<?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="4">

<source>ba-4basis.out</source>

<heading><![CDATA[
Prover9 (32) version August-2006A, August 2006.
Process 11425 was started by mccune on cleo.thornwood,
Sat Aug 12 21:01:14 2006
The command was "/home/mccune/bin/prover9 -f ba-4basis.in".
]]></heading>

<proof number="1" length="115" max_count="39">

<comments><![CDATA[
% Proof 1 at 0.96 (+ 0.01) seconds: CC.
% Length of proof is 115.
% Level of proof is 30.
% Maximum clause weight is 39.
% Given clauses 112.
]]></comments>

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

  <clause id="5">
    <literal><![CDATA[
      x v (y v z) = y v (x v z)
    ]]></literal>
    <attribute><![CDATA[
      label(AJ)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="6">
    <literal><![CDATA[
      x ^ y = (x' v y')'
    ]]></literal>
    <attribute><![CDATA[
      label(DM)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="7">
    <literal><![CDATA[
      x v x' = y v y'
    ]]></literal>
    <attribute><![CDATA[
      label(ONE)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

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

  <clause id="9">
    <literal><![CDATA[
      ((x v y')' v (x v y)')' = x
    ]]></literal>
    <justification jstring="[copy(8),rewrite(6(4))].">
      <j1 rule="copy" parents="8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="10">
    <literal><![CDATA[
      c1'' != c1
    ]]></literal>
    <attribute><![CDATA[
      answer(CC)
    ]]></attribute>
    <justification jstring="[deny(1)].">
      <j1 rule="deny" parents="1"/>
    </justification>
  </clause>

  <clause id="17">
    <literal><![CDATA[
      x v x' = c_0
    ]]></literal>
    <justification jstring="[new_symbol(7)].">
      <j1 rule="new_symbol" parents="7"/>
    </justification>
  </clause>

  <clause id="18">
    <literal><![CDATA[
      x v (y v (z v u)) = z v (x v (y v u))
    ]]></literal>
    <justification jstring="[para(5(a,1),5(a,1,2))].">
      <j1 rule="para" parents="5 5"/>
    </justification>
  </clause>

  <clause id="19">
    <literal><![CDATA[
      ((x v (y v z)')' v (y v (x v z))')' = x
    ]]></literal>
    <justification jstring="[para(5(a,1),9(a,1,1,2,1))].">
      <j1 rule="para" parents="5 9"/>
    </justification>
  </clause>

  <clause id="21">
    <literal><![CDATA[
      (x v (x v ((x v y')' v y))')' = (x v y')'
    ]]></literal>
    <justification jstring="[para(9(a,1),9(a,1,1,1)),rewrite(5(5))].">
      <j1 rule="para" parents="9 9"/>
      <j2 rule="rewrite" parents="5"/>
    </justification>
  </clause>

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

  <clause id="23">
    <literal><![CDATA[
      x v (y v x') = y v c_0
    ]]></literal>
    <justification jstring="[para(17(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24">
    <literal><![CDATA[
      (c_0' v (x v x)')' = x
    ]]></literal>
    <justification jstring="[para(17(a,1),9(a,1,1,1,1))].">
      <j1 rule="para" parents="17 9"/>
    </justification>
  </clause>

  <clause id="25">
    <literal><![CDATA[
      ((x v x'')' v c_0')' = x
    ]]></literal>
    <justification jstring="[para(17(a,1),9(a,1,1,2,1))].">
      <j1 rule="para" parents="17 9"/>
    </justification>
  </clause>

  <clause id="26">
    <literal><![CDATA[
      ((x v y')' v (x v y)') v x = c_0
    ]]></literal>
    <justification jstring="[para(9(a,1),17(a,1,2))].">
      <j1 rule="para" parents="9 17"/>
    </justification>
  </clause>

  <clause id="27">
    <literal><![CDATA[
      x v (y v (z v x')) = y v (z v c_0)
    ]]></literal>
    <justification jstring="[para(23(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="23 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28">
    <literal><![CDATA[
      ((x v (y v x')')' v (y v c_0)')' = x
    ]]></literal>
    <justification jstring="[para(23(a,1),9(a,1,1,2,1))].">
      <j1 rule="para" parents="23 9"/>
    </justification>
  </clause>

  <clause id="30">
    <literal><![CDATA[
      (c_0' v (x v ((x v y) v y))')' = x v y
    ]]></literal>
    <justification jstring="[para(5(a,1),24(a,1,1,2,1))].">
      <j1 rule="para" parents="5 24"/>
    </justification>
  </clause>

  <clause id="32">
    <literal><![CDATA[
      (x v (c_0' v (x v x))')' = c_0'
    ]]></literal>
    <justification jstring="[para(24(a,1),9(a,1,1,1))].">
      <j1 rule="para" parents="24 9"/>
    </justification>
  </clause>

  <clause id="33">
    <literal><![CDATA[
      ((c_0' v (x v x)'')' v x)' = c_0'
    ]]></literal>
    <justification jstring="[para(24(a,1),9(a,1,1,2))].">
      <j1 rule="para" parents="24 9"/>
    </justification>
  </clause>

  <clause id="34">
    <literal><![CDATA[
      (c_0' v (x v x)') v x = c_0
    ]]></literal>
    <justification jstring="[para(24(a,1),17(a,1,2))].">
      <j1 rule="para" parents="24 17"/>
    </justification>
  </clause>

  <clause id="35">
    <literal><![CDATA[
      (c_0' v (x v x)') v (y v x) = y v c_0
    ]]></literal>
    <justification jstring="[para(24(a,1),23(a,1,2,2))].">
      <j1 rule="para" parents="24 23"/>
    </justification>
  </clause>

  <clause id="36">
    <literal><![CDATA[
      x v (y v (z v (u v v))) = z v (x v (u v (y v v)))
    ]]></literal>
    <justification jstring="[para(18(a,1),5(a,1,2))].">
      <j1 rule="para" parents="18 5"/>
    </justification>
  </clause>

  <clause id="40">
    <literal><![CDATA[
      ((x v (y v (z v u))')' v (z v (x v (y v u)))')' = x
    ]]></literal>
    <justification jstring="[para(18(a,1),9(a,1,1,2,1))].">
      <j1 rule="para" parents="18 9"/>
    </justification>
  </clause>

  <clause id="41">
    <literal><![CDATA[
      ((x v (y v (z v u))')' v (y v (z v (x v u)))')' = x
    ]]></literal>
    <justification jstring="[para(18(a,2),9(a,1,1,2,1))].">
      <j1 rule="para" parents="18 9"/>
    </justification>
  </clause>

  <clause id="42">
    <literal><![CDATA[
      x v (y v (z v (u v x'))) = y v (z v (u v c_0))
    ]]></literal>
    <justification jstring="[para(23(a,1),18(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="23 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43">
    <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(18(a,1),24(a,1,1,2,1)),rewrite(5(6))].">
      <j1 rule="para" parents="18 24"/>
      <j2 rule="rewrite" parents="5"/>
    </justification>
  </clause>

  <clause id="56">
    <literal><![CDATA[
      (c_0' v (x' v x')') v c_0 = x v c_0
    ]]></literal>
    <justification jstring="[para(34(a,1),23(a,1,2)),flip(a)].">
      <j1 rule="para" parents="34 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="65">
    <literal><![CDATA[
      (x v ((x v x'')' v c_0)')' = (x v x'')'
    ]]></literal>
    <justification jstring="[para(25(a,1),9(a,1,1,1))].">
      <j1 rule="para" parents="25 9"/>
    </justification>
  </clause>

  <clause id="68">
    <literal><![CDATA[
      ((x v x'')' v c_0') v x = c_0
    ]]></literal>
    <justification jstring="[para(25(a,1),17(a,1,2))].">
      <j1 rule="para" parents="25 17"/>
    </justification>
  </clause>

  <clause id="72">
    <literal><![CDATA[
      (x v (x v (c_0' v x))')' = c_0'
    ]]></literal>
    <justification jstring="[para(5(a,1),32(a,1,1,2,1))].">
      <j1 rule="para" parents="5 32"/>
    </justification>
  </clause>

  <clause id="74">
    <literal><![CDATA[
      (c_0' v (x v (c_0' v (x v x)))')' = x
    ]]></literal>
    <justification jstring="[para(32(a,1),9(a,1,1,1))].">
      <j1 rule="para" parents="32 9"/>
    </justification>
  </clause>

  <clause id="76">
    <literal><![CDATA[
      (x v (c_0' v (x v x))') v c_0' = c_0
    ]]></literal>
    <justification jstring="[para(32(a,1),17(a,1,2))].">
      <j1 rule="para" parents="32 17"/>
    </justification>
  </clause>

  <clause id="126">
    <literal><![CDATA[
      (c_0' v (x v (x v (c_0' v x)))')' = x
    ]]></literal>
    <justification jstring="[para(72(a,1),9(a,1,1,1))].">
      <j1 rule="para" parents="72 9"/>
    </justification>
  </clause>

  <clause id="144">
    <literal><![CDATA[
      ((c_0' v (x v x)'')' v x) v c_0' = c_0
    ]]></literal>
    <justification jstring="[para(24(a,1),26(a,1,1,2))].">
      <j1 rule="para" parents="24 26"/>
    </justification>
  </clause>

  <clause id="169">
    <literal><![CDATA[
      (c_0' v (x v (x v (c_0' v x)))') v x = c_0
    ]]></literal>
    <justification jstring="[para(72(a,1),26(a,1,1,1))].">
      <j1 rule="para" parents="72 26"/>
    </justification>
  </clause>

  <clause id="183">
    <literal><![CDATA[
      (c_0' v ((x v (c_0' v (x v x))') v c_0)')' = x v (c_0' v (x v x))'
    ]]></literal>
    <justification jstring="[para(76(a,1),9(a,1,1,1,1))].">
      <j1 rule="para" parents="76 9"/>
    </justification>
  </clause>

  <clause id="184">
    <literal><![CDATA[
      (x v (c_0' v (x v x))') v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(76(a,1),23(a,1,2)),flip(a)].">
      <j1 rule="para" parents="76 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="193">
    <literal><![CDATA[
      x v (c_0' v (x v x))' = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(183),rewrite(184(10),24(8)),flip(a)].">
      <j1 rule="back_rewrite" parents="183"/>
      <j2 rule="rewrite" parents="184 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="251">
    <literal><![CDATA[
      x v (y v (c_0' v (x v x))') = y v c_0
    ]]></literal>
    <justification jstring="[para(193(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="193 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="254">
    <literal><![CDATA[
      (c_0' v (x v x)) v c_0 = x v c_0
    ]]></literal>
    <justification jstring="[para(193(a,1),23(a,1,2))].">
      <j1 rule="para" parents="193 23"/>
    </justification>
  </clause>

  <clause id="255">
    <literal><![CDATA[
      c_0'' v (c_0'' v c_0)' = c_0
    ]]></literal>
    <justification jstring="[para(23(a,1),193(a,1,2,1))].">
      <j1 rule="para" parents="23 193"/>
    </justification>
  </clause>

  <clause id="280">
    <literal><![CDATA[
      (c_0'' v c_0) v c_0 = c_0'' v c_0
    ]]></literal>
    <justification jstring="[para(23(a,1),254(a,1,1))].">
      <j1 rule="para" parents="23 254"/>
    </justification>
  </clause>

  <clause id="294">
    <literal><![CDATA[
      (c_0' v (c_0'' v (c_0'' v c_0))')' = c_0''
    ]]></literal>
    <justification jstring="[para(255(a,1),9(a,1,1,1,1))].">
      <j1 rule="para" parents="255 9"/>
    </justification>
  </clause>

  <clause id="300">
    <literal><![CDATA[
      (c_0'' v c_0) v (x v c_0) = x v (c_0'' v c_0)
    ]]></literal>
    <justification jstring="[para(255(a,1),27(a,1,2,2))].">
      <j1 rule="para" parents="255 27"/>
    </justification>
  </clause>

  <clause id="540">
    <literal><![CDATA[
      ((c_0' v (x v x)'')' v x) v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(33(a,1),56(a,1,1,2,1,1)),rewrite(33(13),56(11)),flip(a)].">
      <j1 rule="para" parents="33 56"/>
      <j2 rule="rewrite" parents="33 56"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="545">
    <literal><![CDATA[
      (c_0' v ((x v y) v (c_0' v (x v ((x v y) v y))))')' = x v y
    ]]></literal>
    <justification jstring="[para(5(a,1),74(a,1,1,2,1,2,2))].">
      <j1 rule="para" parents="5 74"/>
    </justification>
  </clause>

  <clause id="676">
    <literal><![CDATA[
      (c_0' v (x v x)) v (y v c_0) = x v (y v c_0)
    ]]></literal>
    <justification jstring="[para(251(a,1),27(a,1,2))].">
      <j1 rule="para" parents="251 27"/>
    </justification>
  </clause>

  <clause id="812">
    <literal><![CDATA[
      (c_0' v c_0''')' v c_0' = (c_0' v c_0''')'
    ]]></literal>
    <justification jstring="[para(68(a,1),30(a,1,1,2,1,2)),rewrite(65(15)),flip(a)].">
      <j1 rule="para" parents="68 30"/>
      <j2 rule="rewrite" parents="65"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="821">
    <literal><![CDATA[
      c_0'' v c_0 = c_0''
    ]]></literal>
    <justification jstring="[para(280(a,1),30(a,1,1,2,1,2,1)),rewrite(280(14),5(13),280(12),294(14),280(10)),flip(a)].">
      <j1 rule="para" parents="280 30"/>
      <j2 rule="rewrite" parents="280 5 280 294 280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="851">
    <literal><![CDATA[
      c_0'' v (x v c_0) = x v c_0''
    ]]></literal>
    <justification jstring="[back_rewrite(300),rewrite(821(5),821(11))].">
      <j1 rule="back_rewrite" parents="300"/>
      <j2 rule="rewrite" parents="821 821"/>
    </justification>
  </clause>

  <clause id="853">
    <literal><![CDATA[
      (c_0' v (c_0 v c_0)') v c_0'' = c_0''
    ]]></literal>
    <justification jstring="[para(821(a,1),35(a,1,2)),rewrite(821(16))].">
      <j1 rule="para" parents="821 35"/>
      <j2 rule="rewrite" parents="821"/>
    </justification>
  </clause>

  <clause id="858">
    <literal><![CDATA[
      c_0' v (c_0'' v (x v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[para(851(a,2),23(a,1,2))].">
      <j1 rule="para" parents="851 23"/>
    </justification>
  </clause>

  <clause id="907">
    <literal><![CDATA[
      c_0'' v (x v (c_0' v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[para(858(a,1),18(a,2))].">
      <j1 rule="para" parents="858 18"/>
    </justification>
  </clause>

  <clause id="995">
    <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(34(a,1),907(a,1,2)),rewrite(821(5),5(14)),flip(a)].">
      <j1 rule="para" parents="34 907"/>
      <j2 rule="rewrite" parents="821 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1002">
    <literal><![CDATA[
      x v ((c_0' v (x v (c_0' v ((x v (c_0' v c_0)) v c_0)))') v c_0) = c_0''
    ]]></literal>
    <justification jstring="[para(907(a,1),35(a,1,2)),rewrite(5(13),5(12),5(18),821(23))].">
      <j1 rule="para" parents="907 35"/>
      <j2 rule="rewrite" parents="5 5 5 821"/>
    </justification>
  </clause>

  <clause id="1019">
    <literal><![CDATA[
      (c_0' v c_0''')'' = c_0'
    ]]></literal>
    <justification jstring="[para(853(a,1),28(a,1,1,1,1,2,1)),rewrite(34(17),812(11))].">
      <j1 rule="para" parents="853 28"/>
      <j2 rule="rewrite" parents="34 812"/>
    </justification>
  </clause>

  <clause id="1024">
    <literal><![CDATA[
      (c_0' v c_0''')' = c_0
    ]]></literal>
    <justification jstring="[para(1019(a,1),17(a,1,2)),rewrite(812(11))].">
      <j1 rule="para" parents="1019 17"/>
      <j2 rule="rewrite" parents="812"/>
    </justification>
  </clause>

  <clause id="1029">
    <literal><![CDATA[
      ((c_0' v c_0'''')' v c_0)' = c_0'
    ]]></literal>
    <justification jstring="[para(1024(a,1),9(a,1,1,2))].">
      <j1 rule="para" parents="1024 9"/>
    </justification>
  </clause>

  <clause id="1224">
    <literal><![CDATA[
      ((((c_0' v c_0'''')' v c_0) v c_0'')' v c_0')' = (c_0' v c_0'''')' v c_0
    ]]></literal>
    <justification jstring="[para(1029(a,1),25(a,1,1,1,1,2,1))].">
      <j1 rule="para" parents="1029 25"/>
    </justification>
  </clause>

  <clause id="1447">
    <literal><![CDATA[
      (c_0' v (x v x)'')' v x = c_0
    ]]></literal>
    <justification jstring="[para(144(a,1),9(a,1,1,1,1)),rewrite(540(12),24(8)),flip(a)].">
      <j1 rule="para" parents="144 9"/>
      <j2 rule="rewrite" parents="540 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1462">
    <literal><![CDATA[
      (c_0' v (x v x)'')' v (y v x) = y v c_0
    ]]></literal>
    <justification jstring="[para(1447(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1447 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1519">
    <literal><![CDATA[
      ((x v (y v (z v (u v x')))')' v (z v (y v (u v c_0)))')' = x
    ]]></literal>
    <justification jstring="[para(27(a,1),40(a,1,1,2,1,2))].">
      <j1 rule="para" parents="27 40"/>
    </justification>
  </clause>

