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

<heading><![CDATA[
Prover9 (32) version August-2006A, August 2006.
Process 11364 was started by mccune on cleo.thornwood,
Sat Aug 12 21:00:03 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="1">
    <literal><![CDATA[
      x * y != x * z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="2">
    <literal><![CDATA[
      x * y != z * y
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

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

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

  <clause id="5">
    <literal><![CDATA[
      x * y * z * y * x = y * x * z * x * y
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="6">
    <literal><![CDATA[
      (A @ B) * C != C * (A @ B)
    ]]></literal>
    <attribute><![CDATA[
      answer(N)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="7">
    <literal><![CDATA[
      x * y * z != x * y * u
    ]]></literal>
    <literal><![CDATA[
      z = u
    ]]></literal>
    <justification jstring="[para(3(a,1),1(a,1)),rewrite(3(4))].">
      <j1 rule="para" parents="3 1"/>
      <j2 rule="rewrite" parents="3"/>
    </justification>
  </clause>

  <clause id="8">
    <literal><![CDATA[
      x * y * z != u * z
    ]]></literal>
    <literal><![CDATA[
      x * y = u
    ]]></literal>
    <justification jstring="[para(3(a,1),2(a,1))].">
      <j1 rule="para" parents="3 2"/>
    </justification>
  </clause>

  <clause id="13">
    <literal><![CDATA[
      x * y * (y @ x) * z = y * x * z
    ]]></literal>
    <justification jstring="[para(4(a,1),3(a,1,1)),rewrite(3(2),3(5)),flip(a)].">
      <j1 rule="para" parents="4 3"/>
      <j2 rule="rewrite" parents="3 3"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21">
    <literal><![CDATA[
      x * y * z * u * y * x = y * x * z * u * x * y
    ]]></literal>
    <justification jstring="[para(3(a,1),5(a,1,2,2)),rewrite(3(8))].">
      <j1 rule="para" parents="3 5"/>
      <j2 rule="rewrite" parents="3"/>
    </justification>
  </clause>

  <clause id="24">
    <literal><![CDATA[
      x * (A @ B) * C != x * C * (A @ B)
    ]]></literal>
    <attribute><![CDATA[
      answer(N)
    ]]></attribute>
    <justification jstring="[ur(1,b,6,a)].">
      <j1 rule="ur" parents="1 6"/>
    </justification>
  </clause>

  <clause id="30">
    <literal><![CDATA[
      x * y * (A @ B) * C != x * y * C * (A @ B)
    ]]></literal>
    <attribute><![CDATA[
      answer(N)
    ]]></attribute>
    <justification jstring="[ur(1,b,24,a)].">
      <j1 rule="ur" parents="1 24"/>
    </justification>
  </clause>

  <clause id="47">
    <literal><![CDATA[
      x * y * z * y * x != y * x * u
    ]]></literal>
    <literal><![CDATA[
      z * x * y = u
    ]]></literal>
    <justification jstring="[para(5(a,1),7(a,1))].">
      <j1 rule="para" parents="5 7"/>
    </justification>
  </clause>

  <clause id="169">
    <literal><![CDATA[
      B * A * C * (A @ B) != A * B * C
    ]]></literal>
    <attribute><![CDATA[
      answer(N)
    ]]></attribute>
    <justification jstring="[para(13(a,1),30(a,1)),flip(a)].">
      <j1 rule="para" parents="13 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="173">
    <literal><![CDATA[
      B * A * C * (A @ B) * x != A * B * C * x
    ]]></literal>
    <attribute><![CDATA[
      answer(N)
    ]]></attribute>
    <justification jstring="[ur(8,b,169,a),rewrite(3(9),3(8),3(16),3(15))].">
      <j1 rule="ur" parents="8 169"/>
      <j2 rule="rewrite" parents="3 3 3 3"/>
    </justification>
  </clause>

  <clause id="343">
    <literal><![CDATA[
      A * B * C * (A @ B) * B * A != A * B * C * A * B
    ]]></literal>
    <attribute><![CDATA[
      answer(N)
    ]]></attribute>
    <justification jstring="[para(21(a,1),173(a,1))].">
      <j1 rule="para" parents="21 173"/>
    </justification>
  </clause>

  <clause id="465">
    <literal><![CDATA[
      (x @ y) * y * x = x * y
    ]]></literal>
    <justification jstring="[hyper(47,a,13,a)].">
      <j1 rule="hyper" parents="47 13"/>
    </justification>
  </clause>

  <clause id="468">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer(N)
    ]]></attribute>
    <justification jstring="[back_rewrite(343),rewrite(465(10)),xx(a)].">
      <j1 rule="back_rewrite" parents="343"/>
      <j2 rule="rewrite" parents="465"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

</proofs>
