<?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="2">

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

<heading><![CDATA[
Prover9 (32) version November-2006, November 2006.
Process 4529 was started by mccune on cleo.thornwood,
Wed Nov 22 12:20:45 2006
The command was "/home/mccune/bin/prover9 -f MOL-base.in".
]]></heading>

<proof number="1" length="231" max_count="59">

<comments><![CDATA[
% Proof 1 at 156.46 (+ 0.60) seconds: A_SS.
% Length of proof is 231.
% Level of proof is 50.
% Maximum clause weight is 59.
% Given clauses 1272.
]]></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="3" 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="4" 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="7">
    <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(3(a,1),3(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="3 3"/>
    </justification>
  </clause>

  <clause id="9">
    <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(3(a,1),3(a,1,2,2,2))].">
      <j1 rule="para" parents="3 3"/>
    </justification>
  </clause>

  <clause id="10">
    <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(3(a,1),9(a,1,1,2)),rewrite(3(12),3(12),3(14),3(17),3(30))].">
      <j1 rule="para" parents="3 9"/>
      <j2 rule="rewrite" parents="3 3 3 3 3"/>
    </justification>
  </clause>

  <clause id="11">
    <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)),x))) = f(z,x)
    ]]></literal>
    <justification jstring="[para(3(a,1),9(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="3 9"/>
    </justification>
  </clause>

  <clause id="14">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),z),y)) = y
    ]]></literal>
    <justification jstring="[para(3(a,1),10(a,1,2,2))].">
      <j1 rule="para" parents="3 10"/>
    </justification>
  </clause>

  <clause id="15">
    <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(f(f(y,y),w),f(f(f(f(f(y,v6),w),w),y),f(y,v7)))))))) = y
    ]]></literal>
    <justification jstring="[para(10(a,1),9(a,1,1,2)),rewrite(10(20),10(20),10(22),10(25),10(46))].">
      <j1 rule="para" parents="10 9"/>
      <j2 rule="rewrite" parents="10 10 10 10 10"/>
    </justification>
  </clause>

  <clause id="22">
    <literal><![CDATA[
      f(f(x,y),f(y,y)) = y
    ]]></literal>
    <justification jstring="[para(3(a,1),14(a,1,2,1))].">
      <j1 rule="para" parents="3 14"/>
    </justification>
  </clause>

  <clause id="38">
    <literal><![CDATA[
      f(f(x,f(y,y)),f(f(y,z),f(f(f(f(f(f(y,y),x),z),z),f(y,y)),f(f(y,y),u)))) = f(y,y)
    ]]></literal>
    <justification jstring="[para(22(a,1),3(a,1,2,1,1))].">
      <j1 rule="para" parents="22 3"/>
    </justification>
  </clause>

  <clause id="39">
    <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(22(a,1),3(a,1,2,1))].">
      <j1 rule="para" parents="22 3"/>
    </justification>
  </clause>

  <clause id="40">
    <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(22(a,1),3(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="22 3"/>
    </justification>
  </clause>

  <clause id="41">
    <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(22(a,1),3(a,1,2,2,1,1,1))].">
      <j1 rule="para" parents="22 3"/>
    </justification>
  </clause>

  <clause id="46">
    <literal><![CDATA[
      f(f(f(x,x),f(y,x)),f(f(f(f(y,x),f(y,x)),z),f(f(f(f(x,z),z),f(y,x)),x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(22(a,1),9(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="22 9"/>
    </justification>
  </clause>

  <clause id="47">
    <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(22(a,1),9(a,1,2,2,1,1,1))].">
      <j1 rule="para" parents="22 9"/>
    </justification>
  </clause>

  <clause id="48">
    <literal><![CDATA[
      f(f(x,f(y,y)),y) = f(y,y)
    ]]></literal>
    <justification jstring="[para(22(a,1),9(a,1,2,2,1)),rewrite(22(5),22(5))].">
      <j1 rule="para" parents="22 9"/>
      <j2 rule="rewrite" parents="22 22"/>
    </justification>
  </clause>

  <clause id="52">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),f(x,x)),f(f(f(x,f(x,x)),y),f(f(f(y,y),z),f(f(f(f(f(y,u),z),z),y),f(y,v)))))) = y
    ]]></literal>
    <justification jstring="[para(22(a,1),10(a,1,2,2,1,1,1))].">
      <j1 rule="para" parents="22 10"/>
    </justification>
  </clause>

  <clause id="57">
    <literal><![CDATA[
      f(f(f(x,x),y),x) = f(x,x)
    ]]></literal>
    <justification jstring="[para(14(a,1),22(a,1,1)),rewrite(14(7)),flip(a)].">
      <j1 rule="para" parents="14 22"/>
      <j2 rule="rewrite" parents="14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="59">
    <literal><![CDATA[
      f(f(x,y),f(y,f(f(y,y),f(y,z)))) = y
    ]]></literal>
    <justification jstring="[back_rewrite(39),rewrite(48(7))].">
      <j1 rule="back_rewrite" parents="39"/>
      <j2 rule="rewrite" parents="48"/>
    </justification>
  </clause>

  <clause id="67">
    <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>
    <justification jstring="[para(48(a,1),9(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="48 9"/>
    </justification>
  </clause>

  <clause id="68">
    <literal><![CDATA[
      f(f(f(x,x),f(y,z)),f(f(f(f(y,z),f(y,z)),x),f(f(f(f(x,x),x),f(y,z)),z))) = f(y,z)
    ]]></literal>
    <justification jstring="[para(48(a,1),9(a,1,2,2,1,1,1))].">
      <j1 rule="para" parents="48 9"/>
    </justification>
  </clause>

  <clause id="73">
    <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(57(a,1),3(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="57 3"/>
    </justification>
  </clause>

  <clause id="74">
    <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(57(a,1),3(a,1,2,2,1,1))].">
      <j1 rule="para" parents="57 3"/>
    </justification>
  </clause>

  <clause id="78">
    <literal><![CDATA[
      f(f(f(x,y),f(x,y)),f(f(f(f(x,y),f(x,y)),f(x,y)),f(f(f(f(x,y),f(x,y)),f(x,y)),y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(57(a,1),9(a,1,2,2,1,1))].">
      <j1 rule="para" parents="57 9"/>
    </justification>
  </clause>

  <clause id="82">
    <literal><![CDATA[
      f(f(x,y),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(22(a,1),57(a,1,1,1)),rewrite(22(6))].">
      <j1 rule="para" parents="22 57"/>
      <j2 rule="rewrite" parents="22"/>
    </justification>
  </clause>

  <clause id="86">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),f(f(y,x),f(y,x))),f(f(f(y,x),y),f(y,z)))) = y
    ]]></literal>
    <justification jstring="[para(82(a,1),3(a,1,2,2,1,1))].">
      <j1 rule="para" parents="82 3"/>
    </justification>
  </clause>

  <clause id="88">
    <literal><![CDATA[
      f(x,f(f(y,x),f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(3(a,1),82(a,1,1))].">
      <j1 rule="para" parents="3 82"/>
    </justification>
  </clause>

  <clause id="90">
    <literal><![CDATA[
      f(f(x,f(y,z)),f(f(f(f(y,z),f(y,z)),f(f(f(y,z),x),f(f(y,z),x))),f(f(f(f(y,z),x),f(y,z)),z))) = f(y,z)
    ]]></literal>
    <justification jstring="[para(82(a,1),9(a,1,2,2,1,1))].">
      <j1 rule="para" parents="82 9"/>
    </justification>
  </clause>

  <clause id="92">
    <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(f(f(y,y),z),f(f(f(f(f(y,u),z),z),y),f(y,v)))))) = y
    ]]></literal>
    <justification jstring="[para(82(a,1),10(a,1,2,2,1,1))].">
      <j1 rule="para" parents="82 10"/>
    </justification>
  </clause>

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

  <clause id="100">
    <literal><![CDATA[
      f(f(f(f(x,y),f(x,y)),y),f(f(f(y,y),z),f(f(f(f(f(x,y),z),z),y),f(y,u)))) = y
    ]]></literal>
    <justification jstring="[para(88(a,1),3(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="88 3"/>
    </justification>
  </clause>

  <clause id="102">
    <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(88(a,1),3(a,1,2,2,2))].">
      <j1 rule="para" parents="88 3"/>
    </justification>
  </clause>

  <clause id="103">
    <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(3(a,1),88(a,1,2,1)),rewrite(3(20),3(22))].">
      <j1 rule="para" parents="3 88"/>
      <j2 rule="rewrite" parents="3 3"/>
    </justification>
  </clause>

  <clause id="107">
    <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(v,y),u),u),y),f(y,w)))))) = y
    ]]></literal>
    <justification jstring="[para(88(a,1),10(a,1,2,2,2,2,1,1,1,1))].">
      <j1 rule="para" parents="88 10"/>
    </justification>
  </clause>

  <clause id="113">
    <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)),u),f(f(f(f(x,u),u),f(y,x)),f(f(y,x),v)))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(22(a,1),7(a,1,1,1,2,1,1,1))].">
      <j1 rule="para" parents="22 7"/>
    </justification>
  </clause>

  <clause id="121">
    <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)),f(x,x)),f(f(x,f(z,x)),f(f(z,x),v)))) = f(z,x)
    ]]></literal>
    <justification jstring="[para(82(a,1),7(a,1,2,2,1,1))].">
      <j1 rule="para" parents="82 7"/>
    </justification>
  </clause>

  <clause id="122">
    <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)),z))) = f(z,x)
    ]]></literal>
    <justification jstring="[para(82(a,1),7(a,1,2,2,2))].">
      <j1 rule="para" parents="82 7"/>
    </justification>
  </clause>

  <clause id="123">
    <literal><![CDATA[
      f(f(f(f(f(x,y),f(x,y)),z),f(f(f(f(y,z),z),f(x,y)),f(f(x,y),u))),f(f(x,y),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(7(a,1),88(a,1,2,1)),rewrite(7(37),7(40))].">
      <j1 rule="para" parents="7 88"/>
      <j2 rule="rewrite" parents="7 7"/>
    </justification>
  </clause>

  <clause id="141">
    <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(59(a,1),57(a,1)),flip(a)].">
      <j1 rule="para" parents="59 57"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="201">
    <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(74(a,1),88(a,1,2,1)),rewrite(74(16),74(18))].">
      <j1 rule="para" parents="74 88"/>
      <j2 rule="rewrite" parents="74 74"/>
    </justification>
  </clause>

  <clause id="210">
    <literal><![CDATA[
      f(x,f(f(x,x),f(x,y))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(141(a,1),22(a,1,1)),rewrite(141(9)),flip(a)].">
      <j1 rule="para" parents="141 22"/>
      <j2 rule="rewrite" parents="141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="215">
    <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)),f(f(f(f(y,z),f(y,z)),v),f(f(f(f(z,v),v),f(y,z)),z))))) = f(y,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),9(a,1,1,2)),rewrite(11(24),11(25),11(28),11(32),11(47))].">
      <j1 rule="para" parents="11 9"/>
      <j2 rule="rewrite" parents="11 11 11 11 11"/>
    </justification>
  </clause>

  <clause id="217">
    <literal><![CDATA[
      f(f(f(f(f(x,x),x),f(f(x,x),x)),x),f(f(f(f(x,x),x),f(f(x,x),x)),x)) = f(f(f(x,x),x),f(f(f(f(x,x),x),f(f(x,x),x)),x))
    ]]></literal>
    <justification jstring="[para(11(a,1),48(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="227">
    <literal><![CDATA[
      f(f(x,y),f(f(f(x,y),f(x,y)),y)) = f(f(x,y),f(x,y))
    ]]></literal>
    <justification jstring="[para(3(a,1),210(a,1,2,2))].">
      <j1 rule="para" parents="3 210"/>
    </justification>
  </clause>

  <clause id="231">
    <literal><![CDATA[
      f(f(x,x),f(x,f(f(x,x),y))) = x
    ]]></literal>
    <justification jstring="[para(22(a,1),210(a,1,2,1)),rewrite(82(8))].">
      <j1 rule="para" parents="22 210"/>
      <j2 rule="rewrite" parents="82"/>
    </justification>
  </clause>

  <clause id="234">
    <literal><![CDATA[
      f(f(x,y),f(f(f(x,y),f(x,y)),x)) = f(f(x,y),f(x,y))
    ]]></literal>
    <justification jstring="[para(82(a,1),210(a,1,2,2))].">
      <j1 rule="para" parents="82 210"/>
    </justification>
  </clause>

  <clause id="235">
    <literal><![CDATA[
      f(x,f(f(x,x),f(y,x))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(88(a,1),210(a,1,2,2))].">
      <j1 rule="para" parents="88 210"/>
    </justification>
  </clause>

  <clause id="237">
    <literal><![CDATA[
      f(f(f(f(f(x,x),x),f(f(x,x),x)),x),f(f(f(f(x,x),x),f(f(x,x),x)),x)) = f(f(f(x,x),x),f(f(x,x),x))
    ]]></literal>
    <justification jstring="[back_rewrite(217),rewrite(227(22))].">
      <j1 rule="back_rewrite" parents="217"/>
      <j2 rule="rewrite" parents="227"/>
    </justification>
  </clause>

  <clause id="239">
    <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(231(a,1),3(a,1,2,2,1,1,1)),rewrite(231(6))].">
      <j1 rule="para" parents="231 3"/>
      <j2 rule="rewrite" parents="231"/>
    </justification>
  </clause>

  <clause id="244">
    <literal><![CDATA[
      f(f(x,x),f(x,f(y,f(x,x)))) = x
    ]]></literal>
    <justification jstring="[para(88(a,1),231(a,1,2,2))].">
      <j1 rule="para" parents="88 231"/>
    </justification>
  </clause>

  <clause id="260">
    <literal><![CDATA[
      f(f(f(f(x,x),x),f(f(x,x),x)),x) = f(f(x,x),x)
    ]]></literal>
    <justification jstring="[para(11(a,1),244(a,1,2,2)),rewrite(237(13),57(14),82(11)),flip(a)].">
      <j1 rule="para" parents="11 244"/>
      <j2 rule="rewrite" parents="237 57 82"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="278">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),f(x,f(x,x))),f(x,x)) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(22(a,1),260(a,1,1,1,1)),rewrite(82(5),82(10))].">
      <j1 rule="para" parents="22 260"/>
      <j2 rule="rewrite" parents="82 82"/>
    </justification>
  </clause>

  <clause id="285">
    <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(88(a,1),201(a,1,1,2,2))].">
      <j1 rule="para" parents="88 201"/>
    </justification>
  </clause>

  <clause id="296">
    <literal><![CDATA[
      f(x,f(f(x,x),f(f(f(x,x),y),f(f(f(f(f(x,z),y),y),x),f(x,u))))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(3(a,1),227(a,1,1)),rewrite(3(11),3(11),3(23),3(23))].">
      <j1 rule="para" parents="3 227"/>
      <j2 rule="rewrite" parents="3 3 3 3"/>
    </justification>
  </clause>

  <clause id="327">
    <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(22(a,1),285(a,1,1,1,1)),rewrite(82(5),82(11))].">
      <j1 rule="para" parents="22 285"/>
      <j2 rule="rewrite" parents="82 82"/>
    </justification>
  </clause>

  <clause id="344">
    <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(f(f(y,y),w),f(f(f(f(f(v6,y),w),w),y),f(y,v7)))))))) = y
    ]]></literal>
    <justification jstring="[para(88(a,1),15(a,1,2,2,2,2,2,2,1,1,1,1))].">
      <j1 rule="para" parents="88 15"/>
    </justification>
  </clause>

  <clause id="353">
    <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(88(a,1),239(a,1,2,2,2))].">
      <j1 rule="para" parents="88 239"/>
    </justification>
  </clause>

  <clause id="394">
    <literal><![CDATA[
      f(f(x,x),f(f(x,f(x,f(f(x,x),y))),x)) = x
    ]]></literal>
    <justification jstring="[para(88(a,1),353(a,1,2))].">
      <j1 rule="para" parents="88 353"/>
    </justification>
  </clause>

  <clause id="454">
    <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)),y))) = f(y,z)
    ]]></literal>
    <justification jstring="[para(82(a,1),41(a,1,2,2,2))].">
      <j1 rule="para" parents="82 41"/>
    </justification>
  </clause>

  <clause id="462">
    <literal><![CDATA[
      f(x,f(f(f(x,x),x),f(x,f(f(x,x),y)))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(285(a,1),41(a,1,2,2,1)),rewrite(22(4),82(3),88(6))].">
      <j1 rule="para" parents="285 41"/>
      <j2 rule="rewrite" parents="22 82 88"/>
    </justification>
  </clause>

  <clause id="463">
    <literal><![CDATA[
      f(f(x,x),f(f(x,f(x,x)),f(f(x,x),f(x,y)))) = x
    ]]></literal>
    <justification jstring="[para(327(a,1),41(a,1,2,2,1)),rewrite(48(3),88(8))].">
      <j1 rule="para" parents="327 41"/>
      <j2 rule="rewrite" parents="48 88"/>
    </justification>
  </clause>

