TSTP Solution File: MGT024+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : MGT024+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 : n012.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 10:49:35 EDT 2023
% Result : Theorem 3.97s 1.88s
% Output : CNFRefutation 4.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 23
% Syntax : Number of formulae : 137 ( 49 unt; 16 typ; 0 def)
% Number of atoms : 332 ( 28 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 371 ( 160 ~; 182 |; 18 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 11 >; 9 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 72 (; 72 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subpopulations > in_environment > greater_or_equal > greater > environment > decreases > constant > resources > number_of_organizations > growth_rate > #nlpp > equilibrium > zero > first_movers > efficient_producers > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(subpopulations,type,
subpopulations: ( $i * $i * $i * $i ) > $o ).
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(efficient_producers,type,
efficient_producers: $i ).
tff(growth_rate,type,
growth_rate: ( $i * $i ) > $i ).
tff(decreases,type,
decreases: $i > $o ).
tff('#skF_2',type,
'#skF_2': $i ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(environment,type,
environment: $i > $o ).
tff(first_movers,type,
first_movers: $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(zero,type,
zero: $i ).
tff(f_126,negated_conjecture,
~ ! [E,T] :
( ( environment(E)
& subpopulations(first_movers,efficient_producers,E,T)
& greater_or_equal(T,equilibrium(E)) )
=> ( ( ( growth_rate(first_movers,T) = zero )
& ( growth_rate(efficient_producers,T) = zero ) )
| ( greater(growth_rate(first_movers,T),zero)
& greater(zero,growth_rate(efficient_producers,T)) )
| ( greater(growth_rate(efficient_producers,T),zero)
& greater(zero,growth_rate(first_movers,T)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l6) ).
tff(f_37,axiom,
! [E,T] :
( ( environment(E)
& subpopulations(first_movers,efficient_producers,E,T) )
=> in_environment(E,T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_time_point_occur) ).
tff(f_45,axiom,
! [E,T] :
( ( environment(E)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(number_of_organizations(E,T),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_positive_number_of_organizations) ).
tff(f_69,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_53,axiom,
! [E,T] :
( ( environment(E)
& greater_or_equal(T,equilibrium(E)) )
=> ~ greater(equilibrium(E),T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_equilibrium) ).
tff(f_84,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_105,hypothesis,
! [E,T] :
( ( environment(E)
& subpopulations(first_movers,efficient_producers,E,T)
& constant(number_of_organizations(E,T)) )
=> ( ( ( growth_rate(first_movers,T) = zero )
& ( growth_rate(efficient_producers,T) = zero ) )
| ( greater(growth_rate(first_movers,T),zero)
& greater(zero,growth_rate(efficient_producers,T)) )
| ( greater(growth_rate(efficient_producers,T),zero)
& greater(zero,growth_rate(first_movers,T)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l7) ).
tff(c_32,plain,
( ~ greater(zero,growth_rate(first_movers,'#skF_2'))
| ~ greater(growth_rate(efficient_producers,'#skF_2'),zero) ),
inference(cnfTransformation,[status(thm)],[f_126]) ).
tff(c_203,plain,
~ greater(growth_rate(efficient_producers,'#skF_2'),zero),
inference(splitLeft,[status(thm)],[c_32]) ).
tff(c_52,plain,
~ greater(growth_rate(efficient_producers,'#skF_2'),zero),
inference(splitLeft,[status(thm)],[c_32]) ).
tff(c_34,plain,
( ~ greater(zero,growth_rate(efficient_producers,'#skF_2'))
| ~ greater(growth_rate(first_movers,'#skF_2'),zero) ),
inference(cnfTransformation,[status(thm)],[f_126]) ).
tff(c_51,plain,
~ greater(growth_rate(first_movers,'#skF_2'),zero),
inference(splitLeft,[status(thm)],[c_34]) ).
tff(c_36,plain,
( ( growth_rate(efficient_producers,'#skF_2') != zero )
| ( growth_rate(first_movers,'#skF_2') != zero ) ),
inference(cnfTransformation,[status(thm)],[f_126]) ).
tff(c_43,plain,
growth_rate(first_movers,'#skF_2') != zero,
inference(splitLeft,[status(thm)],[c_36]) ).
