%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : MGT030+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 01:26:26 PM UTC 2026
% Result : Theorem 0.14s 0.63s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 3
% Syntax : Number of formulae : 51 ( 4 unt; 0 def)
% Number of atoms : 258 ( 0 equ)
% Maximal formula atoms : 42 ( 5 avg)
% Number of connectives : 341 ( 134 ~; 153 |; 40 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 70 ( 0 sgn 20 !; 8 ?)
% 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/sandbox/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/sandbox/benchmark/theBenchmark.p',l1) ).
fof(prove_l12,conjecture,
! [X1] :
( ( stable(X1)
& 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/sandbox/benchmark/theBenchmark.p',prove_l12) ).
fof(c_0_3,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_4,plain,
! [X10,X11,X14] :
( ( ~ environment(X10)
| ~ in_environment(X10,X11)
| ~ greater(growth_rate(efficient_producers,esk4_2(X10,X11)),growth_rate(first_movers,esk4_2(X10,X11)))
| greater(growth_rate(efficient_producers,X14),growth_rate(first_movers,X14))
| ~ greater(X14,esk5_1(X10))
| ~ subpopulations(first_movers,efficient_producers,X10,X14) )
& ( ~ environment(X10)
| ~ in_environment(X10,X11)
| ~ greater(growth_rate(efficient_producers,esk4_2(X10,X11)),growth_rate(first_movers,esk4_2(X10,X11)))
| ~ greater(growth_rate(efficient_producers,esk5_1(X10)),growth_rate(first_movers,esk5_1(X10))) )
& ( ~ environment(X10)
| ~ in_environment(X10,X11)
| ~ greater(growth_rate(efficient_producers,esk4_2(X10,X11)),growth_rate(first_movers,esk4_2(X10,X11)))
| in_environment(X10,esk5_1(X10)) )
& ( ~ environment(X10)
| ~ in_environment(X10,X11)
| greater_or_equal(esk4_2(X10,X11),X11)
| greater(growth_rate(efficient_producers,X14),growth_rate(first_movers,X14))
| ~ greater(X14,esk5_1(X10))
| ~ subpopulations(first_movers,efficient_producers,X10,X14) )
& ( ~ environment(X10)
| ~ in_environment(X10,X11)
| greater_or_equal(esk4_2(X10,X11),X11)
| ~ greater(growth_rate(efficient_producers,esk5_1(X10)),growth_rate(first_movers,esk5_1(X10))) )
& ( ~ environment(X10)
| ~ in_environment(X10,X11)
| greater_or_equal(esk4_2(X10,X11),X11)
| in_environment(X10,esk5_1(X10)) )
& ( ~ environment(X10)
| ~ in_environment(X10,X11)
| subpopulations(first_movers,efficient_producers,X10,esk4_2(X10,X11))
| greater(growth_rate(efficient_producers,X14),growth_rate(first_movers,X14))
| ~ greater(X14,esk5_1(X10))
| ~ subpopulations(first_movers,efficient_producers,X10,X14) )
& ( ~ environment(X10)
| ~ in_environment(X10,X11)
| subpopulations(first_movers,efficient_producers,X10,esk4_2(X10,X11))
| ~ greater(growth_rate(efficient_producers,esk5_1(X10)),growth_rate(first_movers,esk5_1(X10))) )
& ( ~ environment(X10)
| ~ in_environment(X10,X11)
| subpopulations(first_movers,efficient_producers,X10,esk4_2(X10,X11))
| in_environment(X10,esk5_1(X10)) ) ),
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_3])])])])])]) ).
fof(c_0_5,hypothesis,
! [X4,X6] :
( ( ~ stable(X4)
| ~ environment(X4)
| greater(growth_rate(efficient_producers,X6),growth_rate(first_movers,X6))
| ~ greater_or_equal(X6,esk1_1(X4))
| ~ subpopulations(first_movers,efficient_producers,X4,X6) )
& ( ~ stable(X4)
| ~ environment(X4)
| in_environment(X4,esk1_1(X4)) ) ),
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_6,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_4]) ).
cnf(c_0_7,hypothesis,
( ~ stable(X1)
| ~ environment(X1)
| in_environment(X1,esk1_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_8,negated_conjecture,
~ ! [X1] :
( ( stable(X1)
& 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(assume_negation,[status(cth)],[prove_l12]) ).
cnf(c_0_9,hypothesis,
( ~ stable(X1)
| ~ environment(X1)
| ~ greater_or_equal(X2,esk1_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_10,hypothesis,
( ~ environment(X1)
| ~ stable(X1)
| in_environment(X1,esk5_1(X1))
| greater_or_equal(esk4_2(X1,esk1_1(X1)),esk1_1(X1)) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
fof(c_0_11,negated_conjecture,
~ ! [X1] :
( ( stable(X1)
& 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)],[c_0_8]) ).
