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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 April-2007, April 2007.
Process 27709 was started by mccune on cleo,
Fri Apr 13 09:43:04 2007
The command was "/home/mccune/bin/prover9 -f dist-both.in".
]]></heading>

<proof number="1" length="324" max_count="40">

<comments><![CDATA[
% Proof 1 at 745.23 (+ 1.29) seconds: dist_both.
% Length of proof is 324.
% Level of proof is 41.
% Maximum clause weight is 44.
% Given clauses 836.
]]></comments>

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

  <clause id="26">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,z,v))) = f(x,z,f(x,y,f(z,u,v)))
    ]]></literal>
    <justification jstring="[para(16(a,2),8(a,1,3))].">
      <j1 rule="para" parents="16 8"/>
    </justification>
  </clause>

  <clause id="28">
    <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="29">
    <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="30">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,u,v))) = f(x,u,f(x,y,f(z,u,v)))
    ]]></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="32">
    <literal><![CDATA[
      f(x,y,f(x,z,f(x,u,v))) = f(x,v,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,v,y)) = f(x,v,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,v))) = f(z,x,f(x,u,f(x,y,v)))
    ]]></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,v))) = f(y,z,f(y,u,f(x,y,v)))
    ]]></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,v,w)))) = f(x,z,f(x,y,f(z,v,f(z,u,w))))
    ]]></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="53">
    <literal><![CDATA[
      f(x,y,f(z,u,f(z,v,f(x,z,w)))) = f(x,z,f(x,y,f(z,u,f(z,v,w))))
    ]]></literal>
    <justification jstring="[para(18(a,2),16(a,1,3)),rewrite(5(1,R),6(1),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,v,f(x,u,w)))) = f(x,u,f(x,y,f(x,z,f(u,v,w))))
    ]]></literal>
    <justification jstring="[para(16(a,2),18(a,1,3,3))].">
      <j1 rule="para" parents="16 18"/>
    </justification>
  </clause>

  <clause id="55">
    <literal><![CDATA[
      f(x,y,f(x,z,f(u,v,f(x,u,w)))) = f(x,z,f(x,u,f(x,y,f(u,v,w))))
    ]]></literal>
    <justification jstring="[para(16(a,2),18(a,2,3,3)),flip(a)].">
      <j1 rule="para" parents="16 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="57">
    <literal><![CDATA[
      f(x,f(x,y,z),f(x,u,v)) = f(x,y,f(x,u,f(x,v,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="70">
    <literal><![CDATA[
      f(x,y,f(z,u,f(y,z,v))) = f(y,z,f(x,y,f(z,u,v)))
    ]]></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="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,v))) = f(y,u,f(x,y,f(z,u,v)))
    ]]></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,v,z)) = f(x,v,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="76">
    <literal><![CDATA[
      f(x,y,f(z,u,f(z,x,v))) = f(z,x,f(x,y,f(z,v,u)))
    ]]></literal>
    <justification jstring="[para(17(a,1),24(a,2,3)),rewrite(5(2,R),6(2),5(6,R),6(6)),flip(a)].">
      <j1 rule="para" parents="17 24"/>
      <j2 rule="rewrite" parents="5 6 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="78">
    <literal><![CDATA[
      f(x,y,f(z,u,f(y,z,f(z,v,w)))) = f(y,z,f(x,y,f(z,v,f(z,u,w))))
    ]]></literal>
    <justification jstring="[para(18(a,1),24(a,1,3)),rewrite(5(2,R),6(2),5(8,R),6(8))].">
      <j1 rule="para" parents="18 24"/>
      <j2 rule="rewrite" parents="5 6 5 6"/>
    </justification>
  </clause>

  <clause id="81">
    <literal><![CDATA[
      f(x,y,f(z,u,f(z,v,f(z,x,w)))) = f(z,x,f(x,y,f(z,u,f(z,v,w))))
    ]]></literal>
    <justification jstring="[para(18(a,2),24(a,2,3)),rewrite(5(3,R),6(3),5(8,R),6(8)),flip(a)].">
      <j1 rule="para" parents="18 24"/>
      <j2 rule="rewrite" parents="5 6 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="95">
    <literal><![CDATA[
      f(x,y,f(x,z,f(y,u,f(x,y,v)))) = f(x,z,f(y,u,f(x,y,v)))
    ]]></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="102">
    <literal><![CDATA[
      f(x,y,f(z,x,f(y,u,f(x,y,v)))) = f(z,x,f(y,u,f(x,y,v)))
    ]]></literal>
    <justification jstring="[para(21(a,1),24(a,1,3)),rewrite(5(1),5(4),5(7,R),6(7)),flip(a)].">
      <j1 rule="para" parents="21 24"/>
      <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,v)))) = f(y,z,f(x,u,f(x,y,v)))
    ]]></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="113">
    <literal><![CDATA[
      f(x,y,f(y,z,f(y,u,v))) = f(x,y,f(y,v,f(y,z,u)))
    ]]></literal>
    <justification jstring="[para(17(a,1),29(a,2,3)),rewrite(29(4))].">
      <j1 rule="para" parents="17 29"/>
      <j2 rule="rewrite" parents="29"/>
    </justification>
  </clause>

  <clause id="116">
    <literal><![CDATA[
      f(x,y,f(y,z,f(x,u,f(x,v,f(x,y,w))))) = f(x,y,f(y,z,f(x,u,f(x,v,w))))
    ]]></literal>
    <justification jstring="[para(18(a,2),29(a,1,3,3))].">
      <j1 rule="para" parents="18 29"/>
    </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="123">
    <literal><![CDATA[
      f(x,y,f(x,z,f(u,y,f(x,y,v)))) = f(x,z,f(u,y,f(x,y,v)))
    ]]></literal>
    <justification jstring="[para(73(a,1),16(a,1,3)),rewrite(5(1,R),6(1),5(4,R),6(4),5(7,R),6(7)),flip(a)].">
      <j1 rule="para" parents="73 16"/>
      <j2 rule="rewrite" parents="5 6 5 6 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="125">
    <literal><![CDATA[
      f(x,y,f(z,u,f(z,x,v))) = f(x,y,f(z,x,f(z,u,v)))
    ]]></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="131">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,v,f(x,z,w)))) = f(x,z,f(x,y,f(z,u,f(x,v,w))))
    ]]></literal>
    <justification jstring="[para(8(a,1),26(a,1,3,3))].">
      <j1 rule="para" parents="8 26"/>
    </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),26(a,1,3)),rewrite(6(4),95(6)),flip(a)].">
      <j1 rule="para" parents="15 26"/>
      <j2 rule="rewrite" parents="6 95"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="133">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,z,f(y,x,u))) = f(y,z,f(y,x,u))
    ]]></literal>
    <justification jstring="[para(15(a,1),26(a,1)),rewrite(5(1,R),6(1),5(3,R),6(3),6(6),5(7,R),6(7),103(7)),flip(a)].">
      <j1 rule="para" parents="15 26"/>
      <j2 rule="rewrite" parents="5 6 5 6 6 5 6 103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="141">
    <literal><![CDATA[
      f(x,y,f(x,z,f(u,v,f(x,u,w)))) = f(x,u,f(x,z,f(x,y,f(u,v,w))))
    ]]></literal>
    <justification jstring="[para(26(a,2),18(a,2,3)),flip(a)].">
      <j1 rule="para" parents="26 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="147">
    <literal><![CDATA[
      f(x,y,f(z,y,f(z,x,u))) = f(z,x,f(z,y,f(x,y,u)))
    ]]></literal>
    <justification jstring="[para(26(a,1),24(a,1)),flip(a)].">
      <j1 rule="para" parents="26 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="151">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,v,f(z,x,w)))) = f(z,x,f(x,y,f(z,u,f(x,v,w))))
    ]]></literal>
    <justification jstring="[para(26(a,2),24(a,2,3)),rewrite(5(3,R),6(3),5(8,R),6(8)),flip(a)].">
      <j1 rule="para" parents="26 24"/>
      <j2 rule="rewrite" parents="5 6 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="156">
    <literal><![CDATA[
      f(x,y,f(x,z,f(y,u,f(x,v,f(x,y,w))))) = f(x,z,f(y,u,f(x,v,f(x,y,w))))
    ]]></literal>
    <justification jstring="[para(21(a,1),26(a,1,3,3)),rewrite(6(1),6(5)),flip(a)].">
      <j1 rule="para" parents="21 26"/>
      <j2 rule="rewrite" parents="6 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="162">
    <literal><![CDATA[
      f(x,y,f(z,u,f(z,x,f(u,v,w)))) = f(x,y,f(z,x,f(u,v,f(z,u,w))))
    ]]></literal>
    <justification jstring="[para(26(a,1),122(a,1,3,3)),rewrite(5(4,R),6(4),103(5),5(8,R),6(8))].">
      <j1 rule="para" parents="26 122"/>
      <j2 rule="rewrite" parents="5 6 103 5 6"/>
    </justification>
  </clause>

  <clause id="163">
    <literal><![CDATA[
      f(x,y,f(z,y,f(x,z,u))) = f(z,y,f(x,z,f(x,y,u)))
    ]]></literal>
    <justification jstring="[para(26(a,1),122(a,1,3)),rewrite(5(2,R),6(2),5(3,R),6(3),95(4),5(4,R),6(4),5(6,R),6(6))].">
      <j1 rule="para" parents="26 122"/>
      <j2 rule="rewrite" parents="5 6 5 6 95 5 6 5 6"/>
    </justification>
  </clause>

  <clause id="169">
    <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(28(a,1),5(a,2)),rewrite(5(2),5(2),5(4),5(6,R),6(6))].">
      <j1 rule="para" parents="28 5"/>
      <j2 rule="rewrite" parents="5 5 5 5 6"/>
    </justification>
  </clause>

  <clause id="170">
    <literal><![CDATA[
      f(x,f(y,z,u),f(z,u,f(x,y,z))) = f(x,z,f(y,z,u))
    ]]></literal>
    <justification jstring="[para(5(a,1),28(a,1,2)),rewrite(6(2),5(5))].">
      <j1 rule="para" parents="5 28"/>
      <j2 rule="rewrite" parents="6 5"/>
    </justification>
  </clause>

  <clause id="188">
    <literal><![CDATA[
      f(x,f(y,z,f(z,u,v)),f(z,u,f(x,u,f(y,z,v)))) = f(x,u,f(z,u,f(y,z,v)))
    ]]></literal>
    <justification jstring="[para(24(a,1),28(a,1,2)),rewrite(5(1,R),6(1),5(5,R),6(5),5(8,R),6(8))].">
      <j1 rule="para" parents="24 28"/>
      <j2 rule="rewrite" parents="5 6 5 6 5 6"/>
    </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="215">
    <literal><![CDATA[
      f(x,y,f(z,x,f(x,u,y))) = f(z,x,f(x,u,y))
    ]]></literal>
    <justification jstring="[para(205(a,1),24(a,1,3)),rewrite(5(1),5(3),5(5,R),6(5)),flip(a)].">
      <j1 rule="para" parents="205 24"/>
      <j2 rule="rewrite" parents="5 5 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="220">
    <literal><![CDATA[
      f(x,y,f(z,u,f(u,y,v))) = f(u,y,f(x,y,f(z,u,v)))
    ]]></literal>
    <justification jstring="[para(30(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="30 5"/>
      <j2 rule="rewrite" parents="5 6 6 5 6 5 6"/>
    </justification>
  </clause>

  <clause id="224">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,u,f(z,v,w)))) = f(x,u,f(x,y,f(z,v,f(z,u,w))))
    ]]></literal>
    <justification jstring="[para(8(a,1),30(a,2,3,3))].">
      <j1 rule="para" parents="8 30"/>
    </justification>
  </clause>

  <clause id="241">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,z,y))) = f(x,z,f(z,y,f(x,y,u)))
    ]]></literal>
    <justification jstring="[para(25(a,2),30(a,2,3)),flip(a)].">
      <j1 rule="para" parents="25 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="255">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,v,f(x,u,f(v,w,v6))))) = f(x,u,f(x,y,f(z,u,f(v,w,f(x,v,v6)))))
    ]]></literal>
    <justification jstring="[para(26(a,1),30(a,1,3,3))].">
      <j1 rule="para" parents="26 30"/>
    </justification>
  </clause>

  <clause id="263">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,z,f(x,z,f(x,y,u)))) = f(x,z,f(x,y,f(y,z,u)))
    ]]></literal>
    <justification jstring="[para(28(a,1),30(a,2,3))].">
      <j1 rule="para" parents="28 30"/>
    </justification>
  </clause>

  <clause id="264">
    <literal><![CDATA[
      f(x,y,f(z,u,f(u,y,v))) = f(x,y,f(u,y,f(z,u,v)))
    ]]></literal>
    <justification jstring="[para(30(a,1),205(a,1,3)),rewrite(5(1,R),6(1),5(4,R),6(4),5(5,R),6(5),188(6),5(4,R),6(4),5(6,R),6(6)),flip(a)].">
      <j1 rule="para" parents="30 205"/>
      <j2 rule="rewrite" parents="5 6 5 6 5 6 188 5 6 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="266">
    <literal><![CDATA[
      f(x,y,f(z,x,f(z,y,u))) = f(z,x,f(z,y,f(x,y,u)))
    ]]></literal>
    <justification jstring="[para(30(a,1),215(a,2)),rewrite(5(4,R),6(4),21(5),5(5,R),6(5)),flip(a)].">
      <j1 rule="para" parents="30 215"/>
      <j2 rule="rewrite" parents="5 6 21 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="320">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,x,v)) = f(x,v,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="321">
    <literal><![CDATA[
      f(x,f(y,z,u),f(v,y,x)) = f(v,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="323">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,u,v)) = f(x,v,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="333">
    <literal><![CDATA[
      f(x,y,f(z,f(x,y,u),f(x,v,f(x,y,u)))) = f(x,f(x,y,u),f(z,v,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="362">
    <literal><![CDATA[
      f(x,y,f(z,f(u,v,w),f(z,x,u))) = f(z,x,f(x,y,f(u,v,f(z,u,w))))
    ]]></literal>
    <justification jstring="[para(38(a,2),24(a,2,3)),rewrite(5(3,R),6(3),5(8,R),6(8)),flip(a)].">
      <j1 rule="para" parents="38 24"/>
      <j2 rule="rewrite" parents="5 6 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="369">
    <literal><![CDATA[
      f(x,f(y,x,z),f(y,x,u)) = f(y,x,f(x,u,z))
    ]]></literal>
    <justification jstring="[para(25(a,2),38(a,2)),rewrite(15(2),6(2)),flip(a)].">
      <j1 rule="para" parents="25 38"/>
      <j2 rule="rewrite" parents="15 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="388">
    <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="394">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,y,v)) = f(x,y,f(x,v,f(y,z,u)))
    ]]></literal>
    <justification jstring="[para(38(a,2),26(a,1)),rewrite(6(2))].">
      <j1 rule="para" parents="38 26"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="439">
    <literal><![CDATA[
      f(x,f(x,y,z),f(y,u,f(x,y,v))) = f(x,y,f(x,z,f(y,u,v)))
    ]]></literal>
    <justification jstring="[para(8(a,1),369(a,1,3)),rewrite(5(1,R),6(1),5(2,R),6(2),6(6),5(7,R),6(7))].">
      <j1 rule="para" parents="8 369"/>
      <j2 rule="rewrite" parents="5 6 5 6 6 5 6"/>
    </justification>
  </clause>

  <clause id="444">
    <literal><![CDATA[
      f(x,f(x,y,z),f(u,f(x,y,z),f(x,y,v))) = f(u,f(x,y,z),f(x,y,f(x,z,v)))
    ]]></literal>
    <justification jstring="[para(369(a,1),24(a,2,3)),rewrite(5(1,R),6(1),5(2,R),6(2),5(3,R),6(3),5(6,R),6(6),6(7),5(8,R),6(8))].">
      <j1 rule="para" parents="369 24"/>
      <j2 rule="rewrite" parents="5 6 5 6 5 6 5 6 6 5 6"/>
    </justification>
  </clause>

