<?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 April-2007, April 2007.
Process 27046 was started by mccune on cleo,
Fri Apr 13 09:19:39 2007
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 1.28 (+ 0.02) 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(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 v))) = u v (x v (y v (z v v)))
    ]]></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="2143">
    <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="2392">
    <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="2420">
    <literal><![CDATA[
      c_0 v (x v (c_0' v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[para(2392(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2392 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2426">
    <literal><![CDATA[
      ((c_0 v (c_0' v c_0)')' v c_0') v c_0 = c_0
    ]]></literal>
    <justification jstring="[para(2392(a,1),26(a,1,1,2,1))].">
      <j1 rule="para" parents="2392 26"/>
    </justification>
  </clause>

  <clause id="2430">
    <literal><![CDATA[
      c_0'' = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(2392(a,1),52(a,1,2)),rewrite(5(11),1157(15))].">
      <j1 rule="para" parents="2392 52"/>
      <j2 rule="rewrite" parents="5 1157"/>
    </justification>
  </clause>

  <clause id="2432">
    <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(2392(a,1),29(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="2392 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2494">
    <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(2430(3),2430(15),5(16),2430(20))].">
      <j1 rule="back_rewrite" parents="1546"/>
      <j2 rule="rewrite" parents="2430 2430 5 2430"/>
    </justification>
  </clause>

  <clause id="2499">
    <literal><![CDATA[
      ((c_0 v (c_0 v c_0))' v c_0')' = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(1519),rewrite(2430(5),1707(11),2430(4),2430(15),1707(21))].">
      <j1 rule="back_rewrite" parents="1519"/>
      <j2 rule="rewrite" parents="2430 1707 2430 2430 1707"/>
    </justification>
  </clause>

  <clause id="2550">
    <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(2430(18))].">
      <j1 rule="back_rewrite" parents="1157"/>
      <j2 rule="rewrite" parents="2430"/>
    </justification>
  </clause>

  <clause id="2571">
    <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(2430(5),5(10))].">
      <j1 rule="back_rewrite" parents="1136"/>
      <j2 rule="rewrite" parents="2430 5"/>
    </justification>
  </clause>

  <clause id="2588">
    <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(2430(3),2430(16),5(17),63(16))].">
      <j1 rule="back_rewrite" parents="1119"/>
      <j2 rule="rewrite" parents="2430 2430 5 63"/>
    </justification>
  </clause>

  <clause id="2607">
    <literal><![CDATA[
      ((c_0 v (x v c_0))' v (x v c_0')')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(1082),rewrite(2430(3),2588(6))].">
      <j1 rule="back_rewrite" parents="1082"/>
      <j2 rule="rewrite" parents="2430 2588"/>
    </justification>
  </clause>

  <clause id="2625">
    <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(2430(5),2430(9),2430(20))].">
      <j1 rule="back_rewrite" parents="672"/>
      <j2 rule="rewrite" parents="2430 2430 2430"/>
    </justification>
  </clause>

  <clause id="3585">
    <literal><![CDATA[
      c_0' v (c_0' v c_0')' = c_0
    ]]></literal>
    <justification jstring="[para(49(a,1),2607(a,1,1,2,1)),rewrite(63(12),2499(10)),flip(a)].">
      <j1 rule="para" parents="49 2607"/>
      <j2 rule="rewrite" parents="63 2499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3594">
    <literal><![CDATA[
      (c_0' v x')' v (c_0' v x)' = c_0
    ]]></literal>
    <justification jstring="[para(26(a,1),2607(a,1,1,2,1)),rewrite(149(13),2499(10)),flip(a)].">
      <j1 rule="para" parents="26 2607"/>
      <j2 rule="rewrite" parents="149 2499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3842">
    <literal><![CDATA[
      c_0' v (x v (c_0' v c_0')') = x v c_0
    ]]></literal>
    <justification jstring="[para(3585(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3585 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3844">
    <literal><![CDATA[
      (c_0' v c_0') v c_0 = c_0' v c_0
    ]]></literal>
    <justification jstring="[para(3585(a,1),23(a,1,2))].">
      <j1 rule="para" parents="3585 23"/>
    </justification>
  </clause>

  <clause id="3854">
    <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(3585(a,1),169(a,1,1,2,1,2,2))].">
      <j1 rule="para" parents="3585 169"/>
    </justification>
  </clause>

  <clause id="3893">
    <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(3594(a,1),18(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3594 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3896">
    <literal><![CDATA[
      (c_0' v x')' v c_0 = (c_0' v x) v c_0
    ]]></literal>
    <justification jstring="[para(3594(a,1),23(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3594 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3953">
    <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(3854),rewrite(3896(16),5(15),3896(14))].">
      <j1 rule="back_rewrite" parents="3854"/>
      <j2 rule="rewrite" parents="3896 5 3896"/>
    </justification>
  </clause>

  <clause id="4055">
    <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="4126">
    <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),3842(a,1,2)),rewrite(3842(28),3896(20),5(19),3896(18)),flip(a)].">
      <j1 rule="para" parents="165 3842"/>
      <j2 rule="rewrite" parents="3842 3896 5 3896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4153">
    <literal><![CDATA[
      (c_0' v c_0')' = c_0' v c_0
    ]]></literal>
    <justification jstring="[para(3896(a,1),21(a,1,1,2,1,2)),rewrite(45(14)),flip(a)].">
      <j1 rule="para" parents="3896 21"/>
      <j2 rule="rewrite" parents="45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4245">
    <literal><![CDATA[
      c_0' v (c_0' v c_0) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(3953),rewrite(4153(21),5(20),4126(19))].">
      <j1 rule="back_rewrite" parents="3953"/>
      <j2 rule="rewrite" parents="4153 5 4126"/>
    </justification>
  </clause>

  <clause id="4281">
    <literal><![CDATA[
      c_0' v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(4245(a,1),52(a,1,2)),rewrite(5(11),2550(15)),flip(a)].">
      <j1 rule="para" parents="4245 52"/>
      <j2 rule="rewrite" parents="5 2550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4282">
    <literal><![CDATA[
      c_0 v (c_0 v c_0) = c_0
    ]]></literal>
    <justification jstring="[para(52(a,2),4245(a,1,2)),rewrite(5(11),49(10),4281(6),5(6),4281(5))].">
      <j1 rule="para" parents="52 4245"/>
      <j2 rule="rewrite" parents="5 49 4281 5 4281"/>
    </justification>
  </clause>

  <clause id="4324">
    <literal><![CDATA[
      (c_0' v c_0') v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[back_rewrite(3844),rewrite(4281(11))].">
      <j1 rule="back_rewrite" parents="3844"/>
      <j2 rule="rewrite" parents="4281"/>
    </justification>
  </clause>

  <clause id="4385">
    <literal><![CDATA[
      (c_0 v c_0)' = c_0'
    ]]></literal>
    <justification jstring="[back_rewrite(2494),rewrite(4281(9),17(11),4281(5),4282(5)),flip(a)].">
      <j1 rule="back_rewrite" parents="2494"/>
      <j2 rule="rewrite" parents="4281 17 4281 4282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4400">
    <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(2432),rewrite(4281(5))].">
      <j1 rule="back_rewrite" parents="2432"/>
      <j2 rule="rewrite" parents="4281"/>
    </justification>
  </clause>

  <clause id="4403">
    <literal><![CDATA[
      c_0 v c_0 = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(2426),rewrite(4281(5),4385(5),17(4),4324(7))].">
      <j1 rule="back_rewrite" parents="2426"/>
      <j2 rule="rewrite" parents="4281 4385 17 4324"/>
    </justification>
  </clause>

