<?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>LT.out</source>

<heading><![CDATA[
Prover9 (32) version 2009-02A, February 2009.
Process 12206 was started by mccune on cleo,
Wed Feb 25 10:10:20 2009
The command was "/home/mccune/bin/prover9 -f LT.in LT-interp.outx".
]]></heading>

<proof number="1" length="63" max_count="29">

<comments><![CDATA[
% Proof 1 at 0.56 (+ 0.01) seconds: H2.
% Length of proof is 63.
% Level of proof is 21.
% Maximum clause weight is 29.
% Given clauses 85.

]]></comments>

  <clause id="1" type="goal">
    <literal><![CDATA[
      x ^ (y v (x ^ z)) = x ^ (y v (z ^ ((x ^ (y v z)) v (y ^ z))))
    ]]></literal>
    <attribute><![CDATA[
      label(H2)
    ]]></attribute>
    <attribute><![CDATA[
      label(non_clause)
    ]]></attribute>
    <attribute><![CDATA[
      label(goal)
    ]]></attribute>
    <justification jstring="[goal].">
      <j1 rule="goal"/>
    </justification>
  </clause>

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

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

  <clause id="4">
    <literal><![CDATA[
      x v (y v z) = z v (x v y)
    ]]></literal>
    <justification jstring="[copy(3),rewrite([2(2)]),flip(a)].">
      <j1 rule="copy" parents="3"/>
      <j2 rule="rewrite" parents="2"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5" type="assumption">
    <literal><![CDATA[
      x ^ y = y ^ x
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="6" type="assumption">
    <literal><![CDATA[
      (x ^ y) ^ z = x ^ (y ^ z)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="7">
    <literal><![CDATA[
      x ^ (y ^ z) = z ^ (x ^ y)
    ]]></literal>
    <justification jstring="[copy(6),rewrite([5(2)]),flip(a)].">
      <j1 rule="copy" parents="6"/>
      <j2 rule="rewrite" parents="5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8" type="assumption">
    <literal><![CDATA[
      x ^ (x v y) = x
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="9" type="assumption">
    <literal><![CDATA[
      x v (x ^ y) = x
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="10" type="assumption">
    <literal><![CDATA[
      (x ^ y) v (x ^ z) = x ^ ((y ^ (x v z)) v (z ^ (x v y)))
    ]]></literal>
    <attribute><![CDATA[
      label(H82)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="11">
    <literal><![CDATA[
      x ^ ((y ^ (x v z)) v (z ^ (x v y))) = (x ^ z) v (x ^ y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[copy(10),rewrite([2(8)]),flip(a),rewrite([2(5),2(9)])].">
      <j1 rule="copy" parents="10"/>
      <j2 rule="rewrite" parents="2"/>
      <j2 rule="flip"/>
      <j2 rule="rewrite" parents="2 2"/>
    </justification>
  </clause>

  <clause id="12" type="deny">
    <literal><![CDATA[
      c1 ^ (c2 v (c3 ^ ((c1 ^ (c2 v c3)) v (c2 ^ c3)))) != c1 ^ (c2 v (c1 ^ c3))
    ]]></literal>
    <attribute><![CDATA[
      label(H2)
    ]]></attribute>
    <attribute><![CDATA[
      answer(H2)
    ]]></attribute>
    <justification jstring="[deny(1)].">
      <j1 rule="deny" parents="1"/>
    </justification>
  </clause>

  <clause id="13">
    <literal><![CDATA[
      c1 ^ (c2 v (c3 ^ ((c2 ^ c3) v (c1 ^ (c2 v c3))))) != c1 ^ (c2 v (c1 ^ c3))
    ]]></literal>
    <attribute><![CDATA[
      answer(H2)
    ]]></attribute>
    <justification jstring="[copy(12),rewrite([2(12)])].">
      <j1 rule="copy" parents="12"/>
      <j2 rule="rewrite" parents="2"/>
    </justification>
  </clause>

