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<!DOCTYPE proofs SYSTEM "proof3.dtd">

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

<proofs number_of_proofs="5">

<source>winner.out</source>

<heading><![CDATA[
Prover9 (32) version June-2007-, 12 June 2007.
Process 10345 was started by mccune on cleo,
Wed Jun 13 10:27:47 2007
The command was "prover9 -f winner.in".
]]></heading>

<proof number="1" length="35" max_count="23">

<comments><![CDATA[
% Proof 1 at 87.93 (+ 0.26) seconds: Winker2a.
% Length of proof is 35.
% Level of proof is 12.
% Maximum clause weight is 23.
% Given clauses 833.
]]></comments>

  <clause id="1" 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>
    <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>
    <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[
      (x + y)' != x'
    ]]></literal>
    <attribute><![CDATA[
      answer(Winker2a)
    ]]></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="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="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="33">
    <literal><![CDATA[
      (h(x) + (x + (x + (x + g(x)))')')' = x
    ]]></literal>
    <justification jstring="[para(12(a,1),8(a,1,1,1))].">
      <j1 rule="para" parents="12 8"/>
    </justification>
  </clause>

  <clause id="36">
    <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="40">
    <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="41">
    <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="42">
    <literal><![CDATA[
      (g(x) + h(x))' = x
    ]]></literal>
    <justification jstring="[back_rewrite(33),rewrite([40(7),6(3)])].">
      <j1 rule="back_rewrite" parents="33"/>
      <j2 rule="rewrite" parents="40 6"/>
    </justification>
  </clause>

  <clause id="43">
    <literal><![CDATA[
      (x + (g(x) + h(x)')')' = g(x)
    ]]></literal>
    <justification jstring="[para(42(a,1),8(a,1,1,1))].">
      <j1 rule="para" parents="42 8"/>
    </justification>
  </clause>

  <clause id="44">
    <literal><![CDATA[
      ((x + y)' + (x + (g(y) + h(y)))')' = x
    ]]></literal>
    <justification jstring="[para(42(a,1),8(a,1,1,2,1,2)),rewrite([6(8)])].">
      <j1 rule="para" parents="42 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="58">
    <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="94">
    <literal><![CDATA[
      ((x + (g(y) + h(y)))' + (y + x)')' = x
    ]]></literal>
    <justification jstring="[para(42(a,1),21(a,1,1,2,1,1))].">
      <j1 rule="para" parents="42 21"/>
    </justification>
  </clause>

  <clause id="113">
    <literal><![CDATA[
      (g(x) + (x + (g(x) + h(x)'))')' = x
    ]]></literal>
    <justification jstring="[para(43(a,1),8(a,1,1,2)),rewrite([6(8)])].">
      <j1 rule="para" parents="43 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="679">
    <literal><![CDATA[
      (x + (x + (g(y) + (h(y) + (x + y)')))')' = (x + y)'
    ]]></literal>
    <justification jstring="[para(44(a,1),8(a,1,1,2)),rewrite([6(7),7(7),7(6),6(9)])].">
      <j1 rule="para" parents="44 8"/>
      <j2 rule="rewrite" parents="6 7 7 6"/>
    </justification>
  </clause>

  <clause id="1653">
    <literal><![CDATA[
      (h(x) + g(g(x) + (x + x)'))' = x + g(x)
    ]]></literal>
    <justification jstring="[para(12(a,1),58(a,1,1,1)),rewrite([7(6),41(7)])].">
      <j1 rule="para" parents="12 58"/>
      <j2 rule="rewrite" parents="7 41"/>
    </justification>
  </clause>

  <clause id="2610">
    <literal><![CDATA[
      (x + (g(x) + (x + (g(x) + (h(x) + (x + x)')))'))' = h(x)
    ]]></literal>
    <justification jstring="[para(1653(a,1),28(a,1,1,1)),rewrite([29(12),6(8),19(9),19(8),7(11)])].">
      <j1 rule="para" parents="1653 28"/>
      <j2 rule="rewrite" parents="29 6 19 19 7"/>
    </justification>
  </clause>

  <clause id="22398">
    <literal><![CDATA[
      (x + h(x))' = g(x)
    ]]></literal>
    <justification jstring="[para(2610(a,1),36(a,1,1,1)),rewrite([679(12),29(6),6(2)])].">
      <j1 rule="para" parents="2610 36"/>
      <j2 rule="rewrite" parents="679 29 6"/>
    </justification>
  </clause>

  <clause id="22424">
    <literal><![CDATA[
      (g(x') + (x + h(x'))')' = h(x')
    ]]></literal>
    <justification jstring="[para(22398(a,1),21(a,1,1,2)),rewrite([6(3),6(7)])].">
      <j1 rule="para" parents="22398 21"/>
      <j2 rule="rewrite" parents="6 6"/>
    </justification>
  </clause>

  <clause id="22439">
    <literal><![CDATA[
      (x + (x + (g(x) + h(x)'))')' = g(x)
    ]]></literal>
    <justification jstring="[para(22398(a,1),25(a,1,1,2,1,2,2)),rewrite([6(4),22398(11)])].">
      <j1 rule="para" parents="22398 25"/>
      <j2 rule="rewrite" parents="6 22398"/>
    </justification>
  </clause>

  <clause id="24379">
    <literal><![CDATA[
      (g(x) + (g(x) + (h(x) + (x + (g(x) + h(x)'))'))')' = h(x)
    ]]></literal>
    <justification jstring="[para(113(a,1),22424(a,1,1,1,1)),rewrite([113(18),6(11),19(11),113(23)])].">
      <j1 rule="para" parents="113 22424"/>
      <j2 rule="rewrite" parents="113 6 19 113"/>
    </justification>
  </clause>

  <clause id="24552">
    <literal><![CDATA[
      (x + (g(x) + h(x)'))' = h(x)
    ]]></literal>
    <justification jstring="[para(22439(a,1),94(a,1,1,2)),rewrite([6(10),7(10),6(13),24379(14)]),flip(a)].">
      <j1 rule="para" parents="22439 94"/>
      <j2 rule="rewrite" parents="6 7 6 24379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24581">
    <literal><![CDATA[
      (h(x) + (h(x)' + (x + g(x))')')' = h(x)'
    ]]></literal>
    <justification jstring="[para(24552(a,1),58(a,1,1,1))].">
      <j1 rule="para" parents="24552 58"/>
    </justification>
  </clause>

  <clause id="24582">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer(Winker2a)
    ]]></attribute>
    <justification jstring="[resolve(24581,a,13,a)].">
      <j1 rule="resolve" parents="24581 13"/>
    </justification>
  </clause>

</proof>

<proof number="2" length="52" max_count="32">

<comments><![CDATA[
% Proof 2 at 99.69 (+ 0.28) seconds: Winker1b.
% Length of proof is 52.
% Level of proof is 18.
% Maximum clause weight is 32.
% Given clauses 920.
]]></comments>

  <clause id="4" 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>
    <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>
    <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 != y
    ]]></literal>
    <attribute><![CDATA[
      answer(Winker1b)
    ]]></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="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="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="33">
    <literal><![CDATA[
      (h(x) + (x + (x + (x + g(x)))')')' = x
    ]]></literal>
    <justification jstring="[para(12(a,1),8(a,1,1,1))].">
      <j1 rule="para" parents="12 8"/>
    </justification>
  </clause>

  <clause id="36">
    <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="40">
    <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="41">
    <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="42">
    <literal><![CDATA[
      (g(x) + h(x))' = x
    ]]></literal>
    <justification jstring="[back_rewrite(33),rewrite([40(7),6(3)])].">
      <j1 rule="back_rewrite" parents="33"/>
      <j2 rule="rewrite" parents="40 6"/>
    </justification>
  </clause>

  <clause id="44">
    <literal><![CDATA[
      ((x + y)' + (x + (g(y) + h(y)))')' = x
    ]]></literal>
    <justification jstring="[para(42(a,1),8(a,1,1,2,1,2)),rewrite([6(8)])].">
      <j1 rule="para" parents="42 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="58">
    <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="62">
    <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="84">
    <literal><![CDATA[
      ((x + ((y + z)' + (y + z')'))' + (y + x)')' = x
    ]]></literal>
    <justification jstring="[para(8(a,1),21(a,1,1,2,1,1))].">
      <j1 rule="para" parents="8 21"/>
    </justification>
  </clause>

  <clause id="85">
    <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="87">
    <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="93">
    <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="109">
    <literal><![CDATA[
      (g(x') + (x + (x' + (x' + g(x')))')')' = (x' + (x' + g(x')))'
    ]]></literal>
    <justification jstring="[para(40(a,1),21(a,1,1,2)),rewrite([6(8),6(12)])].">
      <j1 rule="para" parents="40 21"/>
      <j2 rule="rewrite" parents="6 6"/>
    </justification>
  </clause>

  <clause id="170">
    <literal><![CDATA[
      (h(x) + (x + (x + (x + g(x))'))')' = x + x
    ]]></literal>
    <justification jstring="[para(12(a,1),22(a,1,1,1))].">
      <j1 rule="para" parents="12 22"/>
    </justification>
  </clause>

  <clause id="679">
    <literal><![CDATA[
      (x + (x + (g(y) + (h(y) + (x + y)')))')' = (x + y)'
    ]]></literal>
    <justification jstring="[para(44(a,1),8(a,1,1,2)),rewrite([6(7),7(7),7(6),6(9)])].">
      <j1 rule="para" parents="44 8"/>
      <j2 rule="rewrite" parents="6 7 7 6"/>
    </justification>
  </clause>

  <clause id="833">
    <literal><![CDATA[
      (h(g(x)) + (x + (g(x) + (g(x) + (g(g(x)) + x'))))')' = g(x) + (g(x) + g(g(x)))
    ]]></literal>
    <justification jstring="[para(12(a,1),87(a,1,1,2)),rewrite([19(9),7(8),7(7),6(13)])].">
      <j1 rule="para" parents="12 87"/>
      <j2 rule="rewrite" parents="19 7 7 6"/>
    </justification>
  </clause>

  <clause id="1653">
    <literal><![CDATA[
      (h(x) + g(g(x) + (x + x)'))' = x + g(x)
    ]]></literal>
    <justification jstring="[para(12(a,1),58(a,1,1,1)),rewrite([7(6),41(7)])].">
      <j1 rule="para" parents="12 58"/>
      <j2 rule="rewrite" parents="7 41"/>
    </justification>
  </clause>

  <clause id="2610">
    <literal><![CDATA[
      (x + (g(x) + (x + (g(x) + (h(x) + (x + x)')))'))' = h(x)
    ]]></literal>
    <justification jstring="[para(1653(a,1),28(a,1,1,1)),rewrite([29(12),6(8),19(9),19(8),7(11)])].">
      <j1 rule="para" parents="1653 28"/>
      <j2 rule="rewrite" parents="29 6 19 19 7"/>
    </justification>
  </clause>

  <clause id="2895">
    <literal><![CDATA[
      (x + (x + (h(y) + (y + (y + (y + (g(y) + x))))'))')' = (y + (y + (y + (g(y) + x))))'
    ]]></literal>
    <justification jstring="[para(12(a,1),62(a,1,1,2,1,2,1)),rewrite([7(6),7(5),7(4),7(17),7(16),7(15)])].">
      <j1 rule="para" parents="12 62"/>
      <j2 rule="rewrite" parents="7 7 7 7 7 7"/>
    </justification>
  </clause>

  <clause id="3222">
    <literal><![CDATA[
      (x + (x + (x + (x + (h(x) + (x + g(x))')))'))' = h(x)
    ]]></literal>
    <justification jstring="[para(170(a,1),8(a,1,1,2)),rewrite([19(7),19(6),6(10),7(10)])].">
      <j1 rule="para" parents="170 8"/>
      <j2 rule="rewrite" parents="19 19 6 7"/>
    </justification>
  </clause>

  <clause id="21312">
    <literal><![CDATA[
      (h(x) + (x + (x + (x + (x + (h(x) + (x + g(x))')))')')')' = x
    ]]></literal>
    <justification jstring="[para(3222(a,1),8(a,1,1,1))].">
      <j1 rule="para" parents="3222 8"/>
    </justification>
  </clause>

  <clause id="22398">
    <literal><![CDATA[
      (x + h(x))' = g(x)
    ]]></literal>
    <justification jstring="[para(2610(a,1),36(a,1,1,1)),rewrite([679(12),29(6),6(2)])].">
      <j1 rule="para" parents="2610 36"/>
      <j2 rule="rewrite" parents="679 29 6"/>
    </justification>
  </clause>

  <clause id="22424">
    <literal><![CDATA[
      (g(x') + (x + h(x'))')' = h(x')
    ]]></literal>
    <justification jstring="[para(22398(a,1),21(a,1,1,2)),rewrite([6(3),6(7)])].">
      <j1 rule="para" parents="22398 21"/>
      <j2 rule="rewrite" parents="6 6"/>
    </justification>
  </clause>

  <clause id="22493">
    <literal><![CDATA[
      (x + (x + (y + (h(y) + (x + g(y))')))')' = (x + g(y))'
    ]]></literal>
    <justification jstring="[para(22398(a,1),85(a,1,1,2,1,2,2,1,2)),rewrite([7(6),22398(13)])].">
      <j1 rule="para" parents="22398 85"/>
      <j2 rule="rewrite" parents="7 22398"/>
    </justification>
  </clause>

  <clause id="22532">
    <literal><![CDATA[
      (g(x) + (h(x) + ((x + y)' + (x + y')'))')' = h(x)
    ]]></literal>
    <justification jstring="[para(22398(a,1),84(a,1,1,2)),rewrite([6(11)])].">
      <j1 rule="para" parents="22398 84"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="23021">
    <literal><![CDATA[
      (h(x) + (x + (x + g(x))')')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(21312),rewrite([22493(11)])].">
      <j1 rule="back_rewrite" parents="21312"/>
      <j2 rule="rewrite" parents="22493"/>
    </justification>
  </clause>

