<?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 September-2006, September 2006.
Process 26742 was started by mccune on cleo.thornwood,
Wed Sep 13 14:36:54 2006
The command was "/home/mccune/LADR/bin/prover9 -f wang.in wang3.in".
]]></heading>

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

<comments><![CDATA[
% Proof 1 at 22.51 (+ 0.16) seconds.
% Length of proof is 136.
% Level of proof is 72.
% Maximum clause weight is 27.
% Given clauses 5784.
]]></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="44">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      -(k == x)
    ]]></literal>
    <literal><![CDATA[
      p(b,x)
    ]]></literal>
    <justification jstring="[resolve(35,b,18,b)].">
      <j1 rule="resolve" parents="35 18"/>
    </justification>
  </clause>

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

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

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

  <clause id="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,46,d)].">
      <j1 rule="resolve" parents="31 46"/>
    </justification>
  </clause>

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  <clause id="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,46,d),merge(h),merge(i)].">
      <j1 rule="resolve" parents="1155 46"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="15635">
    <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,50,d),merge(h),merge(i)].">
      <j1 rule="resolve" parents="14967 50"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="15657">
    <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(15635,h,1155,d),merge(h),merge(i),merge(j),merge(k),merge(l),merge(m),merge(n)].">
      <j1 rule="resolve" parents="15635 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="15659">
    <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(15657,e,450,f),merge(g),merge(h),merge(i),merge(k)].">
      <j1 rule="resolve" parents="15657 450"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="15672">
    <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(15659,g,46,d),merge(g),merge(h)].">
      <j1 rule="resolve" parents="15659 46"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="15688">
    <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(15672,g,50,d),merge(g),merge(h)].">
      <j1 rule="resolve" parents="15672 50"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="15694">
    <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(15688,g,15659,g),merge(g),merge(h),merge(i),merge(j),merge(k),merge(l)].">
      <j1 rule="resolve" parents="15688 15659"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="15697">
    <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(15694,e,451,f),merge(f),merge(g),merge(h),merge(j)].">
      <j1 rule="resolve" parents="15694 451"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="15709">
    <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(15697,f,46,d),merge(f),merge(g)].">
      <j1 rule="resolve" parents="15697 46"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="15722">
    <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(15709,f,50,d),merge(f),merge(g)].">
      <j1 rule="resolve" parents="15709 50"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="15737">
    <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(15722,f,15697,f),merge(f),merge(g),merge(h),merge(i),merge(j)].">
      <j1 rule="resolve" parents="15722 15697"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="15738">
    <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(15737,e,1162,f),merge(e),merge(f),merge(g),merge(i)].">
      <j1 rule="resolve" parents="15737 1162"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="15747">
    <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(15738,e,46,d),merge(e),merge(f)].">
      <j1 rule="resolve" parents="15738 46"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="15765">
    <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(15747,e,50,d),merge(e),merge(f)].">
      <j1 rule="resolve" parents="15747 50"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="15772">
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      k == b
    ]]></literal>
    <literal><![CDATA[
      k == m
    ]]></literal>
    <justification jstring="[resolve(15765,e,15738,e),merge(e),merge(f),merge(g),merge(h)].">
      <j1 rule="resolve" parents="15765 15738"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="15790">
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      k == b
    ]]></literal>
    <justification jstring="[resolve(15772,d,15,a),merge(d)].">
      <j1 rule="resolve" parents="15772 15"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="15799">
    <literal><![CDATA[
      m == k
    ]]></literal>
    <literal><![CDATA[
      b == k
    ]]></literal>
    <justification jstring="[resolve(15790,c,15,a),merge(c)].">
      <j1 rule="resolve" parents="15790 15"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="15812">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      k == m
    ]]></literal>
    <justification jstring="[resolve(15799,a,15,a)].">
      <j1 rule="resolve" parents="15799 15"/>
    </justification>
  </clause>

