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

<!DOCTYPE proofs SYSTEM "proof3.dtd">

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

<proofs number_of_proofs="2">

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

<heading><![CDATA[
Prover9 (32) version 2009-02A, February 2009.
Process 12434 was started by mccune on cleo,
Wed Feb 25 10:24:51 2009
The command was "/home/mccune/bin/prover9 -f MOL-base.in".
]]></heading>

<proof number="1" length="253" max_count="59">

<comments><![CDATA[
% Proof 1 at 169.34 (+ 0.49) seconds: A_SS.
% Length of proof is 253.
% Level of proof is 46.
% Maximum clause weight is 59.
% Given clauses 1336.

]]></comments>

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

  <clause id="3" type="assumption">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),z),f(f(f(f(f(y,x),z),z),y),f(y,u)))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(MOL_SS)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="4" type="deny">
    <literal><![CDATA[
      f(c1,f(f(c2,c3),f(c2,c3))) != f(c2,f(f(c1,c3),f(c1,c3)))
    ]]></literal>
    <attribute><![CDATA[
      answer(A_SS)
    ]]></attribute>
    <justification jstring="[deny(1)].">
      <j1 rule="deny" parents="1"/>
    </justification>
  </clause>

  <clause id="6">
    <literal><![CDATA[
      f(f(x,y),f(y,f(f(f(f(f(y,x),f(f(f(y,y),z),f(f(f(f(f(y,y),z),z),y),f(y,u)))),f(f(f(y,y),z),f(f(f(f(f(y,y),z),z),y),f(y,u)))),y),f(y,w)))) = y
    ]]></literal>
    <justification jstring="[para(3(a,1),3(a,1,2,1))].">
      <j1 rule="para" parents="3 3"/>
    </justification>
  </clause>

  <clause id="7">
    <literal><![CDATA[
      f(f(f(f(f(x,x),y),f(f(f(f(f(x,z),y),y),x),f(x,u))),f(z,x)),f(f(f(f(z,x),f(z,x)),w),f(f(f(f(x,w),w),f(z,x)),f(f(z,x),v5)))) = f(z,x)
    ]]></literal>
    <justification jstring="[para(3(a,1),3(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="3 3"/>
    </justification>
  </clause>

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

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

  <clause id="10">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),z),y)) = y
    ]]></literal>
    <justification jstring="[para(6(a,1),3(a,1,2,2))].">
      <j1 rule="para" parents="6 3"/>
    </justification>
  </clause>

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

  <clause id="14">
    <literal><![CDATA[
      f(x,f(f(x,y),f(f(f(f(f(f(x,x),f(z,x)),y),y),f(x,x)),f(f(x,x),u)))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(13(a,1),3(a,1,1)),rewrite([13(3)])].">
      <j1 rule="para" parents="13 3"/>
      <j2 rule="rewrite" parents="13"/>
    </justification>
  </clause>

  <clause id="16">
    <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(13(a,1),3(a,1,2,1))].">
      <j1 rule="para" parents="13 3"/>
    </justification>
  </clause>

  <clause id="17">
    <literal><![CDATA[
      f(f(f(x,x),f(y,x)),f(f(f(f(y,x),f(y,x)),z),f(f(f(f(x,z),z),f(y,x)),f(f(y,x),u)))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(13(a,1),3(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="13 3"/>
    </justification>
  </clause>

  <clause id="18">
    <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(13(a,1),3(a,1,2,2,1,1,1))].">
      <j1 rule="para" parents="13 3"/>
    </justification>
  </clause>

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

  <clause id="24">
    <literal><![CDATA[
      f(f(x,y),f(y,f(f(y,y),f(y,z)))) = y
    ]]></literal>
    <justification jstring="[back_rewrite(16),rewrite([22(7)])].">
      <j1 rule="back_rewrite" parents="16"/>
      <j2 rule="rewrite" parents="22"/>
    </justification>
  </clause>

  <clause id="27">
    <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(22(a,1),3(a,1,2,2,1,1,1))].">
      <j1 rule="para" parents="22 3"/>
    </justification>
  </clause>

  <clause id="34">
    <literal><![CDATA[
      f(f(f(x,x),y),x) = f(x,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),13(a,1,1)),rewrite([10(7)]),flip(a)].">
      <j1 rule="para" parents="10 13"/>
      <j2 rule="rewrite" parents="10"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38">
    <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(34(a,1),3(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="34 3"/>
    </justification>
  </clause>

  <clause id="39">
    <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(34(a,1),3(a,1,2,2,1,1))].">
      <j1 rule="para" parents="34 3"/>
    </justification>
  </clause>

  <clause id="42">
    <literal><![CDATA[
      f(f(x,y),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(13(a,1),34(a,1,1,1)),rewrite([13(6)])].">
      <j1 rule="para" parents="13 34"/>
      <j2 rule="rewrite" parents="13"/>
    </justification>
  </clause>

  <clause id="43">
    <literal><![CDATA[
      f(f(f(f(f(x,x),y),f(f(f(f(f(x,z),y),y),x),f(x,u))),f(z,x)),f(f(f(f(z,x),f(z,x)),w),f(f(f(f(x,w),w),f(z,x)),x))) = f(z,x)
    ]]></literal>
    <justification jstring="[para(3(a,1),7(a,1,2,2,2))].">
      <j1 rule="para" parents="3 7"/>
    </justification>
  </clause>

  <clause id="52">
    <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(34(a,1),7(a,1,1)),rewrite([42(3),42(3)])].">
      <j1 rule="para" parents="34 7"/>
      <j2 rule="rewrite" parents="42 42"/>
    </justification>
  </clause>

  <clause id="55">
    <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(42(a,1),3(a,1,2,2,1,1))].">
      <j1 rule="para" parents="42 3"/>
    </justification>
  </clause>

  <clause id="56">
    <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(42(a,1),3(a,1,2,2,2))].">
      <j1 rule="para" parents="42 3"/>
    </justification>
  </clause>

  <clause id="57">
    <literal><![CDATA[
      f(x,f(f(y,x),f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(3(a,1),42(a,1,1))].">
      <j1 rule="para" parents="3 42"/>
    </justification>
  </clause>

  <clause id="63">
    <literal><![CDATA[
      f(x,f(f(x,y),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(42(a,1),42(a,1,1))].">
      <j1 rule="para" parents="42 42"/>
    </justification>
  </clause>

  <clause id="65">
    <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(57(a,1),3(a,1,2,1))].">
      <j1 rule="para" parents="57 3"/>
    </justification>
  </clause>

  <clause id="68">
    <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(57(a,1),3(a,1,2,2,2))].">
      <j1 rule="para" parents="57 3"/>
    </justification>
  </clause>

  <clause id="69">
    <literal><![CDATA[
      f(f(f(f(x,x),y),f(f(f(f(f(x,z),y),y),x),f(x,u))),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(3(a,1),57(a,1,2,1)),rewrite([3(20),3(22)])].">
      <j1 rule="para" parents="3 57"/>
      <j2 rule="rewrite" parents="3 3"/>
    </justification>
  </clause>

  <clause id="77">
    <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(x,u)))) = x
    ]]></literal>
    <justification jstring="[para(63(a,1),3(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="63 3"/>
    </justification>
  </clause>

  <clause id="84">
    <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(24(a,1),34(a,1)),flip(a)].">
      <j1 rule="para" parents="24 34"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="96">
    <literal><![CDATA[
      f(f(f(f(x,x),f(f(f(y,y),z),f(f(f(f(f(y,x),z),z),y),f(y,u)))),f(f(f(y,f(f(f(y,y),z),f(f(f(f(f(y,x),z),z),y),f(y,u)))),x),f(x,w))),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(8(a,1),57(a,1,2,1)),rewrite([8(52),8(54)])].">
      <j1 rule="para" parents="8 57"/>
      <j2 rule="rewrite" parents="8 8"/>
    </justification>
  </clause>

  <clause id="129">
    <literal><![CDATA[
      f(f(f(x,x),f(y,x)),f(f(f(f(y,x),f(y,x)),z),f(f(f(f(x,z),z),f(y,x)),x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(13(a,1),9(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="13 9"/>
    </justification>
  </clause>

  <clause id="130">
    <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(13(a,1),9(a,1,2,2,1,1,1))].">
      <j1 rule="para" parents="13 9"/>
    </justification>
  </clause>

  <clause id="132">
    <literal><![CDATA[
      f(f(x,f(y,f(x,x))),f(f(f(f(y,f(x,x)),f(y,f(x,x))),z),f(f(f(f(f(x,x),z),z),f(y,f(x,x))),f(x,x)))) = f(y,f(x,x))
    ]]></literal>
    <justification jstring="[para(22(a,1),9(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="22 9"/>
    </justification>
  </clause>

  <clause id="136">
    <literal><![CDATA[
      f(f(f(x,y),f(x,y)),f(f(f(f(x,y),f(x,y)),f(x,y)),f(f(f(f(x,y),f(x,y)),f(x,y)),y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(34(a,1),9(a,1,2,2,1,1))].">
      <j1 rule="para" parents="34 9"/>
    </justification>
  </clause>

  <clause id="138">
    <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)),y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(42(a,1),9(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="42 9"/>
    </justification>
  </clause>

  <clause id="139">
    <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(42(a,1),9(a,1,2,2,1,1))].">
      <j1 rule="para" parents="42 9"/>
    </justification>
  </clause>

  <clause id="159">
    <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(39(a,1),57(a,1,2,1)),rewrite([39(16),39(18)])].">
      <j1 rule="para" parents="39 57"/>
      <j2 rule="rewrite" parents="39 39"/>
    </justification>
  </clause>

  <clause id="160">
    <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(57(a,1),39(a,1,2,2,2))].">
      <j1 rule="para" parents="57 39"/>
    </justification>
  </clause>

  <clause id="167">
    <literal><![CDATA[
      f(x,f(f(x,x),f(x,y))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(84(a,1),13(a,1,1)),rewrite([84(9)]),flip(a)].">
      <j1 rule="para" parents="84 13"/>
      <j2 rule="rewrite" parents="84"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="174">
    <literal><![CDATA[
      f(f(x,y),f(y,f(f(f(f(f(y,x),f(y,f(f(y,y),z))),f(y,f(f(y,y),z))),y),f(y,u)))) = y
    ]]></literal>
    <justification jstring="[para(167(a,1),3(a,1,2,1)),rewrite([42(4),42(5),42(9)])].">
      <j1 rule="para" parents="167 3"/>
      <j2 rule="rewrite" parents="42 42 42"/>
    </justification>
  </clause>

  <clause id="176">
    <literal><![CDATA[
      f(f(x,y),f(f(f(x,y),f(x,y)),y)) = f(f(x,y),f(x,y))
    ]]></literal>
    <justification jstring="[para(3(a,1),167(a,1,2,2))].">
      <j1 rule="para" parents="3 167"/>
    </justification>
  </clause>

  <clause id="177">
    <literal><![CDATA[
      f(f(x,x),f(x,f(f(x,x),y))) = x
    ]]></literal>
    <justification jstring="[para(13(a,1),167(a,1,2,1)),rewrite([42(8)])].">
      <j1 rule="para" parents="13 167"/>
      <j2 rule="rewrite" parents="42"/>
    </justification>
  </clause>

  <clause id="179">
    <literal><![CDATA[
      f(f(x,y),f(f(f(x,y),f(x,y)),x)) = f(f(x,y),f(x,y))
    ]]></literal>
    <justification jstring="[para(42(a,1),167(a,1,2,2))].">
      <j1 rule="para" parents="42 167"/>
    </justification>
  </clause>

  <clause id="180">
    <literal><![CDATA[
      f(x,f(f(x,x),f(y,x))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(57(a,1),167(a,1,2,2))].">
      <j1 rule="para" parents="57 167"/>
    </justification>
  </clause>

  <clause id="184">
    <literal><![CDATA[
      f(f(x,x),f(x,f(f(f(x,f(x,f(f(x,x),y))),x),f(x,z)))) = x
    ]]></literal>
    <justification jstring="[para(177(a,1),3(a,1,2,2,1,1,1)),rewrite([177(6)])].">
      <j1 rule="para" parents="177 3"/>
      <j2 rule="rewrite" parents="177"/>
    </justification>
  </clause>

  <clause id="186">
    <literal><![CDATA[
      f(f(x,x),f(x,f(y,f(x,x)))) = x
    ]]></literal>
    <justification jstring="[para(57(a,1),177(a,1,2,2))].">
      <j1 rule="para" parents="57 177"/>
    </justification>
  </clause>

  <clause id="216">
    <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(57(a,1),159(a,1,1,2,2))].">
      <j1 rule="para" parents="57 159"/>
    </justification>
  </clause>

  <clause id="221">
    <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(13(a,1),160(a,1,1)),rewrite([42(3),42(5)])].">
      <j1 rule="para" parents="13 160"/>
      <j2 rule="rewrite" parents="42 42"/>
    </justification>
  </clause>

  <clause id="226">
    <literal><![CDATA[
      f(f(x,y),f(y,f(f(f(f(f(f(f(x,y),f(x,y)),f(z,f(x,y))),f(y,y)),f(y,y)),f(f(x,y),f(x,y))),f(f(f(x,y),f(x,y)),u)))) = f(f(x,y),f(x,y))
    ]]></literal>
    <justification jstring="[para(13(a,1),14(a,1,2,1))].">
      <j1 rule="para" parents="13 14"/>
    </justification>
  </clause>

  <clause id="252">
    <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(13(a,1),216(a,1,1,1,1)),rewrite([42(5),42(11)])].">
      <j1 rule="para" parents="13 216"/>
      <j2 rule="rewrite" parents="42 42"/>
    </justification>
  </clause>

  <clause id="273">
    <literal><![CDATA[
      f(f(x,x),f(x,f(f(f(x,f(x,f(f(x,x),y))),x),f(z,x)))) = x
    ]]></literal>
    <justification jstring="[para(57(a,1),184(a,1,2,2,2))].">
      <j1 rule="para" parents="57 184"/>
    </justification>
  </clause>

  <clause id="287">
    <literal><![CDATA[
      f(f(x,x),f(f(f(x,f(x,x)),f(f(x,f(x,x)),f(y,f(x,x)))),f(f(x,f(x,x)),f(f(x,f(x,x)),f(y,f(x,x)))))) = f(f(x,f(x,x)),f(f(x,f(x,x)),f(y,f(x,x))))
    ]]></literal>
    <justification jstring="[para(221(a,1),13(a,1,1))].">
      <j1 rule="para" parents="221 13"/>
    </justification>
  </clause>

  <clause id="289">
    <literal><![CDATA[
      f(f(f(f(x,y),f(x,y)),f(z,f(x,y))),f(f(f(f(z,f(x,y)),f(z,f(x,y))),f(y,y)),f(f(f(y,f(y,y)),f(z,f(x,y))),f(f(z,f(x,y)),u)))) = f(z,f(x,y))
    ]]></literal>
    <justification jstring="[para(13(a,1),17(a,1,2,2,1,1,1))].">
      <j1 rule="para" parents="13 17"/>
    </justification>
  </clause>

  <clause id="290">
    <literal><![CDATA[
      f(f(x,f(y,f(x,x))),f(f(f(f(y,f(x,x)),f(y,f(x,x))),x),f(f(f(x,x),f(y,f(x,x))),f(f(y,f(x,x)),z)))) = f(y,f(x,x))
    ]]></literal>
    <justification jstring="[para(34(a,1),17(a,1,2,2,1,1)),rewrite([42(3)])].">
      <j1 rule="para" parents="34 17"/>
      <j2 rule="rewrite" parents="42"/>
    </justification>
  </clause>

  <clause id="309">
    <literal><![CDATA[
      f(f(x,x),f(f(x,f(x,f(f(x,x),y))),x)) = x
    ]]></literal>
    <justification jstring="[para(57(a,1),273(a,1,2))].">
      <j1 rule="para" parents="57 273"/>
    </justification>
  </clause>

  <clause id="316">
    <literal><![CDATA[
      f(x,f(f(f(x,x),f(f(x,x),f(x,y))),f(x,x))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(13(a,1),309(a,1,1)),rewrite([42(5)])].">
      <j1 rule="para" parents="13 309"/>
      <j2 rule="rewrite" parents="42"/>
    </justification>
  </clause>

  <clause id="331">
    <literal><![CDATA[
      f(f(x,x),f(f(y,f(x,x)),f(f(f(f(y,f(x,x)),f(f(y,f(x,x)),f(y,f(x,x)))),x),f(x,z)))) = x
    ]]></literal>
    <justification jstring="[para(22(a,1),18(a,1,1)),rewrite([57(8)])].">
      <j1 rule="para" parents="22 18"/>
      <j2 rule="rewrite" parents="57"/>
    </justification>
  </clause>

  <clause id="333">
    <literal><![CDATA[
      f(f(f(x,x),x),f(f(f(x,x),x),f(f(x,x),f(x,y)))) = x
    ]]></literal>
    <justification jstring="[para(34(a,1),18(a,1,2,2,1)),rewrite([42(6)])].">
      <j1 rule="para" parents="34 18"/>
      <j2 rule="rewrite" parents="42"/>
    </justification>
  </clause>

  <clause id="337">
    <literal><![CDATA[
      f(f(x,f(y,z)),f(f(f(f(y,z),f(y,z)),f(x,x)),f(f(f(x,f(x,x)),f(y,z)),y))) = f(y,z)
    ]]></literal>
    <justification jstring="[para(42(a,1),18(a,1,2,2,2))].">
      <j1 rule="para" parents="42 18"/>
    </justification>
  </clause>

  <clause id="346">
    <literal><![CDATA[
      f(x,f(f(f(x,x),x),f(x,f(f(x,x),y)))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(216(a,1),18(a,1,2,2,1)),rewrite([13(4),42(3),57(6)])].">
      <j1 rule="para" parents="216 18"/>
      <j2 rule="rewrite" parents="13 42 57"/>
    </justification>
  </clause>

  <clause id="347">
    <literal><![CDATA[
      f(f(x,x),f(f(x,f(x,x)),f(f(x,x),f(x,y)))) = x
    ]]></literal>
    <justification jstring="[para(252(a,1),18(a,1,2,2,1)),rewrite([22(3),57(8)])].">
      <j1 rule="para" parents="252 18"/>
      <j2 rule="rewrite" parents="22 57"/>
    </justification>
  </clause>

  <clause id="366">
    <literal><![CDATA[
      f(f(x,x),f(f(x,f(x,x)),f(f(x,x),f(y,x)))) = x
    ]]></literal>
    <justification jstring="[para(57(a,1),347(a,1,2,2,2))].">
      <j1 rule="para" parents="57 347"/>
    </justification>
  </clause>

  <clause id="419">
    <literal><![CDATA[
      f(f(f(x,x),x),f(f(f(x,x),x),f(f(x,x),f(y,x)))) = x
    ]]></literal>
    <justification jstring="[para(57(a,1),333(a,1,2,2,2))].">
      <j1 rule="para" parents="57 333"/>
    </justification>
  </clause>

  <clause id="435">
    <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(27(a,1),57(a,1,2,1)),rewrite([27(19),27(21)])].">
      <j1 rule="para" parents="27 57"/>
      <j2 rule="rewrite" parents="27 27"/>
    </justification>
  </clause>

  <clause id="437">
    <literal><![CDATA[
      f(f(f(x,x),y),f(f(f(y,y),x),f(f(f(f(x,x),x),y),f(z,y)))) = y
    ]]></literal>
    <justification jstring="[para(57(a,1),27(a,1,2,2,2))].">
      <j1 rule="para" parents="57 27"/>
    </justification>
  </clause>

  <clause id="462">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(x,f(x,x)),f(x,f(y,f(x,x))))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(13(a,1),419(a,1,1,1)),rewrite([42(5),42(7)])].">
      <j1 rule="para" parents="13 419"/>
      <j2 rule="rewrite" parents="42 42"/>
    </justification>
  </clause>

  <clause id="526">
    <literal><![CDATA[
      f(f(f(x,f(y,y)),f(f(f(f(x,f(y,y)),f(f(x,f(y,y)),f(x,f(y,y)))),y),f(y,z))),f(y,y)) = y
    ]]></literal>
    <justification jstring="[para(57(a,1),435(a,1,1,1)),rewrite([42(13)])].">
      <j1 rule="para" parents="57 435"/>
      <j2 rule="rewrite" parents="42"/>
    </justification>
  </clause>

  <clause id="555">
    <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(57(a,1),52(a,1,2,2,2))].">
      <j1 rule="para" parents="57 52"/>
    </justification>
  </clause>

  <clause id="574">
    <literal><![CDATA[
      f(f(x,x),f(x,f(f(f(x,f(f(f(x,x),x),f(f(f(x,x),x),f(x,y)))),x),f(z,x)))) = x
    ]]></literal>
    <justification jstring="[para(39(a,1),68(a,1,2,2,1,1,1)),rewrite([39(10)])].">
      <j1 rule="para" parents="39 68"/>
      <j2 rule="rewrite" parents="39"/>
    </justification>
  </clause>

  <clause id="666">
    <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="[para(43(a,1),22(a,1,1)),rewrite([176(9)]),flip(a)].">
      <j1 rule="para" parents="43 22"/>
      <j2 rule="rewrite" parents="176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="673">
    <literal><![CDATA[
      f(f(f(f(x,x),x),f(f(x,x),x)),x) = f(f(x,x),x)
    ]]></literal>
    <justification jstring="[para(43(a,1),186(a,1,2,2)),rewrite([666(13),34(14),42(11)]),flip(a)].">
      <j1 rule="para" parents="43 186"/>
      <j2 rule="rewrite" parents="666 34 42"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="678">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),f(x,f(x,x))),f(x,x)) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(13(a,1),673(a,1,1,1,1)),rewrite([42(5),42(10)])].">
      <j1 rule="para" parents="13 673"/>
      <j2 rule="rewrite" parents="42 42"/>
    </justification>
  </clause>

  <clause id="682">
    <literal><![CDATA[
      f(f(x,f(f(x,x),x)),f(f(f(x,x),x),f(f(f(x,x),f(f(x,x),x)),f(f(f(x,x),x),y)))) = f(f(x,x),x)
    ]]></literal>
    <justification jstring="[para(673(a,1),38(a,1,2,1)),rewrite([34(8)])].">
      <j1 rule="para" parents="673 38"/>
      <j2 rule="rewrite" parents="34"/>
    </justification>
  </clause>

  <clause id="684">
    <literal><![CDATA[
      f(f(f(x,x),x),f(f(f(x,x),y),f(f(f(f(f(f(x,x),x),y),y),x),f(z,x)))) = x
    ]]></literal>
    <justification jstring="[para(673(a,1),68(a,1,1)),rewrite([57(10)])].">
      <j1 rule="para" parents="673 68"/>
      <j2 rule="rewrite" parents="57"/>
    </justification>
  </clause>

  <clause id="890">
    <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(13(a,1),55(a,1,2,2,1)),rewrite([42(5),57(8)])].">
      <j1 rule="para" parents="13 55"/>
      <j2 rule="rewrite" parents="42 57"/>
    </justification>
  </clause>

  <clause id="891">
    <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(22(a,1),55(a,1,2,2,1)),rewrite([57(9)])].">
      <j1 rule="para" parents="22 55"/>
      <j2 rule="rewrite" parents="57"/>
    </justification>
  </clause>

  <clause id="919">
    <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(57(a,1),891(a,1,2,2,2))].">
      <j1 rule="para" parents="57 891"/>
    </justification>
  </clause>

  <clause id="1437">
    <literal><![CDATA[
      f(f(f(x,x),x),f(x,f(f(f(f(f(f(x,x),x),f(x,f(f(x,x),y))),f(x,f(f(x,x),y))),x),f(z,x)))) = x
    ]]></literal>
    <justification jstring="[para(167(a,1),684(a,1,2,1)),rewrite([42(5),42(7),42(11)])].">
      <j1 rule="para" parents="167 684"/>
      <j2 rule="rewrite" parents="42 42 42"/>
    </justification>
  </clause>

  <clause id="1847">
    <literal><![CDATA[
      f(f(x,x),f(f(x,f(f(f(x,x),x),f(f(f(x,x),x),f(x,y)))),x)) = x
    ]]></literal>
    <justification jstring="[para(57(a,1),574(a,1,2))].">
      <j1 rule="para" parents="57 574"/>
    </justification>
  </clause>

  <clause id="2174">
    <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(42(a,1),129(a,1,2,2,1,1))].">
      <j1 rule="para" parents="42 129"/>
    </justification>
  </clause>

