TSTP Solution File: MGT039+2 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : MGT039+2 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n012.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 09:08:35 EDT 2023
% Result : Theorem 0.21s 0.59s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 40
% Syntax : Number of formulae : 135 ( 21 unt; 22 typ; 0 def)
% Number of atoms : 395 ( 32 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 484 ( 202 ~; 218 |; 42 &)
% ( 1 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 32 ( 18 >; 14 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-4 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-2 aty)
% Number of variables : 162 ( 0 sgn; 72 !; 1 ?; 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,
subpopulation: ( $i * $i * $i ) > $o ).
tff(decl_28,type,
cardinality_at_time: ( $i * $i ) > $i ).
tff(decl_29,type,
zero: $i ).
tff(decl_30,type,
observational_period: $i > $o ).
tff(decl_31,type,
first_movers: $i ).
tff(decl_32,type,
propagation_strategy: $i > $o ).
tff(decl_33,type,
efficient_producers: $i ).
tff(decl_34,type,
in_environment: ( $i * $i ) > $o ).
tff(decl_35,type,
end_time: $i > $i ).
tff(decl_36,type,
slow_change: $i > $o ).
tff(decl_37,type,
critical_point: $i > $i ).
tff(decl_38,type,
start_time: $i > $i ).
tff(decl_39,type,
greater_or_equal: ( $i * $i ) > $o ).
tff(decl_40,type,
appear: ( $i * $i ) > $i ).
tff(decl_41,type,
esk1_1: $i > $i ).
tff(decl_42,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_43,type,
esk3_0: $i ).
fof(mp_greater_or_equal,axiom,
! [X6,X7] :
( greater_or_equal(X6,X7)
<=> ( greater(X6,X7)
| X6 = X7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal) ).
fof(mp_time_of_critical_point,axiom,
! [X1] :
( environment(X1)
=> greater_or_equal(critical_point(X1),start_time(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_time_of_critical_point) ).
fof(prove_t8,conjecture,
! [X5] :
( ( observational_period(X5)
& slow_change(X5) )
=> selection_favors(efficient_producers,first_movers,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t8) ).
fof(mp_greater_transitivity,axiom,
! [X6,X7,X8] :
( ( greater(X6,X7)
& greater(X7,X8) )
=> greater(X6,X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_transitivity) ).
fof(mp4_critical_point,axiom,
! [X5] :
( ( observational_period(X5)
& slow_change(X5) )
=> ! [X1] :
( ( environment(X1)
& in_environment(X5,X1) )
=> ? [X4] :
( in_environment(X1,X4)
& greater(X4,critical_point(X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp4_critical_point) ).
fof(mp_environment_end_point,axiom,
! [X1,X4] :
( ( environment(X1)
& in_environment(X1,X4) )
=> greater_or_equal(end_time(X1),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_environment_end_point) ).
fof(mp_time_in_environment,axiom,
! [X1,X4] :
( ( environment(X1)
& greater_or_equal(X4,start_time(X1))
& greater_or_equal(end_time(X1),X4) )
=> in_environment(X1,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_time_in_environment) ).
fof(mp3_favoured_trategy,axiom,
! [X5] :
( ( observational_period(X5)
& propagation_strategy(first_movers)
& propagation_strategy(efficient_producers)
& ! [X1] :
( ( environment(X1)
& in_environment(X5,X1) )
=> selection_favors(efficient_producers,first_movers,end_time(X1)) ) )
=> selection_favors(efficient_producers,first_movers,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp3_favoured_trategy) ).
fof(mp_critical_point_after_EP,axiom,
! [X1] :
( environment(X1)
=> greater_or_equal(critical_point(X1),appear(efficient_producers,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_critical_point_after_EP) ).
fof(mp_organizational_sets1,axiom,
propagation_strategy(first_movers),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_organizational_sets1) ).
fof(mp_organizational_sets2,axiom,
propagation_strategy(efficient_producers),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_organizational_sets2) ).
