%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : MGT039-2 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:26:52 PM UTC 2026
% Result : Unsatisfiable 0.15s 5.47s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 26
% Syntax : Number of clauses : 125 ( 25 unt; 26 nHn; 124 RR)
% Number of literals : 398 ( 31 equ; 252 neg)
% Maximal clause size : 6 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-4 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-2 aty)
% Number of variables : 175 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(mp_greater_or_equal_52,axiom,
( ~ greater_or_equal(X1,X2)
| X1 = X2
| greater(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal_52) ).
cnf(mp_time_of_critical_point_49,axiom,
( ~ environment(X1)
| greater_or_equal(critical_point(X1),start_time(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_time_of_critical_point_49) ).
cnf(mp_greater_transitivity_50,axiom,
( ~ greater(X2,X3)
| ~ greater(X1,X2)
| greater(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_transitivity_50) ).
cnf(mp4_critical_point_38,axiom,
( ~ in_environment(X1,X2)
| ~ environment(X2)
| ~ slow_change(X1)
| ~ observational_period(X1)
| in_environment(X2,sk2(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp4_critical_point_38) ).
cnf(mp4_critical_point_39,axiom,
( ~ in_environment(X1,X2)
| ~ environment(X2)
| ~ slow_change(X1)
| ~ observational_period(X1)
| greater(sk2(X2,X1),critical_point(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp4_critical_point_39) ).
cnf(mp_environment_end_point_43,axiom,
( ~ in_environment(X1,X2)
| ~ environment(X1)
| greater_or_equal(end_time(X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_environment_end_point_43) ).
cnf(prove_t8_59,negated_conjecture,
slow_change(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t8_59) ).
cnf(prove_t8_58,negated_conjecture,
observational_period(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t8_58) ).
cnf(mp_time_in_environment_42,axiom,
( ~ greater_or_equal(end_time(X1),X2)
| ~ greater_or_equal(X2,start_time(X1))
| ~ environment(X1)
| in_environment(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_time_in_environment_42) ).
cnf(mp_greater_or_equal_53,axiom,
( ~ greater(X1,X2)
| greater_or_equal(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal_53) ).
cnf(mp_greater_or_equal_54,axiom,
( X1 != X2
| greater_or_equal(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal_54) ).
cnf(mp3_favoured_trategy_36,axiom,
( ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers)
| ~ observational_period(X1)
| selection_favors(efficient_producers,first_movers,X1)
| in_environment(X1,sk1(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp3_favoured_trategy_36) ).
cnf(mp3_favoured_trategy_35,axiom,
( ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers)
| ~ observational_period(X1)
| selection_favors(efficient_producers,first_movers,X1)
| environment(sk1(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp3_favoured_trategy_35) ).
cnf(mp_critical_point_after_EP_48,axiom,
( ~ environment(X1)
| greater_or_equal(critical_point(X1),appear(efficient_producers,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_critical_point_after_EP_48) ).
cnf(mp_organizational_sets1_40,axiom,
propagation_strategy(first_movers),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_organizational_sets1_40) ).
cnf(mp_organizational_sets2_41,axiom,
propagation_strategy(efficient_producers),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_organizational_sets2_41) ).
cnf(prove_t8_60,negated_conjecture,
~ selection_favors(efficient_producers,first_movers,sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t8_60) ).
cnf(t6_57,hypothesis,
( ~ greater_or_equal(X2,appear(efficient_producers,X1))
| ~ in_environment(X1,X2)
| ~ environment(X1)
| greater(cardinality_at_time(efficient_producers,X2),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_57) ).
cnf(d1_56,hypothesis,
( ~ greater(X3,X2)
| ~ subpopulations(first_movers,efficient_producers,X1,X3)
| X2 != critical_point(X1)
| ~ environment(X1)
| greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_56) ).
cnf(mp2_favour_members_34,axiom,
( cardinality_at_time(X4,X3) != zero
| ~ greater(cardinality_at_time(X2,X3),zero)
| ~ subpopulation(X4,X1,X3)
| ~ subpopulation(X2,X1,X3)
| ~ environment(X1)
| selection_favors(X2,X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp2_favour_members_34) ).
cnf(mp_subpopulations_46,axiom,
( ~ in_environment(X1,X2)
| ~ environment(X1)
| subpopulation(first_movers,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_subpopulations_46) ).
