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

<!DOCTYPE proofs SYSTEM "proof3.dtd">

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

<proofs number_of_proofs="1">

<source>dist-long-short.out</source>

<heading><![CDATA[
Prover9 (32) version June-2006C, June 2006.
Process 13955 was started by mccune on cleo.thornwood,
Mon Jun 19 17:18:29 2006
The command was "/home/mccune/bin/prover9 -f dist-long-short.in".
]]></heading>

<proof number="1" length="115" max_count="45">

<comments><![CDATA[
% Proof 1 at 55.10 (+ 0.09) seconds: dist_short.
% Length of proof is 115.
% Level of proof is 19.
% Maximum clause weight is 45.
% Given clauses 194.
]]></comments>

  <clause id="4">
    <literal><![CDATA[
      f(f(x,y,z),y,u) = f(x,y,f(z,y,u))
    ]]></literal>
    <attribute><![CDATA[
      label(associativity)
    ]]></attribute>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="5">
    <literal><![CDATA[
      f(f(x,y,z),u,v) = f(f(x,u,v),f(y,u,v),f(z,u,v))
    ]]></literal>
    <attribute><![CDATA[
      label(dist_long)
    ]]></attribute>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="6">
    <literal><![CDATA[
      f(f(c1,c2,c3),c4,E) != f(c1,f(c2,c4,E),f(c3,c4,E))
    ]]></literal>
    <attribute><![CDATA[
      answer(dist_short)
    ]]></attribute>
    <justification jstring="[clausify].">
      <j1 rule="clausify"/>
    </justification>
  </clause>

  <clause id="7">
    <literal><![CDATA[
      f(x,x,y) = x
    ]]></literal>
    <attribute><![CDATA[
      label(majority)
    ]]></attribute>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="8">
    <literal><![CDATA[
      f(x,y,z) = f(z,x,y)
    ]]></literal>
    <attribute><![CDATA[
      label(2a)
    ]]></attribute>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="9">
    <literal><![CDATA[
      f(x,y,z) = f(x,z,y)
    ]]></literal>
    <attribute><![CDATA[
      label(2b)
    ]]></attribute>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="10">
    <literal><![CDATA[
      f(x,y,f(z,x,u)) = f(z,x,f(x,u,y))
    ]]></literal>
    <attribute><![CDATA[
      label(associativity)
    ]]></attribute>
    <justification jstring="[copy(4),demod(8(2),8(2),8(3,R),9(3))].">
      <j1 rule="copy" parents="4"/>
      <j2 rule="demod" parents="8 8 8 9"/>
    </justification>
  </clause>

  <clause id="11">
    <literal><![CDATA[
      f(f(x,y,z),f(u,y,z),f(v,y,z)) = f(y,z,f(x,u,v))
    ]]></literal>
    <attribute><![CDATA[
      label(dist_long)
    ]]></attribute>
    <justification jstring="[copy(5),demod(8(2),8(2)),flip(a)].">
      <j1 rule="copy" parents="5"/>
      <j2 rule="demod" parents="8 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12">
    <literal><![CDATA[
      f(c1,f(E,c2,c4),f(E,c3,c4)) != f(E,c4,f(c1,c2,c3))
    ]]></literal>
    <attribute><![CDATA[
      answer(dist_short)
    ]]></attribute>
    <justification jstring="[copy(6),demod(8(7),9(7),8(12),8(16)),flip(a)].">
      <j1 rule="copy" parents="6"/>
      <j2 rule="demod" parents="8 9 8 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13">
    <literal><![CDATA[
      f(x,y,y) = y
    ]]></literal>
    <justification jstring="[para(8(a,1),7(a,1))].">
      <j1 rule="para" parents="8 7"/>
    </justification>
  </clause>

  <clause id="14">
    <literal><![CDATA[
      f(x,y,f(x,z,u)) = f(x,z,f(x,y,u))
    ]]></literal>
    <justification jstring="[para(10(a,2),8(a,1)),demod(8(1,R),9(1),9(3),8(4),9(4))].">
      <j1 rule="para" parents="10 8"/>
      <j2 rule="demod" parents="8 9 9 8 9"/>
    </justification>
  </clause>

  <clause id="15">
    <literal><![CDATA[
      f(x,y,f(z,y,u)) = f(z,y,f(x,y,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),8(a,2)),demod(9(2),8(3))].">
      <j1 rule="para" parents="10 8"/>
      <j2 rule="demod" parents="9 8"/>
    </justification>
  </clause>

  <clause id="18">
    <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(10(a,1),10(a,1,3)),demod(8(1),9(5),8(6,R),9(6))].">
      <j1 rule="para" parents="10 10"/>
      <j2 rule="demod" parents="8 9 8 9"/>
    </justification>
  </clause>

  <clause id="20">
    <literal><![CDATA[
      f(x,y,f(x,z,y)) = f(x,z,y)
    ]]></literal>
    <justification jstring="[para(10(a,2),10(a,1)),demod(8(1,R),13(1),8(2),9(2)),flip(a)].">
      <j1 rule="para" parents="10 10"/>
      <j2 rule="demod" parents="8 13 8 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23">
    <literal><![CDATA[
      f(x,f(x,y,z),f(x,z,u)) = f(x,z,f(x,y,u))
    ]]></literal>
    <justification jstring="[para(7(a,1),11(a,1,1)),demod(8(1,R),9(1),8(2),8(2))].">
      <j1 rule="para" parents="7 11"/>
      <j2 rule="demod" parents="8 9 8 8"/>
    </justification>
  </clause>

  <clause id="24">
    <literal><![CDATA[
      f(x,f(x,y,z),f(u,x,y)) = f(x,y,f(u,x,z))
    ]]></literal>
    <justification jstring="[para(7(a,1),11(a,1,2)),demod(8(2),8(2),8(3,R))].">
      <j1 rule="para" parents="7 11"/>
      <j2 rule="demod" parents="8 8 8"/>
    </justification>
  </clause>

