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<!DOCTYPE proofs SYSTEM "proof3.dtd">

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

<proofs number_of_proofs="1">

<source>idempotent.out</source>

<heading><![CDATA[
Prover9 (32) version June-2006C, June 2006.
Process 13013 was started by mccune on cleo.thornwood,
Mon Jun 19 16:40:06 2006
The command was "/home/mccune/bin/prover9 -f idempotent.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 1.
]]></comments>

  <clause id="6">
    <literal><![CDATA[
      (x * e) * x = x
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="7">
    <literal><![CDATA[
      x * (x * y) = y
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="10">
    <literal><![CDATA[
      e * e != e
    ]]></literal>
    <justification jstring="[clausify].">
      <j1 rule="clausify"/>
    </justification>
  </clause>

  <clause id="11">
    <literal><![CDATA[
      e * e = e
    ]]></literal>
    <justification jstring="[para(6(a,1),6(a,1,1)),demod(7(5)),flip(a)].">
      <j1 rule="para" parents="6 6"/>
      <j2 rule="demod" parents="7"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[resolve(11,a,10,a)].">
      <j1 rule="resolve" parents="11 10"/>
    </justification>
  </clause>

</proof>

</proofs>
