<?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 2009-02A, February 2009.
Process 11688 was started by mccune on cleo,
Wed Feb 25 09:36:43 2009
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 25.40 (+ 0.14) 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="15119">
    <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="15759">
    <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(15119,h,51,d),merge(h),merge(i)].">
      <j1 rule="resolve" parents="15119 51"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="15786">
    <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(15759,h,1155,d),merge(h),merge(i),merge(j),merge(k),merge(l),merge(m),merge(n)].">
      <j1 rule="resolve" parents="15759 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="15788">
    <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(15786,e,450,f),merge(g),merge(h),merge(i),merge(k)].">
      <j1 rule="resolve" parents="15786 450"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="15803">
    <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(15788,g,47,d),merge(g),merge(h)].">
      <j1 rule="resolve" parents="15788 47"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="15815">
    <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(15803,g,51,d),merge(g),merge(h)].">
      <j1 rule="resolve" parents="15803 51"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="15826">
    <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(15815,g,15788,g),merge(g),merge(h),merge(i),merge(j),merge(k),merge(l)].">
      <j1 rule="resolve" parents="15815 15788"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="15827">
    <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(15826,e,451,f),merge(f),merge(g),merge(h),merge(j)].">
      <j1 rule="resolve" parents="15826 451"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="15839">
    <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(15827,f,47,d),merge(f),merge(g)].">
      <j1 rule="resolve" parents="15827 47"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="15858">
    <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(15839,f,51,d),merge(f),merge(g)].">
      <j1 rule="resolve" parents="15839 51"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="15865">
    <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(15858,f,15827,f),merge(f),merge(g),merge(h),merge(i),merge(j)].">
      <j1 rule="resolve" parents="15858 15827"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="15866">
    <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(15865,e,1162,f),merge(e),merge(f),merge(g),merge(i)].">
      <j1 rule="resolve" parents="15865 1162"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="15882">
    <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(15866,e,47,d),merge(e),merge(f)].">
      <j1 rule="resolve" parents="15866 47"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="15894">
    <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(15882,e,51,d),merge(e),merge(f)].">
      <j1 rule="resolve" parents="15882 51"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="15903">
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      k == b
    ]]></literal>
    <literal><![CDATA[
      k == m
    ]]></literal>
    <justification jstring="[resolve(15894,e,15866,e),merge(e),merge(f),merge(g),merge(h)].">
      <j1 rule="resolve" parents="15894 15866"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="15915">
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      k == b
    ]]></literal>
    <justification jstring="[resolve(15903,d,15,a),merge(d)].">
      <j1 rule="resolve" parents="15903 15"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="15924">
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      b == k
    ]]></literal>
    <justification jstring="[resolve(15915,c,15,a),merge(c)].">
      <j1 rule="resolve" parents="15915 15"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="15937">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      k == m
    ]]></literal>
    <justification jstring="[resolve(15924,a,15,a)].">
      <j1 rule="resolve" parents="15924 15"/>
    </justification>
  </clause>

  <clause id="15940">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <justification jstring="[resolve(15937,b,45,b),merge(b)].">
      <j1 rule="resolve" parents="15937 45"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="15945">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      -(x == k)
    ]]></literal>
    <literal><![CDATA[
      x == m
    ]]></literal>
    <justification jstring="[resolve(15937,b,16,b)].">
      <j1 rule="resolve" parents="15937 16"/>
    </justification>
  </clause>

  <clause id="15949">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      p(f(b),b)
    ]]></literal>
    <justification jstring="[resolve(15940,b,7,b),unit_del(b,41)].">
      <j1 rule="resolve" parents="15940 7"/>
      <j2 rule="unit_del" parents="41"/>
    </justification>
  </clause>

  <clause id="15950">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      p(b,f(b))
    ]]></literal>
    <justification jstring="[resolve(15940,b,6,b),unit_del(b,41)].">
      <j1 rule="resolve" parents="15940 6"/>
      <j2 rule="unit_del" parents="41"/>
    </justification>
  </clause>

  <clause id="15951">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      -(f(b) == b)
    ]]></literal>
    <justification jstring="[resolve(15940,b,5,b),unit_del(b,41)].">
      <j1 rule="resolve" parents="15940 5"/>
      <j2 rule="unit_del" parents="41"/>
    </justification>
  </clause>

  <clause id="15952">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      -(f(b) == m)
    ]]></literal>
    <justification jstring="[resolve(15940,b,4,b),unit_del(b,41)].">
      <j1 rule="resolve" parents="15940 4"/>
      <j2 rule="unit_del" parents="41"/>
    </justification>
  </clause>

