%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : MGT034+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 : n016.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 01:26:28 PM UTC 2026
% Result : Theorem 0.11s 0.43s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 17
% Syntax : Number of formulae : 91 ( 16 unt; 0 def)
% Number of atoms : 285 ( 15 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 317 ( 123 ~; 122 |; 47 &)
% ( 3 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 124 ( 0 sgn 78 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_t3,conjecture,
! [X1,X4] :
( ( greater(critical_point(X1),X4)
& greater_or_equal(X4,appear(efficient_producers,X1))
& in_environment(X1,critical_point(X1))
& environment(X1) )
=> selection_favors(first_movers,efficient_producers,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t3) ).
fof(mp_critical_point_means_FM_and_EP,axiom,
! [X1] :
( ( in_environment(X1,critical_point(X1))
& environment(X1) )
=> subpopulations(first_movers,efficient_producers,X1,critical_point(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_critical_point_means_FM_and_EP) ).
fof(mp_critical_time_points,axiom,
! [X1,X4] :
( ( greater(critical_point(X1),X4)
& greater_or_equal(X4,appear(efficient_producers,X1))
& in_environment(X1,critical_point(X1))
& environment(X1) )
=> in_environment(X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_critical_time_points) ).
fof(mp_greater_or_equal,axiom,
! [X8,X9] :
( greater_or_equal(X8,X9)
<=> ( X8 = X9
| greater(X8,X9) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal) ).
fof(mp_FM_and_EP_members_EP_appeared,axiom,
! [X1,X4] :
( ( subpopulations(first_movers,efficient_producers,X1,X4)
& environment(X1) )
=> greater_or_equal(X4,appear(efficient_producers,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_FM_and_EP_members_EP_appeared) ).
fof(a10,hypothesis,
! [X1,X6,X7,X4] :
( ( greater_or_equal(X7,X4)
& greater_or_equal(X4,X6)
& subpopulations(first_movers,efficient_producers,X1,X7)
& subpopulations(first_movers,efficient_producers,X1,X6)
& environment(X1) )
=> subpopulations(first_movers,efficient_producers,X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a10) ).
fof(mp_FM_and_EP_when_EP_appears,axiom,
! [X1] :
( ( in_environment(X1,appear(efficient_producers,X1))
& environment(X1) )
=> subpopulations(first_movers,efficient_producers,X1,appear(efficient_producers,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_FM_and_EP_when_EP_appears) ).
fof(mp_difference_between_founding_rates,axiom,
! [X4] :
( ( ~ decreases(difference(disbanding_rate(first_movers,X4),disbanding_rate(efficient_producers,X4)))
& decreases(difference(founding_rate(first_movers,X4),founding_rate(efficient_producers,X4))) )
=> decreases(difference(growth_rate(first_movers,X4),growth_rate(efficient_producers,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_difference_between_founding_rates) ).
fof(a12,hypothesis,
! [X1,X4] :
( ( subpopulations(first_movers,efficient_producers,X1,X4)
& environment(X1) )
=> decreases(difference(founding_rate(first_movers,X4),founding_rate(efficient_producers,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a12) ).
fof(l3,axiom,
! [X1,X4] :
( ( subpopulations(first_movers,efficient_producers,X1,X4)
& environment(X1) )
=> ~ decreases(difference(disbanding_rate(first_movers,X4),disbanding_rate(efficient_producers,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3) ).
fof(mp_decreasing_function,axiom,
! [X1,X4,X5] :
( ( greater(X5,X4)
& greater_or_equal(X4,appear(efficient_producers,X1))
& greater_or_equal(difference(growth_rate(first_movers,X5),growth_rate(efficient_producers,X5)),zero)
& in_environment(X1,X5)
& environment(X1) )
=> ( decreases(difference(growth_rate(first_movers,X4),growth_rate(efficient_producers,X4)))
=> greater(difference(growth_rate(first_movers,X4),growth_rate(efficient_producers,X4)),zero) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_decreasing_function) ).
fof(mp_relationship_of_growth_rates,axiom,
! [X1,X4] :
( ( ~ greater(zero,difference(growth_rate(first_movers,X4),growth_rate(efficient_producers,X4)))
& subpopulations(first_movers,efficient_producers,X1,X4)
& environment(X1) )
=> greater_or_equal(difference(growth_rate(first_movers,X4),growth_rate(efficient_producers,X4)),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_relationship_of_growth_rates) ).
