%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : MGT025-1 : 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 : n002.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 01:26:05 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.43s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 21
% Syntax : Number of clauses : 113 ( 17 unt; 47 nHn; 113 RR)
% Number of literals : 354 ( 40 equ; 169 neg)
% Maximal clause size : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 137 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(mp_time_point_occur_45,axiom,
( ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ environment(X1)
| in_environment(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_time_point_occur_45) ).
cnf(mp_only_members_29,axiom,
( X2 != first_movers
| ~ subpopulation(X2,X1,X3)
| ~ environment(X1)
| number_of_organizations(X1,X3) = sum(cardinality_at_time(first_movers,X3),cardinality_at_time(efficient_producers,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_only_members_29) ).
cnf(mp_subpopulations_30,axiom,
( ~ in_environment(X1,X2)
| ~ environment(X1)
| subpopulation(first_movers,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_subpopulations_30) ).
cnf(prove_l7_48,negated_conjecture,
subpopulations(first_movers,efficient_producers,sk1,sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l7_48) ).
cnf(prove_l7_47,negated_conjecture,
environment(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l7_47) ).
cnf(mp_growth_rate_42,axiom,
( ~ decreases(cardinality_at_time(X3,X2))
| ~ greater(cardinality_at_time(X3,X2),zero)
| ~ subpopulation(X3,X1,X2)
| ~ in_environment(X1,X2)
| ~ environment(X1)
| greater(zero,growth_rate(X3,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_growth_rate_42) ).
cnf(mp_non_zero_producers_43,axiom,
( ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ environment(X1)
| greater(cardinality_at_time(first_movers,X2),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_non_zero_producers_43) ).
cnf(mp_abc_sum_increase_36,axiom,
( ~ constant(X1)
| X1 != sum(X2,X3)
| decreases(X2)
| increases(X2)
| constant(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_abc_sum_increase_36) ).
cnf(mp_growth_rate_41,axiom,
( ~ increases(cardinality_at_time(X3,X2))
| ~ greater(cardinality_at_time(X3,X2),zero)
| ~ subpopulation(X3,X1,X2)
| ~ in_environment(X1,X2)
| ~ environment(X1)
| greater(growth_rate(X3,X2),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_growth_rate_41) ).
cnf(mp_subpopulations_31,axiom,
( ~ in_environment(X1,X2)
| ~ environment(X1)
| subpopulation(efficient_producers,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_subpopulations_31) ).
cnf(mp_non_zero_producers_44,axiom,
( ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ environment(X1)
| greater(cardinality_at_time(efficient_producers,X2),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_non_zero_producers_44) ).
cnf(mp_abc_sum_increase_37,axiom,
( ~ constant(X1)
| X1 != sum(X2,X3)
| increases(X3)
| increases(X2)
| constant(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_abc_sum_increase_37) ).
cnf(mp_abc_sum_increase_39,axiom,
( ~ constant(X1)
| X1 != sum(X2,X3)
| increases(X3)
| decreases(X3)
| constant(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_abc_sum_increase_39) ).
cnf(mp_abc_sum_increase_38,axiom,
( ~ constant(X1)
| X1 != sum(X2,X3)
| decreases(X2)
| decreases(X3)
| constant(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_abc_sum_increase_38) ).
cnf(prove_l7_49,negated_conjecture,
constant(number_of_organizations(sk1,sk2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l7_49) ).
cnf(prove_l7_52,negated_conjecture,
( ~ greater(zero,growth_rate(first_movers,sk2))
| ~ greater(growth_rate(efficient_producers,sk2),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l7_52) ).
cnf(prove_l7_51,negated_conjecture,
( ~ greater(zero,growth_rate(efficient_producers,sk2))
| ~ greater(growth_rate(first_movers,sk2),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l7_51) ).
cnf(mp_abc_sum_increase_32,axiom,
( ~ constant(X1)
| X1 != sum(X2,X3)
| decreases(X2)
| increases(X2)
| constant(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_abc_sum_increase_32) ).
cnf(mp_growth_rate_40,axiom,
( ~ constant(cardinality_at_time(X3,X2))
| ~ greater(cardinality_at_time(X3,X2),zero)
| ~ subpopulation(X3,X1,X2)
| ~ in_environment(X1,X2)
| ~ environment(X1)
| growth_rate(X3,X2) = zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_growth_rate_40) ).
