<?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>dn1.out</source>

<heading><![CDATA[
Prover9 (32) version August-2006A, August 2006.
Process 11561 was started by mccune on cleo.thornwood,
Sat Aug 12 21:08:38 2006
The command was "/home/mccune/bin/prover9 -f dn1.in".
]]></heading>

<proof number="1" length="136" max_count="90">

<comments><![CDATA[
% Proof 1 at 2.36 (+ 0.03) seconds: robbins_basis.
% Length of proof is 136.
% Level of proof is 41.
% Maximum clause weight is 90.
% Given clauses 272.
]]></comments>

  <clause id="1">
    <literal><![CDATA[
      (((x v y)' v z)' v (x v (z' v (z v u)')')')' = z
    ]]></literal>
    <attribute><![CDATA[
      label(DN1)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="2">
    <literal><![CDATA[
      B v A != A v B
    ]]></literal>
    <literal><![CDATA[
      (A v B) v C != A v (B v C)
    ]]></literal>
    <literal><![CDATA[
      ((A v B)' v (A' v B)')' != B
    ]]></literal>
    <attribute><![CDATA[
      answer(robbins_basis)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

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

  <clause id="12">
    <literal><![CDATA[
      ((x v x')' v x)' = x'
    ]]></literal>
    <justification jstring="[para(1(a,1),7(a,1,1,1,1,1))].">
      <j1 rule="para" parents="1 7"/>
    </justification>
  </clause>

  <clause id="15">
    <literal><![CDATA[
      (x' v (x v (x' v (x v y)')')')' = x
    ]]></literal>
    <justification jstring="[para(12(a,1),1(a,1,1,1))].">
      <j1 rule="para" parents="12 1"/>
    </justification>
  </clause>

  <clause id="23">
    <literal><![CDATA[
      ((x v y)' v (x' v (y' v (y v z)')')')' = y
    ]]></literal>
    <justification jstring="[para(15(a,1),1(a,1,1,1,1,1))].">
      <j1 rule="para" parents="15 1"/>
    </justification>
  </clause>

  <clause id="27">
    <literal><![CDATA[
      (((x v y)' v z)' v (x v z)')' = z
    ]]></literal>
    <justification jstring="[para(15(a,1),1(a,1,1,2,1,2))].">
      <j1 rule="para" parents="15 1"/>
    </justification>
  </clause>

  <clause id="39">
    <literal><![CDATA[
      (x' v (x v x)')' = x
    ]]></literal>
    <justification jstring="[para(15(a,1),15(a,1,1,2,1,2))].">
      <j1 rule="para" parents="15 15"/>
    </justification>
  </clause>

  <clause id="77">
    <literal><![CDATA[
      (((((x' v y)' v (x v z)')' v u)' v x)' v (x v z)')' = x
    ]]></literal>
    <justification jstring="[para(27(a,1),1(a,1,1,2))].">
      <j1 rule="para" parents="27 1"/>
    </justification>
  </clause>

  <clause id="79">
    <literal><![CDATA[
      (((((x v y)' v z)' v u)' v (x v (z' v (z v v)')')')' v z)' = (x v (z' v (z v v)')')'
    ]]></literal>
    <justification jstring="[para(1(a,1),27(a,1,1,2))].">
      <j1 rule="para" parents="1 27"/>
    </justification>
  </clause>

  <clause id="87">
    <literal><![CDATA[
      ((x v y)' v (x' v y)')' = y
    ]]></literal>
    <justification jstring="[para(15(a,1),27(a,1,1,1,1,1))].">
      <j1 rule="para" parents="15 27"/>
    </justification>
  </clause>

  <clause id="93">
    <literal><![CDATA[
      (x v ((y v z)' v (y v x)')')' = (y v x)'
    ]]></literal>
    <justification jstring="[para(27(a,1),27(a,1,1,1))].">
      <j1 rule="para" parents="27 27"/>
    </justification>
  </clause>

  <clause id="95">
    <literal><![CDATA[
      B v A != A v B
    ]]></literal>
    <literal><![CDATA[
      (A v B) v C != A v (B v C)
    ]]></literal>
    <attribute><![CDATA[
      answer(robbins_basis)
    ]]></attribute>
    <justification jstring="[back_rewrite(2),rewrite(87(29)),xx(c)].">
      <j1 rule="back_rewrite" parents="2"/>
      <j2 rule="rewrite" parents="87"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

  <clause id="98">
    <literal><![CDATA[
      ((((x v (x v y)')' v z)' v x)' v (x v y)')' = x
    ]]></literal>
    <justification jstring="[para(87(a,1),1(a,1,1,2))].">
      <j1 rule="para" parents="87 1"/>
    </justification>
  </clause>

  <clause id="107">
    <literal><![CDATA[
      (x' v ((x v x')'' v x)')' = x
    ]]></literal>
    <justification jstring="[para(12(a,1),87(a,1,1,1))].">
      <j1 rule="para" parents="12 87"/>
    </justification>
  </clause>

  <clause id="109">
    <literal><![CDATA[
      (((x v x') v x)' v x')' = x
    ]]></literal>
    <justification jstring="[para(12(a,1),87(a,1,1,2))].">
      <j1 rule="para" parents="12 87"/>
    </justification>
  </clause>

  <clause id="118">
    <literal><![CDATA[
      ((x v y)' v ((z v x)' v y)')' = y
    ]]></literal>
    <justification jstring="[para(87(a,1),27(a,1,1,1,1,1))].">
      <j1 rule="para" parents="87 27"/>
    </justification>
  </clause>

  <clause id="119">
    <literal><![CDATA[
      (x v (y v (y' v x)')')' = (y' v x)'
    ]]></literal>
    <justification jstring="[para(87(a,1),27(a,1,1,1))].">
      <j1 rule="para" parents="87 27"/>
    </justification>
  </clause>

  <clause id="139">
    <literal><![CDATA[
      (x v ((x v x') v x')')' = x'
    ]]></literal>
    <justification jstring="[para(109(a,1),27(a,1,1,1))].">
      <j1 rule="para" parents="109 27"/>
    </justification>
  </clause>

