%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : MGT028+1 : TPTP v9.3.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 06:11:23 AM UTC 2026
% Result : Theorem 0.14s 0.37s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 49 ( 11 unt; 0 def)
% Number of atoms : 144 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 166 ( 71 ~; 70 |; 16 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 33 ( 4 sgn 9 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_l10,plain,
! [E] :
( ( environment(E)
& stable(E) )
=> ? [To] :
( greater(To,appear(efficient_producers,E))
& ! [T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& greater_or_equal(T,To) )
=> greater(zero,growth_rate(first_movers,T)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l10) ).
fof(prove_l10_negated,plain,
~ ! [E] :
( ( environment(E)
& stable(E) )
=> ? [To] :
( greater(To,appear(efficient_producers,E))
& ! [T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& greater_or_equal(T,To) )
=> greater(zero,growth_rate(first_movers,T)) ) ) ),
inference(negate_conjecture,[status(cth)],[prove_l10]) ).
cnf(8,plain,
environment(sK4),
inference(cnf,[status(esa)],[prove_l10_negated]) ).
cnf(l0,plain,
environment(sK4),
inference(instantiation,[status(thm)],[8]) ).
fof(mp_first_movers_negative_growth,plain,
! [E] :
( ( environment(E)
& stable(E)
& ? [T1] :
( in_environment(E,T1)
& ! [T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& greater_or_equal(T,T1) )
=> greater(zero,growth_rate(first_movers,T)) ) ) )
=> ? [T2] :
( greater(T2,appear(efficient_producers,E))
& ! [T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& greater_or_equal(T,T2) )
=> greater(zero,growth_rate(first_movers,T)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_first_movers_negative_growth) ).
cnf(0,plain,
( ~ in_environment(X0,X1)
| ~ environment(X0)
| ~ stable(X0)
| sP0(X0,X2)
| subpopulations(first_movers,efficient_producers,X0,sK1(X0,X1)) ),
inference(cnf,[status(esa)],[mp_first_movers_negative_growth]) ).
cnf(l1,plain,
( ~ in_environment(sK4,sK3(sK4))
| ~ environment(sK4)
| ~ stable(sK4)
| sP0(sK4,sK5(sK2(sK4)))
| subpopulations(first_movers,efficient_producers,sK4,sK1(sK4,sK3(sK4))) ),
inference(instantiation,[status(thm)],[0]) ).
fof(l11,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),zero)
& greater(zero,growth_rate(first_movers,T)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l11) ).
cnf(5,plain,
( ~ environment(X0)
| ~ stable(X0)
| in_environment(X0,sK3(X0)) ),
inference(cnf,[status(esa)],[l11]) ).
cnf(l2,plain,
( ~ environment(sK4)
| ~ stable(sK4)
| in_environment(sK4,sK3(sK4)) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(9,plain,
stable(sK4),
inference(cnf,[status(esa)],[prove_l10_negated]) ).
cnf(l3,plain,
stable(sK4),
inference(instantiation,[status(thm)],[9]) ).
cnf(7,plain,
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ greater_or_equal(X1,sK3(X0))
| ~ environment(X0)
| ~ stable(X0)
| greater(zero,growth_rate(first_movers,X1)) ),
inference(cnf,[status(esa)],[l11]) ).
cnf(l4,plain,
( ~ subpopulations(first_movers,efficient_producers,sK4,sK1(sK4,sK3(sK4)))
| ~ greater_or_equal(sK1(sK4,sK3(sK4)),sK3(sK4))
| ~ environment(sK4)
| ~ stable(sK4)
| greater(zero,growth_rate(first_movers,sK1(sK4,sK3(sK4)))) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(2,plain,
( ~ in_environment(X0,X1)
| ~ environment(X0)
| ~ stable(X0)
| ~ greater(zero,growth_rate(first_movers,sK1(X0,X1)))
| sP0(X0,X2) ),
inference(cnf,[status(esa)],[mp_first_movers_negative_growth]) ).
