TSTP Solution File: MGT026+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : MGT026+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 : n013.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 4.26s 2.18s
% Output : CNFRefutation 4.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 27
% Syntax : Number of formulae : 100 ( 22 unt; 16 typ; 0 def)
% Number of atoms : 247 ( 26 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 294 ( 131 ~; 131 |; 20 &)
% ( 1 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 11 >; 13 *; 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 : 97 (; 97 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subpopulations > subpopulation > selection_favors > in_environment > greater_or_equal > greater > environment > growth_rate > cardinality_at_time > appear > #nlpp > critical_point > 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(in_environment,type,
in_environment: ( $i * $i ) > $o ).
tff(appear,type,
appear: ( $i * $i ) > $i ).
tff(efficient_producers,type,
efficient_producers: $i ).
tff(cardinality_at_time,type,
cardinality_at_time: ( $i * $i ) > $i ).
tff(critical_point,type,
critical_point: $i > $i ).
tff(growth_rate,type,
growth_rate: ( $i * $i ) > $i ).
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(greater_or_equal,type,
greater_or_equal: ( $i * $i ) > $o ).
tff(subpopulation,type,
subpopulation: ( $i * $i * $i ) > $o ).
tff(selection_favors,type,
selection_favors: ( $i * $i * $i ) > $o ).
tff(zero,type,
zero: $i ).
tff(f_137,negated_conjecture,
~ ! [E,T] :
( ( environment(E)
& in_environment(E,T)
& greater(T,critical_point(E)) )
=> selection_favors(efficient_producers,first_movers,T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l8) ).
tff(f_79,axiom,
! [E,T] :
( ( environment(E)
& in_environment(E,T) )
=> ( subpopulation(first_movers,E,T)
& subpopulation(efficient_producers,E,T) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_subpopulations) ).
tff(f_70,axiom,
! [E,T] :
( ( environment(E)
& in_environment(E,T) )
=> greater_or_equal(cardinality_at_time(first_movers,T),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_first_movers_exist) ).
tff(f_99,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_63,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(f_85,axiom,
! [E] :
( environment(E)
=> greater_or_equal(critical_point(E),appear(efficient_producers,E)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_critical_point_after_EP) ).
tff(f_92,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_126,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_116,hypothesis,
! [E,Tc] :
( ( environment(E)
& ( Tc = critical_point(E) ) )
=> ( ~ greater(growth_rate(efficient_producers,Tc),growth_rate(first_movers,Tc))
& ! [T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& greater(T,Tc) )
=> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1) ).
tff(f_37,axiom,
! [E,S1,S2,T] :
( ( environment(E)
& subpopulations(S1,S2,E,T)
& greater(growth_rate(S2,T),growth_rate(S1,T)) )
=> selection_favors(S2,S1,T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp1_high_growth_rates) ).
tff(f_51,axiom,
! [E,S1,S2,T] :
( ( environment(E)
& subpopulation(S1,E,T)
& subpopulation(S2,E,T)
& greater(cardinality_at_time(S1,T),zero)
& ( cardinality_at_time(S2,T) = zero ) )
=> selection_favors(S1,S2,T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp2_favour_members) ).
tff(c_36,plain,
environment('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_137]) ).
tff(c_34,plain,
in_environment('#skF_1','#skF_2'),
inference(cnfTransformation,[status(thm)],[f_137]) ).
tff(c_10,plain,
! [E_13,T_14] :
( subpopulation(efficient_producers,E_13,T_14)
| ~ in_environment(E_13,T_14)
| ~ environment(E_13) ),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_30,plain,
~ selection_favors(efficient_producers,first_movers,'#skF_2'),
inference(cnfTransformation,[status(thm)],[f_137]) ).
tff(c_32,plain,
greater('#skF_2',critical_point('#skF_1')),
inference(cnfTransformation,[status(thm)],[f_137]) ).
tff(c_64,plain,
! [T_41,E_42] :
( greater_or_equal(cardinality_at_time(first_movers,T_41),zero)
| ~ in_environment(E_42,T_41)
| ~ environment(E_42) ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_66,plain,
( greater_or_equal(cardinality_at_time(first_movers,'#skF_2'),zero)
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_34,c_64]) ).
