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<!DOCTYPE proofs SYSTEM "proof3.dtd">

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

<proofs number_of_proofs="1">

<source>w_sk.out</source>

<heading><![CDATA[
Prover9 (32) version June-2006C, June 2006.
Process 13071 was started by mccune on cleo.thornwood,
Mon Jun 19 16:41:08 2006
The command was "/home/mccune/bin/prover9 -f w_sk.in".
]]></heading>

<proof number="1" length="8" max_count="45">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 8.
% Level of proof is 3.
% Maximum clause weight is 45.
% Given clauses 4.
]]></comments>

  <clause id="3">
    <literal><![CDATA[
      a(a(x,f1(x)),f2(x)) != a(a(f1(x),f2(x)),f2(x))
    ]]></literal>
    <justification jstring="[clausify].">
      <j1 rule="clausify"/>
    </justification>
  </clause>

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

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

  <clause id="6">
    <literal><![CDATA[
      a(a(f1(x),f2(x)),f2(x)) != a(a(x,f1(x)),f2(x))
    ]]></literal>
    <justification jstring="[copy(3),flip(a)].">
      <j1 rule="copy" parents="3"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15">
    <literal><![CDATA[
      a(a(a(S,K),x),y) = y
    ]]></literal>
    <justification jstring="[para(5(a,1),4(a,2))].">
      <j1 rule="para" parents="5 4"/>
    </justification>
  </clause>

  <clause id="16">
    <literal><![CDATA[
      a(a(f1(a(a(S,x),y)),f2(a(a(S,x),y))),f2(a(a(S,x),y))) != a(a(a(x,f1(a(a(S,x),y))),a(y,f1(a(a(S,x),y)))),f2(a(a(S,x),y)))
    ]]></literal>
    <justification jstring="[para(4(a,1),6(a,2,1))].">
      <j1 rule="para" parents="4 6"/>
    </justification>
  </clause>

  <clause id="21">
    <literal><![CDATA[
      a(a(a(S,x),a(a(S,K),y)),z) = a(a(x,z),z)
    ]]></literal>
    <justification jstring="[para(15(a,1),4(a,2,2))].">
      <j1 rule="para" parents="15 4"/>
    </justification>
  </clause>

  <clause id="22">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[resolve(21,a,16,a(flip))].">
      <j1 rule="resolve" parents="21 16"/>
    </justification>
  </clause>

</proof>

</proofs>
