"/>
    </justification>
  </clause>

  <clause id="9010">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(y,y)) = y
    ]]></literal>
    <justification jstring="[para(8448(a,1),11(a,1,1))].">
      <j1 rule="para" parents="8448 11"/>
    </justification>
  </clause>

  <clause id="9012">
    <literal><![CDATA[
      f(x,f(f(y,f(y,y)),f(y,f(y,y)))) = f(y,f(y,y))
    ]]></literal>
    <justification jstring="[para(8448(a,1),55(a,1,2,1)),rewrite([8448(6),8448(10)])].">
      <j1 rule="para" parents="8448 55"/>
      <j2 rule="rewrite" parents="8448 8448"/>
    </justification>
  </clause>

  <clause id="9014">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),y),f(f(f(x,f(x,x)),y),f(f(x,f(x,x)),y))) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(61(a,1),8448(a,1,1))].">
      <j1 rule="para" parents="61 8448"/>
    </justification>
  </clause>

  <clause id="9023">
    <literal><![CDATA[
      f(f(x,x),f(y,f(y,y))) = x
    ]]></literal>
    <justification jstring="[para(8448(a,1),544(a,1,2))].">
      <j1 rule="para" parents="8448 544"/>
    </justification>
  </clause>

  <clause id="9025">
    <literal><![CDATA[
      f(x,f(y,f(y,y))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(8448(a,1),607(a,1,2))].">
      <j1 rule="para" parents="8448 607"/>
    </justification>
  </clause>

  <clause id="9029">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),f(x,f(x,x))),y) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(8448(a,1),657(a,1,1,1)),rewrite([8448(6),8448(10)])].">
      <j1 rule="para" parents="8448 657"/>
      <j2 rule="rewrite" parents="8448 8448"/>
    </justification>
  </clause>

  <clause id="9030">
    <literal><![CDATA[
      f(f(f(f(x,y),y),f(x,f(x,x))),x) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(8448(a,1),41(a,1,1,1,2,1,1)),rewrite([20(5),543(5),32(3),2546(3),543(4),2546(2),2546(4),9029(6),2546(6),2615(10),2546(8)])].">
      <j1 rule="para" parents="8448 41"/>
      <j2 rule="rewrite" parents="20 543 32 2546 543 2546 2546 9029 2546 2615 2546"/>
    </justification>
  </clause>

  <clause id="9041">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),y),f(f(x,f(x,x)),f(f(x,f(x,x)),f(f(f(f(x,f(x,x)),y),f(f(x,f(x,x)),y)),z)))) = f(f(f(x,f(x,x)),y),f(f(x,f(x,x)),y))
    ]]></literal>
    <justification jstring="[para(8448(a,1),50(a,1,2,1)),rewrite([8448(9),9014(16)])].">
      <j1 rule="para" parents="8448 50"/>
      <j2 rule="rewrite" parents="8448 9014"/>
    </justification>
  </clause>

  <clause id="9046">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),z),f(f(f(f(f(y,x),z),z),y),f(u,f(u,u))))) = y
    ]]></literal>
    <justification jstring="[para(8448(a,1),66(a,1,2,2,2))].">
      <j1 rule="para" parents="8448 66"/>
    </justification>
  </clause>

  <clause id="9070">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(x,f(x,x)),y)) = y
    ]]></literal>
    <justification jstring="[para(8448(a,1),1368(a,1,1)),rewrite([8448(6),8448(8)])].">
      <j1 rule="para" parents="8448 1368"/>
      <j2 rule="rewrite" parents="8448 8448"/>
    </justification>
  </clause>

  <clause id="9071">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(f(f(y,f(f(x,f(x,x)),y)),f(z,y)),f(z,y)),y)) = y
    ]]></literal>
    <justification jstring="[para(8448(a,1),1369(a,1,1))].">
      <j1 rule="para" parents="8448 1369"/>
    </justification>
  </clause>

  <clause id="9075">
    <literal><![CDATA[
      f(x,f(x,f(y,f(y,y)))) = f(y,f(y,y))
    ]]></literal>
    <justification jstring="[para(8448(a,1),1370(a,1,2,1,1)),rewrite([9070(6),9070(6)])].">
      <j1 rule="para" parents="8448 1370"/>
      <j2 rule="rewrite" parents="9070 9070"/>
    </justification>
  </clause>

  <clause id="9079">
    <literal><![CDATA[
      f(f(x,y),f(f(z,f(z,z)),y)) = y
    ]]></literal>
    <justification jstring="[para(8448(a,1),63(a,1,2,1)),rewrite([9010(8),9010(10),9012(10),9010(9),9010(11),9075(11),20(6),543(6)])].">
      <j1 rule="para" parents="8448 63"/>
      <j2 rule="rewrite" parents="9010 9010 9012 9010 9010 9075 20 543"/>
    </justification>
  </clause>

  <clause id="9090">
    <literal><![CDATA[
      f(x,f(x,x)) = f(y,f(y,y))
    ]]></literal>
    <justification jstring="[para(8448(a,1),1464(a,2)),rewrite([9010(7),55(7)])].">
      <j1 rule="para" parents="8448 1464"/>
      <j2 rule="rewrite" parents="9010 55"/>
    </justification>
  </clause>

  <clause id="9106">
    <literal><![CDATA[
      f(x,f(f(y,f(y,y)),f(f(f(x,f(x,x)),f(y,f(y,y))),x))) = f(y,f(y,y))
    ]]></literal>
    <justification jstring="[para(8448(a,1),2575(a,1,2,1)),rewrite([8448(8),8448(14)])].">
      <j1 rule="para" parents="8448 2575"/>
      <j2 rule="rewrite" parents="8448 8448"/>
    </justification>
  </clause>

  <clause id="9150">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(f(y,y),z),f(f(f(f(f(y,f(f(x,f(x,x)),y)),z),z),y),f(f(f(y,y),u),f(f(f(f(f(y,w),u),u),y),f(y,v5)))))) = y
    ]]></literal>
    <justification jstring="[para(8448(a,1),126(a,1,1))].">
      <j1 rule="para" parents="8448 126"/>
    </justification>
  </clause>

  <clause id="9166">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(f(y,y),z),f(f(f(x,f(x,x)),y),f(y,u)))) = y
    ]]></literal>
    <justification jstring="[para(8448(a,1),679(a,1,1)),rewrite([8448(8),8448(8)])].">
      <j1 rule="para" parents="8448 679"/>
      <j2 rule="rewrite" parents="8448 8448"/>
    </justification>
  </clause>

  <clause id="9182">
    <literal><![CDATA[
      f(x,f(f(x,f(y,y)),f(f(f(y,f(y,y)),f(f(z,f(z,z)),x)),f(z,f(z,z))))) = f(f(z,f(z,z)),x)
    ]]></literal>
    <justification jstring="[para(8448(a,1),762(a,1,2,2,2)),rewrite([9079(7),9079(7)])].">
      <j1 rule="para" parents="8448 762"/>
      <j2 rule="rewrite" parents="9079 9079"/>
    </justification>
  </clause>

  <clause id="9189">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(f(y,y),z),f(f(f(x,f(x,x)),y),f(u,y)))) = y
    ]]></literal>
    <justification jstring="[para(8448(a,1),1005(a,1,1)),rewrite([8448(8),8448(8)])].">
      <j1 rule="para" parents="8448 1005"/>
      <j2 rule="rewrite" parents="8448 8448"/>
    </justification>
  </clause>

  <clause id="9198">
    <literal><![CDATA[
      f(f(x,y),f(f(f(x,x),z),f(f(f(f(f(x,y),z),z),x),f(u,f(u,u))))) = x
    ]]></literal>
    <justification jstring="[para(8448(a,1),1008(a,1,2,2,2))].">
      <j1 rule="para" parents="8448 1008"/>
    </justification>
  </clause>

  <clause id="9203">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),y),f(x,f(x,x))) = y
    ]]></literal>
    <justification jstring="[para(8448(a,1),7848(a,1,2))].">
      <j1 rule="para" parents="8448 7848"/>
    </justification>
  </clause>

  <clause id="9228">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),y),f(y,z)) = y
    ]]></literal>
    <justification jstring="[back_rewrite(9041),rewrite([9079(14),9070(10),9079(12)])].">
      <j1 rule="back_rewrite" parents="9041"/>
      <j2 rule="rewrite" parents="9079 9070 9079"/>
    </justification>
  </clause>

  <clause id="9232">
    <literal><![CDATA[
      f(x,f(x,x)) = c_0
    ]]></literal>
    <justification jstring="[new_symbol(9090)].">
      <j1 rule="new_symbol" parents="9090"/>
    </justification>
  </clause>

  <clause id="9276">
    <literal><![CDATA[
      f(c_0,f(f(f(x,x),y),f(f(c_0,x),f(z,x)))) = x
    ]]></literal>
    <justification jstring="[back_rewrite(9189),rewrite([9232(2),9232(5)])].">
      <j1 rule="back_rewrite" parents="9189"/>
      <j2 rule="rewrite" parents="9232 9232"/>
    </justification>
  </clause>

  <clause id="9397">
    <literal><![CDATA[
      f(f(f(x,x),y),f(f(c_0,x),f(z,x))) = f(x,x)
    ]]></literal>
    <justification jstring="[back_rewrite(5400),rewrite([9232(4),9232(7),9276(11),32(3),9232(5)]),flip(a)].">
      <j1 rule="back_rewrite" parents="5400"/>
      <j2 rule="rewrite" parents="9232 9232 9276 32 9232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9421">
    <literal><![CDATA[
      f(f(x,y),f(c_0,x)) = x
    ]]></literal>
    <justification jstring="[back_rewrite(4650),rewrite([9232(7),9397(10),40(4),9232(6),9397(9),9232(3)])].">
      <j1 rule="back_rewrite" parents="4650"/>
      <j2 rule="rewrite" parents="9232 9397 40 9232 9397 9232"/>
    </justification>
  </clause>

