%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : MGT025+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:26:05 PM UTC 2026
% Result : Theorem 0.14s 0.43s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 89 ( 15 unt; 0 def)
% Number of atoms : 351 ( 42 equ)
% Maximal formula atoms : 40 ( 3 avg)
% Number of connectives : 415 ( 153 ~; 206 |; 44 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 98 ( 4 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_l7,conjecture,
! [X1,X3] :
( ( constant(number_of_organizations(X1,X3))
& subpopulations(first_movers,efficient_producers,X1,X3)
& environment(X1) )
=> ( ( greater(zero,growth_rate(first_movers,X3))
& greater(growth_rate(efficient_producers,X3),zero) )
| ( greater(zero,growth_rate(efficient_producers,X3))
& greater(growth_rate(first_movers,X3),zero) )
| ( growth_rate(efficient_producers,X3) = zero
& growth_rate(first_movers,X3) = zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l7) ).
fof(mp_only_members,axiom,
! [X1,X2,X3] :
( ( ( greater(cardinality_at_time(X2,X3),zero)
=> ( X2 = first_movers
| X2 = efficient_producers ) )
& subpopulation(X2,X1,X3)
& environment(X1) )
=> number_of_organizations(X1,X3) = sum(cardinality_at_time(first_movers,X3),cardinality_at_time(efficient_producers,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_only_members) ).
fof(mp_time_point_occur,axiom,
! [X1,X3] :
( ( subpopulations(first_movers,efficient_producers,X1,X3)
& environment(X1) )
=> in_environment(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_time_point_occur) ).
fof(mp_subpopulations,axiom,
! [X1,X3] :
( ( in_environment(X1,X3)
& environment(X1) )
=> ( subpopulation(efficient_producers,X1,X3)
& subpopulation(first_movers,X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_subpopulations) ).
fof(mp_non_zero_producers,axiom,
! [X1,X3] :
( ( subpopulations(first_movers,efficient_producers,X1,X3)
& environment(X1) )
=> ( greater(cardinality_at_time(efficient_producers,X3),zero)
& greater(cardinality_at_time(first_movers,X3),zero) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_non_zero_producers) ).
fof(mp_growth_rate,axiom,
! [X2,X1,X3] :
( ( greater(cardinality_at_time(X2,X3),zero)
& subpopulation(X2,X1,X3)
& in_environment(X1,X3)
& environment(X1) )
=> ( ( decreases(cardinality_at_time(X2,X3))
=> greater(zero,growth_rate(X2,X3)) )
& ( increases(cardinality_at_time(X2,X3))
=> greater(growth_rate(X2,X3),zero) )
& ( constant(cardinality_at_time(X2,X3))
=> growth_rate(X2,X3) = zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_growth_rate) ).
fof(mp_abc_sum_increase,axiom,
! [X4,X5,X6] :
( ( constant(X4)
& X4 = sum(X5,X6) )
=> ( ( increases(X6)
& decreases(X5) )
| ( decreases(X6)
& increases(X5) )
| ( constant(X6)
& constant(X5) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_abc_sum_increase) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X3] :
( ( constant(number_of_organizations(X1,X3))
& subpopulations(first_movers,efficient_producers,X1,X3)
& environment(X1) )
=> ( ( greater(zero,growth_rate(first_movers,X3))
& greater(growth_rate(efficient_producers,X3),zero) )
| ( greater(zero,growth_rate(efficient_producers,X3))
& greater(growth_rate(first_movers,X3),zero) )
| ( growth_rate(efficient_producers,X3) = zero
& growth_rate(first_movers,X3) = zero ) ) ),
inference(assume_negation,[status(cth)],[prove_l7]) ).
