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<!DOCTYPE proofs SYSTEM "proof3.dtd">

<?xml-stylesheet type="text/xsl" href="proof3.xsl"?>

<proofs number_of_proofs="5">

<source>s0.out</source>

<heading><![CDATA[
Prover9 (32) version June-2007-, 4 June 2007.
Process 10961 was started by mccune on cleo,
Mon Jun 11 11:35:28 2007
The command was "prover9 -f s0.in".
]]></heading>

<proof number="1" length="35" max_count="26">

<comments><![CDATA[
% Proof 1 at 965.62 (+ 1.40) seconds: Winker2b.
% Length of proof is 35.
% Level of proof is 10.
% Maximum clause weight is 26.
% Given clauses 3374.
]]></comments>

  <clause id="5" type="goal">
    <literal><![CDATA[
      (exists a exists b (a + b)' = b')
    ]]></literal>
    <attribute><![CDATA[
      answer(Winker2b)
    ]]></attribute>
    <attribute><![CDATA[
      label(non_clause)
    ]]></attribute>
    <attribute><![CDATA[
      label(goal)
    ]]></attribute>
    <justification jstring="[goal].">
      <j1 rule="goal"/>
    </justification>
  </clause>

  <clause id="6" type="assumption">
    <literal><![CDATA[
      x + y = y + x
    ]]></literal>
    <attribute><![CDATA[
      label(Commutativity)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="7" type="assumption">
    <literal><![CDATA[
      (x + y) + z = x + (y + z)
    ]]></literal>
    <attribute><![CDATA[
      label(Associativity)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

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

  <clause id="9" type="assumption">
    <literal><![CDATA[
      g(x) = (x + x')'
    ]]></literal>
    <attribute><![CDATA[
      label(definition_g)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="10">
    <literal><![CDATA[
      (x + x')' = g(x)
    ]]></literal>
    <justification jstring="[copy(9),flip(a)].">
      <j1 rule="copy" parents="9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11" type="assumption">
    <literal><![CDATA[
      h(x) = x + (x + (x + g(x)))
    ]]></literal>
    <attribute><![CDATA[
      label(definition_h)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="12">
    <literal><![CDATA[
      x + (x + (x + g(x))) = h(x)
    ]]></literal>
    <justification jstring="[copy(11),flip(a)].">
      <j1 rule="copy" parents="11"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17" type="deny">
    <literal><![CDATA[
      (x + y)' != y'
    ]]></literal>
    <attribute><![CDATA[
      answer(Winker2b)
    ]]></attribute>
    <justification jstring="[deny(5)].">
      <j1 rule="deny" parents="5"/>
    </justification>
  </clause>

  <clause id="19">
    <literal><![CDATA[
      x + (y + z) = y + (x + z)
    ]]></literal>
    <justification jstring="[para(6(a,1),7(a,1,1)),rewrite([7(2)])].">
      <j1 rule="para" parents="6 7"/>
      <j2 rule="rewrite" parents="7"/>
    </justification>
  </clause>

  <clause id="20">
    <literal><![CDATA[
      ((x + y)' + (y + x')')' = y
    ]]></literal>
    <justification jstring="[para(6(a,1),8(a,1,1,1,1))].">
      <j1 rule="para" parents="6 8"/>
    </justification>
  </clause>

  <clause id="21">
    <literal><![CDATA[
      ((x + y)' + (y' + x)')' = x
    ]]></literal>
    <justification jstring="[para(6(a,1),8(a,1,1,2,1))].">
      <j1 rule="para" parents="6 8"/>
    </justification>
  </clause>

  <clause id="24">
    <literal><![CDATA[
      ((x + y)' + (x + ((y + z)' + (y + z')'))')' = x
    ]]></literal>
    <justification jstring="[para(8(a,1),8(a,1,1,2,1,2)),rewrite([6(11)])].">
      <j1 rule="para" parents="8 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="28">
    <literal><![CDATA[
      ((x + g(y))' + (x + (y + y'))')' = x
    ]]></literal>
    <justification jstring="[para(10(a,1),8(a,1,1,2,1,2)),rewrite([6(8)])].">
      <j1 rule="para" parents="10 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="29">
    <literal><![CDATA[
      (g(x) + (x + x)')' = x
    ]]></literal>
    <justification jstring="[para(10(a,1),8(a,1,1,2)),rewrite([6(4)])].">
      <j1 rule="para" parents="10 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="35">
    <literal><![CDATA[
      (h(x)' + (x + (x + (x + g(x)))')')' = x
    ]]></literal>
    <justification jstring="[para(12(a,1),8(a,1,1,1,1))].">
      <j1 rule="para" parents="12 8"/>
    </justification>
  </clause>

  <clause id="46">
    <literal><![CDATA[
      (x + (y + z))' != z'
    ]]></literal>
    <attribute><![CDATA[
      answer(Winker2b)
    ]]></attribute>
    <justification jstring="[para(7(a,1),17(a,1,1))].">
      <j1 rule="para" parents="7 17"/>
    </justification>
  </clause>

  <clause id="66">
    <literal><![CDATA[
      (x + (x + (x + g(x)))')' = g(x)
    ]]></literal>
    <justification jstring="[para(29(a,1),8(a,1,1,2)),rewrite([19(3),6(2),6(5)])].">
      <j1 rule="para" parents="29 8"/>
      <j2 rule="rewrite" parents="19 6 6"/>
    </justification>
  </clause>

  <clause id="67">
    <literal><![CDATA[
      (x + (g(x) + (x + x)'))' = g(g(x) + (x + x)')
    ]]></literal>
    <justification jstring="[para(29(a,1),10(a,1,1,2)),rewrite([6(5)])].">
      <j1 rule="para" parents="29 10"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="74">
    <literal><![CDATA[
      (g(x) + h(x)')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(35),rewrite([66(8),6(4)])].">
      <j1 rule="back_rewrite" parents="35"/>
      <j2 rule="rewrite" parents="66 6"/>
    </justification>
  </clause>

  <clause id="76">
    <literal><![CDATA[
      ((x + y)' + (x + (g(y) + h(y)'))')' = x
    ]]></literal>
    <justification jstring="[para(74(a,1),8(a,1,1,2,1,2)),rewrite([6(9)])].">
      <j1 rule="para" parents="74 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="77">
    <literal><![CDATA[
      (x + (g(x) + h(x))')' = g(x)
    ]]></literal>
    <justification jstring="[para(74(a,1),8(a,1,1,2)),rewrite([6(5)])].">
      <j1 rule="para" parents="74 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="103">
    <literal><![CDATA[
      (g(x) + (x + (g(x) + h(x)))')' = x
    ]]></literal>
    <justification jstring="[para(77(a,1),8(a,1,1,2)),rewrite([6(7)])].">
      <j1 rule="para" parents="77 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="113">
    <literal><![CDATA[
      ((x + (y + z))' + (z + (x + y)')')' = z
    ]]></literal>
    <justification jstring="[para(7(a,1),20(a,1,1,1,1))].">
      <j1 rule="para" parents="7 20"/>
    </justification>
  </clause>

  <clause id="154">
    <literal><![CDATA[
      (x + (x + (y + (x + y')'))')' = (x + y')'
    ]]></literal>
    <justification jstring="[para(8(a,1),21(a,1,1,2)),rewrite([6(5),7(5),6(7)])].">
      <j1 rule="para" parents="8 21"/>
      <j2 rule="rewrite" parents="6 7 6"/>
    </justification>
  </clause>

  <clause id="167">
    <literal><![CDATA[
      ((x + (g(y) + h(y)'))' + (y + x)')' = x
    ]]></literal>
    <justification jstring="[para(74(a,1),21(a,1,1,2,1,1))].">
      <j1 rule="para" parents="74 21"/>
    </justification>
  </clause>

  <clause id="574">
    <literal><![CDATA[
      ((x + (g(y) + (y + (g(y) + h(y)))'))' + (y + x)')' = x
    ]]></literal>
    <justification jstring="[para(103(a,1),21(a,1,1,2,1,1))].">
      <j1 rule="para" parents="103 21"/>
    </justification>
  </clause>

  <clause id="675">
    <literal><![CDATA[
      (x + (g(x) + (((x + x)' + y)' + ((x + x)' + y')'))')' = g(x)
    ]]></literal>
    <justification jstring="[para(29(a,1),24(a,1,1,1))].">
      <j1 rule="para" parents="29 24"/>
    </justification>
  </clause>

  <clause id="3769">
    <literal><![CDATA[
      (h(x)' + g(g(x) + (x + x)'))' = x + g(x)
    ]]></literal>
    <justification jstring="[para(12(a,1),113(a,1,1,1,1)),rewrite([7(7),67(8)])].">
      <j1 rule="para" parents="12 113"/>
      <j2 rule="rewrite" parents="7 67"/>
    </justification>
  </clause>

  <clause id="14988">
    <literal><![CDATA[
      (x + (g(x) + (x + (g(x) + (h(x)' + (x + x)')))'))' = h(x)'
    ]]></literal>
    <justification jstring="[para(3769(a,1),28(a,1,1,1)),rewrite([29(13),6(9),19(10),19(9),7(12)])].">
      <j1 rule="para" parents="3769 28"/>
      <j2 rule="rewrite" parents="29 6 19 19 7"/>
    </justification>
  </clause>

  <clause id="34718">
    <literal><![CDATA[
      (x + h(x)')' = g(x)
    ]]></literal>
    <justification jstring="[para(76(a,1),675(a,1,1,2,1,2,2)),rewrite([6(9),7(9),7(8),6(11),19(12),14988(13)])].">
      <j1 rule="para" parents="76 675"/>
      <j2 rule="rewrite" parents="6 7 7 6 19 14988"/>
    </justification>
  </clause>

  <clause id="34840">
    <literal><![CDATA[
      (x + (x + (g(x) + h(x)))')' = g(x)
    ]]></literal>
    <justification jstring="[para(34718(a,1),154(a,1,1,2,1,2,2)),rewrite([6(3),34718(11)])].">
      <j1 rule="para" parents="34718 154"/>
      <j2 rule="rewrite" parents="6 34718"/>
    </justification>
  </clause>

  <clause id="35126">
    <literal><![CDATA[
      (g(x) + (g(x) + (h(x)' + (x + (g(x) + h(x)))'))')' = h(x)'
    ]]></literal>
    <justification jstring="[para(34718(a,1),574(a,1,1,2)),rewrite([19(10),6(13)])].">
      <j1 rule="para" parents="34718 574"/>
      <j2 rule="rewrite" parents="19 6"/>
    </justification>
  </clause>

  <clause id="35609">
    <literal><![CDATA[
      (x + (g(x) + h(x)))' = h(x)'
    ]]></literal>
    <justification jstring="[para(34840(a,1),167(a,1,1,2)),rewrite([6(10),7(10),6(13),35126(14)]),flip(a)].">
      <j1 rule="para" parents="34840 167"/>
      <j2 rule="rewrite" parents="6 7 6 35126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35610">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer(Winker2b)
    ]]></attribute>
    <justification jstring="[resolve(35609,a,46,a)].">
      <j1 rule="resolve" parents="35609 46"/>
    </justification>
  </clause>

</proof>

<proof number="2" length="42" max_count="27">

<comments><![CDATA[
% Proof 2 at 989.94 (+ 1.46) seconds: Winker1a.
% Length of proof is 42.
% Level of proof is 12.
% Maximum clause weight is 27.
% Given clauses 3445.
]]></comments>

  <clause id="2" type="goal">
    <literal><![CDATA[
      (exists a exists b a + b = a)
    ]]></literal>
    <attribute><![CDATA[
      answer(Winker1a)
    ]]></attribute>
    <attribute><![CDATA[
      label(non_clause)
    ]]></attribute>
    <attribute><![CDATA[
      label(goal)
    ]]></attribute>
    <justification jstring="[goal].">
      <j1 rule="goal"/>
    </justification>
  </clause>

  <clause id="6" type="assumption">
    <literal><![CDATA[
      x + y = y + x
    ]]></literal>
    <attribute><![CDATA[
      label(Commutativity)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="7" type="assumption">
    <literal><![CDATA[
      (x + y) + z = x + (y + z)
    ]]></literal>
    <attribute><![CDATA[
      label(Associativity)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

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

  <clause id="9" type="assumption">
    <literal><![CDATA[
      g(x) = (x + x')'
    ]]></literal>
    <attribute><![CDATA[
      label(definition_g)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="10">
    <literal><![CDATA[
      (x + x')' = g(x)
    ]]></literal>
    <justification jstring="[copy(9),flip(a)].">
      <j1 rule="copy" parents="9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11" type="assumption">
    <literal><![CDATA[
      h(x) = x + (x + (x + g(x)))
    ]]></literal>
    <attribute><![CDATA[
      label(definition_h)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="12">
    <literal><![CDATA[
      x + (x + (x + g(x))) = h(x)
    ]]></literal>
    <justification jstring="[copy(11),flip(a)].">
      <j1 rule="copy" parents="11"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14" type="deny">
    <literal><![CDATA[
      x + y != x
    ]]></literal>
    <attribute><![CDATA[
      answer(Winker1a)
    ]]></attribute>
    <justification jstring="[deny(2)].">
      <j1 rule="deny" parents="2"/>
    </justification>
  </clause>

  <clause id="19">
    <literal><![CDATA[
      x + (y + z) = y + (x + z)
    ]]></literal>
    <justification jstring="[para(6(a,1),7(a,1,1)),rewrite([7(2)])].">
      <j1 rule="para" parents="6 7"/>
      <j2 rule="rewrite" parents="7"/>
    </justification>
  </clause>

  <clause id="20">
    <literal><![CDATA[
      ((x + y)' + (y + x')')' = y
    ]]></literal>
    <justification jstring="[para(6(a,1),8(a,1,1,1,1))].">
      <j1 rule="para" parents="6 8"/>
    </justification>
  </clause>

  <clause id="21">
    <literal><![CDATA[
      ((x + y)' + (y' + x)')' = x
    ]]></literal>
    <justification jstring="[para(6(a,1),8(a,1,1,2,1))].">
      <j1 rule="para" parents="6 8"/>
    </justification>
  </clause>

  <clause id="24">
    <literal><![CDATA[
      ((x + y)' + (x + ((y + z)' + (y + z')'))')' = x
    ]]></literal>
    <justification jstring="[para(8(a,1),8(a,1,1,2,1,2)),rewrite([6(11)])].">
      <j1 rule="para" parents="8 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="28">
    <literal><![CDATA[
      ((x + g(y))' + (x + (y + y'))')' = x
    ]]></literal>
    <justification jstring="[para(10(a,1),8(a,1,1,2,1,2)),rewrite([6(8)])].">
      <j1 rule="para" parents="10 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="29">
    <literal><![CDATA[
      (g(x) + (x + x)')' = x
    ]]></literal>
    <justification jstring="[para(10(a,1),8(a,1,1,2)),rewrite([6(4)])].">
      <j1 rule="para" parents="10 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="34">
    <literal><![CDATA[
      x + h(y) = y + (y + (g(y) + (x + y)))
    ]]></literal>
    <justification jstring="[para(12(a,1),7(a,2,2)),rewrite([19(5),19(4),6(3)]),flip(a)].">
      <j1 rule="para" parents="12 7"/>
      <j2 rule="rewrite" parents="19 19 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35">
    <literal><![CDATA[
      (h(x)' + (x + (x + (x + g(x)))')')' = x
    ]]></literal>
    <justification jstring="[para(12(a,1),8(a,1,1,1,1))].">
      <j1 rule="para" parents="12 8"/>
    </justification>
  </clause>

  <clause id="36">
    <literal><![CDATA[
      x + (y + z) != x + y
    ]]></literal>
    <attribute><![CDATA[
      answer(Winker1a)
    ]]></attribute>
    <justification jstring="[para(7(a,1),14(a,1))].">
      <j1 rule="para" parents="7 14"/>
    </justification>
  </clause>

  <clause id="66">
    <literal><![CDATA[
      (x + (x + (x + g(x)))')' = g(x)
    ]]></literal>
    <justification jstring="[para(29(a,1),8(a,1,1,2)),rewrite([19(3),6(2),6(5)])].">
      <j1 rule="para" parents="29 8"/>
      <j2 rule="rewrite" parents="19 6 6"/>
    </justification>
  </clause>

  <clause id="67">
    <literal><![CDATA[
      (x + (g(x) + (x + x)'))' = g(g(x) + (x + x)')
    ]]></literal>
    <justification jstring="[para(29(a,1),10(a,1,1,2)),rewrite([6(5)])].">
      <j1 rule="para" parents="29 10"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="74">
    <literal><![CDATA[
      (g(x) + h(x)')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(35),rewrite([66(8),6(4)])].">
      <j1 rule="back_rewrite" parents="35"/>
      <j2 rule="rewrite" parents="66 6"/>
    </justification>
  </clause>

