<?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 August-2006A, August 2006.
Process 11482 was started by mccune on cleo.thornwood,
Sat Aug 12 21:02:06 2006
The command was "/home/mccune/bin/prover9 -f wang-eq.in wang3-eq.in".
]]></heading>

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

<comments><![CDATA[
% Proof 1 at 39.94 (+ 0.28) seconds.
% Length of proof is 284.
% Level of proof is 127.
% Maximum clause weight is 25.
% Given clauses 3013.
]]></comments>

  <clause id="1">
    <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">
    <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">
    <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">
    <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">
    <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">
    <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">
    <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">
    <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">
    <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">
    <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">
    <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">
    <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">
    <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">
    <literal><![CDATA[
      m != b
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="28">
    <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">
    <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="24548">
    <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="24579">
    <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(24548,c,58,c(flip)),merge(e),merge(f)].">
      <j1 rule="resolve" parents="24548 58"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="24588">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(g(k),k)
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <justification jstring="[para(24579(d,1),11729(b,2)),merge(d),merge(e),merge(f)].">
      <j1 rule="para" parents="24579 11729"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="24602">
    <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(24588,b,6,d),flip(c),flip(d),flip(e)].">
      <j1 rule="resolve" parents="24588 6"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24606">
    <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(24602,c,18,c),flip(e),merge(f)].">
      <j1 rule="resolve" parents="24602 18"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="24623">
    <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(24606(c,1),8986(b,2)),merge(e),merge(f),merge(g)].">
      <j1 rule="para" parents="24606 8986"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="24630">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[resolve(24623,c,16,c),flip(d),merge(d),merge(e)].">
      <j1 rule="resolve" parents="24623 16"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="24650">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <justification jstring="[para(24630(c,1),11729(b,2)),merge(c),merge(d),merge(e)].">
      <j1 rule="para" parents="24630 11729"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="24724">
    <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(24650,b,39,h),flip(d),flip(f),unit_del(d,27)].">
      <j1 rule="resolve" parents="24650 39"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="24728">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      p(f(k),k)
    ]]></literal>
    <justification jstring="[resolve(24650,b,14,b),flip(b)].">
      <j1 rule="resolve" parents="24650 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24729">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      p(k,f(k))
    ]]></literal>
    <justification jstring="[resolve(24650,b,12,b),flip(b)].">
      <j1 rule="resolve" parents="24650 12"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24743">
    <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(24724,a,b),merge(f)].">
      <j1 rule="factor" parents="24724"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="24813">
    <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(24728,b,11711,e),merge(c)].">
      <j1 rule="resolve" parents="24728 11711"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="24819">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(f(k),k)
    ]]></literal>
    <literal><![CDATA[
      p(g(k),k)
    ]]></literal>
    <justification jstring="[resolve(24728,b,58,c(flip)),merge(c)].">
      <j1 rule="resolve" parents="24728 58"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="24865">
    <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(24729,b,11711,e),merge(c)].">
      <j1 rule="resolve" parents="24729 11711"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="24883">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,f(k))
    ]]></literal>
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <justification jstring="[para(24729(b,1),6860(a,2))].">
      <j1 rule="para" parents="24729 6860"/>
    </justification>
  </clause>

  <clause id="24885">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,f(k))
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <justification jstring="[para(24729(b,1),7647(a,1)),merge(d)].">
      <j1 rule="para" parents="24729 7647"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="25142">
    <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(24819,c,6,d),flip(c),flip(d),flip(e)].">
      <j1 rule="resolve" parents="24819 6"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26104">
    <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(24743,c,2192,a)].">
      <j1 rule="resolve" parents="24743 2192"/>
    </justification>
  </clause>

