TSTP Solution File: MGT027+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : MGT027+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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n008.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 10:49:36 EDT 2023
% Result : Theorem 5.40s 2.25s
% Output : CNFRefutation 5.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 25
% Syntax : Number of formulae : 97 ( 15 unt; 16 typ; 0 def)
% Number of atoms : 317 ( 14 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 426 ( 190 ~; 206 |; 19 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 23 ( 12 >; 11 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 100 (; 98 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subpopulations > in_environment > greater_or_equal > greater > contracts_from > stable > environment > growth_rate > cardinality_at_time > appear > #nlpp > zero > first_movers > efficient_producers > #skF_2 > #skF_3 > #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('#skF_2',type,
'#skF_2': $i > $i ).
tff(in_environment,type,
in_environment: ( $i * $i ) > $o ).
tff(appear,type,
appear: ( $i * $i ) > $i ).
tff(efficient_producers,type,
efficient_producers: $i ).
tff(contracts_from,type,
contracts_from: ( $i * $i ) > $o ).
tff(cardinality_at_time,type,
cardinality_at_time: ( $i * $i ) > $i ).
tff(growth_rate,type,
growth_rate: ( $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff(environment,type,
environment: $i > $o ).
tff(first_movers,type,
first_movers: $i ).
tff(greater_or_equal,type,
greater_or_equal: ( $i * $i ) > $o ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(zero,type,
zero: $i ).
tff(stable,type,
stable: $i > $o ).
tff(f_128,negated_conjecture,
~ ! [E] :
( ( environment(E)
& stable(E) )
=> ? [To] :
( greater(To,appear(efficient_producers,E))
& contracts_from(To,first_movers) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l9) ).
tff(f_75,axiom,
! [E] :
( ( environment(E)
& stable(E) )
=> in_environment(E,appear(efficient_producers,E)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_EP_in_stable_environments) ).
tff(f_116,hypothesis,
! [E] :
( ( environment(E)
& stable(E) )
=> ? [To] :
( greater(To,appear(efficient_producers,E))
& ! [T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& greater_or_equal(T,To) )
=> greater(zero,growth_rate(first_movers,T)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l10) ).
tff(f_68,axiom,
! [E,T1,T2] :
( ( environment(E)
& stable(E)
& in_environment(E,T1)
& greater(T2,T1) )
=> in_environment(E,T2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_long_stable_environments) ).
tff(f_45,axiom,
! [E,To] :
( ( environment(E)
& stable(E)
& in_environment(E,To)
& ! [T] :
( ( greater(cardinality_at_time(first_movers,T),zero)
& greater_or_equal(T,To) )
=> greater(zero,growth_rate(first_movers,T)) ) )
=> contracts_from(To,first_movers) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_contracts_from) ).
tff(f_89,axiom,
! [X,Y] :
( greater_or_equal(X,Y)
<=> ( greater(X,Y)
| ( X = Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal) ).
tff(f_82,axiom,
! [X,Y,Z] :
( ( greater(X,Y)
& greater(Y,Z) )
=> greater(X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_transitivity) ).
tff(f_99,hypothesis,
! [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/sandbox/benchmark/theBenchmark.p',t6) ).
tff(f_57,axiom,
! [E,T] :
( ( environment(E)
& in_environment(E,T)
& greater(cardinality_at_time(first_movers,T),zero)
& greater(cardinality_at_time(efficient_producers,T),zero) )
=> subpopulations(first_movers,efficient_producers,E,T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_non_empty_fm_and_ep) ).
tff(c_32,plain,
environment('#skF_3'),
inference(cnfTransformation,[status(thm)],[f_128]) ).
tff(c_30,plain,
stable('#skF_3'),
inference(cnfTransformation,[status(thm)],[f_128]) ).
tff(c_12,plain,
! [E_9] :
( in_environment(E_9,appear(efficient_producers,E_9))
| ~ stable(E_9)
| ~ environment(E_9) ),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_26,plain,
! [E_17] :
( greater('#skF_2'(E_17),appear(efficient_producers,E_17))
| ~ stable(E_17)
| ~ environment(E_17) ),
inference(cnfTransformation,[status(thm)],[f_116]) ).
