TSTP Solution File: MGT034+2 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : MGT034+2 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n024.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 : 600s
% DateTime : Sun Jul 17 22:09:57 EDT 2022
% Result : Theorem 0.23s 1.42s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 17
% Syntax : Number of formulae : 89 ( 14 unt; 0 def)
% Number of atoms : 294 ( 13 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 348 ( 143 ~; 145 |; 40 &)
% ( 3 <=>; 17 =>; 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 : 131 ( 4 sgn 74 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mp_greater_or_equal,axiom,
! [X8,X9] :
( greater_or_equal(X8,X9)
<=> ( greater(X8,X9)
| X8 = X9 ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mp_greater_or_equal) ).
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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mp_critical_time_points) ).
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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',prove_t3) ).
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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mp_FM_and_EP_when_EP_appears) ).
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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mp_critical_point_means_FM_and_EP) ).
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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',a10) ).
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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mp_FM_and_EP_members_EP_appeared) ).
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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',a12) ).
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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mp_difference_between_founding_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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mp_decreasing_function) ).
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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mp_negative_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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d1) ).
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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mp_symmetry_of_subpopulations) ).
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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mp_positive_growth_rate_difference) ).
fof(c_0_17,plain,
! [X10,X11,X10,X11] :
( ( ~ greater_or_equal(X10,X11)
| greater(X10,X11)
| X10 = X11 )
& ( ~ greater(X10,X11)
| greater_or_equal(X10,X11) )
& ( X10 != X11
| greater_or_equal(X10,X11) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_greater_or_equal])])])])]) ).
fof(c_0_18,plain,
! [X5,X6] :
( ~ environment(X5)
| ~ in_environment(X5,critical_point(X5))
| ~ greater_or_equal(X6,appear(efficient_producers,X5))
| ~ greater(critical_point(X5),X6)
| in_environment(X5,X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_critical_time_points])]) ).
cnf(c_0_19,plain,
( greater_or_equal(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_20,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_21,plain,
! [X2] :
( ~ environment(X2)
| ~ in_environment(X2,appear(efficient_producers,X2))
| subpopulations(first_movers,efficient_producers,X2,appear(efficient_producers,X2)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_FM_and_EP_when_EP_appears])]) ).
cnf(c_0_22,plain,
( in_environment(X1,X2)
| ~ greater(critical_point(X1),X2)
| ~ greater_or_equal(X2,appear(efficient_producers,X1))
| ~ in_environment(X1,critical_point(X1))
| ~ environment(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,plain,
greater_or_equal(X1,X1),
inference(er,[status(thm)],[c_0_19]) ).
fof(c_0_24,plain,
! [X2] :
( ~ environment(X2)
| ~ in_environment(X2,critical_point(X2))
| subpopulations(first_movers,efficient_producers,X2,critical_point(X2)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_critical_point_means_FM_and_EP])]) ).
fof(c_0_25,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_20])])]) ).
fof(c_0_26,hypothesis,
! [X8,X9,X10,X11] :
( ~ environment(X8)
| ~ subpopulations(first_movers,efficient_producers,X8,X9)
| ~ subpopulations(first_movers,efficient_producers,X8,X10)
| ~ greater_or_equal(X11,X9)
| ~ greater_or_equal(X10,X11)
| subpopulations(first_movers,efficient_producers,X8,X11) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[a10])]) ).
cnf(c_0_27,plain,
( subpopulations(first_movers,efficient_producers,X1,appear(efficient_producers,X1))
| ~ in_environment(X1,appear(efficient_producers,X1))
| ~ environment(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,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_22,c_0_23]) ).
fof(c_0_29,plain,
! [X5,X6] :
( ~ environment(X5)
| ~ subpopulations(first_movers,efficient_producers,X5,X6)
| greater_or_equal(X6,appear(efficient_producers,X5)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_FM_and_EP_members_EP_appeared])]) ).
cnf(c_0_30,plain,
( subpopulations(first_movers,efficient_producers,X1,critical_point(X1))
| ~ in_environment(X1,critical_point(X1))
| ~ environment(X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,negated_conjecture,
in_environment(esk1_0,critical_point(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,negated_conjecture,
environment(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_33,hypothesis,
( subpopulations(first_movers,efficient_producers,X1,X2)
| ~ greater_or_equal(X3,X2)
| ~ greater_or_equal(X2,X4)
| ~ subpopulations(first_movers,efficient_producers,X1,X3)
| ~ subpopulations(first_movers,efficient_producers,X1,X4)
| ~ environment(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_34,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_27,c_0_28]) ).
