<?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 April-2007, April 2007.
Process 27100 was started by mccune on cleo,
Fri Apr 13 09:20:41 2007
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 44.44 (+ 0.19) seconds.
% Length of proof is 284.
% Level of proof is 127.
% Maximum clause weight is 25.
% Given clauses 2993.
]]></comments>

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

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

  <clause id="3" type="assumption">
    <literal><![CDATA[
      x = b
    ]]></literal>
    <literal><![CDATA[
      -p(x,b)
    ]]></literal>
    <literal><![CDATA[
      y = b
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <literal><![CDATA[
      -p(x,y)
    ]]></literal>
    <literal><![CDATA[
      -p(y,x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="4">
    <literal><![CDATA[
      b = x
    ]]></literal>
    <literal><![CDATA[
      -p(x,b)
    ]]></literal>
    <literal><![CDATA[
      b = y
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <literal><![CDATA[
      -p(x,y)
    ]]></literal>
    <literal><![CDATA[
      -p(y,x)
    ]]></literal>
    <justification jstring="[copy(3),flip(a),flip(c)].">
      <j1 rule="copy" parents="3"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

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

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

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

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

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

  <clause id="10">
    <literal><![CDATA[
      m = x
    ]]></literal>
    <literal><![CDATA[
      -p(x,m)
    ]]></literal>
    <literal><![CDATA[
      f(x) != x
    ]]></literal>
    <justification jstring="[copy(9),flip(a)].">
      <j1 rule="copy" parents="9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11" type="assumption">
    <literal><![CDATA[
      x = m
    ]]></literal>
    <literal><![CDATA[
      -p(x,m)
    ]]></literal>
    <literal><![CDATA[
      p(x,f(x))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  <clause id="28" type="assumption">
    <literal><![CDATA[
      x = j
    ]]></literal>
    <literal><![CDATA[
      -p(x,j)
    ]]></literal>
    <literal><![CDATA[
      x = k
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

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

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

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

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

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

  <clause id="49">
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      p(m,k)
    ]]></literal>
    <justification jstring="[xx_res(24,b)].">
      <j1 rule="xx_res" parents="24"/>
    </justification>
  </clause>

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

  <clause id="57">
    <literal><![CDATA[
      p(x,b)
    ]]></literal>
    <literal><![CDATA[
      p(x,g(x))
    ]]></literal>
    <literal><![CDATA[
      m != x
    ]]></literal>
    <justification jstring="[para(20(a,1),27(a,2))].">
      <j1 rule="para" parents="20 27"/>
    </justification>
  </clause>

  <clause id="58">
    <literal><![CDATA[
      p(x,b)
    ]]></literal>
    <literal><![CDATA[
      p(g(x),x)
    ]]></literal>
    <literal><![CDATA[
      m != x
    ]]></literal>
    <justification jstring="[para(22(a,1),27(a,2))].">
      <j1 rule="para" parents="22 27"/>
    </justification>
  </clause>

  <clause id="61">
    <literal><![CDATA[
      j = k
    ]]></literal>
    <literal><![CDATA[
      p(k,j)
    ]]></literal>
    <justification jstring="[xx_res(31,c)].">
      <j1 rule="xx_res" parents="31"/>
    </justification>
  </clause>

  <clause id="80">
    <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="83">
    <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="88">
    <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="89">
    <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="92">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <justification jstring="[para(52(a,1),88(b,2)),merge(b)].">
      <j1 rule="para" parents="52 88"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="99">
    <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),92(b,2))].">
      <j1 rule="para" parents="22 92"/>
    </justification>
  </clause>

  <clause id="123">
    <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="226">
    <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(89,c,88,b)].">
      <j1 rule="resolve" parents="89 88"/>
    </justification>
  </clause>

  <clause id="232">
    <literal><![CDATA[
      p(k,j)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <justification jstring="[para(226(b,1),61(a,1)),flip(d),merge(d),merge(e)].">
      <j1 rule="para" parents="226 61"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="262">
    <literal><![CDATA[
      p(k,j)
    ]]></literal>
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <justification jstring="[para(232(b,1),52(a,1)),merge(d),unit_del(c,27)].">
      <j1 rule="para" parents="232 52"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="265">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(b,j)
    ]]></literal>
    <justification jstring="[para(52(a,1),262(a,1)),merge(c)].">
      <j1 rule="para" parents="52 262"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="267">
    <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(265,b,2,e),flip(d),unit_del(b,27)].">
      <j1 rule="resolve" parents="265 2"/>
      <j2 rule="flip"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="356">
    <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(99,b,29,b),flip(d),flip(e)].">
      <j1 rule="resolve" parents="99 29"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1993">
    <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="2009">
    <literal><![CDATA[
      p(m,k)
    ]]></literal>
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      g(k) = b
    ]]></literal>
    <justification jstring="[para(1993(c,1),126(b,1)),merge(d),merge(e),merge(f)].">
      <j1 rule="para" parents="1993 126"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="2018">
    <literal><![CDATA[
      p(m,k)
    ]]></literal>
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <justification jstring="[para(2009(c,1),123(b,2)),merge(c),merge(d),merge(e)].">
      <j1 rule="para" parents="2009 123"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="2026">
    <literal><![CDATA[
      p(m,k)
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <justification jstring="[para(49(a,1),2018(b,1)),merge(b)].">
      <j1 rule="para" parents="49 2018"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="3083">
    <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(356,d,18,c),flip(e),merge(f)].">
      <j1 rule="resolve" parents="356 18"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="3091">
    <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(3083(d,1),16(c,1)),flip(e),merge(e),merge(f)].">
      <j1 rule="para" parents="3083 16"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="3112">
    <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(3091,e,52,a),merge(e)].">
      <j1 rule="resolve" parents="3091 52"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="3117">
    <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(3112,d,26,b(flip)),flip(d)].">
      <j1 rule="resolve" parents="3112 26"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3201">
    <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(3117(d,1),265(b,2)),merge(e),merge(f)].">
      <j1 rule="para" parents="3117 265"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="3204">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <justification jstring="[para(52(a,1),3201(d,2)),merge(c),merge(e)].">
      <j1 rule="para" parents="52 3201"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="3205">
    <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(3204,b,267,e),merge(c)].">
      <j1 rule="resolve" parents="3204 267"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="3207">
    <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(3204,b,83,e),flip(d),flip(e),flip(f),merge(c)].">
      <j1 rule="resolve" parents="3204 83"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="3219">
    <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(3205(d,1),265(b,2)),merge(e),merge(f)].">
      <j1 rule="para" parents="3205 265"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="3224">
    <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(3219,d,26,b(flip)),flip(d)].">
      <j1 rule="resolve" parents="3219 26"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3254">
    <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),3207(c,2)),merge(b),merge(f)].">
      <j1 rule="para" parents="52 3207"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="3255">
    <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(3254,d,24,b(flip)),flip(d)].">
      <j1 rule="resolve" parents="3254 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3257">
    <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(3254(d,1),262(a,2)),merge(e)].">
      <j1 rule="para" parents="3254 262"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="3310">
    <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(3224(d,1),265(b,2)),merge(e),merge(f)].">
      <j1 rule="para" parents="3224 265"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="3313">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <justification jstring="[para(3219(d,1),3310(d,1)),merge(d),merge(e),merge(f),merge(g)].">
      <j1 rule="para" parents="3219 3310"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="3318">
    <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(3313,b,29,b)].">
      <j1 rule="resolve" parents="3313 29"/>
    </justification>
  </clause>

