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 v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n029.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 10:49:40 EDT 2023
% Result : Theorem 4.38s 2.09s
% Output : CNFRefutation 4.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 38
% Syntax : Number of formulae : 147 ( 36 unt; 22 typ; 0 def)
% Number of atoms : 396 ( 94 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 473 ( 202 ~; 220 |; 32 &)
% ( 0 <=>; 19 =>; 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 : 130 (; 128 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subpopulation > in_environment > greater_or_equal > greater > environment > decreases > constant > resources > number_of_organizations > growth_rate > cardinality_at_time > appear > #nlpp > resilience > equilibrium > zero > first_movers > efficient_producers > an_organisation > #skF_3 > #skF_4 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(greater,type,
greater: ( $i * $i ) > $o ).
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('#skF_3',type,
'#skF_3': $i ).
tff(environment,type,
environment: $i > $o ).
tff(first_movers,type,
first_movers: $i ).
tff(an_organisation,type,
an_organisation: $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff(equilibrium,type,
equilibrium: $i > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(greater_or_equal,type,
greater_or_equal: ( $i * $i ) > $o ).
tff(resources,type,
resources: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(subpopulation,type,
subpopulation: ( $i * $i * $i ) > $o ).
tff(zero,type,
zero: $i ).
tff(f_203,negated_conjecture,
~ ! [E,T] :
( ( environment(E)
& in_environment(E,T)
& greater_or_equal(T,appear(efficient_producers,E)) )
=> greater(cardinality_at_time(efficient_producers,T),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t6) ).
tff(f_110,axiom,
! [E,T] :
( ( environment(E)
& in_environment(E,T) )
=> ( ( cardinality_at_time(efficient_producers,T) = zero )
| greater(cardinality_at_time(efficient_producers,T),zero) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_efficient_producers_exist) ).
tff(f_46,axiom,
! [E,T] :
( ( environment(E)
& greater_or_equal(T,appear(efficient_producers,E))
& ( cardinality_at_time(efficient_producers,T) = zero ) )
=> ? [To] :
( greater(To,appear(efficient_producers,E))
& in_environment(E,To)
& greater(T,To)
& greater(zero,growth_rate(efficient_producers,To)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_previous_negative_growth) ).
tff(f_181,hypothesis,
greater(resilience(efficient_producers),resilience(first_movers)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2) ).
tff(f_179,hypothesis,
! [E,S1,S2,T] :
( ( environment(E)
& in_environment(E,T)
& ~ greater(zero,growth_rate(S1,T))
& greater(resilience(S2),resilience(S1)) )
=> ~ greater(zero,growth_rate(S2,T)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a12) ).
tff(f_101,axiom,
! [S,T] :
( ( cardinality_at_time(S,T) = zero )
=> ~ greater(zero,growth_rate(S,T)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_empty_not_decreasing) ).
tff(f_74,axiom,
! [E,T] :
( ( environment(E)
& in_environment(E,T)
& ~ decreases(number_of_organizations(E,T)) )
=> ? [X] :
( subpopulation(X,E,T)
& greater(cardinality_at_time(X,T),zero)
& ~ greater(zero,growth_rate(X,T)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_non_decreasing) ).
tff(f_192,hypothesis,
! [E,X,T] :
( ( environment(E)
& subpopulation(X,E,T)
& greater(cardinality_at_time(X,T),zero) )
=> ( ( X = efficient_producers )
| ( X = first_movers ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a9) ).
tff(f_125,axiom,
! [E,T] :
( ( environment(E)
& in_environment(E,T) )
=> ( greater_or_equal(T,appear(an_organisation,E))
| greater(appear(an_organisation,E),T) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_environment_inequality) ).
tff(f_150,hypothesis,
! [E,T] :
( ( environment(E)
& in_environment(E,T)
& greater_or_equal(T,appear(an_organisation,E)) )
=> greater(number_of_organizations(E,T),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1) ).
tff(f_141,hypothesis,
! [E,T] :
( ( environment(E)
& in_environment(E,T)
& greater(number_of_organizations(E,T),zero) )
=> ( ( greater(equilibrium(E),T)
=> decreases(resources(E,T)) )
& ( ~ greater(equilibrium(E),T)
=> constant(resources(E,T)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a3) ).
tff(f_56,axiom,
! [E,T] :
( ( environment(E)
& in_environment(E,T)
& greater(appear(an_organisation,E),T) )
=> ( number_of_organizations(E,T) = zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_start_of_organizations) ).
tff(f_165,hypothesis,
! [E,T] :
( ( environment(E)
& in_environment(E,T) )
=> ( ( decreases(resources(E,T))
=> ~ decreases(number_of_organizations(E,T)) )
& ( constant(resources(E,T))
=> constant(number_of_organizations(E,T)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a6) ).
tff(f_116,axiom,
! [X] :
( constant(X)
=> ~ decreases(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_constant_not_decrease) ).