  <clause id="15815">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <justification jstring="[resolve(15812,b,44,b),merge(b)].">
      <j1 rule="resolve" parents="15812 44"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="15820">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      -(x == k)
    ]]></literal>
    <literal><![CDATA[
      x == m
    ]]></literal>
    <justification jstring="[resolve(15812,b,16,b)].">
      <j1 rule="resolve" parents="15812 16"/>
    </justification>
  </clause>

  <clause id="15824">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      p(f(b),b)
    ]]></literal>
    <justification jstring="[resolve(15815,b,7,b),unit_del(b,41)].">
      <j1 rule="resolve" parents="15815 7"/>
      <j2 rule="unit_del" parents="41"/>
    </justification>
  </clause>

  <clause id="15825">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      p(b,f(b))
    ]]></literal>
    <justification jstring="[resolve(15815,b,6,b),unit_del(b,41)].">
      <j1 rule="resolve" parents="15815 6"/>
      <j2 rule="unit_del" parents="41"/>
    </justification>
  </clause>

  <clause id="15826">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      -(f(b) == b)
    ]]></literal>
    <justification jstring="[resolve(15815,b,5,b),unit_del(b,41)].">
      <j1 rule="resolve" parents="15815 5"/>
      <j2 rule="unit_del" parents="41"/>
    </justification>
  </clause>

  <clause id="15827">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      -(f(b) == m)
    ]]></literal>
    <justification jstring="[resolve(15815,b,4,b),unit_del(b,41)].">
      <j1 rule="resolve" parents="15815 4"/>
      <j2 rule="unit_del" parents="41"/>
    </justification>
  </clause>

  <clause id="15831">
    <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(15824,b,1,e),unit_del(d,41)].">
      <j1 rule="resolve" parents="15824 1"/>
      <j2 rule="unit_del" parents="41"/>
    </justification>
  </clause>

  <clause id="16325">
    <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(15831,e,15825,b),merge(e)].">
      <j1 rule="resolve" parents="15831 15825"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="16870">
    <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(16325,c,18,b)].">
      <j1 rule="resolve" parents="16325 18"/>
    </justification>
  </clause>

  <clause id="18172">
    <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(16870,d,15799,a),merge(e)].">
      <j1 rule="resolve" parents="16870 15799"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="18183">
    <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(18172,d,3,d),merge(e)].">
      <j1 rule="resolve" parents="18172 3"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="20651">
    <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(18183,d,15820,b),merge(e),merge(f)].">
      <j1 rule="resolve" parents="18183 15820"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="20653">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      b == f(b)
    ]]></literal>
    <literal><![CDATA[
      f(b) == b
    ]]></literal>
    <justification jstring="[resolve(20651,b,15827,b),merge(d)].">
      <j1 rule="resolve" parents="20651 15827"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="20660">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      b == f(b)
    ]]></literal>
    <justification jstring="[resolve(20653,c,15826,b),merge(c)].">
      <j1 rule="resolve" parents="20653 15826"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="20673">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <literal><![CDATA[
      f(b) == b
    ]]></literal>
    <justification jstring="[resolve(20660,b,15,a)].">
      <j1 rule="resolve" parents="20660 15"/>
    </justification>
  </clause>

  <clause id="20688">
    <literal><![CDATA[
      b == k
    ]]></literal>
    <justification jstring="[resolve(20673,b,15826,b),merge(b)].">
      <j1 rule="resolve" parents="20673 15826"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="20691">
    <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(20688,a,78,d)].">
      <j1 rule="resolve" parents="20688 78"/>
    </justification>
  </clause>

  <clause id="20695">
    <literal><![CDATA[
      f(b) == f(k)
    ]]></literal>
    <justification jstring="[resolve(20688,a,19,a)].">
      <j1 rule="resolve" parents="20688 19"/>
    </justification>
  </clause>

  <clause id="20696">
    <literal><![CDATA[
      -(x == b)
    ]]></literal>
    <literal><![CDATA[
      x == k
    ]]></literal>
    <justification jstring="[resolve(20688,a,16,b)].">
      <j1 rule="resolve" parents="20688 16"/>
    </justification>
  </clause>

