TSTP Solution File: MGT034+2 by E---3.1
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1
% Problem : MGT034+2 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n004.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 : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 18:35:02 EDT 2023
% Result : Theorem 0.22s 0.55s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 17
% Syntax : Number of formulae : 98 ( 10 unt; 0 def)
% Number of atoms : 318 ( 22 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 370 ( 150 ~; 148 |; 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(mp_greater_or_equal,axiom,
! [X8,X9] :
( greater_or_equal(X8,X9)
<=> ( greater(X8,X9)
| X8 = X9 ) ),
file('/export/starexec/sandbox2/tmp/tmp.Ocn7rEa5zY/E---3.1_3519.p',mp_greater_or_equal) ).
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/tmp/tmp.Ocn7rEa5zY/E---3.1_3519.p',prove_t3) ).
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/tmp/tmp.Ocn7rEa5zY/E---3.1_3519.p',mp_critical_time_points) ).
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/tmp/tmp.Ocn7rEa5zY/E---3.1_3519.p',mp_critical_point_means_FM_and_EP) ).
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/tmp/tmp.Ocn7rEa5zY/E---3.1_3519.p',mp_FM_and_EP_when_EP_appears) ).
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/tmp/tmp.Ocn7rEa5zY/E---3.1_3519.p',mp_FM_and_EP_members_EP_appeared) ).
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/tmp/tmp.Ocn7rEa5zY/E---3.1_3519.p',a10) ).
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/tmp/tmp.Ocn7rEa5zY/E---3.1_3519.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/tmp/tmp.Ocn7rEa5zY/E---3.1_3519.p',a12) ).
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/tmp/tmp.Ocn7rEa5zY/E---3.1_3519.p',mp_decreasing_function) ).
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/tmp/tmp.Ocn7rEa5zY/E---3.1_3519.p',l3) ).
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/tmp/tmp.Ocn7rEa5zY/E---3.1_3519.p',mp_symmetry_of_subpopulations) ).
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/tmp/tmp.Ocn7rEa5zY/E---3.1_3519.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/sandbox2/tmp/tmp.Ocn7rEa5zY/E---3.1_3519.p',mp_positive_growth_rate_difference) ).
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/tmp/tmp.Ocn7rEa5zY/E---3.1_3519.p',d1) ).
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/tmp/tmp.Ocn7rEa5zY/E---3.1_3519.p',mp_relationship_of_growth_rates) ).
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/tmp/tmp.Ocn7rEa5zY/E---3.1_3519.p',mp_negative_growth_rate_difference) ).
fof(c_0_17,plain,
! [X22,X23] :
( ( ~ greater_or_equal(X22,X23)
| greater(X22,X23)
| X22 = X23 )
& ( ~ greater(X22,X23)
| greater_or_equal(X22,X23) )
& ( X22 != X23
| greater_or_equal(X22,X23) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_greater_or_equal])])]) ).
fof(c_0_18,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_19,plain,
! [X31,X32] :
( ~ environment(X31)
| ~ in_environment(X31,critical_point(X31))
| ~ greater_or_equal(X32,appear(efficient_producers,X31))
| ~ greater(critical_point(X31),X32)
| in_environment(X31,X32) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_critical_time_points])]) ).
cnf(c_0_20,plain,
( greater_or_equal(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_21,plain,
! [X30] :
( ~ environment(X30)
| ~ in_environment(X30,critical_point(X30))
| subpopulations(first_movers,efficient_producers,X30,critical_point(X30)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_critical_point_means_FM_and_EP])]) ).
fof(c_0_22,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_18])])]) ).
fof(c_0_23,plain,
! [X47] :
( ~ environment(X47)
| ~ in_environment(X47,appear(efficient_producers,X47))
| subpopulations(first_movers,efficient_producers,X47,appear(efficient_producers,X47)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_FM_and_EP_when_EP_appears])]) ).
cnf(c_0_24,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_19]) ).