  <clause id="9488">
    <literal><![CDATA[
      f(c_0,f(f(f(x,x),y),f(f(c_0,x),f(x,z)))) = x
    ]]></literal>
    <justification jstring="[back_rewrite(9166),rewrite([9232(2),9232(5)])].">
      <j1 rule="back_rewrite" parents="9166"/>
      <j2 rule="rewrite" parents="9232 9232"/>
    </justification>
  </clause>

  <clause id="9506">
    <literal><![CDATA[
      f(c_0,f(f(x,y),f(f(c_0,f(x,y)),f(f(x,y),z)))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(8479),rewrite([9232(2),9232(4)])].">
      <j1 rule="back_rewrite" parents="8479"/>
      <j2 rule="rewrite" parents="9232 9232"/>
    </justification>
  </clause>

  <clause id="9626">
    <literal><![CDATA[
      f(f(f(x,x),y),f(f(c_0,x),f(x,z))) = f(x,x)
    ]]></literal>
    <justification jstring="[back_rewrite(5408),rewrite([9232(4),9232(7),9488(11),32(3),9232(5)]),flip(a)].">
      <j1 rule="back_rewrite" parents="5408"/>
      <j2 rule="rewrite" parents="9232 9232 9488 32 9232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9711">
    <literal><![CDATA[
      f(f(f(x,f(f(c_0,x),f(x,y))),f(z,x)),f(f(f(f(z,x),f(z,x)),u),f(f(f(f(x,u),u),f(z,x)),x))) = f(z,x)
    ]]></literal>
    <justification jstring="[back_rewrite(3145),rewrite([9232(5)])].">
      <j1 rule="back_rewrite" parents="3145"/>
      <j2 rule="rewrite" parents="9232"/>
    </justification>
  </clause>

  <clause id="9732">
    <literal><![CDATA[
      f(f(f(x,f(f(c_0,x),f(x,y))),f(x,y)),f(f(f(f(x,y),f(x,y)),z),f(f(f(f(x,z),z),f(x,y)),x))) = f(x,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(2610),rewrite([9232(5)])].">
      <j1 rule="back_rewrite" parents="2610"/>
      <j2 rule="rewrite" parents="9232"/>
    </justification>
  </clause>

  <clause id="9736">
    <literal><![CDATA[
      f(f(x,f(y,z)),f(f(y,z),f(f(c_0,f(y,z)),y))) = f(y,z)
    ]]></literal>
    <justification jstring="[back_rewrite(1279),rewrite([9232(11),9626(16),9232(8)])].">
      <j1 rule="back_rewrite" parents="1279"/>
      <j2 rule="rewrite" parents="9232 9626 9232"/>
    </justification>
  </clause>

  <clause id="9823">
    <literal><![CDATA[
      f(f(c_0,x),f(x,y)) = x
    ]]></literal>
    <justification jstring="[back_rewrite(9228),rewrite([9232(2)])].">
      <j1 rule="back_rewrite" parents="9228"/>
      <j2 rule="rewrite" parents="9232"/>
    </justification>
  </clause>

  <clause id="9838">
    <literal><![CDATA[
      f(f(c_0,x),c_0) = x
    ]]></literal>
    <justification jstring="[back_rewrite(9203),rewrite([9232(2),9232(4)])].">
      <j1 rule="back_rewrite" parents="9203"/>
      <j2 rule="rewrite" parents="9232 9232"/>
    </justification>
  </clause>

  <clause id="9841">
    <literal><![CDATA[
      f(f(x,y),f(f(f(x,x),z),f(f(f(f(f(x,y),z),z),x),c_0))) = x
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(9198),rewrite([9232(9)])].">
      <j1 rule="back_rewrite" parents="9198"/>
      <j2 rule="rewrite" parents="9232"/>
    </justification>
  </clause>

  <clause id="9850">
    <literal><![CDATA[
      f(c_0,x) = f(x,x)
    ]]></literal>
    <justification jstring="[back_rewrite(9182),rewrite([9232(4),9232(5),9232(8),9838(8),9421(5),9232(3)]),flip(a)].">
      <j1 rule="back_rewrite" parents="9182"/>
      <j2 rule="rewrite" parents="9232 9232 9232 9838 9421 9232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9861">
    <literal><![CDATA[
      f(c_0,f(x,x)) = x
    ]]></literal>
    <justification jstring="[back_rewrite(9150),rewrite([9232(2),9232(5),9850(5),9232(5),9850(5),2546(5),9232(5),9850(5),753(14),32(4)])].">
      <j1 rule="back_rewrite" parents="9150"/>
      <j2 rule="rewrite" parents="9232 9232 9850 9232 9850 2546 9232 9850 753 32"/>
    </justification>
  </clause>

  <clause id="9883">
    <literal><![CDATA[
      f(x,f(c_0,c_0)) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(9106),rewrite([9232(2),9232(3),9232(4),604(6),9232(6)])].">
      <j1 rule="back_rewrite" parents="9106"/>
      <j2 rule="rewrite" parents="9232 9232 9232 604 9232"/>
    </justification>
  </clause>

  <clause id="9901">
    <literal><![CDATA[
      f(c_0,f(f(f(c_0,f(x,y)),f(x,y)),y)) = y
    ]]></literal>
    <justification jstring="[back_rewrite(9071),rewrite([9232(2),9232(3),9850(3),9232(3)])].">
      <j1 rule="back_rewrite" parents="9071"/>
      <j2 rule="rewrite" parents="9232 9232 9850 9232"/>
    </justification>
  </clause>

  <clause id="9910">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),z),f(f(f(f(f(y,x),z),z),y),c_0))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(9046),rewrite([9232(9)])].">
      <j1 rule="back_rewrite" parents="9046"/>
      <j2 rule="rewrite" parents="9232"/>
    </justification>
  </clause>

  <clause id="9912">
    <literal><![CDATA[
      f(f(f(f(x,y),y),c_0),x) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(9030),rewrite([9232(4),9232(7)])].">
      <j1 rule="back_rewrite" parents="9030"/>
      <j2 rule="rewrite" parents="9232 9232"/>
    </justification>
  </clause>

  <clause id="9913">
    <literal><![CDATA[
      f(f(c_0,c_0),x) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(9029),rewrite([9232(2),9232(3),9232(6)])].">
      <j1 rule="back_rewrite" parents="9029"/>
      <j2 rule="rewrite" parents="9232 9232 9232"/>
    </justification>
  </clause>

  <clause id="9914">
    <literal><![CDATA[
      f(x,c_0) = f(x,x)
    ]]></literal>
    <justification jstring="[back_rewrite(9025),rewrite([9232(2)])].">
      <j1 rule="back_rewrite" parents="9025"/>
      <j2 rule="rewrite" parents="9232"/>
    </justification>
  </clause>

  <clause id="9915">
    <literal><![CDATA[
      f(f(x,x),c_0) = x
    ]]></literal>
    <justification jstring="[back_rewrite(9023),rewrite([9232(3)])].">
      <j1 rule="back_rewrite" parents="9023"/>
      <j2 rule="rewrite" parents="9232"/>
    </justification>
  </clause>

  <clause id="9978">
    <literal><![CDATA[
      f(x,f(f(f(x,y),y),c_0)) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(8457),rewrite([9232(4),9232(7)])].">
      <j1 rule="back_rewrite" parents="8457"/>
      <j2 rule="rewrite" parents="9232 9232"/>
    </justification>
  </clause>

  <clause id="10036">
    <literal><![CDATA[
      f(f(f(x,f(y,y)),c_0),y) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(7772),rewrite([9232(4),9232(7)])].">
      <j1 rule="back_rewrite" parents="7772"/>
      <j2 rule="rewrite" parents="9232 9232"/>
    </justification>
  </clause>

  <clause id="10042">
    <literal><![CDATA[
      f(f(x,x),f(f(y,x),c_0)) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(7763),rewrite([9232(4),9232(7)])].">
      <j1 rule="back_rewrite" parents="7763"/>
      <j2 rule="rewrite" parents="9232 9232"/>
    </justification>
  </clause>

  <clause id="10047">
    <literal><![CDATA[
      f(f(x,x),f(f(f(c_0,f(y,f(x,x))),f(c_0,f(z,x))),f(f(f(z,x),f(y,f(x,x))),f(x,x)))) = f(y,f(x,x))
    ]]></literal>
    <justification jstring="[back_rewrite(7758),rewrite([9850(6,R),9232(7)])].">
      <j1 rule="back_rewrite" parents="7758"/>
      <j2 rule="rewrite" parents="9850 9232"/>
    </justification>
  </clause>

  <clause id="10738">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),f(f(f(x,y),f(c_0,f(x,y))),y)) = f(f(x,y),f(c_0,f(x,y)))
    ]]></literal>
    <justification jstring="[back_rewrite(2834),rewrite([9850(3,R),9850(7,R),9850(14,R)])].">
      <j1 rule="back_rewrite" parents="2834"/>
      <j2 rule="rewrite" parents="9850 9850 9850"/>
    </justification>
  </clause>

  <clause id="10801">
    <literal><![CDATA[
      f(f(x,x),f(c_0,f(x,y))) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(2631),rewrite([9232(3),9232(7)])].">
      <j1 rule="back_rewrite" parents="2631"/>
      <j2 rule="rewrite" parents="9232 9232"/>
    </justification>
  </clause>

  <clause id="10802">
    <literal><![CDATA[
      f(f(x,x),f(c_0,f(y,x))) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(2629),rewrite([9232(3),9232(7)])].">
      <j1 rule="back_rewrite" parents="2629"/>
      <j2 rule="rewrite" parents="9232 9232"/>
    </justification>
  </clause>

  <clause id="10806">
    <literal><![CDATA[
      f(x,f(c_0,f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(2617),rewrite([9232(2)])].">
      <j1 rule="back_rewrite" parents="2617"/>
      <j2 rule="rewrite" parents="9232"/>
    </justification>
  </clause>

