<?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-both.out</source>

<heading><![CDATA[
Prover9 (32) version June-2006C, June 2006.
Process 13905 was started by mccune on cleo.thornwood,
Mon Jun 19 17:06:22 2006
The command was "/home/mccune/bin/prover9 -f dist-both.in".
]]></heading>

<proof number="1" length="193" max_count="39">

<comments><![CDATA[
% Proof 1 at 724.21 (+ 1.70) seconds: dist_both.
% Length of proof is 193.
% Level of proof is 31.
% Maximum clause weight is 43.
% Given clauses 858.
]]></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(A,B,C),D,E) != f(f(A,D,E),f(B,D,E),f(C,D,E))
    ]]></literal>
    <literal><![CDATA[
      f(f(A,B,C),D,E) != f(A,f(B,D,E),f(C,D,E))
    ]]></literal>
    <attribute><![CDATA[
      answer(dist_both)
    ]]></attribute>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="6">
    <literal><![CDATA[
      f(x,x,y) = x
    ]]></literal>
    <attribute><![CDATA[
      label(majority)
    ]]></attribute>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="7">
    <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="8">
    <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="9">
    <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(7(2),7(2),7(3,R),8(3))].">
      <j1 rule="copy" parents="4"/>
      <j2 rule="demod" parents="7 7 7 8"/>
    </justification>
  </clause>

  <clause id="10">
    <literal><![CDATA[
      f(f(A,D,E),f(B,D,E),f(C,D,E)) != f(D,E,f(A,B,C))
    ]]></literal>
    <literal><![CDATA[
      f(A,f(B,D,E),f(C,D,E)) != f(D,E,f(A,B,C))
    ]]></literal>
    <attribute><![CDATA[
      answer(dist_both)
    ]]></attribute>
    <justification jstring="[copy(5),demod(7(7),7(7),7(28),7(28)),flip(a),flip(b)].">
      <j1 rule="copy" parents="5"/>
      <j2 rule="demod" parents="7 7 7 7"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11">
    <literal><![CDATA[
      f(x,y,y) = y
    ]]></literal>
    <justification jstring="[para(7(a,1),6(a,1))].">
      <j1 rule="para" parents="7 6"/>
    </justification>
  </clause>

  <clause id="12">
    <literal><![CDATA[
      f(x,y,f(x,z,u)) = f(x,z,f(x,y,u))
    ]]></literal>
    <justification jstring="[para(9(a,2),7(a,1)),demod(7(1,R),8(1),8(3),7(4),8(4))].">
      <j1 rule="para" parents="9 7"/>
      <j2 rule="demod" parents="7 8 8 7 8"/>
    </justification>
  </clause>

  <clause id="13">
    <literal><![CDATA[
      f(x,y,f(z,y,u)) = f(z,y,f(x,y,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),7(a,2)),demod(8(2),7(3))].">
      <j1 rule="para" parents="9 7"/>
      <j2 rule="demod" parents="8 7"/>
    </justification>
  </clause>

  <clause id="14">
    <literal><![CDATA[
      f(x,y,f(x,z,u)) = f(x,u,f(x,z,y))
    ]]></literal>
    <justification jstring="[para(9(a,2),7(a,2)),demod(8(2),7(3),7(3))].">
      <j1 rule="para" parents="9 7"/>
      <j2 rule="demod" parents="8 7 7"/>
    </justification>
  </clause>

  <clause id="16">
    <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(9(a,1),9(a,1,3)),demod(7(1),8(5),7(6,R),8(6))].">
      <j1 rule="para" parents="9 9"/>
      <j2 rule="demod" parents="7 8 7 8"/>
    </justification>
  </clause>

  <clause id="18">
    <literal><![CDATA[
      f(x,y,f(x,z,y)) = f(x,z,y)
    ]]></literal>
    <justification jstring="[para(9(a,2),9(a,1)),demod(7(1,R),11(1),7(2),8(2)),flip(a)].">
      <j1 rule="para" parents="9 9"/>
      <j2 rule="demod" parents="7 11 7 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,y,v)) = f(x,v,f(y,u,f(x,y,z)))
    ]]></literal>
    <justification jstring="[para(9(a,2),9(a,2,3)),demod(7(2),7(2),7(6,R),8(6))].">
      <j1 rule="para" parents="9 9"/>
      <j2 rule="demod" parents="7 7 7 8"/>
    </justification>
  </clause>

  <clause id="22">
    <literal><![CDATA[
      f(x,y,f(x,y,z)) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),9(a,2,3)),demod(7(1),7(1),7(3),7(3))].">
      <j1 rule="para" parents="11 9"/>
      <j2 rule="demod" parents="7 7 7 7"/>
    </justification>
  </clause>

  <clause id="23">
    <literal><![CDATA[
      f(x,y,f(z,x,u)) = f(z,x,f(x,y,u))
    ]]></literal>
    <justification jstring="[para(12(a,1),7(a,2)),demod(8(2),7(3,R),8(3)),flip(a)].">
      <j1 rule="para" parents="12 7"/>
      <j2 rule="demod" parents="8 7 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24">
    <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(12(a,1),9(a,1,3)),demod(7(1,R),8(1),8(5),7(6,R),8(6))].">
      <j1 rule="para" parents="12 9"/>
      <j2 rule="demod" parents="7 8 8 7 8"/>
    </justification>
  </clause>

  <clause id="27">
    <literal><![CDATA[
      f(x,y,f(x,z,f(x,y,u))) = f(x,z,f(x,y,u))
    ]]></literal>
    <justification jstring="[para(18(a,1),9(a,1,3)),demod(7(1),7(3),8(4),7(5,R),8(5)),flip(a)].">
      <j1 rule="para" parents="18 9"/>
      <j2 rule="demod" parents="7 7 8 7 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28">
    <literal><![CDATA[
      f(x,f(x,y,z),f(x,z,u)) = f(x,u,f(x,y,z))
    ]]></literal>
    <justification jstring="[para(18(a,1),9(a,2,3)),demod(7(2),7(2),7(5,R),8(5))].">
      <j1 rule="para" parents="18 9"/>
      <j2 rule="demod" parents="7 7 7 8"/>
    </justification>
  </clause>

  <clause id="31">
    <literal><![CDATA[
      f(x,y,f(x,z,f(x,u,y))) = f(x,z,f(x,u,y))
    ]]></literal>
    <justification jstring="[para(18(a,1),12(a,1,3)),flip(a)].">
      <j1 rule="para" parents="18 12"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33">
    <literal><![CDATA[
      f(x,y,f(y,z,f(x,y,u))) = f(x,y,f(y,z,u))
    ]]></literal>
    <justification jstring="[para(9(a,2),22(a,1,3)),demod(8(4))].">
      <j1 rule="para" parents="9 22"/>
      <j2 rule="demod" parents="8"/>
    </justification>
  </clause>

  <clause id="36">
    <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(9(a,1),13(a,1,3)),demod(7(1),7(6,R),8(6))].">
      <j1 rule="para" parents="9 13"/>
      <j2 rule="demod" parents="7 7 8"/>
    </justification>
  </clause>

  <clause id="37">
    <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(9(a,2),13(a,1,3)),demod(7(1,R),8(1),8(4),7(6,R),8(6)),flip(a)].">
      <j1 rule="para" parents="9 13"/>
      <j2 rule="demod" parents="7 8 8 7 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38">
    <literal><![CDATA[
      f(x,y,f(z,u,f(z,x,v))) = f(z,x,f(x,y,f(z,u,v)))
    ]]></literal>
    <justification jstring="[para(9(a,1),13(a,2,3)),demod(7(1,R),8(1),7(2,R),8(2),8(4),7(5,R),8(5),7(6,R),8(6)),flip(a)].">
      <j1 rule="para" parents="9 13"/>
      <j2 rule="demod" parents="7 8 7 8 8 7 8 7 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40">
    <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(12(a,1),13(a,1,3)),demod(7(1,R),8(1),7(6,R),8(6))].">
      <j1 rule="para" parents="12 13"/>
      <j2 rule="demod" parents="7 8 7 8"/>
    </justification>
  </clause>

