<?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.out</source>

<heading><![CDATA[
Prover9 (32) version August-2006A, August 2006.
Process 11477 was started by mccune on cleo.thornwood,
Sat Aug 12 21:01:43 2006
The command was "/home/mccune/bin/prover9 -f wang.in wang3.in".
]]></heading>

<proof number="1" length="125" max_count="27">

<comments><![CDATA[
% Proof 1 at 12.62 (+ 0.10) seconds.
% Length of proof is 125.
% Level of proof is 74.
% Maximum clause weight is 27.
% Given clauses 5814.
]]></comments>

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

  <clause id="2">
    <literal><![CDATA[
      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="3">
    <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="4">
    <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="5">
    <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="6">
    <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="7">
    <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="9">
    <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="10">
    <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="11">
    <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="12">
    <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="13">
    <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="14">
    <literal><![CDATA[
      x == x
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="15">
    <literal><![CDATA[
      -(x == y)
    ]]></literal>
    <literal><![CDATA[
      y == x
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="16">
    <literal><![CDATA[
      -(x == y)
    ]]></literal>
    <literal><![CDATA[
      -(y == z)
    ]]></literal>
    <literal><![CDATA[
      x == z
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="18">
    <literal><![CDATA[
      -(x == y)
    ]]></literal>
    <literal><![CDATA[
      -p(z,x)
    ]]></literal>
    <literal><![CDATA[
      p(z,y)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="21">
    <literal><![CDATA[
      -(m == b)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="22">
    <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="23">
    <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[
      k == b
    ]]></literal>
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      g(k) == k
    ]]></literal>
    <literal><![CDATA[
      g(k) == m
    ]]></literal>
    <literal><![CDATA[
      g(k) == b
    ]]></literal>
    <justification jstring="[resolve(11,c,3,d)].">
      <j1 rule="resolve" parents="11 3"/>
    </justification>
  </clause>

  <clause id="35">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      p(b,k)
    ]]></literal>
    <justification jstring="[resolve(14,a,13,b)].">
      <j1 rule="resolve" parents="14 13"/>
    </justification>
  </clause>

  <clause id="36">
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      p(m,k)
    ]]></literal>
    <justification jstring="[resolve(14,a,12,b)].">
      <j1 rule="resolve" parents="14 12"/>
    </justification>
  </clause>

  <clause id="40">
    <literal><![CDATA[
      -(g(x) == y)
    ]]></literal>
    <literal><![CDATA[
      p(x,y)
    ]]></literal>
    <literal><![CDATA[
      x == b
    ]]></literal>
    <literal><![CDATA[
      p(x,b)
    ]]></literal>
    <justification jstring="[resolve(18,b,10,c)].">
      <j1 rule="resolve" parents="18 10"/>
    </justification>
  </clause>

  <clause id="41">
    <literal><![CDATA[
      -(b == m)
    ]]></literal>
    <justification jstring="[ur(15,b,21,a)].">
      <j1 rule="ur" parents="15 21"/>
    </justification>
  </clause>

  <clause id="42">
    <literal><![CDATA[
      g(j) == j
    ]]></literal>
    <literal><![CDATA[
      g(j) == k
    ]]></literal>
    <literal><![CDATA[
      j == b
    ]]></literal>
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <justification jstring="[resolve(22,b,11,c)].">
      <j1 rule="resolve" parents="22 11"/>
    </justification>
  </clause>

  <clause id="44">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      -(k == x)
    ]]></literal>
    <literal><![CDATA[
      p(b,x)
    ]]></literal>
    <justification jstring="[resolve(35,b,18,b)].">
      <j1 rule="resolve" parents="35 18"/>
    </justification>
  </clause>

  <clause id="46">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      k == m
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <literal><![CDATA[
      -p(k,b)
    ]]></literal>
    <justification jstring="[resolve(35,b,1,f),merge(e),unit_del(d,41)].">
      <j1 rule="resolve" parents="35 1"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="41"/>
    </justification>
  </clause>

  <clause id="48">
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      -(k == x)
    ]]></literal>
    <literal><![CDATA[
      p(m,x)
    ]]></literal>
    <justification jstring="[resolve(36,b,18,b)].">
      <j1 rule="resolve" parents="36 18"/>
    </justification>
  </clause>

  <clause id="50">
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      k == b
    ]]></literal>
    <literal><![CDATA[
      -p(k,b)
    ]]></literal>
    <literal><![CDATA[
      -p(k,m)
    ]]></literal>
    <justification jstring="[resolve(36,b,2,f),merge(e),unit_del(d,21)].">
      <j1 rule="resolve" parents="36 2"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="21"/>
    </justification>
  </clause>