tff(c_69,plain,
greater_or_equal(cardinality_at_time(first_movers,'#skF_2'),zero),
inference(demodulation,[status(thm),theory(equality)],[c_36,c_66]) ).
tff(c_18,plain,
! [Y_20,X_19] :
( ( Y_20 = X_19 )
| greater(X_19,Y_20)
| ~ greater_or_equal(X_19,Y_20) ),
inference(cnfTransformation,[status(thm)],[f_99]) ).
tff(c_73,plain,
( ( cardinality_at_time(first_movers,'#skF_2') = zero )
| greater(cardinality_at_time(first_movers,'#skF_2'),zero) ),
inference(resolution,[status(thm)],[c_69,c_18]) ).
tff(c_74,plain,
greater(cardinality_at_time(first_movers,'#skF_2'),zero),
inference(splitLeft,[status(thm)],[c_73]) ).
tff(c_185,plain,
! [E_67,T_68] :
( subpopulations(first_movers,efficient_producers,E_67,T_68)
| ~ greater(cardinality_at_time(efficient_producers,T_68),zero)
| ~ greater(cardinality_at_time(first_movers,T_68),zero)
| ~ in_environment(E_67,T_68)
| ~ environment(E_67) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_188,plain,
! [E_67] :
( subpopulations(first_movers,efficient_producers,E_67,'#skF_2')
| ~ greater(cardinality_at_time(efficient_producers,'#skF_2'),zero)
| ~ in_environment(E_67,'#skF_2')
| ~ environment(E_67) ),
inference(resolution,[status(thm)],[c_74,c_185]) ).
tff(c_189,plain,
~ greater(cardinality_at_time(efficient_producers,'#skF_2'),zero),
inference(splitLeft,[status(thm)],[c_188]) ).
tff(c_14,plain,
! [E_15] :
( greater_or_equal(critical_point(E_15),appear(efficient_producers,E_15))
| ~ environment(E_15) ),
inference(cnfTransformation,[status(thm)],[f_85]) ).
tff(c_40,plain,
! [Y_31,X_32] :
( ( Y_31 = X_32 )
| greater(X_32,Y_31)
| ~ greater_or_equal(X_32,Y_31) ),
inference(cnfTransformation,[status(thm)],[f_99]) ).
tff(c_92,plain,
! [E_47] :
( ( appear(efficient_producers,E_47) = critical_point(E_47) )
| greater(critical_point(E_47),appear(efficient_producers,E_47))
| ~ environment(E_47) ),
inference(resolution,[status(thm)],[c_14,c_40]) ).
tff(c_16,plain,
! [X_16,Z_18,Y_17] :
( greater(X_16,Z_18)
| ~ greater(Y_17,Z_18)
| ~ greater(X_16,Y_17) ),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_144,plain,
! [X_58,E_59] :
( greater(X_58,appear(efficient_producers,E_59))
| ~ greater(X_58,critical_point(E_59))
| ( appear(efficient_producers,E_59) = critical_point(E_59) )
| ~ environment(E_59) ),
inference(resolution,[status(thm)],[c_92,c_16]) ).
tff(c_22,plain,
! [X_19,Y_20] :
( ~ greater(X_19,Y_20)
| greater_or_equal(X_19,Y_20) ),
inference(cnfTransformation,[status(thm)],[f_99]) ).
tff(c_99,plain,
! [T_48,E_49] :
( greater(cardinality_at_time(efficient_producers,T_48),zero)
| ~ greater_or_equal(T_48,appear(efficient_producers,E_49))
| ~ in_environment(E_49,T_48)
| ~ environment(E_49) ),
inference(cnfTransformation,[status(thm)],[f_126]) ).
tff(c_112,plain,
! [X_19,E_49] :
( greater(cardinality_at_time(efficient_producers,X_19),zero)
| ~ in_environment(E_49,X_19)
| ~ environment(E_49)
| ~ greater(X_19,appear(efficient_producers,E_49)) ),
inference(resolution,[status(thm)],[c_22,c_99]) ).