cnf(c_0_25,plain,
greater_or_equal(X1,X1),
inference(er,[status(thm)],[c_0_20]) ).
fof(c_0_26,plain,
! [X37,X38] :
( ~ environment(X37)
| ~ subpopulations(first_movers,efficient_producers,X37,X38)
| greater_or_equal(X38,appear(efficient_producers,X37)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_FM_and_EP_members_EP_appeared])]) ).
fof(c_0_27,hypothesis,
! [X14,X15,X16,X17] :
( ~ environment(X14)
| ~ subpopulations(first_movers,efficient_producers,X14,X15)
| ~ subpopulations(first_movers,efficient_producers,X14,X16)
| ~ greater_or_equal(X17,X15)
| ~ greater_or_equal(X16,X17)
| subpopulations(first_movers,efficient_producers,X14,X17) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[a10])]) ).
cnf(c_0_28,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_21]) ).
cnf(c_0_29,negated_conjecture,
in_environment(esk1_0,critical_point(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,negated_conjecture,
environment(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_31,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_23]) ).
cnf(c_0_32,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_24,c_0_25]) ).
cnf(c_0_33,plain,
( greater(X1,X2)
| X1 = X2
| ~ greater_or_equal(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_34,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_26]) ).
cnf(c_0_35,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_27]) ).
cnf(c_0_36,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_28,c_0_29]),c_0_30])]) ).
cnf(c_0_37,plain,
( subpopulations(first_movers,efficient_producers,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_31,c_0_32]) ).
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_33,c_0_34]) ).
cnf(c_0_39,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_35,c_0_36]),c_0_30])]) ).
cnf(c_0_40,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(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_28]) ).
cnf(c_0_41,hypothesis,
( appear(efficient_producers,esk1_0) = critical_point(esk1_0)
| subpopulations(first_movers,efficient_producers,esk1_0,X1)
| ~ greater_or_equal(X1,appear(efficient_producers,esk1_0))
| ~ greater_or_equal(critical_point(esk1_0),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_29]),c_0_30])]) ).
cnf(c_0_42,negated_conjecture,
greater_or_equal(esk2_0,appear(efficient_producers,esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_43,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_44,hypothesis,
! [X18,X19] :
( ~ environment(X18)
| ~ subpopulations(first_movers,efficient_producers,X18,X19)
| decreases(difference(founding_rate(first_movers,X19),founding_rate(efficient_producers,X19))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[a12])]) ).
cnf(c_0_45,negated_conjecture,
( appear(efficient_producers,esk1_0) = critical_point(esk1_0)
| subpopulations(first_movers,efficient_producers,esk1_0,esk2_0)
| ~ greater_or_equal(critical_point(esk1_0),esk2_0) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_46,plain,
( greater_or_equal(X1,X2)
| ~ greater(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_47,negated_conjecture,
greater(critical_point(esk1_0),esk2_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_48,plain,
! [X39,X40,X41] :
( ~ environment(X39)
| ~ in_environment(X39,X41)
| ~ greater_or_equal(difference(growth_rate(first_movers,X41),growth_rate(efficient_producers,X41)),zero)
| ~ greater_or_equal(X40,appear(efficient_producers,X39))
| ~ greater(X41,X40)
| ~ decreases(difference(growth_rate(first_movers,X40),growth_rate(efficient_producers,X40)))
| greater(difference(growth_rate(first_movers,X40),growth_rate(efficient_producers,X40)),zero) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_decreasing_function])]) ).
fof(c_0_49,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_50,plain,
! [X42] :
( ~ decreases(difference(founding_rate(first_movers,X42),founding_rate(efficient_producers,X42)))
| decreases(difference(disbanding_rate(first_movers,X42),disbanding_rate(efficient_producers,X42)))
| decreases(difference(growth_rate(first_movers,X42),growth_rate(efficient_producers,X42))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_43])]) ).
cnf(c_0_51,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_44]) ).
