<?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>wang2-eq.out</source>

<heading><![CDATA[
Prover9 (32) version September-2006, September 2006.
Process 26826 was started by mccune on cleo.thornwood,
Wed Sep 13 14:37:17 2006
The command was "/home/mccune/LADR/bin/prover9 -f wang-eq.in wang2-eq.in".
]]></heading>

<proof number="1" length="155" max_count="23">

<comments><![CDATA[
% Proof 1 at 10.16 (+ 0.06) seconds.
% Length of proof is 155.
% Level of proof is 57.
% Maximum clause weight is 23.
% Given clauses 1085.
]]></comments>

  <clause id="1" type="assumption">
    <literal><![CDATA[
      x = m
    ]]></literal>
    <literal><![CDATA[
      p(x,m)
    ]]></literal>
    <literal><![CDATA[
      y = m
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <literal><![CDATA[
      -p(x,y)
    ]]></literal>
    <literal><![CDATA[
      -p(y,x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="2">
    <literal><![CDATA[
      m = x
    ]]></literal>
    <literal><![CDATA[
      p(x,m)
    ]]></literal>
    <literal><![CDATA[
      m = y
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <literal><![CDATA[
      -p(x,y)
    ]]></literal>
    <literal><![CDATA[
      -p(y,x)
    ]]></literal>
    <justification jstring="[copy(1),flip(a),flip(c)].">
      <j1 rule="copy" parents="1"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5" type="assumption">
    <literal><![CDATA[
      x = k
    ]]></literal>
    <literal><![CDATA[
      x = m
    ]]></literal>
    <literal><![CDATA[
      x = b
    ]]></literal>
    <literal><![CDATA[
      -p(x,k)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="6">
    <literal><![CDATA[
      k = x
    ]]></literal>
    <literal><![CDATA[
      m = x
    ]]></literal>
    <literal><![CDATA[
      b = x
    ]]></literal>
    <literal><![CDATA[
      -p(x,k)
    ]]></literal>
    <justification jstring="[copy(5),flip(a),flip(b),flip(c)].">
      <j1 rule="copy" parents="5"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7" type="assumption">
    <literal><![CDATA[
      x = m
    ]]></literal>
    <literal><![CDATA[
      -p(x,m)
    ]]></literal>
    <literal><![CDATA[
      f(x) != m
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="8">
    <literal><![CDATA[
      m = x
    ]]></literal>
    <literal><![CDATA[
      -p(x,m)
    ]]></literal>
    <literal><![CDATA[
      f(x) != m
    ]]></literal>
    <justification jstring="[copy(7),flip(a)].">
      <j1 rule="copy" parents="7"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9" type="assumption">
    <literal><![CDATA[
      x = m
    ]]></literal>
    <literal><![CDATA[
      -p(x,m)
    ]]></literal>
    <literal><![CDATA[
      f(x) != x
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="10">
    <literal><![CDATA[
      m = x
    ]]></literal>
    <literal><![CDATA[
      -p(x,m)
    ]]></literal>
    <literal><![CDATA[
      f(x) != 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[
      x = m
    ]]></literal>
    <literal><![CDATA[
      -p(x,m)
    ]]></literal>
    <literal><![CDATA[
      p(x,f(x))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