fof(c_0_8,plain,
! [X22,X23,X24] :
( ( number_of_organizations(X22,X24) = sum(cardinality_at_time(first_movers,X24),cardinality_at_time(efficient_producers,X24))
| ~ subpopulation(X23,X22,X24)
| ~ environment(X22)
| X23 != first_movers )
& ( number_of_organizations(X22,X24) = sum(cardinality_at_time(first_movers,X24),cardinality_at_time(efficient_producers,X24))
| ~ subpopulation(X23,X22,X24)
| ~ environment(X22)
| X23 != efficient_producers )
& ( number_of_organizations(X22,X24) = sum(cardinality_at_time(first_movers,X24),cardinality_at_time(efficient_producers,X24))
| ~ subpopulation(X23,X22,X24)
| ~ environment(X22)
| greater(cardinality_at_time(X23,X24),zero) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_only_members])])])]) ).
fof(c_0_9,plain,
! [X25,X26] :
( in_environment(X25,X26)
| ~ subpopulations(first_movers,efficient_producers,X25,X26)
| ~ environment(X25) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_time_point_occur])])]) ).
fof(c_0_10,negated_conjecture,
( ( ~ greater(zero,growth_rate(first_movers,esk2_0))
| ~ greater(growth_rate(efficient_producers,esk2_0),zero) )
& ( ~ greater(zero,growth_rate(efficient_producers,esk2_0))
| ~ greater(growth_rate(first_movers,esk2_0),zero) )
& ( growth_rate(efficient_producers,esk2_0) != zero
| growth_rate(first_movers,esk2_0) != zero )
& constant(number_of_organizations(esk1_0,esk2_0))
& subpopulations(first_movers,efficient_producers,esk1_0,esk2_0)
& environment(esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
cnf(c_0_11,plain,
( ~ subpopulation(X1,X2,X3)
| ~ environment(X2)
| X1 != efficient_producers
| number_of_organizations(X2,X3) = sum(cardinality_at_time(first_movers,X3),cardinality_at_time(efficient_producers,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,plain,
! [X14,X15] :
( ( ~ in_environment(X14,X15)
| ~ environment(X14)
| subpopulation(efficient_producers,X14,X15) )
& ( ~ in_environment(X14,X15)
| ~ environment(X14)
| subpopulation(first_movers,X14,X15) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_subpopulations])])])]) ).
cnf(c_0_13,plain,
( ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ environment(X1)
| in_environment(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,negated_conjecture,
subpopulations(first_movers,efficient_producers,esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
environment(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_16,plain,
! [X12,X13] :
( ( ~ subpopulations(first_movers,efficient_producers,X12,X13)
| ~ environment(X12)
| greater(cardinality_at_time(efficient_producers,X13),zero) )
& ( ~ subpopulations(first_movers,efficient_producers,X12,X13)
| ~ environment(X12)
| greater(cardinality_at_time(first_movers,X13),zero) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_non_zero_producers])])])]) ).
cnf(c_0_17,plain,
( ~ environment(X1)
| ~ subpopulation(efficient_producers,X1,X2)
| number_of_organizations(X1,X2) = sum(cardinality_at_time(first_movers,X2),cardinality_at_time(efficient_producers,X2)) ),
inference(er,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
( ~ in_environment(X1,X2)
| ~ environment(X1)
| subpopulation(efficient_producers,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,negated_conjecture,
in_environment(esk1_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]) ).
fof(c_0_20,plain,
! [X16,X17,X18] :
( ( ~ greater(cardinality_at_time(X16,X18),zero)
| ~ subpopulation(X16,X17,X18)
| ~ in_environment(X17,X18)
| ~ environment(X17)
| greater(zero,growth_rate(X16,X18))
| ~ decreases(cardinality_at_time(X16,X18)) )
& ( ~ greater(cardinality_at_time(X16,X18),zero)
| ~ subpopulation(X16,X17,X18)
| ~ in_environment(X17,X18)
| ~ environment(X17)
| greater(growth_rate(X16,X18),zero)
| ~ increases(cardinality_at_time(X16,X18)) )
& ( ~ greater(cardinality_at_time(X16,X18),zero)
| ~ subpopulation(X16,X17,X18)
| ~ in_environment(X17,X18)
| ~ environment(X17)
| growth_rate(X16,X18) = zero
| ~ constant(cardinality_at_time(X16,X18)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_growth_rate])])])]) ).