  <clause id="25">
    <literal><![CDATA[
      f(x,f(y,x,z),f(x,z,u)) = f(x,z,f(y,x,u))
    ]]></literal>
    <justification jstring="[para(7(a,1),11(a,1,3)),demod(8(2),8(2),8(3),9(4))].">
      <j1 rule="para" parents="7 11"/>
      <j2 rule="demod" parents="8 8 8 9"/>
    </justification>
  </clause>

  <clause id="26">
    <literal><![CDATA[
      f(f(x,y,z),f(x,y,u),f(x,y,v)) = f(x,y,f(u,v,z))
    ]]></literal>
    <justification jstring="[para(11(a,1),8(a,1)),demod(8(3),8(3),8(4),8(4),8(5),8(5)),flip(a)].">
      <j1 rule="para" parents="11 8"/>
      <j2 rule="demod" parents="8 8 8 8 8 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27">
    <literal><![CDATA[
      f(f(x,y,z),f(y,z,u),f(y,z,v)) = f(y,z,f(x,u,v))
    ]]></literal>
    <justification jstring="[para(11(a,1),8(a,2)),demod(8(2),8(2),8(3),8(3),8(5),8(5))].">
      <j1 rule="para" parents="11 8"/>
      <j2 rule="demod" parents="8 8 8 8 8 8"/>
    </justification>
  </clause>

  <clause id="28">
    <literal><![CDATA[
      f(f(x,y,z),f(x,z,u),f(x,z,v)) = f(x,z,f(y,u,v))
    ]]></literal>
    <justification jstring="[para(8(a,1),11(a,1,1)),demod(8(2),9(2),8(3),9(3),8(6,R),9(6))].">
      <j1 rule="para" parents="8 11"/>
      <j2 rule="demod" parents="8 9 8 9 8 9"/>
    </justification>
  </clause>

  <clause id="30">
    <literal><![CDATA[
      f(f(x,y,z),f(y,z,u),f(v,f(x,y,z),f(y,z,w))) = f(v,f(x,y,z),f(y,z,f(x,u,w)))
    ]]></literal>
    <justification jstring="[para(11(a,1),10(a,2,3)),demod(8(2),8(2),8(4),8(4),9(8))].">
      <j1 rule="para" parents="11 10"/>
      <j2 rule="demod" parents="8 8 8 8 9"/>
    </justification>
  </clause>

  <clause id="34">
    <literal><![CDATA[
      f(f(x,y,f(z,u,v)),f(y,w,f(z,u,v)),f(z,u,f(y,u,v))) = f(y,f(z,u,v),f(x,u,w))
    ]]></literal>
    <justification jstring="[para(10(a,1),11(a,1,3)),demod(8(4,R),9(4),8(5),9(9))].">
      <j1 rule="para" parents="10 11"/>
      <j2 rule="demod" parents="8 9 8 9"/>
    </justification>
  </clause>

  <clause id="35">
    <literal><![CDATA[
      f(f(x,y,f(x,z,u)),f(x,v,f(x,y,u)),f(x,w,f(x,y,u))) = f(x,f(x,y,u),f(z,v,w))
    ]]></literal>
    <justification jstring="[para(10(a,2),11(a,1,1)),demod(8(1,R),9(1),9(3),8(4,R),9(4),9(5),8(6,R),9(6),9(8))].">
      <j1 rule="para" parents="10 11"/>
      <j2 rule="demod" parents="8 9 9 8 9 9 8 9 9"/>
    </justification>
  </clause>

  <clause id="39">
    <literal><![CDATA[
      f(x,y,f(z,x,u)) = f(z,x,f(x,y,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),11(a,2)),demod(7(2),8(2),8(2),8(3,R),24(3),9(3))].">
      <j1 rule="para" parents="10 11"/>
      <j2 rule="demod" parents="7 8 8 8 24 9"/>
    </justification>
  </clause>

  <clause id="41">
    <literal><![CDATA[
      f(x,f(x,y,z),f(x,y,u)) = f(x,u,f(x,y,z))
    ]]></literal>
    <justification jstring="[para(10(a,2),11(a,2)),demod(8(1),7(1),8(1),9(1),8(2),9(2),8(4,R),9(4))].">
      <j1 rule="para" parents="10 11"/>
      <j2 rule="demod" parents="8 7 8 9 8 9 8 9"/>
    </justification>
  </clause>

  <clause id="48">
    <literal><![CDATA[
      f(x,y,f(x,y,z)) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(13(a,1),10(a,2,3)),demod(8(1),8(1),8(3),8(3))].">
      <j1 rule="para" parents="13 10"/>
      <j2 rule="demod" parents="8 8 8 8"/>
    </justification>
  </clause>

  <clause id="50">
    <literal><![CDATA[
      f(x,y,f(x,z,f(x,y,u))) = f(x,z,f(x,y,u))
    ]]></literal>
    <justification jstring="[para(20(a,1),10(a,1,3)),demod(8(1),8(3),9(4),8(5,R),9(5)),flip(a)].">
      <j1 rule="para" parents="20 10"/>
      <j2 rule="demod" parents="8 8 9 8 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53">
    <literal><![CDATA[
      f(f(x,y,z),f(z,u,f(x,y,z)),f(z,v,f(x,y,z))) = f(z,f(x,y,z),f(x,u,v))
    ]]></literal>
    <justification jstring="[para(20(a,1),11(a,1,1)),demod(8(3,R),9(3),8(5,R),9(5))].">
      <j1 rule="para" parents="20 11"/>
      <j2 rule="demod" parents="8 9 8 9"/>
    </justification>
  </clause>

  <clause id="56">
    <literal><![CDATA[
      f(x,y,f(y,z,f(x,y,u))) = f(x,y,f(y,z,u))
    ]]></literal>
    <justification jstring="[para(10(a,2),48(a,1,3)),demod(9(4))].">
      <j1 rule="para" parents="10 48"/>
      <j2 rule="demod" parents="9"/>
    </justification>
  </clause>

  <clause id="57">
    <literal><![CDATA[
      f(f(x,y,z),f(y,u,f(x,y,z)),f(y,v,f(x,y,z))) = f(y,f(x,y,z),f(x,u,v))
    ]]></literal>
    <justification jstring="[para(48(a,1),11(a,1,1)),demod(8(3,R),9(3),8(5,R),9(5))].">
      <j1 rule="para" parents="48 11"/>
      <j2 rule="demod" parents="8 9 8 9"/>
    </justification>
  </clause>

