<?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 2009-02A, February 2009.
Process 11668 was started by mccune on cleo,
Wed Feb 25 09:36:13 2009
The command was "/home/mccune/bin/prover9 -f ba-4basis.in".
]]></heading>

<proof number="1" length="129" max_count="39">

<comments><![CDATA[
% Proof 1 at 1.31 (+ 0.01) seconds: CC.
% Length of proof is 129.
% Level of proof is 37.
% Maximum clause weight is 39.
% Given clauses 122.

]]></comments>

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

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

  <clause id="7" type="assumption">
    <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" type="assumption">
    <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" type="deny">
    <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="29">
    <literal><![CDATA[
      x v (y v (z v (u v w))) = u v (x v (y v (z v w)))
    ]]></literal>
    <justification jstring="[para(18(a,2),5(a,1,2))].">
      <j1 rule="para" parents="18 5"/>
    </justification>
  </clause>

  <clause id="31">
    <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="33">
    <literal><![CDATA[
      x v (y v (z v x')) = y v (z v c_0)
    ]]></literal>
    <justification jstring="[para(17(a,1),18(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="17 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42">
    <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="44">
    <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="45">
    <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="47">
    <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="48">
    <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="49">
    <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="50">
    <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="52">
    <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="53">
    <literal><![CDATA[
      x v ((c_0' v (x v ((x v y) v y))') v y) = c_0
    ]]></literal>
    <justification jstring="[para(49(a,1),5(a,1)),rewrite([5(6)]),flip(a)].">
      <j1 rule="para" parents="49 5"/>
      <j2 rule="rewrite" parents="5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="63">
    <literal><![CDATA[
      (c_0' v (x' v x')') v c_0 = x v c_0
    ]]></literal>
    <justification jstring="[para(49(a,1),23(a,1,2)),flip(a)].">
      <j1 rule="para" parents="49 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="85">
    <literal><![CDATA[
      (x v (x v (c_0' v x))')' = c_0'
    ]]></literal>
    <justification jstring="[para(24(a,1),19(a,1,1,1))].">
      <j1 rule="para" parents="24 19"/>
    </justification>
  </clause>

  <clause id="95">
    <literal><![CDATA[
      (c_0' v (x v (c_0' v (x v x)))')' = x
    ]]></literal>
    <justification jstring="[para(47(a,1),9(a,1,1,1))].">
      <j1 rule="para" parents="47 9"/>
    </justification>
  </clause>

  <clause id="97">
    <literal><![CDATA[
      (x v (c_0' v (x v x))') v c_0' = c_0
    ]]></literal>
    <justification jstring="[para(47(a,1),17(a,1,2))].">
      <j1 rule="para" parents="47 17"/>
    </justification>
  </clause>

  <clause id="126">
    <literal><![CDATA[
      (c_0' v (x v (x v (c_0' v x)))')' = x
    ]]></literal>
    <justification jstring="[para(85(a,1),9(a,1,1,1))].">
      <j1 rule="para" parents="85 9"/>
    </justification>
  </clause>

  <clause id="149">
    <literal><![CDATA[
      ((x' v y')' v (x' v y)') v c_0 = x v c_0
    ]]></literal>
    <justification jstring="[para(26(a,1),23(a,1,2)),flip(a)].">
      <j1 rule="para" parents="26 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="152">
    <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="165">
    <literal><![CDATA[
      (c_0' v (x v (c_0' v (x v x)))') v x = c_0
    ]]></literal>
    <justification jstring="[para(47(a,1),26(a,1,1,1))].">
      <j1 rule="para" parents="47 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(85(a,1),26(a,1,1,1))].">
      <j1 rule="para" parents="85 26"/>
    </justification>
  </clause>

  <clause id="243">
    <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(97(a,1),9(a,1,1,1,1))].">
      <j1 rule="para" parents="97 9"/>
    </justification>
  </clause>

  <clause id="248">
    <literal><![CDATA[
      (x v (c_0' v (x v x))') v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(97(a,1),23(a,1,2)),flip(a)].">
      <j1 rule="para" parents="97 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="256">
    <literal><![CDATA[
      x v (c_0' v (x v x))' = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(243),rewrite([248(10),24(8)]),flip(a)].">
      <j1 rule="back_rewrite" parents="243"/>
      <j2 rule="rewrite" parents="248 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="258">
    <literal><![CDATA[
      x v (y v (c_0' v (x v x))') = y v c_0
    ]]></literal>
    <justification jstring="[para(256(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="256 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="266">
    <literal><![CDATA[
      (c_0' v (x v x)) v c_0 = x v c_0
    ]]></literal>
    <justification jstring="[para(256(a,1),23(a,1,2))].">
      <j1 rule="para" parents="256 23"/>
    </justification>
  </clause>

  <clause id="267">
    <literal><![CDATA[
      c_0'' v (c_0'' v c_0)' = c_0
    ]]></literal>
    <justification jstring="[para(23(a,1),256(a,1,2,1))].">
      <j1 rule="para" parents="23 256"/>
    </justification>
  </clause>

  <clause id="322">
    <literal><![CDATA[
      (c_0'' v c_0) v c_0 = c_0'' v c_0
    ]]></literal>
    <justification jstring="[para(23(a,1),266(a,1,1))].">
      <j1 rule="para" parents="23 266"/>
    </justification>
  </clause>

  <clause id="330">
    <literal><![CDATA[
      (c_0' v (c_0'' v (c_0'' v c_0))')' = c_0''
    ]]></literal>
    <justification jstring="[para(267(a,1),9(a,1,1,1,1))].">
      <j1 rule="para" parents="267 9"/>
    </justification>
  </clause>

  <clause id="339">
    <literal><![CDATA[
      (c_0'' v c_0) v (x v c_0) = x v (c_0'' v c_0)
    ]]></literal>
    <justification jstring="[para(267(a,1),33(a,1,2,2))].">
      <j1 rule="para" parents="267 33"/>
    </justification>
  </clause>

  <clause id="651">
    <literal><![CDATA[
      ((c_0' v (x v x)'')' v x) v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(48(a,1),63(a,1,1,2,1,1)),rewrite([48(13),63(11)]),flip(a)].">
      <j1 rule="para" parents="48 63"/>
      <j2 rule="rewrite" parents="48 63"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="672">
    <literal><![CDATA[
      (c_0' v (x v ((x v c_0'') v ((x v c_0'') v c_0)))')' = x v c_0''
    ]]></literal>
    <justification jstring="[para(33(a,1),95(a,1,1,2,1,2)),rewrite([5(13),5(14)])].">
      <j1 rule="para" parents="33 95"/>
      <j2 rule="rewrite" parents="5 5"/>
    </justification>
  </clause>

  <clause id="712">
    <literal><![CDATA[
      (c_0' v (x v (x v (c_0' v x)))') v (y v x) = y v c_0
    ]]></literal>
    <justification jstring="[para(126(a,1),23(a,1,2,2))].">
      <j1 rule="para" parents="126 23"/>
    </justification>
  </clause>

  <clause id="869">
    <literal><![CDATA[
      (c_0' v (x v x)) v (y v c_0) = x v (y v c_0)
    ]]></literal>
    <justification jstring="[para(258(a,1),33(a,1,2))].">
      <j1 rule="para" parents="258 33"/>
    </justification>
  </clause>

  <clause id="955">
    <literal><![CDATA[
      (c_0' v c_0''')' v c_0' = (c_0' v c_0''')'
    ]]></literal>
    <justification jstring="[para(68(a,1),45(a,1,1,2,1,2)),rewrite([65(15)]),flip(a)].">
      <j1 rule="para" parents="68 45"/>
      <j2 rule="rewrite" parents="65"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="963">
    <literal><![CDATA[
      c_0'' v c_0 = c_0''
    ]]></literal>
    <justification jstring="[para(322(a,1),45(a,1,1,2,1,2,1)),rewrite([322(14),5(13),322(12),330(14),322(10)]),flip(a)].">
      <j1 rule="para" parents="322 45"/>
      <j2 rule="rewrite" parents="322 5 322 330 322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="999">
    <literal><![CDATA[
      c_0'' v (x v c_0) = x v c_0''
    ]]></literal>
    <justification jstring="[back_rewrite(339),rewrite([963(5),963(11)])].">
      <j1 rule="back_rewrite" parents="339"/>
      <j2 rule="rewrite" parents="963 963"/>
    </justification>
  </clause>

  <clause id="1028">
    <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(33(a,1),31(a,1,1,2,1,2))].">
      <j1 rule="para" parents="33 31"/>
    </justification>
  </clause>

  <clause id="1078">
    <literal><![CDATA[
      (c_0' v (c_0 v c_0)') v c_0'' = c_0''
    ]]></literal>
    <justification jstring="[para(963(a,1),52(a,1,2)),rewrite([963(16)])].">
      <j1 rule="para" parents="963 52"/>
      <j2 rule="rewrite" parents="963"/>
    </justification>
  </clause>

  <clause id="1082">
    <literal><![CDATA[
      ((c_0'' v (x v c_0))' v (x v c_0')')' = x
    ]]></literal>
    <justification jstring="[para(999(a,2),9(a,1,1,1,1))].">
      <j1 rule="para" parents="999 9"/>
    </justification>
  </clause>

  <clause id="1083">
    <literal><![CDATA[
      c_0' v (c_0'' v (x v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[para(999(a,2),23(a,1,2))].">
      <j1 rule="para" parents="999 23"/>
    </justification>
  </clause>

  <clause id="1119">
    <literal><![CDATA[
      c_0'' v (x v c_0) = (c_0' v (x' v x')') v c_0''
    ]]></literal>
    <justification jstring="[para(63(a,1),999(a,1,2))].">
      <j1 rule="para" parents="63 999"/>
    </justification>
  </clause>

  <clause id="1136">
    <literal><![CDATA[
      c_0' v (c_0'' v (x v (y v c_0))) = x v (y v c_0)
    ]]></literal>
    <justification jstring="[para(1083(a,1),18(a,2,2))].">
      <j1 rule="para" parents="1083 18"/>
    </justification>
  </clause>

  <clause id="1137">
    <literal><![CDATA[
      c_0'' v (x v (c_0' v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[para(1083(a,1),18(a,2))].">
      <j1 rule="para" parents="1083 18"/>
    </justification>
  </clause>

  <clause id="1157">
    <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(49(a,1),1137(a,1,2)),rewrite([963(5),5(14)]),flip(a)].">
      <j1 rule="para" parents="49 1137"/>
      <j2 rule="rewrite" parents="963 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1263">
    <literal><![CDATA[
      (c_0' v c_0''')'' = c_0'
    ]]></literal>
    <justification jstring="[para(1078(a,1),42(a,1,1,1,1,2,1)),rewrite([49(17),955(11)])].">
      <j1 rule="para" parents="1078 42"/>
      <j2 rule="rewrite" parents="49 955"/>
    </justification>
  </clause>

  <clause id="1266">
    <literal><![CDATA[
      (c_0' v c_0''')' = c_0
    ]]></literal>
    <justification jstring="[para(1263(a,1),17(a,1,2)),rewrite([955(11)])].">
      <j1 rule="para" parents="1263 17"/>
      <j2 rule="rewrite" parents="955"/>
    </justification>
  </clause>

  <clause id="1271">
    <literal><![CDATA[
      ((c_0' v c_0'''')' v c_0)' = c_0'
    ]]></literal>
    <justification jstring="[para(1266(a,1),9(a,1,1,2))].">
      <j1 rule="para" parents="1266 9"/>
    </justification>
  </clause>

  <clause id="1284">
    <literal><![CDATA[
      (c_0''' v (c_0' v c_0)')' = c_0''
    ]]></literal>
    <justification jstring="[para(1266(a,1),42(a,1,1,1,1,2)),rewrite([963(5)])].">
      <j1 rule="para" parents="1266 42"/>
      <j2 rule="rewrite" parents="963"/>
    </justification>
  </clause>

  <clause id="1519">
    <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(1271(a,1),25(a,1,1,1,1,2,1))].">
      <j1 rule="para" parents="1271 25"/>
    </justification>
  </clause>

  <clause id="1546">
    <literal><![CDATA[
      ((c_0''' v (c_0' v c_0)'')' v c_0'')' = c_0'''
    ]]></literal>
    <justification jstring="[para(1284(a,1),9(a,1,1,2))].">
      <j1 rule="para" parents="1284 9"/>
    </justification>
  </clause>

  <clause id="1707">
    <literal><![CDATA[
      (c_0' v (x v x)'')' v x = c_0
    ]]></literal>
    <justification jstring="[para(152(a,1),9(a,1,1,1,1)),rewrite([651(12),24(8)]),flip(a)].">
      <j1 rule="para" parents="152 9"/>
      <j2 rule="rewrite" parents="651 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2115">
    <literal><![CDATA[
      ((x v c_0')' v ((c_0' v (y v (y v (c_0' v y)))') v (x v y))')' = x
    ]]></literal>
    <justification jstring="[para(169(a,1),19(a,1,1,1,1,2,1))].">
      <j1 rule="para" parents="169 19"/>
    </justification>
  </clause>

  <clause id="2387">
    <literal><![CDATA[
      c_0 v (c_0' v c_0) = c_0
    ]]></literal>
    <justification jstring="[para(869(a,1),45(a,1,1,2,1,2)),rewrite([5(10),5(9),126(13),5(7)]),flip(a)].">
      <j1 rule="para" parents="869 45"/>
      <j2 rule="rewrite" parents="5 5 126 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2416">
    <literal><![CDATA[
      c_0 v (x v (c_0' v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[para(2387(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2387 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2422">
    <literal><![CDATA[
      ((c_0 v (c_0' v c_0)')' v c_0') v c_0 = c_0
    ]]></literal>
    <justification jstring="[para(2387(a,1),26(a,1,1,2,1))].">
      <j1 rule="para" parents="2387 26"/>
    </justification>
  </clause>

  <clause id="2426">
    <literal><![CDATA[
      c_0'' = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(2387(a,1),52(a,1,2)),rewrite([5(11),1157(15)])].">
      <j1 rule="para" parents="2387 52"/>
      <j2 rule="rewrite" parents="5 1157"/>
    </justification>
  </clause>

  <clause id="2428">
    <literal><![CDATA[
      c_0 v (x v (y v (z v (c_0' v c_0)))) = x v (y v (z v c_0))
    ]]></literal>
    <justification jstring="[para(2387(a,1),29(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="2387 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2488">
    <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(1546),rewrite([2426(3),2426(15),5(16),2426(20)])].">
      <j1 rule="back_rewrite" parents="1546"/>
      <j2 rule="rewrite" parents="2426 2426 5 2426"/>
    </justification>
  </clause>

  <clause id="2493">
    <literal><![CDATA[
      ((c_0 v (c_0 v c_0))' v c_0')' = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(1519),rewrite([2426(5),1707(11),2426(4),2426(15),1707(21)])].">
      <j1 rule="back_rewrite" parents="1519"/>
      <j2 rule="rewrite" parents="2426 1707 2426 2426 1707"/>
    </justification>
  </clause>

  <clause id="2544">
    <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(1157),rewrite([2426(18)])].">
      <j1 rule="back_rewrite" parents="1157"/>
      <j2 rule="rewrite" parents="2426"/>
    </justification>
  </clause>

  <clause id="2565">
    <literal><![CDATA[
      (c_0 v c_0) v (c_0' v (x v (y v c_0))) = x v (y v c_0)
    ]]></literal>
    <justification jstring="[back_rewrite(1136),rewrite([2426(5),5(10)])].">
      <j1 rule="back_rewrite" parents="1136"/>
      <j2 rule="rewrite" parents="2426 5"/>
    </justification>
  </clause>

  <clause id="2582">
    <literal><![CDATA[
      (c_0 v c_0) v (x v c_0) = c_0 v (x v c_0)
    ]]></literal>
    <justification jstring="[back_rewrite(1119),rewrite([2426(3),2426(16),5(17),63(16)])].">
      <j1 rule="back_rewrite" parents="1119"/>
      <j2 rule="rewrite" parents="2426 2426 5 63"/>
    </justification>
  </clause>

  <clause id="2601">
    <literal><![CDATA[
      ((c_0 v (x v c_0))' v (x v c_0')')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(1082),rewrite([2426(3),2582(6)])].">
      <j1 rule="back_rewrite" parents="1082"/>
      <j2 rule="rewrite" parents="2426 2582"/>
    </justification>
  </clause>

  <clause id="2619">
    <literal><![CDATA[
      (c_0' v (x v ((x v (c_0 v c_0)) v ((x v (c_0 v c_0)) v c_0)))')' = x v (c_0 v c_0)
    ]]></literal>
    <justification jstring="[back_rewrite(672),rewrite([2426(5),2426(9),2426(20)])].">
      <j1 rule="back_rewrite" parents="672"/>
      <j2 rule="rewrite" parents="2426 2426 2426"/>
    </justification>
  </clause>

  <clause id="3579">
    <literal><![CDATA[
      c_0' v (c_0' v c_0')' = c_0
    ]]></literal>
    <justification jstring="[para(49(a,1),2601(a,1,1,2,1)),rewrite([63(12),2493(10)]),flip(a)].">
      <j1 rule="para" parents="49 2601"/>
      <j2 rule="rewrite" parents="63 2493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3588">
    <literal><![CDATA[
      (c_0' v x')' v (c_0' v x)' = c_0
    ]]></literal>
    <justification jstring="[para(26(a,1),2601(a,1,1,2,1)),rewrite([149(13),2493(10)]),flip(a)].">
      <j1 rule="para" parents="26 2601"/>
      <j2 rule="rewrite" parents="149 2493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3836">
    <literal><![CDATA[
      c_0' v (x v (c_0' v c_0')') = x v c_0
    ]]></literal>
    <justification jstring="[para(3579(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3579 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3838">
    <literal><![CDATA[
      (c_0' v c_0') v c_0 = c_0' v c_0
    ]]></literal>
    <justification jstring="[para(3579(a,1),23(a,1,2))].">
      <j1 rule="para" parents="3579 23"/>
    </justification>
  </clause>

  <clause id="3847">
    <literal><![CDATA[
      (c_0' v ((c_0' v c_0')' v ((c_0' v c_0')' v c_0))') v (c_0' v c_0')' = c_0
    ]]></literal>
    <justification jstring="[para(3579(a,1),169(a,1,1,2,1,2,2))].">
      <j1 rule="para" parents="3579 169"/>
    </justification>
  </clause>

  <clause id="3887">
    <literal><![CDATA[
      (c_0' v x')' v (y v (z v (c_0' v x)')) = y v (z v c_0)
    ]]></literal>
    <justification jstring="[para(3588(a,1),18(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3588 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3890">
    <literal><![CDATA[
      (c_0' v x')' v c_0 = (c_0' v x) v c_0
    ]]></literal>
    <justification jstring="[para(3588(a,1),23(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3588 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3947">
    <literal><![CDATA[
      (c_0' v ((c_0' v c_0) v ((c_0' v c_0) v c_0))') v (c_0' v c_0')' = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(3847),rewrite([3890(16),5(15),3890(14)])].">
      <j1 rule="back_rewrite" parents="3847"/>
      <j2 rule="rewrite" parents="3890 5 3890"/>
    </justification>
  </clause>

  <clause id="4047">
    <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(44(a,1),22(a,1,1,1,1,2,1,1))].">
      <j1 rule="para" parents="44 22"/>
    </justification>
  </clause>

