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

<heading><![CDATA[
Prover9 (32) version August-2006A, August 2006.
Process 11362 was started by mccune on cleo.thornwood,
Sat Aug 12 21:00:03 2006
The command was "/home/mccune/bin/prover9 -f cs.in ED.in".
]]></heading>

<proof number="1" length="27" max_count="23">

<comments><![CDATA[
% Proof 1 at 0.36 (+ 0.01) seconds: D.
% Length of proof is 27.
% Level of proof is 8.
% Maximum clause weight is 23.
% Given clauses 201.
]]></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 @ C) * (B @ C) != A * B @ C
    ]]></literal>
    <attribute><![CDATA[
      answer(D)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="7">
    <literal><![CDATA[
      A * B @ C != (A @ C) * (B @ C)
    ]]></literal>
    <attribute><![CDATA[
      answer(D)
    ]]></attribute>
    <justification jstring="[copy(6),flip(a)].">
      <j1 rule="copy" parents="6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8">
    <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="9">
    <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="10">
    <literal><![CDATA[
      x * (x @ x) = x
    ]]></literal>
    <justification jstring="[hyper(1,a,4,a)].">
      <j1 rule="hyper" parents="1 4"/>
    </justification>
  </clause>

  <clause id="14">
    <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="20">
    <literal><![CDATA[
      x * y * z * y * x * u = y * x * z * x * y * u
    ]]></literal>
    <justification jstring="[para(5(a,1),3(a,1,1)),rewrite(3(5),3(4),3(3),3(2),3(9),3(8),3(7))].">
      <j1 rule="para" parents="5 3"/>
      <j2 rule="rewrite" parents="3 3 3 3 3 3 3"/>
    </justification>
  </clause>

  <clause id="24">
    <literal><![CDATA[
      (A * B @ C) * x != (A @ C) * (B @ C) * x
    ]]></literal>
    <attribute><![CDATA[
      answer(D)
    ]]></attribute>
    <justification jstring="[ur(2,b,7,a),rewrite(3(14))].">
      <j1 rule="ur" parents="2 7"/>
      <j2 rule="rewrite" parents="3"/>
    </justification>
  </clause>

  <clause id="34">
    <literal><![CDATA[
      x * (x @ x) * y = x * y
    ]]></literal>
    <justification jstring="[para(10(a,1),3(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 3"/>
      <j2 rule="flip"/>
    </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),8(a,1))].">
      <j1 rule="para" parents="5 8"/>
    </justification>
  </clause>

  <clause id="54">
    <literal><![CDATA[
      x * y * z * u != v * u
    ]]></literal>
    <literal><![CDATA[
      x * y * z = v
    ]]></literal>
    <justification jstring="[para(3(a,1),9(a,1,2))].">
      <j1 rule="para" parents="3 9"/>
    </justification>
  </clause>

  <clause id="64">
    <literal><![CDATA[
      (x @ x) * y = y
    ]]></literal>
    <justification jstring="[hyper(8,a,34,a)].">
      <j1 rule="hyper" parents="8 34"/>
    </justification>
  </clause>

  <clause id="68">
    <literal><![CDATA[
      x * y * y * x = y * x * x * y
    ]]></literal>
    <justification jstring="[para(34(a,1),5(a,1,2)),rewrite(64(6))].">
      <j1 rule="para" parents="34 5"/>
      <j2 rule="rewrite" parents="64"/>
    </justification>
  </clause>

  <clause id="147">
    <literal><![CDATA[
      x * y * z != y * x * u
    ]]></literal>
    <literal><![CDATA[
      (x @ y) * z = u
    ]]></literal>
    <justification jstring="[para(14(a,1),8(a,1))].">
      <j1 rule="para" parents="14 8"/>
    </justification>
  </clause>

  <clause id="395">
    <literal><![CDATA[
      (x @ y) * y * x = x * y
    ]]></literal>
    <justification jstring="[hyper(47,a,14,a)].">
      <j1 rule="hyper" parents="47 14"/>
    </justification>
  </clause>

  <clause id="415">
    <literal><![CDATA[
      (x @ y) * y * x * z = x * y * z
    ]]></literal>
    <justification jstring="[para(395(a,1),3(a,1,1)),rewrite(3(2),3(5)),flip(a)].">
      <j1 rule="para" parents="395 3"/>
      <j2 rule="rewrite" parents="3 3"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="418">
    <literal><![CDATA[
      (A @ C) * (B @ C) * C * A * B != A * B * C
    ]]></literal>
    <attribute><![CDATA[
      answer(D)
    ]]></attribute>
    <justification jstring="[para(395(a,1),24(a,1)),rewrite(3(5)),flip(a)].">
      <j1 rule="para" parents="395 24"/>
      <j2 rule="rewrite" parents="3"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="498">
    <literal><![CDATA[
      (A @ C) * (B @ C) * C * A * B * x != A * B * C * x
    ]]></literal>
    <attribute><![CDATA[
      answer(D)
    ]]></attribute>
    <justification jstring="[ur(54,b,418,a),rewrite(3(12),3(11),3(20),3(19))].">
      <j1 rule="ur" parents="54 418"/>
      <j2 rule="rewrite" parents="3 3 3 3"/>
    </justification>
  </clause>

  <clause id="717">
    <literal><![CDATA[
      (A @ C) * B * C * A * A * B != A * B * C * B * A
    ]]></literal>
    <attribute><![CDATA[
      answer(D)
    ]]></attribute>
    <justification jstring="[para(68(a,1),498(a,1,2,2,2)),rewrite(415(16))].">
      <j1 rule="para" parents="68 498"/>
      <j2 rule="rewrite" parents="415"/>
    </justification>
  </clause>

  <clause id="916">
    <literal><![CDATA[
      (A @ C) * B * C * A * A * B != B * A * C * A * B
    ]]></literal>
    <attribute><![CDATA[
      answer(D)
    ]]></attribute>
    <justification jstring="[para(5(a,1),717(a,2))].">
      <j1 rule="para" parents="5 717"/>
    </justification>
  </clause>

  <clause id="1437">
    <literal><![CDATA[
      (x @ y) * z * y * x * u = z * x * y * u
    ]]></literal>
    <justification jstring="[hyper(147,a,20,a)].">
      <j1 rule="hyper" parents="147 20"/>
    </justification>
  </clause>

  <clause id="1438">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer(D)
    ]]></attribute>
    <justification jstring="[resolve(1437,a,916,a)].">
      <j1 rule="resolve" parents="1437 916"/>
    </justification>
  </clause>

</proof>

</proofs>
