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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 2009-11A, November 2009.
Process 6693 was started by mccune on cleo,
Tue Nov  3 10:23:08 2009
The command was "/home/mccune/LADR/bin/prover9 -f MOL-M.in MOL-M-interp.outx".
]]></heading>

<proof number="1" length="539" max_count="59">

<comments><![CDATA[
% Proof 1 at 698.27 (+ 1.84) seconds: MOD_SS.
% Length of proof is 539.
% Level of proof is 71.
% Maximum clause weight is 59.000.
% Given clauses 1791.

]]></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="1897">
    <literal><![CDATA[
      f(f(x,y),f(f(y,f(f(f(f(x,y),f(z,y)),f(z,y)),y)),y)) = y
    ]]></literal>
    <justification jstring="[para(1614(a,1),1614(a,1,2,1,1))].">
      <j1 rule="para" parents="1614 1614"/>
    </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="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="9009">
    <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="9011">
    <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="9013">
    <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="9022">
    <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="9024">
    <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="9028">
    <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="9029">
    <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),9028(6),2546(6),2615(10),2546(8)])].">
      <j1 rule="para" parents="8448 41"/>
      <j2 rule="rewrite" parents="20 543 32 2546 543 2546 2546 9028 2546 2615 2546"/>
    </justification>
  </clause>

  <clause id="9040">
    <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),9013(16)])].">
      <j1 rule="para" parents="8448 50"/>
      <j2 rule="rewrite" parents="8448 9013"/>
    </justification>
  </clause>

  <clause id="9044">
    <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="9066">
    <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="9067">
    <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="9071">
    <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([9066(6),9066(6)])].">
      <j1 rule="para" parents="8448 1370"/>
      <j2 rule="rewrite" parents="9066 9066"/>
    </justification>
  </clause>

  <clause id="9075">
    <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([9009(8),9009(10),9011(10),9009(9),9009(11),9071(11),20(6),543(6)])].">
      <j1 rule="para" parents="8448 63"/>
      <j2 rule="rewrite" parents="9009 9009 9011 9009 9009 9071 20 543"/>
    </justification>
  </clause>

  <clause id="9086">
    <literal><![CDATA[
      f(x,f(x,x)) = f(y,f(y,y))
    ]]></literal>
    <justification jstring="[para(8448(a,1),1464(a,2)),rewrite([9009(7),55(7)])].">
      <j1 rule="para" parents="8448 1464"/>
      <j2 rule="rewrite" parents="9009 55"/>
    </justification>
  </clause>

  <clause id="9102">
    <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="9145">
    <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="9156">
    <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="9172">
    <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([9075(7),9075(7)])].">
      <j1 rule="para" parents="8448 762"/>
      <j2 rule="rewrite" parents="9075 9075"/>
    </justification>
  </clause>

  <clause id="9179">
    <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="9188">
    <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="9193">
    <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="9217">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),y),f(y,z)) = y
    ]]></literal>
    <justification jstring="[back_rewrite(9040),rewrite([9075(14),9066(10),9075(12)])].">
      <j1 rule="back_rewrite" parents="9040"/>
      <j2 rule="rewrite" parents="9075 9066 9075"/>
    </justification>
  </clause>

  <clause id="9222">
    <literal><![CDATA[
      f(x,f(x,x)) = c_0
    ]]></literal>
    <justification jstring="[new_symbol(9086)].">
      <j1 rule="new_symbol" parents="9086"/>
    </justification>
  </clause>

  <clause id="9265">
    <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(9179),rewrite([9222(2),9222(5)])].">
      <j1 rule="back_rewrite" parents="9179"/>
      <j2 rule="rewrite" parents="9222 9222"/>
    </justification>
  </clause>

  <clause id="9386">
    <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([9222(4),9222(7),9265(11),32(3),9222(5)]),flip(a)].">
      <j1 rule="back_rewrite" parents="5400"/>
      <j2 rule="rewrite" parents="9222 9222 9265 32 9222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9410">
    <literal><![CDATA[
      f(f(x,y),f(c_0,x)) = x
    ]]></literal>
    <justification jstring="[back_rewrite(4650),rewrite([9222(7),9386(10),40(4),9222(6),9386(9),9222(3)])].">
      <j1 rule="back_rewrite" parents="4650"/>
      <j2 rule="rewrite" parents="9222 9386 40 9222 9386 9222"/>
    </justification>
  </clause>

  <clause id="9477">
    <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(9156),rewrite([9222(2),9222(5)])].">
      <j1 rule="back_rewrite" parents="9156"/>
      <j2 rule="rewrite" parents="9222 9222"/>
    </justification>
  </clause>

  <clause id="9495">
    <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([9222(2),9222(4)])].">
      <j1 rule="back_rewrite" parents="8479"/>
      <j2 rule="rewrite" parents="9222 9222"/>
    </justification>
  </clause>

  <clause id="9615">
    <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([9222(4),9222(7),9477(11),32(3),9222(5)]),flip(a)].">
      <j1 rule="back_rewrite" parents="5408"/>
      <j2 rule="rewrite" parents="9222 9222 9477 32 9222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9700">
    <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([9222(5)])].">
      <j1 rule="back_rewrite" parents="3145"/>
      <j2 rule="rewrite" parents="9222"/>
    </justification>
  </clause>

  <clause id="9721">
    <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([9222(5)])].">
      <j1 rule="back_rewrite" parents="2610"/>
      <j2 rule="rewrite" parents="9222"/>
    </justification>
  </clause>

  <clause id="9725">
    <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([9222(11),9615(16),9222(8)])].">
      <j1 rule="back_rewrite" parents="1279"/>
      <j2 rule="rewrite" parents="9222 9615 9222"/>
    </justification>
  </clause>

  <clause id="9813">
    <literal><![CDATA[
      f(f(c_0,x),f(x,y)) = x
    ]]></literal>
    <justification jstring="[back_rewrite(9217),rewrite([9222(2)])].">
      <j1 rule="back_rewrite" parents="9217"/>
      <j2 rule="rewrite" parents="9222"/>
    </justification>
  </clause>

  <clause id="9827">
    <literal><![CDATA[
      f(f(c_0,x),c_0) = x
    ]]></literal>
    <justification jstring="[back_rewrite(9193),rewrite([9222(2),9222(4)])].">
      <j1 rule="back_rewrite" parents="9193"/>
      <j2 rule="rewrite" parents="9222 9222"/>
    </justification>
  </clause>

  <clause id="9830">
    <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(9188),rewrite([9222(9)])].">
      <j1 rule="back_rewrite" parents="9188"/>
      <j2 rule="rewrite" parents="9222"/>
    </justification>
  </clause>

  <clause id="9839">
    <literal><![CDATA[
      f(c_0,x) = f(x,x)
    ]]></literal>
    <justification jstring="[back_rewrite(9172),rewrite([9222(4),9222(5),9222(8),9827(8),9410(5),9222(3)]),flip(a)].">
      <j1 rule="back_rewrite" parents="9172"/>
      <j2 rule="rewrite" parents="9222 9222 9222 9827 9410 9222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9849">
    <literal><![CDATA[
      f(c_0,f(x,x)) = x
    ]]></literal>
    <justification jstring="[back_rewrite(9145),rewrite([9222(2),9222(5),9839(5),9222(5),9839(5),2546(5),9222(5),9839(5),753(14),32(4)])].">
      <j1 rule="back_rewrite" parents="9145"/>
      <j2 rule="rewrite" parents="9222 9222 9839 9222 9839 2546 9222 9839 753 32"/>
    </justification>
  </clause>

  <clause id="9870">
    <literal><![CDATA[
      f(x,f(c_0,c_0)) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(9102),rewrite([9222(2),9222(3),9222(4),604(6),9222(6)])].">
      <j1 rule="back_rewrite" parents="9102"/>
      <j2 rule="rewrite" parents="9222 9222 9222 604 9222"/>
    </justification>
  </clause>

  <clause id="9888">
    <literal><![CDATA[
      f(c_0,f(f(f(c_0,f(x,y)),f(x,y)),y)) = y
    ]]></literal>
    <justification jstring="[back_rewrite(9067),rewrite([9222(2),9222(3),9839(3),9222(3)])].">
      <j1 rule="back_rewrite" parents="9067"/>
      <j2 rule="rewrite" parents="9222 9222 9839 9222"/>
    </justification>
  </clause>

  <clause id="9895">
    <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(9044),rewrite([9222(9)])].">
      <j1 rule="back_rewrite" parents="9044"/>
      <j2 rule="rewrite" parents="9222"/>
    </justification>
  </clause>

  <clause id="9897">
    <literal><![CDATA[
      f(f(f(f(x,y),y),c_0),x) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(9029),rewrite([9222(4),9222(7)])].">
      <j1 rule="back_rewrite" parents="9029"/>
      <j2 rule="rewrite" parents="9222 9222"/>
    </justification>
  </clause>

  <clause id="9898">
    <literal><![CDATA[
      f(f(c_0,c_0),x) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(9028),rewrite([9222(2),9222(3),9222(6)])].">
      <j1 rule="back_rewrite" parents="9028"/>
      <j2 rule="rewrite" parents="9222 9222 9222"/>
    </justification>
  </clause>

  <clause id="9899">
    <literal><![CDATA[
      f(x,c_0) = f(x,x)
    ]]></literal>
    <justification jstring="[back_rewrite(9024),rewrite([9222(2)])].">
      <j1 rule="back_rewrite" parents="9024"/>
      <j2 rule="rewrite" parents="9222"/>
    </justification>
  </clause>

  <clause id="9900">
    <literal><![CDATA[
      f(f(x,x),c_0) = x
    ]]></literal>
    <justification jstring="[back_rewrite(9022),rewrite([9222(3)])].">
      <j1 rule="back_rewrite" parents="9022"/>
      <j2 rule="rewrite" parents="9222"/>
    </justification>
  </clause>

  <clause id="9963">
    <literal><![CDATA[
      f(x,f(f(f(x,y),y),c_0)) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(8457),rewrite([9222(4),9222(7)])].">
      <j1 rule="back_rewrite" parents="8457"/>
      <j2 rule="rewrite" parents="9222 9222"/>
    </justification>
  </clause>

  <clause id="10021">
    <literal><![CDATA[
      f(f(f(x,f(y,y)),c_0),y) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(7772),rewrite([9222(4),9222(7)])].">
      <j1 rule="back_rewrite" parents="7772"/>
      <j2 rule="rewrite" parents="9222 9222"/>
    </justification>
  </clause>

  <clause id="10027">
    <literal><![CDATA[
      f(f(x,x),f(f(y,x),c_0)) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(7763),rewrite([9222(4),9222(7)])].">
      <j1 rule="back_rewrite" parents="7763"/>
      <j2 rule="rewrite" parents="9222 9222"/>
    </justification>
  </clause>

  <clause id="10032">
    <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([9839(6,R),9222(7)])].">
      <j1 rule="back_rewrite" parents="7758"/>
      <j2 rule="rewrite" parents="9839 9222"/>
    </justification>
  </clause>

  <clause id="10723">
    <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([9839(3,R),9839(7,R),9839(14,R)])].">
      <j1 rule="back_rewrite" parents="2834"/>
      <j2 rule="rewrite" parents="9839 9839 9839"/>
    </justification>
  </clause>

  <clause id="10786">
    <literal><![CDATA[
      f(f(x,x),f(c_0,f(x,y))) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(2631),rewrite([9222(3),9222(7)])].">
      <j1 rule="back_rewrite" parents="2631"/>
      <j2 rule="rewrite" parents="9222 9222"/>
    </justification>
  </clause>

  <clause id="10787">
    <literal><![CDATA[
      f(f(x,x),f(c_0,f(y,x))) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(2629),rewrite([9222(3),9222(7)])].">
      <j1 rule="back_rewrite" parents="2629"/>
      <j2 rule="rewrite" parents="9222 9222"/>
    </justification>
  </clause>

  <clause id="10791">
    <literal><![CDATA[
      f(x,f(c_0,f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(2617),rewrite([9222(2)])].">
      <j1 rule="back_rewrite" parents="2617"/>
      <j2 rule="rewrite" parents="9222"/>
    </justification>
  </clause>

  <clause id="10793">
    <literal><![CDATA[
      f(x,f(c_0,f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(2615),rewrite([9222(2)])].">
      <j1 rule="back_rewrite" parents="2615"/>
      <j2 rule="rewrite" parents="9222"/>
    </justification>
  </clause>

  <clause id="10812">
    <literal><![CDATA[
      f(x,f(c_0,f(y,f(x,x)))) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(2026),rewrite([9222(2),9222(7)])].">
      <j1 rule="back_rewrite" parents="2026"/>
      <j2 rule="rewrite" parents="9222 9222"/>
    </justification>
  </clause>

  <clause id="10813">
    <literal><![CDATA[
      f(x,f(c_0,f(f(x,x),y))) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(1832),rewrite([9222(2),9222(7)])].">
      <j1 rule="back_rewrite" parents="1832"/>
      <j2 rule="rewrite" parents="9222 9222"/>
    </justification>
  </clause>

  <clause id="10891">
    <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(9721),rewrite([9839(2),543(3),543(3),9839(3,R)])].">
      <j1 rule="back_rewrite" parents="9721"/>
      <j2 rule="rewrite" parents="9839 543 543 9839"/>
    </justification>
  </clause>

  <clause id="10898">
    <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(9700),rewrite([9839(2),543(3),544(3),9839(3,R)])].">
      <j1 rule="back_rewrite" parents="9700"/>
      <j2 rule="rewrite" parents="9839 543 544 9839"/>
    </justification>
  </clause>

  <clause id="10913">
    <literal><![CDATA[
      f(c_0,f(c_0,f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(9495),rewrite([9813(8),9839(4,R)])].">
      <j1 rule="back_rewrite" parents="9495"/>
      <j2 rule="rewrite" parents="9813 9839"/>
    </justification>
  </clause>

  <clause id="10934">
    <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([9839(9,R)])].">
      <j1 rule="back_rewrite" parents="8989"/>
      <j2 rule="rewrite" parents="9839"/>
    </justification>
  </clause>

  <clause id="10967">
    <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([9839(3,R)])].">
      <j1 rule="back_rewrite" parents="8755"/>
      <j2 rule="rewrite" parents="9839"/>
    </justification>
  </clause>

  <clause id="10968">
    <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([9839(3,R)])].">
      <j1 rule="back_rewrite" parents="8754"/>
      <j2 rule="rewrite" parents="9839"/>
    </justification>
  </clause>

  <clause id="10991">
    <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([9839(9,R),9839(13,R),9839(20,R)])].">
      <j1 rule="back_rewrite" parents="8653"/>
      <j2 rule="rewrite" parents="9839 9839 9839"/>
    </justification>
  </clause>

  <clause id="11105">
    <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([9839(5,R),9839(19,R)])].">
      <j1 rule="back_rewrite" parents="8223"/>
      <j2 rule="rewrite" parents="9839 9839"/>
    </justification>
  </clause>

  <clause id="11121">
    <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([9839(5,R),9839(17,R)])].">
      <j1 rule="back_rewrite" parents="8196"/>
      <j2 rule="rewrite" parents="9839 9839"/>
    </justification>
  </clause>

  <clause id="11153">
    <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([9839(5,R)])].">
      <j1 rule="back_rewrite" parents="8049"/>
      <j2 rule="rewrite" parents="9839"/>
    </justification>
  </clause>

  <clause id="11188">
    <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([9839(5,R)])].">
      <j1 rule="back_rewrite" parents="7881"/>
      <j2 rule="rewrite" parents="9839"/>
    </justification>
  </clause>

  <clause id="11959">
    <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([9839(19,R)])].">
      <j1 rule="back_rewrite" parents="1181"/>
      <j2 rule="rewrite" parents="9839"/>
    </justification>
  </clause>

  <clause id="11974">
    <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([9839(3,R),9839(14,R),10787(15)])].">
      <j1 rule="back_rewrite" parents="1156"/>
      <j2 rule="rewrite" parents="9839 9839 10787"/>
    </justification>
  </clause>