  <clause id="26194">
    <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(26104,d,58,c(flip)),merge(e),merge(f)].">
      <j1 rule="resolve" parents="26104 58"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="26197">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(g(k),k)
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <justification jstring="[para(26194(c,1),2192(a,2)),merge(d),merge(e)].">
      <j1 rule="para" parents="26194 2192"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="26207">
    <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(26197,b,6,d),flip(c),flip(d),flip(e)].">
      <j1 rule="resolve" parents="26197 6"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26251">
    <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(24813,d,16,c),flip(e),merge(e),merge(f)].">
      <j1 rule="resolve" parents="24813 16"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="26279">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(f(k),k)
    ]]></literal>
    <literal><![CDATA[
      p(k,k)
    ]]></literal>
    <justification jstring="[para(26251(d,1),24728(b,1)),flip(e),merge(d),merge(f),unit_del(d,27)].">
      <j1 rule="para" parents="26251 24728"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="26288">
    <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(26279,b,6,d),flip(c),flip(d),flip(e)].">
      <j1 rule="resolve" parents="26279 6"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26393">
    <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(24865,d,16,c),flip(e),merge(e),merge(f)].">
      <j1 rule="resolve" parents="24865 16"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="26419">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,f(k))
    ]]></literal>
    <literal><![CDATA[
      p(k,k)
    ]]></literal>
    <justification jstring="[para(26393(d,1),24729(b,1)),flip(e),merge(d),merge(f),unit_del(d,27)].">
      <j1 rule="para" parents="26393 24729"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="27144">
    <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(26207,c,18,c),flip(e),merge(f)].">
      <j1 rule="resolve" parents="26207 18"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="27158">
    <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(27144(c,1),18(c,1)),flip(e),flip(g),merge(e),merge(f)].">
      <j1 rule="para" parents="27144 18"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="27195">
    <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(27158,e,24729,b),merge(e)].">
      <j1 rule="resolve" parents="27158 24729"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="27203">
    <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(27195,c,16,c),flip(e),merge(e),merge(f)].">
      <j1 rule="resolve" parents="27195 16"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="27211">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,f(k))
    ]]></literal>
    <justification jstring="[para(27203(c,1),2192(a,2)),merge(d),merge(e)].">
      <j1 rule="para" parents="27203 2192"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="27327">
    <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(26288(c,1),26279(b,1)),merge(e),merge(f),merge(g)].">
      <j1 rule="para" parents="26288 26279"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="27328">
    <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(27327,c,8,c),flip(d)].">
      <j1 rule="resolve" parents="27327 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27368">
    <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(27328,e,24650,b),merge(e)].">
      <j1 rule="resolve" parents="27328 24650"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="27386">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,k)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[para(27368(c,1),26419(b,2)),merge(d),merge(e),merge(f)].">
      <j1 rule="para" parents="27368 26419"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="27402">
    <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(27386,c,11711,e),merge(c),merge(d)].">
      <j1 rule="resolve" parents="27386 11711"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="27804">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,k)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[resolve(27402,c,16,c),flip(d),merge(d),merge(e)].">
      <j1 rule="resolve" parents="27402 16"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="27843">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,k)
    ]]></literal>
    <justification jstring="[para(27804(c,1),27386(c,1)),flip(e),merge(c),merge(d),unit_del(c,27)].">
      <j1 rule="para" parents="27804 27386"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="31895">
    <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(24728(b,1),25142(c,2)),merge(c),merge(d),merge(f)].">
      <j1 rule="para" parents="24728 25142"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="31900">
    <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(31895(c,1),18(c,1)),flip(d),flip(f),merge(e)].">
      <j1 rule="para" parents="31895 18"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="32103">
    <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(31900,e,24728,b),merge(e),merge(f)].">
      <j1 rule="resolve" parents="31900 24728"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="32110">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(f(k),k)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[resolve(32103,c,16,c),flip(d),merge(d),merge(e)].">
      <j1 rule="resolve" parents="32103 16"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="32132">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(f(k),k)
    ]]></literal>
    <justification jstring="[para(32110(c,1),24728(b,1)),flip(d),merge(c),merge(e),unit_del(c,27)].">
      <j1 rule="para" parents="32110 24728"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="32142">
    <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(32132,b,6,d),flip(b),flip(c),flip(d)].">
      <j1 rule="resolve" parents="32132 6"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32232">
    <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(32142,b,10,c),flip(d)].">
      <j1 rule="resolve" parents="32142 10"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32292">
    <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(32232,e,24650,b),merge(e)].">
      <j1 rule="resolve" parents="32232 24650"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="32293">
    <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(32292,b,8,c),flip(d),merge(d)].">
      <j1 rule="resolve" parents="32292 8"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="32304">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      f(k) = b
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[resolve(32293,d,24650,b),merge(d)].">
      <j1 rule="resolve" parents="32293 24650"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="32319">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <justification jstring="[para(32304(b,1),24883(b,2)),merge(c),merge(d)].">
      <j1 rule="para" parents="32304 24883"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="32320">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <justification jstring="[para(32304(b,1),24885(b,2)),merge(c),merge(d)].">
      <j1 rule="para" parents="32304 24885"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="32328">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <justification jstring="[para(32304(b,1),27211(c,2)),merge(c),merge(e)].">
      <j1 rule="para" parents="32304 27211"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="32507">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <justification jstring="[para(32319(b,1),6860(a,2)),merge(c)].">
      <j1 rule="para" parents="32319 6860"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="32522">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[resolve(32507,a,3445,d),merge(b)].">
      <j1 rule="resolve" parents="32507 3445"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="32568">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <justification jstring="[para(32320(b,1),7647(a,1)),merge(c),merge(d)].">
      <j1 rule="para" parents="32320 7647"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="32573">
    <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(32568,a,6869,d)].">
      <j1 rule="resolve" parents="32568 6869"/>
    </justification>
  </clause>