  <clause id="73">
    <literal><![CDATA[
      k == b
    ]]></literal>
    <literal><![CDATA[
      g(k) == k
    ]]></literal>
    <literal><![CDATA[
      g(k) == m
    ]]></literal>
    <literal><![CDATA[
      g(k) == b
    ]]></literal>
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      k == m
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <justification jstring="[resolve(31,b,46,d)].">
      <j1 rule="resolve" parents="31 46"/>
    </justification>
  </clause>

  <clause id="76">
    <literal><![CDATA[
      k == b
    ]]></literal>
    <literal><![CDATA[
      g(k) == k
    ]]></literal>
    <literal><![CDATA[
      g(k) == m
    ]]></literal>
    <literal><![CDATA[
      g(k) == b
    ]]></literal>
    <literal><![CDATA[
      x == b
    ]]></literal>
    <literal><![CDATA[
      x == k
    ]]></literal>
    <literal><![CDATA[
      -p(k,x)
    ]]></literal>
    <literal><![CDATA[
      -p(x,k)
    ]]></literal>
    <justification jstring="[resolve(31,b,2,b),merge(e)].">
      <j1 rule="resolve" parents="31 2"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="78">
    <literal><![CDATA[
      g(j) == j
    ]]></literal>
    <literal><![CDATA[
      g(j) == k
    ]]></literal>
    <literal><![CDATA[
      j == b
    ]]></literal>
    <literal><![CDATA[
      -(b == x)
    ]]></literal>
    <literal><![CDATA[
      p(j,x)
    ]]></literal>
    <justification jstring="[resolve(42,d,18,b)].">
      <j1 rule="resolve" parents="42 18"/>
    </justification>
  </clause>

  <clause id="146">
    <literal><![CDATA[
      k == b
    ]]></literal>
    <literal><![CDATA[
      g(k) == k
    ]]></literal>
    <literal><![CDATA[
      g(k) == m
    ]]></literal>
    <literal><![CDATA[
      g(k) == b
    ]]></literal>
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      -p(k,m)
    ]]></literal>
    <justification jstring="[resolve(76,h,36,b),merge(h),unit_del(e,21)].">
      <j1 rule="resolve" parents="76 36"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="21"/>
    </justification>
  </clause>

  <clause id="147">
    <literal><![CDATA[
      k == b
    ]]></literal>
    <literal><![CDATA[
      g(k) == k
    ]]></literal>
    <literal><![CDATA[
      g(k) == m
    ]]></literal>
    <literal><![CDATA[
      g(k) == b
    ]]></literal>
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      k == m
    ]]></literal>
    <justification jstring="[resolve(146,f,73,g),merge(f),merge(g),merge(h),merge(i)].">
      <j1 rule="resolve" parents="146 73"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="167">
    <literal><![CDATA[
      k == b
    ]]></literal>
    <literal><![CDATA[
      g(k) == m
    ]]></literal>
    <literal><![CDATA[
      g(k) == b
    ]]></literal>
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      k == m
    ]]></literal>
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <justification jstring="[resolve(147,b,9,c),merge(g)].">
      <j1 rule="resolve" parents="147 9"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="169">
    <literal><![CDATA[
      k == b
    ]]></literal>
    <literal><![CDATA[
      g(k) == m
    ]]></literal>
    <literal><![CDATA[
      g(k) == b
    ]]></literal>
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      k == m
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <justification jstring="[resolve(167,g,46,d),merge(g),merge(h)].">
      <j1 rule="resolve" parents="167 46"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="181">
    <literal><![CDATA[
      k == b
    ]]></literal>
    <literal><![CDATA[
      g(k) == m
    ]]></literal>
    <literal><![CDATA[
      g(k) == b
    ]]></literal>
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      k == m
    ]]></literal>
    <literal><![CDATA[
      -p(k,b)
    ]]></literal>
    <justification jstring="[resolve(169,g,50,d),merge(g),merge(h)].">
      <j1 rule="resolve" parents="169 50"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="188">
    <literal><![CDATA[
      k == b
    ]]></literal>
    <literal><![CDATA[
      g(k) == m
    ]]></literal>
    <literal><![CDATA[
      g(k) == b
    ]]></literal>
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      k == m
    ]]></literal>
    <justification jstring="[resolve(181,g,167,g),merge(g),merge(h),merge(i),merge(j),merge(k),merge(l)].">
      <j1 rule="resolve" parents="181 167"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="196">
    <literal><![CDATA[
      k == b
    ]]></literal>
    <literal><![CDATA[
      g(k) == b
    ]]></literal>
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      k == m
    ]]></literal>
    <literal><![CDATA[
      m == g(k)
    ]]></literal>
    <justification jstring="[resolve(188,b,15,a)].">
      <j1 rule="resolve" parents="188 15"/>
    </justification>
  </clause>