  <clause id="12040">
    <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([9839(5,R)])].">
      <j1 rule="back_rewrite" parents="846"/>
      <j2 rule="rewrite" parents="9839"/>
    </justification>
  </clause>

  <clause id="12075">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),x) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(662),rewrite([9839(3,R)])].">
      <j1 rule="back_rewrite" parents="662"/>
      <j2 rule="rewrite" parents="9839"/>
    </justification>
  </clause>

  <clause id="12078">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),y) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(657),rewrite([9839(3,R)])].">
      <j1 rule="back_rewrite" parents="657"/>
      <j2 rule="rewrite" parents="9839"/>
    </justification>
  </clause>

  <clause id="12170">
    <literal><![CDATA[
      f(f(x,f(y,z)),f(c_0,f(y,z))) = f(y,z)
    ]]></literal>
    <justification jstring="[back_rewrite(9725),rewrite([12075(7),9839(5,R)])].">
      <j1 rule="back_rewrite" parents="9725"/>
      <j2 rule="rewrite" parents="12075 9839"/>
    </justification>
  </clause>

  <clause id="12275">
    <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),9830(a,1,1)),rewrite([9839(3,R),2(15)])].">
      <j1 rule="para" parents="2 9830"/>
      <j2 rule="rewrite" parents="9839 2"/>
    </justification>
  </clause>

  <clause id="12534">
    <literal><![CDATA[
      f(f(x,y),f(f(y,f(f(f(y,y),z),f(f(f(f(f(y,x),z),z),y),c_0))),y)) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(9895(a,1),2257(a,1,2,1,1)),rewrite([9895(22),9895(24)])].">
      <j1 rule="para" parents="9895 2257"/>
      <j2 rule="rewrite" parents="9895 9895"/>
    </justification>
  </clause>

  <clause id="12594">
    <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),9895(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="7716 9895"/>
    </justification>
  </clause>

  <clause id="12638">
    <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),10891(a,1,2,1))].">
      <j1 rule="para" parents="2257 10891"/>
    </justification>
  </clause>

  <clause id="12669">
    <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(9222(a,1),753(a,1,2,2,2))].">
      <j1 rule="para" parents="9222 753"/>
    </justification>
  </clause>

  <clause id="12685">
    <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(9839(a,2),66(a,1,2,2))].">
      <j1 rule="para" parents="9839 66"/>
    </justification>
  </clause>

  <clause id="12716">
    <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(9839(a,2),1005(a,1,2,2))].">
      <j1 rule="para" parents="9839 1005"/>
    </justification>
  </clause>

  <clause id="12718">
    <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(9839(a,2),1008(a,1,2,2))].">
      <j1 rule="para" parents="9839 1008"/>
    </justification>
  </clause>

  <clause id="12742">
    <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([9839(16,R)])].">
      <j1 rule="para" parents="604 294"/>
      <j2 rule="rewrite" parents="9839"/>
    </justification>
  </clause>

  <clause id="12799">
    <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),12685(a,1,2,2,2,1,1,1)),rewrite([543(3),9839(3,R)])].">
      <j1 rule="para" parents="40 12685"/>
      <j2 rule="rewrite" parents="543 9839"/>
    </justification>
  </clause>

  <clause id="12805">
    <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),12685(a,1,2,2,2,1,1,1))].">
      <j1 rule="para" parents="764 12685"/>
    </justification>
  </clause>

  <clause id="12884">
    <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),12685(a,1,2,2,2,1,1,1))].">
      <j1 rule="para" parents="2482 12685"/>
    </justification>
  </clause>

  <clause id="12886">
    <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),12685(a,1,2,2,2,1,1,1))].">
      <j1 rule="para" parents="2648 12685"/>
    </justification>
  </clause>

  <clause id="12950">
    <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(12716(a,1),11(a,1,1)),rewrite([9839(19,R)])].">
      <j1 rule="para" parents="12716 11"/>
      <j2 rule="rewrite" parents="9839"/>
    </justification>
  </clause>

  <clause id="12967">
    <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),12716(a,1,2,2,2,1,1))].">
      <j1 rule="para" parents="2257 12716"/>
    </justification>
  </clause>

  <clause id="12998">
    <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(12716(a,1),7848(a,1,1)),rewrite([12716(11)])].">
      <j1 rule="para" parents="12716 7848"/>
      <j2 rule="rewrite" parents="12716"/>
    </justification>
  </clause>

  <clause id="13014">
    <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),12718(a,1,2,1,1))].">
      <j1 rule="para" parents="11 12718"/>
    </justification>
  </clause>

  <clause id="13036">
    <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),12718(a,1,2,2,2,1,1))].">
      <j1 rule="para" parents="2257 12718"/>
    </justification>
  </clause>

  <clause id="13089">
    <literal><![CDATA[
      f(f(f(c_0,f(x,y)),f(x,y)),y) = f(y,y)
    ]]></literal>
    <justification jstring="[para(1369(a,1),10898(a,1,2,2,1)),rewrite([9222(3),9888(8),9839(3,R),9849(3),9222(3)]),flip(a)].">
      <j1 rule="para" parents="1369 10898"/>
      <j2 rule="rewrite" parents="9222 9888 9839 9849 9222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13416">
    <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),12275(a,1,2,2,1)),rewrite([9839(6,R),9839(13,R),9839(21,R)])].">
      <j1 rule="para" parents="604 12275"/>
      <j2 rule="rewrite" parents="9839 9839 9839"/>
    </justification>
  </clause>

  <clause id="13743">
    <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(12799(a,1),1388(a,1,2,1,2,2,1,1,2,2,1,1,1,1)),rewrite([12799(30),12799(35)])].">
      <j1 rule="para" parents="12799 1388"/>
      <j2 rule="rewrite" parents="12799 12799"/>
    </justification>
  </clause>

  <clause id="13881">
    <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(9897(a,1),679(a,1,2,2,1,1,1)),rewrite([9898(8),9839(7),9900(8),9839(7)])].">
      <j1 rule="para" parents="9897 679"/>
      <j2 rule="rewrite" parents="9898 9839 9900 9839"/>
    </justification>
  </clause>

  <clause id="13926">
    <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(12685(a,1),9897(a,1,1,1,1))].">
      <j1 rule="para" parents="12685 9897"/>
    </justification>
  </clause>

  <clause id="13927">
    <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(12716(a,1),9897(a,1,1,1,1))].">
      <j1 rule="para" parents="12716 9897"/>
    </justification>
  </clause>

  <clause id="13932">
    <literal><![CDATA[
      f(f(c_0,f(f(x,y),y)),x) = c_0
    ]]></literal>
    <justification jstring="[para(9899(a,1),9897(a,1,1)),rewrite([9839(5,R)])].">
      <j1 rule="para" parents="9899 9897"/>
      <j2 rule="rewrite" parents="9839"/>
    </justification>
  </clause>

  <clause id="13955">
    <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(13416),rewrite([13932(6),9898(4),13932(14)])].">
      <j1 rule="back_rewrite" parents="13416"/>
      <j2 rule="rewrite" parents="13932 9898 13932"/>
    </justification>
  </clause>

  <clause id="14141">
    <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(9963(a,1),9895(a,1,2,2,1,1,1))].">
      <j1 rule="para" parents="9963 9895"/>
    </justification>
  </clause>

  <clause id="14143">
    <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(9963(a,1),10891(a,1,2,2,1,1,1))].">
      <j1 rule="para" parents="9963 10891"/>
    </justification>
  </clause>

  <clause id="14150">
    <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(12685(a,1),9963(a,1,2,1,1))].">
      <j1 rule="para" parents="12685 9963"/>
    </justification>
  </clause>

  <clause id="14156">
    <literal><![CDATA[
      f(f(x,y),f(f(x,f(f(f(x,x),z),f(c_0,f(f(f(f(x,y),z),z),x)))),c_0)) = c_0
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(12718(a,1),9963(a,1,2,1,1))].">
      <j1 rule="para" parents="12718 9963"/>
    </justification>
  </clause>

  <clause id="14706">
    <literal><![CDATA[
      f(f(x,y),f(f(y,f(f(f(y,y),f(f(x,f(f(f(f(y,x),f(z,x)),f(z,x)),x)),x)),f(f(f(x,f(f(x,f(f(f(f(y,x),f(z,x)),f(z,x)),x)),x)),y),c_0))),y)) = y
    ]]></literal>
    <justification jstring="[para(1897(a,1),12534(a,1,2,1,2,2,1,1,1))].">
      <j1 rule="para" parents="1897 12534"/>
    </justification>
  </clause>

  <clause id="14797">
    <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),12594(a,1,2,2,1,1,1))].">
      <j1 rule="para" parents="2257 12594"/>
    </justification>
  </clause>

  <clause id="14994">
    <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(10021(a,1),679(a,1,2,2,1,1,1)),rewrite([9898(8),9839(7),9900(8),9839(7)])].">
      <j1 rule="para" parents="10021 679"/>
      <j2 rule="rewrite" parents="9898 9839 9900 9839"/>
    </justification>
  </clause>

  <clause id="15042">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),f(x,x)) = c_0
    ]]></literal>
    <justification jstring="[para(543(a,1),10027(a,1,2,1)),rewrite([9839(3,R),9899(5)])].">
      <j1 rule="para" parents="543 10027"/>
      <j2 rule="rewrite" parents="9839 9899"/>
    </justification>
  </clause>

  <clause id="15043">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),f(y,y)) = c_0
    ]]></literal>
    <justification jstring="[para(544(a,1),10027(a,1,2,1)),rewrite([9839(3,R),9899(5)])].">
      <j1 rule="para" parents="544 10027"/>
      <j2 rule="rewrite" parents="9839 9899"/>
    </justification>
  </clause>

  <clause id="15147">
    <literal><![CDATA[
      f(f(x,y),x) = f(x,f(x,y))
    ]]></literal>
    <justification jstring="[back_rewrite(11188),rewrite([15042(6),10793(5)])].">
      <j1 rule="back_rewrite" parents="11188"/>
      <j2 rule="rewrite" parents="15042 10793"/>
    </justification>
  </clause>

  <clause id="15148">
    <literal><![CDATA[
      f(f(x,y),y) = f(y,f(x,y))
    ]]></literal>
    <justification jstring="[back_rewrite(11153),rewrite([15042(6),10793(5)])].">
      <j1 rule="back_rewrite" parents="11153"/>
      <j2 rule="rewrite" parents="15042 10793"/>
    </justification>
  </clause>

  <clause id="15153">
    <literal><![CDATA[
      f(f(x,y),f(x,f(x,y))) = x
    ]]></literal>
    <justification jstring="[back_rewrite(10967),rewrite([15042(5),15147(4),7716(4),12075(4),15147(3),7716(4),15147(3)])].">
      <j1 rule="back_rewrite" parents="10967"/>
      <j2 rule="rewrite" parents="15042 15147 7716 12075 15147 7716 15147"/>
    </justification>
  </clause>

  <clause id="15155">
    <literal><![CDATA[
      f(x,f(c_0,f(f(x,f(x,y)),y))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(10934),rewrite([15147(2),7716(3),15147(2),15148(4),15153(4),15042(5)])].">
      <j1 rule="back_rewrite" parents="10934"/>
      <j2 rule="rewrite" parents="15147 7716 15147 15148 15153 15042"/>
    </justification>
  </clause>

  <clause id="15163">
    <literal><![CDATA[
      f(f(x,y),f(c_0,f(f(y,f(x,y)),f(y,z)))) = y
    ]]></literal>
    <justification jstring="[back_rewrite(11974),rewrite([15043(5),15147(4),7717(4),12078(4),15148(4)])].">
      <j1 rule="back_rewrite" parents="11974"/>
      <j2 rule="rewrite" parents="15043 15147 7717 12078 15148"/>
    </justification>
  </clause>

  <clause id="15203">
    <literal><![CDATA[
      f(f(x,y),f(y,f(x,y))) = y
    ]]></literal>
    <justification jstring="[back_rewrite(10968),rewrite([15043(5),15147(4),7717(4),12078(4),15148(3),7717(4),15148(3)])].">
      <j1 rule="back_rewrite" parents="10968"/>
      <j2 rule="rewrite" parents="15043 15147 7717 12078 15148 7717 15148"/>
    </justification>
  </clause>

  <clause id="15293">
    <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(14797),rewrite([15147(3),7716(3),15148(5),15148(8),15203(8),15148(8),15148(11),15203(11),15148(6)])].">
      <j1 rule="back_rewrite" parents="14797"/>
      <j2 rule="rewrite" parents="15147 7716 15148 15148 15203 15148 15148 15203 15148"/>
    </justification>
  </clause>

  <clause id="15354">
    <literal><![CDATA[
      f(f(x,y),f(y,f(y,f(f(f(y,y),f(f(f(z,x),f(f(y,x),f(z,x))),x)),f(f(f(x,f(f(f(z,x),f(f(y,x),f(z,x))),x)),y),c_0))))) = y
    ]]></literal>
    <justification jstring="[back_rewrite(14706),rewrite([15148(7),15147(10),7717(10),15148(14),15147(17),7717(17),15147(22)])].">
      <j1 rule="back_rewrite" parents="14706"/>
      <j2 rule="rewrite" parents="15148 15147 7717 15148 15147 7717 15147"/>
    </justification>
  </clause>

  <clause id="15610">
    <literal><![CDATA[
      f(x,f(c_0,f(y,f(x,y)))) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(13955),rewrite([15148(4),15147(7),10913(7)])].">
      <j1 rule="back_rewrite" parents="13955"/>
      <j2 rule="rewrite" parents="15148 15147 10913"/>
    </justification>
  </clause>

  <clause id="15649">
    <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(13743),rewrite([15148(7),15148(17),15147(23),15147(28),7716(28)])].">
      <j1 rule="back_rewrite" parents="13743"/>
      <j2 rule="rewrite" parents="15148 15148 15147 15147 7716"/>
    </justification>
  </clause>

  <clause id="15747">
    <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(13036),rewrite([15148(5),15148(8),15203(8),15148(9),15148(12),15203(12),15148(7)])].">
      <j1 rule="back_rewrite" parents="13036"/>
      <j2 rule="rewrite" parents="15148 15148 15203 15148 15148 15203 15148"/>
    </justification>
  </clause>

  <clause id="15765">
    <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(12967),rewrite([15148(5),15148(8),15203(8),15148(9),15148(12),15203(12),15148(7)])].">
      <j1 rule="back_rewrite" parents="12967"/>
      <j2 rule="rewrite" parents="15148 15148 15203 15148 15148 15203 15148"/>
    </justification>
  </clause>

  <clause id="15774">
    <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(12886),rewrite([15148(3),15147(8),7717(8),15148(11)])].">
      <j1 rule="back_rewrite" parents="12886"/>
      <j2 rule="rewrite" parents="15148 15147 7717 15148"/>
    </justification>
  </clause>

  <clause id="15776">
    <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(12884),rewrite([15148(3),15148(5),15203(5),15148(2),15148(4),15203(4),15148(7)])].">
      <j1 rule="back_rewrite" parents="12884"/>
      <j2 rule="rewrite" parents="15148 15148 15203 15148 15148 15203 15148"/>
    </justification>
  </clause>

  <clause id="15796">
    <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(12805),rewrite([15148(3),15148(5),15203(5),15148(10)])].">
      <j1 rule="back_rewrite" parents="12805"/>
      <j2 rule="rewrite" parents="15148 15148 15203 15148"/>
    </justification>
  </clause>

  <clause id="15820">
    <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(12638),rewrite([15148(9),15148(14),15203(14),15148(10),15148(15),15203(15),15148(6)])].">
      <j1 rule="back_rewrite" parents="12638"/>
      <j2 rule="rewrite" parents="15148 15148 15203 15148 15148 15203 15148"/>
    </justification>
  </clause>

  <clause id="15912">
    <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(12040),rewrite([15148(8),15147(15),15148(23)])].">
      <j1 rule="back_rewrite" parents="12040"/>
      <j2 rule="rewrite" parents="15148 15147 15148"/>
    </justification>
  </clause>