  <clause id="3325">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[para(3318(c,1),265(b,2)),merge(d),merge(e)].">
      <j1 rule="para" parents="3318 265"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="3332">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <justification jstring="[para(3325(c,1),52(a,1)),merge(d),unit_del(c,27)].">
      <j1 rule="para" parents="3325 52"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="3335">
    <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(3332,a,2,e),flip(d),merge(c),unit_del(b,27)].">
      <j1 rule="resolve" parents="3332 2"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="3339">
    <literal><![CDATA[
      p(m,k)
    ]]></literal>
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <justification jstring="[para(49(a,1),3332(a,2)),merge(c)].">
      <j1 rule="para" parents="49 3332"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="3353">
    <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(3339,a,89,c)].">
      <j1 rule="resolve" parents="3339 89"/>
    </justification>
  </clause>

  <clause id="3431">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      p(k,j)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[para(3353(c,1),61(a,1)),flip(d),merge(d),merge(e)].">
      <j1 rule="para" parents="3353 61"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="3446">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      p(k,j)
    ]]></literal>
    <justification jstring="[para(3431(c,1),3332(a,2)),merge(c),merge(d)].">
      <j1 rule="para" parents="3431 3332"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="3817">
    <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),3255(d,2)),merge(b),merge(e)].">
      <j1 rule="para" parents="52 3255"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="3828">
    <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(3817,c,26,b(flip)),flip(d),merge(e)].">
      <j1 rule="resolve" parents="3817 26"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="3840">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      p(j,k)
    ]]></literal>
    <justification jstring="[para(3828(d,1),265(b,2)),merge(d),merge(e)].">
      <j1 rule="para" parents="3828 265"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="3843">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <justification jstring="[para(3257(c,1),3840(c,1)),merge(d),merge(e),merge(f)].">
      <j1 rule="para" parents="3257 3840"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="3844">
    <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(3843,c,14,b),flip(c)].">
      <j1 rule="resolve" parents="3843 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3870">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      p(f(k),k)
    ]]></literal>
    <justification jstring="[para(3844(c,1),52(a,1)),merge(e),unit_del(d,27)].">
      <j1 rule="para" parents="3844 52"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="3875">
    <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(3870,c,6,d),flip(c),flip(d),flip(e)].">
      <j1 rule="resolve" parents="3870 6"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6066">
    <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),3875(c,2)),merge(b),merge(f)].">
      <j1 rule="para" parents="52 3875"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="6071">
    <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(6066,d,8,c),flip(d)].">
      <j1 rule="resolve" parents="6066 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6154">
    <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(6071,e,3843,c),merge(e),merge(f)].">
      <j1 rule="resolve" parents="6071 3843"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="6172">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[para(6154(c,1),3870(c,1)),merge(d),merge(e),merge(f)].">
      <j1 rule="para" parents="6154 3870"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="6185">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <justification jstring="[para(6172(c,1),52(a,1)),merge(d),unit_del(c,27)].">
      <j1 rule="para" parents="6172 52"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="6197">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[resolve(6185,b,29,b)].">
      <j1 rule="resolve" parents="6185 29"/>
    </justification>
  </clause>

  <clause id="6203">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <justification jstring="[para(6197(b,1),262(a,2)),merge(d)].">
      <j1 rule="para" parents="6197 262"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="6214">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <justification jstring="[para(6203(b,1),52(a,1)),merge(d),unit_del(c,27)].">
      <j1 rule="para" parents="6203 52"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="6225">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      p(f(k),k)
    ]]></literal>
    <justification jstring="[resolve(6214,b,14,b),flip(b)].">
      <j1 rule="resolve" parents="6214 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6254">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      p(f(k),k)
    ]]></literal>
    <justification jstring="[para(6225(b,1),52(a,1)),merge(d),unit_del(c,27)].">
      <j1 rule="para" parents="6225 52"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="6261">
    <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(6254,b,6,d),flip(b),flip(c),flip(d)].">
      <j1 rule="resolve" parents="6254 6"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6619">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      f(k) = b
    ]]></literal>
    <literal><![CDATA[
      f(k) = m
    ]]></literal>
    <justification jstring="[para(52(a,1),6261(b,2)),merge(b),merge(e)].">
      <j1 rule="para" parents="52 6261"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="6620">
    <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(6619,c,8,c),flip(c)].">
      <j1 rule="resolve" parents="6619 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6688">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      f(k) = b
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[resolve(6620,d,6214,b),merge(d)].">
      <j1 rule="resolve" parents="6620 6214"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="6709">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[para(6688(b,1),6254(b,1)),merge(c),merge(d)].">
      <j1 rule="para" parents="6688 6254"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="6716">
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <justification jstring="[para(6709(b,1),52(a,1)),merge(c),unit_del(b,27)].">
      <j1 rule="para" parents="6709 52"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="6724">
    <literal><![CDATA[
      p(k,j)
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[resolve(6716,a,89,c)].">
      <j1 rule="resolve" parents="6716 89"/>
    </justification>
  </clause>

