<?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="8">

<source>MGT025+1.out</source>

<heading><![CDATA[
FOF-Prover9 (32) version August-2006A, August 2006.
Process 11255 was started by mccune on cleo.thornwood,
Sat Aug 12 20:59:24 2006
The command was "/home/mccune/bin/fof-prover9 -f MGT025+1.in".
]]></heading>

<proof number="1" length="34" max_count="23">

<comments><![CDATA[
% Proof 1 at 0.01 (+ 0.00) seconds.
% Length of proof is 34.
% Level of proof is 6.
% Maximum clause weight is 21.
% Given clauses 52.
]]></comments>

  <clause id="1">
    <literal><![CDATA[
      environment(c1)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="4">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      first_movers != B
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(B,A,C)
    ]]></literal>
    <literal><![CDATA[
      sum(cardinality_at_time(first_movers,C),cardinality_at_time(efficient_producers,C)) = number_of_organizations(A,C)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="5">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -in_environment(A,B)
    ]]></literal>
    <literal><![CDATA[
      subpopulation(first_movers,A,B)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="6">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -in_environment(A,B)
    ]]></literal>
    <literal><![CDATA[
      subpopulation(efficient_producers,A,B)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="7">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -in_environment(A,B)
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(C,A,B)
    ]]></literal>
    <literal><![CDATA[
      -greater(cardinality_at_time(C,B),zero)
    ]]></literal>
    <literal><![CDATA[
      -constant(cardinality_at_time(C,B))
    ]]></literal>
    <literal><![CDATA[
      growth_rate(C,B) = zero
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="8">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -in_environment(A,B)
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(C,A,B)
    ]]></literal>
    <literal><![CDATA[
      -greater(cardinality_at_time(C,B),zero)
    ]]></literal>
    <literal><![CDATA[
      -increases(cardinality_at_time(C,B))
    ]]></literal>
    <literal><![CDATA[
      greater(growth_rate(C,B),zero)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="10">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -subpopulations(first_movers,efficient_producers,A,B)
    ]]></literal>
    <literal><![CDATA[
      greater(cardinality_at_time(first_movers,B),zero)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="11">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -subpopulations(first_movers,efficient_producers,A,B)
    ]]></literal>
    <literal><![CDATA[
      greater(cardinality_at_time(efficient_producers,B),zero)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="12">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -subpopulations(first_movers,efficient_producers,A,B)
    ]]></literal>
    <literal><![CDATA[
      in_environment(A,B)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="15">
    <literal><![CDATA[
      -constant(A)
    ]]></literal>
    <literal><![CDATA[
      constant(B)
    ]]></literal>
    <literal><![CDATA[
      increases(B)
    ]]></literal>
    <literal><![CDATA[
      sum(B,C) != A
    ]]></literal>
    <literal><![CDATA[
      increases(C)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="22">
    <literal><![CDATA[
      subpopulations(first_movers,efficient_producers,c1,c2)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="23">
    <literal><![CDATA[
      constant(number_of_organizations(c1,c2))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="24">
    <literal><![CDATA[
      growth_rate(first_movers,c2) != zero
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="25">
    <literal><![CDATA[
      -greater(growth_rate(first_movers,c2),zero)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="26">
    <literal><![CDATA[
      -greater(growth_rate(efficient_producers,c2),zero)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="31">
    <literal><![CDATA[
      first_movers != A
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(A,c1,B)
    ]]></literal>
    <literal><![CDATA[
      sum(cardinality_at_time(first_movers,B),cardinality_at_time(efficient_producers,B)) = number_of_organizations(c1,B)
    ]]></literal>
    <justification jstring="[resolve(1,a,4,a)].">
      <j1 rule="resolve" parents="1 4"/>
    </justification>
  </clause>

  <clause id="32">
    <literal><![CDATA[
      first_movers != A
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(A,c1,B)
    ]]></literal>
    <literal><![CDATA[
      number_of_organizations(c1,B) = sum(cardinality_at_time(first_movers,B),cardinality_at_time(efficient_producers,B))
    ]]></literal>
    <justification jstring="[copy(31),flip(c)].">
      <j1 rule="copy" parents="31"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33">
    <literal><![CDATA[
      -in_environment(c1,A)
    ]]></literal>
    <literal><![CDATA[
      subpopulation(first_movers,c1,A)
    ]]></literal>
    <justification jstring="[resolve(1,a,5,a)].">
      <j1 rule="resolve" parents="1 5"/>
    </justification>
  </clause>

  <clause id="34">
    <literal><![CDATA[
      -in_environment(c1,A)
    ]]></literal>
    <literal><![CDATA[
      subpopulation(efficient_producers,c1,A)
    ]]></literal>
    <justification jstring="[resolve(1,a,6,a)].">
      <j1 rule="resolve" parents="1 6"/>
    </justification>
  </clause>

  <clause id="35">
    <literal><![CDATA[
      -in_environment(c1,A)
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(B,c1,A)
    ]]></literal>
    <literal><![CDATA[
      -greater(cardinality_at_time(B,A),zero)
    ]]></literal>
    <literal><![CDATA[
      -constant(cardinality_at_time(B,A))
    ]]></literal>
    <literal><![CDATA[
      growth_rate(B,A) = zero
    ]]></literal>
    <justification jstring="[resolve(1,a,7,a)].">
      <j1 rule="resolve" parents="1 7"/>
    </justification>
  </clause>

  <clause id="36">
    <literal><![CDATA[
      -in_environment(c1,A)
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(B,c1,A)
    ]]></literal>
    <literal><![CDATA[
      -greater(cardinality_at_time(B,A),zero)
    ]]></literal>
    <literal><![CDATA[
      -increases(cardinality_at_time(B,A))
    ]]></literal>
    <literal><![CDATA[
      greater(growth_rate(B,A),zero)
    ]]></literal>
    <justification jstring="[resolve(1,a,8,a)].">
      <j1 rule="resolve" parents="1 8"/>
    </justification>
  </clause>

  <clause id="38">
    <literal><![CDATA[
      -subpopulations(first_movers,efficient_producers,c1,A)
    ]]></literal>
    <literal><![CDATA[
      greater(cardinality_at_time(first_movers,A),zero)
    ]]></literal>
    <justification jstring="[resolve(1,a,10,a)].">
      <j1 rule="resolve" parents="1 10"/>
    </justification>
  </clause>

  <clause id="39">
    <literal><![CDATA[
      -subpopulations(first_movers,efficient_producers,c1,A)
    ]]></literal>
    <literal><![CDATA[
      greater(cardinality_at_time(efficient_producers,A),zero)
    ]]></literal>
    <justification jstring="[resolve(1,a,11,a)].">
      <j1 rule="resolve" parents="1 11"/>
    </justification>
  </clause>

  <clause id="40">
    <literal><![CDATA[
      -subpopulations(first_movers,efficient_producers,c1,A)
    ]]></literal>
    <literal><![CDATA[
      in_environment(c1,A)
    ]]></literal>
    <justification jstring="[resolve(1,a,12,a)].">
      <j1 rule="resolve" parents="1 12"/>
    </justification>
  </clause>

  <clause id="56">
    <literal><![CDATA[
      greater(cardinality_at_time(first_movers,c2),zero)
    ]]></literal>
    <justification jstring="[resolve(38,a,22,a)].">
      <j1 rule="resolve" parents="38 22"/>
    </justification>
  </clause>

  <clause id="57">
    <literal><![CDATA[
      greater(cardinality_at_time(efficient_producers,c2),zero)
    ]]></literal>
    <justification jstring="[resolve(39,a,22,a)].">
      <j1 rule="resolve" parents="39 22"/>
    </justification>
  </clause>

  <clause id="58">
    <literal><![CDATA[
      in_environment(c1,c2)
    ]]></literal>
    <justification jstring="[resolve(40,a,22,a)].">
      <j1 rule="resolve" parents="40 22"/>
    </justification>
  </clause>

  <clause id="59">
    <literal><![CDATA[
      subpopulation(efficient_producers,c1,c2)
    ]]></literal>
    <justification jstring="[resolve(58,a,34,a)].">
      <j1 rule="resolve" parents="58 34"/>
    </justification>
  </clause>

  <clause id="60">
    <literal><![CDATA[
      subpopulation(first_movers,c1,c2)
    ]]></literal>
    <justification jstring="[resolve(58,a,33,a)].">
      <j1 rule="resolve" parents="58 33"/>
    </justification>
  </clause>

  <clause id="62">
    <literal><![CDATA[
      -increases(cardinality_at_time(efficient_producers,c2))
    ]]></literal>
    <justification jstring="[resolve(59,a,36,b),unit_del(a,58),unit_del(b,57),unit_del(d,26)].">
      <j1 rule="resolve" parents="59 36"/>
      <j2 rule="unit_del" parents="58"/>
      <j2 rule="unit_del" parents="57"/>
      <j2 rule="unit_del" parents="26"/>
    </justification>
  </clause>

  <clause id="65">
    <literal><![CDATA[
      -increases(cardinality_at_time(first_movers,c2))
    ]]></literal>
    <justification jstring="[resolve(60,a,36,b),unit_del(a,58),unit_del(b,56),unit_del(d,25)].">
      <j1 rule="resolve" parents="60 36"/>
      <j2 rule="unit_del" parents="58"/>
      <j2 rule="unit_del" parents="56"/>
      <j2 rule="unit_del" parents="25"/>
    </justification>
  </clause>

  <clause id="66">
    <literal><![CDATA[
      -constant(cardinality_at_time(first_movers,c2))
    ]]></literal>
    <justification jstring="[resolve(60,a,35,b),unit_del(a,58),unit_del(b,56),unit_del(d,24)].">
      <j1 rule="resolve" parents="60 35"/>
      <j2 rule="unit_del" parents="58"/>
      <j2 rule="unit_del" parents="56"/>
      <j2 rule="unit_del" parents="24"/>
    </justification>
  </clause>