fof(t6,hypothesis,
! [X1,X4] :
( ( environment(X1)
& in_environment(X1,X4)
& greater_or_equal(X4,appear(efficient_producers,X1)) )
=> greater(cardinality_at_time(efficient_producers,X4),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6) ).
fof(d1,hypothesis,
! [X1,X9] :
( ( environment(X1)
& X9 = critical_point(X1) )
=> ( ~ greater(growth_rate(efficient_producers,X9),growth_rate(first_movers,X9))
& ! [X4] :
( ( subpopulations(first_movers,efficient_producers,X1,X4)
& greater(X4,X9) )
=> greater(growth_rate(efficient_producers,X4),growth_rate(first_movers,X4)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1) ).
fof(mp2_favour_members,axiom,
! [X1,X2,X3,X4] :
( ( environment(X1)
& subpopulation(X2,X1,X4)
& subpopulation(X3,X1,X4)
& greater(cardinality_at_time(X2,X4),zero)
& cardinality_at_time(X3,X4) = zero )
=> selection_favors(X2,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp2_favour_members) ).
fof(mp_subpopulations,axiom,
! [X1,X4] :
( ( environment(X1)
& in_environment(X1,X4) )
=> ( subpopulation(first_movers,X1,X4)
& subpopulation(efficient_producers,X1,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_subpopulations) ).
fof(mp_contains_FM_and_EP,axiom,
! [X1,X4] :
( ( environment(X1)
& in_environment(X1,X4)
& greater(cardinality_at_time(first_movers,X4),zero)
& greater(cardinality_at_time(efficient_producers,X4),zero) )
=> subpopulations(first_movers,efficient_producers,X1,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_contains_FM_and_EP) ).
fof(mp_first_movers_exist,axiom,
! [X1,X4] :
( ( environment(X1)
& in_environment(X1,X4) )
=> greater_or_equal(cardinality_at_time(first_movers,X4),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_first_movers_exist) ).
fof(mp1_high_growth_rates,axiom,
! [X1,X2,X3,X4] :
( ( environment(X1)
& subpopulations(X2,X3,X1,X4)
& greater(growth_rate(X3,X4),growth_rate(X2,X4)) )
=> selection_favors(X3,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp1_high_growth_rates) ).
fof(c_0_18,plain,
! [X40,X41] :
( ( ~ greater_or_equal(X40,X41)
| greater(X40,X41)
| X40 = X41 )
& ( ~ greater(X40,X41)
| greater_or_equal(X40,X41) )
& ( X40 != X41
| greater_or_equal(X40,X41) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_greater_or_equal])])]) ).
fof(c_0_19,plain,
! [X34] :
( ~ environment(X34)
| greater_or_equal(critical_point(X34),start_time(X34)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_time_of_critical_point])]) ).
fof(c_0_20,negated_conjecture,
~ ! [X5] :
( ( observational_period(X5)
& slow_change(X5) )
=> selection_favors(efficient_producers,first_movers,X5) ),
inference(assume_negation,[status(cth)],[prove_t8]) ).
fof(c_0_21,plain,
! [X35,X36,X37] :
( ~ greater(X35,X36)
| ~ greater(X36,X37)
| greater(X35,X37) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_greater_transitivity])]) ).
cnf(c_0_22,plain,
( greater(X1,X2)
| X1 = X2
| ~ greater_or_equal(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,plain,
( greater_or_equal(critical_point(X1),start_time(X1))
| ~ environment(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_24,plain,
! [X20,X21] :
( ( in_environment(X21,esk2_2(X20,X21))
| ~ environment(X21)
| ~ in_environment(X20,X21)
| ~ observational_period(X20)
| ~ slow_change(X20) )
& ( greater(esk2_2(X20,X21),critical_point(X21))
| ~ environment(X21)
| ~ in_environment(X20,X21)
| ~ observational_period(X20)
| ~ slow_change(X20) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp4_critical_point])])])])]) ).