cnf(mp3_favoured_trategy_37,axiom,
( ~ selection_favors(efficient_producers,first_movers,end_time(sk1(X1)))
| ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers)
| ~ observational_period(X1)
| selection_favors(efficient_producers,first_movers,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp3_favoured_trategy_37) ).
cnf(mp_contains_FM_and_EP_44,axiom,
( ~ greater(cardinality_at_time(efficient_producers,X2),zero)
| ~ greater(cardinality_at_time(first_movers,X2),zero)
| ~ in_environment(X1,X2)
| ~ environment(X1)
| subpopulations(first_movers,efficient_producers,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_contains_FM_and_EP_44) ).
cnf(mp_subpopulations_47,axiom,
( ~ in_environment(X1,X2)
| ~ environment(X1)
| subpopulation(efficient_producers,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_subpopulations_47) ).
cnf(mp_first_movers_exist_45,axiom,
( ~ in_environment(X1,X2)
| ~ environment(X1)
| greater_or_equal(cardinality_at_time(first_movers,X2),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_first_movers_exist_45) ).
cnf(mp1_high_growth_rates_33,axiom,
( ~ greater(growth_rate(X3,X4),growth_rate(X2,X4))
| ~ subpopulations(X2,X3,X1,X4)
| ~ environment(X1)
| selection_favors(X3,X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp1_high_growth_rates_33) ).
cnf(c_0_26,plain,
( ~ greater_or_equal(X1,X2)
| X1 = X2
| greater(X1,X2) ),
inference(fof_simplification,[status(thm)],[mp_greater_or_equal_52]) ).
cnf(c_0_27,plain,
( ~ environment(X1)
| greater_or_equal(critical_point(X1),start_time(X1)) ),
inference(fof_simplification,[status(thm)],[mp_time_of_critical_point_49]) ).
cnf(c_0_28,plain,
( ~ greater(X2,X3)
| ~ greater(X1,X2)
| greater(X1,X3) ),
inference(fof_simplification,[status(thm)],[mp_greater_transitivity_50]) ).
cnf(c_0_29,plain,
( ~ greater_or_equal(X1,X2)
| X1 = X2
| greater(X1,X2) ),
c_0_26 ).
cnf(c_0_30,plain,
( ~ environment(X1)
| greater_or_equal(critical_point(X1),start_time(X1)) ),
c_0_27 ).
cnf(c_0_31,plain,
( ~ in_environment(X1,X2)
| ~ environment(X2)
| ~ slow_change(X1)
| ~ observational_period(X1)
| in_environment(X2,sk2(X2,X1)) ),
inference(fof_simplification,[status(thm)],[mp4_critical_point_38]) ).
cnf(c_0_32,plain,
( ~ greater(X2,X3)
| ~ greater(X1,X2)
| greater(X1,X3) ),
c_0_28 ).
cnf(c_0_33,plain,
( ~ environment(X1)
| greater(critical_point(X1),start_time(X1))
| start_time(X1) = critical_point(X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,plain,
( ~ in_environment(X1,X2)
| ~ environment(X2)
| ~ slow_change(X1)
| ~ observational_period(X1)
| greater(sk2(X2,X1),critical_point(X2)) ),
inference(fof_simplification,[status(thm)],[mp4_critical_point_39]) ).
cnf(c_0_35,plain,
( ~ in_environment(X1,X2)
| ~ environment(X1)
| greater_or_equal(end_time(X1),X2) ),
inference(fof_simplification,[status(thm)],[mp_environment_end_point_43]) ).
cnf(c_0_36,plain,
( ~ in_environment(X1,X2)
| ~ environment(X2)
| ~ slow_change(X1)
| ~ observational_period(X1)
| in_environment(X2,sk2(X2,X1)) ),
c_0_31 ).
cnf(c_0_37,negated_conjecture,
slow_change(sk3),
prove_t8_59 ).
cnf(c_0_38,negated_conjecture,
observational_period(sk3),
prove_t8_58 ).
cnf(c_0_39,plain,
( ~ environment(X1)
| ~ greater(X2,critical_point(X1))
| greater(X2,start_time(X1))
| start_time(X1) = critical_point(X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_40,plain,
( ~ in_environment(X1,X2)
| ~ environment(X2)
| ~ slow_change(X1)
| ~ observational_period(X1)
| greater(sk2(X2,X1),critical_point(X2)) ),
c_0_34 ).
