<?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>HWV006-1.out</source>

<heading><![CDATA[
Prover9 (32) version 2009-02A, February 2009.
Process 11198 was started by mccune on cleo,
Wed Feb 25 09:32:26 2009
The command was "/home/mccune/bin/prover9 -f HWV006-1.in".
]]></heading>

<proof number="1" length="125" max_count="21">

<comments><![CDATA[
% Proof 1 at 0.04 (+ 0.00) seconds.
% Length of proof is 125.
% Level of proof is 20.
% Maximum clause weight is 21.
% Given clauses 157.

]]></comments>

  <clause id="1" type="assumption">
    <literal><![CDATA[
      -p1(A,B)
    ]]></literal>
    <literal><![CDATA[
      p2(B,C)
    ]]></literal>
    <literal><![CDATA[
      -p2(A,C)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="2" type="assumption">
    <literal><![CDATA[
      -p9(A,c16)
    ]]></literal>
    <literal><![CDATA[
      p1(f12(c5,f19(A)),f11(c13,f17(A)))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="3" type="assumption">
    <literal><![CDATA[
      p1(f12(c22,A),f12(c5,f18(A)))
    ]]></literal>
    <literal><![CDATA[
      -p9(A,c16)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="4" type="assumption">
    <literal><![CDATA[
      -p9(A,c16)
    ]]></literal>
    <literal><![CDATA[
      p1(f12(c5,f18(A)),f11(c5,f19(A)))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="5" type="assumption">
    <literal><![CDATA[
      p1(f12(c21,A),f12(c5,f17(A)))
    ]]></literal>
    <literal><![CDATA[
      -p9(A,c16)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="6" type="assumption">
    <literal><![CDATA[
      -p9(A,c23)
    ]]></literal>
    <literal><![CDATA[
      p1(f11(c5,A),f11(c5,f25(A)))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="7" type="assumption">
    <literal><![CDATA[
      p1(f12(c21,A),f12(c21,f25(A)))
    ]]></literal>
    <literal><![CDATA[
      -p9(A,c23)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="8" type="assumption">
    <literal><![CDATA[
      p2(A,B)
    ]]></literal>
    <literal><![CDATA[
      -p1(A,C)
    ]]></literal>
    <literal><![CDATA[
      -p2(C,B)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="10" type="assumption">
    <literal><![CDATA[
      -p9(A,c16)
    ]]></literal>
    <literal><![CDATA[
      p1(f12(c5,f20(A)),f11(c5,f17(A)))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="11" type="assumption">
    <literal><![CDATA[
      p1(f12(c21,f24(A)),f11(c13,f25(A)))
    ]]></literal>
    <literal><![CDATA[
      -p9(A,c23)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="12" type="assumption">
    <literal><![CDATA[
      p1(f11(c13,A),f11(c5,f24(A)))
    ]]></literal>
    <literal><![CDATA[
      -p9(A,c23)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="14" type="assumption">
    <literal><![CDATA[
      p1(f12(c22,A),f12(c5,f20(A)))
    ]]></literal>
    <literal><![CDATA[
      -p9(A,c23)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="15" type="assumption">
    <literal><![CDATA[
      -p9(A,c16)
    ]]></literal>
    <literal><![CDATA[
      p1(f11(c13,A),f11(c13,f20(A)))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="16" type="assumption">
    <literal><![CDATA[
      p1(f11(c5,A),f11(c5,f18(A)))
    ]]></literal>
    <literal><![CDATA[
      -p9(A,c16)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="17" type="assumption">
    <literal><![CDATA[
      p1(f11(c22,A),f11(c13,f24(A)))
    ]]></literal>
    <literal><![CDATA[
      -p9(A,c23)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="18" type="assumption">
    <literal><![CDATA[
      -p9(A,c16)
    ]]></literal>
    <literal><![CDATA[
      p1(f11(c13,A),f11(c13,f18(A)))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="19" type="assumption">
    <literal><![CDATA[
      -p9(A,c23)
    ]]></literal>
    <literal><![CDATA[
      p1(f12(c22,f25(A)),f11(c5,f20(A)))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="20" type="assumption">
    <literal><![CDATA[
      p3(A,B)
    ]]></literal>
    <literal><![CDATA[
      -p2(C,B)
    ]]></literal>
    <literal><![CDATA[
      -p2(C,A)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="21" type="assumption">
    <literal><![CDATA[
      -p3(c4,c5)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="23" type="assumption">
    <literal><![CDATA[
      -p2(f12(c5,A),c4)
    ]]></literal>
    <literal><![CDATA[
      -p9(A,c15)
    ]]></literal>
    <literal><![CDATA[
      p2(f11(c5,A),c5)
    ]]></literal>
    <literal><![CDATA[
      -p6(A,c7)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="24" type="assumption">
    <literal><![CDATA[
      p9(f25(A),c16)
    ]]></literal>
    <literal><![CDATA[
      -p9(A,c23)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="26" type="assumption">
    <literal><![CDATA[
      -p2(f12(c5,A),c4)
    ]]></literal>
    <literal><![CDATA[
      -p9(A,c14)
    ]]></literal>
    <literal><![CDATA[
      p2(f11(c5,A),c4)
    ]]></literal>
    <literal><![CDATA[
