%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : MGT023+2 : TPTP v9.2.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n008.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 : Tue May 5 04:47:09 PM UTC 2026
% Result : Theorem 1.27s 1.73s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 4
% Syntax : Number of formulae : 57 ( 11 unt; 0 def)
% Number of atoms : 254 ( 24 equ)
% Maximal formula atoms : 42 ( 4 avg)
% Number of connectives : 306 ( 109 ~; 145 |; 38 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 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 : 64 ( 0 sgn 23 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_l5,conjecture,
! [X1] :
( ( environment(X1)
& stable(X1) )
=> in_environment(X1,critical_point(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l5) ).
fof(mp_earliest_time_growth_rate_exceeds,axiom,
! [X1] :
( ( environment(X1)
& ? [X2] :
( in_environment(X1,X2)
& ! [X3] :
( ( subpopulations(first_movers,efficient_producers,X1,X3)
& greater_or_equal(X3,X2) )
=> greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3)) ) ) )
=> ? [X2] :
( in_environment(X1,X2)
& ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
& ! [X3] :
( ( subpopulations(first_movers,efficient_producers,X1,X3)
& greater(X3,X2) )
=> greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds) ).
fof(l1,hypothesis,
! [X1] :
( ( environment(X1)
& stable(X1) )
=> ? [X2] :
( in_environment(X1,X2)
& ! [X3] :
( ( subpopulations(first_movers,efficient_producers,X1,X3)
& greater_or_equal(X3,X2) )
=> greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1) ).
fof(d1,hypothesis,
! [X1,X2] :
( ( environment(X1)
& ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
& in_environment(X1,X2)
& ! [X3] :
( ( subpopulations(first_movers,efficient_producers,X1,X3)
& greater(X3,X2) )
=> greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3)) ) )
=> X2 = critical_point(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1) ).
fof(c_0_4,negated_conjecture,
~ ! [X1] :
( ( environment(X1)
& stable(X1) )
=> in_environment(X1,critical_point(X1)) ),
inference(assume_negation,[status(cth)],[prove_l5]) ).
fof(c_0_5,plain,
! [X1] :
( ( environment(X1)
& ? [X2] :
( in_environment(X1,X2)
& ! [X3] :
( ( subpopulations(first_movers,efficient_producers,X1,X3)
& greater_or_equal(X3,X2) )
=> greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3)) ) ) )
=> ? [X2] :
( in_environment(X1,X2)
& ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
& ! [X3] :
( ( subpopulations(first_movers,efficient_producers,X1,X3)
& greater(X3,X2) )
=> greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3)) ) ) ),
inference(fof_simplification,[status(thm)],[mp_earliest_time_growth_rate_exceeds]) ).
fof(c_0_6,hypothesis,
! [X24,X26] :
( ( in_environment(X24,esk4_1(X24))
| ~ environment(X24)
| ~ stable(X24) )
& ( ~ subpopulations(first_movers,efficient_producers,X24,X26)
| ~ greater_or_equal(X26,esk4_1(X24))
| greater(growth_rate(efficient_producers,X26),growth_rate(first_movers,X26))
| ~ environment(X24)
| ~ stable(X24) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l1])])])])]) ).