  <clause id="20698">
    <literal><![CDATA[
      k == b
    ]]></literal>
    <justification jstring="[resolve(20688,a,15,a)].">
      <j1 rule="resolve" parents="20688 15"/>
    </justification>
  </clause>

  <clause id="20699">
    <literal><![CDATA[
      -(k == m)
    ]]></literal>
    <justification jstring="[ur(16,a,20688,a,c,41,a)].">
      <j1 rule="ur" parents="16 20688 41"/>
    </justification>
  </clause>

  <clause id="20702">
    <literal><![CDATA[
      k == j
    ]]></literal>
    <literal><![CDATA[
      p(b,j)
    ]]></literal>
    <justification jstring="[resolve(20698,a,54,b)].">
      <j1 rule="resolve" parents="20698 54"/>
    </justification>
  </clause>

  <clause id="20706">
    <literal><![CDATA[
      -(x == k)
    ]]></literal>
    <literal><![CDATA[
      x == b
    ]]></literal>
    <justification jstring="[resolve(20698,a,16,b)].">
      <j1 rule="resolve" parents="20698 16"/>
    </justification>
  </clause>

  <clause id="20708">
    <literal><![CDATA[
      -(m == k)
    ]]></literal>
    <justification jstring="[ur(16,b,20698,a,c,21,a)].">
      <j1 rule="ur" parents="16 20698 21"/>
    </justification>
  </clause>

  <clause id="20711">
    <literal><![CDATA[
      -(k == x)
    ]]></literal>
    <literal><![CDATA[
      p(m,x)
    ]]></literal>
    <justification jstring="[back_unit_del(48),unit_del(a,20708)].">
      <j1 rule="back_unit_del" parents="48"/>
      <j2 rule="unit_del" parents="20708"/>
    </justification>
  </clause>

  <clause id="20737">
    <literal><![CDATA[
      -(f(k) == x)
    ]]></literal>
    <literal><![CDATA[
      f(b) == x
    ]]></literal>
    <justification jstring="[resolve(20695,a,16,a)].">
      <j1 rule="resolve" parents="20695 16"/>
    </justification>
  </clause>

  <clause id="20767">
    <literal><![CDATA[
      k == j
    ]]></literal>
    <literal><![CDATA[
      -(j == x)
    ]]></literal>
    <literal><![CDATA[
      p(b,x)
    ]]></literal>
    <justification jstring="[resolve(20702,b,18,b)].">
      <j1 rule="resolve" parents="20702 18"/>
    </justification>
  </clause>

  <clause id="20902">
    <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(20691,d,3,d),merge(f)].">
      <j1 rule="resolve" parents="20691 3"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="25502">
    <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(20902,a,9,c),merge(e)].">
      <j1 rule="resolve" parents="20902 9"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="25506">
    <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(25502,e,18,b)].">
      <j1 rule="resolve" parents="25502 18"/>
    </justification>
  </clause>

  <clause id="31005">
    <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(25506,e,20688,a)].">
      <j1 rule="resolve" parents="25506 20688"/>
    </justification>
  </clause>

  <clause id="31017">
    <literal><![CDATA[
      g(j) == k
    ]]></literal>
    <literal><![CDATA[
      j == b
    ]]></literal>
    <literal><![CDATA[
      j == k
    ]]></literal>
    <literal><![CDATA[
      j == m
    ]]></literal>
    <justification jstring="[resolve(31005,e,3,d),merge(e),merge(f),merge(g)].">
      <j1 rule="resolve" parents="31005 3"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="31019">
    <literal><![CDATA[
      j == b
    ]]></literal>
    <literal><![CDATA[
      j == k
    ]]></literal>
    <literal><![CDATA[
      j == m
    ]]></literal>
    <literal><![CDATA[
      g(j) == b
    ]]></literal>
    <justification jstring="[resolve(31017,a,20706,a)].">
      <j1 rule="resolve" parents="31017 20706"/>
    </justification>
  </clause>

