TSTP Solution File: MGT037-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : MGT037-1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Aug 22 10:49:39 EDT 2023
% Result : Unsatisfiable 5.12s 2.52s
% Output : CNFRefutation 5.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 46
% Syntax : Number of formulae : 155 ( 40 unt; 22 typ; 0 def)
% Number of atoms : 406 ( 89 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 514 ( 241 ~; 273 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 28 ( 16 >; 12 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-2 aty)
% Number of variables : 132 (; 132 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subpopulation > in_environment > greater_or_equal > greater > environment > decreases > constant > sk2 > sk1 > resources > number_of_organizations > growth_rate > cardinality_at_time > appear > #nlpp > resilience > equilibrium > zero > sk4 > sk3 > first_movers > efficient_producers > an_organisation
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(greater,type,
greater: ( $i * $i ) > $o ).
tff(sk2,type,
sk2: ( $i * $i ) > $i ).
tff(number_of_organizations,type,
number_of_organizations: ( $i * $i ) > $i ).
tff(in_environment,type,
in_environment: ( $i * $i ) > $o ).
tff(constant,type,
constant: $i > $o ).
tff(appear,type,
appear: ( $i * $i ) > $i ).
tff(efficient_producers,type,
efficient_producers: $i ).
tff(resilience,type,
resilience: $i > $i ).
tff(cardinality_at_time,type,
cardinality_at_time: ( $i * $i ) > $i ).
tff(growth_rate,type,
growth_rate: ( $i * $i ) > $i ).
tff(decreases,type,
decreases: $i > $o ).
tff(environment,type,
environment: $i > $o ).
tff(sk4,type,
sk4: $i ).
tff(first_movers,type,
first_movers: $i ).
tff(sk3,type,
sk3: $i ).
tff(an_organisation,type,
an_organisation: $i ).
tff(equilibrium,type,
equilibrium: $i > $i ).
tff(greater_or_equal,type,
greater_or_equal: ( $i * $i ) > $o ).
tff(resources,type,
resources: ( $i * $i ) > $i ).
tff(subpopulation,type,
subpopulation: ( $i * $i * $i ) > $o ).
tff(sk1,type,
sk1: ( $i * $i ) > $i ).
tff(zero,type,
zero: $i ).
tff(f_261,axiom,
environment(sk3),
file(unknown,unknown) ).
tff(f_263,axiom,
greater_or_equal(sk4,appear(efficient_producers,sk3)),
file(unknown,unknown) ).
tff(f_265,axiom,
~ greater(cardinality_at_time(efficient_producers,sk4),zero),
file(unknown,unknown) ).
tff(f_262,axiom,
in_environment(sk3,sk4),
file(unknown,unknown) ).
tff(f_155,axiom,
! [A,B] :
( ~ environment(A)
| ~ in_environment(A,B)
| ( cardinality_at_time(efficient_producers,B) = zero )
| greater(cardinality_at_time(efficient_producers,B),zero) ),
file(unknown,unknown) ).
tff(f_45,axiom,
! [A,B] :
( ~ environment(A)
| ~ greater_or_equal(B,appear(efficient_producers,A))
| ( cardinality_at_time(efficient_producers,B) != zero )
| in_environment(A,sk1(B,A)) ),
file(unknown,unknown) ).
tff(f_247,axiom,
greater(resilience(efficient_producers),resilience(first_movers)),
file(unknown,unknown) ).
tff(f_67,axiom,
! [A,B] :
( ~ environment(A)
| ~ greater_or_equal(B,appear(efficient_producers,A))
| ( cardinality_at_time(efficient_producers,B) != zero )
| greater(zero,growth_rate(efficient_producers,sk1(B,A))) ),
file(unknown,unknown) ).
tff(f_246,axiom,
! [A,B,C,D] :
( ~ environment(A)
| ~ in_environment(A,B)
| greater(zero,growth_rate(C,B))
| ~ greater(resilience(D),resilience(C))
| ~ greater(zero,growth_rate(D,B)) ),
file(unknown,unknown) ).
tff(f_145,axiom,
! [A,B] :
( ( cardinality_at_time(A,B) != zero )
| ~ greater(zero,growth_rate(A,B)) ),
file(unknown,unknown) ).
tff(f_88,axiom,
! [A,B] :
( ~ environment(A)
| ~ in_environment(A,B)
| decreases(number_of_organizations(A,B))
| subpopulation(sk2(B,A),A,B) ),
file(unknown,unknown) ).
tff(f_98,axiom,
! [A,B] :
( ~ environment(A)
| ~ in_environment(A,B)
| decreases(number_of_organizations(A,B))
| greater(cardinality_at_time(sk2(B,A),B),zero) ),
file(unknown,unknown) ).
tff(f_260,axiom,
! [A,B,C] :
( ~ environment(A)
| ~ subpopulation(B,A,C)
| ~ greater(cardinality_at_time(B,C),zero)
| ( B = efficient_producers )
| ( B = first_movers ) ),
file(unknown,unknown) ).