  <clause id="76">
    <literal><![CDATA[
      ((x + y)' + (x + (g(y) + h(y)'))')' = x
    ]]></literal>
    <justification jstring="[para(74(a,1),8(a,1,1,2,1,2)),rewrite([6(9)])].">
      <j1 rule="para" parents="74 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="77">
    <literal><![CDATA[
      (x + (g(x) + h(x))')' = g(x)
    ]]></literal>
    <justification jstring="[para(74(a,1),8(a,1,1,2)),rewrite([6(5)])].">
      <j1 rule="para" parents="74 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="103">
    <literal><![CDATA[
      (g(x) + (x + (g(x) + h(x)))')' = x
    ]]></literal>
    <justification jstring="[para(77(a,1),8(a,1,1,2)),rewrite([6(7)])].">
      <j1 rule="para" parents="77 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="113">
    <literal><![CDATA[
      ((x + (y + z))' + (z + (x + y)')')' = z
    ]]></literal>
    <justification jstring="[para(7(a,1),20(a,1,1,1,1))].">
      <j1 rule="para" parents="7 20"/>
    </justification>
  </clause>

  <clause id="154">
    <literal><![CDATA[
      (x + (x + (y + (x + y')'))')' = (x + y')'
    ]]></literal>
    <justification jstring="[para(8(a,1),21(a,1,1,2)),rewrite([6(5),7(5),6(7)])].">
      <j1 rule="para" parents="8 21"/>
      <j2 rule="rewrite" parents="6 7 6"/>
    </justification>
  </clause>

  <clause id="166">
    <literal><![CDATA[
      ((x + (g(y) + (y + y)'))' + (y + x)')' = x
    ]]></literal>
    <justification jstring="[para(29(a,1),21(a,1,1,2,1,1))].">
      <j1 rule="para" parents="29 21"/>
    </justification>
  </clause>

  <clause id="167">
    <literal><![CDATA[
      ((x + (g(y) + h(y)'))' + (y + x)')' = x
    ]]></literal>
    <justification jstring="[para(74(a,1),21(a,1,1,2,1,1))].">
      <j1 rule="para" parents="74 21"/>
    </justification>
  </clause>

  <clause id="574">
    <literal><![CDATA[
      ((x + (g(y) + (y + (g(y) + h(y)))'))' + (y + x)')' = x
    ]]></literal>
    <justification jstring="[para(103(a,1),21(a,1,1,2,1,1))].">
      <j1 rule="para" parents="103 21"/>
    </justification>
  </clause>

  <clause id="675">
    <literal><![CDATA[
      (x + (g(x) + (((x + x)' + y)' + ((x + x)' + y')'))')' = g(x)
    ]]></literal>
    <justification jstring="[para(29(a,1),24(a,1,1,1))].">
      <j1 rule="para" parents="29 24"/>
    </justification>
  </clause>

  <clause id="1383">
    <literal><![CDATA[
      x + (y + (z + u)) != y + (x + z)
    ]]></literal>
    <attribute><![CDATA[
      answer(Winker1a)
    ]]></attribute>
    <justification jstring="[para(19(a,1),36(a,2)),rewrite([7(2)])].">
      <j1 rule="para" parents="19 36"/>
      <j2 rule="rewrite" parents="7"/>
    </justification>
  </clause>

  <clause id="3769">
    <literal><![CDATA[
      (h(x)' + g(g(x) + (x + x)'))' = x + g(x)
    ]]></literal>
    <justification jstring="[para(12(a,1),113(a,1,1,1,1)),rewrite([7(7),67(8)])].">
      <j1 rule="para" parents="12 113"/>
      <j2 rule="rewrite" parents="7 67"/>
    </justification>
  </clause>

  <clause id="12445">
    <literal><![CDATA[
      (h(x)' + (x + (x + (g(x) + (g(x) + (x + x)'))))')' = x + (x + g(x))
    ]]></literal>
    <justification jstring="[para(12(a,1),166(a,1,1,2,1)),rewrite([19(8),7(7),7(6),19(8),19(7),6(12)])].">
      <j1 rule="para" parents="12 166"/>
      <j2 rule="rewrite" parents="19 7 7 19 19 6"/>
    </justification>
  </clause>

  <clause id="14988">
    <literal><![CDATA[
      (x + (g(x) + (x + (g(x) + (h(x)' + (x + x)')))'))' = h(x)'
    ]]></literal>
    <justification jstring="[para(3769(a,1),28(a,1,1,1)),rewrite([29(13),6(9),19(10),19(9),7(12)])].">
      <j1 rule="para" parents="3769 28"/>
      <j2 rule="rewrite" parents="29 6 19 19 7"/>
    </justification>
  </clause>

  <clause id="33954">
    <literal><![CDATA[
      x + (y + (z + u)) != y + (x + u)
    ]]></literal>
    <attribute><![CDATA[
      answer(Winker1a)
    ]]></attribute>
    <justification jstring="[para(6(a,1),1383(a,1,2,2))].">
      <j1 rule="para" parents="6 1383"/>
    </justification>
  </clause>

  <clause id="34718">
    <literal><![CDATA[
      (x + h(x)')' = g(x)
    ]]></literal>
    <justification jstring="[para(76(a,1),675(a,1,1,2,1,2,2)),rewrite([6(9),7(9),7(8),6(11),19(12),14988(13)])].">
      <j1 rule="para" parents="76 675"/>
      <j2 rule="rewrite" parents="6 7 7 6 19 14988"/>
    </justification>
  </clause>

  <clause id="34840">
    <literal><![CDATA[
      (x + (x + (g(x) + h(x)))')' = g(x)
    ]]></literal>
    <justification jstring="[para(34718(a,1),154(a,1,1,2,1,2,2)),rewrite([6(3),34718(11)])].">
      <j1 rule="para" parents="34718 154"/>
      <j2 rule="rewrite" parents="6 34718"/>
    </justification>
  </clause>

  <clause id="35126">
    <literal><![CDATA[
      (g(x) + (g(x) + (h(x)' + (x + (g(x) + h(x)))'))')' = h(x)'
    ]]></literal>
    <justification jstring="[para(34718(a,1),574(a,1,1,2)),rewrite([19(10),6(13)])].">
      <j1 rule="para" parents="34718 574"/>
      <j2 rule="rewrite" parents="19 6"/>
    </justification>
  </clause>

  <clause id="35609">
    <literal><![CDATA[
      (x + (g(x) + h(x)))' = h(x)'
    ]]></literal>
    <justification jstring="[para(34840(a,1),167(a,1,1,2)),rewrite([6(10),7(10),6(13),35126(14)]),flip(a)].">
      <j1 rule="para" parents="34840 167"/>
      <j2 rule="rewrite" parents="6 7 6 35126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35690">
    <literal><![CDATA[
      (x + (x + (x + (x + (g(x) + g(x))))))' = h(x)'
    ]]></literal>
    <justification jstring="[para(34(a,1),35609(a,1,1,2)),rewrite([6(3),19(4)])].">
      <j1 rule="para" parents="34 35609"/>
      <j2 rule="rewrite" parents="6 19"/>
    </justification>
  </clause>

  <clause id="36259">
    <literal><![CDATA[
      x + (x + (g(x) + g(x))) = x + (x + g(x))
    ]]></literal>
    <justification jstring="[para(35690(a,1),113(a,1,1,1)),rewrite([7(10),7(9),7(8),12445(13)]),flip(a)].">
      <j1 rule="para" parents="35690 113"/>
      <j2 rule="rewrite" parents="7 7 7 12445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36260">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer(Winker1a)
    ]]></attribute>
    <justification jstring="[resolve(36259,a,33954,a)].">
      <j1 rule="resolve" parents="36259 33954"/>
    </justification>
  </clause>

</proof>

<proof number="3" length="41" max_count="27">

<comments><![CDATA[
% Proof 3 at 989.95 (+ 1.46) seconds: Winker1b.
% Length of proof is 41.
% Level of proof is 12.
% Maximum clause weight is 27.
% Given clauses 3445.
]]></comments>

  <clause id="3" type="goal">
    <literal><![CDATA[
      (exists a exists b a + b = b)
    ]]></literal>
    <attribute><![CDATA[
      answer(Winker1b)
    ]]></attribute>
    <attribute><![CDATA[
      label(non_clause)
    ]]></attribute>
    <attribute><![CDATA[
      label(goal)
    ]]></attribute>
    <justification jstring="[goal].">
      <j1 rule="goal"/>
    </justification>
  </clause>

  <clause id="6" type="assumption">
    <literal><![CDATA[
      x + y = y + x
    ]]></literal>
    <attribute><![CDATA[
      label(Commutativity)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="7" type="assumption">
    <literal><![CDATA[
      (x + y) + z = x + (y + z)
    ]]></literal>
    <attribute><![CDATA[
      label(Associativity)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

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

  <clause id="9" type="assumption">
    <literal><![CDATA[
      g(x) = (x + x')'
    ]]></literal>
    <attribute><![CDATA[
      label(definition_g)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="10">
    <literal><![CDATA[
      (x + x')' = g(x)
    ]]></literal>
    <justification jstring="[copy(9),flip(a)].">
      <j1 rule="copy" parents="9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11" type="assumption">
    <literal><![CDATA[
      h(x) = x + (x + (x + g(x)))
    ]]></literal>
    <attribute><![CDATA[
      label(definition_h)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="12">
    <literal><![CDATA[
      x + (x + (x + g(x))) = h(x)
    ]]></literal>
    <justification jstring="[copy(11),flip(a)].">
      <j1 rule="copy" parents="11"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15" type="deny">
    <literal><![CDATA[
      x + y != y
    ]]></literal>
    <attribute><![CDATA[
      answer(Winker1b)
    ]]></attribute>
    <justification jstring="[deny(3)].">
      <j1 rule="deny" parents="3"/>
    </justification>
  </clause>

  <clause id="19">
    <literal><![CDATA[
      x + (y + z) = y + (x + z)
    ]]></literal>
    <justification jstring="[para(6(a,1),7(a,1,1)),rewrite([7(2)])].">
      <j1 rule="para" parents="6 7"/>
      <j2 rule="rewrite" parents="7"/>
    </justification>
  </clause>

  <clause id="20">
    <literal><![CDATA[
      ((x + y)' + (y + x')')' = y
    ]]></literal>
    <justification jstring="[para(6(a,1),8(a,1,1,1,1))].">
      <j1 rule="para" parents="6 8"/>
    </justification>
  </clause>

  <clause id="21">
    <literal><![CDATA[
      ((x + y)' + (y' + x)')' = x
    ]]></literal>
    <justification jstring="[para(6(a,1),8(a,1,1,2,1))].">
      <j1 rule="para" parents="6 8"/>
    </justification>
  </clause>

  <clause id="24">
    <literal><![CDATA[
      ((x + y)' + (x + ((y + z)' + (y + z')'))')' = x
    ]]></literal>
    <justification jstring="[para(8(a,1),8(a,1,1,2,1,2)),rewrite([6(11)])].">
      <j1 rule="para" parents="8 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="28">
    <literal><![CDATA[
      ((x + g(y))' + (x + (y + y'))')' = x
    ]]></literal>
    <justification jstring="[para(10(a,1),8(a,1,1,2,1,2)),rewrite([6(8)])].">
      <j1 rule="para" parents="10 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="29">
    <literal><![CDATA[
      (g(x) + (x + x)')' = x
    ]]></literal>
    <justification jstring="[para(10(a,1),8(a,1,1,2)),rewrite([6(4)])].">
      <j1 rule="para" parents="10 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="34">
    <literal><![CDATA[
      x + h(y) = y + (y + (g(y) + (x + y)))
    ]]></literal>
    <justification jstring="[para(12(a,1),7(a,2,2)),rewrite([19(5),19(4),6(3)]),flip(a)].">
      <j1 rule="para" parents="12 7"/>
      <j2 rule="rewrite" parents="19 19 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35">
    <literal><![CDATA[
      (h(x)' + (x + (x + (x + g(x)))')')' = x
    ]]></literal>
    <justification jstring="[para(12(a,1),8(a,1,1,1,1))].">
      <j1 rule="para" parents="12 8"/>
    </justification>
  </clause>

  <clause id="54">
    <literal><![CDATA[
      x + (y + z) != x + z
    ]]></literal>
    <attribute><![CDATA[
      answer(Winker1b)
    ]]></attribute>
    <justification jstring="[para(19(a,1),15(a,1))].">
      <j1 rule="para" parents="19 15"/>
    </justification>
  </clause>

  <clause id="66">
    <literal><![CDATA[
      (x + (x + (x + g(x)))')' = g(x)
    ]]></literal>
    <justification jstring="[para(29(a,1),8(a,1,1,2)),rewrite([19(3),6(2),6(5)])].">
      <j1 rule="para" parents="29 8"/>
      <j2 rule="rewrite" parents="19 6 6"/>
    </justification>
  </clause>

  <clause id="67">
    <literal><![CDATA[
      (x + (g(x) + (x + x)'))' = g(g(x) + (x + x)')
    ]]></literal>
    <justification jstring="[para(29(a,1),10(a,1,1,2)),rewrite([6(5)])].">
      <j1 rule="para" parents="29 10"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="74">
    <literal><![CDATA[
      (g(x) + h(x)')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(35),rewrite([66(8),6(4)])].">
      <j1 rule="back_rewrite" parents="35"/>
      <j2 rule="rewrite" parents="66 6"/>
    </justification>
  </clause>

  <clause id="76">
    <literal><![CDATA[
      ((x + y)' + (x + (g(y) + h(y)'))')' = x
    ]]></literal>
    <justification jstring="[para(74(a,1),8(a,1,1,2,1,2)),rewrite([6(9)])].">
      <j1 rule="para" parents="74 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="77">
    <literal><![CDATA[
      (x + (g(x) + h(x))')' = g(x)
    ]]></literal>
    <justification jstring="[para(74(a,1),8(a,1,1,2)),rewrite([6(5)])].">
      <j1 rule="para" parents="74 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="103">
    <literal><![CDATA[
      (g(x) + (x + (g(x) + h(x)))')' = x
    ]]></literal>
    <justification jstring="[para(77(a,1),8(a,1,1,2)),rewrite([6(7)])].">
      <j1 rule="para" parents="77 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="113">
    <literal><![CDATA[
      ((x + (y + z))' + (z + (x + y)')')' = z
    ]]></literal>
    <justification jstring="[para(7(a,1),20(a,1,1,1,1))].">
      <j1 rule="para" parents="7 20"/>
    </justification>
  </clause>

  <clause id="154">
    <literal><![CDATA[
      (x + (x + (y + (x + y')'))')' = (x + y')'
    ]]></literal>
    <justification jstring="[para(8(a,1),21(a,1,1,2)),rewrite([6(5),7(5),6(7)])].">
      <j1 rule="para" parents="8 21"/>
      <j2 rule="rewrite" parents="6 7 6"/>
    </justification>
  </clause>

  <clause id="166">
    <literal><![CDATA[
      ((x + (g(y) + (y + y)'))' + (y + x)')' = x
    ]]></literal>
    <justification jstring="[para(29(a,1),21(a,1,1,2,1,1))].">
      <j1 rule="para" parents="29 21"/>
    </justification>
  </clause>

  <clause id="167">
    <literal><![CDATA[
      ((x + (g(y) + h(y)'))' + (y + x)')' = x
    ]]></literal>
    <justification jstring="[para(74(a,1),21(a,1,1,2,1,1))].">
      <j1 rule="para" parents="74 21"/>
    </justification>
  </clause>

  <clause id="574">
    <literal><![CDATA[
      ((x + (g(y) + (y + (g(y) + h(y)))'))' + (y + x)')' = x
    ]]></literal>
    <justification jstring="[para(103(a,1),21(a,1,1,2,1,1))].">
      <j1 rule="para" parents="103 21"/>
    </justification>
  </clause>

  <clause id="675">
    <literal><![CDATA[
      (x + (g(x) + (((x + x)' + y)' + ((x + x)' + y')'))')' = g(x)
    ]]></literal>
    <justification jstring="[para(29(a,1),24(a,1,1,1))].">
      <j1 rule="para" parents="29 24"/>
    </justification>
  </clause>

  <clause id="3769">
    <literal><![CDATA[
      (h(x)' + g(g(x) + (x + x)'))' = x + g(x)
    ]]></literal>
    <justification jstring="[para(12(a,1),113(a,1,1,1,1)),rewrite([7(7),67(8)])].">
      <j1 rule="para" parents="12 113"/>
      <j2 rule="rewrite" parents="7 67"/>
    </justification>
  </clause>

  <clause id="5722">
    <literal><![CDATA[
      x + (y + (z + u)) != x + (y + u)
    ]]></literal>
    <attribute><![CDATA[
      answer(Winker1b)
    ]]></attribute>
    <justification jstring="[para(7(a,1),54(a,1)),rewrite([7(5)])].">
      <j1 rule="para" parents="7 54"/>
      <j2 rule="rewrite" parents="7"/>
    </justification>
  </clause>

  <clause id="12445">
    <literal><![CDATA[
      (h(x)' + (x + (x + (g(x) + (g(x) + (x + x)'))))')' = x + (x + g(x))
    ]]></literal>
    <justification jstring="[para(12(a,1),166(a,1,1,2,1)),rewrite([19(8),7(7),7(6),19(8),19(7),6(12)])].">
      <j1 rule="para" parents="12 166"/>
      <j2 rule="rewrite" parents="19 7 7 19 19 6"/>
    </justification>
  </clause>

