TSTP Solution File: MGT024-1 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : MGT024-1 : 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/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 : n017.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 : Unsatisfiable 4.06s 2.00s
% Output : CNFRefutation 4.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 34
% Syntax : Number of formulae : 154 ( 50 unt; 16 typ; 0 def)
% Number of atoms : 391 ( 41 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 464 ( 211 ~; 253 |; 0 &)
% ( 0 <=>; 0 =>; 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 : 86 (; 86 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subpopulations > in_environment > greater_or_equal > greater > environment > decreases > constant > resources > number_of_organizations > growth_rate > #nlpp > equilibrium > zero > sk2 > sk1 > first_movers > efficient_producers
%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(sk2,type,
sk2: $i ).
tff(constant,type,
constant: $i > $o ).
tff(sk1,type,
sk1: $i ).
tff(efficient_producers,type,
efficient_producers: $i ).
tff(growth_rate,type,
growth_rate: ( $i * $i ) > $i ).
tff(decreases,type,
decreases: $i > $o ).
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_227,axiom,
( ( growth_rate(first_movers,sk2) != zero )
| ( growth_rate(efficient_producers,sk2) != zero ) ),
file(unknown,unknown) ).
tff(f_232,axiom,
( ~ greater(growth_rate(first_movers,sk2),zero)
| ~ greater(zero,growth_rate(efficient_producers,sk2)) ),
file(unknown,unknown) ).
tff(f_237,axiom,
( ~ greater(growth_rate(efficient_producers,sk2),zero)
| ~ greater(zero,growth_rate(first_movers,sk2)) ),
file(unknown,unknown) ).
tff(f_220,axiom,
environment(sk1),
file(unknown,unknown) ).
tff(f_221,axiom,
subpopulations(first_movers,efficient_producers,sk1,sk2),
file(unknown,unknown) ).
tff(f_32,axiom,
! [A,B] :
( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| in_environment(A,B) ),
file(unknown,unknown) ).
tff(f_40,axiom,
! [A,B] :
( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| greater(number_of_organizations(A,B),zero) ),
file(unknown,unknown) ).
tff(f_76,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_222,axiom,
greater_or_equal(sk2,equilibrium(sk1)),
file(unknown,unknown) ).
tff(f_49,axiom,
! [A,B] :
( ~ environment(A)
| ~ greater_or_equal(B,equilibrium(A))
| ~ greater(equilibrium(A),B) ),
file(unknown,unknown) ).
tff(f_99,axiom,
! [A,B] :
( ~ environment(A)
| ~ in_environment(A,B)
| ~ constant(resources(A,B))
| constant(number_of_organizations(A,B)) ),
file(unknown,unknown) ).
tff(f_204,axiom,
! [A,B] :
( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ constant(number_of_organizations(A,B))
| ( growth_rate(efficient_producers,B) = zero )
| greater(zero,growth_rate(efficient_producers,B))
| greater(growth_rate(efficient_producers,B),zero) ),
file(unknown,unknown) ).
tff(f_114,axiom,
! [A,B] :
( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ constant(number_of_organizations(A,B))
| ( growth_rate(first_movers,B) = zero )
| greater(growth_rate(first_movers,B),zero)
| greater(growth_rate(efficient_producers,B),zero) ),
file(unknown,unknown) ).
tff(f_174,axiom,
! [A,B] :
( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ constant(number_of_organizations(A,B))
| ( growth_rate(efficient_producers,B) = zero )
| greater(growth_rate(first_movers,B),zero)
| greater(growth_rate(efficient_producers,B),zero) ),
file(unknown,unknown) ).
tff(f_129,axiom,
! [A,B] :
( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ constant(number_of_organizations(A,B))
| ( growth_rate(first_movers,B) = zero )
| greater(growth_rate(first_movers,B),zero)
| greater(zero,growth_rate(first_movers,B)) ),
file(unknown,unknown) ).
