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<!DOCTYPE proofs SYSTEM "proof3.dtd">

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

<proofs number_of_proofs="3">

<source>dist-both.out</source>

<heading><![CDATA[
Prover9 (32) version 2008-04A, April 2008.
Process 24458 was started by mccune on cleo,
Fri Apr  4 11:56:29 2008
The command was "/home/mccune/LADR/bin/prover9 -f dist-both.in".
]]></heading>

<proof number="1" length="235" max_count="42">

<comments><![CDATA[
% Proof 1 at 637.76 (+ 0.94) seconds: dist_both.
% Length of proof is 235.
% Level of proof is 31.
% Maximum clause weight is 46.
% Given clauses 791.
]]></comments>

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

  <clause id="4" type="assumption">
    <literal><![CDATA[
      f(x,x,y) = x
    ]]></literal>
    <attribute><![CDATA[
      label(majority)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="5" type="assumption">
    <literal><![CDATA[
      f(x,y,z) = f(z,x,y)
    ]]></literal>
    <attribute><![CDATA[
      label(2a)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="6" type="assumption">
    <literal><![CDATA[
      f(x,y,z) = f(x,z,y)
    ]]></literal>
    <attribute><![CDATA[
      label(2b)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="7" type="assumption">
    <literal><![CDATA[
      f(f(x,y,z),y,u) = f(x,y,f(z,y,u))
    ]]></literal>
    <attribute><![CDATA[
      label(associativity)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="8">
    <literal><![CDATA[
      f(x,y,f(x,z,u)) = f(x,z,f(x,y,u))
    ]]></literal>
    <justification jstring="[copy(7),rewrite([5(2),5(2),5(3,R),6(3)]),rewrite([5(1,R),6(1),6(3),5(4,R),6(4)])].">
      <j1 rule="copy" parents="7"/>
      <j2 rule="rewrite" parents="5 5 5 6"/>
      <j2 rule="rewrite" parents="5 6 6 5 6"/>
    </justification>
  </clause>

  <clause id="13" type="deny">
    <literal><![CDATA[
      f(f(c11,c14,c15),f(c12,c14,c15),f(c13,c14,c15)) != f(f(c11,c12,c13),c14,c15)
    ]]></literal>
    <literal><![CDATA[
      f(f(c11,c12,c13),c14,c15) != f(c11,f(c12,c14,c15),f(c13,c14,c15))
    ]]></literal>
    <attribute><![CDATA[
      label(dist_both)
    ]]></attribute>
    <attribute><![CDATA[
      answer(dist_both)
    ]]></attribute>
    <justification jstring="[deny(3)].">
      <j1 rule="deny" parents="3"/>
    </justification>
  </clause>

  <clause id="14">
    <literal><![CDATA[
      f(f(c11,c14,c15),f(c12,c14,c15),f(c13,c14,c15)) != f(c14,c15,f(c11,c12,c13))
    ]]></literal>
    <literal><![CDATA[
      f(c11,f(c12,c14,c15),f(c13,c14,c15)) != f(c14,c15,f(c11,c12,c13))
    ]]></literal>
    <attribute><![CDATA[
      answer(dist_both)
    ]]></attribute>
    <justification jstring="[copy(13),rewrite([5(20),5(20),5(28),5(28)]),flip(b)].">
      <j1 rule="copy" parents="13"/>
      <j2 rule="rewrite" parents="5 5 5 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15">
    <literal><![CDATA[
      f(x,y,y) = y
    ]]></literal>
    <justification jstring="[para(5(a,1),4(a,1))].">
      <j1 rule="para" parents="5 4"/>
    </justification>
  </clause>

  <clause id="16">
    <literal><![CDATA[
      f(x,y,f(z,x,u)) = f(z,x,f(x,y,u))
    ]]></literal>
    <justification jstring="[para(8(a,1),5(a,2)),rewrite([6(2),5(3,R),6(3)]),flip(a)].">
      <j1 rule="para" parents="8 5"/>
      <j2 rule="rewrite" parents="6 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17">
    <literal><![CDATA[
      f(x,y,f(x,z,u)) = f(x,u,f(x,y,z))
    ]]></literal>
    <justification jstring="[para(5(a,1),8(a,1,3)),rewrite([5(1,R),6(1)])].">
      <j1 rule="para" parents="5 8"/>
      <j2 rule="rewrite" parents="5 6"/>
    </justification>
  </clause>

  <clause id="18">
    <literal><![CDATA[
      f(x,y,f(x,z,f(x,u,w))) = f(x,u,f(x,y,f(x,z,w)))
    ]]></literal>
    <justification jstring="[para(8(a,1),8(a,1,3))].">
      <j1 rule="para" parents="8 8"/>
    </justification>
  </clause>

  <clause id="19">
    <literal><![CDATA[
      f(x,y,f(x,z,y)) = f(x,z,y)
    ]]></literal>
    <justification jstring="[para(15(a,1),8(a,1,3)),flip(a)].">
      <j1 rule="para" parents="15 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20">
    <literal><![CDATA[
      f(x,y,f(x,y,z)) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(15(a,1),8(a,1)),rewrite([6(3),19(3)]),flip(a)].">
      <j1 rule="para" parents="15 8"/>
      <j2 rule="rewrite" parents="6 19"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21">
    <literal><![CDATA[
      f(x,y,f(x,z,f(x,u,y))) = f(x,z,f(x,u,y))
    ]]></literal>
    <justification jstring="[para(19(a,1),8(a,1,3)),flip(a)].">
      <j1 rule="para" parents="19 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22">
    <literal><![CDATA[
      f(x,y,f(x,z,f(x,y,u))) = f(x,z,f(x,y,u))
    ]]></literal>
    <justification jstring="[para(19(a,1),8(a,2,3)),rewrite([6(1),6(4)])].">
      <j1 rule="para" parents="19 8"/>
      <j2 rule="rewrite" parents="6 6"/>
    </justification>
  </clause>

  <clause id="24">
    <literal><![CDATA[
      f(x,y,f(z,y,u)) = f(z,y,f(x,y,u))
    ]]></literal>
    <justification jstring="[para(16(a,1),5(a,2)),rewrite([6(2),5(3,R),6(3)])].">
      <j1 rule="para" parents="16 5"/>
      <j2 rule="rewrite" parents="6 5 6"/>
    </justification>
  </clause>

  <clause id="25">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,z,w))) = f(x,z,f(x,y,f(z,u,w)))
    ]]></literal>
    <justification jstring="[para(16(a,2),8(a,1,3))].">
      <j1 rule="para" parents="16 8"/>
    </justification>
  </clause>

  <clause id="27">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,z,f(x,y,u))) = f(x,y,f(y,z,u))
    ]]></literal>
    <justification jstring="[para(16(a,2),19(a,1,3))].">
      <j1 rule="para" parents="16 19"/>
    </justification>
  </clause>

  <clause id="28">
    <literal><![CDATA[
      f(x,y,f(y,z,f(x,y,u))) = f(x,y,f(y,z,u))
    ]]></literal>
    <justification jstring="[para(16(a,2),20(a,1,3))].">
      <j1 rule="para" parents="16 20"/>
    </justification>
  </clause>

  <clause id="29">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,u,w))) = f(x,u,f(x,y,f(z,u,w)))
    ]]></literal>
    <justification jstring="[para(16(a,1),16(a,1,3)),rewrite([5(1,R),6(1),5(6,R),6(6)])].">
      <j1 rule="para" parents="16 16"/>
      <j2 rule="rewrite" parents="5 6 5 6"/>
    </justification>
  </clause>

  <clause id="30">
    <literal><![CDATA[
      f(x,y,f(z,x,u)) = f(z,x,f(x,u,y))
    ]]></literal>
    <justification jstring="[para(17(a,1),5(a,2)),rewrite([6(2),5(3,R),6(3)]),flip(a)].">
      <j1 rule="para" parents="17 5"/>
      <j2 rule="rewrite" parents="6 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32">
    <literal><![CDATA[
      f(x,y,f(x,z,f(x,u,w))) = f(x,u,f(x,y,f(x,w,z)))
    ]]></literal>
    <justification jstring="[para(17(a,1),8(a,2,3)),flip(a)].">
      <j1 rule="para" parents="17 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33">
    <literal><![CDATA[
      f(x,y,f(x,z,f(x,u,w))) = f(x,w,f(x,y,f(x,z,u)))
    ]]></literal>
    <justification jstring="[para(17(a,2),8(a,1,3))].">
      <j1 rule="para" parents="17 8"/>
    </justification>
  </clause>

  <clause id="38">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,w,y)) = f(x,w,f(y,z,f(x,y,u)))
    ]]></literal>
    <justification jstring="[para(16(a,2),17(a,1,3)),flip(a)].">
      <j1 rule="para" parents="16 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40">
    <literal><![CDATA[
      f(x,y,f(z,x,f(x,u,w))) = f(z,x,f(x,u,f(x,y,w)))
    ]]></literal>
    <justification jstring="[para(18(a,1),5(a,2)),rewrite([6(3),5(5,R),6(5)]),flip(a)].">
      <j1 rule="para" parents="18 5"/>
      <j2 rule="rewrite" parents="6 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41">
    <literal><![CDATA[
      f(x,y,f(y,z,f(y,u,w))) = f(y,z,f(y,u,f(x,y,w)))
    ]]></literal>
    <justification jstring="[para(18(a,2),5(a,2)),rewrite([6(3),5(4,R),6(4)])].">
      <j1 rule="para" parents="18 5"/>
      <j2 rule="rewrite" parents="6 5 6"/>
    </justification>
  </clause>

  <clause id="52">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,z,f(z,w,v5)))) = f(x,z,f(x,y,f(z,w,f(z,u,v5))))
    ]]></literal>
    <justification jstring="[para(18(a,1),16(a,1,3)),rewrite([5(2,R),6(2),5(8,R),6(8)])].">
      <j1 rule="para" parents="18 16"/>
      <j2 rule="rewrite" parents="5 6 5 6"/>
    </justification>
  </clause>

  <clause id="54">
    <literal><![CDATA[
      f(x,y,f(x,z,f(u,w,f(x,u,v5)))) = f(x,u,f(x,y,f(x,z,f(u,w,v5))))
    ]]></literal>
    <justification jstring="[para(16(a,2),18(a,1,3,3))].">
      <j1 rule="para" parents="16 18"/>
    </justification>
  </clause>

  <clause id="57">
    <literal><![CDATA[
      f(x,f(x,y,z),f(x,u,w)) = f(x,y,f(x,u,f(x,w,z)))
    ]]></literal>
    <justification jstring="[para(18(a,1),17(a,1)),flip(a)].">
      <j1 rule="para" parents="18 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="61">
    <literal><![CDATA[
      f(x,y,f(x,z,f(x,u,w))) = f(x,u,f(x,w,f(x,y,z)))
    ]]></literal>
    <justification jstring="[para(17(a,1),18(a,2,3))].">
      <j1 rule="para" parents="17 18"/>
    </justification>
  </clause>

  <clause id="70">
    <literal><![CDATA[
      f(x,y,f(z,u,f(y,z,w))) = f(y,z,f(x,y,f(z,u,w)))
    ]]></literal>
    <justification jstring="[para(8(a,1),24(a,1,3)),rewrite([5(1,R),6(1),5(6,R),6(6)])].">
      <j1 rule="para" parents="8 24"/>
      <j2 rule="rewrite" parents="5 6 5 6"/>
    </justification>
  </clause>

  <clause id="71">
    <literal><![CDATA[
      f(x,y,f(z,u,f(z,x,w))) = f(z,x,f(x,y,f(z,u,w)))
    ]]></literal>
    <justification jstring="[para(8(a,1),24(a,2,3)),rewrite([5(2,R),6(2),5(6,R),6(6)]),flip(a)].">
      <j1 rule="para" parents="8 24"/>
      <j2 rule="rewrite" parents="5 6 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="73">
    <literal><![CDATA[
      f(x,y,f(z,x,f(x,y,u))) = f(z,x,f(x,y,u))
    ]]></literal>
    <justification jstring="[para(19(a,1),24(a,1,3)),rewrite([5(1),5(3),5(5,R),6(5)]),flip(a)].">
      <j1 rule="para" parents="19 24"/>
      <j2 rule="rewrite" parents="5 5 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="74">
    <literal><![CDATA[
      f(x,y,f(z,u,f(y,u,w))) = f(y,u,f(x,y,f(z,u,w)))
    ]]></literal>
    <justification jstring="[para(16(a,1),24(a,1,3)),rewrite([5(1,R),6(1),5(6,R),6(6)])].">
      <j1 rule="para" parents="16 24"/>
      <j2 rule="rewrite" parents="5 6 5 6"/>
    </justification>
  </clause>

  <clause id="75">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,w,z)) = f(x,w,f(y,z,f(x,z,u)))
    ]]></literal>
    <justification jstring="[para(24(a,1),17(a,1,3)),flip(a)].">
      <j1 rule="para" parents="24 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="87">
    <literal><![CDATA[
      f(x,y,f(y,z,f(y,u,w))) = f(y,z,f(y,w,f(x,y,u)))
    ]]></literal>
    <justification jstring="[para(30(a,2),24(a,2,3)),rewrite([5(2,R),6(2),5(6,R),6(6)])].">
      <j1 rule="para" parents="30 24"/>
      <j2 rule="rewrite" parents="5 6 5 6"/>
    </justification>
  </clause>

  <clause id="95">
    <literal><![CDATA[
      f(x,y,f(x,z,f(y,u,f(x,y,w)))) = f(x,z,f(y,u,f(x,y,w)))
    ]]></literal>
    <justification jstring="[para(21(a,1),16(a,1,3)),rewrite([5(1),5(4),5(7,R),6(7)]),flip(a)].">
      <j1 rule="para" parents="21 16"/>
      <j2 rule="rewrite" parents="5 5 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="103">
    <literal><![CDATA[
      f(x,y,f(y,z,f(x,u,f(x,y,w)))) = f(y,z,f(x,u,f(x,y,w)))
    ]]></literal>
    <justification jstring="[para(21(a,1),24(a,2,3)),rewrite([6(1),5(3,R),6(3),6(5),5(7,R),6(7)])].">
      <j1 rule="para" parents="21 24"/>
      <j2 rule="rewrite" parents="6 5 6 6 5 6"/>
    </justification>
  </clause>

  <clause id="105">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,u,w))) = f(x,y,f(x,u,f(z,u,w)))
    ]]></literal>
    <justification jstring="[para(24(a,1),21(a,2,3)),rewrite([21(5)]),flip(a)].">
      <j1 rule="para" parents="24 21"/>
      <j2 rule="rewrite" parents="21"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="111">
    <literal><![CDATA[
      f(x,y,f(z,u,f(y,z,w))) = f(x,y,f(y,z,f(z,u,w)))
    ]]></literal>
    <justification jstring="[para(16(a,2),28(a,2,3)),rewrite([28(4)]),flip(a)].">
      <j1 rule="para" parents="16 28"/>
      <j2 rule="rewrite" parents="28"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="113">
    <literal><![CDATA[
      f(x,y,f(y,z,f(y,u,w))) = f(x,y,f(y,w,f(y,z,u)))
    ]]></literal>
    <justification jstring="[para(17(a,1),28(a,2,3)),rewrite([28(4)])].">
      <j1 rule="para" parents="17 28"/>
      <j2 rule="rewrite" parents="28"/>
    </justification>
  </clause>

  <clause id="122">
    <literal><![CDATA[
      f(x,y,f(z,y,f(x,y,u))) = f(z,y,f(x,y,u))
    ]]></literal>
    <justification jstring="[para(73(a,1),5(a,2)),rewrite([5(1,R),6(1),6(3),5(4,R),6(4)])].">
      <j1 rule="para" parents="73 5"/>
      <j2 rule="rewrite" parents="5 6 6 5 6"/>
    </justification>
  </clause>

  <clause id="125">
    <literal><![CDATA[
      f(x,y,f(z,u,f(z,x,w))) = f(x,y,f(z,x,f(z,u,w)))
    ]]></literal>
    <justification jstring="[para(8(a,1),122(a,1,3,3)),rewrite([5(3,R),6(3),103(4),5(6,R),6(6)])].">
      <j1 rule="para" parents="8 122"/>
      <j2 rule="rewrite" parents="5 6 103 5 6"/>
    </justification>
  </clause>

  <clause id="132">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,z,u))) = f(x,y,f(x,z,u))
    ]]></literal>
    <justification jstring="[para(15(a,1),25(a,1,3)),rewrite([6(4),95(6)]),flip(a)].">
      <j1 rule="para" parents="15 25"/>
      <j2 rule="rewrite" parents="6 95"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="168">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,z,f(y,u,x))) = f(y,x,f(y,z,u))
    ]]></literal>
    <justification jstring="[para(27(a,1),5(a,2)),rewrite([5(2),5(2),5(4),5(6,R),6(6)])].">
      <j1 rule="para" parents="27 5"/>
      <j2 rule="rewrite" parents="5 5 5 5 6"/>
    </justification>
  </clause>

  <clause id="187">
    <literal><![CDATA[
      f(x,f(y,z,f(z,u,w)),f(z,u,f(x,u,f(y,z,w)))) = f(x,u,f(z,u,f(y,z,w)))
    ]]></literal>
    <justification jstring="[para(24(a,1),27(a,1,2)),rewrite([5(1,R),6(1),5(5,R),6(5),5(8,R),6(8)])].">
      <j1 rule="para" parents="24 27"/>
      <j2 rule="rewrite" parents="5 6 5 6 5 6"/>
    </justification>
  </clause>

  <clause id="200">
    <literal><![CDATA[
      f(x,f(y,z,f(u,w,f(x,u,v5))),f(y,z,f(x,u,f(x,y,f(u,w,v5))))) = f(x,y,f(y,z,f(u,w,f(x,u,v5))))
    ]]></literal>
    <justification jstring="[para(25(a,1),27(a,1,3,3))].">
      <j1 rule="para" parents="25 27"/>
    </justification>
  </clause>

  <clause id="205">
    <literal><![CDATA[
      f(x,y,f(z,x,y)) = f(z,x,y)
    ]]></literal>
    <justification jstring="[para(132(a,1),15(a,1)),rewrite([6(4),132(4),15(3)]),flip(a)].">
      <j1 rule="para" parents="132 15"/>
      <j2 rule="rewrite" parents="6 132 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="220">
    <literal><![CDATA[
      f(x,y,f(z,u,f(u,y,w))) = f(u,y,f(x,y,f(z,u,w)))
    ]]></literal>
    <justification jstring="[para(29(a,1),5(a,2)),rewrite([5(1,R),6(1),6(3),5(5,R),6(5),5(6,R),6(6)])].">
      <j1 rule="para" parents="29 5"/>
      <j2 rule="rewrite" parents="5 6 6 5 6 5 6"/>
    </justification>
  </clause>

  <clause id="262">
    <literal><![CDATA[
      f(x,y,f(z,u,f(u,y,w))) = f(x,y,f(u,y,f(z,u,w)))
    ]]></literal>
    <justification jstring="[para(29(a,1),205(a,1,3)),rewrite([5(1,R),6(1),5(4,R),6(4),5(5,R),6(5),187(6),5(4,R),6(4),5(6,R),6(6)]),flip(a)].">
      <j1 rule="para" parents="29 205"/>
      <j2 rule="rewrite" parents="5 6 5 6 5 6 187 5 6 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="318">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,x,w)) = f(x,w,f(y,z,f(y,u,x)))
    ]]></literal>
    <justification jstring="[para(38(a,1),5(a,2)),rewrite([5(2),5(3),5(4),5(4)])].">
      <j1 rule="para" parents="38 5"/>
      <j2 rule="rewrite" parents="5 5 5 5"/>
    </justification>
  </clause>

