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

<!DOCTYPE proofs SYSTEM "proof3.dtd">

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

<proofs number_of_proofs="1">

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

<heading><![CDATA[
Prover9 (32) version November-2006, November 2006.
Process 4468 was started by mccune on cleo.thornwood,
Wed Nov 22 12:06:20 2006
The command was "/home/mccune/bin/prover9 -f MOL-M.in MOL-M-interp.outx".
]]></heading>

<proof number="1" length="565" max_count="59">

<comments><![CDATA[
% Proof 1 at 862.65 (+ 1.94) seconds: MOD_SS.
% Length of proof is 565.
% Level of proof is 72.
% Maximum clause weight is 59.
% Given clauses 1965.
]]></comments>

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

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

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

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

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

  <clause id="8">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),z),f(f(f(f(f(y,x),z),z),y),f(f(f(y,y),u),f(f(f(f(f(y,v),u),u),y),f(y,w)))))) = y
    ]]></literal>
    <justification jstring="[para(2(a,1),7(a,1,1,2)),rewrite(2(12),2(12),2(14),2(17),2(30))].">
      <j1 rule="para" parents="2 7"/>
      <j2 rule="rewrite" parents="2 2 2 2 2"/>
    </justification>
  </clause>

  <clause id="9">
    <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(2(a,1),7(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="2 7"/>
    </justification>
  </clause>

  <clause id="12">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),z),y)) = y
    ]]></literal>
    <justification jstring="[para(2(a,1),8(a,1,2,2))].">
      <j1 rule="para" parents="2 8"/>
    </justification>
  </clause>

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

  <clause id="36">
    <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(20(a,1),2(a,1,2,1,1))].">
      <j1 rule="para" parents="20 2"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      f(f(x,y),f(y,f(f(f(f(f(y,x),f(y,y)),f(y,y)),y),f(y,z)))) = y
    ]]></literal>
    <justification jstring="[para(20(a,1),2(a,1,2,1))].">
      <j1 rule="para" parents="20 2"/>
    </justification>
  </clause>

  <clause id="39">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),f(x,x)),f(f(f(x,f(x,x)),y),f(y,z)))) = y
    ]]></literal>
    <justification jstring="[para(20(a,1),2(a,1,2,2,1,1,1))].">
      <j1 rule="para" parents="20 2"/>
    </justification>
  </clause>

  <clause id="44">
    <literal><![CDATA[
      f(f(f(x,x),f(y,x)),f(f(f(f(y,x),f(y,x)),z),f(f(f(f(x,z),z),f(y,x)),x))) = f(y,x)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(20(a,1),7(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="20 7"/>
    </justification>
  </clause>

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

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

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

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

  <clause id="60">
    <literal><![CDATA[
      f(f(f(x,x),y),f(f(f(y,y),x),f(f(f(f(x,x),x),y),f(y,z)))) = y
    ]]></literal>
    <justification jstring="[para(46(a,1),2(a,1,2,2,1,1,1))].">
      <j1 rule="para" parents="46 2"/>
    </justification>
  </clause>

  <clause id="68">
    <literal><![CDATA[
      f(f(x,f(f(x,x),y)),f(f(f(f(f(x,x),y),f(f(x,x),y)),z),f(f(f(f(f(x,x),z),z),f(f(x,x),y)),f(f(f(x,x),y),u)))) = f(f(x,x),y)
    ]]></literal>
    <justification jstring="[para(55(a,1),2(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="55 2"/>
    </justification>
  </clause>

  <clause id="69">
    <literal><![CDATA[
      f(f(x,x),f(f(f(x,x),x),f(f(f(x,x),x),f(x,y)))) = x
    ]]></literal>
    <justification jstring="[para(55(a,1),2(a,1,2,2,1,1))].">
      <j1 rule="para" parents="55 2"/>
    </justification>
  </clause>

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

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

  <clause id="81">
    <literal><![CDATA[
      f(f(x,f(y,z)),f(f(f(f(y,z),f(y,z)),u),f(f(f(f(f(f(y,z),x),u),u),f(y,z)),y))) = f(y,z)
    ]]></literal>
    <justification jstring="[para(77(a,1),2(a,1,2,2,2))].">
      <j1 rule="para" parents="77 2"/>
    </justification>
  </clause>

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

  <clause id="84">
    <literal><![CDATA[
      f(f(x,f(y,z)),f(f(f(f(y,z),f(y,z)),f(f(f(y,z),x),f(f(y,z),x))),f(f(f(f(y,z),x),f(y,z)),z))) = f(y,z)
    ]]></literal>
    <justification jstring="[para(77(a,1),7(a,1,2,2,1,1))].">
      <j1 rule="para" parents="77 7"/>
    </justification>
  </clause>

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

  <clause id="93">
    <literal><![CDATA[
      f(f(x,y),f(f(z,f(y,y)),f(f(f(f(f(y,x),f(f(z,f(y,y)),f(z,f(y,y)))),f(f(z,f(y,y)),f(z,f(y,y)))),y),f(y,u)))) = y
    ]]></literal>
    <justification jstring="[para(82(a,1),2(a,1,2,1))].">
      <j1 rule="para" parents="82 2"/>
    </justification>
  </clause>

  <clause id="94">
    <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(82(a,1),2(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="82 2"/>
    </justification>
  </clause>

  <clause id="96">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),z),f(f(f(f(f(y,x),z),z),y),f(u,y)))) = y
    ]]></literal>
    <justification jstring="[para(82(a,1),2(a,1,2,2,2))].">
      <j1 rule="para" parents="82 2"/>
    </justification>
  </clause>

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

  <clause id="102">
    <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(w,y)))))) = y
    ]]></literal>
    <justification jstring="[para(82(a,1),8(a,1,2,2,2,2,2))].">
      <j1 rule="para" parents="82 8"/>
    </justification>
  </clause>

  <clause id="112">
    <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(44(a,1),46(a,1,1)),flip(a)].">
      <j1 rule="para" parents="44 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="115">
    <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(77(a,1),44(a,1,2,2,1,1))].">
      <j1 rule="para" parents="77 44"/>
    </justification>
  </clause>

  <clause id="136">
    <literal><![CDATA[
      f(f(x,f(f(x,x),f(x,y))),f(x,f(f(x,x),f(x,y)))) = x
    ]]></literal>
    <justification jstring="[para(57(a,1),55(a,1)),flip(a)].">
      <j1 rule="para" parents="57 55"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="139">
    <literal><![CDATA[
      f(f(x,y),f(y,f(f(y,y),f(z,y)))) = y
    ]]></literal>
    <justification jstring="[para(82(a,1),57(a,1,2,2,2))].">
      <j1 rule="para" parents="82 57"/>
    </justification>
  </clause>

  <clause id="156">
    <literal><![CDATA[
      f(x,f(f(x,x),f(x,f(y,f(x,x))))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(20(a,1),139(a,1,1)),rewrite(77(4))].">
      <j1 rule="para" parents="20 139"/>
      <j2 rule="rewrite" parents="77"/>
    </justification>
  </clause>

  <clause id="171">
    <literal><![CDATA[
      f(f(f(x,x),x),f(f(f(f(x,x),x),f(f(x,x),x)),x)) = f(f(f(x,x),x),f(f(x,x),x))
    ]]></literal>
    <justification jstring="[para(44(a,1),156(a,1,2,2,2)),rewrite(112(19),55(24),77(21),55(9),112(18)),flip(a)].">
      <j1 rule="para" parents="44 156"/>
      <j2 rule="rewrite" parents="112 55 77 55 112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="173">
    <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(112),rewrite(171(22))].">
      <j1 rule="back_rewrite" parents="112"/>
      <j2 rule="rewrite" parents="171"/>
    </justification>
  </clause>

  <clause id="188">
    <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(20(a,1),5(a,1,1,1,2,1,1,1))].">
      <j1 rule="para" parents="20 5"/>
    </justification>
  </clause>

  <clause id="190">
    <literal><![CDATA[
      f(x,f(f(x,y),f(f(f(f(x,y),y),f(x,x)),f(f(x,x),z)))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(20(a,1),5(a,1,2,1,1)),rewrite(97(11))].">
      <j1 rule="para" parents="20 5"/>
      <j2 rule="rewrite" parents="97"/>
    </justification>
  </clause>

  <clause id="210">
    <literal><![CDATA[
      f(f(f(f(x,x),x),f(f(f(x,x),x),f(x,y))),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(69(a,1),82(a,1,2,1)),rewrite(69(16),69(18))].">
      <j1 rule="para" parents="69 82"/>
      <j2 rule="rewrite" parents="69 69"/>
    </justification>
  </clause>

  <clause id="211">
    <literal><![CDATA[
      f(f(x,x),f(f(f(x,x),x),f(f(f(x,x),x),f(y,x)))) = x
    ]]></literal>
    <justification jstring="[para(82(a,1),69(a,1,2,2,2))].">
      <j1 rule="para" parents="82 69"/>
    </justification>
  </clause>

  <clause id="219">
    <literal><![CDATA[
      f(x,f(f(x,x),f(x,y))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(136(a,1),20(a,1,1)),rewrite(136(9)),flip(a)].">
      <j1 rule="para" parents="136 20"/>
      <j2 rule="rewrite" parents="136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="230">
    <literal><![CDATA[
      f(f(x,x),f(x,f(f(x,x),y))) = x
    ]]></literal>
    <justification jstring="[para(20(a,1),219(a,1,2,1)),rewrite(77(8))].">
      <j1 rule="para" parents="20 219"/>
      <j2 rule="rewrite" parents="77"/>
    </justification>
  </clause>

  <clause id="233">
    <literal><![CDATA[
      f(x,f(f(x,x),f(y,x))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(82(a,1),219(a,1,2,2))].">
      <j1 rule="para" parents="82 219"/>
    </justification>
  </clause>

  <clause id="244">
    <literal><![CDATA[
      f(f(x,x),f(x,f(y,f(x,x)))) = x
    ]]></literal>
    <justification jstring="[para(82(a,1),230(a,1,2,2))].">
      <j1 rule="para" parents="82 230"/>
    </justification>
  </clause>

  <clause id="261">
    <literal><![CDATA[
      f(f(f(f(x,x),x),f(f(x,x),x)),x) = f(f(x,x),x)
    ]]></literal>
    <justification jstring="[para(44(a,1),244(a,1,2,2)),rewrite(173(13),55(14),77(11)),flip(a)].">
      <j1 rule="para" parents="44 244"/>
      <j2 rule="rewrite" parents="173 55 77"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="275">
    <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(82(a,1),210(a,1,1,2,2))].">
      <j1 rule="para" parents="82 210"/>
    </justification>
  </clause>

  <clause id="292">
    <literal><![CDATA[
      f(x,f(f(x,f(x,x)),f(f(x,f(x,x)),f(y,f(x,x))))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(20(a,1),211(a,1,1)),rewrite(77(3),77(5))].">
      <j1 rule="para" parents="20 211"/>
      <j2 rule="rewrite" parents="77 77"/>
    </justification>
  </clause>

  <clause id="312">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),f(f(x,f(x,x)),f(y,f(x,x)))),x) = f(x,x)
    ]]></literal>
    <justification jstring="[para(20(a,1),275(a,1,1,1,1)),rewrite(77(5),77(11))].">
      <j1 rule="para" parents="20 275"/>
      <j2 rule="rewrite" parents="77 77"/>
    </justification>
  </clause>

  <clause id="399">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),f(x,x)),f(f(f(x,f(x,x)),y),f(z,y)))) = y
    ]]></literal>
    <justification jstring="[para(82(a,1),39(a,1,2,2,2))].">
      <j1 rule="para" parents="82 39"/>
    </justification>
  </clause>

  <clause id="404">
    <literal><![CDATA[
      f(x,f(f(f(x,x),x),f(x,f(f(x,x),y)))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(275(a,1),39(a,1,2,2,1)),rewrite(20(4),77(3),82(6))].">
      <j1 rule="para" parents="275 39"/>
      <j2 rule="rewrite" parents="20 77 82"/>
    </justification>
  </clause>

  <clause id="413">
    <literal><![CDATA[
      f(x,f(f(f(x,x),x),f(x,f(y,f(x,x))))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(82(a,1),404(a,1,2,2,2))].">
      <j1 rule="para" parents="82 404"/>
    </justification>
  </clause>

  <clause id="577">
    <literal><![CDATA[
      f(f(f(f(x,x),y),f(f(f(f(y,y),y),x),f(x,z))),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(60(a,1),82(a,1,2,1)),rewrite(60(19),60(21))].">
      <j1 rule="para" parents="60 82"/>
      <j2 rule="rewrite" parents="60 60"/>
    </justification>
  </clause>

  <clause id="657">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),f(f(y,x),f(y,x))),f(f(f(y,x),y),f(z,y)))) = y
    ]]></literal>
    <justification jstring="[para(77(a,1),96(a,1,2,2,1,1))].">
      <j1 rule="para" parents="77 96"/>
    </justification>
  </clause>

  <clause id="658">
    <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(96(a,1),82(a,1,2,1)),rewrite(96(20),96(22))].">
      <j1 rule="para" parents="96 82"/>
      <j2 rule="rewrite" parents="96 96"/>
    </justification>
  </clause>

  <clause id="661">
    <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(82(a,1),96(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="82 96"/>
    </justification>
  </clause>

  <clause id="665">
    <literal><![CDATA[
      f(f(f(f(x,y),f(x,y)),x),f(f(f(x,x),z),f(f(f(f(f(x,y),z),z),x),f(u,x)))) = x
    ]]></literal>
    <justification jstring="[para(91(a,1),96(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="91 96"/>
    </justification>
  </clause>

  <clause id="668">
    <literal><![CDATA[
      f(x,f(f(x,y),f(f(f(f(x,y),y),f(x,x)),f(z,f(x,x))))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(69(a,1),96(a,1,2,2,1,1,1,1)),rewrite(210(9),77(3))].">
      <j1 rule="para" parents="69 96"/>
      <j2 rule="rewrite" parents="210 77"/>
    </justification>
  </clause>

  <clause id="856">
    <literal><![CDATA[
      f(f(f(f(x,x),y),f(f(f(f(f(z,x),y),y),x),f(u,x))),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(82(a,1),658(a,1,1,2,1,1,1,1))].">
      <j1 rule="para" parents="82 658"/>
    </justification>
  </clause>

  <clause id="967">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(f(x,x),x),f(x,f(f(x,x),y)))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(20(a,1),80(a,1,2,2,1)),rewrite(77(5),82(8))].">
      <j1 rule="para" parents="20 80"/>
      <j2 rule="rewrite" parents="77 82"/>
    </justification>
  </clause>

  <clause id="969">
    <literal><![CDATA[
      f(f(f(x,x),x),f(f(x,f(x,x)),f(f(x,x),f(x,y)))) = x
    ]]></literal>
    <justification jstring="[para(46(a,1),80(a,1,2,2,1)),rewrite(82(9))].">
      <j1 rule="para" parents="46 80"/>
      <j2 rule="rewrite" parents="82"/>
    </justification>
  </clause>

  <clause id="1005">
    <literal><![CDATA[
      f(f(f(x,x),x),f(f(x,f(x,x)),f(f(x,x),f(y,x)))) = x
    ]]></literal>
    <justification jstring="[para(82(a,1),969(a,1,2,2,2))].">
      <j1 rule="para" parents="82 969"/>
    </justification>
  </clause>

  <clause id="1017">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(f(x,x),x),f(x,f(y,f(x,x))))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(20(a,1),1005(a,1,1,1)),rewrite(77(6),77(7))].">
      <j1 rule="para" parents="20 1005"/>
      <j2 rule="rewrite" parents="77 77"/>
    </justification>
  </clause>

  <clause id="1073">
    <literal><![CDATA[
      f(f(f(x,x),x),f(x,f(f(x,x),y))) = x
    ]]></literal>
    <justification jstring="[para(404(a,1),45(a,1,1)),rewrite(967(25),230(21),46(17),77(3)),flip(a)].">
      <j1 rule="para" parents="404 45"/>
      <j2 rule="rewrite" parents="967 230 46 77"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1077">
    <literal><![CDATA[
      f(f(f(x,x),x),f(x,f(y,f(x,x)))) = x
    ]]></literal>
    <justification jstring="[para(413(a,1),45(a,1,1)),rewrite(1017(25),244(21),46(17),77(3)),flip(a)].">
      <j1 rule="para" parents="413 45"/>
      <j2 rule="rewrite" parents="1017 244 46 77"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1085">
    <literal><![CDATA[
      f(f(f(x,x),x),f(f(x,x),f(x,y))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(60(a,1),45(a,1,2,2,1)),rewrite(77(4),77(4),77(8),55(6),77(7),77(11),77(11),77(15),55(13),77(14),77(17),77(17),77(21),55(19),77(20),77(24),77(25),77(27),55(25),77(26),219(26),20(24),55(9),77(4),77(4),77(8),55(6),77(7)),flip(a)].">
      <j1 rule="para" parents="60 45"/>
      <j2 rule="rewrite" parents="77 77 77 55 77 77 77 77 55 77 77 77 77 55 77 77 77 77 55 77 219 20 55 77 77 77 55 77"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1253">
    <literal><![CDATA[
      f(f(f(f(x,x),f(x,y)),f(f(x,x),x)),f(f(f(x,x),x),f(f(f(x,x),f(f(x,x),x)),f(f(f(x,x),x),z)))) = f(f(x,x),x)
    ]]></literal>
    <justification jstring="[para(1085(a,1),80(a,1,2,1,2,1)),rewrite(1085(18),77(14),261(12),1085(14))].">
      <j1 rule="para" parents="1085 80"/>
      <j2 rule="rewrite" parents="1085 77 261 1085"/>
    </justification>
  </clause>

  <clause id="2271">
    <literal><![CDATA[
      f(f(x,f(f(x,x),y)),f(f(f(f(f(x,x),y),f(f(x,x),y)),z),f(f(f(f(f(x,x),z),z),f(f(x,x),y)),f(x,x)))) = f(f(x,x),y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(55(a,1),68(a,1,2,2,2))].">
      <j1 rule="para" parents="55 68"/>
    </justification>
  </clause>

  <clause id="2277">
    <literal><![CDATA[
      f(f(f(x,x),f(x,y)),f(f(f(f(x,y),f(x,y)),z),f(f(f(f(x,z),z),f(x,y)),x))) = f(x,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(20(a,1),2271(a,1,1,2,1)),rewrite(77(6),77(7),77(10),77(12),77(14),77(17))].">
      <j1 rule="para" parents="20 2271"/>
      <j2 rule="rewrite" parents="77 77 77 77 77 77"/>
    </justification>
  </clause>