tff(f_144,axiom,
! [A,B] :
( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ constant(number_of_organizations(A,B))
| ( growth_rate(first_movers,B) = zero )
| greater(zero,growth_rate(efficient_producers,B))
| greater(growth_rate(efficient_producers,B),zero) ),
file(unknown,unknown) ).
tff(f_159,axiom,
! [A,B] :
( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ constant(number_of_organizations(A,B))
| ( growth_rate(first_movers,B) = zero )
| greater(zero,growth_rate(efficient_producers,B))
| greater(zero,growth_rate(first_movers,B)) ),
file(unknown,unknown) ).
tff(f_189,axiom,
! [A,B] :
( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ constant(number_of_organizations(A,B))
| ( growth_rate(efficient_producers,B) = zero )
| greater(growth_rate(first_movers,B),zero)
| greater(zero,growth_rate(first_movers,B)) ),
file(unknown,unknown) ).
tff(c_38,plain,
( ( growth_rate(efficient_producers,sk2) != zero )
| ( growth_rate(first_movers,sk2) != zero ) ),
inference(cnfTransformation,[status(thm)],[f_227]) ).
tff(c_43,plain,
growth_rate(first_movers,sk2) != zero,
inference(splitLeft,[status(thm)],[c_38]) ).
tff(c_40,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk2))
| ~ greater(growth_rate(first_movers,sk2),zero) ),
inference(cnfTransformation,[status(thm)],[f_232]) ).
tff(c_44,plain,
~ greater(growth_rate(first_movers,sk2),zero),
inference(splitLeft,[status(thm)],[c_40]) ).
tff(c_42,plain,
( ~ greater(zero,growth_rate(first_movers,sk2))
| ~ greater(growth_rate(efficient_producers,sk2),zero) ),
inference(cnfTransformation,[status(thm)],[f_237]) ).
tff(c_52,plain,
~ greater(growth_rate(efficient_producers,sk2),zero),
inference(splitLeft,[status(thm)],[c_42]) ).
tff(c_32,plain,
environment(sk1),
inference(cnfTransformation,[status(thm)],[f_220]) ).
tff(c_34,plain,
subpopulations(first_movers,efficient_producers,sk1,sk2),
inference(cnfTransformation,[status(thm)],[f_221]) ).
tff(c_53,plain,
! [A_33,B_34] :
( in_environment(A_33,B_34)
| ~ subpopulations(first_movers,efficient_producers,A_33,B_34)
| ~ environment(A_33) ),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_56,plain,
( in_environment(sk1,sk2)
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_34,c_53]) ).
tff(c_59,plain,
in_environment(sk1,sk2),
inference(demodulation,[status(thm),theory(equality)],[c_32,c_56]) ).
tff(c_4,plain,
! [A_3,B_4] :
( greater(number_of_organizations(A_3,B_4),zero)
| ~ subpopulations(first_movers,efficient_producers,A_3,B_4)
| ~ environment(A_3) ),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_68,plain,
! [A_43,B_44] :
( constant(resources(A_43,B_44))
| greater(equilibrium(A_43),B_44)
| ~ greater(number_of_organizations(A_43,B_44),zero)
| ~ in_environment(A_43,B_44)
| ~ environment(A_43) ),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_75,plain,
! [A_49,B_50] :
( constant(resources(A_49,B_50))
| greater(equilibrium(A_49),B_50)
| ~ in_environment(A_49,B_50)
| ~ subpopulations(first_movers,efficient_producers,A_49,B_50)
| ~ environment(A_49) ),
inference(resolution,[status(thm)],[c_4,c_68]) ).
tff(c_36,plain,
greater_or_equal(sk2,equilibrium(sk1)),
inference(cnfTransformation,[status(thm)],[f_222]) ).
tff(c_45,plain,
! [A_31,B_32] :
( ~ greater(equilibrium(A_31),B_32)
| ~ greater_or_equal(B_32,equilibrium(A_31))
| ~ environment(A_31) ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_48,plain,
( ~ greater(equilibrium(sk1),sk2)
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_36,c_45]) ).