cnf(mp_abc_sum_increase_35,axiom,
( ~ constant(X1)
| X1 != sum(X2,X3)
| increases(X3)
| decreases(X3)
| constant(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_abc_sum_increase_35) ).
cnf(prove_l7_50,negated_conjecture,
( growth_rate(efficient_producers,sk2) != zero
| growth_rate(first_movers,sk2) != zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l7_50) ).
cnf(c_0_21,plain,
( ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ environment(X1)
| in_environment(X1,X2) ),
inference(fof_simplification,[status(thm)],[mp_time_point_occur_45]) ).
cnf(c_0_22,plain,
( X2 != first_movers
| ~ subpopulation(X2,X1,X3)
| ~ environment(X1)
| number_of_organizations(X1,X3) = sum(cardinality_at_time(first_movers,X3),cardinality_at_time(efficient_producers,X3)) ),
inference(fof_simplification,[status(thm)],[mp_only_members_29]) ).
cnf(c_0_23,plain,
( ~ in_environment(X1,X2)
| ~ environment(X1)
| subpopulation(first_movers,X1,X2) ),
inference(fof_simplification,[status(thm)],[mp_subpopulations_30]) ).
cnf(c_0_24,plain,
( ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ environment(X1)
| in_environment(X1,X2) ),
c_0_21 ).
cnf(c_0_25,negated_conjecture,
subpopulations(first_movers,efficient_producers,sk1,sk2),
prove_l7_48 ).
cnf(c_0_26,negated_conjecture,
environment(sk1),
prove_l7_47 ).
cnf(c_0_27,plain,
( ~ decreases(cardinality_at_time(X3,X2))
| ~ greater(cardinality_at_time(X3,X2),zero)
| ~ subpopulation(X3,X1,X2)
| ~ in_environment(X1,X2)
| ~ environment(X1)
| greater(zero,growth_rate(X3,X2)) ),
inference(fof_simplification,[status(thm)],[mp_growth_rate_42]) ).
cnf(c_0_28,plain,
( ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ environment(X1)
| greater(cardinality_at_time(first_movers,X2),zero) ),
inference(fof_simplification,[status(thm)],[mp_non_zero_producers_43]) ).
cnf(c_0_29,plain,
( ~ constant(X1)
| X1 != sum(X2,X3)
| decreases(X2)
| increases(X2)
| constant(X3) ),
inference(fof_simplification,[status(thm)],[mp_abc_sum_increase_36]) ).
cnf(c_0_30,plain,
( X2 != first_movers
| ~ subpopulation(X2,X1,X3)
| ~ environment(X1)
| number_of_organizations(X1,X3) = sum(cardinality_at_time(first_movers,X3),cardinality_at_time(efficient_producers,X3)) ),
c_0_22 ).
cnf(c_0_31,plain,
( ~ in_environment(X1,X2)
| ~ environment(X1)
| subpopulation(first_movers,X1,X2) ),
c_0_23 ).
cnf(c_0_32,negated_conjecture,
in_environment(sk1,sk2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
cnf(c_0_33,plain,
( ~ increases(cardinality_at_time(X3,X2))
| ~ greater(cardinality_at_time(X3,X2),zero)
| ~ subpopulation(X3,X1,X2)
| ~ in_environment(X1,X2)
| ~ environment(X1)
| greater(growth_rate(X3,X2),zero) ),
inference(fof_simplification,[status(thm)],[mp_growth_rate_41]) ).
cnf(c_0_34,plain,
( ~ in_environment(X1,X2)
| ~ environment(X1)
| subpopulation(efficient_producers,X1,X2) ),
inference(fof_simplification,[status(thm)],[mp_subpopulations_31]) ).
cnf(c_0_35,plain,
( ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ environment(X1)
| greater(cardinality_at_time(efficient_producers,X2),zero) ),
inference(fof_simplification,[status(thm)],[mp_non_zero_producers_44]) ).
cnf(c_0_36,plain,
( ~ constant(X1)
| X1 != sum(X2,X3)
| increases(X3)
| increases(X2)
| constant(X3) ),
inference(fof_simplification,[status(thm)],[mp_abc_sum_increase_37]) ).
cnf(c_0_37,plain,
( ~ decreases(cardinality_at_time(X3,X2))
| ~ greater(cardinality_at_time(X3,X2),zero)
| ~ subpopulation(X3,X1,X2)
| ~ in_environment(X1,X2)
| ~ environment(X1)
| greater(zero,growth_rate(X3,X2)) ),
c_0_27 ).