  <clause id="15940">
    <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(11959),rewrite([15148(5),15147(11),15148(22)])].">
      <j1 rule="back_rewrite" parents="11959"/>
      <j2 rule="rewrite" parents="15148 15147 15148"/>
    </justification>
  </clause>

  <clause id="16219">
    <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(10991),rewrite([15148(3),7717(4),15148(3),7717(4)])].">
      <j1 rule="back_rewrite" parents="10991"/>
      <j2 rule="rewrite" parents="15148 7717 15148 7717"/>
    </justification>
  </clause>

  <clause id="16414">
    <literal><![CDATA[
      f(x,f(f(y,f(x,y)),f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(8676),rewrite([15148(2),7717(3),15148(2),15148(4),15203(4),15148(2)])].">
      <j1 rule="back_rewrite" parents="8676"/>
      <j2 rule="rewrite" parents="15148 7717 15148 15148 15203 15148"/>
    </justification>
  </clause>

  <clause id="17035">
    <literal><![CDATA[
      f(f(x,y),f(f(x,f(f(f(x,x),z),f(c_0,f(f(z,f(f(x,y),z)),x)))),c_0)) = c_0
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(14156),rewrite([15148(7)])].">
      <j1 rule="back_rewrite" parents="14156"/>
      <j2 rule="rewrite" parents="15148"/>
    </justification>
  </clause>

  <clause id="17041">
    <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(14150),rewrite([15148(7)])].">
      <j1 rule="back_rewrite" parents="14150"/>
      <j2 rule="rewrite" parents="15148"/>
    </justification>
  </clause>

  <clause id="17048">
    <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(14143),rewrite([15148(5),15148(11)])].">
      <j1 rule="back_rewrite" parents="14143"/>
      <j2 rule="rewrite" parents="15148 15148"/>
    </justification>
  </clause>

  <clause id="17049">
    <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(14141),rewrite([15148(5),15148(12)])].">
      <j1 rule="back_rewrite" parents="14141"/>
      <j2 rule="rewrite" parents="15148 15148"/>
    </justification>
  </clause>

  <clause id="17126">
    <literal><![CDATA[
      f(f(c_0,f(x,f(y,x))),y) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(13932),rewrite([15148(3)])].">
      <j1 rule="back_rewrite" parents="13932"/>
      <j2 rule="rewrite" parents="15148"/>
    </justification>
  </clause>

  <clause id="17130">
    <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(13927),rewrite([15148(6)])].">
      <j1 rule="back_rewrite" parents="13927"/>
      <j2 rule="rewrite" parents="15148"/>
    </justification>
  </clause>

  <clause id="17131">
    <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(13926),rewrite([15148(6)])].">
      <j1 rule="back_rewrite" parents="13926"/>
      <j2 rule="rewrite" parents="15148"/>
    </justification>
  </clause>

  <clause id="17147">
    <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(13881),rewrite([15148(2)])].">
      <j1 rule="back_rewrite" parents="13881"/>
      <j2 rule="rewrite" parents="15148"/>
    </justification>
  </clause>

  <clause id="17406">
    <literal><![CDATA[
      f(f(f(x,y),f(c_0,f(x,y))),y) = f(y,y)
    ]]></literal>
    <justification jstring="[back_rewrite(13089),rewrite([15148(5)])].">
      <j1 rule="back_rewrite" parents="13089"/>
      <j2 rule="rewrite" parents="15148"/>
    </justification>
  </clause>

  <clause id="17439">
    <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(13014),rewrite([15148(8)])].">
      <j1 rule="back_rewrite" parents="13014"/>
      <j2 rule="rewrite" parents="15148"/>
    </justification>
  </clause>

  <clause id="17447">
    <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(12998),rewrite([15148(6),15148(17)])].">
      <j1 rule="back_rewrite" parents="12998"/>
      <j2 rule="rewrite" parents="15148 15148"/>
    </justification>
  </clause>

  <clause id="17476">
    <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(12950),rewrite([15148(7),15148(18)])].">
      <j1 rule="back_rewrite" parents="12950"/>
      <j2 rule="rewrite" parents="15148 15148"/>
    </justification>
  </clause>

  <clause id="17578">
    <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(12742),rewrite([15148(8)])].">
      <j1 rule="back_rewrite" parents="12742"/>
      <j2 rule="rewrite" parents="15148"/>
    </justification>
  </clause>

  <clause id="17601">
    <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(12669),rewrite([15148(6)])].">
      <j1 rule="back_rewrite" parents="12669"/>
      <j2 rule="rewrite" parents="15148"/>
    </justification>
  </clause>

  <clause id="17992">
    <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(11121),rewrite([15148(8),15148(20)])].">
      <j1 rule="back_rewrite" parents="11121"/>
      <j2 rule="rewrite" parents="15148 15148"/>
    </justification>
  </clause>

  <clause id="17995">
    <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(11105),rewrite([15148(10),15148(24)])].">
      <j1 rule="back_rewrite" parents="11105"/>
      <j2 rule="rewrite" parents="15148 15148"/>
    </justification>
  </clause>

  <clause id="18133">
    <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([15148(5),15148(16)])].">
      <j1 rule="back_rewrite" parents="8184"/>
      <j2 rule="rewrite" parents="15148 15148"/>
    </justification>
  </clause>

  <clause id="18540">
    <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([15148(5),15148(14)])].">
      <j1 rule="back_rewrite" parents="783"/>
      <j2 rule="rewrite" parents="15148 15148"/>
    </justification>
  </clause>

  <clause id="18578">
    <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([15153(5),9222(3)])].">
      <j1 rule="back_rewrite" parents="7880"/>
      <j2 rule="rewrite" parents="15153 9222"/>
    </justification>
  </clause>

  <clause id="18622">
    <literal><![CDATA[
      f(f(x,y),f(c_0,f(x,y))) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(10723),rewrite([17406(9),15043(5)]),flip(a)].">
      <j1 rule="back_rewrite" parents="10723"/>
      <j2 rule="rewrite" parents="17406 15043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18689">
    <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(15912),rewrite([17992(15)])].">
      <j1 rule="back_rewrite" parents="15912"/>
      <j2 rule="rewrite" parents="17992"/>
    </justification>
  </clause>

  <clause id="18829">
    <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(15940),rewrite([18133(11)])].">
      <j1 rule="back_rewrite" parents="15940"/>
      <j2 rule="rewrite" parents="18133"/>
    </justification>
  </clause>

  <clause id="18833">
    <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(15649),rewrite([18133(23)])].">
      <j1 rule="back_rewrite" parents="15649"/>
      <j2 rule="rewrite" parents="18133"/>
    </justification>
  </clause>

  <clause id="18865">
    <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(16219),rewrite([18622(6)])].">
      <j1 rule="back_rewrite" parents="16219"/>
      <j2 rule="rewrite" parents="18622"/>
    </justification>
  </clause>

  <clause id="18902">
    <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(15293(a,1),15776(a,1,2,2,2,1,2)),rewrite([17601(12),15148(13),10791(15)])].">
      <j1 rule="para" parents="15293 15776"/>
      <j2 rule="rewrite" parents="17601 15148 10791"/>
    </justification>
  </clause>

  <clause id="18910">
    <literal><![CDATA[
      f(f(x,y),c_0) = f(c_0,f(x,y))
    ]]></literal>
    <justification jstring="[para(10786(a,1),544(a,1,2)),rewrite([9839(7,R),10913(5)])].">
      <j1 rule="para" parents="10786 544"/>
      <j2 rule="rewrite" parents="9839 10913"/>
    </justification>
  </clause>

  <clause id="18914">
    <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(18902),rewrite([18910(9)])].">
      <j1 rule="back_rewrite" parents="18902"/>
      <j2 rule="rewrite" parents="18910"/>
    </justification>
  </clause>

  <clause id="18995">
    <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(17147),rewrite([18910(4)])].">
      <j1 rule="back_rewrite" parents="17147"/>
      <j2 rule="rewrite" parents="18910"/>
    </justification>
  </clause>

  <clause id="19010">
    <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(17131),rewrite([18910(12)])].">
      <j1 rule="back_rewrite" parents="17131"/>
      <j2 rule="rewrite" parents="18910"/>
    </justification>
  </clause>

  <clause id="19011">
    <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(17130),rewrite([18910(12)])].">
      <j1 rule="back_rewrite" parents="17130"/>
      <j2 rule="rewrite" parents="18910"/>
    </justification>
  </clause>

  <clause id="19075">
    <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(17049),rewrite([18910(7),18910(14),10913(15),18910(14)])].">
      <j1 rule="back_rewrite" parents="17049"/>
      <j2 rule="rewrite" parents="18910 18910 10913 18910"/>
    </justification>
  </clause>

  <clause id="19076">
    <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(17048),rewrite([18910(7),18910(13),10913(14)])].">
      <j1 rule="back_rewrite" parents="17048"/>
      <j2 rule="rewrite" parents="18910 18910 10913"/>
    </justification>
  </clause>

  <clause id="19081">
    <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(17041),rewrite([18910(13)])].">
      <j1 rule="back_rewrite" parents="17041"/>
      <j2 rule="rewrite" parents="18910"/>
    </justification>
  </clause>

  <clause id="19085">
    <literal><![CDATA[
      f(f(x,y),f(c_0,f(x,f(f(f(x,x),z),f(c_0,f(f(z,f(f(x,y),z)),x)))))) = c_0
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(17035),rewrite([18910(13)])].">
      <j1 rule="back_rewrite" parents="17035"/>
      <j2 rule="rewrite" parents="18910"/>
    </justification>
  </clause>

  <clause id="19278">
    <literal><![CDATA[
      f(f(x,y),f(y,f(y,f(f(f(y,y),f(f(f(z,x),f(f(y,x),f(z,x))),x)),f(c_0,f(f(x,f(f(f(z,x),f(f(y,x),f(z,x))),x)),y)))))) = y
    ]]></literal>
    <justification jstring="[back_rewrite(15354),rewrite([18910(19)])].">
      <j1 rule="back_rewrite" parents="15354"/>
      <j2 rule="rewrite" parents="18910"/>
    </justification>
  </clause>

  <clause id="19321">
    <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(14994),rewrite([18910(4)])].">
      <j1 rule="back_rewrite" parents="14994"/>
      <j2 rule="rewrite" parents="18910"/>
    </justification>
  </clause>

  <clause id="19449">
    <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(10813(a,1),18914(a,1,2,2,1,2,2,1,2)),rewrite([9839(6,R),9839(14,R),15147(18),10913(18)])].">
      <j1 rule="para" parents="10813 18914"/>
      <j2 rule="rewrite" parents="9839 9839 15147 10913"/>
    </justification>
  </clause>

  <clause id="19513">
    <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(19011(a,1),15820(a,1,2,1)),rewrite([15203(5),17447(12),10793(13)])].">
      <j1 rule="para" parents="19011 15820"/>
      <j2 rule="rewrite" parents="15203 17447 10793"/>
    </justification>
  </clause>

  <clause id="19528">
    <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(15765(a,1),12078(a,1,1,2)),rewrite([9839(2),15765(22)])].">
      <j1 rule="para" parents="15765 12078"/>
      <j2 rule="rewrite" parents="9839 15765"/>
    </justification>
  </clause>

  <clause id="19695">
    <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(17439(a,1),11(a,1,1)),rewrite([9839(22,R)])].">
      <j1 rule="para" parents="17439 11"/>
      <j2 rule="rewrite" parents="9839"/>
    </justification>
  </clause>

  <clause id="19820">
    <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(17439(a,1),15148(a,1,1)),rewrite([17439(35)]),flip(a)].">
      <j1 rule="para" parents="17439 15148"/>
      <j2 rule="rewrite" parents="17439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19883">
    <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(17439(a,1),15203(a,1,1)),rewrite([17439(24),19820(13)])].">
      <j1 rule="para" parents="17439 15203"/>
      <j2 rule="rewrite" parents="17439 19820"/>
    </justification>
  </clause>

  <clause id="20592">
    <literal><![CDATA[
      f(f(x,y),f(f(c_0,f(x,y)),z)) = f(c_0,f(x,y))
    ]]></literal>
    <justification jstring="[para(12170(a,1),543(a,1,1))].">
      <j1 rule="para" parents="12170 543"/>
    </justification>
  </clause>

  <clause id="20601">
    <literal><![CDATA[
      f(f(c_0,f(x,f(y,z))),f(c_0,f(y,z))) = c_0
    ]]></literal>
    <justification jstring="[para(12170(a,1),10786(a,1,2,2)),rewrite([9839(5,R)])].">
      <j1 rule="para" parents="12170 10786"/>
      <j2 rule="rewrite" parents="9839"/>
    </justification>
  </clause>

  <clause id="20605">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),f(c_0,f(z,f(x,y)))) = c_0
    ]]></literal>
    <justification jstring="[para(12170(a,1),10812(a,1,2,2,2))].">
      <j1 rule="para" parents="12170 10812"/>
    </justification>
  </clause>

  <clause id="20615">
    <literal><![CDATA[
      f(f(f(c_0,f(x,y)),z),f(c_0,f(f(c_0,f(x,y)),f(f(f(x,y),u),f(c_0,f(f(u,f(f(f(c_0,f(x,y)),z),u)),f(c_0,f(x,y)))))))) = c_0
    ]]></literal>
    <justification jstring="[para(12170(a,1),19085(a,1,2,2,2,1,1))].">
      <j1 rule="para" parents="12170 19085"/>
    </justification>
  </clause>

  <clause id="20661">
    <literal><![CDATA[
      f(f(f(x,f(x,y)),y),f(c_0,f(x,y))) = c_0
    ]]></literal>
    <justification jstring="[para(15155(a,1),10787(a,1,2,2)),rewrite([9839(11,R),10913(7)])].">
      <j1 rule="para" parents="15155 10787"/>
      <j2 rule="rewrite" parents="9839 10913"/>
    </justification>
  </clause>

  <clause id="20711">
    <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(15155(a,1),15148(a,1,1)),rewrite([15155(18)]),flip(a)].">
      <j1 rule="para" parents="15155 15148"/>
      <j2 rule="rewrite" parents="15155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20818">
    <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(16414(a,1),15155(a,1,2,2,1,2)),rewrite([16414(15)])].">
      <j1 rule="para" parents="16414 15155"/>
      <j2 rule="rewrite" parents="16414"/>
    </justification>
  </clause>

  <clause id="22535">
    <literal><![CDATA[
      f(f(f(x,f(x,y)),y),x) = f(x,f(x,y))
    ]]></literal>
    <justification jstring="[para(20661(a,1),15747(a,1,2,2,2,1,2)),rewrite([9839(8,R),20601(11),15147(10),10913(10),15153(9),9839(6),9849(6)])].">
      <j1 rule="para" parents="20661 15747"/>
      <j2 rule="rewrite" parents="9839 20601 15147 10913 15153 9839 9849"/>
    </justification>
  </clause>

  <clause id="22552">
    <literal><![CDATA[
      f(f(x,f(y,f(y,x))),f(c_0,f(y,x))) = c_0
    ]]></literal>
    <justification jstring="[para(20661(a,1),19081(a,1,2,2,2,2,2,1,2)),rewrite([9839(11,R),20601(14),15147(13),10913(13),15153(12),9839(9),9849(9),15147(7),7716(7)])].">
      <j1 rule="para" parents="20661 19081"/>
      <j2 rule="rewrite" parents="9839 20601 15147 10913 15153 9839 9849 15147 7716"/>
    </justification>
  </clause>

  <clause id="22984">
    <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(16414(a,1),22535(a,1,1,1,2)),rewrite([16414(13)])].">
      <j1 rule="para" parents="16414 22535"/>
      <j2 rule="rewrite" parents="16414"/>
    </justification>
  </clause>