tff(c_59,plain,
! [E_36,T2_37,T1_38] :
( in_environment(E_36,T2_37)
| ~ greater(T2_37,T1_38)
| ~ in_environment(E_36,T1_38)
| ~ stable(E_36)
| ~ environment(E_36) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_141,plain,
! [E_62,E_63] :
( in_environment(E_62,'#skF_2'(E_63))
| ~ in_environment(E_62,appear(efficient_producers,E_63))
| ~ stable(E_62)
| ~ environment(E_62)
| ~ stable(E_63)
| ~ environment(E_63) ),
inference(resolution,[status(thm)],[c_26,c_59]) ).
tff(c_145,plain,
! [E_9] :
( in_environment(E_9,'#skF_2'(E_9))
| ~ stable(E_9)
| ~ environment(E_9) ),
inference(resolution,[status(thm)],[c_12,c_141]) ).
tff(c_48,plain,
! [E_35] :
( greater('#skF_2'(E_35),appear(efficient_producers,E_35))
| ~ stable(E_35)
| ~ environment(E_35) ),
inference(cnfTransformation,[status(thm)],[f_116]) ).
tff(c_28,plain,
! [To_24] :
( ~ contracts_from(To_24,first_movers)
| ~ greater(To_24,appear(efficient_producers,'#skF_3')) ),
inference(cnfTransformation,[status(thm)],[f_128]) ).
tff(c_54,plain,
( ~ contracts_from('#skF_2'('#skF_3'),first_movers)
| ~ stable('#skF_3')
| ~ environment('#skF_3') ),
inference(resolution,[status(thm)],[c_48,c_28]) ).
tff(c_58,plain,
~ contracts_from('#skF_2'('#skF_3'),first_movers),
inference(demodulation,[status(thm),theory(equality)],[c_32,c_30,c_54]) ).
tff(c_78,plain,
! [E_42,To_43] :
( greater_or_equal('#skF_1'(E_42,To_43),To_43)
| contracts_from(To_43,first_movers)
| ~ in_environment(E_42,To_43)
| ~ stable(E_42)
| ~ environment(E_42) ),
inference(cnfTransformation,[status(thm)],[f_45]) ).
tff(c_16,plain,
! [Y_14,X_13] :
( ( Y_14 = X_13 )
| greater(X_13,Y_14)
| ~ greater_or_equal(X_13,Y_14) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_82,plain,
! [E_42,To_43] :
( ( '#skF_1'(E_42,To_43) = To_43 )
| greater('#skF_1'(E_42,To_43),To_43)
| contracts_from(To_43,first_movers)
| ~ in_environment(E_42,To_43)
| ~ stable(E_42)
| ~ environment(E_42) ),
inference(resolution,[status(thm)],[c_78,c_16]) ).
tff(c_14,plain,
! [X_10,Z_12,Y_11] :
( greater(X_10,Z_12)
| ~ greater(Y_11,Z_12)
| ~ greater(X_10,Y_11) ),
inference(cnfTransformation,[status(thm)],[f_82]) ).
tff(c_63,plain,
! [X_39,E_40] :
( greater(X_39,appear(efficient_producers,E_40))
| ~ greater(X_39,'#skF_2'(E_40))
| ~ stable(E_40)
| ~ environment(E_40) ),
inference(resolution,[status(thm)],[c_48,c_14]) ).
tff(c_10,plain,
! [E_6,T2_8,T1_7] :
( in_environment(E_6,T2_8)
| ~ greater(T2_8,T1_7)
| ~ in_environment(E_6,T1_7)
| ~ stable(E_6)
| ~ environment(E_6) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_235,plain,
! [E_84,X_85,E_86] :
( in_environment(E_84,X_85)
| ~ in_environment(E_84,appear(efficient_producers,E_86))
| ~ stable(E_84)
| ~ environment(E_84)
| ~ greater(X_85,'#skF_2'(E_86))
| ~ stable(E_86)
| ~ environment(E_86) ),
inference(resolution,[status(thm)],[c_63,c_10]) ).
