%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : MGT039+2 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 01:26:51 PM UTC 2026
% Result : Theorem 0.17s 0.48s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 18
% Syntax : Number of formulae : 113 ( 21 unt; 0 def)
% Number of atoms : 395 ( 32 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 484 ( 202 ~; 218 |; 42 &)
% ( 1 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 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 : 162 ( 0 sgn 72 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mp_greater_or_equal,axiom,
! [X6,X7] :
( greater_or_equal(X6,X7)
<=> ( X6 = X7
| greater(X6,X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal) ).
fof(mp_time_of_critical_point,axiom,
! [X1] :
( environment(X1)
=> greater_or_equal(critical_point(X1),start_time(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_time_of_critical_point) ).
fof(prove_t8,conjecture,
! [X5] :
( ( slow_change(X5)
& observational_period(X5) )
=> selection_favors(efficient_producers,first_movers,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t8) ).
fof(mp_greater_transitivity,axiom,
! [X6,X7,X8] :
( ( greater(X7,X8)
& greater(X6,X7) )
=> greater(X6,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_transitivity) ).
fof(mp4_critical_point,axiom,
! [X5] :
( ( slow_change(X5)
& observational_period(X5) )
=> ! [X1] :
( ( in_environment(X5,X1)
& environment(X1) )
=> ? [X4] :
( greater(X4,critical_point(X1))
& in_environment(X1,X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp4_critical_point) ).
fof(mp_environment_end_point,axiom,
! [X1,X4] :
( ( in_environment(X1,X4)
& environment(X1) )
=> greater_or_equal(end_time(X1),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_environment_end_point) ).
fof(mp_time_in_environment,axiom,
! [X1,X4] :
( ( greater_or_equal(end_time(X1),X4)
& greater_or_equal(X4,start_time(X1))
& environment(X1) )
=> in_environment(X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_time_in_environment) ).
fof(mp3_favoured_trategy,axiom,
! [X5] :
( ( ! [X1] :
( ( in_environment(X5,X1)
& environment(X1) )
=> selection_favors(efficient_producers,first_movers,end_time(X1)) )
& propagation_strategy(efficient_producers)
& propagation_strategy(first_movers)
& observational_period(X5) )
=> selection_favors(efficient_producers,first_movers,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp3_favoured_trategy) ).
fof(mp_critical_point_after_EP,axiom,
! [X1] :
( environment(X1)
=> greater_or_equal(critical_point(X1),appear(efficient_producers,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_critical_point_after_EP) ).
fof(mp_organizational_sets1,axiom,
propagation_strategy(first_movers),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_organizational_sets1) ).
fof(mp_organizational_sets2,axiom,
propagation_strategy(efficient_producers),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_organizational_sets2) ).
fof(t6,hypothesis,
! [X1,X4] :
( ( greater_or_equal(X4,appear(efficient_producers,X1))
& in_environment(X1,X4)
& environment(X1) )
=> greater(cardinality_at_time(efficient_producers,X4),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6) ).
fof(d1,hypothesis,
! [X1,X9] :
( ( X9 = critical_point(X1)
& environment(X1) )
=> ( ! [X4] :
( ( greater(X4,X9)
& subpopulations(first_movers,efficient_producers,X1,X4) )
=> greater(growth_rate(efficient_producers,X4),growth_rate(first_movers,X4)) )
& ~ greater(growth_rate(efficient_producers,X9),growth_rate(first_movers,X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1) ).
fof(mp2_favour_members,axiom,
! [X1,X2,X3,X4] :
( ( cardinality_at_time(X3,X4) = zero
& greater(cardinality_at_time(X2,X4),zero)
& subpopulation(X3,X1,X4)
& subpopulation(X2,X1,X4)
& environment(X1) )
=> selection_favors(X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp2_favour_members) ).
fof(mp_subpopulations,axiom,
! [X1,X4] :
( ( in_environment(X1,X4)
& environment(X1) )
=> ( subpopulation(efficient_producers,X1,X4)
& subpopulation(first_movers,X1,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_subpopulations) ).
fof(mp_contains_FM_and_EP,axiom,
! [X1,X4] :
( ( greater(cardinality_at_time(efficient_producers,X4),zero)
& greater(cardinality_at_time(first_movers,X4),zero)
& in_environment(X1,X4)
& environment(X1) )
=> subpopulations(first_movers,efficient_producers,X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_contains_FM_and_EP) ).
