%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : MGT023+2 : 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 : n013.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 01:26:04 PM UTC 2026
% Result : Theorem 0.14s 0.42s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 4
% Syntax : Number of formulae : 55 ( 6 unt; 0 def)
% Number of atoms : 316 ( 29 equ)
% Maximal formula atoms : 42 ( 5 avg)
% Number of connectives : 429 ( 168 ~; 209 |; 38 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 92 ( 0 sgn 23 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mp_earliest_time_growth_rate_exceeds,axiom,
! [X1] :
( ( ? [X2] :
( ! [X3] :
( ( greater_or_equal(X3,X2)
& subpopulations(first_movers,efficient_producers,X1,X3) )
=> greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3)) )
& in_environment(X1,X2) )
& environment(X1) )
=> ? [X2] :
( ! [X3] :
( ( greater(X3,X2)
& subpopulations(first_movers,efficient_producers,X1,X3) )
=> greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3)) )
& ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
& in_environment(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds) ).
fof(l1,hypothesis,
! [X1] :
( ( stable(X1)
& environment(X1) )
=> ? [X2] :
( ! [X3] :
( ( greater_or_equal(X3,X2)
& subpopulations(first_movers,efficient_producers,X1,X3) )
=> greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3)) )
& in_environment(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1) ).
fof(d1,hypothesis,
! [X1,X2] :
( ( ! [X3] :
( ( greater(X3,X2)
& subpopulations(first_movers,efficient_producers,X1,X3) )
=> greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3)) )
& in_environment(X1,X2)
& ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
& environment(X1) )
=> X2 = critical_point(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1) ).
fof(prove_l5,conjecture,
! [X1] :
( ( stable(X1)
& environment(X1) )
=> in_environment(X1,critical_point(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l5) ).
fof(c_0_4,plain,
! [X1] :
( ( ? [X2] :
( ! [X3] :
( ( greater_or_equal(X3,X2)
& subpopulations(first_movers,efficient_producers,X1,X3) )
=> greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3)) )
& in_environment(X1,X2) )
& environment(X1) )
=> ? [X2] :
( ! [X3] :
( ( greater(X3,X2)
& subpopulations(first_movers,efficient_producers,X1,X3) )
=> greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3)) )
& ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
& in_environment(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[mp_earliest_time_growth_rate_exceeds]) ).
fof(c_0_5,plain,
! [X11,X12,X15] :
( ( ~ environment(X11)
| ~ in_environment(X11,X12)
| ~ greater(growth_rate(efficient_producers,esk4_2(X11,X12)),growth_rate(first_movers,esk4_2(X11,X12)))
| greater(growth_rate(efficient_producers,X15),growth_rate(first_movers,X15))
| ~ greater(X15,esk5_1(X11))
| ~ subpopulations(first_movers,efficient_producers,X11,X15) )
& ( ~ environment(X11)
| ~ in_environment(X11,X12)
| ~ greater(growth_rate(efficient_producers,esk4_2(X11,X12)),growth_rate(first_movers,esk4_2(X11,X12)))
| ~ greater(growth_rate(efficient_producers,esk5_1(X11)),growth_rate(first_movers,esk5_1(X11))) )
& ( ~ environment(X11)
| ~ in_environment(X11,X12)
| ~ greater(growth_rate(efficient_producers,esk4_2(X11,X12)),growth_rate(first_movers,esk4_2(X11,X12)))
| in_environment(X11,esk5_1(X11)) )
& ( ~ environment(X11)
| ~ in_environment(X11,X12)
| greater_or_equal(esk4_2(X11,X12),X12)
| greater(growth_rate(efficient_producers,X15),growth_rate(first_movers,X15))
| ~ greater(X15,esk5_1(X11))
| ~ subpopulations(first_movers,efficient_producers,X11,X15) )
& ( ~ environment(X11)
| ~ in_environment(X11,X12)
| greater_or_equal(esk4_2(X11,X12),X12)
| ~ greater(growth_rate(efficient_producers,esk5_1(X11)),growth_rate(first_movers,esk5_1(X11))) )
& ( ~ environment(X11)
| ~ in_environment(X11,X12)
| greater_or_equal(esk4_2(X11,X12),X12)
| in_environment(X11,esk5_1(X11)) )
& ( ~ environment(X11)
| ~ in_environment(X11,X12)
| subpopulations(first_movers,efficient_producers,X11,esk4_2(X11,X12))
| greater(growth_rate(efficient_producers,X15),growth_rate(first_movers,X15))
| ~ greater(X15,esk5_1(X11))
| ~ subpopulations(first_movers,efficient_producers,X11,X15) )
& ( ~ environment(X11)
| ~ in_environment(X11,X12)
| subpopulations(first_movers,efficient_producers,X11,esk4_2(X11,X12))
| ~ greater(growth_rate(efficient_producers,esk5_1(X11)),growth_rate(first_movers,esk5_1(X11))) )
& ( ~ environment(X11)
| ~ in_environment(X11,X12)
| subpopulations(first_movers,efficient_producers,X11,esk4_2(X11,X12))
| in_environment(X11,esk5_1(X11)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])])])]) ).