  <clause id="15956">
    <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(15949,b,1,e),unit_del(d,41)].">
      <j1 rule="resolve" parents="15949 1"/>
      <j2 rule="unit_del" parents="41"/>
    </justification>
  </clause>

  <clause id="16450">
    <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(15956,e,15950,b),merge(e)].">
      <j1 rule="resolve" parents="15956 15950"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="16995">
    <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(16450,c,18,b)].">
      <j1 rule="resolve" parents="16450 18"/>
    </justification>
  </clause>

  <clause id="18303">
    <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(16995,d,15924,a),merge(e)].">
      <j1 rule="resolve" parents="16995 15924"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="18308">
    <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(18303,d,3,d),merge(e)].">
      <j1 rule="resolve" parents="18303 3"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="20776">
    <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(18308,d,15945,b),merge(e),merge(f)].">
      <j1 rule="resolve" parents="18308 15945"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="20783">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      b == f(b)
    ]]></literal>
    <literal><![CDATA[
      f(b) == b
    ]]></literal>
    <justification jstring="[resolve(20776,b,15952,b),merge(d)].">
      <j1 rule="resolve" parents="20776 15952"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="20785">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      b == f(b)
    ]]></literal>
    <justification jstring="[resolve(20783,c,15951,b),merge(c)].">
      <j1 rule="resolve" parents="20783 15951"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="20798">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      f(b) == b
    ]]></literal>
    <justification jstring="[resolve(20785,b,15,a)].">
      <j1 rule="resolve" parents="20785 15"/>
    </justification>
  </clause>

  <clause id="20813">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <justification jstring="[resolve(20798,b,15951,b),merge(b)].">
      <j1 rule="resolve" parents="20798 15951"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="20816">
    <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(20813,a,78,d)].">
      <j1 rule="resolve" parents="20813 78"/>
    </justification>
  </clause>

  <clause id="20820">
    <literal><![CDATA[
      f(b) == f(k)
    ]]></literal>
    <justification jstring="[resolve(20813,a,19,a)].">
      <j1 rule="resolve" parents="20813 19"/>
    </justification>
  </clause>

  <clause id="20821">
    <literal><![CDATA[
      -(x == b)
    ]]></literal>
    <literal><![CDATA[
      x == k
    ]]></literal>
    <justification jstring="[resolve(20813,a,16,b)].">
      <j1 rule="resolve" parents="20813 16"/>
    </justification>
  </clause>

  <clause id="20823">
    <literal><![CDATA[
      k == b
    ]]></literal>
    <justification jstring="[resolve(20813,a,15,a)].">
      <j1 rule="resolve" parents="20813 15"/>
    </justification>
  </clause>

  <clause id="20824">
    <literal><![CDATA[
      -(k == m)
    ]]></literal>
    <justification jstring="[ur(16,a,20813,a,c,41,a)].">
      <j1 rule="ur" parents="16 20813 41"/>
    </justification>
  </clause>

  <clause id="20827">
    <literal><![CDATA[
      k == j
    ]]></literal>
    <literal><![CDATA[
      p(b,j)
    ]]></literal>
    <justification jstring="[resolve(20823,a,54,b)].">
      <j1 rule="resolve" parents="20823 54"/>
    </justification>
  </clause>

  <clause id="20831">
    <literal><![CDATA[
      -(x == k)
    ]]></literal>
    <literal><![CDATA[
      x == b
    ]]></literal>
    <justification jstring="[resolve(20823,a,16,b)].">
      <j1 rule="resolve" parents="20823 16"/>
    </justification>
  </clause>

  <clause id="20833">
    <literal><![CDATA[
      -(m == k)
    ]]></literal>
    <justification jstring="[ur(16,b,20823,a,c,21,a)].">
      <j1 rule="ur" parents="16 20823 21"/>
    </justification>
  </clause>

  <clause id="20836">
    <literal><![CDATA[
      -(k == x)
    ]]></literal>
    <literal><![CDATA[
      p(m,x)
    ]]></literal>
    <justification jstring="[back_unit_del(49),unit_del(a,20833)].">
      <j1 rule="back_unit_del" parents="49"/>
      <j2 rule="unit_del" parents="20833"/>
    </justification>
  </clause>

  <clause id="20862">
    <literal><![CDATA[
      -(f(k) == x)
    ]]></literal>
    <literal><![CDATA[
      f(b) == x
    ]]></literal>
    <justification jstring="[resolve(20820,a,16,a)].">
      <j1 rule="resolve" parents="20820 16"/>
    </justification>
  </clause>

  <clause id="20892">
    <literal><![CDATA[
      k == j
    ]]></literal>
    <literal><![CDATA[
      -(j == x)
    ]]></literal>
    <literal><![CDATA[
      p(b,x)
    ]]></literal>
    <justification jstring="[resolve(20827,b,18,b)].">
      <j1 rule="resolve" parents="20827 18"/>
    </justification>
  </clause>