  <clause id="31398">
    <literal><![CDATA[
      j == b
    ]]></literal>
    <literal><![CDATA[
      j == k
    ]]></literal>
    <literal><![CDATA[
      j == m
    ]]></literal>
    <literal><![CDATA[
      p(j,b)
    ]]></literal>
    <justification jstring="[resolve(31019,d,40,a),merge(e),merge(f)].">
      <j1 rule="resolve" parents="31019 40"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="31406">
    <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(31398,d,18,b)].">
      <j1 rule="resolve" parents="31398 18"/>
    </justification>
  </clause>

  <clause id="33423">
    <literal><![CDATA[
      j == b
    ]]></literal>
    <literal><![CDATA[
      j == k
    ]]></literal>
    <literal><![CDATA[
      j == m
    ]]></literal>
    <literal><![CDATA[
      p(j,k)
    ]]></literal>
    <justification jstring="[resolve(31406,d,20688,a)].">
      <j1 rule="resolve" parents="31406 20688"/>
    </justification>
  </clause>

  <clause id="33429">
    <literal><![CDATA[
      j == b
    ]]></literal>
    <literal><![CDATA[
      j == k
    ]]></literal>
    <literal><![CDATA[
      j == m
    ]]></literal>
    <justification jstring="[resolve(33423,d,3,d),merge(d),merge(e),merge(f)].">
      <j1 rule="resolve" parents="33423 3"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="33439">
    <literal><![CDATA[
      j == b
    ]]></literal>
    <literal><![CDATA[
      j == m
    ]]></literal>
    <justification jstring="[resolve(33429,b,20706,a),merge(c)].">
      <j1 rule="resolve" parents="33429 20706"/>
      <j2 rule="merge"/>
    </justification>
  </clause>

  <clause id="33443">
    <literal><![CDATA[
      j == b
    ]]></literal>
    <literal><![CDATA[
      k == j
    ]]></literal>
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <justification jstring="[resolve(33439,b,20767,b)].">
      <j1 rule="resolve" parents="33439 20767"/>
    </justification>
  </clause>

  <clause id="33445">
    <literal><![CDATA[
      j == b
    ]]></literal>
    <literal><![CDATA[
      k == j
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <justification jstring="[resolve(33439,b,53,b)].">
      <j1 rule="resolve" parents="33439 53"/>
    </justification>
  </clause>

  <clause id="33452">
    <literal><![CDATA[
      j == b
    ]]></literal>
    <literal><![CDATA[
      m == j
    ]]></literal>
    <justification jstring="[resolve(33439,b,15,a)].">
      <j1 rule="resolve" parents="33439 15"/>
    </justification>
  </clause>

  <clause id="33459">
    <literal><![CDATA[
      m == j
    ]]></literal>
    <literal><![CDATA[
      j == k
    ]]></literal>
    <justification jstring="[resolve(33452,a,20696,a)].">
      <j1 rule="resolve" parents="33452 20696"/>
    </justification>
  </clause>

  <clause id="33477">
    <literal><![CDATA[
      m == j
    ]]></literal>
    <literal><![CDATA[
      k == j
    ]]></literal>
    <justification jstring="[resolve(33459,b,15,a)].">
      <j1 rule="resolve" parents="33459 15"/>
    </justification>
  </clause>

  <clause id="33496">
    <literal><![CDATA[
      m == j
    ]]></literal>
    <literal><![CDATA[
      p(m,j)
    ]]></literal>
    <justification jstring="[resolve(33477,b,20711,a)].">
      <j1 rule="resolve" parents="33477 20711"/>
    </justification>
  </clause>

  <clause id="33516">
    <literal><![CDATA[
      m == j
    ]]></literal>
    <justification jstring="[resolve(33496,b,22,b),merge(b),unit_del(b,20708)].">
      <j1 rule="resolve" parents="33496 22"/>
      <j2 rule="merge"/>
      <j2 rule="unit_del" parents="20708"/>
    </justification>
  </clause>

  <clause id="33531">
    <literal><![CDATA[
      -(j == k)
    ]]></literal>
    <justification jstring="[ur(16,a,33516,a,c,20708,a)].">
      <j1 rule="ur" parents="16 33516 20708"/>
    </justification>
  </clause>