  <clause id="4117">
    <literal><![CDATA[
      (c_0' v ((c_0' v c_0) v ((c_0' v c_0) v c_0))') v c_0 = c_0' v c_0
    ]]></literal>
    <justification jstring="[para(165(a,1),3836(a,1,2)),rewrite([3836(28),3890(20),5(19),3890(18)]),flip(a)].">
      <j1 rule="para" parents="165 3836"/>
      <j2 rule="rewrite" parents="3836 3890 5 3890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4145">
    <literal><![CDATA[
      (c_0' v c_0')' = c_0' v c_0
    ]]></literal>
    <justification jstring="[para(3890(a,1),21(a,1,1,2,1,2)),rewrite([45(14)]),flip(a)].">
      <j1 rule="para" parents="3890 21"/>
      <j2 rule="rewrite" parents="45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4237">
    <literal><![CDATA[
      c_0' v (c_0' v c_0) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(3947),rewrite([4145(21),5(20),4117(19)])].">
      <j1 rule="back_rewrite" parents="3947"/>
      <j2 rule="rewrite" parents="4145 5 4117"/>
    </justification>
  </clause>

  <clause id="4273">
    <literal><![CDATA[
      c_0' v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(4237(a,1),52(a,1,2)),rewrite([5(11),2544(15)]),flip(a)].">
      <j1 rule="para" parents="4237 52"/>
      <j2 rule="rewrite" parents="5 2544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4274">
    <literal><![CDATA[
      c_0 v (c_0 v c_0) = c_0
    ]]></literal>
    <justification jstring="[para(52(a,2),4237(a,1,2)),rewrite([5(11),49(10),4273(6),5(6),4273(5)])].">
      <j1 rule="para" parents="52 4237"/>
      <j2 rule="rewrite" parents="5 49 4273 5 4273"/>
    </justification>
  </clause>

  <clause id="4316">
    <literal><![CDATA[
      (c_0' v c_0') v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[back_rewrite(3838),rewrite([4273(11)])].">
      <j1 rule="back_rewrite" parents="3838"/>
      <j2 rule="rewrite" parents="4273"/>
    </justification>
  </clause>

  <clause id="4379">
    <literal><![CDATA[
      (c_0 v c_0)' = c_0'
    ]]></literal>
    <justification jstring="[back_rewrite(2488),rewrite([4273(9),17(11),4273(5),4274(5)]),flip(a)].">
      <j1 rule="back_rewrite" parents="2488"/>
      <j2 rule="rewrite" parents="4273 17 4273 4274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4392">
    <literal><![CDATA[
      c_0 v (x v (y v (z v (c_0 v c_0)))) = x v (y v (z v c_0))
    ]]></literal>
    <justification jstring="[back_rewrite(2428),rewrite([4273(5)])].">
      <j1 rule="back_rewrite" parents="2428"/>
      <j2 rule="rewrite" parents="4273"/>
    </justification>
  </clause>

  <clause id="4395">
    <literal><![CDATA[
      c_0 v c_0 = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(2422),rewrite([4273(5),4379(5),17(4),4316(7)])].">
      <j1 rule="back_rewrite" parents="2422"/>
      <j2 rule="rewrite" parents="4273 4379 17 4316"/>
    </justification>
  </clause>

  <clause id="4398">
    <literal><![CDATA[
      c_0 v (x v c_0) = x v c_0
    ]]></literal>
    <justification jstring="[back_rewrite(2416),rewrite([4273(5),4395(4)])].">
      <j1 rule="back_rewrite" parents="2416"/>
      <j2 rule="rewrite" parents="4273 4395"/>
    </justification>
  </clause>

  <clause id="4431">
    <literal><![CDATA[
      c_0 v (x v (y v (z v c_0))) = x v (y v (z v c_0))
    ]]></literal>
    <justification jstring="[back_rewrite(4392),rewrite([4395(4)])].">
      <j1 rule="back_rewrite" parents="4392"/>
      <j2 rule="rewrite" parents="4395"/>
    </justification>
  </clause>

  <clause id="4447">
    <literal><![CDATA[
      c_0' v c_0 = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(4273),rewrite([4395(7)])].">
      <j1 rule="back_rewrite" parents="4273"/>
      <j2 rule="rewrite" parents="4395"/>
    </justification>
  </clause>

  <clause id="4523">
    <literal><![CDATA[
      (c_0' v (x v ((x v c_0) v ((x v c_0) v c_0)))')' = x v c_0
    ]]></literal>
    <justification jstring="[back_rewrite(2619),rewrite([4395(5),4395(7),4395(16)])].">
      <j1 rule="back_rewrite" parents="2619"/>
      <j2 rule="rewrite" parents="4395 4395 4395"/>
    </justification>
  </clause>

  <clause id="4527">
    <literal><![CDATA[
      c_0' v (x v (y v c_0)) = x v (y v c_0)
    ]]></literal>
    <justification jstring="[back_rewrite(2565),rewrite([4395(3),4431(8)])].">
      <j1 rule="back_rewrite" parents="2565"/>
      <j2 rule="rewrite" parents="4395 4431"/>
    </justification>
  </clause>

  <clause id="4530">
    <literal><![CDATA[
      c_0'' = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(2426),rewrite([4395(6)])].">
      <j1 rule="back_rewrite" parents="2426"/>
      <j2 rule="rewrite" parents="4395"/>
    </justification>
  </clause>

  <clause id="4712">
    <literal><![CDATA[
      x v ((x v c_0) v c_0) = x v c_0
    ]]></literal>
    <justification jstring="[para(869(a,1),50(a,1,1,2,1,2,2)),rewrite([5(11),4527(12),5(10),4523(13),5(9),4527(10)]),flip(a)].">
      <j1 rule="para" parents="869 50"/>
      <j2 rule="rewrite" parents="5 4527 5 4523 5 4527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4736">
    <literal><![CDATA[
      (c_0' v (x v c_0)')' = x v c_0
    ]]></literal>
    <justification jstring="[para(3588(a,1),50(a,1,1,2,1,2,2,1,2)),rewrite([3887(16),4712(7),3588(17)])].">
      <j1 rule="para" parents="3588 50"/>
      <j2 rule="rewrite" parents="3887 4712 3588"/>
    </justification>
  </clause>

  <clause id="4742">
    <literal><![CDATA[
      x v ((c_0' v (x v c_0)') v c_0) = c_0
    ]]></literal>
    <justification jstring="[para(4398(a,1),52(a,1,2)),rewrite([5(7),4712(7),5(9),4395(12)])].">
      <j1 rule="para" parents="4398 52"/>
      <j2 rule="rewrite" parents="5 4712 5 4395"/>
    </justification>
  </clause>

  <clause id="4747">
    <literal><![CDATA[
      x v (y v ((x v c_0) v c_0)) = y v (x v c_0)
    ]]></literal>
    <justification jstring="[para(4712(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4712 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4856">
    <literal><![CDATA[
      ((x v c_0)' v c_0')' = x v c_0
    ]]></literal>
    <justification jstring="[para(4736(a,1),42(a,1,1,1,1,2)),rewrite([5(5),4712(5),4447(7)])].">
      <j1 rule="para" parents="4736 42"/>
      <j2 rule="rewrite" parents="5 4712 4447"/>
    </justification>
  </clause>

  <clause id="4869">
    <literal><![CDATA[
      ((x v (y v c_0))' v ((y v c_0)' v (x v c_0'))')' = x
    ]]></literal>
    <justification jstring="[para(4856(a,1),19(a,1,1,1,1,2))].">
      <j1 rule="para" parents="4856 19"/>
    </justification>
  </clause>

  <clause id="4879">
    <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(4856(a,1),21(a,1,1,2,1,2,1)),rewrite([5(11),4856(21)])].">
      <j1 rule="para" parents="4856 21"/>
      <j2 rule="rewrite" parents="5 4856"/>
    </justification>
  </clause>

  <clause id="4887">
    <literal><![CDATA[
      ((x v c_0)' v ((x v c_0)' v c_0)')' = c_0
    ]]></literal>
    <justification jstring="[para(4856(a,1),42(a,1,1,1,1,2)),rewrite([4398(4)])].">
      <j1 rule="para" parents="4856 42"/>
      <j2 rule="rewrite" parents="4398"/>
    </justification>
  </clause>

  <clause id="4988">
    <literal><![CDATA[
      x v ((x v c_0) v ((c_0' v (x v c_0)') v c_0)) = c_0
    ]]></literal>
    <justification jstring="[para(4712(a,1),53(a,1,2,1,2,1,2,1)),rewrite([4747(10),5(7),4712(7),5(11)])].">
      <j1 rule="para" parents="4712 53"/>
      <j2 rule="rewrite" parents="4747 5 4712 5"/>
    </justification>
  </clause>

  <clause id="4999">
    <literal><![CDATA[
      x v (y v ((c_0' v (x v c_0)') v c_0)) = y v c_0
    ]]></literal>
    <justification jstring="[para(4742(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4742 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5007">
    <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(4742(a,1),22(a,1,1,1,1,2,1,1)),rewrite([4530(14)])].">
      <j1 rule="para" parents="4742 22"/>
      <j2 rule="rewrite" parents="4530"/>
    </justification>
  </clause>

  <clause id="5022">
    <literal><![CDATA[
      (x v c_0) v c_0 = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(4988),rewrite([4999(12)])].">
      <j1 rule="back_rewrite" parents="4988"/>
      <j2 rule="rewrite" parents="4999"/>
    </justification>
  </clause>

  <clause id="5040">
    <literal><![CDATA[
      (x v c_0) v (y v c_0) = y v c_0
    ]]></literal>
    <justification jstring="[para(5022(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5022 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5056">
    <literal><![CDATA[
      x v c_0 = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(4879),rewrite([5040(11),4887(11)]),flip(a)].">
      <j1 rule="back_rewrite" parents="4879"/>
      <j2 rule="rewrite" parents="5040 4887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5060">
    <literal><![CDATA[
      (c_0' v x)' = (x v c_0')'
    ]]></literal>
    <justification jstring="[back_rewrite(5007),rewrite([5056(4),5056(7),5056(6),5056(8),5056(11)])].">
      <j1 rule="back_rewrite" parents="5007"/>
      <j2 rule="rewrite" parents="5056 5056 5056 5056 5056"/>
    </justification>
  </clause>

  <clause id="5089">
    <literal><![CDATA[
      (c_0' v (c_0' v (x v c_0'))')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(4869),rewrite([5056(2),5056(2),5056(4)])].">
      <j1 rule="back_rewrite" parents="4869"/>
      <j2 rule="rewrite" parents="5056 5056 5056"/>
    </justification>
  </clause>

  <clause id="5186">
    <literal><![CDATA[
      (x v (y v (z v (u v x')))')' = (c_0' v x)'
    ]]></literal>
    <justification jstring="[back_rewrite(4047),rewrite([5056(9),5056(9),5056(9),4530(10),5056(9)]),flip(a)].">
      <j1 rule="back_rewrite" parents="4047"/>
      <j2 rule="rewrite" parents="5056 5056 5056 4530 5056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5637">
    <literal><![CDATA[
      (c_0' v (c_0' v x)')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(1028),rewrite([5186(7),5056(6),5056(6),5056(6),5060(8,R)])].">
      <j1 rule="back_rewrite" parents="1028"/>
      <j2 rule="rewrite" parents="5186 5056 5056 5056 5060"/>
    </justification>
  </clause>

  <clause id="5717">
    <literal><![CDATA[
      (c_0' v (x v (x v (c_0' v x)))') v (y v x) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(712),rewrite([5056(13)])].">
      <j1 rule="back_rewrite" parents="712"/>
      <j2 rule="rewrite" parents="5056"/>
    </justification>
  </clause>

  <clause id="5887">
    <literal><![CDATA[
      x v c_0' = x
    ]]></literal>
    <justification jstring="[back_rewrite(5089),rewrite([5637(11)])].">
      <j1 rule="back_rewrite" parents="5089"/>
      <j2 rule="rewrite" parents="5637"/>
    </justification>
  </clause>

  <clause id="5917">
    <literal><![CDATA[
      x'' = x
    ]]></literal>
    <justification jstring="[back_rewrite(2115),rewrite([5887(3),5717(12),5887(4)])].">
      <j1 rule="back_rewrite" parents="2115"/>
      <j2 rule="rewrite" parents="5887 5717 5887"/>
    </justification>
  </clause>

  <clause id="5918">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer(CC)
    ]]></attribute>
    <justification jstring="[resolve(5917,a,10,a)].">
      <j1 rule="resolve" parents="5917 10"/>
    </justification>
  </clause>

</proof>

<proof number="2" length="154" max_count="86">

<comments><![CDATA[
% Proof 2 at 1.40 (+ 0.01) seconds: B1.
% Length of proof is 154.
% Level of proof is 41.
% Maximum clause weight is 86.
% Given clauses 122.

]]></comments>

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

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

  <clause id="7" type="assumption">
    <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" type="assumption">
    <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" type="deny">
    <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 (u v w))) = z v (x v (u v (y v w)))
    ]]></literal>
    <justification jstring="[para(18(a,1),5(a,1,2))].">
      <j1 rule="para" parents="18 5"/>
    </justification>
  </clause>

  <clause id="29">
    <literal><![CDATA[
      x v (y v (z v (u v w))) = u v (x v (y v (z v w)))
    ]]></literal>
    <justification jstring="[para(18(a,2),5(a,1,2))].">
      <j1 rule="para" parents="18 5"/>
    </justification>
  </clause>

  <clause id="31">
    <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="33">
    <literal><![CDATA[
      x v (y v (z v x')) = y v (z v c_0)
    ]]></literal>
    <justification jstring="[para(17(a,1),18(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="17 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42">
    <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="44">
    <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="45">
    <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="46">
    <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="47">
    <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="48">
    <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="49">
    <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="50">
    <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="52">
    <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="53">
    <literal><![CDATA[
      x v ((c_0' v (x v ((x v y) v y))') v y) = c_0
    ]]></literal>
    <justification jstring="[para(49(a,1),5(a,1)),rewrite([5(6)]),flip(a)].">
      <j1 rule="para" parents="49 5"/>
      <j2 rule="rewrite" parents="5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="63">
    <literal><![CDATA[
      (c_0' v (x' v x')') v c_0 = x v c_0
    ]]></literal>
    <justification jstring="[para(49(a,1),23(a,1,2)),flip(a)].">
      <j1 rule="para" parents="49 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="85">
    <literal><![CDATA[
      (x v (x v (c_0' v x))')' = c_0'
    ]]></literal>
    <justification jstring="[para(24(a,1),19(a,1,1,1))].">
      <j1 rule="para" parents="24 19"/>
    </justification>
  </clause>

  <clause id="95">
    <literal><![CDATA[
      (c_0' v (x v (c_0' v (x v x)))')' = x
    ]]></literal>
    <justification jstring="[para(47(a,1),9(a,1,1,1))].">
      <j1 rule="para" parents="47 9"/>
    </justification>
  </clause>

  <clause id="97">
    <literal><![CDATA[
      (x v (c_0' v (x v x))') v c_0' = c_0
    ]]></literal>
    <justification jstring="[para(47(a,1),17(a,1,2))].">
      <j1 rule="para" parents="47 17"/>
    </justification>
  </clause>

  <clause id="108">
    <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="126">
    <literal><![CDATA[
      (c_0' v (x v (x v (c_0' v x)))')' = x
    ]]></literal>
    <justification jstring="[para(85(a,1),9(a,1,1,1))].">
      <j1 rule="para" parents="85 9"/>
    </justification>
  </clause>

  <clause id="149">
    <literal><![CDATA[
      ((x' v y')' v (x' v y)') v c_0 = x v c_0
    ]]></literal>
    <justification jstring="[para(26(a,1),23(a,1,2)),flip(a)].">
      <j1 rule="para" parents="26 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="152">
    <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="165">
    <literal><![CDATA[
      (c_0' v (x v (c_0' v (x v x)))') v x = c_0
    ]]></literal>
    <justification jstring="[para(47(a,1),26(a,1,1,1))].">
      <j1 rule="para" parents="47 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(85(a,1),26(a,1,1,1))].">
      <j1 rule="para" parents="85 26"/>
    </justification>
  </clause>

  <clause id="243">
    <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(97(a,1),9(a,1,1,1,1))].">
      <j1 rule="para" parents="97 9"/>
    </justification>
  </clause>

  <clause id="248">
    <literal><![CDATA[
      (x v (c_0' v (x v x))') v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(97(a,1),23(a,1,2)),flip(a)].">
      <j1 rule="para" parents="97 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="256">
    <literal><![CDATA[
      x v (c_0' v (x v x))' = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(243),rewrite([248(10),24(8)]),flip(a)].">
      <j1 rule="back_rewrite" parents="243"/>
      <j2 rule="rewrite" parents="248 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="258">
    <literal><![CDATA[
      x v (y v (c_0' v (x v x))') = y v c_0
    ]]></literal>
    <justification jstring="[para(256(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="256 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="266">
    <literal><![CDATA[
      (c_0' v (x v x)) v c_0 = x v c_0
    ]]></literal>
    <justification jstring="[para(256(a,1),23(a,1,2))].">
      <j1 rule="para" parents="256 23"/>
    </justification>
  </clause>

  <clause id="267">
    <literal><![CDATA[
      c_0'' v (c_0'' v c_0)' = c_0
    ]]></literal>
    <justification jstring="[para(23(a,1),256(a,1,2,1))].">
      <j1 rule="para" parents="23 256"/>
    </justification>
  </clause>

  <clause id="322">
    <literal><![CDATA[
      (c_0'' v c_0) v c_0 = c_0'' v c_0
    ]]></literal>
    <justification jstring="[para(23(a,1),266(a,1,1))].">
      <j1 rule="para" parents="23 266"/>
    </justification>
  </clause>

  <clause id="330">
    <literal><![CDATA[
      (c_0' v (c_0'' v (c_0'' v c_0))')' = c_0''
    ]]></literal>
    <justification jstring="[para(267(a,1),9(a,1,1,1,1))].">
      <j1 rule="para" parents="267 9"/>
    </justification>
  </clause>

  <clause id="339">
    <literal><![CDATA[
      (c_0'' v c_0) v (x v c_0) = x v (c_0'' v c_0)
    ]]></literal>
    <justification jstring="[para(267(a,1),33(a,1,2,2))].">
      <j1 rule="para" parents="267 33"/>
    </justification>
  </clause>

  <clause id="523">
    <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(52(a,2),22(a,1,1,1,1,2,1,1))].">
      <j1 rule="para" parents="52 22"/>
    </justification>
  </clause>

  <clause id="651">
    <literal><![CDATA[
      ((c_0' v (x v x)'')' v x) v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(48(a,1),63(a,1,1,2,1,1)),rewrite([48(13),63(11)]),flip(a)].">
      <j1 rule="para" parents="48 63"/>
      <j2 rule="rewrite" parents="48 63"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="672">
    <literal><![CDATA[
      (c_0' v (x v ((x v c_0'') v ((x v c_0'') v c_0)))')' = x v c_0''
    ]]></literal>
    <justification jstring="[para(33(a,1),95(a,1,1,2,1,2)),rewrite([5(13),5(14)])].">
      <j1 rule="para" parents="33 95"/>
      <j2 rule="rewrite" parents="5 5"/>
    </justification>
  </clause>

  <clause id="682">
    <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(27(a,2),95(a,1,1,2,1))].">
      <j1 rule="para" parents="27 95"/>
    </justification>
  </clause>

  <clause id="712">
    <literal><![CDATA[
      (c_0' v (x v (x v (c_0' v x)))') v (y v x) = y v c_0
    ]]></literal>
    <justification jstring="[para(126(a,1),23(a,1,2,2))].">
      <j1 rule="para" parents="126 23"/>
    </justification>
  </clause>

  <clause id="869">
    <literal><![CDATA[
      (c_0' v (x v x)) v (y v c_0) = x v (y v c_0)
    ]]></literal>
    <justification jstring="[para(258(a,1),33(a,1,2))].">
      <j1 rule="para" parents="258 33"/>
    </justification>
  </clause>

  <clause id="935">
    <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),42(a,1,1,1,1,2))].">
      <j1 rule="para" parents="22 42"/>
    </justification>
  </clause>