fof(c_0_6,hypothesis,
! [X7,X9] :
( ( ~ stable(X7)
| ~ environment(X7)
| greater(growth_rate(efficient_producers,X9),growth_rate(first_movers,X9))
| ~ greater_or_equal(X9,esk2_1(X7))
| ~ subpopulations(first_movers,efficient_producers,X7,X9) )
& ( ~ stable(X7)
| ~ environment(X7)
| in_environment(X7,esk2_1(X7)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l1])])])])])]) ).
cnf(c_0_7,plain,
( ~ environment(X1)
| ~ in_environment(X1,X2)
| greater_or_equal(esk4_2(X1,X2),X2)
| in_environment(X1,esk5_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,hypothesis,
( ~ stable(X1)
| ~ environment(X1)
| in_environment(X1,esk2_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,hypothesis,
( ~ stable(X1)
| ~ environment(X1)
| ~ greater_or_equal(X2,esk2_1(X1))
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,hypothesis,
( ~ environment(X1)
| ~ stable(X1)
| in_environment(X1,esk5_1(X1))
| greater_or_equal(esk4_2(X1,esk2_1(X1)),esk2_1(X1)) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
fof(c_0_11,hypothesis,
! [X1,X2] :
( ( ! [X3] :
( ( greater(X3,X2)
& subpopulations(first_movers,efficient_producers,X1,X3) )
=> greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3)) )
& in_environment(X1,X2)
& ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
& environment(X1) )
=> X2 = critical_point(X1) ),
inference(fof_simplification,[status(thm)],[d1]) ).
cnf(c_0_12,plain,
( ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ greater(growth_rate(efficient_producers,esk4_2(X1,X2)),growth_rate(first_movers,esk4_2(X1,X2)))
| in_environment(X1,esk5_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_13,hypothesis,
( ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,esk4_2(X1,esk2_1(X1)))
| ~ stable(X1)
| in_environment(X1,esk5_1(X1))
| greater(growth_rate(efficient_producers,esk4_2(X1,esk2_1(X1))),growth_rate(first_movers,esk4_2(X1,esk2_1(X1)))) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
fof(c_0_14,hypothesis,
! [X4,X5] :
( ( X5 = critical_point(X4)
| ~ in_environment(X4,X5)
| greater(growth_rate(efficient_producers,X5),growth_rate(first_movers,X5))
| ~ environment(X4)
| ~ greater(growth_rate(efficient_producers,esk1_2(X4,X5)),growth_rate(first_movers,esk1_2(X4,X5))) )
& ( X5 = critical_point(X4)
| ~ in_environment(X4,X5)
| greater(growth_rate(efficient_producers,X5),growth_rate(first_movers,X5))
| ~ environment(X4)
| greater(esk1_2(X4,X5),X5) )
& ( X5 = critical_point(X4)
| ~ in_environment(X4,X5)
| greater(growth_rate(efficient_producers,X5),growth_rate(first_movers,X5))
| ~ environment(X4)
| subpopulations(first_movers,efficient_producers,X4,esk1_2(X4,X5)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])])]) ).