cnf(c_0_21,plain,
( ~ subpopulations(first_movers,efficient_producers,X2,X1)
| ~ environment(X2)
| greater(cardinality_at_time(efficient_producers,X1),zero) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,negated_conjecture,
constant(number_of_organizations(esk1_0,esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_23,plain,
( ~ environment(X3)
| ~ environment(X1)
| ~ subpopulation(efficient_producers,X3,X2)
| ~ subpopulation(efficient_producers,X1,X2)
| number_of_organizations(X1,X2) = number_of_organizations(X3,X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_17]) ).
cnf(c_0_24,negated_conjecture,
subpopulation(efficient_producers,esk1_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_15])]) ).
cnf(c_0_25,plain,
( ~ in_environment(X1,X2)
| ~ environment(X1)
| subpopulation(first_movers,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_26,plain,
( ~ subpopulations(first_movers,efficient_producers,X2,X1)
| ~ environment(X2)
| greater(cardinality_at_time(first_movers,X1),zero) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_27,plain,
( ~ greater(cardinality_at_time(X1,X2),zero)
| ~ subpopulation(X1,X3,X2)
| ~ in_environment(X3,X2)
| ~ environment(X3)
| ~ constant(cardinality_at_time(X1,X2))
| growth_rate(X1,X2) = zero ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,negated_conjecture,
greater(cardinality_at_time(efficient_producers,esk2_0),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_14]),c_0_15])]) ).
fof(c_0_29,plain,
! [X19,X20,X21] :
( ( ~ constant(X19)
| X19 != sum(X20,X21)
| constant(X21)
| decreases(X21)
| increases(X21) )
& ( ~ constant(X19)
| X19 != sum(X20,X21)
| constant(X21)
| decreases(X21)
| decreases(X20) )
& ( ~ constant(X19)
| X19 != sum(X20,X21)
| constant(X21)
| increases(X20)
| increases(X21) )
& ( ~ constant(X19)
| X19 != sum(X20,X21)
| constant(X21)
| increases(X20)
| decreases(X20) )
& ( ~ constant(X19)
| X19 != sum(X20,X21)
| constant(X20)
| decreases(X21)
| increases(X21) )
& ( ~ constant(X19)
| X19 != sum(X20,X21)
| constant(X20)
| decreases(X21)
| decreases(X20) )
& ( ~ constant(X19)
| X19 != sum(X20,X21)
| constant(X20)
| increases(X20)
| increases(X21) )
& ( ~ constant(X19)
| X19 != sum(X20,X21)
| constant(X20)
| increases(X20)
| decreases(X20) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_abc_sum_increase])])])]) ).
cnf(c_0_30,negated_conjecture,
( ~ environment(X1)
| ~ subpopulation(efficient_producers,X1,esk2_0)
| constant(number_of_organizations(X1,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_15])]) ).
cnf(c_0_31,plain,
( ~ greater(cardinality_at_time(X1,X2),zero)
| ~ subpopulation(X1,X3,X2)
| ~ in_environment(X3,X2)
| ~ environment(X3)
| ~ increases(cardinality_at_time(X1,X2))
| greater(growth_rate(X1,X2),zero) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_32,negated_conjecture,
subpopulation(first_movers,esk1_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_19]),c_0_15])]) ).
cnf(c_0_33,negated_conjecture,
greater(cardinality_at_time(first_movers,esk2_0),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_14]),c_0_15])]) ).
cnf(c_0_34,negated_conjecture,
( ~ greater(zero,growth_rate(first_movers,esk2_0))
| ~ greater(growth_rate(efficient_producers,esk2_0),zero) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_35,negated_conjecture,
( ~ constant(cardinality_at_time(efficient_producers,esk2_0))
| growth_rate(efficient_producers,esk2_0) = zero ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_24]),c_0_19]),c_0_28]),c_0_15])]) ).
