%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : MGT034+2 : TPTP v9.2.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:47:34 PM UTC 2026
% Result : Theorem 1.34s 1.73s
% Output : CNFRefutation 1.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 17
% Syntax : Number of formulae : 89 ( 14 unt; 0 def)
% Number of atoms : 292 ( 16 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 333 ( 130 ~; 131 |; 47 &)
% ( 3 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 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 : 130 ( 0 sgn 78 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_t3,conjecture,
! [X1,X4] :
( ( environment(X1)
& in_environment(X1,critical_point(X1))
& greater_or_equal(X4,appear(efficient_producers,X1))
& greater(critical_point(X1),X4) )
=> selection_favors(first_movers,efficient_producers,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t3) ).
fof(mp_critical_point_means_FM_and_EP,axiom,
! [X1] :
( ( environment(X1)
& in_environment(X1,critical_point(X1)) )
=> subpopulations(first_movers,efficient_producers,X1,critical_point(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_critical_point_means_FM_and_EP) ).
fof(mp_greater_or_equal,axiom,
! [X8,X9] :
( greater_or_equal(X8,X9)
<=> ( greater(X8,X9)
| X8 = X9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal) ).
fof(a10,hypothesis,
! [X1,X6,X7,X4] :
( ( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X6)
& subpopulations(first_movers,efficient_producers,X1,X7)
& greater_or_equal(X4,X6)
& greater_or_equal(X7,X4) )
=> subpopulations(first_movers,efficient_producers,X1,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a10) ).
fof(mp_critical_time_points,axiom,
! [X1,X4] :
( ( environment(X1)
& in_environment(X1,critical_point(X1))
& greater_or_equal(X4,appear(efficient_producers,X1))
& greater(critical_point(X1),X4) )
=> in_environment(X1,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_critical_time_points) ).
fof(mp_FM_and_EP_members_EP_appeared,axiom,
! [X1,X4] :
( ( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X4) )
=> greater_or_equal(X4,appear(efficient_producers,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_FM_and_EP_members_EP_appeared) ).
fof(mp_FM_and_EP_when_EP_appears,axiom,
! [X1] :
( ( environment(X1)
& in_environment(X1,appear(efficient_producers,X1)) )
=> subpopulations(first_movers,efficient_producers,X1,appear(efficient_producers,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_FM_and_EP_when_EP_appears) ).
fof(mp_difference_between_founding_rates,axiom,
! [X4] :
( ( decreases(difference(founding_rate(first_movers,X4),founding_rate(efficient_producers,X4)))
& ~ decreases(difference(disbanding_rate(first_movers,X4),disbanding_rate(efficient_producers,X4))) )
=> decreases(difference(growth_rate(first_movers,X4),growth_rate(efficient_producers,X4))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_difference_between_founding_rates) ).
fof(a12,hypothesis,
! [X1,X4] :
( ( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X4) )
=> decreases(difference(founding_rate(first_movers,X4),founding_rate(efficient_producers,X4))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a12) ).
fof(mp_relationship_of_growth_rates,axiom,
! [X1,X4] :
( ( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X4)
& ~ greater(zero,difference(growth_rate(first_movers,X4),growth_rate(efficient_producers,X4))) )
=> greater_or_equal(difference(growth_rate(first_movers,X4),growth_rate(efficient_producers,X4)),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_relationship_of_growth_rates) ).
fof(l3,axiom,
! [X1,X4] :
( ( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X4) )
=> ~ decreases(difference(disbanding_rate(first_movers,X4),disbanding_rate(efficient_producers,X4))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3) ).
fof(mp_decreasing_function,axiom,
! [X1,X4,X5] :
( ( environment(X1)
& in_environment(X1,X5)
& greater_or_equal(difference(growth_rate(first_movers,X5),growth_rate(efficient_producers,X5)),zero)
& greater_or_equal(X4,appear(efficient_producers,X1))
& greater(X5,X4) )
=> ( 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/sandbox2/benchmark/theBenchmark.p',mp_decreasing_function) ).
fof(d1,hypothesis,
! [X1,X10] :
( ( environment(X1)
& X10 = critical_point(X1) )
=> ( ~ greater(growth_rate(efficient_producers,X10),growth_rate(first_movers,X10))
& ! [X4] :
( ( subpopulations(first_movers,efficient_producers,X1,X4)
& greater(X4,X10) )
=> greater(growth_rate(efficient_producers,X4),growth_rate(first_movers,X4)) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mp_negative_growth_rate_difference) ).
