<?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 June-2006C, June 2006.
Process 13586 was started by mccune on cleo.thornwood,
Mon Jun 19 16:43:06 2006
The command was "/home/mccune/bin/prover9 -f ba-4basis.in".
]]></heading>

<proof number="1" length="149" max_count="39">

<comments><![CDATA[
% Proof 1 at 1.39 (+ 0.01) seconds: CC.
% Length of proof is 149.
% Level of proof is 40.
% Maximum clause weight is 39.
% Given clauses 122.
]]></comments>

  <clause id="3">
    <literal><![CDATA[
      x v c(x) = y v c(y)
    ]]></literal>
    <attribute><![CDATA[
      label(ONE)
    ]]></attribute>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="4">
    <literal><![CDATA[
      (x v c(y)) ^ (x v y) = x
    ]]></literal>
    <attribute><![CDATA[
      label(CUT)
    ]]></attribute>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="9">
    <literal><![CDATA[
      x v (y v z) = y v (x v z)
    ]]></literal>
    <attribute><![CDATA[
      label(AJ)
    ]]></attribute>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="10">
    <literal><![CDATA[
      x ^ y = c(c(x) v c(y))
    ]]></literal>
    <attribute><![CDATA[
      label(DM)
    ]]></attribute>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="11">
    <literal><![CDATA[
      x v c(x) = y v c(y)
    ]]></literal>
    <attribute><![CDATA[
      label(ONE)
    ]]></attribute>
    <justification jstring="[copy(3)].">
      <j1 rule="copy" parents="3"/>
    </justification>
  </clause>

  <clause id="12">
    <literal><![CDATA[
      c(c(x v c(y)) v c(x v y)) = x
    ]]></literal>
    <attribute><![CDATA[
      label(CUT)
    ]]></attribute>
    <justification jstring="[copy(4),demod(10(4))].">
      <j1 rule="copy" parents="4"/>
      <j2 rule="demod" parents="10"/>
    </justification>
  </clause>

  <clause id="13">
    <literal><![CDATA[
      x v c(x) = c_0
    ]]></literal>
    <justification jstring="[new_symbol(11)].">
      <j1 rule="new_symbol" parents="11"/>
    </justification>
  </clause>

  <clause id="14">
    <literal><![CDATA[
      c(c(c1)) != c1
    ]]></literal>
    <attribute><![CDATA[
      answer(CC)
    ]]></attribute>
    <justification jstring="[clausify].">
      <j1 rule="clausify"/>
    </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(9(a,1),9(a,1,2))].">
      <j1 rule="para" parents="9 9"/>
    </justification>
  </clause>

  <clause id="19">
    <literal><![CDATA[
      c(c(x v c(y v z)) v c(y v (x v z))) = x
    ]]></literal>
    <justification jstring="[para(9(a,1),12(a,1,1,2,1))].">
      <j1 rule="para" parents="9 12"/>
    </justification>
  </clause>

  <clause id="21">
    <literal><![CDATA[
      c(x v c(x v (c(x v c(y)) v y))) = c(x v c(y))
    ]]></literal>
    <justification jstring="[para(12(a,1),12(a,1,1,1)),demod(9(5))].">
      <j1 rule="para" parents="12 12"/>
      <j2 rule="demod" parents="9"/>
    </justification>
  </clause>

  <clause id="22">
    <literal><![CDATA[
      c(c(c(x v c(y)) v c(c(x v y))) v x) = c(x v c(y))
    ]]></literal>
    <justification jstring="[para(12(a,1),12(a,1,1,2))].">
      <j1 rule="para" parents="12 12"/>
    </justification>
  </clause>

  <clause id="23">
    <literal><![CDATA[
      x v (y v c(x)) = y v c_0
    ]]></literal>
    <justification jstring="[para(13(a,1),9(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24">
    <literal><![CDATA[
      c(c(c_0) v c(x v x)) = x
    ]]></literal>
    <justification jstring="[para(13(a,1),12(a,1,1,1,1))].">
      <j1 rule="para" parents="13 12"/>
    </justification>
  </clause>

  <clause id="25">
    <literal><![CDATA[
      c(c(x v c(c(x))) v c(c_0)) = x
    ]]></literal>
    <justification jstring="[para(13(a,1),12(a,1,1,2,1))].">
      <j1 rule="para" parents="13 12"/>
    </justification>
  </clause>

  <clause id="26">
    <literal><![CDATA[
      (c(x v c(y)) v c(x v y)) v x = c_0
    ]]></literal>
    <justification jstring="[para(12(a,1),13(a,1,2))].">
      <j1 rule="para" parents="12 13"/>
    </justification>
  </clause>

  <clause id="27">
    <literal><![CDATA[
      x v (y v (z v c(x))) = y v (z v c_0)
    ]]></literal>
    <justification jstring="[para(23(a,1),9(a,1,2)),flip(a)].">
      <j1 rule="para" parents="23 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28">
    <literal><![CDATA[
      c(c(x v c(y v c(x))) v c(y v c_0)) = x
    ]]></literal>
    <justification jstring="[para(23(a,1),12(a,1,1,2,1))].">
      <j1 rule="para" parents="23 12"/>
    </justification>
  </clause>

  <clause id="29">
    <literal><![CDATA[
      (c(x v c(y)) v c(x v y)) v (z v x) = z v c_0
    ]]></literal>
    <justification jstring="[para(12(a,1),23(a,1,2,2))].">
      <j1 rule="para" parents="12 23"/>
    </justification>
  </clause>

  <clause id="30">
    <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),9(a,1,2))].">
      <j1 rule="para" parents="18 9"/>
    </justification>
  </clause>

  <clause id="34">
    <literal><![CDATA[
      c(c(x v c(y v (z v u))) v c(z v (x v (y v u)))) = x
    ]]></literal>
    <justification jstring="[para(18(a,1),12(a,1,1,2,1))].">
      <j1 rule="para" parents="18 12"/>
    </justification>
  </clause>

  <clause id="35">
    <literal><![CDATA[
      c(c(x v c(y v (z v u))) v c(y v (z v (x v u)))) = x
    ]]></literal>
    <justification jstring="[para(18(a,2),12(a,1,1,2,1))].">
      <j1 rule="para" parents="18 12"/>
    </justification>
  </clause>

  <clause id="36">
    <literal><![CDATA[
      x v (y v (z v (u v c(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(c(c_0) v c(x v ((x v y) v y))) = x v y
    ]]></literal>
    <justification jstring="[para(9(a,1),24(a,1,1,2,1))].">
      <j1 rule="para" parents="9 24"/>
    </justification>
  </clause>

  <clause id="47">
    <literal><![CDATA[
      c(x v c(c(c_0) v (x v x))) = c(c_0)
    ]]></literal>
    <justification jstring="[para(24(a,1),12(a,1,1,1))].">
      <j1 rule="para" parents="24 12"/>
    </justification>
  </clause>

  <clause id="48">
    <literal><![CDATA[
      c(c(c(c_0) v c(c(x v x))) v x) = c(c_0)
    ]]></literal>
    <justification jstring="[para(24(a,1),12(a,1,1,2))].">
      <j1 rule="para" parents="24 12"/>
    </justification>
  </clause>

  <clause id="49">
    <literal><![CDATA[
      (c(c_0) v c(x v x)) v x = c_0
    ]]></literal>
    <justification jstring="[para(24(a,1),13(a,1,2))].">
      <j1 rule="para" parents="24 13"/>
    </justification>
  </clause>

  <clause id="50">
    <literal><![CDATA[
      (c(c_0) v c(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="51">
    <literal><![CDATA[
      c(c(c_0) v c(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)),demod(9(6))].">
      <j1 rule="para" parents="18 24"/>
      <j2 rule="demod" parents="9"/>
    </justification>
  </clause>

  <clause id="53">
    <literal><![CDATA[
      x v ((c(c_0) v c(x v ((x v y) v y))) v y) = c_0
    ]]></literal>
    <justification jstring="[para(49(a,1),9(a,1)),demod(9(6)),flip(a)].">
      <j1 rule="para" parents="49 9"/>
      <j2 rule="demod" parents="9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="56">
    <literal><![CDATA[
      (c(c_0) v c(c(x) v c(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[
      c(x v c(c(x v c(c(x))) v c_0)) = c(x v c(c(x)))
    ]]></literal>
    <justification jstring="[para(25(a,1),12(a,1,1,1))].">
      <j1 rule="para" parents="25 12"/>
    </justification>
  </clause>

  <clause id="66">
    <literal><![CDATA[
      c(c(c(x v c(c(x))) v c(c(c_0))) v x) = c(x v c(c(x)))
    ]]></literal>
    <justification jstring="[para(25(a,1),12(a,1,1,2))].">
      <j1 rule="para" parents="25 12"/>
    </justification>
  </clause>

  <clause id="68">
    <literal><![CDATA[
      (c(x v c(c(x))) v c(c_0)) v x = c_0
    ]]></literal>
    <justification jstring="[para(25(a,1),13(a,1,2))].">
      <j1 rule="para" parents="25 13"/>
    </justification>
  </clause>

  <clause id="72">
    <literal><![CDATA[
      c(x v c(x v (c(c_0) v x))) = c(c_0)
    ]]></literal>
    <justification jstring="[para(9(a,1),47(a,1,1,2,1))].">
      <j1 rule="para" parents="9 47"/>
    </justification>
  </clause>

  <clause id="74">
    <literal><![CDATA[
      c(c(c_0) v c(x v (c(c_0) v (x v x)))) = x
    ]]></literal>
    <justification jstring="[para(47(a,1),12(a,1,1,1))].">
      <j1 rule="para" parents="47 12"/>
    </justification>
  </clause>

  <clause id="76">
    <literal><![CDATA[
      (x v c(c(c_0) v (x v x))) v c(c_0) = c_0
    ]]></literal>
    <justification jstring="[para(47(a,1),13(a,1,2))].">
      <j1 rule="para" parents="47 13"/>
    </justification>
  </clause>

  <clause id="126">
    <literal><![CDATA[
      c(c(c_0) v c(x v (x v (c(c_0) v x)))) = x
    ]]></literal>
    <justification jstring="[para(72(a,1),12(a,1,1,1))].">
      <j1 rule="para" parents="72 12"/>
    </justification>
  </clause>

  <clause id="141">
    <literal><![CDATA[
      (c(c(x) v c(y)) v c(c(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(c(c_0) v c(c(x v x))) v x) v c(c_0) = c_0
    ]]></literal>
    <justification jstring="[para(24(a,1),26(a,1,1,2))].">
      <j1 rule="para" parents="24 26"/>
    </justification>
  </clause>

  <clause id="158">
    <literal><![CDATA[
      (c(c_0) v c(x v (c(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(c_0) v c(x v (x v (c(c_0) v x)))) v x = c_0
    ]]></literal>
    <justification jstring="[para(72(a,1),26(a,1,1,1))].">
      <j1 rule="para" parents="72 26"/>
    </justification>
  </clause>

  <clause id="243">
    <literal><![CDATA[
      c(c(c_0) v c((x v c(c(c_0) v (x v x))) v c_0)) = x v c(c(c_0) v (x v x))
    ]]></literal>
    <justification jstring="[para(76(a,1),12(a,1,1,1,1))].">
      <j1 rule="para" parents="76 12"/>
    </justification>
  </clause>

  <clause id="244">
    <literal><![CDATA[
      (x v c(c(c_0) v (x v x))) v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(76(a,1),23(a,1,2)),flip(a)].">
      <j1 rule="para" parents="76 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="256">
    <literal><![CDATA[
      x v c(c(c_0) v (x v x)) = c_0
    ]]></literal>
    <justification jstring="[back_demod(243),demod(244(10),24(8)),flip(a)].">
      <j1 rule="back_demod" parents="243"/>
      <j2 rule="demod" parents="244 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="258">
    <literal><![CDATA[
      x v (y v c(c(c_0) v (x v x))) = y v c_0
    ]]></literal>
    <justification jstring="[para(256(a,1),9(a,1,2)),flip(a)].">
      <j1 rule="para" parents="256 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="260">
    <literal><![CDATA[
      x v c(x v (c(c_0) v x)) = c_0
    ]]></literal>
    <justification jstring="[para(9(a,1),256(a,1,2,1))].">
      <j1 rule="para" parents="9 256"/>
    </justification>
  </clause>

  <clause id="261">
    <literal><![CDATA[
      (c(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="262">
    <literal><![CDATA[
      c(c(c_0)) v c(c(c(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="273">
    <literal><![CDATA[
      x v (y v c(x v (c(c_0) v x))) = y v c_0
    ]]></literal>
    <justification jstring="[para(260(a,1),9(a,1,2)),flip(a)].">
      <j1 rule="para" parents="260 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="284">
    <literal><![CDATA[
      (c(c(c_0)) v c_0) v c_0 = c(c(c_0)) v c_0
    ]]></literal>
    <justification jstring="[para(23(a,1),261(a,1,1))].">
      <j1 rule="para" parents="23 261"/>
    </justification>
  </clause>

  <clause id="330">
    <literal><![CDATA[
      c(c(c_0) v c(c(c(c_0)) v (c(c(c_0)) v c_0))) = c(c(c_0))
    ]]></literal>
    <justification jstring="[para(262(a,1),12(a,1,1,1,1))].">
      <j1 rule="para" parents="262 12"/>
    </justification>
  </clause>

  <clause id="336">
    <literal><![CDATA[
      (c(c(c_0)) v c_0) v (x v c_0) = x v (c(c(c_0)) v c_0)
    ]]></literal>
    <justification jstring="[para(262(a,1),27(a,1,2,2))].">
      <j1 rule="para" parents="262 27"/>
    </justification>
  </clause>

  <clause id="547">
    <literal><![CDATA[
      (c(c(c_0) v c(c(x v x))) v x) v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(48(a,1),56(a,1,1,2,1,1)),demod(48(13),56(11)),flip(a)].">
      <j1 rule="para" parents="48 56"/>
      <j2 rule="demod" parents="48 56"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="576">
    <literal><![CDATA[
      c(c(x v c((c(c(c_0)) v c_0) v c(x))) v c(c(c(c_0)) v c_0)) = x
    ]]></literal>
    <justification jstring="[para(284(a,1),28(a,1,1,2,1))].">
      <j1 rule="para" parents="284 28"/>
    </justification>
  </clause>

  <clause id="605">
    <literal><![CDATA[
      c(c(c_0) v c(x v ((x v c(c(c_0))) v ((x v c(c(c_0))) v c_0)))) = x v c(c(c_0))
    ]]></literal>
    <justification jstring="[para(27(a,1),74(a,1,1,2,1,2)),demod(9(13),9(14))].">
      <j1 rule="para" parents="27 74"/>
      <j2 rule="demod" parents="9 9"/>
    </justification>
  </clause>

  <clause id="680">
    <literal><![CDATA[
      (c(c_0) v (x v x)) v (y v c_0) = x v (y v c_0)
    ]]></literal>
    <justification jstring="[para(258(a,1),27(a,1,2))].">
      <j1 rule="para" parents="258 27"/>
    </justification>
  </clause>

  <clause id="805">
    <literal><![CDATA[
      c(c(c(x v c(y v c(x v (c(c_0) v x)))) v c(c(y v c_0))) v x) = c(x v c(y v c(x v (c(c_0) v x))))
    ]]></literal>
    <justification jstring="[para(273(a,1),22(a,1,1,1,1,2,1,1))].">
      <j1 rule="para" parents="273 22"/>
    </justification>
  </clause>

  <clause id="808">
    <literal><![CDATA[
      (c(x v c(y v c(x v (c(c_0) v x)))) v c(y v c_0)) v (z v x) = z v c_0
    ]]></literal>
    <justification jstring="[para(273(a,1),29(a,1,1,2,1))].">
      <j1 rule="para" parents="273 29"/>
    </justification>
  </clause>

  <clause id="817">
    <literal><![CDATA[
      c(c(c_0) v c(c(c(c_0)))) v c(c_0) = c(c(c_0) v c(c(c(c_0))))
    ]]></literal>
    <justification jstring="[para(68(a,1),45(a,1,1,2,1,2)),demod(65(15)),flip(a)].">
      <j1 rule="para" parents="68 45"/>
      <j2 rule="demod" parents="65"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="825">
    <literal><![CDATA[
      c(c(c_0)) v c_0 = c(c(c_0))
    ]]></literal>
    <justification jstring="[para(284(a,1),45(a,1,1,2,1,2,1)),demod(284(14),9(13),284(12),330(14),284(10)),flip(a)].">
      <j1 rule="para" parents="284 45"/>
      <j2 rule="demod" parents="284 9 284 330 284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="842">
    <literal><![CDATA[
      c(c(x v c(c(c(c_0)) v c(x))) v c(c(c(c_0)))) = x
    ]]></literal>
    <justification jstring="[back_demod(576),demod(825(5),825(13))].">
      <j1 rule="back_demod" parents="576"/>
      <j2 rule="demod" parents="825 825"/>
    </justification>
  </clause>

  <clause id="855">
    <literal><![CDATA[
      c(c(c_0)) v (x v c_0) = x v c(c(c_0))
    ]]></literal>
    <justification jstring="[back_demod(336),demod(825(5),825(11))].">
      <j1 rule="back_demod" parents="336"/>
      <j2 rule="demod" parents="825 825"/>
    </justification>
  </clause>

  <clause id="858">
    <literal><![CDATA[
      (c(c_0) v c(c_0 v c_0)) v c(c(c_0)) = c(c(c_0))
    ]]></literal>
    <justification jstring="[para(825(a,1),50(a,1,2)),demod(825(16))].">
      <j1 rule="para" parents="825 50"/>
      <j2 rule="demod" parents="825"/>
    </justification>
  </clause>

  <clause id="861">
    <literal><![CDATA[
      c(c(c(c(c_0)) v (x v c_0)) v c(x v c(c_0))) = x
    ]]></literal>
    <justification jstring="[para(855(a,2),12(a,1,1,1,1))].">
      <j1 rule="para" parents="855 12"/>
    </justification>
  </clause>

