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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 June-2006C, June 2006.
Process 13068 was started by mccune on cleo.thornwood,
Mon Jun 19 16:41:01 2006
The command was "/home/mccune/bin/prover9 -f RBA-2.in".
]]></heading>

<proof number="1" length="29" max_count="21">

<comments><![CDATA[
% Proof 1 at 0.14 (+ 0.00) seconds: Huntington.
% Length of proof is 29.
% Level of proof is 13.
% Maximum clause weight is 21.
% Given clauses 44.
]]></comments>

  <clause id="6">
    <literal><![CDATA[
      x + y = y + x
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="7">
    <literal><![CDATA[
      (x + y) + z = x + (y + z)
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="8">
    <literal><![CDATA[
      ((x + y) ' + (x + y ') ') ' = x
    ]]></literal>
    <attribute><![CDATA[
      label(Robbins)
    ]]></attribute>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="9">
    <literal><![CDATA[
      c + c = c
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="10">
    <literal><![CDATA[
      (c1 + c2 ') ' + (c1 ' + c2 ') ' != c2
    ]]></literal>
    <attribute><![CDATA[
      answer(Huntington)
    ]]></attribute>
    <justification jstring="[clausify].">
      <j1 rule="clausify"/>
    </justification>
  </clause>

  <clause id="11">
    <literal><![CDATA[
      x + (y + z) = y + (x + z)
    ]]></literal>
    <justification jstring="[para(6(a,1),7(a,1,1)),demod(7(2))].">
      <j1 rule="para" parents="6 7"/>
      <j2 rule="demod" parents="7"/>
    </justification>
  </clause>

  <clause id="12">
    <literal><![CDATA[
      ((x + y) ' + (y + x ') ') ' = y
    ]]></literal>
    <justification jstring="[para(6(a,1),8(a,1,1,1,1))].">
      <j1 rule="para" parents="6 8"/>
    </justification>
  </clause>

  <clause id="13">
    <literal><![CDATA[
      ((x + y) ' + (y ' + x) ') ' = x
    ]]></literal>
    <justification jstring="[para(6(a,1),8(a,1,1,2,1))].">
      <j1 rule="para" parents="6 8"/>
    </justification>
  </clause>

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

  <clause id="16">
    <literal><![CDATA[
      ((x + y) ' + (x + ((y + z) ' + (y + z ') ')) ') ' = x
    ]]></literal>
    <justification jstring="[para(8(a,1),8(a,1,1,2,1,2)),demod(6(11))].">
      <j1 rule="para" parents="8 8"/>
      <j2 rule="demod" parents="6"/>
    </justification>
  </clause>

  <clause id="18">
    <literal><![CDATA[
      c + (c + x) = c + x
    ]]></literal>
    <justification jstring="[para(9(a,1),7(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 7"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20">
    <literal><![CDATA[
      (c ' + (c + c ') ') ' = c
    ]]></literal>
    <justification jstring="[para(9(a,1),8(a,1,1,1,1))].">
      <j1 rule="para" parents="9 8"/>
    </justification>
  </clause>

  <clause id="27">
    <literal><![CDATA[
      ((x + c) ' + (x + (c ' + (c + c ') ')) ') ' = x
    ]]></literal>
    <justification jstring="[para(20(a,1),8(a,1,1,2,1,2)),demod(6(14))].">
      <j1 rule="para" parents="20 8"/>
      <j2 rule="demod" parents="6"/>
    </justification>
  </clause>

  <clause id="28">
    <literal><![CDATA[
      (c + (c + (c ' + c ')) ') ' = c '
    ]]></literal>
    <justification jstring="[para(20(a,1),8(a,1,1,2)),demod(11(7),6(10))].">
      <j1 rule="para" parents="20 8"/>
      <j2 rule="demod" parents="11 6"/>
    </justification>
  </clause>

  <clause id="29">
    <literal><![CDATA[
      ((x + y) ' + (x ' + y) ') ' = y
    ]]></literal>
    <justification jstring="[para(6(a,1),12(a,1,1,2,1))].">
      <j1 rule="para" parents="6 12"/>
    </justification>
  </clause>

  <clause id="38">
    <literal><![CDATA[
      ((c + x) ' + (c + (x + c ')) ') ' = c + x
    ]]></literal>
    <justification jstring="[para(18(a,1),12(a,1,1,1,1)),demod(7(8))].">
      <j1 rule="para" parents="18 12"/>
      <j2 rule="demod" parents="7"/>
    </justification>
  </clause>

