<?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 22-May-2007, May 2007.
Process 27610 was started by mccune on cleo,
Tue May 22 14:49:14 2007
The command was "/home/mccune/bin/prover9 -f wang.in wang3.in".
]]></heading>

<proof number="1" length="136" max_count="27">

<comments><![CDATA[
% Proof 1 at 20.47 (+ 0.10) seconds.
% Length of proof is 136.
% Level of proof is 73.
% Maximum clause weight is 27.
% Given clauses 5783.
]]></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" 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="3" 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="4" 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="5" 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="6" 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="7" 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="9" 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="10" 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="11" 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="12" 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="13" 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="14" type="assumption">
    <literal><![CDATA[
      x == x
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

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

  <clause id="16" type="assumption">
    <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="17" type="assumption">
    <literal><![CDATA[
      -(x == y)
    ]]></literal>
    <literal><![CDATA[
      -p(x,z)
    ]]></literal>
    <literal><![CDATA[
      p(y,z)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="18" type="assumption">
    <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="19" type="assumption">
    <literal><![CDATA[
      -(x == y)
    ]]></literal>
    <literal><![CDATA[
      f(x) == f(y)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

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

  <clause id="22" 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="23" 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[
      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="43">
    <literal><![CDATA[
      k == j
    ]]></literal>
    <literal><![CDATA[
      p(k,j)
    ]]></literal>
    <justification jstring="[resolve(23,c,14,a)].">
      <j1 rule="resolve" parents="23 14"/>
    </justification>
  </clause>

  <clause id="45">
    <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="47">
    <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="49">
    <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="51">
    <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="53">
    <literal><![CDATA[
      k == j
    ]]></literal>
    <literal><![CDATA[
      -(j == x)
    ]]></literal>
    <literal><![CDATA[
      p(k,x)
    ]]></literal>
    <justification jstring="[resolve(43,b,18,b)].">
      <j1 rule="resolve" parents="43 18"/>
    </justification>
  </clause>

  <clause id="54">
    <literal><![CDATA[
      k == j
    ]]></literal>
    <literal><![CDATA[
      -(k == x)
    ]]></literal>
    <literal><![CDATA[
      p(x,j)
    ]]></literal>
    <justification jstring="[resolve(43,b,17,b)].">
      <j1 rule="resolve" parents="43 17"/>
    </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,47,d)].">
      <j1 rule="resolve" parents="31 47"/>
    </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="152">
    <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="153">
    <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(152,f,73,g),merge(f),merge(g),merge(h),merge(i)].">
      <j1 rule="resolve" parents="152 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(153,b,9,c),merge(g)].">
      <j1 rule="resolve" parents="153 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,47,d),merge(g),merge(h)].">
      <j1 rule="resolve" parents="167 47"/>
      <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,51,d),merge(g),merge(h)].">
      <j1 rule="resolve" parents="169 51"/>
      <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="202">
    <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(202,b,40,a),merge(g),merge(h)].">
      <j1 rule="resolve" parents="202 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,47,d),merge(f),merge(g)].">
      <j1 rule="resolve" parents="206 47"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="233">
    <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,51,d),merge(f),merge(g)].">
      <j1 rule="resolve" parents="215 51"/>
      <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(233,f,206,f),merge(f),merge(g),merge(h),merge(i),merge(j)].">
      <j1 rule="resolve" parents="233 206"/>
      <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="14967">
    <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,47,d),merge(h),merge(i)].">
      <j1 rule="resolve" parents="1155 47"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="15607">
    <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(14967,h,51,d),merge(h),merge(i)].">
      <j1 rule="resolve" parents="14967 51"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="15634">
    <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(15607,h,1155,d),merge(h),merge(i),merge(j),merge(k),merge(l),merge(m),merge(n)].">
      <j1 rule="resolve" parents="15607 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="15636">
    <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(15634,e,450,f),merge(g),merge(h),merge(i),merge(k)].">
      <j1 rule="resolve" parents="15634 450"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="15651">
    <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(15636,g,47,d),merge(g),merge(h)].">
      <j1 rule="resolve" parents="15636 47"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="15663">
    <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(15651,g,51,d),merge(g),merge(h)].">
      <j1 rule="resolve" parents="15651 51"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="15674">
    <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(15663,g,15636,g),merge(g),merge(h),merge(i),merge(j),merge(k),merge(l)].">
      <j1 rule="resolve" parents="15663 15636"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="15675">
    <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(15674,e,451,f),merge(f),merge(g),merge(h),merge(j)].">
      <j1 rule="resolve" parents="15674 451"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="15687">
    <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(15675,f,47,d),merge(f),merge(g)].">
      <j1 rule="resolve" parents="15675 47"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="15706">
    <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(15687,f,51,d),merge(f),merge(g)].">
      <j1 rule="resolve" parents="15687 51"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="15713">
    <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(15706,f,15675,f),merge(f),merge(g),merge(h),merge(i),merge(j)].">
      <j1 rule="resolve" parents="15706 15675"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="15714">
    <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(15713,e,1162,f),merge(e),merge(f),merge(g),merge(i)].">
      <j1 rule="resolve" parents="15713 1162"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="15730">
    <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(15714,e,47,d),merge(e),merge(f)].">
      <j1 rule="resolve" parents="15714 47"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="15742">
    <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(15730,e,51,d),merge(e),merge(f)].">
      <j1 rule="resolve" parents="15730 51"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="15751">
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      k == b
    ]]></literal>
    <literal><![CDATA[
      k == m
    ]]></literal>
    <justification jstring="[resolve(15742,e,15714,e),merge(e),merge(f),merge(g),merge(h)].">
      <j1 rule="resolve" parents="15742 15714"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="15763">
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      k == b
    ]]></literal>
    <justification jstring="[resolve(15751,d,15,a),merge(d)].">
      <j1 rule="resolve" parents="15751 15"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="15772">
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      b == k
    ]]></literal>
    <justification jstring="[resolve(15763,c,15,a),merge(c)].">
      <j1 rule="resolve" parents="15763 15"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="15785">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      k == m
    ]]></literal>
    <justification jstring="[resolve(15772,a,15,a)].">
      <j1 rule="resolve" parents="15772 15"/>
    </justification>
  </clause>