tff(c_290,plain,
! [X_87,E_88] :
( greater(cardinality_at_time(efficient_producers,X_87),zero)
| ~ in_environment(E_88,X_87)
| ~ greater(X_87,critical_point(E_88))
| ( appear(efficient_producers,E_88) = critical_point(E_88) )
| ~ environment(E_88) ),
inference(resolution,[status(thm)],[c_144,c_112]) ).
tff(c_298,plain,
( greater(cardinality_at_time(efficient_producers,'#skF_2'),zero)
| ~ in_environment('#skF_1','#skF_2')
| ( appear(efficient_producers,'#skF_1') = critical_point('#skF_1') )
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_32,c_290]) ).
tff(c_310,plain,
( greater(cardinality_at_time(efficient_producers,'#skF_2'),zero)
| ( appear(efficient_producers,'#skF_1') = critical_point('#skF_1') ) ),
inference(demodulation,[status(thm),theory(equality)],[c_36,c_34,c_298]) ).
tff(c_311,plain,
appear(efficient_producers,'#skF_1') = critical_point('#skF_1'),
inference(negUnitSimplification,[status(thm)],[c_189,c_310]) ).
tff(c_323,plain,
! [X_19] :
( greater(cardinality_at_time(efficient_producers,X_19),zero)
| ~ in_environment('#skF_1',X_19)
| ~ environment('#skF_1')
| ~ greater(X_19,critical_point('#skF_1')) ),
inference(superposition,[status(thm),theory(equality)],[c_311,c_112]) ).
tff(c_356,plain,
! [X_89] :
( greater(cardinality_at_time(efficient_producers,X_89),zero)
| ~ in_environment('#skF_1',X_89)
| ~ greater(X_89,critical_point('#skF_1')) ),
inference(demodulation,[status(thm),theory(equality)],[c_36,c_323]) ).
tff(c_363,plain,
( ~ in_environment('#skF_1','#skF_2')
| ~ greater('#skF_2',critical_point('#skF_1')) ),
inference(resolution,[status(thm)],[c_356,c_189]) ).
tff(c_373,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_32,c_34,c_363]) ).
tff(c_383,plain,
! [E_91] :
( subpopulations(first_movers,efficient_producers,E_91,'#skF_2')
| ~ in_environment(E_91,'#skF_2')
| ~ environment(E_91) ),
inference(splitRight,[status(thm)],[c_188]) ).
tff(c_116,plain,
! [T_52,E_53] :
( greater(growth_rate(efficient_producers,T_52),growth_rate(first_movers,T_52))
| ~ greater(T_52,critical_point(E_53))
| ~ subpopulations(first_movers,efficient_producers,E_53,T_52)
| ~ environment(E_53) ),
inference(cnfTransformation,[status(thm)],[f_116]) ).
tff(c_120,plain,
( greater(growth_rate(efficient_producers,'#skF_2'),growth_rate(first_movers,'#skF_2'))
| ~ subpopulations(first_movers,efficient_producers,'#skF_1','#skF_2')
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_32,c_116]) ).
tff(c_126,plain,
( greater(growth_rate(efficient_producers,'#skF_2'),growth_rate(first_movers,'#skF_2'))
| ~ subpopulations(first_movers,efficient_producers,'#skF_1','#skF_2') ),
inference(demodulation,[status(thm),theory(equality)],[c_36,c_120]) ).
tff(c_127,plain,
~ subpopulations(first_movers,efficient_producers,'#skF_1','#skF_2'),
inference(splitLeft,[status(thm)],[c_126]) ).
tff(c_386,plain,
( ~ in_environment('#skF_1','#skF_2')
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_383,c_127]) ).
tff(c_390,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_36,c_34,c_386]) ).
tff(c_392,plain,
subpopulations(first_movers,efficient_producers,'#skF_1','#skF_2'),
inference(splitRight,[status(thm)],[c_126]) ).