  <clause id="10808">
    <literal><![CDATA[
      f(x,f(c_0,f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(2615),rewrite([9232(2)])].">
      <j1 rule="back_rewrite" parents="2615"/>
      <j2 rule="rewrite" parents="9232"/>
    </justification>
  </clause>

  <clause id="10827">
    <literal><![CDATA[
      f(x,f(c_0,f(y,f(x,x)))) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(2026),rewrite([9232(2),9232(7)])].">
      <j1 rule="back_rewrite" parents="2026"/>
      <j2 rule="rewrite" parents="9232 9232"/>
    </justification>
  </clause>

  <clause id="10828">
    <literal><![CDATA[
      f(x,f(c_0,f(f(x,x),y))) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(1832),rewrite([9232(2),9232(7)])].">
      <j1 rule="back_rewrite" parents="1832"/>
      <j2 rule="rewrite" parents="9232 9232"/>
    </justification>
  </clause>

  <clause id="10906">
    <literal><![CDATA[
      f(x,f(f(f(c_0,f(x,y)),z),f(f(f(f(x,z),z),f(x,y)),x))) = f(x,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(9732),rewrite([9850(2),543(3),543(3),9850(3,R)])].">
      <j1 rule="back_rewrite" parents="9732"/>
      <j2 rule="rewrite" parents="9850 543 543 9850"/>
    </justification>
  </clause>

  <clause id="10913">
    <literal><![CDATA[
      f(x,f(f(f(c_0,f(y,x)),z),f(f(f(f(x,z),z),f(y,x)),x))) = f(y,x)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(9711),rewrite([9850(2),543(3),544(3),9850(3,R)])].">
      <j1 rule="back_rewrite" parents="9711"/>
      <j2 rule="rewrite" parents="9850 543 544 9850"/>
    </justification>
  </clause>

  <clause id="10928">
    <literal><![CDATA[
      f(c_0,f(c_0,f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(9506),rewrite([9823(8),9850(4,R)])].">
      <j1 rule="back_rewrite" parents="9506"/>
      <j2 rule="rewrite" parents="9823 9850"/>
    </justification>
  </clause>

  <clause id="10949">
    <literal><![CDATA[
      f(f(f(f(x,f(f(x,y),x)),x),f(x,y)),f(f(f(c_0,f(x,y)),f(x,x)),f(f(x,f(x,y)),y))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(8989),rewrite([9850(9,R)])].">
      <j1 rule="back_rewrite" parents="8989"/>
      <j2 rule="rewrite" parents="9850"/>
    </justification>
  </clause>

  <clause id="10982">
    <literal><![CDATA[
      f(f(f(f(f(c_0,f(x,y)),f(x,x)),f(f(x,f(x,y)),x)),x),f(f(x,f(f(x,y),x)),x)) = x
    ]]></literal>
    <justification jstring="[back_rewrite(8755),rewrite([9850(3,R)])].">
      <j1 rule="back_rewrite" parents="8755"/>
      <j2 rule="rewrite" parents="9850"/>
    </justification>
  </clause>

  <clause id="10983">
    <literal><![CDATA[
      f(f(f(f(f(c_0,f(x,y)),f(y,y)),f(f(y,f(x,y)),y)),y),f(f(y,f(f(x,y),y)),y)) = y
    ]]></literal>
    <justification jstring="[back_rewrite(8754),rewrite([9850(3,R)])].">
      <j1 rule="back_rewrite" parents="8754"/>
      <j2 rule="rewrite" parents="9850"/>
    </justification>
  </clause>

  <clause id="11006">
    <literal><![CDATA[
      f(f(x,y),f(y,f(f(f(y,f(f(y,f(f(x,y),y)),y)),f(c_0,f(x,y))),f(z,f(c_0,f(x,y)))))) = f(c_0,f(x,y))
    ]]></literal>
    <justification jstring="[back_rewrite(8653),rewrite([9850(9,R),9850(13,R),9850(20,R)])].">
      <j1 rule="back_rewrite" parents="8653"/>
      <j2 rule="rewrite" parents="9850 9850 9850"/>
    </justification>
  </clause>

  <clause id="11120">
    <literal><![CDATA[
      f(f(x,y),f(f(x,y),f(f(f(c_0,f(x,y)),z),f(f(f(f(f(f(x,y),u),z),z),f(x,y)),x)))) = f(f(f(c_0,f(x,y)),z),f(f(f(f(f(f(x,y),u),z),z),f(x,y)),x))
    ]]></literal>
    <justification jstring="[back_rewrite(8223),rewrite([9850(5,R),9850(19,R)])].">
      <j1 rule="back_rewrite" parents="8223"/>
      <j2 rule="rewrite" parents="9850 9850"/>
    </justification>
  </clause>

  <clause id="11136">
    <literal><![CDATA[
      f(f(x,y),f(f(x,y),f(f(f(c_0,f(x,y)),z),f(f(f(f(x,z),z),f(x,y)),x)))) = f(f(f(c_0,f(x,y)),z),f(f(f(f(x,z),z),f(x,y)),x))
    ]]></literal>
    <justification jstring="[back_rewrite(8196),rewrite([9850(5,R),9850(17,R)])].">
      <j1 rule="back_rewrite" parents="8196"/>
      <j2 rule="rewrite" parents="9850 9850"/>
    </justification>
  </clause>

  <clause id="11163">
    <literal><![CDATA[
      f(f(f(f(c_0,f(x,y)),z),f(f(f(f(f(f(x,y),u),z),z),f(x,y)),x)),f(f(f(f(c_0,f(x,y)),z),f(f(f(f(f(f(x,y),u),z),z),f(x,y)),x)),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(8054),rewrite([9850(3,R),9850(15,R)])].">
      <j1 rule="back_rewrite" parents="8054"/>
      <j2 rule="rewrite" parents="9850 9850"/>
    </justification>
  </clause>

  <clause id="11168">
    <literal><![CDATA[
      f(x,f(f(f(c_0,f(x,f(y,x))),f(x,x)),f(f(y,x),x))) = f(x,f(y,x))
    ]]></literal>
    <justification jstring="[back_rewrite(8049),rewrite([9850(5,R)])].">
      <j1 rule="back_rewrite" parents="8049"/>
      <j2 rule="rewrite" parents="9850"/>
    </justification>
  </clause>

  <clause id="11203">
    <literal><![CDATA[
      f(x,f(f(f(c_0,f(x,f(x,y))),f(x,x)),f(f(x,y),x))) = f(x,f(x,y))
    ]]></literal>
    <justification jstring="[back_rewrite(7881),rewrite([9850(5,R)])].">
      <j1 rule="back_rewrite" parents="7881"/>
      <j2 rule="rewrite" parents="9850"/>
    </justification>
  </clause>

  <clause id="11974">
    <literal><![CDATA[
      f(f(f(x,f(f(f(x,f(f(f(x,x),y),f(f(f(f(f(x,z),y),y),x),f(x,z)))),x),f(x,z))),f(x,z)),f(f(f(c_0,f(x,z)),u),f(f(f(f(x,u),u),f(x,z)),x))) = f(x,z)
    ]]></literal>
    <justification jstring="[back_rewrite(1181),rewrite([9850(19,R)])].">
      <j1 rule="back_rewrite" parents="1181"/>
      <j2 rule="rewrite" parents="9850"/>
    </justification>
  </clause>

  <clause id="11989">
    <literal><![CDATA[
      f(f(f(f(f(c_0,f(x,y)),f(y,y)),f(f(y,f(x,y)),y)),y),f(c_0,f(f(f(x,y),y),f(y,z)))) = y
    ]]></literal>
    <justification jstring="[back_rewrite(1156),rewrite([9850(3,R),9850(14,R),10802(15)])].">
      <j1 rule="back_rewrite" parents="1156"/>
      <j2 rule="rewrite" parents="9850 9850 10802"/>
    </justification>
  </clause>

  <clause id="12055">
    <literal><![CDATA[
      f(f(f(f(x,y),f(f(f(f(x,y),f(f(f(c_0,f(x,y)),z),f(f(f(f(x,z),z),f(x,y)),x))),f(x,y)),x)),x),f(f(f(x,x),u),f(f(f(f(f(x,y),u),u),x),f(x,w)))) = x
    ]]></literal>
    <justification jstring="[back_rewrite(846),rewrite([9850(5,R)])].">
      <j1 rule="back_rewrite" parents="846"/>
      <j2 rule="rewrite" parents="9850"/>
    </justification>
  </clause>

  <clause id="12090">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),x) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(662),rewrite([9850(3,R)])].">
      <j1 rule="back_rewrite" parents="662"/>
      <j2 rule="rewrite" parents="9850"/>
    </justification>
  </clause>

  <clause id="12093">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),y) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(657),rewrite([9850(3,R)])].">
      <j1 rule="back_rewrite" parents="657"/>
      <j2 rule="rewrite" parents="9850"/>
    </justification>
  </clause>

  <clause id="12185">
    <literal><![CDATA[
      f(f(x,f(y,z)),f(c_0,f(y,z))) = f(y,z)
    ]]></literal>
    <justification jstring="[back_rewrite(9736),rewrite([12090(7),9850(5,R)])].">
      <j1 rule="back_rewrite" parents="9736"/>
      <j2 rule="rewrite" parents="12090 9850"/>
    </justification>
  </clause>

  <clause id="12290">
    <literal><![CDATA[
      f(x,f(f(f(c_0,f(y,x)),z),f(f(f(f(x,z),z),f(y,x)),c_0))) = f(y,x)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(2(a,1),9841(a,1,1)),rewrite([9850(3,R),2(15)])].">
      <j1 rule="para" parents="2 9841"/>
      <j2 rule="rewrite" parents="9850 2"/>
    </justification>
  </clause>

  <clause id="12608">
    <literal><![CDATA[
      f(f(f(x,f(x,y)),x),f(f(f(x,x),z),f(f(f(f(f(x,y),z),z),x),c_0))) = x
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(7716(a,1),9910(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="7716 9910"/>
    </justification>
  </clause>