  <clause id="21027">
    <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(20816,d,3,d),merge(f)].">
      <j1 rule="resolve" parents="20816 3"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="25627">
    <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(21027,a,9,c),merge(e)].">
      <j1 rule="resolve" parents="21027 9"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="25636">
    <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(25627,e,18,b)].">
      <j1 rule="resolve" parents="25627 18"/>
    </justification>
  </clause>

  <clause id="31136">
    <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(25636,e,20813,a)].">
      <j1 rule="resolve" parents="25636 20813"/>
    </justification>
  </clause>

  <clause id="31148">
    <literal><![CDATA[
      g(j) == k
    ]]></literal>
    <literal><![CDATA[
      j == b
    ]]></literal>
    <literal><![CDATA[
      j == k
    ]]></literal>
    <literal><![CDATA[
      j == m
    ]]></literal>
    <justification jstring="[resolve(31136,e,3,d),merge(e),merge(f),merge(g)].">
      <j1 rule="resolve" parents="31136 3"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="31150">
    <literal><![CDATA[
      j == b
    ]]></literal>
    <literal><![CDATA[
      j == k
    ]]></literal>
    <literal><![CDATA[
      j == m
    ]]></literal>
    <literal><![CDATA[
      g(j) == b
    ]]></literal>
    <justification jstring="[resolve(31148,a,20831,a)].">
      <j1 rule="resolve" parents="31148 20831"/>
    </justification>
  </clause>

  <clause id="31526">
    <literal><![CDATA[
      j == b
    ]]></literal>
    <literal><![CDATA[
      j == k
    ]]></literal>
    <literal><![CDATA[
      j == m
    ]]></literal>
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <justification jstring="[resolve(31150,d,40,a),merge(e),merge(f)].">
      <j1 rule="resolve" parents="31150 40"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="31534">
    <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(31526,d,18,b)].">
      <j1 rule="resolve" parents="31526 18"/>
    </justification>
  </clause>

  <clause id="33562">
    <literal><![CDATA[
      j == b
    ]]></literal>
    <literal><![CDATA[
      j == k
    ]]></literal>
    <literal><![CDATA[
      j == m
    ]]></literal>
    <literal><![CDATA[
      p(j,k)
    ]]></literal>
    <justification jstring="[resolve(31534,d,20813,a)].">
      <j1 rule="resolve" parents="31534 20813"/>
    </justification>
  </clause>

  <clause id="33573">
    <literal><![CDATA[
      j == b
    ]]></literal>
    <literal><![CDATA[
      j == k
    ]]></literal>
    <literal><![CDATA[
      j == m
    ]]></literal>
    <justification jstring="[resolve(33562,d,3,d),merge(d),merge(e),merge(f)].">
      <j1 rule="resolve" parents="33562 3"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="33583">
    <literal><![CDATA[
      j == b
    ]]></literal>
    <literal><![CDATA[
      j == m
    ]]></literal>
    <justification jstring="[resolve(33573,b,20831,a),merge(c)].">
      <j1 rule="resolve" parents="33573 20831"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="33587">
    <literal><![CDATA[
      j == b
    ]]></literal>
    <literal><![CDATA[
      k == j
    ]]></literal>
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <justification jstring="[resolve(33583,b,20892,b)].">
      <j1 rule="resolve" parents="33583 20892"/>
    </justification>
  </clause>

  <clause id="33589">
    <literal><![CDATA[
      j == b
    ]]></literal>
    <literal><![CDATA[
      k == j
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <justification jstring="[resolve(33583,b,53,b)].">
      <j1 rule="resolve" parents="33583 53"/>
    </justification>
  </clause>

  <clause id="33596">
    <literal><![CDATA[
      j == b
    ]]></literal>
    <literal><![CDATA[
      m == j
    ]]></literal>
    <justification jstring="[resolve(33583,b,15,a)].">
      <j1 rule="resolve" parents="33583 15"/>
    </justification>
  </clause>

  <clause id="33603">
    <literal><![CDATA[
      m == j
    ]]></literal>
    <literal><![CDATA[
      j == k
    ]]></literal>
    <justification jstring="[resolve(33596,a,20821,a)].">
      <j1 rule="resolve" parents="33596 20821"/>
    </justification>
  </clause>

  <clause id="33623">
    <literal><![CDATA[
      m == j
    ]]></literal>
    <literal><![CDATA[
      k == j
    ]]></literal>
    <justification jstring="[resolve(33603,b,15,a)].">
      <j1 rule="resolve" parents="33603 15"/>
    </justification>
  </clause>

