<?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>BA3.out</source>

<heading><![CDATA[
Prover9 (32) version April-2007, April 2007.
Process 26496 was started by mccune on cleo,
Fri Apr 13 09:15:16 2007
The command was "/home/mccune/bin/prover9 -f BA3.in".
]]></heading>

<proof number="1" length="141" max_count="29">

<comments><![CDATA[
% Proof 1 at 2.50 (+ 0.03) seconds: distributivity_1.
% Length of proof is 141.
% Level of proof is 46.
% Maximum clause weight is 29.
% Given clauses 299.
]]></comments>

  <clause id="1" type="goal">
    <literal><![CDATA[
      x ^ (y v z) = (x ^ y) v (x ^ z)
    ]]></literal>
    <attribute><![CDATA[
      label(distributivity_1)
    ]]></attribute>
    <attribute><![CDATA[
      label(goal)
    ]]></attribute>
    <justification jstring="[goal].">
      <j1 rule="goal"/>
    </justification>
  </clause>

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

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

  <clause id="4" type="assumption">
    <literal><![CDATA[
      x v x' = y v y'
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

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

  <clause id="6">
    <literal><![CDATA[
      ((x v y')' v (x v y)')' = x
    ]]></literal>
    <justification jstring="[copy(5),rewrite(3(4))].">
      <j1 rule="copy" parents="5"/>
      <j2 rule="rewrite" parents="3"/>
    </justification>
  </clause>

  <clause id="7" type="deny">
    <literal><![CDATA[
      (c1 ^ c2) v (c1 ^ c3) != c1 ^ (c2 v c3)
    ]]></literal>
    <attribute><![CDATA[
      label(distributivity_1)
    ]]></attribute>
    <attribute><![CDATA[
      answer(distributivity_1)
    ]]></attribute>
    <justification jstring="[deny(1)].">
      <j1 rule="deny" parents="1"/>
    </justification>
  </clause>

  <clause id="8">
    <literal><![CDATA[
      (c1' v (c2 v c3)')' != (c1' v c2')' v (c1' v c3')'
    ]]></literal>
    <attribute><![CDATA[
      answer(distributivity_1)
    ]]></attribute>
    <justification jstring="[copy(7),rewrite(3(3),3(9),3(18)),flip(a)].">
      <j1 rule="copy" parents="7"/>
      <j2 rule="rewrite" parents="3 3 3"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9">
    <literal><![CDATA[
      x v x' = c_0
    ]]></literal>
    <justification jstring="[new_symbol(4)].">
      <j1 rule="new_symbol" parents="4"/>
    </justification>
  </clause>

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

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

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

  <clause id="13">
    <literal><![CDATA[
      (x v (x v ((x v y')' v y))')' = (x v y')'
    ]]></literal>
    <justification jstring="[para(6(a,1),6(a,1,1,1)),rewrite(2(5))].">
      <j1 rule="para" parents="6 6"/>
      <j2 rule="rewrite" parents="2"/>
    </justification>
  </clause>

  <clause id="14">
    <literal><![CDATA[
      (((x v y')' v (x v y)'')' v x)' = (x v y')'
    ]]></literal>
    <justification jstring="[para(6(a,1),6(a,1,1,2))].">
      <j1 rule="para" parents="6 6"/>
    </justification>
  </clause>

  <clause id="15">
    <literal><![CDATA[
      x v (y v x') = y v c_0
    ]]></literal>
    <justification jstring="[para(9(a,1),2(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 2"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16">
    <literal><![CDATA[
      (c_0' v (x v x)')' = x
    ]]></literal>
    <justification jstring="[para(9(a,1),6(a,1,1,1,1))].">
      <j1 rule="para" parents="9 6"/>
    </justification>
  </clause>

  <clause id="17">
    <literal><![CDATA[
      ((x v x'')' v c_0')' = x
    ]]></literal>
    <justification jstring="[para(9(a,1),6(a,1,1,2,1))].">
      <j1 rule="para" parents="9 6"/>
    </justification>
  </clause>

  <clause id="18">
    <literal><![CDATA[
      ((x v y')' v (x v y)') v x = c_0
    ]]></literal>
    <justification jstring="[para(6(a,1),9(a,1,2))].">
      <j1 rule="para" parents="6 9"/>
    </justification>
  </clause>

  <clause id="21">
    <literal><![CDATA[
      x v (y v (z v (u v v))) = u v (x v (y v (z v v)))
    ]]></literal>
    <justification jstring="[para(10(a,2),2(a,1,2))].">
      <j1 rule="para" parents="10 2"/>
    </justification>
  </clause>

  <clause id="25">
    <literal><![CDATA[
      x v (y v (z v x')) = y v (z v c_0)
    ]]></literal>
    <justification jstring="[para(9(a,1),10(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 10"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34">
    <literal><![CDATA[
      ((x v (y v x')')' v (y v c_0)')' = x
    ]]></literal>
    <justification jstring="[para(15(a,1),6(a,1,1,2,1))].">
      <j1 rule="para" parents="15 6"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      (c_0' v (x v ((x v y) v y))')' = x v y
    ]]></literal>
    <justification jstring="[para(2(a,1),16(a,1,1,2,1))].">
      <j1 rule="para" parents="2 16"/>
    </justification>
  </clause>

  <clause id="39">
    <literal><![CDATA[
      (x v (c_0' v (x v x))')' = c_0'
    ]]></literal>
    <justification jstring="[para(16(a,1),6(a,1,1,1))].">
      <j1 rule="para" parents="16 6"/>
    </justification>
  </clause>