cnf(c_0_38,plain,
( ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ environment(X1)
| greater(cardinality_at_time(first_movers,X2),zero) ),
c_0_28 ).
cnf(c_0_39,plain,
( ~ constant(X1)
| X1 != sum(X2,X3)
| decreases(X2)
| increases(X2)
| constant(X3) ),
c_0_29 ).
cnf(c_0_40,plain,
( ~ environment(X1)
| ~ subpopulation(first_movers,X1,X2)
| number_of_organizations(X1,X2) = sum(cardinality_at_time(first_movers,X2),cardinality_at_time(efficient_producers,X2)) ),
inference(er,[status(thm)],[c_0_30]) ).
cnf(c_0_41,negated_conjecture,
subpopulation(first_movers,sk1,sk2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_26])]) ).
cnf(c_0_42,plain,
( ~ increases(cardinality_at_time(X3,X2))
| ~ greater(cardinality_at_time(X3,X2),zero)
| ~ subpopulation(X3,X1,X2)
| ~ in_environment(X1,X2)
| ~ environment(X1)
| greater(growth_rate(X3,X2),zero) ),
c_0_33 ).
cnf(c_0_43,plain,
( ~ in_environment(X1,X2)
| ~ environment(X1)
| subpopulation(efficient_producers,X1,X2) ),
c_0_34 ).
cnf(c_0_44,plain,
( ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ environment(X1)
| greater(cardinality_at_time(efficient_producers,X2),zero) ),
c_0_35 ).
cnf(c_0_45,plain,
( ~ constant(X1)
| X1 != sum(X2,X3)
| increases(X3)
| increases(X2)
| constant(X3) ),
c_0_36 ).
cnf(c_0_46,plain,
( ~ constant(X1)
| X1 != sum(X2,X3)
| increases(X3)
| decreases(X3)
| constant(X3) ),
inference(fof_simplification,[status(thm)],[mp_abc_sum_increase_39]) ).
cnf(c_0_47,plain,
( ~ constant(X1)
| X1 != sum(X2,X3)
| decreases(X2)
| decreases(X3)
| constant(X3) ),
inference(fof_simplification,[status(thm)],[mp_abc_sum_increase_38]) ).
cnf(c_0_48,negated_conjecture,
( ~ subpopulation(X1,sk1,sk2)
| ~ greater(cardinality_at_time(X1,sk2),zero)
| ~ decreases(cardinality_at_time(X1,sk2))
| greater(zero,growth_rate(X1,sk2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_32]),c_0_26])]) ).
cnf(c_0_49,negated_conjecture,
greater(cardinality_at_time(first_movers,sk2),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_25]),c_0_26])]) ).
cnf(c_0_50,plain,
( ~ constant(sum(X1,X2))
| constant(X2)
| increases(X1)
| decreases(X1) ),
inference(er,[status(thm)],[c_0_39]) ).
cnf(c_0_51,negated_conjecture,
sum(cardinality_at_time(first_movers,sk2),cardinality_at_time(efficient_producers,sk2)) = number_of_organizations(sk1,sk2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_26])]) ).
cnf(c_0_52,negated_conjecture,
constant(number_of_organizations(sk1,sk2)),
prove_l7_49 ).
cnf(c_0_53,negated_conjecture,
( ~ subpopulation(X1,sk1,sk2)
| ~ greater(cardinality_at_time(X1,sk2),zero)
| ~ increases(cardinality_at_time(X1,sk2))
| greater(growth_rate(X1,sk2),zero) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_32]),c_0_26])]) ).
cnf(c_0_54,negated_conjecture,
subpopulation(efficient_producers,sk1,sk2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_32]),c_0_26])]) ).
cnf(c_0_55,negated_conjecture,
greater(cardinality_at_time(efficient_producers,sk2),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_25]),c_0_26])]) ).
cnf(c_0_56,plain,
( ~ constant(sum(X2,X1))
| constant(X1)
| increases(X2)
| increases(X1) ),
inference(er,[status(thm)],[c_0_45]) ).
cnf(c_0_57,plain,
( ~ constant(X1)
| X1 != sum(X2,X3)
| increases(X3)
| decreases(X3)
| constant(X3) ),
c_0_46 ).