  <clause id="42">
    <literal><![CDATA[
      f(x,y,f(z,x,f(x,y,u))) = f(z,x,f(x,y,u))
    ]]></literal>
    <justification jstring="[para(18(a,1),13(a,1,3)),demod(7(1),7(3),7(5,R),8(5)),flip(a)].">
      <j1 rule="para" parents="18 13"/>
      <j2 rule="demod" parents="7 7 7 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45">
    <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(9(a,2),14(a,1,3)),demod(8(4),8(5)),flip(a)].">
      <j1 rule="para" parents="9 14"/>
      <j2 rule="demod" parents="8 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47">
    <literal><![CDATA[
      f(x,y,f(x,z,f(x,u,v))) = f(x,u,f(x,y,f(x,v,z)))
    ]]></literal>
    <justification jstring="[para(14(a,1),12(a,2,3)),demod(8(4)),flip(a)].">
      <j1 rule="para" parents="14 12"/>
      <j2 rule="demod" parents="8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49">
    <literal><![CDATA[
      f(x,f(x,y,z),f(x,u,z)) = f(x,u,f(x,y,z))
    ]]></literal>
    <justification jstring="[para(18(a,1),14(a,1,3)),demod(8(4)),flip(a)].">
      <j1 rule="para" parents="18 14"/>
      <j2 rule="demod" parents="8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="51">
    <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(13(a,1),14(a,1,3)),demod(8(5)),flip(a)].">
      <j1 rule="para" parents="13 14"/>
      <j2 rule="demod" parents="8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="54">
    <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(23(a,2),18(a,1,3))].">
      <j1 rule="para" parents="23 18"/>
    </justification>
  </clause>

  <clause id="57">
    <literal><![CDATA[
      f(x,f(x,y,z),f(x,u,f(x,z,v))) = f(x,f(x,u,v),f(x,y,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),28(a,1,3)),demod(8(2),7(3,R),8(3),7(5,R),8(5))].">
      <j1 rule="para" parents="9 28"/>
      <j2 rule="demod" parents="8 7 8 7 8"/>
    </justification>
  </clause>

  <clause id="61">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,z,v))) = f(x,y,f(x,z,f(z,v,u)))
    ]]></literal>
    <justification jstring="[para(9(a,2),28(a,2,3)),demod(8(4),49(5)),flip(a)].">
      <j1 rule="para" parents="9 28"/>
      <j2 rule="demod" parents="8 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="63">
    <literal><![CDATA[
      f(x,f(x,y,z),f(x,u,v)) = f(x,y,f(x,z,f(x,u,v)))
    ]]></literal>
    <justification jstring="[para(28(a,1),12(a,2,3)),demod(57(4))].">
      <j1 rule="para" parents="28 12"/>
      <j2 rule="demod" parents="57"/>
    </justification>
  </clause>

  <clause id="64">
    <literal><![CDATA[
      f(x,y,f(x,z,f(x,u,f(x,y,v)))) = f(x,u,f(x,z,f(x,y,v)))
    ]]></literal>
    <justification jstring="[para(12(a,1),28(a,1,2)),demod(8(4),63(5),63(4),31(3))].">
      <j1 rule="para" parents="12 28"/>
      <j2 rule="demod" parents="8 63 63 31"/>
    </justification>
  </clause>

  <clause id="73">
    <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(27(a,1),9(a,1,3)),demod(7(1,R),8(1),7(4,R),8(4),8(6),7(7,R),8(7)),flip(a)].">
      <j1 rule="para" parents="27 9"/>
      <j2 rule="demod" parents="7 8 7 8 8 7 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="76">
    <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(27(a,1),13(a,2,3)),demod(7(3,R),8(3),7(7,R),8(7))].">
      <j1 rule="para" parents="27 13"/>
      <j2 rule="demod" parents="7 8 7 8"/>
    </justification>
  </clause>

  <clause id="82">
    <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(16(a,1),7(a,2)),demod(7(1,R),8(1),8(3),7(5,R),8(5),7(6,R),8(6))].">
      <j1 rule="para" parents="16 7"/>
      <j2 rule="demod" parents="7 8 8 7 8 7 8"/>
    </justification>
  </clause>

  <clause id="84">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,z,f(u,v,w)))) = f(x,z,f(x,y,f(u,v,f(z,u,w))))
    ]]></literal>
    <justification jstring="[para(16(a,1),9(a,1,3)),demod(7(1,R),8(1),7(2,R),8(2),7(6,R),8(6),8(7),7(8,R),8(8))].">
      <j1 rule="para" parents="16 9"/>
      <j2 rule="demod" parents="7 8 7 8 7 8 8 7 8"/>
    </justification>
  </clause>

  <clause id="87">
    <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(16(a,1),9(a,2)),demod(7(2,R),8(2),7(5,R),8(5))].">
      <j1 rule="para" parents="16 9"/>
      <j2 rule="demod" parents="7 8 7 8"/>
    </justification>
  </clause>

  <clause id="91">
    <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(9(a,1),16(a,2,3,3)),demod(7(1,R),8(1),8(5),7(6,R),8(6))].">
      <j1 rule="para" parents="9 16"/>
      <j2 rule="demod" parents="7 8 8 7 8"/>
    </justification>
  </clause>

  <clause id="93">
    <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(9(a,2),16(a,2,3)),flip(a)].">
      <j1 rule="para" parents="9 16"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="98">
    <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),12(a,2,3)),demod(7(1,R),8(1),7(6,R),8(6)),flip(a)].">
      <j1 rule="para" parents="16 12"/>
      <j2 rule="demod" parents="7 8 7 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="103">
    <literal><![CDATA[
      f(x,y,f(z,u,f(y,v,f(y,z,w)))) = f(y,z,f(x,y,f(z,u,f(y,v,w))))
    ]]></literal>
    <justification jstring="[para(16(a,2),13(a,1,3)),demod(7(1,R),8(1),7(2,R),8(2),7(5,R),8(5),7(8,R),8(8))].">
      <j1 rule="para" parents="16 13"/>
      <j2 rule="demod" parents="7 8 7 8 7 8 7 8"/>
    </justification>
  </clause>

  <clause id="135">
    <literal><![CDATA[
      f(x,y,f(z,y,f(z,x,u))) = f(z,y,f(z,x,f(x,y,u)))
    ]]></literal>
    <justification jstring="[para(33(a,1),16(a,2,3)),demod(76(4))].">
      <j1 rule="para" parents="33 16"/>
      <j2 rule="demod" parents="76"/>
    </justification>
  </clause>

  <clause id="140">
    <literal><![CDATA[
      f(x,y,f(z,y,f(x,y,u))) = f(z,y,f(x,y,u))
    ]]></literal>
    <justification jstring="[para(42(a,1),7(a,2)),demod(7(1,R),8(1),8(3),7(4,R),8(4))].">
      <j1 rule="para" parents="42 7"/>
      <j2 rule="demod" parents="7 8 8 7 8"/>
    </justification>
  </clause>

  <clause id="192">
    <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(20(a,2),7(a,2)),demod(7(1,R),8(1),8(3),8(4),7(5),8(5)),flip(a)].">
      <j1 rule="para" parents="20 7"/>
      <j2 rule="demod" parents="7 8 8 8 7 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="193">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,u,v)) = f(x,v,f(z,u,f(x,y,u)))
    ]]></literal>
    <justification jstring="[para(7(a,2),20(a,1,2)),demod(8(4),7(5,R),8(5))].">
      <j1 rule="para" parents="7 20"/>
      <j2 rule="demod" parents="8 7 8"/>
    </justification>
  </clause>

  <clause id="194">
    <literal><![CDATA[
      f(x,f(x,y,z),f(z,u,v)) = f(x,y,f(z,u,f(x,z,v)))
    ]]></literal>
    <justification jstring="[para(20(a,1),8(a,1)),demod(8(4),8(5)),flip(a)].">
      <j1 rule="para" parents="20 8"/>
      <j2 rule="demod" parents="8 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="195">
    <literal><![CDATA[
      f(x,f(x,y,z),f(y,u,v)) = f(x,z,f(y,v,f(x,y,u)))
    ]]></literal>
    <justification jstring="[para(20(a,1),8(a,2))].">
      <j1 rule="para" parents="20 8"/>
    </justification>
  </clause>

  <clause id="196">
    <literal><![CDATA[
      f(x,f(y,z,u),f(v,f(y,z,u),f(y,x,w))) = f(v,f(y,z,u),f(x,w,f(y,u,f(y,z,x))))
    ]]></literal>
    <justification jstring="[para(20(a,1),9(a,1,3)),demod(7(2),7(2),7(5,R),8(5),7(8,R),8(8),7(9)),flip(a)].">
      <j1 rule="para" parents="20 9"/>
      <j2 rule="demod" parents="7 7 7 8 7 8 7"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="206">
    <literal><![CDATA[
      f(x,f(y,x,z),f(y,x,u)) = f(y,x,f(x,z,u))
    ]]></literal>
    <justification jstring="[para(9(a,2),20(a,2)),demod(11(2),8(2)),flip(a)].">
      <j1 rule="para" parents="9 20"/>
      <j2 rule="demod" parents="11 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="207">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,z,u))) = f(x,z,f(x,u,y))
    ]]></literal>
    <justification jstring="[para(11(a,1),20(a,1,2)),demod(8(3),7(4,R),8(4)),flip(a)].">
      <j1 rule="para" parents="11 20"/>
      <j2 rule="demod" parents="8 7 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="218">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,y,u)) = f(y,u,f(x,u,f(x,y,z)))
    ]]></literal>
    <justification jstring="[para(20(a,2),13(a,1))].">
      <j1 rule="para" parents="20 13"/>
    </justification>
  </clause>