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_4]) ).
cnf(c_0_13,hypothesis,
( ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,esk4_2(X1,esk1_1(X1)))
| ~ stable(X1)
| in_environment(X1,esk5_1(X1))
| greater(growth_rate(efficient_producers,esk4_2(X1,esk1_1(X1))),growth_rate(first_movers,esk4_2(X1,esk1_1(X1)))) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
fof(c_0_14,negated_conjecture,
! [X8] :
( ( greater(growth_rate(efficient_producers,X8),growth_rate(first_movers,X8))
| ~ in_environment(esk2_0,X8)
| ~ greater(growth_rate(efficient_producers,esk3_1(X8)),growth_rate(first_movers,esk3_1(X8))) )
& ( greater(growth_rate(efficient_producers,X8),growth_rate(first_movers,X8))
| ~ in_environment(esk2_0,X8)
| greater(esk3_1(X8),X8) )
& ( greater(growth_rate(efficient_producers,X8),growth_rate(first_movers,X8))
| ~ in_environment(esk2_0,X8)
| subpopulations(first_movers,efficient_producers,esk2_0,esk3_1(X8)) )
& stable(esk2_0)
& environment(esk2_0) ),
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_11])])])])])]) ).
cnf(c_0_15,hypothesis,
( ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,esk4_2(X1,esk1_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_7]) ).
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_4]) ).
cnf(c_0_17,negated_conjecture,
( ~ in_environment(esk2_0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| subpopulations(first_movers,efficient_producers,esk2_0,esk3_1(X1)) ),
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_7]) ).
cnf(c_0_19,negated_conjecture,
stable(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,negated_conjecture,
environment(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,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_4]) ).
cnf(c_0_22,negated_conjecture,
( subpopulations(first_movers,efficient_producers,esk2_0,esk3_1(esk5_1(esk2_0)))
| greater(growth_rate(efficient_producers,esk5_1(esk2_0)),growth_rate(first_movers,esk5_1(esk2_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_20])]) ).
cnf(c_0_23,negated_conjecture,
( ~ in_environment(esk2_0,X1)
| ~ greater(esk3_1(esk5_1(esk2_0)),esk5_1(esk2_0))
| greater_or_equal(esk4_2(esk2_0,X1),X1)
| greater(growth_rate(efficient_producers,esk5_1(esk2_0)),growth_rate(first_movers,esk5_1(esk2_0)))
| greater(growth_rate(efficient_producers,esk3_1(esk5_1(esk2_0))),growth_rate(first_movers,esk3_1(esk5_1(esk2_0)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_20])]) ).
cnf(c_0_24,negated_conjecture,
( ~ in_environment(esk2_0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| greater(esk3_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_25,negated_conjecture,
( ~ in_environment(esk2_0,X1)
| ~ greater(growth_rate(efficient_producers,esk3_1(X1)),growth_rate(first_movers,esk3_1(X1)))
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_26,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_4]) ).
cnf(c_0_27,negated_conjecture,
( ~ in_environment(esk2_0,X1)
| ~ in_environment(esk2_0,esk5_1(esk2_0))
| greater_or_equal(esk4_2(esk2_0,X1),X1)
| greater(growth_rate(efficient_producers,esk5_1(esk2_0)),growth_rate(first_movers,esk5_1(esk2_0))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_28,negated_conjecture,
( ~ in_environment(esk2_0,X1)
| ~ greater(esk3_1(esk5_1(esk2_0)),esk5_1(esk2_0))
| subpopulations(first_movers,efficient_producers,esk2_0,esk4_2(esk2_0,X1))
| greater(growth_rate(efficient_producers,esk5_1(esk2_0)),growth_rate(first_movers,esk5_1(esk2_0)))
| greater(growth_rate(efficient_producers,esk3_1(esk5_1(esk2_0))),growth_rate(first_movers,esk3_1(esk5_1(esk2_0)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_22]),c_0_20])]) ).
