TSTP Solution File: MGT034+2 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : MGT034+2 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n026.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 : Thu Aug 31 09:07:49 EDT 2023
% Result : Theorem 0.20s 0.62s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 37
% Syntax : Number of formulae : 118 ( 10 unt; 20 typ; 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 types : 2 ( 0 usr)
% Number of type conns : 29 ( 15 >; 14 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-2 aty)
% Number of variables : 130 ( 0 sgn; 78 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
environment: $i > $o ).
tff(decl_23,type,
subpopulations: ( $i * $i * $i * $i ) > $o ).
tff(decl_24,type,
growth_rate: ( $i * $i ) > $i ).
tff(decl_25,type,
greater: ( $i * $i ) > $o ).
tff(decl_26,type,
selection_favors: ( $i * $i * $i ) > $o ).
tff(decl_27,type,
first_movers: $i ).
tff(decl_28,type,
efficient_producers: $i ).
tff(decl_29,type,
disbanding_rate: ( $i * $i ) > $i ).
tff(decl_30,type,
difference: ( $i * $i ) > $i ).
tff(decl_31,type,
decreases: $i > $o ).
tff(decl_32,type,
critical_point: $i > $i ).
tff(decl_33,type,
in_environment: ( $i * $i ) > $o ).
tff(decl_34,type,
appear: ( $i * $i ) > $i ).
tff(decl_35,type,
founding_rate: ( $i * $i ) > $i ).
tff(decl_36,type,
zero: $i ).
tff(decl_37,type,
greater_or_equal: ( $i * $i ) > $o ).
tff(decl_38,type,
start_time: $i > $i ).
tff(decl_39,type,
cardinality_at_time: ( $i * $i ) > $i ).
tff(decl_40,type,
esk1_0: $i ).
tff(decl_41,type,
esk2_0: $i ).
fof(mp_greater_or_equal,axiom,
! [X8,X9] :
( greater_or_equal(X8,X9)
<=> ( greater(X8,X9)
| X8 = X9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.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/sandbox/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/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.p',mp1_high_growth_rates) ).
fof(mp_positive_growth_rate_difference,axiom,
! [X4] :
( greater(difference(growth_rate(first_movers,X4),growth_rate(efficient_producers,X4)),zero)
<=> greater(growth_rate(first_movers,X4),growth_rate(efficient_producers,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_positive_growth_rate_difference) ).
fof(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/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.p',mp_negative_growth_rate_difference) ).
fof(c_0_17,plain,
! [X39,X40] :
( ( ~ greater_or_equal(X39,X40)
| greater(X39,X40)
| X39 = X40 )
& ( ~ greater(X39,X40)
| greater_or_equal(X39,X40) )
& ( X39 != X40
| greater_or_equal(X39,X40) ) ),
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,
! [X17] :
( ~ environment(X17)
| ~ in_environment(X17,critical_point(X17))
| subpopulations(first_movers,efficient_producers,X17,critical_point(X17)) ),
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,
! [X18] :
( ~ environment(X18)
| ~ in_environment(X18,appear(efficient_producers,X18))
| subpopulations(first_movers,efficient_producers,X18,appear(efficient_producers,X18)) ),
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,
! [X46,X47,X48,X49] :
( ~ environment(X46)
| ~ subpopulations(first_movers,efficient_producers,X46,X47)
| ~ subpopulations(first_movers,efficient_producers,X46,X48)
| ~ greater_or_equal(X49,X47)
| ~ greater_or_equal(X48,X49)
| subpopulations(first_movers,efficient_producers,X46,X49) ),
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,
! [X50,X51] :
( ~ environment(X50)
| ~ subpopulations(first_movers,efficient_producers,X50,X51)
| decreases(difference(founding_rate(first_movers,X51),founding_rate(efficient_producers,X51))) ),
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,
! [X20,X21,X22] :
( ~ environment(X20)
| ~ in_environment(X20,X22)
