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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 March-2007, March 2007.
Process 20998 was started by mccune on cleo,
Mon Mar 19 17:01:53 2007
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 12.
]]></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 = u @ (v @ w)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="6" type="assumption">
    <literal><![CDATA[
      (A @ B) * C != C * (A @ B)
    ]]></literal>
    <attribute><![CDATA[
      answer(N)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

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

  <clause id="17">
    <literal><![CDATA[
      (x @ y) * z * ((u @ v) @ w) = z * (x @ y)
    ]]></literal>
    <justification jstring="[para(5(a,2),4(a,1,2,2))].">
      <j1 rule="para" parents="5 4"/>
    </justification>
  </clause>

  <clause id="20">
    <literal><![CDATA[
      (A @ B) * C * x != C * (A @ B) * x
    ]]></literal>
    <attribute><![CDATA[
      answer(N)
    ]]></attribute>
    <justification jstring="[ur(2,b,6,a),rewrite(3(6),3(12))].">
      <j1 rule="ur" parents="2 6"/>
      <j2 rule="rewrite" parents="3 3"/>
    </justification>
  </clause>

  <clause id="50">
    <literal><![CDATA[
      (A @ B) * C * ((A @ B) @ (A @ B)) != C * (A @ B)
    ]]></literal>
    <attribute><![CDATA[
      answer(N)
    ]]></attribute>
    <justification jstring="[para(9(a,1),20(a,2,2))].">
      <j1 rule="para" parents="9 20"/>
    </justification>
  </clause>

  <clause id="51">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer(N)
    ]]></attribute>
    <justification jstring="[resolve(50,a,17,a)].">
      <j1 rule="resolve" parents="50 17"/>
    </justification>
  </clause>

</proof>

</proofs>