tff(c_239,plain,
! [E_87,X_88] :
( in_environment(E_87,X_88)
| ~ greater(X_88,'#skF_2'(E_87))
| ~ stable(E_87)
| ~ environment(E_87) ),
inference(resolution,[status(thm)],[c_12,c_235]) ).
tff(c_244,plain,
! [E_87,E_42] :
( in_environment(E_87,'#skF_1'(E_42,'#skF_2'(E_87)))
| ~ stable(E_87)
| ~ environment(E_87)
| ( '#skF_1'(E_42,'#skF_2'(E_87)) = '#skF_2'(E_87) )
| contracts_from('#skF_2'(E_87),first_movers)
| ~ in_environment(E_42,'#skF_2'(E_87))
| ~ stable(E_42)
| ~ environment(E_42) ),
inference(resolution,[status(thm)],[c_82,c_239]) ).
tff(c_185,plain,
! [E_79,To_80] :
( ( '#skF_1'(E_79,To_80) = To_80 )
| greater('#skF_1'(E_79,To_80),To_80)
| contracts_from(To_80,first_movers)
| ~ in_environment(E_79,To_80)
| ~ stable(E_79)
| ~ environment(E_79) ),
inference(resolution,[status(thm)],[c_78,c_16]) ).
tff(c_55,plain,
! [X_10,E_35] :
( greater(X_10,appear(efficient_producers,E_35))
| ~ greater(X_10,'#skF_2'(E_35))
| ~ stable(E_35)
| ~ environment(E_35) ),
inference(resolution,[status(thm)],[c_48,c_14]) ).
tff(c_20,plain,
! [X_13,Y_14] :
( ~ greater(X_13,Y_14)
| greater_or_equal(X_13,Y_14) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_83,plain,
! [T_44,E_45] :
( greater(cardinality_at_time(efficient_producers,T_44),zero)
| ~ greater_or_equal(T_44,appear(efficient_producers,E_45))
| ~ in_environment(E_45,T_44)
| ~ environment(E_45) ),
inference(cnfTransformation,[status(thm)],[f_99]) ).
tff(c_119,plain,
! [X_54,E_55] :
( greater(cardinality_at_time(efficient_producers,X_54),zero)
| ~ in_environment(E_55,X_54)
| ~ environment(E_55)
| ~ greater(X_54,appear(efficient_producers,E_55)) ),
inference(resolution,[status(thm)],[c_20,c_83]) ).
tff(c_124,plain,
! [X_10,E_35] :
( greater(cardinality_at_time(efficient_producers,X_10),zero)
| ~ in_environment(E_35,X_10)
| ~ greater(X_10,'#skF_2'(E_35))
| ~ stable(E_35)
| ~ environment(E_35) ),
inference(resolution,[status(thm)],[c_55,c_119]) ).
tff(c_413,plain,
! [E_167,E_168] :
( greater(cardinality_at_time(efficient_producers,'#skF_1'(E_167,'#skF_2'(E_168))),zero)
| ~ in_environment(E_168,'#skF_1'(E_167,'#skF_2'(E_168)))
| ~ stable(E_168)
| ~ environment(E_168)
| ( '#skF_1'(E_167,'#skF_2'(E_168)) = '#skF_2'(E_168) )
| contracts_from('#skF_2'(E_168),first_movers)
| ~ in_environment(E_167,'#skF_2'(E_168))
| ~ stable(E_167)
| ~ environment(E_167) ),
inference(resolution,[status(thm)],[c_185,c_124]) ).
tff(c_425,plain,
! [E_169,E_170] :
( greater(cardinality_at_time(efficient_producers,'#skF_1'(E_169,'#skF_2'(E_170))),zero)
| ~ stable(E_170)
| ~ environment(E_170)
| ( '#skF_1'(E_169,'#skF_2'(E_170)) = '#skF_2'(E_170) )
| contracts_from('#skF_2'(E_170),first_movers)
| ~ in_environment(E_169,'#skF_2'(E_170))
| ~ stable(E_169)
| ~ environment(E_169) ),
inference(resolution,[status(thm)],[c_244,c_413]) ).