  <clause id="2285">
    <literal><![CDATA[
      f(f(x,x),f(x,y)) = x
    ]]></literal>
    <justification jstring="[para(1073(a,1),2271(a,1,2,2,1)),rewrite(77(4),219(4),77(5),77(8),77(13),46(11),77(3),77(4)),flip(a)].">
      <j1 rule="para" parents="1073 2271"/>
      <j2 rule="rewrite" parents="77 219 77 77 77 46 77 77"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2286">
    <literal><![CDATA[
      f(f(x,x),f(y,x)) = x
    ]]></literal>
    <justification jstring="[para(1077(a,1),2271(a,1,2,2,1)),rewrite(2285(4),233(4),2285(5),2285(8),2285(13),46(11),2285(3),2285(4)),flip(a)].">
      <j1 rule="para" parents="1077 2271"/>
      <j2 rule="rewrite" parents="2285 233 2285 2285 2285 46 2285 2285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2288">
    <literal><![CDATA[
      f(x,f(f(f(f(x,y),f(x,y)),z),f(f(f(f(x,z),z),f(x,y)),x))) = f(x,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(2277),rewrite(2285(3))].">
      <j1 rule="back_rewrite" parents="2277"/>
      <j2 rule="rewrite" parents="2285"/>
    </justification>
  </clause>

  <clause id="2297">
    <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(1253),rewrite(2285(3),2286(9))].">
      <j1 rule="back_rewrite" parents="1253"/>
      <j2 rule="rewrite" parents="2285 2286"/>
    </justification>
  </clause>

  <clause id="2350">
    <literal><![CDATA[
      f(x,f(f(f(f(y,x),f(y,x)),f(x,x)),f(f(x,f(y,x)),x))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(115),rewrite(2286(3))].">
      <j1 rule="back_rewrite" parents="115"/>
      <j2 rule="rewrite" parents="2286"/>
    </justification>
  </clause>

  <clause id="2353">
    <literal><![CDATA[
      f(x,f(f(f(f(y,x),f(y,x)),z),f(f(f(f(x,z),z),f(y,x)),x))) = f(y,x)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(44),rewrite(2286(3))].">
      <j1 rule="back_rewrite" parents="44"/>
      <j2 rule="rewrite" parents="2286"/>
    </justification>
  </clause>

  <clause id="2359">
    <literal><![CDATA[
      f(f(x,f(y,y)),f(f(y,z),f(f(f(f(f(x,f(y,y)),z),z),f(y,y)),f(x,f(y,y))))) = f(y,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(46(a,1),2288(a,1,2,1,1,1)),rewrite(46(6),2285(5),46(10),46(17))].">
      <j1 rule="para" parents="46 2288"/>
      <j2 rule="rewrite" parents="46 2285 46 46"/>
    </justification>
  </clause>

  <clause id="2364">
    <literal><![CDATA[
      f(f(x,y),f(f(f(x,x),z),f(f(f(f(f(x,y),z),z),x),f(x,y)))) = x
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(77(a,1),2288(a,1,2,1,1,1)),rewrite(77(4),77(9),77(14))].">
      <j1 rule="para" parents="77 2288"/>
      <j2 rule="rewrite" parents="77 77 77"/>
    </justification>
  </clause>

  <clause id="2366">
    <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(77(a,1),2288(a,1,2,2,1,1))].">
      <j1 rule="para" parents="77 2288"/>
    </justification>
  </clause>

  <clause id="2380">
    <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(36(a,1),2288(a,1,2,2,1)),rewrite(77(6),77(17),2285(29),46(27),77(3),77(5)),flip(a)].">
      <j1 rule="para" parents="36 2288"/>
      <j2 rule="rewrite" parents="77 77 2285 46 77 77"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2386">
    <literal><![CDATA[
      f(x,f(f(x,x),y)) = f(x,x)
    ]]></literal>
    <justification jstring="[para(1073(a,1),2288(a,1,2,2,1)),rewrite(20(10)),flip(a)].">
      <j1 rule="para" parents="1073 2288"/>
      <j2 rule="rewrite" parents="20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2387">
    <literal><![CDATA[
      f(x,f(y,f(x,x))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(1077(a,1),2288(a,1,2,2,1)),rewrite(20(10)),flip(a)].">
      <j1 rule="para" parents="1077 2288"/>
      <j2 rule="rewrite" parents="20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2396">
    <literal><![CDATA[
      f(f(x,x),f(f(f(x,x),x),f(x,f(f(f(x,x),x),y)))) = f(f(x,x),x)
    ]]></literal>
    <justification jstring="[back_rewrite(2297),rewrite(2386(3))].">
      <j1 rule="back_rewrite" parents="2297"/>
      <j2 rule="rewrite" parents="2386"/>
    </justification>
  </clause>

  <clause id="2455">
    <literal><![CDATA[
      f(f(x,y),f(f(f(x,x),f(y,y)),f(f(f(y,f(y,y)),x),f(x,y)))) = x
    ]]></literal>
    <justification jstring="[para(20(a,1),2364(a,1,2,2,1,1,1))].">
      <j1 rule="para" parents="20 2364"/>
    </justification>
  </clause>

  <clause id="2482">
    <literal><![CDATA[
      f(f(x,y),f(f(f(x,x),f(f(f(x,x),z),f(f(f(f(f(x,y),z),z),x),f(x,y)))),f(f(f(x,f(f(f(x,x),z),f(f(f(f(f(x,y),z),z),x),f(x,y)))),x),f(x,y)))) = x
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(2364(a,1),2364(a,1,2,2,1,1,1))].">
      <j1 rule="para" parents="2364 2364"/>
    </justification>
  </clause>

  <clause id="2483">
    <literal><![CDATA[
      f(f(x,y),f(y,f(f(f(f(f(y,x),f(y,z)),f(y,z)),y),f(y,u)))) = y
    ]]></literal>
    <justification jstring="[para(2285(a,1),2(a,1,2,1))].">
      <j1 rule="para" parents="2285 2"/>
    </justification>
  </clause>

  <clause id="2484">
    <literal><![CDATA[
      f(f(f(x,y),f(x,y)),y) = f(x,y)
    ]]></literal>
    <justification jstring="[para(2(a,1),2285(a,1,2))].">
      <j1 rule="para" parents="2 2285"/>
    </justification>
  </clause>

  <clause id="2489">
    <literal><![CDATA[
      f(f(f(x,y),f(x,y)),x) = f(x,y)
    ]]></literal>
    <justification jstring="[para(77(a,1),2285(a,1,2))].">
      <j1 rule="para" parents="77 2285"/>
    </justification>
  </clause>

  <clause id="2527">
    <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="[back_rewrite(661),rewrite(2484(4))].">
      <j1 rule="back_rewrite" parents="661"/>
      <j2 rule="rewrite" parents="2484"/>
    </justification>
  </clause>

  <clause id="2530">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),z),f(f(f(f(f(x,y),z),z),y),f(y,u)))) = y
    ]]></literal>
    <justification jstring="[back_rewrite(94),rewrite(2484(4))].">
      <j1 rule="back_rewrite" parents="94"/>
      <j2 rule="rewrite" parents="2484"/>
    </justification>
  </clause>

  <clause id="2573">
    <literal><![CDATA[
      f(f(x,y),f(f(f(x,x),z),f(f(f(f(f(x,y),z),z),x),f(u,x)))) = x
    ]]></literal>
    <justification jstring="[back_rewrite(665),rewrite(2489(4))].">
      <j1 rule="back_rewrite" parents="665"/>
      <j2 rule="rewrite" parents="2489"/>
    </justification>
  </clause>

  <clause id="2598">
    <literal><![CDATA[
      f(x,f(f(y,x),f(f(f(f(x,x),x),f(y,x)),x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(2286(a,1),45(a,1,1)),rewrite(2285(6),2484(4),2285(5))].">
      <j1 rule="para" parents="2286 45"/>
      <j2 rule="rewrite" parents="2285 2484 2285"/>
    </justification>
  </clause>

  <clause id="2642">
    <literal><![CDATA[
      f(x,f(f(f(f(x,f(f(f(x,y),y),f(f(x,y),y))),f(x,f(f(f(x,y),y),f(f(x,y),y)))),y),f(f(f(f(x,y),y),f(f(x,y),y)),x))) = f(x,f(f(f(x,y),y),f(f(x,y),y)))
    ]]></literal>
    <justification jstring="[para(2387(a,1),2288(a,1,2,2,1))].">
      <j1 rule="para" parents="2387 2288"/>
    </justification>
  </clause>

  <clause id="2705">
    <literal><![CDATA[
      f(f(x,x),f(f(f(x,x),y),f(f(f(f(f(x,z),y),y),x),f(x,u)))) = x
    ]]></literal>
    <justification jstring="[para(2(a,1),2484(a,1,1,1)),rewrite(2(11),2(22))].">
      <j1 rule="para" parents="2 2484"/>
      <j2 rule="rewrite" parents="2 2"/>
    </justification>
  </clause>

  <clause id="2720">
    <literal><![CDATA[
      f(f(x,x),f(f(f(x,x),f(y,y)),f(f(f(y,f(y,y)),x),f(x,z)))) = x
    ]]></literal>
    <justification jstring="[para(39(a,1),2484(a,1,1,1)),rewrite(39(11),39(22))].">
      <j1 rule="para" parents="39 2484"/>
      <j2 rule="rewrite" parents="39 39"/>
    </justification>
  </clause>

  <clause id="2727">
    <literal><![CDATA[
      f(f(x,x),f(f(f(x,x),y),f(f(f(f(f(x,z),y),y),x),f(u,x)))) = x
    ]]></literal>
    <justification jstring="[para(96(a,1),2484(a,1,1,1)),rewrite(96(11),96(22))].">
      <j1 rule="para" parents="96 2484"/>
      <j2 rule="rewrite" parents="96 96"/>
    </justification>
  </clause>

  <clause id="2743">
    <literal><![CDATA[
      f(x,f(f(x,y),f(f(f(f(x,y),y),f(x,y)),x))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(2484(a,1),2288(a,1,2,1))].">
      <j1 rule="para" parents="2484 2288"/>
    </justification>
  </clause>

  <clause id="2750">
    <literal><![CDATA[
      f(f(x,y),f(x,f(f(f(x,f(f(f(x,x),z),f(f(f(f(f(x,y),z),z),x),f(x,y)))),x),f(x,y)))) = x
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(2482(a,1),2484(a,2)),rewrite(2705(12),2705(28),2705(44),2484(48))].">
      <j1 rule="para" parents="2482 2484"/>
      <j2 rule="rewrite" parents="2705 2705 2705 2484"/>
    </justification>
  </clause>

  <clause id="2765">
    <literal><![CDATA[
      f(f(f(f(f(x,x),y),f(f(f(f(f(x,z),y),y),x),f(x,u))),f(z,x)),f(f(z,x),f(f(f(f(x,z),z),f(z,x)),f(f(z,x),v)))) = f(z,x)
    ]]></literal>
    <justification jstring="[para(2489(a,1),5(a,1,2,1))].">
      <j1 rule="para" parents="2489 5"/>
    </justification>
  </clause>

  <clause id="2777">
    <literal><![CDATA[
      f(f(x,x),f(f(f(x,x),y),f(f(f(f(f(z,x),y),y),x),f(u,x)))) = x
    ]]></literal>
    <justification jstring="[para(856(a,1),2489(a,1,1,1)),rewrite(856(11),856(22))].">
      <j1 rule="para" parents="856 2489"/>
      <j2 rule="rewrite" parents="856 856"/>
    </justification>
  </clause>

  <clause id="2846">
    <literal><![CDATA[
      f(x,f(f(x,y),f(f(f(f(x,y),f(f(f(f(x,y),f(x,y)),z),f(f(f(f(x,z),z),f(x,y)),x))),f(x,y)),x))) = f(x,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(77(a,1),2750(a,1,1)),rewrite(77(9),77(13),77(18))].">
      <j1 rule="para" parents="77 2750"/>
      <j2 rule="rewrite" parents="77 77 77"/>
    </justification>
  </clause>

  <clause id="2895">
    <literal><![CDATA[
      f(f(f(f(x,y),f(f(f(f(x,y),f(f(f(f(x,y),f(x,y)),z),f(f(f(f(x,z),z),f(x,y)),x))),f(x,y)),x)),x),f(f(f(x,x),u),f(f(f(f(f(x,y),u),u),x),f(x,v)))) = x
    ]]></literal>
    <justification jstring="[para(2846(a,1),2(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="2846 2"/>
    </justification>
  </clause>

  <clause id="3098">
    <literal><![CDATA[
      f(f(f(f(f(f(x,y),f(x,y)),f(y,y)),f(f(y,f(x,y)),y)),y),f(f(f(y,y),f(f(x,y),f(x,y))),f(f(f(x,y),y),f(y,z)))) = y
    ]]></literal>
    <justification jstring="[para(2350(a,1),80(a,1,2,1,2,1)),rewrite(2350(22),2350(25))].">
      <j1 rule="para" parents="2350 80"/>
      <j2 rule="rewrite" parents="2350 2350"/>
    </justification>
  </clause>

  <clause id="3147">
    <literal><![CDATA[
      f(f(f(x,f(f(f(x,f(f(f(x,x),y),f(f(f(f(f(x,z),y),y),x),f(x,z)))),x),f(x,z))),f(x,z)),f(f(f(f(x,z),f(x,z)),u),f(f(f(f(x,u),u),f(x,z)),x))) = f(x,z)
    ]]></literal>
    <justification jstring="[para(2750(a,1),81(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="2750 81"/>
    </justification>
  </clause>

  <clause id="3195">
    <literal><![CDATA[
      f(f(f(x,x),y),f(f(f(f(f(x,f(x,x)),y),y),x),f(x,z))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(20(a,1),2380(a,1,2,1,1,1,1,1)),rewrite(2285(9),2285(10))].">
      <j1 rule="para" parents="20 2380"/>
      <j2 rule="rewrite" parents="2285 2285"/>
    </justification>
  </clause>

  <clause id="3226">
    <literal><![CDATA[
      f(x,f(f(f(f(f(x,f(x,x)),f(x,y)),f(x,y)),x),f(x,z))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(2285(a,1),2380(a,1,1)),rewrite(2285(3),2285(9),2285(10))].">
      <j1 rule="para" parents="2285 2380"/>
      <j2 rule="rewrite" parents="2285 2285 2285"/>
    </justification>
  </clause>

  <clause id="3227">
    <literal><![CDATA[
      f(x,f(f(f(f(f(x,f(x,x)),f(y,x)),f(y,x)),x),f(x,z))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(2286(a,1),2380(a,1,1)),rewrite(2285(3),2285(9),2285(10))].">
      <j1 rule="para" parents="2286 2380"/>
      <j2 rule="rewrite" parents="2285 2285 2285"/>
    </justification>
  </clause>

  <clause id="3377">
    <literal><![CDATA[
      f(f(f(f(f(x,x),f(y,y)),f(f(f(y,f(y,y)),x),f(x,y))),f(x,y)),f(f(f(f(x,y),f(x,y)),z),f(f(f(f(x,z),z),f(x,y)),x))) = f(x,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(2455(a,1),81(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="2455 81"/>
    </justification>
  </clause>

  <clause id="3378">
    <literal><![CDATA[
      f(f(x,f(y,z)),f(f(y,z),f(f(f(f(y,z),f(f(f(f(y,z),f(y,z)),f(x,x)),f(f(f(x,f(x,x)),f(y,z)),f(f(y,z),x)))),f(y,z)),y))) = f(y,z)
    ]]></literal>
    <justification jstring="[para(2455(a,1),81(a,1,2,2,1,1,1)),rewrite(2720(19))].">
      <j1 rule="para" parents="2455 81"/>
      <j2 rule="rewrite" parents="2720"/>
    </justification>
  </clause>

  <clause id="3384">
    <literal><![CDATA[
      f(f(f(x,f(f(f(f(f(x,y),f(x,y)),f(x,y)),x),f(x,y))),f(x,y)),f(f(f(f(x,y),f(x,y)),z),f(f(f(f(x,z),z),f(x,y)),x))) = f(x,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(91(a,1),3377(a,1,1,1,2,2)),rewrite(2285(8),2285(3),2285(10),91(13),91(15),91(16),91(21),91(26))].">
      <j1 rule="para" parents="91 3377"/>
      <j2 rule="rewrite" parents="2285 2285 2285 91 91 91 91 91"/>
    </justification>
  </clause>

  <clause id="3414">
    <literal><![CDATA[
      f(f(x,y),f(f(f(f(y,x),f(y,z)),f(y,z)),y)) = y
    ]]></literal>
    <justification jstring="[para(2387(a,1),2483(a,1,2,2)),rewrite(82(15))].">
      <j1 rule="para" parents="2387 2483"/>
      <j2 rule="rewrite" parents="82"/>
    </justification>
  </clause>

  <clause id="3437">
    <literal><![CDATA[
      f(f(x,f(y,z)),f(f(f(f(f(y,z),x),z),z),f(y,z))) = f(y,z)
    ]]></literal>
    <justification jstring="[para(2(a,1),3414(a,1,2,1,1,2)),rewrite(2(16))].">
      <j1 rule="para" parents="2 3414"/>
      <j2 rule="rewrite" parents="2"/>
    </justification>
  </clause>

  <clause id="3443">
    <literal><![CDATA[
      f(x,f(f(f(x,f(f(y,x),z)),f(f(y,x),z)),f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(20(a,1),3414(a,1,2,1,1,1)),rewrite(2286(3))].">
      <j1 rule="para" parents="20 3414"/>
      <j2 rule="rewrite" parents="2286"/>
    </justification>
  </clause>

  <clause id="3447">
    <literal><![CDATA[
      f(x,f(f(f(x,f(f(x,y),z)),f(f(x,y),z)),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(77(a,1),3414(a,1,2,1,1,1)),rewrite(2285(3))].">
      <j1 rule="para" parents="77 3414"/>
      <j2 rule="rewrite" parents="2285"/>
    </justification>
  </clause>

  <clause id="3448">
    <literal><![CDATA[
      f(f(x,f(y,z)),f(f(f(f(f(y,z),x),y),y),f(y,z))) = f(y,z)
    ]]></literal>
    <justification jstring="[para(77(a,1),3414(a,1,2,1,1,2)),rewrite(77(8))].">
      <j1 rule="para" parents="77 3414"/>
      <j2 rule="rewrite" parents="77"/>
    </justification>
  </clause>