fof(mp_first_movers_exist,axiom,
! [X1,X4] :
( ( in_environment(X1,X4)
& environment(X1) )
=> greater_or_equal(cardinality_at_time(first_movers,X4),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_first_movers_exist) ).
fof(mp1_high_growth_rates,axiom,
! [X1,X2,X3,X4] :
( ( 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) ).
fof(c_0_18,plain,
! [X40,X41] :
( ( greater_or_equal(X40,X41)
| X40 != X41 )
& ( greater_or_equal(X40,X41)
| ~ greater(X40,X41) )
& ( X40 = X41
| greater(X40,X41)
| ~ greater_or_equal(X40,X41) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_greater_or_equal])])])]) ).
fof(c_0_19,plain,
! [X34] :
( greater_or_equal(critical_point(X34),start_time(X34))
| ~ environment(X34) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_time_of_critical_point])])]) ).
fof(c_0_20,negated_conjecture,
~ ! [X5] :
( ( slow_change(X5)
& observational_period(X5) )
=> selection_favors(efficient_producers,first_movers,X5) ),
inference(assume_negation,[status(cth)],[prove_t8]) ).
fof(c_0_21,plain,
! [X35,X36,X37] :
( greater(X35,X37)
| ~ greater(X36,X37)
| ~ greater(X35,X36) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_greater_transitivity])])]) ).
cnf(c_0_22,plain,
( ~ greater_or_equal(X1,X2)
| X1 = X2
| greater(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,plain,
( ~ environment(X1)
| greater_or_equal(critical_point(X1),start_time(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_24,plain,
! [X20,X21] :
( ( ~ slow_change(X20)
| ~ observational_period(X20)
| ~ in_environment(X20,X21)
| ~ environment(X21)
| greater(esk2_2(X20,X21),critical_point(X21)) )
& ( ~ slow_change(X20)
| ~ observational_period(X20)
| ~ in_environment(X20,X21)
| ~ environment(X21)
| in_environment(X21,esk2_2(X20,X21)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp4_critical_point])])])])])]) ).
fof(c_0_25,negated_conjecture,
( ~ selection_favors(efficient_producers,first_movers,esk3_0)
& slow_change(esk3_0)
& observational_period(esk3_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])]) ).
cnf(c_0_26,plain,
( ~ greater(X2,X3)
| ~ greater(X1,X2)
| greater(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,plain,
( ~ environment(X1)
| greater(critical_point(X1),start_time(X1))
| start_time(X1) = critical_point(X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
fof(c_0_28,plain,
! [X25,X26] :
( greater_or_equal(end_time(X25),X26)
| ~ in_environment(X25,X26)
| ~ environment(X25) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_environment_end_point])])]) ).
cnf(c_0_29,plain,
( ~ slow_change(X2)
| ~ observational_period(X2)
| ~ in_environment(X2,X1)
| ~ environment(X1)
| in_environment(X1,esk2_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,negated_conjecture,
slow_change(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,negated_conjecture,
observational_period(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,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_26,c_0_27]) ).
cnf(c_0_33,plain,
( ~ slow_change(X1)
| ~ observational_period(X1)
| ~ in_environment(X1,X2)
| ~ environment(X2)
| greater(esk2_2(X1,X2),critical_point(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_34,plain,
( ~ in_environment(X1,X2)
| ~ environment(X1)
| greater_or_equal(end_time(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_35,negated_conjecture,
( ~ environment(X1)
| ~ in_environment(esk3_0,X1)
| in_environment(X1,esk2_2(esk3_0,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]) ).
fof(c_0_36,plain,
! [X23,X24] :
( in_environment(X23,X24)
| ~ greater_or_equal(end_time(X23),X24)
| ~ greater_or_equal(X24,start_time(X23))
| ~ environment(X23) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_time_in_environment])])]) ).
cnf(c_0_37,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_26,c_0_32]) ).
cnf(c_0_38,negated_conjecture,
( ~ environment(X1)
| ~ in_environment(esk3_0,X1)
| greater(esk2_2(esk3_0,X1),critical_point(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_30]),c_0_31])]) ).