  <clause id="4406">
    <literal><![CDATA[
      c_0 v (x v c_0) = x v c_0
    ]]></literal>
    <justification jstring="[back_rewrite(2420),rewrite(4281(5),4403(4))].">
      <j1 rule="back_rewrite" parents="2420"/>
      <j2 rule="rewrite" parents="4281 4403"/>
    </justification>
  </clause>

  <clause id="4439">
    <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(4400),rewrite(4403(4))].">
      <j1 rule="back_rewrite" parents="4400"/>
      <j2 rule="rewrite" parents="4403"/>
    </justification>
  </clause>

  <clause id="4455">
    <literal><![CDATA[
      c_0' v c_0 = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(4281),rewrite(4403(7))].">
      <j1 rule="back_rewrite" parents="4281"/>
      <j2 rule="rewrite" parents="4403"/>
    </justification>
  </clause>

  <clause id="4531">
    <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(2625),rewrite(4403(5),4403(7),4403(16))].">
      <j1 rule="back_rewrite" parents="2625"/>
      <j2 rule="rewrite" parents="4403 4403 4403"/>
    </justification>
  </clause>

  <clause id="4535">
    <literal><![CDATA[
      c_0' v (x v (y v c_0)) = x v (y v c_0)
    ]]></literal>
    <justification jstring="[back_rewrite(2571),rewrite(4403(3),4439(8))].">
      <j1 rule="back_rewrite" parents="2571"/>
      <j2 rule="rewrite" parents="4403 4439"/>
    </justification>
  </clause>

  <clause id="4538">
    <literal><![CDATA[
      c_0'' = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(2430),rewrite(4403(6))].">
      <j1 rule="back_rewrite" parents="2430"/>
      <j2 rule="rewrite" parents="4403"/>
    </justification>
  </clause>

  <clause id="4718">
    <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),4535(12),5(10),4531(13),5(9),4535(10)),flip(a)].">
      <j1 rule="para" parents="869 50"/>
      <j2 rule="rewrite" parents="5 4535 5 4531 5 4535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4744">
    <literal><![CDATA[
      (c_0' v (x v c_0)')' = x v c_0
    ]]></literal>
    <justification jstring="[para(3594(a,1),50(a,1,1,2,1,2,2,1,2)),rewrite(3893(16),4718(7),3594(17))].">
      <j1 rule="para" parents="3594 50"/>
      <j2 rule="rewrite" parents="3893 4718 3594"/>
    </justification>
  </clause>

  <clause id="4750">
    <literal><![CDATA[
      x v ((c_0' v (x v c_0)') v c_0) = c_0
    ]]></literal>
    <justification jstring="[para(4406(a,1),52(a,1,2)),rewrite(5(7),4718(7),5(9),4403(12))].">
      <j1 rule="para" parents="4406 52"/>
      <j2 rule="rewrite" parents="5 4718 5 4403"/>
    </justification>
  </clause>

  <clause id="4755">
    <literal><![CDATA[
      x v (y v ((x v c_0) v c_0)) = y v (x v c_0)
    ]]></literal>
    <justification jstring="[para(4718(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4718 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4864">
    <literal><![CDATA[
      ((x v c_0)' v c_0')' = x v c_0
    ]]></literal>
    <justification jstring="[para(4744(a,1),42(a,1,1,1,1,2)),rewrite(5(5),4718(5),4455(7))].">
      <j1 rule="para" parents="4744 42"/>
      <j2 rule="rewrite" parents="5 4718 4455"/>
    </justification>
  </clause>

  <clause id="4877">
    <literal><![CDATA[
      ((x v (y v c_0))' v ((y v c_0)' v (x v c_0'))')' = x
    ]]></literal>
    <justification jstring="[para(4864(a,1),19(a,1,1,1,1,2))].">
      <j1 rule="para" parents="4864 19"/>
    </justification>
  </clause>

  <clause id="4887">
    <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(4864(a,1),21(a,1,1,2,1,2,1)),rewrite(5(11),4864(21))].">
      <j1 rule="para" parents="4864 21"/>
      <j2 rule="rewrite" parents="5 4864"/>
    </justification>
  </clause>

  <clause id="4895">
    <literal><![CDATA[
      ((x v c_0)' v ((x v c_0)' v c_0)')' = c_0
    ]]></literal>
    <justification jstring="[para(4864(a,1),42(a,1,1,1,1,2)),rewrite(4406(4))].">
      <j1 rule="para" parents="4864 42"/>
      <j2 rule="rewrite" parents="4406"/>
    </justification>
  </clause>

  <clause id="4996">
    <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(4718(a,1),53(a,1,2,1,2,1,2,1)),rewrite(4755(10),5(7),4718(7),5(11))].">
      <j1 rule="para" parents="4718 53"/>
      <j2 rule="rewrite" parents="4755 5 4718 5"/>
    </justification>
  </clause>

  <clause id="5007">
    <literal><![CDATA[
      x v (y v ((c_0' v (x v c_0)') v c_0)) = y v c_0
    ]]></literal>
    <justification jstring="[para(4750(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4750 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5015">
    <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(4750(a,1),22(a,1,1,1,1,2,1,1)),rewrite(4538(14))].">
      <j1 rule="para" parents="4750 22"/>
      <j2 rule="rewrite" parents="4538"/>
    </justification>
  </clause>

  <clause id="5030">
    <literal><![CDATA[
      (x v c_0) v c_0 = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(4996),rewrite(5007(12))].">
      <j1 rule="back_rewrite" parents="4996"/>
      <j2 rule="rewrite" parents="5007"/>
    </justification>
  </clause>

  <clause id="5048">
    <literal><![CDATA[
      (x v c_0) v (y v c_0) = y v c_0
    ]]></literal>
    <justification jstring="[para(5030(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5030 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5064">
    <literal><![CDATA[
      x v c_0 = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(4887),rewrite(5048(11),4895(11)),flip(a)].">
      <j1 rule="back_rewrite" parents="4887"/>
      <j2 rule="rewrite" parents="5048 4895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5068">
    <literal><![CDATA[
      (c_0' v x)' = (x v c_0')'
    ]]></literal>
    <justification jstring="[back_rewrite(5015),rewrite(5064(4),5064(7),5064(6),5064(8),5064(11))].">
      <j1 rule="back_rewrite" parents="5015"/>
      <j2 rule="rewrite" parents="5064 5064 5064 5064 5064"/>
    </justification>
  </clause>

  <clause id="5097">
    <literal><![CDATA[
      (c_0' v (c_0' v (x v c_0'))')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(4877),rewrite(5064(2),5064(2),5064(4))].">
      <j1 rule="back_rewrite" parents="4877"/>
      <j2 rule="rewrite" parents="5064 5064 5064"/>
    </justification>
  </clause>

  <clause id="5194">
    <literal><![CDATA[
      (x v (y v (z v (u v x')))')' = (c_0' v x)'
    ]]></literal>
    <justification jstring="[back_rewrite(4055),rewrite(5064(9),5064(9),5064(9),4538(10),5064(9)),flip(a)].">
      <j1 rule="back_rewrite" parents="4055"/>
      <j2 rule="rewrite" parents="5064 5064 5064 4538 5064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5645">
    <literal><![CDATA[
      (c_0' v (c_0' v x)')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(1028),rewrite(5194(7),5064(6),5064(6),5064(6),5068(8,R))].">
      <j1 rule="back_rewrite" parents="1028"/>
      <j2 rule="rewrite" parents="5194 5064 5064 5064 5068"/>
    </justification>
  </clause>

  <clause id="5725">
    <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(5064(13))].">
      <j1 rule="back_rewrite" parents="712"/>
      <j2 rule="rewrite" parents="5064"/>
    </justification>
  </clause>