  <clause id="3449">
    <literal><![CDATA[
      f(f(x,y),f(f(f(f(x,y),f(y,z)),f(y,z)),y)) = y
    ]]></literal>
    <justification jstring="[para(82(a,1),3414(a,1,2,1,1,1)),rewrite(2484(4))].">
      <j1 rule="para" parents="82 3414"/>
      <j2 rule="rewrite" parents="2484"/>
    </justification>
  </clause>

  <clause id="3450">
    <literal><![CDATA[
      f(f(x,y),f(f(f(f(y,x),f(z,y)),f(z,y)),y)) = y
    ]]></literal>
    <justification jstring="[para(82(a,1),3414(a,1,2,1,1,2)),rewrite(82(8))].">
      <j1 rule="para" parents="82 3414"/>
      <j2 rule="rewrite" parents="82"/>
    </justification>
  </clause>

  <clause id="3451">
    <literal><![CDATA[
      f(f(x,y),f(f(f(f(x,y),f(x,z)),f(x,z)),x)) = x
    ]]></literal>
    <justification jstring="[para(91(a,1),3414(a,1,2,1,1,1)),rewrite(2489(4))].">
      <j1 rule="para" parents="91 3414"/>
      <j2 rule="rewrite" parents="2489"/>
    </justification>
  </clause>

  <clause id="3454">
    <literal><![CDATA[
      f(f(f(f(x,f(x,x)),f(x,y)),f(x,y)),x) = f(x,x)
    ]]></literal>
    <justification jstring="[para(3414(a,1),60(a,1,2,2,1)),rewrite(2286(9),2484(16),3226(18)),flip(a)].">
      <j1 rule="para" parents="3414 60"/>
      <j2 rule="rewrite" parents="2286 2484 3226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3482">
    <literal><![CDATA[
      f(x,f(f(f(x,x),x),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(2359(a,1),3414(a,1,2,1,1)),rewrite(2285(3),77(5),77(9),46(7),77(4))].">
      <j1 rule="para" parents="2359 3414"/>
      <j2 rule="rewrite" parents="2285 77 77 46 77"/>
    </justification>
  </clause>

  <clause id="3486">
    <literal><![CDATA[
      f(f(x,y),f(f(y,f(y,f(f(f(y,f(f(f(y,y),z),f(f(f(f(f(y,x),z),z),y),f(y,x)))),y),f(y,x)))),y)) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(2750(a,1),3414(a,1,2,1,1))].">
      <j1 rule="para" parents="2750 3414"/>
    </justification>
  </clause>

  <clause id="3523">
    <literal><![CDATA[
      f(x,f(f(f(x,x),x),f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(82(a,1),3482(a,1,2,2)),rewrite(82(9))].">
      <j1 rule="para" parents="82 3482"/>
      <j2 rule="rewrite" parents="82"/>
    </justification>
  </clause>

  <clause id="3566">
    <literal><![CDATA[
      f(f(x,x),f(f(f(x,x),x),f(x,y))) = f(f(x,x),x)
    ]]></literal>
    <justification jstring="[para(3482(a,1),2396(a,1,2,2))].">
      <j1 rule="para" parents="3482 2396"/>
    </justification>
  </clause>

  <clause id="3576">
    <literal><![CDATA[
      f(f(x,x),f(f(x,f(x,x)),f(y,f(x,x)))) = f(y,f(x,x))
    ]]></literal>
    <justification jstring="[para(20(a,1),3523(a,1,2,1,1))].">
      <j1 rule="para" parents="20 3523"/>
    </justification>
  </clause>

  <clause id="3750">
    <literal><![CDATA[
      f(f(x,f(y,z)),f(f(f(f(x,f(y,z)),y),y),f(y,z))) = f(y,z)
    ]]></literal>
    <justification jstring="[para(77(a,1),3449(a,1,2,1,1,2)),rewrite(77(8))].">
      <j1 rule="para" parents="77 3449"/>
      <j2 rule="rewrite" parents="77"/>
    </justification>
  </clause>

  <clause id="3751">
    <literal><![CDATA[
      f(f(x,y),f(f(f(f(x,y),f(z,y)),f(z,y)),y)) = y
    ]]></literal>
    <justification jstring="[para(82(a,1),3449(a,1,2,1,1,2)),rewrite(82(8))].">
      <j1 rule="para" parents="82 3449"/>
      <j2 rule="rewrite" parents="82"/>
    </justification>
  </clause>

  <clause id="3791">
    <literal><![CDATA[
      f(x,f(f(f(x,f(y,f(z,x))),f(y,f(z,x))),f(z,x))) = f(z,x)
    ]]></literal>
    <justification jstring="[para(20(a,1),3450(a,1,2,1,1,1)),rewrite(2286(3))].">
      <j1 rule="para" parents="20 3450"/>
      <j2 rule="rewrite" parents="2286"/>
    </justification>
  </clause>

  <clause id="3793">
    <literal><![CDATA[
      f(x,f(f(f(x,f(y,f(x,z))),f(y,f(x,z))),f(x,z))) = f(x,z)
    ]]></literal>
    <justification jstring="[para(77(a,1),3450(a,1,2,1,1,1)),rewrite(2285(3))].">
      <j1 rule="para" parents="77 3450"/>
      <j2 rule="rewrite" parents="2285"/>
    </justification>
  </clause>

  <clause id="3794">
    <literal><![CDATA[
      f(f(x,y),f(f(f(f(x,y),f(z,x)),f(z,x)),x)) = x
    ]]></literal>
    <justification jstring="[para(91(a,1),3450(a,1,2,1,1,1)),rewrite(2489(4))].">
      <j1 rule="para" parents="91 3450"/>
      <j2 rule="rewrite" parents="2489"/>
    </justification>
  </clause>

  <clause id="3797">
    <literal><![CDATA[
      f(f(f(f(x,f(x,x)),f(y,x)),f(y,x)),x) = f(x,x)
    ]]></literal>
    <justification jstring="[para(3450(a,1),60(a,1,2,2,1)),rewrite(2286(9),2484(16),3227(18)),flip(a)].">
      <j1 rule="para" parents="3450 60"/>
      <j2 rule="rewrite" parents="2286 2484 3227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3863">
    <literal><![CDATA[
      f(f(f(x,y),z),f(f(f(f(f(x,y),z),y),y),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(2(a,1),3451(a,1,2,1,1,2)),rewrite(2(16))].">
      <j1 rule="para" parents="2 3451"/>
      <j2 rule="rewrite" parents="2"/>
    </justification>
  </clause>

  <clause id="3906">
    <literal><![CDATA[
      f(x,f(f(f(x,f(x,x)),f(x,y)),f(x,y))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(3454(a,1),2489(a,1,1,1)),rewrite(3454(8),2285(3),3454(14))].">
      <j1 rule="para" parents="3454 2489"/>
      <j2 rule="rewrite" parents="3454 2285 3454"/>
    </justification>
  </clause>

  <clause id="3990">
    <literal><![CDATA[
      f(f(f(x,y),f(x,y)),f(f(f(f(x,y),f(x,y)),f(x,y)),y)) = f(f(f(x,y),f(x,y)),f(x,y))
    ]]></literal>
    <justification jstring="[para(2(a,1),3566(a,1,2,2))].">
      <j1 rule="para" parents="2 3566"/>
    </justification>
  </clause>

  <clause id="3996">
    <literal><![CDATA[
      f(x,f(f(x,f(x,x)),f(f(x,x),y))) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(20(a,1),3566(a,1,1)),rewrite(2285(3),2285(9))].">
      <j1 rule="para" parents="20 3566"/>
      <j2 rule="rewrite" parents="2285 2285"/>
    </justification>
  </clause>

  <clause id="3999">
    <literal><![CDATA[
      f(f(x,x),f(f(f(x,x),x),f(y,x))) = f(f(x,x),x)
    ]]></literal>
    <justification jstring="[para(82(a,1),3566(a,1,2,2))].">
      <j1 rule="para" parents="82 3566"/>
    </justification>
  </clause>

  <clause id="4218">
    <literal><![CDATA[
      f(x,f(f(f(x,f(x,x)),f(y,x)),f(y,x))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(3797(a,1),2489(a,1,1,1)),rewrite(3797(8),2285(3),3797(14))].">
      <j1 rule="para" parents="3797 2489"/>
      <j2 rule="rewrite" parents="3797 2285 3797"/>
    </justification>
  </clause>

  <clause id="4239">
    <literal><![CDATA[
      f(x,f(f(x,f(x,x)),f(y,f(x,x)))) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(82(a,1),3996(a,1,2,2))].">
      <j1 rule="para" parents="82 3996"/>
    </justification>
  </clause>

  <clause id="4283">
    <literal><![CDATA[
      f(f(x,x),f(f(f(f(y,f(x,x)),f(y,f(x,x))),f(f(f(x,x),x),f(z,x))),f(f(f(f(f(x,x),x),f(f(f(x,x),x),f(z,x))),f(y,f(x,x))),f(x,x)))) = f(y,f(x,x))
    ]]></literal>
    <justification jstring="[para(3999(a,1),2353(a,1,2,2,1,1,1))].">
      <j1 rule="para" parents="3999 2353"/>
    </justification>
  </clause>

  <clause id="4399">
    <literal><![CDATA[
      f(x,f(f(x,f(x,x)),f(f(f(f(x,f(x,x)),f(f(x,f(x,x)),f(y,f(x,x)))),f(x,f(x,x))),x))) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(4239(a,1),2743(a,1,2,1)),rewrite(4239(8),4239(16),4239(22))].">
      <j1 rule="para" parents="4239 2743"/>
      <j2 rule="rewrite" parents="4239 4239 4239"/>
    </justification>
  </clause>

  <clause id="4566">
    <literal><![CDATA[
      f(x,f(f(f(x,y),y),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(77(a,1),3437(a,1,2,1,1,1)),rewrite(2285(3))].">
      <j1 rule="para" parents="77 3437"/>
      <j2 rule="rewrite" parents="2285"/>
    </justification>
  </clause>

  <clause id="4841">
    <literal><![CDATA[
      f(f(x,x),f(f(f(f(x,x),x),f(f(f(x,x),x),f(y,x))),f(f(x,x),x))) = f(f(x,x),x)
    ]]></literal>
    <justification jstring="[para(3999(a,1),4566(a,1,2,1,1)),rewrite(3999(14),3999(18))].">
      <j1 rule="para" parents="3999 4566"/>
      <j2 rule="rewrite" parents="3999 3999"/>
    </justification>
  </clause>

  <clause id="4854">
    <literal><![CDATA[
      f(x,f(f(f(x,y),f(f(f(x,y),y),f(x,y))),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(4566(a,1),4566(a,1,2,1,1)),rewrite(4566(11),4566(14))].">
      <j1 rule="para" parents="4566 4566"/>
      <j2 rule="rewrite" parents="4566 4566"/>
    </justification>
  </clause>

  <clause id="4863">
    <literal><![CDATA[
      f(x,f(f(f(x,y),y),f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(77(a,1),3443(a,1,2,1,1,2)),rewrite(77(4))].">
      <j1 rule="para" parents="77 3443"/>
      <j2 rule="rewrite" parents="77"/>
    </justification>
  </clause>

  <clause id="4935">
    <literal><![CDATA[
      f(f(x,x),x) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(55(a,1),4863(a,1,2,1)),rewrite(2285(5))].">
      <j1 rule="para" parents="55 4863"/>
      <j2 rule="rewrite" parents="2285"/>
    </justification>
  </clause>

  <clause id="4936">
    <literal><![CDATA[
      f(f(x,x),f(f(x,f(x,x)),f(f(x,f(x,x)),f(y,x)))) = x
    ]]></literal>
    <justification jstring="[para(4863(a,1),69(a,1,2,2,2)),rewrite(4935(3),4935(5))].">
      <j1 rule="para" parents="4863 69"/>
      <j2 rule="rewrite" parents="4935 4935"/>
    </justification>
  </clause>

  <clause id="4938">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),f(f(x,f(x,x)),f(y,x))),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(4863(a,1),210(a,1,1,2,2)),rewrite(4935(2),4935(4))].">
      <j1 rule="para" parents="4863 210"/>
      <j2 rule="rewrite" parents="4935 4935"/>
    </justification>
  </clause>

  <clause id="4944">
    <literal><![CDATA[
      f(f(f(f(x,x),y),f(f(f(y,f(y,y)),x),f(z,x))),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(4863(a,1),577(a,1,1,2,2)),rewrite(4935(4))].">
      <j1 rule="para" parents="4863 577"/>
      <j2 rule="rewrite" parents="4935"/>
    </justification>
  </clause>

  <clause id="4945">
    <literal><![CDATA[
      f(f(f(f(x,x),y),f(f(f(y,f(y,y)),x),f(x,z))),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(577(a,1),4863(a,1,2,2)),rewrite(4935(6),4935(15),2286(22),4935(4)),flip(a)].">
      <j1 rule="para" parents="577 4863"/>
      <j2 rule="rewrite" parents="4935 4935 2286 4935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5002">
    <literal><![CDATA[
      f(x,f(f(y,x),f(f(f(x,f(x,x)),f(y,x)),x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(2598(a,1),4863(a,1,2,2)),rewrite(4935(3),4935(10),3863(19),4935(4)),flip(a)].">
      <j1 rule="para" parents="2598 4863"/>
      <j2 rule="rewrite" parents="4935 4935 3863 4935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5028">
    <literal><![CDATA[
      f(x,f(f(x,f(x,x)),f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(4863(a,1),3482(a,1,2,2)),rewrite(4935(2),4863(10))].">
      <j1 rule="para" parents="4863 3482"/>
      <j2 rule="rewrite" parents="4935 4863"/>
    </justification>
  </clause>

  <clause id="5030">
    <literal><![CDATA[
      f(x,f(f(x,f(x,x)),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(3482(a,1),4863(a,1,2,2)),rewrite(4935(2),4935(6),3750(13),4935(3)),flip(a)].">
      <j1 rule="para" parents="3482 4863"/>
      <j2 rule="rewrite" parents="4935 4935 3750 4935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5043">
    <literal><![CDATA[
      f(f(x,x),f(f(x,f(x,x)),f(y,x))) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(4863(a,1),3566(a,1,2,2)),rewrite(4935(3),4935(8))].">
      <j1 rule="para" parents="4863 3566"/>
      <j2 rule="rewrite" parents="4935 4935"/>
    </justification>
  </clause>

  <clause id="5045">
    <literal><![CDATA[
      f(f(x,x),f(f(x,f(x,x)),f(x,y))) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(3566(a,1),4863(a,1,2,2)),rewrite(4935(2),4935(6),4935(14),3863(16),4935(5)),flip(a)].">
      <j1 rule="para" parents="3566 4863"/>
      <j2 rule="rewrite" parents="4935 4935 4935 3863 4935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5053">
    <literal><![CDATA[
      f(f(f(x,f(f(f(f(x,y),f(f(x,y),f(x,y))),x),f(x,y))),f(x,y)),f(f(f(f(x,y),f(x,y)),z),f(f(f(f(x,z),z),f(x,y)),x))) = f(x,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(3384(a,1),4863(a,2)),rewrite(4935(25),4935(37),4935(49),4863(68))].">
      <j1 rule="para" parents="3384 4863"/>
      <j2 rule="rewrite" parents="4935 4935 4935 4863"/>
    </justification>
  </clause>

  <clause id="5065">
    <literal><![CDATA[
      f(x,f(f(f(y,x),f(f(f(x,y),y),f(y,x))),f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(4863(a,1),4566(a,1,2,1,1)),rewrite(4863(11),4863(14))].">
      <j1 rule="para" parents="4863 4566"/>
      <j2 rule="rewrite" parents="4863 4863"/>
    </justification>
  </clause>

  <clause id="5086">
    <literal><![CDATA[
      f(f(x,x),f(f(f(x,f(x,x)),f(f(x,f(x,x)),f(y,x))),f(x,f(x,x)))) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[back_rewrite(4841),rewrite(4935(3),4935(5),4935(10),4935(14))].">
      <j1 rule="back_rewrite" parents="4841"/>
      <j2 rule="rewrite" parents="4935 4935 4935 4935"/>
    </justification>
  </clause>

  <clause id="5260">
    <literal><![CDATA[
      f(f(x,x),f(f(f(f(y,f(x,x)),f(y,f(x,x))),f(f(x,f(x,x)),f(z,x))),f(f(f(f(x,f(x,x)),f(f(x,f(x,x)),f(z,x))),f(y,f(x,x))),f(x,x)))) = f(y,f(x,x))
    ]]></literal>
    <justification jstring="[back_rewrite(4283),rewrite(4935(8),4935(13),4935(15))].">
      <j1 rule="back_rewrite" parents="4283"/>
      <j2 rule="rewrite" parents="4935 4935 4935"/>
    </justification>
  </clause>

  <clause id="5371">
    <literal><![CDATA[
      f(f(f(x,y),f(x,y)),f(f(f(x,y),f(f(x,y),f(x,y))),y)) = f(f(x,y),f(f(x,y),f(x,y)))
    ]]></literal>
    <justification jstring="[back_rewrite(3990),rewrite(4935(8),4935(15))].">
      <j1 rule="back_rewrite" parents="3990"/>
      <j2 rule="rewrite" parents="4935 4935"/>
    </justification>
  </clause>

  <clause id="5957">
    <literal><![CDATA[
      f(f(f(f(x,f(x,x)),f(f(x,f(x,x)),f(y,f(x,x)))),f(x,f(x,x))),x) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[back_rewrite(4399),rewrite(5028(16))].">
      <j1 rule="back_rewrite" parents="4399"/>
      <j2 rule="rewrite" parents="5028"/>
    </justification>
  </clause>

  <clause id="5972">
    <literal><![CDATA[
      f(f(f(x,f(f(f(f(x,y),f(f(x,y),f(x,y))),x),f(x,z))),f(y,x)),f(f(f(f(y,x),f(y,x)),u),f(f(f(f(x,u),u),f(y,x)),x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(4935(a,1),9(a,1,1,1,2,1,1)),rewrite(2285(3))].">
      <j1 rule="para" parents="4935 9"/>
      <j2 rule="rewrite" parents="2285"/>
    </justification>
  </clause>

  <clause id="6008">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,x),f(f(y,x),f(y,x))),y)) = y
    ]]></literal>
    <justification jstring="[para(4935(a,1),3414(a,1,2,1))].">
      <j1 rule="para" parents="4935 3414"/>
    </justification>
  </clause>