tff(c_51,plain,
~ greater(equilibrium(sk1),sk2),
inference(demodulation,[status(thm),theory(equality)],[c_32,c_48]) ).
tff(c_81,plain,
( constant(resources(sk1,sk2))
| ~ in_environment(sk1,sk2)
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_75,c_51]) ).
tff(c_85,plain,
constant(resources(sk1,sk2)),
inference(demodulation,[status(thm),theory(equality)],[c_32,c_34,c_59,c_81]) ).
tff(c_14,plain,
! [A_13,B_14] :
( constant(number_of_organizations(A_13,B_14))
| ~ constant(resources(A_13,B_14))
| ~ in_environment(A_13,B_14)
| ~ environment(A_13) ),
inference(cnfTransformation,[status(thm)],[f_99]) ).
tff(c_88,plain,
( constant(number_of_organizations(sk1,sk2))
| ~ in_environment(sk1,sk2)
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_85,c_14]) ).
tff(c_91,plain,
constant(number_of_organizations(sk1,sk2)),
inference(demodulation,[status(thm),theory(equality)],[c_32,c_59,c_88]) ).
tff(c_28,plain,
! [B_28,A_27] :
( greater(growth_rate(efficient_producers,B_28),zero)
| greater(zero,growth_rate(efficient_producers,B_28))
| ( growth_rate(efficient_producers,B_28) = zero )
| ~ constant(number_of_organizations(A_27,B_28))
| ~ subpopulations(first_movers,efficient_producers,A_27,B_28)
| ~ environment(A_27) ),
inference(cnfTransformation,[status(thm)],[f_204]) ).
tff(c_93,plain,
( greater(growth_rate(efficient_producers,sk2),zero)
| greater(zero,growth_rate(efficient_producers,sk2))
| ( growth_rate(efficient_producers,sk2) = zero )
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_91,c_28]) ).
tff(c_96,plain,
( greater(growth_rate(efficient_producers,sk2),zero)
| greater(zero,growth_rate(efficient_producers,sk2))
| ( growth_rate(efficient_producers,sk2) = zero ) ),
inference(demodulation,[status(thm),theory(equality)],[c_32,c_34,c_93]) ).
tff(c_97,plain,
( greater(zero,growth_rate(efficient_producers,sk2))
| ( growth_rate(efficient_producers,sk2) = zero ) ),
inference(negUnitSimplification,[status(thm)],[c_52,c_96]) ).
tff(c_98,plain,
growth_rate(efficient_producers,sk2) = zero,
inference(splitLeft,[status(thm)],[c_97]) ).
tff(c_99,plain,
~ greater(zero,zero),
inference(demodulation,[status(thm),theory(equality)],[c_98,c_52]) ).
tff(c_116,plain,
! [B_55,A_56] :
( greater(growth_rate(efficient_producers,B_55),zero)
| greater(growth_rate(first_movers,B_55),zero)
| ( growth_rate(first_movers,B_55) = zero )
| ~ constant(number_of_organizations(A_56,B_55))
| ~ subpopulations(first_movers,efficient_producers,A_56,B_55)
| ~ environment(A_56) ),
inference(cnfTransformation,[status(thm)],[f_114]) ).
tff(c_118,plain,
( greater(growth_rate(efficient_producers,sk2),zero)
| greater(growth_rate(first_movers,sk2),zero)
| ( growth_rate(first_movers,sk2) = zero )
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_91,c_116]) ).
tff(c_121,plain,
( greater(zero,zero)
| greater(growth_rate(first_movers,sk2),zero)
| ( growth_rate(first_movers,sk2) = zero ) ),
inference(demodulation,[status(thm),theory(equality)],[c_32,c_34,c_98,c_118]) ).
tff(c_123,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_43,c_44,c_99,c_121]) ).
tff(c_125,plain,
growth_rate(efficient_producers,sk2) != zero,
inference(splitRight,[status(thm)],[c_97]) ).