  <clause id="5895">
    <literal><![CDATA[
      x v c_0' = x
    ]]></literal>
    <justification jstring="[back_rewrite(5097),rewrite(5645(11))].">
      <j1 rule="back_rewrite" parents="5097"/>
      <j2 rule="rewrite" parents="5645"/>
    </justification>
  </clause>

  <clause id="5925">
    <literal><![CDATA[
      x'' = x
    ]]></literal>
    <justification jstring="[back_rewrite(2143),rewrite(5895(3),5725(12),5895(4))].">
      <j1 rule="back_rewrite" parents="2143"/>
      <j2 rule="rewrite" parents="5895 5725 5895"/>
    </justification>
  </clause>

  <clause id="5926">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer(CC)
    ]]></attribute>
    <justification jstring="[resolve(5925,a,10,a)].">
      <j1 rule="resolve" parents="5925 10"/>
    </justification>
  </clause>

</proof>

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

<comments><![CDATA[
% Proof 2 at 1.37 (+ 0.02) 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(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 v))) = z v (x v (u v (y v v)))
    ]]></literal>
    <justification jstring="[para(18(a,1),5(a,1,2))].">
      <j1 rule="para" parents="18 5"/>
    </justification>
  </clause>

  <clause id="29">
    <literal><![CDATA[
      x v (y v (z v (u v v))) = u v (x v (y v (z v v)))
    ]]></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="2055">
    <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="2143">
    <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="2392">
    <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="2420">
    <literal><![CDATA[
      c_0 v (x v (c_0' v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[para(2392(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2392 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2426">
    <literal><![CDATA[
      ((c_0 v (c_0' v c_0)')' v c_0') v c_0 = c_0
    ]]></literal>
    <justification jstring="[para(2392(a,1),26(a,1,1,2,1))].">
      <j1 rule="para" parents="2392 26"/>
    </justification>
  </clause>

  <clause id="2430">
    <literal><![CDATA[
      c_0'' = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(2392(a,1),52(a,1,2)),rewrite(5(11),1157(15))].">
      <j1 rule="para" parents="2392 52"/>
      <j2 rule="rewrite" parents="5 1157"/>
    </justification>
  </clause>

  <clause id="2432">
    <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(2392(a,1),29(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="2392 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2494">
    <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(2430(3),2430(15),5(16),2430(20))].">
      <j1 rule="back_rewrite" parents="1546"/>
      <j2 rule="rewrite" parents="2430 2430 5 2430"/>
    </justification>
  </clause>

  <clause id="2499">
    <literal><![CDATA[
      ((c_0 v (c_0 v c_0))' v c_0')' = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(1519),rewrite(2430(5),1707(11),2430(4),2430(15),1707(21))].">
      <j1 rule="back_rewrite" parents="1519"/>
      <j2 rule="rewrite" parents="2430 1707 2430 2430 1707"/>
    </justification>
  </clause>

  <clause id="2550">
    <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(2430(18))].">
      <j1 rule="back_rewrite" parents="1157"/>
      <j2 rule="rewrite" parents="2430"/>
    </justification>
  </clause>

  <clause id="2571">
    <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(2430(5),5(10))].">
      <j1 rule="back_rewrite" parents="1136"/>
      <j2 rule="rewrite" parents="2430 5"/>
    </justification>
  </clause>

  <clause id="2588">
    <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(2430(3),2430(16),5(17),63(16))].">
      <j1 rule="back_rewrite" parents="1119"/>
      <j2 rule="rewrite" parents="2430 2430 5 63"/>
    </justification>
  </clause>

  <clause id="2607">
    <literal><![CDATA[
      ((c_0 v (x v c_0))' v (x v c_0')')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(1082),rewrite(2430(3),2588(6))].">
      <j1 rule="back_rewrite" parents="1082"/>
      <j2 rule="rewrite" parents="2430 2588"/>
    </justification>
  </clause>

  <clause id="2625">
    <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(2430(5),2430(9),2430(20))].">
      <j1 rule="back_rewrite" parents="672"/>
      <j2 rule="rewrite" parents="2430 2430 2430"/>
    </justification>
  </clause>

  <clause id="2640">
    <literal><![CDATA[
      ((c_0 v ((x v x'')' v c_0))' v x)' = (x v x'')'
    ]]></literal>
    <justification jstring="[back_rewrite(66),rewrite(2430(7),5(8))].">
      <j1 rule="back_rewrite" parents="66"/>
      <j2 rule="rewrite" parents="2430 5"/>
    </justification>
  </clause>

  <clause id="3585">
    <literal><![CDATA[
      c_0' v (c_0' v c_0')' = c_0
    ]]></literal>
    <justification jstring="[para(49(a,1),2607(a,1,1,2,1)),rewrite(63(12),2499(10)),flip(a)].">
      <j1 rule="para" parents="49 2607"/>
      <j2 rule="rewrite" parents="63 2499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3594">
    <literal><![CDATA[
      (c_0' v x')' v (c_0' v x)' = c_0
    ]]></literal>
    <justification jstring="[para(26(a,1),2607(a,1,1,2,1)),rewrite(149(13),2499(10)),flip(a)].">
      <j1 rule="para" parents="26 2607"/>
      <j2 rule="rewrite" parents="149 2499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3842">
    <literal><![CDATA[
      c_0' v (x v (c_0' v c_0')') = x v c_0
    ]]></literal>
    <justification jstring="[para(3585(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3585 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3844">
    <literal><![CDATA[
      (c_0' v c_0') v c_0 = c_0' v c_0
    ]]></literal>
    <justification jstring="[para(3585(a,1),23(a,1,2))].">
      <j1 rule="para" parents="3585 23"/>
    </justification>
  </clause>

  <clause id="3854">
    <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(3585(a,1),169(a,1,1,2,1,2,2))].">
      <j1 rule="para" parents="3585 169"/>
    </justification>
  </clause>

  <clause id="3893">
    <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(3594(a,1),18(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3594 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3896">
    <literal><![CDATA[
      (c_0' v x')' v c_0 = (c_0' v x) v c_0
    ]]></literal>
    <justification jstring="[para(3594(a,1),23(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3594 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3953">
    <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(3854),rewrite(3896(16),5(15),3896(14))].">
      <j1 rule="back_rewrite" parents="3854"/>
      <j2 rule="rewrite" parents="3896 5 3896"/>
    </justification>
  </clause>

  <clause id="4055">
    <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="4126">
    <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),3842(a,1,2)),rewrite(3842(28),3896(20),5(19),3896(18)),flip(a)].">
      <j1 rule="para" parents="165 3842"/>
      <j2 rule="rewrite" parents="3842 3896 5 3896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4153">
    <literal><![CDATA[
      (c_0' v c_0')' = c_0' v c_0
    ]]></literal>
    <justification jstring="[para(3896(a,1),21(a,1,1,2,1,2)),rewrite(45(14)),flip(a)].">
      <j1 rule="para" parents="3896 21"/>
      <j2 rule="rewrite" parents="45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4245">
    <literal><![CDATA[
      c_0' v (c_0' v c_0) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(3953),rewrite(4153(21),5(20),4126(19))].">
      <j1 rule="back_rewrite" parents="3953"/>
      <j2 rule="rewrite" parents="4153 5 4126"/>
    </justification>
  </clause>

  <clause id="4281">
    <literal><![CDATA[
      c_0' v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(4245(a,1),52(a,1,2)),rewrite(5(11),2550(15)),flip(a)].">
      <j1 rule="para" parents="4245 52"/>
      <j2 rule="rewrite" parents="5 2550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4282">
    <literal><![CDATA[
      c_0 v (c_0 v c_0) = c_0
    ]]></literal>
    <justification jstring="[para(52(a,2),4245(a,1,2)),rewrite(5(11),49(10),4281(6),5(6),4281(5))].">
      <j1 rule="para" parents="52 4245"/>
      <j2 rule="rewrite" parents="5 49 4281 5 4281"/>
    </justification>
  </clause>