  <clause id="72">
    <literal><![CDATA[
      number_of_organizations(c1,c2) != sum(cardinality_at_time(first_movers,c2),cardinality_at_time(efficient_producers,c2))
    ]]></literal>
    <justification jstring="[ur(15,a,23,a,b,66,a,c,65,a,e,62,a),flip(a)].">
      <j1 rule="ur" parents="15 23 66 65 62"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="73">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[ur(32,b,60,a,c,72,a),xx(a)].">
      <j1 rule="ur" parents="32 60 72"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="2" length="30" max_count="23">

<comments><![CDATA[
% Proof 1 at 0.01 (+ 0.00) seconds.
% Length of proof is 30.
% Level of proof is 6.
% Maximum clause weight is 21.
% Given clauses 47.
]]></comments>

  <clause id="1">
    <literal><![CDATA[
      environment(c1)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="4">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      first_movers != B
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(B,A,C)
    ]]></literal>
    <literal><![CDATA[
      sum(cardinality_at_time(first_movers,C),cardinality_at_time(efficient_producers,C)) = number_of_organizations(A,C)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="5">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -in_environment(A,B)
    ]]></literal>
    <literal><![CDATA[
      subpopulation(first_movers,A,B)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="7">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -in_environment(A,B)
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(C,A,B)
    ]]></literal>
    <literal><![CDATA[
      -greater(cardinality_at_time(C,B),zero)
    ]]></literal>
    <literal><![CDATA[
      -constant(cardinality_at_time(C,B))
    ]]></literal>
    <literal><![CDATA[
      growth_rate(C,B) = zero
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="8">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -in_environment(A,B)
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(C,A,B)
    ]]></literal>
    <literal><![CDATA[
      -greater(cardinality_at_time(C,B),zero)
    ]]></literal>
    <literal><![CDATA[
      -increases(cardinality_at_time(C,B))
    ]]></literal>
    <literal><![CDATA[
      greater(growth_rate(C,B),zero)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="9">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -in_environment(A,B)
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(C,A,B)
    ]]></literal>
    <literal><![CDATA[
      -greater(cardinality_at_time(C,B),zero)
    ]]></literal>
    <literal><![CDATA[
      -decreases(cardinality_at_time(C,B))
    ]]></literal>
    <literal><![CDATA[
      greater(zero,growth_rate(C,B))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="10">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -subpopulations(first_movers,efficient_producers,A,B)
    ]]></literal>
    <literal><![CDATA[
      greater(cardinality_at_time(first_movers,B),zero)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="12">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -subpopulations(first_movers,efficient_producers,A,B)
    ]]></literal>
    <literal><![CDATA[
      in_environment(A,B)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="14">
    <literal><![CDATA[
      -constant(A)
    ]]></literal>
    <literal><![CDATA[
      constant(B)
    ]]></literal>
    <literal><![CDATA[
      increases(B)
    ]]></literal>
    <literal><![CDATA[
      decreases(B)
    ]]></literal>
    <literal><![CDATA[
      sum(B,C) != A
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="22">
    <literal><![CDATA[
      subpopulations(first_movers,efficient_producers,c1,c2)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="23">
    <literal><![CDATA[
      constant(number_of_organizations(c1,c2))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="24">
    <literal><![CDATA[
      growth_rate(first_movers,c2) != zero
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="25">
    <literal><![CDATA[
      -greater(growth_rate(first_movers,c2),zero)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="26">
    <literal><![CDATA[
      -greater(zero,growth_rate(first_movers,c2))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="31">
    <literal><![CDATA[
      first_movers != A
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(A,c1,B)
    ]]></literal>
    <literal><![CDATA[
      sum(cardinality_at_time(first_movers,B),cardinality_at_time(efficient_producers,B)) = number_of_organizations(c1,B)
    ]]></literal>
    <justification jstring="[resolve(1,a,4,a)].">
      <j1 rule="resolve" parents="1 4"/>
    </justification>
  </clause>

  <clause id="32">
    <literal><![CDATA[
      first_movers != A
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(A,c1,B)
    ]]></literal>
    <literal><![CDATA[
      number_of_organizations(c1,B) = sum(cardinality_at_time(first_movers,B),cardinality_at_time(efficient_producers,B))
    ]]></literal>
    <justification jstring="[copy(31),flip(c)].">
      <j1 rule="copy" parents="31"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33">
    <literal><![CDATA[
      -in_environment(c1,A)
    ]]></literal>
    <literal><![CDATA[
      subpopulation(first_movers,c1,A)
    ]]></literal>
    <justification jstring="[resolve(1,a,5,a)].">
      <j1 rule="resolve" parents="1 5"/>
    </justification>
  </clause>

  <clause id="35">
    <literal><![CDATA[
      -in_environment(c1,A)
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(B,c1,A)
    ]]></literal>
    <literal><![CDATA[
      -greater(cardinality_at_time(B,A),zero)
    ]]></literal>
    <literal><![CDATA[
      -constant(cardinality_at_time(B,A))
    ]]></literal>
    <literal><![CDATA[
      growth_rate(B,A) = zero
    ]]></literal>
    <justification jstring="[resolve(1,a,7,a)].">
      <j1 rule="resolve" parents="1 7"/>
    </justification>
  </clause>

  <clause id="36">
    <literal><![CDATA[
      -in_environment(c1,A)
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(B,c1,A)
    ]]></literal>
    <literal><![CDATA[
      -greater(cardinality_at_time(B,A),zero)
    ]]></literal>
    <literal><![CDATA[
      -increases(cardinality_at_time(B,A))
    ]]></literal>
    <literal><![CDATA[
      greater(growth_rate(B,A),zero)
    ]]></literal>
    <justification jstring="[resolve(1,a,8,a)].">
      <j1 rule="resolve" parents="1 8"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      -in_environment(c1,A)
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(B,c1,A)
    ]]></literal>
    <literal><![CDATA[
      -greater(cardinality_at_time(B,A),zero)
    ]]></literal>
    <literal><![CDATA[
      -decreases(cardinality_at_time(B,A))
    ]]></literal>
    <literal><![CDATA[
      greater(zero,growth_rate(B,A))
    ]]></literal>
    <justification jstring="[resolve(1,a,9,a)].">
      <j1 rule="resolve" parents="1 9"/>
    </justification>
  </clause>

  <clause id="38">
    <literal><![CDATA[
      -subpopulations(first_movers,efficient_producers,c1,A)
    ]]></literal>
    <literal><![CDATA[
      greater(cardinality_at_time(first_movers,A),zero)
    ]]></literal>
    <justification jstring="[resolve(1,a,10,a)].">
      <j1 rule="resolve" parents="1 10"/>
    </justification>
  </clause>

  <clause id="40">
    <literal><![CDATA[
      -subpopulations(first_movers,efficient_producers,c1,A)
    ]]></literal>
    <literal><![CDATA[
      in_environment(c1,A)
    ]]></literal>
    <justification jstring="[resolve(1,a,12,a)].">
      <j1 rule="resolve" parents="1 12"/>
    </justification>
  </clause>

  <clause id="56">
    <literal><![CDATA[
      greater(cardinality_at_time(first_movers,c2),zero)
    ]]></literal>
    <justification jstring="[resolve(38,a,22,a)].">
      <j1 rule="resolve" parents="38 22"/>
    </justification>
  </clause>

  <clause id="58">
    <literal><![CDATA[
      in_environment(c1,c2)
    ]]></literal>
    <justification jstring="[resolve(40,a,22,a)].">
      <j1 rule="resolve" parents="40 22"/>
    </justification>
  </clause>

  <clause id="60">
    <literal><![CDATA[
      subpopulation(first_movers,c1,c2)
    ]]></literal>
    <justification jstring="[resolve(58,a,33,a)].">
      <j1 rule="resolve" parents="58 33"/>
    </justification>
  </clause>

  <clause id="64">
    <literal><![CDATA[
      -decreases(cardinality_at_time(first_movers,c2))
    ]]></literal>
    <justification jstring="[resolve(60,a,37,b),unit_del(a,58),unit_del(b,56),unit_del(d,26)].">
      <j1 rule="resolve" parents="60 37"/>
      <j2 rule="unit_del" parents="58"/>
      <j2 rule="unit_del" parents="56"/>
      <j2 rule="unit_del" parents="26"/>
    </justification>
  </clause>

  <clause id="65">
    <literal><![CDATA[
      -increases(cardinality_at_time(first_movers,c2))
    ]]></literal>
    <justification jstring="[resolve(60,a,36,b),unit_del(a,58),unit_del(b,56),unit_del(d,25)].">
      <j1 rule="resolve" parents="60 36"/>
      <j2 rule="unit_del" parents="58"/>
      <j2 rule="unit_del" parents="56"/>
      <j2 rule="unit_del" parents="25"/>
    </justification>
  </clause>

  <clause id="66">
    <literal><![CDATA[
      -constant(cardinality_at_time(first_movers,c2))
    ]]></literal>
    <justification jstring="[resolve(60,a,35,b),unit_del(a,58),unit_del(b,56),unit_del(d,24)].">
      <j1 rule="resolve" parents="60 35"/>
      <j2 rule="unit_del" parents="58"/>
      <j2 rule="unit_del" parents="56"/>
      <j2 rule="unit_del" parents="24"/>
    </justification>
  </clause>

  <clause id="72">
    <literal><![CDATA[
      sum(cardinality_at_time(first_movers,c2),A) != number_of_organizations(c1,c2)
    ]]></literal>
    <justification jstring="[ur(14,a,23,a,b,66,a,c,65,a,d,64,a)].">
      <j1 rule="ur" parents="14 23 66 65 64"/>
    </justification>
  </clause>

  <clause id="73">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[ur(32,b,60,a,c,72,a(flip)),xx(a)].">
      <j1 rule="ur" parents="32 60 72"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="3" length="36" max_count="23">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 36.
% Level of proof is 6.
% Maximum clause weight is 21.
% Given clauses 47.
]]></comments>