  <clause id="15788">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <justification jstring="[resolve(15785,b,45,b),merge(b)].">
      <j1 rule="resolve" parents="15785 45"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="15793">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      -(x == k)
    ]]></literal>
    <literal><![CDATA[
      x == m
    ]]></literal>
    <justification jstring="[resolve(15785,b,16,b)].">
      <j1 rule="resolve" parents="15785 16"/>
    </justification>
  </clause>

  <clause id="15797">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      p(f(b),b)
    ]]></literal>
    <justification jstring="[resolve(15788,b,7,b),unit_del(b,41)].">
      <j1 rule="resolve" parents="15788 7"/>
      <j2 rule="unit_del" parents="41"/>
    </justification>
  </clause>

  <clause id="15798">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      p(b,f(b))
    ]]></literal>
    <justification jstring="[resolve(15788,b,6,b),unit_del(b,41)].">
      <j1 rule="resolve" parents="15788 6"/>
      <j2 rule="unit_del" parents="41"/>
    </justification>
  </clause>

  <clause id="15799">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      -(f(b) == b)
    ]]></literal>
    <justification jstring="[resolve(15788,b,5,b),unit_del(b,41)].">
      <j1 rule="resolve" parents="15788 5"/>
      <j2 rule="unit_del" parents="41"/>
    </justification>
  </clause>

  <clause id="15800">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      -(f(b) == m)
    ]]></literal>
    <justification jstring="[resolve(15788,b,4,b),unit_del(b,41)].">
      <j1 rule="resolve" parents="15788 4"/>
      <j2 rule="unit_del" parents="41"/>
    </justification>
  </clause>

  <clause id="15804">
    <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(15797,b,1,e),unit_del(d,41)].">
      <j1 rule="resolve" parents="15797 1"/>
      <j2 rule="unit_del" parents="41"/>
    </justification>
  </clause>

  <clause id="16298">
    <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(15804,e,15798,b),merge(e)].">
      <j1 rule="resolve" parents="15804 15798"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="16843">
    <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(16298,c,18,b)].">
      <j1 rule="resolve" parents="16298 18"/>
    </justification>
  </clause>

