<?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 June-2006C, June 2006.
Process 13075 was started by mccune on cleo.thornwood,
Mon Jun 19 16:41:11 2006
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 0.02 (+ 0.00) seconds.
% Length of proof is 125.
% Level of proof is 21.
% Maximum clause weight is 21.
% Given clauses 183.
]]></comments>

  <clause id="1">
    <literal><![CDATA[
      - p9(A,c16)
    ]]></literal>
    <literal><![CDATA[
      p1(f12(c5,f19(A)),f11(c13,f17(A)))
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

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

  <clause id="5">
    <literal><![CDATA[
      - p3(c4,c5)
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="6">
    <literal><![CDATA[
      - p9(A,c16)
    ]]></literal>
    <literal><![CDATA[
      p1(f12(c5,f18(A)),f11(c5,f19(A)))
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="7">
    <literal><![CDATA[
      p1(f12(c21,A),f12(c5,f17(A)))
    ]]></literal>
    <literal><![CDATA[
      - p9(A,c16)
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="8">
    <literal><![CDATA[
      - p9(A,c23)
    ]]></literal>
    <literal><![CDATA[
      p1(f11(c5,A),f11(c5,f25(A)))
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="12">
    <literal><![CDATA[
      p1(f12(c21,A),f12(c21,f25(A)))
    ]]></literal>
    <literal><![CDATA[
      - p9(A,c23)
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="14">
    <literal><![CDATA[
      - p1(A,B)
    ]]></literal>
    <literal><![CDATA[
      p2(B,C)
    ]]></literal>
    <literal><![CDATA[
      - p2(A,C)
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="16">
    <literal><![CDATA[
      p2(A,B)
    ]]></literal>
    <literal><![CDATA[
      - p1(A,C)
    ]]></literal>
    <literal><![CDATA[
      - p2(C,B)
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="22">
    <literal><![CDATA[
      - p9(A,c16)
    ]]></literal>
    <literal><![CDATA[
      p1(f12(c5,f20(A)),f11(c5,f17(A)))
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="23">
    <literal><![CDATA[
      p1(f12(c21,f24(A)),f11(c13,f25(A)))
    ]]></literal>
    <literal><![CDATA[
      - p9(A,c23)
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="24">
    <literal><![CDATA[
      p1(f11(c13,A),f11(c5,f24(A)))
    ]]></literal>
    <literal><![CDATA[
      - p9(A,c23)
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="27">
    <literal><![CDATA[
      p1(f12(c22,A),f12(c5,f20(A)))
    ]]></literal>
    <literal><![CDATA[
      - p9(A,c23)
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="32">
    <literal><![CDATA[
      - p9(A,c16)
    ]]></literal>
    <literal><![CDATA[
      p1(f11(c13,A),f11(c13,f20(A)))
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="34">
    <literal><![CDATA[
      p1(f11(c5,A),f11(c5,f18(A)))
    ]]></literal>
    <literal><![CDATA[
      - p9(A,c16)
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="36">
    <literal><![CDATA[
      p1(f11(c22,A),f11(c13,f24(A)))
    ]]></literal>
    <literal><![CDATA[
      - p9(A,c23)
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      - p9(A,c16)
    ]]></literal>
    <literal><![CDATA[
      p1(f11(c13,A),f11(c13,f18(A)))
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="38">
    <literal><![CDATA[
      p3(A,B)
    ]]></literal>
    <literal><![CDATA[
      - p2(C,B)
    ]]></literal>
    <literal><![CDATA[
      - p2(C,A)
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="41">
    <literal><![CDATA[
      - p9(A,c23)
    ]]></literal>
    <literal><![CDATA[
      p1(f12(c22,f25(A)),f11(c5,f20(A)))
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="95">
    <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="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="96">
    <literal><![CDATA[
      p9(f25(A),c16)
    ]]></literal>
    <literal><![CDATA[
      - p9(A,c23)
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="98">
    <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="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="99">
    <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="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="100">
    <literal><![CDATA[
      p6(A,c7)
    ]]></literal>
    <literal><![CDATA[
      - p9(A,B)
    ]]></literal>
    <literal><![CDATA[
      p6(A,c8)
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="102">
    <literal><![CDATA[
      - p9(A,c16)
    ]]></literal>
    <literal><![CDATA[
      p9(f19(A),c15)
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="105">
    <literal><![CDATA[
      p9(f24(A),c16)
    ]]></literal>
    <literal><![CDATA[
      - p9(A,c23)
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="106">
    <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="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="107">
    <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="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="108">
    <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="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="109">
    <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="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="111">
    <literal><![CDATA[
      p9(f17(A),c10)
    ]]></literal>
    <literal><![CDATA[
      - p9(A,c16)
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="112">
    <literal><![CDATA[
      - p9(A,c23)
    ]]></literal>
    <literal><![CDATA[
      p9(f20(A),c14)
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="115">
    <literal><![CDATA[
      p9(f20(A),c14)
    ]]></literal>
    <literal><![CDATA[
      - p9(A,c16)
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="117">
    <literal><![CDATA[
      p9(f18(A),c10)
    ]]></literal>
    <literal><![CDATA[
      - p9(A,c16)
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="118">
    <literal><![CDATA[
      - p6(f19(f24(c26)),c8)
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="119">
    <literal><![CDATA[
      - p6(f17(f24(c26)),c8)
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="120">
    <literal><![CDATA[
      - p6(f18(f25(c26)),c8)
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="121">
    <literal><![CDATA[
      - p6(f18(f24(c26)),c8)
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="122">
    <literal><![CDATA[
      - p6(f17(f25(c26)),c8)
    ]]></literal>
    <literal><![CDATA[
      - p6(f20(c26),c8)
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="123">
    <literal><![CDATA[
      p2(f12(c21,c26),c5)
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="124">
    <literal><![CDATA[
      p2(f11(c13,c26),c4)
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="125">
    <literal><![CDATA[
      p2(f11(c22,c26),c5)
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="126">
    <literal><![CDATA[
      p2(f11(c5,c26),c5)
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="127">
    <literal><![CDATA[
      - p6(f20(f24(c26)),c8)
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="128">
    <literal><![CDATA[
      p9(c26,c23)
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="129">
    <literal><![CDATA[
      - p6(f19(f25(c26)),c8)
    ]]></literal>
    <literal><![CDATA[
      - p6(f20(c26),c8)
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="130">
    <literal><![CDATA[
      p2(f12(c22,c26),c4)
    ]]></literal>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="132">
    <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(14,a,3,a)].">
      <j1 rule="resolve" parents="14 3"/>
    </justification>
  </clause>