      -p6(A,c7)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="27" type="assumption">
    <literal><![CDATA[
      p2(f11(c13,A),c4)
    ]]></literal>
    <literal><![CDATA[
      -p2(f12(c5,A),c4)
    ]]></literal>
    <literal><![CDATA[
      p2(f11(c5,A),c4)
    ]]></literal>
    <literal><![CDATA[
      -p6(A,c7)
    ]]></literal>
    <literal><![CDATA[
      -p9(A,c10)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="28" type="assumption">
    <literal><![CDATA[
      p6(A,c7)
    ]]></literal>
    <literal><![CDATA[
      -p9(A,B)
    ]]></literal>
    <literal><![CDATA[
      p6(A,c8)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="30" type="assumption">
    <literal><![CDATA[
      -p9(A,c16)
    ]]></literal>
    <literal><![CDATA[
      p9(f19(A),c15)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="33" type="assumption">
    <literal><![CDATA[
      p9(f24(A),c16)
    ]]></literal>
    <literal><![CDATA[
      -p9(A,c23)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="34" type="assumption">
    <literal><![CDATA[
      -p9(A,c10)
    ]]></literal>
    <literal><![CDATA[
      -p2(f12(c5,A),c5)
    ]]></literal>
    <literal><![CDATA[
      -p6(A,c7)
    ]]></literal>
    <literal><![CDATA[
      p2(f11(c5,A),c5)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="35" type="assumption">
    <literal><![CDATA[
      -p6(A,c7)
    ]]></literal>
    <literal><![CDATA[
      -p9(A,c10)
    ]]></literal>
    <literal><![CDATA[
      -p2(f12(c5,A),c5)
    ]]></literal>
    <literal><![CDATA[
      p2(f11(c13,A),c5)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      -p2(f12(c5,A),c4)
    ]]></literal>
    <literal><![CDATA[
      p2(f11(c13,A),c4)
    ]]></literal>
    <literal><![CDATA[
      -p6(A,c7)
    ]]></literal>
    <literal><![CDATA[
      -p9(A,c14)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37" type="assumption">
    <literal><![CDATA[
      p2(f11(c5,A),c4)
    ]]></literal>
    <literal><![CDATA[
      -p2(f12(c5,A),c5)
    ]]></literal>
    <literal><![CDATA[
      -p6(A,c7)
    ]]></literal>
    <literal><![CDATA[
      -p9(A,c15)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="39" type="assumption">
    <literal><![CDATA[
      p9(f17(A),c10)
    ]]></literal>
    <literal><![CDATA[
      -p9(A,c16)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="40" type="assumption">
    <literal><![CDATA[
      -p9(A,c23)
    ]]></literal>
    <literal><![CDATA[
      p9(f20(A),c14)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="43" type="assumption">
    <literal><![CDATA[
      p9(f20(A),c14)
    ]]></literal>
    <literal><![CDATA[
      -p9(A,c16)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="45" type="assumption">
    <literal><![CDATA[
      p9(f18(A),c10)
    ]]></literal>
    <literal><![CDATA[
      -p9(A,c16)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="46" type="assumption">
    <literal><![CDATA[
      -p6(f19(f24(c26)),c8)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="47" type="assumption">
    <literal><![CDATA[
      -p6(f17(f24(c26)),c8)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="48" type="assumption">
    <literal><![CDATA[
      -p6(f18(f25(c26)),c8)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="49" type="assumption">
    <literal><![CDATA[
      -p6(f18(f24(c26)),c8)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="50" type="assumption">
    <literal><![CDATA[
      -p6(f17(f25(c26)),c8)
    ]]></literal>
    <literal><![CDATA[
      -p6(f20(c26),c8)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="51" type="assumption">
    <literal><![CDATA[
      p2(f12(c21,c26),c5)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="52" type="assumption">
    <literal><![CDATA[
      p2(f11(c13,c26),c4)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="53" type="assumption">
    <literal><![CDATA[
      p2(f11(c22,c26),c5)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="54" type="assumption">
    <literal><![CDATA[
      p2(f11(c5,c26),c5)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="55" type="assumption">
    <literal><![CDATA[
      -p6(f20(f24(c26)),c8)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="56" type="assumption">
    <literal><![CDATA[
      p9(c26,c23)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="57" type="assumption">
    <literal><![CDATA[
      -p6(f19(f25(c26)),c8)
    ]]></literal>
    <literal><![CDATA[
      -p6(f20(c26),c8)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="58" type="assumption">
    <literal><![CDATA[
      p2(f12(c22,c26),c4)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="60">
    <literal><![CDATA[
      p2(f12(c5,f18(A)),B)
    ]]></literal>
    <literal><![CDATA[
      -p2(f12(c22,A),B)
    ]]></literal>
    <literal><![CDATA[
      -p9(A,c16)
    ]]></literal>
    <justification jstring="[resolve(1,a,3,a)].">
      <j1 rule="resolve" parents="1 3"/>
    </justification>
  </clause>