cnf(c_0_35,plain,
( greater_or_equal(X1,appear(efficient_producers,X2))
| ~ subpopulations(first_movers,efficient_producers,X2,X1)
| ~ environment(X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
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_30,c_0_31]),c_0_32])]) ).
cnf(c_0_37,hypothesis,
( subpopulations(first_movers,efficient_producers,X1,X2)
| ~ greater_or_equal(X2,appear(efficient_producers,X1))
| ~ greater_or_equal(X3,X2)
| ~ in_environment(X1,critical_point(X1))
| ~ greater(critical_point(X1),appear(efficient_producers,X1))
| ~ subpopulations(first_movers,efficient_producers,X1,X3)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,negated_conjecture,
greater_or_equal(esk2_0,appear(efficient_producers,esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_39,plain,
( X1 = X2
| greater(X1,X2)
| ~ greater_or_equal(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_40,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_35,c_0_36]),c_0_32])]) ).
cnf(c_0_41,negated_conjecture,
( subpopulations(first_movers,efficient_producers,esk1_0,esk2_0)
| ~ greater_or_equal(X1,esk2_0)
| ~ greater(critical_point(esk1_0),appear(efficient_producers,esk1_0))
| ~ subpopulations(first_movers,efficient_producers,esk1_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_31]),c_0_32])]) ).
cnf(c_0_42,negated_conjecture,
( appear(efficient_producers,esk1_0) = critical_point(esk1_0)
| greater(critical_point(esk1_0),appear(efficient_producers,esk1_0)) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_43,negated_conjecture,
( appear(efficient_producers,esk1_0) = critical_point(esk1_0)
| subpopulations(first_movers,efficient_producers,esk1_0,esk2_0)
| ~ greater_or_equal(X1,esk2_0)
| ~ subpopulations(first_movers,efficient_producers,esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_44,hypothesis,
( subpopulations(first_movers,efficient_producers,esk1_0,X1)
| ~ greater_or_equal(X1,critical_point(esk1_0))
| ~ greater_or_equal(X2,X1)
| ~ subpopulations(first_movers,efficient_producers,esk1_0,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_36]),c_0_32])]) ).
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_43,c_0_36]) ).
cnf(c_0_46,negated_conjecture,
( subpopulations(first_movers,efficient_producers,esk1_0,X1)
| ~ greater_or_equal(X1,critical_point(esk1_0))
| ~ greater_or_equal(critical_point(esk1_0),X1) ),
inference(spm,[status(thm)],[c_0_44,c_0_36]) ).
fof(c_0_47,hypothesis,
! [X5,X6] :
( ~ environment(X5)
| ~ subpopulations(first_movers,efficient_producers,X5,X6)
| decreases(difference(founding_rate(first_movers,X6),founding_rate(efficient_producers,X6))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[a12])]) ).
cnf(c_0_48,negated_conjecture,
( subpopulations(first_movers,efficient_producers,esk1_0,esk2_0)
| ~ greater_or_equal(critical_point(esk1_0),esk2_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_45]),c_0_46]) ).
cnf(c_0_49,plain,
( greater_or_equal(X1,X2)
| ~ greater(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_50,negated_conjecture,
greater(critical_point(esk1_0),esk2_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_51,plain,
! [X5] :
( ~ decreases(difference(founding_rate(first_movers,X5),founding_rate(efficient_producers,X5)))
| decreases(difference(disbanding_rate(first_movers,X5),disbanding_rate(efficient_producers,X5)))
| decreases(difference(growth_rate(first_movers,X5),growth_rate(efficient_producers,X5))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[mp_difference_between_founding_rates])])]) ).
cnf(c_0_52,hypothesis,
( decreases(difference(founding_rate(first_movers,X1),founding_rate(efficient_producers,X1)))
| ~ subpopulations(first_movers,efficient_producers,X2,X1)
| ~ environment(X2) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_53,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_48,c_0_49]),c_0_50])]) ).
fof(c_0_54,plain,
! [X5,X6] :
( ~ environment(X5)
| ~ subpopulations(first_movers,efficient_producers,X5,X6)
| ~ decreases(difference(disbanding_rate(first_movers,X6),disbanding_rate(efficient_producers,X6))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[l3])])]) ).
cnf(c_0_55,plain,
( decreases(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
| decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ~ decreases(difference(founding_rate(first_movers,X1),founding_rate(efficient_producers,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_56,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_52,c_0_53]),c_0_32])]) ).
cnf(c_0_57,plain,
( ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ~ subpopulations(first_movers,efficient_producers,X2,X1)
| ~ environment(X2) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_58,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_55,c_0_56]) ).