  <clause id="62">
    <literal><![CDATA[
      f(f(x,y,f(z,u,v)),f(z,u,f(y,z,v)),f(y,w,f(z,u,v))) = f(y,f(z,u,v),f(x,z,w))
    ]]></literal>
    <justification jstring="[para(14(a,1),11(a,1,2)),demod(8(3,R),9(3),8(6,R),9(6))].">
      <j1 rule="para" parents="14 11"/>
      <j2 rule="demod" parents="8 9 8 9"/>
    </justification>
  </clause>

  <clause id="64">
    <literal><![CDATA[
      f(x,f(y,x,z),f(z,f(y,x,z),f(x,z,u))) = f(x,z,f(y,u,f(y,x,z)))
    ]]></literal>
    <justification jstring="[para(14(a,1),11(a,1)),demod(8(3),8(3),8(4),8(5,R),9(5))].">
      <j1 rule="para" parents="14 11"/>
      <j2 rule="demod" parents="8 8 8 8 9"/>
    </justification>
  </clause>

  <clause id="65">
    <literal><![CDATA[
      f(f(x,y,z),f(y,z,u),f(v,f(y,z,w),f(x,y,z))) = f(v,f(x,y,z),f(y,z,f(x,u,w)))
    ]]></literal>
    <justification jstring="[para(11(a,1),14(a,1,3)),demod(8(4,R),9(4),8(6),8(6),8(8),8(8),8(9,R)),flip(a)].">
      <j1 rule="para" parents="11 14"/>
      <j2 rule="demod" parents="8 9 8 8 8 8 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="66">
    <literal><![CDATA[
      f(x,f(x,y,z),f(y,f(x,y,z),f(x,y,u))) = f(x,y,f(z,u,f(x,y,z)))
    ]]></literal>
    <justification jstring="[para(11(a,1),14(a,1)),demod(8(1),8(1),8(4),8(4),8(5),8(5),8(6),8(6),8(7),8(8,R),9(8)),flip(a)].">
      <j1 rule="para" parents="11 14"/>
      <j2 rule="demod" parents="8 8 8 8 8 8 8 8 8 8 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="77">
    <literal><![CDATA[
      f(x,f(y,x,z),f(u,y,x)) = f(u,x,f(y,x,z))
    ]]></literal>
    <justification jstring="[para(15(a,1),11(a,2)),demod(8(2,R),13(2),8(2),8(2),8(3,R))].">
      <j1 rule="para" parents="15 11"/>
      <j2 rule="demod" parents="8 13 8 8 8"/>
    </justification>
  </clause>

  <clause id="107">
    <literal><![CDATA[
      f(x,f(x,y,z),f(z,u,f(x,z,v))) = f(x,z,f(x,y,f(z,u,v)))
    ]]></literal>
    <justification jstring="[para(10(a,2),23(a,1,3)),demod(9(5))].">
      <j1 rule="para" parents="10 23"/>
      <j2 rule="demod" parents="9"/>
    </justification>
  </clause>

  <clause id="109">
    <literal><![CDATA[
      f(f(x,y,z),f(u,f(y,z,v),f(x,y,z)),f(y,z,f(x,v,w))) = f(u,f(x,y,z),f(y,z,f(x,v,w)))
    ]]></literal>
    <justification jstring="[para(11(a,1),23(a,1,3)),demod(8(3),8(3),8(4,R),8(9),8(9),8(11),8(11),8(12,R),65(13))].">
      <j1 rule="para" parents="11 23"/>
      <j2 rule="demod" parents="8 8 8 8 8 8 8 8 65"/>
    </justification>
  </clause>

  <clause id="121">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,y,z)) = f(y,z,f(x,y,f(x,z,u)))
    ]]></literal>
    <justification jstring="[para(18(a,1),10(a,2)),demod(8(2,R),9(2),8(5,R),9(5))].">
      <j1 rule="para" parents="18 10"/>
      <j2 rule="demod" parents="8 9 8 9"/>
    </justification>
  </clause>

  <clause id="137">
    <literal><![CDATA[
      f(f(x,y,z),f(y,z,u),f(y,v,f(y,z,f(x,y,z)))) = f(y,z,f(x,y,f(x,u,v)))
    ]]></literal>
    <justification jstring="[para(11(a,1),18(a,2,3)),demod(8(2),8(2),8(4),8(4),8(5,R),9(5),8(10,R),9(10),25(10))].">
      <j1 rule="para" parents="11 18"/>
      <j2 rule="demod" parents="8 8 8 8 8 9 8 9 25"/>
    </justification>
  </clause>

  <clause id="142">
    <literal><![CDATA[
      f(x,y,f(x,z,f(y,u,f(x,y,v)))) = f(x,y,f(x,z,f(y,u,v)))
    ]]></literal>
    <justification jstring="[para(18(a,2),48(a,1,3)),demod(8(2,R),9(2),8(5,R),9(5))].">
      <j1 rule="para" parents="18 48"/>
      <j2 rule="demod" parents="8 9 8 9"/>
    </justification>
  </clause>

  <clause id="159">
    <literal><![CDATA[
      f(x,f(x,y,f(x,z,f(y,u,v))),f(x,w,f(y,u,f(x,y,v)))) = f(x,f(y,u,f(x,y,v)),f(x,z,w))
    ]]></literal>
    <justification jstring="[para(18(a,1),23(a,1,2)),demod(8(1,R),9(1),8(5,R),9(5),9(6),8(9,R),9(9))].">
      <j1 rule="para" parents="18 23"/>
      <j2 rule="demod" parents="8 9 8 9 9 8 9"/>
    </justification>
  </clause>

  <clause id="162">
    <literal><![CDATA[
      f(x,y,f(z,f(x,y,u),f(x,v,f(x,y,u)))) = f(x,y,f(x,u,f(z,v,f(x,y,u))))
    ]]></literal>
    <justification jstring="[para(18(a,2),23(a,1)),demod(9(1),9(2),9(3),9(6),9(7))].">
      <j1 rule="para" parents="18 23"/>
      <j2 rule="demod" parents="9 9 9 9 9"/>
    </justification>
  </clause>