tff(f_171,axiom,
! [A,B] :
( ~ environment(A)
| ~ in_environment(A,B)
| greater_or_equal(B,appear(an_organisation,A))
| greater(appear(an_organisation,A),B) ),
file(unknown,unknown) ).
tff(f_209,axiom,
! [A,B] :
( ~ environment(A)
| ~ in_environment(A,B)
| ~ greater_or_equal(B,appear(an_organisation,A))
| greater(number_of_organizations(A,B),zero) ),
file(unknown,unknown) ).
tff(f_198,axiom,
! [A,B] :
( ~ environment(A)
| ~ in_environment(A,B)
| ~ greater(number_of_organizations(A,B),zero)
| greater(equilibrium(A),B)
| constant(resources(A,B)) ),
file(unknown,unknown) ).
tff(f_78,axiom,
! [A,B] :
( ~ environment(A)
| ~ in_environment(A,B)
| ~ greater(appear(an_organisation,A),B)
| ( number_of_organizations(A,B) = zero ) ),
file(unknown,unknown) ).
tff(f_185,axiom,
! [A,B] :
( ~ environment(A)
| ~ in_environment(A,B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ greater(equilibrium(A),B)
| decreases(resources(A,B)) ),
file(unknown,unknown) ).
tff(f_221,axiom,
! [A,B] :
( ~ environment(A)
| ~ in_environment(A,B)
| ~ decreases(resources(A,B))
| ~ decreases(number_of_organizations(A,B)) ),
file(unknown,unknown) ).
tff(f_232,axiom,
! [A,B] :
( ~ environment(A)
| ~ in_environment(A,B)
| ~ constant(resources(A,B))
| constant(number_of_organizations(A,B)) ),
file(unknown,unknown) ).
tff(f_161,axiom,
! [A] :
( ~ constant(A)
| ~ decreases(A) ),
file(unknown,unknown) ).
tff(f_109,axiom,
! [A,B] :
( ~ environment(A)
| ~ in_environment(A,B)
| decreases(number_of_organizations(A,B))
| ~ greater(zero,growth_rate(sk2(B,A),B)) ),
file(unknown,unknown) ).
tff(f_131,axiom,
! [A,B] :
( ~ environment(A)
| ~ in_environment(A,B)
| subpopulation(first_movers,A,B) ),
file(unknown,unknown) ).
tff(f_123,axiom,
! [A,B,C] :
( ~ environment(A)
| ~ in_environment(A,B)
| ( number_of_organizations(A,B) != zero )
| ~ subpopulation(C,A,B)
| ( cardinality_at_time(C,B) = zero ) ),
file(unknown,unknown) ).
tff(c_48,plain,
environment(sk3),
inference(cnfTransformation,[status(thm)],[f_261]) ).
tff(c_52,plain,
greater_or_equal(sk4,appear(efficient_producers,sk3)),
inference(cnfTransformation,[status(thm)],[f_263]) ).
tff(c_54,plain,
~ greater(cardinality_at_time(efficient_producers,sk4),zero),
inference(cnfTransformation,[status(thm)],[f_265]) ).
tff(c_50,plain,
in_environment(sk3,sk4),
inference(cnfTransformation,[status(thm)],[f_262]) ).
tff(c_62,plain,
! [B_61,A_62] :
( greater(cardinality_at_time(efficient_producers,B_61),zero)
| ( cardinality_at_time(efficient_producers,B_61) = zero )
| ~ in_environment(A_62,B_61)
| ~ environment(A_62) ),
inference(cnfTransformation,[status(thm)],[f_155]) ).
tff(c_64,plain,
( greater(cardinality_at_time(efficient_producers,sk4),zero)
| ( cardinality_at_time(efficient_producers,sk4) = zero )
| ~ environment(sk3) ),
inference(resolution,[status(thm)],[c_50,c_62]) ).
tff(c_67,plain,
( greater(cardinality_at_time(efficient_producers,sk4),zero)
| ( cardinality_at_time(efficient_producers,sk4) = zero ) ),
inference(demodulation,[status(thm),theory(equality)],[c_48,c_64]) ).
tff(c_68,plain,
cardinality_at_time(efficient_producers,sk4) = zero,
inference(negUnitSimplification,[status(thm)],[c_54,c_67]) ).
tff(c_4,plain,
! [A_3,B_4] :
( in_environment(A_3,sk1(B_4,A_3))
| ( cardinality_at_time(efficient_producers,B_4) != zero )
| ~ greater_or_equal(B_4,appear(efficient_producers,A_3))
| ~ environment(A_3) ),
inference(cnfTransformation,[status(thm)],[f_45]) ).
tff(c_44,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(cnfTransformation,[status(thm)],[f_247]) ).
