<?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="4">

<source>SWC339+1.out</source>

<heading><![CDATA[
FOF-Prover9 (32) version 22-May-2007, May 2007.
Process 27407 was started by mccune on cleo,
Tue May 22 14:45:23 2007
The command was "/home/mccune/bin/fof-prover9 -f SWC339+1.in".
]]></heading>

<proof number="1" length="17" max_count="18">

<comments><![CDATA[
% Proof 1 at 4.39 (+ 0.04) seconds.
% Length of proof is 17.
% Level of proof is 3.
% Maximum clause weight is 18.
% Given clauses 678.
]]></comments>

  <clause id="208" type="assumption">
    <literal><![CDATA[
      -ssList(A)
    ]]></literal>
    <literal><![CDATA[
      segmentP(A,A)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="209" type="assumption">
    <literal><![CDATA[
      -ssList(A)
    ]]></literal>
    <literal><![CDATA[
      -ssList(B)
    ]]></literal>
    <literal><![CDATA[
      -segmentP(A,B)
    ]]></literal>
    <literal><![CDATA[
      -ssList(C)
    ]]></literal>
    <literal><![CDATA[
      -ssList(D)
    ]]></literal>
    <literal><![CDATA[
      segmentP(app(app(C,A),D),B)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="253" type="assumption">
    <literal><![CDATA[
      ssList(c3)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="255" type="assumption">
    <literal><![CDATA[
      -segmentP(c4,c3)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="257" type="assumption">
    <literal><![CDATA[
      c5 = c3
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="261" type="assumption">
    <literal><![CDATA[
      c6 = c4
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="262" type="assumption">
    <literal><![CDATA[
      ssList(c7)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="265" type="assumption">
    <literal><![CDATA[
      ssList(c8)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="266" type="assumption">
    <literal><![CDATA[
      app(app(c7,c5),c8) = c6
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="267">
    <literal><![CDATA[
      app(app(c7,c3),c8) = c4
    ]]></literal>
    <justification jstring="[copy(266),rewrite([257(2),261(6)])].">
      <j1 rule="copy" parents="266"/>
      <j2 rule="rewrite" parents="257 261"/>
    </justification>
  </clause>

  <clause id="270" type="assumption">
    <literal><![CDATA[
      nil = c6
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="271">
    <literal><![CDATA[
      c4 = nil
    ]]></literal>
    <justification jstring="[copy(270),rewrite([261(2)]),flip(a)].">
      <j1 rule="copy" parents="270"/>
      <j2 rule="rewrite" parents="261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="769">
    <literal><![CDATA[
      -ssList(A)
    ]]></literal>
    <literal><![CDATA[
      -segmentP(A,A)
    ]]></literal>
    <literal><![CDATA[
      -ssList(B)
    ]]></literal>
    <literal><![CDATA[
      -ssList(C)
    ]]></literal>
    <literal><![CDATA[
      segmentP(app(app(B,A),C),A)
    ]]></literal>
    <justification jstring="[factor(209,a,b)].">
      <j1 rule="factor" parents="209"/>
    </justification>
  </clause>

  <clause id="792">
    <literal><![CDATA[
      app(app(c7,c3),c8) = nil
    ]]></literal>
    <justification jstring="[back_rewrite(267),rewrite([271(6)])].">
      <j1 rule="back_rewrite" parents="267"/>
      <j2 rule="rewrite" parents="271"/>
    </justification>
  </clause>

  <clause id="794">
    <literal><![CDATA[
      -segmentP(nil,c3)
    ]]></literal>
    <justification jstring="[back_rewrite(255),rewrite([271(1)])].">
      <j1 rule="back_rewrite" parents="255"/>
      <j2 rule="rewrite" parents="271"/>
    </justification>
  </clause>

  <clause id="5372">
    <literal><![CDATA[
      segmentP(c3,c3)
    ]]></literal>
    <justification jstring="[resolve(253,a,208,a)].">
      <j1 rule="resolve" parents="253 208"/>
    </justification>
  </clause>

  <clause id="8644">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[para(792(a,1),769(e,1)),unit_del(a,253),unit_del(b,5372),unit_del(c,262),unit_del(d,265),unit_del(e,794)].">
      <j1 rule="para" parents="792 769"/>
      <j2 rule="unit_del" parents="253"/>
      <j2 rule="unit_del" parents="5372"/>
      <j2 rule="unit_del" parents="262"/>
      <j2 rule="unit_del" parents="265"/>
      <j2 rule="unit_del" parents="794"/>
    </justification>
  </clause>

</proof>

<proof number="2" length="4" max_count="3">

<comments><![CDATA[
% Proof 1 at 0.26 (+ 0.00) seconds.
% Length of proof is 4.
% Level of proof is 1.
% Maximum clause weight is 3.
% Given clauses 0.
]]></comments>

