<?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>steam.out</source>

<heading><![CDATA[
Prover9 (32) version June-2006C, June 2006.
Process 13073 was started by mccune on cleo.thornwood,
Mon Jun 19 16:41:11 2006
The command was "/home/mccune/bin/prover9 -f steam.in".
]]></heading>

<proof number="1" length="55" max_count="20">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 55.
% Level of proof is 9.
% Maximum clause weight is 13.
% Given clauses 44.
]]></comments>

  <clause id="1">
    <literal><![CDATA[
      - Wolf(x)
    ]]></literal>
    <literal><![CDATA[
      animal(x)
    ]]></literal>
    <justification jstring="[clausify].">
      <j1 rule="clausify"/>
    </justification>
  </clause>

  <clause id="2">
    <literal><![CDATA[
      - Fox(x)
    ]]></literal>
    <literal><![CDATA[
      animal(x)
    ]]></literal>
    <justification jstring="[clausify].">
      <j1 rule="clausify"/>
    </justification>
  </clause>

  <clause id="3">
    <literal><![CDATA[
      - Bird(x)
    ]]></literal>
    <literal><![CDATA[
      animal(x)
    ]]></literal>
    <justification jstring="[clausify].">
      <j1 rule="clausify"/>
    </justification>
  </clause>

  <clause id="5">
    <literal><![CDATA[
      - Snail(x)
    ]]></literal>
    <literal><![CDATA[
      animal(x)
    ]]></literal>
    <justification jstring="[clausify].">
      <j1 rule="clausify"/>
    </justification>
  </clause>

  <clause id="6">
    <literal><![CDATA[
      - Grain(x)
    ]]></literal>
    <literal><![CDATA[
      plant(x)
    ]]></literal>
    <justification jstring="[clausify].">
      <j1 rule="clausify"/>
    </justification>
  </clause>

  <clause id="7">
    <literal><![CDATA[
      Wolf(c1)
    ]]></literal>
    <justification jstring="[clausify].">
      <j1 rule="clausify"/>
    </justification>
  </clause>

  <clause id="8">
    <literal><![CDATA[
      Fox(c2)
    ]]></literal>
    <justification jstring="[clausify].">
      <j1 rule="clausify"/>
    </justification>
  </clause>

  <clause id="9">
    <literal><![CDATA[
      Bird(c3)
    ]]></literal>
    <justification jstring="[clausify].">
      <j1 rule="clausify"/>
    </justification>
  </clause>

  <clause id="11">
    <literal><![CDATA[
      Snail(c5)
    ]]></literal>
    <justification jstring="[clausify].">
      <j1 rule="clausify"/>
    </justification>
  </clause>

  <clause id="12">
    <literal><![CDATA[
      Grain(c6)
    ]]></literal>
    <justification jstring="[clausify].">
      <j1 rule="clausify"/>
    </justification>
  </clause>

  <clause id="13">
    <literal><![CDATA[
      - animal(x)
    ]]></literal>
    <literal><![CDATA[
      - plant(y)
    ]]></literal>
    <literal><![CDATA[
      eats(x,y)
    ]]></literal>
    <literal><![CDATA[
      - animal(z)
    ]]></literal>
    <literal><![CDATA[
      - Smaller(z,x)
    ]]></literal>
    <literal><![CDATA[
      - plant(u)
    ]]></literal>
    <literal><![CDATA[
      - eats(z,u)
    ]]></literal>
    <literal><![CDATA[
      eats(x,z)
    ]]></literal>
    <justification jstring="[clausify].">
      <j1 rule="clausify"/>
    </justification>
  </clause>

  <clause id="15">
    <literal><![CDATA[
      - Snail(x)
    ]]></literal>
    <literal><![CDATA[
      - Bird(y)
    ]]></literal>
    <literal><![CDATA[
      Smaller(x,y)
    ]]></literal>
    <justification jstring="[clausify].">
      <j1 rule="clausify"/>
    </justification>
  </clause>