  <clause id="196">
    <literal><![CDATA[
      (x' v x')' = x
    ]]></literal>
    <justification jstring="[para(139(a,1),15(a,1,1,2,1,2,1,2)),rewrite(119(9))].">
      <j1 rule="para" parents="139 15"/>
      <j2 rule="rewrite" parents="119"/>
    </justification>
  </clause>

  <clause id="200">
    <literal><![CDATA[
      ((x' v y)' v (x v y)')' = y
    ]]></literal>
    <justification jstring="[para(139(a,1),27(a,1,1,1,1,1))].">
      <j1 rule="para" parents="139 27"/>
    </justification>
  </clause>

  <clause id="216">
    <literal><![CDATA[
      ((x v y)' v z)' v (x v (z' v (z v u)')')' = (z v z)'
    ]]></literal>
    <justification jstring="[para(1(a,1),196(a,1,1,1)),rewrite(1(13)),flip(a)].">
      <j1 rule="para" parents="1 196"/>
      <j2 rule="rewrite" parents="1"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="221">
    <literal><![CDATA[
      (x v x')' v x = x
    ]]></literal>
    <justification jstring="[para(12(a,1),196(a,1,1,1)),rewrite(12(6),196(4)),flip(a)].">
      <j1 rule="para" parents="12 196"/>
      <j2 rule="rewrite" parents="12 196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="225">
    <literal><![CDATA[
      (x'' v x)' = x'
    ]]></literal>
    <justification jstring="[para(196(a,1),39(a,1,1,2))].">
      <j1 rule="para" parents="196 39"/>
    </justification>
  </clause>

  <clause id="228">
    <literal><![CDATA[
      (((x' v y)' v x')' v x)' = x'
    ]]></literal>
    <justification jstring="[para(196(a,1),27(a,1,1,2))].">
      <j1 rule="para" parents="196 27"/>
    </justification>
  </clause>

  <clause id="229">
    <literal><![CDATA[
      (x v x)' = ((y v z)' v x)' v (y v x)'
    ]]></literal>
    <justification jstring="[para(27(a,1),196(a,1,1,1)),rewrite(27(8))].">
      <j1 rule="para" parents="27 196"/>
      <j2 rule="rewrite" parents="27"/>
    </justification>
  </clause>

  <clause id="232">
    <literal><![CDATA[
      (x v x)' = (y v x)' v (y' v x)'
    ]]></literal>
    <justification jstring="[para(87(a,1),196(a,1,1,1)),rewrite(87(7))].">
      <j1 rule="para" parents="87 196"/>
      <j2 rule="rewrite" parents="87"/>
    </justification>
  </clause>

  <clause id="240">
    <literal><![CDATA[
      (x v x)' = x' v x'
    ]]></literal>
    <justification jstring="[para(196(a,1),196(a,1,1,1)),rewrite(196(4))].">
      <j1 rule="para" parents="196 196"/>
      <j2 rule="rewrite" parents="196"/>
    </justification>
  </clause>

  <clause id="245">
    <literal><![CDATA[
      x'' v x'' = x
    ]]></literal>
    <justification jstring="[back_rewrite(1),rewrite(216(12),240(2),240(4))].">
      <j1 rule="back_rewrite" parents="1"/>
      <j2 rule="rewrite" parents="216 240 240"/>
    </justification>
  </clause>

  <clause id="254">
    <literal><![CDATA[
      (x v y)' v (x' v y)' = y' v y'
    ]]></literal>
    <justification jstring="[back_rewrite(232),rewrite(240(2)),flip(a)].">
      <j1 rule="back_rewrite" parents="232"/>
      <j2 rule="rewrite" parents="240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="255">
    <literal><![CDATA[
      ((x v y)' v z)' v (x v z)' = z' v z'
    ]]></literal>
    <justification jstring="[back_rewrite(229),rewrite(240(2)),flip(a)].">
      <j1 rule="back_rewrite" parents="229"/>
      <j2 rule="rewrite" parents="240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="257">
    <literal><![CDATA[
      ((x v y)' v z)' v (x v (z' v (z v u)')')' = z' v z'
    ]]></literal>
    <justification jstring="[back_rewrite(216),rewrite(240(14))].">
      <j1 rule="back_rewrite" parents="216"/>
      <j2 rule="rewrite" parents="240"/>
    </justification>
  </clause>

  <clause id="273">
    <literal><![CDATA[
      x'' v x = x
    ]]></literal>
    <justification jstring="[para(225(a,1),245(a,1,1,1)),rewrite(225(6),245(5)),flip(a)].">
      <j1 rule="para" parents="225 245"/>
      <j2 rule="rewrite" parents="225 245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="287">
    <literal><![CDATA[
      (x' v ((x v x') v x)')' = x
    ]]></literal>
    <justification jstring="[para(221(a,1),200(a,1,1,1,1))].">
      <j1 rule="para" parents="221 200"/>
    </justification>
  </clause>

  <clause id="289">
    <literal><![CDATA[
      (x' v y)' v (x v y)' = y' v y'
    ]]></literal>
    <justification jstring="[para(200(a,1),245(a,1,1,1)),rewrite(200(8)),flip(a)].">
      <j1 rule="para" parents="200 245"/>
      <j2 rule="rewrite" parents="200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="292">
    <literal><![CDATA[
      (x' v (x' v x)')' = x
    ]]></literal>
    <justification jstring="[para(273(a,1),200(a,1,1,1,1))].">
      <j1 rule="para" parents="273 200"/>
    </justification>
  </clause>

  <clause id="295">
    <literal><![CDATA[
      (x v (x v x')')' = x'
    ]]></literal>
    <justification jstring="[para(240(a,1),200(a,1,1,1)),rewrite(245(5))].">
      <j1 rule="para" parents="240 200"/>
      <j2 rule="rewrite" parents="245"/>
    </justification>
  </clause>