cnf(l5,plain,
( ~ in_environment(sK4,sK3(sK4))
| ~ environment(sK4)
| ~ stable(sK4)
| ~ greater(zero,growth_rate(first_movers,sK1(sK4,sK3(sK4))))
| sP0(sK4,sK5(sK2(sK4))) ),
inference(instantiation,[status(thm)],[2]) ).
cnf(l6,plain,
stable(sK4),
inference(instantiation,[status(thm)],[9]) ).
cnf(1,plain,
( ~ in_environment(X0,X1)
| ~ environment(X0)
| ~ stable(X0)
| sP0(X0,X2)
| greater_or_equal(sK1(X0,X1),X1) ),
inference(cnf,[status(esa)],[mp_first_movers_negative_growth]) ).
cnf(l7,plain,
( ~ in_environment(sK4,sK3(sK4))
| ~ environment(sK4)
| ~ stable(sK4)
| sP0(sK4,sK5(sK2(sK4)))
| greater_or_equal(sK1(sK4,sK3(sK4)),sK3(sK4)) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(l8,plain,
stable(sK4),
inference(instantiation,[status(thm)],[9]) ).
cnf(3,plain,
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ greater_or_equal(X1,sK2(X0))
| greater(zero,growth_rate(first_movers,X1))
| ~ sP0(X0,X1) ),
inference(cnf,[status(esa)],[mp_first_movers_negative_growth]) ).
cnf(l9,plain,
( ~ subpopulations(first_movers,efficient_producers,sK4,sK5(sK2(sK4)))
| ~ greater_or_equal(sK5(sK2(sK4)),sK2(sK4))
| greater(zero,growth_rate(first_movers,sK5(sK2(sK4))))
| ~ sP0(sK4,sK5(sK2(sK4))) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(4,plain,
( greater(sK2(X0),appear(efficient_producers,X0))
| ~ sP0(X0,X1) ),
inference(cnf,[status(esa)],[mp_first_movers_negative_growth]) ).
cnf(l10,plain,
( greater(sK2(sK4),appear(efficient_producers,sK4))
| ~ sP0(sK4,sK5(sK2(sK4))) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l11_001,plain,
stable(sK4),
inference(instantiation,[status(thm)],[9]) ).
cnf(l13,plain,
( ~ environment(sK4)
| ~ stable(sK4)
| in_environment(sK4,sK3(sK4)) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(12,plain,
( ~ greater(X0,appear(efficient_producers,sK4))
| ~ greater(zero,growth_rate(first_movers,sK5(X0))) ),
inference(cnf,[status(esa)],[prove_l10_negated]) ).
cnf(l19,plain,
( ~ greater(sK2(sK4),appear(efficient_producers,sK4))
| ~ greater(zero,growth_rate(first_movers,sK5(sK2(sK4)))) ),
inference(instantiation,[status(thm)],[12]) ).
cnf(10,plain,
( ~ greater(X0,appear(efficient_producers,sK4))
| subpopulations(first_movers,efficient_producers,sK4,sK5(X0)) ),
inference(cnf,[status(esa)],[prove_l10_negated]) ).
cnf(l15,plain,
( ~ greater(sK2(sK4),appear(efficient_producers,sK4))
| subpopulations(first_movers,efficient_producers,sK4,sK5(sK2(sK4))) ),
inference(instantiation,[status(thm)],[10]) ).
cnf(l14,plain,
( ~ environment(sK4)
| ~ stable(sK4)
| in_environment(sK4,sK3(sK4)) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(l20,plain,
( greater(sK2(sK4),appear(efficient_producers,sK4))
| ~ sP0(sK4,sK5(sK2(sK4))) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l12,plain,
stable(sK4),
inference(instantiation,[status(thm)],[9]) ).
cnf(l16,plain,
( ~ subpopulations(first_movers,efficient_producers,sK4,sK5(sK2(sK4)))
| ~ greater_or_equal(sK5(sK2(sK4)),sK2(sK4))
| greater(zero,growth_rate(first_movers,sK5(sK2(sK4))))
| ~ sP0(sK4,sK5(sK2(sK4))) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(11,plain,
( ~ greater(X0,appear(efficient_producers,sK4))
| greater_or_equal(sK5(X0),X0) ),
inference(cnf,[status(esa)],[prove_l10_negated]) ).