  <clause id="1822">
    <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(1447(a,1),41(a,1,1,1,1,2,1,2))].">
      <j1 rule="para" parents="1447 41"/>
    </justification>
  </clause>

  <clause id="1916">
    <literal><![CDATA[
      c_0 v (c_0' v c_0) = c_0
    ]]></literal>
    <justification jstring="[para(676(a,1),30(a,1,1,2,1,2)),rewrite(5(10),5(9),126(13),5(7)),flip(a)].">
      <j1 rule="para" parents="676 30"/>
      <j2 rule="rewrite" parents="5 5 126 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1943">
    <literal><![CDATA[
      c_0 v (c_0' v (x v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[para(1916(a,1),18(a,2,2))].">
      <j1 rule="para" parents="1916 18"/>
    </justification>
  </clause>

  <clause id="1948">
    <literal><![CDATA[
      c_0'' = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(1916(a,1),35(a,1,2)),rewrite(5(11),995(15))].">
      <j1 rule="para" parents="1916 35"/>
      <j2 rule="rewrite" parents="5 995"/>
    </justification>
  </clause>

  <clause id="2028">
    <literal><![CDATA[
      ((c_0 v (c_0 v c_0))' v c_0')' = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(1224),rewrite(1948(5),1447(11),1948(4),1948(15),1447(21))].">
      <j1 rule="back_rewrite" parents="1224"/>
      <j2 rule="rewrite" parents="1948 1447 1948 1948 1447"/>
    </justification>
  </clause>

  <clause id="2067">
    <literal><![CDATA[
      x v ((c_0' v (x v (c_0' v ((x v (c_0' v c_0)) v c_0)))') v c_0) = c_0 v c_0
    ]]></literal>
    <justification jstring="[back_rewrite(1002),rewrite(1948(21))].">
      <j1 rule="back_rewrite" parents="1002"/>
      <j2 rule="rewrite" parents="1948"/>
    </justification>
  </clause>

  <clause id="2074">
    <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(995),rewrite(1948(18))].">
      <j1 rule="back_rewrite" parents="995"/>
      <j2 rule="rewrite" parents="1948"/>
    </justification>
  </clause>

  <clause id="2096">
    <literal><![CDATA[
      (c_0 v c_0) v (x v (c_0' v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[back_rewrite(907),rewrite(1948(3))].">
      <j1 rule="back_rewrite" parents="907"/>
      <j2 rule="rewrite" parents="1948"/>
    </justification>
  </clause>

  <clause id="2204">
    <literal><![CDATA[
      (((x v (y v (z v (u v x')))')' v (y v (z v (u v c_0)))'')' v x)' = (x v (y v (z v (u v x')))')'
    ]]></literal>
    <justification jstring="[para(42(a,1),22(a,1,1,1,1,2,1,1))].">
      <j1 rule="para" parents="42 22"/>
    </justification>
  </clause>

  <clause id="2316">
    <literal><![CDATA[
      c_0' v (x v ((x v c_0) v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[para(676(a,1),43(a,1,1,2,1,2,2)),rewrite(5(11),545(16),5(9)),flip(a)].">
      <j1 rule="para" parents="676 43"/>
      <j2 rule="rewrite" parents="5 545 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2318">
    <literal><![CDATA[
      (c_0' v (c_0 v (x v c_0))')' = x v c_0
    ]]></literal>
    <justification jstring="[para(1943(a,1),43(a,1,1,2,1,2,2,1)),rewrite(5(10),5(12),2316(11),1943(16))].">
      <j1 rule="para" parents="1943 43"/>
      <j2 rule="rewrite" parents="5 5 2316 1943"/>
    </justification>
  </clause>

  <clause id="2742">
    <literal><![CDATA[
      x v ((x v c_0) v (c_0' v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[para(2316(a,1),18(a,2))].">
      <j1 rule="para" parents="2316 18"/>
    </justification>
  </clause>

  <clause id="2759">
    <literal><![CDATA[
      x v (y v ((x v c_0) v (c_0' v c_0))) = y v (x v c_0)
    ]]></literal>
    <justification jstring="[para(2316(a,1),36(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2316 36"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2767">
    <literal><![CDATA[
      x v ((x v c_0) v ((c_0' v (x v ((x v ((x v c_0) v c_0)) v ((x v ((x v c_0) v c_0)) v c_0)))') v c_0)) = c_0
    ]]></literal>
    <justification jstring="[para(2316(a,1),169(a,1,1,2,1,2,2)),rewrite(5(15),5(16),5(24),5(23))].">
      <j1 rule="para" parents="2316 169"/>
      <j2 rule="rewrite" parents="5 5 5 5"/>
    </justification>
  </clause>

  <clause id="2793">
    <literal><![CDATA[
      (c_0' v (x v ((x v c_0) v c_0))') v c_0 = (c_0' v (c_0 v (x v c_0))') v c_0
    ]]></literal>
    <justification jstring="[para(2318(a,1),56(a,1,1,2,1,1)),rewrite(2318(13),5(7))].">
      <j1 rule="para" parents="2318 56"/>
      <j2 rule="rewrite" parents="2318 5"/>
    </justification>
  </clause>

  <clause id="2795">
    <literal><![CDATA[
      ((x v ((c_0 v (x v c_0)) v c_0))' v (c_0' v c_0)')' = c_0 v (x v c_0)
    ]]></literal>
    <justification jstring="[para(2318(a,1),28(a,1,1,1,1,2)),rewrite(5(7))].">
      <j1 rule="para" parents="2318 28"/>
      <j2 rule="rewrite" parents="5"/>
    </justification>
  </clause>

  <clause id="2800">
    <literal><![CDATA[
      (c_0' v c_0')' = c_0' v c_0
    ]]></literal>
    <justification jstring="[para(1916(a,1),2318(a,1,1,2,1))].">
      <j1 rule="para" parents="1916 2318"/>
    </justification>
  </clause>

  <clause id="2803">
    <literal><![CDATA[
      (c_0' v c_0') v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[back_rewrite(2074),rewrite(2793(15),1916(8))].">
      <j1 rule="back_rewrite" parents="2074"/>
      <j2 rule="rewrite" parents="2793 1916"/>
    </justification>
  </clause>

  <clause id="2840">
    <literal><![CDATA[
      (c_0' v (c_0' v c_0))' = c_0'
    ]]></literal>
    <justification jstring="[para(2800(a,1),9(a,1,1,2)),rewrite(1948(5),5(6),1916(6))].">
      <j1 rule="para" parents="2800 9"/>
      <j2 rule="rewrite" parents="1948 5 1916"/>
    </justification>
  </clause>

  <clause id="2854">
    <literal><![CDATA[
      (c_0' v (c_0' v c_0)) v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(2800(a,1),56(a,1,1,2))].">
      <j1 rule="para" parents="2800 56"/>
    </justification>
  </clause>

  <clause id="3052">
    <literal><![CDATA[
      c_0' v (c_0' v c_0) = c_0
    ]]></literal>
    <justification jstring="[para(2840(a,1),25(a,1,1,1,1,2,1)),rewrite(1948(10),5(11),2854(10),2028(10)),flip(a)].">
      <j1 rule="para" parents="2840 25"/>
      <j2 rule="rewrite" parents="1948 5 2854 2028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3057">
    <literal><![CDATA[
      c_0' v (x v (c_0' v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[para(3052(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3052 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3063">
    <literal><![CDATA[
      c_0' v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(3052(a,1),35(a,1,2)),rewrite(5(11),2793(15),1916(8),2803(7)),flip(a)].">
      <j1 rule="para" parents="3052 35"/>
      <j2 rule="rewrite" parents="5 2793 1916 2803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3064">
    <literal><![CDATA[
      c_0 v (c_0 v c_0) = c_0
    ]]></literal>
    <justification jstring="[para(35(a,2),3052(a,1,2)),rewrite(5(11),34(10),3063(6),5(6),3063(5))].">
      <j1 rule="para" parents="35 3052"/>
      <j2 rule="rewrite" parents="5 34 3063 5 3063"/>
    </justification>
  </clause>

  <clause id="3065">
    <literal><![CDATA[
      c_0 v c_0 = c_0
    ]]></literal>
    <justification jstring="[para(3052(a,1),22(a,1,1,1,1,2,1,1)),rewrite(3063(6),24(8),1948(4),3064(5),2800(6),3063(4),3063(9),24(11))].">
      <j1 rule="para" parents="3052 22"/>
      <j2 rule="rewrite" parents="3063 24 1948 3064 2800 3063 3063 24"/>
    </justification>
  </clause>

  <clause id="3076">
    <literal><![CDATA[
      c_0' v (x v c_0) = x v c_0
    ]]></literal>
    <justification jstring="[back_rewrite(3057),rewrite(3063(6),3065(5))].">
      <j1 rule="back_rewrite" parents="3057"/>
      <j2 rule="rewrite" parents="3063 3065"/>
    </justification>
  </clause>

  <clause id="3101">
    <literal><![CDATA[
      ((x v ((c_0 v (x v c_0)) v c_0))' v c_0')' = c_0 v (x v c_0)
    ]]></literal>
    <justification jstring="[back_rewrite(2795),rewrite(3063(12),3065(11))].">
      <j1 rule="back_rewrite" parents="2795"/>
      <j2 rule="rewrite" parents="3063 3065"/>
    </justification>
  </clause>

  <clause id="3104">
    <literal><![CDATA[
      x v (y v ((x v c_0) v c_0)) = y v (x v c_0)
    ]]></literal>
    <justification jstring="[back_rewrite(2759),rewrite(3063(6),3065(5))].">
      <j1 rule="back_rewrite" parents="2759"/>
      <j2 rule="rewrite" parents="3063 3065"/>
    </justification>
  </clause>

  <clause id="3106">
    <literal><![CDATA[
      x v ((x v c_0) v c_0) = x v c_0
    ]]></literal>
    <justification jstring="[back_rewrite(2742),rewrite(3063(6),3065(5))].">
      <j1 rule="back_rewrite" parents="2742"/>
      <j2 rule="rewrite" parents="3063 3065"/>
    </justification>
  </clause>

  <clause id="3120">
    <literal><![CDATA[
      c_0 v (x v c_0) = x v c_0
    ]]></literal>
    <justification jstring="[back_rewrite(2096),rewrite(3065(3),3063(5),3065(4))].">
      <j1 rule="back_rewrite" parents="2096"/>
      <j2 rule="rewrite" parents="3065 3063 3065"/>
    </justification>
  </clause>

  <clause id="3125">
    <literal><![CDATA[
      x v ((c_0' v (x v c_0)') v c_0) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(2067),rewrite(3063(8),3065(7),3076(9),3106(7),3065(12))].">
      <j1 rule="back_rewrite" parents="2067"/>
      <j2 rule="rewrite" parents="3063 3065 3076 3106 3065"/>
    </justification>
  </clause>

  <clause id="3177">
    <literal><![CDATA[
      c_0'' = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(1948),rewrite(3065(6))].">
      <j1 rule="back_rewrite" parents="1948"/>
      <j2 rule="rewrite" parents="3065"/>
    </justification>
  </clause>

  <clause id="3191">
    <literal><![CDATA[
      x v ((x v c_0) v ((c_0' v (x v c_0)') v c_0)) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(2767),rewrite(3106(9),3106(11),3104(12),5(9),3106(9))].">
      <j1 rule="back_rewrite" parents="2767"/>
      <j2 rule="rewrite" parents="3106 3106 3104 5 3106"/>
    </justification>
  </clause>

  <clause id="3193">
    <literal><![CDATA[
      ((x v c_0)' v c_0')' = x v c_0
    ]]></literal>
    <justification jstring="[back_rewrite(3101),rewrite(3120(4),3106(5),3120(11))].">
      <j1 rule="back_rewrite" parents="3101"/>
      <j2 rule="rewrite" parents="3120 3106 3120"/>
    </justification>
  </clause>

  <clause id="3877">
    <literal><![CDATA[
      ((x v (y v c_0))' v ((y v c_0)' v (x v c_0'))')' = x
    ]]></literal>
    <justification jstring="[para(3193(a,1),19(a,1,1,1,1,2))].">
      <j1 rule="para" parents="3193 19"/>
    </justification>
  </clause>

  <clause id="3887">
    <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(3193(a,1),21(a,1,1,2,1,2,1)),rewrite(5(11),3193(21))].">
      <j1 rule="para" parents="3193 21"/>
      <j2 rule="rewrite" parents="5 3193"/>
    </justification>
  </clause>

  <clause id="3895">
    <literal><![CDATA[
      ((x v c_0)' v ((x v c_0)' v c_0)')' = c_0
    ]]></literal>
    <justification jstring="[para(3193(a,1),28(a,1,1,1,1,2)),rewrite(3120(4))].">
      <j1 rule="para" parents="3193 28"/>
      <j2 rule="rewrite" parents="3120"/>
    </justification>
  </clause>

  <clause id="3924">
    <literal><![CDATA[
      x v (y v ((c_0' v (x v c_0)') v c_0)) = y v c_0
    ]]></literal>
    <justification jstring="[para(3125(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3125 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3935">
    <literal><![CDATA[
      (((x v ((c_0' v (x v c_0)') v c_0)')' v c_0)' v x)' = (x v ((c_0' v (x v c_0)') v c_0)')'
    ]]></literal>
    <justification jstring="[para(3125(a,1),22(a,1,1,1,1,2,1,1)),rewrite(3177(14))].">
      <j1 rule="para" parents="3125 22"/>
      <j2 rule="rewrite" parents="3177"/>
    </justification>
  </clause>

  <clause id="3948">
    <literal><![CDATA[
      (x v c_0) v c_0 = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(3191),rewrite(3924(12))].">
      <j1 rule="back_rewrite" parents="3191"/>
      <j2 rule="rewrite" parents="3924"/>
    </justification>
  </clause>

  <clause id="4065">
    <literal><![CDATA[
      (x v c_0) v (y v c_0) = y v c_0
    ]]></literal>
    <justification jstring="[para(3948(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3948 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4082">
    <literal><![CDATA[
      x v c_0 = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(3887),rewrite(4065(11),3895(11)),flip(a)].">
      <j1 rule="back_rewrite" parents="3887"/>
      <j2 rule="rewrite" parents="4065 3895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4114">
    <literal><![CDATA[
      (c_0' v x)' = (x v c_0')'
    ]]></literal>
    <justification jstring="[back_rewrite(3935),rewrite(4082(4),4082(7),4082(6),4082(8),4082(11))].">
      <j1 rule="back_rewrite" parents="3935"/>
      <j2 rule="rewrite" parents="4082 4082 4082 4082 4082"/>
    </justification>
  </clause>

  <clause id="4127">
    <literal><![CDATA[
      (c_0' v (c_0' v (x v c_0'))')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(3877),rewrite(4082(2),4082(2),4082(4))].">
      <j1 rule="back_rewrite" parents="3877"/>
      <j2 rule="rewrite" parents="4082 4082 4082"/>
    </justification>
  </clause>

  <clause id="4381">
    <literal><![CDATA[
      (x v (y v (z v (u v x')))')' = (c_0' v x)'
    ]]></literal>
    <justification jstring="[back_rewrite(2204),rewrite(4082(9),4082(9),4082(9),3177(10),4082(9)),flip(a)].">
      <j1 rule="back_rewrite" parents="2204"/>
      <j2 rule="rewrite" parents="4082 4082 4082 3177 4082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4420">
    <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(1822),rewrite(4082(2))].">
      <j1 rule="back_rewrite" parents="1822"/>
      <j2 rule="rewrite" parents="4082"/>
    </justification>
  </clause>

  <clause id="4488">
    <literal><![CDATA[
      (c_0' v (c_0' v x)')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(1519),rewrite(4381(7),4082(6),4082(6),4082(6),4114(8,R))].">
      <j1 rule="back_rewrite" parents="1519"/>
      <j2 rule="rewrite" parents="4381 4082 4082 4082 4114"/>
    </justification>
  </clause>

  <clause id="4507">
    <literal><![CDATA[
      (c_0' v (x v x)'')' v (y v x) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(1462),rewrite(4082(11))].">
      <j1 rule="back_rewrite" parents="1462"/>
      <j2 rule="rewrite" parents="4082"/>
    </justification>
  </clause>

  <clause id="4833">
    <literal><![CDATA[
      x v c_0' = x
    ]]></literal>
    <justification jstring="[back_rewrite(4127),rewrite(4488(11))].">
      <j1 rule="back_rewrite" parents="4127"/>
      <j2 rule="rewrite" parents="4488"/>
    </justification>
  </clause>

  <clause id="4856">
    <literal><![CDATA[
      x'' = x
    ]]></literal>
    <justification jstring="[back_rewrite(4420),rewrite(4833(3),4507(10),4082(3),4833(4))].">
      <j1 rule="back_rewrite" parents="4420"/>
      <j2 rule="rewrite" parents="4833 4507 4082 4833"/>
    </justification>
  </clause>

  <clause id="4857">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer(CC)
    ]]></attribute>
    <justification jstring="[resolve(4856,a,10,a)].">
      <j1 rule="resolve" parents="4856 10"/>
    </justification>
  </clause>