  <clause id="23594">
    <literal><![CDATA[
      (x + (x + g(x)))' = h(x)
    ]]></literal>
    <justification jstring="[para(23021(a,1),109(a,1,1,1,1)),rewrite([23021(16),23021(16),23021(16),6(13),19(13),22532(16),23021(9),23021(9),23021(9)]),flip(a)].">
      <j1 rule="para" parents="23021 109"/>
      <j2 rule="rewrite" parents="23021 23021 23021 6 19 22532 23021 23021 23021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23848">
    <literal><![CDATA[
      ((x + h(y))' + (x + (y + (y + g(y))))')' = x
    ]]></literal>
    <justification jstring="[para(23594(a,1),8(a,1,1,2,1,2)),rewrite([6(9)])].">
      <j1 rule="para" parents="23594 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="23868">
    <literal><![CDATA[
      (h(g(x)) + (x + (g(x) + (g(g(x)) + x')))')' = g(x) + g(g(x))
    ]]></literal>
    <justification jstring="[para(23594(a,1),87(a,1,1,2)),rewrite([19(7),7(6),6(11)])].">
      <j1 rule="para" parents="23594 87"/>
      <j2 rule="rewrite" parents="19 7 6"/>
    </justification>
  </clause>

  <clause id="23892">
    <literal><![CDATA[
      (h(x) + (x + (g(x) + (g(x) + (x + x)')))')' = x + g(x)
    ]]></literal>
    <justification jstring="[para(23594(a,1),93(a,1,1,2)),rewrite([19(7),7(6),19(7),6(10)])].">
      <j1 rule="para" parents="23594 93"/>
      <j2 rule="rewrite" parents="19 7 19 6"/>
    </justification>
  </clause>

  <clause id="25450">
    <literal><![CDATA[
      (x + (x + (x + (g(x) + g(x))))')' = g(x)
    ]]></literal>
    <justification jstring="[para(42(a,1),23848(a,1,1,1)),rewrite([19(5),19(4)])].">
      <j1 rule="para" parents="42 23848"/>
      <j2 rule="rewrite" parents="19 19"/>
    </justification>
  </clause>

  <clause id="25456">
    <literal><![CDATA[
      (g(x) + (x + (x + (x + (g(x) + g(x)))))')' = x
    ]]></literal>
    <justification jstring="[para(25450(a,1),8(a,1,1,2)),rewrite([6(9)])].">
      <j1 rule="para" parents="25450 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="25936">
    <literal><![CDATA[
      (x + (x + (x + (g(x) + g(x)))))' = h(x)
    ]]></literal>
    <justification jstring="[para(25456(a,1),22424(a,1,1,1,1)),rewrite([25456(20),6(12),19(12),2895(15),25456(17)])].">
      <j1 rule="para" parents="25456 22424"/>
      <j2 rule="rewrite" parents="25456 6 19 2895 25456"/>
    </justification>
  </clause>

  <clause id="25950">
    <literal><![CDATA[
      x + (g(x) + g(x)) = x + g(x)
    ]]></literal>
    <justification jstring="[para(25936(a,1),58(a,1,1,1)),rewrite([7(8),7(7),23892(11)]),flip(a)].">
      <j1 rule="para" parents="25936 58"/>
      <j2 rule="rewrite" parents="7 7 23892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25979">
    <literal><![CDATA[
      x + (g(x) + (g(x) + y)) = x + (g(x) + y)
    ]]></literal>
    <justification jstring="[para(25950(a,1),7(a,1,1)),rewrite([7(3),7(7)]),flip(a)].">
      <j1 rule="para" parents="25950 7"/>
      <j2 rule="rewrite" parents="7 7"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26233">
    <literal><![CDATA[
      g(x) + (g(x) + g(g(x))) = g(x) + g(g(x))
    ]]></literal>
    <justification jstring="[back_rewrite(833),rewrite([25979(11),23868(12)]),flip(a)].">
      <j1 rule="back_rewrite" parents="833"/>
      <j2 rule="rewrite" parents="25979 23868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26234">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer(Winker1b)
    ]]></attribute>
    <justification jstring="[resolve(26233,a,16,a)].">
      <j1 rule="resolve" parents="26233 16"/>
    </justification>
  </clause>

</proof>

<proof number="3" length="58" max_count="32">

<comments><![CDATA[
% Proof 3 at 100.42 (+ 0.28) seconds: Winker1a.
% Length of proof is 58.
% Level of proof is 20.
% Maximum clause weight is 32.
% Given clauses 928.
]]></comments>

  <clause id="3" 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>
    <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>
    <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 != x
    ]]></literal>
    <attribute><![CDATA[
      answer(Winker1a)
    ]]></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="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="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="33">
    <literal><![CDATA[
      (h(x) + (x + (x + (x + g(x)))')')' = x
    ]]></literal>
    <justification jstring="[para(12(a,1),8(a,1,1,1))].">
      <j1 rule="para" parents="12 8"/>
    </justification>
  </clause>

  <clause id="36">
    <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="40">
    <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="41">
    <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="42">
    <literal><![CDATA[
      (g(x) + h(x))' = x
    ]]></literal>
    <justification jstring="[back_rewrite(33),rewrite([40(7),6(3)])].">
      <j1 rule="back_rewrite" parents="33"/>
      <j2 rule="rewrite" parents="40 6"/>
    </justification>
  </clause>

  <clause id="44">
    <literal><![CDATA[
      ((x + y)' + (x + (g(y) + h(y)))')' = x
    ]]></literal>
    <justification jstring="[para(42(a,1),8(a,1,1,2,1,2)),rewrite([6(8)])].">
      <j1 rule="para" parents="42 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="58">
    <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="62">
    <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="69">
    <literal><![CDATA[
      ((x + (x + (x + (g(x) + y))))' + (y + h(x))')' = y
    ]]></literal>
    <justification jstring="[para(12(a,1),20(a,1,1,2,1,2)),rewrite([7(5),7(4),7(3)])].">
      <j1 rule="para" parents="12 20"/>
      <j2 rule="rewrite" parents="7 7 7"/>
    </justification>
  </clause>

  <clause id="84">
    <literal><![CDATA[
      ((x + ((y + z)' + (y + z')'))' + (y + x)')' = x
    ]]></literal>
    <justification jstring="[para(8(a,1),21(a,1,1,2,1,1))].">
      <j1 rule="para" parents="8 21"/>
    </justification>
  </clause>

  <clause id="85">
    <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="87">
    <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="93">
    <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="94">
    <literal><![CDATA[
      ((x + (g(y) + h(y)))' + (y + x)')' = x
    ]]></literal>
    <justification jstring="[para(42(a,1),21(a,1,1,2,1,1))].">
      <j1 rule="para" parents="42 21"/>
    </justification>
  </clause>

  <clause id="109">
    <literal><![CDATA[
      (g(x') + (x + (x' + (x' + g(x')))')')' = (x' + (x' + g(x')))'
    ]]></literal>
    <justification jstring="[para(40(a,1),21(a,1,1,2)),rewrite([6(8),6(12)])].">
      <j1 rule="para" parents="40 21"/>
      <j2 rule="rewrite" parents="6 6"/>
    </justification>
  </clause>

  <clause id="170">
    <literal><![CDATA[
      (h(x) + (x + (x + (x + g(x))'))')' = x + x
    ]]></literal>
    <justification jstring="[para(12(a,1),22(a,1,1,1))].">
      <j1 rule="para" parents="12 22"/>
    </justification>
  </clause>

  <clause id="679">
    <literal><![CDATA[
      (x + (x + (g(y) + (h(y) + (x + y)')))')' = (x + y)'
    ]]></literal>
    <justification jstring="[para(44(a,1),8(a,1,1,2)),rewrite([6(7),7(7),7(6),6(9)])].">
      <j1 rule="para" parents="44 8"/>
      <j2 rule="rewrite" parents="6 7 7 6"/>
    </justification>
  </clause>

  <clause id="833">
    <literal><![CDATA[
      (h(g(x)) + (x + (g(x) + (g(x) + (g(g(x)) + x'))))')' = g(x) + (g(x) + g(g(x)))
    ]]></literal>
    <justification jstring="[para(12(a,1),87(a,1,1,2)),rewrite([19(9),7(8),7(7),6(13)])].">
      <j1 rule="para" parents="12 87"/>
      <j2 rule="rewrite" parents="19 7 7 6"/>
    </justification>
  </clause>

  <clause id="1653">
    <literal><![CDATA[
      (h(x) + g(g(x) + (x + x)'))' = x + g(x)
    ]]></literal>
    <justification jstring="[para(12(a,1),58(a,1,1,1)),rewrite([7(6),41(7)])].">
      <j1 rule="para" parents="12 58"/>
      <j2 rule="rewrite" parents="7 41"/>
    </justification>
  </clause>

  <clause id="2610">
    <literal><![CDATA[
      (x + (g(x) + (x + (g(x) + (h(x) + (x + x)')))'))' = h(x)
    ]]></literal>
    <justification jstring="[para(1653(a,1),28(a,1,1,1)),rewrite([29(12),6(8),19(9),19(8),7(11)])].">
      <j1 rule="para" parents="1653 28"/>
      <j2 rule="rewrite" parents="29 6 19 19 7"/>
    </justification>
  </clause>

  <clause id="2895">
    <literal><![CDATA[
      (x + (x + (h(y) + (y + (y + (y + (g(y) + x))))'))')' = (y + (y + (y + (g(y) + x))))'
    ]]></literal>
    <justification jstring="[para(12(a,1),62(a,1,1,2,1,2,1)),rewrite([7(6),7(5),7(4),7(17),7(16),7(15)])].">
      <j1 rule="para" parents="12 62"/>
      <j2 rule="rewrite" parents="7 7 7 7 7 7"/>
    </justification>
  </clause>

  <clause id="3222">
    <literal><![CDATA[
      (x + (x + (x + (x + (h(x) + (x + g(x))')))'))' = h(x)
    ]]></literal>
    <justification jstring="[para(170(a,1),8(a,1,1,2)),rewrite([19(7),19(6),6(10),7(10)])].">
      <j1 rule="para" parents="170 8"/>
      <j2 rule="rewrite" parents="19 19 6 7"/>
    </justification>
  </clause>

  <clause id="21312">
    <literal><![CDATA[
      (h(x) + (x + (x + (x + (x + (h(x) + (x + g(x))')))')')')' = x
    ]]></literal>
    <justification jstring="[para(3222(a,1),8(a,1,1,1))].">
      <j1 rule="para" parents="3222 8"/>
    </justification>
  </clause>

  <clause id="22398">
    <literal><![CDATA[
      (x + h(x))' = g(x)
    ]]></literal>
    <justification jstring="[para(2610(a,1),36(a,1,1,1)),rewrite([679(12),29(6),6(2)])].">
      <j1 rule="para" parents="2610 36"/>
      <j2 rule="rewrite" parents="679 29 6"/>
    </justification>
  </clause>

  <clause id="22424">
    <literal><![CDATA[
      (g(x') + (x + h(x'))')' = h(x')
    ]]></literal>
    <justification jstring="[para(22398(a,1),21(a,1,1,2)),rewrite([6(3),6(7)])].">
      <j1 rule="para" parents="22398 21"/>
      <j2 rule="rewrite" parents="6 6"/>
    </justification>
  </clause>

  <clause id="22493">
    <literal><![CDATA[
      (x + (x + (y + (h(y) + (x + g(y))')))')' = (x + g(y))'
    ]]></literal>
    <justification jstring="[para(22398(a,1),85(a,1,1,2,1,2,2,1,2)),rewrite([7(6),22398(13)])].">
      <j1 rule="para" parents="22398 85"/>
      <j2 rule="rewrite" parents="7 22398"/>
    </justification>
  </clause>

  <clause id="22532">
    <literal><![CDATA[
      (g(x) + (h(x) + ((x + y)' + (x + y')'))')' = h(x)
    ]]></literal>
    <justification jstring="[para(22398(a,1),84(a,1,1,2)),rewrite([6(11)])].">
      <j1 rule="para" parents="22398 84"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="23021">
    <literal><![CDATA[
      (h(x) + (x + (x + g(x))')')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(21312),rewrite([22493(11)])].">
      <j1 rule="back_rewrite" parents="21312"/>
      <j2 rule="rewrite" parents="22493"/>
    </justification>
  </clause>

  <clause id="23594">
    <literal><![CDATA[
      (x + (x + g(x)))' = h(x)
    ]]></literal>
    <justification jstring="[para(23021(a,1),109(a,1,1,1,1)),rewrite([23021(16),23021(16),23021(16),6(13),19(13),22532(16),23021(9),23021(9),23021(9)]),flip(a)].">
      <j1 rule="para" parents="23021 109"/>
      <j2 rule="rewrite" parents="23021 23021 23021 6 19 22532 23021 23021 23021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23848">
    <literal><![CDATA[
      ((x + h(y))' + (x + (y + (y + g(y))))')' = x
    ]]></literal>
    <justification jstring="[para(23594(a,1),8(a,1,1,2,1,2)),rewrite([6(9)])].">
      <j1 rule="para" parents="23594 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="23868">
    <literal><![CDATA[
      (h(g(x)) + (x + (g(x) + (g(g(x)) + x')))')' = g(x) + g(g(x))
    ]]></literal>
    <justification jstring="[para(23594(a,1),87(a,1,1,2)),rewrite([19(7),7(6),6(11)])].">
      <j1 rule="para" parents="23594 87"/>
      <j2 rule="rewrite" parents="19 7 6"/>
    </justification>
  </clause>

  <clause id="23892">
    <literal><![CDATA[
      (h(x) + (x + (g(x) + (g(x) + (x + x)')))')' = x + g(x)
    ]]></literal>
    <justification jstring="[para(23594(a,1),93(a,1,1,2)),rewrite([19(7),7(6),19(7),6(10)])].">
      <j1 rule="para" parents="23594 93"/>
      <j2 rule="rewrite" parents="19 7 19 6"/>
    </justification>
  </clause>

  <clause id="25450">
    <literal><![CDATA[
      (x + (x + (x + (g(x) + g(x))))')' = g(x)
    ]]></literal>
    <justification jstring="[para(42(a,1),23848(a,1,1,1)),rewrite([19(5),19(4)])].">
      <j1 rule="para" parents="42 23848"/>
      <j2 rule="rewrite" parents="19 19"/>
    </justification>
  </clause>

  <clause id="25456">
    <literal><![CDATA[
      (g(x) + (x + (x + (x + (g(x) + g(x)))))')' = x
    ]]></literal>
    <justification jstring="[para(25450(a,1),8(a,1,1,2)),rewrite([6(9)])].">
      <j1 rule="para" parents="25450 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="25936">
    <literal><![CDATA[
      (x + (x + (x + (g(x) + g(x)))))' = h(x)
    ]]></literal>
    <justification jstring="[para(25456(a,1),22424(a,1,1,1,1)),rewrite([25456(20),6(12),19(12),2895(15),25456(17)])].">
      <j1 rule="para" parents="25456 22424"/>
      <j2 rule="rewrite" parents="25456 6 19 2895 25456"/>
    </justification>
  </clause>