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

  <clause id="13" type="assumption">
    <literal><![CDATA[
      x = m
    ]]></literal>
    <literal><![CDATA[
      -p(x,m)
    ]]></literal>
    <literal><![CDATA[
      p(f(x),x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="14">
    <literal><![CDATA[
      m = x
    ]]></literal>
    <literal><![CDATA[
      -p(x,m)
    ]]></literal>
    <literal><![CDATA[
      p(f(x),x)
    ]]></literal>
    <justification jstring="[copy(13),flip(a)].">
      <j1 rule="copy" parents="13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15" type="assumption">
    <literal><![CDATA[
      x = b
    ]]></literal>
    <literal><![CDATA[
      p(x,b)
    ]]></literal>
    <literal><![CDATA[
      g(x) != b
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="16">
    <literal><![CDATA[
      b = x
    ]]></literal>
    <literal><![CDATA[
      p(x,b)
    ]]></literal>
    <literal><![CDATA[
      g(x) != b
    ]]></literal>
    <justification jstring="[copy(15),flip(a)].">
      <j1 rule="copy" parents="15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17" type="assumption">
    <literal><![CDATA[
      x = b
    ]]></literal>
    <literal><![CDATA[
      p(x,b)
    ]]></literal>
    <literal><![CDATA[
      g(x) != x
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="18">
    <literal><![CDATA[
      b = x
    ]]></literal>
    <literal><![CDATA[
      p(x,b)
    ]]></literal>
    <literal><![CDATA[
      g(x) != x
    ]]></literal>
    <justification jstring="[copy(17),flip(a)].">
      <j1 rule="copy" parents="17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19" type="assumption">
    <literal><![CDATA[
      x = b
    ]]></literal>
    <literal><![CDATA[
      p(x,b)
    ]]></literal>
    <literal><![CDATA[
      p(x,g(x))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="20">
    <literal><![CDATA[
      b = x
    ]]></literal>
    <literal><![CDATA[
      p(x,b)
    ]]></literal>
    <literal><![CDATA[
      p(x,g(x))
    ]]></literal>
    <justification jstring="[copy(19),flip(a)].">
      <j1 rule="copy" parents="19"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21" type="assumption">
    <literal><![CDATA[
      x = b
    ]]></literal>
    <literal><![CDATA[
      p(x,b)
    ]]></literal>
    <literal><![CDATA[
      p(g(x),x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="22">
    <literal><![CDATA[
      b = x
    ]]></literal>
    <literal><![CDATA[
      p(x,b)
    ]]></literal>
    <literal><![CDATA[
      p(g(x),x)
    ]]></literal>
    <justification jstring="[copy(21),flip(a)].">
      <j1 rule="copy" parents="21"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23" type="assumption">
    <literal><![CDATA[
      x = k
    ]]></literal>
    <literal><![CDATA[
      x != m
    ]]></literal>
    <literal><![CDATA[
      p(x,k)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="24">
    <literal><![CDATA[
      k = x
    ]]></literal>
    <literal><![CDATA[
      m != x
    ]]></literal>
    <literal><![CDATA[
      p(x,k)
    ]]></literal>
    <justification jstring="[copy(23),flip(a),flip(b)].">
      <j1 rule="copy" parents="23"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25" type="assumption">
    <literal><![CDATA[
      x = k
    ]]></literal>
    <literal><![CDATA[
      x != b
    ]]></literal>
    <literal><![CDATA[
      p(x,k)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="26">
    <literal><![CDATA[
      k = x
    ]]></literal>
    <literal><![CDATA[
      b != x
    ]]></literal>
    <literal><![CDATA[
      p(x,k)
    ]]></literal>
    <justification jstring="[copy(25),flip(a),flip(b)].">
      <j1 rule="copy" parents="25"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27" type="assumption">
    <literal><![CDATA[
      m != b
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="28" type="assumption">
    <literal><![CDATA[
      b = k
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="29">
    <literal><![CDATA[
      k = b
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[copy(28),flip(a)].">
      <j1 rule="copy" parents="28"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30" type="assumption">
    <literal><![CDATA[
      x = j
    ]]></literal>
    <literal><![CDATA[
      -p(x,j)
    ]]></literal>
    <literal><![CDATA[
      x = k
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="31">
    <literal><![CDATA[
      j = x
    ]]></literal>
    <literal><![CDATA[
      -p(x,j)
    ]]></literal>
    <literal><![CDATA[
      k = x
    ]]></literal>
    <justification jstring="[copy(30),flip(a),flip(c)].">
      <j1 rule="copy" parents="30"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32" type="assumption">
    <literal><![CDATA[
      x = j
    ]]></literal>
    <literal><![CDATA[
      p(x,j)
    ]]></literal>
    <literal><![CDATA[
      x != k
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="33">
    <literal><![CDATA[
      j = x
    ]]></literal>
    <literal><![CDATA[
      p(x,j)
    ]]></literal>
    <literal><![CDATA[
      k != x
    ]]></literal>
    <justification jstring="[copy(32),flip(a),flip(c)].">
      <j1 rule="copy" parents="32"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="51">
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      p(m,k)
    ]]></literal>
    <justification jstring="[xx_res(24,b)].">
      <j1 rule="xx_res" parents="24"/>
    </justification>
  </clause>

  <clause id="52">
    <literal><![CDATA[
      k = x
    ]]></literal>
    <literal><![CDATA[
      p(x,k)
    ]]></literal>
    <literal><![CDATA[
      p(x,b)
    ]]></literal>
    <literal><![CDATA[
      p(g(x),x)
    ]]></literal>
    <justification jstring="[resolve(26,b,22,a)].">
      <j1 rule="resolve" parents="26 22"/>
    </justification>
  </clause>

  <clause id="53">
    <literal><![CDATA[
      k = x
    ]]></literal>
    <literal><![CDATA[
      p(x,k)
    ]]></literal>
    <literal><![CDATA[
      p(x,b)
    ]]></literal>
    <literal><![CDATA[
      p(x,g(x))
    ]]></literal>
    <justification jstring="[resolve(26,b,20,a)].">
      <j1 rule="resolve" parents="26 20"/>
    </justification>
  </clause>

  <clause id="54">
    <literal><![CDATA[
      k = b
    ]]></literal>
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <justification jstring="[xx_res(26,b)].">
      <j1 rule="xx_res" parents="26"/>
    </justification>
  </clause>

  <clause id="57">
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      p(g(m),m)
    ]]></literal>
    <justification jstring="[resolve(27,a,22,a(flip))].">
      <j1 rule="resolve" parents="27 22"/>
    </justification>
  </clause>

  <clause id="59">
    <literal><![CDATA[
      p(x,b)
    ]]></literal>
    <literal><![CDATA[
      p(x,g(x))
    ]]></literal>
    <literal><![CDATA[
      m != x
    ]]></literal>
    <justification jstring="[para(20(a,1),27(a,2))].">
      <j1 rule="para" parents="20 27"/>
    </justification>
  </clause>