  <clause id="14">
    <literal><![CDATA[
      x v (y v z) = y v (x v z)
    ]]></literal>
    <justification jstring="[para(4(a,1),2(a,1)),rewrite([2(3),2(4)])].">
      <j1 rule="para" parents="4 2"/>
      <j2 rule="rewrite" parents="2 2"/>
    </justification>
  </clause>

  <clause id="15">
    <literal><![CDATA[
      x ^ (y ^ z) = y ^ (x ^ z)
    ]]></literal>
    <justification jstring="[para(7(a,1),5(a,1)),rewrite([5(3),5(4)])].">
      <j1 rule="para" parents="7 5"/>
      <j2 rule="rewrite" parents="5 5"/>
    </justification>
  </clause>

  <clause id="16">
    <literal><![CDATA[
      x ^ x = x
    ]]></literal>
    <justification jstring="[para(9(a,1),8(a,1,2))].">
      <j1 rule="para" parents="9 8"/>
    </justification>
  </clause>

  <clause id="17">
    <literal><![CDATA[
      x v x = x
    ]]></literal>
    <justification jstring="[para(8(a,1),9(a,1,2))].">
      <j1 rule="para" parents="8 9"/>
    </justification>
  </clause>

  <clause id="18">
    <literal><![CDATA[
      x ^ ((y ^ (z v x)) v (z ^ (x v y))) = (z ^ x) v (x ^ y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(11(a,1),5(a,2)),rewrite([2(3),2(5),5(6),5(8),2(9)])].">
      <j1 rule="para" parents="11 5"/>
      <j2 rule="rewrite" parents="2 2 5 5 2"/>
    </justification>
  </clause>

  <clause id="22">
    <literal><![CDATA[
      x v (y v (x ^ z)) = x v y
    ]]></literal>
    <justification jstring="[para(9(a,1),14(a,2,2)),rewrite([2(4)])].">
      <j1 rule="para" parents="9 14"/>
      <j2 rule="rewrite" parents="2"/>
    </justification>
  </clause>

  <clause id="23">
    <literal><![CDATA[
      x ^ (((x v y) ^ (z v u)) v (y ^ (x v (z v u)))) = (x ^ y) v (x ^ (z v u))
    ]]></literal>
    <justification jstring="[para(14(a,1),11(a,1,2,1,2)),rewrite([14(2),5(6),2(7),2(12)])].">
      <j1 rule="para" parents="14 11"/>
      <j2 rule="rewrite" parents="14 5 2 2"/>
    </justification>
  </clause>

  <clause id="24">
    <literal><![CDATA[
      x ^ ((y ^ (z v x)) v (z ^ (y v x))) = (z ^ x) v (y ^ x)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(18(a,1),5(a,2)),rewrite([2(3),2(5),5(6),5(8),2(9)])].">
      <j1 rule="para" parents="18 5"/>
      <j2 rule="rewrite" parents="2 2 5 5 2"/>
    </justification>
  </clause>

  <clause id="25">
    <literal><![CDATA[
      (x v y) ^ (x v (z ^ (x v (x v y)))) = x v (z ^ (x v y))
    ]]></literal>
    <justification jstring="[para(8(a,1),18(a,2,1)),rewrite([2(6),14(6),2(5),8(7),2(5),5(8)])].">
      <j1 rule="para" parents="8 18"/>
      <j2 rule="rewrite" parents="2 14 2 8 2 5"/>
    </justification>
  </clause>

  <clause id="27">
    <literal><![CDATA[
      x ^ (x ^ y) = x ^ y
    ]]></literal>
    <justification jstring="[para(9(a,1),24(a,2)),rewrite([5(1),2(2),5(4),2(5),9(5),5(4),2(5),9(5),5(3)])].">
      <j1 rule="para" parents="9 24"/>
      <j2 rule="rewrite" parents="5 2 5 2 9 5 2 9 5"/>
    </justification>
  </clause>