  <clause id="1">
    <literal><![CDATA[
      environment(c1)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="4">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      first_movers != B
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(B,A,C)
    ]]></literal>
    <literal><![CDATA[
      sum(cardinality_at_time(first_movers,C),cardinality_at_time(efficient_producers,C)) = number_of_organizations(A,C)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="5">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -in_environment(A,B)
    ]]></literal>
    <literal><![CDATA[
      subpopulation(first_movers,A,B)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="6">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -in_environment(A,B)
    ]]></literal>
    <literal><![CDATA[
      subpopulation(efficient_producers,A,B)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="7">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -in_environment(A,B)
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(C,A,B)
    ]]></literal>
    <literal><![CDATA[
      -greater(cardinality_at_time(C,B),zero)
    ]]></literal>
    <literal><![CDATA[
      -constant(cardinality_at_time(C,B))
    ]]></literal>
    <literal><![CDATA[
      growth_rate(C,B) = zero
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="8">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -in_environment(A,B)
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(C,A,B)
    ]]></literal>
    <literal><![CDATA[
      -greater(cardinality_at_time(C,B),zero)
    ]]></literal>
    <literal><![CDATA[
      -increases(cardinality_at_time(C,B))
    ]]></literal>
    <literal><![CDATA[
      greater(growth_rate(C,B),zero)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="9">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -in_environment(A,B)
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(C,A,B)
    ]]></literal>
    <literal><![CDATA[
      -greater(cardinality_at_time(C,B),zero)
    ]]></literal>
    <literal><![CDATA[
      -decreases(cardinality_at_time(C,B))
    ]]></literal>
    <literal><![CDATA[
      greater(zero,growth_rate(C,B))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="10">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -subpopulations(first_movers,efficient_producers,A,B)
    ]]></literal>
    <literal><![CDATA[
      greater(cardinality_at_time(first_movers,B),zero)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="11">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -subpopulations(first_movers,efficient_producers,A,B)
    ]]></literal>
    <literal><![CDATA[
      greater(cardinality_at_time(efficient_producers,B),zero)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="12">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -subpopulations(first_movers,efficient_producers,A,B)
    ]]></literal>
    <literal><![CDATA[
      in_environment(A,B)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="17">
    <literal><![CDATA[
      -constant(A)
    ]]></literal>
    <literal><![CDATA[
      constant(B)
    ]]></literal>
    <literal><![CDATA[
      sum(B,C) != A
    ]]></literal>
    <literal><![CDATA[
      decreases(C)
    ]]></literal>
    <literal><![CDATA[
      increases(C)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="22">
    <literal><![CDATA[
      subpopulations(first_movers,efficient_producers,c1,c2)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="23">
    <literal><![CDATA[
      constant(number_of_organizations(c1,c2))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="24">
    <literal><![CDATA[
      growth_rate(first_movers,c2) != zero
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="25">
    <literal><![CDATA[
      -greater(zero,growth_rate(efficient_producers,c2))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="26">
    <literal><![CDATA[
      -greater(growth_rate(efficient_producers,c2),zero)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="31">
    <literal><![CDATA[
      first_movers != A
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(A,c1,B)
    ]]></literal>
    <literal><![CDATA[
      sum(cardinality_at_time(first_movers,B),cardinality_at_time(efficient_producers,B)) = number_of_organizations(c1,B)
    ]]></literal>
    <justification jstring="[resolve(1,a,4,a)].">
      <j1 rule="resolve" parents="1 4"/>
    </justification>
  </clause>

  <clause id="32">
    <literal><![CDATA[
      first_movers != A
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(A,c1,B)
    ]]></literal>
    <literal><![CDATA[
      number_of_organizations(c1,B) = sum(cardinality_at_time(first_movers,B),cardinality_at_time(efficient_producers,B))
    ]]></literal>
    <justification jstring="[copy(31),flip(c)].">
      <j1 rule="copy" parents="31"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33">
    <literal><![CDATA[
      -in_environment(c1,A)
    ]]></literal>
    <literal><![CDATA[
      subpopulation(first_movers,c1,A)
    ]]></literal>
    <justification jstring="[resolve(1,a,5,a)].">
      <j1 rule="resolve" parents="1 5"/>
    </justification>
  </clause>

  <clause id="34">
    <literal><![CDATA[
      -in_environment(c1,A)
    ]]></literal>
    <literal><![CDATA[
      subpopulation(efficient_producers,c1,A)
    ]]></literal>
    <justification jstring="[resolve(1,a,6,a)].">
      <j1 rule="resolve" parents="1 6"/>
    </justification>
  </clause>

  <clause id="35">
    <literal><![CDATA[
      -in_environment(c1,A)
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(B,c1,A)
    ]]></literal>
    <literal><![CDATA[
      -greater(cardinality_at_time(B,A),zero)
    ]]></literal>
    <literal><![CDATA[
      -constant(cardinality_at_time(B,A))
    ]]></literal>
    <literal><![CDATA[
      growth_rate(B,A) = zero
    ]]></literal>
    <justification jstring="[resolve(1,a,7,a)].">
      <j1 rule="resolve" parents="1 7"/>
    </justification>
  </clause>

  <clause id="36">
    <literal><![CDATA[
      -in_environment(c1,A)
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(B,c1,A)
    ]]></literal>
    <literal><![CDATA[
      -greater(cardinality_at_time(B,A),zero)
    ]]></literal>
    <literal><![CDATA[
      -increases(cardinality_at_time(B,A))
    ]]></literal>
    <literal><![CDATA[
      greater(growth_rate(B,A),zero)
    ]]></literal>
    <justification jstring="[resolve(1,a,8,a)].">
      <j1 rule="resolve" parents="1 8"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      -in_environment(c1,A)
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(B,c1,A)
    ]]></literal>
    <literal><![CDATA[
      -greater(cardinality_at_time(B,A),zero)
    ]]></literal>
    <literal><![CDATA[
      -decreases(cardinality_at_time(B,A))
    ]]></literal>
    <literal><![CDATA[
      greater(zero,growth_rate(B,A))
    ]]></literal>
    <justification jstring="[resolve(1,a,9,a)].">
      <j1 rule="resolve" parents="1 9"/>
    </justification>
  </clause>

  <clause id="38">
    <literal><![CDATA[
      -subpopulations(first_movers,efficient_producers,c1,A)
    ]]></literal>
    <literal><![CDATA[
      greater(cardinality_at_time(first_movers,A),zero)
    ]]></literal>
    <justification jstring="[resolve(1,a,10,a)].">
      <j1 rule="resolve" parents="1 10"/>
    </justification>
  </clause>

  <clause id="39">
    <literal><![CDATA[
      -subpopulations(first_movers,efficient_producers,c1,A)
    ]]></literal>
    <literal><![CDATA[
      greater(cardinality_at_time(efficient_producers,A),zero)
    ]]></literal>
    <justification jstring="[resolve(1,a,11,a)].">
      <j1 rule="resolve" parents="1 11"/>
    </justification>
  </clause>

  <clause id="40">
    <literal><![CDATA[
      -subpopulations(first_movers,efficient_producers,c1,A)
    ]]></literal>
    <literal><![CDATA[
      in_environment(c1,A)
    ]]></literal>
    <justification jstring="[resolve(1,a,12,a)].">
      <j1 rule="resolve" parents="1 12"/>
    </justification>
  </clause>

  <clause id="56">
    <literal><![CDATA[
      greater(cardinality_at_time(first_movers,c2),zero)
    ]]></literal>
    <justification jstring="[resolve(38,a,22,a)].">
      <j1 rule="resolve" parents="38 22"/>
    </justification>
  </clause>

  <clause id="57">
    <literal><![CDATA[
      greater(cardinality_at_time(efficient_producers,c2),zero)
    ]]></literal>
    <justification jstring="[resolve(39,a,22,a)].">
      <j1 rule="resolve" parents="39 22"/>
    </justification>
  </clause>

  <clause id="58">
    <literal><![CDATA[
      in_environment(c1,c2)
    ]]></literal>
    <justification jstring="[resolve(40,a,22,a)].">
      <j1 rule="resolve" parents="40 22"/>
    </justification>
  </clause>

  <clause id="59">
    <literal><![CDATA[
      subpopulation(efficient_producers,c1,c2)
    ]]></literal>
    <justification jstring="[resolve(58,a,34,a)].">
      <j1 rule="resolve" parents="58 34"/>
    </justification>
  </clause>

  <clause id="60">
    <literal><![CDATA[
      subpopulation(first_movers,c1,c2)
    ]]></literal>
    <justification jstring="[resolve(58,a,33,a)].">
      <j1 rule="resolve" parents="58 33"/>
    </justification>
  </clause>

  <clause id="61">
    <literal><![CDATA[
      -decreases(cardinality_at_time(efficient_producers,c2))
    ]]></literal>
    <justification jstring="[resolve(59,a,37,b),unit_del(a,58),unit_del(b,57),unit_del(d,25)].">
      <j1 rule="resolve" parents="59 37"/>
      <j2 rule="unit_del" parents="58"/>
      <j2 rule="unit_del" parents="57"/>
      <j2 rule="unit_del" parents="25"/>
    </justification>
  </clause>

  <clause id="62">
    <literal><![CDATA[
      -increases(cardinality_at_time(efficient_producers,c2))
    ]]></literal>
    <justification jstring="[resolve(59,a,36,b),unit_del(a,58),unit_del(b,57),unit_del(d,26)].">
      <j1 rule="resolve" parents="59 36"/>
      <j2 rule="unit_del" parents="58"/>
      <j2 rule="unit_del" parents="57"/>
      <j2 rule="unit_del" parents="26"/>
    </justification>
  </clause>

  <clause id="66">
    <literal><![CDATA[
      -constant(cardinality_at_time(first_movers,c2))
    ]]></literal>
    <justification jstring="[resolve(60,a,35,b),unit_del(a,58),unit_del(b,56),unit_del(d,24)].">
      <j1 rule="resolve" parents="60 35"/>
      <j2 rule="unit_del" parents="58"/>
      <j2 rule="unit_del" parents="56"/>
      <j2 rule="unit_del" parents="24"/>
    </justification>
  </clause>

  <clause id="70">
    <literal><![CDATA[
      number_of_organizations(c1,c2) != sum(cardinality_at_time(first_movers,c2),cardinality_at_time(efficient_producers,c2))
    ]]></literal>
    <justification jstring="[ur(17,a,23,a,b,66,a,d,61,a,e,62,a),flip(a)].">
      <j1 rule="ur" parents="17 23 66 61 62"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="79">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[ur(32,b,60,a,c,70,a),xx(a)].">
      <j1 rule="ur" parents="32 60 70"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="4" length="34" max_count="23">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 34.
% Level of proof is 6.
% Maximum clause weight is 21.
% Given clauses 52.
]]></comments>

