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<!DOCTYPE proofs SYSTEM "proof3.dtd">

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

<proofs number_of_proofs="1">

<source>NA-gt.out</source>

<heading><![CDATA[
Prover9 (32) version June-2006C, June 2006.
Process 13130 was started by mccune on cleo.thornwood,
Mon Jun 19 16:41:41 2006
The command was "/home/mccune/bin/prover9 -f gt.in NA.in".
]]></heading>

<proof number="1" length="12" max_count="13">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds: A.
% Length of proof is 12.
% Level of proof is 3.
% Maximum clause weight is 13.
% Given clauses 5.
]]></comments>

  <clause id="4">
    <literal><![CDATA[
      x @ y = x ' * y ' * x * y
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

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

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

  <clause id="9">
    <literal><![CDATA[
      x ' * x = e
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="10">
    <literal><![CDATA[
      x ' * y ' * x * y = x @ y
    ]]></literal>
    <justification jstring="[copy(4),flip(a)].">
      <j1 rule="copy" parents="4"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11">
    <literal><![CDATA[
      (x @ y) * z = z * (x @ y)
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="12">
    <literal><![CDATA[
      (A @ B) @ C != D @ (F @ G)
    ]]></literal>
    <attribute><![CDATA[
      answer(A)
    ]]></attribute>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="13">
    <literal><![CDATA[
      x ' * x * y = y
    ]]></literal>
    <justification jstring="[para(9(a,1),7(a,1,1)),demod(8(2)),flip(a)].">
      <j1 rule="para" parents="9 7"/>
      <j2 rule="demod" parents="8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22">
    <literal><![CDATA[
      (x @ y) * (x @ y) ' = e
    ]]></literal>
    <justification jstring="[para(11(a,2),9(a,1))].">
      <j1 rule="para" parents="11 9"/>
    </justification>
  </clause>

  <clause id="23">
    <literal><![CDATA[
      (x @ y) @ z = e
    ]]></literal>
    <justification jstring="[para(11(a,1),10(a,1,2,2)),demod(13(6),11(4,R),22(4)),flip(a)].">
      <j1 rule="para" parents="11 10"/>
      <j2 rule="demod" parents="13 11 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24">
    <literal><![CDATA[
      x @ (y @ z) = e
    ]]></literal>
    <justification jstring="[para(11(a,2),10(a,1,2,2)),demod(13(6),9(2)),flip(a)].">
      <j1 rule="para" parents="11 10"/>
      <j2 rule="demod" parents="13 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer(A)
    ]]></attribute>
    <justification jstring="[back_demod(12),demod(23(5),24(6)),xx(a)].">
      <j1 rule="back_demod" parents="12"/>
      <j2 rule="demod" parents="23 24"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

</proofs>