  <clause id="862">
    <literal><![CDATA[
      c(c_0) v (c(c(c_0)) v (x v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[para(855(a,2),23(a,1,2))].">
      <j1 rule="para" parents="855 23"/>
    </justification>
  </clause>

  <clause id="898">
    <literal><![CDATA[
      c(c(c_0)) v (x v c_0) = (c(c_0) v c(c(x) v c(x))) v c(c(c_0))
    ]]></literal>
    <justification jstring="[para(56(a,1),855(a,1,2))].">
      <j1 rule="para" parents="56 855"/>
    </justification>
  </clause>

  <clause id="1040">
    <literal><![CDATA[
      c(c(c_0)) v (x v (c(c_0) v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[para(862(a,1),18(a,2))].">
      <j1 rule="para" parents="862 18"/>
    </justification>
  </clause>

  <clause id="1060">
    <literal><![CDATA[
      (c(c_0) v c(c(c_0) v ((c(c_0) v c_0) v c_0))) v c_0 = c(c(c_0))
    ]]></literal>
    <justification jstring="[para(49(a,1),1040(a,1,2)),demod(825(5),9(14)),flip(a)].">
      <j1 rule="para" parents="49 1040"/>
      <j2 rule="demod" parents="825 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1083">
    <literal><![CDATA[
      c(c(c(c_0) v c(c(c(c_0))))) = c(c_0)
    ]]></literal>
    <justification jstring="[para(858(a,1),28(a,1,1,1,1,2,1)),demod(49(17),817(11))].">
      <j1 rule="para" parents="858 28"/>
      <j2 rule="demod" parents="49 817"/>
    </justification>
  </clause>

  <clause id="1087">
    <literal><![CDATA[
      c(c(c_0) v c(c(c(c_0)))) = c_0
    ]]></literal>
    <justification jstring="[para(1083(a,1),13(a,1,2)),demod(817(11))].">
      <j1 rule="para" parents="1083 13"/>
      <j2 rule="demod" parents="817"/>
    </justification>
  </clause>

  <clause id="1234">
    <literal><![CDATA[
      c(c(c(c_0) v c(c(c(c(c_0))))) v c_0) = c(c_0)
    ]]></literal>
    <justification jstring="[para(1087(a,1),12(a,1,1,2))].">
      <j1 rule="para" parents="1087 12"/>
    </justification>
  </clause>

  <clause id="1247">
    <literal><![CDATA[
      c(c(c(c(c_0))) v c(c(c_0) v c_0)) = c(c(c_0))
    ]]></literal>
    <justification jstring="[para(1087(a,1),28(a,1,1,1,1,2)),demod(825(5))].">
      <j1 rule="para" parents="1087 28"/>
      <j2 rule="demod" parents="825"/>
    </justification>
  </clause>

  <clause id="1294">
    <literal><![CDATA[
      c(c((c(c(c_0) v c(c(c(c(c_0))))) v c_0) v c(c(c_0))) v c(c_0)) = c(c(c_0) v c(c(c(c(c_0))))) v c_0
    ]]></literal>
    <justification jstring="[para(1234(a,1),25(a,1,1,1,1,2,1))].">
      <j1 rule="para" parents="1234 25"/>
    </justification>
  </clause>

  <clause id="1333">
    <literal><![CDATA[
      c(c(x v c(y v (z v (u v c(x))))) v c(z v (y v (u v c_0)))) = x
    ]]></literal>
    <justification jstring="[para(27(a,1),34(a,1,1,2,1,2))].">
      <j1 rule="para" parents="27 34"/>
    </justification>
  </clause>

  <clause id="1414">
    <literal><![CDATA[
      c(c(c(c(c(c_0))) v c(c(c(c_0) v c_0))) v c(c(c_0))) = c(c(c(c_0)))
    ]]></literal>
    <justification jstring="[para(1247(a,1),12(a,1,1,2))].">
      <j1 rule="para" parents="1247 12"/>
    </justification>
  </clause>

  <clause id="1455">
    <literal><![CDATA[
      c(c(c_0) v c(c(x v x))) v x = c_0
    ]]></literal>
    <justification jstring="[para(152(a,1),12(a,1,1,1,1)),demod(547(12),24(8)),flip(a)].">
      <j1 rule="para" parents="152 12"/>
      <j2 rule="demod" parents="547 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1477">
    <literal><![CDATA[
      c(c(x v c(y v c_0)) v c(y v ((c(z v c(c(z))) v c(c_0)) v (x v z)))) = x
    ]]></literal>
    <justification jstring="[para(68(a,1),35(a,1,1,1,1,2,1,2))].">
      <j1 rule="para" parents="68 35"/>
    </justification>
  </clause>

  <clause id="1710">
    <literal><![CDATA[
      c(c(c(x v c(y v (z v (u v c(x))))) v c(c(y v (z v (u v c_0))))) v x) = c(x v c(y v (z v (u v c(x)))))
    ]]></literal>
    <justification jstring="[para(36(a,1),22(a,1,1,1,1,2,1,1))].">
      <j1 rule="para" parents="36 22"/>
    </justification>
  </clause>

  <clause id="1864">
    <literal><![CDATA[
      c_0 v (c(c_0) v c_0) = c_0
    ]]></literal>
    <justification jstring="[para(680(a,1),45(a,1,1,2,1,2)),demod(9(10),9(9),126(13),9(7)),flip(a)].">
      <j1 rule="para" parents="680 45"/>
      <j2 rule="demod" parents="9 9 126 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1887">
    <literal><![CDATA[
      c_0 v (x v (c(c_0) v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[para(1864(a,1),9(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1864 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1893">
    <literal><![CDATA[
      (c(c_0 v c(c(c_0) v c_0)) v c(c_0)) v c_0 = c_0
    ]]></literal>
    <justification jstring="[para(1864(a,1),26(a,1,1,2,1))].">
      <j1 rule="para" parents="1864 26"/>
    </justification>
  </clause>

  <clause id="1897">
    <literal><![CDATA[
      c(c(c_0)) = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(1864(a,1),50(a,1,2)),demod(9(11),1060(15))].">
      <j1 rule="para" parents="1864 50"/>
      <j2 rule="demod" parents="9 1060"/>
    </justification>
  </clause>

  <clause id="1898">
    <literal><![CDATA[
      (c(c_0 v c(c(c_0) v c_0)) v c(c_0)) v (x v c_0) = x v c_0
    ]]></literal>
    <justification jstring="[para(1864(a,1),29(a,1,1,2,1))].">
      <j1 rule="para" parents="1864 29"/>
    </justification>
  </clause>

  <clause id="1963">
    <literal><![CDATA[
      c(c_0 v (c(c(c_0 v c_0) v c(c(c(c_0) v c_0))) v c_0)) = c(c_0 v c_0)
    ]]></literal>
    <justification jstring="[back_demod(1414),demod(1897(3),1897(15),9(16),1897(20))].">
      <j1 rule="back_demod" parents="1414"/>
      <j2 rule="demod" parents="1897 1897 9 1897"/>
    </justification>
  </clause>

  <clause id="1975">
    <literal><![CDATA[
      c(c(c_0 v (c_0 v c_0)) v c(c_0)) = c_0
    ]]></literal>
    <justification jstring="[back_demod(1294),demod(1897(5),1455(11),1897(4),1897(15),1455(21))].">
      <j1 rule="back_demod" parents="1294"/>
      <j2 rule="demod" parents="1897 1455 1897 1897 1455"/>
    </justification>
  </clause>

  <clause id="2022">
    <literal><![CDATA[
      (c(c_0) v c(c(c_0) v ((c(c_0) v c_0) v c_0))) v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[back_demod(1060),demod(1897(18))].">
      <j1 rule="back_demod" parents="1060"/>
      <j2 rule="demod" parents="1897"/>
    </justification>
  </clause>

  <clause id="2058">
    <literal><![CDATA[
      (c_0 v c_0) v (x v c_0) = c_0 v (x v c_0)
    ]]></literal>
    <justification jstring="[back_demod(898),demod(1897(3),1897(16),9(17),56(16))].">
      <j1 rule="back_demod" parents="898"/>
      <j2 rule="demod" parents="1897 1897 9 56"/>
    </justification>
  </clause>

  <clause id="2078">
    <literal><![CDATA[
      c(c(c_0 v (x v c_0)) v c(x v c(c_0))) = x
    ]]></literal>
    <justification jstring="[back_demod(861),demod(1897(3),2058(6))].">
      <j1 rule="back_demod" parents="861"/>
      <j2 rule="demod" parents="1897 2058"/>
    </justification>
  </clause>

  <clause id="2087">
    <literal><![CDATA[
      c(c(x v c((c_0 v c_0) v c(x))) v c(c_0 v c_0)) = x
    ]]></literal>
    <justification jstring="[back_demod(842),demod(1897(3),1897(11))].">
      <j1 rule="back_demod" parents="842"/>
      <j2 rule="demod" parents="1897 1897"/>
    </justification>
  </clause>

  <clause id="2093">
    <literal><![CDATA[
      c(c(c_0) v c(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_demod(605),demod(1897(5),1897(9),1897(20))].">
      <j1 rule="back_demod" parents="605"/>
      <j2 rule="demod" parents="1897 1897 1897"/>
    </justification>
  </clause>

  <clause id="2109">
    <literal><![CDATA[
      c(c(c_0 v (c(x v c(c(x))) v c_0)) v x) = c(x v c(c(x)))
    ]]></literal>
    <justification jstring="[back_demod(66),demod(1897(7),9(8))].">
      <j1 rule="back_demod" parents="66"/>
      <j2 rule="demod" parents="1897 9"/>
    </justification>
  </clause>

  <clause id="3326">
    <literal><![CDATA[
      c(c_0) v c(c(c_0) v c(c_0)) = c_0
    ]]></literal>
    <justification jstring="[para(49(a,1),2078(a,1,1,2,1)),demod(56(12),1975(10)),flip(a)].">
      <j1 rule="para" parents="49 2078"/>
      <j2 rule="demod" parents="56 1975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3335">
    <literal><![CDATA[
      c(c(c_0) v c(x)) v c(c(c_0) v x) = c_0
    ]]></literal>
    <justification jstring="[para(26(a,1),2078(a,1,1,2,1)),demod(141(13),1975(10)),flip(a)].">
      <j1 rule="para" parents="26 2078"/>
      <j2 rule="demod" parents="141 1975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3364">
    <literal><![CDATA[
      c(c_0) v (x v c(c(c_0) v c(c_0))) = x v c_0
    ]]></literal>
    <justification jstring="[para(3326(a,1),9(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3326 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3365">
    <literal><![CDATA[
      (c(c_0) v c(c_0)) v c_0 = c(c_0) v c_0
    ]]></literal>
    <justification jstring="[para(3326(a,1),23(a,1,2))].">
      <j1 rule="para" parents="3326 23"/>
    </justification>
  </clause>

  <clause id="3376">
    <literal><![CDATA[
      (c(c_0) v c(c(c(c_0) v c(c_0)) v (c(c(c_0) v c(c_0)) v c_0))) v c(c(c_0) v c(c_0)) = c_0
    ]]></literal>
    <justification jstring="[para(3326(a,1),169(a,1,1,2,1,2,2))].">
      <j1 rule="para" parents="3326 169"/>
    </justification>
  </clause>

  <clause id="3521">
    <literal><![CDATA[
      c(c(c_0) v c(x)) v c_0 = (c(c_0) v x) v c_0
    ]]></literal>
    <justification jstring="[para(3335(a,1),23(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3335 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3523">
    <literal><![CDATA[
      c(c(c_0) v c(x)) v (y v (z v c(c(c_0) v x))) = y v (z v c_0)
    ]]></literal>
    <justification jstring="[para(3335(a,1),18(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3335 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3579">
    <literal><![CDATA[
      (c(c_0) v c((c(c_0) v c_0) v ((c(c_0) v c_0) v c_0))) v c(c(c_0) v c(c_0)) = c_0
    ]]></literal>
    <justification jstring="[back_demod(3376),demod(3521(16),9(15),3521(14))].">
      <j1 rule="back_demod" parents="3376"/>
      <j2 rule="demod" parents="3521 9 3521"/>
    </justification>
  </clause>

  <clause id="3694">
    <literal><![CDATA[
      (c(c_0) v c(c_0)) v (x v c_0) = c(c_0) v (x v c_0)
    ]]></literal>
    <justification jstring="[para(3364(a,1),27(a,1,2))].">
      <j1 rule="para" parents="3364 27"/>
    </justification>
  </clause>

  <clause id="3705">
    <literal><![CDATA[
      (c(c_0) v c((c(c_0) v c_0) v ((c(c_0) v c_0) v c_0))) v c_0 = c(c_0) v c_0
    ]]></literal>
    <justification jstring="[para(158(a,1),3364(a,1,2)),demod(3364(28),3521(20),9(19),3521(18)),flip(a)].">
      <j1 rule="para" parents="158 3364"/>
      <j2 rule="demod" parents="3364 3521 9 3521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3707">
    <literal><![CDATA[
      x v ((c(c_0) v c(x v ((x v c(c(c_0) v c(c_0))) v ((x v c(c(c_0) v c(c_0))) v c_0)))) v c(c(c_0) v c(c_0))) = c_0
    ]]></literal>
    <justification jstring="[para(3364(a,1),169(a,1,1,2,1,2,2)),demod(9(19),9(20),9(30))].">
      <j1 rule="para" parents="3364 169"/>
      <j2 rule="demod" parents="9 9 9"/>
    </justification>
  </clause>

  <clause id="3983">
    <literal><![CDATA[
      c(c(c_0) v c(c_0)) = c(c_0) v c_0
    ]]></literal>
    <justification jstring="[para(3521(a,1),21(a,1,1,2,1,2)),demod(45(14)),flip(a)].">
      <j1 rule="para" parents="3521 21"/>
      <j2 rule="demod" parents="45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4058">
    <literal><![CDATA[
      x v (c(c_0) v ((c(c_0) v c(x v ((x v (c(c_0) v c_0)) v ((x v (c(c_0) v c_0)) v c_0)))) v c_0)) = c_0
    ]]></literal>
    <justification jstring="[back_demod(3707),demod(3983(8),3983(13),3983(24),9(23))].">
      <j1 rule="back_demod" parents="3707"/>
      <j2 rule="demod" parents="3983 3983 3983 9"/>
    </justification>
  </clause>

  <clause id="4071">
    <literal><![CDATA[
      c(c_0) v (c(c_0) v c_0) = c_0
    ]]></literal>
    <justification jstring="[back_demod(3579),demod(3983(21),9(20),3705(19))].">
      <j1 rule="back_demod" parents="3579"/>
      <j2 rule="demod" parents="3983 9 3705"/>
    </justification>
  </clause>

  <clause id="4107">
    <literal><![CDATA[
      c(c_0) v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(4071(a,1),50(a,1,2)),demod(9(11),2022(15)),flip(a)].">
      <j1 rule="para" parents="4071 50"/>
      <j2 rule="demod" parents="9 2022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4108">
    <literal><![CDATA[
      c_0 v (c_0 v c_0) = c_0
    ]]></literal>
    <justification jstring="[para(50(a,2),4071(a,1,2)),demod(9(11),49(10),4107(6),9(6),4107(5))].">
      <j1 rule="para" parents="50 4071"/>
      <j2 rule="demod" parents="9 49 4107 9 4107"/>
    </justification>
  </clause>

  <clause id="4109">
    <literal><![CDATA[
      c(c_0) v (x v (c(c_0) v (y v c_0))) = x v (y v c_0)
    ]]></literal>
    <justification jstring="[para(4071(a,1),30(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4071 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4117">
    <literal><![CDATA[
      x v (c(c_0) v ((c(c_0) v c(x v ((x v (c_0 v c_0)) v ((x v (c_0 v c_0)) v c_0)))) v c_0)) = c_0
    ]]></literal>
    <justification jstring="[back_demod(4058),demod(4107(8),4107(12))].">
      <j1 rule="back_demod" parents="4058"/>
      <j2 rule="demod" parents="4107 4107"/>
    </justification>
  </clause>

  <clause id="4148">
    <literal><![CDATA[
      (c(c_0) v c(c_0)) v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[back_demod(3365),demod(4107(11))].">
      <j1 rule="back_demod" parents="3365"/>
      <j2 rule="demod" parents="4107"/>
    </justification>
  </clause>

  <clause id="4208">
    <literal><![CDATA[
      c(c_0 v c_0) = c(c_0)
    ]]></literal>
    <justification jstring="[back_demod(1963),demod(4107(9),13(11),4107(5),4108(5)),flip(a)].">
      <j1 rule="back_demod" parents="1963"/>
      <j2 rule="demod" parents="4107 13 4107 4108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4225">
    <literal><![CDATA[
      c(c_0) v (x v c_0) = x v c_0
    ]]></literal>
    <justification jstring="[back_demod(1898),demod(4107(5),4208(5),13(4),3694(8))].">
      <j1 rule="back_demod" parents="1898"/>
      <j2 rule="demod" parents="4107 4208 13 3694"/>
    </justification>
  </clause>

  <clause id="4228">
    <literal><![CDATA[
      c_0 v c_0 = c_0
    ]]></literal>
    <justification jstring="[back_demod(1893),demod(4107(5),4208(5),13(4),4148(7))].">
      <j1 rule="back_demod" parents="1893"/>
      <j2 rule="demod" parents="4107 4208 13 4148"/>
    </justification>
  </clause>

  <clause id="4231">
    <literal><![CDATA[
      c_0 v (x v c_0) = x v c_0
    ]]></literal>
    <justification jstring="[back_demod(1887),demod(4107(5),4228(4))].">
      <j1 rule="back_demod" parents="1887"/>
      <j2 rule="demod" parents="4107 4228"/>
    </justification>
  </clause>

  <clause id="4254">
    <literal><![CDATA[
      c(c(x v c(c_0 v c(x))) v c(c_0)) = x
    ]]></literal>
    <justification jstring="[back_demod(2087),demod(4228(3),4228(9))].">
      <j1 rule="back_demod" parents="2087"/>
      <j2 rule="demod" parents="4228 4228"/>
    </justification>
  </clause>