</proof>

<proof number="2" length="141" max_count="86">

<comments><![CDATA[
% Proof 2 at 1.11 (+ 0.01) seconds: B1.
% Length of proof is 141.
% Level of proof is 34.
% Maximum clause weight is 86.
% Given clauses 112.
]]></comments>

  <clause id="2">
    <literal><![CDATA[
      x v (x ^ y) = x
    ]]></literal>
    <attribute><![CDATA[
      answer(B1)
    ]]></attribute>
    <justification jstring="[goal].">
      <j1 rule="goal"/>
    </justification>
  </clause>

  <clause id="5">
    <literal><![CDATA[
      x v (y v z) = y v (x v z)
    ]]></literal>
    <attribute><![CDATA[
      label(AJ)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="6">
    <literal><![CDATA[
      x ^ y = (x' v y')'
    ]]></literal>
    <attribute><![CDATA[
      label(DM)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="7">
    <literal><![CDATA[
      x v x' = y v y'
    ]]></literal>
    <attribute><![CDATA[
      label(ONE)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

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

  <clause id="9">
    <literal><![CDATA[
      ((x v y')' v (x v y)')' = x
    ]]></literal>
    <justification jstring="[copy(8),rewrite(6(4))].">
      <j1 rule="copy" parents="8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="11">
    <literal><![CDATA[
      c2 v (c2 ^ c3) != c2
    ]]></literal>
    <attribute><![CDATA[
      answer(B1)
    ]]></attribute>
    <justification jstring="[deny(2)].">
      <j1 rule="deny" parents="2"/>
    </justification>
  </clause>

  <clause id="12">
    <literal><![CDATA[
      c2 v (c2' v c3')' != c2
    ]]></literal>
    <attribute><![CDATA[
      answer(B1)
    ]]></attribute>
    <justification jstring="[copy(11),rewrite(6(4))].">
      <j1 rule="copy" parents="11"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="17">
    <literal><![CDATA[
      x v x' = c_0
    ]]></literal>
    <justification jstring="[new_symbol(7)].">
      <j1 rule="new_symbol" parents="7"/>
    </justification>
  </clause>

  <clause id="18">
    <literal><![CDATA[
      x v (y v (z v u)) = z v (x v (y v u))
    ]]></literal>
    <justification jstring="[para(5(a,1),5(a,1,2))].">
      <j1 rule="para" parents="5 5"/>
    </justification>
  </clause>

  <clause id="19">
    <literal><![CDATA[
      ((x v (y v z)')' v (y v (x v z))')' = x
    ]]></literal>
    <justification jstring="[para(5(a,1),9(a,1,1,2,1))].">
      <j1 rule="para" parents="5 9"/>
    </justification>
  </clause>

  <clause id="20">
    <literal><![CDATA[
      ((x v y)' v (x v ((y v z')' v (y v z)'))')' = x
    ]]></literal>
    <justification jstring="[para(9(a,1),9(a,1,1,1,1,2))].">
      <j1 rule="para" parents="9 9"/>
    </justification>
  </clause>

  <clause id="21">
    <literal><![CDATA[
      (x v (x v ((x v y')' v y))')' = (x v y')'
    ]]></literal>
    <justification jstring="[para(9(a,1),9(a,1,1,1)),rewrite(5(5))].">
      <j1 rule="para" parents="9 9"/>
      <j2 rule="rewrite" parents="5"/>
    </justification>
  </clause>

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

  <clause id="23">
    <literal><![CDATA[
      x v (y v x') = y v c_0
    ]]></literal>
    <justification jstring="[para(17(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24">
    <literal><![CDATA[
      (c_0' v (x v x)')' = x
    ]]></literal>
    <justification jstring="[para(17(a,1),9(a,1,1,1,1))].">
      <j1 rule="para" parents="17 9"/>
    </justification>
  </clause>

  <clause id="25">
    <literal><![CDATA[
      ((x v x'')' v c_0')' = x
    ]]></literal>
    <justification jstring="[para(17(a,1),9(a,1,1,2,1))].">
      <j1 rule="para" parents="17 9"/>
    </justification>
  </clause>

  <clause id="26">
    <literal><![CDATA[
      ((x v y')' v (x v y)') v x = c_0
    ]]></literal>
    <justification jstring="[para(9(a,1),17(a,1,2))].">
      <j1 rule="para" parents="9 17"/>
    </justification>
  </clause>

  <clause id="27">
    <literal><![CDATA[
      x v (y v (z v x')) = y v (z v c_0)
    ]]></literal>
    <justification jstring="[para(23(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="23 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28">
    <literal><![CDATA[
      ((x v (y v x')')' v (y v c_0)')' = x
    ]]></literal>
    <justification jstring="[para(23(a,1),9(a,1,1,2,1))].">
      <j1 rule="para" parents="23 9"/>
    </justification>
  </clause>

  <clause id="30">
    <literal><![CDATA[
      (c_0' v (x v ((x v y) v y))')' = x v y
    ]]></literal>
    <justification jstring="[para(5(a,1),24(a,1,1,2,1))].">
      <j1 rule="para" parents="5 24"/>
    </justification>
  </clause>

  <clause id="31">
    <literal><![CDATA[
      ((x v y)' v (x v (c_0' v (y v y)'))')' = x
    ]]></literal>
    <justification jstring="[para(24(a,1),9(a,1,1,1,1,2))].">
      <j1 rule="para" parents="24 9"/>
    </justification>
  </clause>

  <clause id="32">
    <literal><![CDATA[
      (x v (c_0' v (x v x))')' = c_0'
    ]]></literal>
    <justification jstring="[para(24(a,1),9(a,1,1,1))].">
      <j1 rule="para" parents="24 9"/>
    </justification>
  </clause>

  <clause id="33">
    <literal><![CDATA[
      ((c_0' v (x v x)'')' v x)' = c_0'
    ]]></literal>
    <justification jstring="[para(24(a,1),9(a,1,1,2))].">
      <j1 rule="para" parents="24 9"/>
    </justification>
  </clause>

  <clause id="34">
    <literal><![CDATA[
      (c_0' v (x v x)') v x = c_0
    ]]></literal>
    <justification jstring="[para(24(a,1),17(a,1,2))].">
      <j1 rule="para" parents="24 17"/>
    </justification>
  </clause>

  <clause id="35">
    <literal><![CDATA[
      (c_0' v (x v x)') v (y v x) = y v c_0
    ]]></literal>
    <justification jstring="[para(24(a,1),23(a,1,2,2))].">
      <j1 rule="para" parents="24 23"/>
    </justification>
  </clause>

  <clause id="36">
    <literal><![CDATA[
      x v (y v (z v (u v v))) = z v (x v (u v (y v v)))
    ]]></literal>
    <justification jstring="[para(18(a,1),5(a,1,2))].">
      <j1 rule="para" parents="18 5"/>
    </justification>
  </clause>

  <clause id="40">
    <literal><![CDATA[
      ((x v (y v (z v u))')' v (z v (x v (y v u)))')' = x
    ]]></literal>
    <justification jstring="[para(18(a,1),9(a,1,1,2,1))].">
      <j1 rule="para" parents="18 9"/>
    </justification>
  </clause>

  <clause id="41">
    <literal><![CDATA[
      ((x v (y v (z v u))')' v (y v (z v (x v u)))')' = x
    ]]></literal>
    <justification jstring="[para(18(a,2),9(a,1,1,2,1))].">
      <j1 rule="para" parents="18 9"/>
    </justification>
  </clause>

  <clause id="42">
    <literal><![CDATA[
      x v (y v (z v (u v x'))) = y v (z v (u v c_0))
    ]]></literal>
    <justification jstring="[para(23(a,1),18(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="23 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43">
    <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(18(a,1),24(a,1,1,2,1)),rewrite(5(6))].">
      <j1 rule="para" parents="18 24"/>
      <j2 rule="rewrite" parents="5"/>
    </justification>
  </clause>

  <clause id="56">
    <literal><![CDATA[
      (c_0' v (x' v x')') v c_0 = x v c_0
    ]]></literal>
    <justification jstring="[para(34(a,1),23(a,1,2)),flip(a)].">
      <j1 rule="para" parents="34 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="65">
    <literal><![CDATA[
      (x v ((x v x'')' v c_0)')' = (x v x'')'
    ]]></literal>
    <justification jstring="[para(25(a,1),9(a,1,1,1))].">
      <j1 rule="para" parents="25 9"/>
    </justification>
  </clause>

  <clause id="66">
    <literal><![CDATA[
      (((x v x'')' v c_0'')' v x)' = (x v x'')'
    ]]></literal>
    <justification jstring="[para(25(a,1),9(a,1,1,2))].">
      <j1 rule="para" parents="25 9"/>
    </justification>
  </clause>

  <clause id="68">
    <literal><![CDATA[
      ((x v x'')' v c_0') v x = c_0
    ]]></literal>
    <justification jstring="[para(25(a,1),17(a,1,2))].">
      <j1 rule="para" parents="25 17"/>
    </justification>
  </clause>

  <clause id="72">
    <literal><![CDATA[
      (x v (x v (c_0' v x))')' = c_0'
    ]]></literal>
    <justification jstring="[para(5(a,1),32(a,1,1,2,1))].">
      <j1 rule="para" parents="5 32"/>
    </justification>
  </clause>

  <clause id="74">
    <literal><![CDATA[
      (c_0' v (x v (c_0' v (x v x)))')' = x
    ]]></literal>
    <justification jstring="[para(32(a,1),9(a,1,1,1))].">
      <j1 rule="para" parents="32 9"/>
    </justification>
  </clause>

  <clause id="76">
    <literal><![CDATA[
      (x v (c_0' v (x v x))') v c_0' = c_0
    ]]></literal>
    <justification jstring="[para(32(a,1),17(a,1,2))].">
      <j1 rule="para" parents="32 17"/>
    </justification>
  </clause>

  <clause id="85">
    <literal><![CDATA[
      (c_0' v (((x' v x''')' v c_0') v x)')' = (x' v x''')' v c_0'
    ]]></literal>
    <justification jstring="[para(68(a,1),9(a,1,1,1,1))].">
      <j1 rule="para" parents="68 9"/>
    </justification>
  </clause>

  <clause id="118">
    <literal><![CDATA[
      (c_0' v (c_0' v (x v (x v x)))')' = x
    ]]></literal>
    <justification jstring="[para(32(a,1),19(a,1,1,1))].">
      <j1 rule="para" parents="32 19"/>
    </justification>
  </clause>

  <clause id="126">
    <literal><![CDATA[
      (c_0' v (x v (x v (c_0' v x)))')' = x
    ]]></literal>
    <justification jstring="[para(72(a,1),9(a,1,1,1))].">
      <j1 rule="para" parents="72 9"/>
    </justification>
  </clause>

  <clause id="144">
    <literal><![CDATA[
      ((c_0' v (x v x)'')' v x) v c_0' = c_0
    ]]></literal>
    <justification jstring="[para(24(a,1),26(a,1,1,2))].">
      <j1 rule="para" parents="24 26"/>
    </justification>
  </clause>

  <clause id="158">
    <literal><![CDATA[
      (c_0' v (x v (c_0' v (x v x)))') v x = c_0
    ]]></literal>
    <justification jstring="[para(32(a,1),26(a,1,1,1))].">
      <j1 rule="para" parents="32 26"/>
    </justification>
  </clause>

  <clause id="169">
    <literal><![CDATA[
      (c_0' v (x v (x v (c_0' v x)))') v x = c_0
    ]]></literal>
    <justification jstring="[para(72(a,1),26(a,1,1,1))].">
      <j1 rule="para" parents="72 26"/>
    </justification>
  </clause>

  <clause id="183">
    <literal><![CDATA[
      (c_0' v ((x v (c_0' v (x v x))') v c_0)')' = x v (c_0' v (x v x))'
    ]]></literal>
    <justification jstring="[para(76(a,1),9(a,1,1,1,1))].">
      <j1 rule="para" parents="76 9"/>
    </justification>
  </clause>

  <clause id="184">
    <literal><![CDATA[
      (x v (c_0' v (x v x))') v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(76(a,1),23(a,1,2)),flip(a)].">
      <j1 rule="para" parents="76 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="193">
    <literal><![CDATA[
      x v (c_0' v (x v x))' = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(183),rewrite(184(10),24(8)),flip(a)].">
      <j1 rule="back_rewrite" parents="183"/>
      <j2 rule="rewrite" parents="184 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="251">
    <literal><![CDATA[
      x v (y v (c_0' v (x v x))') = y v c_0
    ]]></literal>
    <justification jstring="[para(193(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="193 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="254">
    <literal><![CDATA[
      (c_0' v (x v x)) v c_0 = x v c_0
    ]]></literal>
    <justification jstring="[para(193(a,1),23(a,1,2))].">
      <j1 rule="para" parents="193 23"/>
    </justification>
  </clause>

  <clause id="255">
    <literal><![CDATA[
      c_0'' v (c_0'' v c_0)' = c_0
    ]]></literal>
    <justification jstring="[para(23(a,1),193(a,1,2,1))].">
      <j1 rule="para" parents="23 193"/>
    </justification>
  </clause>

  <clause id="280">
    <literal><![CDATA[
      (c_0'' v c_0) v c_0 = c_0'' v c_0
    ]]></literal>
    <justification jstring="[para(23(a,1),254(a,1,1))].">
      <j1 rule="para" parents="23 254"/>
    </justification>
  </clause>

  <clause id="294">
    <literal><![CDATA[
      (c_0' v (c_0'' v (c_0'' v c_0))')' = c_0''
    ]]></literal>
    <justification jstring="[para(255(a,1),9(a,1,1,1,1))].">
      <j1 rule="para" parents="255 9"/>
    </justification>
  </clause>

  <clause id="300">
    <literal><![CDATA[
      (c_0'' v c_0) v (x v c_0) = x v (c_0'' v c_0)
    ]]></literal>
    <justification jstring="[para(255(a,1),27(a,1,2,2))].">
      <j1 rule="para" parents="255 27"/>
    </justification>
  </clause>

  <clause id="480">
    <literal><![CDATA[
      (((x v c_0')' v ((c_0' v (y v y)') v (x v y))'')' v x)' = (x v c_0')'
    ]]></literal>
    <justification jstring="[para(35(a,2),22(a,1,1,1,1,2,1,1))].">
      <j1 rule="para" parents="35 22"/>
    </justification>
  </clause>

  <clause id="540">
    <literal><![CDATA[
      ((c_0' v (x v x)'')' v x) v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(33(a,1),56(a,1,1,2,1,1)),rewrite(33(13),56(11)),flip(a)].">
      <j1 rule="para" parents="33 56"/>
      <j2 rule="rewrite" parents="33 56"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="545">
    <literal><![CDATA[
      (c_0' v ((x v y) v (c_0' v (x v ((x v y) v y))))')' = x v y
    ]]></literal>
    <justification jstring="[para(5(a,1),74(a,1,1,2,1,2,2))].">
      <j1 rule="para" parents="5 74"/>
    </justification>
  </clause>

  <clause id="606">
    <literal><![CDATA[
      ((x v (x' v y')')' v (((x' v y')' v (x' v y)'')' v c_0)')' = x
    ]]></literal>
    <justification jstring="[para(22(a,1),28(a,1,1,1,1,2))].">
      <j1 rule="para" parents="22 28"/>
    </justification>
  </clause>

  <clause id="614">
    <literal><![CDATA[
      (c_0' v (c_0' v (x v ((x v y) v ((x v y) v y))))')' = x v y
    ]]></literal>
    <justification jstring="[para(5(a,1),118(a,1,1,2,1,2,2)),rewrite(5(9))].">
      <j1 rule="para" parents="5 118"/>
      <j2 rule="rewrite" parents="5"/>
    </justification>
  </clause>

  <clause id="676">
    <literal><![CDATA[
      (c_0' v (x v x)) v (y v c_0) = x v (y v c_0)
    ]]></literal>
    <justification jstring="[para(251(a,1),27(a,1,2))].">
      <j1 rule="para" parents="251 27"/>
    </justification>
  </clause>

  <clause id="812">
    <literal><![CDATA[
      (c_0' v c_0''')' v c_0' = (c_0' v c_0''')'
    ]]></literal>
    <justification jstring="[para(68(a,1),30(a,1,1,2,1,2)),rewrite(65(15)),flip(a)].">
      <j1 rule="para" parents="68 30"/>
      <j2 rule="rewrite" parents="65"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="821">
    <literal><![CDATA[
      c_0'' v c_0 = c_0''
    ]]></literal>
    <justification jstring="[para(280(a,1),30(a,1,1,2,1,2,1)),rewrite(280(14),5(13),280(12),294(14),280(10)),flip(a)].">
      <j1 rule="para" parents="280 30"/>
      <j2 rule="rewrite" parents="280 5 280 294 280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="851">
    <literal><![CDATA[
      c_0'' v (x v c_0) = x v c_0''
    ]]></literal>
    <justification jstring="[back_rewrite(300),rewrite(821(5),821(11))].">
      <j1 rule="back_rewrite" parents="300"/>
      <j2 rule="rewrite" parents="821 821"/>
    </justification>
  </clause>

  <clause id="853">
    <literal><![CDATA[
      (c_0' v (c_0 v c_0)') v c_0'' = c_0''
    ]]></literal>
    <justification jstring="[para(821(a,1),35(a,1,2)),rewrite(821(16))].">
      <j1 rule="para" parents="821 35"/>
      <j2 rule="rewrite" parents="821"/>
    </justification>
  </clause>