  <clause id="1">
    <literal><![CDATA[
      environment(c1)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="4">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      first_movers != B
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(B,A,C)
    ]]></literal>
    <literal><![CDATA[
      sum(cardinality_at_time(first_movers,C),cardinality_at_time(efficient_producers,C)) = number_of_organizations(A,C)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="5">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -in_environment(A,B)
    ]]></literal>
    <literal><![CDATA[
      subpopulation(first_movers,A,B)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="6">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -in_environment(A,B)
    ]]></literal>
    <literal><![CDATA[
      subpopulation(efficient_producers,A,B)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="7">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -in_environment(A,B)
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(C,A,B)
    ]]></literal>
    <literal><![CDATA[
      -greater(cardinality_at_time(C,B),zero)
    ]]></literal>
    <literal><![CDATA[
      -constant(cardinality_at_time(C,B))
    ]]></literal>
    <literal><![CDATA[
      growth_rate(C,B) = zero
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="9">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -in_environment(A,B)
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(C,A,B)
    ]]></literal>
    <literal><![CDATA[
      -greater(cardinality_at_time(C,B),zero)
    ]]></literal>
    <literal><![CDATA[
      -decreases(cardinality_at_time(C,B))
    ]]></literal>
    <literal><![CDATA[
      greater(zero,growth_rate(C,B))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="10">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -subpopulations(first_movers,efficient_producers,A,B)
    ]]></literal>
    <literal><![CDATA[
      greater(cardinality_at_time(first_movers,B),zero)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="11">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -subpopulations(first_movers,efficient_producers,A,B)
    ]]></literal>
    <literal><![CDATA[
      greater(cardinality_at_time(efficient_producers,B),zero)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="12">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -subpopulations(first_movers,efficient_producers,A,B)
    ]]></literal>
    <literal><![CDATA[
      in_environment(A,B)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="16">
    <literal><![CDATA[
      -constant(A)
    ]]></literal>
    <literal><![CDATA[
      constant(B)
    ]]></literal>
    <literal><![CDATA[
      decreases(B)
    ]]></literal>
    <literal><![CDATA[
      sum(B,C) != A
    ]]></literal>
    <literal><![CDATA[
      decreases(C)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="22">
    <literal><![CDATA[
      subpopulations(first_movers,efficient_producers,c1,c2)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="23">
    <literal><![CDATA[
      constant(number_of_organizations(c1,c2))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="24">
    <literal><![CDATA[
      growth_rate(first_movers,c2) != zero
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="25">
    <literal><![CDATA[
      -greater(zero,growth_rate(efficient_producers,c2))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="26">
    <literal><![CDATA[
      -greater(zero,growth_rate(first_movers,c2))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="31">
    <literal><![CDATA[
      first_movers != A
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(A,c1,B)
    ]]></literal>
    <literal><![CDATA[
      sum(cardinality_at_time(first_movers,B),cardinality_at_time(efficient_producers,B)) = number_of_organizations(c1,B)
    ]]></literal>
    <justification jstring="[resolve(1,a,4,a)].">
      <j1 rule="resolve" parents="1 4"/>
    </justification>
  </clause>

  <clause id="32">
    <literal><![CDATA[
      first_movers != A
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(A,c1,B)
    ]]></literal>
    <literal><![CDATA[
      number_of_organizations(c1,B) = sum(cardinality_at_time(first_movers,B),cardinality_at_time(efficient_producers,B))
    ]]></literal>
    <justification jstring="[copy(31),flip(c)].">
      <j1 rule="copy" parents="31"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33">
    <literal><![CDATA[
      -in_environment(c1,A)
    ]]></literal>
    <literal><![CDATA[
      subpopulation(first_movers,c1,A)
    ]]></literal>
    <justification jstring="[resolve(1,a,5,a)].">
      <j1 rule="resolve" parents="1 5"/>
    </justification>
  </clause>

  <clause id="34">
    <literal><![CDATA[
      -in_environment(c1,A)
    ]]></literal>
    <literal><![CDATA[
      subpopulation(efficient_producers,c1,A)
    ]]></literal>
    <justification jstring="[resolve(1,a,6,a)].">
      <j1 rule="resolve" parents="1 6"/>
    </justification>
  </clause>

  <clause id="35">
    <literal><![CDATA[
      -in_environment(c1,A)
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(B,c1,A)
    ]]></literal>
    <literal><![CDATA[
      -greater(cardinality_at_time(B,A),zero)
    ]]></literal>
    <literal><![CDATA[
      -constant(cardinality_at_time(B,A))
    ]]></literal>
    <literal><![CDATA[
      growth_rate(B,A) = zero
    ]]></literal>
    <justification jstring="[resolve(1,a,7,a)].">
      <j1 rule="resolve" parents="1 7"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      -in_environment(c1,A)
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(B,c1,A)
    ]]></literal>
    <literal><![CDATA[
      -greater(cardinality_at_time(B,A),zero)
    ]]></literal>
    <literal><![CDATA[
      -decreases(cardinality_at_time(B,A))
    ]]></literal>
    <literal><![CDATA[
      greater(zero,growth_rate(B,A))
    ]]></literal>
    <justification jstring="[resolve(1,a,9,a)].">
      <j1 rule="resolve" parents="1 9"/>
    </justification>
  </clause>

  <clause id="38">
    <literal><![CDATA[
      -subpopulations(first_movers,efficient_producers,c1,A)
    ]]></literal>
    <literal><![CDATA[
      greater(cardinality_at_time(first_movers,A),zero)
    ]]></literal>
    <justification jstring="[resolve(1,a,10,a)].">
      <j1 rule="resolve" parents="1 10"/>
    </justification>
  </clause>

  <clause id="39">
    <literal><![CDATA[
      -subpopulations(first_movers,efficient_producers,c1,A)
    ]]></literal>
    <literal><![CDATA[
      greater(cardinality_at_time(efficient_producers,A),zero)
    ]]></literal>
    <justification jstring="[resolve(1,a,11,a)].">
      <j1 rule="resolve" parents="1 11"/>
    </justification>
  </clause>

  <clause id="40">
    <literal><![CDATA[
      -subpopulations(first_movers,efficient_producers,c1,A)
    ]]></literal>
    <literal><![CDATA[
      in_environment(c1,A)
    ]]></literal>
    <justification jstring="[resolve(1,a,12,a)].">
      <j1 rule="resolve" parents="1 12"/>
    </justification>
  </clause>

  <clause id="56">
    <literal><![CDATA[
      greater(cardinality_at_time(first_movers,c2),zero)
    ]]></literal>
    <justification jstring="[resolve(38,a,22,a)].">
      <j1 rule="resolve" parents="38 22"/>
    </justification>
  </clause>

  <clause id="57">
    <literal><![CDATA[
      greater(cardinality_at_time(efficient_producers,c2),zero)
    ]]></literal>
    <justification jstring="[resolve(39,a,22,a)].">
      <j1 rule="resolve" parents="39 22"/>
    </justification>
  </clause>

  <clause id="58">
    <literal><![CDATA[
      in_environment(c1,c2)
    ]]></literal>
    <justification jstring="[resolve(40,a,22,a)].">
      <j1 rule="resolve" parents="40 22"/>
    </justification>
  </clause>

  <clause id="59">
    <literal><![CDATA[
      subpopulation(efficient_producers,c1,c2)
    ]]></literal>
    <justification jstring="[resolve(58,a,34,a)].">
      <j1 rule="resolve" parents="58 34"/>
    </justification>
  </clause>

  <clause id="60">
    <literal><![CDATA[
      subpopulation(first_movers,c1,c2)
    ]]></literal>
    <justification jstring="[resolve(58,a,33,a)].">
      <j1 rule="resolve" parents="58 33"/>
    </justification>
  </clause>

  <clause id="61">
    <literal><![CDATA[
      -decreases(cardinality_at_time(efficient_producers,c2))
    ]]></literal>
    <justification jstring="[resolve(59,a,37,b),unit_del(a,58),unit_del(b,57),unit_del(d,25)].">
      <j1 rule="resolve" parents="59 37"/>
      <j2 rule="unit_del" parents="58"/>
      <j2 rule="unit_del" parents="57"/>
      <j2 rule="unit_del" parents="25"/>
    </justification>
  </clause>

  <clause id="64">
    <literal><![CDATA[
      -decreases(cardinality_at_time(first_movers,c2))
    ]]></literal>
    <justification jstring="[resolve(60,a,37,b),unit_del(a,58),unit_del(b,56),unit_del(d,26)].">
      <j1 rule="resolve" parents="60 37"/>
      <j2 rule="unit_del" parents="58"/>
      <j2 rule="unit_del" parents="56"/>
      <j2 rule="unit_del" parents="26"/>
    </justification>
  </clause>

  <clause id="66">
    <literal><![CDATA[
      -constant(cardinality_at_time(first_movers,c2))
    ]]></literal>
    <justification jstring="[resolve(60,a,35,b),unit_del(a,58),unit_del(b,56),unit_del(d,24)].">
      <j1 rule="resolve" parents="60 35"/>
      <j2 rule="unit_del" parents="58"/>
      <j2 rule="unit_del" parents="56"/>
      <j2 rule="unit_del" parents="24"/>
    </justification>
  </clause>

  <clause id="72">
    <literal><![CDATA[
      number_of_organizations(c1,c2) != sum(cardinality_at_time(first_movers,c2),cardinality_at_time(efficient_producers,c2))
    ]]></literal>
    <justification jstring="[ur(16,a,23,a,b,66,a,c,64,a,e,61,a),flip(a)].">
      <j1 rule="ur" parents="16 23 66 64 61"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="73">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[ur(32,b,60,a,c,72,a),xx(a)].">
      <j1 rule="ur" parents="32 60 72"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="5" length="34" max_count="23">

<comments><![CDATA[
% Proof 1 at 0.01 (+ 0.00) seconds.
% Length of proof is 34.
% Level of proof is 6.
% Maximum clause weight is 21.
% Given clauses 48.
]]></comments>