  <clause id="23356">
    <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(17578(a,1),15774(a,1,2,2,2,1,2)),rewrite([9839(11,R),9849(11),18578(19),19820(22),15147(24),19883(24),19695(22)])].">
      <j1 rule="para" parents="17578 15774"/>
      <j2 rule="rewrite" parents="9839 9849 18578 19820 15147 19883 19695"/>
    </justification>
  </clause>

  <clause id="23410">
    <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(15774(a,1),15774(a,1,2,2,2,1,2)),rewrite([16414(9),15148(6),19528(24),19513(24),15147(25),17447(25),17476(25)])].">
      <j1 rule="para" parents="15774 15774"/>
      <j2 rule="rewrite" parents="16414 15148 19528 19513 15147 17447 17476"/>
    </justification>
  </clause>

  <clause id="23616">
    <literal><![CDATA[
      f(f(x,f(y,f(y,x))),f(x,f(y,x))) = x
    ]]></literal>
    <justification jstring="[para(22552(a,1),15747(a,1,2,2,2,1,2)),rewrite([10787(8),15147(10),10913(10),15148(7),10913(9)])].">
      <j1 rule="para" parents="22552 15747"/>
      <j2 rule="rewrite" parents="10787 15147 10913 15148 10913"/>
    </justification>
  </clause>

  <clause id="23907">
    <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(16414(a,1),23616(a,1,1,2,2)),rewrite([16414(16),15148(13)])].">
      <j1 rule="para" parents="16414 23616"/>
      <j2 rule="rewrite" parents="16414 15148"/>
    </justification>
  </clause>

  <clause id="24176">
    <literal><![CDATA[
      f(f(f(x,f(y,x)),f(x,z)),f(x,x)) = c_0
    ]]></literal>
    <justification jstring="[para(15163(a,1),10787(a,1,2,2)),rewrite([9839(13,R),10913(8),9839(6)])].">
      <j1 rule="para" parents="15163 10787"/>
      <j2 rule="rewrite" parents="9839 10913 9839"/>
    </justification>
  </clause>

  <clause id="24194">
    <literal><![CDATA[
      f(f(x,f(x,y)),f(c_0,f(f(x,y),f(x,z)))) = x
    ]]></literal>
    <justification jstring="[para(15147(a,1),15163(a,1,1)),rewrite([15147(5),7716(6)])].">
      <j1 rule="para" parents="15147 15163"/>
      <j2 rule="rewrite" parents="15147 7716"/>
    </justification>
  </clause>

  <clause id="24208">
    <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(15203(a,1),15163(a,1,2,2,1))].">
      <j1 rule="para" parents="15203 15163"/>
    </justification>
  </clause>

  <clause id="24326">
    <literal><![CDATA[
      f(f(f(x,y),f(x,z)),f(x,x)) = c_0
    ]]></literal>
    <justification jstring="[para(15147(a,1),24176(a,1,1,1,2)),rewrite([7716(3)])].">
      <j1 rule="para" parents="15147 24176"/>
      <j2 rule="rewrite" parents="7716"/>
    </justification>
  </clause>

  <clause id="24330">
    <literal><![CDATA[
      f(f(f(x,y),f(y,z)),f(y,y)) = c_0
    ]]></literal>
    <justification jstring="[para(15148(a,1),24176(a,1,1,1,2)),rewrite([7717(3)])].">
      <j1 rule="para" parents="15148 24176"/>
      <j2 rule="rewrite" parents="7717"/>
    </justification>
  </clause>

  <clause id="24366">
    <literal><![CDATA[
      f(f(x,x),f(f(x,y),f(x,z))) = c_0
    ]]></literal>
    <justification jstring="[para(24326(a,1),19010(a,1,1,2,2,2,2,1,2)),rewrite([9839(5,R),15042(7),18910(7),9849(7),10913(8),15153(5),9839(2)])].">
      <j1 rule="para" parents="24326 19010"/>
      <j2 rule="rewrite" parents="9839 15042 18910 9849 10913 15153 9839"/>
    </justification>
  </clause>

  <clause id="24374">
    <literal><![CDATA[
      f(f(f(f(f(x,y),f(x,z)),f(f(x,z),f(x,y))),f(x,y)),f(x,f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(24326(a,1),15796(a,1,2,2,2,1,2)),rewrite([9839(12,R),15042(14),18910(14),9849(14),10913(15)])].">
      <j1 rule="para" parents="24326 15796"/>
      <j2 rule="rewrite" parents="9839 15042 18910 9849 10913"/>
    </justification>
  </clause>

  <clause id="24464">
    <literal><![CDATA[
      f(f(f(x,f(y,y)),f(z,f(y,y))),y) = c_0
    ]]></literal>
    <justification jstring="[para(10032(a,1),24330(a,1,1,2)),rewrite([9839(8,R),9849(8)])].">
      <j1 rule="para" parents="10032 24330"/>
      <j2 rule="rewrite" parents="9839 9849"/>
    </justification>
  </clause>

  <clause id="24465">
    <literal><![CDATA[
      f(f(f(f(f(x,y),f(f(y,z),f(x,y))),f(f(x,y),f(y,z))),f(y,z)),f(y,f(y,z))) = f(y,z)
    ]]></literal>
    <justification jstring="[para(24330(a,1),15774(a,1,2,2,2,1,2)),rewrite([9839(14,R),15042(16),18910(16),9849(16),10913(17)])].">
      <j1 rule="para" parents="24330 15774"/>
      <j2 rule="rewrite" parents="9839 15042 18910 9849 10913"/>
    </justification>
  </clause>

  <clause id="24537">
    <literal><![CDATA[
      f(f(f(f(f(x,x),f(c_0,f(y,f(f(x,z),y)))),f(c_0,f(f(y,f(f(x,z),y)),x))),f(z,x)),f(f(f(c_0,f(z,x)),u),f(c_0,f(f(u,f(x,u)),f(z,x))))) = f(z,x)
    ]]></literal>
    <justification jstring="[para(19075(a,1),15776(a,1,2,2,2,1,2,1)),rewrite([9839(19,R)])].">
      <j1 rule="para" parents="19075 15776"/>
      <j2 rule="rewrite" parents="9839"/>
    </justification>
  </clause>

  <clause id="24566">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),f(c_0,f(f(f(y,x),z),f(c_0,f(f(f(y,x),f(f(y,x),z)),z))))),f(c_0,f(f(f(f(y,x),z),f(c_0,f(f(f(y,x),f(f(y,x),z)),z))),y)))) = y
    ]]></literal>
    <justification jstring="[para(15155(a,1),19075(a,1,2,1,2,2,2)),rewrite([20711(13),15155(32),20711(26)])].">
      <j1 rule="para" parents="15155 19075"/>
      <j2 rule="rewrite" parents="20711 15155 20711"/>
    </justification>
  </clause>

  <clause id="24613">
    <literal><![CDATA[
      f(x,y) = f(y,x)
    ]]></literal>
    <justification jstring="[para(15148(a,1),19076(a,1,2,2,1)),rewrite([20605(8),15203(5),10793(4)])].">
      <j1 rule="para" parents="15148 19076"/>
      <j2 rule="rewrite" parents="20605 15203 10793"/>
    </justification>
  </clause>

  <clause id="24620">
    <literal><![CDATA[
      f(x,f(f(x,f(f(x,y),f(z,f(x,z)))),f(f(c_0,f(x,y)),f(c_0,f(z,f(x,z)))))) = f(x,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(15610(a,1),19076(a,1,2,1,2,2,2)),rewrite([24613(10),10913(10),15610(17),24613(14),10913(14),24613(12),24613(13),24613(14)])].">
      <j1 rule="para" parents="15610 19076"/>
      <j2 rule="rewrite" parents="24613 10913 15610 24613 10913 24613 24613 24613"/>
    </justification>
  </clause>

  <clause id="24621">
    <literal><![CDATA[
      f(f(c_0,f(x,f(x,y))),f(f(y,f(c_0,f(x,f(x,y)))),f(z,f(z,f(c_0,f(x,f(x,y))))))) = f(y,f(c_0,f(x,f(x,y))))
    ]]></literal>
    <justification jstring="[para(17126(a,1),19076(a,1,2,1,1,2)),rewrite([24613(2),24613(10),24613(13),543(16),24613(7),24613(10),24613(13),24613(16),24613(17),24613(19),24613(22),10791(24),24613(19),24613(22)])].">
      <j1 rule="para" parents="17126 19076"/>
      <j2 rule="rewrite" parents="24613 24613 24613 543 24613 24613 24613 24613 24613 24613 24613 10791 24613 24613"/>
    </justification>
  </clause>

  <clause id="24622">
    <literal><![CDATA[
      f(x,f(c_0,f(y,f(y,x)))) = c_0
    ]]></literal>
    <justification jstring="[para(17126(a,1),19076(a,2)),rewrite([24613(2),24613(7),24613(10),24613(14),24613(17),24613(22),24613(25),24613(28),24613(31),24613(32),24613(34),24613(37),24621(37),24613(26),20592(26),10793(12)])].">
      <j1 rule="para" parents="17126 19076"/>
      <j2 rule="rewrite" parents="24613 24613 24613 24613 24613 24613 24613 24613 24613 24613 24613 24613 24621 24613 20592 10793"/>
    </justification>
  </clause>

  <clause id="24634">
    <literal><![CDATA[
      f(x,f(f(x,y),f(f(x,y),f(f(x,f(f(x,y),f(z,f(x,z)))),f(f(c_0,f(x,y)),f(c_0,f(z,f(x,z)))))))) = f(x,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(19076(a,1),16414(a,1,2,1,2)),rewrite([24613(12),24613(13),24613(14),24613(16),24613(28),24613(29),24613(30),24613(31),24620(31),24613(18),24613(31),24613(32),24613(33),24613(34),24620(34)])].">
      <j1 rule="para" parents="19076 16414"/>
      <j2 rule="rewrite" parents="24613 24613 24613 24613 24613 24613 24613 24613 24620 24613 24613 24613 24613 24613 24620"/>
    </justification>
  </clause>

  <clause id="24650">
    <literal><![CDATA[
      f(f(x,y),f(f(z,f(x,x)),f(c_0,f(x,f(z,f(z,f(x,y))))))) = x
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(19076(a,1),15774(a,1,1,1,1,2)),rewrite([24613(12),24613(13),24613(14),24613(16),24613(28),24613(29),24613(30),24613(31),24620(31),24613(18),24613(19),24634(19),24613(3),24613(16),24613(17),24613(18),24613(19),24620(19),24613(6),24613(8)])].">
      <j1 rule="para" parents="19076 15774"/>
      <j2 rule="rewrite" parents="24613 24613 24613 24613 24613 24613 24613 24613 24620 24613 24613 24634 24613 24613 24613 24613 24613 24620 24613 24613"/>
    </justification>
  </clause>

  <clause id="24662">
    <literal><![CDATA[
      f(f(x,y),f(f(c_0,f(x,f(z,f(z,f(x,y))))),f(f(x,x),f(c_0,f(z,f(z,f(x,y))))))) = x
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(19076(a,1),19075(a,1,2,1,2,2,2,1)),rewrite([24613(12),24613(13),24613(14),24613(15),24620(15),24613(5),24613(21),24613(22),24613(23),24620(24),24613(11),24613(13),24613(15)])].">
      <j1 rule="para" parents="19076 19075"/>
      <j2 rule="rewrite" parents="24613 24613 24613 24613 24620 24613 24613 24613 24613 24620 24613 24613 24613"/>
    </justification>
  </clause>

  <clause id="24680">
    <literal><![CDATA[
      f(f(x,y),f(f(c_0,f(y,f(f(z,f(x,y)),f(c_0,f(z,f(f(x,y),f(z,f(x,y)))))))),f(f(y,y),f(c_0,f(f(z,f(x,y)),f(c_0,f(z,f(f(x,y),f(z,f(x,y)))))))))) = y
    ]]></literal>
    <justification jstring="[back_rewrite(24566),rewrite([24613(4),24613(5),24613(7),24613(8),24613(9),24613(11),24613(17),24613(18),24613(20),24613(21),24613(22),24613(24),24613(27),24613(29)])].">
      <j1 rule="back_rewrite" parents="24566"/>
      <j2 rule="rewrite" parents="24613 24613 24613 24613 24613 24613 24613 24613 24613 24613 24613 24613 24613 24613"/>
    </justification>
  </clause>

  <clause id="24694">
    <literal><![CDATA[
      f(x,f(f(y,f(c_0,f(x,z))),f(c_0,f(f(x,z),f(y,f(x,y)))))) = f(x,z)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(24537),rewrite([24613(4),24613(10),24613(12),24613(14),24613(15),24613(16),24662(16),24613(2),24613(4),24613(8),24613(9),24613(13)])].">
      <j1 rule="back_rewrite" parents="24537"/>
      <j2 rule="rewrite" parents="24613 24613 24613 24613 24613 24613 24662 24613 24613 24613 24613 24613"/>
    </justification>
  </clause>

  <clause id="24726">
    <literal><![CDATA[
      f(f(x,f(x,y)),f(f(z,x),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(24465),rewrite([24613(4),24613(9),15153(9),24613(6)])].">
      <j1 rule="back_rewrite" parents="24465"/>
      <j2 rule="rewrite" parents="24613 24613 15153 24613"/>
    </justification>
  </clause>

  <clause id="24727">
    <literal><![CDATA[
      f(x,f(f(y,f(x,x)),f(z,f(x,x)))) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(24464),rewrite([24613(6)])].">
      <j1 rule="back_rewrite" parents="24464"/>
      <j2 rule="rewrite" parents="24613"/>
    </justification>
  </clause>

  <clause id="24756">
    <literal><![CDATA[
      f(f(x,f(x,y)),f(f(x,y),f(x,z))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(24374),rewrite([24613(6),9839(7,R),24613(7),10791(7),24613(6)])].">
      <j1 rule="back_rewrite" parents="24374"/>
      <j2 rule="rewrite" parents="24613 9839 24613 10791 24613"/>
    </justification>
  </clause>

  <clause id="24806">
    <literal><![CDATA[
      f(f(x,f(x,y)),f(c_0,f(x,f(z,f(x,y))))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(24208),rewrite([24613(1),24613(4),24613(5),24613(9)])].">
      <j1 rule="back_rewrite" parents="24208"/>
      <j2 rule="rewrite" parents="24613 24613 24613 24613"/>
    </justification>
  </clause>

  <clause id="24885">
    <literal><![CDATA[
      f(f(x,f(x,y)),f(x,f(y,f(x,y)))) = x
    ]]></literal>
    <justification jstring="[back_rewrite(23907),rewrite([24613(1),24613(4),15153(4),24613(5),24613(8),15153(8),24613(5),24613(6),24613(7),24613(10),15153(10)])].">
      <j1 rule="back_rewrite" parents="23907"/>
      <j2 rule="rewrite" parents="24613 24613 15153 24613 24613 15153 24613 24613 24613 24613 15153"/>
    </justification>
  </clause>

  <clause id="24966">
    <literal><![CDATA[
      f(f(x,y),f(f(z,f(y,y)),f(c_0,f(y,f(z,f(z,f(x,y))))))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(23410),rewrite([24613(2),24613(5),15153(5),24613(2),24613(3),24613(6),15153(6),24613(4),15153(4),24613(3),24613(6),24613(8)])].">
      <j1 rule="back_rewrite" parents="23410"/>
      <j2 rule="rewrite" parents="24613 24613 15153 24613 24613 24613 15153 24613 15153 24613 24613 24613"/>
    </justification>
  </clause>

  <clause id="24982">
    <literal><![CDATA[
      f(f(x,f(y,y)),f(f(y,z),f(c_0,f(f(y,y),f(z,f(z,f(x,f(y,y)))))))) = f(y,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(23356),rewrite([24613(2),24613(6),15153(6),24613(6),24613(7),24613(10)])].">
      <j1 rule="back_rewrite" parents="23356"/>
      <j2 rule="rewrite" parents="24613 24613 15153 24613 24613 24613"/>
    </justification>
  </clause>