tff(c_139,plain,
! [B_63,A_64] :
( greater(growth_rate(efficient_producers,B_63),zero)
| greater(growth_rate(first_movers,B_63),zero)
| ( growth_rate(efficient_producers,B_63) = zero )
| ~ constant(number_of_organizations(A_64,B_63))
| ~ subpopulations(first_movers,efficient_producers,A_64,B_63)
| ~ environment(A_64) ),
inference(cnfTransformation,[status(thm)],[f_174]) ).
tff(c_141,plain,
( greater(growth_rate(efficient_producers,sk2),zero)
| greater(growth_rate(first_movers,sk2),zero)
| ( growth_rate(efficient_producers,sk2) = zero )
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_91,c_139]) ).
tff(c_144,plain,
( greater(growth_rate(efficient_producers,sk2),zero)
| greater(growth_rate(first_movers,sk2),zero)
| ( growth_rate(efficient_producers,sk2) = zero ) ),
inference(demodulation,[status(thm),theory(equality)],[c_32,c_34,c_141]) ).
tff(c_146,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_125,c_44,c_52,c_144]) ).
tff(c_147,plain,
~ greater(zero,growth_rate(first_movers,sk2)),
inference(splitRight,[status(thm)],[c_42]) ).
tff(c_149,plain,
! [A_65,B_66] :
( in_environment(A_65,B_66)
| ~ subpopulations(first_movers,efficient_producers,A_65,B_66)
| ~ environment(A_65) ),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_152,plain,
( in_environment(sk1,sk2)
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_34,c_149]) ).
tff(c_155,plain,
in_environment(sk1,sk2),
inference(demodulation,[status(thm),theory(equality)],[c_32,c_152]) ).
tff(c_164,plain,
! [A_75,B_76] :
( constant(resources(A_75,B_76))
| greater(equilibrium(A_75),B_76)
| ~ greater(number_of_organizations(A_75,B_76),zero)
| ~ in_environment(A_75,B_76)
| ~ environment(A_75) ),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_171,plain,
! [A_81,B_82] :
( constant(resources(A_81,B_82))
| greater(equilibrium(A_81),B_82)
| ~ in_environment(A_81,B_82)
| ~ subpopulations(first_movers,efficient_producers,A_81,B_82)
| ~ environment(A_81) ),
inference(resolution,[status(thm)],[c_4,c_164]) ).
tff(c_177,plain,
( constant(resources(sk1,sk2))
| ~ in_environment(sk1,sk2)
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_171,c_51]) ).
tff(c_181,plain,
constant(resources(sk1,sk2)),
inference(demodulation,[status(thm),theory(equality)],[c_32,c_34,c_155,c_177]) ).
tff(c_184,plain,
( constant(number_of_organizations(sk1,sk2))
| ~ in_environment(sk1,sk2)
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_181,c_14]) ).
tff(c_187,plain,
constant(number_of_organizations(sk1,sk2)),
inference(demodulation,[status(thm),theory(equality)],[c_32,c_155,c_184]) ).
tff(c_225,plain,
! [B_93,A_94] :
( greater(zero,growth_rate(first_movers,B_93))
| greater(growth_rate(first_movers,B_93),zero)
| ( growth_rate(first_movers,B_93) = zero )
| ~ constant(number_of_organizations(A_94,B_93))
| ~ subpopulations(first_movers,efficient_producers,A_94,B_93)
| ~ environment(A_94) ),
inference(cnfTransformation,[status(thm)],[f_129]) ).
tff(c_227,plain,
( greater(zero,growth_rate(first_movers,sk2))
| greater(growth_rate(first_movers,sk2),zero)
| ( growth_rate(first_movers,sk2) = zero )
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_187,c_225]) ).
tff(c_230,plain,
( greater(zero,growth_rate(first_movers,sk2))
| greater(growth_rate(first_movers,sk2),zero)
| ( growth_rate(first_movers,sk2) = zero ) ),
inference(demodulation,[status(thm),theory(equality)],[c_32,c_34,c_227]) ).
tff(c_232,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_43,c_44,c_147,c_230]) ).
tff(c_233,plain,
~ greater(zero,growth_rate(efficient_producers,sk2)),
inference(splitRight,[status(thm)],[c_40]) ).