  <clause id="1">
    <literal><![CDATA[
      environment(c1)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="4">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      first_movers != B
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(B,A,C)
    ]]></literal>
    <literal><![CDATA[
      sum(cardinality_at_time(first_movers,C),cardinality_at_time(efficient_producers,C)) = number_of_organizations(A,C)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="5">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -in_environment(A,B)
    ]]></literal>
    <literal><![CDATA[
      subpopulation(first_movers,A,B)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="6">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -in_environment(A,B)
    ]]></literal>
    <literal><![CDATA[
      subpopulation(efficient_producers,A,B)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="7">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -in_environment(A,B)
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(C,A,B)
    ]]></literal>
    <literal><![CDATA[
      -greater(cardinality_at_time(C,B),zero)
    ]]></literal>
    <literal><![CDATA[
      -constant(cardinality_at_time(C,B))
    ]]></literal>
    <literal><![CDATA[
      growth_rate(C,B) = zero
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="8">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -in_environment(A,B)
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(C,A,B)
    ]]></literal>
    <literal><![CDATA[
      -greater(cardinality_at_time(C,B),zero)
    ]]></literal>
    <literal><![CDATA[
      -increases(cardinality_at_time(C,B))
    ]]></literal>
    <literal><![CDATA[
      greater(growth_rate(C,B),zero)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="10">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -subpopulations(first_movers,efficient_producers,A,B)
    ]]></literal>
    <literal><![CDATA[
      greater(cardinality_at_time(first_movers,B),zero)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="11">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -subpopulations(first_movers,efficient_producers,A,B)
    ]]></literal>
    <literal><![CDATA[
      greater(cardinality_at_time(efficient_producers,B),zero)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="12">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -subpopulations(first_movers,efficient_producers,A,B)
    ]]></literal>
    <literal><![CDATA[
      in_environment(A,B)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="19">
    <literal><![CDATA[
      -constant(A)
    ]]></literal>
    <literal><![CDATA[
      increases(B)
    ]]></literal>
    <literal><![CDATA[
      sum(B,C) != A
    ]]></literal>
    <literal><![CDATA[
      constant(C)
    ]]></literal>
    <literal><![CDATA[
      increases(C)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="22">
    <literal><![CDATA[
      subpopulations(first_movers,efficient_producers,c1,c2)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="23">
    <literal><![CDATA[
      constant(number_of_organizations(c1,c2))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="24">
    <literal><![CDATA[
      growth_rate(efficient_producers,c2) != zero
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="25">
    <literal><![CDATA[
      -greater(growth_rate(first_movers,c2),zero)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="26">
    <literal><![CDATA[
      -greater(growth_rate(efficient_producers,c2),zero)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="31">
    <literal><![CDATA[
      first_movers != A
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(A,c1,B)
    ]]></literal>
    <literal><![CDATA[
      sum(cardinality_at_time(first_movers,B),cardinality_at_time(efficient_producers,B)) = number_of_organizations(c1,B)
    ]]></literal>
    <justification jstring="[resolve(1,a,4,a)].">
      <j1 rule="resolve" parents="1 4"/>
    </justification>
  </clause>

  <clause id="32">
    <literal><![CDATA[
      first_movers != A
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(A,c1,B)
    ]]></literal>
    <literal><![CDATA[
      number_of_organizations(c1,B) = sum(cardinality_at_time(first_movers,B),cardinality_at_time(efficient_producers,B))
    ]]></literal>
    <justification jstring="[copy(31),flip(c)].">
      <j1 rule="copy" parents="31"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33">
    <literal><![CDATA[
      -in_environment(c1,A)
    ]]></literal>
    <literal><![CDATA[
      subpopulation(first_movers,c1,A)
    ]]></literal>
    <justification jstring="[resolve(1,a,5,a)].">
      <j1 rule="resolve" parents="1 5"/>
    </justification>
  </clause>

  <clause id="34">
    <literal><![CDATA[
      -in_environment(c1,A)
    ]]></literal>
    <literal><![CDATA[
      subpopulation(efficient_producers,c1,A)
    ]]></literal>
    <justification jstring="[resolve(1,a,6,a)].">
      <j1 rule="resolve" parents="1 6"/>
    </justification>
  </clause>

  <clause id="35">
    <literal><![CDATA[
      -in_environment(c1,A)
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(B,c1,A)
    ]]></literal>
    <literal><![CDATA[
      -greater(cardinality_at_time(B,A),zero)
    ]]></literal>
    <literal><![CDATA[
      -constant(cardinality_at_time(B,A))
    ]]></literal>
    <literal><![CDATA[
      growth_rate(B,A) = zero
    ]]></literal>
    <justification jstring="[resolve(1,a,7,a)].">
      <j1 rule="resolve" parents="1 7"/>
    </justification>
  </clause>

  <clause id="36">
    <literal><![CDATA[
      -in_environment(c1,A)
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(B,c1,A)
    ]]></literal>
    <literal><![CDATA[
      -greater(cardinality_at_time(B,A),zero)
    ]]></literal>
    <literal><![CDATA[
      -increases(cardinality_at_time(B,A))
    ]]></literal>
    <literal><![CDATA[
      greater(growth_rate(B,A),zero)
    ]]></literal>
    <justification jstring="[resolve(1,a,8,a)].">
      <j1 rule="resolve" parents="1 8"/>
    </justification>
  </clause>

  <clause id="38">
    <literal><![CDATA[
      -subpopulations(first_movers,efficient_producers,c1,A)
    ]]></literal>
    <literal><![CDATA[
      greater(cardinality_at_time(first_movers,A),zero)
    ]]></literal>
    <justification jstring="[resolve(1,a,10,a)].">
      <j1 rule="resolve" parents="1 10"/>
    </justification>
  </clause>

  <clause id="39">
    <literal><![CDATA[
      -subpopulations(first_movers,efficient_producers,c1,A)
    ]]></literal>
    <literal><![CDATA[
      greater(cardinality_at_time(efficient_producers,A),zero)
    ]]></literal>
    <justification jstring="[resolve(1,a,11,a)].">
      <j1 rule="resolve" parents="1 11"/>
    </justification>
  </clause>

  <clause id="40">
    <literal><![CDATA[
      -subpopulations(first_movers,efficient_producers,c1,A)
    ]]></literal>
    <literal><![CDATA[
      in_environment(c1,A)
    ]]></literal>
    <justification jstring="[resolve(1,a,12,a)].">
      <j1 rule="resolve" parents="1 12"/>
    </justification>
  </clause>

  <clause id="56">
    <literal><![CDATA[
      greater(cardinality_at_time(first_movers,c2),zero)
    ]]></literal>
    <justification jstring="[resolve(38,a,22,a)].">
      <j1 rule="resolve" parents="38 22"/>
    </justification>
  </clause>

  <clause id="57">
    <literal><![CDATA[
      greater(cardinality_at_time(efficient_producers,c2),zero)
    ]]></literal>
    <justification jstring="[resolve(39,a,22,a)].">
      <j1 rule="resolve" parents="39 22"/>
    </justification>
  </clause>

  <clause id="58">
    <literal><![CDATA[
      in_environment(c1,c2)
    ]]></literal>
    <justification jstring="[resolve(40,a,22,a)].">
      <j1 rule="resolve" parents="40 22"/>
    </justification>
  </clause>

  <clause id="59">
    <literal><![CDATA[
      subpopulation(efficient_producers,c1,c2)
    ]]></literal>
    <justification jstring="[resolve(58,a,34,a)].">
      <j1 rule="resolve" parents="58 34"/>
    </justification>
  </clause>

  <clause id="60">
    <literal><![CDATA[
      subpopulation(first_movers,c1,c2)
    ]]></literal>
    <justification jstring="[resolve(58,a,33,a)].">
      <j1 rule="resolve" parents="58 33"/>
    </justification>
  </clause>

  <clause id="62">
    <literal><![CDATA[
      -increases(cardinality_at_time(efficient_producers,c2))
    ]]></literal>
    <justification jstring="[resolve(59,a,36,b),unit_del(a,58),unit_del(b,57),unit_del(d,26)].">
      <j1 rule="resolve" parents="59 36"/>
      <j2 rule="unit_del" parents="58"/>
      <j2 rule="unit_del" parents="57"/>
      <j2 rule="unit_del" parents="26"/>
    </justification>
  </clause>

  <clause id="63">
    <literal><![CDATA[
      -constant(cardinality_at_time(efficient_producers,c2))
    ]]></literal>
    <justification jstring="[resolve(59,a,35,b),unit_del(a,58),unit_del(b,57),unit_del(d,24)].">
      <j1 rule="resolve" parents="59 35"/>
      <j2 rule="unit_del" parents="58"/>
      <j2 rule="unit_del" parents="57"/>
      <j2 rule="unit_del" parents="24"/>
    </justification>
  </clause>

  <clause id="65">
    <literal><![CDATA[
      -increases(cardinality_at_time(first_movers,c2))
    ]]></literal>
    <justification jstring="[resolve(60,a,36,b),unit_del(a,58),unit_del(b,56),unit_del(d,25)].">
      <j1 rule="resolve" parents="60 36"/>
      <j2 rule="unit_del" parents="58"/>
      <j2 rule="unit_del" parents="56"/>
      <j2 rule="unit_del" parents="25"/>
    </justification>
  </clause>

  <clause id="71">
    <literal><![CDATA[
      number_of_organizations(c1,c2) != sum(cardinality_at_time(first_movers,c2),cardinality_at_time(efficient_producers,c2))
    ]]></literal>
    <justification jstring="[ur(19,a,23,a,b,65,a,d,63,a,e,62,a),flip(a)].">
      <j1 rule="ur" parents="19 23 65 63 62"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="73">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[ur(32,b,60,a,c,71,a),xx(a)].">
      <j1 rule="ur" parents="32 60 71"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="6" length="36" max_count="23">

<comments><![CDATA[
% Proof 1 at 0.01 (+ 0.00) seconds.
% Length of proof is 36.
% Level of proof is 6.
% Maximum clause weight is 21.
% Given clauses 43.
]]></comments>