  <clause id="474">
    <literal><![CDATA[
      f(f(f(x,x),f(y,x)),f(f(f(f(y,x),f(y,x)),f(f(x,x),f(x,z))),f(f(f(f(x,x),f(f(x,x),f(x,z))),f(y,x)),f(f(y,x),u)))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(210(a,1),40(a,1,2,2,1,1,1))].">
      <j1 rule="para" parents="210 40"/>
    </justification>
  </clause>

  <clause id="521">
    <literal><![CDATA[
      f(f(f(x,x),f(y,x)),f(f(f(f(y,x),f(y,x)),f(x,x)),f(f(x,f(y,x)),x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(82(a,1),46(a,1,2,2,1,1))].">
      <j1 rule="para" parents="82 46"/>
    </justification>
  </clause>

  <clause id="564">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(x,f(f(x,x),y))) = x
    ]]></literal>
    <justification jstring="[para(41(a,1),47(a,1,2,2,1)),rewrite(82(3),82(6),82(10),82(13),82(16),82(19),82(27),231(27),48(23),82(9),82(3),82(6)),flip(a)].">
      <j1 rule="para" parents="41 47"/>
      <j2 rule="rewrite" parents="82 82 82 82 82 82 82 231 48 82 82 82"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="577">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(x,f(y,f(x,x)))) = x
    ]]></literal>
    <justification jstring="[para(88(a,1),564(a,1,2,2))].">
      <j1 rule="para" parents="88 564"/>
    </justification>
  </clause>

  <clause id="590">
    <literal><![CDATA[
      f(f(f(x,x),x),f(f(x,x),f(y,x))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(22(a,1),577(a,1,1,2)),rewrite(82(6))].">
      <j1 rule="para" parents="22 577"/>
      <j2 rule="rewrite" parents="82"/>
    </justification>
  </clause>

  <clause id="681">
    <literal><![CDATA[
      f(f(f(f(x,x),y),f(f(f(f(f(x,z),y),y),x),f(u,x))),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(102(a,1),88(a,1,2,1)),rewrite(102(20),102(22))].">
      <j1 rule="para" parents="102 88"/>
      <j2 rule="rewrite" parents="102 102"/>
    </justification>
  </clause>

  <clause id="684">
    <literal><![CDATA[
      f(f(f(f(x,y),f(x,y)),y),f(f(f(y,y),z),f(f(f(f(f(x,y),z),z),y),f(u,y)))) = y
    ]]></literal>
    <justification jstring="[para(88(a,1),102(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="88 102"/>
    </justification>
  </clause>

  <clause id="737">
    <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(564(a,1),102(a,1,2,2,1,1,1)),rewrite(231(7))].">
      <j1 rule="para" parents="564 102"/>
      <j2 rule="rewrite" parents="231"/>
    </justification>
  </clause>

  <clause id="837">
    <literal><![CDATA[
      f(f(x,x),f(f(x,f(x,x)),f(f(x,x),f(f(f(x,x),y),f(f(f(f(f(x,z),y),y),x),f(x,u)))))) = x
    ]]></literal>
    <justification jstring="[para(327(a,1),52(a,1,2,2,1)),rewrite(48(3),88(8))].">
      <j1 rule="para" parents="327 52"/>
      <j2 rule="rewrite" parents="48 88"/>
    </justification>
  </clause>

  <clause id="958">
    <literal><![CDATA[
      f(f(f(x,y),f(f(f(f(x,y),y),f(x,x)),f(z,f(x,x)))),x) = f(x,x)
    ]]></literal>
    <justification jstring="[para(74(a,1),681(a,1,1,2,1,1,1,1)),rewrite(82(3),82(12))].">
      <j1 rule="para" parents="74 681"/>
      <j2 rule="rewrite" parents="82 82"/>
    </justification>
  </clause>

  <clause id="1010">
    <literal><![CDATA[
      f(f(f(x,x),x),f(f(x,f(x,f(f(x,x),y))),x)) = x
    ]]></literal>
    <justification jstring="[para(88(a,1),737(a,1,2))].">
      <j1 rule="para" parents="88 737"/>
    </justification>
  </clause>

  <clause id="1028">
    <literal><![CDATA[
      f(f(x,f(x,f(f(x,x),y))),x) = f(x,x)
    ]]></literal>
    <justification jstring="[para(1010(a,1),46(a,1,2,2,1)),rewrite(394(7),22(14)),flip(a)].">
      <j1 rule="para" parents="1010 46"/>
      <j2 rule="rewrite" parents="394 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1036">
    <literal><![CDATA[
      f(f(x,f(x,f(y,f(x,x)))),x) = f(x,x)
    ]]></literal>
    <justification jstring="[para(88(a,1),1028(a,1,1,2,2))].">
      <j1 rule="para" parents="88 1028"/>
    </justification>
  </clause>

  <clause id="1052">
    <literal><![CDATA[
      f(f(f(x,x),f(f(x,x),f(y,x))),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(22(a,1),1036(a,1,1,2,2,2)),rewrite(82(10))].">
      <j1 rule="para" parents="22 1036"/>
      <j2 rule="rewrite" parents="82"/>
    </justification>
  </clause>

  <clause id="1330">
    <literal><![CDATA[
      f(f(f(x,x),x),f(x,f(f(x,x),y))) = x
    ]]></literal>
    <justification jstring="[para(86(a,1),47(a,1,2,2,1)),rewrite(82(3),88(6),22(6),462(7),82(4),88(7),22(7),82(10),88(13),22(13),22(21),231(21),48(17),82(3),82(3),88(6),22(6)),flip(a)].">
      <j1 rule="para" parents="86 47"/>
      <j2 rule="rewrite" parents="82 88 22 462 82 88 22 82 88 22 22 231 48 82 82 88 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1349">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(x,x),f(x,y))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(86(a,1),68(a,1,2,2,1)),rewrite(88(8),48(6),463(8),88(7),48(5),88(13),48(11),48(17),210(18),22(16),88(8),48(6)),flip(a)].">
      <j1 rule="para" parents="86 68"/>
      <j2 rule="rewrite" parents="88 48 463 88 48 88 48 48 210 22 88 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1359">
    <literal><![CDATA[
      f(f(f(x,x),x),f(x,f(y,f(x,x)))) = x
    ]]></literal>
    <justification jstring="[para(88(a,1),1330(a,1,2,2))].">
      <j1 rule="para" parents="88 1330"/>
    </justification>
  </clause>

  <clause id="1392">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(x,x),f(y,x))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(22(a,1),1359(a,1,1,1)),rewrite(82(6))].">
      <j1 rule="para" parents="22 1359"/>
      <j2 rule="rewrite" parents="82"/>
    </justification>
  </clause>

  <clause id="1413">
    <literal><![CDATA[
      f(f(f(x,y),f(f(x,y),f(x,y))),f(f(f(x,y),f(x,y)),y)) = f(f(x,y),f(x,y))
    ]]></literal>
    <justification jstring="[para(3(a,1),1349(a,1,2,2))].">
      <j1 rule="para" parents="3 1349"/>
    </justification>
  </clause>

  <clause id="1420">
    <literal><![CDATA[
      f(f(f(x,y),f(f(x,y),f(x,y))),f(f(f(x,y),f(x,y)),x)) = f(f(x,y),f(x,y))
    ]]></literal>
    <justification jstring="[para(82(a,1),1349(a,1,2,2))].">
      <j1 rule="para" parents="82 1349"/>
    </justification>
  </clause>

  <clause id="1654">
    <literal><![CDATA[
      f(f(x,f(f(x,x),x)),f(f(f(x,x),x),f(f(f(x,x),f(f(x,x),x)),f(f(f(x,x),x),y)))) = f(f(x,x),x)
    ]]></literal>
    <justification jstring="[para(260(a,1),73(a,1,2,1)),rewrite(57(8))].">
      <j1 rule="para" parents="260 73"/>
      <j2 rule="rewrite" parents="57"/>
    </justification>
  </clause>

  <clause id="1794">
    <literal><![CDATA[
      f(f(f(x,y),f(x,y)),f(f(f(f(x,y),f(x,y)),f(x,y)),f(f(f(f(x,y),f(x,y)),f(x,y)),f(f(f(f(x,y),f(x,y)),z),f(f(f(f(y,z),z),f(x,y)),y))))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(11(a,1),78(a,1,1,1)),rewrite(11(23),11(25),11(26),11(28),11(30),11(31),11(33),11(48))].">
      <j1 rule="para" parents="11 78"/>
      <j2 rule="rewrite" parents="11 11 11 11 11 11 11 11"/>
    </justification>
  </clause>

  <clause id="2381">
    <literal><![CDATA[
      f(f(f(f(x,x),f(y,x)),f(f(x,x),x)),x) = f(f(x,x),x)
    ]]></literal>
    <justification jstring="[para(590(a,1),90(a,1,2,1,2,1)),rewrite(590(18),82(14),260(12),590(14),57(13),22(10))].">
      <j1 rule="para" parents="590 90"/>
      <j2 rule="rewrite" parents="590 82 260 590 57 22"/>
    </justification>
  </clause>

  <clause id="2436">
    <literal><![CDATA[
      f(f(x,x),f(f(f(x,x),f(f(x,x),x)),f(f(f(x,x),x),f(y,x)))) = x
    ]]></literal>
    <justification jstring="[para(2381(a,1),102(a,1,2,2,1))].">
      <j1 rule="para" parents="2381 102"/>
    </justification>
  </clause>

  <clause id="2491">
    <literal><![CDATA[
      f(f(x,x),f(f(x,x),x)) = x
    ]]></literal>
    <justification jstring="[para(22(a,1),2436(a,1,2))].">
      <j1 rule="para" parents="22 2436"/>
    </justification>
  </clause>

  <clause id="2498">
    <literal><![CDATA[
      f(x,f(x,f(x,x))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(278(a,1),2436(a,1,2,2,2)),rewrite(82(3),82(3),82(3),82(6),22(9))].">
      <j1 rule="para" parents="278 2436"/>
      <j2 rule="rewrite" parents="82 82 82 82 22"/>
    </justification>
  </clause>

  <clause id="2537">
    <literal><![CDATA[
      f(f(x,f(f(x,x),x)),f(f(f(x,x),x),f(x,f(f(f(x,x),x),y)))) = f(f(x,x),x)
    ]]></literal>
    <justification jstring="[back_rewrite(1654),rewrite(2491(9))].">
      <j1 rule="back_rewrite" parents="1654"/>
      <j2 rule="rewrite" parents="2491"/>
    </justification>
  </clause>

  <clause id="2576">
    <literal><![CDATA[
      f(f(x,y),f(y,f(f(f(f(f(y,x),f(f(y,y),y)),f(f(y,y),y)),y),f(z,y)))) = y
    ]]></literal>
    <justification jstring="[para(2491(a,1),102(a,1,2,1))].">
      <j1 rule="para" parents="2491 102"/>
    </justification>
  </clause>

  <clause id="2610">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(x,x),f(f(f(x,x),y),f(f(f(f(f(x,z),y),y),x),f(x,u))))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(92(a,1),68(a,1,2,2,1)),rewrite(88(8),48(6),837(16),88(7),48(5),88(21),48(19),48(33),296(42),22(32),88(8),48(6)),flip(a)].">
      <j1 rule="para" parents="92 68"/>
      <j2 rule="rewrite" parents="88 48 837 88 48 88 48 48 296 22 88 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4042">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(x,x),f(f(x,x),f(f(x,x),f(y,x))))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(1052(a,1),1420(a,1,1,1)),rewrite(1052(7),1052(7),1052(9),1052(9),1052(17),1052(17))].">
      <j1 rule="para" parents="1052 1420"/>
      <j2 rule="rewrite" parents="1052 1052 1052 1052 1052 1052"/>
    </justification>
  </clause>

  <clause id="4109">
    <literal><![CDATA[
      f(f(f(f(x,y),f(f(f(f(f(f(x,x),x),y),y),f(x,x)),f(f(x,x),z))),f(x,f(x,x))),x) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(564(a,1),121(a,1,2,2,2)),rewrite(82(3),82(22),57(25),22(22))].">
      <j1 rule="para" parents="564 121"/>
      <j2 rule="rewrite" parents="82 82 57 22"/>
    </justification>
  </clause>

  <clause id="4211">
    <literal><![CDATA[
      f(x,f(f(x,y),f(f(f(f(x,y),y),f(x,x)),f(x,f(x,f(f(x,x),z)))))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(1028(a,1),122(a,1,1,2)),rewrite(103(15),1028(5),1028(6),82(3),1028(8),1028(17))].">
      <j1 rule="para" parents="1028 122"/>
      <j2 rule="rewrite" parents="103 1028 1028 82 1028 1028"/>
    </justification>
  </clause>

  <clause id="4246">
    <literal><![CDATA[
      f(f(f(f(x,x),f(f(x,x),f(f(x,x),f(y,x)))),f(x,f(x,x))),f(f(f(f(x,f(x,x)),f(x,f(x,x))),x),f(f(f(x,x),f(x,f(x,x))),f(f(x,f(x,x)),z)))) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(4042(a,1),86(a,1,2,1,2,1)),rewrite(4042(26),82(18),4042(26))].">
      <j1 rule="para" parents="4042 86"/>
      <j2 rule="rewrite" parents="4042 82 4042"/>
    </justification>
  </clause>

  <clause id="4654">
    <literal><![CDATA[
      f(f(x,y),f(f(f(f(y,x),f(f(y,y),y)),f(f(y,y),y)),y)) = y
    ]]></literal>
    <justification jstring="[para(88(a,1),2576(a,1,2))].">
      <j1 rule="para" parents="88 2576"/>
    </justification>
  </clause>

  <clause id="4731">
    <literal><![CDATA[
      f(f(f(x,x),x),f(f(f(f(f(x,x),x),f(f(x,x),x)),f(f(x,x),x)),x)) = x
    ]]></literal>
    <justification jstring="[para(48(a,1),4654(a,1,2,1,1)),rewrite(260(6))].">
      <j1 rule="para" parents="48 4654"/>
      <j2 rule="rewrite" parents="260"/>
    </justification>
  </clause>

  <clause id="4735">
    <literal><![CDATA[
      f(f(f(x,x),f(x,y)),f(f(f(x,f(f(f(x,y),f(x,y)),f(x,y))),f(f(f(x,y),f(x,y)),f(x,y))),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(82(a,1),4654(a,1,2,1,1,1))].">
      <j1 rule="para" parents="82 4654"/>
    </justification>
  </clause>

  <clause id="4739">
    <literal><![CDATA[
      f(f(f(f(x,y),f(x,y)),x),f(f(f(f(x,y),f(f(x,x),x)),f(f(x,x),x)),x)) = x
    ]]></literal>
    <justification jstring="[para(97(a,1),4654(a,1,2,1,1,1))].">
      <j1 rule="para" parents="97 4654"/>
    </justification>
  </clause>

  <clause id="4922">
    <literal><![CDATA[
      f(f(f(f(x,f(x,x)),f(x,f(x,x))),f(x,f(x,x))),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(4731(a,1),67(a,1,2,2,1)),rewrite(82(3),82(5),82(8),82(14),82(16),82(19),82(24),82(26),82(29),82(37),48(35),82(13),82(3),82(5),82(8)),flip(a)].">
      <j1 rule="para" parents="4731 67"/>
      <j2 rule="rewrite" parents="82 82 82 82 82 82 82 82 82 82 48 82 82 82 82"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4969">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),f(f(f(x,f(x,x)),f(x,f(x,x))),f(x,f(x,x)))),x) = f(f(f(x,f(x,x)),f(x,f(x,x))),f(x,f(x,x)))
    ]]></literal>
    <justification jstring="[para(4922(a,1),2537(a,1,2,2,2)),rewrite(48(22),4922(21))].">
      <j1 rule="para" parents="4922 2537"/>
      <j2 rule="rewrite" parents="48 4922"/>
    </justification>
  </clause>

  <clause id="5567">
    <literal><![CDATA[
      f(x,f(f(x,f(x,x)),f(f(x,f(x,x)),f(x,f(x,f(f(x,x),y)))))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(82(a,1),4211(a,1,2,2,1,1))].">
      <j1 rule="para" parents="82 4211"/>
    </justification>
  </clause>

  <clause id="5640">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),f(f(x,f(x,x)),f(x,f(x,f(f(x,x),y))))),x) = f(x,x)
    ]]></literal>
    <justification jstring="[para(5567(a,1),88(a,1,2,1)),rewrite(5567(22),82(13),5567(22))].">
      <j1 rule="para" parents="5567 88"/>
      <j2 rule="rewrite" parents="5567 82 5567"/>
    </justification>
  </clause>

  <clause id="5691">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),f(f(x,f(x,x)),f(x,f(x,f(y,f(x,x)))))),x) = f(x,x)
    ]]></literal>
    <justification jstring="[para(88(a,1),5640(a,1,1,2,2,2,2))].">
      <j1 rule="para" parents="88 5640"/>
    </justification>
  </clause>

  <clause id="5714">
    <literal><![CDATA[
      f(f(f(f(x,f(x,x)),f(x,f(x,f(y,f(x,x))))),f(x,f(x,x))),f(f(f(f(x,f(x,x)),f(x,f(x,x))),x),f(f(f(f(x,x),x),f(x,f(x,x))),f(x,x)))) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(5691(a,1),9(a,1,2,2,1,1,1))].">
      <j1 rule="para" parents="5691 9"/>
    </justification>
  </clause>