cnf(c_0_15,hypothesis,
( ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,esk4_2(X1,esk2_1(X1)))
| ~ stable(X1)
| in_environment(X1,esk5_1(X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_8]) ).
cnf(c_0_16,plain,
( ~ environment(X1)
| ~ in_environment(X1,X2)
| subpopulations(first_movers,efficient_producers,X1,esk4_2(X1,X2))
| in_environment(X1,esk5_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_17,hypothesis,
( ~ in_environment(X1,X2)
| ~ environment(X1)
| X2 = critical_point(X1)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| subpopulations(first_movers,efficient_producers,X1,esk1_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,hypothesis,
( ~ environment(X1)
| ~ stable(X1)
| in_environment(X1,esk5_1(X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_8]) ).
cnf(c_0_19,plain,
( ~ environment(X1)
| ~ in_environment(X1,X3)
| ~ greater(X2,esk5_1(X1))
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| greater_or_equal(esk4_2(X1,X3),X3)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_20,hypothesis,
( ~ environment(X1)
| ~ stable(X1)
| subpopulations(first_movers,efficient_producers,X1,esk1_2(X1,esk5_1(X1)))
| greater(growth_rate(efficient_producers,esk5_1(X1)),growth_rate(first_movers,esk5_1(X1)))
| critical_point(X1) = esk5_1(X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,plain,
( ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ greater(growth_rate(efficient_producers,esk5_1(X1)),growth_rate(first_movers,esk5_1(X1)))
| greater_or_equal(esk4_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_22,hypothesis,
( ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ greater(esk1_2(X1,esk5_1(X1)),esk5_1(X1))
| ~ stable(X1)
| greater_or_equal(esk4_2(X1,X2),X2)
| greater(growth_rate(efficient_producers,esk1_2(X1,esk5_1(X1))),growth_rate(first_movers,esk1_2(X1,esk5_1(X1))))
| critical_point(X1) = esk5_1(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
cnf(c_0_23,hypothesis,
( ~ in_environment(X1,X2)
| ~ environment(X1)
| X2 = critical_point(X1)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| greater(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_24,hypothesis,
( ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ stable(X1)
| greater_or_equal(esk4_2(X1,X2),X2)
| greater(growth_rate(efficient_producers,esk1_2(X1,esk5_1(X1))),growth_rate(first_movers,esk1_2(X1,esk5_1(X1))))
| critical_point(X1) = esk5_1(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_18]),c_0_21]) ).
cnf(c_0_25,plain,
( ~ environment(X1)
| ~ in_environment(X1,X3)
| ~ greater(X2,esk5_1(X1))
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| subpopulations(first_movers,efficient_producers,X1,esk4_2(X1,X3))
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_26,plain,
( ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ greater(growth_rate(efficient_producers,esk5_1(X1)),growth_rate(first_movers,esk5_1(X1)))
| subpopulations(first_movers,efficient_producers,X1,esk4_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_27,hypothesis,
( ~ in_environment(X1,X2)
| ~ environment(X1)
| ~ greater(growth_rate(efficient_producers,esk1_2(X1,X2)),growth_rate(first_movers,esk1_2(X1,X2)))
| X2 = critical_point(X1)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_28,hypothesis,
( ~ environment(X1)
| ~ stable(X1)
| greater_or_equal(esk4_2(X1,esk2_1(X1)),esk2_1(X1))
| greater(growth_rate(efficient_producers,esk1_2(X1,esk5_1(X1))),growth_rate(first_movers,esk1_2(X1,esk5_1(X1))))
| critical_point(X1) = esk5_1(X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_8]) ).