  <clause id="25950">
    <literal><![CDATA[
      x + (g(x) + g(x)) = x + g(x)
    ]]></literal>
    <justification jstring="[para(25936(a,1),58(a,1,1,1)),rewrite([7(8),7(7),23892(11)]),flip(a)].">
      <j1 rule="para" parents="25936 58"/>
      <j2 rule="rewrite" parents="7 7 23892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25979">
    <literal><![CDATA[
      x + (g(x) + (g(x) + y)) = x + (g(x) + y)
    ]]></literal>
    <justification jstring="[para(25950(a,1),7(a,1,1)),rewrite([7(3),7(7)]),flip(a)].">
      <j1 rule="para" parents="25950 7"/>
      <j2 rule="rewrite" parents="7 7"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25983">
    <literal><![CDATA[
      x + (y + (g(x) + g(x))) = y + (x + g(x))
    ]]></literal>
    <justification jstring="[para(25950(a,1),19(a,1,2)),flip(a)].">
      <j1 rule="para" parents="25950 19"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26233">
    <literal><![CDATA[
      g(x) + (g(x) + g(g(x))) = g(x) + g(g(x))
    ]]></literal>
    <justification jstring="[back_rewrite(833),rewrite([25979(11),23868(12)]),flip(a)].">
      <j1 rule="back_rewrite" parents="833"/>
      <j2 rule="rewrite" parents="25979 23868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26339">
    <literal><![CDATA[
      (h(x) + (g(x) + (g(x) + h(x)))')' = g(x) + g(x)
    ]]></literal>
    <justification jstring="[para(25983(a,1),69(a,1,1,1,1,2,2)),rewrite([19(4),25950(4),12(5),6(6),19(6),6(5)])].">
      <j1 rule="para" parents="25983 69"/>
      <j2 rule="rewrite" parents="19 25950 12 6 19 6"/>
    </justification>
  </clause>

  <clause id="26374">
    <literal><![CDATA[
      (g(x) + g(g(x)))' = h(g(x))
    ]]></literal>
    <justification jstring="[para(26233(a,1),12(a,1,1,2)),rewrite([26233(6)])].">
      <j1 rule="para" parents="26233 12"/>
      <j2 rule="rewrite" parents="26233"/>
    </justification>
  </clause>

  <clause id="26432">
    <literal><![CDATA[
      g(g(x)) + g(g(x)) = g(g(x))
    ]]></literal>
    <justification jstring="[para(26374(a,1),94(a,1,1,2)),rewrite([6(12),26339(13)])].">
      <j1 rule="para" parents="26374 94"/>
      <j2 rule="rewrite" parents="6 26339"/>
    </justification>
  </clause>

  <clause id="26433">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer(Winker1a)
    ]]></attribute>
    <justification jstring="[resolve(26432,a,15,a)].">
      <j1 rule="resolve" parents="26432 15"/>
    </justification>
  </clause>

</proof>

<proof number="4" length="209" max_count="32">

<comments><![CDATA[
% Proof 4 at 117.16 (+ 0.29) seconds: Winker2b.
% Length of proof is 209.
% Level of proof is 44.
% Maximum clause weight is 32.
% Given clauses 932.
]]></comments>

  <clause id="2" 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>
    <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>
    <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)' != y'
    ]]></literal>
    <attribute><![CDATA[
      answer(Winker2b)
    ]]></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="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="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[
      (x + (y + (x + (y + (x + (y + g(x + y)))))))' = h(x + y)
    ]]></literal>
    <justification jstring="[para(7(a,1),12(a,1,1,2,2)),rewrite([19(7),19(6),7(5),19(8),19(7),19(6),19(5),7(4)])].">
      <j1 rule="para" parents="7 12"/>
      <j2 rule="rewrite" parents="19 19 7 19 19 19 19 7"/>
    </justification>
  </clause>

  <clause id="33">
    <literal><![CDATA[
      (h(x) + (x + (x + (x + g(x)))')')' = x
    ]]></literal>
    <justification jstring="[para(12(a,1),8(a,1,1,1))].">
      <j1 rule="para" parents="12 8"/>
    </justification>
  </clause>

  <clause id="36">
    <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="37">
    <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="38">
    <literal><![CDATA[
      (x + (g(x) + (x + x)'')')' = g(x)
    ]]></literal>
    <justification jstring="[para(29(a,1),8(a,1,1,1))].">
      <j1 rule="para" parents="29 8"/>
    </justification>
  </clause>

  <clause id="40">
    <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="41">
    <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="42">
    <literal><![CDATA[
      (g(x) + h(x))' = x
    ]]></literal>
    <justification jstring="[back_rewrite(33),rewrite([40(7),6(3)])].">
      <j1 rule="back_rewrite" parents="33"/>
      <j2 rule="rewrite" parents="40 6"/>
    </justification>
  </clause>

  <clause id="43">
    <literal><![CDATA[
      (x + (g(x) + h(x)')')' = g(x)
    ]]></literal>
    <justification jstring="[para(42(a,1),8(a,1,1,1))].">
      <j1 rule="para" parents="42 8"/>
    </justification>
  </clause>

  <clause id="44">
    <literal><![CDATA[
      ((x + y)' + (x + (g(y) + h(y)))')' = x
    ]]></literal>
    <justification jstring="[para(42(a,1),8(a,1,1,2,1,2)),rewrite([6(8)])].">
      <j1 rule="para" parents="42 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="45">
    <literal><![CDATA[
      (x + (g(x) + h(x)))' = g(g(x) + h(x))
    ]]></literal>
    <justification jstring="[para(42(a,1),10(a,1,1,2)),rewrite([6(4)])].">
      <j1 rule="para" parents="42 10"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="49">
    <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="50">
    <literal><![CDATA[
      (x + (g(x) + (x + x'')'))' = g(g(x) + (x + x'')')
    ]]></literal>
    <justification jstring="[para(27(a,1),10(a,1,1,2)),rewrite([6(7)])].">
      <j1 rule="para" parents="27 10"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="53">
    <literal><![CDATA[
      (g(g(x) + (x + x)') + (g(x) + (x' + (x + x)'))')' = g(x) + (x + x)'
    ]]></literal>
    <justification jstring="[para(29(a,1),27(a,1,1,2,1,2,1)),rewrite([6(11),19(11)])].">
      <j1 rule="para" parents="29 27"/>
      <j2 rule="rewrite" parents="6 19"/>
    </justification>
  </clause>

  <clause id="56">
    <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="58">
    <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="62">
    <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="63">
    <literal><![CDATA[
      (x + ((x + y')' + (x + y)'')')' = (x + y')'
    ]]></literal>
    <justification jstring="[para(8(a,1),20(a,1,1,1))].">
      <j1 rule="para" parents="8 20"/>
    </justification>
  </clause>

  <clause id="66">
    <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="79">
    <literal><![CDATA[
      ((x' + y)' + (y + x)')' = y
    ]]></literal>
    <justification jstring="[para(6(a,1),21(a,1,1))].">
      <j1 rule="para" parents="6 21"/>
    </justification>
  </clause>

  <clause id="84">
    <literal><![CDATA[
      ((x + ((y + z)' + (y + z')'))' + (y + x)')' = x
    ]]></literal>
    <justification jstring="[para(8(a,1),21(a,1,1,2,1,1))].">
      <j1 rule="para" parents="8 21"/>
    </justification>
  </clause>

  <clause id="85">
    <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="87">
    <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="88">
    <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="91">
    <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="93">
    <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="94">
    <literal><![CDATA[
      ((x + (g(y) + h(y)))' + (y + x)')' = x
    ]]></literal>
    <justification jstring="[para(42(a,1),21(a,1,1,2,1,1))].">
      <j1 rule="para" parents="42 21"/>
    </justification>
  </clause>

  <clause id="95">
    <literal><![CDATA[
      ((x + (g(y) + (y + y'')'))' + (y + x)')' = x
    ]]></literal>
    <justification jstring="[para(27(a,1),21(a,1,1,2,1,1))].">
      <j1 rule="para" parents="27 21"/>
    </justification>
  </clause>

  <clause id="108">
    <literal><![CDATA[
      ((x + (y + (y + (y + g(y)))'))' + (g(y) + x)')' = x
    ]]></literal>
    <justification jstring="[para(40(a,1),21(a,1,1,2,1,1))].">
      <j1 rule="para" parents="40 21"/>
    </justification>
  </clause>

  <clause id="109">
    <literal><![CDATA[
      (g(x') + (x + (x' + (x' + g(x')))')')' = (x' + (x' + g(x')))'
    ]]></literal>
    <justification jstring="[para(40(a,1),21(a,1,1,2)),rewrite([6(8),6(12)])].">
      <j1 rule="para" parents="40 21"/>
      <j2 rule="rewrite" parents="6 6"/>
    </justification>
  </clause>

  <clause id="113">
    <literal><![CDATA[
      (g(x) + (x + (g(x) + h(x)'))')' = x
    ]]></literal>
    <justification jstring="[para(43(a,1),8(a,1,1,2)),rewrite([6(8)])].">
      <j1 rule="para" parents="43 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="170">
    <literal><![CDATA[
      (h(x) + (x + (x + (x + g(x))'))')' = x + x
    ]]></literal>
    <justification jstring="[para(12(a,1),22(a,1,1,1))].">
      <j1 rule="para" parents="12 22"/>
    </justification>
  </clause>

  <clause id="172">
    <literal><![CDATA[
      ((x + (y + (z + u)))' + (x + (z + (y + u)'))')' = x + z
    ]]></literal>
    <justification jstring="[para(19(a,1),22(a,1,1,1,1,2))].">
      <j1 rule="para" parents="19 22"/>
    </justification>
  </clause>

  <clause id="173">
    <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="198">
    <literal><![CDATA[
      (g(g(x) + h(x)) + (x + x)')' = x
    ]]></literal>
    <justification jstring="[para(42(a,1),66(a,1,1,2,1,1)),rewrite([42(8),42(12)])].">
      <j1 rule="para" parents="42 66"/>
      <j2 rule="rewrite" parents="42 42"/>
    </justification>
  </clause>

  <clause id="227">
    <literal><![CDATA[
      ((x' + (y + z))' + (y + (z + x))')' = y + z
    ]]></literal>
    <justification jstring="[para(7(a,1),79(a,1,1,2,1))].">
      <j1 rule="para" parents="7 79"/>
    </justification>
  </clause>

  <clause id="254">
    <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="265">
    <literal><![CDATA[
      ((g(x + y) + z)' + (x + (y + ((x + y)' + z)))')' = z
    ]]></literal>
    <justification jstring="[para(26(a,1),56(a,1,1,2,1,1)),rewrite([7(5),7(4),6(11)])].">
      <j1 rule="para" parents="26 56"/>
      <j2 rule="rewrite" parents="7 7 6"/>
    </justification>
  </clause>

  <clause id="278">
    <literal><![CDATA[
      (x + ((x + (g(y) + (y + y)'))' + (x + y)'')')' = (x + (g(y) + (y + y)'))'
    ]]></literal>
    <justification jstring="[para(29(a,1),23(a,1,1,2,1,2,1,1,2))].">
      <j1 rule="para" parents="29 23"/>
    </justification>
  </clause>

  <clause id="286">
    <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="301">
    <literal><![CDATA[
      (((x + y)' + (x + y)')' + g(x + ((x + y)' + (x + y')'')'))' = (x + y)'
    ]]></literal>
    <justification jstring="[para(23(a,1),66(a,1,1,2,1,1)),rewrite([23(22),6(17),23(28)])].">
      <j1 rule="para" parents="23 66"/>
      <j2 rule="rewrite" parents="23 6 23"/>
    </justification>
  </clause>

  <clause id="310">
    <literal><![CDATA[
      (x + ((x + y)' + (x + ((x + y)' + (x + y')'')'')'')')' = (x + y)'
    ]]></literal>
    <justification jstring="[para(23(a,1),23(a,1,1,2,1,1)),rewrite([23(28)])].">
      <j1 rule="para" parents="23 23"/>
      <j2 rule="rewrite" parents="23"/>
    </justification>
  </clause>

  <clause id="324">
    <literal><![CDATA[
      (g(x + x') + (x + (g(x) + x''))')' = x + g(x)
    ]]></literal>
    <justification jstring="[para(31(a,1),22(a,1,1,1))].">
      <j1 rule="para" parents="31 22"/>
    </justification>
  </clause>

  <clause id="335">
    <literal><![CDATA[
      (x + (g(g(x) + h(x)) + (x + x)'))' = g(g(g(x) + h(x)) + (x + x)')
    ]]></literal>
    <justification jstring="[para(198(a,1),10(a,1,1,2)),rewrite([6(8)])].">
      <j1 rule="para" parents="198 10"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="353">
    <literal><![CDATA[
      (g(x + y) + (x' + (y + (y + x)'))')' = y + (y + x)'
    ]]></literal>
    <justification jstring="[para(254(a,1),20(a,1,1,1)),rewrite([6(7)])].">
      <j1 rule="para" parents="254 20"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="369">
    <literal><![CDATA[
      (g(x) + (x + (g(x) + (x + x)''))')' = x
    ]]></literal>
    <justification jstring="[para(38(a,1),8(a,1,1,2)),rewrite([6(9)])].">
      <j1 rule="para" parents="38 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="507">
    <literal><![CDATA[
      (g(x) + (x' + ((x + y)' + (x + y')'))')' = x'
    ]]></literal>
    <justification jstring="[para(8(a,1),88(a,1,1,1,1)),rewrite([8(14),6(9),8(19)])].">
      <j1 rule="para" parents="8 88"/>
      <j2 rule="rewrite" parents="8 6 8"/>
    </justification>
  </clause>

  <clause id="511">
    <literal><![CDATA[
      (g(x) + (g(x) + (x' + (x + x)'))')' = x'
    ]]></literal>
    <justification jstring="[para(29(a,1),88(a,1,1,1,1)),rewrite([29(10),6(7),19(7),29(15)])].">
      <j1 rule="para" parents="29 88"/>
      <j2 rule="rewrite" parents="29 6 19 29"/>
    </justification>
  </clause>