cnf(c_0_29,hypothesis,
( ~ in_environment(esk2_0,X1)
| greater_or_equal(esk4_2(esk2_0,X1),X1)
| greater(growth_rate(efficient_producers,esk5_1(esk2_0)),growth_rate(first_movers,esk5_1(esk2_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_18]),c_0_19]),c_0_20])]) ).
cnf(c_0_30,negated_conjecture,
( ~ in_environment(esk2_0,X1)
| ~ in_environment(esk2_0,esk5_1(esk2_0))
| subpopulations(first_movers,efficient_producers,esk2_0,esk4_2(esk2_0,X1))
| greater(growth_rate(efficient_producers,esk5_1(esk2_0)),growth_rate(first_movers,esk5_1(esk2_0))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_24]),c_0_25]) ).
cnf(c_0_31,hypothesis,
( greater_or_equal(esk4_2(esk2_0,esk1_1(esk2_0)),esk1_1(esk2_0))
| greater(growth_rate(efficient_producers,esk5_1(esk2_0)),growth_rate(first_movers,esk5_1(esk2_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_7]),c_0_19]),c_0_20])]) ).
cnf(c_0_32,hypothesis,
( ~ in_environment(esk2_0,X1)
| subpopulations(first_movers,efficient_producers,esk2_0,esk4_2(esk2_0,X1))
| greater(growth_rate(efficient_producers,esk5_1(esk2_0)),growth_rate(first_movers,esk5_1(esk2_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_18]),c_0_19]),c_0_20])]) ).
cnf(c_0_33,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_4]) ).
cnf(c_0_34,hypothesis,
( ~ subpopulations(first_movers,efficient_producers,esk2_0,esk4_2(esk2_0,esk1_1(esk2_0)))
| greater(growth_rate(efficient_producers,esk5_1(esk2_0)),growth_rate(first_movers,esk5_1(esk2_0)))
| greater(growth_rate(efficient_producers,esk4_2(esk2_0,esk1_1(esk2_0))),growth_rate(first_movers,esk4_2(esk2_0,esk1_1(esk2_0)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_31]),c_0_19]),c_0_20])]) ).
cnf(c_0_35,hypothesis,
( subpopulations(first_movers,efficient_producers,esk2_0,esk4_2(esk2_0,esk1_1(esk2_0)))
| greater(growth_rate(efficient_producers,esk5_1(esk2_0)),growth_rate(first_movers,esk5_1(esk2_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_7]),c_0_19]),c_0_20])]) ).
cnf(c_0_36,hypothesis,
( ~ in_environment(esk2_0,esk1_1(esk2_0))
| ~ subpopulations(first_movers,efficient_producers,esk2_0,X1)
| ~ greater(X1,esk5_1(esk2_0))
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| greater(growth_rate(efficient_producers,esk5_1(esk2_0)),growth_rate(first_movers,esk5_1(esk2_0))) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_20])]),c_0_35]) ).
cnf(c_0_37,hypothesis,
( ~ in_environment(esk2_0,esk1_1(esk2_0))
| ~ subpopulations(first_movers,efficient_producers,esk2_0,esk4_2(esk2_0,esk1_1(esk2_0)))
| in_environment(esk2_0,esk5_1(esk2_0))
| greater(growth_rate(efficient_producers,esk5_1(esk2_0)),growth_rate(first_movers,esk5_1(esk2_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_34]),c_0_20])]) ).
cnf(c_0_38,negated_conjecture,
( ~ in_environment(esk2_0,esk1_1(esk2_0))
| ~ greater(esk3_1(esk5_1(esk2_0)),esk5_1(esk2_0))
| greater(growth_rate(efficient_producers,esk5_1(esk2_0)),growth_rate(first_movers,esk5_1(esk2_0)))
| greater(growth_rate(efficient_producers,esk3_1(esk5_1(esk2_0))),growth_rate(first_movers,esk3_1(esk5_1(esk2_0)))) ),
inference(spm,[status(thm)],[c_0_36,c_0_22]) ).