  <clause id="858">
    <literal><![CDATA[
      c_0' v (c_0'' v (x v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[para(851(a,2),23(a,1,2))].">
      <j1 rule="para" parents="851 23"/>
    </justification>
  </clause>

  <clause id="907">
    <literal><![CDATA[
      c_0'' v (x v (c_0' v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[para(858(a,1),18(a,2))].">
      <j1 rule="para" parents="858 18"/>
    </justification>
  </clause>

  <clause id="995">
    <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(34(a,1),907(a,1,2)),rewrite(821(5),5(14)),flip(a)].">
      <j1 rule="para" parents="34 907"/>
      <j2 rule="rewrite" parents="821 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1002">
    <literal><![CDATA[
      x v ((c_0' v (x v (c_0' v ((x v (c_0' v c_0)) v c_0)))') v c_0) = c_0''
    ]]></literal>
    <justification jstring="[para(907(a,1),35(a,1,2)),rewrite(5(13),5(12),5(18),821(23))].">
      <j1 rule="para" parents="907 35"/>
      <j2 rule="rewrite" parents="5 5 5 821"/>
    </justification>
  </clause>

  <clause id="1019">
    <literal><![CDATA[
      (c_0' v c_0''')'' = c_0'
    ]]></literal>
    <justification jstring="[para(853(a,1),28(a,1,1,1,1,2,1)),rewrite(34(17),812(11))].">
      <j1 rule="para" parents="853 28"/>
      <j2 rule="rewrite" parents="34 812"/>
    </justification>
  </clause>

  <clause id="1024">
    <literal><![CDATA[
      (c_0' v c_0''')' = c_0
    ]]></literal>
    <justification jstring="[para(1019(a,1),17(a,1,2)),rewrite(812(11))].">
      <j1 rule="para" parents="1019 17"/>
      <j2 rule="rewrite" parents="812"/>
    </justification>
  </clause>

  <clause id="1029">
    <literal><![CDATA[
      ((c_0' v c_0'''')' v c_0)' = c_0'
    ]]></literal>
    <justification jstring="[para(1024(a,1),9(a,1,1,2))].">
      <j1 rule="para" parents="1024 9"/>
    </justification>
  </clause>

  <clause id="1224">
    <literal><![CDATA[
      ((((c_0' v c_0'''')' v c_0) v c_0'')' v c_0')' = (c_0' v c_0'''')' v c_0
    ]]></literal>
    <justification jstring="[para(1029(a,1),25(a,1,1,1,1,2,1))].">
      <j1 rule="para" parents="1029 25"/>
    </justification>
  </clause>

  <clause id="1447">
    <literal><![CDATA[
      (c_0' v (x v x)'')' v x = c_0
    ]]></literal>
    <justification jstring="[para(144(a,1),9(a,1,1,1,1)),rewrite(540(12),24(8)),flip(a)].">
      <j1 rule="para" parents="144 9"/>
      <j2 rule="rewrite" parents="540 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1462">
    <literal><![CDATA[
      (c_0' v (x v x)'')' v (y v x) = y v c_0
    ]]></literal>
    <justification jstring="[para(1447(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1447 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1519">
    <literal><![CDATA[
      ((x v (y v (z v (u v x')))')' v (z v (y v (u v c_0)))')' = x
    ]]></literal>
    <justification jstring="[para(27(a,1),40(a,1,1,2,1,2))].">
      <j1 rule="para" parents="27 40"/>
    </justification>
  </clause>

  <clause id="1642">
    <literal><![CDATA[
      (((c_0' v (c_0' 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 x)' v c_0')' = c_0' v (c_0' v ((x v y')' v (((x v y')' v (x v y)') v (((x v y')' v (x v y)') v (x v y)'))))'
    ]]></literal>
    <justification jstring="[para(158(a,1),20(a,1,1,2,1)),rewrite(5(23),5(25),5(24),5(56),5(58),5(57))].">
      <j1 rule="para" parents="158 20"/>
      <j2 rule="rewrite" parents="5 5 5 5 5 5"/>
    </justification>
  </clause>

  <clause id="1656">
    <literal><![CDATA[
      (((c_0' v (c_0' v (c_0' v ((c_0' v (x v x)') v ((c_0' v (x v x)') v (x v x)'))))') v x)' v c_0')' = c_0' v (c_0' v (c_0' v ((c_0' v (x v x)') v ((c_0' v (x v x)') v (x v x)'))))'
    ]]></literal>
    <justification jstring="[para(158(a,1),31(a,1,1,2,1)),rewrite(5(20),5(22),5(21),5(50),5(52),5(51))].">
      <j1 rule="para" parents="158 31"/>
      <j2 rule="rewrite" parents="5 5 5 5 5 5"/>
    </justification>
  </clause>

  <clause id="1822">
    <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(1447(a,1),41(a,1,1,1,1,2,1,2))].">
      <j1 rule="para" parents="1447 41"/>
    </justification>
  </clause>

  <clause id="1916">
    <literal><![CDATA[
      c_0 v (c_0' v c_0) = c_0
    ]]></literal>
    <justification jstring="[para(676(a,1),30(a,1,1,2,1,2)),rewrite(5(10),5(9),126(13),5(7)),flip(a)].">
      <j1 rule="para" parents="676 30"/>
      <j2 rule="rewrite" parents="5 5 126 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1943">
    <literal><![CDATA[
      c_0 v (c_0' v (x v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[para(1916(a,1),18(a,2,2))].">
      <j1 rule="para" parents="1916 18"/>
    </justification>
  </clause>

  <clause id="1948">
    <literal><![CDATA[
      c_0'' = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(1916(a,1),35(a,1,2)),rewrite(5(11),995(15))].">
      <j1 rule="para" parents="1916 35"/>
      <j2 rule="rewrite" parents="5 995"/>
    </justification>
  </clause>

  <clause id="2028">
    <literal><![CDATA[
      ((c_0 v (c_0 v c_0))' v c_0')' = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(1224),rewrite(1948(5),1447(11),1948(4),1948(15),1447(21))].">
      <j1 rule="back_rewrite" parents="1224"/>
      <j2 rule="rewrite" parents="1948 1447 1948 1948 1447"/>
    </justification>
  </clause>

  <clause id="2067">
    <literal><![CDATA[
      x v ((c_0' v (x v (c_0' v ((x v (c_0' v c_0)) v c_0)))') v c_0) = c_0 v c_0
    ]]></literal>
    <justification jstring="[back_rewrite(1002),rewrite(1948(21))].">
      <j1 rule="back_rewrite" parents="1002"/>
      <j2 rule="rewrite" parents="1948"/>
    </justification>
  </clause>

  <clause id="2074">
    <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(995),rewrite(1948(18))].">
      <j1 rule="back_rewrite" parents="995"/>
      <j2 rule="rewrite" parents="1948"/>
    </justification>
  </clause>

  <clause id="2096">
    <literal><![CDATA[
      (c_0 v c_0) v (x v (c_0' v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[back_rewrite(907),rewrite(1948(3))].">
      <j1 rule="back_rewrite" parents="907"/>
      <j2 rule="rewrite" parents="1948"/>
    </justification>
  </clause>

  <clause id="2158">
    <literal><![CDATA[
      ((c_0 v ((x v x'')' v c_0))' v x)' = (x v x'')'
    ]]></literal>
    <justification jstring="[back_rewrite(66),rewrite(1948(7),5(8))].">
      <j1 rule="back_rewrite" parents="66"/>
      <j2 rule="rewrite" parents="1948 5"/>
    </justification>
  </clause>

  <clause id="2204">
    <literal><![CDATA[
      (((x v (y v (z v (u v x')))')' v (y v (z v (u v c_0)))'')' v x)' = (x v (y v (z v (u v x')))')'
    ]]></literal>
    <justification jstring="[para(42(a,1),22(a,1,1,1,1,2,1,1))].">
      <j1 rule="para" parents="42 22"/>
    </justification>
  </clause>

  <clause id="2316">
    <literal><![CDATA[
      c_0' v (x v ((x v c_0) v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[para(676(a,1),43(a,1,1,2,1,2,2)),rewrite(5(11),545(16),5(9)),flip(a)].">
      <j1 rule="para" parents="676 43"/>
      <j2 rule="rewrite" parents="5 545 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2318">
    <literal><![CDATA[
      (c_0' v (c_0 v (x v c_0))')' = x v c_0
    ]]></literal>
    <justification jstring="[para(1943(a,1),43(a,1,1,2,1,2,2,1)),rewrite(5(10),5(12),2316(11),1943(16))].">
      <j1 rule="para" parents="1943 43"/>
      <j2 rule="rewrite" parents="5 5 2316 1943"/>
    </justification>
  </clause>

  <clause id="2742">
    <literal><![CDATA[
      x v ((x v c_0) v (c_0' v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[para(2316(a,1),18(a,2))].">
      <j1 rule="para" parents="2316 18"/>
    </justification>
  </clause>

  <clause id="2759">
    <literal><![CDATA[
      x v (y v ((x v c_0) v (c_0' v c_0))) = y v (x v c_0)
    ]]></literal>
    <justification jstring="[para(2316(a,1),36(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2316 36"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2767">
    <literal><![CDATA[
      x v ((x v c_0) v ((c_0' v (x v ((x v ((x v c_0) v c_0)) v ((x v ((x v c_0) v c_0)) v c_0)))') v c_0)) = c_0
    ]]></literal>
    <justification jstring="[para(2316(a,1),169(a,1,1,2,1,2,2)),rewrite(5(15),5(16),5(24),5(23))].">
      <j1 rule="para" parents="2316 169"/>
      <j2 rule="rewrite" parents="5 5 5 5"/>
    </justification>
  </clause>

  <clause id="2793">
    <literal><![CDATA[
      (c_0' v (x v ((x v c_0) v c_0))') v c_0 = (c_0' v (c_0 v (x v c_0))') v c_0
    ]]></literal>
    <justification jstring="[para(2318(a,1),56(a,1,1,2,1,1)),rewrite(2318(13),5(7))].">
      <j1 rule="para" parents="2318 56"/>
      <j2 rule="rewrite" parents="2318 5"/>
    </justification>
  </clause>

  <clause id="2795">
    <literal><![CDATA[
      ((x v ((c_0 v (x v c_0)) v c_0))' v (c_0' v c_0)')' = c_0 v (x v c_0)
    ]]></literal>
    <justification jstring="[para(2318(a,1),28(a,1,1,1,1,2)),rewrite(5(7))].">
      <j1 rule="para" parents="2318 28"/>
      <j2 rule="rewrite" parents="5"/>
    </justification>
  </clause>

  <clause id="2800">
    <literal><![CDATA[
      (c_0' v c_0')' = c_0' v c_0
    ]]></literal>
    <justification jstring="[para(1916(a,1),2318(a,1,1,2,1))].">
      <j1 rule="para" parents="1916 2318"/>
    </justification>
  </clause>

  <clause id="2803">
    <literal><![CDATA[
      (c_0' v c_0') v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[back_rewrite(2074),rewrite(2793(15),1916(8))].">
      <j1 rule="back_rewrite" parents="2074"/>
      <j2 rule="rewrite" parents="2793 1916"/>
    </justification>
  </clause>

  <clause id="2840">
    <literal><![CDATA[
      (c_0' v (c_0' v c_0))' = c_0'
    ]]></literal>
    <justification jstring="[para(2800(a,1),9(a,1,1,2)),rewrite(1948(5),5(6),1916(6))].">
      <j1 rule="para" parents="2800 9"/>
      <j2 rule="rewrite" parents="1948 5 1916"/>
    </justification>
  </clause>

  <clause id="2854">
    <literal><![CDATA[
      (c_0' v (c_0' v c_0)) v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(2800(a,1),56(a,1,1,2))].">
      <j1 rule="para" parents="2800 56"/>
    </justification>
  </clause>

  <clause id="3052">
    <literal><![CDATA[
      c_0' v (c_0' v c_0) = c_0
    ]]></literal>
    <justification jstring="[para(2840(a,1),25(a,1,1,1,1,2,1)),rewrite(1948(10),5(11),2854(10),2028(10)),flip(a)].">
      <j1 rule="para" parents="2840 25"/>
      <j2 rule="rewrite" parents="1948 5 2854 2028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3057">
    <literal><![CDATA[
      c_0' v (x v (c_0' v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[para(3052(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3052 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3063">
    <literal><![CDATA[
      c_0' v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(3052(a,1),35(a,1,2)),rewrite(5(11),2793(15),1916(8),2803(7)),flip(a)].">
      <j1 rule="para" parents="3052 35"/>
      <j2 rule="rewrite" parents="5 2793 1916 2803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3064">
    <literal><![CDATA[
      c_0 v (c_0 v c_0) = c_0
    ]]></literal>
    <justification jstring="[para(35(a,2),3052(a,1,2)),rewrite(5(11),34(10),3063(6),5(6),3063(5))].">
      <j1 rule="para" parents="35 3052"/>
      <j2 rule="rewrite" parents="5 34 3063 5 3063"/>
    </justification>
  </clause>

  <clause id="3065">
    <literal><![CDATA[
      c_0 v c_0 = c_0
    ]]></literal>
    <justification jstring="[para(3052(a,1),22(a,1,1,1,1,2,1,1)),rewrite(3063(6),24(8),1948(4),3064(5),2800(6),3063(4),3063(9),24(11))].">
      <j1 rule="para" parents="3052 22"/>
      <j2 rule="rewrite" parents="3063 24 1948 3064 2800 3063 3063 24"/>
    </justification>
  </clause>

  <clause id="3076">
    <literal><![CDATA[
      c_0' v (x v c_0) = x v c_0
    ]]></literal>
    <justification jstring="[back_rewrite(3057),rewrite(3063(6),3065(5))].">
      <j1 rule="back_rewrite" parents="3057"/>
      <j2 rule="rewrite" parents="3063 3065"/>
    </justification>
  </clause>

  <clause id="3101">
    <literal><![CDATA[
      ((x v ((c_0 v (x v c_0)) v c_0))' v c_0')' = c_0 v (x v c_0)
    ]]></literal>
    <justification jstring="[back_rewrite(2795),rewrite(3063(12),3065(11))].">
      <j1 rule="back_rewrite" parents="2795"/>
      <j2 rule="rewrite" parents="3063 3065"/>
    </justification>
  </clause>

  <clause id="3104">
    <literal><![CDATA[
      x v (y v ((x v c_0) v c_0)) = y v (x v c_0)
    ]]></literal>
    <justification jstring="[back_rewrite(2759),rewrite(3063(6),3065(5))].">
      <j1 rule="back_rewrite" parents="2759"/>
      <j2 rule="rewrite" parents="3063 3065"/>
    </justification>
  </clause>

  <clause id="3106">
    <literal><![CDATA[
      x v ((x v c_0) v c_0) = x v c_0
    ]]></literal>
    <justification jstring="[back_rewrite(2742),rewrite(3063(6),3065(5))].">
      <j1 rule="back_rewrite" parents="2742"/>
      <j2 rule="rewrite" parents="3063 3065"/>
    </justification>
  </clause>

  <clause id="3120">
    <literal><![CDATA[
      c_0 v (x v c_0) = x v c_0
    ]]></literal>
    <justification jstring="[back_rewrite(2096),rewrite(3065(3),3063(5),3065(4))].">
      <j1 rule="back_rewrite" parents="2096"/>
      <j2 rule="rewrite" parents="3065 3063 3065"/>
    </justification>
  </clause>

  <clause id="3125">
    <literal><![CDATA[
      x v ((c_0' v (x v c_0)') v c_0) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(2067),rewrite(3063(8),3065(7),3076(9),3106(7),3065(12))].">
      <j1 rule="back_rewrite" parents="2067"/>
      <j2 rule="rewrite" parents="3063 3065 3076 3106 3065"/>
    </justification>
  </clause>

  <clause id="3177">
    <literal><![CDATA[
      c_0'' = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(1948),rewrite(3065(6))].">
      <j1 rule="back_rewrite" parents="1948"/>
      <j2 rule="rewrite" parents="3065"/>
    </justification>
  </clause>

  <clause id="3191">
    <literal><![CDATA[
      x v ((x v c_0) v ((c_0' v (x v c_0)') v c_0)) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(2767),rewrite(3106(9),3106(11),3104(12),5(9),3106(9))].">
      <j1 rule="back_rewrite" parents="2767"/>
      <j2 rule="rewrite" parents="3106 3106 3104 5 3106"/>
    </justification>
  </clause>

  <clause id="3193">
    <literal><![CDATA[
      ((x v c_0)' v c_0')' = x v c_0
    ]]></literal>
    <justification jstring="[back_rewrite(3101),rewrite(3120(4),3106(5),3120(11))].">
      <j1 rule="back_rewrite" parents="3101"/>
      <j2 rule="rewrite" parents="3120 3106 3120"/>
    </justification>
  </clause>

  <clause id="3215">
    <literal><![CDATA[
      (((x v x'')' v c_0)' v x)' = (x v x'')'
    ]]></literal>
    <justification jstring="[back_rewrite(2158),rewrite(3120(8))].">
      <j1 rule="back_rewrite" parents="2158"/>
      <j2 rule="rewrite" parents="3120"/>
    </justification>
  </clause>

  <clause id="3877">
    <literal><![CDATA[
      ((x v (y v c_0))' v ((y v c_0)' v (x v c_0'))')' = x
    ]]></literal>
    <justification jstring="[para(3193(a,1),19(a,1,1,1,1,2))].">
      <j1 rule="para" parents="3193 19"/>
    </justification>
  </clause>