  <clause id="30">
    <literal><![CDATA[
      x ^ ((x v y) v (y ^ (x v (x v y)))) = x
    ]]></literal>
    <justification jstring="[para(16(a,1),11(a,1,2,1)),rewrite([8(9),2(8),9(8)])].">
      <j1 rule="para" parents="16 11"/>
      <j2 rule="rewrite" parents="8 2 9"/>
    </justification>
  </clause>

  <clause id="32">
    <literal><![CDATA[
      x v (x v y) = x v y
    ]]></literal>
    <justification jstring="[para(17(a,1),14(a,1)),rewrite([2(3),14(3),17(2)]),flip(a)].">
      <j1 rule="para" parents="17 14"/>
      <j2 rule="rewrite" parents="2 14 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33">
    <literal><![CDATA[
      x ^ ((x v y) v (y ^ (x v y))) = x
    ]]></literal>
    <justification jstring="[back_rewrite(30),rewrite([32(3)])].">
      <j1 rule="back_rewrite" parents="30"/>
      <j2 rule="rewrite" parents="32"/>
    </justification>
  </clause>

  <clause id="34">
    <literal><![CDATA[
      (x v y) ^ (x v (z ^ (x v y))) = x v (z ^ (x v y))
    ]]></literal>
    <justification jstring="[back_rewrite(25),rewrite([32(3)])].">
      <j1 rule="back_rewrite" parents="25"/>
      <j2 rule="rewrite" parents="32"/>
    </justification>
  </clause>

  <clause id="35">
    <literal><![CDATA[
      x ^ ((x ^ y) v (x ^ z)) = (x ^ y) v (x ^ z)
    ]]></literal>
    <justification jstring="[para(11(a,1),27(a,1,2)),rewrite([11(10)])].">
      <j1 rule="para" parents="11 27"/>
      <j2 rule="rewrite" parents="11"/>
    </justification>
  </clause>

  <clause id="38">
    <literal><![CDATA[
      x ^ (y ^ (x v z)) = x ^ y
    ]]></literal>
    <justification jstring="[para(8(a,1),15(a,2,2)),rewrite([5(4)])].">
      <j1 rule="para" parents="8 15"/>
      <j2 rule="rewrite" parents="5"/>
    </justification>
  </clause>

  <clause id="39">
    <literal><![CDATA[
      x ^ (y ^ ((z ^ (x v u)) v (u ^ (x v z)))) = y ^ ((x ^ u) v (x ^ z))
    ]]></literal>
    <justification jstring="[para(11(a,1),15(a,2,2)),rewrite([2(5),2(10)])].">
      <j1 rule="para" parents="11 15"/>
      <j2 rule="rewrite" parents="2 2"/>
    </justification>
  </clause>

  <clause id="43">
    <literal><![CDATA[
      x ^ ((y ^ ((x v z) ^ (x v u))) v (z ^ (x v (y ^ (x v u))))) = (x ^ z) v (x ^ y)
    ]]></literal>
    <justification jstring="[para(38(a,1),11(a,2,1)),rewrite([5(8),15(8),2(9),2(13)])].">
      <j1 rule="para" parents="38 11"/>
      <j2 rule="rewrite" parents="5 15 2 2"/>
    </justification>
  </clause>

  <clause id="44">
    <literal><![CDATA[
      (x ^ (y v z)) ^ ((x ^ y) v (y ^ z)) = x ^ y
    ]]></literal>
    <justification jstring="[para(11(a,1),38(a,1,2)),rewrite([5(4),2(5),5(9),15(9),8(8)])].">
      <j1 rule="para" parents="11 38"/>
      <j2 rule="rewrite" parents="5 2 5 15 8"/>
    </justification>
  </clause>

  <clause id="45">
    <literal><![CDATA[
      (x v y) ^ ((x ^ z) v (x ^ u)) = (x ^ z) v (x ^ u)
    ]]></literal>
    <justification jstring="[para(11(a,1),38(a,2)),rewrite([2(5),5(7),39(8),2(8)])].">
      <j1 rule="para" parents="11 38"/>
      <j2 rule="rewrite" parents="2 5 39 2"/>
    </justification>
  </clause>