  <clause id="60">
    <literal><![CDATA[
      p(x,b)
    ]]></literal>
    <literal><![CDATA[
      p(g(x),x)
    ]]></literal>
    <literal><![CDATA[
      m != x
    ]]></literal>
    <justification jstring="[para(22(a,1),27(a,2))].">
      <j1 rule="para" parents="22 27"/>
    </justification>
  </clause>

  <clause id="61">
    <literal><![CDATA[
      k = b
    ]]></literal>
    <literal><![CDATA[
      k = x
    ]]></literal>
    <literal><![CDATA[
      m = x
    ]]></literal>
    <literal><![CDATA[
      b = x
    ]]></literal>
    <literal><![CDATA[
      -p(x,m)
    ]]></literal>
    <justification jstring="[para(29(b,1),6(d,2))].">
      <j1 rule="para" parents="29 6"/>
    </justification>
  </clause>

  <clause id="65">
    <literal><![CDATA[
      j = k
    ]]></literal>
    <literal><![CDATA[
      p(k,j)
    ]]></literal>
    <justification jstring="[xx_res(33,c)].">
      <j1 rule="xx_res" parents="33"/>
    </justification>
  </clause>

  <clause id="75">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(m,k)
    ]]></literal>
    <justification jstring="[para(54(a,1),51(a,1)),flip(b),unit_del(b,27)].">
      <j1 rule="para" parents="54 51"/>
      <j2 rule="flip"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="77">
    <literal><![CDATA[
      p(k,j)
    ]]></literal>
    <literal><![CDATA[
      j = x
    ]]></literal>
    <literal><![CDATA[
      -p(x,k)
    ]]></literal>
    <literal><![CDATA[
      k = x
    ]]></literal>
    <justification jstring="[para(65(a,1),31(b,2))].">
      <j1 rule="para" parents="65 31"/>
    </justification>
  </clause>

  <clause id="98">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <justification jstring="[para(54(a,1),75(b,2)),merge(b)].">
      <j1 rule="para" parents="54 75"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="101">
    <literal><![CDATA[
      p(x,b)
    ]]></literal>
    <literal><![CDATA[
      p(g(x),x)
    ]]></literal>
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(m,x)
    ]]></literal>
    <justification jstring="[para(22(a,1),98(b,2))].">
      <j1 rule="para" parents="22 98"/>
    </justification>
  </clause>

  <clause id="136">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,g(k))
    ]]></literal>
    <literal><![CDATA[
      p(m,k)
    ]]></literal>
    <justification jstring="[resolve(59,c,51,a(flip))].">
      <j1 rule="resolve" parents="59 51"/>
    </justification>
  </clause>

  <clause id="142">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(g(k),k)
    ]]></literal>
    <literal><![CDATA[
      p(m,k)
    ]]></literal>
    <justification jstring="[resolve(60,c,51,a(flip))].">
      <j1 rule="resolve" parents="60 51"/>
    </justification>
  </clause>

  <clause id="157">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(m,k)
    ]]></literal>
    <literal><![CDATA[
      g(k) = k
    ]]></literal>
    <literal><![CDATA[
      g(k) = m
    ]]></literal>
    <literal><![CDATA[
      g(k) = b
    ]]></literal>
    <justification jstring="[resolve(142,b,6,d),flip(c),flip(d),flip(e)].">
      <j1 rule="resolve" parents="142 6"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="256">
    <literal><![CDATA[
      p(k,j)
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <justification jstring="[resolve(77,c,75,b)].">
      <j1 rule="resolve" parents="77 75"/>
    </justification>
  </clause>

  <clause id="298">
    <literal><![CDATA[
      p(k,j)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <justification jstring="[para(256(b,1),65(a,1)),flip(d),merge(d),merge(e)].">
      <j1 rule="para" parents="256 65"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="304">
    <literal><![CDATA[
      p(k,j)
    ]]></literal>
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <justification jstring="[para(298(b,1),54(a,1)),merge(d),unit_del(c,27)].">
      <j1 rule="para" parents="298 54"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="307">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(b,j)
    ]]></literal>
    <justification jstring="[para(54(a,1),304(a,1)),merge(c)].">
      <j1 rule="para" parents="54 304"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="309">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <literal><![CDATA[
      -p(j,b)
    ]]></literal>
    <justification jstring="[resolve(307,b,2,e),flip(d),unit_del(b,27)].">
      <j1 rule="resolve" parents="307 2"/>
      <j2 rule="flip"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="310">
    <literal><![CDATA[
      p(x,b)
    ]]></literal>
    <literal><![CDATA[
      p(x,g(x))
    ]]></literal>
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(x,j)
    ]]></literal>
    <justification jstring="[para(20(a,1),307(b,1))].">
      <j1 rule="para" parents="20 307"/>
    </justification>
  </clause>