  <clause id="3887">
    <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(3193(a,1),21(a,1,1,2,1,2,1)),rewrite(5(11),3193(21))].">
      <j1 rule="para" parents="3193 21"/>
      <j2 rule="rewrite" parents="5 3193"/>
    </justification>
  </clause>

  <clause id="3895">
    <literal><![CDATA[
      ((x v c_0)' v ((x v c_0)' v c_0)')' = c_0
    ]]></literal>
    <justification jstring="[para(3193(a,1),28(a,1,1,1,1,2)),rewrite(3120(4))].">
      <j1 rule="para" parents="3193 28"/>
      <j2 rule="rewrite" parents="3120"/>
    </justification>
  </clause>

  <clause id="3924">
    <literal><![CDATA[
      x v (y v ((c_0' v (x v c_0)') v c_0)) = y v c_0
    ]]></literal>
    <justification jstring="[para(3125(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3125 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3935">
    <literal><![CDATA[
      (((x v ((c_0' v (x v c_0)') v c_0)')' v c_0)' v x)' = (x v ((c_0' v (x v c_0)') v c_0)')'
    ]]></literal>
    <justification jstring="[para(3125(a,1),22(a,1,1,1,1,2,1,1)),rewrite(3177(14))].">
      <j1 rule="para" parents="3125 22"/>
      <j2 rule="rewrite" parents="3177"/>
    </justification>
  </clause>

  <clause id="3948">
    <literal><![CDATA[
      (x v c_0) v c_0 = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(3191),rewrite(3924(12))].">
      <j1 rule="back_rewrite" parents="3191"/>
      <j2 rule="rewrite" parents="3924"/>
    </justification>
  </clause>

  <clause id="4065">
    <literal><![CDATA[
      (x v c_0) v (y v c_0) = y v c_0
    ]]></literal>
    <justification jstring="[para(3948(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3948 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4082">
    <literal><![CDATA[
      x v c_0 = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(3887),rewrite(4065(11),3895(11)),flip(a)].">
      <j1 rule="back_rewrite" parents="3887"/>
      <j2 rule="rewrite" parents="4065 3895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4114">
    <literal><![CDATA[
      (c_0' v x)' = (x v c_0')'
    ]]></literal>
    <justification jstring="[back_rewrite(3935),rewrite(4082(4),4082(7),4082(6),4082(8),4082(11))].">
      <j1 rule="back_rewrite" parents="3935"/>
      <j2 rule="rewrite" parents="4082 4082 4082 4082 4082"/>
    </justification>
  </clause>

  <clause id="4127">
    <literal><![CDATA[
      (c_0' v (c_0' v (x v c_0'))')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(3877),rewrite(4082(2),4082(2),4082(4))].">
      <j1 rule="back_rewrite" parents="3877"/>
      <j2 rule="rewrite" parents="4082 4082 4082"/>
    </justification>
  </clause>

  <clause id="4279">
    <literal><![CDATA[
      (x v x'')' = (c_0' v x)'
    ]]></literal>
    <justification jstring="[back_rewrite(3215),rewrite(4082(6)),flip(a)].">
      <j1 rule="back_rewrite" parents="3215"/>
      <j2 rule="rewrite" parents="4082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4381">
    <literal><![CDATA[
      (x v (y v (z v (u v x')))')' = (c_0' v x)'
    ]]></literal>
    <justification jstring="[back_rewrite(2204),rewrite(4082(9),4082(9),4082(9),3177(10),4082(9)),flip(a)].">
      <j1 rule="back_rewrite" parents="2204"/>
      <j2 rule="rewrite" parents="4082 4082 4082 3177 4082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4420">
    <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(1822),rewrite(4082(2))].">
      <j1 rule="back_rewrite" parents="1822"/>
      <j2 rule="rewrite" parents="4082"/>
    </justification>
  </clause>

  <clause id="4488">
    <literal><![CDATA[
      (c_0' v (c_0' v x)')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(1519),rewrite(4381(7),4082(6),4082(6),4082(6),4114(8,R))].">
      <j1 rule="back_rewrite" parents="1519"/>
      <j2 rule="rewrite" parents="4381 4082 4082 4082 4114"/>
    </justification>
  </clause>

  <clause id="4507">
    <literal><![CDATA[
      (c_0' v (x v x)'')' v (y v x) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(1462),rewrite(4082(11))].">
      <j1 rule="back_rewrite" parents="1462"/>
      <j2 rule="rewrite" parents="4082"/>
    </justification>
  </clause>

  <clause id="4655">
    <literal><![CDATA[
      (c_0' v (x v (x' v y')')')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(606),rewrite(4082(18),4114(10,R))].">
      <j1 rule="back_rewrite" parents="606"/>
      <j2 rule="rewrite" parents="4082 4114"/>
    </justification>
  </clause>

  <clause id="4724">
    <literal><![CDATA[
      (c_0' v (x v x)') v (y v x) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(35),rewrite(4082(9))].">
      <j1 rule="back_rewrite" parents="35"/>
      <j2 rule="rewrite" parents="4082"/>
    </justification>
  </clause>

  <clause id="4750">
    <literal><![CDATA[
      (c_0' v ((c_0' v (c_0' v (c_0' v ((c_0' v (x v x)') v ((c_0' v (x v x)') v (x v x)'))))') v x)')' = c_0' v (c_0' v (c_0' v ((c_0' v (x v x)') v ((c_0' v (x v x)') v (x v x)'))))'
    ]]></literal>
    <justification jstring="[back_rewrite(1656),rewrite(4114(30,R))].">
      <j1 rule="back_rewrite" parents="1656"/>
      <j2 rule="rewrite" parents="4114"/>
    </justification>
  </clause>

  <clause id="4751">
    <literal><![CDATA[
      (c_0' v ((c_0' v (c_0' 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 x)')' = c_0' v (c_0' v ((x v y')' v (((x v y')' v (x v y)') v (((x v y')' v (x v y)') v (x v y)'))))'
    ]]></literal>
    <justification jstring="[back_rewrite(1642),rewrite(4114(33,R))].">
      <j1 rule="back_rewrite" parents="1642"/>
      <j2 rule="rewrite" parents="4114"/>
    </justification>
  </clause>

  <clause id="4830">
    <literal><![CDATA[
      (c_0' v (((c_0' v x')' v c_0') v x)')' = (c_0' v x')' v c_0'
    ]]></literal>
    <justification jstring="[back_rewrite(85),rewrite(4279(8),4279(20))].">
      <j1 rule="back_rewrite" parents="85"/>
      <j2 rule="rewrite" parents="4279 4279"/>
    </justification>
  </clause>

  <clause id="4833">
    <literal><![CDATA[
      x v c_0' = x
    ]]></literal>
    <justification jstring="[back_rewrite(4127),rewrite(4488(11))].">
      <j1 rule="back_rewrite" parents="4127"/>
      <j2 rule="rewrite" parents="4488"/>
    </justification>
  </clause>

  <clause id="4853">
    <literal><![CDATA[
      x v ((x v y) v ((x v y) v y)) = x v y
    ]]></literal>
    <justification jstring="[back_rewrite(614),rewrite(4488(13))].">
      <j1 rule="back_rewrite" parents="614"/>
      <j2 rule="rewrite" parents="4488"/>
    </justification>
  </clause>

  <clause id="4856">
    <literal><![CDATA[
      x'' = x
    ]]></literal>
    <justification jstring="[back_rewrite(4420),rewrite(4833(3),4507(10),4082(3),4833(4))].">
      <j1 rule="back_rewrite" parents="4420"/>
      <j2 rule="rewrite" parents="4833 4507 4082 4833"/>
    </justification>
  </clause>

  <clause id="4884">
    <literal><![CDATA[
      (c_0' v x)' = x'
    ]]></literal>
    <justification jstring="[back_rewrite(480),rewrite(4833(3),4724(8),4856(4),4082(3),4833(7))].">
      <j1 rule="back_rewrite" parents="480"/>
      <j2 rule="rewrite" parents="4833 4724 4856 4082 4833"/>
    </justification>
  </clause>

  <clause id="4892">
    <literal><![CDATA[
      x v x = x
    ]]></literal>
    <justification jstring="[back_rewrite(4830),rewrite(4884(7),4856(4),4833(5),4884(6),4856(3),4884(6),4856(3),4833(4))].">
      <j1 rule="back_rewrite" parents="4830"/>
      <j2 rule="rewrite" parents="4884 4856 4833 4884 4856 4884 4856 4833"/>
    </justification>
  </clause>

  <clause id="5007">
    <literal><![CDATA[
      (c_0' v x) v x = c_0' v x
    ]]></literal>
    <justification jstring="[back_rewrite(4751),rewrite(4853(26),4884(14),9(11),4884(9),4856(6),4853(28),4884(16),9(13))].">
      <j1 rule="back_rewrite" parents="4751"/>
      <j2 rule="rewrite" parents="4853 4884 9 4884 4856 4853 4884 9"/>
    </justification>
  </clause>

  <clause id="5008">
    <literal><![CDATA[
      c_0' v x = x
    ]]></literal>
    <justification jstring="[back_rewrite(4750),rewrite(4892(11),4892(15),4892(17),5007(18),4892(17),4884(15),4884(12),4884(9),4856(6),5007(6),4884(6),4884(5),4856(2),4892(9),4892(13),4892(15),5007(16),4892(15),4884(13),4884(10),4884(7),4856(4)),flip(a)].">
      <j1 rule="back_rewrite" parents="4750"/>
      <j2 rule="rewrite" parents="4892 4892 4892 5007 4892 4884 4884 4884 4856 5007 4884 4884 4856 4892 4892 4892 5007 4892 4884 4884 4884 4856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5164">
    <literal><![CDATA[
      x v (x' v y')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(4655),rewrite(5008(9),4856(7))].">
      <j1 rule="back_rewrite" parents="4655"/>
      <j2 rule="rewrite" parents="5008 4856"/>
    </justification>
  </clause>

  <clause id="5165">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer(B1)
    ]]></attribute>
    <justification jstring="[resolve(5164,a,12,a)].">
      <j1 rule="resolve" parents="5164 12"/>
    </justification>
  </clause>

</proof>

<proof number="3" length="159" max_count="86">

<comments><![CDATA[
% Proof 3 at 2.84 (+ 0.02) seconds: MOD.
% Length of proof is 159.
% Level of proof is 39.
% Maximum clause weight is 86.
% Given clauses 185.
]]></comments>

  <clause id="4">
    <literal><![CDATA[
      x v (y ^ (x v z)) = x v (z ^ (x v y))
    ]]></literal>
    <attribute><![CDATA[
      answer(MOD)
    ]]></attribute>
    <justification jstring="[goal].">
      <j1 rule="goal"/>
    </justification>
  </clause>

  <clause id="5">
    <literal><![CDATA[
      x v (y v z) = y v (x v z)
    ]]></literal>
    <attribute><![CDATA[
      label(AJ)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="6">
    <literal><![CDATA[
      x ^ y = (x' v y')'
    ]]></literal>
    <attribute><![CDATA[
      label(DM)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="7">
    <literal><![CDATA[
      x v x' = y v y'
    ]]></literal>
    <attribute><![CDATA[
      label(ONE)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

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

  <clause id="9">
    <literal><![CDATA[
      ((x v y')' v (x v y)')' = x
    ]]></literal>
    <justification jstring="[copy(8),rewrite(6(4))].">
      <j1 rule="copy" parents="8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="15">
    <literal><![CDATA[
      c7 v (c9 ^ (c7 v c8)) != c7 v (c8 ^ (c7 v c9))
    ]]></literal>
    <attribute><![CDATA[
      answer(MOD)
    ]]></attribute>
    <justification jstring="[deny(4)].">
      <j1 rule="deny" parents="4"/>
    </justification>
  </clause>

  <clause id="16">
    <literal><![CDATA[
      c7 v (c8' v (c7 v c9)')' != c7 v (c9' v (c7 v c8)')'
    ]]></literal>
    <attribute><![CDATA[
      answer(MOD)
    ]]></attribute>
    <justification jstring="[copy(15),rewrite(6(6),6(16)),flip(a)].">
      <j1 rule="copy" parents="15"/>
      <j2 rule="rewrite" parents="6 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17">
    <literal><![CDATA[
      x v x' = c_0
    ]]></literal>
    <justification jstring="[new_symbol(7)].">
      <j1 rule="new_symbol" parents="7"/>
    </justification>
  </clause>

  <clause id="18">
    <literal><![CDATA[
      x v (y v (z v u)) = z v (x v (y v u))
    ]]></literal>
    <justification jstring="[para(5(a,1),5(a,1,2))].">
      <j1 rule="para" parents="5 5"/>
    </justification>
  </clause>

  <clause id="19">
    <literal><![CDATA[
      ((x v (y v z)')' v (y v (x v z))')' = x
    ]]></literal>
    <justification jstring="[para(5(a,1),9(a,1,1,2,1))].">
      <j1 rule="para" parents="5 9"/>
    </justification>
  </clause>

  <clause id="20">
    <literal><![CDATA[
      ((x v y)' v (x v ((y v z')' v (y v z)'))')' = x
    ]]></literal>
    <justification jstring="[para(9(a,1),9(a,1,1,1,1,2))].">
      <j1 rule="para" parents="9 9"/>
    </justification>
  </clause>

  <clause id="21">
    <literal><![CDATA[
      (x v (x v ((x v y')' v y))')' = (x v y')'
    ]]></literal>
    <justification jstring="[para(9(a,1),9(a,1,1,1)),rewrite(5(5))].">
      <j1 rule="para" parents="9 9"/>
      <j2 rule="rewrite" parents="5"/>
    </justification>
  </clause>

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

  <clause id="23">
    <literal><![CDATA[
      x v (y v x') = y v c_0
    ]]></literal>
    <justification jstring="[para(17(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24">
    <literal><![CDATA[
      (c_0' v (x v x)')' = x
    ]]></literal>
    <justification jstring="[para(17(a,1),9(a,1,1,1,1))].">
      <j1 rule="para" parents="17 9"/>
    </justification>
  </clause>

  <clause id="25">
    <literal><![CDATA[
      ((x v x'')' v c_0')' = x
    ]]></literal>
    <justification jstring="[para(17(a,1),9(a,1,1,2,1))].">
      <j1 rule="para" parents="17 9"/>
    </justification>
  </clause>

  <clause id="26">
    <literal><![CDATA[
      ((x v y')' v (x v y)') v x = c_0
    ]]></literal>
    <justification jstring="[para(9(a,1),17(a,1,2))].">
      <j1 rule="para" parents="9 17"/>
    </justification>
  </clause>

  <clause id="27">
    <literal><![CDATA[
      x v (y v (z v x')) = y v (z v c_0)
    ]]></literal>
    <justification jstring="[para(23(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="23 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28">
    <literal><![CDATA[
      ((x v (y v x')')' v (y v c_0)')' = x
    ]]></literal>
    <justification jstring="[para(23(a,1),9(a,1,1,2,1))].">
      <j1 rule="para" parents="23 9"/>
    </justification>
  </clause>

  <clause id="30">
    <literal><![CDATA[
      (c_0' v (x v ((x v y) v y))')' = x v y
    ]]></literal>
    <justification jstring="[para(5(a,1),24(a,1,1,2,1))].">
      <j1 rule="para" parents="5 24"/>
    </justification>
  </clause>

  <clause id="31">
    <literal><![CDATA[
      ((x v y)' v (x v (c_0' v (y v y)'))')' = x
    ]]></literal>
    <justification jstring="[para(24(a,1),9(a,1,1,1,1,2))].">
      <j1 rule="para" parents="24 9"/>
    </justification>
  </clause>

  <clause id="32">
    <literal><![CDATA[
      (x v (c_0' v (x v x))')' = c_0'
    ]]></literal>
    <justification jstring="[para(24(a,1),9(a,1,1,1))].">
      <j1 rule="para" parents="24 9"/>
    </justification>
  </clause>

  <clause id="33">
    <literal><![CDATA[
      ((c_0' v (x v x)'')' v x)' = c_0'
    ]]></literal>
    <justification jstring="[para(24(a,1),9(a,1,1,2))].">
      <j1 rule="para" parents="24 9"/>
    </justification>
  </clause>

  <clause id="34">
    <literal><![CDATA[
      (c_0' v (x v x)') v x = c_0
    ]]></literal>
    <justification jstring="[para(24(a,1),17(a,1,2))].">
      <j1 rule="para" parents="24 17"/>
    </justification>
  </clause>

  <clause id="35">
    <literal><![CDATA[
      (c_0' v (x v x)') v (y v x) = y v c_0
    ]]></literal>
    <justification jstring="[para(24(a,1),23(a,1,2,2))].">
      <j1 rule="para" parents="24 23"/>
    </justification>
  </clause>

  <clause id="36">
    <literal><![CDATA[
      x v (y v (z v (u v v))) = z v (x v (u v (y v v)))
    ]]></literal>
    <justification jstring="[para(18(a,1),5(a,1,2))].">
      <j1 rule="para" parents="18 5"/>
    </justification>
  </clause>

  <clause id="40">
    <literal><![CDATA[
      ((x v (y v (z v u))')' v (z v (x v (y v u)))')' = x
    ]]></literal>
    <justification jstring="[para(18(a,1),9(a,1,1,2,1))].">
      <j1 rule="para" parents="18 9"/>
    </justification>
  </clause>