  <clause id="25046">
    <literal><![CDATA[
      f(x,f(y,f(x,f(x,y)))) = f(x,f(x,y))
    ]]></literal>
    <justification jstring="[back_rewrite(22984),rewrite([24613(1),24613(5),24613(6),15203(6),24613(3),24613(4),24613(5)])].">
      <j1 rule="back_rewrite" parents="22984"/>
      <j2 rule="rewrite" parents="24613 24613 24613 15203 24613 24613 24613"/>
    </justification>
  </clause>

  <clause id="25284">
    <literal><![CDATA[
      f(x,f(c_0,f(y,f(x,f(x,y))))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(20818),rewrite([24613(2),24613(6),24613(7),15203(7),24613(4),24613(7)])].">
      <j1 rule="back_rewrite" parents="20818"/>
      <j2 rule="rewrite" parents="24613 24613 24613 15203 24613 24613"/>
    </justification>
  </clause>

  <clause id="25327">
    <literal><![CDATA[
      f(f(x,f(c_0,f(y,z))),f(c_0,f(f(c_0,f(y,z)),f(f(u,f(y,z)),f(c_0,f(f(c_0,f(y,z)),f(u,f(u,f(x,f(c_0,f(y,z))))))))))) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(20615),rewrite([24613(4),24613(10),24613(15),24613(16),24613(21)])].">
      <j1 rule="back_rewrite" parents="20615"/>
      <j2 rule="rewrite" parents="24613 24613 24613 24613 24613"/>
    </justification>
  </clause>

  <clause id="25525">
    <literal><![CDATA[
      f(f(x,y),f(y,f(y,f(f(c_0,f(y,f(z,f(c_0,f(x,y))))),f(f(y,y),f(c_0,f(z,f(c_0,f(x,y))))))))) = y
    ]]></literal>
    <justification jstring="[back_rewrite(19449),rewrite([24613(5),24613(7),24613(12),24613(14),24613(15),24613(17),24613(18)])].">
      <j1 rule="back_rewrite" parents="19449"/>
      <j2 rule="rewrite" parents="24613 24613 24613 24613 24613 24613 24613"/>
    </justification>
  </clause>

  <clause id="25546">
    <literal><![CDATA[
      f(f(x,y),f(y,f(y,f(f(c_0,f(y,f(x,f(x,f(f(x,z),f(f(x,y),f(x,z))))))),f(f(y,y),f(x,f(f(x,z),f(f(x,y),f(x,z))))))))) = y
    ]]></literal>
    <justification jstring="[back_rewrite(19278),rewrite([24613(3),24613(4),24613(5),24613(8),24613(11),24613(12),24613(13),24613(16),24613(18),24613(20)])].">
      <j1 rule="back_rewrite" parents="19278"/>
      <j2 rule="rewrite" parents="24613 24613 24613 24613 24613 24613 24613 24613 24613 24613"/>
    </justification>
  </clause>

  <clause id="25611">
    <literal><![CDATA[
      f(f(c_0,f(x,f(x,y))),f(c_0,f(y,f(z,z)))) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(18995),rewrite([24613(2)])].">
      <j1 rule="back_rewrite" parents="18995"/>
      <j2 rule="rewrite" parents="24613"/>
    </justification>
  </clause>

  <clause id="25638">
    <literal><![CDATA[
      f(f(x,y),f(x,f(f(x,y),f(f(z,f(x,x)),f(f(x,y),f(x,f(z,f(z,f(x,y))))))))) = x
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(18833),rewrite([24613(4),24613(9),24613(12),24694(12),24613(3),24613(5),24613(7),24613(9),24613(12)])].">
      <j1 rule="back_rewrite" parents="18833"/>
      <j2 rule="rewrite" parents="24613 24613 24613 24694 24613 24613 24613 24613 24613"/>
    </justification>
  </clause>

  <clause id="25641">
    <literal><![CDATA[
      f(x,f(f(y,f(c_0,f(x,z))),f(x,f(f(x,z),f(y,f(x,y)))))) = f(x,z)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(18829),rewrite([24613(2),24613(4),24613(6),24613(8),24613(11),24613(14),25638(14),24613(4),24613(8),24613(9)])].">
      <j1 rule="back_rewrite" parents="18829"/>
      <j2 rule="rewrite" parents="24613 24613 24613 24613 24613 24613 25638 24613 24613 24613"/>
    </justification>
  </clause>

  <clause id="25669">
    <literal><![CDATA[
      f(f(x,y),f(f(z,f(x,x)),f(f(x,u),f(x,f(z,f(z,f(x,y))))))) = x
    ]]></literal>
    <justification jstring="[back_rewrite(18689),rewrite([24613(5),24613(9),24613(10),24613(12),25641(12),9839(3,R),24613(4),10791(4),24613(3),24613(5),24613(7),24613(9)])].">
      <j1 rule="back_rewrite" parents="18689"/>
      <j2 rule="rewrite" parents="24613 24613 24613 24613 25641 9839 24613 10791 24613 24613 24613 24613"/>
    </justification>
  </clause>

  <clause id="25692">
    <literal><![CDATA[
      f(x,f(f(x,y),f(y,f(z,f(x,y))))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(18540),rewrite([24613(2),24613(4),24613(6),24613(8),24613(10),24613(11),25669(11),24613(1),24613(4),24613(5),15203(5),24613(2),24613(3),24613(7)])].">
      <j1 rule="back_rewrite" parents="18540"/>
      <j2 rule="rewrite" parents="24613 24613 24613 24613 24613 24613 25669 24613 24613 24613 15203 24613 24613 24613"/>
    </justification>
  </clause>

  <clause id="25800">
    <literal><![CDATA[
      f(f(x,y),f(f(x,y),f(f(z,f(c_0,f(x,y))),f(x,f(f(x,y),f(z,f(z,f(u,f(x,y))))))))) = f(f(z,f(c_0,f(x,y))),f(x,f(f(x,y),f(z,f(z,f(u,f(x,y)))))))
    ]]></literal>
    <justification jstring="[back_rewrite(17995),rewrite([24613(6),24613(8),24613(9),24613(12),24613(13),24613(20),24613(22),24613(23),24613(26),24613(27)])].">
      <j1 rule="back_rewrite" parents="17995"/>
      <j2 rule="rewrite" parents="24613 24613 24613 24613 24613 24613 24613 24613 24613 24613"/>
    </justification>
  </clause>

  <clause id="26164">
    <literal><![CDATA[
      f(f(c_0,c_0),f(f(x,y),f(z,z))) = c_0
    ]]></literal>
    <justification jstring="[para(10913(a,1),24366(a,1,2,1)),rewrite([24613(6),9899(6)])].">
      <j1 rule="para" parents="10913 24366"/>
      <j2 rule="rewrite" parents="24613 9899"/>
    </justification>
  </clause>

  <clause id="26177">
    <literal><![CDATA[
      f(x,f(c_0,f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(24966(a,1),543(a,1,2)),rewrite([9899(3,R),24613(3),24613(4)])].">
      <j1 rule="para" parents="24966 543"/>
      <j2 rule="rewrite" parents="9899 24613 24613"/>
    </justification>
  </clause>

  <clause id="26178">
    <literal><![CDATA[
      f(f(x,x),f(c_0,f(y,x))) = c_0
    ]]></literal>
    <justification jstring="[para(24966(a,1),10786(a,1,2,2)),rewrite([9899(3,R),24613(3),24613(5),9899(5),24613(5)])].">
      <j1 rule="para" parents="24966 10786"/>
      <j2 rule="rewrite" parents="9899 24613 24613 9899 24613"/>
    </justification>
  </clause>

  <clause id="26180">
    <literal><![CDATA[
      f(x,f(x,f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(24966(a,1),15153(a,1,2,2)),rewrite([24966(11),24613(2)])].">
      <j1 rule="para" parents="24966 15153"/>
      <j2 rule="rewrite" parents="24966 24613"/>
    </justification>
  </clause>

  <clause id="26187">
    <literal><![CDATA[
      f(f(f(x,f(c_0,f(y,z))),f(c_0,f(f(x,f(x,y)),f(y,z)))),f(f(y,f(c_0,f(x,f(c_0,f(y,z))))),f(c_0,f(f(y,f(y,z)),f(x,f(c_0,f(y,z))))))) = f(x,f(c_0,f(y,z)))
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(24694(a,1),24650(a,1,2,2,2,2,2)),rewrite([24613(7),24613(9),9899(20,R),24613(17),24613(26)])].">
      <j1 rule="para" parents="24694 24650"/>
      <j2 rule="rewrite" parents="24613 24613 9899 24613 24613"/>
    </justification>
  </clause>

  <clause id="26188">
    <literal><![CDATA[
      f(x,f(f(y,f(c_0,f(x,z))),f(c_0,f(f(y,f(y,x)),f(x,z))))) = f(x,z)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(24694(a,1),24613(a,2)),rewrite([24613(7),24613(9),24613(12)])].">
      <j1 rule="para" parents="24694 24613"/>
      <j2 rule="rewrite" parents="24613 24613 24613"/>
    </justification>
  </clause>

  <clause id="26199">
    <literal><![CDATA[
      f(f(x,y),f(f(z,f(y,y)),f(f(x,y),f(y,f(z,f(z,f(x,y))))))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(11(a,1),25641(a,1,2,1,2,2)),rewrite([24613(3),9899(3),11(7),24613(6),11(14)])].">
      <j1 rule="para" parents="11 25641"/>
      <j2 rule="rewrite" parents="24613 9899 11 24613 11"/>
    </justification>
  </clause>

  <clause id="26216">
    <literal><![CDATA[
      f(f(c_0,c_0),f(f(x,y),f(z,u))) = c_0
    ]]></literal>
    <justification jstring="[para(12170(a,1),26164(a,1,2,2))].">
      <j1 rule="para" parents="12170 26164"/>
    </justification>
  </clause>

  <clause id="26248">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),f(f(x,y),f(z,u))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(26216(a,1),24650(a,1,2,2,2,2,2)),rewrite([9899(9,R),24613(9),543(10),24613(11),9222(11),24613(8),10913(9),24613(7)])].">
      <j1 rule="para" parents="26216 24650"/>
      <j2 rule="rewrite" parents="9899 24613 543 24613 9222 24613 10913 24613"/>
    </justification>
  </clause>

  <clause id="26249">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),f(f(z,u),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(26216(a,1),24966(a,1,2,2,2,2,2)),rewrite([9899(9,R),24613(9),543(10),24613(11),9222(11),24613(8),10913(9),24613(7)])].">
      <j1 rule="para" parents="26216 24966"/>
      <j2 rule="rewrite" parents="9899 24613 543 24613 9222 24613 10913 24613"/>
    </justification>
  </clause>

  <clause id="26376">
    <literal><![CDATA[
      f(f(c_0,f(x,f(y,y))),f(c_0,f(y,z))) = c_0
    ]]></literal>
    <justification jstring="[para(11(a,1),19321(a,1,2,2,2))].">
      <j1 rule="para" parents="11 19321"/>
    </justification>
  </clause>

  <clause id="26377">
    <literal><![CDATA[
      f(f(x,x),f(c_0,f(y,f(c_0,f(z,x))))) = c_0
    ]]></literal>
    <justification jstring="[para(11(a,1),19321(a,1,2,2)),rewrite([9899(4,R),24613(4),24613(8),9899(8),24613(8)])].">
      <j1 rule="para" parents="11 19321"/>
      <j2 rule="rewrite" parents="9899 24613 24613 9899 24613"/>
    </justification>
  </clause>

  <clause id="26378">
    <literal><![CDATA[
      f(x,f(c_0,f(f(x,x),f(y,y)))) = c_0
    ]]></literal>
    <justification jstring="[para(607(a,1),19321(a,1,1,2)),rewrite([9849(3)])].">
      <j1 rule="para" parents="607 19321"/>
      <j2 rule="rewrite" parents="9849"/>
    </justification>
  </clause>

  <clause id="26396">
    <literal><![CDATA[
      f(f(x,y),f(y,f(z,f(c_0,f(x,y))))) = y
    ]]></literal>
    <justification jstring="[back_rewrite(25525),rewrite([26377(16),24613(10),10913(10),7716(8)])].">
      <j1 rule="back_rewrite" parents="25525"/>
      <j2 rule="rewrite" parents="26377 24613 10913 7716"/>
    </justification>
  </clause>

  <clause id="26407">
    <literal><![CDATA[
      f(f(x,y),f(x,f(z,f(z,f(x,y))))) = x
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(26199(a,1),24966(a,1,2,2,2,2,2)),rewrite([24613(3),24613(4),24613(10),24613(11),24613(12),24613(17),24613(18),9899(23,R),24613(18),10791(19),24613(17),24613(18),24613(23),24613(24),24613(25),24756(25),24613(19),26248(19),24613(11),25669(11),24613(1),24613(2)]),flip(a)].">
      <j1 rule="para" parents="26199 24966"/>
      <j2 rule="rewrite" parents="24613 24613 24613 24613 24613 24613 24613 9899 24613 10791 24613 24613 24613 24613 24613 24756 24613 26248 24613 25669 24613 24613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26415">
    <literal><![CDATA[
      f(x,f(f(x,y),f(z,f(x,z)))) = f(x,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(11(a,1),26407(a,1,1)),rewrite([24613(1),24613(2),24613(4),543(4),24613(2),24613(6)])].">
      <j1 rule="para" parents="11 26407"/>
      <j2 rule="rewrite" parents="24613 24613 24613 543 24613 24613"/>
    </justification>
  </clause>

  <clause id="26419">
    <literal><![CDATA[
      f(f(f(x,f(y,y)),f(y,f(y,z))),f(f(x,f(y,y)),f(c_0,f(y,f(x,f(x,f(y,z))))))) = f(x,f(y,y))
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(24650(a,1),26407(a,1,2,2,2)),rewrite([24613(13),24613(15)])].">
      <j1 rule="para" parents="24650 26407"/>
      <j2 rule="rewrite" parents="24613 24613"/>
    </justification>
  </clause>

  <clause id="26420">
    <literal><![CDATA[
      f(f(x,y),f(y,f(z,f(z,f(x,y))))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(24613(a,1),26407(a,1,1)),rewrite([24613(2)])].">
      <j1 rule="para" parents="24613 26407"/>
      <j2 rule="rewrite" parents="24613"/>
    </justification>
  </clause>

  <clause id="26421">
    <literal><![CDATA[
      f(f(x,f(y,f(y,f(x,z)))),f(c_0,f(x,f(x,z)))) = c_0
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(26407(a,1),24622(a,1,2,2,2)),rewrite([24613(7)])].">
      <j1 rule="para" parents="26407 24622"/>
      <j2 rule="rewrite" parents="24613"/>
    </justification>
  </clause>

  <clause id="26505">
    <literal><![CDATA[
      f(x,f(c_0,f(f(x,x),f(y,z)))) = c_0
    ]]></literal>
    <justification jstring="[para(12170(a,1),26378(a,1,2,2,2))].">
      <j1 rule="para" parents="12170 26378"/>
    </justification>
  </clause>

  <clause id="26511">
    <literal><![CDATA[
      f(x,f(f(x,y),f(f(x,x),f(z,u)))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(26505(a,1),26415(a,1,2,2,2)),rewrite([24613(8),10913(8)])].">
      <j1 rule="para" parents="26505 26415"/>
      <j2 rule="rewrite" parents="24613 10913"/>
    </justification>
  </clause>

  <clause id="26518">
    <literal><![CDATA[
      f(x,f(f(x,x),f(y,z))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(26505(a,1),25046(a,1,2,2,2)),rewrite([9899(7),24613(7),10791(7),26505(10),9899(6)])].">
      <j1 rule="para" parents="26505 25046"/>
      <j2 rule="rewrite" parents="9899 24613 10791 26505 9899"/>
    </justification>
  </clause>