  <clause id="321">
    <literal><![CDATA[
      p(x,k)
    ]]></literal>
    <literal><![CDATA[
      p(x,b)
    ]]></literal>
    <literal><![CDATA[
      p(g(x),x)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <literal><![CDATA[
      m = x
    ]]></literal>
    <justification jstring="[para(52(a,1),29(b,1)),flip(e)].">
      <j1 rule="para" parents="52 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="341">
    <literal><![CDATA[
      p(x,k)
    ]]></literal>
    <literal><![CDATA[
      p(x,b)
    ]]></literal>
    <literal><![CDATA[
      p(x,g(x))
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <literal><![CDATA[
      m = x
    ]]></literal>
    <justification jstring="[para(53(a,1),29(b,1)),flip(e)].">
      <j1 rule="para" parents="53 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="400">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      g(j) = j
    ]]></literal>
    <literal><![CDATA[
      g(j) = k
    ]]></literal>
    <justification jstring="[resolve(101,b,31,b),flip(d),flip(e)].">
      <j1 rule="resolve" parents="101 31"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="556">
    <literal><![CDATA[
      p(x,b)
    ]]></literal>
    <literal><![CDATA[
      p(x,g(x))
    ]]></literal>
    <literal><![CDATA[
      p(y,b)
    ]]></literal>
    <literal><![CDATA[
      p(y,g(y))
    ]]></literal>
    <literal><![CDATA[
      p(x,k)
    ]]></literal>
    <literal><![CDATA[
      p(y,j)
    ]]></literal>
    <justification jstring="[para(20(a,1),310(c,1))].">
      <j1 rule="para" parents="20 310"/>
    </justification>
  </clause>

  <clause id="570">
    <literal><![CDATA[
      p(x,b)
    ]]></literal>
    <literal><![CDATA[
      p(x,g(x))
    ]]></literal>
    <literal><![CDATA[
      p(x,k)
    ]]></literal>
    <literal><![CDATA[
      p(x,j)
    ]]></literal>
    <justification jstring="[factor(556,a,c),merge(c)].">
      <j1 rule="factor" parents="556"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="1538">
    <literal><![CDATA[
      p(x,k)
    ]]></literal>
    <literal><![CDATA[
      p(x,b)
    ]]></literal>
    <literal><![CDATA[
      p(g(x),x)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[resolve(321,e,60,c),merge(e),merge(f)].">
      <j1 rule="resolve" parents="321 60"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="1605">
    <literal><![CDATA[
      p(x,k)
    ]]></literal>
    <literal><![CDATA[
      p(x,b)
    ]]></literal>
    <literal><![CDATA[
      p(x,g(x))
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[resolve(341,e,59,c),merge(e),merge(f)].">
      <j1 rule="resolve" parents="341 59"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="1624">
    <literal><![CDATA[
      p(x,k)
    ]]></literal>
    <literal><![CDATA[
      p(x,b)
    ]]></literal>
    <literal><![CDATA[
      p(x,g(x))
    ]]></literal>
    <literal><![CDATA[
      p(m,k)
    ]]></literal>
    <justification jstring="[para(1605(d,1),51(a,1)),flip(d),unit_del(d,27)].">
      <j1 rule="para" parents="1605 51"/>
      <j2 rule="flip"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="1650">
    <literal><![CDATA[
      p(x,k)
    ]]></literal>
    <literal><![CDATA[
      p(x,b)
    ]]></literal>
    <literal><![CDATA[
      p(x,g(x))
    ]]></literal>
    <literal><![CDATA[
      p(y,k)
    ]]></literal>
    <literal><![CDATA[
      p(y,b)
    ]]></literal>
    <literal><![CDATA[
      p(y,g(y))
    ]]></literal>
    <literal><![CDATA[
      p(m,x)
    ]]></literal>
    <justification jstring="[para(53(a,1),1624(d,2))].">
      <j1 rule="para" parents="53 1624"/>
    </justification>
  </clause>

  <clause id="1657">
    <literal><![CDATA[
      p(x,k)
    ]]></literal>
    <literal><![CDATA[
      p(x,b)
    ]]></literal>
    <literal><![CDATA[
      p(x,g(x))
    ]]></literal>
    <literal><![CDATA[
      p(y,k)
    ]]></literal>
    <literal><![CDATA[
      p(y,b)
    ]]></literal>
    <literal><![CDATA[
      p(y,g(y))
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <justification jstring="[para(1605(d,1),1624(d,2))].">
      <j1 rule="para" parents="1605 1624"/>
    </justification>
  </clause>

  <clause id="1665">
    <literal><![CDATA[
      p(x,k)
    ]]></literal>
    <literal><![CDATA[
      p(x,b)
    ]]></literal>
    <literal><![CDATA[
      p(x,g(x))
    ]]></literal>
    <literal><![CDATA[
      p(m,x)
    ]]></literal>
    <justification jstring="[factor(1650,a,d),merge(d),merge(e)].">
      <j1 rule="factor" parents="1650"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="1669">
    <literal><![CDATA[
      p(x,k)
    ]]></literal>
    <literal><![CDATA[
      p(x,b)
    ]]></literal>
    <literal><![CDATA[
      p(x,g(x))
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <justification jstring="[factor(1657,a,d),merge(d),merge(e)].">
      <j1 rule="factor" parents="1657"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="1684">
    <literal><![CDATA[
      p(j,k)
    ]]></literal>
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(j,g(j))
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[resolve(1665,d,31,b)].">
      <j1 rule="resolve" parents="1665 31"/>
    </justification>
  </clause>