  <clause id="486">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,z,f(z,y,v)))) = f(x,z,f(z,y,f(x,y,f(z,u,v))))
    ]]></literal>
    <justification jstring="[para(40(a,2),30(a,2,3)),flip(a)].">
      <j1 rule="para" parents="40 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="503">
    <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="548">
    <literal><![CDATA[
      f(x,y,f(z,y,f(z,u,f(x,z,v)))) = f(x,z,f(z,y,f(x,y,f(z,u,v))))
    ]]></literal>
    <justification jstring="[para(41(a,1),30(a,2,3)),flip(a)].">
      <j1 rule="para" parents="41 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="574">
    <literal><![CDATA[
      f(x,f(y,x,z),f(x,u,z)) = f(y,x,f(x,u,z))
    ]]></literal>
    <justification jstring="[para(503(a,1),17(a,1)),rewrite(6(4)),flip(a)].">
      <j1 rule="para" parents="503 17"/>
      <j2 rule="rewrite" parents="6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="577">
    <literal><![CDATA[
      f(x,y,f(z,u,f(z,x,v))) = f(x,y,f(z,v,f(z,x,u)))
    ]]></literal>
    <justification jstring="[para(503(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="503 24"/>
      <j2 rule="rewrite" parents="5 5 5 6 103 6 5 6 5 6"/>
    </justification>
  </clause>

  <clause id="602">
    <literal><![CDATA[
      f(x,f(y,x,z),f(x,z,u)) = f(y,x,f(x,z,u))
    ]]></literal>
    <justification jstring="[para(574(a,1),5(a,2)),rewrite(6(2),5(3),6(4))].">
      <j1 rule="para" parents="574 5"/>
      <j2 rule="rewrite" parents="6 5 6"/>
    </justification>
  </clause>

  <clause id="603">
    <literal><![CDATA[
      f(x,f(x,y,z),f(u,x,z)) = f(u,x,f(x,y,z))
    ]]></literal>
    <justification jstring="[para(574(a,1),6(a,1)),flip(a)].">
      <j1 rule="para" parents="574 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="604">
    <literal><![CDATA[
      f(x,f(y,x,z),f(u,f(x,z,v),f(y,x,z))) = f(u,f(y,x,z),f(y,x,f(x,z,v)))
    ]]></literal>
    <justification jstring="[para(574(a,1),16(a,1,3)),rewrite(6(2),5(4,R),6(4),6(7),5(8,R)),flip(a)].">
      <j1 rule="para" parents="574 16"/>
      <j2 rule="rewrite" parents="6 5 6 6 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="611">
    <literal><![CDATA[
      f(x,f(x,y,z),f(u,f(x,z,v),f(x,y,z))) = f(u,f(x,y,z),f(x,y,f(x,z,v)))
    ]]></literal>
    <justification jstring="[para(574(a,1),29(a,1,3,3)),rewrite(5(1,R),6(1),5(2,R),6(2),6(3),5(4,R),6(4),5(5,R),6(5),444(6),20(3),5(5,R),6(5),5(6,R),6(6),6(7),5(8,R)),flip(a)].">
      <j1 rule="para" parents="574 29"/>
      <j2 rule="rewrite" parents="5 6 5 6 6 5 6 5 6 444 20 5 6 5 6 6 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="617">
    <literal><![CDATA[
      f(x,f(y,f(x,z,u),f(x,v,z)),f(y,f(x,v,z),f(x,v,f(x,z,u)))) = f(y,f(x,v,z),f(x,v,f(x,z,u)))
    ]]></literal>
    <justification jstring="[para(574(a,1),28(a,1,3,3)),rewrite(5(1,R),6(1),6(2),5(3,R),5(4,R),6(4),6(5),5(6,R),6(6),5(7,R),6(7),5(9,R),6(9),5(10,R),6(10),6(11),5(12,R),611(13))].">
      <j1 rule="para" parents="574 28"/>
      <j2 rule="rewrite" parents="5 6 6 5 5 6 6 5 6 5 6 5 6 5 6 6 5 611"/>
    </justification>
  </clause>

  <clause id="638">
    <literal><![CDATA[
      f(x,f(x,y,z),f(u,x,y)) = f(u,x,f(x,y,z))
    ]]></literal>
    <justification jstring="[para(602(a,1),6(a,1)),flip(a)].">
      <j1 rule="para" parents="602 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="639">
    <literal><![CDATA[
      f(x,f(x,y,z),f(u,v,f(x,y,z))) = f(x,z,f(x,y,f(u,v,f(x,y,z))))
    ]]></literal>
    <justification jstring="[para(602(a,1),26(a,2)),rewrite(5(1),5(1),5(2),5(2),6(3),5(4,R),6(4),333(5),5(5),5(5),5(6),5(6),5(8,R),6(8))].">
      <j1 rule="para" parents="602 26"/>
      <j2 rule="rewrite" parents="5 5 5 5 6 5 6 333 5 5 5 5 5 6"/>
    </justification>
  </clause>

  <clause id="641">
    <literal><![CDATA[
      f(x,y,f(x,z,f(u,f(x,y,v),f(x,z,y)))) = f(u,f(x,z,y),f(x,z,f(x,y,v)))
    ]]></literal>
    <justification jstring="[para(602(a,1),28(a,1,3,3)),rewrite(5(1,R),6(1),5(3,R),5(4,R),6(4),5(6,R),6(6),5(7,R),6(7),617(8),5(5,R),6(5),5(6,R),6(6),5(8,R),639(9)),flip(a)].">
      <j1 rule="para" parents="602 28"/>
      <j2 rule="rewrite" parents="5 6 5 5 6 5 6 5 6 617 5 6 5 6 5 639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="670">
    <literal><![CDATA[
      f(f(x,y,z),f(x,u,f(x,y,z)),f(x,v,f(x,y,z))) = f(v,f(x,y,z),f(x,y,f(x,z,u)))
    ]]></literal>
    <justification jstring="[para(603(a,1),369(a,1,2)),rewrite(5(3,R),6(3),6(5),5(9),5(9),5(10,R),639(11),641(11))].">
      <j1 rule="para" parents="603 369"/>
      <j2 rule="rewrite" parents="5 6 6 5 5 5 639 641"/>
    </justification>
  </clause>

  <clause id="785">
    <literal><![CDATA[
      f(x,y,f(x,z,f(y,z,u))) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(638(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),439(6),6(3),57(6),6(4),20(4),20(5)),flip(a)].">
      <j1 rule="para" parents="638 40"/>
      <j2 rule="rewrite" parents="5 15 5 15 5 6 5 6 439 6 57 6 20 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="791">
    <literal><![CDATA[
      f(x,y,f(z,y,f(x,z,u))) = f(x,z,y)
    ]]></literal>
    <justification jstring="[back_rewrite(266),rewrite(5(1,R),6(1),5(2,R),6(2),785(3),5(3,R),6(3),5(4,R),6(4)),flip(a)].">
      <j1 rule="back_rewrite" parents="266"/>
      <j2 rule="rewrite" parents="5 6 5 6 785 5 6 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="793">
    <literal><![CDATA[
      f(x,y,f(y,z,f(x,z,u))) = f(x,y,z)
    ]]></literal>
    <justification jstring="[back_rewrite(147),rewrite(5(1,R),6(1),5(2,R),6(2),5(5,R),6(5),5(6,R),6(6),791(6))].">
      <j1 rule="back_rewrite" parents="147"/>
      <j2 rule="rewrite" parents="5 6 5 6 5 6 5 6 791"/>
    </justification>
  </clause>

  <clause id="794">
    <literal><![CDATA[
      f(x,y,f(z,y,f(z,x,u))) = f(z,x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(163),rewrite(5(2,R),6(2),793(3),5(4,R),6(4)),flip(a)].">
      <j1 rule="back_rewrite" parents="163"/>
      <j2 rule="rewrite" parents="5 6 793 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="795">
    <literal><![CDATA[
      f(x,y,f(y,z,f(z,u,f(x,z,v)))) = f(x,y,z)
    ]]></literal>
    <justification jstring="[back_rewrite(548),rewrite(5(3,R),6(3),5(7,R),6(7),791(8))].">
      <j1 rule="back_rewrite" parents="548"/>
      <j2 rule="rewrite" parents="5 6 5 6 791"/>
    </justification>
  </clause>

  <clause id="796">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,z,f(y,z,v)))) = f(x,y,z)
    ]]></literal>
    <justification jstring="[back_rewrite(486),rewrite(5(1,R),6(1),5(7,R),6(7),791(8))].">
      <j1 rule="back_rewrite" parents="486"/>
      <j2 rule="rewrite" parents="5 6 5 6 791"/>
    </justification>
  </clause>

  <clause id="798">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,y,z))) = f(x,y,z)
    ]]></literal>
    <justification jstring="[back_rewrite(241),rewrite(6(1),5(5,R),6(5),791(6))].">
      <j1 rule="back_rewrite" parents="241"/>
      <j2 rule="rewrite" parents="6 5 6 791"/>
    </justification>
  </clause>

  <clause id="800">
    <literal><![CDATA[
      f(x,y,f(x,z,f(z,y,u))) = f(x,z,y)
    ]]></literal>
    <justification jstring="[back_rewrite(263),rewrite(794(4),394(3),785(3)),flip(a)].">
      <j1 rule="back_rewrite" parents="263"/>
      <j2 rule="rewrite" parents="794 394 785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="802">
    <literal><![CDATA[
      f(x,y,f(z,x,f(z,y,u))) = f(z,x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(388),rewrite(798(4)),flip(a)].">
      <j1 rule="back_rewrite" parents="388"/>
      <j2 rule="rewrite" parents="798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="808">
    <literal><![CDATA[
      f(x,y,f(x,f(y,z,u),f(y,v,f(y,z,u)))) = f(y,z,f(x,y,u))
    ]]></literal>
    <justification jstring="[para(16(a,2),785(a,2)),rewrite(6(3))].">
      <j1 rule="para" parents="16 785"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="815">
    <literal><![CDATA[
      f(x,y,f(z,x,u)) = f(x,u,f(z,x,y))
    ]]></literal>
    <justification jstring="[para(25(a,2),785(a,2)),rewrite(6(3),808(5))].">
      <j1 rule="para" parents="25 785"/>
      <j2 rule="rewrite" parents="6 808"/>
    </justification>
  </clause>

  <clause id="831">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,v,f(x,y,z))) = f(x,v,f(x,y,z))
    ]]></literal>
    <justification jstring="[para(785(a,1),32(a,1,3)),flip(a)].">
      <j1 rule="para" parents="785 32"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="847">
    <literal><![CDATA[
      f(x,y,f(z,u,x)) = f(z,x,f(u,x,y))
    ]]></literal>
    <justification jstring="[para(815(a,1),5(a,2)),rewrite(6(2),5(3)),flip(a)].">
      <j1 rule="para" parents="815 5"/>
      <j2 rule="rewrite" parents="6 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="871">
    <literal><![CDATA[
      f(x,y,f(z,u,y)) = f(z,y,f(x,u,y))
    ]]></literal>
    <justification jstring="[para(847(a,1),5(a,2)),rewrite(6(2),5(3))].">
      <j1 rule="para" parents="847 5"/>
      <j2 rule="rewrite" parents="6 5"/>
    </justification>
  </clause>

  <clause id="884">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,z,y))) = f(x,z,y)
    ]]></literal>
    <justification jstring="[para(847(a,2),26(a,2,3)),rewrite(5(2,R),6(2),793(3),6(2)),flip(a)].">
      <j1 rule="para" parents="847 26"/>
      <j2 rule="rewrite" parents="5 6 793 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="896">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,z,x)) = f(y,z,x)
    ]]></literal>
    <justification jstring="[para(847(a,2),38(a,2)),rewrite(6(2),394(3),785(3)),flip(a)].">
      <j1 rule="para" parents="847 38"/>
      <j2 rule="rewrite" parents="6 394 785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="899">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,x,z)) = f(y,x,z)
    ]]></literal>
    <justification jstring="[para(38(a,2),847(a,2)),rewrite(5(2),394(3),785(3),5(2,R),6(2),5(3,R),6(3)),flip(a)].">
      <j1 rule="para" parents="38 847"/>
      <j2 rule="rewrite" parents="5 394 785 5 6 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="904">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,v,z))) = f(x,z,f(x,y,f(v,z,u)))
    ]]></literal>
    <justification jstring="[para(847(a,2),503(a,2,3)),rewrite(5(3,R),6(3),21(5),5(6,R),6(6)),flip(a)].">
      <j1 rule="para" parents="847 503"/>
      <j2 rule="rewrite" parents="5 6 21 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="964">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,u,y))) = f(x,u,y)
    ]]></literal>
    <justification jstring="[para(20(a,1),871(a,1,3)),rewrite(15(3),639(5),122(4)),flip(a)].">
      <j1 rule="para" parents="20 871"/>
      <j2 rule="rewrite" parents="15 639 122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="966">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,v,f(y,z,u))) = f(v,f(y,z,u),f(y,z,f(x,y,u)))
    ]]></literal>
    <justification jstring="[para(16(a,2),871(a,2,3)),rewrite(5(3,R),6(3))].">
      <j1 rule="para" parents="16 871"/>
      <j2 rule="rewrite" parents="5 6"/>
    </justification>
  </clause>

  <clause id="1004">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,z,u)) = f(x,z,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),896(a,1,2)),rewrite(5(2),5(4))].">
      <j1 rule="para" parents="5 896"/>
      <j2 rule="rewrite" parents="5 5"/>
    </justification>
  </clause>

  <clause id="1005">
    <literal><![CDATA[
      f(x,y,f(x,z,f(y,u,z))) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(5(a,2),896(a,1,2)),rewrite(5(2),6(2),394(3),5(4),6(4))].">
      <j1 rule="para" parents="5 896"/>
      <j2 rule="rewrite" parents="5 6 394 5 6"/>
    </justification>
  </clause>

  <clause id="1006">
    <literal><![CDATA[
      f(x,f(y,z,x),f(y,z,u)) = f(y,z,x)
    ]]></literal>
    <justification jstring="[para(896(a,1),6(a,1)),flip(a)].">
      <j1 rule="para" parents="896 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1007">
    <literal><![CDATA[
      f(x,f(x,y,z),f(y,z,u)) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(896(a,1),6(a,2)),rewrite(5(1),5(4))].">
      <j1 rule="para" parents="896 6"/>
      <j2 rule="rewrite" parents="5 5"/>
    </justification>
  </clause>

  <clause id="1012">
    <literal><![CDATA[
      f(x,f(y,z,f(z,u,v)),f(x,z,u)) = f(x,z,u)
    ]]></literal>
    <justification jstring="[para(16(a,1),896(a,1,2)),rewrite(5(3),5(5))].">
      <j1 rule="para" parents="16 896"/>
      <j2 rule="rewrite" parents="5 5"/>
    </justification>
  </clause>

  <clause id="1015">
    <literal><![CDATA[
      f(x,y,f(x,z,f(y,u,f(y,v,z)))) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(17(a,2),896(a,1,2)),rewrite(5(3),394(4),5(5))].">
      <j1 rule="para" parents="17 896"/>
      <j2 rule="rewrite" parents="5 394 5"/>
    </justification>
  </clause>

  <clause id="1021">
    <literal><![CDATA[
      f(x,f(y,z,f(z,u,v)),f(x,z,v)) = f(x,z,v)
    ]]></literal>
    <justification jstring="[para(25(a,1),896(a,1,2)),rewrite(5(3),5(5))].">
      <j1 rule="para" parents="25 896"/>
      <j2 rule="rewrite" parents="5 5"/>
    </justification>
  </clause>

  <clause id="1066">
    <literal><![CDATA[
      f(x,y,f(x,f(z,u,v),f(y,z,u))) = f(x,y,f(z,u,v))
    ]]></literal>
    <justification jstring="[para(896(a,1),785(a,1,3,3)),rewrite(5(2))].">
      <j1 rule="para" parents="896 785"/>
      <j2 rule="rewrite" parents="5"/>
    </justification>
  </clause>

  <clause id="1074">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,u,f(y,z,v))) = f(x,u,f(y,z,v))
    ]]></literal>
    <justification jstring="[para(896(a,1),896(a,1,2)),rewrite(5(3),5(6))].">
      <j1 rule="para" parents="896 896"/>
      <j2 rule="rewrite" parents="5 5"/>
    </justification>
  </clause>

  <clause id="1075">
    <literal><![CDATA[
      f(x,f(y,x,z),f(y,z,u)) = f(y,x,z)
    ]]></literal>
    <justification jstring="[para(899(a,1),6(a,1)),flip(a)].">
      <j1 rule="para" parents="899 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1091">
    <literal><![CDATA[
      f(x,f(y,z,u),f(v,x,y)) = f(v,x,f(y,z,f(x,y,u)))
    ]]></literal>
    <justification jstring="[para(38(a,2),899(a,2)),rewrite(6(3),5(6,R),6(6),394(7),1005(7),5(5,R),6(5)),flip(a)].">
      <j1 rule="para" parents="38 899"/>
      <j2 rule="rewrite" parents="6 5 6 394 1005 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1106">
    <literal><![CDATA[
      f(x,f(y,z,u),f(z,u,x)) = f(z,u,x)
    ]]></literal>
    <justification jstring="[para(1004(a,1),5(a,2)),rewrite(5(2),5(2),5(3),5(4),5(4))].">
      <j1 rule="para" parents="1004 5"/>
      <j2 rule="rewrite" parents="5 5 5 5 5"/>
    </justification>
  </clause>