tff(c_8,plain,
! [B_8,A_7] :
( greater(zero,growth_rate(efficient_producers,sk1(B_8,A_7)))
| ( cardinality_at_time(efficient_producers,B_8) != zero )
| ~ greater_or_equal(B_8,appear(efficient_producers,A_7))
| ~ environment(A_7) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_170,plain,
! [D_105,B_106,C_107,A_108] :
( ~ greater(zero,growth_rate(D_105,B_106))
| ~ greater(resilience(D_105),resilience(C_107))
| greater(zero,growth_rate(C_107,B_106))
| ~ in_environment(A_108,B_106)
| ~ environment(A_108) ),
inference(cnfTransformation,[status(thm)],[f_246]) ).
tff(c_260,plain,
! [C_138,B_139,A_140,A_141] :
( ~ greater(resilience(efficient_producers),resilience(C_138))
| greater(zero,growth_rate(C_138,sk1(B_139,A_140)))
| ~ in_environment(A_141,sk1(B_139,A_140))
| ~ environment(A_141)
| ( cardinality_at_time(efficient_producers,B_139) != zero )
| ~ greater_or_equal(B_139,appear(efficient_producers,A_140))
| ~ environment(A_140) ),
inference(resolution,[status(thm)],[c_8,c_170]) ).
tff(c_290,plain,
! [B_148,A_149,A_150] :
( greater(zero,growth_rate(first_movers,sk1(B_148,A_149)))
| ~ in_environment(A_150,sk1(B_148,A_149))
| ~ environment(A_150)
| ( cardinality_at_time(efficient_producers,B_148) != zero )
| ~ greater_or_equal(B_148,appear(efficient_producers,A_149))
| ~ environment(A_149) ),
inference(resolution,[status(thm)],[c_44,c_260]) ).
tff(c_293,plain,
! [B_4,A_3] :
( greater(zero,growth_rate(first_movers,sk1(B_4,A_3)))
| ( cardinality_at_time(efficient_producers,B_4) != zero )
| ~ greater_or_equal(B_4,appear(efficient_producers,A_3))
| ~ environment(A_3) ),
inference(resolution,[status(thm)],[c_4,c_290]) ).
tff(c_336,plain,
! [B_151,A_152] :
( greater(zero,growth_rate(first_movers,sk1(B_151,A_152)))
| ( cardinality_at_time(efficient_producers,B_151) != zero )
| ~ greater_or_equal(B_151,appear(efficient_producers,A_152))
| ~ environment(A_152) ),
inference(resolution,[status(thm)],[c_4,c_290]) ).
tff(c_24,plain,
! [A_24,B_25] :
( ~ greater(zero,growth_rate(A_24,B_25))
| ( cardinality_at_time(A_24,B_25) != zero ) ),
inference(cnfTransformation,[status(thm)],[f_145]) ).
tff(c_412,plain,
! [B_155,A_156] :
( ( cardinality_at_time(first_movers,sk1(B_155,A_156)) != zero )
| ( cardinality_at_time(efficient_producers,B_155) != zero )
| ~ greater_or_equal(B_155,appear(efficient_producers,A_156))
| ~ environment(A_156) ),
inference(resolution,[status(thm)],[c_336,c_24]) ).
tff(c_415,plain,
( ( cardinality_at_time(first_movers,sk1(sk4,sk3)) != zero )
| ( cardinality_at_time(efficient_producers,sk4) != zero )
| ~ environment(sk3) ),
inference(resolution,[status(thm)],[c_52,c_412]) ).
tff(c_418,plain,
cardinality_at_time(first_movers,sk1(sk4,sk3)) != zero,
inference(demodulation,[status(thm),theory(equality)],[c_48,c_68,c_415]) ).
tff(c_12,plain,
! [B_12,A_11] :
( subpopulation(sk2(B_12,A_11),A_11,B_12)
| decreases(number_of_organizations(A_11,B_12))
| ~ in_environment(A_11,B_12)
| ~ environment(A_11) ),
inference(cnfTransformation,[status(thm)],[f_88]) ).
tff(c_92,plain,
! [B_78,A_79] :
( greater(cardinality_at_time(sk2(B_78,A_79),B_78),zero)
| decreases(number_of_organizations(A_79,B_78))
| ~ in_environment(A_79,B_78)
| ~ environment(A_79) ),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_46,plain,
! [B_46,C_47,A_45] :
( ( first_movers = B_46 )
| ( efficient_producers = B_46 )
| ~ greater(cardinality_at_time(B_46,C_47),zero)
| ~ subpopulation(B_46,A_45,C_47)
| ~ environment(A_45) ),
inference(cnfTransformation,[status(thm)],[f_260]) ).
tff(c_245,plain,
! [B_131,A_132,A_133] :
( ( sk2(B_131,A_132) = first_movers )
| ( sk2(B_131,A_132) = efficient_producers )
| ~ subpopulation(sk2(B_131,A_132),A_133,B_131)
| ~ environment(A_133)
| decreases(number_of_organizations(A_132,B_131))
| ~ in_environment(A_132,B_131)
| ~ environment(A_132) ),
inference(resolution,[status(thm)],[c_92,c_46]) ).