  <clause id="4324">
    <literal><![CDATA[
      (c_0' v c_0') v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[back_rewrite(3844),rewrite(4281(11))].">
      <j1 rule="back_rewrite" parents="3844"/>
      <j2 rule="rewrite" parents="4281"/>
    </justification>
  </clause>

  <clause id="4385">
    <literal><![CDATA[
      (c_0 v c_0)' = c_0'
    ]]></literal>
    <justification jstring="[back_rewrite(2494),rewrite(4281(9),17(11),4281(5),4282(5)),flip(a)].">
      <j1 rule="back_rewrite" parents="2494"/>
      <j2 rule="rewrite" parents="4281 17 4281 4282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4400">
    <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(2432),rewrite(4281(5))].">
      <j1 rule="back_rewrite" parents="2432"/>
      <j2 rule="rewrite" parents="4281"/>
    </justification>
  </clause>

  <clause id="4403">
    <literal><![CDATA[
      c_0 v c_0 = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(2426),rewrite(4281(5),4385(5),17(4),4324(7))].">
      <j1 rule="back_rewrite" parents="2426"/>
      <j2 rule="rewrite" parents="4281 4385 17 4324"/>
    </justification>
  </clause>

  <clause id="4406">
    <literal><![CDATA[
      c_0 v (x v c_0) = x v c_0
    ]]></literal>
    <justification jstring="[back_rewrite(2420),rewrite(4281(5),4403(4))].">
      <j1 rule="back_rewrite" parents="2420"/>
      <j2 rule="rewrite" parents="4281 4403"/>
    </justification>
  </clause>

  <clause id="4439">
    <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(4400),rewrite(4403(4))].">
      <j1 rule="back_rewrite" parents="4400"/>
      <j2 rule="rewrite" parents="4403"/>
    </justification>
  </clause>

  <clause id="4455">
    <literal><![CDATA[
      c_0' v c_0 = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(4281),rewrite(4403(7))].">
      <j1 rule="back_rewrite" parents="4281"/>
      <j2 rule="rewrite" parents="4403"/>
    </justification>
  </clause>

  <clause id="4531">
    <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(2625),rewrite(4403(5),4403(7),4403(16))].">
      <j1 rule="back_rewrite" parents="2625"/>
      <j2 rule="rewrite" parents="4403 4403 4403"/>
    </justification>
  </clause>

  <clause id="4535">
    <literal><![CDATA[
      c_0' v (x v (y v c_0)) = x v (y v c_0)
    ]]></literal>
    <justification jstring="[back_rewrite(2571),rewrite(4403(3),4439(8))].">
      <j1 rule="back_rewrite" parents="2571"/>
      <j2 rule="rewrite" parents="4403 4439"/>
    </justification>
  </clause>

  <clause id="4538">
    <literal><![CDATA[
      c_0'' = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(2430),rewrite(4403(6))].">
      <j1 rule="back_rewrite" parents="2430"/>
      <j2 rule="rewrite" parents="4403"/>
    </justification>
  </clause>

  <clause id="4544">
    <literal><![CDATA[
      (((x v x'')' v c_0)' v x)' = (x v x'')'
    ]]></literal>
    <justification jstring="[back_rewrite(2640),rewrite(4406(8))].">
      <j1 rule="back_rewrite" parents="2640"/>
      <j2 rule="rewrite" parents="4406"/>
    </justification>
  </clause>

  <clause id="4638">
    <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="4718">
    <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),4535(12),5(10),4531(13),5(9),4535(10)),flip(a)].">
      <j1 rule="para" parents="869 50"/>
      <j2 rule="rewrite" parents="5 4535 5 4531 5 4535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4744">
    <literal><![CDATA[
      (c_0' v (x v c_0)')' = x v c_0
    ]]></literal>
    <justification jstring="[para(3594(a,1),50(a,1,1,2,1,2,2,1,2)),rewrite(3893(16),4718(7),3594(17))].">
      <j1 rule="para" parents="3594 50"/>
      <j2 rule="rewrite" parents="3893 4718 3594"/>
    </justification>
  </clause>

  <clause id="4750">
    <literal><![CDATA[
      x v ((c_0' v (x v c_0)') v c_0) = c_0
    ]]></literal>
    <justification jstring="[para(4406(a,1),52(a,1,2)),rewrite(5(7),4718(7),5(9),4403(12))].">
      <j1 rule="para" parents="4406 52"/>
      <j2 rule="rewrite" parents="5 4718 5 4403"/>
    </justification>
  </clause>

  <clause id="4755">
    <literal><![CDATA[
      x v (y v ((x v c_0) v c_0)) = y v (x v c_0)
    ]]></literal>
    <justification jstring="[para(4718(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4718 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4864">
    <literal><![CDATA[
      ((x v c_0)' v c_0')' = x v c_0
    ]]></literal>
    <justification jstring="[para(4744(a,1),42(a,1,1,1,1,2)),rewrite(5(5),4718(5),4455(7))].">
      <j1 rule="para" parents="4744 42"/>
      <j2 rule="rewrite" parents="5 4718 4455"/>
    </justification>
  </clause>

  <clause id="4877">
    <literal><![CDATA[
      ((x v (y v c_0))' v ((y v c_0)' v (x v c_0'))')' = x
    ]]></literal>
    <justification jstring="[para(4864(a,1),19(a,1,1,1,1,2))].">
      <j1 rule="para" parents="4864 19"/>
    </justification>
  </clause>

  <clause id="4887">
    <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(4864(a,1),21(a,1,1,2,1,2,1)),rewrite(5(11),4864(21))].">
      <j1 rule="para" parents="4864 21"/>
      <j2 rule="rewrite" parents="5 4864"/>
    </justification>
  </clause>

  <clause id="4895">
    <literal><![CDATA[
      ((x v c_0)' v ((x v c_0)' v c_0)')' = c_0
    ]]></literal>
    <justification jstring="[para(4864(a,1),42(a,1,1,1,1,2)),rewrite(4406(4))].">
      <j1 rule="para" parents="4864 42"/>
      <j2 rule="rewrite" parents="4406"/>
    </justification>
  </clause>

  <clause id="4996">
    <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(4718(a,1),53(a,1,2,1,2,1,2,1)),rewrite(4755(10),5(7),4718(7),5(11))].">
      <j1 rule="para" parents="4718 53"/>
      <j2 rule="rewrite" parents="4755 5 4718 5"/>
    </justification>
  </clause>

  <clause id="5007">
    <literal><![CDATA[
      x v (y v ((c_0' v (x v c_0)') v c_0)) = y v c_0
    ]]></literal>
    <justification jstring="[para(4750(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4750 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5015">
    <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(4750(a,1),22(a,1,1,1,1,2,1,1)),rewrite(4538(14))].">
      <j1 rule="para" parents="4750 22"/>
      <j2 rule="rewrite" parents="4538"/>
    </justification>
  </clause>

  <clause id="5030">
    <literal><![CDATA[
      (x v c_0) v c_0 = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(4996),rewrite(5007(12))].">
      <j1 rule="back_rewrite" parents="4996"/>
      <j2 rule="rewrite" parents="5007"/>
    </justification>
  </clause>