  <clause id="319">
    <literal><![CDATA[
      f(x,f(y,z,u),f(w,y,x)) = f(w,x,f(y,z,f(y,x,u)))
    ]]></literal>
    <justification jstring="[para(38(a,2),5(a,2)),rewrite([5(1,R),6(1),6(3),5(5),5(5)]),flip(a)].">
      <j1 rule="para" parents="38 5"/>
      <j2 rule="rewrite" parents="5 6 6 5 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="321">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,u,w)) = f(x,w,f(y,u,f(x,z,u)))
    ]]></literal>
    <justification jstring="[para(5(a,2),38(a,1,2)),rewrite([6(2),6(4),5(5,R),6(5)])].">
      <j1 rule="para" parents="5 38"/>
      <j2 rule="rewrite" parents="6 6 5 6"/>
    </justification>
  </clause>

  <clause id="331">
    <literal><![CDATA[
      f(x,y,f(z,f(x,y,u),f(x,w,f(x,y,u)))) = f(x,f(x,y,u),f(z,w,f(x,y,u)))
    ]]></literal>
    <justification jstring="[para(20(a,1),38(a,1,3)),rewrite([5(2),5(2),6(4),6(7),5(8,R),6(8)]),flip(a)].">
      <j1 rule="para" parents="20 38"/>
      <j2 rule="rewrite" parents="5 5 6 6 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="360">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,z,x)) = f(y,z,f(z,x,f(y,x,u)))
    ]]></literal>
    <justification jstring="[para(38(a,2),24(a,2)),rewrite([5(1,R),6(1),5(2,R),6(2),5(5),6(5)]),flip(a)].">
      <j1 rule="para" parents="38 24"/>
      <j2 rule="rewrite" parents="5 6 5 6 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="385">
    <literal><![CDATA[
      f(x,y,f(z,f(x,y,u),f(x,y,z))) = f(y,z,f(x,y,f(x,z,u)))
    ]]></literal>
    <justification jstring="[para(38(a,2),122(a,1,3)),rewrite([5(2),6(2),5(5,R),6(5),5(7,R),6(7)])].">
      <j1 rule="para" parents="38 122"/>
      <j2 rule="rewrite" parents="5 6 5 6 5 6"/>
    </justification>
  </clause>

  <clause id="392">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,y,w)) = f(x,y,f(x,w,f(y,z,u)))
    ]]></literal>
    <justification jstring="[para(38(a,2),25(a,1)),rewrite([6(2)])].">
      <j1 rule="para" parents="38 25"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="474">
    <literal><![CDATA[
      f(x,y,f(x,z,f(u,x,y))) = f(u,x,f(x,z,y))
    ]]></literal>
    <justification jstring="[para(19(a,1),41(a,1,3)),flip(a)].">
      <j1 rule="para" parents="19 41"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="628">
    <literal><![CDATA[
      f(x,f(y,x,z),f(x,u,z)) = f(y,x,f(x,u,z))
    ]]></literal>
    <justification jstring="[para(474(a,1),17(a,1)),rewrite([6(4)]),flip(a)].">
      <j1 rule="para" parents="474 17"/>
      <j2 rule="rewrite" parents="6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="630">
    <literal><![CDATA[
      f(x,y,f(z,u,f(z,x,w))) = f(x,y,f(z,w,f(z,x,u)))
    ]]></literal>
    <justification jstring="[para(474(a,1),24(a,2,3)),rewrite([5(1),5(1),5(3,R),6(3),103(4),6(4),5(5,R),6(5),5(6,R),6(6)])].">
      <j1 rule="para" parents="474 24"/>
      <j2 rule="rewrite" parents="5 5 5 6 103 6 5 6 5 6"/>
    </justification>
  </clause>

  <clause id="654">
    <literal><![CDATA[
      f(x,f(y,x,z),f(x,z,u)) = f(y,x,f(x,z,u))
    ]]></literal>
    <justification jstring="[para(628(a,1),5(a,2)),rewrite([6(2),5(3),6(4)])].">
      <j1 rule="para" parents="628 5"/>
      <j2 rule="rewrite" parents="6 5 6"/>
    </justification>
  </clause>

  <clause id="695">
    <literal><![CDATA[
      f(x,f(x,y,z),f(u,x,y)) = f(u,x,f(x,y,z))
    ]]></literal>
    <justification jstring="[para(654(a,1),6(a,1)),flip(a)].">
      <j1 rule="para" parents="654 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="696">
    <literal><![CDATA[
      f(x,f(x,y,z),f(u,w,f(x,y,z))) = f(x,z,f(x,y,f(u,w,f(x,y,z))))
    ]]></literal>
    <justification jstring="[para(654(a,1),25(a,2)),rewrite([5(1),5(1),5(2),5(2),6(3),5(4,R),6(4),331(5),5(5),5(5),5(6),5(6),5(8,R),6(8)])].">
      <j1 rule="para" parents="654 25"/>
      <j2 rule="rewrite" parents="5 5 5 5 6 5 6 331 5 5 5 5 5 6"/>
    </justification>
  </clause>

  <clause id="803">
    <literal><![CDATA[
      f(x,y,f(x,z,f(z,y,u))) = f(x,z,y)
    ]]></literal>
    <justification jstring="[para(695(a,1),40(a,1,3)),rewrite([5(4,R),15(4),5(3,R),15(3),5(5),6(5),5(6,R),6(6),696(6),28(5),6(3),57(6),6(4),20(5),22(5)]),flip(a)].">
      <j1 rule="para" parents="695 40"/>
      <j2 rule="rewrite" parents="5 15 5 15 5 6 5 6 696 28 6 57 6 20 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="812">
    <literal><![CDATA[
      f(x,y,f(y,z,f(x,z,u))) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(803(a,1),5(a,2)),rewrite([5(1,R),6(1),6(3),5(4)])].">
      <j1 rule="para" parents="803 5"/>
      <j2 rule="rewrite" parents="5 6 6 5"/>
    </justification>
  </clause>

  <clause id="813">
    <literal><![CDATA[
      f(x,y,f(x,z,f(y,z,u))) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(5(a,1),803(a,1,3,3)),rewrite([5(1),6(1),6(4)])].">
      <j1 rule="para" parents="5 803"/>
      <j2 rule="rewrite" parents="5 6 6"/>
    </justification>
  </clause>

  <clause id="814">
    <literal><![CDATA[
      f(x,y,f(x,z,f(x,u,f(u,y,w)))) = f(x,z,f(x,u,y))
    ]]></literal>
    <justification jstring="[para(803(a,1),8(a,1,3)),flip(a)].">
      <j1 rule="para" parents="803 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="816">
    <literal><![CDATA[
      f(x,y,f(x,z,f(z,u,f(y,z,w)))) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(8(a,1),803(a,1,3,3)),rewrite([5(1,R),6(1),6(5)])].">
      <j1 rule="para" parents="8 803"/>
      <j2 rule="rewrite" parents="5 6 6"/>
    </justification>
  </clause>

  <clause id="820">
    <literal><![CDATA[
      f(x,y,f(x,f(y,z,u),f(y,w,f(y,z,u)))) = f(y,z,f(x,y,u))
    ]]></literal>
    <justification jstring="[para(16(a,2),803(a,2)),rewrite([6(3),392(5),6(4)])].">
      <j1 rule="para" parents="16 803"/>
      <j2 rule="rewrite" parents="6 392 6"/>
    </justification>
  </clause>

  <clause id="826">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,z,f(z,w,f(y,z,u)))) = f(y,z,f(x,z,u))
    ]]></literal>
    <justification jstring="[para(24(a,1),803(a,2)),rewrite([6(3)])].">
      <j1 rule="para" parents="24 803"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="827">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,y,z))) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(30(a,2),803(a,1,3)),rewrite([6(1),6(4)])].">
      <j1 rule="para" parents="30 803"/>
      <j2 rule="rewrite" parents="6 6"/>
    </justification>
  </clause>

  <clause id="828">
    <literal><![CDATA[
      f(x,y,f(z,x,u)) = f(x,u,f(z,x,y))
    ]]></literal>
    <justification jstring="[para(30(a,2),803(a,2)),rewrite([6(3),392(5),6(4),820(5)])].">
      <j1 rule="para" parents="30 803"/>
      <j2 rule="rewrite" parents="6 392 6 820"/>
    </justification>
  </clause>

  <clause id="847">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,w,f(x,y,z))) = f(x,w,f(x,y,z))
    ]]></literal>
    <justification jstring="[para(803(a,1),33(a,1,3)),rewrite([6(4)]),flip(a)].">
      <j1 rule="para" parents="803 33"/>
      <j2 rule="rewrite" parents="6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="866">
    <literal><![CDATA[
      f(x,y,f(z,y,f(z,x,u))) = f(z,x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(360),rewrite([5(2),392(3),813(3),5(2,R),6(2),5(3,R),6(3)]),flip(a)].">
      <j1 rule="back_rewrite" parents="360"/>
      <j2 rule="rewrite" parents="5 392 813 5 6 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="871">
    <literal><![CDATA[
      f(x,y,f(z,x,f(z,y,u))) = f(z,x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(385),rewrite([827(4)]),flip(a)].">
      <j1 rule="back_rewrite" parents="385"/>
      <j2 rule="rewrite" parents="827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="874">
    <literal><![CDATA[
      f(x,y,f(z,u,x)) = f(z,x,f(u,x,y))
    ]]></literal>
    <justification jstring="[para(828(a,1),5(a,2)),rewrite([6(2),5(3)]),flip(a)].">
      <j1 rule="para" parents="828 5"/>
      <j2 rule="rewrite" parents="6 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="897">
    <literal><![CDATA[
      f(x,y,f(z,u,y)) = f(z,y,f(x,u,y))
    ]]></literal>
    <justification jstring="[para(874(a,1),5(a,2)),rewrite([6(2),5(3)])].">
      <j1 rule="para" parents="874 5"/>
      <j2 rule="rewrite" parents="6 5"/>
    </justification>
  </clause>

  <clause id="922">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,z,x)) = f(y,z,x)
    ]]></literal>
    <justification jstring="[para(874(a,2),38(a,2)),rewrite([6(2),392(3),813(3)]),flip(a)].">
      <j1 rule="para" parents="874 38"/>
      <j2 rule="rewrite" parents="6 392 813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="933">
    <literal><![CDATA[
      f(x,y,f(z,u,x)) = f(u,x,f(z,x,y))
    ]]></literal>
    <justification jstring="[para(874(a,2),803(a,2)),rewrite([6(3),826(5)]),flip(a)].">
      <j1 rule="para" parents="874 803"/>
      <j2 rule="rewrite" parents="6 826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1030">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,u,y))) = f(x,u,y)
    ]]></literal>
    <justification jstring="[para(20(a,1),897(a,1,3)),rewrite([15(3),696(5),122(4)]),flip(a)].">
      <j1 rule="para" parents="20 897"/>
      <j2 rule="rewrite" parents="15 696 122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1036">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,w,f(y,z,u))) = f(w,f(y,z,u),f(y,u,f(x,y,z)))
    ]]></literal>
    <justification jstring="[para(30(a,2),897(a,2,3)),rewrite([5(3,R),6(3)])].">
      <j1 rule="para" parents="30 897"/>
      <j2 rule="rewrite" parents="5 6"/>
    </justification>
  </clause>

  <clause id="1050">
    <literal><![CDATA[
      f(x,y,f(x,f(x,y,z),f(u,y,z))) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(897(a,1),29(a,1)),rewrite([20(3),15(3)]),flip(a)].">
      <j1 rule="para" parents="897 29"/>
      <j2 rule="rewrite" parents="20 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1057">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,x,z)) = f(y,x,z)
    ]]></literal>
    <justification jstring="[para(38(a,2),897(a,2)),rewrite([5(1,R),6(1),5(2,R),6(2),696(4),28(3),6(1),803(3),6(2),5(3,R),6(3),5(4),20(4)]),flip(a)].">
      <j1 rule="para" parents="38 897"/>
      <j2 rule="rewrite" parents="5 6 5 6 696 28 6 803 6 5 6 5 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1063">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,u,f(u,w,f(y,z,u)))) = f(y,u,f(x,z,u))
    ]]></literal>
    <justification jstring="[para(897(a,1),803(a,2)),rewrite([6(3)])].">
      <j1 rule="para" parents="897 803"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="1071">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,z,u)) = f(x,z,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),922(a,1,2)),rewrite([5(2),5(4)])].">
      <j1 rule="para" parents="5 922"/>
      <j2 rule="rewrite" parents="5 5"/>
    </justification>
  </clause>

  <clause id="1072">
    <literal><![CDATA[
      f(x,y,f(x,z,f(y,u,z))) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(5(a,2),922(a,1,2)),rewrite([5(2),6(2),392(3),5(4),6(4)])].">
      <j1 rule="para" parents="5 922"/>
      <j2 rule="rewrite" parents="5 6 392 5 6"/>
    </justification>
  </clause>

  <clause id="1073">
    <literal><![CDATA[
      f(x,f(y,z,x),f(y,z,u)) = f(y,z,x)
    ]]></literal>
    <justification jstring="[para(922(a,1),6(a,1)),flip(a)].">
      <j1 rule="para" parents="922 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1079">
    <literal><![CDATA[
      f(x,f(y,z,f(z,u,w)),f(x,z,u)) = f(x,z,u)
    ]]></literal>
    <justification jstring="[para(16(a,1),922(a,1,2)),rewrite([5(3),5(5)])].">
      <j1 rule="para" parents="16 922"/>
      <j2 rule="rewrite" parents="5 5"/>
    </justification>
  </clause>

  <clause id="1082">
    <literal><![CDATA[
      f(x,y,f(x,z,f(y,u,f(y,w,z)))) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(17(a,2),922(a,1,2)),rewrite([5(3),392(4),5(5)])].">
      <j1 rule="para" parents="17 922"/>
      <j2 rule="rewrite" parents="5 392 5"/>
    </justification>
  </clause>

  <clause id="1088">
    <literal><![CDATA[
      f(x,f(y,z,f(z,u,w)),f(x,z,w)) = f(x,z,w)
    ]]></literal>
    <justification jstring="[para(30(a,1),922(a,1,2)),rewrite([5(3),5(5)])].">
      <j1 rule="para" parents="30 922"/>
      <j2 rule="rewrite" parents="5 5"/>
    </justification>
  </clause>

  <clause id="1101">
    <literal><![CDATA[
      f(f(x,y,z),f(y,z,u),f(x,y,z)) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(205(a,1),922(a,1,3)),rewrite([205(6)])].">
      <j1 rule="para" parents="205 922"/>
      <j2 rule="rewrite" parents="205"/>
    </justification>
  </clause>

  <clause id="1136">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,w,f(y,z,w))) = f(x,w,f(y,z,u))
    ]]></literal>
    <justification jstring="[para(922(a,1),803(a,1,3,3))].">
      <j1 rule="para" parents="922 803"/>
    </justification>
  </clause>

  <clause id="1140">
    <literal><![CDATA[
      f(f(x,y,z),f(x,y,u),f(u,w,f(x,y,z))) = f(w,f(x,y,u),f(x,y,z))
    ]]></literal>
    <justification jstring="[para(922(a,1),828(a,2,3)),rewrite([6(4),5(8,R)])].">
      <j1 rule="para" parents="922 828"/>
      <j2 rule="rewrite" parents="6 5"/>
    </justification>
  </clause>

  <clause id="1142">
    <literal><![CDATA[
      f(x,f(y,z,x),f(u,f(y,z,w),f(y,z,x))) = f(y,z,x)
    ]]></literal>
    <justification jstring="[para(922(a,1),874(a,1,3)),rewrite([5(3,R),15(3),5(5)]),flip(a)].">
      <j1 rule="para" parents="922 874"/>
      <j2 rule="rewrite" parents="5 15 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1148">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,u,f(y,z,w))) = f(x,u,f(y,z,w))
    ]]></literal>
    <justification jstring="[para(922(a,1),922(a,1,2)),rewrite([5(3),5(6)])].">
      <j1 rule="para" parents="922 922"/>
      <j2 rule="rewrite" parents="5 5"/>
    </justification>
  </clause>

  <clause id="1149">
    <literal><![CDATA[
      f(x,y,f(z,u,y)) = f(u,y,f(x,z,y))
    ]]></literal>
    <justification jstring="[para(933(a,1),5(a,2)),rewrite([6(2),5(3)])].">
      <j1 rule="para" parents="933 5"/>
      <j2 rule="rewrite" parents="6 5"/>
    </justification>
  </clause>

  <clause id="1150">
    <literal><![CDATA[
      f(x,f(y,z,x),f(y,u,f(y,z,x))) = f(y,z,x)
    ]]></literal>
    <justification jstring="[para(19(a,1),933(a,1,3)),rewrite([5(3,R),15(3),6(4)]),flip(a)].">
      <j1 rule="para" parents="19 933"/>
      <j2 rule="rewrite" parents="5 15 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1176">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,u,w)) = f(x,w,f(z,u,f(x,y,u)))
    ]]></literal>
    <justification jstring="[para(933(a,1),828(a,2,3)),rewrite([5(2,R),6(2),5(4)])].">
      <j1 rule="para" parents="933 828"/>
      <j2 rule="rewrite" parents="5 6 5"/>
    </justification>
  </clause>

  <clause id="1181">
    <literal><![CDATA[
      f(x,f(y,x,z),f(y,z,u)) = f(y,x,z)
    ]]></literal>
    <justification jstring="[para(1057(a,1),6(a,1)),flip(a)].">
      <j1 rule="para" parents="1057 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1197">
    <literal><![CDATA[
      f(x,f(y,z,u),f(w,x,y)) = f(w,x,f(y,z,f(x,y,u)))
    ]]></literal>
    <justification jstring="[para(38(a,2),1057(a,2)),rewrite([6(3),5(6,R),6(6),392(7),1072(7),5(5,R),6(5)]),flip(a)].">
      <j1 rule="para" parents="38 1057"/>
      <j2 rule="rewrite" parents="6 5 6 392 1072 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1253">
    <literal><![CDATA[
      f(x,f(y,z,u),f(z,u,x)) = f(z,u,x)
    ]]></literal>
    <justification jstring="[para(1071(a,1),5(a,2)),rewrite([5(2),5(2),5(3),5(4),5(4)])].">
      <j1 rule="para" parents="1071 5"/>
      <j2 rule="rewrite" parents="5 5 5 5 5"/>
    </justification>
  </clause>

  <clause id="1254">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,w,f(x,z,u))) = f(x,w,f(x,z,u))
    ]]></literal>
    <justification jstring="[para(1071(a,1),8(a,2,3))].">
      <j1 rule="para" parents="1071 8"/>
    </justification>
  </clause>

  <clause id="1286">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,u,f(x,z,w))) = f(x,w,f(x,z,u))
    ]]></literal>
    <justification jstring="[para(1071(a,1),32(a,2,3)),rewrite([6(2)])].">
      <j1 rule="para" parents="1071 32"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="1321">
    <literal><![CDATA[
      f(x,f(y,z,f(z,u,w)),f(x,f(y,z,u),f(z,u,w))) = f(x,f(y,z,u),f(z,u,w))
    ]]></literal>
    <justification jstring="[para(654(a,1),1071(a,1,2))].">
      <j1 rule="para" parents="654 1071"/>
    </justification>
  </clause>