tff(c_6,plain,
! [E_1,To_2] :
( greater(cardinality_at_time(first_movers,'#skF_1'(E_1,To_2)),zero)
| contracts_from(To_2,first_movers)
| ~ in_environment(E_1,To_2)
| ~ stable(E_1)
| ~ environment(E_1) ),
inference(cnfTransformation,[status(thm)],[f_45]) ).
tff(c_177,plain,
! [E_70,T_71] :
( subpopulations(first_movers,efficient_producers,E_70,T_71)
| ~ greater(cardinality_at_time(efficient_producers,T_71),zero)
| ~ greater(cardinality_at_time(first_movers,T_71),zero)
| ~ in_environment(E_70,T_71)
| ~ environment(E_70) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_180,plain,
! [E_70,E_1,To_2] :
( subpopulations(first_movers,efficient_producers,E_70,'#skF_1'(E_1,To_2))
| ~ greater(cardinality_at_time(efficient_producers,'#skF_1'(E_1,To_2)),zero)
| ~ in_environment(E_70,'#skF_1'(E_1,To_2))
| ~ environment(E_70)
| contracts_from(To_2,first_movers)
| ~ in_environment(E_1,To_2)
| ~ stable(E_1)
| ~ environment(E_1) ),
inference(resolution,[status(thm)],[c_6,c_177]) ).
tff(c_455,plain,
! [E_179,E_180,E_181] :
( subpopulations(first_movers,efficient_producers,E_179,'#skF_1'(E_180,'#skF_2'(E_181)))
| ~ in_environment(E_179,'#skF_1'(E_180,'#skF_2'(E_181)))
| ~ environment(E_179)
| ~ stable(E_181)
| ~ environment(E_181)
| ( '#skF_1'(E_180,'#skF_2'(E_181)) = '#skF_2'(E_181) )
| contracts_from('#skF_2'(E_181),first_movers)
| ~ in_environment(E_180,'#skF_2'(E_181))
| ~ stable(E_180)
| ~ environment(E_180) ),
inference(resolution,[status(thm)],[c_425,c_180]) ).
tff(c_4,plain,
! [E_1,To_2] :
( greater_or_equal('#skF_1'(E_1,To_2),To_2)
| contracts_from(To_2,first_movers)
| ~ in_environment(E_1,To_2)
| ~ stable(E_1)
| ~ environment(E_1) ),
inference(cnfTransformation,[status(thm)],[f_45]) ).
tff(c_146,plain,
! [T_64,E_65] :
( greater(zero,growth_rate(first_movers,T_64))
| ~ greater_or_equal(T_64,'#skF_2'(E_65))
| ~ subpopulations(first_movers,efficient_producers,E_65,T_64)
| ~ stable(E_65)
| ~ environment(E_65) ),
inference(cnfTransformation,[status(thm)],[f_116]) ).
tff(c_159,plain,
! [E_1,E_65] :
( greater(zero,growth_rate(first_movers,'#skF_1'(E_1,'#skF_2'(E_65))))
| ~ subpopulations(first_movers,efficient_producers,E_65,'#skF_1'(E_1,'#skF_2'(E_65)))
| ~ stable(E_65)
| ~ environment(E_65)
| contracts_from('#skF_2'(E_65),first_movers)
| ~ in_environment(E_1,'#skF_2'(E_65))
| ~ stable(E_1)
| ~ environment(E_1) ),
inference(resolution,[status(thm)],[c_4,c_146]) ).
tff(c_460,plain,
! [E_182,E_183] :
( greater(zero,growth_rate(first_movers,'#skF_1'(E_182,'#skF_2'(E_183))))
| ~ in_environment(E_183,'#skF_1'(E_182,'#skF_2'(E_183)))
| ~ stable(E_183)
| ~ environment(E_183)
| ( '#skF_1'(E_182,'#skF_2'(E_183)) = '#skF_2'(E_183) )
| contracts_from('#skF_2'(E_183),first_movers)
| ~ in_environment(E_182,'#skF_2'(E_183))
| ~ stable(E_182)
| ~ environment(E_182) ),
inference(resolution,[status(thm)],[c_455,c_159]) ).