  <clause id="41">
    <literal><![CDATA[
      (c_0' v (x v x)') v x = c_0
    ]]></literal>
    <justification jstring="[para(16(a,1),9(a,1,2))].">
      <j1 rule="para" parents="16 9"/>
    </justification>
  </clause>

  <clause id="42">
    <literal><![CDATA[
      (c_0' v (x v (y v ((y v (x v z)) v z)))')' = y v (x v z)
    ]]></literal>
    <justification jstring="[para(10(a,1),16(a,1,1,2,1)),rewrite(2(6))].">
      <j1 rule="para" parents="10 16"/>
      <j2 rule="rewrite" parents="2"/>
    </justification>
  </clause>

  <clause id="44">
    <literal><![CDATA[
      (c_0' v (x v x)') v (y v x) = y v c_0
    ]]></literal>
    <justification jstring="[para(16(a,1),15(a,1,2,2))].">
      <j1 rule="para" parents="16 15"/>
    </justification>
  </clause>

  <clause id="45">
    <literal><![CDATA[
      x v ((c_0' v (x v ((x v y) v y))') v y) = c_0
    ]]></literal>
    <justification jstring="[para(41(a,1),2(a,1)),rewrite(2(6)),flip(a)].">
      <j1 rule="para" parents="41 2"/>
      <j2 rule="rewrite" parents="2"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="54">
    <literal><![CDATA[
      (c_0' v (x' v x')') v c_0 = x v c_0
    ]]></literal>
    <justification jstring="[para(41(a,1),15(a,1,2)),flip(a)].">
      <j1 rule="para" parents="41 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="57">
    <literal><![CDATA[
      (((x v x'')' v c_0'')' v x)' = (x v x'')'
    ]]></literal>
    <justification jstring="[para(17(a,1),6(a,1,1,2))].">
      <j1 rule="para" parents="17 6"/>
    </justification>
  </clause>

  <clause id="73">
    <literal><![CDATA[
      (x v (x v (c_0' v x))')' = c_0'
    ]]></literal>
    <justification jstring="[para(16(a,1),11(a,1,1,1))].">
      <j1 rule="para" parents="16 11"/>
    </justification>
  </clause>

  <clause id="82">
    <literal><![CDATA[
      (x v (c_0' v (x v x))') v c_0' = c_0
    ]]></literal>
    <justification jstring="[para(39(a,1),9(a,1,2))].">
      <j1 rule="para" parents="39 9"/>
    </justification>
  </clause>

  <clause id="88">
    <literal><![CDATA[
      (c_0'' v (c_0'' v c_0)')' = c_0'
    ]]></literal>
    <justification jstring="[para(15(a,1),39(a,1,1,2,1))].">
      <j1 rule="para" parents="15 39"/>
    </justification>
  </clause>

  <clause id="103">
    <literal><![CDATA[
      (c_0' v (x v (x v (c_0' v x)))')' = x
    ]]></literal>
    <justification jstring="[para(73(a,1),6(a,1,1,1))].">
      <j1 rule="para" parents="73 6"/>
    </justification>
  </clause>

  <clause id="121">
    <literal><![CDATA[
      ((x' v y')' v (x' v y)') v c_0 = x v c_0
    ]]></literal>
    <justification jstring="[para(18(a,1),15(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="130">
    <literal><![CDATA[
      (c_0' v (x v (c_0' v (x v x)))') v x = c_0
    ]]></literal>
    <justification jstring="[para(39(a,1),18(a,1,1,1))].">
      <j1 rule="para" parents="39 18"/>
    </justification>
  </clause>

  <clause id="133">
    <literal><![CDATA[
      (c_0' v (x v (x v (c_0' v x)))') v x = c_0
    ]]></literal>
    <justification jstring="[para(73(a,1),18(a,1,1,1))].">
      <j1 rule="para" parents="73 18"/>
    </justification>
  </clause>

  <clause id="154">
    <literal><![CDATA[
      (x v (c_0' v (x v x))') v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(82(a,1),15(a,1,2)),flip(a)].">
      <j1 rule="para" parents="82 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="159">
    <literal><![CDATA[
      (c_0' v (c_0'' v (c_0'' v c_0))')' = c_0''
    ]]></literal>
    <justification jstring="[para(88(a,1),6(a,1,1,1))].">
      <j1 rule="para" parents="88 6"/>
    </justification>
  </clause>

  <clause id="175">
    <literal><![CDATA[
      ((x v x'')' v (x v ((x v x'')' v c_0))')' = x
    ]]></literal>
    <justification jstring="[para(17(a,1),13(a,1,1,2,1,2,1)),rewrite(2(11),17(22))].">
      <j1 rule="para" parents="17 13"/>
      <j2 rule="rewrite" parents="2 17"/>
    </justification>
  </clause>

  <clause id="180">
    <literal><![CDATA[
      (x v (y v ((x v (y v x')')' v c_0))')' = (x v (y v x')')'
    ]]></literal>
    <justification jstring="[para(25(a,1),13(a,1,1,2,1)),rewrite(2(8))].">
      <j1 rule="para" parents="25 13"/>
      <j2 rule="rewrite" parents="2"/>
    </justification>
  </clause>

  <clause id="226">
    <literal><![CDATA[
      ((x v (y v c_0)')' v (y v ((c_0' v (z v z)') v (x v z)))')' = x
    ]]></literal>
    <justification jstring="[para(44(a,2),11(a,1,1,2,1,2))].">
      <j1 rule="para" parents="44 11"/>
    </justification>
  </clause>