tff(c_250,plain,
! [B_134,A_135] :
( ( sk2(B_134,A_135) = first_movers )
| ( sk2(B_134,A_135) = efficient_producers )
| decreases(number_of_organizations(A_135,B_134))
| ~ in_environment(A_135,B_134)
| ~ environment(A_135) ),
inference(resolution,[status(thm)],[c_12,c_245]) ).
tff(c_78,plain,
! [A_68,B_69] :
( greater(appear(an_organisation,A_68),B_69)
| greater_or_equal(B_69,appear(an_organisation,A_68))
| ~ in_environment(A_68,B_69)
| ~ environment(A_68) ),
inference(cnfTransformation,[status(thm)],[f_171]) ).
tff(c_36,plain,
! [A_35,B_36] :
( greater(number_of_organizations(A_35,B_36),zero)
| ~ greater_or_equal(B_36,appear(an_organisation,A_35))
| ~ in_environment(A_35,B_36)
| ~ environment(A_35) ),
inference(cnfTransformation,[status(thm)],[f_209]) ).
tff(c_82,plain,
! [A_68,B_69] :
( greater(number_of_organizations(A_68,B_69),zero)
| greater(appear(an_organisation,A_68),B_69)
| ~ in_environment(A_68,B_69)
| ~ environment(A_68) ),
inference(resolution,[status(thm)],[c_78,c_36]) ).
tff(c_153,plain,
! [A_95,B_96] :
( constant(resources(A_95,B_96))
| greater(equilibrium(A_95),B_96)
| ~ greater(number_of_organizations(A_95,B_96),zero)
| ~ in_environment(A_95,B_96)
| ~ environment(A_95) ),
inference(cnfTransformation,[status(thm)],[f_198]) ).
tff(c_165,plain,
! [A_103,B_104] :
( constant(resources(A_103,B_104))
| greater(equilibrium(A_103),B_104)
| greater(appear(an_organisation,A_103),B_104)
| ~ in_environment(A_103,B_104)
| ~ environment(A_103) ),
inference(resolution,[status(thm)],[c_82,c_153]) ).
tff(c_10,plain,
! [A_9,B_10] :
( ( number_of_organizations(A_9,B_10) = zero )
| ~ greater(appear(an_organisation,A_9),B_10)
| ~ in_environment(A_9,B_10)
| ~ environment(A_9) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_174,plain,
! [A_109,B_110] :
( ( number_of_organizations(A_109,B_110) = zero )
| constant(resources(A_109,B_110))
| greater(equilibrium(A_109),B_110)
| ~ in_environment(A_109,B_110)
| ~ environment(A_109) ),
inference(resolution,[status(thm)],[c_165,c_10]) ).
tff(c_136,plain,
! [A_89,B_90] :
( decreases(resources(A_89,B_90))
| ~ greater(equilibrium(A_89),B_90)
| ~ greater(number_of_organizations(A_89,B_90),zero)
| ~ in_environment(A_89,B_90)
| ~ environment(A_89) ),
inference(cnfTransformation,[status(thm)],[f_185]) ).
tff(c_159,plain,
! [A_99,B_100] :
( decreases(resources(A_99,B_100))
| ~ greater(equilibrium(A_99),B_100)
| greater(appear(an_organisation,A_99),B_100)
| ~ in_environment(A_99,B_100)
| ~ environment(A_99) ),
inference(resolution,[status(thm)],[c_82,c_136]) ).
tff(c_163,plain,
! [A_99,B_100] :
( ( number_of_organizations(A_99,B_100) = zero )
| decreases(resources(A_99,B_100))
| ~ greater(equilibrium(A_99),B_100)
| ~ in_environment(A_99,B_100)
| ~ environment(A_99) ),
inference(resolution,[status(thm)],[c_159,c_10]) ).
tff(c_179,plain,
! [A_111,B_112] :
( decreases(resources(A_111,B_112))
| ( number_of_organizations(A_111,B_112) = zero )
| constant(resources(A_111,B_112))
| ~ in_environment(A_111,B_112)
| ~ environment(A_111) ),
inference(resolution,[status(thm)],[c_174,c_163]) ).
tff(c_38,plain,
! [A_37,B_38] :
( ~ decreases(number_of_organizations(A_37,B_38))
| ~ decreases(resources(A_37,B_38))
| ~ in_environment(A_37,B_38)
| ~ environment(A_37) ),
inference(cnfTransformation,[status(thm)],[f_221]) ).
tff(c_186,plain,
! [A_111,B_112] :
( ~ decreases(number_of_organizations(A_111,B_112))
| ( number_of_organizations(A_111,B_112) = zero )
| constant(resources(A_111,B_112))
| ~ in_environment(A_111,B_112)
| ~ environment(A_111) ),
inference(resolution,[status(thm)],[c_179,c_38]) ).
