<?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>wang3-eq.out</source>

<heading><![CDATA[
Prover9 (32) version September-2006, September 2006.
Process 26828 was started by mccune on cleo.thornwood,
Wed Sep 13 14:37:27 2006
The command was "/home/mccune/LADR/bin/prover9 -f wang-eq.in wang3-eq.in".
]]></heading>

<proof number="1" length="284" max_count="25">

<comments><![CDATA[
% Proof 1 at 52.61 (+ 0.25) seconds.
% Length of proof is 284.
% Level of proof is 127.
% Maximum clause weight is 25.
% Given clauses 3013.
]]></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="3" type="assumption">
    <literal><![CDATA[
      x = b
    ]]></literal>
    <literal><![CDATA[
      -p(x,b)
    ]]></literal>
    <literal><![CDATA[
      y = b
    ]]></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="4">
    <literal><![CDATA[
      b = x
    ]]></literal>
    <literal><![CDATA[
      -p(x,b)
    ]]></literal>
    <literal><![CDATA[
      b = y
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <literal><![CDATA[
      -p(x,y)
    ]]></literal>
    <literal><![CDATA[
      -p(y,x)
    ]]></literal>
    <justification jstring="[copy(3),flip(a),flip(c)].">
      <j1 rule="copy" parents="3"/>
      <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[
      x = j
    ]]></literal>
    <literal><![CDATA[
      -p(x,j)
    ]]></literal>
    <literal><![CDATA[
      x = k
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="29">
    <literal><![CDATA[
      j = x
    ]]></literal>
    <literal><![CDATA[
      -p(x,j)
    ]]></literal>
    <literal><![CDATA[
      k = x
    ]]></literal>
    <justification jstring="[copy(28),flip(a),flip(c)].">
      <j1 rule="copy" parents="28"/>
      <j2 rule="flip"/>
      <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="35">
    <literal><![CDATA[
      p(x,b)
    ]]></literal>
    <literal><![CDATA[
      p(x,g(x))
    ]]></literal>
    <literal><![CDATA[
      b = y
    ]]></literal>
    <literal><![CDATA[
      p(y,b)
    ]]></literal>
    <literal><![CDATA[
      g(y) != x
    ]]></literal>
    <justification jstring="[para(20(a,1),16(c,2))].">
      <j1 rule="para" parents="20 16"/>
    </justification>
  </clause>

  <clause id="39">
    <literal><![CDATA[
      p(x,b)
    ]]></literal>
    <literal><![CDATA[
      p(g(x),x)
    ]]></literal>
    <literal><![CDATA[
      b = y
    ]]></literal>
    <literal><![CDATA[
      -p(y,x)
    ]]></literal>
    <literal><![CDATA[
      b = z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <literal><![CDATA[
      -p(y,z)
    ]]></literal>
    <literal><![CDATA[
      -p(z,y)
    ]]></literal>
    <justification jstring="[para(22(a,1),4(b,2))].">
      <j1 rule="para" parents="22 4"/>
    </justification>
  </clause>

  <clause id="49">
    <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 = 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(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="58">
    <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[
      j = k
    ]]></literal>
    <literal><![CDATA[
      p(k,j)
    ]]></literal>
    <justification jstring="[xx_res(31,c)].">
      <j1 rule="xx_res" parents="31"/>
    </justification>
  </clause>

  <clause id="63">
    <literal><![CDATA[
      p(m,k)
    ]]></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(49(a,1),6(d,2))].">
      <j1 rule="para" parents="49 6"/>
    </justification>
  </clause>

  <clause id="66">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      k = x
    ]]></literal>
    <literal><![CDATA[
      m = x
    ]]></literal>
    <literal><![CDATA[
      b = x
    ]]></literal>
    <literal><![CDATA[
      -p(x,b)
    ]]></literal>
    <justification jstring="[para(52(a,1),6(d,2))].">
      <j1 rule="para" parents="52 6"/>
    </justification>
  </clause>

  <clause id="70">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(m,k)
    ]]></literal>
    <justification jstring="[para(52(a,1),49(a,1)),flip(b),unit_del(b,27)].">
      <j1 rule="para" parents="52 49"/>
      <j2 rule="flip"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="71">
    <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(61(a,1),29(b,2))].">
      <j1 rule="para" parents="61 29"/>
    </justification>
  </clause>

  <clause id="74">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <justification jstring="[para(52(a,1),70(b,2)),merge(b)].">
      <j1 rule="para" parents="52 70"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="95">
    <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),74(b,2))].">
      <j1 rule="para" parents="22 74"/>
    </justification>
  </clause>

  <clause id="119">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,g(k))
    ]]></literal>
    <literal><![CDATA[
      p(m,k)
    ]]></literal>
    <justification jstring="[resolve(57,c,49,a(flip))].">
      <j1 rule="resolve" parents="57 49"/>
    </justification>
  </clause>

  <clause id="126">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(g(k),k)
    ]]></literal>
    <literal><![CDATA[
      p(m,k)
    ]]></literal>
    <justification jstring="[resolve(58,c,49,a(flip))].">
      <j1 rule="resolve" parents="58 49"/>
    </justification>
  </clause>

  <clause id="135">
    <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(126,b,6,d),flip(c),flip(d),flip(e)].">
      <j1 rule="resolve" parents="126 6"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="222">
    <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(71,c,70,b)].">
      <j1 rule="resolve" parents="71 70"/>
    </justification>
  </clause>