  <clause id="243">
    <literal><![CDATA[
      ((x v ((x v x'')' v c_0)'')' v (x v x'')')' = x
    ]]></literal>
    <justification jstring="[para(17(a,1),14(a,1,1,1,1,1)),rewrite(17(24))].">
      <j1 rule="para" parents="17 14"/>
      <j2 rule="rewrite" parents="17"/>
    </justification>
  </clause>

  <clause id="314">
    <literal><![CDATA[
      x v (c_0' v (x v x))' = c_0
    ]]></literal>
    <justification jstring="[para(154(a,1),6(a,1,1,2,1)),rewrite(82(9),16(8)),flip(a)].">
      <j1 rule="para" parents="154 6"/>
      <j2 rule="rewrite" parents="82 16"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="320">
    <literal><![CDATA[
      x v (y v (c_0' v (x v x))') = y v c_0
    ]]></literal>
    <justification jstring="[para(314(a,1),2(a,1,2)),flip(a)].">
      <j1 rule="para" parents="314 2"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="322">
    <literal><![CDATA[
      x v (x v (c_0' v x))' = c_0
    ]]></literal>
    <justification jstring="[para(2(a,1),314(a,1,2,1))].">
      <j1 rule="para" parents="2 314"/>
    </justification>
  </clause>

  <clause id="328">
    <literal><![CDATA[
      (c_0' v (x v x)) v c_0 = x v c_0
    ]]></literal>
    <justification jstring="[para(314(a,1),15(a,1,2))].">
      <j1 rule="para" parents="314 15"/>
    </justification>
  </clause>

  <clause id="329">
    <literal><![CDATA[
      c_0'' v (c_0'' v c_0)' = c_0
    ]]></literal>
    <justification jstring="[para(15(a,1),314(a,1,2,1))].">
      <j1 rule="para" parents="15 314"/>
    </justification>
  </clause>

  <clause id="330">
    <literal><![CDATA[
      ((x v (y v (c_0' v (x v x))')')' v (y v c_0)')' = x
    ]]></literal>
    <justification jstring="[para(314(a,1),11(a,1,1,2,1,2))].">
      <j1 rule="para" parents="314 11"/>
    </justification>
  </clause>

  <clause id="335">
    <literal><![CDATA[
      x v (y v (x v (c_0' v x))') = y v c_0
    ]]></literal>
    <justification jstring="[para(322(a,1),2(a,1,2)),flip(a)].">
      <j1 rule="para" parents="322 2"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="338">
    <literal><![CDATA[
      (x v (c_0' v x)) v c_0 = x v c_0
    ]]></literal>
    <justification jstring="[para(322(a,1),15(a,1,2))].">
      <j1 rule="para" parents="322 15"/>
    </justification>
  </clause>

  <clause id="353">
    <literal><![CDATA[
      (c_0'' v c_0) v c_0 = c_0'' v c_0
    ]]></literal>
    <justification jstring="[para(15(a,1),328(a,1,1))].">
      <j1 rule="para" parents="15 328"/>
    </justification>
  </clause>

  <clause id="393">
    <literal><![CDATA[
      (c_0'' v c_0) v (x v c_0) = x v (c_0'' v c_0)
    ]]></literal>
    <justification jstring="[para(329(a,1),25(a,1,2,2))].">
      <j1 rule="para" parents="329 25"/>
    </justification>
  </clause>

  <clause id="451">
    <literal><![CDATA[
      (c_0' v (x v x)) v (y v c_0) = x v (y v c_0)
    ]]></literal>
    <justification jstring="[para(320(a,1),25(a,1,2))].">
      <j1 rule="para" parents="320 25"/>
    </justification>
  </clause>

  <clause id="456">
    <literal><![CDATA[
      ((x v x)' v ((x v (c_0' v x)')' v c_0)')' = x
    ]]></literal>
    <justification jstring="[para(335(a,1),12(a,1,1,2,1))].">
      <j1 rule="para" parents="335 12"/>
    </justification>
  </clause>

  <clause id="463">
    <literal><![CDATA[
      ((x v y)' v ((y v (z v y')')' v (x v (z v c_0)'))')' = x
    ]]></literal>
    <justification jstring="[para(34(a,1),11(a,1,1,1,1,2))].">
      <j1 rule="para" parents="34 11"/>
    </justification>
  </clause>

  <clause id="486">
    <literal><![CDATA[
      c_0'' v c_0 = c_0''
    ]]></literal>
    <justification jstring="[para(353(a,1),37(a,1,1,2,1,2,1)),rewrite(353(14),2(13),353(12),159(14),353(10)),flip(a)].">
      <j1 rule="para" parents="353 37"/>
      <j2 rule="rewrite" parents="353 2 353 159 353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="500">
    <literal><![CDATA[
      c_0'' v (x v c_0) = x v c_0''
    ]]></literal>
    <justification jstring="[back_rewrite(393),rewrite(486(5),486(11))].">
      <j1 rule="back_rewrite" parents="393"/>
      <j2 rule="rewrite" parents="486 486"/>
    </justification>
  </clause>

  <clause id="514">
    <literal><![CDATA[
      ((c_0'' v (x v c_0))' v (x v c_0')')' = x
    ]]></literal>
    <justification jstring="[para(500(a,2),6(a,1,1,1,1))].">
      <j1 rule="para" parents="500 6"/>
    </justification>
  </clause>