| ~ greater_or_equal(difference(growth_rate(first_movers,X22),growth_rate(efficient_producers,X22)),zero)
| ~ greater_or_equal(X21,appear(efficient_producers,X20))
| ~ greater(X22,X21)
| ~ decreases(difference(growth_rate(first_movers,X21),growth_rate(efficient_producers,X21)))
| greater(difference(growth_rate(first_movers,X21),growth_rate(efficient_producers,X21)),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,
! [X19] :
( ~ decreases(difference(founding_rate(first_movers,X19),founding_rate(efficient_producers,X19)))
| decreases(difference(disbanding_rate(first_movers,X19),disbanding_rate(efficient_producers,X19)))
| decreases(difference(growth_rate(first_movers,X19),growth_rate(efficient_producers,X19))) ),
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,
! [X35,X36] :
( ~ environment(X35)
| ~ subpopulations(first_movers,efficient_producers,X35,X36)
| subpopulations(efficient_producers,first_movers,X35,X36) ),
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,
! [X15,X16] :
( ~ environment(X15)
| ~ subpopulations(first_movers,efficient_producers,X15,X16)
| ~ decreases(difference(disbanding_rate(first_movers,X16),disbanding_rate(efficient_producers,X16))) ),
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,
! [X11,X12,X13,X14] :
( ~ environment(X11)
| ~ subpopulations(X12,X13,X11,X14)
| ~ greater(growth_rate(X13,X14),growth_rate(X12,X14))
| selection_favors(X13,X12,X14) ),
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,
! [X24] :
( ( ~ greater(difference(growth_rate(first_movers,X24),growth_rate(efficient_producers,X24)),zero)
| greater(growth_rate(first_movers,X24),growth_rate(efficient_producers,X24)) )
& ( ~ greater(growth_rate(first_movers,X24),growth_rate(efficient_producers,X24))
| greater(difference(growth_rate(first_movers,X24),growth_rate(efficient_producers,X24)),zero) ) ),
inference(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,
! [X43,X44,X45] :
( ( ~ greater(growth_rate(efficient_producers,X44),growth_rate(first_movers,X44))
| ~ environment(X43)
| X44 != critical_point(X43) )
& ( ~ subpopulations(first_movers,efficient_producers,X43,X45)
| ~ greater(X45,X44)
| greater(growth_rate(efficient_producers,X45),growth_rate(first_movers,X45))
| ~ environment(X43)
| X44 != critical_point(X43) ) ),
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,
! [X41,X42] :
( ~ environment(X41)
| ~ subpopulations(first_movers,efficient_producers,X41,X42)
| greater(zero,difference(growth_rate(first_movers,X42),growth_rate(efficient_producers,X42)))
| greater_or_equal(difference(growth_rate(first_movers,X42),growth_rate(efficient_producers,X42)),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,
! [X23] :
( ( ~ greater(zero,difference(growth_rate(first_movers,X23),growth_rate(efficient_producers,X23)))
| greater(growth_rate(efficient_producers,X23),growth_rate(first_movers,X23)) )
& ( ~ greater(growth_rate(efficient_producers,X23),growth_rate(first_movers,X23))
| greater(zero,difference(growth_rate(first_movers,X23),growth_rate(efficient_producers,X23))) ) ),
inference(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
% 0.00/0.12 % Problem : MGT034+2 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n026.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 : 300
% 0.13/0.34 % DateTime : Mon Aug 28 06:43:04 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 0.20/0.62 % Version : CSE_E---1.5
% 0.20/0.62 % Problem : theBenchmark.p
% 0.20/0.62 % Proof found
% 0.20/0.62 % SZS status Theorem for theBenchmark.p
% 0.20/0.62 % SZS output start Proof
% See solution above
% 0.20/0.63 % Total time : 0.039000 s
% 0.20/0.63 % SZS output end Proof
% 0.20/0.63 % Total time : 0.043000 s
%------------------------------------------------------------------------------