fof(c_0_7,negated_conjecture,
( environment(esk5_0)
& stable(esk5_0)
& ~ in_environment(esk5_0,critical_point(esk5_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_8,plain,
! [X16,X17,X20] :
( ( in_environment(X16,esk2_1(X16))
| subpopulations(first_movers,efficient_producers,X16,esk1_2(X16,X17))
| ~ in_environment(X16,X17)
| ~ environment(X16) )
& ( ~ greater(growth_rate(efficient_producers,esk2_1(X16)),growth_rate(first_movers,esk2_1(X16)))
| subpopulations(first_movers,efficient_producers,X16,esk1_2(X16,X17))
| ~ in_environment(X16,X17)
| ~ environment(X16) )
& ( ~ subpopulations(first_movers,efficient_producers,X16,X20)
| ~ greater(X20,esk2_1(X16))
| greater(growth_rate(efficient_producers,X20),growth_rate(first_movers,X20))
| subpopulations(first_movers,efficient_producers,X16,esk1_2(X16,X17))
| ~ in_environment(X16,X17)
| ~ environment(X16) )
& ( in_environment(X16,esk2_1(X16))
| greater_or_equal(esk1_2(X16,X17),X17)
| ~ in_environment(X16,X17)
| ~ environment(X16) )
& ( ~ greater(growth_rate(efficient_producers,esk2_1(X16)),growth_rate(first_movers,esk2_1(X16)))
| greater_or_equal(esk1_2(X16,X17),X17)
| ~ in_environment(X16,X17)
| ~ environment(X16) )
& ( ~ subpopulations(first_movers,efficient_producers,X16,X20)
| ~ greater(X20,esk2_1(X16))
| greater(growth_rate(efficient_producers,X20),growth_rate(first_movers,X20))
| greater_or_equal(esk1_2(X16,X17),X17)
| ~ in_environment(X16,X17)
| ~ environment(X16) )
& ( in_environment(X16,esk2_1(X16))
| ~ greater(growth_rate(efficient_producers,esk1_2(X16,X17)),growth_rate(first_movers,esk1_2(X16,X17)))
| ~ in_environment(X16,X17)
| ~ environment(X16) )
& ( ~ greater(growth_rate(efficient_producers,esk2_1(X16)),growth_rate(first_movers,esk2_1(X16)))
| ~ greater(growth_rate(efficient_producers,esk1_2(X16,X17)),growth_rate(first_movers,esk1_2(X16,X17)))
| ~ in_environment(X16,X17)
| ~ environment(X16) )
& ( ~ subpopulations(first_movers,efficient_producers,X16,X20)
| ~ greater(X20,esk2_1(X16))
| greater(growth_rate(efficient_producers,X20),growth_rate(first_movers,X20))
| ~ greater(growth_rate(efficient_producers,esk1_2(X16,X17)),growth_rate(first_movers,esk1_2(X16,X17)))
| ~ in_environment(X16,X17)
| ~ environment(X16) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])])]) ).
cnf(c_0_9,hypothesis,
( in_environment(X1,esk4_1(X1))
| ~ environment(X1)
| ~ stable(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
stable(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
environment(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,hypothesis,
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ greater_or_equal(X2,esk4_1(X1))
| ~ environment(X1)
| ~ stable(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_13,hypothesis,
! [X1,X2] :
( ( environment(X1)
& ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
& in_environment(X1,X2)
& ! [X3] :
( ( subpopulations(first_movers,efficient_producers,X1,X3)
& greater(X3,X2) )
=> greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3)) ) )
=> X2 = critical_point(X1) ),
inference(fof_simplification,[status(thm)],[d1]) ).
cnf(c_0_14,plain,
( in_environment(X1,esk2_1(X1))
| greater_or_equal(esk1_2(X1,X2),X2)
| ~ in_environment(X1,X2)
| ~ environment(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,negated_conjecture,
in_environment(esk5_0,esk4_1(esk5_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11])]) ).
cnf(c_0_16,plain,
( in_environment(X1,esk2_1(X1))
| subpopulations(first_movers,efficient_producers,X1,esk1_2(X1,X2))
| ~ in_environment(X1,X2)
| ~ environment(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_17,negated_conjecture,
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ greater_or_equal(X1,esk4_1(esk5_0))
| ~ subpopulations(first_movers,efficient_producers,esk5_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_10]),c_0_11])]) ).
cnf(c_0_18,plain,
( greater_or_equal(esk1_2(X1,X2),X2)
| ~ greater(growth_rate(efficient_producers,esk2_1(X1)),growth_rate(first_movers,esk2_1(X1)))
| ~ in_environment(X1,X2)
| ~ environment(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_19,plain,
( ~ greater(growth_rate(efficient_producers,esk2_1(X1)),growth_rate(first_movers,esk2_1(X1)))
| ~ greater(growth_rate(efficient_producers,esk1_2(X1,X2)),growth_rate(first_movers,esk1_2(X1,X2)))
| ~ in_environment(X1,X2)
| ~ environment(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_20,hypothesis,
! [X21,X22] :
( ( subpopulations(first_movers,efficient_producers,X21,esk3_2(X21,X22))
| ~ environment(X21)
| greater(growth_rate(efficient_producers,X22),growth_rate(first_movers,X22))
| ~ in_environment(X21,X22)
| X22 = critical_point(X21) )
& ( greater(esk3_2(X21,X22),X22)
| ~ environment(X21)
| greater(growth_rate(efficient_producers,X22),growth_rate(first_movers,X22))
| ~ in_environment(X21,X22)
| X22 = critical_point(X21) )
& ( ~ greater(growth_rate(efficient_producers,esk3_2(X21,X22)),growth_rate(first_movers,esk3_2(X21,X22)))
| ~ environment(X21)
| greater(growth_rate(efficient_producers,X22),growth_rate(first_movers,X22))
| ~ in_environment(X21,X22)
| X22 = critical_point(X21) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])]) ).
