<?xml version="1.0" encoding="ISO-8859-1"?>

<!DOCTYPE proofs SYSTEM "proof3.dtd">

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

<proofs number_of_proofs="1">

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

<heading><![CDATA[
Prover9 (32) version November-2006, November 2006.
Process 4443 was started by mccune on cleo.thornwood,
Wed Nov 22 12:05:38 2006
The command was "/home/mccune/bin/prover9 -f MOL-A.in MOL-A-interp.outx".
]]></heading>

<proof number="1" length="315" max_count="59">

<comments><![CDATA[
% Proof 1 at 40.89 (+ 0.12) seconds: A_SS.
% Length of proof is 315.
% Level of proof is 59.
% Maximum clause weight is 59.
% Given clauses 590.
]]></comments>

  <clause id="1" type="goal">
    <literal><![CDATA[
      f(x,f(f(y,z),f(y,z))) = f(y,f(f(x,z),f(x,z)))
    ]]></literal>
    <attribute><![CDATA[
      answer(A_SS)
    ]]></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(f(c2,c3),f(c2,c3))) != f(c2,f(f(c1,c3),f(c1,c3)))
    ]]></literal>
    <attribute><![CDATA[
      answer(A_SS)
    ]]></attribute>
    <justification jstring="[deny(1)].">
      <j1 rule="deny" parents="1"/>
    </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)),v),f(f(f(f(x,v),v),f(z,x)),f(f(z,x),w)))) = 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),f(f(f(f(f(y,x),z),z),y),f(f(f(y,y),u),f(f(f(f(f(y,v),u),u),y),f(y,w)))))) = 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="12">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),z),y)) = y
    ]]></literal>
    <justification jstring="[para(2(a,1),8(a,1,2,2))].">
      <j1 rule="para" parents="2 8"/>
    </justification>
  </clause>

  <clause id="20">
    <literal><![CDATA[
      f(f(x,y),f(y,y)) = y
    ]]></literal>
    <justification jstring="[para(2(a,1),12(a,1,2,1))].">
      <j1 rule="para" parents="2 12"/>
    </justification>
  </clause>

  <clause id="37">
    <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(20(a,1),2(a,1,2,1))].">
      <j1 rule="para" parents="20 2"/>
    </justification>
  </clause>

  <clause id="38">
    <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)),f(f(y,x),u)))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(20(a,1),2(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="20 2"/>
    </justification>
  </clause>

  <clause id="39">
    <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(20(a,1),2(a,1,2,2,1,1,1))].">
      <j1 rule="para" parents="20 2"/>
    </justification>
  </clause>

  <clause id="40">
    <literal><![CDATA[
      f(f(x,f(y,y)),f(f(y,y),f(y,f(f(y,y),z)))) = f(y,y)
    ]]></literal>
    <justification jstring="[para(20(a,1),2(a,1,2,2,1)),rewrite(20(5))].">
      <j1 rule="para" parents="20 2"/>
      <j2 rule="rewrite" parents="20"/>
    </justification>
  </clause>

  <clause id="45">
    <literal><![CDATA[
      f(f(x,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)),z))) = f(y,z)
    ]]></literal>
    <justification jstring="[para(20(a,1),7(a,1,2,2,1,1,1))].">
      <j1 rule="para" parents="20 7"/>
    </justification>
  </clause>

  <clause id="46">
    <literal><![CDATA[
      f(f(x,f(y,y)),y) = f(y,y)
    ]]></literal>
    <justification jstring="[para(20(a,1),7(a,1,2,2,1)),rewrite(20(5),20(5))].">
      <j1 rule="para" parents="20 7"/>
      <j2 rule="rewrite" parents="20 20"/>
    </justification>
  </clause>

  <clause id="55">
    <literal><![CDATA[
      f(f(f(x,x),y),x) = f(x,x)
    ]]></literal>
    <justification jstring="[para(12(a,1),20(a,1,1)),rewrite(12(7)),flip(a)].">
      <j1 rule="para" parents="12 20"/>
      <j2 rule="rewrite" parents="12"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="57">
    <literal><![CDATA[
      f(f(x,y),f(y,f(f(y,y),f(y,z)))) = y
    ]]></literal>
    <justification jstring="[back_rewrite(37),rewrite(46(7))].">
      <j1 rule="back_rewrite" parents="37"/>
      <j2 rule="rewrite" parents="46"/>
    </justification>
  </clause>

  <clause id="60">
    <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(46(a,1),2(a,1,2,2,1,1,1))].">
      <j1 rule="para" parents="46 2"/>
    </justification>
  </clause>

  <clause id="62">
    <literal><![CDATA[
      f(f(x,f(y,f(x,x))),f(f(f(f(y,f(x,x)),f(y,f(x,x))),z),f(f(f(f(f(x,x),z),z),f(y,f(x,x))),f(x,x)))) = f(y,f(x,x))
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(46(a,1),7(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="46 7"/>
    </justification>
  </clause>

  <clause id="68">
    <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(55(a,1),2(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="55 2"/>
    </justification>
  </clause>

  <clause id="69">
    <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(55(a,1),2(a,1,2,2,1,1))].">
      <j1 rule="para" parents="55 2"/>
    </justification>
  </clause>

  <clause id="77">
    <literal><![CDATA[
      f(f(x,y),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(20(a,1),55(a,1,1,1)),rewrite(20(6))].">
      <j1 rule="para" parents="20 55"/>
      <j2 rule="rewrite" parents="20"/>
    </justification>
  </clause>

  <clause id="80">
    <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>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(77(a,1),2(a,1,2,2,1,1))].">
      <j1 rule="para" parents="77 2"/>
    </justification>
  </clause>

  <clause id="82">
    <literal><![CDATA[
      f(x,f(f(y,x),f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(2(a,1),77(a,1,1))].">
      <j1 rule="para" parents="2 77"/>
    </justification>
  </clause>

  <clause id="84">
    <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>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(77(a,1),7(a,1,2,2,1,1))].">
      <j1 rule="para" parents="77 7"/>
    </justification>
  </clause>

  <clause id="91">
    <literal><![CDATA[
      f(x,f(f(x,y),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(77(a,1),77(a,1,1))].">
      <j1 rule="para" parents="77 77"/>
    </justification>
  </clause>

  <clause id="96">
    <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(82(a,1),2(a,1,2,2,2))].">
      <j1 rule="para" parents="82 2"/>
    </justification>
  </clause>

  <clause id="97">
    <literal><![CDATA[
      f(f(f(f(x,x),y),f(f(f(f(f(x,z),y),y),x),f(x,u))),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(2(a,1),82(a,1,2,1)),rewrite(2(20),2(22))].">
      <j1 rule="para" parents="2 82"/>
      <j2 rule="rewrite" parents="2 2"/>
    </justification>
  </clause>

  <clause id="119">
    <literal><![CDATA[
      f(f(f(x,x),x),f(f(x,f(x,x)),f(f(x,x),f(x,y)))) = x
    ]]></literal>
    <justification jstring="[para(46(a,1),80(a,1,2,2,1)),rewrite(82(9))].">
      <j1 rule="para" parents="46 80"/>
      <j2 rule="rewrite" parents="82"/>
    </justification>
  </clause>

  <clause id="124">
    <literal><![CDATA[
      f(f(f(x,x),f(x,y)),f(f(f(f(x,y),f(x,y)),f(x,x)),f(f(x,f(x,y)),f(f(x,y),z)))) = f(x,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(77(a,1),80(a,1,2,1,2,1)),rewrite(77(9),77(11))].">
      <j1 rule="para" parents="77 80"/>
      <j2 rule="rewrite" parents="77 77"/>
    </justification>
  </clause>

  <clause id="125">
    <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)),y))) = f(y,z)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(77(a,1),80(a,1,2,2,2))].">
      <j1 rule="para" parents="77 80"/>
    </justification>
  </clause>

  <clause id="127">
    <literal><![CDATA[
      f(f(f(f(x,y),f(x,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>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(82(a,1),80(a,1,2,1,2,1)),rewrite(82(10),82(13))].">
      <j1 rule="para" parents="82 80"/>
      <j2 rule="rewrite" parents="82 82"/>
    </justification>
  </clause>

  <clause id="128">
    <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(z,y)))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(82(a,1),80(a,1,2,2,2))].">
      <j1 rule="para" parents="82 80"/>
    </justification>
  </clause>

  <clause id="137">
    <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)),f(z,f(y,x))))) = f(y,x)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(20(a,1),128(a,1,2,1,2,1)),rewrite(20(9),20(11))].">
      <j1 rule="para" parents="20 128"/>
      <j2 rule="rewrite" parents="20 20"/>
    </justification>
  </clause>

  <clause id="138">
    <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(20(a,1),128(a,1,2,1,2))].">
      <j1 rule="para" parents="20 128"/>
    </justification>
  </clause>

  <clause id="146">
    <literal><![CDATA[
      f(f(f(x,x),f(x,y)),f(f(f(f(x,y),f(x,y)),f(x,x)),f(f(x,f(x,y)),f(z,f(x,y))))) = f(x,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(77(a,1),128(a,1,2,1,2,1)),rewrite(77(9),77(11))].">
      <j1 rule="para" parents="77 128"/>
      <j2 rule="rewrite" parents="77 77"/>
    </justification>
  </clause>

  <clause id="148">
    <literal><![CDATA[
      f(f(f(f(x,y),f(x,y)),y),f(f(f(y,y),f(f(x,y),f(x,y))),f(f(f(x,y),y),f(z,y)))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(82(a,1),128(a,1,2,1,2,1)),rewrite(82(10),82(13))].">
      <j1 rule="para" parents="82 128"/>
      <j2 rule="rewrite" parents="82 82"/>
    </justification>
  </clause>

  <clause id="169">
    <literal><![CDATA[
      f(f(f(f(x,y),f(x,y)),x),f(f(f(x,x),f(f(x,y),f(x,y))),f(f(f(x,y),x),f(z,x)))) = x
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(91(a,1),128(a,1,2,1,2,1)),rewrite(91(10),91(13))].">
      <j1 rule="para" parents="91 128"/>
      <j2 rule="rewrite" parents="91 91"/>
    </justification>
  </clause>

  <clause id="180">
    <literal><![CDATA[
      f(x,f(f(x,x),f(x,f(f(x,x),y)))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(20(a,1),57(a,1,1)),rewrite(77(4))].">
      <j1 rule="para" parents="20 57"/>
      <j2 rule="rewrite" parents="77"/>
    </justification>
  </clause>

  <clause id="181">
    <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(57(a,1),55(a,1)),flip(a)].">
      <j1 rule="para" parents="57 55"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="184">
    <literal><![CDATA[
      f(f(x,y),f(y,f(f(y,y),f(z,y)))) = y
    ]]></literal>
    <justification jstring="[para(82(a,1),57(a,1,2,2,2))].">
      <j1 rule="para" parents="82 57"/>
    </justification>
  </clause>

  <clause id="207">
    <literal><![CDATA[
      f(f(x,f(f(x,x),f(y,x))),f(x,f(f(x,x),f(y,x)))) = x
    ]]></literal>
    <justification jstring="[para(184(a,1),55(a,1)),flip(a)].">
      <j1 rule="para" parents="184 55"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="237">
    <literal><![CDATA[
      f(f(f(f(x,f(y,y)),f(x,f(y,y))),f(y,y)),f(f(y,f(f(x,f(y,y)),f(x,f(y,y)))),f(f(f(x,f(y,y)),f(y,y)),f(f(y,y),z)))) = f(y,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(20(a,1),127(a,1,2,1,1))].">
      <j1 rule="para" parents="20 127"/>
    </justification>
  </clause>

  <clause id="245">
    <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(20(a,1),148(a,1,1,1,1)),rewrite(20(3),77(3),77(3),20(3),20(3),20(5))].">
      <j1 rule="para" parents="20 148"/>
      <j2 rule="rewrite" parents="20 77 77 20 20 20"/>
    </justification>
  </clause>

  <clause id="246">
    <literal><![CDATA[
      f(f(f(f(x,f(y,y)),f(x,f(y,y))),f(y,y)),f(f(y,f(f(x,f(y,y)),f(x,f(y,y)))),f(f(f(x,f(y,y)),f(y,y)),f(z,f(y,y))))) = f(y,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(20(a,1),148(a,1,2,1,1))].">
      <j1 rule="para" parents="20 148"/>
    </justification>
  </clause>

  <clause id="257">
    <literal><![CDATA[
      f(f(f(f(f(x,x),y),f(f(x,x),y)),f(x,x)),f(f(x,f(f(f(x,x),y),f(f(x,x),y))),f(f(f(f(x,x),y),f(x,x)),f(z,f(x,x))))) = f(x,x)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(20(a,1),169(a,1,2,1,1))].">
      <j1 rule="para" parents="20 169"/>
    </justification>
  </clause>

  <clause id="270">
    <literal><![CDATA[
      f(f(f(x,x),f(x,f(f(x,x),y))),f(f(x,x),f(x,f(f(x,x),y)))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(40(a,1),55(a,1)),flip(a)].">
      <j1 rule="para" parents="40 55"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="287">
    <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(69(a,1),82(a,1,2,1)),rewrite(69(16),69(18))].">
      <j1 rule="para" parents="69 82"/>
      <j2 rule="rewrite" parents="69 69"/>
    </justification>
  </clause>

  <clause id="300">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),f(f(x,x),f(x,y))),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(119(a,1),82(a,1,2,1)),rewrite(119(15),119(17))].">
      <j1 rule="para" parents="119 82"/>
      <j2 rule="rewrite" parents="119 119"/>
    </justification>
  </clause>

  <clause id="325">
    <literal><![CDATA[
      f(f(f(x,x),f(x,y)),f(f(f(f(x,y),f(x,y)),f(x,x)),f(f(x,f(x,y)),x))) = f(x,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(77(a,1),124(a,1,2,2,2))].">
      <j1 rule="para" parents="77 124"/>
    </justification>
  </clause>

  <clause id="360">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),f(f(x,x),f(y,x))),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(82(a,1),300(a,1,1,2,2))].">
      <j1 rule="para" parents="82 300"/>
    </justification>
  </clause>

