%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : MGT023+2 : 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 : n012.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 79.76s 10.39s
% Output : CNFRefutation 79.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 73 ( 16 unt; 0 def)
% Number of atoms : 215 ( 13 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 257 ( 115 ~; 118 |; 15 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 37 ( 5 sgn 10 !; 3 ?)
% 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(11,plain,
environment(sK5),
inference(cnf,[status(esa)],[prove_l5_negated]) ).
cnf(l0,plain,
environment(sK5),
inference(instantiation,[status(thm)],[11]) ).
fof(mp_earliest_time_growth_rate_exceeds,plain,
! [E] :
( ( environment(E)
& ? [To] :
( in_environment(E,To)
& ! [T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& greater_or_equal(T,To) )
=> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) ) ) )
=> ? [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',mp_earliest_time_growth_rate_exceeds) ).
cnf(0,plain,
( ~ environment(X0)
| ~ in_environment(X0,X1)
| subpopulations(first_movers,efficient_producers,X0,sK1(X0,X1))
| sP0(X0,X2) ),
inference(cnf,[status(esa)],[mp_earliest_time_growth_rate_exceeds]) ).
cnf(l1,plain,
( ~ environment(sK5)
| ~ in_environment(sK5,sK4(sK5))
| subpopulations(first_movers,efficient_producers,sK5,sK1(sK5,sK4(sK5)))
| sP0(sK5,sK3(sK5,sK2(sK5))) ),
inference(instantiation,[status(thm)],[0]) ).
fof(l1_001,plain,
! [E] :
( ( environment(E)
& stable(E) )
=> ? [To] :
( in_environment(E,To)
& ! [T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& greater_or_equal(T,To) )
=> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1) ).
cnf(9,plain,
( ~ stable(X0)
| ~ environment(X0)
| in_environment(X0,sK4(X0)) ),
inference(cnf,[status(esa)],[l1]) ).
cnf(l2,plain,
( ~ stable(sK5)
| ~ environment(sK5)
| in_environment(sK5,sK4(sK5)) ),
inference(instantiation,[status(thm)],[9]) ).
cnf(12,plain,
stable(sK5),
inference(cnf,[status(esa)],[prove_l5_negated]) ).
cnf(l56,plain,
stable(sK5),
inference(instantiation,[status(thm)],[12]) ).
cnf(5,plain,
( in_environment(X0,sK2(X0))
| ~ sP0(X0,X1) ),
inference(cnf,[status(esa)],[mp_earliest_time_growth_rate_exceeds]) ).
cnf(l4,plain,
( in_environment(sK5,sK2(sK5))
| ~ sP0(sK5,sK3(sK5,sK2(sK5))) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(10,plain,
( ~ stable(X0)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ greater_or_equal(X1,sK4(X0))
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ),
inference(cnf,[status(esa)],[l1]) ).
cnf(l3,plain,
( ~ stable(sK5)
| ~ environment(sK5)
| ~ subpopulations(first_movers,efficient_producers,sK5,sK1(sK5,sK4(sK5)))
| ~ greater_or_equal(sK1(sK5,sK4(sK5)),sK4(sK5))
| greater(growth_rate(efficient_producers,sK1(sK5,sK4(sK5))),growth_rate(first_movers,sK1(sK5,sK4(sK5)))) ),
inference(instantiation,[status(thm)],[10]) ).
cnf(l10,plain,
stable(sK5),
inference(instantiation,[status(thm)],[12]) ).
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(6,plain,
( ~ environment(X0)
| ~ in_environment(X0,X1)
| subpopulations(first_movers,efficient_producers,X0,sK3(X0,X1))
| X1 = critical_point(X0)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ),
inference(cnf,[status(esa)],[d1]) ).
cnf(l68,plain,
( ~ environment(sK5)
| ~ in_environment(sK5,sK2(sK5))
| subpopulations(first_movers,efficient_producers,sK5,sK3(sK5,sK2(sK5)))
| sK2(sK5) = critical_point(sK5)
| greater(growth_rate(efficient_producers,sK2(sK5)),growth_rate(first_movers,sK2(sK5))) ),
inference(instantiation,[status(thm)],[6]) ).
cnf(4,plain,
( ~ greater(growth_rate(efficient_producers,sK2(X0)),growth_rate(first_movers,sK2(X0)))
| ~ sP0(X0,X1) ),
inference(cnf,[status(esa)],[mp_earliest_time_growth_rate_exceeds]) ).