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/sandbox2/benchmark/theBenchmark.p',mp_positive_growth_rate_difference) ).
fof(mp1_high_growth_rates,axiom,
! [X1,X2,X3,X4] :
( ( environment(X1)
& subpopulations(X2,X3,X1,X4)
& greater(growth_rate(X3,X4),growth_rate(X2,X4)) )
=> selection_favors(X3,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp1_high_growth_rates) ).
fof(mp_symmetry_of_subpopulations,axiom,
! [X1,X4] :
( ( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X4) )
=> subpopulations(efficient_producers,first_movers,X1,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_symmetry_of_subpopulations) ).
fof(c_0_17,negated_conjecture,
~ ! [X1,X4] :
( ( environment(X1)
& in_environment(X1,critical_point(X1))
& greater_or_equal(X4,appear(efficient_producers,X1))
& greater(critical_point(X1),X4) )
=> selection_favors(first_movers,efficient_producers,X4) ),
inference(assume_negation,[status(cth)],[prove_t3]) ).
fof(c_0_18,plain,
! [X60] :
( ~ environment(X60)
| ~ in_environment(X60,critical_point(X60))
| subpopulations(first_movers,efficient_producers,X60,critical_point(X60)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_critical_point_means_FM_and_EP])]) ).
fof(c_0_19,negated_conjecture,
( environment(esk1_0)
& in_environment(esk1_0,critical_point(esk1_0))
& greater_or_equal(esk2_0,appear(efficient_producers,esk1_0))
& greater(critical_point(esk1_0),esk2_0)
& ~ selection_favors(first_movers,efficient_producers,esk2_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])]) ).
fof(c_0_20,plain,
! [X82,X83] :
( ( ~ greater_or_equal(X82,X83)
| greater(X82,X83)
| X82 = X83 )
& ( ~ greater(X82,X83)
| greater_or_equal(X82,X83) )
& ( X82 != X83
| greater_or_equal(X82,X83) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_greater_or_equal])])]) ).
fof(c_0_21,hypothesis,
! [X89,X90,X91,X92] :
( ~ environment(X89)
| ~ subpopulations(first_movers,efficient_producers,X89,X90)
| ~ subpopulations(first_movers,efficient_producers,X89,X91)
| ~ greater_or_equal(X92,X90)
| ~ greater_or_equal(X91,X92)
| subpopulations(first_movers,efficient_producers,X89,X92) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[a10])]) ).
cnf(c_0_22,plain,
( subpopulations(first_movers,efficient_producers,X1,critical_point(X1))
| ~ environment(X1)
| ~ in_environment(X1,critical_point(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,negated_conjecture,
in_environment(esk1_0,critical_point(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,negated_conjecture,
environment(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_25,plain,
! [X74,X75] :
( ~ environment(X74)
| ~ in_environment(X74,critical_point(X74))
| ~ greater_or_equal(X75,appear(efficient_producers,X74))
| ~ greater(critical_point(X74),X75)
| in_environment(X74,X75) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_critical_time_points])]) ).
cnf(c_0_26,plain,
( greater_or_equal(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_27,plain,
! [X80,X81] :
( ~ environment(X80)
| ~ subpopulations(first_movers,efficient_producers,X80,X81)
| greater_or_equal(X81,appear(efficient_producers,X80)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_FM_and_EP_members_EP_appeared])]) ).
cnf(c_0_28,hypothesis,
( subpopulations(first_movers,efficient_producers,X1,X4)
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ subpopulations(first_movers,efficient_producers,X1,X3)
| ~ greater_or_equal(X4,X2)
| ~ greater_or_equal(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
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_22,c_0_23]),c_0_24])]) ).
cnf(c_0_30,plain,
( in_environment(X1,X2)
| ~ environment(X1)
| ~ in_environment(X1,critical_point(X1))
| ~ greater_or_equal(X2,appear(efficient_producers,X1))
| ~ greater(critical_point(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,plain,
greater_or_equal(X1,X1),
inference(er,[status(thm)],[c_0_26]) ).
cnf(c_0_32,plain,
( greater(X1,X2)
| X1 = X2
| ~ greater_or_equal(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_33,plain,
( greater_or_equal(X2,appear(efficient_producers,X1))
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_34,hypothesis,
( subpopulations(first_movers,efficient_producers,esk1_0,X1)
| ~ greater_or_equal(critical_point(esk1_0),X1)
| ~ greater_or_equal(X1,X2)
| ~ subpopulations(first_movers,efficient_producers,esk1_0,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_24])]) ).