  <clause id="955">
    <literal><![CDATA[
      (c_0' v c_0''')' v c_0' = (c_0' v c_0''')'
    ]]></literal>
    <justification jstring="[para(68(a,1),45(a,1,1,2,1,2)),rewrite([65(15)]),flip(a)].">
      <j1 rule="para" parents="68 45"/>
      <j2 rule="rewrite" parents="65"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="963">
    <literal><![CDATA[
      c_0'' v c_0 = c_0''
    ]]></literal>
    <justification jstring="[para(322(a,1),45(a,1,1,2,1,2,1)),rewrite([322(14),5(13),322(12),330(14),322(10)]),flip(a)].">
      <j1 rule="para" parents="322 45"/>
      <j2 rule="rewrite" parents="322 5 322 330 322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="999">
    <literal><![CDATA[
      c_0'' v (x v c_0) = x v c_0''
    ]]></literal>
    <justification jstring="[back_rewrite(339),rewrite([963(5),963(11)])].">
      <j1 rule="back_rewrite" parents="339"/>
      <j2 rule="rewrite" parents="963 963"/>
    </justification>
  </clause>

  <clause id="1028">
    <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(33(a,1),31(a,1,1,2,1,2))].">
      <j1 rule="para" parents="33 31"/>
    </justification>
  </clause>

  <clause id="1078">
    <literal><![CDATA[
      (c_0' v (c_0 v c_0)') v c_0'' = c_0''
    ]]></literal>
    <justification jstring="[para(963(a,1),52(a,1,2)),rewrite([963(16)])].">
      <j1 rule="para" parents="963 52"/>
      <j2 rule="rewrite" parents="963"/>
    </justification>
  </clause>

  <clause id="1082">
    <literal><![CDATA[
      ((c_0'' v (x v c_0))' v (x v c_0')')' = x
    ]]></literal>
    <justification jstring="[para(999(a,2),9(a,1,1,1,1))].">
      <j1 rule="para" parents="999 9"/>
    </justification>
  </clause>

  <clause id="1083">
    <literal><![CDATA[
      c_0' v (c_0'' v (x v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[para(999(a,2),23(a,1,2))].">
      <j1 rule="para" parents="999 23"/>
    </justification>
  </clause>

  <clause id="1119">
    <literal><![CDATA[
      c_0'' v (x v c_0) = (c_0' v (x' v x')') v c_0''
    ]]></literal>
    <justification jstring="[para(63(a,1),999(a,1,2))].">
      <j1 rule="para" parents="63 999"/>
    </justification>
  </clause>

  <clause id="1136">
    <literal><![CDATA[
      c_0' v (c_0'' v (x v (y v c_0))) = x v (y v c_0)
    ]]></literal>
    <justification jstring="[para(1083(a,1),18(a,2,2))].">
      <j1 rule="para" parents="1083 18"/>
    </justification>
  </clause>

  <clause id="1137">
    <literal><![CDATA[
      c_0'' v (x v (c_0' v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[para(1083(a,1),18(a,2))].">
      <j1 rule="para" parents="1083 18"/>
    </justification>
  </clause>

  <clause id="1157">
    <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(49(a,1),1137(a,1,2)),rewrite([963(5),5(14)]),flip(a)].">
      <j1 rule="para" parents="49 1137"/>
      <j2 rule="rewrite" parents="963 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1263">
    <literal><![CDATA[
      (c_0' v c_0''')'' = c_0'
    ]]></literal>
    <justification jstring="[para(1078(a,1),42(a,1,1,1,1,2,1)),rewrite([49(17),955(11)])].">
      <j1 rule="para" parents="1078 42"/>
      <j2 rule="rewrite" parents="49 955"/>
    </justification>
  </clause>

  <clause id="1266">
    <literal><![CDATA[
      (c_0' v c_0''')' = c_0
    ]]></literal>
    <justification jstring="[para(1263(a,1),17(a,1,2)),rewrite([955(11)])].">
      <j1 rule="para" parents="1263 17"/>
      <j2 rule="rewrite" parents="955"/>
    </justification>
  </clause>

  <clause id="1271">
    <literal><![CDATA[
      ((c_0' v c_0'''')' v c_0)' = c_0'
    ]]></literal>
    <justification jstring="[para(1266(a,1),9(a,1,1,2))].">
      <j1 rule="para" parents="1266 9"/>
    </justification>
  </clause>

  <clause id="1284">
    <literal><![CDATA[
      (c_0''' v (c_0' v c_0)')' = c_0''
    ]]></literal>
    <justification jstring="[para(1266(a,1),42(a,1,1,1,1,2)),rewrite([963(5)])].">
      <j1 rule="para" parents="1266 42"/>
      <j2 rule="rewrite" parents="963"/>
    </justification>
  </clause>

  <clause id="1519">
    <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(1271(a,1),25(a,1,1,1,1,2,1))].">
      <j1 rule="para" parents="1271 25"/>
    </justification>
  </clause>

  <clause id="1546">
    <literal><![CDATA[
      ((c_0''' v (c_0' v c_0)'')' v c_0'')' = c_0'''
    ]]></literal>
    <justification jstring="[para(1284(a,1),9(a,1,1,2))].">
      <j1 rule="para" parents="1284 9"/>
    </justification>
  </clause>

  <clause id="1707">
    <literal><![CDATA[
      (c_0' v (x v x)'')' v x = c_0
    ]]></literal>
    <justification jstring="[para(152(a,1),9(a,1,1,1,1)),rewrite([651(12),24(8)]),flip(a)].">
      <j1 rule="para" parents="152 9"/>
      <j2 rule="rewrite" parents="651 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2028">
    <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(165(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="165 20"/>
      <j2 rule="rewrite" parents="5 5 5 5 5 5"/>
    </justification>
  </clause>

  <clause id="2115">
    <literal><![CDATA[
      ((x v c_0')' v ((c_0' v (y v (y v (c_0' v y)))') v (x v y))')' = x
    ]]></literal>
    <justification jstring="[para(169(a,1),19(a,1,1,1,1,2,1))].">
      <j1 rule="para" parents="169 19"/>
    </justification>
  </clause>

  <clause id="2387">
    <literal><![CDATA[
      c_0 v (c_0' v c_0) = c_0
    ]]></literal>
    <justification jstring="[para(869(a,1),45(a,1,1,2,1,2)),rewrite([5(10),5(9),126(13),5(7)]),flip(a)].">
      <j1 rule="para" parents="869 45"/>
      <j2 rule="rewrite" parents="5 5 126 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2416">
    <literal><![CDATA[
      c_0 v (x v (c_0' v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[para(2387(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2387 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2422">
    <literal><![CDATA[
      ((c_0 v (c_0' v c_0)')' v c_0') v c_0 = c_0
    ]]></literal>
    <justification jstring="[para(2387(a,1),26(a,1,1,2,1))].">
      <j1 rule="para" parents="2387 26"/>
    </justification>
  </clause>

  <clause id="2426">
    <literal><![CDATA[
      c_0'' = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(2387(a,1),52(a,1,2)),rewrite([5(11),1157(15)])].">
      <j1 rule="para" parents="2387 52"/>
      <j2 rule="rewrite" parents="5 1157"/>
    </justification>
  </clause>

  <clause id="2428">
    <literal><![CDATA[
      c_0 v (x v (y v (z v (c_0' v c_0)))) = x v (y v (z v c_0))
    ]]></literal>
    <justification jstring="[para(2387(a,1),29(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="2387 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2488">
    <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(1546),rewrite([2426(3),2426(15),5(16),2426(20)])].">
      <j1 rule="back_rewrite" parents="1546"/>
      <j2 rule="rewrite" parents="2426 2426 5 2426"/>
    </justification>
  </clause>

  <clause id="2493">
    <literal><![CDATA[
      ((c_0 v (c_0 v c_0))' v c_0')' = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(1519),rewrite([2426(5),1707(11),2426(4),2426(15),1707(21)])].">
      <j1 rule="back_rewrite" parents="1519"/>
      <j2 rule="rewrite" parents="2426 1707 2426 2426 1707"/>
    </justification>
  </clause>

  <clause id="2544">
    <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(1157),rewrite([2426(18)])].">
      <j1 rule="back_rewrite" parents="1157"/>
      <j2 rule="rewrite" parents="2426"/>
    </justification>
  </clause>

  <clause id="2565">
    <literal><![CDATA[
      (c_0 v c_0) v (c_0' v (x v (y v c_0))) = x v (y v c_0)
    ]]></literal>
    <justification jstring="[back_rewrite(1136),rewrite([2426(5),5(10)])].">
      <j1 rule="back_rewrite" parents="1136"/>
      <j2 rule="rewrite" parents="2426 5"/>
    </justification>
  </clause>

  <clause id="2582">
    <literal><![CDATA[
      (c_0 v c_0) v (x v c_0) = c_0 v (x v c_0)
    ]]></literal>
    <justification jstring="[back_rewrite(1119),rewrite([2426(3),2426(16),5(17),63(16)])].">
      <j1 rule="back_rewrite" parents="1119"/>
      <j2 rule="rewrite" parents="2426 2426 5 63"/>
    </justification>
  </clause>

  <clause id="2601">
    <literal><![CDATA[
      ((c_0 v (x v c_0))' v (x v c_0')')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(1082),rewrite([2426(3),2582(6)])].">
      <j1 rule="back_rewrite" parents="1082"/>
      <j2 rule="rewrite" parents="2426 2582"/>
    </justification>
  </clause>

  <clause id="2619">
    <literal><![CDATA[
      (c_0' v (x v ((x v (c_0 v c_0)) v ((x v (c_0 v c_0)) v c_0)))')' = x v (c_0 v c_0)
    ]]></literal>
    <justification jstring="[back_rewrite(672),rewrite([2426(5),2426(9),2426(20)])].">
      <j1 rule="back_rewrite" parents="672"/>
      <j2 rule="rewrite" parents="2426 2426 2426"/>
    </justification>
  </clause>

  <clause id="2634">
    <literal><![CDATA[
      ((c_0 v ((x v x'')' v c_0))' v x)' = (x v x'')'
    ]]></literal>
    <justification jstring="[back_rewrite(66),rewrite([2426(7),5(8)])].">
      <j1 rule="back_rewrite" parents="66"/>
      <j2 rule="rewrite" parents="2426 5"/>
    </justification>
  </clause>

  <clause id="3579">
    <literal><![CDATA[
      c_0' v (c_0' v c_0')' = c_0
    ]]></literal>
    <justification jstring="[para(49(a,1),2601(a,1,1,2,1)),rewrite([63(12),2493(10)]),flip(a)].">
      <j1 rule="para" parents="49 2601"/>
      <j2 rule="rewrite" parents="63 2493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3588">
    <literal><![CDATA[
      (c_0' v x')' v (c_0' v x)' = c_0
    ]]></literal>
    <justification jstring="[para(26(a,1),2601(a,1,1,2,1)),rewrite([149(13),2493(10)]),flip(a)].">
      <j1 rule="para" parents="26 2601"/>
      <j2 rule="rewrite" parents="149 2493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3836">
    <literal><![CDATA[
      c_0' v (x v (c_0' v c_0')') = x v c_0
    ]]></literal>
    <justification jstring="[para(3579(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3579 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3838">
    <literal><![CDATA[
      (c_0' v c_0') v c_0 = c_0' v c_0
    ]]></literal>
    <justification jstring="[para(3579(a,1),23(a,1,2))].">
      <j1 rule="para" parents="3579 23"/>
    </justification>
  </clause>

  <clause id="3847">
    <literal><![CDATA[
      (c_0' v ((c_0' v c_0')' v ((c_0' v c_0')' v c_0))') v (c_0' v c_0')' = c_0
    ]]></literal>
    <justification jstring="[para(3579(a,1),169(a,1,1,2,1,2,2))].">
      <j1 rule="para" parents="3579 169"/>
    </justification>
  </clause>

  <clause id="3887">
    <literal><![CDATA[
      (c_0' v x')' v (y v (z v (c_0' v x)')) = y v (z v c_0)
    ]]></literal>
    <justification jstring="[para(3588(a,1),18(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3588 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3890">
    <literal><![CDATA[
      (c_0' v x')' v c_0 = (c_0' v x) v c_0
    ]]></literal>
    <justification jstring="[para(3588(a,1),23(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3588 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3947">
    <literal><![CDATA[
      (c_0' v ((c_0' v c_0) v ((c_0' v c_0) v c_0))') v (c_0' v c_0')' = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(3847),rewrite([3890(16),5(15),3890(14)])].">
      <j1 rule="back_rewrite" parents="3847"/>
      <j2 rule="rewrite" parents="3890 5 3890"/>
    </justification>
  </clause>

  <clause id="4047">
    <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(44(a,1),22(a,1,1,1,1,2,1,1))].">
      <j1 rule="para" parents="44 22"/>
    </justification>
  </clause>

  <clause id="4117">
    <literal><![CDATA[
      (c_0' v ((c_0' v c_0) v ((c_0' v c_0) v c_0))') v c_0 = c_0' v c_0
    ]]></literal>
    <justification jstring="[para(165(a,1),3836(a,1,2)),rewrite([3836(28),3890(20),5(19),3890(18)]),flip(a)].">
      <j1 rule="para" parents="165 3836"/>
      <j2 rule="rewrite" parents="3836 3890 5 3890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4145">
    <literal><![CDATA[
      (c_0' v c_0')' = c_0' v c_0
    ]]></literal>
    <justification jstring="[para(3890(a,1),21(a,1,1,2,1,2)),rewrite([45(14)]),flip(a)].">
      <j1 rule="para" parents="3890 21"/>
      <j2 rule="rewrite" parents="45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4237">
    <literal><![CDATA[
      c_0' v (c_0' v c_0) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(3947),rewrite([4145(21),5(20),4117(19)])].">
      <j1 rule="back_rewrite" parents="3947"/>
      <j2 rule="rewrite" parents="4145 5 4117"/>
    </justification>
  </clause>

  <clause id="4273">
    <literal><![CDATA[
      c_0' v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(4237(a,1),52(a,1,2)),rewrite([5(11),2544(15)]),flip(a)].">
      <j1 rule="para" parents="4237 52"/>
      <j2 rule="rewrite" parents="5 2544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4274">
    <literal><![CDATA[
      c_0 v (c_0 v c_0) = c_0
    ]]></literal>
    <justification jstring="[para(52(a,2),4237(a,1,2)),rewrite([5(11),49(10),4273(6),5(6),4273(5)])].">
      <j1 rule="para" parents="52 4237"/>
      <j2 rule="rewrite" parents="5 49 4273 5 4273"/>
    </justification>
  </clause>

  <clause id="4316">
    <literal><![CDATA[
      (c_0' v c_0') v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[back_rewrite(3838),rewrite([4273(11)])].">
      <j1 rule="back_rewrite" parents="3838"/>
      <j2 rule="rewrite" parents="4273"/>
    </justification>
  </clause>

  <clause id="4379">
    <literal><![CDATA[
      (c_0 v c_0)' = c_0'
    ]]></literal>
    <justification jstring="[back_rewrite(2488),rewrite([4273(9),17(11),4273(5),4274(5)]),flip(a)].">
      <j1 rule="back_rewrite" parents="2488"/>
      <j2 rule="rewrite" parents="4273 17 4273 4274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4392">
    <literal><![CDATA[
      c_0 v (x v (y v (z v (c_0 v c_0)))) = x v (y v (z v c_0))
    ]]></literal>
    <justification jstring="[back_rewrite(2428),rewrite([4273(5)])].">
      <j1 rule="back_rewrite" parents="2428"/>
      <j2 rule="rewrite" parents="4273"/>
    </justification>
  </clause>

  <clause id="4395">
    <literal><![CDATA[
      c_0 v c_0 = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(2422),rewrite([4273(5),4379(5),17(4),4316(7)])].">
      <j1 rule="back_rewrite" parents="2422"/>
      <j2 rule="rewrite" parents="4273 4379 17 4316"/>
    </justification>
  </clause>

  <clause id="4398">
    <literal><![CDATA[
      c_0 v (x v c_0) = x v c_0
    ]]></literal>
    <justification jstring="[back_rewrite(2416),rewrite([4273(5),4395(4)])].">
      <j1 rule="back_rewrite" parents="2416"/>
      <j2 rule="rewrite" parents="4273 4395"/>
    </justification>
  </clause>

  <clause id="4431">
    <literal><![CDATA[
      c_0 v (x v (y v (z v c_0))) = x v (y v (z v c_0))
    ]]></literal>
    <justification jstring="[back_rewrite(4392),rewrite([4395(4)])].">
      <j1 rule="back_rewrite" parents="4392"/>
      <j2 rule="rewrite" parents="4395"/>
    </justification>
  </clause>

  <clause id="4447">
    <literal><![CDATA[
      c_0' v c_0 = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(4273),rewrite([4395(7)])].">
      <j1 rule="back_rewrite" parents="4273"/>
      <j2 rule="rewrite" parents="4395"/>
    </justification>
  </clause>

  <clause id="4523">
    <literal><![CDATA[
      (c_0' v (x v ((x v c_0) v ((x v c_0) v c_0)))')' = x v c_0
    ]]></literal>
    <justification jstring="[back_rewrite(2619),rewrite([4395(5),4395(7),4395(16)])].">
      <j1 rule="back_rewrite" parents="2619"/>
      <j2 rule="rewrite" parents="4395 4395 4395"/>
    </justification>
  </clause>

  <clause id="4527">
    <literal><![CDATA[
      c_0' v (x v (y v c_0)) = x v (y v c_0)
    ]]></literal>
    <justification jstring="[back_rewrite(2565),rewrite([4395(3),4431(8)])].">
      <j1 rule="back_rewrite" parents="2565"/>
      <j2 rule="rewrite" parents="4395 4431"/>
    </justification>
  </clause>

  <clause id="4530">
    <literal><![CDATA[
      c_0'' = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(2426),rewrite([4395(6)])].">
      <j1 rule="back_rewrite" parents="2426"/>
      <j2 rule="rewrite" parents="4395"/>
    </justification>
  </clause>

  <clause id="4536">
    <literal><![CDATA[
      (((x v x'')' v c_0)' v x)' = (x v x'')'
    ]]></literal>
    <justification jstring="[back_rewrite(2634),rewrite([4398(8)])].">
      <j1 rule="back_rewrite" parents="2634"/>
      <j2 rule="rewrite" parents="4398"/>
    </justification>
  </clause>

  <clause id="4630">
    <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(165(a,1),46(a,1,1,2,1)),rewrite([5(20),5(22),5(21),5(50),5(52),5(51)])].">
      <j1 rule="para" parents="165 46"/>
      <j2 rule="rewrite" parents="5 5 5 5 5 5"/>
    </justification>
  </clause>

  <clause id="4712">
    <literal><![CDATA[
      x v ((x v c_0) v c_0) = x v c_0
    ]]></literal>
    <justification jstring="[para(869(a,1),50(a,1,1,2,1,2,2)),rewrite([5(11),4527(12),5(10),4523(13),5(9),4527(10)]),flip(a)].">
      <j1 rule="para" parents="869 50"/>
      <j2 rule="rewrite" parents="5 4527 5 4523 5 4527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4736">
    <literal><![CDATA[
      (c_0' v (x v c_0)')' = x v c_0
    ]]></literal>
    <justification jstring="[para(3588(a,1),50(a,1,1,2,1,2,2,1,2)),rewrite([3887(16),4712(7),3588(17)])].">
      <j1 rule="para" parents="3588 50"/>
      <j2 rule="rewrite" parents="3887 4712 3588"/>
    </justification>
  </clause>

  <clause id="4742">
    <literal><![CDATA[
      x v ((c_0' v (x v c_0)') v c_0) = c_0
    ]]></literal>
    <justification jstring="[para(4398(a,1),52(a,1,2)),rewrite([5(7),4712(7),5(9),4395(12)])].">
      <j1 rule="para" parents="4398 52"/>
      <j2 rule="rewrite" parents="5 4712 5 4395"/>
    </justification>
  </clause>