  <clause id="4264">
    <literal><![CDATA[
      x v ((c(c_0) v c(x v ((x v c_0) v ((x v c_0) v c_0)))) v c_0) = c_0
    ]]></literal>
    <justification jstring="[back_demod(4117),demod(4228(7),4228(9),4225(17))].">
      <j1 rule="back_demod" parents="4117"/>
      <j2 rule="demod" parents="4228 4228 4225"/>
    </justification>
  </clause>

  <clause id="4267">
    <literal><![CDATA[
      c(c_0) v (x v (y v c_0)) = x v (y v c_0)
    ]]></literal>
    <justification jstring="[back_demod(4109),demod(4225(7))].">
      <j1 rule="back_demod" parents="4109"/>
      <j2 rule="demod" parents="4225"/>
    </justification>
  </clause>

  <clause id="4284">
    <literal><![CDATA[
      c(c_0) v c_0 = c_0
    ]]></literal>
    <justification jstring="[back_demod(4107),demod(4228(7))].">
      <j1 rule="back_demod" parents="4107"/>
      <j2 rule="demod" parents="4228"/>
    </justification>
  </clause>

  <clause id="4350">
    <literal><![CDATA[
      c(c(c_0) v c(x v ((x v c_0) v ((x v c_0) v c_0)))) = x v c_0
    ]]></literal>
    <justification jstring="[back_demod(2093),demod(4228(5),4228(7),4228(16))].">
      <j1 rule="back_demod" parents="2093"/>
      <j2 rule="demod" parents="4228 4228 4228"/>
    </justification>
  </clause>

  <clause id="4362">
    <literal><![CDATA[
      c(c(c_0)) = c_0
    ]]></literal>
    <justification jstring="[back_demod(1897),demod(4228(6))].">
      <j1 rule="back_demod" parents="1897"/>
      <j2 rule="demod" parents="4228"/>
    </justification>
  </clause>

  <clause id="4367">
    <literal><![CDATA[
      c(c(c(x v c(c(x))) v c_0) v x) = c(x v c(c(x)))
    ]]></literal>
    <justification jstring="[back_demod(2109),demod(4231(8))].">
      <j1 rule="back_demod" parents="2109"/>
      <j2 rule="demod" parents="4231"/>
    </justification>
  </clause>

  <clause id="4719">
    <literal><![CDATA[
      x v ((x v c_0) v c_0) = x v c_0
    ]]></literal>
    <justification jstring="[para(680(a,1),51(a,1,1,2,1,2,2)),demod(9(11),4267(12),9(10),4350(13),9(9),4267(10)),flip(a)].">
      <j1 rule="para" parents="680 51"/>
      <j2 rule="demod" parents="9 4267 9 4350 9 4267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4749">
    <literal><![CDATA[
      c(c(c_0) v c(x v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[para(3335(a,1),51(a,1,1,2,1,2,2,1,2)),demod(3523(16),4719(7),3335(17))].">
      <j1 rule="para" parents="3335 51"/>
      <j2 rule="demod" parents="3523 4719 3335"/>
    </justification>
  </clause>

  <clause id="4768">
    <literal><![CDATA[
      x v (y v ((x v c_0) v c_0)) = y v (x v c_0)
    ]]></literal>
    <justification jstring="[para(4719(a,1),9(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4719 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4804">
    <literal><![CDATA[
      x v ((c(c_0) v c(x v c_0)) v c_0) = c_0
    ]]></literal>
    <justification jstring="[back_demod(4264),demod(4768(10),9(7),4719(7))].">
      <j1 rule="back_demod" parents="4264"/>
      <j2 rule="demod" parents="4768 9 4719"/>
    </justification>
  </clause>

  <clause id="4820">
    <literal><![CDATA[
      c(c(x v c_0) v c(c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[para(4749(a,1),28(a,1,1,1,1,2)),demod(9(5),4719(5),4284(7))].">
      <j1 rule="para" parents="4749 28"/>
      <j2 rule="demod" parents="9 4719 4284"/>
    </justification>
  </clause>

  <clause id="4833">
    <literal><![CDATA[
      c(c(x v (y v c_0)) v c(c(y v c_0) v (x v c(c_0)))) = x
    ]]></literal>
    <justification jstring="[para(4820(a,1),19(a,1,1,1,1,2))].">
      <j1 rule="para" parents="4820 19"/>
    </justification>
  </clause>

  <clause id="4843">
    <literal><![CDATA[
      c(c(x v c_0) v c((x v c_0) v (c(x v c_0) v c_0))) = x v c_0
    ]]></literal>
    <justification jstring="[para(4820(a,1),21(a,1,1,2,1,2,1)),demod(9(11),4820(21))].">
      <j1 rule="para" parents="4820 21"/>
      <j2 rule="demod" parents="9 4820"/>
    </justification>
  </clause>

  <clause id="4851">
    <literal><![CDATA[
      c(c(x v c_0) v c(c(x v c_0) v c_0)) = c_0
    ]]></literal>
    <justification jstring="[para(4820(a,1),28(a,1,1,1,1,2)),demod(4231(4))].">
      <j1 rule="para" parents="4820 28"/>
      <j2 rule="demod" parents="4231"/>
    </justification>
  </clause>

  <clause id="4859">
    <literal><![CDATA[
      x v (y v ((c(c_0) v c(x v c_0)) v c_0)) = y v c_0
    ]]></literal>
    <justification jstring="[para(4804(a,1),9(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4804 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5006">
    <literal><![CDATA[
      c(x v c(c(x v c(c_0 v c(x))) v c_0)) = c(x v c(c_0 v c(x)))
    ]]></literal>
    <justification jstring="[para(4254(a,1),12(a,1,1,1))].">
      <j1 rule="para" parents="4254 12"/>
    </justification>
  </clause>

  <clause id="5007">
    <literal><![CDATA[
      c(c(c(x v c(c_0 v c(x))) v c_0) v x) = c(x v c(c_0 v c(x)))
    ]]></literal>
    <justification jstring="[para(4254(a,1),12(a,1,1,2)),demod(4362(9))].">
      <j1 rule="para" parents="4254 12"/>
      <j2 rule="demod" parents="4362"/>
    </justification>
  </clause>

  <clause id="5250">
    <literal><![CDATA[
      (x v c_0) v c_0 = c_0
    ]]></literal>
    <justification jstring="[para(4719(a,1),53(a,1,2,1,2,1,2,1)),demod(4768(10),9(7),4719(7),9(11),4859(12))].">
      <j1 rule="para" parents="4719 53"/>
      <j2 rule="demod" parents="4768 9 4719 9 4859"/>
    </justification>
  </clause>

  <clause id="5268">
    <literal><![CDATA[
      (x v c_0) v (y v c_0) = y v c_0
    ]]></literal>
    <justification jstring="[para(5250(a,1),9(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5250 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5285">
    <literal><![CDATA[
      x v c_0 = c_0
    ]]></literal>
    <justification jstring="[back_demod(4843),demod(5268(11),4851(11)),flip(a)].">
      <j1 rule="back_demod" parents="4843"/>
      <j2 rule="demod" parents="5268 4851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5408">
    <literal><![CDATA[
      c(x v c(c_0 v c(x))) = c(c(c_0) v x)
    ]]></literal>
    <justification jstring="[back_demod(5007),demod(5285(8)),flip(a)].">
      <j1 rule="back_demod" parents="5007"/>
      <j2 rule="demod" parents="5285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5409">
    <literal><![CDATA[
      c(c(c_0) v x) = c(x v c(c_0))
    ]]></literal>
    <justification jstring="[back_demod(5006),demod(5408(6),5285(6),5408(10)),flip(a)].">
      <j1 rule="back_demod" parents="5006"/>
      <j2 rule="demod" parents="5408 5285 5408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5443">
    <literal><![CDATA[
      c(c(c_0) v c(c(c_0) v (x v c(c_0)))) = x
    ]]></literal>
    <justification jstring="[back_demod(4833),demod(5285(2),5285(2),5285(4))].">
      <j1 rule="back_demod" parents="4833"/>
      <j2 rule="demod" parents="5285 5285 5285"/>
    </justification>
  </clause>

  <clause id="5525">
    <literal><![CDATA[
      c(x v c(c(x))) = c(c(c_0) v x)
    ]]></literal>
    <justification jstring="[back_demod(4367),demod(5285(6)),flip(a)].">
      <j1 rule="back_demod" parents="4367"/>
      <j2 rule="demod" parents="5285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5860">
    <literal><![CDATA[
      c(x v c(y v (z v (u v c(x))))) = c(c(c_0) v x)
    ]]></literal>
    <justification jstring="[back_demod(1710),demod(5285(9),5285(9),5285(9),4362(10),5285(9)),flip(a)].">
      <j1 rule="back_demod" parents="1710"/>
      <j2 rule="demod" parents="5285 5285 5285 4362 5285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5923">
    <literal><![CDATA[
      c(c(x v c(c_0)) v c(y v ((c(c(c_0) v z) v c(c_0)) v (x v z)))) = x
    ]]></literal>
    <justification jstring="[back_demod(1477),demod(5285(2),5525(8))].">
      <j1 rule="back_demod" parents="1477"/>
      <j2 rule="demod" parents="5285 5525"/>
    </justification>
  </clause>

  <clause id="5936">
    <literal><![CDATA[
      c(c(c_0) v c(c(c_0) v x)) = x
    ]]></literal>
    <justification jstring="[back_demod(1333),demod(5860(7),5285(6),5285(6),5285(6),5409(8,R))].">
      <j1 rule="back_demod" parents="1333"/>
      <j2 rule="demod" parents="5860 5285 5285 5285 5409"/>
    </justification>
  </clause>

  <clause id="5995">
    <literal><![CDATA[
      (c(x v c(y v c(x v (c(c_0) v x)))) v c(c_0)) v (z v x) = c_0
    ]]></literal>
    <justification jstring="[back_demod(808),demod(5285(11),5285(16))].">
      <j1 rule="back_demod" parents="808"/>
      <j2 rule="demod" parents="5285 5285"/>
    </justification>
  </clause>

  <clause id="5997">
    <literal><![CDATA[
      c(x v c(y v c(x v (c(c_0) v x)))) = c(c(c_0) v x)
    ]]></literal>
    <justification jstring="[back_demod(805),demod(5285(11),4362(12),5285(11)),flip(a)].">
      <j1 rule="back_demod" parents="805"/>
      <j2 rule="demod" parents="5285 4362 5285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6292">
    <literal><![CDATA[
      x v c(c_0) = x
    ]]></literal>
    <justification jstring="[back_demod(5443),demod(5936(11))].">
      <j1 rule="back_demod" parents="5443"/>
      <j2 rule="demod" parents="5936"/>
    </justification>
  </clause>

  <clause id="6322">
    <literal><![CDATA[
      c(c(c_0) v x) v (y v x) = c_0
    ]]></literal>
    <justification jstring="[back_demod(5995),demod(5997(9),6292(7))].">
      <j1 rule="back_demod" parents="5995"/>
      <j2 rule="demod" parents="5997 6292"/>
    </justification>
  </clause>

  <clause id="6324">
    <literal><![CDATA[
      c(c(x)) = x
    ]]></literal>
    <justification jstring="[back_demod(5923),demod(6292(3),6292(8),6322(7),5285(3),6292(4))].">
      <j1 rule="back_demod" parents="5923"/>
      <j2 rule="demod" parents="6292 6292 6322 5285 6292"/>
    </justification>
  </clause>

  <clause id="6325">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer(CC)
    ]]></attribute>
    <justification jstring="[resolve(6324,a,14,a)].">
      <j1 rule="resolve" parents="6324 14"/>
    </justification>
  </clause>

</proof>

<proof number="2" length="168" max_count="86">

<comments><![CDATA[
% Proof 2 at 1.51 (+ 0.01) seconds: B1.
% Length of proof is 168.
% Level of proof is 44.
% Maximum clause weight is 86.
% Given clauses 122.
]]></comments>

  <clause id="3">
    <literal><![CDATA[
      x v c(x) = y v c(y)
    ]]></literal>
    <attribute><![CDATA[
      label(ONE)
    ]]></attribute>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="4">
    <literal><![CDATA[
      (x v c(y)) ^ (x v y) = x
    ]]></literal>
    <attribute><![CDATA[
      label(CUT)
    ]]></attribute>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="6">
    <literal><![CDATA[
      c2 v (c2 ^ c3) != c2
    ]]></literal>
    <attribute><![CDATA[
      answer(B1)
    ]]></attribute>
    <justification jstring="[clausify].">
      <j1 rule="clausify"/>
    </justification>
  </clause>

  <clause id="9">
    <literal><![CDATA[
      x v (y v z) = y v (x v z)
    ]]></literal>
    <attribute><![CDATA[
      label(AJ)
    ]]></attribute>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="10">
    <literal><![CDATA[
      x ^ y = c(c(x) v c(y))
    ]]></literal>
    <attribute><![CDATA[
      label(DM)
    ]]></attribute>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="11">
    <literal><![CDATA[
      x v c(x) = y v c(y)
    ]]></literal>
    <attribute><![CDATA[
      label(ONE)
    ]]></attribute>
    <justification jstring="[copy(3)].">
      <j1 rule="copy" parents="3"/>
    </justification>
  </clause>

  <clause id="12">
    <literal><![CDATA[
      c(c(x v c(y)) v c(x v y)) = x
    ]]></literal>
    <attribute><![CDATA[
      label(CUT)
    ]]></attribute>
    <justification jstring="[copy(4),demod(10(4))].">
      <j1 rule="copy" parents="4"/>
      <j2 rule="demod" parents="10"/>
    </justification>
  </clause>

  <clause id="13">
    <literal><![CDATA[
      x v c(x) = c_0
    ]]></literal>
    <justification jstring="[new_symbol(11)].">
      <j1 rule="new_symbol" parents="11"/>
    </justification>
  </clause>

  <clause id="15">
    <literal><![CDATA[
      c2 v c(c(c2) v c(c3)) != c2
    ]]></literal>
    <attribute><![CDATA[
      answer(B1)
    ]]></attribute>
    <justification jstring="[copy(6),demod(10(4))].">
      <j1 rule="copy" parents="6"/>
      <j2 rule="demod" parents="10"/>
    </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(9(a,1),9(a,1,2))].">
      <j1 rule="para" parents="9 9"/>
    </justification>
  </clause>

  <clause id="19">
    <literal><![CDATA[
      c(c(x v c(y v z)) v c(y v (x v z))) = x
    ]]></literal>
    <justification jstring="[para(9(a,1),12(a,1,1,2,1))].">
      <j1 rule="para" parents="9 12"/>
    </justification>
  </clause>

  <clause id="20">
    <literal><![CDATA[
      c(c(x v y) v c(x v (c(y v c(z)) v c(y v z)))) = x
    ]]></literal>
    <justification jstring="[para(12(a,1),12(a,1,1,1,1,2))].">
      <j1 rule="para" parents="12 12"/>
    </justification>
  </clause>

  <clause id="21">
    <literal><![CDATA[
      c(x v c(x v (c(x v c(y)) v y))) = c(x v c(y))
    ]]></literal>
    <justification jstring="[para(12(a,1),12(a,1,1,1)),demod(9(5))].">
      <j1 rule="para" parents="12 12"/>
      <j2 rule="demod" parents="9"/>
    </justification>
  </clause>

  <clause id="22">
    <literal><![CDATA[
      c(c(c(x v c(y)) v c(c(x v y))) v x) = c(x v c(y))
    ]]></literal>
    <justification jstring="[para(12(a,1),12(a,1,1,2))].">
      <j1 rule="para" parents="12 12"/>
    </justification>
  </clause>

  <clause id="23">
    <literal><![CDATA[
      x v (y v c(x)) = y v c_0
    ]]></literal>
    <justification jstring="[para(13(a,1),9(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24">
    <literal><![CDATA[
      c(c(c_0) v c(x v x)) = x
    ]]></literal>
    <justification jstring="[para(13(a,1),12(a,1,1,1,1))].">
      <j1 rule="para" parents="13 12"/>
    </justification>
  </clause>

  <clause id="25">
    <literal><![CDATA[
      c(c(x v c(c(x))) v c(c_0)) = x
    ]]></literal>
    <justification jstring="[para(13(a,1),12(a,1,1,2,1))].">
      <j1 rule="para" parents="13 12"/>
    </justification>
  </clause>

  <clause id="26">
    <literal><![CDATA[
      (c(x v c(y)) v c(x v y)) v x = c_0
    ]]></literal>
    <justification jstring="[para(12(a,1),13(a,1,2))].">
      <j1 rule="para" parents="12 13"/>
    </justification>
  </clause>

  <clause id="27">
    <literal><![CDATA[
      x v (y v (z v c(x))) = y v (z v c_0)
    ]]></literal>
    <justification jstring="[para(23(a,1),9(a,1,2)),flip(a)].">
      <j1 rule="para" parents="23 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28">
    <literal><![CDATA[
      c(c(x v c(y v c(x))) v c(y v c_0)) = x
    ]]></literal>
    <justification jstring="[para(23(a,1),12(a,1,1,2,1))].">
      <j1 rule="para" parents="23 12"/>
    </justification>
  </clause>

  <clause id="29">
    <literal><![CDATA[
      (c(x v c(y)) v c(x v y)) v (z v x) = z v c_0
    ]]></literal>
    <justification jstring="[para(12(a,1),23(a,1,2,2))].">
      <j1 rule="para" parents="12 23"/>
    </justification>
  </clause>

  <clause id="30">
    <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),9(a,1,2))].">
      <j1 rule="para" parents="18 9"/>
    </justification>
  </clause>

  <clause id="34">
    <literal><![CDATA[
      c(c(x v c(y v (z v u))) v c(z v (x v (y v u)))) = x
    ]]></literal>
    <justification jstring="[para(18(a,1),12(a,1,1,2,1))].">
      <j1 rule="para" parents="18 12"/>
    </justification>
  </clause>