  <clause id="5048">
    <literal><![CDATA[
      (x v c_0) v (y v c_0) = y v c_0
    ]]></literal>
    <justification jstring="[para(5030(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5030 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5064">
    <literal><![CDATA[
      x v c_0 = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(4887),rewrite(5048(11),4895(11)),flip(a)].">
      <j1 rule="back_rewrite" parents="4887"/>
      <j2 rule="rewrite" parents="5048 4895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5068">
    <literal><![CDATA[
      (c_0' v x)' = (x v c_0')'
    ]]></literal>
    <justification jstring="[back_rewrite(5015),rewrite(5064(4),5064(7),5064(6),5064(8),5064(11))].">
      <j1 rule="back_rewrite" parents="5015"/>
      <j2 rule="rewrite" parents="5064 5064 5064 5064 5064"/>
    </justification>
  </clause>

  <clause id="5097">
    <literal><![CDATA[
      (c_0' v (c_0' v (x v c_0'))')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(4877),rewrite(5064(2),5064(2),5064(4))].">
      <j1 rule="back_rewrite" parents="4877"/>
      <j2 rule="rewrite" parents="5064 5064 5064"/>
    </justification>
  </clause>

  <clause id="5147">
    <literal><![CDATA[
      (x v x'')' = (c_0' v x)'
    ]]></literal>
    <justification jstring="[back_rewrite(4544),rewrite(5064(6)),flip(a)].">
      <j1 rule="back_rewrite" parents="4544"/>
      <j2 rule="rewrite" parents="5064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5194">
    <literal><![CDATA[
      (x v (y v (z v (u v x')))')' = (c_0' v x)'
    ]]></literal>
    <justification jstring="[back_rewrite(4055),rewrite(5064(9),5064(9),5064(9),4538(10),5064(9)),flip(a)].">
      <j1 rule="back_rewrite" parents="4055"/>
      <j2 rule="rewrite" parents="5064 5064 5064 4538 5064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5645">
    <literal><![CDATA[
      (c_0' v (c_0' v x)')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(1028),rewrite(5194(7),5064(6),5064(6),5064(6),5068(8,R))].">
      <j1 rule="back_rewrite" parents="1028"/>
      <j2 rule="rewrite" parents="5194 5064 5064 5064 5068"/>
    </justification>
  </clause>

  <clause id="5662">
    <literal><![CDATA[
      (c_0' v (x v (x' v y')')')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(935),rewrite(5064(18),5068(10,R))].">
      <j1 rule="back_rewrite" parents="935"/>
      <j2 rule="rewrite" parents="5064 5068"/>
    </justification>
  </clause>

  <clause id="5725">
    <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(5064(13))].">
      <j1 rule="back_rewrite" parents="712"/>
      <j2 rule="rewrite" parents="5064"/>
    </justification>
  </clause>

  <clause id="5787">
    <literal><![CDATA[
      (c_0' v (x v x)') v (y v x) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(52),rewrite(5064(9))].">
      <j1 rule="back_rewrite" parents="52"/>
      <j2 rule="rewrite" parents="5064"/>
    </justification>
  </clause>

  <clause id="5801">
    <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(4638),rewrite(5068(30,R))].">
      <j1 rule="back_rewrite" parents="4638"/>
      <j2 rule="rewrite" parents="5068"/>
    </justification>
  </clause>

  <clause id="5818">
    <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(2055),rewrite(5068(33,R))].">
      <j1 rule="back_rewrite" parents="2055"/>
      <j2 rule="rewrite" parents="5068"/>
    </justification>
  </clause>

  <clause id="5888">
    <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(5147(8),5147(20))].">
      <j1 rule="back_rewrite" parents="108"/>
      <j2 rule="rewrite" parents="5147 5147"/>
    </justification>
  </clause>

  <clause id="5895">
    <literal><![CDATA[
      x v c_0' = x
    ]]></literal>
    <justification jstring="[back_rewrite(5097),rewrite(5645(11))].">
      <j1 rule="back_rewrite" parents="5097"/>
      <j2 rule="rewrite" parents="5645"/>
    </justification>
  </clause>

  <clause id="5918">
    <literal><![CDATA[
      x v ((x v y) v ((x v y) v y)) = x v y
    ]]></literal>
    <justification jstring="[back_rewrite(682),rewrite(5645(13))].">
      <j1 rule="back_rewrite" parents="682"/>
      <j2 rule="rewrite" parents="5645"/>
    </justification>
  </clause>

  <clause id="5925">
    <literal><![CDATA[
      x'' = x
    ]]></literal>
    <justification jstring="[back_rewrite(2143),rewrite(5895(3),5725(12),5895(4))].">
      <j1 rule="back_rewrite" parents="2143"/>
      <j2 rule="rewrite" parents="5895 5725 5895"/>
    </justification>
  </clause>

  <clause id="5934">
    <literal><![CDATA[
      (c_0' v x)' = x'
    ]]></literal>
    <justification jstring="[back_rewrite(523),rewrite(5895(3),5787(8),5925(4),5064(3),5895(7))].">
      <j1 rule="back_rewrite" parents="523"/>
      <j2 rule="rewrite" parents="5895 5787 5925 5064 5895"/>
    </justification>
  </clause>

  <clause id="5943">
    <literal><![CDATA[
      x v x = x
    ]]></literal>
    <justification jstring="[back_rewrite(5888),rewrite(5934(7),5925(4),5895(5),5934(6),5925(3),5934(6),5925(3),5895(4))].">
      <j1 rule="back_rewrite" parents="5888"/>
      <j2 rule="rewrite" parents="5934 5925 5895 5934 5925 5934 5925 5895"/>
    </justification>
  </clause>

  <clause id="6069">
    <literal><![CDATA[
      (c_0' v x) v x = c_0' v x
    ]]></literal>
    <justification jstring="[back_rewrite(5818),rewrite(5918(26),5934(14),9(11),5934(9),5925(6),5918(28),5934(16),9(13))].">
      <j1 rule="back_rewrite" parents="5818"/>
      <j2 rule="rewrite" parents="5918 5934 9 5934 5925 5918 5934 9"/>
    </justification>
  </clause>

  <clause id="6071">
    <literal><![CDATA[
      c_0' v x = x
    ]]></literal>
    <justification jstring="[back_rewrite(5801),rewrite(5943(11),5943(15),5943(17),6069(18),5943(17),5934(15),5934(12),5934(9),5925(6),6069(6),5934(6),5934(5),5925(2),5943(9),5943(13),5943(15),6069(16),5943(15),5934(13),5934(10),5934(7),5925(4)),flip(a)].">
      <j1 rule="back_rewrite" parents="5801"/>
      <j2 rule="rewrite" parents="5943 5943 5943 6069 5943 5934 5934 5934 5925 6069 5934 5934 5925 5943 5943 5943 6069 5943 5934 5934 5934 5925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6094">
    <literal><![CDATA[
      x v (x' v y')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(5662),rewrite(6071(9),5925(7))].">
      <j1 rule="back_rewrite" parents="5662"/>
      <j2 rule="rewrite" parents="6071 5925"/>
    </justification>
  </clause>

  <clause id="6095">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer(B1)
    ]]></attribute>
    <justification jstring="[resolve(6094,a,12,a)].">
      <j1 rule="resolve" parents="6094 12"/>
    </justification>
  </clause>

</proof>

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

<comments><![CDATA[
% Proof 3 at 3.46 (+ 0.03) 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(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 v))) = z v (x v (u v (y v v)))
    ]]></literal>
    <justification jstring="[para(18(a,1),5(a,1,2))].">
      <j1 rule="para" parents="18 5"/>
    </justification>
  </clause>