cnf(c_0_39,hypothesis,
( ~ in_environment(esk2_0,esk1_1(esk2_0))
| in_environment(esk2_0,esk5_1(esk2_0))
| greater(growth_rate(efficient_producers,esk5_1(esk2_0)),growth_rate(first_movers,esk5_1(esk2_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_16]),c_0_20])]) ).
cnf(c_0_40,negated_conjecture,
( ~ in_environment(esk2_0,esk1_1(esk2_0))
| ~ greater(esk3_1(esk5_1(esk2_0)),esk5_1(esk2_0))
| greater(growth_rate(efficient_producers,esk5_1(esk2_0)),growth_rate(first_movers,esk5_1(esk2_0))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_38]),c_0_39]) ).
cnf(c_0_41,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_4]) ).
cnf(c_0_42,negated_conjecture,
( ~ in_environment(esk2_0,esk1_1(esk2_0))
| greater(growth_rate(efficient_producers,esk5_1(esk2_0)),growth_rate(first_movers,esk5_1(esk2_0))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_24]),c_0_39]) ).
cnf(c_0_43,negated_conjecture,
( ~ in_environment(esk2_0,X1)
| ~ in_environment(esk2_0,esk1_1(esk2_0))
| greater_or_equal(esk4_2(esk2_0,X1),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_20])]) ).
cnf(c_0_44,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_4]) ).
cnf(c_0_45,hypothesis,
( ~ environment(X1)
| ~ in_environment(esk2_0,esk1_1(X1))
| ~ in_environment(esk2_0,esk1_1(esk2_0))
| ~ subpopulations(first_movers,efficient_producers,X1,esk4_2(esk2_0,esk1_1(X1)))
| ~ stable(X1)
| greater(growth_rate(efficient_producers,esk4_2(esk2_0,esk1_1(X1))),growth_rate(first_movers,esk4_2(esk2_0,esk1_1(X1)))) ),
inference(spm,[status(thm)],[c_0_9,c_0_43]) ).
cnf(c_0_46,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_4]) ).
cnf(c_0_47,hypothesis,
( ~ environment(X1)
| ~ in_environment(esk2_0,esk1_1(X1))
| ~ in_environment(esk2_0,esk1_1(esk2_0))
| ~ subpopulations(first_movers,efficient_producers,X1,esk4_2(esk2_0,esk1_1(X1)))
| ~ stable(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_20])]),c_0_42]) ).
cnf(c_0_48,negated_conjecture,
( ~ in_environment(esk2_0,X1)
| ~ in_environment(esk2_0,esk1_1(esk2_0))
| subpopulations(first_movers,efficient_producers,esk2_0,esk4_2(esk2_0,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_42]),c_0_20])]) ).
cnf(c_0_49,negated_conjecture,
~ in_environment(esk2_0,esk1_1(esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_19]),c_0_20])]) ).
cnf(c_0_50,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_7]),c_0_19]),c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT030+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.56 % Computer : n015.cluster.edu
% 0.09/0.56 % Model : x86_64 x86_64
% 0.09/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.56 % Memory : 8046.5625MB
% 0.09/0.56 % OS : Linux 6.8.0-71-generic
% 0.09/0.56 % CPULimit : 300
% 0.09/0.56 % WCLimit : 300
% 0.09/0.56 % DateTime : Mon Sep 21 01:25:22 UTC 2026
% 0.09/0.56 % CPUTime :
% 0.09/0.56 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.60 Running first-order theorem proving
% 0.09/0.61 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 0.14/0.63 % Version: 3.5.1
% 0.14/0.63 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.63 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.63 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.63 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.63 % Starting sh5l with 300s (1) cores
% 0.14/0.63 % new_bool_3 with pid 254087 completed with status 0
% 0.14/0.63 % Result found by new_bool_3
% 0.14/0.63 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.63 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.63 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.63 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.63 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.63 % Search class: FGHNF-FFMF21-SFFFFFNN
% 0.14/0.63 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.63 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.63 % SubtermCWHack with pid 254093 completed with status 0
% 0.14/0.63 % Result found by SubtermCWHack
% 0.14/0.63 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.63 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.63 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.63 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.63 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.63 % Search class: FGHNF-FFMF21-SFFFFFNN
% 0.14/0.63 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.63 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.63 % Preprocessing time : 0.001 s
% 0.14/0.63
% 0.14/0.63 % Proof found!