  <clause id="515">
    <literal><![CDATA[
      c_0' v (c_0'' v (x v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[para(500(a,2),15(a,1,2))].">
      <j1 rule="para" parents="500 15"/>
    </justification>
  </clause>

  <clause id="545">
    <literal><![CDATA[
      c_0'' v (x v c_0) = (x v (c_0' v x)) v c_0''
    ]]></literal>
    <justification jstring="[para(338(a,1),500(a,1,2))].">
      <j1 rule="para" parents="338 500"/>
    </justification>
  </clause>

  <clause id="554">
    <literal><![CDATA[
      c_0'' v (x v (c_0' v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[para(515(a,1),10(a,2))].">
      <j1 rule="para" parents="515 10"/>
    </justification>
  </clause>

  <clause id="567">
    <literal><![CDATA[
      (c_0' v (c_0' v ((c_0' v c_0) v c_0))') v c_0 = c_0''
    ]]></literal>
    <justification jstring="[para(41(a,1),554(a,1,2)),rewrite(486(5),2(14)),flip(a)].">
      <j1 rule="para" parents="41 554"/>
      <j2 rule="rewrite" parents="486 2"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="736">
    <literal><![CDATA[
      c_0 v (c_0' v c_0) = c_0
    ]]></literal>
    <justification jstring="[para(451(a,1),37(a,1,1,2,1,2)),rewrite(2(10),2(9),103(13),2(7)),flip(a)].">
      <j1 rule="para" parents="451 37"/>
      <j2 rule="rewrite" parents="2 2 103 2"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="747">
    <literal><![CDATA[
      c_0'' = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(736(a,1),44(a,1,2)),rewrite(2(11),567(15))].">
      <j1 rule="para" parents="736 44"/>
      <j2 rule="rewrite" parents="2 567"/>
    </justification>
  </clause>

  <clause id="801">
    <literal><![CDATA[
      (c_0' v (c_0' v ((c_0' v c_0) v c_0))') v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[back_rewrite(567),rewrite(747(18))].">
      <j1 rule="back_rewrite" parents="567"/>
      <j2 rule="rewrite" parents="747"/>
    </justification>
  </clause>

  <clause id="814">
    <literal><![CDATA[
      (c_0 v c_0) v (x v (c_0' v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[back_rewrite(554),rewrite(747(3))].">
      <j1 rule="back_rewrite" parents="554"/>
      <j2 rule="rewrite" parents="747"/>
    </justification>
  </clause>

  <clause id="823">
    <literal><![CDATA[
      (c_0 v c_0) v (x v c_0) = c_0 v (x v c_0)
    ]]></literal>
    <justification jstring="[back_rewrite(545),rewrite(747(3),747(13),2(14),338(13))].">
      <j1 rule="back_rewrite" parents="545"/>
      <j2 rule="rewrite" parents="747 747 2 338"/>
    </justification>
  </clause>

  <clause id="841">
    <literal><![CDATA[
      ((c_0 v (x v c_0))' v (x v c_0')')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(514),rewrite(747(3),823(6))].">
      <j1 rule="back_rewrite" parents="514"/>
      <j2 rule="rewrite" parents="747 823"/>
    </justification>
  </clause>

  <clause id="862">
    <literal><![CDATA[
      ((c_0 v ((x v x'')' v c_0))' v x)' = (x v x'')'
    ]]></literal>
    <justification jstring="[back_rewrite(57),rewrite(747(7),2(8))].">
      <j1 rule="back_rewrite" parents="57"/>
      <j2 rule="rewrite" parents="747 2"/>
    </justification>
  </clause>

  <clause id="876">
    <literal><![CDATA[
      ((c_0 v (c_0 v c_0))' v c_0')' = c_0
    ]]></literal>
    <justification jstring="[para(747(a,1),17(a,1,1,1,1,2))].">
      <j1 rule="para" parents="747 17"/>
    </justification>
  </clause>

  <clause id="1039">
    <literal><![CDATA[
      c_0' v (c_0' v c_0')' = c_0
    ]]></literal>
    <justification jstring="[para(41(a,1),841(a,1,1,2,1)),rewrite(54(12),876(10)),flip(a)].">
      <j1 rule="para" parents="41 841"/>
      <j2 rule="rewrite" parents="54 876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1044">
    <literal><![CDATA[
      (c_0' v x')' v (c_0' v x)' = c_0
    ]]></literal>
    <justification jstring="[para(18(a,1),841(a,1,1,2,1)),rewrite(121(13),876(10)),flip(a)].">
      <j1 rule="para" parents="18 841"/>
      <j2 rule="rewrite" parents="121 876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1055">
    <literal><![CDATA[
      c_0' v (x v (c_0' v c_0')') = x v c_0
    ]]></literal>
    <justification jstring="[para(1039(a,1),2(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1039 2"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1104">
    <literal><![CDATA[
      (c_0' v x')' v c_0 = (c_0' v x) v c_0
    ]]></literal>
    <justification jstring="[para(1044(a,1),15(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1044 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1188">
    <literal><![CDATA[
      (c_0' v ((c_0' v c_0) v ((c_0' v c_0) v c_0))') v (c_0' v c_0')' = c_0
    ]]></literal>
    <justification jstring="[para(1055(a,1),130(a,1,1,2,1,2)),rewrite(1104(16),2(15),1104(14))].">
      <j1 rule="para" parents="1055 130"/>
      <j2 rule="rewrite" parents="1104 2 1104"/>
    </justification>
  </clause>