cnf(c_0_58,plain,
( ~ constant(X1)
| X1 != sum(X2,X3)
| decreases(X2)
| decreases(X3)
| constant(X3) ),
c_0_47 ).
cnf(c_0_59,negated_conjecture,
( ~ greater(zero,growth_rate(first_movers,sk2))
| ~ greater(growth_rate(efficient_producers,sk2),zero) ),
inference(fof_simplification,[status(thm)],[prove_l7_52]) ).
cnf(c_0_60,negated_conjecture,
( ~ decreases(cardinality_at_time(first_movers,sk2))
| greater(zero,growth_rate(first_movers,sk2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_41]),c_0_49])]) ).
cnf(c_0_61,negated_conjecture,
( constant(cardinality_at_time(efficient_producers,sk2))
| increases(cardinality_at_time(first_movers,sk2))
| decreases(cardinality_at_time(first_movers,sk2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52])]) ).
cnf(c_0_62,negated_conjecture,
( ~ increases(cardinality_at_time(efficient_producers,sk2))
| greater(growth_rate(efficient_producers,sk2),zero) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55])]) ).
cnf(c_0_63,negated_conjecture,
( constant(cardinality_at_time(efficient_producers,sk2))
| increases(cardinality_at_time(first_movers,sk2))
| increases(cardinality_at_time(efficient_producers,sk2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_51]),c_0_52])]) ).
cnf(c_0_64,plain,
( ~ constant(sum(X2,X1))
| constant(X1)
| increases(X1)
| decreases(X1) ),
inference(er,[status(thm)],[c_0_57]) ).
cnf(c_0_65,plain,
( ~ constant(sum(X2,X1))
| constant(X1)
| decreases(X2)
| decreases(X1) ),
inference(er,[status(thm)],[c_0_58]) ).
cnf(c_0_66,negated_conjecture,
( ~ greater(zero,growth_rate(first_movers,sk2))
| ~ greater(growth_rate(efficient_producers,sk2),zero) ),
c_0_59 ).
cnf(c_0_67,negated_conjecture,
( greater(zero,growth_rate(first_movers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2))
| increases(cardinality_at_time(first_movers,sk2)) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_68,negated_conjecture,
( greater(growth_rate(efficient_producers,sk2),zero)
| constant(cardinality_at_time(efficient_producers,sk2))
| increases(cardinality_at_time(first_movers,sk2)) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_69,negated_conjecture,
( ~ greater(zero,growth_rate(efficient_producers,sk2))
| ~ greater(growth_rate(first_movers,sk2),zero) ),
inference(fof_simplification,[status(thm)],[prove_l7_51]) ).
cnf(c_0_70,negated_conjecture,
( ~ decreases(cardinality_at_time(efficient_producers,sk2))
| greater(zero,growth_rate(efficient_producers,sk2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_54]),c_0_55])]) ).
cnf(c_0_71,negated_conjecture,
( constant(cardinality_at_time(efficient_producers,sk2))
| increases(cardinality_at_time(efficient_producers,sk2))
| decreases(cardinality_at_time(efficient_producers,sk2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_51]),c_0_52])]) ).
cnf(c_0_72,negated_conjecture,
( constant(cardinality_at_time(efficient_producers,sk2))
| decreases(cardinality_at_time(first_movers,sk2))
| decreases(cardinality_at_time(efficient_producers,sk2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_51]),c_0_52])]) ).
cnf(c_0_73,negated_conjecture,
( ~ increases(cardinality_at_time(first_movers,sk2))
| greater(growth_rate(first_movers,sk2),zero) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_41]),c_0_49])]) ).
cnf(c_0_74,negated_conjecture,
( constant(cardinality_at_time(efficient_producers,sk2))
| increases(cardinality_at_time(first_movers,sk2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68]) ).
cnf(c_0_75,negated_conjecture,
( ~ greater(zero,growth_rate(efficient_producers,sk2))
| ~ greater(growth_rate(first_movers,sk2),zero) ),
c_0_69 ).
cnf(c_0_76,negated_conjecture,
( greater(zero,growth_rate(efficient_producers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2))
| increases(cardinality_at_time(efficient_producers,sk2)) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_77,plain,
( ~ constant(X1)
| X1 != sum(X2,X3)
| decreases(X2)
| increases(X2)
| constant(X2) ),
inference(fof_simplification,[status(thm)],[mp_abc_sum_increase_32]) ).