  <clause id="6577">
    <literal><![CDATA[
      f(f(x,x),f(f(x,f(x,x)),f(f(x,f(x,x)),f(f(x,f(x,x)),f(y,f(x,x)))))) = f(f(x,f(x,x)),f(f(x,f(x,x)),f(y,f(x,x))))
    ]]></literal>
    <justification jstring="[para(292(a,1),6008(a,1,1)),rewrite(312(10),312(11),312(12),2285(5),4935(3))].">
      <j1 rule="para" parents="292 6008"/>
      <j2 rule="rewrite" parents="312 312 312 2285 4935"/>
    </justification>
  </clause>

  <clause id="6771">
    <literal><![CDATA[
      f(x,f(f(x,f(x,x)),f(f(x,f(x,x)),f(f(x,f(x,x)),f(y,x))))) = f(f(x,f(x,x)),f(f(x,f(x,x)),f(y,x)))
    ]]></literal>
    <justification jstring="[para(4936(a,1),6008(a,1,1)),rewrite(4938(9),4938(9),4938(9))].">
      <j1 rule="para" parents="4936 6008"/>
      <j2 rule="rewrite" parents="4938 4938 4938"/>
    </justification>
  </clause>

  <clause id="7560">
    <literal><![CDATA[
      f(x,f(f(f(x,x),f(f(f(x,f(x,x)),f(y,x)),f(y,x))),f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(4218(a,1),3791(a,1,2,1,1))].">
      <j1 rule="para" parents="4218 3791"/>
    </justification>
  </clause>

  <clause id="7663">
    <literal><![CDATA[
      f(x,f(f(f(x,x),f(f(f(x,f(x,x)),f(x,y)),f(x,y))),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(3906(a,1),3793(a,1,2,1,1))].">
      <j1 rule="para" parents="3906 3793"/>
    </justification>
  </clause>

  <clause id="7685">
    <literal><![CDATA[
      f(f(x,y),f(f(f(f(x,y),f(f(f(x,x),f(z,z)),f(f(f(z,f(z,z)),x),f(u,x)))),f(f(f(x,x),f(z,z)),f(f(f(z,f(z,z)),x),f(u,x)))),x)) = x
    ]]></literal>
    <justification jstring="[para(399(a,1),3863(a,1,1,1)),rewrite(399(12),399(33),399(35))].">
      <j1 rule="para" parents="399 3863"/>
      <j2 rule="rewrite" parents="399 399 399"/>
    </justification>
  </clause>

  <clause id="8550">
    <literal><![CDATA[
      f(f(f(x,x),y),f(f(x,f(x,x)),f(f(f(x,x),y),f(f(f(y,f(y,y)),x),f(z,x))))) = f(f(f(x,x),y),f(f(f(y,f(y,y)),x),f(z,x)))
    ]]></literal>
    <justification jstring="[para(4944(a,1),3447(a,1,2,1,1,2)),rewrite(55(5),4944(13),4935(4))].">
      <j1 rule="para" parents="4944 3447"/>
      <j2 rule="rewrite" parents="55 4944 4935"/>
    </justification>
  </clause>

  <clause id="8558">
    <literal><![CDATA[
      f(f(f(x,x),y),f(f(x,f(x,x)),f(f(f(x,x),y),f(f(f(y,f(y,y)),x),f(x,z))))) = f(f(f(x,x),y),f(f(f(y,f(y,y)),x),f(x,z)))
    ]]></literal>
    <justification jstring="[para(4945(a,1),3447(a,1,2,1,1,2)),rewrite(55(5),4945(13),4935(4))].">
      <j1 rule="para" parents="4945 3447"/>
      <j2 rule="rewrite" parents="55 4945 4935"/>
    </justification>
  </clause>

  <clause id="9519">
    <literal><![CDATA[
      f(f(f(f(x,f(x,x)),f(x,y)),f(x,y)),f(f(x,y),f(f(f(x,f(x,x)),f(x,y)),f(f(x,y),z)))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(3454(a,1),2530(a,1,2,2,1,1,1)),rewrite(2489(10),4935(9))].">
      <j1 rule="para" parents="3454 2530"/>
      <j2 rule="rewrite" parents="2489 4935"/>
    </justification>
  </clause>

  <clause id="9649">
    <literal><![CDATA[
      f(f(f(f(f(x,x),y),f(f(f(f(f(x,z),y),y),x),f(u,x))),f(x,z)),f(f(f(f(x,z),f(x,z)),f(x,x)),f(f(x,f(x,z)),z))) = f(x,z)
    ]]></literal>
    <justification jstring="[para(2573(a,1),84(a,1,2,1,2,1)),rewrite(2573(25),2573(27))].">
      <j1 rule="para" parents="2573 84"/>
      <j2 rule="rewrite" parents="2573 2573"/>
    </justification>
  </clause>

  <clause id="10614">
    <literal><![CDATA[
      f(f(f(f(f(f(x,f(x,x)),y),y),x),f(x,z)),x) = f(x,x)
    ]]></literal>
    <justification jstring="[para(3195(a,1),82(a,1,2,1)),rewrite(3195(18),2285(10),3195(18))].">
      <j1 rule="para" parents="3195 82"/>
      <j2 rule="rewrite" parents="3195 2285 3195"/>
    </justification>
  </clause>

  <clause id="10677">
    <literal><![CDATA[
      f(f(f(f(x,f(x,x)),y),y),x) = f(x,x)
    ]]></literal>
    <justification jstring="[para(2387(a,1),10614(a,1,1)),rewrite(2484(12))].">
      <j1 rule="para" parents="2387 10614"/>
      <j2 rule="rewrite" parents="2484"/>
    </justification>
  </clause>

  <clause id="10706">
    <literal><![CDATA[
      f(f(f(f(x,f(x,x)),y),y),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(20(a,1),10677(a,1,1,1,1,2)),rewrite(4935(2),2285(9))].">
      <j1 rule="para" parents="20 10677"/>
      <j2 rule="rewrite" parents="4935 2285"/>
    </justification>
  </clause>

  <clause id="10806">
    <literal><![CDATA[
      f(f(x,x),f(f(f(x,f(x,x)),y),y)) = x
    ]]></literal>
    <justification jstring="[para(10706(a,1),2489(a,1,1,1)),rewrite(10706(6),10706(12))].">
      <j1 rule="para" parents="10706 2489"/>
      <j2 rule="rewrite" parents="10706 10706"/>
    </justification>
  </clause>

  <clause id="10821">
    <literal><![CDATA[
      f(x,f(f(f(x,y),y),f(f(f(x,f(x,x)),y),y))) = f(f(f(x,f(x,x)),y),y)
    ]]></literal>
    <justification jstring="[para(10706(a,1),3437(a,1,2,1,1,1)),rewrite(10806(6))].">
      <j1 rule="para" parents="10706 3437"/>
      <j2 rule="rewrite" parents="10806"/>
    </justification>
  </clause>

  <clause id="10878">
    <literal><![CDATA[
      f(x,f(x,f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(7663),rewrite(10806(8))].">
      <j1 rule="back_rewrite" parents="7663"/>
      <j2 rule="rewrite" parents="10806"/>
    </justification>
  </clause>

  <clause id="10879">
    <literal><![CDATA[
      f(x,f(x,f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(7560),rewrite(10806(8))].">
      <j1 rule="back_rewrite" parents="7560"/>
      <j2 rule="rewrite" parents="10806"/>
    </justification>
  </clause>

  <clause id="10889">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(x,f(x,x)),f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(6771),rewrite(10878(10),5028(5)),flip(a)].">
      <j1 rule="back_rewrite" parents="6771"/>
      <j2 rule="rewrite" parents="10878 5028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10890">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(x,f(x,x)),f(y,f(x,x)))) = f(y,f(x,x))
    ]]></literal>
    <justification jstring="[back_rewrite(6577),rewrite(10878(12),3576(7)),flip(a)].">
      <j1 rule="back_rewrite" parents="6577"/>
      <j2 rule="rewrite" parents="10878 3576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10942">
    <literal><![CDATA[
      f(f(x,x),f(f(f(f(y,f(x,x)),f(y,f(x,x))),f(f(x,f(x,x)),f(z,x))),f(f(f(z,x),f(y,f(x,x))),f(x,x)))) = f(y,f(x,x))
    ]]></literal>
    <justification jstring="[back_rewrite(5260),rewrite(10889(18))].">
      <j1 rule="back_rewrite" parents="5260"/>
      <j2 rule="rewrite" parents="10889"/>
    </justification>
  </clause>

  <clause id="10947">
    <literal><![CDATA[
      f(f(x,x),f(f(y,x),f(x,f(x,x)))) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[back_rewrite(5086),rewrite(10889(8))].">
      <j1 rule="back_rewrite" parents="5086"/>
      <j2 rule="rewrite" parents="10889"/>
    </justification>
  </clause>

  <clause id="10956">
    <literal><![CDATA[
      f(f(f(x,f(y,y)),f(y,f(y,y))),y) = f(y,f(y,y))
    ]]></literal>
    <justification jstring="[back_rewrite(5957),rewrite(10890(8))].">
      <j1 rule="back_rewrite" parents="5957"/>
      <j2 rule="rewrite" parents="10890"/>
    </justification>
  </clause>

  <clause id="11022">
    <literal><![CDATA[
      f(f(x,y),f(f(x,y),y)) = y
    ]]></literal>
    <justification jstring="[para(2(a,1),10878(a,1,2,2)),rewrite(2(15))].">
      <j1 rule="para" parents="2 10878"/>
      <j2 rule="rewrite" parents="2"/>
    </justification>
  </clause>

  <clause id="11032">
    <literal><![CDATA[
      f(f(x,y),f(f(x,y),x)) = x
    ]]></literal>
    <justification jstring="[para(77(a,1),10878(a,1,2,2)),rewrite(77(7))].">
      <j1 rule="para" parents="77 10878"/>
      <j2 rule="rewrite" parents="77"/>
    </justification>
  </clause>

  <clause id="11051">
    <literal><![CDATA[
      f(x,f(f(x,y),f(f(f(f(x,y),f(x,f(x,y))),f(x,x)),f(z,f(x,x))))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(10878(a,1),668(a,1,2,1)),rewrite(10878(4))].">
      <j1 rule="para" parents="10878 668"/>
      <j2 rule="rewrite" parents="10878"/>
    </justification>
  </clause>

  <clause id="11072">
    <literal><![CDATA[
      f(f(x,y),f(f(f(f(x,f(x,y)),f(x,f(x,y))),f(f(f(x,f(x,y)),x),f(f(x,f(x,y)),x))),f(f(f(f(x,f(x,y)),x),f(x,f(x,y))),f(z,f(x,f(x,y)))))) = f(x,f(x,y))
    ]]></literal>
    <justification jstring="[para(10878(a,1),657(a,1,1))].">
      <j1 rule="para" parents="10878 657"/>
    </justification>
  </clause>

  <clause id="11092">
    <literal><![CDATA[
      f(x,f(f(f(f(x,f(x,y)),f(x,f(x,y))),f(x,x)),f(f(x,y),x))) = f(x,f(x,y))
    ]]></literal>
    <justification jstring="[para(10878(a,1),2366(a,1,2,2,1))].">
      <j1 rule="para" parents="10878 2366"/>
    </justification>
  </clause>

  <clause id="11284">
    <literal><![CDATA[
      f(f(x,y),f(f(f(f(y,f(x,y)),f(y,f(x,y))),f(f(f(y,f(x,y)),y),f(f(y,f(x,y)),y))),f(f(f(f(y,f(x,y)),y),f(y,f(x,y))),f(z,f(y,f(x,y)))))) = f(y,f(x,y))
    ]]></literal>
    <justification jstring="[para(10879(a,1),657(a,1,1))].">
      <j1 rule="para" parents="10879 657"/>
    </justification>
  </clause>

  <clause id="11300">
    <literal><![CDATA[
      f(f(f(f(f(x,y),f(x,y)),z),f(f(f(f(f(f(x,y),u),z),z),f(x,y)),x)),f(f(f(f(f(x,y),f(x,y)),z),f(f(f(f(f(f(x,y),u),z),z),f(x,y)),x)),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(81(a,1),10879(a,1,2,2)),rewrite(81(42))].">
      <j1 rule="para" parents="81 10879"/>
      <j2 rule="rewrite" parents="81"/>
    </justification>
  </clause>

  <clause id="11301">
    <literal><![CDATA[
      f(x,f(f(f(f(x,f(y,x)),f(x,f(y,x))),f(x,x)),f(f(y,x),x))) = f(x,f(y,x))
    ]]></literal>
    <justification jstring="[para(10879(a,1),2366(a,1,2,2,1))].">
      <j1 rule="para" parents="10879 2366"/>
    </justification>
  </clause>

  <clause id="11449">
    <literal><![CDATA[
      f(x,f(x,f(f(f(x,x),y),f(f(f(f(f(x,z),y),y),x),f(x,u))))) = f(f(f(x,x),y),f(f(f(f(f(x,z),y),y),x),f(x,u)))
    ]]></literal>
    <justification jstring="[para(2(a,1),11022(a,1,1)),rewrite(2(11))].">
      <j1 rule="para" parents="2 11022"/>
      <j2 rule="rewrite" parents="2"/>
    </justification>
  </clause>

  <clause id="11490">
    <literal><![CDATA[
      f(f(x,y),f(f(x,y),f(f(f(f(x,y),f(x,y)),z),f(f(f(f(x,z),z),f(x,y)),x)))) = f(f(f(f(x,y),f(x,y)),z),f(f(f(f(x,z),z),f(x,y)),x))
    ]]></literal>
    <justification jstring="[para(2288(a,1),11022(a,1,1)),rewrite(2288(12))].">
      <j1 rule="para" parents="2288 11022"/>
      <j2 rule="rewrite" parents="2288"/>
    </justification>
  </clause>

  <clause id="11499">
    <literal><![CDATA[
      f(f(x,y),f(f(x,y),f(f(f(f(x,y),f(x,y)),z),f(f(f(f(f(f(x,y),u),z),z),f(x,y)),x)))) = f(f(f(f(x,y),f(x,y)),z),f(f(f(f(f(f(x,y),u),z),z),f(x,y)),x))
    ]]></literal>
    <justification jstring="[para(81(a,1),11022(a,1,1)),rewrite(81(16))].">
      <j1 rule="para" parents="81 11022"/>
      <j2 rule="rewrite" parents="81"/>
    </justification>
  </clause>

  <clause id="11515">
    <literal><![CDATA[
      f(f(x,y),f(f(y,f(f(x,y),y)),y)) = y
    ]]></literal>
    <justification jstring="[para(11022(a,1),3751(a,1,2,1,1))].">
      <j1 rule="para" parents="11022 3751"/>
    </justification>
  </clause>

  <clause id="11661">
    <literal><![CDATA[
      f(f(x,y),f(f(y,f(f(y,x),y)),y)) = y
    ]]></literal>
    <justification jstring="[para(11032(a,1),3450(a,1,2,1,1))].">
      <j1 rule="para" parents="11032 3450"/>
    </justification>
  </clause>

  <clause id="11665">
    <literal><![CDATA[
      f(f(x,y),f(f(x,f(f(x,y),x)),x)) = x
    ]]></literal>
    <justification jstring="[para(11032(a,1),3794(a,1,2,1,1))].">
      <j1 rule="para" parents="11032 3794"/>
    </justification>
  </clause>

  <clause id="11751">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),y),y) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(10677(a,1),11032(a,1,1)),rewrite(10677(6),10806(7),4935(2)),flip(a)].">
      <j1 rule="para" parents="10677 11032"/>
      <j2 rule="rewrite" parents="10677 10806 4935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11761">
    <literal><![CDATA[
      f(x,f(f(f(x,y),y),f(x,f(x,x)))) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[back_rewrite(10821),rewrite(11751(6),11751(10))].">
      <j1 rule="back_rewrite" parents="10821"/>
      <j2 rule="rewrite" parents="11751 11751"/>
    </justification>
  </clause>

  <clause id="11779">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(x,y),f(f(f(x,f(x,x)),f(x,y)),f(f(x,y),z)))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(9519),rewrite(11751(6))].">
      <j1 rule="back_rewrite" parents="9519"/>
      <j2 rule="rewrite" parents="11751"/>
    </justification>
  </clause>

  <clause id="11957">
    <literal><![CDATA[
      f(f(x,y),f(y,f(f(f(y,f(f(y,f(f(x,y),y)),y)),f(f(x,y),f(x,y))),f(z,f(f(x,y),f(x,y)))))) = f(f(x,y),f(x,y))
    ]]></literal>
    <justification jstring="[para(11515(a,1),668(a,1,2,1)),rewrite(11515(7))].">
      <j1 rule="para" parents="11515 668"/>
      <j2 rule="rewrite" parents="11515"/>
    </justification>
  </clause>

  <clause id="11996">
    <literal><![CDATA[
      f(f(f(f(x,f(f(y,x),x)),x),f(y,x)),f(f(f(x,y),y),f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(11515(a,1),3448(a,1,2,1,1,1))].">
      <j1 rule="para" parents="11515 3448"/>
    </justification>
  </clause>

  <clause id="12085">
    <literal><![CDATA[
      f(f(f(f(f(f(x,y),f(x,y)),f(y,y)),f(f(y,f(x,y)),y)),y),f(f(y,f(f(x,y),y)),y)) = y
    ]]></literal>
    <justification jstring="[para(2350(a,1),11661(a,1,2,1,2,1))].">
      <j1 rule="para" parents="2350 11661"/>
    </justification>
  </clause>

  <clause id="12089">
    <literal><![CDATA[
      f(f(f(f(f(f(x,y),f(x,y)),f(x,x)),f(f(x,f(x,y)),x)),x),f(f(x,f(f(x,y),x)),x)) = x
    ]]></literal>
    <justification jstring="[para(2366(a,1),11661(a,1,2,1,2,1))].">
      <j1 rule="para" parents="2366 11661"/>
    </justification>
  </clause>

  <clause id="12275">
    <literal><![CDATA[
      f(f(f(f(x,f(f(x,y),x)),x),f(x,y)),f(f(f(f(x,y),f(x,y)),f(x,x)),f(f(x,f(x,y)),f(z,f(x,y))))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(11665(a,1),657(a,1,2,1,2,1)),rewrite(11665(15),11665(17))].">
      <j1 rule="para" parents="11665 657"/>
      <j2 rule="rewrite" parents="11665 11665"/>
    </justification>
  </clause>