  <clause id="306">
    <literal><![CDATA[
      x' v (x' v x)' = x' v x'
    ]]></literal>
    <justification jstring="[para(292(a,1),245(a,1,1,1)),rewrite(292(7)),flip(a)].">
      <j1 rule="para" parents="292 245"/>
      <j2 rule="rewrite" parents="292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="315">
    <literal><![CDATA[
      x v (x v x')' = x
    ]]></literal>
    <justification jstring="[para(295(a,1),245(a,1,1,1)),rewrite(295(7),245(5)),flip(a)].">
      <j1 rule="para" parents="295 245"/>
      <j2 rule="rewrite" parents="295 245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="341">
    <literal><![CDATA[
      (((x' v x) v x')' v x)' = x'
    ]]></literal>
    <justification jstring="[para(23(a,1),23(a,1,1,2))].">
      <j1 rule="para" parents="23 23"/>
    </justification>
  </clause>

  <clause id="343">
    <literal><![CDATA[
      x' v ((x v x') v x)' = x' v x'
    ]]></literal>
    <justification jstring="[para(287(a,1),245(a,1,1,1)),rewrite(287(8)),flip(a)].">
      <j1 rule="para" parents="287 245"/>
      <j2 rule="rewrite" parents="287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="363">
    <literal><![CDATA[
      ((x' v x) v x')' v x = x
    ]]></literal>
    <justification jstring="[para(341(a,1),245(a,1,1,1)),rewrite(341(9),245(5)),flip(a)].">
      <j1 rule="para" parents="341 245"/>
      <j2 rule="rewrite" parents="341 245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="371">
    <literal><![CDATA[
      x' v ((x v x')'' v x)' = x' v x'
    ]]></literal>
    <justification jstring="[para(107(a,1),245(a,1,1,1)),rewrite(107(10)),flip(a)].">
      <j1 rule="para" parents="107 245"/>
      <j2 rule="rewrite" parents="107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="372">
    <literal><![CDATA[
      ((x' v x') v (((x v x) v (x' v x'))'' v (x v x))')' = x v x
    ]]></literal>
    <justification jstring="[para(240(a,1),107(a,1,1,1)),rewrite(240(6))].">
      <j1 rule="para" parents="240 107"/>
      <j2 rule="rewrite" parents="240"/>
    </justification>
  </clause>

  <clause id="373">
    <literal><![CDATA[
      x v (x v (x' v x'))' = x v x
    ]]></literal>
    <justification jstring="[para(107(a,1),306(a,1,1)),rewrite(371(8),240(4),245(5),371(8),371(14),240(10),245(11),371(14),240(10),245(11))].">
      <j1 rule="para" parents="107 306"/>
      <j2 rule="rewrite" parents="371 240 245 371 371 240 245 371 240 245"/>
    </justification>
  </clause>

  <clause id="379">
    <literal><![CDATA[
      ((x' v x)' v x')' = x
    ]]></literal>
    <justification jstring="[para(221(a,1),118(a,1,1,2,1))].">
      <j1 rule="para" parents="221 118"/>
    </justification>
  </clause>

  <clause id="380">
    <literal><![CDATA[
      (x v y)' v ((z v x)' v y)' = y' v y'
    ]]></literal>
    <justification jstring="[para(118(a,1),245(a,1,1,1)),rewrite(118(9)),flip(a)].">
      <j1 rule="para" parents="118 245"/>
      <j2 rule="rewrite" parents="118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="408">
    <literal><![CDATA[
      (x' v x)' v x' = x' v x'
    ]]></literal>
    <justification jstring="[para(379(a,1),245(a,1,1,1)),rewrite(379(7)),flip(a)].">
      <j1 rule="para" parents="379 245"/>
      <j2 rule="rewrite" parents="379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="416">
    <literal><![CDATA[
      ((x' v y)' v x')' v x = x
    ]]></literal>
    <justification jstring="[para(228(a,1),245(a,1,1,1)),rewrite(228(10),245(5)),flip(a)].">
      <j1 rule="para" parents="228 245"/>
      <j2 rule="rewrite" parents="228 245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="418">
    <literal><![CDATA[
      x' v x' = x'
    ]]></literal>
    <justification jstring="[para(408(a,1),228(a,1,1,1,1)),rewrite(240(4),245(5),240(2))].">
      <j1 rule="para" parents="408 228"/>
      <j2 rule="rewrite" parents="240 245 240"/>
    </justification>
  </clause>

  <clause id="426">
    <literal><![CDATA[
      (x v y)' v ((z v x)' v y)' = y'
    ]]></literal>
    <justification jstring="[back_rewrite(380),rewrite(418(10))].">
      <j1 rule="back_rewrite" parents="380"/>
      <j2 rule="rewrite" parents="418"/>
    </justification>
  </clause>

  <clause id="429">
    <literal><![CDATA[
      x v x = x
    ]]></literal>
    <justification jstring="[back_rewrite(373),rewrite(418(3),315(4)),flip(a)].">
      <j1 rule="back_rewrite" parents="373"/>
      <j2 rule="rewrite" parents="418 315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="430">
    <literal><![CDATA[
      x'' = x
    ]]></literal>
    <justification jstring="[back_rewrite(372),rewrite(429(3),429(2),429(4),429(6),371(8),429(3),429(3))].">
      <j1 rule="back_rewrite" parents="372"/>
      <j2 rule="rewrite" parents="429 429 429 429 371 429 429"/>
    </justification>
  </clause>

  <clause id="433">
    <literal><![CDATA[
      x' v ((x v x') v x)' = x'
    ]]></literal>
    <justification jstring="[back_rewrite(343),rewrite(429(9))].">
      <j1 rule="back_rewrite" parents="343"/>
      <j2 rule="rewrite" parents="429"/>
    </justification>
  </clause>

  <clause id="442">
    <literal><![CDATA[
      (x' v y)' v (x v y)' = y'
    ]]></literal>
    <justification jstring="[back_rewrite(289),rewrite(429(9))].">
      <j1 rule="back_rewrite" parents="289"/>
      <j2 rule="rewrite" parents="429"/>
    </justification>
  </clause>