cnf(l2954,plain,
( ~ greater(growth_rate(efficient_producers,sK2(sK5)),growth_rate(first_movers,sK2(sK5)))
| ~ sP0(sK5,sK3(sK5,sK2(sK5))) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(1,plain,
( ~ environment(X0)
| ~ in_environment(X0,X1)
| sP0(X0,X2)
| greater_or_equal(sK1(X0,X1),X1) ),
inference(cnf,[status(esa)],[mp_earliest_time_growth_rate_exceeds]) ).
cnf(l5,plain,
( ~ environment(sK5)
| ~ in_environment(sK5,sK4(sK5))
| sP0(sK5,sK3(sK5,sK2(sK5)))
| greater_or_equal(sK1(sK5,sK4(sK5)),sK4(sK5)) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(l32,plain,
( ~ stable(sK5)
| ~ environment(sK5)
| in_environment(sK5,sK4(sK5)) ),
inference(instantiation,[status(thm)],[9]) ).
cnf(3,plain,
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ greater(X1,sK2(X0))
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ sP0(X0,X1) ),
inference(cnf,[status(esa)],[mp_earliest_time_growth_rate_exceeds]) ).
cnf(l170,plain,
( ~ subpopulations(first_movers,efficient_producers,sK5,sK3(sK5,sK2(sK5)))
| ~ greater(sK3(sK5,sK2(sK5)),sK2(sK5))
| greater(growth_rate(efficient_producers,sK3(sK5,sK2(sK5))),growth_rate(first_movers,sK3(sK5,sK2(sK5))))
| ~ sP0(sK5,sK3(sK5,sK2(sK5))) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(l104,plain,
( ~ subpopulations(first_movers,efficient_producers,sK5,sK3(sK5,sK2(sK5)))
| ~ greater(sK3(sK5,sK2(sK5)),sK2(sK5))
| greater(growth_rate(efficient_producers,sK3(sK5,sK2(sK5))),growth_rate(first_movers,sK3(sK5,sK2(sK5))))
| ~ sP0(sK5,sK3(sK5,sK2(sK5))) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(l1423,plain,
stable(sK5),
inference(instantiation,[status(thm)],[12]) ).
cnf(8,plain,
( ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater(growth_rate(efficient_producers,sK3(X0,X1)),growth_rate(first_movers,sK3(X0,X1)))
| X1 = critical_point(X0)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ),
inference(cnf,[status(esa)],[d1]) ).
cnf(l204,plain,
( ~ environment(sK5)
| ~ in_environment(sK5,sK2(sK5))
| ~ greater(growth_rate(efficient_producers,sK3(sK5,sK2(sK5))),growth_rate(first_movers,sK3(sK5,sK2(sK5))))
| sK2(sK5) = critical_point(sK5)
| greater(growth_rate(efficient_producers,sK2(sK5)),growth_rate(first_movers,sK2(sK5))) ),
inference(instantiation,[status(thm)],[8]) ).
cnf(l257,plain,
( ~ environment(sK5)
| ~ in_environment(sK5,sK2(sK5))
| ~ greater(growth_rate(efficient_producers,sK3(sK5,sK2(sK5))),growth_rate(first_movers,sK3(sK5,sK2(sK5))))
| sK2(sK5) = critical_point(sK5)
| greater(growth_rate(efficient_producers,sK2(sK5)),growth_rate(first_movers,sK2(sK5))) ),
inference(instantiation,[status(thm)],[8]) ).
cnf(13,plain,
~ in_environment(sK5,critical_point(sK5)),
inference(cnf,[status(esa)],[prove_l5_negated]) ).
cnf(l102,plain,
~ in_environment(sK5,critical_point(sK5)),
inference(instantiation,[status(thm)],[13]) ).
cnf(2,plain,
( ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater(growth_rate(efficient_producers,sK1(X0,X1)),growth_rate(first_movers,sK1(X0,X1)))
| sP0(X0,X2) ),
inference(cnf,[status(esa)],[mp_earliest_time_growth_rate_exceeds]) ).
cnf(l416,plain,
( ~ environment(sK5)
| ~ in_environment(sK5,sK4(sK5))
| ~ greater(growth_rate(efficient_producers,sK1(sK5,sK4(sK5))),growth_rate(first_movers,sK1(sK5,sK4(sK5))))
| sP0(sK5,sK3(sK5,sK2(sK5))) ),
inference(instantiation,[status(thm)],[2]) ).
cnf(7,plain,
( ~ environment(X0)
| ~ in_environment(X0,X1)
| X1 = critical_point(X0)
| greater(sK3(X0,X1),X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ),
inference(cnf,[status(esa)],[d1]) ).