fof(d1,hypothesis,
! [X1,X10] :
( ( X10 = critical_point(X1)
& environment(X1) )
=> ( ! [X4] :
( ( greater(X4,X10)
& subpopulations(first_movers,efficient_producers,X1,X4) )
=> greater(growth_rate(efficient_producers,X4),growth_rate(first_movers,X4)) )
& ~ greater(growth_rate(efficient_producers,X10),growth_rate(first_movers,X10)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1) ).
fof(mp_negative_growth_rate_difference,axiom,
! [X4] :
( greater(zero,difference(growth_rate(first_movers,X4),growth_rate(efficient_producers,X4)))
<=> greater(growth_rate(efficient_producers,X4),growth_rate(first_movers,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_negative_growth_rate_difference) ).
fof(mp_symmetry_of_subpopulations,axiom,
! [X1,X4] :
( ( subpopulations(first_movers,efficient_producers,X1,X4)
& environment(X1) )
=> subpopulations(efficient_producers,first_movers,X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_symmetry_of_subpopulations) ).
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(mp_positive_growth_rate_difference,axiom,
! [X4] :
( greater(difference(growth_rate(first_movers,X4),growth_rate(efficient_producers,X4)),zero)
<=> greater(growth_rate(first_movers,X4),growth_rate(efficient_producers,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_positive_growth_rate_difference) ).
fof(c_0_17,negated_conjecture,
~ ! [X1,X4] :
( ( greater(critical_point(X1),X4)
& greater_or_equal(X4,appear(efficient_producers,X1))
& in_environment(X1,critical_point(X1))
& environment(X1) )
=> selection_favors(first_movers,efficient_producers,X4) ),
inference(assume_negation,[status(cth)],[prove_t3]) ).
fof(c_0_18,plain,
! [X17] :
( subpopulations(first_movers,efficient_producers,X17,critical_point(X17))
| ~ in_environment(X17,critical_point(X17))
| ~ environment(X17) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_critical_point_means_FM_and_EP])])]) ).
fof(c_0_19,negated_conjecture,
( ~ selection_favors(first_movers,efficient_producers,esk2_0)
& greater(critical_point(esk1_0),esk2_0)
& greater_or_equal(esk2_0,appear(efficient_producers,esk1_0))
& in_environment(esk1_0,critical_point(esk1_0))
& environment(esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])]) ).
fof(c_0_20,plain,
! [X31,X32] :
( in_environment(X31,X32)
| ~ greater(critical_point(X31),X32)
| ~ greater_or_equal(X32,appear(efficient_producers,X31))
| ~ in_environment(X31,critical_point(X31))
| ~ environment(X31) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_critical_time_points])])]) ).
fof(c_0_21,plain,
! [X39,X40] :
( ( greater_or_equal(X39,X40)
| X39 != X40 )
& ( greater_or_equal(X39,X40)
| ~ greater(X39,X40) )
& ( X39 = X40
| greater(X39,X40)
| ~ greater_or_equal(X39,X40) ) ),
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_22,plain,
! [X37,X38] :
( greater_or_equal(X38,appear(efficient_producers,X37))
| ~ subpopulations(first_movers,efficient_producers,X37,X38)
| ~ environment(X37) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_FM_and_EP_members_EP_appeared])])]) ).
cnf(c_0_23,plain,
( ~ in_environment(X1,critical_point(X1))
| ~ environment(X1)
| subpopulations(first_movers,efficient_producers,X1,critical_point(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,negated_conjecture,
in_environment(esk1_0,critical_point(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,negated_conjecture,
environment(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,plain,
( ~ greater(critical_point(X1),X2)
| ~ greater_or_equal(X2,appear(efficient_producers,X1))
| ~ in_environment(X1,critical_point(X1))
| ~ environment(X1)
| in_environment(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,plain,
( X1 != X2
| greater_or_equal(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,plain,
( ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ environment(X1)
| greater_or_equal(X2,appear(efficient_producers,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,negated_conjecture,
subpopulations(first_movers,efficient_producers,esk1_0,critical_point(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).