  <clause id="47">
    <literal><![CDATA[
      x ^ (y ^ (z ^ (x v u))) = x ^ (y ^ z)
    ]]></literal>
    <justification jstring="[para(38(a,1),15(a,2,2)),rewrite([15(6)])].">
      <j1 rule="para" parents="38 15"/>
      <j2 rule="rewrite" parents="15"/>
    </justification>
  </clause>

  <clause id="54">
    <literal><![CDATA[
      (x v y) ^ ((z ^ (x v y)) v ((x v y) ^ (x v (y v z)))) = (x v y) v (z ^ (x v y))
    ]]></literal>
    <justification jstring="[para(16(a,1),23(a,2,2)),rewrite([2(3),14(3),2(2),5(5),17(8),2(8),5(11),2(13)])].">
      <j1 rule="para" parents="16 23"/>
      <j2 rule="rewrite" parents="2 14 2 5 17 2 5 2"/>
    </justification>
  </clause>

  <clause id="56">
    <literal><![CDATA[
      x ^ ((y ^ z) ^ (y v u)) = x ^ (y ^ z)
    ]]></literal>
    <justification jstring="[para(11(a,1),47(a,1,2,2)),rewrite([5(4),2(5),15(7),44(6),15(2),5(1),5(5),5(6),15(6)]),flip(a)].">
      <j1 rule="para" parents="11 47"/>
      <j2 rule="rewrite" parents="5 2 15 44 15 5 5 5 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="68">
    <literal><![CDATA[
      (x ^ y) ^ (x v z) = x ^ y
    ]]></literal>
    <justification jstring="[para(16(a,1),56(a,2)),rewrite([27(5)])].">
      <j1 rule="para" parents="16 56"/>
      <j2 rule="rewrite" parents="27"/>
    </justification>
  </clause>

  <clause id="72">
    <literal><![CDATA[
      (x ^ y) ^ (y v z) = x ^ y
    ]]></literal>
    <justification jstring="[para(5(a,1),68(a,1,1)),rewrite([5(4)])].">
      <j1 rule="para" parents="5 68"/>
      <j2 rule="rewrite" parents="5"/>
    </justification>
  </clause>

  <clause id="80">
    <literal><![CDATA[
      (x ^ y) ^ (z v (x ^ y)) = x ^ y
    ]]></literal>
    <justification jstring="[para(68(a,1),68(a,1,1)),rewrite([2(3),68(7)])].">
      <j1 rule="para" parents="68 68"/>
      <j2 rule="rewrite" parents="2 68"/>
    </justification>
  </clause>

  <clause id="109">
    <literal><![CDATA[
      x ^ (y v ((x v z) v (z ^ (x v z)))) = x
    ]]></literal>
    <justification jstring="[para(33(a,1),72(a,1,1)),rewrite([2(5),33(11)])].">
      <j1 rule="para" parents="33 72"/>
      <j2 rule="rewrite" parents="2 33"/>
    </justification>
  </clause>

  <clause id="129">
    <literal><![CDATA[
      x v ((x v y) v (z ^ (x v y))) = x v y
    ]]></literal>
    <justification jstring="[para(34(a,1),9(a,1,2)),rewrite([14(5)])].">
      <j1 rule="para" parents="34 9"/>
      <j2 rule="rewrite" parents="14"/>
    </justification>
  </clause>

  <clause id="172">
    <literal><![CDATA[
      (x v y) ^ (x v ((y v z) v (z ^ (y v z)))) = x v y
    ]]></literal>
    <justification jstring="[para(109(a,1),34(a,1,2,2)),rewrite([5(7),109(13)])].">
      <j1 rule="para" parents="109 34"/>
      <j2 rule="rewrite" parents="5 109"/>
    </justification>
  </clause>

  <clause id="175">
    <literal><![CDATA[
      x ^ (y ^ ((x ^ z) v (x ^ u))) = y ^ ((x ^ z) v (x ^ u))
    ]]></literal>
    <justification jstring="[para(35(a,1),15(a,2,2))].">
      <j1 rule="para" parents="35 15"/>
    </justification>
  </clause>

