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<!DOCTYPE proofs SYSTEM "proof3.dtd">

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

<proofs number_of_proofs="1">

<source>lifsch.out</source>

<heading><![CDATA[
Prover9 (32) version August-2006A, August 2006.
Process 10893 was started by mccune on cleo.thornwood,
Sat Aug 12 20:59:02 2006
The command was "/home/mccune/bin/prover9 -f lifsch.in".
]]></heading>

<proof number="1" length="32" max_count="62">

<comments><![CDATA[
% Proof 1 at 0.29 (+ 0.01) seconds.
% Length of proof is 32.
% Level of proof is 22.
% Maximum clause weight is 34.
% Given clauses 100.
]]></comments>

  <clause id="1">
    <literal><![CDATA[
      (exists x exists y all z exists u exists v ((-p(z,z) | p(x,x) | -s(u,x)) & (s(x,z) | -s(z,u) | q(v,v)) & (q(y,z) | -q(z,v) | s(y,y))))
    ]]></literal>
    <justification jstring="[goal].">
      <j1 rule="goal"/>
    </justification>
  </clause>

  <clause id="5">
    <literal><![CDATA[
      p(f1(x,y),f1(x,y))
    ]]></literal>
    <literal><![CDATA[
      -s(x,f1(x,y))
    ]]></literal>
    <literal><![CDATA[
      -s(y,y)
    ]]></literal>
    <justification jstring="[deny(1)].">
      <j1 rule="deny" parents="1"/>
    </justification>
  </clause>

  <clause id="7">
    <literal><![CDATA[
      p(f1(x,y),f1(x,y))
    ]]></literal>
    <literal><![CDATA[
      s(f1(x,y),z)
    ]]></literal>
    <literal><![CDATA[
      q(f1(x,y),u)
    ]]></literal>
    <justification jstring="[deny(1)].">
      <j1 rule="deny" parents="1"/>
    </justification>
  </clause>

  <clause id="13">
    <literal><![CDATA[
      -p(x,x)
    ]]></literal>
    <literal><![CDATA[
      -s(x,f1(x,y))
    ]]></literal>
    <literal><![CDATA[
      -s(y,y)
    ]]></literal>
    <justification jstring="[deny(1)].">
      <j1 rule="deny" parents="1"/>
    </justification>
  </clause>

  <clause id="15">
    <literal><![CDATA[
      -p(x,x)
    ]]></literal>
    <literal><![CDATA[
      s(f1(x,y),z)
    ]]></literal>
    <literal><![CDATA[
      q(f1(x,y),u)
    ]]></literal>
    <justification jstring="[deny(1)].">
      <j1 rule="deny" parents="1"/>
    </justification>
  </clause>

  <clause id="22">
    <literal><![CDATA[
      s(x,y)
    ]]></literal>
    <literal><![CDATA[
      -s(y,f1(y,z))
    ]]></literal>
    <literal><![CDATA[
      -s(z,z)
    ]]></literal>
    <justification jstring="[deny(1)].">
      <j1 rule="deny" parents="1"/>
    </justification>
  </clause>

  <clause id="26">
    <literal><![CDATA[
      s(x,y)
    ]]></literal>
    <literal><![CDATA[
      -q(z,z)
    ]]></literal>
    <literal><![CDATA[
      -q(u,f1(y,u))
    ]]></literal>
    <justification jstring="[deny(1)].">
      <j1 rule="deny" parents="1"/>
    </justification>
  </clause>

  <clause id="49">
    <literal><![CDATA[
      -s(f1(x,y),f1(f1(x,y),z))
    ]]></literal>
    <literal><![CDATA[
      -s(z,z)
    ]]></literal>
    <literal><![CDATA[
      -s(x,f1(x,y))
    ]]></literal>
    <literal><![CDATA[
      -s(y,y)
    ]]></literal>
    <justification jstring="[resolve(13,a,5,a)].">
      <j1 rule="resolve" parents="13 5"/>
    </justification>
  </clause>

  <clause id="68">
    <literal><![CDATA[
      s(f1(f1(x,y),z),u)
    ]]></literal>
    <literal><![CDATA[
      q(f1(f1(x,y),z),v)
    ]]></literal>
    <literal><![CDATA[
      s(f1(x,y),w)
    ]]></literal>
    <literal><![CDATA[
      q(f1(x,y),v6)
    ]]></literal>
    <justification jstring="[resolve(15,a,7,a)].">
      <j1 rule="resolve" parents="15 7"/>
    </justification>
  </clause>

  <clause id="100">
    <literal><![CDATA[
      -s(f1(x,y),f1(f1(x,y),y))
    ]]></literal>
    <literal><![CDATA[
      -s(y,y)
    ]]></literal>
    <literal><![CDATA[
      -s(x,f1(x,y))
    ]]></literal>
    <justification jstring="[factor(49,b,d)].">
      <j1 rule="factor" parents="49"/>
    </justification>
  </clause>