  <clause id="206">
    <literal><![CDATA[
      k == b
    ]]></literal>
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      k == m
    ]]></literal>
    <literal><![CDATA[
      m == g(k)
    ]]></literal>
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <justification jstring="[resolve(196,b,40,a),merge(g),merge(h)].">
      <j1 rule="resolve" parents="196 40"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="215">
    <literal><![CDATA[
      k == b
    ]]></literal>
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      k == m
    ]]></literal>
    <literal><![CDATA[
      m == g(k)
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <justification jstring="[resolve(206,f,46,d),merge(f),merge(g)].">
      <j1 rule="resolve" parents="206 46"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="227">
    <literal><![CDATA[
      k == b
    ]]></literal>
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      k == m
    ]]></literal>
    <literal><![CDATA[
      m == g(k)
    ]]></literal>
    <literal><![CDATA[
      -p(k,b)
    ]]></literal>
    <justification jstring="[resolve(215,f,50,d),merge(f),merge(g)].">
      <j1 rule="resolve" parents="215 50"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="240">
    <literal><![CDATA[
      k == b
    ]]></literal>
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      k == m
    ]]></literal>
    <literal><![CDATA[
      m == g(k)
    ]]></literal>
    <justification jstring="[resolve(227,f,206,f),merge(f),merge(g),merge(h),merge(i),merge(j)].">
      <j1 rule="resolve" parents="227 206"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="251">
    <literal><![CDATA[
      k == b
    ]]></literal>
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      m == g(k)
    ]]></literal>
    <justification jstring="[resolve(240,d,15,a),merge(e)].">
      <j1 rule="resolve" parents="240 15"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="259">
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      m == g(k)
    ]]></literal>
    <justification jstring="[resolve(251,a,15,a),merge(d)].">
      <j1 rule="resolve" parents="251 15"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="269">
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      g(k) == m
    ]]></literal>
    <justification jstring="[resolve(259,c,15,a)].">
      <j1 rule="resolve" parents="259 15"/>
    </justification>
  </clause>

  <clause id="275">
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <literal><![CDATA[
      k == b
    ]]></literal>
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <justification jstring="[resolve(269,c,40,a)].">
      <j1 rule="resolve" parents="269 40"/>
    </justification>
  </clause>

  <clause id="448">
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      k == b
    ]]></literal>
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      k == m
    ]]></literal>
    <literal><![CDATA[
      p(f(k),k)
    ]]></literal>
    <justification jstring="[resolve(275,c,7,b)].">
      <j1 rule="resolve" parents="275 7"/>
    </justification>
  </clause>

  <clause id="449">
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      k == b
    ]]></literal>
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      k == m
    ]]></literal>
    <literal><![CDATA[
      p(k,f(k))
    ]]></literal>
    <justification jstring="[resolve(275,c,6,b)].">
      <j1 rule="resolve" parents="275 6"/>
    </justification>
  </clause>

  <clause id="450">
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      k == b
    ]]></literal>
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      k == m
    ]]></literal>
    <literal><![CDATA[
      -(f(k) == k)
    ]]></literal>
    <justification jstring="[resolve(275,c,5,b)].">
      <j1 rule="resolve" parents="275 5"/>
    </justification>
  </clause>

  <clause id="451">
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      k == b
    ]]></literal>
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      k == m
    ]]></literal>
    <literal><![CDATA[
      -(f(k) == m)
    ]]></literal>
    <justification jstring="[resolve(275,c,4,b)].">
      <j1 rule="resolve" parents="275 4"/>
    </justification>
  </clause>

  <clause id="1155">
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      k == b
    ]]></literal>
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      k == m
    ]]></literal>
    <literal><![CDATA[
      f(k) == k
    ]]></literal>
    <literal><![CDATA[
      f(k) == m
    ]]></literal>
    <literal><![CDATA[
      f(k) == b
    ]]></literal>
    <justification jstring="[resolve(448,f,3,d)].">
      <j1 rule="resolve" parents="448 3"/>
    </justification>
  </clause>

  <clause id="1158">
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      k == b
    ]]></literal>
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      k == m
    ]]></literal>
    <literal><![CDATA[
      -(f(k) == x)
    ]]></literal>
    <literal><![CDATA[
      p(k,x)
    ]]></literal>
    <justification jstring="[resolve(449,f,18,b)].">
      <j1 rule="resolve" parents="449 18"/>
    </justification>
  </clause>

  <clause id="1162">
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      k == b
    ]]></literal>
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <literal><![CDATA[
      k == m
    ]]></literal>
    <literal><![CDATA[
      -(f(k) == b)
    ]]></literal>
    <justification jstring="[factor(1158,d,g)].">
      <j1 rule="factor" parents="1158"/>
    </justification>
  </clause>