  <clause id="41">
    <literal><![CDATA[
      ((x v (y v (z v u))')' v (y v (z v (x v u)))')' = x
    ]]></literal>
    <justification jstring="[para(18(a,2),9(a,1,1,2,1))].">
      <j1 rule="para" parents="18 9"/>
    </justification>
  </clause>

  <clause id="42">
    <literal><![CDATA[
      x v (y v (z v (u v x'))) = y v (z v (u v c_0))
    ]]></literal>
    <justification jstring="[para(23(a,1),18(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="23 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43">
    <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(18(a,1),24(a,1,1,2,1)),rewrite(5(6))].">
      <j1 rule="para" parents="18 24"/>
      <j2 rule="rewrite" parents="5"/>
    </justification>
  </clause>

  <clause id="56">
    <literal><![CDATA[
      (c_0' v (x' v x')') v c_0 = x v c_0
    ]]></literal>
    <justification jstring="[para(34(a,1),23(a,1,2)),flip(a)].">
      <j1 rule="para" parents="34 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="65">
    <literal><![CDATA[
      (x v ((x v x'')' v c_0)')' = (x v x'')'
    ]]></literal>
    <justification jstring="[para(25(a,1),9(a,1,1,1))].">
      <j1 rule="para" parents="25 9"/>
    </justification>
  </clause>

  <clause id="66">
    <literal><![CDATA[
      (((x v x'')' v c_0'')' v x)' = (x v x'')'
    ]]></literal>
    <justification jstring="[para(25(a,1),9(a,1,1,2))].">
      <j1 rule="para" parents="25 9"/>
    </justification>
  </clause>

  <clause id="68">
    <literal><![CDATA[
      ((x v x'')' v c_0') v x = c_0
    ]]></literal>
    <justification jstring="[para(25(a,1),17(a,1,2))].">
      <j1 rule="para" parents="25 17"/>
    </justification>
  </clause>

  <clause id="72">
    <literal><![CDATA[
      (x v (x v (c_0' v x))')' = c_0'
    ]]></literal>
    <justification jstring="[para(5(a,1),32(a,1,1,2,1))].">
      <j1 rule="para" parents="5 32"/>
    </justification>
  </clause>

  <clause id="74">
    <literal><![CDATA[
      (c_0' v (x v (c_0' v (x v x)))')' = x
    ]]></literal>
    <justification jstring="[para(32(a,1),9(a,1,1,1))].">
      <j1 rule="para" parents="32 9"/>
    </justification>
  </clause>

  <clause id="76">
    <literal><![CDATA[
      (x v (c_0' v (x v x))') v c_0' = c_0
    ]]></literal>
    <justification jstring="[para(32(a,1),17(a,1,2))].">
      <j1 rule="para" parents="32 17"/>
    </justification>
  </clause>

  <clause id="85">
    <literal><![CDATA[
      (c_0' v (((x' v x''')' v c_0') v x)')' = (x' v x''')' v c_0'
    ]]></literal>
    <justification jstring="[para(68(a,1),9(a,1,1,1,1))].">
      <j1 rule="para" parents="68 9"/>
    </justification>
  </clause>

  <clause id="116">
    <literal><![CDATA[
      ((x v y)' v ((y v y'')' v (x v c_0'))')' = x
    ]]></literal>
    <justification jstring="[para(25(a,1),19(a,1,1,1,1,2))].">
      <j1 rule="para" parents="25 19"/>
    </justification>
  </clause>

  <clause id="118">
    <literal><![CDATA[
      (c_0' v (c_0' v (x v (x v x)))')' = x
    ]]></literal>
    <justification jstring="[para(32(a,1),19(a,1,1,1))].">
      <j1 rule="para" parents="32 19"/>
    </justification>
  </clause>

  <clause id="126">
    <literal><![CDATA[
      (c_0' v (x v (x v (c_0' v x)))')' = x
    ]]></literal>
    <justification jstring="[para(72(a,1),9(a,1,1,1))].">
      <j1 rule="para" parents="72 9"/>
    </justification>
  </clause>

  <clause id="144">
    <literal><![CDATA[
      ((c_0' v (x v x)'')' v x) v c_0' = c_0
    ]]></literal>
    <justification jstring="[para(24(a,1),26(a,1,1,2))].">
      <j1 rule="para" parents="24 26"/>
    </justification>
  </clause>

  <clause id="158">
    <literal><![CDATA[
      (c_0' v (x v (c_0' v (x v x)))') v x = c_0
    ]]></literal>
    <justification jstring="[para(32(a,1),26(a,1,1,1))].">
      <j1 rule="para" parents="32 26"/>
    </justification>
  </clause>

  <clause id="169">
    <literal><![CDATA[
      (c_0' v (x v (x v (c_0' v x)))') v x = c_0
    ]]></literal>
    <justification jstring="[para(72(a,1),26(a,1,1,1))].">
      <j1 rule="para" parents="72 26"/>
    </justification>
  </clause>

  <clause id="183">
    <literal><![CDATA[
      (c_0' v ((x v (c_0' v (x v x))') v c_0)')' = x v (c_0' v (x v x))'
    ]]></literal>
    <justification jstring="[para(76(a,1),9(a,1,1,1,1))].">
      <j1 rule="para" parents="76 9"/>
    </justification>
  </clause>

  <clause id="184">
    <literal><![CDATA[
      (x v (c_0' v (x v x))') v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(76(a,1),23(a,1,2)),flip(a)].">
      <j1 rule="para" parents="76 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="193">
    <literal><![CDATA[
      x v (c_0' v (x v x))' = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(183),rewrite(184(10),24(8)),flip(a)].">
      <j1 rule="back_rewrite" parents="183"/>
      <j2 rule="rewrite" parents="184 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="204">
    <literal><![CDATA[
      ((x v c_0)' v (y v (((x v y') v z')' v ((x v y') v z)'))')' = y
    ]]></literal>
    <justification jstring="[para(23(a,1),20(a,1,1,1,1))].">
      <j1 rule="para" parents="23 20"/>
    </justification>
  </clause>

  <clause id="251">
    <literal><![CDATA[
      x v (y v (c_0' v (x v x))') = y v c_0
    ]]></literal>
    <justification jstring="[para(193(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="193 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="254">
    <literal><![CDATA[
      (c_0' v (x v x)) v c_0 = x v c_0
    ]]></literal>
    <justification jstring="[para(193(a,1),23(a,1,2))].">
      <j1 rule="para" parents="193 23"/>
    </justification>
  </clause>

  <clause id="255">
    <literal><![CDATA[
      c_0'' v (c_0'' v c_0)' = c_0
    ]]></literal>
    <justification jstring="[para(23(a,1),193(a,1,2,1))].">
      <j1 rule="para" parents="23 193"/>
    </justification>
  </clause>

  <clause id="280">
    <literal><![CDATA[
      (c_0'' v c_0) v c_0 = c_0'' v c_0
    ]]></literal>
    <justification jstring="[para(23(a,1),254(a,1,1))].">
      <j1 rule="para" parents="23 254"/>
    </justification>
  </clause>

  <clause id="294">
    <literal><![CDATA[
      (c_0' v (c_0'' v (c_0'' v c_0))')' = c_0''
    ]]></literal>
    <justification jstring="[para(255(a,1),9(a,1,1,1,1))].">
      <j1 rule="para" parents="255 9"/>
    </justification>
  </clause>

  <clause id="300">
    <literal><![CDATA[
      (c_0'' v c_0) v (x v c_0) = x v (c_0'' v c_0)
    ]]></literal>
    <justification jstring="[para(255(a,1),27(a,1,2,2))].">
      <j1 rule="para" parents="255 27"/>
    </justification>
  </clause>

  <clause id="480">
    <literal><![CDATA[
      (((x v c_0')' v ((c_0' v (y v y)') v (x v y))'')' v x)' = (x v c_0')'
    ]]></literal>
    <justification jstring="[para(35(a,2),22(a,1,1,1,1,2,1,1))].">
      <j1 rule="para" parents="35 22"/>
    </justification>
  </clause>

  <clause id="540">
    <literal><![CDATA[
      ((c_0' v (x v x)'')' v x) v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(33(a,1),56(a,1,1,2,1,1)),rewrite(33(13),56(11)),flip(a)].">
      <j1 rule="para" parents="33 56"/>
      <j2 rule="rewrite" parents="33 56"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="545">
    <literal><![CDATA[
      (c_0' v ((x v y) v (c_0' v (x v ((x v y) v y))))')' = x v y
    ]]></literal>
    <justification jstring="[para(5(a,1),74(a,1,1,2,1,2,2))].">
      <j1 rule="para" parents="5 74"/>
    </justification>
  </clause>

  <clause id="614">
    <literal><![CDATA[
      (c_0' v (c_0' v (x v ((x v y) v ((x v y) v y))))')' = x v y
    ]]></literal>
    <justification jstring="[para(5(a,1),118(a,1,1,2,1,2,2)),rewrite(5(9))].">
      <j1 rule="para" parents="5 118"/>
      <j2 rule="rewrite" parents="5"/>
    </justification>
  </clause>

  <clause id="676">
    <literal><![CDATA[
      (c_0' v (x v x)) v (y v c_0) = x v (y v c_0)
    ]]></literal>
    <justification jstring="[para(251(a,1),27(a,1,2))].">
      <j1 rule="para" parents="251 27"/>
    </justification>
  </clause>

  <clause id="812">
    <literal><![CDATA[
      (c_0' v c_0''')' v c_0' = (c_0' v c_0''')'
    ]]></literal>
    <justification jstring="[para(68(a,1),30(a,1,1,2,1,2)),rewrite(65(15)),flip(a)].">
      <j1 rule="para" parents="68 30"/>
      <j2 rule="rewrite" parents="65"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="821">
    <literal><![CDATA[
      c_0'' v c_0 = c_0''
    ]]></literal>
    <justification jstring="[para(280(a,1),30(a,1,1,2,1,2,1)),rewrite(280(14),5(13),280(12),294(14),280(10)),flip(a)].">
      <j1 rule="para" parents="280 30"/>
      <j2 rule="rewrite" parents="280 5 280 294 280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="851">
    <literal><![CDATA[
      c_0'' v (x v c_0) = x v c_0''
    ]]></literal>
    <justification jstring="[back_rewrite(300),rewrite(821(5),821(11))].">
      <j1 rule="back_rewrite" parents="300"/>
      <j2 rule="rewrite" parents="821 821"/>
    </justification>
  </clause>

  <clause id="853">
    <literal><![CDATA[
      (c_0' v (c_0 v c_0)') v c_0'' = c_0''
    ]]></literal>
    <justification jstring="[para(821(a,1),35(a,1,2)),rewrite(821(16))].">
      <j1 rule="para" parents="821 35"/>
      <j2 rule="rewrite" parents="821"/>
    </justification>
  </clause>

  <clause id="858">
    <literal><![CDATA[
      c_0' v (c_0'' v (x v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[para(851(a,2),23(a,1,2))].">
      <j1 rule="para" parents="851 23"/>
    </justification>
  </clause>

  <clause id="907">
    <literal><![CDATA[
      c_0'' v (x v (c_0' v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[para(858(a,1),18(a,2))].">
      <j1 rule="para" parents="858 18"/>
    </justification>
  </clause>

  <clause id="995">
    <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(34(a,1),907(a,1,2)),rewrite(821(5),5(14)),flip(a)].">
      <j1 rule="para" parents="34 907"/>
      <j2 rule="rewrite" parents="821 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1002">
    <literal><![CDATA[
      x v ((c_0' v (x v (c_0' v ((x v (c_0' v c_0)) v c_0)))') v c_0) = c_0''
    ]]></literal>
    <justification jstring="[para(907(a,1),35(a,1,2)),rewrite(5(13),5(12),5(18),821(23))].">
      <j1 rule="para" parents="907 35"/>
      <j2 rule="rewrite" parents="5 5 5 821"/>
    </justification>
  </clause>

  <clause id="1019">
    <literal><![CDATA[
      (c_0' v c_0''')'' = c_0'
    ]]></literal>
    <justification jstring="[para(853(a,1),28(a,1,1,1,1,2,1)),rewrite(34(17),812(11))].">
      <j1 rule="para" parents="853 28"/>
      <j2 rule="rewrite" parents="34 812"/>
    </justification>
  </clause>

  <clause id="1024">
    <literal><![CDATA[
      (c_0' v c_0''')' = c_0
    ]]></literal>
    <justification jstring="[para(1019(a,1),17(a,1,2)),rewrite(812(11))].">
      <j1 rule="para" parents="1019 17"/>
      <j2 rule="rewrite" parents="812"/>
    </justification>
  </clause>

  <clause id="1029">
    <literal><![CDATA[
      ((c_0' v c_0'''')' v c_0)' = c_0'
    ]]></literal>
    <justification jstring="[para(1024(a,1),9(a,1,1,2))].">
      <j1 rule="para" parents="1024 9"/>
    </justification>
  </clause>

  <clause id="1224">
    <literal><![CDATA[
      ((((c_0' v c_0'''')' v c_0) v c_0'')' v c_0')' = (c_0' v c_0'''')' v c_0
    ]]></literal>
    <justification jstring="[para(1029(a,1),25(a,1,1,1,1,2,1))].">
      <j1 rule="para" parents="1029 25"/>
    </justification>
  </clause>

  <clause id="1447">
    <literal><![CDATA[
      (c_0' v (x v x)'')' v x = c_0
    ]]></literal>
    <justification jstring="[para(144(a,1),9(a,1,1,1,1)),rewrite(540(12),24(8)),flip(a)].">
      <j1 rule="para" parents="144 9"/>
      <j2 rule="rewrite" parents="540 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1462">
    <literal><![CDATA[
      (c_0' v (x v x)'')' v (y v x) = y v c_0
    ]]></literal>
    <justification jstring="[para(1447(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1447 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1519">
    <literal><![CDATA[
      ((x v (y v (z v (u v x')))')' v (z v (y v (u v c_0)))')' = x
    ]]></literal>
    <justification jstring="[para(27(a,1),40(a,1,1,2,1,2))].">
      <j1 rule="para" parents="27 40"/>
    </justification>
  </clause>

  <clause id="1642">
    <literal><![CDATA[
      (((c_0' v (c_0' 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 x)' v c_0')' = c_0' v (c_0' v ((x v y')' v (((x v y')' v (x v y)') v (((x v y')' v (x v y)') v (x v y)'))))'
    ]]></literal>
    <justification jstring="[para(158(a,1),20(a,1,1,2,1)),rewrite(5(23),5(25),5(24),5(56),5(58),5(57))].">
      <j1 rule="para" parents="158 20"/>
      <j2 rule="rewrite" parents="5 5 5 5 5 5"/>
    </justification>
  </clause>

  <clause id="1656">
    <literal><![CDATA[
      (((c_0' v (c_0' v (c_0' v ((c_0' v (x v x)') v ((c_0' v (x v x)') v (x v x)'))))') v x)' v c_0')' = c_0' v (c_0' v (c_0' v ((c_0' v (x v x)') v ((c_0' v (x v x)') v (x v x)'))))'
    ]]></literal>
    <justification jstring="[para(158(a,1),31(a,1,1,2,1)),rewrite(5(20),5(22),5(21),5(50),5(52),5(51))].">
      <j1 rule="para" parents="158 31"/>
      <j2 rule="rewrite" parents="5 5 5 5 5 5"/>
    </justification>
  </clause>

  <clause id="1822">
    <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(1447(a,1),41(a,1,1,1,1,2,1,2))].">
      <j1 rule="para" parents="1447 41"/>
    </justification>
  </clause>

  <clause id="1916">
    <literal><![CDATA[
      c_0 v (c_0' v c_0) = c_0
    ]]></literal>
    <justification jstring="[para(676(a,1),30(a,1,1,2,1,2)),rewrite(5(10),5(9),126(13),5(7)),flip(a)].">
      <j1 rule="para" parents="676 30"/>
      <j2 rule="rewrite" parents="5 5 126 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1943">
    <literal><![CDATA[
      c_0 v (c_0' v (x v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[para(1916(a,1),18(a,2,2))].">
      <j1 rule="para" parents="1916 18"/>
    </justification>
  </clause>

  <clause id="1948">
    <literal><![CDATA[
      c_0'' = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(1916(a,1),35(a,1,2)),rewrite(5(11),995(15))].">
      <j1 rule="para" parents="1916 35"/>
      <j2 rule="rewrite" parents="5 995"/>
    </justification>
  </clause>

  <clause id="2028">
    <literal><![CDATA[
      ((c_0 v (c_0 v c_0))' v c_0')' = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(1224),rewrite(1948(5),1447(11),1948(4),1948(15),1447(21))].">
      <j1 rule="back_rewrite" parents="1224"/>
      <j2 rule="rewrite" parents="1948 1447 1948 1948 1447"/>
    </justification>
  </clause>

  <clause id="2067">
    <literal><![CDATA[
      x v ((c_0' v (x v (c_0' v ((x v (c_0' v c_0)) v c_0)))') v c_0) = c_0 v c_0
    ]]></literal>
    <justification jstring="[back_rewrite(1002),rewrite(1948(21))].">
      <j1 rule="back_rewrite" parents="1002"/>
      <j2 rule="rewrite" parents="1948"/>
    </justification>
  </clause>

  <clause id="2074">
    <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(995),rewrite(1948(18))].">
      <j1 rule="back_rewrite" parents="995"/>
      <j2 rule="rewrite" parents="1948"/>
    </justification>
  </clause>