  <clause id="168">
    <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(24(a,1),10(a,1,3)),demod(8(2),8(2),8(4,R),9(4),8(7),8(7),8(8)),flip(a)].">
      <j1 rule="para" parents="24 10"/>
      <j2 rule="demod" parents="8 8 8 9 8 8 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="169">
    <literal><![CDATA[
      f(x,f(x,y,f(x,z,u)),f(x,u,v)) = f(x,u,f(x,v,f(x,y,z)))
    ]]></literal>
    <justification jstring="[para(10(a,1),24(a,1,2)),demod(8(2,R),9(2),8(3),8(3),8(5,R),9(5),8(6,R),9(6))].">
      <j1 rule="para" parents="10 24"/>
      <j2 rule="demod" parents="8 9 8 8 8 9 8 9"/>
    </justification>
  </clause>

  <clause id="171">
    <literal><![CDATA[
      f(x,f(y,z,f(x,y,u)),f(x,y,v)) = f(x,y,f(x,v,f(y,z,u)))
    ]]></literal>
    <justification jstring="[para(10(a,2),24(a,1,2)),demod(8(3),8(3),9(5),8(6,R),9(6))].">
      <j1 rule="para" parents="10 24"/>
      <j2 rule="demod" parents="8 8 9 8 9"/>
    </justification>
  </clause>

  <clause id="172">
    <literal><![CDATA[
      f(x,f(x,y,z),f(x,u,v)) = f(x,z,f(x,u,f(x,y,v)))
    ]]></literal>
    <justification jstring="[para(10(a,2),24(a,1,3)),demod(9(2),8(3),8(3),169(5),9(2),41(3),8(5),8(5)),flip(a)].">
      <j1 rule="para" parents="10 24"/>
      <j2 rule="demod" parents="9 8 8 169 9 41 8 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="197">
    <literal><![CDATA[
      f(x,y,f(x,z,f(x,u,f(x,v,y)))) = f(x,y,f(x,z,f(x,v,u)))
    ]]></literal>
    <justification jstring="[para(24(a,1),24(a,1,2)),demod(8(1,R),9(1),8(4,R),9(4),172(5),48(3),172(4),8(6),8(6),8(7,R),9(7),172(8),48(6))].">
      <j1 rule="para" parents="24 24"/>
      <j2 rule="demod" parents="8 9 8 9 172 48 172 8 8 8 9 172 48"/>
    </justification>
  </clause>

  <clause id="200">
    <literal><![CDATA[
      f(x,f(y,x,z),f(y,x,f(y,z,u))) = f(y,x,f(z,u,f(y,x,z)))
    ]]></literal>
    <justification jstring="[back_demod(66),demod(168(5))].">
      <j1 rule="back_demod" parents="66"/>
      <j2 rule="demod" parents="168"/>
    </justification>
  </clause>

  <clause id="203">
    <literal><![CDATA[
      f(x,f(y,z,f(x,y,u)),f(x,v,w)) = f(x,f(y,z,u),f(x,w,f(x,y,v)))
    ]]></literal>
    <justification jstring="[back_demod(159),demod(172(7),56(5),172(6),197(6)),flip(a)].">
      <j1 rule="back_demod" parents="159"/>
      <j2 rule="demod" parents="172 56 172 197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="205">
    <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="[back_demod(171),demod(203(4),13(2),9(2))].">
      <j1 rule="back_demod" parents="171"/>
      <j2 rule="demod" parents="203 13 9"/>
    </justification>
  </clause>

  <clause id="209">
    <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="[back_demod(121),demod(205(3)),flip(a)].">
      <j1 rule="back_demod" parents="121"/>
      <j2 rule="demod" parents="205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="217">
    <literal><![CDATA[
      f(f(x,y,z),f(y,z,u),f(y,v,f(x,y,z))) = f(v,f(x,y,z),f(y,z,f(x,y,u)))
    ]]></literal>
    <justification jstring="[para(25(a,1),24(a,1,3)),demod(8(4),9(7),30(7),9(3),20(3),9(8)),flip(a)].">
      <j1 rule="para" parents="25 24"/>
      <j2 rule="demod" parents="8 9 30 9 20 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="219">
    <literal><![CDATA[
      f(x,y,f(x,z,f(y,u,f(x,z,y)))) = f(x,y,f(z,u,f(x,z,y)))
    ]]></literal>
    <justification jstring="[back_demod(64),demod(8(1,R),9(1),8(2,R),9(2),107(5),9(2),8(5,R),9(5))].">
      <j1 rule="back_demod" parents="64"/>
      <j2 rule="demod" parents="8 9 8 9 107 9 8 9"/>
    </justification>
  </clause>

  <clause id="234">
    <literal><![CDATA[
      f(f(x,y,z),f(y,z,u),f(y,f(y,z,u),f(z,f(x,y,z),f(y,z,u)))) = f(y,z,f(x,u,f(y,z,u)))
    ]]></literal>
    <justification jstring="[para(11(a,1),56(a,2)),demod(8(2),8(2),8(3),8(3),8(5),8(5),8(6),8(7,R),9(7),8(9),8(9))].">
      <j1 rule="para" parents="11 56"/>
      <j2 rule="demod" parents="8 8 8 8 8 8 8 8 9 8 8"/>
    </justification>
  </clause>

  <clause id="310">
    <literal><![CDATA[
      f(x,f(y,x,z),f(y,x,u)) = f(x,u,f(y,x,z))
    ]]></literal>
    <justification jstring="[para(77(a,1),8(a,2)),demod(8(2),8(2),8(3),8(5,R),9(5))].">
      <j1 rule="para" parents="77 8"/>
      <j2 rule="demod" parents="8 8 8 8 9"/>
    </justification>
  </clause>