  <clause id="62">
    <literal><![CDATA[
      p2(f12(c5,f17(A)),B)
    ]]></literal>
    <literal><![CDATA[
      -p2(f12(c21,A),B)
    ]]></literal>
    <literal><![CDATA[
      -p9(A,c16)
    ]]></literal>
    <justification jstring="[resolve(1,a,5,a)].">
      <j1 rule="resolve" parents="1 5"/>
    </justification>
  </clause>

  <clause id="64">
    <literal><![CDATA[
      p2(f12(c21,f25(A)),B)
    ]]></literal>
    <literal><![CDATA[
      -p2(f12(c21,A),B)
    ]]></literal>
    <literal><![CDATA[
      -p9(A,c23)
    ]]></literal>
    <justification jstring="[resolve(1,a,7,a)].">
      <j1 rule="resolve" parents="1 7"/>
    </justification>
  </clause>

  <clause id="65">
    <literal><![CDATA[
      p2(f12(c5,f19(A)),B)
    ]]></literal>
    <literal><![CDATA[
      -p2(f11(c13,f17(A)),B)
    ]]></literal>
    <literal><![CDATA[
      -p9(A,c16)
    ]]></literal>
    <justification jstring="[resolve(8,b,2,b)].">
      <j1 rule="resolve" parents="8 2"/>
    </justification>
  </clause>

  <clause id="67">
    <literal><![CDATA[
      p2(f12(c5,f18(A)),B)
    ]]></literal>
    <literal><![CDATA[
      -p2(f11(c5,f19(A)),B)
    ]]></literal>
    <literal><![CDATA[
      -p9(A,c16)
    ]]></literal>
    <justification jstring="[resolve(8,b,4,b)].">
      <j1 rule="resolve" parents="8 4"/>
    </justification>
  </clause>

  <clause id="69">
    <literal><![CDATA[
      p2(f11(c5,A),B)
    ]]></literal>
    <literal><![CDATA[
      -p2(f11(c5,f25(A)),B)
    ]]></literal>
    <literal><![CDATA[
      -p9(A,c23)
    ]]></literal>
    <justification jstring="[resolve(8,b,6,b)].">
      <j1 rule="resolve" parents="8 6"/>
    </justification>
  </clause>

  <clause id="74">
    <literal><![CDATA[
      -p9(A,c16)
    ]]></literal>
    <literal><![CDATA[
      p2(f12(c5,f20(A)),B)
    ]]></literal>
    <literal><![CDATA[
      -p2(f11(c5,f17(A)),B)
    ]]></literal>
    <justification jstring="[resolve(10,b,8,b)].">
      <j1 rule="resolve" parents="10 8"/>
    </justification>
  </clause>

  <clause id="76">
    <literal><![CDATA[
      -p9(A,c23)
    ]]></literal>
    <literal><![CDATA[
      p2(f12(c21,f24(A)),B)
    ]]></literal>
    <literal><![CDATA[
      -p2(f11(c13,f25(A)),B)
    ]]></literal>
    <justification jstring="[resolve(11,a,8,b)].">
      <j1 rule="resolve" parents="11 8"/>
    </justification>
  </clause>

  <clause id="78">
    <literal><![CDATA[
      -p9(A,c23)
    ]]></literal>
    <literal><![CDATA[
      p2(f11(c13,A),B)
    ]]></literal>
    <literal><![CDATA[
      -p2(f11(c5,f24(A)),B)
    ]]></literal>
    <justification jstring="[resolve(12,a,8,b)].">
      <j1 rule="resolve" parents="12 8"/>
    </justification>
  </clause>

  <clause id="81">
    <literal><![CDATA[
      -p9(A,c23)
    ]]></literal>
    <literal><![CDATA[
      p2(f12(c5,f20(A)),B)
    ]]></literal>
    <literal><![CDATA[
      -p2(f12(c22,A),B)
    ]]></literal>
    <justification jstring="[resolve(14,a,1,a)].">
      <j1 rule="resolve" parents="14 1"/>
    </justification>
  </clause>