cnf(c_0_41,plain,
( ~ in_environment(X1,X2)
| ~ environment(X1)
| greater_or_equal(end_time(X1),X2) ),
c_0_35 ).
cnf(c_0_42,negated_conjecture,
( ~ environment(X1)
| ~ in_environment(sk3,X1)
| in_environment(X1,sk2(X1,sk3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38])]) ).
cnf(c_0_43,plain,
( ~ greater_or_equal(end_time(X1),X2)
| ~ greater_or_equal(X2,start_time(X1))
| ~ environment(X1)
| in_environment(X1,X2) ),
inference(fof_simplification,[status(thm)],[mp_time_in_environment_42]) ).
cnf(c_0_44,plain,
( ~ greater(X1,X2)
| greater_or_equal(X1,X2) ),
inference(fof_simplification,[status(thm)],[mp_greater_or_equal_53]) ).
cnf(c_0_45,plain,
( X1 != X2
| greater_or_equal(X1,X2) ),
inference(fof_simplification,[status(thm)],[mp_greater_or_equal_54]) ).
cnf(c_0_46,plain,
( ~ environment(X1)
| ~ greater(X2,X3)
| ~ greater(X3,critical_point(X1))
| greater(X2,start_time(X1))
| start_time(X1) = critical_point(X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_39]) ).
cnf(c_0_47,negated_conjecture,
( ~ environment(X1)
| ~ in_environment(sk3,X1)
| greater(sk2(X1,sk3),critical_point(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_37]),c_0_38])]) ).
cnf(c_0_48,negated_conjecture,
( ~ environment(X1)
| ~ in_environment(sk3,X1)
| greater_or_equal(end_time(X1),sk2(X1,sk3)) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_49,plain,
( ~ greater_or_equal(end_time(X1),X2)
| ~ greater_or_equal(X2,start_time(X1))
| ~ environment(X1)
| in_environment(X1,X2) ),
c_0_43 ).
cnf(c_0_50,plain,
( ~ greater(X1,X2)
| greater_or_equal(X1,X2) ),
c_0_44 ).
cnf(c_0_51,plain,
( X1 != X2
| greater_or_equal(X1,X2) ),
c_0_45 ).
cnf(c_0_52,plain,
( ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers)
| ~ observational_period(X1)
| selection_favors(efficient_producers,first_movers,X1)
| in_environment(X1,sk1(X1)) ),
inference(fof_simplification,[status(thm)],[mp3_favoured_trategy_36]) ).
cnf(c_0_53,plain,
( ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers)
| ~ observational_period(X1)
| selection_favors(efficient_producers,first_movers,X1)
| environment(sk1(X1)) ),
inference(fof_simplification,[status(thm)],[mp3_favoured_trategy_35]) ).
cnf(c_0_54,plain,
( ~ environment(X1)
| greater_or_equal(critical_point(X1),appear(efficient_producers,X1)) ),
inference(fof_simplification,[status(thm)],[mp_critical_point_after_EP_48]) ).
cnf(c_0_55,negated_conjecture,
( ~ environment(X1)
| ~ greater(X2,sk2(X1,sk3))
| ~ in_environment(sk3,X1)
| greater(X2,start_time(X1))
| start_time(X1) = critical_point(X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_56,negated_conjecture,
( ~ environment(X1)
| ~ in_environment(sk3,X1)
| greater(end_time(X1),sk2(X1,sk3))
| sk2(X1,sk3) = end_time(X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_48]) ).
cnf(c_0_57,plain,
( ~ environment(X1)
| ~ greater(X2,start_time(X1))
| ~ greater_or_equal(end_time(X1),X2)
| in_environment(X1,X2) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_58,plain,
greater_or_equal(X1,X1),
inference(er,[status(thm)],[c_0_51]) ).
cnf(c_0_59,plain,
( ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers)
| ~ observational_period(X1)
| selection_favors(efficient_producers,first_movers,X1)
| in_environment(X1,sk1(X1)) ),
c_0_52 ).
cnf(c_0_60,axiom,
propagation_strategy(first_movers),
mp_organizational_sets1_40 ).
cnf(c_0_61,axiom,
propagation_strategy(efficient_producers),
mp_organizational_sets2_41 ).
