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<!DOCTYPE proofs SYSTEM "proof3.dtd">

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

<proofs number_of_proofs="1">

<source>H7b.out</source>

<heading><![CDATA[
Prover9 (32) version June-2006C, June 2006.
Process 13802 was started by mccune on cleo.thornwood,
Mon Jun 19 16:51:07 2006
The command was "/home/mccune/bin/prover9 -f lt.in uc.in H7b.in".
]]></heading>

<proof number="1" length="33" max_count="24">

<comments><![CDATA[
% Proof 1 at 17.34 (+ 0.24) seconds.
% Length of proof is 33.
% Level of proof is 13.
% Maximum clause weight is 23.
% Given clauses 1447.
]]></comments>

  <clause id="10">
    <literal><![CDATA[
      x ^ (y v (x ^ z)) = x ^ (y v (x ^ ((x ^ y) v (z ^ (x v y)))))
    ]]></literal>
    <attribute><![CDATA[
      label(H7)
    ]]></attribute>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="12">
    <literal><![CDATA[
      c1 ' != c1 ' v c2 '
    ]]></literal>
    <justification jstring="[clausify].">
      <j1 rule="clausify"/>
    </justification>
  </clause>

  <clause id="13">
    <literal><![CDATA[
      x v y = y v x
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="14">
    <literal><![CDATA[
      (x v y) v z = x v (y v z)
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="15">
    <literal><![CDATA[
      x ^ y = y ^ x
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="16">
    <literal><![CDATA[
      (x ^ y) ^ z = x ^ (y ^ z)
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="17">
    <literal><![CDATA[
      x ^ (x v y) = x
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="18">
    <literal><![CDATA[
      x v (x ^ y) = x
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="19">
    <literal><![CDATA[
      x v x ' = 1
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="20">
    <literal><![CDATA[
      x ^ x ' = 0
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="21">
    <literal><![CDATA[
      x v y != 1
    ]]></literal>
    <literal><![CDATA[
      x ^ y != 0
    ]]></literal>
    <literal><![CDATA[
      x ' = y
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="22">
    <literal><![CDATA[
      x ^ (y v (x ^ ((x ^ y) v (z ^ (x v y))))) = x ^ (y v (x ^ z))
    ]]></literal>
    <attribute><![CDATA[
      label(H7)
    ]]></attribute>
    <justification jstring="[copy(10),flip(a)].">
      <j1 rule="copy" parents="10"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23">
    <literal><![CDATA[
      c1 ^ c2 = c1
    ]]></literal>
    <justification jstring="[clausify].">
      <j1 rule="clausify"/>
    </justification>
  </clause>

  <clause id="24">
    <literal><![CDATA[
      c1 ' v c2 ' != c1 '
    ]]></literal>
    <justification jstring="[copy(12),flip(a)].">
      <j1 rule="copy" parents="12"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25">
    <literal><![CDATA[
      x v (y v z) = y v (x v z)
    ]]></literal>
    <justification jstring="[para(13(a,1),14(a,1,1)),demod(14(2))].">
      <j1 rule="para" parents="13 14"/>
      <j2 rule="demod" parents="14"/>
    </justification>
  </clause>

  <clause id="31">
    <literal><![CDATA[
      x v ((x ^ y) v z) = x v z
    ]]></literal>
    <justification jstring="[para(18(a,1),14(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33">
    <literal><![CDATA[
      x v (y ^ x) = x
    ]]></literal>
    <justification jstring="[para(15(a,1),18(a,1,2))].">
      <j1 rule="para" parents="15 18"/>
    </justification>
  </clause>

  <clause id="39">
    <literal><![CDATA[
      x ^ 1 = x
    ]]></literal>
    <justification jstring="[para(19(a,1),17(a,1,2))].">
      <j1 rule="para" parents="19 17"/>
    </justification>
  </clause>

  <clause id="41">
    <literal><![CDATA[
      x ^ (y ^ (x ^ y) ') = 0
    ]]></literal>
    <justification jstring="[para(20(a,1),16(a,1)),flip(a)].">
      <j1 rule="para" parents="20 16"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49">
    <literal><![CDATA[
      x ^ (y v (x ^ ((x ^ y) v (z ^ (y v x))))) = x ^ (y v (x ^ z))
    ]]></literal>
    <justification jstring="[para(13(a,1),22(a,1,2,2,2,2,2))].">
      <j1 rule="para" parents="13 22"/>
    </justification>
  </clause>