  <clause id="84">
    <literal><![CDATA[
      -p9(A,c16)
    ]]></literal>
    <literal><![CDATA[
      p2(f11(c13,A),B)
    ]]></literal>
    <literal><![CDATA[
      -p2(f11(c13,f20(A)),B)
    ]]></literal>
    <justification jstring="[resolve(15,b,8,b)].">
      <j1 rule="resolve" parents="15 8"/>
    </justification>
  </clause>

  <clause id="86">
    <literal><![CDATA[
      -p9(A,c16)
    ]]></literal>
    <literal><![CDATA[
      p2(f11(c5,A),B)
    ]]></literal>
    <literal><![CDATA[
      -p2(f11(c5,f18(A)),B)
    ]]></literal>
    <justification jstring="[resolve(16,a,8,b)].">
      <j1 rule="resolve" parents="16 8"/>
    </justification>
  </clause>

  <clause id="88">
    <literal><![CDATA[
      -p9(A,c23)
    ]]></literal>
    <literal><![CDATA[
      p2(f11(c22,A),B)
    ]]></literal>
    <literal><![CDATA[
      -p2(f11(c13,f24(A)),B)
    ]]></literal>
    <justification jstring="[resolve(17,a,8,b)].">
      <j1 rule="resolve" parents="17 8"/>
    </justification>
  </clause>

  <clause id="90">
    <literal><![CDATA[
      -p9(A,c16)
    ]]></literal>
    <literal><![CDATA[
      p2(f11(c13,A),B)
    ]]></literal>
    <literal><![CDATA[
      -p2(f11(c13,f18(A)),B)
    ]]></literal>
    <justification jstring="[resolve(18,b,8,b)].">
      <j1 rule="resolve" parents="18 8"/>
    </justification>
  </clause>

  <clause id="92">
    <literal><![CDATA[
      -p9(A,c23)
    ]]></literal>
    <literal><![CDATA[
      p2(f12(c22,f25(A)),B)
    ]]></literal>
    <literal><![CDATA[
      -p2(f11(c5,f20(A)),B)
    ]]></literal>
    <justification jstring="[resolve(19,b,8,b)].">
      <j1 rule="resolve" parents="19 8"/>
    </justification>
  </clause>

  <clause id="93">
    <literal><![CDATA[
      -p2(A,c5)
    ]]></literal>
    <literal><![CDATA[
      -p2(A,c4)
    ]]></literal>
    <justification jstring="[resolve(20,a,21,a)].">
      <j1 rule="resolve" parents="20 21"/>
    </justification>
  </clause>

  <clause id="94">
    <literal><![CDATA[
      p9(f20(c26),c14)
    ]]></literal>
    <justification jstring="[resolve(56,a,40,a)].">
      <j1 rule="resolve" parents="56 40"/>
    </justification>
  </clause>

  <clause id="95">
    <literal><![CDATA[
      p9(f24(c26),c16)
    ]]></literal>
    <justification jstring="[resolve(56,a,33,b)].">
      <j1 rule="resolve" parents="56 33"/>
    </justification>
  </clause>

  <clause id="97">
    <literal><![CDATA[
      p9(f25(c26),c16)
    ]]></literal>
    <justification jstring="[resolve(56,a,24,b)].">
      <j1 rule="resolve" parents="56 24"/>
    </justification>
  </clause>

  <clause id="99">
    <literal><![CDATA[
      p2(f12(c21,f25(c26)),A)
    ]]></literal>
    <literal><![CDATA[
      -p2(f12(c21,c26),A)
    ]]></literal>
    <justification jstring="[resolve(64,c,56,a)].">
      <j1 rule="resolve" parents="64 56"/>
    </justification>
  </clause>

  <clause id="108">
    <literal><![CDATA[
      p2(f12(c5,f20(c26)),A)
    ]]></literal>
    <literal><![CDATA[
      -p2(f12(c22,c26),A)
    ]]></literal>
    <justification jstring="[resolve(81,a,56,a)].">
      <j1 rule="resolve" parents="81 56"/>
    </justification>
  </clause>

  <clause id="115">
    <literal><![CDATA[
      -p2(f11(c13,c26),c5)
    ]]></literal>
    <justification jstring="[resolve(93,b,52,a)].">
      <j1 rule="resolve" parents="93 52"/>
    </justification>
  </clause>

  <clause id="116">
    <literal><![CDATA[
      -p2(f11(c5,c26),c4)
    ]]></literal>
    <justification jstring="[ur(93,a,54,a)].">
      <j1 rule="ur" parents="93 54"/>
    </justification>
  </clause>