  <clause id="196">
    <literal><![CDATA[
      s(f1(f1(x,y),z),u)
    ]]></literal>
    <literal><![CDATA[
      s(f1(x,y),v)
    ]]></literal>
    <literal><![CDATA[
      q(f1(x,y),w)
    ]]></literal>
    <literal><![CDATA[
      s(v6,v7)
    ]]></literal>
    <literal><![CDATA[
      -q(v8,v8)
    ]]></literal>
    <justification jstring="[resolve(68,b,26,c)].">
      <j1 rule="resolve" parents="68 26"/>
    </justification>
  </clause>

  <clause id="243">
    <literal><![CDATA[
      s(f1(f1(x,y),z),u)
    ]]></literal>
    <literal><![CDATA[
      s(f1(x,y),v)
    ]]></literal>
    <literal><![CDATA[
      q(f1(x,y),w)
    ]]></literal>
    <literal><![CDATA[
      -q(v6,v6)
    ]]></literal>
    <justification jstring="[factor(196,a,d)].">
      <j1 rule="factor" parents="196"/>
    </justification>
  </clause>

  <clause id="1035">
    <literal><![CDATA[
      s(f1(f1(x,y),z),u)
    ]]></literal>
    <literal><![CDATA[
      s(f1(x,y),v)
    ]]></literal>
    <literal><![CDATA[
      q(f1(x,y),w)
    ]]></literal>
    <literal><![CDATA[
      s(f1(f1(v6,v7),v8),v9)
    ]]></literal>
    <literal><![CDATA[
      s(f1(v6,v7),v10)
    ]]></literal>
    <literal><![CDATA[
      q(f1(v6,v7),v11)
    ]]></literal>
    <justification jstring="[resolve(243,d,68,b)].">
      <j1 rule="resolve" parents="243 68"/>
    </justification>
  </clause>

  <clause id="1043">
    <literal><![CDATA[
      s(f1(f1(x,y),z),u)
    ]]></literal>
    <literal><![CDATA[
      s(f1(x,y),v)
    ]]></literal>
    <literal><![CDATA[
      q(f1(x,y),w)
    ]]></literal>
    <literal><![CDATA[
      s(f1(x,y),v6)
    ]]></literal>
    <literal><![CDATA[
      q(f1(x,y),v7)
    ]]></literal>
    <justification jstring="[factor(1035,a,d)].">
      <j1 rule="factor" parents="1035"/>
    </justification>
  </clause>

  <clause id="1046">
    <literal><![CDATA[
      s(f1(f1(x,y),z),u)
    ]]></literal>
    <literal><![CDATA[
      s(f1(x,y),v)
    ]]></literal>
    <literal><![CDATA[
      q(f1(x,y),w)
    ]]></literal>
    <literal><![CDATA[
      q(f1(x,y),v6)
    ]]></literal>
    <justification jstring="[factor(1043,b,d)].">
      <j1 rule="factor" parents="1043"/>
    </justification>
  </clause>

  <clause id="1048">
    <literal><![CDATA[
      s(f1(f1(x,y),z),u)
    ]]></literal>
    <literal><![CDATA[
      s(f1(x,y),v)
    ]]></literal>
    <literal><![CDATA[
      q(f1(x,y),w)
    ]]></literal>
    <justification jstring="[factor(1046,c,d)].">
      <j1 rule="factor" parents="1046"/>
    </justification>
  </clause>

  <clause id="1084">
    <literal><![CDATA[
      s(f1(f1(x,y),z),u)
    ]]></literal>
    <literal><![CDATA[
      s(f1(x,y),v)
    ]]></literal>
    <literal><![CDATA[
      s(w,v6)
    ]]></literal>
    <literal><![CDATA[
      -q(v7,v7)
    ]]></literal>
    <justification jstring="[resolve(1048,c,26,c)].">
      <j1 rule="resolve" parents="1048 26"/>
    </justification>
  </clause>

  <clause id="1098">
    <literal><![CDATA[
      s(f1(f1(x,y),z),u)
    ]]></literal>
    <literal><![CDATA[
      s(f1(x,y),v)
    ]]></literal>
    <literal><![CDATA[
      -q(w,w)
    ]]></literal>
    <justification jstring="[factor(1084,a,c)].">
      <j1 rule="factor" parents="1084"/>
    </justification>
  </clause>

  <clause id="1104">
    <literal><![CDATA[
      s(f1(f1(x,y),z),u)
    ]]></literal>
    <literal><![CDATA[
      s(f1(x,y),v)
    ]]></literal>
    <literal><![CDATA[
      s(f1(f1(w,v6),v7),v8)
    ]]></literal>
    <literal><![CDATA[
      s(f1(w,v6),v9)
    ]]></literal>
    <justification jstring="[resolve(1098,c,1048,c)].">
      <j1 rule="resolve" parents="1098 1048"/>
    </justification>
  </clause>