  <clause id="2218">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(x,f(f(x,x),y))) = x
    ]]></literal>
    <justification jstring="[para(18(a,1),130(a,1,2,2,1)),rewrite([42(3),42(6),42(10),42(13),42(16),42(19),42(27),177(27),22(23),42(9),42(3),42(6)]),flip(a)].">
      <j1 rule="para" parents="18 130"/>
      <j2 rule="rewrite" parents="42 42 42 42 42 42 42 177 22 42 42 42"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2220">
    <literal><![CDATA[
      f(f(f(x,x),x),f(x,f(f(x,x),y))) = x
    ]]></literal>
    <justification jstring="[para(346(a,1),130(a,1,1)),rewrite([890(25),177(21),22(17),42(3)]),flip(a)].">
      <j1 rule="para" parents="346 130"/>
      <j2 rule="rewrite" parents="890 177 22 42"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2222">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(x,x),f(x,y))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(347(a,1),130(a,1,1)),rewrite([42(16),42(18),891(23),167(18),13(16)]),flip(a)].">
      <j1 rule="para" parents="347 130"/>
      <j2 rule="rewrite" parents="42 42 891 167 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2226">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(x,x),f(y,x))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(366(a,1),130(a,1,1)),rewrite([42(16),42(18),919(23),180(18),13(16)]),flip(a)].">
      <j1 rule="para" parents="366 130"/>
      <j2 rule="rewrite" parents="42 42 919 180 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2232">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(x,f(y,f(x,x)))) = x
    ]]></literal>
    <justification jstring="[para(462(a,1),130(a,1,2,2,1)),rewrite([186(27),22(23),42(9)]),flip(a)].">
      <j1 rule="para" parents="462 130"/>
      <j2 rule="rewrite" parents="186 22 42"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2238">
    <literal><![CDATA[
      f(f(f(x,x),x),f(f(x,x),f(y,x))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(437(a,1),130(a,1,2,2,1)),rewrite([42(4),42(4),42(8),34(6),42(7),42(11),42(11),42(15),34(13),42(14),42(17),42(17),42(21),34(19),42(20),42(24),42(25),42(27),34(25),42(26),180(26),13(24),34(9),42(4),42(4),42(8),34(6),42(7)]),flip(a)].">
      <j1 rule="para" parents="437 130"/>
      <j2 rule="rewrite" parents="42 42 42 34 42 42 42 42 34 42 42 42 42 34 42 42 42 42 34 42 180 13 34 42 42 42 34 42"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2268">
    <literal><![CDATA[
      f(f(f(x,x),x),f(x,f(f(f(x,f(x,f(f(x,x),y))),x),f(z,x)))) = x
    ]]></literal>
    <justification jstring="[back_rewrite(1437),rewrite([2220(8)])].">
      <j1 rule="back_rewrite" parents="1437"/>
      <j2 rule="rewrite" parents="2220"/>
    </justification>
  </clause>

  <clause id="2436">
    <literal><![CDATA[
      f(f(f(x,y),f(f(x,y),f(x,y))),f(f(f(x,y),f(x,y)),y)) = f(f(x,y),f(x,y))
    ]]></literal>
    <justification jstring="[para(3(a,1),2222(a,1,2,2))].">
      <j1 rule="para" parents="3 2222"/>
    </justification>
  </clause>

  <clause id="2438">
    <literal><![CDATA[
      f(f(f(x,y),f(f(x,y),f(x,y))),f(f(f(x,y),f(x,y)),x)) = f(f(x,y),f(x,y))
    ]]></literal>
    <justification jstring="[para(42(a,1),2222(a,1,2,2))].">
      <j1 rule="para" parents="42 2222"/>
    </justification>
  </clause>

  <clause id="2632">
    <literal><![CDATA[
      f(f(f(x,x),x),f(f(x,f(x,f(f(x,x),y))),x)) = x
    ]]></literal>
    <justification jstring="[para(57(a,1),2268(a,1,2))].">
      <j1 rule="para" parents="57 2268"/>
    </justification>
  </clause>

  <clause id="2679">
    <literal><![CDATA[
      f(f(x,f(x,f(f(x,x),y))),x) = f(x,x)
    ]]></literal>
    <justification jstring="[para(2632(a,1),129(a,1,2,2,1)),rewrite([309(7),13(14)]),flip(a)].">
      <j1 rule="para" parents="2632 129"/>
      <j2 rule="rewrite" parents="309 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2680">
    <literal><![CDATA[
      f(f(f(x,x),f(f(x,x),f(x,y))),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(2632(a,1),132(a,1,2,2,1)),rewrite([42(5),316(8),42(6),42(13),42(21),22(19),42(3),42(5)]),flip(a)].">
      <j1 rule="para" parents="2632 132"/>
      <j2 rule="rewrite" parents="42 316 42 42 42 22 42 42"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2766">
    <literal><![CDATA[
      f(f(f(f(x,y),f(x,y)),f(f(f(x,y),f(x,y)),y)),f(f(x,y),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(3(a,1),2680(a,1,1,2,2))].">
      <j1 rule="para" parents="3 2680"/>
    </justification>
  </clause>

  <clause id="2769">
    <literal><![CDATA[
      f(f(f(f(x,y),f(x,y)),f(f(f(x,y),f(x,y)),x)),f(f(x,y),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(42(a,1),2680(a,1,1,2,2))].">
      <j1 rule="para" parents="42 2680"/>
    </justification>
  </clause>

  <clause id="3062">
    <literal><![CDATA[
      f(f(f(x,y),f(x,y)),f(f(f(f(x,y),f(x,y)),f(x,y)),f(f(f(f(x,y),f(x,y)),f(x,y)),f(f(f(f(x,y),f(x,y)),z),f(f(f(f(x,z),z),f(x,y)),y))))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(138(a,1),136(a,1,1,1)),rewrite([138(15),138(17),138(18),138(20),138(22),138(23),138(25),138(40)])].">
      <j1 rule="para" parents="138 136"/>
      <j2 rule="rewrite" parents="138 138 138 138 138 138 138 138"/>
    </justification>
  </clause>

  <clause id="3136">
    <literal><![CDATA[
      f(f(f(f(x,x),f(y,x)),f(f(x,x),x)),x) = f(f(x,x),x)
    ]]></literal>
    <justification jstring="[para(2238(a,1),139(a,1,2,1,2,1)),rewrite([2238(18),42(14),673(12),2238(14),34(13),13(10)])].">
      <j1 rule="para" parents="2238 139"/>
      <j2 rule="rewrite" parents="2238 42 673 2238 34 13"/>
    </justification>
  </clause>

  <clause id="3159">
    <literal><![CDATA[
      f(f(x,x),f(f(f(x,x),f(f(x,x),x)),f(f(f(x,x),x),f(y,x)))) = x
    ]]></literal>
    <justification jstring="[para(3136(a,1),68(a,1,2,2,1))].">
      <j1 rule="para" parents="3136 68"/>
    </justification>
  </clause>

  <clause id="3163">
    <literal><![CDATA[
      f(f(f(x,y),f(x,y)),f(f(f(f(x,y),f(x,y)),f(f(f(x,y),f(x,y)),f(x,y))),f(f(f(f(x,y),f(x,y)),f(x,y)),x))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(3136(a,1),56(a,1,2,2,1))].">
      <j1 rule="para" parents="3136 56"/>
    </justification>
  </clause>

  <clause id="3398">
    <literal><![CDATA[
      f(f(x,x),f(f(x,x),x)) = x
    ]]></literal>
    <justification jstring="[para(13(a,1),3159(a,1,2))].">
      <j1 rule="para" parents="13 3159"/>
    </justification>
  </clause>

  <clause id="3413">
    <literal><![CDATA[
      f(x,f(x,f(x,x))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(678(a,1),3159(a,1,2,2,2)),rewrite([42(3),42(3),42(3),42(6),13(9)])].">
      <j1 rule="para" parents="678 3159"/>
      <j2 rule="rewrite" parents="42 42 42 42 13"/>
    </justification>
  </clause>

  <clause id="3440">
    <literal><![CDATA[
      f(f(f(x,y),f(x,y)),f(f(x,y),f(f(f(f(x,y),f(x,y)),f(x,y)),x))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(3163),rewrite([3398(12)])].">
      <j1 rule="back_rewrite" parents="3163"/>
      <j2 rule="rewrite" parents="3398"/>
    </justification>
  </clause>

  <clause id="3453">
    <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(682),rewrite([3398(9)])].">
      <j1 rule="back_rewrite" parents="682"/>
      <j2 rule="rewrite" parents="3398"/>
    </justification>
  </clause>

  <clause id="3484">
    <literal><![CDATA[
      f(f(x,y),f(y,f(f(f(f(f(y,x),f(f(y,y),y)),f(f(y,y),y)),y),f(z,y)))) = y
    ]]></literal>
    <justification jstring="[para(3398(a,1),68(a,1,2,1))].">
      <j1 rule="para" parents="3398 68"/>
    </justification>
  </clause>

  <clause id="4511">
    <literal><![CDATA[
      f(f(f(x,y),f(f(x,y),f(x,y))),f(f(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)),y)))) = f(f(x,y),f(x,y))
    ]]></literal>
    <justification jstring="[para(138(a,1),2436(a,1,1,1)),rewrite([138(15),138(16),138(19),138(20),138(34),138(35)])].">
      <j1 rule="para" parents="138 2436"/>
      <j2 rule="rewrite" parents="138 138 138 138 138 138"/>
    </justification>
  </clause>

  <clause id="5302">
    <literal><![CDATA[
      f(f(f(f(x,y),f(x,y)),f(f(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)),y)))),f(f(x,y),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(138(a,1),2766(a,1,1,1,1)),rewrite([138(15),138(17),138(18),138(32),138(33),138(36)])].">
      <j1 rule="para" parents="138 2766"/>
      <j2 rule="rewrite" parents="138 138 138 138 138 138"/>
    </justification>
  </clause>

  <clause id="5967">
    <literal><![CDATA[
      f(f(x,y),f(f(f(f(y,x),f(f(y,y),y)),f(f(y,y),y)),y)) = y
    ]]></literal>
    <justification jstring="[para(57(a,1),3484(a,1,2))].">
      <j1 rule="para" parents="57 3484"/>
    </justification>
  </clause>

  <clause id="6050">
    <literal><![CDATA[
      f(f(f(x,x),x),f(f(f(f(f(x,x),x),f(f(x,x),x)),f(f(x,x),x)),x)) = x
    ]]></literal>
    <justification jstring="[para(22(a,1),5967(a,1,2,1,1)),rewrite([673(6)])].">
      <j1 rule="para" parents="22 5967"/>
      <j2 rule="rewrite" parents="673"/>
    </justification>
  </clause>

  <clause id="6056">
    <literal><![CDATA[
      f(f(f(f(x,y),f(x,y)),y),f(f(f(f(x,y),f(f(y,y),y)),f(f(y,y),y)),y)) = y
    ]]></literal>
    <justification jstring="[para(57(a,1),5967(a,1,2,1,1,1))].">
      <j1 rule="para" parents="57 5967"/>
    </justification>
  </clause>

  <clause id="6058">
    <literal><![CDATA[
      f(f(f(f(x,y),f(x,y)),x),f(f(f(f(x,y),f(f(x,x),x)),f(f(x,x),x)),x)) = x
    ]]></literal>
    <justification jstring="[para(63(a,1),5967(a,1,2,1,1,1))].">
      <j1 rule="para" parents="63 5967"/>
    </justification>
  </clause>

  <clause id="6111">
    <literal><![CDATA[
      f(f(f(f(x,f(x,x)),f(f(x,x),x)),f(f(x,x),x)),x) = f(x,x)
    ]]></literal>
    <justification jstring="[para(5967(a,1),129(a,1,2,2,1)),rewrite([13(33),34(12)]),flip(a)].">
      <j1 rule="para" parents="5967 129"/>
      <j2 rule="rewrite" parents="13 34"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6167">
    <literal><![CDATA[
      f(f(f(x,x),x),f(x,f(f(f(x,f(x,x)),f(f(x,x),x)),f(f(x,x),x)))) = x
    ]]></literal>
    <justification jstring="[para(6111(a,1),2438(a,1,1,1)),rewrite([6111(10),6111(11),42(4),6111(11),6111(12),42(5),6111(21),6111(22),42(15)])].">
      <j1 rule="para" parents="6111 2438"/>
      <j2 rule="rewrite" parents="6111 6111 42 6111 6111 42 6111 6111 42"/>
    </justification>
  </clause>

  <clause id="6230">
    <literal><![CDATA[
      f(f(f(f(f(x,x),x),f(f(x,x),x)),f(f(x,x),x)),x) = f(x,x)
    ]]></literal>
    <justification jstring="[para(6050(a,1),129(a,1,2,2,1)),rewrite([13(33),34(12)]),flip(a)].">
      <j1 rule="para" parents="6050 129"/>
      <j2 rule="rewrite" parents="13 34"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6231">
    <literal><![CDATA[
      f(f(f(f(x,f(x,x)),f(x,f(x,x))),f(x,f(x,x))),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(6050(a,1),132(a,1,2,2,1)),rewrite([42(3),42(5),42(8),42(14),42(16),42(19),42(24),42(26),42(29),42(37),22(35),42(13),42(3),42(5),42(8)]),flip(a)].">
      <j1 rule="para" parents="6050 132"/>
      <j2 rule="rewrite" parents="42 42 42 42 42 42 42 42 42 42 22 42 42 42 42"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6275">
    <literal><![CDATA[
      f(f(f(x,x),f(f(x,x),f(f(f(x,f(x,x)),f(x,f(x,x))),f(x,f(x,x))))),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(6231(a,1),2769(a,1,1,1,1)),rewrite([6231(10),6231(11),6231(11),6231(22),6231(22),6231(24)])].">
      <j1 rule="para" parents="6231 2769"/>
      <j2 rule="rewrite" parents="6231 6231 6231 6231 6231 6231"/>
    </justification>
  </clause>

  <clause id="6278">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),f(f(f(x,f(x,x)),f(x,f(x,x))),f(x,f(x,x)))),x) = f(f(f(x,f(x,x)),f(x,f(x,x))),f(x,f(x,x)))
    ]]></literal>
    <justification jstring="[para(6231(a,1),3453(a,1,2,2,2)),rewrite([22(22),6231(21)])].">
      <j1 rule="para" parents="6231 3453"/>
      <j2 rule="rewrite" parents="22 6231"/>
    </justification>
  </clause>

  <clause id="6360">
    <literal><![CDATA[
      f(f(f(f(x,x),x),f(f(x,x),x)),f(f(f(f(x,x),x),f(f(f(f(f(x,x),x),f(f(x,x),x)),f(f(x,x),x)),f(x,x))),f(f(x,x),x))) = f(f(x,x),x)
    ]]></literal>
    <justification jstring="[para(6167(a,1),1847(a,1,2,1,2,2,2)),rewrite([6230(24)])].">
      <j1 rule="para" parents="6167 1847"/>
      <j2 rule="rewrite" parents="6230"/>
    </justification>
  </clause>

  <clause id="6870">
    <literal><![CDATA[
      f(f(x,y),f(f(f(f(y,x),f(y,f(f(y,y),z))),f(y,f(f(y,y),z))),y)) = y
    ]]></literal>
    <justification jstring="[para(226(a,1),174(a,1,2,2)),rewrite([57(23)])].">
      <j1 rule="para" parents="226 174"/>
      <j2 rule="rewrite" parents="57"/>
    </justification>
  </clause>

  <clause id="6964">
    <literal><![CDATA[
      f(f(f(f(f(f(x,y),f(x,f(f(x,x),z))),f(x,f(f(x,x),z))),x),f(y,x)),f(f(f(x,f(f(f(y,x),f(y,x)),f(y,x))),f(f(f(y,x),f(y,x)),f(y,x))),f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(6870(a,1),5967(a,1,2,1,1,1))].">
      <j1 rule="para" parents="6870 5967"/>
    </justification>
  </clause>

  <clause id="8980">
    <literal><![CDATA[
      f(f(x,x),f(x,f(f(f(x,x),x),f(f(x,x),f(f(x,x),f(f(f(x,f(x,x)),f(x,f(x,x))),f(x,f(x,x)))))))) = x
    ]]></literal>
    <justification jstring="[para(6275(a,1),3440(a,1,1,1)),rewrite([6275(14),6275(15),6275(15),6275(15),6275(16),6275(32)])].">
      <j1 rule="para" parents="6275 3440"/>
      <j2 rule="rewrite" parents="6275 6275 6275 6275 6275 6275"/>
    </justification>
  </clause>

  <clause id="9276">
    <literal><![CDATA[
      f(f(x,x),x) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(2218(a,1),290(a,1,2,2,2)),rewrite([3413(3),34(12),13(9)])].">
      <j1 rule="para" parents="2218 290"/>
      <j2 rule="rewrite" parents="3413 34 13"/>
    </justification>
  </clause>

  <clause id="9278">
    <literal><![CDATA[
      f(f(x,x),f(f(x,f(x,x)),f(f(x,f(x,x)),f(x,y)))) = x
    ]]></literal>
    <justification jstring="[para(2679(a,1),290(a,1,1,2)),rewrite([42(3),42(6),2680(8),42(6),2680(8),9276(3),42(9),2680(11),9276(5),42(10),2680(12),42(14),2680(16)])].">
      <j1 rule="para" parents="2679 290"/>
      <j2 rule="rewrite" parents="42 42 2680 42 2680 9276 42 2680 9276 42 2680 42 2680"/>
    </justification>
  </clause>

  <clause id="9288">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),f(f(x,f(x,x)),f(x,f(x,x)))),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(6111(a,1),290(a,2)),rewrite([42(4),9276(2),42(5),42(8),9276(8),42(15),9276(13),42(16),42(19),9276(19),42(25),9276(23),42(26),42(29),9276(29),42(38),9276(36),42(39),42(42),9276(42),42(49),9276(47),42(50),42(53),9276(53),290(59),42(13)])].">
      <j1 rule="para" parents="6111 290"/>
      <j2 rule="rewrite" parents="42 9276 42 42 9276 42 9276 42 42 9276 42 9276 42 42 9276 42 9276 42 42 9276 42 9276 42 42 9276 290 42"/>
    </justification>
  </clause>

  <clause id="9409">
    <literal><![CDATA[
      f(f(x,x),f(x,f(x,x))) = x
    ]]></literal>
    <justification jstring="[back_rewrite(8980),rewrite([9276(3),9276(13),9278(14),9276(5),63(7)])].">
      <j1 rule="back_rewrite" parents="8980"/>
      <j2 rule="rewrite" parents="9276 9276 9278 9276 63"/>
    </justification>
  </clause>

  <clause id="10071">
    <literal><![CDATA[
      f(f(f(f(f(f(x,y),f(x,f(f(x,x),z))),f(x,f(f(x,x),z))),x),f(y,x)),f(f(f(x,f(f(y,x),f(f(y,x),f(y,x)))),f(f(y,x),f(f(y,x),f(y,x)))),f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(6964),rewrite([9276(17),9276(23)])].">
      <j1 rule="back_rewrite" parents="6964"/>
      <j2 rule="rewrite" parents="9276 9276"/>
    </justification>
  </clause>

  <clause id="10340">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),f(x,f(x,x))),x) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[back_rewrite(6360),rewrite([9276(2),9276(4),9276(7),9276(9),9276(11),9276(14),9276(15),9288(17),22(8),9276(8),9409(9),9276(8)])].">
      <j1 rule="back_rewrite" parents="6360"/>
      <j2 rule="rewrite" parents="9276 9276 9276 9276 9276 9276 9276 9288 22 9276 9409 9276"/>
    </justification>
  </clause>

  <clause id="10382">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(x,f(x,x)),f(x,f(x,x)))) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[back_rewrite(6278),rewrite([9276(10),3413(11),10340(6),9276(10)]),flip(a)].">
      <j1 rule="back_rewrite" parents="6278"/>
      <j2 rule="rewrite" parents="9276 3413 10340 9276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10454">
    <literal><![CDATA[
      f(f(f(f(x,y),f(x,y)),x),f(f(f(f(x,y),f(x,f(x,x))),f(x,f(x,x))),x)) = x
    ]]></literal>
    <justification jstring="[back_rewrite(6058),rewrite([9276(7),9276(10)])].">
      <j1 rule="back_rewrite" parents="6058"/>
      <j2 rule="rewrite" parents="9276 9276"/>
    </justification>
  </clause>

  <clause id="10455">
    <literal><![CDATA[
      f(f(f(f(x,y),f(x,y)),y),f(f(f(f(x,y),f(y,f(y,y))),f(y,f(y,y))),y)) = y
    ]]></literal>
    <justification jstring="[back_rewrite(6056),rewrite([9276(7),9276(10)])].">
      <j1 rule="back_rewrite" parents="6056"/>
      <j2 rule="rewrite" parents="9276 9276"/>
    </justification>
  </clause>

  <clause id="10499">
    <literal><![CDATA[
      f(f(x,y),f(f(f(f(y,x),f(y,f(y,y))),f(y,f(y,y))),y)) = y
    ]]></literal>
    <justification jstring="[back_rewrite(5967),rewrite([9276(4),9276(7)])].">
      <j1 rule="back_rewrite" parents="5967"/>
      <j2 rule="rewrite" parents="9276 9276"/>
    </justification>
  </clause>

  <clause id="11262">
    <literal><![CDATA[
      f(f(f(x,y),f(x,y)),f(f(f(x,y),f(f(x,y),f(x,y))),f(f(f(x,y),f(f(x,y),f(x,y))),f(f(f(f(x,y),f(x,y)),z),f(f(f(f(x,z),z),f(x,y)),y))))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(3062),rewrite([9276(8),9276(13)])].">
      <j1 rule="back_rewrite" parents="3062"/>
      <j2 rule="rewrite" parents="9276 9276"/>
    </justification>
  </clause>

  <clause id="11765">
    <literal><![CDATA[
      f(f(f(x,x),f(y,x)),f(f(f(f(y,x),f(y,x)),f(f(x,f(x,x)),f(x,f(x,x)))),f(f(f(x,f(x,x)),f(y,x)),f(f(y,x),z)))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(9409(a,1),289(a,1,1,1,1)),rewrite([9409(4),9409(5),9409(7),9409(8),10382(20),9409(18),9409(20),9409(25)])].">
      <j1 rule="para" parents="9409 289"/>
      <j2 rule="rewrite" parents="9409 9409 9409 9409 10382 9409 9409 9409"/>
    </justification>
  </clause>

  <clause id="11775">
    <literal><![CDATA[
      f(f(f(f(x,x),f(y,f(y,y))),f(f(f(y,f(y,y)),x),f(x,z))),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(10340(a,1),96(a,1,1,1,2,2,2)),rewrite([42(12),22(21),42(10),42(20),10340(32),22(29),42(18),9276(12),10382(12)])].">
      <j1 rule="para" parents="10340 96"/>
      <j2 rule="rewrite" parents="42 22 42 42 10340 22 42 9276 10382"/>
    </justification>
  </clause>

  <clause id="12287">
    <literal><![CDATA[
      f(f(x,x),f(x,y)) = x
    ]]></literal>
    <justification jstring="[para(167(a,1),337(a,1,1)),rewrite([2222(16),42(13),22(11),42(3)]),flip(a)].">
      <j1 rule="para" parents="167 337"/>
      <j2 rule="rewrite" parents="2222 42 22 42"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12288">
    <literal><![CDATA[
      f(x,f(f(x,x),y)) = f(x,x)
    ]]></literal>
    <justification jstring="[para(177(a,1),337(a,1,1)),rewrite([12287(10),12287(12),9276(10),2218(14),13(10)]),flip(a)].">
      <j1 rule="para" parents="177 337"/>
      <j2 rule="rewrite" parents="12287 12287 9276 2218 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12289">
    <literal><![CDATA[
      f(f(x,x),f(y,x)) = x
    ]]></literal>
    <justification jstring="[para(180(a,1),337(a,1,1)),rewrite([2226(16),12287(13),22(11),12287(3)]),flip(a)].">
      <j1 rule="para" parents="180 337"/>
      <j2 rule="rewrite" parents="2226 12287 22 12287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12290">
    <literal><![CDATA[
      f(x,f(y,f(x,x))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(186(a,1),337(a,1,1)),rewrite([12287(10),12287(12),9276(10),2232(14),13(10)]),flip(a)].">
      <j1 rule="para" parents="186 337"/>
      <j2 rule="rewrite" parents="12287 12287 9276 2232 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12291">
    <literal><![CDATA[
      f(f(f(x,y),f(x,y)),y) = f(x,y)
    ]]></literal>
    <justification jstring="[para(176(a,1),337(a,1,1)),rewrite([2436(26),12287(23),22(18),12287(7)]),flip(a)].">
      <j1 rule="para" parents="176 337"/>
      <j2 rule="rewrite" parents="2436 12287 22 12287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12292">
    <literal><![CDATA[
      f(f(f(x,y),f(x,y)),x) = f(x,y)
    ]]></literal>
    <justification jstring="[para(179(a,1),337(a,1,1)),rewrite([2438(26),12287(23),22(18),12287(7)]),flip(a)].">
      <j1 rule="para" parents="179 337"/>
      <j2 rule="rewrite" parents="2438 12287 22 12287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12298">
    <literal><![CDATA[
      f(f(x,y),f(f(f(f(f(x,f(x,x)),y),y),f(x,x)),f(z,f(x,x)))) = x
    ]]></literal>
    <justification jstring="[para(68(a,1),337(a,1,2,2,1)),rewrite([12287(3),9276(3),12287(15),9276(15),12287(26),9276(26),12287(41),12287(40),22(38),42(14),12287(3),9276(3)]),flip(a)].">
      <j1 rule="para" parents="68 337"/>
      <j2 rule="rewrite" parents="12287 9276 12287 9276 12287 9276 12287 12287 22 42 12287 9276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12323">
    <literal><![CDATA[
      f(f(x,y),f(f(f(x,x),z),f(f(f(f(f(x,y),z),z),x),f(x,u)))) = x
    ]]></literal>
    <justification jstring="[para(77(a,1),337(a,2)),rewrite([12292(4),12292(16),12292(27),12292(43),12292(55),337(55)])].">
      <j1 rule="para" parents="77 337"/>
      <j2 rule="rewrite" parents="12292 12292 12292 12292 12292 337"/>
    </justification>
  </clause>