tff(f_95,axiom,
! [E,T] :
( ( environment(E)
& in_environment(E,T) )
=> ( subpopulation(first_movers,E,T)
& subpopulation(efficient_producers,E,T) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_subpopulations) ).
tff(f_86,axiom,
! [E,T,X] :
( ( environment(E)
& in_environment(E,T)
& ( number_of_organizations(E,T) = zero )
& subpopulation(X,E,T) )
=> ( cardinality_at_time(X,T) = zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_no_members) ).
tff(c_54,plain,
environment('#skF_3'),
inference(cnfTransformation,[status(thm)],[f_203]) ).
tff(c_50,plain,
greater_or_equal('#skF_4',appear(efficient_producers,'#skF_3')),
inference(cnfTransformation,[status(thm)],[f_203]) ).
tff(c_48,plain,
~ greater(cardinality_at_time(efficient_producers,'#skF_4'),zero),
inference(cnfTransformation,[status(thm)],[f_203]) ).
tff(c_52,plain,
in_environment('#skF_3','#skF_4'),
inference(cnfTransformation,[status(thm)],[f_203]) ).
tff(c_62,plain,
! [T_47,E_48] :
( greater(cardinality_at_time(efficient_producers,T_47),zero)
| ( cardinality_at_time(efficient_producers,T_47) = zero )
| ~ in_environment(E_48,T_47)
| ~ environment(E_48) ),
inference(cnfTransformation,[status(thm)],[f_110]) ).
tff(c_64,plain,
( greater(cardinality_at_time(efficient_producers,'#skF_4'),zero)
| ( cardinality_at_time(efficient_producers,'#skF_4') = zero )
| ~ environment('#skF_3') ),
inference(resolution,[status(thm)],[c_52,c_62]) ).
tff(c_67,plain,
( greater(cardinality_at_time(efficient_producers,'#skF_4'),zero)
| ( cardinality_at_time(efficient_producers,'#skF_4') = zero ) ),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_64]) ).
tff(c_68,plain,
cardinality_at_time(efficient_producers,'#skF_4') = zero,
inference(negUnitSimplification,[status(thm)],[c_48,c_67]) ).
tff(c_6,plain,
! [E_1,T_2] :
( in_environment(E_1,'#skF_1'(E_1,T_2))
| ( cardinality_at_time(efficient_producers,T_2) != zero )
| ~ greater_or_equal(T_2,appear(efficient_producers,E_1))
| ~ environment(E_1) ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_44,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(cnfTransformation,[status(thm)],[f_181]) ).
tff(c_2,plain,
! [E_1,T_2] :
( greater(zero,growth_rate(efficient_producers,'#skF_1'(E_1,T_2)))
| ( cardinality_at_time(efficient_producers,T_2) != zero )
| ~ greater_or_equal(T_2,appear(efficient_producers,E_1))
| ~ environment(E_1) ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_170,plain,
! [S2_91,T_92,S1_93,E_94] :
( ~ greater(zero,growth_rate(S2_91,T_92))
| ~ greater(resilience(S2_91),resilience(S1_93))
| greater(zero,growth_rate(S1_93,T_92))
| ~ in_environment(E_94,T_92)
| ~ environment(E_94) ),
inference(cnfTransformation,[status(thm)],[f_179]) ).
tff(c_260,plain,
! [S1_124,E_125,T_126,E_127] :
( ~ greater(resilience(efficient_producers),resilience(S1_124))
| greater(zero,growth_rate(S1_124,'#skF_1'(E_125,T_126)))
| ~ in_environment(E_127,'#skF_1'(E_125,T_126))
| ~ environment(E_127)
| ( cardinality_at_time(efficient_producers,T_126) != zero )
| ~ greater_or_equal(T_126,appear(efficient_producers,E_125))
| ~ environment(E_125) ),
inference(resolution,[status(thm)],[c_2,c_170]) ).
tff(c_351,plain,
! [E_134,T_135,E_136] :
( greater(zero,growth_rate(first_movers,'#skF_1'(E_134,T_135)))
| ~ in_environment(E_136,'#skF_1'(E_134,T_135))
| ~ environment(E_136)
| ( cardinality_at_time(efficient_producers,T_135) != zero )
| ~ greater_or_equal(T_135,appear(efficient_producers,E_134))
| ~ environment(E_134) ),
inference(resolution,[status(thm)],[c_44,c_260]) ).
tff(c_354,plain,
! [E_1,T_2] :
( greater(zero,growth_rate(first_movers,'#skF_1'(E_1,T_2)))
| ( cardinality_at_time(efficient_producers,T_2) != zero )
| ~ greater_or_equal(T_2,appear(efficient_producers,E_1))
| ~ environment(E_1) ),
inference(resolution,[status(thm)],[c_6,c_351]) ).
