<?xml version="1.0" encoding="ISO-8859-1"?>

<!DOCTYPE proofs SYSTEM "proof3.dtd">

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

<proofs number_of_proofs="1">

<source>t4_12.out</source>

<heading><![CDATA[
Prover9 (32) version August-2006A, August 2006.
Process 11455 was started by mccune on cleo.thornwood,
Sat Aug 12 21:01:39 2006
The command was "/home/mccune/bin/prover9 -f head.in t4_12.in".
]]></heading>

<proof number="1" length="72" max_count="39">

<comments><![CDATA[
% Proof 1 at 2.72 (+ 0.03) seconds.
% Length of proof is 72.
% Level of proof is 17.
% Maximum clause weight is 34.
% Given clauses 537.
]]></comments>

  <clause id="2">
    <literal><![CDATA[
      (all x all y all z (B(x,y,z) <-> (x ^ y) v (y ^ z) = y & (x v y) ^ (y v z) = y))
    ]]></literal>
    <attribute><![CDATA[
      label(non_clause)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="24">
    <literal><![CDATA[
      x ^ y = y ^ x
    ]]></literal>
    <attribute><![CDATA[
      label("commutativity_meet")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="25">
    <literal><![CDATA[
      x v y = y v x
    ]]></literal>
    <attribute><![CDATA[
      label("commutativity_join")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="26">
    <literal><![CDATA[
      (x ^ y) ^ z = x ^ (y ^ z)
    ]]></literal>
    <attribute><![CDATA[
      label("associativity_meet")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="27">
    <literal><![CDATA[
      (x v y) v z = x v (y v z)
    ]]></literal>
    <attribute><![CDATA[
      label("associativity_join")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="28">
    <literal><![CDATA[
      (x v y) ^ x = x
    ]]></literal>
    <attribute><![CDATA[
      label("absorption_1")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="29">
    <literal><![CDATA[
      x ^ (x v y) = x
    ]]></literal>
    <justification jstring="[copy(28),rewrite(24(2))].">
      <j1 rule="copy" parents="28"/>
      <j2 rule="rewrite" parents="24"/>
    </justification>
  </clause>

  <clause id="30">
    <literal><![CDATA[
      (x ^ y) v x = x
    ]]></literal>
    <attribute><![CDATA[
      label("absorption_2")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="31">
    <literal><![CDATA[
      x v (x ^ y) = x
    ]]></literal>
    <justification jstring="[copy(30),rewrite(25(2))].">
      <j1 rule="copy" parents="30"/>
      <j2 rule="rewrite" parents="25"/>
    </justification>
  </clause>

  <clause id="32">
    <literal><![CDATA[
      -B(x,y,z)
    ]]></literal>
    <literal><![CDATA[
      (x ^ y) v (y ^ z) = y
    ]]></literal>
    <justification jstring="[clausify(2)].">
      <j1 rule="clausify" parents="2"/>
    </justification>
  </clause>

  <clause id="33">
    <literal><![CDATA[
      -B(x,y,z)
    ]]></literal>
    <literal><![CDATA[
      (x v y) ^ (y v z) = y
    ]]></literal>
    <justification jstring="[clausify(2)].">
      <j1 rule="clausify" parents="2"/>
    </justification>
  </clause>

  <clause id="34">
    <literal><![CDATA[
      B(x,y,z)
    ]]></literal>
    <literal><![CDATA[
      (x ^ y) v (y ^ z) != y
    ]]></literal>
    <literal><![CDATA[
      (x v y) ^ (y v z) != y
    ]]></literal>
    <justification jstring="[clausify(2)].">
      <j1 rule="clausify" parents="2"/>
    </justification>
  </clause>