fof(c_0_25,negated_conjecture,
( observational_period(esk3_0)
& slow_change(esk3_0)
& ~ selection_favors(efficient_producers,first_movers,esk3_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])]) ).
cnf(c_0_26,plain,
( greater(X1,X3)
| ~ greater(X1,X2)
| ~ greater(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,plain,
( start_time(X1) = critical_point(X1)
| greater(critical_point(X1),start_time(X1))
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
fof(c_0_28,plain,
! [X25,X26] :
( ~ environment(X25)
| ~ in_environment(X25,X26)
| greater_or_equal(end_time(X25),X26) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_environment_end_point])]) ).
cnf(c_0_29,plain,
( in_environment(X1,esk2_2(X2,X1))
| ~ environment(X1)
| ~ in_environment(X2,X1)
| ~ observational_period(X2)
| ~ slow_change(X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,negated_conjecture,
slow_change(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,negated_conjecture,
observational_period(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,plain,
( start_time(X1) = critical_point(X1)
| greater(X2,start_time(X1))
| ~ greater(X2,critical_point(X1))
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,plain,
( greater(esk2_2(X1,X2),critical_point(X2))
| ~ environment(X2)
| ~ in_environment(X1,X2)
| ~ observational_period(X1)
| ~ slow_change(X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_34,plain,
( greater_or_equal(end_time(X1),X2)
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_35,negated_conjecture,
( in_environment(X1,esk2_2(esk3_0,X1))
| ~ in_environment(esk3_0,X1)
| ~ environment(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]) ).
fof(c_0_36,plain,
! [X23,X24] :
( ~ environment(X23)
| ~ greater_or_equal(X24,start_time(X23))
| ~ greater_or_equal(end_time(X23),X24)
| in_environment(X23,X24) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_time_in_environment])]) ).
cnf(c_0_37,plain,
( start_time(X1) = critical_point(X1)
| greater(X2,start_time(X1))
| ~ greater(X3,critical_point(X1))
| ~ greater(X2,X3)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_32]) ).
cnf(c_0_38,negated_conjecture,
( greater(esk2_2(esk3_0,X1),critical_point(X1))
| ~ in_environment(esk3_0,X1)
| ~ environment(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_30]),c_0_31])]) ).
cnf(c_0_39,negated_conjecture,
( greater_or_equal(end_time(X1),esk2_2(esk3_0,X1))
| ~ in_environment(esk3_0,X1)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_40,plain,
( in_environment(X1,X2)
| ~ environment(X1)
| ~ greater_or_equal(X2,start_time(X1))
| ~ greater_or_equal(end_time(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_41,plain,
( greater_or_equal(X1,X2)
| ~ greater(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_42,plain,
( greater_or_equal(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_43,plain,
! [X18] :
( ( environment(esk1_1(X18))
| ~ observational_period(X18)
| ~ propagation_strategy(first_movers)
| ~ propagation_strategy(efficient_producers)
| selection_favors(efficient_producers,first_movers,X18) )
& ( in_environment(X18,esk1_1(X18))
| ~ observational_period(X18)
| ~ propagation_strategy(first_movers)
| ~ propagation_strategy(efficient_producers)
| selection_favors(efficient_producers,first_movers,X18) )
& ( ~ selection_favors(efficient_producers,first_movers,end_time(esk1_1(X18)))
| ~ observational_period(X18)
| ~ propagation_strategy(first_movers)
| ~ propagation_strategy(efficient_producers)
| selection_favors(efficient_producers,first_movers,X18) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp3_favoured_trategy])])])]) ).
fof(c_0_44,plain,
! [X33] :
( ~ environment(X33)
| greater_or_equal(critical_point(X33),appear(efficient_producers,X33)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_critical_point_after_EP])]) ).
cnf(c_0_45,negated_conjecture,
( start_time(X1) = critical_point(X1)
| greater(X2,start_time(X1))
| ~ in_environment(esk3_0,X1)
| ~ greater(X2,esk2_2(esk3_0,X1))
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_46,negated_conjecture,
( esk2_2(esk3_0,X1) = end_time(X1)
| greater(end_time(X1),esk2_2(esk3_0,X1))
| ~ in_environment(esk3_0,X1)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_39]) ).