tff(c_403,plain,
! [E_137,T_138] :
( greater(zero,growth_rate(first_movers,'#skF_1'(E_137,T_138)))
| ( cardinality_at_time(efficient_producers,T_138) != zero )
| ~ greater_or_equal(T_138,appear(efficient_producers,E_137))
| ~ environment(E_137) ),
inference(resolution,[status(thm)],[c_6,c_351]) ).
tff(c_24,plain,
! [S_14,T_15] :
( ~ greater(zero,growth_rate(S_14,T_15))
| ( cardinality_at_time(S_14,T_15) != zero ) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_412,plain,
! [E_139,T_140] :
( ( cardinality_at_time(first_movers,'#skF_1'(E_139,T_140)) != zero )
| ( cardinality_at_time(efficient_producers,T_140) != zero )
| ~ greater_or_equal(T_140,appear(efficient_producers,E_139))
| ~ environment(E_139) ),
inference(resolution,[status(thm)],[c_403,c_24]) ).
tff(c_415,plain,
( ( cardinality_at_time(first_movers,'#skF_1'('#skF_3','#skF_4')) != zero )
| ( cardinality_at_time(efficient_producers,'#skF_4') != zero )
| ~ environment('#skF_3') ),
inference(resolution,[status(thm)],[c_50,c_412]) ).
tff(c_418,plain,
cardinality_at_time(first_movers,'#skF_1'('#skF_3','#skF_4')) != zero,
inference(demodulation,[status(thm),theory(equality)],[c_54,c_68,c_415]) ).
tff(c_16,plain,
! [E_6,T_7] :
( subpopulation('#skF_2'(E_6,T_7),E_6,T_7)
| decreases(number_of_organizations(E_6,T_7))
| ~ in_environment(E_6,T_7)
| ~ environment(E_6) ),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_95,plain,
! [E_64,T_65] :
( greater(cardinality_at_time('#skF_2'(E_64,T_65),T_65),zero)
| decreases(number_of_organizations(E_64,T_65))
| ~ in_environment(E_64,T_65)
| ~ environment(E_64) ),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_46,plain,
! [X_32,T_33,E_31] :
( ( first_movers = X_32 )
| ( efficient_producers = X_32 )
| ~ greater(cardinality_at_time(X_32,T_33),zero)
| ~ subpopulation(X_32,E_31,T_33)
| ~ environment(E_31) ),
inference(cnfTransformation,[status(thm)],[f_192]) ).
tff(c_245,plain,
! [E_117,T_118,E_119] :
( ( '#skF_2'(E_117,T_118) = first_movers )
| ( '#skF_2'(E_117,T_118) = efficient_producers )
| ~ subpopulation('#skF_2'(E_117,T_118),E_119,T_118)
| ~ environment(E_119)
| decreases(number_of_organizations(E_117,T_118))
| ~ in_environment(E_117,T_118)
| ~ environment(E_117) ),
inference(resolution,[status(thm)],[c_95,c_46]) ).
tff(c_250,plain,
! [E_120,T_121] :
( ( '#skF_2'(E_120,T_121) = first_movers )
| ( '#skF_2'(E_120,T_121) = efficient_producers )
| decreases(number_of_organizations(E_120,T_121))
| ~ in_environment(E_120,T_121)
| ~ environment(E_120) ),
inference(resolution,[status(thm)],[c_16,c_245]) ).
tff(c_79,plain,
! [E_56,T_57] :
( greater(appear(an_organisation,E_56),T_57)
| greater_or_equal(T_57,appear(an_organisation,E_56))
| ~ in_environment(E_56,T_57)
| ~ environment(E_56) ),
inference(cnfTransformation,[status(thm)],[f_125]) ).
tff(c_36,plain,
! [E_23,T_24] :
( greater(number_of_organizations(E_23,T_24),zero)
| ~ greater_or_equal(T_24,appear(an_organisation,E_23))
| ~ in_environment(E_23,T_24)
| ~ environment(E_23) ),
inference(cnfTransformation,[status(thm)],[f_150]) ).
tff(c_83,plain,
! [E_56,T_57] :
( greater(number_of_organizations(E_56,T_57),zero)
| greater(appear(an_organisation,E_56),T_57)
| ~ in_environment(E_56,T_57)
| ~ environment(E_56) ),
inference(resolution,[status(thm)],[c_79,c_36]) ).
tff(c_149,plain,
! [E_81,T_82] :
( constant(resources(E_81,T_82))
| greater(equilibrium(E_81),T_82)
| ~ greater(number_of_organizations(E_81,T_82),zero)
| ~ in_environment(E_81,T_82)
| ~ environment(E_81) ),
inference(cnfTransformation,[status(thm)],[f_141]) ).
tff(c_159,plain,
! [E_85,T_86] :
( constant(resources(E_85,T_86))
| greater(equilibrium(E_85),T_86)
| greater(appear(an_organisation,E_85),T_86)
| ~ in_environment(E_85,T_86)
| ~ environment(E_85) ),
inference(resolution,[status(thm)],[c_83,c_149]) ).