  <clause id="221">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,z,x)) = f(y,z,f(z,x,f(y,x,u)))
    ]]></literal>
    <justification jstring="[para(20(a,2),13(a,2)),demod(7(1,R),8(1),7(2,R),8(2),8(4),7(5),7(5)),flip(a)].">
      <j1 rule="para" parents="20 13"/>
      <j2 rule="demod" parents="7 8 7 8 8 7 7"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="266">
    <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(20(a,2),140(a,1,3)),demod(8(1),7(2),7(2),7(5,R),8(5),7(7,R),8(7))].">
      <j1 rule="para" parents="20 140"/>
      <j2 rule="demod" parents="8 7 7 7 8 7 8"/>
    </justification>
  </clause>

  <clause id="308">
    <literal><![CDATA[
      f(f(x,y,z),f(u,v,f(x,z,f(x,y,u))),f(u,w,f(x,y,z))) = f(u,f(x,y,z),f(w,f(x,y,z),f(x,u,v)))
    ]]></literal>
    <justification jstring="[para(20(a,1),206(a,1,2)),demod(7(2),7(2),8(6),7(10,R),8(10),7(11))].">
      <j1 rule="para" parents="20 206"/>
      <j2 rule="demod" parents="7 7 8 7 8 7"/>
    </justification>
  </clause>

  <clause id="313">
    <literal><![CDATA[
      f(x,y,f(z,u,y)) = f(z,y,f(x,u,y))
    ]]></literal>
    <justification jstring="[para(207(a,1),7(a,2)),demod(7(1),7(1),22(2),8(2),7(3),8(3),7(4,R),8(4))].">
      <j1 rule="para" parents="207 7"/>
      <j2 rule="demod" parents="7 7 22 8 7 8 7 8"/>
    </justification>
  </clause>

  <clause id="314">
    <literal><![CDATA[
      f(x,y,f(z,u,x)) = f(z,x,f(u,x,y))
    ]]></literal>
    <justification jstring="[para(7(a,1),207(a,1)),demod(7(1),7(1),22(2),7(2),7(2),7(3,R),8(3),7(4,R),8(4))].">
      <j1 rule="para" parents="7 207"/>
      <j2 rule="demod" parents="7 7 22 7 7 7 8 7 8"/>
    </justification>
  </clause>

  <clause id="319">
    <literal><![CDATA[
      f(x,y,f(z,x,y)) = f(z,x,y)
    ]]></literal>
    <justification jstring="[para(207(a,1),11(a,1)),demod(207(3),11(1),22(2)),flip(a)].">
      <j1 rule="para" parents="207 11"/>
      <j2 rule="demod" parents="207 11 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="343">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,u,f(x,z,u))) = f(x,u,f(y,z,u))
    ]]></literal>
    <justification jstring="[para(313(a,1),18(a,1,3))].">
      <j1 rule="para" parents="313 18"/>
    </justification>
  </clause>

  <clause id="345">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,y,z))) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(18(a,1),313(a,2,3)),demod(7(3,R),8(3),194(4),18(2),11(6))].">
      <j1 rule="para" parents="18 313"/>
      <j2 rule="demod" parents="7 8 194 18 11"/>
    </justification>
  </clause>

  <clause id="347">
    <literal><![CDATA[
      f(x,y,f(x,z,f(z,y,u))) = f(x,z,y)
    ]]></literal>
    <justification jstring="[para(22(a,1),313(a,2,3)),demod(7(3,R),8(3),195(4),206(3),11(6))].">
      <j1 rule="para" parents="22 313"/>
      <j2 rule="demod" parents="7 8 195 206 11"/>
    </justification>
  </clause>

  <clause id="378">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,x,z)) = f(y,x,z)
    ]]></literal>
    <justification jstring="[para(20(a,2),313(a,2)),demod(7(1,R),8(1),7(2,R),8(2),195(4),206(3),347(3),7(3,R),8(3),7(4,R),8(4),22(4)),flip(a)].">
      <j1 rule="para" parents="20 313"/>
      <j2 rule="demod" parents="7 8 7 8 195 206 347 7 8 7 8 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="382">
    <literal><![CDATA[
      f(x,y,f(z,x,f(z,y,u))) = f(z,x,y)
    ]]></literal>
    <justification jstring="[back_demod(266),demod(345(4)),flip(a)].">
      <j1 rule="back_demod" parents="266"/>
      <j2 rule="demod" parents="345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="384">
    <literal><![CDATA[
      f(x,y,f(y,z,f(x,z,u))) = f(x,y,z)
    ]]></literal>
    <justification jstring="[back_demod(135),demod(7(1,R),8(1),7(2,R),8(2),7(5,R),8(5),382(6),8(4))].">
      <j1 rule="back_demod" parents="135"/>
      <j2 rule="demod" parents="7 8 7 8 7 8 382 8"/>
    </justification>
  </clause>

  <clause id="385">
    <literal><![CDATA[
      f(x,y,f(z,y,f(x,z,u))) = f(x,z,y)
    ]]></literal>
    <justification jstring="[back_demod(93),demod(8(1),345(3),7(3,R),8(3)),flip(a)].">
      <j1 rule="back_demod" parents="93"/>
      <j2 rule="demod" parents="8 345 7 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="386">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,y,z)) = f(x,y,z)
    ]]></literal>
    <justification jstring="[back_demod(87),demod(382(6))].">
      <j1 rule="back_demod" parents="87"/>
      <j2 rule="demod" parents="382"/>
    </justification>
  </clause>

  <clause id="387">
    <literal><![CDATA[
      f(x,y,f(z,y,f(z,x,u))) = f(z,x,y)
    ]]></literal>
    <justification jstring="[back_demod(221),demod(7(2),386(3),7(2,R),8(2),7(3,R),8(3)),flip(a)].">
      <j1 rule="back_demod" parents="221"/>
      <j2 rule="demod" parents="7 386 7 8 7 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="389">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,y,u)) = f(x,y,u)
    ]]></literal>
    <justification jstring="[back_demod(218),demod(387(6))].">
      <j1 rule="back_demod" parents="218"/>
      <j2 rule="demod" parents="387"/>
    </justification>
  </clause>

  <clause id="392">
    <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(11(a,1),24(a,1)),demod(7(1,R),8(1),7(3,R),8(3),8(6),7(7,R),8(7),76(7)),flip(a)].">
      <j1 rule="para" parents="11 24"/>
      <j2 rule="demod" parents="7 8 7 8 8 7 8 76"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="413">
    <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(24(a,1),20(a,2)),demod(8(4))].">
      <j1 rule="para" parents="24 20"/>
      <j2 rule="demod" parents="8"/>
    </justification>
  </clause>

  <clause id="430">
    <literal><![CDATA[
      f(x,y,f(x,z,f(y,u,z))) = f(x,y,z)
    ]]></literal>
    <justification jstring="[back_demod(389),demod(413(3))].">
      <j1 rule="back_demod" parents="389"/>
      <j2 rule="demod" parents="413"/>
    </justification>
  </clause>

  <clause id="473">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,z,x)) = f(y,z,x)
    ]]></literal>
    <justification jstring="[para(378(a,1),7(a,2)),demod(8(2),7(3),8(4))].">
      <j1 rule="para" parents="378 7"/>
      <j2 rule="demod" parents="8 7 8"/>
    </justification>
  </clause>

  <clause id="474">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,z,u)) = f(x,z,u)
    ]]></literal>
    <justification jstring="[para(7(a,1),378(a,1,2)),demod(7(2,R),8(2),7(4,R),8(4))].">
      <j1 rule="para" parents="7 378"/>
      <j2 rule="demod" parents="7 8 7 8"/>
    </justification>
  </clause>

  <clause id="475">
    <literal><![CDATA[
      f(x,f(y,x,z),f(y,z,u)) = f(y,x,z)
    ]]></literal>
    <justification jstring="[para(378(a,1),8(a,1)),flip(a)].">
      <j1 rule="para" parents="378 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="476">
    <literal><![CDATA[
      f(x,f(y,z,u),f(v,f(y,z,u),f(y,z,x))) = f(v,f(y,z,x),f(y,z,u))
    ]]></literal>
    <justification jstring="[para(378(a,1),9(a,1,3)),demod(8(2),7(3,R),8(6),7(7)),flip(a)].">
      <j1 rule="para" parents="378 9"/>
      <j2 rule="demod" parents="8 7 8 7"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="481">
    <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(378(a,1),12(a,1,3)),demod(7(1,R),8(1),7(4,R),8(4)),flip(a)].">
      <j1 rule="para" parents="378 12"/>
      <j2 rule="demod" parents="7 8 7 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="485">
    <literal><![CDATA[
      f(x,y,f(x,z,f(y,u,f(y,v,z)))) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(14(a,1),378(a,1,2)),demod(7(3,R),8(3),413(4),7(5,R),8(5))].">
      <j1 rule="para" parents="14 378"/>
      <j2 rule="demod" parents="7 8 413 7 8"/>
    </justification>
  </clause>