  <clause id="12360">
    <literal><![CDATA[
      f(x,f(f(f(f(y,x),f(y,x)),f(x,x)),f(f(x,f(y,x)),x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(2174(a,1),337(a,2)),rewrite([12289(3),12289(14),12289(24),12289(39),12289(50),337(50)])].">
      <j1 rule="para" parents="2174 337"/>
      <j2 rule="rewrite" parents="12289 12289 12289 12289 12289 337"/>
    </justification>
  </clause>

  <clause id="12463">
    <literal><![CDATA[
      f(x,f(f(f(x,f(f(y,x),f(f(y,x),f(y,x)))),f(f(y,x),f(f(y,x),f(y,x)))),f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(10071),rewrite([12288(4),42(3),12288(3),22(3),12289(3)])].">
      <j1 rule="back_rewrite" parents="10071"/>
      <j2 rule="rewrite" parents="12288 42 12288 22 12289"/>
    </justification>
  </clause>

  <clause id="12493">
    <literal><![CDATA[
      f(x,f(f(f(f(y,x),f(y,x)),f(f(x,f(x,x)),f(x,f(x,x)))),f(f(f(x,f(x,x)),f(y,x)),f(f(y,x),z)))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(11765),rewrite([12289(3)])].">
      <j1 rule="back_rewrite" parents="11765"/>
      <j2 rule="rewrite" parents="12289"/>
    </justification>
  </clause>

  <clause id="12574">
    <literal><![CDATA[
      f(f(x,y),f(f(f(f(x,y),f(y,f(y,y))),f(y,f(y,y))),y)) = y
    ]]></literal>
    <justification jstring="[back_rewrite(10455),rewrite([12291(4)])].">
      <j1 rule="back_rewrite" parents="10455"/>
      <j2 rule="rewrite" parents="12291"/>
    </justification>
  </clause>

  <clause id="12706">
    <literal><![CDATA[
      f(f(x,y),f(f(f(f(x,y),f(x,f(x,x))),f(x,f(x,x))),x)) = x
    ]]></literal>
    <justification jstring="[back_rewrite(10454),rewrite([12292(4)])].">
      <j1 rule="back_rewrite" parents="10454"/>
      <j2 rule="rewrite" parents="12292"/>
    </justification>
  </clause>

  <clause id="12933">
    <literal><![CDATA[
      f(f(f(f(f(x,x),y),f(f(f(f(f(x,z),y),y),x),f(x,u))),f(z,x)),f(f(z,x),f(f(f(f(x,z),z),f(z,x)),f(f(z,x),w)))) = f(z,x)
    ]]></literal>
    <justification jstring="[para(12292(a,1),7(a,1,2,1))].">
      <j1 rule="para" parents="12292 7"/>
    </justification>
  </clause>

  <clause id="13156">
    <literal><![CDATA[
      f(f(x,y),f(x,f(f(f(x,f(f(f(f(x,y),f(x,f(x,x))),f(x,f(x,x))),x)),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(12706(a,1),555(a,1,2,1)),rewrite([12706(11)])].">
      <j1 rule="para" parents="12706 555"/>
      <j2 rule="rewrite" parents="12706"/>
    </justification>
  </clause>

  <clause id="13241">
    <literal><![CDATA[
      f(f(f(f(f(x,f(x,x)),y),y),f(x,x)),f(f(f(f(x,f(x,x)),y),y),f(x,x))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(12298(a,1),22(a,1,1)),rewrite([12290(7)]),flip(a)].">
      <j1 rule="para" parents="12298 22"/>
      <j2 rule="rewrite" parents="12290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13306">
    <literal><![CDATA[
      f(f(f(f(x,f(x,x)),y),y),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(12298(a,1),331(a,1,2,1)),rewrite([13241(13),13241(15),42(4),13241(15),42(4),13241(15),42(4),12287(20)]),flip(a)].">
      <j1 rule="para" parents="12298 331"/>
      <j2 rule="rewrite" parents="13241 13241 42 13241 42 13241 42 12287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13326">
    <literal><![CDATA[
      f(f(f(f(x,f(x,x)),y),y),x) = f(x,x)
    ]]></literal>
    <justification jstring="[para(13(a,1),13306(a,1,1,1,1,2)),rewrite([9276(2),12287(7)])].">
      <j1 rule="para" parents="13 13306"/>
      <j2 rule="rewrite" parents="9276 12287"/>
    </justification>
  </clause>

  <clause id="13341">
    <literal><![CDATA[
      f(f(f(f(f(x,f(x,x)),y),y),f(f(f(x,f(x,x)),y),y)),x) = f(f(f(x,f(x,x)),y),y)
    ]]></literal>
    <justification jstring="[para(13306(a,1),12287(a,1,2))].">
      <j1 rule="para" parents="13306 12287"/>
    </justification>
  </clause>

  <clause id="13344">
    <literal><![CDATA[
      f(f(x,x),f(f(f(x,f(x,x)),y),y)) = x
    ]]></literal>
    <justification jstring="[para(13306(a,1),12292(a,1,1,1)),rewrite([13306(6),13306(12)])].">
      <j1 rule="para" parents="13306 12292"/>
      <j2 rule="rewrite" parents="13306 13306"/>
    </justification>
  </clause>

  <clause id="13368">
    <literal><![CDATA[
      f(f(x,f(f(f(x,f(x,x)),y),y)),f(f(f(f(x,f(x,x)),y),y),f(x,y))) = f(f(f(x,f(x,x)),y),y)
    ]]></literal>
    <justification jstring="[para(13326(a,1),139(a,1,2,1,2,1)),rewrite([13326(20),12287(17),13341(15),13326(14),13344(15)])].">
      <j1 rule="para" parents="13326 139"/>
      <j2 rule="rewrite" parents="13326 12287 13341 13326 13344"/>
    </justification>
  </clause>

  <clause id="13370">
    <literal><![CDATA[
      f(f(f(f(x,f(x,x)),y),y),f(x,f(x,x))) = f(f(x,f(x,x)),f(x,f(x,x)))
    ]]></literal>
    <justification jstring="[para(10382(a,1),13326(a,1,1,1,1))].">
      <j1 rule="para" parents="10382 13326"/>
    </justification>
  </clause>

  <clause id="13372">
    <literal><![CDATA[
      f(f(f(f(f(x,f(x,x)),y),y),f(f(f(x,f(x,x)),y),y)),f(x,x)) = f(f(f(x,f(x,x)),y),y)
    ]]></literal>
    <justification jstring="[para(13326(a,1),12287(a,1,2))].">
      <j1 rule="para" parents="13326 12287"/>
    </justification>
  </clause>

  <clause id="13375">
    <literal><![CDATA[
      f(x,f(f(f(x,f(x,x)),y),y)) = f(x,x)
    ]]></literal>
    <justification jstring="[para(13326(a,1),12292(a,1,1,1)),rewrite([13326(6),12287(3),13326(10)])].">
      <j1 rule="para" parents="13326 12292"/>
      <j2 rule="rewrite" parents="13326 12287 13326"/>
    </justification>
  </clause>

  <clause id="13381">
    <literal><![CDATA[
      f(f(x,x),f(f(f(f(x,f(x,x)),y),y),f(x,y))) = f(f(f(x,f(x,x)),y),y)
    ]]></literal>
    <justification jstring="[back_rewrite(13368),rewrite([13375(5)])].">
      <j1 rule="back_rewrite" parents="13368"/>
      <j2 rule="rewrite" parents="13375"/>
    </justification>
  </clause>

  <clause id="13465">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(f(x,f(x,x)),y),y)) = f(f(x,f(x,x)),f(x,f(x,x)))
    ]]></literal>
    <justification jstring="[para(10382(a,1),13375(a,1,2,1,1))].">
      <j1 rule="para" parents="10382 13375"/>
    </justification>
  </clause>

  <clause id="13470">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),y),y) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(13375(a,1),337(a,1,1)),rewrite([13372(12),13465(12),12287(14),13370(8),57(7)]),flip(a)].">
      <j1 rule="para" parents="13375 337"/>
      <j2 rule="rewrite" parents="13372 13465 12287 13370 57"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13500">
    <literal><![CDATA[
      f(f(x,x),f(f(x,f(x,x)),f(x,y))) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[back_rewrite(13381),rewrite([13470(5),13470(10)])].">
      <j1 rule="back_rewrite" parents="13381"/>
      <j2 rule="rewrite" parents="13470 13470"/>
    </justification>
  </clause>

  <clause id="13511">
    <literal><![CDATA[
      f(x,f(f(y,f(y,y)),f(y,f(y,y)))) = f(y,f(y,y))
    ]]></literal>
    <justification jstring="[para(10382(a,1),526(a,1,1,2,2)),rewrite([13470(32),12290(27),12291(19)])].">
      <j1 rule="para" parents="10382 526"/>
      <j2 rule="rewrite" parents="13470 12290 12291"/>
    </justification>
  </clause>

  <clause id="13516">
    <literal><![CDATA[
      f(x,f(f(x,f(x,x)),f(f(f(x,f(x,x)),f(y,x)),f(f(y,x),z)))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(12493),rewrite([13511(9)])].">
      <j1 rule="back_rewrite" parents="12493"/>
      <j2 rule="rewrite" parents="13511"/>
    </justification>
  </clause>

  <clause id="13536">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(y,y)) = y
    ]]></literal>
    <justification jstring="[para(13470(a,1),13(a,1,1))].">
      <j1 rule="para" parents="13470 13"/>
    </justification>
  </clause>

  <clause id="13539">
    <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(63(a,1),13470(a,1,1))].">
      <j1 rule="para" parents="63 13470"/>
    </justification>
  </clause>

  <clause id="13547">
    <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(13470(a,1),52(a,1,2,1)),rewrite([13470(9),13539(16)])].">
      <j1 rule="para" parents="13470 52"/>
      <j2 rule="rewrite" parents="13470 13539"/>
    </justification>
  </clause>

  <clause id="13580">
    <literal><![CDATA[
      f(f(x,y),f(f(z,f(z,z)),y)) = y
    ]]></literal>
    <justification jstring="[para(13470(a,1),65(a,1,2,1)),rewrite([13536(8),13536(10),13511(10),13536(9),13536(11),13511(11),22(6),12287(6)])].">
      <j1 rule="para" parents="13470 65"/>
      <j2 rule="rewrite" parents="13536 13536 13511 13536 13536 13511 22 12287"/>
    </justification>
  </clause>

  <clause id="13620">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(x,f(x,x)),f(y,f(y,y)))) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(13470(a,1),287(a,2,2,2)),rewrite([13536(9),13511(9),13536(11),13511(11),57(7)]),flip(a)].">
      <j1 rule="para" parents="13470 287"/>
      <j2 rule="rewrite" parents="13536 13511 13536 13511 57"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13623">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(f(f(y,f(f(x,f(x,x)),y)),f(y,f(y,y))),f(y,f(y,y))),y)) = y
    ]]></literal>
    <justification jstring="[para(13470(a,1),10499(a,1,1))].">
      <j1 rule="para" parents="13470 10499"/>
    </justification>
  </clause>

  <clause id="13640">
    <literal><![CDATA[
      f(f(f(x,f(y,f(y,y))),f(f(f(y,f(y,y)),f(f(z,f(z,z)),x)),f(z,f(z,z)))),x) = f(f(z,f(z,z)),x)
    ]]></literal>
    <justification jstring="[para(13470(a,1),11775(a,1,1,2,2)),rewrite([13580(7),13580(20)])].">
      <j1 rule="para" parents="13470 11775"/>
      <j2 rule="rewrite" parents="13580 13580"/>
    </justification>
  </clause>

  <clause id="13644">
    <literal><![CDATA[
      f(f(x,x),f(y,f(y,y))) = x
    ]]></literal>
    <justification jstring="[para(13470(a,1),12289(a,1,2))].">
      <j1 rule="para" parents="13470 12289"/>
    </justification>
  </clause>

  <clause id="13646">
    <literal><![CDATA[
      f(x,f(y,f(y,y))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(13470(a,1),12290(a,1,2))].">
      <j1 rule="para" parents="13470 12290"/>
    </justification>
  </clause>

  <clause id="13658">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(x,f(x,x)),y)) = y
    ]]></literal>
    <justification jstring="[para(13470(a,1),12574(a,1,1)),rewrite([13470(6),13470(10)])].">
      <j1 rule="para" parents="13470 12574"/>
      <j2 rule="rewrite" parents="13470 13470"/>
    </justification>
  </clause>

  <clause id="13672">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),y),f(y,z)) = y
    ]]></literal>
    <justification jstring="[back_rewrite(13547),rewrite([13580(14),13658(10),13580(12)])].">
      <j1 rule="back_rewrite" parents="13547"/>
      <j2 rule="rewrite" parents="13580 13658 13580"/>
    </justification>
  </clause>

  <clause id="13718">
    <literal><![CDATA[
      f(x,f(x,x)) = f(y,f(y,y))
    ]]></literal>
    <justification jstring="[back_rewrite(13620),rewrite([13658(8)])].">
      <j1 rule="back_rewrite" parents="13620"/>
      <j2 rule="rewrite" parents="13658"/>
    </justification>
  </clause>

  <clause id="13741">
    <literal><![CDATA[
      f(f(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)),y))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(11262),rewrite([13658(25)])].">
      <j1 rule="back_rewrite" parents="11262"/>
      <j2 rule="rewrite" parents="13658"/>
    </justification>
  </clause>

  <clause id="13757">
    <literal><![CDATA[
      f(x,f(f(x,f(x,x)),f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(13516),rewrite([13672(9)])].">
      <j1 rule="back_rewrite" parents="13516"/>
      <j2 rule="rewrite" parents="13672"/>
    </justification>
  </clause>

  <clause id="13766">
    <literal><![CDATA[
      f(x,f(x,x)) = c_0
    ]]></literal>
    <justification jstring="[new_symbol(13718)].">
      <j1 rule="new_symbol" parents="13718"/>
    </justification>
  </clause>

  <clause id="13776">
    <literal><![CDATA[
      f(c_0,f(f(x,y),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(5302),rewrite([13741(17),9276(5),13766(5)])].">
      <j1 rule="back_rewrite" parents="5302"/>
      <j2 rule="rewrite" parents="13741 9276 13766"/>
    </justification>
  </clause>

  <clause id="13777">
    <literal><![CDATA[
      f(f(x,y),f(x,y)) = f(c_0,f(x,y))
    ]]></literal>
    <justification jstring="[back_rewrite(4511),rewrite([13766(5),13741(15)]),flip(a)].">
      <j1 rule="back_rewrite" parents="4511"/>
      <j2 rule="rewrite" parents="13766 13741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13787">
    <literal><![CDATA[
      f(x,f(c_0,f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(13757),rewrite([13766(2)])].">
      <j1 rule="back_rewrite" parents="13757"/>
      <j2 rule="rewrite" parents="13766"/>
    </justification>
  </clause>

  <clause id="13826">
    <literal><![CDATA[
      f(c_0,f(c_0,x)) = x
    ]]></literal>
    <justification jstring="[back_rewrite(13658),rewrite([13766(2),13766(3)])].">
      <j1 rule="back_rewrite" parents="13658"/>
      <j2 rule="rewrite" parents="13766 13766"/>
    </justification>
  </clause>

  <clause id="13832">
    <literal><![CDATA[
      f(x,c_0) = f(x,x)
    ]]></literal>
    <justification jstring="[back_rewrite(13646),rewrite([13766(2)])].">
      <j1 rule="back_rewrite" parents="13646"/>
      <j2 rule="rewrite" parents="13766"/>
    </justification>
  </clause>

  <clause id="13833">
    <literal><![CDATA[
      f(f(x,x),c_0) = x
    ]]></literal>
    <justification jstring="[back_rewrite(13644),rewrite([13766(3)])].">
      <j1 rule="back_rewrite" parents="13644"/>
      <j2 rule="rewrite" parents="13766"/>
    </justification>
  </clause>

  <clause id="13836">
    <literal><![CDATA[
      f(c_0,x) = f(x,x)
    ]]></literal>
    <justification jstring="[back_rewrite(13640),rewrite([13766(2),13832(2),13766(3),13766(4),13826(5),13766(3),13832(3),13832(3,R),13833(3),13766(3)]),flip(a)].">
      <j1 rule="back_rewrite" parents="13640"/>
      <j2 rule="rewrite" parents="13766 13832 13766 13766 13826 13766 13832 13832 13833 13766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13845">
    <literal><![CDATA[
      f(c_0,f(x,x)) = x
    ]]></literal>
    <justification jstring="[back_rewrite(13623),rewrite([13766(2),13766(3),13836(3),13766(3),13766(4),13766(6),9276(6),13766(6),13836(3)])].">
      <j1 rule="back_rewrite" parents="13623"/>
      <j2 rule="rewrite" parents="13766 13766 13836 13766 13766 13766 9276 13766 13836"/>
    </justification>
  </clause>

  <clause id="13877">
    <literal><![CDATA[
      f(f(x,x),f(c_0,f(x,y))) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(13500),rewrite([13766(3),13766(7)])].">
      <j1 rule="back_rewrite" parents="13500"/>
      <j2 rule="rewrite" parents="13766 13766"/>
    </justification>
  </clause>

  <clause id="13898">
    <literal><![CDATA[
      f(f(x,y),f(x,f(f(f(x,f(f(f(f(x,y),c_0),c_0),x)),f(f(x,y),c_0)),f(z,f(f(x,y),c_0))))) = f(f(x,y),c_0)
    ]]></literal>
    <justification jstring="[back_rewrite(13156),rewrite([13766(4),13766(6),13832(11,R),13832(15,R),13832(22,R)])].">
      <j1 rule="back_rewrite" parents="13156"/>
      <j2 rule="rewrite" parents="13766 13766 13832 13832 13832"/>
    </justification>
  </clause>

  <clause id="14049">
    <literal><![CDATA[
      f(f(x,y),f(f(f(f(x,y),c_0),c_0),x)) = x
    ]]></literal>
    <justification jstring="[back_rewrite(12706),rewrite([13766(4),13766(6)])].">
      <j1 rule="back_rewrite" parents="12706"/>
      <j2 rule="rewrite" parents="13766 13766"/>
    </justification>
  </clause>

  <clause id="14072">
    <literal><![CDATA[
      f(f(x,y),f(f(f(f(x,y),c_0),c_0),y)) = y
    ]]></literal>
    <justification jstring="[back_rewrite(12574),rewrite([13766(4),13766(6)])].">
      <j1 rule="back_rewrite" parents="12574"/>
      <j2 rule="rewrite" parents="13766 13766"/>
    </justification>
  </clause>

  <clause id="14101">
    <literal><![CDATA[
      f(x,f(f(f(x,f(f(y,x),f(f(y,x),c_0))),f(f(y,x),f(f(y,x),c_0))),f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(12463),rewrite([13832(4,R),13832(10,R)])].">
      <j1 rule="back_rewrite" parents="12463"/>
      <j2 rule="rewrite" parents="13832 13832"/>
    </justification>
  </clause>

  <clause id="14268">
    <literal><![CDATA[
      f(f(x,x),x) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(9276),rewrite([13766(4)])].">
      <j1 rule="back_rewrite" parents="9276"/>
      <j2 rule="rewrite" parents="13766"/>
    </justification>
  </clause>

  <clause id="14290">
    <literal><![CDATA[
      f(c_0,f(f(x,y),c_0)) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(13776),rewrite([13832(4,R)])].">
      <j1 rule="back_rewrite" parents="13776"/>
      <j2 rule="rewrite" parents="13832"/>
    </justification>
  </clause>

  <clause id="14451">
    <literal><![CDATA[
      f(x,f(f(f(f(y,x),c_0),f(x,x)),f(f(x,f(y,x)),x))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(12360),rewrite([13832(3,R)])].">
      <j1 rule="back_rewrite" parents="12360"/>
      <j2 rule="rewrite" parents="13832"/>
    </justification>
  </clause>

  <clause id="14462">
    <literal><![CDATA[
      f(f(f(x,y),c_0),x) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(12292),rewrite([13832(3,R)])].">
      <j1 rule="back_rewrite" parents="12292"/>
      <j2 rule="rewrite" parents="13832"/>
    </justification>
  </clause>

  <clause id="14463">
    <literal><![CDATA[
      f(f(f(x,y),c_0),y) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(12291),rewrite([13832(3,R)])].">
      <j1 rule="back_rewrite" parents="12291"/>
      <j2 rule="rewrite" parents="13832"/>
    </justification>
  </clause>

  <clause id="14637">
    <literal><![CDATA[
      f(x,f(f(x,y),c_0)) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(63),rewrite([13832(3,R)])].">
      <j1 rule="back_rewrite" parents="63"/>
      <j2 rule="rewrite" parents="13832"/>
    </justification>
  </clause>

  <clause id="14647">
    <literal><![CDATA[
      f(c1,f(f(c2,c3),c_0)) != f(c2,f(f(c1,c3),c_0))
    ]]></literal>
    <attribute><![CDATA[
      answer(A_SS)
    ]]></attribute>
    <justification jstring="[back_rewrite(4),rewrite([13832(8,R),13832(15,R)])].">
      <j1 rule="back_rewrite" parents="4"/>
      <j2 rule="rewrite" parents="13832 13832"/>
    </justification>
  </clause>

  <clause id="14660">
    <literal><![CDATA[
      f(f(x,y),c_0) = f(c_0,f(x,y))
    ]]></literal>
    <justification jstring="[back_rewrite(13777),rewrite([13832(3,R)])].">
      <j1 rule="back_rewrite" parents="13777"/>
      <j2 rule="rewrite" parents="13832"/>
    </justification>
  </clause>

  <clause id="14681">
    <literal><![CDATA[
      f(c1,f(c_0,f(c2,c3))) != f(c2,f(c_0,f(c1,c3)))
    ]]></literal>
    <attribute><![CDATA[
      answer(A_SS)
    ]]></attribute>
    <justification jstring="[back_rewrite(14647),rewrite([14660(6),14660(13)])].">
      <j1 rule="back_rewrite" parents="14647"/>
      <j2 rule="rewrite" parents="14660 14660"/>
    </justification>
  </clause>

  <clause id="14690">
    <literal><![CDATA[
      f(x,f(c_0,f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(14637),rewrite([14660(3)])].">
      <j1 rule="back_rewrite" parents="14637"/>
      <j2 rule="rewrite" parents="14660"/>
    </justification>
  </clause>

  <clause id="14862">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),y) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(14463),rewrite([14660(3)])].">
      <j1 rule="back_rewrite" parents="14463"/>
      <j2 rule="rewrite" parents="14660"/>
    </justification>
  </clause>

  <clause id="14863">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),x) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(14462),rewrite([14660(3)])].">
      <j1 rule="back_rewrite" parents="14462"/>
      <j2 rule="rewrite" parents="14660"/>
    </justification>
  </clause>

  <clause id="14874">
    <literal><![CDATA[
      f(x,f(f(f(c_0,f(y,x)),f(x,x)),f(f(x,f(y,x)),x))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(14451),rewrite([14660(3)])].">
      <j1 rule="back_rewrite" parents="14451"/>
      <j2 rule="rewrite" parents="14660"/>
    </justification>
  </clause>

  <clause id="15035">
    <literal><![CDATA[
      f(c_0,f(c_0,f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(14290),rewrite([14660(4)])].">
      <j1 rule="back_rewrite" parents="14290"/>
      <j2 rule="rewrite" parents="14660"/>
    </justification>
  </clause>

  <clause id="15160">
    <literal><![CDATA[
      f(x,f(f(f(x,f(f(y,x),f(c_0,f(y,x)))),f(f(y,x),f(c_0,f(y,x)))),f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(14101),rewrite([14660(4),14660(10)])].">
      <j1 rule="back_rewrite" parents="14101"/>
      <j2 rule="rewrite" parents="14660 14660"/>
    </justification>
  </clause>

  <clause id="15178">
    <literal><![CDATA[
      f(f(x,y),f(f(x,y),y)) = y
    ]]></literal>
    <justification jstring="[back_rewrite(14072),rewrite([14660(4),14660(6),15035(6)])].">
      <j1 rule="back_rewrite" parents="14072"/>
      <j2 rule="rewrite" parents="14660 14660 15035"/>
    </justification>
  </clause>