  <clause id="1189">
    <literal><![CDATA[
      (c_0' v ((c_0' v c_0) v ((c_0' v c_0) v c_0))') v c_0 = c_0' v c_0
    ]]></literal>
    <justification jstring="[para(130(a,1),1055(a,1,2)),rewrite(1055(28),1104(20),2(19),1104(18)),flip(a)].">
      <j1 rule="para" parents="130 1055"/>
      <j2 rule="rewrite" parents="1055 1104 2 1104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1204">
    <literal><![CDATA[
      (c_0' v c_0')' = c_0' v c_0
    ]]></literal>
    <justification jstring="[para(1104(a,1),13(a,1,1,2,1,2)),rewrite(37(14)),flip(a)].">
      <j1 rule="para" parents="1104 13"/>
      <j2 rule="rewrite" parents="37"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1241">
    <literal><![CDATA[
      c_0' v (c_0' v c_0) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(1188),rewrite(1204(21),2(20),1189(19))].">
      <j1 rule="back_rewrite" parents="1188"/>
      <j2 rule="rewrite" parents="1204 2 1189"/>
    </justification>
  </clause>

  <clause id="1259">
    <literal><![CDATA[
      c_0' v (x v (c_0' v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[back_rewrite(1055),rewrite(1204(8))].">
      <j1 rule="back_rewrite" parents="1055"/>
      <j2 rule="rewrite" parents="1204"/>
    </justification>
  </clause>

  <clause id="1262">
    <literal><![CDATA[
      c_0' v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(1241(a,1),44(a,1,2)),rewrite(2(11),801(15)),flip(a)].">
      <j1 rule="para" parents="1241 44"/>
      <j2 rule="rewrite" parents="2 801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1263">
    <literal><![CDATA[
      c_0 v (c_0 v c_0) = c_0
    ]]></literal>
    <justification jstring="[para(44(a,2),1241(a,1,2)),rewrite(2(11),41(10),1262(6),2(6),1262(5))].">
      <j1 rule="para" parents="44 1241"/>
      <j2 rule="rewrite" parents="2 41 1262 2 1262"/>
    </justification>
  </clause>

  <clause id="1264">
    <literal><![CDATA[
      c_0 v c_0 = c_0
    ]]></literal>
    <justification jstring="[para(1241(a,1),14(a,1,1,1,1,2,1,1)),rewrite(1262(6),16(8),747(4),1263(5),1204(6),1262(4),1262(9),16(11))].">
      <j1 rule="para" parents="1241 14"/>
      <j2 rule="rewrite" parents="1262 16 747 1263 1204 1262 1262 16"/>
    </justification>
  </clause>

  <clause id="1270">
    <literal><![CDATA[
      c_0' v (x v (y v c_0)) = x v (y v c_0)
    ]]></literal>
    <justification jstring="[para(1241(a,1),21(a,1,2,2)),rewrite(1262(9),1264(8)),flip(a)].">
      <j1 rule="para" parents="1241 21"/>
      <j2 rule="rewrite" parents="1262 1264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1282">
    <literal><![CDATA[
      c_0' v (x v c_0) = x v c_0
    ]]></literal>
    <justification jstring="[back_rewrite(1259),rewrite(1262(6),1264(5))].">
      <j1 rule="back_rewrite" parents="1259"/>
      <j2 rule="rewrite" parents="1262 1264"/>
    </justification>
  </clause>

  <clause id="1302">
    <literal><![CDATA[
      c_0 v (x v c_0) = x v c_0
    ]]></literal>
    <justification jstring="[back_rewrite(814),rewrite(1264(3),1262(5),1264(4))].">
      <j1 rule="back_rewrite" parents="814"/>
      <j2 rule="rewrite" parents="1264 1262 1264"/>
    </justification>
  </clause>

  <clause id="1312">
    <literal><![CDATA[
      c_0' v c_0 = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(1262),rewrite(1264(7))].">
      <j1 rule="back_rewrite" parents="1262"/>
      <j2 rule="rewrite" parents="1264"/>
    </justification>
  </clause>

  <clause id="1348">
    <literal><![CDATA[
      c_0'' = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(747),rewrite(1264(6))].">
      <j1 rule="back_rewrite" parents="747"/>
      <j2 rule="rewrite" parents="1264"/>
    </justification>
  </clause>

  <clause id="1353">
    <literal><![CDATA[
      (((x v x'')' v c_0)' v x)' = (x v x'')'
    ]]></literal>
    <justification jstring="[back_rewrite(862),rewrite(1302(8))].">
      <j1 rule="back_rewrite" parents="862"/>
      <j2 rule="rewrite" parents="1302"/>
    </justification>
  </clause>

  <clause id="1357">
    <literal><![CDATA[
      (c_0' v (x v ((x v c_0) v ((x v c_0) v c_0)))')' = x v ((x v c_0) v c_0)
    ]]></literal>
    <justification jstring="[para(451(a,1),42(a,1,1,2,1,2,2)),rewrite(2(11),1270(12),2(10),2(20),1270(21))].">
      <j1 rule="para" parents="451 42"/>
      <j2 rule="rewrite" parents="2 1270 2 2 1270"/>
    </justification>
  </clause>

  <clause id="1371">
    <literal><![CDATA[
      x v ((x v c_0) v c_0) = x v c_0
    ]]></literal>
    <justification jstring="[para(1282(a,1),103(a,1,1,2,1,2,2)),rewrite(2(9),2(10),1357(13))].">
      <j1 rule="para" parents="1282 103"/>
      <j2 rule="rewrite" parents="2 2 1357"/>
    </justification>
  </clause>