  <clause id="12652">
    <literal><![CDATA[
      f(x,f(f(f(c_0,f(x,y)),z),f(f(f(f(x,f(f(f(f(c_0,f(x,y)),z),z),f(f(c_0,f(x,y)),z))),f(f(f(f(c_0,f(x,y)),z),z),f(f(c_0,f(x,y)),z))),f(x,y)),x))) = f(x,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(2257(a,1),10906(a,1,2,1))].">
      <j1 rule="para" parents="2257 10906"/>
    </justification>
  </clause>

  <clause id="12683">
    <literal><![CDATA[
      f(f(x,x),f(f(f(x,x),y),f(f(f(f(f(x,z),y),y),x),c_0))) = x
    ]]></literal>
    <justification jstring="[para(9232(a,1),753(a,1,2,2,2))].">
      <j1 rule="para" parents="9232 753"/>
    </justification>
  </clause>

  <clause id="12699">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),z),f(c_0,f(f(f(f(y,x),z),z),y)))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(9850(a,2),66(a,1,2,2))].">
      <j1 rule="para" parents="9850 66"/>
    </justification>
  </clause>

  <clause id="12730">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),z),f(c_0,f(f(f(f(x,y),z),z),y)))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(9850(a,2),1005(a,1,2,2))].">
      <j1 rule="para" parents="9850 1005"/>
    </justification>
  </clause>

  <clause id="12732">
    <literal><![CDATA[
      f(f(x,y),f(f(f(x,x),z),f(c_0,f(f(f(f(x,y),z),z),x)))) = x
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(9850(a,2),1008(a,1,2,2))].">
      <j1 rule="para" parents="9850 1008"/>
    </justification>
  </clause>

  <clause id="12756">
    <literal><![CDATA[
      f(f(x,f(y,y)),f(f(y,z),f(c_0,f(f(f(f(f(y,y),x),z),z),f(y,y))))) = f(y,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(604(a,1),294(a,1,2,2)),rewrite([9850(16,R)])].">
      <j1 rule="para" parents="604 294"/>
      <j2 rule="rewrite" parents="9850"/>
    </justification>
  </clause>

  <clause id="12813">
    <literal><![CDATA[
      f(x,f(f(f(c_0,f(x,y)),z),f(c_0,f(f(f(x,z),z),f(x,y))))) = f(x,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(40(a,1),12699(a,1,2,2,2,1,1,1)),rewrite([543(3),9850(3,R)])].">
      <j1 rule="para" parents="40 12699"/>
      <j2 rule="rewrite" parents="543 9850"/>
    </justification>
  </clause>

  <clause id="12819">
    <literal><![CDATA[
      f(f(f(f(x,y),f(f(f(f(x,y),y),f(x,y)),x)),x),f(f(f(x,x),z),f(c_0,f(f(f(f(x,y),z),z),x)))) = x
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(764(a,1),12699(a,1,2,2,2,1,1,1))].">
      <j1 rule="para" parents="764 12699"/>
    </justification>
  </clause>

  <clause id="12898">
    <literal><![CDATA[
      f(f(f(f(f(x,y),f(f(f(x,y),y),f(x,y))),f(x,y)),x),f(f(f(x,x),z),f(c_0,f(f(f(f(x,y),z),z),x)))) = x
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(2482(a,1),12699(a,1,2,2,2,1,1,1))].">
      <j1 rule="para" parents="2482 12699"/>
    </justification>
  </clause>

  <clause id="12900">
    <literal><![CDATA[
      f(f(f(f(f(x,y),f(f(f(y,x),x),f(x,y))),f(x,y)),y),f(f(f(y,y),z),f(c_0,f(f(f(f(x,y),z),z),y)))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(2648(a,1),12699(a,1,2,2,2,1,1,1))].">
      <j1 rule="para" parents="2648 12699"/>
    </justification>
  </clause>

  <clause id="12964">
    <literal><![CDATA[
      f(x,f(c_0,f(f(f(x,x),y),f(c_0,f(f(f(f(z,x),y),y),x))))) = f(f(f(x,x),y),f(c_0,f(f(f(f(z,x),y),y),x)))
    ]]></literal>
    <justification jstring="[para(12730(a,1),11(a,1,1)),rewrite([9850(19,R)])].">
      <j1 rule="para" parents="12730 11"/>
      <j2 rule="rewrite" parents="9850"/>
    </justification>
  </clause>

  <clause id="12981">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),f(f(f(f(x,y),z),z),f(f(x,y),z))),f(c_0,f(f(f(f(x,y),z),f(f(f(f(x,y),z),z),f(f(x,y),z))),y)))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(2257(a,1),12730(a,1,2,2,2,1,1))].">
      <j1 rule="para" parents="2257 12730"/>
    </justification>
  </clause>

  <clause id="13012">
    <literal><![CDATA[
      f(x,f(x,f(f(f(x,x),y),f(c_0,f(f(f(f(z,x),y),y),x))))) = f(f(f(x,x),y),f(c_0,f(f(f(f(z,x),y),y),x)))
    ]]></literal>
    <justification jstring="[para(12730(a,1),7848(a,1,1)),rewrite([12730(11)])].">
      <j1 rule="para" parents="12730 7848"/>
      <j2 rule="rewrite" parents="12730"/>
    </justification>
  </clause>

  <clause id="13028">
    <literal><![CDATA[
      f(f(f(x,x),y),f(f(x,z),f(c_0,f(f(f(f(f(x,x),y),z),z),f(x,x))))) = f(x,x)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(11(a,1),12732(a,1,2,1,1))].">
      <j1 rule="para" parents="11 12732"/>
    </justification>
  </clause>

  <clause id="13050">
    <literal><![CDATA[
      f(f(x,y),f(f(f(x,x),f(f(f(f(x,y),z),z),f(f(x,y),z))),f(c_0,f(f(f(f(x,y),z),f(f(f(f(x,y),z),z),f(f(x,y),z))),x)))) = x
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(2257(a,1),12732(a,1,2,2,2,1,1))].">
      <j1 rule="para" parents="2257 12732"/>
    </justification>
  </clause>

  <clause id="13103">
    <literal><![CDATA[
      f(f(f(c_0,f(x,y)),f(x,y)),y) = f(y,y)
    ]]></literal>
    <justification jstring="[para(1369(a,1),10913(a,1,2,2,1)),rewrite([9232(3),9901(8),9850(3,R),9861(3),9232(3)]),flip(a)].">
      <j1 rule="para" parents="1369 10913"/>
      <j2 rule="rewrite" parents="9232 9901 9850 9861 9232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13430">
    <literal><![CDATA[
      f(x,f(f(f(c_0,f(f(c_0,f(f(x,y),y)),x)),y),f(f(c_0,f(f(x,y),y)),c_0))) = f(f(c_0,f(f(x,y),y)),x)
    ]]></literal>
    <justification jstring="[para(604(a,1),12290(a,1,2,2,1)),rewrite([9850(6,R),9850(13,R),9850(21,R)])].">
      <j1 rule="para" parents="604 12290"/>
      <j2 rule="rewrite" parents="9850 9850 9850"/>
    </justification>
  </clause>

  <clause id="13757">
    <literal><![CDATA[
      f(f(f(f(f(c_0,f(x,y)),z),f(c_0,f(f(f(x,z),z),f(x,y)))),x),f(f(x,f(x,f(f(f(x,f(f(f(x,x),u),f(f(f(f(f(x,y),u),u),x),f(x,y)))),x),f(x,y)))),x)) = x
    ]]></literal>
    <justification jstring="[para(12813(a,1),1388(a,1,2,1,2,2,1,1,2,2,1,1,1,1)),rewrite([12813(30),12813(35)])].">
      <j1 rule="para" parents="12813 1388"/>
      <j2 rule="rewrite" parents="12813 12813"/>
    </justification>
  </clause>

  <clause id="13895">
    <literal><![CDATA[
      f(f(f(f(x,y),y),c_0),f(c_0,f(x,f(z,z)))) = c_0
    ]]></literal>
    <justification jstring="[para(9912(a,1),679(a,1,2,2,1,1,1)),rewrite([9913(8),9850(7),9915(8),9850(7)])].">
      <j1 rule="para" parents="9912 679"/>
      <j2 rule="rewrite" parents="9913 9850 9915 9850"/>
    </justification>
  </clause>

  <clause id="13940">
    <literal><![CDATA[
      f(f(f(x,f(f(f(x,x),y),f(c_0,f(f(f(f(x,z),y),y),x)))),c_0),f(z,x)) = c_0
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(12699(a,1),9912(a,1,1,1,1))].">
      <j1 rule="para" parents="12699 9912"/>
    </justification>
  </clause>

  <clause id="13941">
    <literal><![CDATA[
      f(f(f(x,f(f(f(x,x),y),f(c_0,f(f(f(f(z,x),y),y),x)))),c_0),f(z,x)) = c_0
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(12730(a,1),9912(a,1,1,1,1))].">
      <j1 rule="para" parents="12730 9912"/>
    </justification>
  </clause>

  <clause id="13946">
    <literal><![CDATA[
      f(f(c_0,f(f(x,y),y)),x) = c_0
    ]]></literal>
    <justification jstring="[para(9914(a,1),9912(a,1,1)),rewrite([9850(5,R)])].">
      <j1 rule="para" parents="9914 9912"/>
      <j2 rule="rewrite" parents="9850"/>
    </justification>
  </clause>

  <clause id="13969">
    <literal><![CDATA[
      f(x,f(c_0,f(f(c_0,f(f(x,y),y)),c_0))) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(13430),rewrite([13946(6),9913(4),13946(14)])].">
      <j1 rule="back_rewrite" parents="13430"/>
      <j2 rule="rewrite" parents="13946 9913 13946"/>
    </justification>
  </clause>