  <clause id="12279">
    <literal><![CDATA[
      f(f(f(f(x,f(f(x,y),x)),x),f(x,y)),f(f(f(f(x,y),f(x,y)),f(x,x)),f(f(x,f(x,y)),y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(11665(a,1),84(a,1,2,1,2,1)),rewrite(11665(15),11665(17))].">
      <j1 rule="para" parents="11665 84"/>
      <j2 rule="rewrite" parents="11665 11665"/>
    </justification>
  </clause>

  <clause id="12364">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(y,y)) = y
    ]]></literal>
    <justification jstring="[para(11751(a,1),20(a,1,1))].">
      <j1 rule="para" parents="11751 20"/>
    </justification>
  </clause>

  <clause id="12366">
    <literal><![CDATA[
      f(x,f(f(y,f(y,y)),f(y,f(y,y)))) = f(y,f(y,y))
    ]]></literal>
    <justification jstring="[para(11751(a,1),82(a,1,2,1)),rewrite(11751(6),11751(10))].">
      <j1 rule="para" parents="11751 82"/>
      <j2 rule="rewrite" parents="11751 11751"/>
    </justification>
  </clause>

  <clause id="12368">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),y),f(f(f(x,f(x,x)),y),f(f(x,f(x,x)),y))) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(91(a,1),11751(a,1,1))].">
      <j1 rule="para" parents="91 11751"/>
    </justification>
  </clause>

  <clause id="12374">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),z),f(f(f(f(f(y,x),z),z),y),f(u,f(u,u))))) = y
    ]]></literal>
    <justification jstring="[para(11751(a,1),96(a,1,2,2,2))].">
      <j1 rule="para" parents="11751 96"/>
    </justification>
  </clause>

  <clause id="12375">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),y),f(f(x,f(x,x)),f(f(x,f(x,x)),f(f(f(f(x,f(x,x)),y),f(f(x,f(x,x)),y)),z)))) = f(f(f(x,f(x,x)),y),f(f(x,f(x,x)),y))
    ]]></literal>
    <justification jstring="[para(11751(a,1),190(a,1,2,1)),rewrite(11751(9),12368(16))].">
      <j1 rule="para" parents="11751 190"/>
      <j2 rule="rewrite" parents="11751 12368"/>
    </justification>
  </clause>

  <clause id="12410">
    <literal><![CDATA[
      f(f(x,x),f(y,f(y,y))) = x
    ]]></literal>
    <justification jstring="[para(11751(a,1),2286(a,1,2))].">
      <j1 rule="para" parents="11751 2286"/>
    </justification>
  </clause>

  <clause id="12412">
    <literal><![CDATA[
      f(x,f(y,f(y,y))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(11751(a,1),2387(a,1,2))].">
      <j1 rule="para" parents="11751 2387"/>
    </justification>
  </clause>

  <clause id="12416">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),f(x,f(x,x))),y) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(11751(a,1),2484(a,1,1,1)),rewrite(11751(6),11751(10))].">
      <j1 rule="para" parents="11751 2484"/>
      <j2 rule="rewrite" parents="11751 11751"/>
    </justification>
  </clause>

  <clause id="12441">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(x,f(x,x)),y)) = y
    ]]></literal>
    <justification jstring="[para(11751(a,1),3449(a,1,1)),rewrite(11751(6),11751(8))].">
      <j1 rule="para" parents="11751 3449"/>
      <j2 rule="rewrite" parents="11751 11751"/>
    </justification>
  </clause>

  <clause id="12442">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(f(f(y,f(f(x,f(x,x)),y)),f(z,y)),f(z,y)),y)) = y
    ]]></literal>
    <justification jstring="[para(11751(a,1),3450(a,1,1))].">
      <j1 rule="para" parents="11751 3450"/>
    </justification>
  </clause>

  <clause id="12446">
    <literal><![CDATA[
      f(x,f(x,f(y,f(y,y)))) = f(y,f(y,y))
    ]]></literal>
    <justification jstring="[para(11751(a,1),3451(a,1,2,1,1)),rewrite(12441(6),12441(6))].">
      <j1 rule="para" parents="11751 3451"/>
      <j2 rule="rewrite" parents="12441 12441"/>
    </justification>
  </clause>

  <clause id="12454">
    <literal><![CDATA[
      f(f(x,y),f(f(z,f(z,z)),y)) = y
    ]]></literal>
    <justification jstring="[para(11751(a,1),93(a,1,2,1)),rewrite(12364(8),12364(10),12366(10),12364(9),12364(11),12446(11),46(6),2285(6))].">
      <j1 rule="para" parents="11751 93"/>
      <j2 rule="rewrite" parents="12364 12364 12366 12364 12364 12446 46 2285"/>
    </justification>
  </clause>

  <clause id="12459">
    <literal><![CDATA[
      f(x,f(x,x)) = f(y,f(y,y))
    ]]></literal>
    <justification jstring="[para(11751(a,1),3576(a,2)),rewrite(12364(7),82(7))].">
      <j1 rule="para" parents="11751 3576"/>
      <j2 rule="rewrite" parents="12364 82"/>
    </justification>
  </clause>

  <clause id="12475">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(f(y,y),z),f(f(f(f(f(y,f(f(x,f(x,x)),y)),z),z),y),f(f(f(y,y),u),f(f(f(f(f(y,v),u),u),y),f(w,y)))))) = y
    ]]></literal>
    <justification jstring="[para(11751(a,1),102(a,1,1))].">
      <j1 rule="para" parents="11751 102"/>
    </justification>
  </clause>

  <clause id="12480">
    <literal><![CDATA[
      f(x,f(f(y,f(y,y)),f(f(f(x,f(x,x)),f(y,f(y,y))),x))) = f(y,f(y,y))
    ]]></literal>
    <justification jstring="[para(11751(a,1),5002(a,1,2,1)),rewrite(11751(8),11751(14))].">
      <j1 rule="para" parents="11751 5002"/>
      <j2 rule="rewrite" parents="11751 11751"/>
    </justification>
  </clause>

  <clause id="12527">
    <literal><![CDATA[
      f(f(f(f(x,f(x,x)),f(f(f(y,f(y,y)),x),f(x,z))),f(y,f(y,y))),f(f(y,f(y,y)),f(f(f(f(x,u),u),f(y,f(y,y))),f(f(y,f(y,y)),v)))) = f(y,f(y,y))
    ]]></literal>
    <justification jstring="[para(11751(a,1),188(a,1,1,2)),rewrite(12454(8),4935(2),12454(12),11751(6),11751(15),11751(17),12416(17),11751(19),11751(22),11751(28))].">
      <j1 rule="para" parents="11751 188"/>
      <j2 rule="rewrite" parents="12454 4935 12454 11751 11751 11751 12416 11751 11751 11751"/>
    </justification>
  </clause>

  <clause id="12539">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(f(y,y),z),f(f(f(x,f(x,x)),y),f(u,y)))) = y
    ]]></literal>
    <justification jstring="[para(11751(a,1),2527(a,1,1)),rewrite(11751(8),11751(8))].">
      <j1 rule="para" parents="11751 2527"/>
      <j2 rule="rewrite" parents="11751 11751"/>
    </justification>
  </clause>

  <clause id="12543">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(f(y,y),z),f(f(f(x,f(x,x)),y),f(y,u)))) = y
    ]]></literal>
    <justification jstring="[para(11751(a,1),2530(a,1,1)),rewrite(11751(8),11751(8))].">
      <j1 rule="para" parents="11751 2530"/>
      <j2 rule="rewrite" parents="11751 11751"/>
    </justification>
  </clause>

  <clause id="12550">
    <literal><![CDATA[
      f(f(x,y),f(f(f(x,x),z),f(f(f(f(f(x,y),z),z),x),f(u,f(u,u))))) = x
    ]]></literal>
    <justification jstring="[para(11751(a,1),2573(a,1,2,2,2))].">
      <j1 rule="para" parents="11751 2573"/>
    </justification>
  </clause>

  <clause id="12565">
    <literal><![CDATA[
      f(x,f(f(x,f(y,y)),f(f(f(y,f(y,y)),f(f(z,f(z,z)),x)),f(z,f(z,z))))) = f(f(z,f(z,z)),x)
    ]]></literal>
    <justification jstring="[para(11751(a,1),2720(a,1,2,2,2)),rewrite(12454(7),12454(7))].">
      <j1 rule="para" parents="11751 2720"/>
      <j2 rule="rewrite" parents="12454 12454"/>
    </justification>
  </clause>

  <clause id="12583">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),y),f(x,f(x,x))) = y
    ]]></literal>
    <justification jstring="[para(11751(a,1),11022(a,1,2))].">
      <j1 rule="para" parents="11751 11022"/>
    </justification>
  </clause>

  <clause id="12610">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),y),f(y,z)) = y
    ]]></literal>
    <justification jstring="[back_rewrite(12375),rewrite(12454(14),12441(10),12454(12))].">
      <j1 rule="back_rewrite" parents="12375"/>
      <j2 rule="rewrite" parents="12454 12441 12454"/>
    </justification>
  </clause>

  <clause id="12616">
    <literal><![CDATA[
      f(x,f(x,x)) = c_0
    ]]></literal>
    <justification jstring="[new_symbol(12459)].">
      <j1 rule="new_symbol" parents="12459"/>
    </justification>
  </clause>

  <clause id="12660">
    <literal><![CDATA[
      f(c_0,f(f(f(x,x),y),f(f(c_0,x),f(z,x)))) = x
    ]]></literal>
    <justification jstring="[back_rewrite(12539),rewrite(12616(2),12616(5))].">
      <j1 rule="back_rewrite" parents="12539"/>
      <j2 rule="rewrite" parents="12616 12616"/>
    </justification>
  </clause>

  <clause id="12776">
    <literal><![CDATA[
      f(f(f(x,x),y),f(f(c_0,x),f(z,x))) = f(x,x)
    ]]></literal>
    <justification jstring="[back_rewrite(8550),rewrite(12616(4),12616(7),12660(11),55(3),12616(5)),flip(a)].">
      <j1 rule="back_rewrite" parents="8550"/>
      <j2 rule="rewrite" parents="12616 12616 12660 55 12616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12798">
    <literal><![CDATA[
      f(f(x,y),f(c_0,x)) = x
    ]]></literal>
    <justification jstring="[back_rewrite(7685),rewrite(12616(7),12776(10),77(4),12616(6),12776(9),12616(3))].">
      <j1 rule="back_rewrite" parents="7685"/>
      <j2 rule="rewrite" parents="12616 12776 77 12616 12776 12616"/>
    </justification>
  </clause>

  <clause id="12869">
    <literal><![CDATA[
      f(c_0,f(f(f(x,x),y),f(f(c_0,x),f(x,z)))) = x
    ]]></literal>
    <justification jstring="[back_rewrite(12543),rewrite(12616(2),12616(5))].">
      <j1 rule="back_rewrite" parents="12543"/>
      <j2 rule="rewrite" parents="12616 12616"/>
    </justification>
  </clause>

  <clause id="12872">
    <literal><![CDATA[
      f(f(f(c_0,f(f(c_0,x),f(x,y))),c_0),f(c_0,f(f(f(f(x,z),z),c_0),f(c_0,u)))) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(12527),rewrite(12616(2),12616(3),12616(8),12616(10),12616(13),12616(15),12616(20))].">
      <j1 rule="back_rewrite" parents="12527"/>
      <j2 rule="rewrite" parents="12616 12616 12616 12616 12616 12616 12616"/>
    </justification>
  </clause>

  <clause id="12898">
    <literal><![CDATA[
      f(c_0,f(f(x,y),f(f(c_0,f(x,y)),f(f(x,y),z)))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(11779),rewrite(12616(2),12616(4))].">
      <j1 rule="back_rewrite" parents="11779"/>
      <j2 rule="rewrite" parents="12616 12616"/>
    </justification>
  </clause>

  <clause id="13063">
    <literal><![CDATA[
      f(f(f(x,x),y),f(f(c_0,x),f(x,z))) = f(x,x)
    ]]></literal>
    <justification jstring="[back_rewrite(8558),rewrite(12616(4),12616(7),12869(11),55(3),12616(5)),flip(a)].">
      <j1 rule="back_rewrite" parents="8558"/>
      <j2 rule="rewrite" parents="12616 12616 12869 55 12616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13139">
    <literal><![CDATA[
      f(f(f(x,f(f(c_0,x),f(x,y))),f(z,x)),f(f(f(f(z,x),f(z,x)),u),f(f(f(f(x,u),u),f(z,x)),x))) = f(z,x)
    ]]></literal>
    <justification jstring="[back_rewrite(5972),rewrite(12616(5))].">
      <j1 rule="back_rewrite" parents="5972"/>
      <j2 rule="rewrite" parents="12616"/>
    </justification>
  </clause>

  <clause id="13156">
    <literal><![CDATA[
      f(f(f(x,f(f(c_0,x),f(x,y))),f(x,y)),f(f(f(f(x,y),f(x,y)),z),f(f(f(f(x,z),z),f(x,y)),x))) = f(x,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(5053),rewrite(12616(5))].">
      <j1 rule="back_rewrite" parents="5053"/>
      <j2 rule="rewrite" parents="12616"/>
    </justification>
  </clause>

  <clause id="13161">
    <literal><![CDATA[
      f(f(x,f(y,z)),f(f(y,z),f(f(c_0,f(y,z)),y))) = f(y,z)
    ]]></literal>
    <justification jstring="[back_rewrite(3378),rewrite(12616(11),13063(16),12616(8))].">
      <j1 rule="back_rewrite" parents="3378"/>
      <j2 rule="rewrite" parents="12616 13063 12616"/>
    </justification>
  </clause>

  <clause id="13263">
    <literal><![CDATA[
      f(f(c_0,x),f(x,y)) = x
    ]]></literal>
    <justification jstring="[back_rewrite(12610),rewrite(12616(2))].">
      <j1 rule="back_rewrite" parents="12610"/>
      <j2 rule="rewrite" parents="12616"/>
    </justification>
  </clause>

  <clause id="13282">
    <literal><![CDATA[
      f(f(c_0,x),c_0) = x
    ]]></literal>
    <justification jstring="[back_rewrite(12583),rewrite(12616(2),12616(4))].">
      <j1 rule="back_rewrite" parents="12583"/>
      <j2 rule="rewrite" parents="12616 12616"/>
    </justification>
  </clause>

  <clause id="13294">
    <literal><![CDATA[
      f(c_0,x) = f(x,x)
    ]]></literal>
    <justification jstring="[back_rewrite(12565),rewrite(12616(4),12616(5),12616(8),13282(8),12798(5),12616(3)),flip(a)].">
      <j1 rule="back_rewrite" parents="12565"/>
      <j2 rule="rewrite" parents="12616 12616 12616 13282 12798 12616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13303">
    <literal><![CDATA[
      f(f(x,y),f(f(f(x,x),z),f(f(f(f(f(x,y),z),z),x),c_0))) = x
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(12550),rewrite(12616(9))].">
      <j1 rule="back_rewrite" parents="12550"/>
      <j2 rule="rewrite" parents="12616"/>
    </justification>
  </clause>

  <clause id="13330">
    <literal><![CDATA[
      f(x,f(c_0,c_0)) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(12480),rewrite(12616(2),12616(3),12616(4),2386(6),12616(6))].">
      <j1 rule="back_rewrite" parents="12480"/>
      <j2 rule="rewrite" parents="12616 12616 12616 2386 12616"/>
    </justification>
  </clause>

  <clause id="13333">
    <literal><![CDATA[
      f(c_0,f(x,x)) = x
    ]]></literal>
    <justification jstring="[back_rewrite(12475),rewrite(12616(2),12616(5),13294(5),12616(5),13294(5),4935(5),12616(5),13294(5),2727(14),55(4))].">
      <j1 rule="back_rewrite" parents="12475"/>
      <j2 rule="rewrite" parents="12616 12616 13294 12616 13294 4935 12616 13294 2727 55"/>
    </justification>
  </clause>

  <clause id="13346">
    <literal><![CDATA[
      f(c_0,f(f(f(c_0,f(x,y)),f(x,y)),y)) = y
    ]]></literal>
    <justification jstring="[back_rewrite(12442),rewrite(12616(2),12616(3),13294(3),12616(3))].">
      <j1 rule="back_rewrite" parents="12442"/>
      <j2 rule="rewrite" parents="12616 12616 13294 12616"/>
    </justification>
  </clause>

  <clause id="13352">
    <literal><![CDATA[
      f(f(c_0,c_0),x) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(12416),rewrite(12616(2),12616(3),12616(6))].">
      <j1 rule="back_rewrite" parents="12416"/>
      <j2 rule="rewrite" parents="12616 12616 12616"/>
    </justification>
  </clause>

  <clause id="13353">
    <literal><![CDATA[
      f(x,c_0) = f(x,x)
    ]]></literal>
    <justification jstring="[back_rewrite(12412),rewrite(12616(2))].">
      <j1 rule="back_rewrite" parents="12412"/>
      <j2 rule="rewrite" parents="12616"/>
    </justification>
  </clause>

  <clause id="13354">
    <literal><![CDATA[
      f(f(x,x),c_0) = x
    ]]></literal>
    <justification jstring="[back_rewrite(12410),rewrite(12616(3))].">
      <j1 rule="back_rewrite" parents="12410"/>
      <j2 rule="rewrite" parents="12616"/>
    </justification>
  </clause>

  <clause id="13364">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),z),f(f(f(f(f(y,x),z),z),y),c_0))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(12374),rewrite(12616(9))].">
      <j1 rule="back_rewrite" parents="12374"/>
      <j2 rule="rewrite" parents="12616"/>
    </justification>
  </clause>

  <clause id="13428">
    <literal><![CDATA[
      f(x,f(f(f(x,y),y),c_0)) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(11761),rewrite(12616(4),12616(7))].">
      <j1 rule="back_rewrite" parents="11761"/>
      <j2 rule="rewrite" parents="12616 12616"/>
    </justification>
  </clause>

  <clause id="13488">
    <literal><![CDATA[
      f(f(f(x,f(y,y)),c_0),y) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(10956),rewrite(12616(4),12616(7))].">
      <j1 rule="back_rewrite" parents="10956"/>
      <j2 rule="rewrite" parents="12616 12616"/>
    </justification>
  </clause>

  <clause id="13494">
    <literal><![CDATA[
      f(f(x,x),f(f(y,x),c_0)) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(10947),rewrite(12616(4),12616(7))].">
      <j1 rule="back_rewrite" parents="10947"/>
      <j2 rule="rewrite" parents="12616 12616"/>
    </justification>
  </clause>