  <clause id="497">
    <literal><![CDATA[
      f(f(x,y,z),f(x,y,u),f(u,v,f(x,y,z))) = f(v,f(x,y,u),f(x,y,z))
    ]]></literal>
    <justification jstring="[para(378(a,1),206(a,1,2)),demod(8(2),8(4),8(8),7(9),476(10))].">
      <j1 rule="para" parents="378 206"/>
      <j2 rule="demod" parents="8 8 8 7 476"/>
    </justification>
  </clause>

  <clause id="514">
    <literal><![CDATA[
      f(f(x,y,z),f(x,z,u),f(x,y,z)) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(18(a,1),473(a,1,3)),demod(18(6))].">
      <j1 rule="para" parents="18 473"/>
      <j2 rule="demod" parents="18"/>
    </justification>
  </clause>

  <clause id="524">
    <literal><![CDATA[
      f(f(x,y,z),f(y,z,u),f(x,y,z)) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(319(a,1),473(a,1,3)),demod(319(6))].">
      <j1 rule="para" parents="319 473"/>
      <j2 rule="demod" parents="319"/>
    </justification>
  </clause>

  <clause id="532">
    <literal><![CDATA[
      f(x,f(y,z,u),f(z,u,x)) = f(z,u,x)
    ]]></literal>
    <justification jstring="[para(474(a,1),7(a,2)),demod(7(2),7(2),7(3),7(4),7(4))].">
      <j1 rule="para" parents="474 7"/>
      <j2 rule="demod" parents="7 7 7 7 7"/>
    </justification>
  </clause>

  <clause id="573">
    <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(474(a,1),378(a,1,2)),demod(7(2),7(2),7(3,R),8(3),413(4),7(5),7(5),7(6,R),8(6))].">
      <j1 rule="para" parents="474 378"/>
      <j2 rule="demod" parents="7 7 7 8 413 7 7 7 8"/>
    </justification>
  </clause>

  <clause id="612">
    <literal><![CDATA[
      f(x,y,f(z,f(z,y,u),f(x,z,v))) = f(x,z,y)
    ]]></literal>
    <justification jstring="[para(9(a,1),475(a,1,3)),demod(7(1,R),8(1),8(2),7(3,R),8(3),195(4),7(5,R),8(5))].">
      <j1 rule="para" parents="9 475"/>
      <j2 rule="demod" parents="7 8 8 7 8 195 7 8"/>
    </justification>
  </clause>

  <clause id="630">
    <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(474(a,1),475(a,1,3)),demod(7(2,R),8(2),8(4),413(4),7(6,R),8(6))].">
      <j1 rule="para" parents="474 475"/>
      <j2 rule="demod" parents="7 8 8 413 7 8"/>
    </justification>
  </clause>

  <clause id="655">
    <literal><![CDATA[
      f(f(x,y,z),f(y,u,v),f(x,y,f(y,z,v))) = f(y,v,f(x,y,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),532(a,1,3)),demod(7(2,R),8(2))].">
      <j1 rule="para" parents="9 532"/>
      <j2 rule="demod" parents="7 8"/>
    </justification>
  </clause>

  <clause id="705">
    <literal><![CDATA[
      f(x,y,f(z,u,f(z,x,y))) = f(z,x,y)
    ]]></literal>
    <justification jstring="[para(7(a,1),345(a,1)),demod(7(1),7(3),7(3),7(4))].">
      <j1 rule="para" parents="7 345"/>
      <j2 rule="demod" parents="7 7 7 7"/>
    </justification>
  </clause>

  <clause id="706">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,y,u))) = f(x,y,u)
    ]]></literal>
    <justification jstring="[para(7(a,2),345(a,1,3)),demod(8(2))].">
      <j1 rule="para" parents="7 345"/>
      <j2 rule="demod" parents="8"/>
    </justification>
  </clause>

  <clause id="757">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,v,f(y,z,v))) = f(x,v,f(y,z,u))
    ]]></literal>
    <justification jstring="[para(378(a,1),347(a,1,3,3)),demod(8(2))].">
      <j1 rule="para" parents="378 347"/>
      <j2 rule="demod" parents="8"/>
    </justification>
  </clause>

  <clause id="760">
    <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(474(a,1),347(a,1,3,3)),demod(7(2),7(2))].">
      <j1 rule="para" parents="474 347"/>
      <j2 rule="demod" parents="7 7"/>
    </justification>
  </clause>

  <clause id="790">
    <literal><![CDATA[
      f(x,y,f(y,z,f(x,u,f(x,z,v)))) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(16(a,2),382(a,1,3)),demod(7(1,R),8(1),7(2,R),8(2),7(3,R),8(3),7(5),7(5))].">
      <j1 rule="para" parents="16 382"/>
      <j2 rule="demod" parents="7 8 7 8 7 8 7 7"/>
    </justification>
  </clause>

  <clause id="885">
    <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(378(a,1),384(a,1,3,3)),demod(7(2,R),8(2))].">
      <j1 rule="para" parents="378 384"/>
      <j2 rule="demod" parents="7 8"/>
    </justification>
  </clause>

  <clause id="902">
    <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(378(a,1),385(a,1,3,3)),demod(7(2,R),8(2),7(3,R),8(6))].">
      <j1 rule="para" parents="378 385"/>
      <j2 rule="demod" parents="7 8 7 8"/>
    </justification>
  </clause>

  <clause id="1150">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,u,y))) = f(x,u,y)
    ]]></literal>
    <justification jstring="[para(706(a,1),7(a,2)),demod(7(1),7(1),8(3),7(4),7(4))].">
      <j1 rule="para" parents="706 7"/>
      <j2 rule="demod" parents="7 7 8 7 7"/>
    </justification>
  </clause>

  <clause id="1237">
    <literal><![CDATA[
      f(x,f(y,z,x),f(z,x,u)) = f(y,x,f(z,x,u))
    ]]></literal>
    <justification jstring="[para(473(a,1),36(a,2,3)),demod(7(3),8(3),140(4),18(4),7(4),7(5,R)),flip(a)].">
      <j1 rule="para" parents="473 36"/>
      <j2 rule="demod" parents="7 8 140 18 7 7"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1248">
    <literal><![CDATA[
      f(x,f(y,z,x),f(u,z,x)) = f(y,x,f(u,z,x))
    ]]></literal>
    <justification jstring="[para(532(a,1),36(a,2,3)),demod(7(3),8(3),1150(5),7(4),7(5,R)),flip(a)].">
      <j1 rule="para" parents="532 36"/>
      <j2 rule="demod" parents="7 8 1150 7 7"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1298">
    <literal><![CDATA[
      f(f(x,y,f(y,z,u)),f(x,v,f(y,z,u)),f(x,y,f(y,z,u))) = f(y,u,f(x,y,z))
    ]]></literal>
    <justification jstring="[para(9(a,2),514(a,2)),demod(8(4))].">
      <j1 rule="para" parents="9 514"/>
      <j2 rule="demod" parents="8"/>
    </justification>
  </clause>

  <clause id="1396">
    <literal><![CDATA[
      f(x,f(x,y,z),f(u,x,v)) = f(x,y,f(u,x,f(x,v,z)))
    ]]></literal>
    <justification jstring="[para(37(a,2),514(a,2)),demod(8(6),1298(10))].">
      <j1 rule="para" parents="37 514"/>
      <j2 rule="demod" parents="8 1298"/>
    </justification>
  </clause>

  <clause id="1409">
    <literal><![CDATA[
      f(x,y,f(z,f(y,z,u),f(x,z,v))) = f(x,y,z)
    ]]></literal>
    <justification jstring="[back_demod(612),demod(7(1,R),8(1),8(5))].">
      <j1 rule="back_demod" parents="612"/>
      <j2 rule="demod" parents="7 8 8"/>
    </justification>
  </clause>

  <clause id="1483">
    <literal><![CDATA[
      f(x,f(y,x,z),f(x,z,u)) = f(x,u,f(y,x,z))
    ]]></literal>
    <justification jstring="[para(524(a,1),36(a,2,3)),demod(7(4),7(4),22(4),655(5),7(5,R)),flip(a)].">
      <j1 rule="para" parents="524 36"/>
      <j2 rule="demod" parents="7 7 22 655 7"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1523">
    <literal><![CDATA[
      f(f(x,y,z),f(x,y,f(x,z,u)),f(u,v,f(x,y,z))) = f(x,f(x,y,z),f(u,v,f(x,y,z)))
    ]]></literal>
    <justification jstring="[para(12(a,1),1237(a,1,2)),demod(8(2),8(5),8(9))].">
      <j1 rule="para" parents="12 1237"/>
      <j2 rule="demod" parents="8 8 8"/>
    </justification>
  </clause>

