<?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 March-2007, March 2007.
Process 21143 was started by mccune on cleo,
Mon Mar 19 17:05:50 2007
The command was "/home/mccune/bin/prover9 -f wang-eq.in wang2-eq.in".
]]></heading>

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

<comments><![CDATA[
% Proof 1 at 9.36 (+ 0.03) seconds.
% Length of proof is 155.
% Level of proof is 57.
% Maximum clause weight is 23.
% Given clauses 1088.
]]></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="93">
    <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="95">
    <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),93(b,2)),merge(b)].">
      <j1 rule="para" parents="54 93"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="105">
    <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="159">
    <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="280">
    <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(95,c,93,b)].">
      <j1 rule="resolve" parents="95 93"/>
    </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(280(b,1),65(a,1)),flip(d),merge(d),merge(e)].">
      <j1 rule="para" parents="280 65"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="308">
    <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="311">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(b,j)
    ]]></literal>
    <justification jstring="[para(54(a,1),308(a,1)),merge(c)].">
      <j1 rule="para" parents="54 308"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="313">
    <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(311,b,2,e),flip(d),unit_del(b,27)].">
      <j1 rule="resolve" parents="311 2"/>
      <j2 rule="flip"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="314">
    <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),311(b,1))].">
      <j1 rule="para" parents="20 311"/>
    </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(105,b,31,b),flip(d),flip(e)].">
      <j1 rule="resolve" parents="105 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),314(c,1))].">
      <j1 rule="para" parents="20 314"/>
    </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="1542">
    <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="1625">
    <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),1625(d,2))].">
      <j1 rule="para" parents="53 1625"/>
    </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),1625(d,2))].">
      <j1 rule="para" parents="1605 1625"/>
    </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="1693">
    <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="2224">
    <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(1693,d,59,c(flip)),merge(e),merge(f)].">
      <j1 rule="resolve" parents="1693 59"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="2238">
    <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(2224(d,1),1605(d,1)),unit_del(g,27)].">
      <j1 rule="para" parents="2224 1605"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="2242">
    <literal><![CDATA[
      p(j,k)
    ]]></literal>
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(j,g(j))
    ]]></literal>
    <justification jstring="[factor(2238,a,d),merge(d),merge(e)].">
      <j1 rule="factor" parents="2238"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="2323">
    <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),159(c,2)),merge(c),merge(e)].">
      <j1 rule="para" parents="51 159"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="2721">
    <literal><![CDATA[
      p(m,k)
    ]]></literal>
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      g(k) = b
    ]]></literal>
    <justification jstring="[para(2323(c,1),142(b,1)),merge(d),merge(e),merge(f)].">
      <j1 rule="para" parents="2323 142"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="2730">
    <literal><![CDATA[
      p(m,k)
    ]]></literal>
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <justification jstring="[para(2721(c,1),136(b,2)),merge(c),merge(d),merge(e)].">
      <j1 rule="para" parents="2721 136"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="2739">
    <literal><![CDATA[
      p(m,k)
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <justification jstring="[para(51(a,1),2730(b,1)),merge(b)].">
      <j1 rule="para" parents="51 2730"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="2743">
    <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(2739,a,95,c)].">
      <j1 rule="resolve" parents="2739 95"/>
    </justification>
  </clause>

  <clause id="2756">
    <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(1542(d,1),2739(a,2)),merge(e)].">
      <j1 rule="para" parents="1542 2739"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="2901">
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,j)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[para(2743(c,1),65(a,1)),flip(d),merge(d),merge(e)].">
      <j1 rule="para" parents="2743 65"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="2906">
    <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(2901(c,1),95(c,2)),merge(c)].">
      <j1 rule="para" parents="2901 95"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="3315">
    <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(2756,c,31,b),flip(d),flip(e)].">
      <j1 rule="resolve" parents="2756 31"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4092">
    <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(2906,d,57,b),flip(c),flip(d),merge(e)].">
      <j1 rule="resolve" parents="2906 57"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="4095">
    <literal><![CDATA[
      p(k,j)
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      g(m) = k
    ]]></literal>
    <justification jstring="[para(65(a,1),4092(c,2)),merge(c),merge(e)].">
      <j1 rule="para" parents="65 4092"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="4098">
    <literal><![CDATA[
      p(k,j)
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      k != m
    ]]></literal>
    <justification jstring="[para(4095(c,1),18(c,1)),flip(c),merge(d),unit_del(c,27)].">
      <j1 rule="para" parents="4095 18"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="4128">
    <literal><![CDATA[
      p(k,j)
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <justification jstring="[resolve(4098,c,2901,c),merge(c),merge(d)].">
      <j1 rule="resolve" parents="4098 2901"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="4145">
    <literal><![CDATA[
      k = b
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <justification jstring="[para(29(b,1),4128(a,1))].">
      <j1 rule="para" parents="29 4128"/>
    </justification>
  </clause>

