<?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 June-2006C, June 2006.
Process 13127 was started by mccune on cleo.thornwood,
Mon Jun 19 16:41:40 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="6">
    <literal><![CDATA[
      (A @ C) * (B @ C) != A * B @ C
    ]]></literal>
    <attribute><![CDATA[
      answer(D)
    ]]></attribute>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <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 != (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="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="15">
    <literal><![CDATA[
      x * (x @ x) = x
    ]]></literal>
    <justification jstring="[hyper(7,a,10,a)].">
      <j1 rule="hyper" parents="7 10"/>
    </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="25">
    <literal><![CDATA[
      x * y * z * y * x * u = y * x * z * x * y * u
    ]]></literal>
    <justification jstring="[para(11(a,1),9(a,1,1)),demod(9(5),9(4),9(3),9(2),9(9),9(8),9(7))].">
      <j1 rule="para" parents="11 9"/>
      <j2 rule="demod" parents="9 9 9 9 9 9 9"/>
    </justification>
  </clause>

  <clause id="29">
    <literal><![CDATA[
      (A * B @ C) * x != (A @ C) * (B @ C) * x
    ]]></literal>
    <attribute><![CDATA[
      answer(D)
    ]]></attribute>
    <justification jstring="[ur(8,b,12,a),demod(9(14))].">
      <j1 rule="ur" parents="8 12"/>
      <j2 rule="demod" parents="9"/>
    </justification>
  </clause>

  <clause id="39">
    <literal><![CDATA[
      x * (x @ x) * y = x * y
    ]]></literal>
    <justification jstring="[para(15(a,1),9(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52">
    <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="59">
    <literal><![CDATA[
      x * y * z * u != v * u
    ]]></literal>
    <literal><![CDATA[
      x * y * z = v
    ]]></literal>
    <justification jstring="[para(9(a,1),14(a,1,2))].">
      <j1 rule="para" parents="9 14"/>
    </justification>
  </clause>

  <clause id="69">
    <literal><![CDATA[
      (x @ x) * y = y
    ]]></literal>
    <justification jstring="[hyper(13,a,39,a)].">
      <j1 rule="hyper" parents="13 39"/>
    </justification>
  </clause>

  <clause id="73">
    <literal><![CDATA[
      x * y * y * x = y * x * x * y
    ]]></literal>
    <justification jstring="[para(39(a,1),11(a,1,2)),demod(69(6))].">
      <j1 rule="para" parents="39 11"/>
      <j2 rule="demod" parents="69"/>
    </justification>
  </clause>

  <clause id="152">
    <literal><![CDATA[
      x * y * z != y * x * u
    ]]></literal>
    <literal><![CDATA[
      (x @ y) * z = u
    ]]></literal>
    <justification jstring="[para(19(a,1),13(a,1))].">
      <j1 rule="para" parents="19 13"/>
    </justification>
  </clause>

  <clause id="400">
    <literal><![CDATA[
      (x @ y) * y * x = x * y
    ]]></literal>
    <justification jstring="[hyper(52,a,19,a)].">
      <j1 rule="hyper" parents="52 19"/>
    </justification>
  </clause>

  <clause id="420">
    <literal><![CDATA[
      (x @ y) * y * x * z = x * y * z
    ]]></literal>
    <justification jstring="[para(400(a,1),9(a,1,1)),demod(9(2),9(5)),flip(a)].">
      <j1 rule="para" parents="400 9"/>
      <j2 rule="demod" parents="9 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="423">
    <literal><![CDATA[
      (A @ C) * (B @ C) * C * A * B != A * B * C
    ]]></literal>
    <attribute><![CDATA[
      answer(D)
    ]]></attribute>
    <justification jstring="[para(400(a,1),29(a,1)),demod(9(5)),flip(a)].">
      <j1 rule="para" parents="400 29"/>
      <j2 rule="demod" parents="9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="503">
    <literal><![CDATA[
      (A @ C) * (B @ C) * C * A * B * x != A * B * C * x
    ]]></literal>
    <attribute><![CDATA[
      answer(D)
    ]]></attribute>
    <justification jstring="[ur(59,b,423,a),demod(9(12),9(11),9(20),9(19))].">
      <j1 rule="ur" parents="59 423"/>
      <j2 rule="demod" parents="9 9 9 9"/>
    </justification>
  </clause>

  <clause id="722">
    <literal><![CDATA[
      (A @ C) * B * C * A * A * B != A * B * C * B * A
    ]]></literal>
    <attribute><![CDATA[
      answer(D)
    ]]></attribute>
    <justification jstring="[para(73(a,1),503(a,1,2,2,2)),demod(420(16))].">
      <j1 rule="para" parents="73 503"/>
      <j2 rule="demod" parents="420"/>
    </justification>
  </clause>

  <clause id="921">
    <literal><![CDATA[
      (A @ C) * B * C * A * A * B != B * A * C * A * B
    ]]></literal>
    <attribute><![CDATA[
      answer(D)
    ]]></attribute>
    <justification jstring="[para(11(a,1),722(a,2))].">
      <j1 rule="para" parents="11 722"/>
    </justification>
  </clause>

  <clause id="1442">
    <literal><![CDATA[
      (x @ y) * z * y * x * u = z * x * y * u
    ]]></literal>
    <justification jstring="[hyper(152,a,25,a)].">
      <j1 rule="hyper" parents="152 25"/>
    </justification>
  </clause>

  <clause id="1443">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer(D)
    ]]></attribute>
    <justification jstring="[resolve(1442,a,921,a)].">
      <j1 rule="resolve" parents="1442 921"/>
    </justification>
  </clause>

</proof>

</proofs>