cnf(c_0_36,plain,
( ~ greater(cardinality_at_time(X1,X2),zero)
| ~ subpopulation(X1,X3,X2)
| ~ in_environment(X3,X2)
| ~ environment(X3)
| ~ decreases(cardinality_at_time(X1,X2))
| greater(zero,growth_rate(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_37,plain,
( ~ constant(X2)
| X2 != sum(X1,X3)
| constant(X1)
| increases(X1)
| decreases(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_38,negated_conjecture,
( ~ environment(X1)
| ~ subpopulation(efficient_producers,X1,esk2_0)
| constant(sum(cardinality_at_time(first_movers,esk2_0),cardinality_at_time(efficient_producers,esk2_0))) ),
inference(spm,[status(thm)],[c_0_30,c_0_17]) ).
cnf(c_0_39,negated_conjecture,
( growth_rate(efficient_producers,esk2_0) != zero
| growth_rate(first_movers,esk2_0) != zero ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_40,negated_conjecture,
( ~ greater(zero,growth_rate(efficient_producers,esk2_0))
| ~ greater(growth_rate(first_movers,esk2_0),zero) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_41,negated_conjecture,
( ~ increases(cardinality_at_time(first_movers,esk2_0))
| greater(growth_rate(first_movers,esk2_0),zero) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_19]),c_0_33]),c_0_15])]) ).
cnf(c_0_42,plain,
( ~ constant(X3)
| X3 != sum(X2,X1)
| constant(X2)
| decreases(X1)
| increases(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_43,plain,
( ~ constant(X3)
| X3 != sum(X2,X1)
| constant(X2)
| increases(X2)
| increases(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_44,negated_conjecture,
( ~ greater(zero,zero)
| ~ greater(zero,growth_rate(first_movers,esk2_0))
| ~ constant(cardinality_at_time(efficient_producers,esk2_0)) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_45,negated_conjecture,
( ~ decreases(cardinality_at_time(first_movers,esk2_0))
| greater(zero,growth_rate(first_movers,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_32]),c_0_19]),c_0_33]),c_0_15])]) ).
cnf(c_0_46,plain,
( ~ constant(sum(X1,X2))
| constant(X1)
| increases(X1)
| decreases(X1) ),
inference(er,[status(thm)],[c_0_37]) ).
cnf(c_0_47,negated_conjecture,
constant(sum(cardinality_at_time(first_movers,esk2_0),cardinality_at_time(efficient_producers,esk2_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_24]),c_0_15])]) ).
cnf(c_0_48,negated_conjecture,
( ~ constant(cardinality_at_time(efficient_producers,esk2_0))
| growth_rate(first_movers,esk2_0) != zero ),
inference(spm,[status(thm)],[c_0_39,c_0_35]) ).
cnf(c_0_49,negated_conjecture,
( ~ constant(cardinality_at_time(first_movers,esk2_0))
| growth_rate(first_movers,esk2_0) = zero ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_32]),c_0_19]),c_0_33]),c_0_15])]) ).
cnf(c_0_50,negated_conjecture,
( ~ greater(zero,growth_rate(efficient_producers,esk2_0))
| ~ increases(cardinality_at_time(first_movers,esk2_0)) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_51,negated_conjecture,
( ~ decreases(cardinality_at_time(efficient_producers,esk2_0))
| greater(zero,growth_rate(efficient_producers,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_24]),c_0_19]),c_0_28]),c_0_15])]) ).
cnf(c_0_52,plain,
( ~ constant(sum(X2,X1))
| constant(X2)
| increases(X1)
| decreases(X1) ),
inference(er,[status(thm)],[c_0_42]) ).
cnf(c_0_53,plain,
( ~ constant(sum(X1,X2))
| constant(X1)
| increases(X2)
| increases(X1) ),
inference(er,[status(thm)],[c_0_43]) ).
cnf(c_0_54,negated_conjecture,
( ~ greater(zero,zero)
| ~ constant(cardinality_at_time(efficient_producers,esk2_0))
| ~ decreases(cardinality_at_time(first_movers,esk2_0)) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_55,negated_conjecture,
( constant(cardinality_at_time(first_movers,esk2_0))
| increases(cardinality_at_time(first_movers,esk2_0))
| decreases(cardinality_at_time(first_movers,esk2_0)) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_56,negated_conjecture,
( ~ constant(cardinality_at_time(first_movers,esk2_0))
| ~ constant(cardinality_at_time(efficient_producers,esk2_0)) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_57,plain,
( ~ constant(X3)
| X3 != sum(X1,X2)
| constant(X2)
| increases(X1)
| decreases(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_58,negated_conjecture,
( ~ increases(cardinality_at_time(efficient_producers,esk2_0))
| greater(growth_rate(efficient_producers,esk2_0),zero) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_24]),c_0_19]),c_0_28]),c_0_15])]) ).