  <clause id="512">
    <literal><![CDATA[
      (g(x) + (g(x) + (h(x) + x'))')' = x'
    ]]></literal>
    <justification jstring="[para(42(a,1),88(a,1,1,1,1)),rewrite([42(8),7(6),42(13)])].">
      <j1 rule="para" parents="42 88"/>
      <j2 rule="rewrite" parents="42 7 42"/>
    </justification>
  </clause>

  <clause id="575">
    <literal><![CDATA[
      (g(x) + (x + (g(x) + (x + x'')''))')' = x
    ]]></literal>
    <justification jstring="[para(27(a,1),25(a,1,1,2,1,2,2)),rewrite([6(8),19(9),27(19)])].">
      <j1 rule="para" parents="27 25"/>
      <j2 rule="rewrite" parents="6 19 27"/>
    </justification>
  </clause>

  <clause id="679">
    <literal><![CDATA[
      (x + (x + (g(y) + (h(y) + (x + y)')))')' = (x + y)'
    ]]></literal>
    <justification jstring="[para(44(a,1),8(a,1,1,2)),rewrite([6(7),7(7),7(6),6(9)])].">
      <j1 rule="para" parents="44 8"/>
      <j2 rule="rewrite" parents="6 7 7 6"/>
    </justification>
  </clause>

  <clause id="833">
    <literal><![CDATA[
      (h(g(x)) + (x + (g(x) + (g(x) + (g(g(x)) + x'))))')' = g(x) + (g(x) + g(g(x)))
    ]]></literal>
    <justification jstring="[para(12(a,1),87(a,1,1,2)),rewrite([19(9),7(8),7(7),6(13)])].">
      <j1 rule="para" parents="12 87"/>
      <j2 rule="rewrite" parents="19 7 7 6"/>
    </justification>
  </clause>

  <clause id="963">
    <literal><![CDATA[
      (x + (y + (x + (y + (x + (y + g(y + x)))))))' = h(x + y)
    ]]></literal>
    <justification jstring="[para(6(a,1),32(a,1,1,2,2,2,2,2,2,1))].">
      <j1 rule="para" parents="6 32"/>
    </justification>
  </clause>

  <clause id="1345">
    <literal><![CDATA[
      ((x + (y + z))' + (y + (z + x)')')' = y
    ]]></literal>
    <justification jstring="[para(6(a,1),36(a,1,1,2,1,2,1))].">
      <j1 rule="para" parents="6 36"/>
    </justification>
  </clause>

  <clause id="1379">
    <literal><![CDATA[
      ((x + g(y + z))' + (y + (x + (z + (z + y)')))')' = x
    ]]></literal>
    <justification jstring="[para(254(a,1),36(a,1,1,2,1,2)),rewrite([6(11)])].">
      <j1 rule="para" parents="254 36"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="1561">
    <literal><![CDATA[
      (g(x + y) + (y + (x + (y + x)))')' = y + x
    ]]></literal>
    <justification jstring="[para(6(a,1),37(a,1,1,1,1))].">
      <j1 rule="para" parents="6 37"/>
    </justification>
  </clause>

  <clause id="1567">
    <literal><![CDATA[
      (g(x + y) + (x + (x + (y + y)))')' = x + y
    ]]></literal>
    <justification jstring="[para(19(a,1),37(a,1,1,2,1,2))].">
      <j1 rule="para" parents="19 37"/>
    </justification>
  </clause>

  <clause id="1653">
    <literal><![CDATA[
      (h(x) + g(g(x) + (x + x)'))' = x + g(x)
    ]]></literal>
    <justification jstring="[para(12(a,1),58(a,1,1,1)),rewrite([7(6),41(7)])].">
      <j1 rule="para" parents="12 58"/>
      <j2 rule="rewrite" parents="7 41"/>
    </justification>
  </clause>

  <clause id="1746">
    <literal><![CDATA[
      ((x + (y + z))' + ((z + x)' + y)')' = y
    ]]></literal>
    <justification jstring="[para(6(a,1),91(a,1,1,2,1,1,1))].">
      <j1 rule="para" parents="6 91"/>
    </justification>
  </clause>

  <clause id="2017">
    <literal><![CDATA[
      (g(x) + (x + (g(x) + (x + (g(x) + (x + x)''))''))')' = x
    ]]></literal>
    <justification jstring="[para(369(a,1),25(a,1,1,2,1,2,2)),rewrite([6(11),19(12),369(25)])].">
      <j1 rule="para" parents="369 25"/>
      <j2 rule="rewrite" parents="6 19 369"/>
    </justification>
  </clause>

  <clause id="2198">
    <literal><![CDATA[
      ((x' + (y + x))' + (y + g(x))')' = y
    ]]></literal>
    <justification jstring="[para(10(a,1),1345(a,1,1,2,1,2))].">
      <j1 rule="para" parents="10 1345"/>
    </justification>
  </clause>

  <clause id="2203">
    <literal><![CDATA[
      ((x + y)' + (h(y) + (x + g(y)))')' = x
    ]]></literal>
    <justification jstring="[para(42(a,1),1345(a,1,1,2,1,2)),rewrite([6(8)])].">
      <j1 rule="para" parents="42 1345"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="2294">
    <literal><![CDATA[
      ((x + g(y))' + (y' + (x + y))')' = x
    ]]></literal>
    <justification jstring="[para(6(a,1),2198(a,1,1))].">
      <j1 rule="para" parents="6 2198"/>
    </justification>
  </clause>

  <clause id="2348">
    <literal><![CDATA[
      ((x + (y + z))' + (h(z) + (x + (y + g(z))))')' = x + y
    ]]></literal>
    <justification jstring="[para(7(a,1),2203(a,1,1,1,1)),rewrite([7(7)])].">
      <j1 rule="para" parents="7 2203"/>
      <j2 rule="rewrite" parents="7"/>
    </justification>
  </clause>

  <clause id="2453">
    <literal><![CDATA[
      ((x + g(y + z))' + (y + ((y + z)' + (x + z)))')' = x
    ]]></literal>
    <justification jstring="[para(19(a,1),2294(a,1,1,2,1,2)),rewrite([19(9)])].">
      <j1 rule="para" parents="19 2294"/>
      <j2 rule="rewrite" parents="19"/>
    </justification>
  </clause>

  <clause id="2610">
    <literal><![CDATA[
      (x + (g(x) + (x + (g(x) + (h(x) + (x + x)')))'))' = h(x)
    ]]></literal>
    <justification jstring="[para(1653(a,1),28(a,1,1,1)),rewrite([29(12),6(8),19(9),19(8),7(11)])].">
      <j1 rule="para" parents="1653 28"/>
      <j2 rule="rewrite" parents="29 6 19 19 7"/>
    </justification>
  </clause>

  <clause id="2765">
    <literal><![CDATA[
      ((x + (g(x) + y))' + (g(g(x) + (x + x)') + (y + h(x)))')' = y
    ]]></literal>
    <justification jstring="[para(1653(a,1),1746(a,1,1,2,1,1)),rewrite([7(12),6(14)])].">
      <j1 rule="para" parents="1653 1746"/>
      <j2 rule="rewrite" parents="7 6"/>
    </justification>
  </clause>

  <clause id="2892">
    <literal><![CDATA[
      ((x + y)' + (y + (y + (x' + (x + y)')))')' = y
    ]]></literal>
    <justification jstring="[para(62(a,1),8(a,1,1,2)),rewrite([6(10)])].">
      <j1 rule="para" parents="62 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="2895">
    <literal><![CDATA[
      (x + (x + (h(y) + (y + (y + (y + (g(y) + x))))'))')' = (y + (y + (y + (g(y) + x))))'
    ]]></literal>
    <justification jstring="[para(12(a,1),62(a,1,1,2,1,2,1)),rewrite([7(6),7(5),7(4),7(17),7(16),7(15)])].">
      <j1 rule="para" parents="12 62"/>
      <j2 rule="rewrite" parents="7 7 7 7 7 7"/>
    </justification>
  </clause>

  <clause id="3092">
    <literal><![CDATA[
      (g(x + x') + (g(x) + (g(x) + (x' + (x + x)')))')' = g(x) + x'
    ]]></literal>
    <justification jstring="[para(31(a,1),93(a,1,1,2)),rewrite([19(8),7(7),6(13)])].">
      <j1 rule="para" parents="31 93"/>
      <j2 rule="rewrite" parents="19 7 6"/>
    </justification>
  </clause>

  <clause id="3097">
    <literal><![CDATA[
      (g(x) + (g(x) + ((x + x)' + (x + (g(x) + x''))'))')' = (x + (g(x) + x''))'
    ]]></literal>
    <justification jstring="[para(49(a,1),93(a,1,1,2)),rewrite([6(11),7(11),6(14)])].">
      <j1 rule="para" parents="49 93"/>
      <j2 rule="rewrite" parents="6 7 6"/>
    </justification>
  </clause>

  <clause id="3222">
    <literal><![CDATA[
      (x + (x + (x + (x + (h(x) + (x + g(x))')))'))' = h(x)
    ]]></literal>
    <justification jstring="[para(170(a,1),8(a,1,1,2)),rewrite([19(7),19(6),6(10),7(10)])].">
      <j1 rule="para" parents="170 8"/>
      <j2 rule="rewrite" parents="19 19 6 7"/>
    </justification>
  </clause>

  <clause id="4308">
    <literal><![CDATA[
      (g(x) + (x' + (g(x) + (g(x) + (x' + (x + x)')))'')')' = x'
    ]]></literal>
    <justification jstring="[para(511(a,1),63(a,1,1,2,1,1)),rewrite([511(26)])].">
      <j1 rule="para" parents="511 63"/>
      <j2 rule="rewrite" parents="511"/>
    </justification>
  </clause>

  <clause id="5352">
    <literal><![CDATA[
      (g(x) + (g(x) + (g(x) + (h(x) + (x' + x'))))')' = x'
    ]]></literal>
    <justification jstring="[para(512(a,1),85(a,1,1,2,1,2,2)),rewrite([6(9),19(9),19(8),512(22)])].">
      <j1 rule="para" parents="512 85"/>
      <j2 rule="rewrite" parents="6 19 19 512"/>
    </justification>
  </clause>

  <clause id="5499">
    <literal><![CDATA[
      (g(x + y) + h(y + x))' = y + x
    ]]></literal>
    <justification jstring="[para(1561(a,1),85(a,1,1,2,1,2,2)),rewrite([6(9),19(9),19(8),19(7),6(6),19(10),19(9),19(8),19(7),19(6),6(5),963(11),1561(14)])].">
      <j1 rule="para" parents="1561 85"/>
      <j2 rule="rewrite" parents="6 19 19 19 6 19 19 19 19 19 6 963 1561"/>
    </justification>
  </clause>

  <clause id="5522">
    <literal><![CDATA[
      (g(x + (y + z)) + h(z + (x + y)))' = z + (x + y)
    ]]></literal>
    <justification jstring="[para(7(a,1),5499(a,1,1,1,1))].">
      <j1 rule="para" parents="7 5499"/>
    </justification>
  </clause>

  <clause id="5523">
    <literal><![CDATA[
      (g(x + (y + z)) + h(y + (z + x)))' = y + (z + x)
    ]]></literal>
    <justification jstring="[para(7(a,1),5499(a,1,1,2,1)),rewrite([7(10)])].">
      <j1 rule="para" parents="7 5499"/>
      <j2 rule="rewrite" parents="7"/>
    </justification>
  </clause>

  <clause id="7561">
    <literal><![CDATA[
      ((x + (y + z'))' + (y + (x + z))')' = x + y
    ]]></literal>
    <justification jstring="[para(6(a,1),173(a,1,1))].">
      <j1 rule="para" parents="6 173"/>
    </justification>
  </clause>

  <clause id="9115">
    <literal><![CDATA[
      ((x + (y + z))' + (y + (z + (g(g(x) + h(x)) + (x + x)')))')' = y + z
    ]]></literal>
    <justification jstring="[para(198(a,1),227(a,1,1,1,1,1))].">
      <j1 rule="para" parents="198 227"/>
    </justification>
  </clause>

  <clause id="16072">
    <literal><![CDATA[
      (x + (x + ((x + x)' + (x + (x + g(x)))'))')' = (x + x)'
    ]]></literal>
    <justification jstring="[para(29(a,1),108(a,1,1,2)),rewrite([19(8),6(10)])].">
      <j1 rule="para" parents="29 108"/>
      <j2 rule="rewrite" parents="19 6"/>
    </justification>
  </clause>

  <clause id="16519">
    <literal><![CDATA[
      (g(x + (y + z)) + h(z + (y + x)))' = z + (x + y)
    ]]></literal>
    <justification jstring="[para(6(a,1),5522(a,1,1,2,1,2))].">
      <j1 rule="para" parents="6 5522"/>
    </justification>
  </clause>

  <clause id="21312">
    <literal><![CDATA[
      (h(x) + (x + (x + (x + (x + (h(x) + (x + g(x))')))')')')' = x
    ]]></literal>
    <justification jstring="[para(3222(a,1),8(a,1,1,1))].">
      <j1 rule="para" parents="3222 8"/>
    </justification>
  </clause>

  <clause id="22398">
    <literal><![CDATA[
      (x + h(x))' = g(x)
    ]]></literal>
    <justification jstring="[para(2610(a,1),36(a,1,1,1)),rewrite([679(12),29(6),6(2)])].">
      <j1 rule="para" parents="2610 36"/>
      <j2 rule="rewrite" parents="679 29 6"/>
    </justification>
  </clause>

  <clause id="22418">
    <literal><![CDATA[
      (g(x) + (x + h(x)')')' = x
    ]]></literal>
    <justification jstring="[para(22398(a,1),8(a,1,1,1))].">
      <j1 rule="para" parents="22398 8"/>
    </justification>
  </clause>

  <clause id="22419">
    <literal><![CDATA[
      ((x + g(y))' + (x + (y + h(y)))')' = x
    ]]></literal>
    <justification jstring="[para(22398(a,1),8(a,1,1,2,1,2)),rewrite([6(8)])].">
      <j1 rule="para" parents="22398 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="22420">
    <literal><![CDATA[
      g(g(x) + h(x)) = g(x + h(x))
    ]]></literal>
    <justification jstring="[para(22398(a,1),10(a,1,1,2)),rewrite([6(4),19(4),45(5)])].">
      <j1 rule="para" parents="22398 10"/>
      <j2 rule="rewrite" parents="6 19 45"/>
    </justification>
  </clause>