cnf(c_0_52,negated_conjecture,
( appear(efficient_producers,esk1_0) = critical_point(esk1_0)
| subpopulations(first_movers,efficient_producers,esk1_0,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47])]) ).
fof(c_0_53,plain,
! [X28,X29] :
( ~ environment(X28)
| ~ subpopulations(first_movers,efficient_producers,X28,X29)
| subpopulations(efficient_producers,first_movers,X28,X29) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_symmetry_of_subpopulations])]) ).
cnf(c_0_54,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_48]) ).
fof(c_0_55,plain,
! [X48,X49] :
( ~ environment(X48)
| ~ subpopulations(first_movers,efficient_producers,X48,X49)
| ~ decreases(difference(disbanding_rate(first_movers,X49),disbanding_rate(efficient_producers,X49))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_49])]) ).
cnf(c_0_56,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_50]) ).
cnf(c_0_57,hypothesis,
( appear(efficient_producers,esk1_0) = critical_point(esk1_0)
| 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_51,c_0_52]),c_0_30])]) ).
fof(c_0_58,plain,
! [X43,X44,X45,X46] :
( ~ environment(X43)
| ~ subpopulations(X44,X45,X43,X46)
| ~ greater(growth_rate(X45,X46),growth_rate(X44,X46))
| selection_favors(X45,X44,X46) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp1_high_growth_rates])]) ).
cnf(c_0_59,plain,
( subpopulations(efficient_producers,first_movers,X1,X2)
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
fof(c_0_60,plain,
! [X25] :
( ( ~ greater(difference(growth_rate(first_movers,X25),growth_rate(efficient_producers,X25)),zero)
| greater(growth_rate(first_movers,X25),growth_rate(efficient_producers,X25)) )
& ( ~ greater(growth_rate(first_movers,X25),growth_rate(efficient_producers,X25))
| greater(difference(growth_rate(first_movers,X25),growth_rate(efficient_producers,X25)),zero) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_positive_growth_rate_difference])]) ).
cnf(c_0_61,negated_conjecture,
( greater(difference(growth_rate(first_movers,esk2_0),growth_rate(efficient_producers,esk2_0)),zero)
| ~ greater_or_equal(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero)
| ~ in_environment(esk1_0,X1)
| ~ decreases(difference(growth_rate(first_movers,esk2_0),growth_rate(efficient_producers,esk2_0)))
| ~ greater(X1,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_42]),c_0_30])]) ).
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_55]) ).
cnf(c_0_63,hypothesis,
( appear(efficient_producers,esk1_0) = critical_point(esk1_0)
| 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_56,c_0_57]) ).
cnf(c_0_64,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_58]) ).
cnf(c_0_65,negated_conjecture,
( appear(efficient_producers,esk1_0) = critical_point(esk1_0)
| subpopulations(efficient_producers,first_movers,esk1_0,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_52]),c_0_30])]) ).
cnf(c_0_66,negated_conjecture,
~ selection_favors(first_movers,efficient_producers,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_67,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_60]) ).
cnf(c_0_68,negated_conjecture,
( greater(difference(growth_rate(first_movers,esk2_0),growth_rate(efficient_producers,esk2_0)),zero)
| ~ greater_or_equal(difference(growth_rate(first_movers,critical_point(esk1_0)),growth_rate(efficient_producers,critical_point(esk1_0))),zero)
| ~ 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_61,c_0_29]),c_0_47])]) ).
cnf(c_0_69,hypothesis,
( appear(efficient_producers,esk1_0) = critical_point(esk1_0)
| 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]) ).
cnf(c_0_70,negated_conjecture,
( appear(efficient_producers,esk1_0) = critical_point(esk1_0)
| ~ 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_64,c_0_65]),c_0_30])]),c_0_66]) ).