cnf(c_0_59,hypothesis,
( subpopulations(first_movers,efficient_producers,esk1_0,X1)
| ~ greater_or_equal(X1,esk2_0)
| ~ greater_or_equal(X2,X1)
| ~ subpopulations(first_movers,efficient_producers,esk1_0,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_53]),c_0_32])]) ).
fof(c_0_60,plain,
! [X6,X7,X8] :
( ~ environment(X6)
| ~ in_environment(X6,X8)
| ~ greater_or_equal(difference(growth_rate(first_movers,X8),growth_rate(efficient_producers,X8)),zero)
| ~ greater_or_equal(X7,appear(efficient_producers,X6))
| ~ greater(X8,X7)
| ~ decreases(difference(growth_rate(first_movers,X7),growth_rate(efficient_producers,X7)))
| greater(difference(growth_rate(first_movers,X7),growth_rate(efficient_producers,X7)),zero) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_decreasing_function])])])]) ).
cnf(c_0_61,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_57,c_0_58]) ).
cnf(c_0_62,negated_conjecture,
( subpopulations(first_movers,efficient_producers,esk1_0,X1)
| ~ greater_or_equal(X1,esk2_0)
| ~ greater_or_equal(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_59,c_0_53]) ).
cnf(c_0_63,plain,
( greater(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero)
| ~ decreases(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
| ~ greater(X2,X1)
| ~ greater_or_equal(X1,appear(efficient_producers,X3))
| ~ greater_or_equal(difference(growth_rate(first_movers,X2),growth_rate(efficient_producers,X2)),zero)
| ~ in_environment(X3,X2)
| ~ environment(X3) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_64,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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_32]),c_0_23])]) ).
cnf(c_0_65,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)
| ~ greater_or_equal(esk2_0,appear(efficient_producers,X2))
| ~ in_environment(X2,X1)
| ~ greater(X1,esk2_0)
| ~ environment(X2) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
fof(c_0_66,plain,
! [X5,X6] :
( ~ environment(X5)
| ~ subpopulations(first_movers,efficient_producers,X5,X6)
| greater(zero,difference(growth_rate(first_movers,X6),growth_rate(efficient_producers,X6)))
| greater_or_equal(difference(growth_rate(first_movers,X6),growth_rate(efficient_producers,X6)),zero) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[mp_relationship_of_growth_rates])])]) ).
cnf(c_0_67,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)
| ~ greater(X1,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_38]),c_0_32])]) ).
cnf(c_0_68,plain,
( greater_or_equal(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero)
| greater(zero,difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
| ~ subpopulations(first_movers,efficient_producers,X2,X1)
| ~ environment(X2) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
fof(c_0_69,plain,
! [X5,X5] :
( ( ~ greater(zero,difference(growth_rate(first_movers,X5),growth_rate(efficient_producers,X5)))
| greater(growth_rate(efficient_producers,X5),growth_rate(first_movers,X5)) )
& ( ~ greater(growth_rate(efficient_producers,X5),growth_rate(first_movers,X5))
| greater(zero,difference(growth_rate(first_movers,X5),growth_rate(efficient_producers,X5))) ) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_negative_growth_rate_difference])])])]) ).
cnf(c_0_70,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) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_31]),c_0_50])]) ).
cnf(c_0_71,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_68,c_0_36]),c_0_32])]) ).
fof(c_0_72,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(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d1])])])])])])]) ).
cnf(c_0_73,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_69]) ).
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(difference(growth_rate(first_movers,esk2_0),growth_rate(efficient_producers,esk2_0)),zero) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
fof(c_0_75,plain,
! [X5,X6,X7,X8] :
( ~ environment(X5)
| ~ subpopulations(X6,X7,X5,X8)
| ~ greater(growth_rate(X7,X8),growth_rate(X6,X8))
| selection_favors(X7,X6,X8) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp1_high_growth_rates])]) ).
fof(c_0_76,plain,
! [X5,X6] :
( ~ environment(X5)
| ~ subpopulations(first_movers,efficient_producers,X5,X6)
| subpopulations(efficient_producers,first_movers,X5,X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_symmetry_of_subpopulations])]) ).
cnf(c_0_77,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_72]) ).
cnf(c_0_78,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_73,c_0_74]) ).
cnf(c_0_79,plain,
( selection_favors(X1,X2,X3)
| ~ greater(growth_rate(X1,X3),growth_rate(X2,X3))
| ~ subpopulations(X2,X1,X4,X3)
| ~ environment(X4) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_80,plain,
( subpopulations(efficient_producers,first_movers,X1,X2)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ environment(X1) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
fof(c_0_81,plain,
! [X5,X5] :
( ( ~ greater(difference(growth_rate(first_movers,X5),growth_rate(efficient_producers,X5)),zero)
| greater(growth_rate(first_movers,X5),growth_rate(efficient_producers,X5)) )
& ( ~ greater(growth_rate(first_movers,X5),growth_rate(efficient_producers,X5))
| greater(difference(growth_rate(first_movers,X5),growth_rate(efficient_producers,X5)),zero) ) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_positive_growth_rate_difference])])])]) ).