  <clause id="35">
    <literal><![CDATA[
      x v (y ^ (x v z)) = (x v y) ^ (x v z)
    ]]></literal>
    <attribute><![CDATA[
      label("modularity_1")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36">
    <literal><![CDATA[
      x ^ (y v (x ^ z)) = (x ^ y) v (x ^ z)
    ]]></literal>
    <attribute><![CDATA[
      label("modularity_2")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      (x ^ y) v (x ^ z) = x ^ (y v (x ^ z))
    ]]></literal>
    <justification jstring="[copy(36),flip(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38">
    <literal><![CDATA[
      B(ca,cy,cx)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="39">
    <literal><![CDATA[
      B(ca,cx,cb)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="40">
    <literal><![CDATA[
      -B(ca,cy,cb)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="42">
    <literal><![CDATA[
      x ^ (y ^ z) = y ^ (x ^ z)
    ]]></literal>
    <justification jstring="[para(24(a,1),26(a,1,1)),rewrite(26(2))].">
      <j1 rule="para" parents="24 26"/>
      <j2 rule="rewrite" parents="26"/>
    </justification>
  </clause>

  <clause id="44">
    <literal><![CDATA[
      x v (y v z) = y v (x v z)
    ]]></literal>
    <justification jstring="[para(25(a,1),27(a,1,1)),rewrite(27(2))].">
      <j1 rule="para" parents="25 27"/>
      <j2 rule="rewrite" parents="27"/>
    </justification>
  </clause>

  <clause id="45">
    <literal><![CDATA[
      x ^ (y v x) = x
    ]]></literal>
    <justification jstring="[para(25(a,1),29(a,1,2))].">
      <j1 rule="para" parents="25 29"/>
    </justification>
  </clause>

  <clause id="46">
    <literal><![CDATA[
      x ^ ((x v y) ^ z) = x ^ z
    ]]></literal>
    <justification jstring="[para(29(a,1),26(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29 26"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49">
    <literal><![CDATA[
      x v (y ^ x) = x
    ]]></literal>
    <justification jstring="[para(24(a,1),31(a,1,2))].">
      <j1 rule="para" parents="24 31"/>
    </justification>
  </clause>

  <clause id="53">
    <literal><![CDATA[
      x ^ x = x
    ]]></literal>
    <justification jstring="[para(31(a,1),29(a,1,2))].">
      <j1 rule="para" parents="31 29"/>
    </justification>
  </clause>

  <clause id="60">
    <literal><![CDATA[
      B(x,y,z)
    ]]></literal>
    <literal><![CDATA[
      (x ^ y) v (y ^ z) != y
    ]]></literal>
    <literal><![CDATA[
      (x v y) ^ (z v y) != y
    ]]></literal>
    <justification jstring="[para(25(a,1),34(c,1,2))].">
      <j1 rule="para" parents="25 34"/>
    </justification>
  </clause>

  <clause id="70">
    <literal><![CDATA[
      x v (y ^ (z v x)) = (x v y) ^ (x v z)
    ]]></literal>
    <justification jstring="[para(25(a,1),35(a,1,2,2))].">
      <j1 rule="para" parents="25 35"/>
    </justification>
  </clause>

  <clause id="76">
    <literal><![CDATA[
      B(x,y,z ^ (y v u))
    ]]></literal>
    <literal><![CDATA[
      (x ^ y) v (y ^ (z ^ (y v u))) != y
    ]]></literal>
    <literal><![CDATA[
      (x v y) ^ ((y v z) ^ (y v u)) != y
    ]]></literal>
    <justification jstring="[para(35(a,1),34(c,1,2))].">
      <j1 rule="para" parents="35 34"/>
    </justification>
  </clause>

  <clause id="78">
    <literal><![CDATA[
      (x ^ y) v (y ^ z) = y ^ (x v (y ^ z))
    ]]></literal>
    <justification jstring="[para(24(a,1),37(a,1,1))].">
      <j1 rule="para" parents="24 37"/>
    </justification>
  </clause>