  <clause id="57">
    <literal><![CDATA[
      1 ^ x = x
    ]]></literal>
    <justification jstring="[para(39(a,1),15(a,1)),flip(a)].">
      <j1 rule="para" parents="39 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="64">
    <literal><![CDATA[
      1 v x = 1
    ]]></literal>
    <justification jstring="[para(57(a,1),17(a,1))].">
      <j1 rule="para" parents="57 17"/>
    </justification>
  </clause>

  <clause id="72">
    <literal><![CDATA[
      x v 1 = 1
    ]]></literal>
    <justification jstring="[para(64(a,1),13(a,1)),flip(a)].">
      <j1 rule="para" parents="64 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="179">
    <literal><![CDATA[
      x v (x ^ y) ' = 1
    ]]></literal>
    <justification jstring="[para(19(a,1),31(a,1,2)),demod(72(2)),flip(a)].">
      <j1 rule="para" parents="19 31"/>
      <j2 rule="demod" parents="72"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="190">
    <literal><![CDATA[
      x v (y ^ x) ' = 1
    ]]></literal>
    <justification jstring="[para(15(a,1),179(a,1,2,1))].">
      <j1 rule="para" parents="15 179"/>
    </justification>
  </clause>

  <clause id="200">
    <literal><![CDATA[
      c2 v c1 ' = 1
    ]]></literal>
    <justification jstring="[para(23(a,1),190(a,1,2,1))].">
      <j1 rule="para" parents="23 190"/>
    </justification>
  </clause>

  <clause id="299">
    <literal><![CDATA[
      x v (y ^ (x ^ y) ') != 1
    ]]></literal>
    <literal><![CDATA[
      y ^ (x ^ y) ' = x '
    ]]></literal>
    <justification jstring="[para(41(a,1),21(b,1)),flip(c),xx(b)].">
      <j1 rule="para" parents="41 21"/>
      <j2 rule="flip"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

  <clause id="517">
    <literal><![CDATA[
      c1 ' ^ (c2 v (c1 ' ^ ((c2 ^ c1 ') v x))) = c1 ' ^ (c2 v (c1 ' ^ x))
    ]]></literal>
    <justification jstring="[para(200(a,1),49(a,1,2,2,2,2,2)),demod(15(9),39(11))].">
      <j1 rule="para" parents="200 49"/>
      <j2 rule="demod" parents="15 39"/>
    </justification>
  </clause>

  <clause id="13494">
    <literal><![CDATA[
      c1 ' ^ (c2 v (c1 ' ^ (c2 ^ c1 ') ')) = c1 '
    ]]></literal>
    <justification jstring="[para(19(a,1),517(a,1,2,2,2)),demod(15(7),57(7),200(6),15(4),57(4)),flip(a)].">
      <j1 rule="para" parents="19 517"/>
      <j2 rule="demod" parents="15 57 200 15 57"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13502">
    <literal><![CDATA[
      c2 v (c1 ' ^ (c2 ^ c1 ') ') = 1
    ]]></literal>
    <justification jstring="[para(13494(a,1),33(a,1,2)),demod(13(13),25(13),18(12),200(4)),flip(a)].">
      <j1 rule="para" parents="13494 33"/>
      <j2 rule="demod" parents="13 25 18 200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13517">
    <literal><![CDATA[
      c1 ' ^ (c2 ^ c1 ') ' = c2 '
    ]]></literal>
    <justification jstring="[hyper(299,a,13502,a)].">
      <j1 rule="hyper" parents="299 13502"/>
    </justification>
  </clause>

  <clause id="13525">
    <literal><![CDATA[
      c1 ' v c2 ' = c1 '
    ]]></literal>
    <justification jstring="[para(13517(a,1),18(a,1,2))].">
      <j1 rule="para" parents="13517 18"/>
    </justification>
  </clause>

  <clause id="13526">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[resolve(13525,a,24,a)].">
      <j1 rule="resolve" parents="13525 24"/>
    </justification>
  </clause>

</proof>

</proofs>