  <clause id="11682">
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      k == b
    ]]></literal>
    <literal><![CDATA[
      k == m
    ]]></literal>
    <literal><![CDATA[
      f(k) == k
    ]]></literal>
    <literal><![CDATA[
      f(k) == m
    ]]></literal>
    <literal><![CDATA[
      f(k) == b
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <justification jstring="[resolve(1155,d,46,d),merge(h),merge(i)].">
      <j1 rule="resolve" parents="1155 46"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="11832">
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      k == b
    ]]></literal>
    <literal><![CDATA[
      k == m
    ]]></literal>
    <literal><![CDATA[
      f(k) == k
    ]]></literal>
    <literal><![CDATA[
      f(k) == m
    ]]></literal>
    <literal><![CDATA[
      f(k) == b
    ]]></literal>
    <literal><![CDATA[
      -p(k,b)
    ]]></literal>
    <justification jstring="[resolve(11682,h,50,d),merge(h),merge(i)].">
      <j1 rule="resolve" parents="11682 50"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="11846">
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      k == b
    ]]></literal>
    <literal><![CDATA[
      k == m
    ]]></literal>
    <literal><![CDATA[
      f(k) == k
    ]]></literal>
    <literal><![CDATA[
      f(k) == m
    ]]></literal>
    <literal><![CDATA[
      f(k) == b
    ]]></literal>
    <justification jstring="[resolve(11832,h,1155,d),merge(h),merge(i),merge(j),merge(k),merge(l),merge(m),merge(n)].">
      <j1 rule="resolve" parents="11832 1155"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="11848">
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      k == b
    ]]></literal>
    <literal><![CDATA[
      k == m
    ]]></literal>
    <literal><![CDATA[
      f(k) == m
    ]]></literal>
    <literal><![CDATA[
      f(k) == b
    ]]></literal>
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <justification jstring="[resolve(11846,e,450,f),merge(g),merge(h),merge(i),merge(k)].">
      <j1 rule="resolve" parents="11846 450"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="11861">
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      k == b
    ]]></literal>
    <literal><![CDATA[
      k == m
    ]]></literal>
    <literal><![CDATA[
      f(k) == m
    ]]></literal>
    <literal><![CDATA[
      f(k) == b
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <justification jstring="[resolve(11848,g,46,d),merge(g),merge(h)].">
      <j1 rule="resolve" parents="11848 46"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="11873">
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      k == b
    ]]></literal>
    <literal><![CDATA[
      k == m
    ]]></literal>
    <literal><![CDATA[
      f(k) == m
    ]]></literal>
    <literal><![CDATA[
      f(k) == b
    ]]></literal>
    <literal><![CDATA[
      -p(k,b)
    ]]></literal>
    <justification jstring="[resolve(11861,g,50,d),merge(g),merge(h)].">
      <j1 rule="resolve" parents="11861 50"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="11879">
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      k == b
    ]]></literal>
    <literal><![CDATA[
      k == m
    ]]></literal>
    <literal><![CDATA[
      f(k) == m
    ]]></literal>
    <literal><![CDATA[
      f(k) == b
    ]]></literal>
    <justification jstring="[resolve(11873,g,11848,g),merge(g),merge(h),merge(i),merge(j),merge(k),merge(l)].">
      <j1 rule="resolve" parents="11873 11848"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="11880">
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      k == b
    ]]></literal>
    <literal><![CDATA[
      k == m
    ]]></literal>
    <literal><![CDATA[
      f(k) == b
    ]]></literal>
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <justification jstring="[resolve(11879,e,451,f),merge(f),merge(g),merge(h),merge(j)].">
      <j1 rule="resolve" parents="11879 451"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="11892">
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      k == b
    ]]></literal>
    <literal><![CDATA[
      k == m
    ]]></literal>
    <literal><![CDATA[
      f(k) == b
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <justification jstring="[resolve(11880,f,46,d),merge(f),merge(g)].">
      <j1 rule="resolve" parents="11880 46"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="11905">
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      k == b
    ]]></literal>
    <literal><![CDATA[
      k == m
    ]]></literal>
    <literal><![CDATA[
      f(k) == b
    ]]></literal>
    <literal><![CDATA[
      -p(k,b)
    ]]></literal>
    <justification jstring="[resolve(11892,f,50,d),merge(f),merge(g)].">
      <j1 rule="resolve" parents="11892 50"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="11912">
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      k == b
    ]]></literal>
    <literal><![CDATA[
      k == m
    ]]></literal>
    <literal><![CDATA[
      f(k) == b
    ]]></literal>
    <justification jstring="[resolve(11905,f,11880,f),merge(f),merge(g),merge(h),merge(i),merge(j)].">
      <j1 rule="resolve" parents="11905 11880"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="11913">
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      k == b
    ]]></literal>
    <literal><![CDATA[
      k == m
    ]]></literal>
    <literal><![CDATA[
      p(k,b)
    ]]></literal>
    <justification jstring="[resolve(11912,e,1162,f),merge(e),merge(f),merge(g),merge(i)].">
      <j1 rule="resolve" parents="11912 1162"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="11922">
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      k == b
    ]]></literal>
    <literal><![CDATA[
      k == m
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <justification jstring="[resolve(11913,e,46,d),merge(e),merge(f)].">
      <j1 rule="resolve" parents="11913 46"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="11934">
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      k == b
    ]]></literal>
    <literal><![CDATA[
      k == m
    ]]></literal>
    <literal><![CDATA[
      -p(k,b)
    ]]></literal>
    <justification jstring="[resolve(11922,e,50,d),merge(e),merge(f)].">
      <j1 rule="resolve" parents="11922 50"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="11941">
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      k == b
    ]]></literal>
    <literal><![CDATA[
      k == m
    ]]></literal>
    <justification jstring="[resolve(11934,e,11913,e),merge(e),merge(f),merge(g),merge(h)].">
      <j1 rule="resolve" parents="11934 11913"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="11956">
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      k == b
    ]]></literal>
    <justification jstring="[resolve(11941,d,15,a),merge(d)].">
      <j1 rule="resolve" parents="11941 15"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="11965">
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      b == k
    ]]></literal>
    <justification jstring="[resolve(11956,c,15,a),merge(c)].">
      <j1 rule="resolve" parents="11956 15"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="11978">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      k == m
    ]]></literal>
    <justification jstring="[resolve(11965,a,15,a)].">
      <j1 rule="resolve" parents="11965 15"/>
    </justification>
  </clause>