  <clause id="319">
    <literal><![CDATA[
      f(x,f(x,y,z),f(y,u,f(x,y,z))) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(48(a,1),77(a,1,3)),demod(9(3),8(5),7(5),9(4)),flip(a)].">
      <j1 rule="para" parents="48 77"/>
      <j2 rule="demod" parents="9 8 7 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="325">
    <literal><![CDATA[
      f(f(x,y,z),f(x,u,f(x,y,z)),f(x,y,f(x,z,v))) = f(v,f(x,y,z),f(x,u,f(x,y,z)))
    ]]></literal>
    <justification jstring="[para(39(a,2),77(a,1,3)),demod(9(3),8(4),8(4),9(9))].">
      <j1 rule="para" parents="39 77"/>
      <j2 rule="demod" parents="9 8 8 9"/>
    </justification>
  </clause>

  <clause id="347">
    <literal><![CDATA[
      f(x,f(y,z,u),f(z,v,f(y,z,u))) = f(z,f(y,z,u),f(y,v,x))
    ]]></literal>
    <justification jstring="[para(77(a,1),77(a,1,2)),demod(8(3,R),9(3),8(5,R),9(5),57(6),8(6),8(6),310(7)),flip(a)].">
      <j1 rule="para" parents="77 77"/>
      <j2 rule="demod" parents="8 9 8 9 57 8 8 310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="349">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,y,z))) = f(x,z,f(x,y,f(y,z,u)))
    ]]></literal>
    <justification jstring="[back_demod(200),demod(8(1,R),9(1),8(3,R),9(3),172(4),48(3),8(4,R),9(4),8(6,R),9(6)),flip(a)].">
      <j1 rule="back_demod" parents="200"/>
      <j2 rule="demod" parents="8 9 8 9 172 48 8 9 8 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="350">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,y,u))) = f(x,y,u)
    ]]></literal>
    <justification jstring="[back_demod(234),demod(319(7),13(4)),flip(a)].">
      <j1 rule="back_demod" parents="234"/>
      <j2 rule="demod" parents="319 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="353">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,y,z))) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(350(a,1),8(a,1)),demod(8(3,R),9(3),8(4),8(4)),flip(a)].">
      <j1 rule="para" parents="350 8"/>
      <j2 rule="demod" parents="8 9 8 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="391">
    <literal><![CDATA[
      f(x,y,f(x,z,f(z,y,u))) = f(x,z,y)
    ]]></literal>
    <justification jstring="[back_demod(349),demod(353(3)),flip(a)].">
      <j1 rule="back_demod" parents="349"/>
      <j2 rule="demod" parents="353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="392">
    <literal><![CDATA[
      f(x,y,f(x,z,f(y,z,u))) = f(x,y,z)
    ]]></literal>
    <justification jstring="[back_demod(219),demod(9(1),142(4),9(1),9(4),353(6))].">
      <j1 rule="back_demod" parents="219"/>
      <j2 rule="demod" parents="9 142 9 9 353"/>
    </justification>
  </clause>

  <clause id="394">
    <literal><![CDATA[
      f(x,y,f(z,y,f(x,z,u))) = f(x,z,y)
    ]]></literal>
    <justification jstring="[back_demod(209),demod(8(1,R),9(1),8(2,R),9(2),392(3),8(3,R),9(3),8(4,R),9(4)),flip(a)].">
      <j1 rule="back_demod" parents="209"/>
      <j2 rule="demod" parents="8 9 8 9 392 8 9 8 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="401">
    <literal><![CDATA[
      f(x,y,f(z,x,y)) = f(z,x,y)
    ]]></literal>
    <justification jstring="[para(353(a,1),15(a,1)),demod(48(3),8(3,R),9(3)),flip(a)].">
      <j1 rule="para" parents="353 15"/>
      <j2 rule="demod" parents="48 8 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="412">
    <literal><![CDATA[
      f(x,f(y,z,u),f(z,u,f(y,z,v))) = f(z,u,f(y,z,f(y,v,x)))
    ]]></literal>
    <justification jstring="[back_demod(137),demod(401(4),217(5))].">
      <j1 rule="back_demod" parents="137"/>
      <j2 rule="demod" parents="401 217"/>
    </justification>
  </clause>

  <clause id="418">
    <literal><![CDATA[
      f(f(x,y,z),f(x,u,f(x,y,v)),f(x,y,w)) = f(x,y,f(z,w,f(x,u,v)))
    ]]></literal>
    <justification jstring="[para(10(a,1),26(a,1,2)),demod(9(2),8(3,R),9(3),8(6,R),9(6),8(7),9(7))].">
      <j1 rule="para" parents="10 26"/>
      <j2 rule="demod" parents="9 8 9 8 9 8 9"/>
    </justification>
  </clause>

  <clause id="419">
    <literal><![CDATA[
      f(f(x,y,z),f(x,y,u),f(x,v,f(x,y,w))) = f(x,y,f(z,u,f(x,v,w)))
    ]]></literal>
    <justification jstring="[para(10(a,1),26(a,1,3)),demod(9(3),8(4,R),9(4),8(6,R),9(6),8(7))].">
      <j1 rule="para" parents="10 26"/>
      <j2 rule="demod" parents="9 8 9 8 9 8"/>
    </justification>
  </clause>

  <clause id="420">
    <literal><![CDATA[
      f(f(x,y,f(x,z,u)),f(x,z,v),f(x,z,w)) = f(x,z,f(v,w,f(x,y,u)))
    ]]></literal>
    <justification jstring="[para(10(a,2),26(a,1,1)),demod(8(1,R),9(1),8(3,R),9(3),8(4,R),9(4),9(6),8(8,R),9(8))].">
      <j1 rule="para" parents="10 26"/>
      <j2 rule="demod" parents="8 9 8 9 8 9 9 8 9"/>
    </justification>
  </clause>

  <clause id="428">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,v,y))) = f(x,y,f(v,z,u))
    ]]></literal>
    <justification jstring="[para(20(a,1),26(a,1,1)),demod(28(4)),flip(a)].">
      <j1 rule="para" parents="20 26"/>
      <j2 rule="demod" parents="28"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="434">
    <literal><![CDATA[
      f(x,y,f(z,x,u)) = f(x,u,f(z,x,y))
    ]]></literal>
    <justification jstring="[para(39(a,2),26(a,2)),demod(13(2),8(3,R),310(3))].">
      <j1 rule="para" parents="39 26"/>
      <j2 rule="demod" parents="13 8 310"/>
    </justification>
  </clause>