tff(c_42,plain,
environment('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_126]) ).
tff(c_40,plain,
subpopulations(first_movers,efficient_producers,'#skF_1','#skF_2'),
inference(cnfTransformation,[status(thm)],[f_126]) ).
tff(c_53,plain,
! [E_15,T_16] :
( in_environment(E_15,T_16)
| ~ subpopulations(first_movers,efficient_producers,E_15,T_16)
| ~ environment(E_15) ),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_56,plain,
( in_environment('#skF_1','#skF_2')
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_40,c_53]) ).
tff(c_59,plain,
in_environment('#skF_1','#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_42,c_56]) ).
tff(c_4,plain,
! [E_3,T_4] :
( greater(number_of_organizations(E_3,T_4),zero)
| ~ subpopulations(first_movers,efficient_producers,E_3,T_4)
| ~ environment(E_3) ),
inference(cnfTransformation,[status(thm)],[f_45]) ).
tff(c_63,plain,
! [E_23,T_24] :
( constant(resources(E_23,T_24))
| greater(equilibrium(E_23),T_24)
| ~ greater(number_of_organizations(E_23,T_24),zero)
| ~ in_environment(E_23,T_24)
| ~ environment(E_23) ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_73,plain,
! [E_27,T_28] :
( constant(resources(E_27,T_28))
| greater(equilibrium(E_27),T_28)
| ~ in_environment(E_27,T_28)
| ~ subpopulations(first_movers,efficient_producers,E_27,T_28)
| ~ environment(E_27) ),
inference(resolution,[status(thm)],[c_4,c_63]) ).
tff(c_38,plain,
greater_or_equal('#skF_2',equilibrium('#skF_1')),
inference(cnfTransformation,[status(thm)],[f_126]) ).
tff(c_44,plain,
! [E_13,T_14] :
( ~ greater(equilibrium(E_13),T_14)
| ~ greater_or_equal(T_14,equilibrium(E_13))
| ~ environment(E_13) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_47,plain,
( ~ greater(equilibrium('#skF_1'),'#skF_2')
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_38,c_44]) ).
tff(c_50,plain,
~ greater(equilibrium('#skF_1'),'#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_42,c_47]) ).
tff(c_76,plain,
( constant(resources('#skF_1','#skF_2'))
| ~ in_environment('#skF_1','#skF_2')
| ~ subpopulations(first_movers,efficient_producers,'#skF_1','#skF_2')
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_73,c_50]) ).
tff(c_79,plain,
constant(resources('#skF_1','#skF_2')),
inference(demodulation,[status(thm),theory(equality)],[c_42,c_40,c_59,c_76]) ).
tff(c_12,plain,
! [E_9,T_10] :
( constant(number_of_organizations(E_9,T_10))
| ~ constant(resources(E_9,T_10))
| ~ in_environment(E_9,T_10)
| ~ environment(E_9) ),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_82,plain,
( constant(number_of_organizations('#skF_1','#skF_2'))
| ~ in_environment('#skF_1','#skF_2')
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_79,c_12]) ).
tff(c_85,plain,
constant(number_of_organizations('#skF_1','#skF_2')),
inference(demodulation,[status(thm),theory(equality)],[c_42,c_59,c_82]) ).
tff(c_126,plain,
! [T_43,E_44] :
( ( growth_rate(first_movers,T_43) = zero )
| greater(growth_rate(first_movers,T_43),zero)
| greater(growth_rate(efficient_producers,T_43),zero)
| ~ constant(number_of_organizations(E_44,T_43))
| ~ subpopulations(first_movers,efficient_producers,E_44,T_43)
| ~ environment(E_44) ),
inference(cnfTransformation,[status(thm)],[f_105]) ).
tff(c_128,plain,
( ( growth_rate(first_movers,'#skF_2') = zero )
| greater(growth_rate(first_movers,'#skF_2'),zero)
| greater(growth_rate(efficient_producers,'#skF_2'),zero)
| ~ subpopulations(first_movers,efficient_producers,'#skF_1','#skF_2')
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_85,c_126]) ).
tff(c_131,plain,
( ( growth_rate(first_movers,'#skF_2') = zero )
| greater(growth_rate(first_movers,'#skF_2'),zero)
| greater(growth_rate(efficient_producers,'#skF_2'),zero) ),
inference(demodulation,[status(thm),theory(equality)],[c_42,c_40,c_128]) ).