  <clause id="1624">
    <literal><![CDATA[
      f(x,f(y,x,z),f(u,y,x)) = f(x,z,f(u,y,x))
    ]]></literal>
    <justification jstring="[para(7(a,1),1248(a,1)),demod(7(2),7(2),7(3,R),7(5,R),8(5))].">
      <j1 rule="para" parents="7 1248"/>
      <j2 rule="demod" parents="7 7 7 7 8"/>
    </justification>
  </clause>

  <clause id="1660">
    <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(1483(a,1),16(a,2)),demod(7(1),7(1),7(2),7(2),8(3),7(6),7(6),8(7),7(8),7(8),8(9))].">
      <j1 rule="para" parents="1483 16"/>
      <j2 rule="demod" parents="7 7 7 7 8 7 7 8 7 7 8"/>
    </justification>
  </clause>

  <clause id="1736">
    <literal><![CDATA[
      f(x,f(y,z,f(x,y,u)),f(x,v,w)) = f(x,y,f(x,f(y,z,u),f(x,v,w)))
    ]]></literal>
    <justification jstring="[para(36(a,1),1624(a,1,2)),demod(7(1,R),8(1),7(2,R),8(2),7(4),8(4),63(5),63(4),27(4),7(6,R),8(6),7(7),8(7)),flip(a)].">
      <j1 rule="para" parents="36 1624"/>
      <j2 rule="demod" parents="7 8 7 8 7 8 63 63 27 7 8 7 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2394">
    <literal><![CDATA[
      f(x,y,f(z,f(x,z,u),f(z,y,v))) = f(x,z,y)
    ]]></literal>
    <justification jstring="[para(1409(a,1),7(a,2)),demod(7(2,R),8(2),8(4),7(5),7(5))].">
      <j1 rule="para" parents="1409 7"/>
      <j2 rule="demod" parents="7 8 8 7 7"/>
    </justification>
  </clause>

  <clause id="2402">
    <literal><![CDATA[
      f(x,y,f(f(y,z,u),f(y,v,f(y,z,u)),f(x,w,f(y,z,u)))) = f(y,u,f(x,y,z))
    ]]></literal>
    <justification jstring="[para(9(a,2),1409(a,2)),demod(8(3),8(5))].">
      <j1 rule="para" parents="9 1409"/>
      <j2 rule="demod" parents="8 8"/>
    </justification>
  </clause>

  <clause id="2630">
    <literal><![CDATA[
      f(x,f(y,z,u),f(z,f(x,z,v),f(z,w,f(y,z,u)))) = f(y,z,f(x,z,u))
    ]]></literal>
    <justification jstring="[para(13(a,1),2394(a,2)),demod(8(4))].">
      <j1 rule="para" parents="13 2394"/>
      <j2 rule="demod" parents="8"/>
    </justification>
  </clause>

  <clause id="2651">
    <literal><![CDATA[
      f(x,y,f(z,u,x)) = f(u,x,f(z,x,y))
    ]]></literal>
    <justification jstring="[para(314(a,2),2394(a,2)),demod(8(4),2630(6)),flip(a)].">
      <j1 rule="para" parents="314 2394"/>
      <j2 rule="demod" parents="8 2630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2701">
    <literal><![CDATA[
      f(x,y,f(z,u,y)) = f(u,y,f(x,z,y))
    ]]></literal>
    <justification jstring="[para(2651(a,1),7(a,2)),demod(8(2),7(3))].">
      <j1 rule="para" parents="2651 7"/>
      <j2 rule="demod" parents="8 7"/>
    </justification>
  </clause>

  <clause id="2710">
    <literal><![CDATA[
      f(f(x,y,z),f(x,y,u),f(v,z,f(x,y,u))) = f(v,f(x,y,z),f(x,y,u))
    ]]></literal>
    <justification jstring="[para(475(a,1),2651(a,1,3)),demod(8(2),7(3,R),8(4),7(7)),flip(a)].">
      <j1 rule="para" parents="475 2651"/>
      <j2 rule="demod" parents="8 7 8 7"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3352">
    <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(430(a,1),485(a,1,3,3))].">
      <j1 rule="para" parents="430 485"/>
    </justification>
  </clause>

  <clause id="3639">
    <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(51(a,2),45(a,1)),demod(7(3),7(3),8(4),63(5),27(5),8(7),7(8,R),8(8),1660(9)),flip(a)].">
      <j1 rule="para" parents="51 45"/>
      <j2 rule="demod" parents="7 7 8 63 27 8 7 8 1660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3683">
    <literal><![CDATA[
      f(f(x,y,z),f(x,y,f(x,z,u)),f(u,v,f(x,y,z))) = f(x,z,f(x,y,f(u,v,f(x,y,z))))
    ]]></literal>
    <justification jstring="[back_demod(1523),demod(3639(10))].">
      <j1 rule="back_demod" parents="1523"/>
      <j2 rule="demod" parents="3639"/>
    </justification>
  </clause>

  <clause id="4098">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,v,f(y,z,u))) = f(y,u,f(y,z,f(v,x,f(y,z,u))))
    ]]></literal>
    <justification jstring="[para(54(a,1),314(a,2,3)),demod(7(2),7(2),7(5,R),8(5),3683(6),7(7,R),8(7)),flip(a)].">
      <j1 rule="para" parents="54 314"/>
      <j2 rule="demod" parents="7 7 7 8 3683 7 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4206">
    <literal><![CDATA[
      f(x,f(y,z,f(y,u,v)),f(y,x,u)) = f(y,x,u)
    ]]></literal>
    <justification jstring="[para(790(a,1),1409(a,2)),demod(8(7),8(11),2402(13))].">
      <j1 rule="para" parents="790 1409"/>
      <j2 rule="demod" parents="8 8 2402"/>
    </justification>
  </clause>

  <clause id="4221">
    <literal><![CDATA[
      f(x,y,f(z,u,f(x,z,f(z,v,y)))) = f(x,z,y)
    ]]></literal>
    <justification jstring="[para(18(a,1),4206(a,1,3)),demod(7(1),8(2),7(4),8(5),195(5),1396(4),33(3),7(5),7(6,R),8(6),22(6))].">
      <j1 rule="para" parents="18 4206"/>
      <j2 rule="demod" parents="7 8 7 8 195 1396 33 7 7 8 22"/>
    </justification>
  </clause>

  <clause id="4970">
    <literal><![CDATA[
      f(x,y,f(x,z,f(u,z,y))) = f(x,z,y)
    ]]></literal>
    <justification jstring="[para(2701(a,1),61(a,1)),demod(22(3),11(3),7(3),63(5),27(5)),flip(a)].">
      <j1 rule="para" parents="2701 61"/>
      <j2 rule="demod" parents="22 11 7 63 27"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6164">
    <literal><![CDATA[
      f(x,y,f(x,z,f(z,u,f(z,v,y)))) = f(x,z,y)
    ]]></literal>
    <justification jstring="[para(4221(a,1),18(a,1,3)),demod(8(5),195(5),206(4),8(2),4221(8))].">
      <j1 rule="para" parents="4221 18"/>
      <j2 rule="demod" parents="8 195 206 8 4221"/>
    </justification>
  </clause>

  <clause id="6728">
    <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(430(a,1),6164(a,1,3,3)),demod(7(2),7(2))].">
      <j1 rule="para" parents="430 6164"/>
      <j2 rule="demod" parents="7 7"/>
    </justification>
  </clause>

  <clause id="8328">
    <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(192(a,1),8(a,1)),demod(7(1,R),8(1),8(4)),flip(a)].">
      <j1 rule="para" parents="192 8"/>
      <j2 rule="demod" parents="7 8 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8576">
    <literal><![CDATA[
      f(x,f(y,z,u),f(u,x,v)) = f(x,v,f(z,u,f(y,u,x)))
    ]]></literal>
    <justification jstring="[para(193(a,1),7(a,2)),demod(7(2,R),8(2),7(3),7(4),7(4))].">
      <j1 rule="para" parents="193 7"/>
      <j2 rule="demod" parents="7 8 7 7 7"/>
    </justification>
  </clause>