  <clause id="6725">
    <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(6716,a,2,f),flip(a),flip(d),unit_del(c,27)].">
      <j1 rule="resolve" parents="6716 2"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="6726">
    <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),6716(a,1))].">
      <j1 rule="para" parents="20 6716"/>
    </justification>
  </clause>

  <clause id="6727">
    <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),6716(a,1))].">
      <j1 rule="para" parents="22 6716"/>
    </justification>
  </clause>

  <clause id="6738">
    <literal><![CDATA[
      p(k,j)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[para(6724(b,1),61(a,1)),flip(c),merge(c),merge(d)].">
      <j1 rule="para" parents="6724 61"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="6741">
    <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(6738(b,1),6(d,2))].">
      <j1 rule="para" parents="6738 6"/>
    </justification>
  </clause>

  <clause id="6827">
    <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(6727,b,29,b),flip(c),flip(d)].">
      <j1 rule="resolve" parents="6727 29"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6828">
    <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(6727,b,6,d),flip(c),flip(d),flip(e)].">
      <j1 rule="resolve" parents="6727 6"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6954">
    <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),6725(d,2))].">
      <j1 rule="para" parents="22 6725"/>
    </justification>
  </clause>

  <clause id="7336">
    <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(6827,c,18,c),flip(d),merge(e)].">
      <j1 rule="resolve" parents="6827 18"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="7370">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(j,k)
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <justification jstring="[para(7336(c,1),6726(b,2)),merge(d),merge(e),merge(f)].">
      <j1 rule="para" parents="7336 6726"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="7375">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(j,k)
    ]]></literal>
    <literal><![CDATA[
      j = k
    ]]></literal>
    <justification jstring="[resolve(7370,c,26,b(flip)),flip(c),merge(d)].">
      <j1 rule="resolve" parents="7370 26"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="7419">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(j,k)
    ]]></literal>
    <literal><![CDATA[
      g(j) = k
    ]]></literal>
    <justification jstring="[para(7375(c,1),6827(c,2)),merge(c),merge(d),merge(f)].">
      <j1 rule="para" parents="7375 6827"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="7499">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(j,k)
    ]]></literal>
    <justification jstring="[para(7419(c,1),6726(b,2)),merge(c),merge(d),merge(e)].">
      <j1 rule="para" parents="7419 6726"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="7512">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      j = k
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <justification jstring="[resolve(7499,b,6,d),flip(b),flip(c),flip(d)].">
      <j1 rule="resolve" parents="7499 6"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7515">
    <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(7499,b,2,e),flip(b),flip(d),flip(e)].">
      <j1 rule="resolve" parents="7499 2"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7519">
    <literal><![CDATA[
      p(k,j)
    ]]></literal>
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <justification jstring="[para(6738(b,1),7499(b,2)),merge(c)].">
      <j1 rule="para" parents="6738 7499"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="7527">
    <literal><![CDATA[
      p(k,j)
    ]]></literal>
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <justification jstring="[para(61(a,1),7519(b,1)),merge(b)].">
      <j1 rule="para" parents="61 7519"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="7640">
    <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(7512(b,1),29(b,2))].">
      <j1 rule="para" parents="7512 29"/>
    </justification>
  </clause>

  <clause id="7644">
    <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(7640,b,d)].">
      <j1 rule="factor" parents="7640"/>
    </justification>
  </clause>

  <clause id="7645">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[factor(7640,c,d),unit_del(d,6716)].">
      <j1 rule="factor" parents="7640"/>
      <j2 rule="unit_del" parents="6716"/>
    </justification>
  </clause>

  <clause id="7658">
    <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(7645,b,58,c(flip)),merge(d)].">
      <j1 rule="resolve" parents="7645 58"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="7660">
    <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(7645(b,1),29(b,2))].">
      <j1 rule="para" parents="7645 29"/>
    </justification>
  </clause>

  <clause id="7671">
    <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(7660,b,d),merge(e)].">
      <j1 rule="factor" parents="7660"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="7696">
    <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(7658(b,1),7527(a,2)),merge(e)].">
      <j1 rule="para" parents="7658 7527"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="7748">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(g(j),j)
    ]]></literal>
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <justification jstring="[para(7696(b,1),7499(b,2)),merge(d),merge(e)].">
      <j1 rule="para" parents="7696 7499"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="7760">
    <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(7748,b,29,b),flip(c),flip(d)].">
      <j1 rule="resolve" parents="7748 29"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7839">
    <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(7760,c,18,c),flip(d),merge(e)].">
      <j1 rule="resolve" parents="7760 18"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="7852">
    <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(7839,c,35,e),flip(f),merge(d),merge(f),merge(g)].">
      <j1 rule="resolve" parents="7839 35"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="7988">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,g(k))
    ]]></literal>
    <justification jstring="[para(7852(c,1),7527(a,2)),merge(d),merge(e)].">
      <j1 rule="para" parents="7852 7527"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="7996">
    <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),7988(a,2))].">
      <j1 rule="para" parents="20 7988"/>
    </justification>
  </clause>