  <clause id="22424">
    <literal><![CDATA[
      (g(x') + (x + h(x'))')' = h(x')
    ]]></literal>
    <justification jstring="[para(22398(a,1),21(a,1,1,2)),rewrite([6(3),6(7)])].">
      <j1 rule="para" parents="22398 21"/>
      <j2 rule="rewrite" parents="6 6"/>
    </justification>
  </clause>

  <clause id="22430">
    <literal><![CDATA[
      (x + (g(x) + (x + h(x)')'')')' = g(x)
    ]]></literal>
    <justification jstring="[para(22398(a,1),23(a,1,1,2,1,1)),rewrite([22398(13)])].">
      <j1 rule="para" parents="22398 23"/>
      <j2 rule="rewrite" parents="22398"/>
    </justification>
  </clause>

  <clause id="22439">
    <literal><![CDATA[
      (x + (x + (g(x) + h(x)'))')' = g(x)
    ]]></literal>
    <justification jstring="[para(22398(a,1),25(a,1,1,2,1,2,2)),rewrite([6(4),22398(11)])].">
      <j1 rule="para" parents="22398 25"/>
      <j2 rule="rewrite" parents="6 22398"/>
    </justification>
  </clause>

  <clause id="22447">
    <literal><![CDATA[
      (g(x) + (g(x) + (h(x) + h(x)))')' = h(x)
    ]]></literal>
    <justification jstring="[para(22398(a,1),94(a,1,1,2)),rewrite([19(5),6(8)])].">
      <j1 rule="para" parents="22398 94"/>
      <j2 rule="rewrite" parents="19 6"/>
    </justification>
  </clause>

  <clause id="22493">
    <literal><![CDATA[
      (x + (x + (y + (h(y) + (x + g(y))')))')' = (x + g(y))'
    ]]></literal>
    <justification jstring="[para(22398(a,1),85(a,1,1,2,1,2,2,1,2)),rewrite([7(6),22398(13)])].">
      <j1 rule="para" parents="22398 85"/>
      <j2 rule="rewrite" parents="7 22398"/>
    </justification>
  </clause>

  <clause id="22532">
    <literal><![CDATA[
      (g(x) + (h(x) + ((x + y)' + (x + y')'))')' = h(x)
    ]]></literal>
    <justification jstring="[para(22398(a,1),84(a,1,1,2)),rewrite([6(11)])].">
      <j1 rule="para" parents="22398 84"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="22777">
    <literal><![CDATA[
      (x + (g(x) + (x + (g(x) + (x + h(x)')'')'')'')')' = g(x)
    ]]></literal>
    <justification jstring="[para(22398(a,1),310(a,1,1,2,1,1)),rewrite([22398(4),22398(20)])].">
      <j1 rule="para" parents="22398 310"/>
      <j2 rule="rewrite" parents="22398 22398"/>
    </justification>
  </clause>

  <clause id="22949">
    <literal><![CDATA[
      ((x + (y + z))' + (y + (z + (g(x + h(x)) + (x + x)')))')' = y + z
    ]]></literal>
    <justification jstring="[back_rewrite(9115),rewrite([22420(7)])].">
      <j1 rule="back_rewrite" parents="9115"/>
      <j2 rule="rewrite" parents="22420"/>
    </justification>
  </clause>

  <clause id="23014">
    <literal><![CDATA[
      (x + (g(x + h(x)) + (x + x)'))' = g(g(x + h(x)) + (x + x)')
    ]]></literal>
    <justification jstring="[back_rewrite(335),rewrite([22420(4),22420(12)])].">
      <j1 rule="back_rewrite" parents="335"/>
      <j2 rule="rewrite" parents="22420 22420"/>
    </justification>
  </clause>

  <clause id="23018">
    <literal><![CDATA[
      (x + (g(x) + h(x)))' = g(x + h(x))
    ]]></literal>
    <justification jstring="[back_rewrite(45),rewrite([22420(9)])].">
      <j1 rule="back_rewrite" parents="45"/>
      <j2 rule="rewrite" parents="22420"/>
    </justification>
  </clause>

  <clause id="23021">
    <literal><![CDATA[
      (h(x) + (x + (x + g(x))')')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(21312),rewrite([22493(11)])].">
      <j1 rule="back_rewrite" parents="21312"/>
      <j2 rule="rewrite" parents="22493"/>
    </justification>
  </clause>

  <clause id="23203">
    <literal><![CDATA[
      ((x + x)' + g(g(x) + (x + (g(x) + (x + h(x)')'')'')'))' = x
    ]]></literal>
    <justification jstring="[para(22418(a,1),301(a,1,1,1,1,1)),rewrite([22418(7),22418(10),22418(25)])].">
      <j1 rule="para" parents="22418 301"/>
      <j2 rule="rewrite" parents="22418 22418 22418"/>
    </justification>
  </clause>

  <clause id="23594">
    <literal><![CDATA[
      (x + (x + g(x)))' = h(x)
    ]]></literal>
    <justification jstring="[para(23021(a,1),109(a,1,1,1,1)),rewrite([23021(16),23021(16),23021(16),6(13),19(13),22532(16),23021(9),23021(9),23021(9)]),flip(a)].">
      <j1 rule="para" parents="23021 109"/>
      <j2 rule="rewrite" parents="23021 23021 23021 6 19 22532 23021 23021 23021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23739">
    <literal><![CDATA[
      (x + (x + (h(x) + (x + x)'))')' = (x + x)'
    ]]></literal>
    <justification jstring="[back_rewrite(16072),rewrite([23594(6),6(4)])].">
      <j1 rule="back_rewrite" parents="16072"/>
      <j2 rule="rewrite" parents="23594 6"/>
    </justification>
  </clause>

  <clause id="23847">
    <literal><![CDATA[
      (x + (y + (x + (y + g(x + y)))))' = h(x + y)
    ]]></literal>
    <justification jstring="[para(7(a,1),23594(a,1,1,2)),rewrite([19(6),19(5),7(4)])].">
      <j1 rule="para" parents="7 23594"/>
      <j2 rule="rewrite" parents="19 19 7"/>
    </justification>
  </clause>

  <clause id="23848">
    <literal><![CDATA[
      ((x + h(y))' + (x + (y + (y + g(y))))')' = x
    ]]></literal>
    <justification jstring="[para(23594(a,1),8(a,1,1,2,1,2)),rewrite([6(9)])].">
      <j1 rule="para" parents="23594 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="23849">
    <literal><![CDATA[
      (x + (x + (g(x) + h(x))))' = g(x + (x + g(x)))
    ]]></literal>
    <justification jstring="[para(23594(a,1),10(a,1,1,2)),rewrite([6(5),19(5),19(4),6(3)])].">
      <j1 rule="para" parents="23594 10"/>
      <j2 rule="rewrite" parents="6 19 19 6"/>
    </justification>
  </clause>

  <clause id="23868">
    <literal><![CDATA[
      (h(g(x)) + (x + (g(x) + (g(g(x)) + x')))')' = g(x) + g(g(x))
    ]]></literal>
    <justification jstring="[para(23594(a,1),87(a,1,1,2)),rewrite([19(7),7(6),6(11)])].">
      <j1 rule="para" parents="23594 87"/>
      <j2 rule="rewrite" parents="19 7 6"/>
    </justification>
  </clause>

  <clause id="23892">
    <literal><![CDATA[
      (h(x) + (x + (g(x) + (g(x) + (x + x)')))')' = x + g(x)
    ]]></literal>
    <justification jstring="[para(23594(a,1),93(a,1,1,2)),rewrite([19(7),7(6),19(7),6(10)])].">
      <j1 rule="para" parents="23594 93"/>
      <j2 rule="rewrite" parents="19 7 19 6"/>
    </justification>
  </clause>

  <clause id="23946">
    <literal><![CDATA[
      (h(x) + (x + (g(x) + (g(x) + (x + x'')')))')' = x + g(x)
    ]]></literal>
    <justification jstring="[para(23594(a,1),95(a,1,1,2)),rewrite([19(9),7(8),19(9),6(12)])].">
      <j1 rule="para" parents="23594 95"/>
      <j2 rule="rewrite" parents="19 7 19 6"/>
    </justification>
  </clause>

  <clause id="24109">
    <literal><![CDATA[
      (g(x + (x + (x + g(x)))) + (x + (h(x) + h(x)))')' = x + h(x)
    ]]></literal>
    <justification jstring="[para(12(a,1),353(a,1,1,2,1,2,2)),rewrite([6(4),23594(9),19(9),12(17)])].">
      <j1 rule="para" parents="12 353"/>
      <j2 rule="rewrite" parents="6 23594 19 12"/>
    </justification>
  </clause>

  <clause id="24379">
    <literal><![CDATA[
      (g(x) + (g(x) + (h(x) + (x + (g(x) + h(x)'))'))')' = h(x)
    ]]></literal>
    <justification jstring="[para(113(a,1),22424(a,1,1,1,1)),rewrite([113(18),6(11),19(11),113(23)])].">
      <j1 rule="para" parents="113 22424"/>
      <j2 rule="rewrite" parents="113 6 19 113"/>
    </justification>
  </clause>

  <clause id="24475">
    <literal><![CDATA[
      (g(x) + (g(x) + (h(x) + (x + (g(x) + (x + x'')''))'))')' = h(x)
    ]]></literal>
    <justification jstring="[para(575(a,1),22424(a,1,1,1,1)),rewrite([575(24),6(14),19(14),575(29)])].">
      <j1 rule="para" parents="575 22424"/>
      <j2 rule="rewrite" parents="575 6 19 575"/>
    </justification>
  </clause>

  <clause id="24552">
    <literal><![CDATA[
      (x + (g(x) + h(x)'))' = h(x)
    ]]></literal>
    <justification jstring="[para(22439(a,1),94(a,1,1,2)),rewrite([6(10),7(10),6(13),24379(14)]),flip(a)].">
      <j1 rule="para" parents="22439 94"/>
      <j2 rule="rewrite" parents="6 7 6 24379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25108">
    <literal><![CDATA[
      (g(x) + (g(x) + (x' + (x + (g(x) + (x + h(x)')''))'))')' = x'
    ]]></literal>
    <justification jstring="[para(22430(a,1),507(a,1,1,2,1,2,2)),rewrite([6(13),19(14)])].">
      <j1 rule="para" parents="22430 507"/>
      <j2 rule="rewrite" parents="6 19"/>
    </justification>
  </clause>

  <clause id="25355">
    <literal><![CDATA[
      ((x + (y + y)')' + (x + (y + (y + (h(y) + (y + y)'))'))')' = x
    ]]></literal>
    <justification jstring="[para(23739(a,1),8(a,1,1,2,1,2)),rewrite([6(14)])].">
      <j1 rule="para" parents="23739 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="25450">
    <literal><![CDATA[
      (x + (x + (x + (g(x) + g(x))))')' = g(x)
    ]]></literal>
    <justification jstring="[para(42(a,1),23848(a,1,1,1)),rewrite([19(5),19(4)])].">
      <j1 rule="para" parents="42 23848"/>
      <j2 rule="rewrite" parents="19 19"/>
    </justification>
  </clause>

  <clause id="25456">
    <literal><![CDATA[
      (g(x) + (x + (x + (x + (g(x) + g(x)))))')' = x
    ]]></literal>
    <justification jstring="[para(25450(a,1),8(a,1,1,2)),rewrite([6(9)])].">
      <j1 rule="para" parents="25450 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="25493">
    <literal><![CDATA[
      (g(x + (x + g(x))) + (x + (x + x))')' = x + x
    ]]></literal>
    <justification jstring="[para(23849(a,1),22(a,1,1,1)),rewrite([42(8)])].">
      <j1 rule="para" parents="23849 22"/>
      <j2 rule="rewrite" parents="42"/>
    </justification>
  </clause>

  <clause id="25496">
    <literal><![CDATA[
      (g(x + (x + g(x))) + (g(x) + (h(x) + (x + x)'))')' = g(x) + h(x)
    ]]></literal>
    <justification jstring="[para(23849(a,1),58(a,1,1,1)),rewrite([7(10)])].">
      <j1 rule="para" parents="23849 58"/>
      <j2 rule="rewrite" parents="7"/>
    </justification>
  </clause>

  <clause id="25936">
    <literal><![CDATA[
      (x + (x + (x + (g(x) + g(x)))))' = h(x)
    ]]></literal>
    <justification jstring="[para(25456(a,1),22424(a,1,1,1,1)),rewrite([25456(20),6(12),19(12),2895(15),25456(17)])].">
      <j1 rule="para" parents="25456 22424"/>
      <j2 rule="rewrite" parents="25456 6 19 2895 25456"/>
    </justification>
  </clause>

  <clause id="25950">
    <literal><![CDATA[
      x + (g(x) + g(x)) = x + g(x)
    ]]></literal>
    <justification jstring="[para(25936(a,1),58(a,1,1,1)),rewrite([7(8),7(7),23892(11)]),flip(a)].">
      <j1 rule="para" parents="25936 58"/>
      <j2 rule="rewrite" parents="7 7 23892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25979">
    <literal><![CDATA[
      x + (g(x) + (g(x) + y)) = x + (g(x) + y)
    ]]></literal>
    <justification jstring="[para(25950(a,1),7(a,1,1)),rewrite([7(3),7(7)]),flip(a)].">
      <j1 rule="para" parents="25950 7"/>
      <j2 rule="rewrite" parents="7 7"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25996">
    <literal><![CDATA[
      (h(x) + g(x + g(x)))' = x + g(x)
    ]]></literal>
    <justification jstring="[para(25950(a,1),37(a,1,1,1,1)),rewrite([25950(10),6(9),19(9),6(8),19(8),25950(8),19(7),25950(7),23594(7),6(5),25950(10)])].">
      <j1 rule="para" parents="25950 37"/>
      <j2 rule="rewrite" parents="25950 6 19 6 19 25950 19 25950 23594 6 25950"/>
    </justification>
  </clause>