  <clause id="117">
    <literal><![CDATA[
      -p2(f11(c22,c26),c4)
    ]]></literal>
    <justification jstring="[ur(93,a,53,a)].">
      <j1 rule="ur" parents="93 53"/>
    </justification>
  </clause>

  <clause id="119">
    <literal><![CDATA[
      p6(f20(c26),c7)
    ]]></literal>
    <literal><![CDATA[
      p6(f20(c26),c8)
    ]]></literal>
    <justification jstring="[resolve(94,a,28,b)].">
      <j1 rule="resolve" parents="94 28"/>
    </justification>
  </clause>

  <clause id="121">
    <literal><![CDATA[
      -p2(f11(c5,f24(c26)),c5)
    ]]></literal>
    <justification jstring="[ur(78,a,56,a,b,115,a)].">
      <j1 rule="ur" parents="78 56 115"/>
    </justification>
  </clause>

  <clause id="122">
    <literal><![CDATA[
      -p2(f11(c5,f25(c26)),c4)
    ]]></literal>
    <justification jstring="[ur(69,a,116,a,c,56,a)].">
      <j1 rule="ur" parents="69 116 56"/>
    </justification>
  </clause>

  <clause id="123">
    <literal><![CDATA[
      -p2(f11(c13,f24(c26)),c4)
    ]]></literal>
    <justification jstring="[ur(88,a,56,a,b,117,a)].">
      <j1 rule="ur" parents="88 56 117"/>
    </justification>
  </clause>

  <clause id="142">
    <literal><![CDATA[
      p9(f18(f24(c26)),c10)
    ]]></literal>
    <justification jstring="[resolve(95,a,45,b)].">
      <j1 rule="resolve" parents="95 45"/>
    </justification>
  </clause>

  <clause id="143">
    <literal><![CDATA[
      p9(f20(f24(c26)),c14)
    ]]></literal>
    <justification jstring="[resolve(95,a,43,b)].">
      <j1 rule="resolve" parents="95 43"/>
    </justification>
  </clause>

  <clause id="144">
    <literal><![CDATA[
      p9(f17(f24(c26)),c10)
    ]]></literal>
    <justification jstring="[resolve(95,a,39,b)].">
      <j1 rule="resolve" parents="95 39"/>
    </justification>
  </clause>

  <clause id="145">
    <literal><![CDATA[
      p9(f19(f24(c26)),c15)
    ]]></literal>
    <justification jstring="[resolve(95,a,30,a)].">
      <j1 rule="resolve" parents="95 30"/>
    </justification>
  </clause>

  <clause id="165">
    <literal><![CDATA[
      p9(f18(f25(c26)),c10)
    ]]></literal>
    <justification jstring="[resolve(97,a,45,b)].">
      <j1 rule="resolve" parents="97 45"/>
    </justification>
  </clause>

  <clause id="167">
    <literal><![CDATA[
      p9(f17(f25(c26)),c10)
    ]]></literal>
    <justification jstring="[resolve(97,a,39,b)].">
      <j1 rule="resolve" parents="97 39"/>
    </justification>
  </clause>

  <clause id="168">
    <literal><![CDATA[
      p9(f19(f25(c26)),c15)
    ]]></literal>
    <justification jstring="[resolve(97,a,30,a)].">
      <j1 rule="resolve" parents="97 30"/>
    </justification>
  </clause>

  <clause id="170">
    <literal><![CDATA[
      p6(f18(f24(c26)),c7)
    ]]></literal>
    <justification jstring="[resolve(142,a,28,b),unit_del(b,49)].">
      <j1 rule="resolve" parents="142 28"/>
      <j2 rule="unit_del" parents="49"/>
    </justification>
  </clause>

  <clause id="171">
    <literal><![CDATA[
      p6(f20(f24(c26)),c7)
    ]]></literal>
    <justification jstring="[resolve(143,a,28,b),unit_del(b,55)].">
      <j1 rule="resolve" parents="143 28"/>
      <j2 rule="unit_del" parents="55"/>
    </justification>
  </clause>

  <clause id="173">
    <literal><![CDATA[
      -p2(f11(c5,f18(f24(c26))),c5)
    ]]></literal>
    <justification jstring="[ur(86,a,95,a,b,121,a)].">
      <j1 rule="ur" parents="86 95 121"/>
    </justification>
  </clause>

  <clause id="175">
    <literal><![CDATA[
      -p2(f11(c5,f18(f25(c26))),c4)
    ]]></literal>
    <justification jstring="[ur(86,a,97,a,b,122,a)].">
      <j1 rule="ur" parents="86 97 122"/>
    </justification>
  </clause>