tff(c_133,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_52,c_51,c_43,c_131]) ).
tff(c_134,plain,
~ greater(zero,growth_rate(first_movers,'#skF_2')),
inference(splitRight,[status(thm)],[c_32]) ).
tff(c_136,plain,
! [E_45,T_46] :
( in_environment(E_45,T_46)
| ~ subpopulations(first_movers,efficient_producers,E_45,T_46)
| ~ environment(E_45) ),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_139,plain,
( in_environment('#skF_1','#skF_2')
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_40,c_136]) ).
tff(c_142,plain,
in_environment('#skF_1','#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_42,c_139]) ).
tff(c_146,plain,
! [E_53,T_54] :
( constant(resources(E_53,T_54))
| greater(equilibrium(E_53),T_54)
| ~ greater(number_of_organizations(E_53,T_54),zero)
| ~ in_environment(E_53,T_54)
| ~ environment(E_53) ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_156,plain,
! [E_57,T_58] :
( constant(resources(E_57,T_58))
| greater(equilibrium(E_57),T_58)
| ~ in_environment(E_57,T_58)
| ~ subpopulations(first_movers,efficient_producers,E_57,T_58)
| ~ environment(E_57) ),
inference(resolution,[status(thm)],[c_4,c_146]) ).
tff(c_159,plain,
( constant(resources('#skF_1','#skF_2'))
| ~ in_environment('#skF_1','#skF_2')
| ~ subpopulations(first_movers,efficient_producers,'#skF_1','#skF_2')
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_156,c_50]) ).
tff(c_162,plain,
constant(resources('#skF_1','#skF_2')),
inference(demodulation,[status(thm),theory(equality)],[c_42,c_40,c_142,c_159]) ).
tff(c_165,plain,
( constant(number_of_organizations('#skF_1','#skF_2'))
| ~ in_environment('#skF_1','#skF_2')
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_162,c_12]) ).
tff(c_168,plain,
constant(number_of_organizations('#skF_1','#skF_2')),
inference(demodulation,[status(thm),theory(equality)],[c_42,c_142,c_165]) ).
tff(c_193,plain,
! [T_69,E_70] :
( ( growth_rate(first_movers,T_69) = zero )
| greater(growth_rate(first_movers,T_69),zero)
| greater(zero,growth_rate(first_movers,T_69))
| ~ constant(number_of_organizations(E_70,T_69))
| ~ subpopulations(first_movers,efficient_producers,E_70,T_69)
| ~ environment(E_70) ),
inference(cnfTransformation,[status(thm)],[f_105]) ).
tff(c_195,plain,
( ( growth_rate(first_movers,'#skF_2') = zero )
| greater(growth_rate(first_movers,'#skF_2'),zero)
| greater(zero,growth_rate(first_movers,'#skF_2'))
| ~ subpopulations(first_movers,efficient_producers,'#skF_1','#skF_2')
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_168,c_193]) ).
tff(c_198,plain,
( ( growth_rate(first_movers,'#skF_2') = zero )
| greater(growth_rate(first_movers,'#skF_2'),zero)
| greater(zero,growth_rate(first_movers,'#skF_2')) ),
inference(demodulation,[status(thm),theory(equality)],[c_42,c_40,c_195]) ).
tff(c_200,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_134,c_51,c_43,c_198]) ).
tff(c_201,plain,
~ greater(zero,growth_rate(efficient_producers,'#skF_2')),
inference(splitRight,[status(thm)],[c_34]) ).
tff(c_204,plain,
! [E_71,T_72] :
( in_environment(E_71,T_72)
| ~ subpopulations(first_movers,efficient_producers,E_71,T_72)
| ~ environment(E_71) ),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_207,plain,
( in_environment('#skF_1','#skF_2')
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_40,c_204]) ).
tff(c_210,plain,
in_environment('#skF_1','#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_42,c_207]) ).