  <clause id="8394">
    <literal><![CDATA[
      f(f(x,x),f(x,y)) = x
    ]]></literal>
    <justification jstring="[para(210(a,1),454(a,1,1)),rewrite(1349(16),82(13),48(11),82(3)),flip(a)].">
      <j1 rule="para" parents="210 454"/>
      <j2 rule="rewrite" parents="1349 82 48 82"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8395">
    <literal><![CDATA[
      f(x,f(f(x,x),y)) = f(x,x)
    ]]></literal>
    <justification jstring="[para(231(a,1),454(a,1,1)),rewrite(8394(10),8394(12),1330(14),22(10)),flip(a)].">
      <j1 rule="para" parents="231 454"/>
      <j2 rule="rewrite" parents="8394 8394 1330 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8396">
    <literal><![CDATA[
      f(f(x,x),f(y,x)) = x
    ]]></literal>
    <justification jstring="[para(235(a,1),454(a,1,1)),rewrite(1392(16),8394(13),48(11),8394(3)),flip(a)].">
      <j1 rule="para" parents="235 454"/>
      <j2 rule="rewrite" parents="1392 8394 48 8394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8397">
    <literal><![CDATA[
      f(x,f(y,f(x,x))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(244(a,1),454(a,1,1)),rewrite(8394(10),8394(12),1359(14),22(10)),flip(a)].">
      <j1 rule="para" parents="244 454"/>
      <j2 rule="rewrite" parents="8394 8394 1359 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8398">
    <literal><![CDATA[
      f(f(f(x,y),f(x,y)),y) = f(x,y)
    ]]></literal>
    <justification jstring="[para(227(a,1),454(a,1,1)),rewrite(1413(26),8394(23),48(18),8394(7)),flip(a)].">
      <j1 rule="para" parents="227 454"/>
      <j2 rule="rewrite" parents="1413 8394 48 8394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8400">
    <literal><![CDATA[
      f(f(f(x,y),f(x,y)),x) = f(x,y)
    ]]></literal>
    <justification jstring="[para(234(a,1),454(a,1,1)),rewrite(1420(26),8394(23),48(18),8394(7)),flip(a)].">
      <j1 rule="para" parents="234 454"/>
      <j2 rule="rewrite" parents="1420 8394 48 8394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8402">
    <literal><![CDATA[
      f(f(x,y),f(f(f(f(f(f(x,x),x),y),y),f(x,x)),f(f(x,x),z))) = x
    ]]></literal>
    <justification jstring="[para(38(a,1),454(a,1,2,2,1)),rewrite(8394(40),48(38),82(14)),flip(a)].">
      <j1 rule="para" parents="38 454"/>
      <j2 rule="rewrite" parents="8394 48 82"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8436">
    <literal><![CDATA[
      f(f(x,x),f(f(f(x,x),y),f(f(f(f(f(x,z),y),y),x),f(x,u)))) = x
    ]]></literal>
    <justification jstring="[para(296(a,1),454(a,1,1)),rewrite(8400(26),2610(26),8394(15),57(13),8394(3)),flip(a)].">
      <j1 rule="para" parents="296 454"/>
      <j2 rule="rewrite" parents="8400 2610 8394 57 8394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8440">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),z),f(f(f(f(f(x,y),z),z),y),f(y,u)))) = y
    ]]></literal>
    <justification jstring="[para(100(a,1),454(a,2)),rewrite(8398(4),8398(16),8398(27),8398(43),8398(55),454(55))].">
      <j1 rule="para" parents="100 454"/>
      <j2 rule="rewrite" parents="8398 8398 8398 8398 8398 454"/>
    </justification>
  </clause>

  <clause id="8483">
    <literal><![CDATA[
      f(f(x,y),f(f(f(f(x,y),f(f(x,x),x)),f(f(x,x),x)),x)) = x
    ]]></literal>
    <justification jstring="[para(4739(a,1),454(a,2)),rewrite(8400(4),8400(15),8400(25),8400(40),8400(51),454(51))].">
      <j1 rule="para" parents="4739 454"/>
      <j2 rule="rewrite" parents="8400 8400 8400 8400 8400 454"/>
    </justification>
  </clause>

  <clause id="8486">
    <literal><![CDATA[
      f(x,f(f(f(f(y,x),f(y,x)),f(x,x)),f(f(x,f(y,x)),x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(521(a,1),454(a,2)),rewrite(8396(3),8396(14),8396(24),8396(39),8396(50),454(50))].">
      <j1 rule="para" parents="521 454"/>
      <j2 rule="rewrite" parents="8396 8396 8396 8396 8396 454"/>
    </justification>
  </clause>

  <clause id="8488">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),z),f(f(f(f(f(x,y),z),z),y),f(u,y)))) = y
    ]]></literal>
    <justification jstring="[para(684(a,1),454(a,2)),rewrite(8398(4),8398(16),8398(27),8398(43),8398(55),454(55))].">
      <j1 rule="para" parents="684 454"/>
      <j2 rule="rewrite" parents="8398 8398 8398 8398 8398 454"/>
    </justification>
  </clause>

  <clause id="8534">
    <literal><![CDATA[
      f(x,f(f(f(x,f(f(f(x,y),f(x,y)),f(x,y))),f(f(f(x,y),f(x,y)),f(x,y))),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(4735),rewrite(8394(3))].">
      <j1 rule="back_rewrite" parents="4735"/>
      <j2 rule="rewrite" parents="8394"/>
    </justification>
  </clause>

  <clause id="8541">
    <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(4246),rewrite(8396(5),8396(4),2498(3),8400(7),8394(7))].">
      <j1 rule="back_rewrite" parents="4246"/>
      <j2 rule="rewrite" parents="8396 8396 2498 8400 8394"/>
    </justification>
  </clause>

  <clause id="8589">
    <literal><![CDATA[
      f(x,f(f(y,x),f(f(f(f(x,x),x),f(y,x)),f(f(y,x),z)))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(474),rewrite(8396(3),8394(6),8398(4),8394(5))].">
      <j1 rule="back_rewrite" parents="474"/>
      <j2 rule="rewrite" parents="8396 8394 8398 8394"/>
    </justification>
  </clause>

  <clause id="8616">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),f(x,f(x,x))),f(x,f(x,x))) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[back_rewrite(4969),rewrite(8395(11),8400(6)),flip(a)].">
      <j1 rule="back_rewrite" parents="4969"/>
      <j2 rule="rewrite" parents="8395 8400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8681">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(x,f(x,x)),f(f(f(f(x,x),x),f(x,f(x,x))),f(x,x)))) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[back_rewrite(5714),rewrite(8397(5),8616(8),8400(8))].">
      <j1 rule="back_rewrite" parents="5714"/>
      <j2 rule="rewrite" parents="8397 8616 8400"/>
    </justification>
  </clause>

  <clause id="8888">
    <literal><![CDATA[
      f(f(x,x),x) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[back_rewrite(4109),rewrite(8402(11),8397(3))].">
      <j1 rule="back_rewrite" parents="4109"/>
      <j2 rule="rewrite" parents="8402 8397"/>
    </justification>
  </clause>

  <clause id="9157">
    <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="[back_rewrite(8681),rewrite(8888(6),8398(11))].">
      <j1 rule="back_rewrite" parents="8681"/>
      <j2 rule="rewrite" parents="8888 8398"/>
    </justification>
  </clause>

  <clause id="9187">
    <literal><![CDATA[
      f(x,f(f(y,x),f(f(f(x,f(x,x)),f(y,x)),f(f(y,x),z)))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(8589),rewrite(8888(3))].">
      <j1 rule="back_rewrite" parents="8589"/>
      <j2 rule="rewrite" parents="8888"/>
    </justification>
  </clause>

  <clause id="9203">
    <literal><![CDATA[
      f(x,f(f(f(x,f(f(x,y),f(f(x,y),f(x,y)))),f(f(x,y),f(f(x,y),f(x,y)))),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(8534),rewrite(8888(5),8888(11))].">
      <j1 rule="back_rewrite" parents="8534"/>
      <j2 rule="rewrite" parents="8888 8888"/>
    </justification>
  </clause>

  <clause id="9216">
    <literal><![CDATA[
      f(f(x,y),f(f(f(f(x,y),f(x,f(x,x))),f(x,f(x,x))),x)) = x
    ]]></literal>
    <justification jstring="[back_rewrite(8483),rewrite(8888(4),8888(7))].">
      <j1 rule="back_rewrite" parents="8483"/>
      <j2 rule="rewrite" parents="8888 8888"/>
    </justification>
  </clause>

  <clause id="9535">
    <literal><![CDATA[
      f(f(f(x,y),f(x,y)),f(f(f(x,y),f(f(x,y),f(x,y))),f(f(f(x,y),f(f(x,y),f(x,y))),f(f(f(f(x,y),f(x,y)),z),f(f(f(f(y,z),z),f(x,y)),y))))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(1794),rewrite(8888(8),8888(13))].">
      <j1 rule="back_rewrite" parents="1794"/>
      <j2 rule="rewrite" parents="8888 8888"/>
    </justification>
  </clause>

  <clause id="9628">
    <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(285),rewrite(8888(2),8888(4))].">
      <j1 rule="back_rewrite" parents="285"/>
      <j2 rule="rewrite" parents="8888 8888"/>
    </justification>
  </clause>

  <clause id="9638">
    <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(201),rewrite(8888(2),8888(4))].">
      <j1 rule="back_rewrite" parents="201"/>
      <j2 rule="rewrite" parents="8888 8888"/>
    </justification>
  </clause>

  <clause id="9978">
    <literal><![CDATA[
      f(f(x,x),f(f(f(x,x),y),f(f(f(f(f(x,z),y),y),x),f(f(f(x,x),u),f(f(f(f(f(v,x),u),u),x),f(x,w)))))) = x
    ]]></literal>
    <justification jstring="[para(107(a,1),8398(a,1,1,1)),rewrite(107(19),107(38))].">
      <j1 rule="para" parents="107 8398"/>
      <j2 rule="rewrite" parents="107 107"/>
    </justification>
  </clause>

  <clause id="10047">
    <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(y,x),f(f(f(f(x,y),y),f(y,x)),f(f(y,x),u)))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(8400(a,1),113(a,1,2,1))].">
      <j1 rule="para" parents="8400 113"/>
    </justification>
  </clause>

  <clause id="10604">
    <literal><![CDATA[
      f(x,f(f(f(f(x,y),f(x,y)),f(x,x)),f(f(x,f(x,y)),x))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(8400(a,1),8486(a,1,2,1,1,1)),rewrite(8400(5),8400(9),8400(14))].">
      <j1 rule="para" parents="8400 8486"/>
      <j2 rule="rewrite" parents="8400 8400 8400"/>
    </justification>
  </clause>

  <clause id="11076">
    <literal><![CDATA[
      f(x,f(f(x,f(x,x)),f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(8397(a,1),9187(a,1,2,2)),rewrite(88(11))].">
      <j1 rule="para" parents="8397 9187"/>
      <j2 rule="rewrite" parents="88"/>
    </justification>
  </clause>

  <clause id="11140">
    <literal><![CDATA[
      f(f(x,y),f(f(f(x,y),f(f(x,y),f(x,y))),x)) = x
    ]]></literal>
    <justification jstring="[para(8394(a,1),11076(a,1,2,2)),rewrite(8394(11))].">
      <j1 rule="para" parents="8394 11076"/>
      <j2 rule="rewrite" parents="8394"/>
    </justification>
  </clause>

  <clause id="11142">
    <literal><![CDATA[
      f(x,f(f(x,f(x,x)),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(8400(a,1),11076(a,1,2,2)),rewrite(8400(9))].">
      <j1 rule="para" parents="8400 11076"/>
      <j2 rule="rewrite" parents="8400"/>
    </justification>
  </clause>

  <clause id="11170">
    <literal><![CDATA[
      f(f(x,x),f(f(x,f(x,x)),f(y,x))) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(11076(a,1),8541(a,1,2,2))].">
      <j1 rule="para" parents="11076 8541"/>
    </justification>
  </clause>

  <clause id="11226">
    <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(9157(a,1),11142(a,1,2,1))].">
      <j1 rule="para" parents="9157 11142"/>
    </justification>
  </clause>

  <clause id="11328">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(x,f(x,x)),f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(9628(a,1),11140(a,1,1)),rewrite(9628(9),9628(9),9628(9),11226(10),11076(5)),flip(a)].">
      <j1 rule="para" parents="9628 11140"/>
      <j2 rule="rewrite" parents="9628 9628 9628 11226 11076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11329">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(x,f(x,x)),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(9638(a,1),11140(a,1,1)),rewrite(9638(9),9638(9),9638(9),11226(10),11142(5)),flip(a)].">
      <j1 rule="para" parents="9638 11140"/>
      <j2 rule="rewrite" parents="9638 9638 9638 11226 11142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11482">
    <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(8394(a,1),11170(a,1,2,2))].">
      <j1 rule="para" parents="8394 11170"/>
    </justification>
  </clause>

  <clause id="11485">
    <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(8396(a,1),11170(a,1,2,2))].">
      <j1 rule="para" parents="8396 11170"/>
    </justification>
  </clause>

  <clause id="11613">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(y,x),f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(11328(a,1),97(a,1,2,1)),rewrite(11328(10),11328(13))].">
      <j1 rule="para" parents="11328 97"/>
      <j2 rule="rewrite" parents="11328 11328"/>
    </justification>
  </clause>

  <clause id="11617">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(y,x)) = f(f(y,x),f(y,x))
    ]]></literal>
    <justification jstring="[para(11328(a,1),47(a,1,1)),rewrite(11329(24),11328(23),8397(21)),flip(a)].">
      <j1 rule="para" parents="11328 47"/>
      <j2 rule="rewrite" parents="11329 11328 8397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11660">
    <literal><![CDATA[
      f(f(f(x,y),f(x,y)),f(y,f(y,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(11328(a,1),8400(a,1,1,1)),rewrite(11328(8),11328(13))].">
      <j1 rule="para" parents="11328 8400"/>
      <j2 rule="rewrite" parents="11328 11328"/>
    </justification>
  </clause>

  <clause id="11710">
    <literal><![CDATA[
      f(f(f(x,y),f(f(x,y),f(x,y))),f(y,y)) = y
    ]]></literal>
    <justification jstring="[para(8396(a,1),11613(a,1,2,1)),rewrite(8396(8),8396(10))].">
      <j1 rule="para" parents="8396 11613"/>
      <j2 rule="rewrite" parents="8396 8396"/>
    </justification>
  </clause>

  <clause id="11713">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(x,y),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(8400(a,1),11613(a,1,2,1)),rewrite(8400(7),8400(10))].">
      <j1 rule="para" parents="8400 11613"/>
      <j2 rule="rewrite" parents="8400 8400"/>
    </justification>
  </clause>

  <clause id="12000">
    <literal><![CDATA[
      f(f(f(x,y),f(f(x,y),f(x,y))),x) = f(x,x)
    ]]></literal>
    <justification jstring="[para(8394(a,1),11617(a,1,2)),rewrite(8394(9),8394(9))].">
      <j1 rule="para" parents="8394 11617"/>
      <j2 rule="rewrite" parents="8394 8394"/>
    </justification>
  </clause>

  <clause id="12003">
    <literal><![CDATA[
      f(f(f(x,y),f(f(x,y),f(x,y))),y) = f(y,y)
    ]]></literal>
    <justification jstring="[para(8396(a,1),11617(a,1,2)),rewrite(8396(9),8396(9))].">
      <j1 rule="para" parents="8396 11617"/>
      <j2 rule="rewrite" parents="8396 8396"/>
    </justification>
  </clause>

  <clause id="12007">
    <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(11617(a,2),8888(a,2,2)),rewrite(8888(5)),flip(a)].">
      <j1 rule="para" parents="11617 8888"/>
      <j2 rule="rewrite" parents="8888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12125">
    <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(11617(a,2),11328(a,1,1,2))].">
      <j1 rule="para" parents="11617 11328"/>
    </justification>
  </clause>

  <clause id="12140">
    <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(11482),rewrite(12000(9))].">
      <j1 rule="back_rewrite" parents="11482"/>
      <j2 rule="rewrite" parents="12000"/>
    </justification>
  </clause>

  <clause id="12145">
    <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(11485),rewrite(12003(9))].">
      <j1 rule="back_rewrite" parents="11485"/>
      <j2 rule="rewrite" parents="12003"/>
    </justification>
  </clause>

  <clause id="12226">
    <literal><![CDATA[
      f(x,f(f(f(x,y),f(f(x,y),f(x,y))),f(f(x,f(x,y)),x))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(10604),rewrite(12140(5))].">
      <j1 rule="back_rewrite" parents="10604"/>
      <j2 rule="rewrite" parents="12140"/>
    </justification>
  </clause>