cnf(c_0_30,negated_conjecture,
( ~ greater(critical_point(esk1_0),X1)
| ~ greater_or_equal(X1,appear(efficient_producers,esk1_0))
| in_environment(esk1_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_24]),c_0_25])]) ).
cnf(c_0_31,plain,
greater_or_equal(X1,X1),
inference(er,[status(thm)],[c_0_27]) ).
cnf(c_0_32,plain,
( ~ greater_or_equal(X1,X2)
| X1 = X2
| greater(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_33,negated_conjecture,
greater_or_equal(critical_point(esk1_0),appear(efficient_producers,esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_25])]) ).
fof(c_0_34,hypothesis,
! [X46,X47,X48,X49] :
( subpopulations(first_movers,efficient_producers,X46,X49)
| ~ greater_or_equal(X48,X49)
| ~ greater_or_equal(X49,X47)
| ~ subpopulations(first_movers,efficient_producers,X46,X48)
| ~ subpopulations(first_movers,efficient_producers,X46,X47)
| ~ environment(X46) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[a10])])]) ).
fof(c_0_35,plain,
! [X18] :
( subpopulations(first_movers,efficient_producers,X18,appear(efficient_producers,X18))
| ~ in_environment(X18,appear(efficient_producers,X18))
| ~ environment(X18) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_FM_and_EP_when_EP_appears])])]) ).
cnf(c_0_36,negated_conjecture,
( ~ greater(critical_point(esk1_0),appear(efficient_producers,esk1_0))
| in_environment(esk1_0,appear(efficient_producers,esk1_0)) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_37,negated_conjecture,
( greater(critical_point(esk1_0),appear(efficient_producers,esk1_0))
| appear(efficient_producers,esk1_0) = critical_point(esk1_0) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_38,hypothesis,
( ~ greater_or_equal(X3,X4)
| ~ greater_or_equal(X4,X2)
| ~ subpopulations(first_movers,efficient_producers,X1,X3)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ environment(X1)
| subpopulations(first_movers,efficient_producers,X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_39,plain,
( ~ in_environment(X1,appear(efficient_producers,X1))
| ~ environment(X1)
| subpopulations(first_movers,efficient_producers,X1,appear(efficient_producers,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_40,negated_conjecture,
( in_environment(esk1_0,appear(efficient_producers,esk1_0))
| appear(efficient_producers,esk1_0) = critical_point(esk1_0) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_41,negated_conjecture,
( ~ subpopulations(first_movers,efficient_producers,esk1_0,X2)
| ~ greater_or_equal(X1,X2)
| ~ greater_or_equal(critical_point(esk1_0),X1)
| subpopulations(first_movers,efficient_producers,esk1_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_29]),c_0_25])]) ).
cnf(c_0_42,negated_conjecture,
( subpopulations(first_movers,efficient_producers,esk1_0,appear(efficient_producers,esk1_0))
| appear(efficient_producers,esk1_0) = critical_point(esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_25])]) ).
cnf(c_0_43,plain,
( ~ greater(X1,X2)
| greater_or_equal(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_44,negated_conjecture,
greater(critical_point(esk1_0),esk2_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_45,negated_conjecture,
( ~ greater_or_equal(critical_point(esk1_0),X1)
| ~ greater_or_equal(X1,appear(efficient_producers,esk1_0))
| subpopulations(first_movers,efficient_producers,esk1_0,X1)
| appear(efficient_producers,esk1_0) = critical_point(esk1_0) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_46,negated_conjecture,
greater_or_equal(critical_point(esk1_0),esk2_0),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_47,negated_conjecture,
greater_or_equal(esk2_0,appear(efficient_producers,esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_48,negated_conjecture,
( ~ greater_or_equal(X1,critical_point(esk1_0))
| ~ greater_or_equal(critical_point(esk1_0),X1)
| subpopulations(first_movers,efficient_producers,esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_29]) ).
fof(c_0_49,plain,
! [X4] :
( ( ~ decreases(difference(disbanding_rate(first_movers,X4),disbanding_rate(efficient_producers,X4)))
& decreases(difference(founding_rate(first_movers,X4),founding_rate(efficient_producers,X4))) )
=> decreases(difference(growth_rate(first_movers,X4),growth_rate(efficient_producers,X4))) ),
inference(fof_simplification,[status(thm)],[mp_difference_between_founding_rates]) ).
