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<!DOCTYPE proofs SYSTEM "proof3.dtd">

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

<proofs number_of_proofs="1">

<source>EN-cs.out</source>

<heading><![CDATA[
Prover9 (32) version June-2006C, June 2006.
Process 13129 was started by mccune on cleo.thornwood,
Mon Jun 19 16:41:41 2006
The command was "/home/mccune/bin/prover9 -f cs.in EN.in".
]]></heading>

<proof number="1" length="18" max_count="23">

<comments><![CDATA[
% Proof 1 at 0.11 (+ 0.00) seconds: N.
% Length of proof is 18.
% Level of proof is 6.
% Maximum clause weight is 23.
% Given clauses 101.
]]></comments>

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

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

  <clause id="9">
    <literal><![CDATA[
      (x * y) * z = x * y * z
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="10">
    <literal><![CDATA[
      x * y * (y @ x) = y * x
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

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

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

  <clause id="13">
    <literal><![CDATA[
      x * y * z != x * y * u
    ]]></literal>
    <literal><![CDATA[
      z = u
    ]]></literal>
    <justification jstring="[para(9(a,1),7(a,1)),demod(9(4))].">
      <j1 rule="para" parents="9 7"/>
      <j2 rule="demod" parents="9"/>
    </justification>
  </clause>

  <clause id="14">
    <literal><![CDATA[
      x * y * z != u * z
    ]]></literal>
    <literal><![CDATA[
      x * y = u
    ]]></literal>
    <justification jstring="[para(9(a,1),8(a,1))].">
      <j1 rule="para" parents="9 8"/>
    </justification>
  </clause>

  <clause id="19">
    <literal><![CDATA[
      x * y * (y @ x) * z = y * x * z
    ]]></literal>
    <justification jstring="[para(10(a,1),9(a,1,1)),demod(9(2),9(5)),flip(a)].">
      <j1 rule="para" parents="10 9"/>
      <j2 rule="demod" parents="9 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27">
    <literal><![CDATA[
      x * y * z * u * y * x = y * x * z * u * x * y
    ]]></literal>
    <justification jstring="[para(9(a,1),11(a,1,2,2)),demod(9(8))].">
      <j1 rule="para" parents="9 11"/>
      <j2 rule="demod" parents="9"/>
    </justification>
  </clause>

  <clause id="30">
    <literal><![CDATA[
      x * (A @ B) * C != x * C * (A @ B)
    ]]></literal>
    <attribute><![CDATA[
      answer(N)
    ]]></attribute>
    <justification jstring="[ur(7,b,12,a)].">
      <j1 rule="ur" parents="7 12"/>
    </justification>
  </clause>

  <clause id="36">
    <literal><![CDATA[
      x * y * (A @ B) * C != x * y * C * (A @ B)
    ]]></literal>
    <attribute><![CDATA[
      answer(N)
    ]]></attribute>
    <justification jstring="[ur(7,b,30,a)].">
      <j1 rule="ur" parents="7 30"/>
    </justification>
  </clause>

  <clause id="53">
    <literal><![CDATA[
      x * y * z * y * x != y * x * u
    ]]></literal>
    <literal><![CDATA[
      z * x * y = u
    ]]></literal>
    <justification jstring="[para(11(a,1),13(a,1))].">
      <j1 rule="para" parents="11 13"/>
    </justification>
  </clause>

  <clause id="175">
    <literal><![CDATA[
      B * A * C * (A @ B) != A * B * C
    ]]></literal>
    <attribute><![CDATA[
      answer(N)
    ]]></attribute>
    <justification jstring="[para(19(a,1),36(a,1)),flip(a)].">
      <j1 rule="para" parents="19 36"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="179">
    <literal><![CDATA[
      B * A * C * (A @ B) * x != A * B * C * x
    ]]></literal>
    <attribute><![CDATA[
      answer(N)
    ]]></attribute>
    <justification jstring="[ur(14,b,175,a),demod(9(9),9(8),9(16),9(15))].">
      <j1 rule="ur" parents="14 175"/>
      <j2 rule="demod" parents="9 9 9 9"/>
    </justification>
  </clause>

  <clause id="349">
    <literal><![CDATA[
      A * B * C * (A @ B) * B * A != A * B * C * A * B
    ]]></literal>
    <attribute><![CDATA[
      answer(N)
    ]]></attribute>
    <justification jstring="[para(27(a,1),179(a,1))].">
      <j1 rule="para" parents="27 179"/>
    </justification>
  </clause>

  <clause id="471">
    <literal><![CDATA[
      (x @ y) * y * x = x * y
    ]]></literal>
    <justification jstring="[hyper(53,a,19,a)].">
      <j1 rule="hyper" parents="53 19"/>
    </justification>
  </clause>

  <clause id="474">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer(N)
    ]]></attribute>
    <justification jstring="[back_demod(349),demod(471(10)),xx(a)].">
      <j1 rule="back_demod" parents="349"/>
      <j2 rule="demod" parents="471"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

</proofs>
