%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : MGT023+1 : TPTP v9.3.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 : Tue Sep 8 06:11:22 AM UTC 2026
% Result : Theorem 4.34s 0.96s
% Output : CNFRefutation 4.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 41 ( 18 unt; 0 def)
% Number of atoms : 111 ( 7 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 125 ( 55 ~; 54 |; 10 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 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 : 18 ( 0 sgn 7 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_l5,plain,
! [E] :
( ( environment(E)
& stable(E) )
=> in_environment(E,critical_point(E)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l5) ).
fof(prove_l5_negated,plain,
~ ! [E] :
( ( environment(E)
& stable(E) )
=> in_environment(E,critical_point(E)) ),
inference(negate_conjecture,[status(cth)],[prove_l5]) ).
cnf(6,plain,
environment(sK3),
inference(cnf,[status(esa)],[prove_l5_negated]) ).
cnf(l0,plain,
environment(sK3),
inference(instantiation,[status(thm)],[6]) ).
fof(l12,plain,
! [E] :
( ( environment(E)
& stable(E) )
=> ? [To] :
( in_environment(E,To)
& ~ greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
& ! [T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& greater(T,To) )
=> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l12) ).
cnf(5,plain,
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| ~ greater(X1,sK2(X0))
| ~ stable(X0)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ),
inference(cnf,[status(esa)],[l12]) ).
cnf(l1,plain,
( ~ subpopulations(first_movers,efficient_producers,sK3,sK1(sK3,sK2(sK3)))
| ~ environment(sK3)
| ~ greater(sK1(sK3,sK2(sK3)),sK2(sK3))
| ~ stable(sK3)
| greater(growth_rate(efficient_producers,sK1(sK3,sK2(sK3))),growth_rate(first_movers,sK1(sK3,sK2(sK3)))) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(7,plain,
stable(sK3),
inference(cnf,[status(esa)],[prove_l5_negated]) ).
cnf(l63,plain,
stable(sK3),
inference(instantiation,[status(thm)],[7]) ).
fof(d1,plain,
! [E,To] :
( ( environment(E)
& ~ greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
& in_environment(E,To)
& ! [T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& greater(T,To) )
=> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) ) )
=> To = critical_point(E) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1) ).
cnf(0,plain,
( ~ in_environment(X0,X1)
| ~ environment(X0)
| subpopulations(first_movers,efficient_producers,X0,sK1(X0,X1))
| X1 = critical_point(X0)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ),
inference(cnf,[status(esa)],[d1]) ).
cnf(l2,plain,
( ~ in_environment(sK3,sK2(sK3))
| ~ environment(sK3)
| subpopulations(first_movers,efficient_producers,sK3,sK1(sK3,sK2(sK3)))
| sK2(sK3) = critical_point(sK3)
| greater(growth_rate(efficient_producers,sK2(sK3)),growth_rate(first_movers,sK2(sK3))) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(2,plain,
( ~ in_environment(X0,X1)
| ~ environment(X0)
| ~ greater(growth_rate(efficient_producers,sK1(X0,X1)),growth_rate(first_movers,sK1(X0,X1)))
| X1 = critical_point(X0)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ),
inference(cnf,[status(esa)],[d1]) ).
cnf(l4,plain,
( ~ in_environment(sK3,sK2(sK3))
| ~ environment(sK3)
| ~ greater(growth_rate(efficient_producers,sK1(sK3,sK2(sK3))),growth_rate(first_movers,sK1(sK3,sK2(sK3))))
| sK2(sK3) = critical_point(sK3)
| greater(growth_rate(efficient_producers,sK2(sK3)),growth_rate(first_movers,sK2(sK3))) ),
inference(instantiation,[status(thm)],[2]) ).
cnf(3,plain,
( ~ environment(X0)
| ~ stable(X0)
| in_environment(X0,sK2(X0)) ),
inference(cnf,[status(esa)],[l12]) ).
cnf(l22,plain,
( ~ environment(sK3)
| ~ stable(sK3)
| in_environment(sK3,sK2(sK3)) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(4,plain,
( ~ environment(X0)
| ~ greater(growth_rate(efficient_producers,sK2(X0)),growth_rate(first_movers,sK2(X0)))
| ~ stable(X0) ),
inference(cnf,[status(esa)],[l12]) ).