  <clause id="4747">
    <literal><![CDATA[
      x v (y v ((x v c_0) v c_0)) = y v (x v c_0)
    ]]></literal>
    <justification jstring="[para(4712(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4712 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4856">
    <literal><![CDATA[
      ((x v c_0)' v c_0')' = x v c_0
    ]]></literal>
    <justification jstring="[para(4736(a,1),42(a,1,1,1,1,2)),rewrite([5(5),4712(5),4447(7)])].">
      <j1 rule="para" parents="4736 42"/>
      <j2 rule="rewrite" parents="5 4712 4447"/>
    </justification>
  </clause>

  <clause id="4869">
    <literal><![CDATA[
      ((x v (y v c_0))' v ((y v c_0)' v (x v c_0'))')' = x
    ]]></literal>
    <justification jstring="[para(4856(a,1),19(a,1,1,1,1,2))].">
      <j1 rule="para" parents="4856 19"/>
    </justification>
  </clause>

  <clause id="4879">
    <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(4856(a,1),21(a,1,1,2,1,2,1)),rewrite([5(11),4856(21)])].">
      <j1 rule="para" parents="4856 21"/>
      <j2 rule="rewrite" parents="5 4856"/>
    </justification>
  </clause>

  <clause id="4887">
    <literal><![CDATA[
      ((x v c_0)' v ((x v c_0)' v c_0)')' = c_0
    ]]></literal>
    <justification jstring="[para(4856(a,1),42(a,1,1,1,1,2)),rewrite([4398(4)])].">
      <j1 rule="para" parents="4856 42"/>
      <j2 rule="rewrite" parents="4398"/>
    </justification>
  </clause>

  <clause id="4988">
    <literal><![CDATA[
      x v ((x v c_0) v ((c_0' v (x v c_0)') v c_0)) = c_0
    ]]></literal>
    <justification jstring="[para(4712(a,1),53(a,1,2,1,2,1,2,1)),rewrite([4747(10),5(7),4712(7),5(11)])].">
      <j1 rule="para" parents="4712 53"/>
      <j2 rule="rewrite" parents="4747 5 4712 5"/>
    </justification>
  </clause>

  <clause id="4999">
    <literal><![CDATA[
      x v (y v ((c_0' v (x v c_0)') v c_0)) = y v c_0
    ]]></literal>
    <justification jstring="[para(4742(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4742 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5007">
    <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(4742(a,1),22(a,1,1,1,1,2,1,1)),rewrite([4530(14)])].">
      <j1 rule="para" parents="4742 22"/>
      <j2 rule="rewrite" parents="4530"/>
    </justification>
  </clause>

  <clause id="5022">
    <literal><![CDATA[
      (x v c_0) v c_0 = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(4988),rewrite([4999(12)])].">
      <j1 rule="back_rewrite" parents="4988"/>
      <j2 rule="rewrite" parents="4999"/>
    </justification>
  </clause>

  <clause id="5040">
    <literal><![CDATA[
      (x v c_0) v (y v c_0) = y v c_0
    ]]></literal>
    <justification jstring="[para(5022(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5022 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5056">
    <literal><![CDATA[
      x v c_0 = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(4879),rewrite([5040(11),4887(11)]),flip(a)].">
      <j1 rule="back_rewrite" parents="4879"/>
      <j2 rule="rewrite" parents="5040 4887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5060">
    <literal><![CDATA[
      (c_0' v x)' = (x v c_0')'
    ]]></literal>
    <justification jstring="[back_rewrite(5007),rewrite([5056(4),5056(7),5056(6),5056(8),5056(11)])].">
      <j1 rule="back_rewrite" parents="5007"/>
      <j2 rule="rewrite" parents="5056 5056 5056 5056 5056"/>
    </justification>
  </clause>

  <clause id="5089">
    <literal><![CDATA[
      (c_0' v (c_0' v (x v c_0'))')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(4869),rewrite([5056(2),5056(2),5056(4)])].">
      <j1 rule="back_rewrite" parents="4869"/>
      <j2 rule="rewrite" parents="5056 5056 5056"/>
    </justification>
  </clause>

  <clause id="5139">
    <literal><![CDATA[
      (x v x'')' = (c_0' v x)'
    ]]></literal>
    <justification jstring="[back_rewrite(4536),rewrite([5056(6)]),flip(a)].">
      <j1 rule="back_rewrite" parents="4536"/>
      <j2 rule="rewrite" parents="5056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5186">
    <literal><![CDATA[
      (x v (y v (z v (u v x')))')' = (c_0' v x)'
    ]]></literal>
    <justification jstring="[back_rewrite(4047),rewrite([5056(9),5056(9),5056(9),4530(10),5056(9)]),flip(a)].">
      <j1 rule="back_rewrite" parents="4047"/>
      <j2 rule="rewrite" parents="5056 5056 5056 4530 5056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5637">
    <literal><![CDATA[
      (c_0' v (c_0' v x)')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(1028),rewrite([5186(7),5056(6),5056(6),5056(6),5060(8,R)])].">
      <j1 rule="back_rewrite" parents="1028"/>
      <j2 rule="rewrite" parents="5186 5056 5056 5056 5060"/>
    </justification>
  </clause>

  <clause id="5654">
    <literal><![CDATA[
      (c_0' v (x v (x' v y')')')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(935),rewrite([5056(18),5060(10,R)])].">
      <j1 rule="back_rewrite" parents="935"/>
      <j2 rule="rewrite" parents="5056 5060"/>
    </justification>
  </clause>

  <clause id="5717">
    <literal><![CDATA[
      (c_0' v (x v (x v (c_0' v x)))') v (y v x) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(712),rewrite([5056(13)])].">
      <j1 rule="back_rewrite" parents="712"/>
      <j2 rule="rewrite" parents="5056"/>
    </justification>
  </clause>

  <clause id="5779">
    <literal><![CDATA[
      (c_0' v (x v x)') v (y v x) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(52),rewrite([5056(9)])].">
      <j1 rule="back_rewrite" parents="52"/>
      <j2 rule="rewrite" parents="5056"/>
    </justification>
  </clause>

  <clause id="5793">
    <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(4630),rewrite([5060(30,R)])].">
      <j1 rule="back_rewrite" parents="4630"/>
      <j2 rule="rewrite" parents="5060"/>
    </justification>
  </clause>

  <clause id="5810">
    <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(2028),rewrite([5060(33,R)])].">
      <j1 rule="back_rewrite" parents="2028"/>
      <j2 rule="rewrite" parents="5060"/>
    </justification>
  </clause>

  <clause id="5880">
    <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(108),rewrite([5139(8),5139(20)])].">
      <j1 rule="back_rewrite" parents="108"/>
      <j2 rule="rewrite" parents="5139 5139"/>
    </justification>
  </clause>

  <clause id="5887">
    <literal><![CDATA[
      x v c_0' = x
    ]]></literal>
    <justification jstring="[back_rewrite(5089),rewrite([5637(11)])].">
      <j1 rule="back_rewrite" parents="5089"/>
      <j2 rule="rewrite" parents="5637"/>
    </justification>
  </clause>

  <clause id="5910">
    <literal><![CDATA[
      x v ((x v y) v ((x v y) v y)) = x v y
    ]]></literal>
    <justification jstring="[back_rewrite(682),rewrite([5637(13)])].">
      <j1 rule="back_rewrite" parents="682"/>
      <j2 rule="rewrite" parents="5637"/>
    </justification>
  </clause>

  <clause id="5917">
    <literal><![CDATA[
      x'' = x
    ]]></literal>
    <justification jstring="[back_rewrite(2115),rewrite([5887(3),5717(12),5887(4)])].">
      <j1 rule="back_rewrite" parents="2115"/>
      <j2 rule="rewrite" parents="5887 5717 5887"/>
    </justification>
  </clause>

  <clause id="5926">
    <literal><![CDATA[
      (c_0' v x)' = x'
    ]]></literal>
    <justification jstring="[back_rewrite(523),rewrite([5887(3),5779(8),5917(4),5056(3),5887(7)])].">
      <j1 rule="back_rewrite" parents="523"/>
      <j2 rule="rewrite" parents="5887 5779 5917 5056 5887"/>
    </justification>
  </clause>

  <clause id="5935">
    <literal><![CDATA[
      x v x = x
    ]]></literal>
    <justification jstring="[back_rewrite(5880),rewrite([5926(7),5917(4),5887(5),5926(6),5917(3),5926(6),5917(3),5887(4)])].">
      <j1 rule="back_rewrite" parents="5880"/>
      <j2 rule="rewrite" parents="5926 5917 5887 5926 5917 5926 5917 5887"/>
    </justification>
  </clause>

  <clause id="6061">
    <literal><![CDATA[
      (c_0' v x) v x = c_0' v x
    ]]></literal>
    <justification jstring="[back_rewrite(5810),rewrite([5910(26),5926(14),9(11),5926(9),5917(6),5910(28),5926(16),9(13)])].">
      <j1 rule="back_rewrite" parents="5810"/>
      <j2 rule="rewrite" parents="5910 5926 9 5926 5917 5910 5926 9"/>
    </justification>
  </clause>

  <clause id="6063">
    <literal><![CDATA[
      c_0' v x = x
    ]]></literal>
    <justification jstring="[back_rewrite(5793),rewrite([5935(11),5935(15),5935(17),6061(18),5935(17),5926(15),5926(12),5926(9),5917(6),6061(6),5926(6),5926(5),5917(2),5935(9),5935(13),5935(15),6061(16),5935(15),5926(13),5926(10),5926(7),5917(4)]),flip(a)].">
      <j1 rule="back_rewrite" parents="5793"/>
      <j2 rule="rewrite" parents="5935 5935 5935 6061 5935 5926 5926 5926 5917 6061 5926 5926 5917 5935 5935 5935 6061 5935 5926 5926 5926 5917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6086">
    <literal><![CDATA[
      x v (x' v y')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(5654),rewrite([6063(9),5917(7)])].">
      <j1 rule="back_rewrite" parents="5654"/>
      <j2 rule="rewrite" parents="6063 5917"/>
    </justification>
  </clause>

  <clause id="6087">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer(B1)
    ]]></attribute>
    <justification jstring="[resolve(6086,a,12,a)].">
      <j1 rule="resolve" parents="6086 12"/>
    </justification>
  </clause>

</proof>

<proof number="3" length="172" max_count="86">

<comments><![CDATA[
% Proof 3 at 3.55 (+ 0.02) seconds: MOD.
% Length of proof is 172.
% Level of proof is 46.
% Maximum clause weight is 86.
% Given clauses 196.

]]></comments>

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

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

  <clause id="7" type="assumption">
    <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" type="assumption">
    <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" type="deny">
    <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 (u v w))) = z v (x v (u v (y v w)))
    ]]></literal>
    <justification jstring="[para(18(a,1),5(a,1,2))].">
      <j1 rule="para" parents="18 5"/>
    </justification>
  </clause>

  <clause id="29">
    <literal><![CDATA[
      x v (y v (z v (u v w))) = u v (x v (y v (z v w)))
    ]]></literal>
    <justification jstring="[para(18(a,2),5(a,1,2))].">
      <j1 rule="para" parents="18 5"/>
    </justification>
  </clause>

  <clause id="31">
    <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="33">
    <literal><![CDATA[
      x v (y v (z v x')) = y v (z v c_0)
    ]]></literal>
    <justification jstring="[para(17(a,1),18(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="17 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42">
    <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="44">
    <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="45">
    <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="46">
    <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="47">
    <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="48">
    <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="49">
    <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="50">
    <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="52">
    <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="53">
    <literal><![CDATA[
      x v ((c_0' v (x v ((x v y) v y))') v y) = c_0
    ]]></literal>
    <justification jstring="[para(49(a,1),5(a,1)),rewrite([5(6)]),flip(a)].">
      <j1 rule="para" parents="49 5"/>
      <j2 rule="rewrite" parents="5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="63">
    <literal><![CDATA[
      (c_0' v (x' v x')') v c_0 = x v c_0
    ]]></literal>
    <justification jstring="[para(49(a,1),23(a,1,2)),flip(a)].">
      <j1 rule="para" parents="49 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="85">
    <literal><![CDATA[
      (x v (x v (c_0' v x))')' = c_0'
    ]]></literal>
    <justification jstring="[para(24(a,1),19(a,1,1,1))].">
      <j1 rule="para" parents="24 19"/>
    </justification>
  </clause>

  <clause id="91">
    <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="95">
    <literal><![CDATA[
      (c_0' v (x v (c_0' v (x v x)))')' = x
    ]]></literal>
    <justification jstring="[para(47(a,1),9(a,1,1,1))].">
      <j1 rule="para" parents="47 9"/>
    </justification>
  </clause>

  <clause id="97">
    <literal><![CDATA[
      (x v (c_0' v (x v x))') v c_0' = c_0
    ]]></literal>
    <justification jstring="[para(47(a,1),17(a,1,2))].">
      <j1 rule="para" parents="47 17"/>
    </justification>
  </clause>

  <clause id="108">
    <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="126">
    <literal><![CDATA[
      (c_0' v (x v (x v (c_0' v x)))')' = x
    ]]></literal>
    <justification jstring="[para(85(a,1),9(a,1,1,1))].">
      <j1 rule="para" parents="85 9"/>
    </justification>
  </clause>

  <clause id="149">
    <literal><![CDATA[
      ((x' v y')' v (x' v y)') v c_0 = x v c_0
    ]]></literal>
    <justification jstring="[para(26(a,1),23(a,1,2)),flip(a)].">
      <j1 rule="para" parents="26 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="152">
    <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="165">
    <literal><![CDATA[
      (c_0' v (x v (c_0' v (x v x)))') v x = c_0
    ]]></literal>
    <justification jstring="[para(47(a,1),26(a,1,1,1))].">
      <j1 rule="para" parents="47 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(85(a,1),26(a,1,1,1))].">
      <j1 rule="para" parents="85 26"/>
    </justification>
  </clause>

  <clause id="185">
    <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="243">
    <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(97(a,1),9(a,1,1,1,1))].">
      <j1 rule="para" parents="97 9"/>
    </justification>
  </clause>

  <clause id="248">
    <literal><![CDATA[
      (x v (c_0' v (x v x))') v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(97(a,1),23(a,1,2)),flip(a)].">
      <j1 rule="para" parents="97 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="256">
    <literal><![CDATA[
      x v (c_0' v (x v x))' = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(243),rewrite([248(10),24(8)]),flip(a)].">
      <j1 rule="back_rewrite" parents="243"/>
      <j2 rule="rewrite" parents="248 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="258">
    <literal><![CDATA[
      x v (y v (c_0' v (x v x))') = y v c_0
    ]]></literal>
    <justification jstring="[para(256(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="256 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="266">
    <literal><![CDATA[
      (c_0' v (x v x)) v c_0 = x v c_0
    ]]></literal>
    <justification jstring="[para(256(a,1),23(a,1,2))].">
      <j1 rule="para" parents="256 23"/>
    </justification>
  </clause>

  <clause id="267">
    <literal><![CDATA[
      c_0'' v (c_0'' v c_0)' = c_0
    ]]></literal>
    <justification jstring="[para(23(a,1),256(a,1,2,1))].">
      <j1 rule="para" parents="23 256"/>
    </justification>
  </clause>

  <clause id="322">
    <literal><![CDATA[
      (c_0'' v c_0) v c_0 = c_0'' v c_0
    ]]></literal>
    <justification jstring="[para(23(a,1),266(a,1,1))].">
      <j1 rule="para" parents="23 266"/>
    </justification>
  </clause>

  <clause id="330">
    <literal><![CDATA[
      (c_0' v (c_0'' v (c_0'' v c_0))')' = c_0''
    ]]></literal>
    <justification jstring="[para(267(a,1),9(a,1,1,1,1))].">
      <j1 rule="para" parents="267 9"/>
    </justification>
  </clause>

  <clause id="339">
    <literal><![CDATA[
      (c_0'' v c_0) v (x v c_0) = x v (c_0'' v c_0)
    ]]></literal>
    <justification jstring="[para(267(a,1),33(a,1,2,2))].">
      <j1 rule="para" parents="267 33"/>
    </justification>
  </clause>

  <clause id="523">
    <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(52(a,2),22(a,1,1,1,1,2,1,1))].">
      <j1 rule="para" parents="52 22"/>
    </justification>
  </clause>

  <clause id="651">
    <literal><![CDATA[
      ((c_0' v (x v x)'')' v x) v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(48(a,1),63(a,1,1,2,1,1)),rewrite([48(13),63(11)]),flip(a)].">
      <j1 rule="para" parents="48 63"/>
      <j2 rule="rewrite" parents="48 63"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="672">
    <literal><![CDATA[
      (c_0' v (x v ((x v c_0'') v ((x v c_0'') v c_0)))')' = x v c_0''
    ]]></literal>
    <justification jstring="[para(33(a,1),95(a,1,1,2,1,2)),rewrite([5(13),5(14)])].">
      <j1 rule="para" parents="33 95"/>
      <j2 rule="rewrite" parents="5 5"/>
    </justification>
  </clause>

  <clause id="682">
    <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(27(a,2),95(a,1,1,2,1))].">
      <j1 rule="para" parents="27 95"/>
    </justification>
  </clause>

  <clause id="712">
    <literal><![CDATA[
      (c_0' v (x v (x v (c_0' v x)))') v (y v x) = y v c_0
    ]]></literal>
    <justification jstring="[para(126(a,1),23(a,1,2,2))].">
      <j1 rule="para" parents="126 23"/>
    </justification>
  </clause>

  <clause id="869">
    <literal><![CDATA[
      (c_0' v (x v x)) v (y v c_0) = x v (y v c_0)
    ]]></literal>
    <justification jstring="[para(258(a,1),33(a,1,2))].">
      <j1 rule="para" parents="258 33"/>
    </justification>
  </clause>

  <clause id="955">
    <literal><![CDATA[
      (c_0' v c_0''')' v c_0' = (c_0' v c_0''')'
    ]]></literal>
    <justification jstring="[para(68(a,1),45(a,1,1,2,1,2)),rewrite([65(15)]),flip(a)].">
      <j1 rule="para" parents="68 45"/>
      <j2 rule="rewrite" parents="65"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="963">
    <literal><![CDATA[
      c_0'' v c_0 = c_0''
    ]]></literal>
    <justification jstring="[para(322(a,1),45(a,1,1,2,1,2,1)),rewrite([322(14),5(13),322(12),330(14),322(10)]),flip(a)].">
      <j1 rule="para" parents="322 45"/>
      <j2 rule="rewrite" parents="322 5 322 330 322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="999">
    <literal><![CDATA[
      c_0'' v (x v c_0) = x v c_0''
    ]]></literal>
    <justification jstring="[back_rewrite(339),rewrite([963(5),963(11)])].">
      <j1 rule="back_rewrite" parents="339"/>
      <j2 rule="rewrite" parents="963 963"/>
    </justification>
  </clause>

  <clause id="1028">
    <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(33(a,1),31(a,1,1,2,1,2))].">
      <j1 rule="para" parents="33 31"/>
    </justification>
  </clause>

  <clause id="1078">
    <literal><![CDATA[
      (c_0' v (c_0 v c_0)') v c_0'' = c_0''
    ]]></literal>
    <justification jstring="[para(963(a,1),52(a,1,2)),rewrite([963(16)])].">
      <j1 rule="para" parents="963 52"/>
      <j2 rule="rewrite" parents="963"/>
    </justification>
  </clause>

  <clause id="1082">
    <literal><![CDATA[
      ((c_0'' v (x v c_0))' v (x v c_0')')' = x
    ]]></literal>
    <justification jstring="[para(999(a,2),9(a,1,1,1,1))].">
      <j1 rule="para" parents="999 9"/>
    </justification>
  </clause>

