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<!DOCTYPE proofs SYSTEM "proof3.dtd">

<?xml-stylesheet type="text/xsl" href="proof3.xsl"?>

<proofs number_of_proofs="1">

<source>subset_trans.out</source>

<heading><![CDATA[
Prover9 (32) version June-2006C, June 2006.
Process 12522 was started by mccune on cleo.thornwood,
Mon Jun 19 16:15:42 2006
The command was "/home/mccune/bin/prover9 -f subset_trans.in".
]]></heading>

<proof number="1" length="12" max_count="9">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 12.
% Level of proof is 3.
% Maximum clause weight is 6.
% Given clauses 6.
]]></comments>

  <clause id="1">
    <literal><![CDATA[
      - subset(x,y)
    ]]></literal>
    <literal><![CDATA[
      - member(z,x)
    ]]></literal>
    <literal><![CDATA[
      member(z,y)
    ]]></literal>
    <justification jstring="[clausify].">
      <j1 rule="clausify"/>
    </justification>
  </clause>

  <clause id="2">
    <literal><![CDATA[
      subset(x,y)
    ]]></literal>
    <literal><![CDATA[
      member(f1(x,y),x)
    ]]></literal>
    <justification jstring="[clausify].">
      <j1 rule="clausify"/>
    </justification>
  </clause>

  <clause id="3">
    <literal><![CDATA[
      subset(x,y)
    ]]></literal>
    <literal><![CDATA[
      - member(f1(x,y),y)
    ]]></literal>
    <justification jstring="[clausify].">
      <j1 rule="clausify"/>
    </justification>
  </clause>

  <clause id="4">
    <literal><![CDATA[
      subset(c1,c2)
    ]]></literal>
    <justification jstring="[clausify].">
      <j1 rule="clausify"/>
    </justification>
  </clause>

  <clause id="5">
    <literal><![CDATA[
      subset(c2,c3)
    ]]></literal>
    <justification jstring="[clausify].">
      <j1 rule="clausify"/>
    </justification>
  </clause>

  <clause id="6">
    <literal><![CDATA[
      - subset(c1,c3)
    ]]></literal>
    <justification jstring="[clausify].">
      <j1 rule="clausify"/>
    </justification>
  </clause>

  <clause id="15">
    <literal><![CDATA[
      - member(x,c1)
    ]]></literal>
    <literal><![CDATA[
      member(x,c2)
    ]]></literal>
    <justification jstring="[resolve(4,a,1,a)].">
      <j1 rule="resolve" parents="4 1"/>
    </justification>
  </clause>

  <clause id="16">
    <literal><![CDATA[
      - member(x,c2)
    ]]></literal>
    <literal><![CDATA[
      member(x,c3)
    ]]></literal>
    <justification jstring="[resolve(5,a,1,a)].">
      <j1 rule="resolve" parents="5 1"/>
    </justification>
  </clause>

  <clause id="17">
    <literal><![CDATA[
      member(f1(c1,c3),c1)
    ]]></literal>
    <justification jstring="[resolve(6,a,2,a)].">
      <j1 rule="resolve" parents="6 2"/>
    </justification>
  </clause>

  <clause id="18">
    <literal><![CDATA[
      - member(f1(c1,c3),c3)
    ]]></literal>
    <justification jstring="[resolve(6,a,3,a)].">
      <j1 rule="resolve" parents="6 3"/>
    </justification>
  </clause>

  <clause id="19">
    <literal><![CDATA[
      member(f1(c1,c3),c2)
    ]]></literal>
    <justification jstring="[resolve(17,a,15,a)].">
      <j1 rule="resolve" parents="17 15"/>
    </justification>
  </clause>

  <clause id="22">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[ur(16,b,18,a),unit_del(a,19)].">
      <j1 rule="ur" parents="16 18"/>
      <j2 rule="unit_del" parents="19"/>
    </justification>
  </clause>

</proof>

</proofs>