  <clause id="14988">
    <literal><![CDATA[
      (x + (g(x) + (x + (g(x) + (h(x)' + (x + x)')))'))' = h(x)'
    ]]></literal>
    <justification jstring="[para(3769(a,1),28(a,1,1,1)),rewrite([29(13),6(9),19(10),19(9),7(12)])].">
      <j1 rule="para" parents="3769 28"/>
      <j2 rule="rewrite" parents="29 6 19 19 7"/>
    </justification>
  </clause>

  <clause id="34718">
    <literal><![CDATA[
      (x + h(x)')' = g(x)
    ]]></literal>
    <justification jstring="[para(76(a,1),675(a,1,1,2,1,2,2)),rewrite([6(9),7(9),7(8),6(11),19(12),14988(13)])].">
      <j1 rule="para" parents="76 675"/>
      <j2 rule="rewrite" parents="6 7 7 6 19 14988"/>
    </justification>
  </clause>

  <clause id="34840">
    <literal><![CDATA[
      (x + (x + (g(x) + h(x)))')' = g(x)
    ]]></literal>
    <justification jstring="[para(34718(a,1),154(a,1,1,2,1,2,2)),rewrite([6(3),34718(11)])].">
      <j1 rule="para" parents="34718 154"/>
      <j2 rule="rewrite" parents="6 34718"/>
    </justification>
  </clause>

  <clause id="35126">
    <literal><![CDATA[
      (g(x) + (g(x) + (h(x)' + (x + (g(x) + h(x)))'))')' = h(x)'
    ]]></literal>
    <justification jstring="[para(34718(a,1),574(a,1,1,2)),rewrite([19(10),6(13)])].">
      <j1 rule="para" parents="34718 574"/>
      <j2 rule="rewrite" parents="19 6"/>
    </justification>
  </clause>

  <clause id="35609">
    <literal><![CDATA[
      (x + (g(x) + h(x)))' = h(x)'
    ]]></literal>
    <justification jstring="[para(34840(a,1),167(a,1,1,2)),rewrite([6(10),7(10),6(13),35126(14)]),flip(a)].">
      <j1 rule="para" parents="34840 167"/>
      <j2 rule="rewrite" parents="6 7 6 35126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35690">
    <literal><![CDATA[
      (x + (x + (x + (x + (g(x) + g(x))))))' = h(x)'
    ]]></literal>
    <justification jstring="[para(34(a,1),35609(a,1,1,2)),rewrite([6(3),19(4)])].">
      <j1 rule="para" parents="34 35609"/>
      <j2 rule="rewrite" parents="6 19"/>
    </justification>
  </clause>

  <clause id="36259">
    <literal><![CDATA[
      x + (x + (g(x) + g(x))) = x + (x + g(x))
    ]]></literal>
    <justification jstring="[para(35690(a,1),113(a,1,1,1)),rewrite([7(10),7(9),7(8),12445(13)]),flip(a)].">
      <j1 rule="para" parents="35690 113"/>
      <j2 rule="rewrite" parents="7 7 7 12445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36261">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer(Winker1b)
    ]]></attribute>
    <justification jstring="[resolve(36259,a,5722,a)].">
      <j1 rule="resolve" parents="36259 5722"/>
    </justification>
  </clause>

</proof>

<proof number="4" length="45" max_count="27">

<comments><![CDATA[
% Proof 4 at 989.97 (+ 1.46) seconds: Winker2a.
% Length of proof is 45.
% Level of proof is 13.
% Maximum clause weight is 27.
% Given clauses 3445.
]]></comments>

  <clause id="4" type="goal">
    <literal><![CDATA[
      (exists a exists b (a + b)' = a')
    ]]></literal>
    <attribute><![CDATA[
      answer(Winker2a)
    ]]></attribute>
    <attribute><![CDATA[
      label(non_clause)
    ]]></attribute>
    <attribute><![CDATA[
      label(goal)
    ]]></attribute>
    <justification jstring="[goal].">
      <j1 rule="goal"/>
    </justification>
  </clause>

  <clause id="6" type="assumption">
    <literal><![CDATA[
      x + y = y + x
    ]]></literal>
    <attribute><![CDATA[
      label(Commutativity)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="7" type="assumption">
    <literal><![CDATA[
      (x + y) + z = x + (y + z)
    ]]></literal>
    <attribute><![CDATA[
      label(Associativity)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

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

  <clause id="9" type="assumption">
    <literal><![CDATA[
      g(x) = (x + x')'
    ]]></literal>
    <attribute><![CDATA[
      label(definition_g)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="10">
    <literal><![CDATA[
      (x + x')' = g(x)
    ]]></literal>
    <justification jstring="[copy(9),flip(a)].">
      <j1 rule="copy" parents="9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11" type="assumption">
    <literal><![CDATA[
      h(x) = x + (x + (x + g(x)))
    ]]></literal>
    <attribute><![CDATA[
      label(definition_h)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="12">
    <literal><![CDATA[
      x + (x + (x + g(x))) = h(x)
    ]]></literal>
    <justification jstring="[copy(11),flip(a)].">
      <j1 rule="copy" parents="11"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16" type="deny">
    <literal><![CDATA[
      (x + y)' != x'
    ]]></literal>
    <attribute><![CDATA[
      answer(Winker2a)
    ]]></attribute>
    <justification jstring="[deny(4)].">
      <j1 rule="deny" parents="4"/>
    </justification>
  </clause>

  <clause id="19">
    <literal><![CDATA[
      x + (y + z) = y + (x + z)
    ]]></literal>
    <justification jstring="[para(6(a,1),7(a,1,1)),rewrite([7(2)])].">
      <j1 rule="para" parents="6 7"/>
      <j2 rule="rewrite" parents="7"/>
    </justification>
  </clause>

  <clause id="20">
    <literal><![CDATA[
      ((x + y)' + (y + x')')' = y
    ]]></literal>
    <justification jstring="[para(6(a,1),8(a,1,1,1,1))].">
      <j1 rule="para" parents="6 8"/>
    </justification>
  </clause>

  <clause id="21">
    <literal><![CDATA[
      ((x + y)' + (y' + x)')' = x
    ]]></literal>
    <justification jstring="[para(6(a,1),8(a,1,1,2,1))].">
      <j1 rule="para" parents="6 8"/>
    </justification>
  </clause>

  <clause id="24">
    <literal><![CDATA[
      ((x + y)' + (x + ((y + z)' + (y + z')'))')' = x
    ]]></literal>
    <justification jstring="[para(8(a,1),8(a,1,1,2,1,2)),rewrite([6(11)])].">
      <j1 rule="para" parents="8 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="28">
    <literal><![CDATA[
      ((x + g(y))' + (x + (y + y'))')' = x
    ]]></literal>
    <justification jstring="[para(10(a,1),8(a,1,1,2,1,2)),rewrite([6(8)])].">
      <j1 rule="para" parents="10 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="29">
    <literal><![CDATA[
      (g(x) + (x + x)')' = x
    ]]></literal>
    <justification jstring="[para(10(a,1),8(a,1,1,2)),rewrite([6(4)])].">
      <j1 rule="para" parents="10 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="34">
    <literal><![CDATA[
      x + h(y) = y + (y + (g(y) + (x + y)))
    ]]></literal>
    <justification jstring="[para(12(a,1),7(a,2,2)),rewrite([19(5),19(4),6(3)]),flip(a)].">
      <j1 rule="para" parents="12 7"/>
      <j2 rule="rewrite" parents="19 19 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35">
    <literal><![CDATA[
      (h(x)' + (x + (x + (x + g(x)))')')' = x
    ]]></literal>
    <justification jstring="[para(12(a,1),8(a,1,1,1,1))].">
      <j1 rule="para" parents="12 8"/>
    </justification>
  </clause>

  <clause id="66">
    <literal><![CDATA[
      (x + (x + (x + g(x)))')' = g(x)
    ]]></literal>
    <justification jstring="[para(29(a,1),8(a,1,1,2)),rewrite([19(3),6(2),6(5)])].">
      <j1 rule="para" parents="29 8"/>
      <j2 rule="rewrite" parents="19 6 6"/>
    </justification>
  </clause>

  <clause id="67">
    <literal><![CDATA[
      (x + (g(x) + (x + x)'))' = g(g(x) + (x + x)')
    ]]></literal>
    <justification jstring="[para(29(a,1),10(a,1,1,2)),rewrite([6(5)])].">
      <j1 rule="para" parents="29 10"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="74">
    <literal><![CDATA[
      (g(x) + h(x)')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(35),rewrite([66(8),6(4)])].">
      <j1 rule="back_rewrite" parents="35"/>
      <j2 rule="rewrite" parents="66 6"/>
    </justification>
  </clause>

  <clause id="76">
    <literal><![CDATA[
      ((x + y)' + (x + (g(y) + h(y)'))')' = x
    ]]></literal>
    <justification jstring="[para(74(a,1),8(a,1,1,2,1,2)),rewrite([6(9)])].">
      <j1 rule="para" parents="74 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="77">
    <literal><![CDATA[
      (x + (g(x) + h(x))')' = g(x)
    ]]></literal>
    <justification jstring="[para(74(a,1),8(a,1,1,2)),rewrite([6(5)])].">
      <j1 rule="para" parents="74 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="103">
    <literal><![CDATA[
      (g(x) + (x + (g(x) + h(x)))')' = x
    ]]></literal>
    <justification jstring="[para(77(a,1),8(a,1,1,2)),rewrite([6(7)])].">
      <j1 rule="para" parents="77 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="113">
    <literal><![CDATA[
      ((x + (y + z))' + (z + (x + y)')')' = z
    ]]></literal>
    <justification jstring="[para(7(a,1),20(a,1,1,1,1))].">
      <j1 rule="para" parents="7 20"/>
    </justification>
  </clause>

  <clause id="124">
    <literal><![CDATA[
      (x + y)'' != y
    ]]></literal>
    <attribute><![CDATA[
      answer(Winker2a)
    ]]></attribute>
    <justification jstring="[para(20(a,1),16(a,1)),flip(a)].">
      <j1 rule="para" parents="20 16"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="154">
    <literal><![CDATA[
      (x + (x + (y + (x + y')'))')' = (x + y')'
    ]]></literal>
    <justification jstring="[para(8(a,1),21(a,1,1,2)),rewrite([6(5),7(5),6(7)])].">
      <j1 rule="para" parents="8 21"/>
      <j2 rule="rewrite" parents="6 7 6"/>
    </justification>
  </clause>

  <clause id="157">
    <literal><![CDATA[
      (g(x') + (x + x'')')' = x''
    ]]></literal>
    <justification jstring="[para(10(a,1),21(a,1,1,2)),rewrite([6(3),6(7)])].">
      <j1 rule="para" parents="10 21"/>
      <j2 rule="rewrite" parents="6 6"/>
    </justification>
  </clause>

  <clause id="166">
    <literal><![CDATA[
      ((x + (g(y) + (y + y)'))' + (y + x)')' = x
    ]]></literal>
    <justification jstring="[para(29(a,1),21(a,1,1,2,1,1))].">
      <j1 rule="para" parents="29 21"/>
    </justification>
  </clause>

  <clause id="167">
    <literal><![CDATA[
      ((x + (g(y) + h(y)'))' + (y + x)')' = x
    ]]></literal>
    <justification jstring="[para(74(a,1),21(a,1,1,2,1,1))].">
      <j1 rule="para" parents="74 21"/>
    </justification>
  </clause>

  <clause id="574">
    <literal><![CDATA[
      ((x + (g(y) + (y + (g(y) + h(y)))'))' + (y + x)')' = x
    ]]></literal>
    <justification jstring="[para(103(a,1),21(a,1,1,2,1,1))].">
      <j1 rule="para" parents="103 21"/>
    </justification>
  </clause>

  <clause id="675">
    <literal><![CDATA[
      (x + (g(x) + (((x + x)' + y)' + ((x + x)' + y')'))')' = g(x)
    ]]></literal>
    <justification jstring="[para(29(a,1),24(a,1,1,1))].">
      <j1 rule="para" parents="29 24"/>
    </justification>
  </clause>

  <clause id="1180">
    <literal><![CDATA[
      (g(x) + (g(x) + (x' + h(x)'))')' = x'
    ]]></literal>
    <justification jstring="[para(74(a,1),157(a,1,1,1,1)),rewrite([74(10),6(7),19(7),74(15)])].">
      <j1 rule="para" parents="74 157"/>
      <j2 rule="rewrite" parents="74 6 19 74"/>
    </justification>
  </clause>

  <clause id="3769">
    <literal><![CDATA[
      (h(x)' + g(g(x) + (x + x)'))' = x + g(x)
    ]]></literal>
    <justification jstring="[para(12(a,1),113(a,1,1,1,1)),rewrite([7(7),67(8)])].">
      <j1 rule="para" parents="12 113"/>
      <j2 rule="rewrite" parents="7 67"/>
    </justification>
  </clause>

  <clause id="12445">
    <literal><![CDATA[
      (h(x)' + (x + (x + (g(x) + (g(x) + (x + x)'))))')' = x + (x + g(x))
    ]]></literal>
    <justification jstring="[para(12(a,1),166(a,1,1,2,1)),rewrite([19(8),7(7),7(6),19(8),19(7),6(12)])].">
      <j1 rule="para" parents="12 166"/>
      <j2 rule="rewrite" parents="19 7 7 19 19 6"/>
    </justification>
  </clause>

  <clause id="14988">
    <literal><![CDATA[
      (x + (g(x) + (x + (g(x) + (h(x)' + (x + x)')))'))' = h(x)'
    ]]></literal>
    <justification jstring="[para(3769(a,1),28(a,1,1,1)),rewrite([29(13),6(9),19(10),19(9),7(12)])].">
      <j1 rule="para" parents="3769 28"/>
      <j2 rule="rewrite" parents="29 6 19 19 7"/>
    </justification>
  </clause>

  <clause id="34718">
    <literal><![CDATA[
      (x + h(x)')' = g(x)
    ]]></literal>
    <justification jstring="[para(76(a,1),675(a,1,1,2,1,2,2)),rewrite([6(9),7(9),7(8),6(11),19(12),14988(13)])].">
      <j1 rule="para" parents="76 675"/>
      <j2 rule="rewrite" parents="6 7 7 6 19 14988"/>
    </justification>
  </clause>

  <clause id="34748">
    <literal><![CDATA[
      ((x + (y + h(y)'))' + (g(y) + x)')' = x
    ]]></literal>
    <justification jstring="[para(34718(a,1),21(a,1,1,2,1,1))].">
      <j1 rule="para" parents="34718 21"/>
    </justification>
  </clause>

  <clause id="34840">
    <literal><![CDATA[
      (x + (x + (g(x) + h(x)))')' = g(x)
    ]]></literal>
    <justification jstring="[para(34718(a,1),154(a,1,1,2,1,2,2)),rewrite([6(3),34718(11)])].">
      <j1 rule="para" parents="34718 154"/>
      <j2 rule="rewrite" parents="6 34718"/>
    </justification>
  </clause>

  <clause id="35126">
    <literal><![CDATA[
      (g(x) + (g(x) + (h(x)' + (x + (g(x) + h(x)))'))')' = h(x)'
    ]]></literal>
    <justification jstring="[para(34718(a,1),574(a,1,1,2)),rewrite([19(10),6(13)])].">
      <j1 rule="para" parents="34718 574"/>
      <j2 rule="rewrite" parents="19 6"/>
    </justification>
  </clause>

  <clause id="35609">
    <literal><![CDATA[
      (x + (g(x) + h(x)))' = h(x)'
    ]]></literal>
    <justification jstring="[para(34840(a,1),167(a,1,1,2)),rewrite([6(10),7(10),6(13),35126(14)]),flip(a)].">
      <j1 rule="para" parents="34840 167"/>
      <j2 rule="rewrite" parents="6 7 6 35126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35690">
    <literal><![CDATA[
      (x + (x + (x + (x + (g(x) + g(x))))))' = h(x)'
    ]]></literal>
    <justification jstring="[para(34(a,1),35609(a,1,1,2)),rewrite([6(3),19(4)])].">
      <j1 rule="para" parents="34 35609"/>
      <j2 rule="rewrite" parents="6 19"/>
    </justification>
  </clause>

  <clause id="36019">
    <literal><![CDATA[
      (g(x) + y)' != y'
    ]]></literal>
    <attribute><![CDATA[
      answer(Winker2a)
    ]]></attribute>
    <justification jstring="[para(34748(a,1),124(a,1,1)),flip(a)].">
      <j1 rule="para" parents="34748 124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36259">
    <literal><![CDATA[
      x + (x + (g(x) + g(x))) = x + (x + g(x))
    ]]></literal>
    <justification jstring="[para(35690(a,1),113(a,1,1,1)),rewrite([7(10),7(9),7(8),12445(13)]),flip(a)].">
      <j1 rule="para" parents="35690 113"/>
      <j2 rule="rewrite" parents="7 7 7 12445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36273">
    <literal><![CDATA[
      (x + h(x))' = h(x)'
    ]]></literal>
    <justification jstring="[para(35690(a,1),1180(a,2)),rewrite([36259(5),12(4),36259(8),12(7),36259(11),12(10),36259(14),12(13),1180(18)])].">
      <j1 rule="para" parents="35690 1180"/>
      <j2 rule="rewrite" parents="36259 12 36259 12 36259 12 36259 12 1180"/>
    </justification>
  </clause>