tff(c_10,plain,
! [E_4,T_5] :
( ( number_of_organizations(E_4,T_5) = zero )
| ~ greater(appear(an_organisation,E_4),T_5)
| ~ in_environment(E_4,T_5)
| ~ environment(E_4) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_163,plain,
! [E_85,T_86] :
( ( number_of_organizations(E_85,T_86) = zero )
| constant(resources(E_85,T_86))
| greater(equilibrium(E_85),T_86)
| ~ in_environment(E_85,T_86)
| ~ environment(E_85) ),
inference(resolution,[status(thm)],[c_159,c_10]) ).
tff(c_154,plain,
! [E_83,T_84] :
( decreases(resources(E_83,T_84))
| ~ greater(equilibrium(E_83),T_84)
| ~ greater(number_of_organizations(E_83,T_84),zero)
| ~ in_environment(E_83,T_84)
| ~ environment(E_83) ),
inference(cnfTransformation,[status(thm)],[f_141]) ).
tff(c_165,plain,
! [E_89,T_90] :
( decreases(resources(E_89,T_90))
| ~ greater(equilibrium(E_89),T_90)
| greater(appear(an_organisation,E_89),T_90)
| ~ in_environment(E_89,T_90)
| ~ environment(E_89) ),
inference(resolution,[status(thm)],[c_83,c_154]) ).
tff(c_174,plain,
! [E_95,T_96] :
( ( number_of_organizations(E_95,T_96) = zero )
| decreases(resources(E_95,T_96))
| ~ greater(equilibrium(E_95),T_96)
| ~ in_environment(E_95,T_96)
| ~ environment(E_95) ),
inference(resolution,[status(thm)],[c_165,c_10]) ).
tff(c_179,plain,
! [E_97,T_98] :
( decreases(resources(E_97,T_98))
| ( number_of_organizations(E_97,T_98) = zero )
| constant(resources(E_97,T_98))
| ~ in_environment(E_97,T_98)
| ~ environment(E_97) ),
inference(resolution,[status(thm)],[c_163,c_174]) ).
tff(c_40,plain,
! [E_25,T_26] :
( ~ decreases(number_of_organizations(E_25,T_26))
| ~ decreases(resources(E_25,T_26))
| ~ in_environment(E_25,T_26)
| ~ environment(E_25) ),
inference(cnfTransformation,[status(thm)],[f_165]) ).
tff(c_186,plain,
! [E_97,T_98] :
( ~ decreases(number_of_organizations(E_97,T_98))
| ( number_of_organizations(E_97,T_98) = zero )
| constant(resources(E_97,T_98))
| ~ in_environment(E_97,T_98)
| ~ environment(E_97) ),
inference(resolution,[status(thm)],[c_179,c_40]) ).
tff(c_264,plain,
! [E_128,T_129] :
( ( number_of_organizations(E_128,T_129) = zero )
| constant(resources(E_128,T_129))
| ( '#skF_2'(E_128,T_129) = first_movers )
| ( '#skF_2'(E_128,T_129) = efficient_producers )
| ~ in_environment(E_128,T_129)
| ~ environment(E_128) ),
inference(resolution,[status(thm)],[c_250,c_186]) ).
tff(c_38,plain,
! [E_25,T_26] :
( constant(number_of_organizations(E_25,T_26))
| ~ constant(resources(E_25,T_26))
| ~ in_environment(E_25,T_26)
| ~ environment(E_25) ),
inference(cnfTransformation,[status(thm)],[f_165]) ).
tff(c_269,plain,
! [E_130,T_131] :
( constant(number_of_organizations(E_130,T_131))
| ( number_of_organizations(E_130,T_131) = zero )
| ( '#skF_2'(E_130,T_131) = first_movers )
| ( '#skF_2'(E_130,T_131) = efficient_producers )
| ~ in_environment(E_130,T_131)
| ~ environment(E_130) ),
inference(resolution,[status(thm)],[c_264,c_38]) ).
tff(c_28,plain,
! [X_18] :
( ~ decreases(X_18)
| ~ constant(X_18) ),
inference(cnfTransformation,[status(thm)],[f_116]) ).
tff(c_258,plain,
! [E_120,T_121] :
( ~ constant(number_of_organizations(E_120,T_121))
| ( '#skF_2'(E_120,T_121) = first_movers )
| ( '#skF_2'(E_120,T_121) = efficient_producers )
| ~ in_environment(E_120,T_121)
| ~ environment(E_120) ),
inference(resolution,[status(thm)],[c_250,c_28]) ).
tff(c_278,plain,
! [E_132,T_133] :
( ( number_of_organizations(E_132,T_133) = zero )
| ( '#skF_2'(E_132,T_133) = first_movers )
| ( '#skF_2'(E_132,T_133) = efficient_producers )
| ~ in_environment(E_132,T_133)
| ~ environment(E_132) ),
inference(resolution,[status(thm)],[c_269,c_258]) ).
