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<!DOCTYPE proofs SYSTEM "proof3.dtd">

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

<proofs number_of_proofs="1">

<source>RBA-2.out</source>

<heading><![CDATA[
Prover9 (32) version August-2006A, August 2006.
Process 10828 was started by mccune on cleo.thornwood,
Sat Aug 12 20:58:51 2006
The command was "/home/mccune/bin/prover9 -f RBA-2.in".
]]></heading>

<proof number="1" length="29" max_count="23">

<comments><![CDATA[
% Proof 1 at 0.16 (+ 0.00) seconds: Huntington.
% Length of proof is 29.
% Level of proof is 14.
% Maximum clause weight is 23.
% Given clauses 48.
]]></comments>

  <clause id="1">
    <literal><![CDATA[
      (x + y')' + (x' + y')' = y
    ]]></literal>
    <attribute><![CDATA[
      answer(Huntington)
    ]]></attribute>
    <justification jstring="[goal].">
      <j1 rule="goal"/>
    </justification>
  </clause>

  <clause id="2">
    <literal><![CDATA[
      x + y = y + x
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="3">
    <literal><![CDATA[
      (x + y) + z = x + (y + z)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="4">
    <literal><![CDATA[
      ((x + y)' + (x + y')')' = x
    ]]></literal>
    <attribute><![CDATA[
      label(Robbins)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="5">
    <literal><![CDATA[
      c + c = c
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="6">
    <literal><![CDATA[
      (c1 + c2')' + (c1' + c2')' != c2
    ]]></literal>
    <attribute><![CDATA[
      answer(Huntington)
    ]]></attribute>
    <justification jstring="[deny(1)].">
      <j1 rule="deny" parents="1"/>
    </justification>
  </clause>

  <clause id="8">
    <literal><![CDATA[
      x + (y + z) = y + (x + z)
    ]]></literal>
    <justification jstring="[para(2(a,1),3(a,1,1)),rewrite(3(2))].">
      <j1 rule="para" parents="2 3"/>
      <j2 rule="rewrite" parents="3"/>
    </justification>
  </clause>

  <clause id="9">
    <literal><![CDATA[
      ((x + y)' + (y + x')')' = y
    ]]></literal>
    <justification jstring="[para(2(a,1),4(a,1,1,1,1))].">
      <j1 rule="para" parents="2 4"/>
    </justification>
  </clause>

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

  <clause id="13">
    <literal><![CDATA[
      ((x + y)' + (x + ((y + z)' + (y + z')'))')' = x
    ]]></literal>
    <justification jstring="[para(4(a,1),4(a,1,1,2,1,2)),rewrite(2(11))].">
      <j1 rule="para" parents="4 4"/>
      <j2 rule="rewrite" parents="2"/>
    </justification>
  </clause>

  <clause id="15">
    <literal><![CDATA[
      c + (c + x) = c + x
    ]]></literal>
    <justification jstring="[para(5(a,1),3(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5 3"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17">
    <literal><![CDATA[
      (c' + (c + c')')' = c
    ]]></literal>
    <justification jstring="[para(5(a,1),4(a,1,1,1,1))].">
      <j1 rule="para" parents="5 4"/>
    </justification>
  </clause>

  <clause id="24">
    <literal><![CDATA[
      ((x + c)' + (x + (c' + (c + c')'))')' = x
    ]]></literal>
    <justification jstring="[para(17(a,1),4(a,1,1,2,1,2)),rewrite(2(14))].">
      <j1 rule="para" parents="17 4"/>
      <j2 rule="rewrite" parents="2"/>
    </justification>
  </clause>

  <clause id="25">
    <literal><![CDATA[
      (c + (c + (c' + c'))')' = c'
    ]]></literal>
    <justification jstring="[para(17(a,1),4(a,1,1,2)),rewrite(8(7),2(10))].">
      <j1 rule="para" parents="17 4"/>
      <j2 rule="rewrite" parents="8 2"/>
    </justification>
  </clause>

  <clause id="26">
    <literal><![CDATA[
      ((x + y)' + (x' + y)')' = y
    ]]></literal>
    <justification jstring="[para(2(a,1),9(a,1,1,2,1))].">
      <j1 rule="para" parents="2 9"/>
    </justification>
  </clause>

  <clause id="36">
    <literal><![CDATA[
      ((c + x)' + (c + (x + c'))')' = c + x
    ]]></literal>
    <justification jstring="[para(15(a,1),9(a,1,1,1,1)),rewrite(3(8))].">
      <j1 rule="para" parents="15 9"/>
      <j2 rule="rewrite" parents="3"/>
    </justification>
  </clause>