  <clause id="1372">
    <literal><![CDATA[
      (c_0' v (x v c_0)')' = x v c_0
    ]]></literal>
    <justification jstring="[para(1282(a,1),37(a,1,1,2,1,2,1)),rewrite(2(9),1371(9),1282(7),1282(12))].">
      <j1 rule="para" parents="1282 37"/>
      <j2 rule="rewrite" parents="2 1371 1282 1282"/>
    </justification>
  </clause>

  <clause id="1373">
    <literal><![CDATA[
      x v ((c_0' v (x v c_0)') v c_0) = c_0
    ]]></literal>
    <justification jstring="[para(1282(a,1),133(a,1,1,2,1,2,2)),rewrite(2(9),1371(9),2(7),1371(7),2(9))].">
      <j1 rule="para" parents="1282 133"/>
      <j2 rule="rewrite" parents="2 1371 2 1371 2"/>
    </justification>
  </clause>

  <clause id="1378">
    <literal><![CDATA[
      x v (y v ((x v c_0) v c_0)) = y v (x v c_0)
    ]]></literal>
    <justification jstring="[para(1371(a,1),2(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1371 2"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1416">
    <literal><![CDATA[
      x v ((x v c_0) v ((c_0' v (x v c_0)') v c_0)) = c_0
    ]]></literal>
    <justification jstring="[para(1371(a,1),45(a,1,2,1,2,1,2,1)),rewrite(1378(10),2(7),1371(7),2(11))].">
      <j1 rule="para" parents="1371 45"/>
      <j2 rule="rewrite" parents="1378 2 1371 2"/>
    </justification>
  </clause>

  <clause id="1425">
    <literal><![CDATA[
      ((x v c_0)' v c_0')' = x v c_0
    ]]></literal>
    <justification jstring="[para(1372(a,1),34(a,1,1,1,1,2)),rewrite(2(5),1371(5),1312(7))].">
      <j1 rule="para" parents="1372 34"/>
      <j2 rule="rewrite" parents="2 1371 1312"/>
    </justification>
  </clause>

  <clause id="1438">
    <literal><![CDATA[
      ((x v (y v c_0))' v ((y v c_0)' v (x v c_0'))')' = x
    ]]></literal>
    <justification jstring="[para(1425(a,1),11(a,1,1,1,1,2))].">
      <j1 rule="para" parents="1425 11"/>
    </justification>
  </clause>

  <clause id="1445">
    <literal><![CDATA[
      ((x v c_0)' v ((x v c_0) v ((x v c_0)' v c_0))')' = x v c_0
    ]]></literal>
    <justification jstring="[para(1425(a,1),13(a,1,1,2,1,2,1)),rewrite(2(11),1425(21))].">
      <j1 rule="para" parents="1425 13"/>
      <j2 rule="rewrite" parents="2 1425"/>
    </justification>
  </clause>

  <clause id="1450">
    <literal><![CDATA[
      ((x v c_0)' v ((x v c_0)' v c_0)')' = c_0
    ]]></literal>
    <justification jstring="[para(1425(a,1),34(a,1,1,1,1,2)),rewrite(1302(4))].">
      <j1 rule="para" parents="1425 34"/>
      <j2 rule="rewrite" parents="1302"/>
    </justification>
  </clause>

  <clause id="1471">
    <literal><![CDATA[
      x v (y v ((c_0' v (x v c_0)') v c_0)) = y v c_0
    ]]></literal>
    <justification jstring="[para(1373(a,1),2(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1373 2"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1488">
    <literal><![CDATA[
      (x v c_0) v c_0 = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(1416),rewrite(1471(12))].">
      <j1 rule="back_rewrite" parents="1416"/>
      <j2 rule="rewrite" parents="1471"/>
    </justification>
  </clause>

  <clause id="1493">
    <literal><![CDATA[
      (x v c_0) v (y v c_0) = y v c_0
    ]]></literal>
    <justification jstring="[para(1488(a,1),2(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1488 2"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1511">
    <literal><![CDATA[
      x v c_0 = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(1445),rewrite(1493(11),1450(11)),flip(a)].">
      <j1 rule="back_rewrite" parents="1445"/>
      <j2 rule="rewrite" parents="1493 1450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1526">
    <literal><![CDATA[
      (c_0' v (c_0' v (x v c_0'))')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(1438),rewrite(1511(2),1511(2),1511(4))].">
      <j1 rule="back_rewrite" parents="1438"/>
      <j2 rule="rewrite" parents="1511 1511 1511"/>
    </justification>
  </clause>

  <clause id="1537">
    <literal><![CDATA[
      (x v x'')' = (c_0' v x)'
    ]]></literal>
    <justification jstring="[back_rewrite(1353),rewrite(1511(6)),flip(a)].">
      <j1 rule="back_rewrite" parents="1353"/>
      <j2 rule="rewrite" parents="1511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1603">
    <literal><![CDATA[
      ((x v y)' v ((y v (z v y')')' v (x v c_0'))')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(463),rewrite(1511(9))].">
      <j1 rule="back_rewrite" parents="463"/>
      <j2 rule="rewrite" parents="1511"/>
    </justification>
  </clause>

  <clause id="1606">
    <literal><![CDATA[
      ((x v x)' v c_0')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(456),rewrite(1511(10))].">
      <j1 rule="back_rewrite" parents="456"/>
      <j2 rule="rewrite" parents="1511"/>
    </justification>
  </clause>