cnf(c_0_47,plain,
( in_environment(X1,X2)
| ~ greater_or_equal(end_time(X1),X2)
| ~ greater(X2,start_time(X1))
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_48,plain,
greater_or_equal(X1,X1),
inference(er,[status(thm)],[c_0_42]) ).
cnf(c_0_49,plain,
( in_environment(X1,esk1_1(X1))
| selection_favors(efficient_producers,first_movers,X1)
| ~ observational_period(X1)
| ~ propagation_strategy(first_movers)
| ~ propagation_strategy(efficient_producers) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_50,plain,
propagation_strategy(first_movers),
inference(split_conjunct,[status(thm)],[mp_organizational_sets1]) ).
cnf(c_0_51,plain,
propagation_strategy(efficient_producers),
inference(split_conjunct,[status(thm)],[mp_organizational_sets2]) ).
cnf(c_0_52,plain,
( environment(esk1_1(X1))
| selection_favors(efficient_producers,first_movers,X1)
| ~ observational_period(X1)
| ~ propagation_strategy(first_movers)
| ~ propagation_strategy(efficient_producers) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_53,negated_conjecture,
( greater(X1,critical_point(X2))
| ~ in_environment(esk3_0,X2)
| ~ greater(X1,esk2_2(esk3_0,X2))
| ~ environment(X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_38]) ).
fof(c_0_54,hypothesis,
! [X45,X46] :
( ~ environment(X45)
| ~ in_environment(X45,X46)
| ~ greater_or_equal(X46,appear(efficient_producers,X45))
| greater(cardinality_at_time(efficient_producers,X46),zero) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6])]) ).
cnf(c_0_55,plain,
( greater_or_equal(critical_point(X1),appear(efficient_producers,X1))
| ~ environment(X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_56,negated_conjecture,
( esk2_2(esk3_0,X1) = end_time(X1)
| start_time(X1) = critical_point(X1)
| greater(end_time(X1),start_time(X1))
| ~ in_environment(esk3_0,X1)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_57,plain,
( in_environment(X1,end_time(X1))
| ~ greater(end_time(X1),start_time(X1))
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_58,plain,
( in_environment(X1,esk1_1(X1))
| selection_favors(efficient_producers,first_movers,X1)
| ~ observational_period(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50]),c_0_51])]) ).
cnf(c_0_59,negated_conjecture,
~ selection_favors(efficient_producers,first_movers,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_60,plain,
( selection_favors(efficient_producers,first_movers,X1)
| environment(esk1_1(X1))
| ~ observational_period(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_50]),c_0_51])]) ).
cnf(c_0_61,negated_conjecture,
( esk2_2(esk3_0,X1) = end_time(X1)
| greater(end_time(X1),critical_point(X1))
| ~ in_environment(esk3_0,X1)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_53,c_0_46]) ).
fof(c_0_62,hypothesis,
! [X1,X9] :
( ( environment(X1)
& X9 = critical_point(X1) )
=> ( ~ greater(growth_rate(efficient_producers,X9),growth_rate(first_movers,X9))
& ! [X4] :
( ( subpopulations(first_movers,efficient_producers,X1,X4)
& greater(X4,X9) )
=> greater(growth_rate(efficient_producers,X4),growth_rate(first_movers,X4)) ) ) ),
inference(fof_simplification,[status(thm)],[d1]) ).
cnf(c_0_63,hypothesis,
( greater(cardinality_at_time(efficient_producers,X2),zero)
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ greater_or_equal(X2,appear(efficient_producers,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_64,plain,
( appear(efficient_producers,X1) = critical_point(X1)
| greater(critical_point(X1),appear(efficient_producers,X1))
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_55]) ).
cnf(c_0_65,negated_conjecture,
( start_time(X1) = critical_point(X1)
| in_environment(X1,end_time(X1))
| ~ in_environment(esk3_0,X1)
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_56]),c_0_57]) ).
