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<!DOCTYPE proofs SYSTEM "proof3.dtd">

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

<proofs number_of_proofs="1">

<source>cancel1.out</source>

<heading><![CDATA[
Prover9 (32) version August-2006A, August 2006.
Process 10666 was started by mccune on cleo.thornwood,
Sat Aug 12 20:57:46 2006
The command was "/home/mccune/bin/prover9 -f cancel1.in".
]]></heading>

<proof number="1" length="6" max_count="26">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 6.
% Level of proof is 3.
% Maximum clause weight is 7.
% Given clauses 5.
]]></comments>

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

  <clause id="3">
    <literal><![CDATA[
      x * (x * y) = y
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="6">
    <literal><![CDATA[
      c1 * c3 = c1 * c2
    ]]></literal>
    <justification jstring="[deny(1)].">
      <j1 rule="deny" parents="1"/>
    </justification>
  </clause>

  <clause id="7">
    <literal><![CDATA[
      c3 != c2
    ]]></literal>
    <justification jstring="[deny(1)].">
      <j1 rule="deny" parents="1"/>
    </justification>
  </clause>

  <clause id="23">
    <literal><![CDATA[
      c3 = c2
    ]]></literal>
    <justification jstring="[para(6(a,1),3(a,1,2)),rewrite(3(5)),flip(a)].">
      <j1 rule="para" parents="6 3"/>
      <j2 rule="rewrite" parents="3"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[resolve(23,a,7,a)].">
      <j1 rule="resolve" parents="23 7"/>
    </justification>
  </clause>

</proof>

</proofs>