  <clause id="14144">
    <literal><![CDATA[
      f(f(x,y),f(f(y,f(f(y,f(f(y,x),y)),y)),c_0)) = c_0
    ]]></literal>
    <justification jstring="[para(8363(a,1),9978(a,1,2,1,1))].">
      <j1 rule="para" parents="8363 9978"/>
    </justification>
  </clause>

  <clause id="14155">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),f(f(f(f(y,x),z),z),c_0)),f(f(f(c_0,f(f(f(f(y,x),z),z),c_0)),y),c_0))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(9978(a,1),9910(a,1,2,2,1,1,1))].">
      <j1 rule="para" parents="9978 9910"/>
    </justification>
  </clause>

  <clause id="14157">
    <literal><![CDATA[
      f(x,f(f(f(c_0,f(x,y)),f(f(f(x,z),z),c_0)),f(f(f(c_0,f(f(f(x,z),z),c_0)),f(x,y)),x))) = f(x,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(9978(a,1),10906(a,1,2,2,1,1,1))].">
      <j1 rule="para" parents="9978 10906"/>
    </justification>
  </clause>

  <clause id="14164">
    <literal><![CDATA[
      f(f(x,y),f(f(y,f(f(f(y,y),z),f(c_0,f(f(f(f(y,x),z),z),y)))),c_0)) = c_0
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(12699(a,1),9978(a,1,2,1,1))].">
      <j1 rule="para" parents="12699 9978"/>
    </justification>
  </clause>

  <clause id="14825">
    <literal><![CDATA[
      f(f(f(x,f(x,y)),x),f(f(f(x,x),f(f(f(f(x,y),z),z),f(f(x,y),z))),f(f(f(f(f(x,y),z),f(f(f(f(x,y),z),z),f(f(x,y),z))),x),c_0))) = x
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(2257(a,1),12608(a,1,2,2,1,1,1))].">
      <j1 rule="para" parents="2257 12608"/>
    </justification>
  </clause>

  <clause id="15043">
    <literal><![CDATA[
      f(f(f(x,f(y,y)),c_0),f(c_0,f(y,f(z,z)))) = c_0
    ]]></literal>
    <justification jstring="[para(10036(a,1),679(a,1,2,2,1,1,1)),rewrite([9913(8),9850(7),9915(8),9850(7)])].">
      <j1 rule="para" parents="10036 679"/>
      <j2 rule="rewrite" parents="9913 9850 9915 9850"/>
    </justification>
  </clause>

  <clause id="15093">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),f(x,x)) = c_0
    ]]></literal>
    <justification jstring="[para(543(a,1),10042(a,1,2,1)),rewrite([9850(3,R),9914(5)])].">
      <j1 rule="para" parents="543 10042"/>
      <j2 rule="rewrite" parents="9850 9914"/>
    </justification>
  </clause>

  <clause id="15094">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),f(y,y)) = c_0
    ]]></literal>
    <justification jstring="[para(544(a,1),10042(a,1,2,1)),rewrite([9850(3,R),9914(5)])].">
      <j1 rule="para" parents="544 10042"/>
      <j2 rule="rewrite" parents="9850 9914"/>
    </justification>
  </clause>

  <clause id="15201">
    <literal><![CDATA[
      f(f(x,y),x) = f(x,f(x,y))
    ]]></literal>
    <justification jstring="[back_rewrite(11203),rewrite([15093(6),10808(5)])].">
      <j1 rule="back_rewrite" parents="11203"/>
      <j2 rule="rewrite" parents="15093 10808"/>
    </justification>
  </clause>

  <clause id="15202">
    <literal><![CDATA[
      f(f(x,y),y) = f(y,f(x,y))
    ]]></literal>
    <justification jstring="[back_rewrite(11168),rewrite([15093(6),10808(5)])].">
      <j1 rule="back_rewrite" parents="11168"/>
      <j2 rule="rewrite" parents="15093 10808"/>
    </justification>
  </clause>

  <clause id="15207">
    <literal><![CDATA[
      f(f(x,y),f(x,f(x,y))) = x
    ]]></literal>
    <justification jstring="[back_rewrite(10982),rewrite([15093(5),15201(4),7716(4),12090(4),15201(3),7716(4),15201(3)])].">
      <j1 rule="back_rewrite" parents="10982"/>
      <j2 rule="rewrite" parents="15093 15201 7716 12090 15201 7716 15201"/>
    </justification>
  </clause>

  <clause id="15209">
    <literal><![CDATA[
      f(x,f(c_0,f(f(x,f(x,y)),y))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(10949),rewrite([15201(2),7716(3),15201(2),15202(4),15207(4),15093(5)])].">
      <j1 rule="back_rewrite" parents="10949"/>
      <j2 rule="rewrite" parents="15201 7716 15201 15202 15207 15093"/>
    </justification>
  </clause>

  <clause id="15217">
    <literal><![CDATA[
      f(f(x,y),f(c_0,f(f(y,f(x,y)),f(y,z)))) = y
    ]]></literal>
    <justification jstring="[back_rewrite(11989),rewrite([15094(5),15201(4),7717(4),12093(4),15202(4)])].">
      <j1 rule="back_rewrite" parents="11989"/>
      <j2 rule="rewrite" parents="15094 15201 7717 12093 15202"/>
    </justification>
  </clause>

  <clause id="15257">
    <literal><![CDATA[
      f(f(x,y),f(y,f(x,y))) = y
    ]]></literal>
    <justification jstring="[back_rewrite(10983),rewrite([15094(5),15201(4),7717(4),12093(4),15202(3),7717(4),15202(3)])].">
      <j1 rule="back_rewrite" parents="10983"/>
      <j2 rule="rewrite" parents="15094 15201 7717 12093 15202 7717 15202"/>
    </justification>
  </clause>

  <clause id="15356">
    <literal><![CDATA[
      f(f(x,y),f(f(f(x,x),z),f(f(f(z,f(f(x,y),z)),x),c_0))) = x
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(14825),rewrite([15201(3),7716(3),15202(5),15202(8),15257(8),15202(8),15202(11),15257(11),15202(6)])].">
      <j1 rule="back_rewrite" parents="14825"/>
      <j2 rule="rewrite" parents="15201 7716 15202 15202 15257 15202 15202 15257 15202"/>
    </justification>
  </clause>

  <clause id="15632">
    <literal><![CDATA[
      f(f(x,y),f(f(y,x),c_0)) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(14144),rewrite([15201(3),7716(4),15201(3),7716(4)])].">
      <j1 rule="back_rewrite" parents="14144"/>
      <j2 rule="rewrite" parents="15201 7716 15201 7716"/>
    </justification>
  </clause>

  <clause id="15683">
    <literal><![CDATA[
      f(x,f(c_0,f(y,f(x,y)))) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(13969),rewrite([15202(4),15201(7),10928(7)])].">
      <j1 rule="back_rewrite" parents="13969"/>
      <j2 rule="rewrite" parents="15202 15201 10928"/>
    </justification>
  </clause>

  <clause id="15722">
    <literal><![CDATA[
      f(f(f(f(f(c_0,f(x,y)),z),f(c_0,f(f(z,f(x,z)),f(x,y)))),x),f(x,f(f(x,f(x,f(f(f(x,x),u),f(f(f(u,f(f(x,y),u)),x),f(x,y))))),f(x,y)))) = x
    ]]></literal>
    <justification jstring="[back_rewrite(13757),rewrite([15202(7),15202(17),15201(23),15201(28),7716(28)])].">
      <j1 rule="back_rewrite" parents="13757"/>
      <j2 rule="rewrite" parents="15202 15202 15201 15201 7716"/>
    </justification>
  </clause>

  <clause id="15820">
    <literal><![CDATA[
      f(f(x,y),f(f(f(x,x),z),f(c_0,f(f(z,f(f(x,y),z)),x)))) = x
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(13050),rewrite([15202(5),15202(8),15257(8),15202(9),15202(12),15257(12),15202(7)])].">
      <j1 rule="back_rewrite" parents="13050"/>
      <j2 rule="rewrite" parents="15202 15202 15257 15202 15202 15257 15202"/>
    </justification>
  </clause>

  <clause id="15838">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),z),f(c_0,f(f(z,f(f(x,y),z)),y)))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(12981),rewrite([15202(5),15202(8),15257(8),15202(9),15202(12),15257(12),15202(7)])].">
      <j1 rule="back_rewrite" parents="12981"/>
      <j2 rule="rewrite" parents="15202 15202 15257 15202 15202 15257 15202"/>
    </justification>
  </clause>

  <clause id="15847">
    <literal><![CDATA[
      f(f(f(f(x,f(y,x)),f(x,y)),y),f(f(f(y,y),z),f(c_0,f(f(z,f(f(x,y),z)),y)))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(12900),rewrite([15202(3),15201(8),7717(8),15202(11)])].">
      <j1 rule="back_rewrite" parents="12900"/>
      <j2 rule="rewrite" parents="15202 15201 7717 15202"/>
    </justification>
  </clause>

  <clause id="15849">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),z),f(c_0,f(f(z,f(f(y,x),z)),y)))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(12898),rewrite([15202(3),15202(5),15257(5),15202(2),15202(4),15257(4),15202(7)])].">
      <j1 rule="back_rewrite" parents="12898"/>
      <j2 rule="rewrite" parents="15202 15202 15257 15202 15202 15257 15202"/>
    </justification>
  </clause>

  <clause id="15869">
    <literal><![CDATA[
      f(f(f(f(x,y),f(y,x)),x),f(f(f(x,x),z),f(c_0,f(f(z,f(f(x,y),z)),x)))) = x
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(12819),rewrite([15202(3),15202(5),15257(5),15202(10)])].">
      <j1 rule="back_rewrite" parents="12819"/>
      <j2 rule="rewrite" parents="15202 15202 15257 15202"/>
    </justification>
  </clause>