  <clause id="8004">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,g(k))
    ]]></literal>
    <literal><![CDATA[
      p(j,k)
    ]]></literal>
    <justification jstring="[factor(7996,a,d),merge(d)].">
      <j1 rule="factor" parents="7996"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="8019">
    <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(8004,c,6,d),flip(c),flip(d),flip(e)].">
      <j1 rule="resolve" parents="8004 6"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8836">
    <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(8019(c,1),7988(a,1)),merge(e),merge(f),merge(g)].">
      <j1 rule="para" parents="8019 7988"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="8841">
    <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(8836(c,1),7527(a,2)),merge(e)].">
      <j1 rule="para" parents="8836 7527"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="8854">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,g(k))
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <justification jstring="[para(8841(c,1),7527(a,2)),merge(d),merge(e)].">
      <j1 rule="para" parents="8841 7527"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="11701">
    <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(6828(c,1),6726(b,2)),merge(e),merge(f),merge(g)].">
      <j1 rule="para" parents="6828 6726"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="11702">
    <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(11701(c,1),18(c,1)),flip(d),flip(f),merge(e)].">
      <j1 rule="para" parents="11701 18"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="11703">
    <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(11701(c,1),6726(b,2)),merge(d),merge(f)].">
      <j1 rule="para" parents="11701 6726"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="11720">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,k)
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <justification jstring="[para(11703(c,1),6726(b,2)),merge(d),merge(e),merge(f)].">
      <j1 rule="para" parents="11703 6726"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="25718">
    <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(6954,f,11720,b),merge(f),merge(g)].">
      <j1 rule="resolve" parents="6954 11720"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="25740">
    <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(25718,c,58,c(flip)),merge(e),merge(f)].">
      <j1 rule="resolve" parents="25718 58"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="25749">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(g(k),k)
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <justification jstring="[para(25740(d,1),11720(b,2)),merge(d),merge(e),merge(f)].">
      <j1 rule="para" parents="25740 11720"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="25763">
    <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(25749,b,6,d),flip(c),flip(d),flip(e)].">
      <j1 rule="resolve" parents="25749 6"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25767">
    <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(25763,c,18,c),flip(e),merge(f)].">
      <j1 rule="resolve" parents="25763 18"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="25818">
    <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(25767(c,1),8854(b,2)),merge(e),merge(f),merge(g)].">
      <j1 rule="para" parents="25767 8854"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="25825">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[resolve(25818,c,16,c),flip(d),merge(d),merge(e)].">
      <j1 rule="resolve" parents="25818 16"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="25845">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <justification jstring="[para(25825(c,1),11720(b,2)),merge(c),merge(d),merge(e)].">
      <j1 rule="para" parents="25825 11720"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="25922">
    <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(25845,b,39,h),flip(d),flip(f),unit_del(d,27)].">
      <j1 rule="resolve" parents="25845 39"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="25926">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      p(f(k),k)
    ]]></literal>
    <justification jstring="[resolve(25845,b,14,b),flip(b)].">
      <j1 rule="resolve" parents="25845 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25927">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      p(k,f(k))
    ]]></literal>
    <justification jstring="[resolve(25845,b,12,b),flip(b)].">
      <j1 rule="resolve" parents="25845 12"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25941">
    <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(25922,a,b),merge(f)].">
      <j1 rule="factor" parents="25922"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="25967">
    <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(25926,b,11702,e),merge(c)].">
      <j1 rule="resolve" parents="25926 11702"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="25973">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(f(k),k)
    ]]></literal>
    <literal><![CDATA[
      p(g(k),k)
    ]]></literal>
    <justification jstring="[resolve(25926,b,58,c(flip)),merge(c)].">
      <j1 rule="resolve" parents="25926 58"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="26016">
    <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(25927,b,11702,e),merge(c)].">
      <j1 rule="resolve" parents="25927 11702"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="26034">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,f(k))
    ]]></literal>
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <justification jstring="[para(25927(b,1),6716(a,2))].">
      <j1 rule="para" parents="25927 6716"/>
    </justification>
  </clause>

  <clause id="26036">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,f(k))
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <justification jstring="[para(25927(b,1),7527(a,1)),merge(d)].">
      <j1 rule="para" parents="25927 7527"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="26355">
    <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(25973,c,6,d),flip(c),flip(d),flip(e)].">
      <j1 rule="resolve" parents="25973 6"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27683">
    <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(25941,c,2026,a)].">
      <j1 rule="resolve" parents="25941 2026"/>
    </justification>
  </clause>