cnf(c_0_39,negated_conjecture,
( ~ environment(X1)
| ~ in_environment(esk3_0,X1)
| greater_or_equal(end_time(X1),esk2_2(esk3_0,X1)) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_40,plain,
( ~ greater_or_equal(end_time(X1),X2)
| ~ greater_or_equal(X2,start_time(X1))
| ~ environment(X1)
| in_environment(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_41,plain,
( ~ greater(X1,X2)
| greater_or_equal(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_42,plain,
( X1 != X2
| greater_or_equal(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_43,plain,
! [X18] :
( ( selection_favors(efficient_producers,first_movers,X18)
| ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers)
| ~ observational_period(X18)
| ~ selection_favors(efficient_producers,first_movers,end_time(esk1_1(X18))) )
& ( selection_favors(efficient_producers,first_movers,X18)
| ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers)
| ~ observational_period(X18)
| in_environment(X18,esk1_1(X18)) )
& ( selection_favors(efficient_producers,first_movers,X18)
| ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers)
| ~ observational_period(X18)
| environment(esk1_1(X18)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp3_favoured_trategy])])])])]) ).
fof(c_0_44,plain,
! [X33] :
( greater_or_equal(critical_point(X33),appear(efficient_producers,X33))
| ~ environment(X33) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_critical_point_after_EP])])]) ).
cnf(c_0_45,negated_conjecture,
( ~ environment(X1)
| ~ greater(X2,esk2_2(esk3_0,X1))
| ~ in_environment(esk3_0,X1)
| greater(X2,start_time(X1))
| start_time(X1) = critical_point(X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_46,negated_conjecture,
( ~ environment(X1)
| ~ in_environment(esk3_0,X1)
| greater(end_time(X1),esk2_2(esk3_0,X1))
| esk2_2(esk3_0,X1) = end_time(X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_39]) ).
cnf(c_0_47,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_40,c_0_41]) ).
cnf(c_0_48,plain,
greater_or_equal(X1,X1),
inference(er,[status(thm)],[c_0_42]) ).
cnf(c_0_49,plain,
( ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers)
| ~ observational_period(X1)
| selection_favors(efficient_producers,first_movers,X1)
| in_environment(X1,esk1_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_50,plain,
propagation_strategy(first_movers),
inference(split_conjunct,[status(thm)],[mp_organizational_sets1]) ).
cnf(c_0_51,plain,
propagation_strategy(efficient_producers),
inference(split_conjunct,[status(thm)],[mp_organizational_sets2]) ).
cnf(c_0_52,plain,
( ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers)
| ~ observational_period(X1)
| selection_favors(efficient_producers,first_movers,X1)
| environment(esk1_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_53,negated_conjecture,
( ~ environment(X2)
| ~ greater(X1,esk2_2(esk3_0,X2))
| ~ in_environment(esk3_0,X2)
| greater(X1,critical_point(X2)) ),
inference(spm,[status(thm)],[c_0_26,c_0_38]) ).
fof(c_0_54,hypothesis,
! [X45,X46] :
( greater(cardinality_at_time(efficient_producers,X46),zero)
| ~ greater_or_equal(X46,appear(efficient_producers,X45))
| ~ in_environment(X45,X46)
| ~ environment(X45) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6])])]) ).
cnf(c_0_55,plain,
( ~ environment(X1)
| greater_or_equal(critical_point(X1),appear(efficient_producers,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_56,negated_conjecture,
( ~ environment(X1)
| ~ in_environment(esk3_0,X1)
| greater(end_time(X1),start_time(X1))
| start_time(X1) = critical_point(X1)
| esk2_2(esk3_0,X1) = end_time(X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_57,plain,
( ~ environment(X1)
| ~ greater(end_time(X1),start_time(X1))
| in_environment(X1,end_time(X1)) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_58,plain,
( ~ observational_period(X1)
| selection_favors(efficient_producers,first_movers,X1)
| in_environment(X1,esk1_1(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50]),c_0_51])]) ).
cnf(c_0_59,negated_conjecture,
~ selection_favors(efficient_producers,first_movers,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_60,plain,
( ~ observational_period(X1)
| environment(esk1_1(X1))
| selection_favors(efficient_producers,first_movers,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_50]),c_0_51])]) ).
cnf(c_0_61,negated_conjecture,
( ~ environment(X1)
| ~ in_environment(esk3_0,X1)
| greater(end_time(X1),critical_point(X1))
| esk2_2(esk3_0,X1) = end_time(X1) ),
inference(spm,[status(thm)],[c_0_53,c_0_46]) ).