cnf(c_0_78,plain,
( ~ constant(cardinality_at_time(X3,X2))
| ~ greater(cardinality_at_time(X3,X2),zero)
| ~ subpopulation(X3,X1,X2)
| ~ in_environment(X1,X2)
| ~ environment(X1)
| growth_rate(X3,X2) = zero ),
inference(fof_simplification,[status(thm)],[mp_growth_rate_40]) ).
cnf(c_0_79,negated_conjecture,
( greater(zero,growth_rate(efficient_producers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2))
| decreases(cardinality_at_time(first_movers,sk2)) ),
inference(spm,[status(thm)],[c_0_70,c_0_72]) ).
cnf(c_0_80,negated_conjecture,
( greater(growth_rate(first_movers,sk2),zero)
| constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_81,negated_conjecture,
( ~ greater(growth_rate(first_movers,sk2),zero)
| constant(cardinality_at_time(efficient_producers,sk2))
| increases(cardinality_at_time(efficient_producers,sk2)) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_82,plain,
( ~ constant(X1)
| X1 != sum(X2,X3)
| decreases(X2)
| increases(X2)
| constant(X2) ),
c_0_77 ).
cnf(c_0_83,plain,
( ~ constant(X1)
| X1 != sum(X2,X3)
| increases(X3)
| decreases(X3)
| constant(X2) ),
inference(fof_simplification,[status(thm)],[mp_abc_sum_increase_35]) ).
cnf(c_0_84,plain,
( ~ constant(cardinality_at_time(X3,X2))
| ~ greater(cardinality_at_time(X3,X2),zero)
| ~ subpopulation(X3,X1,X2)
| ~ in_environment(X1,X2)
| ~ environment(X1)
| growth_rate(X3,X2) = zero ),
c_0_78 ).
cnf(c_0_85,negated_conjecture,
( constant(cardinality_at_time(efficient_producers,sk2))
| decreases(cardinality_at_time(first_movers,sk2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_79]),c_0_80]) ).
cnf(c_0_86,negated_conjecture,
( constant(cardinality_at_time(efficient_producers,sk2))
| increases(cardinality_at_time(efficient_producers,sk2)) ),
inference(spm,[status(thm)],[c_0_81,c_0_80]) ).
cnf(c_0_87,plain,
( ~ constant(sum(X1,X2))
| constant(X1)
| increases(X1)
| decreases(X1) ),
inference(er,[status(thm)],[c_0_82]) ).
cnf(c_0_88,plain,
( ~ constant(X1)
| X1 != sum(X2,X3)
| increases(X3)
| decreases(X3)
| constant(X2) ),
c_0_83 ).
cnf(c_0_89,negated_conjecture,
( ~ subpopulation(X1,sk1,sk2)
| ~ greater(cardinality_at_time(X1,sk2),zero)
| ~ constant(cardinality_at_time(X1,sk2))
| growth_rate(X1,sk2) = zero ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_32]),c_0_26])]) ).
cnf(c_0_90,negated_conjecture,
( greater(zero,growth_rate(first_movers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(spm,[status(thm)],[c_0_60,c_0_85]) ).
cnf(c_0_91,negated_conjecture,
( greater(growth_rate(efficient_producers,sk2),zero)
| constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(spm,[status(thm)],[c_0_62,c_0_86]) ).
cnf(c_0_92,negated_conjecture,
( constant(cardinality_at_time(first_movers,sk2))
| increases(cardinality_at_time(first_movers,sk2))
| decreases(cardinality_at_time(first_movers,sk2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_51]),c_0_52])]) ).
cnf(c_0_93,plain,
( ~ constant(sum(X2,X1))
| constant(X2)
| increases(X1)
| decreases(X1) ),
inference(er,[status(thm)],[c_0_88]) ).
cnf(c_0_94,negated_conjecture,
( ~ constant(cardinality_at_time(efficient_producers,sk2))
| growth_rate(efficient_producers,sk2) = zero ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_54]),c_0_55])]) ).
cnf(c_0_95,negated_conjecture,
constant(cardinality_at_time(efficient_producers,sk2)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_90]),c_0_91]) ).
cnf(c_0_96,negated_conjecture,
( greater(zero,growth_rate(first_movers,sk2))
| constant(cardinality_at_time(first_movers,sk2))
| increases(cardinality_at_time(first_movers,sk2)) ),
inference(spm,[status(thm)],[c_0_60,c_0_92]) ).