  <clause id="1627">
    <literal><![CDATA[
      ((x v (y v (c_0' v (x v x))')')' v c_0')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(330),rewrite(1511(11))].">
      <j1 rule="back_rewrite" parents="330"/>
      <j2 rule="rewrite" parents="1511"/>
    </justification>
  </clause>

  <clause id="1634">
    <literal><![CDATA[
      (c_0' v (c_0' v x)')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(243),rewrite(1537(4),1511(6),1348(3),1511(2),1537(6))].">
      <j1 rule="back_rewrite" parents="243"/>
      <j2 rule="rewrite" parents="1537 1511 1348 1511 1537"/>
    </justification>
  </clause>

  <clause id="1635">
    <literal><![CDATA[
      ((x v c_0')' v (y v ((c_0' v (z v z)') v (x v z)))')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(226),rewrite(1511(2))].">
      <j1 rule="back_rewrite" parents="226"/>
      <j2 rule="rewrite" parents="1511"/>
    </justification>
  </clause>

  <clause id="1645">
    <literal><![CDATA[
      (x v (y v x')')' = (x v c_0')'
    ]]></literal>
    <justification jstring="[back_rewrite(180),rewrite(1511(7),1511(2)),flip(a)].">
      <j1 rule="back_rewrite" parents="180"/>
      <j2 rule="rewrite" parents="1511 1511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1646">
    <literal><![CDATA[
      ((c_0' v x)' v c_0')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(175),rewrite(1537(4),1537(8),1511(10),1511(6))].">
      <j1 rule="back_rewrite" parents="175"/>
      <j2 rule="rewrite" parents="1537 1537 1511 1511"/>
    </justification>
  </clause>

  <clause id="1662">
    <literal><![CDATA[
      (c_0' v (x v x)') v (y v x) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(44),rewrite(1511(9))].">
      <j1 rule="back_rewrite" parents="44"/>
      <j2 rule="rewrite" parents="1511"/>
    </justification>
  </clause>

  <clause id="1677">
    <literal><![CDATA[
      x v c_0' = x
    ]]></literal>
    <justification jstring="[back_rewrite(1526),rewrite(1634(11))].">
      <j1 rule="back_rewrite" parents="1526"/>
      <j2 rule="rewrite" parents="1634"/>
    </justification>
  </clause>

  <clause id="1685">
    <literal><![CDATA[
      x'' = x
    ]]></literal>
    <justification jstring="[back_rewrite(1635),rewrite(1677(3),1662(8),1511(3),1677(4))].">
      <j1 rule="back_rewrite" parents="1635"/>
      <j2 rule="rewrite" parents="1677 1662 1511 1677"/>
    </justification>
  </clause>

  <clause id="1688">
    <literal><![CDATA[
      ((x v y)' v (y' v x)')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(1603),rewrite(1645(7),1677(5),1677(6))].">
      <j1 rule="back_rewrite" parents="1603"/>
      <j2 rule="rewrite" parents="1645 1677 1677"/>
    </justification>
  </clause>

  <clause id="1694">
    <literal><![CDATA[
      c_0' v x = x
    ]]></literal>
    <justification jstring="[back_rewrite(1646),rewrite(1677(7),1685(5))].">
      <j1 rule="back_rewrite" parents="1646"/>
      <j2 rule="rewrite" parents="1677 1685"/>
    </justification>
  </clause>

  <clause id="1696">
    <literal><![CDATA[
      x v (y v (x v x)')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(1627),rewrite(1694(4),1677(9),1685(7))].">
      <j1 rule="back_rewrite" parents="1627"/>
      <j2 rule="rewrite" parents="1694 1677 1685"/>
    </justification>
  </clause>

  <clause id="1701">
    <literal><![CDATA[
      x v x = x
    ]]></literal>
    <justification jstring="[back_rewrite(1606),rewrite(1677(5),1685(3))].">
      <j1 rule="back_rewrite" parents="1606"/>
      <j2 rule="rewrite" parents="1677 1685"/>
    </justification>
  </clause>

  <clause id="1750">
    <literal><![CDATA[
      x v (y v x')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(1696),rewrite(1701(1))].">
      <j1 rule="back_rewrite" parents="1696"/>
      <j2 rule="rewrite" parents="1701"/>
    </justification>
  </clause>

  <clause id="1761">
    <literal><![CDATA[
      x v (x v ((x v y')' v y))' = x v y'
    ]]></literal>
    <justification jstring="[para(13(a,1),1685(a,1,1)),rewrite(1685(4)),flip(a)].">
      <j1 rule="para" parents="13 1685"/>
      <j2 rule="rewrite" parents="1685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1800">
    <literal><![CDATA[
      x v y = y v x
    ]]></literal>
    <justification jstring="[para(1677(a,1),2(a,1,2)),rewrite(1677(4))].">
      <j1 rule="para" parents="1677 2"/>
      <j2 rule="rewrite" parents="1677"/>
    </justification>
  </clause>

  <clause id="1801">
    <literal><![CDATA[
      x v (y v z) = z v (x v y)
    ]]></literal>
    <justification jstring="[para(1677(a,1),10(a,1,2,2)),rewrite(1677(5))].">
      <j1 rule="para" parents="1677 10"/>
      <j2 rule="rewrite" parents="1677"/>
    </justification>
  </clause>

  <clause id="1826">
    <literal><![CDATA[
      x v (x v y)' = x v y'
    ]]></literal>
    <justification jstring="[back_rewrite(1761),rewrite(1800(4),1750(4))].">
      <j1 rule="back_rewrite" parents="1761"/>
      <j2 rule="rewrite" parents="1800 1750"/>
    </justification>
  </clause>