  <clause id="414">
    <literal><![CDATA[
      f(x,f(f(x,x),f(x,y))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(57(a,1),360(a,1,1,2,2)),rewrite(181(13),181(14),20(7),181(9)),flip(a)].">
      <j1 rule="para" parents="57 360"/>
      <j2 rule="rewrite" parents="181 181 20 181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="415">
    <literal><![CDATA[
      f(x,f(f(x,x),f(y,x))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(184(a,1),360(a,1,1,2,2)),rewrite(207(13),207(14),20(7),207(9)),flip(a)].">
      <j1 rule="para" parents="184 360"/>
      <j2 rule="rewrite" parents="207 207 20 207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="416">
    <literal><![CDATA[
      f(f(x,x),f(x,f(f(x,x),y))) = x
    ]]></literal>
    <justification jstring="[para(180(a,1),360(a,1,1,2,2)),rewrite(270(16),270(18),77(10),46(8),270(12),77(3)),flip(a)].">
      <j1 rule="para" parents="180 360"/>
      <j2 rule="rewrite" parents="270 270 77 46 270 77"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="429">
    <literal><![CDATA[
      f(f(x,x),f(f(f(f(f(x,x),f(x,y)),f(f(x,x),f(x,y))),x),f(f(f(x,x),f(f(x,x),f(x,y))),f(z,f(f(x,x),f(x,y)))))) = f(f(x,x),f(x,y))
    ]]></literal>
    <justification jstring="[para(414(a,1),128(a,1,1)),rewrite(55(12),55(13),77(11),55(13))].">
      <j1 rule="para" parents="414 128"/>
      <j2 rule="rewrite" parents="55 55 77 55"/>
    </justification>
  </clause>

  <clause id="435">
    <literal><![CDATA[
      f(f(x,x),f(f(f(f(f(x,x),f(x,y)),f(f(x,x),f(x,y))),x),f(f(f(x,x),f(f(x,x),f(x,y))),f(x,y)))) = f(f(x,x),f(x,y))
    ]]></literal>
    <justification jstring="[para(414(a,1),84(a,1,1)),rewrite(55(12),55(13),77(11),55(13))].">
      <j1 rule="para" parents="414 84"/>
      <j2 rule="rewrite" parents="55 55 77 55"/>
    </justification>
  </clause>

  <clause id="442">
    <literal><![CDATA[
      f(f(x,x),f(x,f(y,f(x,x)))) = x
    ]]></literal>
    <justification jstring="[para(20(a,1),415(a,1,2,1)),rewrite(77(8))].">
      <j1 rule="para" parents="20 415"/>
      <j2 rule="rewrite" parents="77"/>
    </justification>
  </clause>

  <clause id="453">
    <literal><![CDATA[
      f(f(x,x),f(x,f(f(f(x,f(x,f(f(x,x),y))),x),f(x,z)))) = x
    ]]></literal>
    <justification jstring="[para(416(a,1),2(a,1,2,2,1,1,1)),rewrite(416(6))].">
      <j1 rule="para" parents="416 2"/>
      <j2 rule="rewrite" parents="416"/>
    </justification>
  </clause>

  <clause id="565">
    <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(138(a,1),82(a,1,2,1)),rewrite(138(16),138(18))].">
      <j1 rule="para" parents="138 82"/>
      <j2 rule="rewrite" parents="138 138"/>
    </justification>
  </clause>

  <clause id="822">
    <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(20(a,1),565(a,1,1,1,1)),rewrite(77(5),77(11))].">
      <j1 rule="para" parents="20 565"/>
      <j2 rule="rewrite" parents="77 77"/>
    </justification>
  </clause>

  <clause id="923">
    <literal><![CDATA[
      f(f(f(f(f(x,x),f(y,y)),f(f(f(y,f(y,y)),x),f(x,z))),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>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(39(a,1),84(a,1,2,1,2,1)),rewrite(39(25),39(27))].">
      <j1 rule="para" parents="39 84"/>
      <j2 rule="rewrite" parents="39 39"/>
    </justification>
  </clause>

  <clause id="930">
    <literal><![CDATA[
      f(x,f(f(f(x,x),x),f(x,f(f(x,x),y)))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(565(a,1),39(a,1,2,2,1)),rewrite(20(4),77(3),82(6))].">
      <j1 rule="para" parents="565 39"/>
      <j2 rule="rewrite" parents="20 77 82"/>
    </justification>
  </clause>

  <clause id="951">
    <literal><![CDATA[
      f(f(x,x),f(f(x,f(x,x)),f(f(x,x),f(x,y)))) = x
    ]]></literal>
    <justification jstring="[para(20(a,1),930(a,1,2,1,1)),rewrite(77(7),77(11))].">
      <j1 rule="para" parents="20 930"/>
      <j2 rule="rewrite" parents="77 77"/>
    </justification>
  </clause>

  <clause id="952">
    <literal><![CDATA[
      f(x,f(f(f(x,x),x),f(x,f(y,f(x,x))))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(82(a,1),930(a,1,2,2,2))].">
      <j1 rule="para" parents="82 930"/>
    </justification>
  </clause>

  <clause id="983">
    <literal><![CDATA[
      f(f(f(x,x),x),f(x,f(f(x,x),y))) = x
    ]]></literal>
    <justification jstring="[para(80(a,1),45(a,1,2,2,1)),rewrite(77(3),82(6),20(6),930(7),77(4),82(7),20(7),77(10),82(13),20(13),20(21),416(21),46(17),77(3),77(3),82(6),20(6)),flip(a)].">
      <j1 rule="para" parents="80 45"/>
      <j2 rule="rewrite" parents="77 82 20 930 77 82 20 77 82 20 20 416 46 77 77 82 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="985">
    <literal><![CDATA[
      f(f(f(x,x),x),f(x,f(y,f(x,x)))) = x
    ]]></literal>
    <justification jstring="[para(128(a,1),45(a,1,2,2,1)),rewrite(77(3),82(6),20(6),952(7),77(4),82(7),20(7),77(10),82(13),20(13),20(21),442(21),46(17),77(3),77(3),82(6),20(6)),flip(a)].">
      <j1 rule="para" parents="128 45"/>
      <j2 rule="rewrite" parents="77 82 20 952 77 82 20 77 82 20 20 442 46 77 77 82 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1016">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(x,f(f(x,x),y))) = x
    ]]></literal>
    <justification jstring="[para(39(a,1),45(a,1,2,2,1)),rewrite(77(3),77(6),77(10),77(13),77(16),77(19),77(27),416(27),46(23),77(9),77(3),77(6)),flip(a)].">
      <j1 rule="para" parents="39 45"/>
      <j2 rule="rewrite" parents="77 77 77 77 77 77 77 416 46 77 77 77"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1017">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(x,x),f(x,y))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(951(a,1),45(a,1,1)),rewrite(77(16),77(18),119(23),414(18),20(16)),flip(a)].">
      <j1 rule="para" parents="951 45"/>
      <j2 rule="rewrite" parents="77 77 119 414 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1057">
    <literal><![CDATA[
      f(f(f(x,x),x),f(f(x,x),f(x,y))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(20(a,1),1016(a,1,1,2)),rewrite(77(6))].">
      <j1 rule="para" parents="20 1016"/>
      <j2 rule="rewrite" parents="77"/>
    </justification>
  </clause>

  <clause id="1125">
    <literal><![CDATA[
      f(f(f(f(x,x),f(x,y)),f(x,f(x,x))),x) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(1017(a,1),125(a,1,2,1,2,1)),rewrite(1017(18),77(14),1017(18),55(17),20(14))].">
      <j1 rule="para" parents="1017 125"/>
      <j2 rule="rewrite" parents="1017 77 1017 55 20"/>
    </justification>
  </clause>

  <clause id="1182">
    <literal><![CDATA[
      f(f(x,x),f(f(f(x,x),f(x,f(x,x))),f(f(x,f(x,x)),f(x,y)))) = x
    ]]></literal>
    <justification jstring="[para(1125(a,1),2(a,1,2,2,1))].">
      <j1 rule="para" parents="1125 2"/>
    </justification>
  </clause>

  <clause id="1260">
    <literal><![CDATA[
      f(f(x,x),f(x,f(f(f(x,f(x,f(f(x,x),y))),x),f(z,x)))) = x
    ]]></literal>
    <justification jstring="[para(82(a,1),453(a,1,2,2,2))].">
      <j1 rule="para" parents="82 453"/>
    </justification>
  </clause>

  <clause id="1336">
    <literal><![CDATA[
      f(f(x,x),f(f(x,f(x,f(f(x,x),y))),x)) = x
    ]]></literal>
    <justification jstring="[para(82(a,1),1260(a,1,2))].">
      <j1 rule="para" parents="82 1260"/>
    </justification>
  </clause>

  <clause id="1347">
    <literal><![CDATA[
      f(x,f(f(f(x,x),f(f(x,x),f(x,y))),f(x,x))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(20(a,1),1336(a,1,1)),rewrite(77(5))].">
      <j1 rule="para" parents="20 1336"/>
      <j2 rule="rewrite" parents="77"/>
    </justification>
  </clause>

  <clause id="1403">
    <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(60(a,1),82(a,1,2,1)),rewrite(60(19),60(21))].">
      <j1 rule="para" parents="60 82"/>
      <j2 rule="rewrite" parents="60 60"/>
    </justification>
  </clause>

  <clause id="1483">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),f(f(f(y,x),f(y,x)),f(f(y,x),z))),f(f(f(f(f(y,x),f(y,x)),f(f(f(y,x),f(y,x)),f(f(y,x),z))),y),f(u,y)))) = y
    ]]></literal>
    <justification jstring="[para(414(a,1),96(a,1,2,2,1,1,1))].">
      <j1 rule="para" parents="414 96"/>
    </justification>
  </clause>

  <clause id="1514">
    <literal><![CDATA[
      f(f(f(x,x),x),f(x,f(f(f(x,f(x,f(f(x,x),y))),x),f(z,x)))) = x
    ]]></literal>
    <justification jstring="[para(1016(a,1),96(a,1,2,2,1,1,1)),rewrite(416(7))].">
      <j1 rule="para" parents="1016 96"/>
      <j2 rule="rewrite" parents="416"/>
    </justification>
  </clause>

  <clause id="1567">
    <literal><![CDATA[
      f(f(f(x,y),f(f(f(f(x,y),y),f(x,x)),f(f(x,x),z))),x) = f(x,x)
    ]]></literal>
    <justification jstring="[para(69(a,1),97(a,1,1,2,1,1,1,1)),rewrite(77(3),77(12))].">
      <j1 rule="para" parents="69 97"/>
      <j2 rule="rewrite" parents="77 77"/>
    </justification>
  </clause>

  <clause id="1699">
    <literal><![CDATA[
      f(f(x,x),f(x,f(x,x))) = x
    ]]></literal>
    <justification jstring="[para(20(a,1),1182(a,1,2))].">
      <j1 rule="para" parents="20 1182"/>
    </justification>
  </clause>

  <clause id="1751">
    <literal><![CDATA[
      f(f(x,y),f(y,f(f(f(f(f(y,x),f(y,f(y,y))),f(y,f(y,y))),y),f(y,z)))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(1699(a,1),2(a,1,2,1))].">
      <j1 rule="para" parents="1699 2"/>
    </justification>
  </clause>

  <clause id="1755">
    <literal><![CDATA[
      f(x,f(f(x,x),x)) = f(x,x)
    ]]></literal>
    <justification jstring="[para(20(a,1),1699(a,1,1)),rewrite(77(4))].">
      <j1 rule="para" parents="20 1699"/>
      <j2 rule="rewrite" parents="77"/>
    </justification>
  </clause>

  <clause id="1780">
    <literal><![CDATA[
      f(f(x,y),f(y,f(f(f(f(f(y,x),f(y,f(y,y))),f(y,f(y,y))),y),f(z,y)))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(1699(a,1),96(a,1,2,1))].">
      <j1 rule="para" parents="1699 96"/>
    </justification>
  </clause>

  <clause id="1826">
    <literal><![CDATA[
      f(f(f(f(x,x),f(x,y)),f(f(x,x),x)),f(f(f(x,x),x),f(f(f(x,f(f(f(x,x),x),f(f(f(x,x),x),f(f(x,x),x)))),f(f(x,x),x)),f(f(f(x,x),x),z)))) = f(f(x,x),x)
    ]]></literal>
    <justification jstring="[para(1057(a,1),1751(a,1,2,2,1,1,1,1)),rewrite(138(18))].">
      <j1 rule="para" parents="1057 1751"/>
      <j2 rule="rewrite" parents="138"/>
    </justification>
  </clause>

  <clause id="1860">
    <literal><![CDATA[
      f(f(x,y),f(f(f(f(y,x),f(y,f(y,y))),f(y,f(y,y))),y)) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(82(a,1),1780(a,1,2))].">
      <j1 rule="para" parents="82 1780"/>
    </justification>
  </clause>

  <clause id="1902">
    <literal><![CDATA[
      f(f(x,f(y,y)),f(f(f(f(f(y,y),x),f(f(y,y),y)),f(f(y,y),y)),f(y,y))) = f(y,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(20(a,1),1860(a,1,2,1,1,2,2)),rewrite(77(11))].">
      <j1 rule="para" parents="20 1860"/>
      <j2 rule="rewrite" parents="77"/>
    </justification>
  </clause>

  <clause id="1968">
    <literal><![CDATA[
      f(f(f(x,x),f(y,x)),f(f(f(f(y,x),f(y,x)),f(f(x,x),x)),f(f(f(f(x,x),f(f(x,x),x)),f(y,x)),f(f(y,x),z)))) = f(y,x)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(1755(a,1),38(a,1,2,2,1,1,1))].">
      <j1 rule="para" parents="1755 38"/>
    </justification>
  </clause>

  <clause id="2448">
    <literal><![CDATA[
      f(f(f(x,x),x),f(f(x,f(x,f(f(x,x),y))),x)) = x
    ]]></literal>
    <justification jstring="[para(82(a,1),1514(a,1,2))].">
      <j1 rule="para" parents="82 1514"/>
    </justification>
  </clause>

  <clause id="2472">
    <literal><![CDATA[
      f(f(f(x,x),f(f(x,x),f(x,y))),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(2448(a,1),62(a,1,2,2,1)),rewrite(77(5),1347(8),77(6),77(13),77(21),46(19),77(3),77(5)),flip(a)].">
      <j1 rule="para" parents="2448 62"/>
      <j2 rule="rewrite" parents="77 1347 77 77 77 46 77 77"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2737">
    <literal><![CDATA[
      f(f(f(x,x),f(f(x,x),f(f(x,x),f(x,y)))),f(x,x)) = f(f(x,x),f(f(x,x),f(x,y)))
    ]]></literal>
    <justification jstring="[para(2472(a,1),125(a,1,2,1,2,1)),rewrite(2472(25),2472(27),77(28),46(21))].">
      <j1 rule="para" parents="2472 125"/>
      <j2 rule="rewrite" parents="2472 2472 77 46"/>
    </justification>
  </clause>