cnf(c_0_62,negated_conjecture,
~ selection_favors(efficient_producers,first_movers,sk3),
inference(fof_simplification,[status(thm)],[prove_t8_60]) ).
cnf(c_0_63,plain,
( ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers)
| ~ observational_period(X1)
| selection_favors(efficient_producers,first_movers,X1)
| environment(sk1(X1)) ),
c_0_53 ).
cnf(c_0_64,negated_conjecture,
( ~ environment(X2)
| ~ greater(X1,sk2(X2,sk3))
| ~ in_environment(sk3,X2)
| greater(X1,critical_point(X2)) ),
inference(spm,[status(thm)],[c_0_32,c_0_47]) ).
cnf(c_0_65,hypothesis,
( ~ greater_or_equal(X2,appear(efficient_producers,X1))
| ~ in_environment(X1,X2)
| ~ environment(X1)
| greater(cardinality_at_time(efficient_producers,X2),zero) ),
inference(fof_simplification,[status(thm)],[t6_57]) ).
cnf(c_0_66,plain,
( ~ environment(X1)
| greater_or_equal(critical_point(X1),appear(efficient_producers,X1)) ),
c_0_54 ).
cnf(c_0_67,negated_conjecture,
( ~ environment(X1)
| ~ in_environment(sk3,X1)
| greater(end_time(X1),start_time(X1))
| start_time(X1) = critical_point(X1)
| sk2(X1,sk3) = end_time(X1) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_68,plain,
( ~ environment(X1)
| ~ greater(end_time(X1),start_time(X1))
| in_environment(X1,end_time(X1)) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_69,plain,
( ~ observational_period(X1)
| selection_favors(efficient_producers,first_movers,X1)
| in_environment(X1,sk1(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_60]),c_0_61])]) ).
cnf(c_0_70,negated_conjecture,
~ selection_favors(efficient_producers,first_movers,sk3),
c_0_62 ).
cnf(c_0_71,plain,
( ~ observational_period(X1)
| environment(sk1(X1))
| selection_favors(efficient_producers,first_movers,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_60]),c_0_61])]) ).
cnf(c_0_72,negated_conjecture,
( ~ environment(X1)
| ~ in_environment(sk3,X1)
| greater(end_time(X1),critical_point(X1))
| sk2(X1,sk3) = end_time(X1) ),
inference(spm,[status(thm)],[c_0_64,c_0_56]) ).
cnf(c_0_73,hypothesis,
( ~ greater_or_equal(X2,appear(efficient_producers,X1))
| ~ in_environment(X1,X2)
| ~ environment(X1)
| greater(cardinality_at_time(efficient_producers,X2),zero) ),
c_0_65 ).
cnf(c_0_74,plain,
( ~ environment(X1)
| greater(critical_point(X1),appear(efficient_producers,X1))
| appear(efficient_producers,X1) = critical_point(X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_66]) ).
cnf(c_0_75,negated_conjecture,
( ~ environment(X1)
| ~ in_environment(sk3,X1)
| in_environment(X1,end_time(X1))
| start_time(X1) = critical_point(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_67]),c_0_68]) ).
cnf(c_0_76,negated_conjecture,
in_environment(sk3,sk1(sk3)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_38]),c_0_70]) ).
cnf(c_0_77,negated_conjecture,
environment(sk1(sk3)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_38]),c_0_70]) ).
cnf(c_0_78,negated_conjecture,
( ~ environment(X1)
| ~ in_environment(sk3,X1)
| greater(end_time(X1),critical_point(X1)) ),
inference(spm,[status(thm)],[c_0_47,c_0_72]) ).
cnf(c_0_79,hypothesis,
( ~ greater(X3,X2)
| ~ subpopulations(first_movers,efficient_producers,X1,X3)
| X2 != critical_point(X1)
| ~ environment(X1)
| greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3)) ),
inference(fof_simplification,[status(thm)],[d1_56]) ).
cnf(c_0_80,plain,
( cardinality_at_time(X4,X3) != zero
| ~ greater(cardinality_at_time(X2,X3),zero)
| ~ subpopulation(X4,X1,X3)
| ~ subpopulation(X2,X1,X3)
| ~ environment(X1)
| selection_favors(X2,X4,X3) ),
inference(fof_simplification,[status(thm)],[mp2_favour_members_34]) ).