  <clause id="1">
    <literal><![CDATA[
      environment(c1)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="4">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      first_movers != B
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(B,A,C)
    ]]></literal>
    <literal><![CDATA[
      sum(cardinality_at_time(first_movers,C),cardinality_at_time(efficient_producers,C)) = number_of_organizations(A,C)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="5">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -in_environment(A,B)
    ]]></literal>
    <literal><![CDATA[
      subpopulation(first_movers,A,B)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="6">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -in_environment(A,B)
    ]]></literal>
    <literal><![CDATA[
      subpopulation(efficient_producers,A,B)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="7">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -in_environment(A,B)
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(C,A,B)
    ]]></literal>
    <literal><![CDATA[
      -greater(cardinality_at_time(C,B),zero)
    ]]></literal>
    <literal><![CDATA[
      -constant(cardinality_at_time(C,B))
    ]]></literal>
    <literal><![CDATA[
      growth_rate(C,B) = zero
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="8">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -in_environment(A,B)
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(C,A,B)
    ]]></literal>
    <literal><![CDATA[
      -greater(cardinality_at_time(C,B),zero)
    ]]></literal>
    <literal><![CDATA[
      -increases(cardinality_at_time(C,B))
    ]]></literal>
    <literal><![CDATA[
      greater(growth_rate(C,B),zero)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="9">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -in_environment(A,B)
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(C,A,B)
    ]]></literal>
    <literal><![CDATA[
      -greater(cardinality_at_time(C,B),zero)
    ]]></literal>
    <literal><![CDATA[
      -decreases(cardinality_at_time(C,B))
    ]]></literal>
    <literal><![CDATA[
      greater(zero,growth_rate(C,B))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="10">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -subpopulations(first_movers,efficient_producers,A,B)
    ]]></literal>
    <literal><![CDATA[
      greater(cardinality_at_time(first_movers,B),zero)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="11">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -subpopulations(first_movers,efficient_producers,A,B)
    ]]></literal>
    <literal><![CDATA[
      greater(cardinality_at_time(efficient_producers,B),zero)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="12">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -subpopulations(first_movers,efficient_producers,A,B)
    ]]></literal>
    <literal><![CDATA[
      in_environment(A,B)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="18">
    <literal><![CDATA[
      -constant(A)
    ]]></literal>
    <literal><![CDATA[
      increases(B)
    ]]></literal>
    <literal><![CDATA[
      decreases(B)
    ]]></literal>
    <literal><![CDATA[
      sum(B,C) != A
    ]]></literal>
    <literal><![CDATA[
      constant(C)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="22">
    <literal><![CDATA[
      subpopulations(first_movers,efficient_producers,c1,c2)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="23">
    <literal><![CDATA[
      constant(number_of_organizations(c1,c2))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="24">
    <literal><![CDATA[
      growth_rate(efficient_producers,c2) != zero
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="25">
    <literal><![CDATA[
      -greater(growth_rate(first_movers,c2),zero)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="26">
    <literal><![CDATA[
      -greater(zero,growth_rate(first_movers,c2))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="31">
    <literal><![CDATA[
      first_movers != A
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(A,c1,B)
    ]]></literal>
    <literal><![CDATA[
      sum(cardinality_at_time(first_movers,B),cardinality_at_time(efficient_producers,B)) = number_of_organizations(c1,B)
    ]]></literal>
    <justification jstring="[resolve(1,a,4,a)].">
      <j1 rule="resolve" parents="1 4"/>
    </justification>
  </clause>

  <clause id="32">
    <literal><![CDATA[
      first_movers != A
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(A,c1,B)
    ]]></literal>
    <literal><![CDATA[
      number_of_organizations(c1,B) = sum(cardinality_at_time(first_movers,B),cardinality_at_time(efficient_producers,B))
    ]]></literal>
    <justification jstring="[copy(31),flip(c)].">
      <j1 rule="copy" parents="31"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33">
    <literal><![CDATA[
      -in_environment(c1,A)
    ]]></literal>
    <literal><![CDATA[
      subpopulation(first_movers,c1,A)
    ]]></literal>
    <justification jstring="[resolve(1,a,5,a)].">
      <j1 rule="resolve" parents="1 5"/>
    </justification>
  </clause>

  <clause id="34">
    <literal><![CDATA[
      -in_environment(c1,A)
    ]]></literal>
    <literal><![CDATA[
      subpopulation(efficient_producers,c1,A)
    ]]></literal>
    <justification jstring="[resolve(1,a,6,a)].">
      <j1 rule="resolve" parents="1 6"/>
    </justification>
  </clause>

  <clause id="35">
    <literal><![CDATA[
      -in_environment(c1,A)
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(B,c1,A)
    ]]></literal>
    <literal><![CDATA[
      -greater(cardinality_at_time(B,A),zero)
    ]]></literal>
    <literal><![CDATA[
      -constant(cardinality_at_time(B,A))
    ]]></literal>
    <literal><![CDATA[
      growth_rate(B,A) = zero
    ]]></literal>
    <justification jstring="[resolve(1,a,7,a)].">
      <j1 rule="resolve" parents="1 7"/>
    </justification>
  </clause>

  <clause id="36">
    <literal><![CDATA[
      -in_environment(c1,A)
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(B,c1,A)
    ]]></literal>
    <literal><![CDATA[
      -greater(cardinality_at_time(B,A),zero)
    ]]></literal>
    <literal><![CDATA[
      -increases(cardinality_at_time(B,A))
    ]]></literal>
    <literal><![CDATA[
      greater(growth_rate(B,A),zero)
    ]]></literal>
    <justification jstring="[resolve(1,a,8,a)].">
      <j1 rule="resolve" parents="1 8"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      -in_environment(c1,A)
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(B,c1,A)
    ]]></literal>
    <literal><![CDATA[
      -greater(cardinality_at_time(B,A),zero)
    ]]></literal>
    <literal><![CDATA[
      -decreases(cardinality_at_time(B,A))
    ]]></literal>
    <literal><![CDATA[
      greater(zero,growth_rate(B,A))
    ]]></literal>
    <justification jstring="[resolve(1,a,9,a)].">
      <j1 rule="resolve" parents="1 9"/>
    </justification>
  </clause>

  <clause id="38">
    <literal><![CDATA[
      -subpopulations(first_movers,efficient_producers,c1,A)
    ]]></literal>
    <literal><![CDATA[
      greater(cardinality_at_time(first_movers,A),zero)
    ]]></literal>
    <justification jstring="[resolve(1,a,10,a)].">
      <j1 rule="resolve" parents="1 10"/>
    </justification>
  </clause>

  <clause id="39">
    <literal><![CDATA[
      -subpopulations(first_movers,efficient_producers,c1,A)
    ]]></literal>
    <literal><![CDATA[
      greater(cardinality_at_time(efficient_producers,A),zero)
    ]]></literal>
    <justification jstring="[resolve(1,a,11,a)].">
      <j1 rule="resolve" parents="1 11"/>
    </justification>
  </clause>

  <clause id="40">
    <literal><![CDATA[
      -subpopulations(first_movers,efficient_producers,c1,A)
    ]]></literal>
    <literal><![CDATA[
      in_environment(c1,A)
    ]]></literal>
    <justification jstring="[resolve(1,a,12,a)].">
      <j1 rule="resolve" parents="1 12"/>
    </justification>
  </clause>

  <clause id="56">
    <literal><![CDATA[
      greater(cardinality_at_time(first_movers,c2),zero)
    ]]></literal>
    <justification jstring="[resolve(38,a,22,a)].">
      <j1 rule="resolve" parents="38 22"/>
    </justification>
  </clause>

  <clause id="57">
    <literal><![CDATA[
      greater(cardinality_at_time(efficient_producers,c2),zero)
    ]]></literal>
    <justification jstring="[resolve(39,a,22,a)].">
      <j1 rule="resolve" parents="39 22"/>
    </justification>
  </clause>

  <clause id="58">
    <literal><![CDATA[
      in_environment(c1,c2)
    ]]></literal>
    <justification jstring="[resolve(40,a,22,a)].">
      <j1 rule="resolve" parents="40 22"/>
    </justification>
  </clause>

  <clause id="59">
    <literal><![CDATA[
      subpopulation(efficient_producers,c1,c2)
    ]]></literal>
    <justification jstring="[resolve(58,a,34,a)].">
      <j1 rule="resolve" parents="58 34"/>
    </justification>
  </clause>

  <clause id="60">
    <literal><![CDATA[
      subpopulation(first_movers,c1,c2)
    ]]></literal>
    <justification jstring="[resolve(58,a,33,a)].">
      <j1 rule="resolve" parents="58 33"/>
    </justification>
  </clause>

  <clause id="63">
    <literal><![CDATA[
      -constant(cardinality_at_time(efficient_producers,c2))
    ]]></literal>
    <justification jstring="[resolve(59,a,35,b),unit_del(a,58),unit_del(b,57),unit_del(d,24)].">
      <j1 rule="resolve" parents="59 35"/>
      <j2 rule="unit_del" parents="58"/>
      <j2 rule="unit_del" parents="57"/>
      <j2 rule="unit_del" parents="24"/>
    </justification>
  </clause>

  <clause id="64">
    <literal><![CDATA[
      -decreases(cardinality_at_time(first_movers,c2))
    ]]></literal>
    <justification jstring="[resolve(60,a,37,b),unit_del(a,58),unit_del(b,56),unit_del(d,26)].">
      <j1 rule="resolve" parents="60 37"/>
      <j2 rule="unit_del" parents="58"/>
      <j2 rule="unit_del" parents="56"/>
      <j2 rule="unit_del" parents="26"/>
    </justification>
  </clause>

  <clause id="65">
    <literal><![CDATA[
      -increases(cardinality_at_time(first_movers,c2))
    ]]></literal>
    <justification jstring="[resolve(60,a,36,b),unit_del(a,58),unit_del(b,56),unit_del(d,25)].">
      <j1 rule="resolve" parents="60 36"/>
      <j2 rule="unit_del" parents="58"/>
      <j2 rule="unit_del" parents="56"/>
      <j2 rule="unit_del" parents="25"/>
    </justification>
  </clause>