  <clause id="13499">
    <literal><![CDATA[
      f(f(x,x),f(f(f(c_0,f(y,f(x,x))),f(c_0,f(z,x))),f(f(f(z,x),f(y,f(x,x))),f(x,x)))) = f(y,f(x,x))
    ]]></literal>
    <justification jstring="[back_rewrite(10942),rewrite(13294(6,R),12616(7))].">
      <j1 rule="back_rewrite" parents="10942"/>
      <j2 rule="rewrite" parents="13294 12616"/>
    </justification>
  </clause>

  <clause id="14294">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),f(f(f(x,y),f(c_0,f(x,y))),y)) = f(f(x,y),f(c_0,f(x,y)))
    ]]></literal>
    <justification jstring="[back_rewrite(5371),rewrite(13294(3,R),13294(7,R),13294(14,R))].">
      <j1 rule="back_rewrite" parents="5371"/>
      <j2 rule="rewrite" parents="13294 13294 13294"/>
    </justification>
  </clause>

  <clause id="14382">
    <literal><![CDATA[
      f(f(x,x),f(c_0,f(x,y))) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(5045),rewrite(12616(3),12616(7))].">
      <j1 rule="back_rewrite" parents="5045"/>
      <j2 rule="rewrite" parents="12616 12616"/>
    </justification>
  </clause>

  <clause id="14383">
    <literal><![CDATA[
      f(f(x,x),f(c_0,f(y,x))) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(5043),rewrite(12616(3),12616(7))].">
      <j1 rule="back_rewrite" parents="5043"/>
      <j2 rule="rewrite" parents="12616 12616"/>
    </justification>
  </clause>

  <clause id="14387">
    <literal><![CDATA[
      f(x,f(c_0,f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(5030),rewrite(12616(2))].">
      <j1 rule="back_rewrite" parents="5030"/>
      <j2 rule="rewrite" parents="12616"/>
    </justification>
  </clause>

  <clause id="14389">
    <literal><![CDATA[
      f(x,f(c_0,f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(5028),rewrite(12616(2))].">
      <j1 rule="back_rewrite" parents="5028"/>
      <j2 rule="rewrite" parents="12616"/>
    </justification>
  </clause>

  <clause id="14429">
    <literal><![CDATA[
      f(x,f(c_0,f(y,f(x,x)))) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(4239),rewrite(12616(2),12616(7))].">
      <j1 rule="back_rewrite" parents="4239"/>
      <j2 rule="rewrite" parents="12616 12616"/>
    </justification>
  </clause>

  <clause id="14431">
    <literal><![CDATA[
      f(x,f(c_0,f(f(x,x),y))) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(3996),rewrite(12616(2),12616(7))].">
      <j1 rule="back_rewrite" parents="3996"/>
      <j2 rule="rewrite" parents="12616 12616"/>
    </justification>
  </clause>

  <clause id="14525">
    <literal><![CDATA[
      f(x,f(f(f(c_0,f(x,f(c_0,f(f(x,y),y)))),y),f(f(c_0,f(f(x,y),y)),x))) = f(x,f(c_0,f(f(x,y),y)))
    ]]></literal>
    <justification jstring="[back_rewrite(2642),rewrite(13294(5,R),13294(10,R),13294(11,R),13294(13,R),13294(20,R))].">
      <j1 rule="back_rewrite" parents="2642"/>
      <j2 rule="rewrite" parents="13294 13294 13294 13294 13294"/>
    </justification>
  </clause>

  <clause id="14531">
    <literal><![CDATA[
      f(x,f(f(f(c_0,f(x,y)),z),f(f(f(f(x,z),z),f(x,y)),x))) = f(x,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(13156),rewrite(13294(2),2285(3),2285(3),13294(3,R))].">
      <j1 rule="back_rewrite" parents="13156"/>
      <j2 rule="rewrite" parents="13294 2285 2285 13294"/>
    </justification>
  </clause>

  <clause id="14536">
    <literal><![CDATA[
      f(x,f(f(f(c_0,f(y,x)),z),f(f(f(f(x,z),z),f(y,x)),x))) = f(y,x)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(13139),rewrite(13294(2),2285(3),2286(3),13294(3,R))].">
      <j1 rule="back_rewrite" parents="13139"/>
      <j2 rule="rewrite" parents="13294 2285 2286 13294"/>
    </justification>
  </clause>

  <clause id="14553">
    <literal><![CDATA[
      f(c_0,f(c_0,f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(12898),rewrite(13263(8),13294(4,R))].">
      <j1 rule="back_rewrite" parents="12898"/>
      <j2 rule="rewrite" parents="13263 13294"/>
    </justification>
  </clause>

  <clause id="14555">
    <literal><![CDATA[
      f(x,f(c_0,f(f(f(f(x,y),y),c_0),f(z,z)))) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(12872),rewrite(13294(3),2285(4),13294(2),13354(3),13294(7))].">
      <j1 rule="back_rewrite" parents="12872"/>
      <j2 rule="rewrite" parents="13294 2285 13294 13354 13294"/>
    </justification>
  </clause>

  <clause id="14590">
    <literal><![CDATA[
      f(f(f(f(x,f(f(x,y),x)),x),f(x,y)),f(f(f(c_0,f(x,y)),f(x,x)),f(f(x,f(x,y)),y))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(12279),rewrite(13294(9,R))].">
      <j1 rule="back_rewrite" parents="12279"/>
      <j2 rule="rewrite" parents="13294"/>
    </justification>
  </clause>

  <clause id="14592">
    <literal><![CDATA[
      f(f(f(f(x,f(f(x,y),x)),x),f(x,y)),f(f(f(c_0,f(x,y)),f(x,x)),f(f(x,f(x,y)),f(z,f(x,y))))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(12275),rewrite(13294(9,R))].">
      <j1 rule="back_rewrite" parents="12275"/>
      <j2 rule="rewrite" parents="13294"/>
    </justification>
  </clause>

  <clause id="14621">
    <literal><![CDATA[
      f(f(f(f(f(c_0,f(x,y)),f(x,x)),f(f(x,f(x,y)),x)),x),f(f(x,f(f(x,y),x)),x)) = x
    ]]></literal>
    <justification jstring="[back_rewrite(12089),rewrite(13294(3,R))].">
      <j1 rule="back_rewrite" parents="12089"/>
      <j2 rule="rewrite" parents="13294"/>
    </justification>
  </clause>

  <clause id="14625">
    <literal><![CDATA[
      f(f(f(f(f(c_0,f(x,y)),f(y,y)),f(f(y,f(x,y)),y)),y),f(f(y,f(f(x,y),y)),y)) = y
    ]]></literal>
    <justification jstring="[back_rewrite(12085),rewrite(13294(3,R))].">
      <j1 rule="back_rewrite" parents="12085"/>
      <j2 rule="rewrite" parents="13294"/>
    </justification>
  </clause>

  <clause id="14657">
    <literal><![CDATA[
      f(f(x,y),f(y,f(f(f(y,f(f(y,f(f(x,y),y)),y)),f(c_0,f(x,y))),f(z,f(c_0,f(x,y)))))) = f(c_0,f(x,y))
    ]]></literal>
    <justification jstring="[back_rewrite(11957),rewrite(13294(9,R),13294(13,R),13294(20,R))].">
      <j1 rule="back_rewrite" parents="11957"/>
      <j2 rule="rewrite" parents="13294 13294 13294"/>
    </justification>
  </clause>

  <clause id="14777">
    <literal><![CDATA[
      f(f(x,y),f(f(x,y),f(f(f(c_0,f(x,y)),z),f(f(f(f(f(f(x,y),u),z),z),f(x,y)),x)))) = f(f(f(c_0,f(x,y)),z),f(f(f(f(f(f(x,y),u),z),z),f(x,y)),x))
    ]]></literal>
    <justification jstring="[back_rewrite(11499),rewrite(13294(5,R),13294(19,R))].">
      <j1 rule="back_rewrite" parents="11499"/>
      <j2 rule="rewrite" parents="13294 13294"/>
    </justification>
  </clause>

  <clause id="14783">
    <literal><![CDATA[
      f(f(x,y),f(f(x,y),f(f(f(c_0,f(x,y)),z),f(f(f(f(x,z),z),f(x,y)),x)))) = f(f(f(c_0,f(x,y)),z),f(f(f(f(x,z),z),f(x,y)),x))
    ]]></literal>
    <justification jstring="[back_rewrite(11490),rewrite(13294(5,R),13294(17,R))].">
      <j1 rule="back_rewrite" parents="11490"/>
      <j2 rule="rewrite" parents="13294 13294"/>
    </justification>
  </clause>

  <clause id="14830">
    <literal><![CDATA[
      f(x,f(f(f(c_0,f(x,f(y,x))),f(x,x)),f(f(y,x),x))) = f(x,f(y,x))
    ]]></literal>
    <justification jstring="[back_rewrite(11301),rewrite(13294(5,R))].">
      <j1 rule="back_rewrite" parents="11301"/>
      <j2 rule="rewrite" parents="13294"/>
    </justification>
  </clause>

  <clause id="14831">
    <literal><![CDATA[
      f(f(f(f(c_0,f(x,y)),z),f(f(f(f(f(f(x,y),u),z),z),f(x,y)),x)),f(f(f(f(c_0,f(x,y)),z),f(f(f(f(f(f(x,y),u),z),z),f(x,y)),x)),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(11300),rewrite(13294(3,R),13294(15,R))].">
      <j1 rule="back_rewrite" parents="11300"/>
      <j2 rule="rewrite" parents="13294 13294"/>
    </justification>
  </clause>

  <clause id="14842">
    <literal><![CDATA[
      f(f(x,y),f(f(f(c_0,f(y,f(x,y))),f(c_0,f(f(y,f(x,y)),y))),f(f(f(f(y,f(x,y)),y),f(y,f(x,y))),f(z,f(y,f(x,y)))))) = f(y,f(x,y))
    ]]></literal>
    <justification jstring="[back_rewrite(11284),rewrite(13294(6,R),13294(12,R))].">
      <j1 rule="back_rewrite" parents="11284"/>
      <j2 rule="rewrite" parents="13294 13294"/>
    </justification>
  </clause>

  <clause id="14873">
    <literal><![CDATA[
      f(x,f(f(f(c_0,f(x,f(x,y))),f(x,x)),f(f(x,y),x))) = f(x,f(x,y))
    ]]></literal>
    <justification jstring="[back_rewrite(11092),rewrite(13294(5,R))].">
      <j1 rule="back_rewrite" parents="11092"/>
      <j2 rule="rewrite" parents="13294"/>
    </justification>
  </clause>

  <clause id="14886">
    <literal><![CDATA[
      f(f(x,y),f(f(f(c_0,f(x,f(x,y))),f(c_0,f(f(x,f(x,y)),x))),f(f(f(f(x,f(x,y)),x),f(x,f(x,y))),f(z,f(x,f(x,y)))))) = f(x,f(x,y))
    ]]></literal>
    <justification jstring="[back_rewrite(11072),rewrite(13294(6,R),13294(12,R))].">
      <j1 rule="back_rewrite" parents="11072"/>
      <j2 rule="rewrite" parents="13294 13294"/>
    </justification>
  </clause>

  <clause id="15012">
    <literal><![CDATA[
      f(f(f(f(f(x,x),y),f(f(f(f(f(x,z),y),y),x),f(u,x))),f(x,z)),f(f(f(c_0,f(x,z)),f(x,x)),f(f(x,f(x,z)),z))) = f(x,z)
    ]]></literal>
    <justification jstring="[back_rewrite(9649),rewrite(13294(14,R))].">
      <j1 rule="back_rewrite" parents="9649"/>
      <j2 rule="rewrite" parents="13294"/>
    </justification>
  </clause>

  <clause id="15847">
    <literal><![CDATA[
      f(f(f(x,f(f(f(x,f(f(f(x,x),y),f(f(f(f(f(x,z),y),y),x),f(x,z)))),x),f(x,z))),f(x,z)),f(f(f(c_0,f(x,z)),u),f(f(f(f(x,u),u),f(x,z)),x))) = f(x,z)
    ]]></literal>
    <justification jstring="[back_rewrite(3147),rewrite(13294(19,R))].">
      <j1 rule="back_rewrite" parents="3147"/>
      <j2 rule="rewrite" parents="13294"/>
    </justification>
  </clause>

  <clause id="15856">
    <literal><![CDATA[
      f(f(f(f(f(c_0,f(x,y)),f(y,y)),f(f(y,f(x,y)),y)),y),f(c_0,f(f(f(x,y),y),f(y,z)))) = y
    ]]></literal>
    <justification jstring="[back_rewrite(3098),rewrite(13294(3,R),13294(14,R),14383(15))].">
      <j1 rule="back_rewrite" parents="3098"/>
      <j2 rule="rewrite" parents="13294 13294 14383"/>
    </justification>
  </clause>

  <clause id="15890">
    <literal><![CDATA[
      f(f(f(f(x,y),f(f(f(f(x,y),f(f(f(c_0,f(x,y)),z),f(f(f(f(x,z),z),f(x,y)),x))),f(x,y)),x)),x),f(f(f(x,x),u),f(f(f(f(f(x,y),u),u),x),f(x,v)))) = x
    ]]></literal>
    <justification jstring="[back_rewrite(2895),rewrite(13294(5,R))].">
      <j1 rule="back_rewrite" parents="2895"/>
      <j2 rule="rewrite" parents="13294"/>
    </justification>
  </clause>

  <clause id="15971">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),x) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(2489),rewrite(13294(3,R))].">
      <j1 rule="back_rewrite" parents="2489"/>
      <j2 rule="rewrite" parents="13294"/>
    </justification>
  </clause>

  <clause id="15973">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),y) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(2484),rewrite(13294(3,R))].">
      <j1 rule="back_rewrite" parents="2484"/>
      <j2 rule="rewrite" parents="13294"/>
    </justification>
  </clause>

  <clause id="16159">
    <literal><![CDATA[
      f(f(x,f(y,z)),f(c_0,f(y,z))) = f(y,z)
    ]]></literal>
    <justification jstring="[back_rewrite(13161),rewrite(15971(7),13294(5,R))].">
      <j1 rule="back_rewrite" parents="13161"/>
      <j2 rule="rewrite" parents="15971 13294"/>
    </justification>
  </clause>

  <clause id="16244">
    <literal><![CDATA[
      f(x,f(f(f(c_0,f(x,y)),z),f(f(f(f(x,z),z),f(x,y)),c_0))) = f(x,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(77(a,1),13303(a,1,1)),rewrite(13294(3,R),77(7))].">
      <j1 rule="para" parents="77 13303"/>
      <j2 rule="rewrite" parents="13294 77"/>
    </justification>
  </clause>

  <clause id="16681">
    <literal><![CDATA[
      f(x,f(f(f(c_0,f(x,y)),z),f(f(f(f(x,f(f(f(f(c_0,f(x,y)),z),z),f(f(c_0,f(x,y)),z))),f(f(f(f(c_0,f(x,y)),z),z),f(f(c_0,f(x,y)),z))),f(x,y)),x))) = f(x,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(4566(a,1),14531(a,1,2,1))].">
      <j1 rule="para" parents="4566 14531"/>
    </justification>
  </clause>

  <clause id="16727">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),z),f(c_0,f(f(f(f(y,x),z),z),y)))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(13294(a,2),96(a,1,2,2))].">
      <j1 rule="para" parents="13294 96"/>
    </justification>
  </clause>

  <clause id="16744">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),z),f(c_0,f(f(f(f(x,y),z),z),y)))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(13294(a,2),2527(a,1,2,2))].">
      <j1 rule="para" parents="13294 2527"/>
    </justification>
  </clause>

  <clause id="16745">
    <literal><![CDATA[
      f(f(x,y),f(f(f(x,x),z),f(c_0,f(f(f(f(x,y),z),z),x)))) = x
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(13294(a,2),2573(a,1,2,2))].">
      <j1 rule="para" parents="13294 2573"/>
    </justification>
  </clause>

  <clause id="16746">
    <literal><![CDATA[
      f(f(x,x),f(f(f(x,x),y),f(c_0,f(f(f(f(x,z),y),y),x)))) = x
    ]]></literal>
    <justification jstring="[para(13294(a,2),2727(a,1,2,2))].">
      <j1 rule="para" parents="13294 2727"/>
    </justification>
  </clause>

  <clause id="16747">
    <literal><![CDATA[
      f(f(x,x),f(f(f(x,x),y),f(c_0,f(f(f(f(z,x),y),y),x)))) = x
    ]]></literal>
    <justification jstring="[para(13294(a,2),2777(a,1,2,2))].">
      <j1 rule="para" parents="13294 2777"/>
    </justification>
  </clause>

  <clause id="16795">
    <literal><![CDATA[
      f(f(x,f(y,y)),f(f(y,z),f(c_0,f(f(f(f(f(y,y),x),z),z),f(y,y))))) = f(y,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(20(a,1),16727(a,1,2,1,1))].">
      <j1 rule="para" parents="20 16727"/>
    </justification>
  </clause>

  <clause id="16798">
    <literal><![CDATA[
      f(x,f(f(f(c_0,f(x,y)),z),f(c_0,f(f(f(x,z),z),f(x,y))))) = f(x,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(77(a,1),16727(a,1,2,2,2,1,1,1)),rewrite(2285(3),13294(3,R))].">
      <j1 rule="para" parents="77 16727"/>
      <j2 rule="rewrite" parents="2285 13294"/>
    </justification>
  </clause>

  <clause id="16815">
    <literal><![CDATA[
      f(f(f(f(x,y),f(f(f(f(x,y),y),f(x,y)),x)),x),f(f(f(x,x),z),f(c_0,f(f(f(f(x,y),z),z),x)))) = x
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(2743(a,1),16727(a,1,2,2,2,1,1,1))].">
      <j1 rule="para" parents="2743 16727"/>
    </justification>
  </clause>

  <clause id="16890">
    <literal><![CDATA[
      f(f(f(f(f(x,y),f(f(f(x,y),y),f(x,y))),f(x,y)),x),f(f(f(x,x),z),f(c_0,f(f(f(f(x,y),z),z),x)))) = x
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(4854(a,1),16727(a,1,2,2,2,1,1,1))].">
      <j1 rule="para" parents="4854 16727"/>
    </justification>
  </clause>

  <clause id="16894">
    <literal><![CDATA[
      f(f(f(f(f(x,y),f(f(f(y,x),x),f(x,y))),f(x,y)),y),f(f(f(y,y),z),f(c_0,f(f(f(f(x,y),z),z),y)))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(5065(a,1),16727(a,1,2,2,2,1,1,1))].">
      <j1 rule="para" parents="5065 16727"/>
    </justification>
  </clause>