tff(c_214,plain,
! [E_79,T_80] :
( constant(resources(E_79,T_80))
| greater(equilibrium(E_79),T_80)
| ~ greater(number_of_organizations(E_79,T_80),zero)
| ~ in_environment(E_79,T_80)
| ~ environment(E_79) ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_224,plain,
! [E_83,T_84] :
( constant(resources(E_83,T_84))
| greater(equilibrium(E_83),T_84)
| ~ in_environment(E_83,T_84)
| ~ subpopulations(first_movers,efficient_producers,E_83,T_84)
| ~ environment(E_83) ),
inference(resolution,[status(thm)],[c_4,c_214]) ).
tff(c_227,plain,
( constant(resources('#skF_1','#skF_2'))
| ~ in_environment('#skF_1','#skF_2')
| ~ subpopulations(first_movers,efficient_producers,'#skF_1','#skF_2')
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_224,c_50]) ).
tff(c_230,plain,
constant(resources('#skF_1','#skF_2')),
inference(demodulation,[status(thm),theory(equality)],[c_42,c_40,c_210,c_227]) ).
tff(c_233,plain,
( constant(number_of_organizations('#skF_1','#skF_2'))
| ~ in_environment('#skF_1','#skF_2')
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_230,c_12]) ).
tff(c_236,plain,
constant(number_of_organizations('#skF_1','#skF_2')),
inference(demodulation,[status(thm),theory(equality)],[c_42,c_210,c_233]) ).
tff(c_255,plain,
! [T_93,E_94] :
( ( growth_rate(first_movers,T_93) = zero )
| greater(zero,growth_rate(efficient_producers,T_93))
| greater(growth_rate(efficient_producers,T_93),zero)
| ~ constant(number_of_organizations(E_94,T_93))
| ~ subpopulations(first_movers,efficient_producers,E_94,T_93)
| ~ environment(E_94) ),
inference(cnfTransformation,[status(thm)],[f_105]) ).
tff(c_257,plain,
( ( growth_rate(first_movers,'#skF_2') = zero )
| greater(zero,growth_rate(efficient_producers,'#skF_2'))
| greater(growth_rate(efficient_producers,'#skF_2'),zero)
| ~ subpopulations(first_movers,efficient_producers,'#skF_1','#skF_2')
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_236,c_255]) ).
tff(c_260,plain,
( ( growth_rate(first_movers,'#skF_2') = zero )
| greater(zero,growth_rate(efficient_producers,'#skF_2'))
| greater(growth_rate(efficient_producers,'#skF_2'),zero) ),
inference(demodulation,[status(thm),theory(equality)],[c_42,c_40,c_257]) ).
tff(c_262,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_203,c_201,c_43,c_260]) ).
tff(c_263,plain,
~ greater(zero,growth_rate(first_movers,'#skF_2')),
inference(splitRight,[status(thm)],[c_32]) ).
tff(c_265,plain,
! [E_95,T_96] :
( in_environment(E_95,T_96)
| ~ subpopulations(first_movers,efficient_producers,E_95,T_96)
| ~ environment(E_95) ),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_268,plain,
( in_environment('#skF_1','#skF_2')
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_40,c_265]) ).
tff(c_271,plain,
in_environment('#skF_1','#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_42,c_268]) ).
tff(c_280,plain,
! [E_105,T_106] :
( constant(resources(E_105,T_106))
| greater(equilibrium(E_105),T_106)
| ~ greater(number_of_organizations(E_105,T_106),zero)
| ~ in_environment(E_105,T_106)
| ~ environment(E_105) ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_287,plain,
! [E_111,T_112] :
( constant(resources(E_111,T_112))
| greater(equilibrium(E_111),T_112)
| ~ in_environment(E_111,T_112)
| ~ subpopulations(first_movers,efficient_producers,E_111,T_112)
| ~ environment(E_111) ),
inference(resolution,[status(thm)],[c_4,c_280]) ).
tff(c_293,plain,
( constant(resources('#skF_1','#skF_2'))
| ~ in_environment('#skF_1','#skF_2')
| ~ subpopulations(first_movers,efficient_producers,'#skF_1','#skF_2')
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_287,c_50]) ).
tff(c_297,plain,
constant(resources('#skF_1','#skF_2')),
inference(demodulation,[status(thm),theory(equality)],[c_42,c_40,c_271,c_293]) ).