  <clause id="1329">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,w,f(z,u,w))) = f(x,w,f(y,z,u))
    ]]></literal>
    <justification jstring="[para(1071(a,1),803(a,1,3,3)),rewrite([5(2),5(2)])].">
      <j1 rule="para" parents="1071 803"/>
      <j2 rule="rewrite" parents="5 5"/>
    </justification>
  </clause>

  <clause id="1332">
    <literal><![CDATA[
      f(f(x,y,z),f(y,z,u),f(u,w,f(x,y,z))) = f(w,f(y,z,u),f(x,y,z))
    ]]></literal>
    <justification jstring="[para(1071(a,1),828(a,2,3)),rewrite([5(2),5(2),6(4),5(7),5(7),5(8,R)])].">
      <j1 rule="para" parents="1071 828"/>
      <j2 rule="rewrite" parents="5 5 6 5 5 5"/>
    </justification>
  </clause>

  <clause id="1341">
    <literal><![CDATA[
      f(x,y,f(x,f(z,u,w),f(y,z,u))) = f(x,y,f(z,u,w))
    ]]></literal>
    <justification jstring="[para(1071(a,1),922(a,1,2)),rewrite([5(2),5(2),5(3),392(4),5(5),5(5),5(6)])].">
      <j1 rule="para" parents="1071 922"/>
      <j2 rule="rewrite" parents="5 5 5 392 5 5 5"/>
    </justification>
  </clause>

  <clause id="1344">
    <literal><![CDATA[
      f(f(x,y,z),f(y,z,u),f(u,w,f(y,z,u))) = f(y,z,u)
    ]]></literal>
    <justification jstring="[para(1071(a,1),1057(a,1,3)),rewrite([5(2),5(2),6(3),5(4),5(4),6(5),5(7),5(7),1253(8)])].">
      <j1 rule="para" parents="1071 1057"/>
      <j2 rule="rewrite" parents="5 5 6 5 5 6 5 5 1253"/>
    </justification>
  </clause>

  <clause id="1349">
    <literal><![CDATA[
      f(x,f(x,y,z),f(y,u,f(y,z,w))) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(8(a,1),1073(a,1,3)),rewrite([5(1),5(5)])].">
      <j1 rule="para" parents="8 1073"/>
      <j2 rule="rewrite" parents="5 5"/>
    </justification>
  </clause>

  <clause id="1404">
    <literal><![CDATA[
      f(x,y,f(x,f(z,u,w),f(y,u,w))) = f(x,y,f(z,u,w))
    ]]></literal>
    <justification jstring="[para(1071(a,1),1073(a,1,3)),rewrite([5(2),6(4),392(4),5(6)])].">
      <j1 rule="para" parents="1071 1073"/>
      <j2 rule="rewrite" parents="5 6 392 5"/>
    </justification>
  </clause>

  <clause id="1469">
    <literal><![CDATA[
      f(x,y,f(z,u,y)) = f(u,y,f(z,x,y))
    ]]></literal>
    <justification jstring="[para(1149(a,1),803(a,2)),rewrite([6(3),1063(5)])].">
      <j1 rule="para" parents="1149 803"/>
      <j2 rule="rewrite" parents="6 1063"/>
    </justification>
  </clause>

  <clause id="1605">
    <literal><![CDATA[
      f(f(x,y,z),f(x,z,u),f(y,w,f(x,z,u))) = f(w,f(x,z,u),f(x,y,z))
    ]]></literal>
    <justification jstring="[para(1181(a,1),1469(a,2,3))].">
      <j1 rule="para" parents="1181 1469"/>
    </justification>
  </clause>

  <clause id="1618">
    <literal><![CDATA[
      f(x,y,f(y,f(z,u,f(x,u,w)),f(x,v5,f(z,u,f(x,u,w))))) = f(x,u,f(x,y,f(z,u,w)))
    ]]></literal>
    <justification jstring="[para(29(a,1),812(a,2)),rewrite([6(5)])].">
      <j1 rule="para" parents="29 812"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="1630">
    <literal><![CDATA[
      f(x,y,f(y,f(z,u,w),f(x,z,u))) = f(x,y,f(z,u,w))
    ]]></literal>
    <justification jstring="[para(922(a,1),812(a,1,3,3)),rewrite([5(2)])].">
      <j1 rule="para" parents="922 812"/>
      <j2 rule="rewrite" parents="5"/>
    </justification>
  </clause>

  <clause id="1856">
    <literal><![CDATA[
      f(x,y,f(z,x,f(y,u,f(z,y,w)))) = f(z,x,y)
    ]]></literal>
    <justification jstring="[para(52(a,1),874(a,2)),rewrite([5(3),392(4),813(4),5(2,R),6(2),5(4,R),6(4)]),flip(a)].">
      <j1 rule="para" parents="52 874"/>
      <j2 rule="rewrite" parents="5 392 813 5 6 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1905">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,u,f(y,u,w)))) = f(x,y,u)
    ]]></literal>
    <justification jstring="[para(41(a,2),871(a,1,3)),rewrite([5(1,R),6(1),5(2,R),6(2),5(5),5(5)])].">
      <j1 rule="para" parents="41 871"/>
      <j2 rule="rewrite" parents="5 6 5 6 5 5"/>
    </justification>
  </clause>

  <clause id="1906">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,z,f(z,u,x))) = f(z,x,f(y,z,u))
    ]]></literal>
    <justification jstring="[para(628(a,1),871(a,1,3)),rewrite([6(2),5(4,R),6(4),6(6)])].">
      <j1 rule="para" parents="628 871"/>
      <j2 rule="rewrite" parents="6 5 6 6"/>
    </justification>
  </clause>

  <clause id="1982">
    <literal><![CDATA[
      f(x,y,f(z,u,f(u,x,y))) = f(u,x,y)
    ]]></literal>
    <justification jstring="[para(1030(a,1),922(a,2)),rewrite([5(1,R),6(1),5(4,R),6(4),922(7),5(4,R),6(4)])].">
      <j1 rule="para" parents="1030 922"/>
      <j2 rule="rewrite" parents="5 6 5 6 922 5 6"/>
    </justification>
  </clause>

  <clause id="2276">
    <literal><![CDATA[
      f(x,f(y,z,f(x,y,u)),f(x,w,v5)) = f(x,y,f(x,w,f(x,v5,f(y,z,u))))
    ]]></literal>
    <justification jstring="[para(54(a,1),17(a,1)),flip(a)].">
      <j1 rule="para" parents="54 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2885">
    <literal><![CDATA[
      f(x,f(y,z,f(u,z,w)),f(x,u,z)) = f(x,u,z)
    ]]></literal>
    <justification jstring="[para(1079(a,1),21(a,2)),rewrite([5(1,R),6(1),6(3),22(5),6(5)])].">
      <j1 rule="para" parents="1079 21"/>
      <j2 rule="rewrite" parents="5 6 6 22 6"/>
    </justification>
  </clause>

  <clause id="2997">
    <literal><![CDATA[
      f(x,f(y,z,f(x,z,u)),f(x,w,v5)) = f(x,z,f(x,w,f(x,v5,f(y,z,u))))
    ]]></literal>
    <justification jstring="[para(24(a,1),57(a,1,2))].">
      <j1 rule="para" parents="24 57"/>
    </justification>
  </clause>

  <clause id="3270">
    <literal><![CDATA[
      f(x,f(y,z,x),f(u,y,z)) = f(y,z,x)
    ]]></literal>
    <justification jstring="[para(1050(a,1),1150(a,1,3)),rewrite([5(2),5(2),5(5),5(5),6(6),1332(6),4(4),5(2),5(2)]),flip(a)].">
      <j1 rule="para" parents="1050 1150"/>
      <j2 rule="rewrite" parents="5 5 5 5 6 1332 4 5 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3475">
    <literal><![CDATA[
      f(x,f(y,x,z),f(y,x,f(y,z,u))) = f(y,x,z)
    ]]></literal>
    <justification jstring="[para(1349(a,1),122(a,1,3)),rewrite([5(1,R),6(1),5(2,R),6(2),15(3),5(2,R),6(2),5(3,R),6(3),57(5),6(3),20(4)]),flip(a)].">
      <j1 rule="para" parents="1349 122"/>
      <j2 rule="rewrite" parents="5 6 5 6 15 5 6 5 6 57 6 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3946">
    <literal><![CDATA[
      f(x,f(y,x,z),f(u,y,f(y,x,w))) = f(x,z,f(u,y,f(y,x,w)))
    ]]></literal>
    <justification jstring="[para(2885(a,1),871(a,1,3)),rewrite([5(1,R),6(1),5(3),6(3),5(4,R),5(5,R),6(5),5(7)])].">
      <j1 rule="para" parents="2885 871"/>
      <j2 rule="rewrite" parents="5 6 5 6 5 5 6 5"/>
    </justification>
  </clause>

  <clause id="4005">
    <literal><![CDATA[
      f(x,y,f(x,f(y,z,u),f(w,z,u))) = f(x,y,f(w,z,u))
    ]]></literal>
    <justification jstring="[para(1071(a,1),3475(a,1,3,3)),rewrite([5(2,R),6(2),5(4,R),6(4),57(5),20(5),5(6,R),6(6)])].">
      <j1 rule="para" parents="1071 3475"/>
      <j2 rule="rewrite" parents="5 6 5 6 57 20 5 6"/>
    </justification>
  </clause>

  <clause id="4085">
    <literal><![CDATA[
      f(x,y,f(z,u,f(z,w,f(x,y,z)))) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(61(a,1),866(a,1,3)),rewrite([5(1),6(1),5(5),5(5)])].">
      <j1 rule="para" parents="61 866"/>
      <j2 rule="rewrite" parents="5 6 5 5"/>
    </justification>
  </clause>

  <clause id="4302">
    <literal><![CDATA[
      f(x,y,f(x,f(y,z,u),f(w,f(y,z,u),f(y,v5,f(y,z,u))))) = f(y,z,f(x,y,u))
    ]]></literal>
    <justification jstring="[para(16(a,2),816(a,2)),rewrite([6(4),5(5,R),6(5)])].">
      <j1 rule="para" parents="16 816"/>
      <j2 rule="rewrite" parents="6 5 6"/>
    </justification>
  </clause>

  <clause id="4305">
    <literal><![CDATA[
      f(x,y,f(z,f(y,z,u),f(x,z,w))) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(30(a,2),816(a,1,3))].">
      <j1 rule="para" parents="30 816"/>
    </justification>
  </clause>

  <clause id="4361">
    <literal><![CDATA[
      f(x,f(y,z,f(z,u,w)),f(x,f(x,z,w),f(v5,f(x,z,w),f(v6,f(y,z,f(z,u,w)),f(x,z,w))))) = f(x,z,w)
    ]]></literal>
    <justification jstring="[para(1088(a,1),816(a,2)),rewrite([5(8),5(9,R),6(9)])].">
      <j1 rule="para" parents="1088 816"/>
      <j2 rule="rewrite" parents="5 5 6"/>
    </justification>
  </clause>

  <clause id="4461">
    <literal><![CDATA[
      f(x,y,f(z,f(x,z,u),f(z,y,w))) = f(x,z,y)
    ]]></literal>
    <justification jstring="[para(4305(a,1),5(a,2)),rewrite([5(2,R),6(2),6(4),5(5),5(5)])].">
      <j1 rule="para" parents="4305 5"/>
      <j2 rule="rewrite" parents="5 6 6 5 5"/>
    </justification>
  </clause>

  <clause id="4572">
    <literal><![CDATA[
      f(x,f(y,z,u),f(z,f(x,z,w),f(z,v5,f(y,z,u)))) = f(y,z,f(x,z,u))
    ]]></literal>
    <justification jstring="[para(24(a,1),4461(a,2)),rewrite([6(4)])].">
      <j1 rule="para" parents="24 4461"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="5467">
    <literal><![CDATA[
      f(x,f(y,z,f(u,y,w)),f(u,x,y)) = f(u,x,y)
    ]]></literal>
    <justification jstring="[para(1856(a,1),828(a,1)),flip(a)].">
      <j1 rule="para" parents="1856 828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5502">
    <literal><![CDATA[
      f(x,y,f(z,x,f(x,u,w))) = f(x,u,f(x,w,f(z,x,y)))
    ]]></literal>
    <justification jstring="[para(61(a,1),1856(a,2)),rewrite([6(7),5(8,R),6(8),5(9,R),6(9),392(10),6(9),4302(10),5(4,R),6(4)])].">
      <j1 rule="para" parents="61 1856"/>
      <j2 rule="rewrite" parents="6 5 6 5 6 392 6 4302 5 6"/>
    </justification>
  </clause>

  <clause id="5647">
    <literal><![CDATA[
      f(x,y,f(x,z,f(u,y,f(z,y,w)))) = f(x,z,y)
    ]]></literal>
    <justification jstring="[para(1905(a,1),812(a,2)),rewrite([6(7),1618(9)])].">
      <j1 rule="para" parents="1905 812"/>
      <j2 rule="rewrite" parents="6 1618"/>
    </justification>
  </clause>

  <clause id="6261">
    <literal><![CDATA[
      f(x,y,f(z,u,f(z,w,f(z,x,y)))) = f(z,x,y)
    ]]></literal>
    <justification jstring="[para(4085(a,1),922(a,2)),rewrite([5(1),5(5),922(9),5(5)])].">
      <j1 rule="para" parents="4085 922"/>
      <j2 rule="rewrite" parents="5 5 922 5"/>
    </justification>
  </clause>

  <clause id="6720">
    <literal><![CDATA[
      f(x,f(y,x,z),f(y,x,u)) = f(y,x,f(x,u,z))
    ]]></literal>
    <justification jstring="[para(70(a,1),17(a,1)),rewrite([5(2,R),6(2),20(3),5(4,R),6(4)]),flip(a)].">
      <j1 rule="para" parents="70 17"/>
      <j2 rule="rewrite" parents="5 6 20 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7772">
    <literal><![CDATA[
      f(x,f(y,z,x),f(z,x,u)) = f(y,x,f(z,x,u))
    ]]></literal>
    <justification jstring="[para(922(a,1),74(a,2,3)),rewrite([5(3),6(3),122(4),19(4),5(4),5(5,R)]),flip(a)].">
      <j1 rule="para" parents="922 74"/>
      <j2 rule="rewrite" parents="5 6 122 19 5 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7788">
    <literal><![CDATA[
      f(x,f(y,z,x),f(u,z,x)) = f(y,x,f(u,z,x))
    ]]></literal>
    <justification jstring="[para(1253(a,1),74(a,2,3)),rewrite([5(3),6(3),1030(5),5(4),5(5,R)]),flip(a)].">
      <j1 rule="para" parents="1253 74"/>
      <j2 rule="rewrite" parents="5 6 1030 5 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8028">
    <literal><![CDATA[
      f(f(x,y,z),f(x,u,f(x,y,z)),f(x,z,f(x,y,w))) = f(u,f(x,y,z),f(x,w,f(x,y,z)))
    ]]></literal>
    <justification jstring="[para(30(a,2),7788(a,1,3)),rewrite([5(3,R),6(3),5(4),5(4),5(9,R),6(9)])].">
      <j1 rule="para" parents="30 7788"/>
      <j2 rule="rewrite" parents="5 6 5 5 5 6"/>
    </justification>
  </clause>

  <clause id="8369">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,f(x,z,w),f(v5,f(x,z,w),f(v6,f(y,z,u),f(x,z,w))))) = f(x,w,f(y,z,f(x,z,u)))
    ]]></literal>
    <justification jstring="[para(75(a,1),816(a,2)),rewrite([6(2),6(3),6(5),5(6),5(7,R),6(7)])].">
      <j1 rule="para" parents="75 816"/>
      <j2 rule="rewrite" parents="6 6 6 5 5 6"/>
    </justification>
  </clause>

  <clause id="8635">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,u,f(u,w,y)))) = f(x,u,y)
    ]]></literal>
    <justification jstring="[back_rewrite(4361),rewrite([8369(11)])].">
      <j1 rule="back_rewrite" parents="4361"/>
      <j2 rule="rewrite" parents="8369"/>
    </justification>
  </clause>

  <clause id="8713">
    <literal><![CDATA[
      f(x,y,f(y,z,f(u,x,y))) = f(y,z,f(u,x,y))
    ]]></literal>
    <justification jstring="[para(1253(a,1),5647(a,1,3)),rewrite([5(2),5(2),5(4),5(4),5(6,R),6(6),205(6),5(5),5(5),5(7),6(7),19(7)])].">
      <j1 rule="para" parents="1253 5647"/>
      <j2 rule="rewrite" parents="5 5 5 5 5 6 205 5 5 5 6 19"/>
    </justification>
  </clause>

  <clause id="9281">
    <literal><![CDATA[
      f(f(x,y,z),f(x,z,u),f(y,w,f(y,v5,f(x,y,z)))) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(1181(a,1),6261(a,1,3,3,3)),rewrite([1181(9)])].">
      <j1 rule="para" parents="1181 6261"/>
      <j2 rule="rewrite" parents="1181"/>
    </justification>
  </clause>

  <clause id="9577">
    <literal><![CDATA[
      f(x,y,f(z,u,f(u,x,f(u,w,y)))) = f(u,x,y)
    ]]></literal>
    <justification jstring="[para(8635(a,1),922(a,2)),rewrite([5(2,R),6(2),5(6,R),6(6),922(9),5(5,R),6(5)])].">
      <j1 rule="para" parents="8635 922"/>
      <j2 rule="rewrite" parents="5 6 5 6 922 5 6"/>
    </justification>
  </clause>

  <clause id="10036">
    <literal><![CDATA[
      f(f(x,y,z),f(y,z,u),f(w,f(y,z,u),f(v5,f(y,z,u),f(x,y,z)))) = f(w,f(y,z,u),f(v5,f(x,y,z),f(y,z,u)))
    ]]></literal>
    <justification jstring="[para(1101(a,1),87(a,2,3,3)),rewrite([5(6),5(7,R),6(7),5(12,R),5(13,R),6(13)])].">
      <j1 rule="para" parents="1101 87"/>
      <j2 rule="rewrite" parents="5 5 6 5 5 6"/>
    </justification>
  </clause>

  <clause id="11098">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,w,z))) = f(x,y,f(w,z,f(x,z,u)))
    ]]></literal>
    <justification jstring="[para(874(a,2),105(a,2,3)),flip(a)].">
      <j1 rule="para" parents="874 105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12311">
    <literal><![CDATA[
      f(x,y,f(y,z,f(u,x,z))) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(125(a,1),1469(a,2)),rewrite([20(3),15(3),5(3,R),6(3),6720(5),6(3)]),flip(a)].">
      <j1 rule="para" parents="125 1469"/>
      <j2 rule="rewrite" parents="20 15 5 6 6720 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12402">
    <literal><![CDATA[
      f(x,y,f(x,z,f(u,z,y))) = f(x,z,y)
    ]]></literal>
    <justification jstring="[para(12311(a,1),474(a,2)),rewrite([5(3,R),6(3),21(5),5(4,R),6(4)])].">
      <j1 rule="para" parents="12311 474"/>
      <j2 rule="rewrite" parents="5 6 21 5 6"/>
    </justification>
  </clause>