  <clause id="89">
    <literal><![CDATA[
      B(x,y,z ^ (y v u))
    ]]></literal>
    <literal><![CDATA[
      y ^ (x v (y ^ (z ^ (y v u)))) != y
    ]]></literal>
    <literal><![CDATA[
      (x v y) ^ ((y v z) ^ (y v u)) != y
    ]]></literal>
    <justification jstring="[back_rewrite(76),rewrite(78(8))].">
      <j1 rule="back_rewrite" parents="76"/>
      <j2 rule="rewrite" parents="78"/>
    </justification>
  </clause>

  <clause id="93">
    <literal><![CDATA[
      B(x,y,z)
    ]]></literal>
    <literal><![CDATA[
      y ^ (x v (y ^ z)) != y
    ]]></literal>
    <literal><![CDATA[
      (x v y) ^ (z v y) != y
    ]]></literal>
    <justification jstring="[back_rewrite(60),rewrite(78(4))].">
      <j1 rule="back_rewrite" parents="60"/>
      <j2 rule="rewrite" parents="78"/>
    </justification>
  </clause>

  <clause id="96">
    <literal><![CDATA[
      -B(x,y,z)
    ]]></literal>
    <literal><![CDATA[
      y ^ (x v (y ^ z)) = y
    ]]></literal>
    <justification jstring="[back_rewrite(32),rewrite(78(4))].">
      <j1 rule="back_rewrite" parents="32"/>
      <j2 rule="rewrite" parents="78"/>
    </justification>
  </clause>

  <clause id="99">
    <literal><![CDATA[
      (ca v cy) ^ (cx v cy) = cy
    ]]></literal>
    <justification jstring="[hyper(33,a,38,a),rewrite(25(6))].">
      <j1 rule="hyper" parents="33 38"/>
      <j2 rule="rewrite" parents="25"/>
    </justification>
  </clause>

  <clause id="100">
    <literal><![CDATA[
      (ca v cx) ^ (cx v cb) = cx
    ]]></literal>
    <justification jstring="[hyper(33,a,39,a)].">
      <j1 rule="hyper" parents="33 39"/>
    </justification>
  </clause>

  <clause id="101">
    <literal><![CDATA[
      x ^ (y ^ (x v z)) = y ^ x
    ]]></literal>
    <justification jstring="[para(29(a,1),42(a,1,2)),flip(a)].">
      <j1 rule="para" parents="29 42"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="105">
    <literal><![CDATA[
      B(x,y,z ^ (y v u))
    ]]></literal>
    <literal><![CDATA[
      y ^ (x v (z ^ y)) != y
    ]]></literal>
    <literal><![CDATA[
      (x v y) ^ ((y v z) ^ (y v u)) != y
    ]]></literal>
    <justification jstring="[back_rewrite(89),rewrite(101(6))].">
      <j1 rule="back_rewrite" parents="89"/>
      <j2 rule="rewrite" parents="101"/>
    </justification>
  </clause>

  <clause id="111">
    <literal><![CDATA[
      x ^ (y ^ x) = y ^ x
    ]]></literal>
    <justification jstring="[para(53(a,1),26(a,2,2)),rewrite(24(2))].">
      <j1 rule="para" parents="53 26"/>
      <j2 rule="rewrite" parents="24"/>
    </justification>
  </clause>