cnf(c_0_59,negated_conjecture,
( ~ increases(cardinality_at_time(first_movers,esk2_0))
| ~ decreases(cardinality_at_time(efficient_producers,esk2_0)) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_60,negated_conjecture,
( constant(cardinality_at_time(first_movers,esk2_0))
| increases(cardinality_at_time(efficient_producers,esk2_0))
| decreases(cardinality_at_time(efficient_producers,esk2_0)) ),
inference(spm,[status(thm)],[c_0_52,c_0_47]) ).
cnf(c_0_61,negated_conjecture,
( constant(cardinality_at_time(first_movers,esk2_0))
| increases(cardinality_at_time(first_movers,esk2_0))
| increases(cardinality_at_time(efficient_producers,esk2_0)) ),
inference(spm,[status(thm)],[c_0_53,c_0_47]) ).
cnf(c_0_62,negated_conjecture,
( ~ greater(zero,zero)
| ~ constant(cardinality_at_time(efficient_producers,esk2_0))
| increases(cardinality_at_time(first_movers,esk2_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56]) ).
cnf(c_0_63,plain,
( ~ constant(X3)
| X3 != sum(X2,X1)
| constant(X1)
| increases(X2)
| increases(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_64,plain,
( ~ constant(sum(X1,X2))
| constant(X2)
| increases(X1)
| decreases(X1) ),
inference(er,[status(thm)],[c_0_57]) ).
cnf(c_0_65,negated_conjecture,
( ~ constant(cardinality_at_time(efficient_producers,esk2_0))
| ~ increases(cardinality_at_time(efficient_producers,esk2_0))
| greater(zero,zero) ),
inference(spm,[status(thm)],[c_0_58,c_0_35]) ).
cnf(c_0_66,negated_conjecture,
( constant(cardinality_at_time(first_movers,esk2_0))
| increases(cardinality_at_time(efficient_producers,esk2_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61]) ).
cnf(c_0_67,negated_conjecture,
( ~ greater(zero,zero)
| ~ constant(cardinality_at_time(efficient_producers,esk2_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_35]),c_0_62]) ).
cnf(c_0_68,plain,
( ~ constant(sum(X1,X2))
| constant(X2)
| increases(X2)
| increases(X1) ),
inference(er,[status(thm)],[c_0_63]) ).
cnf(c_0_69,plain,
( ~ constant(X3)
| X3 != sum(X1,X2)
| constant(X2)
| decreases(X2)
| decreases(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_70,negated_conjecture,
( ~ greater(zero,growth_rate(first_movers,esk2_0))
| ~ increases(cardinality_at_time(efficient_producers,esk2_0)) ),
inference(spm,[status(thm)],[c_0_34,c_0_58]) ).
cnf(c_0_71,negated_conjecture,
( constant(cardinality_at_time(efficient_producers,esk2_0))
| increases(cardinality_at_time(first_movers,esk2_0))
| decreases(cardinality_at_time(first_movers,esk2_0)) ),
inference(spm,[status(thm)],[c_0_64,c_0_47]) ).
cnf(c_0_72,negated_conjecture,
~ constant(cardinality_at_time(efficient_producers,esk2_0)),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67]),c_0_56]) ).
cnf(c_0_73,negated_conjecture,
( constant(cardinality_at_time(efficient_producers,esk2_0))
| increases(cardinality_at_time(first_movers,esk2_0))
| increases(cardinality_at_time(efficient_producers,esk2_0)) ),
inference(spm,[status(thm)],[c_0_68,c_0_47]) ).