  <clause id="1110">
    <literal><![CDATA[
      f(x,f(y,z,u),f(v,f(z,u,x),f(y,z,u))) = f(v,f(z,u,x),f(y,z,u))
    ]]></literal>
    <justification jstring="[para(1004(a,1),16(a,1,3)),rewrite(5(2),5(2),5(3,R),5(6),5(6),5(7,R)),flip(a)].">
      <j1 rule="para" parents="1004 16"/>
      <j2 rule="rewrite" parents="5 5 5 5 5 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1182">
    <literal><![CDATA[
      f(x,y,f(x,f(z,u,v),f(y,u,v))) = f(x,y,f(z,u,v))
    ]]></literal>
    <justification jstring="[para(1004(a,1),785(a,1,3,3))].">
      <j1 rule="para" parents="1004 785"/>
    </justification>
  </clause>

  <clause id="1498">
    <literal><![CDATA[
      f(x,y,f(y,f(x,z,u),f(z,u,v))) = f(x,y,f(z,u,v))
    ]]></literal>
    <justification jstring="[para(896(a,1),791(a,1,3,3)),rewrite(5(2),5(3,R),6(6))].">
      <j1 rule="para" parents="896 791"/>
      <j2 rule="rewrite" parents="5 5 6"/>
    </justification>
  </clause>

  <clause id="1502">
    <literal><![CDATA[
      f(x,y,f(y,f(x,z,u),f(v,z,u))) = f(x,y,f(v,z,u))
    ]]></literal>
    <justification jstring="[para(1004(a,1),791(a,1,3,3)),rewrite(5(3,R),6(6))].">
      <j1 rule="para" parents="1004 791"/>
      <j2 rule="rewrite" parents="5 6"/>
    </justification>
  </clause>

  <clause id="1509">
    <literal><![CDATA[
      f(x,y,f(y,f(z,u,f(x,u,v)),f(x,w,f(z,u,f(x,u,v))))) = f(x,u,f(x,y,f(z,u,v)))
    ]]></literal>
    <justification jstring="[para(30(a,1),793(a,2)),rewrite(6(5))].">
      <j1 rule="para" parents="30 793"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="1515">
    <literal><![CDATA[
      f(x,y,f(y,f(z,u,v),f(x,z,u))) = f(x,y,f(z,u,v))
    ]]></literal>
    <justification jstring="[para(896(a,1),793(a,1,3,3)),rewrite(5(2))].">
      <j1 rule="para" parents="896 793"/>
      <j2 rule="rewrite" parents="5"/>
    </justification>
  </clause>

  <clause id="1519">
    <literal><![CDATA[
      f(x,y,f(z,u,f(y,z,f(x,z,v)))) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(18(a,1),794(a,1,3)),rewrite(5(1,R),6(1),5(2,R),6(2),5(5),5(5))].">
      <j1 rule="para" parents="18 794"/>
      <j2 rule="rewrite" parents="5 6 5 6 5 5"/>
    </justification>
  </clause>

  <clause id="1657">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,z,f(z,v,f(y,z,u)))) = f(y,z,f(x,z,u))
    ]]></literal>
    <justification jstring="[para(24(a,1),800(a,2)),rewrite(6(3))].">
      <j1 rule="para" parents="24 800"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="1668">
    <literal><![CDATA[
      f(x,y,f(z,u,x)) = f(u,x,f(z,x,y))
    ]]></literal>
    <justification jstring="[para(847(a,2),800(a,2)),rewrite(6(3),1657(5)),flip(a)].">
      <j1 rule="para" parents="847 800"/>
      <j2 rule="rewrite" parents="6 1657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1669">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,u,f(u,v,f(y,z,u)))) = f(y,u,f(x,z,u))
    ]]></literal>
    <justification jstring="[para(871(a,1),800(a,2)),rewrite(6(3))].">
      <j1 rule="para" parents="871 800"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="1671">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,v,f(z,u,v))) = f(x,v,f(y,z,u))
    ]]></literal>
    <justification jstring="[para(1004(a,1),800(a,1,3,3)),rewrite(5(2),5(2))].">
      <j1 rule="para" parents="1004 800"/>
      <j2 rule="rewrite" parents="5 5"/>
    </justification>
  </clause>

  <clause id="1675">
    <literal><![CDATA[
      f(x,y,f(z,u,y)) = f(u,y,f(x,z,y))
    ]]></literal>
    <justification jstring="[para(1668(a,1),5(a,2)),rewrite(6(2),5(3))].">
      <j1 rule="para" parents="1668 5"/>
      <j2 rule="rewrite" parents="6 5"/>
    </justification>
  </clause>

  <clause id="1717">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,u,f(y,z,v))) = f(y,u,f(y,z,f(v,x,f(y,z,u))))
    ]]></literal>
    <justification jstring="[para(17(a,1),1675(a,2,3)),rewrite(639(4),6(6)),flip(a)].">
      <j1 rule="para" parents="17 1675"/>
      <j2 rule="rewrite" parents="639 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1761">
    <literal><![CDATA[
      f(x,y,f(z,u,y)) = f(u,y,f(z,x,y))
    ]]></literal>
    <justification jstring="[para(1675(a,1),800(a,2)),rewrite(6(3),1669(5))].">
      <j1 rule="para" parents="1675 800"/>
      <j2 rule="rewrite" parents="6 1669"/>
    </justification>
  </clause>

  <clause id="1776">
    <literal><![CDATA[
      f(f(x,y,z),f(x,y,u),f(z,v,f(x,y,u))) = f(v,f(x,y,u),f(x,y,z))
    ]]></literal>
    <justification jstring="[para(1006(a,1),1761(a,2,3))].">
      <j1 rule="para" parents="1006 1761"/>
    </justification>
  </clause>

  <clause id="1810">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,u,f(y,u,v)))) = f(x,y,u)
    ]]></literal>
    <justification jstring="[para(41(a,2),802(a,1,3)),rewrite(5(1,R),6(1),5(2,R),6(2),5(5),5(5))].">
      <j1 rule="para" parents="41 802"/>
      <j2 rule="rewrite" parents="5 6 5 6 5 5"/>
    </justification>
  </clause>

  <clause id="1857">
    <literal><![CDATA[
      f(x,f(x,y,z),f(u,v,f(x,y,f(x,z,v)))) = f(x,v,f(x,y,z))
    ]]></literal>
    <justification jstring="[para(8(a,1),964(a,1,3,3)),rewrite(6(2))].">
      <j1 rule="para" parents="8 964"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="1905">
    <literal><![CDATA[
      f(x,y,f(z,y,f(x,u,f(x,z,v)))) = f(x,z,y)
    ]]></literal>
    <justification jstring="[para(52(a,1),24(a,2)),rewrite(5(2,R),6(2),5(3,R),6(3),793(4),5(4,R),6(4),5(5,R),6(5)),flip(a)].">
      <j1 rule="para" parents="52 24"/>
      <j2 rule="rewrite" parents="5 6 5 6 793 5 6 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1986">
    <literal><![CDATA[
      f(x,y,f(z,x,f(y,u,f(z,y,v)))) = f(z,x,y)
    ]]></literal>
    <justification jstring="[para(52(a,1),847(a,2)),rewrite(5(3),394(4),785(4),5(2,R),6(2),5(4,R),6(4)),flip(a)].">
      <j1 rule="para" parents="52 847"/>
      <j2 rule="rewrite" parents="5 394 785 5 6 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2184">
    <literal><![CDATA[
      f(x,y,f(z,y,f(x,u,f(z,x,v)))) = f(z,x,y)
    ]]></literal>
    <justification jstring="[para(53(a,1),24(a,1)),rewrite(785(4)),flip(a)].">
      <j1 rule="para" parents="53 24"/>
      <j2 rule="rewrite" parents="785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2520">
    <literal><![CDATA[
      f(x,f(y,z,f(x,y,u)),f(x,v,w)) = f(x,y,f(x,v,f(x,w,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="2752">
    <literal><![CDATA[
      f(x,f(y,z,f(u,z,v)),f(x,u,z)) = f(x,u,z)
    ]]></literal>
    <justification jstring="[para(1012(a,1),21(a,2)),rewrite(5(1,R),6(1),6(3),22(5),6(5))].">
      <j1 rule="para" parents="1012 21"/>
      <j2 rule="rewrite" parents="5 6 6 22 6"/>
    </justification>
  </clause>

  <clause id="3281">
    <literal><![CDATA[
      f(x,f(y,z,f(x,z,u)),f(x,v,w)) = f(x,z,f(x,v,f(x,w,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="3835">
    <literal><![CDATA[
      f(x,y,f(y,f(x,z,u),f(v,f(x,z,u),f(x,w,f(x,z,u))))) = f(x,z,f(x,y,u))
    ]]></literal>
    <justification jstring="[para(8(a,1),795(a,2)),rewrite(6(4),5(5,R),6(5))].">
      <j1 rule="para" parents="8 795"/>
      <j2 rule="rewrite" parents="6 5 6"/>
    </justification>
  </clause>

  <clause id="3841">
    <literal><![CDATA[
      f(x,y,f(z,f(x,z,u),f(y,z,v))) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(25(a,2),795(a,1,3))].">
      <j1 rule="para" parents="25 795"/>
    </justification>
  </clause>

  <clause id="3866">
    <literal><![CDATA[
      f(x,y,f(x,z,f(u,y,z))) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(1004(a,1),795(a,2)),rewrite(6(6),5(7,R),6(7),3835(9),6(2))].">
      <j1 rule="para" parents="1004 795"/>
      <j2 rule="rewrite" parents="6 5 6 3835 6"/>
    </justification>
  </clause>

  <clause id="3892">
    <literal><![CDATA[
      f(x,y,f(x,z,f(u,y,f(y,v,z)))) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(1021(a,1),795(a,2)),rewrite(6(8),5(9,R),6(9),3835(11),6(3))].">
      <j1 rule="para" parents="1021 795"/>
      <j2 rule="rewrite" parents="6 5 6 3835 6"/>
    </justification>
  </clause>

  <clause id="3978">
    <literal><![CDATA[
      f(x,y,f(x,z,f(z,u,y))) = f(x,z,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),3866(a,1)),rewrite(5(1),5(3),5(3),6(4))].">
      <j1 rule="para" parents="5 3866"/>
      <j2 rule="rewrite" parents="5 5 5 6"/>
    </justification>
  </clause>

  <clause id="4130">
    <literal><![CDATA[
      f(x,f(y,z,f(z,u,v)),f(f(x,z,v),f(x,w,f(x,z,v)),f(v6,f(y,z,f(z,u,v)),f(x,z,v)))) = f(x,z,v)
    ]]></literal>
    <justification jstring="[para(1021(a,1),3841(a,2)),rewrite(6(5),5(9))].">
      <j1 rule="para" parents="1021 3841"/>
      <j2 rule="rewrite" parents="6 5"/>
    </justification>
  </clause>

  <clause id="4446">
    <literal><![CDATA[
      f(x,y,f(z,u,f(z,v,f(x,y,z)))) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(847(a,2),796(a,1,3,3))].">
      <j1 rule="para" parents="847 796"/>
    </justification>
  </clause>

  <clause id="4720">
    <literal><![CDATA[
      f(x,y,f(x,f(z,u,v),f(y,z,v))) = f(x,y,f(z,u,v))
    ]]></literal>
    <justification jstring="[para(1005(a,1),1015(a,1,3,3))].">
      <j1 rule="para" parents="1005 1015"/>
    </justification>
  </clause>

  <clause id="5052">
    <literal><![CDATA[
      f(x,y,f(x,z,f(u,y,f(z,y,v)))) = f(x,z,y)
    ]]></literal>
    <justification jstring="[para(1810(a,1),793(a,2)),rewrite(6(7),1509(9))].">
      <j1 rule="para" parents="1810 793"/>
      <j2 rule="rewrite" parents="6 1509"/>
    </justification>
  </clause>

  <clause id="5129">
    <literal><![CDATA[
      f(x,f(y,z,f(u,y,v)),f(u,x,y)) = f(u,x,y)
    ]]></literal>
    <justification jstring="[para(1986(a,1),815(a,1)),flip(a)].">
      <j1 rule="para" parents="1986 815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5250">
    <literal><![CDATA[
      f(x,f(y,x,z),f(z,u,f(y,z,v))) = f(y,x,z)
    ]]></literal>
    <justification jstring="[para(5129(a,1),6(a,1)),flip(a)].">
      <j1 rule="para" parents="5129 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5381">
    <literal><![CDATA[
      f(f(x,y,z),f(x,y,u),f(u,f(x,y,u),f(v,f(x,y,z),f(u,w,f(x,y,z))))) = f(x,y,u)
    ]]></literal>
    <justification jstring="[para(896(a,1),2184(a,2)),rewrite(6(6),5(7,R),6(7))].">
      <j1 rule="para" parents="896 2184"/>
      <j2 rule="rewrite" parents="6 5 6"/>
    </justification>
  </clause>

  <clause id="6077">
    <literal><![CDATA[
      f(x,y,f(z,u,f(z,v,f(z,x,y)))) = f(z,x,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),4446(a,1)),rewrite(5(1),5(4),5(4),5(5))].">
      <j1 rule="para" parents="5 4446"/>
      <j2 rule="rewrite" parents="5 5 5 5"/>
    </justification>
  </clause>

  <clause id="6597">
    <literal><![CDATA[
      f(x,y,f(y,z,f(u,x,y))) = f(y,z,f(u,x,y))
    ]]></literal>
    <justification jstring="[para(1106(a,1),5052(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="1106 5052"/>
      <j2 rule="rewrite" parents="5 5 5 5 5 6 205 5 5 5 6 19"/>
    </justification>
  </clause>

  <clause id="6889">
    <literal><![CDATA[
      f(x,y,f(z,f(x,y,u),f(y,v,f(x,y,u)))) = f(x,y,f(y,u,f(z,v,f(x,y,u))))
    ]]></literal>
    <justification jstring="[para(70(a,2),369(a,1)),rewrite(6(3),5(4,R),6(4),5(7),5(7),6(8))].">
      <j1 rule="para" parents="70 369"/>
      <j2 rule="rewrite" parents="6 5 6 5 5 6"/>
    </justification>
  </clause>

  <clause id="6921">
    <literal><![CDATA[
      f(x,f(x,y,z),f(u,y,z)) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(1004(a,1),70(a,2,3)),rewrite(5(3),5(3),3866(4),1004(3),5(4,R)),flip(a)].">
      <j1 rule="para" parents="1004 70"/>
      <j2 rule="rewrite" parents="5 5 3866 1004 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6930">
    <literal><![CDATA[
      f(x,f(y,x,z),f(u,x,z)) = f(y,x,f(u,x,z))
    ]]></literal>
    <justification jstring="[para(1106(a,1),70(a,2,3)),rewrite(5(3),6(3),884(5),5(4),5(5,R)),flip(a)].">
      <j1 rule="para" parents="1106 70"/>
      <j2 rule="rewrite" parents="5 6 884 5 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6992">
    <literal><![CDATA[
      f(x,f(x,y,z),f(u,y,f(y,v,z))) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(1021(a,1),70(a,2,3)),rewrite(5(5),5(5),3892(6),1021(4),5(5,R)),flip(a)].">
      <j1 rule="para" parents="1021 70"/>
      <j2 rule="rewrite" parents="5 5 3892 1021 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7128">
    <literal><![CDATA[
      f(f(x,y,z),f(u,x,y),f(v,z,f(u,x,y))) = f(v,f(x,y,z),f(u,x,y))
    ]]></literal>
    <justification jstring="[para(6921(a,1),1668(a,1,3)),rewrite(5(2),5(2),5(3,R),5(4),5(4),5(7)),flip(a)].">
      <j1 rule="para" parents="6921 1668"/>
      <j2 rule="rewrite" parents="5 5 5 5 5 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7401">
    <literal><![CDATA[
      f(x,f(x,y,z),f(y,u,z)) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(6992(a,1),3978(a,1,3)),rewrite(394(3),1005(3)),flip(a)].">
      <j1 rule="para" parents="6992 3978"/>
      <j2 rule="rewrite" parents="394 1005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7441">
    <literal><![CDATA[
      f(x,f(y,z,u),f(v,f(y,z,u),f(x,y,u))) = f(v,f(y,z,u),f(x,y,u))
    ]]></literal>
    <justification jstring="[para(7401(a,1),1675(a,2,3)),rewrite(5(4,R))].">
      <j1 rule="para" parents="7401 1675"/>
      <j2 rule="rewrite" parents="5"/>
    </justification>
  </clause>