cnf(c_0_66,negated_conjecture,
in_environment(esk3_0,esk1_1(esk3_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_31]),c_0_59]) ).
cnf(c_0_67,negated_conjecture,
environment(esk1_1(esk3_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_31]),c_0_59]) ).
cnf(c_0_68,negated_conjecture,
( greater(end_time(X1),critical_point(X1))
| ~ in_environment(esk3_0,X1)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_61]) ).
fof(c_0_69,hypothesis,
! [X42,X43,X44] :
( ( ~ greater(growth_rate(efficient_producers,X43),growth_rate(first_movers,X43))
| ~ environment(X42)
| X43 != critical_point(X42) )
& ( ~ subpopulations(first_movers,efficient_producers,X42,X44)
| ~ greater(X44,X43)
| greater(growth_rate(efficient_producers,X44),growth_rate(first_movers,X44))
| ~ environment(X42)
| X43 != critical_point(X42) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_62])])])]) ).
fof(c_0_70,plain,
! [X14,X15,X16,X17] :
( ~ environment(X14)
| ~ subpopulation(X15,X14,X17)
| ~ subpopulation(X16,X14,X17)
| ~ greater(cardinality_at_time(X15,X17),zero)
| cardinality_at_time(X16,X17) != zero
| selection_favors(X15,X16,X17) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp2_favour_members])]) ).
fof(c_0_71,plain,
! [X31,X32] :
( ( subpopulation(first_movers,X31,X32)
| ~ environment(X31)
| ~ in_environment(X31,X32) )
& ( subpopulation(efficient_producers,X31,X32)
| ~ environment(X31)
| ~ in_environment(X31,X32) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_subpopulations])])]) ).
cnf(c_0_72,hypothesis,
( greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ in_environment(X2,X1)
| ~ greater(X1,appear(efficient_producers,X2))
| ~ environment(X2) ),
inference(spm,[status(thm)],[c_0_63,c_0_41]) ).
cnf(c_0_73,plain,
( appear(efficient_producers,X1) = critical_point(X1)
| greater(X2,appear(efficient_producers,X1))
| ~ greater(X2,critical_point(X1))
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_64]) ).
cnf(c_0_74,negated_conjecture,
( start_time(esk1_1(esk3_0)) = critical_point(esk1_1(esk3_0))
| in_environment(esk1_1(esk3_0),end_time(esk1_1(esk3_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67])]) ).
cnf(c_0_75,negated_conjecture,
greater(end_time(esk1_1(esk3_0)),critical_point(esk1_1(esk3_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_66]),c_0_67])]) ).
cnf(c_0_76,plain,
( in_environment(X1,critical_point(X1))
| ~ greater_or_equal(end_time(X1),critical_point(X1))
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_23]) ).
cnf(c_0_77,hypothesis,
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ greater(X2,X3)
| ~ environment(X1)
| X3 != critical_point(X1) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
fof(c_0_78,plain,
! [X27,X28] :
( ~ environment(X27)
| ~ in_environment(X27,X28)
| ~ greater(cardinality_at_time(first_movers,X28),zero)
| ~ greater(cardinality_at_time(efficient_producers,X28),zero)
| subpopulations(first_movers,efficient_producers,X27,X28) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_contains_FM_and_EP])]) ).
cnf(c_0_79,plain,
( selection_favors(X2,X4,X3)
| ~ environment(X1)
| ~ subpopulation(X2,X1,X3)
| ~ subpopulation(X4,X1,X3)
| ~ greater(cardinality_at_time(X2,X3),zero)
| cardinality_at_time(X4,X3) != zero ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_80,plain,
( subpopulation(first_movers,X1,X2)
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_81,plain,
( selection_favors(efficient_producers,first_movers,X1)
| ~ selection_favors(efficient_producers,first_movers,end_time(esk1_1(X1)))
| ~ observational_period(X1)
| ~ propagation_strategy(first_movers)
| ~ propagation_strategy(efficient_producers) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_82,hypothesis,
( appear(efficient_producers,X1) = critical_point(X1)
| greater(cardinality_at_time(efficient_producers,X2),zero)
| ~ in_environment(X1,X2)
| ~ greater(X2,critical_point(X1))
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_83,negated_conjecture,
in_environment(esk1_1(esk3_0),end_time(esk1_1(esk3_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_74]),c_0_75]),c_0_67])]) ).