cnf(c_0_21,negated_conjecture,
( greater_or_equal(esk1_2(esk5_0,esk4_1(esk5_0)),esk4_1(esk5_0))
| in_environment(esk5_0,esk2_1(esk5_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_11])]) ).
cnf(c_0_22,negated_conjecture,
( subpopulations(first_movers,efficient_producers,esk5_0,esk1_2(esk5_0,esk4_1(esk5_0)))
| in_environment(esk5_0,esk2_1(esk5_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_15]),c_0_11])]) ).
cnf(c_0_23,negated_conjecture,
( ~ greater(growth_rate(efficient_producers,esk2_1(X1)),growth_rate(first_movers,esk2_1(X1)))
| ~ subpopulations(first_movers,efficient_producers,esk5_0,esk1_2(X1,esk4_1(esk5_0)))
| ~ in_environment(X1,esk4_1(esk5_0))
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_24,plain,
( subpopulations(first_movers,efficient_producers,X1,esk1_2(X1,X2))
| ~ greater(growth_rate(efficient_producers,esk2_1(X1)),growth_rate(first_movers,esk2_1(X1)))
| ~ in_environment(X1,X2)
| ~ environment(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_25,plain,
( in_environment(X1,esk2_1(X1))
| ~ greater(growth_rate(efficient_producers,esk1_2(X1,X2)),growth_rate(first_movers,esk1_2(X1,X2)))
| ~ in_environment(X1,X2)
| ~ environment(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_26,hypothesis,
( greater(esk3_2(X1,X2),X2)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| X2 = critical_point(X1)
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,negated_conjecture,
( greater(growth_rate(efficient_producers,esk1_2(esk5_0,esk4_1(esk5_0))),growth_rate(first_movers,esk1_2(esk5_0,esk4_1(esk5_0))))
| in_environment(esk5_0,esk2_1(esk5_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_21]),c_0_22]) ).
cnf(c_0_28,negated_conjecture,
~ greater(growth_rate(efficient_producers,esk2_1(esk5_0)),growth_rate(first_movers,esk2_1(esk5_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_15]),c_0_11])]) ).
cnf(c_0_29,negated_conjecture,
( in_environment(esk5_0,esk2_1(esk5_0))
| ~ greater(growth_rate(efficient_producers,esk1_2(esk5_0,X1)),growth_rate(first_movers,esk1_2(esk5_0,X1)))
| ~ in_environment(esk5_0,X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_11]) ).
cnf(c_0_30,hypothesis,
( critical_point(esk5_0) = esk2_1(esk5_0)
| greater(growth_rate(efficient_producers,esk1_2(esk5_0,esk4_1(esk5_0))),growth_rate(first_movers,esk1_2(esk5_0,esk4_1(esk5_0))))
| greater(esk3_2(esk5_0,esk2_1(esk5_0)),esk2_1(esk5_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_11])]),c_0_28]) ).
cnf(c_0_31,hypothesis,
( subpopulations(first_movers,efficient_producers,X1,esk3_2(X1,X2))
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| X2 = critical_point(X1)
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_32,negated_conjecture,
( critical_point(esk5_0) = esk2_1(esk5_0)
| greater(esk3_2(esk5_0,esk2_1(esk5_0)),esk2_1(esk5_0))
| in_environment(esk5_0,esk2_1(esk5_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_15])]) ).
cnf(c_0_33,plain,
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| greater_or_equal(esk1_2(X1,X3),X3)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ greater(X2,esk2_1(X1))
| ~ in_environment(X1,X3)
| ~ environment(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_34,negated_conjecture,
( critical_point(esk5_0) = esk2_1(esk5_0)
| greater(growth_rate(efficient_producers,esk1_2(esk5_0,esk4_1(esk5_0))),growth_rate(first_movers,esk1_2(esk5_0,esk4_1(esk5_0))))
| subpopulations(first_movers,efficient_producers,esk5_0,esk3_2(esk5_0,esk2_1(esk5_0))) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_27]),c_0_11])]),c_0_28]) ).