  <clause id="2096">
    <literal><![CDATA[
      (c_0 v c_0) v (x v (c_0' v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[back_rewrite(907),rewrite(1948(3))].">
      <j1 rule="back_rewrite" parents="907"/>
      <j2 rule="rewrite" parents="1948"/>
    </justification>
  </clause>

  <clause id="2158">
    <literal><![CDATA[
      ((c_0 v ((x v x'')' v c_0))' v x)' = (x v x'')'
    ]]></literal>
    <justification jstring="[back_rewrite(66),rewrite(1948(7),5(8))].">
      <j1 rule="back_rewrite" parents="66"/>
      <j2 rule="rewrite" parents="1948 5"/>
    </justification>
  </clause>

  <clause id="2204">
    <literal><![CDATA[
      (((x v (y v (z v (u v x')))')' v (y v (z v (u v c_0)))'')' v x)' = (x v (y v (z v (u v x')))')'
    ]]></literal>
    <justification jstring="[para(42(a,1),22(a,1,1,1,1,2,1,1))].">
      <j1 rule="para" parents="42 22"/>
    </justification>
  </clause>

  <clause id="2316">
    <literal><![CDATA[
      c_0' v (x v ((x v c_0) v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[para(676(a,1),43(a,1,1,2,1,2,2)),rewrite(5(11),545(16),5(9)),flip(a)].">
      <j1 rule="para" parents="676 43"/>
      <j2 rule="rewrite" parents="5 545 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2318">
    <literal><![CDATA[
      (c_0' v (c_0 v (x v c_0))')' = x v c_0
    ]]></literal>
    <justification jstring="[para(1943(a,1),43(a,1,1,2,1,2,2,1)),rewrite(5(10),5(12),2316(11),1943(16))].">
      <j1 rule="para" parents="1943 43"/>
      <j2 rule="rewrite" parents="5 5 2316 1943"/>
    </justification>
  </clause>

  <clause id="2742">
    <literal><![CDATA[
      x v ((x v c_0) v (c_0' v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[para(2316(a,1),18(a,2))].">
      <j1 rule="para" parents="2316 18"/>
    </justification>
  </clause>

  <clause id="2759">
    <literal><![CDATA[
      x v (y v ((x v c_0) v (c_0' v c_0))) = y v (x v c_0)
    ]]></literal>
    <justification jstring="[para(2316(a,1),36(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2316 36"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2767">
    <literal><![CDATA[
      x v ((x v c_0) v ((c_0' v (x v ((x v ((x v c_0) v c_0)) v ((x v ((x v c_0) v c_0)) v c_0)))') v c_0)) = c_0
    ]]></literal>
    <justification jstring="[para(2316(a,1),169(a,1,1,2,1,2,2)),rewrite(5(15),5(16),5(24),5(23))].">
      <j1 rule="para" parents="2316 169"/>
      <j2 rule="rewrite" parents="5 5 5 5"/>
    </justification>
  </clause>

  <clause id="2793">
    <literal><![CDATA[
      (c_0' v (x v ((x v c_0) v c_0))') v c_0 = (c_0' v (c_0 v (x v c_0))') v c_0
    ]]></literal>
    <justification jstring="[para(2318(a,1),56(a,1,1,2,1,1)),rewrite(2318(13),5(7))].">
      <j1 rule="para" parents="2318 56"/>
      <j2 rule="rewrite" parents="2318 5"/>
    </justification>
  </clause>

  <clause id="2795">
    <literal><![CDATA[
      ((x v ((c_0 v (x v c_0)) v c_0))' v (c_0' v c_0)')' = c_0 v (x v c_0)
    ]]></literal>
    <justification jstring="[para(2318(a,1),28(a,1,1,1,1,2)),rewrite(5(7))].">
      <j1 rule="para" parents="2318 28"/>
      <j2 rule="rewrite" parents="5"/>
    </justification>
  </clause>

  <clause id="2800">
    <literal><![CDATA[
      (c_0' v c_0')' = c_0' v c_0
    ]]></literal>
    <justification jstring="[para(1916(a,1),2318(a,1,1,2,1))].">
      <j1 rule="para" parents="1916 2318"/>
    </justification>
  </clause>

  <clause id="2803">
    <literal><![CDATA[
      (c_0' v c_0') v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[back_rewrite(2074),rewrite(2793(15),1916(8))].">
      <j1 rule="back_rewrite" parents="2074"/>
      <j2 rule="rewrite" parents="2793 1916"/>
    </justification>
  </clause>

  <clause id="2840">
    <literal><![CDATA[
      (c_0' v (c_0' v c_0))' = c_0'
    ]]></literal>
    <justification jstring="[para(2800(a,1),9(a,1,1,2)),rewrite(1948(5),5(6),1916(6))].">
      <j1 rule="para" parents="2800 9"/>
      <j2 rule="rewrite" parents="1948 5 1916"/>
    </justification>
  </clause>

  <clause id="2854">
    <literal><![CDATA[
      (c_0' v (c_0' v c_0)) v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(2800(a,1),56(a,1,1,2))].">
      <j1 rule="para" parents="2800 56"/>
    </justification>
  </clause>

  <clause id="3052">
    <literal><![CDATA[
      c_0' v (c_0' v c_0) = c_0
    ]]></literal>
    <justification jstring="[para(2840(a,1),25(a,1,1,1,1,2,1)),rewrite(1948(10),5(11),2854(10),2028(10)),flip(a)].">
      <j1 rule="para" parents="2840 25"/>
      <j2 rule="rewrite" parents="1948 5 2854 2028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3057">
    <literal><![CDATA[
      c_0' v (x v (c_0' v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[para(3052(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3052 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3063">
    <literal><![CDATA[
      c_0' v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(3052(a,1),35(a,1,2)),rewrite(5(11),2793(15),1916(8),2803(7)),flip(a)].">
      <j1 rule="para" parents="3052 35"/>
      <j2 rule="rewrite" parents="5 2793 1916 2803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3064">
    <literal><![CDATA[
      c_0 v (c_0 v c_0) = c_0
    ]]></literal>
    <justification jstring="[para(35(a,2),3052(a,1,2)),rewrite(5(11),34(10),3063(6),5(6),3063(5))].">
      <j1 rule="para" parents="35 3052"/>
      <j2 rule="rewrite" parents="5 34 3063 5 3063"/>
    </justification>
  </clause>

  <clause id="3065">
    <literal><![CDATA[
      c_0 v c_0 = c_0
    ]]></literal>
    <justification jstring="[para(3052(a,1),22(a,1,1,1,1,2,1,1)),rewrite(3063(6),24(8),1948(4),3064(5),2800(6),3063(4),3063(9),24(11))].">
      <j1 rule="para" parents="3052 22"/>
      <j2 rule="rewrite" parents="3063 24 1948 3064 2800 3063 3063 24"/>
    </justification>
  </clause>

  <clause id="3076">
    <literal><![CDATA[
      c_0' v (x v c_0) = x v c_0
    ]]></literal>
    <justification jstring="[back_rewrite(3057),rewrite(3063(6),3065(5))].">
      <j1 rule="back_rewrite" parents="3057"/>
      <j2 rule="rewrite" parents="3063 3065"/>
    </justification>
  </clause>

  <clause id="3101">
    <literal><![CDATA[
      ((x v ((c_0 v (x v c_0)) v c_0))' v c_0')' = c_0 v (x v c_0)
    ]]></literal>
    <justification jstring="[back_rewrite(2795),rewrite(3063(12),3065(11))].">
      <j1 rule="back_rewrite" parents="2795"/>
      <j2 rule="rewrite" parents="3063 3065"/>
    </justification>
  </clause>

  <clause id="3104">
    <literal><![CDATA[
      x v (y v ((x v c_0) v c_0)) = y v (x v c_0)
    ]]></literal>
    <justification jstring="[back_rewrite(2759),rewrite(3063(6),3065(5))].">
      <j1 rule="back_rewrite" parents="2759"/>
      <j2 rule="rewrite" parents="3063 3065"/>
    </justification>
  </clause>

  <clause id="3106">
    <literal><![CDATA[
      x v ((x v c_0) v c_0) = x v c_0
    ]]></literal>
    <justification jstring="[back_rewrite(2742),rewrite(3063(6),3065(5))].">
      <j1 rule="back_rewrite" parents="2742"/>
      <j2 rule="rewrite" parents="3063 3065"/>
    </justification>
  </clause>

  <clause id="3120">
    <literal><![CDATA[
      c_0 v (x v c_0) = x v c_0
    ]]></literal>
    <justification jstring="[back_rewrite(2096),rewrite(3065(3),3063(5),3065(4))].">
      <j1 rule="back_rewrite" parents="2096"/>
      <j2 rule="rewrite" parents="3065 3063 3065"/>
    </justification>
  </clause>

  <clause id="3125">
    <literal><![CDATA[
      x v ((c_0' v (x v c_0)') v c_0) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(2067),rewrite(3063(8),3065(7),3076(9),3106(7),3065(12))].">
      <j1 rule="back_rewrite" parents="2067"/>
      <j2 rule="rewrite" parents="3063 3065 3076 3106 3065"/>
    </justification>
  </clause>

  <clause id="3177">
    <literal><![CDATA[
      c_0'' = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(1948),rewrite(3065(6))].">
      <j1 rule="back_rewrite" parents="1948"/>
      <j2 rule="rewrite" parents="3065"/>
    </justification>
  </clause>

  <clause id="3191">
    <literal><![CDATA[
      x v ((x v c_0) v ((c_0' v (x v c_0)') v c_0)) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(2767),rewrite(3106(9),3106(11),3104(12),5(9),3106(9))].">
      <j1 rule="back_rewrite" parents="2767"/>
      <j2 rule="rewrite" parents="3106 3106 3104 5 3106"/>
    </justification>
  </clause>

  <clause id="3193">
    <literal><![CDATA[
      ((x v c_0)' v c_0')' = x v c_0
    ]]></literal>
    <justification jstring="[back_rewrite(3101),rewrite(3120(4),3106(5),3120(11))].">
      <j1 rule="back_rewrite" parents="3101"/>
      <j2 rule="rewrite" parents="3120 3106 3120"/>
    </justification>
  </clause>

  <clause id="3215">
    <literal><![CDATA[
      (((x v x'')' v c_0)' v x)' = (x v x'')'
    ]]></literal>
    <justification jstring="[back_rewrite(2158),rewrite(3120(8))].">
      <j1 rule="back_rewrite" parents="2158"/>
      <j2 rule="rewrite" parents="3120"/>
    </justification>
  </clause>

  <clause id="3877">
    <literal><![CDATA[
      ((x v (y v c_0))' v ((y v c_0)' v (x v c_0'))')' = x
    ]]></literal>
    <justification jstring="[para(3193(a,1),19(a,1,1,1,1,2))].">
      <j1 rule="para" parents="3193 19"/>
    </justification>
  </clause>

  <clause id="3887">
    <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(3193(a,1),21(a,1,1,2,1,2,1)),rewrite(5(11),3193(21))].">
      <j1 rule="para" parents="3193 21"/>
      <j2 rule="rewrite" parents="5 3193"/>
    </justification>
  </clause>

  <clause id="3895">
    <literal><![CDATA[
      ((x v c_0)' v ((x v c_0)' v c_0)')' = c_0
    ]]></literal>
    <justification jstring="[para(3193(a,1),28(a,1,1,1,1,2)),rewrite(3120(4))].">
      <j1 rule="para" parents="3193 28"/>
      <j2 rule="rewrite" parents="3120"/>
    </justification>
  </clause>

  <clause id="3924">
    <literal><![CDATA[
      x v (y v ((c_0' v (x v c_0)') v c_0)) = y v c_0
    ]]></literal>
    <justification jstring="[para(3125(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3125 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3935">
    <literal><![CDATA[
      (((x v ((c_0' v (x v c_0)') v c_0)')' v c_0)' v x)' = (x v ((c_0' v (x v c_0)') v c_0)')'
    ]]></literal>
    <justification jstring="[para(3125(a,1),22(a,1,1,1,1,2,1,1)),rewrite(3177(14))].">
      <j1 rule="para" parents="3125 22"/>
      <j2 rule="rewrite" parents="3177"/>
    </justification>
  </clause>

  <clause id="3948">
    <literal><![CDATA[
      (x v c_0) v c_0 = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(3191),rewrite(3924(12))].">
      <j1 rule="back_rewrite" parents="3191"/>
      <j2 rule="rewrite" parents="3924"/>
    </justification>
  </clause>

  <clause id="4065">
    <literal><![CDATA[
      (x v c_0) v (y v c_0) = y v c_0
    ]]></literal>
    <justification jstring="[para(3948(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3948 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4082">
    <literal><![CDATA[
      x v c_0 = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(3887),rewrite(4065(11),3895(11)),flip(a)].">
      <j1 rule="back_rewrite" parents="3887"/>
      <j2 rule="rewrite" parents="4065 3895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4114">
    <literal><![CDATA[
      (c_0' v x)' = (x v c_0')'
    ]]></literal>
    <justification jstring="[back_rewrite(3935),rewrite(4082(4),4082(7),4082(6),4082(8),4082(11))].">
      <j1 rule="back_rewrite" parents="3935"/>
      <j2 rule="rewrite" parents="4082 4082 4082 4082 4082"/>
    </justification>
  </clause>

  <clause id="4127">
    <literal><![CDATA[
      (c_0' v (c_0' v (x v c_0'))')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(3877),rewrite(4082(2),4082(2),4082(4))].">
      <j1 rule="back_rewrite" parents="3877"/>
      <j2 rule="rewrite" parents="4082 4082 4082"/>
    </justification>
  </clause>

  <clause id="4279">
    <literal><![CDATA[
      (x v x'')' = (c_0' v x)'
    ]]></literal>
    <justification jstring="[back_rewrite(3215),rewrite(4082(6)),flip(a)].">
      <j1 rule="back_rewrite" parents="3215"/>
      <j2 rule="rewrite" parents="4082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4381">
    <literal><![CDATA[
      (x v (y v (z v (u v x')))')' = (c_0' v x)'
    ]]></literal>
    <justification jstring="[back_rewrite(2204),rewrite(4082(9),4082(9),4082(9),3177(10),4082(9)),flip(a)].">
      <j1 rule="back_rewrite" parents="2204"/>
      <j2 rule="rewrite" parents="4082 4082 4082 3177 4082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4420">
    <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(1822),rewrite(4082(2))].">
      <j1 rule="back_rewrite" parents="1822"/>
      <j2 rule="rewrite" parents="4082"/>
    </justification>
  </clause>

  <clause id="4488">
    <literal><![CDATA[
      (c_0' v (c_0' v x)')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(1519),rewrite(4381(7),4082(6),4082(6),4082(6),4114(8,R))].">
      <j1 rule="back_rewrite" parents="1519"/>
      <j2 rule="rewrite" parents="4381 4082 4082 4082 4114"/>
    </justification>
  </clause>

  <clause id="4507">
    <literal><![CDATA[
      (c_0' v (x v x)'')' v (y v x) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(1462),rewrite(4082(11))].">
      <j1 rule="back_rewrite" parents="1462"/>
      <j2 rule="rewrite" parents="4082"/>
    </justification>
  </clause>

  <clause id="4710">
    <literal><![CDATA[
      (c_0' v (x v (((y v x') v z')' v ((y v x') v z)'))')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(204),rewrite(4082(2))].">
      <j1 rule="back_rewrite" parents="204"/>
      <j2 rule="rewrite" parents="4082"/>
    </justification>
  </clause>

  <clause id="4724">
    <literal><![CDATA[
      (c_0' v (x v x)') v (y v x) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(35),rewrite(4082(9))].">
      <j1 rule="back_rewrite" parents="35"/>
      <j2 rule="rewrite" parents="4082"/>
    </justification>
  </clause>

  <clause id="4750">
    <literal><![CDATA[
      (c_0' v ((c_0' v (c_0' v (c_0' v ((c_0' v (x v x)') v ((c_0' v (x v x)') v (x v x)'))))') v x)')' = c_0' v (c_0' v (c_0' v ((c_0' v (x v x)') v ((c_0' v (x v x)') v (x v x)'))))'
    ]]></literal>
    <justification jstring="[back_rewrite(1656),rewrite(4114(30,R))].">
      <j1 rule="back_rewrite" parents="1656"/>
      <j2 rule="rewrite" parents="4114"/>
    </justification>
  </clause>

  <clause id="4751">
    <literal><![CDATA[
      (c_0' v ((c_0' v (c_0' 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 x)')' = c_0' v (c_0' v ((x v y')' v (((x v y')' v (x v y)') v (((x v y')' v (x v y)') v (x v y)'))))'
    ]]></literal>
    <justification jstring="[back_rewrite(1642),rewrite(4114(33,R))].">
      <j1 rule="back_rewrite" parents="1642"/>
      <j2 rule="rewrite" parents="4114"/>
    </justification>
  </clause>

  <clause id="4827">
    <literal><![CDATA[
      ((x v y)' v ((c_0' v y)' v (x v c_0'))')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(116),rewrite(4279(6))].">
      <j1 rule="back_rewrite" parents="116"/>
      <j2 rule="rewrite" parents="4279"/>
    </justification>
  </clause>