cnf(c_0_71,negated_conjecture,
( greater(growth_rate(first_movers,esk2_0),growth_rate(efficient_producers,esk2_0))
| ~ greater_or_equal(difference(growth_rate(first_movers,critical_point(esk1_0)),growth_rate(efficient_producers,critical_point(esk1_0))),zero)
| ~ decreases(difference(growth_rate(first_movers,esk2_0),growth_rate(efficient_producers,esk2_0))) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_72,negated_conjecture,
( appear(efficient_producers,esk1_0) = critical_point(esk1_0)
| 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_69,c_0_52]),c_0_30])]) ).
cnf(c_0_73,negated_conjecture,
( subpopulations(first_movers,efficient_producers,esk1_0,X1)
| ~ greater_or_equal(critical_point(esk1_0),X1)
| ~ greater_or_equal(X1,critical_point(esk1_0)) ),
inference(spm,[status(thm)],[c_0_39,c_0_36]) ).
cnf(c_0_74,negated_conjecture,
( appear(efficient_producers,esk1_0) = 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(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72]) ).
cnf(c_0_75,negated_conjecture,
( subpopulations(first_movers,efficient_producers,esk1_0,X1)
| ~ greater_or_equal(X1,critical_point(esk1_0))
| ~ greater(critical_point(esk1_0),X1) ),
inference(spm,[status(thm)],[c_0_73,c_0_46]) ).
cnf(c_0_76,negated_conjecture,
( greater_or_equal(esk2_0,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(spm,[status(thm)],[c_0_42,c_0_74]) ).
cnf(c_0_77,negated_conjecture,
( subpopulations(first_movers,efficient_producers,esk1_0,esk2_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_75,c_0_76]),c_0_47])]) ).
cnf(c_0_78,negated_conjecture,
( subpopulations(efficient_producers,first_movers,esk1_0,esk2_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_59,c_0_77]),c_0_30])]) ).
cnf(c_0_79,negated_conjecture,
( ~ greater_or_equal(difference(growth_rate(first_movers,critical_point(esk1_0)),growth_rate(efficient_producers,critical_point(esk1_0))),zero)
| ~ 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_64,c_0_78]),c_0_30])]),c_0_66]) ).
fof(c_0_80,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_81,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]) ).
cnf(c_0_82,hypothesis,
( decreases(difference(founding_rate(first_movers,esk2_0),founding_rate(efficient_producers,esk2_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_51,c_0_77]),c_0_30])]) ).
cnf(c_0_83,negated_conjecture,
( ~ greater_or_equal(difference(growth_rate(first_movers,critical_point(esk1_0)),growth_rate(efficient_producers,critical_point(esk1_0))),zero)
| ~ decreases(difference(growth_rate(first_movers,esk2_0),growth_rate(efficient_producers,esk2_0))) ),
inference(spm,[status(thm)],[c_0_79,c_0_71]) ).
fof(c_0_84,hypothesis,
! [X11,X12,X13] :
( ( ~ greater(growth_rate(efficient_producers,X12),growth_rate(first_movers,X12))
| ~ environment(X11)
| X12 != critical_point(X11) )
& ( ~ subpopulations(first_movers,efficient_producers,X11,X13)
| ~ greater(X13,X12)
| greater(growth_rate(efficient_producers,X13),growth_rate(first_movers,X13))
| ~ environment(X11)
| X12 != critical_point(X11) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_80])])])]) ).
fof(c_0_85,plain,
! [X26,X27] :
( ~ environment(X26)
| ~ subpopulations(first_movers,efficient_producers,X26,X27)
| greater(zero,difference(growth_rate(first_movers,X27),growth_rate(efficient_producers,X27)))
| greater_or_equal(difference(growth_rate(first_movers,X27),growth_rate(efficient_producers,X27)),zero) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_81])]) ).
cnf(c_0_86,hypothesis,
( decreases(difference(disbanding_rate(first_movers,esk2_0),disbanding_rate(efficient_producers,esk2_0)))
| ~ greater_or_equal(difference(growth_rate(first_movers,critical_point(esk1_0)),growth_rate(efficient_producers,critical_point(esk1_0))),zero) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_82]),c_0_83]) ).