  <clause id="134">
    <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(14,a,7,a)].">
      <j1 rule="resolve" parents="14 7"/>
    </justification>
  </clause>

  <clause id="136">
    <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(14,a,12,a)].">
      <j1 rule="resolve" parents="14 12"/>
    </justification>
  </clause>

  <clause id="137">
    <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(16,b,1,b)].">
      <j1 rule="resolve" parents="16 1"/>
    </justification>
  </clause>

  <clause id="139">
    <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(16,b,6,b)].">
      <j1 rule="resolve" parents="16 6"/>
    </justification>
  </clause>

  <clause id="141">
    <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(16,b,8,b)].">
      <j1 rule="resolve" parents="16 8"/>
    </justification>
  </clause>

  <clause id="146">
    <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(22,b,16,b)].">
      <j1 rule="resolve" parents="22 16"/>
    </justification>
  </clause>

  <clause id="148">
    <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(23,a,16,b)].">
      <j1 rule="resolve" parents="23 16"/>
    </justification>
  </clause>

  <clause id="150">
    <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(24,a,16,b)].">
      <j1 rule="resolve" parents="24 16"/>
    </justification>
  </clause>

  <clause id="153">
    <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(27,a,14,a)].">
      <j1 rule="resolve" parents="27 14"/>
    </justification>
  </clause>

  <clause id="156">
    <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(32,b,16,b)].">
      <j1 rule="resolve" parents="32 16"/>
    </justification>
  </clause>

