<?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>bw.out</source>

<heading><![CDATA[
Prover9 (32) version June-2006C, June 2006.
Process 13069 was started by mccune on cleo.thornwood,
Mon Jun 19 16:41:01 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 6.76 (+ 0.04) 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="3">
    <literal><![CDATA[
      a(x,f(x)) != a(f(x),a(x,f(x)))
    ]]></literal>
    <attribute><![CDATA[
      answer(x)
    ]]></attribute>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="4">
    <literal><![CDATA[
      a(a(a(B,x),y),z) = a(x,a(y,z))
    ]]></literal>
    <attribute><![CDATA[
      label(B)
    ]]></attribute>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="5">
    <literal><![CDATA[
      a(a(W,x),y) = a(a(x,y),y)
    ]]></literal>
    <attribute><![CDATA[
      label(W)
    ]]></attribute>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="6">
    <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="10">
    <literal><![CDATA[
      a(a(W,a(a(B,x),y)),z) = a(a(x,a(y,z)),z)
    ]]></literal>
    <justification jstring="[para(4(a,1),5(a,2,1))].">
      <j1 rule="para" parents="4 5"/>
    </justification>
  </clause>

  <clause id="11">
    <literal><![CDATA[
      a(a(W,W),x) = a(a(x,x),x)
    ]]></literal>
    <justification jstring="[para(5(a,2),5(a,1))].">
      <j1 rule="para" parents="5 5"/>
    </justification>
  </clause>

  <clause id="13">
    <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(4(a,1),6(a,1,2)),demod(4(19))].">
      <j1 rule="para" parents="4 6"/>
      <j2 rule="demod" parents="4"/>
    </justification>
  </clause>

  <clause id="16">
    <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(4(a,1),11(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4 11"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45">
    <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(4(a,1),13(a,1,2,2)),demod(4(29))].">
      <j1 rule="para" parents="4 13"/>
      <j2 rule="demod" parents="4"/>
    </justification>
  </clause>

  <clause id="164">
    <literal><![CDATA[
      a(a(W,a(a(B,a(B,x)),y)),z) = a(x,a(a(y,z),z))
    ]]></literal>
    <justification jstring="[para(10(a,2),4(a,1))].">
      <j1 rule="para" parents="10 4"/>
    </justification>
  </clause>

  <clause id="8044">
    <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(164(a,1),16(a,1)),demod(4(17),16(24))].">
      <j1 rule="para" parents="164 16"/>
      <j2 rule="demod" parents="4 16"/>
    </justification>
  </clause>

  <clause id="8597">
    <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(4(a,1),45(a,1,2,2,2)),demod(4(39))].">
      <j1 rule="para" parents="4 45"/>
      <j2 rule="demod" parents="4"/>
    </justification>
  </clause>

  <clause id="8598">
    <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(8597,a,8044,a)].">
      <j1 rule="resolve" parents="8597 8044"/>
    </justification>
  </clause>

</proof>

</proofs>