tff(c_391,plain,
greater(growth_rate(efficient_producers,'#skF_2'),growth_rate(first_movers,'#skF_2')),
inference(splitRight,[status(thm)],[c_126]) ).
tff(c_2,plain,
! [S2_3,S1_2,T_4,E_1] :
( selection_favors(S2_3,S1_2,T_4)
| ~ greater(growth_rate(S2_3,T_4),growth_rate(S1_2,T_4))
| ~ subpopulations(S1_2,S2_3,E_1,T_4)
| ~ environment(E_1) ),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_395,plain,
! [E_1] :
( selection_favors(efficient_producers,first_movers,'#skF_2')
| ~ subpopulations(first_movers,efficient_producers,E_1,'#skF_2')
| ~ environment(E_1) ),
inference(resolution,[status(thm)],[c_391,c_2]) ).
tff(c_405,plain,
! [E_96] :
( ~ subpopulations(first_movers,efficient_producers,E_96,'#skF_2')
| ~ environment(E_96) ),
inference(negUnitSimplification,[status(thm)],[c_30,c_395]) ).
tff(c_408,plain,
~ environment('#skF_1'),
inference(resolution,[status(thm)],[c_392,c_405]) ).
tff(c_412,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_36,c_408]) ).
tff(c_413,plain,
cardinality_at_time(first_movers,'#skF_2') = zero,
inference(splitRight,[status(thm)],[c_73]) ).
tff(c_12,plain,
! [E_13,T_14] :
( subpopulation(first_movers,E_13,T_14)
| ~ in_environment(E_13,T_14)
| ~ environment(E_13) ),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_431,plain,
! [E_100] :
( ( appear(efficient_producers,E_100) = critical_point(E_100) )
| greater(critical_point(E_100),appear(efficient_producers,E_100))
| ~ environment(E_100) ),
inference(resolution,[status(thm)],[c_14,c_40]) ).
tff(c_483,plain,
! [X_111,E_112] :
( greater(X_111,appear(efficient_producers,E_112))
| ~ greater(X_111,critical_point(E_112))
| ( appear(efficient_producers,E_112) = critical_point(E_112) )
| ~ environment(E_112) ),
inference(resolution,[status(thm)],[c_431,c_16]) ).
tff(c_438,plain,
! [T_101,E_102] :
( greater(cardinality_at_time(efficient_producers,T_101),zero)
| ~ greater_or_equal(T_101,appear(efficient_producers,E_102))
| ~ in_environment(E_102,T_101)
| ~ environment(E_102) ),
inference(cnfTransformation,[status(thm)],[f_126]) ).
tff(c_451,plain,
! [X_19,E_102] :
( greater(cardinality_at_time(efficient_producers,X_19),zero)
| ~ in_environment(E_102,X_19)
| ~ environment(E_102)
| ~ greater(X_19,appear(efficient_producers,E_102)) ),
inference(resolution,[status(thm)],[c_22,c_438]) ).
tff(c_586,plain,
! [X_135,E_136] :
( greater(cardinality_at_time(efficient_producers,X_135),zero)
| ~ in_environment(E_136,X_135)
| ~ greater(X_135,critical_point(E_136))
| ( appear(efficient_producers,E_136) = critical_point(E_136) )
| ~ environment(E_136) ),
inference(resolution,[status(thm)],[c_483,c_451]) ).
tff(c_594,plain,
( greater(cardinality_at_time(efficient_producers,'#skF_2'),zero)
| ~ in_environment('#skF_1','#skF_2')
| ( appear(efficient_producers,'#skF_1') = critical_point('#skF_1') )
| ~ environment('#skF_1') ),
inference(resolution,[status(thm)],[c_32,c_586]) ).
tff(c_606,plain,
( greater(cardinality_at_time(efficient_producers,'#skF_2'),zero)
| ( appear(efficient_producers,'#skF_1') = critical_point('#skF_1') ) ),
inference(demodulation,[status(thm),theory(equality)],[c_36,c_34,c_594]) ).