  <clause id="36274">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer(Winker2a)
    ]]></attribute>
    <justification jstring="[resolve(36273,a,36019,a)].">
      <j1 rule="resolve" parents="36273 36019"/>
    </justification>
  </clause>

</proof>

<proof number="5" length="219" max_count="81">

<comments><![CDATA[
% Proof 5 at 1025.36 (+ 1.48) seconds: Huntington.
% Length of proof is 219.
% Level of proof is 36.
% Maximum clause weight is 81.
% Given clauses 3475.
]]></comments>

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

  <clause id="6" type="assumption">
    <literal><![CDATA[
      x + y = y + x
    ]]></literal>
    <attribute><![CDATA[
      label(Commutativity)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="7" type="assumption">
    <literal><![CDATA[
      (x + y) + z = x + (y + z)
    ]]></literal>
    <attribute><![CDATA[
      label(Associativity)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

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

  <clause id="9" type="assumption">
    <literal><![CDATA[
      g(x) = (x + x')'
    ]]></literal>
    <attribute><![CDATA[
      label(definition_g)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="10">
    <literal><![CDATA[
      (x + x')' = g(x)
    ]]></literal>
    <justification jstring="[copy(9),flip(a)].">
      <j1 rule="copy" parents="9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11" type="assumption">
    <literal><![CDATA[
      h(x) = x + (x + (x + g(x)))
    ]]></literal>
    <attribute><![CDATA[
      label(definition_h)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="12">
    <literal><![CDATA[
      x + (x + (x + g(x))) = h(x)
    ]]></literal>
    <justification jstring="[copy(11),flip(a)].">
      <j1 rule="copy" parents="11"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13" type="deny">
    <literal><![CDATA[
      (c1 + c2')' + (c1' + c2')' != c2
    ]]></literal>
    <attribute><![CDATA[
      answer(Huntington)
    ]]></attribute>
    <justification jstring="[deny(1)].">
      <j1 rule="deny" parents="1"/>
    </justification>
  </clause>

  <clause id="19">
    <literal><![CDATA[
      x + (y + z) = y + (x + z)
    ]]></literal>
    <justification jstring="[para(6(a,1),7(a,1,1)),rewrite([7(2)])].">
      <j1 rule="para" parents="6 7"/>
      <j2 rule="rewrite" parents="7"/>
    </justification>
  </clause>

  <clause id="20">
    <literal><![CDATA[
      ((x + y)' + (y + x')')' = y
    ]]></literal>
    <justification jstring="[para(6(a,1),8(a,1,1,1,1))].">
      <j1 rule="para" parents="6 8"/>
    </justification>
  </clause>

  <clause id="21">
    <literal><![CDATA[
      ((x + y)' + (y' + x)')' = x
    ]]></literal>
    <justification jstring="[para(6(a,1),8(a,1,1,2,1))].">
      <j1 rule="para" parents="6 8"/>
    </justification>
  </clause>

  <clause id="22">
    <literal><![CDATA[
      ((x + (y + z))' + (x + (y + z'))')' = x + y
    ]]></literal>
    <justification jstring="[para(7(a,1),8(a,1,1,1,1)),rewrite([7(6)])].">
      <j1 rule="para" parents="7 8"/>
      <j2 rule="rewrite" parents="7"/>
    </justification>
  </clause>

  <clause id="23">
    <literal><![CDATA[
      (x + ((x + y)' + (x + y')'')')' = (x + y)'
    ]]></literal>
    <justification jstring="[para(8(a,1),8(a,1,1,1))].">
      <j1 rule="para" parents="8 8"/>
    </justification>
  </clause>

  <clause id="24">
    <literal><![CDATA[
      ((x + y)' + (x + ((y + z)' + (y + z')'))')' = x
    ]]></literal>
    <justification jstring="[para(8(a,1),8(a,1,1,2,1,2)),rewrite([6(11)])].">
      <j1 rule="para" parents="8 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="25">
    <literal><![CDATA[
      (x + (x + (y' + (x + y)'))')' = (x + y)'
    ]]></literal>
    <justification jstring="[para(8(a,1),8(a,1,1,2)),rewrite([6(5),7(5),6(7)])].">
      <j1 rule="para" parents="8 8"/>
      <j2 rule="rewrite" parents="6 7 6"/>
    </justification>
  </clause>

  <clause id="26">
    <literal><![CDATA[
      (x + (y + (x + y)'))' = g(x + y)
    ]]></literal>
    <justification jstring="[para(7(a,1),10(a,1,1))].">
      <j1 rule="para" parents="7 10"/>
    </justification>
  </clause>

  <clause id="27">
    <literal><![CDATA[
      (g(x) + (x + x'')')' = x
    ]]></literal>
    <justification jstring="[para(10(a,1),8(a,1,1,1))].">
      <j1 rule="para" parents="10 8"/>
    </justification>
  </clause>

  <clause id="28">
    <literal><![CDATA[
      ((x + g(y))' + (x + (y + y'))')' = x
    ]]></literal>
    <justification jstring="[para(10(a,1),8(a,1,1,2,1,2)),rewrite([6(8)])].">
      <j1 rule="para" parents="10 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="29">
    <literal><![CDATA[
      (g(x) + (x + x)')' = x
    ]]></literal>
    <justification jstring="[para(10(a,1),8(a,1,1,2)),rewrite([6(4)])].">
      <j1 rule="para" parents="10 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="31">
    <literal><![CDATA[
      (x + (g(x) + x'))' = g(x + x')
    ]]></literal>
    <justification jstring="[para(10(a,1),10(a,1,1,2)),rewrite([6(4),19(4)])].">
      <j1 rule="para" parents="10 10"/>
      <j2 rule="rewrite" parents="6 19"/>
    </justification>
  </clause>

  <clause id="32">
    <literal><![CDATA[
      h(x) + y = x + (x + (x + (g(x) + y)))
    ]]></literal>
    <justification jstring="[para(12(a,1),7(a,1,1)),rewrite([7(6),7(5)])].">
      <j1 rule="para" parents="12 7"/>
      <j2 rule="rewrite" parents="7 7"/>
    </justification>
  </clause>

  <clause id="34">
    <literal><![CDATA[
      x + h(y) = y + (y + (g(y) + (x + y)))
    ]]></literal>
    <justification jstring="[para(12(a,1),7(a,2,2)),rewrite([19(5),19(4),6(3)]),flip(a)].">
      <j1 rule="para" parents="12 7"/>
      <j2 rule="rewrite" parents="19 19 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35">
    <literal><![CDATA[
      (h(x)' + (x + (x + (x + g(x)))')')' = x
    ]]></literal>
    <justification jstring="[para(12(a,1),8(a,1,1,1,1))].">
      <j1 rule="para" parents="12 8"/>
    </justification>
  </clause>

  <clause id="51">
    <literal><![CDATA[
      ((x + (y + z))' + (y + (x + z)')')' = y
    ]]></literal>
    <justification jstring="[para(19(a,1),8(a,1,1,1,1))].">
      <j1 rule="para" parents="19 8"/>
    </justification>
  </clause>

  <clause id="63">
    <literal><![CDATA[
      (g(x + y) + (x + (y + (x + y)))')' = x + y
    ]]></literal>
    <justification jstring="[para(7(a,1),29(a,1,1,2,1))].">
      <j1 rule="para" parents="7 29"/>
    </justification>
  </clause>

  <clause id="66">
    <literal><![CDATA[
      (x + (x + (x + g(x)))')' = g(x)
    ]]></literal>
    <justification jstring="[para(29(a,1),8(a,1,1,2)),rewrite([19(3),6(2),6(5)])].">
      <j1 rule="para" parents="29 8"/>
      <j2 rule="rewrite" parents="19 6 6"/>
    </justification>
  </clause>

  <clause id="67">
    <literal><![CDATA[
      (x + (g(x) + (x + x)'))' = g(g(x) + (x + x)')
    ]]></literal>
    <justification jstring="[para(29(a,1),10(a,1,1,2)),rewrite([6(5)])].">
      <j1 rule="para" parents="29 10"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="74">
    <literal><![CDATA[
      (g(x) + h(x)')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(35),rewrite([66(8),6(4)])].">
      <j1 rule="back_rewrite" parents="35"/>
      <j2 rule="rewrite" parents="66 6"/>
    </justification>
  </clause>

  <clause id="75">
    <literal><![CDATA[
      (x + (g(x) + h(x)'')')' = g(x)
    ]]></literal>
    <justification jstring="[para(74(a,1),8(a,1,1,1))].">
      <j1 rule="para" parents="74 8"/>
    </justification>
  </clause>

  <clause id="76">
    <literal><![CDATA[
      ((x + y)' + (x + (g(y) + h(y)'))')' = x
    ]]></literal>
    <justification jstring="[para(74(a,1),8(a,1,1,2,1,2)),rewrite([6(9)])].">
      <j1 rule="para" parents="74 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="77">
    <literal><![CDATA[
      (x + (g(x) + h(x))')' = g(x)
    ]]></literal>
    <justification jstring="[para(74(a,1),8(a,1,1,2)),rewrite([6(5)])].">
      <j1 rule="para" parents="74 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="78">
    <literal><![CDATA[
      (x + (g(x) + h(x)'))' = g(g(x) + h(x)')
    ]]></literal>
    <justification jstring="[para(74(a,1),10(a,1,1,2)),rewrite([6(5)])].">
      <j1 rule="para" parents="74 10"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="88">
    <literal><![CDATA[
      (x + (x + (g(x) + x''))')' = g(x)
    ]]></literal>
    <justification jstring="[para(27(a,1),8(a,1,1,2)),rewrite([19(5),6(7)])].">
      <j1 rule="para" parents="27 8"/>
      <j2 rule="rewrite" parents="19 6"/>
    </justification>
  </clause>

  <clause id="103">
    <literal><![CDATA[
      (g(x) + (x + (g(x) + h(x)))')' = x
    ]]></literal>
    <justification jstring="[para(77(a,1),8(a,1,1,2)),rewrite([6(7)])].">
      <j1 rule="para" parents="77 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="111">
    <literal><![CDATA[
      ((x + y)' + (x' + y)')' = y
    ]]></literal>
    <justification jstring="[para(6(a,1),20(a,1,1,2,1))].">
      <j1 rule="para" parents="6 20"/>
    </justification>
  </clause>

  <clause id="113">
    <literal><![CDATA[
      ((x + (y + z))' + (z + (x + y)')')' = z
    ]]></literal>
    <justification jstring="[para(7(a,1),20(a,1,1,1,1))].">
      <j1 rule="para" parents="7 20"/>
    </justification>
  </clause>

  <clause id="117">
    <literal><![CDATA[
      (x + (x + (y' + (y + x)'))')' = (y + x)'
    ]]></literal>
    <justification jstring="[para(20(a,1),8(a,1,1,2)),rewrite([6(5),7(5),6(7)])].">
      <j1 rule="para" parents="20 8"/>
      <j2 rule="rewrite" parents="6 7 6"/>
    </justification>
  </clause>

  <clause id="120">
    <literal><![CDATA[
      (x + ((y + x)' + (x + y')'))' = g((y + x)' + (x + y')')
    ]]></literal>
    <justification jstring="[para(20(a,1),10(a,1,1,2)),rewrite([6(7)])].">
      <j1 rule="para" parents="20 10"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="121">
    <literal><![CDATA[
      (g(x) + (x' + x')')' = x'
    ]]></literal>
    <justification jstring="[para(10(a,1),20(a,1,1,1))].">
      <j1 rule="para" parents="10 20"/>
    </justification>
  </clause>

  <clause id="127">
    <literal><![CDATA[
      ((x + (y + z))' + (x + (z + y'))')' = x + z
    ]]></literal>
    <justification jstring="[para(19(a,1),20(a,1,1,1,1)),rewrite([7(6)])].">
      <j1 rule="para" parents="19 20"/>
      <j2 rule="rewrite" parents="7"/>
    </justification>
  </clause>

  <clause id="135">
    <literal><![CDATA[
      (g((x + y)' + (y + x')') + (y' + ((x + y)' + (y + x')'))')' = (x + y)' + (y + x')'
    ]]></literal>
    <justification jstring="[para(20(a,1),27(a,1,1,2,1,2,1)),rewrite([6(15)])].">
      <j1 rule="para" parents="20 27"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="138">
    <literal><![CDATA[
      (g(x) + (x' + (g(x) + h(x))')')' = (g(x) + h(x))'
    ]]></literal>
    <justification jstring="[para(77(a,1),20(a,1,1,1)),rewrite([6(7)])].">
      <j1 rule="para" parents="77 20"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="154">
    <literal><![CDATA[
      (x + (x + (y + (x + y')'))')' = (x + y')'
    ]]></literal>
    <justification jstring="[para(8(a,1),21(a,1,1,2)),rewrite([6(5),7(5),6(7)])].">
      <j1 rule="para" parents="8 21"/>
      <j2 rule="rewrite" parents="6 7 6"/>
    </justification>
  </clause>

  <clause id="156">
    <literal><![CDATA[
      ((x + (y + y'))' + (g(y) + x)')' = x
    ]]></literal>
    <justification jstring="[para(10(a,1),21(a,1,1,2,1,1))].">
      <j1 rule="para" parents="10 21"/>
    </justification>
  </clause>

  <clause id="157">
    <literal><![CDATA[
      (g(x') + (x + x'')')' = x''
    ]]></literal>
    <justification jstring="[para(10(a,1),21(a,1,1,2)),rewrite([6(3),6(7)])].">
      <j1 rule="para" parents="10 21"/>
      <j2 rule="rewrite" parents="6 6"/>
    </justification>
  </clause>

  <clause id="161">
    <literal><![CDATA[
      ((x + (y + z))' + ((x + z)' + y)')' = y
    ]]></literal>
    <justification jstring="[para(19(a,1),21(a,1,1,1,1))].">
      <j1 rule="para" parents="19 21"/>
    </justification>
  </clause>

  <clause id="166">
    <literal><![CDATA[
      ((x + (g(y) + (y + y)'))' + (y + x)')' = x
    ]]></literal>
    <justification jstring="[para(29(a,1),21(a,1,1,2,1,1))].">
      <j1 rule="para" parents="29 21"/>
    </justification>
  </clause>

  <clause id="167">
    <literal><![CDATA[
      ((x + (g(y) + h(y)'))' + (y + x)')' = x
    ]]></literal>
    <justification jstring="[para(74(a,1),21(a,1,1,2,1,1))].">
      <j1 rule="para" parents="74 21"/>
    </justification>
  </clause>

  <clause id="203">
    <literal><![CDATA[
      ((x + (y + z))' + (y + (x' + z))')' = y + z
    ]]></literal>
    <justification jstring="[para(19(a,1),111(a,1,1,2,1))].">
      <j1 rule="para" parents="19 111"/>
    </justification>
  </clause>

  <clause id="208">
    <literal><![CDATA[
      ((x + y)' + (g(x) + (h(x)' + y))')' = y
    ]]></literal>
    <justification jstring="[para(74(a,1),111(a,1,1,2,1,1)),rewrite([7(5),6(9)])].">
      <j1 rule="para" parents="74 111"/>
      <j2 rule="rewrite" parents="7 6"/>
    </justification>
  </clause>

  <clause id="209">
    <literal><![CDATA[
      (g((x + y)' + (x' + y)') + (y' + ((x + y)' + (x' + y)'))')' = (x + y)' + (x' + y)'
    ]]></literal>
    <justification jstring="[para(111(a,1),27(a,1,1,2,1,2,1)),rewrite([6(15)])].">
      <j1 rule="para" parents="111 27"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="246">
    <literal><![CDATA[
      ((x + (y + z))' + (y + (z' + x))')' = x + y
    ]]></literal>
    <justification jstring="[para(6(a,1),22(a,1,1,2,1)),rewrite([7(6)])].">
      <j1 rule="para" parents="6 22"/>
      <j2 rule="rewrite" parents="7"/>
    </justification>
  </clause>

  <clause id="260">
    <literal><![CDATA[
      ((x + (y + z))' + (y + (x + z'))')' = y + x
    ]]></literal>
    <justification jstring="[para(19(a,1),22(a,1,1,1,1))].">
      <j1 rule="para" parents="19 22"/>
    </justification>
  </clause>

  <clause id="312">
    <literal><![CDATA[
      ((x + x)' + g(g(x) + (x + x)'))' = x
    ]]></literal>
    <justification jstring="[para(29(a,1),121(a,1,1,2,1,1)),rewrite([29(10),6(8),29(14)])].">
      <j1 rule="para" parents="29 121"/>
      <j2 rule="rewrite" parents="29 6 29"/>
    </justification>
  </clause>

  <clause id="319">
    <literal><![CDATA[
      (g((x + y)' + (y + x')') + (y + y)')' = y
    ]]></literal>
    <justification jstring="[para(20(a,1),121(a,1,1,2,1,1)),rewrite([20(14),20(18)])].">
      <j1 rule="para" parents="20 121"/>
      <j2 rule="rewrite" parents="20 20"/>
    </justification>
  </clause>

  <clause id="324">
    <literal><![CDATA[
      (g((x + y)' + (x' + y)') + (y + y)')' = y
    ]]></literal>
    <justification jstring="[para(111(a,1),121(a,1,1,2,1,1)),rewrite([111(14),111(18)])].">
      <j1 rule="para" parents="111 121"/>
      <j2 rule="rewrite" parents="111 111"/>
    </justification>
  </clause>