  <clause id="68">
    <literal><![CDATA[
      number_of_organizations(c1,c2) != sum(cardinality_at_time(first_movers,c2),cardinality_at_time(efficient_producers,c2))
    ]]></literal>
    <justification jstring="[ur(18,a,23,a,b,65,a,c,64,a,e,63,a),flip(a)].">
      <j1 rule="ur" parents="18 23 65 64 63"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="79">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[ur(32,b,60,a,c,68,a),xx(a)].">
      <j1 rule="ur" parents="32 60 68"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="7" length="33" max_count="23">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 33.
% Level of proof is 6.
% Maximum clause weight is 21.
% Given clauses 43.
]]></comments>

  <clause id="1">
    <literal><![CDATA[
      environment(c1)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="4">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      first_movers != B
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(B,A,C)
    ]]></literal>
    <literal><![CDATA[
      sum(cardinality_at_time(first_movers,C),cardinality_at_time(efficient_producers,C)) = number_of_organizations(A,C)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="5">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -in_environment(A,B)
    ]]></literal>
    <literal><![CDATA[
      subpopulation(first_movers,A,B)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="6">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -in_environment(A,B)
    ]]></literal>
    <literal><![CDATA[
      subpopulation(efficient_producers,A,B)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="7">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -in_environment(A,B)
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(C,A,B)
    ]]></literal>
    <literal><![CDATA[
      -greater(cardinality_at_time(C,B),zero)
    ]]></literal>
    <literal><![CDATA[
      -constant(cardinality_at_time(C,B))
    ]]></literal>
    <literal><![CDATA[
      growth_rate(C,B) = zero
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="8">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -in_environment(A,B)
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(C,A,B)
    ]]></literal>
    <literal><![CDATA[
      -greater(cardinality_at_time(C,B),zero)
    ]]></literal>
    <literal><![CDATA[
      -increases(cardinality_at_time(C,B))
    ]]></literal>
    <literal><![CDATA[
      greater(growth_rate(C,B),zero)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="9">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -in_environment(A,B)
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(C,A,B)
    ]]></literal>
    <literal><![CDATA[
      -greater(cardinality_at_time(C,B),zero)
    ]]></literal>
    <literal><![CDATA[
      -decreases(cardinality_at_time(C,B))
    ]]></literal>
    <literal><![CDATA[
      greater(zero,growth_rate(C,B))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="11">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -subpopulations(first_movers,efficient_producers,A,B)
    ]]></literal>
    <literal><![CDATA[
      greater(cardinality_at_time(efficient_producers,B),zero)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="12">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -subpopulations(first_movers,efficient_producers,A,B)
    ]]></literal>
    <literal><![CDATA[
      in_environment(A,B)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="21">
    <literal><![CDATA[
      -constant(A)
    ]]></literal>
    <literal><![CDATA[
      sum(B,C) != A
    ]]></literal>
    <literal><![CDATA[
      constant(C)
    ]]></literal>
    <literal><![CDATA[
      decreases(C)
    ]]></literal>
    <literal><![CDATA[
      increases(C)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="22">
    <literal><![CDATA[
      subpopulations(first_movers,efficient_producers,c1,c2)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="23">
    <literal><![CDATA[
      constant(number_of_organizations(c1,c2))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="24">
    <literal><![CDATA[
      growth_rate(efficient_producers,c2) != zero
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="25">
    <literal><![CDATA[
      -greater(zero,growth_rate(efficient_producers,c2))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="26">
    <literal><![CDATA[
      -greater(growth_rate(efficient_producers,c2),zero)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="31">
    <literal><![CDATA[
      first_movers != A
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(A,c1,B)
    ]]></literal>
    <literal><![CDATA[
      sum(cardinality_at_time(first_movers,B),cardinality_at_time(efficient_producers,B)) = number_of_organizations(c1,B)
    ]]></literal>
    <justification jstring="[resolve(1,a,4,a)].">
      <j1 rule="resolve" parents="1 4"/>
    </justification>
  </clause>

  <clause id="32">
    <literal><![CDATA[
      first_movers != A
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(A,c1,B)
    ]]></literal>
    <literal><![CDATA[
      number_of_organizations(c1,B) = sum(cardinality_at_time(first_movers,B),cardinality_at_time(efficient_producers,B))
    ]]></literal>
    <justification jstring="[copy(31),flip(c)].">
      <j1 rule="copy" parents="31"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33">
    <literal><![CDATA[
      -in_environment(c1,A)
    ]]></literal>
    <literal><![CDATA[
      subpopulation(first_movers,c1,A)
    ]]></literal>
    <justification jstring="[resolve(1,a,5,a)].">
      <j1 rule="resolve" parents="1 5"/>
    </justification>
  </clause>

  <clause id="34">
    <literal><![CDATA[
      -in_environment(c1,A)
    ]]></literal>
    <literal><![CDATA[
      subpopulation(efficient_producers,c1,A)
    ]]></literal>
    <justification jstring="[resolve(1,a,6,a)].">
      <j1 rule="resolve" parents="1 6"/>
    </justification>
  </clause>

  <clause id="35">
    <literal><![CDATA[
      -in_environment(c1,A)
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(B,c1,A)
    ]]></literal>
    <literal><![CDATA[
      -greater(cardinality_at_time(B,A),zero)
    ]]></literal>
    <literal><![CDATA[
      -constant(cardinality_at_time(B,A))
    ]]></literal>
    <literal><![CDATA[
      growth_rate(B,A) = zero
    ]]></literal>
    <justification jstring="[resolve(1,a,7,a)].">
      <j1 rule="resolve" parents="1 7"/>
    </justification>
  </clause>

  <clause id="36">
    <literal><![CDATA[
      -in_environment(c1,A)
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(B,c1,A)
    ]]></literal>
    <literal><![CDATA[
      -greater(cardinality_at_time(B,A),zero)
    ]]></literal>
    <literal><![CDATA[
      -increases(cardinality_at_time(B,A))
    ]]></literal>
    <literal><![CDATA[
      greater(growth_rate(B,A),zero)
    ]]></literal>
    <justification jstring="[resolve(1,a,8,a)].">
      <j1 rule="resolve" parents="1 8"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      -in_environment(c1,A)
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(B,c1,A)
    ]]></literal>
    <literal><![CDATA[
      -greater(cardinality_at_time(B,A),zero)
    ]]></literal>
    <literal><![CDATA[
      -decreases(cardinality_at_time(B,A))
    ]]></literal>
    <literal><![CDATA[
      greater(zero,growth_rate(B,A))
    ]]></literal>
    <justification jstring="[resolve(1,a,9,a)].">
      <j1 rule="resolve" parents="1 9"/>
    </justification>
  </clause>

  <clause id="39">
    <literal><![CDATA[
      -subpopulations(first_movers,efficient_producers,c1,A)
    ]]></literal>
    <literal><![CDATA[
      greater(cardinality_at_time(efficient_producers,A),zero)
    ]]></literal>
    <justification jstring="[resolve(1,a,11,a)].">
      <j1 rule="resolve" parents="1 11"/>
    </justification>
  </clause>

  <clause id="40">
    <literal><![CDATA[
      -subpopulations(first_movers,efficient_producers,c1,A)
    ]]></literal>
    <literal><![CDATA[
      in_environment(c1,A)
    ]]></literal>
    <justification jstring="[resolve(1,a,12,a)].">
      <j1 rule="resolve" parents="1 12"/>
    </justification>
  </clause>

  <clause id="57">
    <literal><![CDATA[
      greater(cardinality_at_time(efficient_producers,c2),zero)
    ]]></literal>
    <justification jstring="[resolve(39,a,22,a)].">
      <j1 rule="resolve" parents="39 22"/>
    </justification>
  </clause>

  <clause id="58">
    <literal><![CDATA[
      in_environment(c1,c2)
    ]]></literal>
    <justification jstring="[resolve(40,a,22,a)].">
      <j1 rule="resolve" parents="40 22"/>
    </justification>
  </clause>

  <clause id="59">
    <literal><![CDATA[
      subpopulation(efficient_producers,c1,c2)
    ]]></literal>
    <justification jstring="[resolve(58,a,34,a)].">
      <j1 rule="resolve" parents="58 34"/>
    </justification>
  </clause>

  <clause id="60">
    <literal><![CDATA[
      subpopulation(first_movers,c1,c2)
    ]]></literal>
    <justification jstring="[resolve(58,a,33,a)].">
      <j1 rule="resolve" parents="58 33"/>
    </justification>
  </clause>

  <clause id="61">
    <literal><![CDATA[
      -decreases(cardinality_at_time(efficient_producers,c2))
    ]]></literal>
    <justification jstring="[resolve(59,a,37,b),unit_del(a,58),unit_del(b,57),unit_del(d,25)].">
      <j1 rule="resolve" parents="59 37"/>
      <j2 rule="unit_del" parents="58"/>
      <j2 rule="unit_del" parents="57"/>
      <j2 rule="unit_del" parents="25"/>
    </justification>
  </clause>

  <clause id="62">
    <literal><![CDATA[
      -increases(cardinality_at_time(efficient_producers,c2))
    ]]></literal>
    <justification jstring="[resolve(59,a,36,b),unit_del(a,58),unit_del(b,57),unit_del(d,26)].">
      <j1 rule="resolve" parents="59 36"/>
      <j2 rule="unit_del" parents="58"/>
      <j2 rule="unit_del" parents="57"/>
      <j2 rule="unit_del" parents="26"/>
    </justification>
  </clause>

  <clause id="63">
    <literal><![CDATA[
      -constant(cardinality_at_time(efficient_producers,c2))
    ]]></literal>
    <justification jstring="[resolve(59,a,35,b),unit_del(a,58),unit_del(b,57),unit_del(d,24)].">
      <j1 rule="resolve" parents="59 35"/>
      <j2 rule="unit_del" parents="58"/>
      <j2 rule="unit_del" parents="57"/>
      <j2 rule="unit_del" parents="24"/>
    </justification>
  </clause>

  <clause id="71">
    <literal><![CDATA[
      sum(A,cardinality_at_time(efficient_producers,c2)) != number_of_organizations(c1,c2)
    ]]></literal>
    <justification jstring="[ur(21,a,23,a,c,63,a,d,61,a,e,62,a)].">
      <j1 rule="ur" parents="21 23 63 61 62"/>
    </justification>
  </clause>

