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<!DOCTYPE proofs SYSTEM "proof3.dtd">

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

<proofs number_of_proofs="1">

<source>3.13.out</source>

<heading><![CDATA[
Prover9 (64) version Aug-2007, Aug 2007.
Process 32341 was started by veroff on io,
Mon Jan 21 11:14:33 2008
The command was "prover9 -f 3.13.in".
]]></heading>

<proof number="1" length="11" max_count="9">

<comments><![CDATA[
% Proof 1 at 0.02 (+ 0.01) seconds: "(3.19)".
% Length of proof is 11.
% Level of proof is 4.
% Maximum clause weight is 9.
% Given clauses 51.
]]></comments>

  <clause id="1" type="goal">
    <literal><![CDATA[
      x => 0 = ~ x
    ]]></literal>
    <attribute><![CDATA[
      label("(3.19)")
    ]]></attribute>
    <attribute><![CDATA[
      label(non_clause)
    ]]></attribute>
    <attribute><![CDATA[
      label(goal)
    ]]></attribute>
    <justification jstring="[goal].">
      <j1 rule="goal"/>
    </justification>
  </clause>

  <clause id="15" type="assumption">
    <literal><![CDATA[
      ~ ~ x = x
    ]]></literal>
    <attribute><![CDATA[
      label("(DN)")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="16" type="assumption">
    <literal><![CDATA[
      ~ 1 = 0
    ]]></literal>
    <attribute><![CDATA[
      label("(2.2)")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="38" type="assumption">
    <literal><![CDATA[
      1 => x = x
    ]]></literal>
    <attribute><![CDATA[
      label("(BCK2)")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="43" type="assumption">
    <literal><![CDATA[
      ~ x => ~ y = y => x
    ]]></literal>
    <attribute><![CDATA[
      label("(3.12)")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="54" type="deny">
    <literal><![CDATA[
      ~ c1 != c1 => 0
    ]]></literal>
    <attribute><![CDATA[
      label("(3.19)")
    ]]></attribute>
    <attribute><![CDATA[
      answer("(3.19)")
    ]]></attribute>
    <justification jstring="[deny(1)].">
      <j1 rule="deny" parents="1"/>
    </justification>
  </clause>

  <clause id="55">
    <literal><![CDATA[
      c1 => 0 != ~ c1
    ]]></literal>
    <attribute><![CDATA[
      answer("(3.19)")
    ]]></attribute>
    <justification jstring="[copy(54),flip(a)].">
      <j1 rule="copy" parents="54"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="600">
    <literal><![CDATA[
      ~ x => ~ 1 = x
    ]]></literal>
    <justification jstring="[para(38(a,1),43(a,2))].">
      <j1 rule="para" parents="38 43"/>
    </justification>
  </clause>

  <clause id="829">
    <literal><![CDATA[
      ~ x => 0 = x
    ]]></literal>
    <justification jstring="[para(16(a,1),600(a,1,2))].">
      <j1 rule="para" parents="16 600"/>
    </justification>
  </clause>

  <clause id="844">
    <literal><![CDATA[
      x => 0 = ~ x
    ]]></literal>
    <justification jstring="[para(15(a,1),829(a,1,1))].">
      <j1 rule="para" parents="15 829"/>
    </justification>
  </clause>

  <clause id="845">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer("(3.19)")
    ]]></attribute>
    <justification jstring="[resolve(844,a,55,a)].">
      <j1 rule="resolve" parents="844 55"/>
    </justification>
  </clause>

</proof>

</proofs>