  <clause id="33642">
    <literal><![CDATA[
      m == j
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <justification jstring="[resolve(33623,b,20836,a)].">
      <j1 rule="resolve" parents="33623 20836"/>
    </justification>
  </clause>

  <clause id="33667">
    <literal><![CDATA[
      m == j
    ]]></literal>
    <justification jstring="[resolve(33642,b,22,b),merge(b),unit_del(b,20833)].">
      <j1 rule="resolve" parents="33642 22"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="20833"/>
    </justification>
  </clause>

  <clause id="33682">
    <literal><![CDATA[
      -(j == k)
    ]]></literal>
    <justification jstring="[ur(16,a,33667,a,c,20833,a)].">
      <j1 rule="ur" parents="16 33667 20833"/>
    </justification>
  </clause>

  <clause id="33683">
    <literal><![CDATA[
      -(j == b)
    ]]></literal>
    <justification jstring="[ur(16,a,33667,a,c,21,a)].">
      <j1 rule="ur" parents="16 33667 21"/>
    </justification>
  </clause>

  <clause id="33691">
    <literal><![CDATA[
      k == j
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <justification jstring="[back_unit_del(33589),unit_del(a,33683)].">
      <j1 rule="back_unit_del" parents="33589"/>
      <j2 rule="unit_del" parents="33683"/>
    </justification>
  </clause>

  <clause id="33692">
    <literal><![CDATA[
      k == j
    ]]></literal>
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <justification jstring="[back_unit_del(33587),unit_del(a,33683)].">
      <j1 rule="back_unit_del" parents="33587"/>
      <j2 rule="unit_del" parents="33683"/>
    </justification>
  </clause>

  <clause id="33912">
    <literal><![CDATA[
      -(k == j)
    ]]></literal>
    <justification jstring="[ur(15,b,33682,a)].">
      <j1 rule="ur" parents="15 33682"/>
    </justification>
  </clause>

  <clause id="33940">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <justification jstring="[back_unit_del(33692),unit_del(a,33912)].">
      <j1 rule="back_unit_del" parents="33692"/>
      <j2 rule="unit_del" parents="33912"/>
    </justification>
  </clause>

  <clause id="33941">
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <justification jstring="[back_unit_del(33691),unit_del(a,33912)].">
      <j1 rule="back_unit_del" parents="33691"/>
      <j2 rule="unit_del" parents="33912"/>
    </justification>
  </clause>

  <clause id="34002">
    <literal><![CDATA[
      -(f(b) == b)
    ]]></literal>
    <justification jstring="[resolve(33940,a,5,b),unit_del(a,41)].">
      <j1 rule="resolve" parents="33940 5"/>
      <j2 rule="unit_del" parents="41"/>
    </justification>
  </clause>

  <clause id="34003">
    <literal><![CDATA[
      -(f(b) == m)
    ]]></literal>
    <justification jstring="[resolve(33940,a,4,b),unit_del(a,41)].">
      <j1 rule="resolve" parents="33940 4"/>
      <j2 rule="unit_del" parents="41"/>
    </justification>
  </clause>

  <clause id="34045">
    <literal><![CDATA[
      -(f(k) == b)
    ]]></literal>
    <justification jstring="[ur(20862,b,34002,a)].">
      <j1 rule="ur" parents="20862 34002"/>
    </justification>
  </clause>

  <clause id="34259">
    <literal><![CDATA[
      -(f(k) == m)
    ]]></literal>
    <justification jstring="[ur(20862,b,34003,a)].">
      <j1 rule="ur" parents="20862 34003"/>
    </justification>
  </clause>

  <clause id="34402">
    <literal><![CDATA[
      -(f(k) == k)
    ]]></literal>
    <justification jstring="[ur(20831,b,34045,a)].">
      <j1 rule="ur" parents="20831 34045"/>
    </justification>
  </clause>

  <clause id="34452">
    <literal><![CDATA[
      p(f(k),k)
    ]]></literal>
    <justification jstring="[resolve(33941,a,7,b),unit_del(a,20824)].">
      <j1 rule="resolve" parents="33941 7"/>
      <j2 rule="unit_del" parents="20824"/>
    </justification>
  </clause>

  <clause id="34488">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[resolve(34452,a,3,d),unit_del(a,34402),unit_del(b,34259),unit_del(c,34045)].">
      <j1 rule="resolve" parents="34452 3"/>
      <j2 rule="unit_del" parents="34402"/>
      <j2 rule="unit_del" parents="34259"/>
      <j2 rule="unit_del" parents="34045"/>
    </justification>
  </clause>

</proof>

</proofs>