  <clause id="12507">
    <literal><![CDATA[
      f(f(x,x),f(f(x,y),f(f(x,y),f(x,y)))) = x
    ]]></literal>
    <justification jstring="[para(8394(a,1),11660(a,1,1,1)),rewrite(8394(3),8394(10))].">
      <j1 rule="para" parents="8394 11660"/>
      <j2 rule="rewrite" parents="8394 8394"/>
    </justification>
  </clause>

  <clause id="12510">
    <literal><![CDATA[
      f(x,f(f(y,f(x,x)),f(f(y,f(x,x)),f(y,f(x,x))))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(8397(a,1),11660(a,1,1,1)),rewrite(8397(4),8394(3),8397(12))].">
      <j1 rule="para" parents="8397 11660"/>
      <j2 rule="rewrite" parents="8397 8394 8397"/>
    </justification>
  </clause>

  <clause id="12614">
    <literal><![CDATA[
      f(x,f(f(f(y,x),f(f(y,x),f(y,x))),f(f(y,x),f(f(y,x),f(y,x))))) = f(f(y,x),f(f(y,x),f(y,x)))
    ]]></literal>
    <justification jstring="[para(11710(a,1),82(a,1,1))].">
      <j1 rule="para" parents="11710 82"/>
    </justification>
  </clause>

  <clause id="12618">
    <literal><![CDATA[
      f(f(f(x,y),f(f(x,y),f(x,y))),f(f(f(x,y),f(f(x,y),f(x,y))),f(f(f(y,f(y,y)),f(x,y)),f(f(f(f(x,y),f(x,y)),z),f(f(f(f(y,z),z),f(x,y)),y))))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(11710(a,1),215(a,1,2,2,1,1,1)),rewrite(8888(5),12145(10))].">
      <j1 rule="para" parents="11710 215"/>
      <j2 rule="rewrite" parents="8888 12145"/>
    </justification>
  </clause>

  <clause id="12633">
    <literal><![CDATA[
      f(f(x,y),f(f(x,f(x,x)),f(x,f(x,x)))) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(11713(a,1),82(a,1,1))].">
      <j1 rule="para" parents="11713 82"/>
    </justification>
  </clause>

  <clause id="12712">
    <literal><![CDATA[
      f(x,f(f(x,y),f(f(x,y),f(x,y)))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(12000(a,1),8400(a,1,1,1)),rewrite(12000(7),8394(3),12000(12))].">
      <j1 rule="para" parents="12000 8400"/>
      <j2 rule="rewrite" parents="12000 8394 12000"/>
    </justification>
  </clause>

  <clause id="12715">
    <literal><![CDATA[
      f(f(x,y),f(f(x,y),f(x,y))) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(12000(a,1),9216(a,1,1)),rewrite(12000(7),12633(19),12507(8),12633(18),12712(7),12507(8),8888(2)),flip(a)].">
      <j1 rule="para" parents="12000 9216"/>
      <j2 rule="rewrite" parents="12000 12633 12507 12633 12712 12507 8888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12722">
    <literal><![CDATA[
      f(f(x,f(x,x)),y) = f(y,y)
    ]]></literal>
    <justification jstring="[para(11076(a,1),12000(a,1,1,1)),rewrite(11076(6),11076(7),12715(5))].">
      <j1 rule="para" parents="11076 12000"/>
      <j2 rule="rewrite" parents="11076 11076 12715"/>
    </justification>
  </clause>

  <clause id="12782">
    <literal><![CDATA[
      f(x,f(x,f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(9203),rewrite(12715(5),8397(3),12715(6),8394(4))].">
      <j1 rule="back_rewrite" parents="9203"/>
      <j2 rule="rewrite" parents="12715 8397 12715 8394"/>
    </justification>
  </clause>

  <clause id="12809">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(x,f(x,x)),f(f(f(y,f(y,y)),f(x,y)),f(f(f(f(x,y),f(x,y)),z),f(f(f(f(y,z),z),f(x,y)),y))))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(12618),rewrite(12715(5),12715(7))].">
      <j1 rule="back_rewrite" parents="12618"/>
      <j2 rule="rewrite" parents="12715 12715"/>
    </justification>
  </clause>

  <clause id="12813">
    <literal><![CDATA[
      f(x,f(f(y,f(y,y)),f(y,f(y,y)))) = f(y,f(y,y))
    ]]></literal>
    <justification jstring="[back_rewrite(12614),rewrite(12715(5),12715(7),12715(11))].">
      <j1 rule="back_rewrite" parents="12614"/>
      <j2 rule="rewrite" parents="12715 12715 12715"/>
    </justification>
  </clause>

  <clause id="12833">
    <literal><![CDATA[
      f(x,f(y,f(y,y))) = f(x,x)
    ]]></literal>
    <justification jstring="[back_rewrite(12510),rewrite(12715(8))].">
      <j1 rule="back_rewrite" parents="12510"/>
      <j2 rule="rewrite" parents="12715"/>
    </justification>
  </clause>

  <clause id="12960">
    <literal><![CDATA[
      f(f(x,f(x,y)),x) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(12226),rewrite(12715(5),11076(7))].">
      <j1 rule="back_rewrite" parents="12226"/>
      <j2 rule="rewrite" parents="12715 11076"/>
    </justification>
  </clause>

  <clause id="13010">
    <literal><![CDATA[
      f(f(f(x,y),f(f(y,f(y,y)),f(x,y))),f(f(x,f(x,x)),f(z,f(x,y)))) = f(z,f(x,y))
    ]]></literal>
    <justification jstring="[back_rewrite(12125),rewrite(12715(11))].">
      <j1 rule="back_rewrite" parents="12125"/>
      <j2 rule="rewrite" parents="12715"/>
    </justification>
  </clause>

  <clause id="13031">
    <literal><![CDATA[
      f(f(x,y),f(f(y,f(y,y)),f(x,y))) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[back_rewrite(12007),rewrite(12715(11))].">
      <j1 rule="back_rewrite" parents="12007"/>
      <j2 rule="rewrite" parents="12715"/>
    </justification>
  </clause>

  <clause id="13140">
    <literal><![CDATA[
      f(f(f(x,y),f(x,y)),f(f(x,f(x,x)),f(f(x,f(x,x)),f(f(f(f(x,y),f(x,y)),z),f(f(f(f(y,z),z),f(x,y)),y))))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(9535),rewrite(12715(8),12715(10))].">
      <j1 rule="back_rewrite" parents="9535"/>
      <j2 rule="rewrite" parents="12715 12715"/>
    </justification>
  </clause>

  <clause id="13429">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(x,f(x,x)),f(y,f(x,z)))) = f(y,f(x,z))
    ]]></literal>
    <justification jstring="[back_rewrite(13010),rewrite(13031(6))].">
      <j1 rule="back_rewrite" parents="13010"/>
      <j2 rule="rewrite" parents="13031"/>
    </justification>
  </clause>

  <clause id="13558">
    <literal><![CDATA[
      f(f(x,y),f(f(z,f(z,z)),y)) = y
    ]]></literal>
    <justification jstring="[para(12722(a,2),22(a,1,2))].">
      <j1 rule="para" parents="12722 22"/>
    </justification>
  </clause>

  <clause id="13573">
    <literal><![CDATA[
      f(x,f(f(y,f(y,y)),f(x,z))) = f(x,z)
    ]]></literal>
    <justification jstring="[para(12722(a,2),97(a,1,2))].">
      <j1 rule="para" parents="12722 97"/>
    </justification>
  </clause>

  <clause id="13607">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),y),f(y,z)) = y
    ]]></literal>
    <justification jstring="[para(12722(a,1),41(a,1,2,1,2)),rewrite(12813(10),12813(13),13573(12))].">
      <j1 rule="para" parents="12722 41"/>
      <j2 rule="rewrite" parents="12813 12813 13573"/>
    </justification>
  </clause>

  <clause id="13821">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),y),y) = f(y,f(y,y))
    ]]></literal>
    <justification jstring="[para(12722(a,2),8888(a,1,1))].">
      <j1 rule="para" parents="12722 8888"/>
    </justification>
  </clause>

  <clause id="13920">
    <literal><![CDATA[
      f(x,f(f(y,x),f(f(f(f(x,y),y),f(y,x)),f(f(y,x),z)))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(10047),rewrite(13607(8),57(4),8396(3))].">
      <j1 rule="back_rewrite" parents="10047"/>
      <j2 rule="rewrite" parents="13607 57 8396"/>
    </justification>
  </clause>

  <clause id="13941">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(f(x,x),y),f(f(f(y,f(y,y)),x),f(f(f(x,x),z),f(f(f(f(f(x,u),z),z),x),f(f(f(x,x),v),f(f(f(f(f(w,x),v),v),x),f(x,v6)))))))) = x
    ]]></literal>
    <justification jstring="[para(8888(a,1),344(a,1,1)),rewrite(13821(8))].">
      <j1 rule="para" parents="8888 344"/>
      <j2 rule="rewrite" parents="13821"/>
    </justification>
  </clause>

  <clause id="13959">
    <literal><![CDATA[
      f(f(x,y),f(f(x,y),x)) = x
    ]]></literal>
    <justification jstring="[para(82(a,1),12782(a,1,2,2)),rewrite(82(7))].">
      <j1 rule="para" parents="82 12782"/>
      <j2 rule="rewrite" parents="82"/>
    </justification>
  </clause>

  <clause id="13960">
    <literal><![CDATA[
      f(x,f(x,f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(88(a,1),12782(a,1,2,2)),rewrite(88(7))].">
      <j1 rule="para" parents="88 12782"/>
      <j2 rule="rewrite" parents="88"/>
    </justification>
  </clause>

  <clause id="13984">
    <literal><![CDATA[
      f(f(f(x,y),f(f(f(f(x,y),f(x,f(x,y))),f(x,x)),f(z,f(x,x)))),x) = f(x,x)
    ]]></literal>
    <justification jstring="[para(12782(a,1),958(a,1,1,1)),rewrite(12782(4))].">
      <j1 rule="para" parents="12782 958"/>
      <j2 rule="rewrite" parents="12782"/>
    </justification>
  </clause>

  <clause id="14078">
    <literal><![CDATA[
      f(f(x,y),f(x,f(z,f(z,z)))) = x
    ]]></literal>
    <justification jstring="[para(12833(a,2),82(a,1,2))].">
      <j1 rule="para" parents="12833 82"/>
    </justification>
  </clause>

  <clause id="14079">
    <literal><![CDATA[
      f(x,f(f(y,x),f(z,f(z,z)))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(12833(a,2),88(a,1,2))].">
      <j1 rule="para" parents="12833 88"/>
    </justification>
  </clause>

  <clause id="14091">
    <literal><![CDATA[
      f(x,f(f(x,y),f(z,f(z,z)))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(12833(a,2),97(a,1,2))].">
      <j1 rule="para" parents="12833 97"/>
    </justification>
  </clause>

  <clause id="14215">
    <literal><![CDATA[
      f(f(f(x,y),f(f(f(y,f(y,y)),f(x,f(z,f(z,z)))),f(f(x,x),u))),x) = f(x,f(z,f(z,z)))
    ]]></literal>
    <justification jstring="[para(12833(a,1),123(a,1,1,2,2,1)),rewrite(14078(7),13821(5),14078(18))].">
      <j1 rule="para" parents="12833 123"/>
      <j2 rule="rewrite" parents="14078 13821 14078"/>
    </justification>
  </clause>

  <clause id="14301">
    <literal><![CDATA[
      f(f(f(x,y),f(z,f(z,z))),x) = f(x,y)
    ]]></literal>
    <justification jstring="[para(12833(a,2),8400(a,1,1))].">
      <j1 rule="para" parents="12833 8400"/>
    </justification>
  </clause>

  <clause id="14306">
    <literal><![CDATA[
      f(x,f(x,x)) = f(y,f(y,y))
    ]]></literal>
    <justification jstring="[para(12833(a,1),9216(a,1,2)),rewrite(12813(14),12813(17),14301(12),12813(17),12813(20),14301(15),13558(10),13821(4))].">
      <j1 rule="para" parents="12833 9216"/>
      <j2 rule="rewrite" parents="12813 12813 14301 12813 12813 14301 13558 13821"/>
    </justification>
  </clause>

  <clause id="14355">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(y,f(x,f(x,x)))) = y
    ]]></literal>
    <justification jstring="[para(12833(a,1),11617(a,1,1,2)),rewrite(12813(8),14078(13))].">
      <j1 rule="para" parents="12833 11617"/>
      <j2 rule="rewrite" parents="12813 14078"/>
    </justification>
  </clause>

  <clause id="14361">
    <literal><![CDATA[
      f(f(x,f(x,x)),y) = f(y,f(z,f(z,z)))
    ]]></literal>
    <justification jstring="[para(12833(a,2),12722(a,2))].">
      <j1 rule="para" parents="12833 12722"/>
    </justification>
  </clause>

  <clause id="14371">
    <literal><![CDATA[
      f(x,f(x,x)) = c_0
    ]]></literal>
    <justification jstring="[new_symbol(14306)].">
      <j1 rule="new_symbol" parents="14306"/>
    </justification>
  </clause>

  <clause id="14403">
    <literal><![CDATA[
      f(c_0,x) = f(x,c_0)
    ]]></literal>
    <justification jstring="[back_rewrite(14361),rewrite(14371(2),14371(4))].">
      <j1 rule="back_rewrite" parents="14361"/>
      <j2 rule="rewrite" parents="14371 14371"/>
    </justification>
  </clause>

  <clause id="14404">
    <literal><![CDATA[
      f(c_0,f(x,c_0)) = x
    ]]></literal>
    <justification jstring="[back_rewrite(14355),rewrite(14371(2),14371(3))].">
      <j1 rule="back_rewrite" parents="14355"/>
      <j2 rule="rewrite" parents="14371 14371"/>
    </justification>
  </clause>

  <clause id="14441">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),x) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(14301),rewrite(14371(3),14403(3,R))].">
      <j1 rule="back_rewrite" parents="14301"/>
      <j2 rule="rewrite" parents="14371 14403"/>
    </justification>
  </clause>

  <clause id="14500">
    <literal><![CDATA[
      f(x,c_0) = f(x,x)
    ]]></literal>
    <justification jstring="[back_rewrite(14215),rewrite(14371(3),14371(4),14404(5),8395(4),82(3),14371(3)),flip(a)].">
      <j1 rule="back_rewrite" parents="14215"/>
      <j2 rule="rewrite" parents="14371 14371 14404 8395 82 14371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14530">
    <literal><![CDATA[
      f(x,f(c_0,f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(14091),rewrite(14371(3),14403(3,R))].">
      <j1 rule="back_rewrite" parents="14091"/>
      <j2 rule="rewrite" parents="14371 14403"/>
    </justification>
  </clause>

  <clause id="14534">
    <literal><![CDATA[
      f(x,f(c_0,f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(14079),rewrite(14371(3),14403(3,R))].">
      <j1 rule="back_rewrite" parents="14079"/>
      <j2 rule="rewrite" parents="14371 14403"/>
    </justification>
  </clause>

  <clause id="14553">
    <literal><![CDATA[
      f(c_0,f(x,x)) = x
    ]]></literal>
    <justification jstring="[back_rewrite(13941),rewrite(14371(2),14371(5),14403(5),14500(5),9978(22),57(4))].">
      <j1 rule="back_rewrite" parents="13941"/>
      <j2 rule="rewrite" parents="14371 14371 14403 14500 9978 57"/>
    </justification>
  </clause>

  <clause id="14621">
    <literal><![CDATA[
      f(c_0,f(c_0,f(x,f(y,z)))) = f(x,f(y,z))
    ]]></literal>
    <justification jstring="[back_rewrite(13429),rewrite(14371(2),14371(3))].">
      <j1 rule="back_rewrite" parents="13429"/>
      <j2 rule="rewrite" parents="14371 14371"/>
    </justification>
  </clause>

  <clause id="14711">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),f(f(f(c_0,f(x,y)),z),f(f(f(f(y,z),z),f(x,y)),y))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(13140),rewrite(14500(3,R),14403(3,R),14371(5),14371(6),14500(8,R),14403(8,R),14621(17))].">
      <j1 rule="back_rewrite" parents="13140"/>
      <j2 rule="rewrite" parents="14500 14403 14371 14371 14500 14403 14621"/>
    </justification>
  </clause>

  <clause id="14874">
    <literal><![CDATA[
      f(c_0,f(c_0,f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(12809),rewrite(14371(2),14371(3),14371(4),14500(8,R),14403(8,R),14711(16))].">
      <j1 rule="back_rewrite" parents="12809"/>
      <j2 rule="rewrite" parents="14371 14371 14371 14500 14403 14711"/>
    </justification>
  </clause>

  <clause id="15158">
    <literal><![CDATA[
      f(f(x,x),x) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(8888),rewrite(14371(4))].">
      <j1 rule="back_rewrite" parents="8888"/>
      <j2 rule="rewrite" parents="14371"/>
    </justification>
  </clause>

  <clause id="15492">
    <literal><![CDATA[
      f(f(f(x,y),c_0),x) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(8400),rewrite(14500(3,R))].">
      <j1 rule="back_rewrite" parents="8400"/>
      <j2 rule="rewrite" parents="14500"/>
    </justification>
  </clause>