  <clause id="15893">
    <literal><![CDATA[
      f(x,f(f(f(c_0,f(x,y)),z),f(f(f(z,f(x,z)),f(x,y)),x))) = f(x,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(12652),rewrite([15202(9),15202(14),15257(14),15202(10),15202(15),15257(15),15202(6)])].">
      <j1 rule="back_rewrite" parents="12652"/>
      <j2 rule="rewrite" parents="15202 15202 15257 15202 15202 15257 15202"/>
    </justification>
  </clause>

  <clause id="15984">
    <literal><![CDATA[
      f(f(f(f(x,y),f(f(f(x,y),f(f(x,y),f(f(f(c_0,f(x,y)),z),f(f(f(z,f(x,z)),f(x,y)),x)))),x)),x),f(f(f(x,x),u),f(f(f(u,f(f(x,y),u)),x),f(x,w)))) = x
    ]]></literal>
    <justification jstring="[back_rewrite(12055),rewrite([15202(8),15201(15),15202(23)])].">
      <j1 rule="back_rewrite" parents="12055"/>
      <j2 rule="rewrite" parents="15202 15201 15202"/>
    </justification>
  </clause>

  <clause id="16012">
    <literal><![CDATA[
      f(f(f(x,f(f(x,f(x,f(f(f(x,x),y),f(f(f(y,f(f(x,z),y)),x),f(x,z))))),f(x,z))),f(x,z)),f(f(f(c_0,f(x,z)),u),f(f(f(u,f(x,u)),f(x,z)),x))) = f(x,z)
    ]]></literal>
    <justification jstring="[back_rewrite(11974),rewrite([15202(5),15201(11),15202(22)])].">
      <j1 rule="back_rewrite" parents="11974"/>
      <j2 rule="rewrite" parents="15202 15201 15202"/>
    </justification>
  </clause>

  <clause id="16291">
    <literal><![CDATA[
      f(f(x,y),f(y,f(f(f(x,y),f(c_0,f(x,y))),f(z,f(c_0,f(x,y)))))) = f(c_0,f(x,y))
    ]]></literal>
    <justification jstring="[back_rewrite(11006),rewrite([15202(3),7717(4),15202(3),7717(4)])].">
      <j1 rule="back_rewrite" parents="11006"/>
      <j2 rule="rewrite" parents="15202 7717 15202 7717"/>
    </justification>
  </clause>

  <clause id="16486">
    <literal><![CDATA[
      f(x,f(f(y,f(x,y)),f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(8676),rewrite([15202(2),7717(3),15202(2),15202(4),15257(4),15202(2)])].">
      <j1 rule="back_rewrite" parents="8676"/>
      <j2 rule="rewrite" parents="15202 7717 15202 15202 15257 15202"/>
    </justification>
  </clause>

  <clause id="17120">
    <literal><![CDATA[
      f(f(x,y),f(f(y,f(f(f(y,y),z),f(c_0,f(f(z,f(f(y,x),z)),y)))),c_0)) = c_0
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(14164),rewrite([15202(7)])].">
      <j1 rule="back_rewrite" parents="14164"/>
      <j2 rule="rewrite" parents="15202"/>
    </justification>
  </clause>

  <clause id="17127">
    <literal><![CDATA[
      f(x,f(f(f(c_0,f(x,y)),f(f(z,f(x,z)),c_0)),f(f(f(c_0,f(f(z,f(x,z)),c_0)),f(x,y)),x))) = f(x,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(14157),rewrite([15202(5),15202(11)])].">
      <j1 rule="back_rewrite" parents="14157"/>
      <j2 rule="rewrite" parents="15202 15202"/>
    </justification>
  </clause>

  <clause id="17128">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),f(f(z,f(f(y,x),z)),c_0)),f(f(f(c_0,f(f(z,f(f(y,x),z)),c_0)),y),c_0))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(14155),rewrite([15202(5),15202(12)])].">
      <j1 rule="back_rewrite" parents="14155"/>
      <j2 rule="rewrite" parents="15202 15202"/>
    </justification>
  </clause>

  <clause id="17205">
    <literal><![CDATA[
      f(f(c_0,f(x,f(y,x))),y) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(13946),rewrite([15202(3)])].">
      <j1 rule="back_rewrite" parents="13946"/>
      <j2 rule="rewrite" parents="15202"/>
    </justification>
  </clause>

  <clause id="17209">
    <literal><![CDATA[
      f(f(f(x,f(f(f(x,x),y),f(c_0,f(f(y,f(f(z,x),y)),x)))),c_0),f(z,x)) = c_0
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(13941),rewrite([15202(6)])].">
      <j1 rule="back_rewrite" parents="13941"/>
      <j2 rule="rewrite" parents="15202"/>
    </justification>
  </clause>

  <clause id="17210">
    <literal><![CDATA[
      f(f(f(x,f(f(f(x,x),y),f(c_0,f(f(y,f(f(x,z),y)),x)))),c_0),f(z,x)) = c_0
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(13940),rewrite([15202(6)])].">
      <j1 rule="back_rewrite" parents="13940"/>
      <j2 rule="rewrite" parents="15202"/>
    </justification>
  </clause>

  <clause id="17226">
    <literal><![CDATA[
      f(f(f(x,f(y,x)),c_0),f(c_0,f(y,f(z,z)))) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(13895),rewrite([15202(2)])].">
      <j1 rule="back_rewrite" parents="13895"/>
      <j2 rule="rewrite" parents="15202"/>
    </justification>
  </clause>

  <clause id="17485">
    <literal><![CDATA[
      f(f(f(x,y),f(c_0,f(x,y))),y) = f(y,y)
    ]]></literal>
    <justification jstring="[back_rewrite(13103),rewrite([15202(5)])].">
      <j1 rule="back_rewrite" parents="13103"/>
      <j2 rule="rewrite" parents="15202"/>
    </justification>
  </clause>

  <clause id="17518">
    <literal><![CDATA[
      f(f(f(x,x),y),f(f(x,z),f(c_0,f(f(z,f(f(f(x,x),y),z)),f(x,x))))) = f(x,x)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(13028),rewrite([15202(8)])].">
      <j1 rule="back_rewrite" parents="13028"/>
      <j2 rule="rewrite" parents="15202"/>
    </justification>
  </clause>

  <clause id="17526">
    <literal><![CDATA[
      f(x,f(x,f(f(f(x,x),y),f(c_0,f(f(y,f(f(z,x),y)),x))))) = f(f(f(x,x),y),f(c_0,f(f(y,f(f(z,x),y)),x)))
    ]]></literal>
    <justification jstring="[back_rewrite(13012),rewrite([15202(6),15202(17)])].">
      <j1 rule="back_rewrite" parents="13012"/>
      <j2 rule="rewrite" parents="15202 15202"/>
    </justification>
  </clause>

  <clause id="17555">
    <literal><![CDATA[
      f(x,f(c_0,f(f(f(x,x),y),f(c_0,f(f(y,f(f(z,x),y)),x))))) = f(f(f(x,x),y),f(c_0,f(f(y,f(f(z,x),y)),x)))
    ]]></literal>
    <justification jstring="[back_rewrite(12964),rewrite([15202(7),15202(18)])].">
      <j1 rule="back_rewrite" parents="12964"/>
      <j2 rule="rewrite" parents="15202 15202"/>
    </justification>
  </clause>

  <clause id="17657">
    <literal><![CDATA[
      f(f(x,f(y,y)),f(f(y,z),f(c_0,f(f(z,f(f(f(y,y),x),z)),f(y,y))))) = f(y,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(12756),rewrite([15202(8)])].">
      <j1 rule="back_rewrite" parents="12756"/>
      <j2 rule="rewrite" parents="15202"/>
    </justification>
  </clause>

  <clause id="17680">
    <literal><![CDATA[
      f(f(x,x),f(f(f(x,x),y),f(f(f(y,f(f(x,z),y)),x),c_0))) = x
    ]]></literal>
    <justification jstring="[back_rewrite(12683),rewrite([15202(6)])].">
      <j1 rule="back_rewrite" parents="12683"/>
      <j2 rule="rewrite" parents="15202"/>
    </justification>
  </clause>

  <clause id="18054">
    <literal><![CDATA[
      f(f(f(f(c_0,f(x,y)),z),f(f(f(z,f(f(f(x,y),u),z)),f(x,y)),x)),f(f(f(f(c_0,f(x,y)),z),f(f(f(z,f(f(f(x,y),u),z)),f(x,y)),x)),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(11163),rewrite([15202(8),15202(20)])].">
      <j1 rule="back_rewrite" parents="11163"/>
      <j2 rule="rewrite" parents="15202 15202"/>
    </justification>
  </clause>

  <clause id="18062">
    <literal><![CDATA[
      f(f(x,y),f(f(x,y),f(f(f(c_0,f(x,y)),z),f(f(f(z,f(x,z)),f(x,y)),x)))) = f(f(f(c_0,f(x,y)),z),f(f(f(z,f(x,z)),f(x,y)),x))
    ]]></literal>
    <justification jstring="[back_rewrite(11136),rewrite([15202(8),15202(20)])].">
      <j1 rule="back_rewrite" parents="11136"/>
      <j2 rule="rewrite" parents="15202 15202"/>
    </justification>
  </clause>

  <clause id="18065">
    <literal><![CDATA[
      f(f(x,y),f(f(x,y),f(f(f(c_0,f(x,y)),z),f(f(f(z,f(f(f(x,y),u),z)),f(x,y)),x)))) = f(f(f(c_0,f(x,y)),z),f(f(f(z,f(f(f(x,y),u),z)),f(x,y)),x))
    ]]></literal>
    <justification jstring="[back_rewrite(11120),rewrite([15202(10),15202(24)])].">
      <j1 rule="back_rewrite" parents="11120"/>
      <j2 rule="rewrite" parents="15202 15202"/>
    </justification>
  </clause>