  <clause id="101">
    <literal><![CDATA[
      ((c + x) ' + (c ' + ((c + c ') ' + x)) ') ' = x
    ]]></literal>
    <justification jstring="[para(20(a,1),29(a,1,1,2,1,1)),demod(7(9),6(14))].">
      <j1 rule="para" parents="20 29"/>
      <j2 rule="demod" parents="7 6"/>
    </justification>
  </clause>

  <clause id="190">
    <literal><![CDATA[
      (c ' + (c + (c ' + c ')) ') ' = c
    ]]></literal>
    <justification jstring="[para(28(a,1),8(a,1,1,2)),demod(18(9),6(11))].">
      <j1 rule="para" parents="28 8"/>
      <j2 rule="demod" parents="18 6"/>
    </justification>
  </clause>

  <clause id="191">
    <literal><![CDATA[
      (c + (c ' + c ')) ' = (c + c ') '
    ]]></literal>
    <justification jstring="[para(28(a,1),12(a,1,1,1)),demod(6(13),190(14),6(4)),flip(a)].">
      <j1 rule="para" parents="28 12"/>
      <j2 rule="demod" parents="6 190 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="200">
    <literal><![CDATA[
      (c + (c + c ') ') ' = c '
    ]]></literal>
    <justification jstring="[para(28(a,1),15(a,2)),demod(191(10),191(18),15(23))].">
      <j1 rule="para" parents="28 15"/>
      <j2 rule="demod" parents="191 191 15"/>
    </justification>
  </clause>

  <clause id="526">
    <literal><![CDATA[
      (c ' + (c + (c ' + (c + c ') ')) ') ' = c
    ]]></literal>
    <justification jstring="[para(9(a,1),27(a,1,1,1,1))].">
      <j1 rule="para" parents="9 27"/>
    </justification>
  </clause>

  <clause id="563">
    <literal><![CDATA[
      c + (c + c ') ' = c
    ]]></literal>
    <justification jstring="[para(200(a,1),38(a,1,1,1)),demod(6(11),526(15)),flip(a)].">
      <j1 rule="para" parents="200 38"/>
      <j2 rule="demod" parents="6 526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="574">
    <literal><![CDATA[
      c + ((c + c ') ' + x) = c + x
    ]]></literal>
    <justification jstring="[para(563(a,1),7(a,1,1)),flip(a)].">
      <j1 rule="para" parents="563 7"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="582">
    <literal><![CDATA[
      (c + c ') ' + x = x
    ]]></literal>
    <justification jstring="[para(574(a,1),12(a,1,1,1,1)),demod(6(12),101(15)),flip(a)].">
      <j1 rule="para" parents="574 12"/>
      <j2 rule="demod" parents="6 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="607">
    <literal><![CDATA[
      (c + c ') ' = (x + x ') '
    ]]></literal>
    <justification jstring="[para(582(a,1),16(a,1,1,1,1)),demod(582(13),8(8),6(2)),flip(a)].">
      <j1 rule="para" parents="582 16"/>
      <j2 rule="demod" parents="582 8 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="759">
    <literal><![CDATA[
      (x + x ' ') ' ' = x
    ]]></literal>
    <justification jstring="[para(607(a,2),8(a,1,1,1)),demod(582(10))].">
      <j1 rule="para" parents="607 8"/>
      <j2 rule="demod" parents="582"/>
    </justification>
  </clause>

  <clause id="767">
    <literal><![CDATA[
      x ' ' = x
    ]]></literal>
    <justification jstring="[para(607(a,2),13(a,1,1,2)),demod(6(3),6(10),582(10),759(5)),flip(a)].">
      <j1 rule="para" parents="607 13"/>
      <j2 rule="demod" parents="6 6 582 759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="914">
    <literal><![CDATA[
      (x + y) ' + (x ' + y) ' = y '
    ]]></literal>
    <justification jstring="[para(29(a,1),767(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29 767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="927">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer(Huntington)
    ]]></attribute>
    <justification jstring="[back_demod(10),demod(914(12),767(3)),xx(a)].">
      <j1 rule="back_demod" parents="10"/>
      <j2 rule="demod" parents="914 767"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

</proofs>