  <clause id="1083">
    <literal><![CDATA[
      c_0' v (c_0'' v (x v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[para(999(a,2),23(a,1,2))].">
      <j1 rule="para" parents="999 23"/>
    </justification>
  </clause>

  <clause id="1119">
    <literal><![CDATA[
      c_0'' v (x v c_0) = (c_0' v (x' v x')') v c_0''
    ]]></literal>
    <justification jstring="[para(63(a,1),999(a,1,2))].">
      <j1 rule="para" parents="63 999"/>
    </justification>
  </clause>

  <clause id="1136">
    <literal><![CDATA[
      c_0' v (c_0'' v (x v (y v c_0))) = x v (y v c_0)
    ]]></literal>
    <justification jstring="[para(1083(a,1),18(a,2,2))].">
      <j1 rule="para" parents="1083 18"/>
    </justification>
  </clause>

  <clause id="1137">
    <literal><![CDATA[
      c_0'' v (x v (c_0' v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[para(1083(a,1),18(a,2))].">
      <j1 rule="para" parents="1083 18"/>
    </justification>
  </clause>

  <clause id="1157">
    <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(49(a,1),1137(a,1,2)),rewrite([963(5),5(14)]),flip(a)].">
      <j1 rule="para" parents="49 1137"/>
      <j2 rule="rewrite" parents="963 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1263">
    <literal><![CDATA[
      (c_0' v c_0''')'' = c_0'
    ]]></literal>
    <justification jstring="[para(1078(a,1),42(a,1,1,1,1,2,1)),rewrite([49(17),955(11)])].">
      <j1 rule="para" parents="1078 42"/>
      <j2 rule="rewrite" parents="49 955"/>
    </justification>
  </clause>

  <clause id="1266">
    <literal><![CDATA[
      (c_0' v c_0''')' = c_0
    ]]></literal>
    <justification jstring="[para(1263(a,1),17(a,1,2)),rewrite([955(11)])].">
      <j1 rule="para" parents="1263 17"/>
      <j2 rule="rewrite" parents="955"/>
    </justification>
  </clause>

  <clause id="1271">
    <literal><![CDATA[
      ((c_0' v c_0'''')' v c_0)' = c_0'
    ]]></literal>
    <justification jstring="[para(1266(a,1),9(a,1,1,2))].">
      <j1 rule="para" parents="1266 9"/>
    </justification>
  </clause>

  <clause id="1284">
    <literal><![CDATA[
      (c_0''' v (c_0' v c_0)')' = c_0''
    ]]></literal>
    <justification jstring="[para(1266(a,1),42(a,1,1,1,1,2)),rewrite([963(5)])].">
      <j1 rule="para" parents="1266 42"/>
      <j2 rule="rewrite" parents="963"/>
    </justification>
  </clause>

  <clause id="1519">
    <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(1271(a,1),25(a,1,1,1,1,2,1))].">
      <j1 rule="para" parents="1271 25"/>
    </justification>
  </clause>

  <clause id="1546">
    <literal><![CDATA[
      ((c_0''' v (c_0' v c_0)'')' v c_0'')' = c_0'''
    ]]></literal>
    <justification jstring="[para(1284(a,1),9(a,1,1,2))].">
      <j1 rule="para" parents="1284 9"/>
    </justification>
  </clause>

  <clause id="1707">
    <literal><![CDATA[
      (c_0' v (x v x)'')' v x = c_0
    ]]></literal>
    <justification jstring="[para(152(a,1),9(a,1,1,1,1)),rewrite([651(12),24(8)]),flip(a)].">
      <j1 rule="para" parents="152 9"/>
      <j2 rule="rewrite" parents="651 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2028">
    <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(165(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="165 20"/>
      <j2 rule="rewrite" parents="5 5 5 5 5 5"/>
    </justification>
  </clause>

  <clause id="2115">
    <literal><![CDATA[
      ((x v c_0')' v ((c_0' v (y v (y v (c_0' v y)))') v (x v y))')' = x
    ]]></literal>
    <justification jstring="[para(169(a,1),19(a,1,1,1,1,2,1))].">
      <j1 rule="para" parents="169 19"/>
    </justification>
  </clause>

  <clause id="2387">
    <literal><![CDATA[
      c_0 v (c_0' v c_0) = c_0
    ]]></literal>
    <justification jstring="[para(869(a,1),45(a,1,1,2,1,2)),rewrite([5(10),5(9),126(13),5(7)]),flip(a)].">
      <j1 rule="para" parents="869 45"/>
      <j2 rule="rewrite" parents="5 5 126 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2416">
    <literal><![CDATA[
      c_0 v (x v (c_0' v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[para(2387(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2387 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2422">
    <literal><![CDATA[
      ((c_0 v (c_0' v c_0)')' v c_0') v c_0 = c_0
    ]]></literal>
    <justification jstring="[para(2387(a,1),26(a,1,1,2,1))].">
      <j1 rule="para" parents="2387 26"/>
    </justification>
  </clause>

  <clause id="2426">
    <literal><![CDATA[
      c_0'' = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(2387(a,1),52(a,1,2)),rewrite([5(11),1157(15)])].">
      <j1 rule="para" parents="2387 52"/>
      <j2 rule="rewrite" parents="5 1157"/>
    </justification>
  </clause>

  <clause id="2428">
    <literal><![CDATA[
      c_0 v (x v (y v (z v (c_0' v c_0)))) = x v (y v (z v c_0))
    ]]></literal>
    <justification jstring="[para(2387(a,1),29(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="2387 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2488">
    <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(1546),rewrite([2426(3),2426(15),5(16),2426(20)])].">
      <j1 rule="back_rewrite" parents="1546"/>
      <j2 rule="rewrite" parents="2426 2426 5 2426"/>
    </justification>
  </clause>

  <clause id="2493">
    <literal><![CDATA[
      ((c_0 v (c_0 v c_0))' v c_0')' = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(1519),rewrite([2426(5),1707(11),2426(4),2426(15),1707(21)])].">
      <j1 rule="back_rewrite" parents="1519"/>
      <j2 rule="rewrite" parents="2426 1707 2426 2426 1707"/>
    </justification>
  </clause>

  <clause id="2544">
    <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(1157),rewrite([2426(18)])].">
      <j1 rule="back_rewrite" parents="1157"/>
      <j2 rule="rewrite" parents="2426"/>
    </justification>
  </clause>

  <clause id="2565">
    <literal><![CDATA[
      (c_0 v c_0) v (c_0' v (x v (y v c_0))) = x v (y v c_0)
    ]]></literal>
    <justification jstring="[back_rewrite(1136),rewrite([2426(5),5(10)])].">
      <j1 rule="back_rewrite" parents="1136"/>
      <j2 rule="rewrite" parents="2426 5"/>
    </justification>
  </clause>

  <clause id="2582">
    <literal><![CDATA[
      (c_0 v c_0) v (x v c_0) = c_0 v (x v c_0)
    ]]></literal>
    <justification jstring="[back_rewrite(1119),rewrite([2426(3),2426(16),5(17),63(16)])].">
      <j1 rule="back_rewrite" parents="1119"/>
      <j2 rule="rewrite" parents="2426 2426 5 63"/>
    </justification>
  </clause>

  <clause id="2601">
    <literal><![CDATA[
      ((c_0 v (x v c_0))' v (x v c_0')')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(1082),rewrite([2426(3),2582(6)])].">
      <j1 rule="back_rewrite" parents="1082"/>
      <j2 rule="rewrite" parents="2426 2582"/>
    </justification>
  </clause>

  <clause id="2619">
    <literal><![CDATA[
      (c_0' v (x v ((x v (c_0 v c_0)) v ((x v (c_0 v c_0)) v c_0)))')' = x v (c_0 v c_0)
    ]]></literal>
    <justification jstring="[back_rewrite(672),rewrite([2426(5),2426(9),2426(20)])].">
      <j1 rule="back_rewrite" parents="672"/>
      <j2 rule="rewrite" parents="2426 2426 2426"/>
    </justification>
  </clause>

  <clause id="2634">
    <literal><![CDATA[
      ((c_0 v ((x v x'')' v c_0))' v x)' = (x v x'')'
    ]]></literal>
    <justification jstring="[back_rewrite(66),rewrite([2426(7),5(8)])].">
      <j1 rule="back_rewrite" parents="66"/>
      <j2 rule="rewrite" parents="2426 5"/>
    </justification>
  </clause>

  <clause id="3579">
    <literal><![CDATA[
      c_0' v (c_0' v c_0')' = c_0
    ]]></literal>
    <justification jstring="[para(49(a,1),2601(a,1,1,2,1)),rewrite([63(12),2493(10)]),flip(a)].">
      <j1 rule="para" parents="49 2601"/>
      <j2 rule="rewrite" parents="63 2493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3588">
    <literal><![CDATA[
      (c_0' v x')' v (c_0' v x)' = c_0
    ]]></literal>
    <justification jstring="[para(26(a,1),2601(a,1,1,2,1)),rewrite([149(13),2493(10)]),flip(a)].">
      <j1 rule="para" parents="26 2601"/>
      <j2 rule="rewrite" parents="149 2493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3836">
    <literal><![CDATA[
      c_0' v (x v (c_0' v c_0')') = x v c_0
    ]]></literal>
    <justification jstring="[para(3579(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3579 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3838">
    <literal><![CDATA[
      (c_0' v c_0') v c_0 = c_0' v c_0
    ]]></literal>
    <justification jstring="[para(3579(a,1),23(a,1,2))].">
      <j1 rule="para" parents="3579 23"/>
    </justification>
  </clause>

  <clause id="3847">
    <literal><![CDATA[
      (c_0' v ((c_0' v c_0')' v ((c_0' v c_0')' v c_0))') v (c_0' v c_0')' = c_0
    ]]></literal>
    <justification jstring="[para(3579(a,1),169(a,1,1,2,1,2,2))].">
      <j1 rule="para" parents="3579 169"/>
    </justification>
  </clause>

  <clause id="3887">
    <literal><![CDATA[
      (c_0' v x')' v (y v (z v (c_0' v x)')) = y v (z v c_0)
    ]]></literal>
    <justification jstring="[para(3588(a,1),18(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3588 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3890">
    <literal><![CDATA[
      (c_0' v x')' v c_0 = (c_0' v x) v c_0
    ]]></literal>
    <justification jstring="[para(3588(a,1),23(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3588 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3947">
    <literal><![CDATA[
      (c_0' v ((c_0' v c_0) v ((c_0' v c_0) v c_0))') v (c_0' v c_0')' = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(3847),rewrite([3890(16),5(15),3890(14)])].">
      <j1 rule="back_rewrite" parents="3847"/>
      <j2 rule="rewrite" parents="3890 5 3890"/>
    </justification>
  </clause>

  <clause id="4047">
    <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(44(a,1),22(a,1,1,1,1,2,1,1))].">
      <j1 rule="para" parents="44 22"/>
    </justification>
  </clause>

  <clause id="4117">
    <literal><![CDATA[
      (c_0' v ((c_0' v c_0) v ((c_0' v c_0) v c_0))') v c_0 = c_0' v c_0
    ]]></literal>
    <justification jstring="[para(165(a,1),3836(a,1,2)),rewrite([3836(28),3890(20),5(19),3890(18)]),flip(a)].">
      <j1 rule="para" parents="165 3836"/>
      <j2 rule="rewrite" parents="3836 3890 5 3890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4145">
    <literal><![CDATA[
      (c_0' v c_0')' = c_0' v c_0
    ]]></literal>
    <justification jstring="[para(3890(a,1),21(a,1,1,2,1,2)),rewrite([45(14)]),flip(a)].">
      <j1 rule="para" parents="3890 21"/>
      <j2 rule="rewrite" parents="45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4237">
    <literal><![CDATA[
      c_0' v (c_0' v c_0) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(3947),rewrite([4145(21),5(20),4117(19)])].">
      <j1 rule="back_rewrite" parents="3947"/>
      <j2 rule="rewrite" parents="4145 5 4117"/>
    </justification>
  </clause>

  <clause id="4273">
    <literal><![CDATA[
      c_0' v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(4237(a,1),52(a,1,2)),rewrite([5(11),2544(15)]),flip(a)].">
      <j1 rule="para" parents="4237 52"/>
      <j2 rule="rewrite" parents="5 2544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4274">
    <literal><![CDATA[
      c_0 v (c_0 v c_0) = c_0
    ]]></literal>
    <justification jstring="[para(52(a,2),4237(a,1,2)),rewrite([5(11),49(10),4273(6),5(6),4273(5)])].">
      <j1 rule="para" parents="52 4237"/>
      <j2 rule="rewrite" parents="5 49 4273 5 4273"/>
    </justification>
  </clause>

  <clause id="4316">
    <literal><![CDATA[
      (c_0' v c_0') v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[back_rewrite(3838),rewrite([4273(11)])].">
      <j1 rule="back_rewrite" parents="3838"/>
      <j2 rule="rewrite" parents="4273"/>
    </justification>
  </clause>

  <clause id="4379">
    <literal><![CDATA[
      (c_0 v c_0)' = c_0'
    ]]></literal>
    <justification jstring="[back_rewrite(2488),rewrite([4273(9),17(11),4273(5),4274(5)]),flip(a)].">
      <j1 rule="back_rewrite" parents="2488"/>
      <j2 rule="rewrite" parents="4273 17 4273 4274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4392">
    <literal><![CDATA[
      c_0 v (x v (y v (z v (c_0 v c_0)))) = x v (y v (z v c_0))
    ]]></literal>
    <justification jstring="[back_rewrite(2428),rewrite([4273(5)])].">
      <j1 rule="back_rewrite" parents="2428"/>
      <j2 rule="rewrite" parents="4273"/>
    </justification>
  </clause>

  <clause id="4395">
    <literal><![CDATA[
      c_0 v c_0 = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(2422),rewrite([4273(5),4379(5),17(4),4316(7)])].">
      <j1 rule="back_rewrite" parents="2422"/>
      <j2 rule="rewrite" parents="4273 4379 17 4316"/>
    </justification>
  </clause>

  <clause id="4398">
    <literal><![CDATA[
      c_0 v (x v c_0) = x v c_0
    ]]></literal>
    <justification jstring="[back_rewrite(2416),rewrite([4273(5),4395(4)])].">
      <j1 rule="back_rewrite" parents="2416"/>
      <j2 rule="rewrite" parents="4273 4395"/>
    </justification>
  </clause>

  <clause id="4431">
    <literal><![CDATA[
      c_0 v (x v (y v (z v c_0))) = x v (y v (z v c_0))
    ]]></literal>
    <justification jstring="[back_rewrite(4392),rewrite([4395(4)])].">
      <j1 rule="back_rewrite" parents="4392"/>
      <j2 rule="rewrite" parents="4395"/>
    </justification>
  </clause>

  <clause id="4447">
    <literal><![CDATA[
      c_0' v c_0 = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(4273),rewrite([4395(7)])].">
      <j1 rule="back_rewrite" parents="4273"/>
      <j2 rule="rewrite" parents="4395"/>
    </justification>
  </clause>

  <clause id="4523">
    <literal><![CDATA[
      (c_0' v (x v ((x v c_0) v ((x v c_0) v c_0)))')' = x v c_0
    ]]></literal>
    <justification jstring="[back_rewrite(2619),rewrite([4395(5),4395(7),4395(16)])].">
      <j1 rule="back_rewrite" parents="2619"/>
      <j2 rule="rewrite" parents="4395 4395 4395"/>
    </justification>
  </clause>

  <clause id="4527">
    <literal><![CDATA[
      c_0' v (x v (y v c_0)) = x v (y v c_0)
    ]]></literal>
    <justification jstring="[back_rewrite(2565),rewrite([4395(3),4431(8)])].">
      <j1 rule="back_rewrite" parents="2565"/>
      <j2 rule="rewrite" parents="4395 4431"/>
    </justification>
  </clause>

  <clause id="4530">
    <literal><![CDATA[
      c_0'' = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(2426),rewrite([4395(6)])].">
      <j1 rule="back_rewrite" parents="2426"/>
      <j2 rule="rewrite" parents="4395"/>
    </justification>
  </clause>

  <clause id="4536">
    <literal><![CDATA[
      (((x v x'')' v c_0)' v x)' = (x v x'')'
    ]]></literal>
    <justification jstring="[back_rewrite(2634),rewrite([4398(8)])].">
      <j1 rule="back_rewrite" parents="2634"/>
      <j2 rule="rewrite" parents="4398"/>
    </justification>
  </clause>

  <clause id="4630">
    <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(165(a,1),46(a,1,1,2,1)),rewrite([5(20),5(22),5(21),5(50),5(52),5(51)])].">
      <j1 rule="para" parents="165 46"/>
      <j2 rule="rewrite" parents="5 5 5 5 5 5"/>
    </justification>
  </clause>

  <clause id="4712">
    <literal><![CDATA[
      x v ((x v c_0) v c_0) = x v c_0
    ]]></literal>
    <justification jstring="[para(869(a,1),50(a,1,1,2,1,2,2)),rewrite([5(11),4527(12),5(10),4523(13),5(9),4527(10)]),flip(a)].">
      <j1 rule="para" parents="869 50"/>
      <j2 rule="rewrite" parents="5 4527 5 4523 5 4527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4736">
    <literal><![CDATA[
      (c_0' v (x v c_0)')' = x v c_0
    ]]></literal>
    <justification jstring="[para(3588(a,1),50(a,1,1,2,1,2,2,1,2)),rewrite([3887(16),4712(7),3588(17)])].">
      <j1 rule="para" parents="3588 50"/>
      <j2 rule="rewrite" parents="3887 4712 3588"/>
    </justification>
  </clause>

  <clause id="4742">
    <literal><![CDATA[
      x v ((c_0' v (x v c_0)') v c_0) = c_0
    ]]></literal>
    <justification jstring="[para(4398(a,1),52(a,1,2)),rewrite([5(7),4712(7),5(9),4395(12)])].">
      <j1 rule="para" parents="4398 52"/>
      <j2 rule="rewrite" parents="5 4712 5 4395"/>
    </justification>
  </clause>

  <clause id="4747">
    <literal><![CDATA[
      x v (y v ((x v c_0) v c_0)) = y v (x v c_0)
    ]]></literal>
    <justification jstring="[para(4712(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4712 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4856">
    <literal><![CDATA[
      ((x v c_0)' v c_0')' = x v c_0
    ]]></literal>
    <justification jstring="[para(4736(a,1),42(a,1,1,1,1,2)),rewrite([5(5),4712(5),4447(7)])].">
      <j1 rule="para" parents="4736 42"/>
      <j2 rule="rewrite" parents="5 4712 4447"/>
    </justification>
  </clause>

  <clause id="4869">
    <literal><![CDATA[
      ((x v (y v c_0))' v ((y v c_0)' v (x v c_0'))')' = x
    ]]></literal>
    <justification jstring="[para(4856(a,1),19(a,1,1,1,1,2))].">
      <j1 rule="para" parents="4856 19"/>
    </justification>
  </clause>

  <clause id="4879">
    <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(4856(a,1),21(a,1,1,2,1,2,1)),rewrite([5(11),4856(21)])].">
      <j1 rule="para" parents="4856 21"/>
      <j2 rule="rewrite" parents="5 4856"/>
    </justification>
  </clause>

  <clause id="4887">
    <literal><![CDATA[
      ((x v c_0)' v ((x v c_0)' v c_0)')' = c_0
    ]]></literal>
    <justification jstring="[para(4856(a,1),42(a,1,1,1,1,2)),rewrite([4398(4)])].">
      <j1 rule="para" parents="4856 42"/>
      <j2 rule="rewrite" parents="4398"/>
    </justification>
  </clause>