fof(c_0_62,hypothesis,
! [X1,X9] :
( ( X9 = critical_point(X1)
& environment(X1) )
=> ( ! [X4] :
( ( greater(X4,X9)
& subpopulations(first_movers,efficient_producers,X1,X4) )
=> greater(growth_rate(efficient_producers,X4),growth_rate(first_movers,X4)) )
& ~ greater(growth_rate(efficient_producers,X9),growth_rate(first_movers,X9)) ) ),
inference(fof_simplification,[status(thm)],[d1]) ).
cnf(c_0_63,hypothesis,
( ~ greater_or_equal(X2,appear(efficient_producers,X1))
| ~ in_environment(X1,X2)
| ~ environment(X1)
| greater(cardinality_at_time(efficient_producers,X2),zero) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_64,plain,
( ~ environment(X1)
| greater(critical_point(X1),appear(efficient_producers,X1))
| appear(efficient_producers,X1) = critical_point(X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_55]) ).
cnf(c_0_65,negated_conjecture,
( ~ environment(X1)
| ~ in_environment(esk3_0,X1)
| in_environment(X1,end_time(X1))
| start_time(X1) = critical_point(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_56]),c_0_57]) ).
cnf(c_0_66,negated_conjecture,
in_environment(esk3_0,esk1_1(esk3_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_31]),c_0_59]) ).
cnf(c_0_67,negated_conjecture,
environment(esk1_1(esk3_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_31]),c_0_59]) ).
cnf(c_0_68,negated_conjecture,
( ~ environment(X1)
| ~ in_environment(esk3_0,X1)
| greater(end_time(X1),critical_point(X1)) ),
inference(spm,[status(thm)],[c_0_38,c_0_61]) ).
fof(c_0_69,hypothesis,
! [X42,X43,X44] :
( ( X43 != critical_point(X42)
| ~ environment(X42)
| greater(growth_rate(efficient_producers,X44),growth_rate(first_movers,X44))
| ~ greater(X44,X43)
| ~ subpopulations(first_movers,efficient_producers,X42,X44) )
& ( X43 != critical_point(X42)
| ~ environment(X42)
| ~ greater(growth_rate(efficient_producers,X43),growth_rate(first_movers,X43)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_62])])])])]) ).
fof(c_0_70,plain,
! [X14,X15,X16,X17] :
( selection_favors(X15,X16,X17)
| cardinality_at_time(X16,X17) != zero
| ~ greater(cardinality_at_time(X15,X17),zero)
| ~ subpopulation(X16,X14,X17)
| ~ subpopulation(X15,X14,X17)
| ~ environment(X14) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp2_favour_members])])]) ).
fof(c_0_71,plain,
! [X31,X32] :
( ( ~ in_environment(X31,X32)
| ~ environment(X31)
| subpopulation(efficient_producers,X31,X32) )
& ( ~ in_environment(X31,X32)
| ~ environment(X31)
| subpopulation(first_movers,X31,X32) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_subpopulations])])])]) ).
cnf(c_0_72,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_63,c_0_41]) ).
cnf(c_0_73,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_26,c_0_64]) ).
cnf(c_0_74,negated_conjecture,
( in_environment(esk1_1(esk3_0),end_time(esk1_1(esk3_0)))
| start_time(esk1_1(esk3_0)) = critical_point(esk1_1(esk3_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67])]) ).
cnf(c_0_75,negated_conjecture,
greater(end_time(esk1_1(esk3_0)),critical_point(esk1_1(esk3_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_66]),c_0_67])]) ).
cnf(c_0_76,plain,
( ~ environment(X1)
| ~ greater_or_equal(end_time(X1),critical_point(X1))
| in_environment(X1,critical_point(X1)) ),
inference(spm,[status(thm)],[c_0_40,c_0_23]) ).
cnf(c_0_77,hypothesis,
( X3 != critical_point(X1)
| ~ environment(X1)
| ~ greater(X2,X3)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
fof(c_0_78,plain,
! [X27,X28] :
( subpopulations(first_movers,efficient_producers,X27,X28)
| ~ greater(cardinality_at_time(efficient_producers,X28),zero)
| ~ greater(cardinality_at_time(first_movers,X28),zero)
| ~ in_environment(X27,X28)
| ~ environment(X27) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_contains_FM_and_EP])])]) ).