tff(c_300,plain,
( constant(number_of_organizations('#skF_1','#skF_2'))
| ~ in_environment('#skF_1','#skF_2')
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_297,c_12]) ).
tff(c_303,plain,
constant(number_of_organizations('#skF_1','#skF_2')),
inference(demodulation,[status(thm),theory(equality)],[c_42,c_271,c_300]) ).
tff(c_315,plain,
! [T_115,E_116] :
( ( growth_rate(efficient_producers,T_115) = zero )
| greater(zero,growth_rate(efficient_producers,T_115))
| greater(zero,growth_rate(first_movers,T_115))
| ~ constant(number_of_organizations(E_116,T_115))
| ~ subpopulations(first_movers,efficient_producers,E_116,T_115)
| ~ environment(E_116) ),
inference(cnfTransformation,[status(thm)],[f_105]) ).
tff(c_317,plain,
( ( growth_rate(efficient_producers,'#skF_2') = zero )
| greater(zero,growth_rate(efficient_producers,'#skF_2'))
| greater(zero,growth_rate(first_movers,'#skF_2'))
| ~ subpopulations(first_movers,efficient_producers,'#skF_1','#skF_2')
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_303,c_315]) ).
tff(c_320,plain,
( ( growth_rate(efficient_producers,'#skF_2') = zero )
| greater(zero,growth_rate(efficient_producers,'#skF_2'))
| greater(zero,growth_rate(first_movers,'#skF_2')) ),
inference(demodulation,[status(thm),theory(equality)],[c_42,c_40,c_317]) ).
tff(c_321,plain,
growth_rate(efficient_producers,'#skF_2') = zero,
inference(negUnitSimplification,[status(thm)],[c_263,c_201,c_320]) ).
tff(c_264,plain,
greater(growth_rate(efficient_producers,'#skF_2'),zero),
inference(splitRight,[status(thm)],[c_32]) ).
tff(c_322,plain,
greater(zero,zero),
inference(demodulation,[status(thm),theory(equality)],[c_321,c_264]) ).
tff(c_323,plain,
~ greater(zero,zero),
inference(demodulation,[status(thm),theory(equality)],[c_321,c_201]) ).
tff(c_329,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_322,c_323]) ).
tff(c_331,plain,
growth_rate(first_movers,'#skF_2') = zero,
inference(splitRight,[status(thm)],[c_36]) ).
tff(c_332,plain,
~ greater(growth_rate(first_movers,'#skF_2'),zero),
inference(splitLeft,[status(thm)],[c_34]) ).
tff(c_337,plain,
~ greater(zero,zero),
inference(demodulation,[status(thm),theory(equality)],[c_331,c_332]) ).
tff(c_330,plain,
growth_rate(efficient_producers,'#skF_2') != zero,
inference(splitRight,[status(thm)],[c_36]) ).
tff(c_346,plain,
! [E_119,T_120] :
( in_environment(E_119,T_120)
| ~ subpopulations(first_movers,efficient_producers,E_119,T_120)
| ~ environment(E_119) ),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_349,plain,
( in_environment('#skF_1','#skF_2')
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_40,c_346]) ).
tff(c_352,plain,
in_environment('#skF_1','#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_42,c_349]) ).
tff(c_356,plain,
! [E_127,T_128] :
( constant(resources(E_127,T_128))
| greater(equilibrium(E_127),T_128)
| ~ greater(number_of_organizations(E_127,T_128),zero)
| ~ in_environment(E_127,T_128)
| ~ environment(E_127) ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_366,plain,
! [E_131,T_132] :
( constant(resources(E_131,T_132))
| greater(equilibrium(E_131),T_132)
| ~ in_environment(E_131,T_132)
| ~ subpopulations(first_movers,efficient_producers,E_131,T_132)
| ~ environment(E_131) ),
inference(resolution,[status(thm)],[c_4,c_356]) ).
tff(c_338,plain,
! [E_117,T_118] :
( ~ greater(equilibrium(E_117),T_118)
| ~ greater_or_equal(T_118,equilibrium(E_117))
| ~ environment(E_117) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_341,plain,
( ~ greater(equilibrium('#skF_1'),'#skF_2')
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_38,c_338]) ).
tff(c_344,plain,
~ greater(equilibrium('#skF_1'),'#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_42,c_341]) ).