  <clause id="29">
    <literal><![CDATA[
      x v (y v (z v (u v v))) = u v (x v (y v (z v v)))
    ]]></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="2055">
    <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="2143">
    <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="2392">
    <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="2420">
    <literal><![CDATA[
      c_0 v (x v (c_0' v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[para(2392(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2392 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2426">
    <literal><![CDATA[
      ((c_0 v (c_0' v c_0)')' v c_0') v c_0 = c_0
    ]]></literal>
    <justification jstring="[para(2392(a,1),26(a,1,1,2,1))].">
      <j1 rule="para" parents="2392 26"/>
    </justification>
  </clause>

  <clause id="2430">
    <literal><![CDATA[
      c_0'' = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(2392(a,1),52(a,1,2)),rewrite(5(11),1157(15))].">
      <j1 rule="para" parents="2392 52"/>
      <j2 rule="rewrite" parents="5 1157"/>
    </justification>
  </clause>

  <clause id="2432">
    <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(2392(a,1),29(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="2392 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2494">
    <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(2430(3),2430(15),5(16),2430(20))].">
      <j1 rule="back_rewrite" parents="1546"/>
      <j2 rule="rewrite" parents="2430 2430 5 2430"/>
    </justification>
  </clause>

  <clause id="2499">
    <literal><![CDATA[
      ((c_0 v (c_0 v c_0))' v c_0')' = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(1519),rewrite(2430(5),1707(11),2430(4),2430(15),1707(21))].">
      <j1 rule="back_rewrite" parents="1519"/>
      <j2 rule="rewrite" parents="2430 1707 2430 2430 1707"/>
    </justification>
  </clause>

  <clause id="2550">
    <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(2430(18))].">
      <j1 rule="back_rewrite" parents="1157"/>
      <j2 rule="rewrite" parents="2430"/>
    </justification>
  </clause>

  <clause id="2571">
    <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(2430(5),5(10))].">
      <j1 rule="back_rewrite" parents="1136"/>
      <j2 rule="rewrite" parents="2430 5"/>
    </justification>
  </clause>

  <clause id="2588">
    <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(2430(3),2430(16),5(17),63(16))].">
      <j1 rule="back_rewrite" parents="1119"/>
      <j2 rule="rewrite" parents="2430 2430 5 63"/>
    </justification>
  </clause>

  <clause id="2607">
    <literal><![CDATA[
      ((c_0 v (x v c_0))' v (x v c_0')')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(1082),rewrite(2430(3),2588(6))].">
      <j1 rule="back_rewrite" parents="1082"/>
      <j2 rule="rewrite" parents="2430 2588"/>
    </justification>
  </clause>

  <clause id="2625">
    <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(2430(5),2430(9),2430(20))].">
      <j1 rule="back_rewrite" parents="672"/>
      <j2 rule="rewrite" parents="2430 2430 2430"/>
    </justification>
  </clause>

  <clause id="2640">
    <literal><![CDATA[
      ((c_0 v ((x v x'')' v c_0))' v x)' = (x v x'')'
    ]]></literal>
    <justification jstring="[back_rewrite(66),rewrite(2430(7),5(8))].">
      <j1 rule="back_rewrite" parents="66"/>
      <j2 rule="rewrite" parents="2430 5"/>
    </justification>
  </clause>

  <clause id="3585">
    <literal><![CDATA[
      c_0' v (c_0' v c_0')' = c_0
    ]]></literal>
    <justification jstring="[para(49(a,1),2607(a,1,1,2,1)),rewrite(63(12),2499(10)),flip(a)].">
      <j1 rule="para" parents="49 2607"/>
      <j2 rule="rewrite" parents="63 2499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3594">
    <literal><![CDATA[
      (c_0' v x')' v (c_0' v x)' = c_0
    ]]></literal>
    <justification jstring="[para(26(a,1),2607(a,1,1,2,1)),rewrite(149(13),2499(10)),flip(a)].">
      <j1 rule="para" parents="26 2607"/>
      <j2 rule="rewrite" parents="149 2499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3842">
    <literal><![CDATA[
      c_0' v (x v (c_0' v c_0')') = x v c_0
    ]]></literal>
    <justification jstring="[para(3585(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3585 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3844">
    <literal><![CDATA[
      (c_0' v c_0') v c_0 = c_0' v c_0
    ]]></literal>
    <justification jstring="[para(3585(a,1),23(a,1,2))].">
      <j1 rule="para" parents="3585 23"/>
    </justification>
  </clause>

  <clause id="3854">
    <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(3585(a,1),169(a,1,1,2,1,2,2))].">
      <j1 rule="para" parents="3585 169"/>
    </justification>
  </clause>

  <clause id="3893">
    <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(3594(a,1),18(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3594 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3896">
    <literal><![CDATA[
      (c_0' v x')' v c_0 = (c_0' v x) v c_0
    ]]></literal>
    <justification jstring="[para(3594(a,1),23(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3594 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3953">
    <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(3854),rewrite(3896(16),5(15),3896(14))].">
      <j1 rule="back_rewrite" parents="3854"/>
      <j2 rule="rewrite" parents="3896 5 3896"/>
    </justification>
  </clause>

  <clause id="4055">
    <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="4126">
    <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),3842(a,1,2)),rewrite(3842(28),3896(20),5(19),3896(18)),flip(a)].">
      <j1 rule="para" parents="165 3842"/>
      <j2 rule="rewrite" parents="3842 3896 5 3896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4153">
    <literal><![CDATA[
      (c_0' v c_0')' = c_0' v c_0
    ]]></literal>
    <justification jstring="[para(3896(a,1),21(a,1,1,2,1,2)),rewrite(45(14)),flip(a)].">
      <j1 rule="para" parents="3896 21"/>
      <j2 rule="rewrite" parents="45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4245">
    <literal><![CDATA[
      c_0' v (c_0' v c_0) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(3953),rewrite(4153(21),5(20),4126(19))].">
      <j1 rule="back_rewrite" parents="3953"/>
      <j2 rule="rewrite" parents="4153 5 4126"/>
    </justification>
  </clause>

  <clause id="4281">
    <literal><![CDATA[
      c_0' v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(4245(a,1),52(a,1,2)),rewrite(5(11),2550(15)),flip(a)].">
      <j1 rule="para" parents="4245 52"/>
      <j2 rule="rewrite" parents="5 2550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4282">
    <literal><![CDATA[
      c_0 v (c_0 v c_0) = c_0
    ]]></literal>
    <justification jstring="[para(52(a,2),4245(a,1,2)),rewrite(5(11),49(10),4281(6),5(6),4281(5))].">
      <j1 rule="para" parents="52 4245"/>
      <j2 rule="rewrite" parents="5 49 4281 5 4281"/>
    </justification>
  </clause>

  <clause id="4324">
    <literal><![CDATA[
      (c_0' v c_0') v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[back_rewrite(3844),rewrite(4281(11))].">
      <j1 rule="back_rewrite" parents="3844"/>
      <j2 rule="rewrite" parents="4281"/>
    </justification>
  </clause>

  <clause id="4385">
    <literal><![CDATA[
      (c_0 v c_0)' = c_0'
    ]]></literal>
    <justification jstring="[back_rewrite(2494),rewrite(4281(9),17(11),4281(5),4282(5)),flip(a)].">
      <j1 rule="back_rewrite" parents="2494"/>
      <j2 rule="rewrite" parents="4281 17 4281 4282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4400">
    <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(2432),rewrite(4281(5))].">
      <j1 rule="back_rewrite" parents="2432"/>
      <j2 rule="rewrite" parents="4281"/>
    </justification>
  </clause>

  <clause id="4403">
    <literal><![CDATA[
      c_0 v c_0 = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(2426),rewrite(4281(5),4385(5),17(4),4324(7))].">
      <j1 rule="back_rewrite" parents="2426"/>
      <j2 rule="rewrite" parents="4281 4385 17 4324"/>
    </justification>
  </clause>