  <clause id="11981">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <justification jstring="[resolve(11978,b,44,b),merge(b)].">
      <j1 rule="resolve" parents="11978 44"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="11986">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      -(x == k)
    ]]></literal>
    <literal><![CDATA[
      x == m
    ]]></literal>
    <justification jstring="[resolve(11978,b,16,b)].">
      <j1 rule="resolve" parents="11978 16"/>
    </justification>
  </clause>

  <clause id="11990">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      p(f(b),b)
    ]]></literal>
    <justification jstring="[resolve(11981,b,7,b),unit_del(b,41)].">
      <j1 rule="resolve" parents="11981 7"/>
      <j2 rule="unit_del" parents="41"/>
    </justification>
  </clause>

  <clause id="11991">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      p(b,f(b))
    ]]></literal>
    <justification jstring="[resolve(11981,b,6,b),unit_del(b,41)].">
      <j1 rule="resolve" parents="11981 6"/>
      <j2 rule="unit_del" parents="41"/>
    </justification>
  </clause>

  <clause id="11992">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      -(f(b) == b)
    ]]></literal>
    <justification jstring="[resolve(11981,b,5,b),unit_del(b,41)].">
      <j1 rule="resolve" parents="11981 5"/>
      <j2 rule="unit_del" parents="41"/>
    </justification>
  </clause>

  <clause id="11993">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      -(f(b) == m)
    ]]></literal>
    <justification jstring="[resolve(11981,b,4,b),unit_del(b,41)].">
      <j1 rule="resolve" parents="11981 4"/>
      <j2 rule="unit_del" parents="41"/>
    </justification>
  </clause>

  <clause id="11997">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      f(b) == m
    ]]></literal>
    <literal><![CDATA[
      p(f(b),m)
    ]]></literal>
    <literal><![CDATA[
      b == f(b)
    ]]></literal>
    <literal><![CDATA[
      -p(b,f(b))
    ]]></literal>
    <justification jstring="[resolve(11990,b,1,e),unit_del(d,41)].">
      <j1 rule="resolve" parents="11990 1"/>
      <j2 rule="unit_del" parents="41"/>
    </justification>
  </clause>

  <clause id="12491">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      f(b) == m
    ]]></literal>
    <literal><![CDATA[
      p(f(b),m)
    ]]></literal>
    <literal><![CDATA[
      b == f(b)
    ]]></literal>
    <justification jstring="[resolve(11997,e,11991,b),merge(e)].">
      <j1 rule="resolve" parents="11997 11991"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="13036">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      f(b) == m
    ]]></literal>
    <literal><![CDATA[
      b == f(b)
    ]]></literal>
    <literal><![CDATA[
      -(m == x)
    ]]></literal>
    <literal><![CDATA[
      p(f(b),x)
    ]]></literal>
    <justification jstring="[resolve(12491,c,18,b)].">
      <j1 rule="resolve" parents="12491 18"/>
    </justification>
  </clause>