% 0.14/0.63 % SZS status Theorem
% 0.14/0.63 % SZS output start CNFRefutation
% See solution above
% 0.14/0.63 % Parsed axioms : 3
% 0.14/0.63 % Removed by relevancy pruning/SinE : 0
% 0.14/0.63 % Initial clauses : 16
% 0.14/0.63 % Removed in clause preprocessing : 0
% 0.14/0.63 % Initial clauses in saturation : 16
% 0.14/0.63 % Processed clauses : 59
% 0.14/0.63 % ...of these trivial : 0
% 0.14/0.63 % ...subsumed : 9
% 0.14/0.63 % ...remaining for further processing : 50
% 0.14/0.63 % Other redundant clauses eliminated : 0
% 0.14/0.63 % Clauses deleted for lack of memory : 0
% 0.14/0.63 % Backward-subsumed : 21
% 0.14/0.63 % Backward-rewritten : 1
% 0.14/0.63 % Generated clauses : 64
% 0.14/0.63 % ...of the previous two non-redundant : 59
% 0.14/0.63 % ...aggressively subsumed : 0
% 0.14/0.63 % Contextual simplify-reflections : 8
% 0.14/0.63 % Paramodulations : 64
% 0.14/0.63 % Factorizations : 0
% 0.14/0.63 % NegExts : 0
% 0.14/0.63 % Equation resolutions : 0
% 0.14/0.63 % Disequality decompositions : 0
% 0.14/0.63 % Total rewrite steps : 64
% 0.14/0.63 % ...of those cached : 61
% 0.14/0.63 % Propositional unsat checks : 0
% 0.14/0.63 % Propositional check models : 0
% 0.14/0.63 % Propositional check unsatisfiable : 0
% 0.14/0.63 % Propositional clauses : 0
% 0.14/0.63 % Propositional clauses after purity: 0
% 0.14/0.63 % Propositional unsat core size : 0
% 0.14/0.63 % Propositional preprocessing time : 0.000
% 0.14/0.63 % Propositional encoding time : 0.000
% 0.14/0.63 % Propositional solver time : 0.000
% 0.14/0.63 % Success case prop preproc time : 0.000
% 0.14/0.63 % Success case prop encoding time : 0.000
% 0.14/0.63 % Success case prop solver time : 0.000
% 0.14/0.63 % Current number of processed clauses : 28
% 0.14/0.63 % Positive orientable unit clauses : 3
% 0.14/0.63 % Positive unorientable unit clauses: 0
% 0.14/0.63 % Negative unit clauses : 1
% 0.14/0.63 % Non-unit-clauses : 24
% 0.14/0.63 % Current number of unprocessed clauses: 9
% 0.14/0.63 % ...number of literals in the above : 52
% 0.14/0.63 % Current number of archived formulas : 0
% 0.14/0.63 % Current number of archived clauses : 22
% 0.14/0.63 % Clause-clause subsumption calls (NU) : 530
% 0.14/0.63 % Rec. Clause-clause subsumption calls : 130
% 0.14/0.63 % Non-unit clause-clause subsumptions : 34
% 0.14/0.63 % Unit Clause-clause subsumption calls : 23
% 0.14/0.63 % Rewrite failures with RHS unbound : 0
% 0.14/0.63 % BW rewrite match attempts : 1
% 0.14/0.63 % BW rewrite match successes : 1
% 0.14/0.63 % Condensation attempts : 0
% 0.14/0.63 % Condensation successes : 0
% 0.14/0.63 % Termbank termtop insertions : 3696
% 0.14/0.63 % Search garbage collected termcells : 291
% 0.14/0.63
% 0.14/0.63 % -------------------------------------------------
% 0.14/0.63 % User time : 0.006 s
% 0.14/0.63 % System time : 0.003 s
% 0.14/0.63 % Total time : 0.009 s
% 0.14/0.63 % Maximum resident set size: 3632 pages
% 0.14/0.63
% 0.14/0.63 % -------------------------------------------------
% 0.14/0.63 % User time : 0.006 s
% 0.14/0.63 % System time : 0.009 s
% 0.14/0.63 % Total time : 0.015 s
% 0.14/0.63 % Maximum resident set size: 4864 pages
% 0.14/0.63 % E exiting
%------------------------------------------------------------------------------