tff(c_419,plain,
! [E_141,T_142] :
( ( number_of_organizations(E_141,'#skF_1'(E_141,T_142)) = zero )
| ( '#skF_2'(E_141,'#skF_1'(E_141,T_142)) = first_movers )
| ( '#skF_2'(E_141,'#skF_1'(E_141,T_142)) = efficient_producers )
| ( cardinality_at_time(efficient_producers,T_142) != zero )
| ~ greater_or_equal(T_142,appear(efficient_producers,E_141))
| ~ environment(E_141) ),
inference(resolution,[status(thm)],[c_6,c_278]) ).
tff(c_421,plain,
( ( number_of_organizations('#skF_3','#skF_1'('#skF_3','#skF_4')) = zero )
| ( '#skF_2'('#skF_3','#skF_1'('#skF_3','#skF_4')) = first_movers )
| ( '#skF_2'('#skF_3','#skF_1'('#skF_3','#skF_4')) = efficient_producers )
| ( cardinality_at_time(efficient_producers,'#skF_4') != zero )
| ~ environment('#skF_3') ),
inference(resolution,[status(thm)],[c_50,c_419]) ).
tff(c_424,plain,
( ( number_of_organizations('#skF_3','#skF_1'('#skF_3','#skF_4')) = zero )
| ( '#skF_2'('#skF_3','#skF_1'('#skF_3','#skF_4')) = first_movers )
| ( '#skF_2'('#skF_3','#skF_1'('#skF_3','#skF_4')) = efficient_producers ) ),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_68,c_421]) ).
tff(c_425,plain,
'#skF_2'('#skF_3','#skF_1'('#skF_3','#skF_4')) = efficient_producers,
inference(splitLeft,[status(thm)],[c_424]) ).
tff(c_435,plain,
( subpopulation(efficient_producers,'#skF_3','#skF_1'('#skF_3','#skF_4'))
| decreases(number_of_organizations('#skF_3','#skF_1'('#skF_3','#skF_4')))
| ~ in_environment('#skF_3','#skF_1'('#skF_3','#skF_4'))
| ~ environment('#skF_3') ),
inference(superposition,[status(thm),theory(equality)],[c_425,c_16]) ).
tff(c_443,plain,
( subpopulation(efficient_producers,'#skF_3','#skF_1'('#skF_3','#skF_4'))
| decreases(number_of_organizations('#skF_3','#skF_1'('#skF_3','#skF_4')))
| ~ in_environment('#skF_3','#skF_1'('#skF_3','#skF_4')) ),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_435]) ).
tff(c_445,plain,
~ in_environment('#skF_3','#skF_1'('#skF_3','#skF_4')),
inference(splitLeft,[status(thm)],[c_443]) ).
tff(c_448,plain,
( ( cardinality_at_time(efficient_producers,'#skF_4') != zero )
| ~ greater_or_equal('#skF_4',appear(efficient_producers,'#skF_3'))
| ~ environment('#skF_3') ),
inference(resolution,[status(thm)],[c_6,c_445]) ).
tff(c_452,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_54,c_50,c_68,c_448]) ).
tff(c_454,plain,
in_environment('#skF_3','#skF_1'('#skF_3','#skF_4')),
inference(splitRight,[status(thm)],[c_443]) ).
tff(c_12,plain,
! [E_6,T_7] :
( ~ greater(zero,growth_rate('#skF_2'(E_6,T_7),T_7))
| decreases(number_of_organizations(E_6,T_7))
| ~ in_environment(E_6,T_7)
| ~ environment(E_6) ),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_429,plain,
( ~ greater(zero,growth_rate(efficient_producers,'#skF_1'('#skF_3','#skF_4')))
| decreases(number_of_organizations('#skF_3','#skF_1'('#skF_3','#skF_4')))
| ~ in_environment('#skF_3','#skF_1'('#skF_3','#skF_4'))
| ~ environment('#skF_3') ),
inference(superposition,[status(thm),theory(equality)],[c_425,c_12]) ).
tff(c_439,plain,
( ~ greater(zero,growth_rate(efficient_producers,'#skF_1'('#skF_3','#skF_4')))
| decreases(number_of_organizations('#skF_3','#skF_1'('#skF_3','#skF_4')))
| ~ in_environment('#skF_3','#skF_1'('#skF_3','#skF_4')) ),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_429]) ).
tff(c_490,plain,
( ~ greater(zero,growth_rate(efficient_producers,'#skF_1'('#skF_3','#skF_4')))
| decreases(number_of_organizations('#skF_3','#skF_1'('#skF_3','#skF_4'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_454,c_439]) ).
tff(c_491,plain,
~ greater(zero,growth_rate(efficient_producers,'#skF_1'('#skF_3','#skF_4'))),
inference(splitLeft,[status(thm)],[c_490]) ).