  <clause id="228">
    <literal><![CDATA[
      p(k,j)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <justification jstring="[para(222(b,1),61(a,1)),flip(d),merge(d),merge(e)].">
      <j1 rule="para" parents="222 61"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="239">
    <literal><![CDATA[
      p(k,j)
    ]]></literal>
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <justification jstring="[para(228(b,1),52(a,1)),merge(d),unit_del(c,27)].">
      <j1 rule="para" parents="228 52"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="242">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(b,j)
    ]]></literal>
    <justification jstring="[para(52(a,1),239(a,1)),merge(c)].">
      <j1 rule="para" parents="52 239"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="244">
    <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(242,b,2,e),flip(d),unit_del(b,27)].">
      <j1 rule="resolve" parents="242 2"/>
      <j2 rule="flip"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="353">
    <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(95,b,29,b),flip(d),flip(e)].">
      <j1 rule="resolve" parents="95 29"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2169">
    <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(49(a,1),135(c,2)),merge(c),merge(e)].">
      <j1 rule="para" parents="49 135"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="2176">
    <literal><![CDATA[
      p(m,k)
    ]]></literal>
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      g(k) = b
    ]]></literal>
    <justification jstring="[para(2169(c,1),126(b,1)),merge(d),merge(e),merge(f)].">
      <j1 rule="para" parents="2169 126"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="2185">
    <literal><![CDATA[
      p(m,k)
    ]]></literal>
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <justification jstring="[para(2176(c,1),119(b,2)),merge(c),merge(d),merge(e)].">
      <j1 rule="para" parents="2176 119"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="2192">
    <literal><![CDATA[
      p(m,k)
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <justification jstring="[para(49(a,1),2185(b,1)),merge(b)].">
      <j1 rule="para" parents="49 2185"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="3207">
    <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(353,d,18,c),flip(e),merge(f)].">
      <j1 rule="resolve" parents="353 18"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="3215">
    <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(3207(d,1),16(c,1)),flip(e),merge(e),merge(f)].">
      <j1 rule="para" parents="3207 16"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="3236">
    <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(3215,e,52,a),merge(e)].">
      <j1 rule="resolve" parents="3215 52"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="3240">
    <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(3236,d,26,b(flip)),flip(d)].">
      <j1 rule="resolve" parents="3236 26"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3324">
    <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(3240(d,1),242(b,2)),merge(e),merge(f)].">
      <j1 rule="para" parents="3240 242"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="3327">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <justification jstring="[para(52(a,1),3324(d,2)),merge(c),merge(e)].">
      <j1 rule="para" parents="52 3324"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="3328">
    <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(3327,b,244,e),merge(c)].">
      <j1 rule="resolve" parents="3327 244"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="3330">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      j = k
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <justification jstring="[resolve(3327,b,66,e),flip(d),flip(e),flip(f),merge(c)].">
      <j1 rule="resolve" parents="3327 66"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="3341">
    <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(3328(d,1),242(b,2)),merge(e),merge(f)].">
      <j1 rule="para" parents="3328 242"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="3345">
    <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(3341,d,26,b(flip)),flip(d)].">
      <j1 rule="resolve" parents="3341 26"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3371">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <justification jstring="[para(52(a,1),3330(c,2)),merge(b),merge(f)].">
      <j1 rule="para" parents="52 3330"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="3372">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <literal><![CDATA[
      j = k
    ]]></literal>
    <literal><![CDATA[
      p(j,k)
    ]]></literal>
    <justification jstring="[resolve(3371,d,24,b(flip)),flip(d)].">
      <j1 rule="resolve" parents="3371 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3374">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <justification jstring="[para(3371(d,1),239(a,2)),merge(e)].">
      <j1 rule="para" parents="3371 239"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="3417">
    <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(3345(d,1),242(b,2)),merge(e),merge(f)].">
      <j1 rule="para" parents="3345 242"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="3420">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <justification jstring="[para(3341(d,1),3417(d,1)),merge(d),merge(e),merge(f),merge(g)].">
      <j1 rule="para" parents="3341 3417"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="3428">
    <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(3420,b,29,b)].">
      <j1 rule="resolve" parents="3420 29"/>
    </justification>
  </clause>

  <clause id="3435">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[para(3428(c,1),242(b,2)),merge(d),merge(e)].">
      <j1 rule="para" parents="3428 242"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="3442">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <justification jstring="[para(3435(c,1),52(a,1)),merge(d),unit_del(c,27)].">
      <j1 rule="para" parents="3435 52"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="3445">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <literal><![CDATA[
      -p(k,b)
    ]]></literal>
    <justification jstring="[resolve(3442,a,2,e),flip(d),merge(c),unit_del(b,27)].">
      <j1 rule="resolve" parents="3442 2"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="3448">
    <literal><![CDATA[
      p(m,k)
    ]]></literal>
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <justification jstring="[para(49(a,1),3442(a,2)),merge(c)].">
      <j1 rule="para" parents="49 3442"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="3461">
    <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(3448,a,71,c)].">
      <j1 rule="resolve" parents="3448 71"/>
    </justification>
  </clause>

  <clause id="3546">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      p(k,j)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[para(3461(c,1),61(a,1)),flip(d),merge(d),merge(e)].">
      <j1 rule="para" parents="3461 61"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="3561">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      p(k,j)
    ]]></literal>
    <justification jstring="[para(3546(c,1),3442(a,2)),merge(c),merge(d)].">
      <j1 rule="para" parents="3546 3442"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="3940">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <literal><![CDATA[
      p(j,k)
    ]]></literal>
    <justification jstring="[para(52(a,1),3372(d,2)),merge(b),merge(e)].">
      <j1 rule="para" parents="52 3372"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="3946">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      p(j,k)
    ]]></literal>
    <literal><![CDATA[
      j = k
    ]]></literal>
    <justification jstring="[resolve(3940,c,26,b(flip)),flip(d),merge(e)].">
      <j1 rule="resolve" parents="3940 26"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="3958">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      p(j,k)
    ]]></literal>
    <justification jstring="[para(3946(d,1),242(b,2)),merge(d),merge(e)].">
      <j1 rule="para" parents="3946 242"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="3961">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <justification jstring="[para(3374(c,1),3958(c,1)),merge(d),merge(e),merge(f)].">
      <j1 rule="para" parents="3374 3958"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="3962">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      p(f(k),k)
    ]]></literal>
    <justification jstring="[resolve(3961,c,14,b),flip(c)].">
      <j1 rule="resolve" parents="3961 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3987">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      p(f(k),k)
    ]]></literal>
    <justification jstring="[para(3962(c,1),52(a,1)),merge(e),unit_del(d,27)].">
      <j1 rule="para" parents="3962 52"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="3992">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      f(k) = k
    ]]></literal>
    <literal><![CDATA[
      f(k) = m
    ]]></literal>
    <literal><![CDATA[
      f(k) = b
    ]]></literal>
    <justification jstring="[resolve(3987,c,6,d),flip(c),flip(d),flip(e)].">
      <j1 rule="resolve" parents="3987 6"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6198">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      f(k) = b
    ]]></literal>
    <literal><![CDATA[
      f(k) = m
    ]]></literal>
    <justification jstring="[para(52(a,1),3992(c,2)),merge(b),merge(f)].">
      <j1 rule="para" parents="52 3992"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="6213">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      f(k) = b
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      -p(k,m)
    ]]></literal>
    <justification jstring="[resolve(6198,d,8,c),flip(d)].">
      <j1 rule="resolve" parents="6198 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6278">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      f(k) = b
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[resolve(6213,e,3961,c),merge(e),merge(f)].">
      <j1 rule="resolve" parents="6213 3961"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="6296">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[para(6278(c,1),3987(c,1)),merge(d),merge(e),merge(f)].">
      <j1 rule="para" parents="6278 3987"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="6309">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <justification jstring="[para(6296(c,1),52(a,1)),merge(d),unit_del(c,27)].">
      <j1 rule="para" parents="6296 52"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="6322">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[resolve(6309,b,29,b)].">
      <j1 rule="resolve" parents="6309 29"/>
    </justification>
  </clause>

  <clause id="6328">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <justification jstring="[para(6322(b,1),239(a,2)),merge(d)].">
      <j1 rule="para" parents="6322 239"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="6339">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <justification jstring="[para(6328(b,1),52(a,1)),merge(d),unit_del(c,27)].">
      <j1 rule="para" parents="6328 52"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="6350">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      p(f(k),k)
    ]]></literal>
    <justification jstring="[resolve(6339,b,14,b),flip(b)].">
      <j1 rule="resolve" parents="6339 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6379">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(f(k),k)
    ]]></literal>
    <justification jstring="[para(6350(b,1),52(a,1)),merge(d),unit_del(c,27)].">
      <j1 rule="para" parents="6350 52"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="6386">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      f(k) = k
    ]]></literal>
    <literal><![CDATA[
      f(k) = m
    ]]></literal>
    <literal><![CDATA[
      f(k) = b
    ]]></literal>
    <justification jstring="[resolve(6379,b,6,d),flip(b),flip(c),flip(d)].">
      <j1 rule="resolve" parents="6379 6"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6765">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      f(k) = b
    ]]></literal>
    <literal><![CDATA[
      f(k) = m
    ]]></literal>
    <justification jstring="[para(52(a,1),6386(b,2)),merge(b),merge(e)].">
      <j1 rule="para" parents="52 6386"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="6766">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      f(k) = b
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      -p(k,m)
    ]]></literal>
    <justification jstring="[resolve(6765,c,8,c),flip(c)].">
      <j1 rule="resolve" parents="6765 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6829">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      f(k) = b
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[resolve(6766,d,6339,b),merge(d)].">
      <j1 rule="resolve" parents="6766 6339"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="6853">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[para(6829(b,1),6379(b,1)),merge(c),merge(d)].">
      <j1 rule="para" parents="6829 6379"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="6860">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <justification jstring="[para(6853(b,1),52(a,1)),merge(c),unit_del(b,27)].">
      <j1 rule="para" parents="6853 52"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="6868">
    <literal><![CDATA[
      p(k,j)
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[resolve(6860,a,71,c)].">
      <j1 rule="resolve" parents="6860 71"/>
    </justification>
  </clause>