  <clause id="18204">
    <literal><![CDATA[
      f(x,f(x,f(f(f(x,x),y),f(f(f(y,f(f(x,z),y)),x),f(x,u))))) = f(f(f(x,x),y),f(f(f(y,f(f(x,z),y)),x),f(x,u)))
    ]]></literal>
    <justification jstring="[back_rewrite(8184),rewrite([15202(5),15202(16)])].">
      <j1 rule="back_rewrite" parents="8184"/>
      <j2 rule="rewrite" parents="15202 15202"/>
    </justification>
  </clause>

  <clause id="18611">
    <literal><![CDATA[
      f(f(f(f(f(x,x),y),f(f(f(y,f(f(x,z),y)),x),f(x,u))),f(z,x)),f(f(z,x),f(f(f(z,f(x,z)),f(z,x)),f(f(z,x),w)))) = f(z,x)
    ]]></literal>
    <justification jstring="[back_rewrite(783),rewrite([15202(5),15202(14)])].">
      <j1 rule="back_rewrite" parents="783"/>
      <j2 rule="rewrite" parents="15202 15202"/>
    </justification>
  </clause>

  <clause id="18649">
    <literal><![CDATA[
      f(x,f(f(x,y),f(c_0,f(z,f(x,x))))) = f(x,x)
    ]]></literal>
    <justification jstring="[back_rewrite(7880),rewrite([15207(5),9232(3)])].">
      <j1 rule="back_rewrite" parents="7880"/>
      <j2 rule="rewrite" parents="15207 9232"/>
    </justification>
  </clause>

  <clause id="18693">
    <literal><![CDATA[
      f(f(x,y),f(c_0,f(x,y))) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(10738),rewrite([17485(9),15094(5)]),flip(a)].">
      <j1 rule="back_rewrite" parents="10738"/>
      <j2 rule="rewrite" parents="17485 15094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18760">
    <literal><![CDATA[
      f(f(f(f(x,y),f(f(f(f(c_0,f(x,y)),z),f(f(f(z,f(x,z)),f(x,y)),x)),x)),x),f(f(f(x,x),u),f(f(f(u,f(f(x,y),u)),x),f(x,w)))) = x
    ]]></literal>
    <justification jstring="[back_rewrite(15984),rewrite([18062(15)])].">
      <j1 rule="back_rewrite" parents="15984"/>
      <j2 rule="rewrite" parents="18062"/>
    </justification>
  </clause>

  <clause id="18900">
    <literal><![CDATA[
      f(f(f(x,f(f(f(f(x,x),y),f(f(f(y,f(f(x,z),y)),x),f(x,z))),f(x,z))),f(x,z)),f(f(f(c_0,f(x,z)),u),f(f(f(u,f(x,u)),f(x,z)),x))) = f(x,z)
    ]]></literal>
    <justification jstring="[back_rewrite(16012),rewrite([18204(11)])].">
      <j1 rule="back_rewrite" parents="16012"/>
      <j2 rule="rewrite" parents="18204"/>
    </justification>
  </clause>

  <clause id="18904">
    <literal><![CDATA[
      f(f(f(f(f(c_0,f(x,y)),z),f(c_0,f(f(z,f(x,z)),f(x,y)))),x),f(x,f(f(f(f(x,x),u),f(f(f(u,f(f(x,y),u)),x),f(x,y))),f(x,y)))) = x
    ]]></literal>
    <justification jstring="[back_rewrite(15722),rewrite([18204(23)])].">
      <j1 rule="back_rewrite" parents="15722"/>
      <j2 rule="rewrite" parents="18204"/>
    </justification>
  </clause>

  <clause id="18936">
    <literal><![CDATA[
      f(f(x,y),f(y,f(c_0,f(z,f(c_0,f(x,y)))))) = f(c_0,f(x,y))
    ]]></literal>
    <justification jstring="[back_rewrite(16291),rewrite([18693(6)])].">
      <j1 rule="back_rewrite" parents="16291"/>
      <j2 rule="rewrite" parents="18693"/>
    </justification>
  </clause>

  <clause id="18973">
    <literal><![CDATA[
      f(f(x,y),f(y,f(f(f(f(y,y),z),f(f(f(z,f(f(y,x),z)),y),c_0)),y))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(15356(a,1),15849(a,1,2,2,2,1,2)),rewrite([17680(12),15202(13),10806(15)])].">
      <j1 rule="para" parents="15356 15849"/>
      <j2 rule="rewrite" parents="17680 15202 10806"/>
    </justification>
  </clause>

  <clause id="18981">
    <literal><![CDATA[
      f(f(x,y),c_0) = f(c_0,f(x,y))
    ]]></literal>
    <justification jstring="[para(10801(a,1),544(a,1,2)),rewrite([9850(7,R),10928(5)])].">
      <j1 rule="para" parents="10801 544"/>
      <j2 rule="rewrite" parents="9850 10928"/>
    </justification>
  </clause>

  <clause id="18985">
    <literal><![CDATA[
      f(f(x,y),f(y,f(f(f(f(y,y),z),f(c_0,f(f(z,f(f(y,x),z)),y))),y))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(18973),rewrite([18981(9)])].">
      <j1 rule="back_rewrite" parents="18973"/>
      <j2 rule="rewrite" parents="18981"/>
    </justification>
  </clause>

  <clause id="19066">
    <literal><![CDATA[
      f(f(c_0,f(x,f(y,x))),f(c_0,f(y,f(z,z)))) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(17226),rewrite([18981(4)])].">
      <j1 rule="back_rewrite" parents="17226"/>
      <j2 rule="rewrite" parents="18981"/>
    </justification>
  </clause>

  <clause id="19081">
    <literal><![CDATA[
      f(f(c_0,f(x,f(f(f(x,x),y),f(c_0,f(f(y,f(f(x,z),y)),x))))),f(z,x)) = c_0
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(17210),rewrite([18981(12)])].">
      <j1 rule="back_rewrite" parents="17210"/>
      <j2 rule="rewrite" parents="18981"/>
    </justification>
  </clause>

  <clause id="19082">
    <literal><![CDATA[
      f(f(c_0,f(x,f(f(f(x,x),y),f(c_0,f(f(y,f(f(z,x),y)),x))))),f(z,x)) = c_0
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(17209),rewrite([18981(12)])].">
      <j1 rule="back_rewrite" parents="17209"/>
      <j2 rule="rewrite" parents="18981"/>
    </justification>
  </clause>

  <clause id="19146">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),f(c_0,f(z,f(f(y,x),z)))),f(c_0,f(f(z,f(f(y,x),z)),y)))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(17128),rewrite([18981(7),18981(14),10928(15),18981(14)])].">
      <j1 rule="back_rewrite" parents="17128"/>
      <j2 rule="rewrite" parents="18981 18981 10928 18981"/>
    </justification>
  </clause>

  <clause id="19147">
    <literal><![CDATA[
      f(x,f(f(f(c_0,f(x,y)),f(c_0,f(z,f(x,z)))),f(f(f(z,f(x,z)),f(x,y)),x))) = f(x,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(17127),rewrite([18981(7),18981(13),10928(14)])].">
      <j1 rule="back_rewrite" parents="17127"/>
      <j2 rule="rewrite" parents="18981 18981 10928"/>
    </justification>
  </clause>

  <clause id="19152">
    <literal><![CDATA[
      f(f(x,y),f(c_0,f(y,f(f(f(y,y),z),f(c_0,f(f(z,f(f(y,x),z)),y)))))) = c_0
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(17120),rewrite([18981(13)])].">
      <j1 rule="back_rewrite" parents="17120"/>
      <j2 rule="rewrite" parents="18981"/>
    </justification>
  </clause>

  <clause id="19279">
    <literal><![CDATA[
      f(f(x,y),f(c_0,f(y,x))) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(15632),rewrite([18981(4)])].">
      <j1 rule="back_rewrite" parents="15632"/>
      <j2 rule="rewrite" parents="18981"/>
    </justification>
  </clause>

  <clause id="19404">
    <literal><![CDATA[
      f(f(c_0,f(x,f(y,y))),f(c_0,f(y,f(z,z)))) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(15043),rewrite([18981(4)])].">
      <j1 rule="back_rewrite" parents="15043"/>
      <j2 rule="rewrite" parents="18981"/>
    </justification>
  </clause>

  <clause id="19532">
    <literal><![CDATA[
      f(f(x,y),f(y,f(f(f(f(y,y),f(c_0,f(f(c_0,f(y,x)),z))),f(c_0,f(f(f(c_0,f(y,x)),z),y))),y))) = y
    ]]></literal>
    <justification jstring="[para(10828(a,1),18985(a,1,2,2,1,2,2,1,2)),rewrite([9850(6,R),9850(14,R),15201(18),10928(18)])].">
      <j1 rule="para" parents="10828 18985"/>
      <j2 rule="rewrite" parents="9850 9850 15201 10928"/>
    </justification>
  </clause>

  <clause id="19596">
    <literal><![CDATA[
      f(f(f(f(x,x),y),f(c_0,f(f(y,f(f(z,x),y)),x))),x) = f(x,f(f(f(x,x),y),f(c_0,f(f(y,f(f(z,x),y)),x))))
    ]]></literal>
    <justification jstring="[para(19082(a,1),15893(a,1,2,1)),rewrite([15257(5),17526(12),10808(13)])].">
      <j1 rule="para" parents="19082 15893"/>
      <j2 rule="rewrite" parents="15257 17526 10808"/>
    </justification>
  </clause>

  <clause id="19611">
    <literal><![CDATA[
      f(f(x,x),f(f(f(x,x),y),f(c_0,f(f(y,f(f(z,x),y)),x)))) = x
    ]]></literal>
    <justification jstring="[para(15838(a,1),12093(a,1,1,2)),rewrite([9850(2),15838(22)])].">
      <j1 rule="para" parents="15838 12093"/>
      <j2 rule="rewrite" parents="9850 15838"/>
    </justification>
  </clause>