fof(c_0_50,hypothesis,
! [X50,X51] :
( decreases(difference(founding_rate(first_movers,X51),founding_rate(efficient_producers,X51)))
| ~ subpopulations(first_movers,efficient_producers,X50,X51)
| ~ environment(X50) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[a12])])]) ).
cnf(c_0_51,negated_conjecture,
( subpopulations(first_movers,efficient_producers,esk1_0,esk2_0)
| appear(efficient_producers,esk1_0) = critical_point(esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47])]) ).
cnf(c_0_52,negated_conjecture,
( ~ greater_or_equal(esk2_0,critical_point(esk1_0))
| subpopulations(first_movers,efficient_producers,esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_48,c_0_46]) ).
fof(c_0_53,plain,
! [X1,X4] :
( ( subpopulations(first_movers,efficient_producers,X1,X4)
& environment(X1) )
=> ~ decreases(difference(disbanding_rate(first_movers,X4),disbanding_rate(efficient_producers,X4))) ),
inference(fof_simplification,[status(thm)],[l3]) ).
fof(c_0_54,plain,
! [X19] :
( decreases(difference(growth_rate(first_movers,X19),growth_rate(efficient_producers,X19)))
| decreases(difference(disbanding_rate(first_movers,X19),disbanding_rate(efficient_producers,X19)))
| ~ decreases(difference(founding_rate(first_movers,X19),founding_rate(efficient_producers,X19))) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_49])])]) ).
cnf(c_0_55,hypothesis,
( ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ environment(X1)
| decreases(difference(founding_rate(first_movers,X2),founding_rate(efficient_producers,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_56,negated_conjecture,
subpopulations(first_movers,efficient_producers,esk1_0,esk2_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_51]),c_0_52]) ).
fof(c_0_57,plain,
! [X15,X16] :
( ~ decreases(difference(disbanding_rate(first_movers,X16),disbanding_rate(efficient_producers,X16)))
| ~ subpopulations(first_movers,efficient_producers,X15,X16)
| ~ environment(X15) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_53])])]) ).
cnf(c_0_58,plain,
( ~ decreases(difference(founding_rate(first_movers,X1),founding_rate(efficient_producers,X1)))
| decreases(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
| decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_59,hypothesis,
decreases(difference(founding_rate(first_movers,esk2_0),founding_rate(efficient_producers,esk2_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_25])]) ).
cnf(c_0_60,plain,
( ~ decreases(difference(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2)))
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ environment(X1) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_61,hypothesis,
( decreases(difference(growth_rate(first_movers,esk2_0),growth_rate(efficient_producers,esk2_0)))
| decreases(difference(disbanding_rate(first_movers,esk2_0),disbanding_rate(efficient_producers,esk2_0))) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
fof(c_0_62,plain,
! [X20,X21,X22] :
( greater(difference(growth_rate(first_movers,X21),growth_rate(efficient_producers,X21)),zero)
| ~ decreases(difference(growth_rate(first_movers,X21),growth_rate(efficient_producers,X21)))
| ~ greater(X22,X21)
| ~ greater_or_equal(X21,appear(efficient_producers,X20))
| ~ greater_or_equal(difference(growth_rate(first_movers,X22),growth_rate(efficient_producers,X22)),zero)
| ~ in_environment(X20,X22)
| ~ environment(X20) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_decreasing_function])])]) ).
cnf(c_0_63,hypothesis,
( ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,esk2_0)
| decreases(difference(growth_rate(first_movers,esk2_0),growth_rate(efficient_producers,esk2_0))) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
fof(c_0_64,plain,
! [X1,X4] :
( ( ~ greater(zero,difference(growth_rate(first_movers,X4),growth_rate(efficient_producers,X4)))
& subpopulations(first_movers,efficient_producers,X1,X4)
& environment(X1) )
=> greater_or_equal(difference(growth_rate(first_movers,X4),growth_rate(efficient_producers,X4)),zero) ),
inference(fof_simplification,[status(thm)],[mp_relationship_of_growth_rates]) ).