  <clause id="15585">
    <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(4),rewrite(14500(8,R),14500(15,R))].">
      <j1 rule="back_rewrite" parents="4"/>
      <j2 rule="rewrite" parents="14500 14500"/>
    </justification>
  </clause>

  <clause id="15810">
    <literal><![CDATA[
      f(f(f(x,y),x),f(x,y)) = x
    ]]></literal>
    <justification jstring="[para(82(a,1),12960(a,1,1,2)),rewrite(82(7))].">
      <j1 rule="para" parents="82 12960"/>
      <j2 rule="rewrite" parents="82"/>
    </justification>
  </clause>

  <clause id="15847">
    <literal><![CDATA[
      f(f(x,x),f(c_0,f(f(f(f(x,y),x),x),f(x,z)))) = x
    ]]></literal>
    <justification jstring="[para(12960(a,1),8436(a,1,2,2,1,1,1)),rewrite(15158(3))].">
      <j1 rule="para" parents="12960 8436"/>
      <j2 rule="rewrite" parents="15158"/>
    </justification>
  </clause>

  <clause id="15848">
    <literal><![CDATA[
      f(f(x,f(x,y)),f(f(x,y),f(x,f(f(x,y),z)))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(12960(a,1),8440(a,1,2,2,1,1,1)),rewrite(14500(5,R),15492(6),15810(7))].">
      <j1 rule="para" parents="12960 8440"/>
      <j2 rule="rewrite" parents="14500 15492 15810"/>
    </justification>
  </clause>

  <clause id="15858">
    <literal><![CDATA[
      f(f(x,y),x) = f(x,f(x,y))
    ]]></literal>
    <justification jstring="[para(12782(a,1),12960(a,1,1))].">
      <j1 rule="para" parents="12782 12960"/>
    </justification>
  </clause>

  <clause id="15880">
    <literal><![CDATA[
      f(f(x,x),f(c_0,f(f(x,y),f(x,z)))) = x
    ]]></literal>
    <justification jstring="[back_rewrite(15847),rewrite(15858(4),15858(5),12782(5))].">
      <j1 rule="back_rewrite" parents="15847"/>
      <j2 rule="rewrite" parents="15858 15858 12782"/>
    </justification>
  </clause>

  <clause id="16188">
    <literal><![CDATA[
      f(f(x,y),f(x,f(x,y))) = x
    ]]></literal>
    <justification jstring="[back_rewrite(13959),rewrite(15858(3))].">
      <j1 rule="back_rewrite" parents="13959"/>
      <j2 rule="rewrite" parents="15858"/>
    </justification>
  </clause>

  <clause id="16266">
    <literal><![CDATA[
      f(f(f(x,y),f(c_0,f(z,f(x,x)))),x) = f(x,x)
    ]]></literal>
    <justification jstring="[back_rewrite(13984),rewrite(16188(5),14371(3))].">
      <j1 rule="back_rewrite" parents="13984"/>
      <j2 rule="rewrite" parents="16188 14371"/>
    </justification>
  </clause>

  <clause id="16430">
    <literal><![CDATA[
      f(f(x,y),c_0) = f(c_0,f(x,y))
    ]]></literal>
    <justification jstring="[para(14441(a,1),82(a,1,1)),rewrite(14500(8,R),15858(6),14874(6),14500(3,R))].">
      <j1 rule="para" parents="14441 82"/>
      <j2 rule="rewrite" parents="14500 15858 14874 14500"/>
    </justification>
  </clause>

  <clause id="16561">
    <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(15585),rewrite(16430(6),16430(13))].">
      <j1 rule="back_rewrite" parents="15585"/>
      <j2 rule="rewrite" parents="16430 16430"/>
    </justification>
  </clause>

  <clause id="17267">
    <literal><![CDATA[
      f(f(x,y),y) = f(y,f(x,y))
    ]]></literal>
    <justification jstring="[para(3(a,1),15858(a,1,1)),rewrite(3(14)),flip(a)].">
      <j1 rule="para" parents="3 15858"/>
      <j2 rule="rewrite" parents="3"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17394">
    <literal><![CDATA[
      f(f(x,y),f(y,f(x,y))) = y
    ]]></literal>
    <justification jstring="[para(15858(a,1),8488(a,1,2,2)),rewrite(15858(3),14371(3),17267(4),15858(5),13960(5),17267(5),15858(6),13960(6),17267(5),14530(8))].">
      <j1 rule="para" parents="15858 8488"/>
      <j2 rule="rewrite" parents="15858 14371 17267 15858 13960 17267 15858 13960 17267 14530"/>
    </justification>
  </clause>

  <clause id="18647">
    <literal><![CDATA[
      f(x,f(f(y,x),f(f(f(y,f(x,y)),f(y,x)),f(f(y,x),z)))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(13920),rewrite(17267(3))].">
      <j1 rule="back_rewrite" parents="13920"/>
      <j2 rule="rewrite" parents="17267"/>
    </justification>
  </clause>

  <clause id="19010">
    <literal><![CDATA[
      f(c_0,f(f(x,y),f(x,z))) = f(x,f(f(x,y),f(x,z)))
    ]]></literal>
    <justification jstring="[para(15880(a,1),22(a,1,1)),rewrite(14500(11,R),15858(7),14874(7)),flip(a)].">
      <j1 rule="para" parents="15880 22"/>
      <j2 rule="rewrite" parents="14500 15858 14874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20062">
    <literal><![CDATA[
      f(f(f(f(x,x),y),f(c_0,f(z,x))),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(22(a,1),16266(a,1,1,2,2,2)),rewrite(14500(11,R),16430(11),14553(11))].">
      <j1 rule="para" parents="22 16266"/>
      <j2 rule="rewrite" parents="14500 16430 14553"/>
    </justification>
  </clause>

  <clause id="26783">
    <literal><![CDATA[
      f(f(x,y),f(x,f(f(x,y),z))) = f(c_0,f(x,f(f(x,y),z)))
    ]]></literal>
    <justification jstring="[para(82(a,1),19010(a,1,2,1)),rewrite(82(9)),flip(a)].">
      <j1 rule="para" parents="82 19010"/>
      <j2 rule="rewrite" parents="82"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26932">
    <literal><![CDATA[
      f(f(x,f(x,y)),f(f(x,y),f(x,z))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(19010(a,2),15848(a,1,2,2)),rewrite(14530(9))].">
      <j1 rule="para" parents="19010 15848"/>
      <j2 rule="rewrite" parents="14530"/>
    </justification>
  </clause>

  <clause id="27256">
    <literal><![CDATA[
      f(f(x,f(y,x)),f(x,f(f(y,x),z))) = x
    ]]></literal>
    <justification jstring="[para(22(a,1),26932(a,1,1,2)),rewrite(17267(2),22(5),22(9))].">
      <j1 rule="para" parents="22 26932"/>
      <j2 rule="rewrite" parents="17267 22 22"/>
    </justification>
  </clause>

  <clause id="27357">
    <literal><![CDATA[
      f(f(x,f(y,x)),f(x,y)) = x
    ]]></literal>
    <justification jstring="[para(82(a,1),27256(a,1,2,2))].">
      <j1 rule="para" parents="82 27256"/>
    </justification>
  </clause>

  <clause id="27434">
    <literal><![CDATA[
      f(x,f(c_0,f(y,f(f(y,x),z)))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(18647),rewrite(27357(5),26783(5))].">
      <j1 rule="back_rewrite" parents="18647"/>
      <j2 rule="rewrite" parents="27357 26783"/>
    </justification>
  </clause>

  <clause id="28082">
    <literal><![CDATA[
      f(x,y) = f(y,x)
    ]]></literal>
    <justification jstring="[para(82(a,1),27434(a,1,2,2,2)),rewrite(14553(3))].">
      <j1 rule="para" parents="82 27434"/>
      <j2 rule="rewrite" parents="14553"/>
    </justification>
  </clause>

  <clause id="28086">
    <literal><![CDATA[
      f(x,f(c_0,f(y,f(z,f(y,x))))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(27434(a,1),13960(a,2)),rewrite(28082(3),28082(8),28082(13),13960(18))].">
      <j1 rule="para" parents="27434 13960"/>
      <j2 rule="rewrite" parents="28082 28082 28082 13960"/>
    </justification>
  </clause>

  <clause id="28173">
    <literal><![CDATA[
      f(f(x,f(y,y)),f(c_0,f(z,y))) = f(z,y)
    ]]></literal>
    <justification jstring="[para(20062(a,1),27434(a,1,2,2,2)),rewrite(28082(6),28082(7),8397(7),14553(6),28082(4),14534(4),28082(3)),flip(a)].">
      <j1 rule="para" parents="20062 27434"/>
      <j2 rule="rewrite" parents="28082 28082 8397 14553 28082 14534 28082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29367">
    <literal><![CDATA[
      f(f(x,x),f(y,f(c_0,f(x,z)))) = x
    ]]></literal>
    <justification jstring="[para(8394(a,1),28173(a,1,2,2)),rewrite(14500(3,R),28082(3),28082(6),14500(6),28082(6),8394(9))].">
      <j1 rule="para" parents="8394 28173"/>
      <j2 rule="rewrite" parents="14500 28082 28082 14500 28082 8394"/>
    </justification>
  </clause>

  <clause id="29418">
    <literal><![CDATA[
      f(x,f(x,f(y,f(c_0,f(x,z))))) = f(y,f(c_0,f(x,z)))
    ]]></literal>
    <justification jstring="[para(29367(a,1),17394(a,1,1)),rewrite(29367(10),28082(5))].">
      <j1 rule="para" parents="29367 17394"/>
      <j2 rule="rewrite" parents="29367 28082"/>
    </justification>
  </clause>

  <clause id="29431">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),f(c_0,f(x,z))) = f(z,f(c_0,f(x,y)))
    ]]></literal>
    <justification jstring="[para(29367(a,1),28086(a,1,2,2,2)),rewrite(28082(5))].">
      <j1 rule="para" parents="29367 28086"/>
      <j2 rule="rewrite" parents="28082"/>
    </justification>
  </clause>

  <clause id="36584">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),f(c_0,f(x,z))) = f(y,f(c_0,f(x,z)))
    ]]></literal>
    <justification jstring="[para(29431(a,1),28082(a,2))].">
      <j1 rule="para" parents="29431 28082"/>
    </justification>
  </clause>

  <clause id="36585">
    <literal><![CDATA[
      f(x,f(c_0,f(y,z))) = f(z,f(c_0,f(y,x)))
    ]]></literal>
    <justification jstring="[para(29431(a,2),28082(a,2)),rewrite(28082(4),36584(11))].">
      <j1 rule="para" parents="29431 28082"/>
      <j2 rule="rewrite" parents="28082 36584"/>
    </justification>
  </clause>

  <clause id="37762">
    <literal><![CDATA[
      f(x,f(c_0,f(y,z))) = f(y,f(c_0,f(x,z)))
    ]]></literal>
    <justification jstring="[para(36585(a,1),12782(a,1,2,2)),rewrite(28082(2),29418(6),28082(6))].">
      <j1 rule="para" parents="36585 12782"/>
      <j2 rule="rewrite" parents="28082 29418 28082"/>
    </justification>
  </clause>

  <clause id="37763">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer(A_SS)
    ]]></attribute>
    <justification jstring="[resolve(37762,a,16561,a)].">
      <j1 rule="resolve" parents="37762 16561"/>
    </justification>
  </clause>

</proof>

<proof number="2" length="257" max_count="59">

<comments><![CDATA[
% Proof 2 at 2632.52 (+ 9.73) seconds: MOD_SS.
% Length of proof is 257.
% Level of proof is 53.
% Maximum clause weight is 59.
% Given clauses 3699.
]]></comments>

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

  <clause id="3" 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="5" type="deny">
    <literal><![CDATA[
      f(c4,f(c6,f(c4,f(c5,c5)))) != f(c4,f(c5,f(c4,f(c6,c6))))
    ]]></literal>
    <attribute><![CDATA[
      answer(MOD_SS)
    ]]></attribute>
    <justification jstring="[deny(2)].">
      <j1 rule="deny" parents="2"/>
    </justification>
  </clause>

  <clause id="7">
    <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(3(a,1),3(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="3 3"/>
    </justification>
  </clause>

  <clause id="9">
    <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(3(a,1),3(a,1,2,2,2))].">
      <j1 rule="para" parents="3 3"/>
    </justification>
  </clause>

  <clause id="10">
    <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(3(a,1),9(a,1,1,2)),rewrite(3(12),3(12),3(14),3(17),3(30))].">
      <j1 rule="para" parents="3 9"/>
      <j2 rule="rewrite" parents="3 3 3 3 3"/>
    </justification>
  </clause>

  <clause id="11">
    <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)),x))) = f(z,x)
    ]]></literal>
    <justification jstring="[para(3(a,1),9(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="3 9"/>
    </justification>
  </clause>

  <clause id="14">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),z),y)) = y
    ]]></literal>
    <justification jstring="[para(3(a,1),10(a,1,2,2))].">
      <j1 rule="para" parents="3 10"/>
    </justification>
  </clause>

  <clause id="15">
    <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(f(f(y,y),w),f(f(f(f(f(y,v6),w),w),y),f(y,v7)))))))) = y
    ]]></literal>
    <justification jstring="[para(10(a,1),9(a,1,1,2)),rewrite(10(20),10(20),10(22),10(25),10(46))].">
      <j1 rule="para" parents="10 9"/>
      <j2 rule="rewrite" parents="10 10 10 10 10"/>
    </justification>
  </clause>

  <clause id="22">
    <literal><![CDATA[
      f(f(x,y),f(y,y)) = y
    ]]></literal>
    <justification jstring="[para(3(a,1),14(a,1,2,1))].">
      <j1 rule="para" parents="3 14"/>
    </justification>
  </clause>

  <clause id="38">
    <literal><![CDATA[
      f(f(x,f(y,y)),f(f(y,z),f(f(f(f(f(f(y,y),x),z),z),f(y,y)),f(f(y,y),u)))) = f(y,y)
    ]]></literal>
    <justification jstring="[para(22(a,1),3(a,1,2,1,1))].">
      <j1 rule="para" parents="22 3"/>
    </justification>
  </clause>

  <clause id="39">
    <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(22(a,1),3(a,1,2,1))].">
      <j1 rule="para" parents="22 3"/>
    </justification>
  </clause>

  <clause id="40">
    <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(22(a,1),3(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="22 3"/>
    </justification>
  </clause>

  <clause id="41">
    <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(22(a,1),3(a,1,2,2,1,1,1))].">
      <j1 rule="para" parents="22 3"/>
    </justification>
  </clause>

  <clause id="46">
    <literal><![CDATA[
      f(f(f(x,x),f(y,x)),f(f(f(f(y,x),f(y,x)),z),f(f(f(f(x,z),z),f(y,x)),x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(22(a,1),9(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="22 9"/>
    </justification>
  </clause>

  <clause id="47">
    <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(22(a,1),9(a,1,2,2,1,1,1))].">
      <j1 rule="para" parents="22 9"/>
    </justification>
  </clause>

  <clause id="48">
    <literal><![CDATA[
      f(f(x,f(y,y)),y) = f(y,y)
    ]]></literal>
    <justification jstring="[para(22(a,1),9(a,1,2,2,1)),rewrite(22(5),22(5))].">
      <j1 rule="para" parents="22 9"/>
      <j2 rule="rewrite" parents="22 22"/>
    </justification>
  </clause>

  <clause id="52">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),f(x,x)),f(f(f(x,f(x,x)),y),f(f(f(y,y),z),f(f(f(f(f(y,u),z),z),y),f(y,v)))))) = y
    ]]></literal>
    <justification jstring="[para(22(a,1),10(a,1,2,2,1,1,1))].">
      <j1 rule="para" parents="22 10"/>
    </justification>
  </clause>

  <clause id="57">
    <literal><![CDATA[
      f(f(f(x,x),y),x) = f(x,x)
    ]]></literal>
    <justification jstring="[para(14(a,1),22(a,1,1)),rewrite(14(7)),flip(a)].">
      <j1 rule="para" parents="14 22"/>
      <j2 rule="rewrite" parents="14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="59">
    <literal><![CDATA[
      f(f(x,y),f(y,f(f(y,y),f(y,z)))) = y
    ]]></literal>
    <justification jstring="[back_rewrite(39),rewrite(48(7))].">
      <j1 rule="back_rewrite" parents="39"/>
      <j2 rule="rewrite" parents="48"/>
    </justification>
  </clause>

  <clause id="67">
    <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>
    <justification jstring="[para(48(a,1),9(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="48 9"/>
    </justification>
  </clause>

  <clause id="68">
    <literal><![CDATA[
      f(f(f(x,x),f(y,z)),f(f(f(f(y,z),f(y,z)),x),f(f(f(f(x,x),x),f(y,z)),z))) = f(y,z)
    ]]></literal>
    <justification jstring="[para(48(a,1),9(a,1,2,2,1,1,1))].">
      <j1 rule="para" parents="48 9"/>
    </justification>
  </clause>

  <clause id="73">
    <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(57(a,1),3(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="57 3"/>
    </justification>
  </clause>