  <clause id="7456">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,v,f(y,u,v))) = f(x,v,f(y,z,u))
    ]]></literal>
    <justification jstring="[para(7401(a,1),3978(a,1,3,3)),rewrite(5(2),5(2))].">
      <j1 rule="para" parents="7401 3978"/>
      <j2 rule="rewrite" parents="5 5"/>
    </justification>
  </clause>

  <clause id="7888">
    <literal><![CDATA[
      f(x,f(y,z,x),f(z,x,u)) = f(y,x,f(z,x,u))
    ]]></literal>
    <justification jstring="[para(896(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="896 74"/>
      <j2 rule="rewrite" parents="5 6 122 19 5 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7901">
    <literal><![CDATA[
      f(x,f(y,x,z),f(u,y,x)) = f(x,z,f(u,y,x))
    ]]></literal>
    <justification jstring="[para(74(a,1),1106(a,1)),rewrite(5(3),5(3),5(6),6(6),7128(6),5(5,R),6(5),19(5),5(5),5(5),6597(6))].">
      <j1 rule="para" parents="74 1106"/>
      <j2 rule="rewrite" parents="5 5 5 6 7128 5 6 19 5 5 6597"/>
    </justification>
  </clause>

  <clause id="7902">
    <literal><![CDATA[
      f(x,f(y,z,x),f(u,z,x)) = f(y,x,f(u,z,x))
    ]]></literal>
    <justification jstring="[para(1106(a,1),74(a,2,3)),rewrite(5(3),6(3),964(5),5(4),5(5,R)),flip(a)].">
      <j1 rule="para" parents="1106 74"/>
      <j2 rule="rewrite" parents="5 6 964 5 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8141">
    <literal><![CDATA[
      f(f(x,y,z),f(y,u,f(x,y,z)),f(v,f(y,z,u),f(x,y,z))) = f(v,f(x,y,z),f(x,y,f(y,z,u)))
    ]]></literal>
    <justification jstring="[para(6930(a,1),7888(a,1,2)),rewrite(5(3,R),6(3),5(4),5(4),5(6),5(9),5(9),5(11),604(12))].">
      <j1 rule="para" parents="6930 7888"/>
      <j2 rule="rewrite" parents="5 6 5 5 5 5 5 5 604"/>
    </justification>
  </clause>

  <clause id="8148">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,z,v)) = f(x,z,f(x,v,f(y,z,u)))
    ]]></literal>
    <justification jstring="[para(16(a,1),7901(a,1,2)),rewrite(5(1,R),6(1),5(3),6(3),3281(4),20(4),5(5),6(5)),flip(a)].">
      <j1 rule="para" parents="16 7901"/>
      <j2 rule="rewrite" parents="5 6 5 6 3281 20 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8153">
    <literal><![CDATA[
      f(f(x,y,z),f(y,u,f(x,y,z)),f(y,v,f(x,y,z))) = f(u,f(x,y,z),f(x,y,f(y,z,v)))
    ]]></literal>
    <justification jstring="[para(24(a,1),7901(a,2,3)),rewrite(6(3),5(5,R),6(5),5(8),5(8),5(10,R),6(10))].">
      <j1 rule="para" parents="24 7901"/>
      <j2 rule="rewrite" parents="6 5 6 5 5 5 6"/>
    </justification>
  </clause>

  <clause id="8248">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,u,f(y,z,x))) = f(y,z,f(y,u,x))
    ]]></literal>
    <justification jstring="[para(7901(a,1),70(a,2,3)),rewrite(5(1,R),6(1),5(2,R),6(2),5(3),6(3),802(4),6(2),57(3),6(1),20(3),5(3,R),6(3),5(4),6(4),5(6,R),6(6)),flip(a)].">
      <j1 rule="para" parents="7901 70"/>
      <j2 rule="rewrite" parents="5 6 5 6 5 6 802 6 57 6 20 5 6 5 6 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8418">
    <literal><![CDATA[
      f(f(x,y,z),f(x,z,u),f(y,v,f(y,w,f(x,y,z)))) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(1075(a,1),6077(a,1,3,3,3)),rewrite(1075(9))].">
      <j1 rule="para" parents="1075 6077"/>
      <j2 rule="rewrite" parents="1075"/>
    </justification>
  </clause>

  <clause id="8456">
    <literal><![CDATA[
      f(x,f(x,y,z),f(u,z,v)) = f(x,y,f(u,z,f(x,z,v)))
    ]]></literal>
    <justification jstring="[para(75(a,1),6(a,1)),flip(a)].">
      <j1 rule="para" parents="75 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8571">
    <literal><![CDATA[
      f(x,f(x,y,f(x,z,f(u,y,v))),f(w,f(u,y,v),f(x,y,z))) = f(x,z,f(u,y,f(x,y,v)))
    ]]></literal>
    <justification jstring="[para(75(a,1),1007(a,2)),rewrite(6(2),8148(3),6(5),5(6))].">
      <j1 rule="para" parents="75 1007"/>
      <j2 rule="rewrite" parents="6 8148 6 5"/>
    </justification>
  </clause>

  <clause id="8687">
    <literal><![CDATA[
      f(x,f(y,z,u),f(f(x,z,v),f(x,w,f(x,z,v)),f(v6,f(y,z,u),f(x,z,v)))) = f(x,v,f(y,z,f(x,z,u)))
    ]]></literal>
    <justification jstring="[para(75(a,1),3841(a,2)),rewrite(6(2),6(3),6(4),6(6),5(7))].">
      <j1 rule="para" parents="75 3841"/>
      <j2 rule="rewrite" parents="6 6 6 6 5"/>
    </justification>
  </clause>

  <clause id="8843">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,u,f(u,v,y)))) = f(x,u,y)
    ]]></literal>
    <justification jstring="[back_rewrite(4130),rewrite(8687(11))].">
      <j1 rule="back_rewrite" parents="4130"/>
      <j2 rule="rewrite" parents="8687"/>
    </justification>
  </clause>

  <clause id="9180">
    <literal><![CDATA[
      f(x,y,f(z,u,f(u,x,f(u,v,y)))) = f(u,x,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),8843(a,1)),rewrite(5(2,R),6(2),5(4),5(4),5(5,R),6(5))].">
      <j1 rule="para" parents="5 8843"/>
      <j2 rule="rewrite" parents="5 6 5 5 5 6"/>
    </justification>
  </clause>

  <clause id="9899">
    <literal><![CDATA[
      f(x,y,f(z,u,f(y,z,v))) = f(x,y,f(z,v,f(y,z,u)))
    ]]></literal>
    <justification jstring="[para(847(a,1),78(a,1,3,3)),rewrite(5(1),5(1),5(2,R),6(2),20(2),5(4),102(7))].">
      <j1 rule="para" parents="847 78"/>
      <j2 rule="rewrite" parents="5 5 5 6 20 5 102"/>
    </justification>
  </clause>

  <clause id="12063">
    <literal><![CDATA[
      f(x,y,f(y,z,f(u,x,z))) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(1675(a,1),125(a,1)),rewrite(5(3,R),6(3),20(3),15(3),5(3,R),6(3),369(5),6(3)),flip(a)].">
      <j1 rule="para" parents="1675 125"/>
      <j2 rule="rewrite" parents="5 6 20 15 5 6 369 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12149">
    <literal><![CDATA[
      f(x,y,f(x,z,f(u,z,y))) = f(x,z,y)
    ]]></literal>
    <justification jstring="[para(12063(a,1),503(a,2)),rewrite(5(3,R),6(3),21(5),5(4,R),6(4))].">
      <j1 rule="para" parents="12063 503"/>
      <j2 rule="rewrite" parents="5 6 21 5 6"/>
    </justification>
  </clause>

  <clause id="12628">
    <literal><![CDATA[
      f(x,y,f(z,y,f(x,u,f(x,v,y)))) = f(z,y,f(x,u,f(x,v,y)))
    ]]></literal>
    <justification jstring="[para(6597(a,1),133(a,1,2)),rewrite(5(1),5(3),5(5,R),6(5),5(6,R),6(6),964(7),5(4),5(6,R),6(6),5(7,R),6(7)),flip(a)].">
      <j1 rule="para" parents="6597 133"/>
      <j2 rule="rewrite" parents="5 5 5 6 5 6 964 5 5 6 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12709">
    <literal><![CDATA[
      f(x,f(y,z,x),f(x,u,f(y,z,v))) = f(x,u,f(y,z,x))
    ]]></literal>
    <justification jstring="[para(896(a,1),169(a,1,3,3)),rewrite(896(6)),flip(a)].">
      <j1 rule="para" parents="896 169"/>
      <j2 rule="rewrite" parents="896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12727">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,u,x)) = f(y,u,x)
    ]]></literal>
    <justification jstring="[para(1005(a,1),169(a,1,3)),rewrite(5(2),5(2),5(3),5(3),15(4),5(3),5(3)),flip(a)].">
      <j1 rule="para" parents="1005 169"/>
      <j2 rule="rewrite" parents="5 5 5 5 15 5 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12752">
    <literal><![CDATA[
      f(x,f(y,z,f(y,u,v)),f(y,v,x)) = f(y,v,x)
    ]]></literal>
    <justification jstring="[para(1015(a,1),169(a,1,3)),rewrite(5(3),5(3),5(4),5(4),15(5),5(4),5(4)),flip(a)].">
      <j1 rule="para" parents="1015 169"/>
      <j2 rule="rewrite" parents="5 5 5 5 15 5 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12961">
    <literal><![CDATA[
      f(x,f(y,z,x),f(z,u,x)) = f(y,x,f(z,u,x))
    ]]></literal>
    <justification jstring="[para(12727(a,1),74(a,2,3)),rewrite(5(3),6(3),964(5),5(4),5(5,R)),flip(a)].">
      <j1 rule="para" parents="12727 74"/>
      <j2 rule="rewrite" parents="5 6 964 5 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12999">
    <literal><![CDATA[
      f(f(x,y,z),f(u,v,x),f(u,v,f(u,x,w))) = f(w,f(u,v,x),f(u,v,f(x,y,f(u,x,z))))
    ]]></literal>
    <justification jstring="[para(38(a,1),12961(a,2,3)),rewrite(5(3,R),6(3),670(7))].">
      <j1 rule="para" parents="38 12961"/>
      <j2 rule="rewrite" parents="5 6 670"/>
    </justification>
  </clause>

  <clause id="13044">
    <literal><![CDATA[
      f(f(x,y,f(x,z,u)),f(x,u,v),f(v,f(x,u,v),f(v,w,f(x,y,f(x,z,u))))) = f(x,u,v)
    ]]></literal>
    <justification jstring="[para(12752(a,1),794(a,2)),rewrite(6(7))].">
      <j1 rule="para" parents="12752 794"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="13589">
    <literal><![CDATA[
      f(x,f(y,z,x),f(u,y,x)) = f(u,x,f(y,z,x))
    ]]></literal>
    <justification jstring="[para(19(a,1),170(a,1,2)),rewrite(7441(5),19(5))].">
      <j1 rule="para" parents="19 170"/>
      <j2 rule="rewrite" parents="7441 19"/>
    </justification>
  </clause>

  <clause id="13734">
    <literal><![CDATA[
      f(x,f(y,z,x),f(y,x,u)) = f(x,u,f(y,z,x))
    ]]></literal>
    <justification jstring="[para(13589(a,1),5(a,2)),rewrite(5(2),5(2),5(3),5(5,R),6(5))].">
      <j1 rule="para" parents="13589 5"/>
      <j2 rule="rewrite" parents="5 5 5 5 6"/>
    </justification>
  </clause>

  <clause id="13752">
    <literal><![CDATA[
      f(x,f(y,z,u),f(z,u,f(y,z,v))) = f(v,f(y,z,u),f(y,z,f(z,u,x)))
    ]]></literal>
    <justification jstring="[para(815(a,1),13589(a,2,3)),rewrite(5(5,R),6(5),8153(6)),flip(a)].">
      <j1 rule="para" parents="815 13589"/>
      <j2 rule="rewrite" parents="5 6 8153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14701">
    <literal><![CDATA[
      f(f(x,y,z),f(y,u,v),f(x,y,z)) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(1075(a,1),320(a,1,3)),rewrite(8418(10))].">
      <j1 rule="para" parents="1075 320"/>
      <j2 rule="rewrite" parents="8418"/>
    </justification>
  </clause>

  <clause id="14835">
    <literal><![CDATA[
      f(x,f(y,z,f(y,x,u)),f(y,v,f(y,x,w))) = f(y,x,f(x,f(y,v,w),f(y,z,u)))
    ]]></literal>
    <justification jstring="[para(81(a,1),320(a,1)),rewrite(29(5),6(7)),flip(a)].">
      <j1 rule="para" parents="81 320"/>
      <j2 rule="rewrite" parents="29 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15028">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,u,f(y,z,f(x,v,f(y,z,u))))) = f(y,u,f(y,z,f(x,v,f(y,z,u))))
    ]]></literal>
    <justification jstring="[para(14701(a,1),795(a,1,3)),rewrite(6(3),5(4,R),6(4),639(4),6(7),5(8,R),6(8),639(8),15(9),6(7),5(8,R),6(8),639(8),6(10)),flip(a)].">
      <j1 rule="para" parents="14701 795"/>
      <j2 rule="rewrite" parents="6 5 6 639 6 5 6 639 15 6 5 6 639 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15182">
    <literal><![CDATA[
      f(x,f(y,x,z),f(z,u,v)) = f(y,x,f(z,u,f(x,z,v)))
    ]]></literal>
    <justification jstring="[para(321(a,1),6(a,1)),rewrite(5(1,R),6(1),6(4)),flip(a)].">
      <j1 rule="para" parents="321 6"/>
      <j2 rule="rewrite" parents="5 6 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15206">
    <literal><![CDATA[
      f(f(x,y,z),f(u,v,f(x,y,z)),f(x,y,f(x,z,f(u,v,f(x,y,z))))) = f(x,z,f(x,y,f(u,v,f(x,y,z))))
    ]]></literal>
    <justification jstring="[para(321(a,1),40(a,2)),rewrite(5(3),5(3),5(6),5(6),5(7,R),7902(7),639(5),5(6,R),6(6),15028(6),5(7),5(7),5(9),5(9),6(10)),flip(a)].">
      <j1 rule="para" parents="321 40"/>
      <j2 rule="rewrite" parents="5 5 5 5 5 7902 639 5 6 15028 5 5 5 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15230">
    <literal><![CDATA[
      f(f(x,y,z),f(x,u,v),f(v,f(x,u,v),f(v,w,f(x,y,z)))) = f(u,v,f(x,y,f(x,z,v)))
    ]]></literal>
    <justification jstring="[para(321(a,1),794(a,2)),rewrite(5(2,R),6(2),5(3,R),6(3),6(5),6(8))].">
      <j1 rule="para" parents="321 794"/>
      <j2 rule="rewrite" parents="5 6 5 6 6 6"/>
    </justification>
  </clause>

  <clause id="15244">
    <literal><![CDATA[
      f(f(x,y,z),f(u,v,w),f(x,y,z)) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(321(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="321 54"/>
      <j2 rule="rewrite" parents="5 5 19 20 5 15 6 4 5 15"/>
    </justification>
  </clause>

  <clause id="15268">
    <literal><![CDATA[
      f(f(x,y,z),f(x,u,v),f(v,f(x,u,v),f(w,f(x,y,z),f(v,v6,f(x,y,z))))) = f(u,v,f(x,y,f(x,z,v)))
    ]]></literal>
    <justification jstring="[para(321(a,1),2184(a,2)),rewrite(5(2,R),6(2),5(3,R),6(3),6(6),5(7,R),6(7),6(10))].">
      <j1 rule="para" parents="321 2184"/>
      <j2 rule="rewrite" parents="5 6 5 6 6 5 6 6"/>
    </justification>
  </clause>