cnf(c_0_65,plain,
( ~ decreases(difference(growth_rate(first_movers,X3),growth_rate(efficient_producers,X3)))
| ~ greater(X2,X3)
| ~ greater_or_equal(X3,appear(efficient_producers,X1))
| ~ greater_or_equal(difference(growth_rate(first_movers,X2),growth_rate(efficient_producers,X2)),zero)
| ~ in_environment(X1,X2)
| ~ environment(X1)
| greater(difference(growth_rate(first_movers,X3),growth_rate(efficient_producers,X3)),zero) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_66,negated_conjecture,
decreases(difference(growth_rate(first_movers,esk2_0),growth_rate(efficient_producers,esk2_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_56]),c_0_25])]) ).
fof(c_0_67,plain,
! [X41,X42] :
( greater_or_equal(difference(growth_rate(first_movers,X42),growth_rate(efficient_producers,X42)),zero)
| greater(zero,difference(growth_rate(first_movers,X42),growth_rate(efficient_producers,X42)))
| ~ subpopulations(first_movers,efficient_producers,X41,X42)
| ~ environment(X41) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_64])])]) ).
fof(c_0_68,hypothesis,
! [X1,X10] :
( ( X10 = critical_point(X1)
& environment(X1) )
=> ( ! [X4] :
( ( greater(X4,X10)
& subpopulations(first_movers,efficient_producers,X1,X4) )
=> greater(growth_rate(efficient_producers,X4),growth_rate(first_movers,X4)) )
& ~ greater(growth_rate(efficient_producers,X10),growth_rate(first_movers,X10)) ) ),
inference(fof_simplification,[status(thm)],[d1]) ).
cnf(c_0_69,negated_conjecture,
( ~ environment(X2)
| ~ greater(X1,esk2_0)
| ~ in_environment(X2,X1)
| ~ greater_or_equal(esk2_0,appear(efficient_producers,X2))
| ~ greater_or_equal(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero)
| greater(difference(growth_rate(first_movers,esk2_0),growth_rate(efficient_producers,esk2_0)),zero) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_70,plain,
( ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ environment(X1)
| greater_or_equal(difference(growth_rate(first_movers,X2),growth_rate(efficient_producers,X2)),zero)
| greater(zero,difference(growth_rate(first_movers,X2),growth_rate(efficient_producers,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
fof(c_0_71,hypothesis,
! [X43,X44,X45] :
( ( X44 != critical_point(X43)
| ~ environment(X43)
| greater(growth_rate(efficient_producers,X45),growth_rate(first_movers,X45))
| ~ greater(X45,X44)
| ~ subpopulations(first_movers,efficient_producers,X43,X45) )
& ( X44 != critical_point(X43)
| ~ environment(X43)
| ~ greater(growth_rate(efficient_producers,X44),growth_rate(first_movers,X44)) ) ),
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_68])])])])]) ).
fof(c_0_72,plain,
! [X23] :
( ( greater(zero,difference(growth_rate(first_movers,X23),growth_rate(efficient_producers,X23)))
| ~ greater(growth_rate(efficient_producers,X23),growth_rate(first_movers,X23)) )
& ( greater(growth_rate(efficient_producers,X23),growth_rate(first_movers,X23))
| ~ greater(zero,difference(growth_rate(first_movers,X23),growth_rate(efficient_producers,X23))) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_negative_growth_rate_difference])])]) ).
cnf(c_0_73,negated_conjecture,
( ~ greater_or_equal(difference(growth_rate(first_movers,critical_point(esk1_0)),growth_rate(efficient_producers,critical_point(esk1_0))),zero)
| greater(difference(growth_rate(first_movers,esk2_0),growth_rate(efficient_producers,esk2_0)),zero) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_24]),c_0_47]),c_0_44]),c_0_25])]) ).
cnf(c_0_74,negated_conjecture,
( greater(zero,difference(growth_rate(first_movers,critical_point(esk1_0)),growth_rate(efficient_producers,critical_point(esk1_0))))
| greater_or_equal(difference(growth_rate(first_movers,critical_point(esk1_0)),growth_rate(efficient_producers,critical_point(esk1_0))),zero) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_29]),c_0_25])]) ).
fof(c_0_75,plain,
! [X35,X36] :
( subpopulations(efficient_producers,first_movers,X35,X36)
| ~ subpopulations(first_movers,efficient_producers,X35,X36)
| ~ environment(X35) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_symmetry_of_subpopulations])])]) ).