  <clause id="18151">
    <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(16843,d,15772,a),merge(e)].">
      <j1 rule="resolve" parents="16843 15772"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="18156">
    <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(18151,d,3,d),merge(e)].">
      <j1 rule="resolve" parents="18151 3"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="20624">
    <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(18156,d,15793,b),merge(e),merge(f)].">
      <j1 rule="resolve" parents="18156 15793"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="20631">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      b == f(b)
    ]]></literal>
    <literal><![CDATA[
      f(b) == b
    ]]></literal>
    <justification jstring="[resolve(20624,b,15800,b),merge(d)].">
      <j1 rule="resolve" parents="20624 15800"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="20633">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      b == f(b)
    ]]></literal>
    <justification jstring="[resolve(20631,c,15799,b),merge(c)].">
      <j1 rule="resolve" parents="20631 15799"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="20646">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      f(b) == b
    ]]></literal>
    <justification jstring="[resolve(20633,b,15,a)].">
      <j1 rule="resolve" parents="20633 15"/>
    </justification>
  </clause>

  <clause id="20661">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <justification jstring="[resolve(20646,b,15799,b),merge(b)].">
      <j1 rule="resolve" parents="20646 15799"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="20664">
    <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(20661,a,78,d)].">
      <j1 rule="resolve" parents="20661 78"/>
    </justification>
  </clause>

  <clause id="20668">
    <literal><![CDATA[
      f(b) == f(k)
    ]]></literal>
    <justification jstring="[resolve(20661,a,19,a)].">
      <j1 rule="resolve" parents="20661 19"/>
    </justification>
  </clause>

  <clause id="20669">
    <literal><![CDATA[
      -(x == b)
    ]]></literal>
    <literal><![CDATA[
      x == k
    ]]></literal>
    <justification jstring="[resolve(20661,a,16,b)].">
      <j1 rule="resolve" parents="20661 16"/>
    </justification>
  </clause>

  <clause id="20671">
    <literal><![CDATA[
      k == b
    ]]></literal>
    <justification jstring="[resolve(20661,a,15,a)].">
      <j1 rule="resolve" parents="20661 15"/>
    </justification>
  </clause>

  <clause id="20672">
    <literal><![CDATA[
      -(k == m)
    ]]></literal>
    <justification jstring="[ur(16,a,20661,a,c,41,a)].">
      <j1 rule="ur" parents="16 20661 41"/>
    </justification>
  </clause>

  <clause id="20675">
    <literal><![CDATA[
      k == j
    ]]></literal>
    <literal><![CDATA[
      p(b,j)
    ]]></literal>
    <justification jstring="[resolve(20671,a,54,b)].">
      <j1 rule="resolve" parents="20671 54"/>
    </justification>
  </clause>

  <clause id="20679">
    <literal><![CDATA[
      -(x == k)
    ]]></literal>
    <literal><![CDATA[
      x == b
    ]]></literal>
    <justification jstring="[resolve(20671,a,16,b)].">
      <j1 rule="resolve" parents="20671 16"/>
    </justification>
  </clause>

  <clause id="20681">
    <literal><![CDATA[
      -(m == k)
    ]]></literal>
    <justification jstring="[ur(16,b,20671,a,c,21,a)].">
      <j1 rule="ur" parents="16 20671 21"/>
    </justification>
  </clause>

  <clause id="20684">
    <literal><![CDATA[
      -(k == x)
    ]]></literal>
    <literal><![CDATA[
      p(m,x)
    ]]></literal>
    <justification jstring="[back_unit_del(49),unit_del(a,20681)].">
      <j1 rule="back_unit_del" parents="49"/>
      <j2 rule="unit_del" parents="20681"/>
    </justification>
  </clause>

  <clause id="20710">
    <literal><![CDATA[
      -(f(k) == x)
    ]]></literal>
    <literal><![CDATA[
      f(b) == x
    ]]></literal>
    <justification jstring="[resolve(20668,a,16,a)].">
      <j1 rule="resolve" parents="20668 16"/>
    </justification>
  </clause>

  <clause id="20740">
    <literal><![CDATA[
      k == j
    ]]></literal>
    <literal><![CDATA[
      -(j == x)
    ]]></literal>
    <literal><![CDATA[
      p(b,x)
    ]]></literal>
    <justification jstring="[resolve(20675,b,18,b)].">
      <j1 rule="resolve" parents="20675 18"/>
    </justification>
  </clause>

  <clause id="20875">
    <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(20664,d,3,d),merge(f)].">
      <j1 rule="resolve" parents="20664 3"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="25475">
    <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(20875,a,9,c),merge(e)].">
      <j1 rule="resolve" parents="20875 9"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="25484">
    <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(25475,e,18,b)].">
      <j1 rule="resolve" parents="25475 18"/>
    </justification>
  </clause>