  <clause id="4406">
    <literal><![CDATA[
      c_0 v (x v c_0) = x v c_0
    ]]></literal>
    <justification jstring="[back_rewrite(2420),rewrite(4281(5),4403(4))].">
      <j1 rule="back_rewrite" parents="2420"/>
      <j2 rule="rewrite" parents="4281 4403"/>
    </justification>
  </clause>

  <clause id="4439">
    <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(4400),rewrite(4403(4))].">
      <j1 rule="back_rewrite" parents="4400"/>
      <j2 rule="rewrite" parents="4403"/>
    </justification>
  </clause>

  <clause id="4455">
    <literal><![CDATA[
      c_0' v c_0 = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(4281),rewrite(4403(7))].">
      <j1 rule="back_rewrite" parents="4281"/>
      <j2 rule="rewrite" parents="4403"/>
    </justification>
  </clause>

  <clause id="4531">
    <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(2625),rewrite(4403(5),4403(7),4403(16))].">
      <j1 rule="back_rewrite" parents="2625"/>
      <j2 rule="rewrite" parents="4403 4403 4403"/>
    </justification>
  </clause>

  <clause id="4535">
    <literal><![CDATA[
      c_0' v (x v (y v c_0)) = x v (y v c_0)
    ]]></literal>
    <justification jstring="[back_rewrite(2571),rewrite(4403(3),4439(8))].">
      <j1 rule="back_rewrite" parents="2571"/>
      <j2 rule="rewrite" parents="4403 4439"/>
    </justification>
  </clause>

  <clause id="4538">
    <literal><![CDATA[
      c_0'' = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(2430),rewrite(4403(6))].">
      <j1 rule="back_rewrite" parents="2430"/>
      <j2 rule="rewrite" parents="4403"/>
    </justification>
  </clause>

  <clause id="4544">
    <literal><![CDATA[
      (((x v x'')' v c_0)' v x)' = (x v x'')'
    ]]></literal>
    <justification jstring="[back_rewrite(2640),rewrite(4406(8))].">
      <j1 rule="back_rewrite" parents="2640"/>
      <j2 rule="rewrite" parents="4406"/>
    </justification>
  </clause>

  <clause id="4638">
    <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="4718">
    <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),4535(12),5(10),4531(13),5(9),4535(10)),flip(a)].">
      <j1 rule="para" parents="869 50"/>
      <j2 rule="rewrite" parents="5 4535 5 4531 5 4535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4744">
    <literal><![CDATA[
      (c_0' v (x v c_0)')' = x v c_0
    ]]></literal>
    <justification jstring="[para(3594(a,1),50(a,1,1,2,1,2,2,1,2)),rewrite(3893(16),4718(7),3594(17))].">
      <j1 rule="para" parents="3594 50"/>
      <j2 rule="rewrite" parents="3893 4718 3594"/>
    </justification>
  </clause>

  <clause id="4750">
    <literal><![CDATA[
      x v ((c_0' v (x v c_0)') v c_0) = c_0
    ]]></literal>
    <justification jstring="[para(4406(a,1),52(a,1,2)),rewrite(5(7),4718(7),5(9),4403(12))].">
      <j1 rule="para" parents="4406 52"/>
      <j2 rule="rewrite" parents="5 4718 5 4403"/>
    </justification>
  </clause>

  <clause id="4755">
    <literal><![CDATA[
      x v (y v ((x v c_0) v c_0)) = y v (x v c_0)
    ]]></literal>
    <justification jstring="[para(4718(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4718 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4864">
    <literal><![CDATA[
      ((x v c_0)' v c_0')' = x v c_0
    ]]></literal>
    <justification jstring="[para(4744(a,1),42(a,1,1,1,1,2)),rewrite(5(5),4718(5),4455(7))].">
      <j1 rule="para" parents="4744 42"/>
      <j2 rule="rewrite" parents="5 4718 4455"/>
    </justification>
  </clause>

  <clause id="4877">
    <literal><![CDATA[
      ((x v (y v c_0))' v ((y v c_0)' v (x v c_0'))')' = x
    ]]></literal>
    <justification jstring="[para(4864(a,1),19(a,1,1,1,1,2))].">
      <j1 rule="para" parents="4864 19"/>
    </justification>
  </clause>

  <clause id="4887">
    <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(4864(a,1),21(a,1,1,2,1,2,1)),rewrite(5(11),4864(21))].">
      <j1 rule="para" parents="4864 21"/>
      <j2 rule="rewrite" parents="5 4864"/>
    </justification>
  </clause>

  <clause id="4895">
    <literal><![CDATA[
      ((x v c_0)' v ((x v c_0)' v c_0)')' = c_0
    ]]></literal>
    <justification jstring="[para(4864(a,1),42(a,1,1,1,1,2)),rewrite(4406(4))].">
      <j1 rule="para" parents="4864 42"/>
      <j2 rule="rewrite" parents="4406"/>
    </justification>
  </clause>

  <clause id="4996">
    <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(4718(a,1),53(a,1,2,1,2,1,2,1)),rewrite(4755(10),5(7),4718(7),5(11))].">
      <j1 rule="para" parents="4718 53"/>
      <j2 rule="rewrite" parents="4755 5 4718 5"/>
    </justification>
  </clause>

  <clause id="5007">
    <literal><![CDATA[
      x v (y v ((c_0' v (x v c_0)') v c_0)) = y v c_0
    ]]></literal>
    <justification jstring="[para(4750(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4750 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5015">
    <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(4750(a,1),22(a,1,1,1,1,2,1,1)),rewrite(4538(14))].">
      <j1 rule="para" parents="4750 22"/>
      <j2 rule="rewrite" parents="4538"/>
    </justification>
  </clause>

  <clause id="5030">
    <literal><![CDATA[
      (x v c_0) v c_0 = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(4996),rewrite(5007(12))].">
      <j1 rule="back_rewrite" parents="4996"/>
      <j2 rule="rewrite" parents="5007"/>
    </justification>
  </clause>

  <clause id="5048">
    <literal><![CDATA[
      (x v c_0) v (y v c_0) = y v c_0
    ]]></literal>
    <justification jstring="[para(5030(a,1),5(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5030 5"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5064">
    <literal><![CDATA[
      x v c_0 = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(4887),rewrite(5048(11),4895(11)),flip(a)].">
      <j1 rule="back_rewrite" parents="4887"/>
      <j2 rule="rewrite" parents="5048 4895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5068">
    <literal><![CDATA[
      (c_0' v x)' = (x v c_0')'
    ]]></literal>
    <justification jstring="[back_rewrite(5015),rewrite(5064(4),5064(7),5064(6),5064(8),5064(11))].">
      <j1 rule="back_rewrite" parents="5015"/>
      <j2 rule="rewrite" parents="5064 5064 5064 5064 5064"/>
    </justification>
  </clause>

  <clause id="5097">
    <literal><![CDATA[
      (c_0' v (c_0' v (x v c_0'))')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(4877),rewrite(5064(2),5064(2),5064(4))].">
      <j1 rule="back_rewrite" parents="4877"/>
      <j2 rule="rewrite" parents="5064 5064 5064"/>
    </justification>
  </clause>