  <clause id="14338">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      f(b) == m
    ]]></literal>
    <literal><![CDATA[
      b == f(b)
    ]]></literal>
    <literal><![CDATA[
      p(f(b),k)
    ]]></literal>
    <justification jstring="[resolve(13036,d,11965,a),merge(e)].">
      <j1 rule="resolve" parents="13036 11965"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="14349">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      f(b) == m
    ]]></literal>
    <literal><![CDATA[
      b == f(b)
    ]]></literal>
    <literal><![CDATA[
      f(b) == k
    ]]></literal>
    <literal><![CDATA[
      f(b) == b
    ]]></literal>
    <justification jstring="[resolve(14338,d,3,d),merge(e)].">
      <j1 rule="resolve" parents="14338 3"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="16817">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      f(b) == m
    ]]></literal>
    <literal><![CDATA[
      b == f(b)
    ]]></literal>
    <literal><![CDATA[
      f(b) == b
    ]]></literal>
    <justification jstring="[resolve(14349,d,11986,b),merge(e),merge(f)].">
      <j1 rule="resolve" parents="14349 11986"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="16819">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      b == f(b)
    ]]></literal>
    <literal><![CDATA[
      f(b) == b
    ]]></literal>
    <justification jstring="[resolve(16817,b,11993,b),merge(d)].">
      <j1 rule="resolve" parents="16817 11993"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="16826">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      b == f(b)
    ]]></literal>
    <justification jstring="[resolve(16819,c,11992,b),merge(c)].">
      <j1 rule="resolve" parents="16819 11992"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="16839">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      f(b) == b
    ]]></literal>
    <justification jstring="[resolve(16826,b,15,a)].">
      <j1 rule="resolve" parents="16826 15"/>
    </justification>
  </clause>

  <clause id="16854">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <justification jstring="[resolve(16839,b,11992,b),merge(b)].">
      <j1 rule="resolve" parents="16839 11992"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="16857">
    <literal><![CDATA[
      g(j) == j
    ]]></literal>
    <literal><![CDATA[
      g(j) == k
    ]]></literal>
    <literal><![CDATA[
      j == b
    ]]></literal>
    <literal><![CDATA[
      p(j,k)
    ]]></literal>
    <justification jstring="[resolve(16854,a,78,d)].">
      <j1 rule="resolve" parents="16854 78"/>
    </justification>
  </clause>

  <clause id="16859">
    <literal><![CDATA[
      b == j
    ]]></literal>
    <literal><![CDATA[
      p(b,j)
    ]]></literal>
    <justification jstring="[resolve(16854,a,23,c)].">
      <j1 rule="resolve" parents="16854 23"/>
    </justification>
  </clause>

  <clause id="16862">
    <literal><![CDATA[
      -(x == b)
    ]]></literal>
    <literal><![CDATA[
      x == k
    ]]></literal>
    <justification jstring="[resolve(16854,a,16,b)].">
      <j1 rule="resolve" parents="16854 16"/>
    </justification>
  </clause>

  <clause id="16864">
    <literal><![CDATA[
      k == b
    ]]></literal>
    <justification jstring="[resolve(16854,a,15,a)].">
      <j1 rule="resolve" parents="16854 15"/>
    </justification>
  </clause>

  <clause id="16872">
    <literal><![CDATA[
      -(x == k)
    ]]></literal>
    <literal><![CDATA[
      x == b
    ]]></literal>
    <justification jstring="[resolve(16864,a,16,b)].">
      <j1 rule="resolve" parents="16864 16"/>
    </justification>
  </clause>

  <clause id="16874">
    <literal><![CDATA[
      -(m == k)
    ]]></literal>
    <justification jstring="[ur(16,b,16864,a,c,21,a)].">
      <j1 rule="ur" parents="16 16864 21"/>
    </justification>
  </clause>

  <clause id="16877">
    <literal><![CDATA[
      -(k == x)
    ]]></literal>
    <literal><![CDATA[
      p(m,x)
    ]]></literal>
    <justification jstring="[back_unit_del(48),unit_del(a,16874)].">
      <j1 rule="back_unit_del" parents="48"/>
      <j2 rule="unit_del" parents="16874"/>
    </justification>
  </clause>

  <clause id="16926">
    <literal><![CDATA[
      b == j
    ]]></literal>
    <literal><![CDATA[
      -(j == x)
    ]]></literal>
    <literal><![CDATA[
      p(b,x)
    ]]></literal>
    <justification jstring="[resolve(16859,b,18,b)].">
      <j1 rule="resolve" parents="16859 18"/>
    </justification>
  </clause>