  <clause id="32727">
    <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(32328,b,27158,e),merge(c),merge(d)].">
      <j1 rule="resolve" parents="32328 27158"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="32820">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[para(32522(b,1),6860(a,2)),merge(c)].">
      <j1 rule="para" parents="32522 6860"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="32839">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <justification jstring="[para(32820(b,1),2192(a,2)),merge(c)].">
      <j1 rule="para" parents="32820 2192"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="32841">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      p(b,j)
    ]]></literal>
    <justification jstring="[para(32820(b,1),3561(b,1)),merge(b)].">
      <j1 rule="para" parents="32820 3561"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="32845">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <justification jstring="[para(32820(b,1),7620(b,2)),merge(c)].">
      <j1 rule="para" parents="32820 7620"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="32863">
    <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(32841,b,2,e),flip(d),merge(c),unit_del(b,27)].">
      <j1 rule="resolve" parents="32841 2"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="34148">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <justification jstring="[resolve(32863,d,32845,b),merge(d)].">
      <j1 rule="resolve" parents="32863 32845"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="34193">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <justification jstring="[para(34148(b,1),32841(b,2)),merge(c),merge(d)].">
      <j1 rule="para" parents="34148 32841"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="34197">
    <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(34193(b,1),29(b,2))].">
      <j1 rule="para" parents="34193 29"/>
    </justification>
  </clause>

  <clause id="34437">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[resolve(34197,c,32839,b),merge(d)].">
      <j1 rule="resolve" parents="34197 32839"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="34448">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[para(34437(b,1),32841(b,2)),merge(c),merge(d)].">
      <j1 rule="para" parents="34437 32841"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="34454">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <justification jstring="[para(34448(b,1),6860(a,2)),merge(b)].">
      <j1 rule="para" parents="34448 6860"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="34458">
    <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,34454)].">
      <j1 rule="back_unit_del" parents="7797"/>
      <j2 rule="unit_del" parents="34454"/>
    </justification>
  </clause>