  <clause id="449">
    <literal><![CDATA[
      ((x v y)' v z)' v (x v (z' v (z v u)')')' = z'
    ]]></literal>
    <justification jstring="[back_rewrite(257),rewrite(429(15))].">
      <j1 rule="back_rewrite" parents="257"/>
      <j2 rule="rewrite" parents="429"/>
    </justification>
  </clause>

  <clause id="451">
    <literal><![CDATA[
      ((x v y)' v z)' v (x v z)' = z'
    ]]></literal>
    <justification jstring="[back_rewrite(255),rewrite(429(10))].">
      <j1 rule="back_rewrite" parents="255"/>
      <j2 rule="rewrite" parents="429"/>
    </justification>
  </clause>

  <clause id="452">
    <literal><![CDATA[
      (x v y)' v (x' v y)' = y'
    ]]></literal>
    <justification jstring="[back_rewrite(254),rewrite(429(9))].">
      <j1 rule="back_rewrite" parents="254"/>
      <j2 rule="rewrite" parents="429"/>
    </justification>
  </clause>

  <clause id="542">
    <literal><![CDATA[
      ((x v y)' v x)' v x' = x'
    ]]></literal>
    <justification jstring="[para(430(a,1),416(a,1,1,1,1,1,1)),rewrite(430(4))].">
      <j1 rule="para" parents="430 416"/>
      <j2 rule="rewrite" parents="430"/>
    </justification>
  </clause>

  <clause id="600">
    <literal><![CDATA[
      x v ((y' v x) v (y v x)')' = y v x
    ]]></literal>
    <justification jstring="[para(442(a,1),442(a,1,1,1)),rewrite(430(2),430(10))].">
      <j1 rule="para" parents="442 442"/>
      <j2 rule="rewrite" parents="430 430"/>
    </justification>
  </clause>

  <clause id="610">
    <literal><![CDATA[
      (((((((x' v x) v x') v y)' v x')' v z)' v ((x' v x) v x')')' v x')' = ((x' v x) v x')'
    ]]></literal>
    <justification jstring="[para(363(a,1),77(a,1,1,1,1,1,1,1,1,2,1)),rewrite(430(6),363(24))].">
      <j1 rule="para" parents="363 77"/>
      <j2 rule="rewrite" parents="430 363"/>
    </justification>
  </clause>

  <clause id="627">
    <literal><![CDATA[
      x v ((y v x) v (y' v x)')' = y' v x
    ]]></literal>
    <justification jstring="[para(452(a,1),442(a,1,1,1)),rewrite(430(2),430(11))].">
      <j1 rule="para" parents="452 442"/>
      <j2 rule="rewrite" parents="430 430"/>
    </justification>
  </clause>

  <clause id="715">
    <literal><![CDATA[
      ((((x v y) v z)' v (x v ((((x v y) v (x v y)') v (x v y)) v ((((x v y) v (x v y)') v (x v y))' v u)')')')' v (((x v y) v (x v y)') v (x v y))')' = (x v ((((x v y) v (x v y)') v (x v y)) v ((((x v y) v (x v y)') v (x v y))' v u)')')'
    ]]></literal>
    <justification jstring="[para(433(a,1),79(a,1,1,1,1,1,1,1,1)),rewrite(430(3),430(11),430(41))].">
      <j1 rule="para" parents="433 79"/>
      <j2 rule="rewrite" parents="430 430 430"/>
    </justification>
  </clause>

  <clause id="767">
    <literal><![CDATA[
      x v ((y v x) v ((z v y)' v x)')' = (z v y)' v x
    ]]></literal>
    <justification jstring="[para(426(a,1),442(a,1,1,1)),rewrite(430(2),430(13))].">
      <j1 rule="para" parents="426 442"/>
      <j2 rule="rewrite" parents="430 430"/>
    </justification>
  </clause>

  <clause id="771">
    <literal><![CDATA[
      (x v (y v x)')' v x = y v x
    ]]></literal>
    <justification jstring="[para(442(a,1),426(a,1,2,1)),rewrite(430(6),430(8))].">
      <j1 rule="para" parents="442 426"/>
      <j2 rule="rewrite" parents="430 430"/>
    </justification>
  </clause>

  <clause id="784">
    <literal><![CDATA[
      x v ((y v (z v x)')' v ((u v z)' v x)')' = (u v z)' v x
    ]]></literal>
    <justification jstring="[para(426(a,1),426(a,1,1,1)),rewrite(430(2),430(16))].">
      <j1 rule="para" parents="426 426"/>
      <j2 rule="rewrite" parents="430 430"/>
    </justification>
  </clause>

  <clause id="785">
    <literal><![CDATA[
      (x v y')' v y = y
    ]]></literal>
    <justification jstring="[para(771(a,1),416(a,1,1,1))].">
      <j1 rule="para" parents="771 416"/>
    </justification>
  </clause>

  <clause id="788">
    <literal><![CDATA[
      (x v y)' v y' = y'
    ]]></literal>
    <justification jstring="[para(771(a,1),542(a,1,1,1))].">
      <j1 rule="para" parents="771 542"/>
    </justification>
  </clause>

  <clause id="797">
    <literal><![CDATA[
      x v (y v x) = y v x
    ]]></literal>
    <justification jstring="[para(442(a,1),785(a,1,1,1)),rewrite(430(2))].">
      <j1 rule="para" parents="442 785"/>
      <j2 rule="rewrite" parents="430"/>
    </justification>
  </clause>

  <clause id="827">
    <literal><![CDATA[
      x v ((y v z)' v (y v x)')' = y v x
    ]]></literal>
    <justification jstring="[para(93(a,1),430(a,1,1)),rewrite(430(3)),flip(a)].">
      <j1 rule="para" parents="93 430"/>
      <j2 rule="rewrite" parents="430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="871">
    <literal><![CDATA[
      x v (y' v (y v x)')' = y v x
    ]]></literal>
    <justification jstring="[para(442(a,1),451(a,1,1,1)),rewrite(430(2),430(9))].">
      <j1 rule="para" parents="442 451"/>
      <j2 rule="rewrite" parents="430 430"/>
    </justification>
  </clause>