cnf(c_0_35,hypothesis,
( critical_point(esk5_0) = esk2_1(esk5_0)
| greater(esk3_2(esk5_0,esk2_1(esk5_0)),esk2_1(esk5_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_32]),c_0_11])]),c_0_28]) ).
cnf(c_0_36,negated_conjecture,
( critical_point(esk5_0) = esk2_1(esk5_0)
| greater(growth_rate(efficient_producers,esk1_2(esk5_0,esk4_1(esk5_0))),growth_rate(first_movers,esk1_2(esk5_0,esk4_1(esk5_0))))
| greater(growth_rate(efficient_producers,esk3_2(esk5_0,esk2_1(esk5_0))),growth_rate(first_movers,esk3_2(esk5_0,esk2_1(esk5_0))))
| greater_or_equal(esk1_2(esk5_0,X1),X1)
| ~ in_environment(esk5_0,X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_11])]),c_0_35]) ).
cnf(c_0_37,plain,
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| subpopulations(first_movers,efficient_producers,X1,esk1_2(X1,X3))
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ greater(X2,esk2_1(X1))
| ~ in_environment(X1,X3)
| ~ environment(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_38,negated_conjecture,
( critical_point(esk5_0) = esk2_1(esk5_0)
| greater(growth_rate(efficient_producers,esk3_2(esk5_0,esk2_1(esk5_0))),growth_rate(first_movers,esk3_2(esk5_0,esk2_1(esk5_0))))
| greater(growth_rate(efficient_producers,esk1_2(esk5_0,esk4_1(esk5_0))),growth_rate(first_movers,esk1_2(esk5_0,esk4_1(esk5_0))))
| greater_or_equal(esk1_2(esk5_0,esk4_1(esk5_0)),esk4_1(esk5_0)) ),
inference(spm,[status(thm)],[c_0_36,c_0_15]) ).
cnf(c_0_39,negated_conjecture,
( critical_point(esk5_0) = esk2_1(esk5_0)
| greater(growth_rate(efficient_producers,esk1_2(esk5_0,esk4_1(esk5_0))),growth_rate(first_movers,esk1_2(esk5_0,esk4_1(esk5_0))))
| greater(growth_rate(efficient_producers,esk3_2(esk5_0,esk2_1(esk5_0))),growth_rate(first_movers,esk3_2(esk5_0,esk2_1(esk5_0))))
| subpopulations(first_movers,efficient_producers,esk5_0,esk1_2(esk5_0,X1))
| ~ in_environment(esk5_0,X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_34]),c_0_11])]),c_0_35]) ).
cnf(c_0_40,negated_conjecture,
( critical_point(esk5_0) = esk2_1(esk5_0)
| greater(growth_rate(efficient_producers,esk3_2(esk5_0,esk2_1(esk5_0))),growth_rate(first_movers,esk3_2(esk5_0,esk2_1(esk5_0))))
| greater(growth_rate(efficient_producers,esk1_2(esk5_0,esk4_1(esk5_0))),growth_rate(first_movers,esk1_2(esk5_0,esk4_1(esk5_0))))
| ~ subpopulations(first_movers,efficient_producers,esk5_0,esk1_2(esk5_0,esk4_1(esk5_0))) ),
inference(spm,[status(thm)],[c_0_17,c_0_38]) ).
cnf(c_0_41,negated_conjecture,
( critical_point(esk5_0) = esk2_1(esk5_0)
| greater(growth_rate(efficient_producers,esk3_2(esk5_0,esk2_1(esk5_0))),growth_rate(first_movers,esk3_2(esk5_0,esk2_1(esk5_0))))
| greater(growth_rate(efficient_producers,esk1_2(esk5_0,esk4_1(esk5_0))),growth_rate(first_movers,esk1_2(esk5_0,esk4_1(esk5_0)))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_15]),c_0_40]) ).
cnf(c_0_42,negated_conjecture,
( critical_point(esk5_0) = esk2_1(esk5_0)
| greater(growth_rate(efficient_producers,esk3_2(esk5_0,esk2_1(esk5_0))),growth_rate(first_movers,esk3_2(esk5_0,esk2_1(esk5_0))))
| in_environment(esk5_0,esk2_1(esk5_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_41]),c_0_15])]) ).
