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<!DOCTYPE proofs SYSTEM "proof3.dtd">

<?xml-stylesheet type="text/xsl" href="proof3.xsl"?>

<proofs number_of_proofs="1">

<source>AN-cs.out</source>

<heading><![CDATA[
Prover9 (32) version June-2006C, June 2006.
Process 13116 was started by mccune on cleo.thornwood,
Mon Jun 19 16:41:29 2006
The command was "/home/mccune/bin/prover9 -f cs.in AN.in".
]]></heading>

<proof number="1" length="11" max_count="19">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds: N.
% Length of proof is 11.
% Level of proof is 3.
% Maximum clause weight is 19.
% Given clauses 9.
]]></comments>

  <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 = u @ (v @ w)
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="12">
    <literal><![CDATA[
      (A @ B) * C != C * (A @ B)
    ]]></literal>
    <attribute><![CDATA[
      answer(N)
    ]]></attribute>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </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="23">
    <literal><![CDATA[
      (x @ y) * z * ((u @ v) @ w) = z * (x @ y)
    ]]></literal>
    <justification jstring="[para(11(a,2),10(a,1,2,2))].">
      <j1 rule="para" parents="11 10"/>
    </justification>
  </clause>

  <clause id="26">
    <literal><![CDATA[
      (A @ B) * C * x != C * (A @ B) * x
    ]]></literal>
    <attribute><![CDATA[
      answer(N)
    ]]></attribute>
    <justification jstring="[ur(8,b,12,a),demod(9(6),9(12))].">
      <j1 rule="ur" parents="8 12"/>
      <j2 rule="demod" parents="9 9"/>
    </justification>
  </clause>

  <clause id="42">
    <literal><![CDATA[
      (A @ B) * C * ((A @ B) @ (A @ B)) != C * (A @ B)
    ]]></literal>
    <attribute><![CDATA[
      answer(N)
    ]]></attribute>
    <justification jstring="[para(15(a,1),26(a,2,2))].">
      <j1 rule="para" parents="15 26"/>
    </justification>
  </clause>

  <clause id="43">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer(N)
    ]]></attribute>
    <justification jstring="[resolve(42,a,23,a)].">
      <j1 rule="resolve" parents="42 23"/>
    </justification>
  </clause>

</proof>

</proofs>
