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<!DOCTYPE proofs SYSTEM "proof3.dtd">

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

<proofs number_of_proofs="1">

<source>bw.out</source>

<heading><![CDATA[
Prover9 (32) version August-2006A, August 2006.
Process 10833 was started by mccune on cleo.thornwood,
Sat Aug 12 20:58:51 2006
The command was "/home/mccune/bin/prover9 -f bw.in".
]]></heading>

<proof number="1" length="13" max_count="60">

<comments><![CDATA[
% Proof 1 at 7.32 (+ 0.03) seconds: a(a(B,a(W,W)),a(a(B,a(B,W)),a(a(B,B),B))).
% Length of proof is 13.
% Level of proof is 5.
% Maximum clause weight is 60.
% Given clauses 96.
]]></comments>

  <clause id="1">
    <literal><![CDATA[
      a(a(a(B,x),y),z) = a(x,a(y,z))
    ]]></literal>
    <attribute><![CDATA[
      label(B)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="2">
    <literal><![CDATA[
      a(a(W,x),y) = a(a(x,y),y)
    ]]></literal>
    <attribute><![CDATA[
      label(W)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="3">
    <literal><![CDATA[
      a(x,f(x)) != a(f(x),a(x,f(x)))
    ]]></literal>
    <attribute><![CDATA[
      answer(x)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="4">
    <literal><![CDATA[
      a(f(x),a(x,f(x))) != a(x,f(x))
    ]]></literal>
    <attribute><![CDATA[
      answer(x)
    ]]></attribute>
    <justification jstring="[copy(3),flip(a)].">
      <j1 rule="copy" parents="3"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8">
    <literal><![CDATA[
      a(a(W,a(a(B,x),y)),z) = a(a(x,a(y,z)),z)
    ]]></literal>
    <justification jstring="[para(1(a,1),2(a,2,1))].">
      <j1 rule="para" parents="1 2"/>
    </justification>
  </clause>

  <clause id="9">
    <literal><![CDATA[
      a(a(W,W),x) = a(a(x,x),x)
    ]]></literal>
    <justification jstring="[para(2(a,2),2(a,1))].">
      <j1 rule="para" parents="2 2"/>
    </justification>
  </clause>

  <clause id="11">
    <literal><![CDATA[
      a(f(a(a(B,x),y)),a(x,a(y,f(a(a(B,x),y))))) != a(x,a(y,f(a(a(B,x),y))))
    ]]></literal>
    <attribute><![CDATA[
      answer(a(a(B,x),y))
    ]]></attribute>
    <justification jstring="[para(1(a,1),4(a,1,2)),rewrite(1(19))].">
      <j1 rule="para" parents="1 4"/>
      <j2 rule="rewrite" parents="1"/>
    </justification>
  </clause>

  <clause id="14">
    <literal><![CDATA[
      a(a(x,a(y,a(a(B,x),y))),a(a(B,x),y)) = a(a(W,W),a(a(B,x),y))
    ]]></literal>
    <justification jstring="[para(1(a,1),9(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43">
    <literal><![CDATA[
      a(f(a(a(B,x),a(a(B,y),z))),a(x,a(y,a(z,f(a(a(B,x),a(a(B,y),z))))))) != a(x,a(y,a(z,f(a(a(B,x),a(a(B,y),z))))))
    ]]></literal>
    <attribute><![CDATA[
      answer(a(a(B,x),a(a(B,y),z)))
    ]]></attribute>
    <justification jstring="[para(1(a,1),11(a,1,2,2)),rewrite(1(29))].">
      <j1 rule="para" parents="1 11"/>
      <j2 rule="rewrite" parents="1"/>
    </justification>
  </clause>

  <clause id="162">
    <literal><![CDATA[
      a(a(W,a(a(B,a(B,x)),y)),z) = a(x,a(a(y,z),z))
    ]]></literal>
    <justification jstring="[para(8(a,2),1(a,1))].">
      <j1 rule="para" parents="8 1"/>
    </justification>
  </clause>

  <clause id="8042">
    <literal><![CDATA[
      a(x,a(a(W,W),a(a(B,W),a(B,a(B,x))))) = a(a(W,W),a(a(B,W),a(B,a(B,x))))
    ]]></literal>
    <justification jstring="[para(162(a,1),14(a,1)),rewrite(1(17),14(24))].">
      <j1 rule="para" parents="162 14"/>
      <j2 rule="rewrite" parents="1 14"/>
    </justification>
  </clause>

  <clause id="8595">
    <literal><![CDATA[
      a(f(a(a(B,x),a(a(B,y),a(a(B,z),u)))),a(x,a(y,a(z,a(u,f(a(a(B,x),a(a(B,y),a(a(B,z),u))))))))) != a(x,a(y,a(z,a(u,f(a(a(B,x),a(a(B,y),a(a(B,z),u))))))))
    ]]></literal>
    <attribute><![CDATA[
      answer(a(a(B,x),a(a(B,y),a(a(B,z),u))))
    ]]></attribute>
    <justification jstring="[para(1(a,1),43(a,1,2,2,2)),rewrite(1(39))].">
      <j1 rule="para" parents="1 43"/>
      <j2 rule="rewrite" parents="1"/>
    </justification>
  </clause>

  <clause id="8596">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer(a(a(B,a(W,W)),a(a(B,a(B,W)),a(a(B,B),B))))
    ]]></attribute>
    <justification jstring="[resolve(8595,a,8042,a)].">
      <j1 rule="resolve" parents="8595 8042"/>
    </justification>
  </clause>

</proof>

</proofs>