cnf(c_0_79,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(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_80,plain,
( ~ in_environment(X1,X2)
| ~ environment(X1)
| subpopulation(first_movers,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_81,plain,
( ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers)
| ~ observational_period(X1)
| ~ selection_favors(efficient_producers,first_movers,end_time(esk1_1(X1)))
| selection_favors(efficient_producers,first_movers,X1) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_82,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_72,c_0_73]) ).
cnf(c_0_83,negated_conjecture,
in_environment(esk1_1(esk3_0),end_time(esk1_1(esk3_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_74]),c_0_75]),c_0_67])]) ).
cnf(c_0_84,plain,
( ~ environment(X1)
| ~ greater(end_time(X1),critical_point(X1))
| in_environment(X1,critical_point(X1)) ),
inference(spm,[status(thm)],[c_0_76,c_0_41]) ).
cnf(c_0_85,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_77]) ).
cnf(c_0_86,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(split_conjunct,[status(thm)],[c_0_78]) ).
fof(c_0_87,plain,
! [X29,X30] :
( greater_or_equal(cardinality_at_time(first_movers,X30),zero)
| ~ in_environment(X29,X30)
| ~ environment(X29) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_first_movers_exist])])]) ).
cnf(c_0_88,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_79,c_0_80]) ).
cnf(c_0_89,plain,
( ~ in_environment(X1,X2)
| ~ environment(X1)
| subpopulation(efficient_producers,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_90,plain,
( ~ selection_favors(efficient_producers,first_movers,end_time(esk1_1(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_81,c_0_50]),c_0_51])]) ).
cnf(c_0_91,negated_conjecture,
( greater(cardinality_at_time(efficient_producers,end_time(esk1_1(esk3_0))),zero)
| appear(efficient_producers,esk1_1(esk3_0)) = critical_point(esk1_1(esk3_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_75]),c_0_83]),c_0_67])]) ).
cnf(c_0_92,negated_conjecture,
in_environment(esk1_1(esk3_0),critical_point(esk1_1(esk3_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_75]),c_0_67])]) ).
cnf(c_0_93,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_85,c_0_86]) ).
cnf(c_0_94,plain,
( ~ in_environment(X1,X2)
| ~ environment(X1)
| greater_or_equal(cardinality_at_time(first_movers,X2),zero) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_95,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_88,c_0_89]) ).
cnf(c_0_96,negated_conjecture,
~ selection_favors(efficient_producers,first_movers,end_time(esk1_1(esk3_0))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_31]),c_0_59]) ).
cnf(c_0_97,hypothesis,
( ~ in_environment(esk1_1(esk3_0),X1)
| ~ greater_or_equal(X1,critical_point(esk1_1(esk3_0)))
| greater(cardinality_at_time(efficient_producers,X1),zero)
| greater(cardinality_at_time(efficient_producers,end_time(esk1_1(esk3_0))),zero) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_91]),c_0_67])]) ).
cnf(c_0_98,negated_conjecture,
greater_or_equal(end_time(esk1_1(esk3_0)),critical_point(esk1_1(esk3_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_92]),c_0_67])]) ).
cnf(c_0_99,hypothesis,
( ~ greater(cardinality_at_time(efficient_producers,end_time(esk1_1(esk3_0))),zero)
| ~ greater(cardinality_at_time(first_movers,end_time(esk1_1(esk3_0))),zero)
| ~ in_environment(esk1_1(esk3_0),end_time(esk1_1(esk3_0)))
| greater(growth_rate(efficient_producers,end_time(esk1_1(esk3_0))),growth_rate(first_movers,end_time(esk1_1(esk3_0)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_75]),c_0_67])]) ).
cnf(c_0_100,negated_conjecture,
greater_or_equal(cardinality_at_time(first_movers,end_time(esk1_1(esk3_0))),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_83]),c_0_67])]) ).
cnf(c_0_101,negated_conjecture,
( ~ greater(cardinality_at_time(efficient_producers,end_time(esk1_1(esk3_0))),zero)
| cardinality_at_time(first_movers,end_time(esk1_1(esk3_0))) != zero ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_83]),c_0_67])]),c_0_96]) ).