cnf(c_0_84,plain,
( in_environment(X1,critical_point(X1))
| ~ greater(end_time(X1),critical_point(X1))
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_76,c_0_41]) ).
cnf(c_0_85,hypothesis,
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ greater(X1,critical_point(X2))
| ~ subpopulations(first_movers,efficient_producers,X2,X1)
| ~ environment(X2) ),
inference(er,[status(thm)],[c_0_77]) ).
cnf(c_0_86,plain,
( subpopulations(first_movers,efficient_producers,X1,X2)
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ greater(cardinality_at_time(first_movers,X2),zero)
| ~ greater(cardinality_at_time(efficient_producers,X2),zero) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
fof(c_0_87,plain,
! [X29,X30] :
( ~ environment(X29)
| ~ in_environment(X29,X30)
| greater_or_equal(cardinality_at_time(first_movers,X30),zero) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_first_movers_exist])]) ).
cnf(c_0_88,plain,
( selection_favors(X1,first_movers,X2)
| cardinality_at_time(first_movers,X2) != zero
| ~ in_environment(X3,X2)
| ~ subpopulation(X1,X3,X2)
| ~ greater(cardinality_at_time(X1,X2),zero)
| ~ environment(X3) ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_89,plain,
( subpopulation(efficient_producers,X1,X2)
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_90,plain,
( selection_favors(efficient_producers,first_movers,X1)
| ~ observational_period(X1)
| ~ selection_favors(efficient_producers,first_movers,end_time(esk1_1(X1))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_50]),c_0_51])]) ).
cnf(c_0_91,negated_conjecture,
( appear(efficient_producers,esk1_1(esk3_0)) = critical_point(esk1_1(esk3_0))
| greater(cardinality_at_time(efficient_producers,end_time(esk1_1(esk3_0))),zero) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_75]),c_0_83]),c_0_67])]) ).
cnf(c_0_92,negated_conjecture,
in_environment(esk1_1(esk3_0),critical_point(esk1_1(esk3_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_75]),c_0_67])]) ).
cnf(c_0_93,hypothesis,
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ in_environment(X2,X1)
| ~ greater(cardinality_at_time(first_movers,X1),zero)
| ~ greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ greater(X1,critical_point(X2))
| ~ environment(X2) ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_94,plain,
( greater_or_equal(cardinality_at_time(first_movers,X2),zero)
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_95,plain,
( selection_favors(efficient_producers,first_movers,X1)
| cardinality_at_time(first_movers,X1) != zero
| ~ in_environment(X2,X1)
| ~ greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ environment(X2) ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_96,negated_conjecture,
~ selection_favors(efficient_producers,first_movers,end_time(esk1_1(esk3_0))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_31]),c_0_59]) ).
cnf(c_0_97,hypothesis,
( greater(cardinality_at_time(efficient_producers,end_time(esk1_1(esk3_0))),zero)
| greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ greater_or_equal(X1,critical_point(esk1_1(esk3_0)))
| ~ in_environment(esk1_1(esk3_0),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_91]),c_0_67])]) ).
cnf(c_0_98,negated_conjecture,
greater_or_equal(end_time(esk1_1(esk3_0)),critical_point(esk1_1(esk3_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_92]),c_0_67])]) ).
cnf(c_0_99,hypothesis,
( greater(growth_rate(efficient_producers,end_time(esk1_1(esk3_0))),growth_rate(first_movers,end_time(esk1_1(esk3_0))))
| ~ in_environment(esk1_1(esk3_0),end_time(esk1_1(esk3_0)))
| ~ greater(cardinality_at_time(first_movers,end_time(esk1_1(esk3_0))),zero)
| ~ greater(cardinality_at_time(efficient_producers,end_time(esk1_1(esk3_0))),zero) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_75]),c_0_67])]) ).