tff(c_249,plain,
~ greater(growth_rate(efficient_producers,sk2),zero),
inference(splitLeft,[status(thm)],[c_42]) ).
tff(c_242,plain,
! [A_97,B_98] :
( in_environment(A_97,B_98)
| ~ subpopulations(first_movers,efficient_producers,A_97,B_98)
| ~ environment(A_97) ),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_245,plain,
( in_environment(sk1,sk2)
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_34,c_242]) ).
tff(c_248,plain,
in_environment(sk1,sk2),
inference(demodulation,[status(thm),theory(equality)],[c_32,c_245]) ).
tff(c_258,plain,
! [A_107,B_108] :
( constant(resources(A_107,B_108))
| greater(equilibrium(A_107),B_108)
| ~ greater(number_of_organizations(A_107,B_108),zero)
| ~ in_environment(A_107,B_108)
| ~ environment(A_107) ),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_264,plain,
! [A_111,B_112] :
( constant(resources(A_111,B_112))
| greater(equilibrium(A_111),B_112)
| ~ in_environment(A_111,B_112)
| ~ subpopulations(first_movers,efficient_producers,A_111,B_112)
| ~ environment(A_111) ),
inference(resolution,[status(thm)],[c_4,c_258]) ).
tff(c_235,plain,
! [A_95,B_96] :
( ~ greater(equilibrium(A_95),B_96)
| ~ greater_or_equal(B_96,equilibrium(A_95))
| ~ environment(A_95) ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_238,plain,
( ~ greater(equilibrium(sk1),sk2)
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_36,c_235]) ).
tff(c_241,plain,
~ greater(equilibrium(sk1),sk2),
inference(demodulation,[status(thm),theory(equality)],[c_32,c_238]) ).
tff(c_270,plain,
( constant(resources(sk1,sk2))
| ~ in_environment(sk1,sk2)
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_264,c_241]) ).
tff(c_274,plain,
constant(resources(sk1,sk2)),
inference(demodulation,[status(thm),theory(equality)],[c_32,c_34,c_248,c_270]) ).
tff(c_277,plain,
( constant(number_of_organizations(sk1,sk2))
| ~ in_environment(sk1,sk2)
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_274,c_14]) ).
tff(c_280,plain,
constant(number_of_organizations(sk1,sk2)),
inference(demodulation,[status(thm),theory(equality)],[c_32,c_248,c_277]) ).
tff(c_294,plain,
! [B_119,A_120] :
( greater(growth_rate(efficient_producers,B_119),zero)
| greater(zero,growth_rate(efficient_producers,B_119))
| ( growth_rate(first_movers,B_119) = zero )
| ~ constant(number_of_organizations(A_120,B_119))
| ~ subpopulations(first_movers,efficient_producers,A_120,B_119)
| ~ environment(A_120) ),
inference(cnfTransformation,[status(thm)],[f_144]) ).
tff(c_296,plain,
( greater(growth_rate(efficient_producers,sk2),zero)
| greater(zero,growth_rate(efficient_producers,sk2))
| ( growth_rate(first_movers,sk2) = zero )
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_280,c_294]) ).
tff(c_299,plain,
( greater(growth_rate(efficient_producers,sk2),zero)
| greater(zero,growth_rate(efficient_producers,sk2))
| ( growth_rate(first_movers,sk2) = zero ) ),
inference(demodulation,[status(thm),theory(equality)],[c_32,c_34,c_296]) ).
tff(c_301,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_43,c_233,c_249,c_299]) ).
tff(c_302,plain,
~ greater(zero,growth_rate(first_movers,sk2)),
inference(splitRight,[status(thm)],[c_42]) ).
