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<!DOCTYPE proofs SYSTEM "proof3.dtd">

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

<proofs number_of_proofs="1">

<source>cg1.out</source>

<heading><![CDATA[
Prover9 (32) version June-2006C, June 2006.
Process 13019 was started by mccune on cleo.thornwood,
Mon Jun 19 16:40:30 2006
The command was "/home/mccune/bin/prover9 -f cg1.in".
]]></heading>

<proof number="1" length="13" max_count="47">

<comments><![CDATA[
% Proof 1 at 0.12 (+ 0.00) seconds.
% Length of proof is 13.
% Level of proof is 5.
% Maximum clause weight is 47.
% Given clauses 34.
]]></comments>

  <clause id="4">
    <literal><![CDATA[
      (c1 * (c4 * c3)) * ((c2 * c5) * c6) != (c1 * (c2 * c3)) * ((c4 * c5) * c6)
    ]]></literal>
    <justification jstring="[clausify].">
      <j1 rule="clausify"/>
    </justification>
  </clause>

  <clause id="5">
    <literal><![CDATA[
      (x * y) * (z * u) = (x * z) * (y * u)
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="6">
    <literal><![CDATA[
      x * y != x * z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[clausify].">
      <j1 rule="clausify"/>
    </justification>
  </clause>

  <clause id="8">
    <literal><![CDATA[
      (c1 * (c2 * c3)) * ((c4 * c5) * c6) != (c1 * (c4 * c3)) * ((c2 * c5) * c6)
    ]]></literal>
    <justification jstring="[copy(4),flip(a)].">
      <j1 rule="copy" parents="4"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9">
    <literal><![CDATA[
      ((x * y) * (z * u)) * (v * w) = ((x * z) * v) * ((y * u) * w)
    ]]></literal>
    <justification jstring="[para(5(a,1),5(a,1,1))].">
      <j1 rule="para" parents="5 5"/>
    </justification>
  </clause>

  <clause id="10">
    <literal><![CDATA[
      (x * (y * z)) * (u * (v * w)) = (x * u) * ((y * v) * (z * w))
    ]]></literal>
    <justification jstring="[para(5(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11">
    <literal><![CDATA[
      (x * y) * (z * u) != (x * z) * v
    ]]></literal>
    <literal><![CDATA[
      y * u = v
    ]]></literal>
    <justification jstring="[para(5(a,1),6(a,1))].">
      <j1 rule="para" parents="5 6"/>
    </justification>
  </clause>

  <clause id="15">
    <literal><![CDATA[
      (c1 * (c4 * c5)) * ((c2 * c3) * c6) != (c1 * (c4 * c3)) * ((c2 * c5) * c6)
    ]]></literal>
    <justification jstring="[para(5(a,1),8(a,1))].">
      <j1 rule="para" parents="5 8"/>
    </justification>
  </clause>

  <clause id="25">
    <literal><![CDATA[
      ((x * y) * z) * ((u * v) * w) = ((x * u) * z) * ((y * v) * w)
    ]]></literal>
    <justification jstring="[para(9(a,1),5(a,1))].">
      <j1 rule="para" parents="9 5"/>
    </justification>
  </clause>

  <clause id="66">
    <literal><![CDATA[
      (x * (c1 * (c4 * c3))) * (y * ((c2 * c5) * c6)) != (x * y) * ((c1 * (c4 * c5)) * ((c2 * c3) * c6))
    ]]></literal>
    <justification jstring="[ur(11,b,15,a(flip))].">
      <j1 rule="ur" parents="11 15"/>
    </justification>
  </clause>

  <clause id="483">
    <literal><![CDATA[
      ((x * (y * z)) * (u * (v * w))) * ((c1 * (c4 * c5)) * ((c2 * c3) * c6)) != ((x * u) * (c1 * (c4 * c3))) * (((y * v) * (z * w)) * ((c2 * c5) * c6))
    ]]></literal>
    <justification jstring="[para(10(a,2),66(a,2,1)),flip(a)].">
      <j1 rule="para" parents="10 66"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="499">
    <literal><![CDATA[
      ((x * (y * z)) * u) * ((v * (w * v6)) * (v7 * v8)) = ((x * v) * u) * (((y * w) * v7) * ((z * v6) * v8))
    ]]></literal>
    <justification jstring="[para(9(a,1),25(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="500">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[resolve(499,a,483,a)].">
      <j1 rule="resolve" parents="499 483"/>
    </justification>
  </clause>

</proof>

</proofs>