  <clause id="177">
    <literal><![CDATA[
      p6(f17(f24(c26)),c7)
    ]]></literal>
    <justification jstring="[resolve(144,a,28,b),unit_del(b,47)].">
      <j1 rule="resolve" parents="144 28"/>
      <j2 rule="unit_del" parents="47"/>
    </justification>
  </clause>

  <clause id="178">
    <literal><![CDATA[
      p6(f19(f24(c26)),c7)
    ]]></literal>
    <justification jstring="[resolve(145,a,28,b),unit_del(b,46)].">
      <j1 rule="resolve" parents="145 28"/>
      <j2 rule="unit_del" parents="46"/>
    </justification>
  </clause>

  <clause id="179">
    <literal><![CDATA[
      p6(f18(f25(c26)),c7)
    ]]></literal>
    <justification jstring="[resolve(165,a,28,b),unit_del(b,48)].">
      <j1 rule="resolve" parents="165 28"/>
      <j2 rule="unit_del" parents="48"/>
    </justification>
  </clause>

  <clause id="183">
    <literal><![CDATA[
      -p2(f11(c13,f20(f24(c26))),c4)
    ]]></literal>
    <justification jstring="[ur(84,a,95,a,b,123,a)].">
      <j1 rule="ur" parents="84 95 123"/>
    </justification>
  </clause>

  <clause id="185">
    <literal><![CDATA[
      p6(f17(f25(c26)),c7)
    ]]></literal>
    <literal><![CDATA[
      p6(f17(f25(c26)),c8)
    ]]></literal>
    <justification jstring="[resolve(167,a,28,b)].">
      <j1 rule="resolve" parents="167 28"/>
    </justification>
  </clause>

  <clause id="186">
    <literal><![CDATA[
      p6(f19(f25(c26)),c7)
    ]]></literal>
    <literal><![CDATA[
      p6(f19(f25(c26)),c8)
    ]]></literal>
    <justification jstring="[resolve(168,a,28,b)].">
      <j1 rule="resolve" parents="168 28"/>
    </justification>
  </clause>

  <clause id="192">
    <literal><![CDATA[
      -p2(f12(c5,f18(f24(c26))),c5)
    ]]></literal>
    <justification jstring="[resolve(170,a,34,c),unit_del(a,142),unit_del(c,173)].">
      <j1 rule="resolve" parents="170 34"/>
      <j2 rule="unit_del" parents="142"/>
      <j2 rule="unit_del" parents="173"/>
    </justification>
  </clause>

  <clause id="200">
    <literal><![CDATA[
      -p2(f12(c5,f20(f24(c26))),c4)
    ]]></literal>
    <justification jstring="[resolve(171,a,36,c),unit_del(b,183),unit_del(c,143)].">
      <j1 rule="resolve" parents="171 36"/>
      <j2 rule="unit_del" parents="183"/>
      <j2 rule="unit_del" parents="143"/>
    </justification>
  </clause>

  <clause id="206">
    <literal><![CDATA[
      p2(f12(c21,f25(c26)),c5)
    ]]></literal>
    <justification jstring="[resolve(99,b,51,a)].">
      <j1 rule="resolve" parents="99 51"/>
    </justification>
  </clause>

  <clause id="215">
    <literal><![CDATA[
      p2(f11(c13,f17(f24(c26))),c4)
    ]]></literal>
    <literal><![CDATA[
      -p2(f12(c5,f17(f24(c26))),c4)
    ]]></literal>
    <literal><![CDATA[
      p2(f11(c5,f17(f24(c26))),c4)
    ]]></literal>
    <justification jstring="[resolve(177,a,27,d),unit_del(d,144)].">
      <j1 rule="resolve" parents="177 27"/>
      <j2 rule="unit_del" parents="144"/>
    </justification>
  </clause>

  <clause id="232">
    <literal><![CDATA[
      -p2(f12(c5,f19(f24(c26))),c4)
    ]]></literal>
    <literal><![CDATA[
      p2(f11(c5,f19(f24(c26))),c5)
    ]]></literal>
    <justification jstring="[resolve(178,a,23,d),unit_del(b,145)].">
      <j1 rule="resolve" parents="178 23"/>
      <j2 rule="unit_del" parents="145"/>
    </justification>
  </clause>

  <clause id="240">
    <literal><![CDATA[
      p2(f11(c13,f18(f25(c26))),c4)
    ]]></literal>
    <literal><![CDATA[
      -p2(f12(c5,f18(f25(c26))),c4)
    ]]></literal>
    <justification jstring="[resolve(179,a,27,d),unit_del(c,175),unit_del(d,165)].">
      <j1 rule="resolve" parents="179 27"/>
      <j2 rule="unit_del" parents="175"/>
      <j2 rule="unit_del" parents="165"/>
    </justification>
  </clause>