  <clause id="35">
    <literal><![CDATA[
      c(c(x v c(y v (z v u))) v c(y v (z v (x v u)))) = x
    ]]></literal>
    <justification jstring="[para(18(a,2),12(a,1,1,2,1))].">
      <j1 rule="para" parents="18 12"/>
    </justification>
  </clause>

  <clause id="36">
    <literal><![CDATA[
      x v (y v (z v (u v c(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(c(c_0) v c(x v ((x v y) v y))) = x v y
    ]]></literal>
    <justification jstring="[para(9(a,1),24(a,1,1,2,1))].">
      <j1 rule="para" parents="9 24"/>
    </justification>
  </clause>

  <clause id="47">
    <literal><![CDATA[
      c(x v c(c(c_0) v (x v x))) = c(c_0)
    ]]></literal>
    <justification jstring="[para(24(a,1),12(a,1,1,1))].">
      <j1 rule="para" parents="24 12"/>
    </justification>
  </clause>

  <clause id="48">
    <literal><![CDATA[
      c(c(c(c_0) v c(c(x v x))) v x) = c(c_0)
    ]]></literal>
    <justification jstring="[para(24(a,1),12(a,1,1,2))].">
      <j1 rule="para" parents="24 12"/>
    </justification>
  </clause>

  <clause id="49">
    <literal><![CDATA[
      (c(c_0) v c(x v x)) v x = c_0
    ]]></literal>
    <justification jstring="[para(24(a,1),13(a,1,2))].">
      <j1 rule="para" parents="24 13"/>
    </justification>
  </clause>

  <clause id="50">
    <literal><![CDATA[
      (c(c_0) v c(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="51">
    <literal><![CDATA[
      c(c(c_0) v c(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)),demod(9(6))].">
      <j1 rule="para" parents="18 24"/>
      <j2 rule="demod" parents="9"/>
    </justification>
  </clause>

  <clause id="53">
    <literal><![CDATA[
      x v ((c(c_0) v c(x v ((x v y) v y))) v y) = c_0
    ]]></literal>
    <justification jstring="[para(49(a,1),9(a,1)),demod(9(6)),flip(a)].">
      <j1 rule="para" parents="49 9"/>
      <j2 rule="demod" parents="9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="56">
    <literal><![CDATA[
      (c(c_0) v c(c(x) v c(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[
      c(x v c(c(x v c(c(x))) v c_0)) = c(x v c(c(x)))
    ]]></literal>
    <justification jstring="[para(25(a,1),12(a,1,1,1))].">
      <j1 rule="para" parents="25 12"/>
    </justification>
  </clause>

  <clause id="66">
    <literal><![CDATA[
      c(c(c(x v c(c(x))) v c(c(c_0))) v x) = c(x v c(c(x)))
    ]]></literal>
    <justification jstring="[para(25(a,1),12(a,1,1,2))].">
      <j1 rule="para" parents="25 12"/>
    </justification>
  </clause>

  <clause id="68">
    <literal><![CDATA[
      (c(x v c(c(x))) v c(c_0)) v x = c_0
    ]]></literal>
    <justification jstring="[para(25(a,1),13(a,1,2))].">
      <j1 rule="para" parents="25 13"/>
    </justification>
  </clause>

  <clause id="72">
    <literal><![CDATA[
      c(x v c(x v (c(c_0) v x))) = c(c_0)
    ]]></literal>
    <justification jstring="[para(9(a,1),47(a,1,1,2,1))].">
      <j1 rule="para" parents="9 47"/>
    </justification>
  </clause>

  <clause id="74">
    <literal><![CDATA[
      c(c(c_0) v c(x v (c(c_0) v (x v x)))) = x
    ]]></literal>
    <justification jstring="[para(47(a,1),12(a,1,1,1))].">
      <j1 rule="para" parents="47 12"/>
    </justification>
  </clause>

  <clause id="76">
    <literal><![CDATA[
      (x v c(c(c_0) v (x v x))) v c(c_0) = c_0
    ]]></literal>
    <justification jstring="[para(47(a,1),13(a,1,2))].">
      <j1 rule="para" parents="47 13"/>
    </justification>
  </clause>

  <clause id="105">
    <literal><![CDATA[
      c(c(c_0) v c(c(c_0) v (x v (x v x)))) = x
    ]]></literal>
    <justification jstring="[para(47(a,1),19(a,1,1,1))].">
      <j1 rule="para" parents="47 19"/>
    </justification>
  </clause>

  <clause id="126">
    <literal><![CDATA[
      c(c(c_0) v c(x v (x v (c(c_0) v x)))) = x
    ]]></literal>
    <justification jstring="[para(72(a,1),12(a,1,1,1))].">
      <j1 rule="para" parents="72 12"/>
    </justification>
  </clause>

  <clause id="141">
    <literal><![CDATA[
      (c(c(x) v c(y)) v c(c(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(c(c_0) v c(c(x v x))) v x) v c(c_0) = c_0
    ]]></literal>
    <justification jstring="[para(24(a,1),26(a,1,1,2))].">
      <j1 rule="para" parents="24 26"/>
    </justification>
  </clause>

  <clause id="158">
    <literal><![CDATA[
      (c(c_0) v c(x v (c(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(c_0) v c(x v (x v (c(c_0) v x)))) v x = c_0
    ]]></literal>
    <justification jstring="[para(72(a,1),26(a,1,1,1))].">
      <j1 rule="para" parents="72 26"/>
    </justification>
  </clause>

  <clause id="243">
    <literal><![CDATA[
      c(c(c_0) v c((x v c(c(c_0) v (x v x))) v c_0)) = x v c(c(c_0) v (x v x))
    ]]></literal>
    <justification jstring="[para(76(a,1),12(a,1,1,1,1))].">
      <j1 rule="para" parents="76 12"/>
    </justification>
  </clause>

  <clause id="244">
    <literal><![CDATA[
      (x v c(c(c_0) v (x v x))) v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(76(a,1),23(a,1,2)),flip(a)].">
      <j1 rule="para" parents="76 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="256">
    <literal><![CDATA[
      x v c(c(c_0) v (x v x)) = c_0
    ]]></literal>
    <justification jstring="[back_demod(243),demod(244(10),24(8)),flip(a)].">
      <j1 rule="back_demod" parents="243"/>
      <j2 rule="demod" parents="244 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="258">
    <literal><![CDATA[
      x v (y v c(c(c_0) v (x v x))) = y v c_0
    ]]></literal>
    <justification jstring="[para(256(a,1),9(a,1,2)),flip(a)].">
      <j1 rule="para" parents="256 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="260">
    <literal><![CDATA[
      x v c(x v (c(c_0) v x)) = c_0
    ]]></literal>
    <justification jstring="[para(9(a,1),256(a,1,2,1))].">
      <j1 rule="para" parents="9 256"/>
    </justification>
  </clause>

  <clause id="261">
    <literal><![CDATA[
      (c(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="262">
    <literal><![CDATA[
      c(c(c_0)) v c(c(c(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="273">
    <literal><![CDATA[
      x v (y v c(x v (c(c_0) v x))) = y v c_0
    ]]></literal>
    <justification jstring="[para(260(a,1),9(a,1,2)),flip(a)].">
      <j1 rule="para" parents="260 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="284">
    <literal><![CDATA[
      (c(c(c_0)) v c_0) v c_0 = c(c(c_0)) v c_0
    ]]></literal>
    <justification jstring="[para(23(a,1),261(a,1,1))].">
      <j1 rule="para" parents="23 261"/>
    </justification>
  </clause>

  <clause id="330">
    <literal><![CDATA[
      c(c(c_0) v c(c(c(c_0)) v (c(c(c_0)) v c_0))) = c(c(c_0))
    ]]></literal>
    <justification jstring="[para(262(a,1),12(a,1,1,1,1))].">
      <j1 rule="para" parents="262 12"/>
    </justification>
  </clause>

  <clause id="336">
    <literal><![CDATA[
      (c(c(c_0)) v c_0) v (x v c_0) = x v (c(c(c_0)) v c_0)
    ]]></literal>
    <justification jstring="[para(262(a,1),27(a,1,2,2))].">
      <j1 rule="para" parents="262 27"/>
    </justification>
  </clause>

  <clause id="526">
    <literal><![CDATA[
      c(c(c(x v c(c_0)) v c(c((c(c_0) v c(y v y)) v (x v y)))) v x) = c(x v c(c_0))
    ]]></literal>
    <justification jstring="[para(50(a,2),22(a,1,1,1,1,2,1,1))].">
      <j1 rule="para" parents="50 22"/>
    </justification>
  </clause>

  <clause id="547">
    <literal><![CDATA[
      (c(c(c_0) v c(c(x v x))) v x) v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(48(a,1),56(a,1,1,2,1,1)),demod(48(13),56(11)),flip(a)].">
      <j1 rule="para" parents="48 56"/>
      <j2 rule="demod" parents="48 56"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="576">
    <literal><![CDATA[
      c(c(x v c((c(c(c_0)) v c_0) v c(x))) v c(c(c(c_0)) v c_0)) = x
    ]]></literal>
    <justification jstring="[para(284(a,1),28(a,1,1,2,1))].">
      <j1 rule="para" parents="284 28"/>
    </justification>
  </clause>

  <clause id="581">
    <literal><![CDATA[
      c(c(x v c(c(x) v c(y))) v c(c(c(c(x) v c(y)) v c(c(c(x) v y))) v c_0)) = x
    ]]></literal>
    <justification jstring="[para(22(a,1),28(a,1,1,1,1,2))].">
      <j1 rule="para" parents="22 28"/>
    </justification>
  </clause>

  <clause id="605">
    <literal><![CDATA[
      c(c(c_0) v c(x v ((x v c(c(c_0))) v ((x v c(c(c_0))) v c_0)))) = x v c(c(c_0))
    ]]></literal>
    <justification jstring="[para(27(a,1),74(a,1,1,2,1,2)),demod(9(13),9(14))].">
      <j1 rule="para" parents="27 74"/>
      <j2 rule="demod" parents="9 9"/>
    </justification>
  </clause>

  <clause id="618">
    <literal><![CDATA[
      c(c(c_0) v c(c(c_0) v (x v ((x v y) v ((x v y) v y))))) = x v y
    ]]></literal>
    <justification jstring="[para(9(a,1),105(a,1,1,2,1,2,2)),demod(9(9))].">
      <j1 rule="para" parents="9 105"/>
      <j2 rule="demod" parents="9"/>
    </justification>
  </clause>

  <clause id="680">
    <literal><![CDATA[
      (c(c_0) v (x v x)) v (y v c_0) = x v (y v c_0)
    ]]></literal>
    <justification jstring="[para(258(a,1),27(a,1,2))].">
      <j1 rule="para" parents="258 27"/>
    </justification>
  </clause>

  <clause id="805">
    <literal><![CDATA[
      c(c(c(x v c(y v c(x v (c(c_0) v x)))) v c(c(y v c_0))) v x) = c(x v c(y v c(x v (c(c_0) v x))))
    ]]></literal>
    <justification jstring="[para(273(a,1),22(a,1,1,1,1,2,1,1))].">
      <j1 rule="para" parents="273 22"/>
    </justification>
  </clause>

  <clause id="808">
    <literal><![CDATA[
      (c(x v c(y v c(x v (c(c_0) v x)))) v c(y v c_0)) v (z v x) = z v c_0
    ]]></literal>
    <justification jstring="[para(273(a,1),29(a,1,1,2,1))].">
      <j1 rule="para" parents="273 29"/>
    </justification>
  </clause>

  <clause id="817">
    <literal><![CDATA[
      c(c(c_0) v c(c(c(c_0)))) v c(c_0) = c(c(c_0) v c(c(c(c_0))))
    ]]></literal>
    <justification jstring="[para(68(a,1),45(a,1,1,2,1,2)),demod(65(15)),flip(a)].">
      <j1 rule="para" parents="68 45"/>
      <j2 rule="demod" parents="65"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="825">
    <literal><![CDATA[
      c(c(c_0)) v c_0 = c(c(c_0))
    ]]></literal>
    <justification jstring="[para(284(a,1),45(a,1,1,2,1,2,1)),demod(284(14),9(13),284(12),330(14),284(10)),flip(a)].">
      <j1 rule="para" parents="284 45"/>
      <j2 rule="demod" parents="284 9 284 330 284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="842">
    <literal><![CDATA[
      c(c(x v c(c(c(c_0)) v c(x))) v c(c(c(c_0)))) = x
    ]]></literal>
    <justification jstring="[back_demod(576),demod(825(5),825(13))].">
      <j1 rule="back_demod" parents="576"/>
      <j2 rule="demod" parents="825 825"/>
    </justification>
  </clause>

  <clause id="855">
    <literal><![CDATA[
      c(c(c_0)) v (x v c_0) = x v c(c(c_0))
    ]]></literal>
    <justification jstring="[back_demod(336),demod(825(5),825(11))].">
      <j1 rule="back_demod" parents="336"/>
      <j2 rule="demod" parents="825 825"/>
    </justification>
  </clause>

  <clause id="858">
    <literal><![CDATA[
      (c(c_0) v c(c_0 v c_0)) v c(c(c_0)) = c(c(c_0))
    ]]></literal>
    <justification jstring="[para(825(a,1),50(a,1,2)),demod(825(16))].">
      <j1 rule="para" parents="825 50"/>
      <j2 rule="demod" parents="825"/>
    </justification>
  </clause>

  <clause id="861">
    <literal><![CDATA[
      c(c(c(c(c_0)) v (x v c_0)) v c(x v c(c_0))) = x
    ]]></literal>
    <justification jstring="[para(855(a,2),12(a,1,1,1,1))].">
      <j1 rule="para" parents="855 12"/>
    </justification>
  </clause>

  <clause id="862">
    <literal><![CDATA[
      c(c_0) v (c(c(c_0)) v (x v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[para(855(a,2),23(a,1,2))].">
      <j1 rule="para" parents="855 23"/>
    </justification>
  </clause>

  <clause id="898">
    <literal><![CDATA[
      c(c(c_0)) v (x v c_0) = (c(c_0) v c(c(x) v c(x))) v c(c(c_0))
    ]]></literal>
    <justification jstring="[para(56(a,1),855(a,1,2))].">
      <j1 rule="para" parents="56 855"/>
    </justification>
  </clause>

  <clause id="1040">
    <literal><![CDATA[
      c(c(c_0)) v (x v (c(c_0) v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[para(862(a,1),18(a,2))].">
      <j1 rule="para" parents="862 18"/>
    </justification>
  </clause>

  <clause id="1060">
    <literal><![CDATA[
      (c(c_0) v c(c(c_0) v ((c(c_0) v c_0) v c_0))) v c_0 = c(c(c_0))
    ]]></literal>
    <justification jstring="[para(49(a,1),1040(a,1,2)),demod(825(5),9(14)),flip(a)].">
      <j1 rule="para" parents="49 1040"/>
      <j2 rule="demod" parents="825 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1083">
    <literal><![CDATA[
      c(c(c(c_0) v c(c(c(c_0))))) = c(c_0)
    ]]></literal>
    <justification jstring="[para(858(a,1),28(a,1,1,1,1,2,1)),demod(49(17),817(11))].">
      <j1 rule="para" parents="858 28"/>
      <j2 rule="demod" parents="49 817"/>
    </justification>
  </clause>

  <clause id="1087">
    <literal><![CDATA[
      c(c(c_0) v c(c(c(c_0)))) = c_0
    ]]></literal>
    <justification jstring="[para(1083(a,1),13(a,1,2)),demod(817(11))].">
      <j1 rule="para" parents="1083 13"/>
      <j2 rule="demod" parents="817"/>
    </justification>
  </clause>

  <clause id="1234">
    <literal><![CDATA[
      c(c(c(c_0) v c(c(c(c(c_0))))) v c_0) = c(c_0)
    ]]></literal>
    <justification jstring="[para(1087(a,1),12(a,1,1,2))].">
      <j1 rule="para" parents="1087 12"/>
    </justification>
  </clause>

  <clause id="1247">
    <literal><![CDATA[
      c(c(c(c(c_0))) v c(c(c_0) v c_0)) = c(c(c_0))
    ]]></literal>
    <justification jstring="[para(1087(a,1),28(a,1,1,1,1,2)),demod(825(5))].">
      <j1 rule="para" parents="1087 28"/>
      <j2 rule="demod" parents="825"/>
    </justification>
  </clause>

  <clause id="1294">
    <literal><![CDATA[
      c(c((c(c(c_0) v c(c(c(c(c_0))))) v c_0) v c(c(c_0))) v c(c_0)) = c(c(c_0) v c(c(c(c(c_0))))) v c_0
    ]]></literal>
    <justification jstring="[para(1234(a,1),25(a,1,1,1,1,2,1))].">
      <j1 rule="para" parents="1234 25"/>
    </justification>
  </clause>

  <clause id="1333">
    <literal><![CDATA[
      c(c(x v c(y v (z v (u v c(x))))) v c(z v (y v (u v c_0)))) = x
    ]]></literal>
    <justification jstring="[para(27(a,1),34(a,1,1,2,1,2))].">
      <j1 rule="para" parents="27 34"/>
    </justification>
  </clause>

  <clause id="1414">
    <literal><![CDATA[
      c(c(c(c(c(c_0))) v c(c(c(c_0) v c_0))) v c(c(c_0))) = c(c(c(c_0)))
    ]]></literal>
    <justification jstring="[para(1247(a,1),12(a,1,1,2))].">
      <j1 rule="para" parents="1247 12"/>
    </justification>
  </clause>

  <clause id="1455">
    <literal><![CDATA[
      c(c(c_0) v c(c(x v x))) v x = c_0
    ]]></literal>
    <justification jstring="[para(152(a,1),12(a,1,1,1,1)),demod(547(12),24(8)),flip(a)].">
      <j1 rule="para" parents="152 12"/>
      <j2 rule="demod" parents="547 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1477">
    <literal><![CDATA[
      c(c(x v c(y v c_0)) v c(y v ((c(z v c(c(z))) v c(c_0)) v (x v z)))) = x
    ]]></literal>
    <justification jstring="[para(68(a,1),35(a,1,1,1,1,2,1,2))].">
      <j1 rule="para" parents="68 35"/>
    </justification>
  </clause>