  <clause id="17068">
    <literal><![CDATA[
      g(j) == j
    ]]></literal>
    <literal><![CDATA[
      g(j) == k
    ]]></literal>
    <literal><![CDATA[
      j == b
    ]]></literal>
    <literal><![CDATA[
      j == k
    ]]></literal>
    <literal><![CDATA[
      j == m
    ]]></literal>
    <justification jstring="[resolve(16857,d,3,d),merge(f)].">
      <j1 rule="resolve" parents="16857 3"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="21668">
    <literal><![CDATA[
      g(j) == k
    ]]></literal>
    <literal><![CDATA[
      j == b
    ]]></literal>
    <literal><![CDATA[
      j == k
    ]]></literal>
    <literal><![CDATA[
      j == m
    ]]></literal>
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <justification jstring="[resolve(17068,a,9,c),merge(e)].">
      <j1 rule="resolve" parents="17068 9"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="21672">
    <literal><![CDATA[
      g(j) == k
    ]]></literal>
    <literal><![CDATA[
      j == b
    ]]></literal>
    <literal><![CDATA[
      j == k
    ]]></literal>
    <literal><![CDATA[
      j == m
    ]]></literal>
    <literal><![CDATA[
      -(b == x)
    ]]></literal>
    <literal><![CDATA[
      p(j,x)
    ]]></literal>
    <justification jstring="[resolve(21668,e,18,b)].">
      <j1 rule="resolve" parents="21668 18"/>
    </justification>
  </clause>

  <clause id="25931">
    <literal><![CDATA[
      g(j) == k
    ]]></literal>
    <literal><![CDATA[
      j == b
    ]]></literal>
    <literal><![CDATA[
      j == k
    ]]></literal>
    <literal><![CDATA[
      j == m
    ]]></literal>
    <literal><![CDATA[
      p(j,k)
    ]]></literal>
    <justification jstring="[resolve(21672,e,16854,a)].">
      <j1 rule="resolve" parents="21672 16854"/>
    </justification>
  </clause>

  <clause id="25943">
    <literal><![CDATA[
      g(j) == k
    ]]></literal>
    <literal><![CDATA[
      j == b
    ]]></literal>
    <literal><![CDATA[
      j == k
    ]]></literal>
    <literal><![CDATA[
      j == m
    ]]></literal>
    <justification jstring="[resolve(25931,e,3,d),merge(e),merge(f),merge(g)].">
      <j1 rule="resolve" parents="25931 3"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="25945">
    <literal><![CDATA[
      j == b
    ]]></literal>
    <literal><![CDATA[
      j == k
    ]]></literal>
    <literal><![CDATA[
      j == m
    ]]></literal>
    <literal><![CDATA[
      g(j) == b
    ]]></literal>
    <justification jstring="[resolve(25943,a,16872,a)].">
      <j1 rule="resolve" parents="25943 16872"/>
    </justification>
  </clause>

  <clause id="26312">
    <literal><![CDATA[
      j == b
    ]]></literal>
    <literal><![CDATA[
      j == k
    ]]></literal>
    <literal><![CDATA[
      j == m
    ]]></literal>
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <justification jstring="[resolve(25945,d,40,a),merge(e),merge(f)].">
      <j1 rule="resolve" parents="25945 40"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="26320">
    <literal><![CDATA[
      j == b
    ]]></literal>
    <literal><![CDATA[
      j == k
    ]]></literal>
    <literal><![CDATA[
      j == m
    ]]></literal>
    <literal><![CDATA[
      -(b == x)
    ]]></literal>
    <literal><![CDATA[
      p(j,x)
    ]]></literal>
    <justification jstring="[resolve(26312,d,18,b)].">
      <j1 rule="resolve" parents="26312 18"/>
    </justification>
  </clause>

  <clause id="28162">
    <literal><![CDATA[
      j == b
    ]]></literal>
    <literal><![CDATA[
      j == k
    ]]></literal>
    <literal><![CDATA[
      j == m
    ]]></literal>
    <literal><![CDATA[
      p(j,k)
    ]]></literal>
    <justification jstring="[resolve(26320,d,16854,a)].">
      <j1 rule="resolve" parents="26320 16854"/>
    </justification>
  </clause>

  <clause id="28168">
    <literal><![CDATA[
      j == b
    ]]></literal>
    <literal><![CDATA[
      j == k
    ]]></literal>
    <literal><![CDATA[
      j == m
    ]]></literal>
    <justification jstring="[resolve(28162,d,3,d),merge(d),merge(e),merge(f)].">
      <j1 rule="resolve" parents="28162 3"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="28178">
    <literal><![CDATA[
      j == b
    ]]></literal>
    <literal><![CDATA[
      j == m
    ]]></literal>
    <justification jstring="[resolve(28168,b,16872,a),merge(c)].">
      <j1 rule="resolve" parents="28168 16872"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="28191">
    <literal><![CDATA[
      j == b
    ]]></literal>
    <literal><![CDATA[
      m == j
    ]]></literal>
    <justification jstring="[resolve(28178,b,15,a)].">
      <j1 rule="resolve" parents="28178 15"/>
    </justification>
  </clause>

  <clause id="28198">
    <literal><![CDATA[
      m == j
    ]]></literal>
    <literal><![CDATA[
      j == k
    ]]></literal>
    <justification jstring="[resolve(28191,a,16862,a)].">
      <j1 rule="resolve" parents="28191 16862"/>
    </justification>
  </clause>

