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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 June-2006C, June 2006.
Process 13076 was started by mccune on cleo.thornwood,
Mon Jun 19 16:41:11 2006
The command was "/home/mccune/bin/prover9 -f lifsch.in".
]]></heading>

<proof number="1" length="31" max_count="34">

<comments><![CDATA[
% Proof 1 at 0.30 (+ 0.00) seconds.
% Length of proof is 31.
% Level of proof is 21.
% Maximum clause weight is 34.
% Given clauses 100.
]]></comments>

  <clause id="3">
    <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="[clausify].">
      <j1 rule="clausify"/>
    </justification>
  </clause>

  <clause id="5">
    <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="[clausify].">
      <j1 rule="clausify"/>
    </justification>
  </clause>

  <clause id="12">
    <literal><![CDATA[
      - p(x,x)
    ]]></literal>
    <literal><![CDATA[
      - s(x,f1(x,y))
    ]]></literal>
    <literal><![CDATA[
      - s(y,y)
    ]]></literal>
    <justification jstring="[clausify].">
      <j1 rule="clausify"/>
    </justification>
  </clause>

  <clause id="14">
    <literal><![CDATA[
      - p(x,x)
    ]]></literal>
    <literal><![CDATA[
      s(f1(x,y),z)
    ]]></literal>
    <literal><![CDATA[
      q(f1(x,y),u)
    ]]></literal>
    <justification jstring="[clausify].">
      <j1 rule="clausify"/>
    </justification>
  </clause>

  <clause id="111">
    <literal><![CDATA[
      s(x,y)
    ]]></literal>
    <literal><![CDATA[
      - s(y,f1(y,z))
    ]]></literal>
    <literal><![CDATA[
      - s(z,z)
    ]]></literal>
    <justification jstring="[clausify].">
      <j1 rule="clausify"/>
    </justification>
  </clause>

  <clause id="115">
    <literal><![CDATA[
      s(x,y)
    ]]></literal>
    <literal><![CDATA[
      - q(z,z)
    ]]></literal>
    <literal><![CDATA[
      - q(u,f1(y,u))
    ]]></literal>
    <justification jstring="[clausify].">
      <j1 rule="clausify"/>
    </justification>
  </clause>

  <clause id="138">
    <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(12,a,3,a)].">
      <j1 rule="resolve" parents="12 3"/>
    </justification>
  </clause>

  <clause id="157">
    <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(14,a,5,a)].">
      <j1 rule="resolve" parents="14 5"/>
    </justification>
  </clause>

  <clause id="189">
    <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(138,b,d)].">
      <j1 rule="factor" parents="138"/>
    </justification>
  </clause>

  <clause id="285">
    <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(157,b,115,c)].">
      <j1 rule="resolve" parents="157 115"/>
    </justification>
  </clause>

  <clause id="332">
    <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(285,a,d)].">
      <j1 rule="factor" parents="285"/>
    </justification>
  </clause>

  <clause id="1124">
    <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(332,d,157,b)].">
      <j1 rule="resolve" parents="332 157"/>
    </justification>
  </clause>

  <clause id="1132">
    <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(1124,a,d)].">
      <j1 rule="factor" parents="1124"/>
    </justification>
  </clause>

  <clause id="1135">
    <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(1132,b,d)].">
      <j1 rule="factor" parents="1132"/>
    </justification>
  </clause>

  <clause id="1137">
    <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(1135,c,d)].">
      <j1 rule="factor" parents="1135"/>
    </justification>
  </clause>

  <clause id="1173">
    <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(1137,c,115,c)].">
      <j1 rule="resolve" parents="1137 115"/>
    </justification>
  </clause>

  <clause id="1187">
    <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(1173,a,c)].">
      <j1 rule="factor" parents="1173"/>
    </justification>
  </clause>

  <clause id="1193">
    <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(1187,c,1137,c)].">
      <j1 rule="resolve" parents="1187 1137"/>
    </justification>
  </clause>

  <clause id="1194">
    <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(1193,a,c)].">
      <j1 rule="factor" parents="1193"/>
    </justification>
  </clause>

  <clause id="1195">
    <literal><![CDATA[
      s(f1(f1(x,y),z),u)
    ]]></literal>
    <literal><![CDATA[
      s(f1(x,y),v)
    ]]></literal>
    <justification jstring="[factor(1194,b,c)].">
      <j1 rule="factor" parents="1194"/>
    </justification>
  </clause>

  <clause id="1198">
    <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(1195,a,189,a)].">
      <j1 rule="resolve" parents="1195 189"/>
    </justification>
  </clause>

  <clause id="1214">
    <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(1195,a,111,b)].">
      <j1 rule="resolve" parents="1195 111"/>
    </justification>
  </clause>

  <clause id="1238">
    <literal><![CDATA[
      s(f1(x,y),f1(f1(x,y),z))
    ]]></literal>
    <literal><![CDATA[
      - s(u,u)
    ]]></literal>
    <justification jstring="[factor(1214,a,b)].">
      <j1 rule="factor" parents="1214"/>
    </justification>
  </clause>

  <clause id="1245">
    <literal><![CDATA[
      s(f1(x,y),f1(f1(x,y),z))
    ]]></literal>
    <literal><![CDATA[
      s(f1(u,v),w)
    ]]></literal>
    <justification jstring="[resolve(1238,b,1195,a)].">
      <j1 rule="resolve" parents="1238 1195"/>
    </justification>
  </clause>

  <clause id="1247">
    <literal><![CDATA[
      s(f1(x,y),f1(f1(x,y),z))
    ]]></literal>
    <justification jstring="[factor(1245,a,b)].">
      <j1 rule="factor" parents="1245"/>
    </justification>
  </clause>

  <clause id="1258">
    <literal><![CDATA[
      s(f1(x,y),z)
    ]]></literal>
    <literal><![CDATA[
      - s(u,u)
    ]]></literal>
    <justification jstring="[back_unit_del(1198),unit_del(c,1247)].">
      <j1 rule="back_unit_del" parents="1198"/>
      <j2 rule="unit_del" parents="1247"/>
    </justification>
  </clause>

  <clause id="1259">
    <literal><![CDATA[
      - s(x,x)
    ]]></literal>
    <literal><![CDATA[
      - s(y,f1(y,x))
    ]]></literal>
    <justification jstring="[back_unit_del(189),unit_del(a,1247)].">
      <j1 rule="back_unit_del" parents="189"/>
      <j2 rule="unit_del" parents="1247"/>
    </justification>
  </clause>

  <clause id="1277">
    <literal><![CDATA[
      s(f1(x,y),z)
    ]]></literal>
    <literal><![CDATA[
      s(f1(u,v),w)
    ]]></literal>
    <justification jstring="[resolve(1258,b,1195,a)].">
      <j1 rule="resolve" parents="1258 1195"/>
    </justification>
  </clause>

  <clause id="1279">
    <literal><![CDATA[
      s(f1(x,y),z)
    ]]></literal>
    <justification jstring="[factor(1277,a,b)].">
      <j1 rule="factor" parents="1277"/>
    </justification>
  </clause>

  <clause id="1280">
    <literal><![CDATA[
      - s(x,x)
    ]]></literal>
    <justification jstring="[resolve(1279,a,1259,b)].">
      <j1 rule="resolve" parents="1279 1259"/>
    </justification>
  </clause>

  <clause id="1281">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[resolve(1280,a,1279,a)].">
      <j1 rule="resolve" parents="1280 1279"/>
    </justification>
  </clause>

</proof>

</proofs>