  <clause id="73">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[ur(32,b,60,a,c,71,a(flip)),xx(a)].">
      <j1 rule="ur" parents="32 60 71"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="8" length="34" max_count="23">

<comments><![CDATA[
% Proof 1 at 0.01 (+ 0.00) seconds.
% Length of proof is 34.
% Level of proof is 6.
% Maximum clause weight is 21.
% Given clauses 48.
]]></comments>

  <clause id="1">
    <literal><![CDATA[
      environment(c1)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="4">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      first_movers != B
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(B,A,C)
    ]]></literal>
    <literal><![CDATA[
      sum(cardinality_at_time(first_movers,C),cardinality_at_time(efficient_producers,C)) = number_of_organizations(A,C)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="5">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -in_environment(A,B)
    ]]></literal>
    <literal><![CDATA[
      subpopulation(first_movers,A,B)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="6">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -in_environment(A,B)
    ]]></literal>
    <literal><![CDATA[
      subpopulation(efficient_producers,A,B)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="7">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -in_environment(A,B)
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(C,A,B)
    ]]></literal>
    <literal><![CDATA[
      -greater(cardinality_at_time(C,B),zero)
    ]]></literal>
    <literal><![CDATA[
      -constant(cardinality_at_time(C,B))
    ]]></literal>
    <literal><![CDATA[
      growth_rate(C,B) = zero
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="9">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -in_environment(A,B)
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(C,A,B)
    ]]></literal>
    <literal><![CDATA[
      -greater(cardinality_at_time(C,B),zero)
    ]]></literal>
    <literal><![CDATA[
      -decreases(cardinality_at_time(C,B))
    ]]></literal>
    <literal><![CDATA[
      greater(zero,growth_rate(C,B))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="10">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -subpopulations(first_movers,efficient_producers,A,B)
    ]]></literal>
    <literal><![CDATA[
      greater(cardinality_at_time(first_movers,B),zero)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="11">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -subpopulations(first_movers,efficient_producers,A,B)
    ]]></literal>
    <literal><![CDATA[
      greater(cardinality_at_time(efficient_producers,B),zero)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="12">
    <literal><![CDATA[
      -environment(A)
    ]]></literal>
    <literal><![CDATA[
      -subpopulations(first_movers,efficient_producers,A,B)
    ]]></literal>
    <literal><![CDATA[
      in_environment(A,B)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

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

  <clause id="22">
    <literal><![CDATA[
      subpopulations(first_movers,efficient_producers,c1,c2)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="23">
    <literal><![CDATA[
      constant(number_of_organizations(c1,c2))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="24">
    <literal><![CDATA[
      growth_rate(efficient_producers,c2) != zero
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="25">
    <literal><![CDATA[
      -greater(zero,growth_rate(efficient_producers,c2))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="26">
    <literal><![CDATA[
      -greater(zero,growth_rate(first_movers,c2))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="31">
    <literal><![CDATA[
      first_movers != A
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(A,c1,B)
    ]]></literal>
    <literal><![CDATA[
      sum(cardinality_at_time(first_movers,B),cardinality_at_time(efficient_producers,B)) = number_of_organizations(c1,B)
    ]]></literal>
    <justification jstring="[resolve(1,a,4,a)].">
      <j1 rule="resolve" parents="1 4"/>
    </justification>
  </clause>

  <clause id="32">
    <literal><![CDATA[
      first_movers != A
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(A,c1,B)
    ]]></literal>
    <literal><![CDATA[
      number_of_organizations(c1,B) = sum(cardinality_at_time(first_movers,B),cardinality_at_time(efficient_producers,B))
    ]]></literal>
    <justification jstring="[copy(31),flip(c)].">
      <j1 rule="copy" parents="31"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33">
    <literal><![CDATA[
      -in_environment(c1,A)
    ]]></literal>
    <literal><![CDATA[
      subpopulation(first_movers,c1,A)
    ]]></literal>
    <justification jstring="[resolve(1,a,5,a)].">
      <j1 rule="resolve" parents="1 5"/>
    </justification>
  </clause>

  <clause id="34">
    <literal><![CDATA[
      -in_environment(c1,A)
    ]]></literal>
    <literal><![CDATA[
      subpopulation(efficient_producers,c1,A)
    ]]></literal>
    <justification jstring="[resolve(1,a,6,a)].">
      <j1 rule="resolve" parents="1 6"/>
    </justification>
  </clause>

  <clause id="35">
    <literal><![CDATA[
      -in_environment(c1,A)
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(B,c1,A)
    ]]></literal>
    <literal><![CDATA[
      -greater(cardinality_at_time(B,A),zero)
    ]]></literal>
    <literal><![CDATA[
      -constant(cardinality_at_time(B,A))
    ]]></literal>
    <literal><![CDATA[
      growth_rate(B,A) = zero
    ]]></literal>
    <justification jstring="[resolve(1,a,7,a)].">
      <j1 rule="resolve" parents="1 7"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      -in_environment(c1,A)
    ]]></literal>
    <literal><![CDATA[
      -subpopulation(B,c1,A)
    ]]></literal>
    <literal><![CDATA[
      -greater(cardinality_at_time(B,A),zero)
    ]]></literal>
    <literal><![CDATA[
      -decreases(cardinality_at_time(B,A))
    ]]></literal>
    <literal><![CDATA[
      greater(zero,growth_rate(B,A))
    ]]></literal>
    <justification jstring="[resolve(1,a,9,a)].">
      <j1 rule="resolve" parents="1 9"/>
    </justification>
  </clause>

  <clause id="38">
    <literal><![CDATA[
      -subpopulations(first_movers,efficient_producers,c1,A)
    ]]></literal>
    <literal><![CDATA[
      greater(cardinality_at_time(first_movers,A),zero)
    ]]></literal>
    <justification jstring="[resolve(1,a,10,a)].">
      <j1 rule="resolve" parents="1 10"/>
    </justification>
  </clause>

  <clause id="39">
    <literal><![CDATA[
      -subpopulations(first_movers,efficient_producers,c1,A)
    ]]></literal>
    <literal><![CDATA[
      greater(cardinality_at_time(efficient_producers,A),zero)
    ]]></literal>
    <justification jstring="[resolve(1,a,11,a)].">
      <j1 rule="resolve" parents="1 11"/>
    </justification>
  </clause>

  <clause id="40">
    <literal><![CDATA[
      -subpopulations(first_movers,efficient_producers,c1,A)
    ]]></literal>
    <literal><![CDATA[
      in_environment(c1,A)
    ]]></literal>
    <justification jstring="[resolve(1,a,12,a)].">
      <j1 rule="resolve" parents="1 12"/>
    </justification>
  </clause>

  <clause id="56">
    <literal><![CDATA[
      greater(cardinality_at_time(first_movers,c2),zero)
    ]]></literal>
    <justification jstring="[resolve(38,a,22,a)].">
      <j1 rule="resolve" parents="38 22"/>
    </justification>
  </clause>

  <clause id="57">
    <literal><![CDATA[
      greater(cardinality_at_time(efficient_producers,c2),zero)
    ]]></literal>
    <justification jstring="[resolve(39,a,22,a)].">
      <j1 rule="resolve" parents="39 22"/>
    </justification>
  </clause>

  <clause id="58">
    <literal><![CDATA[
      in_environment(c1,c2)
    ]]></literal>
    <justification jstring="[resolve(40,a,22,a)].">
      <j1 rule="resolve" parents="40 22"/>
    </justification>
  </clause>

  <clause id="59">
    <literal><![CDATA[
      subpopulation(efficient_producers,c1,c2)
    ]]></literal>
    <justification jstring="[resolve(58,a,34,a)].">
      <j1 rule="resolve" parents="58 34"/>
    </justification>
  </clause>

  <clause id="60">
    <literal><![CDATA[
      subpopulation(first_movers,c1,c2)
    ]]></literal>
    <justification jstring="[resolve(58,a,33,a)].">
      <j1 rule="resolve" parents="58 33"/>
    </justification>
  </clause>

  <clause id="61">
    <literal><![CDATA[
      -decreases(cardinality_at_time(efficient_producers,c2))
    ]]></literal>
    <justification jstring="[resolve(59,a,37,b),unit_del(a,58),unit_del(b,57),unit_del(d,25)].">
      <j1 rule="resolve" parents="59 37"/>
      <j2 rule="unit_del" parents="58"/>
      <j2 rule="unit_del" parents="57"/>
      <j2 rule="unit_del" parents="25"/>
    </justification>
  </clause>

  <clause id="63">
    <literal><![CDATA[
      -constant(cardinality_at_time(efficient_producers,c2))
    ]]></literal>
    <justification jstring="[resolve(59,a,35,b),unit_del(a,58),unit_del(b,57),unit_del(d,24)].">
      <j1 rule="resolve" parents="59 35"/>
      <j2 rule="unit_del" parents="58"/>
      <j2 rule="unit_del" parents="57"/>
      <j2 rule="unit_del" parents="24"/>
    </justification>
  </clause>

  <clause id="64">
    <literal><![CDATA[
      -decreases(cardinality_at_time(first_movers,c2))
    ]]></literal>
    <justification jstring="[resolve(60,a,37,b),unit_del(a,58),unit_del(b,56),unit_del(d,26)].">
      <j1 rule="resolve" parents="60 37"/>
      <j2 rule="unit_del" parents="58"/>
      <j2 rule="unit_del" parents="56"/>
      <j2 rule="unit_del" parents="26"/>
    </justification>
  </clause>

  <clause id="70">
    <literal><![CDATA[
      number_of_organizations(c1,c2) != sum(cardinality_at_time(first_movers,c2),cardinality_at_time(efficient_producers,c2))
    ]]></literal>
    <justification jstring="[ur(20,a,23,a,b,64,a,d,63,a,e,61,a),flip(a)].">
      <j1 rule="ur" parents="20 23 64 63 61"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="73">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[ur(32,b,60,a,c,70,a),xx(a)].">
      <j1 rule="ur" parents="32 60 70"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

</proofs>