cnf(c_0_43,plain,
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ greater(X2,esk2_1(X1))
| ~ greater(growth_rate(efficient_producers,esk1_2(X1,X3)),growth_rate(first_movers,esk1_2(X1,X3)))
| ~ in_environment(X1,X3)
| ~ environment(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_44,hypothesis,
( critical_point(esk5_0) = esk2_1(esk5_0)
| greater(growth_rate(efficient_producers,esk3_2(esk5_0,esk2_1(esk5_0))),growth_rate(first_movers,esk3_2(esk5_0,esk2_1(esk5_0))))
| subpopulations(first_movers,efficient_producers,esk5_0,esk3_2(esk5_0,esk2_1(esk5_0))) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_42]),c_0_11])]),c_0_28]) ).
cnf(c_0_45,hypothesis,
( critical_point(esk5_0) = esk2_1(esk5_0)
| greater(growth_rate(efficient_producers,esk3_2(esk5_0,esk2_1(esk5_0))),growth_rate(first_movers,esk3_2(esk5_0,esk2_1(esk5_0))))
| ~ greater(growth_rate(efficient_producers,esk1_2(esk5_0,X1)),growth_rate(first_movers,esk1_2(esk5_0,X1)))
| ~ in_environment(esk5_0,X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_11])]),c_0_35]) ).
cnf(c_0_46,hypothesis,
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| X2 = critical_point(X1)
| ~ greater(growth_rate(efficient_producers,esk3_2(X1,X2)),growth_rate(first_movers,esk3_2(X1,X2)))
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_47,negated_conjecture,
( critical_point(esk5_0) = esk2_1(esk5_0)
| greater(growth_rate(efficient_producers,esk3_2(esk5_0,esk2_1(esk5_0))),growth_rate(first_movers,esk3_2(esk5_0,esk2_1(esk5_0)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_41]),c_0_15])]) ).
cnf(c_0_48,hypothesis,
( critical_point(esk5_0) = esk2_1(esk5_0)
| ~ in_environment(esk5_0,esk2_1(esk5_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_11])]),c_0_28]) ).
cnf(c_0_49,negated_conjecture,
( critical_point(esk5_0) = esk2_1(esk5_0)
| greater(growth_rate(efficient_producers,esk1_2(esk5_0,esk4_1(esk5_0))),growth_rate(first_movers,esk1_2(esk5_0,esk4_1(esk5_0)))) ),
inference(spm,[status(thm)],[c_0_48,c_0_27]) ).
cnf(c_0_50,negated_conjecture,
~ in_environment(esk5_0,critical_point(esk5_0)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_51,negated_conjecture,
critical_point(esk5_0) = esk2_1(esk5_0),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_49]),c_0_15])]),c_0_48]) ).
cnf(c_0_52,negated_conjecture,
~ in_environment(esk5_0,esk2_1(esk5_0)),
inference(rw,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_53,negated_conjecture,
greater_or_equal(esk1_2(esk5_0,esk4_1(esk5_0)),esk4_1(esk5_0)),
inference(sr,[status(thm)],[c_0_21,c_0_52]) ).
cnf(c_0_54,negated_conjecture,
subpopulations(first_movers,efficient_producers,esk5_0,esk1_2(esk5_0,esk4_1(esk5_0))),
inference(sr,[status(thm)],[c_0_22,c_0_52]) ).
cnf(c_0_55,negated_conjecture,
greater(growth_rate(efficient_producers,esk1_2(esk5_0,esk4_1(esk5_0))),growth_rate(first_movers,esk1_2(esk5_0,esk4_1(esk5_0)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_53]),c_0_54])]) ).
cnf(c_0_56,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_55]),c_0_15])]),c_0_52]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT023+2 : TPTP v9.2.1. Released v2.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32 % Computer : n008.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Mon May 4 23:27:43 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.27/1.73 % Version : CSE_E---1.7
% 1.27/1.73 % Problem : theBenchmark.p
% 1.27/1.73 % SZS status Theorem for theBenchmark.p
% 1.27/1.73 % SZS output start CNFRefutation
% See solution above
% 1.27/1.73 % Total time : 1.370s
%------------------------------------------------------------------------------