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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 2009-02A, February 2009.
Process 11199 was started by mccune on cleo,
Wed Feb 25 09:32:26 2009
The command was "/home/mccune/bin/prover9 -f lifsch.in".
]]></heading>

<proof number="1" length="32" max_count="54">

<comments><![CDATA[
% Proof 1 at 0.38 (+ 0.00) seconds.
% Length of proof is 32.
% Level of proof is 22.
% Maximum clause weight is 34.
% Given clauses 101.

]]></comments>

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

  <clause id="5" type="deny">
    <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" type="deny">
    <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" type="deny">
    <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" type="deny">
    <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" type="deny">
    <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" type="deny">
    <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),w)
    ]]></literal>
    <literal><![CDATA[
      s(f1(x,y),v5)
    ]]></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),w)
    ]]></literal>
    <literal><![CDATA[
      q(f1(x,y),v5)
    ]]></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),w)
    ]]></literal>
    <literal><![CDATA[
      q(f1(x,y),v5)
    ]]></literal>
    <literal><![CDATA[
      -q(v6,v6)
    ]]></literal>
    <justification jstring="[factor(196,a,d)].">
      <j1 rule="factor" parents="196"/>
    </justification>
  </clause>

  <clause id="1199">
    <literal><![CDATA[
      s(f1(f1(x,y),z),u)
    ]]></literal>
    <literal><![CDATA[
      s(f1(x,y),w)
    ]]></literal>
    <literal><![CDATA[
      q(f1(x,y),v5)
    ]]></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="1207">
    <literal><![CDATA[
      s(f1(f1(x,y),z),u)
    ]]></literal>
    <literal><![CDATA[
      s(f1(x,y),w)
    ]]></literal>
    <literal><![CDATA[
      q(f1(x,y),v5)
    ]]></literal>
    <literal><![CDATA[
      s(f1(x,y),v6)
    ]]></literal>
    <literal><![CDATA[
      q(f1(x,y),v7)
    ]]></literal>
    <justification jstring="[factor(1199,a,d)].">
      <j1 rule="factor" parents="1199"/>
    </justification>
  </clause>

  <clause id="1210">
    <literal><![CDATA[
      s(f1(f1(x,y),z),u)
    ]]></literal>
    <literal><![CDATA[
      s(f1(x,y),w)
    ]]></literal>
    <literal><![CDATA[
      q(f1(x,y),v5)
    ]]></literal>
    <literal><![CDATA[
      q(f1(x,y),v6)
    ]]></literal>
    <justification jstring="[factor(1207,b,d)].">
      <j1 rule="factor" parents="1207"/>
    </justification>
  </clause>

  <clause id="1212">
    <literal><![CDATA[
      s(f1(f1(x,y),z),u)
    ]]></literal>
    <literal><![CDATA[
      s(f1(x,y),w)
    ]]></literal>
    <literal><![CDATA[
      q(f1(x,y),v5)
    ]]></literal>
    <justification jstring="[factor(1210,c,d)].">
      <j1 rule="factor" parents="1210"/>
    </justification>
  </clause>

  <clause id="1248">
    <literal><![CDATA[
      s(f1(f1(x,y),z),u)
    ]]></literal>
    <literal><![CDATA[
      s(f1(x,y),w)
    ]]></literal>
    <literal><![CDATA[
      s(v5,v6)
    ]]></literal>
    <literal><![CDATA[
      -q(v7,v7)
    ]]></literal>
    <justification jstring="[resolve(1212,c,26,c)].">
      <j1 rule="resolve" parents="1212 26"/>
    </justification>
  </clause>

  <clause id="1262">
    <literal><![CDATA[
      s(f1(f1(x,y),z),u)
    ]]></literal>
    <literal><![CDATA[
      s(f1(x,y),w)
    ]]></literal>
    <literal><![CDATA[
      -q(v5,v5)
    ]]></literal>
    <justification jstring="[factor(1248,a,c)].">
      <j1 rule="factor" parents="1248"/>
    </justification>
  </clause>

  <clause id="1268">
    <literal><![CDATA[
      s(f1(f1(x,y),z),u)
    ]]></literal>
    <literal><![CDATA[
      s(f1(x,y),w)
    ]]></literal>
    <literal><![CDATA[
      s(f1(f1(v5,v6),v7),v8)
    ]]></literal>
    <literal><![CDATA[
      s(f1(v5,v6),v9)
    ]]></literal>
    <justification jstring="[resolve(1262,c,1212,c)].">
      <j1 rule="resolve" parents="1262 1212"/>
    </justification>
  </clause>