  <clause id="34465">
    <literal><![CDATA[
      p(f(b),b)
    ]]></literal>
    <justification jstring="[resolve(34454,a,14,b),unit_del(a,27)].">
      <j1 rule="resolve" parents="34454 14"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="34466">
    <literal><![CDATA[
      p(b,f(b))
    ]]></literal>
    <justification jstring="[resolve(34454,a,12,b),unit_del(a,27)].">
      <j1 rule="resolve" parents="34454 12"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="34467">
    <literal><![CDATA[
      f(b) != b
    ]]></literal>
    <justification jstring="[ur(10,a,27,a,b,34454,a)].">
      <j1 rule="ur" parents="10 27 34454"/>
    </justification>
  </clause>

  <clause id="34468">
    <literal><![CDATA[
      f(b) != m
    ]]></literal>
    <justification jstring="[ur(8,a,27,a,b,34454,a)].">
      <j1 rule="ur" parents="8 27 34454"/>
    </justification>
  </clause>

  <clause id="34510">
    <literal><![CDATA[
      p(k,j)
    ]]></literal>
    <literal><![CDATA[
      f(b) = k
    ]]></literal>
    <justification jstring="[resolve(34465,a,6885,e),flip(b),flip(c),flip(d),unit_del(c,34468),unit_del(d,34467)].">
      <j1 rule="resolve" parents="34465 6885"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="unit_del" parents="34468"/>
      <j2 rule="unit_del" parents="34467"/>
    </justification>
  </clause>

  <clause id="34512">
    <literal><![CDATA[
      p(f(b),m)
    ]]></literal>
    <justification jstring="[resolve(34465,a,2,e),flip(a),flip(d),unit_del(a,34468),unit_del(c,27),unit_del(d,34467),unit_del(e,34466)].">
      <j1 rule="resolve" parents="34465 2"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="unit_del" parents="34468"/>
      <j2 rule="unit_del" parents="27"/>
      <j2 rule="unit_del" parents="34467"/>
      <j2 rule="unit_del" parents="34466"/>
    </justification>
  </clause>

  <clause id="34561">
    <literal><![CDATA[
      p(m,k)
    ]]></literal>
    <literal><![CDATA[
      f(b) = k
    ]]></literal>
    <justification jstring="[resolve(34512,a,63,e),flip(b),flip(c),flip(d),unit_del(c,34468),unit_del(d,34467)].">
      <j1 rule="resolve" parents="34512 63"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="unit_del" parents="34468"/>
      <j2 rule="unit_del" parents="34467"/>
    </justification>
  </clause>

  <clause id="34569">
    <literal><![CDATA[
      -p(m,f(b))
    ]]></literal>
    <justification jstring="[resolve(34512,a,4,e),flip(a),flip(c),flip(d),unit_del(a,34467),unit_del(b,34465),unit_del(c,27),unit_del(d,34468)].">
      <j1 rule="resolve" parents="34512 4"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="unit_del" parents="34467"/>
      <j2 rule="unit_del" parents="34465"/>
      <j2 rule="unit_del" parents="27"/>
      <j2 rule="unit_del" parents="34468"/>
    </justification>
  </clause>

  <clause id="34622">
    <literal><![CDATA[
      p(k,j)
    ]]></literal>
    <justification jstring="[para(6881(b,1),34510(b,2)),merge(b),unit_del(b,34467)].">
      <j1 rule="para" parents="6881 34510"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="34467"/>
    </justification>
  </clause>

  <clause id="34624">
    <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,34622)].">
      <j1 rule="back_unit_del" parents="7636"/>
      <j2 rule="unit_del" parents="34622"/>
    </justification>
  </clause>

  <clause id="34640">
    <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(34622,a,2,e),flip(a),flip(c)].">
      <j1 rule="resolve" parents="34622 2"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34646">
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[para(32573(b,1),34622(a,1)),merge(d)].">
      <j1 rule="para" parents="32573 34622"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="34652">
    <literal><![CDATA[
      p(m,k)
    ]]></literal>
    <justification jstring="[para(49(a,1),34561(b,2)),merge(b),unit_del(b,34468)].">
      <j1 rule="para" parents="49 34561"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="34468"/>
    </justification>
  </clause>