  <clause id="2217">
    <literal><![CDATA[
      p(j,k)
    ]]></literal>
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(j,g(j))
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[resolve(1684,d,59,c(flip)),merge(e),merge(f)].">
      <j1 rule="resolve" parents="1684 59"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="2231">
    <literal><![CDATA[
      p(j,k)
    ]]></literal>
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(j,g(j))
    ]]></literal>
    <literal><![CDATA[
      p(x,k)
    ]]></literal>
    <literal><![CDATA[
      p(x,b)
    ]]></literal>
    <literal><![CDATA[
      p(x,g(x))
    ]]></literal>
    <justification jstring="[para(2217(d,1),1605(d,1)),unit_del(g,27)].">
      <j1 rule="para" parents="2217 1605"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="2235">
    <literal><![CDATA[
      p(j,k)
    ]]></literal>
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(j,g(j))
    ]]></literal>
    <justification jstring="[factor(2231,a,d),merge(d),merge(e)].">
      <j1 rule="factor" parents="2231"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="2314">
    <literal><![CDATA[
      p(m,k)
    ]]></literal>
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      g(k) = m
    ]]></literal>
    <literal><![CDATA[
      g(k) = b
    ]]></literal>
    <justification jstring="[para(51(a,1),157(c,2)),merge(c),merge(e)].">
      <j1 rule="para" parents="51 157"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="2703">
    <literal><![CDATA[
      p(m,k)
    ]]></literal>
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      g(k) = b
    ]]></literal>
    <justification jstring="[para(2314(c,1),142(b,1)),merge(d),merge(e),merge(f)].">
      <j1 rule="para" parents="2314 142"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="2712">
    <literal><![CDATA[
      p(m,k)
    ]]></literal>
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <justification jstring="[para(2703(c,1),136(b,2)),merge(c),merge(d),merge(e)].">
      <j1 rule="para" parents="2703 136"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="2720">
    <literal><![CDATA[
      p(m,k)
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <justification jstring="[para(51(a,1),2712(b,1)),merge(b)].">
      <j1 rule="para" parents="51 2712"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="2726">
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,j)
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[resolve(2720,a,77,c)].">
      <j1 rule="resolve" parents="2720 77"/>
    </justification>
  </clause>

  <clause id="2738">
    <literal><![CDATA[
      p(x,k)
    ]]></literal>
    <literal><![CDATA[
      p(x,b)
    ]]></literal>
    <literal><![CDATA[
      p(g(x),x)
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <justification jstring="[para(1538(d,1),2720(a,2)),merge(e)].">
      <j1 rule="para" parents="1538 2720"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="2883">
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,j)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[para(2726(c,1),65(a,1)),flip(d),merge(d),merge(e)].">
      <j1 rule="para" parents="2726 65"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="2888">
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,j)
    ]]></literal>
    <literal><![CDATA[
      j = x
    ]]></literal>
    <literal><![CDATA[
      -p(x,m)
    ]]></literal>
    <literal><![CDATA[
      k = x
    ]]></literal>
    <justification jstring="[para(2883(c,1),77(c,2)),merge(c)].">
      <j1 rule="para" parents="2883 77"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="3297">
    <literal><![CDATA[
      p(j,k)
    ]]></literal>
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      g(j) = j
    ]]></literal>
    <literal><![CDATA[
      g(j) = k
    ]]></literal>
    <justification jstring="[resolve(2738,c,31,b),flip(d),flip(e)].">
      <j1 rule="resolve" parents="2738 31"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4075">
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,j)
    ]]></literal>
    <literal><![CDATA[
      g(m) = j
    ]]></literal>
    <literal><![CDATA[
      g(m) = k
    ]]></literal>
    <justification jstring="[resolve(2888,d,57,b),flip(c),flip(d),merge(e)].">
      <j1 rule="resolve" parents="2888 57"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="4078">
    <literal><![CDATA[
      p(k,j)
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      g(m) = k
    ]]></literal>
    <justification jstring="[para(65(a,1),4075(c,2)),merge(c),merge(e)].">
      <j1 rule="para" parents="65 4075"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="4081">
    <literal><![CDATA[
      p(k,j)
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      k != m
    ]]></literal>
    <justification jstring="[para(4078(c,1),18(c,1)),flip(c),merge(d),unit_del(c,27)].">
      <j1 rule="para" parents="4078 18"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="4111">
    <literal><![CDATA[
      p(k,j)
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <justification jstring="[resolve(4081,c,2883,c),merge(c),merge(d)].">
      <j1 rule="resolve" parents="4081 2883"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="4128">
    <literal><![CDATA[
      k = b
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <justification jstring="[para(29(b,1),4111(a,1))].">
      <j1 rule="para" parents="29 4111"/>
    </justification>
  </clause>

  <clause id="4140">
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <justification jstring="[para(4128(a,1),2720(a,2)),merge(c),merge(d)].">
      <j1 rule="para" parents="4128 2720"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="4153">
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[resolve(4140,a,31,b)].">
      <j1 rule="resolve" parents="4140 31"/>
    </justification>
  </clause>

  <clause id="4161">
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(g(j),j)
    ]]></literal>
    <justification jstring="[resolve(4153,b,60,c(flip))].">
      <j1 rule="resolve" parents="4153 60"/>
    </justification>
  </clause>

