%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : MGT028+1 : 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 : n002.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 04:47:10 PM UTC 2026
% Result : Theorem 1.26s 1.72s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 36 ( 10 unt; 0 def)
% Number of atoms : 168 ( 0 equ)
% Maximal formula atoms : 36 ( 4 avg)
% Number of connectives : 223 ( 91 ~; 96 |; 27 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 15 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mp_first_movers_negative_growth,axiom,
! [X1] :
( ( environment(X1)
& stable(X1)
& ? [X2] :
( in_environment(X1,X2)
& ! [X3] :
( ( subpopulations(first_movers,efficient_producers,X1,X3)
& greater_or_equal(X3,X2) )
=> greater(zero,growth_rate(first_movers,X3)) ) ) )
=> ? [X4] :
( greater(X4,appear(efficient_producers,X1))
& ! [X3] :
( ( subpopulations(first_movers,efficient_producers,X1,X3)
& greater_or_equal(X3,X4) )
=> greater(zero,growth_rate(first_movers,X3)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_first_movers_negative_growth) ).
fof(l11,hypothesis,
! [X1] :
( ( environment(X1)
& stable(X1) )
=> ? [X5] :
( in_environment(X1,X5)
& ! [X3] :
( ( subpopulations(first_movers,efficient_producers,X1,X3)
& greater_or_equal(X3,X5) )
=> ( greater(growth_rate(efficient_producers,X3),zero)
& greater(zero,growth_rate(first_movers,X3)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l11) ).
fof(prove_l10,conjecture,
! [X1] :
( ( environment(X1)
& stable(X1) )
=> ? [X5] :
( greater(X5,appear(efficient_producers,X1))
& ! [X3] :
( ( subpopulations(first_movers,efficient_producers,X1,X3)
& greater_or_equal(X3,X5) )
=> greater(zero,growth_rate(first_movers,X3)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l10) ).
fof(c_0_3,plain,
! [X17,X18,X21] :
( ( greater(esk2_1(X17),appear(efficient_producers,X17))
| subpopulations(first_movers,efficient_producers,X17,esk1_2(X17,X18))
| ~ in_environment(X17,X18)
| ~ environment(X17)
| ~ stable(X17) )
& ( ~ subpopulations(first_movers,efficient_producers,X17,X21)
| ~ greater_or_equal(X21,esk2_1(X17))
| greater(zero,growth_rate(first_movers,X21))
| subpopulations(first_movers,efficient_producers,X17,esk1_2(X17,X18))
| ~ in_environment(X17,X18)
| ~ environment(X17)
| ~ stable(X17) )
& ( greater(esk2_1(X17),appear(efficient_producers,X17))
| greater_or_equal(esk1_2(X17,X18),X18)
| ~ in_environment(X17,X18)
| ~ environment(X17)
| ~ stable(X17) )
& ( ~ subpopulations(first_movers,efficient_producers,X17,X21)
| ~ greater_or_equal(X21,esk2_1(X17))
| greater(zero,growth_rate(first_movers,X21))
| greater_or_equal(esk1_2(X17,X18),X18)
| ~ in_environment(X17,X18)
| ~ environment(X17)
| ~ stable(X17) )
& ( greater(esk2_1(X17),appear(efficient_producers,X17))
| ~ greater(zero,growth_rate(first_movers,esk1_2(X17,X18)))
| ~ in_environment(X17,X18)
| ~ environment(X17)
| ~ stable(X17) )
& ( ~ subpopulations(first_movers,efficient_producers,X17,X21)
| ~ greater_or_equal(X21,esk2_1(X17))
| greater(zero,growth_rate(first_movers,X21))
| ~ greater(zero,growth_rate(first_movers,esk1_2(X17,X18)))
| ~ in_environment(X17,X18)
| ~ environment(X17)
| ~ stable(X17) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_first_movers_negative_growth])])])])]) ).