cnf(c_0_76,hypothesis,
( X1 != critical_point(X2)
| ~ environment(X2)
| ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_77,plain,
( ~ greater(zero,difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_78,negated_conjecture,
( greater(difference(growth_rate(first_movers,esk2_0),growth_rate(efficient_producers,esk2_0)),zero)
| greater(zero,difference(growth_rate(first_movers,critical_point(esk1_0)),growth_rate(efficient_producers,critical_point(esk1_0)))) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
fof(c_0_79,plain,
! [X11,X12,X13,X14] :
( selection_favors(X13,X12,X14)
| ~ greater(growth_rate(X13,X14),growth_rate(X12,X14))
| ~ subpopulations(X12,X13,X11,X14)
| ~ environment(X11) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp1_high_growth_rates])])]) ).
cnf(c_0_80,plain,
( ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ environment(X1)
| subpopulations(efficient_producers,first_movers,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
fof(c_0_81,plain,
! [X24] :
( ( greater(difference(growth_rate(first_movers,X24),growth_rate(efficient_producers,X24)),zero)
| ~ greater(growth_rate(first_movers,X24),growth_rate(efficient_producers,X24)) )
& ( greater(growth_rate(first_movers,X24),growth_rate(efficient_producers,X24))
| ~ greater(difference(growth_rate(first_movers,X24),growth_rate(efficient_producers,X24)),zero) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_positive_growth_rate_difference])])]) ).
cnf(c_0_82,hypothesis,
( ~ environment(X1)
| ~ greater(growth_rate(efficient_producers,critical_point(X1)),growth_rate(first_movers,critical_point(X1))) ),
inference(er,[status(thm)],[c_0_76]) ).
cnf(c_0_83,negated_conjecture,
( greater(growth_rate(efficient_producers,critical_point(esk1_0)),growth_rate(first_movers,critical_point(esk1_0)))
| greater(difference(growth_rate(first_movers,esk2_0),growth_rate(efficient_producers,esk2_0)),zero) ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_84,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_79]) ).
cnf(c_0_85,negated_conjecture,
subpopulations(efficient_producers,first_movers,esk1_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_56]),c_0_25])]) ).
cnf(c_0_86,negated_conjecture,
~ selection_favors(first_movers,efficient_producers,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_87,plain,
( ~ greater(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero)
| greater(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_88,hypothesis,
greater(difference(growth_rate(first_movers,esk2_0),growth_rate(efficient_producers,esk2_0)),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_25])]) ).
cnf(c_0_89,negated_conjecture,
~ greater(growth_rate(first_movers,esk2_0),growth_rate(efficient_producers,esk2_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_25])]),c_0_86]) ).
cnf(c_0_90,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_89]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT034+2 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.35 % Computer : n016.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % 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 01:27:09 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 Running first-order theorem proving
% 0.11/0.39 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
% 0.11/0.43 % Version: 3.5.1
% 0.11/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.43 % Starting sh5l with 300s (1) cores
% 0.11/0.43 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1272493 completed with status 0
% 0.11/0.43 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.11/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.43 % No SInE strategy applied
% 0.11/0.43 % Search class: FGHSF-FFMS21-SFFFFFNN
% 0.11/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.11/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.11/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.11/0.43 % Starting 208_C09_12_F1_SE_CS_SP_PS_S070I with 136s (1) cores
% 0.11/0.43 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 0.11/0.43 % Starting new_bool_3 with 136s (1) cores
% 0.11/0.43 % new_bool_3 with pid 1272503 completed with status 0
% 0.11/0.43 % Result found by new_bool_3
% 0.11/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.43 % No SInE strategy applied
% 0.11/0.43 % Search class: FGHSF-FFMS21-SFFFFFNN
% 0.11/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.11/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.11/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.11/0.43 % Starting 208_C09_12_F1_SE_CS_SP_PS_S070I with 136s (1) cores
% 0.11/0.43 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 0.11/0.43 % Starting new_bool_3 with 136s (1) cores
% 0.11/0.43 % Preprocessing time : 0.002 s
% 0.11/0.43 % Presaturation interreduction done
% 0.11/0.43
% 0.11/0.43 % Proof found!