  <clause id="26028">
    <literal><![CDATA[
      g(x) + (g(x) + (y + x)) = x + (g(x) + y)
    ]]></literal>
    <justification jstring="[para(25950(a,1),16519(a,1,1,1,1,2)),rewrite([19(9),7(8),25979(9),5523(10),7(8)]),flip(a)].">
      <j1 rule="para" parents="25950 16519"/>
      <j2 rule="rewrite" parents="19 7 25979 5523 7"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26034">
    <literal><![CDATA[
      ((x + (y + g(y)))' + (x + (g(y) + (y + g(y))'))')' = x + g(y)
    ]]></literal>
    <justification jstring="[para(25950(a,1),172(a,1,1,1,1,2))].">
      <j1 rule="para" parents="25950 172"/>
    </justification>
  </clause>

  <clause id="26125">
    <literal><![CDATA[
      (h(x) + g(g(x) + (x + x'')'))' = x + g(x)
    ]]></literal>
    <justification jstring="[back_rewrite(23946),rewrite([25979(10),50(9)])].">
      <j1 rule="back_rewrite" parents="23946"/>
      <j2 rule="rewrite" parents="25979 50"/>
    </justification>
  </clause>

  <clause id="26233">
    <literal><![CDATA[
      g(x) + (g(x) + g(g(x))) = g(x) + g(g(x))
    ]]></literal>
    <justification jstring="[back_rewrite(833),rewrite([25979(11),23868(12)]),flip(a)].">
      <j1 rule="back_rewrite" parents="833"/>
      <j2 rule="rewrite" parents="25979 23868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26288">
    <literal><![CDATA[
      x + (g(x) + (y + (g(x) + z))) = x + (g(x) + (y + z))
    ]]></literal>
    <justification jstring="[para(19(a,1),25979(a,1,2,2))].">
      <j1 rule="para" parents="19 25979"/>
    </justification>
  </clause>

  <clause id="26346">
    <literal><![CDATA[
      g(x) + (g(x) + (y + (x + z))) = x + (g(x) + (y + z))
    ]]></literal>
    <justification jstring="[para(26028(a,1),7(a,1,1)),rewrite([7(4),7(3),7(9),7(8)]),flip(a)].">
      <j1 rule="para" parents="26028 7"/>
      <j2 rule="rewrite" parents="7 7 7 7"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26370">
    <literal><![CDATA[
      (x + (g(x) + (y + (y + (x + g(x + (g(x) + y)))))))' = h(x + (g(x) + y))
    ]]></literal>
    <justification jstring="[para(26028(a,1),23847(a,1,1,2,2,2,2,1)),rewrite([6(13),19(13),19(12),6(11),26346(14),19(13),19(12),19(11),6(10),19(10),19(9),6(8),26288(13),19(12),25979(12),26028(16)])].">
      <j1 rule="para" parents="26028 23847"/>
      <j2 rule="rewrite" parents="6 19 19 6 26346 19 19 19 6 19 19 6 26288 19 25979 26028"/>
    </justification>
  </clause>

  <clause id="26371">
    <literal><![CDATA[
      g(x) + (g(x) + (g(g(x)) + y)) = g(x) + (g(g(x)) + y)
    ]]></literal>
    <justification jstring="[para(26233(a,1),7(a,1,1)),rewrite([7(5),7(11)]),flip(a)].">
      <j1 rule="para" parents="26233 7"/>
      <j2 rule="rewrite" parents="7 7"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26374">
    <literal><![CDATA[
      (g(x) + g(g(x)))' = h(g(x))
    ]]></literal>
    <justification jstring="[para(26233(a,1),12(a,1,1,2)),rewrite([26233(6)])].">
      <j1 rule="para" parents="26233 12"/>
      <j2 rule="rewrite" parents="26233"/>
    </justification>
  </clause>

  <clause id="26377">
    <literal><![CDATA[
      g(g(x) + h(g(x))) = g(g(x) + g(g(x)))
    ]]></literal>
    <justification jstring="[para(26233(a,1),26(a,1,1,2,2,1)),rewrite([26374(10),6(8),19(8),6(7),26371(9),23018(8),26233(11)])].">
      <j1 rule="para" parents="26233 26"/>
      <j2 rule="rewrite" parents="26374 6 19 6 26371 23018 26233"/>
    </justification>
  </clause>

  <clause id="26394">
    <literal><![CDATA[
      ((g(x) + (y + h(g(x))))' + (y + (g(x) + g(g(x))))')' = g(x) + y
    ]]></literal>
    <justification jstring="[para(26233(a,1),7561(a,1,1,2,1,2)),rewrite([26374(6)])].">
      <j1 rule="para" parents="26233 7561"/>
      <j2 rule="rewrite" parents="26374"/>
    </justification>
  </clause>

  <clause id="26397">
    <literal><![CDATA[
      (h(g(x)) + (g(x) + (g(g(x)) + (h(g(x)) + g(x)')))')' = g(x) + g(g(x))
    ]]></literal>
    <justification jstring="[para(26233(a,1),2892(a,1,1,1,1)),rewrite([26374(5),26233(18),26374(17),6(15),19(16),7(15),19(16),19(15),19(17),19(16),19(15),7(14),19(15),19(14),19(16),25979(16),26371(14)])].">
      <j1 rule="para" parents="26233 2892"/>
      <j2 rule="rewrite" parents="26374 26233 26374 6 19 7 19 19 19 19 19 7 19 19 19 25979 26371"/>
    </justification>
  </clause>

  <clause id="26406">
    <literal><![CDATA[
      ((g(x) + (g(g(x)) + (h(g(x)) + y)))' + (g(g(x) + g(g(x))) + y)')' = y
    ]]></literal>
    <justification jstring="[para(26233(a,1),265(a,1,1,1,1,1,1)),rewrite([26233(18),26374(17),19(16),7(15),19(16),19(15),26371(17),6(17)])].">
      <j1 rule="para" parents="26233 265"/>
      <j2 rule="rewrite" parents="26233 26374 19 7 19 19 26371 6"/>
    </justification>
  </clause>

  <clause id="26409">
    <literal><![CDATA[
      (g(x) + (g(g(x)) + (h(g(x)) + g(x)')))' = g(g(x) + g(g(x)))
    ]]></literal>
    <justification jstring="[para(26233(a,1),286(a,1,1,1,1)),rewrite([26374(5),26374(7),26233(16),26374(15),6(13),19(14),7(13),19(14),19(13),26397(17),19(7),6(6),23018(8),26377(5),26233(17),26374(16),6(14),19(15),7(14),19(15),19(14)]),flip(a)].">
      <j1 rule="para" parents="26233 286"/>
      <j2 rule="rewrite" parents="26374 26374 26233 26374 6 19 7 19 19 26397 19 6 23018 26377 26233 26374 6 19 7 19 19"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26416">
    <literal><![CDATA[
      (g(g(x) + g(g(x))) + (g(x) + (g(x) + g(x)))')' = g(x) + g(x)
    ]]></literal>
    <justification jstring="[para(26233(a,1),2348(a,1,1,2,1,2)),rewrite([19(13),6(12),23018(14),26377(11),6(12)])].">
      <j1 rule="para" parents="26233 2348"/>
      <j2 rule="rewrite" parents="19 6 23018 26377 6"/>
    </justification>
  </clause>

  <clause id="26417">
    <literal><![CDATA[
      (g(g(x) + g(g(x))) + g(g(x) + g(g(x))))' = g(x) + (g(g(x)) + h(g(x)))
    ]]></literal>
    <justification jstring="[para(26233(a,1),353(a,1,1,1,1)),rewrite([6(17),26233(17),26374(16),6(14),19(14),6(13),6(15),7(15),7(14),26409(16),6(22),26233(22),26374(21),6(19),19(19),6(18)])].">
      <j1 rule="para" parents="26233 353"/>
      <j2 rule="rewrite" parents="6 26233 26374 6 19 6 6 7 7 26409 6 26233 26374 6 19 6"/>
    </justification>
  </clause>

  <clause id="26448">
    <literal><![CDATA[
      g(x)' = h(g(x))
    ]]></literal>
    <justification jstring="[para(26374(a,1),62(a,1,1,2,1,2,2)),rewrite([6(9),512(13),26374(7)])].">
      <j1 rule="para" parents="26374 62"/>
      <j2 rule="rewrite" parents="6 512 26374"/>
    </justification>
  </clause>

  <clause id="26451">
    <literal><![CDATA[
      (h(g(x)) + (g(x) + (g(x) + h(g(x))))')' = g(x) + g(x)
    ]]></literal>
    <justification jstring="[para(26374(a,1),170(a,1,1,2,1,2,2))].">
      <j1 rule="para" parents="26374 170"/>
    </justification>
  </clause>

  <clause id="26613">
    <literal><![CDATA[
      ((x + g(g(y) + g(g(y))))' + (g(g(y)) + (x + (g(y) + h(g(y)))))')' = x
    ]]></literal>
    <justification jstring="[para(26374(a,1),1379(a,1,1,2,1,2,2,2)),rewrite([6(4)])].">
      <j1 rule="para" parents="26374 1379"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="26621">
    <literal><![CDATA[
      ((x + g(g(y) + g(g(y))))' + (g(y) + (h(g(y)) + (x + g(g(y)))))')' = x
    ]]></literal>
    <justification jstring="[para(26374(a,1),2453(a,1,1,2,1,2,1))].">
      <j1 rule="para" parents="26374 2453"/>
    </justification>
  </clause>

  <clause id="26623">
    <literal><![CDATA[
      g(x) + g(x) = g(x)
    ]]></literal>
    <justification jstring="[para(26374(a,1),22419(a,1,1,1)),rewrite([26451(11)])].">
      <j1 rule="para" parents="26374 22419"/>
      <j2 rule="rewrite" parents="26451"/>
    </justification>
  </clause>

  <clause id="27105">
    <literal><![CDATA[
      g(x) + (g(g(x)) + h(g(x))) = h(g(g(x) + g(g(x))))
    ]]></literal>
    <justification jstring="[back_rewrite(26417),rewrite([26623(11),26448(6)]),flip(a)].">
      <j1 rule="back_rewrite" parents="26417"/>
      <j2 rule="rewrite" parents="26623 26448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27106">
    <literal><![CDATA[
      g(x) + g(g(x)) = g(x)
    ]]></literal>
    <justification jstring="[back_rewrite(26416),rewrite([26623(9),26623(8),26448(7),6(8),25996(9),26623(7)])].">
      <j1 rule="back_rewrite" parents="26416"/>
      <j2 rule="rewrite" parents="26623 26623 26448 6 25996 26623"/>
    </justification>
  </clause>

  <clause id="27280">
    <literal><![CDATA[
      g(x) + (g(g(x)) + h(g(x))) = h(g(g(x)))
    ]]></literal>
    <justification jstring="[back_rewrite(27105),rewrite([27106(11)])].">
      <j1 rule="back_rewrite" parents="27105"/>
      <j2 rule="rewrite" parents="27106"/>
    </justification>
  </clause>

  <clause id="27283">
    <literal><![CDATA[
      ((x + g(g(y)))' + (g(y) + (h(g(y)) + (x + g(g(y)))))')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(26621),rewrite([27106(4)])].">
      <j1 rule="back_rewrite" parents="26621"/>
      <j2 rule="rewrite" parents="27106"/>
    </justification>
  </clause>

  <clause id="27289">
    <literal><![CDATA[
      ((x + g(g(y)))' + (g(g(y)) + (x + (g(y) + h(g(y)))))')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(26613),rewrite([27106(4)])].">
      <j1 rule="back_rewrite" parents="26613"/>
      <j2 rule="rewrite" parents="27106"/>
    </justification>
  </clause>

  <clause id="27346">
    <literal><![CDATA[
      ((g(g(x)) + y)' + (g(x) + (g(g(x)) + (h(g(x)) + y)))')' = y
    ]]></literal>
    <justification jstring="[back_rewrite(26406),rewrite([27106(13),6(14)])].">
      <j1 rule="back_rewrite" parents="26406"/>
      <j2 rule="rewrite" parents="27106 6"/>
    </justification>
  </clause>

  <clause id="27351">
    <literal><![CDATA[
      ((x + g(y))' + (g(y) + (x + h(g(y))))')' = g(y) + x
    ]]></literal>
    <justification jstring="[back_rewrite(26394),rewrite([27106(10),6(10)])].">
      <j1 rule="back_rewrite" parents="26394"/>
      <j2 rule="rewrite" parents="27106 6"/>
    </justification>
  </clause>

  <clause id="27360">
    <literal><![CDATA[
      g(g(x) + h(g(x))) = g(g(x))
    ]]></literal>
    <justification jstring="[back_rewrite(26377),rewrite([27106(9)])].">
      <j1 rule="back_rewrite" parents="26377"/>
      <j2 rule="rewrite" parents="27106"/>
    </justification>
  </clause>

  <clause id="27375">
    <literal><![CDATA[
      g(g(x)) + h(g(x)) = h(g(x))
    ]]></literal>
    <justification jstring="[para(26448(a,1),53(a,1,1,2,1,2,1)),rewrite([26623(5),26448(4),22420(6),27360(5),26623(9),26448(8),22447(13),26623(7),26448(6)]),flip(a)].">
      <j1 rule="para" parents="26448 53"/>
      <j2 rule="rewrite" parents="26623 26448 22420 27360 26623 26448 22447 26623 26448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27459">
    <literal><![CDATA[
      h(g(x))' = g(x)
    ]]></literal>
    <justification jstring="[para(26448(a,1),324(a,1,1,1,1,2)),rewrite([27360(5),26448(7),24552(11),27375(5),27106(7)])].">
      <j1 rule="para" parents="26448 324"/>
      <j2 rule="rewrite" parents="27360 26448 24552 27375 27106"/>
    </justification>
  </clause>

  <clause id="27514">
    <literal><![CDATA[
      g(x) + h(g(x)) = h(g(g(x)))
    ]]></literal>
    <justification jstring="[back_rewrite(27280),rewrite([27375(6)])].">
      <j1 rule="back_rewrite" parents="27280"/>
      <j2 rule="rewrite" parents="27375"/>
    </justification>
  </clause>

  <clause id="27525">
    <literal><![CDATA[
      g(g(x)) + y = y
    ]]></literal>
    <justification jstring="[back_rewrite(27289),rewrite([27514(10),27351(14)])].">
      <j1 rule="back_rewrite" parents="27289"/>
      <j2 rule="rewrite" parents="27514 27351"/>
    </justification>
  </clause>