cnf(c_0_81,plain,
( ~ in_environment(X1,X2)
| ~ environment(X1)
| subpopulation(first_movers,X1,X2) ),
inference(fof_simplification,[status(thm)],[mp_subpopulations_46]) ).
cnf(c_0_82,plain,
( ~ selection_favors(efficient_producers,first_movers,end_time(sk1(X1)))
| ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers)
| ~ observational_period(X1)
| selection_favors(efficient_producers,first_movers,X1) ),
inference(fof_simplification,[status(thm)],[mp3_favoured_trategy_37]) ).
cnf(c_0_83,hypothesis,
( ~ environment(X2)
| ~ greater(X1,appear(efficient_producers,X2))
| ~ in_environment(X2,X1)
| greater(cardinality_at_time(efficient_producers,X1),zero) ),
inference(spm,[status(thm)],[c_0_73,c_0_50]) ).
cnf(c_0_84,plain,
( ~ environment(X1)
| ~ greater(X2,critical_point(X1))
| greater(X2,appear(efficient_producers,X1))
| appear(efficient_producers,X1) = critical_point(X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_74]) ).
cnf(c_0_85,negated_conjecture,
( in_environment(sk1(sk3),end_time(sk1(sk3)))
| start_time(sk1(sk3)) = critical_point(sk1(sk3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_77])]) ).
cnf(c_0_86,negated_conjecture,
greater(end_time(sk1(sk3)),critical_point(sk1(sk3))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_76]),c_0_77])]) ).
cnf(c_0_87,plain,
( ~ environment(X1)
| ~ greater_or_equal(end_time(X1),critical_point(X1))
| in_environment(X1,critical_point(X1)) ),
inference(spm,[status(thm)],[c_0_49,c_0_30]) ).
cnf(c_0_88,hypothesis,
( ~ greater(X3,X2)
| ~ subpopulations(first_movers,efficient_producers,X1,X3)
| X2 != critical_point(X1)
| ~ environment(X1)
| greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3)) ),
c_0_79 ).
cnf(c_0_89,plain,
( ~ greater(cardinality_at_time(efficient_producers,X2),zero)
| ~ greater(cardinality_at_time(first_movers,X2),zero)
| ~ in_environment(X1,X2)
| ~ environment(X1)
| subpopulations(first_movers,efficient_producers,X1,X2) ),
inference(fof_simplification,[status(thm)],[mp_contains_FM_and_EP_44]) ).
cnf(c_0_90,plain,
( cardinality_at_time(X4,X3) != zero
| ~ greater(cardinality_at_time(X2,X3),zero)
| ~ subpopulation(X4,X1,X3)
| ~ subpopulation(X2,X1,X3)
| ~ environment(X1)
| selection_favors(X2,X4,X3) ),
c_0_80 ).
cnf(c_0_91,plain,
( ~ in_environment(X1,X2)
| ~ environment(X1)
| subpopulation(first_movers,X1,X2) ),
c_0_81 ).
cnf(c_0_92,plain,
( ~ in_environment(X1,X2)
| ~ environment(X1)
| subpopulation(efficient_producers,X1,X2) ),
inference(fof_simplification,[status(thm)],[mp_subpopulations_47]) ).
cnf(c_0_93,plain,
( ~ selection_favors(efficient_producers,first_movers,end_time(sk1(X1)))
| ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers)
| ~ observational_period(X1)
| selection_favors(efficient_producers,first_movers,X1) ),
c_0_82 ).
cnf(c_0_94,hypothesis,
( ~ environment(X1)
| ~ greater(X2,critical_point(X1))
| ~ in_environment(X1,X2)
| greater(cardinality_at_time(efficient_producers,X2),zero)
| appear(efficient_producers,X1) = critical_point(X1) ),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_95,negated_conjecture,
in_environment(sk1(sk3),end_time(sk1(sk3))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_85]),c_0_86]),c_0_77])]) ).
cnf(c_0_96,plain,
( ~ environment(X1)
| ~ greater(end_time(X1),critical_point(X1))
| in_environment(X1,critical_point(X1)) ),
inference(spm,[status(thm)],[c_0_87,c_0_50]) ).
cnf(c_0_97,hypothesis,
( ~ environment(X2)
| ~ subpopulations(first_movers,efficient_producers,X2,X1)
| ~ greater(X1,critical_point(X2))
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ),
inference(er,[status(thm)],[c_0_88]) ).