  <clause id="117">
    <literal><![CDATA[
      x ^ ((y v x) ^ z) = x ^ z
    ]]></literal>
    <justification jstring="[para(45(a,1),26(a,1,1)),flip(a)].">
      <j1 rule="para" parents="45 26"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="120">
    <literal><![CDATA[
      x ^ (y ^ (z v x)) = y ^ x
    ]]></literal>
    <justification jstring="[para(45(a,1),42(a,1,2)),flip(a)].">
      <j1 rule="para" parents="45 42"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="137">
    <literal><![CDATA[
      (ca v cx) ^ ((cx v cb) ^ x) = cx ^ x
    ]]></literal>
    <justification jstring="[para(100(a,1),26(a,1,1)),flip(a)].">
      <j1 rule="para" parents="100 26"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="152">
    <literal><![CDATA[
      ca ^ (cx v cy) = ca ^ cy
    ]]></literal>
    <justification jstring="[para(99(a,1),46(a,1,2)),flip(a)].">
      <j1 rule="para" parents="99 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="153">
    <literal><![CDATA[
      ca ^ (cx v cb) = ca ^ cx
    ]]></literal>
    <justification jstring="[para(100(a,1),46(a,1,2)),flip(a)].">
      <j1 rule="para" parents="100 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="155">
    <literal><![CDATA[
      x ^ (y ^ (z ^ x)) = y ^ (z ^ x)
    ]]></literal>
    <justification jstring="[para(26(a,1),111(a,1,2)),rewrite(26(5))].">
      <j1 rule="para" parents="26 111"/>
      <j2 rule="rewrite" parents="26"/>
    </justification>
  </clause>

  <clause id="156">
    <literal><![CDATA[
      (x v y) ^ (z ^ x) = z ^ x
    ]]></literal>
    <justification jstring="[para(111(a,1),46(a,2)),rewrite(155(4))].">
      <j1 rule="para" parents="111 46"/>
      <j2 rule="rewrite" parents="155"/>
    </justification>
  </clause>

  <clause id="188">
    <literal><![CDATA[
      cx v (ca ^ cy) = (ca v cx) ^ (cx v cy)
    ]]></literal>
    <justification jstring="[para(152(a,1),35(a,1,2)),rewrite(25(8))].">
      <j1 rule="para" parents="152 35"/>
      <j2 rule="rewrite" parents="25"/>
    </justification>
  </clause>

  <clause id="217">
    <literal><![CDATA[
      cx ^ (ca v cy) = cx ^ cy
    ]]></literal>
    <justification jstring="[para(99(a,1),101(a,1,2)),rewrite(24(8)),flip(a)].">
      <j1 rule="para" parents="99 101"/>
      <j2 rule="rewrite" parents="24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="220">
    <literal><![CDATA[
      ca v (cx ^ cy) = (ca v cx) ^ (ca v cy)
    ]]></literal>
    <justification jstring="[para(217(a,1),35(a,1,2))].">
      <j1 rule="para" parents="217 35"/>
    </justification>
  </clause>

  <clause id="222">
    <literal><![CDATA[
      cx ^ (x ^ (ca v cy)) = x ^ (cx ^ cy)
    ]]></literal>
    <justification jstring="[para(217(a,1),42(a,1,2)),flip(a)].">
      <j1 rule="para" parents="217 42"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="256">
    <literal><![CDATA[
      cb ^ (ca v cx) = cx ^ cb
    ]]></literal>
    <justification jstring="[para(100(a,1),120(a,1,2)),rewrite(24(3),24(8)),flip(a)].">
      <j1 rule="para" parents="100 120"/>
      <j2 rule="rewrite" parents="24 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="261">
    <literal><![CDATA[
      cb ^ ((ca v cx) ^ x) = cx ^ (cb ^ x)
    ]]></literal>
    <justification jstring="[para(256(a,1),26(a,1,1)),rewrite(26(4)),flip(a)].">
      <j1 rule="para" parents="256 26"/>
      <j2 rule="rewrite" parents="26"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="262">
    <literal><![CDATA[
      ca v (cx ^ cb) = (ca v cx) ^ (ca v cb)
    ]]></literal>
    <justification jstring="[para(256(a,1),35(a,1,2)),rewrite(24(12))].">
      <j1 rule="para" parents="256 35"/>
      <j2 rule="rewrite" parents="24"/>
    </justification>
  </clause>