  <clause id="15327">
    <literal><![CDATA[
      f(x,f(y,z,u),f(v,f(y,z,u),f(y,x,f(y,z,u)))) = f(y,u,f(y,z,f(x,v,f(y,z,u))))
    ]]></literal>
    <justification jstring="[para(321(a,1),113(a,1)),rewrite(5(3),5(3),5(5),5(5),6(6),15206(8),5(6),5(6),5(10),5(10),5(11,R),6(11),5(12,R),6(12),7888(12)),flip(a)].">
      <j1 rule="para" parents="321 113"/>
      <j2 rule="rewrite" parents="5 5 5 5 6 15206 5 5 5 5 5 6 5 6 7888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15370">
    <literal><![CDATA[
      f(x,y,f(z,u,f(z,y,f(z,v,x)))) = f(z,x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(13044),rewrite(15230(9),6(2))].">
      <j1 rule="back_rewrite" parents="13044"/>
      <j2 rule="rewrite" parents="15230 6"/>
    </justification>
  </clause>

  <clause id="15371">
    <literal><![CDATA[
      f(x,y,f(z,x,f(z,u,y))) = f(z,x,y)
    ]]></literal>
    <justification jstring="[back_rewrite(5381),rewrite(15268(9))].">
      <j1 rule="back_rewrite" parents="5381"/>
      <j2 rule="rewrite" parents="15268"/>
    </justification>
  </clause>

  <clause id="15456">
    <literal><![CDATA[
      f(x,f(y,z,u),f(v,f(y,z,u),f(x,w,f(y,z,u)))) = f(v,f(y,z,u),f(x,w,f(y,z,u)))
    ]]></literal>
    <justification jstring="[para(15244(a,1),795(a,1,3)),rewrite(6(3),5(4,R),6(4),6(7),5(8,R),6(8),15(9),6(7),5(8,R),6(8),6(10)),flip(a)].">
      <j1 rule="para" parents="15244 795"/>
      <j2 rule="rewrite" parents="6 5 6 6 5 6 15 6 5 6 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15461">
    <literal><![CDATA[
      f(f(x,y,z),f(u,v,w),f(x,y,f(x,z,f(u,v,w)))) = f(x,y,f(x,z,f(u,v,w)))
    ]]></literal>
    <justification jstring="[para(15244(a,1),70(a,1)),rewrite(5(2),5(2),5(6),5(6),5(10),6(10),5(11,R),6(11),12628(11)),flip(a)].">
      <j1 rule="para" parents="15244 70"/>
      <j2 rule="rewrite" parents="5 5 5 5 5 6 5 6 12628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15462">
    <literal><![CDATA[
      f(x,f(x,y,z),f(u,v,w)) = f(x,y,f(x,z,f(u,v,w)))
    ]]></literal>
    <justification jstring="[para(15244(a,1),70(a,2,3)),rewrite(5(4),5(4),15461(6),5(6,R)),flip(a)].">
      <j1 rule="para" parents="15244 70"/>
      <j2 rule="rewrite" parents="5 5 15461 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15466">
    <literal><![CDATA[
      f(f(x,y,z),f(u,v,w),f(x,y,f(y,z,f(u,v,w)))) = f(y,f(x,y,z),f(u,v,w))
    ]]></literal>
    <justification jstring="[para(15244(a,1),74(a,2,3)),rewrite(5(4),5(4),5(9,R))].">
      <j1 rule="para" parents="15244 74"/>
      <j2 rule="rewrite" parents="5 5 5"/>
    </justification>
  </clause>

  <clause id="15491">
    <literal><![CDATA[
      f(x,f(y,x,z),f(u,v,w)) = f(y,x,f(x,z,f(u,v,w)))
    ]]></literal>
    <justification jstring="[para(15244(a,1),220(a,1)),rewrite(6(2),6(6),5(10),6(10),15466(10),19(8)),flip(a)].">
      <j1 rule="para" parents="15244 220"/>
      <j2 rule="rewrite" parents="6 6 5 6 15466 19"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15610">
    <literal><![CDATA[
      f(x,y,f(x,z,f(u,f(y,v,w),f(x,y,f(x,z,f(y,v,w)))))) = f(x,z,f(y,v,f(x,y,w)))
    ]]></literal>
    <justification jstring="[back_rewrite(8571),rewrite(5(1,R),6(1),5(4,R),6(4),15462(7),8456(6),394(4),5(9,R),6(9))].">
      <j1 rule="back_rewrite" parents="8571"/>
      <j2 rule="rewrite" parents="5 6 5 6 15462 8456 394 5 6"/>
    </justification>
  </clause>

  <clause id="15751">
    <literal><![CDATA[
      f(x,y,f(x,z,f(u,v,f(x,y,f(x,z,v))))) = f(x,v,f(x,y,z))
    ]]></literal>
    <justification jstring="[back_rewrite(1857),rewrite(15462(5))].">
      <j1 rule="back_rewrite" parents="1857"/>
      <j2 rule="rewrite" parents="15462"/>
    </justification>
  </clause>

  <clause id="15765">
    <literal><![CDATA[
      f(x,f(y,z,u),f(v,y,f(y,z,u))) = f(y,u,f(y,z,f(v,x,f(y,z,u))))
    ]]></literal>
    <justification jstring="[back_rewrite(15327),rewrite(5(4,R),6(4),15456(6))].">
      <j1 rule="back_rewrite" parents="15327"/>
      <j2 rule="rewrite" parents="5 6 15456"/>
    </justification>
  </clause>

  <clause id="15773">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,y,v)) = f(x,v,f(y,z,f(x,y,u)))
    ]]></literal>
    <justification jstring="[back_rewrite(15610),rewrite(15751(7))].">
      <j1 rule="back_rewrite" parents="15610"/>
      <j2 rule="rewrite" parents="15751"/>
    </justification>
  </clause>

  <clause id="15801">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,z,u)) = f(x,z,u)
    ]]></literal>
    <justification jstring="[para(15370(a,1),896(a,1,2)),rewrite(5(2),5(4))].">
      <j1 rule="para" parents="15370 896"/>
      <j2 rule="rewrite" parents="5 5"/>
    </justification>
  </clause>

  <clause id="15824">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,y,u)) = f(x,y,u)
    ]]></literal>
    <justification jstring="[para(15370(a,1),2752(a,1,2))].">
      <j1 rule="para" parents="15370 2752"/>
    </justification>
  </clause>

  <clause id="15852">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,y,z)) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(15370(a,1),5129(a,1,2)),rewrite(5(2,R),6(2),5(4,R),6(4))].">
      <j1 rule="para" parents="15370 5129"/>
      <j2 rule="rewrite" parents="5 6 5 6"/>
    </justification>
  </clause>

  <clause id="16533">
    <literal><![CDATA[
      f(x,f(y,z,u),f(u,x,v)) = f(x,v,f(y,u,f(z,u,x)))
    ]]></literal>
    <justification jstring="[para(323(a,1),5(a,2)),rewrite(5(2,R),6(2),5(3),5(4),5(4))].">
      <j1 rule="para" parents="323 5"/>
      <j2 rule="rewrite" parents="5 6 5 5 5"/>
    </justification>
  </clause>

  <clause id="16618">
    <literal><![CDATA[
      f(x,f(y,z,x),f(y,u,x)) = f(y,x,f(u,z,x))
    ]]></literal>
    <justification jstring="[para(847(a,2),323(a,2)),rewrite(15(2),6(2)),flip(a)].">
      <j1 rule="para" parents="847 323"/>
      <j2 rule="rewrite" parents="15 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16737">
    <literal><![CDATA[
      f(f(x,y,z),f(u,f(x,y,z),f(z,u,v)),f(w,f(z,u,v),f(u,v6,f(z,u,v)))) = f(u,v,f(x,z,f(y,z,u)))
    ]]></literal>
    <justification jstring="[para(323(a,1),5250(a,2)),rewrite(5(3,R),6(3),5(5,R),6(5),5(6,R),6(6),6(7),5(8,R),6(8),5(10),5(10))].">
      <j1 rule="para" parents="323 5250"/>
      <j2 rule="rewrite" parents="5 6 5 6 5 6 6 5 6 5 5"/>
    </justification>
  </clause>

  <clause id="16964">
    <literal><![CDATA[
      f(f(x,y,z),f(x,z,u),f(v,f(x,z,u),f(x,z,f(y,z,u)))) = f(v,f(x,z,u),f(z,u,f(x,y,z)))
    ]]></literal>
    <justification jstring="[para(16618(a,1),6597(a,1,3,3)),rewrite(6(2),6(3),5(4),5(4),5(6,R),6(6),6(8),6(10),13734(11),5(11,R),6(11))].">
      <j1 rule="para" parents="16618 6597"/>
      <j2 rule="rewrite" parents="6 6 5 5 5 6 6 6 13734 5 6"/>
    </justification>
  </clause>

  <clause id="18416">
    <literal><![CDATA[
      f(x,y,f(z,u,f(y,u,f(x,z,u)))) = f(x,y,u)
    ]]></literal>
    <justification jstring="[para(577(a,1),9180(a,1,3)),rewrite(5(1),6(1),5(2,R),6(2),5(5),5(5))].">
      <j1 rule="para" parents="577 9180"/>
      <j2 rule="rewrite" parents="5 6 5 6 5 5"/>
    </justification>
  </clause>

  <clause id="18567">
    <literal><![CDATA[
      f(x,y,f(z,y,f(x,u,z))) = f(x,z,y)
    ]]></literal>
    <justification jstring="[para(18416(a,1),6(a,2)),rewrite(5(2,R),6(2),6597(3),6(3),6(4))].">
      <j1 rule="para" parents="18416 6"/>
      <j2 rule="rewrite" parents="5 6 6597 6 6"/>
    </justification>
  </clause>

  <clause id="19342">
    <literal><![CDATA[
      f(x,f(y,x,f(y,z,u)),f(z,u,v)) = f(y,x,f(z,u,v))
    ]]></literal>
    <justification jstring="[para(831(a,1),74(a,2,3)),rewrite(5(4,R),1498(5),19(4),5(6,R)),flip(a)].">
      <j1 rule="para" parents="831 74"/>
      <j2 rule="rewrite" parents="5 1498 19 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19365">
    <literal><![CDATA[
      f(x,f(y,z,u),f(v,x,f(v,y,z))) = f(v,x,f(y,z,u))
    ]]></literal>
    <justification jstring="[para(831(a,1),220(a,2,3)),rewrite(1515(5),19(4)),flip(a)].">
      <j1 rule="para" parents="831 220"/>
      <j2 rule="rewrite" parents="1515 19"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19704">
    <literal><![CDATA[
      f(x,f(y,z,f(x,u,v)),f(y,z,f(y,f(x,u,v),f(x,w,f(x,y,v6))))) = f(y,z,f(x,v,f(x,y,u)))
    ]]></literal>
    <justification jstring="[para(904(a,2),2184(a,2)),rewrite(5(1,R),6(1),5(3,R),6(3),5(5,R),6(5),15462(7),5(9))].">
      <j1 rule="para" parents="904 2184"/>
      <j2 rule="rewrite" parents="5 6 5 6 5 6 15462 5"/>
    </justification>
  </clause>

  <clause id="20060">
    <literal><![CDATA[
      f(x,f(y,z,u),f(v,z,f(v,x,y))) = f(v,x,f(y,z,u))
    ]]></literal>
    <justification jstring="[para(1066(a,1),2184(a,2)),rewrite(5(7,R),6(7),15462(9),19704(10),5(6,R),6(6))].">
      <j1 rule="para" parents="1066 2184"/>
      <j2 rule="rewrite" parents="5 6 15462 19704 5 6"/>
    </justification>
  </clause>

  <clause id="20775">
    <literal><![CDATA[
      f(x,y,f(x,z,f(x,f(y,u,v),f(u,v,w)))) = f(x,z,f(x,y,f(u,v,w)))
    ]]></literal>
    <justification jstring="[para(1074(a,1),18(a,1,3)),rewrite(5(4)),flip(a)].">
      <j1 rule="para" parents="1074 18"/>
      <j2 rule="rewrite" parents="5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20924">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,y,f(x,v,w))) = f(x,y,f(x,v,f(x,w,f(y,z,u))))
    ]]></literal>
    <justification jstring="[para(1091(a,2),7901(a,1,2)),rewrite(5(2),5(2),5(4),6(4),15462(5),15462(4),20(3),5(7),6(7),2520(8))].">
      <j1 rule="para" parents="1091 7901"/>
      <j2 rule="rewrite" parents="5 5 5 6 15462 15462 20 5 6 2520"/>
    </justification>
  </clause>

  <clause id="21536">
    <literal><![CDATA[
      f(x,y,f(x,f(y,z,u),f(v,z,f(x,y,u)))) = f(x,y,f(v,z,f(x,y,u)))
    ]]></literal>
    <justification jstring="[para(26(a,1),1182(a,1,3)),rewrite(6(4),20(6))].">
      <j1 rule="para" parents="26 1182"/>
      <j2 rule="rewrite" parents="6 20"/>
    </justification>
  </clause>

  <clause id="22733">
    <literal><![CDATA[
      f(x,y,f(y,z,f(x,u,f(y,z,v)))) = f(x,y,f(z,u,f(y,z,v)))
    ]]></literal>
    <justification jstring="[para(26(a,1),1502(a,1,3)),rewrite(6(4),21536(5))].">
      <j1 rule="para" parents="26 1502"/>
      <j2 rule="rewrite" parents="6 21536"/>
    </justification>
  </clause>

  <clause id="24883">
    <literal><![CDATA[
      f(x,y,f(z,y,f(u,z,x))) = f(z,x,y)
    ]]></literal>
    <justification jstring="[para(3866(a,1),8248(a,1,3)),rewrite(5(2),6(2),5(3),5(3),15(4),5(3,R),6(3),5(4,R),6(4)),flip(a)].">
      <j1 rule="para" parents="3866 8248"/>
      <j2 rule="rewrite" parents="5 6 5 5 15 5 6 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25820">
    <literal><![CDATA[
      f(x,y,f(y,f(z,u,v),f(z,u,f(z,x,v)))) = f(x,y,f(z,u,v))
    ]]></literal>
    <justification jstring="[para(1675(a,1),162(a,1)),rewrite(5(5,R),6(5),20(5),15(5),5(5,R),6(5),369(8),6(6)),flip(a)].">
      <j1 rule="para" parents="1675 162"/>
      <j2 rule="rewrite" parents="5 6 20 15 5 6 369 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25837">
    <literal><![CDATA[
      f(x,f(y,x,z),f(y,u,v)) = f(x,z,f(y,u,f(y,v,x)))
    ]]></literal>
    <justification jstring="[para(5(a,1),15182(a,1)),rewrite(5(2),6(2),5(3,R),5(4),5(4),5(6,R),6(6))].">
      <j1 rule="para" parents="5 15182"/>
      <j2 rule="rewrite" parents="5 6 5 5 5 5 6"/>
    </justification>
  </clause>

  <clause id="25903">
    <literal><![CDATA[
      f(x,y,f(x,z,f(u,v,f(x,z,y)))) = f(x,y,f(z,u,f(x,z,v)))
    ]]></literal>
    <justification jstring="[para(15182(a,1),1671(a,2)),rewrite(5(2),5(2),5(3),5(3),15462(5),20924(6),6(4),20775(6),5(7,R),6(7))].">
      <j1 rule="para" parents="15182 1671"/>
      <j2 rule="rewrite" parents="5 5 5 5 15462 20924 6 20775 5 6"/>
    </justification>
  </clause>

  <clause id="25932">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,v,f(y,z,u))) = f(y,u,f(x,z,f(y,z,v)))
    ]]></literal>
    <justification jstring="[back_rewrite(15765),rewrite(5(3,R),6(3),5(6,R),6(6),25903(8),5(6,R),6(6))].">
      <j1 rule="back_rewrite" parents="15765"/>
      <j2 rule="rewrite" parents="5 6 5 6 25903 5 6"/>
    </justification>
  </clause>

  <clause id="25958">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,u,f(y,z,v))) = f(y,u,f(x,z,f(y,z,v)))
    ]]></literal>
    <justification jstring="[back_rewrite(1717),rewrite(5(6,R),6(6),25903(8),5(6,R),6(6))].">
      <j1 rule="back_rewrite" parents="1717"/>
      <j2 rule="rewrite" parents="5 6 25903 5 6"/>
    </justification>
  </clause>

  <clause id="26078">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,z,f(v,y,u))) = f(y,u,f(v,z,f(y,z,x)))
    ]]></literal>
    <justification jstring="[back_rewrite(966),rewrite(25932(4)),flip(a)].">
      <j1 rule="back_rewrite" parents="966"/>
      <j2 rule="rewrite" parents="25932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26105">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,v,f(y,z,v)))) = f(x,y,f(z,v,u))
    ]]></literal>
    <justification jstring="[back_rewrite(25820),rewrite(5(2,R),6(2),26078(4),5(1))].">
      <j1 rule="back_rewrite" parents="25820"/>
      <j2 rule="rewrite" parents="5 6 26078 5"/>
    </justification>
  </clause>