  <clause id="27545">
    <literal><![CDATA[
      (x' + (g(y) + (h(g(y)) + x))')' = x
    ]]></literal>
    <justification jstring="[back_rewrite(27346),rewrite([27525(3),27525(8)])].">
      <j1 rule="back_rewrite" parents="27346"/>
      <j2 rule="rewrite" parents="27525 27525"/>
    </justification>
  </clause>

  <clause id="27563">
    <literal><![CDATA[
      g(x) + (g(x) + y) = g(x) + y
    ]]></literal>
    <justification jstring="[back_rewrite(26371),rewrite([27525(5),27525(8)])].">
      <j1 rule="back_rewrite" parents="26371"/>
      <j2 rule="rewrite" parents="27525 27525"/>
    </justification>
  </clause>

  <clause id="27602">
    <literal><![CDATA[
      x + g(g(y)) = x
    ]]></literal>
    <justification jstring="[back_rewrite(27283),rewrite([27545(15)])].">
      <j1 rule="back_rewrite" parents="27283"/>
      <j2 rule="rewrite" parents="27545"/>
    </justification>
  </clause>

  <clause id="27708">
    <literal><![CDATA[
      (g(x) + (g(x) + (h(x) + (x' + x')))')' = x'
    ]]></literal>
    <justification jstring="[back_rewrite(5352),rewrite([27563(10)])].">
      <j1 rule="back_rewrite" parents="5352"/>
      <j2 rule="rewrite" parents="27563"/>
    </justification>
  </clause>

  <clause id="27713">
    <literal><![CDATA[
      (g(x) + (x' + (g(x) + (x' + (x + x)'))'')')' = x'
    ]]></literal>
    <justification jstring="[back_rewrite(4308),rewrite([27563(10)])].">
      <j1 rule="back_rewrite" parents="4308"/>
      <j2 rule="rewrite" parents="27563"/>
    </justification>
  </clause>

  <clause id="27719">
    <literal><![CDATA[
      (g(x + x') + (g(x) + (x' + (x + x)'))')' = g(x) + x'
    ]]></literal>
    <justification jstring="[back_rewrite(3092),rewrite([27563(11)])].">
      <j1 rule="back_rewrite" parents="3092"/>
      <j2 rule="rewrite" parents="27563"/>
    </justification>
  </clause>

  <clause id="27725">
    <literal><![CDATA[
      g(h(g(x))) = g(g(x))
    ]]></literal>
    <justification jstring="[para(27459(a,1),10(a,1,1,2)),rewrite([6(4),27514(4),27459(4)]),flip(a)].">
      <j1 rule="para" parents="27459 10"/>
      <j2 rule="rewrite" parents="6 27514 27459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27787">
    <literal><![CDATA[
      (x + x'')'' = x''
    ]]></literal>
    <justification jstring="[para(27525(a,1),85(a,1,1,2,1,2,2,1)),rewrite([27525(8),27525(7),27525(9)])].">
      <j1 rule="para" parents="27525 85"/>
      <j2 rule="rewrite" parents="27525 27525 27525"/>
    </justification>
  </clause>

  <clause id="27826">
    <literal><![CDATA[
      (g(x) + (h(x) + x'))'' = x'
    ]]></literal>
    <justification jstring="[para(27525(a,1),679(a,1,1,2,1,2,2,2,1)),rewrite([27525(10),27525(9),27525(10)])].">
      <j1 rule="para" parents="27525 679"/>
      <j2 rule="rewrite" parents="27525 27525 27525"/>
    </justification>
  </clause>

  <clause id="27855">
    <literal><![CDATA[
      x'' = x
    ]]></literal>
    <justification jstring="[para(27525(a,1),278(a,1,1,2,1,1,1)),rewrite([29(7),27525(5),27525(7),27787(5),27525(9),29(7)])].">
      <j1 rule="para" parents="27525 278"/>
      <j2 rule="rewrite" parents="29 27525 27525 27787 27525 29"/>
    </justification>
  </clause>

  <clause id="27856">
    <literal><![CDATA[
      x + x = x
    ]]></literal>
    <justification jstring="[para(27525(a,1),278(a,1,1,2,1,2,1,1)),rewrite([27525(9),29(7),27855(4),27525(5),27855(3),27525(8),29(6)])].">
      <j1 rule="para" parents="27525 278"/>
      <j2 rule="rewrite" parents="27525 29 27855 27525 27855 27525 29"/>
    </justification>
  </clause>

  <clause id="27871">
    <literal><![CDATA[
      (x + g(x))' = x'
    ]]></literal>
    <justification jstring="[para(27525(a,1),301(a,1,1,1,1,1,1)),rewrite([27525(4),27856(3),27855(2),27525(5),27525(7),27855(5),27856(5),27855(4),27525(3),27525(6)])].">
      <j1 rule="para" parents="27525 301"/>
      <j2 rule="rewrite" parents="27525 27856 27855 27525 27525 27855 27856 27855 27525 27525"/>
    </justification>
  </clause>

  <clause id="27911">
    <literal><![CDATA[
      x' = h(x)
    ]]></literal>
    <justification jstring="[back_rewrite(24475),rewrite([27855(6),27856(5),27855(6),6(5),23594(7),27856(5),42(5),6(2),27871(3)])].">
      <j1 rule="back_rewrite" parents="24475"/>
      <j2 rule="rewrite" parents="27855 27856 27855 6 23594 27856 42 6 27871"/>
    </justification>
  </clause>

  <clause id="28007">
    <literal><![CDATA[
      h(h(g(x) + h(x))) = h(x)
    ]]></literal>
    <justification jstring="[back_rewrite(27826),rewrite([27911(3),27856(4),27911(4),27911(5),27911(6)])].">
      <j1 rule="back_rewrite" parents="27826"/>
      <j2 rule="rewrite" parents="27911 27856 27911 27911 27911"/>
    </justification>
  </clause>

  <clause id="28013">
    <literal><![CDATA[
      h(h(x + h(h(x)))) = h(h(x))
    ]]></literal>
    <justification jstring="[back_rewrite(27787),rewrite([27911(1),27911(2),27911(4),27911(5),27911(6),27911(7)])].">
      <j1 rule="back_rewrite" parents="27787"/>
      <j2 rule="rewrite" parents="27911 27911 27911 27911 27911 27911"/>
    </justification>
  </clause>

  <clause id="28039">
    <literal><![CDATA[
      h(g(x) + h(h(x))) = h(x)
    ]]></literal>
    <justification jstring="[back_rewrite(27713),rewrite([27911(2),27911(4),27856(5),27911(5),27856(6),27911(6),27911(7),28007(7),27856(4),27911(3),27911(5),27911(6)])].">
      <j1 rule="back_rewrite" parents="27713"/>
      <j2 rule="rewrite" parents="27911 27911 27856 27911 27856 27911 27911 28007 27856 27911 27911 27911"/>
    </justification>
  </clause>

  <clause id="28208">
    <literal><![CDATA[
      h(h(x) + g(g(x) + h(x + h(h(x))))) = x + g(x)
    ]]></literal>
    <justification jstring="[back_rewrite(26125),rewrite([27911(3),27911(4),27911(6),27911(10)])].">
      <j1 rule="back_rewrite" parents="26125"/>
      <j2 rule="rewrite" parents="27911 27911 27911 27911"/>
    </justification>
  </clause>

  <clause id="28259">
    <literal><![CDATA[
      h(g(x) + h(g(x) + (h(x) + h(x + (g(x) + h(h(x))))))) = h(x)
    ]]></literal>
    <justification jstring="[back_rewrite(25108),rewrite([27911(3),27911(6),27911(8),27911(9),28013(9),27911(9),27911(12),27911(14),27911(15)])].">
      <j1 rule="back_rewrite" parents="25108"/>
      <j2 rule="rewrite" parents="27911 27911 27911 27911 28013 27911 27911 27911 27911"/>
    </justification>
  </clause>

  <clause id="28394">
    <literal><![CDATA[
      x + g(x) = x
    ]]></literal>
    <justification jstring="[back_rewrite(23203),rewrite([27856(1),27911(1),27911(5),27911(7),27911(8),28013(8),27911(7),28039(7),27911(4),27911(6),27911(10),28208(10)])].">
      <j1 rule="back_rewrite" parents="23203"/>
      <j2 rule="rewrite" parents="27856 27911 27911 27911 27911 28013 27911 28039 27911 27911 27911 28208"/>
    </justification>
  </clause>

  <clause id="28414">
    <literal><![CDATA[
      h(x + h(x)) = g(x)
    ]]></literal>
    <justification jstring="[back_rewrite(22777),rewrite([27911(4),27911(6),27911(7),28013(7),27911(6),28039(6),27911(3),27911(5),27911(6),28013(6),27911(5),28039(5),27911(3)])].">
      <j1 rule="back_rewrite" parents="22777"/>
      <j2 rule="rewrite" parents="27911 27911 27911 28013 27911 28039 27911 27911 27911 28013 27911 28039 27911"/>
    </justification>
  </clause>

  <clause id="29275">
    <literal><![CDATA[
      h(x + (g(x) + h(h(x)))) = h(x)
    ]]></literal>
    <justification jstring="[back_rewrite(3097),rewrite([27856(3),27911(3),27911(5),27911(6),27911(9),27911(12),27911(14),28259(14),27911(3),27911(4),27911(7)]),flip(a)].">
      <j1 rule="back_rewrite" parents="3097"/>
      <j2 rule="rewrite" parents="27856 27911 27911 27911 27911 27911 27911 28259 27911 27911 27911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29369">
    <literal><![CDATA[
      h(g(x) + h(x)) = x
    ]]></literal>
    <justification jstring="[back_rewrite(2017),rewrite([27856(4),27911(4),27911(5),27911(8),29275(8),27911(4),27911(7),29275(7),27911(4)])].">
      <j1 rule="back_rewrite" parents="2017"/>
      <j2 rule="rewrite" parents="27856 27911 27911 27911 29275 27911 27911 29275 27911"/>
    </justification>
  </clause>

  <clause id="29478">
    <literal><![CDATA[
      g(x) + h(x) = h(x + g(x + h(x)))
    ]]></literal>
    <justification jstring="[back_rewrite(27719),rewrite([27911(1),27911(5),27856(6),27911(6),27856(7),27911(7),29369(7),6(4),27911(5),27911(7)]),flip(a)].">
      <j1 rule="back_rewrite" parents="27719"/>
      <j2 rule="rewrite" parents="27911 27911 27856 27911 27856 27911 29369 6 27911 27911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29482">
    <literal><![CDATA[
      h(g(x) + h(h(x + g(x + h(x))))) = h(x)
    ]]></literal>
    <justification jstring="[back_rewrite(27708),rewrite([27911(4),27911(5),27856(6),27856(5),29478(4),27911(7),27911(9),27911(10)])].">
      <j1 rule="back_rewrite" parents="27708"/>
      <j2 rule="rewrite" parents="27911 27911 27856 27856 29478 27911 27911 27911"/>
    </justification>
  </clause>

  <clause id="29668">
    <literal><![CDATA[
      h(x + g(x + h(x))) = h(x)
    ]]></literal>
    <justification jstring="[back_rewrite(25496),rewrite([28394(2),27856(1),27856(4),27911(4),27856(5),29478(4),27911(7),27911(9),29482(9),29478(4)]),flip(a)].">
      <j1 rule="back_rewrite" parents="25496"/>
      <j2 rule="rewrite" parents="28394 27856 27856 27911 27856 29478 27911 27911 29482 29478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29669">
    <literal><![CDATA[
      h(h(x)) = x
    ]]></literal>
    <justification jstring="[back_rewrite(25493),rewrite([28394(2),27856(1),27856(2),27856(2),27911(2),29478(3),29668(5),27911(2),27856(3)])].">
      <j1 rule="back_rewrite" parents="25493"/>
      <j2 rule="rewrite" parents="28394 27856 27856 27856 27911 29478 29668 27911 27856"/>
    </justification>
  </clause>

  <clause id="29697">
    <literal><![CDATA[
      h(h(x + y) + h(x + h(y))) = x
    ]]></literal>
    <justification jstring="[back_rewrite(25355),rewrite([27856(1),27911(1),27911(3),27856(5),27911(5),27856(6),27911(6),28414(6),28394(5),27911(5),6(6),27911(7)])].">
      <j1 rule="back_rewrite" parents="25355"/>
      <j2 rule="rewrite" parents="27856 27911 27911 27856 27911 27856 27911 28414 28394 27911 6 27911"/>
    </justification>
  </clause>

  <clause id="29805">
    <literal><![CDATA[
      x + h(x) = h(g(x))
    ]]></literal>
    <justification jstring="[back_rewrite(24109),rewrite([28394(2),27856(1),27856(1),27856(4),27911(4),28414(4),27856(3),27911(2)]),flip(a)].">
      <j1 rule="back_rewrite" parents="24109"/>
      <j2 rule="rewrite" parents="28394 27856 27856 27856 27911 28414 27856 27911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29876">
    <literal><![CDATA[
      g(h(x)) = g(x)
    ]]></literal>
    <justification jstring="[back_rewrite(23014),rewrite([29805(2),27725(3),27856(3),27911(3),27525(4),29805(2),27911(3),29669(3),29805(3),27725(4),27856(4),27911(4),27525(5)]),flip(a)].">
      <j1 rule="back_rewrite" parents="23014"/>
      <j2 rule="rewrite" parents="29805 27725 27856 27911 27525 29805 27911 29669 29805 27725 27856 27911 27525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29888">
    <literal><![CDATA[
      h(h(x + (y + z)) + h(y + (z + h(x)))) = y + z
    ]]></literal>
    <justification jstring="[back_rewrite(22949),rewrite([27911(3),29805(5),29876(6),27856(6),27911(6),27525(7),27911(7),27911(9)])].">
      <j1 rule="back_rewrite" parents="22949"/>
      <j2 rule="rewrite" parents="27911 29805 29876 27856 27911 27525 27911 27911"/>
    </justification>
  </clause>

  <clause id="31541">
    <literal><![CDATA[
      g(x) + y = y
    ]]></literal>
    <justification jstring="[back_rewrite(2765),rewrite([27911(4),27856(6),27911(6),29478(7),29805(6),29876(7),27602(7),29876(6),27911(9),27911(11),29888(11)])].">
      <j1 rule="back_rewrite" parents="2765"/>
      <j2 rule="rewrite" parents="27911 27856 27911 29478 29805 29876 27602 29876 27911 27911 29888"/>
    </justification>
  </clause>