  <clause id="27836">
    <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(27683,d,58,c(flip)),merge(e),merge(f)].">
      <j1 rule="resolve" parents="27683 58"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="27839">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(g(k),k)
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <justification jstring="[para(27836(c,1),2026(a,2)),merge(d),merge(e)].">
      <j1 rule="para" parents="27836 2026"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="27852">
    <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(27839,b,6,d),flip(c),flip(d),flip(e)].">
      <j1 rule="resolve" parents="27839 6"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27926">
    <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(25967,d,16,c),flip(e),merge(e),merge(f)].">
      <j1 rule="resolve" parents="25967 16"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="27954">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(f(k),k)
    ]]></literal>
    <literal><![CDATA[
      p(k,k)
    ]]></literal>
    <justification jstring="[para(27926(d,1),25926(b,1)),flip(e),merge(d),merge(f),unit_del(d,27)].">
      <j1 rule="para" parents="27926 25926"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="27980">
    <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(27954,b,6,d),flip(c),flip(d),flip(e)].">
      <j1 rule="resolve" parents="27954 6"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28180">
    <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(26016,d,16,c),flip(e),merge(e),merge(f)].">
      <j1 rule="resolve" parents="26016 16"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="28206">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,f(k))
    ]]></literal>
    <literal><![CDATA[
      p(k,k)
    ]]></literal>
    <justification jstring="[para(28180(d,1),25927(b,1)),flip(e),merge(d),merge(f),unit_del(d,27)].">
      <j1 rule="para" parents="28180 25927"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="30106">
    <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(27852,c,18,c),flip(e),merge(f)].">
      <j1 rule="resolve" parents="27852 18"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="30119">
    <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(30106(c,1),18(c,1)),flip(e),flip(g),merge(e),merge(f)].">
      <j1 rule="para" parents="30106 18"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="30158">
    <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(30119,e,25927,b),merge(e)].">
      <j1 rule="resolve" parents="30119 25927"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="30191">
    <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(30158,c,16,c),flip(e),merge(e),merge(f)].">
      <j1 rule="resolve" parents="30158 16"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="30199">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,f(k))
    ]]></literal>
    <justification jstring="[para(30191(c,1),2026(a,2)),merge(d),merge(e)].">
      <j1 rule="para" parents="30191 2026"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="30358">
    <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(27980(c,1),27954(b,1)),merge(e),merge(f),merge(g)].">
      <j1 rule="para" parents="27980 27954"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="30359">
    <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(30358,c,8,c),flip(d)].">
      <j1 rule="resolve" parents="30358 8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30366">
    <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(30359,e,25845,b),merge(e)].">
      <j1 rule="resolve" parents="30359 25845"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="30386">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,k)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[para(30366(c,1),28206(b,2)),merge(d),merge(e),merge(f)].">
      <j1 rule="para" parents="30366 28206"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="30415">
    <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(30386,c,11702,e),merge(c),merge(d)].">
      <j1 rule="resolve" parents="30386 11702"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="31143">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,k)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[resolve(30415,c,16,c),flip(d),merge(d),merge(e)].">
      <j1 rule="resolve" parents="30415 16"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="31182">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,k)
    ]]></literal>
    <justification jstring="[para(31143(c,1),30386(c,1)),flip(e),merge(c),merge(d),unit_del(c,27)].">
      <j1 rule="para" parents="31143 30386"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="37406">
    <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(25926(b,1),26355(c,2)),merge(c),merge(d),merge(f)].">
      <j1 rule="para" parents="25926 26355"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="37411">
    <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(37406(c,1),18(c,1)),flip(d),flip(f),merge(e)].">
      <j1 rule="para" parents="37406 18"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="37869">
    <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(37411,e,25926,b),merge(e),merge(f)].">
      <j1 rule="resolve" parents="37411 25926"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="37876">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(f(k),k)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[resolve(37869,c,16,c),flip(d),merge(d),merge(e)].">
      <j1 rule="resolve" parents="37869 16"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="37898">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(f(k),k)
    ]]></literal>
    <justification jstring="[para(37876(c,1),25926(b,1)),flip(d),merge(c),merge(e),unit_del(c,27)].">
      <j1 rule="para" parents="37876 25926"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="37912">
    <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(37898,b,6,d),flip(b),flip(c),flip(d)].">
      <j1 rule="resolve" parents="37898 6"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38073">
    <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(37912,b,10,c),flip(d)].">
      <j1 rule="resolve" parents="37912 10"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38165">
    <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(38073,e,25845,b),merge(e)].">
      <j1 rule="resolve" parents="38073 25845"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="38168">
    <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(38165,b,8,c),flip(d),merge(d)].">
      <j1 rule="resolve" parents="38165 8"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="38179">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      f(k) = b
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[resolve(38168,d,25845,b),merge(d)].">
      <j1 rule="resolve" parents="38168 25845"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="38194">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <justification jstring="[para(38179(b,1),26034(b,2)),merge(c),merge(d)].">
      <j1 rule="para" parents="38179 26034"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="38195">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <justification jstring="[para(38179(b,1),26036(b,2)),merge(c),merge(d)].">
      <j1 rule="para" parents="38179 26036"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="38203">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <justification jstring="[para(38179(b,1),30199(c,2)),merge(c),merge(e)].">
      <j1 rule="para" parents="38179 30199"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="38411">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <justification jstring="[para(38194(b,1),6716(a,2)),merge(c)].">
      <j1 rule="para" parents="38194 6716"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="38425">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[resolve(38411,a,3335,d),merge(b)].">
      <j1 rule="resolve" parents="38411 3335"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="38471">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <justification jstring="[para(38195(b,1),7527(a,1)),merge(c),merge(d)].">
      <j1 rule="para" parents="38195 7527"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="38477">
    <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(38471,a,6725,d)].">
      <j1 rule="resolve" parents="38471 6725"/>
    </justification>
  </clause>

  <clause id="38638">
    <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(38203,b,30119,e),merge(c),merge(d)].">
      <j1 rule="resolve" parents="38203 30119"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="38734">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[para(38425(b,1),6716(a,2)),merge(c)].">
      <j1 rule="para" parents="38425 6716"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="38822">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <justification jstring="[para(38734(b,1),2026(a,2)),merge(c)].">
      <j1 rule="para" parents="38734 2026"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="38824">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      p(b,j)
    ]]></literal>
    <justification jstring="[para(38734(b,1),3446(b,1)),merge(b)].">
      <j1 rule="para" parents="38734 3446"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="38828">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <justification jstring="[para(38734(b,1),7499(b,2)),merge(c)].">
      <j1 rule="para" parents="38734 7499"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="38846">
    <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(38824,b,2,e),flip(d),merge(c),unit_del(b,27)].">
      <j1 rule="resolve" parents="38824 2"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="40226">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <justification jstring="[resolve(38846,d,38828,b),merge(d)].">
      <j1 rule="resolve" parents="38846 38828"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="40231">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <justification jstring="[para(40226(b,1),38824(b,2)),merge(c),merge(d)].">
      <j1 rule="para" parents="40226 38824"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="40235">
    <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(40231(b,1),29(b,2))].">
      <j1 rule="para" parents="40231 29"/>
    </justification>
  </clause>