  <clause id="26150">
    <literal><![CDATA[
      f(f(x,y,z),f(x,u,v),f(u,v,f(x,u,w))) = f(w,f(x,u,v),f(u,v,f(x,y,f(x,z,u))))
    ]]></literal>
    <justification jstring="[back_rewrite(12999),rewrite(5(2),5(3,R),6(3),5(6),5(7),5(7))].">
      <j1 rule="back_rewrite" parents="12999"/>
      <j2 rule="rewrite" parents="5 5 6 5 5 5"/>
    </justification>
  </clause>

  <clause id="26264">
    <literal><![CDATA[
      f(x,f(y,z,f(x,y,u)),f(v,w,v6)) = f(x,y,f(x,f(y,z,u),f(v,w,v6)))
    ]]></literal>
    <justification jstring="[para(16(a,2),15462(a,1,2))].">
      <j1 rule="para" parents="16 15462"/>
    </justification>
  </clause>

  <clause id="26268">
    <literal><![CDATA[
      f(x,f(y,z,f(x,z,u)),f(v,w,v6)) = f(x,z,f(x,f(y,z,u),f(v,w,v6)))
    ]]></literal>
    <justification jstring="[para(24(a,1),15462(a,1,2))].">
      <j1 rule="para" parents="24 15462"/>
    </justification>
  </clause>

  <clause id="26977">
    <literal><![CDATA[
      f(f(x,y,z),f(y,u,f(x,y,z)),f(v,w,v6)) = f(x,y,f(y,z,f(u,f(v,w,v6),f(x,y,z))))
    ]]></literal>
    <justification jstring="[para(15491(a,2),15491(a,1)),rewrite(6(3),5(8,R))].">
      <j1 rule="para" parents="15491 15491"/>
      <j2 rule="rewrite" parents="6 5"/>
    </justification>
  </clause>

  <clause id="27034">
    <literal><![CDATA[
      f(x,y,f(y,z,f(u,f(y,z,v),f(x,y,z)))) = f(u,f(x,y,z),f(x,y,f(y,z,v)))
    ]]></literal>
    <justification jstring="[back_rewrite(8141),rewrite(26977(7),6(5),1110(5))].">
      <j1 rule="back_rewrite" parents="8141"/>
      <j2 rule="rewrite" parents="26977 6 1110"/>
    </justification>
  </clause>

  <clause id="27174">
    <literal><![CDATA[
      f(x,y,f(x,z,f(y,u,f(x,z,v)))) = f(x,f(z,u,v),f(x,y,z))
    ]]></literal>
    <justification jstring="[para(15773(a,2),1182(a,2)),rewrite(26264(5),21536(5),6(6))].">
      <j1 rule="para" parents="15773 1182"/>
      <j2 rule="rewrite" parents="26264 21536 6"/>
    </justification>
  </clause>

  <clause id="28447">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,v,f(x,y,z))) = f(v,f(x,y,z),f(x,y,f(y,z,u)))
    ]]></literal>
    <justification jstring="[para(1519(a,1),16533(a,2,3)),rewrite(5(1,R),6(1),5(3),6(3),5(4,R),6(4),6(6),5(7,R),6(7),25932(7),5(4,R),25837(4),6(2),20(3),5(5,R),6(5),5(7),5(7),5(8),5(8))].">
      <j1 rule="para" parents="1519 16533"/>
      <j2 rule="rewrite" parents="5 6 5 6 5 6 6 5 6 25932 5 25837 6 20 5 6 5 5 5 5"/>
    </justification>
  </clause>

  <clause id="29680">
    <literal><![CDATA[
      f(x,f(y,x,z),f(u,y,v)) = f(x,z,f(u,y,f(y,v,x)))
    ]]></literal>
    <justification jstring="[para(75(a,1),19342(a,2)),rewrite(4(3),5(3),4(3),5(2),5(3,R),5(4),5(4))].">
      <j1 rule="para" parents="75 19342"/>
      <j2 rule="rewrite" parents="4 5 4 5 5 5 5"/>
    </justification>
  </clause>

  <clause id="29693">
    <literal><![CDATA[
      f(f(x,y,z),f(y,z,u),f(y,z,v)) = f(u,f(x,y,z),f(y,z,v))
    ]]></literal>
    <justification jstring="[para(15801(a,1),19342(a,1,2)),rewrite(5(2),5(2))].">
      <j1 rule="para" parents="15801 19342"/>
      <j2 rule="rewrite" parents="5 5"/>
    </justification>
  </clause>

  <clause id="29695">
    <literal><![CDATA[
      f(f(x,y,z),f(x,z,u),f(x,z,v)) = f(u,f(x,y,z),f(x,z,v))
    ]]></literal>
    <justification jstring="[para(15824(a,1),19342(a,1,2)),rewrite(5(2),5(2))].">
      <j1 rule="para" parents="15824 19342"/>
      <j2 rule="rewrite" parents="5 5"/>
    </justification>
  </clause>

  <clause id="29696">
    <literal><![CDATA[
      f(f(x,y,z),f(x,y,u),f(x,y,v)) = f(u,f(x,y,z),f(x,y,v))
    ]]></literal>
    <justification jstring="[para(15852(a,1),19342(a,1,2)),rewrite(5(2),5(2))].">
      <j1 rule="para" parents="15852 19342"/>
      <j2 rule="rewrite" parents="5 5"/>
    </justification>
  </clause>

  <clause id="29827">
    <literal><![CDATA[
      f(x,f(y,z,u),f(z,u,v)) = f(v,f(y,z,u),f(z,u,x))
    ]]></literal>
    <justification jstring="[para(15801(a,1),19365(a,1,3)),rewrite(5(3),5(3),29693(4))].">
      <j1 rule="para" parents="15801 19365"/>
      <j2 rule="rewrite" parents="5 5 29693"/>
    </justification>
  </clause>

  <clause id="29828">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,u,v)) = f(v,f(y,z,u),f(y,u,x))
    ]]></literal>
    <justification jstring="[para(15824(a,1),19365(a,1,3)),rewrite(5(3),5(3),29695(4))].">
      <j1 rule="para" parents="15824 19365"/>
      <j2 rule="rewrite" parents="5 5 29695"/>
    </justification>
  </clause>

  <clause id="29829">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,z,v)) = f(v,f(y,z,u),f(y,z,x))
    ]]></literal>
    <justification jstring="[para(15852(a,1),19365(a,1,3)),rewrite(5(3),5(3),29696(4))].">
      <j1 rule="para" parents="15852 19365"/>
      <j2 rule="rewrite" parents="5 5 29696"/>
    </justification>
  </clause>

  <clause id="29874">
    <literal><![CDATA[
      f(x,f(y,z,u),f(v,y,z)) = f(v,f(y,z,u),f(y,z,x))
    ]]></literal>
    <justification jstring="[para(5(a,2),29827(a,1,2)),rewrite(5(4),5(4),5(5)),flip(a)].">
      <j1 rule="para" parents="5 29827"/>
      <j2 rule="rewrite" parents="5 5 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29875">
    <literal><![CDATA[
      f(x,f(y,z,u),f(v,z,u)) = f(y,f(v,z,u),f(z,u,x))
    ]]></literal>
    <justification jstring="[para(29827(a,1),6(a,1)),rewrite(5(4)),flip(a)].">
      <j1 rule="para" parents="29827 6"/>
      <j2 rule="rewrite" parents="5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29876">
    <literal><![CDATA[
      f(x,f(y,z,u),f(v,y,z)) = f(v,f(y,z,x),f(y,z,u))
    ]]></literal>
    <justification jstring="[para(29827(a,1),6(a,2)),rewrite(5(2),5(2),5(4),5(4),5(5)),flip(a)].">
      <j1 rule="para" parents="29827 6"/>
      <j2 rule="rewrite" parents="5 5 5 5 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29885">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,v,z)) = f(u,f(y,v,z),f(y,z,x))
    ]]></literal>
    <justification jstring="[para(19(a,1),29827(a,2,3)),rewrite(5(2),5(2),29695(4),5(4),5(4)),flip(a)].">
      <j1 rule="para" parents="19 29827"/>
      <j2 rule="rewrite" parents="5 5 29695 5 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29886">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,z,v)) = f(v,f(y,z,x),f(y,z,u))
    ]]></literal>
    <justification jstring="[para(20(a,1),29827(a,2,3)),rewrite(5(2),5(2),29696(4),5(4),5(4))].">
      <j1 rule="para" parents="20 29827"/>
      <j2 rule="rewrite" parents="5 5 29696 5 5"/>
    </justification>
  </clause>

  <clause id="30000">
    <literal><![CDATA[
      f(x,f(y,z,u),f(v,z,u)) = f(v,f(z,u,x),f(y,z,u))
    ]]></literal>
    <justification jstring="[para(29827(a,1),1005(a,2)),rewrite(5(5,R),12149(7),5(5)),flip(a)].">
      <j1 rule="para" parents="29827 1005"/>
      <j2 rule="rewrite" parents="5 12149 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30106">
    <literal><![CDATA[
      f(f(x,y,z),f(y,z,u),f(x,z,u)) = f(x,z,f(y,z,u))
    ]]></literal>
    <justification jstring="[para(29827(a,1),170(a,1)),rewrite(5(3))].">
      <j1 rule="para" parents="29827 170"/>
      <j2 rule="rewrite" parents="5"/>
    </justification>
  </clause>

  <clause id="30208">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,v,f(x,z,f(y,z,u)))) = f(u,f(y,z,v),f(x,y,z))
    ]]></literal>
    <justification jstring="[para(29827(a,1),7456(a,2)),rewrite(5(2),5(2),5(3),5(3),25932(5),5(6),5(6),5(7))].">
      <j1 rule="para" parents="29827 7456"/>
      <j2 rule="rewrite" parents="5 5 5 5 25932 5 5 5"/>
    </justification>
  </clause>

  <clause id="30415">
    <literal><![CDATA[
      f(x,f(y,z,u),f(z,v,u)) = f(y,f(z,v,u),f(z,u,x))
    ]]></literal>
    <justification jstring="[para(29828(a,1),6(a,1)),rewrite(5(4)),flip(a)].">
      <j1 rule="para" parents="29828 6"/>
      <j2 rule="rewrite" parents="5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30445">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,u,f(x,y,v))) = f(x,y,f(v,f(y,z,u),f(x,y,u)))
    ]]></literal>
    <justification jstring="[para(29828(a,1),26(a,2,3)),rewrite(5(6))].">
      <j1 rule="para" parents="29828 26"/>
      <j2 rule="rewrite" parents="5"/>
    </justification>
  </clause>

  <clause id="30543">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,v,f(x,y,u))) = f(x,y,f(v,f(y,z,u),f(x,y,u)))
    ]]></literal>
    <justification jstring="[para(29828(a,1),76(a,2,3)),rewrite(5(2,R),6(2),5(6),5(8,R),6(8))].">
      <j1 rule="para" parents="29828 76"/>
      <j2 rule="rewrite" parents="5 6 5 5 6"/>
    </justification>
  </clause>

  <clause id="30622">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,v,f(y,u,f(x,y,w)))) = f(x,y,f(x,v,f(w,f(y,z,u),f(x,y,u))))
    ]]></literal>
    <justification jstring="[para(29828(a,1),141(a,2,3,3)),rewrite(5(7))].">
      <j1 rule="para" parents="29828 141"/>
      <j2 rule="rewrite" parents="5"/>
    </justification>
  </clause>

  <clause id="30875">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,v,f(x,y,z))) = f(x,y,f(v,f(y,z,u),f(x,y,z)))
    ]]></literal>
    <justification jstring="[para(29829(a,1),76(a,2,3)),rewrite(5(2,R),6(2),5(6),5(8,R),6(8))].">
      <j1 rule="para" parents="29829 76"/>
      <j2 rule="rewrite" parents="5 6 5 5 6"/>
    </justification>
  </clause>

  <clause id="30960">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,z,f(x,v,f(x,y,w)))) = f(x,y,f(f(x,v,w),f(y,z,u),f(x,y,z)))
    ]]></literal>
    <justification jstring="[para(29829(a,1),131(a,2,3)),rewrite(5(8))].">
      <j1 rule="para" parents="29829 131"/>
      <j2 rule="rewrite" parents="5"/>
    </justification>
  </clause>

  <clause id="30979">
    <literal><![CDATA[
      f(x,f(y,z,u),f(v,y,z)) = f(u,f(y,z,x),f(v,y,z))
    ]]></literal>
    <justification jstring="[para(29829(a,1),4720(a,2)),rewrite(5(4),5(4),25958(5),30208(5),5(5))].">
      <j1 rule="para" parents="29829 4720"/>
      <j2 rule="rewrite" parents="5 5 25958 30208 5"/>
    </justification>
  </clause>

  <clause id="31092">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,z,f(z,u,v))) = f(y,z,f(x,f(z,u,v),f(y,z,u)))
    ]]></literal>
    <justification jstring="[back_rewrite(28447),rewrite(30875(4)),flip(a)].">
      <j1 rule="back_rewrite" parents="28447"/>
      <j2 rule="rewrite" parents="30875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31246">
    <literal><![CDATA[
      f(x,y,f(z,f(y,u,v),f(x,y,u))) = f(x,y,f(y,u,f(z,v,f(x,y,u))))
    ]]></literal>
    <justification jstring="[para(29874(a,1),123(a,1,3)),rewrite(6(2),5(4),20(4),6(4),6889(5),6(6),5(8,R),6(8),26264(9),6(5),30875(8),20(9)),flip(a)].">
      <j1 rule="para" parents="29874 123"/>
      <j2 rule="rewrite" parents="6 5 20 6 6889 6 5 6 26264 6 30875 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31254">
    <literal><![CDATA[
      f(x,f(y,z,u),f(v,y,z)) = f(v,f(y,x,z),f(y,z,u))
    ]]></literal>
    <justification jstring="[para(5(a,1),29875(a,1,2)),rewrite(5(2),6(2),5(4),6(4),5(5),6(5)),flip(a)].">
      <j1 rule="para" parents="5 29875"/>
      <j2 rule="rewrite" parents="5 6 5 6 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31255">
    <literal><![CDATA[
      f(x,f(y,z,u),f(z,u,v)) = f(y,f(x,z,u),f(z,u,v))
    ]]></literal>
    <justification jstring="[para(29875(a,2),6(a,1)),rewrite(5(2),5(2),5(4),5(5),5(5))].">
      <j1 rule="para" parents="29875 6"/>
      <j2 rule="rewrite" parents="5 5 5 5 5"/>
    </justification>
  </clause>

  <clause id="31400">
    <literal><![CDATA[
      f(x,y,f(z,f(y,u,v),f(x,y,v))) = f(x,y,f(y,v,f(u,z,f(x,y,v))))
    ]]></literal>
    <justification jstring="[para(29875(a,1),123(a,1,3)),rewrite(5(2,R),6(2),5(4),20(4),6(4),6889(5),5(6,R),6(6),5(8,R),6(8),26264(9),30543(8),20(9)),flip(a)].">
      <j1 rule="para" parents="29875 123"/>
      <j2 rule="rewrite" parents="5 6 5 20 6 6889 5 6 5 6 26264 30543 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31414">
    <literal><![CDATA[
      f(x,y,f(y,z,f(u,f(v,y,z),f(x,y,z)))) = f(v,f(x,y,z),f(y,u,f(x,y,z)))
    ]]></literal>
    <justification jstring="[para(29875(a,2),9899(a,2)),rewrite(5(3),5(3),205(3),5(6),5(6),5(9),26977(9)),flip(a)].">
      <j1 rule="para" parents="29875 9899"/>
      <j2 rule="rewrite" parents="5 5 205 5 5 5 26977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31505">
    <literal><![CDATA[
      f(f(x,y,z),f(x,y,u),f(v,w,f(x,y,z))) = f(w,f(x,y,z),f(u,f(x,y,v),f(x,y,z)))
    ]]></literal>
    <justification jstring="[para(29876(a,1),815(a,2,3)),rewrite(5(2),5(2),6(4),5(10,R),6(10))].">
      <j1 rule="para" parents="29876 815"/>
      <j2 rule="rewrite" parents="5 5 6 5 6"/>
    </justification>
  </clause>