cnf(l18,plain,
( ~ greater(sK2(sK4),appear(efficient_producers,sK4))
| greater_or_equal(sK5(sK2(sK4)),sK2(sK4)) ),
inference(instantiation,[status(thm)],[11]) ).
cnf(l21,plain,
stable(sK4),
inference(instantiation,[status(thm)],[9]) ).
cnf(l25,plain,
( greater(sK2(sK4),appear(efficient_producers,sK4))
| ~ sP0(sK4,sK5(sK2(sK4))) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l26,plain,
stable(sK4),
inference(instantiation,[status(thm)],[9]) ).
cnf(l22,plain,
( greater(sK2(sK4),appear(efficient_producers,sK4))
| ~ sP0(sK4,sK5(sK2(sK4))) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l23,plain,
( ~ greater(sK2(sK4),appear(efficient_producers,sK4))
| subpopulations(first_movers,efficient_producers,sK4,sK5(sK2(sK4))) ),
inference(instantiation,[status(thm)],[10]) ).
cnf(l27,plain,
( ~ greater(sK2(sK4),appear(efficient_producers,sK4))
| subpopulations(first_movers,efficient_producers,sK4,sK5(sK2(sK4))) ),
inference(instantiation,[status(thm)],[10]) ).
cnf(l31,plain,
( ~ greater(sK2(sK4),appear(efficient_producers,sK4))
| ~ greater(zero,growth_rate(first_movers,sK5(sK2(sK4)))) ),
inference(instantiation,[status(thm)],[12]) ).
cnf(l28,plain,
( ~ subpopulations(first_movers,efficient_producers,sK4,sK5(sK2(sK4)))
| ~ greater_or_equal(sK5(sK2(sK4)),sK2(sK4))
| greater(zero,growth_rate(first_movers,sK5(sK2(sK4))))
| ~ sP0(sK4,sK5(sK2(sK4))) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(l33,plain,
( ~ greater(sK2(sK4),appear(efficient_producers,sK4))
| greater_or_equal(sK5(sK2(sK4)),sK2(sK4)) ),
inference(instantiation,[status(thm)],[11]) ).
cnf(l24,plain,
( ~ greater(sK2(sK4),appear(efficient_producers,sK4))
| greater_or_equal(sK5(sK2(sK4)),sK2(sK4)) ),
inference(instantiation,[status(thm)],[11]) ).
cnf(l32,plain,
( greater(sK2(sK4),appear(efficient_producers,sK4))
| ~ sP0(sK4,sK5(sK2(sK4))) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l34,plain,
( ~ greater(sK2(sK4),appear(efficient_producers,sK4))
| ~ greater(zero,growth_rate(first_movers,sK5(sK2(sK4)))) ),
inference(instantiation,[status(thm)],[12]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l2,l3,l4,l5,l6,l7,l8,l9,l10,l11,l13,l19,l15,l14,l20,l12,l16,l18,l21,l25,l26,l22,l23,l27,l31,l28,l33,l24,l32,l34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT028+1 : TPTP v9.3.0. Released v2.0.0.
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n011.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 7 12:14:30 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.14/0.37 % launching worker at depth: 1
% 0.14/0.37 % launching worker at depth: 6
% 0.14/0.37 % launching worker at depth: 5
% 0.14/0.37 % launching worker at depth: 2
% 0.14/0.37 % launching worker at depth: 3
% 0.14/0.37 % launching worker at depth: 4
% 0.14/0.37 % launching worker at depth: 7
% 0.14/0.37 % launching worker at depth: 8
% 0.14/0.37 % launching worker at depth: 9
% 0.14/0.37 % launching worker at depth: 10
% 0.14/0.37 % SZS status Theorem for theBenchmark
% 0.14/0.37 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------