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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 November-2006, November 2006.
Process 3318 was started by mccune on cleo.thornwood,
Wed Nov 22 11:22:01 2006
The command was "/home/mccune/bin/prover9 -f idempotent.in".
]]></heading>

<proof number="1" length="6" max_count="7">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 6.
% Level of proof is 2.
% Maximum clause weight is 7.
% Given clauses 1.
]]></comments>

  <clause id="1" type="goal">
    <literal><![CDATA[
      e * e = e
    ]]></literal>
    <attribute><![CDATA[
      label(goal)
    ]]></attribute>
    <justification jstring="[goal].">
      <j1 rule="goal"/>
    </justification>
  </clause>

  <clause id="2" type="assumption">
    <literal><![CDATA[
      (x * e) * x = x
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

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

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

  <clause id="7">
    <literal><![CDATA[
      e * e = e
    ]]></literal>
    <justification jstring="[para(2(a,1),2(a,1,1)),rewrite(3(5)),flip(a)].">
      <j1 rule="para" parents="2 2"/>
      <j2 rule="rewrite" parents="3"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[resolve(7,a,6,a)].">
      <j1 rule="resolve" parents="7 6"/>
    </justification>
  </clause>

</proof>

</proofs>