tff(c_369,plain,
( constant(resources('#skF_1','#skF_2'))
| ~ in_environment('#skF_1','#skF_2')
| ~ subpopulations(first_movers,efficient_producers,'#skF_1','#skF_2')
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_366,c_344]) ).
tff(c_372,plain,
constant(resources('#skF_1','#skF_2')),
inference(demodulation,[status(thm),theory(equality)],[c_42,c_40,c_352,c_369]) ).
tff(c_375,plain,
( constant(number_of_organizations('#skF_1','#skF_2'))
| ~ in_environment('#skF_1','#skF_2')
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_372,c_12]) ).
tff(c_378,plain,
constant(number_of_organizations('#skF_1','#skF_2')),
inference(demodulation,[status(thm),theory(equality)],[c_42,c_352,c_375]) ).
tff(c_417,plain,
! [T_147,E_148] :
( ( growth_rate(efficient_producers,T_147) = zero )
| greater(growth_rate(first_movers,T_147),zero)
| greater(zero,growth_rate(first_movers,T_147))
| ~ constant(number_of_organizations(E_148,T_147))
| ~ subpopulations(first_movers,efficient_producers,E_148,T_147)
| ~ environment(E_148) ),
inference(cnfTransformation,[status(thm)],[f_105]) ).
tff(c_419,plain,
( ( growth_rate(efficient_producers,'#skF_2') = zero )
| greater(growth_rate(first_movers,'#skF_2'),zero)
| greater(zero,growth_rate(first_movers,'#skF_2'))
| ~ subpopulations(first_movers,efficient_producers,'#skF_1','#skF_2')
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_378,c_417]) ).
tff(c_422,plain,
( ( growth_rate(efficient_producers,'#skF_2') = zero )
| greater(zero,zero) ),
inference(demodulation,[status(thm),theory(equality)],[c_42,c_40,c_331,c_331,c_419]) ).
tff(c_424,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_337,c_330,c_422]) ).
tff(c_426,plain,
greater(growth_rate(first_movers,'#skF_2'),zero),
inference(splitRight,[status(thm)],[c_34]) ).
tff(c_431,plain,
greater(zero,zero),
inference(demodulation,[status(thm),theory(equality)],[c_331,c_426]) ).
tff(c_433,plain,
~ greater(growth_rate(efficient_producers,'#skF_2'),zero),
inference(demodulation,[status(thm),theory(equality)],[c_431,c_331,c_32]) ).
tff(c_425,plain,
~ greater(zero,growth_rate(efficient_producers,'#skF_2')),
inference(splitRight,[status(thm)],[c_34]) ).
tff(c_441,plain,
! [E_151,T_152] :
( in_environment(E_151,T_152)
| ~ subpopulations(first_movers,efficient_producers,E_151,T_152)
| ~ environment(E_151) ),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_444,plain,
( in_environment('#skF_1','#skF_2')
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_40,c_441]) ).
tff(c_447,plain,
in_environment('#skF_1','#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_42,c_444]) ).
tff(c_451,plain,
! [E_159,T_160] :
( constant(resources(E_159,T_160))
| greater(equilibrium(E_159),T_160)
| ~ greater(number_of_organizations(E_159,T_160),zero)
| ~ in_environment(E_159,T_160)
| ~ environment(E_159) ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_462,plain,
! [E_165,T_166] :
( constant(resources(E_165,T_166))
| greater(equilibrium(E_165),T_166)
| ~ in_environment(E_165,T_166)
| ~ subpopulations(first_movers,efficient_producers,E_165,T_166)
| ~ environment(E_165) ),
inference(resolution,[status(thm)],[c_4,c_451]) ).
tff(c_434,plain,
! [E_149,T_150] :
( ~ greater(equilibrium(E_149),T_150)
| ~ greater_or_equal(T_150,equilibrium(E_149))
| ~ environment(E_149) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_437,plain,
( ~ greater(equilibrium('#skF_1'),'#skF_2')
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_38,c_434]) ).
tff(c_440,plain,
~ greater(equilibrium('#skF_1'),'#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_42,c_437]) ).