tff(c_472,plain,
! [E_184,E_185] :
( greater(zero,growth_rate(first_movers,'#skF_1'(E_184,'#skF_2'(E_185))))
| ~ stable(E_185)
| ~ environment(E_185)
| ( '#skF_1'(E_184,'#skF_2'(E_185)) = '#skF_2'(E_185) )
| contracts_from('#skF_2'(E_185),first_movers)
| ~ in_environment(E_184,'#skF_2'(E_185))
| ~ stable(E_184)
| ~ environment(E_184) ),
inference(resolution,[status(thm)],[c_244,c_460]) ).
tff(c_2,plain,
! [E_1,To_2] :
( ~ greater(zero,growth_rate(first_movers,'#skF_1'(E_1,To_2)))
| contracts_from(To_2,first_movers)
| ~ in_environment(E_1,To_2)
| ~ stable(E_1)
| ~ environment(E_1) ),
inference(cnfTransformation,[status(thm)],[f_45]) ).
tff(c_486,plain,
! [E_186,E_187] :
( ~ stable(E_186)
| ~ environment(E_186)
| ( '#skF_1'(E_187,'#skF_2'(E_186)) = '#skF_2'(E_186) )
| contracts_from('#skF_2'(E_186),first_movers)
| ~ in_environment(E_187,'#skF_2'(E_186))
| ~ stable(E_187)
| ~ environment(E_187) ),
inference(resolution,[status(thm)],[c_472,c_2]) ).
tff(c_491,plain,
! [E_188] :
( ( '#skF_1'(E_188,'#skF_2'(E_188)) = '#skF_2'(E_188) )
| contracts_from('#skF_2'(E_188),first_movers)
| ~ stable(E_188)
| ~ environment(E_188) ),
inference(resolution,[status(thm)],[c_145,c_486]) ).
tff(c_537,plain,
( ( '#skF_1'('#skF_3','#skF_2'('#skF_3')) = '#skF_2'('#skF_3') )
| ~ stable('#skF_3')
| ~ environment('#skF_3') ),
inference(resolution,[status(thm)],[c_491,c_58]) ).
tff(c_545,plain,
'#skF_1'('#skF_3','#skF_2'('#skF_3')) = '#skF_2'('#skF_3'),
inference(demodulation,[status(thm),theory(equality)],[c_32,c_30,c_537]) ).
tff(c_599,plain,
( greater(cardinality_at_time(first_movers,'#skF_2'('#skF_3')),zero)
| contracts_from('#skF_2'('#skF_3'),first_movers)
| ~ in_environment('#skF_3','#skF_2'('#skF_3'))
| ~ stable('#skF_3')
| ~ environment('#skF_3') ),
inference(superposition,[status(thm),theory(equality)],[c_545,c_6]) ).
tff(c_648,plain,
( greater(cardinality_at_time(first_movers,'#skF_2'('#skF_3')),zero)
| contracts_from('#skF_2'('#skF_3'),first_movers)
| ~ in_environment('#skF_3','#skF_2'('#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_32,c_30,c_599]) ).
tff(c_649,plain,
( greater(cardinality_at_time(first_movers,'#skF_2'('#skF_3')),zero)
| ~ in_environment('#skF_3','#skF_2'('#skF_3')) ),
inference(negUnitSimplification,[status(thm)],[c_58,c_648]) ).
tff(c_657,plain,
~ in_environment('#skF_3','#skF_2'('#skF_3')),
inference(splitLeft,[status(thm)],[c_649]) ).
tff(c_660,plain,
( ~ stable('#skF_3')
| ~ environment('#skF_3') ),
inference(resolution,[status(thm)],[c_145,c_657]) ).
tff(c_664,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_32,c_30,c_660]) ).
tff(c_666,plain,
in_environment('#skF_3','#skF_2'('#skF_3')),
inference(splitRight,[status(thm)],[c_649]) ).
tff(c_162,plain,
! [E_66] :
( in_environment(E_66,'#skF_2'(E_66))
| ~ stable(E_66)
| ~ environment(E_66) ),
inference(resolution,[status(thm)],[c_12,c_141]) ).