  <clause id="328">
    <literal><![CDATA[
      (g((x + (y + z))' + (x + (y + z'))') + (x + (y + (x + y)))')' = x + y
    ]]></literal>
    <justification jstring="[para(22(a,1),121(a,1,1,2,1,1)),rewrite([22(19),19(12),6(11),22(24)])].">
      <j1 rule="para" parents="22 121"/>
      <j2 rule="rewrite" parents="22 19 6 22"/>
    </justification>
  </clause>

  <clause id="363">
    <literal><![CDATA[
      (x + (y + (y + x)'))' = g(x + y)
    ]]></literal>
    <justification jstring="[para(6(a,1),26(a,1,1,2,2,1))].">
      <j1 rule="para" parents="6 26"/>
    </justification>
  </clause>

  <clause id="365">
    <literal><![CDATA[
      (g(x + y) + (x + (y + (x + y)')')')' = x
    ]]></literal>
    <justification jstring="[para(26(a,1),8(a,1,1,1))].">
      <j1 rule="para" parents="26 8"/>
    </justification>
  </clause>

  <clause id="368">
    <literal><![CDATA[
      (x + (x + (x + (g(x) + h(x)'))))' = g(h(x))
    ]]></literal>
    <justification jstring="[para(12(a,1),26(a,1,1,2,2,1)),rewrite([7(6),7(5),12(12)])].">
      <j1 rule="para" parents="12 26"/>
      <j2 rule="rewrite" parents="7 7 12"/>
    </justification>
  </clause>

  <clause id="456">
    <literal><![CDATA[
      ((x + y)' + (y' + (y + (x' + (x + y)'))')')' = (y + (x' + (x + y)'))'
    ]]></literal>
    <justification jstring="[para(20(a,1),23(a,1,1,2,1,2,1)),rewrite([6(7),7(7),6(10),6(18),7(18)])].">
      <j1 rule="para" parents="20 23"/>
      <j2 rule="rewrite" parents="6 7 6 6 7"/>
    </justification>
  </clause>

  <clause id="538">
    <literal><![CDATA[
      (g(x) + (x + (g(x) + h(x)''))')' = x
    ]]></literal>
    <justification jstring="[para(75(a,1),8(a,1,1,2)),rewrite([6(9)])].">
      <j1 rule="para" parents="75 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="574">
    <literal><![CDATA[
      ((x + (g(y) + (y + (g(y) + h(y)))'))' + (y + x)')' = x
    ]]></literal>
    <justification jstring="[para(103(a,1),21(a,1,1,2,1,1))].">
      <j1 rule="para" parents="103 21"/>
    </justification>
  </clause>

  <clause id="577">
    <literal><![CDATA[
      ((x + (y + z))' + (x + (y + (g(z) + (z + (g(z) + h(z)))')))')' = x + y
    ]]></literal>
    <justification jstring="[para(103(a,1),22(a,1,1,2,1,2,2)),rewrite([6(14)])].">
      <j1 rule="para" parents="103 22"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="587">
    <literal><![CDATA[
      (x + (y + (z + (y + (z + x))')))' = g(x + (y + z))
    ]]></literal>
    <justification jstring="[para(7(a,1),363(a,1,1,2,2,1)),rewrite([7(5)])].">
      <j1 rule="para" parents="7 363"/>
      <j2 rule="rewrite" parents="7"/>
    </justification>
  </clause>

  <clause id="589">
    <literal><![CDATA[
      (g(x + y) + (x + (y + (y + x)')')')' = x
    ]]></literal>
    <justification jstring="[para(363(a,1),8(a,1,1,1))].">
      <j1 rule="para" parents="363 8"/>
    </justification>
  </clause>

  <clause id="600">
    <literal><![CDATA[
      (g(x + y) + (x' + (y + (y + x)'))')' = y + (y + x)'
    ]]></literal>
    <justification jstring="[para(363(a,1),20(a,1,1,1)),rewrite([6(7)])].">
      <j1 rule="para" parents="363 20"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="603">
    <literal><![CDATA[
      (g(x' + y) + (x + (y + (y + x')'))')' = y + (y + x')'
    ]]></literal>
    <justification jstring="[para(363(a,1),21(a,1,1,2)),rewrite([6(5),6(10)])].">
      <j1 rule="para" parents="363 21"/>
      <j2 rule="rewrite" parents="6 6"/>
    </justification>
  </clause>

  <clause id="620">
    <literal><![CDATA[
      x + h(y) = y + (y + (y + (g(y) + x)))
    ]]></literal>
    <justification jstring="[para(32(a,1),6(a,1)),flip(a)].">
      <j1 rule="para" parents="32 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="621">
    <literal><![CDATA[
      x + (x + (x + (x + (x + (x + (x + (x + (x + (g(x) + (g(x) + (g(x) + g(h(x))))))))))))) = h(h(x))
    ]]></literal>
    <justification jstring="[para(32(a,1),12(a,1,2,2)),rewrite([19(10),19(9),19(8),19(7),32(6),19(10),19(9),19(8),19(14),19(13),19(12),19(11),19(10),19(9),19(8),19(7),32(6),19(10),19(9),19(8),19(11),19(10),19(9)])].">
      <j1 rule="para" parents="32 12"/>
      <j2 rule="rewrite" parents="19 19 19 19 32 19 19 19 19 19 19 19 19 19 19 19 32 19 19 19 19 19 19"/>
    </justification>
  </clause>

  <clause id="649">
    <literal><![CDATA[
      (x + (x + (x + (g(x) + (g(h(x)) + h(x)')))))' = g(x + (x + (x + (g(x) + h(x)'))))
    ]]></literal>
    <justification jstring="[para(32(a,1),31(a,1,1)),rewrite([32(15)])].">
      <j1 rule="para" parents="32 31"/>
      <j2 rule="rewrite" parents="32"/>
    </justification>
  </clause>

  <clause id="657">
    <literal><![CDATA[
      (x + (x + (x + (g(x) + (y + (y + h(x))')))))' = g(x + (x + (x + (g(x) + y))))
    ]]></literal>
    <justification jstring="[para(32(a,1),363(a,1,1)),rewrite([32(12)])].">
      <j1 rule="para" parents="32 363"/>
      <j2 rule="rewrite" parents="32"/>
    </justification>
  </clause>

  <clause id="675">
    <literal><![CDATA[
      (x + (g(x) + (((x + x)' + y)' + ((x + x)' + y')'))')' = g(x)
    ]]></literal>
    <justification jstring="[para(29(a,1),24(a,1,1,1))].">
      <j1 rule="para" parents="29 24"/>
    </justification>
  </clause>

  <clause id="816">
    <literal><![CDATA[
      x + (g(x) + (y + (x + (z + x)))) = y + (z + h(x))
    ]]></literal>
    <justification jstring="[para(34(a,2),7(a,2,2)),rewrite([19(6),19(5),7(4)])].">
      <j1 rule="para" parents="34 7"/>
      <j2 rule="rewrite" parents="19 19 7"/>
    </justification>
  </clause>

  <clause id="848">
    <literal><![CDATA[
      ((x + h(y))' + (y + (y + (g(y) + (x + y))'))')' = y + y
    ]]></literal>
    <justification jstring="[para(34(a,2),22(a,1,1,1,1))].">
      <j1 rule="para" parents="34 22"/>
    </justification>
  </clause>

  <clause id="938">
    <literal><![CDATA[
      (g(x) + (x + (x + (g(x) + x'')))')' = x
    ]]></literal>
    <justification jstring="[para(88(a,1),8(a,1,1,2)),rewrite([6(9)])].">
      <j1 rule="para" parents="88 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="995">
    <literal><![CDATA[
      (x + (x + (h(x)' + (x + (x + g(x)))'))')' = h(x)'
    ]]></literal>
    <justification jstring="[para(12(a,1),25(a,1,1,2,1,2,2,1)),rewrite([6(7),12(15)])].">
      <j1 rule="para" parents="12 25"/>
      <j2 rule="rewrite" parents="6 12"/>
    </justification>
  </clause>

  <clause id="1168">
    <literal><![CDATA[
      (x'' + (g(x') + (x + x'')'')')' = g(x')
    ]]></literal>
    <justification jstring="[para(157(a,1),8(a,1,1,1))].">
      <j1 rule="para" parents="157 8"/>
    </justification>
  </clause>

  <clause id="1171">
    <literal><![CDATA[
      (g(x) + (x' + ((x + y)' + (x + y')'))')' = x'
    ]]></literal>
    <justification jstring="[para(8(a,1),157(a,1,1,1,1)),rewrite([8(14),6(9),8(19)])].">
      <j1 rule="para" parents="8 157"/>
      <j2 rule="rewrite" parents="8 6 8"/>
    </justification>
  </clause>

  <clause id="1180">
    <literal><![CDATA[
      (g(x) + (g(x) + (x' + h(x)'))')' = x'
    ]]></literal>
    <justification jstring="[para(74(a,1),157(a,1,1,1,1)),rewrite([74(10),6(7),19(7),74(15)])].">
      <j1 rule="para" parents="74 157"/>
      <j2 rule="rewrite" parents="74 6 19 74"/>
    </justification>
  </clause>

  <clause id="1186">
    <literal><![CDATA[
      (g(x) + (x' + ((y + x)' + (x + y')'))')' = x'
    ]]></literal>
    <justification jstring="[para(20(a,1),157(a,1,1,1,1)),rewrite([20(14),6(9),20(19)])].">
      <j1 rule="para" parents="20 157"/>
      <j2 rule="rewrite" parents="20 6 20"/>
    </justification>
  </clause>

  <clause id="1191">
    <literal><![CDATA[
      (g(x) + (x' + ((y + x)' + (y' + x)'))')' = x'
    ]]></literal>
    <justification jstring="[para(111(a,1),157(a,1,1,1,1)),rewrite([111(14),6(9),111(19)])].">
      <j1 rule="para" parents="111 157"/>
      <j2 rule="rewrite" parents="111 6 111"/>
    </justification>
  </clause>

  <clause id="1278">
    <literal><![CDATA[
      x + (y + h(z)) = y + (z + (z + (z + (g(z) + x))))
    ]]></literal>
    <justification jstring="[para(620(a,1),19(a,1,2)),flip(a)].">
      <j1 rule="para" parents="620 19"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1835">
    <literal><![CDATA[
      (x + (x + (x' + h(x)'))')' = h(x)'
    ]]></literal>
    <justification jstring="[para(74(a,1),156(a,1,1,2)),rewrite([6(5),7(5),6(7)])].">
      <j1 rule="para" parents="74 156"/>
      <j2 rule="rewrite" parents="6 7 6"/>
    </justification>
  </clause>

  <clause id="2362">
    <literal><![CDATA[
      ((x + (x + (x + (g(x) + h(x)))))' + g(g(h(x)) + (x + (x + (x + (g(x) + h(x)))))'))' = h(x)
    ]]></literal>
    <justification jstring="[para(32(a,1),312(a,1,1,1,1)),rewrite([32(12)])].">
      <j1 rule="para" parents="32 312"/>
      <j2 rule="rewrite" parents="32"/>
    </justification>
  </clause>

  <clause id="2859">
    <literal><![CDATA[
      (x + (x + (x + (g(x) + (x + (x + (x + (g(x) + (h(x)' + h(h(x))')))))'))))' = h(h(x))'
    ]]></literal>
    <justification jstring="[para(32(a,1),1835(a,1,1,2,1)),rewrite([32(14)])].">
      <j1 rule="para" parents="32 1835"/>
      <j2 rule="rewrite" parents="32"/>
    </justification>
  </clause>

  <clause id="3202">
    <literal><![CDATA[
      ((x + (y + z))' + (y + (z + x)')')' = y
    ]]></literal>
    <justification jstring="[para(6(a,1),51(a,1,1,2,1,2,1))].">
      <j1 rule="para" parents="6 51"/>
    </justification>
  </clause>

  <clause id="3212">
    <literal><![CDATA[
      ((x + y)' + (g(y) + (x + h(y)'))')' = x
    ]]></literal>
    <justification jstring="[para(74(a,1),51(a,1,1,2,1,2)),rewrite([6(9)])].">
      <j1 rule="para" parents="74 51"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="3326">
    <literal><![CDATA[
      (x + (x + (g(y) + (h(y)' + (x + y)')))')' = (x + y)'
    ]]></literal>
    <justification jstring="[para(76(a,1),8(a,1,1,2)),rewrite([6(8),7(8),7(7),6(10)])].">
      <j1 rule="para" parents="76 8"/>
      <j2 rule="rewrite" parents="6 7 7 6"/>
    </justification>
  </clause>

  <clause id="3328">
    <literal><![CDATA[
      (g(x) + (x + (g(x') + h(x')'))')' = x
    ]]></literal>
    <justification jstring="[para(10(a,1),76(a,1,1,1))].">
      <j1 rule="para" parents="10 76"/>
    </justification>
  </clause>

  <clause id="3761">
    <literal><![CDATA[
      ((x + (y + z))' + (z + (y + x)')')' = z
    ]]></literal>
    <justification jstring="[para(6(a,1),113(a,1,1,2,1,2,1))].">
      <j1 rule="para" parents="6 113"/>
    </justification>
  </clause>

  <clause id="3769">
    <literal><![CDATA[
      (h(x)' + g(g(x) + (x + x)'))' = x + g(x)
    ]]></literal>
    <justification jstring="[para(12(a,1),113(a,1,1,1,1)),rewrite([7(7),67(8)])].">
      <j1 rule="para" parents="12 113"/>
      <j2 rule="rewrite" parents="7 67"/>
    </justification>
  </clause>

  <clause id="4030">
    <literal><![CDATA[
      ((x + (y + z))' + ((z + x)' + y)')' = y
    ]]></literal>
    <justification jstring="[para(6(a,1),161(a,1,1,2,1,1,1))].">
      <j1 rule="para" parents="6 161"/>
    </justification>
  </clause>

  <clause id="6022">
    <literal><![CDATA[
      (g((x + y)' + (g(x) + (h(x)' + y))') + (y' + ((x + y)' + ((x + y)' + ((g(x) + (h(x)' + y))' + ((g(x) + (h(x)' + y))' + g((x + y)' + (g(x) + (h(x)' + y))'))))))')' = (x + y)' + (g(x) + (h(x)' + y))'
    ]]></literal>
    <justification jstring="[para(208(a,1),938(a,1,1,2,1,2,2,2,1)),rewrite([6(40),19(41),7(40),19(42),19(41),19(40),7(39),19(40)])].">
      <j1 rule="para" parents="208 938"/>
      <j2 rule="rewrite" parents="6 19 7 19 19 19 7 19"/>
    </justification>
  </clause>

  <clause id="8272">
    <literal><![CDATA[
      ((x + y)' + ((y + y)' + (x + g(y)))')' = x
    ]]></literal>
    <justification jstring="[para(29(a,1),3202(a,1,1,2,1,2)),rewrite([6(9)])].">
      <j1 rule="para" parents="29 3202"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="9666">
    <literal><![CDATA[
      (g(g(x) + (x + (g(x) + h(x)''))') + (g(x) + (g(x) + (h(x)' + (x + (g(x) + h(x)''))')))')' = g(x) + (x + (g(x) + h(x)''))'
    ]]></literal>
    <justification jstring="[para(538(a,1),3328(a,1,1,2,1,2,1,1)),rewrite([538(30),6(24),19(24),7(23)])].">
      <j1 rule="para" parents="538 3328"/>
      <j2 rule="rewrite" parents="538 6 19 7"/>
    </justification>
  </clause>

  <clause id="10222">
    <literal><![CDATA[
      ((x + y)' + (h(x)' + (y + g(x)))')' = y
    ]]></literal>
    <justification jstring="[para(74(a,1),4030(a,1,1,2,1,1)),rewrite([6(9)])].">
      <j1 rule="para" parents="74 4030"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="11704">
    <literal><![CDATA[
      ((x + (y + z))' + (h(x)' + (y + (z + g(x))))')' = y + z
    ]]></literal>
    <justification jstring="[para(7(a,1),10222(a,1,1,2,1,2))].">
      <j1 rule="para" parents="7 10222"/>
    </justification>
  </clause>

  <clause id="11812">
    <literal><![CDATA[
      ((x + y)' + (y + (y + (x' + (x + y)')))')' = y
    ]]></literal>
    <justification jstring="[para(117(a,1),8(a,1,1,2)),rewrite([6(10)])].">
      <j1 rule="para" parents="117 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="12445">
    <literal><![CDATA[
      (h(x)' + (x + (x + (g(x) + (g(x) + (x + x)'))))')' = x + (x + g(x))
    ]]></literal>
    <justification jstring="[para(12(a,1),166(a,1,1,2,1)),rewrite([19(8),7(7),7(6),19(8),19(7),6(12)])].">
      <j1 rule="para" parents="12 166"/>
      <j2 rule="rewrite" parents="19 7 7 19 19 6"/>
    </justification>
  </clause>

  <clause id="14988">
    <literal><![CDATA[
      (x + (g(x) + (x + (g(x) + (h(x)' + (x + x)')))'))' = h(x)'
    ]]></literal>
    <justification jstring="[para(3769(a,1),28(a,1,1,1)),rewrite([29(13),6(9),19(10),19(9),7(12)])].">
      <j1 rule="para" parents="3769 28"/>
      <j2 rule="rewrite" parents="29 6 19 19 7"/>
    </justification>
  </clause>