tff(c_264,plain,
! [A_142,B_143] :
( ( number_of_organizations(A_142,B_143) = zero )
| constant(resources(A_142,B_143))
| ( sk2(B_143,A_142) = first_movers )
| ( sk2(B_143,A_142) = efficient_producers )
| ~ in_environment(A_142,B_143)
| ~ environment(A_142) ),
inference(resolution,[status(thm)],[c_250,c_186]) ).
tff(c_40,plain,
! [A_39,B_40] :
( constant(number_of_organizations(A_39,B_40))
| ~ constant(resources(A_39,B_40))
| ~ in_environment(A_39,B_40)
| ~ environment(A_39) ),
inference(cnfTransformation,[status(thm)],[f_232]) ).
tff(c_269,plain,
! [A_144,B_145] :
( constant(number_of_organizations(A_144,B_145))
| ( number_of_organizations(A_144,B_145) = zero )
| ( sk2(B_145,A_144) = first_movers )
| ( sk2(B_145,A_144) = efficient_producers )
| ~ in_environment(A_144,B_145)
| ~ environment(A_144) ),
inference(resolution,[status(thm)],[c_264,c_40]) ).
tff(c_28,plain,
! [A_28] :
( ~ decreases(A_28)
| ~ constant(A_28) ),
inference(cnfTransformation,[status(thm)],[f_161]) ).
tff(c_258,plain,
! [A_135,B_134] :
( ~ constant(number_of_organizations(A_135,B_134))
| ( sk2(B_134,A_135) = first_movers )
| ( sk2(B_134,A_135) = efficient_producers )
| ~ in_environment(A_135,B_134)
| ~ environment(A_135) ),
inference(resolution,[status(thm)],[c_250,c_28]) ).
tff(c_278,plain,
! [A_146,B_147] :
( ( number_of_organizations(A_146,B_147) = zero )
| ( sk2(B_147,A_146) = first_movers )
| ( sk2(B_147,A_146) = efficient_producers )
| ~ in_environment(A_146,B_147)
| ~ environment(A_146) ),
inference(resolution,[status(thm)],[c_269,c_258]) ).
tff(c_427,plain,
! [A_157,B_158] :
( ( number_of_organizations(A_157,sk1(B_158,A_157)) = zero )
| ( sk2(sk1(B_158,A_157),A_157) = first_movers )
| ( sk2(sk1(B_158,A_157),A_157) = efficient_producers )
| ( cardinality_at_time(efficient_producers,B_158) != zero )
| ~ greater_or_equal(B_158,appear(efficient_producers,A_157))
| ~ environment(A_157) ),
inference(resolution,[status(thm)],[c_4,c_278]) ).
tff(c_429,plain,
( ( number_of_organizations(sk3,sk1(sk4,sk3)) = zero )
| ( sk2(sk1(sk4,sk3),sk3) = first_movers )
| ( sk2(sk1(sk4,sk3),sk3) = efficient_producers )
| ( cardinality_at_time(efficient_producers,sk4) != zero )
| ~ environment(sk3) ),
inference(resolution,[status(thm)],[c_52,c_427]) ).
tff(c_432,plain,
( ( number_of_organizations(sk3,sk1(sk4,sk3)) = zero )
| ( sk2(sk1(sk4,sk3),sk3) = first_movers )
| ( sk2(sk1(sk4,sk3),sk3) = efficient_producers ) ),
inference(demodulation,[status(thm),theory(equality)],[c_48,c_68,c_429]) ).
tff(c_433,plain,
sk2(sk1(sk4,sk3),sk3) = efficient_producers,
inference(splitLeft,[status(thm)],[c_432]) ).
tff(c_443,plain,
( subpopulation(efficient_producers,sk3,sk1(sk4,sk3))
| decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| ~ in_environment(sk3,sk1(sk4,sk3))
| ~ environment(sk3) ),
inference(superposition,[status(thm),theory(equality)],[c_433,c_12]) ).
tff(c_451,plain,
( subpopulation(efficient_producers,sk3,sk1(sk4,sk3))
| decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| ~ in_environment(sk3,sk1(sk4,sk3)) ),
inference(demodulation,[status(thm),theory(equality)],[c_48,c_443]) ).
tff(c_453,plain,
~ in_environment(sk3,sk1(sk4,sk3)),
inference(splitLeft,[status(thm)],[c_451]) ).
tff(c_456,plain,
( ( cardinality_at_time(efficient_producers,sk4) != zero )
| ~ greater_or_equal(sk4,appear(efficient_producers,sk3))
| ~ environment(sk3) ),
inference(resolution,[status(thm)],[c_4,c_453]) ).
tff(c_460,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_48,c_52,c_68,c_456]) ).
tff(c_462,plain,
in_environment(sk3,sk1(sk4,sk3)),
inference(splitRight,[status(thm)],[c_451]) ).