  <clause id="1269">
    <literal><![CDATA[
      s(f1(f1(x,y),z),u)
    ]]></literal>
    <literal><![CDATA[
      s(f1(x,y),w)
    ]]></literal>
    <literal><![CDATA[
      s(f1(x,y),v5)
    ]]></literal>
    <justification jstring="[factor(1268,a,c)].">
      <j1 rule="factor" parents="1268"/>
    </justification>
  </clause>

  <clause id="1270">
    <literal><![CDATA[
      s(f1(f1(x,y),z),u)
    ]]></literal>
    <literal><![CDATA[
      s(f1(x,y),w)
    ]]></literal>
    <justification jstring="[factor(1269,b,c)].">
      <j1 rule="factor" parents="1269"/>
    </justification>
  </clause>

  <clause id="1273">
    <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(1270,a,100,a)].">
      <j1 rule="resolve" parents="1270 100"/>
    </justification>
  </clause>

  <clause id="1289">
    <literal><![CDATA[
      s(f1(x,y),z)
    ]]></literal>
    <literal><![CDATA[
      s(u,f1(f1(x,y),w))
    ]]></literal>
    <literal><![CDATA[
      -s(v5,v5)
    ]]></literal>
    <justification jstring="[resolve(1270,a,22,b)].">
      <j1 rule="resolve" parents="1270 22"/>
    </justification>
  </clause>

  <clause id="1313">
    <literal><![CDATA[
      s(f1(x,y),f1(f1(x,y),z))
    ]]></literal>
    <literal><![CDATA[
      -s(u,u)
    ]]></literal>
    <justification jstring="[factor(1289,a,b)].">
      <j1 rule="factor" parents="1289"/>
    </justification>
  </clause>

  <clause id="1320">
    <literal><![CDATA[
      s(f1(x,y),f1(f1(x,y),z))
    ]]></literal>
    <literal><![CDATA[
      s(f1(u,w),v5)
    ]]></literal>
    <justification jstring="[resolve(1313,b,1270,a)].">
      <j1 rule="resolve" parents="1313 1270"/>
    </justification>
  </clause>

  <clause id="1322">
    <literal><![CDATA[
      s(f1(x,y),f1(f1(x,y),z))
    ]]></literal>
    <justification jstring="[factor(1320,a,b)].">
      <j1 rule="factor" parents="1320"/>
    </justification>
  </clause>

  <clause id="1333">
    <literal><![CDATA[
      s(f1(x,y),z)
    ]]></literal>
    <literal><![CDATA[
      -s(u,u)
    ]]></literal>
    <justification jstring="[back_unit_del(1273),unit_del(c,1322)].">
      <j1 rule="back_unit_del" parents="1273"/>
      <j2 rule="unit_del" parents="1322"/>
    </justification>
  </clause>

  <clause id="1334">
    <literal><![CDATA[
      -s(x,x)
    ]]></literal>
    <literal><![CDATA[
      -s(y,f1(y,x))
    ]]></literal>
    <justification jstring="[back_unit_del(100),unit_del(a,1322)].">
      <j1 rule="back_unit_del" parents="100"/>
      <j2 rule="unit_del" parents="1322"/>
    </justification>
  </clause>

  <clause id="1346">
    <literal><![CDATA[
      s(f1(x,y),z)
    ]]></literal>
    <literal><![CDATA[
      s(f1(u,w),v5)
    ]]></literal>
    <justification jstring="[resolve(1333,b,1270,a)].">
      <j1 rule="resolve" parents="1333 1270"/>
    </justification>
  </clause>

  <clause id="1348">
    <literal><![CDATA[
      s(f1(x,y),z)
    ]]></literal>
    <justification jstring="[factor(1346,a,b)].">
      <j1 rule="factor" parents="1346"/>
    </justification>
  </clause>

  <clause id="1349">
    <literal><![CDATA[
      -s(x,x)
    ]]></literal>
    <justification jstring="[resolve(1348,a,1334,b)].">
      <j1 rule="resolve" parents="1348 1334"/>
    </justification>
  </clause>

  <clause id="1350">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[resolve(1349,a,1348,a)].">
      <j1 rule="resolve" parents="1349 1348"/>
    </justification>
  </clause>

</proof>

</proofs>