tff(c_494,plain,
( ( cardinality_at_time(efficient_producers,'#skF_4') != zero )
| ~ greater_or_equal('#skF_4',appear(efficient_producers,'#skF_3'))
| ~ environment('#skF_3') ),
inference(resolution,[status(thm)],[c_2,c_491]) ).
tff(c_498,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_54,c_50,c_68,c_494]) ).
tff(c_499,plain,
decreases(number_of_organizations('#skF_3','#skF_1'('#skF_3','#skF_4'))),
inference(splitRight,[status(thm)],[c_490]) ).
tff(c_511,plain,
~ constant(number_of_organizations('#skF_3','#skF_1'('#skF_3','#skF_4'))),
inference(resolution,[status(thm)],[c_499,c_28]) ).
tff(c_137,plain,
! [E_77,T_78] :
( greater(zero,growth_rate(efficient_producers,'#skF_1'(E_77,T_78)))
| ( cardinality_at_time(efficient_producers,T_78) != zero )
| ~ greater_or_equal(T_78,appear(efficient_producers,E_77))
| ~ environment(E_77) ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_142,plain,
! [E_79,T_80] :
( ( cardinality_at_time(efficient_producers,'#skF_1'(E_79,T_80)) != zero )
| ( cardinality_at_time(efficient_producers,T_80) != zero )
| ~ greater_or_equal(T_80,appear(efficient_producers,E_79))
| ~ environment(E_79) ),
inference(resolution,[status(thm)],[c_137,c_24]) ).
tff(c_145,plain,
( ( cardinality_at_time(efficient_producers,'#skF_1'('#skF_3','#skF_4')) != zero )
| ( cardinality_at_time(efficient_producers,'#skF_4') != zero )
| ~ environment('#skF_3') ),
inference(resolution,[status(thm)],[c_50,c_142]) ).
tff(c_148,plain,
cardinality_at_time(efficient_producers,'#skF_1'('#skF_3','#skF_4')) != zero,
inference(demodulation,[status(thm),theory(equality)],[c_54,c_68,c_145]) ).
tff(c_20,plain,
! [E_12,T_13] :
( subpopulation(efficient_producers,E_12,T_13)
| ~ in_environment(E_12,T_13)
| ~ environment(E_12) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_100,plain,
! [X_68,T_69,E_70] :
( ( cardinality_at_time(X_68,T_69) = zero )
| ~ subpopulation(X_68,E_70,T_69)
| ( number_of_organizations(E_70,T_69) != zero )
| ~ in_environment(E_70,T_69)
| ~ environment(E_70) ),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_112,plain,
! [T_13,E_12] :
( ( cardinality_at_time(efficient_producers,T_13) = zero )
| ( number_of_organizations(E_12,T_13) != zero )
| ~ in_environment(E_12,T_13)
| ~ environment(E_12) ),
inference(resolution,[status(thm)],[c_20,c_100]) ).
tff(c_460,plain,
( ( cardinality_at_time(efficient_producers,'#skF_1'('#skF_3','#skF_4')) = zero )
| ( number_of_organizations('#skF_3','#skF_1'('#skF_3','#skF_4')) != zero )
| ~ environment('#skF_3') ),
inference(resolution,[status(thm)],[c_454,c_112]) ).
tff(c_472,plain,
( ( cardinality_at_time(efficient_producers,'#skF_1'('#skF_3','#skF_4')) = zero )
| ( number_of_organizations('#skF_3','#skF_1'('#skF_3','#skF_4')) != zero ) ),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_460]) ).
tff(c_473,plain,
number_of_organizations('#skF_3','#skF_1'('#skF_3','#skF_4')) != zero,
inference(negUnitSimplification,[status(thm)],[c_148,c_472]) ).
tff(c_503,plain,
( ( number_of_organizations('#skF_3','#skF_1'('#skF_3','#skF_4')) = zero )
| constant(resources('#skF_3','#skF_1'('#skF_3','#skF_4')))
| ~ in_environment('#skF_3','#skF_1'('#skF_3','#skF_4'))
| ~ environment('#skF_3') ),
inference(resolution,[status(thm)],[c_499,c_186]) ).
tff(c_509,plain,
( ( number_of_organizations('#skF_3','#skF_1'('#skF_3','#skF_4')) = zero )
| constant(resources('#skF_3','#skF_1'('#skF_3','#skF_4'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_454,c_503]) ).
tff(c_510,plain,
constant(resources('#skF_3','#skF_1'('#skF_3','#skF_4'))),
inference(negUnitSimplification,[status(thm)],[c_473,c_509]) ).
tff(c_514,plain,
( constant(number_of_organizations('#skF_3','#skF_1'('#skF_3','#skF_4')))
| ~ in_environment('#skF_3','#skF_1'('#skF_3','#skF_4'))
| ~ environment('#skF_3') ),
inference(resolution,[status(thm)],[c_510,c_38]) ).
tff(c_517,plain,
constant(number_of_organizations('#skF_3','#skF_1'('#skF_3','#skF_4'))),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_454,c_514]) ).