  <clause id="4157">
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <justification jstring="[para(4145(a,1),2739(a,2)),merge(c),merge(d)].">
      <j1 rule="para" parents="4145 2739"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="4170">
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[resolve(4157,a,31,b)].">
      <j1 rule="resolve" parents="4157 31"/>
    </justification>
  </clause>

  <clause id="4178">
    <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(4170,b,60,c(flip))].">
      <j1 rule="resolve" parents="4170 60"/>
    </justification>
  </clause>

  <clause id="5761">
    <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="5770">
    <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(5761(d,1),16(c,1)),flip(e),merge(e),merge(f)].">
      <j1 rule="para" parents="5761 16"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="5796">
    <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(5770,e,54,a),merge(e)].">
      <j1 rule="resolve" parents="5770 54"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="5827">
    <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(5796,d,26,b(flip)),flip(d)].">
      <j1 rule="resolve" parents="5796 26"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5912">
    <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(5827(d,1),311(b,2)),merge(e),merge(f)].">
      <j1 rule="para" parents="5827 311"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="5915">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <justification jstring="[para(54(a,1),5912(d,2)),merge(c),merge(e)].">
      <j1 rule="para" parents="54 5912"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="5925">
    <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(5915,b,313,e),merge(c)].">
      <j1 rule="resolve" parents="5915 313"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="5938">
    <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(5925(d,1),311(b,2)),merge(e),merge(f)].">
      <j1 rule="para" parents="5925 311"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="5943">
    <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(5938,d,26,b(flip)),flip(d)].">
      <j1 rule="resolve" parents="5938 26"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6043">
    <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(5943(d,1),311(b,2)),merge(e),merge(f)].">
      <j1 rule="para" parents="5943 311"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="6059">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <justification jstring="[para(5938(d,1),6043(d,1)),merge(d),merge(e),merge(f),merge(g)].">
      <j1 rule="para" parents="5938 6043"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="6062">
    <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(6059,b,31,b)].">
      <j1 rule="resolve" parents="6059 31"/>
    </justification>
  </clause>

  <clause id="6069">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[para(6062(c,1),311(b,2)),merge(d),merge(e)].">
      <j1 rule="para" parents="6062 311"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="6076">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <justification jstring="[para(6069(c,1),54(a,1)),merge(d),unit_del(c,27)].">
      <j1 rule="para" parents="6069 54"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="6100">
    <literal><![CDATA[
      k = b
    ]]></literal>
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <justification jstring="[para(29(b,1),6076(a,2)),merge(c)].">
      <j1 rule="para" parents="29 6076"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="6102">
    <literal><![CDATA[
      p(m,k)
    ]]></literal>
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <justification jstring="[para(51(a,1),6076(a,2)),merge(c)].">
      <j1 rule="para" parents="51 6076"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="6172">
    <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(6102,a,95,c)].">
      <j1 rule="resolve" parents="6102 95"/>
    </justification>
  </clause>