cnf(l197,plain,
( ~ environment(sK5)
| ~ in_environment(sK5,sK2(sK5))
| sK2(sK5) = critical_point(sK5)
| greater(sK3(sK5,sK2(sK5)),sK2(sK5))
| greater(growth_rate(efficient_producers,sK2(sK5)),growth_rate(first_movers,sK2(sK5))) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l161,plain,
( ~ environment(sK5)
| ~ in_environment(sK5,sK2(sK5))
| sK2(sK5) = critical_point(sK5)
| greater(sK3(sK5,sK2(sK5)),sK2(sK5))
| greater(growth_rate(efficient_producers,sK2(sK5)),growth_rate(first_movers,sK2(sK5))) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l1759,plain,
( in_environment(sK5,sK2(sK5))
| ~ sP0(sK5,sK3(sK5,sK2(sK5))) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(l4213,plain,
( ~ greater(growth_rate(efficient_producers,sK2(sK5)),growth_rate(first_movers,sK2(sK5)))
| ~ sP0(sK5,sK3(sK5,sK2(sK5))) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l227,plain,
( in_environment(sK5,sK2(sK5))
| ~ sP0(sK5,sK3(sK5,sK2(sK5))) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(l417,plain,
( ~ stable(sK5)
| ~ environment(sK5)
| in_environment(sK5,sK4(sK5)) ),
inference(instantiation,[status(thm)],[9]) ).
cnf(l436,plain,
stable(sK5),
inference(instantiation,[status(thm)],[12]) ).
cnf(l6066,plain,
( ~ greater(growth_rate(efficient_producers,sK2(sK5)),growth_rate(first_movers,sK2(sK5)))
| ~ sP0(sK5,sK3(sK5,sK2(sK5))) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l4033,plain,
( ~ greater(growth_rate(efficient_producers,sK2(sK5)),growth_rate(first_movers,sK2(sK5)))
| ~ sP0(sK5,sK3(sK5,sK2(sK5))) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l159,plain,
( ~ environment(sK5)
| ~ in_environment(sK5,sK2(sK5))
| subpopulations(first_movers,efficient_producers,sK5,sK3(sK5,sK2(sK5)))
| sK2(sK5) = critical_point(sK5)
| greater(growth_rate(efficient_producers,sK2(sK5)),growth_rate(first_movers,sK2(sK5))) ),
inference(instantiation,[status(thm)],[6]) ).
cnf(l3949,plain,
~ in_environment(sK5,critical_point(sK5)),
inference(instantiation,[status(thm)],[13]) ).
cnf(l7459,plain,
( ~ greater(growth_rate(efficient_producers,sK2(sK5)),growth_rate(first_movers,sK2(sK5)))
| ~ sP0(sK5,sK3(sK5,sK2(sK5))) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l338,plain,
( in_environment(sK5,sK2(sK5))
| ~ sP0(sK5,sK3(sK5,sK2(sK5))) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(l3954,plain,
( in_environment(sK5,sK2(sK5))
| ~ sP0(sK5,sK3(sK5,sK2(sK5))) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(l3971,plain,
( ~ greater(growth_rate(efficient_producers,sK2(sK5)),growth_rate(first_movers,sK2(sK5)))
| ~ sP0(sK5,sK3(sK5,sK2(sK5))) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l426,plain,
( ~ subpopulations(first_movers,efficient_producers,sK5,sK3(sK5,sK2(sK5)))
| ~ greater(sK3(sK5,sK2(sK5)),sK2(sK5))
| greater(growth_rate(efficient_producers,sK3(sK5,sK2(sK5))),growth_rate(first_movers,sK3(sK5,sK2(sK5))))
| ~ sP0(sK5,sK3(sK5,sK2(sK5))) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(l509,plain,
( ~ environment(sK5)
| ~ in_environment(sK5,sK2(sK5))
| sK2(sK5) = critical_point(sK5)
| greater(sK3(sK5,sK2(sK5)),sK2(sK5))
| greater(growth_rate(efficient_producers,sK2(sK5)),growth_rate(first_movers,sK2(sK5))) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l705,plain,
( in_environment(sK5,sK2(sK5))
| ~ sP0(sK5,sK3(sK5,sK2(sK5))) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(l444,plain,
( ~ environment(sK5)
| ~ in_environment(sK5,sK2(sK5))
| subpopulations(first_movers,efficient_producers,sK5,sK3(sK5,sK2(sK5)))
| sK2(sK5) = critical_point(sK5)
| greater(growth_rate(efficient_producers,sK2(sK5)),growth_rate(first_movers,sK2(sK5))) ),
inference(instantiation,[status(thm)],[6]) ).