  <clause id="31526">
    <literal><![CDATA[
      f(f(x,y,z),f(x,y,u),f(v,w,f(x,y,u))) = f(w,f(x,y,u),f(z,f(x,y,u),f(x,y,v)))
    ]]></literal>
    <justification jstring="[para(29876(a,2),1761(a,2,3)),rewrite(5(8),5(8))].">
      <j1 rule="para" parents="29876 1761"/>
      <j2 rule="rewrite" parents="5 5"/>
    </justification>
  </clause>

  <clause id="31565">
    <literal><![CDATA[
      f(x,y,f(z,f(x,y,u),f(y,u,f(x,y,v)))) = f(x,y,f(v,f(y,z,u),f(x,y,u)))
    ]]></literal>
    <justification jstring="[para(29876(a,2),95(a,1,3)),rewrite(6(4),6(6),30445(9))].">
      <j1 rule="para" parents="29876 95"/>
      <j2 rule="rewrite" parents="6 6 30445"/>
    </justification>
  </clause>

  <clause id="31784">
    <literal><![CDATA[
      f(x,y,f(y,f(x,z,u),f(x,z,v))) = f(x,z,f(y,v,f(x,y,u)))
    ]]></literal>
    <justification jstring="[para(29885(a,1),103(a,2)),rewrite(6(2),14835(5),6(1),6(2),20(5),6(8),20(8),6(8),25932(8),5(6,R),6(6))].">
      <j1 rule="para" parents="29885 103"/>
      <j2 rule="rewrite" parents="6 14835 6 6 20 6 20 6 25932 5 6"/>
    </justification>
  </clause>

  <clause id="31811">
    <literal><![CDATA[
      f(f(x,y,f(x,z,u)),f(x,z,v),f(z,v,w)) = f(z,v,f(x,y,f(x,u,f(x,z,w))))
    ]]></literal>
    <justification jstring="[para(29885(a,2),151(a,1)),rewrite(5(1,R),6(1),5(3),6(4),6(6),31784(10),5(7,R),6(7),15462(8))].">
      <j1 rule="para" parents="29885 151"/>
      <j2 rule="rewrite" parents="5 6 5 6 6 31784 5 6 15462"/>
    </justification>
  </clause>

  <clause id="31817">
    <literal><![CDATA[
      f(x,y,f(f(x,z,u),f(y,v,w),f(x,y,v))) = f(x,y,f(y,v,f(x,z,f(x,u,w))))
    ]]></literal>
    <justification jstring="[para(29885(a,2),156(a,1,3)),rewrite(5(3),6(4),31811(5),116(5),6(5),30960(9)),flip(a)].">
      <j1 rule="para" parents="29885 156"/>
      <j2 rule="rewrite" parents="5 6 31811 116 6 30960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31820">
    <literal><![CDATA[
      f(x,y,f(x,z,f(u,f(y,z,v),f(x,y,v)))) = f(x,f(y,u,v),f(x,y,z))
    ]]></literal>
    <justification jstring="[para(29885(a,1),12709(a,1,3)),rewrite(5(1),5(3),15462(5),6(6),5(7))].">
      <j1 rule="para" parents="29885 12709"/>
      <j2 rule="rewrite" parents="5 5 15462 6 5"/>
    </justification>
  </clause>

  <clause id="31856">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,z,f(x,v,f(x,y,w)))) = f(x,y,f(y,z,f(x,v,f(x,u,w))))
    ]]></literal>
    <justification jstring="[back_rewrite(30960),rewrite(31817(10),6(6))].">
      <j1 rule="back_rewrite" parents="30960"/>
      <j2 rule="rewrite" parents="31817 6"/>
    </justification>
  </clause>

  <clause id="31888">
    <literal><![CDATA[
      f(x,y,f(y,z,f(u,f(v,x,y),f(x,y,z)))) = f(v,f(x,y,z),f(y,z,f(x,y,u)))
    ]]></literal>
    <justification jstring="[para(264(a,1),29886(a,1)),rewrite(25837(4),6(2),20(3),6(6),5(7),5(9),26977(9)),flip(a)].">
      <j1 rule="para" parents="264 29886"/>
      <j2 rule="rewrite" parents="25837 6 20 6 5 5 26977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31898">
    <literal><![CDATA[
      f(x,y,f(z,f(x,y,u),f(y,u,f(x,v,w)))) = f(x,y,f(y,u,f(x,v,f(x,z,w))))
    ]]></literal>
    <justification jstring="[para(29886(a,2),131(a,2,3)),rewrite(31856(5),5(7),6(8)),flip(a)].">
      <j1 rule="para" parents="29886 131"/>
      <j2 rule="rewrite" parents="31856 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31924">
    <literal><![CDATA[
      f(x,y,f(z,f(y,u,v),f(x,y,v))) = f(x,y,f(y,v,f(x,u,z)))
    ]]></literal>
    <justification jstring="[back_rewrite(31565),rewrite(31898(5),29(4)),flip(a)].">
      <j1 rule="back_rewrite" parents="31565"/>
      <j2 rule="rewrite" parents="31898 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31937">
    <literal><![CDATA[
      f(x,y,f(y,z,f(u,v,f(x,y,z)))) = f(x,y,f(y,z,f(x,u,v)))
    ]]></literal>
    <justification jstring="[back_rewrite(31400),rewrite(31924(4),6(1),5(5,R),6(5)),flip(a)].">
      <j1 rule="back_rewrite" parents="31400"/>
      <j2 rule="rewrite" parents="31924 6 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31945">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,u,f(x,y,v))) = f(x,y,f(y,u,f(x,z,v)))
    ]]></literal>
    <justification jstring="[back_rewrite(30445),rewrite(31924(8))].">
      <j1 rule="back_rewrite" parents="30445"/>
      <j2 rule="rewrite" parents="31924"/>
    </justification>
  </clause>

  <clause id="31947">
    <literal><![CDATA[
      f(x,f(y,z,u),f(z,u,f(y,z,v))) = f(z,u,f(y,v,f(y,z,x)))
    ]]></literal>
    <justification jstring="[back_rewrite(31888),rewrite(5(1),5(1),31937(5),103(4)),flip(a)].">
      <j1 rule="back_rewrite" parents="31888"/>
      <j2 rule="rewrite" parents="5 5 31937 103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31948">
    <literal><![CDATA[
      f(x,f(y,z,u),f(z,v,f(y,z,u))) = f(y,z,f(u,v,f(z,u,x)))
    ]]></literal>
    <justification jstring="[back_rewrite(31414),rewrite(5(1),5(1),31937(5),22733(4)),flip(a)].">
      <j1 rule="back_rewrite" parents="31414"/>
      <j2 rule="rewrite" parents="5 5 31937 22733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31949">
    <literal><![CDATA[
      f(x,y,f(z,f(y,u,v),f(x,y,u))) = f(x,y,f(y,u,f(x,z,v)))
    ]]></literal>
    <justification jstring="[back_rewrite(31246),rewrite(31937(8))].">
      <j1 rule="back_rewrite" parents="31246"/>
      <j2 rule="rewrite" parents="31937"/>
    </justification>
  </clause>

  <clause id="31952">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,z,f(z,u,v))) = f(y,z,f(u,x,f(z,u,v)))
    ]]></literal>
    <justification jstring="[back_rewrite(27034),rewrite(31937(5),22733(4)),flip(a)].">
      <j1 rule="back_rewrite" parents="27034"/>
      <j2 rule="rewrite" parents="31937 22733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31985">
    <literal><![CDATA[
      f(x,f(y,z,u),f(z,u,f(y,v,f(y,w,z)))) = f(z,u,f(y,x,f(y,z,f(y,v,w))))
    ]]></literal>
    <justification jstring="[back_rewrite(26150),rewrite(31947(5)),flip(a)].">
      <j1 rule="back_rewrite" parents="26150"/>
      <j2 rule="rewrite" parents="31947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31995">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,z,f(v,z,u))) = f(z,u,f(y,x,f(v,y,z)))
    ]]></literal>
    <justification jstring="[back_rewrite(13752),rewrite(31947(4),5(1),5(5)),flip(a)].">
      <j1 rule="back_rewrite" parents="13752"/>
      <j2 rule="rewrite" parents="31947 5 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32044">
    <literal><![CDATA[
      f(x,y,f(z,u,f(v,u,x))) = f(u,x,f(x,y,f(z,v,u)))
    ]]></literal>
    <justification jstring="[back_rewrite(16737),rewrite(31948(8),29680(8),26264(6),6(3),31952(8),15371(6)),flip(a)].">
      <j1 rule="back_rewrite" parents="16737"/>
      <j2 rule="rewrite" parents="31948 29680 26264 6 31952 15371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32078">
    <literal><![CDATA[
      f(x,y,f(z,u,f(y,u,v))) = f(x,y,f(y,u,f(z,x,v)))
    ]]></literal>
    <justification jstring="[back_rewrite(31092),rewrite(31952(4),5(2,R),6(2),31949(7),5(4,R),6(4))].">
      <j1 rule="back_rewrite" parents="31092"/>
      <j2 rule="rewrite" parents="31952 5 6 31949 5 6"/>
    </justification>
  </clause>

  <clause id="32171">
    <literal><![CDATA[
      f(x,f(y,z,u),f(z,u,f(y,v,z))) = f(z,u,f(y,z,f(y,v,x)))
    ]]></literal>
    <justification jstring="[back_rewrite(16964),rewrite(31995(6),5(3,R),6(3),31985(6),6(2),15462(4),20(3),22(3)),flip(a)].">
      <j1 rule="back_rewrite" parents="16964"/>
      <j2 rule="rewrite" parents="31995 5 6 31985 6 15462 20 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32354">
    <literal><![CDATA[
      f(x,y,f(x,f(z,y,u),f(v,z,f(x,y,u)))) = f(x,y,f(v,z,f(x,y,u)))
    ]]></literal>
    <justification jstring="[para(30000(a,1),1905(a,1,3)),rewrite(6(4),26268(7),21(8))].">
      <j1 rule="para" parents="30000 1905"/>
      <j2 rule="rewrite" parents="6 26268 21"/>
    </justification>
  </clause>

  <clause id="32360">
    <literal><![CDATA[
      f(x,f(y,z,u),f(v,y,u)) = f(v,f(x,y,u),f(y,z,u))
    ]]></literal>
    <justification jstring="[para(30000(a,1),1074(a,2)),rewrite(5(1,R),6(1),5(3,R),6(3),1074(6),5(4),5(5,R),6(5))].">
      <j1 rule="para" parents="30000 1074"/>
      <j2 rule="rewrite" parents="5 6 5 6 1074 5 5 6"/>
    </justification>
  </clause>

  <clause id="32488">
    <literal><![CDATA[
      f(f(x,y,z),f(u,x,y),f(u,y,z)) = f(u,y,f(x,y,z))
    ]]></literal>
    <justification jstring="[para(30106(a,1),18567(a,2)),rewrite(5(7,R),24883(9))].">
      <j1 rule="para" parents="30106 18567"/>
      <j2 rule="rewrite" parents="5 24883"/>
    </justification>
  </clause>

  <clause id="32513">
    <literal><![CDATA[
      f(x,y,f(z,f(x,y,u),f(y,v,u))) = f(x,y,f(y,u,f(x,v,z)))
    ]]></literal>
    <justification jstring="[para(30415(a,2),26(a,2,3)),rewrite(31945(4)),flip(a)].">
      <j1 rule="para" parents="30415 26"/>
      <j2 rule="rewrite" parents="31945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32520">
    <literal><![CDATA[
      f(x,y,f(x,z,f(u,f(y,v,w),f(x,y,w)))) = f(x,z,f(x,y,f(y,w,f(x,v,u))))
    ]]></literal>
    <justification jstring="[para(30415(a,2),55(a,2,3,3)),rewrite(30622(5),32513(9))].">
      <j1 rule="para" parents="30415 55"/>
      <j2 rule="rewrite" parents="30622 32513"/>
    </justification>
  </clause>

  <clause id="32529">
    <literal><![CDATA[
      f(x,f(y,z,u),f(u,v,f(y,u,f(x,y,z)))) = f(v,f(x,y,u),f(y,z,u))
    ]]></literal>
    <justification jstring="[para(30415(a,2),1182(a,2)),rewrite(5(4),5(4),32171(5),5(2))].">
      <j1 rule="para" parents="30415 1182"/>
      <j2 rule="rewrite" parents="5 5 32171 5"/>
    </justification>
  </clause>

  <clause id="32545">
    <literal><![CDATA[
      f(x,y,f(x,z,f(z,u,f(x,y,v)))) = f(x,f(z,v,u),f(x,z,y))
    ]]></literal>
    <justification jstring="[back_rewrite(31820),rewrite(32520(5))].">
      <j1 rule="back_rewrite" parents="31820"/>
      <j2 rule="rewrite" parents="32520"/>
    </justification>
  </clause>

  <clause id="32666">
    <literal><![CDATA[
      f(x,f(y,z,u),f(z,u,v)) = f(y,f(z,x,u),f(z,u,v))
    ]]></literal>
    <justification jstring="[para(5(a,2),30979(a,1,2)),rewrite(5(2),6(2),5(4),6(4),5(5),6(5)),flip(a)].">
      <j1 rule="para" parents="5 30979"/>
      <j2 rule="rewrite" parents="5 6 5 6 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32691">
    <literal><![CDATA[
      f(x,f(y,z,f(z,u,v)),f(y,u,f(z,u,v))) = f(z,u,f(x,y,f(z,u,v)))
    ]]></literal>
    <justification jstring="[para(30979(a,1),26(a,1)),rewrite(6(2),5(4,R),6(4),5(7),5(8,R),6(8),6(9),32354(10))].">
      <j1 rule="para" parents="30979 26"/>
      <j2 rule="rewrite" parents="6 5 6 5 5 6 6 32354"/>
    </justification>
  </clause>

  <clause id="32882">
    <literal><![CDATA[
      f(x,f(y,z,u),f(v,y,z)) = f(u,f(v,y,z),f(y,x,z))
    ]]></literal>
    <justification jstring="[para(31254(a,2),1182(a,2)),rewrite(5(4),5(4),32171(5),5(2),32529(5)),flip(a)].">
      <j1 rule="para" parents="31254 1182"/>
      <j2 rule="rewrite" parents="5 5 32171 5 32529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32927">
    <literal><![CDATA[
      f(f(x,y,z),f(x,y,u),f(v,w,f(x,y,u))) = f(v,f(x,y,u),f(z,f(x,y,w),f(x,y,u)))
    ]]></literal>
    <justification jstring="[para(31255(a,1),1668(a,1,3)),rewrite(5(2),5(2),5(5,R),6(5),5(6),5(6),5(9)),flip(a)].">
      <j1 rule="para" parents="31255 1668"/>
      <j2 rule="rewrite" parents="5 5 5 6 5 5 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33322">
    <literal><![CDATA[
      f(x,y,f(y,f(z,x,u),f(v,z,f(x,y,u)))) = f(x,y,f(v,z,f(x,y,u)))
    ]]></literal>
    <justification jstring="[para(32360(a,2),30(a,1)),rewrite(5(1,R),6(1),5(3,R),6(3),5(4,R),6(4),32691(5),5(4,R),6(4),6(7),5(8,R),6(8)),flip(a)].">
      <j1 rule="para" parents="32360 30"/>
      <j2 rule="rewrite" parents="5 6 5 6 5 6 32691 5 6 6 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33446">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,z,f(u,x,v))) = f(y,z,f(u,x,v))
    ]]></literal>
    <justification jstring="[para(32488(a,1),224(a,2,3)),rewrite(5(3),5(3),5(6,R),6(6),5(7),5(7),33322(8),5(7,R),6(7),1776(7),6(4),5(9,R),6(9),5(10,R),6(10),31948(10),6(7),5(8,R),6(8),15462(8),964(7),20(6))].">
      <j1 rule="para" parents="32488 224"/>
      <j2 rule="rewrite" parents="5 5 5 6 5 5 33322 5 6 1776 6 5 6 5 6 31948 6 5 6 15462 964 20"/>
    </justification>
  </clause>

  <clause id="33536">
    <literal><![CDATA[
      f(x,f(y,z,u),f(z,v,u)) = f(v,f(y,z,u),f(z,u,x))
    ]]></literal>
    <justification jstring="[para(32666(a,2),1182(a,2)),rewrite(5(4),5(4),32171(5),5(2),32529(5))].">
      <j1 rule="para" parents="32666 1182"/>
      <j2 rule="rewrite" parents="5 5 32171 5 32529"/>
    </justification>
  </clause>