cnf(c_0_98,plain,
( ~ greater(cardinality_at_time(efficient_producers,X2),zero)
| ~ greater(cardinality_at_time(first_movers,X2),zero)
| ~ in_environment(X1,X2)
| ~ environment(X1)
| subpopulations(first_movers,efficient_producers,X1,X2) ),
c_0_89 ).
cnf(c_0_99,plain,
( ~ in_environment(X1,X2)
| ~ environment(X1)
| greater_or_equal(cardinality_at_time(first_movers,X2),zero) ),
inference(fof_simplification,[status(thm)],[mp_first_movers_exist_45]) ).
cnf(c_0_100,plain,
( ~ environment(X3)
| ~ greater(cardinality_at_time(X1,X2),zero)
| ~ subpopulation(X1,X3,X2)
| ~ in_environment(X3,X2)
| cardinality_at_time(first_movers,X2) != zero
| selection_favors(X1,first_movers,X2) ),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_101,plain,
( ~ in_environment(X1,X2)
| ~ environment(X1)
| subpopulation(efficient_producers,X1,X2) ),
c_0_92 ).
cnf(c_0_102,plain,
( ~ selection_favors(efficient_producers,first_movers,end_time(sk1(X1)))
| ~ observational_period(X1)
| selection_favors(efficient_producers,first_movers,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_60]),c_0_61])]) ).
cnf(c_0_103,negated_conjecture,
( greater(cardinality_at_time(efficient_producers,end_time(sk1(sk3))),zero)
| appear(efficient_producers,sk1(sk3)) = critical_point(sk1(sk3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_86]),c_0_95]),c_0_77])]) ).
cnf(c_0_104,negated_conjecture,
in_environment(sk1(sk3),critical_point(sk1(sk3))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_86]),c_0_77])]) ).
cnf(c_0_105,hypothesis,
( ~ environment(X2)
| ~ greater(X1,critical_point(X2))
| ~ greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ greater(cardinality_at_time(first_movers,X1),zero)
| ~ in_environment(X2,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_106,plain,
( ~ in_environment(X1,X2)
| ~ environment(X1)
| greater_or_equal(cardinality_at_time(first_movers,X2),zero) ),
c_0_99 ).
cnf(c_0_107,plain,
( ~ environment(X2)
| ~ greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ in_environment(X2,X1)
| cardinality_at_time(first_movers,X1) != zero
| selection_favors(efficient_producers,first_movers,X1) ),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_108,negated_conjecture,
~ selection_favors(efficient_producers,first_movers,end_time(sk1(sk3))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_38]),c_0_70]) ).
cnf(c_0_109,hypothesis,
( ~ in_environment(sk1(sk3),X1)
| ~ greater_or_equal(X1,critical_point(sk1(sk3)))
| greater(cardinality_at_time(efficient_producers,X1),zero)
| greater(cardinality_at_time(efficient_producers,end_time(sk1(sk3))),zero) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_103]),c_0_77])]) ).
cnf(c_0_110,negated_conjecture,
greater_or_equal(end_time(sk1(sk3)),critical_point(sk1(sk3))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_104]),c_0_77])]) ).
cnf(c_0_111,hypothesis,
( ~ greater(cardinality_at_time(efficient_producers,end_time(sk1(sk3))),zero)
| ~ greater(cardinality_at_time(first_movers,end_time(sk1(sk3))),zero)
| ~ in_environment(sk1(sk3),end_time(sk1(sk3)))
| greater(growth_rate(efficient_producers,end_time(sk1(sk3))),growth_rate(first_movers,end_time(sk1(sk3)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_86]),c_0_77])]) ).
cnf(c_0_112,negated_conjecture,
greater_or_equal(cardinality_at_time(first_movers,end_time(sk1(sk3))),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_95]),c_0_77])]) ).
cnf(c_0_113,negated_conjecture,
( ~ greater(cardinality_at_time(efficient_producers,end_time(sk1(sk3))),zero)
| cardinality_at_time(first_movers,end_time(sk1(sk3))) != zero ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_95]),c_0_77])]),c_0_108]) ).
cnf(c_0_114,negated_conjecture,
greater(cardinality_at_time(efficient_producers,end_time(sk1(sk3))),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_95])]) ).