  <clause id="6306">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      p(k,j)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[para(6172(c,1),65(a,1)),flip(d),merge(d),merge(e)].">
      <j1 rule="para" parents="6172 65"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="6329">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      p(k,j)
    ]]></literal>
    <justification jstring="[para(6306(c,1),6076(a,2)),merge(c),merge(d)].">
      <j1 rule="para" parents="6306 6076"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="6342">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      p(b,j)
    ]]></literal>
    <justification jstring="[para(6100(a,1),6329(b,1)),merge(b)].">
      <j1 rule="para" parents="6100 6329"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="6345">
    <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(6342,b,2,e),flip(d),merge(c),unit_del(b,27)].">
      <j1 rule="resolve" parents="6342 2"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="10987">
    <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(3315,d,18,c),flip(e),merge(f)].">
      <j1 rule="resolve" parents="3315 18"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="10999">
    <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(10987(d,1),1669(c,2)),merge(e),merge(f),merge(g),merge(h)].">
      <j1 rule="para" parents="10987 1669"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="11102">
    <literal><![CDATA[
      p(j,k)
    ]]></literal>
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <justification jstring="[para(10999(d,1),4157(a,2)),merge(d),merge(e)].">
      <j1 rule="para" parents="10999 4157"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="11111">
    <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(11102,a,6,d),flip(c),flip(d),flip(e)].">
      <j1 rule="resolve" parents="11102 6"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11611">
    <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(4178(b,1),11111(c,2)),merge(d),merge(e),merge(g)].">
      <j1 rule="para" parents="4178 11111"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="11840">
    <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(11611,d,60,c(flip)),merge(e),merge(f)].">
      <j1 rule="resolve" parents="11611 60"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="11846">
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(g(j),j)
    ]]></literal>
    <justification jstring="[para(11840(d,1),4157(a,2)),merge(d),merge(e)].">
      <j1 rule="para" parents="11840 4157"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="11858">
    <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(11846,c,31,b),flip(c),flip(d)].">
      <j1 rule="resolve" parents="11846 31"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11895">
    <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(11858,c,18,c),flip(d),merge(e)].">
      <j1 rule="resolve" parents="11858 18"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="11911">
    <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(11895(c,1),18(c,1)),flip(d),flip(f),merge(d),merge(e)].">
      <j1 rule="para" parents="11895 18"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="11946">
    <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(11911,d,11111,c),merge(d),merge(e),merge(g)].">
      <j1 rule="resolve" parents="11911 11111"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="11985">
    <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(11946(d,1),11911(d,1)),flip(g),merge(d),merge(e),merge(f)].">
      <j1 rule="para" parents="11946 11911"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="11995">
    <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(11985,d,29,b)].">
      <j1 rule="resolve" parents="11985 29"/>
    </justification>
  </clause>

  <clause id="12007">
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[para(11995(c,1),4157(a,2)),merge(d),merge(e)].">
      <j1 rule="para" parents="11995 4157"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="12017">
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <justification jstring="[para(12007(c,1),2739(a,2)),merge(c),merge(d)].">
      <j1 rule="para" parents="12007 2739"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="12034">
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[para(4170(b,1),12017(b,1)),merge(c),merge(d)].">
      <j1 rule="para" parents="4170 12017"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="12035">
    <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(12034(b,1),6(d,2))].">
      <j1 rule="para" parents="12034 6"/>
    </justification>
  </clause>

  <clause id="12091">
    <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(12035,e,57,b),flip(b),flip(c),flip(d),merge(e)].">
      <j1 rule="resolve" parents="12035 57"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="12118">
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      g(m) = m
    ]]></literal>
    <literal><![CDATA[
      g(m) = b
    ]]></literal>
    <justification jstring="[para(12034(b,1),12091(b,2)),merge(b),merge(d)].">
      <j1 rule="para" parents="12034 12091"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="12127">
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      g(m) = b
    ]]></literal>
    <justification jstring="[resolve(12118,b,18,c),flip(c),merge(d),unit_del(c,27)].">
      <j1 rule="resolve" parents="12118 18"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="12132">
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <justification jstring="[resolve(12127,b,16,c),flip(b),merge(c),unit_del(b,27)].">
      <j1 rule="resolve" parents="12127 16"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="12150">
    <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),12132(a,2))].">
      <j1 rule="para" parents="20 12132"/>
    </justification>
  </clause>

  <clause id="12151">
    <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),12132(a,2))].">
      <j1 rule="para" parents="22 12132"/>
    </justification>
  </clause>

  <clause id="12188">
    <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(12151,b,31,b),flip(c),flip(d)].">
      <j1 rule="resolve" parents="12151 31"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12363">
    <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(12188,c,18,c),flip(d),merge(e)].">
      <j1 rule="resolve" parents="12188 18"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="12417">
    <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(12188(c,1),12150(b,2)),merge(d),merge(f)].">
      <j1 rule="para" parents="12188 12150"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="12438">
    <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(12363(c,1),2242(c,2)),merge(e),merge(f)].">
      <j1 rule="para" parents="12363 2242"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="12838">
    <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(12417(c,1),570(b,2)),merge(d),merge(f),merge(g)].">
      <j1 rule="para" parents="12417 570"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="12855">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      p(j,k)
    ]]></literal>
    <justification jstring="[para(12438(c,1),12838(c,2)),merge(d),merge(e),merge(f),merge(g)].">
      <j1 rule="para" parents="12438 12838"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="12876">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <justification jstring="[para(6100(a,1),12855(c,2)),merge(d)].">
      <j1 rule="para" parents="6100 12855"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="12880">
    <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(12876,b,6345,d),merge(c)].">
      <j1 rule="resolve" parents="12876 6345"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="12965">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <justification jstring="[para(12880(c,1),6342(b,2)),merge(d),merge(e)].">
      <j1 rule="para" parents="12880 6342"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="12969">
    <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(12965(c,1),31(b,2))].">
      <j1 rule="para" parents="12965 31"/>
    </justification>
  </clause>

