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<!DOCTYPE proofs SYSTEM "proof3.dtd">

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

<proofs number_of_proofs="1">

<source>4.5.out</source>

<heading><![CDATA[
Prover9 (64) version Aug-2007, Aug 2007.
Process 26278 was started by veroff on titan,
Sat Jan 19 14:18:57 2008
The command was "prover9 -f 4.5.in".
]]></heading>

<proof number="1" length="7" max_count="9">

<comments><![CDATA[
% Proof 1 at 0.01 (+ 0.00) seconds: "(N2)".
% Length of proof is 7.
% Level of proof is 3.
% Maximum clause weight is 9.
% Given clauses 30.
]]></comments>

  <clause id="1" type="goal">
    <literal><![CDATA[
      x -> x = 1
    ]]></literal>
    <attribute><![CDATA[
      label("(N2)")
    ]]></attribute>
    <attribute><![CDATA[
      label(non_clause)
    ]]></attribute>
    <attribute><![CDATA[
      label(goal)
    ]]></attribute>
    <justification jstring="[goal].">
      <j1 rule="goal"/>
    </justification>
  </clause>

  <clause id="20" type="assumption">
    <literal><![CDATA[
      x -> y = x => (x => y)
    ]]></literal>
    <attribute><![CDATA[
      label("(-> def)")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="21">
    <literal><![CDATA[
      x => (x => y) = x -> y
    ]]></literal>
    <justification jstring="[copy(20),flip(a)].">
      <j1 rule="copy" parents="20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34" type="assumption">
    <literal><![CDATA[
      x => (y => x) = 1
    ]]></literal>
    <attribute><![CDATA[
      label("(3.17)")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="47" type="deny">
    <literal><![CDATA[
      c1 -> c1 != 1
    ]]></literal>
    <attribute><![CDATA[
      label("(N2)")
    ]]></attribute>
    <attribute><![CDATA[
      answer("(N2)")
    ]]></attribute>
    <justification jstring="[deny(1)].">
      <j1 rule="deny" parents="1"/>
    </justification>
  </clause>

  <clause id="344">
    <literal><![CDATA[
      x -> x = 1
    ]]></literal>
    <justification jstring="[para(34(a,1),21(a,1)),flip(a)].">
      <j1 rule="para" parents="34 21"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="345">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer("(N2)")
    ]]></attribute>
    <justification jstring="[resolve(344,a,47,a)].">
      <j1 rule="resolve" parents="344 47"/>
    </justification>
  </clause>

</proof>

</proofs>