cnf(c_0_29,hypothesis,
( ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ greater(esk1_2(X1,esk5_1(X1)),esk5_1(X1))
| ~ stable(X1)
| subpopulations(first_movers,efficient_producers,X1,esk4_2(X1,X2))
| greater(growth_rate(efficient_producers,esk1_2(X1,esk5_1(X1))),growth_rate(first_movers,esk1_2(X1,esk5_1(X1))))
| critical_point(X1) = esk5_1(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_20]),c_0_26]) ).
cnf(c_0_30,hypothesis,
( ~ environment(X1)
| ~ stable(X1)
| greater_or_equal(esk4_2(X1,esk2_1(X1)),esk2_1(X1))
| greater(growth_rate(efficient_producers,esk5_1(X1)),growth_rate(first_movers,esk5_1(X1)))
| critical_point(X1) = esk5_1(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_18]) ).
cnf(c_0_31,hypothesis,
( ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ stable(X1)
| subpopulations(first_movers,efficient_producers,X1,esk4_2(X1,X2))
| greater(growth_rate(efficient_producers,esk1_2(X1,esk5_1(X1))),growth_rate(first_movers,esk1_2(X1,esk5_1(X1))))
| critical_point(X1) = esk5_1(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_23]),c_0_18]),c_0_26]) ).
cnf(c_0_32,plain,
( ~ environment(X1)
| ~ in_environment(X1,X3)
| ~ greater(growth_rate(efficient_producers,esk4_2(X1,X3)),growth_rate(first_movers,esk4_2(X1,X3)))
| ~ greater(X2,esk5_1(X1))
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_33,hypothesis,
( ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,esk4_2(X1,esk2_1(X1)))
| ~ stable(X1)
| greater(growth_rate(efficient_producers,esk5_1(X1)),growth_rate(first_movers,esk5_1(X1)))
| greater(growth_rate(efficient_producers,esk4_2(X1,esk2_1(X1))),growth_rate(first_movers,esk4_2(X1,esk2_1(X1))))
| critical_point(X1) = esk5_1(X1) ),
inference(spm,[status(thm)],[c_0_9,c_0_30]) ).
cnf(c_0_34,hypothesis,
( ~ environment(X1)
| ~ stable(X1)
| subpopulations(first_movers,efficient_producers,X1,esk4_2(X1,esk2_1(X1)))
| greater(growth_rate(efficient_producers,esk1_2(X1,esk5_1(X1))),growth_rate(first_movers,esk1_2(X1,esk5_1(X1))))
| critical_point(X1) = esk5_1(X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_8]) ).
cnf(c_0_35,hypothesis,
( ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ subpopulations(first_movers,efficient_producers,X1,esk4_2(X1,esk2_1(X1)))
| ~ greater(X2,esk5_1(X1))
| ~ stable(X1)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| greater(growth_rate(efficient_producers,esk5_1(X1)),growth_rate(first_movers,esk5_1(X1)))
| critical_point(X1) = esk5_1(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_8]) ).
cnf(c_0_36,hypothesis,
( ~ environment(X1)
| ~ stable(X1)
| subpopulations(first_movers,efficient_producers,X1,esk4_2(X1,esk2_1(X1)))
| greater(growth_rate(efficient_producers,esk5_1(X1)),growth_rate(first_movers,esk5_1(X1)))
| critical_point(X1) = esk5_1(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_34]),c_0_18]) ).
cnf(c_0_37,hypothesis,
( ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ greater(X2,esk5_1(X1))
| ~ stable(X1)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| greater(growth_rate(efficient_producers,esk5_1(X1)),growth_rate(first_movers,esk5_1(X1)))
| critical_point(X1) = esk5_1(X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_38,hypothesis,
( ~ environment(X1)
| ~ greater(esk1_2(X1,esk5_1(X1)),esk5_1(X1))
| ~ stable(X1)
| greater(growth_rate(efficient_producers,esk5_1(X1)),growth_rate(first_movers,esk5_1(X1)))
| greater(growth_rate(efficient_producers,esk1_2(X1,esk5_1(X1))),growth_rate(first_movers,esk1_2(X1,esk5_1(X1))))
| critical_point(X1) = esk5_1(X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_20]) ).