tff(c_312,plain,
! [A_129,B_130] :
( constant(resources(A_129,B_130))
| greater(equilibrium(A_129),B_130)
| ~ greater(number_of_organizations(A_129,B_130),zero)
| ~ in_environment(A_129,B_130)
| ~ environment(A_129) ),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_318,plain,
! [A_133,B_134] :
( constant(resources(A_133,B_134))
| greater(equilibrium(A_133),B_134)
| ~ in_environment(A_133,B_134)
| ~ subpopulations(first_movers,efficient_producers,A_133,B_134)
| ~ environment(A_133) ),
inference(resolution,[status(thm)],[c_4,c_312]) ).
tff(c_324,plain,
( constant(resources(sk1,sk2))
| ~ in_environment(sk1,sk2)
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_318,c_241]) ).
tff(c_328,plain,
constant(resources(sk1,sk2)),
inference(demodulation,[status(thm),theory(equality)],[c_32,c_34,c_248,c_324]) ).
tff(c_331,plain,
( constant(number_of_organizations(sk1,sk2))
| ~ in_environment(sk1,sk2)
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_328,c_14]) ).
tff(c_334,plain,
constant(number_of_organizations(sk1,sk2)),
inference(demodulation,[status(thm),theory(equality)],[c_32,c_248,c_331]) ).
tff(c_362,plain,
! [B_145,A_146] :
( greater(zero,growth_rate(first_movers,B_145))
| greater(zero,growth_rate(efficient_producers,B_145))
| ( growth_rate(first_movers,B_145) = zero )
| ~ constant(number_of_organizations(A_146,B_145))
| ~ subpopulations(first_movers,efficient_producers,A_146,B_145)
| ~ environment(A_146) ),
inference(cnfTransformation,[status(thm)],[f_159]) ).
tff(c_364,plain,
( greater(zero,growth_rate(first_movers,sk2))
| greater(zero,growth_rate(efficient_producers,sk2))
| ( growth_rate(first_movers,sk2) = zero )
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_334,c_362]) ).
tff(c_367,plain,
( greater(zero,growth_rate(first_movers,sk2))
| greater(zero,growth_rate(efficient_producers,sk2))
| ( growth_rate(first_movers,sk2) = zero ) ),
inference(demodulation,[status(thm),theory(equality)],[c_32,c_34,c_364]) ).
tff(c_369,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_43,c_233,c_302,c_367]) ).
tff(c_370,plain,
growth_rate(efficient_producers,sk2) != zero,
inference(splitRight,[status(thm)],[c_38]) ).
tff(c_371,plain,
growth_rate(first_movers,sk2) = zero,
inference(splitRight,[status(thm)],[c_38]) ).
tff(c_376,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk2))
| ~ greater(zero,zero) ),
inference(demodulation,[status(thm),theory(equality)],[c_371,c_40]) ).
tff(c_377,plain,
~ greater(zero,zero),
inference(splitLeft,[status(thm)],[c_376]) ).
tff(c_386,plain,
! [A_149,B_150] :
( in_environment(A_149,B_150)
| ~ subpopulations(first_movers,efficient_producers,A_149,B_150)
| ~ environment(A_149) ),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_389,plain,
( in_environment(sk1,sk2)
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_34,c_386]) ).
tff(c_392,plain,
in_environment(sk1,sk2),
inference(demodulation,[status(thm),theory(equality)],[c_32,c_389]) ).
tff(c_396,plain,
! [A_157,B_158] :
( constant(resources(A_157,B_158))
| greater(equilibrium(A_157),B_158)
| ~ greater(number_of_organizations(A_157,B_158),zero)
| ~ in_environment(A_157,B_158)
| ~ environment(A_157) ),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_406,plain,
! [A_161,B_162] :
( constant(resources(A_161,B_162))
| greater(equilibrium(A_161),B_162)
| ~ in_environment(A_161,B_162)
| ~ subpopulations(first_movers,efficient_producers,A_161,B_162)
| ~ environment(A_161) ),
inference(resolution,[status(thm)],[c_4,c_396]) ).
tff(c_378,plain,
! [A_147,B_148] :
( ~ greater(equilibrium(A_147),B_148)
| ~ greater_or_equal(B_148,equilibrium(A_147))
| ~ environment(A_147) ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_381,plain,
( ~ greater(equilibrium(sk1),sk2)
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_36,c_378]) ).