  <clause id="6869">
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <literal><![CDATA[
      -p(k,b)
    ]]></literal>
    <justification jstring="[resolve(6860,a,2,f),flip(a),flip(d),unit_del(c,27)].">
      <j1 rule="resolve" parents="6860 2"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="6870">
    <literal><![CDATA[
      p(x,b)
    ]]></literal>
    <literal><![CDATA[
      p(x,g(x))
    ]]></literal>
    <literal><![CDATA[
      p(x,k)
    ]]></literal>
    <justification jstring="[para(20(a,1),6860(a,1))].">
      <j1 rule="para" parents="20 6860"/>
    </justification>
  </clause>

  <clause id="6871">
    <literal><![CDATA[
      p(x,b)
    ]]></literal>
    <literal><![CDATA[
      p(g(x),x)
    ]]></literal>
    <literal><![CDATA[
      p(x,k)
    ]]></literal>
    <justification jstring="[para(22(a,1),6860(a,1))].">
      <j1 rule="para" parents="22 6860"/>
    </justification>
  </clause>

  <clause id="6881">
    <literal><![CDATA[
      p(k,j)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[para(6868(b,1),61(a,1)),flip(c),merge(c),merge(d)].">
      <j1 rule="para" parents="6868 61"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="6885">
    <literal><![CDATA[
      p(k,j)
    ]]></literal>
    <literal><![CDATA[
      k = x
    ]]></literal>
    <literal><![CDATA[
      m = x
    ]]></literal>
    <literal><![CDATA[
      b = x
    ]]></literal>
    <literal><![CDATA[
      -p(x,b)
    ]]></literal>
    <justification jstring="[para(6881(b,1),6(d,2))].">
      <j1 rule="para" parents="6881 6"/>
    </justification>
  </clause>

  <clause id="6971">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(j,k)
    ]]></literal>
    <literal><![CDATA[
      g(j) = j
    ]]></literal>
    <literal><![CDATA[
      g(j) = k
    ]]></literal>
    <justification jstring="[resolve(6871,b,29,b),flip(c),flip(d)].">
      <j1 rule="resolve" parents="6871 29"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6972">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,k)
    ]]></literal>
    <literal><![CDATA[
      g(k) = k
    ]]></literal>
    <literal><![CDATA[
      g(k) = m
    ]]></literal>
    <literal><![CDATA[
      g(k) = b
    ]]></literal>
    <justification jstring="[resolve(6871,b,6,d),flip(c),flip(d),flip(e)].">
      <j1 rule="resolve" parents="6871 6"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7098">
    <literal><![CDATA[
      p(x,b)
    ]]></literal>
    <literal><![CDATA[
      p(g(x),x)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <literal><![CDATA[
      -p(k,x)
    ]]></literal>
    <justification jstring="[para(22(a,1),6869(d,2))].">
      <j1 rule="para" parents="22 6869"/>
    </justification>
  </clause>

  <clause id="7474">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(j,k)
    ]]></literal>
    <literal><![CDATA[
      g(j) = k
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <justification jstring="[resolve(6971,c,18,c),flip(d),merge(e)].">
      <j1 rule="resolve" parents="6971 18"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="7508">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(j,k)
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <justification jstring="[para(7474(c,1),6870(b,2)),merge(d),merge(e),merge(f)].">
      <j1 rule="para" parents="7474 6870"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="7513">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(j,k)
    ]]></literal>
    <literal><![CDATA[
      j = k
    ]]></literal>
    <justification jstring="[resolve(7508,c,26,b(flip)),flip(c),merge(d)].">
      <j1 rule="resolve" parents="7508 26"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="7544">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(j,k)
    ]]></literal>
    <literal><![CDATA[
      g(j) = k
    ]]></literal>
    <justification jstring="[para(7513(c,1),6971(c,2)),merge(c),merge(d),merge(f)].">
      <j1 rule="para" parents="7513 6971"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="7620">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(j,k)
    ]]></literal>
    <justification jstring="[para(7544(c,1),6870(b,2)),merge(c),merge(d),merge(e)].">
      <j1 rule="para" parents="7544 6870"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="7633">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      j = k
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <justification jstring="[resolve(7620,b,6,d),flip(b),flip(c),flip(d)].">
      <j1 rule="resolve" parents="7620 6"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7636">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      p(j,m)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      j = k
    ]]></literal>
    <literal><![CDATA[
      -p(k,j)
    ]]></literal>
    <justification jstring="[resolve(7620,b,2,e),flip(b),flip(d),flip(e)].">
      <j1 rule="resolve" parents="7620 2"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7640">
    <literal><![CDATA[
      p(k,j)
    ]]></literal>
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <justification jstring="[para(6881(b,1),7620(b,2)),merge(c)].">
      <j1 rule="para" parents="6881 7620"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="7647">
    <literal><![CDATA[
      p(k,j)
    ]]></literal>
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <justification jstring="[para(61(a,1),7640(b,1)),merge(b)].">
      <j1 rule="para" parents="61 7640"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="7766">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <literal><![CDATA[
      j = x
    ]]></literal>
    <literal><![CDATA[
      -p(x,k)
    ]]></literal>
    <literal><![CDATA[
      k = x
    ]]></literal>
    <justification jstring="[para(7633(b,1),29(b,2))].">
      <j1 rule="para" parents="7633 29"/>
    </justification>
  </clause>

  <clause id="7770">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <literal><![CDATA[
      -p(m,k)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[factor(7766,b,d)].">
      <j1 rule="factor" parents="7766"/>
    </justification>
  </clause>

  <clause id="7771">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[factor(7766,c,d),unit_del(d,6860)].">
      <j1 rule="factor" parents="7766"/>
      <j2 rule="unit_del" parents="6860"/>
    </justification>
  </clause>

  <clause id="7784">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <literal><![CDATA[
      p(g(j),j)
    ]]></literal>
    <justification jstring="[resolve(7771,b,58,c(flip)),merge(d)].">
      <j1 rule="resolve" parents="7771 58"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="7786">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <literal><![CDATA[
      j = x
    ]]></literal>
    <literal><![CDATA[
      -p(x,m)
    ]]></literal>
    <literal><![CDATA[
      k = x
    ]]></literal>
    <justification jstring="[para(7771(b,1),29(b,2))].">
      <j1 rule="para" parents="7771 29"/>
    </justification>
  </clause>