  <clause id="12982">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,u,x)) = f(y,u,x)
    ]]></literal>
    <justification jstring="[para(1072(a,1),168(a,1,3)),rewrite([5(2),5(2),5(3),5(3),15(4),5(3),5(3)]),flip(a)].">
      <j1 rule="para" parents="1072 168"/>
      <j2 rule="rewrite" parents="5 5 5 5 15 5 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12992">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,w,f(z,u,x))) = f(x,w,f(z,u,x))
    ]]></literal>
    <justification jstring="[para(3270(a,1),168(a,1,3,3)),rewrite([15(6)]),flip(a)].">
      <j1 rule="para" parents="3270 168"/>
      <j2 rule="rewrite" parents="15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13008">
    <literal><![CDATA[
      f(x,f(y,z,f(y,u,w)),f(y,w,x)) = f(y,w,x)
    ]]></literal>
    <justification jstring="[para(1082(a,1),168(a,1,3)),rewrite([5(3),5(3),5(4),5(4),15(5),5(4),5(4)]),flip(a)].">
      <j1 rule="para" parents="1082 168"/>
      <j2 rule="rewrite" parents="5 5 5 5 15 5 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13139">
    <literal><![CDATA[
      f(x,f(y,z,x),f(z,u,x)) = f(y,x,f(z,u,x))
    ]]></literal>
    <justification jstring="[para(12982(a,1),74(a,2,3)),rewrite([5(3),6(3),1030(5),5(4),5(5,R)]),flip(a)].">
      <j1 rule="para" parents="12982 74"/>
      <j2 rule="rewrite" parents="5 6 1030 5 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13180">
    <literal><![CDATA[
      f(x,f(y,x,z),f(y,u,x)) = f(x,z,f(y,u,x))
    ]]></literal>
    <justification jstring="[para(13139(a,1),922(a,2)),rewrite([5(2),5(2),6(3),5(4),5(4),12982(7),5(5,R),6(5)])].">
      <j1 rule="para" parents="13139 922"/>
      <j2 rule="rewrite" parents="5 5 6 5 5 12982 5 6"/>
    </justification>
  </clause>

  <clause id="13417">
    <literal><![CDATA[
      f(f(x,y,f(x,z,u)),f(x,u,w),f(w,f(x,u,w),f(w,v5,f(x,y,f(x,z,u))))) = f(x,u,w)
    ]]></literal>
    <justification jstring="[para(13008(a,1),866(a,2)),rewrite([6(7)])].">
      <j1 rule="para" parents="13008 866"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="14376">
    <literal><![CDATA[
      f(x,y,f(z,u,f(y,w,z))) = f(x,y,f(w,z,f(y,z,u)))
    ]]></literal>
    <justification jstring="[para(828(a,1),262(a,2,3)),rewrite([5(1,R),6(1),5(4)]),flip(a)].">
      <j1 rule="para" parents="828 262"/>
      <j2 rule="rewrite" parents="5 6 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14673">
    <literal><![CDATA[
      f(f(x,y,z),f(y,u,w),f(x,y,z)) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(1181(a,1),318(a,1,3)),rewrite([9281(10)])].">
      <j1 rule="para" parents="1181 318"/>
      <j2 rule="rewrite" parents="9281"/>
    </justification>
  </clause>

  <clause id="14946">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,u,f(y,z,f(w,x,f(y,z,u))))) = f(w,f(y,z,u),f(y,x,f(y,z,u)))
    ]]></literal>
    <justification jstring="[para(14673(a,1),40(a,1,3)),rewrite([5(3),5(3),5(4,R),6(4),5(6),5(6),5(10),5(10),5(11,R),6(11),696(11),5(12,R),6(12),8028(12),6(9),696(9)]),flip(a)].">
      <j1 rule="para" parents="14673 40"/>
      <j2 rule="rewrite" parents="5 5 5 6 5 5 5 5 5 6 696 5 6 8028 6 696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14966">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,u,f(y,z,f(x,w,f(y,z,u))))) = f(y,u,f(y,z,f(x,w,f(y,z,u))))
    ]]></literal>
    <justification jstring="[para(14673(a,1),816(a,1,3)),rewrite([6(3),5(4,R),6(4),696(4),6(7),5(8,R),6(8),696(8),5(9,R),15(9),6(7),5(8,R),6(8),696(8),5(10),5(10)]),flip(a)].">
      <j1 rule="para" parents="14673 816"/>
      <j2 rule="rewrite" parents="6 5 6 696 6 5 6 696 5 15 6 5 6 696 5 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15096">
    <literal><![CDATA[
      f(x,f(y,x,z),f(z,u,w)) = f(y,x,f(z,u,f(x,z,w)))
    ]]></literal>
    <justification jstring="[para(319(a,1),6(a,1)),rewrite([5(1,R),6(1),6(4)]),flip(a)].">
      <j1 rule="para" parents="319 6"/>
      <j2 rule="rewrite" parents="5 6 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15120">
    <literal><![CDATA[
      f(f(x,y,z),f(u,w,f(x,y,z)),f(x,y,f(x,z,f(u,w,f(x,y,z))))) = f(x,z,f(x,y,f(u,w,f(x,y,z))))
    ]]></literal>
    <justification jstring="[para(319(a,1),40(a,2)),rewrite([5(3),5(3),5(6),5(6),5(7,R),7788(7),696(5),5(6,R),6(6),14966(6),5(7),5(7),5(9),5(9),6(10)]),flip(a)].">
      <j1 rule="para" parents="319 40"/>
      <j2 rule="rewrite" parents="5 5 5 5 5 7788 696 5 6 14966 5 5 5 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15153">
    <literal><![CDATA[
      f(f(x,y,z),f(x,u,w),f(w,f(x,u,w),f(w,v5,f(x,y,z)))) = f(u,w,f(x,y,f(x,z,w)))
    ]]></literal>
    <justification jstring="[para(319(a,1),866(a,2)),rewrite([5(2,R),6(2),5(3,R),6(3),6(5),6(8)])].">
      <j1 rule="para" parents="319 866"/>
      <j2 rule="rewrite" parents="5 6 5 6 6 6"/>
    </justification>
  </clause>

  <clause id="15161">
    <literal><![CDATA[
      f(f(x,y,z),f(u,w,v5),f(x,y,z)) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(319(a,1),54(a,2,3)),rewrite([5(5),5(5),19(5),20(5),5(5,R),15(5),6(9),4(11),5(7,R),15(7)])].">
      <j1 rule="para" parents="319 54"/>
      <j2 rule="rewrite" parents="5 5 19 20 5 15 6 4 5 15"/>
    </justification>
  </clause>

  <clause id="15213">
    <literal><![CDATA[
      f(x,f(y,z,u),f(z,x,u)) = f(z,x,u)
    ]]></literal>
    <justification jstring="[para(319(a,2),8713(a,2)),rewrite([5(4,R),6(4),5(5,R),6(5),3946(5),1982(4),15(3),5(2,R),6(2),5(4),5(4),20(4)]),flip(a)].">
      <j1 rule="para" parents="319 8713"/>
      <j2 rule="rewrite" parents="5 6 5 6 3946 1982 15 5 6 5 5 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15245">
    <literal><![CDATA[
      f(x,f(y,z,u),f(w,f(y,z,u),f(y,x,f(y,z,u)))) = f(y,u,f(y,z,f(x,w,f(y,z,u))))
    ]]></literal>
    <justification jstring="[para(319(a,1),113(a,1)),rewrite([5(3),5(3),5(5),5(5),6(6),15120(8),5(6),5(6),5(10),5(10),5(11,R),6(11),5(12,R),6(12),7772(12)]),flip(a)].">
      <j1 rule="para" parents="319 113"/>
      <j2 rule="rewrite" parents="5 5 5 5 6 15120 5 5 5 5 5 6 5 6 7772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15288">
    <literal><![CDATA[
      f(x,y,f(z,u,f(z,y,f(z,w,x)))) = f(z,x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(13417),rewrite([15153(9),6(2)])].">
      <j1 rule="back_rewrite" parents="13417"/>
      <j2 rule="rewrite" parents="15153 6"/>
    </justification>
  </clause>

  <clause id="15375">
    <literal><![CDATA[
      f(x,f(y,z,u),f(w,f(y,z,u),f(x,v5,f(y,z,u)))) = f(w,f(y,z,u),f(x,v5,f(y,z,u)))
    ]]></literal>
    <justification jstring="[para(15161(a,1),816(a,1,3)),rewrite([6(3),5(4,R),6(4),6(7),5(8,R),6(8),5(9,R),15(9),6(7),5(8,R),6(8),5(10),5(10)]),flip(a)].">
      <j1 rule="para" parents="15161 816"/>
      <j2 rule="rewrite" parents="6 5 6 6 5 6 5 15 6 5 6 5 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15402">
    <literal><![CDATA[
      f(f(x,y,z),f(u,w,f(u,v5,f(x,y,z))),f(u,f(u,w,v5),f(x,y,z))) = f(u,w,f(u,v5,f(x,y,z)))
    ]]></literal>
    <justification jstring="[para(15161(a,1),111(a,1)),rewrite([5(2),5(2),5(5),5(5),5(10,R),5(11,R),6(11)]),flip(a)].">
      <j1 rule="para" parents="15161 111"/>
      <j2 rule="rewrite" parents="5 5 5 5 5 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15403">
    <literal><![CDATA[
      f(x,f(x,y,z),f(u,w,v5)) = f(x,y,f(x,z,f(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(15161(a,1),111(a,2)),rewrite([5(3,R),5(6),5(6),5(8),5(8),15402(8),5(6,R)]),flip(a)].">
      <j1 rule="para" parents="15161 111"/>
      <j2 rule="rewrite" parents="5 5 5 5 5 15402 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15417">
    <literal><![CDATA[
      f(x,f(y,z,u),f(w,y,f(y,z,u))) = f(y,u,f(y,z,f(w,x,f(y,z,u))))
    ]]></literal>
    <justification jstring="[back_rewrite(15245),rewrite([5(4,R),6(4),15375(6)])].">
      <j1 rule="back_rewrite" parents="15245"/>
      <j2 rule="rewrite" parents="5 6 15375"/>
    </justification>
  </clause>

  <clause id="15771">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,z,u)) = f(x,z,u)
    ]]></literal>
    <justification jstring="[para(15288(a,1),922(a,1,2)),rewrite([5(2),5(4)])].">
      <j1 rule="para" parents="15288 922"/>
      <j2 rule="rewrite" parents="5 5"/>
    </justification>
  </clause>

  <clause id="15796">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,y,u)) = f(x,y,u)
    ]]></literal>
    <justification jstring="[para(15288(a,1),2885(a,1,2))].">
      <j1 rule="para" parents="15288 2885"/>
    </justification>
  </clause>

  <clause id="15821">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,y,z)) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(15288(a,1),5467(a,1,2)),rewrite([5(2,R),6(2),5(4,R),6(4)])].">
      <j1 rule="para" parents="15288 5467"/>
      <j2 rule="rewrite" parents="5 6 5 6"/>
    </justification>
  </clause>

  <clause id="15868">
    <literal><![CDATA[
      f(x,f(y,z,f(u,x,y)),f(w,u,x)) = f(x,y,f(w,u,x))
    ]]></literal>
    <justification jstring="[para(12402(a,1),15288(a,1,3,3)),rewrite([5(2),5(2),5(4,R),5(6)])].">
      <j1 rule="para" parents="12402 15288"/>
      <j2 rule="rewrite" parents="5 5 5 5"/>
    </justification>
  </clause>

  <clause id="15909">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,y,f(z,u,w))) = f(x,y,f(z,u,w))
    ]]></literal>
    <justification jstring="[para(15771(a,1),922(a,1,2)),rewrite([5(2),5(2),5(3),5(5),5(5),5(6)])].">
      <j1 rule="para" parents="15771 922"/>
      <j2 rule="rewrite" parents="5 5 5 5 5 5"/>
    </justification>
  </clause>

  <clause id="15921">
    <literal><![CDATA[
      f(x,y,f(x,f(z,u,y),f(w,z,u))) = f(x,y,f(w,z,u))
    ]]></literal>
    <justification jstring="[para(15771(a,1),866(a,1,3,3)),rewrite([5(2),5(2),5(3,R),6(3),5(4,R),15403(4),5(6)])].">
      <j1 rule="para" parents="15771 866"/>
      <j2 rule="rewrite" parents="5 5 5 6 5 15403 5"/>
    </justification>
  </clause>

  <clause id="15972">
    <literal><![CDATA[
      f(x,f(y,z,f(u,x,z)),f(w,u,x)) = f(x,z,f(w,u,x))
    ]]></literal>
    <justification jstring="[para(15771(a,1),9577(a,1,3,3)),rewrite([5(2),5(2),5(4,R),5(6)])].">
      <j1 rule="para" parents="15771 9577"/>
      <j2 rule="rewrite" parents="5 5 5 5"/>
    </justification>
  </clause>

  <clause id="16471">
    <literal><![CDATA[
      f(x,y,f(z,y,f(x,u,y))) = f(x,y,f(z,u,y))
    ]]></literal>
    <justification jstring="[para(15(a,1),321(a,1,3)),rewrite([6(2)]),flip(a)].">
      <j1 rule="para" parents="15 321"/>
      <j2 rule="rewrite" parents="6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16711">
    <literal><![CDATA[
      f(x,y,f(z,u,f(y,w,u))) = f(y,u,f(x,y,f(z,w,u)))
    ]]></literal>
    <justification jstring="[para(321(a,2),74(a,1,3)),rewrite([15(2),6(2),19(5)])].">
      <j1 rule="para" parents="321 74"/>
      <j2 rule="rewrite" parents="15 6 19"/>
    </justification>
  </clause>

  <clause id="18363">
    <literal><![CDATA[
      f(x,y,f(z,u,f(y,u,f(x,z,u)))) = f(x,y,u)
    ]]></literal>
    <justification jstring="[para(630(a,1),9577(a,1,3)),rewrite([5(1),6(1),5(2,R),6(2),5(5),5(5)])].">
      <j1 rule="para" parents="630 9577"/>
      <j2 rule="rewrite" parents="5 6 5 6 5 5"/>
    </justification>
  </clause>

  <clause id="18491">
    <literal><![CDATA[
      f(x,y,f(z,y,f(z,u,x))) = f(z,x,y)
    ]]></literal>
    <justification jstring="[para(18363(a,1),4461(a,2)),rewrite([5(2,R),6(2),8713(3),5(5,R),6(5),8713(6),6(6),4572(8),6(4)])].">
      <j1 rule="para" parents="18363 4461"/>
      <j2 rule="rewrite" parents="5 6 8713 5 6 8713 6 4572 6"/>
    </justification>
  </clause>

  <clause id="18837">
    <literal><![CDATA[
      f(x,f(y,z,u),f(w,x,f(w,y,z))) = f(w,x,f(y,z,u))
    ]]></literal>
    <justification jstring="[para(847(a,1),220(a,2,3)),rewrite([1630(5),19(4)]),flip(a)].">
      <j1 rule="para" parents="847 220"/>
      <j2 rule="rewrite" parents="1630 19"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19724">
    <literal><![CDATA[
      f(x,y,f(x,z,f(x,f(y,u,w),f(u,w,v5)))) = f(x,z,f(x,y,f(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(1136(a,1),32(a,1,3)),rewrite([5(4)]),flip(a)].">
      <j1 rule="para" parents="1136 32"/>
      <j2 rule="rewrite" parents="5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19762">
    <literal><![CDATA[
      f(x,f(y,z,u),f(z,w,f(x,y,w))) = f(x,w,f(y,z,u))
    ]]></literal>
    <justification jstring="[para(1149(a,1),1136(a,1,3))].">
      <j1 rule="para" parents="1149 1136"/>
    </justification>
  </clause>

  <clause id="20436">
    <literal><![CDATA[
      f(x,y,f(f(z,u,w),f(u,w,v5),f(x,u,f(u,w,v5)))) = f(x,f(z,u,f(u,w,v5)),f(x,y,f(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(654(a,1),1176(a,1,2)),rewrite([6(4)]),flip(a)].">
      <j1 rule="para" parents="654 1176"/>
      <j2 rule="rewrite" parents="6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20765">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,y,f(x,w,v5))) = f(x,y,f(x,w,f(x,v5,f(y,z,u))))
    ]]></literal>
    <justification jstring="[para(1197(a,2),13180(a,1,2)),rewrite([5(2),5(2),5(4),15403(5),15403(4),20(3),5(7),2276(8)])].">
      <j1 rule="para" parents="1197 13180"/>
      <j2 rule="rewrite" parents="5 5 5 15403 15403 20 5 2276"/>
    </justification>
  </clause>

  <clause id="20959">
    <literal><![CDATA[
      f(x,f(y,z,u),f(w,x,f(x,z,u))) = f(w,x,f(x,z,u))
    ]]></literal>
    <justification jstring="[para(1254(a,1),74(a,1,3)),rewrite([15771(3),15771(6)]),flip(a)].">
      <j1 rule="para" parents="1254 74"/>
      <j2 rule="rewrite" parents="15771 15771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21385">
    <literal><![CDATA[
      f(x,f(y,z,u),f(z,w,f(x,u,w))) = f(x,w,f(y,z,u))
    ]]></literal>
    <justification jstring="[para(897(a,1),1329(a,1,3))].">
      <j1 rule="para" parents="897 1329"/>
    </justification>
  </clause>

  <clause id="21496">
    <literal><![CDATA[
      f(x,y,f(x,f(y,z,u),f(z,w,f(x,y,u)))) = f(x,y,f(z,w,f(x,y,u)))
    ]]></literal>
    <justification jstring="[para(25(a,1),1341(a,1,3)),rewrite([6(2),6(4),20(6),6(7)])].">
      <j1 rule="para" parents="25 1341"/>
      <j2 rule="rewrite" parents="6 6 20 6"/>
    </justification>
  </clause>

  <clause id="21883">
    <literal><![CDATA[
      f(x,f(y,z,x),f(u,f(w,y,z),f(y,z,x))) = f(y,z,x)
    ]]></literal>
    <justification jstring="[para(1344(a,1),16471(a,2)),rewrite([5(6,R),10036(8)])].">
      <j1 rule="para" parents="1344 16471"/>
      <j2 rule="rewrite" parents="5 10036"/>
    </justification>
  </clause>

  <clause id="22316">
    <literal><![CDATA[
      f(x,f(y,z,u),f(z,u,f(x,w,f(y,z,u)))) = f(z,u,f(x,w,f(y,z,u)))
    ]]></literal>
    <justification jstring="[para(1404(a,1),1142(a,1,3)),rewrite([6(2),5(3),5(3),6(6),5(7),5(7),6(10),6(12),19(12),5(11),21883(11),6(6),5(7),5(7)]),flip(a)].">
      <j1 rule="para" parents="1404 1142"/>
      <j2 rule="rewrite" parents="6 5 5 6 5 5 6 6 19 5 21883 6 5 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23721">
    <literal><![CDATA[
      f(x,y,f(x,z,f(u,w,y))) = f(x,z,f(x,y,f(z,u,w)))
    ]]></literal>
    <justification jstring="[para(4005(a,1),54(a,2,3)),rewrite([6(2),5(3,R),6(3),21385(4),5(4),5(4)]),flip(a)].">
      <j1 rule="para" parents="4005 54"/>
      <j2 rule="rewrite" parents="6 5 6 21385 5 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23961">
    <literal><![CDATA[
      f(x,y,f(z,x,f(u,x,y))) = f(z,x,f(u,x,y))
    ]]></literal>
    <justification jstring="[para(5502(a,2),1469(a,2)),rewrite([4(3),6(2),5(4),122(5)]),flip(a)].">
      <j1 rule="para" parents="5502 1469"/>
      <j2 rule="rewrite" parents="4 6 5 122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24846">
    <literal><![CDATA[
      f(x,f(y,z,f(x,u,y)),f(x,w,v5)) = f(x,y,f(x,w,f(x,v5,f(u,y,z))))
    ]]></literal>
    <justification jstring="[para(11098(a,1),1286(a,1,3,3)),rewrite([1286(6),2997(4)]),flip(a)].">
      <j1 rule="para" parents="11098 1286"/>
      <j2 rule="rewrite" parents="1286 2997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25097">
    <literal><![CDATA[
      f(x,y,f(x,z,f(u,w,f(x,z,y)))) = f(x,y,f(z,u,f(x,z,w)))
    ]]></literal>
    <justification jstring="[para(15096(a,1),1329(a,2)),rewrite([5(2),5(2),5(3),5(3),15403(5),20765(6),6(4),19724(6),5(7,R),6(7)])].">
      <j1 rule="para" parents="15096 1329"/>
      <j2 rule="rewrite" parents="5 5 5 5 15403 20765 6 19724 5 6"/>
    </justification>
  </clause>