  <clause id="2791">
    <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(55(a,1),68(a,1,2,2,2))].">
      <j1 rule="para" parents="55 68"/>
    </justification>
  </clause>

  <clause id="2951">
    <literal><![CDATA[
      f(f(f(x,x),f(y,x)),f(f(f(f(y,x),f(y,x)),f(f(x,x),x)),f(f(f(f(x,x),f(f(x,x),x)),f(y,x)),f(z,f(y,x))))) = f(y,x)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(82(a,1),1968(a,1,2,2,2))].">
      <j1 rule="para" parents="82 1968"/>
    </justification>
  </clause>

  <clause id="2956">
    <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(20(a,1),2791(a,1,1,2,1)),rewrite(77(6),77(7),77(10),77(12),77(14),77(17))].">
      <j1 rule="para" parents="20 2791"/>
      <j2 rule="rewrite" parents="77 77 77 77 77 77"/>
    </justification>
  </clause>

  <clause id="2962">
    <literal><![CDATA[
      f(f(x,x),f(x,y)) = x
    ]]></literal>
    <justification jstring="[para(983(a,1),2791(a,1,2,2,1)),rewrite(77(4),414(4),77(5),77(8),77(13),46(11),77(3),77(4)),flip(a)].">
      <j1 rule="para" parents="983 2791"/>
      <j2 rule="rewrite" parents="77 414 77 77 77 46 77 77"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2963">
    <literal><![CDATA[
      f(f(x,x),f(y,x)) = x
    ]]></literal>
    <justification jstring="[para(985(a,1),2791(a,1,2,2,1)),rewrite(2962(4),415(4),2962(5),2962(8),2962(13),46(11),2962(3),2962(4)),flip(a)].">
      <j1 rule="para" parents="985 2791"/>
      <j2 rule="rewrite" parents="2962 415 2962 2962 2962 46 2962 2962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2966">
    <literal><![CDATA[
      f(x,f(f(f(f(x,f(x,f(x,x))),f(x,f(x,f(x,x)))),y),f(f(f(f(x,y),y),f(x,f(x,f(x,x)))),x))) = f(x,f(x,f(x,x)))
    ]]></literal>
    <justification jstring="[para(1902(a,1),2791(a,1,1,2)),rewrite(2962(3),2962(3),2962(3),1755(3),2963(4),2962(6),2962(6),1755(6),2963(7),2962(11),2962(13),2962(13),1755(13),2963(14),2962(17),2962(20),2962(20),1755(20),2963(21))].">
      <j1 rule="para" parents="1902 2791"/>
      <j2 rule="rewrite" parents="2962 2962 2962 1755 2963 2962 2962 1755 2963 2962 2962 2962 1755 2963 2962 2962 2962 1755 2963"/>
    </justification>
  </clause>

  <clause id="2970">
    <literal><![CDATA[
      f(x,f(x,f(x,x))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(1902(a,1),2791(a,2)),rewrite(2962(4),2962(4),1755(4),2963(5),2962(5),2962(3),2962(3),1755(3),2963(4),2962(6),2962(6),1755(6),2963(7),2962(11),2962(13),2962(13),1755(13),2963(14),2962(17),2966(17))].">
      <j1 rule="para" parents="1902 2791"/>
      <j2 rule="rewrite" parents="2962 2962 1755 2963 2962 2962 2962 1755 2963 2962 2962 1755 2963 2962 2962 2962 1755 2963 2962 2966"/>
    </justification>
  </clause>

  <clause id="2975">
    <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(2956),rewrite(2962(3))].">
      <j1 rule="back_rewrite" parents="2956"/>
      <j2 rule="rewrite" parents="2962"/>
    </justification>
  </clause>

  <clause id="2989">
    <literal><![CDATA[
      f(f(x,x),x) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[back_rewrite(2737),rewrite(2962(5),2963(4),2962(6)),flip(a)].">
      <j1 rule="back_rewrite" parents="2737"/>
      <j2 rule="rewrite" parents="2962 2963 2962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3020">
    <literal><![CDATA[
      f(f(x,x),f(f(x,f(x,x)),f(x,f(f(x,f(x,x)),y)))) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[back_rewrite(1826),rewrite(2962(3),2989(2),2970(3),2989(3),2989(5),2989(7),2989(9),245(12),2989(6),2962(7),2989(5),2989(11))].">
      <j1 rule="back_rewrite" parents="1826"/>
      <j2 rule="rewrite" parents="2962 2989 2970 2989 2989 2989 2989 245 2989 2962 2989 2989"/>
    </justification>
  </clause>

  <clause id="3024">
    <literal><![CDATA[
      f(f(x,y),f(y,f(f(f(f(y,x),f(f(y,x),f(y,x))),y),f(z,y)))) = y
    ]]></literal>
    <justification jstring="[back_rewrite(1483),rewrite(2962(8),2962(4),2962(10),2989(6))].">
      <j1 rule="back_rewrite" parents="1483"/>
      <j2 rule="rewrite" parents="2962 2962 2962 2989"/>
    </justification>
  </clause>

  <clause id="3043">
    <literal><![CDATA[
      f(f(x,x),f(f(x,f(x,x)),f(f(x,f(x,x)),f(x,y)))) = x
    ]]></literal>
    <justification jstring="[back_rewrite(435),rewrite(2962(4),2962(4),2989(3),2962(7),2989(5),2962(12))].">
      <j1 rule="back_rewrite" parents="435"/>
      <j2 rule="rewrite" parents="2962 2962 2989 2962 2989 2962"/>
    </justification>
  </clause>

  <clause id="3045">
    <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="[back_rewrite(429),rewrite(2962(4),2962(4),2989(3),2962(7),2989(5),2962(8),2962(12))].">
      <j1 rule="back_rewrite" parents="429"/>
      <j2 rule="rewrite" parents="2962 2962 2989 2962 2989 2962 2962"/>
    </justification>
  </clause>

  <clause id="3047">
    <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>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(325),rewrite(2962(3))].">
      <j1 rule="back_rewrite" parents="325"/>
      <j2 rule="rewrite" parents="2962"/>
    </justification>
  </clause>

  <clause id="3049">
    <literal><![CDATA[
      f(x,f(f(f(f(x,y),f(x,y)),f(x,x)),f(f(x,f(x,y)),f(z,f(x,y))))) = f(x,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(146),rewrite(2962(3))].">
      <j1 rule="back_rewrite" parents="146"/>
      <j2 rule="rewrite" parents="2962"/>
    </justification>
  </clause>

  <clause id="3055">
    <literal><![CDATA[
      f(x,f(f(f(f(y,x),f(y,x)),f(x,f(x,x))),f(f(x,f(y,x)),f(z,f(y,x))))) = f(y,x)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(2951),rewrite(2963(3),2989(5),2989(9),2962(10))].">
      <j1 rule="back_rewrite" parents="2951"/>
      <j2 rule="rewrite" parents="2963 2989 2989 2962"/>
    </justification>
  </clause>

  <clause id="3130">
    <literal><![CDATA[
      f(x,f(f(f(f(y,x),f(y,x)),f(x,x)),f(f(x,f(y,x)),f(z,f(y,x))))) = f(y,x)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(137),rewrite(2963(3))].">
      <j1 rule="back_rewrite" parents="137"/>
      <j2 rule="rewrite" parents="2963"/>
    </justification>
  </clause>

  <clause id="3393">
    <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="[back_rewrite(1403),rewrite(2989(4))].">
      <j1 rule="back_rewrite" parents="1403"/>
      <j2 rule="rewrite" parents="2989"/>
    </justification>
  </clause>

  <clause id="3450">
    <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="[back_rewrite(565),rewrite(2989(2),2989(4))].">
      <j1 rule="back_rewrite" parents="565"/>
      <j2 rule="rewrite" parents="2989 2989"/>
    </justification>
  </clause>

  <clause id="3480">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),f(f(x,f(x,x)),f(x,y))),f(x,x)) = x
    ]]></literal>
    <justification jstring="[back_rewrite(287),rewrite(2989(2),2989(4))].">
      <j1 rule="back_rewrite" parents="287"/>
      <j2 rule="rewrite" parents="2989 2989"/>
    </justification>
  </clause>

  <clause id="3541">
    <literal><![CDATA[
      f(f(f(x,y),f(x,y)),y) = f(x,y)
    ]]></literal>
    <justification jstring="[para(2(a,1),2962(a,1,2))].">
      <j1 rule="para" parents="2 2962"/>
    </justification>
  </clause>

  <clause id="3547">
    <literal><![CDATA[
      f(f(f(x,y),f(x,y)),x) = f(x,y)
    ]]></literal>
    <justification jstring="[para(77(a,1),2962(a,1,2))].">
      <j1 rule="para" parents="77 2962"/>
    </justification>
  </clause>

  <clause id="3549">
    <literal><![CDATA[
      f(f(f(f(f(f(x,y),f(x,y)),z),f(f(f(f(x,z),z),f(x,y)),f(f(x,y),u))),x),f(f(f(x,x),v),f(f(f(f(f(x,y),v),v),x),f(x,w)))) = x
    ]]></literal>
    <justification jstring="[para(2962(a,1),5(a,1,1,2)),rewrite(77(7),2962(16),2962(16),2962(21),2962(22),2962(26))].">
      <j1 rule="para" parents="2962 5"/>
      <j2 rule="rewrite" parents="77 2962 2962 2962 2962 2962"/>
    </justification>
  </clause>

  <clause id="3564">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),f(f(x,y),f(x,y))),f(f(f(x,y),y),f(y,z)))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(2962(a,1),237(a,1,1,1,1,2)),rewrite(2962(4),2962(6),3541(4),2962(5),2962(6),2962(9),2962(10),2962(11),2962(15))].">
      <j1 rule="para" parents="2962 237"/>
      <j2 rule="rewrite" parents="2962 2962 3541 2962 2962 2962 2962 2962 2962"/>
    </justification>
  </clause>

  <clause id="3565">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),f(f(x,y),f(x,y))),f(f(f(x,y),y),f(z,y)))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(2962(a,1),246(a,1,1,1,1,2)),rewrite(2962(4),2962(6),3541(4),2962(5),2962(6),2962(9),2962(10),2962(11),2962(15))].">
      <j1 rule="para" parents="2962 246"/>
      <j2 rule="rewrite" parents="2962 2962 3541 2962 2962 2962 2962 2962 2962"/>
    </justification>
  </clause>

  <clause id="3567">
    <literal><![CDATA[
      f(f(x,y),f(f(f(x,x),f(f(x,y),f(x,y))),f(f(f(x,y),x),f(z,x)))) = x
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(2962(a,1),257(a,1,1,1,1,1)),rewrite(2962(4),2962(6),3547(4),2962(5),2962(6),2962(9),2962(10),2962(11),2962(15))].">
      <j1 rule="para" parents="2962 257"/>
      <j2 rule="rewrite" parents="2962 2962 3547 2962 2962 2962 2962 2962 2962"/>
    </justification>
  </clause>

  <clause id="3571">
    <literal><![CDATA[
      f(f(f(f(x,y),f(f(f(x,f(x,x)),f(x,y)),f(f(x,y),z))),x),f(f(f(x,x),f(f(x,y),f(x,y))),f(f(f(x,y),x),f(x,y)))) = x
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(2962(a,1),923(a,1,1,2)),rewrite(2962(6),3547(4),2962(5),2989(3),2962(13),2962(13),2962(19),2962(24))].">
      <j1 rule="para" parents="2962 923"/>
      <j2 rule="rewrite" parents="2962 3547 2962 2989 2962 2962 2962 2962"/>
    </justification>
  </clause>

  <clause id="3576">
    <literal><![CDATA[
      f(f(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))))),f(x,x)) = f(f(x,f(x,x)),f(f(x,f(x,x)),f(y,f(x,x))))
    ]]></literal>
    <justification jstring="[para(822(a,1),2962(a,1,2))].">
      <j1 rule="para" parents="822 2962"/>
    </justification>
  </clause>

  <clause id="3680">
    <literal><![CDATA[
      f(x,f(y,f(x,x))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(20(a,1),2963(a,1,1))].">
      <j1 rule="para" parents="20 2963"/>
    </justification>
  </clause>

  <clause id="3712">
    <literal><![CDATA[
      f(f(x,y),f(f(y,f(y,y)),f(f(f(f(f(y,x),y),y),y),f(y,z)))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(2989(a,1),2(a,1,2,1))].">
      <j1 rule="para" parents="2989 2"/>
    </justification>
  </clause>

  <clause id="3737">
    <literal><![CDATA[
      f(f(x,y),f(f(y,f(y,y)),f(f(f(f(f(y,x),y),y),y),f(z,y)))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(2989(a,1),96(a,1,2,1))].">
      <j1 rule="para" parents="2989 96"/>
    </justification>
  </clause>

  <clause id="3808">
    <literal><![CDATA[
      f(f(x,y),f(f(y,f(y,y)),f(f(f(f(f(x,y),y),y),y),f(y,z)))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(82(a,1),3712(a,1,2,2,1,1,1,1)),rewrite(3541(4))].">
      <j1 rule="para" parents="82 3712"/>
      <j2 rule="rewrite" parents="3541"/>
    </justification>
  </clause>

  <clause id="3811">
    <literal><![CDATA[
      f(f(x,y),f(f(x,f(x,x)),f(f(f(f(f(x,y),x),x),x),f(x,z)))) = x
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(91(a,1),3712(a,1,2,2,1,1,1,1)),rewrite(3547(4))].">
      <j1 rule="para" parents="91 3712"/>
      <j2 rule="rewrite" parents="3547"/>
    </justification>
  </clause>

  <clause id="3841">
    <literal><![CDATA[
      f(f(x,y),f(f(y,f(y,y)),f(f(f(f(f(x,y),y),y),y),f(z,y)))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(82(a,1),3737(a,1,2,2,1,1,1,1)),rewrite(3541(4))].">
      <j1 rule="para" parents="82 3737"/>
      <j2 rule="rewrite" parents="3541"/>
    </justification>
  </clause>

  <clause id="3943">
    <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),v)))) = f(z,x)
    ]]></literal>
    <justification jstring="[para(3547(a,1),5(a,1,2,1))].">
      <j1 rule="para" parents="3547 5"/>
    </justification>
  </clause>