  <clause id="16968">
    <literal><![CDATA[
      f(x,f(c_0,f(f(f(x,x),y),f(c_0,f(f(f(f(z,x),y),y),x))))) = f(f(f(x,x),y),f(c_0,f(f(f(f(z,x),y),y),x)))
    ]]></literal>
    <justification jstring="[para(16744(a,1),20(a,1,1)),rewrite(13294(19,R))].">
      <j1 rule="para" parents="16744 20"/>
      <j2 rule="rewrite" parents="13294"/>
    </justification>
  </clause>

  <clause id="16988">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),f(f(f(f(x,y),z),z),f(f(x,y),z))),f(c_0,f(f(f(f(x,y),z),f(f(f(f(x,y),z),z),f(f(x,y),z))),y)))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(4566(a,1),16744(a,1,2,2,2,1,1))].">
      <j1 rule="para" parents="4566 16744"/>
    </justification>
  </clause>

  <clause id="17030">
    <literal><![CDATA[
      f(x,f(x,f(f(f(x,x),y),f(c_0,f(f(f(f(z,x),y),y),x))))) = f(f(f(x,x),y),f(c_0,f(f(f(f(z,x),y),y),x)))
    ]]></literal>
    <justification jstring="[para(16744(a,1),11022(a,1,1)),rewrite(16744(11))].">
      <j1 rule="para" parents="16744 11022"/>
      <j2 rule="rewrite" parents="16744"/>
    </justification>
  </clause>

  <clause id="17044">
    <literal><![CDATA[
      f(f(f(x,x),y),f(f(x,z),f(c_0,f(f(f(f(f(x,x),y),z),z),f(x,x))))) = f(x,x)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(20(a,1),16745(a,1,2,1,1))].">
      <j1 rule="para" parents="20 16745"/>
    </justification>
  </clause>

  <clause id="17074">
    <literal><![CDATA[
      f(f(x,y),f(f(f(x,x),f(f(f(f(x,y),z),z),f(f(x,y),z))),f(c_0,f(f(f(f(x,y),z),f(f(f(f(x,y),z),z),f(f(x,y),z))),x)))) = x
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(4566(a,1),16745(a,1,2,2,2,1,1))].">
      <j1 rule="para" parents="4566 16745"/>
    </justification>
  </clause>

  <clause id="17147">
    <literal><![CDATA[
      f(f(f(c_0,f(x,y)),f(x,y)),y) = f(y,y)
    ]]></literal>
    <justification jstring="[para(3450(a,1),14536(a,1,2,2,1)),rewrite(12616(3),13346(8),13294(3,R),13333(3),12616(3)),flip(a)].">
      <j1 rule="para" parents="3450 14536"/>
      <j2 rule="rewrite" parents="12616 13346 13294 13333 12616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17165">
    <literal><![CDATA[
      f(f(f(f(c_0,f(x,y)),z),f(f(f(f(y,z),z),f(x,y)),y)),f(f(f(x,y),f(f(f(f(f(f(c_0,f(x,y)),z),f(f(f(f(y,z),z),f(x,y)),y)),y),y),f(x,y))),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(14536(a,1),5065(a,1,2,1,1)),rewrite(14536(34),14536(37),14536(40))].">
      <j1 rule="para" parents="14536 5065"/>
      <j2 rule="rewrite" parents="14536 14536 14536"/>
    </justification>
  </clause>

  <clause id="17589">
    <literal><![CDATA[
      f(x,f(f(f(c_0,f(x,f(c_0,f(f(x,y),y)))),y),f(f(c_0,f(f(x,y),y)),c_0))) = f(x,f(c_0,f(f(x,y),y)))
    ]]></literal>
    <justification jstring="[para(2387(a,1),16244(a,1,2,2,1)),rewrite(13294(6,R),13294(13,R),13294(21,R))].">
      <j1 rule="para" parents="2387 16244"/>
      <j2 rule="rewrite" parents="13294 13294 13294"/>
    </justification>
  </clause>

  <clause id="17801">
    <literal><![CDATA[
      f(f(f(f(f(c_0,f(x,y)),z),f(c_0,f(f(f(x,z),z),f(x,y)))),x),f(f(x,f(x,f(f(f(x,f(f(f(x,x),u),f(f(f(f(f(x,y),u),u),x),f(x,y)))),x),f(x,y)))),x)) = x
    ]]></literal>
    <justification jstring="[para(16798(a,1),3486(a,1,2,1,2,2,1,1,2,2,1,1,1,1)),rewrite(16798(30),16798(35))].">
      <j1 rule="para" parents="16798 3486"/>
      <j2 rule="rewrite" parents="16798 16798"/>
    </justification>
  </clause>

  <clause id="18080">
    <literal><![CDATA[
      f(f(x,y),f(f(y,f(f(y,f(f(y,x),y)),y)),c_0)) = c_0
    ]]></literal>
    <justification jstring="[para(11661(a,1),13428(a,1,2,1,1))].">
      <j1 rule="para" parents="11661 13428"/>
    </justification>
  </clause>

  <clause id="18093">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),f(f(f(f(y,x),z),z),c_0)),f(f(f(c_0,f(f(f(f(y,x),z),z),c_0)),y),c_0))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(13428(a,1),13364(a,1,2,2,1,1,1))].">
      <j1 rule="para" parents="13428 13364"/>
    </justification>
  </clause>

  <clause id="18095">
    <literal><![CDATA[
      f(x,f(f(f(c_0,f(x,y)),f(f(f(x,z),z),c_0)),f(f(f(c_0,f(f(f(x,z),z),c_0)),f(x,y)),x))) = f(x,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(13428(a,1),14531(a,1,2,2,1,1,1))].">
      <j1 rule="para" parents="13428 14531"/>
    </justification>
  </clause>

  <clause id="18102">
    <literal><![CDATA[
      f(f(x,y),f(f(y,f(f(f(y,y),z),f(c_0,f(f(f(f(y,x),z),z),y)))),c_0)) = c_0
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(16727(a,1),13428(a,1,2,1,1))].">
      <j1 rule="para" parents="16727 13428"/>
    </justification>
  </clause>

  <clause id="18111">
    <literal><![CDATA[
      f(x,f(c_0,f(f(x,y),y))) = c_0
    ]]></literal>
    <justification jstring="[para(13353(a,1),13428(a,1,2)),rewrite(13294(5,R))].">
      <j1 rule="para" parents="13353 13428"/>
      <j2 rule="rewrite" parents="13294"/>
    </justification>
  </clause>

  <clause id="18120">
    <literal><![CDATA[
      f(x,f(c_0,f(f(c_0,f(f(x,y),y)),c_0))) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(17589),rewrite(18111(6),13352(4),18111(14))].">
      <j1 rule="back_rewrite" parents="17589"/>
      <j2 rule="rewrite" parents="18111 13352 18111"/>
    </justification>
  </clause>

  <clause id="18121">
    <literal><![CDATA[
      f(f(c_0,f(f(x,y),y)),x) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(14525),rewrite(18111(6),13352(4),14389(8),18111(10))].">
      <j1 rule="back_rewrite" parents="14525"/>
      <j2 rule="rewrite" parents="18111 13352 14389 18111"/>
    </justification>
  </clause>

  <clause id="19039">
    <literal><![CDATA[
      f(f(f(x,f(y,y)),c_0),f(c_0,f(y,f(z,z)))) = c_0
    ]]></literal>
    <justification jstring="[para(13488(a,1),2527(a,1,2,2,1,1,1)),rewrite(13352(8),13294(7),13354(8),13353(7))].">
      <j1 rule="para" parents="13488 2527"/>
      <j2 rule="rewrite" parents="13352 13294 13354 13353"/>
    </justification>
  </clause>

  <clause id="19101">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),f(x,x)) = c_0
    ]]></literal>
    <justification jstring="[para(2285(a,1),13494(a,1,2,1)),rewrite(13294(3,R),13353(5))].">
      <j1 rule="para" parents="2285 13494"/>
      <j2 rule="rewrite" parents="13294 13353"/>
    </justification>
  </clause>

  <clause id="19102">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),f(y,y)) = c_0
    ]]></literal>
    <justification jstring="[para(2286(a,1),13494(a,1,2,1)),rewrite(13294(3,R),13353(5))].">
      <j1 rule="para" parents="2286 13494"/>
      <j2 rule="rewrite" parents="13294 13353"/>
    </justification>
  </clause>

  <clause id="19138">
    <literal><![CDATA[
      f(f(c_0,f(x,f(x,y))),f(f(x,y),c_0)) = c_0
    ]]></literal>
    <justification jstring="[para(10878(a,1),13494(a,1,2,1)),rewrite(13294(5,R))].">
      <j1 rule="para" parents="10878 13494"/>
      <j2 rule="rewrite" parents="13294"/>
    </justification>
  </clause>

  <clause id="19139">
    <literal><![CDATA[
      f(f(c_0,f(x,f(y,x))),f(f(y,x),c_0)) = c_0
    ]]></literal>
    <justification jstring="[para(10879(a,1),13494(a,1,2,1)),rewrite(13294(5,R))].">
      <j1 rule="para" parents="10879 13494"/>
      <j2 rule="rewrite" parents="13294"/>
    </justification>
  </clause>

  <clause id="19216">
    <literal><![CDATA[
      f(f(f(f(f(x,x),y),f(f(f(f(f(x,z),y),y),x),f(u,x))),f(x,z)),f(c_0,f(f(x,f(x,z)),z))) = f(x,z)
    ]]></literal>
    <justification jstring="[back_rewrite(15012),rewrite(19101(16))].">
      <j1 rule="back_rewrite" parents="15012"/>
      <j2 rule="rewrite" parents="19101"/>
    </justification>
  </clause>

  <clause id="19221">
    <literal><![CDATA[
      f(f(x,y),x) = f(x,f(x,y))
    ]]></literal>
    <justification jstring="[back_rewrite(14873),rewrite(19101(6),14389(5))].">
      <j1 rule="back_rewrite" parents="14873"/>
      <j2 rule="rewrite" parents="19101 14389"/>
    </justification>
  </clause>

  <clause id="19222">
    <literal><![CDATA[
      f(f(x,y),y) = f(y,f(x,y))
    ]]></literal>
    <justification jstring="[back_rewrite(14830),rewrite(19101(6),14389(5))].">
      <j1 rule="back_rewrite" parents="14830"/>
      <j2 rule="rewrite" parents="19101 14389"/>
    </justification>
  </clause>

  <clause id="19228">
    <literal><![CDATA[
      f(f(x,y),f(x,f(x,y))) = x
    ]]></literal>
    <justification jstring="[back_rewrite(14621),rewrite(19101(5),19221(4),10878(4),15971(4),19221(3),10878(4),19221(3))].">
      <j1 rule="back_rewrite" parents="14621"/>
      <j2 rule="rewrite" parents="19101 19221 10878 15971 19221 10878 19221"/>
    </justification>
  </clause>

  <clause id="19230">
    <literal><![CDATA[
      f(x,f(c_0,f(f(x,f(x,y)),f(z,f(x,y))))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(14592),rewrite(19221(2),10878(3),19221(2),19222(4),19228(4),19101(5))].">
      <j1 rule="back_rewrite" parents="14592"/>
      <j2 rule="rewrite" parents="19221 10878 19221 19222 19228 19101"/>
    </justification>
  </clause>

  <clause id="19231">
    <literal><![CDATA[
      f(x,f(c_0,f(f(x,f(x,y)),y))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(14590),rewrite(19221(2),10878(3),19221(2),19222(4),19228(4),19101(5))].">
      <j1 rule="back_rewrite" parents="14590"/>
      <j2 rule="rewrite" parents="19221 10878 19221 19222 19228 19101"/>
    </justification>
  </clause>

  <clause id="19248">
    <literal><![CDATA[
      f(f(x,y),f(c_0,f(f(y,f(x,y)),f(y,z)))) = y
    ]]></literal>
    <justification jstring="[back_rewrite(15856),rewrite(19102(5),19221(4),10879(4),15973(4),19222(4))].">
      <j1 rule="back_rewrite" parents="15856"/>
      <j2 rule="rewrite" parents="19102 19221 10879 15973 19222"/>
    </justification>
  </clause>

  <clause id="19304">
    <literal><![CDATA[
      f(f(x,y),f(y,f(x,y))) = y
    ]]></literal>
    <justification jstring="[back_rewrite(14625),rewrite(19102(5),19221(4),10879(4),15973(4),19222(3),10879(4),19222(3))].">
      <j1 rule="back_rewrite" parents="14625"/>
      <j2 rule="rewrite" parents="19102 19221 10879 15973 19222 10879 19222"/>
    </justification>
  </clause>

  <clause id="19696">
    <literal><![CDATA[
      f(x,f(c_0,f(y,f(x,y)))) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(18120),rewrite(19222(4),19221(7),14553(7))].">
      <j1 rule="back_rewrite" parents="18120"/>
      <j2 rule="rewrite" parents="19222 19221 14553"/>
    </justification>
  </clause>

  <clause id="19697">
    <literal><![CDATA[
      f(f(x,y),f(f(y,x),c_0)) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(18080),rewrite(19221(3),10878(4),19221(3),10878(4))].">
      <j1 rule="back_rewrite" parents="18080"/>
      <j2 rule="rewrite" parents="19221 10878 19221 10878"/>
    </justification>
  </clause>

  <clause id="19758">
    <literal><![CDATA[
      f(f(f(f(f(c_0,f(x,y)),z),f(c_0,f(f(z,f(x,z)),f(x,y)))),x),f(x,f(f(x,f(x,f(f(f(x,x),u),f(f(f(u,f(f(x,y),u)),x),f(x,y))))),f(x,y)))) = x
    ]]></literal>
    <justification jstring="[back_rewrite(17801),rewrite(19222(7),19222(17),19221(23),19221(28),10878(28))].">
      <j1 rule="back_rewrite" parents="17801"/>
      <j2 rule="rewrite" parents="19222 19222 19221 19221 10878"/>
    </justification>
  </clause>

  <clause id="19830">
    <literal><![CDATA[
      f(f(f(f(c_0,f(x,y)),z),f(f(f(z,f(y,z)),f(x,y)),y)),f(f(y,f(f(f(f(c_0,f(x,y)),z),f(f(f(z,f(y,z)),f(x,y)),y)),y)),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(17165),rewrite(19222(6),19222(17),19222(23),19221(28),10879(28))].">
      <j1 rule="back_rewrite" parents="17165"/>
      <j2 rule="rewrite" parents="19222 19222 19222 19221 10879"/>
    </justification>
  </clause>

  <clause id="19857">
    <literal><![CDATA[
      f(f(x,y),f(f(f(x,x),z),f(c_0,f(f(z,f(f(x,y),z)),x)))) = x
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(17074),rewrite(19222(5),19222(8),19304(8),19222(9),19222(12),19304(12),19222(7))].">
      <j1 rule="back_rewrite" parents="17074"/>
      <j2 rule="rewrite" parents="19222 19222 19304 19222 19222 19304 19222"/>
    </justification>
  </clause>

  <clause id="19875">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),z),f(c_0,f(f(z,f(f(x,y),z)),y)))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(16988),rewrite(19222(5),19222(8),19304(8),19222(9),19222(12),19304(12),19222(7))].">
      <j1 rule="back_rewrite" parents="16988"/>
      <j2 rule="rewrite" parents="19222 19222 19304 19222 19222 19304 19222"/>
    </justification>
  </clause>

  <clause id="19886">
    <literal><![CDATA[
      f(f(f(f(x,f(y,x)),f(x,y)),y),f(f(f(y,y),z),f(c_0,f(f(z,f(f(x,y),z)),y)))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(16894),rewrite(19222(3),19221(8),10879(8),19222(11))].">
      <j1 rule="back_rewrite" parents="16894"/>
      <j2 rule="rewrite" parents="19222 19221 10879 19222"/>
    </justification>
  </clause>

  <clause id="19889">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),z),f(c_0,f(f(z,f(f(y,x),z)),y)))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(16890),rewrite(19222(3),19222(5),19304(5),19222(2),19222(4),19304(4),19222(7))].">
      <j1 rule="back_rewrite" parents="16890"/>
      <j2 rule="rewrite" parents="19222 19222 19304 19222 19222 19304 19222"/>
    </justification>
  </clause>

  <clause id="19909">
    <literal><![CDATA[
      f(f(f(f(x,y),f(y,x)),x),f(f(f(x,x),z),f(c_0,f(f(z,f(f(x,y),z)),x)))) = x
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(16815),rewrite(19222(3),19222(5),19304(5),19222(10))].">
      <j1 rule="back_rewrite" parents="16815"/>
      <j2 rule="rewrite" parents="19222 19222 19304 19222"/>
    </justification>
  </clause>

  <clause id="19924">
    <literal><![CDATA[
      f(x,f(f(f(c_0,f(x,y)),z),f(f(f(z,f(x,z)),f(x,y)),x))) = f(x,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(16681),rewrite(19222(9),19222(14),19304(14),19222(10),19222(15),19304(15),19222(6))].">
      <j1 rule="back_rewrite" parents="16681"/>
      <j2 rule="rewrite" parents="19222 19222 19304 19222 19222 19304 19222"/>
    </justification>
  </clause>

  <clause id="20061">
    <literal><![CDATA[
      f(f(f(f(x,y),f(f(f(x,y),f(f(x,y),f(f(f(c_0,f(x,y)),z),f(f(f(z,f(x,z)),f(x,y)),x)))),x)),x),f(f(f(x,x),u),f(f(f(u,f(f(x,y),u)),x),f(x,v)))) = x
    ]]></literal>
    <justification jstring="[back_rewrite(15890),rewrite(19222(8),19221(15),19222(23))].">
      <j1 rule="back_rewrite" parents="15890"/>
      <j2 rule="rewrite" parents="19222 19221 19222"/>
    </justification>
  </clause>

  <clause id="20080">
    <literal><![CDATA[
      f(f(f(x,f(f(x,f(x,f(f(f(x,x),y),f(f(f(y,f(f(x,z),y)),x),f(x,z))))),f(x,z))),f(x,z)),f(f(f(c_0,f(x,z)),u),f(f(f(u,f(x,u)),f(x,z)),x))) = f(x,z)
    ]]></literal>
    <justification jstring="[back_rewrite(15847),rewrite(19222(5),19221(11),19222(22))].">
      <j1 rule="back_rewrite" parents="15847"/>
      <j2 rule="rewrite" parents="19222 19221 19222"/>
    </justification>
  </clause>