  <clause id="1653">
    <literal><![CDATA[
      c(c((c(c_0) v c(c(c_0) v (c(x v c(y)) v ((c(x v c(y)) v c(x v y)) v ((c(x v c(y)) v c(x v y)) v c(x v y)))))) v x) v c(c_0)) = c(c_0) v c(c(c_0) v (c(x v c(y)) v ((c(x v c(y)) v c(x v y)) v ((c(x v c(y)) v c(x v y)) v c(x v y)))))
    ]]></literal>
    <justification jstring="[para(158(a,1),20(a,1,1,2,1)),demod(9(23),9(25),9(24),9(56),9(58),9(57))].">
      <j1 rule="para" parents="158 20"/>
      <j2 rule="demod" parents="9 9 9 9 9 9"/>
    </justification>
  </clause>

  <clause id="1710">
    <literal><![CDATA[
      c(c(c(x v c(y v (z v (u v c(x))))) v c(c(y v (z v (u v c_0))))) v x) = c(x v c(y v (z v (u v c(x)))))
    ]]></literal>
    <justification jstring="[para(36(a,1),22(a,1,1,1,1,2,1,1))].">
      <j1 rule="para" parents="36 22"/>
    </justification>
  </clause>

  <clause id="1864">
    <literal><![CDATA[
      c_0 v (c(c_0) v c_0) = c_0
    ]]></literal>
    <justification jstring="[para(680(a,1),45(a,1,1,2,1,2)),demod(9(10),9(9),126(13),9(7)),flip(a)].">
      <j1 rule="para" parents="680 45"/>
      <j2 rule="demod" parents="9 9 126 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1887">
    <literal><![CDATA[
      c_0 v (x v (c(c_0) v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[para(1864(a,1),9(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1864 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1893">
    <literal><![CDATA[
      (c(c_0 v c(c(c_0) v c_0)) v c(c_0)) v c_0 = c_0
    ]]></literal>
    <justification jstring="[para(1864(a,1),26(a,1,1,2,1))].">
      <j1 rule="para" parents="1864 26"/>
    </justification>
  </clause>

  <clause id="1897">
    <literal><![CDATA[
      c(c(c_0)) = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(1864(a,1),50(a,1,2)),demod(9(11),1060(15))].">
      <j1 rule="para" parents="1864 50"/>
      <j2 rule="demod" parents="9 1060"/>
    </justification>
  </clause>

  <clause id="1898">
    <literal><![CDATA[
      (c(c_0 v c(c(c_0) v c_0)) v c(c_0)) v (x v c_0) = x v c_0
    ]]></literal>
    <justification jstring="[para(1864(a,1),29(a,1,1,2,1))].">
      <j1 rule="para" parents="1864 29"/>
    </justification>
  </clause>

  <clause id="1963">
    <literal><![CDATA[
      c(c_0 v (c(c(c_0 v c_0) v c(c(c(c_0) v c_0))) v c_0)) = c(c_0 v c_0)
    ]]></literal>
    <justification jstring="[back_demod(1414),demod(1897(3),1897(15),9(16),1897(20))].">
      <j1 rule="back_demod" parents="1414"/>
      <j2 rule="demod" parents="1897 1897 9 1897"/>
    </justification>
  </clause>

  <clause id="1975">
    <literal><![CDATA[
      c(c(c_0 v (c_0 v c_0)) v c(c_0)) = c_0
    ]]></literal>
    <justification jstring="[back_demod(1294),demod(1897(5),1455(11),1897(4),1897(15),1455(21))].">
      <j1 rule="back_demod" parents="1294"/>
      <j2 rule="demod" parents="1897 1455 1897 1897 1455"/>
    </justification>
  </clause>

  <clause id="2022">
    <literal><![CDATA[
      (c(c_0) v c(c(c_0) v ((c(c_0) v c_0) v c_0))) v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[back_demod(1060),demod(1897(18))].">
      <j1 rule="back_demod" parents="1060"/>
      <j2 rule="demod" parents="1897"/>
    </justification>
  </clause>

  <clause id="2058">
    <literal><![CDATA[
      (c_0 v c_0) v (x v c_0) = c_0 v (x v c_0)
    ]]></literal>
    <justification jstring="[back_demod(898),demod(1897(3),1897(16),9(17),56(16))].">
      <j1 rule="back_demod" parents="898"/>
      <j2 rule="demod" parents="1897 1897 9 56"/>
    </justification>
  </clause>

  <clause id="2078">
    <literal><![CDATA[
      c(c(c_0 v (x v c_0)) v c(x v c(c_0))) = x
    ]]></literal>
    <justification jstring="[back_demod(861),demod(1897(3),2058(6))].">
      <j1 rule="back_demod" parents="861"/>
      <j2 rule="demod" parents="1897 2058"/>
    </justification>
  </clause>

  <clause id="2087">
    <literal><![CDATA[
      c(c(x v c((c_0 v c_0) v c(x))) v c(c_0 v c_0)) = x
    ]]></literal>
    <justification jstring="[back_demod(842),demod(1897(3),1897(11))].">
      <j1 rule="back_demod" parents="842"/>
      <j2 rule="demod" parents="1897 1897"/>
    </justification>
  </clause>

  <clause id="2093">
    <literal><![CDATA[
      c(c(c_0) v c(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_demod(605),demod(1897(5),1897(9),1897(20))].">
      <j1 rule="back_demod" parents="605"/>
      <j2 rule="demod" parents="1897 1897 1897"/>
    </justification>
  </clause>

  <clause id="2109">
    <literal><![CDATA[
      c(c(c_0 v (c(x v c(c(x))) v c_0)) v x) = c(x v c(c(x)))
    ]]></literal>
    <justification jstring="[back_demod(66),demod(1897(7),9(8))].">
      <j1 rule="back_demod" parents="66"/>
      <j2 rule="demod" parents="1897 9"/>
    </justification>
  </clause>

  <clause id="2380">
    <literal><![CDATA[
      (c(x v (c_0 v c_0)) v c(x v c(c_0))) v x = c_0
    ]]></literal>
    <justification jstring="[para(1897(a,1),26(a,1,1,1,1,2))].">
      <j1 rule="para" parents="1897 26"/>
    </justification>
  </clause>

  <clause id="3326">
    <literal><![CDATA[
      c(c_0) v c(c(c_0) v c(c_0)) = c_0
    ]]></literal>
    <justification jstring="[para(49(a,1),2078(a,1,1,2,1)),demod(56(12),1975(10)),flip(a)].">
      <j1 rule="para" parents="49 2078"/>
      <j2 rule="demod" parents="56 1975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3335">
    <literal><![CDATA[
      c(c(c_0) v c(x)) v c(c(c_0) v x) = c_0
    ]]></literal>
    <justification jstring="[para(26(a,1),2078(a,1,1,2,1)),demod(141(13),1975(10)),flip(a)].">
      <j1 rule="para" parents="26 2078"/>
      <j2 rule="demod" parents="141 1975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3364">
    <literal><![CDATA[
      c(c_0) v (x v c(c(c_0) v c(c_0))) = x v c_0
    ]]></literal>
    <justification jstring="[para(3326(a,1),9(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3326 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3365">
    <literal><![CDATA[
      (c(c_0) v c(c_0)) v c_0 = c(c_0) v c_0
    ]]></literal>
    <justification jstring="[para(3326(a,1),23(a,1,2))].">
      <j1 rule="para" parents="3326 23"/>
    </justification>
  </clause>

  <clause id="3376">
    <literal><![CDATA[
      (c(c_0) v c(c(c(c_0) v c(c_0)) v (c(c(c_0) v c(c_0)) v c_0))) v c(c(c_0) v c(c_0)) = c_0
    ]]></literal>
    <justification jstring="[para(3326(a,1),169(a,1,1,2,1,2,2))].">
      <j1 rule="para" parents="3326 169"/>
    </justification>
  </clause>

  <clause id="3521">
    <literal><![CDATA[
      c(c(c_0) v c(x)) v c_0 = (c(c_0) v x) v c_0
    ]]></literal>
    <justification jstring="[para(3335(a,1),23(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3335 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3523">
    <literal><![CDATA[
      c(c(c_0) v c(x)) v (y v (z v c(c(c_0) v x))) = y v (z v c_0)
    ]]></literal>
    <justification jstring="[para(3335(a,1),18(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3335 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3579">
    <literal><![CDATA[
      (c(c_0) v c((c(c_0) v c_0) v ((c(c_0) v c_0) v c_0))) v c(c(c_0) v c(c_0)) = c_0
    ]]></literal>
    <justification jstring="[back_demod(3376),demod(3521(16),9(15),3521(14))].">
      <j1 rule="back_demod" parents="3376"/>
      <j2 rule="demod" parents="3521 9 3521"/>
    </justification>
  </clause>

  <clause id="3694">
    <literal><![CDATA[
      (c(c_0) v c(c_0)) v (x v c_0) = c(c_0) v (x v c_0)
    ]]></literal>
    <justification jstring="[para(3364(a,1),27(a,1,2))].">
      <j1 rule="para" parents="3364 27"/>
    </justification>
  </clause>

  <clause id="3705">
    <literal><![CDATA[
      (c(c_0) v c((c(c_0) v c_0) v ((c(c_0) v c_0) v c_0))) v c_0 = c(c_0) v c_0
    ]]></literal>
    <justification jstring="[para(158(a,1),3364(a,1,2)),demod(3364(28),3521(20),9(19),3521(18)),flip(a)].">
      <j1 rule="para" parents="158 3364"/>
      <j2 rule="demod" parents="3364 3521 9 3521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3707">
    <literal><![CDATA[
      x v ((c(c_0) v c(x v ((x v c(c(c_0) v c(c_0))) v ((x v c(c(c_0) v c(c_0))) v c_0)))) v c(c(c_0) v c(c_0))) = c_0
    ]]></literal>
    <justification jstring="[para(3364(a,1),169(a,1,1,2,1,2,2)),demod(9(19),9(20),9(30))].">
      <j1 rule="para" parents="3364 169"/>
      <j2 rule="demod" parents="9 9 9"/>
    </justification>
  </clause>

  <clause id="3983">
    <literal><![CDATA[
      c(c(c_0) v c(c_0)) = c(c_0) v c_0
    ]]></literal>
    <justification jstring="[para(3521(a,1),21(a,1,1,2,1,2)),demod(45(14)),flip(a)].">
      <j1 rule="para" parents="3521 21"/>
      <j2 rule="demod" parents="45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4058">
    <literal><![CDATA[
      x v (c(c_0) v ((c(c_0) v c(x v ((x v (c(c_0) v c_0)) v ((x v (c(c_0) v c_0)) v c_0)))) v c_0)) = c_0
    ]]></literal>
    <justification jstring="[back_demod(3707),demod(3983(8),3983(13),3983(24),9(23))].">
      <j1 rule="back_demod" parents="3707"/>
      <j2 rule="demod" parents="3983 3983 3983 9"/>
    </justification>
  </clause>

  <clause id="4071">
    <literal><![CDATA[
      c(c_0) v (c(c_0) v c_0) = c_0
    ]]></literal>
    <justification jstring="[back_demod(3579),demod(3983(21),9(20),3705(19))].">
      <j1 rule="back_demod" parents="3579"/>
      <j2 rule="demod" parents="3983 9 3705"/>
    </justification>
  </clause>

  <clause id="4107">
    <literal><![CDATA[
      c(c_0) v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(4071(a,1),50(a,1,2)),demod(9(11),2022(15)),flip(a)].">
      <j1 rule="para" parents="4071 50"/>
      <j2 rule="demod" parents="9 2022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4108">
    <literal><![CDATA[
      c_0 v (c_0 v c_0) = c_0
    ]]></literal>
    <justification jstring="[para(50(a,2),4071(a,1,2)),demod(9(11),49(10),4107(6),9(6),4107(5))].">
      <j1 rule="para" parents="50 4071"/>
      <j2 rule="demod" parents="9 49 4107 9 4107"/>
    </justification>
  </clause>

  <clause id="4109">
    <literal><![CDATA[
      c(c_0) v (x v (c(c_0) v (y v c_0))) = x v (y v c_0)
    ]]></literal>
    <justification jstring="[para(4071(a,1),30(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4071 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4117">
    <literal><![CDATA[
      x v (c(c_0) v ((c(c_0) v c(x v ((x v (c_0 v c_0)) v ((x v (c_0 v c_0)) v c_0)))) v c_0)) = c_0
    ]]></literal>
    <justification jstring="[back_demod(4058),demod(4107(8),4107(12))].">
      <j1 rule="back_demod" parents="4058"/>
      <j2 rule="demod" parents="4107 4107"/>
    </justification>
  </clause>

  <clause id="4148">
    <literal><![CDATA[
      (c(c_0) v c(c_0)) v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[back_demod(3365),demod(4107(11))].">
      <j1 rule="back_demod" parents="3365"/>
      <j2 rule="demod" parents="4107"/>
    </justification>
  </clause>

  <clause id="4208">
    <literal><![CDATA[
      c(c_0 v c_0) = c(c_0)
    ]]></literal>
    <justification jstring="[back_demod(1963),demod(4107(9),13(11),4107(5),4108(5)),flip(a)].">
      <j1 rule="back_demod" parents="1963"/>
      <j2 rule="demod" parents="4107 13 4107 4108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4225">
    <literal><![CDATA[
      c(c_0) v (x v c_0) = x v c_0
    ]]></literal>
    <justification jstring="[back_demod(1898),demod(4107(5),4208(5),13(4),3694(8))].">
      <j1 rule="back_demod" parents="1898"/>
      <j2 rule="demod" parents="4107 4208 13 3694"/>
    </justification>
  </clause>

  <clause id="4228">
    <literal><![CDATA[
      c_0 v c_0 = c_0
    ]]></literal>
    <justification jstring="[back_demod(1893),demod(4107(5),4208(5),13(4),4148(7))].">
      <j1 rule="back_demod" parents="1893"/>
      <j2 rule="demod" parents="4107 4208 13 4148"/>
    </justification>
  </clause>

  <clause id="4231">
    <literal><![CDATA[
      c_0 v (x v c_0) = x v c_0
    ]]></literal>
    <justification jstring="[back_demod(1887),demod(4107(5),4228(4))].">
      <j1 rule="back_demod" parents="1887"/>
      <j2 rule="demod" parents="4107 4228"/>
    </justification>
  </clause>

  <clause id="4254">
    <literal><![CDATA[
      c(c(x v c(c_0 v c(x))) v c(c_0)) = x
    ]]></literal>
    <justification jstring="[back_demod(2087),demod(4228(3),4228(9))].">
      <j1 rule="back_demod" parents="2087"/>
      <j2 rule="demod" parents="4228 4228"/>
    </justification>
  </clause>

  <clause id="4264">
    <literal><![CDATA[
      x v ((c(c_0) v c(x v ((x v c_0) v ((x v c_0) v c_0)))) v c_0) = c_0
    ]]></literal>
    <justification jstring="[back_demod(4117),demod(4228(7),4228(9),4225(17))].">
      <j1 rule="back_demod" parents="4117"/>
      <j2 rule="demod" parents="4228 4228 4225"/>
    </justification>
  </clause>

  <clause id="4267">
    <literal><![CDATA[
      c(c_0) v (x v (y v c_0)) = x v (y v c_0)
    ]]></literal>
    <justification jstring="[back_demod(4109),demod(4225(7))].">
      <j1 rule="back_demod" parents="4109"/>
      <j2 rule="demod" parents="4225"/>
    </justification>
  </clause>

  <clause id="4284">
    <literal><![CDATA[
      c(c_0) v c_0 = c_0
    ]]></literal>
    <justification jstring="[back_demod(4107),demod(4228(7))].">
      <j1 rule="back_demod" parents="4107"/>
      <j2 rule="demod" parents="4228"/>
    </justification>
  </clause>

  <clause id="4344">
    <literal><![CDATA[
      (c(x v c_0) v c(x v c(c_0))) v x = c_0
    ]]></literal>
    <justification jstring="[back_demod(2380),demod(4228(3))].">
      <j1 rule="back_demod" parents="2380"/>
      <j2 rule="demod" parents="4228"/>
    </justification>
  </clause>

  <clause id="4350">
    <literal><![CDATA[
      c(c(c_0) v c(x v ((x v c_0) v ((x v c_0) v c_0)))) = x v c_0
    ]]></literal>
    <justification jstring="[back_demod(2093),demod(4228(5),4228(7),4228(16))].">
      <j1 rule="back_demod" parents="2093"/>
      <j2 rule="demod" parents="4228 4228 4228"/>
    </justification>
  </clause>

  <clause id="4362">
    <literal><![CDATA[
      c(c(c_0)) = c_0
    ]]></literal>
    <justification jstring="[back_demod(1897),demod(4228(6))].">
      <j1 rule="back_demod" parents="1897"/>
      <j2 rule="demod" parents="4228"/>
    </justification>
  </clause>

  <clause id="4367">
    <literal><![CDATA[
      c(c(c(x v c(c(x))) v c_0) v x) = c(x v c(c(x)))
    ]]></literal>
    <justification jstring="[back_demod(2109),demod(4231(8))].">
      <j1 rule="back_demod" parents="2109"/>
      <j2 rule="demod" parents="4231"/>
    </justification>
  </clause>

  <clause id="4719">
    <literal><![CDATA[
      x v ((x v c_0) v c_0) = x v c_0
    ]]></literal>
    <justification jstring="[para(680(a,1),51(a,1,1,2,1,2,2)),demod(9(11),4267(12),9(10),4350(13),9(9),4267(10)),flip(a)].">
      <j1 rule="para" parents="680 51"/>
      <j2 rule="demod" parents="9 4267 9 4350 9 4267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4749">
    <literal><![CDATA[
      c(c(c_0) v c(x v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[para(3335(a,1),51(a,1,1,2,1,2,2,1,2)),demod(3523(16),4719(7),3335(17))].">
      <j1 rule="para" parents="3335 51"/>
      <j2 rule="demod" parents="3523 4719 3335"/>
    </justification>
  </clause>

