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

<heading><![CDATA[
Prover9 (32) version June-2006C, June 2006.
Process 13133 was started by mccune on cleo.thornwood,
Mon Jun 19 16:41:41 2006
The command was "/home/mccune/bin/prover9 -f cs.in ND.in".
]]></heading>

<proof number="1" length="12" max_count="19">

<comments><![CDATA[
% Proof 1 at 0.07 (+ 0.00) seconds: D.
% Length of proof is 12.
% Level of proof is 4.
% Maximum clause weight is 19.
% Given clauses 71.
]]></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="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 = 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="16">
    <literal><![CDATA[
      x * y != z * x
    ]]></literal>
    <literal><![CDATA[
      z * (z @ x) = y
    ]]></literal>
    <justification jstring="[para(10(a,1),7(a,1)),flip(a)].">
      <j1 rule="para" parents="10 7"/>
      <j2 rule="flip"/>
    </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="26">
    <literal><![CDATA[
      (x @ y) * z * u = z * (x @ y) * u
    ]]></literal>
    <justification jstring="[para(11(a,1),9(a,1,1)),demod(9(3)),flip(a)].">
      <j1 rule="para" parents="11 9"/>
      <j2 rule="demod" parents="9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

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

  <clause id="103">
    <literal><![CDATA[
      C * A * B * (A @ C) * (B @ C) != A * B * C
    ]]></literal>
    <attribute><![CDATA[
      answer(D)
    ]]></attribute>
    <justification jstring="[ur(16,b,30,a),demod(9(12),9(18))].">
      <j1 rule="ur" parents="16 30"/>
      <j2 rule="demod" parents="9 9"/>
    </justification>
  </clause>

  <clause id="394">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer(D)
    ]]></attribute>
    <justification jstring="[para(26(a,2),103(a,1,2,2)),demod(19(13),10(8)),xx(a)].">
      <j1 rule="para" parents="26 103"/>
      <j2 rule="demod" parents="19 10"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

</proofs>