  <clause id="879">
    <literal><![CDATA[
      x v (y v ((z v y)' v x)')' = (z v y)' v x
    ]]></literal>
    <justification jstring="[para(426(a,1),451(a,1,1,1)),rewrite(430(2),430(12))].">
      <j1 rule="para" parents="426 451"/>
      <j2 rule="rewrite" parents="430 430"/>
    </justification>
  </clause>

  <clause id="882">
    <literal><![CDATA[
      x' v (y v x)' = x'
    ]]></literal>
    <justification jstring="[para(785(a,1),451(a,1,1,1))].">
      <j1 rule="para" parents="785 451"/>
    </justification>
  </clause>

  <clause id="883">
    <literal><![CDATA[
      x v (y v x')' = x
    ]]></literal>
    <justification jstring="[para(788(a,1),451(a,1,1,1)),rewrite(430(2),430(6))].">
      <j1 rule="para" parents="788 451"/>
      <j2 rule="rewrite" parents="430 430"/>
    </justification>
  </clause>

  <clause id="898">
    <literal><![CDATA[
      x v (x v y) = x v y
    ]]></literal>
    <justification jstring="[para(98(a,1),785(a,1,1))].">
      <j1 rule="para" parents="98 785"/>
    </justification>
  </clause>

  <clause id="899">
    <literal><![CDATA[
      (x' v (x v y)')' = x
    ]]></literal>
    <justification jstring="[para(785(a,1),98(a,1,1,1,1))].">
      <j1 rule="para" parents="785 98"/>
    </justification>
  </clause>

  <clause id="901">
    <literal><![CDATA[
      (x v (x' v y)')' = x'
    ]]></literal>
    <justification jstring="[para(788(a,1),98(a,1,1,1,1)),rewrite(430(2))].">
      <j1 rule="para" parents="788 98"/>
      <j2 rule="rewrite" parents="430"/>
    </justification>
  </clause>

  <clause id="904">
    <literal><![CDATA[
      x v y = y v x
    ]]></literal>
    <justification jstring="[back_rewrite(871),rewrite(899(5))].">
      <j1 rule="back_rewrite" parents="871"/>
      <j2 rule="rewrite" parents="899"/>
    </justification>
  </clause>

  <clause id="938">
    <literal><![CDATA[
      (x v y)' v ((x v z)' v y)' = y'
    ]]></literal>
    <justification jstring="[back_rewrite(449),rewrite(899(9),904(7))].">
      <j1 rule="back_rewrite" parents="449"/>
      <j2 rule="rewrite" parents="899 904"/>
    </justification>
  </clause>

  <clause id="945">
    <literal><![CDATA[
      (((x v y) v (x v y)')' v (((x v y) v z)' v (x v ((x v y) v (x v y)')')')')' = (x v ((x v y) v (x v y)')')'
    ]]></literal>
    <justification jstring="[back_rewrite(715),rewrite(904(9),898(9),904(13),898(13),901(16),904(18),898(18),904(18),904(25),898(25),904(29),898(29),901(32))].">
      <j1 rule="back_rewrite" parents="715"/>
      <j2 rule="rewrite" parents="904 898 904 898 901 904 898 904 904 898 904 898 901"/>
    </justification>
  </clause>

  <clause id="1003">
    <literal><![CDATA[
      (x' v ((x v x')' v ((x' v ((x v x') v y)')' v z)')')' = (x v x')'
    ]]></literal>
    <justification jstring="[back_rewrite(610),rewrite(904(2),904(4),797(4),904(6),904(11),904(13),797(13),904(13),904(16),904(19),904(21),797(21))].">
      <j1 rule="back_rewrite" parents="610"/>
      <j2 rule="rewrite" parents="904 904 797 904 904 904 797 904 904 904 904 797"/>
    </justification>
  </clause>

  <clause id="1007">
    <literal><![CDATA[
      C v (A v B) != A v (B v C)
    ]]></literal>
    <attribute><![CDATA[
      answer(robbins_basis)
    ]]></attribute>
    <justification jstring="[back_rewrite(95),rewrite(904(3),904(12)),xx(a)].">
      <j1 rule="back_rewrite" parents="95"/>
      <j2 rule="rewrite" parents="904 904"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

  <clause id="1009">
    <literal><![CDATA[
      (x v y)' v (y' v x)' = x'
    ]]></literal>
    <justification jstring="[para(904(a,1),452(a,1,1,1))].">
      <j1 rule="para" parents="904 452"/>
    </justification>
  </clause>

  <clause id="1011">
    <literal><![CDATA[
      (x v y)' v ((z v y)' v x)' = x'
    ]]></literal>
    <justification jstring="[para(904(a,1),426(a,1,1,1))].">
      <j1 rule="para" parents="904 426"/>
    </justification>
  </clause>

  <clause id="1053">
    <literal><![CDATA[
      x v ((y' v x)' v (z v (x v y)')')' = y' v x
    ]]></literal>
    <justification jstring="[para(1009(a,1),426(a,1,1,1)),rewrite(430(2),904(8),430(14))].">
      <j1 rule="para" parents="1009 426"/>
      <j2 rule="rewrite" parents="430 904 430"/>
    </justification>
  </clause>

  <clause id="1056">
    <literal><![CDATA[
      (x v y)' v (x v y')' = x'
    ]]></literal>
    <justification jstring="[para(904(a,1),1009(a,1,2,1))].">
      <j1 rule="para" parents="904 1009"/>
    </justification>
  </clause>

  <clause id="1071">
    <literal><![CDATA[
      ((x v y) v (x' v y)')' v ((x' v y)' v (y' v ((x v y) v (x' v y)')'))' = x' v y
    ]]></literal>
    <justification jstring="[para(627(a,1),600(a,1,2,1,2,1)),rewrite(904(18),627(27))].">
      <j1 rule="para" parents="627 600"/>
      <j2 rule="rewrite" parents="904 627"/>
    </justification>
  </clause>

  <clause id="1080">
    <literal><![CDATA[
      x v ((x v y')' v (z v (x v y)')')' = x v y'
    ]]></literal>
    <justification jstring="[para(1056(a,1),426(a,1,1,1)),rewrite(430(2),904(8),430(14))].">
      <j1 rule="para" parents="1056 426"/>
      <j2 rule="rewrite" parents="430 904 430"/>
    </justification>
  </clause>