tff(c_16,plain,
! [B_16,A_15] :
( ~ greater(zero,growth_rate(sk2(B_16,A_15),B_16))
| decreases(number_of_organizations(A_15,B_16))
| ~ in_environment(A_15,B_16)
| ~ environment(A_15) ),
inference(cnfTransformation,[status(thm)],[f_109]) ).
tff(c_440,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk1(sk4,sk3)))
| decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| ~ in_environment(sk3,sk1(sk4,sk3))
| ~ environment(sk3) ),
inference(superposition,[status(thm),theory(equality)],[c_433,c_16]) ).
tff(c_449,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk1(sk4,sk3)))
| decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| ~ in_environment(sk3,sk1(sk4,sk3)) ),
inference(demodulation,[status(thm),theory(equality)],[c_48,c_440]) ).
tff(c_508,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk1(sk4,sk3)))
| decreases(number_of_organizations(sk3,sk1(sk4,sk3))) ),
inference(demodulation,[status(thm),theory(equality)],[c_462,c_449]) ).
tff(c_509,plain,
~ greater(zero,growth_rate(efficient_producers,sk1(sk4,sk3))),
inference(splitLeft,[status(thm)],[c_508]) ).
tff(c_512,plain,
( ( cardinality_at_time(efficient_producers,sk4) != zero )
| ~ greater_or_equal(sk4,appear(efficient_producers,sk3))
| ~ environment(sk3) ),
inference(resolution,[status(thm)],[c_8,c_509]) ).
tff(c_516,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_48,c_52,c_68,c_512]) ).
tff(c_517,plain,
decreases(number_of_organizations(sk3,sk1(sk4,sk3))),
inference(splitRight,[status(thm)],[c_508]) ).
tff(c_529,plain,
~ constant(number_of_organizations(sk3,sk1(sk4,sk3))),
inference(resolution,[status(thm)],[c_517,c_28]) ).
tff(c_20,plain,
! [A_20,B_21] :
( subpopulation(first_movers,A_20,B_21)
| ~ in_environment(A_20,B_21)
| ~ environment(A_20) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_100,plain,
! [C_82,B_83,A_84] :
( ( cardinality_at_time(C_82,B_83) = zero )
| ~ subpopulation(C_82,A_84,B_83)
| ( number_of_organizations(A_84,B_83) != zero )
| ~ in_environment(A_84,B_83)
| ~ environment(A_84) ),
inference(cnfTransformation,[status(thm)],[f_123]) ).
tff(c_112,plain,
! [B_21,A_20] :
( ( cardinality_at_time(first_movers,B_21) = zero )
| ( number_of_organizations(A_20,B_21) != zero )
| ~ in_environment(A_20,B_21)
| ~ environment(A_20) ),
inference(resolution,[status(thm)],[c_20,c_100]) ).
tff(c_468,plain,
( ( cardinality_at_time(first_movers,sk1(sk4,sk3)) = zero )
| ( number_of_organizations(sk3,sk1(sk4,sk3)) != zero )
| ~ environment(sk3) ),
inference(resolution,[status(thm)],[c_462,c_112]) ).
tff(c_480,plain,
( ( cardinality_at_time(first_movers,sk1(sk4,sk3)) = zero )
| ( number_of_organizations(sk3,sk1(sk4,sk3)) != zero ) ),
inference(demodulation,[status(thm),theory(equality)],[c_48,c_468]) ).
tff(c_481,plain,
number_of_organizations(sk3,sk1(sk4,sk3)) != zero,
inference(negUnitSimplification,[status(thm)],[c_418,c_480]) ).
tff(c_521,plain,
( ( number_of_organizations(sk3,sk1(sk4,sk3)) = zero )
| constant(resources(sk3,sk1(sk4,sk3)))
| ~ in_environment(sk3,sk1(sk4,sk3))
| ~ environment(sk3) ),
inference(resolution,[status(thm)],[c_517,c_186]) ).
tff(c_527,plain,
( ( number_of_organizations(sk3,sk1(sk4,sk3)) = zero )
| constant(resources(sk3,sk1(sk4,sk3))) ),
inference(demodulation,[status(thm),theory(equality)],[c_48,c_462,c_521]) ).
tff(c_528,plain,
constant(resources(sk3,sk1(sk4,sk3))),
inference(negUnitSimplification,[status(thm)],[c_481,c_527]) ).
tff(c_539,plain,
( constant(number_of_organizations(sk3,sk1(sk4,sk3)))
| ~ in_environment(sk3,sk1(sk4,sk3))
| ~ environment(sk3) ),
inference(resolution,[status(thm)],[c_528,c_40]) ).
tff(c_542,plain,
constant(number_of_organizations(sk3,sk1(sk4,sk3))),
inference(demodulation,[status(thm),theory(equality)],[c_48,c_462,c_539]) ).
tff(c_543,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_529,c_542]) ).
tff(c_544,plain,
( ( sk2(sk1(sk4,sk3),sk3) = first_movers )
| ( number_of_organizations(sk3,sk1(sk4,sk3)) = zero ) ),
inference(splitRight,[status(thm)],[c_432]) ).