  <clause id="74">
    <literal><![CDATA[
      ((c + x)' + (c' + ((c + c')' + x))')' = x
    ]]></literal>
    <justification jstring="[para(17(a,1),26(a,1,1,2,1,1)),rewrite(3(9),2(14))].">
      <j1 rule="para" parents="17 26"/>
      <j2 rule="rewrite" parents="3 2"/>
    </justification>
  </clause>

  <clause id="145">
    <literal><![CDATA[
      (c' + (c + (c' + c'))')' = c
    ]]></literal>
    <justification jstring="[para(25(a,1),4(a,1,1,2)),rewrite(15(9),2(11))].">
      <j1 rule="para" parents="25 4"/>
      <j2 rule="rewrite" parents="15 2"/>
    </justification>
  </clause>

  <clause id="146">
    <literal><![CDATA[
      (c + (c' + c'))' = (c + c')'
    ]]></literal>
    <justification jstring="[para(25(a,1),9(a,1,1,1)),rewrite(2(13),145(14),2(4)),flip(a)].">
      <j1 rule="para" parents="25 9"/>
      <j2 rule="rewrite" parents="2 145 2"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="155">
    <literal><![CDATA[
      (c + (c + c')')' = c'
    ]]></literal>
    <justification jstring="[back_rewrite(25),rewrite(146(9))].">
      <j1 rule="back_rewrite" parents="25"/>
      <j2 rule="rewrite" parents="146"/>
    </justification>
  </clause>

  <clause id="534">
    <literal><![CDATA[
      (c' + (c + (c' + (c + c')'))')' = c + (c + c')'
    ]]></literal>
    <justification jstring="[para(155(a,1),36(a,1,1,1)),rewrite(2(11))].">
      <j1 rule="para" parents="155 36"/>
      <j2 rule="rewrite" parents="2"/>
    </justification>
  </clause>

  <clause id="647">
    <literal><![CDATA[
      c + (c + c')' = c
    ]]></literal>
    <justification jstring="[para(5(a,1),24(a,1,1,1,1)),rewrite(534(15))].">
      <j1 rule="para" parents="5 24"/>
      <j2 rule="rewrite" parents="534"/>
    </justification>
  </clause>

  <clause id="668">
    <literal><![CDATA[
      c + ((c + c')' + x) = c + x
    ]]></literal>
    <justification jstring="[para(647(a,1),3(a,1,1)),flip(a)].">
      <j1 rule="para" parents="647 3"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="677">
    <literal><![CDATA[
      (c + c')' + x = x
    ]]></literal>
    <justification jstring="[para(668(a,1),9(a,1,1,1,1)),rewrite(2(12),74(15)),flip(a)].">
      <j1 rule="para" parents="668 9"/>
      <j2 rule="rewrite" parents="2 74"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="704">
    <literal><![CDATA[
      (c + c')' = (x + x')'
    ]]></literal>
    <justification jstring="[para(677(a,1),13(a,1,1,1,1)),rewrite(677(13),4(8),2(2)),flip(a)].">
      <j1 rule="para" parents="677 13"/>
      <j2 rule="rewrite" parents="677 4 2"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="866">
    <literal><![CDATA[
      (x + x'')'' = x
    ]]></literal>
    <justification jstring="[para(704(a,2),4(a,1,1,1)),rewrite(677(10))].">
      <j1 rule="para" parents="704 4"/>
      <j2 rule="rewrite" parents="677"/>
    </justification>
  </clause>

  <clause id="874">
    <literal><![CDATA[
      x'' = x
    ]]></literal>
    <justification jstring="[para(704(a,2),10(a,1,1,2)),rewrite(2(3),2(10),677(10),866(5)),flip(a)].">
      <j1 rule="para" parents="704 10"/>
      <j2 rule="rewrite" parents="2 2 677 866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1035">
    <literal><![CDATA[
      (x + y)' + (x' + y)' = y'
    ]]></literal>
    <justification jstring="[para(26(a,1),874(a,1,1)),flip(a)].">
      <j1 rule="para" parents="26 874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1050">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer(Huntington)
    ]]></attribute>
    <justification jstring="[back_rewrite(6),rewrite(1035(12),874(3)),xx(a)].">
      <j1 rule="back_rewrite" parents="6"/>
      <j2 rule="rewrite" parents="1035 874"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

</proofs>