  <clause id="31559">
    <literal><![CDATA[
      x + (x + y) = x + y
    ]]></literal>
    <justification jstring="[back_rewrite(1567),rewrite([27856(3),27911(5),31541(6),27911(4),29669(4)])].">
      <j1 rule="back_rewrite" parents="1567"/>
      <j2 rule="rewrite" parents="27856 27911 31541 27911 29669"/>
    </justification>
  </clause>

  <clause id="31578">
    <literal><![CDATA[
      x + g(y) = x
    ]]></literal>
    <justification jstring="[back_rewrite(26034),rewrite([28394(2),27911(2),28394(5),27911(4),31541(5),27911(5),27911(7),29697(7)]),flip(a)].">
      <j1 rule="back_rewrite" parents="26034"/>
      <j2 rule="rewrite" parents="28394 27911 28394 27911 31541 27911 27911 29697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31753">
    <literal><![CDATA[
      h(x + (y + x)) = h(x + y)
    ]]></literal>
    <justification jstring="[back_rewrite(26370),rewrite([31541(3),31578(4),31559(3),31541(3),27911(3),31541(5)])].">
      <j1 rule="back_rewrite" parents="26370"/>
      <j2 rule="rewrite" parents="31541 31578 31559 31541 27911 31541"/>
    </justification>
  </clause>

  <clause id="36217">
    <literal><![CDATA[
      h(x + y) != h(y)
    ]]></literal>
    <attribute><![CDATA[
      answer(Winker2b)
    ]]></attribute>
    <justification jstring="[back_rewrite(14),rewrite([27911(2),27911(3)])].">
      <j1 rule="back_rewrite" parents="14"/>
      <j2 rule="rewrite" parents="27911 27911"/>
    </justification>
  </clause>

  <clause id="36218">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer(Winker2b)
    ]]></attribute>
    <justification jstring="[resolve(36217,a,31753,a)].">
      <j1 rule="resolve" parents="36217 31753"/>
    </justification>
  </clause>

</proof>

<proof number="5" length="171" max_count="32">

<comments><![CDATA[
% Proof 5 at 118.62 (+ 0.30) seconds: Huntington.
% Length of proof is 171.
% Level of proof is 42.
% Maximum clause weight is 32.
% Given clauses 973.
]]></comments>

  <clause id="5" 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>
    <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>
    <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[
      (c1 + c2')' + (c1' + c2')' != c2
    ]]></literal>
    <attribute><![CDATA[
      answer(Huntington)
    ]]></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="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="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="33">
    <literal><![CDATA[
      (h(x) + (x + (x + (x + g(x)))')')' = x
    ]]></literal>
    <justification jstring="[para(12(a,1),8(a,1,1,1))].">
      <j1 rule="para" parents="12 8"/>
    </justification>
  </clause>

  <clause id="36">
    <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="37">
    <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="38">
    <literal><![CDATA[
      (x + (g(x) + (x + x)'')')' = g(x)
    ]]></literal>
    <justification jstring="[para(29(a,1),8(a,1,1,1))].">
      <j1 rule="para" parents="29 8"/>
    </justification>
  </clause>

  <clause id="40">
    <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="41">
    <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="42">
    <literal><![CDATA[
      (g(x) + h(x))' = x
    ]]></literal>
    <justification jstring="[back_rewrite(33),rewrite([40(7),6(3)])].">
      <j1 rule="back_rewrite" parents="33"/>
      <j2 rule="rewrite" parents="40 6"/>
    </justification>
  </clause>

  <clause id="43">
    <literal><![CDATA[
      (x + (g(x) + h(x)')')' = g(x)
    ]]></literal>
    <justification jstring="[para(42(a,1),8(a,1,1,1))].">
      <j1 rule="para" parents="42 8"/>
    </justification>
  </clause>

  <clause id="44">
    <literal><![CDATA[
      ((x + y)' + (x + (g(y) + h(y)))')' = x
    ]]></literal>
    <justification jstring="[para(42(a,1),8(a,1,1,2,1,2)),rewrite([6(8)])].">
      <j1 rule="para" parents="42 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="45">
    <literal><![CDATA[
      (x + (g(x) + h(x)))' = g(g(x) + h(x))
    ]]></literal>
    <justification jstring="[para(42(a,1),10(a,1,1,2)),rewrite([6(4)])].">
      <j1 rule="para" parents="42 10"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="49">
    <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="50">
    <literal><![CDATA[
      (x + (g(x) + (x + x'')'))' = g(g(x) + (x + x'')')
    ]]></literal>
    <justification jstring="[para(27(a,1),10(a,1,1,2)),rewrite([6(7)])].">
      <j1 rule="para" parents="27 10"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="53">
    <literal><![CDATA[
      (g(g(x) + (x + x)') + (g(x) + (x' + (x + x)'))')' = g(x) + (x + x)'
    ]]></literal>
    <justification jstring="[para(29(a,1),27(a,1,1,2,1,2,1)),rewrite([6(11),19(11)])].">
      <j1 rule="para" parents="29 27"/>
      <j2 rule="rewrite" parents="6 19"/>
    </justification>
  </clause>

  <clause id="56">
    <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="58">
    <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="62">
    <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="63">
    <literal><![CDATA[
      (x + ((x + y')' + (x + y)'')')' = (x + y')'
    ]]></literal>
    <justification jstring="[para(8(a,1),20(a,1,1,1))].">
      <j1 rule="para" parents="8 20"/>
    </justification>
  </clause>

  <clause id="66">
    <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="84">
    <literal><![CDATA[
      ((x + ((y + z)' + (y + z')'))' + (y + x)')' = x
    ]]></literal>
    <justification jstring="[para(8(a,1),21(a,1,1,2,1,1))].">
      <j1 rule="para" parents="8 21"/>
    </justification>
  </clause>

  <clause id="85">
    <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="87">
    <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="88">
    <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="93">
    <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="94">
    <literal><![CDATA[
      ((x + (g(y) + h(y)))' + (y + x)')' = x
    ]]></literal>
    <justification jstring="[para(42(a,1),21(a,1,1,2,1,1))].">
      <j1 rule="para" parents="42 21"/>
    </justification>
  </clause>

  <clause id="95">
    <literal><![CDATA[
      ((x + (g(y) + (y + y'')'))' + (y + x)')' = x
    ]]></literal>
    <justification jstring="[para(27(a,1),21(a,1,1,2,1,1))].">
      <j1 rule="para" parents="27 21"/>
    </justification>
  </clause>

  <clause id="109">
    <literal><![CDATA[
      (g(x') + (x + (x' + (x' + g(x')))')')' = (x' + (x' + g(x')))'
    ]]></literal>
    <justification jstring="[para(40(a,1),21(a,1,1,2)),rewrite([6(8),6(12)])].">
      <j1 rule="para" parents="40 21"/>
      <j2 rule="rewrite" parents="6 6"/>
    </justification>
  </clause>

  <clause id="113">
    <literal><![CDATA[
      (g(x) + (x + (g(x) + h(x)'))')' = x
    ]]></literal>
    <justification jstring="[para(43(a,1),8(a,1,1,2)),rewrite([6(8)])].">
      <j1 rule="para" parents="43 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="170">
    <literal><![CDATA[
      (h(x) + (x + (x + (x + g(x))'))')' = x + x
    ]]></literal>
    <justification jstring="[para(12(a,1),22(a,1,1,1))].">
      <j1 rule="para" parents="12 22"/>
    </justification>
  </clause>

  <clause id="173">
    <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="198">
    <literal><![CDATA[
      (g(g(x) + h(x)) + (x + x)')' = x
    ]]></literal>
    <justification jstring="[para(42(a,1),66(a,1,1,2,1,1)),rewrite([42(8),42(12)])].">
      <j1 rule="para" parents="42 66"/>
      <j2 rule="rewrite" parents="42 42"/>
    </justification>
  </clause>

  <clause id="254">
    <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="278">
    <literal><![CDATA[
      (x + ((x + (g(y) + (y + y)'))' + (x + y)'')')' = (x + (g(y) + (y + y)'))'
    ]]></literal>
    <justification jstring="[para(29(a,1),23(a,1,1,2,1,2,1,1,2))].">
      <j1 rule="para" parents="29 23"/>
    </justification>
  </clause>

  <clause id="286">
    <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="301">
    <literal><![CDATA[
      (((x + y)' + (x + y)')' + g(x + ((x + y)' + (x + y')'')'))' = (x + y)'
    ]]></literal>
    <justification jstring="[para(23(a,1),66(a,1,1,2,1,1)),rewrite([23(22),6(17),23(28)])].">
      <j1 rule="para" parents="23 66"/>
      <j2 rule="rewrite" parents="23 6 23"/>
    </justification>
  </clause>

  <clause id="310">
    <literal><![CDATA[
      (x + ((x + y)' + (x + ((x + y)' + (x + y')'')'')'')')' = (x + y)'
    ]]></literal>
    <justification jstring="[para(23(a,1),23(a,1,1,2,1,1)),rewrite([23(28)])].">
      <j1 rule="para" parents="23 23"/>
      <j2 rule="rewrite" parents="23"/>
    </justification>
  </clause>

  <clause id="324">
    <literal><![CDATA[
      (g(x + x') + (x + (g(x) + x''))')' = x + g(x)
    ]]></literal>
    <justification jstring="[para(31(a,1),22(a,1,1,1))].">
      <j1 rule="para" parents="31 22"/>
    </justification>
  </clause>

  <clause id="335">
    <literal><![CDATA[
      (x + (g(g(x) + h(x)) + (x + x)'))' = g(g(g(x) + h(x)) + (x + x)')
    ]]></literal>
    <justification jstring="[para(198(a,1),10(a,1,1,2)),rewrite([6(8)])].">
      <j1 rule="para" parents="198 10"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="339">
    <literal><![CDATA[
      ((x + y)' + (g(g(x) + h(x)) + ((x + x)' + y))')' = y
    ]]></literal>
    <justification jstring="[para(198(a,1),56(a,1,1,2,1,1)),rewrite([7(8),6(12)])].">
      <j1 rule="para" parents="198 56"/>
      <j2 rule="rewrite" parents="7 6"/>
    </justification>
  </clause>

  <clause id="353">
    <literal><![CDATA[
      (g(x + y) + (x' + (y + (y + x)'))')' = y + (y + x)'
    ]]></literal>
    <justification jstring="[para(254(a,1),20(a,1,1,1)),rewrite([6(7)])].">
      <j1 rule="para" parents="254 20"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="369">
    <literal><![CDATA[
      (g(x) + (x + (g(x) + (x + x)''))')' = x
    ]]></literal>
    <justification jstring="[para(38(a,1),8(a,1,1,2)),rewrite([6(9)])].">
      <j1 rule="para" parents="38 8"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="507">
    <literal><![CDATA[
      (g(x) + (x' + ((x + y)' + (x + y')'))')' = x'
    ]]></literal>
    <justification jstring="[para(8(a,1),88(a,1,1,1,1)),rewrite([8(14),6(9),8(19)])].">
      <j1 rule="para" parents="8 88"/>
      <j2 rule="rewrite" parents="8 6 8"/>
    </justification>
  </clause>

  <clause id="511">
    <literal><![CDATA[
      (g(x) + (g(x) + (x' + (x + x)'))')' = x'
    ]]></literal>
    <justification jstring="[para(29(a,1),88(a,1,1,1,1)),rewrite([29(10),6(7),19(7),29(15)])].">
      <j1 rule="para" parents="29 88"/>
      <j2 rule="rewrite" parents="29 6 19 29"/>
    </justification>
  </clause>

  <clause id="512">
    <literal><![CDATA[
      (g(x) + (g(x) + (h(x) + x'))')' = x'
    ]]></literal>
    <justification jstring="[para(42(a,1),88(a,1,1,1,1)),rewrite([42(8),7(6),42(13)])].">
      <j1 rule="para" parents="42 88"/>
      <j2 rule="rewrite" parents="42 7 42"/>
    </justification>
  </clause>

  <clause id="575">
    <literal><![CDATA[
      (g(x) + (x + (g(x) + (x + x'')''))')' = x
    ]]></literal>
    <justification jstring="[para(27(a,1),25(a,1,1,2,1,2,2)),rewrite([6(8),19(9),27(19)])].">
      <j1 rule="para" parents="27 25"/>
      <j2 rule="rewrite" parents="6 19 27"/>
    </justification>
  </clause>

  <clause id="679">
    <literal><![CDATA[
      (x + (x + (g(y) + (h(y) + (x + y)')))')' = (x + y)'
    ]]></literal>
    <justification jstring="[para(44(a,1),8(a,1,1,2)),rewrite([6(7),7(7),7(6),6(9)])].">
      <j1 rule="para" parents="44 8"/>
      <j2 rule="rewrite" parents="6 7 7 6"/>
    </justification>
  </clause>

  <clause id="833">
    <literal><![CDATA[
      (h(g(x)) + (x + (g(x) + (g(x) + (g(g(x)) + x'))))')' = g(x) + (g(x) + g(g(x)))
    ]]></literal>
    <justification jstring="[para(12(a,1),87(a,1,1,2)),rewrite([19(9),7(8),7(7),6(13)])].">
      <j1 rule="para" parents="12 87"/>
      <j2 rule="rewrite" parents="19 7 7 6"/>
    </justification>
  </clause>

  <clause id="1345">
    <literal><![CDATA[
      ((x + (y + z))' + (y + (z + x)')')' = y
    ]]></literal>
    <justification jstring="[para(6(a,1),36(a,1,1,2,1,2,1))].">
      <j1 rule="para" parents="6 36"/>
    </justification>
  </clause>

  <clause id="1379">
    <literal><![CDATA[
      ((x + g(y + z))' + (y + (x + (z + (z + y)')))')' = x
    ]]></literal>
    <justification jstring="[para(254(a,1),36(a,1,1,2,1,2)),rewrite([6(11)])].">
      <j1 rule="para" parents="254 36"/>
      <j2 rule="rewrite" parents="6"/>
    </justification>
  </clause>

  <clause id="1653">
    <literal><![CDATA[
      (h(x) + g(g(x) + (x + x)'))' = x + g(x)
    ]]></literal>
    <justification jstring="[para(12(a,1),58(a,1,1,1)),rewrite([7(6),41(7)])].">
      <j1 rule="para" parents="12 58"/>
      <j2 r