  <clause id="40435">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[resolve(40235,c,38822,b),merge(d)].">
      <j1 rule="resolve" parents="40235 38822"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="40446">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[para(40435(b,1),38824(b,2)),merge(c),merge(d)].">
      <j1 rule="para" parents="40435 38824"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="40452">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <justification jstring="[para(40446(b,1),6716(a,2)),merge(b)].">
      <j1 rule="para" parents="40446 6716"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="40456">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[back_unit_del(7671),unit_del(d,40452)].">
      <j1 rule="back_unit_del" parents="7671"/>
      <j2 rule="unit_del" parents="40452"/>
    </justification>
  </clause>

  <clause id="40463">
    <literal><![CDATA[
      p(f(b),b)
    ]]></literal>
    <justification jstring="[resolve(40452,a,14,b),unit_del(a,27)].">
      <j1 rule="resolve" parents="40452 14"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="40464">
    <literal><![CDATA[
      p(b,f(b))
    ]]></literal>
    <justification jstring="[resolve(40452,a,12,b),unit_del(a,27)].">
      <j1 rule="resolve" parents="40452 12"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="40465">
    <literal><![CDATA[
      f(b) != b
    ]]></literal>
    <justification jstring="[ur(10,a,27,a,b,40452,a)].">
      <j1 rule="ur" parents="10 27 40452"/>
    </justification>
  </clause>

  <clause id="40466">
    <literal><![CDATA[
      f(b) != m
    ]]></literal>
    <justification jstring="[ur(8,a,27,a,b,40452,a)].">
      <j1 rule="ur" parents="8 27 40452"/>
    </justification>
  </clause>

  <clause id="40514">
    <literal><![CDATA[
      p(k,j)
    ]]></literal>
    <literal><![CDATA[
      f(b) = k
    ]]></literal>
    <justification jstring="[resolve(40463,a,6741,e),flip(b),flip(c),flip(d),unit_del(c,40466),unit_del(d,40465)].">
      <j1 rule="resolve" parents="40463 6741"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="unit_del" parents="40466"/>
      <j2 rule="unit_del" parents="40465"/>
    </justification>
  </clause>

  <clause id="40516">
    <literal><![CDATA[
      p(f(b),m)
    ]]></literal>
    <justification jstring="[resolve(40463,a,2,e),flip(a),flip(d),unit_del(a,40466),unit_del(c,27),unit_del(d,40465),unit_del(e,40464)].">
      <j1 rule="resolve" parents="40463 2"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="unit_del" parents="40466"/>
      <j2 rule="unit_del" parents="27"/>
      <j2 rule="unit_del" parents="40465"/>
      <j2 rule="unit_del" parents="40464"/>
    </justification>
  </clause>

  <clause id="40562">
    <literal><![CDATA[
      p(m,k)
    ]]></literal>
    <literal><![CDATA[
      f(b) = k
    ]]></literal>
    <justification jstring="[resolve(40516,a,80,e),flip(b),flip(c),flip(d),unit_del(c,40466),unit_del(d,40465)].">
      <j1 rule="resolve" parents="40516 80"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="unit_del" parents="40466"/>
      <j2 rule="unit_del" parents="40465"/>
    </justification>
  </clause>

  <clause id="40572">
    <literal><![CDATA[
      -p(m,f(b))
    ]]></literal>
    <justification jstring="[resolve(40516,a,4,e),flip(a),flip(c),flip(d),unit_del(a,40465),unit_del(b,40463),unit_del(c,27),unit_del(d,40466)].">
      <j1 rule="resolve" parents="40516 4"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="unit_del" parents="40465"/>
      <j2 rule="unit_del" parents="40463"/>
      <j2 rule="unit_del" parents="27"/>
      <j2 rule="unit_del" parents="40466"/>
    </justification>
  </clause>

  <clause id="40623">
    <literal><![CDATA[
      p(k,j)
    ]]></literal>
    <justification jstring="[para(6738(b,1),40514(b,2)),merge(b),unit_del(b,40465)].">
      <j1 rule="para" parents="6738 40514"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="40465"/>
    </justification>
  </clause>

  <clause id="40629">
    <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(7515),unit_del(f,40623)].">
      <j1 rule="back_unit_del" parents="7515"/>
      <j2 rule="unit_del" parents="40623"/>
    </justification>
  </clause>

  <clause id="40646">
    <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(40623,a,2,e),flip(a),flip(c)].">
      <j1 rule="resolve" parents="40623 2"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40652">
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[para(38477(b,1),40623(a,1)),merge(d)].">
      <j1 rule="para" parents="38477 40623"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="40659">
    <literal><![CDATA[
      p(m,k)
    ]]></literal>
    <justification jstring="[para(49(a,1),40562(b,2)),merge(b),unit_del(b,40466)].">
      <j1 rule="para" parents="49 40562"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="40466"/>
    </justification>
  </clause>

  <clause id="40703">
    <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(7644),unit_del(d,40659)].">
      <j1 rule="back_unit_del" parents="7644"/>
      <j2 rule="unit_del" parents="40659"/>
    </justification>
  </clause>

  <clause id="40769">
    <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(40659,a,4,f),flip(a),flip(c),flip(d),unit_del(c,27)].">
      <j1 rule="resolve" parents="40659 4"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="42200">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[resolve(38638,c,16,c),flip(d),merge(d),merge(e)].">
      <j1 rule="resolve" parents="38638 16"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="42244">
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <justification jstring="[para(42200(c,1),31182(b,2)),merge(c),merge(d)].">
      <j1 rule="para" parents="42200 31182"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="42251">
    <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(42244,a,6725,d)].">
      <j1 rule="resolve" parents="42244 6725"/>
    </justification>
  </clause>