  <clause id="254" type="assumption">
    <literal><![CDATA[
      -totalorderedP(c3)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="257" type="assumption">
    <literal><![CDATA[
      c5 = c3
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="258" type="assumption">
    <literal><![CDATA[
      totalorderedP(c5)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="259">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(258),rewrite([257(1)]),unit_del(a,254)].">
      <j1 rule="copy" parents="258"/>
      <j2 rule="rewrite" parents="257"/>
      <j2 rule="unit_del" parents="254"/>
    </justification>
  </clause>

</proof>

<proof number="3" length="13" max_count="18">

<comments><![CDATA[
% Proof 1 at 4.44 (+ 0.05) seconds.
% Length of proof is 13.
% Level of proof is 2.
% Maximum clause weight is 18.
% Given clauses 659.
]]></comments>

  <clause id="208" type="assumption">
    <literal><![CDATA[
      -ssList(A)
    ]]></literal>
    <literal><![CDATA[
      segmentP(A,A)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="209" type="assumption">
    <literal><![CDATA[
      -ssList(A)
    ]]></literal>
    <literal><![CDATA[
      -ssList(B)
    ]]></literal>
    <literal><![CDATA[
      -segmentP(A,B)
    ]]></literal>
    <literal><![CDATA[
      -ssList(C)
    ]]></literal>
    <literal><![CDATA[
      -ssList(D)
    ]]></literal>
    <literal><![CDATA[
      segmentP(app(app(C,A),D),B)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="253" type="assumption">
    <literal><![CDATA[
      ssList(c3)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="255" type="assumption">
    <literal><![CDATA[
      -segmentP(c4,c3)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="257" type="assumption">
    <literal><![CDATA[
      c5 = c3
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="263" type="assumption">
    <literal><![CDATA[
      c6 = c4
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="264" type="assumption">
    <literal><![CDATA[
      ssList(c7)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="267" type="assumption">
    <literal><![CDATA[
      ssList(c8)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="268" type="assumption">
    <literal><![CDATA[
      app(app(c7,c5),c8) = c6
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="269">
    <literal><![CDATA[
      app(app(c7,c3),c8) = c4
    ]]></literal>
    <justification jstring="[copy(268),rewrite([257(2),263(6)])].">
      <j1 rule="copy" parents="268"/>
      <j2 rule="rewrite" parents="257 263"/>
    </justification>
  </clause>

  <clause id="769">
    <literal><![CDATA[
      -ssList(A)
    ]]></literal>
    <literal><![CDATA[
      -segmentP(A,A)
    ]]></literal>
    <literal><![CDATA[
      -ssList(B)
    ]]></literal>
    <literal><![CDATA[
      -ssList(C)
    ]]></literal>
    <literal><![CDATA[
      segmentP(app(app(B,A),C),A)
    ]]></literal>
    <justification jstring="[factor(209,a,b)].">
      <j1 rule="factor" parents="209"/>
    </justification>
  </clause>

  <clause id="5365">
    <literal><![CDATA[
      segmentP(c3,c3)
    ]]></literal>
    <justification jstring="[resolve(253,a,208,a)].">
      <j1 rule="resolve" parents="253 208"/>
    </justification>
  </clause>

  <clause id="8831">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[para(269(a,1),769(e,1)),unit_del(a,253),unit_del(b,5365),unit_del(c,264),unit_del(d,267),unit_del(e,255)].">
      <j1 rule="para" parents="269 769"/>
      <j2 rule="unit_del" parents="253"/>
      <j2 rule="unit_del" parents="5365"/>
      <j2 rule="unit_del" parents="264"/>
      <j2 rule="unit_del" parents="267"/>
      <j2 rule="unit_del" parents="255"/>
    </justification>
  </clause>

</proof>

<proof number="4" length="4" max_count="3">

<comments><![CDATA[
% Proof 1 at 0.26 (+ 0.00) seconds.
% Length of proof is 4.
% Level of proof is 1.
% Maximum clause weight is 3.
% Given clauses 0.
]]></comments>

  <clause id="254" type="assumption">
    <literal><![CDATA[
      -totalorderedP(c3)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="257" type="assumption">
    <literal><![CDATA[
      c5 = c3
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="258" type="assumption">
    <literal><![CDATA[
      totalorderedP(c5)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="259">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(258),rewrite([257(1)]),unit_del(a,254)].">
      <j1 rule="copy" parents="258"/>
      <j2 rule="rewrite" parents="257"/>
      <j2 rule="unit_del" parents="254"/>
    </justification>
  </clause>

</proof>

</proofs>