  <clause id="4988">
    <literal><![CDATA[
      x v ((x v c_0) v ((c_0' v (x v c_0)') v c_0)) = c_0
    ]]></literal>
    <justification jstring="[para(4712(a,1),53(a,1,2,1,2,1,2,1)),rewrite([4747(10),5(7),4712(7),5(11)])].">
      <j1 rule="para" parents="4712 53"/>
      <j2 rule="rewrite" parents="4747 5 4712 5"/>
    </justification>
  </clause>

  <clause id="4999">
    <literal><![CDATA[
      x v (y v ((c_0' v (x v c_0)') v c_0)) = y v c_0
    ]]></literal>
    <justification jstring="[para(4742(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4742 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5007">
    <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(4742(a,1),22(a,1,1,1,1,2,1,1)),rewrite([4530(14)])].">
      <j1 rule="para" parents="4742 22"/>
      <j2 rule="rewrite" parents="4530"/>
    </justification>
  </clause>

  <clause id="5022">
    <literal><![CDATA[
      (x v c_0) v c_0 = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(4988),rewrite([4999(12)])].">
      <j1 rule="back_rewrite" parents="4988"/>
      <j2 rule="rewrite" parents="4999"/>
    </justification>
  </clause>

  <clause id="5040">
    <literal><![CDATA[
      (x v c_0) v (y v c_0) = y v c_0
    ]]></literal>
    <justification jstring="[para(5022(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5022 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5056">
    <literal><![CDATA[
      x v c_0 = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(4879),rewrite([5040(11),4887(11)]),flip(a)].">
      <j1 rule="back_rewrite" parents="4879"/>
      <j2 rule="rewrite" parents="5040 4887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5060">
    <literal><![CDATA[
      (c_0' v x)' = (x v c_0')'
    ]]></literal>
    <justification jstring="[back_rewrite(5007),rewrite([5056(4),5056(7),5056(6),5056(8),5056(11)])].">
      <j1 rule="back_rewrite" parents="5007"/>
      <j2 rule="rewrite" parents="5056 5056 5056 5056 5056"/>
    </justification>
  </clause>

  <clause id="5089">
    <literal><![CDATA[
      (c_0' v (c_0' v (x v c_0'))')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(4869),rewrite([5056(2),5056(2),5056(4)])].">
      <j1 rule="back_rewrite" parents="4869"/>
      <j2 rule="rewrite" parents="5056 5056 5056"/>
    </justification>
  </clause>

  <clause id="5139">
    <literal><![CDATA[
      (x v x'')' = (c_0' v x)'
    ]]></literal>
    <justification jstring="[back_rewrite(4536),rewrite([5056(6)]),flip(a)].">
      <j1 rule="back_rewrite" parents="4536"/>
      <j2 rule="rewrite" parents="5056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5186">
    <literal><![CDATA[
      (x v (y v (z v (u v x')))')' = (c_0' v x)'
    ]]></literal>
    <justification jstring="[back_rewrite(4047),rewrite([5056(9),5056(9),5056(9),4530(10),5056(9)]),flip(a)].">
      <j1 rule="back_rewrite" parents="4047"/>
      <j2 rule="rewrite" parents="5056 5056 5056 4530 5056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5637">
    <literal><![CDATA[
      (c_0' v (c_0' v x)')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(1028),rewrite([5186(7),5056(6),5056(6),5056(6),5060(8,R)])].">
      <j1 rule="back_rewrite" parents="1028"/>
      <j2 rule="rewrite" parents="5186 5056 5056 5056 5060"/>
    </justification>
  </clause>

  <clause id="5717">
    <literal><![CDATA[
      (c_0' v (x v (x v (c_0' v x)))') v (y v x) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(712),rewrite([5056(13)])].">
      <j1 rule="back_rewrite" parents="712"/>
      <j2 rule="rewrite" parents="5056"/>
    </justification>
  </clause>

  <clause id="5768">
    <literal><![CDATA[
      (c_0' v (x v (((y v x') v z')' v ((y v x') v z)'))')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(185),rewrite([5056(2)])].">
      <j1 rule="back_rewrite" parents="185"/>
      <j2 rule="rewrite" parents="5056"/>
    </justification>
  </clause>

  <clause id="5779">
    <literal><![CDATA[
      (c_0' v (x v x)') v (y v x) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(52),rewrite([5056(9)])].">
      <j1 rule="back_rewrite" parents="52"/>
      <j2 rule="rewrite" parents="5056"/>
    </justification>
  </clause>

  <clause id="5793">
    <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(4630),rewrite([5060(30,R)])].">
      <j1 rule="back_rewrite" parents="4630"/>
      <j2 rule="rewrite" parents="5060"/>
    </justification>
  </clause>

  <clause id="5810">
    <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(2028),rewrite([5060(33,R)])].">
      <j1 rule="back_rewrite" parents="2028"/>
      <j2 rule="rewrite" parents="5060"/>
    </justification>
  </clause>

  <clause id="5880">
    <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(108),rewrite([5139(8),5139(20)])].">
      <j1 rule="back_rewrite" parents="108"/>
      <j2 rule="rewrite" parents="5139 5139"/>
    </justification>
  </clause>

  <clause id="5882">
    <literal><![CDATA[
      ((x v y)' v ((c_0' v y)' v (x v c_0'))')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(91),rewrite([5139(6)])].">
      <j1 rule="back_rewrite" parents="91"/>
      <j2 rule="rewrite" parents="5139"/>
    </justification>
  </clause>

  <clause id="5887">
    <literal><![CDATA[
      x v c_0' = x
    ]]></literal>
    <justification jstring="[back_rewrite(5089),rewrite([5637(11)])].">
      <j1 rule="back_rewrite" parents="5089"/>
      <j2 rule="rewrite" parents="5637"/>
    </justification>
  </clause>

  <clause id="5910">
    <literal><![CDATA[
      x v ((x v y) v ((x v y) v y)) = x v y
    ]]></literal>
    <justification jstring="[back_rewrite(682),rewrite([5637(13)])].">
      <j1 rule="back_rewrite" parents="682"/>
      <j2 rule="rewrite" parents="5637"/>
    </justification>
  </clause>

  <clause id="5917">
    <literal><![CDATA[
      x'' = x
    ]]></literal>
    <justification jstring="[back_rewrite(2115),rewrite([5887(3),5717(12),5887(4)])].">
      <j1 rule="back_rewrite" parents="2115"/>
      <j2 rule="rewrite" parents="5887 5717 5887"/>
    </justification>
  </clause>

  <clause id="5926">
    <literal><![CDATA[
      (c_0' v x)' = x'
    ]]></literal>
    <justification jstring="[back_rewrite(523),rewrite([5887(3),5779(8),5917(4),5056(3),5887(7)])].">
      <j1 rule="back_rewrite" parents="523"/>
      <j2 rule="rewrite" parents="5887 5779 5917 5056 5887"/>
    </justification>
  </clause>

  <clause id="5933">
    <literal><![CDATA[
      ((x v y)' v (y' v x)')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(5882),rewrite([5926(6),5887(6)])].">
      <j1 rule="back_rewrite" parents="5882"/>
      <j2 rule="rewrite" parents="5926 5887"/>
    </justification>
  </clause>

  <clause id="5935">
    <literal><![CDATA[
      x v x = x
    ]]></literal>
    <justification jstring="[back_rewrite(5880),rewrite([5926(7),5917(4),5887(5),5926(6),5917(3),5926(6),5917(3),5887(4)])].">
      <j1 rule="back_rewrite" parents="5880"/>
      <j2 rule="rewrite" parents="5926 5917 5887 5926 5917 5926 5917 5887"/>
    </justification>
  </clause>

  <clause id="6061">
    <literal><![CDATA[
      (c_0' v x) v x = c_0' v x
    ]]></literal>
    <justification jstring="[back_rewrite(5810),rewrite([5910(26),5926(14),9(11),5926(9),5917(6),5910(28),5926(16),9(13)])].">
      <j1 rule="back_rewrite" parents="5810"/>
      <j2 rule="rewrite" parents="5910 5926 9 5926 5917 5910 5926 9"/>
    </justification>
  </clause>

  <clause id="6063">
    <literal><![CDATA[
      c_0' v x = x
    ]]></literal>
    <justification jstring="[back_rewrite(5793),rewrite([5935(11),5935(15),5935(17),6061(18),5935(17),5926(15),5926(12),5926(9),5917(6),6061(6),5926(6),5926(5),5917(2),5935(9),5935(13),5935(15),6061(16),5935(15),5926(13),5926(10),5926(7),5917(4)]),flip(a)].">
      <j1 rule="back_rewrite" parents="5793"/>
      <j2 rule="rewrite" parents="5935 5935 5935 6061 5935 5926 5926 5926 5917 6061 5926 5926 5917 5935 5935 5935 6061 5935 5926 5926 5926 5917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6077">
    <literal><![CDATA[
      x v (((y v x') v z')' v ((y v x') v z)') = x
    ]]></literal>
    <justification jstring="[back_rewrite(5768),rewrite([6063(15),5917(13)])].">
      <j1 rule="back_rewrite" parents="5768"/>
      <j2 rule="rewrite" parents="6063 5917"/>
    </justification>
  </clause>

  <clause id="6578">
    <literal><![CDATA[
      (x v y')' v (x v y)' = x'
    ]]></literal>
    <justification jstring="[para(9(a,1),5917(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 5917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6581">
    <literal><![CDATA[
      x v (x v ((x v y')' v y))' = x v y'
    ]]></literal>
    <justification jstring="[para(21(a,1),5917(a,1,1)),rewrite([5917(4)]),flip(a)].">
      <j1 rule="para" parents="21 5917"/>
      <j2 rule="rewrite" parents="5917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6587">
    <literal><![CDATA[
      x v (y v x')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(6077),rewrite([6578(10)])].">
      <j1 rule="back_rewrite" parents="6077"/>
      <j2 rule="rewrite" parents="6578"/>
    </justification>
  </clause>

  <clause id="6642">
    <literal><![CDATA[
      x v y = y v x
    ]]></literal>
    <justification jstring="[para(5887(a,1),5(a,1,2)),rewrite([5887(4)])].">
      <j1 rule="para" parents="5887 5"/>
      <j2 rule="rewrite" parents="5887"/>
    </justification>
  </clause>

  <clause id="6643">
    <literal><![CDATA[
      x v (y v z) = z v (x v y)
    ]]></literal>
    <justification jstring="[para(5887(a,1),18(a,1,2,2)),rewrite([5887(5)])].">
      <j1 rule="para" parents="5887 18"/>
      <j2 rule="rewrite" parents="5887"/>
    </justification>
  </clause>

  <clause id="6667">
    <literal><![CDATA[
      x v (x v y)' = x v y'
    ]]></literal>
    <justification jstring="[back_rewrite(6581),rewrite([6642(4),6587(4)])].">
      <j1 rule="back_rewrite" parents="6581"/>
      <j2 rule="rewrite" parents="6642 6587"/>
    </justification>
  </clause>

  <clause id="7269">
    <literal><![CDATA[
      x v (y v (z v x')') = y v x
    ]]></literal>
    <justification jstring="[para(6587(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6587 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7273">
    <literal><![CDATA[
      x v (x' v y)' = x
    ]]></literal>
    <justification jstring="[para(6642(a,1),6587(a,1,2,1))].">
      <j1 rule="para" parents="6642 6587"/>
    </justification>
  </clause>

  <clause id="7318">
    <literal><![CDATA[
      x v (y v (x' v z))' = x
    ]]></literal>
    <justification jstring="[para(5(a,1),7273(a,1,2,1))].">
      <j1 rule="para" parents="5 7273"/>
    </justification>
  </clause>

  <clause id="8516">
    <literal><![CDATA[
      (x v y) v z = x v (y v z)
    ]]></literal>
    <justification jstring="[para(6643(a,2),6642(a,1)),flip(a)].">
      <j1 rule="para" parents="6643 6642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8771">
    <literal><![CDATA[
      x v (y v x)' = x v y'
    ]]></literal>
    <justification jstring="[para(6642(a,1),6667(a,1,2,1))].">
      <j1 rule="para" parents="6642 6667"/>
    </justification>
  </clause>

  <clause id="8832">
    <literal><![CDATA[
      x v ((y v (x' v z))' v u) = x v u
    ]]></literal>
    <justification jstring="[para(7318(a,1),8516(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7318 8516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8848">
    <literal><![CDATA[
      x v (y v (z v x)') = y v (x v z')
    ]]></literal>
    <justification jstring="[para(8771(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8771 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8902">
    <literal><![CDATA[
      (x v y)' v (y' v x)' = x'
    ]]></literal>
    <justification jstring="[para(5933(a,1),5917(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5933 5917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9756">
    <literal><![CDATA[
      (x v (y v z)')' = (x v (z v y'))' v (x v z')'
    ]]></literal>
    <justification jstring="[para(7269(a,1),8902(a,1,2,1)),rewrite([5917(2),6642(4),8848(4),5917(10)]),flip(a)].">
      <j1 rule="para" parents="7269 8902"/>
      <j2 rule="rewrite" parents="5917 6642 8848 5917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9813">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer(MOD)
    ]]></attribute>
    <justification jstring="[back_rewrite(16),rewrite([9756(9),6642(8),8516(8),8832(17),9756(17),6642(16),8516(16),6642(22),8832(25)]),xx(a)].">
      <j1 rule="back_rewrite" parents="16"/>
      <j2 rule="rewrite" parents="9756 6642 8516 8832 9756 6642 8516 6642 8832"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="4" length="181" max_count="86">

<comments><![CDATA[
% Proof 4 at 6.33 (+ 0.03) seconds: DIST1.
% Length of proof is 181.
% Level of proof is 50.
% Maximum clause weight is 86.
% Given clauses 303.

]]></comments>

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

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

  <clause id="7" type="assumption">
    <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" type="assumption">
    <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" type="deny">
    <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 (u v w))) = z v (x v (u v (y v w)))
    ]]></literal>
    <justification jstring="[para(18(a,1),5(a,1,2))].">
      <j1 rule="para" parents="18 5"/>
    </justification>
  </clause>

  <clause id="29">
    <literal><![CDATA[
      x v (y v (z v (u v w))) = u v (x v (y v (z v w)))
    ]]></literal>
    <justification jstring="[para(18(a,2),5(a,1,2))].">
      <j1 rule="para" parents="18 5"/>
    </justification>
  </clause>

  <clause id="31">
    <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="33">
    <literal><![CDATA[
      x v (y v (z v x')) = y v (z v c_0)
    ]]></literal>
    <justification jstring="[para(17(a,1),18(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="17 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42">
    <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="44">
    <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="45">
    <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="46">
    <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="47">
    <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="48">
    <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="49">
    <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="50">
    <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="52">
    <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="53">
    <literal><![CDATA[
      x v ((c_0' v (x v ((x v y) v y))') v y) = c_0
    ]]></literal>
    <justification jstring="[para(49(a,1),5(a,1)),rewrite([5(6)]),flip(a)].">
      <j1 rule="para" parents="49 5"/>
      <j2 rule="rewrite" parents="5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="63">
    <literal><![CDATA[
      (c_0' v (x' v x')') v c_0 = x v c_0
    ]]></literal>
    <justification jstring="[para(49(a,1),23(a,1,2)),flip(a)].">
      <j1 rule="para" parents="49 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="85">
    <literal><![CDATA[
      (x v (x v (c_0' v x))')' = c_0'
    ]]></literal>
    <justification jstring="[para(24(a,1),19(a,1,1,1))].">
      <j1 rule="para" parents="24 19"/>
    </justification>
  </clause>

  <clause id="91">
    <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="95">
    <literal><![CDATA[
      (c_0' v (x v (c_0' v (x v x)))')' = x
    ]]></literal>
    <justification jstring="[para(47(a,1),9(a,1,1,1))].">
      <j1 rule="para" parents="47 9"/>
    </justification>
  </clause>

  <clause id="97">
    <literal><![CDATA[
      (x v (c_0' v (x v x))') v c_0' = c_0
    ]]></literal>
    <justification jstring="[para(47(a,1),17(a,1,2))].">
      <j1 rule="para" parents="47 17"/>
    </justification>
  </clause>

  <clause id="108">
    <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="126">
    <literal><![CDATA[
      (c_0' v (x v (x v (c_0' v x)))')' = x
    ]]></literal>
    <justification jstring="[para(85(a,1),9(a,1,1,1))].">
      <j1 rule="para" parents="85 9"/>
    </justification>
  </clause>

  <clause id="149">
    <literal><![CDATA[
      ((x' v y')' v (x' v y)') v c_0 = x v c_0
    ]]></literal>
    <justification jstring="[para(26(a,1),23(a,1,2)),flip(a)].">
      <j1 rule="para" parents="26 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="152">
    <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="165">
    <literal><![CDATA[
      (c_0' v (x v (c_0' v (x v x)))') v x = c_0
    ]]></literal>
    <justification jstring="[para(47(a,1),26(a,1,1,1))].">
      <j1 rule="para" parents="47 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(85(a,1),26(a,1,1,1))].">
      <j1 rule="para" parents="85 26"/>
    </justification>
  </clause>

  <clause id="185">
    <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="243">
    <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(97(a,1),9(a,1,1,1,1))].">
      <j1 rule="para" parents="97 9"/>
    </justification>
  </clause>

  <clause id="248">
    <literal><![CDATA[
      (x v (c_0' v (x v x))') v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(97(a,1),23(a,1,2)),flip(a)].">
      <j1 rule="para" parents="97 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="256">
    <literal><![CDATA[
      x v (c_0' v (x v x))' = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(243),rewrite([248(10),24(8)]),flip(a)].">
      <j1 rule="back_rewrite" parents="243"/>
      <j2 rule="rewrite" parents="248 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="258">
    <literal><![CDATA[
      x v (y v (c_0' v (x v x))') = y v c_0
    ]]></literal>
    <justification jstring="[para(256(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="256 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="266">
    <literal><![CDATA[
      (c_0' v (x v x)) v c_0 = x v c_0
    ]]></literal>
    <justification jstring="[para(256(a,1),23(a,1,2))].">
      <j1 rule="para" parents="256 23"/>
    </justification>
  </clause>

  <clause id="267">
    <literal><![CDATA[
      c_0'' v (c_0'' v c_0)' = c_0
    ]]></literal>
    <justification jstring="[para(23(a,1),256(a,1,2,1))].">
      <j1 rule="para" parents="23 256"/>
    </justification>
  </clause>

  <clause id="322">
    <literal><![CDATA[
      (c_0'' v c_0) v c_0 = c_0'' v c_0
    ]]></literal>
    <justification jstring="[para(23(a,1),266(a,1,1))].">
      <j1 rule="para" parents="23 266"/>
    </justification>
  </clause>

  <clause id="330">
    <literal><![CDATA[
      (c_0' v (c_0'' v (c_0'' v c_0))')' = c_0''
    ]]></literal>
    <justification jstring="[para(267(a,1),9(a,1,1,1,1))].">
      <j1 rule="para" parents="267 9"/>
    </justification>
  </clause>

  <clause id="339">
    <literal><![CDATA[
      (c_0'' v c_0) v (x v c_0) = x v (c_0'' v c_0)
    ]]></literal>
    <justification jstring="[para(267(a,1),33(a,1,2,2))].">
      <j1 rule="para" parents="267 33"/>
    </justification>
  </clause>

  <clause id="523">
    <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(52(a,2),22(a,1,1,1,1,2,1,1))].">
      <j1 rule="para" parents="52 22"/>
    </justification>
  </clause>