  <clause id="74">
    <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(57(a,1),3(a,1,2,2,1,1))].">
      <j1 rule="para" parents="57 3"/>
    </justification>
  </clause>

  <clause id="78">
    <literal><![CDATA[
      f(f(f(x,y),f(x,y)),f(f(f(f(x,y),f(x,y)),f(x,y)),f(f(f(f(x,y),f(x,y)),f(x,y)),y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(57(a,1),9(a,1,2,2,1,1))].">
      <j1 rule="para" parents="57 9"/>
    </justification>
  </clause>

  <clause id="82">
    <literal><![CDATA[
      f(f(x,y),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(22(a,1),57(a,1,1,1)),rewrite(22(6))].">
      <j1 rule="para" parents="22 57"/>
      <j2 rule="rewrite" parents="22"/>
    </justification>
  </clause>

  <clause id="86">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),f(f(y,x),f(y,x))),f(f(f(y,x),y),f(y,z)))) = y
    ]]></literal>
    <justification jstring="[para(82(a,1),3(a,1,2,2,1,1))].">
      <j1 rule="para" parents="82 3"/>
    </justification>
  </clause>

  <clause id="88">
    <literal><![CDATA[
      f(x,f(f(y,x),f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(3(a,1),82(a,1,1))].">
      <j1 rule="para" parents="3 82"/>
    </justification>
  </clause>

  <clause id="90">
    <literal><![CDATA[
      f(f(x,f(y,z)),f(f(f(f(y,z),f(y,z)),f(f(f(y,z),x),f(f(y,z),x))),f(f(f(f(y,z),x),f(y,z)),z))) = f(y,z)
    ]]></literal>
    <justification jstring="[para(82(a,1),9(a,1,2,2,1,1))].">
      <j1 rule="para" parents="82 9"/>
    </justification>
  </clause>

  <clause id="92">
    <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(f(f(y,y),z),f(f(f(f(f(y,u),z),z),y),f(y,v)))))) = y
    ]]></literal>
    <justification jstring="[para(82(a,1),10(a,1,2,2,1,1))].">
      <j1 rule="para" parents="82 10"/>
    </justification>
  </clause>

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

  <clause id="100">
    <literal><![CDATA[
      f(f(f(f(x,y),f(x,y)),y),f(f(f(y,y),z),f(f(f(f(f(x,y),z),z),y),f(y,u)))) = y
    ]]></literal>
    <justification jstring="[para(88(a,1),3(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="88 3"/>
    </justification>
  </clause>

  <clause id="102">
    <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(88(a,1),3(a,1,2,2,2))].">
      <j1 rule="para" parents="88 3"/>
    </justification>
  </clause>

  <clause id="103">
    <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(3(a,1),88(a,1,2,1)),rewrite(3(20),3(22))].">
      <j1 rule="para" parents="3 88"/>
      <j2 rule="rewrite" parents="3 3"/>
    </justification>
  </clause>

  <clause id="107">
    <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(v,y),u),u),y),f(y,w)))))) = y
    ]]></literal>
    <justification jstring="[para(88(a,1),10(a,1,2,2,2,2,1,1,1,1))].">
      <j1 rule="para" parents="88 10"/>
    </justification>
  </clause>

  <clause id="113">
    <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)),u),f(f(f(f(x,u),u),f(y,x)),f(f(y,x),v)))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(22(a,1),7(a,1,1,1,2,1,1,1))].">
      <j1 rule="para" parents="22 7"/>
    </justification>
  </clause>

  <clause id="121">
    <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)),f(x,x)),f(f(x,f(z,x)),f(f(z,x),v)))) = f(z,x)
    ]]></literal>
    <justification jstring="[para(82(a,1),7(a,1,2,2,1,1))].">
      <j1 rule="para" parents="82 7"/>
    </justification>
  </clause>

  <clause id="122">
    <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)),z))) = f(z,x)
    ]]></literal>
    <justification jstring="[para(82(a,1),7(a,1,2,2,2))].">
      <j1 rule="para" parents="82 7"/>
    </justification>
  </clause>

  <clause id="123">
    <literal><![CDATA[
      f(f(f(f(f(x,y),f(x,y)),z),f(f(f(f(y,z),z),f(x,y)),f(f(x,y),u))),f(f(x,y),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(7(a,1),88(a,1,2,1)),rewrite(7(37),7(40))].">
      <j1 rule="para" parents="7 88"/>
      <j2 rule="rewrite" parents="7 7"/>
    </justification>
  </clause>

  <clause id="141">
    <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(59(a,1),57(a,1)),flip(a)].">
      <j1 rule="para" parents="59 57"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="201">
    <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(74(a,1),88(a,1,2,1)),rewrite(74(16),74(18))].">
      <j1 rule="para" parents="74 88"/>
      <j2 rule="rewrite" parents="74 74"/>
    </justification>
  </clause>

  <clause id="210">
    <literal><![CDATA[
      f(x,f(f(x,x),f(x,y))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(141(a,1),22(a,1,1)),rewrite(141(9)),flip(a)].">
      <j1 rule="para" parents="141 22"/>
      <j2 rule="rewrite" parents="141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="215">
    <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)),f(f(f(f(y,z),f(y,z)),v),f(f(f(f(z,v),v),f(y,z)),z))))) = f(y,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),9(a,1,1,2)),rewrite(11(24),11(25),11(28),11(32),11(47))].">
      <j1 rule="para" parents="11 9"/>
      <j2 rule="rewrite" parents="11 11 11 11 11"/>
    </justification>
  </clause>

  <clause id="217">
    <literal><![CDATA[
      f(f(f(f(f(x,x),x),f(f(x,x),x)),x),f(f(f(f(x,x),x),f(f(x,x),x)),x)) = f(f(f(x,x),x),f(f(f(f(x,x),x),f(f(x,x),x)),x))
    ]]></literal>
    <justification jstring="[para(11(a,1),48(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="227">
    <literal><![CDATA[
      f(f(x,y),f(f(f(x,y),f(x,y)),y)) = f(f(x,y),f(x,y))
    ]]></literal>
    <justification jstring="[para(3(a,1),210(a,1,2,2))].">
      <j1 rule="para" parents="3 210"/>
    </justification>
  </clause>

  <clause id="231">
    <literal><![CDATA[
      f(f(x,x),f(x,f(f(x,x),y))) = x
    ]]></literal>
    <justification jstring="[para(22(a,1),210(a,1,2,1)),rewrite(82(8))].">
      <j1 rule="para" parents="22 210"/>
      <j2 rule="rewrite" parents="82"/>
    </justification>
  </clause>

  <clause id="234">
    <literal><![CDATA[
      f(f(x,y),f(f(f(x,y),f(x,y)),x)) = f(f(x,y),f(x,y))
    ]]></literal>
    <justification jstring="[para(82(a,1),210(a,1,2,2))].">
      <j1 rule="para" parents="82 210"/>
    </justification>
  </clause>

  <clause id="235">
    <literal><![CDATA[
      f(x,f(f(x,x),f(y,x))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(88(a,1),210(a,1,2,2))].">
      <j1 rule="para" parents="88 210"/>
    </justification>
  </clause>

  <clause id="237">
    <literal><![CDATA[
      f(f(f(f(f(x,x),x),f(f(x,x),x)),x),f(f(f(f(x,x),x),f(f(x,x),x)),x)) = f(f(f(x,x),x),f(f(x,x),x))
    ]]></literal>
    <justification jstring="[back_rewrite(217),rewrite(227(22))].">
      <j1 rule="back_rewrite" parents="217"/>
      <j2 rule="rewrite" parents="227"/>
    </justification>
  </clause>

  <clause id="239">
    <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(231(a,1),3(a,1,2,2,1,1,1)),rewrite(231(6))].">
      <j1 rule="para" parents="231 3"/>
      <j2 rule="rewrite" parents="231"/>
    </justification>
  </clause>

  <clause id="244">
    <literal><![CDATA[
      f(f(x,x),f(x,f(y,f(x,x)))) = x
    ]]></literal>
    <justification jstring="[para(88(a,1),231(a,1,2,2))].">
      <j1 rule="para" parents="88 231"/>
    </justification>
  </clause>

  <clause id="260">
    <literal><![CDATA[
      f(f(f(f(x,x),x),f(f(x,x),x)),x) = f(f(x,x),x)
    ]]></literal>
    <justification jstring="[para(11(a,1),244(a,1,2,2)),rewrite(237(13),57(14),82(11)),flip(a)].">
      <j1 rule="para" parents="11 244"/>
      <j2 rule="rewrite" parents="237 57 82"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="278">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),f(x,f(x,x))),f(x,x)) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(22(a,1),260(a,1,1,1,1)),rewrite(82(5),82(10))].">
      <j1 rule="para" parents="22 260"/>
      <j2 rule="rewrite" parents="82 82"/>
    </justification>
  </clause>

  <clause id="285">
    <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(88(a,1),201(a,1,1,2,2))].">
      <j1 rule="para" parents="88 201"/>
    </justification>
  </clause>

  <clause id="296">
    <literal><![CDATA[
      f(x,f(f(x,x),f(f(f(x,x),y),f(f(f(f(f(x,z),y),y),x),f(x,u))))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(3(a,1),227(a,1,1)),rewrite(3(11),3(11),3(23),3(23))].">
      <j1 rule="para" parents="3 227"/>
      <j2 rule="rewrite" parents="3 3 3 3"/>
    </justification>
  </clause>

  <clause id="327">
    <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(22(a,1),285(a,1,1,1,1)),rewrite(82(5),82(11))].">
      <j1 rule="para" parents="22 285"/>
      <j2 rule="rewrite" parents="82 82"/>
    </justification>
  </clause>

  <clause id="344">
    <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(f(f(y,y),w),f(f(f(f(f(v6,y),w),w),y),f(y,v7)))))))) = y
    ]]></literal>
    <justification jstring="[para(88(a,1),15(a,1,2,2,2,2,2,2,1,1,1,1))].">
      <j1 rule="para" parents="88 15"/>
    </justification>
  </clause>

  <clause id="353">
    <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(88(a,1),239(a,1,2,2,2))].">
      <j1 rule="para" parents="88 239"/>
    </justification>
  </clause>

  <clause id="394">
    <literal><![CDATA[
      f(f(x,x),f(f(x,f(x,f(f(x,x),y))),x)) = x
    ]]></literal>
    <justification jstring="[para(88(a,1),353(a,1,2))].">
      <j1 rule="para" parents="88 353"/>
    </justification>
  </clause>

  <clause id="454">
    <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)),y))) = f(y,z)
    ]]></literal>
    <justification jstring="[para(82(a,1),41(a,1,2,2,2))].">
      <j1 rule="para" parents="82 41"/>
    </justification>
  </clause>

  <clause id="462">
    <literal><![CDATA[
      f(x,f(f(f(x,x),x),f(x,f(f(x,x),y)))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(285(a,1),41(a,1,2,2,1)),rewrite(22(4),82(3),88(6))].">
      <j1 rule="para" parents="285 41"/>
      <j2 rule="rewrite" parents="22 82 88"/>
    </justification>
  </clause>

  <clause id="463">
    <literal><![CDATA[
      f(f(x,x),f(f(x,f(x,x)),f(f(x,x),f(x,y)))) = x
    ]]></literal>
    <justification jstring="[para(327(a,1),41(a,1,2,2,1)),rewrite(48(3),88(8))].">
      <j1 rule="para" parents="327 41"/>
      <j2 rule="rewrite" parents="48 88"/>
    </justification>
  </clause>

  <clause id="474">
    <literal><![CDATA[
      f(f(f(x,x),f(y,x)),f(f(f(f(y,x),f(y,x)),f(f(x,x),f(x,z))),f(f(f(f(x,x),f(f(x,x),f(x,z))),f(y,x)),f(f(y,x),u)))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(210(a,1),40(a,1,2,2,1,1,1))].">
      <j1 rule="para" parents="210 40"/>
    </justification>
  </clause>

  <clause id="521">
    <literal><![CDATA[
      f(f(f(x,x),f(y,x)),f(f(f(f(y,x),f(y,x)),f(x,x)),f(f(x,f(y,x)),x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(82(a,1),46(a,1,2,2,1,1))].">
      <j1 rule="para" parents="82 46"/>
    </justification>
  </clause>

  <clause id="564">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(x,f(f(x,x),y))) = x
    ]]></literal>
    <justification jstring="[para(41(a,1),47(a,1,2,2,1)),rewrite(82(3),82(6),82(10),82(13),82(16),82(19),82(27),231(27),48(23),82(9),82(3),82(6)),flip(a)].">
      <j1 rule="para" parents="41 47"/>
      <j2 rule="rewrite" parents="82 82 82 82 82 82 82 231 48 82 82 82"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="577">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(x,f(y,f(x,x)))) = x
    ]]></literal>
    <justification jstring="[para(88(a,1),564(a,1,2,2))].">
      <j1 rule="para" parents="88 564"/>
    </justification>
  </clause>

  <clause id="590">
    <literal><![CDATA[
      f(f(f(x,x),x),f(f(x,x),f(y,x))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(22(a,1),577(a,1,1,2)),rewrite(82(6))].">
      <j1 rule="para" parents="22 577"/>
      <j2 rule="rewrite" parents="82"/>
    </justification>
  </clause>

  <clause id="681">
    <literal><![CDATA[
      f(f(f(f(x,x),y),f(f(f(f(f(x,z),y),y),x),f(u,x))),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(102(a,1),88(a,1,2,1)),rewrite(102(20),102(22))].">
      <j1 rule="para" parents="102 88"/>
      <j2 rule="rewrite" parents="102 102"/>
    </justification>
  </clause>

  <clause id="684">
    <literal><![CDATA[
      f(f(f(f(x,y),f(x,y)),y),f(f(f(y,y),z),f(f(f(f(f(x,y),z),z),y),f(u,y)))) = y
    ]]></literal>
    <justification jstring="[para(88(a,1),102(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="88 102"/>
    </justification>
  </clause>

  <clause id="737">
    <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(564(a,1),102(a,1,2,2,1,1,1)),rewrite(231(7))].">
      <j1 rule="para" parents="564 102"/>
      <j2 rule="rewrite" parents="231"/>
    </justification>
  </clause>

  <clause id="772">
    <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(74(a,1),103(a,1,1,2,1,1,1,1)),rewrite(82(3),82(12))].">
      <j1 rule="para" parents="74 103"/>
      <j2 rule="rewrite" parents="82 82"/>
    </justification>
  </clause>

  <clause id="837">
    <literal><![CDATA[
      f(f(x,x),f(f(x,f(x,x)),f(f(x,x),f(f(f(x,x),y),f(f(f(f(f(x,z),y),y),x),f(x,u)))))) = x
    ]]></literal>
    <justification jstring="[para(327(a,1),52(a,1,2,2,1)),rewrite(48(3),88(8))].">
      <j1 rule="para" parents="327 52"/>
      <j2 rule="rewrite" parents="48 88"/>
    </justification>
  </clause>

  <clause id="958">
    <literal><![CDATA[
      f(f(f(x,y),f(f(f(f(x,y),y),f(x,x)),f(z,f(x,x)))),x) = f(x,x)
    ]]></literal>
    <justification jstring="[para(74(a,1),681(a,1,1,2,1,1,1,1)),rewrite(82(3),82(12))].">
      <j1 rule="para" parents="74 681"/>
      <j2 rule="rewrite" parents="82 82"/>
    </justification>
  </clause>

  <clause id="1010">
    <literal><![CDATA[
      f(f(f(x,x),x),f(f(x,f(x,f(f(x,x),y))),x)) = x
    ]]></literal>
    <justification jstring="[para(88(a,1),737(a,1,2))].">
      <j1 rule="para" parents="88 737"/>
    </justification>
  </clause>

  <clause id="1028">
    <literal><![CDATA[
      f(f(x,f(x,f(f(x,x),y))),x) = f(x,x)
    ]]></literal>
    <justification jstring="[para(1010(a,1),46(a,1,2,2,1)),rewrite(394(7),22(14)),flip(a)].">
      <j1 rule="para" parents="1010 46"/>
      <j2 rule="rewrite" parents="394 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1036">
    <literal><![CDATA[
      f(f(x,f(x,f(y,f(x,x)))),x) = f(x,x)
    ]]></literal>
    <justification jstring="[para(88(a,1),1028(a,1,1,2,2))].">
      <j1 rule="para" parents="88 1028"/>
    </justification>
  </clause>

  <clause id="1052">
    <literal><![CDATA[
      f(f(f(x,x),f(f(x,x),f(y,x))),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(22(a,1),1036(a,1,1,2,2,2)),rewrite(82(10))].">
      <j1 rule="para" parents="22 1036"/>
      <j2 rule="rewrite" parents="82"/>
    </justification>
  </clause>