  <clause id="26522">
    <literal><![CDATA[
      f(f(x,x),f(f(c_0,f(x,y)),f(f(x,x),f(z,u)))) = x
    ]]></literal>
    <justification jstring="[para(26518(a,1),18865(a,1,1)),rewrite([26518(10),9849(8),24613(6),24613(8),26518(14),9849(12)])].">
      <j1 rule="para" parents="26518 18865"/>
      <j2 rule="rewrite" parents="26518 9849 24613 24613 26518 9849"/>
    </justification>
  </clause>

  <clause id="26578">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),f(f(x,f(x,y)),f(z,f(x,z)))) = c_0
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(24885(a,1),26421(a,1,1,2,2,2)),rewrite([24613(3),24885(14),24613(9),7716(9),24613(9)])].">
      <j1 rule="para" parents="24885 26421"/>
      <j2 rule="rewrite" parents="24613 24885 24613 7716 24613"/>
    </justification>
  </clause>

  <clause id="26622">
    <literal><![CDATA[
      f(f(x,y),f(f(z,f(z,f(x,y))),f(c_0,f(y,f(x,f(x,y)))))) = f(c_0,f(y,f(x,f(x,y))))
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(25284(a,1),26420(a,1,1)),rewrite([25284(12),24613(10)])].">
      <j1 rule="para" parents="25284 26420"/>
      <j2 rule="rewrite" parents="25284 24613"/>
    </justification>
  </clause>

  <clause id="26644">
    <literal><![CDATA[
      f(f(c_0,f(x,f(y,z))),f(c_0,f(u,f(c_0,f(y,z))))) = c_0
    ]]></literal>
    <justification jstring="[para(12170(a,1),26376(a,1,1,2,2)),rewrite([24613(9)])].">
      <j1 rule="para" parents="12170 26376"/>
      <j2 rule="rewrite" parents="24613"/>
    </justification>
  </clause>

  <clause id="27135">
    <literal><![CDATA[
      f(c_0,f(f(x,y),f(x,z))) = f(x,f(f(x,y),f(x,z)))
    ]]></literal>
    <justification jstring="[para(24194(a,1),11(a,1,1)),rewrite([9899(11,R),24613(7),10913(7)]),flip(a)].">
      <j1 rule="para" parents="24194 11"/>
      <j2 rule="rewrite" parents="9899 24613 10913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27148">
    <literal><![CDATA[
      f(f(x,x),f(c_0,f(f(x,y),f(x,z)))) = x
    ]]></literal>
    <justification jstring="[para(24194(a,1),26177(a,1,2,2)),rewrite([24613(7),9899(7),24613(7),24194(15)])].">
      <j1 rule="para" parents="24194 26177"/>
      <j2 rule="rewrite" parents="24613 9899 24613 24194"/>
    </justification>
  </clause>

  <clause id="27179">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),f(c_0,f(y,f(z,f(x,y))))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(11(a,1),27148(a,1,2,2,1)),rewrite([9899(3,R),24613(3),24613(6)])].">
      <j1 rule="para" parents="11 27148"/>
      <j2 rule="rewrite" parents="9899 24613 24613"/>
    </justification>
  </clause>

  <clause id="27297">
    <literal><![CDATA[
      f(f(x,f(y,x)),f(x,f(z,f(y,x)))) = x
    ]]></literal>
    <justification jstring="[para(11(a,1),24726(a,1,1,2)),rewrite([24613(2),11(7),24613(5),11(9)])].">
      <j1 rule="para" parents="11 24726"/>
      <j2 rule="rewrite" parents="24613 11 24613 11"/>
    </justification>
  </clause>

  <clause id="27301">
    <literal><![CDATA[
      f(f(x,f(x,y)),f(x,f(z,f(x,y)))) = x
    ]]></literal>
    <justification jstring="[para(15153(a,1),24726(a,1,1,2)),rewrite([24613(2),15153(8),24613(5),15153(10)])].">
      <j1 rule="para" parents="15153 24726"/>
      <j2 rule="rewrite" parents="24613 15153 24613 15153"/>
    </justification>
  </clause>

  <clause id="27357">
    <literal><![CDATA[
      f(c_0,f(x,f(f(x,y),f(x,z)))) = f(f(x,y),f(x,z))
    ]]></literal>
    <justification jstring="[para(24194(a,1),27297(a,1,2,2)),rewrite([18622(9),24613(5)])].">
      <j1 rule="para" parents="24194 27297"/>
      <j2 rule="rewrite" parents="18622 24613"/>
    </justification>
  </clause>

  <clause id="27823">
    <literal><![CDATA[
      f(f(f(x,y),f(f(x,x),f(z,f(x,x)))),f(f(x,y),f(c_0,f(f(x,x),f(y,f(y,f(z,f(x,x)))))))) = f(x,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(24982(a,1),26407(a,1,2,2,2)),rewrite([24613(15),24613(17)])].">
      <j1 rule="para" parents="24982 26407"/>
      <j2 rule="rewrite" parents="24613 24613"/>
    </justification>
  </clause>

  <clause id="27943">
    <literal><![CDATA[
      f(f(x,x),f(c_0,f(y,f(y,f(z,x))))) = c_0
    ]]></literal>
    <justification jstring="[para(11(a,1),25611(a,1,2,2)),rewrite([24613(7),9899(7),24613(7)])].">
      <j1 rule="para" parents="11 25611"/>
      <j2 rule="rewrite" parents="24613 9899 24613"/>
    </justification>
  </clause>

  <clause id="28089">
    <literal><![CDATA[
      f(f(c_0,f(x,f(x,y))),f(f(z,f(z,x)),f(x,y))) = c_0
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(26188(a,1),27943(a,1,2,2,2)),rewrite([9899(13,R),24613(8),10913(8),24613(9)])].">
      <j1 rule="para" parents="26188 27943"/>
      <j2 rule="rewrite" parents="9899 24613 10913 24613"/>
    </justification>
  </clause>

  <clause id="28208">
    <literal><![CDATA[
      f(x,f(f(y,f(y,x)),f(x,z))) = f(x,z)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(28089(a,1),24966(a,1,2,2,2,2,2)),rewrite([9899(11,R),24613(11),24613(12),20605(12),24613(13),10913(13),15153(10),24613(7),9899(7),9849(7),24613(5)])].">
      <j1 rule="para" parents="28089 24966"/>
      <j2 rule="rewrite" parents="9899 24613 24613 20605 24613 10913 15153 24613 9899 9849 24613"/>
    </justification>
  </clause>

  <clause id="29596">
    <literal><![CDATA[
      f(f(x,f(y,f(y,x))),f(f(z,f(z,f(y,x))),f(f(y,x),f(c_0,f(x,f(y,f(y,x))))))) = c_0
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(26622(a,1),26578(a,1,2,1,2)),rewrite([26622(12),10913(7),24613(12),24613(14)])].">
      <j1 rule="para" parents="26622 26578"/>
      <j2 rule="rewrite" parents="26622 10913 24613 24613"/>
    </justification>
  </clause>

  <clause id="30737">
    <literal><![CDATA[
      f(f(x,f(y,x)),f(c_0,f(f(y,x),f(x,z)))) = x
    ]]></literal>
    <justification jstring="[para(11(a,1),24806(a,1,1,2)),rewrite([24613(2),11(7),24613(5),11(11)])].">
      <j1 rule="para" parents="11 24806"/>
      <j2 rule="rewrite" parents="24613 11 24613 11"/>
    </justification>
  </clause>

  <clause id="30846">
    <literal><![CDATA[
      f(c_0,f(x,f(f(y,x),f(x,z)))) = f(f(y,x),f(x,z))
    ]]></literal>
    <justification jstring="[para(30737(a,1),27297(a,1,2,2)),rewrite([18622(9),24613(5)])].">
      <j1 rule="para" parents="30737 27297"/>
      <j2 rule="rewrite" parents="18622 24613"/>
    </justification>
  </clause>

  <clause id="32225">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),f(f(x,x),f(z,u))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(26522(a,1),25692(a,1,2,2,2)),rewrite([24613(14),26518(14),24613(12),26522(12),24613(4),10791(4)]),flip(a)].">
      <j1 rule="para" parents="26522 25692"/>
      <j2 rule="rewrite" parents="24613 26518 24613 26522 24613 10791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32226">
    <literal><![CDATA[
      f(f(x,y),f(c_0,f(f(x,x),f(z,u)))) = f(f(x,x),f(z,u))
    ]]></literal>
    <justification jstring="[para(26522(a,1),24680(a,1,2,1,2,2,1)),rewrite([32225(7),32225(14),32225(16),543(11),24613(9),543(10),24613(7),9899(7),9222(7),24613(7),10913(8),9899(11,R),24613(9),32225(18),543(13),32225(19),32225(21),543(16),24613(14),543(15),24613(12),9899(12),9222(12),24613(13),543(13),24613(6)])].">
      <j1 rule="para" parents="26522 24680"/>
      <j2 rule="rewrite" parents="32225 32225 32225 543 24613 543 24613 9899 9222 24613 10913 9899 24613 32225 543 32225 32225 543 24613 543 24613 9899 9222 24613 543 24613"/>
    </justification>
  </clause>

  <clause id="32233">
    <literal><![CDATA[
      f(f(x,y),f(y,f(x,f(x,f(f(x,z),f(f(x,y),f(x,z))))))) = y
    ]]></literal>
    <justification jstring="[back_rewrite(25546),rewrite([32225(20),7716(11)])].">
      <j1 rule="back_rewrite" parents="25546"/>
      <j2 rule="rewrite" parents="32225 7716"/>
    </justification>
  </clause>

  <clause id="32296">
    <literal><![CDATA[
      f(f(f(x,x),f(y,f(y,f(z,f(x,x))))),f(f(x,y),f(f(x,x),f(z,f(x,x))))) = f(x,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(27823),rewrite([32226(16),24613(13)])].">
      <j1 rule="back_rewrite" parents="27823"/>
      <j2 rule="rewrite" parents="32226 24613"/>
    </justification>
  </clause>

  <clause id="32315">
    <literal><![CDATA[
      f(f(x,x),f(f(y,z),f(c_0,f(x,u)))) = x
    ]]></literal>
    <justification jstring="[para(11(a,1),32225(a,1,1,2)),rewrite([24613(2),9899(2),24613(2),24613(3),9899(4,R),24613(4),24613(6),24613(8),24613(10),543(10)])].">
      <j1 rule="para" parents="11 32225"/>
      <j2 rule="rewrite" parents="24613 9899 24613 24613 9899 24613 24613 24613 24613 543"/>
    </justification>
  </clause>

  <clause id="32317">
    <literal><![CDATA[
      f(f(x,f(y,y)),f(c_0,f(y,z))) = f(y,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),32225(a,1,2,2)),rewrite([24613(5),24613(6)])].">
      <j1 rule="para" parents="11 32225"/>
      <j2 rule="rewrite" parents="24613 24613"/>
    </justification>
  </clause>

  <clause id="32319">
    <literal><![CDATA[
      f(f(x,y),f(f(x,y),f(f(x,x),f(z,u)))) = f(f(x,x),f(z,u))
    ]]></literal>
    <justification jstring="[para(32225(a,1),15203(a,1,1)),rewrite([32225(11),24613(6)])].">
      <j1 rule="para" parents="32225 15203"/>
      <j2 rule="rewrite" parents="32225 24613"/>
    </justification>
  </clause>

  <clause id="32415">
    <literal><![CDATA[
      f(f(x,f(y,f(y,f(x,z)))),f(f(y,f(x,x)),f(x,f(x,z)))) = f(y,f(x,x))
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(26419),rewrite([32317(14),24613(10)])].">
      <j1 rule="back_rewrite" parents="26419"/>
      <j2 rule="rewrite" parents="32317 24613"/>
    </justification>
  </clause>

  <clause id="32448">
    <literal><![CDATA[
      f(f(x,x),f(y,f(c_0,f(x,z)))) = x
    ]]></literal>
    <justification jstring="[para(11(a,1),32315(a,1,2,1))].">
      <j1 rule="para" parents="11 32315"/>
    </justification>
  </clause>

  <clause id="32456">
    <literal><![CDATA[
      f(f(x,x),f(f(c_0,f(x,y)),f(c_0,f(z,u)))) = x
    ]]></literal>
    <justification jstring="[para(18865(a,1),32315(a,1,2,1)),rewrite([24613(8)])].">
      <j1 rule="para" parents="18865 32315"/>
      <j2 rule="rewrite" parents="24613"/>
    </justification>
  </clause>

  <clause id="32517">
    <literal><![CDATA[
      f(x,f(c_0,f(y,f(c_0,f(x,z))))) = f(y,f(c_0,f(x,z)))
    ]]></literal>
    <justification jstring="[para(32448(a,1),11(a,1,1)),rewrite([9899(9,R),24613(6)])].">
      <j1 rule="para" parents="32448 11"/>
      <j2 rule="rewrite" parents="9899 24613"/>
    </justification>
  </clause>

  <clause id="32519">
    <literal><![CDATA[
      f(f(x,f(y,y)),f(c_0,f(z,y))) = f(z,y)
    ]]></literal>
    <justification jstring="[para(11(a,1),32448(a,1,2,2,2)),rewrite([9899(3,R),24613(3),24613(5),9899(5),24613(6)])].">
      <j1 rule="para" parents="11 32448"/>
      <j2 rule="rewrite" parents="9899 24613 24613 9899 24613"/>
    </justification>
  </clause>

  <clause id="32522">
    <literal><![CDATA[
      f(f(x,f(c_0,f(y,z))),f(c_0,f(u,f(y,z)))) = f(u,f(y,z))
    ]]></literal>
    <justification jstring="[para(12170(a,1),32448(a,1,2,2,2)),rewrite([9899(5,R),24613(4),24613(9)])].">
      <j1 rule="para" parents="12170 32448"/>
      <j2 rule="rewrite" parents="9899 24613 24613"/>
    </justification>
  </clause>

  <clause id="32544">
    <literal><![CDATA[
      f(f(x,y),f(x,f(x,f(c_0,f(y,z))))) = x
    ]]></literal>
    <justification jstring="[para(32448(a,1),27301(a,1,2,2)),rewrite([24613(7)])].">
      <j1 rule="para" parents="32448 27301"/>
      <j2 rule="rewrite" parents="24613"/>
    </justification>
  </clause>

  <clause id="32575">
    <literal><![CDATA[
      f(f(f(x,f(x,y)),f(y,z)),f(f(y,f(y,z)),f(x,f(c_0,f(y,z))))) = f(x,f(c_0,f(y,z)))
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(26187),rewrite([32522(11),32517(11),26177(18)])].">
      <j1 rule="back_rewrite" parents="26187"/>
      <j2 rule="rewrite" parents="32522 32517 26177"/>
    </justification>
  </clause>

  <clause id="32800">
    <literal><![CDATA[
      f(f(x,x),f(y,f(c_0,f(z,x)))) = x
    ]]></literal>
    <justification jstring="[para(11(a,1),32317(a,1,2,2)),rewrite([9899(3,R),24613(3),24613(6),9899(6),24613(6),11(9)])].">
      <j1 rule="para" parents="11 32317"/>
      <j2 rule="rewrite" parents="9899 24613 24613 9899 24613 11"/>
    </justification>
  </clause>

  <clause id="32801">
    <literal><![CDATA[
      f(f(x,y),f(c_0,f(z,f(x,x)))) = f(z,f(x,x))
    ]]></literal>
    <justification jstring="[para(32317(a,1),543(a,1,2)),rewrite([9899(5,R),24613(4),24613(6)])].">
      <j1 rule="para" parents="32317 543"/>
      <j2 rule="rewrite" parents="9899 24613 24613"/>
    </justification>
  </clause>

  <clause id="32902">
    <literal><![CDATA[
      f(f(x,f(c_0,f(y,z))),f(z,f(x,f(c_0,f(y,z))))) = z
    ]]></literal>
    <justification jstring="[para(32800(a,1),26180(a,1,2,2)),rewrite([24613(9),32800(16)])].">
      <j1 rule="para" parents="32800 26180"/>
      <j2 rule="rewrite" parents="24613 32800"/>
    </justification>
  </clause>