  <clause id="33626">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,v,z)) = f(v,f(y,z,x),f(y,z,u))
    ]]></literal>
    <justification jstring="[para(32882(a,2),896(a,2)),rewrite(5(2),5(2),6(3),5(4),5(4),12727(7),5(5),5(5))].">
      <j1 rule="para" parents="32882 896"/>
      <j2 rule="rewrite" parents="5 5 6 5 5 12727 5 5"/>
    </justification>
  </clause>

  <clause id="34330">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,v,z)) = f(x,f(v,y,u),f(x,v,z))
    ]]></literal>
    <justification jstring="[para(20060(a,1),255(a,2,3)),rewrite(5(2),5(2),5(3,R),6(3),22(5),794(5),6(4),15462(4),32545(4),5(1,R),6(1),6(2),5(5),5(5),5(6,R),6(6),27174(7),6(4),6(5))].">
      <j1 rule="para" parents="20060 255"/>
      <j2 rule="rewrite" parents="5 5 5 6 22 794 6 15462 32545 5 6 6 5 5 5 6 27174 6 6"/>
    </justification>
  </clause>

  <clause id="34335">
    <literal><![CDATA[
      f(x,f(y,z,u),f(v,x,u)) = f(x,f(y,v,z),f(v,x,u))
    ]]></literal>
    <justification jstring="[para(34330(a,1),5(a,2)),rewrite(5(2),5(3),5(4),5(4),5(5)),flip(a)].">
      <j1 rule="para" parents="34330 5"/>
      <j2 rule="rewrite" parents="5 5 5 5 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35057">
    <literal><![CDATA[
      f(f(x,y,z),f(x,y,u),f(v,w,f(x,y,u))) = f(f(x,y,z),f(v,w,u),f(x,y,u))
    ]]></literal>
    <justification jstring="[para(896(a,1),34335(a,1,3)),rewrite(6(5),6(7),896(10))].">
      <j1 rule="para" parents="896 34335"/>
      <j2 rule="rewrite" parents="6 6 896"/>
    </justification>
  </clause>

  <clause id="35114">
    <literal><![CDATA[
      f(x,f(y,z,u),f(v,f(y,z,w),f(y,z,u))) = f(f(y,z,v),f(u,x,w),f(y,z,u))
    ]]></literal>
    <justification jstring="[back_rewrite(32927),rewrite(35057(5),5(2)),flip(a)].">
      <j1 rule="back_rewrite" parents="32927"/>
      <j2 rule="rewrite" parents="35057 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35115">
    <literal><![CDATA[
      f(x,f(y,z,u),f(v,f(y,z,u),f(y,z,w))) = f(f(y,z,v),f(u,w,x),f(y,z,u))
    ]]></literal>
    <justification jstring="[back_rewrite(31526),rewrite(35057(5),5(2)),flip(a)].">
      <j1 rule="back_rewrite" parents="31526"/>
      <j2 rule="rewrite" parents="35057 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35143">
    <literal><![CDATA[
      f(f(x,y,z),f(x,y,u),f(v,w,f(x,y,z))) = f(f(x,y,u),f(z,v,w),f(x,y,z))
    ]]></literal>
    <justification jstring="[back_rewrite(31505),rewrite(35114(10),6(7))].">
      <j1 rule="back_rewrite" parents="31505"/>
      <j2 rule="rewrite" parents="35114 6"/>
    </justification>
  </clause>

  <clause id="39763">
    <literal><![CDATA[
      f(f(x,y,z),f(u,v,w),f(x,y,u)) = f(z,f(x,y,u),f(x,y,f(u,v,w)))
    ]]></literal>
    <justification jstring="[para(362(a,1),32044(a,1,3)),rewrite(26078(5),5(2),26105(5),5(4,R),6(4),5(9,R),6(9),5(10,R),6(10),35115(11),15(8)),flip(a)].">
      <j1 rule="para" parents="362 32044"/>
      <j2 rule="rewrite" parents="26078 5 26105 5 6 5 6 5 6 35115 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39771">
    <literal><![CDATA[
      f(f(x,y,z),f(x,y,u),f(v,w,f(x,y,z))) = f(u,f(x,y,z),f(x,y,f(z,v,w)))
    ]]></literal>
    <justification jstring="[back_rewrite(35143),rewrite(39763(9))].">
      <j1 rule="back_rewrite" parents="35143"/>
      <j2 rule="rewrite" parents="39763"/>
    </justification>
  </clause>

  <clause id="39829">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,z,v)) = f(y,z,f(v,u,x))
    ]]></literal>
    <justification jstring="[para(32078(a,1),320(a,2,3)),rewrite(5(2),5(2),6(4),39771(5),33446(4),4(4),5(5,R),6(5),19(5),5(5,R)),flip(a)].">
      <j1 rule="para" parents="32078 320"/>
      <j2 rule="rewrite" parents="5 5 6 39771 33446 4 5 6 19 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39834">
    <literal><![CDATA[
      f(x,y,f(z,u,f(v,x,y))) = f(x,y,f(z,u,v))
    ]]></literal>
    <justification jstring="[para(1066(a,1),32078(a,2,3)),rewrite(5(2),5(2),20(4),5(4,R),15462(4),39829(3),6(1),5(7,R),6(7),19(7))].">
      <j1 rule="para" parents="1066 32078"/>
      <j2 rule="rewrite" parents="5 5 20 5 15462 39829 6 5 6 19"/>
    </justification>
  </clause>

  <clause id="39963">
    <literal><![CDATA[
      f(x,f(y,z,u),f(z,u,v)) = f(z,u,f(y,v,x))
    ]]></literal>
    <justification jstring="[back_rewrite(33626),rewrite(6(2),39829(3),5(1),6(1),5(3)),flip(a)].">
      <j1 rule="back_rewrite" parents="33626"/>
      <j2 rule="rewrite" parents="6 39829 5 6 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40158">
    <literal><![CDATA[
      f(x,f(y,z,u),f(v,z,u)) = f(z,u,f(v,y,x))
    ]]></literal>
    <justification jstring="[back_rewrite(33536),rewrite(6(2),39963(3),5(1),5(4)),flip(a)].">
      <j1 rule="back_rewrite" parents="33536"/>
      <j2 rule="rewrite" parents="6 39963 5 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40478">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer(dist_both)
    ]]></attribute>
    <justification jstring="[back_rewrite(14),rewrite(40158(13),5(9,R),6(9),39834(10),5(6),40158(25),5(21),6(21)),xx(a),xx(b)].">
      <j1 rule="back_rewrite" parents="14"/>
      <j2 rule="rewrite" parents="40158 5 6 39834 5 40158 5 6"/>
      <j2 rule="xx"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="2" length="323" max_count="39">

<comments><![CDATA[
% Proof 2 at 745.23 (+ 1.30) seconds: dist_short.
% Length of proof is 323.
% Level of proof is 41.
% Maximum clause weight is 44.
% Given clauses 836.
]]></comments>

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

  <clause id="26">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,z,v))) = f(x,z,f(x,y,f(z,u,v)))
    ]]></literal>
    <justification jstring="[para(16(a,2),8(a,1,3))].">
      <j1 rule="para" parents="16 8"/>
    </justification>
  </clause>

  <clause id="28">
    <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="29">
    <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="30">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,u,v))) = f(x,u,f(x,y,f(z,u,v)))
    ]]></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="32">
    <literal><![CDATA[
      f(x,y,f(x,z,f(x,u,v))) = f(x,v,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,v,y)) = f(x,v,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,v))) = f(z,x,f(x,u,f(x,y,v)))
    ]]></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,v))) = f(y,z,f(y,u,f(x,y,v)))
    ]]></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,v,w)))) = f(x,z,f(x,y,f(z,v,f(z,u,w))))
    ]]></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="53">
    <literal><![CDATA[
      f(x,y,f(z,u,f(z,v,f(x,z,w)))) = f(x,z,f(x,y,f(z,u,f(z,v,w))))
    ]]></literal>
    <justification jstring="[para(18(a,2),16(a,1,3)),rewrite(5(1,R),6(1),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,v,f(x,u,w)))) = f(x,u,f(x,y,f(x,z,f(u,v,w))))
    ]]></literal>
    <justification jstring="[para(16(a,2),18(a,1,3,3))].">
      <j1 rule="para" parents="16 18"/>
    </justification>
  </clause>

  <clause id="55">
    <literal><![CDATA[
      f(x,y,f(x,z,f(u,v,f(x,u,w)))) = f(x,z,f(x,u,f(x,y,f(u,v,w))))
    ]]></literal>
    <justification jstring="[para(16(a,2),18(a,2,3,3)),flip(a)].">
      <j1 rule="para" parents="16 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="57">
    <literal><![CDATA[
      f(x,f(x,y,z),f(x,u,v)) = f(x,y,f(x,u,f(x,v,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="70">
    <literal><![CDATA[
      f(x,y,f(z,u,f(y,z,v))) = f(y,z,f(x,y,f(z,u,v)))
    ]]></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="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,v))) = f(y,u,f(x,y,f(z,u,v)))
    ]]></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,v,z)) = f(x,v,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="76">
    <literal><![CDATA[
      f(x,y,f(z,u,f(z,x,v))) = f(z,x,f(x,y,f(z,v,u)))
    ]]></literal>
    <justification jstring="[para(17(a,1),24(a,2,3)),rewrite(5(2,R),6(2),5(6,R),6(6)),flip(a)].">
      <j1 rule="para" parents="17 24"/>
      <j2 rule="rewrite" parents="5 6 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="78">
    <literal><![CDATA[
      f(x,y,f(z,u,f(y,z,f(z,v,w)))) = f(y,z,f(x,y,f(z,v,f(z,u,w))))
    ]]></literal>
    <justification jstring="[para(18(a,1),24(a,1,3)),rewrite(5(2,R),6(2),5(8,R),6(8))].">
      <j1 rule="para" parents="18 24"/>
      <j2 rule="rewrite" parents="5 6 5 6"/>
    </justification>
  </clause>

  <clause id="81">
    <literal><![CDATA[
      f(x,y,f(z,u,f(z,v,f(z,x,w)))) = f(z,x,f(x,y,f(z,u,f(z,v,w))))
    ]]></literal>
    <justification jstring="[para(18(a,2),24(a,2,3)),rewrite(5(3,R),6(3),5(8,R),6(8)),flip(a)].">
      <j1 rule="para" parents="18 24"/>
      <j2 rule="rewrite" parents="5 6 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="95">
    <literal><![CDATA[
      f(x,y,f(x,z,f(y,u,f(x,y,v)))) = f(x,z,f(y,u,f(x,y,v)))
    ]]></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="102">
    <literal><![CDATA[
      f(x,y,f(z,x,f(y,u,f(x,y,v)))) = f(z,x,f(y,u,f(x,y,v)))
    ]]></literal>
    <justification jstring="[para(21(a,1),24(a,1,3)),rewrite(5(1),5(4),5(7,R),6(7)),flip(a)].">
      <j1 rule="para" parents="21 24"/>
      <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,v)))) = f(y,z,f(x,u,f(x,y,v)))
    ]]></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="113">
    <literal><![CDATA[
      f(x,y,f(y,z,f(y,u,v))) = f(x,y,f(y,v,f(y,z,u)))
    ]]></literal>
    <justification jstring="[para(17(a,1),29(a,2,3)),rewrite(29(4))].">
      <j1 rule="para" parents="17 29"/>
      <j2 rule="rewrite" parents="29"/>
    </justification>
  </clause>

  <clause id="116">
    <literal><![CDATA[
      f(x,y,f(y,z,f(x,u,f(x,v,f(x,y,w))))) = f(x,y,f(y,z,f(x,u,f(x,v,w))))
    ]]></literal>
    <justification jstring="[para(18(a,2),29(a,1,3,3))].">
      <j1 rule="para" parents="18 29"/>
    </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="123">
    <literal><![CDATA[
      f(x,y,f(x,z,f(u,y,f(x,y,v)))) = f(x,z,f(u,y,f(x,y,v)))
    ]]></literal>
    <justification jstring="[para(73(a,1),16(a,1,3)),rewrite(5(1,R),6(1),5(4,R),6(4),5(7,R),6(7)),flip(a)].">
      <j1 rule="para" parents="73 16"/>
      <j2 rule="rewrite" parents="5 6 5 6 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="125">
    <literal><![CDATA[
      f(x,y,f(z,u,f(z,x,v))) = f(x,y,f(z,x,f(z,u,v)))
    ]]></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="131">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,v,f(x,z,w)))) = f(x,z,f(x,y,f(z,u,f(x,v,w))))
    ]]></literal>
    <justification jstring="[para(8(a,1),26(a,1,3,3))].">
      <j1 rule="para" parents="8 26"/>
    </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),26(a,1,3)),rewrite(6(4),95(6)),flip(a)].">
      <j1 rule="para" parents="15 26"/>
      <j2 rule="rewrite" parents="6 95"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="133">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,z,f(y,x,u))) = f(y,z,f(y,x,u))
    ]]></literal>
    <justification jstring="[para(15(a,1),26(a,1)),rewrite(5(1,R),6(1),5(3,R),6(3),6(6),5(7,R),6(7),103(7)),flip(a)].">
      <j1 rule="para" parents="15 26"/>
      <j2 rule="rewrite" parents="5 6 5 6 6 5 6 103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="141">
    <literal><![CDATA[
      f(x,y,f(x,z,f(u,v,f(x,u,w)))) = f(x,u,f(x,z,f(x,y,f(u,v,w))))
    ]]></literal>
    <justification jstring="[para(26(a,2),18(a,2,3)),flip(a)].">
      <j1 rule="para" parents="26 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="147">
    <literal><![CDATA[
      f(x,y,f(z,y,f(z,x,u))) = f(z,x,f(z,y,f(x,y,u)))
    ]]></literal>
    <justification jstring="[para(26(a,1),24(a,1)),flip(a)].">
      <j1 rule="para" parents="26 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="151">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,v,f(z,x,w)))) = f(z,x,f(x,y,f(z,u,f(x,v,w))))
    ]]></literal>
    <justification jstring="[para(26(a,2),24(a,2,3)),rewrite(5(3,R),6(3),5(8,R),6(8)),flip(a)].">
      <j1 rule="para" parents="26 24"/>
      <j2 rule="rewrite" parents="5 6 5 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="156">
    <literal><![CDATA[
      f(x,y,f(x,z,f(y,u,f(x,v,f(x,y,w))))) = f(x,z,f(y,u,f(x,v,f(x,y,w))))
    ]]></literal>
    <justification jstring="[para(21(a,1),26(a,1,3,3)),rewrite(6(1),6(5)),flip(a)].">
      <j1 rule="para" parents="21 26"/>
      <j2 rule="rewrite" parents="6 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="162">
    <literal><![CDATA[
      f(x,y,f(z,u,f(z,x,f(u,v,w)))) = f(x,y,f(z,x,f(u,v,f(z,u,w))))
    ]]></literal>
    <justification jstring="[para(26(a,1),122(a,1,3,3)),rewrite(5(4,R),6(4),103(5),5(8,R),6(8))].">
      <j1 rule="para" parents="26 122"/>
      <j2 rule="rewrite" parents="5 6 103 5 6"/>
    </justification>
  </clause>

  <clause id="163">
    <literal><![CDATA[
      f(x,y,f(z,y,f(x,z,u))) = f(z,y,f(x,z,f(x,y,u)))
    ]]></literal>
    <justification jstring="[para(26(a,1),122(a,1,3)),rewrite(5(2,R),6(2),5(3,R),6(3),95(4),5(4,R),6(4),5(6,R),6(6))].">
      <j1 rule="para" parents="26 122"/>
      <j2 rule="rewrite" parents="5 6 5 6 95 5 6 5 6"/>
    </justification>
  </clause>

  <clause id="169">
    <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(28(a,1),5(a,2)),rewrite(5(2),5(2),5(4),5(6,R),6(6))].">
      <j1 rule="para" parents="28 5"/>
      <j2 rule="rewrite" parents="5 5 5 5 6"/>
    </justification>
  </clause>

  <clause id="170">
    <literal><![CDATA[
      f(x,f(y,z,u),f(z,u,f(x,y,z))) = f(x,z,f(y,z,u))
    ]]></literal>
    <justification jstring="[para(5(a,1),28(a,1,2)),rewrite(6(2),5(5))].">
      <j1 rule="para" parents="5 28"/>
      <j2 rule="rewrite" parents="6 5"/>
    </justification>
  </clause>

  <clause id="188">
    <literal><![CDATA[
      f(x,f(y,z,f(z,u,v)),f(z,u,f(x,u,f(y,z,v)))) = f(x,u,f(z,u,f(y,z,v)))
    ]]>