  <clause id="452">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,v,f(x,y,w)))) = f(x,y,f(z,u,f(x,v,w)))
    ]]></literal>
    <justification jstring="[para(50(a,1),26(a,1,1)),demod(420(5)),flip(a)].">
      <j1 rule="para" parents="50 26"/>
      <j2 rule="demod" parents="420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="469">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,v,f(y,z,u))) = f(y,z,f(u,v,f(y,u,x)))
    ]]></literal>
    <justification jstring="[back_demod(325),demod(418(6),9(2),310(3)),flip(a)].">
      <j1 rule="back_demod" parents="325"/>
      <j2 rule="demod" parents="418 9 310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="473">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,v,z))) = f(x,y,f(x,z,f(y,v,u)))
    ]]></literal>
    <justification jstring="[back_demod(162),demod(469(4),9(1),48(4),428(6))].">
      <j1 rule="back_demod" parents="162"/>
      <j2 rule="demod" parents="469 9 48 428"/>
    </justification>
  </clause>

  <clause id="509">
    <literal><![CDATA[
      f(x,y,f(z,u,f(v,x,y))) = f(x,y,f(v,z,u))
    ]]></literal>
    <justification jstring="[para(401(a,1),26(a,1,1)),demod(27(4)),flip(a)].">
      <j1 rule="para" parents="401 26"/>
      <j2 rule="demod" parents="27"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="523">
    <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(15(a,1),391(a,2)),demod(9(3))].">
      <j1 rule="para" parents="15 391"/>
      <j2 rule="demod" parents="9"/>
    </justification>
  </clause>

  <clause id="547">
    <literal><![CDATA[
      f(x,y,f(z,x,f(z,y,u))) = f(z,x,y)
    ]]></literal>
    <justification jstring="[para(8(a,1),394(a,1)),demod(8(1,R),9(1),8(3),9(3),8(4),8(4))].">
      <j1 rule="para" parents="8 394"/>
      <j2 rule="demod" parents="8 9 8 9 8 8"/>
    </justification>
  </clause>

  <clause id="568">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,x,z)) = f(y,x,z)
    ]]></literal>
    <justification jstring="[para(394(a,1),26(a,2)),demod(13(4),8(4),9(4),310(4),9(4))].">
      <j1 rule="para" parents="394 26"/>
      <j2 rule="demod" parents="13 8 9 310 9"/>
    </justification>
  </clause>

  <clause id="575">
    <literal><![CDATA[
      f(x,f(y,z,x),f(z,x,u)) = f(z,x,f(y,x,u))
    ]]></literal>
    <justification jstring="[para(13(a,1),27(a,1,3)),demod(8(3),9(4))].">
      <j1 rule="para" parents="13 27"/>
      <j2 rule="demod" parents="8 9"/>
    </justification>
  </clause>

  <clause id="598">
    <literal><![CDATA[
      f(x,y,f(z,u,x)) = f(z,x,f(u,x,y))
    ]]></literal>
    <justification jstring="[para(434(a,1),8(a,2)),demod(9(2),8(3)),flip(a)].">
      <j1 rule="para" parents="434 8"/>
      <j2 rule="demod" parents="9 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="624">
    <literal><![CDATA[
      f(x,y,f(z,u,x)) = f(u,x,f(z,x,y))
    ]]></literal>
    <justification jstring="[para(434(a,1),547(a,2)),demod(9(3),8(4,R),9(4),523(5),8(3)),flip(a)].">
      <j1 rule="para" parents="434 547"/>
      <j2 rule="demod" parents="9 8 9 523 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="636">
    <literal><![CDATA[
      f(f(x,y,f(y,z,u)),f(y,v,f(x,y,z)),f(y,w,f(x,y,z))) = f(y,f(x,y,z),f(u,v,w))
    ]]></literal>
    <justification jstring="[para(10(a,1),28(a,1,1)),demod(9(4),9(6))].">
      <j1 rule="para" parents="10 28"/>
      <j2 rule="demod" parents="9 9"/>
    </justification>
  </clause>

  <clause id="664">
    <literal><![CDATA[
      f(x,f(y,x,z),f(u,v,f(x,z,w))) = f(x,f(y,x,z),f(w,u,v))
    ]]></literal>
    <justification jstring="[para(77(a,1),28(a,1,1)),demod(8(1,R),9(1),9(3),9(4),9(5),9(6),636(7),9(4),8(5,R),9(5),8(6),8(6)),flip(a)].">
      <j1 rule="para" parents="77 28"/>
      <j2 rule="demod" parents="8 9 9 9 9 9 636 9 8 9 8 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="690">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,z,x)) = f(y,z,x)
    ]]></literal>
    <justification jstring="[para(568(a,1),8(a,2)),demod(9(2),8(3),9(4))].">
      <j1 rule="para" parents="568 8"/>
      <j2 rule="demod" parents="9 8 9"/>
    </justification>
  </clause>

  <clause id="691">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,z,u)) = f(x,z,u)
    ]]></literal>
    <justification jstring="[para(8(a,1),568(a,1,2)),demod(8(2,R),9(2),8(4,R),9(4))].">
      <j1 rule="para" parents="8 568"/>
      <j2 rule="demod" parents="8 9 8 9"/>
    </justification>
  </clause>

  <clause id="692">
    <literal><![CDATA[
      f(x,y,f(x,z,f(y,u,z))) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(8(a,2),568(a,1,2)),demod(8(2),8(2),205(3),8(4),8(4))].">
      <j1 rule="para" parents="8 568"/>
      <j2 rule="demod" parents="8 8 205 8 8"/>
    </justification>
  </clause>

  <clause id="704">
    <literal><![CDATA[
      f(x,f(y,z,f(z,u,v)),f(x,z,u)) = f(x,z,u)
    ]]></literal>
    <justification jstring="[para(15(a,1),568(a,1,2)),demod(8(1,R),9(1),8(3),8(3),8(5),8(5))].">
      <j1 rule="para" parents="15 568"/>
      <j2 rule="demod" parents="8 9 8 8 8 8"/>
    </justification>
  </clause>