cnf(c_0_97,negated_conjecture,
( constant(cardinality_at_time(first_movers,sk2))
| increases(cardinality_at_time(efficient_producers,sk2))
| decreases(cardinality_at_time(efficient_producers,sk2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_51]),c_0_52])]) ).
cnf(c_0_98,negated_conjecture,
growth_rate(efficient_producers,sk2) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_94,c_0_95])]) ).
cnf(c_0_99,negated_conjecture,
( ~ greater(growth_rate(efficient_producers,sk2),zero)
| constant(cardinality_at_time(first_movers,sk2))
| increases(cardinality_at_time(first_movers,sk2)) ),
inference(spm,[status(thm)],[c_0_66,c_0_96]) ).
cnf(c_0_100,negated_conjecture,
( greater(zero,growth_rate(efficient_producers,sk2))
| constant(cardinality_at_time(first_movers,sk2))
| increases(cardinality_at_time(efficient_producers,sk2)) ),
inference(spm,[status(thm)],[c_0_70,c_0_97]) ).
cnf(c_0_101,negated_conjecture,
( ~ increases(cardinality_at_time(efficient_producers,sk2))
| greater(zero,zero) ),
inference(rw,[status(thm)],[c_0_62,c_0_98]) ).
cnf(c_0_102,negated_conjecture,
( ~ greater(zero,zero)
| constant(cardinality_at_time(first_movers,sk2))
| increases(cardinality_at_time(first_movers,sk2)) ),
inference(rw,[status(thm)],[c_0_99,c_0_98]) ).
cnf(c_0_103,negated_conjecture,
( greater(zero,zero)
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[c_0_100,c_0_98]),c_0_101]) ).
cnf(c_0_104,negated_conjecture,
( ~ greater(zero,zero)
| ~ greater(growth_rate(first_movers,sk2),zero) ),
inference(rw,[status(thm)],[c_0_75,c_0_98]) ).
cnf(c_0_105,negated_conjecture,
( growth_rate(efficient_producers,sk2) != zero
| growth_rate(first_movers,sk2) != zero ),
inference(fof_simplification,[status(thm)],[prove_l7_50]) ).
cnf(c_0_106,negated_conjecture,
( constant(cardinality_at_time(first_movers,sk2))
| increases(cardinality_at_time(first_movers,sk2)) ),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_107,negated_conjecture,
( ~ greater(growth_rate(first_movers,sk2),zero)
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(spm,[status(thm)],[c_0_104,c_0_103]) ).
cnf(c_0_108,negated_conjecture,
( growth_rate(efficient_producers,sk2) != zero
| growth_rate(first_movers,sk2) != zero ),
c_0_105 ).
cnf(c_0_109,negated_conjecture,
( ~ constant(cardinality_at_time(first_movers,sk2))
| growth_rate(first_movers,sk2) = zero ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_41]),c_0_49])]) ).
cnf(c_0_110,negated_conjecture,
constant(cardinality_at_time(first_movers,sk2)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_106]),c_0_107]) ).
cnf(c_0_111,negated_conjecture,
growth_rate(first_movers,sk2) != zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_108,c_0_98])]) ).
cnf(c_0_112,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_109,c_0_110])]),c_0_111]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT025-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n002.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 01:24:16 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.43 % Version: 3.5.1
% 0.10/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.43 % Starting sh5l with 300s (1) cores
% 0.10/0.43 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2148175 completed with status 0
% 0.10/0.43 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.10/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.43 % No SInE strategy applied
% 0.10/0.43 % Search class: FGHSF-FFMS22-SFFFFFNN
% 0.10/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.10/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.10/0.43 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.10/0.43 % Starting new_bool_3 with 136s (1) cores
% 0.10/0.43 % Starting new_bool_1 with 136s (1) cores
% 0.10/0.43 % new_bool_3 with pid 2148182 completed with status 0
% 0.10/0.43 % Result found by new_bool_3
% 0.10/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.43 % No SInE strategy applied
% 0.10/0.43 % Search class: FGHSF-FFMS22-SFFFFFNN
% 0.10/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.10/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.10/0.43 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.10/0.43 % Starting new_bool_3 with 136s (1) cores
% 0.10/0.43 % Preprocessing time : 0.001 s
% 0.10/0.43 % Presaturation interreduction done
% 0.10/0.43
% 0.10/0.43 % Proof found!
