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<!DOCTYPE proofs SYSTEM "proof3.dtd">

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

<proofs number_of_proofs="1">

<source>3.6.out</source>

<heading><![CDATA[
Prover9 (64) version Aug-2007, Aug 2007.
Process 32412 was started by veroff on io,
Mon Jan 21 11:14:54 2008
The command was "prover9 -f 3.6.in".
]]></heading>

<proof number="1" length="12" max_count="13">

<comments><![CDATA[
% Proof 1 at 0.03 (+ 0.00) seconds: "(E2)".
% Length of proof is 12.
% Level of proof is 4.
% Maximum clause weight is 13.
% Given clauses 53.
]]></comments>

  <clause id="1" type="goal">
    <literal><![CDATA[
      x => (x => (x => y)) = x => (x => y)
    ]]></literal>
    <attribute><![CDATA[
      label("(E2)")
    ]]></attribute>
    <attribute><![CDATA[
      label(non_clause)
    ]]></attribute>
    <attribute><![CDATA[
      label(goal)
    ]]></attribute>
    <justification jstring="[goal].">
      <j1 rule="goal"/>
    </justification>
  </clause>

  <clause id="33" type="assumption">
    <literal><![CDATA[
      x -> (x -> y) = x -> y
    ]]></literal>
    <attribute><![CDATA[
      label("(3.5)")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="40" type="assumption">
    <literal><![CDATA[
      x => y != 1
    ]]></literal>
    <literal><![CDATA[
      y => x != 1
    ]]></literal>
    <literal><![CDATA[
      x = y
    ]]></literal>
    <attribute><![CDATA[
      label("(BCK4)")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="46" type="assumption">
    <literal><![CDATA[
      x => (x => y) = x -> y
    ]]></literal>
    <attribute><![CDATA[
      label("(3.15)")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="50" 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="52" type="deny">
    <literal><![CDATA[
      c1 => (c1 => (c1 => c2)) != c1 => (c1 => c2)
    ]]></literal>
    <attribute><![CDATA[
      label("(E2)")
    ]]></attribute>
    <attribute><![CDATA[
      answer("(E2)")
    ]]></attribute>
    <justification jstring="[deny(1)].">
      <j1 rule="deny" parents="1"/>
    </justification>
  </clause>

  <clause id="711">
    <literal><![CDATA[
      (x => y) => (x -> y) = 1
    ]]></literal>
    <justification jstring="[para(46(a,1),50(a,1,2))].">
      <j1 rule="para" parents="46 50"/>
    </justification>
  </clause>

  <clause id="744">
    <literal><![CDATA[
      c1 => (c1 -> c2) != c1 => (c1 => c2)
    ]]></literal>
    <attribute><![CDATA[
      answer("(E2)")
    ]]></attribute>
    <justification jstring="[para(46(a,1),52(a,1,2))].">
      <j1 rule="para" parents="46 52"/>
    </justification>
  </clause>

  <clause id="752">
    <literal><![CDATA[
      (x => (x -> y)) => (x -> y) = 1
    ]]></literal>
    <justification jstring="[para(33(a,1),711(a,1,2))].">
      <j1 rule="para" parents="33 711"/>
    </justification>
  </clause>

  <clause id="775">
    <literal><![CDATA[
      x => (x -> y) = x -> y
    ]]></literal>
    <justification jstring="[hyper(40,a,50,a,b,752,a),flip(a)].">
      <j1 rule="hyper" parents="40 50 752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="871">
    <literal><![CDATA[
      c1 => (c1 -> c2) != c1 -> c2
    ]]></literal>
    <attribute><![CDATA[
      answer("(E2)")
    ]]></attribute>
    <justification jstring="[para(46(a,1),744(a,2))].">
      <j1 rule="para" parents="46 744"/>
    </justification>
  </clause>

  <clause id="872">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer("(E2)")
    ]]></attribute>
    <justification jstring="[resolve(871,a,775,a)].">
      <j1 rule="resolve" parents="871 775"/>
    </justification>
  </clause>

</proof>

</proofs>