  <clause id="748">
    <literal><![CDATA[
      f(x,y,f(z,u,y)) = f(z,y,f(x,u,y))
    ]]></literal>
    <justification jstring="[para(598(a,1),8(a,2)),demod(9(2),8(3))].">
      <j1 rule="para" parents="598 8"/>
      <j2 rule="demod" parents="9 8"/>
    </justification>
  </clause>

  <clause id="752">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,z,f(z,u,v))) = f(z,f(y,z,u),f(y,x,v))
    ]]></literal>
    <justification jstring="[para(15(a,1),598(a,1,3)),demod(8(2),8(2),8(4,R),9(4),9(7),347(8))].">
      <j1 rule="para" parents="15 598"/>
      <j2 rule="demod" parents="8 8 8 9 9 347"/>
    </justification>
  </clause>

  <clause id="753">
    <literal><![CDATA[
      f(x,f(y,x,z),f(u,v,f(y,x,z))) = f(x,f(y,x,z),f(y,u,v))
    ]]></literal>
    <justification jstring="[para(39(a,1),598(a,1,3)),demod(9(2),8(4,R),9(4),752(4),8(6)),flip(a)].">
      <j1 rule="para" parents="39 598"/>
      <j2 rule="demod" parents="9 8 9 752 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="758">
    <literal><![CDATA[
      f(x,f(y,x,z),f(y,u,v)) = f(x,z,f(y,x,f(y,u,v)))
    ]]></literal>
    <justification jstring="[para(24(a,1),598(a,1,3)),demod(8(4,R),9(4),412(4),9(1),8(7),753(8),664(7),8(5),8(5)),flip(a)].">
      <j1 rule="para" parents="24 598"/>
      <j2 rule="demod" parents="8 9 412 9 8 753 664 8 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="779">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,z,f(z,u,v))) = f(z,f(y,z,u),f(x,y,v))
    ]]></literal>
    <justification jstring="[back_demod(752),demod(8(6,R),9(6))].">
      <j1 rule="back_demod" parents="752"/>
      <j2 rule="demod" parents="8 9"/>
    </justification>
  </clause>

  <clause id="783">
    <literal><![CDATA[
      f(x,f(y,z,u),f(z,v,f(y,z,u))) = f(z,f(y,z,u),f(x,y,v))
    ]]></literal>
    <justification jstring="[back_demod(347),demod(8(6))].">
      <j1 rule="back_demod" parents="347"/>
      <j2 rule="demod" parents="8"/>
    </justification>
  </clause>

  <clause id="788">
    <literal><![CDATA[
      f(x,y,f(z,u,y)) = f(u,y,f(x,z,y))
    ]]></literal>
    <justification jstring="[para(624(a,1),8(a,2)),demod(9(2),8(3))].">
      <j1 rule="para" parents="624 8"/>
      <j2 rule="demod" parents="9 8"/>
    </justification>
  </clause>

  <clause id="792">
    <literal><![CDATA[
      f(x,f(y,x,z),f(u,v,f(y,x,z))) = f(x,z,f(y,x,f(y,u,v)))
    ]]></literal>
    <justification jstring="[para(15(a,1),624(a,1,3)),demod(8(2),8(2),8(4,R),9(4),779(4),8(2,R),9(2),758(3),8(6)),flip(a)].">
      <j1 rule="para" parents="15 624"/>
      <j2 rule="demod" parents="8 8 8 9 779 8 9 758 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="835">
    <literal><![CDATA[
      f(x,f(y,z,x),f(u,v,f(y,z,w))) = f(x,f(y,z,x),f(y,u,v))
    ]]></literal>
    <justification jstring="[para(690(a,1),28(a,1,1)),demod(9(3),9(5),53(6),8(6),8(6)),flip(a)].">
      <j1 rule="para" parents="690 28"/>
      <j2 rule="demod" parents="9 9 53 8 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1090">
    <literal><![CDATA[
      f(x,f(y,x,z),f(u,y,v)) = f(x,z,f(y,x,f(u,y,v)))
    ]]></literal>
    <justification jstring="[para(10(a,1),748(a,1,3)),demod(779(4),792(7),8(4,R),9(4))].">
      <j1 rule="para" parents="10 748"/>
      <j2 rule="demod" parents="779 792 8 9"/>
    </justification>
  </clause>

  <clause id="1095">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,z,f(v,z,u))) = f(z,u,f(y,z,f(v,y,x)))
    ]]></literal>
    <justification jstring="[para(15(a,1),748(a,2,3)),demod(8(3,R),9(3),783(4),1090(3)),flip(a)].">
      <j1 rule="para" parents="15 748"/>
      <j2 rule="demod" parents="8 9 783 1090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1102">
    <literal><![CDATA[
      f(x,y,f(z,x,f(u,z,y))) = f(z,x,y)
    ]]></literal>
    <justification jstring="[para(401(a,1),748(a,1,3)),demod(13(3),792(5),8(2,R),9(2)),flip(a)].">
      <j1 rule="para" parents="401 748"/>
      <j2 rule="demod" parents="13 792 8 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1331">
    <literal><![CDATA[
      f(x,f(y,z,x),f(u,y,z)) = f(y,z,x)
    ]]></literal>
    <justification jstring="[para(401(a,1),788(a,1,3)),demod(13(3),835(5),8(3,R),9(3)),flip(a)].">
      <j1 rule="para" parents="401 788"/>
      <j2 rule="demod" parents="13 835 8 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2154">
    <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(14(a,1),35(a,1,2)),demod(9(3),419(7),9(3),28(4)),flip(a)].">
      <j1 rule="para" parents="14 35"/>
      <j2 rule="demod" parents="9 419 9 28"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2230">
    <literal><![CDATA[
      f(x,y,f(x,z,f(u,v,f(y,z,w)))) = f(x,y,f(z,v,f(x,u,z)))
    ]]></literal>
    <justification jstring="[para(691(a,1),35(a,1,2)),demod(469(6),428(3),8(1),8(1),452(4),9(1),8(5),8(5),9(6),2154(7)),flip(a)].">
      <j1 rule="para" parents="691 35"/>
      <j2 rule="demod" parents="469 428 8 8 452 9 8 8 9 2154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2393">
    <literal><![CDATA[
      f(x,f(y,z,u),f(v,w,f(z,u,f(x,y,z)))) = f(x,f(y,z,u),f(z,v,w))
    ]]></literal>
    <justification jstring="[para(598(a,2),428(a,1,3,3))].">
      <j1 rule="para" parents="598 428"/>
    </justification>
  </clause>