tff(c_465,plain,
( constant(resources('#skF_1','#skF_2'))
| ~ in_environment('#skF_1','#skF_2')
| ~ subpopulations(first_movers,efficient_producers,'#skF_1','#skF_2')
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_462,c_440]) ).
tff(c_468,plain,
constant(resources('#skF_1','#skF_2')),
inference(demodulation,[status(thm),theory(equality)],[c_42,c_40,c_447,c_465]) ).
tff(c_471,plain,
( constant(number_of_organizations('#skF_1','#skF_2'))
| ~ in_environment('#skF_1','#skF_2')
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_468,c_12]) ).
tff(c_474,plain,
constant(number_of_organizations('#skF_1','#skF_2')),
inference(demodulation,[status(thm),theory(equality)],[c_42,c_447,c_471]) ).
tff(c_498,plain,
! [T_175,E_176] :
( ( growth_rate(efficient_producers,T_175) = zero )
| greater(zero,growth_rate(efficient_producers,T_175))
| greater(growth_rate(efficient_producers,T_175),zero)
| ~ constant(number_of_organizations(E_176,T_175))
| ~ subpopulations(first_movers,efficient_producers,E_176,T_175)
| ~ environment(E_176) ),
inference(cnfTransformation,[status(thm)],[f_105]) ).
tff(c_500,plain,
( ( growth_rate(efficient_producers,'#skF_2') = zero )
| greater(zero,growth_rate(efficient_producers,'#skF_2'))
| greater(growth_rate(efficient_producers,'#skF_2'),zero)
| ~ subpopulations(first_movers,efficient_producers,'#skF_1','#skF_2')
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_474,c_498]) ).
tff(c_503,plain,
( ( growth_rate(efficient_producers,'#skF_2') = zero )
| greater(zero,growth_rate(efficient_producers,'#skF_2'))
| greater(growth_rate(efficient_producers,'#skF_2'),zero) ),
inference(demodulation,[status(thm),theory(equality)],[c_42,c_40,c_500]) ).
tff(c_505,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_433,c_425,c_330,c_503]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : MGT024+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.14 % 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
% 0.13/0.35 % Computer : n012.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 3 20:25:07 EDT 2023
% 0.13/0.35 % CPUTime :
% 3.97/1.88 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.01/1.89
% 4.01/1.89 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.16/1.94
% 4.16/1.94 Inference rules
% 4.16/1.94 ----------------------
% 4.16/1.94 #Ref : 0
% 4.16/1.94 #Sup : 71
% 4.16/1.94 #Fact : 0
% 4.16/1.94 #Define : 0
% 4.16/1.94 #Split : 6
% 4.16/1.94 #Chain : 0
% 4.16/1.94 #Close : 0
% 4.16/1.94
% 4.16/1.94 Ordering : KBO
% 4.16/1.94
% 4.16/1.94 Simplification rules
% 4.16/1.94 ----------------------
% 4.16/1.94 #Subsume : 1
% 4.16/1.94 #Demod : 111
% 4.16/1.94 #Tautology : 17
% 4.16/1.94 #SimpNegUnit : 16
% 4.16/1.94 #BackRed : 2
% 4.16/1.94
% 4.16/1.94 #Partial instantiations: 0
% 4.16/1.94 #Strategies tried : 1
% 4.16/1.94
% 4.16/1.94 Timing (in seconds)
% 4.16/1.94 ----------------------
% 4.16/1.94 Preprocessing : 0.45
% 4.16/1.94 Parsing : 0.25
% 4.16/1.94 CNF conversion : 0.03
% 4.16/1.94 Main loop : 0.44
% 4.16/1.94 Inferencing : 0.19
% 4.16/1.94 Reduction : 0.11
% 4.16/1.94 Demodulation : 0.07
% 4.16/1.94 BG Simplification : 0.02
% 4.16/1.94 Subsumption : 0.09
% 4.16/1.94 Abstraction : 0.01
% 4.16/1.94 MUC search : 0.00
% 4.16/1.94 Cooper : 0.00
% 4.16/1.94 Total : 0.96
% 4.16/1.94 Index Insertion : 0.00
% 4.16/1.94 Index Deletion : 0.00
% 4.16/1.94 Index Matching : 0.00
% 4.16/1.94 BG Taut test : 0.00
%------------------------------------------------------------------------------