cnf(c_0_87,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_84]) ).
fof(c_0_88,plain,
! [X24] :
( ( ~ greater(zero,difference(growth_rate(first_movers,X24),growth_rate(efficient_producers,X24)))
| greater(growth_rate(efficient_producers,X24),growth_rate(first_movers,X24)) )
& ( ~ greater(growth_rate(efficient_producers,X24),growth_rate(first_movers,X24))
| greater(zero,difference(growth_rate(first_movers,X24),growth_rate(efficient_producers,X24))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_negative_growth_rate_difference])]) ).
cnf(c_0_89,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_85]) ).
cnf(c_0_90,hypothesis,
( ~ greater_or_equal(difference(growth_rate(first_movers,critical_point(esk1_0)),growth_rate(efficient_producers,critical_point(esk1_0))),zero)
| ~ subpopulations(first_movers,efficient_producers,X1,esk2_0)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_62,c_0_86]) ).
cnf(c_0_91,hypothesis,
( ~ greater(growth_rate(efficient_producers,critical_point(X1)),growth_rate(first_movers,critical_point(X1)))
| ~ environment(X1) ),
inference(er,[status(thm)],[c_0_87]) ).
cnf(c_0_92,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_88]) ).
cnf(c_0_93,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_89,c_0_36]),c_0_30])]) ).
cnf(c_0_94,negated_conjecture,
~ 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_90,c_0_77]),c_0_30])]) ).
cnf(c_0_95,hypothesis,
( ~ greater(zero,difference(growth_rate(first_movers,critical_point(X1)),growth_rate(efficient_producers,critical_point(X1))))
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_96,negated_conjecture,
greater(zero,difference(growth_rate(first_movers,critical_point(esk1_0)),growth_rate(efficient_producers,critical_point(esk1_0)))),
inference(sr,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_97,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_30])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : MGT034+2 : TPTP v8.1.2. Released v2.0.0.
% 0.07/0.14 % Command : run_E %s %d THM
% 0.15/0.36 % Computer : n004.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 2400
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Tue Oct 3 00:20:45 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.50 Running first-order theorem proving
% 0.22/0.50 Running: /export/starexec/sandbox2/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/sandbox2/tmp/tmp.Ocn7rEa5zY/E---3.1_3519.p
% 0.22/0.55 # Version: 3.1pre001
% 0.22/0.55 # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/0.55 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.55 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/0.55 # Starting new_bool_3 with 300s (1) cores
% 0.22/0.55 # Starting new_bool_1 with 300s (1) cores
% 0.22/0.55 # Starting sh5l with 300s (1) cores
% 0.22/0.55 # new_bool_3 with pid 3599 completed with status 0
% 0.22/0.55 # Result found by new_bool_3
% 0.22/0.55 # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/0.55 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.55 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/0.55 # Starting new_bool_3 with 300s (1) cores
% 0.22/0.55 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.22/0.55 # Search class: FGHSF-FFMS21-SFFFFFNN
% 0.22/0.55 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.55 # Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S5PRR_S0Y with 181s (1) cores
% 0.22/0.55 # G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S5PRR_S0Y with pid 3603 completed with status 0
% 0.22/0.55 # Result found by G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S5PRR_S0Y
% 0.22/0.55 # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/0.55 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.55 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/0.55 # Starting new_bool_3 with 300s (1) cores
% 0.22/0.55 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.22/0.55 # Search class: FGHSF-FFMS21-SFFFFFNN
% 0.22/0.55 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.55 # Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S5PRR_S0Y with 181s (1) cores
% 0.22/0.55 # Preprocessing time : 0.002 s
% 0.22/0.55 # Presaturation interreduction done
% 0.22/0.55
% 0.22/0.55 # Proof found!