  <clause id="8578">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,x,u)) = f(y,x,u)
    ]]></literal>
    <justification jstring="[para(193(a,2),9(a,2)),demod(7(2,R),8(2),413(3),430(3),7(2,R),8(2),7(3)),flip(a)].">
      <j1 rule="para" parents="193 9"/>
      <j2 rule="demod" parents="7 8 413 430 7 8 7"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8585">
    <literal><![CDATA[
      f(x,y,f(z,y,f(x,u,y))) = f(x,y,f(u,z,y))
    ]]></literal>
    <justification jstring="[para(11(a,1),193(a,1,3)),demod(8(2)),flip(a)].">
      <j1 rule="para" parents="11 193"/>
      <j2 rule="demod" parents="8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8626">
    <literal><![CDATA[
      f(x,f(y,z,x),f(y,u,x)) = f(y,x,f(z,u,x))
    ]]></literal>
    <justification jstring="[para(314(a,2),193(a,2)),demod(11(2),8(2)),flip(a)].">
      <j1 rule="para" parents="314 193"/>
      <j2 rule="demod" parents="11 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8655">
    <literal><![CDATA[
      f(x,y,f(z,u,f(y,v,u))) = f(y,u,f(x,y,f(z,v,u)))
    ]]></literal>
    <justification jstring="[para(193(a,2),36(a,1,3)),demod(7(1,R),8(1),11(2),8(2),18(5))].">
      <j1 rule="para" parents="193 36"/>
      <j2 rule="demod" parents="7 8 11 8 18"/>
    </justification>
  </clause>

  <clause id="8846">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,u,x)) = f(y,u,x)
    ]]></literal>
    <justification jstring="[para(8578(a,1),7(a,2)),demod(8(2),7(3),8(4))].">
      <j1 rule="para" parents="8578 7"/>
      <j2 rule="demod" parents="8 7 8"/>
    </justification>
  </clause>

  <clause id="8937">
    <literal><![CDATA[
      f(x,f(y,z,x),f(z,u,x)) = f(y,x,f(z,u,x))
    ]]></literal>
    <justification jstring="[para(8846(a,1),36(a,2,3)),demod(7(3),8(3),8585(4),7(2,R),8(2),343(4),7(4),7(5,R)),flip(a)].">
      <j1 rule="para" parents="8846 36"/>
      <j2 rule="demod" parents="7 8 8585 7 8 343 7 7"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8941">
    <literal><![CDATA[
      f(x,f(y,z,x),f(u,y,x)) = f(u,x,f(y,z,x))
    ]]></literal>
    <justification jstring="[para(8846(a,1),82(a,2,3)),demod(7(3),8585(4),7(2,R),8(2),343(4),7(4)),flip(a)].">
      <j1 rule="para" parents="8846 82"/>
      <j2 rule="demod" parents="7 8585 7 8 343 7"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9134">
    <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(9(a,2),8941(a,2,3)),demod(7(3,R),8(3),7(5,R),8(5),8937(6),3639(4),7(6),7(6)),flip(a)].">
      <j1 rule="para" parents="9 8941"/>
      <j2 rule="demod" parents="7 8 7 8 8937 3639 7 7"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9135">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,z,f(y,u,v))) = f(y,u,f(y,z,f(v,x,f(y,z,u))))
    ]]></literal>
    <justification jstring="[para(12(a,1),8941(a,2,3)),demod(7(5,R),8(5),8626(6),3639(4),8(6)),flip(a)].">
      <j1 rule="para" parents="12 8941"/>
      <j2 rule="demod" parents="7 8 8626 3639 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9237">
    <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(7(a,1),194(a,1)),demod(7(2),7(3,R),7(4),7(4))].">
      <j1 rule="para" parents="7 194"/>
      <j2 rule="demod" parents="7 7 7 7"/>
    </justification>
  </clause>

  <clause id="9404">
    <literal><![CDATA[
      f(x,y,f(z,y,f(u,x,z))) = f(x,z,y)
    ]]></literal>
    <justification jstring="[para(2701(a,1),195(a,1)),demod(22(3),11(3),7(3),1624(4)),flip(a)].">
      <j1 rule="para" parents="2701 195"/>
      <j2 rule="demod" parents="22 11 7 1624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9967">
    <literal><![CDATA[
      f(f(x,y,z),f(u,v,w),f(x,y,z)) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(192(a,1),91(a,2,3)),demod(8(4),7(5,R),378(5),22(4),8(8),7(11,R),8(11),9237(11),8(9),63(10),27(10),387(10))].">
      <j1 rule="para" parents="192 91"/>
      <j2 rule="demod" parents="8 7 378 22 8 7 8 9237 8 63 27 387"/>
    </justification>
  </clause>

  <clause id="9980">
    <literal><![CDATA[
      f(f(x,y,z),f(u,v,w),f(x,y,f(x,z,f(u,v,w)))) = f(x,f(x,y,z),f(u,v,w))
    ]]></literal>
    <justification jstring="[para(9967(a,1),40(a,2,3)),demod(7(4),7(4),7(9,R))].">
      <j1 rule="para" parents="9967 40"/>
      <j2 rule="demod" parents="7 7 7"/>
    </justification>
  </clause>

  <clause id="9981">
    <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(40(a,1),9967(a,1)),demod(7(3),7(3),7(7),8(7),9980(7),7(5,R),8(5),18(5),7(5),7(5))].">
      <j1 rule="para" parents="40 9967"/>
      <j2 rule="demod" parents="7 7 7 8 9980 7 8 18 7 7"/>
    </justification>
  </clause>

  <clause id="10315">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,y,z)) = f(x,y,z)
    ]]></literal>
    <justification jstring="[para(392(a,1),16(a,2,3)),demod(7(2,R),8(2),387(4),7(4,R),8(4),385(6))].">
      <j1 rule="para" parents="392 16"/>
      <j2 rule="demod" parents="7 8 387 7 8 385"/>
    </justification>
  </clause>

  <clause id="10440">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,z,u)) = f(x,z,u)
    ]]></literal>
    <justification jstring="[para(7(a,1),10315(a,1,2))].">
      <j1 rule="para" parents="7 10315"/>
    </justification>
  </clause>

  <clause id="10441">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,y,u)) = f(x,y,u)
    ]]></literal>
    <justification jstring="[para(7(a,2),10315(a,1,2)),demod(8(2),8(4))].">
      <j1 rule="para" parents="7 10315"/>
      <j2 rule="demod" parents="8 8"/>
    </justification>
  </clause>

  <clause id="11023">
    <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(481(a,1),36(a,2,3)),demod(7(4,R),902(5),18(4),7(6,R)),flip(a)].">
      <j1 rule="para" parents="481 36"/>
      <j2 rule="demod" parents="7 902 18 7"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11078">
    <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(481(a,1),82(a,2,3)),demod(885(5),18(4)),flip(a)].">
      <j1 rule="para" parents="481 82"/>
      <j2 rule="demod" parents="885 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11509">
    <literal><![CDATA[
      f(x,f(y,z,u),f(v,y,f(x,v,z))) = f(x,v,f(y,z,u))
    ]]></literal>
    <justification jstring="[para(573(a,1),98(a,2,3)),demod(73(5),22(7))].">
      <j1 rule="para" parents="573 98"/>
      <j2 rule="demod" parents="73 22"/>
    </justification>
  </clause>

  <clause id="11722">
    <literal><![CDATA[
      f(x,y,f(y,f(x,z,u),f(z,v,f(x,y,u)))) = f(x,y,f(z,v,f(x,y,u)))
    ]]></literal>
    <justification jstring="[para(103(a,1),573(a,1)),demod(8(2),8(4),7(5,R),8(5),22(6),8(7),7(8,R),8(8))].">
      <j1 rule="para" parents="103 573"/>
      <j2 rule="demod" parents="8 8 7 8 22 8 7 8"/>
    </justification>
  </clause>

  <clause id="12630">
    <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(757(a,1),47(a,1,3)),demod(7(4)),flip(a)].">
      <j1 rule="para" parents="757 47"/>
      <j2 rule="demod" parents="7"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12660">
    <literal><![CDATA[
      f(x,f(y,z,u),f(x,y,f(x,v,w))) = f(x,y,f(x,w,f(x,v,f(y,z,u))))
    ]]></literal>
    <justification jstring="[para(98(a,1),757(a,2)),demod(18(5),9981(5),1736(4),64(5))].">
      <j1 rule="para" parents="98 757"/>
      <j2 rule="demod" parents="18 9981 1736 64"/>
    </justification>
  </clause>

  <clause id="14763">
    <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(8328(a,1),760(a,2)),demod(7(2),7(2),7(3),7(3),9981(5),12660(6),8(5),9981(5),12630(6),7(7,R),8(7))].">
      <j1 rule="para" parents="8328 760"/>
      <j2 rule="demod" parents="7 7 7 7 9981 12660 8 9981 12630 7 8"/>
    </justification>
  </clause>

  <clause id="14778">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,z,f(y,u,v))) = f(y,u,f(x,z,f(y,z,v)))
    ]]></literal>
    <justification jstring="[back_demod(9135),demod(7(6,R),8(6),14763(8),7(6,R),8(6))].">
      <j1 rule="back_demod" parents="9135"/>
      <j2 rule="demod" parents="7 8 14763 7 8"/>
    </justification>
  </clause>

  <clause id="14779">
    <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_demod(9134),demod(7(6,R),8(6),14763(8),7(6,R),8(6))].">
      <j1 rule="back_demod" parents="9134"/>
      <j2 rule="demod" parents="7 8 14763 7 8"/>
    </justification>
  </clause>