tff(c_607,plain,
appear(efficient_producers,'#skF_1') = critical_point('#skF_1'),
inference(splitLeft,[status(thm)],[c_606]) ).
tff(c_629,plain,
! [X_19] :
( greater(cardinality_at_time(efficient_producers,X_19),zero)
| ~ in_environment('#skF_1',X_19)
| ~ environment('#skF_1')
| ~ greater(X_19,critical_point('#skF_1')) ),
inference(superposition,[status(thm),theory(equality)],[c_607,c_451]) ).
tff(c_659,plain,
! [X_139] :
( greater(cardinality_at_time(efficient_producers,X_139),zero)
| ~ in_environment('#skF_1',X_139)
| ~ greater(X_139,critical_point('#skF_1')) ),
inference(demodulation,[status(thm),theory(equality)],[c_36,c_629]) ).
tff(c_4,plain,
! [S1_6,S2_7,T_8,E_5] :
( selection_favors(S1_6,S2_7,T_8)
| ( cardinality_at_time(S2_7,T_8) != zero )
| ~ greater(cardinality_at_time(S1_6,T_8),zero)
| ~ subpopulation(S2_7,E_5,T_8)
| ~ subpopulation(S1_6,E_5,T_8)
| ~ environment(E_5) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_718,plain,
! [S2_154,X_155,E_156] :
( selection_favors(efficient_producers,S2_154,X_155)
| ( cardinality_at_time(S2_154,X_155) != zero )
| ~ subpopulation(S2_154,E_156,X_155)
| ~ subpopulation(efficient_producers,E_156,X_155)
| ~ environment(E_156)
| ~ in_environment('#skF_1',X_155)
| ~ greater(X_155,critical_point('#skF_1')) ),
inference(resolution,[status(thm)],[c_659,c_4]) ).
tff(c_725,plain,
! [T_157,E_158] :
( selection_favors(efficient_producers,first_movers,T_157)
| ( cardinality_at_time(first_movers,T_157) != zero )
| ~ subpopulation(efficient_producers,E_158,T_157)
| ~ in_environment('#skF_1',T_157)
| ~ greater(T_157,critical_point('#skF_1'))
| ~ in_environment(E_158,T_157)
| ~ environment(E_158) ),
inference(resolution,[status(thm)],[c_12,c_718]) ).
tff(c_729,plain,
! [T_159,E_160] :
( selection_favors(efficient_producers,first_movers,T_159)
| ( cardinality_at_time(first_movers,T_159) != zero )
| ~ in_environment('#skF_1',T_159)
| ~ greater(T_159,critical_point('#skF_1'))
| ~ in_environment(E_160,T_159)
| ~ environment(E_160) ),
inference(resolution,[status(thm)],[c_10,c_725]) ).
tff(c_737,plain,
! [E_160] :
( selection_favors(efficient_producers,first_movers,'#skF_2')
| ( cardinality_at_time(first_movers,'#skF_2') != zero )
| ~ in_environment('#skF_1','#skF_2')
| ~ in_environment(E_160,'#skF_2')
| ~ environment(E_160) ),
inference(resolution,[status(thm)],[c_32,c_729]) ).
tff(c_743,plain,
! [E_160] :
( selection_favors(efficient_producers,first_movers,'#skF_2')
| ~ in_environment(E_160,'#skF_2')
| ~ environment(E_160) ),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_413,c_737]) ).
tff(c_745,plain,
! [E_161] :
( ~ in_environment(E_161,'#skF_2')
| ~ environment(E_161) ),
inference(negUnitSimplification,[status(thm)],[c_30,c_743]) ).
tff(c_748,plain,
~ environment('#skF_1'),
inference(resolution,[status(thm)],[c_34,c_745]) ).
tff(c_752,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_36,c_748]) ).
tff(c_753,plain,
greater(cardinality_at_time(efficient_producers,'#skF_2'),zero),
inference(splitRight,[status(thm)],[c_606]) ).