  <clause id="15182">
    <literal><![CDATA[
      f(f(x,y),f(f(x,y),x)) = x
    ]]></literal>
    <justification jstring="[back_rewrite(14049),rewrite([14660(4),14660(6),15035(6)])].">
      <j1 rule="back_rewrite" parents="14049"/>
      <j2 rule="rewrite" parents="14660 14660 15035"/>
    </justification>
  </clause>

  <clause id="15230">
    <literal><![CDATA[
      f(f(x,y),f(x,f(f(f(x,f(f(x,y),x)),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(13898),rewrite([14660(4),14660(6),15035(6),14660(7),14660(11),14660(18)])].">
      <j1 rule="back_rewrite" parents="13898"/>
      <j2 rule="rewrite" parents="14660 14660 15035 14660 14660 14660"/>
    </justification>
  </clause>

  <clause id="15421">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),f(y,y)) = c_0
    ]]></literal>
    <justification jstring="[para(3(a,1),13877(a,1,2,2)),rewrite([13832(3,R),14660(3),13836(5)])].">
      <j1 rule="para" parents="3 13877"/>
      <j2 rule="rewrite" parents="13832 14660 13836"/>
    </justification>
  </clause>

  <clause id="15490">
    <literal><![CDATA[
      f(f(x,f(y,x)),x) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(14874),rewrite([15421(5),13787(6)])].">
      <j1 rule="back_rewrite" parents="14874"/>
      <j2 rule="rewrite" parents="15421 13787"/>
    </justification>
  </clause>

  <clause id="15602">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),f(x,y)) = c_0
    ]]></literal>
    <justification jstring="[para(14660(a,1),13877(a,1,2,2)),rewrite([13832(3,R),14660(3),15035(8)])].">
      <j1 rule="para" parents="14660 13877"/>
      <j2 rule="rewrite" parents="13832 14660 15035"/>
    </justification>
  </clause>

  <clause id="15654">
    <literal><![CDATA[
      f(f(x,y),f(c_0,f(x,y))) = c_0
    ]]></literal>
    <justification jstring="[para(14862(a,1),13877(a,1,2,2)),rewrite([13832(7,R),14660(5),15035(5)])].">
      <j1 rule="para" parents="14862 13877"/>
      <j2 rule="rewrite" parents="13832 14660 15035"/>
    </justification>
  </clause>

  <clause id="15677">
    <literal><![CDATA[
      f(x,f(x,f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(15160),rewrite([15654(5),13832(2),15654(6),14660(3),13845(3)])].">
      <j1 rule="back_rewrite" parents="15160"/>
      <j2 rule="rewrite" parents="15654 13832 15654 14660 13845"/>
    </justification>
  </clause>

  <clause id="16030">
    <literal><![CDATA[
      f(f(f(x,y),x),f(x,y)) = x
    ]]></literal>
    <justification jstring="[para(12287(a,1),15490(a,1,1,2)),rewrite([12287(7)])].">
      <j1 rule="para" parents="12287 15490"/>
      <j2 rule="rewrite" parents="12287"/>
    </justification>
  </clause>

  <clause id="16031">
    <literal><![CDATA[
      f(f(f(x,y),y),f(x,y)) = y
    ]]></literal>
    <justification jstring="[para(12289(a,1),15490(a,1,1,2)),rewrite([12289(7)])].">
      <j1 rule="para" parents="12289 15490"/>
      <j2 rule="rewrite" parents="12289"/>
    </justification>
  </clause>

  <clause id="16036">
    <literal><![CDATA[
      f(f(x,f(x,y)),x) = f(x,y)
    ]]></literal>
    <justification jstring="[para(14863(a,1),15490(a,1,1,2)),rewrite([14863(7)])].">
      <j1 rule="para" parents="14863 15490"/>
      <j2 rule="rewrite" parents="14863"/>
    </justification>
  </clause>

  <clause id="16038">
    <literal><![CDATA[
      f(f(x,f(y,x)),f(y,x)) = x
    ]]></literal>
    <justification jstring="[para(15490(a,1),15182(a,1,2))].">
      <j1 rule="para" parents="15490 15182"/>
    </justification>
  </clause>

  <clause id="16146">
    <literal><![CDATA[
      f(x,f(f(y,x),f(f(f(f(y,x),f(x,f(y,x))),f(x,x)),f(f(x,x),z)))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(15677(a,1),52(a,1,2,1)),rewrite([15677(4)])].">
      <j1 rule="para" parents="15677 52"/>
      <j2 rule="rewrite" parents="15677"/>
    </justification>
  </clause>

  <clause id="16339">
    <literal><![CDATA[
      f(f(f(x,y),x),x) = f(x,y)
    ]]></literal>
    <justification jstring="[para(16030(a,1),15182(a,1,2))].">
      <j1 rule="para" parents="16030 15182"/>
    </justification>
  </clause>

  <clause id="16342">
    <literal><![CDATA[
      f(f(x,y),f(y,f(x,y))) = y
    ]]></literal>
    <justification jstring="[para(15490(a,1),16030(a,1,1))].">
      <j1 rule="para" parents="15490 16030"/>
    </justification>
  </clause>

  <clause id="16346">
    <literal><![CDATA[
      f(x,f(f(x,y),x)) = f(x,y)
    ]]></literal>
    <justification jstring="[para(16030(a,1),16030(a,1,1))].">
      <j1 rule="para" parents="16030 16030"/>
    </justification>
  </clause>

  <clause id="16379">
    <literal><![CDATA[
      f(x,f(f(y,x),f(c_0,f(f(x,x),z)))) = f(x,x)
    ]]></literal>
    <justification jstring="[back_rewrite(16146),rewrite([16342(5),13766(3)])].">
      <j1 rule="back_rewrite" parents="16146"/>
      <j2 rule="rewrite" parents="16342 13766"/>
    </justification>
  </clause>

  <clause id="16395">
    <literal><![CDATA[
      f(f(x,y),f(x,f(c_0,f(z,f(c_0,f(x,y)))))) = f(c_0,f(x,y))
    ]]></literal>
    <justification jstring="[back_rewrite(15230),rewrite([16346(4),15654(6)])].">
      <j1 rule="back_rewrite" parents="15230"/>
      <j2 rule="rewrite" parents="16346 15654"/>
    </justification>
  </clause>

  <clause id="16410">
    <literal><![CDATA[
      f(f(x,f(y,x)),f(c_0,f(x,f(f(y,x),z)))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(16031(a,1),3(a,1,2,2,1,1,1)),rewrite([13832(5,R),14660(5),15602(7),16038(7)])].">
      <j1 rule="para" parents="16031 3"/>
      <j2 rule="rewrite" parents="13832 14660 15602 16038"/>
    </justification>
  </clause>

  <clause id="16474">
    <literal><![CDATA[
      f(f(c_0,f(f(x,y),f(x,z))),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(16036(a,1),69(a,1,1,2,1,1,1)),rewrite([14268(2),16339(4)])].">
      <j1 rule="para" parents="16036 69"/>
      <j2 rule="rewrite" parents="14268 16339"/>
    </justification>
  </clause>

  <clause id="16498">
    <literal><![CDATA[
      f(f(x,y),y) = f(y,f(x,y))
    ]]></literal>
    <justification jstring="[para(15178(a,1),16036(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15178 16036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16500">
    <literal><![CDATA[
      f(f(x,y),x) = f(x,f(x,y))
    ]]></literal>
    <justification jstring="[para(15182(a,1),16036(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15182 16036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17408">
    <literal><![CDATA[
      f(f(f(f(f(x,x),y),f(f(f(y,f(f(x,z),y)),x),f(x,u))),f(z,x)),f(f(z,x),f(f(f(z,f(x,z)),f(z,x)),f(f(z,x),w)))) = f(z,x)
    ]]></literal>
    <justification jstring="[back_rewrite(12933),rewrite([16498(5),16498(14)])].">
      <j1 rule="back_rewrite" parents="12933"/>
      <j2 rule="rewrite" parents="16498 16498"/>
    </justification>
  </clause>

  <clause id="17478">
    <literal><![CDATA[
      f(f(x,y),f(f(f(x,x),z),f(f(f(z,f(f(x,y),z)),x),f(x,u)))) = x
    ]]></literal>
    <justification jstring="[back_rewrite(12323),rewrite([16498(6)])].">
      <j1 rule="back_rewrite" parents="12323"/>
      <j2 rule="rewrite" parents="16498"/>
    </justification>
  </clause>

  <clause id="17804">
    <literal><![CDATA[
      f(c_0,f(f(x,y),f(x,z))) = f(x,f(f(x,y),f(x,z)))
    ]]></literal>
    <justification jstring="[para(16474(a,1),42(a,1,1)),rewrite([13832(11,R),16500(7),15035(7)]),flip(a)].">
      <j1 rule="para" parents="16474 42"/>
      <j2 rule="rewrite" parents="13832 16500 15035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19912">
    <literal><![CDATA[
      f(f(x,x),f(f(y,f(x,x)),f(c_0,f(x,z)))) = x
    ]]></literal>
    <justification jstring="[para(13(a,1),16379(a,1,2,2,2,1)),rewrite([13832(11,R),14660(11),13845(11)])].">
      <j1 rule="para" parents="13 16379"/>
      <j2 rule="rewrite" parents="13832 14660 13845"/>
    </justification>
  </clause>

  <clause id="24396">
    <literal><![CDATA[
      f(f(x,y),f(y,f(f(x,y),z))) = f(c_0,f(y,f(f(x,y),z)))
    ]]></literal>
    <justification jstring="[para(16410(a,1),13(a,1,1)),rewrite([13832(12,R),16500(8),15035(8)])].">
      <j1 rule="para" parents="16410 13"/>
      <j2 rule="rewrite" parents="13832 16500 15035"/>
    </justification>
  </clause>

  <clause id="24398">
    <literal><![CDATA[
      f(f(x,f(y,x)),f(c_0,f(x,y))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(42(a,1),16410(a,1,2,2,2))].">
      <j1 rule="para" parents="42 16410"/>
    </justification>
  </clause>

  <clause id="24399">
    <literal><![CDATA[
      f(f(x,f(f(y,x),z)),f(y,x)) = f(c_0,f(x,f(f(y,x),z)))
    ]]></literal>
    <justification jstring="[para(16410(a,1),12289(a,1,2)),rewrite([13832(11,R),16500(7),15035(7)])].">
      <j1 rule="para" parents="16410 12289"/>
      <j2 rule="rewrite" parents="13832 16500 15035"/>
    </justification>
  </clause>

  <clause id="24577">
    <literal><![CDATA[
      f(f(x,y),f(y,x)) = f(c_0,f(y,x))
    ]]></literal>
    <justification jstring="[para(24398(a,1),13(a,1,1)),rewrite([13832(8,R),16500(6),15035(6)])].">
      <j1 rule="para" parents="24398 13"/>
      <j2 rule="rewrite" parents="13832 16500 15035"/>
    </justification>
  </clause>

  <clause id="24578">
    <literal><![CDATA[
      f(c_0,f(x,y)) = f(c_0,f(y,x))
    ]]></literal>
    <justification jstring="[para(24398(a,1),12289(a,1,2)),rewrite([13832(7,R),16500(5),15035(5),24577(3)])].">
      <j1 rule="para" parents="24398 12289"/>
      <j2 rule="rewrite" parents="13832 16500 15035 24577"/>
    </justification>
  </clause>

  <clause id="24579">
    <literal><![CDATA[
      f(x,y) = f(y,x)
    ]]></literal>
    <justification jstring="[para(24398(a,1),13787(a,1,2,2)),rewrite([24578(6),13832(7,R),16500(5),15035(5),24398(7)])].">
      <j1 rule="para" parents="24398 13787"/>
      <j2 rule="rewrite" parents="24578 13832 16500 15035 24398"/>
    </justification>
  </clause>

  <clause id="25062">
    <literal><![CDATA[
      f(f(x,y),f(x,f(z,f(x,y)))) = f(c_0,f(x,f(z,f(x,y))))
    ]]></literal>
    <justification jstring="[back_rewrite(24399),rewrite([24579(1),24579(2),24579(4),24579(5),24579(7),24579(8)])].">
      <j1 rule="back_rewrite" parents="24399"/>
      <j2 rule="rewrite" parents="24579 24579 24579 24579 24579 24579"/>
    </justification>
  </clause>

  <clause id="25063">
    <literal><![CDATA[
      f(f(x,y),f(y,f(z,f(x,y)))) = f(c_0,f(y,f(z,f(x,y))))
    ]]></literal>
    <justification jstring="[back_rewrite(24396),rewrite([24579(3),24579(8)])].">
      <j1 rule="back_rewrite" parents="24396"/>
      <j2 rule="rewrite" parents="24579 24579"/>
    </justification>
  </clause>

  <clause id="25210">
    <literal><![CDATA[
      f(f(x,y),f(f(z,f(x,x)),f(f(x,u),f(x,f(z,f(z,f(x,y))))))) = x
    ]]></literal>
    <justification jstring="[back_rewrite(17478),rewrite([24579(3),24579(5),24579(7),24579(9)])].">
      <j1 rule="back_rewrite" parents="17478"/>
      <j2 rule="rewrite" parents="24579 24579 24579 24579"/>
    </justification>
  </clause>

  <clause id="25228">
    <literal><![CDATA[
      f(x,f(c_0,f(y,f(z,f(x,y))))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(17408),rewrite([24579(2),24579(4),24579(6),24579(8),24579(10),24579(11),25210(11),24579(1),24579(4),24579(5),16342(5),24579(2),24579(3),25063(5),24579(7)])].">
      <j1 rule="back_rewrite" parents="17408"/>
      <j2 rule="rewrite" parents="24579 24579 24579 24579 24579 24579 25210 24579 24579 24579 16342 24579 24579 25063 24579"/>
    </justification>
  </clause>

  <clause id="25354">
    <literal><![CDATA[
      f(x,f(c_0,f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(14862),rewrite([24579(4)])].">
      <j1 rule="back_rewrite" parents="14862"/>
      <j2 rule="rewrite" parents="24579"/>
    </justification>
  </clause>

  <clause id="25514">
    <literal><![CDATA[
      f(x,f(c_0,f(y,f(z,f(y,x))))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(25228(a,1),24579(a,2)),rewrite([24579(2),24579(6),24579(7)])].">
      <j1 rule="para" parents="25228 24579"/>
      <j2 rule="rewrite" parents="24579 24579 24579"/>
    </justification>
  </clause>

  <clause id="25518">
    <literal><![CDATA[
      f(x,f(y,f(x,f(y,z)))) = f(x,f(y,z))
    ]]></literal>
    <justification jstring="[para(17804(a,1),25228(a,1,2)),rewrite([25062(5),14690(6)])].">
      <j1 rule="para" parents="17804 25228"/>
      <j2 rule="rewrite" parents="25062 14690"/>
    </justification>
  </clause>

  <clause id="25556">
    <literal><![CDATA[
      f(f(x,f(y,y)),f(c_0,f(y,z))) = f(y,z)
    ]]></literal>
    <justification jstring="[para(19912(a,1),25514(a,1,2,2,2)),rewrite([24579(7),12290(7),13845(6),24579(4),14690(4)]),flip(a)].">
      <j1 rule="para" parents="19912 25514"/>
      <j2 rule="rewrite" parents="24579 12290 13845 24579 14690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25557">
    <literal><![CDATA[
      f(x,f(c_0,f(y,f(c_0,f(x,z))))) = f(y,f(c_0,f(x,z)))
    ]]></literal>
    <justification jstring="[para(16395(a,1),25514(a,1,2,2,2)),rewrite([14690(11),24579(10),25354(10)]),flip(a)].">
      <j1 rule="para" parents="16395 25514"/>
      <j2 rule="rewrite" parents="14690 24579 25354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25687">
    <literal><![CDATA[
      f(f(x,x),f(y,f(c_0,f(z,x)))) = x
    ]]></literal>
    <justification jstring="[para(13(a,1),25556(a,1,2,2)),rewrite([13832(3,R),24579(3),24579(6),13832(6),24579(6),13(9)])].">
      <j1 rule="para" parents="13 25556"/>
      <j2 rule="rewrite" parents="13832 24579 24579 13832 24579 13"/>
    </justification>
  </clause>

  <clause id="25792">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),f(c_0,f(y,z))) = f(z,f(c_0,f(x,y)))
    ]]></literal>
    <justification jstring="[para(25687(a,1),25514(a,1,2,2,2)),rewrite([24579(5)])].">
      <j1 rule="para" parents="25687 25514"/>
      <j2 rule="rewrite" parents="24579"/>
    </justification>
  </clause>

  <clause id="32400">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),f(c_0,f(z,y))) = f(x,f(c_0,f(z,y)))
    ]]></literal>
    <justification jstring="[para(25792(a,2),14690(a,2)),rewrite([25518(7),24579(9),24579(11)]),flip(a)].">
      <j1 rule="para" parents="25792 14690"/>
      <j2 rule="rewrite" parents="25518 24579 24579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32746">
    <literal><![CDATA[
      f(x,f(c_0,f(y,z))) = f(y,f(c_0,f(x,z)))
    ]]></literal>
    <justification jstring="[para(25792(a,2),25557(a,2)),rewrite([25557(7),24579(9),32400(11)])].">
      <j1 rule="para" parents="25792 25557"/>
      <j2 rule="rewrite" parents="25557 24579 32400"/>
    </justification>
  </clause>

  <clause id="32747">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer(A_SS)
    ]]></attribute>
    <justification jstring="[resolve(32746,a,14681,a)].">
      <j1 rule="resolve" parents="32746 14681"/>
    </justification>
  </clause>

</proof>

<proof number="2" length="287" max_count="59">

<comments><![CDATA[
% Proof 2 at 2297.78 (+ 7.82) seconds: MOD_SS.
% Length of proof is 287.
% Level of proof is 51.
% Maximum clause weight is 59.
% Given clauses 3799.

]]></comments>

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

  <clause id="3" type="assumption">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),z),f(f(f(f(f(y,x),z),z),y),f(y,u)))) = y
    ]]></literal>
    <attribute><![CDATA[
      label(MOL_SS)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

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

  <clause id="6">
    <literal><![CDATA[
      f(f(x,y),f(y,f(f(f(f(f(y,x),f(f(f(y,y),z),f(f(f(f(f(y,y),z),z),y),f(y,u)))),f(f(f(y,y),z),f(f(f(f(f(y,y),z),z),y),f(y,u)))),y),f(y,w)))) = y
    ]]></literal>
    <justification jstring="[para(3(a,1),3(a,1,2,1))].">
      <j1 rule="para" parents="3 3"/>
    </justification>
  </clause>

  <clause id="7">
    <literal><![CDATA[
      f(f(f(f(f(x,x),y),f(f(f(f(f(x,z),y),y),x),f(x,u))),f(z,x)),f(f(f(f(z,x),f(z,x)),w),f(f(f(f(x,w),w),f(z,x)),f(f(z,x),v5)))) = f(z,x)
    ]]></literal>
    <justification jstring="[para(3(a,1),3(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="3 3"/>
    </justification>
  </clause>

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

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

  <clause id="10">
    <literal><![CDATA[
      f(f(x,y),f(f(f(y,y),z),y)) = y
    ]]></literal>
    <justification jstring="[para(6(a,1),3(a,1,2,2))].">
      <j1 rule="para" parents="6 3"/>
    </justification>
  </clause>

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

  <clause id="14">
    <literal><![CDATA[
      f(x,f(f(x,y),f(f(f(f(f(f(x,x),f(z,x)),y),y),f(x,x)),f(f(x,x),u)))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(13(a,1),3(a,1,1)),rewrite([13(3)])].">
      <j1 rule="para" parents="13 3"/>
      <j2 rule="rewrite" parents="13"/>
    </justification>
  </clause>

  <clause id="16">
    <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(13(a,1),3(a,1,2,1))].">
      <j1 rule="para" parents="13 3"/>
    </justification>
  </clause>

  <clause id="17">
    <literal><![CDATA[
      f(f(f(x,x),f(y,x)),f(f(f(f(y,x),f(y,x)),z),f(f(f(f(x,z),z),f(y,x)),f(f(y,x),u)))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(13(a,1),3(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="13 3"/>
    </justification>
  </clause>

  <clause id="18">
    <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(13(a,1),3(a,1,2,2,1,1,1))].">
      <j1 rule="para" parents="13 3"/>
    </justification>
  </clause>

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

  <clause id="24">
    <literal><![CDATA[
      f(f(x,y),f(y,f(f(y,y),f(y,z)))) = y
    ]]></literal>
    <justification jstring="[back_rewrite(16),rewrite([22(7)])].">
      <j1 rule="back_rewrite" parents="16"/>
      <j2 rule="rewrite" parents="22"/>
    </justification>
  </clause>

  <clause id="27">
    <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(22(a,1),3(a,1,2,2,1,1,1))].">
      <j1 rule="para" parents="22 3"/>
    </justification>
  </clause>

  <clause id="34">
    <literal><![CDATA[
      f(f(f(x,x),y),x) = f(x,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),13(a,1,1)),rewrite([10(7)]),flip(a)].">
      <j1 rule="para" parents="10 13"/>
      <j2 rule="rewrite" parents="10"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38">
    <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(34(a,1),3(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="34 3"/>
    </justification>
  </clause>

  <clause id="39">
    <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(34(a,1),3(a,1,2,2,1,1))].">
      <j1 rule="para" parents="34 3"/>
    </justification>
  </clause>

  <clause id="42">
    <literal><![CDATA[
      f(f(x,y),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(13(a,1),34(a,1,1,1)),rewrite([13(6)])].">
      <j1 rule="para" parents="13 34"/>
      <j2 rule="rewrite" parents="13"/>
    </justification>
  </clause>

  <clause id="43">
    <literal><![CDATA[
      f(f(f(f(f(x,x),y),f(f(f(f(f(x,z),y),y),x),f(x,u))),f(z,x)),f(f(f(f(z,x),f(z,x)),w),f(f(f(f(x,w),w),f(z,x)),x))) = f(z,x)
    ]]></literal>
    <justification jstring="[para(3(a,1),7(a,1,2,2,2))].">
      <j1 rule="para" parents="3 7"/>
    </justification>
  </clause>

  <clause id="45">
    <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),w)))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(13(a,1),7(a,1,1,1,2,1,1,1))].">
      <j1 rule="para" parents="13 7"/>
    </justification>
  </clause>

  <clause id="52">
    <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(34(a,1),7(a,1,1)),rewrite([42(3),42(3)])].">
      <j1 rule="para" parents="34 7"/>
      <j2 rule="rewrite" parents="42 42"/>
    </justification>
  </clause>

  <clause id="55">
    <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(42(a,1),3(a,1,2,2,1,1))].">
      <j1 rule="para" parents="42 3"/>
    </justification>
  </clause>

  <clause id="56">
    <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(42(a,1),3(a,1,2,2,2))].">
      <j1 rule="para" parents="42 3"/>
    </justification>
  </clause>

  <clause id="57">
    <literal><![CDATA[
      f(x,f(f(y,x),f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(3(a,1),42(a,1,1))].">
      <j1 rule="para" parents="3 42"/>
    </justification>
  </clause>

  <clause id="63">
    <literal><![CDATA[
      f(x,f(f(x,y),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(42(a,1),42(a,1,1))].">
      <j1 rule="para" parents="42 42"/>
    </justification>
  </clause>

  <clause id="65">
    <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(57(a,1),3(a,1,2,1))].">
      <j1 rule="para" parents="57 3"/>
    </justification>
  </clause>

  <clause id="68">
    <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(57(a,1),3(a,1,2,2,2))].">
      <j1 rule="para" parents="57 3"/>
    </justification>
  </clause>

  <clause id="69">
    <literal><![CDATA[
      f(f(f(f(x,x),y),f(f(f(f(f(x,z),y),y),x),f(x,u))),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(3(a,1),57(a,1,2,1)),rewrite([3(20),3(22)])].">
      <j1 rule="para" parents="3 57"/>
      <j2 rule="rewrite" parents="3 3"/>
    </justification>
  </clause>

  <clause id="77">
    <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(x,u)))) = x
    ]]></literal>
    <justification jstring="[para(63(a,1),3(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="63 3"/>
    </justification>
  </clause>

  <clause id="84">
    <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(24(a,1),34(a,1)),flip(a)].">
      <j1 rule="para" parents="24 34"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="96">
    <literal><![CDATA[
      f(f(f(f(x,x),f(f(f(y,y),z),f(f(f(f(f(y,x),z),z),y),f(y,u)))),f(f(f(y,f(f(f(y,y),z),f(f(f(f(f(y,x),z),z),y),f(y,u)))),x),f(x,w))),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(8(a,1),57(a,1,2,1)),rewrite([8(52),8(54)])].">
      <j1 rule="para" parents="8 57"/>
      <j2 rule="rewrite" parents="8 8"/>
    </justification>
  </clause>