tff(c_125,plain,
! [E_17] :
( greater(cardinality_at_time(efficient_producers,'#skF_2'(E_17)),zero)
| ~ in_environment(E_17,'#skF_2'(E_17))
| ~ stable(E_17)
| ~ environment(E_17) ),
inference(resolution,[status(thm)],[c_26,c_119]) ).
tff(c_165,plain,
! [E_66] :
( greater(cardinality_at_time(efficient_producers,'#skF_2'(E_66)),zero)
| ~ stable(E_66)
| ~ environment(E_66) ),
inference(resolution,[status(thm)],[c_162,c_125]) ).
tff(c_665,plain,
greater(cardinality_at_time(first_movers,'#skF_2'('#skF_3')),zero),
inference(splitRight,[status(thm)],[c_649]) ).
tff(c_8,plain,
! [E_4,T_5] :
( subpopulations(first_movers,efficient_producers,E_4,T_5)
| ~ greater(cardinality_at_time(efficient_producers,T_5),zero)
| ~ greater(cardinality_at_time(first_movers,T_5),zero)
| ~ in_environment(E_4,T_5)
| ~ environment(E_4) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_695,plain,
! [E_4] :
( subpopulations(first_movers,efficient_producers,E_4,'#skF_2'('#skF_3'))
| ~ greater(cardinality_at_time(efficient_producers,'#skF_2'('#skF_3')),zero)
| ~ in_environment(E_4,'#skF_2'('#skF_3'))
| ~ environment(E_4) ),
inference(resolution,[status(thm)],[c_665,c_8]) ).
tff(c_717,plain,
~ greater(cardinality_at_time(efficient_producers,'#skF_2'('#skF_3')),zero),
inference(splitLeft,[status(thm)],[c_695]) ).
tff(c_720,plain,
( ~ stable('#skF_3')
| ~ environment('#skF_3') ),
inference(resolution,[status(thm)],[c_165,c_717]) ).
tff(c_724,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_32,c_30,c_720]) ).
tff(c_829,plain,
! [E_200] :
( subpopulations(first_movers,efficient_producers,E_200,'#skF_2'('#skF_3'))
| ~ in_environment(E_200,'#skF_2'('#skF_3'))
| ~ environment(E_200) ),
inference(splitRight,[status(thm)],[c_695]) ).
tff(c_602,plain,
( ~ greater(zero,growth_rate(first_movers,'#skF_2'('#skF_3')))
| contracts_from('#skF_2'('#skF_3'),first_movers)
| ~ in_environment('#skF_3','#skF_2'('#skF_3'))
| ~ stable('#skF_3')
| ~ environment('#skF_3') ),
inference(superposition,[status(thm),theory(equality)],[c_545,c_2]) ).
tff(c_651,plain,
( ~ greater(zero,growth_rate(first_movers,'#skF_2'('#skF_3')))
| contracts_from('#skF_2'('#skF_3'),first_movers)
| ~ in_environment('#skF_3','#skF_2'('#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_32,c_30,c_602]) ).
tff(c_652,plain,
( ~ greater(zero,growth_rate(first_movers,'#skF_2'('#skF_3')))
| ~ in_environment('#skF_3','#skF_2'('#skF_3')) ),
inference(negUnitSimplification,[status(thm)],[c_58,c_651]) ).
tff(c_667,plain,
~ in_environment('#skF_3','#skF_2'('#skF_3')),
inference(splitLeft,[status(thm)],[c_652]) ).
tff(c_676,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_666,c_667]) ).
tff(c_677,plain,
~ greater(zero,growth_rate(first_movers,'#skF_2'('#skF_3'))),
inference(splitRight,[status(thm)],[c_652]) ).