  <clause id="7797">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <literal><![CDATA[
      -p(b,m)
    ]]></literal>
    <justification jstring="[factor(7786,b,d),merge(e)].">
      <j1 rule="factor" parents="7786"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="7832">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <literal><![CDATA[
      p(g(j),j)
    ]]></literal>
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <justification jstring="[para(7784(b,1),7647(a,2)),merge(e)].">
      <j1 rule="para" parents="7784 7647"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="7888">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(g(j),j)
    ]]></literal>
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <justification jstring="[para(7832(b,1),7620(b,2)),merge(d),merge(e)].">
      <j1 rule="para" parents="7832 7620"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="7900">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      g(j) = j
    ]]></literal>
    <literal><![CDATA[
      g(j) = k
    ]]></literal>
    <justification jstring="[resolve(7888,b,29,b),flip(c),flip(d)].">
      <j1 rule="resolve" parents="7888 29"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7980">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      g(j) = k
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <justification jstring="[resolve(7900,c,18,c),flip(d),merge(e)].">
      <j1 rule="resolve" parents="7900 18"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="7993">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <literal><![CDATA[
      p(k,g(k))
    ]]></literal>
    <justification jstring="[resolve(7980,c,35,e),flip(f),merge(d),merge(f),merge(g)].">
      <j1 rule="resolve" parents="7980 35"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="8108">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,g(k))
    ]]></literal>
    <justification jstring="[para(7993(c,1),7647(a,2)),merge(d),merge(e)].">
      <j1 rule="para" parents="7993 7647"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="8116">
    <literal><![CDATA[
      p(x,b)
    ]]></literal>
    <literal><![CDATA[
      p(x,g(x))
    ]]></literal>
    <literal><![CDATA[
      p(j,x)
    ]]></literal>
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,g(k))
    ]]></literal>
    <justification jstring="[para(20(a,1),8108(a,2))].">
      <j1 rule="para" parents="20 8108"/>
    </justification>
  </clause>

  <clause id="8124">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,g(k))
    ]]></literal>
    <literal><![CDATA[
      p(j,k)
    ]]></literal>
    <justification jstring="[factor(8116,a,d),merge(d)].">
      <j1 rule="factor" parents="8116"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="8139">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,g(k))
    ]]></literal>
    <literal><![CDATA[
      j = k
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <justification jstring="[resolve(8124,c,6,d),flip(c),flip(d),flip(e)].">
      <j1 rule="resolve" parents="8124 6"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8968">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,g(k))
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <justification jstring="[para(8139(c,1),8108(a,1)),merge(e),merge(f),merge(g)].">
      <j1 rule="para" parents="8139 8108"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="8973">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,g(k))
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <justification jstring="[para(8968(c,1),7647(a,2)),merge(e)].">
      <j1 rule="para" parents="8968 7647"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="8986">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,g(k))
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <justification jstring="[para(8973(c,1),7647(a,2)),merge(d),merge(e)].">
      <j1 rule="para" parents="8973 7647"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="11696">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,k)
    ]]></literal>
    <literal><![CDATA[
      g(k) = m
    ]]></literal>
    <literal><![CDATA[
      g(k) = b
    ]]></literal>
    <justification jstring="[para(6972(c,1),6870(b,2)),merge(e),merge(f),merge(g)].">
      <j1 rule="para" parents="6972 6870"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="11711">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,k)
    ]]></literal>
    <literal><![CDATA[
      g(k) = b
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <literal><![CDATA[
      k != m
    ]]></literal>
    <justification jstring="[para(11696(c,1),18(c,1)),flip(d),flip(f),merge(e)].">
      <j1 rule="para" parents="11696 18"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="11712">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,k)
    ]]></literal>
    <literal><![CDATA[
      g(k) = b
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <justification jstring="[para(11696(c,1),6870(b,2)),merge(d),merge(f)].">
      <j1 rule="para" parents="11696 6870"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="11729">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,k)
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <justification jstring="[para(11712(c,1),6870(b,2)),merge(d),merge(e),merge(f)].">
      <j1 rule="para" parents="11712 6870"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="25616">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(g(k),k)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[resolve(7098,f,11729,b),merge(f),merge(g)].">
      <j1 rule="resolve" parents="7098 11729"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="25647">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(g(k),k)
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[resolve(25616,c,58,c(flip)),merge(e),merge(f)].">
      <j1 rule="resolve" parents="25616 58"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="25656">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(g(k),k)
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <justification jstring="[para(25647(d,1),11729(b,2)),merge(d),merge(e),merge(f)].">
      <j1 rule="para" parents="25647 11729"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="25670">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <literal><![CDATA[
      g(k) = k
    ]]></literal>
    <literal><![CDATA[
      g(k) = m
    ]]></literal>
    <literal><![CDATA[
      g(k) = b
    ]]></literal>
    <justification jstring="[resolve(25656,b,6,d),flip(c),flip(d),flip(e)].">
      <j1 rule="resolve" parents="25656 6"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25674">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <literal><![CDATA[
      g(k) = m
    ]]></literal>
    <literal><![CDATA[
      g(k) = b
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[resolve(25670,c,18,c),flip(e),merge(f)].">
      <j1 rule="resolve" parents="25670 18"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="25719">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <literal><![CDATA[
      g(k) = b
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[para(25674(c,1),8986(b,2)),merge(e),merge(f),merge(g)].">
      <j1 rule="para" parents="25674 8986"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="25726">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[resolve(25719,c,16,c),flip(d),merge(d),merge(e)].">
      <j1 rule="resolve" parents="25719 16"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="25746">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <justification jstring="[para(25726(c,1),11729(b,2)),merge(c),merge(d),merge(e)].">
      <j1 rule="para" parents="25726 11729"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="25820">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(x,b)
    ]]></literal>
    <literal><![CDATA[
      p(g(x),x)
    ]]></literal>
    <literal><![CDATA[
      -p(m,x)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      -p(m,k)
    ]]></literal>
    <justification jstring="[resolve(25746,b,39,h),flip(d),flip(f),unit_del(d,27)].">
      <j1 rule="resolve" parents="25746 39"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="25824">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      p(f(k),k)
    ]]></literal>
    <justification jstring="[resolve(25746,b,14,b),flip(b)].">
      <j1 rule="resolve" parents="25746 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25825">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      p(k,f(k))
    ]]></literal>
    <justification jstring="[resolve(25746,b,12,b),flip(b)].">
      <j1 rule="resolve" parents="25746 12"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25839">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(g(k),k)
    ]]></literal>
    <literal><![CDATA[
      -p(m,k)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[factor(25820,a,b),merge(f)].">
      <j1 rule="factor" parents="25820"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="25924">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(f(k),k)
    ]]></literal>
    <literal><![CDATA[
      p(k,k)
    ]]></literal>
    <literal><![CDATA[
      g(k) = b
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[resolve(25824,b,11711,e),merge(c)].">
      <j1 rule="resolve" parents="25824 11711"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="25930">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(f(k),k)
    ]]></literal>
    <literal><![CDATA[
      p(g(k),k)
    ]]></literal>
    <justification jstring="[resolve(25824,b,58,c(flip)),merge(c)].">
      <j1 rule="resolve" parents="25824 58"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="25976">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,f(k))
    ]]></literal>
    <literal><![CDATA[
      p(k,k)
    ]]></literal>
    <literal><![CDATA[
      g(k) = b
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[resolve(25825,b,11711,e),merge(c)].">
      <j1 rule="resolve" parents="25825 11711"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="25994">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,f(k))
    ]]></literal>
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <justification jstring="[para(25825(b,1),6860(a,2))].">
      <j1 rule="para" parents="25825 6860"/>
    </justification>
  </clause>