  <clause id="1974">
    <literal><![CDATA[
      x v (y v (z v x')') = y v x
    ]]></literal>
    <justification jstring="[para(1750(a,1),2(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1750 2"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1979">
    <literal><![CDATA[
      x' v (y v x)' = x'
    ]]></literal>
    <justification jstring="[para(1685(a,1),1750(a,1,2,1,2))].">
      <j1 rule="para" parents="1685 1750"/>
    </justification>
  </clause>

  <clause id="1980">
    <literal><![CDATA[
      x v (x' v y)' = x
    ]]></literal>
    <justification jstring="[para(1800(a,1),1750(a,1,2,1))].">
      <j1 rule="para" parents="1800 1750"/>
    </justification>
  </clause>

  <clause id="1996">
    <literal><![CDATA[
      x v (y v (x' v z)') = y v x
    ]]></literal>
    <justification jstring="[para(1980(a,1),2(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1980 2"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2107">
    <literal><![CDATA[
      (x v y)' v (x v (z v y))' = (x v y)'
    ]]></literal>
    <justification jstring="[para(2(a,1),1979(a,1,2,1))].">
      <j1 rule="para" parents="2 1979"/>
    </justification>
  </clause>

  <clause id="2559">
    <literal><![CDATA[
      (x v y) v z = x v (y v z)
    ]]></literal>
    <justification jstring="[para(1801(a,2),1800(a,1)),flip(a)].">
      <j1 rule="para" parents="1801 1800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2703">
    <literal><![CDATA[
      x v (y v x)' = x v y'
    ]]></literal>
    <justification jstring="[para(1800(a,1),1826(a,1,2,1))].">
      <j1 rule="para" parents="1800 1826"/>
    </justification>
  </clause>

  <clause id="2732">
    <literal><![CDATA[
      x' v ((y v x)' v z) = x' v z
    ]]></literal>
    <justification jstring="[para(1979(a,1),2559(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1979 2559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2741">
    <literal><![CDATA[
      x v (y v (z v x)') = y v (x v z')
    ]]></literal>
    <justification jstring="[para(2703(a,1),2(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2703 2"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2778">
    <literal><![CDATA[
      (x v y)' v (y' v x)' = x'
    ]]></literal>
    <justification jstring="[para(1688(a,1),1685(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1688 1685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2881">
    <literal><![CDATA[
      (x v y)' v (z v (y' v x)') = z v x'
    ]]></literal>
    <justification jstring="[para(2778(a,1),2(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2778 2"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2886">
    <literal><![CDATA[
      (x v (y v z)')' = (x v (z v y'))' v (x v z')'
    ]]></literal>
    <justification jstring="[para(1974(a,1),2778(a,1,2,1)),rewrite(1685(2),1800(4),2741(4),1685(10)),flip(a)].">
      <j1 rule="para" parents="1974 2778"/>
      <j2 rule="rewrite" parents="1685 1800 2741 1685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2895">
    <literal><![CDATA[
      (c3 v (c1' v c2'))' v (c1' v c3')' != (c1' v c2')' v (c1' v c3')'
    ]]></literal>
    <attribute><![CDATA[
      answer(distributivity_1)
    ]]></attribute>
    <justification jstring="[back_rewrite(8),rewrite(2886(8),2(7))].">
      <j1 rule="back_rewrite" parents="8"/>
      <j2 rule="rewrite" parents="2886 2"/>
    </justification>
  </clause>

  <clause id="3052">
    <literal><![CDATA[
      (x v y)' v ((x v (z v y))' v u) = (x v y)' v u
    ]]></literal>
    <justification jstring="[para(2(a,1),2732(a,1,2,1,1))].">
      <j1 rule="para" parents="2 2732"/>
    </justification>
  </clause>

  <clause id="3340">
    <literal><![CDATA[
      (x v (y v z))' v (x v y')' = (x v z)' v (x v y')'
    ]]></literal>
    <justification jstring="[para(1980(a,1),2107(a,1,2,1,2)),rewrite(2886(5),1685(2),1800(10),3052(10),2886(11),1685(8)),flip(a)].">
      <j1 rule="para" parents="1980 2107"/>
      <j2 rule="rewrite" parents="2886 1685 1800 3052 2886 1685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3352">
    <literal><![CDATA[
      (x v (y v z)')' = (x v y')' v (x v z')'
    ]]></literal>
    <justification jstring="[back_rewrite(2886),rewrite(3340(12))].">
      <j1 rule="back_rewrite" parents="2886"/>
      <j2 rule="rewrite" parents="3340"/>
    </justification>
  </clause>

  <clause id="3785">
    <literal><![CDATA[
      (x v (y v z))' v (y v x')' = (y v z)' v (y v x')'
    ]]></literal>
    <justification jstring="[para(2881(a,1),2778(a,1,2,1)),rewrite(1800(6),2559(6),1996(5),3352(12),1685(9))].">
      <j1 rule="para" parents="2881 2778"/>
      <j2 rule="rewrite" parents="1800 2559 1996 3352 1685"/>
    </justification>
  </clause>

  <clause id="3786">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer(distributivity_1)
    ]]></attribute>
    <justification jstring="[resolve(3785,a,2895,a)].">
      <j1 rule="resolve" parents="3785 2895"/>
    </justification>
  </clause>

</proof>

</proofs>