  <clause id="25130">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,w,f(y,z,u))) = f(y,u,f(x,z,f(y,z,w)))
    ]]></literal>
    <justification jstring="[back_rewrite(15417),rewrite([5(3,R),6(3),5(6,R),6(6),25097(8),5(6,R),6(6)])].">
      <j1 rule="back_rewrite" parents="15417"/>
      <j2 rule="rewrite" parents="5 6 5 6 25097 5 6"/>
    </justification>
  </clause>

  <clause id="25132">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,u,f(x,z,f(y,z,w)))) = f(y,u,f(x,z,f(y,z,w)))
    ]]></literal>
    <justification jstring="[back_rewrite(14966),rewrite([25097(5),5(3,R),6(3),25097(9),5(7,R),6(7)])].">
      <j1 rule="back_rewrite" parents="14966"/>
      <j2 rule="rewrite" parents="25097 5 6 25097 5 6"/>
    </justification>
  </clause>

  <clause id="25133">
    <literal><![CDATA[
      f(x,f(y,z,u),f(w,y,f(y,z,u))) = f(y,u,f(w,z,f(y,z,x)))
    ]]></literal>
    <justification jstring="[back_rewrite(14946),rewrite([5(3,R),6(3),25097(5),5(3,R),6(3),25132(5),5(6,R),6(6)]),flip(a)].">
      <j1 rule="back_rewrite" parents="14946"/>
      <j2 rule="rewrite" parents="5 6 25097 5 6 25132 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25262">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,u,f(w,y,z))) = f(y,u,f(w,z,f(y,z,x)))
    ]]></literal>
    <justification jstring="[back_rewrite(1036),rewrite([25130(4)]),flip(a)].">
      <j1 rule="back_rewrite" parents="1036"/>
      <j2 rule="rewrite" parents="25130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25278">
    <literal><![CDATA[
      f(x,f(y,z,f(z,u,w)),f(x,v5,f(z,u,w))) = f(x,v5,f(z,w,f(x,u,f(y,z,u))))
    ]]></literal>
    <justification jstring="[back_rewrite(20436),rewrite([25133(5),205(2)]),flip(a)].">
      <j1 rule="back_rewrite" parents="20436"/>
      <j2 rule="rewrite" parents="25133 205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25399">
    <literal><![CDATA[
      f(x,f(y,z,u),f(z,w,f(x,u,f(y,z,u)))) = f(x,f(y,z,u),f(z,u,w))
    ]]></literal>
    <justification jstring="[back_rewrite(1321),rewrite([25278(6)])].">
      <j1 rule="back_rewrite" parents="1321"/>
      <j2 rule="rewrite" parents="25278"/>
    </justification>
  </clause>

  <clause id="26704">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,z,f(x,u,w))) = f(x,w,f(x,z,u))
    ]]></literal>
    <justification jstring="[para(15868(a,1),12992(a,2)),rewrite([5(2,R),6(2),5(4),24846(5),814(5),5(5)])].">
      <j1 rule="para" parents="15868 12992"/>
      <j2 rule="rewrite" parents="5 6 5 24846 814 5"/>
    </justification>
  </clause>

  <clause id="27091">
    <literal><![CDATA[
      f(x,f(y,z,f(z,u,x)),f(u,x,w)) = f(z,x,f(u,x,w))
    ]]></literal>
    <justification jstring="[para(15972(a,1),5(a,2)),rewrite([5(1),5(3),5(3),5(4),5(5),5(5),5(6,R),6(6)])].">
      <j1 rule="para" parents="15972 5"/>
      <j2 rule="rewrite" parents="5 5 5 5 5 5 5 6"/>
    </justification>
  </clause>

  <clause id="27912">
    <literal><![CDATA[
      f(f(x,y,z),f(y,z,u),f(w,x,f(y,z,u))) = f(w,f(y,z,u),f(x,y,z))
    ]]></literal>
    <justification jstring="[para(15909(a,1),16711(a,2,3)),rewrite([5(5,R),15821(5),19(5)]),flip(a)].">
      <j1 rule="para" parents="15909 16711"/>
      <j2 rule="rewrite" parents="5 15821 19"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28511">
    <literal><![CDATA[
      f(f(x,y,z),f(y,z,u),f(y,z,w)) = f(w,f(x,y,z),f(y,z,u))
    ]]></literal>
    <justification jstring="[para(15771(a,1),18837(a,1,3)),rewrite([5(3),5(3)])].">
      <j1 rule="para" parents="15771 18837"/>
      <j2 rule="rewrite" parents="5 5"/>
    </justification>
  </clause>

  <clause id="28512">
    <literal><![CDATA[
      f(f(x,y,z),f(x,z,u),f(x,z,w)) = f(w,f(x,y,z),f(x,z,u))
    ]]></literal>
    <justification jstring="[para(15796(a,1),18837(a,1,3)),rewrite([5(3),5(3)])].">
      <j1 rule="para" parents="15796 18837"/>
      <j2 rule="rewrite" parents="5 5"/>
    </justification>
  </clause>

  <clause id="28513">
    <literal><![CDATA[
      f(f(x,y,z),f(x,y,u),f(x,y,w)) = f(w,f(x,y,z),f(x,y,u))
    ]]></literal>
    <justification jstring="[para(15821(a,1),18837(a,1,3)),rewrite([5(3),5(3)])].">
      <j1 rule="para" parents="15821 18837"/>
      <j2 rule="rewrite" parents="5 5"/>
    </justification>
  </clause>

  <clause id="28531">
    <literal><![CDATA[
      f(f(x,y,z),f(u,x,y),f(u,x,z)) = f(x,z,f(u,x,y))
    ]]></literal>
    <justification jstring="[para(1906(a,1),18837(a,2)),rewrite([5(5),5(5),922(6),6(5),28513(5)])].">
      <j1 rule="para" parents="1906 18837"/>
      <j2 rule="rewrite" parents="5 5 922 6 28513"/>
    </justification>
  </clause>

  <clause id="28539">
    <literal><![CDATA[
      f(x,f(y,z,f(x,u,w)),f(x,w,f(y,u,w))) = f(x,w,f(y,z,f(x,u,w)))
    ]]></literal>
    <justification jstring="[para(14376(a,1),18837(a,1,3)),rewrite([6(2),6(3),5(5,R),6(5),16471(5),5(3,R),6(3),6(7),5(8,R),6(8)])].">
      <j1 rule="para" parents="14376 18837"/>
      <j2 rule="rewrite" parents="6 6 5 6 16471 5 6 6 5 6"/>
    </justification>
  </clause>

  <clause id="28566">
    <literal><![CDATA[
      f(f(x,y,z),f(x,y,u),f(y,z,u)) = f(y,u,f(x,y,z))
    ]]></literal>
    <justification jstring="[para(28531(a,1),5(a,2))].">
      <j1 rule="para" parents="28531 5"/>
    </justification>
  </clause>

  <clause id="28568">
    <literal><![CDATA[
      f(f(x,y,z),f(x,z,u),f(y,z,u)) = f(y,z,f(x,z,u))
    ]]></literal>
    <justification jstring="[para(5(a,2),28531(a,1,1)),rewrite([5(2),6(2),5(3),6(3),5(5),6(5),5(6,R),6(6)])].">
      <j1 rule="para" parents="5 28531"/>
      <j2 rule="rewrite" parents="5 6 5 6 5 6 5 6"/>
    </justification>
  </clause>

  <clause id="29055">
    <literal><![CDATA[
      f(f(x,y,z),f(u,x,z),f(u,w,f(x,y,z))) = f(w,f(u,x,z),f(x,y,z))
    ]]></literal>
    <justification jstring="[para(12982(a,1),28566(a,1,2)),rewrite([6(2),5(3),5(5),5(6,R),5(7,R),6(7),15213(7),5(5),6(7)]),flip(a)].">
      <j1 rule="para" parents="12982 28566"/>
      <j2 rule="rewrite" parents="6 5 5 5 5 6 15213 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29200">
    <literal><![CDATA[
      f(f(x,y,z),f(x,u,y),f(u,y,z)) = f(u,y,f(x,y,z))
    ]]></literal>
    <justification jstring="[para(28568(a,1),19(a,1,3)),rewrite([28511(5),28568(8)])].">
      <j1 rule="para" parents="28568 19"/>
      <j2 rule="rewrite" parents="28511 28568"/>
    </justification>
  </clause>

  <clause id="29568">
    <literal><![CDATA[
      f(x,f(y,z,u),f(z,w,f(y,x,w))) = f(y,f(z,x,w),f(x,w,f(y,z,u)))
    ]]></literal>
    <justification jstring="[para(29200(a,1),200(a,1,2)),rewrite([5(2,R),6(2),5(5,R),6(5),5(6),5(6),5(8,R),6(8),6(10),21496(11),5(10,R),6(10),27912(10),6(7),25278(8),25399(6),5(6,R),6(6),5(8,R),6(8),5(9),5(9),5(12,R),28566(12),25262(10),5(6)]),flip(a)].">
      <j1 rule="para" parents="29200 200"/>
      <j2 rule="rewrite" parents="5 6 5 6 5 5 5 6 6 21496 5 6 27912 6 25278 25399 5 6 5 6 5 5 5 28566 25262 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30122">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,u,f(x,z,w))) = f(y,u,f(x,z,w))
    ]]></literal>
    <justification jstring="[back_rewrite(29568),rewrite([5(2,R),6(2),19762(4),5(3,R),6(3)]),flip(a)].">
      <j1 rule="back_rewrite" parents="29568"/>
      <j2 rule="rewrite" parents="5 6 19762 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30898">
    <literal><![CDATA[
      f(x,y,f(z,y,f(u,x,z))) = f(x,z,y)
    ]]></literal>
    <justification jstring="[para(20959(a,1),71(a,2)),rewrite([5(3),5(4,R),6(4),5(5,R),6(5),23961(5),5(5),5(5),5(6,R),3270(6)])].">
      <j1 rule="para" parents="20959 71"/>
      <j2 rule="rewrite" parents="5 5 6 5 6 23961 5 5 5 3270"/>
    </justification>
  </clause>

  <clause id="32772">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,w,y)) = f(x,f(w,z,u),f(x,w,y))
    ]]></literal>
    <justification jstring="[para(23721(a,1),1286(a,1,3)),rewrite([26704(5),5(4)]),flip(a)].">
      <j1 rule="para" parents="23721 1286"/>
      <j2 rule="rewrite" parents="26704 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32850">
    <literal><![CDATA[
      f(x,f(y,z,u),f(w,x,u)) = f(x,f(w,y,z),f(w,x,u))
    ]]></literal>
    <justification jstring="[para(32772(a,1),5(a,2)),rewrite([5(2),5(3),5(4),5(4),5(5)]),flip(a)].">
      <j1 rule="para" parents="32772 5"/>
      <j2 rule="rewrite" parents="5 5 5 5 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33448">
    <literal><![CDATA[
      f(f(x,y,z),f(x,y,u),f(w,v5,f(x,y,u))) = f(f(x,y,z),f(w,v5,u),f(x,y,u))
    ]]></literal>
    <justification jstring="[para(922(a,1),32850(a,1,3)),rewrite([6(5),5(7),5(7),922(10)])].">
      <j1 rule="para" parents="922 32850"/>
      <j2 rule="rewrite" parents="6 5 5 922"/>
    </justification>
  </clause>

  <clause id="33505">
    <literal><![CDATA[
      f(f(x,y,z),f(x,z,u),f(w,v5,f(x,z,u))) = f(f(x,y,z),f(w,v5,u),f(x,z,u))
    ]]></literal>
    <justification jstring="[para(12982(a,1),32850(a,1,3)),rewrite([6(5),5(7),5(7),12982(10)])].">
      <j1 rule="para" parents="12982 32850"/>
      <j2 rule="rewrite" parents="6 5 5 12982"/>
    </justification>
  </clause>

  <clause id="33573">
    <literal><![CDATA[
      f(f(x,y,z),f(y,u,w),f(x,z,u)) = f(w,f(x,z,u),f(x,y,z))
    ]]></literal>
    <justification jstring="[back_rewrite(1605),rewrite([33505(5),6(2)])].">
      <j1 rule="back_rewrite" parents="1605"/>
      <j2 rule="rewrite" parents="33505 6"/>
    </justification>
  </clause>

  <clause id="35717">
    <literal><![CDATA[
      f(f(x,y,z),f(u,z,w),f(x,y,u)) = f(w,f(x,y,z),f(x,y,u))
    ]]></literal>
    <justification jstring="[para(1148(a,1),27091(a,1,2)),rewrite([5(4,R),922(4),6(4),1140(5),6(7),33448(8),5(5)]),flip(a)].">
      <j1 rule="para" parents="1148 27091"/>
      <j2 rule="rewrite" parents="5 922 6 1140 6 33448 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36738">
    <literal><![CDATA[
      f(f(x,y,z),f(u,x,w),f(u,w,y)) = f(u,w,f(x,y,z))
    ]]></literal>
    <justification jstring="[para(30122(a,1),18837(a,2)),rewrite([5(2,R),6(2),5(5),5(5),12982(6),6(5),28512(5),5(5,R),6(5)])].">
      <j1 rule="para" parents="30122 18837"/>
      <j2 rule="rewrite" parents="5 6 5 5 12982 6 28512 5 6"/>
    </justification>
  </clause>

  <clause id="36780">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,z,w)) = f(y,z,f(w,u,x))
    ]]></literal>
    <justification jstring="[para(36738(a,1),5(a,1)),rewrite([6(5),35717(6)]),flip(a)].">
      <j1 rule="para" parents="36738 5"/>
      <j2 rule="rewrite" parents="6 35717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36790">
    <literal><![CDATA[
      f(x,f(y,z,u),f(z,w,u)) = f(z,u,f(y,x,f(z,w,u)))
    ]]></literal>
    <justification jstring="[para(19(a,1),36738(a,1,3)),rewrite([6(2),5(3,R),6(3),5(5),6(5),29055(5),6(5)])].">
      <j1 rule="para" parents="19 36738"/>
      <j2 rule="rewrite" parents="6 5 6 5 6 29055 6"/>
    </justification>
  </clause>

  <clause id="36856">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,w,z)) = f(y,z,f(w,u,x))
    ]]></literal>
    <justification jstring="[para(36738(a,1),18491(a,2)),rewrite([5(7,R),30898(9),33573(4)])].">
      <j1 rule="para" parents="36738 18491"/>
      <j2 rule="rewrite" parents="5 30898 33573"/>
    </justification>
  </clause>

  <clause id="36866">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,w,y))) = f(x,y,f(z,u,w))
    ]]></literal>
    <justification jstring="[para(1341(a,1),36738(a,2)),rewrite([5(2),5(2),36780(3),5(1),6(1),4(3),5(5),5(5),15403(5),36780(4),5(2),6(2),20(2)])].">
      <j1 rule="para" parents="1341 36738"/>
      <j2 rule="rewrite" parents="5 5 36780 5 6 4 5 5 15403 36780 5 6 20"/>
    </justification>
  </clause>

  <clause id="36880">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,y,w))) = f(x,y,f(z,u,w))
    ]]></literal>
    <justification jstring="[para(15921(a,1),36738(a,2)),rewrite([5(2),5(2),36780(3),5(1),6(1),4(3),5(5,R),15403(5),36780(4),5(2),6(2),20(2),5(4),5(4)])].">
      <j1 rule="para" parents="15921 36738"/>
      <j2 rule="rewrite" parents="5 5 36780 5 6 4 5 15403 36780 5 6 20 5 5"/>
    </justification>
  </clause>

  <clause id="37170">
    <literal><![CDATA[
      f(x,f(y,z,u),f(z,u,w)) = f(z,u,f(x,y,w))
    ]]></literal>
    <justification jstring="[back_rewrite(36790),rewrite([6(2),6(4),5(5,R),6(5),36880(6)])].">
      <j1 rule="back_rewrite" parents="36790"/>
      <j2 rule="rewrite" parents="6 6 5 6 36880"/>
    </justification>
  </clause>

  <clause id="37187">
    <literal><![CDATA[
      f(x,f(y,z,f(x,u,w)),f(x,w,f(y,u,w))) = f(x,w,f(y,z,u))
    ]]></literal>
    <justification jstring="[back_rewrite(28539),rewrite([36866(8)])].">
      <j1 rule="back_rewrite" parents="28539"/>
      <j2 rule="rewrite" parents="36866"/>
    </justification>
  </clause>

  <clause id="37194">
    <literal><![CDATA[
      f(x,y,f(z,u,f(w,x,y))) = f(x,y,f(z,w,u))
    ]]></literal>
    <justification jstring="[back_rewrite(22316),rewrite([36866(5),37170(3)]),flip(a)].">
      <j1 rule="back_rewrite" parents="22316"/>
      <j2 rule="rewrite" parents="36866 37170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38298">
    <literal><![CDATA[
      f(x,f(y,z,f(u,w,v5)),f(u,v5,f(y,w,v5))) = f(y,f(u,w,v5),f(x,v5,z))
    ]]></literal>
    <justification jstring="[para(897(a,1),36856(a,1,3)),rewrite([6(2),5(7)])].">
      <j1 rule="para" parents="897 36856"/>
      <j2 rule="rewrite" parents="6 5"/>
    </justification>
  </clause>

  <clause id="38353">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,w,u)) = f(y,u,f(x,w,z))
    ]]></literal>
    <justification jstring="[back_rewrite(37187),rewrite([38298(5),6(2)])].">
      <j1 rule="back_rewrite" parents="37187"/>
      <j2 rule="rewrite" parents="38298 6"/>
    </justification>
  </clause>

  <clause id="38852">
    <literal><![CDATA[
      f(x,f(y,z,u),f(w,z,u)) = f(z,u,f(w,x,y))
    ]]></literal>
    <justification jstring="[para(37170(a,1),36780(a,2)),rewrite([6(2),6(4),38353(5),5(4)])].">
      <j1 rule="para" parents="37170 36780"/>
      <j2 rule="rewrite" parents="6 6 38353 5"/>
    </justification>
  </clause>

  <clause id="38910">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer(dist_both)
    ]]></attribute>
    <justification jstring="[back_rewrite(14),rewrite([38852(13),5(9),37194(10),5(6,R),6(6),38852(25),5(21),5(21)]),xx(a),xx(b)].">
      <j1 rule="back_rewrite" parents="14"/>
      <j2 rule="rewrite" parents="38852 5 37194 5 6 38852 5 5"/>
      <j2 rule="xx"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="2" length="226" max_count="39">