  <clause id="16509">
    <literal><![CDATA[
      ((x + y')' + (x + (x + (y + (x + y')')))')' = x
    ]]></literal>
    <justification jstring="[para(154(a,1),8(a,1,1,2)),rewrite([6(11)])].">
      <j1 rule="para" parents="154 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="18784">
    <literal><![CDATA[
      ((x + (y' + z))' + (z + (x + y))')' = z + x
    ]]></literal>
    <justification jstring="[para(6(a,1),246(a,1,1))].">
      <j1 rule="para" parents="6 246"/>
    </justification>
  </clause>

  <clause id="19850">
    <literal><![CDATA[
      ((x + x)' + g((y + x)' + (y' + x)'))' = x
    ]]></literal>
    <justification jstring="[para(6(a,1),324(a,1,1))].">
      <j1 rule="para" parents="6 324"/>
    </justification>
  </clause>

  <clause id="20953">
    <literal><![CDATA[
      x + (g(x) + (y + (x + (x + z)))) = y + (z + h(x))
    ]]></literal>
    <justification jstring="[para(6(a,1),816(a,1,2,2,2,2))].">
      <j1 rule="para" parents="6 816"/>
    </justification>
  </clause>

  <clause id="20968">
    <literal><![CDATA[
      x + (g(x) + (y + (z + (x + x)))) = y + (z + h(x))
    ]]></literal>
    <justification jstring="[para(19(a,1),816(a,1,2,2,2))].">
      <j1 rule="para" parents="19 816"/>
    </justification>
  </clause>

  <clause id="22090">
    <literal><![CDATA[
      x + (y + (z + h(u))) = y + (z + (u + (u + (u + (g(u) + x)))))
    ]]></literal>
    <justification jstring="[para(1278(a,2),7(a,1)),rewrite([7(3)])].">
      <j1 rule="para" parents="1278 7"/>
      <j2 rule="rewrite" parents="7"/>
    </justification>
  </clause>

  <clause id="24615">
    <literal><![CDATA[
      ((x + x)' + g((y + x)' + (g(y) + (h(y)' + x))'))' = x
    ]]></literal>
    <justification jstring="[para(74(a,1),19850(a,1,1,2,1,2,1,1)),rewrite([7(7),6(11)])].">
      <j1 rule="para" parents="74 19850"/>
      <j2 rule="rewrite" parents="7 6"/>
    </justification>
  </clause>

  <clause id="25262">
    <literal><![CDATA[
      ((x + (y + h(z)))' + (z + (g(z) + (y + (z + (z + x')))))')' = y + h(z)
    ]]></literal>
    <justification jstring="[para(20953(a,2),203(a,1,1,2,1))].">
      <j1 rule="para" parents="20953 203"/>
    </justification>
  </clause>

  <clause id="25423">
    <literal><![CDATA[
      x + (y + (g(x) + (z + (x + x)))) = y + (z + h(x))
    ]]></literal>
    <justification jstring="[para(19(a,1),20968(a,1,2))].">
      <j1 rule="para" parents="19 20968"/>
    </justification>
  </clause>

  <clause id="26022">
    <literal><![CDATA[
      x + (g(x) + (y + (x + x))) = y + h(x)
    ]]></literal>
    <justification jstring="[para(25423(a,1),127(a,1,1,1,1)),rewrite([7(10),7(9),7(8),25262(14)]),flip(a)].">
      <j1 rule="para" parents="25423 127"/>
      <j2 rule="rewrite" parents="7 7 7 25262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26033">
    <literal><![CDATA[
      g(x) + (y + (x + (z + (x + x)))) = y + (z + h(x))
    ]]></literal>
    <justification jstring="[para(26022(a,1),7(a,2,2)),rewrite([19(6),7(5)])].">
      <j1 rule="para" parents="26022 7"/>
      <j2 rule="rewrite" parents="19 7"/>
    </justification>
  </clause>

  <clause id="26051">
    <literal><![CDATA[
      ((x + h(y))' + (g(y) + (y + (x + (y + y)))')')' = g(y)
    ]]></literal>
    <justification jstring="[para(26022(a,1),51(a,1,1,1,1))].">
      <j1 rule="para" parents="26022 51"/>
    </justification>
  </clause>

  <clause id="26121">
    <literal><![CDATA[
      g(x) + (y + (x + (x + (z + x)))) = y + (z + h(x))
    ]]></literal>
    <justification jstring="[para(19(a,1),26033(a,1,2,2,2))].">
      <j1 rule="para" parents="19 26033"/>
    </justification>
  </clause>

  <clause id="27211">
    <literal><![CDATA[
      (g(x) + (x' + (x + (x + (x + (g(x) + g(x)))))')')' = (g(x) + h(x))'
    ]]></literal>
    <justification jstring="[para(34(a,1),138(a,1,1,2,1,2,1)),rewrite([6(5),19(6)])].">
      <j1 rule="para" parents="34 138"/>
      <j2 rule="rewrite" parents="6 19"/>
    </justification>
  </clause>

  <clause id="33607">
    <literal><![CDATA[
      (g(x + (g(x) + h(x))) + (x + (x + h(x)))')' = x + h(x)
    ]]></literal>
    <justification jstring="[para(587(a,1),577(a,1,1,2)),rewrite([19(3),6(2),19(8),6(7),6(10),6(13)])].">
      <j1 rule="para" parents="587 577"/>
      <j2 rule="rewrite" parents="19 6 19 6 6 6"/>
    </justification>
  </clause>

  <clause id="34718">
    <literal><![CDATA[
      (x + h(x)')' = g(x)
    ]]></literal>
    <justification jstring="[para(76(a,1),675(a,1,1,2,1,2,2)),rewrite([6(9),7(9),7(8),6(11),19(12),14988(13)])].">
      <j1 rule="para" parents="76 675"/>
      <j2 rule="rewrite" parents="6 7 7 6 19 14988"/>
    </justification>
  </clause>

  <clause id="34738">
    <literal><![CDATA[
      (g(x) + (x + h(x))')' = x
    ]]></literal>
    <justification jstring="[para(34718(a,1),8(a,1,1,2)),rewrite([6(5)])].">
      <j1 rule="para" parents="34718 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="34739">
    <literal><![CDATA[
      g(g(x) + h(x)') = g(x + h(x)')
    ]]></literal>
    <justification jstring="[para(34718(a,1),10(a,1,1,2)),rewrite([6(5),19(5),78(6)])].">
      <j1 rule="para" parents="34718 10"/>
      <j2 rule="rewrite" parents="6 19 78"/>
    </justification>
  </clause>

  <clause id="34746">
    <literal><![CDATA[
      (g(x) + (x' + h(x)')')' = h(x)'
    ]]></literal>
    <justification jstring="[para(34718(a,1),20(a,1,1,1)),rewrite([6(5)])].">
      <j1 rule="para" parents="34718 20"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="34748">
    <literal><![CDATA[
      ((x + (y + h(y)'))' + (g(y) + x)')' = x
    ]]></literal>
    <justification jstring="[para(34718(a,1),21(a,1,1,2,1,1))].">
      <j1 rule="para" parents="34718 21"/>
    </justification>
  </clause>

  <clause id="34749">
    <literal><![CDATA[
      (g(x') + (x + h(x')')')' = h(x')'
    ]]></literal>
    <justification jstring="[para(34718(a,1),21(a,1,1,2)),rewrite([6(4),6(8)])].">
      <j1 rule="para" parents="34718 21"/>
      <j2 rule="rewrite" parents="6 6"/>
    </justification>
  </clause>

  <clause id="34840">
    <literal><![CDATA[
      (x + (x + (g(x) + h(x)))')' = g(x)
    ]]></literal>
    <justification jstring="[para(34718(a,1),154(a,1,1,2,1,2,2)),rewrite([6(3),34718(11)])].">
      <j1 rule="para" parents="34718 154"/>
      <j2 rule="rewrite" parents="6 34718"/>
    </justification>
  </clause>

  <clause id="35083">
    <literal><![CDATA[
      (g(x) + (x + (x + (g(x) + h(x))))')' = x
    ]]></literal>
    <justification jstring="[para(34718(a,1),16509(a,1,1,1)),rewrite([34718(6),6(4)])].">
      <j1 rule="para" parents="34718 16509"/>
      <j2 rule="rewrite" parents="34718 6"/>
    </justification>
  </clause>

  <clause id="35126">
    <literal><![CDATA[
      (g(x) + (g(x) + (h(x)' + (x + (g(x) + h(x)))'))')' = h(x)'
    ]]></literal>
    <justification jstring="[para(34718(a,1),574(a,1,1,2)),rewrite([19(10),6(13)])].">
      <j1 rule="para" parents="34718 574"/>
      <j2 rule="rewrite" parents="19 6"/>
    </justification>
  </clause>

  <clause id="35235">
    <literal><![CDATA[
      (g(x + h(x)') + (x + (g(x) + h(x)))')' = x + g(x)
    ]]></literal>
    <justification jstring="[para(34718(a,1),603(a,1,1,2,1,2,2)),rewrite([6(3),19(8),6(7),34718(15)])].">
      <j1 rule="para" parents="34718 603"/>
      <j2 rule="rewrite" parents="6 19 6 34718"/>
    </justification>
  </clause>

  <clause id="35434">
    <literal><![CDATA[
      (x + (x + (x + (g(x) + (g(x) + h(x)))))')' = g(x)
    ]]></literal>
    <justification jstring="[para(34738(a,1),16509(a,1,1,1)),rewrite([34738(10),6(5),19(6),19(5),19(7),19(6)])].">
      <j1 rule="para" parents="34738 16509"/>
      <j2 rule="rewrite" parents="34738 6 19 19 19 19"/>
    </justification>
  </clause>

  <clause id="35609">
    <literal><![CDATA[
      (x + (g(x) + h(x)))' = h(x)'
    ]]></literal>
    <justification jstring="[para(34840(a,1),167(a,1,1,2)),rewrite([6(10),7(10),6(13),35126(14)]),flip(a)].">
      <j1 rule="para" parents="34840 167"/>
      <j2 rule="rewrite" parents="6 7 6 35126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35671">
    <literal><![CDATA[
      (h(x)' + g(x + h(x)'))' = x + g(x)
    ]]></literal>
    <justification jstring="[back_rewrite(35235),rewrite([35609(9),6(7)])].">
      <j1 rule="back_rewrite" parents="35235"/>
      <j2 rule="rewrite" parents="35609 6"/>
    </justification>
  </clause>

  <clause id="35690">
    <literal><![CDATA[
      (x + (x + (x + (x + (g(x) + g(x))))))' = h(x)'
    ]]></literal>
    <justification jstring="[para(34(a,1),35609(a,1,1,2)),rewrite([6(3),19(4)])].">
      <j1 rule="para" parents="34 35609"/>
      <j2 rule="rewrite" parents="6 19"/>
    </justification>
  </clause>

  <clause id="35999">
    <literal><![CDATA[
      (g(x) + (x + (x + (x + (x + (x + (g(x) + g(x)))))))')' = x
    ]]></literal>
    <justification jstring="[para(34(a,1),35083(a,1,1,2,1,2,2)),rewrite([6(4),19(5)])].">
      <j1 rule="para" parents="34 35083"/>
      <j2 rule="rewrite" parents="6 19"/>
    </justification>
  </clause>

  <clause id="36016">
    <literal><![CDATA[
      (x + (x + (h(x)' + (x + x)'))')' = (x + x)'
    ]]></literal>
    <justification jstring="[para(29(a,1),34748(a,1,1,2)),rewrite([6(6),7(6),6(8)])].">
      <j1 rule="para" parents="29 34748"/>
      <j2 rule="rewrite" parents="6 7 6"/>
    </justification>
  </clause>

  <clause id="36259">
    <literal><![CDATA[
      x + (x + (g(x) + g(x))) = x + (x + g(x))
    ]]></literal>
    <justification jstring="[para(35690(a,1),113(a,1,1,1)),rewrite([7(10),7(9),7(8),12445(13)]),flip(a)].">
      <j1 rule="para" parents="35690 113"/>
      <j2 rule="rewrite" parents="7 7 7 12445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36273">
    <literal><![CDATA[
      (x + h(x))' = h(x)'
    ]]></literal>
    <justification jstring="[para(35690(a,1),1180(a,2)),rewrite([36259(5),12(4),36259(8),12(7),36259(11),12(10),36259(14),12(13),1180(18)])].">
      <j1 rule="para" parents="35690 1180"/>
      <j2 rule="rewrite" parents="36259 12 36259 12 36259 12 36259 12 1180"/>
    </justification>
  </clause>

  <clause id="36292">
    <literal><![CDATA[
      (g(x + h(x)) + (x + g(h(x)))')' = x
    ]]></literal>
    <justification jstring="[para(35690(a,1),365(a,1,1,2,1,2,1,2)),rewrite([36259(5),12(4),36259(8),12(7),32(7),368(11)])].">
      <j1 rule="para" parents="35690 365"/>
      <j2 rule="rewrite" parents="36259 12 36259 12 32 368"/>
    </justification>
  </clause>

  <clause id="36293">
    <literal><![CDATA[
      (g(x + h(x)) + (g(x) + h(x))')' = h(x)
    ]]></literal>
    <justification jstring="[para(35690(a,1),589(a,1,1,2,1,2,1,2)),rewrite([36259(5),12(4),6(2),36259(8),12(7),34718(8),6(6),36259(14),12(13)])].">
      <j1 rule="para" parents="35690 589"/>
      <j2 rule="rewrite" parents="36259 12 6 36259 12 34718 6 36259 12"/>
    </justification>
  </clause>

  <clause id="36373">
    <literal><![CDATA[
      (x + (x + (g(h(x)) + (h(x)' + h(h(x))')))')' = h(x)'
    ]]></literal>
    <justification jstring="[para(35690(a,1),3326(a,1,1,2,1,2,2,2)),rewrite([36259(5),12(4),36259(7),12(6),6(8),36259(18),12(17),36273(16)])].">
      <j1 rule="para" parents="35690 3326"/>
      <j2 rule="rewrite" parents="36259 12 36259 12 6 36259 12 36273"/>
    </justification>
  </clause>

  <clause id="36393">
    <literal><![CDATA[
      (g(h(x)) + h(x)')' = h(x)
    ]]></literal>
    <justification jstring="[para(35690(a,1),11704(a,1,1,1)),rewrite([36259(9),6(9),19(9),19(8),36259(9),12(8),6(6),32(6),368(10),6(5),36259(11),12(10)])].">
      <j1 rule="para" parents="35690 11704"/>
      <j2 rule="rewrite" parents="36259 6 19 19 36259 12 6 32 368 6 36259 12"/>
    </justification>
  </clause>

  <clause id="36414">
    <literal><![CDATA[
      (g(x) + (x + (x + h(x)))')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(35999),rewrite([36259(6),12(5)])].">
      <j1 rule="back_rewrite" parents="35999"/>
      <j2 rule="rewrite" parents="36259 12"/>
    </justification>
  </clause>

  <clause id="36417">
    <literal><![CDATA[
      (g(x) + h(x))' = h(x)'
    ]]></literal>
    <justification jstring="[back_rewrite(27211),rewrite([36259(7),12(6),34746(8)]),flip(a)].">
      <j1 rule="back_rewrite" parents="27211"/>
      <j2 rule="rewrite" parents="36259 12 34746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36423">
    <literal><![CDATA[
      (g(x + h(x)) + h(x)')' = h(x)
    ]]></literal>
    <justification jstring="[back_rewrite(36293),rewrite([36417(7)])].">
      <j1 rule="back_rewrite" parents="36293"/>
      <j2 rule="rewrite" parents="36417"/>
    </justification>
  </clause>

  <clause id="37076">
    <literal><![CDATA[
      (x + (x + (x + (g(x) + (g(x) + h(x)')))))' = g(g(x) + h(x))
    ]]></literal>
    <justification jstring="[para(36417(a,1),10(a,1,1,2)),rewrite([7(6),32(5),19(9),19(8),19(7)])].">
      <j1 rule="para" parents="36417 10"/>
      <j2 rule="rewrite" parents="7 32 19 19 19"/>
    </justification>
  </clause>

  <clause id="37133">
    <literal><![CDATA[
      (g(g(x) + h(x)) + (g(x) + g(h(x)))')' = g(x)
    ]]></literal>
    <justification jstring="[para(36417(a,1),365(a,1,1,2,1,2,1,2)),rewrite([32(9),368(13)])].">
      <j1 rule="para" parents="36417 365"/>
      <j2 rule="rewrite" parents="32 368"/>
    </justification>
  </clause>

  <clause id="37704">
    <literal><![CDATA[
      g(g(x) + h(x)) = g(h(x))
    ]]></literal>
    <justification jstring="[para(36417(a,1),657(a,1,1,2,2,2,2,2)),rewrite([37076(10),36259(9),12(8)])].">
      <j1 rule="para" parents="36417 657"/>
      <j2 rule="rewrite" parents="37076 36259 12"/>
    </justification>
  </clause>