  <clause id="25996">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,f(k))
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <justification jstring="[para(25825(b,1),7647(a,1)),merge(d)].">
      <j1 rule="para" parents="25825 7647"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="26287">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(f(k),k)
    ]]></literal>
    <literal><![CDATA[
      g(k) = k
    ]]></literal>
    <literal><![CDATA[
      g(k) = m
    ]]></literal>
    <literal><![CDATA[
      g(k) = b
    ]]></literal>
    <justification jstring="[resolve(25930,c,6,d),flip(c),flip(d),flip(e)].">
      <j1 rule="resolve" parents="25930 6"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27643">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(g(k),k)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <justification jstring="[resolve(25839,c,2192,a)].">
      <j1 rule="resolve" parents="25839 2192"/>
    </justification>
  </clause>

  <clause id="27771">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(g(k),k)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <justification jstring="[resolve(27643,d,58,c(flip)),merge(e),merge(f)].">
      <j1 rule="resolve" parents="27643 58"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="27774">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(g(k),k)
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <justification jstring="[para(27771(c,1),2192(a,2)),merge(d),merge(e)].">
      <j1 rule="para" parents="27771 2192"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="27788">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      g(k) = k
    ]]></literal>
    <literal><![CDATA[
      g(k) = m
    ]]></literal>
    <literal><![CDATA[
      g(k) = b
    ]]></literal>
    <justification jstring="[resolve(27774,b,6,d),flip(c),flip(d),flip(e)].">
      <j1 rule="resolve" parents="27774 6"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27862">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(f(k),k)
    ]]></literal>
    <literal><![CDATA[
      p(k,k)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[resolve(25924,d,16,c),flip(e),merge(e),merge(f)].">
      <j1 rule="resolve" parents="25924 16"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="27890">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(f(k),k)
    ]]></literal>
    <literal><![CDATA[
      p(k,k)
    ]]></literal>
    <justification jstring="[para(27862(d,1),25824(b,1)),flip(e),merge(d),merge(f),unit_del(d,27)].">
      <j1 rule="para" parents="27862 25824"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="27903">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,k)
    ]]></literal>
    <literal><![CDATA[
      f(k) = k
    ]]></literal>
    <literal><![CDATA[
      f(k) = m
    ]]></literal>
    <literal><![CDATA[
      f(k) = b
    ]]></literal>
    <justification jstring="[resolve(27890,b,6,d),flip(c),flip(d),flip(e)].">
      <j1 rule="resolve" parents="27890 6"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28106">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,f(k))
    ]]></literal>
    <literal><![CDATA[
      p(k,k)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[resolve(25976,d,16,c),flip(e),merge(e),merge(f)].">
      <j1 rule="resolve" parents="25976 16"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="28132">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,f(k))
    ]]></literal>
    <literal><![CDATA[
      p(k,k)
    ]]></literal>
    <justification jstring="[para(28106(d,1),25825(b,1)),flip(e),merge(d),merge(f),unit_del(d,27)].">
      <j1 rule="para" parents="28106 25825"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="29860">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      g(k) = m
    ]]></literal>
    <literal><![CDATA[
      g(k) = b
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[resolve(27788,c,18,c),flip(e),merge(f)].">
      <j1 rule="resolve" parents="27788 18"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="29892">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      g(k) = b
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <literal><![CDATA[
      k != m
    ]]></literal>
    <justification jstring="[para(29860(c,1),18(c,1)),flip(e),flip(g),merge(e),merge(f)].">
      <j1 rule="para" parents="29860 18"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="29929">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      g(k) = b
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <literal><![CDATA[
      p(k,f(k))
    ]]></literal>
    <justification jstring="[resolve(29892,e,25825,b),merge(e)].">
      <j1 rule="resolve" parents="29892 25825"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="29937">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <literal><![CDATA[
      p(k,f(k))
    ]]></literal>
    <justification jstring="[resolve(29929,c,16,c),flip(e),merge(e),merge(f)].">
      <j1 rule="resolve" parents="29929 16"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="29945">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,f(k))
    ]]></literal>
    <justification jstring="[para(29937(c,1),2192(a,2)),merge(d),merge(e)].">
      <j1 rule="para" parents="29937 2192"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="30116">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,k)
    ]]></literal>
    <literal><![CDATA[
      f(k) = m
    ]]></literal>
    <literal><![CDATA[
      f(k) = b
    ]]></literal>
    <justification jstring="[para(27903(c,1),27890(b,1)),merge(e),merge(f),merge(g)].">
      <j1 rule="para" parents="27903 27890"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="30117">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,k)
    ]]></literal>
    <literal><![CDATA[
      f(k) = b
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      -p(k,m)
    ]]></literal>
    <justification jstring="[resolve(30116,c,8,c),flip(d)].">
      <j1 rule="resolve" parents="30116 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30195">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,k)
    ]]></literal>
    <literal><![CDATA[
      f(k) = b
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[resolve(30117,e,25746,b),merge(e)].">
      <j1 rule="resolve" parents="30117 25746"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="30215">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,k)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[para(30195(c,1),28132(b,2)),merge(d),merge(e),merge(f)].">
      <j1 rule="para" parents="30195 28132"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="30231">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,k)
    ]]></literal>
    <literal><![CDATA[
      g(k) = b
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[resolve(30215,c,11711,e),merge(c),merge(d)].">
      <j1 rule="resolve" parents="30215 11711"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="30900">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,k)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[resolve(30231,c,16,c),flip(d),merge(d),merge(e)].">
      <j1 rule="resolve" parents="30231 16"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="30939">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,k)
    ]]></literal>
    <justification jstring="[para(30900(c,1),30215(c,1)),flip(e),merge(c),merge(d),unit_del(c,27)].">
      <j1 rule="para" parents="30900 30215"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="37807">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(f(k),k)
    ]]></literal>
    <literal><![CDATA[
      g(k) = m
    ]]></literal>
    <literal><![CDATA[
      g(k) = b
    ]]></literal>
    <justification jstring="[para(25824(b,1),26287(c,2)),merge(c),merge(d),merge(f)].">
      <j1 rule="para" parents="25824 26287"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="37812">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(f(k),k)
    ]]></literal>
    <literal><![CDATA[
      g(k) = b
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <literal><![CDATA[
      k != m
    ]]></literal>
    <justification jstring="[para(37807(c,1),18(c,1)),flip(d),flip(f),merge(e)].">
      <j1 rule="para" parents="37807 18"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="38165">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(f(k),k)
    ]]></literal>
    <literal><![CDATA[
      g(k) = b
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[resolve(37812,e,25824,b),merge(e),merge(f)].">
      <j1 rule="resolve" parents="37812 25824"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="38172">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(f(k),k)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[resolve(38165,c,16,c),flip(d),merge(d),merge(e)].">
      <j1 rule="resolve" parents="38165 16"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="38194">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(f(k),k)
    ]]></literal>
    <justification jstring="[para(38172(c,1),25824(b,1)),flip(d),merge(c),merge(e),unit_del(c,27)].">
      <j1 rule="para" parents="38172 25824"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="38208">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      f(k) = k
    ]]></literal>
    <literal><![CDATA[
      f(k) = m
    ]]></literal>
    <literal><![CDATA[
      f(k) = b
    ]]></literal>
    <justification jstring="[resolve(38194,b,6,d),flip(b),flip(c),flip(d)].">
      <j1 rule="resolve" parents="38194 6"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38369">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      f(k) = m
    ]]></literal>
    <literal><![CDATA[
      f(k) = b
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      -p(k,m)
    ]]></literal>
    <justification jstring="[resolve(38208,b,10,c),flip(d)].">
      <j1 rule="resolve" parents="38208 10"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38461">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      f(k) = m
    ]]></literal>
    <literal><![CDATA[
      f(k) = b
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[resolve(38369,e,25746,b),merge(e)].">
      <j1 rule="resolve" parents="38369 25746"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="38464">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      f(k) = b
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      -p(k,m)
    ]]></literal>
    <justification jstring="[resolve(38461,b,8,c),flip(d),merge(d)].">
      <j1 rule="resolve" parents="38461 8"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="38475">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      f(k) = b
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[resolve(38464,d,25746,b),merge(d)].">
      <j1 rule="resolve" parents="38464 25746"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="38490">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <justification jstring="[para(38475(b,1),25994(b,2)),merge(c),merge(d)].">
      <j1 rule="para" parents="38475 25994"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="38491">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <justification jstring="[para(38475(b,1),25996(b,2)),merge(c),merge(d)].">
      <j1 rule="para" parents="38475 25996"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="38499">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <justification jstring="[para(38475(b,1),29945(c,2)),merge(c),merge(e)].">
      <j1 rule="para" parents="38475 29945"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="38766">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <justification jstring="[para(38490(b,1),6860(a,2)),merge(c)].">
      <j1 rule="para" parents="38490 6860"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="38780">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[resolve(38766,a,3445,d),merge(b)].">
      <j1 rule="resolve" parents="38766 3445"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="38826">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <justification jstring="[para(38491(b,1),7647(a,1)),merge(c),merge(d)].">
      <j1 rule="para" parents="38491 7647"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="38832">
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[resolve(38826,a,6869,d)].">
      <j1 rule="resolve" parents="38826 6869"/>
    </justification>
  </clause>