  <clause id="4019">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(x,f(x,x)),f(x,f(x,x)))) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(3811(a,1),39(a,1,2,2)),rewrite(245(9),3576(20),46(12),82(7)),flip(a)].">
      <j1 rule="para" parents="3811 39"/>
      <j2 rule="rewrite" parents="245 3576 46 82"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4180">
    <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(3541(a,1),2975(a,1,2,1))].">
      <j1 rule="para" parents="3541 2975"/>
    </justification>
  </clause>

  <clause id="4343">
    <literal><![CDATA[
      f(f(f(f(f(x,x),f(f(y,x),f(y,x))),f(f(f(y,x),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)),f(f(y,x),v)))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(3564(a,1),2(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="3564 2"/>
    </justification>
  </clause>

  <clause id="4414">
    <literal><![CDATA[
      f(f(x,x),f(f(f(x,x),y),f(f(f(y,f(y,y)),x),f(x,z)))) = x
    ]]></literal>
    <justification jstring="[para(3393(a,1),3547(a,1,1,1)),rewrite(3393(10),3393(20))].">
      <j1 rule="para" parents="3393 3547"/>
      <j2 rule="rewrite" parents="3393 3393"/>
    </justification>
  </clause>

  <clause id="4747">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,x),f(f(y,x),f(y,x))),y)) = y
    ]]></literal>
    <justification jstring="[para(82(a,1),3024(a,1,2))].">
      <j1 rule="para" parents="82 3024"/>
    </justification>
  </clause>

  <clause id="4975">
    <literal><![CDATA[
      f(x,f(f(x,f(x,x)),f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(20(a,1),4747(a,1,2,1,1)),rewrite(2963(3),20(3),20(3))].">
      <j1 rule="para" parents="20 4747"/>
      <j2 rule="rewrite" parents="2963 20 20"/>
    </justification>
  </clause>

  <clause id="4978">
    <literal><![CDATA[
      f(x,f(f(x,f(x,x)),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(77(a,1),4747(a,1,2,1,1)),rewrite(2962(3),77(3),77(3))].">
      <j1 rule="para" parents="77 4747"/>
      <j2 rule="rewrite" parents="2962 77 77"/>
    </justification>
  </clause>

  <clause id="4979">
    <literal><![CDATA[
      f(f(x,y),f(f(f(x,y),f(f(x,y),f(x,y))),y)) = y
    ]]></literal>
    <justification jstring="[para(82(a,1),4747(a,1,2,1,1)),rewrite(3541(4),82(6),82(7))].">
      <j1 rule="para" parents="82 4747"/>
      <j2 rule="rewrite" parents="3541 82 82"/>
    </justification>
  </clause>

  <clause id="4984">
    <literal><![CDATA[
      f(f(x,y),f(f(f(x,y),f(f(x,y),f(x,y))),x)) = x
    ]]></literal>
    <justification jstring="[para(91(a,1),4747(a,1,2,1,1)),rewrite(3547(4),91(6),91(7))].">
      <j1 rule="para" parents="91 4747"/>
      <j2 rule="rewrite" parents="3547 91 91"/>
    </justification>
  </clause>

  <clause id="5024">
    <literal><![CDATA[
      f(x,f(f(x,f(x,x)),f(f(x,f(x,x)),f(f(x,f(x,x)),f(x,y))))) = f(f(x,f(x,x)),f(f(x,f(x,x)),f(x,y)))
    ]]></literal>
    <justification jstring="[para(3043(a,1),4747(a,1,1)),rewrite(3480(9),3480(9),3480(9))].">
      <j1 rule="para" parents="3043 4747"/>
      <j2 rule="rewrite" parents="3480 3480 3480"/>
    </justification>
  </clause>

  <clause id="5030">
    <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(3045(a,1),4747(a,1,1)),rewrite(3450(9),3450(9),3450(9))].">
      <j1 rule="para" parents="3045 4747"/>
      <j2 rule="rewrite" parents="3450 3450 3450"/>
    </justification>
  </clause>

  <clause id="5126">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(x,f(x,x)),f(y,f(x,f(x,x))))) = f(y,f(x,f(x,x)))
    ]]></literal>
    <justification jstring="[para(4019(a,1),4975(a,1,2,1))].">
      <j1 rule="para" parents="4019 4975"/>
    </justification>
  </clause>

  <clause id="5136">
    <literal><![CDATA[
      f(f(x,x),f(f(x,f(x,x)),f(y,x))) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(4975(a,1),3020(a,1,2,2))].">
      <j1 rule="para" parents="4975 3020"/>
    </justification>
  </clause>

  <clause id="5182">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(x,f(x,x)),f(f(x,f(x,x)),y))) = f(f(x,f(x,x)),y)
    ]]></literal>
    <justification jstring="[para(4019(a,1),4978(a,1,2,1))].">
      <j1 rule="para" parents="4019 4978"/>
    </justification>
  </clause>

  <clause id="5192">
    <literal><![CDATA[
      f(f(x,x),f(f(x,f(x,x)),f(x,y))) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(4978(a,1),3020(a,1,2,2))].">
      <j1 rule="para" parents="4978 3020"/>
    </justification>
  </clause>

  <clause id="5201">
    <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(5030),rewrite(5182(10),4975(5)),flip(a)].">
      <j1 rule="back_rewrite" parents="5030"/>
      <j2 rule="rewrite" parents="5182 4975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5202">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(x,f(x,x)),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(5024),rewrite(5182(10),4978(5)),flip(a)].">
      <j1 rule="back_rewrite" parents="5024"/>
      <j2 rule="rewrite" parents="5182 4978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5246">
    <literal><![CDATA[
      f(f(f(f(f(x,y),f(f(x,y),f(x,y))),y),f(x,y)),f(f(f(f(x,y),f(x,y)),f(y,y)),f(f(y,f(x,y)),y))) = f(x,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(4979(a,1),84(a,1,2,1,2,1)),rewrite(4979(19),4979(21))].">
      <j1 rule="para" parents="4979 84"/>
      <j2 rule="rewrite" parents="4979 4979"/>
    </justification>
  </clause>

  <clause id="5247">
    <literal><![CDATA[
      f(f(f(f(f(x,y),f(f(x,y),f(x,y))),y),f(x,y)),f(f(f(f(x,y),f(x,y)),f(y,y)),f(f(y,f(x,y)),x))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(4979(a,1),125(a,1,2,1,2,1)),rewrite(4979(19),4979(21))].">
      <j1 rule="para" parents="4979 125"/>
      <j2 rule="rewrite" parents="4979 4979"/>
    </justification>
  </clause>

  <clause id="5271">
    <literal><![CDATA[
      f(x,f(f(x,f(x,x)),f(f(f(x,x),f(f(y,x),f(y,x))),f(f(f(y,x),x),f(x,z))))) = f(f(f(x,x),f(f(y,x),f(y,x))),f(f(f(y,x),x),f(x,z)))
    ]]></literal>
    <justification jstring="[para(3564(a,1),4979(a,1,1)),rewrite(3564(12),3564(12),3564(12))].">
      <j1 rule="para" parents="3564 4979"/>
      <j2 rule="rewrite" parents="3564 3564 3564"/>
    </justification>
  </clause>

  <clause id="5272">
    <literal><![CDATA[
      f(x,f(f(x,f(x,x)),f(f(f(x,x),f(f(y,x),f(y,x))),f(f(f(y,x),x),f(z,x))))) = f(f(f(x,x),f(f(y,x),f(y,x))),f(f(f(y,x),x),f(z,x)))
    ]]></literal>
    <justification jstring="[para(3565(a,1),4979(a,1,1)),rewrite(3565(12),3565(12),3565(12))].">
      <j1 rule="para" parents="3565 4979"/>
      <j2 rule="rewrite" parents="3565 3565 3565"/>
    </justification>
  </clause>

  <clause id="5440">
    <literal><![CDATA[
      f(f(f(f(f(x,y),f(f(x,y),f(x,y))),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(4984(a,1),84(a,1,2,1,2,1)),rewrite(4984(19),4984(21))].">
      <j1 rule="para" parents="4984 84"/>
      <j2 rule="rewrite" parents="4984 4984"/>
    </justification>
  </clause>

  <clause id="5499">
    <literal><![CDATA[
      f(f(f(x,y),f(x,y)),f(f(f(x,y),f(f(x,y),f(x,y))),x)) = f(f(x,y),f(f(x,y),f(x,y)))
    ]]></literal>
    <justification jstring="[para(2962(a,1),5136(a,1,2,2))].">
      <j1 rule="para" parents="2962 5136"/>
    </justification>
  </clause>

  <clause id="5500">
    <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="[para(2963(a,1),5136(a,1,2,2))].">
      <j1 rule="para" parents="2963 5136"/>
    </justification>
  </clause>

  <clause id="5589">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(y,x),f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(5201(a,1),91(a,1,2,1)),rewrite(5201(10),5201(13))].">
      <j1 rule="para" parents="5201 91"/>
      <j2 rule="rewrite" parents="5201 5201"/>
    </justification>
  </clause>

  <clause id="5596">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(y,x)) = f(f(y,x),f(y,x))
    ]]></literal>
    <justification jstring="[para(5201(a,1),45(a,1,1)),rewrite(5202(24),5201(23),3680(21)),flip(a)].">
      <j1 rule="para" parents="5201 45"/>
      <j2 rule="rewrite" parents="5202 5201 3680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5609">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(f(f(y,x),f(y,x)),f(f(x,f(x,x)),f(x,f(x,x)))),f(f(f(x,f(x,x)),f(y,x)),f(x,f(x,x))))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(5201(a,1),3047(a,1,2,1,1,1)),rewrite(5201(10),5201(20),5201(27))].">
      <j1 rule="para" parents="5201 3047"/>
      <j2 rule="rewrite" parents="5201 5201 5201"/>
    </justification>
  </clause>

  <clause id="5620">
    <literal><![CDATA[
      f(f(f(x,y),f(x,y)),f(y,f(y,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(5201(a,1),3547(a,1,1,1)),rewrite(5201(8),5201(13))].">
      <j1 rule="para" parents="5201 3547"/>
      <j2 rule="rewrite" parents="5201 5201"/>
    </justification>
  </clause>

  <clause id="5675">
    <literal><![CDATA[
      f(x,f(f(y,x),f(f(x,f(y,x)),f(z,f(y,x))))) = f(y,x)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(3055),rewrite(5620(6))].">
      <j1 rule="back_rewrite" parents="3055"/>
      <j2 rule="rewrite" parents="5620"/>
    </justification>
  </clause>

  <clause id="5885">
    <literal><![CDATA[
      f(f(x,y),f(f(f(f(y,f(y,y)),f(y,f(y,y))),f(f(x,y),f(x,y))),f(f(f(x,y),f(y,f(y,y))),y))) = f(y,f(y,y))
    ]]></literal>
    <justification jstring="[para(5589(a,1),125(a,1,2,1,2,1)),rewrite(5620(6),5589(13),5589(16))].">
      <j1 rule="para" parents="5589 125"/>
      <j2 rule="rewrite" parents="5620 5589 5589"/>
    </justification>
  </clause>

  <clause id="5905">
    <literal><![CDATA[
      f(f(f(f(f(x,x),y),f(f(f(y,f(y,y)),x),f(x,z))),f(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))))),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(4414(a,1),5589(a,1,2,1)),rewrite(4414(36),4414(38))].">
      <j1 rule="para" parents="4414 5589"/>
      <j2 rule="rewrite" parents="4414 4414"/>
    </justification>
  </clause>

  <clause id="5931">
    <literal><![CDATA[
      f(f(f(x,y),f(x,y)),f(f(y,f(y,y)),f(y,f(y,y)))) = f(y,f(y,y))
    ]]></literal>
    <justification jstring="[para(5596(a,1),77(a,1,1))].">
      <j1 rule="para" parents="5596 77"/>
    </justification>
  </clause>

  <clause id="6046">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),f(x,f(x,x))),f(f(y,x),f(y,x))) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(5596(a,1),2962(a,1,2))].">
      <j1 rule="para" parents="5596 2962"/>
    </justification>
  </clause>

  <clause id="6047">
    <literal><![CDATA[
      f(f(f(x,y),f(f(x,y),f(x,y))),x) = f(x,x)
    ]]></literal>
    <justification jstring="[para(2962(a,1),5596(a,1,2)),rewrite(2962(9),2962(9))].">
      <j1 rule="para" parents="2962 5596"/>
      <j2 rule="rewrite" parents="2962 2962"/>
    </justification>
  </clause>

  <clause id="6048">
    <literal><![CDATA[
      f(f(f(x,y),f(f(x,y),f(x,y))),y) = f(y,y)
    ]]></literal>
    <justification jstring="[para(2963(a,1),5596(a,1,2)),rewrite(2963(9),2963(9))].">
      <j1 rule="para" parents="2963 5596"/>
      <j2 rule="rewrite" parents="2963 2963"/>
    </justification>
  </clause>

  <clause id="6049">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),f(y,x)),f(y,x)) = f(f(y,x),f(f(y,x),f(y,x)))
    ]]></literal>
    <justification jstring="[para(5596(a,2),2989(a,1,1))].">
      <j1 rule="para" parents="5596 2989"/>
    </justification>
  </clause>

  <clause id="6050">
    <literal><![CDATA[
      f(f(x,y),f(f(y,f(y,y)),f(x,y))) = f(f(x,y),f(f(x,y),f(x,y)))
    ]]></literal>
    <justification jstring="[para(5596(a,2),2989(a,2,2)),rewrite(2989(5)),flip(a)].">
      <j1 rule="para" parents="5596 2989"/>
      <j2 rule="rewrite" parents="2989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6101">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),f(f(x,y),f(x,y))),f(f(y,f(y,y)),f(f(x,y),y)))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(5596(a,2),3565(a,1,2,2))].">
      <j1 rule="para" parents="5596 3565"/>
    </justification>
  </clause>

  <clause id="6130">
    <literal><![CDATA[
      f(x,f(f(f(f(x,y),f(x,y)),f(x,x)),f(f(f(x,y),f(f(x,y),f(x,y))),f(x,f(x,y))))) = f(x,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(5596(a,2),3049(a,1,2,2))].">
      <j1 rule="para" parents="5596 3049"/>
    </justification>
  </clause>

  <clause id="6138">
    <literal><![CDATA[
      f(x,f(f(f(f(y,x),f(y,x)),f(x,x)),f(f(f(y,x),f(f(y,x),f(y,x))),f(x,f(y,x))))) = f(y,x)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(5596(a,2),3130(a,1,2,2))].">
      <j1 rule="para" parents="5596 3130"/>
    </justification>
  </clause>

