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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 August-2006A, August 2006.
Process 10674 was started by mccune on cleo.thornwood,
Sat Aug 12 20:58:11 2006
The command was "/home/mccune/bin/prover9 -f cg1.in".
]]></heading>

<proof number="1" length="14" max_count="39">

<comments><![CDATA[
% Proof 1 at 0.09 (+ 0.00) seconds.
% Length of proof is 14.
% Level of proof is 5.
% Maximum clause weight is 39.
% Given clauses 30.
]]></comments>

  <clause id="1">
    <literal><![CDATA[
      (all x all y all z (x * y = x * z -> y = z))
    ]]></literal>
    <attribute><![CDATA[
      label(non_clause)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="3">
    <literal><![CDATA[
      (x * (y * z)) * ((u * v) * w) = (x * (u * z)) * ((y * v) * w)
    ]]></literal>
    <justification jstring="[goal].">
      <j1 rule="goal"/>
    </justification>
  </clause>

  <clause id="4">
    <literal><![CDATA[
      x * y != x * z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[clausify(1)].">
      <j1 rule="clausify" parents="1"/>
    </justification>
  </clause>

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

  <clause id="7">
    <literal><![CDATA[
      (c1 * (c4 * c3)) * ((c2 * c5) * c6) != (c1 * (c2 * c3)) * ((c4 * c5) * c6)
    ]]></literal>
    <justification jstring="[deny(3)].">
      <j1 rule="deny" parents="3"/>
    </justification>
  </clause>

  <clause id="8">
    <literal><![CDATA[
      (c1 * (c2 * c3)) * ((c4 * c5) * c6) != (c1 * (c4 * c3)) * ((c2 * c5) * c6)
    ]]></literal>
    <justification jstring="[copy(7),flip(a)].">
      <j1 rule="copy" parents="7"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9">
    <literal><![CDATA[
      (x * y) * (z * u) != (x * z) * v
    ]]></literal>
    <literal><![CDATA[
      y * u = v
    ]]></literal>
    <justification jstring="[para(6(a,1),4(a,1))].">
      <j1 rule="para" parents="6 4"/>
    </justification>
  </clause>

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

  <clause id="12">
    <literal><![CDATA[
      (x * (y * z)) * (u * (v * w)) = (x * u) * ((y * v) * (z * w))
    ]]></literal>
    <justification jstring="[para(6(a,1),6(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17">
    <literal><![CDATA[
      (x * (c1 * (c2 * c3))) * (y * ((c4 * c5) * c6)) != (x * y) * ((c1 * (c4 * c3)) * ((c2 * c5) * c6))
    ]]></literal>
    <justification jstring="[ur(9,b,8,a)].">
      <j1 rule="ur" parents="9 8"/>
    </justification>
  </clause>

  <clause id="58">
    <literal><![CDATA[
      ((x * y) * z) * ((u * v) * w) = ((x * u) * z) * ((y * v) * w)
    ]]></literal>
    <justification jstring="[para(11(a,1),6(a,1))].">
      <j1 rule="para" parents="11 6"/>
    </justification>
  </clause>

  <clause id="417">
    <literal><![CDATA[
      ((x * y) * ((z * u) * (v * w))) * ((v6 * v7) * v8) = ((x * v6) * (y * (u * w))) * (((z * v) * v7) * v8)
    ]]></literal>
    <justification jstring="[para(12(a,1),58(a,1,1))].">
      <j1 rule="para" parents="12 58"/>
    </justification>
  </clause>

  <clause id="427">
    <literal><![CDATA[
      (x * ((y * z) * u)) * ((c1 * (c4 * c3)) * ((c2 * c5) * c6)) != (x * (c1 * (c2 * c3))) * (((y * c4) * u) * ((z * c5) * c6))
    ]]></literal>
    <justification jstring="[para(58(a,1),17(a,1,2)),flip(a)].">
      <j1 rule="para" parents="58 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="428">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[resolve(427,a,417,a)].">
      <j1 rule="resolve" parents="427 417"/>
    </justification>
  </clause>

</proof>

</proofs>