  <clause id="651">
    <literal><![CDATA[
      ((c_0' v (x v x)'')' v x) v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(48(a,1),63(a,1,1,2,1,1)),rewrite([48(13),63(11)]),flip(a)].">
      <j1 rule="para" parents="48 63"/>
      <j2 rule="rewrite" parents="48 63"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="672">
    <literal><![CDATA[
      (c_0' v (x v ((x v c_0'') v ((x v c_0'') v c_0)))')' = x v c_0''
    ]]></literal>
    <justification jstring="[para(33(a,1),95(a,1,1,2,1,2)),rewrite([5(13),5(14)])].">
      <j1 rule="para" parents="33 95"/>
      <j2 rule="rewrite" parents="5 5"/>
    </justification>
  </clause>

  <clause id="682">
    <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(27(a,2),95(a,1,1,2,1))].">
      <j1 rule="para" parents="27 95"/>
    </justification>
  </clause>

  <clause id="712">
    <literal><![CDATA[
      (c_0' v (x v (x v (c_0' v x)))') v (y v x) = y v c_0
    ]]></literal>
    <justification jstring="[para(126(a,1),23(a,1,2,2))].">
      <j1 rule="para" parents="126 23"/>
    </justification>
  </clause>

  <clause id="869">
    <literal><![CDATA[
      (c_0' v (x v x)) v (y v c_0) = x v (y v c_0)
    ]]></literal>
    <justification jstring="[para(258(a,1),33(a,1,2))].">
      <j1 rule="para" parents="258 33"/>
    </justification>
  </clause>

  <clause id="955">
    <literal><![CDATA[
      (c_0' v c_0''')' v c_0' = (c_0' v c_0''')'
    ]]></literal>
    <justification jstring="[para(68(a,1),45(a,1,1,2,1,2)),rewrite([65(15)]),flip(a)].">
      <j1 rule="para" parents="68 45"/>
      <j2 rule="rewrite" parents="65"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="963">
    <literal><![CDATA[
      c_0'' v c_0 = c_0''
    ]]></literal>
    <justification jstring="[para(322(a,1),45(a,1,1,2,1,2,1)),rewrite([322(14),5(13),322(12),330(14),322(10)]),flip(a)].">
      <j1 rule="para" parents="322 45"/>
      <j2 rule="rewrite" parents="322 5 322 330 322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="999">
    <literal><![CDATA[
      c_0'' v (x v c_0) = x v c_0''
    ]]></literal>
    <justification jstring="[back_rewrite(339),rewrite([963(5),963(11)])].">
      <j1 rule="back_rewrite" parents="339"/>
      <j2 rule="rewrite" parents="963 963"/>
    </justification>
  </clause>

  <clause id="1012">
    <literal><![CDATA[
      (((((x v y) v (x v y)'')' v c_0') v (x v (z v y))')' v (z v c_0)')' = ((x v y) v (x v y)'')' v c_0'
    ]]></literal>
    <justification jstring="[para(68(a,1),31(a,1,1,2,1,2))].">
      <j1 rule="para" parents="68 31"/>
    </justification>
  </clause>

  <clause id="1028">
    <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(33(a,1),31(a,1,1,2,1,2))].">
      <j1 rule="para" parents="33 31"/>
    </justification>
  </clause>

  <clause id="1078">
    <literal><![CDATA[
      (c_0' v (c_0 v c_0)') v c_0'' = c_0''
    ]]></literal>
    <justification jstring="[para(963(a,1),52(a,1,2)),rewrite([963(16)])].">
      <j1 rule="para" parents="963 52"/>
      <j2 rule="rewrite" parents="963"/>
    </justification>
  </clause>

  <clause id="1082">
    <literal><![CDATA[
      ((c_0'' v (x v c_0))' v (x v c_0')')' = x
    ]]></literal>
    <justification jstring="[para(999(a,2),9(a,1,1,1,1))].">
      <j1 rule="para" parents="999 9"/>
    </justification>
  </clause>

  <clause id="1083">
    <literal><![CDATA[
      c_0' v (c_0'' v (x v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[para(999(a,2),23(a,1,2))].">
      <j1 rule="para" parents="999 23"/>
    </justification>
  </clause>

  <clause id="1119">
    <literal><![CDATA[
      c_0'' v (x v c_0) = (c_0' v (x' v x')') v c_0''
    ]]></literal>
    <justification jstring="[para(63(a,1),999(a,1,2))].">
      <j1 rule="para" parents="63 999"/>
    </justification>
  </clause>

  <clause id="1136">
    <literal><![CDATA[
      c_0' v (c_0'' v (x v (y v c_0))) = x v (y v c_0)
    ]]></literal>
    <justification jstring="[para(1083(a,1),18(a,2,2))].">
      <j1 rule="para" parents="1083 18"/>
    </justification>
  </clause>

  <clause id="1137">
    <literal><![CDATA[
      c_0'' v (x v (c_0' v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[para(1083(a,1),18(a,2))].">
      <j1 rule="para" parents="1083 18"/>
    </justification>
  </clause>

  <clause id="1157">
    <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(49(a,1),1137(a,1,2)),rewrite([963(5),5(14)]),flip(a)].">
      <j1 rule="para" parents="49 1137"/>
      <j2 rule="rewrite" parents="963 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1263">
    <literal><![CDATA[
      (c_0' v c_0''')'' = c_0'
    ]]></literal>
    <justification jstring="[para(1078(a,1),42(a,1,1,1,1,2,1)),rewrite([49(17),955(11)])].">
      <j1 rule="para" parents="1078 42"/>
      <j2 rule="rewrite" parents="49 955"/>
    </justification>
  </clause>

  <clause id="1266">
    <literal><![CDATA[
      (c_0' v c_0''')' = c_0
    ]]></literal>
    <justification jstring="[para(1263(a,1),17(a,1,2)),rewrite([955(11)])].">
      <j1 rule="para" parents="1263 17"/>
      <j2 rule="rewrite" parents="955"/>
    </justification>
  </clause>

  <clause id="1271">
    <literal><![CDATA[
      ((c_0' v c_0'''')' v c_0)' = c_0'
    ]]></literal>
    <justification jstring="[para(1266(a,1),9(a,1,1,2))].">
      <j1 rule="para" parents="1266 9"/>
    </justification>
  </clause>

  <clause id="1284">
    <literal><![CDATA[
      (c_0''' v (c_0' v c_0)')' = c_0''
    ]]></literal>
    <justification jstring="[para(1266(a,1),42(a,1,1,1,1,2)),rewrite([963(5)])].">
      <j1 rule="para" parents="1266 42"/>
      <j2 rule="rewrite" parents="963"/>
    </justification>
  </clause>

  <clause id="1519">
    <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(1271(a,1),25(a,1,1,1,1,2,1))].">
      <j1 rule="para" parents="1271 25"/>
    </justification>
  </clause>

  <clause id="1546">
    <literal><![CDATA[
      ((c_0''' v (c_0' v c_0)'')' v c_0'')' = c_0'''
    ]]></literal>
    <justification jstring="[para(1284(a,1),9(a,1,1,2))].">
      <j1 rule="para" parents="1284 9"/>
    </justification>
  </clause>

  <clause id="1707">
    <literal><![CDATA[
      (c_0' v (x v x)'')' v x = c_0
    ]]></literal>
    <justification jstring="[para(152(a,1),9(a,1,1,1,1)),rewrite([651(12),24(8)]),flip(a)].">
      <j1 rule="para" parents="152 9"/>
      <j2 rule="rewrite" parents="651 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2028">
    <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(165(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="165 20"/>
      <j2 rule="rewrite" parents="5 5 5 5 5 5"/>
    </justification>
  </clause>

  <clause id="2115">
    <literal><![CDATA[
      ((x v c_0')' v ((c_0' v (y v (y v (c_0' v y)))') v (x v y))')' = x
    ]]></literal>
    <justification jstring="[para(169(a,1),19(a,1,1,1,1,2,1))].">
      <j1 rule="para" parents="169 19"/>
    </justification>
  </clause>

  <clause id="2387">
    <literal><![CDATA[
      c_0 v (c_0' v c_0) = c_0
    ]]></literal>
    <justification jstring="[para(869(a,1),45(a,1,1,2,1,2)),rewrite([5(10),5(9),126(13),5(7)]),flip(a)].">
      <j1 rule="para" parents="869 45"/>
      <j2 rule="rewrite" parents="5 5 126 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2416">
    <literal><![CDATA[
      c_0 v (x v (c_0' v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[para(2387(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2387 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2422">
    <literal><![CDATA[
      ((c_0 v (c_0' v c_0)')' v c_0') v c_0 = c_0
    ]]></literal>
    <justification jstring="[para(2387(a,1),26(a,1,1,2,1))].">
      <j1 rule="para" parents="2387 26"/>
    </justification>
  </clause>

  <clause id="2426">
    <literal><![CDATA[
      c_0'' = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(2387(a,1),52(a,1,2)),rewrite([5(11),1157(15)])].">
      <j1 rule="para" parents="2387 52"/>
      <j2 rule="rewrite" parents="5 1157"/>
    </justification>
  </clause>

  <clause id="2428">
    <literal><![CDATA[
      c_0 v (x v (y v (z v (c_0' v c_0)))) = x v (y v (z v c_0))
    ]]></literal>
    <justification jstring="[para(2387(a,1),29(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="2387 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2488">
    <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(1546),rewrite([2426(3),2426(15),5(16),2426(20)])].">
      <j1 rule="back_rewrite" parents="1546"/>
      <j2 rule="rewrite" parents="2426 2426 5 2426"/>
    </justification>
  </clause>

  <clause id="2493">
    <literal><![CDATA[
      ((c_0 v (c_0 v c_0))' v c_0')' = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(1519),rewrite([2426(5),1707(11),2426(4),2426(15),1707(21)])].">
      <j1 rule="back_rewrite" parents="1519"/>
      <j2 rule="rewrite" parents="2426 1707 2426 2426 1707"/>
    </justification>
  </clause>

  <clause id="2544">
    <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(1157),rewrite([2426(18)])].">
      <j1 rule="back_rewrite" parents="1157"/>
      <j2 rule="rewrite" parents="2426"/>
    </justification>
  </clause>

  <clause id="2565">
    <literal><![CDATA[
      (c_0 v c_0) v (c_0' v (x v (y v c_0))) = x v (y v c_0)
    ]]></literal>
    <justification jstring="[back_rewrite(1136),rewrite([2426(5),5(10)])].">
      <j1 rule="back_rewrite" parents="1136"/>
      <j2 rule="rewrite" parents="2426 5"/>
    </justification>
  </clause>

  <clause id="2582">
    <literal><![CDATA[
      (c_0 v c_0) v (x v c_0) = c_0 v (x v c_0)
    ]]></literal>
    <justification jstring="[back_rewrite(1119),rewrite([2426(3),2426(16),5(17),63(16)])].">
      <j1 rule="back_rewrite" parents="1119"/>
      <j2 rule="rewrite" parents="2426 2426 5 63"/>
    </justification>
  </clause>

  <clause id="2601">
    <literal><![CDATA[
      ((c_0 v (x v c_0))' v (x v c_0')')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(1082),rewrite([2426(3),2582(6)])].">
      <j1 rule="back_rewrite" parents="1082"/>
      <j2 rule="rewrite" parents="2426 2582"/>
    </justification>
  </clause>

  <clause id="2619">
    <literal><![CDATA[
      (c_0' v (x v ((x v (c_0 v c_0)) v ((x v (c_0 v c_0)) v c_0)))')' = x v (c_0 v c_0)
    ]]></literal>
    <justification jstring="[back_rewrite(672),rewrite([2426(5),2426(9),2426(20)])].">
      <j1 rule="back_rewrite" parents="672"/>
      <j2 rule="rewrite" parents="2426 2426 2426"/>
    </justification>
  </clause>

  <clause id="2634">
    <literal><![CDATA[
      ((c_0 v ((x v x'')' v c_0))' v x)' = (x v x'')'
    ]]></literal>
    <justification jstring="[back_rewrite(66),rewrite([2426(7),5(8)])].">
      <j1 rule="back_rewrite" parents="66"/>
      <j2 rule="rewrite" parents="2426 5"/>
    </justification>
  </clause>

  <clause id="3579">
    <literal><![CDATA[
      c_0' v (c_0' v c_0')' = c_0
    ]]></literal>
    <justification jstring="[para(49(a,1),2601(a,1,1,2,1)),rewrite([63(12),2493(10)]),flip(a)].">
      <j1 rule="para" parents="49 2601"/>
      <j2 rule="rewrite" parents="63 2493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3588">
    <literal><![CDATA[
      (c_0' v x')' v (c_0' v x)' = c_0
    ]]></literal>
    <justification jstring="[para(26(a,1),2601(a,1,1,2,1)),rewrite([149(13),2493(10)]),flip(a)].">
      <j1 rule="para" parents="26 2601"/>
      <j2 rule="rewrite" parents="149 2493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3836">
    <literal><![CDATA[
      c_0' v (x v (c_0' v c_0')') = x v c_0
    ]]></literal>
    <justification jstring="[para(3579(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3579 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3838">
    <literal><![CDATA[
      (c_0' v c_0') v c_0 = c_0' v c_0
    ]]></literal>
    <justification jstring="[para(3579(a,1),23(a,1,2))].">
      <j1 rule="para" parents="3579 23"/>
    </justification>
  </clause>

  <clause id="3847">
    <literal><![CDATA[
      (c_0' v ((c_0' v c_0')' v ((c_0' v c_0')' v c_0))') v (c_0' v c_0')' = c_0
    ]]></literal>
    <justification jstring="[para(3579(a,1),169(a,1,1,2,1,2,2))].">
      <j1 rule="para" parents="3579 169"/>
    </justification>
  </clause>

  <clause id="3887">
    <literal><![CDATA[
      (c_0' v x')' v (y v (z v (c_0' v x)')) = y v (z v c_0)
    ]]></literal>
    <justification jstring="[para(3588(a,1),18(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3588 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3890">
    <literal><![CDATA[
      (c_0' v x')' v c_0 = (c_0' v x) v c_0
    ]]></literal>
    <justification jstring="[para(3588(a,1),23(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3588 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3947">
    <literal><![CDATA[
      (c_0' v ((c_0' v c_0) v ((c_0' v c_0) v c_0))') v (c_0' v c_0')' = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(3847),rewrite([3890(16),5(15),3890(14)])].">
      <j1 rule="back_rewrite" parents="3847"/>
      <j2 rule="rewrite" parents="3890 5 3890"/>
    </justification>
  </clause>

  <clause id="4047">
    <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(44(a,1),22(a,1,1,1,1,2,1,1))].">
      <j1 rule="para" parents="44 22"/>
    </justification>
  </clause>

  <clause id="4117">
    <literal><![CDATA[
      (c_0' v ((c_0' v c_0) v ((c_0' v c_0) v c_0))') v c_0 = c_0' v c_0
    ]]></literal>
    <justification jstring="[para(165(a,1),3836(a,1,2)),rewrite([3836(28),3890(20),5(19),3890(18)]),flip(a)].">
      <j1 rule="para" parents="165 3836"/>
      <j2 rule="rewrite" parents="3836 3890 5 3890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4145">
    <literal><![CDATA[
      (c_0' v c_0')' = c_0' v c_0
    ]]></literal>
    <justification jstring="[para(3890(a,1),21(a,1,1,2,1,2)),rewrite([45(14)]),flip(a)].">
      <j1 rule="para" parents="3890 21"/>
      <j2 rule="rewrite" parents="45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4237">
    <literal><![CDATA[
      c_0' v (c_0' v c_0) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(3947),rewrite([4145(21),5(20),4117(19)])].">
      <j1 rule="back_rewrite" parents="3947"/>
      <j2 rule="rewrite" parents="4145 5 4117"/>
    </justification>
  </clause>

  <clause id="4273">
    <literal><![CDATA[
      c_0' v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(4237(a,1),52(a,1,2)),rewrite([5(11),2544(15)]),flip(a)].">
      <j1 rule="para" parents="4237 52"/>
      <j2 rule="rewrite" parents="5 2544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4274">
    <literal><![CDATA[
      c_0 v (c_0 v c_0) = c_0
    ]]></literal>
    <justification jstring="[para(52(a,2),4237(a,1,2)),rewrite([5(11),49(10),4273(6),5(6),4273(5)])].">
      <j1 rule="para" parents="52 4237"/>
      <j2 rule="rewrite" parents="5 49 4273 5 4273"/>
    </justification>
  </clause>

  <clause id="4316">
    <literal><![CDATA[
      (c_0' v c_0') v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[back_rewrite(3838),rewrite([4273(11)])].">
      <j1 rule="back_rewrite" parents="3838"/>
      <j2 rule="rewrite" parents="4273"/>
    </justification>
  </clause>

  <clause id="4379">
    <literal><![CDATA[
      (c_0 v c_0)' = c_0'
    ]]></literal>
    <justification jstring="[back_rewrite(2488),rewrite([4273(9),17(11),4273(5),4274(5)]),flip(a)].">
      <j1 rule="back_rewrite" parents="2488"/>
      <j2 rule="rewrite" parents="4273 17 4273 4274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4392">
    <literal><![CDATA[
      c_0 v (x v (y v (z v (c_0 v c_0)))) = x v (y v (z v c_0))
    ]]></literal>
    <justification jstring="[back_rewrite(2428),rewrite([4273(5)])].">
      <j1 rule="back_rewrite" parents="2428"/>
      <j2 rule="rewrite" parents="4273"/>
    </justification>
  </clause>

  <clause id="4395">
    <literal><![CDATA[
      c_0 v c_0 = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(2422),rewrite([4273(5),4379(5),17(4),4316(7)])].">
      <j1 rule="back_rewrite" parents="2422"/>
      <j2 rule="rewrite" parents="4273 4379 17 4316"/>
    </justification>
  </clause>

  <clause id="4398">
    <literal><![CDATA[
      c_0 v (x v c_0) = x v c_0
    ]]></literal>
    <justification jstring="[back_rewrite(2416),rewrite([4273(5),4395(4)])].">
      <j1 rule="back_rewrite" parents="2416"/>
      <j2 rule="rewrite" parents="4273 4395"/>
    </justification>
  </clause>

  <clause id="4431">
    <literal><![CDATA[
      c_0 v (x v (y v (z v c_0))) = x v (y v (z v c_0))
    ]]></literal>
    <justification jstring="[back_rewrite(4392),rewrite([4395(4)])].">
      <j1 rule="back_rewrite" parents="4392"/>
      <j2 rule="rewrite" parents="4395"/>
    </justification>
  </clause>

  <clause id="4447">
    <literal><![CDATA[
      c_0' v c_0 = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(4273),rewrite([4395(7)])].">
      <j1 rule="back_rewrite" parents="4273"/>
      <j2 rule="rewrite" parents="4395"/>
    </justification>
  </clause>

  <clause id="4523">
    <literal><![CDATA[
      (c_0' v (x v ((x v c_0) v ((x v c_0) v c_0)))')' = x v c_0
    ]]></literal>
    <justification jstring="[back_rewrite(2619),rewrite([4395(5),4395(7),4395(16)])].">
      <j1 rule="back_rewrite" parents="2619"/>
      <j2 rule="rewrite" parents="4395 4395 4395"/>
    </justification>
  </clause>

  <clause id="4527">
    <literal><![CDATA[
      c_0' v (x v (y v c_0)) = x v (y v c_0)
    ]]></literal>
    <justification jstring="[back_rewrite(2565),rewrite([4395(3),4431(8)])].">
      <j1 rule="back_rewrite" parents="2565"/>
      <j2 rule="rewrite" parents="4395 4431"/>
    </justification>
  </clause>

  <clause id="4530">
    <literal><![CDATA[
      c_0'' = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(2426),rewrite([4395(6)])].">
      <j1 rule="back_rewrite" parents="2426"/>
      <j2 rule="rewrite" parents="4395"/>
    </justification>
  </clause>

  <clause id="4536">
    <literal><![CDATA[
      (((x v x'')' v c_0)' v x)' = (x v x'')'
    ]]></literal>
    <justification jstring="[back_rewrite(2634),rewrite([4398(8)])].">
      <j1 rule="back_rewrite" parents="2634"/>
      <j2 rule="rewrite" parents="4398"/>
    </justification>
  </clause>