  <clause id="1330">
    <literal><![CDATA[
      f(f(f(x,x),x),f(x,f(f(x,x),y))) = x
    ]]></literal>
    <justification jstring="[para(86(a,1),47(a,1,2,2,1)),rewrite(82(3),88(6),22(6),462(7),82(4),88(7),22(7),82(10),88(13),22(13),22(21),231(21),48(17),82(3),82(3),88(6),22(6)),flip(a)].">
      <j1 rule="para" parents="86 47"/>
      <j2 rule="rewrite" parents="82 88 22 462 82 88 22 82 88 22 22 231 48 82 82 88 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1349">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(x,x),f(x,y))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(86(a,1),68(a,1,2,2,1)),rewrite(88(8),48(6),463(8),88(7),48(5),88(13),48(11),48(17),210(18),22(16),88(8),48(6)),flip(a)].">
      <j1 rule="para" parents="86 68"/>
      <j2 rule="rewrite" parents="88 48 463 88 48 88 48 48 210 22 88 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1359">
    <literal><![CDATA[
      f(f(f(x,x),x),f(x,f(y,f(x,x)))) = x
    ]]></literal>
    <justification jstring="[para(88(a,1),1330(a,1,2,2))].">
      <j1 rule="para" parents="88 1330"/>
    </justification>
  </clause>

  <clause id="1392">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(x,x),f(y,x))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(22(a,1),1359(a,1,1,1)),rewrite(82(6))].">
      <j1 rule="para" parents="22 1359"/>
      <j2 rule="rewrite" parents="82"/>
    </justification>
  </clause>

  <clause id="1413">
    <literal><![CDATA[
      f(f(f(x,y),f(f(x,y),f(x,y))),f(f(f(x,y),f(x,y)),y)) = f(f(x,y),f(x,y))
    ]]></literal>
    <justification jstring="[para(3(a,1),1349(a,1,2,2))].">
      <j1 rule="para" parents="3 1349"/>
    </justification>
  </clause>

  <clause id="1420">
    <literal><![CDATA[
      f(f(f(x,y),f(f(x,y),f(x,y))),f(f(f(x,y),f(x,y)),x)) = f(f(x,y),f(x,y))
    ]]></literal>
    <justification jstring="[para(82(a,1),1349(a,1,2,2))].">
      <j1 rule="para" parents="82 1349"/>
    </justification>
  </clause>

  <clause id="1654">
    <literal><![CDATA[
      f(f(x,f(f(x,x),x)),f(f(f(x,x),x),f(f(f(x,x),f(f(x,x),x)),f(f(f(x,x),x),y)))) = f(f(x,x),x)
    ]]></literal>
    <justification jstring="[para(260(a,1),73(a,1,2,1)),rewrite(57(8))].">
      <j1 rule="para" parents="260 73"/>
      <j2 rule="rewrite" parents="57"/>
    </justification>
  </clause>

  <clause id="1794">
    <literal><![CDATA[
      f(f(f(x,y),f(x,y)),f(f(f(f(x,y),f(x,y)),f(x,y)),f(f(f(f(x,y),f(x,y)),f(x,y)),f(f(f(f(x,y),f(x,y)),z),f(f(f(f(y,z),z),f(x,y)),y))))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(11(a,1),78(a,1,1,1)),rewrite(11(23),11(25),11(26),11(28),11(30),11(31),11(33),11(48))].">
      <j1 rule="para" parents="11 78"/>
      <j2 rule="rewrite" parents="11 11 11 11 11 11 11 11"/>
    </justification>
  </clause>

  <clause id="2381">
    <literal><![CDATA[
      f(f(f(f(x,x),f(y,x)),f(f(x,x),x)),x) = f(f(x,x),x)
    ]]></literal>
    <justification jstring="[para(590(a,1),90(a,1,2,1,2,1)),rewrite(590(18),82(14),260(12),590(14),57(13),22(10))].">
      <j1 rule="para" parents="590 90"/>
      <j2 rule="rewrite" parents="590 82 260 590 57 22"/>
    </justification>
  </clause>

  <clause id="2436">
    <literal><![CDATA[
      f(f(x,x),f(f(f(x,x),f(f(x,x),x)),f(f(f(x,x),x),f(y,x)))) = x
    ]]></literal>
    <justification jstring="[para(2381(a,1),102(a,1,2,2,1))].">
      <j1 rule="para" parents="2381 102"/>
    </justification>
  </clause>

  <clause id="2491">
    <literal><![CDATA[
      f(f(x,x),f(f(x,x),x)) = x
    ]]></literal>
    <justification jstring="[para(22(a,1),2436(a,1,2))].">
      <j1 rule="para" parents="22 2436"/>
    </justification>
  </clause>

  <clause id="2498">
    <literal><![CDATA[
      f(x,f(x,f(x,x))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(278(a,1),2436(a,1,2,2,2)),rewrite(82(3),82(3),82(3),82(6),22(9))].">
      <j1 rule="para" parents="278 2436"/>
      <j2 rule="rewrite" parents="82 82 82 82 22"/>
    </justification>
  </clause>

  <clause id="2537">
    <literal><![CDATA[
      f(f(x,f(f(x,x),x)),f(f(f(x,x),x),f(x,f(f(f(x,x),x),y)))) = f(f(x,x),x)
    ]]></literal>
    <justification jstring="[back_rewrite(1654),rewrite(2491(9))].">
      <j1 rule="back_rewrite" parents="1654"/>
      <j2 rule="rewrite" parents="2491"/>
    </justification>
  </clause>

  <clause id="2576">
    <literal><![CDATA[
      f(f(x,y),f(y,f(f(f(f(f(y,x),f(f(y,y),y)),f(f(y,y),y)),y),f(z,y)))) = y
    ]]></literal>
    <justification jstring="[para(2491(a,1),102(a,1,2,1))].">
      <j1 rule="para" parents="2491 102"/>
    </justification>
  </clause>

  <clause id="2610">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(x,x),f(f(f(x,x),y),f(f(f(f(f(x,z),y),y),x),f(x,u))))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(92(a,1),68(a,1,2,2,1)),rewrite(88(8),48(6),837(16),88(7),48(5),88(21),48(19),48(33),296(42),22(32),88(8),48(6)),flip(a)].">
      <j1 rule="para" parents="92 68"/>
      <j2 rule="rewrite" parents="88 48 837 88 48 88 48 48 296 22 88 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4042">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(x,x),f(f(x,x),f(f(x,x),f(y,x))))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(1052(a,1),1420(a,1,1,1)),rewrite(1052(7),1052(7),1052(9),1052(9),1052(17),1052(17))].">
      <j1 rule="para" parents="1052 1420"/>
      <j2 rule="rewrite" parents="1052 1052 1052 1052 1052 1052"/>
    </justification>
  </clause>

  <clause id="4109">
    <literal><![CDATA[
      f(f(f(f(x,y),f(f(f(f(f(f(x,x),x),y),y),f(x,x)),f(f(x,x),z))),f(x,f(x,x))),x) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(564(a,1),121(a,1,2,2,2)),rewrite(82(3),82(22),57(25),22(22))].">
      <j1 rule="para" parents="564 121"/>
      <j2 rule="rewrite" parents="82 82 57 22"/>
    </justification>
  </clause>

  <clause id="4211">
    <literal><![CDATA[
      f(x,f(f(x,y),f(f(f(f(x,y),y),f(x,x)),f(x,f(x,f(f(x,x),z)))))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(1028(a,1),122(a,1,1,2)),rewrite(103(15),1028(5),1028(6),82(3),1028(8),1028(17))].">
      <j1 rule="para" parents="1028 122"/>
      <j2 rule="rewrite" parents="103 1028 1028 82 1028 1028"/>
    </justification>
  </clause>

  <clause id="4246">
    <literal><![CDATA[
      f(f(f(f(x,x),f(f(x,x),f(f(x,x),f(y,x)))),f(x,f(x,x))),f(f(f(f(x,f(x,x)),f(x,f(x,x))),x),f(f(f(x,x),f(x,f(x,x))),f(f(x,f(x,x)),z)))) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(4042(a,1),86(a,1,2,1,2,1)),rewrite(4042(26),82(18),4042(26))].">
      <j1 rule="para" parents="4042 86"/>
      <j2 rule="rewrite" parents="4042 82 4042"/>
    </justification>
  </clause>

  <clause id="4654">
    <literal><![CDATA[
      f(f(x,y),f(f(f(f(y,x),f(f(y,y),y)),f(f(y,y),y)),y)) = y
    ]]></literal>
    <justification jstring="[para(88(a,1),2576(a,1,2))].">
      <j1 rule="para" parents="88 2576"/>
    </justification>
  </clause>

  <clause id="4731">
    <literal><![CDATA[
      f(f(f(x,x),x),f(f(f(f(f(x,x),x),f(f(x,x),x)),f(f(x,x),x)),x)) = x
    ]]></literal>
    <justification jstring="[para(48(a,1),4654(a,1,2,1,1)),rewrite(260(6))].">
      <j1 rule="para" parents="48 4654"/>
      <j2 rule="rewrite" parents="260"/>
    </justification>
  </clause>

  <clause id="4735">
    <literal><![CDATA[
      f(f(f(x,x),f(x,y)),f(f(f(x,f(f(f(x,y),f(x,y)),f(x,y))),f(f(f(x,y),f(x,y)),f(x,y))),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(82(a,1),4654(a,1,2,1,1,1))].">
      <j1 rule="para" parents="82 4654"/>
    </justification>
  </clause>

  <clause id="4739">
    <literal><![CDATA[
      f(f(f(f(x,y),f(x,y)),x),f(f(f(f(x,y),f(f(x,x),x)),f(f(x,x),x)),x)) = x
    ]]></literal>
    <justification jstring="[para(97(a,1),4654(a,1,2,1,1,1))].">
      <j1 rule="para" parents="97 4654"/>
    </justification>
  </clause>

  <clause id="4922">
    <literal><![CDATA[
      f(f(f(f(x,f(x,x)),f(x,f(x,x))),f(x,f(x,x))),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(4731(a,1),67(a,1,2,2,1)),rewrite(82(3),82(5),82(8),82(14),82(16),82(19),82(24),82(26),82(29),82(37),48(35),82(13),82(3),82(5),82(8)),flip(a)].">
      <j1 rule="para" parents="4731 67"/>
      <j2 rule="rewrite" parents="82 82 82 82 82 82 82 82 82 82 48 82 82 82 82"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4969">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),f(f(f(x,f(x,x)),f(x,f(x,x))),f(x,f(x,x)))),x) = f(f(f(x,f(x,x)),f(x,f(x,x))),f(x,f(x,x)))
    ]]></literal>
    <justification jstring="[para(4922(a,1),2537(a,1,2,2,2)),rewrite(48(22),4922(21))].">
      <j1 rule="para" parents="4922 2537"/>
      <j2 rule="rewrite" parents="48 4922"/>
    </justification>
  </clause>

  <clause id="5567">
    <literal><![CDATA[
      f(x,f(f(x,f(x,x)),f(f(x,f(x,x)),f(x,f(x,f(f(x,x),y)))))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(82(a,1),4211(a,1,2,2,1,1))].">
      <j1 rule="para" parents="82 4211"/>
    </justification>
  </clause>

  <clause id="5640">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),f(f(x,f(x,x)),f(x,f(x,f(f(x,x),y))))),x) = f(x,x)
    ]]></literal>
    <justification jstring="[para(5567(a,1),88(a,1,2,1)),rewrite(5567(22),82(13),5567(22))].">
      <j1 rule="para" parents="5567 88"/>
      <j2 rule="rewrite" parents="5567 82 5567"/>
    </justification>
  </clause>

  <clause id="5691">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),f(f(x,f(x,x)),f(x,f(x,f(y,f(x,x)))))),x) = f(x,x)
    ]]></literal>
    <justification jstring="[para(88(a,1),5640(a,1,1,2,2,2,2))].">
      <j1 rule="para" parents="88 5640"/>
    </justification>
  </clause>

  <clause id="5714">
    <literal><![CDATA[
      f(f(f(f(x,f(x,x)),f(x,f(x,f(y,f(x,x))))),f(x,f(x,x))),f(f(f(f(x,f(x,x)),f(x,f(x,x))),x),f(f(f(f(x,x),x),f(x,f(x,x))),f(x,x)))) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(5691(a,1),9(a,1,2,2,1,1,1))].">
      <j1 rule="para" parents="5691 9"/>
    </justification>
  </clause>

  <clause id="8394">
    <literal><![CDATA[
      f(f(x,x),f(x,y)) = x
    ]]></literal>
    <justification jstring="[para(210(a,1),454(a,1,1)),rewrite(1349(16),82(13),48(11),82(3)),flip(a)].">
      <j1 rule="para" parents="210 454"/>
      <j2 rule="rewrite" parents="1349 82 48 82"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8395">
    <literal><![CDATA[
      f(x,f(f(x,x),y)) = f(x,x)
    ]]></literal>
    <justification jstring="[para(231(a,1),454(a,1,1)),rewrite(8394(10),8394(12),1330(14),22(10)),flip(a)].">
      <j1 rule="para" parents="231 454"/>
      <j2 rule="rewrite" parents="8394 8394 1330 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8396">
    <literal><![CDATA[
      f(f(x,x),f(y,x)) = x
    ]]></literal>
    <justification jstring="[para(235(a,1),454(a,1,1)),rewrite(1392(16),8394(13),48(11),8394(3)),flip(a)].">
      <j1 rule="para" parents="235 454"/>
      <j2 rule="rewrite" parents="1392 8394 48 8394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8397">
    <literal><![CDATA[
      f(x,f(y,f(x,x))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(244(a,1),454(a,1,1)),rewrite(8394(10),8394(12),1359(14),22(10)),flip(a)].">
      <j1 rule="para" parents="244 454"/>
      <j2 rule="rewrite" parents="8394 8394 1359 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8398">
    <literal><![CDATA[
      f(f(f(x,y),f(x,y)),y) = f(x,y)
    ]]></literal>
    <justification jstring="[para(227(a,1),454(a,1,1)),rewrite(1413(26),8394(23),48(18),8394(7)),flip(a)].">
      <j1 rule="para" parents="227 454"/>
      <j2 rule="rewrite" parents="1413 8394 48 8394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8400">
    <literal><![CDATA[
      f(f(f(x,y),f(x,y)),x) = f(x,y)
    ]]></literal>
    <justification jstring="[para(234(a,1),454(a,1,1)),rewrite(1420(26),8394(23),48(18),8394(7)),flip(a)].">
      <j1 rule="para" parents="234 454"/>
      <j2 rule="rewrite" parents="1420 8394 48 8394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8402">
    <literal><![CDATA[
      f(f(x,y),f(f(f(f(f(f(x,x),x),y),y),f(x,x)),f(f(x,x),z))) = x
    ]]></literal>
    <justification jstring="[para(38(a,1),454(a,1,2,2,1)),rewrite(8394(40),48(38),82(14)),flip(a)].">
      <j1 rule="para" parents="38 454"/>
      <j2 rule="rewrite" parents="8394 48 82"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8436">
    <literal><![CDATA[
      f(f(x,x),f(f(f(x,x),y),f(f(f(f(f(x,z),y),y),x),f(x,u)))) = x
    ]]></literal>
    <justification jstring="[para(296(a,1),454(a,1,1)),rewrite(8400(26),2610(26),8394(15),57(13),8394(3)),flip(a)].">
      <j1 rule="para" parents="296 454"/>
      <j2 rule="rewrite" parents="8400 2610 8394 57 8394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8440">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),z),f(f(f(f(f(x,y),z),z),y),f(y,u)))) = y
    ]]></literal>
    <justification jstring="[para(100(a,1),454(a,2)),rewrite(8398(4),8398(16),8398(27),8398(43),8398(55),454(55))].">
      <j1 rule="para" parents="100 454"/>
      <j2 rule="rewrite" parents="8398 8398 8398 8398 8398 454"/>
    </justification>
  </clause>

  <clause id="8483">
    <literal><![CDATA[
      f(f(x,y),f(f(f(f(x,y),f(f(x,x),x)),f(f(x,x),x)),x)) = x
    ]]></literal>
    <justification jstring="[para(4739(a,1),454(a,2)),rewrite(8400(4),8400(15),8400(25),8400(40),8400(51),454(51))].">
      <j1 rule="para" parents="4739 454"/>
      <j2 rule="rewrite" parents="8400 8400 8400 8400 8400 454"/>
    </justification>
  </clause>

  <clause id="8486">
    <literal><![CDATA[
      f(x,f(f(f(f(y,x),f(y,x)),f(x,x)),f(f(x,f(y,x)),x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(521(a,1),454(a,2)),rewrite(8396(3),8396(14),8396(24),8396(39),8396(50),454(50))].">
      <j1 rule="para" parents="521 454"/>
      <j2 rule="rewrite" parents="8396 8396 8396 8396 8396 454"/>
    </justification>
  </clause>

  <clause id="8488">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),z),f(f(f(f(f(x,y),z),z),y),f(u,y)))) = y
    ]]></literal>
    <justification jstring="[para(684(a,1),454(a,2)),rewrite(8398(4),8398(16),8398(27),8398(43),8398(55),454(55))].">
      <j1 rule="para" parents="684 454"/>
      <j2 rule="rewrite" parents="8398 8398 8398 8398 8398 454"/>
    </justification>
  </clause>