  <clause id="28204">
    <literal><![CDATA[
      m == j
    ]]></literal>
    <literal><![CDATA[
      b == j
    ]]></literal>
    <justification jstring="[resolve(28191,a,15,a)].">
      <j1 rule="resolve" parents="28191 15"/>
    </justification>
  </clause>

  <clause id="28216">
    <literal><![CDATA[
      m == j
    ]]></literal>
    <literal><![CDATA[
      k == j
    ]]></literal>
    <justification jstring="[resolve(28198,b,15,a)].">
      <j1 rule="resolve" parents="28198 15"/>
    </justification>
  </clause>

  <clause id="28230">
    <literal><![CDATA[
      b == j
    ]]></literal>
    <literal><![CDATA[
      j == m
    ]]></literal>
    <justification jstring="[resolve(28204,a,15,a)].">
      <j1 rule="resolve" parents="28204 15"/>
    </justification>
  </clause>

  <clause id="28235">
    <literal><![CDATA[
      m == j
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <justification jstring="[resolve(28216,b,16877,a)].">
      <j1 rule="resolve" parents="28216 16877"/>
    </justification>
  </clause>

  <clause id="28250">
    <literal><![CDATA[
      b == j
    ]]></literal>
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <justification jstring="[resolve(28230,b,16926,b),merge(b)].">
      <j1 rule="resolve" parents="28230 16926"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="28255">
    <literal><![CDATA[
      m == j
    ]]></literal>
    <justification jstring="[resolve(28235,b,22,b),merge(b),unit_del(b,16874)].">
      <j1 rule="resolve" parents="28235 22"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="16874"/>
    </justification>
  </clause>

  <clause id="28271">
    <literal><![CDATA[
      -(j == b)
    ]]></literal>
    <justification jstring="[ur(16,a,28255,a,c,21,a)].">
      <j1 rule="ur" parents="16 28255 21"/>
    </justification>
  </clause>

  <clause id="28495">
    <literal><![CDATA[
      -(b == j)
    ]]></literal>
    <justification jstring="[ur(15,b,28271,a)].">
      <j1 rule="ur" parents="15 28271"/>
    </justification>
  </clause>

  <clause id="28524">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <justification jstring="[back_unit_del(28250),unit_del(a,28495)].">
      <j1 rule="back_unit_del" parents="28250"/>
      <j2 rule="unit_del" parents="28495"/>
    </justification>
  </clause>

  <clause id="28585">
    <literal><![CDATA[
      p(f(b),b)
    ]]></literal>
    <justification jstring="[resolve(28524,a,7,b),unit_del(a,41)].">
      <j1 rule="resolve" parents="28524 7"/>
      <j2 rule="unit_del" parents="41"/>
    </justification>
  </clause>

  <clause id="28587">
    <literal><![CDATA[
      -(f(b) == b)
    ]]></literal>
    <justification jstring="[resolve(28524,a,5,b),unit_del(a,41)].">
      <j1 rule="resolve" parents="28524 5"/>
      <j2 rule="unit_del" parents="41"/>
    </justification>
  </clause>

  <clause id="28588">
    <literal><![CDATA[
      -(f(b) == m)
    ]]></literal>
    <justification jstring="[resolve(28524,a,4,b),unit_del(a,41)].">
      <j1 rule="resolve" parents="28524 4"/>
      <j2 rule="unit_del" parents="41"/>
    </justification>
  </clause>

  <clause id="28779">
    <literal><![CDATA[
      -(b == x)
    ]]></literal>
    <literal><![CDATA[
      p(f(b),x)
    ]]></literal>
    <justification jstring="[resolve(28585,a,18,b)].">
      <j1 rule="resolve" parents="28585 18"/>
    </justification>
  </clause>

  <clause id="28873">
    <literal><![CDATA[
      p(f(b),k)
    ]]></literal>
    <justification jstring="[resolve(28779,a,16854,a)].">
      <j1 rule="resolve" parents="28779 16854"/>
    </justification>
  </clause>

  <clause id="28877">
    <literal><![CDATA[
      f(b) == k
    ]]></literal>
    <justification jstring="[resolve(28873,a,3,d),unit_del(b,28588),unit_del(c,28587)].">
      <j1 rule="resolve" parents="28873 3"/>
      <j2 rule="unit_del" parents="28588"/>
      <j2 rule="unit_del" parents="28587"/>
    </justification>
  </clause>

  <clause id="28882">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[resolve(28877,a,16872,a),unit_del(a,28587)].">
      <j1 rule="resolve" parents="28877 16872"/>
      <j2 rule="unit_del" parents="28587"/>
    </justification>
  </clause>

</proof>

</proofs>