  <clause id="4768">
    <literal><![CDATA[
      x v (y v ((x v c_0) v c_0)) = y v (x v c_0)
    ]]></literal>
    <justification jstring="[para(4719(a,1),9(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4719 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4804">
    <literal><![CDATA[
      x v ((c(c_0) v c(x v c_0)) v c_0) = c_0
    ]]></literal>
    <justification jstring="[back_demod(4264),demod(4768(10),9(7),4719(7))].">
      <j1 rule="back_demod" parents="4264"/>
      <j2 rule="demod" parents="4768 9 4719"/>
    </justification>
  </clause>

  <clause id="4820">
    <literal><![CDATA[
      c(c(x v c_0) v c(c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[para(4749(a,1),28(a,1,1,1,1,2)),demod(9(5),4719(5),4284(7))].">
      <j1 rule="para" parents="4749 28"/>
      <j2 rule="demod" parents="9 4719 4284"/>
    </justification>
  </clause>

  <clause id="4833">
    <literal><![CDATA[
      c(c(x v (y v c_0)) v c(c(y v c_0) v (x v c(c_0)))) = x
    ]]></literal>
    <justification jstring="[para(4820(a,1),19(a,1,1,1,1,2))].">
      <j1 rule="para" parents="4820 19"/>
    </justification>
  </clause>

  <clause id="4843">
    <literal><![CDATA[
      c(c(x v c_0) v c((x v c_0) v (c(x v c_0) v c_0))) = x v c_0
    ]]></literal>
    <justification jstring="[para(4820(a,1),21(a,1,1,2,1,2,1)),demod(9(11),4820(21))].">
      <j1 rule="para" parents="4820 21"/>
      <j2 rule="demod" parents="9 4820"/>
    </justification>
  </clause>

  <clause id="4851">
    <literal><![CDATA[
      c(c(x v c_0) v c(c(x v c_0) v c_0)) = c_0
    ]]></literal>
    <justification jstring="[para(4820(a,1),28(a,1,1,1,1,2)),demod(4231(4))].">
      <j1 rule="para" parents="4820 28"/>
      <j2 rule="demod" parents="4231"/>
    </justification>
  </clause>

  <clause id="4859">
    <literal><![CDATA[
      x v (y v ((c(c_0) v c(x v c_0)) v c_0)) = y v c_0
    ]]></literal>
    <justification jstring="[para(4804(a,1),9(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4804 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5006">
    <literal><![CDATA[
      c(x v c(c(x v c(c_0 v c(x))) v c_0)) = c(x v c(c_0 v c(x)))
    ]]></literal>
    <justification jstring="[para(4254(a,1),12(a,1,1,1))].">
      <j1 rule="para" parents="4254 12"/>
    </justification>
  </clause>

  <clause id="5007">
    <literal><![CDATA[
      c(c(c(x v c(c_0 v c(x))) v c_0) v x) = c(x v c(c_0 v c(x)))
    ]]></literal>
    <justification jstring="[para(4254(a,1),12(a,1,1,2)),demod(4362(9))].">
      <j1 rule="para" parents="4254 12"/>
      <j2 rule="demod" parents="4362"/>
    </justification>
  </clause>

  <clause id="5064">
    <literal><![CDATA[
      c(c(c_0) v c((c(c(x) v c_0) v c(c(x) v c(c_0))) v x)) = c(c(x) v c_0) v c(c(x) v c(c_0))
    ]]></literal>
    <justification jstring="[para(4344(a,1),12(a,1,1,1,1))].">
      <j1 rule="para" parents="4344 12"/>
    </justification>
  </clause>

  <clause id="5250">
    <literal><![CDATA[
      (x v c_0) v c_0 = c_0
    ]]></literal>
    <justification jstring="[para(4719(a,1),53(a,1,2,1,2,1,2,1)),demod(4768(10),9(7),4719(7),9(11),4859(12))].">
      <j1 rule="para" parents="4719 53"/>
      <j2 rule="demod" parents="4768 9 4719 9 4859"/>
    </justification>
  </clause>

  <clause id="5268">
    <literal><![CDATA[
      (x v c_0) v (y v c_0) = y v c_0
    ]]></literal>
    <justification jstring="[para(5250(a,1),9(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5250 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5285">
    <literal><![CDATA[
      x v c_0 = c_0
    ]]></literal>
    <justification jstring="[back_demod(4843),demod(5268(11),4851(11)),flip(a)].">
      <j1 rule="back_demod" parents="4843"/>
      <j2 rule="demod" parents="5268 4851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5388">
    <literal><![CDATA[
      c(c(c_0) v c((c(c_0) v c(c(x) v c(c_0))) v x)) = c(c_0) v c(c(x) v c(c_0))
    ]]></literal>
    <justification jstring="[back_demod(5064),demod(5285(5),5285(17))].">
      <j1 rule="back_demod" parents="5064"/>
      <j2 rule="demod" parents="5285 5285"/>
    </justification>
  </clause>

  <clause id="5408">
    <literal><![CDATA[
      c(x v c(c_0 v c(x))) = c(c(c_0) v x)
    ]]></literal>
    <justification jstring="[back_demod(5007),demod(5285(8)),flip(a)].">
      <j1 rule="back_demod" parents="5007"/>
      <j2 rule="demod" parents="5285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5409">
    <literal><![CDATA[
      c(c(c_0) v x) = c(x v c(c_0))
    ]]></literal>
    <justification jstring="[back_demod(5006),demod(5408(6),5285(6),5408(10)),flip(a)].">
      <j1 rule="back_demod" parents="5006"/>
      <j2 rule="demod" parents="5408 5285 5408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5443">
    <literal><![CDATA[
      c(c(c_0) v c(c(c_0) v (x v c(c_0)))) = x
    ]]></literal>
    <justification jstring="[back_demod(4833),demod(5285(2),5285(2),5285(4))].">
      <j1 rule="back_demod" parents="4833"/>
      <j2 rule="demod" parents="5285 5285 5285"/>
    </justification>
  </clause>

  <clause id="5525">
    <literal><![CDATA[
      c(x v c(c(x))) = c(c(c_0) v x)
    ]]></literal>
    <justification jstring="[back_demod(4367),demod(5285(6)),flip(a)].">
      <j1 rule="back_demod" parents="4367"/>
      <j2 rule="demod" parents="5285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5860">
    <literal><![CDATA[
      c(x v c(y v (z v (u v c(x))))) = c(c(c_0) v x)
    ]]></literal>
    <justification jstring="[back_demod(1710),demod(5285(9),5285(9),5285(9),4362(10),5285(9)),flip(a)].">
      <j1 rule="back_demod" parents="1710"/>
      <j2 rule="demod" parents="5285 5285 5285 4362 5285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5923">
    <literal><![CDATA[
      c(c(x v c(c_0)) v c(y v ((c(c(c_0) v z) v c(c_0)) v (x v z)))) = x
    ]]></literal>
    <justification jstring="[back_demod(1477),demod(5285(2),5525(8))].">
      <j1 rule="back_demod" parents="1477"/>
      <j2 rule="demod" parents="5285 5525"/>
    </justification>
  </clause>

  <clause id="5936">
    <literal><![CDATA[
      c(c(c_0) v c(c(c_0) v x)) = x
    ]]></literal>
    <justification jstring="[back_demod(1333),demod(5860(7),5285(6),5285(6),5285(6),5409(8,R))].">
      <j1 rule="back_demod" parents="1333"/>
      <j2 rule="demod" parents="5860 5285 5285 5285 5409"/>
    </justification>
  </clause>

  <clause id="5995">
    <literal><![CDATA[
      (c(x v c(y v c(x v (c(c_0) v x)))) v c(c_0)) v (z v x) = c_0
    ]]></literal>
    <justification jstring="[back_demod(808),demod(5285(11),5285(16))].">
      <j1 rule="back_demod" parents="808"/>
      <j2 rule="demod" parents="5285 5285"/>
    </justification>
  </clause>

  <clause id="5997">
    <literal><![CDATA[
      c(x v c(y v c(x v (c(c_0) v x)))) = c(c(c_0) v x)
    ]]></literal>
    <justification jstring="[back_demod(805),demod(5285(11),4362(12),5285(11)),flip(a)].">
      <j1 rule="back_demod" parents="805"/>
      <j2 rule="demod" parents="5285 4362 5285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6073">
    <literal><![CDATA[
      c(c(c_0) v c(x v c(c(x) v c(y)))) = x
    ]]></literal>
    <justification jstring="[back_demod(581),demod(5285(18),5409(10,R))].">
      <j1 rule="back_demod" parents="581"/>
      <j2 rule="demod" parents="5285 5409"/>
    </justification>
  </clause>

  <clause id="6142">
    <literal><![CDATA[
      (c(c_0) v c(x v x)) v (y v x) = c_0
    ]]></literal>
    <justification jstring="[back_demod(50),demod(5285(9))].">
      <j1 rule="back_demod" parents="50"/>
      <j2 rule="demod" parents="5285"/>
    </justification>
  </clause>

  <clause id="6214">
    <literal><![CDATA[
      c(c(c_0) v c((c(c_0) v c(c(c_0) v (c(x v c(y)) v ((c(x v c(y)) v c(x v y)) v ((c(x v c(y)) v c(x v y)) v c(x v y)))))) v x)) = c(c_0) v c(c(c_0) v (c(x v c(y)) v ((c(x v c(y)) v c(x v y)) v ((c(x v c(y)) v c(x v y)) v c(x v y)))))
    ]]></literal>
    <justification jstring="[back_demod(1653),demod(5409(33,R))].">
      <j1 rule="back_demod" parents="1653"/>
      <j2 rule="demod" parents="5409"/>
    </justification>
  </clause>

  <clause id="6292">
    <literal><![CDATA[
      x v c(c_0) = x
    ]]></literal>
    <justification jstring="[back_demod(5443),demod(5936(11))].">
      <j1 rule="back_demod" parents="5443"/>
      <j2 rule="demod" parents="5936"/>
    </justification>
  </clause>

  <clause id="6316">
    <literal><![CDATA[
      x v ((x v y) v ((x v y) v y)) = x v y
    ]]></literal>
    <justification jstring="[back_demod(618),demod(5936(13))].">
      <j1 rule="back_demod" parents="618"/>
      <j2 rule="demod" parents="5936"/>
    </justification>
  </clause>

  <clause id="6322">
    <literal><![CDATA[
      c(c(c_0) v x) v (y v x) = c_0
    ]]></literal>
    <justification jstring="[back_demod(5995),demod(5997(9),6292(7))].">
      <j1 rule="back_demod" parents="5995"/>
      <j2 rule="demod" parents="5997 6292"/>
    </justification>
  </clause>

  <clause id="6324">
    <literal><![CDATA[
      c(c(x)) = x
    ]]></literal>
    <justification jstring="[back_demod(5923),demod(6292(3),6292(8),6322(7),5285(3),6292(4))].">
      <j1 rule="back_demod" parents="5923"/>
      <j2 rule="demod" parents="6292 6292 6322 5285 6292"/>
    </justification>
  </clause>

  <clause id="6334">
    <literal><![CDATA[
      c(c(c_0) v x) = c(x)
    ]]></literal>
    <justification jstring="[back_demod(526),demod(6292(3),6142(8),6324(4),5285(3),6292(7))].">
      <j1 rule="back_demod" parents="526"/>
      <j2 rule="demod" parents="6292 6142 6324 5285 6292"/>
    </justification>
  </clause>

  <clause id="6427">
    <literal><![CDATA[
      (c(c_0) v x) v x = c(c_0) v x
    ]]></literal>
    <justification jstring="[back_demod(5388),demod(6292(8),6324(6),6334(9),6324(6),6292(10),6324(8))].">
      <j1 rule="back_demod" parents="5388"/>
      <j2 rule="demod" parents="6292 6324 6334 6324 6292 6324"/>
    </justification>
  </clause>

  <clause id="6483">
    <literal><![CDATA[
      c(c_0) v x = x
    ]]></literal>
    <justification jstring="[back_demod(6214),demod(6316(26),6334(14),12(11),6427(6),6334(6),6334(5),6324(2),6316(24),6334(12),12(9)),flip(a)].">
      <j1 rule="back_demod" parents="6214"/>
      <j2 rule="demod" parents="6316 6334 12 6427 6334 6334 6324 6316 6334 12"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6533">
    <literal><![CDATA[
      x v c(c(x) v c(y)) = x
    ]]></literal>
    <justification jstring="[back_demod(6073),demod(6483(9),6324(7))].">
      <j1 rule="back_demod" parents="6073"/>
      <j2 rule="demod" parents="6483 6324"/>
    </justification>
  </clause>

  <clause id="6534">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer(B1)
    ]]></attribute>
    <justification jstring="[resolve(6533,a,15,a)].">
      <j1 rule="resolve" parents="6533 15"/>
    </justification>
  </clause>

</proof>

<proof number="3" length="201" max_count="86">

<comments><![CDATA[
% Proof 3 at 5.71 (+ 0.04) seconds: MOD.
% Length of proof is 201.
% Level of proof is 49.
% Maximum clause weight is 86.
% Given clauses 257.
]]></comments>

  <clause id="3">
    <literal><![CDATA[
      x v c(x) = y v c(y)
    ]]></literal>
    <attribute><![CDATA[
      label(ONE)
    ]]></attribute>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="4">
    <literal><![CDATA[
      (x v c(y)) ^ (x v y) = x
    ]]></literal>
    <attribute><![CDATA[
      label(CUT)
    ]]></attribute>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="8">
    <literal><![CDATA[
      c7 v (c9 ^ (c7 v c8)) != c7 v (c8 ^ (c7 v c9))
    ]]></literal>
    <attribute><![CDATA[
      answer(MOD)
    ]]></attribute>
    <justification jstring="[clausify].">
      <j1 rule="clausify"/>
    </justification>
  </clause>

  <clause id="9">
    <literal><![CDATA[
      x v (y v z) = y v (x v z)
    ]]></literal>
    <attribute><![CDATA[
      label(AJ)
    ]]></attribute>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="10">
    <literal><![CDATA[
      x ^ y = c(c(x) v c(y))
    ]]></literal>
    <attribute><![CDATA[
      label(DM)
    ]]></attribute>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="11">
    <literal><![CDATA[
      x v c(x) = y v c(y)
    ]]></literal>
    <attribute><![CDATA[
      label(ONE)
    ]]></attribute>
    <justification jstring="[copy(3)].">
      <j1 rule="copy" parents="3"/>
    </justification>
  </clause>

  <clause id="12">
    <literal><![CDATA[
      c(c(x v c(y)) v c(x v y)) = x
    ]]></literal>
    <attribute><![CDATA[
      label(CUT)
    ]]></attribute>
    <justification jstring="[copy(4),demod(10(4))].">
      <j1 rule="copy" parents="4"/>
      <j2 rule="demod" parents="10"/>
    </justification>
  </clause>

  <clause id="13">
    <literal><![CDATA[
      x v c(x) = c_0
    ]]></literal>
    <justification jstring="[new_symbol(11)].">
      <j1 rule="new_symbol" parents="11"/>
    </justification>
  </clause>

  <clause id="17">
    <literal><![CDATA[
      c7 v c(c(c8) v c(c7 v c9)) != c7 v c(c(c9) v c(c7 v c8))
    ]]></literal>
    <attribute><![CDATA[
      answer(MOD)
    ]]></attribute>
    <justification jstring="[copy(8),demod(10(6),10(16)),flip(a)].">
      <j1 rule="copy" parents="8"/>
      <j2 rule="demod" parents="10 10"/>
      <j2 rule="flip"/>
    </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(9(a,1),9(a,1,2))].">
      <j1 rule="para" parents="9 9"/>
    </justification>
  </clause>

  <clause id="19">
    <literal><![CDATA[
      c(c(x v c(y v z)) v c(y v (x v z))) = x
    ]]></literal>
    <justification jstring="[para(9(a,1),12(a,1,1,2,1))].">
      <j1 rule="para" parents="9 12"/>
    </justification>
  </clause>

  <clause id="20">
    <literal><![CDATA[
      c(c(x v y) v c(x v (c(y v c(z)) v c(y v z)))) = x
    ]]></literal>
    <justification jstring="[para(12(a,1),12(a,1,1,1,1,2))].">
      <j1 rule="para" parents="12 12"/>
    </justification>
  </clause>

  <clause id="21">
    <literal><![CDATA[
      c(x v c(x v (c(x v c(y)) v y))) = c(x v c(y))
    ]]></literal>
    <justification jstring="[para(12(a,1),12(a,1,1,1)),demod(9(5))].">
      <j1 rule="para" parents="12 12"/>
      <j2 rule="demod" parents="9"/>
    </justification>
  </clause>

  <clause id="22">
    <literal><![CDATA[
      c(c(c(x v c(y)) v c(c(x v y))) v x) = c(x v c(y))
    ]]></literal>
    <justification jstring="[para(12(a,1),12(a,1,1,2))].">
      <j1 rule="para" parents="12 12"/>
    </justification>
  </clause>

  <clause id="23">
    <literal><![CDATA[
      x v (y v c(x)) = y v c_0
    ]]></literal>
    <justification jstring="[para(13(a,1),9(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24">
    <literal><![CDATA[
      c(c(c_0) v c(x v x)) = x
    ]]></literal>
    <justification jstring="[para(13(a,1),12(a,1,1,1,1))].">
      <j1 rule="para" parents="13 12"/>
    </justification>
  </clause>

  <clause id="25">
    <literal><![CDATA[
      c(c(x v c(c(x))) v c(c_0)) = x
    ]]></literal>
    <justification jstring="[para(13(a,1),12(a,1,1,2,1))].">
      <j1 rule="para" parents="13 12"/>
    </justification>
  </clause>

  <clause id="26">
    <literal><![CDATA[
      (c(x v c(y)) v c(x v y)) v x = c_0
    ]]></literal>
    <justification jstring="[para(12(a,1),13(a,1,2))].">
      <j1 rule="para" parents="12 13"/>
    </justification>
  </clause>