  <clause id="3032">
    <literal><![CDATA[
      f(x,y,f(z,y,f(z,u,f(x,v,z)))) = f(x,z,y)
    ]]></literal>
    <justification jstring="[para(704(a,1),34(a,2)),demod(7(3),2154(7),1095(6),8(2),7(2),8(2),2154(3))].">
      <j1 rule="para" parents="704 34"/>
      <j2 rule="demod" parents="7 2154 1095 8 7 8 2154"/>
    </justification>
  </clause>

  <clause id="6431">
    <literal><![CDATA[
      f(x,f(y,z,f(x,u,v)),f(z,v,f(x,u,v))) = f(x,v,f(y,z,u))
    ]]></literal>
    <justification jstring="[para(691(a,1),3032(a,1,3)),demod(8(4,R),9(4),428(8),8(6),8(6))].">
      <j1 rule="para" parents="691 3032"/>
      <j2 rule="demod" parents="8 9 428 8 8"/>
    </justification>
  </clause>

  <clause id="6568">
    <literal><![CDATA[
      f(x,y,f(y,z,f(u,x,z))) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(568(a,1),62(a,1,3)),demod(8(1,R),9(1),8(4,R),9(4),48(4),8(4,R),9(4),13(5),8(2,R),9(2),2154(5),2230(5),8(2,R),9(2),8(3,R),9(3)),flip(a)].">
      <j1 rule="para" parents="568 62"/>
      <j2 rule="demod" parents="8 9 8 9 48 8 9 13 8 9 2154 2230 8 9 8 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6576">
    <literal><![CDATA[
      f(x,f(y,z,f(u,v,w)),f(x,f(z,v6,f(u,v,w)),f(z,f(u,v,w),f(y,u,v6)))) = f(x,f(y,z,f(u,v,w)),f(z,v6,f(u,v,w)))
    ]]></literal>
    <justification jstring="[para(62(a,1),692(a,1,3,3))].">
      <j1 rule="para" parents="62 692"/>
    </justification>
  </clause>

  <clause id="6794">
    <literal><![CDATA[
      f(x,f(y,z,u),f(u,v,f(z,u,f(y,z,x)))) = f(x,f(z,u,v),f(y,z,u))
    ]]></literal>
    <justification jstring="[para(575(a,1),6568(a,1,3,3)),demod(1095(5),8(5,R),9(5),8(8,R))].">
      <j1 rule="para" parents="575 6568"/>
      <j2 rule="demod" parents="1095 8 9 8"/>
    </justification>
  </clause>

  <clause id="11571">
    <literal><![CDATA[
      f(x,f(y,z,u),f(z,u,f(y,x,v))) = f(z,u,f(y,x,v))
    ]]></literal>
    <justification jstring="[para(1331(a,1),109(a,1,2)),demod(27(5),48(2)),flip(a)].">
      <j1 rule="para" parents="1331 109"/>
      <j2 rule="demod" parents="27 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12275">
    <literal><![CDATA[
      f(x,f(y,z,u),f(v,y,z)) = f(y,z,f(v,x,u))
    ]]></literal>
    <justification jstring="[para(11(a,1),473(a,2,3)),demod(8(2),8(2),8(4),8(4),8(5,R),2154(5),509(5),8(5,R),9(5),758(5),48(4),1102(4),8(3,R),9(5),8(7,R),9(7),11571(7))].">
      <j1 rule="para" parents="11 473"/>
      <j2 rule="demod" parents="8 8 8 8 8 2154 509 8 9 758 48 1102 8 9 8 9 11571"/>
    </justification>
  </clause>

  <clause id="12418">
    <literal><![CDATA[
      f(x,f(y,z,u),f(z,u,v)) = f(z,u,f(x,y,v))
    ]]></literal>
    <justification jstring="[back_demod(6794),demod(8(2),2393(5),12275(6),8(4,R),9(4))].">
      <j1 rule="back_demod" parents="6794"/>
      <j2 rule="demod" parents="8 2393 12275 8 9"/>
    </justification>
  </clause>

  <clause id="12864">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,u,v)) = f(y,u,f(x,z,v))
    ]]></literal>
    <justification jstring="[para(8(a,2),12275(a,1,2)),demod(8(2),9(2),8(4),8(4),8(5,R),9(5))].">
      <j1 rule="para" parents="8 12275"/>
      <j2 rule="demod" parents="8 9 8 8 8 9"/>
    </justification>
  </clause>

  <clause id="13094">
    <literal><![CDATA[
      f(x,f(y,z,f(u,v,w)),f(z,v6,f(u,v,w))) = f(z,f(u,v,w),f(x,y,v6))
    ]]></literal>
    <justification jstring="[back_demod(6576),demod(12864(8),12418(7),692(4)),flip(a)].">
      <j1 rule="back_demod" parents="6576"/>
      <j2 rule="demod" parents="12864 12418 692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13388">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,v,u)) = f(y,u,f(v,x,z))
    ]]></literal>
    <justification jstring="[back_demod(6431),demod(13094(5))].">
      <j1 rule="back_demod" parents="6431"/>
      <j2 rule="demod" parents="13094"/>
    </justification>
  </clause>

  <clause id="13548">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer(dist_short)
    ]]></attribute>
    <justification jstring="[back_demod(12),demod(13388(10),8(6),8(6)),xx(a)].">
      <j1 rule="back_demod" parents="12"/>
      <j2 rule="demod" parents="13388 8 8"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

</proofs>