tff(c_518,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_511,c_517]) ).
tff(c_519,plain,
( ( '#skF_2'('#skF_3','#skF_1'('#skF_3','#skF_4')) = first_movers )
| ( number_of_organizations('#skF_3','#skF_1'('#skF_3','#skF_4')) = zero ) ),
inference(splitRight,[status(thm)],[c_424]) ).
tff(c_522,plain,
number_of_organizations('#skF_3','#skF_1'('#skF_3','#skF_4')) = zero,
inference(splitLeft,[status(thm)],[c_519]) ).
tff(c_22,plain,
! [E_12,T_13] :
( subpopulation(first_movers,E_12,T_13)
| ~ in_environment(E_12,T_13)
| ~ environment(E_12) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_113,plain,
! [T_71,E_72] :
( ( cardinality_at_time(first_movers,T_71) = zero )
| ( number_of_organizations(E_72,T_71) != zero )
| ~ in_environment(E_72,T_71)
| ~ environment(E_72) ),
inference(resolution,[status(thm)],[c_22,c_100]) ).
tff(c_120,plain,
! [E_1,T_2] :
( ( cardinality_at_time(first_movers,'#skF_1'(E_1,T_2)) = zero )
| ( number_of_organizations(E_1,'#skF_1'(E_1,T_2)) != zero )
| ( cardinality_at_time(efficient_producers,T_2) != zero )
| ~ greater_or_equal(T_2,appear(efficient_producers,E_1))
| ~ environment(E_1) ),
inference(resolution,[status(thm)],[c_6,c_113]) ).
tff(c_531,plain,
( ( cardinality_at_time(first_movers,'#skF_1'('#skF_3','#skF_4')) = zero )
| ( cardinality_at_time(efficient_producers,'#skF_4') != zero )
| ~ greater_or_equal('#skF_4',appear(efficient_producers,'#skF_3'))
| ~ environment('#skF_3') ),
inference(superposition,[status(thm),theory(equality)],[c_522,c_120]) ).
tff(c_562,plain,
cardinality_at_time(first_movers,'#skF_1'('#skF_3','#skF_4')) = zero,
inference(demodulation,[status(thm),theory(equality)],[c_54,c_50,c_68,c_531]) ).
tff(c_564,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_418,c_562]) ).
tff(c_565,plain,
'#skF_2'('#skF_3','#skF_1'('#skF_3','#skF_4')) = first_movers,
inference(splitRight,[status(thm)],[c_519]) ).
tff(c_577,plain,
( subpopulation(first_movers,'#skF_3','#skF_1'('#skF_3','#skF_4'))
| decreases(number_of_organizations('#skF_3','#skF_1'('#skF_3','#skF_4')))
| ~ in_environment('#skF_3','#skF_1'('#skF_3','#skF_4'))
| ~ environment('#skF_3') ),
inference(superposition,[status(thm),theory(equality)],[c_565,c_16]) ).
tff(c_585,plain,
( subpopulation(first_movers,'#skF_3','#skF_1'('#skF_3','#skF_4'))
| decreases(number_of_organizations('#skF_3','#skF_1'('#skF_3','#skF_4')))
| ~ in_environment('#skF_3','#skF_1'('#skF_3','#skF_4')) ),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_577]) ).
tff(c_587,plain,
~ in_environment('#skF_3','#skF_1'('#skF_3','#skF_4')),
inference(splitLeft,[status(thm)],[c_585]) ).
tff(c_590,plain,
( ( cardinality_at_time(efficient_producers,'#skF_4') != zero )
| ~ greater_or_equal('#skF_4',appear(efficient_producers,'#skF_3'))
| ~ environment('#skF_3') ),
inference(resolution,[status(thm)],[c_6,c_587]) ).
tff(c_594,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_54,c_50,c_68,c_590]) ).
tff(c_596,plain,
in_environment('#skF_3','#skF_1'('#skF_3','#skF_4')),
inference(splitRight,[status(thm)],[c_585]) ).
tff(c_571,plain,
( ~ greater(zero,growth_rate(first_movers,'#skF_1'('#skF_3','#skF_4')))
| decreases(number_of_organizations('#skF_3','#skF_1'('#skF_3','#skF_4')))
| ~ in_environment('#skF_3','#skF_1'('#skF_3','#skF_4'))
| ~ environment('#skF_3') ),
inference(superposition,[status(thm),theory(equality)],[c_565,c_12]) ).
tff(c_581,plain,
( ~ greater(zero,growth_rate(first_movers,'#skF_1'('#skF_3','#skF_4')))
| decreases(number_of_organizations('#skF_3','#skF_1'('#skF_3','#skF_4')))
| ~ in_environment('#skF_3','#skF_1'('#skF_3','#skF_4')) ),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_571]) ).
