<?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 March-2007, March 2007.
Process 21014 was started by mccune on cleo,
Mon Mar 19 17:02:09 2007
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 0.71 (+ 0.01) seconds: D.
% Length of proof is 27.
% Level of proof is 8.
% Maximum clause weight is 23.
% Given clauses 326.
]]></comments>

  <clause id="1" type="assumption">
    <literal><![CDATA[
      x * y != x * z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

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

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

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

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

  <clause id="6" type="assumption">
    <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="17">
    <literal><![CDATA[
      x * y * z * y * x != y * u
    ]]></literal>
    <literal><![CDATA[
      x * z * x * y = u
    ]]></literal>
    <justification jstring="[para(5(a,1),1(a,1))].">
      <j1 rule="para" parents="5 1"/>
    </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="43">
    <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="65">
    <literal><![CDATA[
      (x @ x) * y = y
    ]]></literal>
    <justification jstring="[hyper(8,a,43,a)].">
      <j1 rule="hyper" parents="8 43"/>
    </justification>
  </clause>

  <clause id="69">
    <literal><![CDATA[
      x * y * y * x = y * x * x * y
    ]]></literal>
    <justification jstring="[para(43(a,1),5(a,1,2)),rewrite(65(6))].">
      <j1 rule="para" parents="43 5"/>
      <j2 rule="rewrite" parents="65"/>
    </justification>
  </clause>

  <clause id="190">
    <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="290">
    <literal><![CDATA[
      x * (y @ x) * x * y = x * y * x
    ]]></literal>
    <justification jstring="[hyper(17,a,14,a)].">
      <j1 rule="hyper" parents="17 14"/>
    </justification>
  </clause>

  <clause id="436">
    <literal><![CDATA[
      (x @ y) * y * x = x * y
    ]]></literal>
    <justification jstring="[hyper(1,a,290,a)].">
      <j1 rule="hyper" parents="1 290"/>
    </justification>
  </clause>

  <clause id="462">
    <literal><![CDATA[
      (x @ y) * y * x * z = x * y * z
    ]]></literal>
    <justification jstring="[para(436(a,1),3(a,1,1)),rewrite(3(2),3(5)),flip(a)].">
      <j1 rule="para" parents="436 3"/>
      <j2 rule="rewrite" parents="3 3"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="469">
    <literal><![CDATA[
      (A @ C) * (B @ C) * C * A * B != A * B * C
    ]]></literal>
    <attribute><![CDATA[
      answer(D)
    ]]></attribute>
    <justification jstring="[para(436(a,1),24(a,1)),rewrite(3(5)),flip(a)].">
      <j1 rule="para" parents="436 24"/>
      <j2 rule="rewrite" parents="3"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="548">
    <literal><![CDATA[
      (A @ C) * (B @ C) * C * A * B * x != A * B * C * x
    ]]></literal>
    <attribute><![CDATA[
      answer(D)
    ]]></attribute>
    <justification jstring="[ur(9,b,469,a),rewrite(3(13),3(12),3(11),3(20),3(19))].">
      <j1 rule="ur" parents="9 469"/>
      <j2 rule="rewrite" parents="3 3 3 3 3"/>
    </justification>
  </clause>

  <clause id="783">
    <literal><![CDATA[
      (A @ C) * B * C * A * A * B != A * B * C * B * A
    ]]></literal>
    <attribute><![CDATA[
      answer(D)
    ]]></attribute>
    <justification jstring="[para(69(a,1),548(a,1,2,2,2)),rewrite(462(16))].">
      <j1 rule="para" parents="69 548"/>
      <j2 rule="rewrite" parents="462"/>
    </justification>
  </clause>

  <clause id="870">
    <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),783(a,2))].">
      <j1 rule="para" parents="5 783"/>
    </justification>
  </clause>

  <clause id="2576">
    <literal><![CDATA[
      (x @ y) * z * y * x * u = z * x * y * u
    ]]></literal>
    <justification jstring="[hyper(190,a,20,a)].">
      <j1 rule="hyper" parents="190 20"/>
    </justification>
  </clause>

  <clause id="2577">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer(D)
    ]]></attribute>
    <justification jstring="[resolve(2576,a,870,a)].">
      <j1 rule="resolve" parents="2576 870"/>
    </justification>
  </clause>

</proof>

</proofs>