cnf(c_0_74,plain,
( ~ constant(X2)
| X2 != sum(X3,X1)
| constant(X1)
| decreases(X1)
| increases(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_75,plain,
( ~ constant(sum(X2,X1))
| constant(X1)
| decreases(X2)
| decreases(X1) ),
inference(er,[status(thm)],[c_0_69]) ).
cnf(c_0_76,negated_conjecture,
( ~ increases(cardinality_at_time(efficient_producers,esk2_0))
| ~ decreases(cardinality_at_time(first_movers,esk2_0)) ),
inference(spm,[status(thm)],[c_0_70,c_0_45]) ).
cnf(c_0_77,negated_conjecture,
( increases(cardinality_at_time(first_movers,esk2_0))
| decreases(cardinality_at_time(first_movers,esk2_0)) ),
inference(sr,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_78,negated_conjecture,
( increases(cardinality_at_time(efficient_producers,esk2_0))
| increases(cardinality_at_time(first_movers,esk2_0)) ),
inference(sr,[status(thm)],[c_0_73,c_0_72]) ).
cnf(c_0_79,plain,
( ~ constant(sum(X2,X1))
| constant(X1)
| increases(X1)
| decreases(X1) ),
inference(er,[status(thm)],[c_0_74]) ).
cnf(c_0_80,negated_conjecture,
( constant(cardinality_at_time(efficient_producers,esk2_0))
| decreases(cardinality_at_time(efficient_producers,esk2_0))
| decreases(cardinality_at_time(first_movers,esk2_0)) ),
inference(spm,[status(thm)],[c_0_75,c_0_47]) ).
cnf(c_0_81,negated_conjecture,
increases(cardinality_at_time(first_movers,esk2_0)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_78]) ).
cnf(c_0_82,negated_conjecture,
( constant(cardinality_at_time(efficient_producers,esk2_0))
| increases(cardinality_at_time(efficient_producers,esk2_0))
| decreases(cardinality_at_time(efficient_producers,esk2_0)) ),
inference(spm,[status(thm)],[c_0_79,c_0_47]) ).
cnf(c_0_83,negated_conjecture,
( decreases(cardinality_at_time(first_movers,esk2_0))
| decreases(cardinality_at_time(efficient_producers,esk2_0)) ),
inference(sr,[status(thm)],[c_0_80,c_0_72]) ).
cnf(c_0_84,negated_conjecture,
~ decreases(cardinality_at_time(efficient_producers,esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_81])]) ).
cnf(c_0_85,negated_conjecture,
( increases(cardinality_at_time(efficient_producers,esk2_0))
| decreases(cardinality_at_time(efficient_producers,esk2_0)) ),
inference(sr,[status(thm)],[c_0_82,c_0_72]) ).
cnf(c_0_86,negated_conjecture,
decreases(cardinality_at_time(first_movers,esk2_0)),
inference(sr,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_87,negated_conjecture,
increases(cardinality_at_time(efficient_producers,esk2_0)),
inference(sr,[status(thm)],[c_0_85,c_0_84]) ).
cnf(c_0_88,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_86])]),c_0_87])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT025+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.35 % Computer : n016.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 01:26:22 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.43 % Version: 3.5.1
% 0.14/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.43 % Starting sh5l with 300s (1) cores
% 0.14/0.43 % new_bool_1 with pid 1270184 completed with status 0
% 0.14/0.43 % Result found by new_bool_1
% 0.14/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.43 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.43 % Search class: FGHSF-FFMS22-SFFFFFNN
% 0.14/0.43 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.43 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.43 % SubtermCWHack with pid 1270191 completed with status 0
% 0.14/0.43 % Result found by SubtermCWHack
% 0.14/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.43 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.43 % Search class: FGHSF-FFMS22-SFFFFFNN
% 0.14/0.43 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.43 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.43 % Preprocessing time : 0.001 s
% 0.14/0.43
% 0.14/0.43 % Proof found!