  <clause id="6146">
    <literal><![CDATA[
      f(f(f(f(f(x,x),y),f(f(f(y,f(y,y)),x),f(x,z))),f(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))))),x) = f(x,x)
    ]]></literal>
    <justification jstring="[para(4414(a,1),5596(a,1,2)),rewrite(4414(37),4414(37))].">
      <j1 rule="para" parents="4414 5596"/>
      <j2 rule="rewrite" parents="4414 4414"/>
    </justification>
  </clause>

  <clause id="6193">
    <literal><![CDATA[
      f(f(x,x),f(f(y,x),f(y,x))) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(5596(a,1),5136(a,1,2))].">
      <j1 rule="para" parents="5596 5136"/>
    </justification>
  </clause>

  <clause id="6199">
    <literal><![CDATA[
      f(f(f(x,y),f(f(y,f(y,y)),f(x,y))),f(f(f(x,y),f(f(x,y),f(x,y))),f(z,f(x,y)))) = f(z,f(x,y))
    ]]></literal>
    <justification jstring="[para(5596(a,2),5201(a,1,1,2))].">
      <j1 rule="para" parents="5596 5201"/>
    </justification>
  </clause>

  <clause id="6203">
    <literal><![CDATA[
      f(f(f(x,y),f(f(y,f(y,y)),f(x,y))),f(z,f(x,y))) = f(f(z,f(x,y)),f(z,f(x,y)))
    ]]></literal>
    <justification jstring="[para(5596(a,2),5596(a,1,1,2))].">
      <j1 rule="para" parents="5596 5596"/>
    </justification>
  </clause>

  <clause id="6204">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),f(y,x)),f(x,f(x,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(5609),rewrite(5931(11),5126(13))].">
      <j1 rule="back_rewrite" parents="5609"/>
      <j2 rule="rewrite" parents="5931 5126"/>
    </justification>
  </clause>

  <clause id="6208">
    <literal><![CDATA[
      f(f(x,y),f(f(y,f(y,y)),f(f(f(x,y),f(y,f(y,y))),y))) = f(y,f(y,y))
    ]]></literal>
    <justification jstring="[back_rewrite(5885),rewrite(6046(10))].">
      <j1 rule="back_rewrite" parents="5885"/>
      <j2 rule="rewrite" parents="6046"/>
    </justification>
  </clause>

  <clause id="6211">
    <literal><![CDATA[
      f(f(f(x,y),f(x,y)),f(x,x)) = f(f(x,y),f(f(x,y),f(x,y)))
    ]]></literal>
    <justification jstring="[back_rewrite(5499),rewrite(6047(9))].">
      <j1 rule="back_rewrite" parents="5499"/>
      <j2 rule="rewrite" parents="6047"/>
    </justification>
  </clause>

  <clause id="6216">
    <literal><![CDATA[
      f(x,f(f(f(x,y),f(f(x,y),f(x,y))),f(f(x,f(x,y)),y))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(5440),rewrite(6047(6),2962(3),6211(5))].">
      <j1 rule="back_rewrite" parents="5440"/>
      <j2 rule="rewrite" parents="6047 2962 6211"/>
    </justification>
  </clause>

  <clause id="6221">
    <literal><![CDATA[
      f(f(f(x,y),f(x,y)),f(y,y)) = f(f(x,y),f(f(x,y),f(x,y)))
    ]]></literal>
    <justification jstring="[back_rewrite(5500),rewrite(6048(9))].">
      <j1 rule="back_rewrite" parents="5500"/>
      <j2 rule="rewrite" parents="6048"/>
    </justification>
  </clause>

  <clause id="6225">
    <literal><![CDATA[
      f(x,f(f(f(y,x),f(f(y,x),f(y,x))),f(f(x,f(y,x)),y))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(5247),rewrite(6048(6),2963(3),6221(5))].">
      <j1 rule="back_rewrite" parents="5247"/>
      <j2 rule="rewrite" parents="6048 2963 6221"/>
    </justification>
  </clause>

  <clause id="6226">
    <literal><![CDATA[
      f(x,f(f(f(y,x),f(f(y,x),f(y,x))),f(f(x,f(y,x)),x))) = f(y,x)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(5246),rewrite(6048(6),2963(3),6221(5))].">
      <j1 rule="back_rewrite" parents="5246"/>
      <j2 rule="rewrite" parents="6048 2963 6221"/>
    </justification>
  </clause>

  <clause id="6232">
    <literal><![CDATA[
      f(f(x,y),f(f(x,y),y)) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(6101),rewrite(6193(6),5201(9))].">
      <j1 rule="back_rewrite" parents="6101"/>
      <j2 rule="rewrite" parents="6193 5201"/>
    </justification>
  </clause>

  <clause id="6244">
    <literal><![CDATA[
      f(x,f(f(x,f(x,x)),f(f(x,f(x,x)),f(f(f(y,x),x),f(z,x))))) = f(f(x,f(x,x)),f(f(f(y,x),x),f(z,x)))
    ]]></literal>
    <justification jstring="[back_rewrite(5272),rewrite(6193(7),6193(16))].">
      <j1 rule="back_rewrite" parents="5272"/>
      <j2 rule="rewrite" parents="6193 6193"/>
    </justification>
  </clause>

  <clause id="6245">
    <literal><![CDATA[
      f(x,f(f(x,f(x,x)),f(f(x,f(x,x)),f(f(f(y,x),x),f(x,z))))) = f(f(x,f(x,x)),f(f(f(y,x),x),f(x,z)))
    ]]></literal>
    <justification jstring="[back_rewrite(5271),rewrite(6193(7),6193(16))].">
      <j1 rule="back_rewrite" parents="5271"/>
      <j2 rule="rewrite" parents="6193 6193"/>
    </justification>
  </clause>

  <clause id="6277">
    <literal><![CDATA[
      f(f(f(f(x,f(x,x)),f(f(f(y,x),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)),f(f(y,x),v)))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(4343),rewrite(6193(5))].">
      <j1 rule="back_rewrite" parents="4343"/>
      <j2 rule="rewrite" parents="6193"/>
    </justification>
  </clause>

  <clause id="6315">
    <literal><![CDATA[
      f(x,f(x,f(x,y))) = f(x,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(6130),rewrite(6211(5),5201(14))].">
      <j1 rule="back_rewrite" parents="6130"/>
      <j2 rule="rewrite" parents="6211 5201"/>
    </justification>
  </clause>

  <clause id="6425">
    <literal><![CDATA[
      f(x,f(x,f(y,x))) = f(y,x)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(6138),rewrite(6221(5),5201(14))].">
      <j1 rule="back_rewrite" parents="6138"/>
      <j2 rule="rewrite" parents="6221 5201"/>
    </justification>
  </clause>

  <clause id="6696">
    <literal><![CDATA[
      f(x,f(f(f(f(f(y,x),x),f(f(y,x),x)),f(f(f(f(y,x),x),f(y,x)),f(f(f(y,x),x),f(y,x)))),f(f(f(f(f(y,x),x),f(y,x)),f(f(y,x),x)),f(y,x)))) = f(f(y,x),x)
    ]]></literal>
    <justification jstring="[para(6232(a,1),125(a,1,1))].">
      <j1 rule="para" parents="6232 125"/>
    </justification>
  </clause>

  <clause id="6732">
    <literal><![CDATA[
      f(f(x,y),f(f(x,y),x)) = x
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(3547(a,1),6232(a,1,1)),rewrite(3547(5))].">
      <j1 rule="para" parents="3547 6232"/>
      <j2 rule="rewrite" parents="3547"/>
    </justification>
  </clause>

  <clause id="6878">
    <literal><![CDATA[
      f(f(x,y),f(f(f(f(y,f(x,y)),f(y,f(x,y))),f(f(f(y,f(x,y)),y),f(f(y,f(x,y)),y))),f(f(f(f(y,f(x,y)),y),f(y,f(x,y))),f(z,f(y,f(x,y)))))) = f(y,f(x,y))
    ]]></literal>
    <justification jstring="[para(6425(a,1),128(a,1,1))].">
      <j1 rule="para" parents="6425 128"/>
    </justification>
  </clause>

  <clause id="6945">
    <literal><![CDATA[
      f(f(f(x,y),f(f(f(f(x,y),f(y,f(x,y))),f(y,y)),f(f(y,y),z))),y) = f(y,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(6425(a,1),1567(a,1,1,1)),rewrite(6425(4))].">
      <j1 rule="para" parents="6425 1567"/>
      <j2 rule="rewrite" parents="6425"/>
    </justification>
  </clause>

  <clause id="6956">
    <literal><![CDATA[
      f(f(x,y),f(f(x,y),f(x,y))) = f(y,f(y,y))
    ]]></literal>
    <justification jstring="[para(5136(a,1),6425(a,1,2,2)),rewrite(6204(11),6049(6),5136(11))].">
      <j1 rule="para" parents="5136 6425"/>
      <j2 rule="rewrite" parents="6204 6049 5136"/>
    </justification>
  </clause>

  <clause id="7257">
    <literal><![CDATA[
      f(f(x,f(y,x)),x) = f(y,x)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(6226),rewrite(6956(5),4975(7))].">
      <j1 rule="back_rewrite" parents="6226"/>
      <j2 rule="rewrite" parents="6956 4975"/>
    </justification>
  </clause>

  <clause id="7258">
    <literal><![CDATA[
      f(x,f(f(x,f(x,x)),f(f(x,f(y,x)),y))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(6225),rewrite(6956(5))].">
      <j1 rule="back_rewrite" parents="6225"/>
      <j2 rule="rewrite" parents="6956"/>
    </justification>
  </clause>

  <clause id="7260">
    <literal><![CDATA[
      f(f(f(x,y),f(x,y)),f(y,y)) = f(y,f(y,y))
    ]]></literal>
    <justification jstring="[back_rewrite(6221),rewrite(6956(10))].">
      <j1 rule="back_rewrite" parents="6221"/>
      <j2 rule="rewrite" parents="6956"/>
    </justification>
  </clause>

  <clause id="7263">
    <literal><![CDATA[
      f(x,f(f(y,f(y,y)),f(f(x,f(x,y)),y))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(6216),rewrite(6956(5))].">
      <j1 rule="back_rewrite" parents="6216"/>
      <j2 rule="rewrite" parents="6956"/>
    </justification>
  </clause>

  <clause id="7267">
    <literal><![CDATA[
      f(f(f(x,y),f(x,y)),f(x,x)) = f(y,f(y,y))
    ]]></literal>
    <justification jstring="[back_rewrite(6211),rewrite(6956(10))].">
      <j1 rule="back_rewrite" parents="6211"/>
      <j2 rule="rewrite" parents="6956"/>
    </justification>
  </clause>

  <clause id="7271">
    <literal><![CDATA[
      f(f(f(x,y),f(f(y,f(y,y)),f(x,y))),f(f(y,f(y,y)),f(z,f(x,y)))) = f(z,f(x,y))
    ]]></literal>
    <justification jstring="[back_rewrite(6199),rewrite(6956(11))].">
      <j1 rule="back_rewrite" parents="6199"/>
      <j2 rule="rewrite" parents="6956"/>
    </justification>
  </clause>

  <clause id="7286">
    <literal><![CDATA[
      f(f(x,f(x,x)),y) = f(y,y)
    ]]></literal>
    <justification jstring="[back_rewrite(6146),rewrite(6956(26),6956(17),6956(5))].">
      <j1 rule="back_rewrite" parents="6146"/>
      <j2 rule="rewrite" parents="6956 6956 6956"/>
    </justification>
  </clause>

  <clause id="7298">
    <literal><![CDATA[
      f(f(x,y),f(f(y,f(y,y)),f(x,y))) = f(y,f(y,y))
    ]]></literal>
    <justification jstring="[back_rewrite(6050),rewrite(6956(11))].">
      <j1 rule="back_rewrite" parents="6050"/>
      <j2 rule="rewrite" parents="6956"/>
    </justification>
  </clause>

  <clause id="7308">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(y,y)) = y
    ]]></literal>
    <justification jstring="[back_rewrite(5905),rewrite(6956(26),6956(17),6956(5))].">
      <j1 rule="back_rewrite" parents="5905"/>
      <j2 rule="rewrite" parents="6956 6956 6956"/>
    </justification>
  </clause>

  <clause id="7471">
    <literal><![CDATA[
      f(f(x,y),f(f(y,f(y,y)),f(f(f(x,y),f(y,f(x,y))),f(z,f(y,f(x,y)))))) = f(y,f(x,y))
    ]]></literal>
    <justification jstring="[back_rewrite(6878),rewrite(7257(9),7257(10),7260(10),6956(6),7257(6))].">
      <j1 rule="back_rewrite" parents="6878"/>
      <j2 rule="rewrite" parents="7257 7257 7260 6956 7257"/>
    </justification>
  </clause>

  <clause id="7483">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(x,f(x,x)),f(y,f(z,x)))) = f(y,f(z,x))
    ]]></literal>
    <justification jstring="[back_rewrite(7271),rewrite(7298(6))].">
      <j1 rule="back_rewrite" parents="7271"/>
      <j2 rule="rewrite" parents="7298"/>
    </justification>
  </clause>

  <clause id="7492">
    <literal><![CDATA[
      f(f(x,f(y,z)),f(x,f(y,z))) = f(f(z,f(z,z)),f(x,f(y,z)))
    ]]></literal>
    <justification jstring="[back_rewrite(6203),rewrite(7298(6)),flip(a)].">
      <j1 rule="back_rewrite" parents="6203"/>
      <j2 rule="rewrite" parents="7298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7525">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(f(y,x),x),f(z,x))) = f(x,f(f(f(y,x),x),f(z,x)))
    ]]></literal>
    <justification jstring="[back_rewrite(6244),rewrite(7483(10)),flip(a)].">
      <j1 rule="back_rewrite" parents="6244"/>
      <j2 rule="rewrite" parents="7483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7629">
    <literal><![CDATA[
      f(f(x,y),f(y,f(f(f(f(f(x,y),y),y),y),f(z,y)))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(3841),rewrite(7525(10))].">
      <j1 rule="back_rewrite" parents="3841"/>
      <j2 rule="rewrite" parents="7525"/>
    </justification>
  </clause>

  <clause id="7636">
    <literal><![CDATA[
      f(f(x,y),f(y,f(f(f(y,x),y),f(y,z)))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(6732(a,1),2(a,1,2,2,1,1,1)),rewrite(2963(5),7257(5))].">
      <j1 rule="para" parents="6732 2"/>
      <j2 rule="rewrite" parents="2963 7257"/>
    </justification>
  </clause>