  <clause id="244">
    <literal><![CDATA[
      -p2(f11(c5,f19(f24(c26))),c5)
    ]]></literal>
    <justification jstring="[ur(67,a,192,a,c,95,a)].">
      <j1 rule="ur" parents="67 192 95"/>
    </justification>
  </clause>

  <clause id="246">
    <literal><![CDATA[
      -p2(f12(c5,f19(f24(c26))),c4)
    ]]></literal>
    <justification jstring="[back_unit_del(232),unit_del(b,244)].">
      <j1 rule="back_unit_del" parents="232"/>
      <j2 rule="unit_del" parents="244"/>
    </justification>
  </clause>

  <clause id="252">
    <literal><![CDATA[
      -p2(f11(c5,f17(f24(c26))),c4)
    ]]></literal>
    <justification jstring="[ur(74,a,95,a,b,200,a)].">
      <j1 rule="ur" parents="74 95 200"/>
    </justification>
  </clause>

  <clause id="254">
    <literal><![CDATA[
      p2(f11(c13,f17(f24(c26))),c4)
    ]]></literal>
    <literal><![CDATA[
      -p2(f12(c5,f17(f24(c26))),c4)
    ]]></literal>
    <justification jstring="[back_unit_del(215),unit_del(c,252)].">
      <j1 rule="back_unit_del" parents="215"/>
      <j2 rule="unit_del" parents="252"/>
    </justification>
  </clause>

  <clause id="256">
    <literal><![CDATA[
      -p2(f11(c13,f17(f24(c26))),c4)
    ]]></literal>
    <justification jstring="[ur(65,a,246,a,c,95,a)].">
      <j1 rule="ur" parents="65 246 95"/>
    </justification>
  </clause>

  <clause id="257">
    <literal><![CDATA[
      -p2(f12(c5,f17(f24(c26))),c4)
    ]]></literal>
    <justification jstring="[back_unit_del(254),unit_del(a,256)].">
      <j1 rule="back_unit_del" parents="254"/>
      <j2 rule="unit_del" parents="256"/>
    </justification>
  </clause>

  <clause id="260">
    <literal><![CDATA[
      -p2(f12(c21,f24(c26)),c4)
    ]]></literal>
    <justification jstring="[ur(62,a,257,a,c,95,a)].">
      <j1 rule="ur" parents="62 257 95"/>
    </justification>
  </clause>

  <clause id="261">
    <literal><![CDATA[
      p6(f17(f25(c26)),c7)
    ]]></literal>
    <literal><![CDATA[
      -p6(f20(c26),c8)
    ]]></literal>
    <justification jstring="[resolve(185,b,50,a)].">
      <j1 rule="resolve" parents="185 50"/>
    </justification>
  </clause>

  <clause id="262">
    <literal><![CDATA[
      p6(f17(f25(c26)),c7)
    ]]></literal>
    <literal><![CDATA[
      p6(f20(c26),c7)
    ]]></literal>
    <justification jstring="[resolve(261,b,119,b)].">
      <j1 rule="resolve" parents="261 119"/>
    </justification>
  </clause>

  <clause id="267">
    <literal><![CDATA[
      p6(f20(c26),c7)
    ]]></literal>
    <literal><![CDATA[
      -p2(f12(c5,f17(f25(c26))),c5)
    ]]></literal>
    <literal><![CDATA[
      p2(f11(c13,f17(f25(c26))),c5)
    ]]></literal>
    <justification jstring="[resolve(262,a,35,a),unit_del(b,167)].">
      <j1 rule="resolve" parents="262 35"/>
      <j2 rule="unit_del" parents="167"/>
    </justification>
  </clause>

  <clause id="271">
    <literal><![CDATA[
      -p2(f11(c13,f25(c26)),c4)
    ]]></literal>
    <justification jstring="[ur(76,a,56,a,b,260,a)].">
      <j1 rule="ur" parents="76 56 260"/>
    </justification>
  </clause>

  <clause id="272">
    <literal><![CDATA[
      -p2(f11(c13,f18(f25(c26))),c4)
    ]]></literal>
    <justification jstring="[ur(90,a,97,a,b,271,a)].">
      <j1 rule="ur" parents="90 97 271"/>
    </justification>
  </clause>

  <clause id="274">
    <literal><![CDATA[
      -p2(f12(c5,f18(f25(c26))),c4)
    ]]></literal>
    <justification jstring="[back_unit_del(240),unit_del(a,272)].">
      <j1 rule="back_unit_del" parents="240"/>
      <j2 rule="unit_del" parents="272"/>
    </justification>
  </clause>

  <clause id="277">
    <literal><![CDATA[
      p6(f19(f25(c26)),c7)
    ]]></literal>
    <literal><![CDATA[
      -p6(f20(c26),c8)
    ]]></literal>
    <justification jstring="[resolve(186,b,57,a)].">
      <j1 rule="resolve" parents="186 57"/>
    </justification>
  </clause>