  <clause id="1087">
    <literal><![CDATA[
      (x v y)' v ((y v z)' v x)' = x'
    ]]></literal>
    <justification jstring="[para(904(a,1),938(a,1,1,1))].">
      <j1 rule="para" parents="904 938"/>
    </justification>
  </clause>

  <clause id="1088">
    <literal><![CDATA[
      (x v y)' v (y v (x v z)')' = y'
    ]]></literal>
    <justification jstring="[para(904(a,1),938(a,1,2,1))].">
      <j1 rule="para" parents="904 938"/>
    </justification>
  </clause>

  <clause id="1152">
    <literal><![CDATA[
      ((x v y)' v z)' v (z v y)' = z'
    ]]></literal>
    <justification jstring="[para(1011(a,1),904(a,1)),flip(a)].">
      <j1 rule="para" parents="1011 904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1264">
    <literal><![CDATA[
      x v (y v (y v x)')' = x
    ]]></literal>
    <justification jstring="[para(1087(a,1),784(a,1,2,1)),rewrite(430(2),429(1),904(3),904(5)),flip(a)].">
      <j1 rule="para" parents="1087 784"/>
      <j2 rule="rewrite" parents="430 429 904 904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1274">
    <literal><![CDATA[
      x v (y v (x v y)')' = x
    ]]></literal>
    <justification jstring="[para(904(a,1),1264(a,1,2,1,2,1))].">
      <j1 rule="para" parents="904 1264"/>
    </justification>
  </clause>

  <clause id="1280">
    <literal><![CDATA[
      (x v y)' v (y v y')' = (x v y)'
    ]]></literal>
    <justification jstring="[para(882(a,1),1264(a,1,2,1,2,1)),rewrite(430(5),904(4))].">
      <j1 rule="para" parents="882 1264"/>
      <j2 rule="rewrite" parents="430 904"/>
    </justification>
  </clause>

  <clause id="1315">
    <literal><![CDATA[
      x v ((y v x) v (y v x)')' = x
    ]]></literal>
    <justification jstring="[para(797(a,1),1274(a,1,2,1,2,1))].">
      <j1 rule="para" parents="797 1274"/>
    </justification>
  </clause>

  <clause id="1317">
    <literal><![CDATA[
      x v ((x v y) v (x v y)')' = x
    ]]></literal>
    <justification jstring="[para(898(a,1),1274(a,1,2,1,2,1))].">
      <j1 rule="para" parents="898 1274"/>
    </justification>
  </clause>

  <clause id="1340">
    <literal><![CDATA[
      (((x v y) v (x v y)')' v (x' v ((x v y) v z)')')' = x'
    ]]></literal>
    <justification jstring="[back_rewrite(945),rewrite(1317(14),904(10),1317(19))].">
      <j1 rule="back_rewrite" parents="945"/>
      <j2 rule="rewrite" parents="1317 904 1317"/>
    </justification>
  </clause>

  <clause id="1359">
    <literal><![CDATA[
      ((x v y) v (x v y)')' v ((z v y')' v ((u v y)' v ((x v y) v (x v y)')')')' = (u v y)' v ((x v y) v (x v y)')'
    ]]></literal>
    <justification jstring="[para(1315(a,1),784(a,1,2,1,1,1,2,1))].">
      <j1 rule="para" parents="1315 784"/>
    </justification>
  </clause>

  <clause id="1362">
    <literal><![CDATA[
      (x v x')' v ((y v x) v (y v x)')' = ((y v x) v (y v x)')'
    ]]></literal>
    <justification jstring="[para(1315(a,1),1264(a,1,2,1,2,1)),rewrite(904(9))].">
      <j1 rule="para" parents="1315 1264"/>
      <j2 rule="rewrite" parents="904"/>
    </justification>
  </clause>

  <clause id="1365">
    <literal><![CDATA[
      x' v ((y v x)' v ((x v z) v (x v z)')')' = (x v z) v (x v z)'
    ]]></literal>
    <justification jstring="[para(1317(a,1),426(a,1,1,1)),rewrite(430(17))].">
      <j1 rule="para" parents="1317 426"/>
      <j2 rule="rewrite" parents="430"/>
    </justification>
  </clause>

  <clause id="1369">
    <literal><![CDATA[
      ((x v y) v (x v y)')' v (x' v ((x v y) v (x v y)')')' = x
    ]]></literal>
    <justification jstring="[para(1317(a,1),600(a,1,2,1,2,1)),rewrite(904(14),898(14),1317(20))].">
      <j1 rule="para" parents="1317 600"/>
      <j2 rule="rewrite" parents="904 898 1317"/>
    </justification>
  </clause>

  <clause id="1378">
    <literal><![CDATA[
      ((x v y) v (x v y)')' v ((z v x')' v ((u v x)' v ((x v y) v (x v y)')')')' = (u v x)' v ((x v y) v (x v y)')'
    ]]></literal>
    <justification jstring="[para(1317(a,1),784(a,1,2,1,1,1,2,1))].">
      <j1 rule="para" parents="1317 784"/>
    </justification>
  </clause>

  <clause id="1381">
    <literal><![CDATA[
      (x v x')' v ((x v y) v (x v y)')' = ((x v y) v (x v y)')'
    ]]></literal>
    <justification jstring="[para(1317(a,1),1264(a,1,2,1,2,1)),rewrite(904(9))].">
      <j1 rule="para" parents="1317 1264"/>
      <j2 rule="rewrite" parents="904"/>
    </justification>
  </clause>

  <clause id="1414">
    <literal><![CDATA[
      x v ((y v x)' v ((y v z)' v (y v x)')')' = x
    ]]></literal>
    <justification jstring="[para(827(a,1),1274(a,1,2,1,2,1)),rewrite(904(9))].">
      <j1 rule="para" parents="827 1274"/>
      <j2 rule="rewrite" parents="904"/>
    </justification>
  </clause>