  <clause id="14787">
    <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_demod(4098),demod(7(6,R),8(6),14763(8),7(6,R),8(6))].">
      <j1 rule="back_demod" parents="4098"/>
      <j2 rule="demod" parents="7 8 14763 7 8"/>
    </justification>
  </clause>

  <clause id="15616">
    <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(13(a,1),9981(a,1,2))].">
      <j1 rule="para" parents="13 9981"/>
    </justification>
  </clause>

  <clause id="16856">
    <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(10315(a,1),11023(a,1,2)),demod(7(2),7(2))].">
      <j1 rule="para" parents="10315 11023"/>
      <j2 rule="demod" parents="7 7"/>
    </justification>
  </clause>

  <clause id="16857">
    <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(10440(a,1),11023(a,1,2)),demod(7(2),7(2))].">
      <j1 rule="para" parents="10440 11023"/>
      <j2 rule="demod" parents="7 7"/>
    </justification>
  </clause>

  <clause id="16858">
    <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(10441(a,1),11023(a,1,2)),demod(7(2),7(2))].">
      <j1 rule="para" parents="10441 11023"/>
      <j2 rule="demod" parents="7 7"/>
    </justification>
  </clause>

  <clause id="16909">
    <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(10315(a,1),11078(a,1,3)),demod(7(3),7(3),16856(4))].">
      <j1 rule="para" parents="10315 11078"/>
      <j2 rule="demod" parents="7 7 16856"/>
    </justification>
  </clause>

  <clause id="16910">
    <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(10440(a,1),11078(a,1,3)),demod(7(3),7(3),16857(4))].">
      <j1 rule="para" parents="10440 11078"/>
      <j2 rule="demod" parents="7 7 16857"/>
    </justification>
  </clause>

  <clause id="16911">
    <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(10441(a,1),11078(a,1,3)),demod(7(3),7(3),16858(4))].">
      <j1 rule="para" parents="10441 11078"/>
      <j2 rule="demod" parents="7 7 16858"/>
    </justification>
  </clause>

  <clause id="16923">
    <literal><![CDATA[
      f(x,f(y,z,u),f(z,u,v)) = f(y,f(z,u,v),f(z,u,x))
    ]]></literal>
    <justification jstring="[para(16909(a,1),8(a,1)),demod(7(4)),flip(a)].">
      <j1 rule="para" parents="16909 8"/>
      <j2 rule="demod" parents="7"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16924">
    <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(16909(a,1),8(a,2)),demod(7(5)),flip(a)].">
      <j1 rule="para" parents="16909 8"/>
      <j2 rule="demod" parents="7"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16972">
    <literal><![CDATA[
      f(f(x,y,f(y,z,u)),f(x,z,v),f(x,z,w)) = f(w,f(x,z,v),f(x,y,z))
    ]]></literal>
    <justification jstring="[para(347(a,1),16909(a,2,3))].">
      <j1 rule="para" parents="347 16909"/>
    </justification>
  </clause>

  <clause id="17014">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,v,f(x,z,f(y,z,u)))) = f(v,f(y,z,u),f(x,y,z))
    ]]></literal>
    <justification jstring="[para(16909(a,1),3352(a,2)),demod(7(4),7(4),14779(5),7(7))].">
      <j1 rule="para" parents="16909 3352"/>
      <j2 rule="demod" parents="7 7 14779 7"/>
    </justification>
  </clause>

  <clause id="17015">
    <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(16909(a,1),6728(a,2)),demod(14787(5),17014(5),7(5))].">
      <j1 rule="para" parents="16909 6728"/>
      <j2 rule="demod" parents="14787 17014 7"/>
    </justification>
  </clause>

  <clause id="17054">
    <literal><![CDATA[
      f(f(x,y,z),f(y,u,v),f(x,y,v)) = f(x,y,f(x,f(y,u,v),f(y,z,v)))
    ]]></literal>
    <justification jstring="[para(16910(a,1),16(a,1)),demod(7(2),7(3),8(3),7(5),7(6),7(6))].">
      <j1 rule="para" parents="16910 16"/>
      <j2 rule="demod" parents="7 7 8 7 7 7"/>
    </justification>
  </clause>

  <clause id="17149">
    <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(16911(a,1),24(a,2,3)),demod(7(6))].">
      <j1 rule="para" parents="16911 24"/>
      <j2 rule="demod" parents="7"/>
    </justification>
  </clause>

  <clause id="17164">
    <literal><![CDATA[
      f(x,y,f(z,f(y,u,v),f(x,y,v))) = f(x,y,f(x,f(y,u,v),f(y,z,v)))
    ]]></literal>
    <justification jstring="[para(16911(a,1),73(a,1,3)),demod(7(3),17054(4),22(5),17149(8)),flip(a)].">
      <j1 rule="para" parents="16911 73"/>
      <j2 rule="demod" parents="7 17054 22 17149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17259">
    <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(7(a,1),16923(a,1,2)),demod(7(2,R),8(2),7(4,R),8(4),7(5),8(5)),flip(a)].">
      <j1 rule="para" parents="7 16923"/>
      <j2 rule="demod" parents="7 8 7 8 7 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17260">
    <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(16923(a,2),8(a,1)),demod(7(4))].">
      <j1 rule="para" parents="16923 8"/>
      <j2 rule="demod" parents="7"/>
    </justification>
  </clause>

  <clause id="17290">
    <literal><![CDATA[
      f(x,y,f(y,f(z,x,u),f(x,u,v))) = f(x,y,f(z,u,f(x,u,v)))
    ]]></literal>
    <justification jstring="[para(16923(a,1),24(a,1)),demod(7(1,R),8(1),8(4),14778(4),7(7,R),8(7)),flip(a)].">
      <j1 rule="para" parents="16923 24"/>
      <j2 rule="demod" parents="7 8 8 14778 7 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17295">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,v,z)) = f(u,f(y,z,x),f(y,v,z))
    ]]></literal>
    <justification jstring="[para(347(a,1),16923(a,2,3)),demod(7(3),7(3),16972(5))].">
      <j1 rule="para" parents="347 16923"/>
      <j2 rule="demod" parents="7 7 16972"/>
    </justification>
  </clause>

  <clause id="17398">
    <literal><![CDATA[
      f(x,y,f(x,f(z,y,u),f(z,v,f(x,y,u)))) = f(x,y,f(z,v,f(x,y,u)))
    ]]></literal>
    <justification jstring="[para(16924(a,1),24(a,1)),demod(7(1,R),8(1),8(2),7(3,R),8(3),8(4),15616(5),7(6,R),8(6),8(7),8(9),7(10,R),8(10),11722(10))].">
      <j1 rule="para" parents="16924 24"/>
      <j2 rule="demod" parents="7 8 8 7 8 8 15616 7 8 8 8 7 8 11722"/>
    </justification>
  </clause>

  <clause id="17581">
    <literal><![CDATA[
      f(f(x,y,z),f(u,y,z),f(y,z,v)) = f(u,f(x,y,z),f(y,z,v))
    ]]></literal>
    <justification jstring="[para(319(a,1),17015(a,1,2)),demod(7(2),7(2),7(5),7(6),7(6)),flip(a)].">
      <j1 rule="para" parents="319 17015"/>
      <j2 rule="demod" parents="7 7 7 7 7"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17687">
    <literal><![CDATA[
      f(x,f(y,z,u),f(v,y,z)) = f(v,f(y,z,u),f(y,x,z))
    ]]></literal>
    <justification jstring="[para(17259(a,2),430(a,2)),demod(7(5,R),4970(7)),flip(a)].">
      <j1 rule="para" parents="17259 430"/>
      <j2 rule="demod" parents="7 4970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17720">
    <literal><![CDATA[
      f(x,f(y,z,u),f(z,u,f(y,z,v))) = f(y,z,f(x,u,f(z,u,v)))
    ]]></literal>
    <justification jstring="[para(17260(a,1),38(a,1)),demod(7(2,R),8(2),17290(8),7(7,R),8(7))].">
      <j1 rule="para" parents="17260 38"/>
      <j2 rule="demod" parents="7 8 17290 7 8"/>
    </justification>
  </clause>

