%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : MGT023+1 : TPTP v9.2.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n010.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 1.25s 1.71s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 23 ( 4 unt; 0 def)
% Number of atoms : 108 ( 11 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 133 ( 48 ~; 51 |; 24 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 16 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox/benchmark/theBenchmark.p',d1) ).
fof(l12,hypothesis,
! [X1] :
( ( environment(X1)
& stable(X1) )
=> ? [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/sandbox/benchmark/theBenchmark.p',l12) ).
fof(prove_l5,conjecture,
! [X1] :
( ( environment(X1)
& stable(X1) )
=> in_environment(X1,critical_point(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l5) ).
fof(c_0_3,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]) ).
fof(c_0_4,hypothesis,
! [X1] :
( ( environment(X1)
& stable(X1) )
=> ? [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)],[l12]) ).
fof(c_0_5,hypothesis,
! [X11,X12] :
( ( subpopulations(first_movers,efficient_producers,X11,esk1_2(X11,X12))
| ~ environment(X11)
| greater(growth_rate(efficient_producers,X12),growth_rate(first_movers,X12))
| ~ in_environment(X11,X12)
| X12 = critical_point(X11) )
& ( greater(esk1_2(X11,X12),X12)
| ~ environment(X11)
| greater(growth_rate(efficient_producers,X12),growth_rate(first_movers,X12))
| ~ in_environment(X11,X12)
| X12 = critical_point(X11) )
& ( ~ greater(growth_rate(efficient_producers,esk1_2(X11,X12)),growth_rate(first_movers,esk1_2(X11,X12)))
| ~ environment(X11)
| greater(growth_rate(efficient_producers,X12),growth_rate(first_movers,X12))
| ~ in_environment(X11,X12)
| X12 = critical_point(X11) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])]) ).
fof(c_0_6,hypothesis,
! [X14,X16] :
( ( in_environment(X14,esk2_1(X14))
| ~ environment(X14)
| ~ stable(X14) )
& ( ~ greater(growth_rate(efficient_producers,esk2_1(X14)),growth_rate(first_movers,esk2_1(X14)))
| ~ environment(X14)
| ~ stable(X14) )
& ( ~ subpopulations(first_movers,efficient_producers,X14,X16)
| ~ greater(X16,esk2_1(X14))
| greater(growth_rate(efficient_producers,X16),growth_rate(first_movers,X16))
| ~ environment(X14)
| ~ stable(X14) ) ),
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_4])])])])]) ).
cnf(c_0_7,hypothesis,
( subpopulations(first_movers,efficient_producers,X1,esk1_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_5]) ).
cnf(c_0_8,hypothesis,
( in_environment(X1,esk2_1(X1))
| ~ environment(X1)
| ~ stable(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,hypothesis,
( ~ greater(growth_rate(efficient_producers,esk2_1(X1)),growth_rate(first_movers,esk2_1(X1)))
| ~ environment(X1)
| ~ stable(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,hypothesis,
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ greater(X2,esk2_1(X1))
| ~ environment(X1)
| ~ stable(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,hypothesis,
( esk2_1(X1) = critical_point(X1)
| subpopulations(first_movers,efficient_producers,X1,esk1_2(X1,esk2_1(X1)))
| ~ stable(X1)
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9]) ).
fof(c_0_12,negated_conjecture,
~ ! [X1] :
( ( environment(X1)
& stable(X1) )
=> in_environment(X1,critical_point(X1)) ),
inference(assume_negation,[status(cth)],[prove_l5]) ).
cnf(c_0_13,hypothesis,
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| X2 = critical_point(X1)
| ~ greater(growth_rate(efficient_producers,esk1_2(X1,X2)),growth_rate(first_movers,esk1_2(X1,X2)))
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_14,hypothesis,
( esk2_1(X1) = critical_point(X1)
| greater(growth_rate(efficient_producers,esk1_2(X1,esk2_1(X1))),growth_rate(first_movers,esk1_2(X1,esk2_1(X1))))
| ~ stable(X1)
| ~ greater(esk1_2(X1,esk2_1(X1)),esk2_1(X1))
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,hypothesis,
( greater(esk1_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_5]) ).
fof(c_0_16,negated_conjecture,
( environment(esk3_0)
& stable(esk3_0)
& ~ in_environment(esk3_0,critical_point(esk3_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
cnf(c_0_17,hypothesis,
( esk2_1(X1) = critical_point(X1)
| ~ stable(X1)
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_8]),c_0_9]) ).
cnf(c_0_18,negated_conjecture,
~ in_environment(esk3_0,critical_point(esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_19,hypothesis,
( in_environment(X1,critical_point(X1))
| ~ stable(X1)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_8,c_0_17]) ).
cnf(c_0_20,negated_conjecture,
stable(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,negated_conjecture,
environment(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_21])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT023+1 : TPTP v9.2.1. Released v2.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.33 % Computer : n010.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon May 4 23:27:06 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.25/1.71 % Version : CSE_E---1.7
% 1.25/1.71 % Problem : theBenchmark.p
% 1.25/1.71 % SZS status Theorem for theBenchmark.p
% 1.25/1.71 % SZS output start CNFRefutation
% See solution above
% 1.25/1.71 % Total time : 1.370s
%------------------------------------------------------------------------------