% 0.14/0.43 % SZS status Theorem
% 0.14/0.43 % SZS output start CNFRefutation
% See solution above
% 0.14/0.43 % Parsed axioms : 8
% 0.14/0.43 % Removed by relevancy pruning/SinE : 0
% 0.14/0.43 % Initial clauses : 26
% 0.14/0.43 % Removed in clause preprocessing : 0
% 0.14/0.43 % Initial clauses in saturation : 26
% 0.14/0.43 % Processed clauses : 113
% 0.14/0.43 % ...of these trivial : 0
% 0.14/0.43 % ...subsumed : 19
% 0.14/0.43 % ...remaining for further processing : 93
% 0.14/0.43 % Other redundant clauses eliminated : 10
% 0.14/0.43 % Clauses deleted for lack of memory : 0
% 0.14/0.43 % Backward-subsumed : 19
% 0.14/0.43 % Backward-rewritten : 11
% 0.14/0.43 % Generated clauses : 191
% 0.14/0.43 % ...of the previous two non-redundant : 181
% 0.14/0.43 % ...aggressively subsumed : 0
% 0.14/0.43 % Contextual simplify-reflections : 10
% 0.14/0.43 % Paramodulations : 175
% 0.14/0.43 % Factorizations : 0
% 0.14/0.43 % NegExts : 0
% 0.14/0.43 % Equation resolutions : 10
% 0.14/0.43 % Disequality decompositions : 0
% 0.14/0.43 % Total rewrite steps : 62
% 0.14/0.43 % ...of those cached : 52
% 0.14/0.43 % Propositional unsat checks : 0
% 0.14/0.43 % Propositional check models : 0
% 0.14/0.43 % Propositional check unsatisfiable : 0
% 0.14/0.43 % Propositional clauses : 0
% 0.14/0.43 % Propositional clauses after purity: 0
% 0.14/0.43 % Propositional unsat core size : 0
% 0.14/0.43 % Propositional preprocessing time : 0.000
% 0.14/0.43 % Propositional encoding time : 0.000
% 0.14/0.43 % Propositional solver time : 0.000
% 0.14/0.43 % Success case prop preproc time : 0.000
% 0.14/0.43 % Success case prop encoding time : 0.000
% 0.14/0.43 % Success case prop solver time : 0.000
% 0.14/0.43 % Current number of processed clauses : 47
% 0.14/0.43 % Positive orientable unit clauses : 12
% 0.14/0.43 % Positive unorientable unit clauses: 0
% 0.14/0.43 % Negative unit clauses : 2
% 0.14/0.43 % Non-unit-clauses : 33
% 0.14/0.43 % Current number of unprocessed clauses: 94
% 0.14/0.43 % ...number of literals in the above : 546
% 0.14/0.43 % Current number of archived formulas : 0
% 0.14/0.43 % Current number of archived clauses : 36
% 0.14/0.43 % Clause-clause subsumption calls (NU) : 427
% 0.14/0.43 % Rec. Clause-clause subsumption calls : 176
% 0.14/0.43 % Non-unit clause-clause subsumptions : 38
% 0.14/0.43 % Unit Clause-clause subsumption calls : 36
% 0.14/0.43 % Rewrite failures with RHS unbound : 0
% 0.14/0.43 % BW rewrite match attempts : 4
% 0.14/0.43 % BW rewrite match successes : 4
% 0.14/0.43 % Condensation attempts : 0
% 0.14/0.43 % Condensation successes : 0
% 0.14/0.43 % Termbank termtop insertions : 5067
% 0.14/0.43 % Search garbage collected termcells : 381
% 0.14/0.43
% 0.14/0.43 % -------------------------------------------------
% 0.14/0.43 % User time : 0.007 s
% 0.14/0.43 % System time : 0.003 s
% 0.14/0.43 % Total time : 0.010 s
% 0.14/0.43 % Maximum resident set size: 3648 pages
% 0.14/0.43
% 0.14/0.43 % -------------------------------------------------
% 0.14/0.43 % User time : 0.008 s
% 0.14/0.43 % System time : 0.005 s
% 0.14/0.43 % Total time : 0.014 s
% 0.14/0.43 % Maximum resident set size: 4864 pages
% 0.14/0.43 % E exiting
%------------------------------------------------------------------------------