  <clause id="42272">
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[para(42251(b,1),42244(a,1)),merge(d),merge(e)].">
      <j1 rule="para" parents="42251 42244"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="42284">
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <justification jstring="[para(42272(c,1),40659(a,2)),merge(c)].">
      <j1 rule="para" parents="42272 40659"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="42313">
    <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(42284,b,40769,d)].">
      <j1 rule="resolve" parents="42284 40769"/>
    </justification>
  </clause>

  <clause id="42393">
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[resolve(42313,c,42244,a),merge(d)].">
      <j1 rule="resolve" parents="42313 42244"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="42404">
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[para(42393(c,1),42244(a,1)),merge(c),merge(d)].">
      <j1 rule="para" parents="42393 42244"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="42422">
    <literal><![CDATA[
      p(m,b)
    ]]></literal>
    <justification jstring="[para(42404(b,1),40659(a,2)),merge(b)].">
      <j1 rule="para" parents="42404 40659"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="42440">
    <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(42422,a,4,b),flip(a),flip(c),unit_del(a,27)].">
      <j1 rule="resolve" parents="42422 4"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="45698">
    <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(40629(e,1),29(b,2))].">
      <j1 rule="para" parents="40629 29"/>
    </justification>
  </clause>

  <clause id="45712">
    <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(45698,b,e),merge(f),unit_del(e,40659)].">
      <j1 rule="factor" parents="45698"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="40659"/>
    </justification>
  </clause>

  <clause id="45714">
    <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(45712(b,1),40456(b,1)),merge(d),unit_del(d,27)].">
      <j1 rule="para" parents="45712 40456"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="45729">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(j,m)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[para(45714(c,1),7499(b,2)),merge(d),merge(e)].">
      <j1 rule="para" parents="45714 7499"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="45952">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(j,m)
    ]]></literal>
    <justification jstring="[para(45729(c,1),7499(b,2)),merge(c),merge(d)].">
      <j1 rule="para" parents="45729 7499"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="45954">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      p(f(j),j)
    ]]></literal>
    <justification jstring="[resolve(45952,b,14,b),flip(b)].">
      <j1 rule="resolve" parents="45952 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45955">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      p(j,f(j))
    ]]></literal>
    <justification jstring="[resolve(45952,b,12,b),flip(b)].">
      <j1 rule="resolve" parents="45952 12"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45970">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(f(j),j)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[para(45954(b,1),40456(b,1)),merge(c),unit_del(c,27)].">
      <j1 rule="para" parents="45954 40456"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="45987">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(j,f(j))
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[para(45955(b,1),40456(b,1)),merge(c),unit_del(c,27)].">
      <j1 rule="para" parents="45955 40456"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="46009">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(f(j),j)
    ]]></literal>
    <justification jstring="[para(45970(c,1),7499(b,2)),merge(c),merge(d)].">
      <j1 rule="para" parents="45970 7499"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="46033">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      f(j) = j
    ]]></literal>
    <literal><![CDATA[
      f(j) = k
    ]]></literal>
    <justification jstring="[resolve(46009,b,29,b),flip(b),flip(c)].">
      <j1 rule="resolve" parents="46009 29"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46041">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <literal><![CDATA[
      p(f(j),b)
    ]]></literal>
    <justification jstring="[para(40456(b,1),46009(b,2)),merge(c)].">
      <j1 rule="para" parents="40456 46009"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="46079">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(j,f(j))
    ]]></literal>
    <justification jstring="[para(45987(c,1),7499(b,2)),merge(c),merge(d)].">
      <j1 rule="para" parents="45987 7499"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="46112">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <literal><![CDATA[
      p(j,f(b))
    ]]></literal>
    <justification jstring="[para(40456(b,1),46079(b,2,1)),merge(c)].">
      <j1 rule="para" parents="40456 46079"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="46157">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(f(j),b)
    ]]></literal>
    <justification jstring="[para(46041(b,1),7499(b,2)),merge(c),merge(d)].">
      <j1 rule="para" parents="46041 7499"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="46205">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      p(j,f(b))
    ]]></literal>
    <justification jstring="[para(46112(b,1),7499(b,2)),merge(c),merge(d)].">
      <j1 rule="para" parents="46112 7499"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="46219">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[para(40703(b,1),46205(b,1)),merge(d),unit_del(d,40572)].">
      <j1 rule="para" parents="40703 46205"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="40572"/>
    </justification>
  </clause>

  <clause id="46239">
    <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(46219(b,1),29(b,2))].">
      <j1 rule="para" parents="46219 29"/>
    </justification>
  </clause>

  <clause id="46251">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <justification jstring="[factor(46239,b,e),unit_del(d,42422)].">
      <j1 rule="factor" parents="46239"/>
      <j2 rule="unit_del" parents="42422"/>
    </justification>
  </clause>

  <clause id="46290">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[para(46251(c,1),46205(b,1)),merge(c),unit_del(c,40572)].">
      <j1 rule="para" parents="46251 46205"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="40572"/>
    </justification>
  </clause>

  <clause id="46294">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <justification jstring="[para(46290(b,1),7512(b,2)),merge(b),merge(d)].">
      <j1 rule="para" parents="46290 7512"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="46336">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <justification jstring="[para(46294(b,1),46205(b,1)),merge(c),unit_del(c,40572)].">
      <j1 rule="para" parents="46294 46205"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="40572"/>
    </justification>
  </clause>

  <clause id="46358">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      f(j) = k
    ]]></literal>
    <justification jstring="[para(46033(b,1),46157(b,1)),merge(c),merge(d)].">
      <j1 rule="para" parents="46033 46157"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="46367">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <literal><![CDATA[
      f(j) = m
    ]]></literal>
    <justification jstring="[para(46290(b,1),46358(b,2)),merge(b)].">
      <j1 rule="para" parents="46290 46358"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="46397">
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <justification jstring="[para(46336(b,1),46367(b,1,1)),merge(b),unit_del(b,40466)].">
      <j1 rule="para" parents="46336 46367"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="40466"/>
    </justification>
  </clause>