  <clause id="17728">
    <literal><![CDATA[
      f(x,y,f(z,f(y,u,v),f(x,y,v))) = f(x,y,f(u,v,f(y,v,z)))
    ]]></literal>
    <justification jstring="[para(17260(a,1),73(a,1,3)),demod(17720(4),22(4),7(4,R),8(4),17149(7)),flip(a)].">
      <j1 rule="para" parents="17260 73"/>
      <j2 rule="demod" parents="17720 22 7 8 17149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17748">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,f(v,z,u),f(z,u,x))) = f(v,f(y,z,u),f(z,u,x))
    ]]></literal>
    <justification jstring="[para(17260(a,1),8655(a,2,3)),demod(7(3),7(3),9404(4),7(8,R),8(8)),flip(a)].">
      <j1 rule="para" parents="17260 8655"/>
      <j2 rule="demod" parents="7 7 9404 7 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17765">
    <literal><![CDATA[
      f(x,y,f(x,f(y,z,u),f(y,v,u))) = f(x,y,f(z,u,f(y,v,u)))
    ]]></literal>
    <justification jstring="[back_demod(17164),demod(17728(4),8(1)),flip(a)].">
      <j1 rule="back_demod" parents="17164"/>
      <j2 rule="demod" parents="17728 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17828">
    <literal><![CDATA[
      f(f(x,y,z),f(y,u,v),f(x,y,v)) = f(x,y,f(u,v,f(y,z,v)))
    ]]></literal>
    <justification jstring="[back_demod(17054),demod(17765(8))].">
      <j1 rule="back_demod" parents="17054"/>
      <j2 rule="demod" parents="17765"/>
    </justification>
  </clause>

  <clause id="18112">
    <literal><![CDATA[
      f(f(x,y,z),f(x,y,u),f(y,z,u)) = f(x,y,f(y,z,u))
    ]]></literal>
    <justification jstring="[para(8576(a,2),196(a,2)),demod(7(2),7(4,R),8(4),17828(5),319(3),18(4),7(3),7(4,R),8(4),7(5),532(7)),flip(a)].">
      <j1 rule="para" parents="8576 196"/>
      <j2 rule="demod" parents="7 7 8 17828 319 18 7 7 8 7 532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18131">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,v,z)) = f(v,f(y,z,u),f(y,z,x))
    ]]></literal>
    <justification jstring="[para(17687(a,2),473(a,2)),demod(8(3),8846(7),7(5),7(5))].">
      <j1 rule="para" parents="17687 473"/>
      <j2 rule="demod" parents="8 8846 7 7"/>
    </justification>
  </clause>

  <clause id="18166">
    <literal><![CDATA[
      f(f(x,y,z),f(u,x,y),f(u,x,z)) = f(u,x,f(x,y,z))
    ]]></literal>
    <justification jstring="[para(18112(a,1),7(a,1)),flip(a)].">
      <j1 rule="para" parents="18112 7"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18279">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,z,f(x,u,v))) = f(y,z,f(x,u,v))
    ]]></literal>
    <justification jstring="[para(18166(a,1),84(a,2,3)),demod(7(3),7(3),7(6,R),8(6),7(7),7(7),17398(8),7(7,R),8(7),2710(7),7(9,R),8(9),7(10,R),8(10),14787(10),7(7,R),8(7),11509(8))].">
      <j1 rule="para" parents="18166 84"/>
      <j2 rule="demod" parents="7 7 7 8 7 7 17398 7 8 2710 7 8 7 8 14787 7 8 11509"/>
    </justification>
  </clause>

  <clause id="20032">
    <literal><![CDATA[
      f(x,f(y,z,u),f(u,f(y,z,v),f(y,z,x))) = f(v,f(y,z,x),f(y,z,u))
    ]]></literal>
    <justification jstring="[para(17295(a,1),308(a,2,3)),demod(7(4,R),8(4),705(4),497(5),8(6)),flip(a)].">
      <j1 rule="para" parents="17295 308"/>
      <j2 rule="demod" parents="7 8 705 497 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20843">
    <literal><![CDATA[
      f(f(x,y,z),f(u,v,y),f(u,v,x)) = f(u,v,f(x,y,z))
    ]]></literal>
    <justification jstring="[para(18279(a,1),16909(a,1)),flip(a)].">
      <j1 rule="para" parents="18279 16909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20846">
    <literal><![CDATA[
      f(f(x,y,z),f(x,u,v),f(y,u,v)) = f(u,v,f(x,y,z))
    ]]></literal>
    <justification jstring="[para(18279(a,1),16923(a,2)),demod(7(3))].">
      <j1 rule="para" parents="18279 16923"/>
      <j2 rule="demod" parents="7"/>
    </justification>
  </clause>

  <clause id="20860">
    <literal><![CDATA[
      f(f(x,y,z),f(x,y,u),f(z,u,v)) = f(x,y,f(z,u,v))
    ]]></literal>
    <justification jstring="[para(20843(a,1),7(a,2)),demod(7(3,R),8(3),7(5,R),8(5))].">
      <j1 rule="para" parents="20843 7"/>
      <j2 rule="demod" parents="7 8 7 8"/>
    </justification>
  </clause>

  <clause id="20922">
    <literal><![CDATA[
      f(f(x,y,z),f(z,u,v),f(u,v,f(x,y,w))) = f(u,v,f(x,y,z))
    ]]></literal>
    <justification jstring="[para(473(a,1),20846(a,1,1)),demod(7(4),7(4),473(8))].">
      <j1 rule="para" parents="473 20846"/>
      <j2 rule="demod" parents="7 7 473"/>
    </justification>
  </clause>

  <clause id="20968">
    <literal><![CDATA[
      f(x,f(y,z,u),f(y,z,v)) = f(y,z,f(v,u,x))
    ]]></literal>
    <justification jstring="[para(20860(a,1),630(a,2)),demod(7(6),7(6),20922(7),497(5))].">
      <j1 rule="para" parents="20860 630"/>
      <j2 rule="demod" parents="7 7 20922 497"/>
    </justification>
  </clause>

  <clause id="20975">
    <literal><![CDATA[
      f(x,y,f(z,f(u,v,w),f(v,w,v6))) = f(x,y,f(v,w,f(u,v6,z)))
    ]]></literal>
    <justification jstring="[para(20860(a,1),16909(a,1,2)),demod(7(5),20968(5),7(3,R),8(3),20968(5),7(3),20968(3),7(1),20860(7),7(8),20968(8),7(6),8(6),20968(8),7(6)),flip(a)].">
      <j1 rule="para" parents="20860 16909"/>
      <j2 rule="demod" parents="7 20968 7 8 20968 7 20968 7 20860 7 20968 7 8 20968 7"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20977">
    <literal><![CDATA[
      f(x,y,f(z,f(u,v,w),f(v6,u,v))) = f(x,y,f(u,v,f(z,v6,w)))
    ]]></literal>
    <justification jstring="[para(20860(a,1),16910(a,1,3)),demod(20968(3),7(1),8(1),20968(5),7(3),20968(8),7(6),8(6),7(10),20968(10),7(8),8(8),20968(10),17581(8),20975(8),8(5))].">
      <j1 rule="para" parents="20860 16910"/>
      <j2 rule="demod" parents="20968 7 8 20968 7 20968 7 8 7 20968 7 8 20968 17581 20975 8"/>
    </justification>
  </clause>

  <clause id="20991">
    <literal><![CDATA[
      f(x,f(y,z,u),f(z,u,v)) = f(z,u,f(y,v,x))
    ]]></literal>
    <justification jstring="[back_demod(20032),demod(7(3),20977(5),7(2,R),8(2),20968(4),7(2),8(2),22(2),7(3)),flip(a)].">
      <j1 rule="back_demod" parents="20032"/>
      <j2 rule="demod" parents="7 20977 7 8 20968 7 8 22 7"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20997">
    <literal><![CDATA[
      f(x,f(y,z,u),f(v,y,z)) = f(y,z,f(v,u,x))
    ]]></literal>
    <justification jstring="[back_demod(18131),demod(8(2),20968(3),7(1),8(1),7(4)),flip(a)].">
      <j1 rule="back_demod" parents="18131"/>
      <j2 rule="demod" parents="8 20968 7 8 7"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21030">
    <literal><![CDATA[
      f(x,y,f(z,u,f(v,x,y))) = f(x,y,f(v,z,u))
    ]]></literal>
    <justification jstring="[back_demod(16857),demod(20968(4),7(2,R),8(2),20991(6),8(4))].">
      <j1 rule="back_demod" parents="16857"/>
      <j2 rule="demod" parents="20968 7 8 20991 8"/>
    </justification>
  </clause>

  <clause id="21062">
    <literal><![CDATA[
      f(x,f(y,z,u),f(v,z,u)) = f(z,u,f(v,y,x))
    ]]></literal>
    <justification jstring="[back_demod(17748),demod(7(2),7(2),7(3),20997(4),8(2),20991(4),7(2),22(2),7(4)),flip(a)].">
      <j1 rule="back_demod" parents="17748"/>
      <j2 rule="demod" parents="7 7 7 20997 8 20991 7 22 7"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21162">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer(dist_both)
    ]]></attribute>
    <justification jstring="[back_demod(10),demod(21062(13),7(9,R),8(9),21030(10),21062(25),7(21),8(21)),xx(a),xx(b)].">
      <j1 rule="back_demod" parents="10"/>
      <j2 rule="demod" parents="21062 7 8 21030 21062 7 8"/>
      <j2 rule="xx"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

</proofs>