  <clause id="158">
    <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(34,a,16,b)].">
      <j1 rule="resolve" parents="34 16"/>
    </justification>
  </clause>

  <clause id="160">
    <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(36,a,16,b)].">
      <j1 rule="resolve" parents="36 16"/>
    </justification>
  </clause>

  <clause id="162">
    <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(37,b,16,b)].">
      <j1 rule="resolve" parents="37 16"/>
    </justification>
  </clause>

  <clause id="164">
    <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(41,b,16,b)].">
      <j1 rule="resolve" parents="41 16"/>
    </justification>
  </clause>

  <clause id="165">
    <literal><![CDATA[
      - p2(A,c5)
    ]]></literal>
    <literal><![CDATA[
      - p2(A,c4)
    ]]></literal>
    <justification jstring="[resolve(38,a,5,a)].">
      <j1 rule="resolve" parents="38 5"/>
    </justification>
  </clause>

  <clause id="166">
    <literal><![CDATA[
      p9(f20(c26),c14)
    ]]></literal>
    <justification jstring="[resolve(128,a,112,a)].">
      <j1 rule="resolve" parents="128 112"/>
    </justification>
  </clause>

  <clause id="167">
    <literal><![CDATA[
      p9(f24(c26),c16)
    ]]></literal>
    <justification jstring="[resolve(128,a,105,b)].">
      <j1 rule="resolve" parents="128 105"/>
    </justification>
  </clause>

  <clause id="169">
    <literal><![CDATA[
      p9(f25(c26),c16)
    ]]></literal>
    <justification jstring="[resolve(128,a,96,b)].">
      <j1 rule="resolve" parents="128 96"/>
    </justification>
  </clause>

  <clause id="171">
    <literal><![CDATA[
      p2(f12(c21,f25(c26)),A)
    ]]></literal>
    <literal><![CDATA[
      - p2(f12(c21,c26),A)
    ]]></literal>
    <justification jstring="[resolve(136,c,128,a)].">
      <j1 rule="resolve" parents="136 128"/>
    </justification>
  </clause>

  <clause id="175">
    <literal><![CDATA[
      p2(f12(c21,f24(c26)),A)
    ]]></literal>
    <literal><![CDATA[
      - p2(f11(c13,f25(c26)),A)
    ]]></literal>
    <justification jstring="[resolve(148,a,128,a)].">
      <j1 rule="resolve" parents="148 128"/>
    </justification>
  </clause>

  <clause id="180">
    <literal><![CDATA[
      p2(f12(c5,f20(c26)),A)
    ]]></literal>
    <literal><![CDATA[
      - p2(f12(c22,c26),A)
    ]]></literal>
    <justification jstring="[resolve(153,a,128,a)].">
      <j1 rule="resolve" parents="153 128"/>
    </justification>
  </clause>

  <clause id="187">
    <literal><![CDATA[
      - p2(f11(c13,c26),c5)
    ]]></literal>
    <justification jstring="[resolve(165,b,124,a)].">
      <j1 rule="resolve" parents="165 124"/>
    </justification>
  </clause>

  <clause id="188">
    <literal><![CDATA[
      - p2(f11(c5,c26),c4)
    ]]></literal>
    <justification jstring="[ur(165,a,126,a)].">
      <j1 rule="ur" parents="165 126"/>
    </justification>
  </clause>

  <clause id="189">
    <literal><![CDATA[
      - p2(f11(c22,c26),c4)
    ]]></literal>
    <justification jstring="[ur(165,a,125,a)].">
      <j1 rule="ur" parents="165 125"/>
    </justification>
  </clause>

  <clause id="192">
    <literal><![CDATA[
      - p2(f11(c5,f24(c26)),c5)
    ]]></literal>
    <justification jstring="[ur(150,a,128,a,b,187,a)].">
      <j1 rule="ur" parents="150 128 187"/>
    </justification>
  </clause>

  <clause id="193">
    <literal><![CDATA[
      p6(f20(c26),c7)
    ]]></literal>
    <literal><![CDATA[
      p6(f20(c26),c8)
    ]]></literal>
    <justification jstring="[resolve(166,a,100,b)].">
      <j1 rule="resolve" parents="166 100"/>
    </justification>
  </clause>