  <clause id="37889">
    <literal><![CDATA[
      (g(h(x)) + (g(x) + g(h(x)))')' = g(x)
    ]]></literal>
    <justification jstring="[back_rewrite(37133),rewrite([37704(4)])].">
      <j1 rule="back_rewrite" parents="37133"/>
      <j2 rule="rewrite" parents="37704"/>
    </justification>
  </clause>

  <clause id="38250">
    <literal><![CDATA[
      g(g(h(x)) + h(x)') = g(x + (x + (x + (g(x) + h(x)'))))
    ]]></literal>
    <justification jstring="[para(36393(a,1),10(a,1,1,2)),rewrite([6(7),32(7),649(11)]),flip(a)].">
      <j1 rule="para" parents="36393 10"/>
      <j2 rule="rewrite" parents="6 32 649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38251">
    <literal><![CDATA[
      (g(x + (x + (x + (g(x) + h(x)')))) + (g(h(x)) + (h(x)' + h(x)'))')' = g(h(x)) + h(x)'
    ]]></literal>
    <justification jstring="[para(36393(a,1),27(a,1,1,2,1,2,1)),rewrite([38250(6),6(16),19(16)])].">
      <j1 rule="para" parents="36393 27"/>
      <j2 rule="rewrite" parents="38250 6 19"/>
    </justification>
  </clause>

  <clause id="38268">
    <literal><![CDATA[
      (g(h(x)) + (g(h(x)) + (h(x)' + h(x)'))')' = h(x)'
    ]]></literal>
    <justification jstring="[para(36393(a,1),157(a,1,1,1,1)),rewrite([36393(13),6(10),19(10),36393(19)])].">
      <j1 rule="para" parents="36393 157"/>
      <j2 rule="rewrite" parents="36393 6 19 36393"/>
    </justification>
  </clause>

  <clause id="38418">
    <literal><![CDATA[
      (h(x)' + (g(h(x)) + (g(h(x)) + (h(x)' + h(x)'))'')')' = g(h(x))
    ]]></literal>
    <justification jstring="[para(36393(a,1),1168(a,1,1,1,1)),rewrite([36393(8),36393(15),6(12),19(12),36393(24)])].">
      <j1 rule="para" parents="36393 1168"/>
      <j2 rule="rewrite" parents="36393 36393 6 19 36393"/>
    </justification>
  </clause>

  <clause id="38645">
    <literal><![CDATA[
      h(h(x))' = h(x)'
    ]]></literal>
    <justification jstring="[para(36393(a,1),34748(a,1,1,2)),rewrite([32(7),19(11),19(10),19(9),19(8),6(14),32(14),2859(18)])].">
      <j1 rule="para" parents="36393 34748"/>
      <j2 rule="rewrite" parents="32 19 19 19 19 6 32 2859"/>
    </justification>
  </clause>

  <clause id="38657">
    <literal><![CDATA[
      (x + (x + (g(h(x)) + (h(x)' + h(x)')))')' = h(x)'
    ]]></literal>
    <justification jstring="[back_rewrite(36373),rewrite([38645(7)])].">
      <j1 rule="back_rewrite" parents="36373"/>
      <j2 rule="rewrite" parents="38645"/>
    </justification>
  </clause>

  <clause id="38859">
    <literal><![CDATA[
      (h(x)' + g(x + (x + (x + (g(x) + h(x)')))))' = x + (x + (x + (g(x) + g(h(x)))))
    ]]></literal>
    <justification jstring="[para(38645(a,1),35671(a,1,1,1)),rewrite([38645(6),32(6),32(16)])].">
      <j1 rule="para" parents="38645 35671"/>
      <j2 rule="rewrite" parents="38645 32 32"/>
    </justification>
  </clause>

  <clause id="39262">
    <literal><![CDATA[
      (g(x) + (g(x) + (h(x)' + (x + (x + h(x)))'))')' = h(x)'
    ]]></literal>
    <justification jstring="[para(36414(a,1),34749(a,1,1,1,1)),rewrite([36414(14),6(10),19(10),36414(20)])].">
      <j1 rule="para" parents="36414 34749"/>
      <j2 rule="rewrite" parents="36414 6 19 36414"/>
    </justification>
  </clause>

  <clause id="39673">
    <literal><![CDATA[
      (g(x + h(x)) + (x + (g(x + h(x)) + (x + g(h(x)))'')'')')' = x
    ]]></literal>
    <justification jstring="[para(36292(a,1),23(a,1,1,2,1,1)),rewrite([36292(27)])].">
      <j1 rule="para" parents="36292 23"/>
      <j2 rule="rewrite" parents="36292"/>
    </justification>
  </clause>

  <clause id="39811">
    <literal><![CDATA[
      (g(x) + (x' + ((y + x)' + (g(y + h(y)) + ((y + g(h(y)))' + x))'))')' = x'
    ]]></literal>
    <justification jstring="[para(36292(a,1),1191(a,1,1,2,1,2,2,1,1)),rewrite([7(11),6(15)])].">
      <j1 rule="para" parents="36292 1191"/>
      <j2 rule="rewrite" parents="7 6"/>
    </justification>
  </clause>

  <clause id="40628">
    <literal><![CDATA[
      x + (x + (g(x) + (g(x) + y))) = x + (x + (g(x) + y))
    ]]></literal>
    <justification jstring="[para(36259(a,1),7(a,1,1)),rewrite([7(4),7(3),7(9),7(8)]),flip(a)].">
      <j1 rule="para" parents="36259 7"/>
      <j2 rule="rewrite" parents="7 7 7 7"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40637">
    <literal><![CDATA[
      g(x) + h(x) = h(x)
    ]]></literal>
    <justification jstring="[para(36259(a,1),32(a,2,2)),rewrite([6(3),12(7)])].">
      <j1 rule="para" parents="36259 32"/>
      <j2 rule="rewrite" parents="6 12"/>
    </justification>
  </clause>

  <clause id="40662">
    <literal><![CDATA[
      g(x) + (y + h(x)) = y + h(x)
    ]]></literal>
    <justification jstring="[para(36259(a,1),1278(a,2,2,2)),rewrite([12(8)])].">
      <j1 rule="para" parents="36259 1278"/>
      <j2 rule="rewrite" parents="12"/>
    </justification>
  </clause>

  <clause id="40782">
    <literal><![CDATA[
      g(x) + (y + (z + h(x))) = y + (z + h(x))
    ]]></literal>
    <justification jstring="[para(36259(a,1),22090(a,2,2,2,2)),rewrite([12(9)])].">
      <j1 rule="para" parents="36259 22090"/>
      <j2 rule="rewrite" parents="12"/>
    </justification>
  </clause>

  <clause id="40913">
    <literal><![CDATA[
      (x + (x + (x + h(x)))')' = g(x)
    ]]></literal>
    <justification jstring="[back_rewrite(35434),rewrite([40637(4),40637(3)])].">
      <j1 rule="back_rewrite" parents="35434"/>
      <j2 rule="rewrite" parents="40637 40637"/>
    </justification>
  </clause>

  <clause id="40976">
    <literal><![CDATA[
      x + (x + (x + (x + (x + (x + (x + (x + (x + (g(x) + g(h(x))))))))))) = h(h(x))
    ]]></literal>
    <justification jstring="[back_rewrite(621),rewrite([40628(10),40628(8)])].">
      <j1 rule="back_rewrite" parents="621"/>
      <j2 rule="rewrite" parents="40628 40628"/>
    </justification>
  </clause>

  <clause id="41013">
    <literal><![CDATA[
      (g(x + h(x)) + (x + (x + h(x)))')' = x + h(x)
    ]]></literal>
    <justification jstring="[back_rewrite(33607),rewrite([40637(3)])].">
      <j1 rule="back_rewrite" parents="33607"/>
      <j2 rule="rewrite" parents="40637"/>
    </justification>
  </clause>

  <clause id="41031">
    <literal><![CDATA[
      ((x + (x + (x + h(x))))' + g(g(h(x)) + (x + (x + (x + h(x))))'))' = h(x)
    ]]></literal>
    <justification jstring="[back_rewrite(2362),rewrite([40637(3),40637(10)])].">
      <j1 rule="back_rewrite" parents="2362"/>
      <j2 rule="rewrite" parents="40637 40637"/>
    </justification>
  </clause>

  <clause id="41066">
    <literal><![CDATA[
      g(x) + h(h(x)) = h(h(x))
    ]]></literal>
    <justification jstring="[para(40637(a,1),34(a,2,2,2,2)),rewrite([6(10),32(10),19(14),19(13),19(12),19(11),32(10),19(14),19(13),19(12),40628(13),19(16),19(15),19(14),19(13),19(12),19(11),19(10),32(9),19(13),19(12),19(11),40628(12),40976(17)])].">
      <j1 rule="para" parents="40637 34"/>
      <j2 rule="rewrite" parents="6 32 19 19 19 19 32 19 19 19 40628 19 19 19 19 19 19 19 32 19 19 19 40628 40976"/>
    </justification>
  </clause>

  <clause id="41082">
    <literal><![CDATA[
      x + (x + (x + (g(x) + (g(h(x)) + (y + (x + (x + (x + h(x))))))))) = y + h(h(x))
    ]]></literal>
    <justification jstring="[para(40637(a,1),816(a,1,2,2,2,2)),rewrite([32(6),40637(6),32(10),41066(17)])].">
      <j1 rule="para" parents="40637 816"/>
      <j2 rule="rewrite" parents="32 40637 32 41066"/>
    </justification>
  </clause>

  <clause id="41090">
    <literal><![CDATA[
      ((g(x) + (h(x)' + y))' + (y + h(x))')' = y + g(x)
    ]]></literal>
    <justification jstring="[para(40637(a,1),18784(a,1,1,2,1,2))].">
      <j1 rule="para" parents="40637 18784"/>
    </justification>
  </clause>

  <clause id="41093">
    <literal><![CDATA[
      g(h(x)) + (y + (x + (x + (x + (x + (x + (x + h(x)))))))) = y + h(h(x))
    ]]></literal>
    <justification jstring="[para(40637(a,1),26121(a,1,2,2,2,2)),rewrite([32(6),40637(6),19(8),19(7),19(6),32(5),40637(5),41066(15)])].">
      <j1 rule="para" parents="40637 26121"/>
      <j2 rule="rewrite" parents="32 40637 19 19 19 32 40637 41066"/>
    </justification>
  </clause>

  <clause id="41691">
    <literal><![CDATA[
      (x + (x + h(x)))' = h(x)'
    ]]></literal>
    <justification jstring="[para(40913(a,1),167(a,1,1,2)),rewrite([6(9),7(9),6(12),39262(13)]),flip(a)].">
      <j1 rule="para" parents="40913 167"/>
      <j2 rule="rewrite" parents="6 7 6 39262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41943">
    <literal><![CDATA[
      x + h(x) = h(x)
    ]]></literal>
    <justification jstring="[back_rewrite(41013),rewrite([41691(7),36423(7)]),flip(a)].">
      <j1 rule="back_rewrite" parents="41013"/>
      <j2 rule="rewrite" parents="41691 36423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41954">
    <literal><![CDATA[
      g(h(x)) + (y + h(x)) = y + h(h(x))
    ]]></literal>
    <justification jstring="[back_rewrite(41093),rewrite([41943(4),41943(4),41943(4),41943(4),41943(4),41943(4)])].">
      <j1 rule="back_rewrite" parents="41093"/>
      <j2 rule="rewrite" parents="41943 41943 41943 41943 41943 41943"/>
    </justification>
  </clause>

  <clause id="41955">
    <literal><![CDATA[
      x + h(h(y)) = y + (y + (y + (g(h(y)) + (x + h(y)))))
    ]]></literal>
    <justification jstring="[back_rewrite(41082),rewrite([41943(5),41943(5),41943(5),40782(7)]),flip(a)].">
      <j1 rule="back_rewrite" parents="41082"/>
      <j2 rule="rewrite" parents="41943 41943 41943 40782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41956">
    <literal><![CDATA[
      x + (x + (x + (g(x) + g(h(x))))) = h(x)
    ]]></literal>
    <justification jstring="[back_rewrite(41031),rewrite([41943(2),41943(2),41943(2),41943(6),41943(6),41943(6),38250(8),38859(12)])].">
      <j1 rule="back_rewrite" parents="41031"/>
      <j2 rule="rewrite" parents="41943 41943 41943 41943 41943 41943 38250 38859"/>
    </justification>
  </clause>

  <clause id="42085">
    <literal><![CDATA[
      (g(x) + (x' + ((y + x)' + (g(h(y)) + ((y + g(h(y)))' + x))'))')' = x'
    ]]></literal>
    <justification jstring="[back_rewrite(39811),rewrite([41943(6)])].">
      <j1 rule="back_rewrite" parents="39811"/>
      <j2 rule="rewrite" parents="41943"/>
    </justification>
  </clause>

  <clause id="42221">
    <literal><![CDATA[
      (g(h(x)) + (x + (g(h(x)) + (x + g(h(x)))'')'')')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(39673),rewrite([41943(2),41943(4)])].">
      <j1 rule="back_rewrite" parents="39673"/>
      <j2 rule="rewrite" parents="41943 41943"/>
    </justification>
  </clause>

  <clause id="42268">
    <literal><![CDATA[
      (g(h(x)) + (x + g(h(x)))')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(36292),rewrite([41943(2)])].">
      <j1 rule="back_rewrite" parents="36292"/>
      <j2 rule="rewrite" parents="41943"/>
    </justification>
  </clause>

  <clause id="42272">
    <literal><![CDATA[
      h(h(x)) = h(x)
    ]]></literal>
    <justification jstring="[back_rewrite(40976),rewrite([41956(7),41943(2),41943(2),41943(2),41943(2),41943(2),41943(2)]),flip(a)].">
      <j1 rule="back_rewrite" parents="40976"/>
      <j2 rule="rewrite" parents="41956 41943 41943 41943 41943 41943 41943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42288">
    <literal><![CDATA[
      x + (x + (x + (g(h(x)) + (y + h(x))))) = y + h(x)
    ]]></literal>
    <justification jstring="[back_rewrite(41955),rewrite([42272(2)]),flip(a)].">
      <j1 rule="back_rewrite" parents="41955"/>
      <j2 rule="rewrite" parents="42272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42289">
    <literal><![CDATA[
      g(h(x)) + (y + h(x)) = y + h(x)
    ]]></literal>
    <justification jstring="[back_rewrite(41954),rewrite([42272(7)])].">
      <j1 rule="back_rewrite" parents="41954"/>
      <j2 rule="rewrite" parents="42272"/>
    </justification>
  </clause>

  <clause id="42312">
    <literal><![CDATA[
      x + (x + (x + (y + h(x)))) = y + h(x)
    ]]></literal>
    <justification jstring="[back_rewrite(42288),rewrite([42289(5)])].">
      <j1 rule="back_rewrite" parents="42288"/>
      <j2 rule="rewrite" parents="42289"/>
    </justification>
  </clause>

  <clause id="42327">
    <literal><![CDATA[
      ((x + h(y))' + (g(h(y)) + (x + h(y))')')' = g(h(y))
    ]]></literal>
    <justification jstring="[para(42272(a,1),26051(a,1,1,1,1,2)),rewrite([32(9),40637(9),41943(8),41943(8),41943(8),32(9),40662(9),42312(10)])].">
      <j1 rule="para" parents="42272 26051"/>
      <j2 rule="rewrite" parents="32 40637 41943 41943 41943 32 40662 42312"/>
    </justification>
  </clause>

  <clause id="42333">
    <literal><![CDATA[
      (g(h(x)) + (g(h(x)) + g(h(x)))')' = g(h(x))
    ]]></literal>
    <justification jstring="[para(42272(a,1),37889(a,1,1,1,1)),rewrite([42272(6)])].">
      <j1 rule="para" parents="42272 37889"/>
      <j2 rule="rewrite" parents="42272"/>
    </justification>
  </clause>

  <clause id="42349">
    <literal><![CDATA[
      x + (x + (x + (x + (g(x) + y)))) = x + (x + (x + (g(x) + y)))
    ]]></literal>
    <justification jstring="[para(41943(a,1),7(a,1,1)),rewrite([32(2),32(7)]),flip(a)].">
      <j1 rule="para" parents="41943 7"/>
      <j2 rule="rewrite" parents="32 32"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42352">
    <literal><![CDATA[
      x + (y + h(x)) = y + h(x)
    ]]></literal>
    <justification jstring="[para(41943(a,1),19(a,1,2)),flip(a)].">
      <j1 rule="para" parents="41943 19"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42389">
    <literal><![CDATA[
      (h(x)' + (x + (x + (x + (g(x) + (x' + h(x)')))))')' = h(x)
    ]]></literal>
    <justification jstring="[para(41943(a,1),11812(a,1,1,1,1)),rewrite([41943(7),32(9),19(13),19(12),19(11),19(10),32(9),19(13),19(12),19(11),40628(12),42349(12),42349(12),42349(12)])].">
      <j1 rule="para" parents="41943 11812"/>
      <j2 rule="rewrite" parents="41943 32 19 19 19 19 32 19 19 19 40628 42349 42349 42349"/>
    </justification>
  </clause>