  <clause id="1638">
    <literal><![CDATA[
      x' v (y v x) = x v x'
    ]]></literal>
    <justification jstring="[para(1280(a,1),426(a,1,2,1)),rewrite(883(4),430(4),430(7))].">
      <j1 rule="para" parents="1280 426"/>
      <j2 rule="rewrite" parents="883 430 430"/>
    </justification>
  </clause>

  <clause id="1653">
    <literal><![CDATA[
      ((x v y) v (x v y)')' = (y v y')'
    ]]></literal>
    <justification jstring="[para(1280(a,1),1264(a,1,2,1,2,1)),rewrite(430(8),904(7),1362(9))].">
      <j1 rule="para" parents="1280 1264"/>
      <j2 rule="rewrite" parents="430 904 1362"/>
    </justification>
  </clause>

  <clause id="1656">
    <literal><![CDATA[
      x v (y v y')' = x
    ]]></literal>
    <justification jstring="[para(1088(a,1),1280(a,1,1,1)),rewrite(430(2),430(9),904(8),1653(9),430(5),904(4),1653(5),1088(11),430(6))].">
      <j1 rule="para" parents="1088 1280"/>
      <j2 rule="rewrite" parents="430 430 904 1653 430 904 1653 1088 430"/>
    </justification>
  </clause>

  <clause id="1657">
    <literal><![CDATA[
      (x v y) v y' = y v y'
    ]]></literal>
    <justification jstring="[para(1280(a,1),1152(a,1,1,1)),rewrite(430(3),904(5),883(5),430(7))].">
      <j1 rule="para" parents="1280 1152"/>
      <j2 rule="rewrite" parents="430 904 883 430"/>
    </justification>
  </clause>

  <clause id="1664">
    <literal><![CDATA[
      (x v x')' = (y v y')'
    ]]></literal>
    <justification jstring="[back_rewrite(1381),rewrite(1653(8),1656(7),1653(8))].">
      <j1 rule="back_rewrite" parents="1381"/>
      <j2 rule="rewrite" parents="1653 1656 1653"/>
    </justification>
  </clause>

  <clause id="1667">
    <literal><![CDATA[
      (x v x')' v ((y v z')' v (u v z))' = (u v z)'
    ]]></literal>
    <justification jstring="[back_rewrite(1378),rewrite(1653(5),1653(13),1656(12),430(9),1653(17),1656(16))].">
      <j1 rule="back_rewrite" parents="1378"/>
      <j2 rule="rewrite" parents="1653 1653 1656 430 1653 1656"/>
    </justification>
  </clause>

  <clause id="1675">
    <literal><![CDATA[
      (x v x')' v y = y
    ]]></literal>
    <justification jstring="[back_rewrite(1369),rewrite(1653(5),1653(9),1656(8),430(5))].">
      <j1 rule="back_rewrite" parents="1369"/>
      <j2 rule="rewrite" parents="1653 1653 1656 430"/>
    </justification>
  </clause>

  <clause id="1676">
    <literal><![CDATA[
      (x v y) v (x v y)' = x v x'
    ]]></literal>
    <justification jstring="[back_rewrite(1365),rewrite(1653(8),1656(7),430(4),1638(3)),flip(a)].">
      <j1 rule="back_rewrite" parents="1365"/>
      <j2 rule="rewrite" parents="1653 1656 430 1638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1678">
    <literal><![CDATA[
      ((x v y')' v (z v y))' = (z v y)'
    ]]></literal>
    <justification jstring="[back_rewrite(1359),rewrite(1676(4),1676(12),1656(12),430(9),1675(10),1676(12),1656(12))].">
      <j1 rule="back_rewrite" parents="1359"/>
      <j2 rule="rewrite" parents="1676 1676 1656 430 1675 1676 1656"/>
    </justification>
  </clause>

  <clause id="1682">
    <literal><![CDATA[
      x' v ((x v y) v z)' = x'
    ]]></literal>
    <justification jstring="[back_rewrite(1340),rewrite(1676(4),1675(10),430(7))].">
      <j1 rule="back_rewrite" parents="1340"/>
      <j2 rule="rewrite" parents="1676 1675 430"/>
    </justification>
  </clause>

  <clause id="1683">
    <literal><![CDATA[
      (x v x')' = c_0
    ]]></literal>
    <justification jstring="[new_symbol(1664)].">
      <j1 rule="new_symbol" parents="1664"/>
    </justification>
  </clause>

  <clause id="1685">
    <literal><![CDATA[
      c_0 v (x v y)' = (x v y)'
    ]]></literal>
    <justification jstring="[back_rewrite(1667),rewrite(1683(3),1678(7))].">
      <j1 rule="back_rewrite" parents="1667"/>
      <j2 rule="rewrite" parents="1683 1678"/>
    </justification>
  </clause>

  <clause id="1689">
    <literal><![CDATA[
      (x' v (x v y))' = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(1003),rewrite(1683(4),1682(8),430(4),1685(5),430(4),1683(7))].">
      <j1 rule="back_rewrite" parents="1003"/>
      <j2 rule="rewrite" parents="1683 1682 430 1685 430 1683"/>
    </justification>
  </clause>

  <clause id="1713">
    <literal><![CDATA[
      c_0 v x = x
    ]]></literal>
    <justification jstring="[back_rewrite(1675),rewrite(1683(3))].">
      <j1 rule="back_rewrite" parents="1675"/>
      <j2 rule="rewrite" parents="1683"/>
    </justification>
  </clause>

  <clause id="1714">
    <literal><![CDATA[
      x v c_0 = x
    ]]></literal>
    <justification jstring="[back_rewrite(1656),rewrite(1683(3))].">
      <j1 rule="back_rewrite" parents="1656"/>
      <j2 rule="rewrite" parents="1683"/>
    </justification>
  </clause>