fof(c_0_4,hypothesis,
! [X22,X24] :
( ( in_environment(X22,esk3_1(X22))
| ~ environment(X22)
| ~ stable(X22) )
& ( greater(growth_rate(efficient_producers,X24),zero)
| ~ subpopulations(first_movers,efficient_producers,X22,X24)
| ~ greater_or_equal(X24,esk3_1(X22))
| ~ environment(X22)
| ~ stable(X22) )
& ( greater(zero,growth_rate(first_movers,X24))
| ~ subpopulations(first_movers,efficient_producers,X22,X24)
| ~ greater_or_equal(X24,esk3_1(X22))
| ~ environment(X22)
| ~ stable(X22) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l11])])])])]) ).
cnf(c_0_5,plain,
( greater(esk2_1(X1),appear(efficient_producers,X1))
| greater_or_equal(esk1_2(X1,X2),X2)
| ~ in_environment(X1,X2)
| ~ environment(X1)
| ~ stable(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_6,hypothesis,
( in_environment(X1,esk3_1(X1))
| ~ environment(X1)
| ~ stable(X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,plain,
( greater(esk2_1(X1),appear(efficient_producers,X1))
| subpopulations(first_movers,efficient_producers,X1,esk1_2(X1,X2))
| ~ in_environment(X1,X2)
| ~ environment(X1)
| ~ stable(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
fof(c_0_8,negated_conjecture,
~ ! [X1] :
( ( environment(X1)
& stable(X1) )
=> ? [X5] :
( greater(X5,appear(efficient_producers,X1))
& ! [X3] :
( ( subpopulations(first_movers,efficient_producers,X1,X3)
& greater_or_equal(X3,X5) )
=> greater(zero,growth_rate(first_movers,X3)) ) ) ),
inference(assume_negation,[status(cth)],[prove_l10]) ).
cnf(c_0_9,hypothesis,
( greater(zero,growth_rate(first_movers,X1))
| ~ subpopulations(first_movers,efficient_producers,X2,X1)
| ~ greater_or_equal(X1,esk3_1(X2))
| ~ environment(X2)
| ~ stable(X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_10,hypothesis,
( greater(esk2_1(X1),appear(efficient_producers,X1))
| greater_or_equal(esk1_2(X1,esk3_1(X1)),esk3_1(X1))
| ~ stable(X1)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_11,hypothesis,
( greater(esk2_1(X1),appear(efficient_producers,X1))
| subpopulations(first_movers,efficient_producers,X1,esk1_2(X1,esk3_1(X1)))
| ~ stable(X1)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_7,c_0_6]) ).
fof(c_0_12,negated_conjecture,
! [X26] :
( environment(esk4_0)
& stable(esk4_0)
& ( subpopulations(first_movers,efficient_producers,esk4_0,esk5_1(X26))
| ~ greater(X26,appear(efficient_producers,esk4_0)) )
& ( greater_or_equal(esk5_1(X26),X26)
| ~ greater(X26,appear(efficient_producers,esk4_0)) )
& ( ~ greater(zero,growth_rate(first_movers,esk5_1(X26)))
| ~ greater(X26,appear(efficient_producers,esk4_0)) ) ),
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_8])])])])]) ).
cnf(c_0_13,hypothesis,
( greater(zero,growth_rate(first_movers,esk1_2(X1,esk3_1(X1))))
| greater(esk2_1(X1),appear(efficient_producers,X1))
| ~ stable(X1)
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).
cnf(c_0_14,negated_conjecture,
stable(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_15,negated_conjecture,
environment(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
( greater(esk2_1(X1),appear(efficient_producers,X1))
| ~ greater(zero,growth_rate(first_movers,esk1_2(X1,X2)))
| ~ in_environment(X1,X2)
| ~ environment(X1)
| ~ stable(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_17,negated_conjecture,
( greater(zero,growth_rate(first_movers,esk1_2(esk4_0,esk3_1(esk4_0))))
| greater(esk2_1(esk4_0),appear(efficient_producers,esk4_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]) ).
cnf(c_0_18,negated_conjecture,
( greater(esk2_1(esk4_0),appear(efficient_producers,esk4_0))
| ~ in_environment(esk4_0,esk3_1(esk4_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_14]),c_0_15])]) ).