  <clause id="728">
    <literal><![CDATA[
      cb v (ca ^ cx) = (ca v cb) ^ (cx v cb)
    ]]></literal>
    <justification jstring="[para(153(a,1),70(a,1,2)),rewrite(25(8),25(11))].">
      <j1 rule="para" parents="153 70"/>
      <j2 rule="rewrite" parents="25 25"/>
    </justification>
  </clause>

  <clause id="2610">
    <literal><![CDATA[
      cx ^ (ca v cb) = cx
    ]]></literal>
    <justification jstring="[hyper(96,a,39,a),rewrite(262(6),117(9))].">
      <j1 rule="hyper" parents="96 39"/>
      <j2 rule="rewrite" parents="262 117"/>
    </justification>
  </clause>

  <clause id="2611">
    <literal><![CDATA[
      cy ^ (ca v cx) = cy
    ]]></literal>
    <justification jstring="[hyper(96,a,38,a),rewrite(24(5),220(6),120(9),24(5))].">
      <j1 rule="hyper" parents="96 38"/>
      <j2 rule="rewrite" parents="24 220 120 24"/>
    </justification>
  </clause>

  <clause id="2617">
    <literal><![CDATA[
      ca v (cx v cb) = ca v cb
    ]]></literal>
    <justification jstring="[para(2610(a,1),49(a,1,2)),rewrite(25(5),44(5))].">
      <j1 rule="para" parents="2610 49"/>
      <j2 rule="rewrite" parents="25 44"/>
    </justification>
  </clause>

  <clause id="2624">
    <literal><![CDATA[
      (ca v cb) ^ (cx v cb) = cx v cb
    ]]></literal>
    <justification jstring="[para(2610(a,1),70(a,1,2)),rewrite(25(3),25(6),25(9),24(10)),flip(a)].">
      <j1 rule="para" parents="2610 70"/>
      <j2 rule="rewrite" parents="25 25 25 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2659">
    <literal><![CDATA[
      cb v (ca ^ cx) = cx v cb
    ]]></literal>
    <justification jstring="[back_rewrite(728),rewrite(2624(12))].">
      <j1 rule="back_rewrite" parents="728"/>
      <j2 rule="rewrite" parents="2624"/>
    </justification>
  </clause>

  <clause id="2661">
    <literal><![CDATA[
      (ca v cx) ^ (ca v cy) = ca v cy
    ]]></literal>
    <justification jstring="[para(2611(a,1),35(a,1,2)),rewrite(24(10)),flip(a)].">
      <j1 rule="para" parents="2611 35"/>
      <j2 rule="rewrite" parents="24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2669">
    <literal><![CDATA[
      cy ^ (ca v (cx v x)) = cy
    ]]></literal>
    <justification jstring="[para(2611(a,1),156(a,1,2)),rewrite(27(4),24(6),2611(11))].">
      <j1 rule="para" parents="2611 156"/>
      <j2 rule="rewrite" parents="27 24 2611"/>
    </justification>
  </clause>

  <clause id="2671">
    <literal><![CDATA[
      (ca v cx) ^ (cx v cy) = cx v cy
    ]]></literal>
    <justification jstring="[para(2611(a,1),70(a,1,2)),rewrite(25(9),24(10)),flip(a)].">
      <j1 rule="para" parents="2611 70"/>
      <j2 rule="rewrite" parents="25 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2703">
    <literal><![CDATA[
      cx v (ca ^ cy) = cx v cy
    ]]></literal>
    <justification jstring="[back_rewrite(188),rewrite(2671(12))].">
      <j1 rule="back_rewrite" parents="188"/>
      <j2 rule="rewrite" parents="2671"/>
    </justification>
  </clause>

  <clause id="3106">
    <literal><![CDATA[
      cy ^ (ca v cb) = cy
    ]]></literal>
    <justification jstring="[para(2617(a,1),2669(a,1,2))].">
      <j1 rule="para" parents="2617 2669"/>
    </justification>
  </clause>