  <clause id="16">
    <literal><![CDATA[
      - Bird(x)
    ]]></literal>
    <literal><![CDATA[
      - Fox(y)
    ]]></literal>
    <literal><![CDATA[
      Smaller(x,y)
    ]]></literal>
    <justification jstring="[clausify].">
      <j1 rule="clausify"/>
    </justification>
  </clause>

  <clause id="17">
    <literal><![CDATA[
      - Fox(x)
    ]]></literal>
    <literal><![CDATA[
      - Wolf(y)
    ]]></literal>
    <literal><![CDATA[
      Smaller(x,y)
    ]]></literal>
    <justification jstring="[clausify].">
      <j1 rule="clausify"/>
    </justification>
  </clause>

  <clause id="21">
    <literal><![CDATA[
      - Snail(x)
    ]]></literal>
    <literal><![CDATA[
      plant(f2(x))
    ]]></literal>
    <justification jstring="[clausify].">
      <j1 rule="clausify"/>
    </justification>
  </clause>

  <clause id="22">
    <literal><![CDATA[
      - Snail(x)
    ]]></literal>
    <literal><![CDATA[
      eats(x,f2(x))
    ]]></literal>
    <justification jstring="[clausify].">
      <j1 rule="clausify"/>
    </justification>
  </clause>

  <clause id="23">
    <literal><![CDATA[
      - Wolf(x)
    ]]></literal>
    <literal><![CDATA[
      - Fox(y)
    ]]></literal>
    <literal><![CDATA[
      - eats(x,y)
    ]]></literal>
    <justification jstring="[clausify].">
      <j1 rule="clausify"/>
    </justification>
  </clause>

  <clause id="24">
    <literal><![CDATA[
      - Wolf(x)
    ]]></literal>
    <literal><![CDATA[
      - Grain(y)
    ]]></literal>
    <literal><![CDATA[
      - eats(x,y)
    ]]></literal>
    <justification jstring="[clausify].">
      <j1 rule="clausify"/>
    </justification>
  </clause>

  <clause id="25">
    <literal><![CDATA[
      - Bird(x)
    ]]></literal>
    <literal><![CDATA[
      - Snail(y)
    ]]></literal>
    <literal><![CDATA[
      - eats(x,y)
    ]]></literal>
    <justification jstring="[clausify].">
      <j1 rule="clausify"/>
    </justification>
  </clause>

  <clause id="26">
    <literal><![CDATA[
      - animal(x)
    ]]></literal>
    <literal><![CDATA[
      - animal(y)
    ]]></literal>
    <literal><![CDATA[
      - eats(x,y)
    ]]></literal>
    <literal><![CDATA[
      Grain(f3(x,y))
    ]]></literal>
    <justification jstring="[clausify].">
      <j1 rule="clausify"/>
    </justification>
  </clause>

  <clause id="29">
    <literal><![CDATA[
      - Fox(x)
    ]]></literal>
    <literal><![CDATA[
      Smaller(x,c1)
    ]]></literal>
    <justification jstring="[resolve(17,b,7,a)].">
      <j1 rule="resolve" parents="17 7"/>
    </justification>
  </clause>

  <clause id="30">
    <literal><![CDATA[
      - Fox(x)
    ]]></literal>
    <literal><![CDATA[
      - eats(c1,x)
    ]]></literal>
    <justification jstring="[resolve(23,a,7,a)].">
      <j1 rule="resolve" parents="23 7"/>
    </justification>
  </clause>

  <clause id="31">
    <literal><![CDATA[
      - Grain(x)
    ]]></literal>
    <literal><![CDATA[
      - eats(c1,x)
    ]]></literal>
    <justification jstring="[resolve(24,a,7,a)].">
      <j1 rule="resolve" parents="24 7"/>
    </justification>
  </clause>

  <clause id="33">
    <literal><![CDATA[
      - Bird(x)
    ]]></literal>
    <literal><![CDATA[
      Smaller(x,c2)
    ]]></literal>
    <justification jstring="[resolve(16,b,8,a)].">
      <j1 rule="resolve" parents="16 8"/>
    </justification>
  </clause>

