<?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 November-2006, November 2006.
Process 3800 was started by mccune on cleo.thornwood,
Wed Nov 22 11:23:48 2006
The command was "/home/mccune/bin/fof-prover9 -f SWC339+1.in".
]]></heading>

<proof number="1" length="15" max_count="18">

<comments><![CDATA[
% Proof 1 at 2.02 (+ 0.04) seconds.
% Length of proof is 15.
% Level of proof is 3.
% Maximum clause weight is 18.
% Given clauses 680.
]]></comments>

  <clause id="82" 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[
      app(app(C,B),D) != A
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="157" type="assumption">
    <literal><![CDATA[
      ssList(nil)
    ]]></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="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="3696">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[resolve(792,a,82,f),unit_del(a,157),unit_del(b,253),unit_del(c,794),unit_del(d,262),unit_del(e,265)].">
      <j1 rule="resolve" parents="792 82"/>
      <j2 rule="unit_del" parents="157"/>
      <j2 rule="unit_del" parents="253"/>
      <j2 rule="unit_del" parents="794"/>
      <j2 rule="unit_del" parents="262"/>
      <j2 rule="unit_del" parents="265"/>
    </justification>
  </clause>

</proof>

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

<comments><![CDATA[
% Proof 1 at 0.29 (+ 0.01) 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="11" max_count="18">

<comments><![CDATA[
% Proof 1 at 1.83 (+ 0.02) seconds.
% Length of proof is 11.
% Level of proof is 2.
% Maximum clause weight is 18.
% Given clauses 205.
]]></comments>

  <clause id="82" 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[
      app(app(C,B),D) != A
    ]]></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="254" type="assumption">
    <literal><![CDATA[
      ssList(c4)
    ]]></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="3426">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[resolve(269,a,82,f),unit_del(a,254),unit_del(b,253),unit_del(c,255),unit_del(d,264),unit_del(e,267)].">
      <j1 rule="resolve" parents="269 82"/>
      <j2 rule="unit_del" parents="254"/>
      <j2 rule="unit_del" parents="253"/>
      <j2 rule="unit_del" parents="255"/>
      <j2 rule="unit_del" parents="264"/>
      <j2 rule="unit_del" parents="267"/>
    </justification>
  </clause>

</proof>

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

<comments><![CDATA[
% Proof 1 at 0.29 (+ 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>