  <clause id="32917">
    <literal><![CDATA[
      f(f(x,y),f(x,f(x,f(c_0,f(z,y))))) = x
    ]]></literal>
    <justification jstring="[para(32800(a,1),27301(a,1,2,2)),rewrite([24613(7)])].">
      <j1 rule="para" parents="32800 27301"/>
      <j2 rule="rewrite" parents="24613"/>
    </justification>
  </clause>

  <clause id="33032">
    <literal><![CDATA[
      f(f(x,x),f(y,f(f(x,z),f(x,u)))) = x
    ]]></literal>
    <justification jstring="[para(24194(a,1),32519(a,1,2,2)),rewrite([9899(11,R),24613(7),10913(7),24613(6),9899(6),24613(6),24194(14)])].">
      <j1 rule="para" parents="24194 32519"/>
      <j2 rule="rewrite" parents="9899 24613 10913 24613 9899 24613 24194"/>
    </justification>
  </clause>

  <clause id="33047">
    <literal><![CDATA[
      f(f(x,x),f(y,f(f(z,x),f(x,u)))) = x
    ]]></literal>
    <justification jstring="[para(30737(a,1),32519(a,1,2,2)),rewrite([9899(11,R),24613(7),10913(7),24613(6),9899(6),24613(6),30737(14)])].">
      <j1 rule="para" parents="30737 32519"/>
      <j2 rule="rewrite" parents="9899 24613 10913 24613 9899 24613 30737"/>
    </justification>
  </clause>

  <clause id="33057">
    <literal><![CDATA[
      f(f(x,x),f(y,f(c_0,f(z,f(c_0,f(u,x)))))) = x
    ]]></literal>
    <justification jstring="[para(32800(a,1),32519(a,1,2,2)),rewrite([9899(9,R),24613(6),24613(9),9899(9),24613(9),32800(15)])].">
      <j1 rule="para" parents="32800 32519"/>
      <j2 rule="rewrite" parents="9899 24613 24613 9899 24613 32800"/>
    </justification>
  </clause>

  <clause id="33384">
    <literal><![CDATA[
      f(f(x,f(x,f(y,y))),f(x,f(y,z))) = x
    ]]></literal>
    <justification jstring="[para(15153(a,1),32544(a,1,2,2,2,2)),rewrite([24613(4),9899(4),24613(6)])].">
      <j1 rule="para" parents="15153 32544"/>
      <j2 rule="rewrite" parents="24613 9899 24613"/>
    </justification>
  </clause>

  <clause id="33474">
    <literal><![CDATA[
      f(f(x,f(x,y)),f(x,f(f(y,y),f(z,u)))) = x
    ]]></literal>
    <justification jstring="[para(26518(a,1),32917(a,1,2,2,2,2)),rewrite([9849(7),24613(7)])].">
      <j1 rule="para" parents="26518 32917"/>
      <j2 rule="rewrite" parents="9849 24613"/>
    </justification>
  </clause>

  <clause id="33512">
    <literal><![CDATA[
      f(x,f(x,f(y,f(f(x,z),f(x,u))))) = f(y,f(f(x,z),f(x,u)))
    ]]></literal>
    <justification jstring="[para(33032(a,1),15203(a,1,1)),rewrite([33032(10),24613(5)])].">
      <j1 rule="para" parents="33032 15203"/>
      <j2 rule="rewrite" parents="33032 24613"/>
    </justification>
  </clause>

  <clause id="33573">
    <literal><![CDATA[
      f(f(x,y),f(y,f(f(x,z),f(f(x,y),f(x,z))))) = y
    ]]></literal>
    <justification jstring="[back_rewrite(32233),rewrite([33512(8)])].">
      <j1 rule="back_rewrite" parents="32233"/>
      <j2 rule="rewrite" parents="33512"/>
    </justification>
  </clause>

  <clause id="33760">
    <literal><![CDATA[
      f(f(x,y),f(x,f(x,f(f(z,y),f(y,u))))) = x
    ]]></literal>
    <justification jstring="[para(33047(a,1),27301(a,1,2,2)),rewrite([24613(7)])].">
      <j1 rule="para" parents="33047 27301"/>
      <j2 rule="rewrite" parents="24613"/>
    </justification>
  </clause>

  <clause id="33963">
    <literal><![CDATA[
      f(f(f(x,y),f(f(y,y),f(z,f(y,y)))),f(f(y,y),f(x,f(x,f(z,f(y,y)))))) = f(x,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(24613(a,1),32296(a,1,1)),rewrite([24613(6),24613(7),24613(13),24613(14)])].">
      <j1 rule="para" parents="24613 32296"/>
      <j2 rule="rewrite" parents="24613 24613 24613 24613"/>
    </justification>
  </clause>

  <clause id="35994">
    <literal><![CDATA[
      f(f(x,f(y,y)),f(f(y,z),f(f(y,y),f(f(y,y),f(z,f(z,f(x,f(y,y)))))))) = f(y,z)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(33963(a,1),32415(a,1,1,2,2)),rewrite([24613(2),24613(8),24613(9),32319(9),26180(6),24613(3),9899(11,R),24613(11),9849(11),24613(9),26511(9),24613(14),9899(22,R),24613(22),9849(22),24613(20),26511(20)])].">
      <j1 rule="para" parents="33963 32415"/>
      <j2 rule="rewrite" parents="24613 24613 24613 32319 26180 24613 9899 24613 9849 24613 26511 24613 9899 24613 9849 24613 26511"/>
    </justification>
  </clause>

  <clause id="36523">
    <literal><![CDATA[
      f(f(x,f(c_0,f(y,f(c_0,f(z,u))))),f(c_0,f(f(w,v5),f(z,u)))) = f(f(w,v5),f(z,u))
    ]]></literal>
    <justification jstring="[para(26249(a,1),33057(a,1,2,2,2,2,2)),rewrite([9899(7,R),24613(5),24613(13)])].">
      <j1 rule="para" parents="26249 33057"/>
      <j2 rule="rewrite" parents="9899 24613 24613"/>
    </justification>
  </clause>

  <clause id="36796">
    <literal><![CDATA[
      f(x,f(f(y,f(c_0,f(x,z))),f(f(x,z),f(f(x,z),f(y,f(x,y)))))) = f(y,f(c_0,f(x,z)))
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(32448(a,1),35994(a,1,1)),rewrite([24613(4),9899(11,R),24613(9),10913(9),9899(12,R),24613(10),10913(10),9899(14,R),24613(12),10913(12),543(9),24613(7),24613(16)])].">
      <j1 rule="para" parents="32448 35994"/>
      <j2 rule="rewrite" parents="24613 9899 24613 10913 9899 24613 10913 9899 24613 10913 543 24613 24613"/>
    </justification>
  </clause>

  <clause id="37135">
    <literal><![CDATA[
      f(x,f(f(x,y),f(y,z))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(33760(a,1),26407(a,1,2)),rewrite([24613(4)])].">
      <j1 rule="para" parents="33760 26407"/>
      <j2 rule="rewrite" parents="24613"/>
    </justification>
  </clause>

  <clause id="37351">
    <literal><![CDATA[
      f(x,f(y,f(x,f(z,y)))) = f(x,f(z,y))
    ]]></literal>
    <justification jstring="[para(11(a,1),37135(a,1,2,2)),rewrite([24613(3)])].">
      <j1 rule="para" parents="11 37135"/>
      <j2 rule="rewrite" parents="24613"/>
    </justification>
  </clause>

  <clause id="37352">
    <literal><![CDATA[
      f(x,f(y,f(x,f(y,z)))) = f(x,f(y,z))
    ]]></literal>
    <justification jstring="[para(15153(a,1),37135(a,1,2,2)),rewrite([24613(3)])].">
      <j1 rule="para" parents="15153 37135"/>
      <j2 rule="rewrite" parents="24613"/>
    </justification>
  </clause>

  <clause id="37556">
    <literal><![CDATA[
      f(x,f(f(x,y),f(z,f(c_0,f(y,u))))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(32448(a,1),37351(a,1,2,2,2)),rewrite([24613(6),32448(13)])].">
      <j1 rule="para" parents="32448 37351"/>
      <j2 rule="rewrite" parents="24613 32448"/>
    </justification>
  </clause>

  <clause id="37558">
    <literal><![CDATA[
      f(x,f(f(x,y),f(z,f(c_0,f(u,y))))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(32800(a,1),37351(a,1,2,2,2)),rewrite([24613(6),32800(13)])].">
      <j1 rule="para" parents="32800 37351"/>
      <j2 rule="rewrite" parents="24613 32800"/>
    </justification>
  </clause>

  <clause id="37572">
    <literal><![CDATA[
      f(x,f(y,f(x,f(x,f(y,y))))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(33384(a,1),37351(a,1,2)),flip(a)].">
      <j1 rule="para" parents="33384 37351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37904">
    <literal><![CDATA[
      f(x,f(y,f(y,f(x,x)))) = f(x,f(y,y))
    ]]></literal>
    <justification jstring="[para(37572(a,1),37352(a,1,2)),flip(a)].">
      <j1 rule="para" parents="37572 37352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38050">
    <literal><![CDATA[
      f(f(x,x),f(y,f(x,y))) = f(f(x,x),f(y,y))
    ]]></literal>
    <justification jstring="[para(11(a,1),37904(a,1,2,2,2)),rewrite([24613(2)])].">
      <j1 rule="para" parents="11 37904"/>
      <j2 rule="rewrite" parents="24613"/>
    </justification>
  </clause>

  <clause id="38056">
    <literal><![CDATA[
      f(x,f(f(x,y),f(f(x,f(z,z)),f(z,f(z,f(x,x)))))) = f(x,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(37904(a,1),26415(a,1,2,2,2)),rewrite([24613(7)])].">
      <j1 rule="para" parents="37904 26415"/>
      <j2 rule="rewrite" parents="24613"/>
    </justification>
  </clause>

  <clause id="38238">
    <literal><![CDATA[
      f(f(x,y),f(y,f(f(z,f(z,f(c_0,f(x,y)))),f(f(x,y),f(z,z))))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(11(a,1),38056(a,1,2,1)),rewrite([9899(7,R),24613(7),24613(10),11(15)])].">
      <j1 rule="para" parents="11 38056"/>
      <j2 rule="rewrite" parents="9899 24613 24613 11"/>
    </justification>
  </clause>

  <clause id="38300">
    <literal><![CDATA[
      f(f(x,y),f(y,f(f(z,f(x,y)),f(f(z,z),f(f(z,z),f(c_0,f(x,y))))))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(11(a,1),38238(a,1,2,2,2,2)),rewrite([24613(10),24613(11)])].">
      <j1 rule="para" parents="11 38238"/>
      <j2 rule="rewrite" parents="24613 24613"/>
    </justification>
  </clause>

  <clause id="39697">
    <literal><![CDATA[
      f(f(x,y),f(x,f(c_0,f(y,z)))) = f(c_0,f(x,y))
    ]]></literal>
    <justification jstring="[para(37556(a,1),37352(a,1,2)),rewrite([9899(3,R),24613(3)]),flip(a)].">
      <j1 rule="para" parents="37556 37352"/>
      <j2 rule="rewrite" parents="9899 24613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40466">
    <literal><![CDATA[
      f(x,f(x,f(y,f(c_0,f(z,x))))) = f(y,f(c_0,f(z,x)))
    ]]></literal>
    <justification jstring="[para(37558(a,1),15203(a,1,2)),rewrite([24613(5),24613(10),32902(10),24613(5)])].">
      <j1 rule="para" parents="37558 15203"/>
      <j2 rule="rewrite" parents="24613 24613 32902 24613"/>
    </justification>
  </clause>

  <clause id="40645">
    <literal><![CDATA[
      f(f(x,f(x,y)),f(y,y)) = f(f(x,x),f(y,y))
    ]]></literal>
    <justification jstring="[para(38050(a,1),24613(a,2)),rewrite([24613(1),24613(7)])].">
      <j1 rule="para" parents="38050 24613"/>
      <j2 rule="rewrite" parents="24613 24613"/>
    </justification>
  </clause>

  <clause id="40654">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),f(c_0,f(y,f(z,f(c_0,f(x,y)))))) = f(f(c_0,f(x,y)),f(z,f(c_0,f(x,y))))
    ]]></literal>
    <justification jstring="[para(26396(a,1),38050(a,1,2,2)),rewrite([9899(3,R),24613(3),24613(9),40466(9),9899(11,R),24613(11),9899(22,R),24613(18)]),flip(a)].">
      <j1 rule="para" parents="26396 38050"/>
      <j2 rule="rewrite" parents="9899 24613 24613 40466 9899 24613 9899 24613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41403">
    <literal><![CDATA[
      f(f(x,y),f(y,f(z,f(x,x)))) = f(c_0,f(y,f(z,f(x,x))))
    ]]></literal>
    <justification jstring="[para(32519(a,1),39697(a,1,2)),rewrite([24613(3),24613(4),24613(5),24613(9)])].">
      <j1 rule="para" parents="32519 39697"/>
      <j2 rule="rewrite" parents="24613 24613 24613 24613"/>
    </justification>
  </clause>

  <clause id="41777">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),f(f(z,z),f(x,x))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(40645(a,1),32317(a,1,1)),rewrite([24613(7)])].">
      <j1 rule="para" parents="40645 32317"/>
      <j2 rule="rewrite" parents="24613"/>
    </justification>
  </clause>

  <clause id="41819">
    <literal><![CDATA[
      f(f(x,f(x,y)),f(c_0,f(f(x,y),f(y,z)))) = f(f(x,x),f(c_0,f(f(x,y),f(y,z))))
    ]]></literal>
    <justification jstring="[para(37135(a,1),40645(a,1,1,2)),rewrite([9899(9,R),24613(7),9899(16,R),24613(14)])].">
      <j1 rule="para" parents="37135 40645"/>
      <j2 rule="rewrite" parents="9899 24613 9899 24613"/>
    </justification>
  </clause>

  <clause id="42729">
    <literal><![CDATA[
      f(f(c_0,f(x,f(c_0,f(y,z)))),f(c_0,f(f(c_0,f(x,u)),f(c_0,f(y,z))))) = f(f(c_0,f(x,u)),f(c_0,f(y,z)))
    ]]></literal>
    <justification jstring="[para(32456(a,1),27179(a,1,2,2,2)),rewrite([24613(14),24613(16)])].">
      <j1 rule="para" parents="32456 27179"/>
      <j2 rule="rewrite" parents="24613 24613"/>
    </justification>
  </clause>

  <clause id="42739">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),f(c_0,f(y,z))) = f(x,f(c_0,f(y,z)))
    ]]></literal>
    <justification jstring="[para(39697(a,1),27179(a,1,2,2,2)),rewrite([24613(14),42729(16)])].">
      <j1 rule="para" parents="39697 27179"/>
      <j2 rule="rewrite" parents="24613 42729"/>
    </justification>
  </clause>

  <clause id="42744">
    <literal><![CDATA[
      f(x,f(c_0,f(y,f(z,f(x,y))))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(27179(a,1),41777(a,1,1,2)),rewrite([9899(11,R),24613(9),10913(9),24613(6),26248(7),42739(10)]),flip(a)].">
      <j1 rule="para" parents="27179 41777"/>
      <j2 rule="rewrite" parents="9899 24613 10913 24613 26248 42739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42764">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),f(z,f(c_0,f(x,y)))) = f(x,f(c_0,f(y,f(z,f(c_0,f(x,y))))))
    ]]></literal>
    <justification jstring="[back_rewrite(40654),rewrite([42739(11)]),flip(a)].">
      <j1 rule="back_rewrite" parents="40654"/>
      <j2 rule="rewrite" parents="42739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43126">
    <literal><![CDATA[
      f(x,f(c_0,f(y,f(z,f(y,x))))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(42744(a,1),24613(a,2)),rewrite([24613(2),24613(6),24613(7)])].">
      <j1 rule="para" parents="42744 24613"/>
      <j2 rule="rewrite" parents="24613 24613 24613"/>
    </justification>
  </clause>