  <clause id="46484">
    <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(40652(c,1),40646(e,2)),merge(d),unit_del(f,46397)].">
      <j1 rule="para" parents="40652 40646"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="46397"/>
    </justification>
  </clause>

  <clause id="46971">
    <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(46484(e,1),29(b,2))].">
      <j1 rule="para" parents="46484 29"/>
    </justification>
  </clause>

  <clause id="46974">
    <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(46971,c,g),merge(e),unit_del(e,40659)].">
      <j1 rule="factor" parents="46971"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="40659"/>
    </justification>
  </clause>

  <clause id="46977">
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[para(46974(d,1),40623(a,2)),merge(d)].">
      <j1 rule="para" parents="46974 40623"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="46981">
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <justification jstring="[para(46977(c,1),40623(a,1)),merge(c)].">
      <j1 rule="para" parents="46977 40623"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="46982">
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[resolve(46981,b,42440,d),flip(b),flip(c),unit_del(d,40659)].">
      <j1 rule="resolve" parents="46981 42440"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="unit_del" parents="40659"/>
    </justification>
  </clause>

  <clause id="46983">
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      p(f(k),k)
    ]]></literal>
    <justification jstring="[resolve(46981,b,14,b),flip(b)].">
      <j1 rule="resolve" parents="46981 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46992">
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[para(46982(c,1),40623(a,1)),merge(c)].">
      <j1 rule="para" parents="46982 40623"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="47010">
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      p(f(k),k)
    ]]></literal>
    <justification jstring="[para(46983(b,1),40623(a,1)),merge(c)].">
      <j1 rule="para" parents="46983 40623"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="47013">
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      p(f(b),k)
    ]]></literal>
    <justification jstring="[para(46992(b,1),47010(b,1,1)),merge(b)].">
      <j1 rule="para" parents="46992 47010"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="47019">
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <literal><![CDATA[
      f(b) = k
    ]]></literal>
    <justification jstring="[resolve(47013,b,6,d),flip(b),flip(c),flip(d),unit_del(c,40466),unit_del(d,40465)].">
      <j1 rule="resolve" parents="47013 6"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="unit_del" parents="40466"/>
      <j2 rule="unit_del" parents="40465"/>
    </justification>
  </clause>

  <clause id="47053">
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <justification jstring="[para(47019(b,1),40572(a,2)),unit_del(b,40659)].">
      <j1 rule="para" parents="47019 40572"/>
      <j2 rule="unit_del" parents="40659"/>
    </justification>
  </clause>

  <clause id="47055">
    <literal><![CDATA[
      j = m
    ]]></literal>
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[resolve(47053,a,29,b)].">
      <j1 rule="resolve" parents="47053 29"/>
    </justification>
  </clause>

  <clause id="47062">
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      j = x
    ]]></literal>
    <literal><![CDATA[
      -p(x,m)
    ]]></literal>
    <literal><![CDATA[
      k = x
    ]]></literal>
    <justification jstring="[para(47055(a,1),29(b,2))].">
      <j1 rule="para" parents="47055 29"/>
    </justification>
  </clause>

  <clause id="47083">
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      f(b) = j
    ]]></literal>
    <literal><![CDATA[
      f(b) = k
    ]]></literal>
    <justification jstring="[resolve(47062,c,40516,a),flip(b),flip(c)].">
      <j1 rule="resolve" parents="47062 40516"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47084">
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      j = b
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[resolve(47062,c,40452,a)].">
      <j1 rule="resolve" parents="47062 40452"/>
    </justification>
  </clause>

  <clause id="47110">
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      k = b
    ]]></literal>
    <justification jstring="[para(47084(b,1),47055(a,1)),flip(c),merge(d),unit_del(c,27)].">
      <j1 rule="para" parents="47084 47055"/>
      <j2 rule="flip"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="47111">
    <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(47110(a,1),6(d,2))].">
      <j1 rule="para" parents="47110 6"/>
    </justification>
  </clause>

  <clause id="47125">
    <literal><![CDATA[
      k = m
    ]]></literal>
    <literal><![CDATA[
      f(b) = k
    ]]></literal>
    <justification jstring="[para(47083(b,1),40572(a,2)),unit_del(c,47053)].">
      <j1 rule="para" parents="47083 40572"/>
      <j2 rule="unit_del" parents="47053"/>
    </justification>
  </clause>

  <clause id="47136">
    <literal><![CDATA[
      k = m
    ]]></literal>
    <justification jstring="[para(47125(b,1),40572(a,2)),unit_del(b,40659)].">
      <j1 rule="para" parents="47125 40572"/>
      <j2 rule="unit_del" parents="40659"/>
    </justification>
  </clause>

  <clause id="47138">
    <literal><![CDATA[
      m = x
    ]]></literal>
    <literal><![CDATA[
      b = x
    ]]></literal>
    <literal><![CDATA[
      -p(x,m)
    ]]></literal>
    <justification jstring="[back_rewrite(47111),rewrite(47136(1),47136(4)),merge(c),unit_del(a,27)].">
      <j1 rule="back_rewrite" parents="47111"/>
      <j2 rule="rewrite" parents="47136 47136"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="27"/>
    </justification>
  </clause>

  <clause id="47289">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[resolve(47138,c,40516,a),flip(a),flip(b),unit_del(a,40466),unit_del(b,40465)].">
      <j1 rule="resolve" parents="47138 40516"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
      <j2 rule="unit_del" parents="40466"/>
      <j2 rule="unit_del" parents="40465"/>
    </justification>
  </clause>

</proof>

</proofs>