  <clause id="129">
    <literal><![CDATA[
      f(f(f(x,x),f(y,x)),f(f(f(f(y,x),f(y,x)),z),f(f(f(f(x,z),z),f(y,x)),x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(13(a,1),9(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="13 9"/>
    </justification>
  </clause>

  <clause id="130">
    <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(13(a,1),9(a,1,2,2,1,1,1))].">
      <j1 rule="para" parents="13 9"/>
    </justification>
  </clause>

  <clause id="132">
    <literal><![CDATA[
      f(f(x,f(y,f(x,x))),f(f(f(f(y,f(x,x)),f(y,f(x,x))),z),f(f(f(f(f(x,x),z),z),f(y,f(x,x))),f(x,x)))) = f(y,f(x,x))
    ]]></literal>
    <justification jstring="[para(22(a,1),9(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="22 9"/>
    </justification>
  </clause>

  <clause id="136">
    <literal><![CDATA[
      f(f(f(x,y),f(x,y)),f(f(f(f(x,y),f(x,y)),f(x,y)),f(f(f(f(x,y),f(x,y)),f(x,y)),y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(34(a,1),9(a,1,2,2,1,1))].">
      <j1 rule="para" parents="34 9"/>
    </justification>
  </clause>

  <clause id="138">
    <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)),y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(42(a,1),9(a,1,2,2,1,1,1,1))].">
      <j1 rule="para" parents="42 9"/>
    </justification>
  </clause>

  <clause id="139">
    <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(42(a,1),9(a,1,2,2,1,1))].">
      <j1 rule="para" parents="42 9"/>
    </justification>
  </clause>

  <clause id="159">
    <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(39(a,1),57(a,1,2,1)),rewrite([39(16),39(18)])].">
      <j1 rule="para" parents="39 57"/>
      <j2 rule="rewrite" parents="39 39"/>
    </justification>
  </clause>

  <clause id="160">
    <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(57(a,1),39(a,1,2,2,2))].">
      <j1 rule="para" parents="57 39"/>
    </justification>
  </clause>

  <clause id="167">
    <literal><![CDATA[
      f(x,f(f(x,x),f(x,y))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(84(a,1),13(a,1,1)),rewrite([84(9)]),flip(a)].">
      <j1 rule="para" parents="84 13"/>
      <j2 rule="rewrite" parents="84"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="174">
    <literal><![CDATA[
      f(f(x,y),f(y,f(f(f(f(f(y,x),f(y,f(f(y,y),z))),f(y,f(f(y,y),z))),y),f(y,u)))) = y
    ]]></literal>
    <justification jstring="[para(167(a,1),3(a,1,2,1)),rewrite([42(4),42(5),42(9)])].">
      <j1 rule="para" parents="167 3"/>
      <j2 rule="rewrite" parents="42 42 42"/>
    </justification>
  </clause>

  <clause id="176">
    <literal><![CDATA[
      f(f(x,y),f(f(f(x,y),f(x,y)),y)) = f(f(x,y),f(x,y))
    ]]></literal>
    <justification jstring="[para(3(a,1),167(a,1,2,2))].">
      <j1 rule="para" parents="3 167"/>
    </justification>
  </clause>

  <clause id="177">
    <literal><![CDATA[
      f(f(x,x),f(x,f(f(x,x),y))) = x
    ]]></literal>
    <justification jstring="[para(13(a,1),167(a,1,2,1)),rewrite([42(8)])].">
      <j1 rule="para" parents="13 167"/>
      <j2 rule="rewrite" parents="42"/>
    </justification>
  </clause>

  <clause id="179">
    <literal><![CDATA[
      f(f(x,y),f(f(f(x,y),f(x,y)),x)) = f(f(x,y),f(x,y))
    ]]></literal>
    <justification jstring="[para(42(a,1),167(a,1,2,2))].">
      <j1 rule="para" parents="42 167"/>
    </justification>
  </clause>

  <clause id="180">
    <literal><![CDATA[
      f(x,f(f(x,x),f(y,x))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(57(a,1),167(a,1,2,2))].">
      <j1 rule="para" parents="57 167"/>
    </justification>
  </clause>

  <clause id="184">
    <literal><![CDATA[
      f(f(x,x),f(x,f(f(f(x,f(x,f(f(x,x),y))),x),f(x,z)))) = x
    ]]></literal>
    <justification jstring="[para(177(a,1),3(a,1,2,2,1,1,1)),rewrite([177(6)])].">
      <j1 rule="para" parents="177 3"/>
      <j2 rule="rewrite" parents="177"/>
    </justification>
  </clause>

  <clause id="186">
    <literal><![CDATA[
      f(f(x,x),f(x,f(y,f(x,x)))) = x
    ]]></literal>
    <justification jstring="[para(57(a,1),177(a,1,2,2))].">
      <j1 rule="para" parents="57 177"/>
    </justification>
  </clause>

  <clause id="216">
    <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(57(a,1),159(a,1,1,2,2))].">
      <j1 rule="para" parents="57 159"/>
    </justification>
  </clause>

  <clause id="221">
    <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(13(a,1),160(a,1,1)),rewrite([42(3),42(5)])].">
      <j1 rule="para" parents="13 160"/>
      <j2 rule="rewrite" parents="42 42"/>
    </justification>
  </clause>

  <clause id="226">
    <literal><![CDATA[
      f(f(x,y),f(y,f(f(f(f(f(f(f(x,y),f(x,y)),f(z,f(x,y))),f(y,y)),f(y,y)),f(f(x,y),f(x,y))),f(f(f(x,y),f(x,y)),u)))) = f(f(x,y),f(x,y))
    ]]></literal>
    <justification jstring="[para(13(a,1),14(a,1,2,1))].">
      <j1 rule="para" parents="13 14"/>
    </justification>
  </clause>

  <clause id="252">
    <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(13(a,1),216(a,1,1,1,1)),rewrite([42(5),42(11)])].">
      <j1 rule="para" parents="13 216"/>
      <j2 rule="rewrite" parents="42 42"/>
    </justification>
  </clause>

  <clause id="273">
    <literal><![CDATA[
      f(f(x,x),f(x,f(f(f(x,f(x,f(f(x,x),y))),x),f(z,x)))) = x
    ]]></literal>
    <justification jstring="[para(57(a,1),184(a,1,2,2,2))].">
      <j1 rule="para" parents="57 184"/>
    </justification>
  </clause>

  <clause id="287">
    <literal><![CDATA[
      f(f(x,x),f(f(f(x,f(x,x)),f(f(x,f(x,x)),f(y,f(x,x)))),f(f(x,f(x,x)),f(f(x,f(x,x)),f(y,f(x,x)))))) = f(f(x,f(x,x)),f(f(x,f(x,x)),f(y,f(x,x))))
    ]]></literal>
    <justification jstring="[para(221(a,1),13(a,1,1))].">
      <j1 rule="para" parents="221 13"/>
    </justification>
  </clause>

  <clause id="289">
    <literal><![CDATA[
      f(f(f(f(x,y),f(x,y)),f(z,f(x,y))),f(f(f(f(z,f(x,y)),f(z,f(x,y))),f(y,y)),f(f(f(y,f(y,y)),f(z,f(x,y))),f(f(z,f(x,y)),u)))) = f(z,f(x,y))
    ]]></literal>
    <justification jstring="[para(13(a,1),17(a,1,2,2,1,1,1))].">
      <j1 rule="para" parents="13 17"/>
    </justification>
  </clause>

  <clause id="290">
    <literal><![CDATA[
      f(f(x,f(y,f(x,x))),f(f(f(f(y,f(x,x)),f(y,f(x,x))),x),f(f(f(x,x),f(y,f(x,x))),f(f(y,f(x,x)),z)))) = f(y,f(x,x))
    ]]></literal>
    <justification jstring="[para(34(a,1),17(a,1,2,2,1,1)),rewrite([42(3)])].">
      <j1 rule="para" parents="34 17"/>
      <j2 rule="rewrite" parents="42"/>
    </justification>
  </clause>

  <clause id="309">
    <literal><![CDATA[
      f(f(x,x),f(f(x,f(x,f(f(x,x),y))),x)) = x
    ]]></literal>
    <justification jstring="[para(57(a,1),273(a,1,2))].">
      <j1 rule="para" parents="57 273"/>
    </justification>
  </clause>

  <clause id="316">
    <literal><![CDATA[
      f(x,f(f(f(x,x),f(f(x,x),f(x,y))),f(x,x))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(13(a,1),309(a,1,1)),rewrite([42(5)])].">
      <j1 rule="para" parents="13 309"/>
      <j2 rule="rewrite" parents="42"/>
    </justification>
  </clause>

  <clause id="331">
    <literal><![CDATA[
      f(f(x,x),f(f(y,f(x,x)),f(f(f(f(y,f(x,x)),f(f(y,f(x,x)),f(y,f(x,x)))),x),f(x,z)))) = x
    ]]></literal>
    <justification jstring="[para(22(a,1),18(a,1,1)),rewrite([57(8)])].">
      <j1 rule="para" parents="22 18"/>
      <j2 rule="rewrite" parents="57"/>
    </justification>
  </clause>

  <clause id="333">
    <literal><![CDATA[
      f(f(f(x,x),x),f(f(f(x,x),x),f(f(x,x),f(x,y)))) = x
    ]]></literal>
    <justification jstring="[para(34(a,1),18(a,1,2,2,1)),rewrite([42(6)])].">
      <j1 rule="para" parents="34 18"/>
      <j2 rule="rewrite" parents="42"/>
    </justification>
  </clause>

  <clause id="337">
    <literal><![CDATA[
      f(f(x,f(y,z)),f(f(f(f(y,z),f(y,z)),f(x,x)),f(f(f(x,f(x,x)),f(y,z)),y))) = f(y,z)
    ]]></literal>
    <justification jstring="[para(42(a,1),18(a,1,2,2,2))].">
      <j1 rule="para" parents="42 18"/>
    </justification>
  </clause>

  <clause id="346">
    <literal><![CDATA[
      f(x,f(f(f(x,x),x),f(x,f(f(x,x),y)))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(216(a,1),18(a,1,2,2,1)),rewrite([13(4),42(3),57(6)])].">
      <j1 rule="para" parents="216 18"/>
      <j2 rule="rewrite" parents="13 42 57"/>
    </justification>
  </clause>

  <clause id="347">
    <literal><![CDATA[
      f(f(x,x),f(f(x,f(x,x)),f(f(x,x),f(x,y)))) = x
    ]]></literal>
    <justification jstring="[para(252(a,1),18(a,1,2,2,1)),rewrite([22(3),57(8)])].">
      <j1 rule="para" parents="252 18"/>
      <j2 rule="rewrite" parents="22 57"/>
    </justification>
  </clause>

  <clause id="366">
    <literal><![CDATA[
      f(f(x,x),f(f(x,f(x,x)),f(f(x,x),f(y,x)))) = x
    ]]></literal>
    <justification jstring="[para(57(a,1),347(a,1,2,2,2))].">
      <j1 rule="para" parents="57 347"/>
    </justification>
  </clause>

  <clause id="419">
    <literal><![CDATA[
      f(f(f(x,x),x),f(f(f(x,x),x),f(f(x,x),f(y,x)))) = x
    ]]></literal>
    <justification jstring="[para(57(a,1),333(a,1,2,2,2))].">
      <j1 rule="para" parents="57 333"/>
    </justification>
  </clause>

  <clause id="435">
    <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(27(a,1),57(a,1,2,1)),rewrite([27(19),27(21)])].">
      <j1 rule="para" parents="27 57"/>
      <j2 rule="rewrite" parents="27 27"/>
    </justification>
  </clause>

  <clause id="437">
    <literal><![CDATA[
      f(f(f(x,x),y),f(f(f(y,y),x),f(f(f(f(x,x),x),y),f(z,y)))) = y
    ]]></literal>
    <justification jstring="[para(57(a,1),27(a,1,2,2,2))].">
      <j1 rule="para" parents="57 27"/>
    </justification>
  </clause>

  <clause id="462">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(x,f(x,x)),f(x,f(y,f(x,x))))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(13(a,1),419(a,1,1,1)),rewrite([42(5),42(7)])].">
      <j1 rule="para" parents="13 419"/>
      <j2 rule="rewrite" parents="42 42"/>
    </justification>
  </clause>

  <clause id="526">
    <literal><![CDATA[
      f(f(f(x,f(y,y)),f(f(f(f(x,f(y,y)),f(f(x,f(y,y)),f(x,f(y,y)))),y),f(y,z))),f(y,y)) = y
    ]]></literal>
    <justification jstring="[para(57(a,1),435(a,1,1,1)),rewrite([42(13)])].">
      <j1 rule="para" parents="57 435"/>
      <j2 rule="rewrite" parents="42"/>
    </justification>
  </clause>

  <clause id="554">
    <literal><![CDATA[
      f(f(f(x,y),f(f(f(f(x,y),y),f(x,x)),f(f(x,x),z))),x) = f(x,x)
    ]]></literal>
    <justification jstring="[para(52(a,1),57(a,1,2,1)),rewrite([52(20),42(12),52(20)])].">
      <j1 rule="para" parents="52 57"/>
      <j2 rule="rewrite" parents="52 42 52"/>
    </justification>
  </clause>

  <clause id="574">
    <literal><![CDATA[
      f(f(x,x),f(x,f(f(f(x,f(f(f(x,x),x),f(f(f(x,x),x),f(x,y)))),x),f(z,x)))) = x
    ]]></literal>
    <justification jstring="[para(39(a,1),68(a,1,2,2,1,1,1)),rewrite([39(10)])].">
      <j1 rule="para" parents="39 68"/>
      <j2 rule="rewrite" parents="39"/>
    </justification>
  </clause>

  <clause id="666">
    <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="[para(43(a,1),22(a,1,1)),rewrite([176(9)]),flip(a)].">
      <j1 rule="para" parents="43 22"/>
      <j2 rule="rewrite" parents="176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="673">
    <literal><![CDATA[
      f(f(f(f(x,x),x),f(f(x,x),x)),x) = f(f(x,x),x)
    ]]></literal>
    <justification jstring="[para(43(a,1),186(a,1,2,2)),rewrite([666(13),34(14),42(11)]),flip(a)].">
      <j1 rule="para" parents="43 186"/>
      <j2 rule="rewrite" parents="666 34 42"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="678">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),f(x,f(x,x))),f(x,x)) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(13(a,1),673(a,1,1,1,1)),rewrite([42(5),42(10)])].">
      <j1 rule="para" parents="13 673"/>
      <j2 rule="rewrite" parents="42 42"/>
    </justification>
  </clause>

  <clause id="682">
    <literal><![CDATA[
      f(f(x,f(f(x,x),x)),f(f(f(x,x),x),f(f(f(x,x),f(f(x,x),x)),f(f(f(x,x),x),y)))) = f(f(x,x),x)
    ]]></literal>
    <justification jstring="[para(673(a,1),38(a,1,2,1)),rewrite([34(8)])].">
      <j1 rule="para" parents="673 38"/>
      <j2 rule="rewrite" parents="34"/>
    </justification>
  </clause>

  <clause id="684">
    <literal><![CDATA[
      f(f(f(x,x),x),f(f(f(x,x),y),f(f(f(f(f(f(x,x),x),y),y),x),f(z,x)))) = x
    ]]></literal>
    <justification jstring="[para(673(a,1),68(a,1,1)),rewrite([57(10)])].">
      <j1 rule="para" parents="673 68"/>
      <j2 rule="rewrite" parents="57"/>
    </justification>
  </clause>

  <clause id="890">
    <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(13(a,1),55(a,1,2,2,1)),rewrite([42(5),57(8)])].">
      <j1 rule="para" parents="13 55"/>
      <j2 rule="rewrite" parents="42 57"/>
    </justification>
  </clause>

  <clause id="891">
    <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(22(a,1),55(a,1,2,2,1)),rewrite([57(9)])].">
      <j1 rule="para" parents="22 55"/>
      <j2 rule="rewrite" parents="57"/>
    </justification>
  </clause>

  <clause id="919">
    <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(57(a,1),891(a,1,2,2,2))].">
      <j1 rule="para" parents="57 891"/>
    </justification>
  </clause>

  <clause id="1437">
    <literal><![CDATA[
      f(f(f(x,x),x),f(x,f(f(f(f(f(f(x,x),x),f(x,f(f(x,x),y))),f(x,f(f(x,x),y))),x),f(z,x)))) = x
    ]]></literal>
    <justification jstring="[para(167(a,1),684(a,1,2,1)),rewrite([42(5),42(7),42(11)])].">
      <j1 rule="para" parents="167 684"/>
      <j2 rule="rewrite" parents="42 42 42"/>
    </justification>
  </clause>

  <clause id="1847">
    <literal><![CDATA[
      f(f(x,x),f(f(x,f(f(f(x,x),x),f(f(f(x,x),x),f(x,y)))),x)) = x
    ]]></literal>
    <justification jstring="[para(57(a,1),574(a,1,2))].">
      <j1 rule="para" parents="57 574"/>
    </justification>
  </clause>

  <clause id="2174">
    <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(42(a,1),129(a,1,2,2,1,1))].">
      <j1 rule="para" parents="42 129"/>
    </justification>
  </clause>

  <clause id="2218">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(x,f(f(x,x),y))) = x
    ]]></literal>
    <justification jstring="[para(18(a,1),130(a,1,2,2,1)),rewrite([42(3),42(6),42(10),42(13),42(16),42(19),42(27),177(27),22(23),42(9),42(3),42(6)]),flip(a)].">
      <j1 rule="para" parents="18 130"/>
      <j2 rule="rewrite" parents="42 42 42 42 42 42 42 177 22 42 42 42"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2220">
    <literal><![CDATA[
      f(f(f(x,x),x),f(x,f(f(x,x),y))) = x
    ]]></literal>
    <justification jstring="[para(346(a,1),130(a,1,1)),rewrite([890(25),177(21),22(17),42(3)]),flip(a)].">
      <j1 rule="para" parents="346 130"/>
      <j2 rule="rewrite" parents="890 177 22 42"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2222">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(x,x),f(x,y))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(347(a,1),130(a,1,1)),rewrite([42(16),42(18),891(23),167(18),13(16)]),flip(a)].">
      <j1 rule="para" parents="347 130"/>
      <j2 rule="rewrite" parents="42 42 891 167 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2226">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(x,x),f(y,x))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(366(a,1),130(a,1,1)),rewrite([42(16),42(18),919(23),180(18),13(16)]),flip(a)].">
      <j1 rule="para" parents="366 130"/>
      <j2 rule="rewrite" parents="42 42 919 180 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2232">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(x,f(y,f(x,x)))) = x
    ]]></literal>
    <justification jstring="[para(462(a,1),130(a,1,2,2,1)),rewrite([186(27),22(23),42(9)]),flip(a)].">
      <j1 rule="para" parents="462 130"/>
      <j2 rule="rewrite" parents="186 22 42"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2238">
    <literal><![CDATA[
      f(f(f(x,x),x),f(f(x,x),f(y,x))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(437(a,1),130(a,1,2,2,1)),rewrite([42(4),42(4),42(8),34(6),42(7),42(11),42(11),42(15),34(13),42(14),42(17),42(17),42(21),34(19),42(20),42(24),42(25),42(27),34(25),42(26),180(26),13(24),34(9),42(4),42(4),42(8),34(6),42(7)]),flip(a)].">
      <j1 rule="para" parents="437 130"/>
      <j2 rule="rewrite" parents="42 42 42 34 42 42 42 42 34 42 42 42 42 34 42 42 42 42 34 42 180 13 34 42 42 42 34 42"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2268">
    <literal><![CDATA[
      f(f(f(x,x),x),f(x,f(f(f(x,f(x,f(f(x,x),y))),x),f(z,x)))) = x
    ]]></literal>
    <justification jstring="[back_rewrite(1437),rewrite([2220(8)])].">
      <j1 rule="back_rewrite" parents="1437"/>
      <j2 rule="rewrite" parents="2220"/>
    </justification>
  </clause>

  <clause id="2436">
    <literal><![CDATA[
      f(f(f(x,y),f(f(x,y),f(x,y))),f(f(f(x,y),f(x,y)),y)) = f(f(x,y),f(x,y))
    ]]></literal>
    <justification jstring="[para(3(a,1),2222(a,1,2,2))].">
      <j1 rule="para" parents="3 2222"/>
    </justification>
  </clause>

  <clause id="2438">
    <literal><![CDATA[
      f(f(f(x,y),f(f(x,y),f(x,y))),f(f(f(x,y),f(x,y)),x)) = f(f(x,y),f(x,y))
    ]]></literal>
    <justification jstring="[para(42(a,1),2222(a,1,2,2))].">
      <j1 rule="para" parents="42 2222"/>
    </justification>
  </clause>

  <clause id="2632">
    <literal><![CDATA[
      f(f(f(x,x),x),f(f(x,f(x,f(f(x,x),y))),x)) = x
    ]]></literal>
    <justification jstring="[para(57(a,1),2268(a,1,2))].">
      <j1 rule="para" parents="57 2268"/>
    </justification>
  </clause>

  <clause id="2679">
    <literal><![CDATA[
      f(f(x,f(x,f(f(x,x),y))),x) = f(x,x)
    ]]></literal>
    <justification jstring="[para(2632(a,1),129(a,1,2,2,1)),rewrite([309(7),13(14)]),flip(a)].">
      <j1 rule="para" parents="2632 129"/>
      <j2 rule="rewrite" parents="309 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2680">
    <literal><![CDATA[
      f(f(f(x,x),f(f(x,x),f(x,y))),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(2632(a,1),132(a,1,2,2,1)),rewrite([42(5),316(8),42(6),42(13),42(21),22(19),42(3),42(5)]),flip(a)].">
      <j1 rule="para" parents="2632 132"/>
      <j2 rule="rewrite" parents="42 316 42 42 42 22 42 42"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2766">
    <literal><![CDATA[
      f(f(f(f(x,y),f(x,y)),f(f(f(x,y),f(x,y)),y)),f(f(x,y),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(3(a,1),2680(a,1,1,2,2))].">
      <j1 rule="para" parents="3 2680"/>
    </justification>
  </clause>

  <clause id="2769">
    <literal><![CDATA[
      f(f(f(f(x,y),f(x,y)),f(f(f(x,y),f(x,y)),x)),f(f(x,y),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(42(a,1),2680(a,1,1,2,2))].">
      <j1 rule="para" parents="42 2680"/>
    </justification>
  </clause>

  <clause id="3046">
    <literal><![CDATA[
      f(f(f(x,x),f(x,y)),f(f(f(f(x,y),f(x,y)),f(f(x,x),f(z,x))),f(f(f(f(x,x),f(f(x,x),f(z,x))),f(x,y)),y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(180(a,1),138(a,1,2,2,1,1,1))].">
      <j1 rule="para" parents="180 138"/>
    </justification>
  </clause>

  <clause id="3062">
    <literal><![CDATA[
      f(f(f(x,y),f(x,y)),f(f(f(f(x,y),f(x,y)),f(x,y)),f(f(f(f(x,y),f(x,y)),f(x,y)),f(f(f(f(x,y),f(x,y)),z),f(f(f(f(x,z),z),f(x,y)),y))))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(138(a,1),136(a,1,1,1)),rewrite([138(15),138(17),138(18),138(20),138(22),138(23),138(25),138(40)])].">
      <j1 rule="para" parents="138 136"/>
      <j2 rule="rewrite" parents="138 138 138 138 138 138 138 138"/>
    </justification>
  </clause>

  <clause id="3136">
    <literal><![CDATA[
      f(f(f(f(x,x),f(y,x)),f(f(x,x),x)),x) = f(f(x,x),x)
    ]]></literal>
    <justification jstring="[para(2238(a,1),139(a,1,2,1,2,1)),rewrite([2238(18),42(14),673(12),2238(14),34(13),13(10)])].">
      <j1 rule="para" parents="2238 139"/>
      <j2 rule="rewrite" parents="2238 42 673 2238 34 13"/>
    </justification>
  </clause>

  <clause id="3159">
    <literal><![CDATA[
      f(f(x,x),f(f(f(x,x),f(f(x,x),x)),f(f(f(x,x),x),f(y,x)))) = x
    ]]></literal>
    <justification jstring="[para(3136(a,1),68(a,1,2,2,1))].">
      <j1 rule="para" parents="3136 68"/>
    </justification>
  </clause>

  <clause id="3163">
    <literal><![CDATA[
      f(f(f(x,y),f(x,y)),f(f(f(f(x,y),f(x,y)),f(f(f(x,y),f(x,y)),f(x,y))),f(f(f(f(x,y),f(x,y)),f(x,y)),x))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(3136(a,1),56(a,1,2,2,1))].">
      <j1 rule="para" parents="3136 56"/>
    </justification>
  </clause>

  <clause id="3398">
    <literal><![CDATA[
      f(f(x,x),f(f(x,x),x)) = x
    ]]></literal>
    <justification jstring="[para(13(a,1),3159(a,1,2))].">
      <j1 rule="para" parents="13 3159"/>
    </justification>
  </clause>