% 0.22/0.55 # SZS status Theorem
% 0.22/0.55 # SZS output start CNFRefutation
% See solution above
% 0.22/0.55 # Parsed axioms : 21
% 0.22/0.55 # Removed by relevancy pruning/SinE : 3
% 0.22/0.55 # Initial clauses : 27
% 0.22/0.55 # Removed in clause preprocessing : 0
% 0.22/0.55 # Initial clauses in saturation : 27
% 0.22/0.55 # Processed clauses : 292
% 0.22/0.55 # ...of these trivial : 0
% 0.22/0.55 # ...subsumed : 68
% 0.22/0.55 # ...remaining for further processing : 224
% 0.22/0.55 # Other redundant clauses eliminated : 3
% 0.22/0.55 # Clauses deleted for lack of memory : 0
% 0.22/0.55 # Backward-subsumed : 47
% 0.22/0.55 # Backward-rewritten : 16
% 0.22/0.55 # Generated clauses : 425
% 0.22/0.55 # ...of the previous two non-redundant : 319
% 0.22/0.55 # ...aggressively subsumed : 0
% 0.22/0.55 # Contextual simplify-reflections : 5
% 0.22/0.55 # Paramodulations : 421
% 0.22/0.55 # Factorizations : 0
% 0.22/0.55 # NegExts : 0
% 0.22/0.55 # Equation resolutions : 3
% 0.22/0.55 # Total rewrite steps : 261
% 0.22/0.55 # Propositional unsat checks : 0
% 0.22/0.55 # Propositional check models : 0
% 0.22/0.55 # Propositional check unsatisfiable : 0
% 0.22/0.55 # Propositional clauses : 0
% 0.22/0.55 # Propositional clauses after purity: 0
% 0.22/0.55 # Propositional unsat core size : 0
% 0.22/0.55 # Propositional preprocessing time : 0.000
% 0.22/0.55 # Propositional encoding time : 0.000
% 0.22/0.55 # Propositional solver time : 0.000
% 0.22/0.55 # Success case prop preproc time : 0.000
% 0.22/0.55 # Success case prop encoding time : 0.000
% 0.22/0.55 # Success case prop solver time : 0.000
% 0.22/0.55 # Current number of processed clauses : 130
% 0.22/0.55 # Positive orientable unit clauses : 11
% 0.22/0.55 # Positive unorientable unit clauses: 0
% 0.22/0.55 # Negative unit clauses : 2
% 0.22/0.55 # Non-unit-clauses : 117
% 0.22/0.55 # Current number of unprocessed clauses: 78
% 0.22/0.55 # ...number of literals in the above : 475
% 0.22/0.55 # Current number of archived formulas : 0
% 0.22/0.55 # Current number of archived clauses : 91
% 0.22/0.55 # Clause-clause subsumption calls (NU) : 6263
% 0.22/0.55 # Rec. Clause-clause subsumption calls : 1684
% 0.22/0.55 # Non-unit clause-clause subsumptions : 87
% 0.22/0.55 # Unit Clause-clause subsumption calls : 61
% 0.22/0.55 # Rewrite failures with RHS unbound : 0
% 0.22/0.55 # BW rewrite match attempts : 28
% 0.22/0.55 # BW rewrite match successes : 2
% 0.22/0.55 # Condensation attempts : 0
% 0.22/0.55 # Condensation successes : 0
% 0.22/0.55 # Termbank termtop insertions : 16750
% 0.22/0.55
% 0.22/0.55 # -------------------------------------------------
% 0.22/0.55 # User time : 0.038 s
% 0.22/0.55 # System time : 0.004 s
% 0.22/0.55 # Total time : 0.042 s
% 0.22/0.55 # Maximum resident set size: 1904 pages
% 0.22/0.55
% 0.22/0.55 # -------------------------------------------------
% 0.22/0.55 # User time : 0.039 s
% 0.22/0.55 # System time : 0.006 s
% 0.22/0.55 # Total time : 0.046 s
% 0.22/0.55 # Maximum resident set size: 1704 pages
% 0.22/0.55 % E---3.1 exiting
% 0.22/0.55 % E---3.1 exiting
%------------------------------------------------------------------------------