  <clause id="212">
    <literal><![CDATA[
      p9(f18(f24(c26)),c10)
    ]]></literal>
    <justification jstring="[resolve(167,a,117,b)].">
      <j1 rule="resolve" parents="167 117"/>
    </justification>
  </clause>

  <clause id="213">
    <literal><![CDATA[
      p9(f20(f24(c26)),c14)
    ]]></literal>
    <justification jstring="[resolve(167,a,115,b)].">
      <j1 rule="resolve" parents="167 115"/>
    </justification>
  </clause>

  <clause id="214">
    <literal><![CDATA[
      p9(f17(f24(c26)),c10)
    ]]></literal>
    <justification jstring="[resolve(167,a,111,b)].">
      <j1 rule="resolve" parents="167 111"/>
    </justification>
  </clause>

  <clause id="215">
    <literal><![CDATA[
      p9(f19(f24(c26)),c15)
    ]]></literal>
    <justification jstring="[resolve(167,a,102,a)].">
      <j1 rule="resolve" parents="167 102"/>
    </justification>
  </clause>

  <clause id="217">
    <literal><![CDATA[
      - p2(f11(c5,f25(c26)),c4)
    ]]></literal>
    <justification jstring="[ur(141,a,188,a,c,128,a)].">
      <j1 rule="ur" parents="141 188 128"/>
    </justification>
  </clause>

  <clause id="218">
    <literal><![CDATA[
      - p2(f11(c13,f24(c26)),c4)
    ]]></literal>
    <justification jstring="[ur(160,a,128,a,b,189,a)].">
      <j1 rule="ur" parents="160 128 189"/>
    </justification>
  </clause>

  <clause id="237">
    <literal><![CDATA[
      p9(f18(f25(c26)),c10)
    ]]></literal>
    <justification jstring="[resolve(169,a,117,b)].">
      <j1 rule="resolve" parents="169 117"/>
    </justification>
  </clause>

  <clause id="239">
    <literal><![CDATA[
      p9(f17(f25(c26)),c10)
    ]]></literal>
    <justification jstring="[resolve(169,a,111,b)].">
      <j1 rule="resolve" parents="169 111"/>
    </justification>
  </clause>

  <clause id="240">
    <literal><![CDATA[
      p9(f19(f25(c26)),c15)
    ]]></literal>
    <justification jstring="[resolve(169,a,102,a)].">
      <j1 rule="resolve" parents="169 102"/>
    </justification>
  </clause>

  <clause id="242">
    <literal><![CDATA[
      p6(f18(f24(c26)),c7)
    ]]></literal>
    <justification jstring="[resolve(212,a,100,b),unit_del(b,121)].">
      <j1 rule="resolve" parents="212 100"/>
      <j2 rule="unit_del" parents="121"/>
    </justification>
  </clause>

  <clause id="245">
    <literal><![CDATA[
      p6(f20(f24(c26)),c7)
    ]]></literal>
    <justification jstring="[resolve(213,a,100,b),unit_del(b,127)].">
      <j1 rule="resolve" parents="213 100"/>
      <j2 rule="unit_del" parents="127"/>
    </justification>
  </clause>

  <clause id="246">
    <literal><![CDATA[
      p6(f17(f24(c26)),c7)
    ]]></literal>
    <justification jstring="[resolve(214,a,100,b),unit_del(b,119)].">
      <j1 rule="resolve" parents="214 100"/>
      <j2 rule="unit_del" parents="119"/>
    </justification>
  </clause>

  <clause id="247">
    <literal><![CDATA[
      p2(f12(c21,f25(c26)),c5)
    ]]></literal>
    <justification jstring="[resolve(171,b,123,a)].">
      <j1 rule="resolve" parents="171 123"/>
    </justification>
  </clause>

  <clause id="248">
    <literal><![CDATA[
      - p2(f11(c5,f18(f24(c26))),c5)
    ]]></literal>
    <justification jstring="[ur(158,a,167,a,b,192,a)].">
      <j1 rule="ur" parents="158 167 192"/>
    </justification>
  </clause>