tff(c_639,plain,
( ~ greater(zero,growth_rate(first_movers,'#skF_1'('#skF_3','#skF_4')))
| decreases(number_of_organizations('#skF_3','#skF_1'('#skF_3','#skF_4'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_596,c_581]) ).
tff(c_640,plain,
~ greater(zero,growth_rate(first_movers,'#skF_1'('#skF_3','#skF_4'))),
inference(splitLeft,[status(thm)],[c_639]) ).
tff(c_643,plain,
( ( cardinality_at_time(efficient_producers,'#skF_4') != zero )
| ~ greater_or_equal('#skF_4',appear(efficient_producers,'#skF_3'))
| ~ environment('#skF_3') ),
inference(resolution,[status(thm)],[c_354,c_640]) ).
tff(c_647,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_54,c_50,c_68,c_643]) ).
tff(c_648,plain,
decreases(number_of_organizations('#skF_3','#skF_1'('#skF_3','#skF_4'))),
inference(splitRight,[status(thm)],[c_639]) ).
tff(c_663,plain,
~ constant(number_of_organizations('#skF_3','#skF_1'('#skF_3','#skF_4'))),
inference(resolution,[status(thm)],[c_648,c_28]) ).
tff(c_566,plain,
number_of_organizations('#skF_3','#skF_1'('#skF_3','#skF_4')) != zero,
inference(splitRight,[status(thm)],[c_519]) ).
tff(c_655,plain,
( ( number_of_organizations('#skF_3','#skF_1'('#skF_3','#skF_4')) = zero )
| constant(resources('#skF_3','#skF_1'('#skF_3','#skF_4')))
| ~ in_environment('#skF_3','#skF_1'('#skF_3','#skF_4'))
| ~ environment('#skF_3') ),
inference(resolution,[status(thm)],[c_648,c_186]) ).
tff(c_661,plain,
( ( number_of_organizations('#skF_3','#skF_1'('#skF_3','#skF_4')) = zero )
| constant(resources('#skF_3','#skF_1'('#skF_3','#skF_4'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_596,c_655]) ).
tff(c_662,plain,
constant(resources('#skF_3','#skF_1'('#skF_3','#skF_4'))),
inference(negUnitSimplification,[status(thm)],[c_566,c_661]) ).
tff(c_667,plain,
( constant(number_of_organizations('#skF_3','#skF_1'('#skF_3','#skF_4')))
| ~ in_environment('#skF_3','#skF_1'('#skF_3','#skF_4'))
| ~ environment('#skF_3') ),
inference(resolution,[status(thm)],[c_662,c_38]) ).
tff(c_670,plain,
constant(number_of_organizations('#skF_3','#skF_1'('#skF_3','#skF_4'))),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_596,c_667]) ).
tff(c_672,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_663,c_670]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT037+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.16/0.34 % Computer : n029.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Thu Aug 3 20:47:38 EDT 2023
% 0.16/0.35 % CPUTime :
% 4.38/2.09 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.64/2.10
% 4.64/2.10 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.64/2.15
% 4.64/2.15 Inference rules
% 4.64/2.15 ----------------------
% 4.64/2.15 #Ref : 0
% 4.64/2.15 #Sup : 111
% 4.64/2.15 #Fact : 2
% 4.64/2.15 #Define : 0
% 4.64/2.15 #Split : 11
% 4.64/2.15 #Chain : 0
% 4.64/2.15 #Close : 0
% 4.64/2.15
% 4.64/2.15 Ordering : KBO
% 4.64/2.15
% 4.64/2.15 Simplification rules
% 4.64/2.15 ----------------------
% 4.64/2.15 #Subsume : 18
% 4.64/2.15 #Demod : 94
% 4.64/2.15 #Tautology : 25
% 4.64/2.15 #SimpNegUnit : 30
% 4.64/2.15 #BackRed : 2
% 4.64/2.15
% 4.64/2.15 #Partial instantiations: 0
% 4.64/2.15 #Strategies tried : 1
% 4.64/2.15
% 4.64/2.15 Timing (in seconds)
% 4.64/2.15 ----------------------
% 4.64/2.15 Preprocessing : 0.53
% 4.64/2.15 Parsing : 0.30
% 4.64/2.15 CNF conversion : 0.03
% 4.64/2.15 Main loop : 0.49
% 4.64/2.15 Inferencing : 0.21
% 4.64/2.15 Reduction : 0.13
% 4.64/2.15 Demodulation : 0.09
% 4.64/2.15 BG Simplification : 0.02
% 4.64/2.15 Subsumption : 0.09
% 4.64/2.15 Abstraction : 0.02
% 4.64/2.15 MUC search : 0.00
% 4.64/2.15 Cooper : 0.00
% 4.64/2.15 Total : 1.10
% 4.64/2.15 Index Insertion : 0.00
% 4.64/2.15 Index Deletion : 0.00
% 4.64/2.15 Index Matching : 0.00
% 4.64/2.15 BG Taut test : 0.00
%------------------------------------------------------------------------------