  <clause id="34">
    <literal><![CDATA[
      Smaller(c2,c1)
    ]]></literal>
    <justification jstring="[resolve(29,a,8,a)].">
      <j1 rule="resolve" parents="29 8"/>
    </justification>
  </clause>

  <clause id="38">
    <literal><![CDATA[
      - Snail(x)
    ]]></literal>
    <literal><![CDATA[
      Smaller(x,c3)
    ]]></literal>
    <justification jstring="[resolve(15,b,9,a)].">
      <j1 rule="resolve" parents="15 9"/>
    </justification>
  </clause>

  <clause id="40">
    <literal><![CDATA[
      - Snail(x)
    ]]></literal>
    <literal><![CDATA[
      - eats(c3,x)
    ]]></literal>
    <justification jstring="[resolve(25,a,9,a)].">
      <j1 rule="resolve" parents="25 9"/>
    </justification>
  </clause>

  <clause id="41">
    <literal><![CDATA[
      Smaller(c3,c2)
    ]]></literal>
    <justification jstring="[resolve(33,a,9,a)].">
      <j1 rule="resolve" parents="33 9"/>
    </justification>
  </clause>

  <clause id="50">
    <literal><![CDATA[
      Smaller(c5,c3)
    ]]></literal>
    <justification jstring="[resolve(38,a,11,a)].">
      <j1 rule="resolve" parents="38 11"/>
    </justification>
  </clause>

  <clause id="56">
    <literal><![CDATA[
      - animal(c1)
    ]]></literal>
    <literal><![CDATA[
      - plant(x)
    ]]></literal>
    <literal><![CDATA[
      eats(c1,x)
    ]]></literal>
    <literal><![CDATA[
      - animal(c2)
    ]]></literal>
    <literal><![CDATA[
      - plant(y)
    ]]></literal>
    <literal><![CDATA[
      - eats(c2,y)
    ]]></literal>
    <literal><![CDATA[
      eats(c1,c2)
    ]]></literal>
    <justification jstring="[resolve(34,a,13,e)].">
      <j1 rule="resolve" parents="34 13"/>
    </justification>
  </clause>

  <clause id="57">
    <literal><![CDATA[
      - animal(c2)
    ]]></literal>
    <literal><![CDATA[
      - plant(x)
    ]]></literal>
    <literal><![CDATA[
      eats(c2,x)
    ]]></literal>
    <literal><![CDATA[
      - animal(c3)
    ]]></literal>
    <literal><![CDATA[
      - plant(y)
    ]]></literal>
    <literal><![CDATA[
      - eats(c3,y)
    ]]></literal>
    <literal><![CDATA[
      eats(c2,c3)
    ]]></literal>
    <justification jstring="[resolve(41,a,13,e)].">
      <j1 rule="resolve" parents="41 13"/>
    </justification>
  </clause>

  <clause id="59">
    <literal><![CDATA[
      - animal(c3)
    ]]></literal>
    <literal><![CDATA[
      - plant(x)
    ]]></literal>
    <literal><![CDATA[
      eats(c3,x)
    ]]></literal>
    <literal><![CDATA[
      - animal(c5)
    ]]></literal>
    <literal><![CDATA[
      - plant(y)
    ]]></literal>
    <literal><![CDATA[
      - eats(c5,y)
    ]]></literal>
    <literal><![CDATA[
      eats(c3,c5)
    ]]></literal>
    <justification jstring="[resolve(50,a,13,e)].">
      <j1 rule="resolve" parents="50 13"/>
    </justification>
  </clause>

  <clause id="60">
    <literal><![CDATA[
      - animal(x)
    ]]></literal>
    <literal><![CDATA[
      - animal(y)
    ]]></literal>
    <literal><![CDATA[
      - eats(x,y)
    ]]></literal>
    <literal><![CDATA[
      - eats(y,f3(x,y))
    ]]></literal>
    <justification jstring="[clausify].">
      <j1 rule="clausify"/>
    </justification>
  </clause>