  <clause id="250">
    <literal><![CDATA[
      - p2(f11(c5,f18(f25(c26))),c4)
    ]]></literal>
    <justification jstring="[ur(158,a,169,a,b,217,a)].">
      <j1 rule="ur" parents="158 169 217"/>
    </justification>
  </clause>

  <clause id="252">
    <literal><![CDATA[
      p6(f19(f24(c26)),c7)
    ]]></literal>
    <justification jstring="[resolve(215,a,100,b),unit_del(b,118)].">
      <j1 rule="resolve" parents="215 100"/>
      <j2 rule="unit_del" parents="118"/>
    </justification>
  </clause>

  <clause id="253">
    <literal><![CDATA[
      p6(f18(f25(c26)),c7)
    ]]></literal>
    <justification jstring="[resolve(237,a,100,b),unit_del(b,120)].">
      <j1 rule="resolve" parents="237 100"/>
      <j2 rule="unit_del" parents="120"/>
    </justification>
  </clause>

  <clause id="255">
    <literal><![CDATA[
      - p2(f11(c13,f20(f24(c26))),c4)
    ]]></literal>
    <justification jstring="[ur(156,a,167,a,b,218,a)].">
      <j1 rule="ur" parents="156 167 218"/>
    </justification>
  </clause>

  <clause id="258">
    <literal><![CDATA[
      p6(f17(f25(c26)),c7)
    ]]></literal>
    <literal><![CDATA[
      p6(f17(f25(c26)),c8)
    ]]></literal>
    <justification jstring="[resolve(239,a,100,b)].">
      <j1 rule="resolve" parents="239 100"/>
    </justification>
  </clause>

  <clause id="259">
    <literal><![CDATA[
      p6(f19(f25(c26)),c7)
    ]]></literal>
    <literal><![CDATA[
      p6(f19(f25(c26)),c8)
    ]]></literal>
    <justification jstring="[resolve(240,a,100,b)].">
      <j1 rule="resolve" parents="240 100"/>
    </justification>
  </clause>

  <clause id="265">
    <literal><![CDATA[
      - p2(f12(c5,f18(f24(c26))),c5)
    ]]></literal>
    <justification jstring="[resolve(242,a,106,c),unit_del(a,212),unit_del(c,248)].">
      <j1 rule="resolve" parents="242 106"/>
      <j2 rule="unit_del" parents="212"/>
      <j2 rule="unit_del" parents="248"/>
    </justification>
  </clause>

  <clause id="273">
    <literal><![CDATA[
      - p2(f12(c5,f20(f24(c26))),c4)
    ]]></literal>
    <justification jstring="[resolve(245,a,108,c),unit_del(b,255),unit_del(c,213)].">
      <j1 rule="resolve" parents="245 108"/>
      <j2 rule="unit_del" parents="255"/>
      <j2 rule="unit_del" parents="213"/>
    </justification>
  </clause>

  <clause id="287">
    <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(246,a,99,d),unit_del(d,214)].">
      <j1 rule="resolve" parents="246 99"/>
      <j2 rule="unit_del" parents="214"/>
    </justification>
  </clause>

  <clause id="304">
    <literal><![CDATA[
      - p2(f12(c5,f19(f24(c26))),c4)
    ]]></literal>
    <literal><![CDATA[
      p2(f11(c5,f19(f24(c26))),c5)
    ]]></literal>
    <justification jstring="[resolve(252,a,95,d),unit_del(b,215)].">
      <j1 rule="resolve" parents="252 95"/>
      <j2 rule="unit_del" parents="215"/>
    </justification>
  </clause>

  <clause id="312">
    <literal><![CDATA[
      p2(f11(c13,f18(f25(c26))),c4)
    ]]></literal>
    <literal><![CDATA[
      - p2(f12(c5,f18(f25(c26))),c4)
    ]]></literal>
    <justification jstring="[resolve(253,a,99,d),unit_del(c,250),unit_del(d,237)].">
      <j1 rule="resolve" parents="253 99"/>
      <j2 rule="unit_del" parents="250"/>
      <j2 rule="unit_del" parents="237"/>
    </justification>
  </clause>