cnf(c_0_115,plain,
( ~ greater(growth_rate(X3,X4),growth_rate(X2,X4))
| ~ subpopulations(X2,X3,X1,X4)
| ~ environment(X1)
| selection_favors(X3,X2,X4) ),
inference(fof_simplification,[status(thm)],[mp1_high_growth_rates_33]) ).
cnf(c_0_116,hypothesis,
( ~ greater(cardinality_at_time(efficient_producers,end_time(sk1(sk3))),zero)
| ~ greater(cardinality_at_time(first_movers,end_time(sk1(sk3))),zero)
| greater(growth_rate(efficient_producers,end_time(sk1(sk3))),growth_rate(first_movers,end_time(sk1(sk3)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_111,c_0_95])]) ).
cnf(c_0_117,negated_conjecture,
( greater(cardinality_at_time(first_movers,end_time(sk1(sk3))),zero)
| cardinality_at_time(first_movers,end_time(sk1(sk3))) = zero ),
inference(spm,[status(thm)],[c_0_29,c_0_112]) ).
cnf(c_0_118,negated_conjecture,
cardinality_at_time(first_movers,end_time(sk1(sk3))) != zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_113,c_0_114])]) ).
cnf(c_0_119,plain,
( ~ greater(growth_rate(X3,X4),growth_rate(X2,X4))
| ~ subpopulations(X2,X3,X1,X4)
| ~ environment(X1)
| selection_favors(X3,X2,X4) ),
c_0_115 ).
cnf(c_0_120,hypothesis,
( ~ greater(cardinality_at_time(first_movers,end_time(sk1(sk3))),zero)
| greater(growth_rate(efficient_producers,end_time(sk1(sk3))),growth_rate(first_movers,end_time(sk1(sk3)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_116,c_0_114])]) ).
cnf(c_0_121,negated_conjecture,
greater(cardinality_at_time(first_movers,end_time(sk1(sk3))),zero),
inference(sr,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_122,plain,
( ~ environment(X2)
| ~ greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ greater(cardinality_at_time(first_movers,X1),zero)
| ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ in_environment(X2,X1)
| selection_favors(efficient_producers,first_movers,X1) ),
inference(spm,[status(thm)],[c_0_119,c_0_98]) ).
cnf(c_0_123,hypothesis,
greater(growth_rate(efficient_producers,end_time(sk1(sk3))),growth_rate(first_movers,end_time(sk1(sk3)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_120,c_0_121])]) ).
cnf(c_0_124,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_95]),c_0_77])]),c_0_108]),c_0_123]),c_0_121]),c_0_114])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT039-2 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/5.38 % Computer : n014.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Mon Sep 21 01:22:55 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/5.42 Running first-order theorem proving
% 0.15/5.42 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/5.46 % Version: 3.5.1
% 0.15/5.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/5.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/5.46 % Starting new_bool_3 with 300s (1) cores
% 0.15/5.46 % Starting new_bool_1 with 300s (1) cores
% 0.15/5.46 % Starting sh5l with 300s (1) cores
% 0.15/5.46 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2855134 completed with status 0
% 0.15/5.46 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.15/5.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/5.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/5.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/5.46 % No SInE strategy applied
% 0.15/5.46 % Search class: FGHSF-FFMS21-SFFFFFNN
% 0.15/5.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/5.46 % Starting SubtermCWHack with 136s (1) cores
% 0.15/5.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.15/5.46 % Starting 208_C09_12_F1_SE_CS_SP_PS_S070I with 136s (1) cores
% 0.15/5.47 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 0.15/5.47 % Starting new_bool_3 with 136s (1) cores
% 0.15/5.47 % G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0Y with pid 2855144 completed with status 0
% 0.15/5.47 % Result found by G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0Y
% 0.15/5.47 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/5.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/5.47 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/5.47 % No SInE strategy applied
% 0.15/5.47 % Search class: FGHSF-FFMS21-SFFFFFNN
% 0.15/5.47 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/5.47 % Starting SubtermCWHack with 136s (1) cores
% 0.15/5.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.15/5.47 % Starting 208_C09_12_F1_SE_CS_SP_PS_S070I with 136s (1) cores
% 0.15/5.47 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 0.15/5.47 % Preprocessing time : 0.002 s
% 0.15/5.47 % Presaturation interreduction done
% 0.15/5.47
% 0.15/5.47 % Proof found!