tff(c_384,plain,
~ greater(equilibrium(sk1),sk2),
inference(demodulation,[status(thm),theory(equality)],[c_32,c_381]) ).
tff(c_409,plain,
( constant(resources(sk1,sk2))
| ~ in_environment(sk1,sk2)
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_406,c_384]) ).
tff(c_412,plain,
constant(resources(sk1,sk2)),
inference(demodulation,[status(thm),theory(equality)],[c_32,c_34,c_392,c_409]) ).
tff(c_415,plain,
( constant(number_of_organizations(sk1,sk2))
| ~ in_environment(sk1,sk2)
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_412,c_14]) ).
tff(c_418,plain,
constant(number_of_organizations(sk1,sk2)),
inference(demodulation,[status(thm),theory(equality)],[c_32,c_392,c_415]) ).
tff(c_467,plain,
! [B_179,A_180] :
( greater(zero,growth_rate(first_movers,B_179))
| greater(growth_rate(first_movers,B_179),zero)
| ( growth_rate(efficient_producers,B_179) = zero )
| ~ constant(number_of_organizations(A_180,B_179))
| ~ subpopulations(first_movers,efficient_producers,A_180,B_179)
| ~ environment(A_180) ),
inference(cnfTransformation,[status(thm)],[f_189]) ).
tff(c_469,plain,
( greater(zero,growth_rate(first_movers,sk2))
| greater(growth_rate(first_movers,sk2),zero)
| ( growth_rate(efficient_producers,sk2) = zero )
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_418,c_467]) ).
tff(c_472,plain,
( greater(zero,zero)
| ( growth_rate(efficient_producers,sk2) = zero ) ),
inference(demodulation,[status(thm),theory(equality)],[c_32,c_34,c_371,c_371,c_469]) ).
tff(c_474,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_370,c_377,c_472]) ).
tff(c_475,plain,
~ greater(zero,growth_rate(efficient_producers,sk2)),
inference(splitRight,[status(thm)],[c_376]) ).
tff(c_476,plain,
greater(zero,zero),
inference(splitRight,[status(thm)],[c_376]) ).
tff(c_492,plain,
~ greater(growth_rate(efficient_producers,sk2),zero),
inference(demodulation,[status(thm),theory(equality)],[c_476,c_371,c_42]) ).
tff(c_484,plain,
! [A_183,B_184] :
( in_environment(A_183,B_184)
| ~ subpopulations(first_movers,efficient_producers,A_183,B_184)
| ~ environment(A_183) ),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_487,plain,
( in_environment(sk1,sk2)
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_34,c_484]) ).
tff(c_490,plain,
in_environment(sk1,sk2),
inference(demodulation,[status(thm),theory(equality)],[c_32,c_487]) ).
tff(c_496,plain,
! [A_191,B_192] :
( constant(resources(A_191,B_192))
| greater(equilibrium(A_191),B_192)
| ~ greater(number_of_organizations(A_191,B_192),zero)
| ~ in_environment(A_191,B_192)
| ~ environment(A_191) ),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_506,plain,
! [A_195,B_196] :
( constant(resources(A_195,B_196))
| greater(equilibrium(A_195),B_196)
| ~ in_environment(A_195,B_196)
| ~ subpopulations(first_movers,efficient_producers,A_195,B_196)
| ~ environment(A_195) ),
inference(resolution,[status(thm)],[c_4,c_496]) ).
tff(c_477,plain,
! [A_181,B_182] :
( ~ greater(equilibrium(A_181),B_182)
| ~ greater_or_equal(B_182,equilibrium(A_181))
| ~ environment(A_181) ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_480,plain,
( ~ greater(equilibrium(sk1),sk2)
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_36,c_477]) ).
tff(c_483,plain,
~ greater(equilibrium(sk1),sk2),
inference(demodulation,[status(thm),theory(equality)],[c_32,c_480]) ).
tff(c_509,plain,
( constant(resources(sk1,sk2))
| ~ in_environment(sk1,sk2)
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_506,c_483]) ).