cnf(c_0_100,negated_conjecture,
greater_or_equal(cardinality_at_time(first_movers,end_time(esk1_1(esk3_0))),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_83]),c_0_67])]) ).
cnf(c_0_101,negated_conjecture,
( cardinality_at_time(first_movers,end_time(esk1_1(esk3_0))) != zero
| ~ greater(cardinality_at_time(efficient_producers,end_time(esk1_1(esk3_0))),zero) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_83]),c_0_67])]),c_0_96]) ).
cnf(c_0_102,negated_conjecture,
greater(cardinality_at_time(efficient_producers,end_time(esk1_1(esk3_0))),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_83])]) ).
fof(c_0_103,plain,
! [X10,X11,X12,X13] :
( ~ environment(X10)
| ~ subpopulations(X11,X12,X10,X13)
| ~ greater(growth_rate(X12,X13),growth_rate(X11,X13))
| selection_favors(X12,X11,X13) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp1_high_growth_rates])]) ).
cnf(c_0_104,hypothesis,
( greater(growth_rate(efficient_producers,end_time(esk1_1(esk3_0))),growth_rate(first_movers,end_time(esk1_1(esk3_0))))
| ~ greater(cardinality_at_time(first_movers,end_time(esk1_1(esk3_0))),zero)
| ~ greater(cardinality_at_time(efficient_producers,end_time(esk1_1(esk3_0))),zero) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_99,c_0_83])]) ).
cnf(c_0_105,negated_conjecture,
( cardinality_at_time(first_movers,end_time(esk1_1(esk3_0))) = zero
| greater(cardinality_at_time(first_movers,end_time(esk1_1(esk3_0))),zero) ),
inference(spm,[status(thm)],[c_0_22,c_0_100]) ).
cnf(c_0_106,negated_conjecture,
cardinality_at_time(first_movers,end_time(esk1_1(esk3_0))) != zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_101,c_0_102])]) ).
cnf(c_0_107,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_103]) ).
cnf(c_0_108,hypothesis,
( greater(growth_rate(efficient_producers,end_time(esk1_1(esk3_0))),growth_rate(first_movers,end_time(esk1_1(esk3_0))))
| ~ greater(cardinality_at_time(first_movers,end_time(esk1_1(esk3_0))),zero) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_104,c_0_102])]) ).
cnf(c_0_109,negated_conjecture,
greater(cardinality_at_time(first_movers,end_time(esk1_1(esk3_0))),zero),
inference(sr,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_110,plain,
( selection_favors(efficient_producers,first_movers,X1)
| ~ in_environment(X2,X1)
| ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ greater(cardinality_at_time(first_movers,X1),zero)
| ~ greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ environment(X2) ),
inference(spm,[status(thm)],[c_0_107,c_0_86]) ).
cnf(c_0_111,hypothesis,
greater(growth_rate(efficient_producers,end_time(esk1_1(esk3_0))),growth_rate(first_movers,end_time(esk1_1(esk3_0)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_108,c_0_109])]) ).
cnf(c_0_112,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_83]),c_0_67])]),c_0_96]),c_0_111]),c_0_109]),c_0_102])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT039+2 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n012.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 28 06:30:40 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.56 start to proof: theBenchmark
% 0.21/0.59 % Version : CSE_E---1.5
% 0.21/0.59 % Problem : theBenchmark.p
% 0.21/0.59 % Proof found
% 0.21/0.59 % SZS status Theorem for theBenchmark.p
% 0.21/0.59 % SZS output start Proof
% See solution above
% 0.21/0.60 % Total time : 0.018000 s
% 0.21/0.60 % SZS output end Proof
% 0.21/0.60 % Total time : 0.022000 s
%------------------------------------------------------------------------------