cnf(c_0_35,plain,
( greater_or_equal(X1,X2)
| ~ greater(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_36,plain,
! [X61] :
( ~ environment(X61)
| ~ in_environment(X61,appear(efficient_producers,X61))
| subpopulations(first_movers,efficient_producers,X61,appear(efficient_producers,X61)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_FM_and_EP_when_EP_appears])]) ).
cnf(c_0_37,plain,
( in_environment(X1,appear(efficient_producers,X1))
| ~ in_environment(X1,critical_point(X1))
| ~ greater(critical_point(X1),appear(efficient_producers,X1))
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_38,plain,
( X1 = appear(efficient_producers,X2)
| greater(X1,appear(efficient_producers,X2))
| ~ subpopulations(first_movers,efficient_producers,X2,X1)
| ~ environment(X2) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_39,hypothesis,
( subpopulations(first_movers,efficient_producers,esk1_0,X1)
| ~ greater_or_equal(X1,X2)
| ~ greater(critical_point(esk1_0),X1)
| ~ subpopulations(first_movers,efficient_producers,esk1_0,X2) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_40,negated_conjecture,
greater(critical_point(esk1_0),esk2_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_41,plain,
( subpopulations(first_movers,efficient_producers,X1,appear(efficient_producers,X1))
| ~ environment(X1)
| ~ in_environment(X1,appear(efficient_producers,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_42,plain,
( appear(efficient_producers,X1) = critical_point(X1)
| in_environment(X1,appear(efficient_producers,X1))
| ~ in_environment(X1,critical_point(X1))
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_22]) ).
cnf(c_0_43,negated_conjecture,
( subpopulations(first_movers,efficient_producers,esk1_0,esk2_0)
| ~ greater_or_equal(esk2_0,X1)
| ~ subpopulations(first_movers,efficient_producers,esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_44,negated_conjecture,
greater_or_equal(esk2_0,appear(efficient_producers,esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_45,plain,
( appear(efficient_producers,X1) = critical_point(X1)
| subpopulations(first_movers,efficient_producers,X1,appear(efficient_producers,X1))
| ~ in_environment(X1,critical_point(X1))
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_46,negated_conjecture,
( subpopulations(first_movers,efficient_producers,esk1_0,esk2_0)
| ~ subpopulations(first_movers,efficient_producers,esk1_0,appear(efficient_producers,esk1_0)) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_47,negated_conjecture,
( appear(efficient_producers,esk1_0) = critical_point(esk1_0)
| subpopulations(first_movers,efficient_producers,esk1_0,appear(efficient_producers,esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_23]),c_0_24])]) ).
fof(c_0_48,plain,
! [X4] :
( ( decreases(difference(founding_rate(first_movers,X4),founding_rate(efficient_producers,X4)))
& ~ decreases(difference(disbanding_rate(first_movers,X4),disbanding_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_49,hypothesis,
! [X93,X94] :
( ~ environment(X93)
| ~ subpopulations(first_movers,efficient_producers,X93,X94)
| decreases(difference(founding_rate(first_movers,X94),founding_rate(efficient_producers,X94))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[a12])]) ).
cnf(c_0_50,negated_conjecture,
( appear(efficient_producers,esk1_0) = critical_point(esk1_0)
| subpopulations(first_movers,efficient_producers,esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
fof(c_0_51,plain,
! [X1,X4] :
( ( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X4)
& ~ greater(zero,difference(growth_rate(first_movers,X4),growth_rate(efficient_producers,X4))) )
=> 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]) ).
fof(c_0_52,plain,
! [X1,X4] :
( ( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X4) )
=> ~ decreases(difference(disbanding_rate(first_movers,X4),disbanding_rate(efficient_producers,X4))) ),
inference(fof_simplification,[status(thm)],[l3]) ).
fof(c_0_53,plain,
! [X62] :
( ~ decreases(difference(founding_rate(first_movers,X62),founding_rate(efficient_producers,X62)))
| decreases(difference(disbanding_rate(first_movers,X62),disbanding_rate(efficient_producers,X62)))
| decreases(difference(growth_rate(first_movers,X62),growth_rate(efficient_producers,X62))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_48])]) ).
cnf(c_0_54,hypothesis,
( decreases(difference(founding_rate(first_movers,X2),founding_rate(efficient_producers,X2)))
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_55,negated_conjecture,
subpopulations(first_movers,efficient_producers,esk1_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_50]),c_0_29])]) ).