  <clause id="278">
    <literal><![CDATA[
      p6(f19(f25(c26)),c7)
    ]]></literal>
    <literal><![CDATA[
      p6(f20(c26),c7)
    ]]></literal>
    <justification jstring="[resolve(277,b,119,b)].">
      <j1 rule="resolve" parents="277 119"/>
    </justification>
  </clause>

  <clause id="283">
    <literal><![CDATA[
      p6(f20(c26),c7)
    ]]></literal>
    <literal><![CDATA[
      p2(f11(c5,f19(f25(c26))),c4)
    ]]></literal>
    <literal><![CDATA[
      -p2(f12(c5,f19(f25(c26))),c5)
    ]]></literal>
    <justification jstring="[resolve(278,a,37,c),unit_del(d,168)].">
      <j1 rule="resolve" parents="278 37"/>
      <j2 rule="unit_del" parents="168"/>
    </justification>
  </clause>

  <clause id="294">
    <literal><![CDATA[
      -p2(f11(c5,f19(f25(c26))),c4)
    ]]></literal>
    <justification jstring="[ur(67,a,274,a,c,97,a)].">
      <j1 rule="ur" parents="67 274 97"/>
    </justification>
  </clause>

  <clause id="295">
    <literal><![CDATA[
      -p2(f12(c22,f25(c26)),c4)
    ]]></literal>
    <justification jstring="[ur(60,a,274,a,c,97,a)].">
      <j1 rule="ur" parents="60 274 97"/>
    </justification>
  </clause>

  <clause id="298">
    <literal><![CDATA[
      p6(f20(c26),c7)
    ]]></literal>
    <literal><![CDATA[
      -p2(f12(c5,f19(f25(c26))),c5)
    ]]></literal>
    <justification jstring="[back_unit_del(283),unit_del(b,294)].">
      <j1 rule="back_unit_del" parents="283"/>
      <j2 rule="unit_del" parents="294"/>
    </justification>
  </clause>

  <clause id="299">
    <literal><![CDATA[
      -p2(f11(c5,f20(c26)),c4)
    ]]></literal>
    <justification jstring="[ur(92,a,56,a,b,295,a)].">
      <j1 rule="ur" parents="92 56 295"/>
    </justification>
  </clause>

  <clause id="300">
    <literal><![CDATA[
      p2(f12(c5,f20(c26)),c4)
    ]]></literal>
    <justification jstring="[resolve(108,b,58,a)].">
      <j1 rule="resolve" parents="108 58"/>
    </justification>
  </clause>

  <clause id="301">
    <literal><![CDATA[
      -p6(f20(c26),c7)
    ]]></literal>
    <justification jstring="[ur(26,a,300,a,b,94,a,c,299,a)].">
      <j1 rule="ur" parents="26 300 94 299"/>
    </justification>
  </clause>

  <clause id="302">
    <literal><![CDATA[
      -p2(f12(c5,f19(f25(c26))),c5)
    ]]></literal>
    <justification jstring="[back_unit_del(298),unit_del(a,301)].">
      <j1 rule="back_unit_del" parents="298"/>
      <j2 rule="unit_del" parents="301"/>
    </justification>
  </clause>

  <clause id="314">
    <literal><![CDATA[
      -p2(f12(c5,f17(f25(c26))),c5)
    ]]></literal>
    <literal><![CDATA[
      p2(f11(c13,f17(f25(c26))),c5)
    ]]></literal>
    <justification jstring="[back_unit_del(267),unit_del(a,301)].">
      <j1 rule="back_unit_del" parents="267"/>
      <j2 rule="unit_del" parents="301"/>
    </justification>
  </clause>

  <clause id="323">
    <literal><![CDATA[
      -p2(f11(c13,f17(f25(c26))),c5)
    ]]></literal>
    <justification jstring="[ur(65,a,302,a,c,97,a)].">
      <j1 rule="ur" parents="65 302 97"/>
    </justification>
  </clause>

  <clause id="324">
    <literal><![CDATA[
      -p2(f12(c5,f17(f25(c26))),c5)
    ]]></literal>
    <justification jstring="[back_unit_del(314),unit_del(b,323)].">
      <j1 rule="back_unit_del" parents="314"/>
      <j2 rule="unit_del" parents="323"/>
    </justification>
  </clause>

  <clause id="330">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[ur(62,a,324,a,c,97,a),unit_del(a,206)].">
      <j1 rule="ur" parents="62 324 97"/>
      <j2 rule="unit_del" parents="206"/>
    </justification>
  </clause>

</proof>

</proofs>