% 0.15/5.47 % SZS status Unsatisfiable
% 0.15/5.47 % SZS output start CNFRefutation
% See solution above
% 0.15/5.47 % Parsed axioms : 28
% 0.15/5.47 % Removed by relevancy pruning/SinE : 0
% 0.15/5.47 % Initial clauses : 28
% 0.15/5.47 % Removed in clause preprocessing : 0
% 0.15/5.47 % Initial clauses in saturation : 28
% 0.15/5.47 % Processed clauses : 192
% 0.15/5.47 % ...of these trivial : 0
% 0.15/5.47 % ...subsumed : 5
% 0.15/5.47 % ...remaining for further processing : 186
% 0.15/5.47 % Other redundant clauses eliminated : 3
% 0.15/5.47 % Clauses deleted for lack of memory : 0
% 0.15/5.47 % Backward-subsumed : 11
% 0.15/5.47 % Backward-rewritten : 14
% 0.15/5.47 % Generated clauses : 272
% 0.15/5.47 % ...of the previous two non-redundant : 248
% 0.15/5.47 % ...aggressively subsumed : 0
% 0.15/5.47 % Contextual simplify-reflections : 1
% 0.15/5.47 % Paramodulations : 268
% 0.15/5.47 % Factorizations : 0
% 0.15/5.47 % NegExts : 0
% 0.15/5.47 % Equation resolutions : 3
% 0.15/5.47 % Disequality decompositions : 0
% 0.15/5.47 % Total rewrite steps : 131
% 0.15/5.47 % ...of those cached : 111
% 0.15/5.47 % Propositional unsat checks : 0
% 0.15/5.47 % Propositional check models : 0
% 0.15/5.47 % Propositional check unsatisfiable : 0
% 0.15/5.47 % Propositional clauses : 0
% 0.15/5.47 % Propositional clauses after purity: 0
% 0.15/5.47 % Propositional unsat core size : 0
% 0.15/5.47 % Propositional preprocessing time : 0.000
% 0.15/5.47 % Propositional encoding time : 0.000
% 0.15/5.47 % Propositional solver time : 0.000
% 0.15/5.47 % Success case prop preproc time : 0.000
% 0.15/5.47 % Success case prop encoding time : 0.000
% 0.15/5.47 % Success case prop solver time : 0.000
% 0.15/5.47 % Current number of processed clauses : 129
% 0.15/5.47 % Positive orientable unit clauses : 16
% 0.15/5.47 % Positive unorientable unit clauses: 0
% 0.15/5.47 % Negative unit clauses : 3
% 0.15/5.47 % Non-unit-clauses : 110
% 0.15/5.47 % Current number of unprocessed clauses: 97
% 0.15/5.47 % ...number of literals in the above : 544
% 0.15/5.47 % Current number of archived formulas : 0
% 0.15/5.47 % Current number of archived clauses : 54
% 0.15/5.47 % Clause-clause subsumption calls (NU) : 2730
% 0.15/5.47 % Rec. Clause-clause subsumption calls : 1131
% 0.15/5.47 % Non-unit clause-clause subsumptions : 13
% 0.15/5.47 % Unit Clause-clause subsumption calls : 60
% 0.15/5.47 % Rewrite failures with RHS unbound : 0
% 0.15/5.47 % BW rewrite match attempts : 12
% 0.15/5.47 % BW rewrite match successes : 4
% 0.15/5.47 % Condensation attempts : 0
% 0.15/5.47 % Condensation successes : 0
% 0.15/5.47 % Termbank termtop insertions : 9036
% 0.15/5.47 % Search garbage collected termcells : 109
% 0.15/5.47
% 0.15/5.47 % -------------------------------------------------
% 0.15/5.47 % User time : 0.021 s
% 0.15/5.47 % System time : 0.006 s
% 0.15/5.47 % Total time : 0.027 s
% 0.15/5.47 % Maximum resident set size: 3608 pages
% 0.15/5.47
% 0.15/5.47 % -------------------------------------------------
% 0.15/5.47 % User time : 0.112 s
% 0.15/5.47 % System time : 0.020 s
% 0.15/5.47 % Total time : 0.133 s
% 0.15/5.47 % Maximum resident set size: 4864 pages
% 0.15/5.47 % E exiting
%------------------------------------------------------------------------------