% 0.11/0.43 % SZS status Theorem
% 0.11/0.43 % SZS output start CNFRefutation
% See solution above
% 0.11/0.43 % Parsed axioms : 21
% 0.11/0.43 % Removed by relevancy pruning/SinE : 0
% 0.11/0.43 % Initial clauses : 30
% 0.11/0.43 % Removed in clause preprocessing : 0
% 0.11/0.43 % Initial clauses in saturation : 30
% 0.11/0.43 % Processed clauses : 158
% 0.11/0.43 % ...of these trivial : 0
% 0.11/0.43 % ...subsumed : 12
% 0.11/0.43 % ...remaining for further processing : 146
% 0.11/0.43 % Other redundant clauses eliminated : 3
% 0.11/0.43 % Clauses deleted for lack of memory : 0
% 0.11/0.43 % Backward-subsumed : 0
% 0.11/0.43 % Backward-rewritten : 11
% 0.11/0.43 % Generated clauses : 153
% 0.11/0.43 % ...of the previous two non-redundant : 111
% 0.11/0.43 % ...aggressively subsumed : 0
% 0.11/0.43 % Contextual simplify-reflections : 1
% 0.11/0.43 % Paramodulations : 150
% 0.11/0.43 % Factorizations : 0
% 0.11/0.43 % NegExts : 0
% 0.11/0.43 % Equation resolutions : 3
% 0.11/0.43 % Disequality decompositions : 0
% 0.11/0.43 % Total rewrite steps : 128
% 0.11/0.43 % ...of those cached : 113
% 0.11/0.43 % Propositional unsat checks : 0
% 0.11/0.43 % Propositional check models : 0
% 0.11/0.43 % Propositional check unsatisfiable : 0
% 0.11/0.43 % Propositional clauses : 0
% 0.11/0.43 % Propositional clauses after purity: 0
% 0.11/0.43 % Propositional unsat core size : 0
% 0.11/0.43 % Propositional preprocessing time : 0.000
% 0.11/0.43 % Propositional encoding time : 0.000
% 0.11/0.43 % Propositional solver time : 0.000
% 0.11/0.43 % Success case prop preproc time : 0.000
% 0.11/0.43 % Success case prop encoding time : 0.000
% 0.11/0.43 % Success case prop solver time : 0.000
% 0.11/0.43 % Current number of processed clauses : 102
% 0.11/0.43 % Positive orientable unit clauses : 16
% 0.11/0.43 % Positive unorientable unit clauses: 0
% 0.11/0.43 % Negative unit clauses : 2
% 0.11/0.43 % Non-unit-clauses : 84
% 0.11/0.43 % Current number of unprocessed clauses: 10
% 0.11/0.43 % ...number of literals in the above : 28
% 0.11/0.43 % Current number of archived formulas : 0
% 0.11/0.43 % Current number of archived clauses : 41
% 0.11/0.43 % Clause-clause subsumption calls (NU) : 1248
% 0.11/0.43 % Rec. Clause-clause subsumption calls : 534
% 0.11/0.43 % Non-unit clause-clause subsumptions : 13
% 0.11/0.43 % Unit Clause-clause subsumption calls : 16
% 0.11/0.43 % Rewrite failures with RHS unbound : 0
% 0.11/0.43 % BW rewrite match attempts : 28
% 0.11/0.43 % BW rewrite match successes : 3
% 0.11/0.43 % Condensation attempts : 0
% 0.11/0.43 % Condensation successes : 0
% 0.11/0.43 % Termbank termtop insertions : 7409
% 0.11/0.43 % Search garbage collected termcells : 559
% 0.11/0.43
% 0.11/0.43 % -------------------------------------------------
% 0.11/0.43 % User time : 0.018 s
% 0.11/0.43 % System time : 0.004 s
% 0.11/0.43 % Total time : 0.022 s
% 0.11/0.43 % Maximum resident set size: 3664 pages
% 0.11/0.43
% 0.11/0.43 % -------------------------------------------------
% 0.11/0.43 % User time : 0.083 s
% 0.11/0.43 % System time : 0.014 s
% 0.11/0.43 % Total time : 0.097 s
% 0.11/0.43 % Maximum resident set size: 4608 pages
% 0.11/0.43 % E exiting
%------------------------------------------------------------------------------