  <clause id="8534">
    <literal><![CDATA[
      f(x,f(f(f(x,f(f(f(x,y),f(x,y)),f(x,y))),f(f(f(x,y),f(x,y)),f(x,y))),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(4735),rewrite(8394(3))].">
      <j1 rule="back_rewrite" parents="4735"/>
      <j2 rule="rewrite" parents="8394"/>
    </justification>
  </clause>

  <clause id="8541">
    <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(4246),rewrite(8396(5),8396(4),2498(3),8400(7),8394(7))].">
      <j1 rule="back_rewrite" parents="4246"/>
      <j2 rule="rewrite" parents="8396 8396 2498 8400 8394"/>
    </justification>
  </clause>

  <clause id="8589">
    <literal><![CDATA[
      f(x,f(f(y,x),f(f(f(f(x,x),x),f(y,x)),f(f(y,x),z)))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(474),rewrite(8396(3),8394(6),8398(4),8394(5))].">
      <j1 rule="back_rewrite" parents="474"/>
      <j2 rule="rewrite" parents="8396 8394 8398 8394"/>
    </justification>
  </clause>

  <clause id="8616">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),f(x,f(x,x))),f(x,f(x,x))) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[back_rewrite(4969),rewrite(8395(11),8400(6)),flip(a)].">
      <j1 rule="back_rewrite" parents="4969"/>
      <j2 rule="rewrite" parents="8395 8400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8681">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(x,f(x,x)),f(f(f(f(x,x),x),f(x,f(x,x))),f(x,x)))) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[back_rewrite(5714),rewrite(8397(5),8616(8),8400(8))].">
      <j1 rule="back_rewrite" parents="5714"/>
      <j2 rule="rewrite" parents="8397 8616 8400"/>
    </justification>
  </clause>

  <clause id="8888">
    <literal><![CDATA[
      f(f(x,x),x) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[back_rewrite(4109),rewrite(8402(11),8397(3))].">
      <j1 rule="back_rewrite" parents="4109"/>
      <j2 rule="rewrite" parents="8402 8397"/>
    </justification>
  </clause>

  <clause id="9157">
    <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="[back_rewrite(8681),rewrite(8888(6),8398(11))].">
      <j1 rule="back_rewrite" parents="8681"/>
      <j2 rule="rewrite" parents="8888 8398"/>
    </justification>
  </clause>

  <clause id="9187">
    <literal><![CDATA[
      f(x,f(f(y,x),f(f(f(x,f(x,x)),f(y,x)),f(f(y,x),z)))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(8589),rewrite(8888(3))].">
      <j1 rule="back_rewrite" parents="8589"/>
      <j2 rule="rewrite" parents="8888"/>
    </justification>
  </clause>

  <clause id="9203">
    <literal><![CDATA[
      f(x,f(f(f(x,f(f(x,y),f(f(x,y),f(x,y)))),f(f(x,y),f(f(x,y),f(x,y)))),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(8534),rewrite(8888(5),8888(11))].">
      <j1 rule="back_rewrite" parents="8534"/>
      <j2 rule="rewrite" parents="8888 8888"/>
    </justification>
  </clause>

  <clause id="9216">
    <literal><![CDATA[
      f(f(x,y),f(f(f(f(x,y),f(x,f(x,x))),f(x,f(x,x))),x)) = x
    ]]></literal>
    <justification jstring="[back_rewrite(8483),rewrite(8888(4),8888(7))].">
      <j1 rule="back_rewrite" parents="8483"/>
      <j2 rule="rewrite" parents="8888 8888"/>
    </justification>
  </clause>

  <clause id="9535">
    <literal><![CDATA[
      f(f(f(x,y),f(x,y)),f(f(f(x,y),f(f(x,y),f(x,y))),f(f(f(x,y),f(f(x,y),f(x,y))),f(f(f(f(x,y),f(x,y)),z),f(f(f(f(y,z),z),f(x,y)),y))))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(1794),rewrite(8888(8),8888(13))].">
      <j1 rule="back_rewrite" parents="1794"/>
      <j2 rule="rewrite" parents="8888 8888"/>
    </justification>
  </clause>

  <clause id="9628">
    <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(285),rewrite(8888(2),8888(4))].">
      <j1 rule="back_rewrite" parents="285"/>
      <j2 rule="rewrite" parents="8888 8888"/>
    </justification>
  </clause>

  <clause id="9638">
    <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(201),rewrite(8888(2),8888(4))].">
      <j1 rule="back_rewrite" parents="201"/>
      <j2 rule="rewrite" parents="8888 8888"/>
    </justification>
  </clause>

  <clause id="9978">
    <literal><![CDATA[
      f(f(x,x),f(f(f(x,x),y),f(f(f(f(f(x,z),y),y),x),f(f(f(x,x),u),f(f(f(f(f(v,x),u),u),x),f(x,w)))))) = x
    ]]></literal>
    <justification jstring="[para(107(a,1),8398(a,1,1,1)),rewrite(107(19),107(38))].">
      <j1 rule="para" parents="107 8398"/>
      <j2 rule="rewrite" parents="107 107"/>
    </justification>
  </clause>

  <clause id="10047">
    <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(y,x),f(f(f(f(x,y),y),f(y,x)),f(f(y,x),u)))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(8400(a,1),113(a,1,2,1))].">
      <j1 rule="para" parents="8400 113"/>
    </justification>
  </clause>

  <clause id="10604">
    <literal><![CDATA[
      f(x,f(f(f(f(x,y),f(x,y)),f(x,x)),f(f(x,f(x,y)),x))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(8400(a,1),8486(a,1,2,1,1,1)),rewrite(8400(5),8400(9),8400(14))].">
      <j1 rule="para" parents="8400 8486"/>
      <j2 rule="rewrite" parents="8400 8400 8400"/>
    </justification>
  </clause>

  <clause id="11076">
    <literal><![CDATA[
      f(x,f(f(x,f(x,x)),f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(8397(a,1),9187(a,1,2,2)),rewrite(88(11))].">
      <j1 rule="para" parents="8397 9187"/>
      <j2 rule="rewrite" parents="88"/>
    </justification>
  </clause>

  <clause id="11140">
    <literal><![CDATA[
      f(f(x,y),f(f(f(x,y),f(f(x,y),f(x,y))),x)) = x
    ]]></literal>
    <justification jstring="[para(8394(a,1),11076(a,1,2,2)),rewrite(8394(11))].">
      <j1 rule="para" parents="8394 11076"/>
      <j2 rule="rewrite" parents="8394"/>
    </justification>
  </clause>

  <clause id="11142">
    <literal><![CDATA[
      f(x,f(f(x,f(x,x)),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(8400(a,1),11076(a,1,2,2)),rewrite(8400(9))].">
      <j1 rule="para" parents="8400 11076"/>
      <j2 rule="rewrite" parents="8400"/>
    </justification>
  </clause>

  <clause id="11170">
    <literal><![CDATA[
      f(f(x,x),f(f(x,f(x,x)),f(y,x))) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(11076(a,1),8541(a,1,2,2))].">
      <j1 rule="para" parents="11076 8541"/>
    </justification>
  </clause>

  <clause id="11226">
    <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(9157(a,1),11142(a,1,2,1))].">
      <j1 rule="para" parents="9157 11142"/>
    </justification>
  </clause>

  <clause id="11328">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(x,f(x,x)),f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(9628(a,1),11140(a,1,1)),rewrite(9628(9),9628(9),9628(9),11226(10),11076(5)),flip(a)].">
      <j1 rule="para" parents="9628 11140"/>
      <j2 rule="rewrite" parents="9628 9628 9628 11226 11076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11329">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(x,f(x,x)),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(9638(a,1),11140(a,1,1)),rewrite(9638(9),9638(9),9638(9),11226(10),11142(5)),flip(a)].">
      <j1 rule="para" parents="9638 11140"/>
      <j2 rule="rewrite" parents="9638 9638 9638 11226 11142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11482">
    <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(8394(a,1),11170(a,1,2,2))].">
      <j1 rule="para" parents="8394 11170"/>
    </justification>
  </clause>

  <clause id="11485">
    <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(8396(a,1),11170(a,1,2,2))].">
      <j1 rule="para" parents="8396 11170"/>
    </justification>
  </clause>

  <clause id="11613">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(y,x),f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(11328(a,1),97(a,1,2,1)),rewrite(11328(10),11328(13))].">
      <j1 rule="para" parents="11328 97"/>
      <j2 rule="rewrite" parents="11328 11328"/>
    </justification>
  </clause>

  <clause id="11617">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(y,x)) = f(f(y,x),f(y,x))
    ]]></literal>
    <justification jstring="[para(11328(a,1),47(a,1,1)),rewrite(11329(24),11328(23),8397(21)),flip(a)].">
      <j1 rule="para" parents="11328 47"/>
      <j2 rule="rewrite" parents="11329 11328 8397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11660">
    <literal><![CDATA[
      f(f(f(x,y),f(x,y)),f(y,f(y,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(11328(a,1),8400(a,1,1,1)),rewrite(11328(8),11328(13))].">
      <j1 rule="para" parents="11328 8400"/>
      <j2 rule="rewrite" parents="11328 11328"/>
    </justification>
  </clause>

  <clause id="11710">
    <literal><![CDATA[
      f(f(f(x,y),f(f(x,y),f(x,y))),f(y,y)) = y
    ]]></literal>
    <justification jstring="[para(8396(a,1),11613(a,1,2,1)),rewrite(8396(8),8396(10))].">
      <j1 rule="para" parents="8396 11613"/>
      <j2 rule="rewrite" parents="8396 8396"/>
    </justification>
  </clause>

  <clause id="11713">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(x,y),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(8400(a,1),11613(a,1,2,1)),rewrite(8400(7),8400(10))].">
      <j1 rule="para" parents="8400 11613"/>
      <j2 rule="rewrite" parents="8400 8400"/>
    </justification>
  </clause>

  <clause id="12000">
    <literal><![CDATA[
      f(f(f(x,y),f(f(x,y),f(x,y))),x) = f(x,x)
    ]]></literal>
    <justification jstring="[para(8394(a,1),11617(a,1,2)),rewrite(8394(9),8394(9))].">
      <j1 rule="para" parents="8394 11617"/>
      <j2 rule="rewrite" parents="8394 8394"/>
    </justification>
  </clause>

  <clause id="12003">
    <literal><![CDATA[
      f(f(f(x,y),f(f(x,y),f(x,y))),y) = f(y,y)
    ]]></literal>
    <justification jstring="[para(8396(a,1),11617(a,1,2)),rewrite(8396(9),8396(9))].">
      <j1 rule="para" parents="8396 11617"/>
      <j2 rule="rewrite" parents="8396 8396"/>
    </justification>
  </clause>

  <clause id="12007">
    <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(11617(a,2),8888(a,2,2)),rewrite(8888(5)),flip(a)].">
      <j1 rule="para" parents="11617 8888"/>
      <j2 rule="rewrite" parents="8888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12125">
    <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(11617(a,2),11328(a,1,1,2))].">
      <j1 rule="para" parents="11617 11328"/>
    </justification>
  </clause>

  <clause id="12140">
    <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(11482),rewrite(12000(9))].">
      <j1 rule="back_rewrite" parents="11482"/>
      <j2 rule="rewrite" parents="12000"/>
    </justification>
  </clause>

  <clause id="12145">
    <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(11485),rewrite(12003(9))].">
      <j1 rule="back_rewrite" parents="11485"/>
      <j2 rule="rewrite" parents="12003"/>
    </justification>
  </clause>

  <clause id="12226">
    <literal><![CDATA[
      f(x,f(f(f(x,y),f(f(x,y),f(x,y))),f(f(x,f(x,y)),x))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(10604),rewrite(12140(5))].">
      <j1 rule="back_rewrite" parents="10604"/>
      <j2 rule="rewrite" parents="12140"/>
    </justification>
  </clause>

  <clause id="12507">
    <literal><![CDATA[
      f(f(x,x),f(f(x,y),f(f(x,y),f(x,y)))) = x
    ]]></literal>
    <justification jstring="[para(8394(a,1),11660(a,1,1,1)),rewrite(8394(3),8394(10))].">
      <j1 rule="para" parents="8394 11660"/>
      <j2 rule="rewrite" parents="8394 8394"/>
    </justification>
  </clause>

  <clause id="12510">
    <literal><![CDATA[
      f(x,f(f(y,f(x,x)),f(f(y,f(x,x)),f(y,f(x,x))))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(8397(a,1),11660(a,1,1,1)),rewrite(8397(4),8394(3),8397(12))].">
      <j1 rule="para" parents="8397 11660"/>
      <j2 rule="rewrite" parents="8397 8394 8397"/>
    </justification>
  </clause>

  <clause id="12614">
    <literal><![CDATA[
      f(x,f(f(f(y,x),f(f(y,x),f(y,x))),f(f(y,x),f(f(y,x),f(y,x))))) = f(f(y,x),f(f(y,x),f(y,x)))
    ]]></literal>
    <justification jstring="[para(11710(a,1),82(a,1,1))].">
      <j1 rule="para" parents="11710 82"/>
    </justification>
  </clause>

  <clause id="12618">
    <literal><![CDATA[
      f(f(f(x,y),f(f(x,y),f(x,y))),f(f(f(x,y),f(f(x,y),f(x,y))),f(f(f(y,f(y,y)),f(x,y)),f(f(f(f(x,y),f(x,y)),z),f(f(f(f(y,z),z),f(x,y)),y))))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(11710(a,1),215(a,1,2,2,1,1,1)),rewrite(8888(5),12145(10))].">
      <j1 rule="para" parents="11710 215"/>
      <j2 rule="rewrite" parents="8888 12145"/>
    </justification>
  </clause>

  <clause id="12633">
    <literal><![CDATA[
      f(f(x,y),f(f(x,f(x,x)),f(x,f(x,x)))) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(11713(a,1),82(a,1,1))].">
      <j1 rule="para" parents="11713 82"/>
    </justification>
  </clause>

  <clause id="12712">
    <literal><![CDATA[
      f(x,f(f(x,y),f(f(x,y),f(x,y)))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(12000(a,1),8400(a,1,1,1)),rewrite(12000(7),8394(3),12000(12))].">
      <j1 rule="para" parents="12000 8400"/>
      <j2 rule="rewrite" parents="12000 8394 12000"/>
    </justification>
  </clause>

  <clause id="12715">
    <literal><![CDATA[
      f(f(x,y),f(f(x,y),f(x,y))) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(12000(a,1),9216(a,1,1)),rewrite(12000(7),12633(19),12507(8),12633(18),12712(7),12507(8),8888(2)),flip(a)].">
      <j1 rule="para" parents="12000 9216"/>
      <j2 rule="rewrite" parents="12000 12633 12507 12633 12712 12507 8888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12722">
    <literal><![CDATA[
      f(f(x,f(x,x)),y) = f(y,y)
    ]]></literal>
    <justification jstring="[para(11076(a,1),12000(a,1,1,1)),rewrite(11076(6),11076(7),12715(5))].">
      <j1 rule="para" parents="11076 12000"/>
      <j2 rule="rewrite" parents="11076 11076 12715"/>
    </justification>
  </clause>

  <clause id="12782">
    <literal><![CDATA[
      f(x,f(x,f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(9203),rewrite(12715(5),8397(3),12715(6),8394(4))].">
      <j1 rule="back_rewrite" parents="9203"/>
      <j2 rule="rewrite" parents="12715 8397 12715 8394"/>
    </justification>
  </clause>

  <clause id="12809">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(x,f(x,x)),f(f(f(y,f(y,y)),f(x,y)),f(f(f(f(x,y),f(x,y)),z),f(f(f(f(y,z),z),f(x,y)),y))))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(12618),rewrite(12715(5),12715(7))].">
      <j1 rule="back_rewrite" parents="12618"/>
      <j2 rule="rewrite" parents="12715 12715"/>
    </justification>
  </clause>

  <clause id="12813">
    <literal><![CDATA[
      f(x,f(f(y,f(y,y)),f(y,f(y,y)))) = f(y,f(y,y))
    ]]></literal>
    <justification jstring="[back_rewrite(12614),rewrite(12715(5),12715(7),12715(11))].">
      <j1 rule="back_rewrite" parents="12614"/>
      <j2 rule="rewrite" parents="12715 12715 12715"/>
    </justification>
  </clause>

  <clause id="12833">
    <literal><![CDATA[
      f(x,f(y,f(y,y))) = f(x,x)
    ]]></literal>
    <justification jstring="[back_rewrite(12510),rewrite(12715(8))].">
      <j1 rule="back_rewrite" parents="12510"/>
      <j2 rule="rewrite" parents="12715"/>
    </justification>
  </clause>

  <clause id="12960">
    <literal><![CDATA[
      f(f(x,f(x,y)),x) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(12226),rewrite(12715(5),11076(7))].">
      <j1 rule="back_rewrite" parents="12226"/>
      <j2 rule="rewrite" parents="12715 11076"/>
    </justification>
  </clause>

  <clause id="13010">
    <literal><![CDATA[
      f(f(f(x,y),f(f(y,f(y,y)),f(x,y))),f(f(x,f(x,x)),f(z,f(x,y)))) = f(z,f(x,y))
    ]]></literal>
    <justification jstring="[back_rewrite(12125),rewrite(12715(11))].">
      <j1 rule="back_rewrite"