cnf(c_0_19,negated_conjecture,
( greater_or_equal(esk5_1(X1),X1)
| ~ greater(X1,appear(efficient_producers,esk4_0)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,hypothesis,
greater(esk2_1(esk4_0),appear(efficient_producers,esk4_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_6]),c_0_14]),c_0_15])]) ).
cnf(c_0_21,negated_conjecture,
( subpopulations(first_movers,efficient_producers,esk4_0,esk5_1(X1))
| ~ greater(X1,appear(efficient_producers,esk4_0)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_22,negated_conjecture,
( ~ greater(zero,growth_rate(first_movers,esk5_1(X1)))
| ~ greater(X1,appear(efficient_producers,esk4_0)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_23,plain,
( greater(zero,growth_rate(first_movers,X2))
| greater_or_equal(esk1_2(X1,X3),X3)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ greater_or_equal(X2,esk2_1(X1))
| ~ in_environment(X1,X3)
| ~ environment(X1)
| ~ stable(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_24,negated_conjecture,
greater_or_equal(esk5_1(esk2_1(esk4_0)),esk2_1(esk4_0)),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,negated_conjecture,
subpopulations(first_movers,efficient_producers,esk4_0,esk5_1(esk2_1(esk4_0))),
inference(spm,[status(thm)],[c_0_21,c_0_20]) ).
cnf(c_0_26,negated_conjecture,
~ greater(zero,growth_rate(first_movers,esk5_1(esk2_1(esk4_0)))),
inference(spm,[status(thm)],[c_0_22,c_0_20]) ).
cnf(c_0_27,plain,
( greater(zero,growth_rate(first_movers,X2))
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ greater_or_equal(X2,esk2_1(X1))
| ~ greater(zero,growth_rate(first_movers,esk1_2(X1,X3)))
| ~ in_environment(X1,X3)
| ~ environment(X1)
| ~ stable(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_28,negated_conjecture,
( greater_or_equal(esk1_2(esk4_0,X1),X1)
| ~ in_environment(esk4_0,X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_14]),c_0_15])]),c_0_26]) ).
cnf(c_0_29,negated_conjecture,
( ~ greater(zero,growth_rate(first_movers,esk1_2(esk4_0,X1)))
| ~ in_environment(esk4_0,X1) ),
inference(sr,[status(thm)],[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_25]),c_0_14]),c_0_15])]),c_0_26]) ).
cnf(c_0_30,plain,
( greater(zero,growth_rate(first_movers,X2))
| subpopulations(first_movers,efficient_producers,X1,esk1_2(X1,X3))
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ greater_or_equal(X2,esk2_1(X1))
| ~ in_environment(X1,X3)
| ~ environment(X1)
| ~ stable(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_31,hypothesis,
greater_or_equal(esk1_2(esk4_0,esk3_1(esk4_0)),esk3_1(esk4_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_6]),c_0_14]),c_0_15])]) ).
cnf(c_0_32,hypothesis,
~ greater(zero,growth_rate(first_movers,esk1_2(esk4_0,esk3_1(esk4_0)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_6]),c_0_14]),c_0_15])]) ).
cnf(c_0_33,negated_conjecture,
( subpopulations(first_movers,efficient_producers,esk4_0,esk1_2(esk4_0,X1))
| ~ in_environment(esk4_0,X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_24]),c_0_25]),c_0_14]),c_0_15])]),c_0_26]) ).
cnf(c_0_34,hypothesis,
~ subpopulations(first_movers,efficient_producers,esk4_0,esk1_2(esk4_0,esk3_1(esk4_0))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_31]),c_0_14]),c_0_15])]),c_0_32]) ).
cnf(c_0_35,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_6]),c_0_14]),c_0_15])]),c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT028+1 : 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
% 0.17/0.33 % Computer : n002.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Mon May 4 23:28:16 EDT 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.34 % start to proof: theBenchmark
% 1.26/1.72 % Version : CSE_E---1.7
% 1.26/1.72 % Problem : theBenchmark.p
% 1.26/1.72 % SZS status Theorem for theBenchmark.p
% 1.26/1.72 % SZS output start CNFRefutation
% See solution above
% 1.26/1.72 % Total time : 1.374s
%------------------------------------------------------------------------------