  <clause id="61">
    <literal><![CDATA[
      animal(c1)
    ]]></literal>
    <justification jstring="[resolve(7,a,1,a)].">
      <j1 rule="resolve" parents="7 1"/>
    </justification>
  </clause>

  <clause id="62">
    <literal><![CDATA[
      animal(c2)
    ]]></literal>
    <justification jstring="[resolve(8,a,2,a)].">
      <j1 rule="resolve" parents="8 2"/>
    </justification>
  </clause>

  <clause id="63">
    <literal><![CDATA[
      - eats(c1,c2)
    ]]></literal>
    <justification jstring="[resolve(30,a,8,a)].">
      <j1 rule="resolve" parents="30 8"/>
    </justification>
  </clause>

  <clause id="64">
    <literal><![CDATA[
      animal(c3)
    ]]></literal>
    <justification jstring="[resolve(9,a,3,a)].">
      <j1 rule="resolve" parents="9 3"/>
    </justification>
  </clause>

  <clause id="69">
    <literal><![CDATA[
      animal(c5)
    ]]></literal>
    <justification jstring="[resolve(11,a,5,a)].">
      <j1 rule="resolve" parents="11 5"/>
    </justification>
  </clause>

  <clause id="70">
    <literal><![CDATA[
      plant(f2(c5))
    ]]></literal>
    <justification jstring="[resolve(21,a,11,a)].">
      <j1 rule="resolve" parents="21 11"/>
    </justification>
  </clause>

  <clause id="71">
    <literal><![CDATA[
      eats(c5,f2(c5))
    ]]></literal>
    <justification jstring="[resolve(22,a,11,a)].">
      <j1 rule="resolve" parents="22 11"/>
    </justification>
  </clause>

  <clause id="72">
    <literal><![CDATA[
      - eats(c3,c5)
    ]]></literal>
    <justification jstring="[resolve(40,a,11,a)].">
      <j1 rule="resolve" parents="40 11"/>
    </justification>
  </clause>

  <clause id="73">
    <literal><![CDATA[
      plant(c6)
    ]]></literal>
    <justification jstring="[resolve(12,a,6,a)].">
      <j1 rule="resolve" parents="12 6"/>
    </justification>
  </clause>

  <clause id="74">
    <literal><![CDATA[
      - animal(x)
    ]]></literal>
    <literal><![CDATA[
      - animal(y)
    ]]></literal>
    <literal><![CDATA[
      - eats(x,y)
    ]]></literal>
    <literal><![CDATA[
      plant(f3(x,y))
    ]]></literal>
    <justification jstring="[resolve(26,d,6,a)].">
      <j1 rule="resolve" parents="26 6"/>
    </justification>
  </clause>

  <clause id="75">
    <literal><![CDATA[
      - eats(c1,c6)
    ]]></literal>
    <justification jstring="[resolve(31,a,12,a)].">
      <j1 rule="resolve" parents="31 12"/>
    </justification>
  </clause>

  <clause id="77">
    <literal><![CDATA[
      - plant(x)
    ]]></literal>
    <literal><![CDATA[
      eats(c1,x)
    ]]></literal>
    <literal><![CDATA[
      - plant(y)
    ]]></literal>
    <literal><![CDATA[
      - eats(c2,y)
    ]]></literal>
    <justification jstring="[copy(56),unit_del(a,61),unit_del(d,62),unit_del(g,63)].">
      <j1 rule="copy" parents="56"/>
      <j2 rule="unit_del" parents="61"/>
      <j2 rule="unit_del" parents="62"/>
      <j2 rule="unit_del" parents="63"/>
    </justification>
  </clause>