  <clause id="30984">
    <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(25484,e,20661,a)].">
      <j1 rule="resolve" parents="25484 20661"/>
    </justification>
  </clause>

  <clause id="30996">
    <literal><![CDATA[
      g(j) == k
    ]]></literal>
    <literal><![CDATA[
      j == b
    ]]></literal>
    <literal><![CDATA[
      j == k
    ]]></literal>
    <literal><![CDATA[
      j == m
    ]]></literal>
    <justification jstring="[resolve(30984,e,3,d),merge(e),merge(f),merge(g)].">
      <j1 rule="resolve" parents="30984 3"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="30998">
    <literal><![CDATA[
      j == b
    ]]></literal>
    <literal><![CDATA[
      j == k
    ]]></literal>
    <literal><![CDATA[
      j == m
    ]]></literal>
    <literal><![CDATA[
      g(j) == b
    ]]></literal>
    <justification jstring="[resolve(30996,a,20679,a)].">
      <j1 rule="resolve" parents="30996 20679"/>
    </justification>
  </clause>

  <clause id="31374">
    <literal><![CDATA[
      j == b
    ]]></literal>
    <literal><![CDATA[
      j == k
    ]]></literal>
    <literal><![CDATA[
      j == m
    ]]></literal>
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <justification jstring="[resolve(30998,d,40,a),merge(e),merge(f)].">
      <j1 rule="resolve" parents="30998 40"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="31382">
    <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(31374,d,18,b)].">
      <j1 rule="resolve" parents="31374 18"/>
    </justification>
  </clause>

  <clause id="33404">
    <literal><![CDATA[
      j == b
    ]]></literal>
    <literal><![CDATA[
      j == k
    ]]></literal>
    <literal><![CDATA[
      j == m
    ]]></literal>
    <literal><![CDATA[
      p(j,k)
    ]]></literal>
    <justification jstring="[resolve(31382,d,20661,a)].">
      <j1 rule="resolve" parents="31382 20661"/>
    </justification>
  </clause>

  <clause id="33415">
    <literal><![CDATA[
      j == b
    ]]></literal>
    <literal><![CDATA[
      j == k
    ]]></literal>
    <literal><![CDATA[
      j == m
    ]]></literal>
    <justification jstring="[resolve(33404,d,3,d),merge(d),merge(e),merge(f)].">
      <j1 rule="resolve" parents="33404 3"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="33425">
    <literal><![CDATA[
      j == b
    ]]></literal>
    <literal><![CDATA[
      j == m
    ]]></literal>
    <justification jstring="[resolve(33415,b,20679,a),merge(c)].">
      <j1 rule="resolve" parents="33415 20679"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="33429">
    <literal><![CDATA[
      j == b
    ]]></literal>
    <literal><![CDATA[
      k == j
    ]]></literal>
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <justification jstring="[resolve(33425,b,20740,b)].">
      <j1 rule="resolve" parents="33425 20740"/>
    </justification>
  </clause>

  <clause id="33431">
    <literal><![CDATA[
      j == b
    ]]></literal>
    <literal><![CDATA[
      k == j
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <justification jstring="[resolve(33425,b,53,b)].">
      <j1 rule="resolve" parents="33425 53"/>
    </justification>
  </clause>

  <clause id="33438">
    <literal><![CDATA[
      j == b
    ]]></literal>
    <literal><![CDATA[
      m == j
    ]]></literal>
    <justification jstring="[resolve(33425,b,15,a)].">
      <j1 rule="resolve" parents="33425 15"/>
    </justification>
  </clause>

  <clause id="33445">
    <literal><![CDATA[
      m == j
    ]]></literal>
    <literal><![CDATA[
      j == k
    ]]></literal>
    <justification jstring="[resolve(33438,a,20669,a)].">
      <j1 rule="resolve" parents="33438 20669"/>
    </justification>
  </clause>

  <clause id="33465">
    <literal><![CDATA[
      m == j
    ]]></literal>
    <literal><![CDATA[
      k == j
    ]]></literal>
    <justification jstring="[resolve(33445,b,15,a)].">
      <j1 rule="resolve" parents="33445 15"/>
    </justification>
  </clause>

  <clause id="33484">
    <literal><![CDATA[
      m == j
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <justification jstring="[resolve(33465,b,20684,a)].">
      <j1 rule="resolve" parents="33465 20684"/>
    </justification>
  </clause>