<comments><![CDATA[
% Proof 2 at 637.76 (+ 0.94) seconds: dist_short.
% Length of proof is 226.
% Level of proof is 31.
% Maximum clause weight is 45.
% Given clauses 791.
]]></comments>

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

  <clause id="4" type="assumption">
    <literal><![CDATA[
      f(x,x,y) = x
    ]]></literal>
    <attribute><![CDATA[
      label(majority)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="5" type="assumption">
    <literal><![CDATA[
      f(x,y,z) = f(z,x,y)
    ]]></literal>
    <attribute><![CDATA[
      label(2a)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="6" type="assumption">
    <literal><![CDATA[
      f(x,y,z) = f(x,z,y)
    ]]></literal>
    <attribute><![CDATA[
      label(2b)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="7" type="assumption">
    <literal><![CDATA[
      f(f(x,y,z),y,u) = f(x,y,f(z,y,u))
    ]]></literal>
    <attribute><![CDATA[
      label(associativity)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="8">
    <literal><![CDATA[
      f(x,y,f(x,z,u)) = f(x,z,f(x,y,u))
    ]]></literal>
    <justification jstring="[copy(7),rewrite([5(2),5(2),5(3,R),6(3)]),rewrite([5(1,R),6(1),6(3),5(4,R),6(4)])].">
      <j1 rule="copy" parents="7"/>
      <j2 rule="rewrite" parents="5 5 5 6"/>
      <j2 rule="rewrite" parents="5 6 6 5 6"/>
    </justification>
  </clause>

  <clause id="11" type="deny">
    <literal><![CDATA[
      f(f(c6,c7,c8),c9,c10) != f(c6,f(c7,c9,c10),f(c8,c9,c10))
    ]]></literal>
    <attribute><![CDATA[
      label(dist_short)
    ]]></attribute>
    <attribute><![CDATA[
      answer(dist_short)
    ]]></attribute>
    <justification jstring="[deny(2)].">
      <j1 rule="deny" parents="2"/>
    </justification>
  </clause>

  <clause id="12">
    <literal><![CDATA[
      f(c6,f(c7,c9,c10),f(c8,c9,c10)) != f(c9,c10,f(c6,c7,c8))
    ]]></literal>
    <attribute><![CDATA[
      answer(dist_short)
    ]]></attribute>
    <justification jstring="[copy(11),rewrite([5(7),5(7)]),flip(a)].">
      <j1 rule="copy" parents="11"/>
      <j2 rule="rewrite" parents="5 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15">
    <literal><![CDATA[
      f(x,y,y) = y
    ]]></literal>
    <justification jstring="[para(5(a,1),4(a,1))].">
      <j1 rule="para" parents="5 4"/>
    </justification>
  </clause>

  <clause id="16">
    <literal><![CDATA[
      f(x,y,f(z,x,u)) = f(z,x,f(x,y,u))
    ]]></literal>
    <justification jstring="[para(8(a,1),5(a,2)),rewrite([6(2),5(3,R),6(3)]),flip(a)].">
      <j1 rule="para" parents="8 5"/>
      <j2 rule="rewrite" parents="6 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17">
    <literal><![CDATA[
      f(x,y,f(x,z,u)) = f(x,u,f(x,y,z))
    ]]></literal>
    <justification jstring="[para(5(a,1),8(a,1,3)),rewrite([5(1,R),6(1)])].">
      <j1 rule="para" parents="5 8"/>
      <j2 rule="rewrite" parents="5 6"/>
    </justification>
  </clause>

  <clause id="18">
    <literal><![CDATA[
      f(x,y,f(x,z,f(x,u,w))) = f(x,u,f(x,y,f(x,z,w)))
    ]]></literal>
    <justification jstring="[para(8(a,1),8(a,1,3))].">
      <j1 rule="para" parents="8 8"/>
    </justification>
  </clause>

  <clause id="19">
    <literal><![CDATA[
      f(x,y,f(x,z,y)) = f(x,z,y)
    ]]></literal>
    <justification jstring="[para(15(a,1),8(a,1,3)),flip(a)].">
      <j1 rule="para" parents="15 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20">
    <literal><![CDATA[
      f(x,y,f(x,y,z)) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(15(a,1),8(a,1)),rewrite([6(3),19(3)]),flip(a)].">
      <j1 rule="para" parents="15 8"/>
      <j2 rule="rewrite" parents="6 19"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21">
    <literal><![CDATA[
      f(x,y,f(x,z,f(x,u,y))) = f(x,z,f(x,u,y))
    ]]></literal>
    <justification jstring="[para(19(a,1),8(a,1,3)),flip(a)].">
      <j1 rule="para" parents="19 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22">
    <literal><![CDATA[
      f(x,y,f(x,z,f(x,y,u))) = f(x,z,f(x,y,u))
    ]]></literal>
    <justification jstring="[para(19(a,1),8(a,2,3)),rewrite([6(1),6(4)])].">
      <j1 rule="para" parents="19 8"/>
      <j2 rule="rewrite" parents="6 6"/>
    </justification>
  </clause>

  <clause id="24">
    <literal><![CDATA[
      f(x,y,f(z,y,u)) = f(z,y,f(x,y,u))
    ]]></literal>
    <justification jstring="[para(16(a,1),5(a,2)),rewrite([6(2),5(3,R),6(3)])].">
      <j1 rule="para" parents="16 5"/>
      <j2 rule="rewrite" parents="6 5 6"/>
    </justification>
  </clause>

  <clause id="25">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,z,w))) = f(x,z,f(x,y,f(z,u,w)))
    ]]></literal>
    <justification jstring="[para(16(a,2),8(a,1,3))].">
      <j1 rule="para" parents="16 8"/>
    </justification>
  </clause>

  <clause id="27">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,z,f(x,y,u))) = f(x,y,f(y,z,u))
    ]]></literal>
    <justification jstring="[para(16(a,2),19(a,1,3))].">
      <j1 rule="para" parents="16 19"/>
    </justification>
  </clause>

  <clause id="28">
    <literal><![CDATA[
      f(x,y,f(y,z,f(x,y,u))) = f(x,y,f(y,z,u))
    ]]></literal>
    <justification jstring="[para(16(a,2),20(a,1,3))].">
      <j1 rule="para" parents="16 20"/>
    </justification>
  </clause>

  <clause id="29">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,u,w))) = f(x,u,f(x,y,f(z,u,w)))
    ]]></literal>
    <justification jstring="[para(16(a,1),16(a,1,3)),rewrite([5(1,R),6(1),5(6,R),6(6)])].">
      <j1 rule="para" parents="16 16"/>
      <j2 rule="rewrite" parents="5 6 5 6"/>
    </justification>
  </clause>

  <clause id="30">
    <literal><![CDATA[
      f(x,y,f(z,x,u)) = f(z,x,f(x,u,y))
    ]]></literal>
    <justification jstring="[para(17(a,1),5(a,2)),rewrite([6(2),5(3,R),6(3)]),flip(a)].">
      <j1 rule="para" parents="17 5"/>
      <j2 rule="rewrite" parents="6 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32">
    <literal><![CDATA[
      f(x,y,f(x,z,f(x,u,w))) = f(x,u,f(x,y,f(x,w,z)))
    ]]></literal>
    <justification jstring="[para(17(a,1),8(a,2,3)),flip(a)].">
      <j1 rule="para" parents="17 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33">
    <literal><![CDATA[
      f(x,y,f(x,z,f(x,u,w))) = f(x,w,f(x,y,f(x,z,u)))
    ]]></literal>
    <justification jstring="[para(17(a,2),8(a,1,3))].">
      <j1 rule="para" parents="17 8"/>
    </justification>
  </clause>

  <clause id="38">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,w,y)) = f(x,w,f(y,z,f(x,y,u)))
    ]]></literal>
    <justification jstring="[para(16(a,2),17(a,1,3)),flip(a)].">
      <j1 rule="para" parents="16 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40">
    <literal><![CDATA[
      f(x,y,f(z,x,f(x,u,w))) = f(z,x,f(x,u,f(x,y,w)))
    ]]></literal>
    <justification jstring="[para(18(a,1),5(a,2)),rewrite([6(3),5(5,R),6(5)]),flip(a)].">
      <j1 rule="para" parents="18 5"/>
      <j2 rule="rewrite" parents="6 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41">
    <literal><![CDATA[
      f(x,y,f(y,z,f(y,u,w))) = f(y,z,f(y,u,f(x,y,w)))
    ]]></literal>
    <justification jstring="[para(18(a,2),5(a,2)),rewrite([6(3),5(4,R),6(4)])].">
      <j1 rule="para" parents="18 5"/>
      <j2 rule="rewrite" parents="6 5 6"/>
    </justification>
  </clause>

  <clause id="52">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,z,f(z,w,v5)))) = f(x,z,f(x,y,f(z,w,f(z,u,v5))))
    ]]></literal>
    <justification jstring="[para(18(a,1),16(a,1,3)),rewrite([5(2,R),6(2),5(8,R),6(8)])].">
      <j1 rule="para" parents="18 16"/>
      <j2 rule="rewrite" parents="5 6 5 6"/>
    </justification>
  </clause>

  <clause id="54">
    <literal><![CDATA[
      f(x,y,f(x,z,f(u,w,f(x,u,v5)))) = f(x,u,f(x,y,f(x,z,f(u,w,v5))))
    ]]></literal>
    <justification jstring="[para(16(a,2),18(a,1,3,3))].">
      <j1 rule="para" parents="16 18"/>
    </justification>
  </clause>

  <clause id="57">
    <literal><![CDATA[
      f(x,f(x,y,z),f(x,u,w)) = f(x,y,f(x,u,f(x,w,z)))
    ]]></literal>
    <justification jstring="[para(18(a,1),17(a,1)),flip(a)].">
      <j1 rule="para" parents="18 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="61">
    <literal><![CDATA[
      f(x,y,f(x,z,f(x,u,w))) = f(x,u,f(x,w,f(x,y,z)))
    ]]></literal>
    <justification jstring="[para(17(a,1),18(a,2,3))].">
      <j1 rule="para" parents="17 18"/>
    </justification>
  </clause>

  <clause id="70">
    <literal><![CDATA[
      f(x,y,f(z,u,f(y,z,w))) = f(y,z,f(x,y,f(z,u,w)))
    ]]></literal>
    <justification jstring="[para(8(a,1),24(a,1,3)),rewrite([5(1,R),6(1),5(6,R),6(6)])].">
      <j1 rule="para" parents="8 24"/>
      <j2 rule="rewrite" parents="5 6 5 6"/>
    </justification>
  </clause>

  <clause id="71">
    <literal><![CDATA[
      f(x,y,f(z,u,f(z,x,w))) = f(z,x,f(x,y,f(z,u,w)))
    ]]></literal>
    <justification jstring="[para(8(a,1),24(a,2,3)),rewrite([5(2,R),6(2),5(6,R),6(6)]),flip(a)].">
      <j1 rule="para" parents="8 24"/>
      <j2 rule="rewrite" parents="5 6 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="73">
    <literal><![CDATA[
      f(x,y,f(z,x,f(x,y,u))) = f(z,x,f(x,y,u))
    ]]></literal>
    <justification jstring="[para(19(a,1),24(a,1,3)),rewrite([5(1),5(3),5(5,R),6(5)]),flip(a)].">
      <j1 rule="para" parents="19 24"/>
      <j2 rule="rewrite" parents="5 5 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="74">
    <literal><![CDATA[
      f(x,y,f(z,u,f(y,u,w))) = f(y,u,f(x,y,f(z,u,w)))
    ]]></literal>
    <justification jstring="[para(16(a,1),24(a,1,3)),rewrite([5(1,R),6(1),5(6,R),6(6)])].">
      <j1 rule="para" parents="16 24"/>
      <j2 rule="rewrite" parents="5 6 5 6"/>
    </justification>
  </clause>

  <clause id="75">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,w,z)) = f(x,w,f(y,z,f(x,z,u)))
    ]]></literal>
    <justification jstring="[para(24(a,1),17(a,1,3)),flip(a)].">
      <j1 rule="para" parents="24 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="95">
    <literal><![CDATA[
      f(x,y,f(x,z,f(y,u,f(x,y,w)))) = f(x,z,f(y,u,f(x,y,w)))
    ]]></literal>
    <justification jstring="[para(21(a,1),16(a,1,3)),rewrite([5(1),5(4),5(7,R),6(7)]),flip(a)].">
      <j1 rule="para" parents="21 16"/>
      <j2 rule="rewrite" parents="5 5 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="103">
    <literal><![CDATA[
      f(x,y,f(y,z,f(x,u,f(x,y,w)))) = f(y,z,f(x,u,f(x,y,w)))
    ]]></literal>
    <justification jstring="[para(21(a,1),24(a,2,3)),rewrite([6(1),5(3,R),6(3),6(5),5(7,R),6(7)])].">
      <j1 rule="para" parents="21 24"/>
      <j2 rule="rewrite" parents="6 5 6 6 5 6"/>
    </justification>
  </clause>

  <clause id="105">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,u,w))) = f(x,y,f(x,u,f(z,u,w)))
    ]]></literal>
    <justification jstring="[para(24(a,1),21(a,2,3)),rewrite([21(5)]),flip(a)].">
      <j1 rule="para" parents="24 21"/>
      <j2 rule="rewrite" parents="21"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="111">
    <literal><![CDATA[
      f(x,y,f(z,u,f(y,z,w))) = f(x,y,f(y,z,f(z,u,w)))
    ]]></literal>
    <justification jstring="[para(16(a,2),28(a,2,3)),rewrite([28(4)]),flip(a)].">
      <j1 rule="para" parents="16 28"/>
      <j2 rule="rewrite" parents="28"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="113">
    <literal><![CDATA[
      f(x,y,f(y,z,f(y,u,w))) = f(x,y,f(y,w,f(y,z,u)))
    ]]></literal>
    <justification jstring="[para(17(a,1),28(a,2,3)),rewrite([28(4)])].">
      <j1 rule="para" parents="17 28"/>
      <j2 rule="rewrite" parents="28"/>
    </justification>
  </clause>

  <clause id="122">
    <literal><![CDATA[
      f(x,y,f(z,y,f(x,y,u))) = f(z,y,f(x,y,u))
    ]]></literal>
    <justification jstring="[para(73(a,1),5(a,2)),rewrite([5(1,R),6(1),6(3),5(4,R),6(4)])].">
      <j1 rule="para" parents="73 5"/>
      <j2 rule="rewrite" parents="5 6 6 5 6"/>
    </justification>
  </clause>

  <clause id="125">
    <literal><![CDATA[
      f(x,y,f(z,u,f(z,x,w))) = f(x,y,f(z,x,f(z,u,w)))
    ]]></literal>
    <justification jstring="[para(8(a,1),122(a,1,3,3)),rewrite([5(3,R),6(3),103(4),5(6,R),6(6)])].">
      <j1 rule="para" parents="8 122"/>
      <j2 rule="rewrite" parents="5 6 103 5 6"/>
    </justification>
  </clause>

  <clause id="132">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,z,u))) = f(x,y,f(x,z,u))
    ]]></literal>
    <justification jstring="[para(15(a,1),25(a,1,3)),rewrite([6(4),95(6)]),flip(a)].">
      <j1 rule="para" parents="15 25"/>
      <j2 rule="rewrite" parents="6 95"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="168">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,z,f(y,u,x))) = f(y,x,f(y,z,u))
    ]]></literal>
    <justification jstring="[para(27(a,1),5(a,2)),rewrite([5(2),5(2),5(4),5(6,R),6(6)])].">
      <j1 rule="para" parents="27 5"/>
      <j2 rule="rewrite" parents="5 5 5 5 6"/>
    </justification>
  </clause>

  <clause id="187">
    <literal><![CDATA[
      f(x,f(y,z,f(z,u,w)),f(z,u,f(x,u,f(y,z,w)))) = f(x,u,f(z,u,f(y,z,w)))
    ]]></literal>
    <justification jstring="[para(24(a,1),27(a,1,2)),rewrite([5(1,R),6(1),5(5,R),6(5),5(8,R),6(8)])].">
      <j1 rule="para" parents="24 27"/>
      <j2 rule="rewrite" parents="5 6 5 6 5 6"/>
    </justification>
  </clause>

  <clause id="200">
    <literal><![CDATA[
      f(x,f(y,z,f(u,w,f(x,u,v5))),f(y,z,f(x,u,f(x,y,f(u,w,v5))))) = f(x,y,f(y,z,f(u,w,f(x,u,v5))))
    ]]></literal>
    <justification jstring="[para(25(a,1),27(a,1,3,3))].">
      <j1 rule="para" parents="25 27"/>
    </justification>
  </clause>

  <clause id="205">
    <literal><![CDATA[
      f(x,y,f(z,x,y)) = f(z,x,y)
    ]]></literal>
    <justification jstring="[para(132(a,1),15(a,1)),rewrite([6(4),132(4),15(3)]),flip(a)].">
      <j1 rule="para" parents="132 15"/>
      <j2 rule="rewrite" parents="6 132 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="220">
    <literal><![CDATA[
      f(x,y,f(z,u,f(u,y,w))) = f(u,y,f(x,y,f(z,u,w)))
    ]]></literal>
    <justification jstring="[para(29(a,1),5(a,2)),rewrite([5(1,R),6(1),6(3),5(5,R),6(5),5(6,R),6(6)])].">
      <j1 rule="para" parents="29 5"/>
      <j2 rule="rewrite" parents="5 6 6 5 6 5 6"/>
    </justification>
  </clause>

  <clause id="262">
    <literal><![CDATA[
      f(x,y,f(z,u,f(u,y,w))) = f(x,y,f(u,y,f(z,u,w)))
    ]]></literal>
    <justification jstring="[para(29(a,1),205(a,1,3)),rewrite([5(1,R),6(1),5(4,R),6(4),5(5,R),6(5),187(6),5(4,R),6(4),5(6,R),6(6)]),flip(a)].">
      <j1 rule="para" parents="29 205"/>
      <j2 rule="rewrite" parents="5 6 5 6 5 6 187 5 6 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="318">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,x,w)) = f(x,w,f(y,z,f(y,u,x)))
    ]]></literal>
    <justification jstring="[para(38(a,1),5(a,2)),rewrite([5(2),5(3),5(4),5(4)])].">
      <j1 rule="para" parents="38 5"/>
      <j2 rule="rewrite" parents="5 5 5 5"/>
    </justification>
  </clause>

  <clause id="319">
    <literal><![CDATA[
      f(x,f(y,z,u),f(w,y,x)) = f(w,x,f(y,z,f(y,x,u)))
    ]]></literal>
    <justification jstring="[para(38(a,2),5(a,2)),rewrite([5(1,R),6(1),6(3),5(5),5(5)]),flip(a)].">
      <j1 rule="para" parents="38 5"/>
      <j2 rule="rewrite" parents="5 6 6 5 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="321">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,u,w)) = f(x,w,f(y,u,f(x,z,u)))
    ]]></literal>
    <justification jstring="[para(5(a,2),38(a,1,2)),rewrite([6(2),6(4),5(5,R),6(5)])].">
      <j1 rule="para" parents="5 38"/>
      <j2 rule="rewrite" parents="6 6 5 6"/>
    </justification>
  </clause>