  <clause id="1719">
    <literal><![CDATA[
      c_0' = x v x'
    ]]></literal>
    <justification jstring="[para(1713(a,1),1009(a,1,1,1)),rewrite(904(4),1713(4),430(3),904(2)),flip(a)].">
      <j1 rule="para" parents="1713 1009"/>
      <j2 rule="rewrite" parents="904 1713 430 904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1794">
    <literal><![CDATA[
      (x v y) v (x v y)' = c_0'
    ]]></literal>
    <justification jstring="[para(1719(a,2),767(a,2)),rewrite(430(3),430(4),797(3),430(7),904(6),1683(7),904(4),1713(4))].">
      <j1 rule="para" parents="1719 767"/>
      <j2 rule="rewrite" parents="430 430 797 430 904 1683 904 1713"/>
    </justification>
  </clause>

  <clause id="1868">
    <literal><![CDATA[
      (x v ((y v x) v z))' = ((y v x) v z)'
    ]]></literal>
    <justification jstring="[para(1689(a,1),426(a,1,2)),rewrite(904(6),1713(6))].">
      <j1 rule="para" parents="1689 426"/>
      <j2 rule="rewrite" parents="904 1713"/>
    </justification>
  </clause>

  <clause id="1875">
    <literal><![CDATA[
      (x v y)' v ((x v y) v z) = c_0'
    ]]></literal>
    <justification jstring="[para(1689(a,1),767(a,1,2,1,2)),rewrite(904(7),1713(7),1868(6),1794(6)),flip(a)].">
      <j1 rule="para" parents="1689 767"/>
      <j2 rule="rewrite" parents="904 1713 1868 1794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1880">
    <literal><![CDATA[
      ((x v y) v (x' v z)')' = (x v y)'
    ]]></literal>
    <justification jstring="[para(1689(a,1),1088(a,1,1)),rewrite(1713(8))].">
      <j1 rule="para" parents="1689 1088"/>
      <j2 rule="rewrite" parents="1713"/>
    </justification>
  </clause>

  <clause id="1907">
    <literal><![CDATA[
      x v (y v x)' = y' v x
    ]]></literal>
    <justification jstring="[back_rewrite(1071),rewrite(1880(6),1880(12),882(9),904(7),882(7),430(4),904(3))].">
      <j1 rule="back_rewrite" parents="1071"/>
      <j2 rule="rewrite" parents="1880 1880 882 904 882 430 904"/>
    </justification>
  </clause>

  <clause id="1916">
    <literal><![CDATA[
      x v ((y v z) v (y v x)')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(1414),rewrite(1907(9),430(3))].">
      <j1 rule="back_rewrite" parents="1414"/>
      <j2 rule="rewrite" parents="1907 430"/>
    </justification>
  </clause>

  <clause id="2007">
    <literal><![CDATA[
      c_0' = ((x v y) v z) v y'
    ]]></literal>
    <justification jstring="[para(1689(a,1),879(a,1,2,1,2)),rewrite(1714(4),1875(9)),flip(a)].">
      <j1 rule="para" parents="1689 879"/>
      <j2 rule="rewrite" parents="1714 1875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2154">
    <literal><![CDATA[
      (x' v (y v (z v x))')' = x
    ]]></literal>
    <justification jstring="[para(1638(a,1),1011(a,1,1,1)),rewrite(1683(3),904(6),1713(8),430(8))].">
      <j1 rule="para" parents="1638 1011"/>
      <j2 rule="rewrite" parents="1683 904 1713 430"/>
    </justification>
  </clause>

  <clause id="2176">
    <literal><![CDATA[
      x' v (y v (z v x))' = x'
    ]]></literal>
    <justification jstring="[para(1657(a,1),784(a,1,2,1,1,1,2,1)),rewrite(1683(4),1714(3),904(7),2154(8),882(5),904(6)),flip(a)].">
      <j1 rule="para" parents="1657 784"/>
      <j2 rule="rewrite" parents="1683 1714 904 2154 882 904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2475">
    <literal><![CDATA[
      x' v ((y v x) v z)' = x'
    ]]></literal>
    <justification jstring="[para(2007(a,2),1907(a,1,2,1)),rewrite(430(4),904(3),1713(3),904(6)),flip(a)].">
      <j1 rule="para" parents="2007 1907"/>
      <j2 rule="rewrite" parents="430 904 1713 904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4696">
    <literal><![CDATA[
      (x v y) v (x v z) = (x v z) v y
    ]]></literal>
    <justification jstring="[para(1916(a,1),1053(a,1,2,1,2,1)),rewrite(430(4),904(7),2475(7),430(3),430(5)),flip(a)].">
      <j1 rule="para" parents="1916 1053"/>
      <j2 rule="rewrite" parents="430 904 2475 430 430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5500">
    <literal><![CDATA[
      (x v y) v (x v z) = (x v y) v z
    ]]></literal>
    <justification jstring="[para(1916(a,1),1080(a,1,2,1,2,1)),rewrite(430(5),904(7),2176(7),430(3),430(6)),flip(a)].">
      <j1 rule="para" parents="1916 1080"/>
      <j2 rule="rewrite" parents="430 904 2176 430 430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5503">
    <literal><![CDATA[
      (x v y) v z = (x v z) v y
    ]]></literal>
    <justification jstring="[back_rewrite(4696),rewrite(5500(3))].">
      <j1 rule="back_rewrite" parents="4696"/>
      <j2 rule="rewrite" parents="5500"/>
    </justification>
  </clause>

  <clause id="5509">
    <literal><![CDATA[
      (x v y) v z = y v (x v z)
    ]]></literal>
    <justification jstring="[para(5503(a,1),904(a,1))].">
      <j1 rule="para" parents="5503 904"/>
    </justification>
  </clause>

  <clause id="5510">
    <literal><![CDATA[
      x v (y v z) = z v (x v y)
    ]]></literal>
    <justification jstring="[para(904(a,1),5503(a,1,1)),rewrite(5509(2),5509(4))].">
      <j1 rule="para" parents="904 5503"/>
      <j2 rule="rewrite" parents="5509 5509"/>
    </justification>
  </clause>

  <clause id="5511">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer(robbins_basis)
    ]]></attribute>
    <justification jstring="[resolve(5510,a,1007,a(flip))].">
      <j1 rule="resolve" parents="5510 1007"/>
    </justification>
  </clause>

</proof>

</proofs>
