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<!DOCTYPE proofs SYSTEM "proof3.dtd">

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

<proofs number_of_proofs="1">

<source>4.7.out</source>

<heading><![CDATA[
Prover9 (64) version Aug-2007, Aug 2007.
Process 26302 was started by veroff on titan,
Sat Jan 19 14:19:03 2008
The command was "prover9 -f 4.7.in".
]]></heading>

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

<comments><![CDATA[
% Proof 1 at 0.02 (+ 0.01) seconds: "(N3)".
% Length of proof is 12.
% Level of proof is 5.
% Maximum clause weight is 13.
% Given clauses 46.
]]></comments>

  <clause id="1" type="goal">
    <literal><![CDATA[
      (x -> y) ^ (~ x v y) = ~ x v y
    ]]></literal>
    <attribute><![CDATA[
      label("(N3)")
    ]]></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 * y) => z = x => (y => z)
    ]]></literal>
    <attribute><![CDATA[
      label("(P)")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </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="41" type="assumption">
    <literal><![CDATA[
      (x => y) ^ y = y
    ]]></literal>
    <attribute><![CDATA[
      label("(3.13)")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="46" type="assumption">
    <literal><![CDATA[
      x -> (~ x v y) = x -> y
    ]]></literal>
    <attribute><![CDATA[
      label("(4.10)")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="49" type="deny">
    <literal><![CDATA[
      ~ c1 v c2 != (c1 -> c2) ^ (~ c1 v c2)
    ]]></literal>
    <attribute><![CDATA[
      label("(N3)")
    ]]></attribute>
    <attribute><![CDATA[
      answer("(N3)")
    ]]></attribute>
    <justification jstring="[deny(1)].">
      <j1 rule="deny" parents="1"/>
    </justification>
  </clause>

  <clause id="50">
    <literal><![CDATA[
      (c1 -> c2) ^ (~ c1 v c2) != ~ c1 v c2
    ]]></literal>
    <attribute><![CDATA[
      answer("(N3)")
    ]]></attribute>
    <justification jstring="[copy(49),flip(a)].">
      <j1 rule="copy" parents="49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="143">
    <literal><![CDATA[
      (x * x) => y = x -> y
    ]]></literal>
    <justification jstring="[para(21(a,1),15(a,2))].">
      <j1 rule="para" parents="21 15"/>
    </justification>
  </clause>

  <clause id="778">
    <literal><![CDATA[
      (x -> y) ^ y = y
    ]]></literal>
    <justification jstring="[para(143(a,1),41(a,1,1))].">
      <j1 rule="para" parents="143 41"/>
    </justification>
  </clause>

  <clause id="795">
    <literal><![CDATA[
      (x -> y) ^ (~ x v y) = ~ x v y
    ]]></literal>
    <justification jstring="[para(46(a,1),778(a,1,1))].">
      <j1 rule="para" parents="46 778"/>
    </justification>
  </clause>

  <clause id="796">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer("(N3)")
    ]]></attribute>
    <justification jstring="[resolve(795,a,50,a)].">
      <j1 rule="resolve" parents="795 50"/>
    </justification>
  </clause>

</proof>

</proofs>