  <clause id="7728">
    <literal><![CDATA[
      f(f(x,y),f(f(z,f(z,z)),y)) = y
    ]]></literal>
    <justification jstring="[para(7286(a,2),20(a,1,2))].">
      <j1 rule="para" parents="7286 20"/>
    </justification>
  </clause>

  <clause id="7732">
    <literal><![CDATA[
      f(x,f(f(y,f(y,y)),f(z,x))) = f(z,x)
    ]]></literal>
    <justification jstring="[para(7286(a,2),82(a,1,2))].">
      <j1 rule="para" parents="7286 82"/>
    </justification>
  </clause>

  <clause id="7738">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),y),f(y,z)) = y
    ]]></literal>
    <justification jstring="[para(7286(a,2),80(a,1,1)),rewrite(2962(7),2989(5),2989(7),5202(10))].">
      <j1 rule="para" parents="7286 80"/>
      <j2 rule="rewrite" parents="2962 2989 2989 5202"/>
    </justification>
  </clause>

  <clause id="7747">
    <literal><![CDATA[
      f(x,f(f(y,f(y,y)),f(x,z))) = f(x,z)
    ]]></literal>
    <justification jstring="[para(7286(a,2),91(a,1,2))].">
      <j1 rule="para" parents="7286 91"/>
    </justification>
  </clause>

  <clause id="7780">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),f(y,z)),z) = f(y,z)
    ]]></literal>
    <justification jstring="[para(7286(a,2),84(a,1,1)),rewrite(2962(14),2989(9),6956(9),2989(11),6956(11),7257(9),77(8))].">
      <j1 rule="para" parents="7286 84"/>
      <j2 rule="rewrite" parents="2962 2989 6956 2989 6956 7257 77"/>
    </justification>
  </clause>

  <clause id="7826">
    <literal><![CDATA[
      f(f(x,y),f(f(f(f(f(f(y,x),y),y),y),f(z,y)),f(f(f(f(f(y,x),y),y),y),f(z,y)))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(7286(a,1),96(a,1,2)),rewrite(2962(5),2962(6),2962(11),2962(12))].">
      <j1 rule="para" parents="7286 96"/>
      <j2 rule="rewrite" parents="2962 2962 2962 2962"/>
    </justification>
  </clause>

  <clause id="7856">
    <literal><![CDATA[
      f(x,f(f(y,f(y,y)),x)) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(7286(a,2),2989(a,2,2)),rewrite(2989(2)),flip(a)].">
      <j1 rule="para" parents="7286 2989"/>
      <j2 rule="rewrite" parents="2989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7880">
    <literal><![CDATA[
      f(f(x,f(x,x)),y) = f(y,f(x,f(x,x)))
    ]]></literal>
    <justification jstring="[para(7286(a,1),3547(a,1,1,1)),rewrite(2963(5)),flip(a)].">
      <j1 rule="para" parents="7286 3547"/>
      <j2 rule="rewrite" parents="2963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7881">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),f(y,z)),y) = f(y,z)
    ]]></literal>
    <justification jstring="[para(7286(a,2),3547(a,1,1))].">
      <j1 rule="para" parents="7286 3547"/>
    </justification>
  </clause>

  <clause id="7882">
    <literal><![CDATA[
      f(x,f(y,f(y,y))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(7286(a,1),3547(a,2)),rewrite(7728(7))].">
      <j1 rule="para" parents="7286 3547"/>
      <j2 rule="rewrite" parents="7728"/>
    </justification>
  </clause>

  <clause id="7890">
    <literal><![CDATA[
      f(f(x,y),f(f(y,f(f(z,f(z,z)),y)),f(f(f(f(f(x,y),y),y),y),f(y,u)))) = y
    ]]></literal>
    <justification jstring="[para(7286(a,2),3808(a,1,2,1,2))].">
      <j1 rule="para" parents="7286 3808"/>
    </justification>
  </clause>

  <clause id="7900">
    <literal><![CDATA[
      f(f(x,f(x,y)),x) = f(x,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(7286(a,1),2975(a,1,2,2,1,1)),rewrite(7267(5),2962(5),7732(7))].">
      <j1 rule="para" parents="7286 2975"/>
      <j2 rule="rewrite" parents="7267 2962 7732"/>
    </justification>
  </clause>

  <clause id="7920">
    <literal><![CDATA[
      f(f(x,y),f(f(f(f(z,f(z,z)),x),f(f(x,y),f(x,y))),f(f(f(x,y),x),f(u,x)))) = x
    ]]></literal>
    <justification jstring="[para(7286(a,2),3567(a,1,2,1,1))].">
      <j1 rule="para" parents="7286 3567"/>
    </justification>
  </clause>

  <clause id="7992">
    <literal><![CDATA[
      f(f(x,x),f(f(x,f(f(y,f(y,y)),x)),f(z,x))) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(7286(a,2),5136(a,1,2,1,2))].">
      <j1 rule="para" parents="7286 5136"/>
    </justification>
  </clause>

  <clause id="7994">
    <literal><![CDATA[
      f(f(x,x),f(f(x,y),f(x,y))) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(7286(a,1),5192(a,1,2))].">
      <j1 rule="para" parents="7286 5192"/>
    </justification>
  </clause>

  <clause id="8021">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),y),f(f(y,y),f(x,f(x,x)))) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(7286(a,1),6732(a,1,2,1))].">
      <j1 rule="para" parents="7286 6732"/>
    </justification>
  </clause>

  <clause id="8028">
    <literal><![CDATA[
      f(f(f(x,y),x),f(x,y)) = x
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(3571),rewrite(7738(8),3547(4),7994(6),7732(9))].">
      <j1 rule="back_rewrite" parents="3571"/>
      <j2 rule="rewrite" parents="7738 3547 7994 7732"/>
    </justification>
  </clause>

  <clause id="8165">
    <literal><![CDATA[
      f(f(x,y),y) = f(y,f(x,y))
    ]]></literal>
    <justification jstring="[back_rewrite(6696),rewrite(7994(15),6956(8),8028(9),7308(6)),flip(a)].">
      <j1 rule="back_rewrite" parents="6696"/>
      <j2 rule="rewrite" parents="7994 6956 8028 7308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8439">
    <literal><![CDATA[
      f(f(x,y),f(f(y,f(f(z,f(z,z)),y)),f(f(y,f(x,y)),f(y,u)))) = y
    ]]></literal>
    <justification jstring="[back_rewrite(7890),rewrite(8165(7),7257(8),8165(7))].">
      <j1 rule="back_rewrite" parents="7890"/>
      <j2 rule="rewrite" parents="8165 7257 8165"/>
    </justification>
  </clause>

  <clause id="8468">
    <literal><![CDATA[
      f(f(x,y),f(f(f(f(y,x),y),f(z,y)),f(f(f(y,x),y),f(z,y)))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(7826),rewrite(8165(4),7257(5),8165(8),7257(9))].">
      <j1 rule="back_rewrite" parents="7826"/>
      <j2 rule="rewrite" parents="8165 7257 8165 7257"/>
    </justification>
  </clause>

  <clause id="8528">
    <literal><![CDATA[
      f(f(x,y),f(y,f(f(y,f(x,y)),f(z,y)))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(7629),rewrite(8165(3),7257(4),8165(3))].">
      <j1 rule="back_rewrite" parents="7629"/>
      <j2 rule="rewrite" parents="8165 7257 8165"/>
    </justification>
  </clause>

  <clause id="8873">
    <literal><![CDATA[
      f(f(f(f(x,f(x,x)),f(f(x,f(y,x)),f(x,z))),f(y,x)),f(f(f(f(y,x),f(y,x)),u),f(f(f(u,f(x,u)),f(y,x)),f(f(y,x),v)))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(6277),rewrite(8165(4),8165(15))].">
      <j1 rule="back_rewrite" parents="6277"/>
      <j2 rule="rewrite" parents="8165 8165"/>
    </justification>
  </clause>

  <clause id="8883">
    <literal><![CDATA[
      f(x,f(f(x,f(x,x)),f(f(x,f(x,x)),f(f(x,f(y,x)),f(x,z))))) = f(f(x,f(x,x)),f(f(x,f(y,x)),f(x,z)))
    ]]></literal>
    <justification jstring="[back_rewrite(6245),rewrite(8165(6),8165(15))].">
      <j1 rule="back_rewrite" parents="6245"/>
      <j2 rule="rewrite" parents="8165 8165"/>
    </justification>
  </clause>

  <clause id="8888">
    <literal><![CDATA[
      f(f(x,y),f(y,f(x,y))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(6232),rewrite(8165(3))].">
      <j1 rule="back_rewrite" parents="6232"/>
      <j2 rule="rewrite" parents="8165"/>
    </justification>
  </clause>

  <clause id="9223">
    <literal><![CDATA[
      f(x,f(f(x,y),f(y,x))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(4180),rewrite(8165(3),8165(5),8888(5))].">
      <j1 rule="back_rewrite" parents="4180"/>
      <j2 rule="rewrite" parents="8165 8165 8888"/>
    </justification>
  </clause>

  <clause id="9261">
    <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),v)))) = f(z,x)
    ]]></literal>
    <justification jstring="[back_rewrite(3943),rewrite(8165(5),8165(14))].">
      <j1 rule="back_rewrite" parents="3943"/>
      <j2 rule="rewrite" parents="8165 8165"/>
    </justification>
  </clause>

  <clause id="9368">
    <literal><![CDATA[
      f(f(f(f(f(f(x,y),f(x,y)),z),f(f(f(z,f(x,z)),f(x,y)),f(f(x,y),u))),x),f(f(f(x,x),v),f(f(f(v,f(f(x,y),v)),x),f(x,w)))) = x
    ]]></literal>
    <justification jstring="[back_rewrite(3549),rewrite(8165(6),8165(18))].">
      <j1 rule="back_rewrite" parents="3549"/>
      <j2 rule="rewrite" parents="8165 8165"/>
    </justification>
  </clause>

  <clause id="9532">
    <literal><![CDATA[
      f(f(x,y),f(f(y,f(y,y)),f(y,f(z,f(y,f(x,y)))))) = f(y,f(x,y))
    ]]></literal>
    <justification jstring="[back_rewrite(7471),rewrite(8888(7))].">
      <j1 rule="back_rewrite" parents="7471"/>
      <j2 rule="rewrite" parents="8888"/>
    </justification>
  </clause>

  <clause id="9535">
    <literal><![CDATA[
      f(f(f(x,y),f(f(y,f(y,y)),f(f(y,y),z))),y) = f(y,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(6945),rewrite(8888(5))].">
      <j1 rule="back_rewrite" parents="6945"/>
      <j2 rule="rewrite" parents="8888"/>
    </justification>
  </clause>

  <clause id="9547">
    <literal><![CDATA[
      f(x,f(f(y,f(y,y)),f(y,f(y,y)))) = f(y,f(y,y))
    ]]></literal>
    <justification jstring="[para(7308(a,1),77(a,1,1))].">
      <j1 rule="para" parents="7308 77"/>
    </justification>
  </clause>

  <clause id="9548">
    <literal><![CDATA[
      f(f(x,x),f(y,f(y,y))) = x
    ]]></literal>
    <justification jstring="[para(7308(a,1),3547(a,1,1,1)),rewrite(7308(4),7308(8))].">
      <j1 rule="para" parents="7308 3547"/>
      <j2 rule="rewrite" parents="7308 7308"/>
    </justification>
  </clause>

  <clause id="9549">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(x,f(x,x)),y)) = y
    ]]></literal>
    <justification jstring="[para(7308(a,1),6315(a,1,2,2)),rewrite(7308(10))].">
      <j1 rule="para" parents="7308 6315"/>
      <j2 rule="rewrite" parents="7308"/>
    </justification>
  </clause>

  <clause id="9560">
    <literal><![CDATA[
      f(x,f(f(y,f(y,y)),x)) = f(y,f(y,y))
    ]]></literal>
    <justification jstring="[back_rewrite(8021),rewrite(9548(7),8165(4))].">
      <j1 rule="back_rewrite" parents="8021"/>
      <j2 rule="rewrite" parents="9548 8165"/>
    </justification>
  </clause>

  <clause id="9563">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(x,f(y,x)),f(x,z))) = f(x,f(f(x,f(y,x)),f(x,z)))
    ]]></literal>
    <justification jstring="[back_rewrite(8883),rewrite(9549(10)),flip(a)].">
      <j1 rule="back_rewrite" parents="8883"/>
      <j2 rule="rewrite" parents="9549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9566">
    <literal><![CDATA[
      f(f(x,y),f(f(z,f(z,z)),f(f(y,f(x,y)),f(y,u)))) = y
    ]]></literal>
    <justification jstring="[back_rewrite(8439),rewrite(9560(5))].">
      <j1 rule="back_rewrite" parents="8439"/>
      <j2 rule="rewrite" parents="9560"/>
    </justification>
  </clause>

  <clause id="9569">
    <literal><![CDATA[
      f(f(x,x),f(f(y,f(y,y)),f(z,x))) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[back_rewrite(7992),rewrite(9560(5))].">
      <j1 rule="back_rewrite" parents="7992"/>
      <j2 rule="rewrite" parents="9560"/>
    </justification>
  </clause>

  <clause id="9584">
    <literal><![CDATA[
      f(x,f(x,x)) = f(y,f(y,y))
    ]]></literal>
    <justification jstring="[back_rewrite(7856),rewrite(9560(4))].">
      <j1 rule="back_rewrite" parents="7856"/>
      <j2 rule="rewrite" parents="9560"/>
    </justification>
  </clause>

  <clause id="9602">
    <literal><![CDATA[
      f(f(f(x,f(f(x,f(y,x)),f(x,z))),f(y,x)),f(f(f(f(y,x),f(y,x)),u),f(f(f(u,f(x,u)),f(y,x)),f(f(y,x),v)))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(8873),rewrite(9563(7))].">
      <j1 rule="back_rewrite" parents="8873"/>
      <j2 rule="rewrite" parents="9563"/>
    </justification>
  </clause>

  <clause id="9654">
    <literal><![CDATA[
      f(x,f(x,x)) = c_0
    ]]></literal>
    <justification jstring="[new_symbol(9584)].">
      <j1 rule="new_symbol" parents="9584"/>
    </justification>
  </clause>

  <clause id="9680">
    <literal><![CDATA[
      f(f(x,x),f(c_0,f(y,x))) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(9569),rewrite(9654(3),9654(7))].">
      <j1 rule="back_rewrite" parents="9569"/>
      <j2 rule="rewrite" parents="9654 9654"/>
    </justification>
  </clause>