  <clause id="5736">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      g(j) = k
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <justification jstring="[resolve(400,d,18,c),flip(e),merge(f)].">
      <j1 rule="resolve" parents="400 18"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="5745">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <literal><![CDATA[
      k != b
    ]]></literal>
    <justification jstring="[para(5736(d,1),16(c,1)),flip(e),merge(e),merge(f)].">
      <j1 rule="para" parents="5736 16"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="5771">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <justification jstring="[resolve(5745,e,54,a),merge(e)].">
      <j1 rule="resolve" parents="5745 54"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="5791">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      j = k
    ]]></literal>
    <literal><![CDATA[
      p(j,k)
    ]]></literal>
    <justification jstring="[resolve(5771,d,26,b(flip)),flip(d)].">
      <j1 rule="resolve" parents="5771 26"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5885">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      p(j,k)
    ]]></literal>
    <justification jstring="[para(5791(d,1),307(b,2)),merge(e),merge(f)].">
      <j1 rule="para" parents="5791 307"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="5888">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <justification jstring="[para(54(a,1),5885(d,2)),merge(c),merge(e)].">
      <j1 rule="para" parents="54 5885"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="5911">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <justification jstring="[resolve(5888,b,309,e),merge(c)].">
      <j1 rule="resolve" parents="5888 309"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="5924">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <justification jstring="[para(5911(d,1),307(b,2)),merge(e),merge(f)].">
      <j1 rule="para" parents="5911 307"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="5929">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      j = k
    ]]></literal>
    <literal><![CDATA[
      p(j,k)
    ]]></literal>
    <justification jstring="[resolve(5924,d,26,b(flip)),flip(d)].">
      <j1 rule="resolve" parents="5924 26"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6034">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      p(j,k)
    ]]></literal>
    <justification jstring="[para(5929(d,1),307(b,2)),merge(e),merge(f)].">
      <j1 rule="para" parents="5929 307"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="6043">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <justification jstring="[para(5924(d,1),6034(d,1)),merge(d),merge(e),merge(f),merge(g)].">
      <j1 rule="para" parents="5924 6034"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="6046">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[resolve(6043,b,31,b)].">
      <j1 rule="resolve" parents="6043 31"/>
    </justification>
  </clause>

  <clause id="6053">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[para(6046(c,1),307(b,2)),merge(d),merge(e)].">
      <j1 rule="para" parents="6046 307"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="6060">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <justification jstring="[para(6053(c,1),54(a,1)),merge(d),unit_del(c,27)].">
      <j1 rule="para" parents="6053 54"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="6084">
    <literal><![CDATA[
      k = b
    ]]></literal>
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <justification jstring="[para(29(b,1),6060(a,2)),merge(c)].">
      <j1 rule="para" parents="29 6060"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="6085">
    <literal><![CDATA[
      p(m,k)
    ]]></literal>
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <justification jstring="[para(51(a,1),6060(a,2)),merge(c)].">
      <j1 rule="para" parents="51 6060"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="6157">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      p(k,j)
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[resolve(6085,a,77,c)].">
      <j1 rule="resolve" parents="6085 77"/>
    </justification>
  </clause>

  <clause id="6290">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      p(k,j)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[para(6157(c,1),65(a,1)),flip(d),merge(d),merge(e)].">
      <j1 rule="para" parents="6157 65"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="6313">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      p(k,j)
    ]]></literal>
    <justification jstring="[para(6290(c,1),6060(a,2)),merge(c),merge(d)].">
      <j1 rule="para" parents="6290 6060"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="6326">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      p(b,j)
    ]]></literal>
    <justification jstring="[para(6084(a,1),6313(b,1)),merge(b)].">
      <j1 rule="para" parents="6084 6313"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="6329">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <literal><![CDATA[
      -p(j,b)
    ]]></literal>
    <justification jstring="[resolve(6326,b,2,e),flip(d),merge(c),unit_del(b,27)].">
      <j1 rule="resolve" parents="6326 2"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="10963">
    <literal><![CDATA[
      p(j,k)
    ]]></literal>
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      g(j) = k
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <justification jstring="[resolve(3297,d,18,c),flip(e),merge(f)].">
      <j1 rule="resolve" parents="3297 18"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="10975">
    <literal><![CDATA[
      p(j,k)
    ]]></literal>
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <justification jstring="[para(10963(d,1),1669(c,2)),merge(e),merge(f),merge(g),merge(h)].">
      <j1 rule="para" parents="10963 1669"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="11078">
    <literal><![CDATA[
      p(j,k)
    ]]></literal>
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <justification jstring="[para(10975(d,1),4140(a,2)),merge(d),merge(e)].">
      <j1 rule="para" parents="10975 4140"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="11087">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      j = k
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <justification jstring="[resolve(11078,a,6,d),flip(c),flip(d),flip(e)].">
      <j1 rule="resolve" parents="11078 6"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11587">
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(g(j),j)
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <justification jstring="[para(4161(b,1),11087(c,2)),merge(d),merge(e),merge(g)].">
      <j1 rule="para" parents="4161 11087"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="11816">
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(g(j),j)
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <justification jstring="[resolve(11587,d,60,c(flip)),merge(e),merge(f)].">
      <j1 rule="resolve" parents="11587 60"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="11822">
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(g(j),j)
    ]]></literal>
    <justification jstring="[para(11816(d,1),4140(a,2)),merge(d),merge(e)].">
      <j1 rule="para" parents="11816 4140"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="11834">
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      g(j) = j
    ]]></literal>
    <literal><![CDATA[
      g(j) = k
    ]]></literal>
    <justification jstring="[resolve(11822,c,31,b),flip(c),flip(d)].">
      <j1 rule="resolve" parents="11822 31"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11871">
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      g(j) = k
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <justification jstring="[resolve(11834,c,18,c),flip(d),merge(e)].">
      <j1 rule="resolve" parents="11834 18"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="11887">
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <literal><![CDATA[
      j != k
    ]]></literal>
    <justification jstring="[para(11871(c,1),18(c,1)),flip(d),flip(f),merge(d),merge(e)].">
      <j1 rule="para" parents="11871 18"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="11922">
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <justification jstring="[resolve(11887,d,11087,c),merge(d),merge(e),merge(g)].">
      <j1 rule="resolve" parents="11887 11087"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="11961">
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <literal><![CDATA[
      k != m
    ]]></literal>
    <justification jstring="[para(11922(d,1),11887(d,1)),flip(g),merge(d),merge(e),merge(f)].">
      <j1 rule="para" parents="11922 11887"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="11971">
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[resolve(11961,d,29,b)].">
      <j1 rule="resolve" parents="11961 29"/>
    </justification>
  </clause>

