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<!DOCTYPE proofs SYSTEM "proof3.dtd">

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

<proofs number_of_proofs="1">

<source>4.6.out</source>

<heading><![CDATA[
Prover9 (64) version Aug-2007, Aug 2007.
Process 26290 was started by veroff on titan,
Sat Jan 19 14:19:00 2008
The command was "prover9 -f 4.6.in".
]]></heading>

<proof number="1" length="13" max_count="17">

<comments><![CDATA[
% Proof 1 at 0.03 (+ 0.01) seconds: "(N5)".
% Length of proof is 13.
% Level of proof is 8.
% Maximum clause weight is 17.
% Given clauses 48.
]]></comments>

  <clause id="1" type="goal">
    <literal><![CDATA[
      (x -> y) ^ (x -> z) = x -> (y ^ z)
    ]]></literal>
    <attribute><![CDATA[
      label("(N5)")
    ]]></attribute>
    <attribute><![CDATA[
      label(non_clause)
    ]]></attribute>
    <attribute><![CDATA[
      label(goal)
    ]]></attribute>
    <justification jstring="[goal].">
      <j1 rule="goal"/>
    </justification>
  </clause>

  <clause id="5" type="assumption">
    <literal><![CDATA[
      x ^ y = y ^ x
    ]]></literal>
    <attribute><![CDATA[
      label("(D4)")
    ]]></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="37" type="assumption">
    <literal><![CDATA[
      (x => y) ^ (x => z) = x => (y ^ z)
    ]]></literal>
    <attribute><![CDATA[
      label("(4.2)")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="48" type="deny">
    <literal><![CDATA[
      (c1 -> c2) ^ (c1 -> c3) != c1 -> (c2 ^ c3)
    ]]></literal>
    <attribute><![CDATA[
      label("(N5)")
    ]]></attribute>
    <attribute><![CDATA[
      answer("(N5)")
    ]]></attribute>
    <justification jstring="[deny(1)].">
      <j1 rule="deny" parents="1"/>
    </justification>
  </clause>

  <clause id="430">
    <literal><![CDATA[
      x => ((x => y) ^ z) = (x -> y) ^ (x => z)
    ]]></literal>
    <justification jstring="[para(21(a,1),37(a,1,1)),flip(a)].">
      <j1 rule="para" parents="21 37"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="708">
    <literal><![CDATA[
      x => (y ^ (x => z)) = (x -> z) ^ (x => y)
    ]]></literal>
    <justification jstring="[para(5(a,1),430(a,1,2))].">
      <j1 rule="para" parents="5 430"/>
    </justification>
  </clause>

  <clause id="803">
    <literal><![CDATA[
      x => ((x => y) ^ (x => z)) = (x -> z) ^ (x -> y)
    ]]></literal>
    <justification jstring="[para(21(a,1),708(a,2,2))].">
      <j1 rule="para" parents="21 708"/>
    </justification>
  </clause>

  <clause id="908">
    <literal><![CDATA[
      x => (x => (y ^ z)) = (x -> z) ^ (x -> y)
    ]]></literal>
    <justification jstring="[para(37(a,1),803(a,1,2))].">
      <j1 rule="para" parents="37 803"/>
    </justification>
  </clause>

  <clause id="960">
    <literal><![CDATA[
      (x -> y) ^ (x -> z) = x -> (z ^ y)
    ]]></literal>
    <justification jstring="[para(908(a,1),21(a,1))].">
      <j1 rule="para" parents="908 21"/>
    </justification>
  </clause>

  <clause id="1011">
    <literal><![CDATA[
      (x -> y) ^ (x -> z) = x -> (y ^ z)
    ]]></literal>
    <justification jstring="[para(960(a,1),5(a,1)),flip(a)].">
      <j1 rule="para" parents="960 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1012">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer("(N5)")
    ]]></attribute>
    <justification jstring="[resolve(1011,a,48,a)].">
      <j1 rule="resolve" parents="1011 48"/>
    </justification>
  </clause>

</proof>

</proofs>