  <clause id="38993">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      g(k) = b
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[resolve(38499,b,29892,e),merge(c),merge(d)].">
      <j1 rule="resolve" parents="38499 29892"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="39089">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[para(38780(b,1),6860(a,2)),merge(c)].">
      <j1 rule="para" parents="38780 6860"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="39177">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <justification jstring="[para(39089(b,1),2192(a,2)),merge(c)].">
      <j1 rule="para" parents="39089 2192"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="39179">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      p(b,j)
    ]]></literal>
    <justification jstring="[para(39089(b,1),3561(b,1)),merge(b)].">
      <j1 rule="para" parents="39089 3561"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="39183">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <justification jstring="[para(39089(b,1),7620(b,2)),merge(c)].">
      <j1 rule="para" parents="39089 7620"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="39201">
    <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(39179,b,2,e),flip(d),merge(c),unit_del(b,27)].">
      <j1 rule="resolve" parents="39179 2"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="40583">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <justification jstring="[resolve(39201,d,39183,b),merge(d)].">
      <j1 rule="resolve" parents="39201 39183"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="40588">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <justification jstring="[para(40583(b,1),39179(b,2)),merge(c),merge(d)].">
      <j1 rule="para" parents="40583 39179"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="40592">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      j = x
    ]]></literal>
    <literal><![CDATA[
      -p(x,b)
    ]]></literal>
    <literal><![CDATA[
      k = x
    ]]></literal>
    <justification jstring="[para(40588(b,1),29(b,2))].">
      <j1 rule="para" parents="40588 29"/>
    </justification>
  </clause>

  <clause id="40794">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[resolve(40592,c,39177,b),merge(d)].">
      <j1 rule="resolve" parents="40592 39177"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="40805">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[para(40794(b,1),39179(b,2)),merge(c),merge(d)].">
      <j1 rule="para" parents="40794 39179"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="40811">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <justification jstring="[para(40805(b,1),6860(a,2)),merge(b)].">
      <j1 rule="para" parents="40805 6860"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="40815">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[back_unit_del(7797),unit_del(d,40811)].">
      <j1 rule="back_unit_del" parents="7797"/>
      <j2 rule="unit_del" parents="40811"/>
    </justification>
  </clause>

  <clause id="40822">
    <literal><![CDATA[
      p(f(b),b)
    ]]></literal>
    <justification jstring="[resolve(40811,a,14,b),unit_del(a,27)].">
      <j1 rule="resolve" parents="40811 14"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="40823">
    <literal><![CDATA[
      p(b,f(b))
    ]]></literal>
    <justification jstring="[resolve(40811,a,12,b),unit_del(a,27)].">
      <j1 rule="resolve" parents="40811 12"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="40824">
    <literal><![CDATA[
      f(b) != b
    ]]></literal>
    <justification jstring="[ur(10,a,27,a,b,40811,a)].">
      <j1 rule="ur" parents="10 27 40811"/>
    </justification>
  </clause>

  <clause id="40825">
    <literal><![CDATA[
      f(b) != m
    ]]></literal>
    <justification jstring="[ur(8,a,27,a,b,40811,a)].">
      <j1 rule="ur" parents="8 27 40811"/>
    </justification>
  </clause>

  <clause id="40866">
    <literal><![CDATA[
      p(k,j)
    ]]></literal>
    <literal><![CDATA[
      f(b) = k
    ]]></literal>
    <justification jstring="[resolve(40822,a,6885,e),flip(b),flip(c),flip(d),unit_del(c,40825),unit_del(d,40824)].">
      <j1 rule="resolve" parents="40822 6885"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="unit_del" parents="40825"/>
      <j2 rule="unit_del" parents="40824"/>
    </justification>
  </clause>

  <clause id="40868">
    <literal><![CDATA[
      p(f(b),m)
    ]]></literal>
    <justification jstring="[resolve(40822,a,2,e),flip(a),flip(d),unit_del(a,40825),unit_del(c,27),unit_del(d,40824),unit_del(e,40823)].">
      <j1 rule="resolve" parents="40822 2"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="unit_del" parents="40825"/>
      <j2 rule="unit_del" parents="27"/>
      <j2 rule="unit_del" parents="40824"/>
      <j2 rule="unit_del" parents="40823"/>
    </justification>
  </clause>

  <clause id="40924">
    <literal><![CDATA[
      p(m,k)
    ]]></literal>
    <literal><![CDATA[
      f(b) = k
    ]]></literal>
    <justification jstring="[resolve(40868,a,63,e),flip(b),flip(c),flip(d),unit_del(c,40825),unit_del(d,40824)].">
      <j1 rule="resolve" parents="40868 63"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="unit_del" parents="40825"/>
      <j2 rule="unit_del" parents="40824"/>
    </justification>
  </clause>