cnf(l461,plain,
( ~ environment(sK3)
| ~ greater(growth_rate(efficient_producers,sK2(sK3)),growth_rate(first_movers,sK2(sK3)))
| ~ stable(sK3) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l12_001,plain,
( ~ environment(sK3)
| ~ stable(sK3)
| in_environment(sK3,sK2(sK3)) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(l17,plain,
( ~ environment(sK3)
| ~ greater(growth_rate(efficient_producers,sK2(sK3)),growth_rate(first_movers,sK2(sK3)))
| ~ stable(sK3) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l511,plain,
stable(sK3),
inference(instantiation,[status(thm)],[7]) ).
cnf(l41,plain,
stable(sK3),
inference(instantiation,[status(thm)],[7]) ).
cnf(l53,plain,
stable(sK3),
inference(instantiation,[status(thm)],[7]) ).
cnf(l35,plain,
stable(sK3),
inference(instantiation,[status(thm)],[7]) ).
cnf(1,plain,
( ~ in_environment(X0,X1)
| ~ environment(X0)
| X1 = critical_point(X0)
| greater(sK1(X0,X1),X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ),
inference(cnf,[status(esa)],[d1]) ).
cnf(l3,plain,
( ~ in_environment(sK3,sK2(sK3))
| ~ environment(sK3)
| sK2(sK3) = critical_point(sK3)
| greater(sK1(sK3,sK2(sK3)),sK2(sK3))
| greater(growth_rate(efficient_producers,sK2(sK3)),growth_rate(first_movers,sK2(sK3))) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(l197,plain,
( ~ environment(sK3)
| ~ stable(sK3)
| in_environment(sK3,sK2(sK3)) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(8,plain,
~ in_environment(sK3,critical_point(sK3)),
inference(cnf,[status(esa)],[prove_l5_negated]) ).
cnf(l285,plain,
~ in_environment(sK3,critical_point(sK3)),
inference(instantiation,[status(thm)],[8]) ).
cnf(l5,plain,
( ~ environment(sK3)
| ~ greater(growth_rate(efficient_producers,sK2(sK3)),growth_rate(first_movers,sK2(sK3)))
| ~ stable(sK3) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l240,plain,
stable(sK3),
inference(instantiation,[status(thm)],[7]) ).
cnf(l43,plain,
( ~ environment(sK3)
| ~ stable(sK3)
| in_environment(sK3,sK2(sK3)) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(l15,plain,
~ in_environment(sK3,critical_point(sK3)),
inference(instantiation,[status(thm)],[8]) ).
cnf(l542,plain,
~ in_environment(sK3,critical_point(sK3)),
inference(instantiation,[status(thm)],[8]) ).
cnf(l18,plain,
( ~ environment(sK3)
| ~ stable(sK3)
| in_environment(sK3,sK2(sK3)) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(l69,plain,
stable(sK3),
inference(instantiation,[status(thm)],[7]) ).
cnf(l78,plain,
stable(sK3),
inference(instantiation,[status(thm)],[7]) ).
cnf(l266,plain,
stable(sK3),
inference(instantiation,[status(thm)],[7]) ).
cnf(l535,plain,
( ~ environment(sK3)
| ~ stable(sK3)
| in_environment(sK3,sK2(sK3)) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(l537,plain,
stable(sK3),
inference(instantiation,[status(thm)],[7]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l63,l2,l4,l22,l461,l12,l17,l511,l41,l53,l35,l3,l197,l285,l5,l240,l43,l15,l542,l18,l69,l78,l266,l535,l537]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT023+1 : TPTP v9.3.0. Released v2.0.0.
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n005.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 7 12:06:20 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % launching worker at depth: 1
% 0.09/0.36 % launching worker at depth: 5
% 0.09/0.36 % launching worker at depth: 6
% 0.09/0.36 % launching worker at depth: 7
% 0.09/0.36 % launching worker at depth: 3
% 0.09/0.36 % launching worker at depth: 8
% 0.09/0.36 % launching worker at depth: 4
% 0.09/0.36 % launching worker at depth: 2
% 0.09/0.36 % launching worker at depth: 9
% 0.09/0.36 % launching worker at depth: 10
% 0.13/0.37 % launching worker at depth: 11
% 0.13/0.42 % launching worker at depth: 12
% 4.34/0.96 % SZS status Theorem for theBenchmark
% 4.34/0.96 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------