  <clause id="42507">
    <literal><![CDATA[
      (x + (x + (x + (g(x) + (x' + h(x)')))))' = g(h(x))
    ]]></literal>
    <justification jstring="[para(41943(a,1),456(a,1,1,1,1)),rewrite([41943(8),32(10),42389(16),6(4),32(4),368(8),41943(6),32(8)]),flip(a)].">
      <j1 rule="para" parents="41943 456"/>
      <j2 rule="rewrite" parents="41943 32 42389 6 32 368 41943 32"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42526">
    <literal><![CDATA[
      (g(h(x)) + g(h(x)))' = x + (x + (x + (g(x) + h(x)')))
    ]]></literal>
    <justification jstring="[para(41943(a,1),600(a,1,1,1,1)),rewrite([6(6),41943(6),32(7),19(11),19(10),19(9),19(8),42507(12),6(9),41943(9),32(10)])].">
      <j1 rule="para" parents="41943 600"/>
      <j2 rule="rewrite" parents="6 41943 32 19 19 19 19 42507 6 41943 32"/>
    </justification>
  </clause>

  <clause id="42671">
    <literal><![CDATA[
      g(x + (x + (x + (g(x) + h(x)')))) = g(h(x))
    ]]></literal>
    <justification jstring="[back_rewrite(42333),rewrite([42526(8),19(10),19(9),19(8),19(7),649(11)])].">
      <j1 rule="back_rewrite" parents="42333"/>
      <j2 rule="rewrite" parents="42526 19 19 19 19 649"/>
    </justification>
  </clause>

  <clause id="42701">
    <literal><![CDATA[
      g(h(x)) + h(x)' = h(x)'
    ]]></literal>
    <justification jstring="[back_rewrite(38251),rewrite([42671(8),38268(13)]),flip(a)].">
      <j1 rule="back_rewrite" parents="38251"/>
      <j2 rule="rewrite" parents="42671 38268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42702">
    <literal><![CDATA[
      g(h(x)') = g(h(x))
    ]]></literal>
    <justification jstring="[back_rewrite(38250),rewrite([42701(5),42671(11)])].">
      <j1 rule="back_rewrite" parents="38250"/>
      <j2 rule="rewrite" parents="42701 42671"/>
    </justification>
  </clause>

  <clause id="42715">
    <literal><![CDATA[
      h(x)'' = h(x)
    ]]></literal>
    <justification jstring="[back_rewrite(36393),rewrite([42701(5)])].">
      <j1 rule="back_rewrite" parents="36393"/>
      <j2 rule="rewrite" parents="42701"/>
    </justification>
  </clause>

  <clause id="42755">
    <literal><![CDATA[
      (g(x + h(x)') + (g(x) + (g(x) + (h(x)' + h(x)')))')' = g(x) + h(x)'
    ]]></literal>
    <justification jstring="[back_rewrite(9666),rewrite([42715(5),40637(4),41943(3),34739(5),42715(12),40637(11),41943(10),42715(21),40637(20),41943(19)])].">
      <j1 rule="back_rewrite" parents="9666"/>
      <j2 rule="rewrite" parents="42715 40637 41943 34739 42715 40637 41943 42715 40637 41943"/>
    </justification>
  </clause>

  <clause id="42995">
    <literal><![CDATA[
      (h(x)' + h(x)')' = h(h(x)')'
    ]]></literal>
    <justification jstring="[para(42702(a,1),995(a,1,1,2,1,2,2,1,2,2)),rewrite([6(15),42701(15),36016(19)])].">
      <j1 rule="para" parents="42702 995"/>
      <j2 rule="rewrite" parents="6 42701 36016"/>
    </justification>
  </clause>

  <clause id="43738">
    <literal><![CDATA[
      ((x + (x + h(y)))' + g((x + h(y))' + (h(y)' + (x + h(y)))'))' = x + h(y)
    ]]></literal>
    <justification jstring="[para(42352(a,1),24615(a,1,1,2,1,1,1)),rewrite([19(5),6(4),32(4),40662(4),42352(3),42352(3),42352(3),40782(14)])].">
      <j1 rule="para" parents="42352 24615"/>
      <j2 rule="rewrite" parents="19 6 32 40662 42352 42352 42352 40782"/>
    </justification>
  </clause>

  <clause id="43821">
    <literal><![CDATA[
      x + g(h(y)) = x
    ]]></literal>
    <justification jstring="[para(42701(a,1),22(a,1,1,1,1,2)),rewrite([42715(9),6(8),32(8),41956(11),6(8),8(9)]),flip(a)].">
      <j1 rule="para" parents="42701 22"/>
      <j2 rule="rewrite" parents="42715 6 32 41956 6 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43833">
    <literal><![CDATA[
      g(h(x)) = g(x)
    ]]></literal>
    <justification jstring="[para(42701(a,1),3212(a,1,1,2,1,2)),rewrite([6(3),43821(3),74(6),6(2),10(3)]),flip(a)].">
      <j1 rule="para" parents="42701 3212"/>
      <j2 rule="rewrite" parents="6 43821 74 6 10"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43835">
    <literal><![CDATA[
      x + g(y) = x
    ]]></literal>
    <justification jstring="[para(42701(a,1),3761(a,1,1,2,1,2,1)),rewrite([43833(4),19(5),42715(9),41090(11)])].">
      <j1 rule="para" parents="42701 3761"/>
      <j2 rule="rewrite" parents="43833 19 42715 41090"/>
    </justification>
  </clause>

  <clause id="43838">
    <literal><![CDATA[
      g(x) + h(x)' = h(x)'
    ]]></literal>
    <justification jstring="[para(42701(a,1),63(a,2)),rewrite([43833(2),34739(5),43833(6),43833(9),19(12),42755(16)])].">
      <j1 rule="para" parents="42701 63"/>
      <j2 rule="rewrite" parents="43833 34739 43833 43833 19 42755"/>
    </justification>
  </clause>

  <clause id="43849">
    <literal><![CDATA[
      (g(x) + h(h(x)')')' = h(x)'
    ]]></literal>
    <justification jstring="[para(42701(a,1),589(a,1,1,2,1,2,1,2,1)),rewrite([43833(4),6(4),43838(4),42702(3),43833(2),43833(5),42715(7),40637(6),42995(7)])].">
      <j1 rule="para" parents="42701 589"/>
      <j2 rule="rewrite" parents="43833 6 43838 42702 43833 43833 42715 40637 42995"/>
    </justification>
  </clause>

  <clause id="43850">
    <literal><![CDATA[
      (x + (x + (x + h(x)')))' = g(x)
    ]]></literal>
    <justification jstring="[para(42701(a,1),8272(a,1,1,1,1)),rewrite([42715(3),42995(7),43833(7),42702(9),43833(8),43835(8),6(7),43849(8),32(4),43838(4),43833(8)])].">
      <j1 rule="para" parents="42701 8272"/>
      <j2 rule="rewrite" parents="42715 42995 43833 42702 43833 43835 6 43849 32 43838 43833"/>
    </justification>
  </clause>

  <clause id="43861">
    <literal><![CDATA[
      g(x) + y = y
    ]]></literal>
    <justification jstring="[para(42701(a,1),260(a,1,1,1,1,2)),rewrite([43833(6),42715(8),40662(8),6(8),8(9),43833(2)]),flip(a)].">
      <j1 rule="para" parents="42701 260"/>
      <j2 rule="rewrite" parents="43833 42715 40662 6 8 43833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43863">
    <literal><![CDATA[
      h(h(x)') = h(x)'
    ]]></literal>
    <justification jstring="[para(42701(a,1),319(a,1,1,1,1,1,1)),rewrite([42715(3),43833(5),6(6),32(8),43861(8),42995(16),6(15),43835(15),42715(5)])].">
      <j1 rule="para" parents="42701 319"/>
      <j2 rule="rewrite" parents="42715 43833 6 32 43861 42995 6 43835 42715"/>
    </justification>
  </clause>

  <clause id="43876">
    <literal><![CDATA[
      g(x + (x + (x + h(x)'))) = g(x)
    ]]></literal>
    <justification jstring="[para(42701(a,1),120(a,1,1,2,2,1)),rewrite([43833(2),43833(4),6(4),43861(4),42715(6),6(5),32(5),43861(5),19(7),19(6),19(5),43861(4),43850(6),43833(4),6(4),43861(4),43833(5),43861(7),42715(6),6(5),32(5),43861(5)]),flip(a)].">
      <j1 rule="para" parents="42701 120"/>
      <j2 rule="rewrite" parents="43833 43833 6 43861 42715 6 32 43861 19 19 19 43861 43850 43833 6 43861 43833 43861 42715 6 32 43861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43879">
    <literal><![CDATA[
      (x + (x + (x + (g(x)' + h(x)'))))'' = x + (x + (x + h(x)'))
    ]]></literal>
    <justification jstring="[para(42701(a,1),135(a,1,1,1,1,2,1)),rewrite([43833(3),6(3),43861(3),42715(5),6(4),32(4),43861(4),43876(6),43833(3),43833(6),6(6),43861(6),43833(7),43861(9),42715(8),6(7),32(7),43861(7),19(9),19(8),19(7),43861(11),43833(13),6(13),43861(13),43833(14),43861(16),42715(15),6(14),32(14),43861(14)])].">
      <j1 rule="para" parents="42701 135"/>
      <j2 rule="rewrite" parents="43833 6 43861 42715 6 32 43861 43876 43833 43833 6 43861 43833 43861 42715 6 32 43861 19 19 19 43861 43833 6 43861 43833 43861 42715 6 32 43861"/>
    </justification>
  </clause>

  <clause id="43893">
    <literal><![CDATA[
      x + (x + (x + h(x)')) = g(x)'
    ]]></literal>
    <justification jstring="[para(42701(a,1),1171(a,1,1,2,1,2,1,1)),rewrite([43833(2),43833(4),42715(7),43833(7),42715(9),43861(8),32(8),43861(8),19(10),19(9),19(8),43861(12),43879(10),43833(7)])].">
      <j1 rule="para" parents="42701 1171"/>
      <j2 rule="rewrite" parents="43833 43833 42715 43833 42715 43861 32 43861 19 19 19 43861 43879 43833"/>
    </justification>
  </clause>

  <clause id="43895">
    <literal><![CDATA[
      (x + (x + (x + (x + (x + (x + (g(x)' + h(x)')'))))))'' = h(x)
    ]]></literal>
    <justification jstring="[para(42701(a,1),1186(a,1,1,2,1,2,1,1)),rewrite([42702(3),43833(2),42715(4),42715(5),43833(7),6(8),32(10),43861(10),19(12),19(11),19(10),32(9),43861(9),43861(15),42715(17)])].">
      <j1 rule="para" parents="42701 1186"/>
      <j2 rule="rewrite" parents="42702 43833 42715 42715 43833 6 32 43861 19 19 19 32 43861 43861 42715"/>
    </justification>
  </clause>

  <clause id="43899">
    <literal><![CDATA[
      x + (x + (x + (g(x)' + h(x)')')) = h(x)
    ]]></literal>
    <justification jstring="[para(42701(a,1),209(a,1,1,1,1,1,1)),rewrite([42715(3),43833(3),32(8),43861(8),42715(13),43833(13),43861(15),42715(14),43833(14),32(19),43861(19),19(21),19(20),19(19),32(18),43861(18),43861(24),43895(14),43833(3),43861(5),42715(4),43833(4),32(9),43861(9)]),flip(a)].">
      <j1 rule="para" parents="42701 209"/>
      <j2 rule="rewrite" parents="42715 43833 32 43861 42715 43833 43861 42715 43833 32 43861 19 19 19 32 43861 43861 43895 43833 43861 42715 43833 32 43861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43955">
    <literal><![CDATA[
      (x + x)'' = x
    ]]></literal>
    <justification jstring="[para(42701(a,1),328(a,1,1,1,1,1,1,2)),rewrite([43833(6),42715(8),43861(7),6(8),43833(11),43833(12),43835(12),43861(11),43861(12),43833(5),43835(5)])].">
      <j1 rule="para" parents="42701 328"/>
      <j2 rule="rewrite" parents="43833 42715 43861 6 43833 43833 43835 43861 43861 43833 43835"/>
    </justification>
  </clause>

  <clause id="43987">
    <literal><![CDATA[
      h(x)' + h(x)' = h(x)'
    ]]></literal>
    <justification jstring="[para(42701(a,1),848(a,1,1,2,1,2,2,1,2)),rewrite([43833(2),43863(4),43861(4),42715(3),42702(8),43833(7),43861(9),42715(8),6(7),32(7),43861(7),43893(8),6(6),32(8),43861(8),43899(9)]),flip(a)].">
      <j1 rule="para" parents="42701 848"/>
      <j2 rule="rewrite" parents="43833 43863 43861 42715 42702 43833 43861 42715 6 32 43861 43893 6 32 43861 43899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44155">
    <literal><![CDATA[
      h(x)' = x'
    ]]></literal>
    <justification jstring="[back_rewrite(38657),rewrite([43833(2),43987(6),43861(4),34718(4),43835(2)]),flip(a)].">
      <j1 rule="back_rewrite" parents="38657"/>
      <j2 rule="rewrite" parents="43833 43987 43861 34718 43835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44200">
    <literal><![CDATA[
      g(x') = g(x)
    ]]></literal>
    <justification jstring="[back_rewrite(38418),rewrite([44155(2),43833(3),43833(4),44155(5),44155(6),43861(7),43955(7),43861(4),10(5),43833(4)])].">
      <j1 rule="back_rewrite" parents="38418"/>
      <j2 rule="rewrite" parents="44155 43833 43833 44155 44155 43861 43955 43861 10 43833"/>
    </justification>
  </clause>

  <clause id="44410">
    <literal><![CDATA[
      x'' = x
    ]]></literal>
    <justification jstring="[back_rewrite(42268),rewrite([43833(2),43833(3),43835(3),43861(3)])].">
      <j1 rule="back_rewrite" parents="42268"/>
      <j2 rule="rewrite" parents="43833 43833 43835 43861"/>
    </justification>
  </clause>

  <clause id="44413">
    <literal><![CDATA[
      x + x = x
    ]]></literal>
    <justification jstring="[back_rewrite(42221),rewrite([43833(2),43833(3),43833(4),43835(4),44410(4),6(3),43835(3),44410(3),43861(4),44410(3)])].">
      <j1 rule="back_rewrite" parents="42221"/>
      <j2 rule="rewrite" parents="43833 43833 43833 43835 44410 6 43835 44410 43861 44410"/>
    </justification>
  </clause>

  <clause id="44428">
    <literal><![CDATA[
      x' + ((y + x)' + (y' + x)') = x'
    ]]></literal>
    <justification jstring="[back_rewrite(42085),rewrite([43833(6),43833(7),43835(7),43861(8),43861(11),44410(10)])].">
      <j1 rule="back_rewrite" parents="42085"/>
      <j2 rule="rewrite" parents="43833 43833 43835 43861 43861 44410"/>
    </justification>
  </clause>

  <clause id="44447">
    <literal><![CDATA[
      h(x) = x
    ]]></literal>
    <justification jstring="[back_rewrite(41956),rewrite([43833(3),44413(3),43835(2),44413(1),44413(1)]),flip(a)].">
      <j1 rule="back_rewrite" parents="41956"/>
      <j2 rule="rewrite" parents="43833 44413 43835 44413 44413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44536">
    <literal><![CDATA[
      g(x + y) = g(y)
    ]]></literal>
    <justification jstring="[back_rewrite(42327),rewrite([44447(1),44447(3),44447(4),43861(6),44410(5),6(4),7(4),26(5),44447(3)])].">
      <j1 rule="back_rewrite" parents="42327"/>
      <j2 rule="rewrite" parents="44447 44447 44447 43861 44410 6 7 26 44447"/>
    </justification>
  </clause>

  <clause id="44567">
    <literal><![CDATA[
      x + (x + y) = x + y
    ]]></literal>
    <justification jstring="[back_rewrite(43738),rewrite([44447(1),44447(4),44447(6),44447(7),44536(11),44200(8),44536(7),44536(5),6(5),43861(5),44410(4),44447(3)])].">
      <j1 rule="back_rewrite" parents="43738"/>
      <j2 rule="rewrite" parents="44447 44447 44447 44447 44536 44200 44536 44536 6 43861 44410 44447"/>
    </justification>
  </clause>

  <clause id="44895">
    <literal><![CDATA[
      (x + y)' + (x' + y)' = y'
    ]]></literal>
    <justification jstring="[back_rewrite(6022),rewrite([44447(4),43861(6),44536(7),44200(4),44536(3),44447(8),43861(10),44447(11),43861(13),44447(16),43861(18),44536(19),44200(16),44536(15),6(14),43861(14),44413(13),44567(11),44428(9),44410(3),6(2),43835(2),44447(5),43861(7)]),flip(a)].">
      <j1 rule="back_rewrite" parents="6022"/>
      <j2 rule="rewrite" parents="44447 43861 44536 44200 44536 44447 43861 44447 43861 44447 43861 44536 44200 44536 6 43861 44413 44567 44428 44410 6 43835 44447 43861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45188">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer(Huntington)
    ]]></attribute>
    <justification jstring="[back_rewrite(13),rewrite([44895(12),44410(3)]),xx(a)].">
      <j1 rule="back_rewrite" parents="13"/>
      <j2 rule="rewrite" parents="44895 44410"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

</proofs>