  <clause id="40932">
    <literal><![CDATA[
      -p(m,f(b))
    ]]></literal>
    <justification jstring="[resolve(40868,a,4,e),flip(a),flip(c),flip(d),unit_del(a,40824),unit_del(b,40822),unit_del(c,27),unit_del(d,40825)].">
      <j1 rule="resolve" parents="40868 4"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="unit_del" parents="40824"/>
      <j2 rule="unit_del" parents="40822"/>
      <j2 rule="unit_del" parents="27"/>
      <j2 rule="unit_del" parents="40825"/>
    </justification>
  </clause>

  <clause id="40983">
    <literal><![CDATA[
      p(k,j)
    ]]></literal>
    <justification jstring="[para(6881(b,1),40866(b,2)),merge(b),unit_del(b,40824)].">
      <j1 rule="para" parents="6881 40866"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="40824"/>
    </justification>
  </clause>

  <clause id="40989">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      p(j,m)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      j = k
    ]]></literal>
    <justification jstring="[back_unit_del(7636),unit_del(f,40983)].">
      <j1 rule="back_unit_del" parents="7636"/>
      <j2 rule="unit_del" parents="40983"/>
    </justification>
  </clause>

  <clause id="41006">
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      j = k
    ]]></literal>
    <literal><![CDATA[
      -p(j,k)
    ]]></literal>
    <justification jstring="[resolve(40983,a,2,e),flip(a),flip(c)].">
      <j1 rule="resolve" parents="40983 2"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41012">
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[para(38832(b,1),40983(a,1)),merge(d)].">
      <j1 rule="para" parents="38832 40983"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="41018">
    <literal><![CDATA[
      p(m,k)
    ]]></literal>
    <justification jstring="[para(49(a,1),40924(b,2)),merge(b),unit_del(b,40825)].">
      <j1 rule="para" parents="49 40924"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="40825"/>
    </justification>
  </clause>

  <clause id="41062">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[back_unit_del(7770),unit_del(d,41018)].">
      <j1 rule="back_unit_del" parents="7770"/>
      <j2 rule="unit_del" parents="41018"/>
    </justification>
  </clause>

  <clause id="41076">
    <literal><![CDATA[
      k = b
    ]]></literal>
    <literal><![CDATA[
      -p(k,b)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      -p(k,m)
    ]]></literal>
    <justification jstring="[resolve(41018,a,4,f),flip(a),flip(c),flip(d),unit_del(c,27)].">
      <j1 rule="resolve" parents="41018 4"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="42555">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[resolve(38993,c,16,c),flip(d),merge(d),merge(e)].">
      <j1 rule="resolve" parents="38993 16"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="42567">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <justification jstring="[para(42555(c,1),30939(b,2)),merge(c),merge(d)].">
      <j1 rule="para" parents="42555 30939"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="42590">
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[resolve(42567,a,6869,d)].">
      <j1 rule="resolve" parents="42567 6869"/>
    </justification>
  </clause>

  <clause id="42615">
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[para(42590(b,1),42567(a,1)),merge(d),merge(e)].">
      <j1 rule="para" parents="42590 42567"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="42627">
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <justification jstring="[para(42615(c,1),41018(a,2)),merge(c)].">
      <j1 rule="para" parents="42615 41018"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="42628">
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <literal><![CDATA[
      -p(k,b)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[resolve(42627,b,41076,d)].">
      <j1 rule="resolve" parents="42627 41076"/>
    </justification>
  </clause>

  <clause id="42738">
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[resolve(42628,c,42567,a),merge(d)].">
      <j1 rule="resolve" parents="42628 42567"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="42757">
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[para(42738(c,1),42567(a,1)),merge(c),merge(d)].">
      <j1 rule="para" parents="42738 42567"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="42775">
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <justification jstring="[para(42757(b,1),41018(a,2)),merge(b)].">
      <j1 rule="para" parents="42757 41018"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="42793">
    <literal><![CDATA[
      b = x
    ]]></literal>
    <literal><![CDATA[
      m = x
    ]]></literal>
    <literal><![CDATA[
      -p(m,x)
    ]]></literal>
    <literal><![CDATA[
      -p(x,m)
    ]]></literal>
    <justification jstring="[resolve(42775,a,4,b),flip(a),flip(c),unit_del(a,27)].">
      <j1 rule="resolve" parents="42775 4"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="46117">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      p(j,m)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      j = x
    ]]></literal>
    <literal><![CDATA[
      -p(x,k)
    ]]></literal>
    <literal><![CDATA[
      k = x
    ]]></literal>
    <justification jstring="[para(40989(e,1),29(b,2))].">
      <j1 rule="para" parents="40989 29"/>
    </justification>
  </clause>

  <clause id="46131">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      p(j,m)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[factor(46117,b,e),merge(f),unit_del(e,41018)].">
      <j1 rule="factor" parents="46117"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="41018"/>
    </justification>
  </clause>

  <clause id="46133">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(j,m)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[para(46131(b,1),40815(b,1)),merge(d),unit_del(d,27)].">
      <j1 rule="para" parents="46131 40815"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="46148">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(j,m)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[para(46133(c,1),7620(b,2)),merge(d),merge(e)].">
      <j1 rule="para" parents="46133 7620"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="46160">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(j,m)
    ]]></literal>
    <justification jstring="[para(46148(c,1),7620(b,2)),merge(c),merge(d)].">
      <j1 rule="para" parents="46148 7620"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="46373">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      p(f(j),j)
    ]]></literal>
    <justification jstring="[resolve(46160,b,14,b),flip(b)].">
      <j1 rule="resolve" parents="46160 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46374">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      p(j,f(j))
    ]]></literal>
    <justification jstring="[resolve(46160,b,12,b),flip(b)].">
      <j1 rule="resolve" parents="46160 12"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46389">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(f(j),j)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[para(46373(b,1),40815(b,1)),merge(c),unit_del(c,27)].">
      <j1 rule="para" parents="46373 40815"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="46406">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(j,f(j))
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[para(46374(b,1),40815(b,1)),merge(c),unit_del(c,27)].">
      <j1 rule="para" parents="46374 40815"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="46428">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(f(j),j)
    ]]></literal>
    <justification jstring="[para(46389(c,1),7620(b,2)),merge(c),merge(d)].">
      <j1 rule="para" parents="46389 7620"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="46452">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      f(j) = j
    ]]></literal>
    <literal><![CDATA[
      f(j) = k
    ]]></literal>
    <justification jstring="[resolve(46428,b,29,b),flip(b),flip(c)].">
      <j1 rule="resolve" parents="46428 29"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46460">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <literal><![CDATA[
      p(f(j),b)
    ]]></literal>
    <justification jstring="[para(40815(b,1),46428(b,2)),merge(c)].">
      <j1 rule="para" parents="40815 46428"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="46498">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(j,f(j))
    ]]></literal>
    <justification jstring="[para(46406(c,1),7620(b,2)),merge(c),merge(d)].">
      <j1 rule="para" parents="46406 7620"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="46530">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <literal><![CDATA[
      p(j,f(b))
    ]]></literal>
    <justification jstring="[para(40815(b,1),46498(b,2,1)),merge(c)].">
      <j1 rule="para" parents="40815 46498"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="46576">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(f(j),b)
    ]]></literal>
    <justification jstring="[para(46460(b,1),7620(b,2)),merge(c),merge(d)].">
      <j1 rule="para" parents="46460 7620"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="46624">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(j,f(b))
    ]]></literal>
    <justification jstring="[para(46530(b,1),7620(b,2)),merge(c),merge(d)].">
      <j1 rule="para" parents="46530 7620"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="46636">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[para(41062(b,1),46624(b,1)),merge(d),unit_del(d,40932)].">
      <j1 rule="para" parents="41062 46624"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="40932"/>
    </justification>
  </clause>