  <clause id="34692">
    <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,34652)].">
      <j1 rule="back_unit_del" parents="7770"/>
      <j2 rule="unit_del" parents="34652"/>
    </justification>
  </clause>

  <clause id="34706">
    <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(34652,a,4,f),flip(a),flip(c),flip(d),unit_del(c,27)].">
      <j1 rule="resolve" parents="34652 4"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="36216">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[resolve(32727,c,16,c),flip(d),merge(d),merge(e)].">
      <j1 rule="resolve" parents="32727 16"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="36228">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <justification jstring="[para(36216(c,1),27843(b,2)),merge(c),merge(d)].">
      <j1 rule="para" parents="36216 27843"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="36248">
    <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(36228,a,6869,d)].">
      <j1 rule="resolve" parents="36228 6869"/>
    </justification>
  </clause>

  <clause id="36276">
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[para(36248(b,1),36228(a,1)),merge(d),merge(e)].">
      <j1 rule="para" parents="36248 36228"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="36292">
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <justification jstring="[para(36276(c,1),34652(a,2)),merge(c)].">
      <j1 rule="para" parents="36276 34652"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="36293">
    <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(36292,b,34706,d)].">
      <j1 rule="resolve" parents="36292 34706"/>
    </justification>
  </clause>

  <clause id="36396">
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[resolve(36293,c,36228,a),merge(d)].">
      <j1 rule="resolve" parents="36293 36228"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="36414">
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[para(36396(c,1),36228(a,1)),merge(c),merge(d)].">
      <j1 rule="para" parents="36396 36228"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="36436">
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <justification jstring="[para(36414(b,1),34652(a,2)),merge(b)].">
      <j1 rule="para" parents="36414 34652"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="36454">
    <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(36436,a,4,b),flip(a),flip(c),unit_del(a,27)].">
      <j1 rule="resolve" parents="36436 4"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="39809">
    <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(34624(e,1),29(b,2))].">
      <j1 rule="para" parents="34624 29"/>
    </justification>
  </clause>

  <clause id="39823">
    <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(39809,b,e),merge(f),unit_del(e,34652)].">
      <j1 rule="factor" parents="39809"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="34652"/>
    </justification>
  </clause>

  <clause id="39825">
    <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(39823(b,1),34458(b,1)),merge(d),unit_del(d,27)].">
      <j1 rule="para" parents="39823 34458"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="39840">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(j,m)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[para(39825(c,1),7620(b,2)),merge(d),merge(e)].">
      <j1 rule="para" parents="39825 7620"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="39852">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(j,m)
    ]]></literal>
    <justification jstring="[para(39840(c,1),7620(b,2)),merge(c),merge(d)].">
      <j1 rule="para" parents="39840 7620"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="39855">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      p(f(j),j)
    ]]></literal>
    <justification jstring="[resolve(39852,b,14,b),flip(b)].">
      <j1 rule="resolve" parents="39852 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39856">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      p(j,f(j))
    ]]></literal>
    <justification jstring="[resolve(39852,b,12,b),flip(b)].">
      <j1 rule="resolve" parents="39852 12"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39871">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(f(j),j)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[para(39855(b,1),34458(b,1)),merge(c),unit_del(c,27)].">
      <j1 rule="para" parents="39855 34458"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="39889">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(j,f(j))
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[para(39856(b,1),34458(b,1)),merge(c),unit_del(c,27)].">
      <j1 rule="para" parents="39856 34458"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="39918">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(f(j),j)
    ]]></literal>
    <justification jstring="[para(39871(c,1),7620(b,2)),merge(c),merge(d)].">
      <j1 rule="para" parents="39871 7620"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="39939">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      f(j) = j
    ]]></literal>
    <literal><![CDATA[
      f(j) = k
    ]]></literal>
    <justification jstring="[resolve(39918,b,29,b),flip(b),flip(c)].">
      <j1 rule="resolve" parents="39918 29"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39947">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <literal><![CDATA[
      p(f(j),b)
    ]]></literal>
    <justification jstring="[para(34458(b,1),39918(b,2)),merge(c)].">
      <j1 rule="para" parents="34458 39918"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="39982">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(j,f(j))
    ]]></literal>
    <justification jstring="[para(39889(c,1),7620(b,2)),merge(c),merge(d)].">
      <j1 rule="para" parents="39889 7620"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="40011">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <literal><![CDATA[
      p(j,f(b))
    ]]></literal>
    <justification jstring="[para(34458(b,1),39982(b,2,1)),merge(c)].">
      <j1 rule="para" parents="34458 39982"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="40081">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(f(j),b)
    ]]></literal>
    <justification jstring="[para(39947(b,1),7620(b,2)),merge(c),merge(d)].">
      <j1 rule="para" parents="39947 7620"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="40139">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(j,f(b))
    ]]></literal>
    <justification jstring="[para(40011(b,1),7620(b,2)),merge(c),merge(d)].">
      <j1 rule="para" parents="40011 7620"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="40151">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[para(34692(b,1),40139(b,1)),merge(d),unit_del(d,34569)].">
      <j1 rule="para" parents="34692 40139"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="34569"/>
    </justification>
  </clause>