  <clause id="9683">
    <literal><![CDATA[
      f(f(x,y),f(c_0,f(f(y,f(x,y)),f(y,z)))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(9566),rewrite(9654(3))].">
      <j1 rule="back_rewrite" parents="9566"/>
      <j2 rule="rewrite" parents="9654"/>
    </justification>
  </clause>

  <clause id="9695">
    <literal><![CDATA[
      f(x,f(c_0,c_0)) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(9547),rewrite(9654(2),9654(3),9654(6))].">
      <j1 rule="back_rewrite" parents="9547"/>
      <j2 rule="rewrite" parents="9654 9654 9654"/>
    </justification>
  </clause>

  <clause id="9699">
    <literal><![CDATA[
      f(f(f(x,y),f(c_0,f(f(y,y),z))),y) = f(y,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(9535),rewrite(9654(3))].">
      <j1 rule="back_rewrite" parents="9535"/>
      <j2 rule="rewrite" parents="9654"/>
    </justification>
  </clause>

  <clause id="9701">
    <literal><![CDATA[
      f(f(x,y),f(c_0,f(y,f(z,f(y,f(x,y)))))) = f(y,f(x,y))
    ]]></literal>
    <justification jstring="[back_rewrite(9532),rewrite(9654(3))].">
      <j1 rule="back_rewrite" parents="9532"/>
      <j2 rule="rewrite" parents="9654"/>
    </justification>
  </clause>

  <clause id="10228">
    <literal><![CDATA[
      f(f(x,x),f(f(x,y),f(x,y))) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(7994),rewrite(9654(7))].">
      <j1 rule="back_rewrite" parents="7994"/>
      <j2 rule="rewrite" parents="9654"/>
    </justification>
  </clause>

  <clause id="10245">
    <literal><![CDATA[
      f(f(x,y),f(f(f(c_0,x),f(f(x,y),f(x,y))),f(f(f(x,y),x),f(z,x)))) = x
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(7920),rewrite(9654(3))].">
      <j1 rule="back_rewrite" parents="7920"/>
      <j2 rule="rewrite" parents="9654"/>
    </justification>
  </clause>

  <clause id="10248">
    <literal><![CDATA[
      f(x,c_0) = f(x,x)
    ]]></literal>
    <justification jstring="[back_rewrite(7882),rewrite(9654(2))].">
      <j1 rule="back_rewrite" parents="7882"/>
      <j2 rule="rewrite" parents="9654"/>
    </justification>
  </clause>

  <clause id="10249">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),x) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(7881),rewrite(9654(2))].">
      <j1 rule="back_rewrite" parents="7881"/>
      <j2 rule="rewrite" parents="9654"/>
    </justification>
  </clause>

  <clause id="10250">
    <literal><![CDATA[
      f(c_0,x) = f(x,x)
    ]]></literal>
    <justification jstring="[back_rewrite(7880),rewrite(9654(2),9654(4),10248(4))].">
      <j1 rule="back_rewrite" parents="7880"/>
      <j2 rule="rewrite" parents="9654 9654 10248"/>
    </justification>
  </clause>

  <clause id="10254">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),y) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(7780),rewrite(9654(2))].">
      <j1 rule="back_rewrite" parents="7780"/>
      <j2 rule="rewrite" parents="9654"/>
    </justification>
  </clause>

  <clause id="10260">
    <literal><![CDATA[
      f(x,f(c_0,f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(7747),rewrite(9654(2))].">
      <j1 rule="back_rewrite" parents="7747"/>
      <j2 rule="rewrite" parents="9654"/>
    </justification>
  </clause>

  <clause id="10263">
    <literal><![CDATA[
      f(x,f(c_0,f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(7732),rewrite(9654(2))].">
      <j1 rule="back_rewrite" parents="7732"/>
      <j2 rule="rewrite" parents="9654"/>
    </justification>
  </clause>

  <clause id="10265">
    <literal><![CDATA[
      f(f(x,f(y,z)),c_0) = f(c_0,f(x,f(y,z)))
    ]]></literal>
    <justification jstring="[back_rewrite(7492),rewrite(10248(5,R),9654(6))].">
      <j1 rule="back_rewrite" parents="7492"/>
      <j2 rule="rewrite" parents="10248 9654"/>
    </justification>
  </clause>

  <clause id="10270">
    <literal><![CDATA[
      f(c_0,f(x,x)) = x
    ]]></literal>
    <justification jstring="[back_rewrite(7308),rewrite(9654(2))].">
      <j1 rule="back_rewrite" parents="7308"/>
      <j2 rule="rewrite" parents="9654"/>
    </justification>
  </clause>

  <clause id="10271">
    <literal><![CDATA[
      f(x,f(c_0,f(f(x,f(x,y)),y))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(7263),rewrite(9654(2))].">
      <j1 rule="back_rewrite" parents="7263"/>
      <j2 rule="rewrite" parents="9654"/>
    </justification>
  </clause>

  <clause id="10275">
    <literal><![CDATA[
      f(x,f(c_0,f(f(x,f(y,x)),y))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(7258),rewrite(9654(2))].">
      <j1 rule="back_rewrite" parents="7258"/>
      <j2 rule="rewrite" parents="9654"/>
    </justification>
  </clause>

  <clause id="10318">
    <literal><![CDATA[
      f(f(x,y),f(c_0,f(f(f(x,y),c_0),y))) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(6208),rewrite(9654(3),9654(5),9654(10))].">
      <j1 rule="back_rewrite" parents="6208"/>
      <j2 rule="rewrite" parents="9654 9654 9654"/>
    </justification>
  </clause>

  <clause id="10346">
    <literal><![CDATA[
      f(f(x,y),f(f(f(x,x),f(f(x,y),c_0)),f(f(f(x,y),x),f(z,x)))) = x
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(10245),rewrite(10250(3),10248(5,R))].">
      <j1 rule="back_rewrite" parents="10245"/>
      <j2 rule="rewrite" parents="10250 10248"/>
    </justification>
  </clause>

  <clause id="10347">
    <literal><![CDATA[
      f(f(x,x),f(f(x,y),c_0)) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(10228),rewrite(10248(4,R))].">
      <j1 rule="back_rewrite" parents="10228"/>
      <j2 rule="rewrite" parents="10248"/>
    </justification>
  </clause>

  <clause id="10514">
    <literal><![CDATA[
      f(f(f(x,f(f(x,f(y,x)),f(x,z))),f(y,x)),f(f(f(f(y,x),c_0),u),f(f(f(u,f(x,u)),f(y,x)),f(f(y,x),v)))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(9602),rewrite(10248(10,R))].">
      <j1 rule="back_rewrite" parents="9602"/>
      <j2 rule="rewrite" parents="10248"/>
    </justification>
  </clause>

  <clause id="10579">
    <literal><![CDATA[
      f(f(f(f(f(f(x,y),c_0),z),f(f(f(z,f(x,z)),f(x,y)),f(f(x,y),u))),x),f(f(f(x,x),v),f(f(f(v,f(f(x,y),v)),x),f(x,w)))) = x
    ]]></literal>
    <justification jstring="[back_rewrite(9368),rewrite(10248(3,R))].">
      <j1 rule="back_rewrite" parents="9368"/>
      <j2 rule="rewrite" parents="10248"/>
    </justification>
  </clause>

  <clause id="10759">
    <literal><![CDATA[
      f(f(x,y),f(c_0,f(f(f(y,x),y),f(z,y)))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(8468),rewrite(10248(10,R),10265(7))].">
      <j1 rule="back_rewrite" parents="8468"/>
      <j2 rule="rewrite" parents="10248 10265"/>
    </justification>
  </clause>

  <clause id="10839">
    <literal><![CDATA[
      f(f(f(x,y),c_0),y) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(3541),rewrite(10248(3,R))].">
      <j1 rule="back_rewrite" parents="3541"/>
      <j2 rule="rewrite" parents="10248"/>
    </justification>
  </clause>

  <clause id="10847">
    <literal><![CDATA[
      f(c1,f(f(c2,c3),c_0)) != f(c2,f(f(c1,c3),c_0))
    ]]></literal>
    <attribute><![CDATA[
      answer(A_SS)
    ]]></attribute>
    <justification jstring="[back_rewrite(3),rewrite(10248(8,R),10248(15,R))].">
      <j1 rule="back_rewrite" parents="3"/>
      <j2 rule="rewrite" parents="10248 10248"/>
    </justification>
  </clause>

  <clause id="10863">
    <literal><![CDATA[
      f(f(x,y),f(c_0,f(f(f(x,y),x),f(z,x)))) = x
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(10346),rewrite(10347(6))].">
      <j1 rule="back_rewrite" parents="10346"/>
      <j2 rule="rewrite" parents="10347"/>
    </justification>
  </clause>

  <clause id="10864">
    <literal><![CDATA[
      f(f(x,y),f(c_0,f(x,y))) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(10318),rewrite(10839(6))].">
      <j1 rule="back_rewrite" parents="10318"/>
      <j2 rule="rewrite" parents="10839"/>
    </justification>
  </clause>

  <clause id="10866">
    <literal><![CDATA[
      f(f(x,y),x) = f(x,f(x,y))
    ]]></literal>
    <justification jstring="[para(6315(a,1),7900(a,1,1))].">
      <j1 rule="para" parents="6315 7900"/>
    </justification>
  </clause>

  <clause id="10868">
    <literal><![CDATA[
      f(f(x,y),f(c_0,f(f(x,f(x,y)),f(z,x)))) = x
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(10863),rewrite(10866(4))].">
      <j1 rule="back_rewrite" parents="10863"/>
      <j2 rule="rewrite" parents="10866"/>
    </justification>
  </clause>

  <clause id="10909">
    <literal><![CDATA[
      f(f(x,y),f(c_0,f(f(y,f(y,x)),f(z,y)))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(10759),rewrite(10866(4))].">
      <j1 rule="back_rewrite" parents="10759"/>
      <j2 rule="rewrite" parents="10866"/>
    </justification>
  </clause>

  <clause id="11114">
    <literal><![CDATA[
      f(f(x,y),f(y,f(f(y,f(y,x)),f(y,z)))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(7636),rewrite(10866(3))].">
      <j1 rule="back_rewrite" parents="7636"/>
      <j2 rule="rewrite" parents="10866"/>
    </justification>
  </clause>

  <clause id="11197">
    <literal><![CDATA[
      f(f(x,y),c_0) = f(c_0,f(x,y))
    ]]></literal>
    <justification jstring="[para(9680(a,1),5675(a,1,2,2,2)),rewrite(10864(9),9695(8))].">
      <j1 rule="para" parents="9680 5675"/>
      <j2 rule="rewrite" parents="10864 9695"/>
    </justification>
  </clause>

  <clause id="11306">
    <literal><![CDATA[
      f(c1,f(c_0,f(c2,c3))) != f(c2,f(c_0,f(c1,c3)))
    ]]></literal>
    <attribute><![CDATA[
      answer(A_SS)
    ]]></attribute>
    <justification jstring="[back_rewrite(10847),rewrite(11197(6),11197(13))].">
      <j1 rule="back_rewrite" parents="10847"/>
      <j2 rule="rewrite" parents="11197 11197"/>
    </justification>
  </clause>

  <clause id="11480">
    <literal><![CDATA[
      f(f(f(f(f(c_0,f(x,y)),z),f(f(f(z,f(x,z)),f(x,y)),f(f(x,y),u))),x),f(f(f(x,x),v),f(f(f(v,f(f(x,y),v)),x),f(x,w)))) = x
    ]]></literal>
    <justification jstring="[back_rewrite(10579),rewrite(11197(3))].">
      <j1 rule="back_rewrite" parents="10579"/>
      <j2 rule="rewrite" parents="11197"/>
    </justification>
  </clause>

  <clause id="11522">
    <literal><![CDATA[
      f(f(f(x,f(f(x,f(y,x)),f(x,z))),f(y,x)),f(f(f(c_0,f(y,x)),u),f(f(f(u,f(x,u)),f(y,x)),f(f(y,x),v)))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(10514),rewrite(11197(10))].">
      <j1 rule="back_rewrite" parents="10514"/>
      <j2 rule="rewrite" parents="11197"/>
    </justification>
  </clause>

  <clause id="11742">
    <literal><![CDATA[
      f(c_0,f(c_0,f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(10249(a,1),6315(a,1,2,2)),rewrite(8165(8),10864(8),10866(5),10249(9))].">
      <j1 rule="para" parents="10249 6315"/>
      <j2 rule="rewrite" parents="8165 10864 10866 10249"/>
    </justification>
  </clause>

  <clause id="11775">
    <literal><![CDATA[
      f(f(x,y),f(z,f(c_0,f(x,y)))) = f(c_0,f(x,y))
    ]]></literal>
    <justification jstring="[para(10260(a,1),8528(a,1,1)),rewrite(10260(11),8165(9),10864(9),10263(11))].">
      <j1 rule="para" parents="10260 8528"/>
      <j2 rule="rewrite" parents="10260 8165 10864 10263"/>
    </justification>
  </clause>

  <clause id="11793">
    <literal><![CDATA[
      f(f(x,y),f(c_0,f(f(y,f(x,y)),f(z,y)))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(6425(a,1),9683(a,1,2,2,2))].">
      <j1 rule="para" parents="6425 9683"/>
    </justification>
  </clause>

  <clause id="11883">
    <literal><![CDATA[
      f(f(x,f(x,y)),f(c_0,f(f(x,y),f(x,z)))) = x
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(10866(a,1),9683(a,1,1)),rewrite(10866(5),6315(6))].">
      <j1 rule="para" parents="10866 9683"/>
      <j2 rule="rewrite" parents="10866 6315"/>
    </justification>
  </clause>

  <clause id="11902">
    <literal><![CDATA[
      f(f(f(x,f(y,y)),f(c_0,f(y,z))),f(y,y)) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(20(a,1),9699(a,1,1,2,2,1)),rewrite(10248(11,R),11197(11),10270(11))].">
      <j1 rule="para" parents="20 9699"/>
      <j2 rule="rewrite" parents="10248 11197 10270"/>
    </justification>
  </clause>

  <clause id="11914">
    <literal><![CDATA[
      f(f(x,f(x,y)),f(c_0,f(f(x,y),f(z,x)))) = x
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(6315(a,1),10868(a,1,2,2,1))].">
      <j1 rule="para" parents="6315 10868"/>
    </justification>
  </clause>