  <clause id="27">
    <literal><![CDATA[
      x v (y v (z v c(x))) = y v (z v c_0)
    ]]></literal>
    <justification jstring="[para(23(a,1),9(a,1,2)),flip(a)].">
      <j1 rule="para" parents="23 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28">
    <literal><![CDATA[
      c(c(x v c(y v c(x))) v c(y v c_0)) = x
    ]]></literal>
    <justification jstring="[para(23(a,1),12(a,1,1,2,1))].">
      <j1 rule="para" parents="23 12"/>
    </justification>
  </clause>

  <clause id="29">
    <literal><![CDATA[
      (c(x v c(y)) v c(x v y)) v (z v x) = z v c_0
    ]]></literal>
    <justification jstring="[para(12(a,1),23(a,1,2,2))].">
      <j1 rule="para" parents="12 23"/>
    </justification>
  </clause>

  <clause id="30">
    <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),9(a,1,2))].">
      <j1 rule="para" parents="18 9"/>
    </justification>
  </clause>

  <clause id="34">
    <literal><![CDATA[
      c(c(x v c(y v (z v u))) v c(z v (x v (y v u)))) = x
    ]]></literal>
    <justification jstring="[para(18(a,1),12(a,1,1,2,1))].">
      <j1 rule="para" parents="18 12"/>
    </justification>
  </clause>

  <clause id="35">
    <literal><![CDATA[
      c(c(x v c(y v (z v u))) v c(y v (z v (x v u)))) = x
    ]]></literal>
    <justification jstring="[para(18(a,2),12(a,1,1,2,1))].">
      <j1 rule="para" parents="18 12"/>
    </justification>
  </clause>

  <clause id="36">
    <literal><![CDATA[
      x v (y v (z v (u v c(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(c(c_0) v c(x v ((x v y) v y))) = x v y
    ]]></literal>
    <justification jstring="[para(9(a,1),24(a,1,1,2,1))].">
      <j1 rule="para" parents="9 24"/>
    </justification>
  </clause>

  <clause id="47">
    <literal><![CDATA[
      c(x v c(c(c_0) v (x v x))) = c(c_0)
    ]]></literal>
    <justification jstring="[para(24(a,1),12(a,1,1,1))].">
      <j1 rule="para" parents="24 12"/>
    </justification>
  </clause>

  <clause id="48">
    <literal><![CDATA[
      c(c(c(c_0) v c(c(x v x))) v x) = c(c_0)
    ]]></literal>
    <justification jstring="[para(24(a,1),12(a,1,1,2))].">
      <j1 rule="para" parents="24 12"/>
    </justification>
  </clause>

  <clause id="49">
    <literal><![CDATA[
      (c(c_0) v c(x v x)) v x = c_0
    ]]></literal>
    <justification jstring="[para(24(a,1),13(a,1,2))].">
      <j1 rule="para" parents="24 13"/>
    </justification>
  </clause>

  <clause id="50">
    <literal><![CDATA[
      (c(c_0) v c(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="51">
    <literal><![CDATA[
      c(c(c_0) v c(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)),demod(9(6))].">
      <j1 rule="para" parents="18 24"/>
      <j2 rule="demod" parents="9"/>
    </justification>
  </clause>

  <clause id="53">
    <literal><![CDATA[
      x v ((c(c_0) v c(x v ((x v y) v y))) v y) = c_0
    ]]></literal>
    <justification jstring="[para(49(a,1),9(a,1)),demod(9(6)),flip(a)].">
      <j1 rule="para" parents="49 9"/>
      <j2 rule="demod" parents="9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="56">
    <literal><![CDATA[
      (c(c_0) v c(c(x) v c(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[
      c(x v c(c(x v c(c(x))) v c_0)) = c(x v c(c(x)))
    ]]></literal>
    <justification jstring="[para(25(a,1),12(a,1,1,1))].">
      <j1 rule="para" parents="25 12"/>
    </justification>
  </clause>

  <clause id="66">
    <literal><![CDATA[
      c(c(c(x v c(c(x))) v c(c(c_0))) v x) = c(x v c(c(x)))
    ]]></literal>
    <justification jstring="[para(25(a,1),12(a,1,1,2))].">
      <j1 rule="para" parents="25 12"/>
    </justification>
  </clause>

  <clause id="68">
    <literal><![CDATA[
      (c(x v c(c(x))) v c(c_0)) v x = c_0
    ]]></literal>
    <justification jstring="[para(25(a,1),13(a,1,2))].">
      <j1 rule="para" parents="25 13"/>
    </justification>
  </clause>

  <clause id="72">
    <literal><![CDATA[
      c(x v c(x v (c(c_0) v x))) = c(c_0)
    ]]></literal>
    <justification jstring="[para(9(a,1),47(a,1,1,2,1))].">
      <j1 rule="para" parents="9 47"/>
    </justification>
  </clause>

  <clause id="74">
    <literal><![CDATA[
      c(c(c_0) v c(x v (c(c_0) v (x v x)))) = x
    ]]></literal>
    <justification jstring="[para(47(a,1),12(a,1,1,1))].">
      <j1 rule="para" parents="47 12"/>
    </justification>
  </clause>

  <clause id="76">
    <literal><![CDATA[
      (x v c(c(c_0) v (x v x))) v c(c_0) = c_0
    ]]></literal>
    <justification jstring="[para(47(a,1),13(a,1,2))].">
      <j1 rule="para" parents="47 13"/>
    </justification>
  </clause>

  <clause id="103">
    <literal><![CDATA[
      c(c(x v y) v c(c(y v c(c(y))) v (x v c(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="105">
    <literal><![CDATA[
      c(c(c_0) v c(c(c_0) v (x v (x v x)))) = x
    ]]></literal>
    <justification jstring="[para(47(a,1),19(a,1,1,1))].">
      <j1 rule="para" parents="47 19"/>
    </justification>
  </clause>

  <clause id="122">
    <literal><![CDATA[
      c(c((c(x v c(c(x))) v c(c_0)) v c(y v x)) v c(y v c_0)) = c(x v c(c(x))) v c(c_0)
    ]]></literal>
    <justification jstring="[para(68(a,1),19(a,1,1,2,1,2))].">
      <j1 rule="para" parents="68 19"/>
    </justification>
  </clause>

  <clause id="126">
    <literal><![CDATA[
      c(c(c_0) v c(x v (x v (c(c_0) v x)))) = x
    ]]></literal>
    <justification jstring="[para(72(a,1),12(a,1,1,1))].">
      <j1 rule="para" parents="72 12"/>
    </justification>
  </clause>

  <clause id="141">
    <literal><![CDATA[
      (c(c(x) v c(y)) v c(c(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(c(c_0) v c(c(x v x))) v x) v c(c_0) = c_0
    ]]></literal>
    <justification jstring="[para(24(a,1),26(a,1,1,2))].">
      <j1 rule="para" parents="24 26"/>
    </justification>
  </clause>

  <clause id="158">
    <literal><![CDATA[
      (c(c_0) v c(x v (c(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(c_0) v c(x v (x v (c(c_0) v x)))) v x = c_0
    ]]></literal>
    <justification jstring="[para(72(a,1),26(a,1,1,1))].">
      <j1 rule="para" parents="72 26"/>
    </justification>
  </clause>

  <clause id="191">
    <literal><![CDATA[
      c(c(x v c_0) v c(y v (c((x v c(y)) v c(z)) v c((x v c(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(c(c_0) v c((x v c(c(c_0) v (x v x))) v c_0)) = x v c(c(c_0) v (x v x))
    ]]></literal>
    <justification jstring="[para(76(a,1),12(a,1,1,1,1))].">
      <j1 rule="para" parents="76 12"/>
    </justification>
  </clause>

  <clause id="244">
    <literal><![CDATA[
      (x v c(c(c_0) v (x v x))) v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(76(a,1),23(a,1,2)),flip(a)].">
      <j1 rule="para" parents="76 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="256">
    <literal><![CDATA[
      x v c(c(c_0) v (x v x)) = c_0
    ]]></literal>
    <justification jstring="[back_demod(243),demod(244(10),24(8)),flip(a)].">
      <j1 rule="back_demod" parents="243"/>
      <j2 rule="demod" parents="244 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="258">
    <literal><![CDATA[
      x v (y v c(c(c_0) v (x v x))) = y v c_0
    ]]></literal>
    <justification jstring="[para(256(a,1),9(a,1,2)),flip(a)].">
      <j1 rule="para" parents="256 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="260">
    <literal><![CDATA[
      x v c(x v (c(c_0) v x)) = c_0
    ]]></literal>
    <justification jstring="[para(9(a,1),256(a,1,2,1))].">
      <j1 rule="para" parents="9 256"/>
    </justification>
  </clause>

  <clause id="261">
    <literal><![CDATA[
      (c(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="262">
    <literal><![CDATA[
      c(c(c_0)) v c(c(c(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="273">
    <literal><![CDATA[
      x v (y v c(x v (c(c_0) v x))) = y v c_0
    ]]></literal>
    <justification jstring="[para(260(a,1),9(a,1,2)),flip(a)].">
      <j1 rule="para" parents="260 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="284">
    <literal><![CDATA[
      (c(c(c_0)) v c_0) v c_0 = c(c(c_0)) v c_0
    ]]></literal>
    <justification jstring="[para(23(a,1),261(a,1,1))].">
      <j1 rule="para" parents="23 261"/>
    </justification>
  </clause>

  <clause id="330">
    <literal><![CDATA[
      c(c(c_0) v c(c(c(c_0)) v (c(c(c_0)) v c_0))) = c(c(c_0))
    ]]></literal>
    <justification jstring="[para(262(a,1),12(a,1,1,1,1))].">
      <j1 rule="para" parents="262 12"/>
    </justification>
  </clause>

  <clause id="336">
    <literal><![CDATA[
      (c(c(c_0)) v c_0) v (x v c_0) = x v (c(c(c_0)) v c_0)
    ]]></literal>
    <justification jstring="[para(262(a,1),27(a,1,2,2))].">
      <j1 rule="para" parents="262 27"/>
    </justification>
  </clause>

  <clause id="526">
    <literal><![CDATA[
      c(c(c(x v c(c_0)) v c(c((c(c_0) v c(y v y)) v (x v y)))) v x) = c(x v c(c_0))
    ]]></literal>
    <justification jstring="[para(50(a,2),22(a,1,1,1,1,2,1,1))].">
      <j1 rule="para" parents="50 22"/>
    </justification>
  </clause>

  <clause id="547">
    <literal><![CDATA[
      (c(c(c_0) v c(c(x v x))) v x) v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(48(a,1),56(a,1,1,2,1,1)),demod(48(13),56(11)),flip(a)].">
      <j1 rule="para" parents="48 56"/>
      <j2 rule="demod" parents="48 56"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="576">
    <literal><![CDATA[
      c(c(x v c((c(c(c_0)) v c_0) v c(x))) v c(c(c(c_0)) v c_0)) = x
    ]]></literal>
    <justification jstring="[para(284(a,1),28(a,1,1,2,1))].">
      <j1 rule="para" parents="284 28"/>
    </justification>
  </clause>

  <clause id="605">
    <literal><![CDATA[
      c(c(c_0) v c(x v ((x v c(c(c_0))) v ((x v c(c(c_0))) v c_0)))) = x v c(c(c_0))
    ]]></literal>
    <justification jstring="[para(27(a,1),74(a,1,1,2,1,2)),demod(9(13),9(14))].">
      <j1 rule="para" parents="27 74"/>
      <j2 rule="demod" parents="9 9"/>
    </justification>
  </clause>

  <clause id="618">
    <literal><![CDATA[
      c(c(c_0) v c(c(c_0) v (x v ((x v y) v ((x v y) v y))))) = x v y
    ]]></literal>
    <justification jstring="[para(9(a,1),105(a,1,1,2,1,2,2)),demod(9(9))].">
      <j1 rule="para" parents="9 105"/>
      <j2 rule="demod" parents="9"/>
    </justification>
  </clause>

  <clause id="680">
    <literal><![CDATA[
      (c(c_0) v (x v x)) v (y v c_0) = x v (y v c_0)
    ]]></literal>
    <justification jstring="[para(258(a,1),27(a,1,2))].">
      <j1 rule="para" parents="258 27"/>
    </justification>
  </clause>

  <clause id="771">
    <literal><![CDATA[
      (c(x v c(c_0)) v c((c(c_0) v c(y v y)) v (x v y))) v (z v x) = z v c_0
    ]]></literal>
    <justification jstring="[para(50(a,2),29(a,1,1,2,1))].">
      <j1 rule="para" parents="50 29"/>
    </justification>
  </clause>

  <clause id="805">
    <literal><![CDATA[
      c(c(c(x v c(y v c(x v (c(c_0) v x)))) v c(c(y v c_0))) v x) = c(x v c(y v c(x v (c(c_0) v x))))
    ]]></literal>
    <justification jstring="[para(273(a,1),22(a,1,1,1,1,2,1,1))].">
      <j1 rule="para" parents="273 22"/>
    </justification>
  </clause>

  <clause id="808">
    <literal><![CDATA[
      (c(x v c(y v c(x v (c(c_0) v x)))) v c(y v c_0)) v (z v x) = z v c_0
    ]]></literal>
    <justification jstring="[para(273(a,1),29(a,1,1,2,1))].">
      <j1 rule="para" parents="273 29"/>
    </justification>
  </clause>

  <clause id="817">
    <literal><![CDATA[
      c(c(c_0) v c(c(c(c_0)))) v c(c_0) = c(c(c_0) v c(c(c(c_0))))
    ]]></literal>
    <justification jstring="[para(68(a,1),45(a,1,1,2,1,2)),demod(65(15)),flip(a)].">
      <j1 rule="para" parents="68 45"/>
      <j2 rule="demod" parents="65"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="825">
    <literal><![CDATA[
      c(c(c_0)) v c_0 = c(c(c_0))
    ]]></literal>
    <justification jstring="[para(284(a,1),45(a,1,1,2,1,2,1)),demod(284(14),9(13),284(12),330(14),284(10)),flip(a)].">
      <j1 rule="para" parents="284 45"/>
      <j2 rule="demod" parents="284 9 284 330 284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="842">
    <literal><![CDATA[
      c(c(x v c(c(c(c_0)) v c(x))) v c(c(c(c_0)))) = x
    ]]></literal>
    <justification jstring="[back_demod(576),demod(825(5),825(13))].">
      <j1 rule="back_demod" parents="576"/>
      <j2 rule="demod" parents="825 825"/>
    </justification>
  </clause>

  <clause id="855">
    <literal><![CDATA[
      c(c(c_0)) v (x v c_0) = x v c(c(c_0))
    ]]></literal>
    <justification jstring="[back_demod(336),demod(825(5),825(11))].">
      <j1 rule="back_demod" parents="336"/>
      <j2 rule="demod" parents="825 825"/>
    </justification>
  </clause>

  <clause id="858">
    <literal><![CDATA[
      (c(c_0) v c(c_0 v c_0)) v c(c(c_0)) = c(c(c_0))
    ]]></literal>
    <justification jstring="[para(825(a,1),50(a,1,2)),demod(825(16))].">
      <j1 rule="para" parents="825 50"/>
      <j2 rule="demod" parents="825"/>
    </justification>
  </clause>

  <clause id="861">
    <literal><![CDATA[
      c(c(c(c(c_0)) v (x v c_0)) v c(x v c(c_0))) = x
    ]]></literal>
    <justification jstring="[para(855(a,2),12(a,1,1,1,1))].">
      <j1 rule="para" parents="855 12"/>
    </justification>
  </clause>

  <clause id="862">
    <literal><![CDATA[
      c(c_0) v (c(c(c_0)) v (x v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[para(855(a,2),23(a,1,2))].">
      <j1 rule="para" parents="855 23"/>
    </justification>
  </clause>

  <clause id="898">
    <literal><![CDATA[
      c(c(c_0)) v (x v c_0) = (c(c_0) v c(c(x) v c(x))) v c(c(c_0))
    ]]></literal>
    <justification jstring="[para(56(a,1),855(a,1,2))].">
      <j1 rule="para" parents="56 855"/>
    </justification>
  </clause>

  <clause id="1040">
    <literal><![CDATA[
      c(c(c_0)) v (x v (c(c_0) v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[para(862(a,1),18(a,2))].">
      <j1 rule="para" parents="862 18"/>
    </justification>
  </clause>

  <clause id="1060">
    <literal><![CDATA[
      (c(c_0) v c(c(c_0) v ((c(c_0) v c_0) v c_0))) v c_0 = c(c(c_0))
    ]]></literal>
    <justification jstring="[para(49(a,1),1040(a,1,2)),demod(825(5),9(14)),flip(a)].">
      <j1 rule="para" parents="49 1040"/>
      <j2 rule="demod" parents="825 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1083">
    <literal><![CDATA[
      c(c(c(c_0) v c(c(c(c_0))))) = c(c_0)
    ]]></literal>
    <justification jstring="[para(858(a,1),28(a,1,1,1,1,2,1)),demod(49(17),817(11))].">
      <j1 rule="para" parents="858 28"/>
      <j2 rule="demod" parents="49 817"/>
    </justification>
  </clause>

  <clause id="1087">
    <literal><![CDATA[
      c(c(c_0) v c(c(c(c_0)))) = c_0
    ]]></literal>
    <justification jstring="[para(1083(a,1),13(a,1,2)),demod(817(11))].">
      <j1 rule="para" parents="1083 13"/>
      <j2 rule="demod" parents="817"/>
    </justification>
  </clause>

  <clause id="1234">
    <literal><![CDATA[
      c(c(c(c_0) v c(c(c(c(c_0))))) v c_0) = c(c_0)
    ]]></literal>
    <justification jstring="[para(1087(a,1),12(a,1,1,2))].">
      <j1 rule="para" parents="1087 12"/>
    </justification>
  </clause>

  <clause id="1247">
    <literal><![CDATA[
      c(c(c(c(c_0))) v c(c(c_0) v c_0)) = c(c(c_0))
    ]]></literal>
    <justification jstring="[para(1087(a,1),28(a,1,1,1,1,2)),demod(825(5))].">
      <j1 rule="para" parents="1087 28"/>
      <j2 rule="demod" parents="825"/>
    </justification>
  </clause>