  <clause id="40182">
    <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(40151(b,1),29(b,2))].">
      <j1 rule="para" parents="40151 29"/>
    </justification>
  </clause>

  <clause id="40193">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <justification jstring="[factor(40182,b,e),unit_del(d,36436)].">
      <j1 rule="factor" parents="40182"/>
      <j2 rule="unit_del" parents="36436"/>
    </justification>
  </clause>

  <clause id="40231">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[para(40193(c,1),40139(b,1)),merge(c),unit_del(c,34569)].">
      <j1 rule="para" parents="40193 40139"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="34569"/>
    </justification>
  </clause>

  <clause id="40238">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <justification jstring="[para(40231(b,1),7633(b,2)),merge(b),merge(d)].">
      <j1 rule="para" parents="40231 7633"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="40282">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <justification jstring="[para(40238(b,1),40139(b,1)),merge(c),unit_del(c,34569)].">
      <j1 rule="para" parents="40238 40139"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="34569"/>
    </justification>
  </clause>

  <clause id="40314">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      f(j) = k
    ]]></literal>
    <justification jstring="[para(39939(b,1),40081(b,1)),merge(c),merge(d)].">
      <j1 rule="para" parents="39939 40081"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="40323">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      f(j) = m
    ]]></literal>
    <justification jstring="[para(40231(b,1),40314(b,2)),merge(b)].">
      <j1 rule="para" parents="40231 40314"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="40354">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <justification jstring="[para(40282(b,1),40323(b,1,1)),merge(b),unit_del(b,34468)].">
      <j1 rule="para" parents="40282 40323"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="34468"/>
    </justification>
  </clause>

  <clause id="40450">
    <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(34646(c,1),34640(e,2)),merge(d),unit_del(f,40354)].">
      <j1 rule="para" parents="34646 34640"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="40354"/>
    </justification>
  </clause>

  <clause id="41222">
    <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(40450(e,1),29(b,2))].">
      <j1 rule="para" parents="40450 29"/>
    </justification>
  </clause>

  <clause id="41225">
    <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(41222,c,g),merge(e),unit_del(e,34652)].">
      <j1 rule="factor" parents="41222"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="34652"/>
    </justification>
  </clause>

  <clause id="41228">
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[para(41225(d,1),34622(a,2)),merge(d)].">
      <j1 rule="para" parents="41225 34622"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="41236">
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <justification jstring="[para(41228(c,1),34622(a,1)),merge(c)].">
      <j1 rule="para" parents="41228 34622"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="41237">
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[resolve(41236,b,36454,d),flip(b),flip(c),unit_del(d,34652)].">
      <j1 rule="resolve" parents="41236 36454"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="unit_del" parents="34652"/>
    </justification>
  </clause>