  <clause id="3413">
    <literal><![CDATA[
      f(x,f(x,f(x,x))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(678(a,1),3159(a,1,2,2,2)),rewrite([42(3),42(3),42(3),42(6),13(9)])].">
      <j1 rule="para" parents="678 3159"/>
      <j2 rule="rewrite" parents="42 42 42 42 13"/>
    </justification>
  </clause>

  <clause id="3440">
    <literal><![CDATA[
      f(f(f(x,y),f(x,y)),f(f(x,y),f(f(f(f(x,y),f(x,y)),f(x,y)),x))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(3163),rewrite([3398(12)])].">
      <j1 rule="back_rewrite" parents="3163"/>
      <j2 rule="rewrite" parents="3398"/>
    </justification>
  </clause>

  <clause id="3453">
    <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(682),rewrite([3398(9)])].">
      <j1 rule="back_rewrite" parents="682"/>
      <j2 rule="rewrite" parents="3398"/>
    </justification>
  </clause>

  <clause id="3484">
    <literal><![CDATA[
      f(f(x,y),f(y,f(f(f(f(f(y,x),f(f(y,y),y)),f(f(y,y),y)),y),f(z,y)))) = y
    ]]></literal>
    <justification jstring="[para(3398(a,1),68(a,1,2,1))].">
      <j1 rule="para" parents="3398 68"/>
    </justification>
  </clause>

  <clause id="4511">
    <literal><![CDATA[
      f(f(f(x,y),f(f(x,y),f(x,y))),f(f(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)),y)))) = f(f(x,y),f(x,y))
    ]]></literal>
    <justification jstring="[para(138(a,1),2436(a,1,1,1)),rewrite([138(15),138(16),138(19),138(20),138(34),138(35)])].">
      <j1 rule="para" parents="138 2436"/>
      <j2 rule="rewrite" parents="138 138 138 138 138 138"/>
    </justification>
  </clause>

  <clause id="5302">
    <literal><![CDATA[
      f(f(f(f(x,y),f(x,y)),f(f(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)),y)))),f(f(x,y),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(138(a,1),2766(a,1,1,1,1)),rewrite([138(15),138(17),138(18),138(32),138(33),138(36)])].">
      <j1 rule="para" parents="138 2766"/>
      <j2 rule="rewrite" parents="138 138 138 138 138 138"/>
    </justification>
  </clause>

  <clause id="5967">
    <literal><![CDATA[
      f(f(x,y),f(f(f(f(y,x),f(f(y,y),y)),f(f(y,y),y)),y)) = y
    ]]></literal>
    <justification jstring="[para(57(a,1),3484(a,1,2))].">
      <j1 rule="para" parents="57 3484"/>
    </justification>
  </clause>

  <clause id="6050">
    <literal><![CDATA[
      f(f(f(x,x),x),f(f(f(f(f(x,x),x),f(f(x,x),x)),f(f(x,x),x)),x)) = x
    ]]></literal>
    <justification jstring="[para(22(a,1),5967(a,1,2,1,1)),rewrite([673(6)])].">
      <j1 rule="para" parents="22 5967"/>
      <j2 rule="rewrite" parents="673"/>
    </justification>
  </clause>

  <clause id="6054">
    <literal><![CDATA[
      f(f(f(x,x),f(x,y)),f(f(f(x,f(f(f(x,y),f(x,y)),f(x,y))),f(f(f(x,y),f(x,y)),f(x,y))),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[para(42(a,1),5967(a,1,2,1,1,1))].">
      <j1 rule="para" parents="42 5967"/>
    </justification>
  </clause>

  <clause id="6056">
    <literal><![CDATA[
      f(f(f(f(x,y),f(x,y)),y),f(f(f(f(x,y),f(f(y,y),y)),f(f(y,y),y)),y)) = y
    ]]></literal>
    <justification jstring="[para(57(a,1),5967(a,1,2,1,1,1))].">
      <j1 rule="para" parents="57 5967"/>
    </justification>
  </clause>

  <clause id="6058">
    <literal><![CDATA[
      f(f(f(f(x,y),f(x,y)),x),f(f(f(f(x,y),f(f(x,x),x)),f(f(x,x),x)),x)) = x
    ]]></literal>
    <justification jstring="[para(63(a,1),5967(a,1,2,1,1,1))].">
      <j1 rule="para" parents="63 5967"/>
    </justification>
  </clause>

  <clause id="6111">
    <literal><![CDATA[
      f(f(f(f(x,f(x,x)),f(f(x,x),x)),f(f(x,x),x)),x) = f(x,x)
    ]]></literal>
    <justification jstring="[para(5967(a,1),129(a,1,2,2,1)),rewrite([13(33),34(12)]),flip(a)].">
      <j1 rule="para" parents="5967 129"/>
      <j2 rule="rewrite" parents="13 34"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6167">
    <literal><![CDATA[
      f(f(f(x,x),x),f(x,f(f(f(x,f(x,x)),f(f(x,x),x)),f(f(x,x),x)))) = x
    ]]></literal>
    <justification jstring="[para(6111(a,1),2438(a,1,1,1)),rewrite([6111(10),6111(11),42(4),6111(11),6111(12),42(5),6111(21),6111(22),42(15)])].">
      <j1 rule="para" parents="6111 2438"/>
      <j2 rule="rewrite" parents="6111 6111 42 6111 6111 42 6111 6111 42"/>
    </justification>
  </clause>

  <clause id="6230">
    <literal><![CDATA[
      f(f(f(f(f(x,x),x),f(f(x,x),x)),f(f(x,x),x)),x) = f(x,x)
    ]]></literal>
    <justification jstring="[para(6050(a,1),129(a,1,2,2,1)),rewrite([13(33),34(12)]),flip(a)].">
      <j1 rule="para" parents="6050 129"/>
      <j2 rule="rewrite" parents="13 34"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6231">
    <literal><![CDATA[
      f(f(f(f(x,f(x,x)),f(x,f(x,x))),f(x,f(x,x))),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(6050(a,1),132(a,1,2,2,1)),rewrite([42(3),42(5),42(8),42(14),42(16),42(19),42(24),42(26),42(29),42(37),22(35),42(13),42(3),42(5),42(8)]),flip(a)].">
      <j1 rule="para" parents="6050 132"/>
      <j2 rule="rewrite" parents="42 42 42 42 42 42 42 42 42 42 22 42 42 42 42"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6275">
    <literal><![CDATA[
      f(f(f(x,x),f(f(x,x),f(f(f(x,f(x,x)),f(x,f(x,x))),f(x,f(x,x))))),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(6231(a,1),2769(a,1,1,1,1)),rewrite([6231(10),6231(11),6231(11),6231(22),6231(22),6231(24)])].">
      <j1 rule="para" parents="6231 2769"/>
      <j2 rule="rewrite" parents="6231 6231 6231 6231 6231 6231"/>
    </justification>
  </clause>

  <clause id="6278">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),f(f(f(x,f(x,x)),f(x,f(x,x))),f(x,f(x,x)))),x) = f(f(f(x,f(x,x)),f(x,f(x,x))),f(x,f(x,x)))
    ]]></literal>
    <justification jstring="[para(6231(a,1),3453(a,1,2,2,2)),rewrite([22(22),6231(21)])].">
      <j1 rule="para" parents="6231 3453"/>
      <j2 rule="rewrite" parents="22 6231"/>
    </justification>
  </clause>

  <clause id="6360">
    <literal><![CDATA[
      f(f(f(f(x,x),x),f(f(x,x),x)),f(f(f(f(x,x),x),f(f(f(f(f(x,x),x),f(f(x,x),x)),f(f(x,x),x)),f(x,x))),f(f(x,x),x))) = f(f(x,x),x)
    ]]></literal>
    <justification jstring="[para(6167(a,1),1847(a,1,2,1,2,2,2)),rewrite([6230(24)])].">
      <j1 rule="para" parents="6167 1847"/>
      <j2 rule="rewrite" parents="6230"/>
    </justification>
  </clause>

  <clause id="6870">
    <literal><![CDATA[
      f(f(x,y),f(f(f(f(y,x),f(y,f(f(y,y),z))),f(y,f(f(y,y),z))),y)) = y
    ]]></literal>
    <justification jstring="[para(226(a,1),174(a,1,2,2)),rewrite([57(23)])].">
      <j1 rule="para" parents="226 174"/>
      <j2 rule="rewrite" parents="57"/>
    </justification>
  </clause>

  <clause id="6964">
    <literal><![CDATA[
      f(f(f(f(f(f(x,y),f(x,f(f(x,x),z))),f(x,f(f(x,x),z))),x),f(y,x)),f(f(f(x,f(f(f(y,x),f(y,x)),f(y,x))),f(f(f(y,x),f(y,x)),f(y,x))),f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(6870(a,1),5967(a,1,2,1,1,1))].">
      <j1 rule="para" parents="6870 5967"/>
    </justification>
  </clause>

  <clause id="8980">
    <literal><![CDATA[
      f(f(x,x),f(x,f(f(f(x,x),x),f(f(x,x),f(f(x,x),f(f(f(x,f(x,x)),f(x,f(x,x))),f(x,f(x,x)))))))) = x
    ]]></literal>
    <justification jstring="[para(6275(a,1),3440(a,1,1,1)),rewrite([6275(14),6275(15),6275(15),6275(15),6275(16),6275(32)])].">
      <j1 rule="para" parents="6275 3440"/>
      <j2 rule="rewrite" parents="6275 6275 6275 6275 6275 6275"/>
    </justification>
  </clause>

  <clause id="9276">
    <literal><![CDATA[
      f(f(x,x),x) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(2218(a,1),290(a,1,2,2,2)),rewrite([3413(3),34(12),13(9)])].">
      <j1 rule="para" parents="2218 290"/>
      <j2 rule="rewrite" parents="3413 34 13"/>
    </justification>
  </clause>

  <clause id="9278">
    <literal><![CDATA[
      f(f(x,x),f(f(x,f(x,x)),f(f(x,f(x,x)),f(x,y)))) = x
    ]]></literal>
    <justification jstring="[para(2679(a,1),290(a,1,1,2)),rewrite([42(3),42(6),2680(8),42(6),2680(8),9276(3),42(9),2680(11),9276(5),42(10),2680(12),42(14),2680(16)])].">
      <j1 rule="para" parents="2679 290"/>
      <j2 rule="rewrite" parents="42 42 2680 42 2680 9276 42 2680 9276 42 2680 42 2680"/>
    </justification>
  </clause>

  <clause id="9288">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),f(f(x,f(x,x)),f(x,f(x,x)))),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(6111(a,1),290(a,2)),rewrite([42(4),9276(2),42(5),42(8),9276(8),42(15),9276(13),42(16),42(19),9276(19),42(25),9276(23),42(26),42(29),9276(29),42(38),9276(36),42(39),42(42),9276(42),42(49),9276(47),42(50),42(53),9276(53),290(59),42(13)])].">
      <j1 rule="para" parents="6111 290"/>
      <j2 rule="rewrite" parents="42 9276 42 42 9276 42 9276 42 42 9276 42 9276 42 42 9276 42 9276 42 42 9276 42 9276 42 42 9276 290 42"/>
    </justification>
  </clause>

  <clause id="9409">
    <literal><![CDATA[
      f(f(x,x),f(x,f(x,x))) = x
    ]]></literal>
    <justification jstring="[back_rewrite(8980),rewrite([9276(3),9276(13),9278(14),9276(5),63(7)])].">
      <j1 rule="back_rewrite" parents="8980"/>
      <j2 rule="rewrite" parents="9276 9276 9278 9276 63"/>
    </justification>
  </clause>

  <clause id="10071">
    <literal><![CDATA[
      f(f(f(f(f(f(x,y),f(x,f(f(x,x),z))),f(x,f(f(x,x),z))),x),f(y,x)),f(f(f(x,f(f(y,x),f(f(y,x),f(y,x)))),f(f(y,x),f(f(y,x),f(y,x)))),f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(6964),rewrite([9276(17),9276(23)])].">
      <j1 rule="back_rewrite" parents="6964"/>
      <j2 rule="rewrite" parents="9276 9276"/>
    </justification>
  </clause>

  <clause id="10340">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),f(x,f(x,x))),x) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[back_rewrite(6360),rewrite([9276(2),9276(4),9276(7),9276(9),9276(11),9276(14),9276(15),9288(17),22(8),9276(8),9409(9),9276(8)])].">
      <j1 rule="back_rewrite" parents="6360"/>
      <j2 rule="rewrite" parents="9276 9276 9276 9276 9276 9276 9276 9288 22 9276 9409 9276"/>
    </justification>
  </clause>

  <clause id="10382">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(x,f(x,x)),f(x,f(x,x)))) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[back_rewrite(6278),rewrite([9276(10),3413(11),10340(6),9276(10)]),flip(a)].">
      <j1 rule="back_rewrite" parents="6278"/>
      <j2 rule="rewrite" parents="9276 3413 10340 9276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10454">
    <literal><![CDATA[
      f(f(f(f(x,y),f(x,y)),x),f(f(f(f(x,y),f(x,f(x,x))),f(x,f(x,x))),x)) = x
    ]]></literal>
    <justification jstring="[back_rewrite(6058),rewrite([9276(7),9276(10)])].">
      <j1 rule="back_rewrite" parents="6058"/>
      <j2 rule="rewrite" parents="9276 9276"/>
    </justification>
  </clause>

  <clause id="10455">
    <literal><![CDATA[
      f(f(f(f(x,y),f(x,y)),y),f(f(f(f(x,y),f(y,f(y,y))),f(y,f(y,y))),y)) = y
    ]]></literal>
    <justification jstring="[back_rewrite(6056),rewrite([9276(7),9276(10)])].">
      <j1 rule="back_rewrite" parents="6056"/>
      <j2 rule="rewrite" parents="9276 9276"/>
    </justification>
  </clause>

  <clause id="10456">
    <literal><![CDATA[
      f(f(f(x,x),f(x,y)),f(f(f(x,f(f(x,y),f(f(x,y),f(x,y)))),f(f(x,y),f(f(x,y),f(x,y)))),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(6054),rewrite([9276(8),9276(14)])].">
      <j1 rule="back_rewrite" parents="6054"/>
      <j2 rule="rewrite" parents="9276 9276"/>
    </justification>
  </clause>

  <clause id="10499">
    <literal><![CDATA[
      f(f(x,y),f(f(f(f(y,x),f(y,f(y,y))),f(y,f(y,y))),y)) = y
    ]]></literal>
    <justification jstring="[back_rewrite(5967),rewrite([9276(4),9276(7)])].">
      <j1 rule="back_rewrite" parents="5967"/>
      <j2 rule="rewrite" parents="9276 9276"/>
    </justification>
  </clause>

  <clause id="11262">
    <literal><![CDATA[
      f(f(f(x,y),f(x,y)),f(f(f(x,y),f(f(x,y),f(x,y))),f(f(f(x,y),f(f(x,y),f(x,y))),f(f(f(f(x,y),f(x,y)),z),f(f(f(f(x,z),z),f(x,y)),y))))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(3062),rewrite([9276(8),9276(13)])].">
      <j1 rule="back_rewrite" parents="3062"/>
      <j2 rule="rewrite" parents="9276 9276"/>
    </justification>
  </clause>

  <clause id="11765">
    <literal><![CDATA[
      f(f(f(x,x),f(y,x)),f(f(f(f(y,x),f(y,x)),f(f(x,f(x,x)),f(x,f(x,x)))),f(f(f(x,f(x,x)),f(y,x)),f(f(y,x),z)))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(9409(a,1),289(a,1,1,1,1)),rewrite([9409(4),9409(5),9409(7),9409(8),10382(20),9409(18),9409(20),9409(25)])].">
      <j1 rule="para" parents="9409 289"/>
      <j2 rule="rewrite" parents="9409 9409 9409 9409 10382 9409 9409 9409"/>
    </justification>
  </clause>

  <clause id="11775">
    <literal><![CDATA[
      f(f(f(f(x,x),f(y,f(y,y))),f(f(f(y,f(y,y)),x),f(x,z))),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(10340(a,1),96(a,1,1,1,2,2,2)),rewrite([42(12),22(21),42(10),42(20),10340(32),22(29),42(18),9276(12),10382(12)])].">
      <j1 rule="para" parents="10340 96"/>
      <j2 rule="rewrite" parents="42 22 42 42 10340 22 42 9276 10382"/>
    </justification>
  </clause>

  <clause id="12287">
    <literal><![CDATA[
      f(f(x,x),f(x,y)) = x
    ]]></literal>
    <justification jstring="[para(167(a,1),337(a,1,1)),rewrite([2222(16),42(13),22(11),42(3)]),flip(a)].">
      <j1 rule="para" parents="167 337"/>
      <j2 rule="rewrite" parents="2222 42 22 42"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12288">
    <literal><![CDATA[
      f(x,f(f(x,x),y)) = f(x,x)
    ]]></literal>
    <justification jstring="[para(177(a,1),337(a,1,1)),rewrite([12287(10),12287(12),9276(10),2218(14),13(10)]),flip(a)].">
      <j1 rule="para" parents="177 337"/>
      <j2 rule="rewrite" parents="12287 12287 9276 2218 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12289">
    <literal><![CDATA[
      f(f(x,x),f(y,x)) = x
    ]]></literal>
    <justification jstring="[para(180(a,1),337(a,1,1)),rewrite([2226(16),12287(13),22(11),12287(3)]),flip(a)].">
      <j1 rule="para" parents="180 337"/>
      <j2 rule="rewrite" parents="2226 12287 22 12287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12290">
    <literal><![CDATA[
      f(x,f(y,f(x,x))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(186(a,1),337(a,1,1)),rewrite([12287(10),12287(12),9276(10),2232(14),13(10)]),flip(a)].">
      <j1 rule="para" parents="186 337"/>
      <j2 rule="rewrite" parents="12287 12287 9276 2232 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12291">
    <literal><![CDATA[
      f(f(f(x,y),f(x,y)),y) = f(x,y)
    ]]></literal>
    <justification jstring="[para(176(a,1),337(a,1,1)),rewrite([2436(26),12287(23),22(18),12287(7)]),flip(a)].">
      <j1 rule="para" parents="176 337"/>
      <j2 rule="rewrite" parents="2436 12287 22 12287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12292">
    <literal><![CDATA[
      f(f(f(x,y),f(x,y)),x) = f(x,y)
    ]]></literal>
    <justification jstring="[para(179(a,1),337(a,1,1)),rewrite([2438(26),12287(23),22(18),12287(7)]),flip(a)].">
      <j1 rule="para" parents="179 337"/>
      <j2 rule="rewrite" parents="2438 12287 22 12287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12298">
    <literal><![CDATA[
      f(f(x,y),f(f(f(f(f(x,f(x,x)),y),y),f(x,x)),f(z,f(x,x)))) = x
    ]]></literal>
    <justification jstring="[para(68(a,1),337(a,1,2,2,1)),rewrite([12287(3),9276(3),12287(15),9276(15),12287(26),9276(26),12287(41),12287(40),22(38),42(14),12287(3),9276(3)]),flip(a)].">
      <j1 rule="para" parents="68 337"/>
      <j2 rule="rewrite" parents="12287 9276 12287 9276 12287 9276 12287 12287 22 42 12287 9276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12323">
    <literal><![CDATA[
      f(f(x,y),f(f(f(x,x),z),f(f(f(f(f(x,y),z),z),x),f(x,u)))) = x
    ]]></literal>
    <justification jstring="[para(77(a,1),337(a,2)),rewrite([12292(4),12292(16),12292(27),12292(43),12292(55),337(55)])].">
      <j1 rule="para" parents="77 337"/>
      <j2 rule="rewrite" parents="12292 12292 12292 12292 12292 337"/>
    </justification>
  </clause>

  <clause id="12360">
    <literal><![CDATA[
      f(x,f(f(f(f(y,x),f(y,x)),f(x,x)),f(f(x,f(y,x)),x))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(2174(a,1),337(a,2)),rewrite([12289(3),12289(14),12289(24),12289(39),12289(50),337(50)])].">
      <j1 rule="para" parents="2174 337"/>
      <j2 rule="rewrite" parents="12289 12289 12289 12289 12289 337"/>
    </justification>
  </clause>

  <clause id="12425">
    <literal><![CDATA[
      f(x,f(f(f(x,f(f(x,y),f(f(x,y),f(x,y)))),f(f(x,y),f(f(x,y),f(x,y)))),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(10456),rewrite([12287(3)])].">
      <j1 rule="back_rewrite" parents="10456"/>
      <j2 rule="rewrite" parents="12287"/>
    </justification>
  </clause>

  <clause id="12431">
    <literal><![CDATA[
      f(x,f(f(x,y),f(f(f(x,f(x,x)),f(x,y)),y))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(3046),rewrite([12287(3),12289(6),12292(4),12289(5),9276(3)])].">
      <j1 rule="back_rewrite" parents="3046"/>
      <j2 rule="rewrite" parents="12287 12289 12292 12289 9276"/>
    </justification>
  </clause>

  <clause id="12463">
    <literal><![CDATA[
      f(x,f(f(f(x,f(f(y,x),f(f(y,x),f(y,x)))),f(f(y,x),f(f(y,x),f(y,x)))),f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(10071),rewrite([12288(4),42(3),12288(3),22(3),12289(3)])].">
      <j1 rule="back_rewrite" parents="10071"/>
      <j2 rule="rewrite" parents="12288 42 12288 22 12289"/>
    </justification>
  </clause>

  <clause id="12493">
    <literal><![CDATA[
      f(x,f(f(f(f(y,x),f(y,x)),f(f(x,f(x,x)),f(x,f(x,x)))),f(f(f(x,f(x,x)),f(y,x)),f(f(y,x),z)))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(11765),rewrite([12289(3)])].">
      <j1 rule="back_rewrite" parents="11765"/>
      <j2 rule="rewrite" parents="12289"/>
    </justification>
  </clause>

  <clause id="12574">
    <literal><![CDATA[
      f(f(x,y),f(f(f(f(x,y),f(y,f(y,y))),f(y,f(y,y))),y)) = y
    ]]></literal>
    <justification jstring="[back_rewrite(10455),rewrite([12291(4)])].">
      <j1 rule="back_rewrite" parents="10455"/>
      <j2 rule="rewrite" parents="12291"/>
    </justification>
  </clause>

  <clause id="12706">
    <literal><![CDATA[
      f(f(x,y),f(f(f(f(x,y),f(x,f(x,x))),f(x,f(x,x))),x)) = x
    ]]></literal>
    <justification jstring="[back_rewrite(10454),rewrite([12292(4)])].">
      <j1 rule="back_rewrite" parents="10454"/>
      <j2 rule="rewrite" parents="12292"/>
    </justification>
  </clause>

  <clause id="12933">
    <literal><![CDATA[
      f(f(f(f(f(x,x),y),f(f(f(f(f(x,z),y),y),x),f(x,u))),f(z,x)),f(f(z,x),f(f(f(f(x,z),z),f(z,x)),f(f(z,x),w)))) = f(z,x)
    ]]></literal>
    <justification jstring="[para(12292(a,1),7(a,1,2,1))].">
      <j1 rule="para" parents="12292 7"/>
    </justification>
  </clause>

  <clause id="13025">
    <literal><![CDATA[
      f(f(x,f(y,z)),f(f(y,z),f(f(f(f(x,f(y,z)),f(f(x,f(y,z)),f(x,f(y,z)))),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(130(a,1),12431(a,1,2,1)),rewrite([130(25),130(41)])].">
      <j1 rule="para" parents="130 12431"/>
      <j2 rule="rewrite" parents="130 130"/>
    </justification>
  </clause>

  <clause id="13241">
    <literal><![CDATA[
      f(f(f(f(f(x,f(x,x)),y),y),f(x,x)),f(f(f(f(x,f(x,x)),y),y),f(x,x))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(12298(a,1),22(a,1,1)),rewrite([12290(7)]),flip(a)].">
      <j1 rule="para" parents="12298 22"/>
      <j2 rule="rewrite" parents="12290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13306">
    <literal><![CDATA[
      f(f(f(f(x,f(x,x)),y),y),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(12298(a,1),331(a,1,2,1)),rewrite([13241(13),13241(15),42(4),13241(15),42(4),13241(15),42(4),12287(20)]),flip(a)].">
      <j1 rule="para" parents="12298 331"/>
      <j2 rule="rewrite" parents="13241 13241 42 13241 42 13241 42 12287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13326">
    <literal><![CDATA[
      f(f(f(f(x,f(x,x)),y),y),x) = f(x,x)
    ]]></literal>
    <justification jstring="[para(13(a,1),13306(a,1,1,1,1,2)),rewrite([9276(2),12287(7)])].">
      <j1 rule="para" parents="13 13306"/>
      <j2 rule="rewrite" parents="9276 12287"/>
    </justification>
  </clause>

  <clause id="13341">
    <literal><![CDATA[
      f(f(f(f(f(x,f(x,x)),y),y),f(f(f(x,f(x,x)),y),y)),x) = f(f(f(x,f(x,x)),y),y)
    ]]></literal>
    <justification jstring="[para(13306(a,1),12287(a,1,2))].">
      <j1 rule="para" parents="13306 12287"/>
    </justification>
  </clause>