tff(c_571,plain,
( greater(zero,growth_rate(first_movers,'#skF_1'('#skF_3','#skF_2'('#skF_3'))))
| ~ subpopulations(first_movers,efficient_producers,'#skF_3','#skF_2'('#skF_3'))
| ~ stable('#skF_3')
| ~ environment('#skF_3')
| contracts_from('#skF_2'('#skF_3'),first_movers)
| ~ in_environment('#skF_3','#skF_2'('#skF_3'))
| ~ stable('#skF_3')
| ~ environment('#skF_3') ),
inference(superposition,[status(thm),theory(equality)],[c_545,c_159]) ).
tff(c_619,plain,
( greater(zero,growth_rate(first_movers,'#skF_2'('#skF_3')))
| ~ subpopulations(first_movers,efficient_producers,'#skF_3','#skF_2'('#skF_3'))
| contracts_from('#skF_2'('#skF_3'),first_movers)
| ~ in_environment('#skF_3','#skF_2'('#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_32,c_30,c_32,c_30,c_545,c_571]) ).
tff(c_620,plain,
( greater(zero,growth_rate(first_movers,'#skF_2'('#skF_3')))
| ~ subpopulations(first_movers,efficient_producers,'#skF_3','#skF_2'('#skF_3'))
| ~ in_environment('#skF_3','#skF_2'('#skF_3')) ),
inference(negUnitSimplification,[status(thm)],[c_58,c_619]) ).
tff(c_712,plain,
( greater(zero,growth_rate(first_movers,'#skF_2'('#skF_3')))
| ~ subpopulations(first_movers,efficient_producers,'#skF_3','#skF_2'('#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_666,c_620]) ).
tff(c_713,plain,
~ subpopulations(first_movers,efficient_producers,'#skF_3','#skF_2'('#skF_3')),
inference(negUnitSimplification,[status(thm)],[c_677,c_712]) ).
tff(c_832,plain,
( ~ in_environment('#skF_3','#skF_2'('#skF_3'))
| ~ environment('#skF_3') ),
inference(resolution,[status(thm)],[c_829,c_713]) ).
tff(c_839,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_32,c_666,c_832]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT027+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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.17/0.34 % Computer : n008.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Thu Aug 3 20:35:33 EDT 2023
% 0.17/0.34 % CPUTime :
% 5.40/2.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.40/2.26
% 5.40/2.26 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.40/2.31
% 5.40/2.31 Inference rules
% 5.40/2.31 ----------------------
% 5.40/2.31 #Ref : 0
% 5.40/2.31 #Sup : 175
% 5.40/2.31 #Fact : 0
% 5.40/2.31 #Define : 0
% 5.40/2.31 #Split : 7
% 5.40/2.31 #Chain : 0
% 5.40/2.31 #Close : 0
% 5.40/2.31
% 5.40/2.31 Ordering : KBO
% 5.40/2.31
% 5.40/2.31 Simplification rules
% 5.40/2.31 ----------------------
% 5.40/2.31 #Subsume : 60
% 5.40/2.31 #Demod : 91
% 5.40/2.31 #Tautology : 16
% 5.40/2.31 #SimpNegUnit : 21
% 5.40/2.31 #BackRed : 0
% 5.40/2.31
% 5.40/2.31 #Partial instantiations: 0
% 5.40/2.31 #Strategies tried : 1
% 5.40/2.31
% 5.40/2.31 Timing (in seconds)
% 5.40/2.31 ----------------------
% 5.40/2.31 Preprocessing : 0.52
% 5.40/2.31 Parsing : 0.28
% 5.40/2.31 CNF conversion : 0.03
% 5.40/2.31 Main loop : 0.71
% 5.40/2.31 Inferencing : 0.29
% 5.40/2.31 Reduction : 0.16
% 5.40/2.31 Demodulation : 0.11
% 5.40/2.31 BG Simplification : 0.03
% 5.40/2.31 Subsumption : 0.18
% 5.40/2.31 Abstraction : 0.03
% 5.40/2.31 MUC search : 0.00
% 5.40/2.31 Cooper : 0.00
% 5.40/2.31 Total : 1.30
% 5.40/2.31 Index Insertion : 0.00
% 5.40/2.31 Index Deletion : 0.00
% 5.40/2.31 Index Matching : 0.00
% 5.40/2.31 BG Taut test : 0.00
%------------------------------------------------------------------------------