  <clause id="206">
    <literal><![CDATA[
      (x v y) v (y ^ (x v y)) = x v y
    ]]></literal>
    <justification jstring="[para(33(a,1),129(a,1,2,2)),rewrite([2(6),129(6),17(3)]),flip(a)].">
      <j1 rule="para" parents="33 129"/>
      <j2 rule="rewrite" parents="2 129 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="211">
    <literal><![CDATA[
      (x v y) ^ (x v (y v z)) = x v y
    ]]></literal>
    <justification jstring="[back_rewrite(172),rewrite([206(5)])].">
      <j1 rule="back_rewrite" parents="172"/>
      <j2 rule="rewrite" parents="206"/>
    </justification>
  </clause>

  <clause id="212">
    <literal><![CDATA[
      (x v y) v (z ^ (x v y)) = x v y
    ]]></literal>
    <justification jstring="[back_rewrite(54),rewrite([211(7),2(5),8(6)]),flip(a)].">
      <j1 rule="back_rewrite" parents="54"/>
      <j2 rule="rewrite" parents="211 2 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="219">
    <literal><![CDATA[
      x ^ ((x v y) ^ (z v u)) = x ^ (z v u)
    ]]></literal>
    <justification jstring="[para(211(a,1),47(a,2,2)),rewrite([5(5),15(6),211(5)])].">
      <j1 rule="para" parents="211 47"/>
      <j2 rule="rewrite" parents="5 15 211"/>
    </justification>
  </clause>

  <clause id="244">
    <literal><![CDATA[
      (x ^ y) ^ (z v u) = x ^ (y ^ (z v u))
    ]]></literal>
    <justification jstring="[para(212(a,1),47(a,1,2,2,2)),rewrite([15(5),15(4),16(3),5(6)]),flip(a)].">
      <j1 rule="para" parents="212 47"/>
      <j2 rule="rewrite" parents="15 15 16 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="293">
    <literal><![CDATA[
      x ^ (y ^ (z v (x ^ y))) = x ^ y
    ]]></literal>
    <justification jstring="[back_rewrite(80),rewrite([244(4)])].">
      <j1 rule="back_rewrite" parents="80"/>
      <j2 rule="rewrite" parents="244"/>
    </justification>
  </clause>

  <clause id="327">
    <literal><![CDATA[
      x ^ (y v (x ^ (y v z))) = x ^ (y v z)
    ]]></literal>
    <justification jstring="[para(34(a,1),293(a,1,2))].">
      <j1 rule="para" parents="34 293"/>
    </justification>
  </clause>

  <clause id="356">
    <literal><![CDATA[
      (x ^ y) v (x ^ z) = x ^ ((y ^ (x v z)) v (z ^ (x v (y ^ (x v z)))))
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(16(a,1),43(a,1,2,1,2)),rewrite([2(11)]),flip(a)].">
      <j1 rule="para" parents="16 43"/>
      <j2 rule="rewrite" parents="2"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="364">
    <literal><![CDATA[
      x ^ ((y ^ (x v z)) v (z ^ (x v (y ^ (x v z))))) = (x ^ z) v (x ^ y)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(356(a,1),2(a,2)),flip(a)].">
      <j1 rule="para" parents="356 2"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="371">
    <literal><![CDATA[
      x ^ ((y ^ x) v (y ^ z)) = y ^ x
    ]]></literal>
    <justification jstring="[para(356(a,1),293(a,1,2,2)),rewrite([364(8),175(5)])].">
      <j1 rule="para" parents="356 293"/>
      <j2 rule="rewrite" parents="364 175"/>
    </justification>
  </clause>

  <clause id="386">
    <literal><![CDATA[
      (x v y) ^ ((z v u) ^ ((x ^ w) v (x ^ (z v u)))) = x ^ (z v u)
    ]]></literal>
    <justification jstring="[para(219(a,1),371(a,1,2,1)),rewrite([2(7),244(8),219(12)])].">
      <j1 rule="para" parents="219 371"/>
      <j2 rule="rewrite" parents="2 244 219"/>
    </justification>
  </clause>