  <clause id="3166">
    <literal><![CDATA[
      (ca v cb) ^ (ca v cy) = ca v cy
    ]]></literal>
    <justification jstring="[para(3106(a,1),35(a,1,2)),rewrite(24(10)),flip(a)].">
      <j1 rule="para" parents="3106 35"/>
      <j2 rule="rewrite" parents="24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3436">
    <literal><![CDATA[
      B(cb,cx,ca ^ (cx v x))
    ]]></literal>
    <justification jstring="[para(2659(a,1),105(b,1,2)),rewrite(29(12),25(13),25(16),42(20),137(20),29(14)),xx(b),xx(c)].">
      <j1 rule="para" parents="2659 105"/>
      <j2 rule="rewrite" parents="29 25 25 42 137 29"/>
      <j2 rule="xx"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

  <clause id="3457">
    <literal><![CDATA[
      B(cb,cx,ca ^ cy)
    ]]></literal>
    <justification jstring="[para(152(a,1),3436(a,3))].">
      <j1 rule="para" parents="152 3436"/>
    </justification>
  </clause>

  <clause id="3459">
    <literal><![CDATA[
      (cx v cb) ^ (cx v cy) = cx
    ]]></literal>
    <justification jstring="[hyper(33,a,3457,a),rewrite(25(3),2703(8))].">
      <j1 rule="hyper" parents="33 3457"/>
      <j2 rule="rewrite" parents="25 2703"/>
    </justification>
  </clause>

  <clause id="4590">
    <literal><![CDATA[
      cb ^ (cx v cy) = cx ^ cb
    ]]></literal>
    <justification jstring="[para(3459(a,1),117(a,1,2)),rewrite(24(3)),flip(a)].">
      <j1 rule="para" parents="3459 117"/>
      <j2 rule="rewrite" parents="24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4702">
    <literal><![CDATA[
      cx ^ (cb ^ cy) = cb ^ cy
    ]]></literal>
    <justification jstring="[para(4590(a,1),120(a,1,2)),rewrite(42(5),24(4))].">
      <j1 rule="para" parents="4590 120"/>
      <j2 rule="rewrite" parents="42 24"/>
    </justification>
  </clause>

  <clause id="11726">
    <literal><![CDATA[
      cb ^ (ca v cy) = cb ^ cy
    ]]></literal>
    <justification jstring="[para(222(a,1),261(a,2)),rewrite(2661(8),42(10),4702(10))].">
      <j1 rule="para" parents="222 261"/>
      <j2 rule="rewrite" parents="2661 42 4702"/>
    </justification>
  </clause>

  <clause id="11733">
    <literal><![CDATA[
      ca v (cb ^ cy) = ca v cy
    ]]></literal>
    <justification jstring="[para(11726(a,1),35(a,1,2)),rewrite(3166(12))].">
      <j1 rule="para" parents="11726 35"/>
      <j2 rule="rewrite" parents="3166"/>
    </justification>
  </clause>

  <clause id="11736">
    <literal><![CDATA[
      (ca v cy) ^ (cb v cy) = cy
    ]]></literal>
    <justification jstring="[para(11726(a,1),70(a,1,2)),rewrite(49(5),25(4),25(7),24(8)),flip(a)].">
      <j1 rule="para" parents="11726 70"/>
      <j2 rule="rewrite" parents="49 25 25 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11800">
    <literal><![CDATA[
      B(ca,cy,cb)
    ]]></literal>
    <justification jstring="[para(11736(a,1),93(c,1)),rewrite(24(9),11733(10),45(9)),xx(b),xx(c)].">
      <j1 rule="para" parents="11736 93"/>
      <j2 rule="rewrite" parents="24 11733 45"/>
      <j2 rule="xx"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

  <clause id="11801">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[resolve(11800,a,40,a)].">
      <j1 rule="resolve" parents="11800 40"/>
    </justification>
  </clause>

</proof>

</proofs>