  <clause id="331">
    <literal><![CDATA[
      f(x,y,f(z,f(x,y,u),f(x,w,f(x,y,u)))) = f(x,f(x,y,u),f(z,w,f(x,y,u)))
    ]]></literal>
    <justification jstring="[para(20(a,1),38(a,1,3)),rewrite([5(2),5(2),6(4),6(7),5(8,R),6(8)]),flip(a)].">
      <j1 rule="para" parents="20 38"/>
      <j2 rule="rewrite" parents="5 5 6 6 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="360">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,z,x)) = f(y,z,f(z,x,f(y,x,u)))
    ]]></literal>
    <justification jstring="[para(38(a,2),24(a,2)),rewrite([5(1,R),6(1),5(2,R),6(2),5(5),6(5)]),flip(a)].">
      <j1 rule="para" parents="38 24"/>
      <j2 rule="rewrite" parents="5 6 5 6 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="385">
    <literal><![CDATA[
      f(x,y,f(z,f(x,y,u),f(x,y,z))) = f(y,z,f(x,y,f(x,z,u)))
    ]]></literal>
    <justification jstring="[para(38(a,2),122(a,1,3)),rewrite([5(2),6(2),5(5,R),6(5),5(7,R),6(7)])].">
      <j1 rule="para" parents="38 122"/>
      <j2 rule="rewrite" parents="5 6 5 6 5 6"/>
    </justification>
  </clause>

  <clause id="392">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,y,w)) = f(x,y,f(x,w,f(y,z,u)))
    ]]></literal>
    <justification jstring="[para(38(a,2),25(a,1)),rewrite([6(2)])].">
      <j1 rule="para" parents="38 25"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="474">
    <literal><![CDATA[
      f(x,y,f(x,z,f(u,x,y))) = f(u,x,f(x,z,y))
    ]]></literal>
    <justification jstring="[para(19(a,1),41(a,1,3)),flip(a)].">
      <j1 rule="para" parents="19 41"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="628">
    <literal><![CDATA[
      f(x,f(y,x,z),f(x,u,z)) = f(y,x,f(x,u,z))
    ]]></literal>
    <justification jstring="[para(474(a,1),17(a,1)),rewrite([6(4)]),flip(a)].">
      <j1 rule="para" parents="474 17"/>
      <j2 rule="rewrite" parents="6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="630">
    <literal><![CDATA[
      f(x,y,f(z,u,f(z,x,w))) = f(x,y,f(z,w,f(z,x,u)))
    ]]></literal>
    <justification jstring="[para(474(a,1),24(a,2,3)),rewrite([5(1),5(1),5(3,R),6(3),103(4),6(4),5(5,R),6(5),5(6,R),6(6)])].">
      <j1 rule="para" parents="474 24"/>
      <j2 rule="rewrite" parents="5 5 5 6 103 6 5 6 5 6"/>
    </justification>
  </clause>

  <clause id="654">
    <literal><![CDATA[
      f(x,f(y,x,z),f(x,z,u)) = f(y,x,f(x,z,u))
    ]]></literal>
    <justification jstring="[para(628(a,1),5(a,2)),rewrite([6(2),5(3),6(4)])].">
      <j1 rule="para" parents="628 5"/>
      <j2 rule="rewrite" parents="6 5 6"/>
    </justification>
  </clause>

  <clause id="695">
    <literal><![CDATA[
      f(x,f(x,y,z),f(u,x,y)) = f(u,x,f(x,y,z))
    ]]></literal>
    <justification jstring="[para(654(a,1),6(a,1)),flip(a)].">
      <j1 rule="para" parents="654 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="696">
    <literal><![CDATA[
      f(x,f(x,y,z),f(u,w,f(x,y,z))) = f(x,z,f(x,y,f(u,w,f(x,y,z))))
    ]]></literal>
    <justification jstring="[para(654(a,1),25(a,2)),rewrite([5(1),5(1),5(2),5(2),6(3),5(4,R),6(4),331(5),5(5),5(5),5(6),5(6),5(8,R),6(8)])].">
      <j1 rule="para" parents="654 25"/>
      <j2 rule="rewrite" parents="5 5 5 5 6 5 6 331 5 5 5 5 5 6"/>
    </justification>
  </clause>

  <clause id="803">
    <literal><![CDATA[
      f(x,y,f(x,z,f(z,y,u))) = f(x,z,y)
    ]]></literal>
    <justification jstring="[para(695(a,1),40(a,1,3)),rewrite([5(4,R),15(4),5(3,R),15(3),5(5),6(5),5(6,R),6(6),696(6),28(5),6(3),57(6),6(4),20(5),22(5)]),flip(a)].">
      <j1 rule="para" parents="695 40"/>
      <j2 rule="rewrite" parents="5 15 5 15 5 6 5 6 696 28 6 57 6 20 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="812">
    <literal><![CDATA[
      f(x,y,f(y,z,f(x,z,u))) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(803(a,1),5(a,2)),rewrite([5(1,R),6(1),6(3),5(4)])].">
      <j1 rule="para" parents="803 5"/>
      <j2 rule="rewrite" parents="5 6 6 5"/>
    </justification>
  </clause>

  <clause id="813">
    <literal><![CDATA[
      f(x,y,f(x,z,f(y,z,u))) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(5(a,1),803(a,1,3,3)),rewrite([5(1),6(1),6(4)])].">
      <j1 rule="para" parents="5 803"/>
      <j2 rule="rewrite" parents="5 6 6"/>
    </justification>
  </clause>

  <clause id="814">
    <literal><![CDATA[
      f(x,y,f(x,z,f(x,u,f(u,y,w)))) = f(x,z,f(x,u,y))
    ]]></literal>
    <justification jstring="[para(803(a,1),8(a,1,3)),flip(a)].">
      <j1 rule="para" parents="803 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="816">
    <literal><![CDATA[
      f(x,y,f(x,z,f(z,u,f(y,z,w)))) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(8(a,1),803(a,1,3,3)),rewrite([5(1,R),6(1),6(5)])].">
      <j1 rule="para" parents="8 803"/>
      <j2 rule="rewrite" parents="5 6 6"/>
    </justification>
  </clause>

  <clause id="820">
    <literal><![CDATA[
      f(x,y,f(x,f(y,z,u),f(y,w,f(y,z,u)))) = f(y,z,f(x,y,u))
    ]]></literal>
    <justification jstring="[para(16(a,2),803(a,2)),rewrite([6(3),392(5),6(4)])].">
      <j1 rule="para" parents="16 803"/>
      <j2 rule="rewrite" parents="6 392 6"/>
    </justification>
  </clause>

  <clause id="826">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,z,f(z,w,f(y,z,u)))) = f(y,z,f(x,z,u))
    ]]></literal>
    <justification jstring="[para(24(a,1),803(a,2)),rewrite([6(3)])].">
      <j1 rule="para" parents="24 803"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="827">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,y,z))) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(30(a,2),803(a,1,3)),rewrite([6(1),6(4)])].">
      <j1 rule="para" parents="30 803"/>
      <j2 rule="rewrite" parents="6 6"/>
    </justification>
  </clause>

  <clause id="828">
    <literal><![CDATA[
      f(x,y,f(z,x,u)) = f(x,u,f(z,x,y))
    ]]></literal>
    <justification jstring="[para(30(a,2),803(a,2)),rewrite([6(3),392(5),6(4),820(5)])].">
      <j1 rule="para" parents="30 803"/>
      <j2 rule="rewrite" parents="6 392 6 820"/>
    </justification>
  </clause>

  <clause id="847">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,w,f(x,y,z))) = f(x,w,f(x,y,z))
    ]]></literal>
    <justification jstring="[para(803(a,1),33(a,1,3)),rewrite([6(4)]),flip(a)].">
      <j1 rule="para" parents="803 33"/>
      <j2 rule="rewrite" parents="6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="866">
    <literal><![CDATA[
      f(x,y,f(z,y,f(z,x,u))) = f(z,x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(360),rewrite([5(2),392(3),813(3),5(2,R),6(2),5(3,R),6(3)]),flip(a)].">
      <j1 rule="back_rewrite" parents="360"/>
      <j2 rule="rewrite" parents="5 392 813 5 6 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="871">
    <literal><![CDATA[
      f(x,y,f(z,x,f(z,y,u))) = f(z,x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(385),rewrite([827(4)]),flip(a)].">
      <j1 rule="back_rewrite" parents="385"/>
      <j2 rule="rewrite" parents="827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="874">
    <literal><![CDATA[
      f(x,y,f(z,u,x)) = f(z,x,f(u,x,y))
    ]]></literal>
    <justification jstring="[para(828(a,1),5(a,2)),rewrite([6(2),5(3)]),flip(a)].">
      <j1 rule="para" parents="828 5"/>
      <j2 rule="rewrite" parents="6 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="897">
    <literal><![CDATA[
      f(x,y,f(z,u,y)) = f(z,y,f(x,u,y))
    ]]></literal>
    <justification jstring="[para(874(a,1),5(a,2)),rewrite([6(2),5(3)])].">
      <j1 rule="para" parents="874 5"/>
      <j2 rule="rewrite" parents="6 5"/>
    </justification>
  </clause>

  <clause id="922">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,z,x)) = f(y,z,x)
    ]]></literal>
    <justification jstring="[para(874(a,2),38(a,2)),rewrite([6(2),392(3),813(3)]),flip(a)].">
      <j1 rule="para" parents="874 38"/>
      <j2 rule="rewrite" parents="6 392 813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="933">
    <literal><![CDATA[
      f(x,y,f(z,u,x)) = f(u,x,f(z,x,y))
    ]]></literal>
    <justification jstring="[para(874(a,2),803(a,2)),rewrite([6(3),826(5)]),flip(a)].">
      <j1 rule="para" parents="874 803"/>
      <j2 rule="rewrite" parents="6 826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1030">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,u,y))) = f(x,u,y)
    ]]></literal>
    <justification jstring="[para(20(a,1),897(a,1,3)),rewrite([15(3),696(5),122(4)]),flip(a)].">
      <j1 rule="para" parents="20 897"/>
      <j2 rule="rewrite" parents="15 696 122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1036">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,w,f(y,z,u))) = f(w,f(y,z,u),f(y,u,f(x,y,z)))
    ]]></literal>
    <justification jstring="[para(30(a,2),897(a,2,3)),rewrite([5(3,R),6(3)])].">
      <j1 rule="para" parents="30 897"/>
      <j2 rule="rewrite" parents="5 6"/>
    </justification>
  </clause>

  <clause id="1050">
    <literal><![CDATA[
      f(x,y,f(x,f(x,y,z),f(u,y,z))) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(897(a,1),29(a,1)),rewrite([20(3),15(3)]),flip(a)].">
      <j1 rule="para" parents="897 29"/>
      <j2 rule="rewrite" parents="20 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1057">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,x,z)) = f(y,x,z)
    ]]></literal>
    <justification jstring="[para(38(a,2),897(a,2)),rewrite([5(1,R),6(1),5(2,R),6(2),696(4),28(3),6(1),803(3),6(2),5(3,R),6(3),5(4),20(4)]),flip(a)].">
      <j1 rule="para" parents="38 897"/>
      <j2 rule="rewrite" parents="5 6 5 6 696 28 6 803 6 5 6 5 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1063">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,u,f(u,w,f(y,z,u)))) = f(y,u,f(x,z,u))
    ]]></literal>
    <justification jstring="[para(897(a,1),803(a,2)),rewrite([6(3)])].">
      <j1 rule="para" parents="897 803"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="1071">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,z,u)) = f(x,z,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),922(a,1,2)),rewrite([5(2),5(4)])].">
      <j1 rule="para" parents="5 922"/>
      <j2 rule="rewrite" parents="5 5"/>
    </justification>
  </clause>

  <clause id="1072">
    <literal><![CDATA[
      f(x,y,f(x,z,f(y,u,z))) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(5(a,2),922(a,1,2)),rewrite([5(2),6(2),392(3),5(4),6(4)])].">
      <j1 rule="para" parents="5 922"/>
      <j2 rule="rewrite" parents="5 6 392 5 6"/>
    </justification>
  </clause>

  <clause id="1073">
    <literal><![CDATA[
      f(x,f(y,z,x),f(y,z,u)) = f(y,z,x)
    ]]></literal>
    <justification jstring="[para(922(a,1),6(a,1)),flip(a)].">
      <j1 rule="para" parents="922 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1079">
    <literal><![CDATA[
      f(x,f(y,z,f(z,u,w)),f(x,z,u)) = f(x,z,u)
    ]]></literal>
    <justification jstring="[para(16(a,1),922(a,1,2)),rewrite([5(3),5(5)])].">
      <j1 rule="para" parents="16 922"/>
      <j2 rule="rewrite" parents="5 5"/>
    </justification>
  </clause>

  <clause id="1082">
    <literal><![CDATA[
      f(x,y,f(x,z,f(y,u,f(y,w,z)))) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(17(a,2),922(a,1,2)),rewrite([5(3),392(4),5(5)])].">
      <j1 rule="para" parents="17 922"/>
      <j2 rule="rewrite" parents="5 392 5"/>
    </justification>
  </clause>

  <clause id="1088">
    <literal><![CDATA[
      f(x,f(y,z,f(z,u,w)),f(x,z,w)) = f(x,z,w)
    ]]></literal>
    <justification jstring="[para(30(a,1),922(a,1,2)),rewrite([5(3),5(5)])].">
      <j1 rule="para" parents="30 922"/>
      <j2 rule="rewrite" parents="5 5"/>
    </justification>
  </clause>

  <clause id="1136">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,w,f(y,z,w))) = f(x,w,f(y,z,u))
    ]]></literal>
    <justification jstring="[para(922(a,1),803(a,1,3,3))].">
      <j1 rule="para" parents="922 803"/>
    </justification>
  </clause>

  <clause id="1140">
    <literal><![CDATA[
      f(f(x,y,z),f(x,y,u),f(u,w,f(x,y,z))) = f(w,f(x,y,u),f(x,y,z))
    ]]></literal>
    <justification jstring="[para(922(a,1),828(a,2,3)),rewrite([6(4),5(8,R)])].">
      <j1 rule="para" parents="922 828"/>
      <j2 rule="rewrite" parents="6 5"/>
    </justification>
  </clause>

  <clause id="1148">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,u,f(y,z,w))) = f(x,u,f(y,z,w))
    ]]></literal>
    <justification jstring="[para(922(a,1),922(a,1,2)),rewrite([5(3),5(6)])].">
      <j1 rule="para" parents="922 922"/>
      <j2 rule="rewrite" parents="5 5"/>
    </justification>
  </clause>

  <clause id="1149">
    <literal><![CDATA[
      f(x,y,f(z,u,y)) = f(u,y,f(x,z,y))
    ]]></literal>
    <justification jstring="[para(933(a,1),5(a,2)),rewrite([6(2),5(3)])].">
      <j1 rule="para" parents="933 5"/>
      <j2 rule="rewrite" parents="6 5"/>
    </justification>
  </clause>

  <clause id="1150">
    <literal><![CDATA[
      f(x,f(y,z,x),f(y,u,f(y,z,x))) = f(y,z,x)
    ]]></literal>
    <justification jstring="[para(19(a,1),933(a,1,3)),rewrite([5(3,R),15(3),6(4)]),flip(a)].">
      <j1 rule="para" parents="19 933"/>
      <j2 rule="rewrite" parents="5 15 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1176">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,u,w)) = f(x,w,f(z,u,f(x,y,u)))
    ]]></literal>
    <justification jstring="[para(933(a,1),828(a,2,3)),rewrite([5(2,R),6(2),5(4)])].">
      <j1 rule="para" parents="933 828"/>
      <j2 rule="rewrite" parents="5 6 5"/>
    </justification>
  </clause>

  <clause id="1181">
    <literal><![CDATA[
      f(x,f(y,x,z),f(y,z,u)) = f(y,x,z)
    ]]></literal>
    <justification jstring="[para(1057(a,1),6(a,1)),flip(a)].">
      <j1 rule="para" parents="1057 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1197">
    <literal><![CDATA[
      f(x,f(y,z,u),f(w,x,y)) = f(w,x,f(y,z,f(x,y,u)))
    ]]></literal>
    <justification jstring="[para(38(a,2),1057(a,2)),rewrite([6(3),5(6,R),6(6),392(7),1072(7),5(5,R),6(5)]),flip(a)].">
      <j1 rule="para" parents="38 1057"/>
      <j2 rule="rewrite" parents="6 5 6 392 1072 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1253">
    <literal><![CDATA[
      f(x,f(y,z,u),f(z,u,x)) = f(z,u,x)
    ]]></literal>
    <justification jstring="[para(1071(a,1),5(a,2)),rewrite([5(2),5(2),5(3),5(4),5(4)])].">
      <j1 rule="para" parents="1071 5"/>
      <j2 rule="rewrite" parents="5 5 5 5 5"/>
    </justification>
  </clause>

  <clause id="1254">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,w,f(x,z,u))) = f(x,w,f(x,z,u))
    ]]></literal>
    <justification jstring="[para(1071(a,1),8(a,2,3))].">
      <j1 rule="para" parents="1071 8"/>
    </justification>
  </clause>

  <clause id="1286">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,u,f(x,z,w))) = f(x,w,f(x,z,u))
    ]]></literal>
    <justification jstring="[para(1071(a,1),32(a,2,3)),rewrite([6(2)])].">
      <j1 rule="para" parents="1071 32"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="1321">
    <literal><![CDATA[
      f(x,f(y,z,f(z,u,w)),f(x,f(y,z,u),f(z,u,w))) = f(x,f(y,z,u),f(z,u,w))
    ]]></literal>
    <justification jstring="[para(654(a,1),1071(a,1,2))].">
      <j1 rule="para" parents="654 1071"/>
    </justification>
  </clause>

  <clause id="1329">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,w,f(z,u,w))) = f(x,w,f(y,z,u))
    ]]></literal>
    <justification jstring="[para(1071(a,1),803(a,1,3,3)),rewrite([5(2),5(2)])].">
      <j1 rule="para" parents="1071 803"/>
      <j2 rule="rewrite" parents="5 5"/>
    </justification>
  </clause>

  <clause id="1332">
    <literal><![CDATA[
      f(f(x,y,z),f(y,z,u),f(u,w,f(x,y,z))) = f(w,f(y,z,u),f(x,y,z))
    ]]></literal>
    <justification jstring="[para(1071(a,1),828(a,2,3)),rewrite([5(2),5(2),6(4),5(7),5(7),5(8,R)])].">
      <j1 rule="para" parents="1071 828"/>
      <j2 rule="rewrite" parents="5 5 6 5 5 5"/>
    </justification>
  </clause>

  <clause id="1341">
    <literal><![CDATA[
      f(x,y,f(x,f(z,u,w),f(y,z,u))) = f(x,y,f(z,u,w))
    ]]></literal>
    <justification jstring="[para(1071(a,1),922(a,1,2)),rewrite([5(2),5(2),5(3),392(4),5(5),5(5),5(6)])].">
      <j1 rule="para" parents="1071 922"/>
      <j2 rule="rewrite" parents="5 5 5 392 5 5 5"/>
    </justification>
  </clause>

  <clause id="1349">
    <literal><![CDATA[
      f(x,f(x,y,z),f(y,u,f(y,z,w))) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(8(a,1),1073(a,1,3)),rewrite([5(1),5(5)])].">
      <j1 rule="para" parents="8 1073"/>
      <j2 rule="rewrite" parents="5 5"/>
    </justification>
  </clause>

  <clause id="1469">
    <literal><![CDATA[
      f(x,y,f(z,u,y)) = f(u,y,f(z,x,y))
    ]]></literal>
    <justification jstring="[para(1149(a,1),803(a,2)),rewrite([6(3),1063(5)])].">
      <j1 rule="para" parents="1149 803"/>
      <j2 rule="rewrite" parents="6 1063"/>
    </justification>
  </clause>