  <clause id="13344">
    <literal><![CDATA[
      f(f(x,x),f(f(f(x,f(x,x)),y),y)) = x
    ]]></literal>
    <justification jstring="[para(13306(a,1),12292(a,1,1,1)),rewrite([13306(6),13306(12)])].">
      <j1 rule="para" parents="13306 12292"/>
      <j2 rule="rewrite" parents="13306 13306"/>
    </justification>
  </clause>

  <clause id="13368">
    <literal><![CDATA[
      f(f(x,f(f(f(x,f(x,x)),y),y)),f(f(f(f(x,f(x,x)),y),y),f(x,y))) = f(f(f(x,f(x,x)),y),y)
    ]]></literal>
    <justification jstring="[para(13326(a,1),139(a,1,2,1,2,1)),rewrite([13326(20),12287(17),13341(15),13326(14),13344(15)])].">
      <j1 rule="para" parents="13326 139"/>
      <j2 rule="rewrite" parents="13326 12287 13341 13326 13344"/>
    </justification>
  </clause>

  <clause id="13370">
    <literal><![CDATA[
      f(f(f(f(x,f(x,x)),y),y),f(x,f(x,x))) = f(f(x,f(x,x)),f(x,f(x,x)))
    ]]></literal>
    <justification jstring="[para(10382(a,1),13326(a,1,1,1,1))].">
      <j1 rule="para" parents="10382 13326"/>
    </justification>
  </clause>

  <clause id="13372">
    <literal><![CDATA[
      f(f(f(f(f(x,f(x,x)),y),y),f(f(f(x,f(x,x)),y),y)),f(x,x)) = f(f(f(x,f(x,x)),y),y)
    ]]></literal>
    <justification jstring="[para(13326(a,1),12287(a,1,2))].">
      <j1 rule="para" parents="13326 12287"/>
    </justification>
  </clause>

  <clause id="13375">
    <literal><![CDATA[
      f(x,f(f(f(x,f(x,x)),y),y)) = f(x,x)
    ]]></literal>
    <justification jstring="[para(13326(a,1),12292(a,1,1,1)),rewrite([13326(6),12287(3),13326(10)])].">
      <j1 rule="para" parents="13326 12292"/>
      <j2 rule="rewrite" parents="13326 12287 13326"/>
    </justification>
  </clause>

  <clause id="13381">
    <literal><![CDATA[
      f(f(x,x),f(f(f(f(x,f(x,x)),y),y),f(x,y))) = f(f(f(x,f(x,x)),y),y)
    ]]></literal>
    <justification jstring="[back_rewrite(13368),rewrite([13375(5)])].">
      <j1 rule="back_rewrite" parents="13368"/>
      <j2 rule="rewrite" parents="13375"/>
    </justification>
  </clause>

  <clause id="13437">
    <literal><![CDATA[
      f(f(f(f(f(x,x),f(y,y)),f(f(f(y,f(y,y)),x),f(x,z))),f(y,x)),f(f(f(f(y,x),f(y,x)),f(f(f(x,f(x,x)),u),u)),f(f(x,f(y,x)),f(f(y,x),w)))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(13375(a,1),45(a,1,2,2,1,1,1)),rewrite([13344(25)])].">
      <j1 rule="para" parents="13375 45"/>
      <j2 rule="rewrite" parents="13344"/>
    </justification>
  </clause>

  <clause id="13465">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(f(x,f(x,x)),y),y)) = f(f(x,f(x,x)),f(x,f(x,x)))
    ]]></literal>
    <justification jstring="[para(10382(a,1),13375(a,1,2,1,1))].">
      <j1 rule="para" parents="10382 13375"/>
    </justification>
  </clause>

  <clause id="13470">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),y),y) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(13375(a,1),337(a,1,1)),rewrite([13372(12),13465(12),12287(14),13370(8),57(7)]),flip(a)].">
      <j1 rule="para" parents="13375 337"/>
      <j2 rule="rewrite" parents="13372 13465 12287 13370 57"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13492">
    <literal><![CDATA[
      f(f(f(f(f(x,x),f(y,y)),f(f(f(y,f(y,y)),x),f(x,z))),f(y,x)),f(f(f(f(y,x),f(y,x)),f(x,f(x,x))),f(f(x,f(y,x)),f(f(y,x),u)))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(13437),rewrite([13470(18)])].">
      <j1 rule="back_rewrite" parents="13437"/>
      <j2 rule="rewrite" parents="13470"/>
    </justification>
  </clause>

  <clause id="13500">
    <literal><![CDATA[
      f(f(x,x),f(f(x,f(x,x)),f(x,y))) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[back_rewrite(13381),rewrite([13470(5),13470(10)])].">
      <j1 rule="back_rewrite" parents="13381"/>
      <j2 rule="rewrite" parents="13470 13470"/>
    </justification>
  </clause>

  <clause id="13511">
    <literal><![CDATA[
      f(x,f(f(y,f(y,y)),f(y,f(y,y)))) = f(y,f(y,y))
    ]]></literal>
    <justification jstring="[para(10382(a,1),526(a,1,1,2,2)),rewrite([13470(32),12290(27),12291(19)])].">
      <j1 rule="para" parents="10382 526"/>
      <j2 rule="rewrite" parents="13470 12290 12291"/>
    </justification>
  </clause>

  <clause id="13516">
    <literal><![CDATA[
      f(x,f(f(x,f(x,x)),f(f(f(x,f(x,x)),f(y,x)),f(f(y,x),z)))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(12493),rewrite([13511(9)])].">
      <j1 rule="back_rewrite" parents="12493"/>
      <j2 rule="rewrite" parents="13511"/>
    </justification>
  </clause>

  <clause id="13536">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(y,y)) = y
    ]]></literal>
    <justification jstring="[para(13470(a,1),13(a,1,1))].">
      <j1 rule="para" parents="13470 13"/>
    </justification>
  </clause>

  <clause id="13539">
    <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(63(a,1),13470(a,1,1))].">
      <j1 rule="para" parents="63 13470"/>
    </justification>
  </clause>

  <clause id="13547">
    <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(13470(a,1),52(a,1,2,1)),rewrite([13470(9),13539(16)])].">
      <j1 rule="para" parents="13470 52"/>
      <j2 rule="rewrite" parents="13470 13539"/>
    </justification>
  </clause>

  <clause id="13551">
    <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(13470(a,1),68(a,1,2,2,2))].">
      <j1 rule="para" parents="13470 68"/>
    </justification>
  </clause>

  <clause id="13580">
    <literal><![CDATA[
      f(f(x,y),f(f(z,f(z,z)),y)) = y
    ]]></literal>
    <justification jstring="[para(13470(a,1),65(a,1,2,1)),rewrite([13536(8),13536(10),13511(10),13536(9),13536(11),13511(11),22(6),12287(6)])].">
      <j1 rule="para" parents="13470 65"/>
      <j2 rule="rewrite" parents="13536 13536 13511 13536 13536 13511 22 12287"/>
    </justification>
  </clause>

  <clause id="13620">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(x,f(x,x)),f(y,f(y,y)))) = f(x,f(x,x))
    ]]></literal>
    <justification jstring="[para(13470(a,1),287(a,2,2,2)),rewrite([13536(9),13511(9),13536(11),13511(11),57(7)]),flip(a)].">
      <j1 rule="para" parents="13470 287"/>
      <j2 rule="rewrite" parents="13536 13511 13536 13511 57"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13623">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(f(f(y,f(f(x,f(x,x)),y)),f(y,f(y,y))),f(y,f(y,y))),y)) = y
    ]]></literal>
    <justification jstring="[para(13470(a,1),10499(a,1,1))].">
      <j1 rule="para" parents="13470 10499"/>
    </justification>
  </clause>

  <clause id="13640">
    <literal><![CDATA[
      f(f(f(x,f(y,f(y,y))),f(f(f(y,f(y,y)),f(f(z,f(z,z)),x)),f(z,f(z,z)))),x) = f(f(z,f(z,z)),x)
    ]]></literal>
    <justification jstring="[para(13470(a,1),11775(a,1,1,2,2)),rewrite([13580(7),13580(20)])].">
      <j1 rule="para" parents="13470 11775"/>
      <j2 rule="rewrite" parents="13580 13580"/>
    </justification>
  </clause>

  <clause id="13644">
    <literal><![CDATA[
      f(f(x,x),f(y,f(y,y))) = x
    ]]></literal>
    <justification jstring="[para(13470(a,1),12289(a,1,2))].">
      <j1 rule="para" parents="13470 12289"/>
    </justification>
  </clause>

  <clause id="13646">
    <literal><![CDATA[
      f(x,f(y,f(y,y))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(13470(a,1),12290(a,1,2))].">
      <j1 rule="para" parents="13470 12290"/>
    </justification>
  </clause>

  <clause id="13658">
    <literal><![CDATA[
      f(f(x,f(x,x)),f(f(x,f(x,x)),y)) = y
    ]]></literal>
    <justification jstring="[para(13470(a,1),12574(a,1,1)),rewrite([13470(6),13470(10)])].">
      <j1 rule="para" parents="13470 12574"/>
      <j2 rule="rewrite" parents="13470 13470"/>
    </justification>
  </clause>

  <clause id="13672">
    <literal><![CDATA[
      f(f(f(x,f(x,x)),y),f(y,z)) = y
    ]]></literal>
    <justification jstring="[back_rewrite(13547),rewrite([13580(14),13658(10),13580(12)])].">
      <j1 rule="back_rewrite" parents="13547"/>
      <j2 rule="rewrite" parents="13580 13658 13580"/>
    </justification>
  </clause>

  <clause id="13686">
    <literal><![CDATA[
      f(x,f(f(y,x),f(f(x,f(y,x)),f(f(y,x),z)))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(13492),rewrite([13672(8),34(4),12289(3),13644(6)])].">
      <j1 rule="back_rewrite" parents="13492"/>
      <j2 rule="rewrite" parents="13672 34 12289 13644"/>
    </justification>
  </clause>

  <clause id="13718">
    <literal><![CDATA[
      f(x,f(x,x)) = f(y,f(y,y))
    ]]></literal>
    <justification jstring="[back_rewrite(13620),rewrite([13658(8)])].">
      <j1 rule="back_rewrite" parents="13620"/>
      <j2 rule="rewrite" parents="13658"/>
    </justification>
  </clause>

  <clause id="13741">
    <literal><![CDATA[
      f(f(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)),y))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(11262),rewrite([13658(25)])].">
      <j1 rule="back_rewrite" parents="11262"/>
      <j2 rule="rewrite" parents="13658"/>
    </justification>
  </clause>

  <clause id="13757">
    <literal><![CDATA[
      f(x,f(f(x,f(x,x)),f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(13516),rewrite([13672(9)])].">
      <j1 rule="back_rewrite" parents="13516"/>
      <j2 rule="rewrite" parents="13672"/>
    </justification>
  </clause>

  <clause id="13766">
    <literal><![CDATA[
      f(x,f(x,x)) = c_0
    ]]></literal>
    <justification jstring="[new_symbol(13718)].">
      <j1 rule="new_symbol" parents="13718"/>
    </justification>
  </clause>

  <clause id="13776">
    <literal><![CDATA[
      f(c_0,f(f(x,y),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(5302),rewrite([13741(17),9276(5),13766(5)])].">
      <j1 rule="back_rewrite" parents="5302"/>
      <j2 rule="rewrite" parents="13741 9276 13766"/>
    </justification>
  </clause>

  <clause id="13777">
    <literal><![CDATA[
      f(f(x,y),f(x,y)) = f(c_0,f(x,y))
    ]]></literal>
    <justification jstring="[back_rewrite(4511),rewrite([13766(5),13741(15)]),flip(a)].">
      <j1 rule="back_rewrite" parents="4511"/>
      <j2 rule="rewrite" parents="13766 13741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13787">
    <literal><![CDATA[
      f(x,f(c_0,f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(13757),rewrite([13766(2)])].">
      <j1 rule="back_rewrite" parents="13757"/>
      <j2 rule="rewrite" parents="13766"/>
    </justification>
  </clause>

  <clause id="13826">
    <literal><![CDATA[
      f(c_0,f(c_0,x)) = x
    ]]></literal>
    <justification jstring="[back_rewrite(13658),rewrite([13766(2),13766(3)])].">
      <j1 rule="back_rewrite" parents="13658"/>
      <j2 rule="rewrite" parents="13766 13766"/>
    </justification>
  </clause>

  <clause id="13832">
    <literal><![CDATA[
      f(x,c_0) = f(x,x)
    ]]></literal>
    <justification jstring="[back_rewrite(13646),rewrite([13766(2)])].">
      <j1 rule="back_rewrite" parents="13646"/>
      <j2 rule="rewrite" parents="13766"/>
    </justification>
  </clause>

  <clause id="13833">
    <literal><![CDATA[
      f(f(x,x),c_0) = x
    ]]></literal>
    <justification jstring="[back_rewrite(13644),rewrite([13766(3)])].">
      <j1 rule="back_rewrite" parents="13644"/>
      <j2 rule="rewrite" parents="13766"/>
    </justification>
  </clause>

  <clause id="13836">
    <literal><![CDATA[
      f(c_0,x) = f(x,x)
    ]]></literal>
    <justification jstring="[back_rewrite(13640),rewrite([13766(2),13832(2),13766(3),13766(4),13826(5),13766(3),13832(3),13832(3,R),13833(3),13766(3)]),flip(a)].">
      <j1 rule="back_rewrite" parents="13640"/>
      <j2 rule="rewrite" parents="13766 13832 13766 13766 13826 13766 13832 13832 13833 13766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13845">
    <literal><![CDATA[
      f(c_0,f(x,x)) = x
    ]]></literal>
    <justification jstring="[back_rewrite(13623),rewrite([13766(2),13766(3),13836(3),13766(3),13766(4),13766(6),9276(6),13766(6),13836(3)])].">
      <j1 rule="back_rewrite" parents="13623"/>
      <j2 rule="rewrite" parents="13766 13766 13836 13766 13766 13766 9276 13766 13836"/>
    </justification>
  </clause>

  <clause id="13871">
    <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>
    <justification jstring="[back_rewrite(13551),rewrite([13766(9)])].">
      <j1 rule="back_rewrite" parents="13551"/>
      <j2 rule="rewrite" parents="13766"/>
    </justification>
  </clause>

  <clause id="13877">
    <literal><![CDATA[
      f(f(x,x),f(c_0,f(x,y))) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(13500),rewrite([13766(3),13766(7)])].">
      <j1 rule="back_rewrite" parents="13500"/>
      <j2 rule="rewrite" parents="13766 13766"/>
    </justification>
  </clause>

  <clause id="13977">
    <literal><![CDATA[
      f(f(x,f(y,z)),f(f(y,z),f(f(f(f(x,f(y,z)),f(f(x,f(y,z)),c_0)),f(y,z)),f(f(f(f(y,z),c_0),f(x,x)),f(f(c_0,f(y,z)),z))))) = f(y,z)
    ]]></literal>
    <justification jstring="[back_rewrite(13025),rewrite([13832(10,R),13832(15,R),13766(19)])].">
      <j1 rule="back_rewrite" parents="13025"/>
      <j2 rule="rewrite" parents="13832 13832 13766"/>
    </justification>
  </clause>

  <clause id="14049">
    <literal><![CDATA[
      f(f(x,y),f(f(f(f(x,y),c_0),c_0),x)) = x
    ]]></literal>
    <justification jstring="[back_rewrite(12706),rewrite([13766(4),13766(6)])].">
      <j1 rule="back_rewrite" parents="12706"/>
      <j2 rule="rewrite" parents="13766 13766"/>
    </justification>
  </clause>

  <clause id="14072">
    <literal><![CDATA[
      f(f(x,y),f(f(f(f(x,y),c_0),c_0),y)) = y
    ]]></literal>
    <justification jstring="[back_rewrite(12574),rewrite([13766(4),13766(6)])].">
      <j1 rule="back_rewrite" parents="12574"/>
      <j2 rule="rewrite" parents="13766 13766"/>
    </justification>
  </clause>

  <clause id="14101">
    <literal><![CDATA[
      f(x,f(f(f(x,f(f(y,x),f(f(y,x),c_0))),f(f(y,x),f(f(y,x),c_0))),f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(12463),rewrite([13832(4,R),13832(10,R)])].">
      <j1 rule="back_rewrite" parents="12463"/>
      <j2 rule="rewrite" parents="13832 13832"/>
    </justification>
  </clause>

  <clause id="14110">
    <literal><![CDATA[
      f(x,f(f(f(x,f(f(x,y),f(f(x,y),c_0))),f(f(x,y),f(f(x,y),c_0))),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(12425),rewrite([13832(4,R),13832(10,R)])].">
      <j1 rule="back_rewrite" parents="12425"/>
      <j2 rule="rewrite" parents="13832 13832"/>
    </justification>
  </clause>

  <clause id="14268">
    <literal><![CDATA[
      f(f(x,x),x) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(9276),rewrite([13766(4)])].">
      <j1 rule="back_rewrite" parents="9276"/>
      <j2 rule="rewrite" parents="13766"/>
    </justification>
  </clause>

  <clause id="14290">
    <literal><![CDATA[
      f(c_0,f(f(x,y),c_0)) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(13776),rewrite([13832(4,R)])].">
      <j1 rule="back_rewrite" parents="13776"/>
      <j2 rule="rewrite" parents="13832"/>
    </justification>
  </clause>

  <clause id="14451">
    <literal><![CDATA[
      f(x,f(f(f(f(y,x),c_0),f(x,x)),f(f(x,f(y,x)),x))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(12360),rewrite([13832(3,R)])].">
      <j1 rule="back_rewrite" parents="12360"/>
      <j2 rule="rewrite" parents="13832"/>
    </justification>
  </clause>

  <clause id="14462">
    <literal><![CDATA[
      f(f(f(x,y),c_0),x) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(12292),rewrite([13832(3,R)])].">
      <j1 rule="back_rewrite" parents="12292"/>
      <j2 rule="rewrite" parents="13832"/>
    </justification>
  </clause>

  <clause id="14463">
    <literal><![CDATA[
      f(f(f(x,y),c_0),y) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(12291),rewrite([13832(3,R)])].">
      <j1 rule="back_rewrite" parents="12291"/>
      <j2 rule="rewrite" parents="13832"/>
    </justification>
  </clause>

  <clause id="14637">
    <literal><![CDATA[
      f(x,f(f(x,y),c_0)) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(63),rewrite([13832(3,R)])].">
      <j1 rule="back_rewrite" parents="63"/>
      <j2 rule="rewrite" parents="13832"/>
    </justification>
  </clause>

  <clause id="14660">
    <literal><![CDATA[
      f(f(x,y),c_0) = f(c_0,f(x,y))
    ]]></literal>
    <justification jstring="[back_rewrite(13777),rewrite([13832(3,R)])].">
      <j1 rule="back_rewrite" parents="13777"/>
      <j2 rule="rewrite" parents="13832"/>
    </justification>
  </clause>

  <clause id="14690">
    <literal><![CDATA[
      f(x,f(c_0,f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(14637),rewrite([14660(3)])].">
      <j1 rule="back_rewrite" parents="14637"/>
      <j2 rule="rewrite" parents="14660"/>
    </justification>
  </clause>

  <clause id="14862">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),y) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(14463),rewrite([14660(3)])].">
      <j1 rule="back_rewrite" parents="14463"/>
      <j2 rule="rewrite" parents="14660"/>
    </justification>
  </clause>

  <clause id="14863">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),x) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(14462),rewrite([14660(3)])].">
      <j1 rule="back_rewrite" parents="14462"/>
      <j2 rule="rewrite" parents="14660"/>
    </justification>
  </clause>

  <clause id="14874">
    <literal><![CDATA[
      f(x,f(f(f(c_0,f(y,x)),f(x,x)),f(f(x,f(y,x)),x))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(14451),rewrite([14660(3)])].">
      <j1 rule="back_rewrite" parents="14451"/>
      <j2 rule="rewrite" parents="14660"/>
    </justification>
  </clause>

  <clause id="15035">
    <literal><![CDATA[
      f(c_0,f(c_0,f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(14290),rewrite([14660(4)])].">
      <j1 rule="back_rewrite" parents="14290"/>
      <j2 rule="rewrite" parents="14660"/>
    </justification>
  </clause>

  <clause id="15154">
    <literal><![CDATA[
      f(x,f(f(f(x,f(f(x,y),f(c_0,f(x,y)))),f(f(x,y),f(c_0,f(x,y)))),f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(14110),rewrite([14660(4),14660(10)])].">
      <j1 rule="back_rewrite" parents="14110"/>
      <j2 rule="rewrite" parents="14660 14660"/>
    </justification>
  </clause>

  <clause id="15160">
    <literal><![CDATA[
      f(x,f(f(f(x,f(f(y,x),f(c_0,f(y,x)))),f(f(y,x),f(c_0,f(y,x)))),f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(14101),rewrite([14660(4),14660(10)])].">
      <j1 rule="back_rewrite" parents="14101"/>
      <j2 rule="rewrite" parents="14660 14660"/>
    </justification>
  </clause>

  <clause id="15178">
    <literal><![CDATA[
      f(f(x,y),f(f(x,y),y)) = y
    ]]></literal>
    <justification jstring="[back_rewrite(14072),rewrite([14660(4),14660(6),15035(6)])].">
      <j1 rule="back_rewrite" parents="14072"/>
      <j2 rule="rewrite" parents="14660 14660 15035"/>
    </justification>
  </clause>

  <clause id="15182">
    <literal><![CDATA[
      f(f(x,y),f(f(x,y),x)) = x
    ]]></literal>
    <justification jstring="[back_rewrite(14049),rewrite([14660(4),14660(6),15035(6)])].">
      <j1 rule="back_rewrite" parents="14049"/>
      <j2 rule="rewrite" parents="14660 14660 15035"/>
    </justification>
  </clause>

  <clause id="15199">
    <literal><![CDATA[
      f(f(x,f(y,z)),f(f(y,z),f(f(f(f(x,f(y,z)),f(c_0,f(x,f(y,z)))),f(y,z)),f(f(f(c_0,f(y,z)),f(x,x)),f(y,z))))) = f(y,z)
    ]]></literal>
    <justification jstring="[back_rewrite(13977),rewrite([14660(9),14660(15),14862(21)])].">
      <j1 rule="back_rewrite" parents="13977"/>
      <j2 rule="rewrite" parents="14660 14660 14862"/>
    </justification>
  </clause>

  <clause id="15252">
    <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>
    <justification jstring="[back_rewrite(13871),rewrite([14660(9)])].">
      <j1 rule="back_rewrite" parents="13871"/>
      <j2 rule="rewrite" parents="14660"/>
    </justification>
  </clause>

  <clause id="15421">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),f(y,y)) = c_0
    ]]></literal>
    <justification jstring="[para(3(a,1),13877(a,1,2,2)),rewrite([13832(3,R),14660(3),13836(5)])].">
      <j1 rule="para" parents="3 13877"/>
      <j2 rule="rewrite" parents="13832 14660 13836"/>
    </justification>
  </clause>

  <clause id="15490">
    <literal><![CDATA[
      f(f(x,f(y,x)),x) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(14874),rewrite([15421(5),13787(6)])].">
      <j1 rule="back_rewrite" parents="14874"/>
      <j2 rule="rewrite" parents="15421 13787"/>
    </justification>
  </clause>

  <clause id="15586">
    <literal><![CDATA[
      f(f(f(c_0,f(x,y)),f(f(f(x,y),f(c_0,f(x,y))),f(f(c_0,f(x,y)),z))),f(x,y)) = f(c_0,f(x,y))
    ]]></literal>
    <justification jstring="[para(14660(a,1),554(a,1,1,1)),rewrite([14660(6),14660(8),15035(8),13832(7,R),14660(7),13832(11,R),14660(11),13832(19,R),14660(19)])].">
      <j1 rule="para" parents="14660 554"/>
      <j2 rule="rewrite" parents="14660 14660 15035 13832 14660 13832 14660 13832 14660"/>
    </justification>
  </clause>

  <clause id="15602">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),f(x,y)) = c_0
    ]]></literal>
    <justification jstring="[para(14660(a,1),13877(a,1,2,2)),rewrite([13832(3,R),14660(3),15035(8)])].">
      <j1 rule="para" parents="14660 13877"/>
      <j2 rule="rewrite" parents="13832 14660 15035"/>
    </justification>
  </clause>

  <clause id="15654">
    <literal><![CDATA[
      f(f(x,y),f(c_0,f(x,y))) = c_0
    ]]></literal>
    <justification jstring="[para(14862(a,1),13877(a,1,2,2)),rewrite([13832(7,R),14660(5),15035(5)])].">
      <j1 rule="para" parents="14862 13877"/>
      <j2 rule="rewrite" parents="13832 14660 15035"/>
    </justification>
  </clause>