  <clause id="19778">
    <literal><![CDATA[
      f(f(x,x),f(c_0,f(f(x,y),f(c_0,f(f(y,f(f(f(x,x),z),y)),f(x,x)))))) = f(f(x,y),f(c_0,f(f(y,f(f(f(x,x),z),y)),f(x,x))))
    ]]></literal>
    <justification jstring="[para(17518(a,1),11(a,1,1)),rewrite([9850(22,R)])].">
      <j1 rule="para" parents="17518 11"/>
      <j2 rule="rewrite" parents="9850"/>
    </justification>
  </clause>

  <clause id="19903">
    <literal><![CDATA[
      f(f(f(x,y),f(c_0,f(f(y,f(f(f(x,x),z),y)),f(x,x)))),f(x,x)) = f(f(x,x),f(f(x,y),f(c_0,f(f(y,f(f(f(x,x),z),y)),f(x,x)))))
    ]]></literal>
    <justification jstring="[para(17518(a,1),15202(a,1,1)),rewrite([17518(35)]),flip(a)].">
      <j1 rule="para" parents="17518 15202"/>
      <j2 rule="rewrite" parents="17518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19966">
    <literal><![CDATA[
      f(f(x,x),f(f(x,x),f(f(x,y),f(c_0,f(f(y,f(f(f(x,x),z),y)),f(x,x)))))) = f(f(x,y),f(c_0,f(f(y,f(f(f(x,x),z),y)),f(x,x))))
    ]]></literal>
    <justification jstring="[para(17518(a,1),15257(a,1,1)),rewrite([17518(24),19903(13)])].">
      <j1 rule="para" parents="17518 15257"/>
      <j2 rule="rewrite" parents="17518 19903"/>
    </justification>
  </clause>

  <clause id="20347">
    <literal><![CDATA[
      f(f(x,y),f(x,f(y,x))) = x
    ]]></literal>
    <justification jstring="[para(19279(a,1),15820(a,1,2,2,2,1,2)),rewrite([10802(6),15201(8),10928(8),15202(5),10928(7)])].">
      <j1 rule="para" parents="19279 15820"/>
      <j2 rule="rewrite" parents="10802 15201 10928 15202 10928"/>
    </justification>
  </clause>

  <clause id="20675">
    <literal><![CDATA[
      f(f(x,y),f(f(c_0,f(x,y)),z)) = f(c_0,f(x,y))
    ]]></literal>
    <justification jstring="[para(12185(a,1),543(a,1,1))].">
      <j1 rule="para" parents="12185 543"/>
    </justification>
  </clause>

  <clause id="20676">
    <literal><![CDATA[
      f(f(x,y),f(z,f(c_0,f(x,y)))) = f(c_0,f(x,y))
    ]]></literal>
    <justification jstring="[para(12185(a,1),544(a,1,1))].">
      <j1 rule="para" parents="12185 544"/>
    </justification>
  </clause>

  <clause id="20684">
    <literal><![CDATA[
      f(f(c_0,f(x,f(y,z))),f(c_0,f(y,z))) = c_0
    ]]></literal>
    <justification jstring="[para(12185(a,1),10801(a,1,2,2)),rewrite([9850(5,R)])].">
      <j1 rule="para" parents="12185 10801"/>
      <j2 rule="rewrite" parents="9850"/>
    </justification>
  </clause>

  <clause id="20688">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),f(c_0,f(z,f(x,y)))) = c_0
    ]]></literal>
    <justification jstring="[para(12185(a,1),10827(a,1,2,2,2))].">
      <j1 rule="para" parents="12185 10827"/>
    </justification>
  </clause>

  <clause id="20744">
    <literal><![CDATA[
      f(f(f(x,f(x,y)),y),f(c_0,f(x,y))) = c_0
    ]]></literal>
    <justification jstring="[para(15209(a,1),10802(a,1,2,2)),rewrite([9850(11,R),10928(7)])].">
      <j1 rule="para" parents="15209 10802"/>
      <j2 rule="rewrite" parents="9850 10928"/>
    </justification>
  </clause>

  <clause id="20794">
    <literal><![CDATA[
      f(f(c_0,f(f(x,f(x,y)),y)),f(x,y)) = f(f(x,y),f(c_0,f(f(x,f(x,y)),y)))
    ]]></literal>
    <justification jstring="[para(15209(a,1),15202(a,1,1)),rewrite([15209(18)]),flip(a)].">
      <j1 rule="para" parents="15209 15202"/>
      <j2 rule="rewrite" parents="15209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20901">
    <literal><![CDATA[
      f(x,f(c_0,f(f(x,f(y,x)),f(f(y,f(x,y)),f(y,x))))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(16486(a,1),15209(a,1,2,2,1,2)),rewrite([16486(15)])].">
      <j1 rule="para" parents="16486 15209"/>
      <j2 rule="rewrite" parents="16486"/>
    </justification>
  </clause>

  <clause id="22618">
    <literal><![CDATA[
      f(f(f(x,f(x,y)),y),x) = f(x,f(x,y))
    ]]></literal>
    <justification jstring="[para(20744(a,1),15820(a,1,2,2,2,1,2)),rewrite([9850(8,R),20684(11),15201(10),10928(10),15207(9),9850(6),9861(6)])].">
      <j1 rule="para" parents="20744 15820"/>
      <j2 rule="rewrite" parents="9850 20684 15201 10928 15207 9850 9861"/>
    </justification>
  </clause>

  <clause id="22635">
    <literal><![CDATA[
      f(f(x,f(y,f(y,x))),f(c_0,f(y,x))) = c_0
    ]]></literal>
    <justification jstring="[para(20744(a,1),19152(a,1,2,2,2,2,2,1,2)),rewrite([9850(11,R),20684(14),15201(13),10928(13),15207(12),9850(9),9861(9),15201(7),7716(7)])].">
      <j1 rule="para" parents="20744 19152"/>
      <j2 rule="rewrite" parents="9850 20684 15201 10928 15207 9850 9861 15201 7716"/>
    </justification>
  </clause>

  <clause id="23067">
    <literal><![CDATA[
      f(f(f(x,f(y,x)),f(f(y,f(x,y)),f(y,x))),x) = f(x,f(y,x))
    ]]></literal>
    <justification jstring="[para(16486(a,1),22618(a,1,1,1,2)),rewrite([16486(13)])].">
      <j1 rule="para" parents="16486 22618"/>
      <j2 rule="rewrite" parents="16486"/>
    </justification>
  </clause>

  <clause id="23439">
    <literal><![CDATA[
      f(f(f(f(x,f(f(y,y),x)),f(x,f(y,y))),f(y,y)),f(f(y,z),f(c_0,f(f(z,f(f(f(y,y),x),z)),f(y,y))))) = f(y,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(17657(a,1),15847(a,1,2,2,2,1,2)),rewrite([9850(11,R),9861(11),18649(19),19903(22),15201(24),19966(24),19778(22)])].">
      <j1 rule="para" parents="17657 15847"/>
      <j2 rule="rewrite" parents="9850 9861 18649 19903 15201 19966 19778"/>
    </justification>
  </clause>

  <clause id="23493">
    <literal><![CDATA[
      f(f(f(f(f(x,y),f(f(x,f(y,x)),f(x,y))),f(f(f(x,f(y,x)),f(x,y)),y)),y),f(f(f(y,y),z),f(c_0,f(f(z,f(f(x,y),z)),y)))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(15847(a,1),15847(a,1,2,2,2,1,2)),rewrite([16486(9),15202(6),19611(24),19596(24),15201(25),17526(25),17555(25)])].">
      <j1 rule="para" parents="15847 15847"/>
      <j2 rule="rewrite" parents="16486 15202 19611 19596 15201 17526 17555"/>
    </justification>
  </clause>

  <clause id="23699">
    <literal><![CDATA[
      f(f(x,f(y,f(y,x))),f(x,f(y,x))) = x
    ]]></literal>
    <justification jstring="[para(22635(a,1),15820(a,1,2,2,2,1,2)),rewrite([10802(8),15201(10),10928(10),15202(7),10928(9)])].">
      <j1 rule="para" parents="22635 15820"/>
      <j2 rule="rewrite" parents="10802 15201 10928 15202 10928"/>
    </justification>
  </clause>

  <clause id="23994">
    <literal><![CDATA[
      f(f(f(f(x,f(y,x)),f(x,y)),f(y,f(x,y))),f(f(x,y),f(f(x,f(y,x)),f(x,y)))) = f(f(x,f(y,x)),f(x,y))
    ]]></literal>
    <justification jstring="[para(16486(a,1),23699(a,1,1,2,2)),rewrite([16486(16),15202(13)])].">
      <j1 rule="para" parents="16486 23699"/>
      <j2 rule="rewrite" parents="16486 15202"/>
    </justification>
  </clause>

  <clause id="24288">
    <literal><![CDATA[
      f(f(f(x,f(y,x)),f(x,z)),f(x,x)) = c_0
    ]]></literal>
    <justification jstring="[para(15217(a,1),10802(a,1,2,2)),rewrite([9850(13,R),10928(8),9850(6)])].">
      <j1 rule="para" parents="15217 10802"/>
      <j2 rule="rewrite" parents="9850 10928 9850"/>
    </justification>
  </clause>

  <clause id="24306">
    <literal><![CDATA[
      f(f(x,f(x,y)),f(c_0,f(f(x,y),f(x,z)))) = x
    ]]></literal>
    <justification jstring="[para(15201(a,1),15217(a,1,1)),rewrite([15201(5),7716(6)])].">
      <j1 rule="para" parents="15201 15217"/>
      <j2 rule="rewrite" parents="15201 7716"/>
    </justification>
  </clause>

  <clause id="24320">
    <literal><![CDATA[
      f(f(x,f(y,x)),f(c_0,f(x,f(f(y,x),z)))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(15257(a,1),15217(a,1,2,2,1))].">
      <j1 rule="para" parents="15257 15217"/>
    </justification>
  </clause>

  <clause id="24454">
    <literal><![CDATA[
      f(f(f(x,y),f(x,z)),f(x,x)) = c_0
    ]]