  <clause id="11983">
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[para(11971(c,1),4140(a,2)),merge(d),merge(e)].">
      <j1 rule="para" parents="11971 4140"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="11993">
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <justification jstring="[para(11983(c,1),2720(a,2)),merge(c),merge(d)].">
      <j1 rule="para" parents="11983 2720"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="12010">
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[para(4153(b,1),11993(b,1)),merge(c),merge(d)].">
      <j1 rule="para" parents="4153 11993"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="12011">
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      k = x
    ]]></literal>
    <literal><![CDATA[
      m = x
    ]]></literal>
    <literal><![CDATA[
      b = x
    ]]></literal>
    <literal><![CDATA[
      -p(x,m)
    ]]></literal>
    <justification jstring="[para(12010(b,1),6(d,2))].">
      <j1 rule="para" parents="12010 6"/>
    </justification>
  </clause>

  <clause id="12067">
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      g(m) = k
    ]]></literal>
    <literal><![CDATA[
      g(m) = m
    ]]></literal>
    <literal><![CDATA[
      g(m) = b
    ]]></literal>
    <justification jstring="[resolve(12011,e,57,b),flip(b),flip(c),flip(d),merge(e)].">
      <j1 rule="resolve" parents="12011 57"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="12094">
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      g(m) = m
    ]]></literal>
    <literal><![CDATA[
      g(m) = b
    ]]></literal>
    <justification jstring="[para(12010(b,1),12067(b,2)),merge(b),merge(d)].">
      <j1 rule="para" parents="12010 12067"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="12103">
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      g(m) = b
    ]]></literal>
    <justification jstring="[resolve(12094,b,18,c),flip(c),merge(d),unit_del(c,27)].">
      <j1 rule="resolve" parents="12094 18"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="12108">
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <justification jstring="[resolve(12103,b,16,c),flip(b),merge(c),unit_del(b,27)].">
      <j1 rule="resolve" parents="12103 16"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="12126">
    <literal><![CDATA[
      p(x,b)
    ]]></literal>
    <literal><![CDATA[
      p(x,g(x))
    ]]></literal>
    <literal><![CDATA[
      p(m,x)
    ]]></literal>
    <justification jstring="[para(20(a,1),12108(a,2))].">
      <j1 rule="para" parents="20 12108"/>
    </justification>
  </clause>

  <clause id="12127">
    <literal><![CDATA[
      p(x,b)
    ]]></literal>
    <literal><![CDATA[
      p(g(x),x)
    ]]></literal>
    <literal><![CDATA[
      p(m,x)
    ]]></literal>
    <justification jstring="[para(22(a,1),12108(a,2))].">
      <j1 rule="para" parents="22 12108"/>
    </justification>
  </clause>