  <clause id="46658">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      j = x
    ]]></literal>
    <literal><![CDATA[
      -p(x,b)
    ]]></literal>
    <literal><![CDATA[
      k = x
    ]]></literal>
    <justification jstring="[para(46636(b,1),29(b,2))].">
      <j1 rule="para" parents="46636 29"/>
    </justification>
  </clause>

  <clause id="46670">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <justification jstring="[factor(46658,b,e),unit_del(d,42775)].">
      <j1 rule="factor" parents="46658"/>
      <j2 rule="unit_del" parents="42775"/>
    </justification>
  </clause>

  <clause id="46709">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[para(46670(c,1),46624(b,1)),merge(c),unit_del(c,40932)].">
      <j1 rule="para" parents="46670 46624"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="40932"/>
    </justification>
  </clause>

  <clause id="46713">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <justification jstring="[para(46709(b,1),7633(b,2)),merge(b),merge(d)].">
      <j1 rule="para" parents="46709 7633"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="46755">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <justification jstring="[para(46713(b,1),46624(b,1)),merge(c),unit_del(c,40932)].">
      <j1 rule="para" parents="46713 46624"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="40932"/>
    </justification>
  </clause>

  <clause id="46777">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      f(j) = k
    ]]></literal>
    <justification jstring="[para(46452(b,1),46576(b,1)),merge(c),merge(d)].">
      <j1 rule="para" parents="46452 46576"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="46786">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      f(j) = m
    ]]></literal>
    <justification jstring="[para(46709(b,1),46777(b,2)),merge(b)].">
      <j1 rule="para" parents="46709 46777"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="46816">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <justification jstring="[para(46755(b,1),46786(b,1,1)),merge(b),unit_del(b,40825)].">
      <j1 rule="para" parents="46755 46786"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="40825"/>
    </justification>
  </clause>

  <clause id="46903">
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      j = k
    ]]></literal>
    <justification jstring="[para(41012(c,1),41006(e,2)),merge(d),unit_del(f,46816)].">
      <j1 rule="para" parents="41012 41006"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="46816"/>
    </justification>
  </clause>

  <clause id="47385">
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      j = x
    ]]></literal>
    <literal><![CDATA[
      -p(x,k)
    ]]></literal>
    <literal><![CDATA[
      k = x
    ]]></literal>
    <justification jstring="[para(46903(e,1),29(b,2))].">
      <j1 rule="para" parents="46903 29"/>
    </justification>
  </clause>

  <clause id="47388">
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <justification jstring="[factor(47385,c,g),merge(e),unit_del(e,41018)].">
      <j1 rule="factor" parents="47385"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="41018"/>
    </justification>
  </clause>

  <clause id="47396">
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[para(47388(d,1),40983(a,2)),merge(d)].">
      <j1 rule="para" parents="47388 40983"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="47400">
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <justification jstring="[para(47396(c,1),40983(a,1)),merge(c)].">
      <j1 rule="para" parents="47396 40983"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="47401">
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[resolve(47400,b,42793,d),flip(b),flip(c),unit_del(d,41018)].">
      <j1 rule="resolve" parents="47400 42793"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="unit_del" parents="41018"/>
    </justification>
  </clause>

  <clause id="47402">
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      p(f(k),k)
    ]]></literal>
    <justification jstring="[resolve(47400,b,14,b),flip(b)].">
      <j1 rule="resolve" parents="47400 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47407">
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[para(47401(c,1),40983(a,1)),merge(c)].">
      <j1 rule="para" parents="47401 40983"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="47429">
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      p(f(k),k)
    ]]></literal>
    <justification jstring="[para(47402(b,1),40983(a,1)),merge(c)].">
      <j1 rule="para" parents="47402 40983"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="47432">
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      p(f(b),k)
    ]]></literal>
    <justification jstring="[para(47407(b,1),47429(b,1,1)),merge(b)].">
      <j1 rule="para" parents="47407 47429"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="47434">
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      f(b) = k
    ]]></literal>
    <justification jstring="[resolve(47432,b,6,d),flip(b),flip(c),flip(d),unit_del(c,40825),unit_del(d,40824)].">
      <j1 rule="resolve" parents="47432 6"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="unit_del" parents="40825"/>
      <j2 rule="unit_del" parents="40824"/>
    </justification>
  </clause>

  <clause id="47472">
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <justification jstring="[para(47434(b,1),40932(a,2)),unit_del(b,41018)].">
      <j1 rule="para" parents="47434 40932"/>
      <j2 rule="unit_del" parents="41018"/>
    </justification>
  </clause>

  <clause id="47474">
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[resolve(47472,a,29,b)].">
      <j1 rule="resolve" parents="47472 29"/>
    </justification>
  </clause>

  <clause id="47476">
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      j = x
    ]]></literal>
    <literal><![CDATA[
      -p(x,m)
    ]]></literal>
    <literal><![CDATA[
      k = x
    ]]></literal>
    <justification jstring="[para(47474(a,1),29(b,2))].">
      <j1 rule="para" parents="47474 29"/>
    </justification>
  </clause>

  <clause id="47502">
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      f(b) = j
    ]]></literal>
    <literal><![CDATA[
      f(b) = k
    ]]></literal>
    <justification jstring="[resolve(47476,c,40868,a),flip(b),flip(c)].">
      <j1 rule="resolve" parents="47476 40868"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47503">
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[resolve(47476,c,40811,a)].">
      <j1 rule="resolve" parents="47476 40811"/>
    </justification>
  </clause>

  <clause id="47516">
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[para(47503(b,1),47474(a,1)),flip(c),merge(d),unit_del(c,27)].">
      <j1 rule="para" parents="47503 47474"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="47530">
    <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(47516(a,1),6(d,2))].">
      <j1 rule="para" parents="47516 6"/>
    </justification>
  </clause>

  <clause id="47544">
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      f(b) = k
    ]]></literal>
    <justification jstring="[para(47502(b,1),40932(a,2)),unit_del(c,47472)].">
      <j1 rule="para" parents="47502 40932"/>
      <j2 rule="unit_del" parents="47472"/>
    </justification>
  </clause>

  <clause id="47555">
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[para(47544(b,1),40932(a,2)),unit_del(b,41018)].">
      <j1 rule="para" parents="47544 40932"/>
      <j2 rule="unit_del" parents="41018"/>
    </justification>
  </clause>

  <clause id="47557">
    <literal><![CDATA[
      m = x
    ]]></literal>
    <literal><![CDATA[
      b = x
    ]]></literal>
    <literal><![CDATA[
      -p(x,m)
    ]]></literal>
    <justification jstring="[back_rewrite(47530),rewrite(47555(1),47555(4)),merge(c),unit_del(a,27)].">
      <j1 rule="back_rewrite" parents="47530"/>
      <j2 rule="rewrite" parents="47555 47555"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="47708">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[resolve(47557,c,40868,a),flip(a),flip(b),unit_del(a,40825),unit_del(b,40824)].">
      <j1 rule="resolve" parents="47557 40868"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="unit_del" parents="40825"/>
      <j2 rule="unit_del" parents="40824"/>
    </justification>
  </clause>

</proof>

</proofs>