  <clause id="15656">
    <literal><![CDATA[
      f(f(f(c_0,f(x,y)),z),f(x,y)) = f(c_0,f(x,y))
    ]]></literal>
    <justification jstring="[back_rewrite(15586),rewrite([15654(8),14690(10)])].">
      <j1 rule="back_rewrite" parents="15586"/>
      <j2 rule="rewrite" parents="15654 14690"/>
    </justification>
  </clause>

  <clause id="15667">
    <literal><![CDATA[
      f(f(x,f(y,z)),f(c_0,f(y,z))) = f(y,z)
    ]]></literal>
    <justification jstring="[back_rewrite(15199),rewrite([15654(10),15656(13),13832(10,R),14660(8),15035(8),13832(5,R),14660(5)])].">
      <j1 rule="back_rewrite" parents="15199"/>
      <j2 rule="rewrite" parents="15654 15656 13832 14660 15035 13832 14660"/>
    </justification>
  </clause>

  <clause id="15677">
    <literal><![CDATA[
      f(x,f(x,f(y,x))) = f(y,x)
    ]]></literal>
    <justification jstring="[back_rewrite(15160),rewrite([15654(5),13832(2),15654(6),14660(3),13845(3)])].">
      <j1 rule="back_rewrite" parents="15160"/>
      <j2 rule="rewrite" parents="15654 13832 15654 14660 13845"/>
    </justification>
  </clause>

  <clause id="15678">
    <literal><![CDATA[
      f(x,f(x,f(x,y))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(15154),rewrite([15654(5),13832(2),15654(6),14660(3),13845(3)])].">
      <j1 rule="back_rewrite" parents="15154"/>
      <j2 rule="rewrite" parents="15654 13832 15654 14660 13845"/>
    </justification>
  </clause>

  <clause id="16030">
    <literal><![CDATA[
      f(f(f(x,y),x),f(x,y)) = x
    ]]></literal>
    <justification jstring="[para(12287(a,1),15490(a,1,1,2)),rewrite([12287(7)])].">
      <j1 rule="para" parents="12287 15490"/>
      <j2 rule="rewrite" parents="12287"/>
    </justification>
  </clause>

  <clause id="16031">
    <literal><![CDATA[
      f(f(f(x,y),y),f(x,y)) = y
    ]]></literal>
    <justification jstring="[para(12289(a,1),15490(a,1,1,2)),rewrite([12289(7)])].">
      <j1 rule="para" parents="12289 15490"/>
      <j2 rule="rewrite" parents="12289"/>
    </justification>
  </clause>

  <clause id="16036">
    <literal><![CDATA[
      f(f(x,f(x,y)),x) = f(x,y)
    ]]></literal>
    <justification jstring="[para(14863(a,1),15490(a,1,1,2)),rewrite([14863(7)])].">
      <j1 rule="para" parents="14863 15490"/>
      <j2 rule="rewrite" parents="14863"/>
    </justification>
  </clause>

  <clause id="16038">
    <literal><![CDATA[
      f(f(x,f(y,x)),f(y,x)) = x
    ]]></literal>
    <justification jstring="[para(15490(a,1),15182(a,1,2))].">
      <j1 rule="para" parents="15490 15182"/>
    </justification>
  </clause>

  <clause id="16146">
    <literal><![CDATA[
      f(x,f(f(y,x),f(f(f(f(y,x),f(x,f(y,x))),f(x,x)),f(f(x,x),z)))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(15677(a,1),52(a,1,2,1)),rewrite([15677(4)])].">
      <j1 rule="para" parents="15677 52"/>
      <j2 rule="rewrite" parents="15677"/>
    </justification>
  </clause>

  <clause id="16339">
    <literal><![CDATA[
      f(f(f(x,y),x),x) = f(x,y)
    ]]></literal>
    <justification jstring="[para(16030(a,1),15182(a,1,2))].">
      <j1 rule="para" parents="16030 15182"/>
    </justification>
  </clause>

  <clause id="16342">
    <literal><![CDATA[
      f(f(x,y),f(y,f(x,y))) = y
    ]]></literal>
    <justification jstring="[para(15490(a,1),16030(a,1,1))].">
      <j1 rule="para" parents="15490 16030"/>
    </justification>
  </clause>

  <clause id="16379">
    <literal><![CDATA[
      f(x,f(f(y,x),f(c_0,f(f(x,x),z)))) = f(x,x)
    ]]></literal>
    <justification jstring="[back_rewrite(16146),rewrite([16342(5),13766(3)])].">
      <j1 rule="back_rewrite" parents="16146"/>
      <j2 rule="rewrite" parents="16342 13766"/>
    </justification>
  </clause>

  <clause id="16410">
    <literal><![CDATA[
      f(f(x,f(y,x)),f(c_0,f(x,f(f(y,x),z)))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(16031(a,1),3(a,1,2,2,1,1,1)),rewrite([13832(5,R),14660(5),15602(7),16038(7)])].">
      <j1 rule="para" parents="16031 3"/>
      <j2 rule="rewrite" parents="13832 14660 15602 16038"/>
    </justification>
  </clause>

  <clause id="16474">
    <literal><![CDATA[
      f(f(c_0,f(f(x,y),f(x,z))),f(x,x)) = x
    ]]></literal>
    <justification jstring="[para(16036(a,1),69(a,1,1,2,1,1,1)),rewrite([14268(2),16339(4)])].">
      <j1 rule="para" parents="16036 69"/>
      <j2 rule="rewrite" parents="14268 16339"/>
    </justification>
  </clause>

  <clause id="16498">
    <literal><![CDATA[
      f(f(x,y),y) = f(y,f(x,y))
    ]]></literal>
    <justification jstring="[para(15178(a,1),16036(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15178 16036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16499">
    <literal><![CDATA[
      f(f(x,y),f(x,f(x,y))) = x
    ]]></literal>
    <justification jstring="[para(16036(a,1),15182(a,1,2)),rewrite([16498(4)])].">
      <j1 rule="para" parents="16036 15182"/>
      <j2 rule="rewrite" parents="16498"/>
    </justification>
  </clause>

  <clause id="16500">
    <literal><![CDATA[
      f(f(x,y),x) = f(x,f(x,y))
    ]]></literal>
    <justification jstring="[para(15182(a,1),16036(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15182 16036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17145">
    <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>
    <justification jstring="[back_rewrite(15252),rewrite([16498(7)])].">
      <j1 rule="back_rewrite" parents="15252"/>
      <j2 rule="rewrite" parents="16498"/>
    </justification>
  </clause>

  <clause id="17408">
    <literal><![CDATA[
      f(f(f(f(f(x,x),y),f(f(f(y,f(f(x,z),y)),x),f(x,u))),f(z,x)),f(f(z,x),f(f(f(z,f(x,z)),f(z,x)),f(f(z,x),w)))) = f(z,x)
    ]]></literal>
    <justification jstring="[back_rewrite(12933),rewrite([16498(5),16498(14)])].">
      <j1 rule="back_rewrite" parents="12933"/>
      <j2 rule="rewrite" parents="16498 16498"/>
    </justification>
  </clause>

  <clause id="17478">
    <literal><![CDATA[
      f(f(x,y),f(f(f(x,x),z),f(f(f(z,f(f(x,y),z)),x),f(x,u)))) = x
    ]]></literal>
    <justification jstring="[back_rewrite(12323),rewrite([16498(6)])].">
      <j1 rule="back_rewrite" parents="12323"/>
      <j2 rule="rewrite" parents="16498"/>
    </justification>
  </clause>

  <clause id="17678">
    <literal><![CDATA[
      f(f(x,f(x,y)),f(x,f(f(x,y),f(x,z)))) = x
    ]]></literal>
    <justification jstring="[para(16499(a,1),13686(a,1,2,1)),rewrite([16499(8),16500(5),15678(5),16499(7),16499(11)])].">
      <j1 rule="para" parents="16499 13686"/>
      <j2 rule="rewrite" parents="16499 16500 15678 16499 16499"/>
    </justification>
  </clause>

  <clause id="17804">
    <literal><![CDATA[
      f(c_0,f(f(x,y),f(x,z))) = f(x,f(f(x,y),f(x,z)))
    ]]></literal>
    <justification jstring="[para(16474(a,1),42(a,1,1)),rewrite([13832(11,R),16500(7),15035(7)]),flip(a)].">
      <j1 rule="para" parents="16474 42"/>
      <j2 rule="rewrite" parents="13832 16500 15035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19912">
    <literal><![CDATA[
      f(f(x,x),f(f(y,f(x,x)),f(c_0,f(x,z)))) = x
    ]]></literal>
    <justification jstring="[para(13(a,1),16379(a,1,2,2,2,1)),rewrite([13832(11,R),14660(11),13845(11)])].">
      <j1 rule="para" parents="13 16379"/>
      <j2 rule="rewrite" parents="13832 14660 13845"/>
    </justification>
  </clause>

  <clause id="24396">
    <literal><![CDATA[
      f(f(x,y),f(y,f(f(x,y),z))) = f(c_0,f(y,f(f(x,y),z)))
    ]]></literal>
    <justification jstring="[para(16410(a,1),13(a,1,1)),rewrite([13832(12,R),16500(8),15035(8)])].">
      <j1 rule="para" parents="16410 13"/>
      <j2 rule="rewrite" parents="13832 16500 15035"/>
    </justification>
  </clause>

  <clause id="24398">
    <literal><![CDATA[
      f(f(x,f(y,x)),f(c_0,f(x,y))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(42(a,1),16410(a,1,2,2,2))].">
      <j1 rule="para" parents="42 16410"/>
    </justification>
  </clause>

  <clause id="24399">
    <literal><![CDATA[
      f(f(x,f(f(y,x),z)),f(y,x)) = f(c_0,f(x,f(f(y,x),z)))
    ]]></literal>
    <justification jstring="[para(16410(a,1),12289(a,1,2)),rewrite([13832(11,R),16500(7),15035(7)])].">
      <j1 rule="para" parents="16410 12289"/>
      <j2 rule="rewrite" parents="13832 16500 15035"/>
    </justification>
  </clause>

  <clause id="24577">
    <literal><![CDATA[
      f(f(x,y),f(y,x)) = f(c_0,f(y,x))
    ]]></literal>
    <justification jstring="[para(24398(a,1),13(a,1,1)),rewrite([13832(8,R),16500(6),15035(6)])].">
      <j1 rule="para" parents="24398 13"/>
      <j2 rule="rewrite" parents="13832 16500 15035"/>
    </justification>
  </clause>

  <clause id="24578">
    <literal><![CDATA[
      f(c_0,f(x,y)) = f(c_0,f(y,x))
    ]]></literal>
    <justification jstring="[para(24398(a,1),12289(a,1,2)),rewrite([13832(7,R),16500(5),15035(5),24577(3)])].">
      <j1 rule="para" parents="24398 12289"/>
      <j2 rule="rewrite" parents="13832 16500 15035 24577"/>
    </justification>
  </clause>

  <clause id="24579">
    <literal><![CDATA[
      f(x,y) = f(y,x)
    ]]></literal>
    <justification jstring="[para(24398(a,1),13787(a,1,2,2)),rewrite([24578(6),13832(7,R),16500(5),15035(5),24398(7)])].">
      <j1 rule="para" parents="24398 13787"/>
      <j2 rule="rewrite" parents="24578 13832 16500 15035 24398"/>
    </justification>
  </clause>

  <clause id="24993">
    <literal><![CDATA[
      f(f(x,y),f(f(z,f(y,y)),f(c_0,f(y,f(z,f(z,f(x,y))))))) = y
    ]]></literal>
    <justification jstring="[back_rewrite(17145),rewrite([24579(3),24579(5),24579(6),24579(8)])].">
      <j1 rule="back_rewrite" parents="17145"/>
      <j2 rule="rewrite" parents="24579 24579 24579 24579"/>
    </justification>
  </clause>

  <clause id="25062">
    <literal><![CDATA[
      f(f(x,y),f(x,f(z,f(x,y)))) = f(c_0,f(x,f(z,f(x,y))))
    ]]></literal>
    <justification jstring="[back_rewrite(24399),rewrite([24579(1),24579(2),24579(4),24579(5),24579(7),24579(8)])].">
      <j1 rule="back_rewrite" parents="24399"/>
      <j2 rule="rewrite" parents="24579 24579 24579 24579 24579 24579"/>
    </justification>
  </clause>

  <clause id="25063">
    <literal><![CDATA[
      f(f(x,y),f(y,f(z,f(x,y)))) = f(c_0,f(y,f(z,f(x,y))))
    ]]></literal>
    <justification jstring="[back_rewrite(24396),rewrite([24579(3),24579(8)])].">
      <j1 rule="back_rewrite" parents="24396"/>
      <j2 rule="rewrite" parents="24579 24579"/>
    </justification>
  </clause>

  <clause id="25210">
    <literal><![CDATA[
      f(f(x,y),f(f(z,f(x,x)),f(f(x,u),f(x,f(z,f(z,f(x,y))))))) = x
    ]]></literal>
    <justification jstring="[back_rewrite(17478),rewrite([24579(3),24579(5),24579(7),24579(9)])].">
      <j1 rule="back_rewrite" parents="17478"/>
      <j2 rule="rewrite" parents="24579 24579 24579 24579"/>
    </justification>
  </clause>

  <clause id="25228">
    <literal><![CDATA[
      f(x,f(c_0,f(y,f(z,f(x,y))))) = f(x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(17408),rewrite([24579(2),24579(4),24579(6),24579(8),24579(10),24579(11),25210(11),24579(1),24579(4),24579(5),16342(5),24579(2),24579(3),25063(5),24579(7)])].">
      <j1 rule="back_rewrite" parents="17408"/>
      <j2 rule="rewrite" parents="24579 24579 24579 24579 24579 24579 25210 24579 24579 24579 16342 24579 24579 25063 24579"/>
    </justification>
  </clause>

  <clause id="25437">
    <literal><![CDATA[
      f(c_0,f(x,f(f(x,y),f(x,z)))) = f(f(x,y),f(x,z))
    ]]></literal>
    <justification jstring="[para(17804(a,1),15035(a,1,2))].">
      <j1 rule="para" parents="17804 15035"/>
    </justification>
  </clause>

  <clause id="25514">
    <literal><![CDATA[
      f(x,f(c_0,f(y,f(z,f(y,x))))) = f(y,x)
    ]]></literal>
    <justification jstring="[para(25228(a,1),24579(a,2)),rewrite([24579(2),24579(6),24579(7)])].">
      <j1 rule="para" parents="25228 24579"/>
      <j2 rule="rewrite" parents="24579 24579 24579"/>
    </justification>
  </clause>

  <clause id="25518">
    <literal><![CDATA[
      f(x,f(y,f(x,f(y,z)))) = f(x,f(y,z))
    ]]></literal>
    <justification jstring="[para(17804(a,1),25228(a,1,2)),rewrite([25062(5),14690(6)])].">
      <j1 rule="para" parents="17804 25228"/>
      <j2 rule="rewrite" parents="25062 14690"/>
    </justification>
  </clause>

  <clause id="25556">
    <literal><![CDATA[
      f(f(x,f(y,y)),f(c_0,f(y,z))) = f(y,z)
    ]]></literal>
    <justification jstring="[para(19912(a,1),25514(a,1,2,2,2)),rewrite([24579(7),12290(7),13845(6),24579(4),14690(4)]),flip(a)].">
      <j1 rule="para" parents="19912 25514"/>
      <j2 rule="rewrite" parents="24579 12290 13845 24579 14690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25561">
    <literal><![CDATA[
      f(x,f(f(x,x),f(y,y))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(17804(a,1),25514(a,1,2,2)),rewrite([24579(4),13832(4),24579(5),13832(5),24579(5),15035(7),24579(6),13832(6)])].">
      <j1 rule="para" parents="17804 25514"/>
      <j2 rule="rewrite" parents="24579 13832 24579 13832 24579 15035 24579 13832"/>
    </justification>
  </clause>

  <clause id="25603">
    <literal><![CDATA[
      f(f(x,y),f(y,f(z,f(z,f(x,y))))) = y
    ]]></literal>
    <justification jstring="[back_rewrite(24993),rewrite([25556(10)])].">
      <j1 rule="back_rewrite" parents="24993"/>
      <j2 rule="rewrite" parents="25556"/>
    </justification>
  </clause>

  <clause id="25617">
    <literal><![CDATA[
      f(x,f(f(x,x),f(y,z))) = f(x,x)
    ]]></literal>
    <justification jstring="[para(15667(a,1),25561(a,1,2,2))].">
      <j1 rule="para" parents="15667 25561"/>
    </justification>
  </clause>

  <clause id="25670">
    <literal><![CDATA[
      f(f(x,f(x,y)),f(x,f(z,f(x,y)))) = x
    ]]></literal>
    <justification jstring="[para(25518(a,1),17678(a,1,2)),rewrite([24579(4)])].">
      <j1 rule="para" parents="25518 17678"/>
      <j2 rule="rewrite" parents="24579"/>
    </justification>
  </clause>

  <clause id="25687">
    <literal><![CDATA[
      f(f(x,x),f(y,f(c_0,f(z,x)))) = x
    ]]></literal>
    <justification jstring="[para(13(a,1),25556(a,1,2,2)),rewrite([13832(3,R),24579(3),24579(6),13832(6),24579(6),13(9)])].">
      <j1 rule="para" parents="13 25556"/>
      <j2 rule="rewrite" parents="13832 24579 24579 13832 24579 13"/>
    </justification>
  </clause>

  <clause id="25792">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),f(c_0,f(y,z))) = f(z,f(c_0,f(x,y)))
    ]]></literal>
    <justification jstring="[para(25687(a,1),25514(a,1,2,2,2)),rewrite([24579(5)])].">
      <j1 rule="para" parents="25687 25514"/>
      <j2 rule="rewrite" parents="24579"/>
    </justification>
  </clause>

  <clause id="25884">
    <literal><![CDATA[
      f(f(x,y),f(f(z,f(z,f(x,y))),f(c_0,f(y,f(u,f(x,y)))))) = f(c_0,f(y,f(u,f(x,y))))
    ]]></literal>
    <justification jstring="[para(25228(a,1),25603(a,1,1)),rewrite([25228(12),24579(10)])].">
      <j1 rule="para" parents="25228 25603"/>
      <j2 rule="rewrite" parents="25228 24579"/>
    </justification>
  </clause>

  <clause id="25887">
    <literal><![CDATA[
      f(f(x,y),f(f(z,f(z,f(x,y))),f(c_0,f(x,f(u,f(x,y)))))) = f(c_0,f(x,f(u,f(x,y))))
    ]]></literal>
    <justification jstring="[para(25514(a,1),25603(a,1,1)),rewrite([25514(12),24579(10)])].">
      <j1 rule="para" parents="25514 25603"/>
      <j2 rule="rewrite" parents="25514 24579"/>
    </justification>
  </clause>

  <clause id="25979">
    <literal><![CDATA[
      f(f(x,y),f(x,f(x,f(c_0,f(z,y))))) = x
    ]]></literal>
    <justification jstring="[para(25687(a,1),25670(a,1,2,2)),rewrite([24579(7)])].">
      <j1 rule="para" parents="25687 25670"/>
      <j2 rule="rewrite" parents="24579"/>
    </justification>
  </clause>

  <clause id="26249">
    <literal><![CDATA[
      f(f(x,f(x,y)),f(x,f(f(y,y),f(z,u)))) = x
    ]]></literal>
    <justification jstring="[para(25617(a,1),25979(a,1,2,2,2,2)),rewrite([13845(7),24579(7)])].">
      <j1 rule="para" parents="25617 25979"/>
      <j2 rule="rewrite" parents="13845 24579"/>
    </justification>
  </clause>

  <clause id="32396">
    <literal><![CDATA[
      f(f(x,x),f(c_0,f(y,f(x,z)))) = f(y,f(x,x))
    ]]></literal>
    <justification jstring="[para(12287(a,1),25792(a,1,1,2)),rewrite([24579(2),13832(2),24579(4),12287(10),24579(8),13832(8)])].">
      <j1 rule="para" parents="12287 25792"/>
      <j2 rule="rewrite" parents="24579 13832 24579 12287 24579 13832"/>
    </justification>
  </clause>

  <clause id="32431">
    <literal><![CDATA[
      f(f(c_0,f(x,y)),f(c_0,f(x,z))) = f(y,f(c_0,f(x,z)))
    ]]></literal>
    <justification jstring="[para(25792(a,1),24579(a,2)),rewrite([24579(5),24579(9)])].">
      <j1 rule="para" parents="25792 24579"/>
      <j2 rule="rewrite" parents="24579 24579"/>
    </justification>
  </clause>

  <clause id="32432">
    <literal><![CDATA[
      f(x,f(c_0,f(y,z))) = f(z,f(c_0,f(y,x)))
    ]]></literal>
    <justification jstring="[para(24579(a,1),25792(a,1,1,2)),rewrite([32431(7),24579(6)])].">
      <j1 rule="para" parents="24579 25792"/>
      <j2 rule="rewrite" parents="32431 24579"/>
    </justification>
  </clause>

  <clause id="33282">
    <literal><![CDATA[
      f(f(x,y),f(c_0,f(z,f(x,u)))) = f(z,f(x,f(f(x,u),f(x,y))))
    ]]></literal>
    <justification jstring="[para(17804(a,1),32432(a,1,2)),rewrite([24579(9)]),flip(a)].">
      <j1 rule="para" parents="17804 32432"/>
      <j2 rule="rewrite" parents="24579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33491">
    <literal><![CDATA[
      f(f(x,y),f(z,f(c_0,f(x,u)))) = f(f(x,y),f(x,f(c_0,f(u,z))))
    ]]></literal>
    <justification jstring="[para(32432(a,1),25437(a,2,1)),rewrite([24579(7),25437(9),24579(8),24579(12)]),flip(a)].">
      <j1 rule="para" parents="32432 25437"/>
      <j2 rule="rewrite" parents="24579 25437 24579 24579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="74307">
    <literal><![CDATA[
      f(f(x,y),f(y,f(z,z))) = f(c_0,f(y,f(z,f(x,y))))
    ]]></literal>
    <justification jstring="[para(33282(a,1),25884(a,1,2)),rewrite([16499(7)])].">
      <j1 rule="para" parents="33282 25884"/>
      <j2 rule="rewrite" parents="16499"/>
    </justification>
  </clause>

  <clause id="74308">
    <literal><![CDATA[
      f(f(x,y),f(x,f(z,z))) = f(c_0,f(x,f(z,f(x,y))))
    ]]></literal>
    <justification jstring="[para(33282(a,1),25887(a,1,2)),rewrite([16499(7)])].">
      <j1 rule="para" parents="33282 25887"/>
      <j2 rule="rewrite" parents="16499"/>
    </justification>
  </clause>

  <clause id="74400">
    <literal><![CDATA[
      f(x,f(f(x,y),f(x,f(z,z)))) = f(x,f(z,f(x,y)))
    ]]></literal>
    <justification jstring="[para(74307(a,2),14690(a,1,2)),rewrite([24579(1),24579(6)])].">
      <j1 rule="para" parents="74307 14690"/>
      <j2 rule="rewrite" parents="24579 24579"/>
    </justification>
  </clause>

  <clause id="74518">
    <literal><![CDATA[
      f(f(x,y),f(x,f(c_0,f(z,u)))) = f(c_0,f(x,f(f(x,y),f(z,u))))
    ]]></literal>
    <justification jstring="[para(26249(a,1),74308(a,1,2,2)),rewrite([13832(4,R),24579(4),13832(10,R),24579(10),13832(13,R),24579(13),24579(15),15654(15),24579(12),15035(12),24579(10)])].">
      <j1 rule="para" parents="26249 74308"/>
      <j2 rule="rewrite" parents="13832 24579 13832 24579 13832 24579 24579 15654 24579 15035 24579"/>
    </justification>
  </clause>

  <clause id="74589">
    <literal><![CDATA[
      f(f(x,y),f(z,f(c_0,f(x,u)))) = f(c_0,f(x,f(f(x,y),f(z,u))))
    ]]></literal>
    <justification jstring="[back_rewrite(33491),rewrite([24579(9),74518(12)])].">
      <j1 rule="back_rewrite" parents="33491"/>
      <j2 rule="rewrite" parents="24579 74518"/>
    </justification>
  </clause>

  <clause id="74935">
    <literal><![CDATA[
      f(x,f(y,f(x,f(z,z)))) = f(x,f(z,f(x,f(y,y))))
    ]]></literal>
    <justification jstring="[para(32396(a,2),74400(a,1,2,1)),rewrite([24579(9),74589(9),12287(6),24579(4),14690(7)])].">
      <j1 rule="para" parents="32396 74400"/>
      <j2 rule="rewrite" parents="24579 74589 12287 24579 14690"/>
    </justification>
  </clause>

  <clause id="74936">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer(MOD_SS)
    ]]></attribute>
    <justification jstring="[resolve(74935,a,5,a)].">
      <j1 rule="resolve" parents="74935 5"/>
    </justification>
  </clause>

</proof>

</proofs>