cnf(c_0_39,hypothesis,
( ~ environment(X1)
| ~ greater(esk1_2(X1,esk5_1(X1)),esk5_1(X1))
| ~ stable(X1)
| greater(growth_rate(efficient_producers,esk5_1(X1)),growth_rate(first_movers,esk5_1(X1)))
| critical_point(X1) = esk5_1(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_38]),c_0_18]) ).
cnf(c_0_40,hypothesis,
( ~ environment(X1)
| ~ stable(X1)
| greater(growth_rate(efficient_producers,esk5_1(X1)),growth_rate(first_movers,esk5_1(X1)))
| critical_point(X1) = esk5_1(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_23]),c_0_18]) ).
cnf(c_0_41,hypothesis,
( ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ stable(X1)
| greater_or_equal(esk4_2(X1,X2),X2)
| critical_point(X1) = esk5_1(X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_40]) ).
cnf(c_0_42,plain,
( ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ greater(growth_rate(efficient_producers,esk4_2(X1,X2)),growth_rate(first_movers,esk4_2(X1,X2)))
| ~ greater(growth_rate(efficient_producers,esk5_1(X1)),growth_rate(first_movers,esk5_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_43,hypothesis,
( ~ environment(X1)
| ~ environment(X2)
| ~ in_environment(X1,esk2_1(X2))
| ~ subpopulations(first_movers,efficient_producers,X2,esk4_2(X1,esk2_1(X2)))
| ~ stable(X1)
| ~ stable(X2)
| greater(growth_rate(efficient_producers,esk4_2(X1,esk2_1(X2))),growth_rate(first_movers,esk4_2(X1,esk2_1(X2))))
| critical_point(X1) = esk5_1(X1) ),
inference(spm,[status(thm)],[c_0_9,c_0_41]) ).
fof(c_0_44,negated_conjecture,
~ ! [X1] :
( ( stable(X1)
& environment(X1) )
=> in_environment(X1,critical_point(X1)) ),
inference(assume_negation,[status(cth)],[prove_l5]) ).
cnf(c_0_45,hypothesis,
( ~ environment(X2)
| ~ environment(X1)
| ~ in_environment(X1,esk2_1(X2))
| ~ subpopulations(first_movers,efficient_producers,X2,esk4_2(X1,esk2_1(X2)))
| ~ stable(X1)
| ~ stable(X2)
| critical_point(X1) = esk5_1(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_40]) ).
cnf(c_0_46,hypothesis,
( ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ stable(X1)
| subpopulations(first_movers,efficient_producers,X1,esk4_2(X1,X2))
| critical_point(X1) = esk5_1(X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_40]) ).
fof(c_0_47,negated_conjecture,
( ~ in_environment(esk3_0,critical_point(esk3_0))
& stable(esk3_0)
& environment(esk3_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_44])])])]) ).
cnf(c_0_48,hypothesis,
( ~ environment(X1)
| ~ stable(X1)
| critical_point(X1) = esk5_1(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_8]) ).
cnf(c_0_49,negated_conjecture,
stable(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_50,negated_conjecture,
environment(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_51,negated_conjecture,
~ in_environment(esk3_0,critical_point(esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_52,negated_conjecture,
critical_point(esk3_0) = esk5_1(esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50])]) ).
cnf(c_0_53,negated_conjecture,
~ in_environment(esk3_0,esk5_1(esk3_0)),
inference(rw,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_54,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_18]),c_0_49]),c_0_50])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT023+2 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n013.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 01:21:21 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 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
% 0.14/0.42 % Version: 3.5.1
% 0.14/0.42 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.42 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.42 % Starting sh5l with 300s (1) cores
% 0.14/0.42 % new_bool_3 with pid 3853040 completed with status 0
% 0.14/0.42 % Result found by new_bool_3
% 0.14/0.42 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.42 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.42 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.42 % Search class: FGHSF-FFMF21-SFFFFFNN
% 0.14/0.42 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.42 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.42 % SubtermCWHack with pid 3853045 completed with status 0
% 0.14/0.42 % Result found by SubtermCWHack
% 0.14/0.42 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.42 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.42 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.42 % Search class: FGHSF-FFMF21-SFFFFFNN
% 0.14/0.42 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.42 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.42 % Preprocessing time : 0.001 s
% 0.14/0.42
% 0.14/0.42 % Proof found!