% 0.10/0.43 % SZS status Unsatisfiable
% 0.10/0.43 % SZS output start CNFRefutation
% See solution above
% 0.10/0.43 % Parsed axioms : 26
% 0.10/0.43 % Removed by relevancy pruning/SinE : 0
% 0.10/0.43 % Initial clauses : 26
% 0.10/0.43 % Removed in clause preprocessing : 0
% 0.10/0.43 % Initial clauses in saturation : 26
% 0.10/0.43 % Processed clauses : 115
% 0.10/0.43 % ...of these trivial : 1
% 0.10/0.43 % ...subsumed : 2
% 0.10/0.43 % ...remaining for further processing : 112
% 0.10/0.43 % Other redundant clauses eliminated : 10
% 0.10/0.43 % Clauses deleted for lack of memory : 0
% 0.10/0.43 % Backward-subsumed : 14
% 0.10/0.43 % Backward-rewritten : 20
% 0.10/0.43 % Generated clauses : 62
% 0.10/0.43 % ...of the previous two non-redundant : 68
% 0.10/0.43 % ...aggressively subsumed : 0
% 0.10/0.43 % Contextual simplify-reflections : 5
% 0.10/0.43 % Paramodulations : 52
% 0.10/0.43 % Factorizations : 0
% 0.10/0.43 % NegExts : 0
% 0.10/0.43 % Equation resolutions : 10
% 0.10/0.43 % Disequality decompositions : 0
% 0.10/0.43 % Total rewrite steps : 48
% 0.10/0.43 % ...of those cached : 40
% 0.10/0.43 % Propositional unsat checks : 0
% 0.10/0.43 % Propositional check models : 0
% 0.10/0.43 % Propositional check unsatisfiable : 0
% 0.10/0.43 % Propositional clauses : 0
% 0.10/0.43 % Propositional clauses after purity: 0
% 0.10/0.43 % Propositional unsat core size : 0
% 0.10/0.43 % Propositional preprocessing time : 0.000
% 0.10/0.43 % Propositional encoding time : 0.000
% 0.10/0.43 % Propositional solver time : 0.000
% 0.10/0.43 % Success case prop preproc time : 0.000
% 0.10/0.43 % Success case prop encoding time : 0.000
% 0.10/0.43 % Success case prop solver time : 0.000
% 0.10/0.43 % Current number of processed clauses : 42
% 0.10/0.43 % Positive orientable unit clauses : 12
% 0.10/0.43 % Positive unorientable unit clauses: 0
% 0.10/0.43 % Negative unit clauses : 1
% 0.10/0.43 % Non-unit-clauses : 29
% 0.10/0.43 % Current number of unprocessed clauses: 4
% 0.10/0.43 % ...number of literals in the above : 11
% 0.10/0.43 % Current number of archived formulas : 0
% 0.10/0.43 % Current number of archived clauses : 60
% 0.10/0.43 % Clause-clause subsumption calls (NU) : 350
% 0.10/0.43 % Rec. Clause-clause subsumption calls : 226
% 0.10/0.43 % Non-unit clause-clause subsumptions : 21
% 0.10/0.43 % Unit Clause-clause subsumption calls : 24
% 0.10/0.43 % Rewrite failures with RHS unbound : 0
% 0.10/0.43 % BW rewrite match attempts : 3
% 0.10/0.43 % BW rewrite match successes : 3
% 0.10/0.43 % Condensation attempts : 0
% 0.10/0.43 % Condensation successes : 0
% 0.10/0.44 % Termbank termtop insertions : 2619
% 0.10/0.44 % Search garbage collected termcells : 89
% 0.10/0.44
% 0.10/0.44 % -------------------------------------------------
% 0.10/0.44 % User time : 0.006 s
% 0.10/0.44 % System time : 0.001 s
% 0.10/0.44 % Total time : 0.007 s
% 0.10/0.44 % Maximum resident set size: 3652 pages
% 0.10/0.44
% 0.10/0.44 % -------------------------------------------------
% 0.10/0.44 % User time : 0.036 s
% 0.10/0.44 % System time : 0.012 s
% 0.10/0.44 % Total time : 0.048 s
% 0.10/0.44 % Maximum resident set size: 4864 pages
% 0.10/0.44 % E exiting
%------------------------------------------------------------------------------