  <clause id="317">
    <literal><![CDATA[
      - p2(f11(c5,f19(f24(c26))),c5)
    ]]></literal>
    <justification jstring="[ur(139,a,265,a,c,167,a)].">
      <j1 rule="ur" parents="139 265 167"/>
    </justification>
  </clause>

  <clause id="319">
    <literal><![CDATA[
      - p2(f12(c5,f19(f24(c26))),c4)
    ]]></literal>
    <justification jstring="[back_unit_del(304),unit_del(b,317)].">
      <j1 rule="back_unit_del" parents="304"/>
      <j2 rule="unit_del" parents="317"/>
    </justification>
  </clause>

  <clause id="325">
    <literal><![CDATA[
      - p2(f11(c5,f17(f24(c26))),c4)
    ]]></literal>
    <justification jstring="[ur(146,a,167,a,b,273,a)].">
      <j1 rule="ur" parents="146 167 273"/>
    </justification>
  </clause>

  <clause id="327">
    <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(287),unit_del(c,325)].">
      <j1 rule="back_unit_del" parents="287"/>
      <j2 rule="unit_del" parents="325"/>
    </justification>
  </clause>

  <clause id="329">
    <literal><![CDATA[
      - p2(f11(c13,f17(f24(c26))),c4)
    ]]></literal>
    <justification jstring="[ur(137,a,319,a,c,167,a)].">
      <j1 rule="ur" parents="137 319 167"/>
    </justification>
  </clause>

  <clause id="330">
    <literal><![CDATA[
      - p2(f12(c5,f17(f24(c26))),c4)
    ]]></literal>
    <justification jstring="[back_unit_del(327),unit_del(a,329)].">
      <j1 rule="back_unit_del" parents="327"/>
      <j2 rule="unit_del" parents="329"/>
    </justification>
  </clause>

  <clause id="333">
    <literal><![CDATA[
      - p2(f12(c21,f24(c26)),c4)
    ]]></literal>
    <justification jstring="[ur(134,a,330,a,c,167,a)].">
      <j1 rule="ur" parents="134 330 167"/>
    </justification>
  </clause>

  <clause id="334">
    <literal><![CDATA[
      p6(f17(f25(c26)),c7)
    ]]></literal>
    <literal><![CDATA[
      - p6(f20(c26),c8)
    ]]></literal>
    <justification jstring="[resolve(258,b,122,a)].">
      <j1 rule="resolve" parents="258 122"/>
    </justification>
  </clause>

  <clause id="335">
    <literal><![CDATA[
      p2(f12(c5,f20(c26)),c4)
    ]]></literal>
    <justification jstring="[resolve(180,b,130,a)].">
      <j1 rule="resolve" parents="180 130"/>
    </justification>
  </clause>

  <clause id="336">
    <literal><![CDATA[
      - p2(f11(c13,f25(c26)),c4)
    ]]></literal>
    <justification jstring="[ur(175,a,333,a)].">
      <j1 rule="ur" parents="175 333"/>
    </justification>
  </clause>

  <clause id="337">
    <literal><![CDATA[
      - p2(f11(c13,f18(f25(c26))),c4)
    ]]></literal>
    <justification jstring="[ur(162,a,169,a,b,336,a)].">
      <j1 rule="ur" parents="162 169 336"/>
    </justification>
  </clause>

  <clause id="339">
    <literal><![CDATA[
      - p2(f12(c5,f18(f25(c26))),c4)
    ]]></literal>
    <justification jstring="[back_unit_del(312),unit_del(a,337)].">
      <j1 rule="back_unit_del" parents="312"/>
      <j2 rule="unit_del" parents="337"/>
    </justification>
  </clause>

  <clause id="342">
    <literal><![CDATA[
      p6(f17(f25(c26)),c7)
    ]]></literal>
    <literal><![CDATA[
      p6(f20(c26),c7)
    ]]></literal>
    <justification jstring="[resolve(334,b,193,b)].">
      <j1 rule="resolve" parents="334 193"/>
    </justification>
  </clause>