tff(c_797,plain,
! [S2_167,E_168] :
( selection_favors(efficient_producers,S2_167,'#skF_2')
| ( cardinality_at_time(S2_167,'#skF_2') != zero )
| ~ subpopulation(S2_167,E_168,'#skF_2')
| ~ subpopulation(efficient_producers,E_168,'#skF_2')
| ~ environment(E_168) ),
inference(resolution,[status(thm)],[c_753,c_4]) ).
tff(c_800,plain,
! [E_13] :
( selection_favors(efficient_producers,first_movers,'#skF_2')
| ( cardinality_at_time(first_movers,'#skF_2') != zero )
| ~ subpopulation(efficient_producers,E_13,'#skF_2')
| ~ in_environment(E_13,'#skF_2')
| ~ environment(E_13) ),
inference(resolution,[status(thm)],[c_12,c_797]) ).
tff(c_806,plain,
! [E_13] :
( selection_favors(efficient_producers,first_movers,'#skF_2')
| ~ subpopulation(efficient_producers,E_13,'#skF_2')
| ~ in_environment(E_13,'#skF_2')
| ~ environment(E_13) ),
inference(demodulation,[status(thm),theory(equality)],[c_413,c_800]) ).
tff(c_809,plain,
! [E_169] :
( ~ subpopulation(efficient_producers,E_169,'#skF_2')
| ~ in_environment(E_169,'#skF_2')
| ~ environment(E_169) ),
inference(negUnitSimplification,[status(thm)],[c_30,c_806]) ).
tff(c_815,plain,
! [E_170] :
( ~ in_environment(E_170,'#skF_2')
| ~ environment(E_170) ),
inference(resolution,[status(thm)],[c_10,c_809]) ).
tff(c_818,plain,
~ environment('#skF_1'),
inference(resolution,[status(thm)],[c_34,c_815]) ).
tff(c_822,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_36,c_818]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : MGT026+1 : TPTP v8.1.2. Released v2.0.0.
% 0.08/0.15 % 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
% 0.15/0.36 % Computer : n013.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Aug 3 20:28:32 EDT 2023
% 0.15/0.36 % CPUTime :
% 4.26/2.18 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.26/2.19
% 4.26/2.19 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.26/2.23
% 4.26/2.23 Inference rules
% 4.26/2.23 ----------------------
% 4.26/2.23 #Ref : 0
% 4.26/2.23 #Sup : 178
% 4.26/2.23 #Fact : 0
% 4.26/2.23 #Define : 0
% 4.26/2.23 #Split : 16
% 4.26/2.23 #Chain : 0
% 4.26/2.23 #Close : 0
% 4.26/2.23
% 4.26/2.23 Ordering : KBO
% 4.26/2.23
% 4.26/2.23 Simplification rules
% 4.26/2.23 ----------------------
% 4.26/2.23 #Subsume : 28
% 4.26/2.23 #Demod : 72
% 4.26/2.23 #Tautology : 20
% 4.26/2.23 #SimpNegUnit : 5
% 4.26/2.23 #BackRed : 3
% 4.26/2.23
% 4.26/2.23 #Partial instantiations: 0
% 4.26/2.23 #Strategies tried : 1
% 4.26/2.23
% 4.26/2.23 Timing (in seconds)
% 4.26/2.23 ----------------------
% 4.26/2.24 Preprocessing : 0.51
% 4.26/2.24 Parsing : 0.28
% 4.26/2.24 CNF conversion : 0.03
% 4.26/2.24 Main loop : 0.55
% 4.26/2.24 Inferencing : 0.22
% 4.26/2.24 Reduction : 0.14
% 4.26/2.24 Demodulation : 0.09
% 4.26/2.24 BG Simplification : 0.02
% 4.26/2.24 Subsumption : 0.13
% 4.26/2.24 Abstraction : 0.02
% 4.26/2.24 MUC search : 0.00
% 4.26/2.24 Cooper : 0.00
% 4.26/2.24 Total : 1.13
% 4.26/2.24 Index Insertion : 0.00
% 4.26/2.24 Index Deletion : 0.00
% 4.26/2.24 Index Matching : 0.00
% 4.26/2.24 BG Taut test : 0.00
%------------------------------------------------------------------------------