cnf(c_0_82,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_77,c_0_78]) ).
cnf(c_0_83,plain,
( selection_favors(first_movers,efficient_producers,X1)
| ~ greater(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1))
| ~ subpopulations(first_movers,efficient_producers,X2,X1)
| ~ environment(X2) ),
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_25]) ).
cnf(c_0_85,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_81]) ).
cnf(c_0_86,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(er,[status(thm)],[c_0_82]),c_0_32])]) ).
cnf(c_0_87,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_83,c_0_53]),c_0_32])]),c_0_84]) ).
cnf(c_0_88,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_87]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : MGT034+2 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.13 % Command : run_ET %s %d
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 9 10:24:34 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.23/1.42 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.23/1.42 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.23/1.42 # Preprocessing time : 0.017 s
% 0.23/1.42
% 0.23/1.42 # Proof found!
% 0.23/1.42 # SZS status Theorem
% 0.23/1.42 # SZS output start CNFRefutation
% See solution above
% 0.23/1.42 # Proof object total steps : 89
% 0.23/1.42 # Proof object clause steps : 54
% 0.23/1.42 # Proof object formula steps : 35
% 0.23/1.42 # Proof object conjectures : 26
% 0.23/1.42 # Proof object clause conjectures : 23
% 0.23/1.42 # Proof object formula conjectures : 3
% 0.23/1.42 # Proof object initial clauses used : 23
% 0.23/1.42 # Proof object initial formulas used : 17
% 0.23/1.42 # Proof object generating inferences : 30
% 0.23/1.42 # Proof object simplifying inferences : 32
% 0.23/1.42 # Training examples: 0 positive, 0 negative
% 0.23/1.42 # Parsed axioms : 21
% 0.23/1.42 # Removed by relevancy pruning/SinE : 3
% 0.23/1.42 # Initial clauses : 27
% 0.23/1.42 # Removed in clause preprocessing : 0
% 0.23/1.42 # Initial clauses in saturation : 27
% 0.23/1.42 # Processed clauses : 569
% 0.23/1.42 # ...of these trivial : 0
% 0.23/1.42 # ...subsumed : 199
% 0.23/1.42 # ...remaining for further processing : 370
% 0.23/1.42 # Other redundant clauses eliminated : 1
% 0.23/1.42 # Clauses deleted for lack of memory : 0
% 0.23/1.42 # Backward-subsumed : 44
% 0.23/1.42 # Backward-rewritten : 35
% 0.23/1.42 # Generated clauses : 1034
% 0.23/1.42 # ...of the previous two non-trivial : 877
% 0.23/1.42 # Contextual simplify-reflections : 330
% 0.23/1.42 # Paramodulations : 1028
% 0.23/1.42 # Factorizations : 0
% 0.23/1.42 # Equation resolutions : 6
% 0.23/1.42 # Current number of processed clauses : 290
% 0.23/1.42 # Positive orientable unit clauses : 16
% 0.23/1.42 # Positive unorientable unit clauses: 0
% 0.23/1.42 # Negative unit clauses : 4
% 0.23/1.42 # Non-unit-clauses : 270
% 0.23/1.42 # Current number of unprocessed clauses: 189
% 0.23/1.42 # ...number of literals in the above : 1459
% 0.23/1.42 # Current number of archived formulas : 0
% 0.23/1.42 # Current number of archived clauses : 79
% 0.23/1.42 # Clause-clause subsumption calls (NU) : 31050
% 0.23/1.42 # Rec. Clause-clause subsumption calls : 6593
% 0.23/1.42 # Non-unit clause-clause subsumptions : 563
% 0.23/1.42 # Unit Clause-clause subsumption calls : 526
% 0.23/1.42 # Rewrite failures with RHS unbound : 0
% 0.23/1.42 # BW rewrite match attempts : 52
% 0.23/1.42 # BW rewrite match successes : 5
% 0.23/1.42 # Condensation attempts : 0
% 0.23/1.42 # Condensation successes : 0
% 0.23/1.42 # Termbank termtop insertions : 35384
% 0.23/1.42
% 0.23/1.42 # -------------------------------------------------
% 0.23/1.42 # User time : 0.098 s
% 0.23/1.42 # System time : 0.004 s
% 0.23/1.42 # Total time : 0.102 s
% 0.23/1.42 # Maximum resident set size: 4072 pages
%------------------------------------------------------------------------------