cnf(c_0_102,negated_conjecture,
greater(cardinality_at_time(efficient_producers,end_time(esk1_1(esk3_0))),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_83])]) ).
fof(c_0_103,plain,
! [X10,X11,X12,X13] :
( selection_favors(X12,X11,X13)
| ~ greater(growth_rate(X12,X13),growth_rate(X11,X13))
| ~ subpopulations(X11,X12,X10,X13)
| ~ environment(X10) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp1_high_growth_rates])])]) ).
cnf(c_0_104,hypothesis,
( ~ greater(cardinality_at_time(efficient_producers,end_time(esk1_1(esk3_0))),zero)
| ~ greater(cardinality_at_time(first_movers,end_time(esk1_1(esk3_0))),zero)
| greater(growth_rate(efficient_producers,end_time(esk1_1(esk3_0))),growth_rate(first_movers,end_time(esk1_1(esk3_0)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_99,c_0_83])]) ).
cnf(c_0_105,negated_conjecture,
( greater(cardinality_at_time(first_movers,end_time(esk1_1(esk3_0))),zero)
| cardinality_at_time(first_movers,end_time(esk1_1(esk3_0))) = zero ),
inference(spm,[status(thm)],[c_0_22,c_0_100]) ).
cnf(c_0_106,negated_conjecture,
cardinality_at_time(first_movers,end_time(esk1_1(esk3_0))) != zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_101,c_0_102])]) ).
cnf(c_0_107,plain,
( ~ greater(growth_rate(X3,X4),growth_rate(X2,X4))
| ~ subpopulations(X2,X3,X1,X4)
| ~ environment(X1)
| selection_favors(X3,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_108,hypothesis,
( ~ greater(cardinality_at_time(first_movers,end_time(esk1_1(esk3_0))),zero)
| greater(growth_rate(efficient_producers,end_time(esk1_1(esk3_0))),growth_rate(first_movers,end_time(esk1_1(esk3_0)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_104,c_0_102])]) ).
cnf(c_0_109,negated_conjecture,
greater(cardinality_at_time(first_movers,end_time(esk1_1(esk3_0))),zero),
inference(sr,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_110,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_107,c_0_86]) ).
cnf(c_0_111,hypothesis,
greater(growth_rate(efficient_producers,end_time(esk1_1(esk3_0))),growth_rate(first_movers,end_time(esk1_1(esk3_0)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_108,c_0_109])]) ).
cnf(c_0_112,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_110,c_0_83]),c_0_67])]),c_0_96]),c_0_111]),c_0_109]),c_0_102])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT039+2 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n026.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 01:25:38 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.17/0.48 % Version: 3.5.1
% 0.17/0.48 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.17/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.48 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.17/0.48 % Starting new_bool_3 with 300s (1) cores
% 0.17/0.48 % Starting new_bool_1 with 300s (1) cores
% 0.17/0.48 % Starting sh5l with 300s (1) cores
% 0.17/0.48 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1065667 completed with status 0
% 0.17/0.48 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.17/0.48 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.17/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.48 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.17/0.48 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.17/0.48 % No SInE strategy applied
% 0.17/0.48 % Search class: FGHSF-FFMS21-SFFFFFNN
% 0.17/0.48 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.17/0.48 % Starting SubtermCWHack with 136s (1) cores
% 0.17/0.48 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.17/0.48 % Starting 208_C09_12_F1_SE_CS_SP_PS_S070I with 136s (1) cores
% 0.17/0.48 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 0.17/0.48 % Starting new_bool_3 with 136s (1) cores
% 0.17/0.48 % G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0Y with pid 1065676 completed with status 0
% 0.17/0.48 % Result found by G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0Y
% 0.17/0.48 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.17/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.48 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.17/0.48 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.17/0.48 % No SInE strategy applied
% 0.17/0.48 % Search class: FGHSF-FFMS21-SFFFFFNN
% 0.17/0.48 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.17/0.48 % Starting SubtermCWHack with 136s (1) cores
% 0.17/0.48 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.17/0.48 % Starting 208_C09_12_F1_SE_CS_SP_PS_S070I with 136s (1) cores
% 0.17/0.48 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 0.17/0.48 % Preprocessing time : 0.002 s
% 0.17/0.48 % Presaturation interreduction done
% 0.17/0.48
% 0.17/0.48 % Proof found!