tff(c_512,plain,
constant(resources(sk1,sk2)),
inference(demodulation,[status(thm),theory(equality)],[c_32,c_34,c_490,c_509]) ).
tff(c_516,plain,
( constant(number_of_organizations(sk1,sk2))
| ~ in_environment(sk1,sk2)
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_512,c_14]) ).
tff(c_519,plain,
constant(number_of_organizations(sk1,sk2)),
inference(demodulation,[status(thm),theory(equality)],[c_32,c_490,c_516]) ).
tff(c_571,plain,
! [B_215,A_216] :
( greater(growth_rate(efficient_producers,B_215),zero)
| greater(zero,growth_rate(efficient_producers,B_215))
| ( growth_rate(efficient_producers,B_215) = zero )
| ~ constant(number_of_organizations(A_216,B_215))
| ~ subpopulations(first_movers,efficient_producers,A_216,B_215)
| ~ environment(A_216) ),
inference(cnfTransformation,[status(thm)],[f_204]) ).
tff(c_573,plain,
( greater(growth_rate(efficient_producers,sk2),zero)
| greater(zero,growth_rate(efficient_producers,sk2))
| ( growth_rate(efficient_producers,sk2) = zero )
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_519,c_571]) ).
tff(c_576,plain,
( greater(growth_rate(efficient_producers,sk2),zero)
| greater(zero,growth_rate(efficient_producers,sk2))
| ( growth_rate(efficient_producers,sk2) = zero ) ),
inference(demodulation,[status(thm),theory(equality)],[c_32,c_34,c_573]) ).
tff(c_578,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_370,c_475,c_492,c_576]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : MGT024-1 : TPTP v8.1.2. Released v2.4.0.
% 0.13/0.14 % 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
% 0.15/0.35 % Computer : n017.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu Aug 3 19:59:36 EDT 2023
% 0.15/0.35 % CPUTime :
% 4.06/2.00 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.06/2.01
% 4.06/2.01 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.39/2.06
% 4.39/2.06 Inference rules
% 4.39/2.06 ----------------------
% 4.39/2.06 #Ref : 0
% 4.39/2.06 #Sup : 81
% 4.39/2.06 #Fact : 0
% 4.39/2.06 #Define : 0
% 4.39/2.06 #Split : 7
% 4.39/2.06 #Chain : 0
% 4.39/2.06 #Close : 0
% 4.39/2.06
% 4.39/2.06 Ordering : KBO
% 4.39/2.06
% 4.39/2.06 Simplification rules
% 4.39/2.06 ----------------------
% 4.39/2.06 #Subsume : 1
% 4.39/2.06 #Demod : 140
% 4.39/2.06 #Tautology : 22
% 4.39/2.06 #SimpNegUnit : 27
% 4.39/2.06 #BackRed : 2
% 4.39/2.06
% 4.39/2.06 #Partial instantiations: 0
% 4.39/2.06 #Strategies tried : 1
% 4.39/2.06
% 4.39/2.06 Timing (in seconds)
% 4.39/2.06 ----------------------
% 4.39/2.07 Preprocessing : 0.50
% 4.39/2.07 Parsing : 0.28
% 4.39/2.07 CNF conversion : 0.03
% 4.39/2.07 Main loop : 0.48
% 4.39/2.07 Inferencing : 0.20
% 4.39/2.07 Reduction : 0.13
% 4.39/2.07 Demodulation : 0.09
% 4.39/2.07 BG Simplification : 0.03
% 4.39/2.07 Subsumption : 0.09
% 4.39/2.07 Abstraction : 0.01
% 4.39/2.07 MUC search : 0.00
% 4.39/2.07 Cooper : 0.00
% 4.39/2.07 Total : 1.06
% 4.39/2.07 Index Insertion : 0.00
% 4.39/2.07 Index Deletion : 0.00
% 4.39/2.07 Index Matching : 0.00
% 4.39/2.07 BG Taut test : 0.00
%------------------------------------------------------------------------------