  <clause id="78">
    <literal><![CDATA[
      - plant(x)
    ]]></literal>
    <literal><![CDATA[
      eats(c2,x)
    ]]></literal>
    <literal><![CDATA[
      - plant(y)
    ]]></literal>
    <literal><![CDATA[
      - eats(c3,y)
    ]]></literal>
    <literal><![CDATA[
      eats(c2,c3)
    ]]></literal>
    <justification jstring="[copy(57),unit_del(a,62),unit_del(d,64)].">
      <j1 rule="copy" parents="57"/>
      <j2 rule="unit_del" parents="62"/>
      <j2 rule="unit_del" parents="64"/>
    </justification>
  </clause>

  <clause id="79">
    <literal><![CDATA[
      - plant(x)
    ]]></literal>
    <literal><![CDATA[
      eats(c3,x)
    ]]></literal>
    <literal><![CDATA[
      - plant(y)
    ]]></literal>
    <literal><![CDATA[
      - eats(c5,y)
    ]]></literal>
    <justification jstring="[copy(59),unit_del(a,64),unit_del(d,69),unit_del(g,72)].">
      <j1 rule="copy" parents="59"/>
      <j2 rule="unit_del" parents="64"/>
      <j2 rule="unit_del" parents="69"/>
      <j2 rule="unit_del" parents="72"/>
    </justification>
  </clause>

  <clause id="84">
    <literal><![CDATA[
      - plant(x)
    ]]></literal>
    <literal><![CDATA[
      eats(c2,x)
    ]]></literal>
    <literal><![CDATA[
      - eats(c3,x)
    ]]></literal>
    <literal><![CDATA[
      eats(c2,c3)
    ]]></literal>
    <justification jstring="[factor(78,a,c)].">
      <j1 rule="factor" parents="78"/>
    </justification>
  </clause>

  <clause id="97">
    <literal><![CDATA[
      - eats(c2,c6)
    ]]></literal>
    <justification jstring="[ur(77,a,73,a,b,75,a,c,73,a)].">
      <j1 rule="ur" parents="77 73 75 73"/>
    </justification>
  </clause>

  <clause id="103">
    <literal><![CDATA[
      - plant(x)
    ]]></literal>
    <literal><![CDATA[
      eats(c3,x)
    ]]></literal>
    <justification jstring="[resolve(79,d,71,a),unit_del(c,70)].">
      <j1 rule="resolve" parents="79 71"/>
      <j2 rule="unit_del" parents="70"/>
    </justification>
  </clause>

  <clause id="107">
    <literal><![CDATA[
      eats(c3,c6)
    ]]></literal>
    <justification jstring="[resolve(103,a,73,a)].">
      <j1 rule="resolve" parents="103 73"/>
    </justification>
  </clause>

  <clause id="111">
    <literal><![CDATA[
      eats(c2,c3)
    ]]></literal>
    <justification jstring="[resolve(107,a,84,c),unit_del(a,73),unit_del(b,97)].">
      <j1 rule="resolve" parents="107 84"/>
      <j2 rule="unit_del" parents="73"/>
      <j2 rule="unit_del" parents="97"/>
    </justification>
  </clause>

  <clause id="118">
    <literal><![CDATA[
      plant(f3(c2,c3))
    ]]></literal>
    <justification jstring="[resolve(111,a,74,c),unit_del(a,62),unit_del(b,64)].">
      <j1 rule="resolve" parents="111 74"/>
      <j2 rule="unit_del" parents="62"/>
      <j2 rule="unit_del" parents="64"/>
    </justification>
  </clause>

  <clause id="119">
    <literal><![CDATA[
      - eats(c3,f3(c2,c3))
    ]]></literal>
    <justification jstring="[resolve(111,a,60,c),unit_del(a,62),unit_del(b,64)].">
      <j1 rule="resolve" parents="111 60"/>
      <j2 rule="unit_del" parents="62"/>
      <j2 rule="unit_del" parents="64"/>
    </justification>
  </clause>

  <clause id="127">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[resolve(118,a,103,a),unit_del(a,119)].">
      <j1 rule="resolve" parents="118 103"/>
      <j2 rule="unit_del" parents="119"/>
    </justification>
  </clause>

</proof>

</proofs>