cnf(l1758,plain,
( in_environment(sK5,sK2(sK5))
| ~ sP0(sK5,sK3(sK5,sK2(sK5))) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(l512,plain,
( ~ greater(growth_rate(efficient_producers,sK2(sK5)),growth_rate(first_movers,sK2(sK5)))
| ~ sP0(sK5,sK3(sK5,sK2(sK5))) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l430,plain,
( ~ environment(sK5)
| ~ in_environment(sK5,sK2(sK5))
| ~ greater(growth_rate(efficient_producers,sK3(sK5,sK2(sK5))),growth_rate(first_movers,sK3(sK5,sK2(sK5))))
| sK2(sK5) = critical_point(sK5)
| greater(growth_rate(efficient_producers,sK2(sK5)),growth_rate(first_movers,sK2(sK5))) ),
inference(instantiation,[status(thm)],[8]) ).
cnf(l7486,plain,
~ in_environment(sK5,critical_point(sK5)),
inference(instantiation,[status(thm)],[13]) ).
cnf(l433,plain,
( in_environment(sK5,sK2(sK5))
| ~ sP0(sK5,sK3(sK5,sK2(sK5))) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(l6983,plain,
( in_environment(sK5,sK2(sK5))
| ~ sP0(sK5,sK3(sK5,sK2(sK5))) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(l608,plain,
( ~ greater(growth_rate(efficient_producers,sK2(sK5)),growth_rate(first_movers,sK2(sK5)))
| ~ sP0(sK5,sK3(sK5,sK2(sK5))) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l5408,plain,
( ~ greater(growth_rate(efficient_producers,sK2(sK5)),growth_rate(first_movers,sK2(sK5)))
| ~ sP0(sK5,sK3(sK5,sK2(sK5))) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l7384,plain,
~ in_environment(sK5,critical_point(sK5)),
inference(instantiation,[status(thm)],[13]) ).
cnf(l6115,plain,
~ in_environment(sK5,critical_point(sK5)),
inference(instantiation,[status(thm)],[13]) ).
cnf(l6113,plain,
( in_environment(sK5,sK2(sK5))
| ~ sP0(sK5,sK3(sK5,sK2(sK5))) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(l7342,plain,
~ in_environment(sK5,critical_point(sK5)),
inference(instantiation,[status(thm)],[13]) ).
cnf(l7364,plain,
( in_environment(sK5,sK2(sK5))
| ~ sP0(sK5,sK3(sK5,sK2(sK5))) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(l607,plain,
( in_environment(sK5,sK2(sK5))
| ~ sP0(sK5,sK3(sK5,sK2(sK5))) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(l1730,plain,
( in_environment(sK5,sK2(sK5))
| ~ sP0(sK5,sK3(sK5,sK2(sK5))) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(l1811,plain,
~ in_environment(sK5,critical_point(sK5)),
inference(instantiation,[status(thm)],[13]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l2,l56,l4,l3,l10,l68,l2954,l5,l32,l170,l104,l1423,l204,l257,l102,l416,l197,l161,l1759,l4213,l227,l417,l436,l6066,l4033,l159,l3949,l7459,l338,l3954,l3971,l426,l509,l705,l444,l1758,l512,l430,l7486,l433,l6983,l608,l5408,l7384,l6115,l6113,l7342,l7364,l607,l1730,l1811]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : MGT023+2 : TPTP v9.3.0. Released v2.0.0.
% 0.00/0.02 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Mon Sep 7 12:07:11 UTC 2026
% 0.03/0.29 % CPUTime :
% 0.03/0.30 % launching worker at depth: 2
% 0.03/0.30 % launching worker at depth: 6
% 0.03/0.30 % launching worker at depth: 1
% 0.03/0.30 % launching worker at depth: 4
% 0.03/0.30 % launching worker at depth: 8
% 0.03/0.30 % launching worker at depth: 5
% 0.03/0.30 % launching worker at depth: 7
% 0.03/0.30 % launching worker at depth: 3
% 0.03/0.30 % launching worker at depth: 9
% 0.03/0.30 % launching worker at depth: 10
% 0.03/0.31 % launching worker at depth: 11
% 0.32/0.35 % launching worker at depth: 12
% 3.17/0.72 % launching worker at depth: 13
% 28.72/3.97 % launching worker at depth: 14
% 79.76/10.39 % SZS status Theorem for theBenchmark
% 79.76/10.39 % SZS output start CNFRefutation
% See solution above
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