  <clause id="418">
    <literal><![CDATA[
      (x v y) ^ ((z v u) ^ ((x ^ w) v (x ^ v5))) = (z v u) ^ ((x ^ w) v (x ^ v5))
    ]]></literal>
    <justification jstring="[para(45(a,1),244(a,1,1)),rewrite([5(5),5(11)]),flip(a)].">
      <j1 rule="para" parents="45 244"/>
      <j2 rule="rewrite" parents="5 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="419">
    <literal><![CDATA[
      (x v y) ^ ((z ^ u) v (z ^ (x v y))) = z ^ (x v y)
    ]]></literal>
    <justification jstring="[back_rewrite(386),rewrite([418(8)])].">
      <j1 rule="back_rewrite" parents="386"/>
      <j2 rule="rewrite" parents="418"/>
    </justification>
  </clause>

  <clause id="459">
    <literal><![CDATA[
      x ^ ((x ^ y) v ((x ^ z) v (y ^ (x v z)))) = (x ^ y) v (x ^ z)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(11(a,1),327(a,1,2,2)),rewrite([2(5),14(6),2(5),2(12),11(13)])].">
      <j1 rule="para" parents="11 327"/>
      <j2 rule="rewrite" parents="2 14 2 2 11"/>
    </justification>
  </clause>

  <clause id="460">
    <literal><![CDATA[
      (x ^ y) v (x ^ (y v z)) = x ^ (y v z)
    ]]></literal>
    <justification jstring="[para(327(a,1),18(a,1,2,1)),rewrite([2(7),9(7),5(5),2(6),244(7),419(6),27(3),15(5),8(4),5(6),27(6)]),flip(a)].">
      <j1 rule="para" parents="327 18"/>
      <j2 rule="rewrite" parents="2 9 5 2 244 419 27 15 8 5 27"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="534">
    <literal><![CDATA[
      x ^ ((x ^ y) v ((x ^ z) v (z ^ (x v y)))) = (x ^ y) v (x ^ z)
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(2(a,1),459(a,1,2)),rewrite([2(6),14(6),2(10)])].">
      <j1 rule="para" parents="2 459"/>
      <j2 rule="rewrite" parents="2 14 2"/>
    </justification>
  </clause>

  <clause id="577">
    <literal><![CDATA[
      (x ^ y) v (y ^ (x v z)) = y ^ (x v z)
    ]]></literal>
    <justification jstring="[para(5(a,1),460(a,1,1))].">
      <j1 rule="para" parents="5 460"/>
    </justification>
  </clause>

  <clause id="604">
    <literal><![CDATA[
      (x ^ y) v (x ^ z) = x ^ ((x ^ y) v (z ^ (x v y)))
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(534(a,1),460(a,1,2)),rewrite([27(2),32(5),577(8)])].">
      <j1 rule="para" parents="534 460"/>
      <j2 rule="rewrite" parents="27 32 577"/>
    </justification>
  </clause>

  <clause id="680">
    <literal><![CDATA[
      (x ^ y) v (y ^ z) = y ^ ((x ^ y) v (z ^ (x v y)))
    ]]></literal>
    <attribute><![CDATA[
      label(false)
    ]]></attribute>
    <justification jstring="[para(5(a,1),604(a,1,1)),rewrite([5(4),2(5)])].">
      <j1 rule="para" parents="5 604"/>
      <j2 rule="rewrite" parents="5 2"/>
    </justification>
  </clause>

  <clause id="762">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer(H2)
    ]]></attribute>
    <justification jstring="[para(680(a,2),13(a,1,2,2)),rewrite([5(8),2(9),22(10)]),xx(a)].">
      <j1 rule="para" parents="680 13"/>
      <j2 rule="rewrite" parents="5 2 22"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

</proofs>