  <clause id="14391">
    <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(12969,d,12132,a)].">
      <j1 rule="resolve" parents="12969 12132"/>
    </justification>
  </clause>

  <clause id="14394">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[para(14391(c,1),6342(b,2)),merge(d),merge(e)].">
      <j1 rule="para" parents="14391 6342"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="14398">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <justification jstring="[para(14394(c,1),6076(a,2)),merge(c),merge(d)].">
      <j1 rule="para" parents="14394 6076"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="14400">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[resolve(14398,b,31,b)].">
      <j1 rule="resolve" parents="14398 31"/>
    </justification>
  </clause>

  <clause id="14415">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[para(14400(b,1),6342(b,2)),merge(c),merge(d)].">
      <j1 rule="para" parents="14400 6342"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="14422">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <justification jstring="[para(14415(b,1),6076(a,2)),merge(b),merge(c)].">
      <j1 rule="para" parents="14415 6076"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="14454">
    <literal><![CDATA[
      p(f(b),b)
    ]]></literal>
    <justification jstring="[resolve(14422,a,14,b),unit_del(a,27)].">
      <j1 rule="resolve" parents="14422 14"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="14455">
    <literal><![CDATA[
      p(b,f(b))
    ]]></literal>
    <justification jstring="[resolve(14422,a,12,b),unit_del(a,27)].">
      <j1 rule="resolve" parents="14422 12"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="14456">
    <literal><![CDATA[
      f(b) != b
    ]]></literal>
    <justification jstring="[ur(10,a,27,a,b,14422,a)].">
      <j1 rule="ur" parents="10 27 14422"/>
    </justification>
  </clause>

  <clause id="14457">
    <literal><![CDATA[
      f(b) != m
    ]]></literal>
    <justification jstring="[ur(8,a,27,a,b,14422,a)].">
      <j1 rule="ur" parents="8 27 14422"/>
    </justification>
  </clause>

  <clause id="14503">
    <literal><![CDATA[
      p(f(b),m)
    ]]></literal>
    <justification jstring="[resolve(14454,a,2,e),flip(a),flip(d),unit_del(a,14457),unit_del(c,27),unit_del(d,14456),unit_del(e,14455)].">
      <j1 rule="resolve" parents="14454 2"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="unit_del" parents="14457"/>
      <j2 rule="unit_del" parents="27"/>
      <j2 rule="unit_del" parents="14456"/>
      <j2 rule="unit_del" parents="14455"/>
    </justification>
  </clause>

  <clause id="14533">
    <literal><![CDATA[
      k = b
    ]]></literal>
    <literal><![CDATA[
      f(b) = k
    ]]></literal>
    <justification jstring="[resolve(14503,a,61,e),flip(b),flip(c),flip(d),unit_del(c,14457),unit_del(d,14456)].">
      <j1 rule="resolve" parents="14503 61"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="unit_del" parents="14457"/>
      <j2 rule="unit_del" parents="14456"/>
    </justification>
  </clause>

  <clause id="14718">
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[para(29(b,1),14533(b,2)),merge(b),unit_del(b,14457)].">
      <j1 rule="para" parents="29 14533"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="14457"/>
    </justification>
  </clause>

  <clause id="14858">
    <literal><![CDATA[
      b = x
    ]]></literal>
    <literal><![CDATA[
      m = x
    ]]></literal>
    <literal><![CDATA[
      -p(x,b)
    ]]></literal>
    <justification jstring="[back_rewrite(6),rewrite(14718(1),14718(7)),merge(c)].">
      <j1 rule="back_rewrite" parents="6"/>
      <j2 rule="rewrite" parents="14718 14718"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="14870">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[resolve(14858,c,14454,a),flip(a),flip(b),unit_del(a,14456),unit_del(b,14457)].">
      <j1 rule="resolve" parents="14858 14454"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="unit_del" parents="14456"/>
      <j2 rule="unit_del" parents="14457"/>
    </justification>
  </clause>

</proof>

</proofs>
