<?xml version="1.0" encoding="ISO-8859-1"?>

<!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 June-2006C, June 2006.
Process 13011 was started by mccune on cleo.thornwood,
Mon Jun 19 16:40:06 2006
The command was "/home/mccune/bin/prover9 -f cancel1.in".
]]></heading>

<proof number="1" length="5" max_count="7">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 5.
% Level of proof is 2.
% Maximum clause weight is 7.
% Given clauses 5.
]]></comments>

  <clause id="8">
    <literal><![CDATA[
      x * (x * y) = y
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="11">
    <literal><![CDATA[
      c1 * c3 = c1 * c2
    ]]></literal>
    <justification jstring="[clausify].">
      <j1 rule="clausify"/>
    </justification>
  </clause>

  <clause id="12">
    <literal><![CDATA[
      c3 != c2
    ]]></literal>
    <justification jstring="[clausify].">
      <j1 rule="clausify"/>
    </justification>
  </clause>

  <clause id="28">
    <literal><![CDATA[
      c3 = c2
    ]]></literal>
    <justification jstring="[para(11(a,1),8(a,1,2)),demod(8(5)),flip(a)].">
      <j1 rule="para" parents="11 8"/>
      <j2 rule="demod" parents="8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[resolve(28,a,12,a)].">
      <j1 rule="resolve" parents="28 12"/>
    </justification>
  </clause>

</proof>

</proofs>