tff(c_547,plain,
number_of_organizations(sk3,sk1(sk4,sk3)) = zero,
inference(splitLeft,[status(thm)],[c_544]) ).
tff(c_124,plain,
! [B_87,A_88] :
( ( cardinality_at_time(first_movers,B_87) = zero )
| ( number_of_organizations(A_88,B_87) != zero )
| ~ in_environment(A_88,B_87)
| ~ environment(A_88) ),
inference(resolution,[status(thm)],[c_20,c_100]) ).
tff(c_131,plain,
! [B_4,A_3] :
( ( cardinality_at_time(first_movers,sk1(B_4,A_3)) = zero )
| ( number_of_organizations(A_3,sk1(B_4,A_3)) != zero )
| ( cardinality_at_time(efficient_producers,B_4) != zero )
| ~ greater_or_equal(B_4,appear(efficient_producers,A_3))
| ~ environment(A_3) ),
inference(resolution,[status(thm)],[c_4,c_124]) ).
tff(c_556,plain,
( ( cardinality_at_time(first_movers,sk1(sk4,sk3)) = zero )
| ( cardinality_at_time(efficient_producers,sk4) != zero )
| ~ greater_or_equal(sk4,appear(efficient_producers,sk3))
| ~ environment(sk3) ),
inference(superposition,[status(thm),theory(equality)],[c_547,c_131]) ).
tff(c_587,plain,
cardinality_at_time(first_movers,sk1(sk4,sk3)) = zero,
inference(demodulation,[status(thm),theory(equality)],[c_48,c_52,c_68,c_556]) ).
tff(c_589,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_418,c_587]) ).
tff(c_590,plain,
sk2(sk1(sk4,sk3),sk3) = first_movers,
inference(splitRight,[status(thm)],[c_544]) ).
tff(c_602,plain,
( subpopulation(first_movers,sk3,sk1(sk4,sk3))
| decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| ~ in_environment(sk3,sk1(sk4,sk3))
| ~ environment(sk3) ),
inference(superposition,[status(thm),theory(equality)],[c_590,c_12]) ).
tff(c_610,plain,
( subpopulation(first_movers,sk3,sk1(sk4,sk3))
| decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| ~ in_environment(sk3,sk1(sk4,sk3)) ),
inference(demodulation,[status(thm),theory(equality)],[c_48,c_602]) ).
tff(c_612,plain,
~ in_environment(sk3,sk1(sk4,sk3)),
inference(splitLeft,[status(thm)],[c_610]) ).
tff(c_615,plain,
( ( cardinality_at_time(efficient_producers,sk4) != zero )
| ~ greater_or_equal(sk4,appear(efficient_producers,sk3))
| ~ environment(sk3) ),
inference(resolution,[status(thm)],[c_4,c_612]) ).
tff(c_619,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_48,c_52,c_68,c_615]) ).
tff(c_621,plain,
in_environment(sk3,sk1(sk4,sk3)),
inference(splitRight,[status(thm)],[c_610]) ).
tff(c_14,plain,
! [B_14,A_13] :
( greater(cardinality_at_time(sk2(B_14,A_13),B_14),zero)
| decreases(number_of_organizations(A_13,B_14))
| ~ in_environment(A_13,B_14)
| ~ environment(A_13) ),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_596,plain,
( greater(cardinality_at_time(first_movers,sk1(sk4,sk3)),zero)
| decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| ~ in_environment(sk3,sk1(sk4,sk3))
| ~ environment(sk3) ),
inference(superposition,[status(thm),theory(equality)],[c_590,c_14]) ).
tff(c_606,plain,
( greater(cardinality_at_time(first_movers,sk1(sk4,sk3)),zero)
| decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| ~ in_environment(sk3,sk1(sk4,sk3)) ),
inference(demodulation,[status(thm),theory(equality)],[c_48,c_596]) ).
tff(c_656,plain,
( greater(cardinality_at_time(first_movers,sk1(sk4,sk3)),zero)
| decreases(number_of_organizations(sk3,sk1(sk4,sk3))) ),
inference(demodulation,[status(thm),theory(equality)],[c_621,c_606]) ).
tff(c_657,plain,
decreases(number_of_organizations(sk3,sk1(sk4,sk3))),
inference(splitLeft,[status(thm)],[c_656]) ).
tff(c_668,plain,
~ constant(number_of_organizations(sk3,sk1(sk4,sk3))),
inference(resolution,[status(thm)],[c_657,c_28]) ).
tff(c_591,plain,
number_of_organizations(sk3,sk1(sk4,sk3)) != zero,
inference(splitRight,[status(thm)],[c_544]) ).
tff(c_660,plain,
( ( number_of_organizations(sk3,sk1(sk4,sk3)) = zero )
| constant(resources(sk3,sk1(sk4,sk3)))
| ~ in_environment(sk3,sk1(sk4,sk3))
| ~ environment(sk3) ),
inference(resolution,[status(thm)],[c_657,c_186]) ).