  <clause id="43151">
    <literal><![CDATA[
      f(f(x,x),f(c_0,f(f(x,y),f(z,u)))) = f(f(x,x),f(z,u))
    ]]></literal>
    <justification jstring="[para(32225(a,1),42744(a,1,2,2,2)),rewrite([24613(5)])].">
      <j1 rule="para" parents="32225 42744"/>
      <j2 rule="rewrite" parents="24613"/>
    </justification>
  </clause>

  <clause id="43256">
    <literal><![CDATA[
      f(f(x,f(x,y)),f(c_0,f(f(x,y),f(y,z)))) = f(f(x,x),f(y,z))
    ]]></literal>
    <justification jstring="[back_rewrite(41819),rewrite([43151(15)])].">
      <j1 rule="back_rewrite" parents="41819"/>
      <j2 rule="rewrite" parents="43151"/>
    </justification>
  </clause>

  <clause id="43337">
    <literal><![CDATA[
      f(x,f(c_0,f(y,z))) = f(z,f(c_0,f(x,y)))
    ]]></literal>
    <justification jstring="[para(32800(a,1),43126(a,1,2,2,2)),rewrite([24613(5),42739(7)])].">
      <j1 rule="para" parents="32800 43126"/>
      <j2 rule="rewrite" parents="24613 42739"/>
    </justification>
  </clause>

  <clause id="43343">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),f(f(x,z),f(x,u))) = f(y,f(f(x,z),f(x,u)))
    ]]></literal>
    <justification jstring="[para(33032(a,1),43126(a,1,2,2,2)),rewrite([24613(5),24613(7)])].">
      <j1 rule="para" parents="33032 43126"/>
      <j2 rule="rewrite" parents="24613 24613"/>
    </justification>
  </clause>

  <clause id="43450">
    <literal><![CDATA[
      f(f(x,x),f(c_0,f(y,f(x,z)))) = f(y,f(x,x))
    ]]></literal>
    <justification jstring="[para(11(a,1),43337(a,1,2,2)),rewrite([24613(2),9899(2),24613(5)]),flip(a)].">
      <j1 rule="para" parents="11 43337"/>
      <j2 rule="rewrite" parents="24613 9899 24613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43465">
    <literal><![CDATA[
      f(f(x,y),f(c_0,f(z,f(y,f(x,y))))) = f(z,f(y,y))
    ]]></literal>
    <justification jstring="[para(15203(a,1),43337(a,2,2,2)),rewrite([24613(5),24613(9),9899(9)])].">
      <j1 rule="para" parents="15203 43337"/>
      <j2 rule="rewrite" parents="24613 24613 9899"/>
    </justification>
  </clause>

  <clause id="43484">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),f(x,f(c_0,f(y,f(z,f(c_0,f(x,y))))))) = f(y,f(c_0,f(x,z)))
    ]]></literal>
    <justification jstring="[para(43337(a,1),26180(a,2)),rewrite([42764(11),24613(14)])].">
      <j1 rule="para" parents="43337 26180"/>
      <j2 rule="rewrite" parents="42764 24613"/>
    </justification>
  </clause>

  <clause id="43796">
    <literal><![CDATA[
      f(f(x,f(y,f(x,y))),f(f(x,f(y,y)),f(z,f(z,f(x,y))))) = c_0
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(43337(a,2),29596(a,1,2,2)),rewrite([24613(1),24613(4),24613(8),24613(10),24613(11),15203(11),24613(8),9899(8),24613(9)])].">
      <j1 rule="para" parents="43337 29596"/>
      <j2 rule="rewrite" parents="24613 24613 24613 24613 24613 15203 24613 9899 24613"/>
    </justification>
  </clause>

  <clause id="43989">
    <literal><![CDATA[
      f(f(x,y),f(y,f(f(z,f(x,y)),f(f(z,z),f(y,f(c_0,f(x,f(z,z)))))))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(43337(a,1),38300(a,1,2,2,2,2)),rewrite([24613(7)])].">
      <j1 rule="para" parents="43337 38300"/>
      <j2 rule="rewrite" parents="24613"/>
    </justification>
  </clause>

  <clause id="44134">
    <literal><![CDATA[
      f(c_0,f(f(x,y),f(x,f(c_0,f(z,u))))) = f(x,f(f(x,y),f(z,f(c_0,f(x,u)))))
    ]]></literal>
    <justification jstring="[para(43337(a,2),27135(a,2,2,1)),rewrite([24613(7),24613(10),24613(14)])].">
      <j1 rule="para" parents="43337 27135"/>
      <j2 rule="rewrite" parents="24613 24613 24613"/>
    </justification>
  </clause>

  <clause id="45033">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),f(c_0,f(z,u))) = f(y,f(c_0,f(x,f(c_0,f(z,u)))))
    ]]></literal>
    <justification jstring="[para(25327(a,1),32415(a,1,1,2,2,2)),rewrite([9899(6),9222(6),24613(6),9899(15,R),24613(12),25327(43),24613(19),24613(20),42764(20),43484(21),24613(7),9899(16,R),24613(13)])].">
      <j1 rule="para" parents="25327 32415"/>
      <j2 rule="rewrite" parents="9899 9222 24613 9899 24613 25327 24613 24613 42764 43484 24613 9899 24613"/>
    </justification>
  </clause>

  <clause id="45042">
    <literal><![CDATA[
      f(x,f(c_0,f(y,f(c_0,f(z,f(y,x)))))) = c_0
    ]]></literal>
    <justification jstring="[para(26644(a,1),25327(a,1,2,2,2,2,2,2,2)),rewrite([10913(6),10913(9),24613(13),45033(13),10913(19),24613(21),10913(21),36523(20),26180(10),45033(8)])].">
      <j1 rule="para" parents="26644 25327"/>
      <j2 rule="rewrite" parents="10913 10913 24613 45033 10913 24613 10913 36523 26180 45033"/>
    </justification>
  </clause>

  <clause id="45439">
    <literal><![CDATA[
      f(f(f(x,y),f(z,f(z,f(x,f(y,y))))),f(x,f(f(y,y),f(x,f(y,y))))) = c_0
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(11(a,1),43796(a,1,2,1,2)),rewrite([24613(12)])].">
      <j1 rule="para" parents="11 43796"/>
      <j2 rule="rewrite" parents="24613"/>
    </justification>
  </clause>

  <clause id="46110">
    <literal><![CDATA[
      f(x,f(c_0,f(y,f(y,f(f(x,y),f(y,z)))))) = c_0
    ]]></literal>
    <justification jstring="[para(27135(a,1),45042(a,1,2,2,2)),rewrite([24613(3),24613(4)])].">
      <j1 rule="para" parents="27135 45042"/>
      <j2 rule="rewrite" parents="24613 24613"/>
    </justification>
  </clause>

  <clause id="47073">
    <literal><![CDATA[
      f(f(f(x,y),f(y,z)),f(f(x,f(x,y)),f(y,f(y,f(f(x,y),f(y,z)))))) = c_0
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(46110(a,1),32575(a,1,2,2)),rewrite([7716(14),24613(14),30846(14),24613(12),46110(20)])].">
      <j1 rule="para" parents="46110 32575"/>
      <j2 rule="rewrite" parents="7716 24613 30846 24613 46110"/>
    </justification>
  </clause>

  <clause id="47159">
    <literal><![CDATA[
      f(f(f(x,f(x,y)),f(y,z)),f(f(y,y),f(f(x,x),f(y,y)))) = f(y,z)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(28208(a,1),43989(a,1,2,2,1)),rewrite([40645(13),32801(14),32319(13)])].">
      <j1 rule="para" parents="28208 43989"/>
      <j2 rule="rewrite" parents="40645 32801 32319"/>
    </justification>
  </clause>

  <clause id="47189">
    <literal><![CDATA[
      f(f(x,f(y,f(y,f(z,x)))),f(z,f(c_0,f(x,f(f(y,y),f(c_0,f(z,x))))))) = x
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(11(a,1),47159(a,1,1,2)),rewrite([24613(4),9899(7,R),24613(7),9899(11,R),24613(11),42764(13),11(17)])].">
      <j1 rule="para" parents="11 47159"/>
      <j2 rule="rewrite" parents="24613 9899 24613 9899 24613 42764 11"/>
    </justification>
  </clause>

  <clause id="47311">
    <literal><![CDATA[
      f(c_0,f(x,f(f(x,y),f(z,f(c_0,f(x,u)))))) = f(f(x,y),f(z,f(c_0,f(x,u))))
    ]]></literal>
    <justification jstring="[para(36796(a,1),27357(a,1,2,2,1)),rewrite([24613(7),36796(21),24613(15)])].">
      <j1 rule="para" parents="36796 27357"/>
      <j2 rule="rewrite" parents="24613 36796 24613"/>
    </justification>
  </clause>

  <clause id="50135">
    <literal><![CDATA[
      f(f(x,x),f(y,f(z,f(z,f(x,y))))) = f(f(x,x),f(y,y))
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(47189(a,1),43450(a,1,2,2)),rewrite([24613(3),9899(3),24613(9)]),flip(a)].">
      <j1 rule="para" parents="47189 43450"/>
      <j2 rule="rewrite" parents="24613 9899 24613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="51127">
    <literal><![CDATA[
      f(f(x,y),f(x,f(y,y))) = f(c_0,f(x,f(y,f(x,y))))
    ]]></literal>
    <justification jstring="[para(26178(a,1),25800(a,1,2,2,2,2,2,2)),rewrite([26178(7),24613(7),9849(7),24613(5),43465(8),26178(9),26178(12),24613(9),9849(9),24613(7)])].">
      <j1 rule="para" parents="26178 25800"/>
      <j2 rule="rewrite" parents="26178 24613 9849 24613 43465 26178 26178 24613 9849 24613"/>
    </justification>
  </clause>

  <clause id="51128">
    <literal><![CDATA[
      f(c_0,f(x,f(f(y,y),f(x,f(y,y))))) = f(c_0,f(x,f(y,f(x,y))))
    ]]></literal>
    <justification jstring="[para(24727(a,1),25800(a,1,2,2,2,2,2,2)),rewrite([10812(9),9899(9),24613(9),43465(12),9899(5,R),24613(5),9849(5),24613(4),51127(4),10812(10),24613(13),24727(14),9899(10),24613(10)]),flip(a)].">
      <j1 rule="para" parents="24727 25800"/>
      <j2 rule="rewrite" parents="10812 9899 24613 43465 9899 24613 9849 24613 51127 10812 24613 24727 9899 24613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="51174">
    <literal><![CDATA[
      f(f(x,f(y,f(y,f(x,z)))),f(z,z)) = f(f(x,x),f(z,z))
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(50135(a,1),24613(a,2)),rewrite([24613(1),24613(9)])].">
      <j1 rule="para" parents="50135 24613"/>
      <j2 rule="rewrite" parents="24613 24613"/>
    </justification>
  </clause>

  <clause id="51422">
    <literal><![CDATA[
      f(x,f(f(y,y),f(x,f(y,y)))) = f(x,f(y,f(x,y)))
    ]]></literal>
    <justification jstring="[para(45439(a,1),33573(a,1,1)),rewrite([24613(13),45439(25),24613(21),18622(23),24613(8),51128(8),10913(7)]),flip(a)].">
      <j1 rule="para" parents="45439 33573"/>
      <j2 rule="rewrite" parents="24613 45439 24613 18622 24613 51128 10913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="51542">
    <literal><![CDATA[
      f(f(f(x,x),f(y,z)),f(c_0,f(y,f(y,f(f(x,y),f(y,z)))))) = c_0
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(47073(a,1),51174(a,1,1,2,2)),rewrite([24613(7),43256(8),9899(14,R),24613(10),9899(16,R),24613(15),9899(26,R),24613(22),45033(23),46110(21),9870(16)])].">
      <j1 rule="para" parents="47073 51174"/>
      <j2 rule="rewrite" parents="24613 43256 9899 24613 9899 24613 9899 24613 45033 46110 9870"/>
    </justification>
  </clause>

  <clause id="52270">
    <literal><![CDATA[
      f(f(x,f(y,z)),f(c_0,f(y,f(y,f(f(y,z),f(y,f(x,x))))))) = c_0
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(11(a,1),51542(a,1,1,1)),rewrite([24613(5),24613(7)])].">
      <j1 rule="para" parents="11 51542"/>
      <j2 rule="rewrite" parents="24613 24613"/>
    </justification>
  </clause>

  <clause id="52514">
    <literal><![CDATA[
      f(f(c_0,f(x,f(y,f(x,z)))),f(x,f(f(x,z),f(x,f(y,y))))) = c_0
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(52270(a,1),43337(a,1)),rewrite([24613(10),24613(12)]),flip(a)].">
      <j1 rule="para" parents="52270 43337"/>
      <j2 rule="rewrite" parents="24613 24613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="61357">
    <literal><![CDATA[
      f(c_0,f(f(x,y),f(x,f(z,z)))) = f(x,f(z,f(x,y)))
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(52514(a,1),51422(a,2,2,2)),rewrite([9899(16,R),24613(12),27357(12),9899(25,R),24613(21),27357(21),43343(19),41403(16),18622(16),24613(7),10913(7),24613(15),27357(15),43343(13),41403(10)]),flip(a)].">
      <j1 rule="para" parents="52514 51422"/>
      <j2 rule="rewrite" parents="9899 24613 27357 9899 24613 27357 43343 41403 18622 24613 10913 24613 27357 43343 41403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="61724">
    <literal><![CDATA[
      f(x,f(f(x,y),f(x,f(z,z)))) = f(x,f(z,f(x,y)))
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(61357(a,2),10791(a,1,2,2)),rewrite([10913(8)])].">
      <j1 rule="para" parents="61357 10791"/>
      <j2 rule="rewrite" parents="10913"/>
    </justification>
  </clause>

  <clause id="61763">
    <literal><![CDATA[
      f(c_0,f(f(x,y),f(x,f(c_0,f(z,u))))) = f(x,f(f(x,y),f(z,u)))
    ]]></literal>
    <justification jstring="[para(33474(a,1),61357(a,1,2,2,2)),rewrite([9899(5,R),24613(5),9899(11,R),24613(11),9899(14,R),24613(14),24613(16),18622(16),24613(13),10913(13),24613(11)])].">
      <j1 rule="para" parents="33474 61357"/>
      <j2 rule="rewrite" parents="9899 24613 9899 24613 9899 24613 24613 18622 24613 10913 24613"/>
    </justification>
  </clause>

  <clause id="61888">
    <literal><![CDATA[
      f(x,f(f(x,y),f(z,f(c_0,f(x,u))))) = f(x,f(f(x,y),f(z,u)))
    ]]></literal>
    <justification jstring="[back_rewrite(44134),rewrite([61763(8)]),flip(a)].">
      <j1 rule="back_rewrite" parents="44134"/>
      <j2 rule="rewrite" parents="61763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="61899">
    <literal><![CDATA[
      f(f(x,y),f(z,f(c_0,f(x,u)))) = f(c_0,f(x,f(f(x,y),f(z,u))))
    ]]></literal>
    <justification jstring="[back_rewrite(47311),rewrite([61888(8)]),flip(a)].">
      <j1 rule="back_rewrite" parents="47311"/>
      <j2 rule="rewrite" parents="61888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="63019">
    <literal><![CDATA[
      f(x,f(y,f(x,f(z,z)))) = f(x,f(z,f(x,f(y,y))))
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(43450(a,2),61724(a,1,2,1)),rewrite([24613(9),61899(9),543(6),24613(4),10791(7)])].">
      <j1 rule="para" parents="43450 61724"/>
      <j2 rule="rewrite" parents="24613 61899 543 24613 10791"/>
    </justification>
  </clause>

  <clause id="63020">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer(MOD_SS)
    ]]></attribute>
    <justification jstring="[resolve(63019,a,3,a)].">
      <j1 rule="resolve" parents="63019 3"/>
    </justification>
  </clause>

</proof>

</proofs>