  <clause id="41238">
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      p(f(k),k)
    ]]></literal>
    <justification jstring="[resolve(41236,b,14,b),flip(b)].">
      <j1 rule="resolve" parents="41236 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41247">
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[para(41237(c,1),34622(a,1)),merge(c)].">
      <j1 rule="para" parents="41237 34622"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="41269">
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      p(f(k),k)
    ]]></literal>
    <justification jstring="[para(41238(b,1),34622(a,1)),merge(c)].">
      <j1 rule="para" parents="41238 34622"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="41272">
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      p(f(b),k)
    ]]></literal>
    <justification jstring="[para(41247(b,1),41269(b,1,1)),merge(b)].">
      <j1 rule="para" parents="41247 41269"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="41274">
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      f(b) = k
    ]]></literal>
    <justification jstring="[resolve(41272,b,6,d),flip(b),flip(c),flip(d),unit_del(c,34468),unit_del(d,34467)].">
      <j1 rule="resolve" parents="41272 6"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="unit_del" parents="34468"/>
      <j2 rule="unit_del" parents="34467"/>
    </justification>
  </clause>

  <clause id="41308">
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <justification jstring="[para(41274(b,1),34569(a,2)),unit_del(b,34652)].">
      <j1 rule="para" parents="41274 34569"/>
      <j2 rule="unit_del" parents="34652"/>
    </justification>
  </clause>

  <clause id="41310">
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[resolve(41308,a,29,b)].">
      <j1 rule="resolve" parents="41308 29"/>
    </justification>
  </clause>

  <clause id="41312">
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      j = x
    ]]></literal>
    <literal><![CDATA[
      -p(x,m)
    ]]></literal>
    <literal><![CDATA[
      k = x
    ]]></literal>
    <justification jstring="[para(41310(a,1),29(b,2))].">
      <j1 rule="para" parents="41310 29"/>
    </justification>
  </clause>

  <clause id="41345">
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      f(b) = j
    ]]></literal>
    <literal><![CDATA[
      f(b) = k
    ]]></literal>
    <justification jstring="[resolve(41312,c,34512,a),flip(b),flip(c)].">
      <j1 rule="resolve" parents="41312 34512"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41346">
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[resolve(41312,c,34454,a)].">
      <j1 rule="resolve" parents="41312 34454"/>
    </justification>
  </clause>

  <clause id="41359">
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[para(41346(b,1),41310(a,1)),flip(c),merge(d),unit_del(c,27)].">
      <j1 rule="para" parents="41346 41310"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="41360">
    <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(41359(a,1),6(d,2))].">
      <j1 rule="para" parents="41359 6"/>
    </justification>
  </clause>

  <clause id="41378">
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      f(b) = k
    ]]></literal>
    <justification jstring="[para(41345(b,1),34569(a,2)),unit_del(c,41308)].">
      <j1 rule="para" parents="41345 34569"/>
      <j2 rule="unit_del" parents="41308"/>
    </justification>
  </clause>

  <clause id="41389">
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[para(41378(b,1),34569(a,2)),unit_del(b,34652)].">
      <j1 rule="para" parents="41378 34569"/>
      <j2 rule="unit_del" parents="34652"/>
    </justification>
  </clause>

  <clause id="41392">
    <literal><![CDATA[
      m = x
    ]]></literal>
    <literal><![CDATA[
      b = x
    ]]></literal>
    <literal><![CDATA[
      -p(x,m)
    ]]></literal>
    <justification jstring="[back_rewrite(41360),rewrite(41389(1),41389(4)),merge(c),unit_del(a,27)].">
      <j1 rule="back_rewrite" parents="41360"/>
      <j2 rule="rewrite" parents="41389 41389"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="41514">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[resolve(41392,c,34512,a),flip(a),flip(b),unit_del(a,34468),unit_del(b,34467)].">
      <j1 rule="resolve" parents="41392 34512"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="unit_del" parents="34468"/>
      <j2 rule="unit_del" parents="34467"/>
    </justification>
  </clause>

</proof>

</proofs>
