<?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="2">

<source>SWC258+1.out</source>

<heading><![CDATA[
FOF-Prover9 (32) version 2009-02A, February 2009.
Process 11578 was started by mccune on cleo,
Wed Feb 25 09:32:38 2009
The command was "/home/mccune/bin/fof-prover9 -f SWC258+1.in".
]]></heading>

<proof number="1" length="7" max_count="6">

<comments><![CDATA[
% Proof 1 at 3.13 (+ 0.05) seconds.
% Length of proof is 7.
% Level of proof is 2.
% Maximum clause weight is 6.
% Given clauses 200.

]]></comments>

  <clause id="213" type="assumption">
    <literal><![CDATA[
      -ssItem(A)
    ]]></literal>
    <literal><![CDATA[
      totalorderedP(cons(A,nil))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <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="260" type="assumption">
    <literal><![CDATA[
      ssItem(c7)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="261" type="assumption">
    <literal><![CDATA[
      cons(c7,nil) = c5
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="262">
    <literal><![CDATA[
      cons(c7,nil) = c3
    ]]></literal>
    <justification jstring="[copy(261),rewrite([257(4)])].">
      <j1 rule="copy" parents="261"/>
      <j2 rule="rewrite" parents="257"/>
    </justification>
  </clause>

  <clause id="5673">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[resolve(260,a,213,a),rewrite([262(3)]),unit_del(a,254)].">
      <j1 rule="resolve" parents="260 213"/>
      <j2 rule="rewrite" parents="262"/>
      <j2 rule="unit_del" parents="254"/>
    </justification>
  </clause>

</proof>

<proof number="2" length="6" max_count="3">

<comments><![CDATA[
% Proof 1 at 0.42 (+ 0.00) seconds.
% Length of proof is 6.
% Level of proof is 2.
% Maximum clause weight is 3.
% Given clauses 0.

]]></comments>

  <clause id="214" type="assumption">
    <literal><![CDATA[
      totalorderedP(nil)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="259" type="assumption">
    <literal><![CDATA[
      -totalorderedP(c5)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="261" type="assumption">
    <literal><![CDATA[
      c6 = c5
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="262" type="assumption">
    <literal><![CDATA[
      nil = c6
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="263">
    <literal><![CDATA[
      c5 = nil
    ]]></literal>
    <justification jstring="[copy(262),rewrite([261(2)]),flip(a)].">
      <j1 rule="copy" parents="262"/>
      <j2 rule="rewrite" parents="261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="782">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[back_rewrite(259),rewrite([263(1)]),unit_del(a,214)].">
      <j1 rule="back_rewrite" parents="259"/>
      <j2 rule="rewrite" parents="263"/>
      <j2 rule="unit_del" parents="214"/>
    </justification>
  </clause>

</proof>

</proofs>