  <clause id="5147">
    <literal><![CDATA[
      (x v x'')' = (c_0' v x)'
    ]]></literal>
    <justification jstring="[back_rewrite(4544),rewrite(5064(6)),flip(a)].">
      <j1 rule="back_rewrite" parents="4544"/>
      <j2 rule="rewrite" parents="5064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5194">
    <literal><![CDATA[
      (x v (y v (z v (u v x')))')' = (c_0' v x)'
    ]]></literal>
    <justification jstring="[back_rewrite(4055),rewrite(5064(9),5064(9),5064(9),4538(10),5064(9)),flip(a)].">
      <j1 rule="back_rewrite" parents="4055"/>
      <j2 rule="rewrite" parents="5064 5064 5064 4538 5064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5645">
    <literal><![CDATA[
      (c_0' v (c_0' v x)')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(1028),rewrite(5194(7),5064(6),5064(6),5064(6),5068(8,R))].">
      <j1 rule="back_rewrite" parents="1028"/>
      <j2 rule="rewrite" parents="5194 5064 5064 5064 5068"/>
    </justification>
  </clause>

  <clause id="5725">
    <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(5064(13))].">
      <j1 rule="back_rewrite" parents="712"/>
      <j2 rule="rewrite" parents="5064"/>
    </justification>
  </clause>

  <clause id="5776">
    <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(5064(2))].">
      <j1 rule="back_rewrite" parents="185"/>
      <j2 rule="rewrite" parents="5064"/>
    </justification>
  </clause>

  <clause id="5787">
    <literal><![CDATA[
      (c_0' v (x v x)') v (y v x) = c_0
    ]]></literal>
    <justification jstring="[back_rewrite(52),rewrite(5064(9))].">
      <j1 rule="back_rewrite" parents="52"/>
      <j2 rule="rewrite" parents="5064"/>
    </justification>
  </clause>

  <clause id="5801">
    <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(4638),rewrite(5068(30,R))].">
      <j1 rule="back_rewrite" parents="4638"/>
      <j2 rule="rewrite" parents="5068"/>
    </justification>
  </clause>

  <clause id="5818">
    <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(2055),rewrite(5068(33,R))].">
      <j1 rule="back_rewrite" parents="2055"/>
      <j2 rule="rewrite" parents="5068"/>
    </justification>
  </clause>

  <clause id="5888">
    <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(5147(8),5147(20))].">
      <j1 rule="back_rewrite" parents="108"/>
      <j2 rule="rewrite" parents="5147 5147"/>
    </justification>
  </clause>

  <clause id="5890">
    <literal><![CDATA[
      ((x v y)' v ((c_0' v y)' v (x v c_0'))')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(91),rewrite(5147(6))].">
      <j1 rule="back_rewrite" parents="91"/>
      <j2 rule="rewrite" parents="5147"/>
    </justification>
  </clause>

  <clause id="5895">
    <literal><![CDATA[
      x v c_0' = x
    ]]></literal>
    <justification jstring="[back_rewrite(5097),rewrite(5645(11))].">
      <j1 rule="back_rewrite" parents="5097"/>
      <j2 rule="rewrite" parents="5645"/>
    </justification>
  </clause>

  <clause id="5918">
    <literal><![CDATA[
      x v ((x v y) v ((x v y) v y)) = x v y
    ]]></literal>
    <justification jstring="[back_rewrite(682),rewrite(5645(13))].">
      <j1 rule="back_rewrite" parents="682"/>
      <j2 rule="rewrite" parents="5645"/>
    </justification>
  </clause>

  <clause id="5925">
    <literal><![CDATA[
      x'' = x
    ]]></literal>
    <justification jstring="[back_rewrite(2143),rewrite(5895(3),5725(12),5895(4))].">
      <j1 rule="back_rewrite" parents="2143"/>
      <j2 rule="rewrite" parents="5895 5725 5895"/>
    </justification>
  </clause>

  <clause id="5934">
    <literal><![CDATA[
      (c_0' v x)' = x'
    ]]></literal>
    <justification jstring="[back_rewrite(523),rewrite(5895(3),5787(8),5925(4),5064(3),5895(7))].">
      <j1 rule="back_rewrite" parents="523"/>
      <j2 rule="rewrite" parents="5895 5787 5925 5064 5895"/>
    </justification>
  </clause>

  <clause id="5941">
    <literal><![CDATA[
      ((x v y)' v (y' v x)')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(5890),rewrite(5934(6),5895(6))].">
      <j1 rule="back_rewrite" parents="5890"/>
      <j2 rule="rewrite" parents="5934 5895"/>
    </justification>
  </clause>

  <clause id="5943">
    <literal><![CDATA[
      x v x = x
    ]]></literal>
    <justification jstring="[back_rewrite(5888),rewrite(5934(7),5925(4),5895(5),5934(6),5925(3),5934(6),5925(3),5895(4))].">
      <j1 rule="back_rewrite" parents="5888"/>
      <j2 rule="rewrite" parents="5934 5925 5895 5934 5925 5934 5925 5895"/>
    </justification>
  </clause>

  <clause id="6069">
    <literal><![CDATA[
      (c_0' v x) v x = c_0' v x
    ]]></literal>
    <justification jstring="[back_rewrite(5818),rewrite(5918(26),5934(14),9(11),5934(9),5925(6),5918(28),5934(16),9(13))].">
      <j1 rule="back_rewrite" parents="5818"/>
      <j2 rule="rewrite" parents="5918 5934 9 5934 5925 5918 5934 9"/>
    </justification>
  </clause>

  <clause id="6071">
    <literal><![CDATA[
      c_0' v x = x
    ]]></literal>
    <justification jstring="[back_rewrite(5801),rewrite(5943(11),5943(15),5943(17),6069(18),5943(17),5934(15),5934(12),5934(9),5925(6),6069(6),5934(6),5934(5),5925(2),5943(9),5943(13),5943(15),6069(16),5943(15),5934(13),5934(10),5934(7),5925(4)),flip(a)].">
      <j1 rule="back_rewrite" parents="5801"/>
      <j2 rule="rewrite" parents="5943 5943 5943 6069 5943 5934 5934 5934 5925 6069 5934 5934 5925 5943 5943 5943 6069 5943 5934 5934 5934 5925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6085">
    <literal><![CDATA[
      x v (((y v x') v z')' v ((y v x') v z)') = x
    ]]></literal>
    <justification jstring="[back_rewrite(5776),rewrite(6071(15),5925(13))].">
      <j1 rule="back_rewrite" parents="5776"/>
      <j2 rule="rewrite" parents="6071 5925"/>
    </justification>
  </clause>

  <clause id="6586">
    <literal><![CDATA[
      (x v y')' v (x v y)' = x'
    ]]></literal>
    <justification jstring="[para(9(a,1),5925(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 5925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6589">
    <literal><![CDATA[
      x v (x v ((x v y')' v y))' = x v y'
    ]]></literal>
    <justification jstring="[para(21(a,1),5925(a,1,1)),rewrite(5925(4)),flip(a)].">
      <j1 rule="para" parents="21 5925"/>
      <j2 rule="rewrite" parents="5925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6595">
    <literal><![CDATA[
      x v (y v x')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(6085),rewrite(6586(10))].">
      <j1 rule="back_rewrite" parents="6085"/>
      <j2 rule="rewrite" parents="6586"/>
    </justification>
  </clause>

  <clause id="6650">
    <literal><![CDATA[
      x v y = y v x
    ]]></literal>
    <justification jstring="[para(5895(a,1),5(a,1,2)),rewrite(5895(4))].">
      <j1 rule="para" parents="5895 5"/>
      <j2 rule="rewrite" parents="5895"/>
    </justification>
  </clause>

  <clause id="6651">
    <literal><![CDATA[
      x v (y v z) = z v (x v y)
    ]]></literal>
    <justification jstring="[para(5895(a,1),18(a,1,2,2)),rewrite(5895(5))].">
      <j1 rule="para" parents="5895 18"/>
      <j2 rule="rewrite" parents="5895"/>
    