tff(c_666,plain,
( ( number_of_organizations(sk3,sk1(sk4,sk3)) = zero )
| constant(resources(sk3,sk1(sk4,sk3))) ),
inference(demodulation,[status(thm),theory(equality)],[c_48,c_621,c_660]) ).
tff(c_667,plain,
constant(resources(sk3,sk1(sk4,sk3))),
inference(negUnitSimplification,[status(thm)],[c_591,c_666]) ).
tff(c_671,plain,
( constant(number_of_organizations(sk3,sk1(sk4,sk3)))
| ~ in_environment(sk3,sk1(sk4,sk3))
| ~ environment(sk3) ),
inference(resolution,[status(thm)],[c_667,c_40]) ).
tff(c_674,plain,
constant(number_of_organizations(sk3,sk1(sk4,sk3))),
inference(demodulation,[status(thm),theory(equality)],[c_48,c_621,c_671]) ).
tff(c_675,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_668,c_674]) ).
tff(c_677,plain,
~ decreases(number_of_organizations(sk3,sk1(sk4,sk3))),
inference(splitRight,[status(thm)],[c_656]) ).
tff(c_599,plain,
( ~ greater(zero,growth_rate(first_movers,sk1(sk4,sk3)))
| decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| ~ in_environment(sk3,sk1(sk4,sk3))
| ~ environment(sk3) ),
inference(superposition,[status(thm),theory(equality)],[c_590,c_16]) ).
tff(c_608,plain,
( ~ greater(zero,growth_rate(first_movers,sk1(sk4,sk3)))
| decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| ~ in_environment(sk3,sk1(sk4,sk3)) ),
inference(demodulation,[status(thm),theory(equality)],[c_48,c_599]) ).
tff(c_706,plain,
( ~ greater(zero,growth_rate(first_movers,sk1(sk4,sk3)))
| decreases(number_of_organizations(sk3,sk1(sk4,sk3))) ),
inference(demodulation,[status(thm),theory(equality)],[c_621,c_608]) ).
tff(c_707,plain,
~ greater(zero,growth_rate(first_movers,sk1(sk4,sk3))),
inference(negUnitSimplification,[status(thm)],[c_677,c_706]) ).
tff(c_710,plain,
( ( cardinality_at_time(efficient_producers,sk4) != zero )
| ~ greater_or_equal(sk4,appear(efficient_producers,sk3))
| ~ environment(sk3) ),
inference(resolution,[status(thm)],[c_293,c_707]) ).
tff(c_714,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_48,c_52,c_68,c_710]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.10 % Problem : MGT037-1 : TPTP v8.1.2. Released v2.4.0.
% 0.04/0.11 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.09/0.30 % Computer : n003.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Thu Aug 3 20:34:23 EDT 2023
% 0.09/0.30 % CPUTime :
% 5.12/2.52 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.12/2.54
% 5.12/2.54 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.12/2.62
% 5.12/2.62 Inference rules
% 5.12/2.62 ----------------------
% 5.12/2.62 #Ref : 0
% 5.12/2.62 #Sup : 118
% 5.12/2.62 #Fact : 2
% 5.12/2.62 #Define : 0
% 5.12/2.62 #Split : 10
% 5.12/2.62 #Chain : 0
% 5.12/2.62 #Close : 0
% 5.12/2.62
% 5.12/2.62 Ordering : KBO
% 5.12/2.62
% 5.12/2.62 Simplification rules
% 5.12/2.62 ----------------------
% 5.12/2.62 #Subsume : 20
% 5.12/2.62 #Demod : 105
% 5.12/2.62 #Tautology : 28
% 5.12/2.62 #SimpNegUnit : 35
% 5.12/2.62 #BackRed : 2
% 5.12/2.62
% 5.12/2.62 #Partial instantiations: 0
% 5.12/2.62 #Strategies tried : 1
% 5.12/2.62
% 5.12/2.62 Timing (in seconds)
% 5.12/2.62 ----------------------
% 5.12/2.62 Preprocessing : 0.71
% 5.12/2.62 Parsing : 0.41
% 5.12/2.62 CNF conversion : 0.04
% 5.12/2.62 Main loop : 0.71
% 5.12/2.62 Inferencing : 0.30
% 5.12/2.62 Reduction : 0.19
% 5.12/2.62 Demodulation : 0.13
% 5.12/2.62 BG Simplification : 0.03
% 5.12/2.62 Subsumption : 0.13
% 5.12/2.62 Abstraction : 0.02
% 5.12/2.62 MUC search : 0.00
% 5.12/2.62 Cooper : 0.00
% 5.12/2.62 Total : 1.54
% 5.12/2.62 Index Insertion : 0.00
% 5.12/2.62 Index Deletion : 0.00
% 5.12/2.62 Index Matching : 0.00
% 5.12/2.62 BG Taut test : 0.00
%------------------------------------------------------------------------------