  <clause id="1105">
    <literal><![CDATA[
      s(f1(f1(x,y),z),u)
    ]]></literal>
    <literal><![CDATA[
      s(f1(x,y),v)
    ]]></literal>
    <literal><![CDATA[
      s(f1(x,y),w)
    ]]></literal>
    <justification jstring="[factor(1104,a,c)].">
      <j1 rule="factor" parents="1104"/>
    </justification>
  </clause>

  <clause id="1106">
    <literal><![CDATA[
      s(f1(f1(x,y),z),u)
    ]]></literal>
    <literal><![CDATA[
      s(f1(x,y),v)
    ]]></literal>
    <justification jstring="[factor(1105,b,c)].">
      <j1 rule="factor" parents="1105"/>
    </justification>
  </clause>

  <clause id="1109">
    <literal><![CDATA[
      s(f1(x,y),z)
    ]]></literal>
    <literal><![CDATA[
      -s(u,u)
    ]]></literal>
    <literal><![CDATA[
      -s(f1(x,y),f1(f1(x,y),u))
    ]]></literal>
    <justification jstring="[resolve(1106,a,100,a)].">
      <j1 rule="resolve" parents="1106 100"/>
    </justification>
  </clause>

  <clause id="1125">
    <literal><![CDATA[
      s(f1(x,y),z)
    ]]></literal>
    <literal><![CDATA[
      s(u,f1(f1(x,y),v))
    ]]></literal>
    <literal><![CDATA[
      -s(w,w)
    ]]></literal>
    <justification jstring="[resolve(1106,a,22,b)].">
      <j1 rule="resolve" parents="1106 22"/>
    </justification>
  </clause>

  <clause id="1149">
    <literal><![CDATA[
      s(f1(x,y),f1(f1(x,y),z))
    ]]></literal>
    <literal><![CDATA[
      -s(u,u)
    ]]></literal>
    <justification jstring="[factor(1125,a,b)].">
      <j1 rule="factor" parents="1125"/>
    </justification>
  </clause>

  <clause id="1156">
    <literal><![CDATA[
      s(f1(x,y),f1(f1(x,y),z))
    ]]></literal>
    <literal><![CDATA[
      s(f1(u,v),w)
    ]]></literal>
    <justification jstring="[resolve(1149,b,1106,a)].">
      <j1 rule="resolve" parents="1149 1106"/>
    </justification>
  </clause>

  <clause id="1158">
    <literal><![CDATA[
      s(f1(x,y),f1(f1(x,y),z))
    ]]></literal>
    <justification jstring="[factor(1156,a,b)].">
      <j1 rule="factor" parents="1156"/>
    </justification>
  </clause>

  <clause id="1169">
    <literal><![CDATA[
      s(f1(x,y),z)
    ]]></literal>
    <literal><![CDATA[
      -s(u,u)
    ]]></literal>
    <justification jstring="[back_unit_del(1109),unit_del(c,1158)].">
      <j1 rule="back_unit_del" parents="1109"/>
      <j2 rule="unit_del" parents="1158"/>
    </justification>
  </clause>

  <clause id="1170">
    <literal><![CDATA[
      -s(x,x)
    ]]></literal>
    <literal><![CDATA[
      -s(y,f1(y,x))
    ]]></literal>
    <justification jstring="[back_unit_del(100),unit_del(a,1158)].">
      <j1 rule="back_unit_del" parents="100"/>
      <j2 rule="unit_del" parents="1158"/>
    </justification>
  </clause>

  <clause id="1188">
    <literal><![CDATA[
      s(f1(x,y),z)
    ]]></literal>
    <literal><![CDATA[
      s(f1(u,v),w)
    ]]></literal>
    <justification jstring="[resolve(1169,b,1106,a)].">
      <j1 rule="resolve" parents="1169 1106"/>
    </justification>
  </clause>

  <clause id="1190">
    <literal><![CDATA[
      s(f1(x,y),z)
    ]]></literal>
    <justification jstring="[factor(1188,a,b)].">
      <j1 rule="factor" parents="1188"/>
    </justification>
  </clause>

  <clause id="1191">
    <literal><![CDATA[
      -s(x,x)
    ]]></literal>
    <justification jstring="[resolve(1190,a,1170,b)].">
      <j1 rule="resolve" parents="1190 1170"/>
    </justification>
  </clause>

  <clause id="1192">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[resolve(1191,a,1190,a)].">
      <j1 rule="resolve" parents="1191 1190"/>
    </justification>
  </clause>

</proof>

</proofs>