  <clause id="11961">
    <literal><![CDATA[
      f(f(x,f(x,y)),f(y,x)) = x
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(10909(a,1),10263(a,1)),flip(a)].">
      <j1 rule="para" parents="10909 10263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12109">
    <literal><![CDATA[
      f(f(f(f(x,y),f(y,x)),f(f(f(x,y),f(y,x)),x)),f(x,y)) = f(f(x,y),f(y,x))
    ]]></literal>
    <justification jstring="[para(9223(a,1),11961(a,1,2))].">
      <j1 rule="para" parents="9223 11961"/>
    </justification>
  </clause>

  <clause id="12225">
    <literal><![CDATA[
      f(f(f(c_0,f(f(x,f(x,y)),y)),x),f(x,f(f(x,f(x,y)),f(x,z)))) = x
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(10271(a,1),11114(a,1,2,2,1,2))].">
      <j1 rule="para" parents="10271 11114"/>
    </justification>
  </clause>

  <clause id="12268">
    <literal><![CDATA[
      f(f(c_0,f(f(x,f(y,x)),y)),f(c_0,f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(10275(a,1),10263(a,1,2,2)),rewrite(10275(15))].">
      <j1 rule="para" parents="10275 10263"/>
      <j2 rule="rewrite" parents="10275"/>
    </justification>
  </clause>

  <clause id="12291">
    <literal><![CDATA[
      f(f(c_0,f(f(x,f(y,x)),y)),f(f(f(c_0,f(f(x,f(y,x)),y)),x),f(y,x))) = f(f(c_0,f(f(x,f(y,x)),y)),x)
    ]]></literal>
    <justification jstring="[para(10275(a,1),9223(a,1,2,2))].">
      <j1 rule="para" parents="10275 9223"/>
    </justification>
  </clause>

  <clause id="12904">
    <literal><![CDATA[
      f(f(c_0,f(f(x,f(y,x)),f(z,x))),f(f(f(c_0,f(f(x,f(y,x)),f(z,x))),f(y,x)),x)) = f(f(c_0,f(f(x,f(y,x)),f(z,x))),f(y,x))
    ]]></literal>
    <justification jstring="[para(11793(a,1),9223(a,1,2,2))].">
      <j1 rule="para" parents="11793 9223"/>
    </justification>
  </clause>

  <clause id="13259">
    <literal><![CDATA[
      f(f(x,x),f(c_0,f(f(x,y),f(x,z)))) = x
    ]]></literal>
    <justification jstring="[para(11883(a,1),10254(a,1,1,2)),rewrite(10250(2),11883(15))].">
      <j1 rule="para" parents="11883 10254"/>
      <j2 rule="rewrite" parents="10250 11883"/>
    </justification>
  </clause>

  <clause id="13318">
    <literal><![CDATA[
      f(f(f(x,f(c_0,f(y,z))),f(y,y)),f(c_0,f(y,z))) = f(y,z)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(77(a,1),11902(a,1,1,2,2)),rewrite(10248(3,R),11197(3),10250(6),10248(9,R),11197(9))].">
      <j1 rule="para" parents="77 11902"/>
      <j2 rule="rewrite" parents="10248 11197 10250 10248 11197"/>
    </justification>
  </clause>

  <clause id="13347">
    <literal><![CDATA[
      f(f(f(x,y),f(z,x)),x) = f(c_0,f(f(x,y),f(z,x)))
    ]]></literal>
    <justification jstring="[para(11914(a,1),2963(a,1,2)),rewrite(10248(11,R),10866(7),11742(7))].">
      <j1 rule="para" parents="11914 2963"/>
      <j2 rule="rewrite" parents="10248 10866 11742"/>
    </justification>
  </clause>

  <clause id="13446">
    <literal><![CDATA[
      f(f(x,y),f(y,x)) = f(c_0,f(x,y))
    ]]></literal>
    <justification jstring="[back_rewrite(12109),rewrite(13347(7),10864(9)),flip(a)].">
      <j1 rule="back_rewrite" parents="12109"/>
      <j2 rule="rewrite" parents="13347 10864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13467">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),f(c_0,f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(13446(a,1),20(a,1,1)),rewrite(10248(6,R),11197(6))].">
      <j1 rule="para" parents="13446 20"/>
      <j2 rule="rewrite" parents="10248 11197"/>
    </justification>
  </clause>

  <clause id="13468">
    <literal><![CDATA[
      f(x,y) = f(y,x)
    ]]></literal>
    <justification jstring="[para(13446(a,1),2963(a,1,2)),rewrite(10248(3,R),11197(3),13467(7))].">
      <j1 rule="para" parents="13446 2963"/>
      <j2 rule="rewrite" parents="10248 11197 13467"/>
    </justification>
  </clause>

  <clause id="13472">
    <literal><![CDATA[
      f(c_0,f(f(x,y),f(c_0,f(f(x,z),f(x,f(x,y)))))) = f(x,x)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(10868(a,1),13446(a,2,2)),rewrite(13468(5),13468(6),13468(12),13468(13),13468(16),10248(17,R),13468(10),13468(12),10248(12))].">
      <j1 rule="para" parents="10868 13446"/>
      <j2 rule="rewrite" parents="13468 13468 13468 13468 13468 10248 13468 13468 10248"/>
    </justification>
  </clause>

  <clause id="13473">
    <literal><![CDATA[
      f(x,f(f(x,y),f(c_0,f(f(x,z),f(x,f(x,y)))))) = f(x,x)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(10909(a,1),13446(a,1,1)),rewrite(13468(4),13468(5),13468(7),13468(8),13468(11),13468(15),13468(16),13472(19))].">
      <j1 rule="para" parents="10909 13446"/>
      <j2 rule="rewrite" parents="13468 13468 13468 13468 13468 13468 13468 13472"/>
    </justification>
  </clause>

  <clause id="13475">
    <literal><![CDATA[
      f(f(x,y),f(x,f(c_0,f(y,f(x,f(x,y)))))) = f(c_0,f(x,f(c_0,f(y,f(x,f(x,y))))))
    ]]></literal>
    <justification jstring="[para(10271(a,1),13446(a,1,1)),rewrite(13468(5),13468(7),13468(13))].">
      <j1 rule="para" parents="10271 13446"/>
      <j2 rule="rewrite" parents="13468 13468 13468"/>
    </justification>
  </clause>

  <clause id="13476">
    <literal><![CDATA[
      f(c_0,f(x,f(c_0,f(y,f(x,f(x,y)))))) = f(c_0,f(x,y))
    ]]></literal>
    <justification jstring="[para(10271(a,1),13446(a,2,2)),rewrite(13468(4),13468(10),13468(12),10248(13,R),13468(8))].">
      <j1 rule="para" parents="10271 13446"/>
      <j2 rule="rewrite" parents="13468 13468 13468 10248 13468"/>
    </justification>
  </clause>

  <clause id="13510">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),f(f(x,x),f(z,f(c_0,f(x,y))))) = f(x,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(13318),rewrite(13468(6),13468(10))].">
      <j1 rule="back_rewrite" parents="13318"/>
      <j2 rule="rewrite" parents="13468 13468"/>
    </justification>
  </clause>

  <clause id="13561">
    <literal><![CDATA[
      f(f(x,y),f(c_0,f(f(x,z),f(x,f(x,y))))) = x
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(12904),rewrite(13468(2),13468(4),13468(5),13468(8),13468(10),13468(11),13468(13),13468(14),13468(15),13473(15),13468(8),13259(8),13468(2),13468(4),13468(5),13468(7),13468(8)),flip(a)].">
      <j1 rule="back_rewrite" parents="12904"/>
      <j2 rule="rewrite" parents="13468 13468 13468 13468 13468 13468 13468 13468 13468 13473 13468 13259 13468 13468 13468 13468 13468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13635">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),f(c_0,f(y,f(x,f(x,y))))) = f(x,f(c_0,f(y,f(x,f(x,y)))))
    ]]></literal>
    <justification jstring="[back_rewrite(12291),rewrite(13468(2),13468(4),13468(7),13468(9),13468(11),13468(12),13468(13),13475(13),13476(13),13468(9),13468(11),13468(13),13468(15))].">
      <j1 rule="back_rewrite" parents="12291"/>
      <j2 rule="rewrite" parents="13468 13468 13468 13468 13468 13468 13468 13475 13476 13468 13468 13468 13468"/>
    </justification>
  </clause>

  <clause id="13644">
    <literal><![CDATA[
      f(x,f(c_0,f(y,f(x,f(x,y))))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(12268),rewrite(13468(2),13468(4),13468(7),13468(9),13635(9),13468(7))].">
      <j1 rule="back_rewrite" parents="12268"/>
      <j2 rule="rewrite" parents="13468 13468 13468 13468 13635 13468"/>
    </justification>
  </clause>

  <clause id="13651">
    <literal><![CDATA[
      f(f(x,y),f(x,f(f(x,z),f(x,f(x,y))))) = x
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(12225),rewrite(13468(4),13468(6),13644(6),13468(5))].">
      <j1 rule="back_rewrite" parents="12225"/>
      <j2 rule="rewrite" parents="13468 13468 13644 13468"/>
    </justification>
  </clause>

  <clause id="13704">
    <literal><![CDATA[
      f(x,f(f(y,f(c_0,f(x,z))),f(f(u,f(x,z)),f(f(x,z),f(y,f(x,y)))))) = f(x,z)
    ]]></literal>
    <justification jstring="[back_rewrite(11522),rewrite(13468(1),13468(4),13468(6),13468(7),13651(7),13468(2),13468(4),13468(7),13468(8),13468(9),13468(10),13468(11),13468(14))].">
      <j1 rule="back_rewrite" parents="11522"/>
      <j2 rule="rewrite" parents="13468 13468 13468 13468 13651 13468 13468 13468 13468 13468 13468 13468 13468"/>
    </justification>
  </clause>

  <clause id="13731">
    <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(11480),rewrite(13468(4),13468(8),13468(10),13468(11),13468(13),13704(13),13468(3),13468(5),13468(7),13468(9))].">
      <j1 rule="back_rewrite" parents="11480"/>
      <j2 rule="rewrite" parents="13468 13468 13468 13468 13468 13704 13468 13468 13468 13468"/>
    </justification>
  </clause>

  <clause id="13907">
    <literal><![CDATA[
      f(x,f(f(x,y),f(y,f(z,f(x,y))))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(9261),rewrite(13468(2),13468(4),13468(6),13468(8),13468(10),13468(11),13731(11),13468(1),13468(4),13468(5),8888(5),13468(2),13468(3),13468(7))].">
      <j1 rule="back_rewrite" parents="9261"/>
      <j2 rule="rewrite" parents="13468 13468 13468 13468 13468 13468 13731 13468 13468 13468 8888 13468 13468 13468"/>
    </justification>
  </clause>

  <clause id="13956">
    <literal><![CDATA[
      f(f(x,f(y,x)),f(c_0,f(x,f(z,f(y,x))))) = f(y,x)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(9701(a,1),13561(a,1,2,2,2,2)),rewrite(9701(8),13468(5),8888(9),13468(6))].">
      <j1 rule="para" parents="9701 13561"/>
      <j2 rule="rewrite" parents="9701 13468 8888 13468"/>
    </justification>
  </clause>

  <clause id="14062">
    <literal><![CDATA[
      f(f(x,y),f(y,f(z,f(x,y)))) = f(c_0,f(y,f(z,f(x,y))))
    ]]></literal>
    <justification jstring="[para(13956(a,1),20(a,1,1)),rewrite(10248(12,R),13468(8),11742(8))].">
      <j1 rule="para" parents="13956 20"/>
      <j2 rule="rewrite" parents="10248 13468 11742"/>
    </justification>
  </clause>

  <clause id="14081">
    <literal><![CDATA[
      f(x,f(c_0,f(y,f(z,f(x,y))))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(13907),rewrite(14062(5))].">
      <j1 rule="back_rewrite" parents="13907"/>
      <j2 rule="rewrite" parents="14062"/>
    </justification>
  </clause>

  <clause id="14329">
    <literal><![CDATA[
      f(x,f(c_0,f(y,f(z,f(y,x))))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(14081(a,1),13468(a,2)),rewrite(13468(2),13468(6),13468(7))].">
      <j1 rule="para" parents="14081 13468"/>
      <j2 rule="rewrite" parents="13468 13468 13468"/>
    </justification>
  </clause>

  <clause id="14341">
    <literal><![CDATA[
      f(f(x,x),f(y,f(c_0,f(x,z)))) = x
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(13510(a,1),14081(a,1,2,2,2)),rewrite(13468(8),11775(8),11742(6),2962(3)),flip(a)].">
      <j1 rule="para" parents="13510 14081"/>
      <j2 rule="rewrite" parents="13468 11775 11742 2962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14411">
    <literal><![CDATA[
      f(x,f(x,f(y,f(c_0,f(x,z))))) = f(y,f(c_0,f(x,z)))
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(14341(a,1),8888(a,1,1)),rewrite(14341(10),13468(5))].">
      <j1 rule="para" parents="14341 8888"/>
      <j2 rule="rewrite" parents="14341 13468"/>
    </justification>
  </clause>

  <clause id="14440">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),f(c_0,f(x,z))) = f(z,f(c_0,f(x,y)))
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(14341(a,1),14329(a,1,2,2,2)),rewrite(13468(5))].">
      <j1 rule="para" parents="14341 14329"/>
      <j2 rule="rewrite" parents="13468"/>
    </justification>
  </clause>

  <clause id="16911">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),f(c_0,f(x,z))) = f(y,f(c_0,f(x,z)))
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(14440(a,1),13468(a,2))].">
      <j1 rule="para" parents="14440 13468"/>
    </justification>
  </clause>

  <clause id="16912">
    <literal><![CDATA[
      f(x,f(c_0,f(y,z))) = f(z,f(c_0,f(y,x)))
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(14440(a,2),13468(a,2)),rewrite(13468(4),16911(11))].">
      <j1 rule="para" parents="14440 13468"/>
      <j2 rule="rewrite" parents="13468 16911"/>
    </justification>
  </clause>

  <clause id="17426">
    <literal><![CDATA[
      f(x,f(c_0,f(y,z))) = f(y,f(c_0,f(x,z)))
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(16912(a,1),6315(a,1,2,2)),rewrite(13468(2),14411(6),13468(6))].">
      <j1 rule="para" parents="16912 6315"/>
      <j2 rule="rewrite" parents="13468 14411 13468"/>
    </justification>
  </clause>

  <clause id="17427">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer(A_SS)
    ]]></attribute>
    <justification jstring="[resolve(17426,a,11306,a)].">
      <j1 rule="resolve" parents="17426 11306"/>
    </justification>
  </clause>

</proof>

</proofs>