  <clause id="1294">
    <literal><![CDATA[
      c(c((c(c(c_0) v c(c(c(c(c_0))))) v c_0) v c(c(c_0))) v c(c_0)) = c(c(c_0) v c(c(c(c(c_0))))) v c_0
    ]]></literal>
    <justification jstring="[para(1234(a,1),25(a,1,1,1,1,2,1))].">
      <j1 rule="para" parents="1234 25"/>
    </justification>
  </clause>

  <clause id="1333">
    <literal><![CDATA[
      c(c(x v c(y v (z v (u v c(x))))) v c(z v (y v (u v c_0)))) = x
    ]]></literal>
    <justification jstring="[para(27(a,1),34(a,1,1,2,1,2))].">
      <j1 rule="para" parents="27 34"/>
    </justification>
  </clause>

  <clause id="1414">
    <literal><![CDATA[
      c(c(c(c(c(c_0))) v c(c(c(c_0) v c_0))) v c(c(c_0))) = c(c(c(c_0)))
    ]]></literal>
    <justification jstring="[para(1247(a,1),12(a,1,1,2))].">
      <j1 rule="para" parents="1247 12"/>
    </justification>
  </clause>

  <clause id="1455">
    <literal><![CDATA[
      c(c(c_0) v c(c(x v x))) v x = c_0
    ]]></literal>
    <justification jstring="[para(152(a,1),12(a,1,1,1,1)),demod(547(12),24(8)),flip(a)].">
      <j1 rule="para" parents="152 12"/>
      <j2 rule="demod" parents="547 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1477">
    <literal><![CDATA[
      c(c(x v c(y v c_0)) v c(y v ((c(z v c(c(z))) v c(c_0)) v (x v z)))) = x
    ]]></literal>
    <justification jstring="[para(68(a,1),35(a,1,1,1,1,2,1,2))].">
      <j1 rule="para" parents="68 35"/>
    </justification>
  </clause>

  <clause id="1653">
    <literal><![CDATA[
      c(c((c(c_0) v c(c(c_0) v (c(x v c(y)) v ((c(x v c(y)) v c(x v y)) v ((c(x v c(y)) v c(x v y)) v c(x v y)))))) v x) v c(c_0)) = c(c_0) v c(c(c_0) v (c(x v c(y)) v ((c(x v c(y)) v c(x v y)) v ((c(x v c(y)) v c(x v y)) v c(x v y)))))
    ]]></literal>
    <justification jstring="[para(158(a,1),20(a,1,1,2,1)),demod(9(23),9(25),9(24),9(56),9(58),9(57))].">
      <j1 rule="para" parents="158 20"/>
      <j2 rule="demod" parents="9 9 9 9 9 9"/>
    </justification>
  </clause>

  <clause id="1710">
    <literal><![CDATA[
      c(c(c(x v c(y v (z v (u v c(x))))) v c(c(y v (z v (u v c_0))))) v x) = c(x v c(y v (z v (u v c(x)))))
    ]]></literal>
    <justification jstring="[para(36(a,1),22(a,1,1,1,1,2,1,1))].">
      <j1 rule="para" parents="36 22"/>
    </justification>
  </clause>

  <clause id="1864">
    <literal><![CDATA[
      c_0 v (c(c_0) v c_0) = c_0
    ]]></literal>
    <justification jstring="[para(680(a,1),45(a,1,1,2,1,2)),demod(9(10),9(9),126(13),9(7)),flip(a)].">
      <j1 rule="para" parents="680 45"/>
      <j2 rule="demod" parents="9 9 126 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1887">
    <literal><![CDATA[
      c_0 v (x v (c(c_0) v c_0)) = x v c_0
    ]]></literal>
    <justification jstring="[para(1864(a,1),9(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1864 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1893">
    <literal><![CDATA[
      (c(c_0 v c(c(c_0) v c_0)) v c(c_0)) v c_0 = c_0
    ]]></literal>
    <justification jstring="[para(1864(a,1),26(a,1,1,2,1))].">
      <j1 rule="para" parents="1864 26"/>
    </justification>
  </clause>

  <clause id="1897">
    <literal><![CDATA[
      c(c(c_0)) = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(1864(a,1),50(a,1,2)),demod(9(11),1060(15))].">
      <j1 rule="para" parents="1864 50"/>
      <j2 rule="demod" parents="9 1060"/>
    </justification>
  </clause>

  <clause id="1898">
    <literal><![CDATA[
      (c(c_0 v c(c(c_0) v c_0)) v c(c_0)) v (x v c_0) = x v c_0
    ]]></literal>
    <justification jstring="[para(1864(a,1),29(a,1,1,2,1))].">
      <j1 rule="para" parents="1864 29"/>
    </justification>
  </clause>

  <clause id="1963">
    <literal><![CDATA[
      c(c_0 v (c(c(c_0 v c_0) v c(c(c(c_0) v c_0))) v c_0)) = c(c_0 v c_0)
    ]]></literal>
    <justification jstring="[back_demod(1414),demod(1897(3),1897(15),9(16),1897(20))].">
      <j1 rule="back_demod" parents="1414"/>
      <j2 rule="demod" parents="1897 1897 9 1897"/>
    </justification>
  </clause>

  <clause id="1975">
    <literal><![CDATA[
      c(c(c_0 v (c_0 v c_0)) v c(c_0)) = c_0
    ]]></literal>
    <justification jstring="[back_demod(1294),demod(1897(5),1455(11),1897(4),1897(15),1455(21))].">
      <j1 rule="back_demod" parents="1294"/>
      <j2 rule="demod" parents="1897 1455 1897 1897 1455"/>
    </justification>
  </clause>

  <clause id="2022">
    <literal><![CDATA[
      (c(c_0) v c(c(c_0) v ((c(c_0) v c_0) v c_0))) v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[back_demod(1060),demod(1897(18))].">
      <j1 rule="back_demod" parents="1060"/>
      <j2 rule="demod" parents="1897"/>
    </justification>
  </clause>

  <clause id="2058">
    <literal><![CDATA[
      (c_0 v c_0) v (x v c_0) = c_0 v (x v c_0)
    ]]></literal>
    <justification jstring="[back_demod(898),demod(1897(3),1897(16),9(17),56(16))].">
      <j1 rule="back_demod" parents="898"/>
      <j2 rule="demod" parents="1897 1897 9 56"/>
    </justification>
  </clause>

  <clause id="2078">
    <literal><![CDATA[
      c(c(c_0 v (x v c_0)) v c(x v c(c_0))) = x
    ]]></literal>
    <justification jstring="[back_demod(861),demod(1897(3),2058(6))].">
      <j1 rule="back_demod" parents="861"/>
      <j2 rule="demod" parents="1897 2058"/>
    </justification>
  </clause>

  <clause id="2087">
    <literal><![CDATA[
      c(c(x v c((c_0 v c_0) v c(x))) v c(c_0 v c_0)) = x
    ]]></literal>
    <justification jstring="[back_demod(842),demod(1897(3),1897(11))].">
      <j1 rule="back_demod" parents="842"/>
      <j2 rule="demod" parents="1897 1897"/>
    </justification>
  </clause>

  <clause id="2093">
    <literal><![CDATA[
      c(c(c_0) v c(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_demod(605),demod(1897(5),1897(9),1897(20))].">
      <j1 rule="back_demod" parents="605"/>
      <j2 rule="demod" parents="1897 1897 1897"/>
    </justification>
  </clause>

  <clause id="2109">
    <literal><![CDATA[
      c(c(c_0 v (c(x v c(c(x))) v c_0)) v x) = c(x v c(c(x)))
    ]]></literal>
    <justification jstring="[back_demod(66),demod(1897(7),9(8))].">
      <j1 rule="back_demod" parents="66"/>
      <j2 rule="demod" parents="1897 9"/>
    </justification>
  </clause>

  <clause id="2380">
    <literal><![CDATA[
      (c(x v (c_0 v c_0)) v c(x v c(c_0))) v x = c_0
    ]]></literal>
    <justification jstring="[para(1897(a,1),26(a,1,1,1,1,2))].">
      <j1 rule="para" parents="1897 26"/>
    </justification>
  </clause>

  <clause id="3326">
    <literal><![CDATA[
      c(c_0) v c(c(c_0) v c(c_0)) = c_0
    ]]></literal>
    <justification jstring="[para(49(a,1),2078(a,1,1,2,1)),demod(56(12),1975(10)),flip(a)].">
      <j1 rule="para" parents="49 2078"/>
      <j2 rule="demod" parents="56 1975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3335">
    <literal><![CDATA[
      c(c(c_0) v c(x)) v c(c(c_0) v x) = c_0
    ]]></literal>
    <justification jstring="[para(26(a,1),2078(a,1,1,2,1)),demod(141(13),1975(10)),flip(a)].">
      <j1 rule="para" parents="26 2078"/>
      <j2 rule="demod" parents="141 1975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3364">
    <literal><![CDATA[
      c(c_0) v (x v c(c(c_0) v c(c_0))) = x v c_0
    ]]></literal>
    <justification jstring="[para(3326(a,1),9(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3326 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3365">
    <literal><![CDATA[
      (c(c_0) v c(c_0)) v c_0 = c(c_0) v c_0
    ]]></literal>
    <justification jstring="[para(3326(a,1),23(a,1,2))].">
      <j1 rule="para" parents="3326 23"/>
    </justification>
  </clause>

  <clause id="3376">
    <literal><![CDATA[
      (c(c_0) v c(c(c(c_0) v c(c_0)) v (c(c(c_0) v c(c_0)) v c_0))) v c(c(c_0) v c(c_0)) = c_0
    ]]></literal>
    <justification jstring="[para(3326(a,1),169(a,1,1,2,1,2,2))].">
      <j1 rule="para" parents="3326 169"/>
    </justification>
  </clause>

  <clause id="3521">
    <literal><![CDATA[
      c(c(c_0) v c(x)) v c_0 = (c(c_0) v x) v c_0
    ]]></literal>
    <justification jstring="[para(3335(a,1),23(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3335 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3523">
    <literal><![CDATA[
      c(c(c_0) v c(x)) v (y v (z v c(c(c_0) v x))) = y v (z v c_0)
    ]]></literal>
    <justification jstring="[para(3335(a,1),18(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3335 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3579">
    <literal><![CDATA[
      (c(c_0) v c((c(c_0) v c_0) v ((c(c_0) v c_0) v c_0))) v c(c(c_0) v c(c_0)) = c_0
    ]]></literal>
    <justification jstring="[back_demod(3376),demod(3521(16),9(15),3521(14))].">
      <j1 rule="back_demod" parents="3376"/>
      <j2 rule="demod" parents="3521 9 3521"/>
    </justification>
  </clause>

  <clause id="3694">
    <literal><![CDATA[
      (c(c_0) v c(c_0)) v (x v c_0) = c(c_0) v (x v c_0)
    ]]></literal>
    <justification jstring="[para(3364(a,1),27(a,1,2))].">
      <j1 rule="para" parents="3364 27"/>
    </justification>
  </clause>

  <clause id="3705">
    <literal><![CDATA[
      (c(c_0) v c((c(c_0) v c_0) v ((c(c_0) v c_0) v c_0))) v c_0 = c(c_0) v c_0
    ]]></literal>
    <justification jstring="[para(158(a,1),3364(a,1,2)),demod(3364(28),3521(20),9(19),3521(18)),flip(a)].">
      <j1 rule="para" parents="158 3364"/>
      <j2 rule="demod" parents="3364 3521 9 3521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3707">
    <literal><![CDATA[
      x v ((c(c_0) v c(x v ((x v c(c(c_0) v c(c_0))) v ((x v c(c(c_0) v c(c_0))) v c_0)))) v c(c(c_0) v c(c_0))) = c_0
    ]]></literal>
    <justification jstring="[para(3364(a,1),169(a,1,1,2,1,2,2)),demod(9(19),9(20),9(30))].">
      <j1 rule="para" parents="3364 169"/>
      <j2 rule="demod" parents="9 9 9"/>
    </justification>
  </clause>

  <clause id="3983">
    <literal><![CDATA[
      c(c(c_0) v c(c_0)) = c(c_0) v c_0
    ]]></literal>
    <justification jstring="[para(3521(a,1),21(a,1,1,2,1,2)),demod(45(14)),flip(a)].">
      <j1 rule="para" parents="3521 21"/>
      <j2 rule="demod" parents="45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4058">
    <literal><![CDATA[
      x v (c(c_0) v ((c(c_0) v c(x v ((x v (c(c_0) v c_0)) v ((x v (c(c_0) v c_0)) v c_0)))) v c_0)) = c_0
    ]]></literal>
    <justification jstring="[back_demod(3707),demod(3983(8),3983(13),3983(24),9(23))].">
      <j1 rule="back_demod" parents="3707"/>
      <j2 rule="demod" parents="3983 3983 3983 9"/>
    </justification>
  </clause>

  <clause id="4071">
    <literal><![CDATA[
      c(c_0) v (c(c_0) v c_0) = c_0
    ]]></literal>
    <justification jstring="[back_demod(3579),demod(3983(21),9(20),3705(19))].">
      <j1 rule="back_demod" parents="3579"/>
      <j2 rule="demod" parents="3983 9 3705"/>
    </justification>
  </clause>

  <clause id="4107">
    <literal><![CDATA[
      c(c_0) v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[para(4071(a,1),50(a,1,2)),demod(9(11),2022(15)),flip(a)].">
      <j1 rule="para" parents="4071 50"/>
      <j2 rule="demod" parents="9 2022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4108">
    <literal><![CDATA[
      c_0 v (c_0 v c_0) = c_0
    ]]></literal>
    <justification jstring="[para(50(a,2),4071(a,1,2)),demod(9(11),49(10),4107(6),9(6),4107(5))].">
      <j1 rule="para" parents="50 4071"/>
      <j2 rule="demod" parents="9 49 4107 9 4107"/>
    </justification>
  </clause>

  <clause id="4109">
    <literal><![CDATA[
      c(c_0) v (x v (c(c_0) v (y v c_0))) = x v (y v c_0)
    ]]></literal>
    <justification jstring="[para(4071(a,1),30(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4071 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4117">
    <literal><![CDATA[
      x v (c(c_0) v ((c(c_0) v c(x v ((x v (c_0 v c_0)) v ((x v (c_0 v c_0)) v c_0)))) v c_0)) = c_0
    ]]></literal>
    <justification jstring="[back_demod(4058),demod(4107(8),4107(12))].">
      <j1 rule="back_demod" parents="4058"/>
      <j2 rule="demod" parents="4107 4107"/>
    </justification>
  </clause>

  <clause id="4148">
    <literal><![CDATA[
      (c(c_0) v c(c_0)) v c_0 = c_0 v c_0
    ]]></literal>
    <justification jstring="[back_demod(3365),demod(4107(11))].">
      <j1 rule="back_demod" parents="3365"/>
      <j2 rule="demod" parents="4107"/>
    </justification>
  </clause>

  <clause id="4208">
    <literal><![CDATA[
      c(c_0 v c_0) = c(c_0)
    ]]></literal>
    <justification jstring="[back_demod(1963),demod(4107(9),13(11),4107(5),4108(5)),flip(a)].">
      <j1 rule="back_demod" parents="1963"/>
      <j2 rule="demod" parents="4107 13 4107 4108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4225">
    <literal><![CDATA[
      c(c_0) v (x v c_0) = x v c_0
    ]]></literal>
    <justification jstring="[back_demod(1898),demod(4107(5),4208(5),13(4),3694(8))].">
      <j1 rule="back_demod" parents="1898"/>
      <j2 rule="demod" parents="4107 4208 13 3694"/>
    </justification>
  </clause>

  <clause id="4228">
    <literal><![CDATA[
      c_0 v c_0 = c_0
    ]]></literal>
    <justification jstring="[back_demod(1893),demod(4107(5),4208(5),13(4),4148(7))].">
      <j1 rule="back_demod" parents="1893"/>
      <j2 rule="demod" parents="4107 4208 13 4148"/>
    </justification>
  </clause>

  <clause id="4231">
    <literal><![CDATA[
      c_0 v (x v c_0) = x v c_0
    ]]></literal>
    <justification jstring="[back_demod(1887),demod(4107(5),4228(4))].">
      <j1 rule="back_demod" parents="1887"/>
      <j2 rule="demod" parents="4107 4228"/>
    </justification>
  </clause>

  <clause id="4254">
    <literal><![CDATA[
      c(c(x v c(c_0 v c(x))) v c(c_0)) = x
    ]]></literal>
    <justification jstring="[back_demod(2087),demod(4228(3),4228(9))].">
      <j1 rule="back_demod" parents="2087"/>
      <j2 rule="demod" parents="4228 4228"/>
    </justification>
  </clause>

  <clause id="4264">
    <literal><![CDATA[
      x v ((c(c_0) v c(x v ((x v c_0) v ((x v c_0) v c_0)))) v c_0) = c_0
    ]]></literal>
    <justification jstring="[back_demod(4117),demod(4228(7),4228(9),4225(17))].">
      <j1 rule="back_demod" parents="4117"/>
      <j2 rule="demod" parents="4228 4228 4225"/>
    </justification>
  </clause>

  <clause id="4267">
    <literal><![CDATA[
      c(c_0) v (x v (y v c_0)) = x v (y v c_0)
    ]]></literal>
    <justification jstring="[back_demod(4109),demod(4225(7))].">
      <j1 rule="back_demod" parents="4109"/>
      <j2 rule="demod" parents="4225"/>
    </justification>
  </clause>

  <clause id="4284">
    <literal><![CDATA[
      c(c_0) v c_0 = c_0
    ]]></literal>
    <justification jstring="[back_demod(4107),demod(4228(7))].">
      <j1 rule="back_demod" parents="4107"/>
      <j2 rule="demod" parents="4228"/>
    </justification>
  </clause>

  <clause id="4344">
    <literal><![CDATA[
      (c(x v c_0) v c(x v c(c_0))) v x = c_0
    ]]></literal>
    <justification js