fof(c_0_56,plain,
! [X84,X85] :
( ~ environment(X84)
| ~ subpopulations(first_movers,efficient_producers,X84,X85)
| greater(zero,difference(growth_rate(first_movers,X85),growth_rate(efficient_producers,X85)))
| greater_or_equal(difference(growth_rate(first_movers,X85),growth_rate(efficient_producers,X85)),zero) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_51])]) ).
fof(c_0_57,plain,
! [X58,X59] :
( ~ environment(X58)
| ~ subpopulations(first_movers,efficient_producers,X58,X59)
| ~ decreases(difference(disbanding_rate(first_movers,X59),disbanding_rate(efficient_producers,X59))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_52])]) ).
cnf(c_0_58,plain,
( decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| decreases(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
| ~ decreases(difference(founding_rate(first_movers,X1),founding_rate(efficient_producers,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
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_54,c_0_55]),c_0_24])]) ).
fof(c_0_60,plain,
! [X63,X64,X65] :
( ~ environment(X63)
| ~ in_environment(X63,X65)
| ~ greater_or_equal(difference(growth_rate(first_movers,X65),growth_rate(efficient_producers,X65)),zero)
| ~ greater_or_equal(X64,appear(efficient_producers,X63))
| ~ greater(X65,X64)
| ~ decreases(difference(growth_rate(first_movers,X64),growth_rate(efficient_producers,X64)))
| greater(difference(growth_rate(first_movers,X64),growth_rate(efficient_producers,X64)),zero) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_decreasing_function])]) ).
cnf(c_0_61,plain,
( greater(zero,difference(growth_rate(first_movers,X2),growth_rate(efficient_producers,X2)))
| greater_or_equal(difference(growth_rate(first_movers,X2),growth_rate(efficient_producers,X2)),zero)
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_62,plain,
( ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ decreases(difference(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_63,hypothesis,
( decreases(difference(disbanding_rate(first_movers,esk2_0),disbanding_rate(efficient_producers,esk2_0)))
| decreases(difference(growth_rate(first_movers,esk2_0),growth_rate(efficient_producers,esk2_0))) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_64,plain,
( greater(difference(growth_rate(first_movers,X3),growth_rate(efficient_producers,X3)),zero)
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ greater_or_equal(difference(growth_rate(first_movers,X2),growth_rate(efficient_producers,X2)),zero)
| ~ greater_or_equal(X3,appear(efficient_producers,X1))
| ~ greater(X2,X3)
| ~ decreases(difference(growth_rate(first_movers,X3),growth_rate(efficient_producers,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_65,negated_conjecture,
( greater_or_equal(difference(growth_rate(first_movers,critical_point(esk1_0)),growth_rate(efficient_producers,critical_point(esk1_0))),zero)
| greater(zero,difference(growth_rate(first_movers,critical_point(esk1_0)),growth_rate(efficient_producers,critical_point(esk1_0)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_29]),c_0_24])]) ).
cnf(c_0_66,hypothesis,
( decreases(difference(growth_rate(first_movers,esk2_0),growth_rate(efficient_producers,esk2_0)))
| ~ subpopulations(first_movers,efficient_producers,X1,esk2_0)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
fof(c_0_67,hypothesis,
! [X1,X10] :
( ( environment(X1)
& X10 = critical_point(X1) )
=> ( ~ greater(growth_rate(efficient_producers,X10),growth_rate(first_movers,X10))
& ! [X4] :
( ( subpopulations(first_movers,efficient_producers,X1,X4)
& greater(X4,X10) )
=> greater(growth_rate(efficient_producers,X4),growth_rate(first_movers,X4)) ) ) ),
inference(fof_simplification,[status(thm)],[d1]) ).
fof(c_0_68,plain,
! [X66] :
( ( ~ greater(zero,difference(growth_rate(first_movers,X66),growth_rate(efficient_producers,X66)))
| greater(growth_rate(efficient_producers,X66),growth_rate(first_movers,X66)) )
& ( ~ greater(growth_rate(efficient_producers,X66),growth_rate(first_movers,X66))
| greater(zero,difference(growth_rate(first_movers,X66),growth_rate(efficient_producers,X66))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_negative_growth_rate_difference])]) ).