  <clause id="4630">
    <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(165(a,1),46(a,1,1,2,1)),rewrite([5(20),5(22),5(21),5(50),5(52),5(51)])].">
      <j1 rule="para" parents="165 46"/>
      <j2 rule="rewrite" parents="5 5 5 5 5 5"/>
    </justification>
  </clause>

  <clause id="4712">
    <literal><![CDATA[
      x v ((x v c_0) v c_0) = x v c_0
    ]]></literal>
    <justification jstring="[para(869(a,1),50(a,1,1,2,1,2,2)),rewrite([5(11),4527(12),5(10),4523(13),5(9),4527(10)]),flip(a)].">
      <j1 rule="para" parents="869 50"/>
      <j2 rule="rewrite" parents="5 4527 5 4523 5 4527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4736">
    <literal><![CDATA[
      (c_0' v (x v c_0)')' = x v c_0
    ]]></literal>
    <justification jstring="[para(3588(a,1),50(a,1,1,2,1,2,2,1,2)),rewrite([3887(16),4712(7),3588(17)])].">
      <j1 rule="para" parents="3588 50"/>
      <j2 rule="rewrite" parents="3887 4712 3588"/>
    </justification>
  </clause>

  <clause id="4742">
    <literal><![CDATA[
      x v ((c_0' v (x v c_0)') v c_0) = c_0
    ]]></literal>
    <justification jstring="[para(4398(a,1),52(a,1,2)),rewrite([5(7),4712(7),5(9),4395(12)])].">
      <j1 rule="para" parents="4398 52"/>
      <j2 rule="rewrite" parents="5 4712 5 4395"/>
    </justification>
  </clause>

  <clause id="4747">
    <literal><![CDATA[
      x v (y v ((x v c_0) v c_0)) = y v (x v c_0)
    ]]></literal>
    <justification jstring="[para(4712(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4712 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4856">
    <literal><![CDATA[
      ((x v c_0)' v c_0')' = x v c_0
    ]]></literal>
    <justification jstring="[para(4736(a,1),42(a,1,1,1,1,2)),rewrite([5(5),4712(5),4447(7)])].">
      <j1 rule="para" parents="4736 42"/>
      <j2 rule="rewrite" parents="5 4712 4447"/>
    </justification>
  </clause>

  <clause id="4869">
    <literal><![CDATA[
      ((x v (y v c_0))' v ((y v c_0)' v (x v c_0'))')' = x
    ]]></literal>
    <justification jstring="[para(4856(a,1),19(a,1,1,1,1,2))].">
      <j1 rule="para" parents="4856 19"/>
    </justification>
  </clause>

  <clause id="4879">
    <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(4856(a,1),21(a,1,1,2,1,2,1)),rewrite([5(11),4856(21)])].">
      <j1 rule="para" parents="4856 21"/>
      <j2 rule="rewrite" parents="5 4856"/>
    </justification>
  </clause>

  <clause id="4887">
    <literal><![CDATA[
      ((x v c_0)' v ((x v c_0)' v c_0)')' = c_0
    ]]></literal>
    <justification jstring="[para(4856(a,1),42(a,1,1,1,1,2)),rewrite([4398(4)])].">
      <j1 rule="para" parents="4856 42"/>
      <j2 rule="rewrite" parents="4398"/>
    </justification>
  </clause>

  <clause id="4988">
    <literal><![CDATA[
      x v ((x v c_0) v ((c_0' v (x v c_0)') v c_0)) = c_0
    ]]></literal>
    <justification jstring="[para(4712(a,1),53(a,1,2,1,2,1,2,1)),rewrite([4747(10),5(7),4712(7),5(11)])].">
      <j1 rule="para" parents="4712 53"/>
      <j2 rule="rewrite" parents="4747 5 4712 5"/>
    </justification>
  </clause>

  <clause id="4999">
    <literal><![CDATA[
      x v (y v ((c_0' v (x v c_0)') v c_0)) = y v c_0
    ]]></literal>
    <justification jstring="[para(4742(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4742 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5007">
    <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(4742(a,1),22(a,1,1,1,1,2,1,1)),rewrite([4530(14)])].">
      <j1 rule="para" parents="4742 22"/>
      <j2 rule="rewrite" parents="4530"/>
    </justification>
  </clause>

  <clause id="5022">
    <literal><![CDATA[
      (x v c_0) v c_0 = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(4988),rewrite([4999(12)])].">
      <j1 rule="back_rewrite" parents="4988"/>
      <j2 rule="rewrite" parents="4999"/>
    </justification>
  </clause>

  <clause id="5040">
    <literal><![CDATA[
      (x v c_0) v (y v c_0) = y v c_0
    ]]></literal>
    <justification jstring="[para(5022(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5022 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5056">
    <literal><![CDATA[
      x v c_0 = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(4879),rewrite([5040(11),4887(11)]),flip(a)].">
      <j1 rule="back_rewrite" parents="4879"/>
      <j2 rule="rewrite" parents="5040 4887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5060">
    <literal><![CDATA[
      (c_0' v x)' = (x v c_0')'
    ]]></literal>
    <justification jstring="[back_rewrite(5007),rewrite([5056(4),5056(7),5056(6),5056(8),5056(11)])].">
      <j1 rule="back_rewrite" parents="5007"/>
      <j2 rule="rewrite" parents="5056 5056 5056 5056 5056"/>
    </justification>
  </clause>

  <clause id="5089">
    <literal><![CDATA[
      (c_0' v (c_0' v (x v c_0'))')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(4869),rewrite([5056(2),5056(2),5056(4)])].">
      <j1 rule="back_rewrite" parents="4869"/>
      <j2 rule="rewrite" parents="5056 5056 5056"/>
    </justification>
  </clause>

  <clause id="5139">
    <literal><![CDATA[
      (x v x'')' = (c_0' v x)'
    ]]></literal>
    <justification jstring="[back_rewrite(4536),rewrite([5056(6)]),flip(a)].">
      <j1 rule="back_rewrite" parents="4536"/>
      <j2 rule="rewrite" parents="5056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5186">
    <literal><![CDATA[
      (x v (y v (z v (u v x')))')' = (c_0' v x)'
    ]]></literal>
    <justification jstring="[back_rewrite(4047),rewrite([5056(9),5056(9),5056(9),4530(10),5056(9)]),flip(a)].">
      <j1 rule="back_rewrite" parents="4047"/>
      <j2 rule="rewrite" parents="5056 5056 5056 4530 5056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5637">
    <literal><![CDATA[
      (c_0' v (c_0' v x)')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(1028),rewrite([5186(7),5056(6),5056(6),5056(6),5060(8,R)])].">
      <j1 rule="back_rewrite" parents="1028"/>
      <j2 rule="rewrite" parents="5186 5056 5056 5056 5060"/>
    </justification>
  </clause>

  <clause id="5642">
    <literal><![CDATA[
      (c_0' v (((c_0' v (x v y))' v c_0') v (x v (z v y))')')' = (c_0' v (x v y))' v c_0'
    ]]></literal>
    <justification jstring="[back_rewrite(1012),rewrite([5139(6),5056(15),5060(17,R),5139(23)])].">
      <j1 rule="back_rewrite" parents="1012"/>
      <j2 rule="rewrite" parents="5139 5056 5060 5139"/>
    </justification>
  </clause>

  <clause id="5717">
    <literal><![CDATA[
      (c_0' v (x v (x v (c_0' v x)))') v (y v x) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(712),rewrite([5056(13)])].">
      <j1 rule="back_rewrite" parents="712"/>
      <j2 rule="rewrite" parents="5056"/>
    </justification>
  </clause>

  <clause id="5768">
    <literal><![CDATA[
      (c_0' v (x v (((y v x') v z')' v ((y v x') v z)'))')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(185),rewrite([5056(2)])].">
      <j1 rule="back_rewrite" parents="185"/>
      <j2 rule="rewrite" parents="5056"/>
    </justification>
  </clause>

  <clause id="5779">
    <literal><![CDATA[
      (c_0' v (x v x)') v (y v x) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(52),rewrite([5056(9)])].">
      <j1 rule="back_rewrite" parents="52"/>
      <j2 rule="rewrite" parents="5056"/>
    </justification>
  </clause>

  <clause id="5793">
    <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(4630),rewrite([5060(30,R)])].">
      <j1 rule="back_rewrite" parents="4630"/>
      <j2 rule="rewrite" parents="5060"/>
    </justification>
  </clause>

  <clause id="5810">
    <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(2028),rewrite([5060(33,R)])].">
      <j1 rule="back_rewrite" parents="2028"/>
      <j2 rule="rewrite" parents="5060"/>
    </justification>
  </clause>

  <clause id="5880">
    <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(108),rewrite([5139(8),5139(20)])].">
      <j1 rule="back_rewrite" parents="108"/>
      <j2 rule="rewrite" parents="5139 5139"/>
    </justification>
  </clause>

  <clause id="5882">
    <literal><![CDATA[
      ((x v y)' v ((c_0' v y)' v (x v c_0'))')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(91),rewrite([5139(6)])].">
      <j1 rule="back_rewrite" parents="91"/>
      <j2 rule="rewrite" parents="5139"/>
    </justification>
  </clause>

  <clause id="5887">
    <literal><![CDATA[
      x v c_0' = x
    ]]></literal>
    <justification jstring="[back_rewrite(5089),rewrite([5637(11)])].">
      <j1 rule="back_rewrite" parents="5089"/>
      <j2 rule="rewrite" parents="5637"/>
    </justification>
  </clause>

  <clause id="5910">
    <literal><![CDATA[
      x v ((x v y) v ((x v y) v y)) = x v y
    ]]></literal>
    <justification jstring="[back_rewrite(682),rewrite([5637(13)])].">
      <j1 rule="back_rewrite" parents="682"/>
      <j2 rule="rewrite" parents="5637"/>
    </justification>
  </clause>

  <clause id="5917">
    <literal><![CDATA[
      x'' = x
    ]]></literal>
    <justification jstring="[back_rewrite(2115),rewrite([5887(3),5717(12),5887(4)])].">
      <j1 rule="back_rewrite" parents="2115"/>
      <j2 rule="rewrite" parents="5887 5717 5887"/>
    </justification>
  </clause>

  <clause id="5926">
    <literal><![CDATA[
      (c_0' v x)' = x'
    ]]></literal>
    <justification jstring="[back_rewrite(523),rewrite([5887(3),5779(8),5917(4),5056(3),5887(7)])].">
      <j1 rule="back_rewrite" parents="523"/>
      <j2 rule="rewrite" parents="5887 5779 5917 5056 5887"/>
    </justification>
  </clause>

  <clause id="5933">
    <literal><![CDATA[
      ((x v y)' v (y' v x)')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(5882),rewrite([5926(6),5887(6)])].">
      <j1 rule="back_rewrite" parents="5882"/>
      <j2 rule="rewrite" parents="5926 5887"/>
    </justification>
  </clause>

  <clause id="5935">
    <literal><![CDATA[
      x v x = x
    ]]></literal>
    <justification jstring="[back_rewrite(5880),rewrite([5926(7),5917(4),5887(5),5926(6),5917(3),5926(6),5917(3),5887(4)])].">
      <j1 rule="back_rewrite" parents="5880"/>
      <j2 rule="rewrite" parents="5926 5917 5887 5926 5917 5926 5917 5887"/>
    </justification>
  </clause>

  <clause id="5975">
    <literal><![CDATA[
      (x v y)' v (x v (z v y))' = (x v y)'
    ]]></literal>
    <justification jstring="[back_rewrite(5642),rewrite([5926(7),5887(7),5926(11),5917(8),5926(11),5887(11)])].">
      <j1 rule="back_rewrite" parents="5642"/>
      <j2 rule="rewrite" parents="5926 5887 5926 5917 5926 5887"/>
    </justification>
  </clause>

  <clause id="6061">
    <literal><![CDATA[
      (c_0' v x) v x = c_0' v x
    ]]></literal>
    <justification jstring="[back_rewrite(5810),rewrite([5910(26),5926(14),9(11),5926(9),5917(6),5910(28),5926(16),9(13)])].">
      <j1 rule="back_rewrite" parents="5810"/>
      <j2 rule="rewrite" parents="5910 5926 9 5926 5917 5910 5926 9"/>
    </justification>
  </clause>

  <clause id="6063">
    <literal><![CDATA[
      c_0' v x = x
    ]]></literal>
    <justification jstring="[back_rewrite(5793),rewrite([5935(11),5935(15),5935(17),6061(18),5935(17),5926(15),5926(12),5926(9),5917(6),6061(6),5926(6),5926(5),5917(2),5935(9),5935(13),5935(15),6061(16),5935(15),5926(13),5926(10),5926(7),5917(4)]),flip(a)].">
      <j1 rule="back_rewrite" parents="5793"/>
      <j2 rule="rewrite" parents="5935 5935 5935 6061 5935 5926 5926 5926 5917 6061 5926 5926 5917 5935 5935 5935 6061 5935 5926 5926 5926 5917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6077">
    <literal><![CDATA[
      x v (((y v x') v z')' v ((y v x') v z)') = x
    ]]></literal>
    <justification jstring="[back_rewrite(5768),rewrite([6063(15),5917(13)])].">
      <j1 rule="back_rewrite" parents="5768"/>
      <j2 rule="rewrite" parents="6063 5917"/>
    </justification>
  </clause>

  <clause id="6578">
    <literal><![CDATA[
      (x v y')' v (x v y)' = x'
    ]]></literal>
    <justification jstring="[para(9(a,1),5917(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 5917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6581">
    <literal><![CDATA[
      x v (x v ((x v y')' v y))' = x v y'
    ]]></literal>
    <justification jstring="[para(21(a,1),5917(a,1,1)),rewrite([5917(4)]),flip(a)].">
      <j1 rule="para" parents="21 5917"/>
      <j2 rule="rewrite" parents="5917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6587">
    <literal><![CDATA[
      x v (y v x')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(6077),rewrite([6578(10)])].">
      <j1 rule="back_rewrite" parents="6077"/>
      <j2 rule="rewrite" parents="6578"/>
    </justification>
  </clause>

  <clause id="6642">
    <literal><![CDATA[
      x v y = y v x
    ]]></literal>
    <justification jstring="[para(5887(a,1),5(a,1,2)),rewrite([5887(4)])].">
      <j1 rule="para" parents="5887 5"/>
      <j2 rule="rewrite" parents="5887"/>
    </justification>
  </clause>

  <clause id="6643">
    <literal><![CDATA[
      x v (y v z) = z v (x v y)
    ]]></literal>
    <justification jstring="[para(5887(a,1),18(a,1,2,2)),rewrite([5887(5)])].">
      <j1 rule="para" parents="5887 18"/>
      <j2 rule="rewrite" parents="5887"/>
    </justification>
  </clause>

  <clause id="6667">
    <literal><![CDATA[
      x v (x v y)' = x v y'
    ]]></literal>
    <justification jstring="[back_rewrite(6581),rewrite([6642(4),6587(4)])].">
      <j1 rule="back_rewrite" parents="6581"/>
      <j2 rule="rewrite" parents="6642 6587"/>
    </justification>
  </clause>

  <clause id="7269">
    <literal><![CDATA[
      x v (y v (z v x')') = y v x
    ]]></literal>
    <justification jstring="[para(6587(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6587 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7273">
    <literal><![CDATA[
      x v (x' v y)' = x
    ]]></literal>
    <justification jstring="[para(6642(a,1),6587(a,1,2,1))].">
      <j1 rule="para" parents="6642 6587"/>
    </justification>
  </clause>

  <clause id="7317">
    <literal><![CDATA[
      x v (y v (x' v z)') = y v x
    ]]></literal>
    <justification jstring="[para(7273(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7273 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8516">
    <literal><![CDATA[
      (x v y) v z = x v (y v z)
    ]]></literal>
    <justification jstring="[para(6643(a,2),6642(a,1)),flip(a)].">
      <j1 rule="para" parents="6643 6642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8771">
    <literal><![CDATA[
      x v (y v x)' = x v y'
    ]]></literal>
    <justification jstring="[para(6642(a,1),6667(a,1,2,1))].">
      <j1 rule="para" parents="6642 6667"/>
    </justification>
  </clause>

  <clause id="8848">
    <literal><![CDATA[
      x v (y v (z v x)') = y v (x v z')
    ]]></literal>
    <justification jstring="[para(8771(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8771 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8902">
    <literal><![CDATA[
      (x v y)' v (y' v x)' = x'
    ]]></literal>
    <justification jstring="[para(5933(a,1),5917(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5933 5917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9751">
    <literal><![CDATA[
      (x v y)' v (z v (y' v x)') = z v x'
    ]]></literal>
    <justification jstring="[para(8902(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8902 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9756">
    <literal><![CDATA[
      (x v (y v z)')' = (x v (z v y'))' v (x v z')'
    ]]></literal>
    <justification jstring="[para(7269(a,1),8902(a,1,2,1)),rewrite([5917(2),6642(4),8848(4),5917(10)]),flip(a)].">
      <j1 rule="para" parents="7269 8902"/>
      <j2 rule="rewrite" parents="5917 6642 8848 5917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9814">
    <literal><![CDATA[
      (c6 v (c4' v c5'))' v (c4' v c6')' != (c4' v c5')' v (c4' v c6')'
    ]]></literal>
    <attribute><![CDATA[
      answer(DIST1)
    ]]></attribute>
    <justification jstring="[back_rewrite(14),rewrite([9756(8),5(7)])].">
      <j1 rule="back_rewrite" parents="14"/>
      <j2 rule="rewrite" parents="9756 5"/>
    </justification>
  </clause>

  <clause id="10120">
    <literal><![CDATA[
      (x v y)' v ((x v (z v y))' v (x v z')') = (x v (z v y))' v (x v z')'
    ]]></literal>
    <justification jstring="[para(7273(a,1),5975(a,1,2,1,2)),rewrite([9756(5),5917(2),6642(10),9756(15),5917(12)])].">
      <j1 rule="para" parents="7273 5975"/>
      <j2 rule="rewrite" parents="9756 5917 6642 9756 5917"/>
    </justification>
  </clause>

  <clause id="10122">
    <literal><![CDATA[
      (x v y)' v ((x v (z v y))' v u) = (x v y)' v u
    ]]></literal>
    <justification jstring="[para(5975(a,1),8516(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5975 8516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10142">
    <literal><![CDATA[
      (x v (y v z))' v (x v y')' = (x v z)' v (x v y')'
    ]]></literal>
    <justification jstring="[back_rewrite(10120),rewrite([10122(10)]),flip(a)].">
      <j1 rule="back_rewrite" parents="10120"/>
      <j2 rule="rewrite" parents="10122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10157">
    <literal><![CDATA[
      (x v (y v z)')' = (x v y')' v (x v z')'
    ]]></literal>
    <justification jstring="[back_rewrite(9756),rewrite([10142(12)])].">
      <j1 rule="back_rewrite" parents="9756"/>
      <j2 rule="rewrite" parents="10142"/>
    </justification>
  </clause>

  <clause id="12752">
    <literal><![CDATA[
      (x v (y v z))' v (y v x')' = (y v z)' v (y v x')'
    ]]></literal>
    <justification jstring="[para(9751(a,1),8902(a,1,2,1)),rewrite([6642(6),8516(6),7317(5),10157(12),5917(9)])].">
      <j1 rule="para" parents="9751 8902"/>
      <j2 rule="rewrite" parents="6642 8516 7317 10157 5917"/>
    </justification>
  </clause>

  <clause id="12753">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer(DIST1)
    ]]></attribute>
    <justification jstring="[resolve(12752,a,9814,a)].">
      <j1 rule="resolve" parents="12752 9814"/>
    </justification>
  </clause>

</proof>

</proofs>