  <clause id="20369">
    <literal><![CDATA[
      f(f(x,y),f(f(f(c_0,f(x,f(x,y))),f(c_0,f(x,y))),f(x,f(z,f(x,f(x,y)))))) = f(x,f(x,y))
    ]]></literal>
    <justification jstring="[back_rewrite(14886),rewrite(19221(9),10878(9),19221(12),10878(12),19228(13))].">
      <j1 rule="back_rewrite" parents="14886"/>
      <j2 rule="rewrite" parents="19221 10878 19221 10878 19228"/>
    </justification>
  </clause>

  <clause id="20387">
    <literal><![CDATA[
      f(f(x,y),f(f(f(c_0,f(y,f(x,y))),f(c_0,f(x,y))),f(y,f(z,f(y,f(x,y)))))) = f(y,f(x,y))
    ]]></literal>
    <justification jstring="[back_rewrite(14842),rewrite(19221(9),10879(9),19221(12),10879(12),19304(13))].">
      <j1 rule="back_rewrite" parents="14842"/>
      <j2 rule="rewrite" parents="19221 10879 19221 10879 19304"/>
    </justification>
  </clause>

  <clause id="20459">
    <literal><![CDATA[
      f(f(x,y),f(y,f(f(f(x,y),f(c_0,f(x,y))),f(z,f(c_0,f(x,y)))))) = f(c_0,f(x,y))
    ]]></literal>
    <justification jstring="[back_rewrite(14657),rewrite(19222(3),10879(4),19222(3),10879(4))].">
      <j1 rule="back_rewrite" parents="14657"/>
      <j2 rule="rewrite" parents="19222 10879 19222 10879"/>
    </justification>
  </clause>

  <clause id="20687">
    <literal><![CDATA[
      f(x,f(f(y,f(x,y)),f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(11996),rewrite(19222(2),10879(3),19222(2),19222(4),19304(4),19222(2))].">
      <j1 rule="back_rewrite" parents="11996"/>
      <j2 rule="rewrite" parents="19222 10879 19222 19222 19304 19222"/>
    </justification>
  </clause>

  <clause id="21214">
    <literal><![CDATA[
      f(f(f(f(f(x,x),y),f(f(f(y,f(f(x,z),y)),x),f(u,x))),f(x,z)),f(c_0,f(f(x,f(x,z)),z))) = f(x,z)
    ]]></literal>
    <justification jstring="[back_rewrite(19216),rewrite(19222(5))].">
      <j1 rule="back_rewrite" parents="19216"/>
      <j2 rule="rewrite" parents="19222"/>
    </justification>
  </clause>

  <clause id="21388">
    <literal><![CDATA[
      f(f(c_0,f(x,f(y,x))),y) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(18121),rewrite(19222(3))].">
      <j1 rule="back_rewrite" parents="18121"/>
      <j2 rule="rewrite" parents="19222"/>
    </justification>
  </clause>

  <clause id="21405">
    <literal><![CDATA[
      f(f(x,y),f(f(y,f(f(f(y,y),z),f(c_0,f(f(z,f(f(y,x),z)),y)))),c_0)) = c_0
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(18102),rewrite(19222(7))].">
      <j1 rule="back_rewrite" parents="18102"/>
      <j2 rule="rewrite" parents="19222"/>
    </justification>
  </clause>

  <clause id="21412">
    <literal><![CDATA[
      f(x,f(f(f(c_0,f(x,y)),f(f(z,f(x,z)),c_0)),f(f(f(c_0,f(f(z,f(x,z)),c_0)),f(x,y)),x))) = f(x,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(18095),rewrite(19222(5),19222(11))].">
      <j1 rule="back_rewrite" parents="18095"/>
      <j2 rule="rewrite" parents="19222 19222"/>
    </justification>
  </clause>

  <clause id="21413">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),f(f(z,f(f(y,x),z)),c_0)),f(f(f(c_0,f(f(z,f(f(y,x),z)),c_0)),y),c_0))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(18093),rewrite(19222(5),19222(12))].">
      <j1 rule="back_rewrite" parents="18093"/>
      <j2 rule="rewrite" parents="19222 19222"/>
    </justification>
  </clause>

  <clause id="21751">
    <literal><![CDATA[
      f(f(f(x,y),f(c_0,f(x,y))),y) = f(y,y)
    ]]></literal>
    <justification jstring="[back_rewrite(17147),rewrite(19222(5))].">
      <j1 rule="back_rewrite" parents="17147"/>
      <j2 rule="rewrite" parents="19222"/>
    </justification>
  </clause>

  <clause id="21790">
    <literal><![CDATA[
      f(f(f(x,x),y),f(f(x,z),f(c_0,f(f(z,f(f(f(x,x),y),z)),f(x,x))))) = f(x,x)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(17044),rewrite(19222(8))].">
      <j1 rule="back_rewrite" parents="17044"/>
      <j2 rule="rewrite" parents="19222"/>
    </justification>
  </clause>

  <clause id="21797">
    <literal><![CDATA[
      f(x,f(x,f(f(f(x,x),y),f(c_0,f(f(y,f(f(z,x),y)),x))))) = f(f(f(x,x),y),f(c_0,f(f(y,f(f(z,x),y)),x)))
    ]]></literal>
    <justification jstring="[back_rewrite(17030),rewrite(19222(6),19222(17))].">
      <j1 rule="back_rewrite" parents="17030"/>
      <j2 rule="rewrite" parents="19222 19222"/>
    </justification>
  </clause>

  <clause id="21830">
    <literal><![CDATA[
      f(x,f(c_0,f(f(f(x,x),y),f(c_0,f(f(y,f(f(z,x),y)),x))))) = f(f(f(x,x),y),f(c_0,f(f(y,f(f(z,x),y)),x)))
    ]]></literal>
    <justification jstring="[back_rewrite(16968),rewrite(19222(7),19222(18))].">
      <j1 rule="back_rewrite" parents="16968"/>
      <j2 rule="rewrite" parents="19222 19222"/>
    </justification>
  </clause>

  <clause id="21914">
    <literal><![CDATA[
      f(f(x,f(y,y)),f(f(y,z),f(c_0,f(f(z,f(f(f(y,y),x),z)),f(y,y))))) = f(y,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(16795),rewrite(19222(8))].">
      <j1 rule="back_rewrite" parents="16795"/>
      <j2 rule="rewrite" parents="19222"/>
    </justification>
  </clause>

  <clause id="21944">
    <literal><![CDATA[
      f(f(x,x),f(f(f(x,x),y),f(c_0,f(f(y,f(f(z,x),y)),x)))) = x
    ]]></literal>
    <justification jstring="[back_rewrite(16747),rewrite(19222(7))].">
      <j1 rule="back_rewrite" parents="16747"/>
      <j2 rule="rewrite" parents="19222"/>
    </justification>
  </clause>

  <clause id="21945">
    <literal><![CDATA[
      f(f(x,x),f(f(f(x,x),y),f(c_0,f(f(y,f(f(x,z),y)),x)))) = x
    ]]></literal>
    <justification jstring="[back_rewrite(16746),rewrite(19222(7))].">
      <j1 rule="back_rewrite" parents="16746"/>
      <j2 rule="rewrite" parents="19222"/>
    </justification>
  </clause>

  <clause id="22411">
    <literal><![CDATA[
      f(f(f(f(c_0,f(x,y)),z),f(f(f(z,f(f(f(x,y),u),z)),f(x,y)),x)),f(f(f(f(c_0,f(x,y)),z),f(f(f(z,f(f(f(x,y),u),z)),f(x,y)),x)),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(14831),rewrite(19222(8),19222(20))].">
      <j1 rule="back_rewrite" parents="14831"/>
      <j2 rule="rewrite" parents="19222 19222"/>
    </justification>
  </clause>

  <clause id="22420">
    <literal><![CDATA[
      f(f(x,y),f(f(x,y),f(f(f(c_0,f(x,y)),z),f(f(f(z,f(x,z)),f(x,y)),x)))) = f(f(f(c_0,f(x,y)),z),f(f(f(z,f(x,z)),f(x,y)),x))
    ]]></literal>
    <justification jstring="[back_rewrite(14783),rewrite(19222(8),19222(20))].">
      <j1 rule="back_rewrite" parents="14783"/>
      <j2 rule="rewrite" parents="19222 19222"/>
    </justification>
  </clause>

  <clause id="22421">
    <literal><![CDATA[
      f(f(x,y),f(f(x,y),f(f(f(c_0,f(x,y)),z),f(f(f(z,f(f(f(x,y),u),z)),f(x,y)),x)))) = f(f(f(c_0,f(x,y)),z),f(f(f(z,f(f(f(x,y),u),z)),f(x,y)),x))
    ]]></literal>
    <justification jstring="[back_rewrite(14777),rewrite(19222(10),19222(24))].">
      <j1 rule="back_rewrite" parents="14777"/>
      <j2 rule="rewrite" parents="19222 19222"/>
    </justification>
  </clause>

  <clause id="22437">
    <literal><![CDATA[
      f(x,f(c_0,f(f(f(y,f(x,y)),c_0),f(z,z)))) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(14555),rewrite(19222(3))].">
      <j1 rule="back_rewrite" parents="14555"/>
      <j2 rule="rewrite" parents="19222"/>
    </justification>
  </clause>

  <clause id="22612">
    <literal><![CDATA[
      f(x,f(x,f(f(f(x,x),y),f(f(f(y,f(f(x,z),y)),x),f(x,u))))) = f(f(f(x,x),y),f(f(f(y,f(f(x,z),y)),x),f(x,u)))
    ]]></literal>
    <justification jstring="[back_rewrite(11449),rewrite(19222(5),19222(16))].">
      <j1 rule="back_rewrite" parents="11449"/>
      <j2 rule="rewrite" parents="19222 19222"/>
    </justification>
  </clause>

  <clause id="23114">
    <literal><![CDATA[
      f(f(f(f(f(x,x),y),f(f(f(y,f(f(x,z),y)),x),f(x,u))),f(z,x)),f(f(z,x),f(f(f(z,f(x,z)),f(z,x)),f(f(z,x),v)))) = f(z,x)
    ]]></literal>
    <justification jstring="[back_rewrite(2765),rewrite(19222(5),19222(14))].">
      <j1 rule="back_rewrite" parents="2765"/>
      <j2 rule="rewrite" parents="19222 19222"/>
    </justification>
  </clause>

  <clause id="23189">
    <literal><![CDATA[
      f(x,f(f(x,y),f(c_0,f(z,f(x,x))))) = f(x,x)
    ]]></literal>
    <justification jstring="[back_rewrite(11051),rewrite(19228(5),12616(3))].">
      <j1 rule="back_rewrite" parents="11051"/>
      <j2 rule="rewrite" parents="19228 12616"/>
    </justification>
  </clause>

  <clause id="23245">
    <literal><![CDATA[
      f(f(x,y),f(c_0,f(x,y))) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(14294),rewrite(21751(9),19102(5)),flip(a)].">
      <j1 rule="back_rewrite" parents="14294"/>
      <j2 rule="rewrite" parents="21751 19102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23331">
    <literal><![CDATA[
      f(f(f(f(x,y),f(f(f(f(c_0,f(x,y)),z),f(f(f(z,f(x,z)),f(x,y)),x)),x)),x),f(f(f(x,x),u),f(f(f(u,f(f(x,y),u)),x),f(x,v)))) = x
    ]]></literal>
    <justification jstring="[back_rewrite(20061),rewrite(22420(15))].">
      <j1 rule="back_rewrite" parents="20061"/>
      <j2 rule="rewrite" parents="22420"/>
    </justification>
  </clause>

  <clause id="23456">
    <literal><![CDATA[
      f(f(f(x,f(f(f(f(x,x),y),f(f(f(y,f(f(x,z),y)),x),f(x,z))),f(x,z))),f(x,z)),f(f(f(c_0,f(x,z)),u),f(f(f(u,f(x,u)),f(x,z)),x))) = f(x,z)
    ]]></literal>
    <justification jstring="[back_rewrite(20080),rewrite(22612(11))].">
      <j1 rule="back_rewrite" parents="20080"/>
      <j2 rule="rewrite" parents="22612"/>
    </justification>
  </clause>

  <clause id="23459">
    <literal><![CDATA[
      f(f(f(f(f(c_0,f(x,y)),z),f(c_0,f(f(z,f(x,z)),f(x,y)))),x),f(x,f(f(f(f(x,x),u),f(f(f(u,f(f(x,y),u)),x),f(x,y))),f(x,y)))) = x
    ]]></literal>
    <justification jstring="[back_rewrite(19758),rewrite(22612(23))].">
      <j1 rule="back_rewrite" parents="19758"/>
      <j2 rule="rewrite" parents="22612"/>
    </justification>
  </clause>

  <clause id="23487">
    <literal><![CDATA[
      f(f(x,y),f(y,f(c_0,f(z,f(c_0,f(x,y)))))) = f(c_0,f(x,y))
    ]]></literal>
    <justification jstring="[back_rewrite(20459),rewrite(23245(6))].">
      <j1 rule="back_rewrite" parents="20459"/>
      <j2 rule="rewrite" parents="23245"/>
    </justification>
  </clause>

  <clause id="23529">
    <literal><![CDATA[
      f(f(x,y),f(y,f(f(f(f(y,y),z),f(c_0,f(f(z,f(f(y,x),z)),y))),y))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(19857(a,1),19889(a,1,2,2,2,1,2)),rewrite(21945(12),19222(13),14387(15))].">
      <j1 rule="para" parents="19857 19889"/>
      <j2 rule="rewrite" parents="21945 19222 14387"/>
    </justification>
  </clause>

  <clause id="23534">
    <literal><![CDATA[
      f(f(x,y),c_0) = f(c_0,f(x,y))
    ]]></literal>
    <justification jstring="[para(14382(a,1),2286(a,1,2)),rewrite(13294(7,R),14553(5))].">
      <j1 rule="para" parents="14382 2286"/>
      <j2 rule="rewrite" parents="13294 14553"/>
    </justification>
  </clause>

  <clause id="23548">
    <literal><![CDATA[
      f(x,f(c_0,f(f(c_0,f(y,f(x,y))),f(z,z)))) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(22437),rewrite(23534(5))].">
      <j1 rule="back_rewrite" parents="22437"/>
      <j2 rule="rewrite" parents="23534"/>
    </justification>
  </clause>

  <clause id="23653">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),f(c_0,f(z,f(f(y,x),z)))),f(c_0,f(f(z,f(f(y,x),z)),y)))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(21413),rewrite(23534(7),23534(14),14553(15),23534(14))].">
      <j1 rule="back_rewrite" parents="21413"/>
      <j2 rule="rewrite" parents="23534 23534 14553 23534"/>
    </justification>
  </clause>

  <clause id="23654">
    <literal><![CDATA[
      f(x,f(f(f(c_0,f(x,y)),f(c_0,f(z,f(x,z)))),f(f(f(z,f(x,z)),f(x,y)),x))) = f(x,y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(21412),rewrite(23534(7),23534(13),14553(14))].">
      <j1 rule="back_rewrite" parents="21412"/>
      <j2 rule="rewrite" parents="23534 23534 14553"/>
    </justification>
  </clause>

  <clause id="23659">
    <literal><![CDATA[
      f(f(x,y),f(c_0,f(y,f(f(f(y,y),z),f(c_0,f(f(z,f(f(y,x),z)),y)))))) = c_0
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[back_rewrite(21405),rewrite(23534(13))].">
      <j1 rule="back_rewrite" parents="21405"/>
      <j2 rule="rewrite" parents="23534"/>
    </justification>
  </clause>

  <clause id="23776">
    <literal><![CDATA[
      f(f(x,y),f(c_0,f(y,x))) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(19697),rewrite(23534(4))].">
      <j1 rule="back_rewrite" parents="19697"/>
      <j2 rule="rewrite" parents="23534"/>
    </justification>
  </clause>

  <clause id="23890">
    <literal><![CDATA[
      f(f(c_0,f(x,f(y,x))),f(c_0,f(y,x))) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(19139),rewrite(23534(7))].">
      <j1 rule="back_rewrite" parents="19139"/>
      <j2 rule="rewrite" parents="23534"/>
    </justification>
  </clause>

  <clause id="23891">
    <literal><![CDATA[
      f(f(c_0,f(x,f(x,y))),f(c_0,f(x,y))) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(19138),rewrite(23534(7))].">
      <j1 rule="back_rewrite" parents="19138"/>
      <j2 rule="rewrite" parents="23534"/>
    </justification>
  </clause>

  <clause id="23905">
    <literal><![CDATA[
      f(f(c_0,f(x,f(y,y))),f(c_0,f(y,f(z,z)))) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(19039),rewrite(23534(4))].">
      <j1 rule="back_rewrite" parents="19039"/>
      <j2 rule="rewrite" parents="23534"/>
    </justification>
  </clause>

  <clause id="23970">
    <literal><![CDATA[
      f(f(x,y),f(c_0,f(y,f(z,f(y,f(x,y)))))) = f(y,f(x,y))
    ]]></literal>
    <justification jstring="[back_rewrite(20387),rewrite(23890(9))].">
      <j1 rule="back_rewrite" parents="20387"/>
      <j2 rule="rewrite" parents="23890"/>
    </justification>
  </clause>

  <clause id="23972">
    <literal><![CDATA[
      f(f(x,y),f(c_0,f(x,f(z,f(x,f(x,y)))))) = f(x,f(x,y))
    ]]></literal>
    <justification jstring="[back_rewrite(20369),rewrite(23891(9))].">
      <j1 rule="back_rewrite" parents="20369"/>
      <j2 rule="rewrite" parents="23891"/>
    </justification>
  </clause>

  <clause id="24065">
    <literal><![CDATA[
      f(f(x,y),f(y,f(f(f(f(y,y),f(c_0,f(f(c_0,f(y,x)),z))),f(c_0,f(f(f(c_0,f(y,x)),z),y))),y))) = y
    ]]></literal>
    <justification jstring="[para(14431(a,1),23529(a,1,2,2,1,2,2,1,2)),rewrite(13294(6,R),13294(14,R),19221(18),14553(18))].">
      <j1 rule="para" parents="14431 23529"/>
      <j2 rule="rewrite" parents="13294 13294 19221 14553"/>
    </justification>
  </clause>

  <clause id="24269">
    <literal><![CDATA[
      f(f(f(f(x,x),y),f(c_0,f(f(y,f(f(z,x),y