  <clause id="33509">
    <literal><![CDATA[
      m == j
    ]]></literal>
    <justification jstring="[resolve(33484,b,22,b),merge(b),unit_del(b,20681)].">
      <j1 rule="resolve" parents="33484 22"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="20681"/>
    </justification>
  </clause>

  <clause id="33524">
    <literal><![CDATA[
      -(j == k)
    ]]></literal>
    <justification jstring="[ur(16,a,33509,a,c,20681,a)].">
      <j1 rule="ur" parents="16 33509 20681"/>
    </justification>
  </clause>

  <clause id="33525">
    <literal><![CDATA[
      -(j == b)
    ]]></literal>
    <justification jstring="[ur(16,a,33509,a,c,21,a)].">
      <j1 rule="ur" parents="16 33509 21"/>
    </justification>
  </clause>

  <clause id="33533">
    <literal><![CDATA[
      k == j
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <justification jstring="[back_unit_del(33431),unit_del(a,33525)].">
      <j1 rule="back_unit_del" parents="33431"/>
      <j2 rule="unit_del" parents="33525"/>
    </justification>
  </clause>

  <clause id="33534">
    <literal><![CDATA[
      k == j
    ]]></literal>
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <justification jstring="[back_unit_del(33429),unit_del(a,33525)].">
      <j1 rule="back_unit_del" parents="33429"/>
      <j2 rule="unit_del" parents="33525"/>
    </justification>
  </clause>

  <clause id="33755">
    <literal><![CDATA[
      -(k == j)
    ]]></literal>
    <justification jstring="[ur(15,b,33524,a)].">
      <j1 rule="ur" parents="15 33524"/>
    </justification>
  </clause>

  <clause id="33783">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <justification jstring="[back_unit_del(33534),unit_del(a,33755)].">
      <j1 rule="back_unit_del" parents="33534"/>
      <j2 rule="unit_del" parents="33755"/>
    </justification>
  </clause>

  <clause id="33784">
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <justification jstring="[back_unit_del(33533),unit_del(a,33755)].">
      <j1 rule="back_unit_del" parents="33533"/>
      <j2 rule="unit_del" parents="33755"/>
    </justification>
  </clause>

  <clause id="33845">
    <literal><![CDATA[
      -(f(b) == b)
    ]]></literal>
    <justification jstring="[resolve(33783,a,5,b),unit_del(a,41)].">
      <j1 rule="resolve" parents="33783 5"/>
      <j2 rule="unit_del" parents="41"/>
    </justification>
  </clause>

  <clause id="33846">
    <literal><![CDATA[
      -(f(b) == m)
    ]]></literal>
    <justification jstring="[resolve(33783,a,4,b),unit_del(a,41)].">
      <j1 rule="resolve" parents="33783 4"/>
      <j2 rule="unit_del" parents="41"/>
    </justification>
  </clause>

  <clause id="33888">
    <literal><![CDATA[
      -(f(k) == b)
    ]]></literal>
    <justification jstring="[ur(20710,b,33845,a)].">
      <j1 rule="ur" parents="20710 33845"/>
    </justification>
  </clause>

  <clause id="34112">
    <literal><![CDATA[
      -(f(k) == m)
    ]]></literal>
    <justification jstring="[ur(20710,b,33846,a)].">
      <j1 rule="ur" parents="20710 33846"/>
    </justification>
  </clause>

  <clause id="34265">
    <literal><![CDATA[
      -(f(k) == k)
    ]]></literal>
    <justification jstring="[ur(20679,b,33888,a)].">
      <j1 rule="ur" parents="20679 33888"/>
    </justification>
  </clause>

  <clause id="34315">
    <literal><![CDATA[
      p(f(k),k)
    ]]></literal>
    <justification jstring="[resolve(33784,a,7,b),unit_del(a,20672)].">
      <j1 rule="resolve" parents="33784 7"/>
      <j2 rule="unit_del" parents="20672"/>
    </justification>
  </clause>

  <clause id="34351">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[resolve(34315,a,3,d),unit_del(a,34265),unit_del(b,34112),unit_del(c,33888)].">
      <j1 rule="resolve" parents="34315 3"/>
      <j2 rule="unit_del" parents="34265"/>
      <j2 rule="unit_del" parents="34112"/>
      <j2 rule="unit_del" parents="33888"/>
    </justification>
  </clause>

</proof>

</proofs>