  <clause id="1605">
    <literal><![CDATA[
      f(f(x,y,z),f(x,z,u),f(y,w,f(x,z,u))) = f(w,f(x,z,u),f(x,y,z))
    ]]></literal>
    <justification jstring="[para(1181(a,1),1469(a,2,3))].">
      <j1 rule="para" parents="1181 1469"/>
    </justification>
  </clause>

  <clause id="1618">
    <literal><![CDATA[
      f(x,y,f(y,f(z,u,f(x,u,w)),f(x,v5,f(z,u,f(x,u,w))))) = f(x,u,f(x,y,f(z,u,w)))
    ]]></literal>
    <justification jstring="[para(29(a,1),812(a,2)),rewrite([6(5)])].">
      <j1 rule="para" parents="29 812"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="1630">
    <literal><![CDATA[
      f(x,y,f(y,f(z,u,w),f(x,z,u))) = f(x,y,f(z,u,w))
    ]]></literal>
    <justification jstring="[para(922(a,1),812(a,1,3,3)),rewrite([5(2)])].">
      <j1 rule="para" parents="922 812"/>
      <j2 rule="rewrite" parents="5"/>
    </justification>
  </clause>

  <clause id="1856">
    <literal><![CDATA[
      f(x,y,f(z,x,f(y,u,f(z,y,w)))) = f(z,x,y)
    ]]></literal>
    <justification jstring="[para(52(a,1),874(a,2)),rewrite([5(3),392(4),813(4),5(2,R),6(2),5(4,R),6(4)]),flip(a)].">
      <j1 rule="para" parents="52 874"/>
      <j2 rule="rewrite" parents="5 392 813 5 6 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1905">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,u,f(y,u,w)))) = f(x,y,u)
    ]]></literal>
    <justification jstring="[para(41(a,2),871(a,1,3)),rewrite([5(1,R),6(1),5(2,R),6(2),5(5),5(5)])].">
      <j1 rule="para" parents="41 871"/>
      <j2 rule="rewrite" parents="5 6 5 6 5 5"/>
    </justification>
  </clause>

  <clause id="1906">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,z,f(z,u,x))) = f(z,x,f(y,z,u))
    ]]></literal>
    <justification jstring="[para(628(a,1),871(a,1,3)),rewrite([6(2),5(4,R),6(4),6(6)])].">
      <j1 rule="para" parents="628 871"/>
      <j2 rule="rewrite" parents="6 5 6 6"/>
    </justification>
  </clause>

  <clause id="1982">
    <literal><![CDATA[
      f(x,y,f(z,u,f(u,x,y))) = f(u,x,y)
    ]]></literal>
    <justification jstring="[para(1030(a,1),922(a,2)),rewrite([5(1,R),6(1),5(4,R),6(4),922(7),5(4,R),6(4)])].">
      <j1 rule="para" parents="1030 922"/>
      <j2 rule="rewrite" parents="5 6 5 6 922 5 6"/>
    </justification>
  </clause>

  <clause id="2276">
    <literal><![CDATA[
      f(x,f(y,z,f(x,y,u)),f(x,w,v5)) = f(x,y,f(x,w,f(x,v5,f(y,z,u))))
    ]]></literal>
    <justification jstring="[para(54(a,1),17(a,1)),flip(a)].">
      <j1 rule="para" parents="54 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2885">
    <literal><![CDATA[
      f(x,f(y,z,f(u,z,w)),f(x,u,z)) = f(x,u,z)
    ]]></literal>
    <justification jstring="[para(1079(a,1),21(a,2)),rewrite([5(1,R),6(1),6(3),22(5),6(5)])].">
      <j1 rule="para" parents="1079 21"/>
      <j2 rule="rewrite" parents="5 6 6 22 6"/>
    </justification>
  </clause>

  <clause id="2997">
    <literal><![CDATA[
      f(x,f(y,z,f(x,z,u)),f(x,w,v5)) = f(x,z,f(x,w,f(x,v5,f(y,z,u))))
    ]]></literal>
    <justification jstring="[para(24(a,1),57(a,1,2))].">
      <j1 rule="para" parents="24 57"/>
    </justification>
  </clause>

  <clause id="3270">
    <literal><![CDATA[
      f(x,f(y,z,x),f(u,y,z)) = f(y,z,x)
    ]]></literal>
    <justification jstring="[para(1050(a,1),1150(a,1,3)),rewrite([5(2),5(2),5(5),5(5),6(6),1332(6),4(4),5(2),5(2)]),flip(a)].">
      <j1 rule="para" parents="1050 1150"/>
      <j2 rule="rewrite" parents="5 5 5 5 6 1332 4 5 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3475">
    <literal><![CDATA[
      f(x,f(y,x,z),f(y,x,f(y,z,u))) = f(y,x,z)
    ]]></literal>
    <justification jstring="[para(1349(a,1),122(a,1,3)),rewrite([5(1,R),6(1),5(2,R),6(2),15(3),5(2,R),6(2),5(3,R),6(3),57(5),6(3),20(4)]),flip(a)].">
      <j1 rule="para" parents="1349 122"/>
      <j2 rule="rewrite" parents="5 6 5 6 15 5 6 5 6 57 6 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3946">
    <literal><![CDATA[
      f(x,f(y,x,z),f(u,y,f(y,x,w))) = f(x,z,f(u,y,f(y,x,w)))
    ]]></literal>
    <justification jstring="[para(2885(a,1),871(a,1,3)),rewrite([5(1,R),6(1),5(3),6(3),5(4,R),5(5,R),6(5),5(7)])].">
      <j1 rule="para" parents="2885 871"/>
      <j2 rule="rewrite" parents="5 6 5 6 5 5 6 5"/>
    </justification>
  </clause>

  <clause id="4005">
    <literal><![CDATA[
      f(x,y,f(x,f(y,z,u),f(w,z,u))) = f(x,y,f(w,z,u))
    ]]></literal>
    <justification jstring="[para(1071(a,1),3475(a,1,3,3)),rewrite([5(2,R),6(2),5(4,R),6(4),57(5),20(5),5(6,R),6(6)])].">
      <j1 rule="para" parents="1071 3475"/>
      <j2 rule="rewrite" parents="5 6 5 6 57 20 5 6"/>
    </justification>
  </clause>

  <clause id="4085">
    <literal><![CDATA[
      f(x,y,f(z,u,f(z,w,f(x,y,z)))) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(61(a,1),866(a,1,3)),rewrite([5(1),6(1),5(5),5(5)])].">
      <j1 rule="para" parents="61 866"/>
      <j2 rule="rewrite" parents="5 6 5 5"/>
    </justification>
  </clause>

  <clause id="4302">
    <literal><![CDATA[
      f(x,y,f(x,f(y,z,u),f(w,f(y,z,u),f(y,v5,f(y,z,u))))) = f(y,z,f(x,y,u))
    ]]></literal>
    <justification jstring="[para(16(a,2),816(a,2)),rewrite([6(4),5(5,R),6(5)])].">
      <j1 rule="para" parents="16 816"/>
      <j2 rule="rewrite" parents="6 5 6"/>
    </justification>
  </clause>

  <clause id="4305">
    <literal><![CDATA[
      f(x,y,f(z,f(y,z,u),f(x,z,w))) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(30(a,2),816(a,1,3))].">
      <j1 rule="para" parents="30 816"/>
    </justification>
  </clause>

  <clause id="4361">
    <literal><![CDATA[
      f(x,f(y,z,f(z,u,w)),f(x,f(x,z,w),f(v5,f(x,z,w),f(v6,f(y,z,f(z,u,w)),f(x,z,w))))) = f(x,z,w)
    ]]></literal>
    <justification jstring="[para(1088(a,1),816(a,2)),rewrite([5(8),5(9,R),6(9)])].">
      <j1 rule="para" parents="1088 816"/>
      <j2 rule="rewrite" parents="5 5 6"/>
    </justification>
  </clause>

  <clause id="4461">
    <literal><![CDATA[
      f(x,y,f(z,f(x,z,u),f(z,y,w))) = f(x,z,y)
    ]]></literal>
    <justification jstring="[para(4305(a,1),5(a,2)),rewrite([5(2,R),6(2),6(4),5(5),5(5)])].">
      <j1 rule="para" parents="4305 5"/>
      <j2 rule="rewrite" parents="5 6 6 5 5"/>
    </justification>
  </clause>

  <clause id="4572">
    <literal><![CDATA[
      f(x,f(y,z,u),f(z,f(x,z,w),f(z,v5,f(y,z,u)))) = f(y,z,f(x,z,u))
    ]]></literal>
    <justification jstring="[para(24(a,1),4461(a,2)),rewrite([6(4)])].">
      <j1 rule="para" parents="24 4461"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="5467">
    <literal><![CDATA[
      f(x,f(y,z,f(u,y,w)),f(u,x,y)) = f(u,x,y)
    ]]></literal>
    <justification jstring="[para(1856(a,1),828(a,1)),flip(a)].">
      <j1 rule="para" parents="1856 828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5502">
    <literal><![CDATA[
      f(x,y,f(z,x,f(x,u,w))) = f(x,u,f(x,w,f(z,x,y)))
    ]]></literal>
    <justification jstring="[para(61(a,1),1856(a,2)),rewrite([6(7),5(8,R),6(8),5(9,R),6(9),392(10),6(9),4302(10),5(4,R),6(4)])].">
      <j1 rule="para" parents="61 1856"/>
      <j2 rule="rewrite" parents="6 5 6 5 6 392 6 4302 5 6"/>
    </justification>
  </clause>

  <clause id="5647">
    <literal><![CDATA[
      f(x,y,f(x,z,f(u,y,f(z,y,w)))) = f(x,z,y)
    ]]></literal>
    <justification jstring="[para(1905(a,1),812(a,2)),rewrite([6(7),1618(9)])].">
      <j1 rule="para" parents="1905 812"/>
      <j2 rule="rewrite" parents="6 1618"/>
    </justification>
  </clause>

  <clause id="6261">
    <literal><![CDATA[
      f(x,y,f(z,u,f(z,w,f(z,x,y)))) = f(z,x,y)
    ]]></literal>
    <justification jstring="[para(4085(a,1),922(a,2)),rewrite([5(1),5(5),922(9),5(5)])].">
      <j1 rule="para" parents="4085 922"/>
      <j2 rule="rewrite" parents="5 5 922 5"/>
    </justification>
  </clause>

  <clause id="6720">
    <literal><![CDATA[
      f(x,f(y,x,z),f(y,x,u)) = f(y,x,f(x,u,z))
    ]]></literal>
    <justification jstring="[para(70(a,1),17(a,1)),rewrite([5(2,R),6(2),20(3),5(4,R),6(4)]),flip(a)].">
      <j1 rule="para" parents="70 17"/>
      <j2 rule="rewrite" parents="5 6 20 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7772">
    <literal><![CDATA[
      f(x,f(y,z,x),f(z,x,u)) = f(y,x,f(z,x,u))
    ]]></literal>
    <justification jstring="[para(922(a,1),74(a,2,3)),rewrite([5(3),6(3),122(4),19(4),5(4),5(5,R)]),flip(a)].">
      <j1 rule="para" parents="922 74"/>
      <j2 rule="rewrite" parents="5 6 122 19 5 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7788">
    <literal><![CDATA[
      f(x,f(y,z,x),f(u,z,x)) = f(y,x,f(u,z,x))
    ]]></literal>
    <justification jstring="[para(1253(a,1),74(a,2,3)),rewrite([5(3),6(3),1030(5),5(4),5(5,R)]),flip(a)].">
      <j1 rule="para" parents="1253 74"/>
      <j2 rule="rewrite" parents="5 6 1030 5 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8028">
    <literal><![CDATA[
      f(f(x,y,z),f(x,u,f(x,y,z)),f(x,z,f(x,y,w))) = f(u,f(x,y,z),f(x,w,f(x,y,z)))
    ]]></literal>
    <justification jstring="[para(30(a,2),7788(a,1,3)),rewrite([5(3,R),6(3),5(4),5(4),5(9,R),6(9)])].">
      <j1 rule="para" parents="30 7788"/>
      <j2 rule="rewrite" parents="5 6 5 5 5 6"/>
    </justification>
  </clause>

  <clause id="8369">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,f(x,z,w),f(v5,f(x,z,w),f(v6,f(y,z,u),f(x,z,w))))) = f(x,w,f(y,z,f(x,z,u)))
    ]]></literal>
    <justification jstring="[para(75(a,1),816(a,2)),rewrite([6(2),6(3),6(5),5(6),5(7,R),6(7)])].">
      <j1 rule="para" parents="75 816"/>
      <j2 rule="rewrite" parents="6 6 6 5 5 6"/>
    </justification>
  </clause>

  <clause id="8635">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,u,f(u,w,y)))) = f(x,u,y)
    ]]></literal>
    <justification jstring="[back_rewrite(4361),rewrite([8369(11)])].">
      <j1 rule="back_rewrite" parents="4361"/>
      <j2 rule="rewrite" parents="8369"/>
    </justification>
  </clause>

  <clause id="8713">
    <literal><![CDATA[
      f(x,y,f(y,z,f(u,x,y))) = f(y,z,f(u,x,y))
    ]]></literal>
    <justification jstring="[para(1253(a,1),5647(a,1,3)),rewrite([5(2),5(2),5(4),5(4),5(6,R),6(6),205(6),5(5),5(5),5(7),6(7),19(7)])].">
      <j1 rule="para" parents="1253 5647"/>
      <j2 rule="rewrite" parents="5 5 5 5 5 6 205 5 5 5 6 19"/>
    </justification>
  </clause>

  <clause id="9281">
    <literal><![CDATA[
      f(f(x,y,z),f(x,z,u),f(y,w,f(y,v5,f(x,y,z)))) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(1181(a,1),6261(a,1,3,3,3)),rewrite([1181(9)])].">
      <j1 rule="para" parents="1181 6261"/>
      <j2 rule="rewrite" parents="1181"/>
    </justification>
  </clause>

  <clause id="9577">
    <literal><![CDATA[
      f(x,y,f(z,u,f(u,x,f(u,w,y)))) = f(u,x,y)
    ]]></literal>
    <justification jstring="[para(8635(a,1),922(a,2)),rewrite([5(2,R),6(2),5(6,R),6(6),922(9),5(5,R),6(5)])].">
      <j1 rule="para" parents="8635 922"/>
      <j2 rule="rewrite" parents="5 6 5 6 922 5 6"/>
    </justification>
  </clause>

  <clause id="11098">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,w,z))) = f(x,y,f(w,z,f(x,z,u)))
    ]]></literal>
    <justification jstring="[para(874(a,2),105(a,2,3)),flip(a)].">
      <j1 rule="para" parents="874 105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12311">
    <literal><![CDATA[
      f(x,y,f(y,z,f(u,x,z))) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(125(a,1),1469(a,2)),rewrite([20(3),15(3),5(3,R),6(3),6720(5),6(3)]),flip(a)].">
      <j1 rule="para" parents="125 1469"/>
      <j2 rule="rewrite" parents="20 15 5 6 6720 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12402">
    <literal><![CDATA[
      f(x,y,f(x,z,f(u,z,y))) = f(x,z,y)
    ]]></literal>
    <justification jstring="[para(12311(a,1),474(a,2)),rewrite([5(3,R),6(3),21(5),5(4,R),6(4)])].">
      <j1 rule="para" parents="12311 474"/>
      <j2 rule="rewrite" parents="5 6 21 5 6"/>
    </justification>
  </clause>

  <clause id="12982">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,u,x)) = f(y,u,x)
    ]]></literal>
    <justification jstring="[para(1072(a,1),168(a,1,3)),rewrite([5(2),5(2),5(3),5(3),15(4),5(3),5(3)]),flip(a)].">
      <j1 rule="para" parents="1072 168"/>
      <j2 rule="rewrite" parents="5 5 5 5 15 5 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12992">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,w,f(z,u,x))) = f(x,w,f(z,u,x))
    ]]></literal>
    <justification jstring="[para(3270(a,1),168(a,1,3,3)),rewrite([15(6)]),flip(a)].">
      <j1 rule="para" parents="3270 168"/>
      <j2 rule="rewrite" parents="15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13008">
    <literal><![CDATA[
      f(x,f(y,z,f(y,u,w)),f(y,w,x)) = f(y,w,x)
    ]]></literal>
    <justification jstring="[para(1082(a,1),168(a,1,3)),rewrite([5(3),5(3),5(4),5(4),15(5),5(4),5(4)]),flip(a)].">
      <j1 rule="para" parents="1082 168"/>
      <j2 rule="rewrite" parents="5 5 5 5 15 5 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13139">
    <literal><![CDATA[
      f(x,f(y,z,x),f(z,u,x)) = f(y,x,f(z,u,x))
    ]]></literal>
    <justification jstring="[para(12982(a,1),74(a,2,3)),rewrite([5(3),6(3),1030(5),5(4),5(5,R)]),flip(a)].">
      <j1 rule="para" parents="12982 74"/>
      <j2 rule="rewrite" parents="5 6 1030 5 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13180">
    <literal><![CDATA[
      f(x,f(y,x,z),f(y,u,x)) = f(x,z,f(y,u,x))
    ]]></literal>
    <justification jstring="[para(13139(a,1),922(a,2)),rewrite([5(2),5(2),6(3),5(4),5(4),12982(7),5(5,R),6(5)])].">
      <j1 rule="para" parents="13139 922"/>
      <j2 rule="rewrite" parents="5 5 6 5 5 12982 5 6"/>
    </justification>
  </clause>

  <clause id="13417">
    <literal><![CDATA[
      f(f(x,y,f(x,z,u)),f(x,u,w),f(w,f(x,u,w),f(w,v5,f(x,y,f(x,z,u))))) = f(x,u,w)
    ]]></literal>
    <justification jstring="[para(13008(a,1),866(a,2)),rewrite([6(7)])].">
      <j1 rule="para" parents="13008 866"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="14376">
    <literal><![CDATA[
      f(x,y,f(z,u,f(y,w,z))) = f(x,y,f(w,z,f(y,z,u)))
    ]]></literal>
    <justification jstring="[para(828(a,1),262(a,2,3)),rewrite([5(1,R),6(1),5(4)]),flip(a)].">
      <j1 rule="para" parents="828 262"/>
      <j2 rule="rewrite" parents="5 6 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14673">
    <literal><![CDATA[
      f(f(x,y,z),f(y,u,w),f(x,y,z)) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(1181(a,1),318(a,1,3)),rewrite([9281(10)])].">
      <j1 rule="para" parents="1181 318"/>
      <j2 rule="rewrite" parents="9281"/>
    </justification>
  </clause>

  <clause id="14946">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,u,f(y,z,f(w,x,f(y,z,u))))) = f(w,f(y,z,u),f(y,x,f(y,z,u)))
    ]]></literal>
    <justification jstring="[para(14673(a,1),40(a,1,3)),rewrite([5(3),5(3),5(4,R),6(4),5(6),5(6),5(10),5(10),5(11,R),6(11),696(11),5(12,R),6(12),8028(12),6(9),696(9)]),flip(a)].">
      <j1 rule="para" parents="14673 40"/>
      <j2 rule="rewrite" parents="5 5 5 6 5 5 5 5 5 6 696 5 6 8028 6 696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14966">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,u,f(y,z,f(x,w,f(y,z,u))))) = f(y,u,f(y,z,f(x,w,f(y,z,u))))
    ]]></literal>
    <justification jstring="[para(14673(a,1),816(a,1,3)),rewrite([6(3)