cnf(c_0_69,negated_conjecture,
( greater(zero,difference(growth_rate(first_movers,critical_point(esk1_0)),growth_rate(efficient_producers,critical_point(esk1_0))))
| greater(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero)
| ~ greater_or_equal(X1,appear(efficient_producers,X2))
| ~ in_environment(X2,critical_point(esk1_0))
| ~ decreases(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
| ~ greater(critical_point(esk1_0),X1)
| ~ environment(X2) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_70,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_66,c_0_24]),c_0_55])]) ).
fof(c_0_71,hypothesis,
! [X86,X87,X88] :
( ( ~ greater(growth_rate(efficient_producers,X87),growth_rate(first_movers,X87))
| ~ environment(X86)
| X87 != critical_point(X86) )
& ( ~ subpopulations(first_movers,efficient_producers,X86,X88)
| ~ greater(X88,X87)
| greater(growth_rate(efficient_producers,X88),growth_rate(first_movers,X88))
| ~ environment(X86)
| X87 != critical_point(X86) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_67])])])]) ).
cnf(c_0_72,plain,
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ greater(zero,difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_73,negated_conjecture,
( greater(zero,difference(growth_rate(first_movers,critical_point(esk1_0)),growth_rate(efficient_producers,critical_point(esk1_0))))
| 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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_44]),c_0_23]),c_0_70]),c_0_40]),c_0_24])]) ).
cnf(c_0_74,hypothesis,
( ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X2)
| X1 != critical_point(X2) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_75,negated_conjecture,
( greater(difference(growth_rate(first_movers,esk2_0),growth_rate(efficient_producers,esk2_0)),zero)
| greater(growth_rate(efficient_producers,critical_point(esk1_0)),growth_rate(first_movers,critical_point(esk1_0))) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
fof(c_0_76,plain,
! [X67] :
( ( ~ greater(difference(growth_rate(first_movers,X67),growth_rate(efficient_producers,X67)),zero)
| greater(growth_rate(first_movers,X67),growth_rate(efficient_producers,X67)) )
& ( ~ greater(growth_rate(first_movers,X67),growth_rate(efficient_producers,X67))
| greater(difference(growth_rate(first_movers,X67),growth_rate(efficient_producers,X67)),zero) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_positive_growth_rate_difference])]) ).
cnf(c_0_77,hypothesis,
( greater(difference(growth_rate(first_movers,esk2_0),growth_rate(efficient_producers,esk2_0)),zero)
| critical_point(esk1_0) != critical_point(X1)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
fof(c_0_78,plain,
! [X54,X55,X56,X57] :
( ~ environment(X54)
| ~ subpopulations(X55,X56,X54,X57)
| ~ greater(growth_rate(X56,X57),growth_rate(X55,X57))
| selection_favors(X56,X55,X57) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp1_high_growth_rates])]) ).
cnf(c_0_79,plain,
( greater(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1))
| ~ greater(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_80,negated_conjecture,
greater(difference(growth_rate(first_movers,esk2_0),growth_rate(efficient_producers,esk2_0)),zero),
inference(spm,[status(thm)],[c_0_77,c_0_24]) ).
fof(c_0_81,plain,
! [X78,X79] :
( ~ environment(X78)
| ~ subpopulations(first_movers,efficient_producers,X78,X79)
| subpopulations(efficient_producers,first_movers,X78,X79) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_symmetry_of_subpopulations])]) ).
cnf(c_0_82,plain,
( selection_favors(X3,X2,X4)
| ~ environment(X1)
| ~ subpopulations(X2,X3,X1,X4)
| ~ greater(growth_rate(X3,X4),growth_rate(X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_83,negated_conjecture,
greater(growth_rate(first_movers,esk2_0),growth_rate(efficient_producers,esk2_0)),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_84,negated_conjecture,
~ selection_favors(first_movers,efficient_producers,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_85,plain,
( subpopulations(efficient_producers,first_movers,X1,X2)
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_86,negated_conjecture,
( ~ subpopulations(efficient_producers,first_movers,X1,esk2_0)
| ~ environment(X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_84]) ).
cnf(c_0_87,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_85,c_0_55]),c_0_24])]) ).
cnf(c_0_88,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_24]),c_0_87])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : MGT034+2 : TPTP v9.2.1. Released v2.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32 % Computer : n005.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Mon May 4 23:28:45 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.34/1.73 % Version : CSE_E---1.7
% 1.34/1.73 % Problem : theBenchmark.p
% 1.34/1.73 % SZS status Theorem for theBenchmark.p
% 1.34/1.73 % SZS output start CNFRefutation
% See solution above
% 1.34/1.73 % Total time : 1.371s
%------------------------------------------------------------------------------