% 0.14/0.42 % SZS status Theorem
% 0.14/0.42 % SZS output start CNFRefutation
% See solution above
% 0.14/0.43 % Parsed axioms : 4
% 0.14/0.43 % Removed by relevancy pruning/SinE : 0
% 0.14/0.43 % Initial clauses : 17
% 0.14/0.43 % Removed in clause preprocessing : 0
% 0.14/0.43 % Initial clauses in saturation : 17
% 0.14/0.43 % Processed clauses : 60
% 0.14/0.43 % ...of these trivial : 0
% 0.14/0.43 % ...subsumed : 9
% 0.14/0.43 % ...remaining for further processing : 51
% 0.14/0.43 % Other redundant clauses eliminated : 0
% 0.14/0.43 % Clauses deleted for lack of memory : 0
% 0.14/0.43 % Backward-subsumed : 27
% 0.14/0.43 % Backward-rewritten : 1
% 0.14/0.43 % Generated clauses : 56
% 0.14/0.43 % ...of the previous two non-redundant : 54
% 0.14/0.43 % ...aggressively subsumed : 0
% 0.14/0.43 % Contextual simplify-reflections : 17
% 0.14/0.43 % Paramodulations : 56
% 0.14/0.43 % Factorizations : 0
% 0.14/0.43 % NegExts : 0
% 0.14/0.43 % Equation resolutions : 0
% 0.14/0.43 % Disequality decompositions : 0
% 0.14/0.43 % Total rewrite steps : 4
% 0.14/0.43 % ...of those cached : 1
% 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 : 23
% 0.14/0.43 % Positive orientable unit clauses : 3
% 0.14/0.43 % Positive unorientable unit clauses: 0
% 0.14/0.43 % Negative unit clauses : 1
% 0.14/0.43 % Non-unit-clauses : 19
% 0.14/0.43 % Current number of unprocessed clauses: 2
% 0.14/0.43 % ...number of literals in the above : 15
% 0.14/0.43 % Current number of archived formulas : 0
% 0.14/0.43 % Current number of archived clauses : 28
% 0.14/0.43 % Clause-clause subsumption calls (NU) : 1290
% 0.14/0.43 % Rec. Clause-clause subsumption calls : 92
% 0.14/0.43 % Non-unit clause-clause subsumptions : 53
% 0.14/0.43 % Unit Clause-clause subsumption calls : 17
% 0.14/0.43 % Rewrite failures with RHS unbound : 0
% 0.14/0.43 % BW rewrite match attempts : 1
% 0.14/0.43 % BW rewrite match successes : 1
% 0.14/0.43 % Condensation attempts : 0
% 0.14/0.43 % Condensation successes : 0
% 0.14/0.43 % Termbank termtop insertions : 4317
% 0.14/0.43 % Search garbage collected termcells : 308
% 0.14/0.43
% 0.14/0.43 % -------------------------------------------------
% 0.14/0.43 % User time : 0.009 s
% 0.14/0.43 % System time : 0.001 s
% 0.14/0.43 % Total time : 0.010 s
% 0.14/0.43 % Maximum resident set size: 3584 pages
% 0.14/0.43
% 0.14/0.43 % -------------------------------------------------
% 0.14/0.43 % User time : 0.011 s
% 0.14/0.43 % System time : 0.003 s
% 0.14/0.43 % Total time : 0.013 s
% 0.14/0.43 % Maximum resident set size: 4864 pages
% 0.14/0.43 % E exiting
%------------------------------------------------------------------------------