  <clause id="4830">
    <literal><![CDATA[
      (c_0' v (((c_0' v x')' v c_0') v x)')' = (c_0' v x')' v c_0'
    ]]></literal>
    <justification jstring="[back_rewrite(85),rewrite(4279(8),4279(20))].">
      <j1 rule="back_rewrite" parents="85"/>
      <j2 rule="rewrite" parents="4279 4279"/>
    </justification>
  </clause>

  <clause id="4833">
    <literal><![CDATA[
      x v c_0' = x
    ]]></literal>
    <justification jstring="[back_rewrite(4127),rewrite(4488(11))].">
      <j1 rule="back_rewrite" parents="4127"/>
      <j2 rule="rewrite" parents="4488"/>
    </justification>
  </clause>

  <clause id="4853">
    <literal><![CDATA[
      x v ((x v y) v ((x v y) v y)) = x v y
    ]]></literal>
    <justification jstring="[back_rewrite(614),rewrite(4488(13))].">
      <j1 rule="back_rewrite" parents="614"/>
      <j2 rule="rewrite" parents="4488"/>
    </justification>
  </clause>

  <clause id="4856">
    <literal><![CDATA[
      x'' = x
    ]]></literal>
    <justification jstring="[back_rewrite(4420),rewrite(4833(3),4507(10),4082(3),4833(4))].">
      <j1 rule="back_rewrite" parents="4420"/>
      <j2 rule="rewrite" parents="4833 4507 4082 4833"/>
    </justification>
  </clause>

  <clause id="4884">
    <literal><![CDATA[
      (c_0' v x)' = x'
    ]]></literal>
    <justification jstring="[back_rewrite(480),rewrite(4833(3),4724(8),4856(4),4082(3),4833(7))].">
      <j1 rule="back_rewrite" parents="480"/>
      <j2 rule="rewrite" parents="4833 4724 4856 4082 4833"/>
    </justification>
  </clause>

  <clause id="4892">
    <literal><![CDATA[
      x v x = x
    ]]></literal>
    <justification jstring="[back_rewrite(4830),rewrite(4884(7),4856(4),4833(5),4884(6),4856(3),4884(6),4856(3),4833(4))].">
      <j1 rule="back_rewrite" parents="4830"/>
      <j2 rule="rewrite" parents="4884 4856 4833 4884 4856 4884 4856 4833"/>
    </justification>
  </clause>

  <clause id="4895">
    <literal><![CDATA[
      ((x v y)' v (y' v x)')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(4827),rewrite(4884(6),4833(6))].">
      <j1 rule="back_rewrite" parents="4827"/>
      <j2 rule="rewrite" parents="4884 4833"/>
    </justification>
  </clause>

  <clause id="5007">
    <literal><![CDATA[
      (c_0' v x) v x = c_0' v x
    ]]></literal>
    <justification jstring="[back_rewrite(4751),rewrite(4853(26),4884(14),9(11),4884(9),4856(6),4853(28),4884(16),9(13))].">
      <j1 rule="back_rewrite" parents="4751"/>
      <j2 rule="rewrite" parents="4853 4884 9 4884 4856 4853 4884 9"/>
    </justification>
  </clause>

  <clause id="5008">
    <literal><![CDATA[
      c_0' v x = x
    ]]></literal>
    <justification jstring="[back_rewrite(4750),rewrite(4892(11),4892(15),4892(17),5007(18),4892(17),4884(15),4884(12),4884(9),4856(6),5007(6),4884(6),4884(5),4856(2),4892(9),4892(13),4892(15),5007(16),4892(15),4884(13),4884(10),4884(7),4856(4)),flip(a)].">
      <j1 rule="back_rewrite" parents="4750"/>
      <j2 rule="rewrite" parents="4892 4892 4892 5007 4892 4884 4884 4884 4856 5007 4884 4884 4856 4892 4892 4892 5007 4892 4884 4884 4884 4856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5156">
    <literal><![CDATA[
      x v (((y v x') v z')' v ((y v x') v z)') = x
    ]]></literal>
    <justification jstring="[back_rewrite(4710),rewrite(5008(15),4856(13))].">
      <j1 rule="back_rewrite" parents="4710"/>
      <j2 rule="rewrite" parents="5008 4856"/>
    </justification>
  </clause>

  <clause id="5361">
    <literal><![CDATA[
      (x v y')' v (x v y)' = x'
    ]]></literal>
    <justification jstring="[para(9(a,1),4856(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 4856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5364">
    <literal><![CDATA[
      x v (x v ((x v y')' v y))' = x v y'
    ]]></literal>
    <justification jstring="[para(21(a,1),4856(a,1,1)),rewrite(4856(4)),flip(a)].">
      <j1 rule="para" parents="21 4856"/>
      <j2 rule="rewrite" parents="4856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5369">
    <literal><![CDATA[
      x v (y v x')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(5156),rewrite(5361(10))].">
      <j1 rule="back_rewrite" parents="5156"/>
      <j2 rule="rewrite" parents="5361"/>
    </justification>
  </clause>

  <clause id="5510">
    <literal><![CDATA[
      x v y = y v x
    ]]></literal>
    <justification jstring="[para(4833(a,1),5(a,1,2)),rewrite(4833(4))].">
      <j1 rule="para" parents="4833 5"/>
      <j2 rule="rewrite" parents="4833"/>
    </justification>
  </clause>

  <clause id="5511">
    <literal><![CDATA[
      x v (y v z) = z v (x v y)
    ]]></literal>
    <justification jstring="[para(4833(a,1),18(a,1,2,2)),rewrite(4833(5))].">
      <j1 rule="para" parents="4833 18"/>
      <j2 rule="rewrite" parents="4833"/>
    </justification>
  </clause>

  <clause id="5534">
    <literal><![CDATA[
      x v (x v y)' = x v y'
    ]]></literal>
    <justification jstring="[back_rewrite(5364),rewrite(5510(4),5369(4))].">
      <j1 rule="back_rewrite" parents="5364"/>
      <j2 rule="rewrite" parents="5510 5369"/>
    </justification>
  </clause>

  <clause id="5960">
    <literal><![CDATA[
      x v (y v (z v x')') = y v x
    ]]></literal>
    <justification jstring="[para(5369(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5369 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5964">
    <literal><![CDATA[
      x v (x' v y)' = x
    ]]></literal>
    <justification jstring="[para(5510(a,1),5369(a,1,2,1))].">
      <j1 rule="para" parents="5510 5369"/>
    </justification>
  </clause>

  <clause id="6116">
    <literal><![CDATA[
      x v (y v (x' v z))' = x
    ]]></literal>
    <justification jstring="[para(5(a,1),5964(a,1,2,1))].">
      <j1 rule="para" parents="5 5964"/>
    </justification>
  </clause>

  <clause id="7298">
    <literal><![CDATA[
      (x v y) v z = x v (y v z)
    ]]></literal>
    <justification jstring="[para(5511(a,2),5510(a,1)),flip(a)].">
      <j1 rule="para" parents="5511 5510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7555">
    <literal><![CDATA[
      x v (y v x)' = x v y'
    ]]></literal>
    <justification jstring="[para(5510(a,1),5534(a,1,2,1))].">
      <j1 rule="para" parents="5510 5534"/>
    </justification>
  </clause>

  <clause id="7610">
    <literal><![CDATA[
      x v ((y v (x' v z))' v u) = x v u
    ]]></literal>
    <justification jstring="[para(6116(a,1),7298(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6116 7298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7625">
    <literal><![CDATA[
      x v (y v (z v x)') = y v (x v z')
    ]]></literal>
    <justification jstring="[para(7555(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7555 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7679">
    <literal><![CDATA[
      (x v y)' v (y' v x)' = x'
    ]]></literal>
    <justification jstring="[para(4895(a,1),4856(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4895 4856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8476">
    <literal><![CDATA[
      (x v (y v z)')' = (x v (z v y'))' v (x v z')'
    ]]></literal>
    <justification jstring="[para(5960(a,1),7679(a,1,2,1)),rewrite(4856(2),5510(4),7625(4),4856(10)),flip(a)].">
      <j1 rule="para" parents="5960 7679"/>
      <j2 rule="rewrite" parents="4856 5510 7625 4856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8531">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer(MOD)
    ]]></attribute>
    <justification jstring="[back_rewrite(16),rewrite(8476(9),5510(8),7298(8),7610(17),8476(17),5510(16),7298(16),5510(22),7610(25)),xx(a)].">
      <j1 rule="back_rewrite" parents="16"/>
      <j2 rule="rewrite" parents="8476 5510 7298 7610 8476 5510 7298 5510 7610"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="4" length="168" max_count="86">

<comments><![CDATA[
% Proof 4 at 5.52 (+ 0.04) seconds: DIST1.
% Length of proof is 168.
% Level of proof is 43.
% Maximum clause weight is 86.
% Given clauses 290.
]]></comments>

  <clause id="3">
    <literal><![CDATA[
      x ^ (y v z) = (x ^ y) v (x ^ z)
    ]]></literal>
    <attribute><![CDATA[
      answer(DIST1)
    ]]></attribute>
    <justification jstring="[goal].">
      <j1 rule="goal"/>
    </justification>
  </clause>

  <clause id="5">
    <literal><![CDATA[
      x v (y v z) = y v (x v z)
    ]]></literal>
    <attribute><![CDATA[
      label(AJ)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="6">
    <literal><![CDATA[
      x ^ y = (x' v y')'
    ]]></literal>
    <attribute><![CDATA[
      label(DM)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="7">
    <literal><![CDATA[
      x v x' = y v y'
    ]]></literal>
    <attribute><![CDATA[
      label(ONE)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

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

  <clause id="9">
    <literal><![CDATA[
      ((x v y')' v (x v y)')' = x
    ]]></literal>
    <justification jstring="[copy(8),rewrite(6(4))].">
      <j1 rule="copy" parents="8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="13">
    <literal><![CDATA[
      (c4 ^ c5) v (c4 ^ c6) != c4 ^ (c5 v c6)
    ]]></literal>
    <attribute><![CDATA[
      answer(DIST1)
    ]]></attribute>
    <justification jstring="[deny(3)].">
      <j1 rule="deny" parents="3"/>
    </justification>
  </clause>

  <clause id="14">
    <literal><![CDATA[
      (c4' v (c5 v c6)')' != (c4' v c5')' v (c4' v c6')'
    ]]></literal>
    <attribute><![CDATA[
      answer(DIST1)
    ]]></attribute>
    <justification jstring="[copy(13),rewrite(6(3),6(9),6(18)),flip(a)].">
      <j1 rule="copy" parents="13"/>
      <j2 rule="rewrite" parents="6 6 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17">
    <literal><![CDATA[
      x v x' = c_0
    ]]></literal>
    <justification jstring="[new_symbol(7)].">
      <j1 rule="new_symbol" parents="7"/>
    </justification>
  </clause>

  <clause id="18">
    <literal><![CDATA[
      x v (y v (z v u)) = z v (x v (y v u))
    ]]></literal>
    <justification jstring="[para(5(a,1),5(a,1,2))].">
      <j1 rule="para" parents="5 5"/>
    </justification>
  </clause>

  <clause id="19">
    <literal><![CDATA[
      ((x v (y v z)')' v (y v (x v z))')' = x
    ]]></literal>
    <justification jstring="[para(5(a,1),9(a,1,1,2,1))].">
      <j1 rule="para" parents="5 9"/>
    </justification>
  </clause>

  <clause id="20">
    <literal><![CDATA[
      ((x v y)' v (x v ((y v z')' v (y v z)'))')' = x
    ]]></literal>
    <justification jstring="[para(9(a,1),9(a,1,1,1,1,2))].">
      <j1 rule="para" parents="9 9"/>
    </justification>
  </clause>

  <clause id="21">
    <literal><![CDATA[
      (x v (x v ((x v y')' v y))')' = (x v y')'
    ]]></literal>
    <justification jstring="[para(9(a,1),9(a,1,1,1)),rewrite(5(5))].">
      <j1 rule="para" parents="9 9"/>
      <j2 rule="rewrite" parents="5"/>
    </justification>
  </clause>

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

  <clause id="23">
    <literal><![CDATA[
      x v (y v x') = y v c_0
    ]]></literal>
    <justification jstring="[para(17(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24">
    <literal><![CDATA[
      (c_0' v (x v x)')' = x
    ]]></literal>
    <justification jstring="[para(17(a,1),9(a,1,1,1,1))].">
      <j1 rule="para" parents="17 9"/>
    </justification>
  </clause>

  <clause id="25">
    <literal><![CDATA[
      ((x v x'')' v c_0')' = x
    ]]></literal>
    <justification jstring="[para(17(a,1),9(a,1,1,2,1))].">
      <j1 rule="para" parents="17 9"/>
    </justification>
  </clause>

  <clause id="26">
    <literal><![CDATA[
      ((x v y')' v (x v y)') v x = c_0
    ]]></literal>
    <justification jstring="[para(9(a,1),17(a,1,2))].">
      <j1 rule="para" parents="9 17"/>
    </justification>
  </clause>

  <clause id="27">
    <literal><![CDATA[
      x v (y v (z v x')) = y v (z v c_0)
    ]]></literal>
    <justification jstring="[para(23(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="23 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28">
    <literal><![CDATA[
      ((x v (y v x')')' v (y v c_0)')' = x
    ]]></literal>
    <justification jstring="[para(23(a,1),9(a,1,1,2,1))].">
      <j1 rule="para" parents="23 9"/>
    </justification>
  </clause>

  <clause id="30">
    <literal><![CDATA[
      (c_0' v (x v ((x v y) v y))')' = x v y
    ]]></literal>
    <justification jstring="[para(5(a,1),24(a,1,1,2,1))].">
      <j1 rule="para" parents="5 24"/>
    </justification>
  </clause>

  <clause id="31">
    <literal><![CDATA[
      ((x v y)' v (x v (c_0' v (y v y)'))')' = x
    ]]></literal>
    <justification jstring="[para(24(a,1),9(a,1,1,1,1,2))].">
      <j1 rule="para" parents="24 9"/>
    </justification>
  </clause>

  <clause id="32">
    <literal><![CDATA[
      (x v (c_0' v (x v x))')' = c_0'
    ]]></literal>
    <justification jstring="[para(24(a,1),9(a,1,1,1))].">
      <j1 rule="para" parents="24 9"/>
    </justification>
  </clause>

  <clause id="33">
    <literal><![CDATA[
      ((c_0' v (x v x)'')' v x)' = c_0'
    ]]></literal>
    <justification jstring="[para(24(a,1),9(a,1,1,2))].">
      <j1 rule="para" parents="24 9"/>
    </justification>
  </clause>

  <clause id="34">
    <literal><![CDATA[
      (c_0' v (x v x)') v x = c_0
    ]]></literal>
    <justification jstring="[para(24(a,1),17(a,1,2))].">
      <j1 rule="para" parents="24 17"/>
    </justification>
  </clause>

  <clause id="35">
    <literal><![CDATA[
      (c_0' v (x v x)') v (y v x) = y v c_0
    ]]></literal>
    <justification jstring="[para(24(a,1),23(a,1,2,2))].">
      <j1 rule="para" parents="24 23"/>
    </justification>
  </clause>

  <clause id="36">
    <literal><![CDATA[
      x v (y v (z v (u v v))) = z v (x v (u v (y v v)))
    ]]></literal>
    <justification jstring="[para(18(a,1),5(a,1,2))].">
      <j1 rule="para" parents="18 5"/>
    </justification>
  </clause>

  <clause id="40">
    <literal><![CDATA[
      ((x v (y v (z v u))')' v (z v (x v (y v u)))')' = x
    ]]></literal>
    <justification jstring="[para(18(a,1),9(a,1,1,2,1))].">
      <j1 rule="para" parents="18 9"/>
    </justification>
  </clause>

  <clause id="41">
    <literal><![CDATA[
      ((x v (y v (z v u))')' v (y v (z v (x v u)))')' = x
    ]]></literal>
    <justification jstring="[para(18(a,2),9(a,1,1,2,1))].">
      <j1 rule="para" parents="18 9"/>
    </justification>
  </clause>

  <clause id="42">
    <literal><![CDATA[
      x v (y v (z v (u v x'))) = y v (z v (u v c_0))
    ]]></literal>
    <justification jstring="[para(23(a,1),18(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="23 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43">
    <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(18(a,1),24(a,1,1,2,1)),rewrite(5(6))].">
      <j1 rule="para" parents="18 24"/>
      <j2 rule="rewrite" parents="5"/>
    </justification>
  </clause>

  <clause id="56">
    <literal><![CDATA[
      (c_0' v (x' v x')') v c_0 = x v c_0
    ]]></literal>
    <justification jstring="[para(34(a,1),23(a,1,2)),flip(a)].">
      <j1 rule="para" parents="34 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="65">
    <literal><![CDATA[
      (x v ((x v x'')' v c_0)')' = (x v x'')'
    ]]></literal>
    <justification jstring="[para(25(a,1),9(a,1,1,1))].">
      <j1 rule="para" parents="25 9"/>
    </justification>
  </clause>

  <clause id="66">
    <literal><![CDATA[
      (((x v x'')' v c_0'')' v x)' = (x v x'')'
    ]]></literal>
    <justification jstring="[para(25(a,1),9(a,1,1,2))].">
      <j1 rule="para" parents="25 9"/>
    </justification>
  </clause>

  <clause id="68">
    <literal><![CDATA[
      ((x v x'')' v c_0') v x = c_0
    ]]></literal>
    <justification jstring="[para(25(a,1),17(a,1,2))].">
      <j1 rule="para" parents="25 17"/>
    </justific