  <clause id="33532">
    <literal><![CDATA[
      -(j == b)
    ]]></literal>
    <justification jstring="[ur(16,a,33516,a,c,21,a)].">
      <j1 rule="ur" parents="16 33516 21"/>
    </justification>
  </clause>

  <clause id="33540">
    <literal><![CDATA[
      k == j
    ]]></literal>
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <justification jstring="[back_unit_del(33445),unit_del(a,33532)].">
      <j1 rule="back_unit_del" parents="33445"/>
      <j2 rule="unit_del" parents="33532"/>
    </justification>
  </clause>

  <clause id="33541">
    <literal><![CDATA[
      k == j
    ]]></literal>
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <justification jstring="[back_unit_del(33443),unit_del(a,33532)].">
      <j1 rule="back_unit_del" parents="33443"/>
      <j2 rule="unit_del" parents="33532"/>
    </justification>
  </clause>

  <clause id="33759">
    <literal><![CDATA[
      -(k == j)
    ]]></literal>
    <justification jstring="[ur(15,b,33531,a)].">
      <j1 rule="ur" parents="15 33531"/>
    </justification>
  </clause>

  <clause id="33787">
    <literal><![CDATA[
      p(b,m)
    ]]></literal>
    <justification jstring="[back_unit_del(33541),unit_del(a,33759)].">
      <j1 rule="back_unit_del" parents="33541"/>
      <j2 rule="unit_del" parents="33759"/>
    </justification>
  </clause>

  <clause id="33788">
    <literal><![CDATA[
      p(k,m)
    ]]></literal>
    <justification jstring="[back_unit_del(33540),unit_del(a,33759)].">
      <j1 rule="back_unit_del" parents="33540"/>
      <j2 rule="unit_del" parents="33759"/>
    </justification>
  </clause>

  <clause id="33854">
    <literal><![CDATA[
      -(f(b) == b)
    ]]></literal>
    <justification jstring="[resolve(33787,a,5,b),unit_del(a,41)].">
      <j1 rule="resolve" parents="33787 5"/>
      <j2 rule="unit_del" parents="41"/>
    </justification>
  </clause>

  <clause id="33855">
    <literal><![CDATA[
      -(f(b) == m)
    ]]></literal>
    <justification jstring="[resolve(33787,a,4,b),unit_del(a,41)].">
      <j1 rule="resolve" parents="33787 4"/>
      <j2 rule="unit_del" parents="41"/>
    </justification>
  </clause>

  <clause id="33896">
    <literal><![CDATA[
      -(f(k) == b)
    ]]></literal>
    <justification jstring="[ur(20737,b,33854,a)].">
      <j1 rule="ur" parents="20737 33854"/>
    </justification>
  </clause>

  <clause id="34120">
    <literal><![CDATA[
      -(f(k) == m)
    ]]></literal>
    <justification jstring="[ur(20737,b,33855,a)].">
      <j1 rule="ur" parents="20737 33855"/>
    </justification>
  </clause>

  <clause id="34275">
    <literal><![CDATA[
      p(f(k),k)
    ]]></literal>
    <justification jstring="[resolve(33788,a,7,b),unit_del(a,20699)].">
      <j1 rule="resolve" parents="33788 7"/>
      <j2 rule="unit_del" parents="20699"/>
    </justification>
  </clause>

  <clause id="34277">
    <literal><![CDATA[
      -(f(k) == k)
    ]]></literal>
    <justification jstring="[resolve(33788,a,5,b),unit_del(a,20699)].">
      <j1 rule="resolve" parents="33788 5"/>
      <j2 rule="unit_del" parents="20699"/>
    </justification>
  </clause>

  <clause id="34372">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[resolve(34275,a,3,d),unit_del(a,34277),unit_del(b,34120),unit_del(c,33896)].">
      <j1 rule="resolve" parents="34275 3"/>
      <j2 rule="unit_del" parents="34277"/>
      <j2 rule="unit_del" parents="34120"/>
      <j2 rule="unit_del" parents="33896"/>
    </justification>
  </clause>

</proof>

</proofs>