% 0.17/0.48 % SZS status Theorem
% 0.17/0.48 % SZS output start CNFRefutation
% See solution above
% 0.17/0.48 % Parsed axioms : 19
% 0.17/0.48 % Removed by relevancy pruning/SinE : 0
% 0.17/0.48 % Initial clauses : 28
% 0.17/0.48 % Removed in clause preprocessing : 0
% 0.17/0.48 % Initial clauses in saturation : 28
% 0.17/0.48 % Processed clauses : 192
% 0.17/0.48 % ...of these trivial : 0
% 0.17/0.48 % ...subsumed : 5
% 0.17/0.48 % ...remaining for further processing : 186
% 0.17/0.48 % Other redundant clauses eliminated : 3
% 0.17/0.48 % Clauses deleted for lack of memory : 0
% 0.17/0.48 % Backward-subsumed : 11
% 0.17/0.48 % Backward-rewritten : 14
% 0.17/0.48 % Generated clauses : 271
% 0.17/0.48 % ...of the previous two non-redundant : 247
% 0.17/0.48 % ...aggressively subsumed : 0
% 0.17/0.48 % Contextual simplify-reflections : 1
% 0.17/0.48 % Paramodulations : 267
% 0.17/0.48 % Factorizations : 0
% 0.17/0.48 % NegExts : 0
% 0.17/0.48 % Equation resolutions : 3
% 0.17/0.48 % Disequality decompositions : 0
% 0.17/0.48 % Total rewrite steps : 129
% 0.17/0.48 % ...of those cached : 109
% 0.17/0.48 % Propositional unsat checks : 0
% 0.17/0.48 % Propositional check models : 0
% 0.17/0.48 % Propositional check unsatisfiable : 0
% 0.17/0.48 % Propositional clauses : 0
% 0.17/0.48 % Propositional clauses after purity: 0
% 0.17/0.48 % Propositional unsat core size : 0
% 0.17/0.48 % Propositional preprocessing time : 0.000
% 0.17/0.48 % Propositional encoding time : 0.000
% 0.17/0.48 % Propositional solver time : 0.000
% 0.17/0.48 % Success case prop preproc time : 0.000
% 0.17/0.48 % Success case prop encoding time : 0.000
% 0.17/0.48 % Success case prop solver time : 0.000
% 0.17/0.48 % Current number of processed clauses : 129
% 0.17/0.48 % Positive orientable unit clauses : 16
% 0.17/0.48 % Positive unorientable unit clauses: 0
% 0.17/0.48 % Negative unit clauses : 3
% 0.17/0.48 % Non-unit-clauses : 110
% 0.17/0.48 % Current number of unprocessed clauses: 96
% 0.17/0.48 % ...number of literals in the above : 538
% 0.17/0.48 % Current number of archived formulas : 0
% 0.17/0.48 % Current number of archived clauses : 54
% 0.17/0.48 % Clause-clause subsumption calls (NU) : 3467
% 0.17/0.48 % Rec. Clause-clause subsumption calls : 1109
% 0.17/0.48 % Non-unit clause-clause subsumptions : 13
% 0.17/0.48 % Unit Clause-clause subsumption calls : 79
% 0.17/0.48 % Rewrite failures with RHS unbound : 0
% 0.17/0.48 % BW rewrite match attempts : 12
% 0.17/0.48 % BW rewrite match successes : 4
% 0.17/0.48 % Condensation attempts : 0
% 0.17/0.48 % Condensation successes : 0
% 0.17/0.48 % Termbank termtop insertions : 10338
% 0.17/0.48 % Search garbage collected termcells : 492
% 0.17/0.48
% 0.17/0.48 % -------------------------------------------------
% 0.17/0.48 % User time : 0.024 s
% 0.17/0.48 % System time : 0.006 s
% 0.17/0.48 % Total time : 0.030 s
% 0.17/0.48 % Maximum resident set size: 3624 pages
% 0.17/0.48
% 0.17/0.48 % -------------------------------------------------
% 0.17/0.48 % User time : 0.161 s
% 0.17/0.48 % System time : 0.023 s
% 0.17/0.48 % Total time : 0.184 s
% 0.17/0.48 % Maximum resident set size: 4608 pages
% 0.17/0.48 % E exiting
%------------------------------------------------------------------------------