  <clause id="347">
    <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(342,a,107,a),unit_del(b,239)].">
      <j1 rule="resolve" parents="342 107"/>
      <j2 rule="unit_del" parents="239"/>
    </justification>
  </clause>

  <clause id="351">
    <literal><![CDATA[
      p6(f19(f25(c26)),c7)
    ]]></literal>
    <literal><![CDATA[
      - p6(f20(c26),c8)
    ]]></literal>
    <justification jstring="[resolve(259,b,129,a)].">
      <j1 rule="resolve" parents="259 129"/>
    </justification>
  </clause>

  <clause id="353">
    <literal><![CDATA[
      - p2(f11(c5,f19(f25(c26))),c4)
    ]]></literal>
    <justification jstring="[ur(139,a,339,a,c,169,a)].">
      <j1 rule="ur" parents="139 339 169"/>
    </justification>
  </clause>

  <clause id="354">
    <literal><![CDATA[
      - p2(f12(c22,f25(c26)),c4)
    ]]></literal>
    <justification jstring="[ur(132,a,339,a,c,169,a)].">
      <j1 rule="ur" parents="132 339 169"/>
    </justification>
  </clause>

  <clause id="355">
    <literal><![CDATA[
      - p2(f11(c5,f20(c26)),c4)
    ]]></literal>
    <justification jstring="[ur(164,a,128,a,b,354,a)].">
      <j1 rule="ur" parents="164 128 354"/>
    </justification>
  </clause>

  <clause id="356">
    <literal><![CDATA[
      p6(f19(f25(c26)),c7)
    ]]></literal>
    <literal><![CDATA[
      p6(f20(c26),c7)
    ]]></literal>
    <justification jstring="[resolve(351,b,193,b)].">
      <j1 rule="resolve" parents="351 193"/>
    </justification>
  </clause>

  <clause id="357">
    <literal><![CDATA[
      - p6(f20(c26),c7)
    ]]></literal>
    <justification jstring="[ur(98,a,335,a,b,166,a,c,355,a)].">
      <j1 rule="ur" parents="98 335 166 355"/>
    </justification>
  </clause>

  <clause id="358">
    <literal><![CDATA[
      p6(f19(f25(c26)),c7)
    ]]></literal>
    <justification jstring="[back_unit_del(356),unit_del(b,357)].">
      <j1 rule="back_unit_del" parents="356"/>
      <j2 rule="unit_del" parents="357"/>
    </justification>
  </clause>

  <clause id="362">
    <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(347),unit_del(a,357)].">
      <j1 rule="back_unit_del" parents="347"/>
      <j2 rule="unit_del" parents="357"/>
    </justification>
  </clause>

  <clause id="373">
    <literal><![CDATA[
      - p2(f12(c5,f19(f25(c26))),c5)
    ]]></literal>
    <justification jstring="[resolve(358,a,109,c),unit_del(a,353),unit_del(c,240)].">
      <j1 rule="resolve" parents="358 109"/>
      <j2 rule="unit_del" parents="353"/>
      <j2 rule="unit_del" parents="240"/>
    </justification>
  </clause>

  <clause id="388">
    <literal><![CDATA[
      - p2(f11(c13,f17(f25(c26))),c5)
    ]]></literal>
    <justification jstring="[ur(137,a,373,a,c,169,a)].">
      <j1 rule="ur" parents="137 373 169"/>
    </justification>
  </clause>

  <clause id="389">
    <literal><![CDATA[
      - p2(f12(c5,f17(f25(c26))),c5)
    ]]></literal>
    <justification jstring="[back_unit_del(362),unit_del(b,388)].">
      <j1 rule="back_unit_del" parents="362"/>
      <j2 rule="unit_del" parents="388"/>
    </justification>
  </clause>

  <clause id="398">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[ur(134,a,389,a,c,169,a),unit_del(a,247)].">
      <j1 rule="ur" parents="134 389 169"/>
      <j2 rule="unit_del" parents="247"/>
    </justification>
  </clause>

</proof>

</proofs>