  <clause id="12164">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      g(j) = j
    ]]></literal>
    <literal><![CDATA[
      g(j) = k
    ]]></literal>
    <justification jstring="[resolve(12127,b,31,b),flip(c),flip(d)].">
      <j1 rule="resolve" parents="12127 31"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12339">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      g(j) = k
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <justification jstring="[resolve(12164,c,18,c),flip(d),merge(e)].">
      <j1 rule="resolve" parents="12164 18"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="12393">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      g(j) = k
    ]]></literal>
    <literal><![CDATA[
      p(j,j)
    ]]></literal>
    <justification jstring="[para(12164(c,1),12126(b,2)),merge(d),merge(f)].">
      <j1 rule="para" parents="12164 12126"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="12414">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <literal><![CDATA[
      p(j,k)
    ]]></literal>
    <justification jstring="[para(12339(c,1),2235(c,2)),merge(e),merge(f)].">
      <j1 rule="para" parents="12339 2235"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="12814">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      p(j,j)
    ]]></literal>
    <literal><![CDATA[
      p(j,k)
    ]]></literal>
    <justification jstring="[para(12393(c,1),570(b,2)),merge(d),merge(f),merge(g)].">
      <j1 rule="para" parents="12393 570"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="12831">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      p(j,k)
    ]]></literal>
    <justification jstring="[para(12414(c,1),12814(c,2)),merge(d),merge(e),merge(f),merge(g)].">
      <j1 rule="para" parents="12414 12814"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="12852">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <justification jstring="[para(6084(a,1),12831(c,2)),merge(d)].">
      <j1 rule="para" parents="6084 12831"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="12856">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <justification jstring="[resolve(12852,b,6329,d),merge(c)].">
      <j1 rule="resolve" parents="12852 6329"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="12940">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <justification jstring="[para(12856(c,1),6326(b,2)),merge(d),merge(e)].">
      <j1 rule="para" parents="12856 6326"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="12944">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      j = x
    ]]></literal>
    <literal><![CDATA[
      -p(x,b)
    ]]></literal>
    <literal><![CDATA[
      k = x
    ]]></literal>
    <justification jstring="[para(12940(c,1),31(b,2))].">
      <j1 rule="para" parents="12940 31"/>
    </justification>
  </clause>

  <clause id="14264">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[resolve(12944,d,12108,a)].">
      <j1 rule="resolve" parents="12944 12108"/>
    </justification>
  </clause>

  <clause id="14267">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[para(14264(c,1),6326(b,2)),merge(d),merge(e)].">
      <j1 rule="para" parents="14264 6326"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="14309">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <justification jstring="[para(14267(c,1),6060(a,2)),merge(c),merge(d)].">
      <j1 rule="para" parents="14267 6060"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="14311">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[resolve(14309,b,31,b)].">
      <j1 rule="resolve" parents="14309 31"/>
    </justification>
  </clause>

  <clause id="14326">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[para(14311(b,1),6326(b,2)),merge(c),merge(d)].">
      <j1 rule="para" parents="14311 6326"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="14333">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <justification jstring="[para(14326(b,1),6060(a,2)),merge(b),merge(c)].">
      <j1 rule="para" parents="14326 6060"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="14375">
    <literal><![CDATA[
      p(f(b),b)
    ]]></literal>
    <justification jstring="[resolve(14333,a,14,b),unit_del(a,27)].">
      <j1 rule="resolve" parents="14333 14"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="14376">
    <literal><![CDATA[
      p(b,f(b))
    ]]></literal>
    <justification jstring="[resolve(14333,a,12,b),unit_del(a,27)].">
      <j1 rule="resolve" parents="14333 12"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="14377">
    <literal><![CDATA[
      f(b) != b
    ]]></literal>
    <justification jstring="[ur(10,a,27,a,b,14333,a)].">
      <j1 rule="ur" parents="10 27 14333"/>
    </justification>
  </clause>

  <clause id="14378">
    <literal><![CDATA[
      f(b) != m
    ]]></literal>
    <justification jstring="[ur(8,a,27,a,b,14333,a)].">
      <j1 rule="ur" parents="8 27 14333"/>
    </justification>
  </clause>

  <clause id="14436">
    <literal><![CDATA[
      p(f(b),m)
    ]]></literal>
    <justification jstring="[resolve(14375,a,2,e),flip(a),flip(d),unit_del(a,14378),unit_del(c,27),unit_del(d,14377),unit_del(e,14376)].">
      <j1 rule="resolve" parents="14375 2"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="unit_del" parents="14378"/>
      <j2 rule="unit_del" parents="27"/>
      <j2 rule="unit_del" parents="14377"/>
      <j2 rule="unit_del" parents="14376"/>
    </justification>
  </clause>

  <clause id="14501">
    <literal><![CDATA[
      k = b
    ]]></literal>
    <literal><![CDATA[
      f(b) = k
    ]]></literal>
    <justification jstring="[resolve(14436,a,61,e),flip(b),flip(c),flip(d),unit_del(c,14378),unit_del(d,14377)].">
      <j1 rule="resolve" parents="14436 61"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="unit_del" parents="14378"/>
      <j2 rule="unit_del" parents="14377"/>
    </justification>
  </clause>

  <clause id="14645">
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[para(29(b,1),14501(b,2)),merge(b),unit_del(b,14378)].">
      <j1 rule="para" parents="29 14501"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="14378"/>
    </justification>
  </clause>

  <clause id="14793">
    <literal><![CDATA[
      b = x
    ]]></literal>
    <literal><![CDATA[
      m = x
    ]]></literal>
    <literal><![CDATA[
      -p(x,b)
    ]]></literal>
    <justification jstring="[back_rewrite(6),rewrite(14645(1),14645(7)),merge(c)].">
      <j1 rule="back_rewrite" parents="6"/>
      <j2 rule="rewrite" parents="14645 14645"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="14805">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[resolve(14793,c,14375,a),flip(a),flip(b),unit_del(a,14377),unit_del(b,14378)].">
      <j1 rule="resolve" parents="14793 14375"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="unit_del" parents="14377"/>
      <j2 rule="unit_del" parents="14378"/>
    </justification>
  </clause>

</proof>

</proofs>
